Answer:
Option B. 59%Explanation:
The function that represents the number of E.coli bacteria cells per 100 mL of water as the time t years elapses is:
[tex]A(t)=136(1.123)^{4t}[/tex]The base, 1.123, represents the multiplicative constant rate of change of the function, so you just must substitute 1 for t in the power part of the function:
[tex]rate=(1.123)^{4t}=(1.123)^4=1.590[/tex]Then, the multiplicative rate of change is 1.590, which means that every year the number of E.coli bacteria cells per 100 mL of water increases by a factor of 1.590, and that is 1.59 - 1 = 0.590 or 59% increase.
Solve for x.
3x - 1/5 = 10
A) 1
B) 17
C) 3
D) 6
Answer:
The answer to your question is None of the answers is correct
Step-by-step explanation:
[tex]3x - \frac{1}{5} = 10[/tex]
Solve for x
[tex]3x = 10 + \frac{1}{5}[/tex]
[tex]3x = \frac{50 + 1}{5}[/tex]
[tex]3x = \frac{51}{5}[/tex]
[tex][tex]x = \frac{17}{5} [/tex]x = \frac{51}{(3)(5)}[/tex]
[tex]x = \frac{17}{5}[/tex]
A consumer claims that the mean lifetime of a brand of fluorescent bulbs is less than1500 hours. She selects 25 bulbs and finds the mean lifetime to be 1480 hours with the standard deviation of 80 hours. If you were to test the consumer's claimat the 0.05 significance level, what would you conclude?
Answer:
We conclude that the mean lifetime of a brand of fluorescent bulbs is equal to 1500 hours.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 1500 hours
Sample mean, [tex]\bar{x}[/tex] = 1480 hours
Sample size, n = 25
Alpha, α = 0.05
Sample standard deviation, s = 80 hours
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 1500\text{ hours}\\H_A: \mu < 1500\text{ hours}[/tex]
We use one-tailed(left) t test to perform this hypothesis.
Formula:
[tex]t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }[/tex]
Putting all the values, we have
[tex]t_{stat} = \displaystyle\frac{1480-1500}{\frac{80}{\sqrt{25}}}= -1.25[/tex]
Now,
[tex]t_{critical} \text{ at 0.05 level of significance, 24 degree of freedom } = -1.71[/tex]
Since,
[tex]t_{stat} > t_{critical}[/tex]
We fail to reject the null hypothesis and accept the null hypothesis.
We conclude that the mean lifetime of a brand of fluorescent bulbs is equal to 1500 hours.
After performing a one-sample t-test, the calculated t value of -1.25 does not exceed the critical value of -1.711 at the 0.05 significance level. Therefore, we do not have sufficient evidence to support the claim that the mean lifetime of the bulbs is less than 1500 hours.
Explanation:The question asks to test the claim that the mean lifetime of a certain brand of fluorescent bulbs is less than 1500 hours. To test this at the 0.05 significance level, we would perform a one-sample t-test since the sample size is less than 30, and we do not know the population standard deviation.
First, we formulate our null hypothesis (H0) as the mean lifetime of the bulbs being 1500 hours or more, and the alternative hypothesis (Ha) being the mean lifetime less than 1500 hours.
Next, we calculate the test statistic using the sample mean, population mean, standard deviation, and sample size:
[tex]t = (Sample Mean - Population Mean) / (Standard Deviation / \sqrt(Sample Size))[/tex]
[tex]= (1480 - 1500) / (80 / \sqrt(25))[/tex]
= -20 / (80 / 5)
= -20 / 16
= -1.25
Then, we check this t value against the t-distribution table for 24 degrees of freedom (df = n - 1) at the 0.05 significance level. The critical value for a one-tailed test with df = 24 at alpha = 0.05 is approximately -1.711. Since our calculated t value of -1.25 is not less than -1.711, we do not reject the null hypothesis.
Conclusion: At the 0.05 significance level, we do not have sufficient evidence to support the consumer's claim that the mean lifetime of the bulbs is less than 1500 hours.
3/5 of a certain class left on a field trip. 1/3 of the students who stayed behind did not want to go on the field trip (all the others did want to go). When another vehicle was located, 1/2 of the students who did want to go on the field trip but had been left behind were able to join. What fraction of the class ended up going on the field trip?A. 1/2B. 2/3C. 11/15D. 23/30E. 4/5
Answer:
option C
Step-by-step explanation:
[tex]\dfrac{3}{5}[/tex] class left [tex]\dfrac{2}{5}[/tex] of the class left.
now,
[tex]\dfrac{1}{3}[/tex] of stayed did not want to go so, [tex]\dfrac{2}{3}[/tex] of the student wanted to go.
