The equation that gives the relationship between cost (c) and area (a) is c = 2a
How to determine an equation that gives the relationship between cost and area?A variation is a relation between a set of values of one variable and a set of values of other variables
Given that: the cost (c) to paint a building varies directly with the area of the surface being painted (a) in square feet
We can write:
c α a
c = ka
where k is the constant of proportionality
since c = $3,000 and a = 1500
c = ka
3000 = 1500k
k = 3000/1500
k = 2
Thus, the equation of the relationship is c = 2a
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Seven days a year, Tiger Stadium becomes the fifth largest city in the state of Louisiana. Over 92,000 fans pack the stadium to watch the Tigers play. After the game, if the fans leave at a rate of 10% per minute, how long will it take before the stadium is half empty?
It will take 5 minutes before the stadium is half empty
Given that:
Over 92,000 fans pack the stadium to watch the Tigers play
The fans leave at a rate of 10% per minute
The number of fans that leave per minute will be:
10% of 92,000 = 10/100 × 92, 000 = 9,200
The stadium will be fully empty in:
time = 92,000/9,200 = 10 minutes
The stadium will be half empty in:
time = 10 minutes / 2 = 5 minutes
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a square room has a floor area of 64 square meters. the height of the room is 9 meters. what is the area of all 4 walls?
Answer:
288 m^2
Step-by-step explanation:
each side of the room is 8 m ( 8x8 = 64)
So you have FOUR walls of widht 8 and height 9
area = FOUR * ( 9 *8) = 288 m^2
read the picture plsss
Answer:
Step-by-step explanation:
The Population of New York State can be modeled by
Answer: 19.71 Million.
Question
Solve for x.
3/5(x−7/10)=−314
Enter your answer as a mixed number in simplest form in the box.
x =
Answer:
x = -522 19/30
Step-by-step explanation:
To solve for x, distribute the 3/5. This gives us 3/5x - 21/50 = -314. Add over 21/50 to the other side, allowing for 3/5x to equal -313 29/50. Divide by 3/5 on both sides and we get x equal to -522 19/30. This is the final answer as a mixed number and is also in simplest form.
Brian started cleaning at 3:33 PM and finished at 4:21 PM. How long did it take him.
Brian started cleaning at 3:33 PM and finished at 4:21 PM. The correct answer is 48 minutes
How did we figure this out?First, we are figuring out what is given we are counting numbers or we can add to get to 4:21 PM.
Counting numbers:
[tex]\boxed{3:33=3:34=3:35=3:36=3:37=3:38=3:39=3:40 }[/tex]
Add the numbers:
[tex]\boxed{3:33+7=3:40+10=3:50+10=4:00+21=4:21}[/tex]
If we add the numbers it would be faster.
Therefore, when we add we get are answer.
Therefore, Brian started cleaning at 3:33 PM and finished at 4:21 PM. The correct answer is 48 minutes
Answer:
48
Step-by-step explanation:
x^4-2x^2-16x-15=0 find the zeros with work please
ANSWER : -1 , 3 , (-1 - 2i) , (-1 + 2i)
steps
find the zeros JUST MEANS SOLVE FOR X
x⁴-2x²-16x-15=0
break it up
let u = x²
x⁴ = (x²)² = u²
-16x+u²-2u-15=0
hold off on -16x
u²-2u-15=0
what 2 numbers when multiplied give you -15 & when added give you -2?
-5 and 3
(u-5) (u+3)
-16x + (u-5) (u+3) = 0
go back x
-16x + (x²-5) (x²+3) = 0
factor -1 out
( looks horrible so far lol )
-1 ((- x²+ 5) (x²+3) + 16x) = 0
multiply (- x²+ 5) with ( x² + 3 )
-1 (( - x² ( x² + 3 ) + 5 ( x² + 3 ) ) + 16x ) = 0
-1 (( - x² ( x² + 3 ) + 5 ( x² + 3 ) ) + 16x ) = 0
-1 (( - x² ( x² + 3 ) + 5 ( x² + 3 ) ) + 16x ) = 0
-1 (( - x² * x² + -x² * 3 ) + 5x² + 15 ) + 16x ) = 0
-1 (( - x⁴ + -2x² + 15 ) + 16x ) = 0
I understand A and B but I do not understand what they are asking for C. I have no idea what the answer is, please help! Thanks
Mike sells grapes at a farmers market. Each pound of grapes sells for the same amount. The table below shows the total prices for different numbers of pounds of grapes sold.
