In the diagram, b || c. Find the value of y

to solve for m

distribute into parentheses

176 = -16 - 24m

get m on one side

176 + 16 = -24m

192 = -24m

divide by -24

-8 = m

m = -8

Approximately 95% of men must duck when walking through a door that is 72 inches high. Approximately 5% of women must duck when walking through the door. The door height that would allow at least 95% of men to walk through the door without ducking is 74 inches.

The mean height of men is 69.0 inches and the standard deviation is 2.8 inches, while the mean height of women is 63.6 inches and the standard deviation is 2.5 inches.

(a) To find the percentage of men who must duck when walking through a door that is 72 inches high, we first need to find the percentage of men whose height is less than 72 inches.

The height of the door is 72 inches, which is 3 inches above the mean height of men.

Since the standard deviation is 2.8 inches, this means that approximately 95% of men are within 2.8 * 2 = 5.6 inches of the mean height.

Therefore, approximately 95% of men are between 69.0 - 5.6 = 63.4 inches and 69.0 + 5.6 = 74.6 inches tall.

If the height of the door is 72 inches, approximately 95% of men must duck when walking through the door.

(b) To find the percentage of women who must duck when walking through a door that is 70 inches high, we first need to find the percentage of women whose height is less than 70 inches.

The height of the door is 70 inches, which is 6.4 inches above the mean height of women.

Since the standard deviation is 2.5 inches, this means that approximately 95% of women are within 2.5 * 2 = 5 inches of the mean height. Therefore, approximately 95% of women are between 63.6 - 5 = 58.6 inches and 63.6 + 5 = 68.6 inches tall.

If the height of the door is 70 inches, approximately 5% of women must duck when walking through the door.

(c) To find the door height that would allow at least 95% of men to walk through the door without ducking, we need to find the height that is within 2 standard deviations of the mean height of men.

Since the standard deviation is 2.8 inches, this means that approximately 95% of men are within 2.8 * 2 = 5.6 inches of the mean height.

Therefore, the door height that would allow at least 95% of men to walk through the door without ducking is 69.0 + 5.6 = 74

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Answer:

148 cm²

Step-by-step explanation:

Using the formula for the total surface area of a cuboid,

[tex]2(6 \times 4+6 \times 5+4 \times 5)=148[/tex]

Answer: 2nd first 1st second third 4th fourth 3rd and 5th in 5th

Step-by-step explanation:

The area for the shaded region is obtained as 2 units.

In order to find the area, first find the intersection points of the two curves. Then, the area of the region can be found by taking the integration from the intersection point.

The curves in the graph in the form of equation are as follows,

y = x² + 3                     (1)

x = (y - 5)² - 2

=> y = √(x+ 2) + 5       (2)  

Part A :

The intersection points of the two curves are (-1.5, 5.5), (-1, 4) and (0.5, 3.5).

Thus, to calculate the area the limit is from x = -1.5 to x = 0.5.

Part B :

The expression of the integral is given as,

[tex]\int\limits^{-1}_{-1.5} {(x^{2} + 3 ) - (5 + \sqrt{x + 2} )} \, dx + \int\limits^{0.5}_{-1} {(5 + \sqrt{x + 2} ) -(x^{2} + 3 ) } \, dx[/tex]

Part C :

The area is found by evaluating the integral as follows,

[tex]\int\limits^{-1}_{-1.5} {(x^{2} + 3 ) - (5 + \sqrt{x + 2} )} \, dx + \int\limits^{0.5}_{-1} {(5 + \sqrt{x + 2} ) -(x^{2} + 3 ) } \, dx[/tex]

= [-1/3 + 3.375/3 + 3(-1 - (-1.5))] - [5(-1 - (-1.5)) + 2/3([tex]1^{3/2} - 0.5^{3/2}[/tex])] + [5(0.5 - (-1)) -(0.125/3 + 1/3 + 3(0.5 - (-1))]

= 2.291 - [2.5 + 2/3 × 0.647] + [5 × 1.5 - 4.8716]

= 2.291 - 2.927 + 2.6284

= 1.9924

Which is approximately 2.

Hence, the area between the curves is given as 2 units.

