Elizabeth has 4 posters she wants to hang on the wall. How many different ways can the posters be arranged in a row?

Answer:

Option b (28 + 63)

Step-by-step explanation:

7(4+9)

7(13)

7×13= 91

28 + 63 = 91

Both give the same answer

Answer:

The sum 28 + 63 can be expressed as 7 ( 4 + 9 )

Step-by-step explanation:

To solve the problem you need to be aware of the distributive property of multiplication.  This property simply says that a multiple of a group of addens, aka the sum in the parenthesis, can be multiplied individually and summed.

The 7 infront of the parenthesis implies the multiplication operation on the grouping of the sum of 4 and 9.

You can rewrite it as such:

7 * ( 4 + 9 )

= 7 * 4 + 7 * 9

= 28 + 63

Note, how we simply used the multiplier 7 distributed to each term within the parenthesis to create our desired sum.

Cheers.

The line plot, histogram, and box plot provide different visual representations of the reading time data. By analyzing these plots, we can observe the distribution and characteristics of the data, such as central tendency, spread, and outliers.

Line Plot:

A line plot displays data points on a number line, representing the frequency or count of each value.

In this case, the line plot will show the minutes spent reading on the x-axis and the count of students on the y-axis.

For the given data, the line plot will show 10, 20, 30, 40, and 60 on the x-axis, with the corresponding counts displayed above each value.

Histogram:

A histogram displays data distribution by dividing the range of values into intervals or bins and representing the frequency of values falling into each bin.

The histogram will have the minutes spent reading on the x-axis and the count or frequency of students on the y-axis.

The intervals will be 10-19, 20-29, 30-39, 40-49, and 50-59, with the last interval being 60+.

The height of each bar in the histogram will represent the number of students falling into each interval.

Box Plot:

A box plot (also known as a box-and-whisker plot) provides a visual representation of the distribution of data, including measures of central tendency and variability.

The box plot will show a horizontal line inside a box, with whiskers extending from the box, and possibly individual data points beyond the whiskers.

The box will represent the interquartile range (IQR), showing the middle 50% of the data.

The line within the box will represent the median value.

The whiskers will indicate the minimum and maximum values, excluding outliers.

By analyzing these plots, you can observe the central tendency, spread, and distribution of the reading time data. For example, you can identify any outliers, notice the most common reading durations, and observe any patterns or trends within the dataset.

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Answer: Simple regression

Step-by-step explanation:

A regression analysis that involves one independent variable and one dependent variable is called the simple regression.

The Simple Regression Analysis shows the relationship that exist between the dependent variable which is the value that's to be predicted and the independent variable. The dependent variable depends on the independent variable

The cost of 20 T-Shirt will be 2560 when cost of one t-shirt is 128.

When a selling price and profit are provided, cost price equals selling price plus profit. When the selling price and loss are disclosed, cost price equals selling price plus loss.

Profit is calculated as S.P. - C.P. If the selling price is less than the cost price, the difference between the two is the loss incurred. Loss is also equal to C.P. - S.P.

We must divide the gross profit by the entire revenue for the year, multiply by 100, and then find the gross profit margin. We must divide net income (or net profit) by the entire annual revenue before multiplying the result by 100 to get the net profit margin.

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Answer:

Step-by-step explanation:

With calculations I can say it's 4, hurry hurry and get your answer in haha! Good luck

Answer:

Step-by-step explanation:

The events are not independentd) The events are not mutually exclusiveStep-by-step explanation:Hi!Lets call: Gar = {homes with garage}Pool

The day, from the following two days, which would be the best to sell both stocks with the closing price is day 3 by an amount of $2.45.

Given are the closing prices of two stocks in three days.

If you purchase 65 shares of Metropolis stock and 50 shares of Suburbia stock on Day 1 at the closing price,

Amount invested = (65 × 17.95) + (50 × 5.63) = $1448.25

If the stock is sold in day 2,

Amount received = (65 × 18.25) + (50 × 4.98) = $1435.25

Profit = $1435.25 - $1448.25 = -$13

If the stock is sold in day 3,

Amount received = (65 × 18.28) + (50 × 5.25) = $1450.7

Profit = $1450.7 - $1448.25 = $2.45

The profit is more for day 3 than day 2.

Hence it is best to sell on day 3 by $2.45.

