A circle has its center at (-1, 2) and a radius of 3 units. What is the equation of the circle? (1 point) (x - 1)2 + (y + 2)2 = 3 (x + 1)2 + (y - 2)2 = 3 (x + 1)2 + (y + 2)2 = 9 (x + 1)2 + (y - 2)2 = 9

Answer:

Step-by-step explanation:

The formula for the area of a sector is

[tex]A_{s} =\frac{\theta }{360}*\pi r^2[/tex]

where theta is the angle given as 45 and r is the radius (7).  Plugging in we get

[tex]A_{s}=\frac{45}{360}*\pi  (7)^2[/tex]

Simplify a bit to get

[tex]A_{s}=\frac{1}{8}*49\pi[/tex]

which gives you, in terms of pi:

[tex]A_{s}=\frac{49\pi }{8}[/tex]

or if you need to use the decimal form, rounded to the hundredths position:

A = 19.24

Answer:

The period of given function is  [tex]Period = 16\pi [/tex]

So, Option B is correct.

Step-by-step explanation:

In this question we need to find the period of the function y= 3 sin x/8

The formula used to find period of function is: [tex]\frac{2\pi }{b}[/tex]

We need to know the value of b.

To find the value of b we compare the standard equation with the equation of function given.

Standard Equation: y = a sin(bx - c) +d

Given Equation: y= 3 sin(x/8)

Comparing we get:

a= 3

b= 1/8

c= 0

d=0

So, we get the value of b i.e 1/8. Putting it in the formula to find period of given function.

[tex]Period = \frac{2\pi }{b}[/tex]

[tex]Period = \frac{2\pi }{\frac{1}{8}}[/tex]

Solving,

[tex]Period = 2\pi *8[/tex]

[tex]Period = 16\pi [/tex]

So, the period of given function is  [tex]Period = 16\pi [/tex]

The equation for the volume of a cube is V=s^3, where V is volume and s is side length.  Plug in and solve:

V=4.5^3

V=4.5*4.5*4.5

V=91.125ft^3

Hope this helps!!

The selection of "Yes" or "No" to state whether each data set is likely to be normally distributed is as follows: A) No. B) Yes. C) Yes. D) Yes

A normal distribution of data occurs when the majority of data points are relatively similar and the data set has a small range of values.

1. The number of coupons used at a supermarket is no.

2. The weights of the pumpkins that are delivered to a supermarket is yes.

3. The number of raisins in each 8-oz box of raisins at a supermarket is yes.

4. The amount of time customers spend waiting in the checkout line at a supermarket is yes.

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The selection of "Yes" or "No" to state whether each data set is likely to be normally distributed is as follows: A) No. B) Yes. C) Yes. D) No

1. The number of coupons used at a supermarket is likely to follow a discrete distribution rather than a normal distribution. Customers may use 0, 1, 2, or more coupons, but the number of coupons used is not continuous and typically has a lower bound of 0. The distribution may be skewed to the right with a large number of transactions involving no coupons and a decreasing frequency as the number of coupons increases.

2. The weights of pumpkins are likely to be normally distributed because they are a result of many different factors, such as genetics, soil quality, water intake, etc., which tend to produce a bell-shaped curve when combined. This is an example of a continuous measurement that can be modeled well with a normal distribution.

3. The number of raisins in each 8-oz box is likely to be normally distributed due to the central limit theorem. Although the distribution of raisins per box might be uniform or have some other distribution, when the sample size (number of raisins per box) is large, the distribution of the sample mean (total number of raisins in many boxes) will approach a normal distribution. Since an 8-oz box contains a large number of raisins, the count in each box should be approximately normal.

4. The amount of time customers spend waiting in the checkout line is likely not to be normally distributed. This is because the waiting time is bounded below by zero and may have an upper limit depending on the store's operating hours or customer patience. The distribution of waiting times is often skewed to the right, with many customers experiencing short waits and a few experiencing longer waits. This results in a distribution with a long tail on the right side, which is not characteristic of a normal distribution.

ANSWER

C. f(x) = (x+3)(x+5)

EXPLANATION

The given function is

[tex]f(x) = x^2 +8x+15[/tex]

The factored form of the function reveals the zeros of the function.

From the factored form, we apply the zero product principle to get the zeros.

From the given options, the factored form of the polynomial is

[tex]f(x) = (x+3)(x+5)[/tex]

Answer:

Both the mean and median will decrease, but the mean will decrease more than the median.

Step-by-step explanation:

Removing the wheel of cheese will decrease the median a little bit, because the median shifts from between two data points to the lower of the two data points:

       With the wheel of cheese, the median is the middle number, but there's no middle number in this data set! So, to find the median we take the mean of the two middle numbers, $4.79 and $5.19 which is $4.99.

