Given f(x) = 5x - 3 and g(x) = 3x, find f(8) - g(2)

Answer:

一/7

0.392 X 1 = 0.392

0.392 × 10 = 3.92

0.392 × 102 = 39.2

0.392 × 103 = 392

0.392 X 104 = 3,920

There are  212520  ways by which guests arrange themselves on a four person coach.

The term permutation refers to a mathematical calculation of the number of ways a particular set can be arranged. Put simply, a permutation is a word that describes the number of ways things can be ordered or arranged. With permutations, the order of the arrangement matters.

there are total 23 guests and they arranged themselves in 4 person coach,

so,

n = 23 and r = 4

npr = n!/(n-r)!

= 23!/(23-4)!

= 23!/19!

= 23x 22 x 21 x 20x 19!/19!

now cancel the factorial 19 from numerator as well as denominator

=  23x 22 x 21 x 20

= 212520

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Answer:

\(5mn^{2} (2+ 5m^{2} n)\)

Step-by-step explanation:

I assumed the polynomial is \(10mn^{2} +25m^{3}n^{2}\)

FIRST: Highlight the common factors{ 5 , m and\(n^{2}\))

\(5mn^{2} (2+ 5m^{2} n)\)

3x-2y=  7

Slope intercept form y= mx+b

   3x- 2y=  7

-   3x           -3x

-2y/-2=  3x/-2 - 7/2  

y=   3x/-2 -7/2

Answer:

3x/2 and the second 7/-2y

Step-by-step explanation:

thats how is what i got

Answer:

Route A is 0.75 km longer than route B.

Step-by-step explanation:

Length of route A is 1.5 times the length of route B.

a = 1.5b

\(\frac{a}{b}=\frac{15}{10}\)

\(\frac{a}{b}=\frac{3}{2}\) --------(1)

Here, a = Length of route A

b = Length of route B

Length of route A is \(\frac{3}{4}\) of route C.

a = \(\frac{3}{4}c\)

\(\frac{a}{c}=\frac{3}{4}\) ------(2)

Here, c = Length of route C

Length of route C = 3 km

Length of route A = \(\frac{3}{4}\times 3\) [From equation (2)]

                             = 2.25 km

Length of route B = \(\frac{2}{3}\times 2.25\) [From equation (1)]

                             = 1.5 km

Difference in route A and route B = 2.25 - 1.5

                                                       = 0.75 km

Therefore, route A is 0.75 km longer than route B.

The measure of line segment PG from the given triangle is 17 units.

A line segment is a path between two points that can be measured. Since line segments have a defined length, they can form the sides of any polygon.

From the given triangle MPT,

GH=GJ

x+3=2x-1

2x-x=3+1

x=4

So, PG=4x+1

PG=17 units

Therefore, the measure of line segment PG from the given triangle is 17 units.

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The ACT Math section tests a wide range of mathematical concepts and skills, so there are many formulas and concepts that you should be familiar with.

Here are some of the most important ACT math formulas that you should know:

1. Basic operations: addition, subtraction, multiplication, and division.

2. Exponents and roots: \(a^n\) means a multiplied by itself n times; the nth root of a is the number that, when raised to the nth power, gives a.

3. Order of operations: parentheses, exponents, multiplication/division (from left to right), and addition/subtraction (from left to right).

4. Fractions: converting between fractions, decimals, and percents; adding, subtracting, multiplying, and dividing fractions.

5. Algebra: solving equations and inequalities; simplifying algebraic expressions; factoring quadratics; understanding linear and quadratic functions.

6. Geometry: properties of lines, angles, and polygons; Pythagorean theorem; trigonometric functions; volume and surface area of 3D shapes.

7. Probability and statistics: calculating probabilities; mean, median, and mode; standard deviation.

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Answer:

m = -1/2, y-intercept = -3, x-intercept = -6,0

Step-by-step explanation:

M is the gradient (or slope) and is always in front of the x coefficient. -1/2 in this case.

To find the y-intercept, we have to know that it is at the point where the graph passes through the y-axis. At this point x = 0. So just substitute 0 for x and solve for y to give -3.

To find the x-intercept, do the opposite. When the graph passes through the x-axis, y = 0. So when y = 0, x = -6

Based on the formula of the quadratic function y=-x^2+6x-5, we know that its graph is a downward-facing parabola that opens wide, with a vertex at (3,-14), and an axis of symmetry at x=3.

Based on the formula of the quadratic function y=-x^2+6x-5, we can determine several properties of its graph, including its shape, vertex, and axis of symmetry.

First, the negative coefficient of the x-squared term (-1) tells us that the graph will be a downward-facing parabola. The leading coefficient also tells us whether the parabola is narrow or wide. Since the coefficient is -1, the parabola will be wide.

