What is the smallest angle of rotational symmetry that maps a regular pentagon onto itself?

Enter your answer in the box.

___Â°

Answers

Answer 1

Answer:

72º

Step-by-step explanation:

In order to calculate this you have to remember that the center angle of any polygon measures 360º, so what we do is just divide those 360 by the number of angles that you will find in the polygon, the number of angles equals the number of sides, so the pentagon has 5 sides, it will also have 5 angles. So we just divide the 360/5=72

So the smallest angle of rotational symmetry that maps a regular pentagon onto itself will be 72º

Related Questions

Find the probability that the person is frequently or occasionally involved in charity work.

Answers

Given the table below which shows the result of a survey that asked 2,881 people whether they are involved in any type of charity work.

[tex]\begin{tabular} {|c|c|c|c|c|c|} &Frequently&Occassionally&Not at all&Total\\[1ex] Male&227&454&798&1,479\\ Female &205&450&747&1,402\\ Total&432&904&1,545&2,881 \end{tabular}[/tex]

Part A:

If a person is chosen at random, the probability that the person is frequently or occassinally involved in charity work is given by

[tex]P(being \ frequently \ involved \ or \ being \ occassionally \ involved)\\ \\= \frac{432}{2881} + \frac{904}{2881} = \frac{1336}{2881}=\bold{0.464}[/tex]

Part B:

If a person is chosen at random, the probability that the person is female or not involved in charity work at all is given by

[tex]P(being \ female \ or \ not \ being \ involved)\\ \\= \frac{1402}{2881} + \frac{1545}{2881}-\frac{747}{2881} = \frac{2200}{2881}=\bold{0.764}[/tex]

Part C:

If a person is chosen at random, the probability that the person is male or frequently involved in charity work is given by

[tex]P(being \ male \ or \ being \ frequently \ involved)\\ \\= \frac{1479}{2881} + \frac{432}{2881}-\frac{227}{2881} = \frac{1684}{2881}=\bold{0.585}[/tex]

Part D:

If a person is chosen at random, the probability that the person is female or not frequently involved in charity work is given by

[tex]P(being \ female \ or \ not \ being \ frequently \ involved)\\ \\= \frac{1402}{2881} + \frac{904}{2881} + \frac{1545}{2881}-\frac{450}{2881}-\frac{747}{2881} = \frac{2654}{2881}=\bold{0.921}[/tex]

Part E:

The events "being female" and "being frequently involved in charity work" are not mutually exclusive because being a female does not prevent a person from being frequently involved in charity work.

Indeed from the table, there are 205 females who are frequently involved in charity work.

Therefore, the answer to the question is "No, because 205 females are frequently involved charity work".

(a) The probability is [tex]\[\boxed{0.464}\][/tex]. (b) The probability is [tex]\[\boxed{0.763}\][/tex]. (c) The probability is [tex]\[\boxed{0.585}\][/tex]. (d) The probability is [tex]\[\boxed{0.921}\][/tex]. (e) No, because 205 females are frequently involved in charity work. The option (A) is correct.

To address the given questions based on the provided table, let's go through each question step-by-step:

(a) Find the probability that the person is frequently or occasionally involved in charity work.

First, we need the total number of people who are frequently or occasionally involved in charity work. This is the sum of people in the "Frequently" and "Occasionally" columns.

[tex]\[\text{Total frequently or occasionally involved} = 432 + 904 = 1336\][/tex]

Now, we divide this by the total number of people surveyed:

[tex]\[P(\text{frequently or occasionally involved}) = \frac{1336}{2881} \approx 0.464\][/tex]

So, the probability is [tex]\[\boxed{0.464}\][/tex].

(b) Find the probability that the person is female or not involved in charity work at all.

To solve this, we need to find the number of females and those not involved in charity work at all.

[tex]\[\text{Total females} = 1402\][/tex]

[tex]\[\text{Total not involved at all} = 1545\][/tex]

We need to subtract the overlap (females not involved in charity work) to avoid double-counting. From the table, the number of females not involved at all is 747.

