The number of units of tiles he will need is 18.96 units
Step-by-step explanation:
The parallelogram ABCD has a right triangle ABD with A as 90°
The length of segment AB is given as 3.16 units and that of the diagonal BD is 7.07 units.
Apply Pythagorean relationship to find length of segment AD=BC
The sum of squares of the sides equals the square of the hypotenuse.
a²+b²=c²
In this case, side a=3.16 units, b=AD and c=hypotenuse=7.07
Applying the formula;
a²+b²=c²
3.16²+b²=7.07²
9.99+b²=49.99
b²=49.99-9.99
b²=40
b=√40=6.3245 =6.32
AD=BC=6.32 units
Find the perimeter of the quadrilateral
=3.16+3.16+6.32+6.32=18.96 units
Learn More
Perimeter of a quadrilateral :https://brainly.com/question/12708927
Keywords : single line of tiles, pool,quadrilateral,length,hundredth
#LearnwithBrainly
Answer:
18.96 units
Step-by-step explanation:
I took the test.
Which is more economical: purchasing the economy size of a detergent at 7 kilograms for $7.15 or purchasing the regular size at 920 grams for 60cents?
Select the correct choice below and fill in the answer box to complete your choice.
(Round to four decimal places as needed.)
A.
Purchasing the economy size is more economical because the economy size costs $
____ less per gram.
B.
Purchasing the regular size is more economical because the regular size costs $
_____ less per gram.
Purchasing the regular size is more economical because the regular size costs $0.0369 less per gram.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
The economy size of a detergent at 7 kilograms for $7.15 or purchase the regular size at 920 grams for 60 cents.
As we know.
1 kg = 1000 grams
7 kg = 7000 grams
$7.15 = 715 cents
7000 grams cost 715 cents
1 gram cost:
Per gram cost = 715/7000 = cent 0.1021 per gram
920 grams cost 60 cents
Per gram cost:
= 60/920
= cent 0.0652 per gram
Difference in cost = 0.0369
Purchasing the regular size is more economical because the regular size costs $0.0369 less per gram.
Thus, purchasing the regular size is more economical because the regular size costs $0.0369 less per gram.
Learn more about the fraction here:
brainly.com/question/1301963
#SPJ2
A moose population is growing exponentially following the pattern in the table shown below. Assuming that the pattern continues, what will be the population of moose after 12 years? Show all your work! Round your answer to the nearest whole number.
Answer:
7,692 moose.Explanation:
The table that shows the pattern for this question is:
Time (year) Population
0 40
1 62
2 96
3 149
4 231
A growing exponentially pattern may be modeled by a function of the form P(x) = P₀(r)ˣ.
Where P₀ represents the initial population (year = 0), r represents the multiplicative growing rate, and P(x0 represents the population at the year x.
Thus you must find both P₀ and r.
1) P₀
Using the first term of the sequence (0, 40) you get:
P(0) = 40 = P₀ (r)⁰ = P₀ (1) = P₀
Then, P₀ = 40
2) r
Take two consecutive terms of the sequence:
P(0) = 40 r⁰ = 40P(1) = 40 r¹ = 40r = 62P(1) / P(0) = 40r / 40 = 62/40r = 62/40 = 1.55
You can verify that, for any other two consecutive terms you get the same result: 96/62 ≈ 149/96 ≈ 231/149 ≈ 1.55
3) Model
Thus, your model is P(x) = 40(1.55)ˣ
4) Population of moose after 12 years
P(12) = 40 (1.55)¹² ≈ 7,692.019 ≈ 7,692, which is round to the nearest whole number.George is twice as old as Edward, and Edward's age exceeds Robert's age by 4 years. If the sum of the three ages is at least 56 years, what is Robert's minimum age?
Answer:Robert's minimum age is 11 years.
Step-by-step explanation:
Let x represent George's age.
Let y represent Edward's age.
Let z represent Robert's age.
