A plane veered off its course at an angle of 11 degrees. If the plane ended up 170 miles due west of its planned destination, how far did it fly? Estimate your answer to two decimal places.

Answer:

She ate 8 donuts the first day, 14 on the second, 20 on the third, 26 on the fourth, and 32 on the fifth day

Step-by-step explanation:

Over the course of 5 days, she ate 100 donuts, each day eating 6 more than the day before.  Let n be the number of donuts she ate on the first day, then she ate...

Day 1: n donuts

Day 2: n + 6 donuts    

Day 3: n + 12 donuts

Day 4: n + 18 donuts

Day 5: n + 24 donuts

Add the days together and get the equation...

n + (n + 6) + (n + 12) + (n + 18) + (n + 24) = 100

Now combine like terms and solve for n...

5n + 60 = 100

    5n = 40

    n = 8

She ate 8 donuts the first day, 14 on the second, 20 on the third, 26 on the fourth, and 32 on the fifth day

The range of the sample means calculated from the provided data is 2.2.

To find the range of the sample means, we first need to calculate the mean for each row and then find the range of these means.

Calculating the mean for each row:

1st row: (3 + 1 + 0 + 4 + 1) / 5 = 9 / 5 = 1.8

2nd row: (4 + 2 + 3 + 0 + 5) / 5 = 14 / 5 = 2.8

3rd row: (0 + 1 + 1 + 2 + 0) / 5 = 4 / 5 = 0.8

4th row: (4 + 1 + 4 + 4 + 2) / 5 = 15 / 5 = 3

5th row: (3 + 2 + 0 + 1 + 4) / 5 = 10 / 5 = 2

Now, let's find the range of these means:

Range = Maximum mean - Minimum mean

Range = 3 - 0.8 = 2.2

Therefore, the range of the values for the sample means is 2.2.

Answer:

Step-by-step explanation:

Use the formula of a midpoint:

[tex]\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)[/tex]

We have the points P(-2a, 0) and Q(0, 2b). Substitute:

[tex]x=\dfrac{-2a+0}{2}=\dfrac{-2a}{2}=-a\\\\y=\dfrac{0+2b}{2}=\dfrac{2b}{2}=b[/tex]

Answer:

138 apples

Step-by-step explanation:

7x12=84

9x6=54

84+54=138

Answer:

3 hours

Step-by-step explanation:

39 miles/ 13 miles per hour means 3 hours. SIMPLE!

Answer: B) Addition Property

Step-by-step explanation:

The Step 3 is: [tex]3x-30=0[/tex]

The idea is to solve the equation, which means that you have to find the value of the variable [tex]x[/tex].

As [tex]3x-30[/tex] is a subtraction, you need to add 30 to both sides of the equation to keep the equation balanced. This property is known as "Addition property of equality".

This property states that adding the same number to both sides of the equation, the equality does not change:

[tex]a=b\\a+n=b+n[/tex]

Then, the Addition property of equality applied in Step 3, get you to Step 4:

[tex]3x-30+(30)=0+(30)\\3x=30[/tex]

Answer: B. Addition Property

Step-by-step explanation:

The output is -20 to this question

The output of the given linear function at x = 7 is -20.

A straight line on the coordinate plane is represented by a linear function.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

In another word, a linear function is a function that varies linearly with respect to the changing variable.

As per the given function,

y = -3x + 1

Here x is the input and y is the output.

Put x = 7

y = -3 ×7 + 1

y = -21 + 1 = -20

Hence "The output of the given linear function at x = 7 is -20".

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Answer:

The solution in the attached figure

Step-by-step explanation:

we have

[tex]y<16x^{2}[/tex]

we know that

The solution of the inequality is the shaded area below the dashed line of the parabola

The equation of the dashed line is the vertical parabola [tex]y=16x^{2}[/tex]

therefore

The solution in the attached figure

The graph that represents the inequality is in the image at the end.

Which graph represents the inequality?