[tex]P(\text{female or not involved at all}) = \frac{\text{Total females} + \text{Total not involved at all} - \text{Females not involved}}{\text{Total}}[/tex]

[tex]= \frac{1402 + 1545 - 747}{2881} = \frac{2200}{2881} \approx 0.763[/tex]

So, the probability is [tex]\[\boxed{0.763}\][/tex].

[tex]\[\text{Total males} = 1479\][/tex]

[tex]\[\text{Total frequently involved} = 432\][/tex]

We need to subtract the overlap (males frequently involved) to avoid double-counting. From the table, the number of males frequently involved is 227.

[tex]P(\text{male or frequently involved}) = \frac{\text{Total males} + \text{Total frequently involved} - \text{Males frequently involved}}{\text{Total}}[/tex]

[tex]= \frac{1479 + 432 - 227}{2881} = \frac{1684}{2881} \approx 0.585[/tex]

So, the probability is [tex]\[\boxed{0.585}\][/tex].

(d) Find the probability that the person is female or not frequently involved in charity work.

[tex]\[\text{Total females} = 1402\][/tex]

[tex]\[\text{Total not frequently involved} = 2881 - 432 = 2449\][/tex]

We need to subtract the overlap (females not frequently involved) to avoid double-counting. From the table, the number of females not frequently involved is 1197 (450 + 747).

[tex]P(\text{female or not frequently involved})=\frac{1402 + 2449 - 1197}{2881} = \frac{2654}{2881} \approx 0.921[/tex]

So, the probability is [tex]\[\boxed{0.921}\][/tex].

(e) Are the events "being female" and "being frequently involved in charity work" mutually exclusive?

Two events are mutually exclusive if they cannot occur at the same time.

From the table, 205 females are frequently involved in charity work.

Since there are females who are frequently involved in charity work, the events "being female" and "being frequently involved in charity work" are not mutually exclusive.

So, the answer is A. No, because 205 females are frequently involved in charity work.

The complete question is:

The table below shows the results of a survey that asked 2881 people whether they are involved in any type of charity work. A per selected at random from the sample. Complete parts (a) through (e).

(a) Find the probability that the person is frequently or occasionally involved in charity work.

P(being frequently involved or being occasionally involved) - (Round to the nearest thousandth as needed.)

(b) Find the probability that the person is female or not involved in charity work at all.

P(being female or not being involved) (Round to the nearest thousandth as needed.)

P(being male or being frequently involved) (Round to the nearest thousandth as needed.)

P(being male or being frequently involved) - (Round to the nearest thousandth as needed.)

(d) Find the probability that the person is female or not frequently involved in charity work.

P(being female or not being frequently involved) = (Round to the nearest thousandth as needed.)

(e) Are the events "being female" and "being frequently involved in charity work" mutually exclusive? Explain.

A. No, because 205 females are frequently involved in charity work.

B. Yes, because no females are frequently involved in charity work.

C. Yes, because 205 females are frequently involved in charity work.

D. No, because no females are frequently involved in charity work.

Mr. Small, the store manager for Jay's Appliance, is having a difficult time placing a selling price on a refrigerator that cost $410. Mr. Small knows his boss would like to have a 45% markup based on cost. The selling price should be

Answers

Answer:

$594.50

Step-by-step explanation:

1. Divide markup into decimal form

45/100 = .45

2. multiply by cost of Refrigerator

.45 x 410 = $184.50

3. Add markup cost to original Refrigerator cost.

184.50 + 410 = $594.50

what is the approximate value of the square root of 8

Answers

2.828427 for your information

Answer:

2.828427

Step-by-step explanation:

I looked it up

A sample of 12 measurements has a mean of 8.5 and a sample of 20 measurements has a mean of 7.5. Find the mean of all 32 measurements.

