8. A vase contains four white roses and one red rose. You randomly select two roses to take home. Use a sample space to determine whether randomly selecting a white rose first and randomly selecting a white rose second are independent events.​

Answer:

a. To find the factor by which the area decreases in 10 years, we can use the formula for exponential decay: A(t) = A0 * e^(-kt) where A0 is the initial area, k is the decay constant, and t is the time in years.

Given that A(t) = 11 -0.98^t.

so, we can say k =0.98

The area after 10 years will be:

A(10) = 11 - 0.98^10

The decrease factor is:

(A(10)/A(0)) = (11 - 0.98^10)/11

b. To find the factor by which the area decreases each month, we can first convert the annual decay rate to a monthly rate by dividing by 12, since there are 12 months in a year.

So, the monthly decay rate is 0.98/12 = 0.0816

Then we can use the formula for exponential decay again with the new decay rate:

A(t) = A0 * e^(-kt)

The area after 1 month will be:

A(1/12) = 11 - 0.0816^(1/12)

The decrease factor is :

(A(1/12)/A(0)) = (11 - 0.0816^(1/12))/11

if i helped you, can you mark my answer as best?

The percentile for a redwood tree that is 375 feet tall would be 93rd percentile. This is because the z-score of 1.5 (375-360/10) corresponds to a percentile of 93.

Step 1: Find z-score

z-score = (375-360)/10 = 1.5

Step 2: Find percentile

Using a z-score table, the percentile corresponding to a z-score of 1.5 is 93.

Therefore, the percentile for a redwood tree that is 375 feet tall is 93rd percentile.

The percentile of a redwood tree that is 375 feet tall can be determined using a z-score table. The z-score of a data point is the difference between the data point and the mean, divided by the standard deviation. In this case, the z-score is (375-360)/10 = 1.5. This z-score corresponds to a percentile of 93 on a z-score table. Therefore, the percentile for a redwood tree that is 375 feet tall is 93rd percentile. This means that 93% of redwood trees are shorter than 375 feet tall. It also means that only 7% of redwood trees are taller than 375 feet tall. This information can be used to compare the size of a particular redwood tree to other redwood trees.

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Answer:

6(45 + 25)

Step-by-step explanation:

The total number of coins in the jar is 10.

The total number of coins in the jar can be determined using the following formula:

Number of Coins = (1-cent coins) + (5-cent coins) + (10-cent coins) + (25-cent coins) + (50-cent coins)

Since the jar contains a total of 100 cents, we can calculate the number of coins in the jar by solving the following equation:

1x + 5x + 10x + 25x + 50x = 100

The solution to this equation is x = 2. This means that the jar contains 2 coins of each denomination, for a total of 10 coins in the jar. Therefore, the total number of coins in the jar is 10.

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Given the following histogram (image now attached), for a set of data, the number of values in the data set that are greater than 6.5 and less than 9.5 is: 14 (Option D)

A histogram is a rough depiction of the numerical data distribution. Karl Pearson was the first to coin the phrase.

A histogram is a graph that depicts the frequency distribution of a few data points from a single variable. Histograms frequently divide data into "bins" or "range groups" and count the number of data points that belong to each of those bins.

Between 6.5 and 9.5 there are 3 bars. Their heights are:

3, 6, 5, 4, and 3. Adding the values, we have:

3 + 6 + 5 = 14

Thus, the values in the data set are greater than 6.5 and less than 9.5 are 14.

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Full Question:

See attached image.

The isosceles trapezoid has rotational symmetry about the marked point. This means that when the trapezoid is rotated by an angle of 360°, it will look the same as it did before. Since the trapezoid has 4 sides, the rotational symmetry is 4-fold, or 4 magnitude. Therefore, the answer is b) 4.

The correct answer is b) 4, as the isosceles trapezoid has 4-fold rotational symmetry about the marked point.The answer is b) 4, as the isosceles trapezoid has 4-fold rotational symmetry about the marked point.

The isosceles trapezoid has rotational symmetry about the marked point. This means that when the trapezoid is rotated by an angle of 360°, it will look the same as it did before. Since the trapezoid has 4 sides, the rotational symmetry is 4-fold, or 4 magnitude. Therefore, the answer is b) 4.

The correct answer is b) 4, as the isosceles trapezoid has 4-fold rotational symmetry about the marked point.The answer is b) 4, as the isosceles trapezoid has 4-fold rotational symmetry about the marked point.

The complete question is :

Which of the following are magnitudes for rotational symmetry of the isosceles trapezoid below about the marked point?

a) 2

b) 4

c) 6

d) 8

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The measure of CD and CE in the centroid are 22 and 33 respectively.