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\(\hspace{34em}|\\ (\stackrel{x_1}{1}~,~\stackrel{y_1}{k})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{1}) ~\hspace{10em} \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{k}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{1}}}~~ ~~\stackrel{\stackrel{slope}{\downarrow }}{-2} \\\\\\ \cfrac{1-k}{3}= -2\implies 1-k=-6\implies -k=-7\implies k = \cfrac{-7}{-1}\implies \boxed{k = 7}\)

Answer:

Below

Step-by-step explanation:

Calculate the unit price of $ per ounce of the 4 options to find the smallest

$2 / 4 = .50 per ounce

4.25 /8 = .53

6/12 = .50

6.75/18 = .375 per ounce   <=====cheapest

The graph of the equation is shown below

The x-intercept is -2

The y-intercept is undefined

From the question, we are to solve the equation by graphing and determine the x- and y-intercepts

The given equation is

3x + 1 = -5

To determine the x-intercepts, we will solve the equation

3x + 1 =-5

3x = -5 - 1

3x = -6

Divide both sides by 3

x = -2

Since, y is not defined in the equation, the y-intercept is undefined

The graph of the equation is shown below.

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The compound interest implies that Juan owes $163.52 today

The given variables can be represented as:

The amount from a compound interest can be calculated using:

A = P(1 + r/n)^nt

Also from the question, we have

n = 12

This is so because the loan is compounded 12 times in a year as a result of being compounded monthly

So, we have

A = P(1 + r/n)^nt

A = 128 * (1 + (50%/12))^(0.5*12)

Evaluate

A = 163.52

Hence, the amount owed is $163.52

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Answer:

225 quarters are easy to loose and who will accept that many quarters

Step-by-step explanation:

Answer:

quarters

You will get more money

Answer:

\( m = \sqrt{125} \)

Step-by-step explanation:

By geometric mean property:

\( {n}^{2} = 5 \times 20 \\ {n}^{2} = 100 \\ \\ By \: Pythagoras \: Theorem \\ {m}^{2} = {n}^{2} + {5}^{2} \\ {m}^{2} = 100 + 25 \\ {m}^{2} = 125 \\ m = \sqrt{125} \)

The estimate of 179% of 41 by rounding is about 73.19.

To find this estimate, first convert the percentage to a decimal by dividing it by 100: 179/100 = 1.79. Then, multiply this decimal by 41: 1.79 * 41 = 73.39.

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\(\bold{\huge{\underline{ Solution }}}\)

Here, we will use the concept of integration and algebric identities

We have,

\(\bold{\displaystyle\int}{\bold{\dfrac{ cos^{2}x}{1 + sinx}}}{\bold{dx}}\)

By using trigonometric identity,

\(\sf{\displaystyle\int}{\sf{\dfrac{ 1 -sin^{2}x }{1 + sinx}}}{\sf{dx}}\)

By using algebraic identity :-

\(\sf{\displaystyle\int}{\sf{\dfrac{ (1 + sinx) (1 - sinx) }{1 + sinx}}}{\sf{dx}}\)

\(\sf{\displaystyle\int}{\sf{( 1 - Sinx)dx}}\)

\(\sf{ {\displaystyle\int} dx - {\displaystyle\int}sinxdx}\)

We know that,

\(\sf{ x - (-cosx) + c}\)

\(\bold{ x + cosx + c}\)

Hence, The answer is x + Cosx + c.

We are given with an integral and need to solve the integral , so let's start ;

\({:\implies \quad \displaystyle \int \sf \dfrac{\cos^{2}(x)}{1+\sin (x)}dx}\)

As we know that sin²(x) + cos²(x) = 1 , using this

\({:\implies \quad \displaystyle \int \sf \dfrac{1-\sin^{2}(x)}{1+\sin (x)}dx}\)

Can be further written as

\({:\implies \quad \displaystyle \int \sf \dfrac{1^{2}-\sin^{2}(x)}{1+\sin (x)}dx}\)

\({:\implies \quad \displaystyle \int \sf \dfrac{\cancel{\{1+\sin (x)\}}\{1-\sin (x)\}}{\cancel{\{1+\sin (x)\}}}dx\quad \qquad \{\because a^{2}-b^{2}=(a+b)(a-b)\}}\)

\({:\implies \quad \displaystyle \int \sf \{1-\sin (x)\}dx}\)

Now , as integrals follow distributive property , so ;

\({:\implies \quad \displaystyle \int \sf 1\: dx-\int \sin (x)dx}\)

Now , as antiderivative (Integration) of sin(x) is -cos(x) + C and that of dx is x + C So ;

\({:\implies \quad \displaystyle \bf \therefore \underline{\underline{\int \bf \dfrac{\cos^{2}(x)}{1+\sin (x)}=x+\cos (x)+C}}}\)

This is the Required answer

The equivalent value of the exponential expression is A = 0.0625 which is equal to \(A=\frac{1}{16}\).