Here we have the inequality:

y < 16x²

This is a parabola that opens upwards, with a vertex at the point (0, 0).

The area shaded must be the area below the parabola, and because we have the symbol "<" we must graph the parabola with a dashed line instead of a solid line.

With this in mind, we can see that the correct option is the third graph.

Answer:

x = 5.75

Step-by-step explanation:

4^(x+7) = 8^(2x-3)

But; 4^(x+7) = 2^2(x+7)

8^(2x-3) = 2^3(2x-3)

2^2(x+7) = 2^3(2x-3)

Since the bases are the same;

2(x+7) = 3(2x-3)

2x + 14 = 6x -9

14 + 9 = 6x - 2x

23 = 4x

x = 23/4

x = 5.75

Answer:

[tex]946[/tex]

Step-by-step explanation:

we know that

The formula to find the sum is equal to

[tex]S=(a1+an)n/2[/tex]

where

a1 is the first term

an is the last term

n is the number of terms

In this problem we have

[tex]n=11[/tex]

[tex]a1=(98-2(1))=96[/tex]

[tex]an=(98-2(11))=76[/tex]

substitute the values in the formula

[tex]S=(96+76)(11/2)=946[/tex]

Answer:

C is your answer...

Answer:

Its C

Step-by-step explanation:

Edge 2020

Answer:

2*sqrt(x + 8)

Step-by-step explanation:

You could use the distributive property to answer your question

[sqrt(x + 8) + sqrt(x + 8)]

=sqrt(x + 8) [1 + 1]

=2*sqrt(x + 8)

Answer:

Volume

Figure 1 = 56 cube units

figure 2 = 60 cube units

figure 3 =72 cube units

Surface area

Figure 1 = 100 square units

figure 2 = 104 square units

figure 3 =108 square units

Step-by-step explanation:

From the all figure we can see that each figure made up of unit cubes

Figure 1

Surface area

Large cuboid portion =2 x (6 x 2 ) +  (6 x 4) + 2 x(4 x 2) + 16

  = 24 + 24 + 16 + 16 = 80 unit square

Small cuboid portion = (4 x 2) + (2 x 2) + (4 x 2) = 8 + 4 + 8 = 20

Total surface area = 80 + 20 = 100 unit square

Volume

Small cuboid = 4 x 2 = 8

Large cuboid = 6 x 4 x 2 = 48 cube unit

Total volume = 48 + 8 = 56 cubs units

Figure 2

Surface area

Total surface area =24 + 18 + 36 + 20 + 6 = 104 unit square

Volume

Small cuboid = 6 x 2 = 12

Large cuboid = 6 x 4 x 2 = 48 unit square

Total volume = 48 + 12 = 60 cube units

Figure 3

Surface area

Total surface area = 48 + 36 + 24 = 108 square units

Volume

Total volume = 6 x 4 x 3 = 72 cube units

27,459 --- 7,000

40,735 --- 700

7,000÷700 =10 times greater

The surface area is 300 therefore its B

So the answer is (C)

c.2/5

hope this HELP

Answer:

2 to the power of 5

Step-by-step explanation:

Answer:

Step-by-step explanation:

There would be 216 outcomes because

6*6=36 outcomes so

6*6*6, or 36*6, = 216.

When 3 fair dice are rolled then there are 216 possible outcomes.

What is mean by Probability?

The term probability refers to the likelihood of an event occurring.

Given that;

When 2 fair dice are rolled there are 36 possible outcomes.

Now,

Since, When 2 fair dice are rolled then possible outcomes = 6 x 6 = 36

So, When 3 fair dice are rolled then possible outcomes = 6 x 6 x 6

                                                                                      = 216

Thus, When 3 fair dice are rolled then there are 216 possible outcomes.

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Answer:

B) 200 + 4c - 6b

Step-by-step explanation:

Be,

c = number of cards sold at $4

b = number of cards purchased at $6

x = money at the beginning of the day = $200

y = money at the end of the day

The variables x and c owe positive values because they represent possession or income of money, while b must be negative because purchases are expenses.

