If the area of one circle with radius 7 is 153.86 square units, what's the area of another circle that has a radius of 12 units?

The values of the function y = (x +3)(x - 2) at x = 1 and x = 2 are -4 and 0, respectively

The function is given as:

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

When x = 1, we have:

y = (1 +3)(1 - 2)

y = -4

When x = 2, we have:

y = (2 +3)(2 - 2)

y = 0

Hence, the values of the function y = (x +3)(x - 2) at x = 1 and x = 2 are -4 and 0, respectively

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Answer: 2277 Newtons

Step-by-step explanation:

I will show you how to do this the Physics way, so first we must write down our given values.

gravitational field = gravity = 25.3 N/kg

Mass of the astronaut = 90kg

Fun fact: know that if you convert the Newtons to a different unit, Newtons = kg (m/s^2) so we can say that instead of N/kg, we can write it as m/s^2 because if we divide kg(m/s^2) with kg, you’ll end with m/s^2

If you’re in physics, we always work with m/s^2 for every acceleration that exists. So we basically have 25.3 m/s^2 for gravity.

To find the weight, we can use the F=ma formula but rewritten as Weight = mass * gravity

Weight = (90kg)(25.3 m/s^2) = Option D = 2277 Newtons

Answer:

the answer is letter E.

see the attachment.

Answer:

7[tex]\sqrt{7}[/tex]

Step-by-step explanation:

Take 9 out of [tex]\sqrt{63}[/tex]

You get 3[tex]\sqrt{7}[/tex]

Take 4 out of [tex]\sqrt{28}[/tex]

You get 2[tex]\sqrt{7}[/tex]

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

= 9  [tex]\sqrt{7}[/tex] - 2[tex]\sqrt{7}[/tex]

=7[tex]\sqrt{7}[/tex]

Answer:

See below

Step-by-step explanation:

[tex]\displaystyle \frac{\sec x\sin x}{\tan x+\cot x}\\\\=\frac{\frac{1}{\cos x} \sin x}{\frac{\sin x}{\cos x} + \frac{\cos x}{\sin x}}\\ \\=\frac{\frac{\sin x}{\cos x} }{\frac{\sin x \sin x}{\cos x \sin x} + \frac{\cos x \cos x}{\cos x \sin x}}\\\\=\frac{\frac{\sin x}{\cos x} }{\frac{\sin^2 x}{\cos x \sin x} + \frac{\cos^2 x}{\cos x \sin x}}\\\\=\frac{\frac{\sin x}{\cos x}}{\frac{\sin^2 x+\cos^2 x}{\cos x \sin x} }\\ \\=\frac{\frac{\sin x}{\cos x} }{\frac{1}{\cos x \sin x} }[/tex]

[tex]=\frac{\sin x}{\cos x}\cdot \sin x \cos x\\ \\=\frac{\sin x \sin x \cos x}{\cos x}\\ \\=\sin^2x[/tex]

Thus, the identity is proven. Match the options up accordingly to my step-by-step process.

Answer:

Volume in terms of pi is 24

Step-by-step explanation:

formula for volume is pi x radius squared x height

3.14 x [tex]2^{2}[/tex] x 6=

75.36 then divide by pi

75.36/3.14=24pi in[tex]^{2}[/tex]

Answer:

It would be d

Step-by-step explanation:

Its d because its in a staright line

Answer:

D.

Step-by-step explanation: the rest are either non-linear , have no correlation, have a curvilinear relationship, or have no association.

The number of people out of 2000 expected to use the app will be 1300.

A survey is a research method used for collecting data from a predefined group of respondents to gain information and insights into various topics.

It is given that:-

A store employee conducted a survey of 325 randomly selected customers. According to survey 212, customers often use the app to shop.

We need to find the data for 2000 people who visited the store.

So the percentage of the people who are using the app will be calculated as:-

[tex]= \dfrac{212}{3254}=65\%[/tex]

So the number of the people out of 2000 will be:-

[tex]N\ = 2000\times \dfrac{65}{100}=1300\ \[/tex]

Hence the number of people out of 2000 expected to use the app will be 1300.

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Answer:

  (a) $1.92

  (b) $11.68

  (c) $19.21

Step-by-step explanation:

The tax is the product of the tax rate (7.5%) and the taxed amount.

__

  0.075 × $25.55 ≈ $1.92

  0.075 × $155.75 ≈ $11.68

  0.075 × $256.18 ≈ $19.21

_____

It is convenient to use a calculator for these values. A suitable calculator can do the rounding for you.

