Mr. Clauson bought boxes of lights to decorate his house for the holidays. He used 998 boxes containing 24 lights per box. How many lights did Mr. Clauson use to decorate his house?

The range of the function is {0.16, 0.4, 1, 2.5, 6.25}. With an increase in the value of the domain, the range of the function is increasing.

What is a function?

A function from a set X to a set Y allocates exactly one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain.

The given function is

f(x) = 2.5^x.

Given domain is {-2, -1, 0, 1, 2}.

Now putting x = -2, -1, 0, 1, 2 in the function f(x) = 2.5^x.

When x = -2:

f(-2) = 2.5^(-2)

f(-2) = 0.16.

When x = -1:

f(-1) = 2.5^(-1)

f(-1) = 0.4

When x = 0:

f(0) = 2.5^(0)

f(0) = 1.

When x = 1:

f(1) = 2.5^(1)

f(1) = 2.5

When x = 2:

f(2) = 2.5^(2)

f(2) = 6.25

The range of the function is {0.16, 0.4, 1, 2.5, 6.25}

The values of the range increase with the increase of domain.

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The median and mode only are resistant measures of central tendency.

The correct option is B.

Statistics that are resistant to outliers don't change as a result. We assert that the median is a resistive measure of centre, in contrast to the mean, which is not. In a way, the median is able to reject distant values whereas the mean is drawn to them. It cannot withstand the impact of excessive values. The measurement that is least subject to sample variation is the median, which is defined as the middle of ranking data, where 50% of values are above it and 50% below it. As a result, the extreme figures have no bearing on the median. For symmetric data, nonresistant measures perform better because they are less affected by skewness and outliers. Resistant measures can be used since they are less negatively influenced.

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Answer:

BC = 56 units

Step-by-step explanation:

since the main diagonal AK bisects the diagonal BC , then the figure is a kite.

• the disjoint pairs of consecutive sides are congruent in a kite, that is

AB = AC and BK = CK

using the pair AB = AC  to solve for x

9x - 14 = 6x + 7 ( subtract 6x from both sides )

3x - 14 = 7 ( add 14 to both sides )

3x = 21 ( divide both sides by 3 )

x = 7

Since m bisects BC , then

CP = PB and

BC = CP + PB = 4x + 4x = 8x

then

BC = 8x = 8 × 7 = 56

25% percent of Amanda's day was spent on either meals or homework.

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The commission made by Jill for a $480 sale at the rate of commission 30% is $144.

What is meant by the rate of commission?

A commission is a payment made to a salesperson by a company in exchange for his or her assistance in facilitating or closing a sale. The design of the underlying commission agreement determines how a sales commission is calculated.

The rate of commission is a percentage or fixed sum that is linked to a specific amount of sales.

Given,

     Sales = $300

     Commission = $90

Then, rate of commission = (Commission/ sales) * 100

                                           = ( 90/300) * 100 = 30%

For this rate of commission, the commission she makes for a $480 sale is

                            = 480 * (30/100) = 480 * 0.3 = $144

Therefore, the commission made by Jill for a $480 sale at the rate of commission 30% is $144.

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Joe pushes a 200 kg car with a force of 125 N, In the scenario when the car does not move, Joe not be doing work or the car.

Static friction, sliding friction, rolling friction, and fluid friction are the four main categories of friction. Normal force and friction are independent of the hardness of the contacting surfaces and are directly proportional to the contacting surfaces.

The tiny bumps push against each other as two surfaces slide over one another. A surface is subject to a force from friction equivalent that opposes the direction of the surface's motion. Application of lubricants can reduce friction.

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Therefore , the solution of subtraction after subtraction, amount of water left on Tuesday is 98500 liters.

One of the most crucial mathematical operations, which is obtained by removing two numbers, produces difference in mathematics. It reveals how much one number deviates from another. To determine how many numbers are between the two given numbers is the goal of finding the difference in math.

