functions please helpp​

The length of side AD is,

⇒ AD = 16

We have to given that;

The given figure is a right triangular prism.

In the prism:

• DF = 22 in.

• EG = 11 in.

• Volume of the prism = 1936 cubic in.

Since, Volume of right triangular prism is,

V = 1/2 (bh) x L

Substitute all the values we get;

V = 1/2 (22 × 11) × AD

1936 = 121 × AD

AD = 16

Thus, The length of side AD is, 16

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Answer:

\(\displaystyle x=\frac{7\pm\sqrt{37}}{6}\)

Step-by-step explanation:

\(\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\frac{-(-7)\pm\sqrt{(-7)^2-4(3)(1)}}{2(3)}\\\\x=\frac{7\pm\sqrt{49-12}}{6}\\ \\x=\frac{7\pm\sqrt{37}}{6}\)

Rested numbers in group is 33 out of 76.

A percentage is expressed as a number or ratio that can be expressed as fraction of 100. It is denoted by % symbol.

Total numbers in a group = 76.

44% of them were rested.

That is 44% of 76.

To find how many are rested we have to find the value in numbers.

Convert 44% of 76 to numbers.

For this, it can be written as

\(\frac{44}{100} *76\) = 33.44

Therefore 44% of 76  ≅ 33 numbers.(approximately)

Hence, rested numbers in group is 33.

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Answer:

\(n^2 -3n - 6\)

Step-by-step explanation:

Looking at the image attached, you must first work out the difference between each term. This is +0, +2, +4, +6, +8, +10 (shown in orange).

Because you now have a linear sequence, the difference is now the same each time. This is +2 (shown in blue).

Because the original sequence is a quadratic, you have to halve the second difference (the +2). This means that the value of \(n^2\) is 1, so 1\(n^2\) or just \(n^2\) .

If you write out the values of \(n^2\), you can work out how much more you need to add or take away. For example, take the first three terms in the sequence.

n = 1, 2, 3

x = -8, -8, -6

\(n^2\) = 1, 4, 9

Work out the difference between \(n^2\) and x:

1 - -8 = 9

4 - -8 = 12

9 - -6 = 15

This gives you yet another linear sequence, 9, 12, 15.

Working out the formula for this, the difference is 3 each time, so it is 3n. The first value of n is 1, so 3n is 1. The difference is 6, so the formula for this linear sequence is 3n + 6.

Because \(n^2\) is greater than x, you need to take 3n + 6 away from \(n^2\).

This gives \(n^2\) - (3n+6), so the final answer is:

\(n^2\) - 3n - 6.

Answer:

YU = 4.82.  angle STR = 23°

Step-by-step explanation:

7) Angle between U and V = 72°, since angles on a straight line add up to 180°. so angle UV = 180 - 108 = 72°.

similarly, angle YU = 180 - 85 - 72 = 23°.

length of circumference of full circle = π X diameter = π (2r)

= 2πr (radius = half of diameter).

circumference = 2π(12) = 24π.

there are 360° in full circle.

remember that angle YU = 23°.

length YU = (23/360) X 24π

= (23π)/15

= 4.817

= 4.82 to nearest one hundredth.

8) triangle RST sits inside of half the circle, ie in the semicircle.

angle RST = 90° because the angle in a semicircle =  90°.

there are 180° in a full triangle.

since angle RST = 90°, angle STR must be less than 180 - 90.

angle STR < 90°. so STR must be 23°.

Answer:

X=7

Step-by-step explanation:

5x - 15 =20

5x=15+30

5x=35

Divide by 5

X=7

First: Find out their decimal form.

- 2 1/6 as a decimal is 2.16

7/3 as a decimal

To get 7/3 converted to decimal, you simply divide 7 by 3. Don't worry. You don't need to get the calculator out, because we did this for you.

7/3 as a decimal is:

2.333333333

Answer:

Step-by-step explanation:

You want to fill a table using the given rules, then describe the relationship between the table values.

Starting with 100, you want to subtract 20 to get next terms:

  100

  100 -20 = 80

  80 -20 = 60

  60 -20 = 40

The next terms are 80, 60, 40.