What is Centroid?

Centroid is a term used in mathematics to refer to the center of mass of a geometric object. It is typically represented by a point, which is the average of all points in the object. The centroid is often used as a reference point for other calculations or for the positioning of objects.

From the given diagram, the following are true:

CD = 2DE

Given that DE = 11

CD = 2(11)

CD =22

Similarly;

CE = CD + DE

CE = 22 + 11

CE = 33

Hence the measure of CD and CE are 22 and 33 respectively.

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It would take 12 minute for them to mow their lawn if they work together

An equation is an expression showing the relationship between numbers and variables.

John can mow his lawn in 3 hours and his sister, Julie, can mow it in 2 hours.

Let t represent the time it would take them to mow their lawn if they work together, hence:

(1/3hours) * t + (1/2hours) * 2 = 1

t(1/3 + 1/2) = 1

(5/6)t = 1

t = 6/5 hours = 1 hour 12 minutes

It would take 12 minutes

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The simplified form of the given expression is 1073741824x¹⁵.

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.

The given expression is ((4x)³)⁵

= (4x)¹⁵

= 1073741824x¹⁵

Therefore, the simplified form of the given expression is 1073741824x¹⁵.

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There is 99% confidence that the population mean number of books read is between 1.51 and 26.69. This confidence interval indicates that there is a 99% probability that the true mean number of books read by people in the past year falls between 1.51 and 26.69.

Confidence interval for the mean = (x - z(s/√n), x + z(s/√n))

Where x is the sample mean, s is the sample standard deviation, n is the sample size, and z is the critical value for the given confidence level (in this case, 99%).

Therefore, the confidence interval for the mean number of books read is:

(14.1 - 2.58(16.6/√1018), 14.1 + 2.58(16.6/√1018))

= (1.51, 26.69)

This confidence interval indicates that there is a 99% probability that the true mean number of books read by people in the past year falls between 1.51 and 26.69. In other words, it is likely that the average number of books read by people in the past year is between these values. This interval is an estimate of the population mean and the confidence level indicates how confident we can be that the true mean falls within this range.

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The multiplication equation and division equation can

help Raelyn determine how many key chains she can make is 9

When solving multiplication equations, these equations may have the form ax = c, bx = d, or cx = f

The question says that Raelyn has 33 red beads and 21 blue beads. She mixes the

beads together and uses 6 beads for each key chain she

makes.

Based on the given conditions, formulate:: (33+21) /6

Calculate the sum or difference: 54/6

Cross out the common factor: 9

Therefore, the multiplication equation and division equation gives 9

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Answer:360 minutes

Step-by-step explanation: 15 x 26 = 360

360 minutes = to 6 HOURS

Answer: 390 minutes

Step-by-step explanation:

If the data were graphed with x on the horizontal axis and y on the vertical axis, this would be the approximate slope of the line between points C and D.

E. 0.17

The approximate slope between points C and D can be calculated by taking the difference in the y-values (9-15) and dividing it by the difference in the x-values (4-2). This yields a slope of -0.17.

The approximate slope between points C and D can be determined by first calculating the change in y-values (9-15) and the change in x-values (4-2). Then, the change in y-values is divided by the change in x-values to calculate the slope. In this case, the slope is -0.17. This means that for every unit of increase in x-values, the corresponding y-values decrease by 0.17. If the data were graphed with x on the horizontal axis and y on the vertical axis, this would be the approximate slope of the line between points C and D.

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Answer:

Step-by-step explanation:

Let's call the number we're trying to find "x".

We know that:
25% of x is 60 (0.25x = 60)
90% of x is 216 (0.9x = 216)

We can use the first equation to solve for x:
x = 60 / 0.25 = 240

Now we can use this value of x to find 65% of it:
65% of x = 0.65 * 240 = 156

So, 65% of that number is 156.

The total amount of money that the phone will cost including tax would be = $31.03

Cost price is the amount of money that a seller tags a particular product which is usually after the tax fees and other service fees has been added apart from the actual price of the product.

The price of the phone = $29

The percentage of tax = 7% of 29

= 7/100 × 29

= 203/100 = $2.03

Therefore, the total amount of money that the phone will cost including tax would be = 29 + 2.03 = $31.03

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Answer:

Solution in attached photo.

Step-by-step explanation:

Steps are in the attached photo, do note for this question, the units for vectors are called 'units'. Also do note that square roots and squared will cancel out each other (Power 2 x Power Half = Power 1).

Edit: I have included solutions for both scenarios for reference.