George is twice as old as Edward. It means that
x = 2y
Edward's age exceeds Robert's age by 4 years. It means that
z = y - 4
If the sum of the three ages is at least 56 years, it means that
x + y + z ≥ 56 - - - - - - - - - - 1
Substituting x = 2y and z = y - 4 into equation 1, it becomes
2y + y + y - 4 ≥ 56
4y - 4 ≥ 56
4y ≥ 56 + 4
y ≥ 60/4
y ≥ 15
z = y - 4 = 15 - 4
z ≥ 11
Final answer:
To find Robert's minimum age, we need to calculate the ages of Edward, George, and Robert based on the given information.
Explanation:
Minimum Age Calculation:
Let's denote the age of Edward as E, George as 2E (twice as old as Edward), and Robert as E - 4 (Edward's age exceeds Robert's by 4 years).
The sum of their ages is at least 56, so E + 2E + (E - 4) ≥ 56.
Solving the inequality, we get E ≥ 20, George's age (2E) is at least 40, and Robert's minimum age (E - 4) is at least 16.
To estimate the percentage of defects in a recent manufacturing batch, a quality control manager at General Foods General Foods selects every 14th soup cansoup can that comes off the assembly line starting with the sixth sixth until she obtains a sample of 130 soup canssoup cans. What type of sampling is used?
Answer:
Systematic sampling.
Step-by-step explanation:
The systematic sampling is the type of random sampling when the first unit is selected at random from k units and then every kth unit is selected. The k is known as sampling interval which is equal to the population size divided by sample size i.e. N/n.
In the given scenario a quality control manager start with 6th and then every 14th soup canssoup is selected. The sampling units can be selected as 6, 20, 34, 48, 62, 76... and so on. Here the value of k is 14. Thus, the given sampling is the systematic sampling.
The material used to make a storage box costs $1.10 per square foot. The boxes have the same volume. How much does a company save on materials by choosing to make 900 boxes using the box with the least surface area?
We need more data about the box dimensions to calculate the savings. The formula involves multiplying the cost per square foot with the difference in surface areas and number of boxes. The idea of economies of scale isn't directly applicable in this context.
Explanation:In order to answer this question, we would require additional information about the dimensions of the boxes and their surface areas. The cost difference between making boxes with different surface areas can be found by multiplying the difference in surface areas by the cost per square foot and then by the number of boxes.
The formula used would be: $1.10 (Cost per Square Foot) * Difference in Surface Areas * 900 (Number of Boxes).
In case of economies of scale, like the information provided about alarm clocks, the cost per box would decrease as the number of boxes produced increases. But this concept isn't directly applicable here as we're dealing with the material cost of the boxes, not the production cost.
Learn more about Box Material Cost here:https://brainly.com/question/33064251
#SPJ12
"A serving of fish contains 50 g protein and 4 g of fat. If protein has a caloric value of 4 kcal/g and fat has 9 kcal/g, how many kcal are in the serving?"
The total caloric content in the serving of fish can be calculated by adding the calories from protein (200 kcal) and the calories from fat (36 kcal). Therefore, the serving of fish contains a total of 236 kcal.
Explanation:To calculate the total calories in a serving of fish, we need to add the caloric content of both the protein and the fat. The protein content of the fish is 50 g, and we know that protein has a caloric value of 4 kcal/g. Thus, the total caloric content from protein is 50 g x 4 kcal/g = 200 kcal. The fat content of this serving of fish is 4 g, and fat has a caloric value of 9 kcal/g. This makes the total caloric content from fat 4 g x 9 kcal/g = 36 kcal.
To find the total caloric content of the serving, we need to add together the calories from protein and fat. So, 200 kcal + 36 kcal = 236 kcal. Therefore, the serving of fish contains a total of 236 kcal.
Learn more about Caloric Calculation here:https://brainly.com/question/32880642
#SPJ3
Lisa and Bill made 60 magnets for a craft fair. They sold about 55% of the magnets. Lisa says they sold about 30 magnets. Bill says that they sold about 36 magnets. Could they both be correct? Explain.
Answer:
Step-by-step explanation:
The total number of magnets that Lisa and Bill made for the craft fair is 60.