[tex]\dfrac{1}{2}[/tex] of the stayed student join the trip.
number of student that stayed and wanted to go are
=[tex]\dfrac{2}{5}\times \dfrac{2}{3}\times \dfrac{1}{2}[/tex]
=[tex]\dfrac{2}{15}[/tex]
fraction of class on the field trip
= [tex]\dfrac{3}{5}+\dfrac{2}{15}[/tex]
= [tex]\dfrac{11}{15}[/tex]
Hence, the correct answer is option C
John sells tickets to a school concert. Adult tickets cost $6.50 and children's tickets cost $4.50. John collects a total of 157.50 from the ticket sales and he sells twice as many adult tickets as children's tickets. How many tickets does he sell all together?
Answer: The total number of tickets that John sold is 27
Step-by-step explanation:
Let x represent the number of adult tickets that John sold at the concert.
Let y represent the number of children's tickets that John sold at the concert.
Adult tickets cost $6.50 and children's tickets cost $4.50. John collects a total of 157.50 from the ticket sales it means that
6.5x + 4.5y = 157.5 - - - - - - - - - -1
John sells twice as many adult tickets as children's tickets. This means that
x = 2y
Substituting x = 2y into equation 1, it becomes
6.5 × 2y + 4.5y = 157.5
13y + 4.5x = 157.5
17.5y = 157.5
y = 157.5/17.5 = 9
x = 2×9 = 18
The total number of tickets that John sold is 9 + 18 = 27
Please... ?
The first term of an infinite geometric progression is 5 and the sum of its terms is 20. What is the common ratio of the progression?
Answer:
The common ratio of the progression is 3/4Explanation:
A geometric progression is a sequence of terms in which the consecutive terms have a constant ratio; thus, each term is equal to the previous one multiplied by a constant value:
[tex]First\ term=a_1\\\\ Second\ term=a_2=a_1\times r\\\\ Third\ term=a_3=a_2\times r=a_1\times r^2\\\\n_{th}\ term=a_n=a_{n-1}\times r=a_1\times r^{n-1}[/tex]
A infinite geometric progression may have a finite sum. When the absolute value of the ratio is less than 1, the sum of the infinite geometric progression has a finite value equal to:
[tex]S_{\infty}=\frac{a_1}{1-r}[/tex]Thus, the information given translates to:
[tex]a_1=5\\ \\ S_{\infty}=20=\frac{5}{1-r}[/tex]
Now you can solve for the constant ratio, r:
[tex]1-r=\frac{5}{20}\\ \\ r=1-\frac{5}{20}\\ \\ r=\frac{15}{20}\\ \\ r=3/4[/tex]
The common ratio of the infinite geometric progression with the first term of 5 and a sum of 20 is 0.75.
The question pertains to finding the common ratio of an infinite geometric progression (GP) when given the first term and the sum of all its terms. The first term is known as 5, and the sum of the infinite GP is 20. To find the common ratio, we use the formula for the sum of an infinite GP, which is S = a / (1 - r), where S is the sum, a is the first term, and r is the common ratio.
Plugging in the given values, we have:
20 = 5 / (1 - r)
We can solve for r by multiplying both sides by (1 - r) and then simplifying:
20(1 - r) = 5
20 - 20r = 5
15 = 20r
r = 0.75
Thus, the common ratio of the infinite GP with a first term of 5 and a sum of 20 is 0.75.
Mitch and Tom are playing a video game. Mitch has eight less than triple the points that Tom has. If Mitch has 79 points how many points does Tom have?
Tom has 29 points in the video game whereas mitch has 79 points.
What is a linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given, Tom and Mitch are engaged in video game gaming. Tom has eight more points than Mitch does, but not by much. Let points of mitch be y and points of tom be x.
Based on the given conditions, formulate y = 3x -8
Rearrange unknown terms to the left side of the equation: 3x = 79 + 8
Calculate the sum or difference: 3x = 87
Divide both sides of the equation by the coefficient of the variable: x = 87/3
Cross out the common factor: x = 29
Therefore, Tom has 29 points in the video game.
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By solving the equation 3T - 8 = 79, we find that Tom has 29 points.
Explanation:The student is asking a mathematical word problem that involves forming and solving an equation. To find how many points Tom has, we need to work with the information given: Mitch has eight less than triple the points that Tom has, and Mitch has 79 points.
