What is the equivalent of 7(7q+5)

Answer:

\(V(x) = 4x^3 - 24x^2+35x\)

Step-by-step explanation:

Given

\(V(x) = (7 - 2x)(5 - 2x)(x)\)

Required

Expand the expression

\(V(x) = (7 - 2x)(5 - 2x)x\)

Expand bracket

\(V(x) = (7 - 2x)(5 * x - 2x * x)\)

\(V(x) = (7 - 2x)(5x - 2x^2)\)

Further expand bracket

\(V(x) = 7(5x - 2x^2) - 2x(5x - 2x^2)\)

\(V(x) = 35x - 14x^2 - 10x^2 + 4x^3\)

\(V(x) = 35x - 24x^2 + 4x^3\)

\(V(x) = 4x^3 - 24x^2+35x\)

The given information is: Liam commutes to work, and the amount of time it takes him to arrive is normally distributed with a mean of 55 minutes and a standard deviation of 4.5 minutes. Now, we have to find how many times Liam's commute be between 46 and 60 minutes in a year. So, Liam's commute would be between 46 and 60 minutes for 175 days.

Let X be the amount of time Liam's commute takes him to arrive. Hence, X ~ N(μ = 55, σ = 4.5).

Using the Z-score formula, we have: Z = (X - μ) / σ

Let Z1 be the Z-score when X = 46.

Z1 = (46 - 55) / 4.5 = -2Let Z2 be the Z-score when X = 60.

Z2 = (60 - 55) / 4.5 = 1.111So, P(46 ≤ X ≤ 60) = P(-2 ≤ Z ≤ 1.111)

To find this probability, we can use the standard normal table or calculator. By using the standard normal table, we have: P(-2 ≤ Z ≤ 1.111) = 0.8665 - 0.0228 = 0.8437

So, the probability of Liam's commute time to be between 46 and 60 minutes is 0.8437.

Out of the 207 days that Liam commutes to work per year, the number of times his commute would be between 46 and 60 minutes is given by: Number of times = Probability × Total number of days = 0.8437 × 207≈ 175. Therefore, to the nearest whole number, Liam's commute would be between 46 and 60 minutes for 175 days.

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Answer:

293 miles

Step-by-step explanation:

284.58-17.95=266.63

266.63/0.91=293

293 miles

Answer:

30x - 18

Step-by-step explanation:

6(5x - 3)

Apply the distributive property.

6(5x) + 6(-3)

30x + - 18

Answer:

30x - 18 is your final answer

Answer:

Step-by-step explanation:

-6.3

Answer:

-6.3431 ot -6.3

Step-by-step explanation:

The difference between the actual quotient and the estimated quotient of 54,114 ÷ 29 is approximately 66.3448275862068965517241379.

To find the difference between the actual quotient and the estimated quotient of 54,114 ÷ 29, we need to first calculate the actual quotient and then the estimated quotient.

Actual quotient:

Dividing 54,114 by 29, we get:

54,114 ÷ 29 = 1,866.3448275862068965517241379 (approximated to 28 decimal places)

Estimated quotient:

Rounding the dividend, 54,114, to the nearest thousand gives us 54,000. Rounding the divisor, 29, to the nearest ten gives us 30. Now, we can perform the division with the rounded values:

54,000 ÷ 30 = 1,800

Difference between actual and estimated quotient:

Actual quotient - Estimated quotient = 1,866.3448275862068965517241379 - 1,800 = 66.3448275862068965517241379

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The number of square feet needed to cover the hole is 44ft²

To find this, we need to find the area of the green region and subtract the little square that it has inside.

Remember that for a rectangle, the area is the product between the dimensions, then the area of the green region is:

A = 12ft*4ft = 48ft²

The little square has an area:

a = 2ft*2ft = 4ft²

Then the area needed is:

area = 48ft² - 4ft² = 44ft²

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a. The stand form is f(x) = x^3 - 13x - 12

degree = 3

constant term = - 12

b. The stand form is g(x) = 3 x^3 - 39x - 36

degree = 3

constant term = - 36

Given data

f(x) = (x + 1)(x+3)(x-4)

g(x) = 3(x + 1)(x+3)(x-4)

for f(x) = (x + 1)(x+3)(x-4) we have

f(x) = (x + 1)(x+3)(x-4)

f(x) = ( x + 1 ) ( x^2 - 4x + 3x - 12 )

f(x) = (x + 1) ( x^2 - x - 12 )

f(x) =  x^3 - x^2  - 12x +  x^2 - x - 12

f(x) = x^3 - 13x - 12

degree = 3

constant term = -12

g(x) = 3(x + 1)(x+3)(x-4)

g(x) = 3(x + 1) ( x^2 - 4x + 3x - 12 )

g(x) = 3(x + 1) ( x^2 - x - 12 )

g(x) = 3 (  x^3 - x^2  - 12x +  x^2 - x - 12 )

g(x) = 3 ( x^3 - 13x - 12 )

g(x) = 3 x^3 - 39x - 36

degree = 3

constant term = - 36

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Answer: ∠16 and ∠11

Step-by-step explanation:

      All of these answer options include ∠16, so we know we're looking for an angle that is corresponding to ∠16. A corresponding angle is an angle that is in the same relative position. We will look at ∠9, ∠11, ∠2, and ∠12 since those are the given answer options, and see which is corresponding.

