Find the expression for the area of the figure. Give your answer as a simplified radical.

Answer:

D. -6.

Step-by-step explanation:

The inverse is the number when added to 6  results in 0.

So it is 0 - 6 = -6.   (6 + -6 = 0)

Answer:

C

Step-by-step explanation: I big brain

Answer:

D. Both data sets have the same number of data points.

Step-by-step explanation:

Answer:

itd d on egeunity

Step-by-step explanation:

Answer:

7/4

Step-by-step explanation:

We know that US = RU, so we can just set those expressions equal to each other.

US = 3m + 2

RU = -m + 9

US = RU  ⇒  3m + 2 = -m + 9  ⇒  4m = 7  ⇒  m = 7/4

Hope this helps!

Answer:

7/4 or 1¾

Step-by-step explanation:

Since US = UR

3m + 2 = -m + 9

4m = 7

m = 7/4

m = 1¾

Answer:

y=−259x+8

Step-by-step explanation:

i think this might be the answer but not sure

Answer:D

Step-by-step explanation:

He had saved 320 initially

Step-by-step explanation:

Let the amount he saved be 'a'

Amount spent = 20 + 40 + 30

= 90

His grand father gave 50

At the end he has 280

280 = a - 90 +50

a = 280 -50 +90

= 320

He had saved 320 initially

Answer:

9

Step-by-step explanation:

To find the common ratio, take the second term and divide by the first

36/72 = 1/2

To find the next term, take the last term and multiply by the common ratio

18*1/2 = 9

Answer:

9.

Step-by-step explanation:

The common ratio = 36/72 = 18/36 = 1/2.

So the next term is 18 * 1/2 = 9.

Answer:

56.6 square yards.

Step-by-step explanation:

Given:

A fountain in the park has two circular pools that are the same size.

Question asked:

What is the total area of the pools if the radius is 3 yards ?

Solution:

First of all we will calculate the area of a circular pool.

As we know:

[tex]Area\ of\ circle=\pi r^{2}[/tex]

                       [tex]=\frac{22}{7} \times(3)^{2} \\ \\ =\frac{22}{7}\times9\\ \\ =\frac{198}{7} \\ \\ =28.28\ square\ yards[/tex]

Area of circular pool nearest tenth = 28.3 square yards

Now, as given that both pools are of same size.

Total area of the pools = 28.3 square yards + 28.3 square yards

                                      = 56.6 square yards.

Thus, the total area of the pools are 56.6 square yards.

Answer:

ur answer is 56.5 and 18

Step-by-step explanation:

The angle subtended by an arc [tex]\widehat{AU}[/tex] is given by the angle ∠UOA.

Response:

According to circle theorem, we have;

∠QUA = 111°

Therefore;

[tex]m\widehat{QDA}[/tex] = 2 × ∠QUA

[tex]m\widehat{QDA}[/tex] = 2 × 111° = 222°

Which gives;

Angle ∠QOA = [tex]m\widehat{QUA}[/tex] = 360° - 222° = 138°

∠QOA = ∠QOU + ∠UOA by angle addition property

Which gives;

∠QOA = 138° = 88° + ∠UOA

∠UOA = 138° - 88° = 50°

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Answer:16

Step-by-step explanation:AC is half of ED

Slope-intercept form: [tex]y=mx+b[/tex]

Slope formula: [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We're given:

1) First, find the slope using the slope formula:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\dfrac{8-(-9)}{6-3}\\\\m=\dfrac{8+9}{6-3}\\\\m=\dfrac{17}{3}[/tex]

Therefore, the slope of this line (m) is [tex]\dfrac{17}{3}[/tex]. Plug this into slope-intercept form:

[tex]y=\dfrac{17}{3}x+b[/tex]

2) Now, find the y-intercept by using one of the given points:

[tex]y=\dfrac{17}{3}x+b[/tex]

Plug in one of the given points as (x,y):

[tex]8=\dfrac{17}{3}(6)+b\\\\8=34+b\\b=8-34\\b=-26[/tex]

Therefore, the y-intercept of the line is -26. Plug this into our original equation:

[tex]y=\dfrac{17}{3}x+b\\\\y=\dfrac{17}{3}x-26[/tex]

[tex]y=\dfrac{17}{3}x-26[/tex]

To write the equation of the line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept, we need to determine the slope first and then use one of the points to find the y-intercept.