Next, we can find the vertex using the formula:

Vertex = (-b/2a, f(-b/2a))

where a is the coefficient of the x-squared term, b is the coefficient of the x term, and f(x) is the quadratic function. Plugging in the values for our function, we get:

Vertex = (-b/2a, f(-b/2a))

= (-6/(2*-1), f(6/(2*-1)))

= (3, -14)

So the vertex of the parabola is at the point (3,-14).

Finally, we know that the axis of symmetry is a vertical line passing through the vertex. In this case, it is the line x=3.

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Answer:

4:7

Step-by-step explanation:

The area of a semicircle with radius r is given by the formula A = (πr^2)/2.

Substituting r = 98cm, we get:

A = (π(98cm)^2)/2

A = 4,801.089 cm^2 (using π = 3.14159265)

Rounding to 1 decimal place we get 4,801.1 cm^2.

Therefore the area of semi-circle rounding to 1 decimal point is

4,801.1 cm^2.

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Answer:

It 5 would not be x

Step-by-step explanation:

If 5 was x, then it would be equivalent, because 5+3 = 8. I hope this helped.

The solution is x > 5 of the set of x+3 > 8.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

Here 5 is no solution to the given problem because there is no sign of equality.

Due to the fact that 5+3 = 8, if 5 were x, it would be equivalent.

We have to determine the solution set of x+3 > 8

Given inequality as

⇒ x + 3 > 8

Subtract 3 from both sides of the inequality,

⇒ x + 3 - 3 > 8 - 3

⇒ x > 5

Therefore, the solution is x > 5 of the set of x+3 > 8.

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The equation is x² + 11x = 12. Here x represents the width of the decorative border and no, it is not reasonable to be 2.5 inches wide.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

We have an area of border  48 square inches.

Menu dimensions without border =  13-inch by 9-inch

The area of the border can be expressed by the equation:

area of border = area of rectangle with border—area of rectangle without

                            border

48 = (13 + 2x)(9 + 2x) - 13×9

\(\rm 48=4x^2+44x\)

After simplification:

\(\rm 4x^2+44x-48=0\)

or

x² + 11x = 12

Find the solution of the above quadratic equation:

x = 1 or x = -12(width cannot be negative)

Width should be 1 inches.

We have given x = 2.5 it is not reasonable for the border to be 2.5 inches wide. Due to the cost of printing, the border should have an area of 48 square inches.

Thus, the equation is x² + 11x = 12 here x represents the width of the decorative border and no, it is not reasonable to be 2.5 inches wide.

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Answer:

the first table is a non-linear relationship and the second table is a linear relation ship because the first table as a curve in its line and it is not straight making it non-linear the second table is linear because it forms a straight line making it linear

Step-by-step explanation:

to find a linear relationship place the points on the graph. then if the they form a straight line then your table is linear

Also to find a nonlinear relation ship place the points that are given to you on a graph and if they are not a straight line then they are a nonlinear relationship

Step-by-step explanation:

the first hint is in the word itself : linear.

it means it is a line. everything goes straight. no changes in the slope.

so, you see already in the graph ; the first table is non-linear, the second one is linear.

a bit more formally and mathematically :

if you look at any pair of points (x1, y1) and (x2, y2) on the curve, the ratio (y2-y1)/(x2-x1) is constant, always the same value. then it is a linear function.

if this changes from 1 pair of points to any other, it is non-linear.

take table 2 :

(16-20)/(6-5) = -4/1 = -4

(12-8)/(7-6) = -4/1 = -4

(12-20)/(7-5) = -8/2 = -4

=> for the observed range it is linear. all the ratios are the same.

but table 1

(2-1)/(1-0) = 1/1 = 1

(5-2)/(2-1) = 3/1 = 3

(5-1)/(2-0) = 4/2 = 2

the ratios are continuously changing.

=> non-linear.

In quantitative research, data collection from the same respondents at 2 or more points (waves) in time is referring to "longitudinal."

A method for gathering and interpreting numerical data is known as quantitative research. It can be used to discover patterns and averages, to make predictions, to verify causal linkages, and to generalize results to larger groups.

Some features regarding quantitative research are-

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Answer:

12Mph

Step-by-step explanation:

I already did this question it is 12 Mph which can be done by taking 6 divided by 30, the answer is A

PLS GIVE ME BRAINLIEST

Harry bought 6 apples and 5 oranges.

One or many equations having the same number of unknowns that can be solved simultaneously are called simultaneous equations. And the simultaneous equation is the system of equations.

Given:

At a store, apples cost 0.80 each and oranges cost 0.95 each.

Harry buys some apples and oranges and spends 9.55.

