1. Homer has an idea for a new donut shop. He wants to design the donut shop so that the rectangular
store has a perimeter of 63.5 metres and an area of 225 metres. Is Homer's design possible?
Justify your answer algebraically.

The equation of the line containing the point (6,−2) and perpendicular to the line 5x+4y=7 in slope-intercept form is y = (-5/4)x + (17/4).

To write an equation of the line containing the given point (6, -2) and perpendicular to the given line 5x + 4y = 7 in slope-intercept form, we need to follow the steps given below :

Step 1: First, we need to find the slope of the given line.5x + 4y = 7The given line can be written in slope-intercept form as:4y = -5x + 7y = (-5/4)x + (7/4)Thus, the slope of the given line is -5/4.

Step 2: Since the given line is perpendicular to the line we need to find, the slope of the line we need to find can be found using the formula :Slope of the line we need to find = -1 / slope of the given line Substituting the values in the formula :Slope of the line we need to find = -1 / (-5/4) = 4/5Therefore, the slope of the line containing the point (6, -2) and perpendicular to the given line is 4/5.

Step 3: We have the slope of the line and a point on it. Using the point-slope form of the equation, we can write the equation of the line as : y - y1 = m(x - x1)where (x1, y1) is the given point and m is the slope of the line. Substituting the values in the formula : y - (-2) = (4/5)(x - 6)y + 2 = (4/5)x - (24/5)y = (4/5)x - (24/5) - 2y = (4/5)x - (34/5)Thus, the equation of the line containing the point (6,−2) and perpendicular to the given line 5x + 4y = 7 in slope-intercept form is y = (-5/4)x + (17/4).

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The distribution of the number of cars on the highway during two hours follows a binomial distribution with parameters n=2 and p=0.86, and the expected number of cars that will pass the highway before the first truck is approximately 1.16 cars.

(a) The distribution of the number of cars on the highway during two hours follows a Poisson distribution with a rate of 300 cars per hour. Since each vehicle is a car with a probability of 86%, we can use the binomial distribution to determine the probability of a specific number of cars in the two hours. The probability mass function of the number of cars, denoted by X, can be calculated as \(P(X = k) = (2Ck) * (0.86)^k * (0.14)^2^-^k\), where k ranges from 0 to 2. This gives us the probability distribution of the number of cars in the two hours.

(b) To determine the expected number of cars that will pass the highway before the first truck, we can utilize the geometric distribution. The probability of a car passing the highway before the first truck is 86%. Therefore, the expected number of cars, denoted by Y, can be calculated as \(E(Y) = 1 / 0.86 = 1.16\) cars. This means that on average, approximately 1.16 cars will pass the highway before the first truck.

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the maximum value of the function is y = -1 + 6cos(2π/7(26.75-5)) = 5.

The function y = -1 + 6cos(2π/7(x-5)) is a periodic function with a period of 7. The maximum value of the function occurs when the cosine function reaches its maximum value of 1.

So, we need to find the value of x that makes the argument of the cosine function equal to an odd multiple of π/2, which is when the cosine function is equal to 1.

2π/7(x-5) = (2n + 1)π/2, where n is an integer

Simplifying this equation, we get:

x - 5 = (7/4)(2n + 1)

x = 5 + (7/4)(2n + 1)

Since the function has a period of 7, we can restrict our attention to the interval [5, 12].

For n = 0, we get x = 5 + 7/4 = 23/4

For n = 1, we get x = 5 + (7/4)(3) = 26.75

For n = 2, we get x = 5 + (7/4)(5) = 33.25

For n = -1, we get x = 5 + (7/4)(-1) = 1.75

For n = -2, we get x = 5 + (7/4)(-3) = -4.75

Out of these values of x, the only one that lies in the interval [5, 12] is x = 26.75.

