(06.02)
Match the verbal expression (term) with its algebraic expression (definition).
Match
Term
A variable cubed
Quotient of some number and three
Product of an unknown value and three
Three less than a variable
Three more than some number
Definition
A) 3a
B) b + 3
C) z + 3
D) y - 3
E) x³

The expression to find how many more customers visited the store on the first day is 5x - 2.

It's important to note that an expression is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Since the number of customers in a store on the first day is represented by (6x-3) and the number of customers on the second day is represented by (x-1).

The number of more customers will be:

= Customers on first day - Customers on second day

= 6x - 3 - (x - 1)

= 6x - 3 - x + 1

= 5x - 2

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Answer: A) 5.8

Step-by-step explanation: Hard guess

Answer:

40, leg

Step-by-step explanation:

The triangle has side lengths of 9, 40, and 41.

41 is the hypotenuse, so 40 is a leg.

Answer:

58,5km/h

Step-by-step explanation:

Vyork-leeds=45km/h

Vleeds-blackpool=72km/h

(45+72):2=58,5km/h

Answer:

67.5

Step-by-step explanation:

Answer:67.5

Step-by-step explanation:0.675*100=67.5

Taking into account the definition of a system of linear equations, the system of equations to be solved is

r= g+2

2g + 4.75r= 50

where "g" is the number of games Lauren played and "r" is the number of rides Lauren went on.

A system of linear equations is a set of two or more first degree equations, in which two or more unknowns are related and it is desired to find their value.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. Thit is, the values ​​of the unknowns must be find, and when the are replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

r= g+2

2g + 4.75r= 50

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This is 100% correct. Just got it right.

"g" is the number of games.

"r" is the number of rides.

System of equations

r =  g + 2

2g + 4.75r = 50

No, Is it not possible that creating a Boxplot could show outliers but z-scores show no outlier. This is because Any z-score that is either higher than +3 or lower than -3 is viewed as an issue.

When you declare a data point to be an outlier and reject it, you are indicating that even if you have already observed the point, it is unlikely to happen again.

Z scores make it easier to determine whether a data value is larger or less than the mean and how far from the mean it is. The Z score precisely indicates the number of standard deviations a data point deviates from the mean.

So, Outliers can be highlighted using scatterplots, histograms, and boxplots. Asterisks or other symbols are displayed on the graph in boxplots to plainly show the presence of outliers in a dataset.

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Using the simplification, company y has 17 number of part-time employees.

In the given question we have to find how many part-time employees does company y have.

From the question, company x has 50 employees and company y has 60 employees.

Both companies have the same number of full-time employees, but company y has 3 more than twice the number of part-time employees that company x has.

Let company x has A number of part-time employees.

According the given statement

Company y has number of part-time employees = 2A+3

Let company X and Y have B number of full-time employees.

So the total number of employees in company x;

A+B = 50....................(1)

The total number of employees in company x;

2A+3+B = 60

Subtract 3 on both side we get

2A+B=57....................(2)

Subtract Equation 2 and 1

2A+B-(A+B)=57-50

2A+B-A-B=57-50

A=7

Now putting the value of A in equation 1

7+B=50

Subtract 7 on both side we get

B=43

As, Company y has number of part-time employees = 2A+3

Company y has number of part-time employees = 2×7+3

Company y has number of part-time employees = 14+3

Company y has number of part-time employees = 17

Hence, company y has 17 number of part-time employees.

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The probability that both marbles are of the same color is 31/66

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Here, we have

5 red and 7 green marbles.

We have to calculate the probability of two marbles being drawn consecutively without replacing them.

The first is that if we define events R to be two red marbles, and G to be two green marbles, then we can verify that:

P(R) = (5/12)(4/11)

P(G) = (7/12)(6/11)

Then, P(R ∪ G) = P(R) + P(G)

                        = (5/12)(4/11) +  (7/12)(6/11)

                        = 5/33 + 7/22

                        =  31/66

Hence, the probability that both marbles are of the same color is 31/66

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Answer:

the answer is c.

Step-by-step explanation:

the slope will always have an x behind it and the y intercept is exactly as written

The solution to the system of equations (0.4, 1).