He buys a total of 11 pieces of fruit.

Let x be the number of apples and y be the number of oranges.

Then, we have a system of equations,

x + y = 11  {equation 1}

0.80x + 0.95y = 9.55   {equation 2}

Substituting the value of y = 11 -x from equation 1 to equation 2,

we get,

0.80x + 0.95(11 -x) = 9.55

0.80x - 0.95x = 9.55 - 10.45

-0.15x = -0.9

x = 6,

and y = 5

Therefore, the solution is x = 6, and y = 5.

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The number of trees more than 10m tall but not more than 20m tall is 18 trees.

0 < h ≤ 5 = 5

height greater than 0m less than or equal to 5m

5 < h ≤ 10 = 9

height greater than 5m less than or equal to 10m

10 < h ≤ 15 = 13

height greater than 10m less than or equal to 15m

15 < h ≤ 20 = 5

height greater than 15m less than or equal to 20m

20 < h ≤ 25 = 1

height greater than 20m less than or equal to 25m

The number of trees that are more than 10m tall but not more than 20m tall are;

10 < h ≤ 15 = 13

15 < h ≤ 20 = 5

So,

13 + 5 = 18 trees

Therefore, the total number of trees which are 10m tall but not more than 20m tall is 18 trees.

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The polynomial x³ - 2x² - 13x - 10 divided by x + 2 will have quotient of x² - 4x - 5x and a remainder of zero.

The polynomial x³ - 2x² - 13x - 10 divided by x + 2 as follows;

We divide the first of the polynomial x³ by x to give x²

multiply x - 1 by x² to get x³ + 2x²,

then subtract x³ + 2x² from x³ - 2x² - 13x - 10 to get -4x² - 13x - 10

divide -4x² by x to get -4x

multiply x - 1 by -4x to get -4x² - 8x

then subtract -4x² - 8x from -4x² - 13x - 10 to get -5x - 10

divide -5x by x to get -5

multiply x - 1 by -5 to get -5x - 10,

then subtract -5x - 10 from -5x - 10 to get a remainder of zero.

Therefore, the division of the polynomial x³ - 2x² - 13x - 10 by x + 2 using long division give us the quotient x² - 4x - 5x and a remainder of zero.

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a. The probability of success (hitting the target) is constant for each trial (88% or 0.88).

b. The probability of hitting the 6th target is:

P(X = 1) = C(1, 1) * 0.88^1 * (1 - 0.88)^(1 - 1) = 0.88

c. Using the binomial probability formula as before, with p = 0.88 and n = 3:

P(X = 1) = C(3, 1) * 0.88^1 * (1 - 0.88)^(3 - 1)

P(X = 2) = C(3, 2) * 0.88^2 * (1 - 0.88)^(3 - 2)

P(X = 3) = C(3, 3) * 0.88^3 * (1 - 0.88)^(3 - 3)

a) The three characteristics of this scenario that indicate we are working with Bernoulli trials are:

The experiment consists of a fixed number of trials (eight shots).

Each trial (shot) has two possible outcomes: hitting the target or missing the target.

The probability of success (hitting the target) is constant for each trial (88% or 0.88).

b) To find the probability of hitting the 6th target (considered as a single trial), we can use the binomial probability formula:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

where:

P(X = k) is the probability of getting exactly k successes,

C(n, k) is the binomial coefficient or number of ways to choose k successes out of n trials,

p is the probability of success in a single trial, and

n is the total number of trials.

In this case, k = 1 (hitting the target once), p = 0.88, and n = 1. Therefore, the probability of hitting the 6th target is:

P(X = 1) = C(1, 1) * 0.88^1 * (1 - 0.88)^(1 - 1) = 0.88

c) To find the probability that the first time hitting the target is not until the 4th shot, we need to consider the complementary event. The complementary event is hitting the target before the 4th shot.

P(not hitting until the 4th shot) = P(hitting on the 4th shot or later) = 1 - P(hitting on or before the 3rd shot)

The probability of hitting on or before the 3rd shot is the sum of the probabilities of hitting on the 1st, 2nd, and 3rd shots:

P(hitting on or before the 3rd shot) = P(X ≤ 3) = P(X = 1) + P(X = 2) + P(X = 3)

Using the binomial probability formula as before, with p = 0.88 and n = 3:

P(X = 1) = C(3, 1) * 0.88^1 * (1 - 0.88)^(3 - 1)

P(X = 2) = C(3, 2) * 0.88^2 * (1 - 0.88)^(3 - 2)

P(X = 3) = C(3, 3) * 0.88^3 * (1 - 0.88)^(3 - 3)

Calculate these probabilities and sum them up to find P(hitting on or before the 3rd shot), and then subtract from 1 to find the desired probability.

