A circle has an area of 30in². What is the area of a 60° sector of this circle?

Answer:

A.

Step-by-step explanation:

Answer:

370 mm²

Step-by-step explanation:

The area of this figure can be calculated by taking the whole figure as a full rectangle, and consider the part that is cut out from the middle of the shape as another rectangle.

Find the area of the cut-out part and subtract from the area of the full rectangular shape to get the area of the composite figure.

=>Area of full rectangular shape:

Length = 30 mm

Width = 15 mm

Area = L * B = 30*15 = 450 mm²

=>Area of the cut-out Rectangle part:

Length = 10 mm

Width = 8 mm

Area = 10*8 = 80 mm²

=>Area of composite figure = 450 mm² - 80 mm² = 370 mm²

Answer:

(7x^3+2y^3)(2x^3−7y^3)

Answer:

d)aa  (AA is not congruence theorem, it is similarity postulate)

Step-by-step explanation:

Answer:

aa

Step-by-step explanation:

Answer:

c.the area method

Step-by-step explanation:

A scatterplot is a plotting of data that represents the relationship between the two variables that should be numerical in nature. The data points i.e to be shown in a horizontal and vertical axis represent that how much one variable affected by another variable.

In the area method, we plot a data and then draw a shape which can be in oval but it does not include the outliers but the other methods like oval method, divide center method, regression calculator includes the outliers

Therefore the option c is correct

Answer:

c.the area method

Step-by-step explanation:

c.the area method c.the area method c.the area method c.the area methodc.the area methodc.the area methodc.the area method c.the area method c.the area method c.the area method   c.the area method  c.the area method

Step-by-step explanation:

The perimer of a traingle is the saum of its sides

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

Answer:

The 500th term is 3,517

Step-by-step explanation:

Here in this question, we are given an explicit formula to calculate the 500th term of the sequence

The formula to use is ;

a + (n-1)d

where a refers to the first term which is 24 in this case, while d is the common difference which is the difference between success terms and that is 52-45 = 45-38 = 7 and finally n is 500

Now we make a substitution into the formula and we have

24 + (500-1)7

= 24 + (499)7

= 24 + 3493 = 3,517

Answer:

The p-value is 0.025

Step-by-step explanation:

Given that:

30% of the people in Washington state want cell phone use banned in cafes

sample size N = 1450

X = 474 people have the same opinion.

The objective is to calculate the p-value.

Let's assume the level of significance = 5% = 0.05

From the information given ; the null and alternative hypothesis can be computed as:

[tex]\mathbf{H_o: p = 0.30 } \\ \\ \mathbf{H_a: p \neq 0.30}}[/tex]

USING MINITAB; the simulation on what we compute on our MINITAB can be written as:

Test for p = 0.3  vs p not  = 0.3

Sample  X       N         Sample p    95 C.I                            Z-value     P-value

1             474   1450   0.326897    (0.302752, 0.351041)   2.23            0.025

From what we have in our MINITAB Output;

Z - value = 2.23

P-Value = 0.025

Answer:

-5

Step-by-step explanation:

Given the two box plots showing the number of seconds the students completes the 50-meter-dash race before and after the program, we are to determine the difference between the median value of seconds before and after the program.

Median in a box plot is represented by the vertical line that divides the rectangular box in a box plot.

Thus, the median before the program = 15 seconds

The Median after the program = 10 seconds

The median change = 10 - 15 = -5 seconds.

This means, after the program, most of the students now finish the 50-meter-dash faster, about 5 seconds less the former seconds used before the program.

Answer:

-5

Step-by-step explanation:

i did it on Imagine Math and i got it correct!

Answer:

$14,580

Step-by-step explanation:

To start off, 10% of 20,000-one easy way to do this is to multiply 20,000 by 0.1, which is 10% in decimal form

-In doing that, you get 2,000

-Now the question says that the value is depreciated which means it goes down in value, so subtract 2,000 from 20,000 to 18,000

-the value of the car after one year is now $18,000

Now, let's move to the second year.  This time find 10% of 18,000

-multiply 18,000 by 0.1 to get 1,800

-since the value is depreciating, or becoming less, we will subtract 1,800 from 18,000 to get 16,200

-the value of the car after two years is now $16,200

Finally, let's look at the value of the car after three years.  Only this time, we will now find 10% of 16,200

-multiply 16,200 by 0.1 to get 1,620

-since value is being depreciated, or lessened, we will once again be subtracting.  Subtract 1,620 from 16,200 to get 14,580

Therefore, the value of the car after three years is now $14,580.