Answers

multiply 8.5 by 12, multiply 7.5 by 20, add them together to get 252, then divide that by 32 to get 7.875. 7.875 is the mean of all 32 measurements

The formula for any arithmetic sequence is a n = a 1 + d(n - 1), where a n represents the value of the nth term, a 1 represents the value of the first term, d represents the common difference, and n represents the term number. What is the formula for the arithmetic sequence -7, -3, 1, 5, ...?
Plz help

Answers

-7, -3, 1, 5, ..... from -7 to -3, is +4, from -3 to 1, is +4.

so, is really just adding 4 to get the next term's value, thus the "common difference" is 4, and notice, the first term is -7.

[tex]\bf n^{th}\textit{ term of an arithmetic sequence}\\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\ ----------\\ a_1=-7\\ d=4 \end{cases} \\\\\\ a_n=-7+(n-1)4[/tex]

Find the point in the first octant where the tangent plane to x2+116y2+14z2=1 is parallel to the plane x+y+z=10

Answers

2x+3=yx bc it makes the most sence

Solve the Pythagorean Theorem for the variable a.
c²=a²+b²

Answers

you need the values of A, B, and C to solve the problem

a = sqrt (c-b)
Subtract the b value
Take the square root

tina wants to save money for school. tina invests 1100 in an account that pays an interest of 7.25%. how many years will it take the account to reach 6600?

Answers

Final answer:

It would take approximately 19 years for Tina's investment to grow from $1100 to $6600 with an annual interest rate of 7.25% if the interest is compounded annually.

Explanation:

This problem deals with the concept of compound interest. To find out how many years it will take for Tina's investment to grow from $1100 to $6600 with an interest rate of 7.25%, we would use the formula for compound interest: A = P(1 + r/n)_(nt), where A is the final amount, P is the principal amount (initial investment), r is the annual interest rate (in decimal form), n is the number of times interest is compounded per time unit (year), t is the time the money is invested for in years.

In Tina's case, she does not make additional contributions, so we assume the interest is compounded once per year (n=1). Our formula becomes A = P*(1 + r)_t. Arranging for t, we get t = log(A/P) / log(1+r).

Using these values: A=$6600, P=$1100, r=7.25/100=0.0725, we can find t = log(6600/1100) / log(1+0.0725). Calculating this, you would get around 19 years.

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Look at the triangle what is the value of sin X ?

Answers

the sin of an angle is the opposite ÷ hypotenuse

The side opposite angle x is 5cm, and the hypotenuse is 13 cm.
So, the sin (x) = 5 ÷13

a jar of jelly beans that weigh 4.25 ounces costs 2.89. what is the cost of one ounce of jelly

Answers

You have:
Cost in dollars --> $2.89
Total ounces --> 4.25

But you want to know the per unit cost for *1* ounce.

You have the right method. You want cost ($) per ounce so put the price over the amount in ounces.
2.89 / 4.25 = x / 1

If you notice, since the denominator is 1, this is simply:
x = 2.89 / 4.25

So the unit cost is just $2.89 divided by the number of ounces (4.25).

Plug that into your calculator and you get:
0.68

That's in dollars. So if you want it in cents, move the decimal point 2 places to the right.

Answer:
$0.68 per ounce
or
68 cents per ounce

Can someone walk me through the steps in solving this question

Answers

so, we know that, in 1oz of baked potato, there are 48.3 calories, ok..how many calories in 3 and 1/3 oz then?

now, bear in mind, we first convert the mixed fraction to "improper", and then use that,

[tex]\bf \begin{array}{ccll} \stackrel{\stackrel{baked}{potato}}{oz}&calories\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 1&48.3\\ 3\frac{1}{3}&p \end{array}\implies \cfrac{1}{3\frac{1}{3}}=\cfrac{48.3}{p}\implies \cfrac{\frac{1}{1}}{\frac{3\cdot 3+1}{3}}=\cfrac{48.3}{p}[/tex]

[tex]\bf \cfrac{\frac{1}{1}}{\frac{10}{3}}=\cfrac{48.3}{p}\implies \cfrac{1}{1}\cdot \cfrac{3}{10}=\cfrac{48.3}{p}\implies \cfrac{3}{10}=\cfrac{48.3}{p} \\\\\\ 3p=483\implies p=\cfrac{483}{3}\implies \boxed{p=\stackrel{calories}{161}}[/tex]

now, we know that in 1oz of chicken gas 24.6 calories, so, how many calories then in 5 and 1/4 oz?

