The table defines the observed data values and the corresponding predicted values, based on a line of fit. Observed Predicted 9 7.77 12 12.87 12 11.17 15 14.57 17 16.27 24 24.77 28 26.47 33 31.57
How many negative residuals does the data set have? How many positive residuals does the data set have?
2 negative residuals and 6 positive residuals 3 negative residuals and 5 positive residuals 5 negative residuals and 3 positive residuals 6 negative residuals and 2 positive residuals

The multiple of 2, 5, and 7, such that the sum of the 3 digits is 10 is:

630

We want to find a number that is a multiple of 2, 5 and 7, such that the sum of the 3 digits is 10. (such that the number is not 280)

So our number N is of the form:

N = a*(2*5*7)

Where a is an integer.

N = a*70

Here we just need to find the value of a such that the sum of the 3 digits of the outcome is equal to 10.

For example, if a = 2 then:

N = 2*70 = 140

The sum gives 1 + 4 + 0 = 5

Now we jut need to keep trying values of a.

Eventually, we will get to:

if a = 9 then:

N = 9*70 = 630

The sum gives: 6 + 3 + 0 = 10

So this is our number.

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The function that represents the 6% popularity growth per month is P(x) = 500 + 0.06x

Function:

Function also known as an expression, rule, or law that defines a relationship between one variable called independent variable and another variable called dependent variable.

Given,

Before gaining popularity in the music industry, a young artist had 500 social media followers. As her popularity grew, her social media following increased at a rate of 6% per month.

Here we need to find the function that represents the given situation.

Let us consider the number of months to be modeled as x.

Then P(x) is the function that represents the situation.

And from the given question we know that, the initial population was 500.

And the population growth per month is 6%.

When we convert this percentage value into decimal then we get the growth rate as, 0.06.

Through this details, the function is written as,

P(x) = 500 + 0.06x

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Answer:

(3z)^3

Step-by-step explanation:

27 = 3 * 3 * 3 = 3^3

3^3 z^3   = (3z)^3

Answer:

D = 30/7; R =32/7

Step-by-step explanation:

First, we need to find the scale of the number line.  We can see that there are 7 ticks between 4 and 5.  Thus, we can use (5-4)/7 to find the scale which is 1/7.  

Since D is two ticks away from 4, we can use the equation:

[tex]4+2(\frac{1}{7})=D\\ 4+\frac{2}{7}=D\\ 4\frac{2}{7}=D\\ 4*7=28+2=\frac{30}{7}=D[/tex]

Since R is two ticks away from D or 30/7, we can use a similar equation:

[tex]\frac{30}{7}+2(\frac{1}{7})=R\\ \frac{30}{7}+\frac{2}{7}=R\\ \frac{32}{7}=R\\ 4\frac{4}{7}=R[/tex]

Your problem doesn't tell us whether we need to we use improper or mixed fractions, but I've included both for you.

Answer:

A decimal or consecutive tenths decimals. Also 0.1 away from each other.

Step-by-step explanation:

They have decimal endings: .1 and .2

And are 0.1 away.

The domain of the given function is the hours or time taken whereas the range will be the concentration and greatest concentration of the medication that a patient will have in their body is 8 mg/L.

What is Domain of a function?

Inputs are assigned outputs by functions. The collection of all potential inputs for a function is its domain. For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.

Therefore, The domain of the given function is the hours or time taken.

What is range of a function?

The collection of potential output values for a function is known as its range.

Therefore, the range of the function is concentration.

B) Graph of the function is attached and we can see from the graph that greatest concentration of the medication that a patient will have in their body is 8 mg/L.

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Answer:

y=-1/2x+4

y=2x+5

y=x+2

Step-by-step explanation:

1. The equation of the line is y = - 4 / 9 x + 25 / 9.

2. The equation of the line is y = 5 /3 x -  14 / 3

3. The equation of the line is  y = x + 2

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, the equation of the line can be found as follows:

1.

(4, 1)(-5, 5)

m = 5 - 1 / -5 -4

m = 4 / -9

m = - 4 / 9

Let's find y-intercept

1 = - 4 / 9(4) + b

1 + 16 / 9 = b

b =  9 + 16 / 9

b = 25 / 9

Hence, thee equation of the line is  y = - 4 / 9 x + 25 / 9

2.

