Make x the subject of the formula

If the height of a right triangular prism is 1⁵/₆ inches. The surface area of the solid formed is 598.33 in².

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.

First step:-

Right triangular prism=1⁵/₆ inches= 11/6 inches

Height of the base=8²/₃ inches = 26/3 inches

Second step:-

Surface area = 5(10× 10) + (0.5÷ 10 × 26/3) + 3(10× 11/6)

Surface area = 5(100) +43.33+ 3(18.33)

Surface area = 500) +43.33 + 55

Surface area = 598.33 in²

Therefore the surface area of the solid formed is about 598.33 in²

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Answer:

3, 2√2, √7

Step-by-step explanation:

compute the square roots of the next three prime numbers:

√7

√11

√13

Therefore, the next three terms of the sequence are:

{1, √2, √3, 2, √5, √7, √11, √13}

chatgpt

chat

Answer:

They're all manufactured

Step-by-step explanation:

i think so

They are all consumable products

You need to buy more gas every now and then.

Yogurt runs out.

Cereal runs out.

Glue don't last forever.

Soap gets used up.

Yarn gets used up.

Step-by-step explanation:

If f(x) =x, is the father function, then all it's child function would be equally inclined to x and y-axis respectively.

If f(x) =x, is the father function, then all its child functions would be equally inclined to the x and y-axis respectively.

Each family of capabilities has a determining feature. A discern function is the best function that also satisfies the definition of a certain sort of function. As an instance, whilst we think about the linear capabilities which make up our own family of capabilities, the parent feature could be y = x.

Key commonplace points of linear determine features encompass the reality that the equation is y = x. Domain and variety are actual numbers. Slope, or fee of alternate, is steady.

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Answer:20

Step-by-step explanation:this is wrong

Answer:

40

Step-by-step explanation:

subtract median of dogs and median of cats

Answer:

7

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let h(x) = y

The exponentail function is of the form :

\(y = ab^x\)

We have :

\(y_{_1} = ab^{x_{_1}}\\y_{_2} = ab^{x_{_2}}\\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{ab^{x_{1}}}{ab^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{b^{x_{1}}}{b^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = b^{(x_1-x_2)}\)

Given points : (4, 9) and (5, 34.2)

We have:

\(\frac{34.2}{9} = b^{(5-4)}\\\\\implies 3.8 = b\)

Writing the equation with x, y and b:

\(y = ab^x\\\\\implies 9 = a(3.8^4)\\\\a = \frac{9}{3.8^4} \\\\a = 0.043\)

a = 0.043

b = 3.8

When x = 6, y will be:

\(y = (0.043)(3.8^6)\\\\y = 128.47\)

This is not the y value in the question y = 59.4

Therefore (6, 59.4) does not lie on the graph h(x)

Answer:

p = 6

Step-by-step explanation:

5 + 2/3 (2p - 6) = 9

5 + 4/3p - 4 = 9

1 + 4/3p = 9

4/3p = 8

p = 6

Answer:

p= 6

Step-by-step explanation:

Solve for p:

(2 (2 p - 6))/3 + 5 = 9

Put each term in (2 (2 p - 6))/3 + 5 over the common denominator 3: (2 (2 p - 6))/3 + 5 = 15/3 + (2 (2 p - 6))/3:

(15/3 + (2 (2 p - 6))/3) = 9

15/3 + (2 (2 p - 6))/3 = (2 (2 p - 6) + 15)/3:

((2 (2 p - 6) + 15)/3) = 9

2 (2 p - 6) = 4 p - 12:

((4 p - 12) + 15)/3 = 9

Grouping like terms, 4 p - 12 + 15 = 4 p + (15 - 12):

(4 p + (15 - 12))/3 = 9

15 - 12 = 3:

(4 p + 3)/3 = 9

Multiply both sides of (4 p + 3)/3 = 9 by 3:

(3 (4 p + 3))/3 = 3×9

(3 (4 p + 3))/3 = 3/3×(4 p + 3) = 4 p + 3:

