It will take 1.5 hours (or 1 hour and 30 minutes) before Taylor and Blair are 225 miles apart.
To find out how many hours it will be before Taylor and Blair are 225 miles apart, we can set up an equation based on the distance they travel.
Since they are driving away from each other in opposite directions, their distances add up to the total distance they will be apart.
Let t be the number of hours it takes for them to be 225 miles apart.
Distance traveled by Blair = Blair's speed * time (d = r * t)
Distance traveled by Taylor = Taylor's speed * time (d = r * t)
The total distance they will be apart is 225 miles:
Blair's distance + Taylor's distance = 225 miles
(70 mph * t) + (80 mph * t) = 225 miles
Now, solve for t:
70t + 80t = 225
150t = 225
t = 225 / 150
t = 1.5
So, it will take 1.5 hours (or 1 hour and 30 minutes) before Taylor and Blair are 225 miles apart.
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if the average (arithmetic mean) of two, seven, and X is 12, what is the value of X?
Find the area of the regular polygon.
pentagon with a radius of 4 ft
Shawn wants to buy a cd player that costs $48.00. If he has already saved $30.00, what percent of the price of the cd player has he saved?
Substituting x-4=y and -5y+8x=29
Gary earns $12 an hour plus $16 an hour for every hour of overtime. Overtime hours are any hours more than 30 hours for the week. Part A: Create an equation that shows the amount of money earned, M, for working x hours in a week when there is no overtime. (3 points) Part B: Create an equation that shows the amount of wages earned, T, for working y hours of overtime. Hint: Remember to include in the equation the amount earned from working 30 hours. (3 points) Part C: Gary earned $408 in 1 week. How many hours (regular plus overtime) did he work? Show your work. (4 points)
Part A.
Amount of money earned = Regular rate per hour * Number of working hours
M = 12 x
Part B.
Amount of wages earned = Regular rate per hour * Maximum number of regular working hours + Overtime rate per hour * Excess working hours
T = 12 * 30 + 16 * y
T = 360 + 16 y
or
T = 16 y + 360
Part C.
Given T = 408, find y:
408 = 16 y + 360
y = 3 hrs
Therefore the total hours Gary worked that week is,
x + y = 30 + 3 = 33 hrs
(x = 30 since that is the maximum limit for regular working hours)
Translate the sentence into an equation. Twice the difference of a number and 2 equals 9 . Use the variable y for the unknown number.
The value of variable y in the equation,
2y + 2 = 9 is y = 7/2.
What is an equation?An equation is a pair of algebraic equations with the equal sign (=) in the middle and the same value.
Given:
A phrase: Twice the difference of a number and 2 equals 9.
Let the number be y.
Then according to the question,
twice the difference of a number means,
2 x y
= 2y.
And the 2y and 2 equals 9.
That means,
we have an equation,
2y + 2 = 9
Subtract 2 from both sides,
we get,
2y = 7
y = 7/2.
Therefore, the value of y is 7/2.
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3x+2y+4z=12
X+y+2z=6
(X=0,y=4,z=1)
Determine if the given 2 lines intersect at the given point. Explain your reasoning.
-2x-4y+z=8
4x+2y=-5
(x=-2,y=0,z=3) same as up above
In the diagram below, an and bc are tangent to o. What is the measure of adc
Answer:
mADC = 220°
Step-by-step explanation:
In the given diagram AB and BC are tangents to the given circle O. We have to find the measure of arc ADC.
By theorem of tangents and arcs.
m∠ABC = [tex]\frac{1}{2}[/tex] [m ADC- m AC ]
Since it is given in the question
∠ABC = 40 & AC = 140°
Therefore, 40 = [tex]\frac{1}{2}[/tex] [ m ADC - 140 ]
40 × 2 = m ADC - 140
80 + 140 = m ADC
mADC = 220°
The perimeter of a scalene triangle is 14.5 cm. The longest side is twice that of the shortest side. Which equation can be used to find the side lengths if the longest side measures 6.2 cm?
Choose the correct answer.
6.2 + b = 14.5
9.3 + b = 14.5
12.4 + b = 14.5
18.6 + b = 14.5
What is the average of three checks, one for $16.00, one for $40.00 and one for $130?
add them then divide by 3
16.00 + 40.00 + 130 = 186.00
186.00/3 = 62.00
the average is 62.00
Conjecture for interior angles of complex polygons
Final answer:
The conjecture for interior angles of complex polygons involves using the formula (n-2)×180 degrees for regular polygons and more complex considerations for 3D shapes like pentagonal bipyramids or square antiprisms. As the number of sides increases, calculations become more intricate and the interior angles can approach 180 degrees in very large polygons.
