Select the correct answer.
Solve the following compound inequality.
2x − 2 > -8 or -4x ≤ -36

The length of side RQ in triangle PQR is 7.5.

Given,

ΔJKL ≈ ΔPQR

Therefore, sides are in same ratio to each other i.e.

[tex]\frac{QP}{JK}=\frac{RP}{JL}=\frac{RQ}{LK}[/tex]

[tex]\frac{25}{5} =\frac{22.5}{4.5}= \frac{t}{1.5}[/tex]

Therefore,

5 = t/1.5

t = 5*1.5

t = 7.5

Hence, length of RQ is 7.5.

Correct question,

Triangle JKL is similar to triangle PQR, find t. The sides of JKL measures

sJL = 4.5 sLK = 1.5 sJK = 5. The sides of PQR measures sQP = 25 sRP = 22.5 and sRQ = t. Find the length of RQ.

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Answer:

$2.5

Step-by-step explanation:

15 divided by 6 because its asking to split into groups equally

Answer:2.5

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

calculate slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, - 8 ) and (x₂, y₂ ) = (2, - 4 )

m = [tex]\frac{-4-(-8)}{2-2}[/tex] = [tex]\frac{-4+8}{0}[/tex] = [tex]\frac{4}{0}[/tex]

since division by zero is undefined then the slope is undefined

a line with undefined slope is a vertical line parallel to the y- axis with equation

x = c ( c is the value of the x- coordinates the line passes through )

the line passes through (2, - 8 ) and (2, - 4 ) with x- coordinates 2 , then

x = 2 ← equation of line

Answer:

2.8

Step-by-step explanation:

mean = 54+45+76+33+76= 284

284÷5=56.8

median ,to find median you first arrange the numbers in an accending order

33,45,54,76,76 then you find the middle number which is 54

56.8-54=2.8

Answer:

2.8 marks

Step-by-step explanation:

33, 45, 54, 76, 76

mean score = (54 + 45 + 76 + 33 + 76) ÷ 5

= 56.8

median score = (5 + 1) ÷ 2

= 3rd place

= 54

diff between mean and median score = 56.8 - 54

= 2.8

$0.4 is the price per gallon at Miguels gasoline station

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Six customers are buying Gasoline at Miguels gasoline station.

Gasoline bought is marked on x axis and cost on the y axis.

We need to find price per gallon at Miguels gasoline station

If gasoline bought are 4 then cost is 10

Four divided by ten is zero point four.

4/10=0.4

Hence $0.4 is the price per gallon at Miguels gasoline station

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In order to make profit of 1,200,000, the company should publish 180 copies of magazine.

The formula for the profit is given by:

Profit = revenues - total cost.

Meanwhile, the total cost consists of fixed cost and variable cost.

Total cost = fixed cost + price per unit x number of units sold

Parameters given in the problem:

Fixed cost = 600,000

variable cost = 50,000 per unit

selling price = 60,000 per copy

profit = 1,200,000

Let q be the number of copies sold, then:

Revenues = 60,000 q

Total cost = 600,000 + 50,000 q

Profit = 60,000 q - (600,000 + 50,000 q)

1,200,000 = 60,000 q - (600,000 + 50,000 q)

10,000 q = 1,800,000

q = 1,800,000 / 10,000 = 180

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The probability of outcome to be a 5 is 1/13. The probability of outcome not be 5 is 12/13. The probability of outcome to be a diamond or a king is 4/13. The probability of the outcomes to be a jack or a queen is 2/13. The probability of The outcome to be a heart and a club is 0 and the probability of the outcomes to be a card greater than 6 and less than 9 is  2/13.

A deck contains a total of 52 cards.

Total outcomes if the selected number of cards is one=52

Case A:

Each suit contain one 5 numbered card. There are four suits. Therefore, The required outcome would be 4.

Probability of an outcome is the ratio of desired outcomes to the total outcomes.

The probability of outcome to be 5, P(A):
P(A)=4/52

P(A)=1/13

Case B:

The total probability of outcomes=52/52=1

The probability of the outcome to be 5=1/13

Therefore, the probability of the outcome not to be 5, P(B):

P(B)=1-(1/13)

P(B)=12/13

Case C:

Each suit carries a king. Therefore, the probability of the outcome to be a king, P(M):

P(M)=4/52

P(M)=1/13

A suit carries 13 cards. Therefore, there will be 13 cards of diamonds.

