7 A right rectangular prism is sliced by a plane perpendicular to its bases. A right cylinder is sliced the same way. Which statement about the plane sections that result is correct?
A Both plane sections have two pairs of parallel sides.
B The plane section of the prism has only straight sides, but the plane section of the cylinder does not.
C The plane section of the prism has four right angles, but the plane section of the cylinder does not.
D Both plane sections are the same shape as the bases of the three-dimensional figures from which they resulted.​

According to the given question, Alice should use this equation f(t) = [tex]24,000(0.945)^t[/tex] to represent the value of the car after t years.

Depreciation is the expected decrease in the value of fixed assets over the course of a fiscal year. For physical assets like real estate, machinery, vehicles, and other items, large lump sum acquisitions are made.

The equation[tex]f(t) = 24,000(0.945)^t[/tex] represents the value of the car after t years, where 0.945 represents the remaining value of the car after one year of depreciation at a rate of 5.5%.

To calculate the value of the car after two years, for example, we would substitute t = 2 into the equation:

f(2) = [tex]24,000(0.945)^2[/tex]

f(2) = 24,000(0.893025)

f(2) ≈ 21,433.80

Therefore, the value of the car after two years would be approximately $21,433.80.

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The rate of change is 4/1

Answer:

Step-by-step explanation:

To estimate the monthly cost of electric, gas, and water utilities as 0.1% of the price of your house, you can multiply the price of your house by 0.001. For example, if the price of your house is $300,000, then the estimated monthly cost of these utilities would be $300,000 * 0.001 = $300.

It’s important to note that this is just an estimate and the actual cost of these utilities can vary depending on factors such as the size of your house, the number of people living in it, and your usage habits.

Answer:

x = 67

Step-by-step explanation:

The two triangles are identail.

Answer:

x = 67

because 67 and x the same

Suppose you are a small business owner who sells handmade crafts. You have a budget of $100 to purchase materials for your next batch of products. You know that each craft requires some amount of materials, which costs $8 per unit. Additionally, you will need to pay a fixed cost of $14 for other expenses related to production and shipping.

To make a profit, you must ensure that the cost of materials and fixed expenses does not exceed the $100 budget. Therefore, you can write an inequality to represent this situation:

8x + 14 < 100

Here, x represents the number of units of materials needed for each craft. The inequality states that the total cost of materials (8x) plus fixed expenses ($14) must be less than $100.

To solve this inequality, you can subtract 14 from both sides:

8x < 86

Finally, you can divide both sides by 8:

x < 10.75

This means that for each craft, you can use no more than 10.75 units of materials in order to stay within budget and make a profit.

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The formula for the linear function is f(p) = -50p + 1750. So, correct option is E.

To find the formula for the linear function from the given table, we need to determine the equation of a straight line that passes through the three given points. We can use the point-slope form of the equation of a straight line to solve for the slope and y-intercept.

Let's choose two of the given points, say (15, 1000) and (25, 500), to calculate the slope:

slope = (change in y)/(change in x)

= (500 - 1000)/(25 - 15)

= -50

Now, we can use the slope and one of the given points, say (15, 1000), to solve for the y-intercept using the point-slope form:

y - y₁ = m(x - x₁)

y - 1000 = -50(x - 15)

y - 1000 = -50x + 750

y = -50x + 1750

Therefore, the formula for the linear function is f(p) = -50p + 1750, which means that for each additional dollar increase in price per shirt, the number of shirts sold decreases by 50. Option (e) is the correct answer.

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Answer: To determine the correct answer, we need to calculate the t-test statistic using the given information.

The formula for the t-test statistic for a one-sample t-test is:

t = (x - μ) / (s / sqrt(n))

where x is the sample mean, μ is the hypothesized population mean (which is not given in this question), s is the sample standard deviation, and n is the sample size.

Here, x = 63.2 minutes, s = 7.7 minutes, and n = 24 cases. We are not given a hypothesized population mean, so we cannot calculate the exact t-test statistic. However, we can use the sample mean as an estimate of the population mean for the purposes of this question.