Step 1: Find the slope (m)
The slope of a line passing through two points, (x1, y1) and (x2, y2), can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

Given our points (6, 8) and (3, -9), we can substitute them into our formula:

x1 = 6, y1 = 8
x2 = 3, y2 = -9

m = (-9 - 8) / (3 - 6)
m = (-17) / (-3)
m = 17/3
m = 5.666666666666667 (rounded to 5.67 for simplicity)

Step 2: Find the y-intercept (b) using one of the points
Next, we can use the point-slope form of a line equation, which is:

y - y1 = m(x - x1)

We will use the first point (6, 8) and the slope m = 5.67 that we calculated.

Substitute the point and the slope into the point-slope form equation:

8 - y1 = 5.67(6 - x1)

Since we know that (x1, y1) is (6, 8), this simplifies to:

8 - 8 = 5.67(6 - 6)
b = 8 - 5.67(6)

Now, we do the multiplication and subtraction:

b = 8 - 34.02
b = -26

So now we have our y-intercept, which is b = -26.

Step 3: Write the equation in slope-intercept form
Now that we have both m and b, we can write the equation of the line:

y = mx + b

Substitute m and b into the equation:

y = 5.67x - 26

This is the equation of the line in slope-intercept form that passes through the points (6, 8) and (3, -9). For exact calculations, you may want to use the more precise value of the slope (5.666666666666667) in the equation:

y = 5.666666666666667x - 26

By doing so, we obtain a more accurate representation of the line's equation.

Answer:

[tex]\£465.31[/tex]

Step-by-step explanation:

we know that

The insurance company reduces the price by 2.1%

Remember that

The actual cost of £475.29 a year represent the 100%

so

[tex]100\%-2.1\%=97.9\%=97.9/100=0.979[/tex]

To find out the new insurance cost, multiply the original cost by the factor 0.979

[tex]\£475.29(0.979)=\£465.31[/tex]

Brian's car insurance, after a 2.1% reduction from the original cost of £475.29, is now £465.31 when rounded to two decimal places.

Brian's original car insurance cost is £475.29, and the company is offering a reduction of 2.1% on this cost. To calculate the reduced cost, we first find the discount amount by multiplying the original cost by the reduction percentage:

Discount = Original Cost x Reduction Percentage

Discount = £475.29 x 0.021

Discount = £9.98109

Now, we subtract the discount from the original cost to find the new cost of the insurance:

New Cost = Original Cost - Discount

New Cost = £475.29 - £9.98109

New Cost = £465.30891

When rounding to two decimal places, Brian's new cost for car insurance is:

New Cost = £465.31

Answer:

$40.05

Step-by-step explanation:

You would add up 2.70+15.45+22.90 then, subtract the total by 1.00

Answer:

40.05

Step-by-step explanation:

you basically add up all the prices then subtract the 1 dollar the he has and u get ur answer

Answer:

Step-by-step explanation:

The Venn diagram representing this situation is shown in the attached photo.

P represents the set of college graduates that donated to a political campaign.

M represents the set of college graduates that donated to assist medical research.

E represents the set of college graduates that donated to preserve the environment.

From the diagram,

The number of college graduates that donated to all three is 25

The number of college graduates that donated to a political campaign and medical research only is

38 - 25 = 13

The number of college graduates that donated to a political campaign and preserve the environment only is

54 - 25 = 29

The number of college graduates that donated to medical research and to preserve the environment only is 46 - 25 = 21

The number of college graduates that donated to a political campaign only is

95 - (29 + 25 + 13) = 28

The number of college graduates that donated to medical research only is

76 - (13 + 25 + 21) = 17

The number of college graduates that donated to preserve the environment only is

133 - (29 + 25 + 21) = 58

a) the number of college graduates that donated to none is

489 - (28 + 17 + 58 + 13 + 21 + 29 + 25)

= 298 college graduates

b) the number of college graduates that donated to exactly one of the three listed causes is

28 + 17 + 58 = 103

The percentage would be

103/489 × 100 = 21.1%

Answer:

487.5 miles

Step-by-step explanation:

The actual distance between the cities is 487.5 miles.