They sold about 55% of the magnets. The number of magnets that they sold would be about
55/100 × 60 = 0.55 × 60 = 33
If Lisa says that they sold about 30 magnets, she is correct because if we round off 33 to the nearest ten, it would be 30 magnets.
If Bill says that they sold about 36 magnets, he is wrong because if we round off 36 to the nearest ten, it would be 40 magnets.
The cold water faucet can fill a sink in 2 minutes. The drain can empty a full sink in 3 minutes. If the faucet were left on and the drain was left open, how long would it take to fill the sink?
Answer:
6 minutes
Step-by-step explanation:
Let the volume of the sink be Xm^3
The rate of filling the sink by the first faucet is R1 while the rate of draining the faucet is -R2(negative since it’s draining)
R1 = x/2
R2 = -x/3 ( negative as it is draining)
The time it would take both of them working at the same rate to fill the sink is as follows:
x/(R1 - R2) = T
x/( x/2 - x/3) = T
x = T(x/2 - x/3)
x = T( (3x - 2x)/6)
x = T(x/6)
x = Tx/6
6x = Tx
T = 6 minutes
What is (-7)^2 × (-7)?
I will mark the Brainliest, thank, and comment!
Thank you!
Answer:
The answer is -343.
Step-by-step explanation:
If a term doesn't have an exponent, it's considered that the exponent is 1 (so basically, (-7)² x (-7)^1.
Multiply the terms with the same base (by adding the exponents - (-7)²+1<- (as the exponential value) (couldn't find the sign so sorry.)
Add the numbers: (-7)³
A negative base raised to an odd power equals a negative: -7³
Write the problem out: -(7 x 7 x 7).
Multiply: -343
Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 5 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps?A. 5 : 1B. 10 : 5C. 15 : 2D. 20 : 2E. 25 : 2
Final Answer:
The correct simplified ratio of US to British stamps is 25 : 2, which corresponds to answer choice E.
Explanation:
To determine the ratio of US to British stamps, we must use the given ratios of US to Indian and Indian to British stamps.
The given ratio of US to Indian stamps is 5 to 2. This means for every 5 US stamps there are 2 Indian stamps. We can represent this as:
US : Indian = 5 : 2
The given ratio of Indian to British stamps is 5 to 1. This implies that for every 5 Indian stamps, there is 1 British stamp. We can write this as:
Indian : British = 5 : 1
To find the ratio of US to British stamps, we need to combine these two ratios. To do this, we should express each ratio such that the Indian stamp part of each ratio is the same. Since the ratios already have the same number of Indian stamps (5 of them), we can directly multiply the US part by the British part across these ratios.
Thus, we multiply the number of US stamps (5 from the first ratio) by the number of British stamps (1 from the second ratio):
US to British = 5 (US) * 1 (British)
US to British = 5
Since we did not have to multiply the number of British stamps by anything (they were only multiplied by 1), the British part of the ratio remains unchanged.
Next, we multiply the Indian part of the first ratio by the British part of the second ratio:
Indian to British = 2 (Indian from the first ratio) * 5 (British from the second ratio)
Indian to British = 10
Now we can combine these two results to express the US to British ratio:
US to British = 5 (US) : 10 (British)
To simplify this ratio, we divide both sides by the common factor between them. In this case, that common factor is 5. So when we divide both numbers by 5, we have:
US to British = (5/5) : (10/5)
US to British = 1 : 2
However, this is not the option given in the question. Let's revisit the calculation and see if there was an error:
The correct approach to combining the ratios is to multiply the two ratios directly:
US : Indian = 5 : 2
Indian : British = 5 : 1
Multiplying across gives us:
US : British = (5 * 5) : (2 * 1)
US : British = 25 : 2
The correct simplified ratio of US to British stamps is 25 : 2, which corresponds to answer choice E.
A jar contains 10 red marbles and 15 blue marbles. If you randomly draw two marbles from the jar (without replacement), what is the probability that they are the same color?
Answer:
0.5
Step-by-step explanation:
Probability is the possibility of an event happening,
probability = number of required outcomes/ number of possible outcomes
number of red marbles = 10
number of blue marbles = 15
The selection of two marbles is done without replacement.