The probability of the outcome to be a diamond, P(N):

P(N)=13/52

P(N)=1/4

The probability that the outcome is a king of diamonds, P(M[tex]\cap[/tex]N):

P(M[tex]\cap[/tex]N)=1/52

Hence, the probability that the outcome is a diamond or a king, P(M[tex]\cup[/tex]N):

P(M[tex]\cup[/tex]N)=P(M)+P(N)-P(M[tex]\cap[/tex]N)

P(M[tex]\cup[/tex]N)=(1/13)+(1/4)-(1/52)

P(M[tex]\cup[/tex]N)=16/52

P(M[tex]\cup[/tex]N)=4/13

Case D:

Each suit carries a Jack. Therefore, the probability of the outcome to be a jack, P(P):

P(P)=4/52

P(P)=1/13

Each suit carries a Queen. Therefore, the probability of the outcome to be a Queen, P(Q):

P(Q)=4/52

P(Q)=1/13

The probability that the outcome is a jack and a queen, P(P[tex]\cap[/tex]Q):

P(P[tex]\cap[/tex]Q)=0/52

P(P[tex]\cap[/tex]Q)=0

Hence, the probability that the outcome is a jack or a queen, P(P[tex]\cup[/tex]Q):

P(P[tex]\cup[/tex]Q)=P(P)+P(Q)-P(P[tex]\cap[/tex]Q)

P(P[tex]\cup[/tex]Q)=(1/13)+(1/13)-0

P(P[tex]\cup[/tex]Q)=2/13

Case E:

A card is never a heart and a club. Therefore, the probability of a card to be a heart and a club is 0.

Case F:

The numbers greater than 6 and less than 9 are the numbers between 6 and 9. The numbers between 6 and 9 are 7 and 8.

Each suit carries one 7 numbered card and one 8 numbered card. There is a total of 4 suits.

Therefore the desirable outcomes=8

The probability of the outcome required=8/52

=2/13

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When distance is halved, force increases by 4 times.

What is gravitational force?

Each body in the universe attracts other bodies towards itself with a force known as Gravitational Force

According to Newton’s law of gravitation, “Every particle in universe attracts every other particle with a force whose magnitude is,

On combining these equations, we get

F = G × [M1M2]/r²

F ∝ M1M2/r²

Now , r' = r/2 ( given)

so, F' ∝ (m1m2) / (r/2)²

F' ∝(4 m1m2) / r²

Thus F' = 4×F

So, we can conclude that, when distance is halved, force increases by 4 times.

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The value  of  x the subject of the formula is 2c(4+a)

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.

Equation with Lines

More than one variable may be present in a linear equation. An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.

Given ,

X/2c = a+4 by simplifying ,

x=2c(4+a)

Therefore the value of x the subject of the formula is 2c(4+a)

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Answer:

The percent being represented by the shaded area is [tex]175\%[/tex]

Step-by-step explanation:

The percent being represented by the shaded area can be calculated as follows

The first step is to evaluate the left square

Since each square represents one whole, and since the left square is all shaded in of [tex]4[/tex] then the percent being represented by the shaded area in the left square is

[tex]1=\frac{4}{4}=\frac{100}{100}=100\%[/tex]

The percent being represented by the shaded area in the first or the left square is [tex]100\%[/tex]

The second step is to evaluate the right square

Since the right or the second square is [tex]3[/tex] shaded in of [tex]4[/tex], then the fraction being represented by the shaded area in the second square is

[tex]\frac{3}{4}[/tex]

The third step is to convert [tex]\frac{3}{4}[/tex] into the percent form by the following equation

[tex]\frac{3}{4}=\frac{x}{100}[/tex]

Where [tex]x[/tex] is the percent value for the second square

Multiply both side by [tex]100[/tex] to isolate [tex]x[/tex]

[tex]\frac{3}{4}\times 100=\frac{x}{100}\times 100[/tex]

Simplify the equation

[tex]\frac{300}{4}=x[/tex]

Simplify the left side of the equation

[tex]75=x[/tex]

Since the value of [tex]x[/tex] is [tex]75[/tex], then the percent being represented by the shaded area in the second square is [tex]75\%[/tex]

The fourth step is to calculate the total percent being represented by the all shaded area

Since the total percent is the sum of the percent for the first square and the percent for the second square, then it follows

[tex]\text{Total percent}=100\%+75\%[/tex]

Simplify the equation

[tex]\text{Total percent}=175\%[/tex]

Hence the percent being represented by the shaded are is [tex]175\%[/tex]

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A timestamp is a signal that lets us know when the pertinent text was spoken and at what time. They are displayed in the format [HH:MM:SS], where HH stands for hours, MM for minutes, and SS for seconds.