Then, the following equation is formed:

y = x + 4c - 6b

Substituting x for its value, you get

y = 200 + 4c - 6b

Hope this helps!

Answer:

  16

Step-by-step explanation:

The quotient of a number (x) and 4 is written x/4. 56 less than that is ...

  (x/4) -56

The problem statement tells us the value of this is -52, so we have ...

  (x/4) -56 = -52

Add 56 to both sides of this equation, and you get ...

  x/4 = 4

Multiply both sides of this equation by 4 and you get ...

  x = 16

The value of the unknown number is 16.

x = 4.8

With angles like this these ones, the 2 lines equal the same amount. To find the length of one of the lines, you multiply the given lengths.

So, for the first angle, the line with both angles has a 4 and 6, so the length of the line is 24.

Since the lines are equal, to find the length of x you take 24 and divide it by 5, which gives you 4.8, or 24/5.

This means x = 4.8.

To double check, you can simply multiply 4 and 6, then 5 and 4.8. If the answers are the same, it is correct.

This applies to all 3 angles shown.

Hope this helps!

Visual Explanation:

Answer:

The size of the small play area is [tex]400\ ft^{2}[/tex]

Step-by-step explanation:

Let

x-----> the small play area

y-----> the large play area

we know that

[tex]x+y=2,000[/tex] ----> equation A

[tex]x=\frac{1}{4}y[/tex]

[tex]y=4x[/tex] ----> equation B

substitute equation B in equation A and solve for x

[tex]x+(4x)=2,000[/tex]

[tex]5x=2,000[/tex]

[tex]x=2,000/5[/tex]

[tex]x=400\ ft^{2}[/tex]

Final answer:

To find the volume of the soup can, one must use the formula for the volume of a cylinder, [tex]V = (pi)r^2h[/tex]. After substituting the given measurements, the calculated volume, rounded to the nearest tenth, is approximately 673.9 cubic centimeters.

Explanation:

The student asked about the volume of a cylindrical soup can with a given radius and height. To calculate this, the formula for the volume of a cylinder, which is V = \\(pi)r^2h, is used. Here, r represents the radius of the cylinder's base, and h represents the height of the cylinder. Substituting the given values into the formula, we get [tex]V = (pi)(4.3 cm)^2(11.6 cm)[/tex]. The calculated volume will give us the amount of space inside the soup can, measured in cubic centimeters (cm^3).

Step-by-step calculation:

Answer:

The volume of the similar prism is [tex]336\ cm^{3}[/tex]

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z-----> the scale factor

x----> the volume of the larger prism

y----> the volume of the smaller prism

so

[tex]z^{3}=\frac{x}{y}[/tex]

In this problem we have

[tex]z=2[/tex] -----> the scale factor

[tex]y=42\ cm^{3}[/tex]

substitute and solve for x

[tex]x=42(2^{3})=336\ cm^{3}[/tex]

Answer: first option.

Step-by-step explanation:

The formula you must use to calculate the volume of the figure shown is the following:

[tex]V=\frac{BH}{3}[/tex]

Where B is the area of the base and  H is the height.

Assuming that the base of the pyramid is a square, you have that B is:

[tex]B=(10units)^2=100units^2[/tex]

Substitute values into the formula, Then you obtain:

 [tex]V=\frac{(100units^2)(12units)}{3}=400units^3[/tex]

Answer:

Final answer is 400 cubic units.

Step-by-step explanation:

We have been given length of the base edge of square pyramid = a = 10 units

vertical height of the square pyramid = h = 12 units

Now we need to find the volume of the square pyramid.

So apply formula :

[tex]Volume = \frac{1}{3}a^2h[/tex]

[tex]Volume = \frac{1}{3}(10)^2(12)[/tex]

[tex]Volume = \frac{1}{3}(100)(12)[/tex]

[tex]Volume = \frac{1}{3}(1200)[/tex]

[tex]Volume = 400[/tex]

Hence final answer is 400 cubic units.

