Given that F(x)=6x+4 and g(x)=4-x^2, calculate (a) F(g(0))=(b) g(F(0))=

Step-by-step explanation:

Step one:

Firstly we need to determine the place value of 8 in the term 78

in the term, we have 7 tens and 8 units

hence the place value of 8 in 78 is the units

Step two:

Now 1/10 of 8 is given as

0.1*8= 0.8

According to the problem statement, we are expected to find a number that has an 8 that is the same as 0.8.

Say 5.8, 6.8, 9.8

we cannot say exactly, but any number that has an 8 that is one decimal away is an equivalent

Answer:

$312.50

Step-by-step explanation:

240 + 25% = 300

300 + 12.50 =

312.50

Answer:

Step-by-step explanation:

The solutions to the answers are given below :

1) option c

2) option f

3) option b

4) option d

\(a)\frac{5x -7}{7(x+1)} \\\\\\b) 7(5x-7) (x+ 1 )\\\\\\)

  \(c)\frac{5x^3 + 7x +1}{5}\)

  \(d) \frac{5x-1 }{7(x+1)}\)

An Expression is a mathematical term consisting of variables, connected using some operators.

Example :  2x + 3

where x is the coefficient of 2 and both the terms are joined using the addition operator.

The verbal description of the corresponding expression is:

 1) The cube of the difference of 5 times  x and divided by the sum of 7 times x  and 1

 ans.\(\frac{5x - 7}{7(x+1)}\)

2) 7 times the difference of 5 times 6 and 7 and the sum of x and 1.

ans. \(7( 5x - 7 )( x+1)\)

3) The sum of 5 times the cube of x , 1 and 7 times x , divided by 5 .

ans. \(\frac{5x^3 = 7x +1}{5}\)

4) The difference of 5 times the cube of x and 7 divided by 7 times the sum of x and 1.

ans  \(\frac{5x -7}{7(x+ 1)}\).

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Answer:

I can explain how to complete each of the steps you have provided.

1. Draw a point at (1, -2)

This is a simple step. Just mark a dot on your paper at the coordinates (1, -2).

2.

Draw an 8-unit long radius

Using your compass, set the radius to 8 units. Place the compass on the point you drew in step 1 and draw a circle around it, making sure that the radius is 8 units long.

3. Using a compass

Draw a circle with your point from step one as your center and the point from step two as the side: This step is already completed in step 2.

4. Using a protractor draw a 70 degree arc

Place your protractor on the center of the circle (the point you drew in step 1) and draw a 70 degree arc on the circle.

5. Draw a central angle which intercepts your arc

Use a straight edge to draw a line from the center of the circle to each endpoint of the arc you drew in step 4. This creates a central angle, which is an angle whose vertex is at the center of the circle and whose sides intercept the circle.

6. Draw an inscribed angle which intercepts a 40 degree arc

Use a straight edge to draw a line from one endpoint of the 70 degree arc to the other endpoint. Then, draw a perpendicular bisector of this line, which intersects the center of the circle. This creates a 40 degree arc on the circle. Draw a line from the center of the circle to one endpoint of the 40 degree arc, and draw a line from that endpoint to the other endpoint of the 40 degree arc. This creates an inscribed angle, which is an angle whose vertex is on the circle and whose sides intercept the circle.

7. Draw a tangent line

Choose a point on the circle that is not on the 70 degree arc. Draw a line from that point tangent to the circle.

8. Draw a secant line

Choose two points on the circle that are not on the 70 degree arc. Draw a line through those points, which intersects the circle at two points.

9. Equation of your circle

The equation of a circle with center (a,b) and radius r is (x-a)^2 + (y-b)^2 = r^2. Using the coordinates of the center from step 1 and the radius from step 2, the equation of the circle is (x-1)^2 + (y+2)^2 = 64.

Answer:

2

Step-by-step explanation:

Answer:

the answer is 2

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

as 2.5 × 10-^5 is 250000 and b is 3100 and if you do 10-5 + 10-3 it is 10-8 which will give u 0.0008cm I think if my calculations r correct

Answer:

a

Step-by-step explanation:

just did it and got right

Answer: A null hypothesis is a statistical hypothesis that is tested for possible rejection under the assumption that it is true.

Step-by-step explanation:

The null hypothesis\((H_0)\) and alternative hypothesis\((H_a)\) both are statements as per the researcher's claim that involves population parameter .

