a student has scores of 8480 and 80 on 3 music theory exams what score is needed on a fourth exam for the student to earn an average grade of 90

Answer:The area of the walkway around is 26 x + 16 as the sum of two terms

Step-by-step explanation:

A rectangular garden has a walkway around it

1. The area of the garden is 4(4.5 x + 1.5)

2. The combined area of the garden and the walkway is 5.5(8 x + 4)

We need to find the area of the the walkway

To find the area of the walkway by subtracting the area of the

rectangle from the combined area

∵ The combined area = 5.5(8 x + 4) ⇒ simplify it

∴ The combined area = 5.5(8 x) + 5.5(4)

∴ The combined area = 44 x + 22

∵ The area of the garden = 4(4.5 x + 1.5) ⇒ simplify it

∴ The area of the garden = 4(4.5 x) + 4(1.5)

∴ The area of the garden = 18 x + 6

Now subtract the area of the garden from the combined area

∵ Area of the walkway = (44 x + 22) - (18 x + 6)

∴ Area of the walkway = 44x + 22 - 18 x - 6

- Add like terms

∴ Area of the walkway = (44 x - 18 x) + (22 - 6)

∴ Area of the walkway = 26 x + 16

The area of the walkway around is 26 x + 16 as the sum of two terms

Step-by-step explanation:

Answer:

7/3

Step-by-step explanation:

The center point of an ordered data set is the: mean.

The mean of any data set is the middle or center data point of the data set when the data set is ordered in increasing or descending order.

For example, the center point of the data set, 4, 6, 7, 8, 9 is 7. 7 is the mean of the data set.

Therefore, the center point is the mean.

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Answer:

112 cm (red, 4)

Step-by-step explanation:

length = b

width = a

b = 7a

42 = b - a

42 = 7a - a

42 = 6a

a = 7          => b = 7a       b = 7*7 = 49

Perimeter = 2*(a+b)

= 2*(7+49)

= 2*(56)

= 112 cm

Answer:

y=-2x-10

this is slope-intercept form, if this is what you're asking for?

Step-by-step explanation:

simplify: y-4 = -2x-6

y= -2x -10

Binary integer variables are variables whose values consist of two values, 0 and 1.

Correct answer will be :- b. Variables with values 0 and 1.

These values are also known as bits, which are represented as 0 and 1 in computers. Binary integer variables are used in computing as a way to represent numbers, characters, and instructions. Binary integer variables are used to represent information in digital systems, because they can be used to represent any value with a single bit.

For example, a single bit can represent a number, letter, or instruction. Binary integer variables are also used in computer programming, as they can be used to represent boolean values, such as true and false. Additionally, they can be used to represent various types of data, such as numbers, characters, and images.

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Adjusted R² is a modified version of R² that accounts for the number of independent variables in the model, making it more suitable for comparing models with different numbers of independent variables.

(a) To analyze this data using the multiple linear regression model, the theoretical linear model can be written as:

y = β0 + β1 * x1 + β2 * x2 + ε

where y is the dependent variable, x1 and x2 are the independent variables, β0 is the intercept, β1 and β2 are the coefficients of x1 and x2, respectively, and ε is the error term.

The standard assumptions in this model are:
1. Linearity: The relationship between the dependent and independent variables is linear.
2. Independence: The observations are independent of each other.
3. Homoscedasticity: The variance of the error term is constant across all levels of the independent variables.
4. Normality: The error term is normally distributed.

(b) Unfortunately, I cannot run SAS to find the regression line for the above model. Please use the SAS software on your computer to perform this task.

(c) To test whether the model is overall useful, set up the null and alternative hypotheses as follows:

H0: β1 = β2 = 0 (The model is not useful; the independent variables x1 and x2 do not explain any variation in y)
Ha: At least one of β1 or β2 is not equal to 0 (The model is useful; at least one of the independent variables explains the variation in y)

(d) The test statistic used for the above test is the F-statistic, calculated as (explained variance / number of independent variables) / (unexplained variance / degrees of freedom of residuals). Check the SAS output for the F-statistic and its corresponding p-value to determine if you should reject or fail to reject the null hypothesis.

(e) The R² and adjusted R² values can also be found in the SAS output. R² represents the proportion of the total variation in y that is explained by the independent variables in the model.

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Answer:

A) V + 6 B = 372

B) 4V + 12B = 780

We'll divide B) by -4

B) -V -3B = -195 Then we add A)

A) V + 6 B = 372 which equals

3B = 177

1 Bus carries 59 Students

For the Van let's use equation A)

V + 6 * 59 = 372

Van = 372 -354

Each Van Carries 18 Students

Step-by-step explanation:

Answer:

4.8 miles

Step-by-step explanation:

Set up a ratio, Kelvin.

