Marisa recorded the number of hours she babysat each day last summer. She plotted the data in the box plot. A number line goes from 0 to 7. The whiskers range from 2 to 7, and the box ranges from 3.5 to 7. A line divides the box at 4. Which statement must be true according to the box plot? The data is symmetric and shows that she was equally likely to work more than 3.5 hours or less than 5 hours. The data is symmetric and shows that she never worked more than 5 hours. The data is skewed and shows that she was equally likely to work more than 3.5 hours or less than 5 hours. The data is skewed and shows that she never worked more than 5 hours.

Answer:

185/198

Step-by-step explanation:

Since the are 12 Cd and we require them to be selected in 5 ways, the number of selections is ¹²C₅ = 12 × 11 × 10 × 9 × 8/5! = 95040/120 = 792 ways

Since we have Four are rap music, five are country music, and three are heavy metal music, the number of ways to select them in groups of five so as to have at least one of each CD from each category, we have

For the first selection 3 of one category, and 1 each of the other categories.

The second selection is 2 each of two categories and 1 of the last category.

So, doing this for each category, we have

⁴C₃ × ⁵C₁ × ³C₁ + ⁴C₂ × ⁵C₂ × ³C₁ + ³C₃ × ⁴C₁ × ⁵C₁ + ³C₂ × ⁴C₂ × ⁵C₁ + ⁵C₃ × ⁴C₁ × ³C₁ + ⁵C₂ × ³C₂ × ⁴C₁

= (4 × 3 × 2/3! × 5 × 3) + (4 × 3/2! × 5 × 4/2! × 3) + (1 × 4 × 5) + (3 × 2/2! × 4 × 3/2! × 5) + (5 × 4 × 3/2! × 4 × 3) + (5 × 4/2! × 3 × 2/2! × 4)

= 360/6 + 720/4 + 20 + 360/4 + 720/2 + 120/4

= 60 + 180 + 20 + 90 + 360 + 30

= 740 ways

So, the required probability is P = number of ways of selecting at least one CD/ total number of ways = 740/792 = 185/198

Part A: Rebecca's credit card balance can be calculated using the equation x = (51 - 1) 0.02 if her finance charge is $51.

Part B: By making the purchase on the final day of the billing cycle rather than the first day, Rebecca will be able to avoid paying $27 in finance charges.

How do equations work?

A mathematical statement proving the equality of values between two or more mathematical expressions is called an equation.

Equation symbols (=) are used to represent equations.

A finance charge is what?

The interest and other fees levied on credit cards are included in a finance charge.

Typically, the finance charge is based on a stated APR (annual percentage rate).

The month's billing cycle lasts for 28 days.

Balance at current starting = x.

APR = 24%, or annual percentage rate.

The monthly percentage rate (MPR) equals 2% (24% divided by 12).

The final day's purchase cost $1,400.

$51 is the total finance fee for the month.

($1,400 x 2% x 1/28) = $1 finance fee for the last-minute purchase.

$50 ($51 - $1) serves as the initial balance's finance charge.

The starting balance at this time is x = $2,500 ($50 x 2%).

Current Beginning Balance Equation: x = 51 - 1 0.02

($1,400 x 2%) Equals $28 in total loan charges for the last-minute purchase.

Finance charge savings from buying on the last day equals $27 ($28 - $1).

By buying the $1,400 gift for her friend on the last day of the billing cycle rather than the first, Rebecca can avoid paying $27 in finance charges.

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Answer:

1.62 per pen

Step-by-step explanation:

Take the total cost and divide by the number of pens

9.69/6

1.615

Round to the nearest cent

1.62 per pen

After approximately 12.13 years, the revenue of this firm is going to drop to $1 million.

The value of shares t years after their floatation on the stock market, is modelled by V = 10e0.09t

The initial value of shares = V when t = 0. So, putting t = 0 in V = 10e0.09t,

we get

V = 10e0.09 × 0= 10e0 = 10 × 1 = 10 million dollars.

The values after 5 years, 10 years and 12 years, respectively are:

For t = 5, V = 10e0.09 × 5 ≈ 19.65 million dollarsFor t = 10, V = 10e0.09 × 10 ≈ 38.43 million dollarsFor t = 12, V = 10e0.09 × 12 ≈ 47.43 million dollars

The total revenue (TR) in t years' time is modelled as TR = 10e−0.19t (in million dollars)

The current revenue is the total revenue when t = 0.