Null hypothesis has  ≤,≥ ,= signs

Alternative hypotheses has < , > , ≠ signs.

A null hypothesis is a statistical hypothesis that is tested for possible rejection under the assumption that it is true.

The ratio of rainy days to total days written as a percent will be 75%.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

Ratio is used to compare two or more numbers. It is also used to indicate how big or small a quantity is when it is compared to another. It should be noted that in a ratio, two quantities are compared using division.

Since in the last 24 days, it rained 18 days.

Number of rainy days = 18.

Number of total days = 24

The ratio of rainy days to total days written as a percent will be:

= Number of rainy days / Total days × 100

= 18/24 × 100

= 3/4 × 100

= 75%

Therefore, the ratio is 3:4 which is 75%.

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The correct statement is; Pentagon M’N’P’Q’R is smaller than pentagon MNPQR because the scale factor is smaller than 1.

The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.

If a polygon is dilated by a scale factor = k

Rule to be followed as;

(x, y) → (kx, ky)

Here, k = Scale factor

If 0 < k < 1, size of the image will be reduced.

Similarly, k > 1, size of the image will be enlarged.

We are given that Pentagon MNPQR is dilated with the origin as the center of dilation to form an image M'N'P'Q'R'.

Rule used for the transformation,

(x, y) → (1/4x, 1/4y)

Here, the scale factor through which MNPQR has been dilated is 1/4.

Since, scale factor is between zero and 1/4, size of M'N'P'Q'R' will be reduced.

Therefore, the size of pentagon M'N'P'Q'R' will be 1/4 smaller than pentagon MNPQR.

Option (2) is the answer.

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The complete question is: Pentagon MNPQR is shown on the coordinate grid. Pentagon MNPQR is dilated with the origin as the center of dilation using the rule (x, y)→(1/4x, 1/4y) to create pentagon M'N'P'Q'R'.

Which statement is true?

a. Pentagon M'N'P'Q'R' is larger than pentagon MNPQR, because the scale factor is greater than 1.

b. Pentagon M'N'P'Q'R' is smaller than pentagon MNPQR, because the scale factor is less than 1.

c. Pentagon M'N'P'Q'R' is larger than pentagon MNPQR, because the scale factor is less than 1.

d. Pentagon M'N'P'Q'R' is smaller than pentagon MNPQR, because the scale factor is greater than 1.

The group of individuals fitting a description is called option D: Population, this is because, in statistics, a population is seen as am entire group of individuals, items, or elements that tends to have or share a common characteristics.

The term "population" describes the complete group of people or things that you are interested in investigating. It is the group of individuals or thing(s) about which you are attempting to draw conclusions.

There are infinite and finite populations. A population with a set quantity of people or things is said to be finite. An endless population is one that has an infinite amount of people or things.

Therefore, the correct option is D

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See full text below

A group of individuals fitting a description is the _____

Which of the term below fit the description above.

A.census

B.sample

C.parameter

D.population

Answer:

7,200 words

Step-by-step explanation:

Answer: 4,800

I multiplied 120 by 20 because 60 divided by 3 is 20. Then I multiplied my answer by 2 because the question is asking how many words could they type in 2 hours

The value of x is approximately 49.4 units.

What is volume ?

Volume is a measure of the amount of space occupied by a three-dimensional object. It is typically expressed in cubic units such as cubic meters, cubic centimeters, or cubic feet. Volume is a fundamental concept in mathematics and physics, and it is an important property for describing the size, capacity, or amount of material contained within an object.

Let's start by defining some variables:

r: radius of the cone

h: height of the cone

V: volume of the cone

A right cone has a circular base, and its volume can be calculated as follows:

V = (1/3) * π * r² * h

If the diameter of the base is 12 units, then the radius is half of that:

r = 6 units

We also know that the volume is 2767 units³, so we can write:

2767 = (1/3) * π * 6² * h

Simplifying:

h = (2767 * 3) / (π * 6²)

h ≈ 49.15 units

Now, we need to find the value of x. We can use the Pythagorean theorem to relate x, r, and h:

x² = r² + h²

Substituting the values we have:

x² = 6² + 49.15²

x ≈ 49.4 units

Therefore, the value of x is approximately 49.4 units.

In summary, we used the formula for the volume of a cone to relate the radius and height of the cone to its volume. Then, we used the Pythagorean theorem to relate the unknown value of x to the known values of r and h. Finally, we substituted the known values to find the approximate value of x.