Pr( of same color) = RR or BB
which means; (the first is red and second is red) or (the first is blue and the second is blue)
OR in probability means adition while AND means multiplication.
Pr( of same color) = [tex](\frac{10}{25}*\frac{15}{24})+(\frac{15}{25}*\frac{10}{24})[/tex]
=[tex]\frac{1}{4} +\frac{1}{4}[/tex]
=0.5
Probabilities are used to illustrate the chances of an event
The probability that marbles of the same color are picked is 0.50
The numbers of marbles are given as:
[tex]\mathbf{Red =10}[/tex]
[tex]\mathbf{Blue =15}[/tex]
[tex]\mathbf{Total =25}[/tex]
The probability that marbles of the same color are picked is:
[tex]\mathbf{Pr = (Red\ and\ Red) + (Blue\ and\ Blue)}[/tex]
So, we have:
[tex]\mathbf{Pr = (10/25 \times 9/24) + (15/25 \times 14/24)}[/tex]
[tex]\mathbf{Pr = (0.15) + (0.35)}[/tex]
Add
[tex]\mathbf{Pr = 0.50}[/tex]
Hence, the probability that marbles of the same color are picked is 0.50
Read more about probabilities at:
https://brainly.com/question/11234923
A moose population is growing exponentially following the pattern in the table shown below. Assuming that the pattern continues, what will be the population of moose after 12 years? Show all your work! Round your answer to the nearest whole number.
Time (year) Population
0 40
1 62
2 96
3 149
4 231
Answer:
7,692 moose.Explanation:
First, you must find the pattern behind the set of data in the table shown in the question.
It is said that this is a growing exponentially pattern. Thus, the data should be modeled by a function of the form P(x) = A(B)ˣ.
And you must find both A and B.
Finding the multiplicative rate of change (B).B is the multiplicative rate of change of the function which is a constant that you can find by dividing consecutive terms:
62/40 = 1.5596/62 ≈ 1.548 ≈ 1.55149/96 ≈ = 1.552 ≈ 1.55231/149 ≈ 1.550 ≈ 1.55Thus, B = 1.55
Finding the initial value ASo far, you know P(x) = A (1.55)ˣ
To find A, you can use P(0)=40, which drives to:
40 = A (1.55)⁰ = A(1) = AThus, your function is P(x) = 40(1.55)ˣ
Finding the answer to the questionThe population of moose after 12 years, is given by P(12):
P(12) = 40 (1.55)¹² ≈ 7,692.019 ≈ 7,692Thus, round to the nearest whole number, those are 7,692 moose.
If y(x) = -2x2+3 and v(x) = x, what is the range of (Jov(x)?
(3.00)
(-60,3)
0 (0o,00)
Answer:
The answer to your question is (-∞, 3)
Step-by-step explanation:
Data
y(x) = -2x² + 3
v(x) = x
Process
1.- Evaluate y(x) in v(x)
yov(x) = -2(x)² + 3
yov(x) = -2x² + 3
2.- Graph the function
In the graph we observe that the posible values of "y" are from (-∞, 3) that is the range.
Tara ran 3 laps around her neighbor for a total of 1 mile yesterday. Today she wants to run 2 over 3 of a mile. How many laps she will need to run around her neighbor
Answer:
Tara need to run 2 laps today.
Step-by-step explanation:
Number of laps in 1 mile = 3 laps
number of miles she wants to run today = [tex]\frac{2}{3}[/tex]
We need to find the number of lap she need to run today;
Solution:
Now we know that;
in 1 mile = 3 laps
In [tex]\frac{2}{3}[/tex] miles = number of laps in [tex]\frac{2}{3}[/tex] miles
By using Unitary method we get;
number of laps in [tex]\frac{2}{3}[/tex] miles = [tex]3\times\frac{2}{3} = 2\ laps[/tex]
Hence Tara need to run 2 laps today.
Samples of size n=600 are taken from a telephone survey and the mean age is taken from each sample. What is the distribution of the sample means?