So, putting t = 0 in TR = 10e−0.19t, we get

TR = 10e−0.19 × 0= 10e0= 10 million dollars

Revenue in 5 years' time is TR when t = 5.

So, putting t = 5 in TR = 10e−0.19t, we get

TR = 10e−0.19 × 5≈ 4.35 million dollars

To find when the revenue of this firm is going to drop to $1 million, we need to solve the equation TR = 1.

Substituting TR = 1 in TR = 10e−0.19t, we get1 = 10e−0.19t⟹ e−0.19t= 0.1

Taking natural logarithm on both sides, we get−0.19t = ln 0.1 = −2.303

Therefore, t = 2.303 ÷ 0.19 ≈ 12.13 years.

So, after approximately 12.13 years, the revenue of this firm is going to drop to $1 million.

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Answer:

6x + 1

Step-by-step explanation:

Add up like terms

4x + 2x + 1
= 6x + 1

Answer: 11 hours :)

Step-by-step explanation: 1215-445=770, 770 divided by 70=11 so 11 days

Answer:

is D

Step-by-step explanation:

because it just makes more sense and my teacher told me the answer

Answer:

Sorry if it is not clear enough

The difference quotient of \(f(x) = x^2 - 6x + 5\) is is 2x - 6 + h.

To find the difference quotient for the function \(f(x) = x^2 - 6x + 5\), we need to evaluate

(f(x + h) - f(x)) / h, where h is not equal to 0.

First, let's find f(x + h):

\(f(x + h) = (x + h)^2 - 6(x + h) + 5\)

\(= x^2 + 2hx + h^2 - 6x - 6h + 5\)

\(= x^2 - 6x + 5 + 2hx - 6h + h^2\)

Now, we can substitute the values of f(x + h) and f(x) into the difference quotient:

\((f(x + h) - f(x)) / h = ((x^2 - 6x + 5 + 2hx - 6h + h^2) - (x^2 - 6x + 5)) / h\)

= (2hx - 6h + h^2) / h

= 2x - 6 + h

Therefore, the difference quotient of \(f(x) = x^2 - 6x + 5\) is 2x - 6 + h.

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Using the Central Limit Theorem, it is found that the conditions for inference are not met, as there are less than 10 successes and less than 10 failures.

It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1 - p)}{n}}\), as long as \(np \geq 10\) and \(n(1 - p) \geq 10\).

In this problem, we have that np = 6 < 10, n(1-p) = 4 < 10, hence the conditions for inference are not met.

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Answer:

X = Y times 8

Step-by-step explanation:

You need to figure out how many miles you can go in an hour.

160/x and 20/1

20x=160

x=8

You can go 8 miles in 1 hour.

Therefore, if X is 1 and Y is 1

1 = 8

1 hour equals 8 miles

Answer:

0.625 : 1

Step-by-step explanation:

5 : 8

→ Divide both sides by 8 to get it to 1

(5 ÷ 8) : (8 ÷ 8)

→ Simplify

0.625 : 1

The area of the parallelogram spanned by AB and AC is 14.697

We have two vectors AB = î - 2ĵ + 2k and AC = 2î + 3ĵ - 4k.

We need to determine the area of the parallelogram spanned by AB and AC, the following formula can be used to find the area:

Area = |AB × AC|

AB = î - 2ĵ + 2k and AC = 2î + 3ĵ - 4k.

AB × AC = i j k î -2 2 2 2 3 -4

On simplification, we get AB × AC = 10î + 12ĵ + 8k

We know that |AB × AC| = √(10² + 12² + 8²)

                                       = √(100 + 144 + 64)

                                       = √308

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The maximum volume of the prism is 1728 cubic centimeters.

To find the dimensions of the prism with maximum volume, we need to consider the relationship between the volume of the prism and its dimensions.

Let's assume the base of the right triangular prism is an isosceles right triangle with legs of length 'a'. The height of the prism will be 'h'. The prism is inscribed in a hemisphere with a radius of 12 cm.

First, let's determine the relationship between 'a' and 'h'. Since the base of the prism is on the great circle of the hemisphere, the hypotenuse of the triangular base is equal to the diameter of the hemisphere, which is twice the radius. Therefore, the hypotenuse of the base is 2 * 12 = 24 cm.

By using the Pythagorean theorem, we can find 'a':

a^2 + a^2 = 24^2

2a^2 = 576

a^2 = 288

a = √288

Now, let's find the height 'h' of the prism. The height 'h' is equal to the radius of the hemisphere, which is 12 cm.