Here,

Given:

Amount of water on Monday=10000

Amount of water used=1500

Water left on Tuesday=10000-1500=98500

Thus ,  amount of water left on Tuesday is 98500 liters.

Therefore , the solution of subtraction after subtraction, amount of water left on Tuesday is 98500 liters.

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Answer:

x=15

Step-by-step explanation:

6(5)=30

3(5)=15

The length of the missing side Triangle is 3

As it is given that the given triangle is similar which shows all three sides of both the triangle will be in the same ratio by CPST (corresponding parts of similar Triangles).

so

15/x=30/6 .................  the ratio of two sides of the triangle

x  =  15*6/30

x= 3

here the value of x is 3.

Also, the ratio of the side comes out to be 5:1 as 6 and 30 are the length so the first triangle has a side of 15 and the length of another triangle will be 3 to make the ratio 5:1.

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The graphed line is y = 5x passing through points (0, 0) and (1, 5)

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

The linear equation is in the form:

y = mx + b

where m is the rate of change and b is the y intercept.

The graphed line passes through (0, 0) and (1, 5), hence the equation is:

y - 0 = [(5-0)/(1 - 0)](x - 0)

y = 5x

The graphed line is y = 5x.

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The automobile travels at an average speed of 65.71 mph.

Put r = d/t to use.You are moving at a rate of 12 miles per hour since 24 miles are multiplied by two hours.Become familiar with the distance formula, a Pythagorean theorem application that can be used to determine the separation between two places.

Sal Khan and the CK-12 Foundation created it.

The car's average speed is 65.71 miles per hour.

the settings provided;Initially, the automobile is traveling at 50 mph.

motion time, t = 3 hours

v = 70 mph is the motion's final speed.

motion time, t = 11 hours

The following formula is used to determine the car's average speed:

average speed = total distance /total speed

Total distance traveled divided by total motion duration equals average speed.

The entire distance is equal to 920 miles (50 x 3 + 70 x 11).

The duration of the motion was (3 + 11) hours, or 14 hours.

The car's typical speed is;

Consequently, the car's average speed is 65.71 mph.

average speed  =920/14

                        = 65.71 mph.

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Answer:

3x-18

Step-by-step explanation:

The season the team scored more consistently will be this season because the Standard deviation is less.

Statistics is the study of collection, analysis, interpretation, and presentation of data or discipline to collect and summarise the data.

Last Season: 10, 3, 20, 27, 35, 17, 20, 13, 17

The mean is given as,

Mean = (10 + 3 + ...... + 17) / 9

Mean = 18

Then the standard deviation is given as,

Standard deviation = [(10 - 18)² + (3 - 18)² + ...... + (17 - 18)²] / 9

Standard deviation = 8.78

This Season: 23, 17, 28, 16, 23, 16, 16, 10, 13

The mean is given as,

Mean = (23 + 17 + ... + 13) / 9

Mean = 18

Then the standard deviation is given as,

Standard deviation = (23 - 18)² + (17 - 18)² + ...... + (13 - 18)²

Standard deviation = 5.29

The season the team scored more consistently will be this season because the Standard deviation is less.

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Answer:

Option D: 224

Step-by-step explanation:

[tex] \sf (20 + d)d[/tex]

Insert the value d = 8

[tex] \sf(20 + 8)8[/tex]

Add

[tex] \sf (28)8[/tex]

multiply

[tex] \sf 224[/tex]

Answer:

x = 108

Step-by-step explanation:

78-(x-60)=30

Solving for x,

x = 78-30+60

x = 108

The value of x in the figure is 40°.

In a linear pair, the total of two angles is always 180°. All neighboring angles are linear pairs, however not all adjacent angles are linear pairs.

∠DBA + ∠ABC = 180° ( ∵ linear pair)

∠100° + ∠ABC = 180°

∠ABC = 180° - 100°

∠ABC = 80°

The sum of angles of a triangle is 180° .

