Please help asap need it please

The x-intercept will be (5/3, 0) and the y-intercept will be (0, -5/2).

The x-intercept of an equation is the point at which the graph of the equation intersects the x-axis, which means that the y-coordinate of that point is 0. To find a x-intercept, we can set y = 0 in equation and solve for x.

Given the equation: 3x - 2y = 5

Setting y = 0, we get;

3x - 2(0) = 5

3x = 5

x = 5/3

So, the x-intercept is (5/3, 0).

The y-intercept of an equation is the point at which the graph of the equation intersects the y-axis, which means that the x-coordinate of that point is 0. To find y-intercept, we can set x = 0 in equation and solve for y.

Setting x = 0, we get;

3(0) - 2y = 5

-2y = 5

y = -5/2

So, the y-intercept is (0, -5/2).

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For 3 personal training session both gym cost same.

We have,

At Silver gym, membership is $25 per month and personal training sessions are $30 each.

At Fit Factor, membership is $65 per month, the and personal training sessions are $20 each.

let the number of personal session be x.

So, 25+ 30x = 65 + 20x

30x - 20x = 65 - 25

10x = 30

x= 3 sessions

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We will conduct a one-sample t-test to determine if the mean length of the particular size of dress is significantly different from 29 inches.

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We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.005 level of significance that the mean length of the particular size of the dress is found to be significantly longer or shorter than 29 inches and the machines must be adjusted.

What is the null hypothesis?

The null hypothesis is the assertion that there is no association between the two sets of data or variables being investigated in a scientific study. The term "null" refers to the idea that any empirically observed difference is entirely attributable to chance and that no underlying causal relationship exists.

Here, we have

Given: A children's clothing company sells hand-smocked dresses for girls. The length of one particular size of the dress is designed to be 29 inches. The most recent simple random sample of 22 dresses had a mean length of 31.53 inches with a standard deviation of 8.24 inches.

We will conduct a one-sample t-test to determine if the mean length of the particular size of the dress is significantly different from 29 inches.

In the null hypothesis, the mean length of the particular size of the dress is equal to 29 inches.

In the alternative hypothesis, the mean length of the particular size of the dress is significantly longer or shorter than 29 inches.

We will use a 0.005 level of significance, which corresponds to a critical value of ±2.807 for a two-tailed test with 21 degrees of freedom.

Our test statistic is: t = (31.53 - 29) / (8.24 / sqrt(22)) = 1.774

Since our test statistic (1.774) is not greater than the critical value (2.807) or less than the negative of the critical value (-2.807), we fail to reject the null hypothesis.

Hence, We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.005 level of significance that the mean length of the particular size of the dress is found to be significantly longer or shorter than 29 inches and the machines must be adjusted.

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The missing lengths of the following two triangles:

Case 1: x = 50 km

Case 2: x = 40 km

Case 3: Obtuse

Case 4: Acute

Case 5: Right

Case 6: m = 16, n = 8√3

Case 7: x = 3√2, y = 3

In this problem we must determine all missing lenghts in a triangle, this can be done by law of cosine:

x² = a² + b² - 2 · a · b · cos X

Where X is the angle opposite to side x.

Now we proceed to determine the missing lengths of the following two triangles:

Case 1

x = √[(14 km)² + (48 km)² - 2 · (14 km) · (48 km) · cos 90°]

x = 50 km

Case 2

x = √[(24 km)² + (32 km)² - 2 · (24 km) · (32 km) · cos 90°]

x = 40 km

In addition, we can determine if any triangle is acute, obtuse and right also by law of cosine:

cos X = - (x² - a² - b²) / (2 · a · b)

Case 3

cos X = - [(18 in)² - (12 in)² - (9 in)²] / [2 · (12 in) · (9 in)]

cos X = - 0.458 (Obtuse)

Case 4

cos X = - [(15 ft)² - (12 in)² - (14 in)²] / [2 · (12 in) · (14 in)]

cos X = 0.342 (Acute)

Case 5

cos X = - [(5 ft)² - (3 in)² - (4 in)²] / [2 · (3 in) · (4 in)]

cos X = 0 (Right)

Finaly, we determine the missing lengths of two right triangles by trigonometric functions:

sin θ = y / r

cos θ = x / r

tan θ = y / x

Now we find the missing lengths:

Case 6

m = 8 / cos 60°

m = 16

n = 8 · tan 60°

n = 8√3

Case 7

x = 3 / sin 45°

x = 3√2

y = 3 / tan 45°

y = 3

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Answer:

X can be any number greater than -2 and less than or equal to 1/4.