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Answer:

541.1 square feet

Step-by-step explanation:

A = πr²

1) convert in. to ft because answer is in sq. ft

78 in => 6.5 ft

2) Find radius of entire area

6.5 ft + radius of inner circle

6.5 + 10 = 16.5

3) Calculate area of combined circles

A = π(16.5)²

A = 855.3 sq. ft

4) Find area of inner circle

A = π(10)²

A = 314.2 sq. ft

5) Subtract area of inner circle from combined area

855.3 sq ft - 314.2 sq. ft = 541.1 sq. ft

Answer:

false

Step-by-step explanation:

numbers on a number line get bigger as you go right and smaller as you go left

2.9375 is the answer

3 is the rounded up answer

i cant show steps cuz :p

sorry

anyway hope tis helps

Answer:

47/16

is basically dividing  

47÷16  

Long Division for 47 divided by 16  

=2.9375

Answer:

10

Step-by-step explanation:

Should be right

Answer:

Step-by-step explanation:

Let side be x

Using Pythagoras theorem

diagonal =hypotenuse

x²+x²=20²

2x²=400

x²=200

x=10√2

Side is 10√2

Perimeter=4×10√2=>40√2cm

Answer: B. 3x + 1/5

tom's pencil is longer than Ellen's pencil:

5x + 2/5 - (2x + 1/5) = 5x - 2x + 2/5 - 1/5 = 3x + 1/5 (cm)

Step-by-step explanation:

Answer:

45 cause any value inside mod function always return to postive

The original price is $171.59 and the price during sales is $148.37 then the percent markdown will be 13.53%.

The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.

As per the given information in the question,

Original selling price = $171.59

Price during sales = $148.37

Then, the percentage markdown will be,

% markdown = (171.59 - 148.37)/171.59 × 100

= 23.22/171.59 × 100

% markdown = 13.53%

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Answer:

1/64

Step-by-step explanation:

You divide by 4 each time.

It goes 16,4,1,1/4,1/16, 1/64 and so on

The probability of the horse winning the race is 11/13, which is approximately 0.846 or 84.6%

To find the probability of the horse winning the race, we need to use the odds against the horse. The odds against the horse winning are given as 2:11, which means that for every 2 chances the horse loses, it wins 11 times.
We can find the probability of the horse winning by dividing the number of times it wins by the total number of outcomes. In this case, the total number of outcomes is the sum of the chances of winning and losing, which is 2+11 = 13.
So, the probability of the horse winning the race is 11/13. This can be simplified by dividing the numerator and denominator by their greatest common factor, which is 1. Therefore, the probability of the horse winning the race is 11/13.
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The number of atoms present in 8.500 mole of chlorine atoms can be calculated using Avogadro's number, which is 6.022 x \(10^{23}\) atoms per mole. Therefore:

Number of atoms = 8.500 mole x 6.022 x \(10^{23}\)atoms/mole

Number of atoms = 5.1177 x \(10^{24}\) atoms

The mass of 15.50 mole of oxygen can be calculated using the molar mass of oxygen, which is 16.00 g/mol. Therefore:

Mass = 15.50 mole x 16.00 g/mole

Mass = 248 g

The number of moles of helium in 1.953 x \(10^{8}\) g of helium can be calculated using the molar mass of helium, which is 4.00 g/mol. Therefore:

Number of moles = 1.953 x \(10^{8}\) g / 4.00 g/mol

Number of moles = 4.883 x \(10^{7}\) mol

The number of atoms in 147.82 g of sulfur can be calculated using the molar mass of sulfur, which is 32.06 g/mol, and Avogadro's number. Therefore:

Number of moles = 147.82 g / 32.06 g/mol

Number of moles = 4.608 mol

Number of atoms = 4.608 mol x 6.022 x \(10^{23}\) atoms/mol

Number of atoms = 2.773 x \(10^{24}\) atoms

The molar mass of Co (cobalt) is 58.93 g/mol.