Starting with 20, you want to subtract 4 to get next terms:

  20

  20 -4 = 16

  16 -4 = 12

  12 -4 = 8

The next terms are 16, 12, 8.

Looking at second terms, we can determine which description is true:

  80 -80 = 0 ≠ 16 . . . . . the description "subtract 80" fails

  80/5 = 16 . . . . . . . . . . the description "divide by 5" works

Each term in pattern B can be found by dividing the corresponding term in pattern A by 5.

The triangle (call it T ) has base and height 4, so its area is 1/2*4*4 = 8. Then the joint density function is

\(f_{X,Y}(x,y)=\begin{cases}\frac18&\text{for }(x,y)\in T\\0&\text{otherwise}\end{cases}\)

where T is the set

\(T=\{(x,y)\mid 0\le x\le4\land0\le y\le4-x\}\)

(a) I've attached an image of the integration region.

\(P(X<3,Y<3)=\displaystyle\int_0^1\int_0^3f_{X,Y}(x,y)\,\mathrm dy\,\mathrm dx+\int_1^3\int_0^{4-x}f_{X,Y}(x,y)\,\mathrm dy\,\mathrm dx=\frac12\)

(b) X and Y are independent if the joint distribution is equal to the product of their marginal distributions.

Get the marginal distributions of one random variable by integrating the joint density over all values of the other variable:

\(f_X(x)=\displaystyle\int_{-\infty}^\infty f_{X,Y}(x,y)\,\mathrm dy=\int_0^{4-x}\frac{\mathrm dy}8=\begin{cases}\frac{4-x}8&\text{for }0\le x\le4\\0&\text{otherwise}\end{cases}\)

\(f_Y(y)=\displaystyle\int_{-\infty}^\infty f_{X,Y}(x,y)\,\mathrm dx=\int_0^{4-y}\frac{\mathrm dx}8=\begin{cases}\frac{4-y}8&\text{for }0\le y\le4\\0&\text{otherwise}\end{cases}\)

Clearly, \(f_{X,Y}(x,y)\neq f_X(x)f_Y(y)\), so they are not independent.

Answer:

The last one is correct.

Step-by-step explanation:

[] Rewrite 4/5 as 8/10

[] 8/10 / 3/10 = 8/10 * 10/3 = 80/30 = 2 2/3 days

Have a nice day! - This is only correct if your models look like the ones I have attached

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:157.5

Step-by-step explanation:becuase mutilpy 4.5x35 that equals 157.5

Answer:

Step-by-step explanation:

(10 - 4)/(2 - 5) = -6/3 = -2

Answer:

1. 8t

2. 510 + 6t

3. 510 - 2t

Step-by-step explanation:

1. Since the hare moves at a speed of 8 metres per second, the distance it moves from the starting line is d = speed × time = 8t

2. Since the rabbit moves at a speed of 6 metres per second, and gets a head start of 510 metres, the distance it moves from the starting line is d = 510 m + speed × time = 510 + 6t

3. The distance the tortoise is ahead of the hare is thus, distance moved by rabbit - distance moved by hare in time, t.

d' = 510 + 6t - 8t

= 510 - 2t  

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!

The growth rate function indicates that the number of years The Iron Man's net worth will reach the net worth of T'Challa is about 87 years

The growth rate is the rate of growth of a function with regards to the input variable.

T'Challa's net worth in the Marvel comics = 80 trillion (8 × 10¹³) Dollars

The Iron Man's net worth = 20 billion (2 × 10¹⁰) Dollars

The growth rate per annum of The Iron Man's net worth = 10% per annum

The number of years it will take to reach T'Challa can therefore, be found as follows;;

(2 × 10¹⁰) × (1 + 0.1)ˣ = (8 × 10¹³)

(1 + 0.1)ˣ = (8 × 10¹³)/(2 × 10¹⁰)

x·ln(1 + 0.1) = ln((8 × 10¹³)/(2 × 10¹⁰))

x = (ln((8 × 10¹³)/(2 × 10¹⁰)))/(ln(1 + 0.1)) ≈ 87 years

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The formula for obtaining the value of a term of a sequence is given as a

as a recursive formula.

