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The value of the function, f(g(x)), is [tex]f(g(x)) = 2(\sqrt{x+7} )- 3[/tex]. The correct option is the second option [tex]2(\sqrt{x+7} )- 3[/tex]

From the question, we are to determine the value of the given function, f(g(x))

From the given information,

The given functions are

[tex]f(x) = 2x- 3[/tex]

and

[tex]g(x) = \sqrt{x+7}[/tex]

To determine the value of f(g(x)), we will substitute the value of g(x) into the function, f(x)

That is,

[tex]f(x) = 2x- 3[/tex] becomes

[tex]f(g(x)) = 2(\sqrt{x+7} )- 3[/tex]

Hence, the value of f(g(x)) is [tex]2(\sqrt{x+7} )- 3[/tex]

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Answer:

Here is the work

Step-by-step explanation:

The equation of a line perpendicular to y = (-2/3)x - 7 is  y = (3/2)x + 17.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

We know lines perpendicular to each other have slopes that are negative reciprocals of each other.

So, the slope of the perpendicular line to the given line y = (-2/3)x - 7 is (3/2)

which passes through the point (-4, 11) is,

11 = (3/2)(-4) + b.

b = 11 + 6.

b = 17.

∴ y = (3/2)x + 17 is our required line.

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Answer:

Step-by-step explanation:

You are going to want to use the substitution method to solve. Substitute the given value of x (which is x=-3+y) into the equation x+y=3. Now solve the equation for y.You get y = 3. Plug in 3 for x in the other equation. You get x-3=-3 ---> x = 0.

So x = 0, y = 3

The total volume of the fruits is 640 when Syrup is poured over fruit pieces in a cylindrical can and then the lid is closed. The can's height is 10 cm, and its base has a surface area of 75 cm².

Given that,

Syrup is poured over fruit pieces in a cylindrical can and then the lid is closed. The can's height is 10 cm, and its base has a surface area of 75 cm².

We have to find which of the following comes closest to the total volume of the fruit pieces in the can if 110 cm³ of syrup is required to fill the can completely.

We know that,

Total volume of the cylinder can is equal to the sum of the total volume of fruits and total volume of Syrup.

So,

The total volume of the fruits is we have to find take x

The total volume of the cylinder is base× height=75×10

The total volume of the syrup is 110

So,

75×10=x+110

x=750-110

x=640

Therefore, The total volume of the fruits is 640 when Syrup is poured over fruit pieces in a cylindrical can and then the lid is closed. The can's height is 10 cm, and its base has a surface area of 75 cm².

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Time taken for the both train to meet each other is 1.8  hours

The distance between two stations = 360 miles

The speed of one train = 95 miles per hour

The speed of the second train = 105 miles per hour

The relative speed of the trains = 95 + 105

Add the numbers

= 200 miles per hour

We know

Speed = Distance / Time

The time = Distance / Speed

The time taken for the two trains to meet = Distance / relative speed

Substitute the values in the equation

= 360 / 200

= 1.8 hours

Therefore, both trains will meet each other after 1.8 hours

I have answered the question in general, as the given question is incomplete

The complete question is:

Two trains leave stations 360 miles apart at the same time and travel toward each other. One train travels at 95 miles per hour while the other travels at 105 miles per hour. How long will it take for the two trains to meet?

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Step-by-step explanation:

1.What is the equation of a parabola with a vertex at (0, 0)?

y = ax²; y = -ax²; x = ay²; x = -ay² where a = [½, 1 , 2]

Also an infinity of others at various values of a and various angles.

2.The focus lies above the vertex, so the parabola is vertical and the focal length p=10.25

Equation for up-opening parabola with vertex (h,k) and focal length p:

y=14p(x−h)2+k

y=14p(x−0)2+0y=141x2

3.Since the directrix is the line y=−10.25 , a point (x,y) is on the parabola if, and only if,

x2+(y−10.25)2=(y+10.25)2.

Therefore, x2−20.5y=20.5y and y=141x2.

hope I helped

No: of ways can the disk jockey select no more than 11 CDs is 1012

Combinations are mathematical operations that count the number of possible configurations for a set of items where the order of the selection is irrelevant. You can choose the components of combinations in any order. Permutations and combinations can be mixed up.

Combinations with Repetition. ...

Combinations without Repetition. ...

Combinations with Repetition.

There are more options for him to pick from than just 11 CDs when choosing "no more than 8 CDs," including 11,10,9,8,7, 6, 5, 4, 3, and 1.

Ways to choose 9 CDs: 13C9=10

​Ways to choose 8 CDs: 13C8= 45

Ways to choose 7 CDs: 13C7 = 120

Ways to choose 6 CDs: 13C6= 210

Ways to choose 5 CDs: 13C5 = 252

Ways to choose 4 CDs: 13C4 = 210

Ways to choose 3 CDs: 13C3= 120

Ways to choose 2 CDs: 13C= 45

Ways to choose 1 CD: 13C1 = 10

10+45 + 120 + 210 + 252 + 210 + 120 + 45 + 10 = 1012

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The coordinates of the resulting point, g' is :

(-1,1)

Given:

The coordinate plane allows for the translation of any object both horizontally (left/right) and  vertically (up/down).

Rules are:

The point g(2,1) is translated 3 units left.

we are asked to find the coordinates of the resulting point, g'.

By translating 2 units left, it means the x-axis value is made more negative by 2 units

So we are going to subtract two from the x-coordinate

So we have;

(2-3,1)

= (-1,1)

Hence we get the required coordinates.