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Answer:216

Step-by-step explanation:

Answer:

6x-3=15

Step-by-step explanation:

The situation that is best described by the situation is that D. The temperature at 2:00 am is -2 degrees celsius and drops 2 degrees each hour for x hours.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, the equation is given as:

y = 2x - 2.

This illustrates that the temperature at 2:00 am is -2 degrees celsius and drops 2 degrees each hour for x hours.

In conclusion, the correct option is D.

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Answer:

-13

Step-by-step explanation:

The ys can combine and so can the numbers so if you take -5y + 5y you get 0. so those completely cancel out, so then you would add -12 + -1 which is -13.

Answer:

15

Step-by-step explanation:

Answer:

12 Pieces left!

Step-by-step explanation:

Because, Look. 6 is 1 quarter, He gave some of his other friends less.

If you add 2 + 4, thats 6! 6 is 1 quarter. There is 4 quarters in a cake. SO 6 + 6 12, thats half of a quarter. And then he gets the other half! Good luck!

(24 pieces in his cake)

Answer:

To find the value of the quartiles, we need to first find the median of the data set. The median is the middle value of the data set, or the value that separates the lower half of the data from the upper half. In this data set, the median is 68, as it is the middle value when the data is arranged in ascending order.

Once we have the median, we can find the first and third quartiles. The first quartile, also known as Q1, is the median of the lower half of the data set, and the third quartile, also known as Q3, is the median of the upper half of the data set. In this data set, the lower half of the data is {56, 58, 64}, and the upper half of the data is {72, 75, 78}. The median of the lower half is 58, and the median of the upper half is 75.

Therefore, the value of the quartiles is Q1 = 58, Q2 = 68, and Q3 = 75.

Option D, Q1 = 58; Q2 = 68; Q3 = 75, is the correct answer.

Step-by-step explanation:

The slope of the line in the graph is 2/3.

A line's slope is defined as

Slope = Rise / Run

Can also be written as,

slope(m) = y2 - y1 / x2 - x1

Choose any two points on the line, such as A and B.

It is clear from the graph below that

Rise = y Change = -3-(-1) = -2

Run = x Change = 1 - 4 = -3

In the above formula, substitute these values.

Slope = -2 / -3

          = 2/3

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The value of n in the given equation is 1.

Define Algebraic Expression

In mathematics, an expression that includes variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.)

Given equation,

-1/2 (2n + 4) + 6 = -9 + 4(2n + 1)

Now, solve for n

first, solve the brackets

-1/2 * 2n + (-1/2) * 4 + 6 = -9 + 4*2n + 4 * 1

-n - 2 + 6 = -9 + 8n + 4

Solve the constants on both the sides,

-n + 4 = 8n - 5

Now, take out n value one side and constant terms other side

-n - 8n = -5 - 4

-9n = -9

Cancel out -9 from both the sides,

n = 1

Hence, the value of n in the given equation is 1.

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The full price when the sales price is ;

£32.24 = £96.72

£86.08 is  £258.24

£105.48 is £316.44

£230.62 is £691.86

The sales price is one third of the full price of the items. Thus, in order to determine the full price, multiply the sales price by 3.

Full price = sales price x 3

Full price when the sales price is £32.24 would be;

= 3 x £32.24

= £96.72

Full price when the sales price is £86.08  would be;

= 3 x £86.08 = £258.24

Full price when the sales price is £105.48 would be;

= 3 x £105.48 = £316.44

Full price when the sales price is £230.62  would be;

= 3 x £230.62 = £691.86

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Answer:

35 and 1/4

Step-by-step explanation:

6x47/8

6/1x47/8

282/8

35 1/4 or 35.25

Answer:

3 / 5

Step-by-step explanation:

TOA-CAH-SOH are 3 trigonometry ratios. They are:

TOA - tan(theta) = Opposite ÷ Adjacent

CAH - cos(theta) = Adjacent ÷ Hypotenuse

SOH - sin(theta) = Opposite ÷ Hypotenuse

We are finding Cos(A)

Cos(A) = Adjacent ÷ Hypotenuse

= AB ÷ AC

=

[tex] \frac{30}{50} \\ = \frac{3}{5} [/tex]

Therefore Cos(A) = 3 / 5.