A. not enough infomation
B. skewed to left
C. normal
D. skewed to right
Final answer:
The distribution of the sample means from samples of size n=600 is a normal distribution, according to the Central Limit Theorem, option C.
Explanation:
When samples of size n=600 are taken and the mean age is calculated from each sample, the distribution of sample means is best described by a normal distribution. This is due to the Central Limit Theorem which states that as the sample size becomes large (n ≥ 30 is a commonly used threshold), the sampling distribution of the sample means will tend to be normal regardless of the shape of the population distribution.
This property of the distribution of sample means applies as long as the samples are taken with replacement or if sampling without replacement, the population is at least ten times larger than the sample. In this case, with a sample size of 600, which is well above 30, we can confidently expect the distribution of sample means to follow a normal distribution.
c. Two sculptures are similar. The height of one sculpture is four times the height of the other sculpture. The smaller sculpture is 2.5 feet tall. How tall is the larger sculpture?
Answer:
The larger sculpture is 10.0 feet tall
Step-by-step explanation:
The height of one sculpture (larger sculpture) is four times the height of the other sculpture (smaller sculpture)
Let the height of the larger sculpture be x and the height of the smaller sculpture be y
Therefore, x = 4y (y = 2.5 feet)
x = 4×2.5 feet = 10.0 feet
The larger sculpture is 10 feet tall.
Explanation:To find the height of the larger sculpture, we can use the information given. We know that the smaller sculpture is 2.5 feet tall, and the larger sculpture is four times as tall. So, we can multiply the height of the smaller sculpture by 4.
Larger sculpture height = 2.5 feet × 4 = 10 feet
Therefore, the height of the larger sculpture is 10 feet.
Learn more about Sculpture heights here:https://brainly.com/question/35551773
#SPJ3
Levi went to the bookstore traveling 12 mph and returned home traveling 24 mph. If the total trip took 9 hours, how long did Levi travel at each speed?
Answer:
The answer to your question is
a) t₁ = 6 h
b) t₂ = 3h
Step-by-step explanation:
Data
v1 = 12 mph
v2 = 24 mph
total time = 9 h
Process
1.- Write equations to solve the problem
d₁ = v₁t₁ ------------------ Equation l
d₂ = v₂t₂
d₁ = d₂ because the distance is the same in both directions
t₁ = t₁
t₂ = 9 - t₁
d₂ = v₂(9 - t₁) -------------- Equation 2
- Equal both equations
v₁t₁ = v₂(9 - t₁)
- Substitute v₁ and v₂
12t₁ = 24(9 - t₁)
- Solve for t₁
12t₁ = 216 - 24t₁
12t₁ + 24t₁ = 216
36t₁ = 216
t₁ = 216 / 36
t₁ = 6 h
- Calculate t₂
t₂ = 9 - 6
t₂ = 3 h
A pet store has 19 goldfish tanks. The store can place 12 fish in each tank. How many goldfish can it keep? Write a division equation with a variable.
The division equation is: [tex]\frac{x}{19} = 12[/tex]
228 goldfish can be kept
Solution:
Given that,
A pet store has 19 goldfish tanks
The store can place 12 fish in each tank
Let "x" be the number of gold fish that can be kept in tank
From given information,
Number of goldfish tanks = 19
Number of fish kept in 1 tank = 12 fish
We know that,
number of gold fish that can be kept in tank = Number of goldfish tanks x Number of fish kept in 1 tank
[tex]x = 19 \times 12[/tex]
[tex]\frac{x}{19} = 12[/tex]
Thus the division equation is found
On solving we get,
x = 19 x 12 = 228
Thus 228 goldfish can be kept
Stephen and Rocco were playing video games Stephen scored 2,500 points which is 5 time's as many points as Rocco scored how many points did Rocco score
Answer:
500 points
Step-by-step explanation:
Rocco scored 1/5 as many points as Stephen, so scored ...
(1/5) × (2500 points) = 500 points
Rocco scored 500 points.