Explanation:
The question involves making a conjecture for the interior angles of complex polygons. A commonly used theorem related to this is that the sum of the interior angles of a polygon can be found using the formula (n-2)×180 degrees, where n is the number of sides in the polygon. For instance, to find the sum of the interior angles of a pentagon (a polygon with five sides), we calculate (5-2)×180 degrees = 540 degrees. As the number of sides increases, our calculations can become more complex, especially when dealing with non-regular polygons (where the sides and angles don't all have the same length/measure).
When considering the interior angles of complex geometries like a pentagonal bipyramid or a square antiprism, it's essential to recognize that their interior angles may involve multiple planes and hence cannot be calculated using the simple 2D polygon interior angle sum formula. These shapes involve three-dimensional calculations and often require advanced geometry or trigonometry to dissect into understandable components.
Considering large numbers of sides and complex figures, the interior angle measures can approach different limits. For example, as the number of sides I becomes very large, the interior angle measures can become very close to 180 degrees, which is suggested by the idea that for a polygon with infinitely many sides (approaching a circle), each interior angle would be 180 degrees.
Which expression is equivalent to (x^27y)^1/3?
A) x^3 (3√y)
B) x^9 (3√y)
C) x^27 (3√y)
D) x^24 (3√y)
Answer:
Option B).[tex]x^{9}.(\sqrt[3]{y} )[/tex].
Step-by-step explanation:
The given expression is [tex](x^{27}y)^{\frac{1}{3} }[/tex].
We have to further simplify so that we can get the answer as shown in the options.
[tex](x^{27}y)^{\frac{1}{3} }=(x^{27})^{\frac{1}{3}}(y)^{\frac{1}{3}}[/tex]
[ As [tex](x^{a}.y^{b})^{m}=(x^{a})^{m}.(y^{b})^{m}[/tex] ]
Now ([tex](x^{27})^{\frac{1}{3}}(y)^{\frac{1}{3}}=(x^{\frac{27}{3} }).(y^{\frac{1}{3} } )=x^{9}.(\sqrt[3]{y} )[/tex]
Therefore Option B. is the answer.
Do the ratios 1/12 and 8/96 form a proportion? Explain.
Which of the numbers listed below are solutions to the equation? Check all that apply. x2 = 81 A. 18 B. 40.5 C. -9 D. 162 E. 9 F. 6561
Raquel and Van live in two different cities. As part of a project, they each record the lowest prices for a gallon of gas at gas stations around their cities on the same day. Raquel’s data reflect a mean price of $3.42 with a standard deviation of 0.07. Van’s data reflect a mean price of $3.78 with a standard deviation of 0.23. Which statement is true about their gas-price data? Raquel’s data are most likely closer to $3.42 than Van’s data are to $3.78. Van’s data are most likely closer to $3.42 than Raquel’s data are to $3.78. Raquel’s data are most likely closer to $3.78 than Van’s data are to $3.42. Van’s data are most likely closer to $3.78 than Raquel’s data are to $3.42.
Answer:
Raquel’s data are most likely closer to $3.42 than Van’s data are to $3.78.
Step-by-step explanation:
We know that a standard deviation is a measure that is used to find the amount of dispersion or variation of the data set.If standard deviation is low this means that the data points tends close to the mean of the data set.while a higher standard deviation means that the data values are spread to a greater range.Hence, form the given information we may imply that:
Raquel’s data are most likely closer to $3.42 than Van’s data are to $3.78.
( Since, the standard deviation of Raquel's data is low which is 0.07 as compared to Van's data ( which is 0.23).
Hence, the Raquel's data will tend close to the mean which is $ 3.42. )
In a certain? country, the true probability of a baby being a boy is 0.534. among the next six randomly selected births in the? country, what is the probability that at least one of them is a girl??
The probability that at least one of them is a girl is about 0.977
Further explanationThe probability of an event is defined as the possibility of an event occurring against sample space.
[tex]\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }[/tex]
Permutation ( Arrangement )Permutation is the number of ways to arrange objects.
[tex]\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }[/tex]
Combination ( Selection )Combination is the number of ways to select objects.
[tex]\large {\boxed {^nC_r = \frac{n!}{r! (n - r)!} } }[/tex]
Let us tackle the problem.
This problem is about Probability.