(-2, -8)(4, 2)

m = 2 + 8 / 4 + 2

m = 10 / 6

m = 5 / 3

Let's find y-intercept

2 = 5 / 3 (4) + b

2 - 20 / 3 = b

b =  6 - 20/ 3

b = - 14 / 3

Therefore, the equation of the line is y = 5 /3 x -  14 / 3

3.

(0, 2)(-2, 0)

m = 0 - 2 / -2 -0

m = - 2 / -2

m = 1

Let's find y-intercept

2 = 1(0) + b

b = 2

Therefore, the equation of the line is y = x + 2

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A graph which represents the solutions of p + 1 < -1 or p - 5 > 7 is shown in the image attached below.

In Mathematics, an interval notation simply refers to a set of real numbers which consist of all the real numbers that represents a continuous function and lies between two set of numbers.

This ultimately implies that, an interval notation should be used for writing all of the subsets of a real number line (graph) as shown below:

For the first interval, we have:

p + 1 < -1

p < -1 - 1

p < -2

Therefore, in interval notation, we have:

p = {∞, -2}

For the second  interval, we have:

p - 5 > 7

p < 7 + 5

p < 12

Therefore, in interval notation, we have:

p = {12, ∞}

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The sales Sam need to make $733.50 per week before taxes is $3475.

Given, Sam is paid $14 per hour plus 6% of sales.

If he worked 37.5 hours in one week, what would his sales need to make

$733.50 per week before taxes = ?

Let the sales be represented by x

Amount made from no of hours worked :

= $14 × 37.5 hours

=$525

Sales made = 6% of x

=0.06x

Total = 0.06x+$525

=$733.50

0.06x=733.50-$525

=$208.5

x=$3,475

Hence we get the required answer.

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The rocket reaches its maximum height at 2.25 second(s) after launch

The maximum height reached by the object is 88 feet.

The function is given as

h(t) = -16t² + 72t + 7

Differentiate the above function

So, we have the following representation

h'(t) = -32t + 72

Set to 0

-32t + 72 = 0

So, we have

32t = 72

Divide by 32

t = 2.25

Hence, the time is 2.25 seconds

In (a), we have

t = 2.25

Substitute t = 2.25 in h(t) = -16t² + 72t + 7

h(2.25) = -16(2.25)² + 72(2.25) + 7

Evaluate

h(2.25) = 88

Hence, the maximum height is 88 feet

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Answer:

[tex]y=80(1.1)^x[/tex]

Step-by-step explanation:

Please, tell me if I did this wrong as I'm not really sure of this. Thx

The measures of  the angles formed by the common transversal to the parallel lines are;

1. Angle 1 = 87°

Angle 2 = 100°

2. Angle 1 = 78°

Angle 2 = 78°

Parallel lines are lines that have the same slope but pass throuh different points.

The diagram consists of parallel lines that have a common transversal, therefore;

1. The 87° angle and the Angle 1 are alternate interior angles, therefore;

87° ≅ Angle 1

87° = Angle 1

The 87° angle and the Angle 2 are same side interior angles

Therefore;

87° + Angle 2 = 180°

Angle 2 = 180° - 80° = 100°

Angle 2 = 100°

2. The 78° angle and the Angle 1 are corresponding angles, therefore;

78° ≅ Angle 1

Angle 1 = 78° (by the definition of congruency)

Angle 1 and Angle 2 are vertical angles

Therefore, Angle 1 is congruent to Angle 2 by vertical angle theorem

Angle 1 = Angle 2 by definition of congruency

Angle 1 = 78° = Angle 2

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The slope is, 1/4.

And the y - intercept is (0, -1).

What is slope and y-intercept?

A number that describes a line's direction and steepness is known as the slope or gradient of a line in mathematics.

A y-intercept, also known as a vertical intercept, is a point in analytical geometry where the graph of a function or relation meets the y-axis of the coordinate system, employing the convention that the horizontal axis represents a variable x and the vertical axis represents a variable y. Thus,

x = 0 is satisfied at these sites.