Two or more ratios made to be equivalent to each other is termed as the method of proportion.

That is, if 'a' related to 'b' is proportional to 'p' related to 'q', then,

a : b : : p : q

⇒ a/b = p/q

⇒ aq = bp

Here we have the scale on a map reads 1/2 inch as 75 miles.

We have to find the actual distance of two cities if the distance between the cities in the map is 3 and 1/4 inches.

3 and 1/4 inches = (3 × 4 + 1) / 4 = 13/4 inches.

Let x be the actual distance between the cities.

Using proportion,

1/2 : 75 : : 13/4 : x

[tex]\frac{1/2}{75}[/tex] = [tex]\frac{13/4}{x}[/tex]

1/2 × x = 13/4 × 75

1/2 × x = 243.75

x = 487.5

Hence the actual distance between the cities is 487.5 miles.

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Answer:

D is correct E is correct F is correct

Step-by-step explanation:

72/12=6 ft per year

2 yards= 6 ft per year

18/3=6 ft per year

The equivalent rates to 6 feet per year are 18 inches per year, 12 feet in 4 years, 72 inches per year, 2 yards per year, and 18 feet in 3 years.

The student is asking about equivalent rates. To determine which rates are equivalent to 6 feet per year, we need to compare each option against the given rate. The conversion factors needed for this problem are:

Option A: 2 inches per year is not equivalent to 6 feet per year.

Option B: 18 inches per year is equivalent to 6 feet per year because 18 inches is 1.5 feet, and thus, 1.5 feet multiplied by 4 would give us 6 feet in 4 years.

Option C: 12 feet in 4 years is equivalent to 6 feet per year because dividing 12 feet by 4 years gives us 3 feet per year, which is half of the given rate.

Option D: 72 inches per year is equivalent to 6 feet per year because 72 divided by 12 is 6.

Option E: 2 yards per year is equivalent to 6 feet per year because 2 multiplied by 3 is 6.

Option F: 18 feet in 3 years is equivalent to 6 feet per year because dividing 18 feet by 3 years gives us 6 feet per year.

Thus, the equivalent rates to 6 feet per year from the options given are 18 inches per year, 12 feet in 4 years, 72 inches per year, 2 yards per year, and 18 feet in 3 years.

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Answer:

2

Step-by-step explanation:

4 -2f

Let f =1

4 - 2(1)

Multiply and divide first

4 -2

2

Answer and Step-by-step explanation:

Since this is a quadrilateral, we know that all the angles will add up to 360 degrees (by definition). We are given that angle A is 90 degrees and that the ratio of A to B is 5 to 3. This means that we can set up a proportion and solve for B:

A/B = 5/3  ⇒  90/B = 5/3  ⇒  5B = 270  ⇒  B = 54

So, we know that angle B is 54 degrees.

Now that we know angle B is 54 and A is 90, we can find the sum of the remaining two angles X and Y because A + B + X + Y = 360:

90 + 54 + X + Y = 360

X + Y = 216 degrees

We also know that the ratio of X to Y is 1 to 3, so we can set up another proportion:

X/Y = 1/3  ⇒  Y = 3X

Substitute 3X in for Y in X + Y  = 216:

X + 3X = 216

4X = 216

X = 54

Thus, we see that both angles B and X equal 54, so B = X.

Hope this helps!

Answer:

[tex]\frac{a}{b}=\frac{5}{3}=>b=\frac{3a}{5}=\frac{270}{5}=54 \\\\x+y=360-(90+54)=360-144=216\\\\\frac{x}{y}=\frac{1}{3}=>y=3x\\ \\x+3x=216\\\\4x=216\\\\x=216:4\\\\x=54\\\\x=b\\[/tex]

10 cards would have 5 even cards.

First pick would be 5/10 = 1/2 probability of getting an even card.

Without replacing there are 9 cards left with 4 even ones. The probability of picking an even card would be 4/9

The probability of both happening would be Found by multiplying the two probability’s together:

1/2 x 4/9 = 4/18 = 2/9

Two cards are selected from a deck of cards numbered from [tex]1[/tex] to [tex]10[/tex] and once a card is selected, it is not replaced, then Probability of two even numbers is [tex]\frac{2}{9}[/tex] .