[tex]\bf \begin{array}{ccll} \stackrel{chicken}{oz}&calories\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 1&24.6\\ 5\frac{1}{4}&c \end{array}\implies \cfrac{1}{5\frac{1}{4}}=\cfrac{24.6}{c}\implies \cfrac{\frac{1}{1}}{\frac{5\cdot 4+1}{4}}=\cfrac{24.6}{c}[/tex]

[tex]\bf \cfrac{\frac{1}{1}}{\frac{21}{4}}=\cfrac{24.6}{c}\implies \cfrac{1}{1}\cdot \cfrac{4}{21}=\cfrac{24.6}{c}\implies \cfrac{4}{21}=\cfrac{24.6}{c} \\\\\\ 4c=516.6\implies c=\cfrac{516.6}{4}\implies \boxed{c=\stackrel{calories}{129.15}}[/tex]

so, how many calories in that meal? well, p + c.

Read the following statement: Line segment CD is congruent to line segment XY.

Which of the following is an equivalent statement?

-CD overbar is similar to XY overbar

- CD overbar is congruent to XY overbar

-CD overbar equals XY overbar

-CD overbar is an element of XY overbar

SOMEONE PLEASE HELP I HAVE A TEST IN 5 MIN!!

Answers

CD overbar is congruent to XY overbar

The statement which is equivalent to line segment CD is congruent to line segment XY is CD overbar is congruent to XY overbar.

What is a line?

A line is made up of an infinite no. of points it can extend in both directions indefinitely.

We know a line has two subsets they are a ray and a line segment.

A ray is a type of line that has one initial point and the other end can extend indefinitely and a line segment is a type of line which has two endpoints.

Given a line, segment CD is congruent to line segment XY.

∴ [tex]\overline{CD}[/tex] ≅ [tex]\overline{XY}[/tex].

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For the function f(x) = −2(x + 3)2 − 1, identify the vertex, domain, and range.
The vertex is (3, −1), the domain is all real numbers, and the range is y ≥ −1.
The vertex is (3, −1), the domain is all real numbers, and the range is y ≤ −1.
The vertex is (−3, −1), the domain is all real numbers, and the range is y ≤ −1.
The vertex is (−3, −1), the domain is all real numbers, and the range is y ≥ −1.

Answers

"For the function f(x) = −2(x + 3)^2 − 1, identify the vertex, domain, and range. "

Note: You meant x^2, not x2. "^" indicates exponentiation.

This is a quadratic function of the form f(x) = ax^2 + bx + c. Its graph is a vertical parabola that opens down. We know this because a is negative 1 here, and the highest power of x is 2.

We can identify the vertex as being (-3, -1).

The domain of all quadratic functions is "the set of all real numbers."

You must find the maximum value of this function, which will represent the upper limit of the range (-infinity, y-value at vertex). Know how to do this? If not, please ask.

Answer:

C. The vertex is [tex](-3,-1)[/tex], the domain is all real numbers, and the range is [tex]y\leq -1[/tex].

Step-by-step explanation:

We have been given a function [tex]f(x)=-2(x+3)^2-1[/tex]. We are asked to identify the vertex, domain and range of the given function.

We can see that our given parabola is in vertex form [tex]y=a(x-h)^2+k[/tex], where [tex](h,k)[/tex] represents vertex of parabola.