So, in triangle ABC

∠A + ∠B + ∠C = 180°

x + 80 + 60 = 180°

x + 140 = 180°

x = 180° - 140°

x = 40°

So, ∠A = x = 40°

The complete question is,

Find the value of x in the figure below :

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On solving the provided question, the equation will be  and the factors - This cannot be determined from the information given

When points on a curve are equally spaced from a fixed point and line, the curve is said to have a parabola as its equation. The parabola's fixed point is referred to as the focus, and its fixed line is referred to as the directrix. Remember that the fixed point is not on the fixed line as well. A parabola is the locus of any point that is equidistant from both a focus and a straight line. A conical curve of interest in coordinate geometry is a parabola.

The equation will be

=> 4x+9 = 20x - 2.3y

x = 989-32y

y = 5.4x - 10

Factors - This cannot be determined from the information given

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(-4,-3)

x=-4,y=-3

Step-by-step explanation:

solve for the first variable in one of the equations, then substitute the results into the other equation. point form:

Answer: we have

--------> inequality A

--------> inequality B

Using a graphing tool

the solution of the inequality A is the shaded area above the dashed line  

see the attached figure N        

the solution of the inequality B is the shaded area below the dashed line  

see the attached figure N

therefore

the solution of the compound system of inequalities is the shaded area between the two dashed lines

see the attached figure N

therefor

the answer in the attached figure N

The probability of unscheduled maintenance in exactly 5,000 hours is 4/5.

What is the probability?

We know that the probability deals with the fact that an event may or many not occur. It deals with a chance event. In this case, we have been told that the hospital's CT scan facility is 4,000 operating hours.

We know that the probability can be obtained from;

P = Number of unscheduled maintenance hours/Total operating hours

This would now give us that;

P = 4000/5000

P = 4/5

Hence, there is a probability of 4/5.

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Rearranging the given expression into quadratic form gives x² + 0.2x - 15 = 0.

The values of a, b, and c include the following:

a = 1

b = 0.2

c = -15

In Mathematics, the standard form of a quadratic function is given by this mathematical expression;

ax² + bx + c = 0

Where:

Next, we would multiply both sides of the quadratic function by (75 - x) as follows;

0.20 × (75 - x) = x²/(75 - x) × (75 - x)

0.20 × (75 - x) = x²

By applying the distributive property to the mathematical expression, we have the following:

0.20(75) - 0.20(x) = x²

15 - 0.2x = x²

By rearranging the mathematical expression, we have the following:

x² + 0.2x - 15 = 0

Therefore, the quadratic function is equal to x² + 0.2x - 15 = 0.

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The missing length of the right-angle triangle will be 6x - 3.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The perimeter of the triangle is determined by adding together all of its sides.

The third side of the triangle is given as,

11x - 6 = H + 4x + 2 + x - 5

H = 11x - 6 - 4x - 2 - x + 5

H = 6x - 3

The missing length of the right-angle triangle will be 6x - 3.

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The complete question is given below.

The slope of line exists -2 then the value of x is 12 seconds.

The simplest definition of point-slope form is a line equation expressed using a single line point and the line's slope. The slope is the ratio of the change in the y values over the change in the x values, or the rise over run, and the point form is written as (x, y).

The relationship between x and y is linear because the rate at which the kite is being drawn in is constant. The height reaches 16 feet after 4 seconds, making the point (4, 16) on the line. After 5 seconds, the height is 14 feet since the kite is being dragged in at a rate of 2 feet per second. Therefore, (5, 14) is another point on the line.

slope of line = (16-14)/(4-5) = -2

Using the point-slope form, an equation of the line exists:

y - 16 = -2(x - 4)

y - 16 = -2x + 8

y = -2x + 24

To estimate the original height,

Let x = 0:  y = -2(0) + 24 = 24 feet

The kite hits the ground when y = 0:  

0 = -2x + 24

x = 12 seconds

Therefore, the value of x = 12 seconds.

