A school needs to buy new notebook and desktop computers for its computer lab. The notebook computers cost $275 each, and the desktop computers cost $150 each. How much would it cost to buy 14 notebooks and 16 desktop computers? How much would it cost to buy n n notebooks and d d desktop computers?

Answer:

Function g(x) has the greater average rate of change over the given interval.

Step-by-step explanation:

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:

[tex]\sf \dfrac{f(b)-f(a)}{b-a}[/tex]

Given:

Therefore, the average rate of change for the function f(x) over the given interval 4 ≤ x ≤ 8 is:

[tex]\sf \implies\dfrac{f(8)-f(4)}{8-4}=\dfrac{14-0}{8-4}=3.5[/tex]

Work out values of function g(x) for x = 4 and x = 8:

[tex]\implies \sf g(4)=2(4)^2+(4)-1=35[/tex]

[tex]\implies \sf g(8)=2(8)^2+(8)-1=135[/tex]

Therefore, the average rate of change for the function g(x) over the given interval 4 ≤ x ≤ 8 is:

[tex]\implies \sf \dfrac{g(8)-g(4)}{8-4}=\dfrac{135-35}{8-4}=\dfrac{100}{4}=25[/tex]

Therefore, function g(x) has the greater average rate of change over the interval 4 ≤ x ≤ 8, as 25 > 3.5.

Angles that are vertical are opposite ones that only have one common vertex.

Two sets of vertical angles result from the intersection of two lines.

When two lines intersect, we obtain two linear pairs, which are two angles that make a straight line.

Knowing one of the angles formed when two lines intersect enables us to determine that the vertical angle, which is the angle directly across from it, has the same measurement.

Additionally, we know that the angle next to it, which creates a linear pair, will be added to it (add to 180), allowing us to discover its measure by subtracting it from 180.

Since they are both vertical angles, the remaining missing angle will be the same as this supplementary angle.

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Answer:

Part A:

(0.20)(10) = (0.05)(x) + (0.40)(10 - x)

Part B:

5.7 litres of 5% and 4.3 litres of 40%

Step-by-step explanation:

Let's assume she will stick with 10 litres in total for her mixture. (Maybe that's the size of her container.)

Let the volume of 5% by x litres.

Therefore the volume of 40% will equal 10 - x.

Reason: 10 litres total, if we use 2 litres of the one, we'll use 8 litres of the other. Get it?

Moving along...

So:

(0.20)(10) = (0.05)(x) + (0.40)(10 - x)

Now we solve the equation...

2 = 0.05x + 4 - 0.4x

2 - 4 = - 0.35x

-2 = -0.35x

let's multiply both sides by 100 to get rid of the decimal

-200 = -35x

x = 200/35

x = 5.7 litres (volume of 5% solution needed)

volume of 40% = 10 - 5.7 = 4.3 litres

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Work below. :)

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First, find a common denominator. You can do so by listing the denominators' factors and finding a common number. (For the sake of space I'll skip).

1/2 = 6/12

3/4 = 9/12

1/3 = 4/12

Now, simply add the top numbers (aka numerator) but keep the denominator the same.

6 + 9 + 4 = 19

19/12 is an improper fraction, so make it proper.

1 7/12

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Good luck!

~pinetreee

The maximum containers Dodi will use will be  3

She plans to store the slime in containers that each hold a maximum of 6 fluid ounces how many containers will she need

number of containers is 3

The time period "equal" in math refers to two meanings, numbers, or quantities which can be the same. The equivalence of two such portions shall be denoted by a bar over an equivalent symbol or equivalent sign. It also means a logical equivalence among  values or a fixed of quantities.

what is a equivalent instance?

The definition of equal is something that is essentially the same or identical to some thing else. An instance of equivalent is (2+2) and the wide variety four. due to the fact that 2+2= 4, these  matters are equal.

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Answer:

f'(1) = -64

Step-by-step explanation:

To find f'(1), we will be finding the f'(x) first which means the first derivative of f(x), we can find the derivative by using chain rule to this function.

The formula of chain rule is:

[tex]\displaystyle f(u) = u^n \to f'(u) = nu^{n-1}\cdot u'[/tex]

In simple explanation, we derive normally (power rule) then multiply by the derivative of inside (u).

Applying the formula, we will have:

[tex]\displaystyle{f'(x)=4(x^2-3)^{4-1}\cdot (x^2-3)'}\\\\\displaystyle{f'(x)=4(x^2-3)^{3}\cdot 2x}\\\\\displaystyle{f'(x)=8x(x^2-3)^{3}}[/tex]

Substitute x = 1 in the f'(x):

[tex]\displaystyle{f'(1)=8(1)(1^2-3)^3}\\\\\displaystyle{f'(1)=8(1-3)^3}\\\\\displaystyle{f'(1)=8(-2)^3}\\\\\displaystyle{f'(1)=8(-8)}\\\\\displaystyle{f'(1)=-64}[/tex]

Answer:

$0.85/lb

Step-by-step explanation:

unit rate = dollar amount / pounds

unit rate = ($18.70)/(22 lb)

unit rate = $0.85/lb

Answer:

.85 per pound

Step-by-step explanation:

Answer:

Her annual salary is $62,400

Step-by-step explanation:

Michelle Hong noticed that her gross pay per period increased by 2,800 when her employer changed from a bi weekly pay plan to a monthly pay plan.

Bi weekly is a check every 2 weeks, so she would get 26 checks per year.

Monthly would be 12 checks per year.

When she gets paid monthly her pay increased by $2,800 each check.

Let x be one bi-weekly paycheck.

The equation we get is:

12(x+2800) = 26x

Multiply the bracket by 12:

12x +33600 = 26x

Subtract 12x from both sides

33600 = 14x

Divide both sides by 14:

x = 33600/14

x = 2400

Her pay increased by 2800 each period:

2400 + 2800 = 5200 per check.

5200 x 12 months = 62400

Her annual salary is $62,400

According to the given statement :

(1/4)c  + 3d= 45/2 when c = 6   & d = 7

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator as well as the denominator of a complex fraction.

Fractions can be used to represent decimals. Place your decimal number above its place value to convert it to a fraction. For instance, since the number six occupies the tenths place in the fraction 0.6, we must multiply it by 10 to get the comparable fraction, 6/10.

Evaluate  (1/4)c  + 3d

when c = 6   & d = 7

x  =  (1/4)c  + 3d

putting c = 6

& d = 7

=> x = (1/4) * 6  + 3*7

=> x = 3/2  + 21

=> x = (3 + 42)/2

=> x = 45/2

=> x = 22.5

=>  (1/4)c  + 3d= 22.5  when c = 6   & d = 7

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since the year 2000, the law no longer permits people to indicate multiple racial identities to the u.s. census but must select just one. The statement is false.

US Census is a typical comprehensive count of a population specifically: an annual population count conducted by the government.

Now,

According to the laws of the US, it is true that the law permits people to indicate multiple racial identities to the US Census, in order to complete the data and determine the population of the States.

Hence, it is false that: since the year 2000, the law no longer permits people to indicate multiple racial identities to the u.s. census but must select just one.

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Answer:

d) 188.64

Step-by-step explanation:

Let's solve the problem,

→ -78.6(-2.4)

→ -78.6 × -2.4

→ 188.64

Thus, option (d) is correct.

Answer:

D. 188.64 is the correct answer!

Step-by-step explanation:

The zero(s) of function f(x) = -4x + 6 is [tex]x=\frac{3}{2}[/tex]

As per the question statement, We are given a function [tex]f(x) = -4x + 6[/tex]   and we are supposed to find the zero(s) of the function.

We know that zero of a function is the value of the function at which the value of function becomes absolute zero.

For that we have to equate the function to zero first.

f(x) indicates the function with variable in "x"

For zero(s), of f(x)

Let f(x) = 0

[tex]f(x) = -4x+6=0\\4x=6\\x=\frac{6}{4} \\x=\frac{3}{2}[/tex]

Therefore value of x at which f(x) is zero is [tex]x=\frac{3}{2}[/tex]

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Answer:

1,218 Inches

101.5 Feet

33.8333333 Yards

Step-by-step explanation:

8 yards is the radius of the base

In linear equations, -6 was in his account then .

What are instances of linear equations?

Kiran had $24 in her account

24-16=8

28-8=20 he deposited $20

he spent $34 on lunches in the next week.

28-34= -6 his account balance was -6

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The complete question is -

At the Beginning of the month Kiran had $24 in his school cafeteria account. Then he spent $34 on lunches in the next week. How much was in his account then?

Answer: about 7300 thousand per month

about 1700 per week

10 an hour? it doesn't sound right but it doesn't go into detail about how many hours he works so i don't know but i hope it helps.

Step-by-step explanation:

The ordered pairs of the solutions for this system of equations is (-2,11) and (-1,6)

Two integers written in a certain order make up an ordered pair. As a result, we may define an ordered pair as a pair of components that appear in brackets and in a specific order.

These equations are composed of a line and a parabola. The intersection points between them must be located:

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

y=-5x+1

Thus,

[tex]x^2-2x+3=-5x+1[/tex]

[tex]x^2-2x+5x+3-1=0[/tex]

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

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

[tex]x(x+1)+2(x+1)=0[/tex]

x+2=0, x=-2

x+1=0, x=-1

Since the quadratic expression may be factored out, the following x-values represent the system's solution:

x=-2 and x=-1

Now, we may obtain the corresponding y values using either of the system's original equations. We decide to use a linear equation as an illustration:

When x =-2,

y=11

x=-1,

y=6

Thus the two points solution us (-2,11) and (-1,6)

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Answer:

400

Step-by-step explanation:

The possibility that something will occur, prior measures, and conventional objective measurements all influence the likelihood that something will occur.

What is probability and what types are there in total?

The study of probability is a field of mathematics that determines the probability of an event occurring, which is represented by a number between 1 and 0. When an event has a probability of 1, it can be said to be a certainty. For instance, if the coin lands flat, the likelihood that it will come up  "heads or  tails" is 1. There are no other possible outcomes. A probability of .5 indicates that there is an equal chance that an event will occur or not.

Probability can be quantitatively represented in the simplest form as follows: the total number of possible outcomes multiplied by the ratio of the number of occurrences of a targeted event divided by the sum of the occurrences and failures of occurrences:

P(a) = P(a)/[P(a) + P(b)]

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Answer: i knew this before but i forgot

Step-by-step explanation:

.

Outliers are any observations that fall more than 1.5 IQR below Q1 or more than 1.5 IQR above Q3.

Outliers:

While observing the data in the observations some of data may fall outside the general scope of the other observations. Such observations are called outliers.

Given,

An outlier is an observation which is less than IQR or greater than Q3 times IQR.

Here we need to find in Q1 and Q3 place variations.

When we use the IQR method of identifying outliers to set up a “fence” outside of Q1 and Q3.  Any values which fall outside of the identified  fence are considered outliers.

To build this fence we take 1.5 times the IQR and then subtract this value from Q1 and add this value to Q3.

Like,

IQR = (1.5 - Q1)

IQR = (1.5 + Q3)

This gives us the minimum and maximum fence posts that we compare each observation to.

Therefore, any observations that are more than 1.5 IQR below Q1 or more than 1.5 IQR above Q3 are considered outliers.

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Answer:

remember: we are rounding!

313 × 489

Where 313 ≈ 300

Where 489 ≈ 500

Step-by-step explanation:

300 × 500 = 150,000 because 3 × 5 = 15

Hope this helps!

Since, we have to find the sides of the given triangle we will make it a right angle triangle.

Construction: Extend XY to 1 unit and name it Z and join the point W with Z.

Now, the triangle YWZ is a right angle triangle where

YZ = 1 unit

WZ = 3 units

Then [tex]WY = \sqrt{(YZ)^{2}+ (WZ)^{2} }[/tex]     [By Pythagoras Theorem]

= [tex]WY = \sqrt{(1)^{2}+ (3)^{2} }[/tex]

= [tex]WY = \sqrt{(10) }[/tex]

= [tex]WY = 3.16[/tex] units

Now, the triangle XWZ is also a right angle triangle where

XZ = 3 units

WZ = 3 units

Then [tex]WX = \sqrt{(XZ)^{2}+ (WZ)^{2} }[/tex]    [By Pythagoras Theorem]

= [tex]WX = \sqrt{(3)^{2}+ (3)^{2} }[/tex]

= [tex]WX = \sqrt{18[/tex]

= [tex]WX =4.23[/tex] units

Now, In triangle XYW

XY = 2 units

WY = 3.16 units

WX = 4.23 units

∴ The perimeter of the triangle XYW will be

XY + WY + WX

= 2 + 3.16 + 4.23

= 9.39 units

To the nearest hundred, 9.39 rounds to 9

⇒ The perimeter of the triangle XYW is 9 units.

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Answer:

124.67 feet per second

Step-by-step explanation:

First: multiply the feet per mile by the amount of miles that the car is going in order to get the feet per hour

5280 x 85 = 448,800

Second: divide the answer from the first step by 60 in order to get the number of feet per minute

448,800 ÷ 60 = 7480

Third: divide the answer from the second step by 60 in order to get the number of feet per second

7480 ÷ 60 = 124.67

Answer:

27 28 29

Step-by-step explanation:

Let the first be n , and if they are consecutive then the next two numbers are n+1 and n+2.

n+(n+1)+(n+2)=84.

3n+3=84.

⇒3n=81.

⇒n=27.

Hence numbers are n,n+1,n+2→27,28 and 29

Answer:

= 6(4 + 5)

Step-by-step explanation:

GCF = The greatest common factor, example: GCF of 12 and 16 = 12 is divisible by all of these numbers. The factors for 16 are 1, 2, 4, 8, 16. The two numbers (12 and 16) share common factors (1, 2, 4). The greatest of these is 4 and that is the greatest common factor.

Distributive property = allows us to multiply the number by a group of numbers, which are added together. The distributive property is given by: a(b+c) = ab + ac

The Greatest Common Factor of 24 and 30 is 6 because it is the largest number they have together (24 = 6*4 and 30 = 6*5)

24 divided by 6 = 4

30 divided by 6 = 5

This fits B the most: 6(4 + 5)

Step-by-step explanation:

Answer:

35

Step-by-step explanation:

There 3 sides of a triangle.There are three corners called verticals in a triangle.So you will need to add 62+45=107.The you need to divide.107/3=35.

Hope this helps you

The length of the mural is 75 feet.

From the information, it was stated that a 2:15 scaled pattern for a mural is 10 feet long.

Therefore, the length of the mural will be:

= 10 ÷ 2/15

= 10 × 15/2

= 75

Therefore the length of the mural is 75 feet

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