Grapes
Number of Pounds Sold Total Price ($)
2 $4.50
4 $9.00
10 $22.50
A. Write an equation that describes the relationship between the number of pounds of grapes sold(x) and the total price (y), in dollars.
Mike also sells red peppers at the farmers market. The equation below can be used to find the total price (p) in dollars of r pounds of red peppers.
p = 1.80r
B. What is the total price, in dollars, of 17 pounds of red peppers? Explain what the 1.80 represents in the context of the situation.
The farmer decides to increase the price per pound of the grapes. A graph is created to represent both the original equation from Part A and a new equation based on the increased price per pound of the grapes.
C. Thinking about what this graph would look like, explain why the graphs representing the equations will share one point even though the prices per pound are different.
A. The relationship between the number of pounds of grapes sold (x) and the total price (y) can be described by the equation y = 2.25x.
The required details for pounds in given paragraph
This equation can be derived from the data in the table by substituting the values for x and y and solving for the coefficient 2.25. For example, for x = 2 pounds of grapes, we have y = $4.50, so 4.50 = 2.25 * 2. Similarly, for x = 4 pounds of grapes, we have y = $9.00, so 9.00 = 2.25 * 4. We can use this equation to find the total price for any number of pounds of grapes sold.
B. The total price of 17 pounds of red peppers is $31.60. The 1.80 in the equation p = 1.80r represents the price per pound of red peppers. In this case, 1.80 dollars is the price per pound of red peppers, and r is the number of pounds of red peppers that are being purchased. Therefore, the total price of r pounds of red peppers is equal to 1.80 dollars per pound multiplied by the number of pounds of red peppers being purchased.
C. The graphs representing the equations for the original and increased price per pound of grapes will share one point because the two equations will be tangent to each other at that point.
what is pound?
A pound is a unit of weight that is commonly used in the United States and some other parts of the world. It is defined as the weight of a standard reference object, called the international pound, which is kept at the International Bureau of Weights and Measures in France.
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Write the coordinates of the vertices after a reflection over the line y=-5.
The coordinates of the vertices after a reflection over the line y = -5 is given as follows:
T'(-2,-5), U'(2,-7), V'(-2,-9), W'(-3,-7).
How to obtain the coordinates of the vertices after the reflection?The vertices of the original quadrilateral are given as follows:
T(-2,-5), U(2,-3), V(-2,-1), W(-3,-3).
The reflection line y = -5 is an horizontal line, meaning that after the reflection:
The x-coordinate remains constant.The y-coordinate will be equidistant to y = -5, however in an opposite direction.For example, the distance of the y-coordinate of the vertex U from -2 is of:
2 units above.
Then the y-coordinate of the vertex U' will be also 2 units from -5, just two units below, hence:
U'(2,-7).
Applying this rule for all the other vertices, they will be given as follows:
T'(-2,-5), U'(2,-7), V'(-2,-9), W'(-3,-7).
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Write an equation of the line that passes through the points.
4.(-3,0), (-2, 3)
5. (-6, 10), (6, -10)
4.
find slope;
3 - 0/-2 -(-3) = 3/1 = 3
y = 3x + b
0 = (3)(-3) + b
0 = -9 + b
b = 9
y = 3x + 9
Given △
△
M
T
S
and △
△
S
Q
P
, find SP.
Answer:
22
Step-by-step explanation:
Corresponding sides of similar triangles are proportional.
[tex]\frac{3x+2}{5x-4}=\frac{15}{20}=\frac{3}{4} \\ \\ 12x+8=15x-12 \\ \\ 3x=20 \\ \\ \therefore SP=20+2=22[/tex]
6x-7=1-3x[tex]6x-7=1-3x[/tex]
Answer:
x=8/9
Step-by-step explanation:
step one: move x to one side. to do this, we are going to use inverse operations which means adding 3x to both sides.
3x+-3x cancels itself out and 3x+6x=9x.
now, the equation looks like: 9x-7=1
step two: isolate the variable, x. we want to just get x to be by itself so we need to get rid of the -7 next to it by using inverse operations again. this means we're going to add 7 to both sides.