Let the x - intercept is 4.

The x - intercept is the point on x - axis, when y = 0.

So, the x - intercept is (4, 0).

The y - intercept is -1.

y-intercept is the point on the y - axis, when x is zero.

So, the y - intercept is (0, -1).

Here we have two points (4, 0) and (0, -1).

By using these points we can find the slope.

Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m = \frac{-1-0}{0-4}= \frac{-1}{-4} = \frac{1}{4}[/tex]

Hence, the slope is 1/4 and the y - intercept is (0, -1).

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Answer:

The answer is B false

Step-by-step explanation:

According to the graph of the function the real zeros of the functions are (-0.33, 0)

Real zeros of the function

Based on the graph methods, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.

Given,

Here we have the function f(x) = -9x² - 6x - 1

Now, we have to plot the graph for the function by using the graphing calculator and then we have to find the real zeros of the function.

Here we have to take the expression and input it in the graphing calculator.

Then we get the graph like the following.

Now, we have to identify the real zeros of the function through this plotted graph.

The real zeros of the function means the x intercept points of the graph.

Here we have the x intercepts is (-0.33,0)

Therefore, the real zeros on the function are (-0.33 , 0)

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Answer:

I believe this should be it,

Step-by-step explanation:

344.8572

Answer of the following questions:

As given in the question,

For a coordinate plane,

Line passes through the points (-6, 8) and (2,6).

Slope of the line = ( y₂ - y₁)/ (x₂ - x₁)

                          = ( 6 - 8) / (2- (-6))

                          = -2 /8

                          = -1/4

Slopes of the parallel line are always equal.

Equation of the line parallel to the given line and passes through (-2, -4)

is given by:

y -(-4) = (-1/4)(x -(-2))

⇒y + 4 = -x/4-1/2

⇒ y = -x/4 -9/2

y-intercept of the line which is parallel to the given line and passes through (-2, -4) is given by:

x = 0

y = -9/2 is the y-intercept.

Therefore,  answer of the questions for the given condition :

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Answer:

Step-by-step explanation:

89,83,91,92,93,x

n=6

average=91

total=91*6=546

89+83+91+92+93+x=546

448+x=546

x=546-448=98

Answer:

Step-by-step explanation:

1)

Let Andre's grade needs to be a x on his next test

Hence,

[tex]\displaystyle\\\frac{89+83+91+92+93+x}{6} =91\\\\\frac{448+x}{6} =91[/tex]

Multiply both parts of the equation by 6:

[tex]448+x=91(6)\\\\448+x=546\\\\448+x-448=546-448\\\\x=98[/tex]

2)

[tex]\displaystyle\\\frac{1000+1181+1191+1200+1268+1328+2584+x}{8} =1344\\\\\frac{9752+x}{8}=1344[/tex]

Multiply both parts of the equation by 8:

9752+x=1344(8)

9752+x=10752

9752+x-9752=10752-9752

x=$1000

3)

302, 293, 218, 330, 199, 253, 288

Arrange this series:

199, 218, 253, 288, 293, 302, 330

[tex]\displaystyle\\a)\ the \ median = \$288\\\\b) \ the\ mean =\frac{199+218+253+288+293+302+330}{7} \\\\=\frac{1883}{7} \\\\=\$269\\c)\\\\\frac{1883+x}{8} =269+5\\\\\frac{1883+x}{8} =274[/tex]

Multiply both parts of the equation by 8:

1883+x=274(8)

1883+x=2192

1883+x-1883=2192-1883

x=$309

The solution in set builder notation is given by = {y:3>y≥-1}

Given the inequalities are,

y-1<2 ............(i)

y+2 ≥ 1 ..............(ii)

Solving the first inequality we get,

y-1 < 2

y-1+1 < 2+1, adding 1 to both sides

y < 3

Solving second inequality we get,

y+2 ≥ 1

y+2-2 ≥ 1-2

y ≥ -1

So the range is 3>y≥-1

So the solution in set builder notation is = {y:3>y≥-1}

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Answer:

gpaph C.

Step-by-step explanation:

graph 'C' represents the provided function. Its equation is

[tex]y=-\frac{5}{2}x +4.[/tex]

There are 12.3553 square miles are in 32 square kilometers.