(4 p + 3) = 3×9

3×9 = 27:

4 p + 3 = 27

Subtract 3 from both sides:

4 p + (3 - 3) = 27 - 3

3 - 3 = 0:

4 p = 27 - 3

27 - 3 = 24:

4 p = 24

Divide both sides of 4 p = 24 by 4:

(4 p)/4 = 24/4

4/4 = 1:

p = 24/4

The gcd of 24 and 4 is 4, so 24/4 = (4×6)/(4×1) = 4/4×6 = 6:

Answer: p = 6

Answer:

Step-by-step explanation:

9x-3y=-10 ...............(1)

3x-4y=1...............(2)

multiplying equation (2) by 3

9x-12y=3...................(3)

Using elimination method, then

9x-3y=-10 ...............(1)

9x-12y=3...................(3

9y= -13

y= -13/9

substituting y= -13/9 in equation (1) then

9x-3(-13/9)= -10

9x+13/3= -10

multiplying throughout by 3

27x+13= -30

27x= -30-13

27x= -43

x= -43/27

since x and y values are known, then

12x-7y = 12(-43/27) - 7(-13/9)

12x-7y = -516/27 + 91/9

12x-7y = -9

Answer:

Step-by-step explanation:

Answer:

SD = 27.

Step-by-step explanation:

It is given that,

SA = 5x-8

AD = 2x

SD = 4x+7

Note : A should be the mid point of S and D.

SD = SA+AD

Putting all the values,

4x+7=5x-8+2x

taking like terms together

4x-5x-2x=-8-7

-3x=-15

x = 5

The value of x is 5

Put x = 5 in SD = 4x + 7

So,

SD = 4(5) + 7

SD = 27 units

So, the value of SD = 27.

Answer:

1,449

Step-by-step explanation:

Given the points:

You can find the slope of the line using this formula:

Where these two points are on the line:

In this case, you can set up that:

Therefore:

By definition, the Slope-Intercept Form of the equation of a line is:

Where "m" is the slope and "b" is the y-intercept.

In order to find the y-intercept, substitute the slope and the coordinates of one of the points on the line into the equation, and then solve for "b":

Answer:

y=2/3x

Step-by-step explanation:

Since they cross at (3,2) the formula would be y=2/3x

Using the z-distribution, it is found that a sample size of 97 is required.

The confidence interval is as follows:

\(\overline{x} \pm z\frac{\sigma}{\sqrt{n}}\)

The margin of error is given by the following rule:

\(M = z\frac{\sigma}{\sqrt{n}}\)

In which:

For this problem, considering a margin of error of 10, the parameters are given by:

\(M = 10, \sigma = 50\)

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so the critical value is z = 1.96.

Then we take the margin of error equation and solve for n as follows:

\(M = z\frac{\sigma}{\sqrt{n}}\)

\(10 = 1.96\frac{50}{\sqrt{n}}\)

\(10\sqrt{n} = 50 \times 1.96\)

\(\sqrt{n} = 5 \times 1.96\)

\((\sqrt{n})^2 = (5 \times 1.96)^2\)

n = 96.04

Rounding up, as a sample size of 96 results in M > 10, we have that:

A sample size of 97 is required.

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Answer:

Step-by-step explanation:

81 texts in 9 hours

So you do 81 divided by 9

Which givrs you 9 text an hour

Answer:

the sum of 0.349,5.246,3.2 and 8.41? is 17.25

Answer:

The answer is 17.205

Step-by-step explanation:

0.349

+5.246

+3.2

+8.41

that is the first set of numbers on the right added up =9+6=15

you will write 5 then carry 1 to the second set of numbers on the right then add it up =1+4+4+1=10

you will write 0 and carry the 1 to the third set of numbers on the right then add it up=1+3+2+2+4=12

you will write 2 and carry the 1 to the first set of numbers on the left then add it up=1+0+5+3+8=17

Then your answer will be 17.205

note; always arrange the numbers as the point is given

Jane will have traveled a average of 7 miles, so she will be 5 miles away from her starting point. This can be approximated to 5.00 miles, which can be rounded to the nearest hundredth.