The formula mass of Ca3(PO4)2 can be calculated by adding the atomic masses of each element in the compound. The atomic masses are:

Ca = 40.08 g/mol

P = 30.97 g/mol

O = 16.00 g/mol

Formula mass = (3 x Ca) + (2 x P) + (8 x O)

Formula mass = (3 x 40.08 g/mol) + (2 x 30.97 g/mol) + (8 x 16.00 g/mol)

Formula mass = 310.18 g/mol

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Answer: option C, y = 4

Step-by-step explanation:

first, i simplified the equation.

y = ^3sqt64

then, i just calculated that.

y = 4

Answer: C

Step-by-step explanation:

got it right on ape x

Answer:

true

Step-by-step explanation:

Both the angles will be 105°

Just add up the given angles, subtract the result by 360, and divide by 2.

To find the line equation of the form: y = mx, we can proceed as follows:

As we can see, if we multiply the variable, x, times 8, we obtain the value for y, that is:

Therefore, we have here a proportional relationship between the variable, hr (represented above as x), and the variable, earnings (represented above as y).

Hence, the relationship is of the for y = 8x.

Answer

If my answer is ok for you rate my answer

Answer:

-5 and -10

Step-by-step explanation:

-9-5(-5)

-9+25

=16

-9-5(-10)

-9+50

=41

Answer:

No.

Step-by-step explanation:

No, Bob is not correct.

The formula he's using is the following:

\(A=\frac{1}{2} ab\sin(C)\)

The important thing here is that the angle is between the two sides.

In the given triangle, 120 is not between 8 and 18. Therefore, using this formula will not be valid.

Either Bob needs to find the other side first or find the angle between 8 and 18.

\(\huge \text{Answer:}\)

3,000 Minutes is your answer.........

Step-by-step explanation:

hyy.................

Answer:

300 points

Step-by-step explanation:

Since we have a constant rate (12.5 points/game), we can find the number of points by setting up a proportion:

\(\frac{12.5}{1}=\frac{x}{24}\\\\x=(12.5*24)=300\)

ZW is 37 units long. By subtracting the length of WY, which is found to be -1, from ZW, we found that ZY is 38 units long. However, the lengths of TX and WY are negative, suggesting a potential error in the given information.

In the given figure, we are provided with the lengths of various line segments. Using this information, we can determine the length of ZW. Given that XY = 15 and ZX = 52, we can subtract the length of XY from ZX to find the length of ZW. Therefore, ZW = ZX - XY = 52 - 15 = 37.

Now let's provide a detailed explanation of each length:

ZY = 37

To find the length of ZY, we need to subtract the length of WY from ZW. From the previous calculation, we know that ZW = 37. However, the length of WY is not given directly. To find it, we can use the fact that WX = 22 and WT = 23. Since WY is a part of WX and WT, we can subtract WT from WX to get WY. Therefore, WY = WX - WT = 22 - 23 = -1.

Now, we can substitute the value of WY into the equation for ZY: ZY = ZW - WY = 37 - (-1) = 38. Thus, ZY is equal to 38.

TX = 15

To find the length of TX, we need to subtract the length of WT from XY. We know that XY = 15 and WT = 23. Therefore, TX = XY - WT = 15 - 23 = -8. However, it is important to note that lengths cannot be negative, so TX cannot be -8. This indicates that there might be an error in the given information or measurements.

WY = -1

As calculated earlier, the length of WY is -1. However, it is important to note that lengths cannot be negative in a geometrical context. Therefore, we can conclude that there might be an error in the given information or measurements. It is advisable to double-check the given lengths or clarify any inconsistencies before proceeding with further calculations.

In summary, using the given information, we determined that ZW is 37 units long. By subtracting the length of WY, which is found to be -1, from ZW, we found that ZY is 38 units long. However, the lengths of TX and WY are negative, suggesting a potential error in the given information. It is recommended to verify the measurements to ensure accurate results.

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Answer:

slope = \(\frac{3}{5}\)

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (1, - 1) and (x₂, y₂ ) = (6,  2)

m = \(\frac{2+1}{6-1}\) = \(\frac{3}{5}\)

Step-by-step explanation:

Using the integer rule, we can determine:

\( - 35 + 4 - 65 - 8\)

Simplify from left to right:

\( - 31 - 65 - 8 \)

\( -96 - 8\)

\( - 104\)

Answer:

64

Step-by-step explanation:

The exponent of a number says how many times to use the number in a multiplication.

