Suzie solved a linear equation for y. This equivalent equation was her result. y = 7x + 23 Which equations could have been the linear equation Suzie manipulated? Check all that apply. y + 7x = 23 –7x + y = 23 2y – 14x = 46 y – 7x = –23 7x – y = –23

Answer:

P(t) = 300e^0.15t

Step-by-step explanation:

The exponential equation for calculating the growth rate is expressed as;

P = P0e^rt

P0 is the initial value =300,

r is the growth rate = 15% = 0.15

t  is the time

Substitute;

P = 300e^0.15t

Hence the function that represent the information is P = 300e^0.15t

The correct answers are:

Functions are expressions separated by an equal sign. They have both dependent and independent variables.

* Lets explain how to solve the problem

- The table of the function has two column

# First column labeled x with entries:

 -6 , 7 , 4 , 3 , -5

# Second column labeled f(x) with entries:

  8 , 3 , -5 , -2 , 12

∴ The ordered pairs of the function f(x) are:

 (-6 , 8) , (7 , 3) , (4 , -5) , (3 , -2) , (-5 , 12)

* Lets complete the missing

∵ The value of x in the first row is -6

∵ The value of f(x) in the first row is 8

∴ The function notation in the 1st row is f(-6) = 8

- The ordered pair given in the first row of the table can be

 written using function notation as f(-6) = 8

∵ The ordered pair whose x = 3 is (3 , -2)

∴ The value of f(x) when x = 3 is -2

∴ f(3) = -2

∵ The ordered pair whose f(x) = -5 is (4 , -5)

∴ The value of x when f(x) = -5 is 4

∴ f(x) = -5 when x is 4

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By using normal Distribution we found 15 women ran faster than Joan

The  average amount of variability in our data set is known as Standard Deviation.

A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.

standard deviations from the mean is used to measure Z-score

If data point's score is identical to the mean score then the z score will be zero

 Standard deviations a score X is above or below the mean measures z-score measures

From z- table we find the p values respectively.

By given , Joan’s finishing time for the Bolder Boulder 10K race was 1.83 standard deviations faster than the women’s average for her age group.

So,  Z - score = 1.83

From z - table,

If  Z =1.83 , then p-value is 0.9591.

It means that Joan was faster than 95.91% of the participants and slower than 100-95.91 = 4.09% of the participants.

Since, There were 375 women who ran in her age group.

we computed that, 4.09% faster than Joan

Number of women run faster than Joan is, = 375/100*4.09= , nearly = 15

Thus, 15 women ran faster than Joan.

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Answer:

Multiply 10 and 2 each by 4 and .07. Then add.

Step-by-step explanation:

Answer:

Multiply 10 and 2 each by 4 and .07. Then add.

Step-by-step explanation:

Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.

How to Interpret a Box-and-whisker Plot?

In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.

The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.

Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.

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Answer:

1/12

Step-by-step explanation:

Given the following :

Actual height of pyramid = 24 ft

Dimension of scaled model :

Height = 2ft ; width = 1ft

a scale factor is a number used to reproduce a reduced dimension of a model by multiplying the actual dimeznsion or size of the model or object.

Since the height is of the scaled model is less than the actual height of the pyramid ; then it could be said that the scale factor is a fraction, because reduction has occurred.

(Height of scaled model / height of actual pyramid)

(2ft / 24ft) = 1/12

The equation of the line in slope - intercept form is -

y = - 5x + 77.

The equation of a straight line in slope - intercept form is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is the equation as -

77 - y = 5x

We have the equation in the slope - intercept form as -

77 - y = 5x

y = 77 - 5x

y = - 5x + 77

Therefore, the equation of the line in slope - intercept form is -

y = - 5x + 77.

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Answer:

1. a. A

2. c. C

3. a. A > C

Step-by-step explanation:

Absolute value is the translation of the number inside | ? | into a positive number.

Examples:

| -245 | = 245

| -47 | = 47

| 69 | = 69

| 21 | = 21

| -4 | = 4

a) The probability that the test comes back negative for all six people is  95.8%,

b)  The probability that the test comes back positive for at least one of the six people is 4.2%.

(a) To find the probability that the test comes back negative for all six people, we can use the fact that the test is 99.3% effective in accurately detecting the absence of the antibody.

Since the test is 99.3% effective, the probability of it coming back negative for each individual who does not have the antibody is 0.993. Therefore, the probability that the test comes back negative for all six people is calculated as follows:

P(negative for all 6) = (0.993)^6 ≈ 0.958

Therefore, the probability that the test comes back negative for all six people is approximately 0.958, or 95.8%.

(b) To find the probability that the test comes back positive for at least one of the six people, we need to consider the probability of a false positive.

The probability of a false positive, which is the probability of the test coming back positive when the antibody is not present, is given as 0.007. Therefore, the probability of the test correctly identifying the absence of the antibody is 1 - 0.007 = 0.993.