Let's define Tom's points as 'T'. The problem tells us that Mitch's points are eight less than triple Tom's points, which can be written as the equation: 3T - 8 = 79.
Now we solve for 'T':
Add 8 to both sides of the equation: 3T = 79 + 8Calculate the sum: 3T = 87Divide both sides by 3: T = 87 / 3Calculate the division: T = 29Tom has 29 points.
Three consecutive odd integers have a sum of 27. What is the greatest of these integers?
Answer:
11
Step-by-step explanation:
The middle of the three is their average, their sum divided by 3:
middle = 27/3 = 9
Then the largest is 2 more. It is 11.
The researcher has limited resources. He sends 9 emails from a Latino name, and 14 emails from a non-Latino name. For the Latino names, the mean response time was 421 minutes (standard deviation of 82 minutes). For the non-Latino names, it was 366 minutes (standard deviation of 101 minutes). Calculate the standard error for the difference in means.
Answer: 38.41 minutes
Step-by-step explanation:
The standard error for the difference in means is given by :-
[tex]SE.=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma^2_2}{n_2}}[/tex]
where , [tex]\sigma_1[/tex] = Standard deviation for sample 1.
[tex]n_1[/tex]= Size of sample 1.
[tex]\sigma_2[/tex] = Standard deviation for sample 2.
[tex]n_2[/tex]= Size of sample 2.
Let the sample of Latino name is first and non -Latino is second.
As per given , we have
[tex]\sigma_1=82[/tex]
[tex]n_1=9[/tex]
[tex]\sigma_2=101[/tex]
[tex]n_2=14[/tex]
The standard error for the difference in means will be :
[tex]SE.=\sqrt{\dfrac{(82)^2}{9}+\dfrac{(101)^2}{14}}[/tex]
[tex]SE.=\sqrt{\dfrac{6724}{9}+\dfrac{10201}{14}}[/tex]
[tex]SE.=\sqrt{747.111111111+728.642857143}[/tex]
[tex]SE.=\sqrt{1475.75396825}=38.4155433158\approx38.41[/tex]
Hence, the standard error for the difference in means =38.41 minutes
How many positive multiples of 7 that are less than 1000 end with the digit 3?
Answer:
14
Step-by-step explanation:
Ordinarily, a quick multiplication of 7 by other integers up to 10 indicates that only 7*9 yields 63, i.e ends with 3 as required.
Thus the set of possible multiples of the integer 7 ending with the digit 3 will form the arithmetic series with the first term being Ao = 63 and the common difference being d= 7*10= 70. That is we can see the series in details....
the nth term could be evaluated from the formular
An=Ao+(n-1)d (1)
The series could be explicitly depicted as follows:
9*7=63= 63+70*0
(10+9)*7=133 = 63+70*1
(20+9)*7=203=63+70*2
(30+9)*7=273=63+70*3
.................................
(130+9)*7=973=63+70*13
The last 'n' corresponding to the problem statement could be evaluated from equation (1), assuming An=1000:
1000=63+(n-1)*70
1000-63=70(n-1)
937/70=13.38=n-1
n=14.38
Thus the number of possible multiples of 7 less than 1000 ending with digit 3 will be 14.
Check: 7 times 142 is 994, so there are exactly 142 positive multiples of 7 less than 1000.
One tenth of these, ignoring the decimal fraction, end with a digit of 3.
Got three questions need with .
Answer:
14.
Center = (-7,4)
Radius = 7
15. 189 square yards
16. 84 square inches
Step-by-step explanation:
14.
The standard form of a circle is given as:
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
Where
(h,k) is the center
and
r is the radius of the circle
Given, the circle equation in this problem as:
[tex](x+7)^2+(y-4)^2=49[/tex]
We re arrange this:
[tex](x-(-7))^2+(y-(4))^2=7^2[/tex]
Now, we clearly see that the center is (-7,4) and the radius is 7
Hence,
Center = (-7,4)
Radius = 7
15.
For simplicity, let the point at DE, where it makes the right angle, be the point "H".
DEF is the triangle.
So, we see now that:
DE = 21 yd
FH = 18 yd
DE is the base of the triangle and FH is the height of the triangle.
The area of a triangle is:
Area = 0.5 * base * height
So, we now find the area to be:
Area = 0.5 * 21 * 18 = 189 square yards
16.
Rhombus is a quadrilateral (figure with 4 sides) whose 4 sides have equal length.
The diagonal is the length from one corner to the opposite corner. So, a rhombus has 2 diagonals.