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Answer:

answer = 19.2

Step-by-step explanation:

48 = 24 + 1.25x

48 - 24 = 1.25x

24 = 1.25x

24/1.25 = x

19.2 = x

Answer:b e and g

Step-by-step explanation:

because between e and g it increases the most

Answer:

y = 0.5x

Step-by-step explanation:

Slope = m = (2-0)/(1-0) = 1/2 or 0.5

y-intercept = b = 0 since it passes through (0,0)

Slope-Intercept form of a line is y = mx + b

So the equation is
y = 0.5x + 0

or

y = 0.5x

None of the tables represent a proportional relationship.

Proportional relationships are those in which the ratios of two variables are equal. Another way to think about them is that one variable in a proportional relationship is always a constant value multiplied by the other. This is known as the "constant of proportionality."

To determine whether a relationship is proportional, examine the ratios between the two variables. The relationship is proportional if the ratio is always the same. The relationship is not proportional if the ratio changes.

Fir the first table, the ratio varies. Also, the second table isn't constant.

Therefore, none has a proportional relationship.

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Answer:

the value of x is 9

Step-by-step explanation:

the sum of all angles of a triangle is 180

one side is 90 so,

90+7x+3x = 180

10x = 180-90

10x = 90

x=9

Answer:

See attached worksheet

Step-by-step explanation:

Taylor conducted a study using a 2x2 factorial design, and one of the independent variables was linked to a substantial main effect with significant difference.

A post-hoc test is not appropriate in this situation because it cannot provide reliable information about the conditions that are causing the significant difference. Post-hoc tests are only appropriate for small sample sizes and cannot be used to draw any definitive conclusions about the causes of a significant main effect.

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The distance in units of 2√5 between the point A(-2,3) and the line y =1/2x1.

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 points on a line is calculated using the slope of a line formula.

We will comprehend the slope-finding method and its applications in this article.

According to our question-

10/√5 *√5/√5*105/√5

Hence, The distance in units of 2√5 between the point A(-2,3) and the line y =1/2x1.

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The new sale price of the product after the deduction of discount is $60

Based on the given task content; percentage is the concept that can be used to solve for the new sale price.

New price of the product = Regular price of the product - (Percentage discount × Regular price of the product)

= 150 - (60% × 150)

= 150 - (0.6 × 150)

= 150 - 90

= $60

Consequently, new selling price of the product is $60

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Yes , there is convincing evidence that Brayden has improved his free-throw percentage when compared to previous year.

Brayden made 60 % free throws last year

P(Making  free throw last year) = 0.6

This year,

X% of 16 = 12

X/100 * 16 =12

75%

therefore, this year

P(Making  free throw this year) = 7.5

This clearly shows that he improved his free throw percentage compared to last year.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Probability has been introduced in Maths to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment.

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The required product will be 6 when 9 is multiplied by 2/3.

In mathematics, Multiplication operations perform Multiplying values on either side of the operator.

For example 4×2 = 8

We have to determine whether the product will be between 2/3 and 9

As per the given question, we have

2/3 and 9

⇒ 2/3 × 9

Apply the multiplication operation,

⇒ 18/3

Reduce the above fraction into the simplest form, and we get

⇒ 6

Thus, the required product will be 6 between 2/3 and 9.

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Answer: y=(1x)^x + 5000

Step-by-step explanation:

So the original equation is y=mx + b

And we know that each year the house increase by 5000, so the b is 5000

For the x which is the slope, we don't know what the slope is so we just say it as x and the ^x is for the number of years, let's say 3 years then it is ^3 and keep increasing like that up.

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Answer:

y = 4

Step-by-step explanation:

note that the y- coordinates of the 2 points are equal, both 4

This indicates that the line passing through them is horizontal with equation

y = c ( c is the value of the y- coordinates the line passes through ), then

y = 4 ← equation of line

Answer:

Step-by-step explanation:

answer is c

Answer:

Step-by-step explanation:

First, multiply the bases together. Then, add the exponent. Instead of adding the two exponents together, keep it the same. This is because of the fourth exponent rule: distribute power to each base when raising several variables by a power.

A clothing store offers customers a holiday sale of 30% off the price of x items. A customer then has an additional 15% off coupon that can be used when checking out then the function is  P(x) = 0.595x

Original price = x

Sale price  = 30% off:

x - 30%  =

x - 0.3x =

0.7x

Further discount 15% off:

0.7x - 15% =

0.7x - 0.7x*0.15 =

0.7x - 0.105x =

0.595x

The function is:

P(x) = 0.595x

Correct choice is C

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We know that Maya's earnings will be $498 for working 41 hours using simple mathematical operations.

A rule that specifies the right procedure to follow while evaluating a mathematical equation is known as the order of operations.

Parentheses, Exponents, Multiplication, Division (from Left to Right), Addition, and Subtraction are the steps that we can remember in that order using PEMDAS (from left to right).

So, earnings of Maya when she works for 41 hours are:

We know that Maya works for $12.00 per hour.

She's paid 1.5 times her hourly income when she works for more hours after 40 hours.

That will be: 12 × 1.5 = $18

Hence, Maya's income for 41 hours will be:

40 hours + 1 hour (Extra hour)

(12 × 40) + 18

480 + 18

$498

Therefore, we know that Maya's earnings will be $498 for working 41 hours using simple mathematical operations.

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