What is square miles and square kilometers?

A square mile is equivalent to 2.59 square kilometres. A square mile must be multiplied by a factor of 2.59 in order to be converted to a square kilometre. For instance, 3 square miles are equivalent to 7.77 square kilometers when multiplied by 2.59, or square meters.

We have to find how many square miles are in 32 square kilometers.

Since, 1 square mile = 2.59 square kilometer

Suppose x square miles = 32 square kilometer

Consider, the ratio

[tex]\frac{1}{x} = \frac{2.59}{32} \\x = \frac{32}{2.59}\\ x=12.3553[/tex]

Therefore, 12.3553 square miles are in 32 square kilometer.

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The probability that you select two rock concert tickets is 0.25.

What is the probability?

Probability is the branch of mathematics concerned with numerical descriptions of the likelihood of an event occurring or of a proposition being true. The probability of an event is a number between 0 and 1, where 0 represents the event's impossibility and 1 represents certainty.

We have,

[tex]Probability =\frac{number \ of favorable outcomes}{total number \ of outcomes}[/tex]

Number of favorable outcomes  = 6

Total number of outcomes = 24

Probability rock concert tickets = 6/24

= 1/4

Probability rock concert tickets =  0.25

Hence, the probability that you select two rock concert tickets is 0.25

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The dimensions of the shape will be 175 meters and 87.5 meters

The largest area that can be enclosed is 15312.5m².

Based on the information given, the equation to illustrate this will be:

2x + y = 350

y = 350 - 2x

Note that area = length × width

= x × y

We'll substitute the value into the equation. This will be:

A = x × (350 - 2x)

A(x) = 350x - 2x²

Differentiating the area, x will be 87.5

Width = 87.5m

Since y = 350 - 2x

= 350 - 2(87.5)

= 350 - 175

= 175

Length = 175m

Area = Length * Width

= 175 × 87.5

= 15312.5m²

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The quotient for both the parts are 9.375 and 175.01.

What is quotient?

In arithmetic, a quotient may be a amount created by the division of 2 numbers. The quotient has widespread use throughout arithmetic, and is usually brought up because the number a part of a division, or as a fraction or a quantitative relation.

Main body:

A) 3.75/ 0.4

 first removing the decimals,

= 375/ 40

=  9.375

B) 8750.50/50

same process of removing decimals,

= 8755050/ 5000

= 175.01

Hence the value of quotient for both the parts are 9.375 and 175.01.

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The equation, [tex]g(x) = \sqrt{\frac{1}{4}x }-2[/tex], represents the transformation formed by horizontally stretching the graph of [tex]f(x) = \sqrt{x}[/tex]  by a factor of 4 and then vertically shifting the graph 2 units down.

What is transformation of graph?

The process of algorithmically producing a new graph from an original graph is known as graph transformation, sometimes known as graph rewriting. It has several uses, including software engineering, layout algorithms, and image.

Consider, the given function [tex]f(x) = \sqrt{x}[/tex].

If horizontally stretching the graph by 4 units then, the graph  becomes,

[tex]f(x) = \sqrt{\frac{x}{4} }[/tex].

If vertically shifting the graph 2 units, then the graph becomes,

[tex]h(x) = \sqrt{\frac{x}{4} } - 2[/tex].

Hence, the transformed form of the graph is, [tex]h(x) = \sqrt{\frac{x}{4} } - 2[/tex].

So, the third option is correct.

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Answer:

1

Step-by-step explanation:

anything to the power of 0 is equal to 1

Hopes this helps please mark brainliest

According to the given square root value, the resulting value of the expression 2√4 × √9 is 12

Square root:

Square root refers any number that is equal to a number, which when squared gives the original number.

Given,

Here we have the expression 2√4 × √9.

Now, we have to find the value of the expression.

While we looking the given expression we have identified that the value of the square roots are

√4 = √(2 x 2) = 2

Similarly, the value of

√9 = √(3 x 3) = 3

So, now we have to replace the root with these values, then we get,

=> (2 x 2) x 3

=> 4 x 3

=> 12

Therefore, the resulting value is 12.

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