The area of the rhombus, in terms of diagonals, would be:
Area = (Diagonal1 * Diagonal2)/2
So, we multiply the 2 diagonal's length and divide the answer by 2.
We have:
Diagonal 1 = 12
Diagonal 2 = 14
Hence, area would be:
Area = (12*14)/2 = 84 square inches
1. In the triangle below, determine the value of c.
2. In the triangle below, what ratio is tan P?
a. p/r
b. r/q
c. r/p
d. p/q
Answer:
2. a. [tex]\displaystyle \frac{p}{r}[/tex]
1. [tex]\displaystyle 15,35842773 ≈ c[/tex]
Step-by-step explanation:
2. Extended Information on Trigonometric Ratios
[tex]\displaystyle \frac{OPPOSITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOSITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOSITE} = csc\:θ \\ \frac{ADJACENT}{OPPOSITE} = cot\:θ[/tex]
__________________________________________________________
1. We have to determine which trigonometric ratio[s] to use, depending on what is given to us, and in this case, we will be using the secant [or cosine] ratio:
[tex]\displaystyle sec\:43° = \frac{21}{c} → \frac{21}{sec\:43°} ≈ c → 15,35842773 ≈ c \\ \\ OR \\ \\ cos\:43° = \frac{c}{21} → 21cos\:43° ≈ c → 15,35842773 ≈ c[/tex]
ONCE AGAIN...
Extended Information on Trigonometric Ratios
[tex]\displaystyle \frac{OPPOSITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOSITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOSITE} = csc\:θ \\ \frac{ADJACENT}{OPPOSITE} = cot\:θ[/tex]
I am joyous to assist you anytime.
Answer:
15.36.
p/r.
Step-by-step explanation:
cos 43 = c/21
c = 21 cos 43
c = 15.36.
Tan P = opposite side / adjacent side
= p/r.
Susan wanted to know if aerobic exercise caused more weight loss than just walking. Susan had her experimental group do aerobic exercise for 20 minutes, 4 days a week. She weighed each subject before the experiment started and again 3 months into the experiment. The independent variable in her experimental research was _____
Answer:
Independent variable : Anaerobic Exercise
Step-by-step explanation:
The dependent variable is known as the variable of interest or "Y" and usually the independent variables are expressed by "X".
The independent variable is the "variable that is changed or controlled in a scientific experiment to test the effects on the dependent variable"
For this case our independent variable would be the anerobic exercise, since we want to se the effect of the exercise on the weigth loss, so then our dependent variable would be th weigth loss.
And for this case we can check the hypothesis with a paired t-test if we use the same individuals.
A paired t-test is used to compare two population means where you have two samples in which observations in one sample can be paired with observations in the other sample. For example if we have Before-and-after observations we can use it.
The independent variable in Susan's experimental research on weight loss is the introduction of aerobic exercise. How much weight loss is achieved can have multiple contributing factors, including individual differences. Incorporating moderate to vigorous physical activity is crucial for weight control and may need to be adjusted based on individual needs.
The independent variable in Susan's experimental research is the type of exercise performed by the subjects — specifically, the aerobic exercise. This is because the independent variable is the factor that the researcher manipulates to determine if it causes a change in another variable. In this case, the independent variable is the introduction of aerobic exercise compared to just walking. Susan's goal is to measure the effects of aerobic exercise on weight loss among the participants over a period of 3 months.
Variations in weight loss outcomes in a workout program can be attributed to individual differences such as metabolism, diet, genetics, lifestyle, and adherence to the exercise regimen. For effective weight control, research suggests a combination of aerobic activity and muscle-strengthening exercises. Susan can compare her findings to these variables to gain insight into the weight loss effects of aerobic exercise.
For those looking to use physical activity for weight loss and control, it might make sense to increase either the intensity or the minutes per week of physical activity, depending on their individual circumstances. Incorporating moderate to vigorous aerobic activity combined with a reduction in caloric intake can help meet weight-control goals for many adults.
Strawberries are $2.50 A pound and cantaloupes are $2.25 at the local supermarket. Sally bought 7 pounds of the two kinds of fruit for a family breakfast. If she spent exactly $16.75 and bought at least 1 pound of each fruit how many pounds of fruit did she buy there is no sales tax
Answer:
Sally bought 4 pounds of Strawberries and 3 pounds of Cantaloupes.
