A librarian measured the number of young adult books in a library. The number of books in the library as a function of time (in years since 2008) is shown in the scatterplot.

scatterplot with points at 0 comma 10, 4 comma 42, 8 comma 74 and 12 comma 106

Choose the linear function that best describes the scatterplot relating the number of books in the library, y, to time, x. (1 point)

Group of answer choices

y = 8 − 10x

y = 8 + 10x

y = 10 − 8x

y = 10 + 8x

The values which are less than -7 on the number line makes the value true.

b≤-6

-7≤-6

-9≤-6

-256≤-6

only in the case where b = -6 satisfy only equality condition not less than condition. Other than this remaining other values which are less than -7 on the number line including rational numbers , decimal numbers, all negative numbers which are less than -6 satisfy.

The values which are less than -7 on the number line makes the value true

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Question what makes the value Inequality b≤-6 is true for what values of b?

Equation for each option to model the value A of the account after x years is 5+ 5/nⁿ and 2ˣ 0.01.

What is an equation?

In arithmetic,an equation may be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.

Main body:

for option 1

initial investment is $5 after 1 year investment is

5+5/2

after 2 year 5+5/2+(5+5/2)/2=5+5/2+5/2²

continuing this way we get the formula

5+ 5/nⁿ

for option 2

after 1 year money becomes 2*0.01

after 2 year money becomes 2²*0.01

after x year money becomes 2ˣ 0.01

Hence the forumla for each option is as provided.

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Answer:

D. 0.53

Step-by-step explanation:

California = 90

Total of those who prefer Brand A = 170

To find the percentage, you do:

90/170 × 100 = 52.941...

However you have to round it to two decimal points, hence you do:

52.941 ≈ 53%

53% = 0.53

This is due to 53% representing 53/100 = 0.53

Therefore, the probability that the person that likes brand A is from California is 0.53

:)

The solution is, the following expressions are equivalent to 4⁻³ / 4⁻⁸

A.  4^8/4^3

D. 4⁵

An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.

here, we have,

We have to calculate to find the result -

The expression is = 4^(-3)/4^(-8)

According to the indices rule, the power will be deducted if it is a division.

Therefore, a^m/a^n = a^(m-n)

Using that formula,

4⁻³ / 4⁻⁸

= 4⁸ / 4³

= 4⁽⁸⁻³⁾

=4⁵

Therefore, the answer choice D is the option, and the answer is 4^5.

Option A is also correct.

Because we can find 4^5 with the help of that option.

Alternative way,

4^(-3)/4^(-8)

= 4^(-3+8)

= 4^(8-3)

= 4^8/4^3

In the is way, we can also find option A is correct.

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complete question:

Which of the following expressions are equivalent to 4^-3/4^-8?

Answer:

not possible

Step-by-step explanation:

Answer:

[tex]493.039 \;in^3[/tex]

Step-by-step explanation:

If each side of the cube is [tex]a[/tex] then the volume of the cube is given by [tex]a^3[/tex]

If Volume is [tex]V[/tex] then each side [tex]a = \sqrt[3]{V}[/tex]

Here we are given the volume of the smaller cube as [tex]85\; in^3[/tex]

So each side of this cube = [tex]\sqrt[3]{85} = 4.396 \approx 4.4 \;in[/tex]

and each side of the larger cube [tex]= 4.4 + 3.5 = 7.9\;in[/tex]

Volume of larger cube [tex]= 7.9^3 = 493.039 \; in^3[/tex]

Answer:

19.25

Step-by-step explanation:

t = .55m

t = .55(35)

t = 19.25

I am not sure what you mean by 5 give the total cost in dollars T.  I am not sure where the comes from.

Answer:

$24.25

Step-by-step explanation:

Given equation:

[tex]T=0.55m+5[/tex]

where:

To find the total cost of renting a jet ski for 35 minutes, substitute m = 35 into the given equation and solve for T:

[tex]\implies T=0.55(35)+5[/tex]

[tex]\implies T=19.25+5[/tex]

[tex]\implies T=24.25[/tex]

Therefore, the total cost of renting a jet ski for 35 minutes is $24.25.

Willka covers 4.5 m² in 1L paint and 45 m² in 10L in paint according to the table.

What are equivalent ratios?

We know that the equivalent ratio is defined as the ratio which is having the same proportion as given ratio.

Now, using the division property of the ratio, we will divide the given ratio with the same number both sides.

According to the given question:

If Willka covers 13.5 m² with 3L paint, to cover x m² she will need 1L paint

By equivalent ratios

13.5 : 3 = x : 1

x = 13.5 / 3

x = 4.5

Similarly to cover y m² she needs 10L paint

13.5 : 3 = y : 10

y = 13.5 x 10/3

y = 45

Therefore the answer for the blanks is 4.5 and 45.

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Answer:

Solve for x

by simplifying both sides of the inequality, then isolating the variable.

Inequality Form: x>10.4

Interval Notation: (10.4,∞)

Step-by-step explanation:

Answer:

  8.2 m

Step-by-step explanation:

You want the length of the shadow whose tip is 34 m from the top of a 33 m building.

The described geometry can be modeled by a right triangle with one leg 33 m and hypotenuse 34 m. The Pythagorean theorem tells us the length of the other leg is ...

  a² +b² = c²

  b² = c² -a²

  b = √(c² -a²)

  b = √(34² -33²) ≈ 8.2 . . . . meters

The length of the shadow is about 8.2 meters.

__

Additional comment

The angle of elevation to the top of the building can be found from the trig relation ...

  Sin = Opposite/Hypotenuse

And the length of the shadow can be found from the relation ...

  Cos = Adjacent/Hypotenuse

If α is the angle of elevation, then ...

   sin(α) = 33/34   ⇒   α = arcsin(33/34)

and

  Adjacent = Hypotenuse × cos(α)

  Adjacent = 34·cos(arcsin(33/34)) ≈ 8.2 . . . . meters

where the "adjacent" side of the triangle is the side between the building and the tip of the shadow, along the ground.

Probability to get at most 2 heads after flipping coin for 5 times is 1/2.

Probability is the ratio of good outcomes to all possible outcomes of an event is known as the probability.

The number of positive results for an experiment with n outcomes can be represented by the symbol x.

The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

With a fair coin, there are [tex]2^{5}[/tex] = 32 possible combinations of heads and tails after 5 flips.With 0 heads,5C0 = 5!/0!5! = 1 ways

get one head 5C1 = 5!/ 4!1! = 5 ways

To obtain precisely 2 heads,5C2 = 5!/ 2!3! = 10 ways

Obtain 3 heads,5C3 = 5!/ 3!2! = 10 ways

Total methods to gain at most 2 heads are 1+5+10 = 16.

Probability to get at most 2 heads is = ( total methods to gain at most 2 heads)/(total ways)

P(total methods to gain at most 2 heads) = 16/32 =1/2.

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Answer:

Below

Step-by-step explanation:

From the data , the miles per gallon is  

199.2 mi  / 6 gal       or      265.6 mi / 8 gal      or     863.2 / 26    

   = 33.2 mi/gal

for 50 gallons this would be

    33.2 mi / gal   *  50 gal = 1660 mi

The slope of AB -3

The slope of BC 1/3

The slope of AC -1/2

△ABC a right triangle because two lines are perpendicular shown by a negative reciprocal slope -3 and 1/3

The slope is represented as m, The slope by definition is the ratio change of the output values to the input values

The slope, m using the points A(-2, 4), and B(-1, 1)

m = (y₀ - y₁) / (x₀ - x₁)

m = (4 - 1) / (-2 - -1)

m = (3) / (-1)

m = -3

The slope, m using the points B(-1, 1), and C(2, 2)

m = (1 - 2) / (-1 - 2)

m = (-1) / (-3)

m = 1/3

The slope, m using the points A(-2, 4), and C(2, 2)

m = (4 - 2) / (-2 - 2)

m = (2) / (-4)

m = -1/2

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Answer: x=5

Step-by-step explanation:

isolate x

8x-4+4=36+4

8x=40

x=5

Answer:

x=5

Step-by-step explanation:

You would first want to add 4 to both sides. Then divide 40 and 8 by 8 and you get x=5.

When the temperature is 30° in Celsius, the temperature in Fahrenheit is 86.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The given equation to find the temperature,

C= 5/9(F-32)          (1)

Here, C represents the temperature in Celsius,

And F represents the temperature in Fahrenheit.