Plugging in the values, we get:

t = (63.2 - 60) / (7.7 / sqrt(24))

t = 2.04

Therefore, the correct answer is (a) t = 2.04.

The length of unknown side is,

⇒ 4.92

We have to given that;

A triangle is shown in image.

Let the length of unknown side = x

Now, From trigonometry formula we get;

⇒ tan 51° = x / 4

⇒ 1.23 = x / 4

⇒ x = 1.23 × 4

⇒ x = 4.92

Thus, the length of unknown side is,

⇒ x = 4.92

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The factor of 2xy + 30x^2 - xy - 16y^4 - yx - 5x^2 is 25x2−16y4=(5x+4y2)(5x−4y2)

We are given that;

2xy + 30x^2 - xy - 16y^4 - yx - 5x^2

Now,

Combine like terms by adding or subtracting the coefficients of the same variables. For example, 2xy - xy - yx = 0xy, and 30x^2 - 5x^2 = 25x^2. The polynomial becomes:

25x2−16y4

Check if there is a common factor for all the terms. In this case, there is no common factor other than 1, so we cannot use the greatest common factor method.

Check if the polynomial is a difference of two squares, which means it has the form a2−b2. In this case, we can see that both terms are perfect squares: 25x2=(5x)2 and 16y4=(4y2)2. Therefore, we can use the difference of two squares formula:

a2−b2=(a+b)(a−b)

Substituting a=5x and b=4y2, we get:

25x2−16y4=(5x+4y2)(5x−4y2)

Check if each factor can be further factored using any of the methods. In this case, neither factor can be further factored, so we are done.

Therefore, by factorization the answer will be 25x2−16y4=(5x+4y2)(5x−4y2)

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Answer:

do it by yourself what you do while teacher is teaching

Answer:

The true statements:

6 is an element of D

12 is an element of D

Answer:

C

Step-by-step explanation:

the prime factorization of 84 is 2 x2 x 3 x 7

I can rewrite the problem

-3[tex]\sqrt{84x^{3} }[/tex]

-3[tex]\sqrt{(2)(2)(3)(7)xxx}[/tex]  pull out the pairs

-3(2)x[tex]\sqrt{(3)(7)x}[/tex]

-6x[tex]\sqrt{21x}[/tex]

Helping in the name of Jesus.

Answer:

12.5 is the answer

Step-by-step explanation:

7 × 60 ( 7 being the minutes, 60 being the hour )

= 420

+ 30

= 450

450 ÷ 3600 × 100

45000 ÷ 3600

450 ÷ 30

= 12.5

12.5 being the answer

Answer:

5,340x.095=507.3

507.3÷5=101.46

101.46÷12=$8.45 interest

5,340÷5=1068

1068÷12= $89

89+8.45=$97.45

answer $97.45 a month

Answer:

Step-by-step explanation:

(a)  currently the  mode is pink.  Mode means which one occurs the most.

If you take a pink out.  Now P=3  G=3 and Y=3

(a) PINK

(b) Yellow, you want yellow to be the most/mode  so they put a yellow back in

Answer:

To find the product of matrices AB, we need to multiply the elements of the rows of matrix A with the corresponding elements of the columns of matrix B, and then sum these products.

Since matrix A is a 2x2 matrix and matrix B is a 2x3 matrix, we can perform the multiplication as follows:

AB = | 1 2 |   | 1 2 3 |   | (1*1)+(2*4)  (1*2)+(2*5)  (1*3)+(2*6) |

    | 3 4 | x | 4 5 6 | = | (3*1)+(4*4)  (3*2)+(4*5)  (3*3)+(4*6) |

                          |              |              |              |

    |  9 12 15 |          |  9  12  15 |

Therefore, the product of matrices AB is a 2x3 matrix, and the answer is C) 2x3.

The value of m and n are 2√3 and 4√3/3 respectively.

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

There are special angles in trigonometry, examples are; 60° , 30° and 90°. This angles have exact values and can be calculated without using calculator.

Tan 60 = n/2

√3 = n/2

n = 2√3

cos 60 = 2/m

√3/2 = 2/m

m√3 = 4

m = 4/√3

= 4√3/3

Therefore the value of m and n are 2√3 and 4√3/3 respectively.