Answer:

9

Step-by-step explanation:

3 times the sum of 4 and 2 = 3*(4+2)

                                            = 3 * 6

                                           = 18

18 - 9 = 9

Answer:

(x + 9) (x - 7)

Step-by-step explanation:

when we put x + 9 = 0 then x = -9 as it's the root of the fuction.

same thing here: x - 7 = 0 then x = 7

Answer:

4.5%

Step-by-step explanation:

Simple interest:

I = Prt

112.5 = 1250(r)(2)

1250r = 56.25

r = 0.045 = 4.5%

Answer: 4.5%

Answer:ITS A

Step-by-step explanation:

SAS: side angle side

SSA: is not a congruence theorem

AAS:angle angle side

SSS:side side side

Answer:

The answer is A.

Step-by-step explanation:

Just took the test

Answer:

Binomial probability online calculator gives P([tex]\hat p[/tex]>0.60) =0.1054

Step-by-step explanation:

Given that n = 111

p = 0.54

To find P([tex]\hat p[/tex]>0.60)

We have;

P([tex]\hat p[/tex]>0.60) = [tex]P \left (\dfrac{0.6 - p}{\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}} > Z \right )[/tex]

P([tex]\hat p[/tex]>0.60) = [tex]P \left (\dfrac{0.6 - 0.54}{\sqrt{\dfrac{0.54(1-0.54)}{111}}} > Z \right )[/tex]

P([tex]\hat p[/tex]>0.60) = P(1.268 > Z) = 1 - 0.8962 = 0.1038

The above result was obtained from calculation

Binomial probability online calculator gives P([tex]\hat p[/tex]>0.60) =0.1054.

Answer:

? = 33

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan ? = opp / adj

tan ? = 13/20

Take the inverse tan of each side

tan ^-1 tan ? = tan ^-1 ( 13/20)

? = 33.02386756

To the nearest degree

? = 33

Answer:

33.

Step-by-step explanation:

inverse tan (13/20) = 33.023867579302

The correlation coefficient r is always between -1 and 1, inclusive of both endpoints. We can write [tex]-1 \le r \le 1[/tex]

If r = 0, then we have no linear correlation at all. If r = 1, then we have perfect positive correlation. If r = -1, then we have perfect negative correlation.

We see that r = 0.9 is close to r = 1, so we have strong positive linear correlation going on here.

Answer:

x = -4/5 and x = 3/5.

Step-by-step explanation:

The coefficient of x^2 is 25, which is 5 * 5. 5 * -3 = -15, and 5 * 4 = 20. 20 - 15 = 5.

So...

25x^2 + 5x - 12 = 0

(5x + 4)(5x - 3) = 0

5x + 4 = 0

5x = -4

x = -4/5

5x - 3 = 0

5x = 3

x = 3/5

So, x = -4/5 and x = 3/5.

Hope this helps!

You are correct. The higher the standard deviation is, the more spread out the data set will be. Nice work.

Answer:

Hey there! The correct answer is A. Data set C.

---

Standard deviation is simply defined as the spread of a data set in relation to the mean of the data set. The standard deviation can be calculated with a formula as shown below.

[tex]\displaystyle \sigma = \sqrt{\frac{\Sigma(x_i-\mu)^2}{N}[/tex]

Each variable has a significant meaning for this formula.

With this information, we can find the standard deviation of a data set.

Generally speaking, statisticians want a standard deviation that is on the lower end so that conclusions can be drawn about the data that was observed.

If a standard deviation is large, that means that most of the data is quite far from the mean and the data usually disproves a hypothesis. This is undesirable since the original hypothesis cannot be proven with this experiment.

When the standard deviation is quite low, this points to data that can be relied upon since it fulfills the initial requirement to prove the hypothesis.

Therefore, since the highest standard deviation correlates with the most spread out data, A. Data set C is the answer.

Answer:

12

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

This is because it has a constant rate of change.

5 x 1.5 = 7.5

6 x 1.5 = 9

7 x 1.5 = 10.5

You can find this image by dividing y by x and testing this rate of change on the other y values. Thus C is correct.

Answer:

The quantity of clover seeds the worker will add is 11.14 pounds

Step-by-step explanation:

Let

x=Poppy seed

y=clover seed

24x+13y=20.70(x+y)

x=26 pounds

Substitute x=26 pounds into the equation

24x+13y=20.70(x+y)

24(26)+13y=20.70(26+y)

624+13y=538.2 +20.70y

Collect like terms

624-538.2=20.70y-13y

85.8=7.7y

Divide both sides by 7.7

y=85.8/7.7

=11.14 pounds

Therefore, the quantity of clover seeds the worker will add is 11.14 pounds

Answer:

A 11.14

Step-by-step explanation:

To solve this, add the total cost of the poppy seed ($24 × 26) to the cost of the clover seeds ($13x), then divide both by the total number of pounds the finished mixture will weigh.

Answer:

a

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

Let x be that missing number

One third of it is x/3

One-ninth of it is x/9

Multiply x/3 and x/9

● (x/3)*(x/9) = (x^2/27)

● (x^2/27) = 108

Multiply both sides by 27

● (x^2/27)*27 = 108*27

● x^2 = 2916

● x = √(2,916) or x = -√(2,916)

● x = 54 or x = -54

So there are two possibilities 54 and -54.

a1/3×1/9=!08

if you multiply you should get 1/27a=108

in order to let a alone multiply both sides by 27

and now your a which is unknown will equal 2916.