Step-by-step explanation:
Let the number of pounds of Strawberries bought by Sally = x
Let the number of pounds of Cantaloupes bought by Sally = y
[tex]\[x + y = 7\][/tex] ---------------------------------(1)
Moreover,
[tex]\[2.5 x + 2.25 y = 16.75\][/tex] ---------------(2)
Solving (1) and (2) by substitution:
[tex]\[x = 7 - y\][/tex]
=> [tex]\[2.5 *(7-y) + 2.25 y = 16.75\][/tex]
=> [tex]\[17.5 - 2.5y + 2.25 y = 16.75\][/tex]
=> [tex]\[0.25y = 0.75\][/tex]
=> [tex]\[y = 3\][/tex]
From (1), x = 7-3 = 4
Which statements are true about reflections? Check all that apply.
An image created by a reflection will always be congruent to its pre-image.
An image and its pre-image are always the same distance from the line of reflection
If a point on the pre-image lies on the line of reflection, the image of that point is the same as the pre-image.
The line of reflection is perpendicular to the line segments connecting corresponding vertices.
The line segments connecting corresponding vertices are all congruent to each other.
The line segments connecting corresponding vertices are all parallel to each other.
Answer:1 2 34 6
Step-by-step explanation:
Just answered it
Answer:
1,2,3,4,6
Step-by-step explanation:
Edge 2021
In the parallelogram below, W = ?
The value of w in the given figure of parallelogram is, w = 37 degrees.
We can see that the diagonals of the parallelogram divided it into four number of parallelogram.
We know that the sum of all interior angles of a triangle is 180 degrees according to Angle Sum Property of Triangle.
So, from the given figure we can see that in a triangle the interior angles are w, 2w and 69 degrees.
According to Angle Sum Property,
w + 2w + 69 = 180
3w = 180 - 69 = 111
w = 111/3 = 37
Hence the value of w in the given parallelogram is 37 degrees.
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A vegetable garden and it's around a pasta shaped like a square that together are 12 ft wide. A path is 1 feet wide. If one bag of gravel covers 9 square feet, how many bags are needed to cover the path? Round your answers to the nearest tenth.
The overall width of the path and garden is 12 feet.
The area of the entire garden and path is 12 x 12 = 144 square feet.
The path is 1 foot wide, so the garden would be 12 - 2 = 20 feet wide.
The area of the garden only would be 10 x 10 = 100 square feet.
The area of the path only = 144 - 100 = 44 square feet.
1 bag covers 9 square feet:
44 / 9 = 4.88
You would need 5 bags.
A costumer walked into a restaurant and purchased 4 chicken sandwiches and 5 large sodas for $22.50. The customer behind him bought 7 chicken sandwiches and 6 large sodas for $35.25. How much does a chicken sandwich cost and how much is a large soda?
Set up an equation for each customer:
4C + 5S = 22.50
7C + 6S = 35.25
Multipyy the first equation by -1.75 to make the 4C the inverse of 7c:
4C + 5S = 22.50 x -1.75 = -7C - 8.75S = -39.375
Now add the two equations to eliminate the C variable:
7C +6S = 35.25 + -7C - 8.75S = -39.375
= -2.75S = -4.125
Divide both sides by -2.75 to solve for S:
S = -4.125 / -2.75
S = 1.50
The price of a soda is $1.50
Now replace S in an equation with 1.50 and solve for C:
4C + 5(1.50) = 22.50
Simplify:
4C + 7.50 = 22.50
Subtract 7.50 from both sides:
4C = 15
Divide both sides by 4:
C = 15/4
C = 3.75
The sandwich costs $3.75
Soda = $1.50
Sandwich = $3.75
Answer: the cost of a chicken sandwich is $3.75
the cost of a large soda is $1.5
Step-by-step explanation:
Let x represent the cost of a chicken sandwich.
Let y represent the cost of a large soda.
A costumer walked into a restaurant and purchased 4 chicken sandwiches and 5 large sodas for $22.50. This means that
4x + 5y = 22.5 - - - - - - - -1
The customer behind him bought 7 chicken sandwiches and 6 large sodas for $35.25. This means that
7x + 6y = 35.25 - - - - - - - - - -2
Multiplying equation 1 by 7 and equation 2 by 4, it becomes
28x + 35y = 157.5
28x + 24y = 141
Subtracting
11y = 16.5
y = 16.5/11 = 1.5
Substituting y = 1.5 into equation 1, it becomes
4x + 5 × 1.5 = 22.5
4x + 7.5 = 22.5
4x = 22.5 - 7.5 = 15
x = 15/4 = 3.75
In Mathopolis, an adult is a person 21 years of age or older and a child is a person under 21 years of age. Exactly half of the adults in Mathopolis are female, and exactly half of the female adults have exactly one biological child. Nobody else has a child, and there are no other children. What percent of the people of Mathopolis are children?