We can rewrite our given equation as:

[tex]f(x)=-2(x-(-3))^2-1[/tex]

Therefore, the vertex of our given parabola would be [tex](-3,-1)[/tex].

We know that parabola is a quadratic function and the domain of a quadratic function is all real numbers.

We know that range of a quadratic function in form [tex]f(x)=a(x-h)^2+k[/tex] is:

[tex]f(x)\leq k[/tex], when [tex]a<0[/tex] and,

[tex]f(x)\geq k[/tex], when [tex]a>0[/tex]

Upon looking at our given function, we can see that [tex]a=-2[/tex], which is less than 0, therefore, the range of our given function would be [tex]y\leq -1[/tex].

Solve for x.

x−1/4=38

Enter your simplified answer in the box.

Answers

Simplified answer is 5/8. This is how it has been solved:

1. x - 1/4 = 3/8;
2. x = 1/4 + 3/8;
3. x = 2/8 + 3/8;
4. x = 5/8;

Hope everything is clear.

Find the probability of a couple having a baby boy when their fourth child is born, given that the first three children were all boys. assume boys and girls are equally likely. is the result the same as the probability of getting sall boys among four children

Answers

The probability of having a baby boy on the fourth child, given that the first three children were all boys, is 0.5. This result is not the same as the probability of getting all boys among four children, which is 0.0625. The conditional probability accounts for the information about the first three births.

To solve this probability problem, let's break it down step by step.

Probability of Having a Boy on the Fourth Child:

Assuming boys and girls are equally likely, the probability of having a boy or a girl is 1/2 or 0.5. When considering each child's gender independently, the probability of having a boy on the fourth child is 0.5, regardless of the genders of the previous children.

However, the question specifies that the first three children were all boys. This information is crucial for the conditional probability calculation.

Conditional Probability:

The probability of having a boy on the fourth child given that the first three children were all boys is denoted as [tex]$ P(B_4 | B_1, B_2, B_3) $[/tex].

Since the events are assumed to be independent (the gender of one child does not affect the gender of another), the conditional probability is the same as the probability of having a boy on any single birth: 0.5.

Comparison with Getting All Boys:

The probability of getting all boys among four children [tex]($ P(B_1 \cap B_2 \cap B_3 \cap B_4) $)[/tex] is the product of the probabilities of having a boy for each birth.

[tex]\[ P(B_1 \cap B_2 \cap B_3 \cap B_4) = P(B_1) \times P(B_2) \times P(B_3) \times P(B_4) \][/tex]

Given that [tex]$ P(B_4) = 0.5 $[/tex] and the previous births are all boys, [tex]$ P(B_1 \cap B_2 \cap B_3 \cap B_4) = (0.5)^4 = 0.0625 $[/tex].

The question probable may be:

Find the probability of a couple having a baby boy when their fourth child is born, given that the first three children were all boys. Assume boys and girls are equally likely. Is the result the same as the probability of getting all boys among four children?

Determine the inverse of f(x) = x^3 - x^2 - 2x show steps

Answers

Switch the x and y values to find the inverse.

y=x−3x+2

The inverse is given by

x=y−3y+2

Solve for y now:

x(y+2)=y−3

xy+2x=y−3

2x+3=y−xy

2x+3=y(1−x)

2x+31−x=y

The inverse, f−1(x), is given by f−1(x)=2x+31−x.

The function can be graphed using knowledge of asymptotes, invariant points, and intercepts. Prepare a table of values for f(x). Recall that f−1(x) is simply a transformation of(x) over the line y=x, so f−1(x) has a table of values where X and y are inverted relative to f(x).

For example, if the point (2,3) belongs on the graph of f(x), the point (3,2) belongs on f−1(x).