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Note that where the cylindrical and the cuboidal containers shown below have the same height. the same amount of water was poured into each container. The water filled 1/2 of the cylindrical container and 1/3 of the cuboidal container. If the base area of the cylindrical container is 154 sq cm, the base area of the Cuboidal Container is 15.2

Let the height of the cylinder and cuboidal container be h m

We know that the base of the cylinder container is given as: 154 sq cm.

Recall that the volume for a cylinder is = Base x Height

That means in this case:

The volume for the cylinder is = 154 x Height

Thus,

1/2 * 154h = 1/3h³

77h =  1/3h³; divide both side by h to get

77 = 1/3h²

Collecting like terms and make h subject of the formula, we have;

h² = 77 * 3

h² = 231

h = √231

h= 15.1986841536

h = 15.199 or [tex]\approx[/tex] 15.2

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The time that Mrs James have her eyes open than closed will be 13 19/20 hours.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split.

From the information, the average person spends about 1/10 of their walking hours with their eyes closed. If Mrs. James was awake for 15 1/2 hours today.

The more time that she have her eyes open than closed will be:

= 15 1/2 - (1/10 × 15 1/2)

= 15 1/2 - 1 11/20

= 13 19/20

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When lines a and b overlap, angle 1 equals angle 3.

The intersection of two lines in Euclidean geometry might be the empty set, a point, or another line. Distinguishing these circumstances and locating the intersection have applications in computer graphics, motion planning, and collision detection, among others. When two or more lines intersect on a plane, they are referred to as intersecting lines. The crossing lines have a common point, which exists on all of them and is known as the point of intersection. The intersecting lines are two lines that have precisely one common point. The crossing lines have a point in common. The point of intersection is the common point that exists on all intersecting lines.

Here,

To prove ∠1 ≅ ∠ 3, we can use the congruent supplements theorem. According to the congruent supplements theorem, If two angles are supplements of the same angle then two angles are congruent.

Line a and line b intersect                                         (given)

∠3 is supplementary to ∠2 because of linear pair theorem (given)

So, if we take ∠2 as the common angle

And  ∠1 is supplementary to ∠2  by linear pair theorem     ( option D)

Then, ∠1 is supplementary to ∠2 which is supplementary to ∠3

Therefore, ∠1 ≅ ∠3 (according to the congruent supplements theorem)

This is proved when line a and line b intersect, angle 1=angle 3.

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The following are the solutions for the student data:

a. 25 students like exactly two of the composers

b. 31 students like exactly one these composers

c. 10 students like only Mozart

d. 19 students like haydn and exactly one of the other two composers

e. Only one student like none of these composers.

Venn diagrams are commonly used in mathematics, statistics, and logic to illustrate relationships between sets of data. It consists of circles that overlap to show the similarities and differences between the sets like in the case of students data.

Students who like:

All three composers = 8

Only Mozart and Beethoven = 14 - 8 = 6

Only Mozart and Haydn = 20 - 8 = 12

Only Beethoven and Haydn = 15 - 8 = 7

Only Mozart = 36 - (6 + 12 + 8) = 10

Only Beethoven = 37 - (6 + 7 + 8) = 16

Only Haydn = 32 - (12 + 7 + 8) = 5

Students who like none of the composers:

65 - (10 + 16 + 5 + 12 + 6 + 7 + 8)

65 - 64 = 1

Therefore, students who like:

exactly two of the composers = 12 + 6 7 = 25 students

exactly one these composers = 10 + 16 + 5 = 31 students

only Mozart = 10 students

Haydn and exactly one of the other two composers = 12 + 7 = 19 students

none of the composers = 1 student

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Answer:

125

Step-by-step explanation:

Answer: 6 or 7 square inches

Step-by-step explanation:                                                                                   Chicks need enough space under the brooder so that they can keep warm without crowding, piling up or smothering. Under normal conditions, each replacement chick needs about 6 or 7 square inches of brooder space