The correct answer is Option C.

Given data:

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The expression is represented as A = "one fourth raised to the seventh power divided by one fourth raised to the sixth power comma all raised to the second power."

On simplifying the expression:

\(A=[\frac{\frac{1}{4}^7}{\frac{1}{4}^6}]^2\)

From the laws of exponents:

\(\frac{m^{a}}{m^{b}}=m^{a-b}\)

So, on simplifying:

\(A=[\frac{1}{4}^{7-6}]^2\)

\(A=[\frac{1}{4}]^2\)

\(A=\frac{1}{16}\)

Hence, the expression is \(A=\frac{1}{16}\).

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Answer:

The digit that fit into the blank space is 6

Step-by-step explanation:

Here, we want to enter digits into the blank space that can make the expression valid.

Let’s try 6;

6583 < 6612 < 6687

This is actually correct.

Can we have any other digit here?

No, i don’t think so.

Putting in a 5 will make the first number greater than the middle

Putting in a 7 will make the middle number greater than the last and thus render the expression invalid

The inequality that represents the values of x is expressed as:

7/4 < x < 11/2.

According to the triangle inequality theorem, any two sides of a triangle, when added, must be greater than the length of the third side.

Therefore, applying the triangle inequality theorem, we have:

2x + 4 + 6x > 18

8x + 4 > 18

8x > 18 - 4

8x > 14

x > 14/8

x > 7/4 or 7/4 < x

Therefore, the possible value of x would be: 7/4 < x < 11/2

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Answer:

D. 8%

Step-by-step explanation:

I took the test on Edmentum/Plato & it was correct!

Answer: (x > -3).

Step-by-step explanation:

To solve the inequality 4(1 - x) < 16, we will simplify and solve for x:

4(1 - x) < 16

Distribute the 4:

4 - 4x < 16

Subtract 4 from both sides:

-4x < 12

Divide both sides by -4. Note that when dividing by a negative number, the inequality sign flips:

x > -3

The solution to the inequality is x > -3. This means that x must be greater than -3 for the inequality to hold true.

To graph the solution on a number line, we mark a shaded region to the right of -3, indicating that all values greater than -3 satisfy the inequality:

The open circle at -3 indicates that -3 is not included in the solution since the inequality is strict (x > -3).

here's the graph for 4(1-x)<16

Answer:

\(\displaystyle y=\frac{1}{3}x-6\)

Step-by-step explanation:

Dilation of a Line

Given a line that passes through points A(-3,-4) and B(-6,-5). We'll apply a dilation with a scale factor of 2 centered at the origin by multiplying each coordinate by 2. The points map to:

A'(-6,-8) and B'(-12,-10)

Now we find the equation of the line passing through A' and B'.

The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:

\(\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\)

Substituting:

\(\displaystyle y+8=\frac{-10+8}{-12+6}(x+6)\)

\(\displaystyle y+8=\frac{-2}{-6}(x+6)\)

\(\displaystyle y+8=\frac{1}{3}(x+6)\)

Operating:

\(\displaystyle y=\frac{1}{3}x+\frac{1}{3}*6-8\)

\(\displaystyle y=\frac{1}{3}x+2-8\)

\(\boxed{\displaystyle y=\frac{1}{3}x-6}\)

Answer:

Step-by-step explanation:

In the equation y = 10 - 0.1x, the coefficient 0.1 represents the slope of the line.

it represents the rate of change of y with respect to x, which is the amount by which y changes for every unit increase in x.

In this case, the slope is negative (-0.1), which means that as the number of minutes on hold (x) increases by 1 unit, the level of satisfaction (y) decreases by 0.1 units.

In other words, the longer a customer spends on hold, the lower their level of satisfaction is likely to be. The slope is a key parameter in the equation and provides valuable information about the relationship between the two variables.

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The distance between point C  (-3, 3) and point D (0, -4) is equal to: √58 units.

In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represent the data points (coordinates) on a cartesian coordinate.

