Question 10(Multiple Choice Worth 2 points)
(Adding and Subtracting with Scientific Notation MC)
Simplify (3.7 x 10-9) - (8.2 x 10-8). Write the final answer in scientific notation.
O-7.83 x 10-8
-7.83 x 10-9
O-4.5 x 10¹
O-4.5 x 10-¹

Assuming no deposits or withdrawals are made,  the amount in the  account after 19 years is: 11,454. 133.

Using this formula

A = P(1+r/100)ⁿ

Where:

A = Amount =?

P = Principal = $4700

r = Interest rate =4.8%

n = the number of periods =19 years

Let plug in the formula

A = 4,700 (1 + 4.8/100)¹⁹

A = 4,700 (1 + 0.048)¹⁹

A = 4,700 (1.048)¹⁹

A = $11,454. 133

Therefore the amount is $11,454. 133.

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The height should you drop an object in order for it to have a velocity of 60 ft/sec is 55.9 feet

The equation given in the problem is written below

v = √2ha

velocity, v =  60 ft/sec

height, h = ?

acceleration due to gravity, a = 32.2ft/sec^2

The problem asks for height hence we make h the subject of the formula

v = √2ha

v^2 = 2ha

h = v^2 / 2a

substituting the values in to the equation

h = 60^2 / (2 * 32.2)

h = 3600 / 64.4

h = 55.9 feet

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Answer: x∈(-3,-1)

Step-by-step explanation:

13<-5x+8<23

13-8<-5x+8-8<23-8

5<-5x<15

Divide the double inequality by 5:

1<-x<3

Multiply the double inequality by -1:

-1>x>-3

Thus, x∈(-3,-1)

The probability that a randomly selected passenger has a waiting time greater than 4.25 minutes is 0.5278

The uniform distributed between a and b minutes.

The probability of finding a value above x is:

P(X > x) = [tex]\frac{b-x}{b-a}[/tex]

The time is evenly distributed between 0 and 9 minutes.

This implies that a=0 , b=9

Determine the likelihood that a randomly selected passenger will have to wait longer than 4.25 minutes.

p(X > 4.25) = [tex]\frac{9-4.25}{9-0}[/tex]

                 = 0.5278

There is a 52.78% chance that a randomly selected passenger will have to wait longer than 4.25 minutes.

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Answer:

9 dimes, 4 nickels, 12 quarters

90 cents + 20 cents + 300 cents = 410 cents = $6.83

Step-by-step explanation:

q=5+d

n=d-7

q+n+d=25

5 + d + d - 7 + d = 25

3d-2=25

3d=27

d=9

25 - 9 = 16 nickels and quarters

q + n = 16 ---> q=16-n

n=d-7 ---> d=n+7

q=5 + n + 7

q=n+12

n+12 = 16-n

2n=4

n=4

25-(9+4)= 12 quarters

He has 2 nickels, 9 dimes, and 14 quarters, with a total value of $4.50

I am going to assume that the "and" in "five more quarters and dimes" and the "and" in "seven fewer nickels and dimes" is actually "than" because otherwise, there is no context in this question. If my answer is incorrect, please tell me how to correctly interpret this question.

In this scenario, the "and" in "five more quarters and dimes" and the "and" in "seven fewer nickels and dimes" is actually "than."

Amount of nickels - x

If there are seven fewer nickels than dimes, the amount of dimes is x + 7. There are five more quarters than dimes, so the amount of quarters is x + 7 + 5, which equals x + 12.

Therefore, there are 2 nickels. Now we must figure out the number of quarters and dimes.

x + 7 = 9

x + 12 = 14

There are 9 dimes and 14 quarters.

Nickels are each worth 5 cents. 2 times 5 is 10 cents.

Dimes are each worth 10 cents. 9 times 10 is 90 cents.

Quarters are each worth 25 cents. 14 times 25 is 350 cents.

Now, we add. 10 + 90 + 350 = 100 + 350 = 450.

REMEMBER, THIS IS IN CENTS. WE MUST STILL CONVERT IT INTO DOLLARS.

450 divided by 100 is $4.50

The missing number to complete the proportion is 1

Proportion defines that the two given ratios are equivalent to each other. That is two ratios (or fractions) are equal e.g 2:6 = 1:3

Given: 14 seats in 2 rows = 7 seats in ___rows

If each row in a classroom has equal seats. If there are 14 seats in 2 rows of the classroom then we can say there are 7 seats in each row (1 row).

Thus, 14 seats in 2 rows = 7 seats in 1 row

Therefore,  the missing number to complete the proportion is 1. You should type 1

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Points scored by the last player is 10 points. this can be calculated by using BODMAS rule by forming equation.

What is an equation ?

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

Main body:

Points scored by 4 players = 6 each

Total points scored by 4 players = 4*6

                                                      = 24

Total points scored by team = 34

Points scored by last player or 5th player = total points - points scored by 4 players

Points scored by 5th player = 34-24

                                              = 10

Hence point scored by last player is 10.

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After solving the value of x is 2.