The probability that the test comes back positive for at least one person is the complement of the probability that the test comes back negative for all six people. So we can calculate it as follows:

P(positive for at least one person) = 1 - P(negative for all 6) ≈ 1 - 0.958 = 0.042

Therefore, the probability that the test comes back positive for at least one of the six people is approximately 0.042, or 4.2%.

In summary, the probability that the test comes back negative for all six people is approximately 95.8%, while the probability that the test comes back positive for at least one of the six people is approximately 4.2%.

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Answer: -3

Step-by-step explanation:

The common ratio of the geometric sequence –4, 12, -36,... is -3.

12/(-4) =-3

-36/(12) = -3

They both multiply -3 for the next number.

A and B are events defined on a sample space, with P(A) = 0.6 and P(BIA) = 0.3. then P(A and B) = 0.18

Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.

If A and B are events defined on the sample space with P(A) = 0.6 and P(BIA) = 0.3.

To find P(A and B),

we use the formula of conditional probability,

P( A and B ) = P (BIA) P(A)

P( A and B ) = 0.6 × 0.3

P( A and B ) = 0.18

Therefore, P ( A and B ) is 0.18.

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Answer:

30 more dollars

Step-by-step explanation:

Answer:

no ;)

Step-by-step explanation:

Answer:

8.15

Step-by-step explanation:

We have 4 quoters in an hour. 15, 30, 45, 60(00)

so 09 minutes is closer to 15 than to 00. making 8.15 the correct answer.

There will be 16 possibilities for flipping the coin four times.

A sample space is a collection or a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”. The subset of possible outcomes of an experiment is called events. A sample space may contain a number of outcomes that depends on the experiment.

Given that, A two-sided coin has heads on one side and tails on the other side. flipped for four times.

We need to determine the sample space for flipping the coin four times.

Since, four coins are tossed, so the possibilities are either :-

HHHH or TTTT or HHHT or HHTH or

HTHH or THHH or HHTT or HTTH or

HTHT or THHT or THTH or TTHH or

HTTT or THTT or TTHT or TTTH

It means number of elements in sample space =

2⁴ = 16

Therefore, the sample space =

S = {HHHH, TTTT, HHHT, HHTH,

HTHH, THHH, HHTT, HTTH, HTHT,

THHT, THTH, TTHH, HTTT, THTT,

TTHT, TTTH}

Hence, there will be 16 possibilities for flipping the coin four times.

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You have points R(2, 10) and S(6, - 8).

There two ways to construct a right triangle with RS being a hypotenuse.

Please see both ways reflected in the attached.

One triangle is RST and another one is RSU with red or blue legs.

The augmented matrix of the solution to the system of equations is x = 4 and y = -1/2.

The augmented matrix of the system of equations 2x + y = 8 and 3x - y = 7 can be written as follows:

|2x + y = 8 |

|3x - y = 7 |

This can be rewritten in matrix form as:

|2 1 | |x | | 8 |

|3 -1| |y | | 7 |

To solve this system of linear equations, we can use the Gauss-Jordan elimination method. First, we add the first row to the second row to eliminate the x coefficient from the second equation:

|2 1 | |x | | 8 |

|0 -2| |y | | 1 |

Then, we can divide the second row by -2 to get the coefficient of y to be 1:

|2 1 | |x | | 8 |

|0 1 | |y | |-1/2|

Finally, we can subtract the second row from the first row to eliminate the y coefficient from the first equation:

|2 0 | |x | | 8/2|

|0 1 | |y | |-1/2|

Therefore, the solution to the system of equations is x = 4 and y = -1/2.

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Answer:

The change should Sara receive from the $10 bill is $3.56.

Step-by-step explanation:

Given:

The table shows the prices of some breakfast items at a restaurant.

Item                                      Price

One egg                               $1.69

Slice of bacon                      $1.49

Glass of orange juice          

$1.09

Sara ordered 2 eggs, a slice of bacon, and  a glass of orange juice for breakfast.

The sales tax for the order was $0.48.

She paid for her breakfast with a  $10 bill.

Now, to find the change should Sara receive from the $10 bill.

Bill for the Sara's breakfast:

2 eggs =

A slice of bacon = $1.49.

A glass of orange = $1.09.

The sales tax = $0.48.

Total bill =

Sara paid for the breakfast bill = $10.

Now, to get the change Sara should receive we subtract the amount of bill from the money Sara paid for the bill:

Therefore, the change should Sara receive from the $10 bill is $3.56.

Answer:

Her change would be 3 dollars and 56 cents

Step-by-step explanation:

1.69 times 2 because she ordered 2 eggs

1.49 for the bacon

1.09 for the orange juice

0.48 for the sales tax

add them all up

it would equal 6.44

then subtract 6.44 from 10 which would equal 3.56

Answer:

3,000

Step-by-step explanation:

Answer:

I got 3,000

Step-by-step explanation:

The profit function is the difference between the cost and the revenue functions.

The true statement is (a) If material 2 is used, Carrie will earn a profit if she sells chairs for more than $150 each.