8 to the Power 2

In 82 the "2" says to use 8 twice in a multiplication,

so 82 = 8 × 8 = 64

In words: 82 could be called "8 to the power 2" or "8 to the second power", or simply "8 squared"

Answer:

-9 = d

Step-by-step explanation:

Answer:

d= -9

Step-by-step explanation:

The better buy is given by the following brand:

Brand A.

The better buy is obtained applying the proportions in the context of the problem.

A proportion is applied as the cost per ounce is given dividing the total cost by the number of ounces.

Then the better buy is given by the option with the lowest cost per ounce.

The cost per ounce for each brand is given as follows:

$8 per ounce is a lesser cost than $9.3 per ounce, hence the better buy is given by Brand A.

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The equation for the transformed logarithm that passes through the points (3,0) and (0,2) can be written as f(x) = -b * log(base a)(x - h) + k, where a, b, h, and k are constants to be determined.

To find the equation for the transformed logarithm, we need to use the given points (3,0) and (0,2) to determine the values of a, b, h, and k. Let's start with the point (3,0). Plugging the x-coordinate (3) into the equation, we have:

0 = -b * log(base a)(3 - h) + k

Next, we'll use the point (0,2) to obtain another equation. Plugging the x-coordinate (0) into the equation, we get:

2 = -b * log(base a)(0 - h) + k

Simplifying these equations, we have a system of equations to solve for a, b, h, and k. However, since the equation involves a logarithm, we need more information to determine the specific values of a, b, h, and k.The transformed logarithm function includes transformations such as vertical stretches/compressions (b), horizontal shifts (h), and vertical shifts (k). Without more specific information about these transformations or the base of the logarithm, it is not possible to determine the equation uniquely.

In general, the equation for a transformed logarithm can be written as f(x) = -b * log(base a)(x - h) + k, where a, b, h, and k are constants determined by the specific transformations applied to the logarithm function. It's important to have additional information or instructions to determine the values of a, b, h, and k and provide an equation that accurately represents the given transformed logarithm.

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The Answer is D. -63/16

The exact value of \(\tan (x+y)\) is \(-\frac{63}{16}\).

To find the exact value of \(\tan (x+y)\), we shall use the following trigonometric identities:

\(\csc x = \frac{1}{\sin x}\) (1)

\(\tan (x+y) = \frac{\tan x + \tan y}{1-\tan x\cdot \tan y}\) (2)

\(\tan x = \frac{\sin x}{\cos x}\) (3)

\(\tan y = \frac{\sin y}{\cos y}\) (4)

\(\cos x = \sqrt{1-\sin^{2}x}\) (5)

\(\sin y = \sqrt{1-\cos^{2}y}\) (6)

By (1), we find that the sine of \(x\) is:

\(\sin x = \frac{3}{5}\)

And the remaining trigonometric identities are determined below:

\(\cos x = \sqrt{1-\left(\frac{3}{5} \right)^{2}}\)

\(\cos x = \frac{4}{5}\)

\(\sin y = \sqrt{1-\left(\frac{5}{13} \right)^{2}}\)

\(\sin y = \frac{12}{13}\)

Lastly, we determine the exact value:

\(\tan (x+y) = \frac{\tan x + \tan y}{1-\tan x\cdot \tan y}\)

\(\tan (x+y) = \frac{\frac{\sin x}{\cos x} + \frac{\sin y}{\cos y} }{1 -\left(\frac{\sin x}{\cos x} \right)\cdot \left(\frac{\sin y}{\cos y} \right)}\)

\(\tan (x+y) = \frac{\frac{3}{4}+\frac{12}{5}}{1-\left(\frac{3}{4} \right)\cdot \left(\frac{12}{5} \right)}\)

\(\tan (x+y) = -\frac{63}{16}\)

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Answer:

11

Step-by-step explanation:

\(\frac{1}{8}\) of 88

= \(\frac{88}{8}\)

= 11