There are various types of timestamps, as follows:-

1.  Periodic timestamps: These timestamps are repeated frequently. They can show up every 15 or 30 seconds, or once or twice every minute.

2.  Timestamps for paragraphs

3. Timestamps of sentences

4.  Timestamps for speakers

When transcribing audio recordings, the following time-stamping format is used:

[00:00:00]

in which [hour: minute: second]

Therefore, [00:05:00] is the fifth minute.

If an audio file has five to fifteen minute segment, needs to be transcribed, stamping should begin at [00:05:00].

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Answer:

Step-by-step explanation:

Proportional relationship equation:

In the given table, number of buckets represent input values (x) and the price represents output values (y).

We have for the first column:

Find the value of k by plugging in the values of x and y:

Same result will be obtained with the other columns, therefore the constant of proportionality is 7.25.

Answer:

b) 7.25

Step-by-step explanation:

Formula we use,

→ y = kx

→ k = y/x

Now the value of k will be,

→ k = y/x || → k = y/x

→ k = 14.5/2 || → k = 36.25/5

→ [ k = 7.25 ] || → [ k = 7.25 ]

Hence, the answer is 7.25.

The equation for the line given on the graph is y = 30x , the correct option is (c) .

In the question ,

it is given that

the cable length varies directly with the amount of time it passes .

let the cable length that is wound on the spool be " y " , and

let the time it passes be " x " .

since they vary directly , it can be denoted by

y ∝ x

So , the equation is , y [tex]=[/tex] k*x

from the graph we see that when x = 1 , the value of y is 30 .

On substituting x = 1 and y = 30 in the equation y = k*x

we get ,

30 = k*1

So , k = 30 .

Substituting k = 30 , we get

the equation as y = 30x .

Therefore , The equation for the line given on the graph is y = 30x .

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Answer:

6·3+6-4+6·5

6 · 3 + 6 · 4 + 6 · 5 + 6 · 8 + 2[3 · 4+ (3 · 4)]=168

Answer:

one on top is 50

Step-by-step explanation:

The required height of the cliff is  5√3/(√3)-1.

The angle of depression is defined as the If a human looks down at an object, then the angle of depression of that human is the angle between the horizontal line of sight and the object.

we have, angle of depression to top of pole = 45°

that of to foot of pole = 60°

Height of pole is 5 meter.

Then distance between tower is = 5+x/√3        ∴  tan(theta)=P/B

and, tan(45) = x/5+x/√3 = √3x/5+x   =1               ∴  tan(45) =1

5+x =√3x

X = 5/(√3)-1

Now height of cliff = 5+5/(√3)-1 = 5√3/(√3)-1 meter

Thus, the height of cliff is  5√3/(√3)-1.

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The only true statement is line segment ED intersects line segment AB.

We know when a transversal intersects two parallel lines at two distinct points,

Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.

From the given diagram and going through the options we can surely conclude that line segment ED intersects line segment AB.

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Answer:

111

Step-by-step explanation:

1 is squared of the right one so ya

Graph D represent the function.

Function is a representation of continue graph which can't be break so B and C are eliminated from the option.

1. Draw all possible linea parallel to Y- axis

2. If any line cuts the graph at two or more than two points then it is not a function

Reason:- function ka definition hai, element of A related to Only single (one/unique) element in set B.

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Graph D represent the function

Function is a representation of continue graph which can't be break so B and C are eliminated from the option.

1. Draw all possible linea parallel to Y- axis

2. If any line cuts the graph at two or more than two points then it is not a function

Reason:- function ka definition hai, element of A related to Only single (one/unique) element in set B.