Given equations according to the question,

y = -5x+3

y = 1

Now we can use y = 1 and substitute the value of y in y = -5x+3

After substituting we get, the value of y we get,

= 1 = -5x+3

Now given points according to the questions are

(0.4, 1) , (0.8, 1), (1, 0.4), (1, 0.8).

We substitute these points in the equation to see which points satisfy the equation, the point satisfying the equation is our point.

First, we will use (0.4, 1)

= 1 = -5x+3

= 1 = -5×0.4 + 3

= 1 = -2+3

= 1 = 1

Hence (0.4, 1) is our first solution of the equation.

Then we will use (0.8 ,1)

= 1 = -5x+3

= 1 = -5×0.8 + 3

= 1 = -4+3

= 1 = -1

Hence (0.8, 1) is not out the solution to the equation.

Then we will use (1,0.4)

= 1 = -5x+3

= 1 = -5×1 + 3

= 1 = -5+3

= 1 = -2

Hence (1, 0.4) is not the solution to the equation.

Then we will use (1,0.8)

= 1 = -5x+3

= 1 = -5×1 + 3

= 1 = -5+3

= 1 = -2

Hence (1, 0.8) is not the solution to the equation.

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The distance is 252 inches.

What is distance?

The distance between two points is the length of a straight line segment that links them. The distance of a point from a line is the length of the shortest line segment from the point to the line.

Given

the length of shoes = 12 inch

The distance is equal to length of 21 of the shoes.

The total distance = 12×21

=252 inch

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Answer: 115

Step-by-step explanation: trust me bro free lee

Two angles are supplementary if their sum is 180° thus the angle supplementary to angles m∠AED are m∠DEB and m∠AEC and their measure is 115° both.

The angle is the measurement of the angular distance for example for linear motion we have a meter inch but for angular rotation, we don't have the measurement so the angle is useful to measure the angular rotation.

As per the given lines, AB intersect CD at E has been drawn below,

m∠AED = 65° (given)

m∠AED + m∠DEB = 180° (supplementary)

m∠DEB = 180° - 65° = 115°.

m∠AED + m∠AEC = 180° (supplementary)

m∠AEC = 180° - 65° = 115°.

Hence "Two angles are supplementary if their sum is 180° thus the angle supplementary to angles m∠AED are m∠DEB and m∠AEC and their measure is 115° both".

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Answer:

y = -x - 4

Step-by-step explanation:

Given line: y = x - 1

Slope of given line = 1

The slopes of perpendicular lines are negative reciprocals, so the slope of the perpendicular line is -1.

slope = -1

point: (-6, 2)

y = mx + b

y = -x + b

2 = -(-6) + b

2 = 6 + b

b = -4

Equation:

y = -x - 4

Answer:

m∠1 = 88°

m∠2 = 42°

m∠3 = 113°

Step-by-step explanation:

All of the angles in a triangle add up to 180°. This knowledge can be used to find angle 3, which I will rename c to make writing an equation easier.

[tex]180=25+42+c\\180=67+c\\113=c[/tex]

Angle 3 is 113°

Two angles on either side of the intersection of two straight lines are equal, therefore angle 2, or b:

[tex]b=42[/tex]

Angle 2 is 42°

Now that two angles are known in the leftmost triangle, we can solve for the last one: Angle 1, or a:

[tex]180=50+42+a\\180=92+a\\88=a[/tex]

Angle 1 is 88°

From given set, 3x and x; 1/4 and 0.5; –m and 8m; –xy² and 2xy²;  –7 and 6 are the like terms combinations

In algebraic terms, the terms that contain the same variable and the same power or degree are called like terms, In algebraic like terms, the numerical coefficients can vary but are not variables.