Bryan earned $9 per hour walking dogs. He paid $20 to print some flyers to advertise his dog walking business. After his expenses, he had $52. How many hours did he walk dogs? Let h= the number of hours Bryan walked the do
Answer:
bryan walked dogs for 5.8 hours
Step-by-step explanation:
if he had $52 and the walk per hour is $9
you have to divide 52/9
52/9 is 5.77777777777...
after you roud it to the nearest tenth that is 5.8
Bryan earned $9 per hour and had a $20 expense for flyers. After subtracting his expenses from his net income of $52, we can set up an equation to find the number of hours he worked, which is 8 hours.
Let h equal the number of hours Bryan walked dogs.
Calculate his earnings by multiplying h by the rate per hour, which is $9.
Subtract his expenses, which are $20 for the flyers, from his earnings to find his net income.
Set up the equation: 9h - 20 = $52.
Add $20 to both sides of the equation to isolate the term with h on one side: 9h = $52 + $20.
Simplify the right side of the equation: 9h = $72.
Divide both sides by 9 to solve for h: h = $72 ÷ 9.
Solve for h: h = 8.
Therefore, Bryan walked dogs for 8 hours to earn a net income of $52 after his $20 expense on flyers.
Which table represents points on the graph of h(x) = RootIndex 3 StartRoot negative x + 2 EndRoot?
Answer:
Table 3
Step-by-step explanation:
The third one.
We have the function
[tex]h(x) = \sqrt[3]{-x+2}[/tex]
Now we will insert values of x in that definition o h(x) and see if the values we obtain match the corresponding y values in the table:
[tex]h(-6) = \sqrt[3]{-(-6)+2}= \sqrt[3]{6+2}= \sqrt[3]{8} = 2\\h(1) = \sqrt[3]{-1+2}= \sqrt[3]{1}= 1\\h(2) = \sqrt[3]{-2+2}= \sqrt[3]{0}= 0\\h(3) = \sqrt[3]{-3+2}= \sqrt[3]{1}= 1\\h(10) = \sqrt[3]{-10+2}= \sqrt[3]{-8}= -2[/tex]
We can see that the values match the table 3, so the table 3 represents points on the graph of h(x)
Answer:
C
Step-by-step explanation:
22. Model each situation below with an equation. Select the correct equation for each situation. Then solve each problem. A. A company employs 72 workers. It plans to increase the number of employees by 6 per month until it has twice its current workforce. How many months will it take to double the number of employees?
Answer:
The equation representing the the scenario is [tex]72+6m=144[/tex].
It will take 12 month for the company to doubled the number of employees.
Step-by-step explanation:
Given:
Number of employees in the company =72
Number of employee increase per month = 6
We need to find the number of months required to double the number of employees.
Solution:
Doubled number of employees = [tex]2\times[/tex] Number of employees = 144
Let the number of months be 'm'
So we can say that;
Doubled number of employees is equal to Current number of employees in the company plus Number of employee increase per month multiplied by number of months.
framing in equation form we get;
[tex]72+6m=144[/tex]
Hence The equation representing the the scenario is [tex]72+6m=144[/tex].
On solving the above equation we get;
we will subtract both side by 72 we get;
[tex]72+6m-72=144-72\\\\6m=72[/tex]
Dividing both side by 6 we get;
[tex]\frac{6m}{6}=\frac{72}{6}\\\\m =12[/tex]
Hence It will take 12 month for the company to doubled the number of employees.
The distribution of the number of hours people spend at work per day is unimodal and symmetric with a mean of 8 hours and a standard deviation of 0.5 hours. 95% of all people work between ___ and ___ hours per day? a.7 and 9 hours (T/F)
Answer: 95% of all people work between 7 hours and 9 hours per day and It is true.
Step-by-step explanation:
Since we have given that
Mean = 8 hours
Standard deviation = 0.5 hours
According to Empirical Rule,
at 95% confidence, it lies within 2 standard deviations from the mean
so, lower value is given by
[tex]mean-2\times sd\\\\=8-2\times 0.5\\\\\=8-1\\\\=7\ hours[/tex]
upper value is given by
[tex]mean+2\times s.d\\\\=8+2\times 0.5\\\\=8+1\\\\=9\ hours[/tex]
Hence, 95% of all people work between 7 hours and 9 hours per day.
