If a fair die is rolled 7 times, what is the probability, rounded to the nearest thousandth, of getting at least 4 threes?

Answer:

Volume: 203,594

Surface Area: 105,237

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Let's start with surface area because it is a bit complex.

[tex]A = 5 ah + \frac{1}{2} \sqrt{5(5 + 2 \sqrt{5})}~a^2[/tex]

Now, we must break all of these factors into an equation.

remember, the height is 4, the base is 172

[tex]A = 5 * 172 * 4 + \frac{1}{2} * \sqrt{5 * (5 + 2 * \sqrt{5})} * 172^2[/tex]

[tex]A = \sf 1.05237 * 10^5 = 105,237[/tex]

So that should wrap things up for surface area, being 105,237

________________________________________________________

Now, we move on to the volume of this pentagonal prism.

[tex]A = \frac{1}{4} \sqrt{5(5 + 2 \sqrt{5})}~a^2h[/tex]

Similar to surface area, but different.

[tex]A = \frac{1}{4} * \sqrt{5 * (5 + 2 * \sqrt{5})} * 172^2 * 4[/tex]

And the result of this is...

[tex]A = \sf 2.03594 * 10^5[/tex]

Which is also equal to ⇒ 203,594

please let me know if this helped or was correct, I really spent a lot of time on this and would like to hear any good or bad feedback. Thanks!

Answer:

c)  124.96

Step-by-step explanation:

Geometric series:  100 + 20 + ... + 0.16

First we need to find which term 0.16 is.

General form of a geometric sequence: [tex]a_n=ar^{n-1}[/tex]

(where a is the first term and r is the common ratio)

To find the common ratio r, divide one term by the previous term:

[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{20}{100}=0.2[/tex]

Therefore, [tex]a_n=100(0.2)^{n-1}[/tex]

Substitute [tex]a_n=0.16[/tex] into the equation and solve for n:

[tex]\implies 100(0.2)^{n-1}=0.16[/tex]

[tex]\implies (0.2)^{n-1}=0.0016[/tex]

[tex]\implies \ln(0.2)^{n-1}=\ln0.0016[/tex]

[tex]\implies (n-1)\ln(0.2)=\ln0.0016[/tex]

[tex]\implies n-1=\dfrac{\ln0.0016}{\ln(0.2)}[/tex]

[tex]\implies n=\dfrac{\ln0.0016}{\ln(0.2)}+1[/tex]

[tex]\implies n=5[/tex]

Therefore, we need to find the sum of the first 5 terms.

Sum of the first n terms of a geometric series:

[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]

Therefore, sum of the first 5 terms:

[tex]\implies S_5=\dfrac{100(1-0.2^5)}{1-0.2}[/tex]

[tex]\implies S_5=124.96[/tex]

Answer:

2/300, or simplified: 1/150. Decimal: 0.006

Step-by-step explanation:

Answer:

The answer is 24π because r=12

and c=2πr

=2×π×12

=24π

The value of the quotient expression [tex]\sqrt[3]{60} \div \sqrt[3]{20}[/tex] is [tex]\sqrt[3]{3}[/tex]

The quotient of numbers or expressions is the division of a number or expression by another

The quotient expression is given as:

[tex]\sqrt[3]{60} \div \sqrt[3]{20}[/tex]

Write as a single expression by applying the law of indices

[tex]\sqrt[3]{60 \div 20}[/tex]

Divide 60 by 20

[tex]\sqrt[3]{3}[/tex]

Hence, the value of the quotient expression [tex]\sqrt[3]{60} \div \sqrt[3]{20}[/tex] is [tex]\sqrt[3]{3}[/tex]

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Answer:

A

Step-by-step explanation:

Endgenuity 2022

Answer:

[tex]{f}^{2} - 2f - 120[/tex]

Goodluck

Answer:

≈ 11.7 m

Step-by-step explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

let x be the measure of the second leg , then

x² + 15² = 19²

x² + 225 = 361 ( subtract 225 from both sides )

x² = 136 ( take square root of both sides )

x = [tex]\sqrt{136}[/tex] ≈ 11.7 m ( to the nearest tenth )

Answer:

slope is 1/3 or 0.33333333333333

Step-by-step explanation:

just ask

Answer:

-0.6/0.2

Step-by-step explanation:

rise over run, the equation is: x1-x2/y1-y2

Answer:

3 3/4 x 2 10/11 = 120/11 which is equal to 10 10/11 which is the simplified answer

Step-by-step explanation:

make them inproper so you have 15/4 and 32/11 which the product is 120/11 which you can make a proper fraction which is 10 10/11

Answer:

59.4

Step-by-step explanation:

Answer:

200.96 square feet

Step-by-step explanation:

SA = 2pi(r²) + 2pi(r)h

r = 2

pi = 3.14

h = 14

SA = 2(3.14)2² + 2(3.14)(2)14

SA = 6.28(4) + 6.28(2)14

SA = 25.12 + 175.84

SA = 200.96

Answer:

  D) 80%

Step-by-step explanation:

To find the fraction of women surveyed who prefer salads, we need to know something about how many were surveyed, and how many of those preferred salads.