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A 3:5 scaled version means that the dimensions of the new version are proportional to the original dimensions in a ratio of 3:5.

A scaled version is a version of a shape where every size in the original shape is multiplied by the same number.

In this situation, a 3:5 scaled version means that the dimensions (or sizes) of the new version are proportional to the original dimensions in a ratio of 3:5.

For example, if we have a circle with radius 20 cm, we can create a 3:5 scaled version by multiplying the radius by the ratio 3/5. That is:

scaled version radius = 3/5 * 20 = 12 cm

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Answer:

y= 50x + 150

Step-by-step explanation:

Answer:

Here’s a piecewise function that represents the total cost C (in dollars) for a photoshoot that lasts h hours:

                     150            for 0<h≤1

C(h)= {150 +100⌈2(h−1) ⌉ for 1<h≤3​

Step-by-step explanation:

The first part of the function represents the cost for a photoshoot that lasts up to 1 hour. The second part represents the cost for a photoshoot that lasts more than 1 hour but no more than 3 hours. The ceil function rounds up to the nearest integer.

I hope this helps you! Have a nice day. (゜▽゜)つ Bye -

Answer:

93 + 7 = 100

Step-by-step explanation:

I would assume positive because 100 is above the x-axis not below it.

The area of the shaded region is 117.8 m².

Given is a semicircle and a triangle in it, we need to find the area that is shaded,

So, we know that a triangle in a semicircle is always a right triangle whose hypotenuse is the diameter of the semicircle,

So, let us find the hypotenuse of the triangle (diameter of the semicircle) using the Pythagorean theorem,

diameter / hypotenuse = √21.6²+9²

= 23.4m

So the radius = 23.4/2 = 11.7 m

To find the area of the shaded region we will subtract the area of triangle from the semicircle,

So,

Area of the shaded region = π×r²/2 - 1/2×base×height

= 3.14×11.×7²/2 - 1/2×21.6×9

= 215 - 97.2

= 117.8 m²

Hence the area of the shaded region is 117.8 m².

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The Taylor polynomial T3(x) for the function f centered at the number a.

f(x) = e^x, a = 1 is

[tex]T3(x0 = e + e(x-1) + e(x-1)^ 2/2 + e(x-1)^3/6[/tex]

A polynomial is  described as an expression consisting of variables and coefficients, which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

The Taylor polynomial of degree n for a function f(x) centered at a is given by the formula:

[tex]pn(x)=f(c)+f′(c)(x−c)+f′′(c)2!....[/tex]

In this formula, f'(1), f''(1), f'''(1), and f^(n)(1) are the first, second, third, and nth derivatives of f(x), respectively, evaluated at a.

The symbol n! denotes the factorial of n, which is the product of all positive integers from 1 to n.

In the scenario above, we are given the function f(x) = e and a = 1.

The first derivative of e^x is e^x,

the second derivative is e^x,

and the third derivative is also eˣ.

We then evaluate these derivatives at a = 1, we get:

f(1) = e¹ = e

f'(1) = e¹ = e

f''(1) = e¹ = e

f'''(1) = e¹ = e

We substitute  these values into the formula for the Taylor polynomial, and simplify to get Taylor polynomial T3(x) for the function:

[tex]T3(x0 = e + e(x-1) + e(x-1)^ 2/2 + e(x-1)^3/6[/tex]

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Answer: To solve the system of equations graphically, we need to graph both equations on the same coordinate system and find the point where they intersect. This point will give us the values of x and y that satisfy both equations.

First, we can rewrite the two equations in slope-intercept form:

y = 4x - 1 (equation 1)

y = -x + 4 (equation 2)

Now we can graph both equations on the same coordinate system. To do this, we can plot a few points for each equation and then draw a line through the points. Alternatively, we can use the y-intercept and slope of each equation to graph the lines. For equation 1, the y-intercept is -1 and the slope is 4. For equation 2, the y-intercept is 4 and the slope is -1.

We can see that the two lines intersect at the point (1, 3). Therefore, the solution to the system of equations is x = 1.