6/55 = x/44

55x = 6(44)

55x = 264

x = 264/55 = 4.8 miles

Answer:

225 km^2

Step-by-step explanation:

Area of a trapezoid: ((Base 1 + Base 2) x h) / 2

(11 + 19) x 15 / 2

= 225 km^2

Answer:

\(\frac{x^4-x^3-19x^2-10x+17}{x-5}=x^3+4x^2+x-5+\frac{-8}{x-5}\)

Step-by-step explanation:

5 | 1  -1  -19  -10   17

___   5  20_ 5  -25____

    1   4    1   -5  | -8

So, we show our answer as \(1x^3+4x^2+1x-5+\frac{-8}{x-5}=x^3+4x^2+x-5+\frac{-8}{x-5}\)

Answer:

222

Step-by-step explanation:

Find the average of the 2 numbers , that is

average = \(\frac{sum}{count}\) = \(\frac{123+321}{2}\) = \(\frac{444}{2}\) = 222

One meter is equal to 100 centimeters.

Now, we need to know 3.06 meters in centimeters:

Use the rule of three to find this value

1meter-------------------- 100cm

3.06------------------------- x cm

Where x is = (3.06*100)/1

Then x=306

The ceiling is 306 centimeters tall.

The sales price of the item is $48.

The sale price of an item that costs 60% of its original price which is $80 is $48. The original price of the item is $80, and it costs 60% of the original price. The amount of money we'll be spending is calculated as follows: 60 per cent of $80 (60/100) × $80= $48 Therefore, the sales price is $48. The percentage discount for the item is calculated as follows:$80 - $48 = $32

$32 is the amount of money saved due to the discount, which is then divided by the original price, $32/$80 = 0.4 or 40%. Thus, there was a 40% discount on the original price.

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By using Algebraic methods It will take 5 seconds for the rock to hit the ground when dropped from a building that is 64 feet tall, given the equation y = -16t^2 + 400.

The equation is y = -16t^2 + 400, where y represents the height of the rock in feet and t represents the time in seconds.
To find out how many seconds it will take for the rock to hit the ground, we need to set the equation equal to zero because the ground is at a height of zero.
0 = -16t^2 + 400
Now, we can solve for t using  Algebraic methods.
First, we can subtract 400 from both sides of the equation:
-400 = -16t^2
Next, we can divide both sides by -16:
25 = t^2
Finally, we can take the square root of both sides:
t = ±5
Since we can't have negative time, we know that it will take 5 seconds for the rock to hit the ground.
So, to summarize, it will take 5 seconds for the rock to hit the ground when dropped from a building that is 64 feet tall, given the equation y = -16t^2 + 400.

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The output of 0.7326 represents the test statistic (Z-score) computed from the 1-sample Z-test in Excel.

It tells you how many standard deviations the sample mean is from the population mean under the null hypothesis.

A test statistic (Z-score) is a numerical value used in statistical hypothesis testing to assess the evidence against the null hypothesis.

A test statistic measures the difference between a sample statistic (eg sample mean) and the corresponding population parameter (eg population mean) assuming the null hypothesis is true.

For the Z-test, the test statistic is computed as

z = (x - μ) / (σ / √n)

where x = sample mean,

μ = population mean,

σ= population standard deviation,

and n = sample size.

The resulting Z-score indicates how many standard deviations the sample mean is from the population mean, assuming the null hypothesis is true.

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Answer:

The output of y = 1

Step-by-step explanation:

Answer: 48 feet

In order to get the answer you have to plug 12 into the equation you made in part a.

Firstly, let's check your answer to part A.

We know that there is no y-intercept because the line crosses the origin (0,0).

Let's use the slope formula to find the slope:

\(\frac{y2 - y1}{x2 - x1} = \frac{20 - 0}{5-0} = \frac{20}{5} = 4\)

So, the slope is actually 4x.

Now, we go on to answer part b.

y = 4x

Plug in the 12

y = 4(12)

y = 48

Therefore Kelvin will have walked 48 feet after 12 seconds.

I hope this helps!!

- Kay :)

The solution of x when solving x/2 + 1 = √3 is :

x is 2√3 - 2 .

Here in the question given equation ,

x/2 + 1 = √3

To find solution,

we have to subtract 1 from LHS and RHS of equation,

⇒ x/2 + 1 - 1 = √3 - 1

⇒ x/2 = √3 - 1

Next multiply both sides  by 2

2( x/2) = 2(√3 -1)

By simplifying both sides we get,

x = 2√3 - 2

So the value of x = 2√3 -2.

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The probability of x taking on a value between 75 to 90 is 0.25.

Given that x is a continuous random variable uniformly distributed between 65 and 85.To find the probability that x lies between 75 and 90, we need to find the area under the curve between the values 75 and 85, and add to that the area under the curve between 85 and 90.

The curve represents a rectangular shape, the height of which is the maximum probability. So, the height is given by the formula height of the curve = 1/ (b-a) = 1/ (85-65) = 1/20.Area under the curve between 75 and 85 is = (85-75) * (1/20) = (10/20) = 0.5Area under the curve between 85 and 90 is = (90-85) * (1/20) = (5/20) = 0.25.

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The volume of the solid is 4/5π.

The volume of a solid generated by revolving a region around a line is given by V = ∫a b π(y)2dy, where a and b are the lower and upper limits of the region, respectively, and y is a function of x.