For this purpose, we can effectively ignore the percent signs in the table, and consider that it represent 100 people surveyed.

__

Of the 100 people surveyed, 40 were women. Of the 40 women, 32 preferred salads. That is, 32/40 = 8/10 = 80% of the women surveyed preferred salads.

_____

Additional comment

When dealing with percentages, one must always keep in mind the base the percentage is referring to. For all of the numbers in the table, the base is the total number of participants in the survey.

For the percentage that is the answer to the question, the base is the number of women surveyed (or something proportional to that number).

A: Yes, the sum of two sides are greater than the third side.

B: Yes, the sum of two sides are greater than the third side. (Would be an equiilateral triangl.)

C: No, the sum of two sides are less than the third side.

In general, To determine if 3 side lengths are a triangle, use the triangle inequality theorem, which states that the sum of 2 sides of a triangle must be greater than the third side. Therefore, all you have to do is add together each combination of 2 sides to see if it's greater than the third side.

The lower bound of the confidence interval is 0.55.

A confidence interval for a proportion is a range of values that is likely to contain a population proportion with a certain level of confidence.

Construct a confidence interval of the population proportion at the given level of confidence x equals = 540, n equals = 900, 96% confidence.

The value of p is;

[tex]\rm p=\dfrac{x}{n}\\\\p =\dfrac{540}{900}\\\\p=0.6[/tex]

The standard error of the proportion is:

[tex]\rm \sigma_p=\sqrt{\dfrac{p(1-p)}{n}} \\\\ \sigma_p=\sqrt{\dfrac{0.6(1-0.6)}{540}} \\\\ \sigma_p=\sqrt{\dfrac{0.6\times 0.4}{540}} \\\\ \sigma_p=\sqrt{\dfrac{0.24}{540}} \\\\ \sigma_p=\sqrt{0.00044}\\\\ \sigma_p=0.02[/tex]

The critical z-value for a 94% confidence interval is z = 2.04

The margin of error (MOE) can be calculated as:

[tex]\rm Margin \ of \ error=\sigma_p \times z =2.04 \times0.02 =0.04[/tex]

Then, the lower bound of the confidence interval is;

[tex]Lower \ bound =p-x\times \sigma_p=0.6-0.04=0.55[/tex]

Hence, the lower bound of the confidence interval is 0.55.

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The statement second, statement fourth, and statement fifth are correct as the reflection line is y = -4.

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

We have:

Jorge needs to reflect a figure across the line y =  -4

Here, y = -4 is a vertical line.

The correct statements regarding the steps he could take to complete the reflection are:

Thus, the statement second, statement fourth, and statement fifth are correct.

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Answer:

D

Step-by-step explanation:

Answer:

1 out of 10 i think

Step-by-step explanation

2 sides of a coin + 5 days + 3 movements = 10 outcomes?

Answer:

$115

Step-by-step explanation:

The cost of the labor per hour is $115.

The total amount that the technician charged her is the sum of the cost for the total hours worked and the costs of the parts.

Total charge = cost of total hours worked + cost of parts

$749 = $59 +  cost of total hours worked

Cost of total hours worked = $749 - $59

Cost of total hours worked = $690.

The first trigonometric expression cot x and sin x in terms of the second expression is one over tan x and one over cosec x.

Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.

Write the first trigonometric expression in terms of the second expression.

The cotangent can be written as

[tex]\cot x= \dfrac{1}{\tan x}[/tex]

And the sine can be written as

[tex]\sin x = \dfrac{1}{\csc x}[/tex]

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Answer:

-6

Step-by-step explanation:

-15from both sides then divide the -24 from the left by 4 because you only need one x and your answer is x=-6

Answer:

A.  5.19 units

Step-by-step explanation:

[tex]\textsf{Arc length}=2 \pi r\left(\dfrac{\theta}{360^{\circ}}\right) \quad \textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle)}[/tex]

Given:

Substituting given values into the equation and solving for r:

[tex]\implies 7.34=2 \pi r\left(\dfrac{81^{\circ}}{360^{\circ}}\right)[/tex]

[tex]\implies 7.34=r\left(\dfrac{18 \pi}{40}\right)[/tex]

[tex]\implies 7.34 \cdot 40=18 \pi r[/tex]

[tex]\implies 293.6=18 \pi r[/tex]

[tex]\implies r=\dfrac{293.6}{18 \pi}[/tex]

[tex]\implies r=5.19 \sf \: units \:(2\:dp)[/tex]

Answer:

A) 5.19 units

Step-by-step explanation:

Formula for arc length :

Answer:

x = 15,  45 degree angle

Step-by-step explanation:

2x + 15 and 6x - 45 adds up to 90 degrees

(2x + 15) + (6x - 45) = 90

combine like terms:

2x + 6x = 8x

15 + (-45) = -30

8x - 30 = 90

8x - 30 + 30 = 90 + 30

8x = 120

8x / 8 = 120 / 8

x = 15

2(15) + 15

30 + 15 = 45 degree angle

6(15) - 45

90 - 45 = 45

Answer:

x = 15.