From the complete questions, the profit functions are calculated as follows:

Material 1

\(P(x) = 5000000- 20000x - 200000x + 2000x^2\)

\(P(x) = 5000000-220000x + 2000x^2\)

Material 2

\(P(x) = 4000000 - 10000x - 160000x+ 1000x^2\)

\(P(x) = 4000000-170000x+ 1000x^2\)

Material 3

\(P(x) = 2000000 - 5000x - 54000x - 270x^2\)

\(P(x) = 2000000 -59000x - 270x^2\)

Next, we test the options

Option 1: When material 2 is used

A price is greater than $150 is $151.

Calculate P(151) using \(P(x) = 4000000-170000x+ 1000x^2\)

So, we have:

\(P(151) = 4000000-170000 * 151+ 1000* 151^2\)

\(P(151) = 1131000\)

P(151) is greater than 0; this represents a profit

Hence, option (1) is true

Option 2: When material 1 is used

A price is less than $50 is $49.

Calculate P(49) using \(P(x) = 5000000-220000x + 2000x^2\)

So, we have:

\(P(49) = 5000000-220000 * 49 + 2000* 49^2\)

\(P(49) =-978000\)

P(49) is less than 0; this represents loss

Hence, option (2) is false

Option 3: When material 3 is used

Calculate P(45) and P(160) using \(P(x) = 2000000 -59000x - 270x^2\)

So, we have:

\(P(45) = 2000000 -59000 * 45 - 270 * 45^2\)

\(P(45) = -1201750\)

P(45) is less than 0; this represents loss

Hence, option (3) is false

Option 1: When material 2 is used

Calculate P(30) and P(120) using \(P(x) = 4000000-170000x+ 1000x^2\)

So, we have:

\(P(30) = 4000000-170000*30+ 1000*30^2\)

\(P(30) = -200000\)

P(30) is less than 0; this represents a loss

Hence, option (4) is false

Option 2: When material 1 is used

Calculate P(40) and P(70) using \(P(x) = 5000000-220000x + 2000x^2\)

So, we have:

\(P(40) = 5000000-220000*40 + 2000*40^2\)

\(P(40) = -600000\)

P(49) is less than 0; this represents loss

Hence, option (5) is false

The above means that:

The true statement is (a) If material 2 is used, Carrie will earn a profit if she sells chairs for more than $150 each.

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Answer:

The correct answer is A.

Step-by-step explanation:

The correct answer is A.

To find the length of one side of the square, we need to take the square root of the area. Therefore, the square root of 90 is approximately 9.49 feet. Since this value falls between 9 feet and 10 feet, but is closer to 9 feet, the statement "√90 feet is between 9 feet and 10 feet but is closer to 9 feet" is true. So, Jimmy should cut the carpet to 9.49 feet to fit the square-shaped room.

Value of variable x in the equation is 2.

In mathematics, an equation is a statement that two expressions are equivalent. It comprises of two sides with a phrase on each, usually divided by an equal symbol (=). An equation declares that for some or all of the values of the variables in the equation, the two expressions have the same value. Equations can include one or more variables and can be either linear or nonlinear. Finding the values of the variables that make the equation true is the first step in solving an equation.

Given equation

3(x+6)=24

Dividing the terms by 3, we get

x+6=8

x=8-6

x=2

Hence, value of variable x in the equation is 2.

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Answer:

Yes, you do have enough money for the jeans.

Step-by-step explanation:

Answer:

5%

Step-by-step explanation:

50.40 - 48 = 2.4.

The sales total sales tax was $2.40.

2.4 is 5% of the original $48 that was the listed price of the phone.

The largest ratio, among the following ratios: 5/36, 2:9, 3 to 18, 1:3 is 1:3.

The ratio refers to the relative size of one quantity compared to another.

The ratio, which is the quotient of two quantities or values, can be expressed as a decimal, percentage, or fraction.  We can also express the ratio in its standard form (:).

Given   Sum of     Equivalent

Ratio     Ratios          Ratios

5/36        36         13.89% or 0.1389

2:9           11          18.18% or 0.1818

3 to 18     21          14.28% or 0.14.28

1:3            4           25% or 0.25

Thus, we can conclude that 1:3 is the largest ratio amont the others.

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The end-points of the line segment will be negative 1.25 and 0.25.

A number line refers to a straight line in mathematics that has numbers arranged at regular intervals or portions along its width. A number line is often shown horizontally and can be postponed in any direction.

The length of the line segment is 1.50 units and the midpoint of the line segment is negative 0.50. Then the end-points of the line segment are given as,

⇒ - 0.50 ± (1.50) / 2

Simplify the expression, then we have

⇒ - 0.50 ± (1.50) / 2

⇒ - 0.50 - (1.50) / 2, - 0.50 + (1.50) / 2

⇒ - 0.50 - 0.75, - 0.50 + 0.75

⇒ - 1.25, 0.25

The end-points of the line fragment will be negative 1.25 and 0.25.

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