Therefore , it is true.
Final answer:
95% of people work between 7 and 9 hours per day according to the empirical rule of the normal distribution. The statement is true.
Explanation:
The distribution of the number of hours people spend at work per day is unimodal and symmetric with a mean of 8 hours and a standard deviation of 0.5 hours. Since the distribution is symmetric, and we are looking for the range that includes 95% of the distribution for a standard normal distribution, we can use the empirical rule. The empirical rule states that approximately 95% of the data in a normal distribution falls within two standard deviations of the mean.
To find the range, we calculate as follows:
Lower bound = Mean - 2(Standard Deviation) = 8 - 2(0.5) = 7 hoursUpper bound = Mean + 2(Standard Deviation) = 8 + 2(0.5) = 9 hoursTherefore, 95% of all people work between 7 and 9 hours per day. The statement is true.
A small farm field is a square measuring 350 ft on a side. What is the perimeter of the field? If you double the length of each side of the field what is the new perimeter
Answer:The new perimeter of the field is 2800 feet.
Step-by-step explanation:
The formula for determining the area of a square is expressed as
Area = 4L
Where L represents length of each side of the square.
The small farm field is a square measuring 350 ft on a side. This means that the perimeter of the field would be
Perimeter = 350 × 4 = 1400 feet.
If you double the length of each side of the field, the new length would be
350 × 2 = 700 feet.
The new perimeter of the field would be
700 × 4 = 2800 feet
Solve the following inequality using both the graphical and algebraic approach:
8 - X ≥ 5(8-x)
a. x
FIRST PHOTO IS GRAPH A
SECOND PHOTO IS GRAPH B
Algebraically, x ≤ 5π - 32 solves the inequality. Graphically, the solution lies in the shaded region below the line y = 8 - x and above y = 5(8 - π) on the coordinate plane.
Algebraic Approach:
To solve the inequality 8 - x ≥ 5(8 - π), begin by distributing 5 on the right side: 8 - x ≥ 40 - 5π. Next, isolate x by subtracting 8 from both sides: -x ≥ -5π + 32. Multiply both sides by -1, and reverse the inequality sign: x ≤ 5π - 32. This gives the solution for the inequality.
Graphical Approach:
Represent the functions y = 8 - x and y = 5(8 - π) on a graph. The point of intersection is the solution to the inequality. The line y = 8 - x is a downward-sloping line passing through the point (0, 8). The line y = 5(8 - π) is a horizontal line parallel to the x-axis at a height of 5(8 - π). The shaded region below the line y = 8 - x and above y = 5(8 - π) represents the solution to the inequality.
The question probable may be:
Solve the following inequality using both the graphical and algebraic approach: 8-x≥ 5(8-π)
How to graph. y = 1/3x + 3
A garden contains 110110 flowers, each of which is either red or orange. There are 5555 orange flowers. If R represents the number of red flowers in the garden, what equation could you use to find the value of R?
Answer:
The equation use to find the value of R is [tex]55+R=110[/tex].
Step-by-step explanation:
Given:
Total Number of flowers = 110
Number of orange flowers = 55
Let the number of red flowers be represented by 'R'
We need to find the equation used to find the value of R.
Solution:
Now we know that;
Total Number of flowers is equal to sum of Number of orange flowers and Number of red flowers.
representing in equation form we get;
[tex]55+R=110[/tex]
Hence The equation use to find the value of R is [tex]55+R=110[/tex].
On Solving the above equation we get;
We will subtract both side by 55 using Subtraction property of equality.
[tex]55+R-55=110-55\\\\R=55[/tex]
Hence There are 55 red flowers in the garden.
An urn contains four colored balls: two orange and two blue. Two balls are selected at random without replacement, and you are told that at least one of them is orange. What is the probability that the other ball is also orange?
Answer: 1/5
Step-by-step explanation:
P(both are Orange)
P(at least one is orange)
By using conditional probability:
-The P(both are Orange) is (2C2)/4C2)=1/6
-at least one orange is 1 - 1/6=5/6
P(both are Orange / at least one is orange)=(1/6) / (5/6)
=6/30
=1/5
Given one ball has been established to be orange with no replacement, there are three possible outcomes left in the urn (OO, OB, BO). Only one outcome contains both balls as orange, hence, the probability is 1/3 or approximately 0.333.