To find the temperature in Fahrenheit, when C = 30°,

Substitute C = 30° in equation (1),

30 = 5/9(F - 32)

6 x 9 = F - 32

54 = F - 32

F = 86

The temperature in Fahrenheit is 86.

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When forces are balanced the sum of the net force is 0 N

The total of all forces exerted on an object is known as the net force.

A mass can accelerate due to net force. A body is subject to another force whether it is at rest or in motion.

When there are a lot of forces acting on a system, the term "net force" is employed.

When the net force is summed to zero then the forces are said to be balanced

Hence a zero net force is a balanced force and will result to 0 N

N is the short form of Newton which is the unit of force

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The standard form is y= 1/2x+ 4.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

(2,5) and (-4,2)

So, slope

= (2- 5)/ ( -4 - 2)

= -3 / (-6)

= 1/2

and, using slope- intercept form

y- 5 = 1/2( x - 2)

y-5 = 1/2x -1

y= 1/2x + 4

Hence, the standard form is y= 1/2x+ 4.

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The equations of the proportional relationships from the table are k = 5h, k = 5/4h and k = 1/5h

From the question, we have the following parameters that can be used in our computation:

The equation of a proportional relationship is represented as

k = Y/X * h

Where

(X, Y) is the coordinate of any ordered pair from the function or table

Using the above as a guide, we have the following:

Table 1

k = 10/2 * h

Evaluate the products and the quotient

k = 5h

Table 2

k = 5/4 * h

Evaluate the products and the quotient

k = 5/4h

Table 3

k = 5/25 * h

Evaluate the products and the quotient

k = 1/5h

Hence, the equations are k = 5h, k = 5/4h and k = 1/5h

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Answer:

£ 178.34 tax amount

Step-by-step explanation:

A computer costs £ 964. A tax of 18.5% is then added to the cost of the computer. Work out the amount of tax that is added to the cost of the computer.

18.5% tax = 0.185 tax rate

0.185 tax rate * £ 964 = £ 178.34 tax amount

T is not a function of G as they don't have a constant of proportionality.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

It should be noted that the constant of proportionality simply means the ratio that relates two given values in what is known as a proportional relationship. In this case, other names for the constant of proportionality are the constant ratio, constant rate, unit rate, constant of variation, or the rate of change

Since the parking garage charges $5 for the first hour, $10 for up to two hours, and $12 for the entire day. This implies that they don't have a constant of proportionality.

In this case, the time doesn't have an effect on amount paid.

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The amount of money left on the gift card, in term of the number of cups, a Lauren has bought is represented by the equation would be A = 10 - 2a.

An equation is an expression that shows the relationship between two or more numbers and variables.

We are given that from the task content that the total amount of money Lauren has initially is $10.

Hence, each cup of coffee costs $2.

Since the amount of money Lauren has left each time,

That is related to the number of coffee cups bought by the equation;

A = 10 -2a.

where a ranges be between 0 and 5.

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are NOT true for binary search algorithm.

Now, According to the question:

Options 1, 3 are NOT true for binary search algorithm

Hence, Binary search algorithm can be used for any arrays.

and, The worst-case time complexity of binary search is greater than sequential search

are NOT true for binary search algorithm.

In the question:

Which of the following statement(s) is/are NOT TRUE for binary search algorithm? (select all that apply]

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The difference between the number of passenger cars produced in Asia and the number produced in Eastern Europe/Russia is given as follows:

3 million.

The bar graph given by the image at the end of the answer shows the number of passenger cars produced in each of the regions.

From the graph, the numbers for each region are given as follows:

Then the difference between the number of passenger cars produced in Asia and the number produced in Eastern Europe/Russia is calculated as follows:

11 - 8 = 3 million.

The bar graph is given by the image shown at the end of the answer.

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Answer:

250 meters per minute.

Step-by-step explanation:

1 km = 1000 m

15 km = 15*1000 = 15000 m

1 hour = 60 min

Then:

15km/h = 15000km/60minutes

= 250 meter per minute

Answer:250 meters / minute

Step-by-step explanation:1 km/h = 16.66667 m/min

On solving the given equation y=(x+4)(x-1) the point on the graph are as follows:

(-4,0), (-1,0), (2,6), (-3,-4) &(0,-4)

What is a graph?

A relation is a specific instance of a function graph. A function is truly equivalent to its graph in set theory and the current mathematical underpinnings.