Step-by-step explanation:

To solve for x in the inequality 3x + 1 ≤ 2 - x < 18 + 7x, we will first isolate the variable x on one side of the inequality.

3x + 1 ≤ 2 - x

Adding x to both sides, we get:

4x + 1 ≤ 2

Subtracting 1 from both sides, we get:

4x ≤ 1

Dividing both sides by 4, we get:

x ≤ 1/4

Next, we solve the second inequality:

2 - x < 18 + 7x

Adding x to both sides, we get:

2 < 18 + 8x

Subtracting 18 from both sides, we get:

-16 < 8x

Dividing both sides by 8, we get:

-2 < x

Therefore, the solution to the inequality 3x + 1 ≤ 2 - x < 18 + 7x is:

-2 < x ≤ 1/4

This means that x can be any number greater than -2 and less than or equal to 1/4.

The area of the composite figure in this problem is given as follows:

A = 87 ft².

When we want to obtain the area of a composite figure, we must add the areas of all the components of the figure.

The figure in this problem is composed as follows:

The areas are calculated as follows:

Hence the area of the composite figure is given as follows:

A = 10 x 6 + 6 x 3 + 0.5 x 6 x 3

A = 87 ft².

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Answer:7

Step-by-step explanation:

use the Pythagoras theorem to find su (40^2-32^2) take the square root =24 use this to solve for ru. (25^2-24^2=49) square root of 49 is

Answer:

Starting with the equation:

(x + 1)^2 = 13/4

We can use the square root property, which states that if a^2 = b, then a is equal to the positive or negative square root of b.

Taking the square root of both sides, we get:

x + 1 = ±√(13/4)

Simplifying under the radical:

x + 1 = ±(√13)/2

Now we can solve for x by subtracting 1 from both sides:

x = -1 ± (√13)/2

Therefore, the solutions to the equation are:

x = -1 + (√13)/2 or x = -1 - (√13)/2

Step-by-step explanation:

The linear regression equation is y = 22.6x + 52.33

The profit would reach 234 thousand dollars during the calendar year of 2020.

Replacing the means, the intercept a is given by:

108.8 = 22.6(2.5) + a.

a = 108.8 - 22.6(2.5)

a = 52.33

Therefore, the linear regression equation is y = 22.6x + 52.33

The profit would reach 234 thousand dollars during the calendar year of 2020.

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Answer:

Step-by-step explanation:

Answer:

144π = (1/2)(4/3)π(r^3)

144 = (2/3)(r^3)

r^3 = 216, so r = 6 mm, meaning the diameter is 2 × 6 mm = 12 mm.

m² × m² is equal to m⁴.

w³ × w² is equal to w⁵.

5k³ × 4k⁴ × k is equal to 20k⁸.

The length of each side of the square is 9x.

A simplification of the expression 28x³ ÷ 4x is 7x².

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = LB

Where:

By substituting the given parameters into the formula for the area of a rectangle, we have the following;

Area of rectangle = (27x) × (3x)

Area of rectangle = 81x²

Note: Area of square = Area of rectangle

Area of square = (side length)²

81x² = (side length)²

Side length = √(81x²)

Side length = 9x

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Note that the upper bound for v is 2.356.

To find the upper bound for v, divide te upper bound for s by the lower bound for t,    because dividing by a   smaller integer give a bigger quotient.

Adding 0.5 x 0.1 t to the value of s yields the upper bound for s with t decimal places.

As a result, the upper bound for s with two decimal places is......

8.24 + 0.5 x 0.1² = 8.245

The lower bound for t with 1   decimal place is simply the given value of 3.5.

So, the upper bound for v is  ..

v = s/t = 8.245/3.5 = 2.355714...