Answer:
20%
Step-by-step explanation:
If there are 4 adults, 2 are female, and 1 of those has 1 child. Then the population is 4 adults and 1 child. The children make up 1/5 = 20% of the population.
Answer
20%
Step-by-step explanation:
Aops Question
A collection of dimes and quarters is worth $9.55. If the quarters were dimes and the dimes were quarters, the total value would be 7.60. Find the number of each coin.
Number of dimes are 18 and number of quarters are 31
Solution:
Let "d" be the number of dimes
Let "q" be the number of quarters
value of 1 dime = $ 0.10
value of 1 quarter = $ 0.25
A collection of dimes and quarters is worth $9.55
value of 1 dime x number of dimes + value of 1 dime x number of quarters = 9.55
0.10d + 0.25q = 9.55 ---------- eqn 1
If the quarters were dimes and the dimes were quarters, the total value would be 7.60
quarters were dimes means , q = d
dimes were quarters means d = q
0.25d + 0.10q = 7.60 ----- eqn 2
Let us solve eqn 1 and eqn 2 to find "d" and "q"
Multiply eqn 1 by 2.5
0.25d + 0.625q = 23.875 ---- eqn 3
Subtract eqn 2 from eqn 3
0.25d + 0.625q = 23.875
0.25d + 0.10q = 7.60
( - ) ----------------------
0.525q = 16.275
q = 31
Substitute q = 31 in eqn 1
0.10d + 0.25q = 9.55
0.10d + 0.25(31) = 9.55
0.10d + 7.75 = 9.55
0.10d = 1.8
d = 18
Thus dimes are 18 and number of quarters are 31
Answer:
i needed the answer to this too!! have a good life
The points A, B, and C reside on a line segment. B is the midpoint of AC. If line AB measures 6 units in length, what is the length of line AC?
Answer:
12 units
Step-by-step explanation:
A-------6--------B-------?--------C
Midpoint is center that divides the line segment into two equal halves.
∴ AB = BC
If line AB measures 6 units in length, then, line BC will measure 6 units in length.
AB = BC = 6 units
AC = AB + BC
AC = 6 units + 6 units
AC = 12 units
OR
We can say If B is the midpoint of AC, then AC is twice as long as AB.
AC = 2AB
AC = 2 × 6 units
AC = 12 units
Therefore, the length of line AC is 12 units.
In the election for presidency, Stan Fitz received 542 votes, Elizabeth Stuckey received 430 votes and Gene Sterner received 130 votes. Ninety percent of those eligible to vote did so. What was the number of eligible voters?
Answer:
The total number of eligible voters in the town = 1224 ( app.)
Step-by-step explanation:
Let us assume the total number of eligible voters = p
Now, the number of votes received by Stan Fitz = 542
The number of votes received by Elizabeth Stuckey = 430
The number of votes received by Gene Sterner = 130
So, the total number of votes received in total = 542 + 430 + 130 = 1,102
Now, only the 90% of total voters p voted in the election.
⇒ 90% of p = 1102
[tex]\implies \frac{90}{100} \times p = 1102\\ \implies p = \frac{1102\times 100}{90} = 1224[/tex]
or, p ≈ 1224
Hence, the total number of eligible voters in the town = 1224 ( app.)
Suppose the profit the company makes on each customer visit is $0.75 per DVD minus $0.05 "fixed costs." That is, if P = profit, then P X 0.75 0.05. Use a linear transformation of your results in (a) and (b) to find the mean and standard deviation for P.
Answer:
Step-by-step explanation:
Given that the profit the company makes on each customer visit is $0.75 per DVD minus $0.05 "fixed costs."
i.e. Profit
= P(x) = 0.75 x - 0.05 where x is the no of dvds sold
E(x) = [tex]E(0.75x-0.05)\\= E(0.75x) -E(0.05)\\= 0.75E(x) -0.05[/tex]
(using linear transformation rules for mean)
VarP(x) = [tex]Var(0.75 x - 0.05)\\= Var(0.75x)\\= 0.75^2 Var(x)[/tex]
Hence std dev P(X) = 0.75 std dev (x)
Johnny has 7 different colored marbles in his bag. In how many ways can he choose three different marbles from his bag to play a game?