Answer:

Step-by-step explanation: Can u show the picture of the table so i can understand this better

The difference between fundamental theorem of calculus part 1 and 2 is explained below:

The basic theorem of calculus is a theorem that connects the ideas of differentiating and integrating functions. A constant value that relies on where one begins to compute area makes the two procedures the inverses of one another. The relationship between the integral and derivative is established by the calculus fundamental theorem. Simply put, it says that the height of the area at a point x equals the rate of change of the area under the curve up to that point. We can find definite integrals with the aid of this theorem.

The connection between the integral and the derivative is demonstrated in The Fundamental Theorem of Calculus, Part 1. Take note. A definite integral can be assessed in terms of an antiderivative of its integrand using the Fundamental Theorem of Calculus, Part 2. This formula will calculate the total area under a curve.

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The z score that has 70.54% of the distribution area is 9.92

The z-score is a numerical measurement used in statistics to refer to how much a given value differs from the standard deviation.

For the random variable x, the z-score is;

z = (x - 11)/2

therefore, 70.54% of the area under the curve lies to the right of x,

then the area to the left of x is;

100 - 70.54 = 29.46%

From the standard table, a z-score of -0.54 will yield an area of 29.46% to the left of x.

Therefore, we get;

(x - 11)/2 = -0.54

x - 11 = -0.54(2)

x = 9.92

The z score  is 9.92

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Answer: z=34 degrees

Step-by-step explanation:

the total angle of a triangle always adds up to 180

180=44+2z+2z

combine like terms

4z+44=180

4z+44-44=180-44

4z=136

z=34

The strategic decision based on the p-value is given as follows:

Allow the machine to continue operating as it is.

The decision depends if we reject or do not reject the null hypothesis in this problem, as follows:

The decision rule to accept or reject the null hypothesis is given as follows:

The p-value in this problem is given as follows:

0.06811.

Which is greater than the significance level, hence the null hypothesis is not rejected and the first option is correct, as the machine should be allowed to continue operating as it is.

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Since -153/4 + 4i is equivalent to -63/4 + 4i, we should multiply D) –153∕4 + 4i to complex numbers (1∕2 + 4i)².

Complex numbers are those that are expressed as a+ib, where a and b are actual numbers and I is a fictitious number called a "iota." I has the value (-1). As an illustration, the complex number 2+3i is made up of the real number 2 (Re) and the imaginary number 3i (Im). In the case of quadratic equations, the unknown roots are simplified using complex numbers if the roots are not real. In computer science and engineering, complex numbers are used. Both mechanical and civil engineering use complex numbers. Control systems employ complex numbers.

Given,

Complex numbers:;

(1/2 + 4i)²

(a +b )² = a² + b² + 2ab

Multiplying,

(1/2)² + (4i)² + 2(1/2)(4i)

1/4 + 16i² + 4i

i² = -1

1 - 64/4 + 4i

-63/4 + 4i

Since -153/4 + 4i is equivalent to -63/4 + 4i, we should multiply D) –153∕4 + 4i to (1∕2 + 4i)².

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Answer:

A. true

Step-by-step explanation:

I believe you pay most of your interest when you first receive the loan.

Answer:

-4

Step-by-step explanation:

So we have f(x) = x + 1 and g(x) = 5x. We need to find f(g(x))(-1). So let's put g(x) into f(x): f(g(x)) = f(5x) = 5x + 1. Now we have x = -1. Let's substitute this into 5x + 1 = -5 + 1 = -4.

Answer:

17

Step-by-step explanation:

13 + 4 = 17

Answer:

[tex]h=\pm 21[/tex]

Step-by-step explanation:

[tex]h^2=441 \implies h=\pm \sqrt{441}=\pm 21[/tex]

The length of the side a is 112.1664 cm.

The ratios of a triangle's side lengths to each of its opposite angles are related by the law of sines. There is no change in this ratio for the three sides or the opposing angles.

The Law of sines;

Sin A / a = Sin B / b = Sin C/ c

Here, we have two angles 35° and 25° and a side b = 5 ft

Now, sin35°/5 = sin25°/a

a = (0.42) x 5 / (0.57)

a = 3.68

Now the length in feet is 3.68 cm.

Therefore, the length of the side a is 112.1664 cm.

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