It is frequently more helpful to think about functions as mappings, which include the sets that constitute the domain and the codomain in addition to the relationship between input and output. For instance, the codomain should be considered while determining if a function is onto (surjective) or not. The codomain of a function is not determined by the graph alone.

It is typical to use the phrases function and graph of a function interchangeably since, although referring to the same thing, they suggest distinct ways of looking at it.

1)

let   y=0

0=(x+4)(x-1)

i.e. x = -4 and -1

2)

Let x =0

y=(0+4)(0-1)

y=-4

3)

Let x = 2

y=(2+4)(2-1)

y=6

4)

Let x = -3

y=(-3+4)(-3-1)

y=-4

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Answer:

25 Questions

Step-by-step explanation:

This Question tests on the concept of Rationing using percentages.

Eg. 45% of 100 = 45, therefore 100% of 100 = 100.

Given information from the question:

56% = 14 Questions

1% = (14 ÷ 56) Questions

Total number of questions in the test = 100%

100% = (14 ÷ 56) × 100 Questions = 25

Answer:

[tex]\huge\boxed{\sf 25\ questions}[/tex]

Step-by-step explanation:

Let the total questions be x.

Given that,

56% of total questions = 14

Key: "of" means "to multiply", % means out of hundred.

[tex]\displaystyle \frac{56}{100} \times x = 14\\\\0.56 \times x = 14\\\\Divide\ 0.56\ to\ both\ sides\\\\x = 14/0.56\\\\x = 25[/tex]

So, there were 25 questions on the test.

[tex]\rule[225]{225}{2}[/tex]

the answer is 14

simply multiply mika age by 2

since the difference is 7

meaning that mika is seven

and twice is 14

Answer:

Step-by-step explanation:

a. The equation for the cost of AT&T would be $100 + $15n, where n is the number of phones on the account. The equation for the cost of Sprint would be $200.

We can graph these equations on a coordinate plane with the x-axis representing the number of phones on the account and the y-axis representing the monthly cost. The graph for the cost of AT&T would be a straight line starting at the point (0,100) and going through the point (1,115), (2,130), etc. The graph for the cost of Sprint would be a horizontal line at the y-coordinate of 200.

b. In order to determine which company would be cheaper for Carly's family, we can simply plug in the number of phones they have (5) into each of the equations we derived in part a. This would give us a cost of $200 for AT&T and $200 for Sprint. In this case, both companies would be equally cheap for Carly's family.

Alternatively, we could graph the equations and see which company's line is lower on the y-axis for the given number of phones (5). This would also show that both companies would be equally cheap for Carly's family in this case.

The given 4th degree polynomial is ,[tex]f(x)=(x+5)(x+1)^2(x-2)[/tex] zeroes of the equation are -5,-1,2

A fourth-degree polynomial, or quartic function, is one that has a variable raised to the fourth power as its highest order term.

If the highest order term is positive or negative, a fourth-degree polynomial's graph will frequently resemble a M or a W.

The function will reach infinity on both sides if the leading term's coefficient, a, is positive.

The function will extend to minus infinity on both sides if the coefficient an is negative.

The function's y-intercept, or the point at which the function crosses the y-axis, is indicated by the word a0. The x-intercepts are revealed by the function's roots.

Inflection Points are roots of double derivate equation.

Given;

From the graph, x-intercepts are -5,-1,2.

That gives us (x+5),(x+1),(x-2) are factors of the function;

As at [tex]x=-1[/tex] graph touches x axis (x+1) is a double factor of f(x)

That leaves us with [tex](x+5),(x+1)^2,(x-2)[/tex] as factors of f(x);

[tex]f(x)=(x+5)(x+1)^2(x-2)[/tex];

From graph inflections points are -2.686,0.186;

That gives [tex]f^|^|(x)=(x+2.686)(x-0.186)[/tex]

The given 4th degree polynomial is ,[tex]f(x)=(x+5)(x+1)^2(x-2)[/tex] zeroes of the equation are -5,-1,2

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The text messages that Rhonda can send and still pay less than a total of $70 is less than 80 messages.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Let the number of tests be represented by t.

The inequality will then be:

50 + 0.25t < 70

0.25t < 70 - 50

0.25t < 20

Divide

t < 20/0.25

t < 80

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