From the figure:

Let ABCDE be the figure such that:

AB = 6x , BC = 6 , CD = 4,and DE = CE - CD  = 12 - 4 = 8.

BD and AE are parallel lines such that:

AB/BC = ED/CD

6x/6 = 8/4

x = 8/4

x = 2.

Therefore After solving the value of x is 2.

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34 students red is their favorite color

2 out of 7 of the pupils in year 9 say their favourite colour is red

Fraction of pupil that say red is their favorite colour is 7/9

There are 119 pupils in year 9

We need to calculate the number of students out of 119 that would say that their favourite colour is red

To find that,

we multiply the fraction of students that like red with the total number of students

2/7 * 119

= 34

Therefore, if 2 out of 7 of the pupils in year 9 say their favourite colour is red. Then 34 out of 119 pupil will say that their favourite colour is red.

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Answer:

Multiples of 2 = 2, 4, 6, 8, 10, 12

Multiples of 3 = 3, 6, 9, 12, 15,18

The LCM is 6.

Step-by-step explanation:

The equation of the line with slope -1/7 is (y-3) = -1/7(x-3).

According to the question,

We have the following information:

Slope of the line = -1/7

Points through which line is passing = (3,3)

We know that the following formula is used to find the equation of the line:

(y-y') = m(x-x') where m is the slope of the line

In this case, we have x' = 3 and y' = 3.

(y-3) = -1/7(x-3)

This expression can be solved further by multiplying -1/7 into the bracket and then by moving 3 from the left hand side to the right hand side. Then this equation will be in slope-intercept form.

Hence, the correct option is B.

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[tex]{ \boxed{ \orange{ \sf{421.875 \: {cm}^{3}}}}} [/tex]

Step-by-step explanation:-

[tex]{ \red{ \sf{Volume \: of \: the \: cube }}} = { \green{ \sf{ {a}^{3}}}} [/tex]

[tex]{ \red{ \sf{Volume \: of \: the \: cube } = }} \: \: { \green{ \sf{7.5 \times 7.5 \times 7.5}}}[/tex]

[tex]{ \red{ \sf{Volume \: of \: the \: cube = { \green{ \sf{56.25 \times 7.5}}}}}}[/tex]

[tex]{ \boxed{ \sf{Volume \: of \: the \: cube = 421.875 {cm}^{3}}}} [/tex]

The image of the point (3, 6) by means of the translation formula described in the statement is (5, 1).

Herein we find the coordinates of an ordered pair set on Cartesian plane, whose image has to be found by using a rigid transformation formula known as translation formula, whose definition is described and explained below:

P'(x, y) = P(x, y) + T(x, y)

Where:

If we know that P(x, y) = (3, 6) and T(x, y) = (2, - 5), then the image of the original point according to the translation formula is now determined:

P'(x, y) = (3, 6) + (2, - 5)

P'(x, y) = (3 + 2, 6 - 5)

P'(x, y) = (5, 1)

The image of the point by translation formula is (5, 1).

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it represents a distance between observed and predicted values

What is residual?

A residual in statistics is the discrepancy between an observed value and a value that was predicted.

Typically, the anticipated value is based on a model, like a linear regression model. The prediction error is represented by a residual, which can be either positive or negative. A positive residual indicates a difference between the observed and expected values, whereas a negative residual indicates the opposite. Specifically, the residual's absolute value is the distance between the observed value and the predicted value.

For evaluating a model's correctness, residuals are crucial. The residuals should be randomly distributed in the vicinity of zero if the model is valid. The residuals will be biased either in favor of or against the null hypothesis if the model is not accurate. A model's goodness of fit can also be evaluated using the residual. Relatively small residuals characterize a model with a high goodness of fit. Remainders that are far from zero will be present in a model with a low goodness of fit.

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Answer:

67%

Step-by-step explanation:

[tex]\frac{268}{400}[/tex] X 100

Answer:

67%

Step-by-step explanation:

268 ÷ 400 = 0.67 = 67%

The Slope of the first function is greater than the slope of the second function.  We can say that the function f(x) =x is steeper than the second function

What is a Slope?

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, m = y/x, where m is the slope, can be used to express the change in the y coordinate with regard to the change in the x coordinate.

Take notice that tan = y/x.

In the given question, we have: two functions:

So, finding the slope of each of the functions;

The slope of the first function;  f(x) =x is 1;

The slope of the second function: m(x) =[tex]\frac{3}{5} f(x)[/tex];
Since the Slope of the first function is greater than the slope of the second function.  We can say that the function f(x) =x is steeper than the second function because the graph depends on the slope.

Hence,

the Slope of the first function is greater than the slope of the second function.  We can say that the function f(x) =x is steeper than the second function.

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The correct statement regarding the solution of the inequality 8x - 6 < 3x + 19 is given as follows:

D. She knows that the solution must be either all the values less than 5 or all the values greater than 5.

The inequality is presented as follows:

8x - 6 < 3x + 19.

Lin finds the value of x = 5 for which the two sides of the inequality are equal. Then, there are only two cases for the solution, which are listed as follows:

Thus option D gives the correct option regarding how to find the solution.