Answer: A. 51%

Step-by-step explanation:

Area of circle = [tex]\pi r^2[/tex] , where r = radius of the circle.

In the figure below, we have the complete question.

According to that,

Radius of outer circle = 7ft

Radius of inner circle = 5ft

The probability that the thumbtack will be placed on the inner circle

[tex]=\dfrac{\text{Area of inner circle}}{\text{Area of outer circle}}\\\\=\dfrac{\pi (5)^2}{\pi (7)^2}\\\\=\dfrac{25}{49}[/tex][π is canceled from numerator and denominator

in percent, [tex]\dfrac{25}{49}\times100=51.0204081633\%\approx51\%[/tex]

So, the probability that the thumbtack will be placed on the inner circle = 51%

Hence, the correct option is A. 51%.

Answer:

m=0.5

Step-by-step explanation:

Copy the equation.

3.6m-2.7=-1.8m

Subtract 3.6m from both sides.

-2.7=-5.4m

Divide by -5.4 on both sides.

0.5

Answer:

a) 10x - 14y = -4

Step-by-step explanation:

Two equations linear dependent if you can write one as a multiple of the other. It means that the equation that is a linear dependent with -5x+7y=2 is:

10x - 14y = -4

Because it can be written as:

-2(-5x+7y) = -2(2)

So, this equation is equivalent to -5x + 7y = 2

Answer:

The correct option is;

Both spreads are best described by the standard deviation

Step-by-step explanation:

The given information are;

,                                    College                       High School

High,                              20                               20

Low,                                6                                 3

Q₁,                                   8                                 5.5

Q₃,                                  18                                16

IQR,                                 10                                10.5

Median,                           14                                11

Mean,                              13.3                             11

σ,                                      5.2                             5.4

Checking for outliers, we have

College

Q₁ - 1.5×IQR gives 8 - 1.5×10 = -7

Q₃ + 1.5×IQR gives 18 + 1.5×10 = 33

For high school

Q₁ - 1.5×IQR gives 5.5 - 1.5×10.5 = -10.25

Q₃ + 1.5×IQR gives 16 + 1.5×10.5 = 31.75

Therefore, there are no outliers and the data is representative of the population

From the data, for the college students, it is observed that the difference between the mean, 13.3 and Q₁, 8, and between Q₃, 18 and the mean,13.3 is approximately the standard deviation, σ, 5.2

The difference between the low and the high is also approximately 3 standard deviations

Therefore the college spread is best described by the standard deviation

Similarly for the high school students, the IQR is approximately two standard deviations, the  difference between the mean, 11 and Q₁, 5.5, and between Q₃, 16 and the mean,11 is approximately the standard deviation, σ, 5.4

Therefore the high school spread is also best described by the standard deviation.

Answer:

Both spreads are best described by the standard deviation

Step-by-step explanation:

Answer:

The last choice (3,2), because both lines pass through this point.

Step-by-step explanation:

For a point to be a solution to a system of linear equations, both equation's lines have to pass through that same point.

Answer: (3, 2), because both lines pass through this point

Step-by-stepexplanation:

This can be solved by substitution. The graph will show the same result.

Answer:

Area of the composite figure = 75.25 cm²

Step-by-step explanation:

Question (4). Given figure is a composite figure having,

(1). Right triangle STU

(2). A kite PSUV

(3). A trapezoid PQRS

Now we will calculate the area of each figure.

(1). Area of the right triangle = [tex]\frac{1}{2}(\text{ST})(\text{TU})[/tex]

                                              = [tex]\frac{1}{2}(3.5)(3)[/tex]

                                              = 5.25 cm²

(2). Area of the kite PSUV = [tex]\frac{1}{2}(\text{Diagonal 1})(\text{Diagonal 2})[/tex]

                                           = [tex]\frac{1}{2}(\text{PU})(\text{SV})[/tex]

                                           = [tex]\frac{1}{2}(\text{TS+RQ})(\text{SV})[/tex]

                                           = [tex]\frac{1}{2}(3.5+7)(6)[/tex] [Since SV = 2 × 3 = 6 cm]

                                           = [tex]3\times 10.5[/tex]

                                           = 31.5 cm²

(3). Area of the trapezium = [tex]\frac{1}{2}(b_1+b_2)(h)[/tex] [Where [tex]b_1[/tex] and [tex]b_2[/tex] are the bases and h is the distance between the bases]

                                           = [tex]\frac{1}{2}[(7-3)+7](7)[/tex]

                                           = [tex]\frac{77}{2}[/tex]

                                           = 38.5 cm²

Total area of the given figure = 5.25 + 31.5 + 38.5

                                                 = 75.25 cm²