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Your complete question is :-The volume of the right cone below is 2767 units³. Find the value of x if it's diameter is 12

Answer: 72.36

Step-by-step explanation:

To find the total amount of salt in the bowl after Omar poured 13.2 grams, we need to add the initial amount of salt in the bowl to the amount of salt Omar added.

The initial amount of salt in the bowl was 59.16 grams.

Omar added 13.2 grams of salt to the bowl.

To find the total amount of salt in the bowl now, we add these two amounts: 59.16 + 13.2 = 72.36

Therefore, the bowl contains 72.36 grams of salt now.

If we have 360 degrees and need to divide it into 12 equal angles, then all we have to do is a simple division problem.

360 / 12 = 30

There are 30 degrees in each angle.

Hope this helps!

Answer:

30 i think ???

Step-by-step explanation:

Answer:

C) \(\{x|x\neq-4 \:or \:4\}\)

Step-by-step explanation:

\(\frac{x^2+2x-8}{x^2-16}\\ \\\frac{(x+4)(x-2)}{(x+4)(x-4)}\\ \\x\neq-4 \:or \:4\)

Here, \(x\neq-4\) is a hole on the graph since \(x+4\) exists in both the numerator and denominator.

Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.

Answer:

\(x = \frac{17}{18}\)

\(y = \frac{23}{6}\)

Step-by-step explanation:

Given

\(y = 3x + 1\)

\(Points = (0,0)\ to\ (-3,4)\)

Required

Determine (x,y) equidistant from the equation and the given point

This question will be answered using distance formula;

\(d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\)

Considering The first Point \((0,0)\ to\ (x,y)\)

\((x_1 ,y_1) = (0,0)\)

\((x_2,y_2) = (x,y)\)

The distance is:

\(d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\)

\(d = \sqrt{0 - x)^2 + (0 - y)^2}\)

\(d = \sqrt{(- x)^2 + (- y)^2}\)

\(d = \sqrt{x^2 + y^2}\)

Considering the second point: \((x,y)\ to\ (-3,4)\)

\((x_1,y_1) = (x,y)\)

\((x_2,y_2) = (-3,4)\)

The distance is:

\(d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\)

\(d = \sqrt{(x - (-3))^2 + (y - 4)^2}\)

\(d = \sqrt{(x + 3)^2 + (y- 4)^2}\)

\(d = \sqrt{x^2 + 6x + 9 + y^2- 8y + 16}\)

\(d = \sqrt{x^2 + 6x + y^2- 8y + 16 + 9}\)

\(d = \sqrt{x^2 + 6x + y^2- 8y + 25}\)

Equate both values of d

\(\sqrt{x^2 + 6x + y^2- 8y + 25} = \sqrt{x^2 + y^2}\)

Square both sides

\(x^2 + 6x + y^2- 8y + 25 = x^2 + y^2\)

Collect Like Terms

\(6x - 8y + 25 = x^2 -x^2+ y^2 -y^2\)

\(6x - 8y + 25 =0\)

Recall that \(y = 3x + 1\)

\(6x - 8(3x + 1) + 25 = 0\)

\(6x - 24x - 8 + 25 = 0\)

\(-18x+ 17 = 0\)

\(-18x=- 17\)

Solve for x

\(x = \frac{-17}{-18}\)

\(x = \frac{17}{18}\)

Substitute \(\frac{17}{18}\) for x in \(y = 3x + 1\)

\(y = 3 * \frac{17}{18} + 1\)

\(y = \frac{17}{6} + 1\)

\(y = \frac{17 + 6}{6}\)

\(y = \frac{23}{6}\)

The length of side PS according to the quadrilateral descriptions is; 21.

Since, it follows from the task content that the two quadrilaterals given are congruent, hence, the corresponding sides are congruent and are in proportion to each other.

On this note, we have;

x/35 = 15/25

x = (35×15)/25

x = 21.

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Answer:

Option G'(-4, -1) is correct.

Step-by-step explanation:

Given the coordinates of the point

We know that when an object is dilated by a scale factor, it gets reduced, stretched, or remains the same, depending upon the value of the scale factor.

Rule to calculate the dilation by a scale factor 1/2 centered at the origin

P(x, y) → P'(1/2x, 1/2y)

Here, P'(1/2, 1/2y) is the image of P(x, y).