Probability is a ratio of the number of favorable outcomes to the number of possible outcomes of the experiment.

Probability[tex](E)[/tex] [tex]=\frac{Number \ of \ favorable \ outcomes}{Number \ of \ possible \ outcomes \ of \ the \ experiment}[/tex]

We have,

Let [tex]E[/tex] be event of drawing cards.

A deck of cards numbered from [tex]1[/tex] to [tex]10[/tex] .

i.e. total number of possible outcomes [tex]=10[/tex]

And,

Even numbers from [tex]1[/tex] to [tex]10[/tex]  are [tex]2,4,6,8,10[/tex]

[tex]=10[/tex]

Total even numbers are [tex]5[/tex].

So,

Probability[tex](E)[/tex] [tex]=\frac{Number \ of \ favorable \ outcomes}{Number \ of \ possible \ outcomes \ of \ the \ experiment}[/tex]

Probability[tex](E)[/tex] [tex]=\frac{5}{10}*\frac{4}{9}[/tex]

                           [tex]=\frac{2}{9}[/tex]

So, the Probability of two even numbers is [tex]\frac{2}{9}[/tex] , as there are total [tex]10[/tex] cards and it is said that once a card is selected, it is not replaced, so when one card is selected there remains only [tex]9[/tex] cards, so when next time we select a card then Probability will be from those [tex]9[/tex] cards.

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Answer:

The 95% confidence interval has Minimum = 6.053 and Maximum = 7.467

Step-by-step explanation:

Here we have

Data as

1 5 6 7 8 8 8 9 9 9 9 10 3 4 5 5 7 6 8 9 10 5 4 6 5 7 3 1 9 8 8 9 9 10 7 6 4 8 10 2 5 1 8 6 9 6 8 8 10 10

The sum is 338

∴ Mean, [tex]\bar x[/tex] = 6.76, Standard Deviation, s = 2.55

Sample size, n = 50

For a 95% confidence interval, we have

[tex]CI=\bar{x}\pm z\frac{s}{\sqrt{n}}[/tex]

Where z is;

z at 95% z = [tex]\pm[/tex]1.96

Therefore, we have

95% confidence interval as Minimum = 6.053 to Maximum = 7.467.

Answer:

C 5/7

Step-by-step explanation:

We can find the slope of a line using

m = (y2-y1)/(x2-x1)

   = (-5 - -10) /(-2 - -9)

   = (-5 +10)/(-2+9)

   5/7

Answer:

46 feet

Step-by-step explanation:

Perimeter of rectangle needed =

[tex]14+14+7= 35\\[/tex]

Half of the circumference of a circle needed =

[tex]\frac{1}{2} \pi d = \frac{1}{2} * \frac{22}{7} * 7= 11[/tex]

Total perimeter needed =

[tex]35 + 11=46[/tex]

Answer:

46 ft

Step-by-step explanation:

John will need to put a fence along 3 sides of the rectangle: 14 ft, 7 ft, 14 ft

He also needs to put a fence along the half circle:

C (circumference) = 2×π×r = π×d

⇒C÷2 = π×d÷2 = 22/7×7÷2 = 22÷2 = 11 ft

Together: 14 + 7 + 14 + 11 = 46 ft

Answer:

[tex]\frac{\pi }{6}[/tex]

Step-by-step explanation:

[tex]\frac{\pi}{180}[/tex] = [tex]\frac{x}{30}[/tex]

180x = 30π

x = [tex]\frac{30\pi }{180}[/tex]

x = [tex]\frac{3\pi }{18}[/tex]

x= [tex]\frac{\pi}{6}[/tex]

Given:

The given equation of the line is [tex]y=0.216x+32.575[/tex]

We need to determine the slope of the equation.

Slope:

Let us determine the slope of the equation.

The general form of the equation of the line is given by

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

where m is the slope of the equation and b is the y - intercept.

Now, we shall compare the general form of the equation of the line with the given equation, we have;

[tex]m= 0.216[/tex]  and  [tex]b=32.575[/tex]

Thus, the slope of the equation of the line is [tex]m= 0.216[/tex]

the slope is 0.216

And just in case you need it the y-intercept is 32.575

I hope this was helpful :)

Answer:

There will be one person on 1 square yard of land after 1,892,147.588 years.

