Charlie used a regression calculator to generate the
equation f(x) = -0.15x + 20.1 for the ordered pairs (2,
15), (4, 21), (6, 26), (8, 20), and (10, 14).
Is a linear representation the best way to represent the
data? If it is, explain why. If not, explain why and suggest
a better alternative.

Answer:

HE will have 10 fingers

Step-by-step explanation:

Answer: A. 80.61

Step-by-step explanation:

Answer:

what region

Step-by-step explanation:

The solutions to quadratic equation are:

[tex]x = \frac{3 + i \sqrt{3}}{2}\\\\x = \frac{3 - i \sqrt{3}}{2}[/tex]

Solution:

Given is:

[tex]x^2 - 3x + 3 = 0[/tex]

We have to find the solutions to quadratic equation

[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\mathrm{For\:}\quad a=1,\:b=-3,\:c=3:\\\\x=\frac{-\left(-3\right)\pm \sqrt{\left(-3\right)^2-4\cdot \:1\cdot \:3}}{2\cdot \:1}[/tex]

[tex]x=\frac{3 \pm \sqrt{\left(-3\right)^2-4\cdot \:1\cdot \:3}}{2\cdot \:1}\\\\x = \frac{3 \pm \sqrt{-3}}{2}\\\\x = \frac{3 \pm i \sqrt{3}}{2}[/tex]

We have two solutions :

[tex]x = \frac{3 + i \sqrt{3}}{2}\\\\x = \frac{3 - i \sqrt{3}}{2}[/tex]

The solutions to the quadratic equation x^2 - 3x + 3 = 0 can be found using the Quadratic Formula. The solutions are complex numbers: x = 3/2 ± (i*sqrt(3))/2.

The given equation is a quadratic equation of the form ax^2 + bx + c = 0. To find the solutions to this equation, we can use the Quadratic Formula: x = [-b ± sqrt(b^2 - 4ac)] / (2a).

Here a=1, b=-3, c=3.

Plugging these values into the formula,

we get x = [3 ± sqrt((-3)^2 - 4*1*3)] / (2*1).

Simplifying this equation will give us x = [3 ± sqrt((9 - 12)] / 2.

Now, note that the value under the square root is negative, indicating that the solutions will be complex.

Finally, we have the solutions:

x = [3 ± sqrt(-3)] / 2

= 3/2 ± (i*sqrt(3))/2, where 'i' is the imaginary unit.

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Answer:

6

Step-by-step explanation:

The question might be trying to be tricky. If Prince Humperdinck has 17 henchmen and ALL BUT 6 die. That means that 6 are alive.

Answer:

12% decrease

Step-by-step explanation:

think of 1000 as 100% and thin 880 as 88% subtract those 12%

The price decrease from $1000 to $880 represents a 12% decrease. This is figured out by taking the difference in price, dividing it by the original price, and then multiplying by 100%.

The percentage decrease is calculated by taking the difference in price divided by the original price, and then multiplying by 100 to get a percentage. In this case, the difference in price is the original price minus the sale price. This would be $1000 - $880 = $120. So, the formula would be ($120/$1000)*100. The calculated percentage decrease is 12%, meaning the price of the TV has been reduced by 12%.

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Answer:

x = 32

Step-by-step explanation:

Step 1:  Subtract 12 from both sides

x/8 + 12 - 12 = 16 - 12

x/8 = 4

Step 2:  Multiply both sides by 8

x/8 * 8 = 4 * 8

x = 32

Answer:  x = 32

Answer:

Step-by-step explanation:

[tex]\frac{x}{8}+12=16\\\\\frac{x}{8}=16-12\\\\\frac{x}{8}=4\\\\x=4*8\\\\x=32[/tex]

Answer:

6x-15 = 4x+12

Step-by-step explanation:

3*2x = 6x

3*-5 = -15

4*x=4x

4*3=12

6x-15 = 4x+12

Answer:

6x - 15 = 4x + 12

Explanation:

Simplify 3 * 2x = 6x. 3 * -5 =  -15. 4 * x = 4x. And 4 * 3 = 12. Then just put 'em together! :D

five acute angles: the rest of this text does not matter.

Answer:

$35

Step-by-step explanation:

To solve this problem you need to know how what and how is percentage work.

Percentage(%) is a unit that equals to 1/100 or one hundredths. So, 7% will be equal to 7*1/100= 7/100. The commission is given based on the price of the boat. If the boat sold at $500 the commission will be:

commission= percentage * boat price

commission= 7/100 * $500

commission= $35

Answer:

A

Step-by-step explanation:

The cookies ordered is the dependent quantity/variable because the other variables don't depend on anything that is quantifiable.

The dependent quantity in this functional relationship is A. The number of cookies ordered.

A dependent quantity simply refers to the quantity that depends on another quantity or is determined by another quantity.

Based on the information given, the dependent quantity in this functional relationship is the number of cookies ordered since it depends on other factors such as the number of trays and students.

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Square B

The complete question is written in a comment above. The doctor's office where you work needs to store eight filing cabinets with patient information in one of three secure storage rooms. We know that the filing cabinets need a total of 55 square feet of space. You need to identify in which room the filing cabinets will fit. So we have three rooms:

FIRST OFFICE:

[tex]Square \ A = 8 \times 5[/tex]

In other words, for this room we have the following area:

[tex]Square \ A =40ft^2[/tex]

SECOND OFFICE:

[tex]Square \ B = 9 \times 7.5[/tex]

In other words, for this room we have the following area:

[tex]Square \ B =67.5ft^2[/tex]

THIRD OFFICE:

[tex]Square \ C = 5 \times 10[/tex]

In other words, for this room we have the following area:

[tex]Square \ C =50ft^2[/tex]

How can we know what is the room we need to choose?

Well, the room we need to choose is the one whose area is greater than the area of the filling cabinets. In other words, let's call square x the unknown room, then:

[tex]Square \ x>55ft^2[/tex]

From the, choices the only room that meets our requirements is square B because:

[tex]Square \ B>55ft^2 \\ \\ 67.5ft^2>55ft^2[/tex]

Measure the length and width of a room in feet to calculate its area. Multiply these dimensions to get the area in square feet. The filing cabinets need a room with at least 55 square feet.

To determine whether the filing cabinets will fit into a room, we must calculate the area of the room and see if it is at least 55 square feet, the space required for the filing cabinets.

To calculate the area of a room in square feet, measure the length and width of the room in feet and then multiply these numbers together.

For example, if a room is 10 feet wide and 5.5 feet long, its area would be 10 feet times 5.5 feet, which equals 55 square feet. Therefore, the filing cabinets would fit in a room of this size.

Both expressions (20 – 4) – 2 and 20 – (4 – 2) are equivalent, simplifying to 14. The equivalence exemplifies the Associative Property of Addition.

The question asks to determine whether the two expressions (20 – 4) – 2 and 20 – (4 – 2) are equivalent, and if so, to identify the property applied. To determine equivalence, we need to simplify both expressions. The first expression, (20 – 4) – 2, simplifies to 16 – 2 which equals 14. The second expression, 20 – (4 – 2), simplifies to 20 – 2 which also equals 14. Therefore, both expressions are equivalent, and the property applied here is the Associative Property of Addition, which allows us to change the grouping of the numbers we're adding (or subtracting, in this case) without changing the result.

Answer:

[tex]0.125 \ in^3[/tex]

Step-by-step explanation:

Given the sides of the cube as 0.5 inch.

#the volume of a cube is calculated as the product of the three sides:

[tex]V=s^3, \ \ \ \ s=0.5in\\\\V=0.5\ in\times 0.5\ in\times 0.5\ in\\\\V=(0.5\ in)^3\\\\V=0.125\ in^3[/tex]

Hence, the volume of Mary's cube is 0.125 cubic inches

Answer:

Step-by-step explanation: first multiply 342 and 135

then put the decimal just before the ones digit.

answer is

4617.0

please mark  as brainliest

Answer:

$486

Step-by-step explanation:

Step 1:  Solve

(450 * 0.9) * 1.2

405 * 1.2

486

Answer:  $486

x = 7 and x = –7.

Solution:

Given data:

[tex]$f(x)=x^{2}+15[/tex] and [tex]f(x)=64[/tex]

To find the solutions when f(x) = 64.

Both are equations of f(x), so equate the given equations, we get

[tex]x^2+15=64[/tex]

To isolate the constant term subtract 15 from both sides.

[tex]x^2+15-15=64-15[/tex]

[tex]x^2=49[/tex]

49 can be written as 7².

[tex]x^2=7^2[/tex]

Taking square root on both sides of the equation, we get

x = ±7

The solutions to f(x) = 64 is x = 7 and x = –7.

The length of SK = 10 units while the length of BK = 8.6602 units.

Step-by-step explanation:

Step 1:

In the given triangle, there are two right-angles triangles with 60° angles. The central line BK is the opposite side for both the triangles. For triangle RK the hypotenuse's length is 10 m. Assume BK = x units and SK = y units.

Step 2:

So first we calculate the length of BK (x).

As we have the values of the angle of the triangle and the hypotenuse, we can calculate the sine of the angle to determine the value of x.

[tex]sin R = \frac{oppositeside}{hypotenuse}, sin 60 = \frac{x}{10}.[/tex]

[tex]sin 60 = 0.86602, x = 0.86602 (10) = 8.6602 units.[/tex]

So x = BK = 8.6602 units.

Step 3:

So now we calculate the length of SK (y).

As we have the values of the angle of the triangle and the opposite side's length, we can calculate the sine of the angle to determine the value of y.

[tex]sin S = \frac{oppositeside}{hypotenuse}, sin 60 = \frac{86.602}{y}.[/tex]

[tex]sin 60 = 0.86602, y = \frac{8.6602}{0.86602} = 9.999units = 10 units[/tex]

So y = SK = 10 units.

Answer: the man is 58!

Step-by-step explanation: please mark brainliest

we could use this equation

168=400-4a         an a= uknown age

-400     -400

-232=-4a

divide by -4 on both sides to get the variable by itself

58=a

a=58

and to double check we can do this

168=400-4(58)     by susbtuting the variable

168=400-232

168=168     correct

Answer:

x = 4, y = -5 OR (4, -5)

Step-by-step explanation:

Step 1:  Solve for y in the first equation

2x + y - 2x = 3 - 2x

y = 3 - 2x

Step 2:  Plug in that into the second equation to get x

4x + 3(3 - 2x) = 1

4x + 9 - 6x = 1

-2x + 9 - 9 = 1 - 9

-2x / -2 = -8 / -2

x = 4

Step 3:  Use x to find y

y = 3 - 2(4)

y = 3 - 8

y = -5

Answer:  x = 4, y = -5 OR (4, -5)

8320 cubes can fit into the prism.

Solution:

Convert mixed fraction into improper fraction.

Length of the prism = 20 in

Width of the prism = 2 in

Height of the prism = [tex]3\frac{1}{4}=\frac{13}{4}[/tex] in

Volume of the prism = length × width × height

                                 [tex]$=20\times2\times\frac{13}{4}[/tex]

                                 = 130 in³

Volume of the prism = 130 in³

Length of the cube = [tex]\frac{1}{4}[/tex] in

Volume of the cube = length × length × length

                                 [tex]$=\frac{1}{4} \times\frac{1}{4} \times\frac{1}{4}[/tex]

                                 [tex]$=\frac{1}{64} \ \text{in}^3[/tex]

Volume of the cube = 0.015625 in³

[tex]$\text{Number of cubes}=\frac{\text{Volume of the prism}}{\text{Volume of cube}}[/tex]      

                            [tex]$=\frac{130}{0.015625}[/tex]

                            = 8320

Number of cubes = 8320

Hence 8320 cubes can fit into the prism.

Step-by-step explanation:

Given:

Number of packets at the beginning of the day, Nb = 36 packets

Number of packets at the end of the day, Ne = 8 packets

A.

Number of packets sold, Ns = Nb - Ne

36 - Number of packets sold, Ns = Ne

8 = 36 - Ns

Ns = 28

B.

8 = 36 - Ns

8 = 36 - 28

Final answer:

The expression representing the number of juice boxes sold is 28 multiplied by x, where x is the number of juice boxes per package. Since x is unknown, the expression cannot be simplified further and remains as 28 × x.

Explanation:

Part A: Representing the Number of Juice Boxes Sold

To represent the number of juice boxes sold, let's denote the number of juice boxes in each package as x. The store started with 36 packages and ended with 8. We are looking for the number of juice boxes in the packages that were sold. The expression is:

28 × x (since 36 - 8 = 28, and 28 packages were sold)

Part B: Simplifying the Expression

To simplify the expression, we do not have further information to simplify 28 × x more because x represents an unknown number of juice boxes per package. The simplified expression remains as:

28 × x

48=4x can be used to determine the miles covered by Trisha that is 12 miles.

Total distance covered comprises the sum of distances covered by individual entities. Sum means adding like terms in mathematics.

Given, the total number of miles covered by both of them, t= 48 miles

If miles covered by Trisha = x

Then, miles covered by Brandy = 3x (as Brandy drove three times as far as Trisha ).

The total distance covered comprises miles covered by Trisha as well as Brandy.

t=x+3x

On adding the like terms.

t=4x

Substituting t=48,

48=4x

Dividing 4 both sides of the equation,

48/4=4x/4

12=x

x=12 miles

So, the Number of miles Trisha drove is 12.

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Hey there!

This is slope intercept form, where y=mx+b, where b is the y-intercept (where the line hits the y-axis) and the slope (rate of change).

If you wanted to graph this line, we can see that the y intercept in 35. Therefore, our line is going have one point on (0,35). Our slope is 15, which is positive, showing that our line will go up. Because the slope is fifteen, for every single increase of 1 there is in x, there will be an increase of 15 in y. This will give us points like (1,15) (2,30) (3,45). Therefore, this will be a very steep line.

You can use this info to graph your line.

Answer:

PLS PASS BRAINLIEST

Step-by-step explanation:

put the first point on 35 on y axis

now count 15 from 35 which is 50 and move one to the right

which is (50,1)

and keep on reapeting that

Answer: 8 tablespoons

Step-by-step explanation:

If 1 doz muffins= 4 teapoons = 4/3 tablespoon

6 dozens muffin= 4/3 × 6

24/3 = 8 tablespoon

Answer:

8 tablespoons

Step-by-step explanation:

Answer: 2^4+7 -5^3

Step-by-step explanation:

Answer:

(2 to the power of 4 )plus 7 minus( 5 to the power of 3)

Step-by-step explanation:

Answer:

Part A) The graph in the attached figure

Part B) see the explanation

Step-by-step explanation:

Part A) Graph the function

we have the quadratic function

[tex]y=3x^2-12x-36[/tex]

This is a vertical parabola open upward

The vertex is a minimum

using a graphing tool

The graph in the attached figure

Part B) What are the values of a, b and c?

we know that

The values of a and b represent the x-intercepts of the quadratic equation

The x-intercepts are

(-2,0) and (6,0)

so

[tex]a=-2\\b=6[/tex]

Find the value of c

we know that

The x-coordinate of the vertex in a vertical parabola is equal to the midpoint of the roots

so

The value of c is equal to

[tex]c=\frac{a+b}{2}[/tex]

substitute the given values

[tex]c=\frac{-2+6}{2}=2[/tex]

see the attached figure