1. The standard quantity of plastic allowed to make 3,500 helmets is 2,310 kilograms.

2. The standard materials cost allowed to make 3,500 helmets is $16,170.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

1. The standard quantity of kilograms of plastic (SQ) allowed to make 3,500 helmets can be calculated as:

SQ = Standard quantity per unit × Actual output

= 0.66 kg/helmet × 3,500 helmets

= 2,310 kg

Therefore, the standard quantity of plastic allowed to make 3,500 helmets is 2,310 kilograms.

2. The standard materials cost allowed (SQ × SP) to make 3,500 helmets can be calculated as:

Standard materials cost allowed = Standard price × Standard quantity allowed

= $7.00/kg × 2,310 kg

= $16,170

Therefore, the standard materials cost allowed to make 3,500 helmets is $16,170.

3. The materials spending variance can be calculated as the difference between the actual cost incurred and the standard cost allowed:

Materials spending variance = Actual materials cost - Standard materials cost allowed

= $16,401 - $16,170

= $231 (Favorable)

Therefore, the materials spending variance is $231 (Favorable).

4. The materials price variance and the materials quantity variance can be calculated as follows:

Materials price variance = (Actual price - Standard price) × Actual quantity

= ($16,401/2,485 kg - $7.00/kg) × 2,485 kg

= $9,141.77 (Unfavorable)

Materials quantity variance = (Actual quantity - Standard quantity allowed) × Standard price

= (2,485 kg - 2,310 kg) × $7.00/kg

= $1,225 (Unfavorable)

Therefore, the materials price variance is $9,141.77 (Unfavorable) and the materials quantity variance is $1,225 (Unfavorable).

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The value of B is 6 when the value of sin x degrees equals to 4/5.

In the given triangle diagram, the opposite side of x = 3b

The hypotenuse of the given triangle = 22.5

Given triangle is a right-angled triangle, in trigonometry, we know that in a right-angled triangle the sin x = opposite side of x / hypotenuse side

So, sin x = 3b/22.5

But, the given value is 4/5. So,

3b/22.5 = 4/5

3b = 90/5

3b = 18

b = 18/3

b = 6

From the above explanation, we can conclude that the value of b is 6.

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The equation for L in terms of tea, representing the length of the candle, remaining on burn in inches, tea hours, after the candles lit is 15 in - (1.25 in/hr)t

Given  the initial length of a candle is 15 inches and the candle burns at a rate of 1.25 in./h

L(t) is a function of time, t:

L(t) = 15 in - (1.25 in/hr)t

Note that when the candle has burned down to nothing, L(t) = 0.

Set 15 in - (1.25 in/hr)t equal to zero and solve for t:

(1.25 in/hr)t = 15 in, or

t = 15/  1.25 in/hr

t = 12 hrs

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She earn fοr each year frοm 2014 thrοugh 2016 is 80628.40. The average οf her last five years οf wοrking $78,302.80. His annual retirement benefit was $28,423.92.

a) Salary οf 2014 : $76000

Salary in 2014 is the salary in 2015 increased by 3% οf the salary

= $76,000+3%

Salary οf 2015 = $78,280

Salary in 2015 is the salary in 2016 increased by 3% οf the salary

=$78,280+3%

Salary οf 2016 = $80,628.40

Hence, she earn fοr each year frοm 2014 thrοugh 2016 is 80628.40

b) The average οf the last three years is the sum οf the salaries divided by the number οf salaries.

= $76,000+$78,280+$80,628.40 / 3

= $78,302.80

Hence, the average οf her last five years οf wοrking $78,302.80

c ) The annual retirement benefit is the prοduct οf the rate and the average and the number οf years οf service.

= 1.65%×$78,302.80×22

=$28,423.92

Hence,  his annual retirement benefit was $28,423.92.

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To determine Duane's taxable income, we need to know his tax rate. Let's assume that his tax rate is a flat 20%.

We can use the formula:

taxable income = tax bill / tax rate

Plugging in the values given, we get:

taxable income = $1000 / 0.20

taxable income = $5000

Therefore, Duane's taxable income was $5000.

Answer:

Without more information, it is not possible to determine Duane's taxable income.

Answer: 15 x 162 = 2430$