A school had 1 200 students last year and only 1 080 students this year.
What was the percent decrease in the number of students?

Answer:

x=5

Step-by-step explanation:

Follow the steps in the image.

-Hope this helped

Answer:

(-4,-1) and (3,1), respectively.

Step-by-step explanation:

I am not quite sure if the question is necessarily asking for this, but the x and y values are switched to get the points of the inverse. (-1,-4) --> (-4,-1) and (1,3) --> (3,1). I hope that makes sense!

The solution to the expression given as 5x + 3y > 12 has the ordered pair of (3, 0)

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

5x + 3y > 12

Solving further, we need to collect the like terms

So, the expression becomes

3y > 12 - 5x

Next, we divide through the inequality by 3

So, we have the following representation

y > 12/3 - 5/3x

Evaluate

The equation becomes

y > 4 - 5/3x

At this point, we assume any value for x and then solve for y

Assume that the value of x is 3

So, we have the following representation

y > 4 - 5/3 * 3

Evaluate the products

y > -1

A value greater than -1 is 0

So, we have

x = 3 and y = 0

Express as ordered pairs

(x, y) = (3, 0)

Hence, the ordered pair of the solution is (3, 0)

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The number of soda bottles the machine can make each minute = 40

In this question, we have been given the graph shows the relationship between time and the number of soda bottles a machine can make.

Also, we have been given two points ​(​4,160​) and ​(6​,​240)

We need to find the number of soda bottles the machine can make each minute.

i.e., we need to find the slope of line passing through points  ​(​4,160​) and ​(6​,​240)

Using the formula of slope,

m = (240 - 160) / (6 - 4)

m = 80/2

m = 40

Therefore, the number of soda bottles the machine can make each minute = 40

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Answer:Use the slope-intercept form to find the slope.

m=4

The equation of a perpendicular line to

y

=

4

x

−

9

must have a slope that is the negative reciprocal of the original slope.

m

perpendicular

=

-1/4

Step-by-step explanation:

hii lily how are u

Answer: f(4) = -171

Step-by-step explanation:

      To answer this question, we will solve the function for 4. In other words, we will input 4 into the function and simplify. Don't forget the order of PEMDAS when simplifying.

Given:

     f(x) = -11x² + 5

Input of 4:

     f(4) = -11(4)² + 5

Raise to the power of 2:

     f(4) = -11(16) + 5

Multiply:

     f(4) = -176 + 5

Add:

     f(4) = -171

The probability that the component requires both painting and galvanizing is 0.06.

Considering the values provided in the question,

P(Painted) = 0.20

P(Galvanized) = 0.30

Both the events are independent of each other.

The probability of the part needs both painted and galvanized is

= P(Painted and Galvanized)

= P(Painted) × P(Galvanized)

= 0.20 × 0.30

= 0.06

Therefore, The probability of the part needs both painted and galvanized is 0.06.

The possibility of an event happening is determined by probability. We may need to forecast an event's result in a variety of real-world circumstances. The outcomes of an event may be certain or uncertain to us. In these circumstances, we say if there is a chance the event will happen or not.

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Answer:

26x-56y

Step-by-step explanation:

First you open the bracket and collect like terms

55x-29x-46y-10y

26x-56y

The unit of price per oz = 114.2

According to our question-

the price of a 2 liter bottle of sprite holds 67.6 oz

and costs $3.38.

2 = 67.6

67.6/2= 33.8

33.8*3.38= 114.24

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Answer: K 35

Step-by-step explanation:

We're given the inequality : 15n < 580.5

Divide both sides by 15.

-> 15n : 15 < 580.5 : 15
-> n < 38.7

Therefore, the final inequality is : n < 38.7

The volume of the cone is 15393.80 cm³

The curved surface area of a cone is 4068.36 cm²

The total surface area of the cone is 7916.81 cm²

Given parameters;

The base radius( r ) of the cone is 35cm

The height( h ) of the cone is 12cm

Case (I): To find the volume of the cone;

The volume of the cone = [tex]\pi r^{2}\frac{h}{3}[/tex]

                                        = π *(35)² * 12/3

                                        = 15393.80 cm³

Case (II): To find the curved surface area of the cone;

The curved surface area of the cone = πrl

We know that;

Slant height l = [tex]\sqrt{(r^2 + h^2)}[/tex]

By substituting the values;

l = [tex]\sqrt{35^2 + 12^2}[/tex]

l = 37

We know that;

The curved surface area of a cone = πrl

                                                          = π * 35 *37

                                                          = 4068.36 cm²

Case (III): The total surface area of the cone;

The total surface area of the cone = πr(l + r)

                                                         = π * 35 * (37 + 35)

                                                         = 7916.81 cm²

Therefore,

The volume of the cone is 15393.80 cm³

The curved surface area of a cone is 4068.36 cm²

The total surface area of the cone is 7916.81 cm²

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The person from the 4 people that will reach his or her goal is Friend C.