The 15 children get an opportunity to ride a horse before they rest if the horse ride lasts 5 minutes with a 1-minute pause in between the next ride. After every hour and a half, the horse is given a rest

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have:

Each horse ride lasts 5 minutes, with a 1-minute pause in between the next ride. After every hour and a half, the horse is given a rest.

Let's assume the number of children that rides the horse is x

Then we can frame a linear equation in one variable:

5x + 1x = 60+30  (After every hour and a half, the horse is given a rest.)

After solving we get:

6x = 90

x = 15 rides

Thus, the 15 children get an opportunity to ride a horse before they rest if the horse ride lasts 5 minutes with a 1-minute pause in between the next ride. After every hour and a half, the horse is given a rest

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Answer:

-4585

Step-by-step explanation:

answer: 15

steps:

i means √-1

but in this problem treat

i like x

(7-i) + (5 + 3i) - (-3 + 2i) =

(7-i) + (5 + 3i) +3 - 2i

7-i + 5 + 3i +3 - 2i =

7-i + 5 + 3i +3 - 2i

7+5+3-i+3i-2i

7+5+3+2i-2i

7+5+3 =

15

Answer:

(2, 0) and (-7, 0)

N

C.

b.

(2, 0) and (-2, 0)

There are no x-intercepts

d.

(9, 0) and (-2, 0)

Please select the best answer from the choices provided

O A

B

C

Step-by-step explanation:

Answer:

cos(2x) = [tex]\frac{119}{169}[/tex]

                      ➢◇✳︎✧✥---------------------------------------------✥✧✳︎◇⤎

[tex]Hello[/tex] [tex]There![/tex]

   We need to find the slope of the line that's parallel to 6x+5y=-5.

It's not hard, I promise! I'm going to take you through a few steps, and we'll find the answer.

Are you ready? Let's start. :)

[tex]Procedure:[/tex]

➢ First, subtract 6x from both sides:

5y=-5-6x

✦ Switch the order of the terms:

5y=-6x-5

➢ Now, divide both sides by 5:

y=-6/5x-5/5

✦ Which is the same as

[tex]\bold{y=-\displaystyle\frac{6}{5} x-1}[/tex]

➢ Part of the problem's already solved! :)

  Now, parallel lines have the same slope.

✦So the slope of the line parallel to 6x+5y=-5 is also:

◉ [tex]\bold{-\displaystyle\frac{6}{5}}[/tex] ☑︎

Problem solved! :)

[tex]Greetings ![/tex]

     ◆     •     ❖ _____________________________________❖   •. ◆

Answer:

the answer is 126 cm

sana makatulong

The correct option regarding the difference in the length of the worms is given by:

6.5 cm; this is found by determining the range which is found by finding the difference between the greatest length and the least length.

It is given by the difference of the highest value by the lowest value in the data-set.

In this problem, the difference is exactly what we want to estimate, hence we need to consider all measures(which removes the mode and the median), and find the largest lowest and the highest, which is the range, hence:

19 cm - 12.5 cm = 6.5 cm.

Which means that the correct option is given by:

6.5 cm; this is found by determining the range which is found by finding the difference between the greatest length and the least length.

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Answer:

x=5.11

Step-by-step explanation:

Hi there!

We are given a right triangle (notice the right angle), with one of the angles being equal to 64 degrees

We also know one of the sides is 42, another is x, and the other one is not marked

We want to find the value of x, which we can do using trigonometry

The 3 main trigonometric functions are:
Sine, which is opposite/hypotenuse

Cosine, which is adjacent/hypotenuse

Tangent, which is opposite/adjacent

First, let's find which side is which

The side opposite the 64 degree angle is the opposite; this side is the side marked as 42

The adjacent side would be the other leg (one of the sides creating the right angle); in this case, that would be the side marked as x

The hypotenuse in this case would be the side that hasn't been marked yet

Since we are given values for both the opposite and the adjacent, let's use tangent to find x

Since 64° was the angle we referenced to determine which side was which, we will also make the ratio with this angle.

Therefore, the ratio will be:

[tex]tan(64)=\frac{42}{x}[/tex]

Now we need to solve for x; start by multiplying both sides by x

x * tan(64) = 12

Now divide both sides by tan(64)

x = [tex]\frac{12}{tan(64)}[/tex]

Plug [tex]\frac{12}{tan(64)}[/tex] into your calculator; make sure the calculator is on degree, not radian mode

[tex]\frac{12}{tan(64)}[/tex] ≈ 5.11 (rounded to the nearest hundreth)

So x is about 5.11

Hope this helps!