The correct corresponding angles are ∠16 and ∠11.

The different 2-member groups that are possible is 28

From the question, we have

Total number of members, n = 8

Numbers to selection, r = 2

The number of ways of selection could be drawn is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 8 and r = 2

Substitute the known values in the above equation

Total = ⁸C₂

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 8!/(6! * 2!)

Evaluate

Total = 28

Hence, the number of ways is 28

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To find (g+h)(t), we need to add the two functions g(t) and h(t) together, which means adding their respective outputs for any given input   \(t. (g+h)(t) = t^2 - 3t - 2.\)

First, let's write out the functions:

\(g(t) = -2t - 4\)

\(h(t) = t^2 + 2 - t\)

Now, we can add them together:

\((g+h)(t) = g(t) + h(t)\)

\(= (-2t - 4) + (t^2 + 2 - t)\)

\(= t^2 - 3t - 2\)

Therefore, the function (g+h)(t) is given by the equation:

\((g+h)(t) = t^2 - 3t - 2\)

This function is a quadratic polynomial in t, with the coefficient of the t^2 term being 1, the coefficient of the t term being -3, and the constant term being -2.

To find (g+h)(t), we simply add the two functions g(t) and h(t) together and simplify:

\((g+h)(t) = g(t) + h(t)\)

\(= (-2t-4) + (t^2 + 2 - t)\)

\(= t^2 - 3t - 2\)

Therefore,  \((g+h)(t) = t^2 - 3t - 2.\)

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The solution for all three is mathematically given as

Generally, the equation for students taking only PE and not Bio and Eng is  mathematically given as

P(PBE)= 28 – (5+6+4)

= 28 - 15

= 13

Students taking only Bio and not PE and Eng

P(BP)= 31 – (5+4+2)

= 31 - 11

= 20  

Students who are merely studying English and are not also taking Bio and PE

P(EP)= 42 – (6+4+2)

= 42 - 12

= 30  

Now, students who have taken three different classes

P(3)= 100 - ( 13 + 5 + 4 + 20 + 2 + 30 + 6 )

= 100 - 80

= 20

In conclusion, Students who have taken BIO and PE but not ENG will get a = 5 for their efforts.

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Answer:

\(\frac{1}{32} yards^{3}\)

Step-by-step explanation:

\(V=w*h*l\)

↓

\(V= \frac{1}{4} *\frac{1}{4} *\frac{1}{2}\)

=

\(\frac{1}{32} yards^{3}\\\)

Hope this helps!

Both figures have an area of 4 units squared, so yea, the area is the same.

The area of a square of side length S is equal to S squared, for the square, we can see that:

S = 2 units.

Then the area is:

A = (2 units)² = 4 square units.

For the triangle, we know that the area is equal to:

A = B*H/2

Where B = base, H = height.

We can see that:

B = 2 units.

H = 4 units.

Then:

A = (2 units)*(4 units)/2= 4 square units.

So yea, both have the same area.

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Answer:

Round both numbers to 1 significant figure.

400+400=800

800 is the answer.

The triangle with points at (2, 4), (4, 2), (9, 6) was reflected across the line y = 3 to get the points (2, 2), (4, 4), (9, 0)

Transformation is the movement of a point from its initial point to a new location. Types of transformation are reflection, rotation, translation and dilation.

The triangle with points at (2, 4), (4, 2), (9, 6) was reflected across the line y = 3 to get the points (2, 2), (4, 4), (9, 0)

Thus, option (D) is correct.

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Answer:

1 hour and 50 minutes

Step-by-step explanation:

Time Connie takes to clean the house: 210 minutes

Time takes for both of them at the same time: 100 minutes.
210 - 100 = 110 minutes

Therefore, Alvaro takes one hour and 50 minutes to clean the house by himself.

Answer:Alvaro can clean the house alone in approximately 3.89 hours.

Step-by-step explanation:

If Connie can clean her house in 3.5 hours, then her rate of work is 1/3.5 of the house per hour. Together, Connie and Alvaro can clean the house in 1 hour and 40 minutes, or 1.67 hours.

To find how long it would take Alvaro to clean the house alone, we can use the formula:

combined rate of work = sum of individual rates of work

So, (1/3.5 + 1/a) * 5/3 = 1, where "a" is the time it takes Alvaro to clean the house alone.