Rounding this to 3 decimal places, we get:

v ≈ 2.356

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Based on these factors, the polynomial that graph crosses the x-axis at only one point is A. f ⁡ ( x ) = x ³ − 7 ⁢x² + 3 ⁢x − 21

A polynomial in mathematics is a mathematical statement made up of variables (also known as indeterminates) and coefficients that only include the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

Polynomials are a fundamental algebra topic that is used in many areas of mathematics. A polynomial's degree is the largest exponent of the variable x in the expression. The correct option is A.

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The perimeter of the rectangle is P = 18 units

Given data ,

Let the rectangle be represented as ΔWXYZ

Now , the coordinates of the triangle are

W ( 3 , 3 ) , X ( 8 , 3 ) , Y ( 8 , 7 ) and Z ( 3 , 7 )

The perimeter of the rectangle = 2 ( length + width )

The width of the rectangle W = ( 7 - 3 ) = 4 units

The length of the rectangle L = ( ( 8 - 3 ) = 5 units

So , P = 2 ( 4 + 5 )

P = 2 x 9

P = 18 units

Hence , the perimeter is 18 units

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Answer:

The correct function is y = 4(.25^x).

Since the waiting times are uniformly distributed between 0 and 7 minutes, the probability density function (PDF) of the waiting time is:

f(x) = 1/7 for 0 ≤ x ≤ 7

0 otherwise

To find the probability that the waiting time is less than 0.75 minutes, we need to integrate the PDF from 0 to 0.75:

P(X < 0.75) = ∫[0,0.75] f(x) dx

P(X < 0.75) = ∫[0,0.75] 1/7 dx

P(X < 0.75) = [1/7 * x] [0,0.75]

P(X < 0.75) = 1/7 * 0.75

P(X < 0.75) = 0.1071

Therefore, the probability that the waiting time is less than 0.75 minutes is 0.1071 (rounded to three decimal places).

Answer:

18. The end behavior of the graph of f(x) = x³ + 2x² - 5x + 1 is as follows: as x approaches negative infinity, the function f(x) approaches negative infinity, and as x approaches positive infinity, the function f(x) approaches positive infinity. This is because the leading term of the polynomial is x³, which has a positive coefficient, so the graph of the function will have a "smile" shape, with the ends of the graph pointing upwards.

19. The end behavior of the graph of g(x) = -2x³ - 8x² + 18x + 72 is as follows: as x approaches negative infinity, the function g(x) approaches negative infinity, and as x approaches positive infinity, the function g(x) approaches negative infinity. This is because the leading term of the polynomial is -2x³, which has a negative coefficient, so the graph of the function will have a "frown" shape, with the ends of the graph pointing downwards.

Step-by-step explanation:

The Function is linear with a common first difference of 2.

We have,

x     y

-3   -2

-2   0

0    4

4    12

For the first set of points

m=(0-(-2))/(-2--3)

m = (0+2)/(-2+3)

m= 2/1 = 2

For the second set of points

m = (4-0)/(0-(-2))

m = 4/(0+2)

m = 4/2 = 2

For the third set of points

m = (12-4)/(4-0)

m = 8/4

m = 2

Thus, the function is linear with a common first difference of 2.

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The ratio of sec θ is determined as 5/3.

option A.

The ratio is sec θ is calculated by applying the following method;

sec θ =  1/cosθ

Given that tanθ = -4/3 = oppo/adjacent

The hypotenuse side is calculated by applying Pythagoras theorem as shown below;

h = √ 4² + 3²

h = 5

The ratio of sec θ is calculated as follows;

sec θ =  1/cosθ

1/cosθ = 1/(3/5)

1/cosθ = 5/3

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Answer:

-6x - 2y = 12

Step-by-step explanation:

The sketches of the graphs are added as an attachment and the gradient of the perpendicular line l₂ is 1

Given that

3x + 4y + 12 = 0

Set x = 0 to determine the y-intercept

4y + 12 = 0

So, we have

y-intercept = -3

Set y = 0 to determine the x-intercept

3x + 12 = 0

So, we have

x-intercept = -4

For the gradient, we make y the subject in 3x + 4y + 12 = 0.

y = -3/4x - 12/4

y = -3/4x - 3

So, the gradient is -3/4

The sketch of the graph is attached.