In this case, the region is bounded by the graph of y=x3, the y-axis, and the horizontal line y=1. Therefore, the volume of the solid generated when the region is revolved about the y-axis is given by

V = ∫0 1 π(y)2dy

= ∫0 1 πx6dx

= π/7

= 4/5π

The volume of the solid is calculated using the formula V = ∫a b π(y)2dy, where a and b are the lower and upper limits of the region and y is a function of x. In this case, the lower limit is a=0 and the upper limit is b=1, since the region is bounded by the graph of y=x3, the y-axis, and the horizontal line y=1. Integrating from a=0 to b=1 gives the volume of the solid as V = ∫0 1 πx6dx = π/7 = 4/5π.

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Answer: 0=30 degrees

Step-by-step explanation: divide each by 6

Answer: revenue from last year 20n

number of cards sold this year if students sell 200 more cards than last year n + 200

revenue this year if student sell 200 more cards than last year 20(n + 200)

Step-by-step explanation:

An expression is defined as a set of numbers, variables, and mathematical operations. The given pairs can be matched as shown below.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

Given that n represents the number of cards that students sold last year. Also, it is given that each card is sold for $20. Therefore, the given pairs can be matched as shown below.

1.) Revenue from last year

Revenue = Number of tickets sold last year × Cost of each ticket

               = n × $20

               = 20n

2.) Number of cards sold this year if students sell 200 more cards than last year

Number of cards sold this year = Number of tickets sold last year + 200

                                                    = n + 200

3.) Revenue this year if students sell 200 more cards than last year

Revenue this year = Number of cards sold this year × Cost of each ticket

                               = (n + 200) × 20

                               = 20(n+200)

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Answer:

the two numbers are 36 and 25 sum=61

Step-by-step explanation:

√900=30

closest square numbers to 30=25 and 36

to make sure multiply 36 by 25=900

The given expression 106(1.087)^t represents the population of deer in a state park. Here's an explanation of the components and their meanings:

106: This is the initial population of deer in the state park, as of the base year (2010).

(1.087)^t: This part represents the growth factor of the deer population over time. The value 1.087 represents the growth rate per year, and t represents the number of years since 2010.

To calculate the predicted population of deer in a given year, you would substitute the corresponding value of t into the expression. For example, if you wanted to predict the population in the year 2023 (13 years since 2010), you would substitute t = 13 into the expression:

Population in 2023 = 106(1.087)^13

By evaluating this expression, you can calculate the predicted population of deer in the state park in the year 2023.

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a) The slope of the regression equation: 1.6172

b) The equation of the line of best fit that can be used to predict bean heights is: height = (1.6172 x width) + 2.3349

c) The fraction of the variability in bean heights = 0.7484

d) If the students use the height of the beans to predict the width then the slope =  0.4628

e) The equation of the line of best fit that can be used to predict bean widths is: width = (0.4628 × height) - 16.0299

Here, the summary statistics of a random sample of beans are:

Mean width:  7.586

Stdev width:  0.873

Mean height:  14.603

Stdev height:  1.632

Correlation coefficient:  0.8651

Let us assume that  x represents the width and y represents the height. a) First we find the slope.

slope = r × Sy/Sx

where Sx is the Stdev width and Sy is the Stdev height.

So, slope = (0.8651) × (1.632/0.873)

                =  1.6172

b) First we find the intercept.

intercept = ( \(\bar{y}\) - slope × \(\bar{x}\))

where \(\bar{y}\) = mean height and \(\bar{x}\) = mean width

intercept = ( 14.603 - (1.6172)× (7.586))

intercept = 2.3349

So, the equation of the line of best fit that can be used to predict bean heights would be,

y = (1.6172)x + 2.3349

i.e., height = (1.6172 x width) + 2.3349

c) Now we find the fraction of the variability in bean heights can be explained by the linear model of bean height vs. width:

r²

= (0.8651)²

= 0.7484

d) Now let us assume that  x represents the height and y represents the width.

Then the slope would be,

slope = r × Sy/Sx

where Sx is the Stdev height and Sy is the Stdev width.

So, slope = (0.8651) × (0.873/1.632)

                = 0.4628

e) Now we find the intercept.

intercept = ( \(\bar{y}\) - slope × \(\bar{x}\))

where \(\bar{y}\) = mean width and \(\bar{x}\) = mean height

intercept = (7.586 - (1.6172)× (14.603))

intercept = -16.0299

Thus the equation of the line of best fit that can be used to predict bean widths.

width = (0.4628 × height) - 16.0299

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Find the complete question below.

The relationships between the numerator and denominator coefficients of a circuit and the values of resistance (R), inductance (L), and capacitance (C) depend on the specific circuit configuration and the transfer function associated with it.

In general, the numerator coefficients of the transfer function represent the output variables of the circuit, while the denominator coefficients represent the input variables. The coefficients are determined by the circuit elements (R, L, C) and their interconnections.

For example, in a simple RC circuit (resistor and capacitor), the transfer function can be written as a ratio of polynomials in the Laplace domain. The denominator coefficients correspond to the characteristic equation of the circuit and involve the resistance and capacitance values. The numerator coefficients may be related to the initial conditions or external inputs.

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