Friend A: Works 6 hours per week at $13.90 per hour. The amount in 8 weeks will be:

= 6 × $13.90 × 8

= $667.2

b) Friend B: Works 7.5 hours per week at $11.70 per hour. The amount in 8 weeks will be:

= 7.5 × 11.70 × 8

= $702

c) Friend C: Works 9 hours per week at $10.50 per hour. The amount in 8 weeks will be:

= 9 × $10.50 × 8

= $756

d) Friend D: Works 5.5 hours per week at $15.60 per hour. The amount in 8 weeks will be:

= 5.5 × $15.60 × 8

= $686.40

In this case, C had $756 which is above the amount needed.

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Sophie's favorite number is 83

We have that;

A two-digit number is Sophie's preferred number. Her favorite number is 45 less when the digits are in reverse. Her favorite number has digits that add out to 11 in total.

To get Sophie's favorite number, we need to assume the case as;

Let,

⇒10x + y = 10y + x + 45

   x + y = 11

   y = 11-x

⇒10x + 11 - x = 10(11 - x) + x + 45

  10x + 11 - x = 110 - 10x + x + 45

  9x + 11 = 155 - 9x

  18x + 11 = 155

  18x = 144

  x = 8

Therefore, y = 11 - 8

                  y = 3

Sum = x + y = 8 + 3 = 11

Hence, the given condition is satisfied.

Sophie's favorite number is 83.

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9% of the volume of the original volume is removed.

Given that the dimensions of solid box is 15 cm by 10 cm by 8 cm.

So the volume of solid box = 15*10*8 cubic cm = 1200 cubic centimeter

The volume of the cube with side 3 cm = 3*3*3 = 27 cubic centimeter

For each corner one cube so the number of cube is 4

So total volume removed = 4*27 = 108 cubic centimeters

The percent of volume is removed = (108/1200)*100% = 9%

Hence the percentage of volume removed is 9%.

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Prior to cellular radio, mobile radio and telephone services required

a. high-power transmitter/receiver.

A radio transmitter, also known as a transmitter, is an electronic device that generates radio waves using an antenna in electronics and telecommunications. The transmitter generates alternating current with a radio frequency that is applied to the antenna. The antenna emits radio waves when it is excited by this alternating current.

Typically, the term transmitter refers to equipment that generates radio waves for communication or radiolocation, such as radar and navigational transmitters. Even though they frequently use similar circuits, radio wave generators for heating or industrial purposes, such as microwave ovens or diathermy equipment, are not typically referred to as transmitters.

Transmitters are required components of all radio-communication devices, including radio and television broadcasting stations, cell phones, walkie-talkies, wireless computer networks, and Bluetooth-enabled devices.

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Answer:

-0.67

Step-by-step explanation:

What is the slope of the line created by this equation? Round your answer out to the two nearest decimal places. 6x + 9y = 1

_____________________________________________

Slope intercept form solves for y:

y = mx + b when m = slope and b = y-intercept

First, solve for y:

6x + 9y = 1

subtract 6x from both sides:

6x + 9y - 6x = 1 - 6x

9y = 1 - 6x

divide both sides by 9:

9y/9 = (1 - 6x)/9

y = 1/9 - 6/9x

reduce right side:

y = 1/9 - 2/3x

rearrange right side:

y =  - 2/3x + 1/9

Back to the equation: y = mx + b when m = slope and b = y-intercept

your slope is -2/3

in decimal form, rounded to two digits: -0.67

Answer:I am not fully going to do it for you, but here is the best way i can explain, it if not i am sorry.

Step-by-step explanation: Simply take the sales price minus the unit cost, and divide that number by the unit cost. Then, multiply by 100 to determine the markup percentage. For example, if your product costs $50 to make and the selling price is $75, then the markup percentage would be 50%: ( $75 – $50) / $50 = . 50 x 100 = 50%.