7+-7 cancels itself out and 7+1=8.
now, the equation looks like 9x=8
step three: divide to get x by itself. we want to know what x alone is, not 9x. to do this we are going to use inverse operations one last time. this means dividing each side by 9, because 9x means "9 times x".
9x/9= x, 8/9
so the answer is x=8/9
hope this helped!!
One angle measures 130°, and another angle measures (8k + 58)°. If the angles are vertical angles, determine the value of k.
Vertical angles are pairs of angles that are located on opposite sides of a line and are equal in measure, the value of k is 9.
How to find value of k ?Vertical angles are pairs of angles that are located on opposite sides of a line and are equal in measure. They are formed when two lines intersect, and they are always congruent, or equal in measure.
That if one angle measures 130°, the measure of its vertical angle must also be 130°.
If the other angle has a measure of (8k + 58)°, and it is a vertical angle to the angle that measures 130°, then it must also have a measure of 130°.
We can set up the equation 130 = 8k + 58 and solve for k to find the value of k.
Subtracting 58 from both sides gives us 72 = 8k. Dividing both sides by 8 gives us k = 9.
Therefore, the value of k is 9.
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Solve for c.
4(c + 17) = 16
C =
Please help
What is the radius of the circumscribed circle of ABC?
Answer:
Given: △ABC, m∠A=120°, AB=AC=1 Find: The radius of circumscribed circle
Step-by-step explanation:
:]
a company makes wax candles in the shape of a cylinder. each candle has a diameter of 4 inches and a height 8 of inches. if the company used of wax, how many candles did it make? use for , and do not round your answer.
If the company has made 6732.16 in³ wax , Total number of candles made is 67
According to the question,
It is given that a wax candle is in cylindrical shape
Diameter of candle = 4 in
Radius will be = 4 / 2
=> 2 in
Height of each candles = 8 in
Company has used 6732.16 in³ of wax
We have to calculate number of candles company has made
Volume of cylinder = πr²h
Where r is radius and h is height
Substituting all the values,
Volume of candle = π (2)² (8)
=> V = 3.14 × 4 × 8 (putting π = 3.14)
=> V = 100.48
Therefore , Number of candles made = Total volume /volume of one candles
=> 6732.16 / 100.48
=> 67 candles are made by company
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forty percent (40%) of consumers believe that cash will be obsolete in the next twenty years. assume that 8 consumers are randomly selected. find the probability that:
The probability that less than three of the chosen consumers think that currency won't be used in 20 years is 0.293.
According to the statement, 40% of consumers think cash will be unnecessary in 20 years. Let us assume that eight consumers are chosen at random.
We need to determine the likelihood that fewer than three of the chosen consumers think currency will be obsolete in 20 years.
We will use the properties of probability distribution in the given scenario.
We know that for randomly selected variable the properties of combination are used.
P(X=1) + P(X=2) = C¹₈ × 40 × 60⁷ + C²₈ × 40² × 60⁶
P(X=1) + P(X=2) = 0.293
Therefore, there is a 0.293 percent chance that fewer than 3 of the chosen customers think that cash will be obsolete in 20 years.
The ratio of likely outcomes to all scenarios that are feasible, to all possible outcomes is called probability.
Normal distributions are crucial to statistics because they are commonly used in the natural and social sciences to describe real-valued random variables with uncertain distributions. They are important in part because of the central limit theorem.
This claim asserts that under certain conditions, the average of many samples (observations) of a random variable without finite mean and variance is itself a random variable, whose distribution converging to either a normal distribution as the number of samples increases.
Disclaimer: The complete question is :
40% of consumers believe that cash will be obsolete in the next 20 years. Assume that only 8 consumers are randomly selected. Find the probability that less than 3 of the selected consumers believe that cash will be obsolete in the next 20 years .
(Round to three decimal places as needed.)
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for what values of x and y are the triangles congruent by HL?
For the given congruent triangles, the values of x = -1 and y = 3.
What do you mean by congruence of triangle?Two triangles are congruent if all three corresponding sides are equal and all three corresponding angles are equal. These triangles can be moved, rotated, flipped, and flipped to look identical. When rearranged they match each other.
The congruence symbol is "≅".As both the triangles are congruent therefore their corresponding sides will be equal.