Topic: trigonometry in right triangles

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Answer:

[tex]a_n=3n-2[/tex]

Step-by-step explanation:

General form of an arithmetic sequence: [tex]a_n=a+(n-1)d[/tex]

where:

Create expressions for the 4th and 6th terms:

[tex]\implies a_4=a+(4-1)d=a+3d[/tex]

[tex]\implies a_6=a+(6-1)d=a+5d[/tex]

The ratio of the 4th term to the 6th term is 5:8, therefore:

[tex]\implies \dfrac{a_4}{a_6}=\dfrac{5}{8}[/tex]

[tex]\implies \dfrac{a+3d}{a+5d}=\dfrac{5}{8}[/tex]

[tex]\implies 8(a+3d)=5(a+5d)[/tex]

[tex]\implies 8a+24d=5a+25d[/tex]

[tex]\implies 8a-5a=25d-24d[/tex]

[tex]\implies 3a=d \quad \leftarrow \textsf{Equation 1}[/tex]

Sum of the first n terms of an arithmetic series:

[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]

The sum of the first 7 terms of an arithmetic progression is 70:

[tex]\implies S_7=70[/tex]

[tex]\implies \dfrac{7}{2}[2a+(7-1)d]=70[/tex]

[tex]\implies 2a+6d=20[/tex]

[tex]\implies a+3d=10 \quad \leftarrow \textsf{Equation 2}[/tex]

Substitute Equation 1 into Equation 2 and solve for [tex]a[/tex]:

[tex]\implies a+3(3a)=10[/tex]

[tex]\implies a+9a=10[/tex]

[tex]\implies 10a=10[/tex]

[tex]\implies a=1[/tex]

Substitute found value of [tex]a[/tex] into Equation 1 and solve for [tex]d[/tex]:

[tex]\implies 3(1)=d[/tex]

[tex]\implies d=3[/tex]

Finally, substitute found values of [tex]a[/tex] and [tex]d[/tex] into the general form of the arithmetic sequence:

[tex]\implies a_n=1+(n-1)3[/tex]

[tex]\implies a_n=1+3n-3[/tex]

[tex]\implies a_n=3n-2[/tex]

Convert the cm to feet for the base and the height:

12/2 = 6 x 3 = 18 feet

9/2 = 4.5 x 3 = 13.5 feet

area = 1/2 x base x height

Area = 1/2 x 18 x 13.5

Area = 121.5 square feet

answer: 121.5 square feet

Answer:

Francis has $1,993.46 left of his pay stub

Step-by-step explanation:

earns $3437 dollars

42% to tax (yikes! almost half of their pay)

42% of $3437 dollars: $3437 x 0.42 = 1,443.54

Francis is paying $1,443.54 in taxes

$3437 - $1,443.54 = $1,993.46

Part A: The IQR for the males' data.  23

Part B: The difference between the median values of each data set. 13

Part C: The distribution of the data and if the mean or median would be a better measure of center for each Median for the males and Mean for the females

Part D:The possible reason for the outlier in the data set. The day the movie premiered

The likely missing part of the question; The Box Plots are to compare The Number of Males and The Number of Females attending the latest superhero movie every day in a given month

The known parameters

The 5 number summary in a are;

Minimum                                         0           0

FIrst Quarlite Q1                             2           5

Second Quarlite, Mediun Q2        20         7

Third Quarlite                                 25         40

Maximum                                        50         18

Outlier                                                           46

Part A:

The Inter Quartile Range, IQR = Q₃ - Q₁

For the males, we have, IQR = 25 - 2 = 23

Part B:

The difference between the median values for the males and females is given as follows;

Difference between median = Q₂ Males - Q₂ Females

∴ Difference between median = 20 - 7 = 13

The difference between the median values for the males and females = 13

Part C:

The distribution of the data for the males is skewed left, with almost all the data in the first half

The better measure of center for the skewed data is the median, given

that three quarter of the data have values that are less than half of the

range of values in the data set, and that the median is close to the third

quartile, the mean will be located further towards the minimum value of

the data than the median

The distribution of the data for the females consists of the interquartile range located approximately in the middle between the max and the min values with the median being close to the first quartile, therefore, the mean will be a better measure of center as it will be located further from the first quartile and closer midway in the IQR

Part D;