The only correct option that is minimized by the least squares regression line is. Option B the sum of the squared residuals.

lets check all the option -

Option A - This claim is untrue because the residuals' summation would provide a value of 0.

Option B - Because error must be kept to a minimum, the residuals must sum to zero and the line must be as close to the points as possible. Prior to summing them, we must first square the residuals, which will always result in a positive value. This option is accurate since the Least Square Regression Line minimizes the total of residuals.

Option C - This choice is incorrect because the least squares regression line cannot be created by adding the absolute values of the residuals.

Option D - This alternative is incorrect since the influence of outliers has nothing to do with the subject at hand.

Option E - Due to slope's lack of relevance to the subject at hand, this choice is also incorrect.

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Answer:

~62.35°

Step-by-step explanation:

To find the degree of an angle from side lengths, use reverse trigonometric function.

arcsin, arccos, arctan / [tex]sin^-1, cos^-1, tan^-1[/tex]

Because we have adjacent and opposite, lets use arctan.

Set up the equation.

[tex]x = arctan\frac{21}{11}[/tex]

Use a calculator to solve.

The solution to the expression is given as 3 exponent 4 x (20.3 - 9) + 14.5 is 929.8

From the question, the expression is given as

3 exponent 4 x (20.3 - 9) + 14.5

When the expression is rewritten, we have the following representation

3⁴ x (20.3 - 9) + 14.5

Evaluate the exponent

So, we have

3⁴ x (20.3 - 9) + 14.5 = 81 x (20.3 - 9) + 14.5

Evaluate the expression in the bracket

3⁴ x (20.3 - 9) + 14.5 = 81 x 11.3 + 14.5

Solving further, we have

3⁴ x (20.3 - 9) + 14.5 = 915.3 + 14.5

Lastly, we have

3⁴ x (20.3 - 9) + 14.5 = 929.8

Hence, the solution is 929.8

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The scale on the map is of 1 mile: 0.477 inches.

From the question, we have

65 miles - 31 inches

1 mile - x inches

Applying cross multiplication:

65x = 31

x = 31/65

x=0.477

The ratio of inches on a map to feet, miles, or another unit of measurement on the ground is known as the scale.

Scale (map):

The ratio between a distance on a map and its actual distance on the ground is known as the map's scale. Since scale must vary across a map due to the curvature of the Earth's surface, this straightforward idea is made more difficult. This change makes the idea of scale significant in two different ways.

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Answer:

The decemial is 7

Step-by-step explanation:

0.7. Because 04 plus 0.3 equal to 0.7

The half-life of this sample is 535.1 days.

Half-life is defined as the time it will took a substance to reduce to half of its initial amount. The half-life of a substance is determined with respect to the rate of the reaction. It can be calculated using the formula below.

N(t) = N₀(1/2)^(t/T)

where N(t) = amount of substance remaining after time t

N₀ = initial amount of substance

t = time

T = half-life

If a sample of a certain substance decayed to 67.8% of its original amount after 300 days, then N(300) = 0.678N₀.

Plug in the given values to the equation.

N(t) = N₀(1/2)^(t/T)

0.678N₀ = N₀(1/2)^(300/T)

0.678 = (1/2)^(300/T)

T = 535.1 days

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The probability of an event is given by dividing the favorable outcomes by total number of outcomes. The sum of all the probabilities of events is always 1.

The probability that 2 red cards and 11 black cards are dealt is .

The probability of an event is given by dividing the favorable outcomes by total number of outcomes. The sum of all the probabilities of events is always 1. If for finding probability we have to select r out of n. Combination is used to select r items out of n, the formula is as follows,

[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

Finding the probability that 2 red cards and 11 black cards are dealt,

Number of favorable outcomes will be [tex]^{26}C_2\times^{26}C_{11}[/tex].

Total number of outcomes will be [tex]^{52}C_{13}[/tex]

Now, the probability will be,

[tex]P()=\frac{^{26}C_2\times^{26}C_{11}}{^{52}C_{13}} \\\\=\frac{325\times7726160}{635013559600} \\\\=0.00395[/tex]

Therefore, the probability that 2 red cards and 11 black cards are dealt is 0.00395.

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[tex]\fbox{1.333333}[/tex]

[tex]4\frac{2}{15} \div3.1[/tex]

Simplify:

[tex]4\frac{2}{15} \div3.1[/tex]

[tex]=1.333333[/tex]

let's firstly convert the  mixed fraction to improper fraction and the decimal one to a fraction.

[tex]\stackrel{mixed}{4\frac{2}{15}}\implies \cfrac{4\cdot 15+2}{15}\implies \stackrel{improper}{\cfrac{62}{15}}\hspace{10em} 3.\underline{1}\implies \cfrac{31}{1\underline{0}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{62}{15}\div \cfrac{31}{10}\implies \cfrac{62}{15}\cdot \cfrac{10}{31}\implies \cfrac{62}{31}\cdot \cfrac{10}{15}\implies \cfrac{2}{1}\cdot \cfrac{2}{3}\implies \cfrac{4}{3}\implies 1\frac{1}{3}[/tex]

The level of water in the swimming pool after a specified duration of the water draining at a constant rate is found as follows;

10. a. The water level is changing (reducing) at a rate of 1.75 inches per hour.

b. After 9 hours, the change in the water ls 15.75 inches

c. The change in the water level after 23 hours is 40.25 inches

A constant rate is a rate that is fixed or steady and does not vary following a change of the other variables?

The table of values for the draining swimming pool obtained from a similar question on the internet is as follows;

Hours Draining  [tex]{}[/tex]           Change in Water Level (inches)

2   [tex]{}[/tex]                                   -35

9  [tex]{}[/tex]                                     ?

17  [tex]{}[/tex]                                    -29.75

23  [tex]{}[/tex]                                    ?

The relationship between the hours the swimming pool drains and the water level is a proportional relationship., such that the ratio of each coordinate pair in the table is a constant.

Let H represent the hours draining and let C represent the change in water level, we have;

C ∝ H

C = k·H
[tex]k = \dfrac{C}{H}[/tex]

Where;

k = The constant of proportionality, which is the rate at which the water level is changing per hour

a. The rate at which the water level changes per hour can be found from the first pair of points on the table as follows;

The first pair of points = (2, -3.5)

[tex]k = \dfrac{-3.5}{2} = -1.75[/tex]

The rate at which the water level is changing per hour is -1.75 inches per hour

The water level is decreasing at 1.75 inches per hour

b. The change in water level after 9 hours is found by using the formula;

C = k × H

Where, H = 9, we have;

Change in water level, C = -1.75 × 9 = -15.75

The change in water level after 9 hours is 15.75 inches

c. The change in water level after 23 hours is found by plugging in H = 23 as follows;

C = -1.75 × 23 = -40.25

The change in water level after 23 hours is -40.25 inches

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( 0 , -1 , 5) point lies on xyz plane .

The xy-plane is the plane that houses the x- and y-axes, while the yz-plane and the xz-plane house the y- and z-axes, respectively. Space is divided into eight sections known as octants by these three coordinate planes. The positive axes determine the first octant, which is in the front.

To be expressed, everything needs a perspective and a point of view. The three spatial dimensions are represented by the X, Y, and Z coordinates. These stand for length, width, and depth. We employ the same X, Y, and Z denotations when referring to machines, but we assign them different values or meanings. Even more intriguingly, there are no clear laws defining the meaning, which makes it difficult to converse on these levels.

this given point lies on xyz plane bcz the point itself shows coordinates which is only possible in xyz plane .

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The new x-coordinate must be 2-2 = 0.

acc to our question-

Finding the distance between the known endpoint and the midpoint, then applying the same transformation to the midpoint, is the quickest technique to locate the missing endpoint. The x-coordinate changes in this situation from 4 to 2, or down by 2, hence the new x-coordinate is 2-2 = 0.

Hence,The new x-coordinate must be  = 0.

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Answer:

Step-by-step explanation:

Thevalueof theAC segmentknown asthe AB and BC segmentsis:

AC = 12x + 2y + 18

What is a segment?

It is the distance or vector obtained from the sum of the differences of the coordinates of the ends of that segment.

AB = B - A

What are mathematical operations?

They are those such as addition, subtraction, multiplication and division, being the most basic and also have the roots, exponents, among others ...

Thesumis addition to one number to another.

Subtraction is subtractingone number from another.

Multiplicationis adding the same number as many times as the multiplier indicates.

Divisionis the decomposition or separation of one number from another.

What is the value of AC?

Assume that AC is the length of the segment containing AB and BC.

AC = AB + BC

Being;

AB= 8x + 2y

BC = 4x + 18

Replace

AC = 8x +2y + 4x + 18

AC = 12x + 2y + 18