Thus,

G (-8, -2)  → A'(1/2(-8), 1/2(-2)) = G'(-4, -1)

Therefore, the image coordinates of G (-8, -2)  after dilation by a scale factor of 1/2 will be: G'(-4, -1)

Thus, option G'(-4, -1) is correct.

Answer:

The probability that a randomly chosen postmenopausal woman has a healthy bone density is 0.45.

Step-by-step explanation:

Probability of the postmenopausal woman having osteopenia = 0.46

Probability of the postmenopausal woman having osteoporosis = 0.09

Probability of having either osteopenia or osteoporosis = 0.55 (0.46 + 0.09).

Therefore, the probability that the postmenopausal woman does not have either osteopenia or osteoporosis, which is the same as having a healthy bone density = 0.45 (1 - 0.55).  

The proposed skyscraper is 172.8 m tall

From the question, we are to determine the how tall the proposed skyscraper is in meters

From the given information,

The scale of the model is

1 in : 7.2 m

and

The model is 2 ft tall

First, convert 2 ft to inches

NOTE: 1 foot = 12 inches

∴ 2 feet = 2 × 12 inches

= 24 inches

Now,

If 1 inch represents 7.2 m

Then,

24 inches will represent 24 × 7.2 m

24 × 7.2 m = 172.8 m

Hence, the proposed skyscraper is 172.8 m tall

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Here is the attached image for the answer. If you write it in in slope-intercept form, y=mx+b. You will get the answer below in the attached image.

The surface area of the sphere is 1810 cm²

A sphere is a three-dimensional object that is round in shape. Examples of object with spherical shape is a ball, an egg e.t.c.

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The surface area of sphere is expressed as;

A = 4πr². where r is the radius.

A = 4 × 3.14 × 12²

A = 1809.7 cm²

approximately to the nearest whole number

A = 1810 cm²

Therefore the surface area of the sphere to the nearest whole number is 1810 cm².

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Answer:

huh?

Step-by-step explanation:

Minute? Hour?

Answer:

Step-by-step explanation:

r=4*l

t=r-8

t=4l-8

r+t+l=100

4l+4l-8+l=100

9l-8=100

+8 +8

9l=108

:9. :9

l=12 Layla score

4*12=48 Rani score

48-8=40 Tash score

verify 12+40+48=100 correct

Answer:

(x+5y)^2

trust me bro yardy know whole lotta math

Answer:

choice 4 (or D)

Step-by-step explanation:

1) the initial argument (x/2) and the final one (x) shows horizontal compression of the given function;

2) the different between (-1) and (-5) is (-4); it means shifting down 4 units;

3) the correct answer is: the graph is compressed horizontally by a factor 2 and shifted down 4 units.

The monthly payment is $1727.82.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Price of the house = $218,500

Down payment = 3.5%

This means,

= 3.5/100 x 218,500

= 7647.5

Now,

Time of loan = 30 years.

This means,

30 years = 30 x 12 = 360 months.

Now,

Rate = 6.5%

This means,

The amount of interest rate for 30 years.

Simple interest.

SI = PRT/100

So,

P = 218,500 - 7647.5 = 210852.5

T = 30

R = 6.5

SI = (210852.5 x 6.5 x 30)/100

SI = 411162.375

Now,

Total amount to pay in 30 years.

= SI + P

= 411162.375 +  210852.5

= 622014.875

Now,

Monthly payment.

= 622014.875 / 360

= $1727.82

Thus,

$1727.82 is the monthly payment.

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Let's image any function f(x):

We have that the function g(x) is the same f(x) but translated:

Let's analyze the ways of translate a function, by observing the relation between f(x) and g(x) in the given equation:

g(x) = f(x - 1) - 5

If we want to translate the function horizontally we add the number of unities to the x:

- if the number is positive it will be translated to the left.

- if the number is negative it will be translated to the right.

In this equation the x has added -1:

f(x - 1) - 5 ⇒ x - 1

since -1 is negative then the function is translated one unity to the right:

If we want to translate the function vertically we add the number of unities outside the equation:

- if the number is positive it will be translated upwards.

- if the number is negative it will be translated downwards.

In the equation, there is added -5 to the whole equation f(x - 1):

f(x - 1) - 5 ⇒ - 5

since -5 is negative, then the function is translated five unities downwards:

Then, the function is translated one unity to the right and five unities downwards