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Answer:

Q1 - 3.7

Q2 - 5.6

Q3- 300.8

Q4 - 1860.9

Step-by-step explanation:

hope this helps :)

Answer:

Step-by-step explanation:

a. ³√50 = 3.68

b.  ³√180 = 5.64

c.  6.7³ = 300.76

d.  12.3³ = 1860.867

Answer:

12.5

Step-by-step explanation:

there are eight triangles and one yellow so 1/8=12.5%

Answer: 12.5%

Step-by-step explanation:

There are 8 sections and 1 of them is yellow so 1 divided by 8 is 0.125 or 12.5%

The value of  tan(A - B)  will be 15/8.

As mentioned,  cscA= -17/15 and A is in Quadrant III and sinB=12/13 where B is in Quadrant I To find tan(A - B), we need to have the values of sin (A - B) and cos (A - B).We know that, sin(A - B) = sinAcosB - cosAsinB and cos(A - B) = cosAcosB + sinAsinB.Since we have the values of sinA, cosA, and sinB, let's find the values of cosA and cosB.First, let's find cosA. We know that cscA = 1/sinA. Therefore, sinA = -15/17.Since A is in Quadrant III, sinA < 0, cosA < 0, and tanA > 0.

By using the Pythagorean identity sin^2A + cos^2A = 1, we get cosA = -8/17.Next, let's find cosB. We know that sin^2B + cos^2B = 1.

Therefore, cosB = sqrt(1 - sin^2B) = 5/13.

Since B is in Quadrant I, sinB > 0, cosB > 0, and tanB > 0.

Now, we have sinA, cosA, sinB, and cosB.

Using the values of sinA, cosA, sinB, and cosB, let's find sin(A - B) and cos(A - B).

sin(A - B) = sinAcosB - cosAsinB= (-15/17)(12/13) - (-8/17)(5/13)= -180/221

cos(A - B) = cosAcosB + sinAsinB= (-8/17)(12/13) + (-15/17)(5/13)= -96/221

Finally, tan(A - B) = sin(A - B) / cos(A - B)= (-180/221) / (-96/221)= 15/8. Therefore, tan(A - B) = 15/8.

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A minimum sample size of 121 individuals needs to be surveyed, ensuring a rounded-up value to estimate the proportion of non-graduates within the 25 to 30 age group with a 10% margin of error and 90% confidence.

To determine the sample size required to estimate the proportion of non-graduates within the 25 to 30 age group with a certain level of confidence and margin of error, we can use the formula:

n = (Z^2 * p * (1 - p)) / E^2

Where:

n is the required sample size

Z is the Z-score corresponding to the desired confidence level (90% confidence corresponds to a Z-score of approximately 1.645)

p is the estimated proportion of non-graduates (0.21 based on the information provided)

E is the desired margin of error (10% or 0.10)

Substituting the values into the formula:

n = (1.645^2 * 0.21 * (1 - 0.21)) / 0.10^2

n ≈ 120.41

Rounding up to the nearest integer, the required sample size is 121.

Therefore, you would need to survey at least 121 individuals in the 25 to 30 age group to estimate the proportion of non-graduates within 10% margin of error with 90% confidence.

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Step-by-step explanation:

Area = (17.6)²mm²

=309.76 mm²

Given:

Principal value = $240,000

Rate of interest = 6% compounded continuously.

Time = 30 years

To find:

The amount after interest.

Solution:

The formula for amount after continuous compounding the interest is:

\(A=Pe^{rt}\)

Where, P is principal, r is rate of interest and t is the number of years.

Putting \(P=240,000,r=0.06,t=30\), we get

\(A=240,000e^{0.06(30)}\)

\(A=240,000e^{1.8}\)

\(A=1451,915.39146\)

\(A\approx 1451,915.39\)

Therefore, Martins will pay $1451,915.39 for the house, including interest.

Answer: To determine whether the condition of equal standard deviations is met in this case, we can perform a quick check by comparing the sample standard deviations of each group. If the sample standard deviations are roughly equal, then we can assume that the condition of equal standard deviations is met.

Alternatively, we can use Levene's test for equality of variances, which tests the null hypothesis that the population variances are equal across all groups. If the p-value of the test is greater than the significance level (usually 0.05), then we can assume that the condition of equal standard deviations is met.

Without the data or the sample standard deviations, it is not possible to determine whether the condition of equal standard deviations is met in this case.

Step-by-step explanation:

Answer:

Even though it's in fraction form it's still a whole number.

Step-by-step explanation:

Here's an example to make this easier-

If you cut an orange into 8 slices and count all the parts it's 8/8, but you still have 1 whole orange. I hope this makes sense! have a great day! ^^