Therefore, the dimensions of the prism for maximum volume are:

Base length (a) = √288 cm

Height (h) = 12 cm

To find the maximum volume, we can use the formula for the volume of a right triangular prism:

Volume = (1/2) * a^2 * h

Substituting the values, we get:

Volume = (1/2) * (√288)^2 * 12

= (1/2) * 288 * 12

= 1728

Hence, the maximum volume of the prism is 1728 cubic centimeters.

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Answer:

Answer is the last

Step-by-step explanation:

My answer from plato/edmentum unit practice:

Answer:

7x+80

Step-by-step explanation:

x represents the number of weeks

Answer:

\(y= \frac{x}{2x−1}\)

Step-by-step explanation:

To find the inverse function, swap x and y, and solve the resulting equation for x.

If the initial function is not one-to-one, then there will be more than one inverse.

So, swap the variables: y=x/2x−1 becomes x=y/2y−1.

Now, solve the equation x=y/2y−1 for y.

y=x/2x−1

In an analysis of variance (ANOVA), the F-ratio is used to determine whether there are significant differences between the means of two or more groups.

When the null hypothesis is true, it means that there are no significant differences between the group means, and any observed differences are due to random chance.

In this scenario, the F-ratio is balanced in such a way that the numerator and the denominator both measure the same sources of variance.

The F-ratio is calculated by dividing the variability between the group means (numerator) by the variability within the groups (denominator).

When the null hypothesis is true, both the numerator and the denominator represent the same underlying variation.

This ensures that the F-ratio is balanced and close to 1.0, indicating that the group means are similar and any observed differences are likely due to chance.

The balanced F-ratio is a crucial aspect of ANOVA as it allows researchers to assess the significance of group differences accurately.

If the F-ratio deviates significantly from 1.0, it suggests that the observed differences between the group means are unlikely to be due to random chance alone, and the null hypothesis is rejected in favor of the alternative hypothesis.

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Answer:

She can travel for 10 days

Step-by-step explanation:

first you do 1,250 divided by 1,250 will equal 0. Then you do the other side 1,700- 1,250 =450. Then you do 450 divided by 45 and you will get 10

Hope this helps you out!

Kaylee will have to pay $28 in interest.

The interest on a loan or principal sum can be easily calculated using simple interest. Simple interest is a notion that is employed across a wide range of industries, including banking, finance, automobiles, and more.

The interest Kaylee will have to pay is calculated as follows:

Interest = Principal x Rate x Time

where Principal is the amount borrowed, Rate is the interest rate as a decimal, and Time is the time period in years. Since Kaylee has to pay back the loan in 24 months, or 2 years, we can plug in the given values to get:

Interest = 700 x 0.02 x 2 = $28

Therefore, Kaylee will have to pay $28 in interest.

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Answer:

[SHOWN IN IMAGE]

Step-by-step explanation:

I have done the simplifying work only... sorry

Simplify;

4x + 5xy – 3x² – 6xy + 6

= – xy – 3x² + 4x + 6

__o__o__

3x + 2x(x+2) – 6x²

= 3x + 2x² + 4x – 6x²

= – 4x² + 7x

___o__o__

(6a + 2b - 3c ) - ( 4a - 4b + 9c + 12 )

(6a + 2b - 3c ) + ( - 4a + 4b - 9c - 12 )

= 2a + 6b – 12c - 12

___o___o__

Subtract ( 3y + xy ) from ( - 5y + 12xy)

Ans; ( – 5y + 12xy ) – (3y + xy)

( – 5y + 12xy ) + ( - 3y - xy)

= – 8y + 11 xy

= 11xy – 8y

___o___o___

Find the product of 6ab and –3a²b³

\((6ab) \times ( - 3 {a}^{2} {b}^{3} ) = - 18 {a}^{3} {b}^{4} \)

___o___o__

\(( - 3 {x}^{2} y) \times (4 {x}^{2} y - 3x {y}^{2} + 4x - 5y) \\ \\ = - 12 {x}^{4} {y}^{2} + 9 {x}^{3} {y}^{3} - 12 {x}^{3} y + 15 {x}^{2} {y}^{2} \)

___o___o___

Example 1; Ans ;

perimeter of triangle = Length of the first side + Length of the second side + Length of the third side

perimeter of triangle = A + B + C

4x² + 17xy + 5 = ( 5xy -3x² ) + ( x² + 5xy - 2 ) + c

4x² + 17xy + 5 = - 2x² + 10xy - 2 + c

c = (4x² + 17xy + 5 ) – ( - 2x² + 10xy - 2)

c = (4x² + 17xy + 5 ) + ( 2x² - 10xy + 2)

c = 6x² + 7xy + 7

So; Length of the third side = ( 6x² + 7xy + 7 )

___o___o___

Example 2 ; Ans;

To find the length of the smallest part, we must subtract the total length from the length of the largest part .