       Without the wheel of cheese,

Removing the wheel of cheese will decrease the mean significantly, because the total cost will decrease by $39.99, and the number of items decreases by only 1.

Answer: B

Step-by-step explanation:

the answer for this question is (B) 5,-2

Answer:

option A

Step-by-step explanation:

We can find the standard form by expanding the equation:

y = 3(x-4)^2 - 22

y = 3(x^2 - 8x + 16) - 22

y = 3x^2 - 24x + 48 - 22

y= 3x^2 - 24x + 26

So the correct option is option A

Answer:

option A) y= 3x²-24x+26 ~apex

Step-by-step explanation:

[tex]f(x)[/tex] is continuous on [0, 3] and differentiable on (0, 3), so the mean value theorem applies here. It says that there is some [tex]c[/tex] in the open interval (0, 3) such that

[tex]f'(c)=\dfrac{f(3)-f(0)}{3-0}[/tex]

We have

[tex]f'(x)=-2\sin2x-e^{-x}[/tex]

so

[tex]-2\sin2c-e^{-c}=\dfrac{\cos6+e^{-3}-2}3\implies c\approx1.5418[/tex]

Answer:

[tex]\frac{9}{20}[/tex]

Step-by-step explanation:

We want probability that 1st is girl AND 2nd is girl as well.

In probability "AND" means multiplication and "OR" means "addition".

We find the probabilities separately and multiply them together, since "AND".

=9/10

=2/4

P(both girls) = 9/10 * 2/4 =9/20

Answer:

Not 100% sure but i will say (B)

Step-by-step explanation:

Answer:

It is not a real number.

Step-by-step explanation:

Answer:

The degree of a polynomial is the highest degree of its monomials with non-zero coefficients

Step-by-step explanation:

not sure

The maximum power of the polynomial x⁶ + 4x - 3 that is degree will be 6.

A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.

A polynomial's degree is the greatest exponent of its variable term. The variable in this example is x, and the maximum exponent of x is 6, which is the degree of the polynomial. As a result, the polynomial x⁶ + 4x - 3 has a degree of 6.

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a. 9 cm 2 because each side would be 3 and length x width would be 3 x 3 = 9

Answer:

hello : answer : a) 9 cm 2

Step-by-step explanation:

A square has a perimeter of 12 : p = 4×c.....c is the length

12 = 4c

c = 12/4

c = 3

the area  A= c²

   A= 3² = 9  cm 2

Answer:

the answer is 82

Step-by-step explanation:

The answer would be 82

Answer:

F

Step-by-step explanation:

In congruent triangles, or similar triangles, the letters in the same place will also be congruent

Answer:

the answer is A

Step-by-step explanation:

Answer:

  B)  9/2

Step-by-step explanation:

Subtracting 5x+7 from both sides leaves 2x = 9.

Dividing the 9 into two parts, we find ...

  x = 9/2

Answer: 9/2 your welcome i got a 100% on the test by the way

Step-by-step explanation:

Answer:

81.75 ft²

Step-by-step explanation:

The area (A) of a trapezoid is calculated using the formula

A = [tex]\frac{1}{2}[/tex] h (a + b)

where a, b are the parallel bases and h is the perpendicular height

Calculate h using the right triangle and the sine ratio

sin30° = [tex]\frac{opposite }{hypotenuse}[/tex] = [tex]\frac{h}{10}[/tex]

Multiply both sides by 10

10 × sin30° = h, thus

h = 5

a = 12 and b = 8.7 + 12 = 20.7, hence

A = [tex]\frac{1}{2}[/tex] × 5 × (12 + 20.7)

   = 0.5 × 5 ×32.7

   = 81.75 ft²

Answer:

Step-by-step explanation:

Observe in the attached image that the final balance in your account on 9/1 is $578.30.

Then:

*On 9/6 he makes a payment of $140.30

*On 9/8, he makes a withdrawal from an ATM of $120

This means that:

$140.30 + $120 = $260.30

Then:

*On 9/18 you receive a deposit of $356.22

This means that:

$356.22

So, we have:

Beginning Balance: $578.30.

Total Withdrawals: $260.30

Total Deposits: $356.22

Final Balance = Beginning balance + Total Deposits - Total Withdrawals

Final Balance= $578.30 + $356.22 - $260.30

Final balance= $674.22

Then:

Date     Description    Debits(-) Credits(+)    Balance

9/6        Auto Pay         140.30                       438.00

9/8         ATM               120.0                         318.00

9/18       Deposit                           356.22      674.22

The balance in Arianna's register after the transactions will be $587.88. Then the correct option is C.