Answer:
35
Step-by-step explanation:
Use the combination formula:
[tex]C(n,r)=\frac{n!}{r!(n-r)!}[/tex]
Substitute known values:
[tex]C(7,3)=\frac{7!}{3!(7-3)!}=35[/tex]
We don't use the permutation formula since the order of the drawn marbles does not matter.
Answer: 35
Step-by-step explanation:
He can choose 3 marbles from 7 distinct marbles in (7/3) ways
C(7/3) = 7!/(3!-(7-3)!)
= 7*6*5*4/4*3*2
= 35
A football team plays in a large stadium. With a ticket price of $19, the average attendance at recent games has been 50 comma 000. A market survey indicates that for each $1 increase in the ticket price, attendance decreases by 300. a. Express the number of spectators at a football game, N, as a function of the ticket price, x. b. Express the revenue from a football game, R, as a function of the ticket price, x.
Answer:
Part 1: N(x) = 50,000 - 300(x-19)
Part 2: R(x) =-300x² + 55700x
Step-by-step explanation:
Given,
The original price of each ticket = $ 19,
The original attendance = 50,000
Part 1 :
∵ For the each $1 increase in the ticket price, attendance decreases by 300.
Let x represents the price of each ticket after increment,
Thus, if price increment = (x-19) dollars,
New attendance, N(x) = 50,000 - 300(x-19)
Part 2 :
Since, revenue = price of each ticket × attendance
Thus, the revenue from the football game,
R(x) = x(50,000 - 300(x-19))
R(x) = 50000x - 300x²+ 5700x
⇒ R(x) =-300x² + 55700x
What term is used to describe the graphical representation of the change in microbial population over time?
Answer:
The term exponential is often used.
Step-by-step explanation:
The term exponential is used to represent changes in population over time. The idea of (positive) exponential is that the higher the number, the higher the growth. You can relate this with a population, because the higher the population, the more opportunities for it to multiply, thus, the higher it grows.
Usually the way to meassure the population of an species after certain number of years x, you use an exponential function of the form
[tex] f(x) = K_0 * a^x [/tex]
For certain constants K₀ and a. K₀ is the initial population at the start of the experiment and a number of exponential growth. Essentially, the population of the species is multiplied by a during each year.
For example, if K₀ = 1000 and a = 2, then the population at the start of the experiment is 1000. After the first year is 1000*2 = 2000 and after the second year it is 2000*2 = 4000. Note that, not only the population grow during the years, but also the amount that the population increases also grow: in the first year it grows 1000, and between the first and second year it grows 2000.
A solid object may be drawn as a flat plane object showing all sides, or it may be drawn as an isometric drawing. From the list below, choose which statements about solid objects drawn as isometric drawings are true. I. Circles are drawn exactly as circles. II. Circles are drawn as ellipses and not as exact circles. III. Horizontal lines are drawn at 30° angles above the horizontal. IV. Horizontal lines are drawn at 60° angles above the horizontal. V. Vertical lines are drawn at 90° angles above the horizontal. VI. Vertical lines are drawn at 120° angles above the horizontal.
Answer:
For isometric drawings, these are true :
II. Circles are drawn as ellipses and not as exact circles.
III. Horizontal lines are drawn at 30° angles above the horizontal.
V. Vertical lines are drawn at 90° angles above the horizontal.
Step-by-step explanation:
Now,
An isometric drawing allows the designer to draw an object in three dimensions. Isometric drawings are also called isometric projections. This type of drawing is often used by engineers and illustrators that specialize in technical drawings.
For example, when an engineer has an idea for a new product, he or she will probably create a sketch to show a client or investor. And chances are, the sketch will be an isometric drawing.
In isometric projections, horizontal lines are drawn at 30° to the original horizontal, where as vertical lines are remained unchanged.
Even though horizontal lines are at 30°. the measurements of length does not change. so, the circle look like an ellipse.
⇒ The true statements are:
II. Circles are drawn as ellipses and not as exact circles.
III. Horizontal lines are drawn at 30° angles above the horizontal.
V. Vertical lines are drawn at 90° angles above the horizontal.
In an isometric drawing, circles are represented as ellipses (II), the horizontal lines are commonly drawn at 30° angles above the horizontal (III), and the vertical lines are drawn at 90° angles above the horizontal (V).
Explanation:From the given list, statements II, III, and V about isometric drawings of solid objects are true. II. In isometric drawings, circles are not drawn as exact circles but are instead represented as ellipses. This is due to the three-dimensional perspective presented in isometric drawings making the circle appear distorted. III. Horizontal lines in isometric drawings are commonly drawn at 30° angles above the horizontal line that forms part of the axonometric grid. This provides a consistent upward inclination for all lines sketched or perceived as horizontal in the actual object. V. Vertical lines are drawn at 90° angles above the horizontal. In isometric projections, just like in any form, the vertical lines always maintain the same 90° angle with respect to ground regardless of the viewpoint.