Given:
The true probability of a baby being a boy P(B) = 0.534
The true probability that all of six randomly selected births in the country are boys is :
[tex]P(6B) = P(B) \times P(B) \times P(B) \times P(B) \times P(B) \times P(B)[/tex]
[tex]P(6B) = \boxed {(P(B))^6}[/tex]
The true probability that at least one of them is a girl is:
[tex]P(G\geq 1) = 1 - P(6B)[/tex]
[tex]P(G\geq 1) = 1 - (P(B))^6[/tex]
[tex]P(G\geq 1) = 1 - (0.534)^6[/tex]
[tex]P(G\geq 1) \approx \boxed {0.977}[/tex]
Learn moreDifferent Birthdays : https://brainly.com/question/7567074Dependent or Independent Events : https://brainly.com/question/12029535Mutually exclusive : https://brainly.com/question/3464581Answer detailsGrade: High School
Subject: Mathematics
Chapter: Probability
Keywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation
The probability that out of the next six randomly selected births, at least one of them is a girl is 0.98.
What is Probability in Mathematics?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur. Mathematically -
P (Event A) = n(A)/n(S)
where -
n(A) → Number of outcomes favorable to event A.
n(B) → Total number of possible outcomes.
Given is the true probability of a baby being a boy. Its value is -
P(A) = 0.534
Assume that for the next six randomely selected births, the probability that it will be a baby boy is P(B). In one of the six randomely selected births, the probability that it will be a boy is 0.534. Therefore, the probability of being a boy in all the six cases will be -
P(B) = [P(A)]⁶
P(B) = 0.023
Now, for at least one of them to be girl, the probability of the event will be -
P(C) = P(B)' = 1 - 0.023 = 0.98
Therefore, the probability that out of the next six randomly selected births, at least one of them is a girl is 0.98.
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What is the factored form of the expression
What is the shape of the graph of any geometric sequence?
Final answer:
The graph of a geometric sequence forms either an exponential decay or growth curve, depending on the common ratio, with the sequence appearing as a straight line on a semi-logarithmic scale.
Explanation:
The graph of any geometric sequence takes on a distinctive shape. If the common ratio of the geometric sequence is between -1 and 1 (excluding 0), the points of the graph will form a curve that approaches the x-axis as the number of terms increases, which is known as an exponential decay if the common ratio is positive, and an oscillating decay if it is negative. Similarly, if the common ratio is greater than 1 or less than -1, the sequence will exhibit exponential growth with each subsequent term becoming larger, and the points will diverge away from the x-axis forming an upward curve if the common ratio is positive or oscillating upward if it is negative. The graph may have a y-intercept, where it crosses the y-axis, and when graphed on a semi-logarithmic scale, the sequence with a positive common ratio will appear as a straight line.
A quadratic equation is shown below:
25x2 + 10x + 1 = 0
Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)
Part B: Solve 4x2 − 4x + 1 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)
hello :
help :
the discriminat of each quadratic equation : ax²+bx+c=0 ....(a ≠ 0) is :
Δ = b² -4ac
1 ) Δ > 0 the equation has two reals solutions : x = (-b±√Δ)/2a
2 ) Δ = 0 : one solution : x = -b/2a
3 ) Δ < 0 : no reals solutions
the area of the cross section of a sphere at the largest point is 100 Pi square miles. What is the total surface area of the sphere?
The distance between two cities on a map is 3 1/2 inches. The actual distance between the two cities is 28 miles.
a. What is the scale used on the map?
b. If the scale on a different map of the same area is inch = 1 mile, how separate the same two cities?
The width of a rectangle is 7 inches less than its length. The area of the rectangle is 120 square inches. Solve for the dimensions of the rectangle. Length: inches Width: inches
area = L x W
W=L-7
120 = L x L-7
120 = L^2-7L
L^2-7L+120 =0
(L-15) (L+8)
L=15, L=-8. It can't be a negative number so L=15
W=15-7 = 8
15*8 =120
length = 15 inches
width = 8 inches
Answer:
The dimensions of the rectangle. Length= 15 inches and Width= 8 inches
Step-by-step explanation:
Let width of rectangle be W and length be L then
L=W+7 ---- (A)
Also given that area of rectangle = 120 square inches
=> WxL=120 -----(B)
From equation (A) and (B)
Wx(W+7) = 120
=> [tex]W^{2}+7W-120=0[/tex]
=>[tex]W^{2}+15W-8W-120=0 =>(W+15)(W-8)=0[/tex]
=> [tex]W=-15 or 8[/tex]
Since the width can not be a negative quantity , so W= 8 inches
=> L= W+7= (8+7) inches = 15 inches
Thus the dimensions of the rectangle. Length= 15 inches and Width= 8 inches
Choose the equation below whose axis of symmetry is x = 2.
y = x^2 + 4x + 2
y = x^2 - 4
y = x^2 - 2
y =x^2 - 4x + 2
Answer:
Hi!