Explanation:Here, we already know that one ball selected is orange from an urn containing two orange and two blue balls. There was no replacement after the first draw, reforming the context of the problem and the counts of the balls in the urn for the second draw.
For the two-draw scenario under question, there are a total of six possible outcomes: (Orange, Orange), (Orange, Blue), (Blue, Orange), (Blue, Blue) - but since we know that at least one ball is orange, the (Blue, Blue) outcome is impossible, leaving us with three valid outcomes. Among these, only one outcome has both balls Orange.
Therefore, the probability that the other ball is also orange, given that at least one is Orange, is 1/3 or approximately 0.333, assuming that all outcomes are equally likely.
Learn more about Conditional Probability here:https://brainly.com/question/32171649
#SPJ3
Sophia pays a$9.99 membership fee for Apple Music. A. If Sophia purchases n songs for $0.99 each,write an expression for the total cost. B. If she buys two songs from a new album at a price of $0.99 each ,use your expression from part A to determine the total cost?.
Answer: A) 0.99n + 9.9
B) the total cost is $11.88
Step-by-step explanation:
Let n represent the number of songs that Sophia purchases.
A) Sophia pays a $9.99 membership fee for Apple Music. If Sophia purchases n songs for $0.99 each,then an expression for the total cost would be
0.99n + 9.9
B) If she buys two songs from a new album at a price of $0.99 each, it means that the total cost would be
0.99 × 2 + 9.9
= 1.98 + 9.9
= $11.88
Find the six trigonometric function values of the angle θ in standard position, if the terminal side of θ is defined by x + 2y = 0, x ≥ 0.
Answer:
[tex]\sin \theta = \frac{y}r} = \frac{-1}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}} = -\frac{\sqrt{5}}{5}\\\\\cos \theta = \frac{x}{r} = \frac{2}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}} = -\frac{2\sqrt{5}}{5} \\\\\tan \theta = \frac{y}{x} = \frac{-1}{2} = -\frac{1}{2} \\\\\cot \theta = \frac{x}{y} = \frac{2}{-1} = -2\\\\\sec \theta = \frac{r}{x} = \frac{\sqrt{5}}{2} \\\\\csc \theta = \frac{r}{y} = \frac{\sqrt{5}}{-1} = -\sqrt{5}[/tex]
Step-by-step explanation:
First, we need to draw the terminal position of the given angle. To do so, we need to find a point that lies on the straight line [tex] x + 2y= 0, x\geq 0 [/tex]
If we choose [tex] x = 2 [/tex] (we can do so because of the condition [tex] x \geq 0 [/tex], which means that any positive value is suitable for [tex] x [/tex]), then we have
[tex] 2 +2y = 0\implies 2 = -2y \implies y = -1 [/tex]
Therefore, the terminal side of the angle [tex] \theta [/tex] is passing through the origin and the point [tex] (2,-1) [/tex] and now we can draw it.
The angle [tex] \theta [/tex] is presented below.
The distance of the point [tex] (2,-1) [/tex] from the origin equals
[tex]r = \sqrt{2^2 + (-1)^2} = \sqrt{5}[/tex]
Now, we can determine the values of the six trigonometric function, by using their definitions.
[tex]\sin \theta = \frac{y}r} = \frac{-1}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}} = -\frac{\sqrt{5}}{5}\\\\\cos \theta = \frac{x}{r} = \frac{2}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}} = -\frac{2\sqrt{5}}{5} \\\\\tan \theta = \frac{y}{x} = \frac{-1}{2} = -\frac{1}{2} \\\\\cot \theta = \frac{x}{y} = \frac{2}{-1} = -2\\\\\sec \theta = \frac{r}{x} = \frac{\sqrt{5}}{2} \\\\\csc \theta = \frac{r}{y} = \frac{\sqrt{5}}{-1} = -\sqrt{5}[/tex]