A monetary transfer is a record of money entering and exiting your account and is known as a bank transaction.

Arianna's register shows a deposit on 9/5 in the amount of $310.25 an ATM withdrawal on 9/8 in the amount of $60.00 and checks #149 on 9/14 in the amount of $240.67.

No other Transactions were made.

Then the balance be in Arianna's register will be

→ $ 578.37 + $ 310.25 - $ 60 - $ 240.67

→ $ 587.88

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ANSWER

[tex]\frac{\pi}{2} [/tex]

EXPLANATION

The period refers to the interval over which the function completes one full cycle.

The given function completed four cycles in on the the interval.

[-π,π]

The period is

[tex] = \frac{\pi - - \pi}{4} [/tex]

[tex]= \frac{\pi + \pi}{4} [/tex]

Simplify;

[tex]= \frac{2 \pi}{4} [/tex]

[tex]= \frac{\pi}{2} [/tex]

The last choice is correct.

Answer: letter a should be the correct answer

Step-by-step explanation:

D is the answer for this question

Monthly periodic rate = 1.95%

The APR is the annual periodic rate

The annual periodic rate is the monthly rate multiplied by 12, because there are 12 months in a year

APR = monthly periodic rate X number of months in a year

= 1.95% X 12

= 23.4%

By using the concept of Annual Periodic rate and Monthly periodic rate,

Annual periodic rate of Shelby = 23.4%

What is Annual Periodic Rate and Monthly periodic rate?

At first it is important to know about Periodic rate.

Periodic rate is the rate that can be charged on loans for a certain period.

If the periodic rate is calculated over a month then it is called monthly periodic rate.

If the periodic rate is calculated over a year then it is called Annual periodic rate.

Here,

Monthly periodic rate of Shelby = 1.95%

Annual periodic rate of Shelby = [tex]1.95 \times 12[/tex]

                                                   = 23.4%

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The original negative number in the problem is found by setting up the equation 6x = x - 20 and solving for x, which results in the original number being -4.

If a certain negative number is multiplied by six, the result is the same as 20 less than the original number. To solve for the original number, we can set up an equation based on the given condition. Let's assume the original number is x.

According to the problem, 6 times x equals x subtracted by 20:

6x = x - 20

To solve for x, we'll first move all terms involving x to one side of the equation by subtracting x from both sides:

6x - x = -20

This simplifies to:

5x = -20

Now, divide both sides by 5 to isolate x:

x = -20/5

x = -4

Therefore, the value of the original number is -4.

By the binomial theorem,

[tex](x+y)^8=\displaystyle\sum_{n=0}^8\binom8nx^{8-n}y^n[/tex]

The [tex]x^3y^5[/tex] term occurs for [tex]n=5[/tex]; this gives the term

[tex]\dbinom85x^{8-5}y^5=\dfrac{8!}{5!(8-5)!}x^3y^5=56x^3y^5[/tex]

so the coefficient is 56.

option D is the answer.!!!!

Answer:

Step-by-step explanation:

The formula for the area of a circle of radius r is A = πr².

Here, the area is A = π(18 units)² = 324π units²  (Answer D)

Answer:

[tex]\left(fog\right)\left(-5\right)=-59[/tex]

Step-by-step explanation:

Given functions are [tex]f\left(x\right)=-2x-7[/tex] and [tex]g\left(x\right)=-4x+6[/tex].

Using both functions we need to find about what is the value of [tex]\left(fog\right)\left(-5\right)[/tex]. That can be done as shown below:

[tex]\left(fog\right)\left(-5\right)[/tex]

[tex]=f\left(g\left(-5\right)\right)[/tex]

[tex]=f\left(-4\left(-5\right)+6\right)[/tex]

[tex]=f\left(20+6\right)[/tex]

[tex]=f\left(26\right)[/tex]

[tex]=-2\left(26\right)-7[/tex]

[tex]=-52-7[/tex]

[tex]=-59[/tex]

Hence final answer is [tex]\left(fog\right)\left(-5\right)=-59[/tex].