By substituting the given end points into the distance formula, we have the following;

Distance = √[(0 + 3)² + (-4 - 3)²]

Distance = √[(3)² + (-7)²]

Distance = √[9 + 49]

Distance = √58 units.

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The girl which is correct between kate and her friend Margo is Margo.

The correct answer option is option B

If each friend gets the same number of pens;

Number of pens each friend get = Number of pens Kate has / Number of Kate's friends

= 63 / 9

= 7

Check:

Number of pens each friend get × Number of Kate's friends = Number of pens Kate has

7 × 9 = 63

Therefore, Kate's friend, Margo is correct.

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Answer: 12

Step-by-step explanation:

Answer:

The answer toy our problem is, The maximum number of days by which the completion of work can be delayed is 15.

Step-by-step explanation:

We are given that the penalty amount paid by the construction company from the first day as sequence, 4000, 5000, 6000, ‘ and so on ‘. The company can pay 165000 as penalty for this delay at maximum that is

 \(S_{n}\)​ = 165000.

Let us find the amount as arithmetic series as follows:

4000 + 5000 + 6000

The arithmetic series being, first term is \(a_{1}\) = 4000, second term is \(a_{2}\) = 5000.

We would have to find our common difference ‘ d ‘ by subtracting the first term from the second term as shown below:

\(d = a_{2} - a_{1} = 5000 - 4000 = 1000\)

The sum of the arithmetic series with our first term ‘ a ‘ which the common difference being, \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\) ( ‘ d ‘ being the difference. )

Next we can substitute a = 4000, d = 1000 and \(S_{n}\) = 165000 in “ \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\) “ which can be represented as:

Determining, \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\)

⇒ 165000 = \(\frac{n}{2}\) [( 2 x 4000 ) + ( n - 1 ) 1000 ]

⇒ 2 x 165000 = n(8000 + 1000n - 1000 )

⇒ 330000 = n(7000 + 1000n)

⇒ 330000 = 7000n + \(1000n^2\)

⇒ \(1000n^2\) + 7000n - 330000 = 0

⇒ \(1000n^2\) ( \(n^2\) + 7n - 330 ) = 0

⇒  \(n^2\) + 7n - 330 = 0

⇒ \(n^2\) + 22n - 15n - 330 = 0

⇒ n( n + 22 ) - 15 ( n + 22 ) = 0

⇒ ( n + 22 )( n - 15 ) = 0

⇒ n = -22, n = 15

We need to ‘ forget ‘ the negative value of ‘ n ‘ which will represent number of days delayed, therefore, we get n=15.

Thus the answer to your problem is, The maximum number of days by which the completion of work can be delayed is 15.

The number of standard deviations from the mean that include all

data values is two.

From the gathering of information, we will see that the minimum worth is $19.95 and also the most worth is $29.95. So , we would like to seek out the amount of normal deviations, let's decision it "a" , such that\(\overline x $\color \ - a\cdot\sigma \le 19.95}\) and   \(\overline x $\color \ +a\cdot\sigma \geq 29.95}\)

Use the given values of mean  \(\overline x\) and normal deviation (σ) to notice the worth of "a".

         \(\overline x $\color \ - a\cdot\sigma \le 19.95}\\25.07\ - 2.62a \leq 19.95\\5.12\leq 2.62a\\1.9541\leq a\)

On rounding off we get a = 2

Checking another inequality

         \(\overline x $\color \ + a\cdot\sigma \geq 29.95}\\25.07 \ + 2(2.62) \geq 29.95\\25.07 + 5.24 \geq 29.95\\30.31\geq 29.95\)

Thus , 2 standard deviation include the all values from the given set of data .

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The area of the trapezoid MNRS is 378 square feet.

An open, flat object with four straight sides and one set of parallel sides is referred to as a trapezoid or trapezium. A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases.

In the figure below, trapezoid MNRS is made up of trapezoid MNPT,

triangle TPQ, and parallelogram TQRS.

The area of triangle TPQ is 84 square feet.

The lengths of NP, PQ, and QR are in the ratio 2 : 1.5 : 1.

The heights of the parallel base are,

a = 18 feet and b = 16 + 12 + 8 = 36 feet.

Let h be the perpendicular height.

So,

1/2 x h x 12 = 84

h = 14 feet.

The area of the trapezoid MNRS,

= 1/2 x (36 + 18) x 14

= 378 square feet.

Hence, the area is 378 square feet.

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Answer:

1/6

Step-by-step explanation:

3/6 for even 3/6*2/6-----1/2*1/3