Here, we have the points P (-1,4) and Q (3,0).

The gradient is

gradient = (0 - 4)/(3 + 1)

gradient = -1

From the point, we have

x-intercept = 3

For the y-intercept, we have

(0 - 4)/(3 + 1) = (y - 4)/(0 + 1)

(y - 4)/(0 + 1) = -1

y - 4 = -1

y-intercept = 3

So, the equation is

y = -x + 3

The sketch of the graph is attached.

We understand that l₂ is perpendicular to l

The gradients of perpendicular lines are

Gradient 1 = -1/Gradient 2

So, we have

l₂ = -1/-1

Evaluate

l₂ = 1

Hence, the gradient of line l₂ is 1

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Answer:

Step-by-step explanation:

considering that it is not an equation but an algebraic expression we solve it like this

10 + 6k6k =

10 + 36k²

The z-score for 71 is -1.

z-score is a measure of how many standard deviations an observation or data point is away from the mean of a distribution.

It is calculated by subtracting the mean from the observation and then dividing the result by the standard deviation: z = (x - μ) / σ

A positive z-score means that the data point is above the mean, while a negative z-score means that it is below the mean.

Applying the formula to solve our question

Here is a proven formula to use:

z = (x - μ) / σ

where:

x = the data item (x = 71)

μ = the mean of the distribution (μ = 80)

σ = the standard deviation of the distribution (σ = 9)

Substituting the values, we get:

z = (71 - 80) / 9

z = -1

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The surface area of the triangular prism is 70.2 yd²

A prism is a solid shape that is bound on all its sides by plane faces.

The surface area of a prism is expressed as ;

SA = 2B +ph

where h is the height,

B is the base area and

p is the perimeter of the base

Base area = 1/2 bh( since the base Is a triangle)

Base area = 1/2 × 3 ×3 = 4.5yd²

The other side of the triangle is calculated as;

x= √ 3²+3²

x = √9+9

x = √18

x = 4.2

Therefore perimeter = 4.2 + 3+3 = 10.2yds

SA = 2× 4.5 + 10.2 × 6

SA = 9 + 61.2

SA = 70.2 yd²

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The angle BFC is the angle that is complementary to AFB

Whenever the sum of two angles adds up to 90 degrees, they are defined as complementary angles. Take 30 and 60 degrees, for instance; they are complementary angles.

From the definition we have to find the angle when if added to AFB would give us the sum of 90 degrees

AFC is a 90 degree angles

We have AFC = AFB + BFC

90 = 78 + BFC

BFC  = 90 - 78

= 12

Hence the angle BFC is the complementary angle

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Work Shown:

(A'C')/(AC) = 12/5 = 2.4

or you could say

(B'C')/(BC) = 16.8/7 = 2.4

or

(A'B')/(AB) = 9.6/4 = 2.4

The sides of triangle A'B'C' are 2.4 times longer compared to the corresponding sides of triangle ABC.

The two inequalities of the graph are:

y ≥ 3x - 1

y < -¹/₂x + 4

The general form of the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

An inequality can be represented graphically as a region on one side of a line. Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region. Inequalities that use ≤ or ≥ symbols are plotted with a solid line to show that the line is included in the region.

The first inequality with a solid line has a y-intercept of -1 and since it is shaded above the line, we will use ≥.

Two coordinates on the line are: (0, -1) and (1, 2)

The slope = (2 + 1)/(1 - 0) = 3

Thus, inequality is:

y ≥ 3x - 1

The second inequality with a dashed line has a y-intercept of 4 and since it is shaded below the line, we will use <.

Two coordinates on the line are: (4, 0) and (0, 2)

The slope = (2 - 0)/(0 - 4) = -1/2

Thus, inequality is:

y < -¹/₂x + 4

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Answer:

Step-by-step explanation:

Blue line: 0 + -4<x

Black line: 8 - 7<7

Orange: 0=0>y

Green: 1-9<y

Starting points and ending

Answer: 7.35 km = 7350000 mm

Step-by-step explanation:

Multiply km by 1000000

7.35 * 1000000 = 7350000 mm