1. Jane has walked north for 3 miles.

2. Jane has turned 45 degrees to the right.

3. Jane has walked 4 miles after turning 45 degrees to the right.

4. Jane is now 5 miles away from her starting point. This can be approximated to 5.00 miles, which can be rounded to the nearest hundredth.

Jane has walked 3 miles north and then turned 45 degrees to the right and walked 4 more miles. This means that she has traveled a total of 7 miles from her starting point. To calculate the exact distance, we use trigonometry. We can approximate the distance to 5.00 miles, which can then be rounded to the nearest hundredth. This means that Jane is 5 miles away from her starting point.

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Therefore, the measure of angle ∠Y to the nearest tenth of a degree is approximately 103.2 degrees.

To find the measure of angle ∠Y, we need to use the law of cosines, which relates the lengths of the sides of a triangle to the cosine of its angles.

The formula for the law of cosines is:

\(c^2 = a^2 + b^2 - 2ab cos(C)\)

Where a, b, and c are the lengths of the sides of the triangle, and C is the angle opposite to side c.

In our case, we know the lengths of the sides w, x, and y, and we want to find the angle ∠Y, which is opposite to side y. So, we can use the formula as follows:

\(y^2 = w^2 + x^2 - 2wx cos(Y)\)

Substituting the values, we have:

\(630^2 = 170^2 + 590^2 - 2(170)(590) cos(Y)\)

Simplifying and solving for cos(Y):

\(cos(Y) = (170^2 + 590^2 - 630^2) / (2170590)\)

cos(Y) ≈ -0.236

Note that the cosine of an angle is negative if the angle is between 90 and 180 degrees, which is the case for angle ∠Y in this triangle. Therefore, we need to use the inverse cosine function to find the measure of angle ∠Y:

Y ≈ 103.2 degrees

Rounding to the nearest tenth of a degree, we get:

Y ≈ 103.2°

Therefore, the measure of angle ∠Y to the nearest tenth of a degree is approximately 103.2 degrees.

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The number of cubes with 1/2 ft each side that will pack the box of dimensions 3 ft x 2.5 ft x 2 ft completely full are 120, as the sum of the volume of 120 cubes is equal to the volume of box.

What is volume?

The volume is the space occupied by any three dimensional shape or a solid shape like cube, cuboid, sphere, cylinder, cone, etc.

The formula for the volume of cube and cuboid are as follows:

Volume of cube:( Side )³

Volume of cuboid: Length x width x Height

Here, we need to fit the cubes inside the box, as the cubes will occupy the space inside the box, hence we'll find the volume of cube and the box.

Given Dimensions of cube: Side= 1/2 feet

                                                     =0.5 ft or 6 inches

volume of each cube= 0.5 x 0.5 x 0.5

                         =0.125 cubic ft.

Given dimensions of cuboid: Length=3 ft, Width=2.5 ft & Height=2 ft

Volume of Cuboid=3 x 2.5 x 2

                              =15 cubic feet.

As we know that the sum of the volume of all cubes will be equal to that of volume of box:

Volume of 'N' cubes=volume of box

N x Volume of each cube = volume of box

N x 0.125 = 15

            N = 15 ÷ 0.125

            N = 120 cubes

∴ 120 cubes will pack the box completely full.

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Refer to the attached figure for the dimensions of the box.

hm this is weird, i thought i answered the question. or maybe they're two different questions? line graph because i said so. i know im so helpful

Answer:

Y intercept (0,120), x-intercept (10,0)

Step-by-step explanation:

Person 3's payment exceeded person 2's payment by $20.

To find out how much more person 3 paid than person 2, we need to calculate the amounts each person paid based on the given ratio and then compare their payments.

The ratio given is 1:2:3, which means that person 1 gets 1 part, person 2 gets 2 parts, and person 3 gets 3 parts of the total amount.