Here are some examples of like terms and unlike terms,  

4x and 9x are like terms

3x²y and 10x²y are like terms

2xy and 10yx  are like terms

3x and 19y  are unlike terms  [ ∵ variable is different ]

2xyz and 2xy are unlike terms [ ∵ variables is missing in 2nd term ]

Here we have a set of algebraic terms that can be classified as given below

=> 3x and x    - like terms

=> 1/4 and 0.5 - like terms

=> –m and 8m - like terms

=>  –xy² and 2xy² - like terms

=> y and y² - unlike terms             [ ∵ powers are not same ]

=>  4xy and –5x²y  - unlike term  [ ∵ powers are not same ]

=> m and n  - unlike term              [ ∵ variables are not same ]  

=> –7 and 6  like terms

Therefore,

From given set, 3x and x; 1/4 and 0.5; –m and 8m; –xy² and 2xy²;  –7 and 6 are the like terms combinations

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The complete Question

Juan is learning about like terms in his math class. He must check all the combinations below that are like terms. Which ones should he check? Choose all that apply.

=> 3x and x    

=> 1/4 and 0.5

=> –m and 8m

=>  –xy² and 2xy²

=> y and y²

=>  4xy and –5x²y

=> m and n

=> –7 and 6

Answer:

$0.42

Step-by-step explanation:

3ton=6000pounds

2,520/6000=$0.42

The rate of the square increasing when the area is 16 cm² is 64 cm²/s. The result is obtained by using basic derivative rules.

The rate of a square increasing can be counted by the derivative of the area of the square as a function of time.

dA/dt = 2s ds/dt

Where s is side length.

If each side of a square is increasing at a rate of 8 cm/s, what is the rate of the square increasing when the area is 16 cm²?

We have the side of the square as the function of time.

ds/dt = 8 cm/s

When the area is 16 cm², the side length is

A = s²

16 = s²

s = √16

s = 4 cm

The rate of the square increasing is

dA/dt = 2s ds/dt

dA/dt = 2 × 4 × 8

dA/dt = 64 cm²/s

Hence, the rate of the square increasing when the area is 16 cm² is 64 cm²/s.

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Answer:

33, 34

Step-by-step explanation:

we must start solving this equation by letting a variable equal the smaller number

let n = smaller number

now the larger number is consecutive so you add one to n to get it

n + 1 is the bigger number

if you add them you get 67

n + n + 1 = 67

now solve

add like terms

2n + 1 = 67

subtract 1 from both sides

2n = 66

n = 33

the smaller number is 33

adding one to that will get you the larger integer

33 + 1 = 34

that is the larger integer

[tex]y < -3x+1[/tex]

Graph below:

Using front end estimation, the correct decimal solutions to the given problems are;

1) 25.72

2) 137.521

3) 17.1

Front end estimation is defined as one way to round numbers  in such a manner that an approximate answer can be easily found.

1) 32.47 - 6.75

First of all, deal with the whole numbers portion to get;

32 - 6 = 26

Next step is to handle the decimal part to get;

0.47 is approximately equal to 0.5 while 0.75 is approximately equal to 0.8. Thus;

0.5 - 0.8 = - 0.3

Therefore, we have;

26 + (-0.3) = 25.70

Therefore, the correct decimal solution can be written as; 25.72

2) 118.234 + 19.287

First of all, deal with the whole numbers portion to get;

118 + 19 = 137

Next step is to handle the decimal part to get;

0.234 is approximately equal to 0.2 while 0.287 is approximately equal to 0.3. Thus;

0.2 + 0.3 =0.5

Therefore, we have;

137 + 0.5 = 137.5

Therefore, the correct decimal solution can be written as; 137.521

C)  17.9 - 0.8

First of all, deal with the whole numbers portion to get;

17 - 0 = 17

Next step is to handle the decimal part to get;

0.9 - 0.8 = 0.1

Therefore, we have;

17 + 0.1 = 17.1

Therefore, the correct decimal solution can be written as; 17.1

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The probability that she wins the next two matches is 36% or 0.36

How to calculate the probability of two matches?

Given,

She believes that the outcome of each match is independent. So, the outcome of next match does not depend on the previous match, is called independent event.

The probability of winning one match is 0.6

Since the outcome of each match is independent, we easily get the probability of she winning the next two matches by multiplying the probability of she winning per match. So,

Probability she wins the next two matches = 0.6 x 0.6

= 0.36 or 36%

Thus, the probability that she wins the next two matches is 36% or 0.36

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Frequency of radiation with a wave length of 5.2 cm is 57.7x[tex]10^{8}[/tex]

The number of waves that pass a fixed point in unit time.

