A regular pentagon has an apothem measuring 20 cm and a perimeter of 145.3 cm what is the area of the pentagon ?

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: a) 0.6, b) [tex]\dfrac{4}{15}[/tex]

Step-by-step explanation:

Since we have given that

Total number of people were surveyed = 150

Number of people that like comedies they bought popcorn that day = 90

Number of people that said they do not buy popcorn = 40

So, Probability of getting who like comedies and bought popcorn = [tex]\dfrac{90}{150}=\dfrac{3}{5}=0.6[/tex]

Probability of getting who said they do not buy popcorn = [tex]\dfrac{40}{150}=\dfrac{4}{15}[/tex]

Hence, a) 0.6, b) [tex]\dfrac{4}{15}[/tex]

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

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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The scale of the drawing to the new barn is 1:1.5.

To find the scale of the new barn compared to the existing barn, we can use the ratio of their sides. Let's call the shortest side of the new barn x meters. The ratio of the lengths of the shortest sides of the new and existing barns is given as 2/3. Setting up the proportion, we have 2/3 = x/150. Cross-multiplying, we find x = (2/3) * 150 = 100 meters. Therefore, the shortest side of the new barn measures 100 meters. The scale of the drawing to the new barn can be determined by dividing the length of the shortest side of the drawing by the length of the shortest side of the new barn. Let's call the scale factor y. We have y = 150/100 = 1.5. Therefore, the scale of the drawing to the new barn is 1:1.5.

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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]

Answer:

E

Step-by-step explanation:

-18x + 21 > -15

-18x > -36

x < 2

20x - 13》17

20x》40

x》2

Or is union

Union of x < 2 and x》2 is all real numbers

-6.75 is a rational number since it can be expressed as a fraction of two integers. It's also a real number, but it's not a natural, whole, integer, or irrational number.

The number -6.75 is a Rational Number. Here's why:

A Natural Number is a number that is a positive integer, which would not include -6.75 because it is negative. A Whole Number is a number without fractional components, so -6.75 isn't a whole number as it has a fractional part. An Integer is a whole number that can be positive, negative, or zero, but does not include fractions or decimals, therefore, -6.75 isn't an integer. A Rational Number is a number that can be expressed as a fraction of two integers, and since -6.75 can be written as -675/100, it falls into this category. Since all rational numbers are included in the Real Number set, -6.75 is also a real number. However, an Irrational Number cannot be expressed as a ratio of two integers, which means that -6.75 isn't irrational.

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Answer:

C.1/6

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

just replace the x with 2 and solve

4(2)+1

8+1

= 9

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]

Part a)

We have that,the distribution of finishing time for men was approximately normal with mean 242 minutes and standard deviation 29 minutes.

We want to calculate and interpret the standardized score for Clay's marathon time, if the finishing time for Clay was 289 minutes.

We use the formula:

[tex]z = \frac{x - \bar x}{s} [/tex]

we substitute the values to get:

[tex]z = \frac{289 - 242}{29} [/tex]

[tex]z = 1.62[/tex]

This means Clay's finishing time is 1.62 standard deviation above the mean finishing time.

Part b)

This time, we have that, the distribution of finishing time for women was approximately normal with mean 259 minutes and standard deviation 32 minutes.

We want to find the proportion of women who ran the marathon that had a finishing time less than Kathy if the finishing time for Kathy was 272 minutes.

We first calculate the z-score to get:

[tex]z = \frac{272 - 259}{32} = 0.41[/tex]

From the normal standard distribution table P(z<0.41)=0.6591.

This means 65.91% of women had a finishing time less than Kathy's finishing time.

Part c

The standard deviation of a data set tells us how far away the individual data are from the mean.

If the standard deviation of finishing time is greater for women than men, it means the finishing time for women are farther from the mean finishing time than that of men.

Using the normal distribution, it is found that:

a) His standardized score was of z = 1.6, which means that his finishing time is of 1.6 standard deviations above the mean finishing time for all men.

b) 0.6591 = 65.91% of women who ran the marathon had a finishing time less than Kathy's.

c) The higher standard deviation shows that the finishing times of the women who ran the marathon are more spread out compared to the finishing times of the men who ran the marathon.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Item a:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{289 - 242}{29}[/tex]

[tex]Z = 1.6[/tex]

His standardized score was of z = 1.6, which means that his finishing time is of 1.6 standard deviations above the mean finishing time for all men.

Item b:

The proportion is the p-value of Z when X = 272, thus:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{272 - 259}{32}[/tex]

[tex]Z = 0.41[/tex]

[tex]Z = 0.41[/tex] has a p-value of 0.6591.

0.6591 = 65.91% of women who ran the marathon had a finishing time less than Kathy's.

Item c:

The higher standard deviation shows that the finishing times of the women who ran the marathon are more spread out compared to the finishing times of the men who ran the marathon.