The justifications for the other options being wrong are given as follows:

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Answer:

I think its D.... id/k I think it is.

Step-by-step explanation:

if we just randomly guess on each of the 4 questions, Then the probability that you get exactly 1 question correct is 1/4.

Probability formula: P(E) = favourable outcomes/Total outcomes

The number of questions is 10

The options for each question are 4.

Possible answers are 1.

Then,

favourable events = 1 × 10= 10

Total events = 4× 10= 40

Now, find the probability by putting the values as follows:

P(E) = favourable outcomes/Total outcomes

P(E) = 10/40

P(E) = 1/4

Therefore, the probability of doing all questions correct is 1/4

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Answer:

Angle CEB

Step-by-step explanation:

They are vertical angles

:]

From the data in the table relating time and depth, we have that:

a) The scatter plot is graphed at the end of the answer.

b) The scatter plot has negative correlation.

c) The estimate for the depth at a time of 15 seconds is of 50.37 cm.

The scatter plot is built inserting all the points of the table in a graph, which are in the following format:

(Time in seconds, Depth in cm).

Hence the scatter plot will be composed by a set of points, without an image, as is shown at the end of the answer.

The points from the table are listed as follows:

(2, 47), (4, 41), (6, 38), (8, 37), (10, 32), (12, 24), (14, 20), (16, 19).

As the input variable time increases, the output variable depth decreases, meaning that the points in the scatter plot also follow the format of a decreasing line, hence there is negative correlation in the scatter plot.

These points are also inserted into a linear regression calculator to built the line of best fit, which is defined as follows:

y = -2.07x + 50.89.

At 15 seconds, the estimate is obtained replacing the lone instance of x in the equation by 15, hence:

y = -2.07 x 0.25 + 50.89 = 50.37 cm.

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Answer:

21. A basket holds n apples. You pick (2n - 3) apples, and your friend picks

(n+4) apples. How many apples do you and your friend pick together?

How many baskets do you need to carry all the apples? Justify your answer.

Step-by-step explanation:

(2n - 3)(n + 4) binomial times a binomial equals

2n^2 + 5n - 12

The sum of consecutive odd cubes of 8128 is 1³+3³+5³+7³+9³+11³+13³+15³

Therefore, 1+27+125+343+729+1331+2197+3375=8128

Consecutive numbers are those that come after each other in descending order from the smallest to the largest. The difference between consecutive numbers is always fixed and follows a predictable pattern. For example, the first three consecutive natural numbers are 1, 2, 3. The simplest way to find consecutive numbers is to look at the number set and find the number that is either before or after the term of interest.

We know that consecutive odd numbers are 1,3,5,7,9,11,13,15,17..

Here 8128 is a perfect square

And it can be written as the sum of consecutive odd cubes as follows:

1³=1

3³=27

5³=125

7³=343

9³=729

11³=1331

13³=2197

15³=3375

The sum of consecutive odd cubes of 8128 is

=1³+3³+5³+7³+9³+11³+13³+15³

=1+27+125+343+729+1331+2197+3375

=8128

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If Lines J and k are perpendicular. The slope of line k is 3, the slope of line j is -1/3

When two lines are perpendicular to each other, the product of their slope results in -1

slope of line j x slope of line k = -1

slope of line j x 3 = -1

slope of line j  is 1/3

Therefore, if Lines J and k are perpendicular. The slope of line k is 3, the slope of line j is -1/3

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Out of 3000 students at the school , 200 student plays foot ball .

In the question ,

it is given that ,

fraction of students that are involved in sports at Greenville High School = 1/3 of total students ,

percent of students that plays football = 20% of sports students .

given that the total number of students present at the school = 3000

So , the number of students involved in sports = (1/3) × 3000

= 1000

number of students who plays football = 20% of 1000

= 0.20 × 1000            ....because 20% = 0.20

= 200

Therefore , Out of 3000 students at the school , 200 student plays foot ball .

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Answer:

12-12-12+i-12+i =0-i

.

.

.

,

The linear function that models the data-set is given as follows:

v = 4 + 0.4x.

The slope-intercept representation of a linear function is presented as follows:

y = mx + b

The coefficients of the function and their meaning are obtained as follows:

For this problem, the values of these parameters are given as follows:

Hence the equation is given as follows:

v = 4 + 0.4x.

The table is given by:

Money Spent (x) $0 $20 $40 $60

Pounds of Food (v) 4 12 20 28

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Answer:

Circle, hexagon, and oval

Step-by-step explanation:

They are all 2d.  

The two points that are collinear with the point D are points A and B which are on the same plane, K, as the point D

Collinearity of a set of points in geometry is the property of their being on a single line. A set of points with this property is known as a collinear set. In a broader sense, the term has been applied to aligned objects, that is, things that are "in a line" or "in a row."

If two or more points lie on the same line, they are said to be collinear in geometry. As a result, collinear points are the points that lie on a single straight line.

Therefore, the points are A and B.

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$21.00

25% off 28= 7

28-7=21