The possible reason for the outlier in the data set may be due to the first day the latest super hero movie is premiered

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Answer:

[tex]\displaystyle \boxed{ \frac{dz}{du} = \frac{e^\big{\frac{u(2u + v)}{v}}}{v} \Bigg[ 4u + v \Bigg] }[/tex]

[tex]\displaystyle \boxed{ \frac{dz}{dv} = \frac{ue^\big{\frac{u(2u + v)}{v}}}{v} \Bigg[ 1 - \frac{2u + v}{v} \Bigg] }[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:
[tex]\displaystyle (cu)' = cu'[/tex]

Derivative Property [Addition/Subtraction]:
[tex]\displaystyle (u + v)' = u' + v'[/tex]

Derivative Rule [Basic Power Rule]:

Multivariable Calculus

Partial Derivatives

Partial Derivative Rule [Chain Rule]:
[tex]\displaystyle \frac{dw}{dt} = \frac{\partial w}{\partial x} \frac{\partial x}{\partial t} + \frac{\partial w}{\partial y} \frac{\partial y}{\partial t} + \frac{\partial w}{\partial z} \frac{\partial z}{\partial t}[/tex]

Step-by-step explanation:

Step 1: Define

Identify given.

[tex]\displaystyle x = 2u + v[/tex]

[tex]\displaystyle y = \frac{u}{v}[/tex]

[tex]\displaystyle z = e^{xy}[/tex]

Step 2: Find Derivatives

[tex]\displaystyle \frac{dz}{du}[/tex]:

We can find the partial derivatives by differentiating using basic differentiation rules found under "Calculus":

[tex]\displaystyle\begin{aligned}\frac{\partial z}{\partial x} & = ye^{xy} \\\frac{\partial x}{\partial u} & = 2 \\\frac{\partial z}{\partial y} & = xe^{xy} \\\frac{\partial y}{\partial u} & = \frac{1}{v} \\\end{aligned}[/tex]

Substituting in our partial derivatives and our variables x and y, we can obtain a final derivative:

[tex]\displaystyle\begin{aligned}\frac{dz}{du} & = 2ye^{xy} + \frac{xe^{xy}}{v} \\& = \frac{2ue^\big{\frac{u(2u + v)}{v}}}{v} + \frac{(2u + v)e^\big{\frac{u(2u + v)}{v}}}{v} \\& = \boxed{ \frac{e^\big{\frac{u(2u + v)}{v}}}{v} \Bigg[ 4u + v \Bigg] }\end{aligned}[/tex]

∴ we have found the derivative of z with respect to u.

[tex]\displaystyle \frac{dz}{dv}[/tex]:

We can find the partial derivatives by using the same method(s):

[tex]\displaystyle\begin{aligned}\frac{\partial z}{\partial x} & = ye^{xy} \\\frac{\partial x}{\partial v} & = 1 \\ \frac{\partial z}{\partial y} & = xe^{xy} \\\frac{\partial x}{\partial v} & = \frac{-u}{v^2} \\ \end{aligned}[/tex]

Substituting in our partial derivatives and our variables x and y, we can obtain a final derivative:

[tex]\displaystyle\begin{aligned}\frac{dz}{dv} & = ye^{xy} + \frac{-uxe^{xy}}{v^2} \\& = \frac{ue^\big{\frac{u(2u + v)}{v}}}{v} + \frac{-u(2u + v)e^\big{\frac{u(2u + v)}{v}}}{v^2} \\& = \boxed{ \frac{ue^\big{\frac{u(2u + v)}{v}}}{v} \Bigg[ 1 - \frac{2u + v}{v} \Bigg] }\end{aligned}[/tex]

∴ we have found the derivative of z with respect to v.

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Topic: Multivariable Calculus

Unit: Partial Derivatives and Applications

Answer:

178

Step-by-step explanation:

100 plus 78 equal s 179

Answer:

3

Step-by-step explanation:

Prime factorization

60 = 2 x 2 x 5 x 3  

9  15  and 6   are NOT prime numbers !

Based on the rate the bird is flying and the distance above your head, the speed of change in the angle of elevation is 0.018 rad/sec.

First use the Pythogoreous theorem to find the distance between you and the bird at 80 m:

= √(60² + 80²)

= √(3,600 + 6,400

= 100 m

Cos² = 80² / 100²

= 16 /25

Differentiate this to get:

= ((-60 x 16/25) / 80²) x (-3)

= 9/500

= 0.018 rad/sec

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Answer:

depends on where you look