3y + x = y + 5 ...........(1)
y - x = x + 5 ..............(2)
Equation
1:3y + x = y + 5
3y - y = 5 - x
2y = 5 - x
x = 5 - 2y ..............(3)
Substitute this value of x in equation (2)
y - x = x + 5 y = x + x + 5y
= 2x + 5 y = 2(5 - 2y) + 5y
= 10 - 4y + 54y + y = 15
5y = 15 y = 15/ 5
y = 3
Substitute this value of y in equation (3) x = 5 - 2(3) = 5 - 6 = -1
Therefore, x = -1 and y = 3
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JKLM is a parallelogram.
What is the measure of ZKLJ?
Enter your answer in the box.
Theres no point 'Z', so i'm gussing you want the angle of <KLJ?
<K and <M are the same, therefore <M = 130
<J + <K + <M + <L = 360
130 + 130 = 260, 360 - 260 = 100
<J and <L are the same
<MJK = 50 and <KLM = 50
<KLM/2 = <KLJ
50/2 = 25
your statistics class has 26 students in it what is the probability that both students are girls given that the second student chosen is a girl
Given that the second student chosen is a girl, the probability that both students are female is 0.175.
The occurrence of likely events is referred to as probability. It is the branch of mathematics concerned with numerical estimates of the likelihood of an event occurring or a statement being true.
Probability is nothing but likelihood of something is to occur. When we are unsure about the outcome of an event, we can discuss the probabilities of certain outcomes—how likely they are.
The probability of selecting a girl from the class is
[tex]= \frac{Number\ of\ girls}{ Total\ number\ of\ students}= \frac{14}{26}\\\\= \frac{7}{13}[/tex]
It is known that the one of the chosen student from 2 students is girl, the probability of having both girls will be:
[tex]= \frac{7}{16} * \frac{6}{15}\\\\= 0.175[/tex]
Hence, the probability is 0.175.
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Your question is incomplete, here is the complete question.
Your statistics class has 26 students in it - 14 girls and 12 boys.Your teacher uses a calculator to select two students at random to solve a problem on the board. Given that the second student chosen is a girl, what is the probability that the first student was also a girl?
Find the y intercept y = – 17 x + 12.
Answer: 12
Step-by-step explanation:
The y-intercept in the equation that is in slope-intercept form is the constant.
what is the point estimate of the proportion of the population of adults who do think that today's children will be better off than their parents? if required, round your answer to two decimal places.
The point estimate of the proportion of the population adults who think that today's children will be better off than their parents is 0.24.
The point estimate of P, is defined as the proportion of successes in the sample.
P' = X/N ; where X = number of successes; N = total trials.
Here, N = 1000
According to the Child outlook file, number of "yes" = 240.
Hence, P' = 240/1000
P' = 0.24
Therefore, the point estimate of the proportion of the population adults who think that today's children will be better off than their parents is 0.24.
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Simplify 4x - 7 + 12x - 3.
Answer:2(8x-5)
Hope this helps!
I NEED HELP ON THIS QUESTION!!
Answer:
B
Step-by-step explanation:
Determine the equation of the line given by the table and compare with given options.
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, 9) and (x₂, y₂ ) = (7, 19) ← 2 ordered pairs from the table
m = [tex]\frac{19-9}{7-2}[/tex] = [tex]\frac{10}{5}[/tex] = 2 , then
y = 2x + c ← is the partial equation of the line
to find c substitute any ordered pair from the table into the partial equation.
using (6, 17 ), that is x = 6, y = 17 , then
17 = 12 + c ⇒ c = 17 - 12 = 5
y = 2x + 5 ← equation of line from table, with y- intercept c = 5
thus the function with a y- intercept greater than the table line is B
Geometry Suppose that a pizza must fit into a box with a
base that is 12 in. long and 12 in. wide. You can use the
quadratic function A Tr² to find the area of a pizza in
terms of its radius.
a. What values of r make sense for the function?
b. What values of A make sense for the function?
c. Graph the function. Round values of A to the
nearest tenth.
Question 39
The value of (a) r that make sense is 6 in. and (b) the value of A that make sense is 113.1 in²
How to determine the Radius of the circle?You should understand that the pizza is fit inside the square box making all circumference of the circle to touch all the sides of the square box
The quadratic function reads
A= πr²
Where A= Area of circle,
π = 22/7
and r= radius of the circle
A= (22/7)*6
Width of the box is 12
Therefore 12/2 = r=6
A= (22*6*6)/7
A=113.1 in²
In conclusion, he value of (a) r that make sense is 6 in. and (b) the value of A that make sense is 113.1 in²
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Given AB CD , what is the m∠ x and m∠ y in this diagram?
Justify your answer using geometry vocabulary.
Answer:
m∠ x is 130° and m∠ y is 130°
Step-by-step explanation:
Based on the drawn example I gave would explain why
So because ∠AGF = ∠CHF that would make these two angles Corresponding angles and corresponding angles are congruent
Thus making ∠AGH or m∠ x equals 130°
Now we look at ∠DHE and ∠AGF these two angles would be classified as Alternate interior angles which would make them congruent to each other aswell
Thus making ∠DHG or m∠ y equals 130°
Reason also includes the fact that m∠ x and m∠ y would be alternate interior angles also
d) if 36 reindeer are randomly selected, what is the probability their mean weight is less than 100kg
When 36 reindeer are chosen at random, the probability that the mean weight is less than 100 kg is 0.1492.
A standard error is the standard deviation of its sampling distribution or an interpretation of that standard deviation.
Given,
Mean of the weights = 102.4 kg
Standard deviation = 13.9 kg
To determine the probability that the mean weight of 36 reindeer will be less than 100 kg, first compute the standard error using the formula,standard error, [tex]\sigma_x=\frac{\sigma}{\sqrt{n}}[/tex]
Where, [tex]\sigma[/tex]=standard deviation
n= number of reindeer
substitute the values in the formula,
[tex]\sigma_x=\frac{13.9}{\sqrt{36}}\\\\\sigma_x=2.31667[/tex]
Now,
[tex]P(x < 100)=P(x < \frac{100-102.4}{2.316})\\\\=P(z < -1.04)[/tex]
from z-score table,
=0.1492
Thus, the probability the their mean weight is less than 100 kg is 0.1492.
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Your question is incomplete, here is the complete question.
The weight of male reindeer of the R. Santa Claus subspecies is normally distributed with mean 102.4 kg and standard deviation 13.9 kg
if 36 reindeer are randomly selected, what is the probability their mean weight is less than 100kg?
Tabatha and Horatio each leave their separate houses and drive to a restaurant to meet for dinner. Tabatha lives 15 miles from the restaurant, and she drives at a rate of 3 miles every 2 minutes. The graph represents Horatio’s distance, in miles, y, from the restaurant after driving for x minutes.
Tabatha drives 1/12 mile more per minute than Horatio drives.
Tabatha drives 1/6 mile more per minute than Horatio drives
Tabatha drives 3 miles more per minute than Horatio drives.
Tabatha drives 9 miles more per minute than Horatio drives.
Answer:
Tabatha drives 1/6 mile more per minute than Horatio drives
Step-by-step explanation:
Fatimah ate f cookies. Satvinder ate six fewer than two times the number that Fatimah ate. If Satvinder ate 4 cookies, write and solve an equation to find f, the number of cookies Fatimah ate.
If Satvinder ate 4 cookies, then the number of cookies that Fatimah ate will be 5.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Fatimah ate f treats. Satvinder ate six less than twice the number that Fatimah ate.
Let 's' be the number of cookies eaten by Satvinder. Then the equation is given as,
s = 2f - 6
If Satvinder ate 4 cookies, then the number of cookies that Fatimah ate will be given as,
4 = 2f - 6
2f = 10
f = 5
On the off chance that Satvinder ate 4 treats, the number of treats that Fatimah ate will be 5.
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Solve the inequality. Enter the answer as an inequality that shows the value of
the variable; for example f> 7, or 6 < w. Where necessary, use <= to write <
and use >= to write 2.
v-(-5) <-9
Solve the inequality. v - (-5) < -9 the solution for the inequality is
v < -14What is inequality?Inequality, A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.
How to solve the inequalityThe given algebraic expression is v - (-5) < -9
This is solved as follows
v - (-5) < -9
v + 5 < -9
v < -9 - 5
v < -14
The value of v is -14
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