Answer:

B

Step-by-step explanation:

Range of the graph is the ALLOWED y-values. The y-axis is number of gallons left in tank. So, it cannot be NEGATIVE number of gallons, so 0 is the lower limit of the range.

As we can see from the axis of the graph, we see where the line cuts the y-axis, that is the upper limit of number of gallons he starts off with. The y-intercept (y-axis cutting point) is 12.

So we can say that the range is  0 ≤ y ≤ 12

Correct answer is B

ANSWER

[tex]A. \: \: y = 5x + \frac{3}{4} [/tex]

EXPLANATION

The slope-intercept form of an equation is given by;

[tex]y = mx + c[/tex]

wherever m is the slope and c is y-value of the y-intercept.

It was given that the slope is 5.

This implies that,

[tex] m = 5[/tex]

The y-intercept is

[tex](0, \frac{3}{4})[/tex]

This means that,

[tex]c = \frac{3}{4} [/tex]

We plug in the values to obtain,

[tex]y = 5x + \frac{3}{4} [/tex]

The correct choice is A.

Answer:

[tex]s = 21\ ft\\\\a = -6\ \frac{ft}{s^2}[/tex]

Step-by-step explanation:

To find the changes in the slope of the function s(t) we find its derivative

[tex]\frac{ds(t)}{dt} = 3t^2 - 18t +24\\[/tex]

Now we make [tex]\frac{ds(t)}{dt} = 0[/tex]

[tex]3t^2 - 18t +24 = 0[/tex]

[tex]3t^2 - 18t +24\\\\3(t^2-6t + 8)\\\\3(t-4)(t-2)\\\\t_1 =4\\t_2=2\\[/tex]

The particle changes direction for the first time at t = 2 sec

The position at t = 2 sec is:

[tex]s(t=2) = (2)^3 - 9(2)^2 + 24(2) + 1\\\\\s(2) = 21\ ft[/tex]

The acceleration after t = 2 sec is the second derivative of s(t), evaluated at t = 2:

[tex]\frac{d^2s(t)}{d^2t} = 6t -18\\\\\frac{d^2s(t)}{d^2t}(2) = 6(2) -18\\\\ a = 12-18\\\\a = -6\ \frac{ft}{s^2}[/tex]

Answer:

The position is 21 feet

The acceleration is -6 ft/sec²

Step-by-step explanation:

∵ s(t) = t³ - 9t² + 24t + 1

- where s is the displacement in feet and t is the time in second

∵ v(t) = ds/dt ⇒ velocity is the differentiation of s(t)

∵ a(t) = d²s/dt² = dv/dt ⇒ acceleration is the differentiation of v(t)

∴ v(t) = 3t² - 18t + 24

∵ When the particle reverses means v(t) = 0

∴ 3t² - 18t + 24 = 0 ⇒ ÷ 3

∴ t² - 6t + 8 = 0

∴ (t - 2)(t - 4) = 0

∴ t - 2 = 0 ⇒ t = 2 seconds

∴ t - 4 = 0 ⇒ t = 4 seconds

- That means the particle will change its direction first after 2 seconds

  and again after 4 seconds

∵ a(t) = dv/dt

∴ a(t) = 6t - 18

∵ t = 2

∴ a(2) = 6(2) - 18 = 12 - 18 = -6 ft/sec²

∵ s(t) = t³ - 9t² + 24t + 1

∴ s(2) = 2³ - 9(2)² + 24(2) + 1 = 21 feet

First you would need to move the variable causing it to change its sign

5x=10-y

Then divide both sides by 5

X=2-1/5y

Then you are left with your answer:

x=2-1/5y

Hope this helps! :3

Answer:

The measure of each angle is [tex]20\°[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

Let

x------> the angle on each side

we know that

[tex]x\°+140\°+x\°=180\°[/tex]

solve for x

[tex]2x\°=180\°-140\°[/tex]

[tex]2x\°=40\°[/tex]

[tex]x=20\°[/tex]