Replace F(X)FX with yy.y=X3+2X−3Xy=X3+2X-3XInterchange the variables.X=y3+2y−3yX=y3+2y-3y

Find the saving plan balance after 4 years with an apr of 7% and monthly payments of 100

Answers

APR=7%, monthly interest rate, i=7%/12=0.07/12
Monthly payment, A=100
After 4 years, n=4*12 = 48 months,
the balance F is therefore
F = A((1+i)^n-1)/i
=100((1+0.07/12)^48-1)/(0.07/12)
=5520.92

Answer: the balance after 4 years at APR=7% with monthly payment of $100 is $5520.92 to the nearest cent.

What is the justification for each step in solving the inequality?

−2(x+1)≥3x+8−2(x+1)≥3x+8
Select from the drop-down menus to correctly justify each step.

2nd picture is the dropdown box answers

Answers

The given is: −2(x+1)≥3x+8
The first step is getting rid of the brackets using the distributive property.
The second and third steps is isolating the term containing the x on one side of the inequality using addition or subtraction property of order
The last step is getting rid of the coefficient of the x using the multiplication or division property of order.

So, the correct order of choices is:
1- distributive property.
2- addition or subtraction property of order
3- addition or subtraction property of order
4- multiplication or division property of order.

First step is : Distributive property, as -2 is being distributed over x and 1.

Second step: Addition property of order, because we are adding 2 to both sides (or Subtraction: we are subtracting -2 to both sides)

Third step: Subtraction property of order, because we are subtracting 3x to both sides of the inequality.

Fourth step: Division property of order, as we are dividing both sides by -5.
(or multiplication property of order: we are multiplying both sides by -1/5

Three consecutive integers have a sum of 297 . Find the integers.

Answers

297 /3 = 99

99-1 = 98

99 +1 = 100

98 + 99 + 100 = 297

the numbers are 98, 99 , 100

We will put X to the first integer. Since they're consecutive (meaning that the 2nd number will be X+1 and the third number will be X+2 and they should all add up to 297) Here is how you can write the equation.
X+X+1+X+2 = 297
To solve for X, you have to add the integers together and the X variables together. Then, you must subtract 3 from each side and then dividing by 3 on each side.
X + X + 1 + X + 2 = 297
3X + 3 = 297
3X + 3 - 3 = 297 - 3
3X = 294
3X/3 = 294/3
X = 98
Which means that the first number is 98, the second number is 98+1 and third number is 98+2. Which give us three consecutive integers that add up to 297.
98+99+100= 297

Choose all the doubles facts that can help you solve 8+7

Answers

the answer is 15
if you do 8+7=15
i think it help

Answer: 7 + 7 = 14

8 + 8 = 16

Step-by-step explanation: doubles facts are simply additions where a number is added to it self. The strategy sums up two consecutive numbers when they are next to each other to give their result as given by the question above (8 + 7). We simply add the smaller number together then add one (double-plus-one) OR add the larger number together then subtract one (double-minus-one)

All doubles that can be used in solving 8 + 7 are:

A) 8 + 7 = 7 + (7 + 1) = (7 + 7) + 1 = 14 + 1 = 15 [double-plus-one]

B) 8 + 7 = (8 + 8) - 1 = 16 - 1 = 15 [double-minus-one]

The doubles fact makes use of the associative property of addition —changing the grouping of addends does not change the sum.

The distance of planet Mercury from the Sun is approximately 5.8 ⋅ 107 kilometers, and the distance of planet Venus from the Sun is 1.1 ⋅ 108 kilometers. About how many more kilometers is the distance of Venus from the Sun than the distance of Mercury from the Sun? (1 point)
Select one:
a. 5.2 ⋅ 107 kilometers
b. 4.7 ⋅ 108 kilometers
c. 5.2 ⋅ 108 kilometers
d. 5.7 ⋅ 109 kilometers

Answers

a 5.2.107 kilometers

Answer:

a) 5.2 *10^7 km

Step-by-step explanation:

If we could describe our Solar System, in order of appearance nearer the Sun, it would be like this:

Sun --- Mercury --- Venus --- Earth

Sun --------------------- Venus

1.1 * 10^8 km

Sun -------Mercury

5.8 * 10^7 Km

To find out how many more kilometers is the distance of Venus from the Sun than the distance of Mercury from the Sun, all we have to do is simply subtract the distance Sun ---Venus minus Sun ---Mercury

So,

1.1 * 10^8 - 5.8 * 10^7 =

Adjusting the first distance to the same power

110*10^7- 5.8*10^7 =

Subtracting the factors

5.2 * 10^7

a cell phone company charges a monthly fee of $0.25 for each text. message the monthly fee is $30.00 and you owe $59.50. how many text messages did you have

Answers

now, the cell company charges a monthly usually for network access and routing to the device, this company charges 30 bucks monthly for it.

after that, you pay for the txt messages you use, the more you use, the more you pay, in this case is 25 cents for each.

so if you use say hmm 100 txt messages, then you owe for a month 30 + 0.25(100)

and if you use "x" txt messages, then you owe 30 + 0.25x.

[tex]\bf \stackrel{cost}{y}=\stackrel{monthly~fee}{30}+\stackrel{txt~charges}{0.25x}\implies 59.50=30+0.25x \\\\\\ 29.5=0.25x\implies \cfrac{29.5}{0.25}=x\implies 118=x[/tex]

The student body of a large university consists of 60% female students. a random sample of 8 students is selected. what is the probability that among the students in the sample at least 7 are female?

Answers

I believe it would be around 1%

The probability of selecting at least 7 female students from the sample of 8 students is 0.2797.

To solve this problem, we'll use the binomial probability formula, which calculates the probability of a certain number of successes (in this case, selecting female students) in a fixed number of trials (the sample size).

Given:

Probability of selecting a female student (success), ( p = 0.60 )

Probability of selecting a male student (failure), ( q = 1 - p = 0.40 )

Sample size, ( n = 8 )

We need to calculate the probability of selecting at least 7 female students from the sample.

Calculate the probability of selecting exactly 7 female students:

[tex]\[ P(X = 7) = \binom{8}{7} \times (0.60)^7 \times (0.40)^{8-7} \][/tex]

[tex]\[ = \frac{8!}{7!(8-7)!} \times (0.60)^7 \times (0.40)^{1} \][/tex]

[tex]\[ = 8 \times 0.60^7 \times 0.40 \][/tex]

[tex]\[ = 8 \times 0.0279936 \times 0.40 \][/tex]

[tex]\[ = 0.1119744 \][/tex]

Calculate the probability of selecting exactly 8 female students:

[tex]\[ P(X = 8) = \binom{8}{8} \times (0.60)^8 \times (0.40)^{8-8} \][/tex]

[tex]\[ = (0.60)^8 \][/tex]

[tex]\[ = 0.60^8 \][/tex]

[tex]\[ = 0.16777216 \][/tex]

Add the probabilities from Step 1 and Step 2 to get the final probability:

[tex]\[ P(X \geq 7) = P(X = 7) + P(X = 8) \][/tex]

[tex]\[ = 0.1119744 + 0.16777216 \][/tex]

[tex]\[ = 0.27974656 \][/tex]

So, the probability of selecting at least 7 female students from the sample of 8 students is 0.2797.

a law firm charges $100 per hour plus a $300 origination fee for its services find a function notation

Answers

F(t)= $100 x h + 300 A reasonable domain is (1,2,3) and the range is ($400,$500,$600)

The required function notations for the total law firm charges is expressed as f(t) = 100t + 300

Given the following

Law firm charges = $100 per hour

The amount of charge for "t" hours will be 100t hours

Also, the original fee = $300

In other to get the total charge using function notation;

f(t) = Law firm charges for "t" hours + Original fee

f(t) = 100t + 300

The required function notations for the total law firm charges is expressed as f(t) = 100t + 300

Learn more here: https://brainly.com/question/11207409

The degree of the Boolean function given by f(x,y,z,w) = xy + yz + zw is........