Given that, a frequency with a wave length of 5.2 cm

5.2 cm = 0.052 m

Frequency = f = c/λ

f = 3x[tex]10^{8}[/tex]/0.052 = 57.7x[tex]10^{8}[/tex] Hz

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The number of hours Jackson worked washing cars is 8 hours and the number of hours he worked landscaping is 6 hours

The payment of car washing per hour = $10

The payment for landscaping = $12

Total number of hours worked = 14  hours

Number of hours worked in car washing = x

Number of hours worked in landscaping = y

Then the first equation will be

x + y = 14

x = 14 - y

Total amount he earned = $152

Next equation will be

10x + 12y = 152
Here we have to use substitution method

10(14-y) + 12y = 152

140 - 10y +12y = 152

140 + 2y = 152

2y = 152 - 140

2y = 12

y = 12/2

y = 6 hours

Then

x = 14 - y

x = 14 -6

x = 8  hours

Hence, the number of hours Jackson worked washing cars is 8 hours and the number of hours he worked landscaping is 6 hours

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After simplification of |2-5|-(6/2+1)², the resultant answer is (A) -13.

To simplify simply means to make anything easier.

In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler.

Calculations and problem-solving techniques simplify the issue.

Substitute "of" for "multiplication," and "/" for "division."

Always carry out operations in accordance with "BODMAS."

Division and multiplication are equally important (Start from left) Both addition and subtraction are equally important.

So, simplify |2-5|-(6/2+1)² as follows:

|2-5|-(6/2+1)²

|-3| - (6/2 + 1)²

We know that : |-3| = 3 and (6/2 + 1)² = 16

Then, we have:
3 - 16

- 13

Therefore, after simplification of |2-5|-(6/2+1)², the resultant answer is (A) -13.

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Yes y = 7 - 3x is a linear function

A linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

Definition of variables of a linear function

y = output variable

m = slope

x = input variable

c = y intercept

In comparison to the question asked

y = 7-3x

m = slope = -3

x = input variable

c = 7

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The time between when the rock was dropped and when it landed is 2.7 seconds.

What is function?  

    A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a function is defined as a relation f between a set A (the function's domain) and a set B (its co-domain). For any a A and b B, f = (a,b)| .Every element of set A must have exactly one image in set B for a relation to be considered a function. A relation from a non-empty set B is called a function if it has the property that no two separate ordered pairs in f have the same first element.

Here the given height h(t) = 100 feet

Now the given function is,

=> h(t)=25[tex]t^2[/tex]-81 .

Put h(t)=100 then ,

=> 100= 25[tex]t^2[/tex]-81 .

=> 100+81=25[tex]t^2[/tex]

=>[tex]t^2[/tex]= 181/25

=> t = 2.69=2.7 sec.

Hence the time between when the rock was dropped and when it landed is 2.7 seconds.

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It would have cost Louisa $200 in interest charges.

The simple interest amount is calculated as follows;

SI = P*I*t

That is where we have

The balance is P.

The interest rate is I.

The time is t.

Regarding this issue;

Balance of $1,000, 19.99% APR, and 1 year.

She will pay the following sum;

SI = 1000 *0.199*1

SI = 199.9

SI ≅ 200

Louisa would have had to pay $200 in interest fees.

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The system of equations representing these costs is y = 7.5x and y = 5..5x + 10

Given,

Anna desires to enroll in fitness courses. She contrasts two gyms to see which offers the best value. Each class at Fit Fast costs a specified amount. Stepping up costs a monthly fee as well as a price for each lesson.

We have to find the system of equations representing these costs;

Fit Fast: a certain number of feet per class = y = Ax

Stepping Up: a monthly charge plus a cost for each additional class = h = Bx + C

The second and fourth systems can be ignored since they lack the form that is implied by the statement.

Given that it reflects a choice that is always preferable to the alternative, the first system produces an obvious result. There is no need to compare because, for any positive value of x, 5.5x will be less than 7.5x + 10,

The third system is

It is necessary to solve the equations y = 7.5x and y = 5.5x + 10 to decide when one rate is more practical than the other.

That is,

The system of equations representing these costs is y = 7.5x and y = 5..5x + 10

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