Answer:

A [tex]y=8\sin \dfrac{1}{2}x[/tex]

Step-by-step explanation:

From the graph you can see that the period of the function is

[tex]720^{\circ}=4\pi[/tex]

Now the period of the function [tex]y=8\sin kx[/tex] is

[tex]T=\dfrac{2\pi}{k}[/tex]

Thus,

[tex]4\pi=\dfrac{2\pi}{k}\Rightarrow 4\pi k=2\pi\\ \\k=\dfrac{2\pi}{4\pi}=\dfrac{1}{2}[/tex]

and the expression for the function is

[tex]y=8\sin \dfrac{1}{2}x[/tex]

Answer:

A. 18 divided by 2/9

Step-by-step explanation:

To determine the number of boos that will fit into a box that is 18 inches long, we divide the length of the box by the length of the books

18 inches  divided by 2/9 inches per book

This tells us how many books

copy dot flip

18 * 9/2

81 books

To solve this problem we will use Heron's formula:

[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]

Where [tex]a, \ b \ and \ c[/tex] are the side lengths of the triangle and [tex]s[/tex] is the semiperimeter (half the perimeter of the triangle). We know that:

[tex]Perimeter \ P=\triangle PSQ=PS+PQ+SQ: \\ \\ \triangle PSQ=P=50 \\ \\ Semiperimeter \ s: \\ \\ s=\frac{P}{2}=25[/tex]

Also:

[tex](I) \ PS=SQ \\ \\ (II) \ SQ-PQ = 1 \\ \\ (III) \ PS+PQ+SQ=50 \\ \\ \\ (I) \ into \ (III): \\ \\ SQ+PQ+SQ=50 \\ \\ \therefore (IV) \ 2SQ+PQ=50 \\ \\ From \ (II): \\ \\ PQ=SQ-1 \\ \\ (II) \ into \ (IV): \\ \\ 2SQ+(SQ-1)=50 \\ 3SQ-1=50 \\ 3SQ=51 \\ \\ \boxed{SQ=17} \\ \\ \boxed{PS=17} \\ \\ PQ=SQ-1=17-1 \therefore \boxed{PQ=16}[/tex]

Finally:

[tex]A=\sqrt{s(s-a)(s-b)(s-c)} \\ \\ A=\sqrt{s(s-PS)(s-SQ)(s-PQ)} \\ \\ A=\sqrt{s(s-17)(s-17)(s-16)} \\ \\ A=\sqrt{25(25-17)(25-17)(25-16)} \\ \\ \boxed{A=120}[/tex]

Answer:

< 2.11, 4.53 >, < -3.03, -1.75 >, <2.93 cos 108.26, 2.93 sin 108.26 >

Step-by-step explanation:

First, let's decompose Bruce's velocity along the x- and y- direction. Bruce is moving 5 m/s at 25 degrees east of north, so its angle with respect to the positive x-direction is actually 90 - 25 = 65 degrees. So its components are

[tex]b_x = (5 m/s) cos 65^{\circ} =2.11 m/s\\b_y = (5 m/s) sin 65^{\circ} =4.53 m/s[/tex]

So, Bruce's vector is

< 2.11, 4.53 >

The current is moving 3.5 m/s at an angle 60 degrees west of south, which means an overall angle of 210 degrees, measured counterclockwise from the positive x-axis. So, the components of the current's velocity are

[tex]c_x = (3.5 m/s) cos 210^{\circ}=-3.03 m/s\\c_y = (3.5 m/s) sin 210^{\circ}=-1.75 m/s[/tex]

So, the current's vector is

< -3.03, -1.75 >

Finally, we can add the components of the two vectors to find Bruce's actual velocity:

[tex]v_x = b_x + c_x = 2.11 + (-3.03)=-0.92 m/s\\v_y = b_y + c_y = 4.53+(-1.75)=2.78 m/s[/tex]

So, Bruce's actual velocity is

< -0.92, 2.78 >

The magnitude is

[tex]v=\sqrt{(-0.92)^2+(2.78)^2}=2.93 m/s[/tex]

And the direction is

[tex]\theta=180^{\circ} - tan^{-1} (\frac{v_y}{v_x})=180^{\circ} - tan^{-1}(\frac{2.78}{-0.92})=180^{\circ}-71.7^{\circ}=108.3^{\circ}[/tex]

< 2.11, 4.53 >, < -3.03, -1.75 >, <2.93 cos 108.26, 2.93 sin 108.26 >

A) There is a positive correlation between plant growth and the time spent in light.

Hope this helps chu

Have a great day

The correlation coefficient helps us to know how strong is the relation between two variables. The correct option is A.

The correlation coefficient helps us to know how strong is the relation between two variables. Its value is always between +1 to -1, where, the numerical value shows how strong is the relation between them and, the '+' or '-' sign shows whether the relationship is positive or negative.

Since in the given scatterplot as the value of the percent of the time the plant is exposed to light is increased there is a simultaneous growth in the height of the plant in inches.

Therefore, For the given scatterplot the conclusion that can be made is that there is a positive correlation between plant growth and the time spent in light.

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