[tex]\bold{n + (n+1)^{2}}[/tex]

An unknown number can be interpreted with any letter of the alphabet, they will be our unknowns to be able to form an algebraic expression.

Well, in this case, I will use the variable n, to name the unknown number.

Let "n" be the number, the square of it is; n² and the following number results from adding the unit; then (n + 1) will be the next of the number.

(grouping the data the following algebraic expression is obtained):

[tex]\bold{n + (n+1)^{2}}[/tex]

Answer:

(n + 1 )

Let "n" be the number, the square of it is; n² and the following number results from adding the unit; then (n + 1) will be the next of the number.

..

Based on the functions, the statements that are true about these functions include the following: C. I, II, and III.

In Mathematics, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).

In order to determine the inverse of any function, you should swap both the input value (x-value) and output value (y-value) as follows;

x = 3y³ + 2

3y³ = x - 2

y³ = (x - 2)/3

y = ∛[(x - 2)/3]

Therefore, the function f(g(x)) is given by:

Function, f(g(x)) = 3[∛((x - 2)/3)]³ + 2

Function, f(g(x)) = 3[(x - 2)/3] + 2

Function, f(g(x)) = x

For the function g(f(x)), we have:

Function, g(f(x)) = ∛[(3x³ + 2 - 2)/3]

Function, g(f(x)) = ∛x³

g(f(x)) = x

In conclusion, the input value (x-value) and output value (y-value) of these functions are interchangeable.

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The Line chart should be used by the data analyst.

Option (A) is correct.

What is a line chart?

A line chart is a type of chart that is used to display a series of data points over time. It shows how a variable changes over time by connecting data points with lines. The line chart is commonly used to display trends, patterns and changes over time in continuous data.

Line chart

This type of chart is called a line chart. A line chart is a type of chart that is used to display a series of data points over time. It shows how a variable changes over time by connecting data points with lines. The line chart is commonly used to display trends, patterns and changes over time in continuous data.

It uses a horizontal x-axis and a vertical y-axis, with the data points connected by a line. It is great for visualizing trends and changes in data over a period of time, and it can be used to compare multiple variables at once.

Hence, the Line chart should be used by the data analyst.

Option (A) is correct.

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Answer:

21°

Step-by-step explanation:

Let smaller angle be x

Bigger angle = 2x + 27

Since they are complementary they all sum up to 90°

Therefore 2x + 27 + x = 90

3x = 90 - 27

3x = 63

x = 21, therefore the smaller angle is 21°

The parameterization equation for (0,0,0) and (5,3,7/2) is[tex]\frac{x}{5}=\frac{y}{3}=\frac{z}{3.5}[/tex]. Equation of parameterization is what it is.

mathematical formulas

[tex]$$\begin{aligned}& x=0+5 t \\& y=0+3 t \\& z=0+3.5 t\end{aligned}$$[/tex]

Equations with symmetry

[tex]\frac{x}{5}=\frac{y}{3}=\frac{z}{3.5}[/tex]

A straight line is the most straightforward curve to parametrize. It is possible to parametrize a line that passes through the origin along the vectors a, b. X is equal to AT and Y is BT. Two vectors parallel to the plane and a point on the plane must be located in order to find a parametrization. On the plane, finding a location is simple. We may use any number for x and y to determine z using the plane's equation. In the event when x and y are both 0, equation (1) states that

z= 18 x + 2 y 3 = 180 + 2 (0) 3= 6.

The process of locating parametric equations of a curve, a surface, or, more generally, a manifold or a variety, described by an implicit equation, is known as in mathematics, and is most commonly used in geometry.

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Step-by-step explanation:

The area of a rectangular room is given by the formula A = l * w, where l is the length and w is the width. In this case, we know that A = 750 square feet and w = l - 5 feet. We can use this information to create equations to solve for the length of the room.

Three options that can be used to solve for y are:

y(y + 5) = 750

This equation can be obtained by substituting the given information into the formula for the area of a rectangular room.

y(l - 5) = 750

y(l) - 5y = 750

y2 – 5y = 750

This equation can be obtained by expanding the first equation and moving all the terms to one side of the equation.

y(l) - 5y = 750

y2 - 5y = 750

(y + 25)(y - 30) = 0

This equation can be obtained by factoring the second equation, in which you get two solutions, y = -25 and y = 30. The first solution is not a valid solution because the length of a room can not be negative but the second one is a valid solution.

Note that 750 - y(y - 5) = 0 and y(y - 5) + 750 = 0 are not valid options as they are not equation that can be used to solve for y.

The value of k is -1 in the given matrix.