Total length = The length of the largest part + The length of the smallest part

The length of the smallest part = Total length – The length of the largest part

The length of the smallest part = ( 5mn – 2n +1 ) – ( 3mn +n )

The length of the smallest part = ( 5mn – 2n +1 ) + ( – 3mn – n )

The length of the smallest part = 2mn – 3n +1

So ; the length of the smallest part = ( 2mn – 3n + 1 )

I hope I helped you^_^

The statement that shows equivalent measurements is "52 meters = 520 decimeters." Option C.

To determine the equivalent measurements, we need to understand the relationship between different metric units.

In the metric system, each unit is related to others by factors of 10, where prefixes indicate the magnitude. For example, "deci-" represents one-tenth (1/10), "centi-" represents one-hundredth (1/100), and "kilo-" represents one thousand (1,000).

Let's analyze each statement:

5.2 meters = 0.52 centimeters: This statement is incorrect. One meter is equal to 100 centimeters, so 5.2 meters would be equal to 520 centimeters, not 0.52 centimeters.

5.2 meters = 52 decameters: This statement is incorrect. "Deca-" represents ten, so 52 decameters would be equal to 520 meters, not 5.2 meters.

52 meters = 520 decimeters: This statement is correct. "Deci-" represents one-tenth, so 520 decimeters is equal to 52 meters.

5.2 meters = 5,200 kilometers: This statement is incorrect. "Kilo-" represents one thousand, so 5.2 kilometers would be equal to 5,200 meters, not 5.2 meters.

Based on the analysis, the statement "52 meters = 520 decimeters" shows equivalent measurements. So Option C is correct.

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Note the correct and the complete question is

Select the statement that shows equivalent measurements.

A.) 5.2 meters = 0.52 centimeters

B.) 5.2 meters = 52 decameters

C.) 52 meters = 520 decimeters

D.) 5.2 meters = 5,200 kilometers

A BAR graph would be most suitable for displaying the given data.

The visual representation of numerical data is a graph. Graphs offer a visual means of presenting complicated data and demonstrating the link between various variables or data sets. Graphs are a fantastic tool for highlighting patterns and connections in data.

Given data, The number of pets in each student's household.

Stem-and-leaf plot:

A stem and leaf plot, often known as a stem plot, is a method for categorizing discrete or continuous data. As data are gathered, they are organised using a stem and leaf plot. A stem and leaf plot resembles a bar graph in appearance. The term stems from the fact that each number in the data is divided into a stem and a leaf.

Thus it is not suitable for given data.

Line graph:

An individual data point is connected by a line in a line graph, sometimes referred to as a line plot or a line chart. A line graph shows numerical values over a predetermined period of time. Line graphs are frequently used in finance to show the historical price movement of an asset or instrument.

Since, we have similar but Discrete with three variables in our data thus this graph is also not suitable.

Bar graph:

A bar graph (also known as a bar chart or bar diagram) is a visual tool that uses bars to compare data among categories. A bar graph may run horizontally or vertically.

Since we need to compare the data thus, bar graph is most suitable for the giving condition.

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Answer:

D would be your answer. I used my algebra calculator and it shows you step by step how to do the problem

The translation of point C, helped to fill the blank as

C = (-1, 1)

The coordinate of vertex C before translation is (-2, 4),

Applying the translation with the rule, (x+1, y-3)  results to

(-2, 4) → (-2 + 1, 4 - 3) → (-1, 1)

hence the image coordinate is (-1, 1) and the blank spaces are

-1 and 1

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Answer:

10/a

Step-by-step explanation:

Answer:

15g+16n=294

Step-by-step explanation:

15g=15*12=180

16n=16*9=114

total=g+n=180+114=294

Where the above humanities terms are give, the matches for the labels you provided are given below.

With regard to the above terms, note that under the Articles of Confederation, the federal government had the power to run the post office, declare war, and negotiate with foreign powers.

The states had the power to exercise all other powers not specifically mentioned in the document, collect taxes, and control the militia.

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