Step-by-step explanation:

The figure is a square so opposite sides are congruent and parallel.

The 2 angles marked are interior alternate angles, so they are congruent.

Therefore:

2x + 15 = 6x - 45

15 + 45 = 6x - 2x

4x = 60

x = 15.

Answer:

8. P = 48 cm A = 83

9. P =32 cm A = 60

Step-by-step explanation:

P = add all sides together

A = base times height

Answer:

8. P = 48 cm, A = 83 cm²

9. P = 36 cm, A = 56 cm²

Step-by-step explanation:

The trick with irregular shaped objects areas is to split them up into several rectangles. Perimeters is just filling in the missing sides using the other sides and adding them all up.

After finding the missing sides for the first figure, the perimeter would be:

5 + 10 + 4 + 3 + 11 + 3 + 2 + 10 = 48 cm

For the area, we split the figure into the vertical rectangle on top and the horizontal rectangle on the bottom. You'll see that the vertical rectangle has an area of 50 squared cm (5 * 10), while the area of the other rectangle is 33 squared cm (3 * 11), so the area of the whole figure is 50 + 33 = 83 squared cm.

Use this same method for the next figure, and you should get that the perimeter is 36 cm and the area is 56 squared cm.

Hope this helps

Answer:

216°

Step-by-step explanation:

Conversion from Radians to degrees : -

( θ * 360 ) / π

θ = 3π / 5

θ = ( 3π / 5 * 360 / π )

= ( 3 * 360 * π ) / ( 5 * π )

= ( 3 * 360 ) / 5

= 3 * 72

θ = 216°

Answer: If replaced: 0.075 or 7.5%

If not replaced: 0.00455 or 0.455%

Step-by-step explanation:

If the diamonds are replaced after each draw:

The probability of drawing a real diamond is 9/12, found by making the numerator the number of real diamonds and adding the total number of diamonds to find the denominator. 3+9 = 12.

9/12 can be reduced to 3/4 by dividing the numerator and denominator by 3.

To find the probability of all 9 diamonds drawn being real, multiply 3/4 by itself 9 times. [tex]3^9[/tex] = 19683. [tex]4^9[/tex] = 262144. This creates a probability of 19683/262144. This cannot be reduced because there is no common factor. To express as a decimal, divide. 19683/262144 = 0.07508. To turn this into a percent, multiply by 100. 0.07508*100 = 7.508

If the diamonds are not replaced after each draw:

Start with the probability of drawing a single diamond: 9/12. After each draw, both the numerator and denominator have 1 subtracted from them, since there is 1 less real diamond and 1 less diamond in total. This will give you the equation (9/12)*(8/11)*(7/10)*(6/9)*(5/8)*(4/7)*(3/6)*(2/5)*(1/4). This equals 0.00455. To find as a percent, multiply by 100. 0.00455*100 = 0.455

Answer:

f(x) ≈ −2.42x3 + 15.89x2 − 7.55x + 12

Step-by-step explanation:

Notice that the year data are evenly spaced. Check the first differences between the total number or units to see if the data set is linear.

First Differences

41 − 18 = 23

67 − 41 = 26

82 − 67 = 15

69 − 82 = −13

17 − 69 = −52

Because the first differences are not constant, a linear model is not the best model of the data. Check the second differences to see if the data set can be modeled by a quadratic function.

Second Differences

26 − 23 = 3

15 − 26 = −11

−13 − 15 = −28

−52 − (−13) = −39

Because the second differences of the independent variable are not constant, a quadratic model is not the best model of the data. Check the third differences to see if the data set can be modeled by a cubic function.

Third Differences

−11 − 3 = −14

−28 − (−11) = −17

−39 − (−28) = −11

The third differences are approximately the same so we will use a cubic function to represent the data.

Enter the data into a calculator. Plot the data and find the cubic regression equation that best models the data.

f(x) ≈ −2.42x3 + 15.89x2 − 7.55x + 12

Answer:

45 kg

Step-by-step explanation:

Formula for force :

Solving :

Answer:

x= 14

Step-by-step explanation:

When the triangles are similar, they should have a similar ratio that makes one side equal to another. In this case, the ratio is 1.5 as 24 divided by 16 is 1.5. Now, taking the side that is "similar" to the x-value which is 21, we divided 21 by 1.5 resulting in x= 14.

Answer:

x = 14

Step-by-step explanation:

24/21 = 1.14285714286

16/14 = 1.14285714286

Have a nice day! :)

Answer:

T is 5 and n is 10

Step-by-step explanation:

just relate the (b+Tv)^n with 3075072b^5v^10