In mathematics, a matrix is a rectangular array or table of digits, characters, or expressions that is used to represent a mathematical object or a characteristic of one.

Matrixes represent linear maps and allow for explicit linear algebraic calculations in the absence of additional information.

Due to the fact that matrices can be used to express the majority of abstract linear algebra's properties and operations, a significant portion of linear algebra is devoted to their study. Matrix multiplication, for instance, can be used to represent how linear maps are put together.

the det(Y)=|Y| value is 0. Expanding through third column we get

[tex]0 - 7 \times \left[\begin{array}{ccc}2&-1\\k&2\\\end{array}\right] + 3 \times \left[\begin{array}{ccc}2&-1\\-1&4\\\end{array}\right][/tex]

0 - 7(4 -(-k)) + 3(8 -(1)) = 0

- 7(4 +k) + 3(8 -1) = 0

-28 - 7k + 24 -3 = 0

-7k -7 = 0

-7k = 7

k = -7/7

k = -1

Thus, The value of k is -1 in given matrix.

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Answer:

44.57

Step-by-step explanation:

area of two semicircles = πr²

3.142×2×2= 12.568

area of rectangle=L×W2

4×8=32

32+12.568

44.568

=44.57

The answer of the given question based on the compound interest is     (a)  Noah will have £4995.45 in the account after 9 years. (b)  Noah will have earned £995.45 in interest from this account after 9 years.

Compound interest is  type of the interest that is calculated on the both principal (initial amount) and any accumulated interest from the previous periods. In other words, interest is earned not only on the initial investment, but also on the interest earned in previous periods.

a) The formula for compound interest is given by:

A = P(1 + r/n)^(n*t)

In this case, P = £4000, r = 0.025 (2.5% as a decimal), n = 1 (since the interest is compounded annually), and t = 9. Substituting the values into  formula, we will get:

A = £4000(1 + 0.025/1)⁽¹*⁹⁾ = £4995.45

Therefore, Noah will have £4995.45 in the account after 9 years.

b) The amount of interest earned is simply the difference between the amount at the end of the time period and the initial deposit, i.e.,

Interest = A - P = £4995.45 - £4000 = £995.45

Therefore, Noah will have earned £995.45 in interest from this account after 9 years.

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Based on the information given in the bar chart, it should be noted that the most popular last names are Smith, Johnson, and Williams.

The complete question is,

Most Popular Last Names. In alphabetical order, the six most common last names in the United States in 2018 are Brown, Garcia, Johnson, Jones, Smith, and Williams (United States Census Bureau website). Assume that a sample of 50 individuals with one of these last names provided the following data:

Brown Williams Williams Williams Brown

Smith Johnson Williams Smith Miller

Johnson Williams William Johnson Jones

Miller Jones Jones Smith Smith

Miller Johnson Smith Jones Jones

Johnson Smith Brown Smith Johnson

Jones Smith Smith Williams Brown

Johnson Johnson William Smith Brown

Smith Miller Johnson Brown Johnson

Brown Jones Miller Smith Miller

Summarize the data by constructing the following:

A. Relative and percent frequency distributions

B. A bar chart

C. A pie chart

D. Based on these data, what are the three most common last names?

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In this example, the expected value is 1.90 children, and it is more likely that a married adult will have two to three children (with a probability of 0.55) than four to six children (with a probability of 0.15).

a) The probability that a married adult has three children is 0.30.

b) The expected value in this example represents the average number of children married adults in the country have.

c) The expected value is 1.90 children.

d) It is more likely that a married adult will have two to three children, with p = 0.55. This is because the probability of having two to three children (0.30 + 0.25 = 0.55) is greater than the probability of having four to six children (0.10 + 0.05 = 0.15).

In this example, the expected value is 1.90 children, and it is more likely that a married adult will have two to three children (with a probability of 0.55) than four to six children (with a probability of 0.15).

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Answer:

[tex]\frac{1}{x} ; x > 2[/tex]

Step-by-step explanation:

A fraction less than one half would have to be one out of a larger number than two.

Basically, let's change the denominator to "x"

[tex]\frac{1}{x}[/tex] -> for this fraction to be less than 2, x always has to be greater than two

There is no real nth root. Option C

You should understand that a square root of a number is a number that when multiplied by itself yields the original number.

Also, to indicate that we want both the positive and the negative square root of a radicand we put the symbol ± (read as plus minus) in front of the root. ... Zero has one square root which is 0. ... Negative numbers doesn't have real square roots since a square is either positive or 0.

The formula is

nth root of x

Where x ≥0

-729≥0

In conclusion there is no real root for the figure -729

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