Simplifying the equation, we get 1/a = 9/35, which means that Alvaro can clean the house alone in approximately 3.89 hours (or 3 hours and 53 minutes).

Answer: Length = 11

              Width = 9

Step-by-step explanation:

Let x represent the unknown length.

Let x - 2 represent the unknown width.

The perimeter is equal to 2 times x + (x -2)

Equation:

2 (x + (x - 2)) = 40

x + (x - 2) = 40/2

x + x - 2 = 20

2x - 2 = 20

2x -2 + 2 = 20 + 2

The length is: 2x = 22 -> x = 22/2 -> x = 11

The width is: x - 2 = 9

The evaluation of the sinusoidal sine function y = 2·sin(x) + 1 indicates;

Maximum value: 3 at x = π/2

Minimum value: -1 at x = 3·π/2

A sinusoidal function is a periodic function based on either the sine or cosine functions, which oscillates, smoothly, between high and low values.

The specified function is; y = 2·sin(x) + 1

The domain of the input value x is; 0 ≤ x < 2·π

The function is a sinusoidal function which has the form; y = a·sin(b·(x - h)) + k

Therefore, we get;

The amplitude, a = 2

The frequency factor, b = 1

The horizontal shift, h = 0

The vertical shift, k = 1

The points in the interval 0 ≤ x < 2·π, where the sine of the angle is a maximum is; x = π/2, such that we get; sin(π/2) = 1

The points in the interval 0 ≤ x < 2·π, where the sine of the angle is a minimum is; x = 3·π/2, such that we get; sin(3·π/2) = -1

Therefore; Maximum value is;2 × sin(π/2) + 1 = 3 at the point x = π/2

Minimum value is; 2 × sin(3·π/2) + 1 = -1, at the point x = 3·π/2

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Answer:

6000 \(yd^{2}\)

Step-by-step explanation:

Take the length and multiply it by the width.

100 x 60 = 6000

Answer:6,000 yards

Step-by-step explanation:

100 yards x 60 yards = 6,000yards

Answer:

It costs $948.60 per person

Step-by-step explanation:

When you divide 2,845.80 by 3 we get 948.6.

I hope this helps you in any way:)

The equation of the line in the slope-intercept form is y = -3x + 7.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of a line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

Given:

The slope of the line is -3 and the line passes through the point (1, 4).

So, the equation of the line is,

y - 4 = -3(x - 1)

y - 4 = -3x + 3

y = -3x + 7

Therefore, y = -3x + 7.

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Answer:

0.648

Step-by-step explanation:

I added multiplyed

In 15 minutes, Jada would have covered about 2.5 miles, while the cousin would have covered 0.625 miles.

Speed is the ratio of distance to time.

For Jada:

Speed = 2 miles / 12 minutes = 0.167 miles per minute

For Jada cousin:

Speed = 1 mile / 24 min = 0.0417 miles per minute.

Hence, in 15 minutes:

Jada distance = 15 min * 0.167 miles per minute = 2.5 miles

Jada cousin distance = 15 min * 0.167 miles per minute = 0.625 miles

In 15 minutes, Jada would have covered about 2.5 miles, while the cousin would have covered 0.625 miles.

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Answer:

\(M.E=0.046\)

Step-by-step explanation:

From the question we are told that:

Sample size \(n=300\)

No. of rental \(x=111\)

Confidence Interval \(CI=0.90\ \alpha=0.10\)

Probability of rental

\(P(x)=\frac{111}{300}\)

\(P(x)=0.370\)

Generally the equation for Margin of Error is mathematically given by

\(M.E=Z_c*\sqrt{\frac{P(1-P)}{n}}\)

\(M.E=1.645*\sqrt{\frac{0.370(1-0.370)}{300}}\)

\(M.E=0.046\)

The cost of the molding is given as follows:

$119.30.

The circumference of a circle of radius r is given by the equation presented as follows:

C = 2πr.

The parameters for this problem are given as follows:

d = 9 -> r = 4.5.

(as the radius is half the diameter)

Hence the circumference is given as follows:

C = 2 x π x 4.5

C = 28.27 ft.

The cost is of $4.22 per ft, hence the total cost is given as follows:

4.22 x 28.27 = $119.30.

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Answer:

11.2

Step-by-step explanation:

yz = 11.2

since the corresponding arc of yz and xy are same, their measures will ba same too

Answered by GAUTHMATH

Answer:

11.2

Step-by-step explanation:

good luck!

In the given fraction, we have the value of 1 divided in four portions and we just have to identify which portion does A and B fall into

This can be defined as a part of portion of a complete value.

In the first part, the portion A is representing 1 out of 5 parts. So, the fraction of A is

\(A = \frac{1}{5}\)

In the second fraction B, we can say that B is representing 3 out of 5 parts.

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

From the above, the value of A and B are

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