Step-by-step explanation:

Continuous exponential growth formula:

[tex]P(t)=Pe^{rt}[/tex]

P(t)= Population after t years.

P= Initial population

r=rate of growth.

t= time in year

Given that,

Growth rate of country A (r)= 4.9% per year=0.049 per year.

Initial population (P)= 151,000.

Land area of country area= 14,000,000,000 square yards.

There will be one person on one  square yard of land.

So, there will be 14,000,000,000  person for 14,000,000,000 square yard of land in country A.

P(t)=14,000,000,000 person

[tex]\therefore 14,000,000,000= 151,000 e^{0.049t}[/tex]

[tex]\Rightarrow e^{0.049t}=\frac{ 14,000,000,000}{ 151,000}[/tex]

Taking ln both sides

[tex]\Rightarrow ln|e^{0.049t}|=ln|\frac{ 14,000,000,000}{ 151,000}|[/tex]

[tex]\Rightarrow {0.049t}=ln|\frac{ 14,000,000,000}{ 151,000}|[/tex]

[tex]\Rightarrow t}=\frac{ln|\frac{ 14,000,000,000}{ 151,000}|}{0.049}[/tex]

[tex]\Rightarrow t}=1,892,147.588[/tex] years

There will be one person for every square yard of land after 1,892,147.588 years.

The mean is 59

Add all the scores together, then divide by the number of test scores

The mean of the scores to the nearest 10th Score Number of Students is 59.

We have given a data,

80,85,6,90,95,100,6,8

Mean is the adding all the scores together, then divide by the number of test scores.

So we have given a data,

80,85,6,90,95,100,6,8

80+85+6+90+95+100+6+8=470

The number of of test scores=8

[tex]mean=\frac{470}{8}=58.75[/tex]

Mean≈59

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Answer:

[tex]x \approx 21.080\,ft[/tex], [tex]y = 29.080\,ft[/tex]

Step-by-step explanation:

The total area of the pool and the walkway is:

[tex](x + 6\,ft)\cdot (y + 6\,ft) = 950\,ft^{2}[/tex]

[tex](x + 6\,ft)\cdot (x + 14\,ft) = 950\,ft^{2}[/tex]

[tex]x^{2} + 20\cdot x + 84\,ft^{2} = 950\,ft^{2}[/tex]

[tex]x^{2} + 20\cdot x - 866\,ft^{2} = 0[/tex]

The roots of the second-order polynomial is:

[tex]x_{1} \approx 21.080\,ft[/tex] and [tex]x_{2} \approx -41.081\,ft[/tex]

The only possible root is:

[tex]x \approx 21.080\,ft[/tex]

The other dimension of the pool is:

[tex]y = x + 8\,ft[/tex]

[tex]y = 21.080\,ft + 8\,ft[/tex]

[tex]y = 29.080\,ft[/tex]

Answer:

The first option....x^2-x-12

Step-by-step explanation:

Answer: x^2-x-12

Step-by-step explanation: correct answer

Answer:

This depends on the way the triangle

Step-by-step explanation:

Anyway angles that apply includes: 55 and 70

Answer:

Δπ Min = -0.0709

Δπ Max = -0.0535

Step-by-step explanation:

Here we have

[tex]z=\frac{(\hat{p_{1}}-\hat{p_{2}})-(\mu_{1}-\mu _{2} )}{\sqrt{\frac{\hat{p_{1}}(1-\hat{p_{1}}) }{n_{1}}-\frac{\hat{p_{2}}(1-\hat{p_{2}})}{n_{2}}}}[/tex]

Where:

[tex]{\hat{p_{1}}[/tex] = 13% = 0.13

[tex]\hat p_{2}[/tex] = 14% = 0.14

n₁ = 163

n₂ = 160

Therefore, we have;

[tex]z=\frac{(\hat{p_{1}}-\hat{p_{2}})}{\sqrt{\frac{\hat{p_{1}}(1-\hat{p_{1}}) }{n_{1}}-\frac{\hat{p_{2}}(1-\hat{p_{2}})}{n_{2}}}}[/tex]

Plugging the values gives

z = -0.263

CI 90% =  critical z = [tex]\pm[/tex]1.644

The minimum difference in true proportion = -0.0709

The maximum difference in true proportion = 0.0535.