Responses:

The amount of pocket money Smith gets = 2 × The amount he gets in the previous day

The amount Smith gets on the first day = R1

Required:

The given information expressed as a sequence.

Solution:

The amount of money smith gets can be expressed as follows;

Amount he gets on day 1 = R1

On day 2, R2 = 2·R1

On day 3, R3 = 2·R2 = 2·2·R1 = 4·R1

On day 4, R4 = 2·R3 = 2·2·2·R1 = 8·R1

On day 5, R5 = 2·R4 = 2·2·2·2··R1 = 16·R1

The information written as a sequence is therefore;

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The volume of the sphere is 32 cubic feet.

To calculate the volume of sphere, apply the formula given below;

The formula for the volume of a sphere can be described as:

V = (4/3)πr³

where r is the representation of the radius of the sphere.

Given that the radius of the sphere is 2 feet and π = 3, we can substitute these values into the formula to get:

V = (4/3)π(2³)

  = (4/3)π(8)

As per the given information π = 3,

V = (4/3)(3)(8)

V = 32 cubic feet.

Therefore, the required volume is 32 cubic feet.

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The remaining angles of the triangle are approximately 72.7 degrees and 76.3 degrees.

What is the law of sine?

A law in trigonometry the ratio of each side of a plane triangle to the sine of the opposite angle is the same for all three sides and angles.

To solve the triangle, we can use the law of sines and the fact that the angles of a triangle add up to 180 degrees.

Using the law of sines, we have:

a/sin(A) = b/sin(B) = c/sin(C)

where c is the unknown side and B and C are the unknown angles.

We can use the given values to solve for sin(A) and plug them into the equation to get:

sin(A) = sin(31) ≈ 0.515

c/sin(C) = 12/0.515

c ≈ 27.89 inches

So the length of the remaining side is approximately 27.89 inches.

To find the angles, we can use the fact that the angles of a triangle add up to 180 degrees. So we have:

B + C = 180 - A

sin(B) = b/c * sin(C)

Substituting the values we know, we get:

B + C = 180 - 31 = 149

sin(B) = 5/27.89 * sin(C)

We can solve the second equation for sin(C) by rearranging to get:

sin(C) = sin(B) * 27.89/5

Then we can substitute into the first equation to get:

B + arcsin(sin(B) * 27.89/5) = 149

We can solve for B using algebra or by using a calculator to evaluate the left side of the equation. Either way, we get:

B ≈ 72.7 degrees

Then we can use the fact that the angles of a triangle add up to 180 degrees to find C:

C = 180 - A - B

= 180 - 31 - 72.7

= 76.3 degrees

hence, the remaining angles of the triangle are approximately 72.7 degrees and 76.3 degrees.

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*Answer*

15:47

Step-by-step explanation:

He left; 15:03

Walk for; 12mins

Spends extra;4min

So by my side,

I'll sum up those values we're having to find the total time that was spent

12+4= 16mins

So, at that time when he reached at the station it was 15:19 when we add those extra mins

And so I think it'll 15:47

My thought told me so though

Answer:

\(slope=-\frac{1}{3}\)

Step-by-step explanation:

To find the slope of the two points (1, -1) and (4, -2) we have to use the slope formula.

\(slope=\frac{y_{2}- y_{1} }{x_{2} -x_{1} }\)             \(slope=\frac{(-2)- (-1)}{4 -1}\)      

\(slope=\frac{-1 }{3}=-\frac{1}{3}\)  can also be written as a decimal  \(slope=-0.333333\)

Answer:

The answer is 14512

Step-by-step explanation:

106,688

- 89,176

During the entire drive from the first city to the second city, you will be within the signal range of the transmitter.

To determine how much of the drive you will pick up a signal from the transmitter, we need to find the distance between the two cities and compare it to the radius of the transmitter's broadcast.