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The distance from the base to the summit of the mountain is 3600 meters

The speed when going from base to summit = 45 meter / minute

The time taken for going from base to summit  = x minutes

The speed when descents from top to bottom = 60 meter / minute

The time taken for descents from top to bottom = x - 20 minutes

The speed = Distance / Time

The Distance = Speed × Time

Here in both case the distance is same

Then

45x = 60(x-20)

Solve the equation

45x = 60x - 1200

60x - 45x = 1200

15x = 1200

x = 1200/15

x = 80 minutes

Then the distance = 45x

= 45×80

= 3600 meters

Hence, the distance from the base to the summit of the mountain is 3600 meters

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The sum of the first 'n' terms can be expressed as [tex]S_n=\frac{n}{2}[2+(n-1)][/tex]

and the last term will be [tex]t_n = 1+(n-1)[/tex], where a is the first term of A.P. and 'd' is a common difference.

What is an arithmetic progression?

An arithmetic progression or arithmetic sequence is a number sequence in which the difference between consecutive terms is constant. For example, the sequence 5, 7, 9, 11, 13, 15.. is an arithmetic progression with a common difference of 2.

The first 'n' terms will be 1, 2, 3, 4, 5, 6, ...., n

The above sequence is an A.P. because it has a constant common difference of '1' between each consecutive number.

So a = 1, d = 1

By using the standard formula, we get

       [tex]S_n=\frac{n}{2}[2a+(n-1)d]\\\\S_n=\frac{n}{2}[2+(n-1)][/tex]

and for the last term

       [tex]t_n=a+(n-1)d\\\\t_n=1+(n-1)[/tex]

Hence, the sum of the first 'n' terms can be expressed as[tex]S_n=\frac{n}{2}[2+(n-1)][/tex]

and the last term will be [tex]t_n = 1+(n-1)[/tex], where a is the first term of A.P. and 'd' is a common difference.

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Answer:

v=-14

Step-by-step explanation:

Subtract 5 from both sides

5+v=-9

-5 -5

v=-14

The product is greater than 1 < 8.4375

Given:

In the question:

Product the following question:

1/2 x 4[tex]\frac{1}{2}[/tex] x [tex]1\frac{1}{4}[/tex] x 3

Now, According to the question;

1/2 x 4[tex]\frac{1}{2}[/tex] x [tex]1\frac{1}{4}[/tex] x 3

Solve the mixed fraction:

1/2 x 9/2 x 5/4 x 3

Write as a single fraction:

(9 x 5 x 3) / (2 x 2 x4)

Calculate the product or quotient:

= 135/ 16

= 8.4375

Hence, The product is greater than 1 < 8.4375

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We move all terms to the left:

Multiply

We add all the numbers and all the variables.

We move all terms containing x to the left hand side, all other terms to the right hand side

The car can go 28.5 miles in 1 gallon of gas.

According to the question,

We have the following information:

Mamadou’s car used [tex]2\frac{2}{3}[/tex] gallons to travel 76 miles.

Now, we can easily find the distance covered by car in one gallon of gas but we will first convert the gas given from mixed fraction.

8/3 gallons of gas = 76 miles

Now, the distance covered in 1 gallon of gas can be found by dividing 76 by 8/3.

1 gallon of gas = 76/(8/3)

1 gallon of gas = 57/2 miles

1 gallon of gas = [tex]28\frac{1}{2}[/tex] miles or 28.5 miles

Hence, the car can go 28.5 miles in 1 gallon of gas.

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Answer:

42 games

Step-by-step explanation:

she lost 6 and won 6 so if she played 84 games she will win 42 and lose 42

Edit:

The standard form would be:

3y = 20 - 4x

or

3y = -4x + 20

Answer/Step-by-step explanation:

Standard form of the equation should be in the form:

Ax + By = C

A, B and C must be whole numbers not fractions or decimals. B and C can be negative, but A must be positive.

Correctly written in standard form, this equation just needs one small tweak, multiply the whole thing by -1 to change all the signs so that the A will be positive.

-4x + 3y = 20

-1(-4x + 3y = 20)



4x - 3y = -20 this is proper standard form.

The linear function that represents the total cost per week is y = 4x + 250

A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line. The y-intercept and slope are represented by c and m respectively.

The equation can be represented in the form of y = mx + c

Data;

The equation to represent the amount spent weekly is y = 4x + 250

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