Step 1: Calculate the total number of parts in the ratio.

1 + 2 + 3 = 6

Step 2: Determine the value of one part.

$120 (total amount) divided by 6 (total number of parts) = $20

Step 3: Calculate the payments for each person based on the ratio.

Person 1: 1 part * $20 = $20

Person 2: 2 parts * $20 = $40

Person 3: 3 parts * $20 = $60

Therefore, person 3 paid $60, while person 2 paid $40. To find out how much more person 3 paid than person 2, we subtract the amount person 2 paid from the amount person 3 paid:

$60 - $40 = $20

Hence, person 3 paid $20 more than person 2.

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Answer:

Part A) The potato hit the ground at t=5.70 seconds (see the explanation)

Part B) The potato is 40 feet off the ground at the time t=5.28 seconds (see the explanation)

Step-by-step explanation:

The total gross salary for FICA taxes is $4896 with the tax rates 6.2% and 1.45%.

The amount you earn each month before taxes and other deductions is referred to as your monthly gross income. In other words, it's your annual salary divided by 12. It's only a simple metric to aid in budgeting and other routine financial computations.

Annual Salary Amount / Number of Pay Periods = Gross Pay.

Gross pay equals the number of hours worked in a pay period multiplied by the hourly rate (+ overtime hours multiplied by the hourly overtime rate).

Given,

Tax rate=6.2%

=64000(6.2/100)

=3968

And also given another tax rate is 1.45%

=64000(1.45/100)

=92.8

Total=3968+928

=$4896

Therefore, the total gross salary for FICA taxes is $4896.

The total gross salary for FICA taxes is $4896 with the tax rates 6.2% and 1.45%.

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Answer:

\(x + y - x = 6 - y - 4 \\ y = 2 - y \\ 2y = y \\ y = 1 \\ x + y = 6 \\ x + 1 = 6 \\ x = 5\)

Answer:

Step-by-step explanation:

Area of the trapezoid:

Area of trapizoid:-

\(\blue{A=\dfrac{1}{2}(b_1 +b_2)×h }\)

According to the question,

\(\bold{\dfrac{1}{2}×(4+15)×4 }\)

\(\bold{\dfrac{1}{2}×(19)×4 }\)

\(\bold{\dfrac{1}{\cancel{2}}×(19)×\cancel{4}}\)

\(\bold{19×2 ~m^2 }\)

\(\bold{ 38~m^2 }\)

Answer:

33

Step-by-step explanation:

11 * 11 - 6 * 17 + 14

121 - 102 + 14

19 + 14

33

Best of Luck!

Hey there!☺

\(Answer:\boxed{64}\)

\(Explanation:\)

\(11*11-6\times17+45\)

In order to solve, we will need to use the order of operations(PEMDAS). Start from left side multiplication.

\(11*11=121\)

Now move to the right side multiplication.

\(6*17=102\)

Now subtract the two products.

\(121-102=19\)

Now add what is left over.

\(19+45=64\)

\(64\) is your answer.

Hope this helps!

\(\text{-TestedHyperr}\)

Answer:

ŷ = -0.47876X + 11.17724

$6.4

Step-by-step explanation:

Given the data :

Car Age (years) Selling Price ($000) Car Age (years) Selling Price ($000)

1 9 8.1 7 8 7.6

2 7 6 8 11 8

3 11 3.6 9 10 8

4 12 4 10 12 6

5 8 5 11 6 8.6

6 7 10 12 6 8

The estimated regression equation using a linear regression calculator is :

y = -0.47876X + 11.17724

With - 0.47876 being the slope ; and 11.17724 being the intercept

y = predicted variable (price of car) ; x = predictor variable (Age of car)

Selling price of a 10 year old car : x = 10

ŷ = -0.47876(10) + 11.17724

Price = 6.38964

About 6.4(000) dollars ($6,400)

According to the regression equation : The starting price of cars is about $11.18 (intercept) with the proved of cars declining by a value of $0.479(negative slope value) each year.