Answers

The degree of the Boolean function given by f(x, y, z, w) = xy + yz + zw is 1. Booleans are supposedly simple in that they can result in only two possible answers: yes/no, true/false, or 0/1.

A girl is now one-third as old as her mother. In three years, she will be two-fifths as old as her mother will be. What are their present ages?

A girl is 9; mom is 27
B girl is 18; mom is 54
C girl is 25; mom is 75

Answers

I really want to say A, I mean all of these would fit for the one third of their ages but the two-fifths is kinda tricky. But I am sticking with A.

Answer:

Option: A is the correct answer.

A girl is 9; mom is 27

Step-by-step explanation:

A girl is now one-third as old as her mother.

i.e. if x is the present age of girl.

and y is the present age of her mother.

Then,

[tex]x=\dfrac{1}{3}y[/tex]

i.e.

[tex]y=3x-----------(1)[/tex]

In three years, she will be two-fifths as old as her mother will be.

This means after three years.

The age of girl will be: x+3

and the age of her mother will be: y+3

This means that:

[tex](x+3)=\dfrac{2}{5}\times (y+3)[/tex]

[tex]5(x+3)=2(y+3)\\\\i.e.\\\\5x+15=2y+6[/tex]

i.e.

[tex]5x+15=2\times 3x+6[/tex]

( since on using equation (1) )

i.e.

[tex]5x+15=6x+6\\\\i.e.\\\\6x-5x=15-6\\\\i.e.\\\\x=9[/tex]

and the value of y from equation (1) is:

[tex]y=27[/tex]

A store sells toaster ovenstoaster ovens for $4646 each, retail price. The wholesale cost to stock the ovensovens is $ 28$28 each. The fixed cost associated with acquiring the ovensovens, storing them in inventory, using shelf space, and advertising the ovensovens for sale is $25002500. a. Write a function for the total cost of stocking the ovensovens for sale. b. Write a function for the total revenue received from selling the ovensovens. c. Write a system of equations and determine the number of ovensovens that must be sold to break even.

Answers

Selling price = $46 per toaster

Stocking cost = $28 per toaster
Fixed cost = $2500

a) Let the number of toasters be 'x'
The total cost of stocking for sale = 28x + 2500

b) Let the number of toasters be 'x'
Total revenue received from selling the toasters = 46x

c) Break-even is when the cost of production is equal to profit made
So, we can set up the break-even equation as:
Production cost = Revenue cost
28x + 2500 = 46x
2500 = 46x - 28x
2500 = 18x
x = 138.9 ⇒ Rounded to 139 ovens

A customer has six (6) $1 bills, three (3) $5 bills, four (4) $10 bills, seven (7) quarters, ten (10) dimes, seven (7) nickels, and nine (9) pennies. The customer buys a pair of shoes for $49.86. Based on the combination of bills and coins the customer has, what are the least number of bills and coins the customer can give the cashier in order to buy the shoes for the exact amount and not require any change back?

Answers

He would use 9 bills, and 5 coins. (fours $10, one $5, four $1. three quarters, one dime, and one penny). I calculated it all to make sure the total came out as 49.86

The Leukemia and Lymphoma Society sponsors a 5k race to raise money. It receives $55 per race entry and $10,000 in donations, but it must spend $15 per race entry to cover the cost of the race.

Write and solve an inequality to determine the number of race entries the charity needs to raise at least $55,000.

Answers

p=people subtract 10,000 already raised from 55,000 profit/p = 40 40p=45000 p=1125 1125 entries

Find the slope of a line that passes through the points (-3,-1) and (0,-5)

Answers

[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -3}}\quad ,&{{ -1}})\quad % (c,d) &({{ 0}}\quad ,&{{ -5}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-5-(-1)}{0-(-3)}\implies \cfrac{-5+1}{0+3} \\\\\\ \cfrac{-4}{3}[/tex]

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What is the smallest angle of rotational symmetry that maps a regular pentagon onto itself?

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___Â°