The correct answer is y =x^2 - 4x + 2
Step-by-step explanation:
The axis of symmetry is the x-coordinate vertex of the parabola.
The general form to find the axis of symmetry is:
[tex]x=-\frac{-b}{2*a} [/tex]
For y =x^2 - 4x + 2, a=1, b=−4 and c=2:
[tex]x=-\frac{-4}{2*1} = - \frac{-4}{2} = -(-2) = 2[/tex]
[tex]x = 2[/tex]
Find the 6th term of a geometric sequence t3 = 444 and t7 = 7104.
The 6th term of the geometric sequence is 3552
How to determine the 6th term of the geometric sequenceTo find the 6th term of a geometric sequence, we need to determine the common ratio (r) first.
Given that t3 = 444 and t7 = 7104, we can use these two terms to find the common ratio.
t3 = t1 * r^(3-1)
444 = t1 * r^2
t7 = t1 * r^(7-1)
7104 = t1 * r^6
Dividing the two equations, we get:
7104/444 = (t1 * r^6) / (t1 * r^2)
16 = r^4
Taking the fourth root of both sides, we find:
r = ∛16 = 2
Now that we have the common ratio (r = 2), we can find the first term (t1) by substituting the values of t3 and r into the equation t3 = t1 * r^(3-1):
444 = t1 * 2^2
444 = 4t1
t1 = 111
To find the 6th term (t6), we substitute the values of t1 and r into the general formula for the nth term of a geometric sequence:
t6 = t1 * r^(6-1)
t6 = 111 * 2^5
t6 = 111 * 32
t6 = 3552
Therefore, the 6th term of the geometric sequence is 3552.
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What is something that multipys to 72 and adds -27?
Candida bought 334 yards of fabric. If she uses 23 of the fabric to make a dress, how much fabric will she have left?
Are 60 meters equal to, greater than, or less than 6 km?
Final answer:
60 meters is significantly less than 6 kilometers, as 6 kilometers is equal to 6,000 meters.
Explanation:
To answer this, we need to compare the two measurements in the same unit. We know that 1 kilometer is equivalent to 1,000 meters, so to convert 6 kilometers to meters, we multiply by 1,000:
6 km imes 1,000 = 6,000 m
Now we can compare the two measurements:
60 m
6,000 m
Since 60 is less than 6,000, we can conclude that 60 meters is less than 6 kilometers.
A school did a survey among 100 students to find their sports preferences. The students were asked about their preferences for football or baseball. Out of the total 77 people who liked football, 48 also liked baseball. There were 65 people who liked baseball. Part A: Summarize the data by writing the values that the letters A to I in the table below represent. (5 points)A school did a survey among 100 students to find their sports preferences. The students were asked about their preferences for football or baseball. Out of the total 77 people who liked football, 48 also liked baseball. There were 65 people who liked baseball. Part A: Summarize the data by writing the values that the letters A to I in the table below represent. (5 points) Like football Do not like football Total Like baseball A D G Do not like baseball B E H Total C F I Part B: What percentage of the survey respondents did not like either football or baseball? (3 points) Part C: Do the survey results reveal a greater dislike for football or baseball? Justify your answer. (2 points)
Answer:
Part A: A=48 B=29 C=77 D=17 E=6 F=23 G=65 H=35 I=100
Part B: 6% of the survey respondents did not like either football or baseball.
Part C: The survey results reveal a great dislike for baseball this is because 35% of the survey respondents dislike baseball while only 23% of the survey respondents dislike football.
What is the square root of pi?
If you flip a coin twice, what is the probability that you flip tails both times?
Answer: 1/4
Step-by-step explanation: In this problem, we are tossing two coins and we want to find the probability of tossing a tails and a tails. Tossing two coins are independent events because the outcome of tossing one coin does not affect the outcome of tossing the other coin.
We can find the probability of independent events by multiplying the probability of the first event by the probability of the second event. Note that we are talking about the theoretical probability because we aren't going to actually toss the coins.
If we want to find the probability of tossing a tails and a tails, we multiply the probability of tossing a tails by the probability of tossing a tails.
Now, let's find the probability of tossing a tails on the first coin. Remember that a coin has two sides which are heads and tails. Tails is one of these sides so the probability of tossing a heads is 1 out of 2 or 1/2. On the second coin the same is true so the probability is 1 out of 2 or 1/2.
Finally, we can simply multiply 1/2 by 1/2 which gives us 1/4. Therefore, the probability of tossing tails and tails is 1/4.