Learn more about Isometric Drawings here:
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A researcher computes the definitional formula for SS, and finds that Σ(x − M) = 44. If this is a sample of 12 scores, then what would the value of sample variance be using the computational formula?
A. 3.7
B. 4.0
C. 44
D. not possible to know because the scores are not given
Answer:
Option B.
Step-by-step explanation:
Given information:
Σ(x − M) = 44
where, M is mean.
Sample size = 12
The computational formula for sample variance is
[tex]s^2=\dfrac{\sum (x-M)^2}{N-1}[/tex]
where, M is sample mean and N is sample size.
Substitute Σ(x − M) = 44 and N=12 in the above formula.
[tex]s^2=\dfrac{44}{12-1}[/tex]
[tex]s^2=\dfrac{44}{11}[/tex]
[tex]s^2=4.0[/tex]
The sample variance is 4.0.
Therefore, the correct option is B.
In the figure, BP is an angle bisector of ∠CBD.
Find x if m∠1 = 4x - 8 and m∠2 = 3x + 2.
A) 5
B) 7
C) 9
D) 10
Answer:
9
Step-by-step explanation:
Nell's mom makes chocolate milk with 30\text{ mL}30 mL30, start text, space, m, L, end text of chocolate syrup for every 222 ounces of milk. Nell's dad adds 65\text{ mL}65 mL65, start text, space, m, L, end text of chocolate syrup for every 555 ounces of milk. Whose chocolate milk is more chocolatey?
Answer:
Hence Nell's mom Chocolate milk is more Chocolaty.
Step-by-step explanation:
Given:
Chocolate syrup used by Nell's mom = 30 ml
Amount of milk used = 2 ounces.
We will first find Amount of chocolate syrup used in 1 ounce of milk.
Now In 2 ounces of milk = 30 ml of chocolate syrup.
So in 1 ounce of milk = Amount of Chocolate syrup used for 1 ounce milk.
By using Unitary method we get;
Amount of Chocolate syrup used for 1 ounce milk= [tex]\frac{30}{2}=15\ ml[/tex]
Hence For every 1 ounce of milk Nell's mom uses 15 ml of chocolate syrup.
Also Given:
Chocolate syrup used by Nell's dad = 65 ml
Amount of milk used = 5 ounces.
We will first find Amount of chocolate syrup used in 1 ounce of milk.
Now In 5 ounces of milk = 65 ml of chocolate syrup.
So in 1 ounce of milk = Amount of Chocolate syrup used for 1 ounce milk.
By using Unitary method we get;
Amount of Chocolate syrup used for 1 ounce milk= [tex]\frac{65}{5}=13\ ml[/tex]
Hence For every 1 ounce of milk Nell's dad uses 13 ml of chocolate syrup.
Since The amount of chocolate syrup used by Nell's mom is more than Nell's dad.
Hence Nell's mom Chocolate milk is more Chocolaty.
Answer:
They are both the same
Step-by-step explanation:
Eddy MS plans to collect more than 3,000 can of food to donate to the EG Food Bank. So far, 500 can have been collected. WRITE an inequality to find the number of can the school can collect on each of the final 5 days to meet their goal.
Answer:
The in equality representing the number of can school can collect each day is [tex]500+5x\geq 3000[/tex].
Eddy MS school has to collect at least 500 cans in each day.
Step-by-step explanation:
Number of cans Eddy has = 500
Number of days left = 5
Target to achieve = 3000
Let number of cans which can be collected in each day be 'x'.
Now we know that;
Number of can he has plus number of can which can be collected in each day multiplied with number of days left should be greater than or equal to 3000
Framing in equation form we get;
[tex]500+5x\geq 3000[/tex]
Hence, The in equality representing the number of can school can collect each day is [tex]500+5x\geq 3000[/tex].
Solving the same we get;
[tex]500+5x\geq 3000[/tex].
Subtracting Both side with 500 using Subtraction property for Inequality we get;
[tex]500+5x-500\geq 3000-500\\\\5x\geq 2500[/tex]
Now Dividing both side by 5 using Division property of Inequality we get;
[tex]\frac{5x}{5}\geq\frac{2500}{5}\\\\x\geq 500[/tex]
Hence Eddy MS school has to collect at least 500 cans in each day.