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Answer:

3

Step-by-step explanation:

logb(8)

logb(2³)

3 × logb(2)

3 × 1

3

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:

1.12 = 28 / 25

Step-by-step explanation:

28 over 25

28

---

25

BRAINLIST please have a great day

Answer:

28/25

Step-by-step explanation:

hope this helps.

Answer:$15

Step-by-step explanation:

45 divided by 3 =15

Answer:

her brother has $15

Step-by-step explanation:

m= molly

b= brother

m=45

b= 45÷3

b=15

Answer:

15

Step-by-step explanation:

Hello!

To find the median, all you have to do is order the number of terms in ascending order and then count to the middlemost number(s).

Arranging in ascending order:

[tex]6,\:12,\:14,\:15,\:15,\:18,\:19,\:19[/tex]

Since this is an even number, our two medians are 15 and 15.

(15 + 15) / 2 = 15.

Thus, the median of successful free throws is [tex]\boxed{15}[/tex].

[tex](x - 17.7) + 19.6 = 27.8 \\ x - 17.7 = 27.8 - 19.6 \\ x - 17.7 = 8.2 \\ x = 17.7 + 8.2 \\ x = 25.9[/tex]

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:

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:

$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:

so f(0) = g(0)   and f(2) = g(2)

Step-by-step explanation:

f(x) = g(x) where the two graphs intersect

The graphs cross at the x coordinate 0  and x coordinate 2

so f(0) = g(0)   and f(2) = g(2)

Answer:

First one

Step-by-step explanation:

f(x) = g(x)

Is the point of intersection of the two graphs

(0,4) and (2,0)

Solutions are: x = 0 and x = 2

Answer:

79 years old

Step-by-step explanation:

Let's say your age is x.

The problem says "500 reduced by 4 times my age is 184", so we convert this to math:

- "4 times my age" ⇒ 4 * x = 4x

- "500 reduced by" ⇒ 500 - (something)

- "500 reduced by 4 times my age" ⇒ 500 - 4x

- "is 184" ⇒ = 184

- "500 reduced by 4 times my age is 184" ⇒ 500 - 4x = 184

Now, we simply solve for x:

500 - 4x = 184

4x = 500 - 184 = 316

x = 79

Thus, you are 79 years old.

Hope this helps!

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:

Scale factor = 1/2

Ratio R:T = 2:1

Attached is the missing image;

Step-by-step explanation:

From the image attached;

The height of the triangle T is = 5 units

Base of triangle T = 4 units

Since the two triangles are scaled versions;

Area of a triangle = 1/2 × h × b

For triangle R;

Area = 40 = 1/2 × h × b

hb = 80

And, h : b = 5:4

h= 5/4 b

5/4 ×b × b = 80

b^2 = 64

b = 8

h = 5/4 × 8 = 10

The height of the triangle R = 10 units

Base of triangle R = 8 units

Scale factor = h2/h1 = 5/10 = 1/2

Scale factor = 1/2

Answer:

This depends on the way the triangle

Step-by-step explanation:

Anyway angles that apply includes: 55 and 70

Answer:

The distance between them is 366.75 feet.

She doesn't need to sound a warning yet.

Step-by-step explanation:

Please see the attached files for explanation.

To find the Distance between ships, we can use trigonometry. The distance between the ships is the absolute difference between their heights above the horizontal.

To find the distance between the two ships, we can use trigonometry. Let's consider the triangle formed by the lighthouse, ship 1, and ship 2. The angle of depression to ship 1 is 20°, so the angle between the line of sight and the horizontal is also 20°. Similarly, the angle of depression to ship 2 is 12.5°, so the angle between the line of sight and the horizontal is also 12.5°.

We can use the tangent function to find the height of ship 1 and ship 2 above the horizontal. Using the formula tan(angle) = opposite/adjacent, we have: tan(20°) = height of ship 1/208 and tan(12.5°) = height of ship 2/208. Rearranging these equations, we get the heights: height of ship 1 = 208 * tan(20°) and height of ship 2 = 208 * tan(12.5°).

Now, to find the distance between the ships, we need to subtract the heights of the ships from each other. If the distance is less than 300 feet, the keeper will sound a warning. So, the distance between the ships is: distance = |height of ship 1 - height of ship 2|. If this distance is less than 300 feet, she will sound the warning.

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Answer:

Correct option is (c).

Step-by-step explanation:

The experiment is conducted to determine whether a new fertilizer affects the yield of tomato plants.

The procedure involves randomly assigning the new fertilizer to 20 plants and the other 20 will be assigned the current fertilizer.

Then the mean number of tomatoes produced per plant will be recorded for each fertilizer, and the difference in the sample means will be calculated.

The collected sample data will then be used to make conclusion about the population.

The researchers main aim is to determine whether the new fertilizer is effective or not, i.e. if on using the new fertilizer the yield of tomatoes increases or not.

So, the parameter under study id the difference between tow population means.

To make inferences about the experiment the researcher can construct a two-sample t-interval for a difference between population means. The confidence interval has a certain specific probability of including the true parameter value.

Thus, the correct option is (c).

The correct answer is (c) option.

The following information should be considered:

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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: