a. Evaluate the expression 2(2x² - x) - 3(x² - x) + x² - x for x=3 . Do not simplify the expression before evaluating it.

The inequality given by 3n < -4(2 + n) has the solution n < -8/7 or (-∞ , -8/7).

Inequality refers to the relationship between two non-equal expressions. It can be denoted by > for greater than, < for less than, >/= for greater than and equal to, and </= for less than and equal to.

To solve an inequality is to find the values of x such that when we substitute that number for x we have a true statement.

Given the inequality 3n < -4(2 + n), expand the right term by distributing -4 inside the parenthesis.

3n < -4(2 + n)

3n < -8 - 4n

Add 4n to both sides.

3n + 4n < -8 - 4n + 4n

7n < -8

Divide both sides by 7

7n < -8

n < -8/7

To check, let n = -9/7

n = -9/7 < -8/7

Substitute this value to the inequality.

3n < -4(2 + n)

3(-9/7) < -4(2 + -9/7)

-27/7 < -20/7

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If the top 2% of athletes will go pro, then the Z-Score that is required to be 0.0438.

Given that the top 2% of athletes will go pro.

We are required to find the Z-Score that is required to be the top 2%.

A Z-score is basically a numerical measurement that describes a value's relationship to the mean of a group of values. Z-score is measured basically in terms of standard deviations from the mean.

Because only 2% of the top is pro then it will be a two tailed test. The required percentage will be 2/2=1%

The value which we will require to catch up from table=0.01

Z value will be 0.0438 (Z table is attached)

Hence if the top 2% of athletes will go pro, then the Z-Score that is required to be 0.0438.

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Answer:

 15,  10,  6

Step-by-step explanation:

Gavin: 2.52 + 6.25 + 6.25 =15.02 = 15

Jason:  6.25 = 6

Evan:  6.25 + 3.72 = 9.97 = 10

i hope this helped if did pls mark brainliest

150 is   the cost of renting a car from YourPal.

What is surface area of cuboid ?

Let y = total charge for a car rental and x = miles driven

Proxy car equation: y = 0.32x + 18

YourPal equation: y = 0.36x + 12

Set equations right sides equal to each other... meaning their cost, y, are equal

0.32x + 18 = 0.36x + 12

18 = 0.04x + 12  (subtract 0.32x from both sides of the equation)

6 = 0.04x            (subtract 12 from both sides of the equation)

150 = x               (divide both sides of the equation by 0.04)

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Answer:

No, because 2(21) + 13 is not equal to 43.

The Dolphins scored 10 points.

Step-by-step explanation:

A = 13 + 2D

43 = 13 + A + D

43 = 13 + 3D

43 - 13 = 30

30 = 3D

30/3 = 10

D = 10

A = 13 + 2(10)

A = 33

D + A = 43

33 + 10 = 43

Therefore, the Atlanta Falcons scored 33 points which is 13 points more than twice what the Dolphins scored.

Answer:

17

Step-by-step explanation:

3(2)2+(35÷5) = 12+7 = 19

[hope it helps, im not sure if its exactly what you need]

2.4 f of snow would fall in March.

Given that

Delphine's home received 40% 40% 40% 40% more snowfall in March compared to February.

now find the Delphine's house had fff centimeters of snowfall in February.

Let f represent the volume of snow that fell in February.

If there is 40% more snowfall in February than there was in March,

Consequently, the snowfall would be

[tex]f+( \frac{100+40}{100} )f[/tex]

[tex]f+( \frac{140}{100} )f[/tex]

f + 1.4f

2.4f

Therefore, 2.4f of snow would fall in march.

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Answer:

BC = 1 [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion, that is

[tex]\frac{BC}{EF}[/tex] = [tex]\frac{AB}{DE}[/tex] ( substitute values )

[tex]\frac{BC}{4}[/tex] = [tex]\frac{\frac{3}{4} }{\frac{5}{2} }[/tex] ( 2 [tex]\frac{1}{2}[/tex] = [tex]\frac{5}{2}[/tex] )

cross- multiply

[tex]\frac{5}{2}[/tex] BC = 4 × [tex]\frac{3}{4}[/tex] = 3 ( multiply both sides by 2 to clear the fraction )

5 BC = 6 ( divide both sides by 5 )

BC = [tex]\frac{6}{5}[/tex] = 1 [tex]\frac{1}{5}[/tex]

The answer is 6, 12, 18, 24, 30, 36, 42.

The pattern is in increasing order i.e., +6.

Given,

6,12,18,24, . . .

Solution:

Note the difference in the given number series 6,12,18,24, . . .

12 - 6 = 6

18 - 12 = 6

24 - 18 = 6

The difference is common and is 6.

The sequence is in increasing order.

So, add 6 to 24 and the consecutive numbers to get the answer.

24 +6 = 30

30 +6 = 36

36 + 6 = 42

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Answer:

x=ay/4 +3

Step-by-step explanation:

Answer:

[tex]\boxed{y = \dfrac{1}{4}x -4}[/tex]

Step-by-step explanation:

The slope-intercept form of a line equation is y = mx + b[tex]\sf\\\\To\;find\;b, \;plug \;in \;the \;values\; of\; (4, - 3) \;which \;corresponds\; to\; x = 4, y = -3 \;into \;the \;above \;equation:\\== > - 3 = \dfrac{1}{4}\cdot 4 + b\\\\Switching\;sides,\\\dfrac{1}{4}\cdot 4 + b = -3\\\\Simplifying\\1 + b = -3\\\\b = -3 -1 = -4\\So\; the\; equation \;of \;the\; perpendicular\; line \;is: \boxed{y = \dfrac{1}{4}x -4}[/tex]

A perpendicular line will have slope is  [tex]-\dfrac{1}{m}[/tex]

The perpendicular line will have a slope which is the negative of the reciprocal of the first line

Here the line is 4x + y =3

This can be re-written as y = -4x + 3

Slope of this line is -4

[tex]\sf Reciprocal \; of-4 = -\dfrac{1}{4}[/tex]

[tex]\sf Negative \; of \; reciprocal = -(-\dfrac{1}{4}) = \dfrac{1}{4}[/tex]

[tex]\sf So\;slope\;of\;perpendicular\;line=\dfrac{1}{4}\\Equation \;of \;the \;perpendicular\; line\; is \;y = \dfrac{1}{4}x + b \;where \;b \;is \;the\; y\; intercept[/tex]

Answer:

[tex] \frac{2}{10} \\ \\ 0.2[/tex]

After evaluating the given expression at a = -2, we get 24.

We have the following expression -

[tex]2a^{2} -5a +6[/tex]

We have to evaluate it for a = -2.

To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations.

According to the question, we have -

[tex]2a^{2} -5a +6[/tex]

Evaluating the expression for a = -2, we get -

2(-2)(-2) - 5(-2) + 6 = 8 + 10 + 6 =24

Hence, after evaluating the given expression at a = -2, we get 24.

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Answer:

25

Step-by-step explanation:

Work shown in the attached screenshot!! Please let me know if you have any questions! :)

The required value of p(e and f) is 0.24, which is calculated using the conditional probability formula.

What is conditional probability?

Conditional probability is the measure in probability theory that depicts the probability of occurrence of an event given that another event has already occurred. Its mathematical formulation is given by:

P(A/B) = P(A∩B) / P(B)

Here, A is the event and B has already occurred

The calculation for the value of p(e and f)

The assigned value of p(e) = 0.6

Conditional probability, p(f/e) is given as 0.4

We know, that conditional probability = p(e∩f) / p(e)

W need to calculate p(e∩f) which is equal to p(f/e) × p(e)

p(e∩f) = 0.4 × 0.6

= 0.24

Hence, the value of p(e and f) is 0.24.

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The number of games that will be played will be 8 games.

It should be noted that the mathematical relationship between the total cost for a person to bowl at the local bowling alley and the number of games played is represented by

y = 3.50x + 6.00.

The games that you can bowl for $34 will be:

y = 3.50x + 6.00.

34 = 3.50x + 6.00.

Collect like terms

3.50x = 34 - 6

3.50x = 28

Divide

x = 28 / 3.50

x = 8

Therefore, the number of games will be 8 games.

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The sales increased exponentially at the rate of $6,65,00,000/year for the next three consecutive years.

We have sales record of communication industry.

We have to determine the increase in sales over the three-year period.

The advantage of using prepaid phone plans is you only pay for the data you use, and you're not tied into a lengthy service contract.

According to the question -

Initial Sales -  $500,000

Sales after 3 years -  $200,000,000

Therefore, the rate at which the sales increased is -

r = [tex]$\frac{2\times 10^{8}- 5\times 10^{5} }{3}[/tex] = $6,65,00,000

Hence, the sales increased exponentially at the rate of $6,65,00,000/year for the next three consecutive years.

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The amount of apple juice needed in a 64 fluid ounce bottle of cranapple juice is 40.8 fluid ounce.

The beverage company makes 100% cranapple juice which is made up of 3 1/4 cranberry juice to 5 3/4 apple juice. Converting to decimal, it is made up of 3.25 cranberry juice to 5.75 apple juice. The ratio of cranberry juice to apple juice in the cranapple juice would be

=3.25/5.75

=> Total ratio = 3.25 + 5.75 = 9

The amount of apple juice needed in a 64 fluid ounce cranapple juice would be

5.75/9 × 64 = 40.8  fluid ounce

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Missing terms of the geometric sequence = -10, -5, -2.5

For the geometric sequence to the nth term, the formula is

[tex]t_{n}[/tex] = a [tex]r^{n-1}[/tex]

Here the sequence is -20, __ , __, __, -1.25...

So we have to find the 2nd, 3rd and 4th terms of the sequence.

We know the 5th term of the series by which we can find out the common ratio.

[tex]t_{5}[/tex] = -20 [tex]r^{5-1}[/tex]

-1.25 = -20 [tex]r^{4}[/tex]

[tex]r^{4}[/tex] = 1.25/20

   = 1/16

r = 1/2

The common ratio is 1/2

[tex]t_{2}[/tex] = -20 [tex](\frac{1}{2})[/tex]

   = -10

[tex]t_{3}[/tex] = -20 [tex](\frac{1}{2} )^{2}[/tex]

  = -20 [tex]\frac{1}{4}[/tex]

  = -5

[tex]t_{4}[/tex] = -20 [tex](\frac{1}{2} )^{3}[/tex]

   = -20[tex]\frac{1}{8}[/tex]

   = -2.5

Therefore the missing terms are -10, -5 and -2.5.

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The equation of the line satisfies the given conditions. the line passes through (25,24) and is perpendicular to y=6 is x = 25.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

The line passes through the point (25, 24)

y - 24 = m(x - 25)

y = 6

The slope of the line perpendicular to the line y = 6

m = not defined

m = 1/0

y - 24 = [1/0](x - 25)

x - 25 = 0

x = 25

Thus, the equation of the line satisfies the given conditions. the line passes through (25,24) and is perpendicular to y=6 is x = 25.

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Answer:

(3x,3y) if you're representing the dilation from A' -> A

Step-by-step explanation:

I think that it would be (3x, 3y) bc the original point was dilated by 1/3 (3 x 1/3 = 1, 9 x 1/3= 3), so I'm wondering which dilation it specifies for exactly, b/c if its for A', then the answer would be Betty. Hope this helps somewhat tho

The linear equation, he makes approximately 9 balls in the next three baskets and the balls in the first match.

According to the statement

We have to find that the Number of the basket in the each of the game.

So, For this purpose, we know that the

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

From the given information:

Marcus made 6 baskets in his first basketball game. In each of the next 4 games,he made the same number of baskets. If he made a total of 34 baskets.

Then

In first game = 6 basket ball.

The linear equation form is a

3x +6 = 34

Then

3x =  34 - 6

3x  = 28

x = 28/3

x = 9.3

After conclusion, The basket in the first game is a 6 baskets and in the next 3 games he makes a 28 baskets.

So, The linear equation, he makes approximately 9 balls in the next three baskets and the balls in the first match.

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The population of the seven countries, arranged from least to greatest in scientific notation is: 1.38 x 10², 1.48 x 10², 1.9 x 10², 2.75 x 10², 6.53 x 10², 6.81 x 10² and 8.64 x 10².

To arrange from least to the greatest means to arrange from the smallest number to the largest number. Before we can arrange the population of the seven countries from the least to the greatest, we would need to resolve the numbers and convert to scientific notation, hence:

Therefore, if we are to arrange the population of the seven countries, starting with the smallest number and ending with the largest number in scientific notation, we will have: 1.38 x 10², 1.48 x 10², 1.9 x 10², 2.75 x 10², 6.53 x 10², 6.81 x 10² and 8.64 x 10².

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A. The mistake that Nia made when solving her expression is that she added all the numbers before multiplying by 4.

B. The expression, if n represents the number of teams, will be 3 + 4n.

C. The expression be different if there were two coaches for each team will be 1 + 6n 4.

It should be noted that the mistake that Nia made when solving her expression is that she added all the numbers before multiplying by 4.

Therefore, the correct answer will be:

= 1 + 2 + 3 × 4

= 1 + 2 + (3 × 4)

= 3 + 12

= 15

B When the number of teams is n, with four dancers in each, then the expression is:

1 + 2 + 4n  = 3 + 4n

C When the number of teams is n and each team consists of two coaches and 4 dancers then the expression is:

1 + (2 + 4)n = 1 + 6n

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Correct way of calculation, using PEMDAS

The mistake was incorrect order of operations. Addition (A)  comes after multiplication (M) or division (D) if no parenthesis (P) or exponents (E) present.

If the number of teams is n, with four dancers in each, then the expression is:

Here 4n is the number of dancers in n teams.

If the number of teams is n and each team consists of two coaches and 4 dancers then the expression is:

Here 6n is the number of coaches and dancers in n teams.

Answer:

NAH THIS ANSWER IS EASY: ANSWER 2500

Step-by-step explanation:

Answer:

198.5

Step-by-step explanation:

The equation of the line passing through points (-2,5) and (3,-4) is 9x + 5y = 7.

Hence, option C) 9x + 5y = 7 is the correct answer.

Given the data in the question;

Point1 (-2,5)

Point2 (3,-4)

First, we determine the slope of the of the line,

m = (y₂-y₁)/(x₂-x₁)

m = ( -4-5 )/( 3-(-2) )

m = -9/5

Using the formula for equation, we determine the y-intercept

y = mx + b

Plug in the first point (-2,5) and the slope and then solve for the y-intercept b.

5 = -9/5(-2) + b

5 = 18/5 + b

b = 5 - 18/5

b = ( 25 - 18 )/5

b = 7/5

Now, plug the slope and y-intercept into y = mx + b to determine the equation of the line.

y = mx + b

y = -(9/5)x + 7/5

Convert to standard form

y = -(9/5)x + 7/5

Multiply each term by 5

5y = -9x + 7

5y + 9x = 7

9x + 5y = 7

The equation of the line passing through points (-2,5) and (3,-4) is 9x + 5y = 7.

Hence, option C) 9x + 5y = 7 is the correct answer.

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Applying addition of integers, it is found that this number is of -5.

The addition of these following three pairs is given as follows:

Hence, we got three pairs of values from these cards, all cards are used, and all the additions result in -5, hence, this number is of -5.

The addition of integers used in this problem is as follows:

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For 90 trials , expected no. of times of rolling doubles will be 15 times.

It is given that Clarence roll doubles with two cubes.

We have to find out the expected number of times of rolling doubles in 90 trials.

What do you mean by probability ?

Probability is the ratio of the number of favorable outcomes to the total number of outcomes of an event.

As per the question ;

Clarence roll doubles in 90 trials with two cubes.

We know that ;

There are 36 outcomes for a pair of dice.

So ;

In a pair , there are 6 possible doubles.

i.e.,

1-1 , 2-2 , 3-3 , 4-4 , 5-5 and 6-6

So ;

Probability will be ;

= 6 / 36

or

= 1 / 6

And

For 90 trials , expected no. of times of rolling doubles will be ;

= [tex]\frac{1}{6}[/tex] × 90

= 15 times

Thus , for 90 trials , expected no. of times of rolling doubles will be 15 times.

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