Using the Pythagorean theorem, we can calculate the distance between the two cities:

Distance = sqrt((65^2) + (68^2))

Distance = sqrt(4225 + 4624)

Distance = sqrt(8849)

Distance ≈ 94.03 miles

Since the distance between the two cities is 94.03 miles and the transmitter's broadcast radius is 56 miles, we can conclude that for the entire duration of the drive, you will be within the broadcast range of the transmitter.

Thus, you will pick up a signal from the transmitter throughout the entire drive.

During the entire drive from the first city to the second city, you will be within the signal range of the transmitter.

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Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

The correct answer is a. -∞, f(x) → -∞; x → ∞, f(x) → ∞b. -∞, f(x) → -∞; x → ∞, f(x) → ∞c. -∞, f(x) → -∞; x → ∞, f(x) → ∞d. -∞, f(x) → -∞; x → ∞, f(x) → -∞

For the polynomial function f(x) = 6x^5 + 7x^2 + 7x + 9, the leading coefficient is 6 (the coefficient of the highest-degree term). The degree of the polynomial is 5, which is odd.

According to the Leading Coefficient Test, when the degree of the polynomial is odd and the leading coefficient is positive (in this case, positive 6), the end behavior of the graph is as follows:

- As x approaches negative infinity (-∞), f(x) approaches negative infinity (-∞).

- As x approaches positive infinity (∞), f(x) approaches positive infinity (∞).

For the polynomial function f(x) = 61x^11 + 7x^2 + 2x + 8, the leading coefficient is 61 (the coefficient of the highest-degree term). The degree of the polynomial is 11, which is odd.

Using the Leading Coefficient Test, we can determine the end behavior:

- As x approaches negative infinity (-∞), f(x) approaches negative infinity (-∞) since the leading coefficient is positive.

- As x approaches positive infinity (∞), f(x) also approaches positive infinity (∞) due to the same reason.

For the polynomial function f(x) = 5x^8 + 3x^2 + 2x + 9, the leading coefficient is 5 (the coefficient of the highest-degree term). The degree of the polynomial is 8, which is even.

Applying the Leading Coefficient Test:

- As x approaches negative infinity (-∞), f(x) approaches positive infinity (∞) because the leading coefficient is positive.

- As x approaches positive infinity (∞), f(x) also approaches positive infinity (∞) for the same reason.

For the polynomial function f(x) = -2x^8 + 6x^2 + 4x + 9, the leading coefficient is -2 (the coefficient of the highest-degree term). The degree of the polynomial is 8, which is even.

Using the Leading Coefficient Test:

- As x approaches negative infinity (-∞), f(x) approaches negative infinity (-∞) since the leading coefficient is negative.

- As x approaches positive infinity (∞), f(x) approaches negative infinity (-∞) due to the same reason.

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Answer: y = -6.

Step-by-step explanation: -6^3 is -216. Sorry if this isn't a clear explanation, but it seems like the correct choice.

Have a great day! :)

Answer:

A = 35 cm²

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × width

by counting the squares on the sides

length = 7 cm and width = 5 cm , then

A = 7 × 5 = 35 cm²

Based on the information, there are 25 cars with good brakes and good tires.

Total cars = 50

Cars with faulty brakes = 10

Cars with faulty tires = 15

Cars with faulty brakes and good tires = 2

Let's calculate the number of cars with good brakes and good tires:

Cars with faulty brakes or faulty tires = Cars with faulty brakes + Cars with faulty tires - Cars with faulty brakes and good tires

= 10 + 15 - 2

= 25

Cars with good brakes and good tires = Total cars - Cars with faulty brakes or faulty tires

= 50 - 25

= 25

Therefore, there are 25 cars with good brakes and good tires.

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The equation of the line with slope 1/3 and y-intercept as -1 is y = x/3-1 in slope-intercept form.

According to the question,

We have the following information:

Slope of the line = 1/3

We know that the slope of the line is denoted by m.

y-intercept of the line = -1

We know that the y-intercept is denoted by b.

We have the following equation for the line in slope-intercept form:

y = mx+b

Putting the above values in this equation:

y = x/3-1

Hence, the equation of the line with slope 1/3 and y-intercept as -1 is y = x/3-1 in slope-intercept form.

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