Write the equation of the line in slope-intercept form with the following slope and y-intercept:
m= 0
y-intercept = (0, 2)

Answer:

The best bet would be x=40

Step-by-step explanation:

answer

a. 5,8

explanation

use numbers in each answer choice

+5 * -8 = - 40

+5 -8 = -3

Consider the form \(x^2+bx+c\). Find a pair of integers whose product is \(c\) and whose sum is \(b\). In this case, whose product is -40 and whose sum is -3.

\(\longrightarrow\boxed{\bold{(-8,5)}}\)

Write the factored form using these integers.

\((x-8) \ (x+5)\)

Answer:

90

Step-by-step explanation:

Let the whole number be x.

100% is to x as 70% is to 63

100/x = 70/63

10/x = 10/9

10x = 90 * 10

x = 90

Answer: 90

Step-by-step explanation:

0.7x = 63, x = 63/0.7 = 90

Answer: 0.166666667 yards OR 0.1524 meters OR 0.5 feet

Step-by-step explanation:

1 / 6 = 0.166666667 yards

1 yard = 0.9144 meters

0.9144 / 6 = 0.1524 meters

1 yard = 3 feet

3 / 6 = 0.5 feet

Answer:

165

Step-by-step explanation:

Answer:

D the amount of money he pays for each lunch

Step-by-step explanation:

In each lunch Devante has, he pays 2,50 $ according to:

Money in t = t₀     he has  35,50 $      paid 3 lunches and spent

35,50 - 28  =  7,5

Then the cost of each lunch is    7,5 / 3   =  2,5 $

After that

bought    5 lunches and spent   28  - 15,5  = 12,50

Again    12,5 / 5   =  2,5 $

Now the model for the situation is a straight line with a slope 2,5

In an  x , y cartesian system in which  y is money in the account  and x is the number of lunches, such a straight line will be

y  =  b  -  m*x      ( b the intercept on y  and  m the negative slope)

y  =  35,50 - 2,5*x

So  answering the question is lyrics  D  the amount of money he pays for each lunch

If X ~ Exponential(µ), then the mean of X is 1/µ. So if the mean of X is twice the mean of Y, then the mean of Y is 1/(2µ), so that Y ~ Exponential(2µ).

We're given that

P(X > 50) = 1 - P(X ≤ 50) = 1 - Fx (50) ≈ 0.7788

==>   Fx (50) = P(X ≤ 50) ≈ 0.2212

where Fx is the CDF of X, which is given for 0 ≤ x < ∞ to be

Fx (x) = 1 - exp(-µx)

Solve for µ :

1 - exp(-50µ) ≈ 0.2212   ==>   µ ≈ -ln(0.7788)/50 ≈ 0.005

Then we have

P (Y > 40) = 1 - P (Y ≤ 40) = 1 - Fy (40)

where Fy is the CDF of Y,

Fy (y) = 1 - exp(-2µy)

so that

P (Y > 40) ≈ 1 - exp(-2 × 0.005 × 40) ≈ 0.3297

Let f(x, y, z) = z - arctan(x y). Compute the gradient of f at the point (0, 3, 0):

∇ f(x, y, z) = (-y / (1 + x²y²), -x / (1 + x²y²), 1)

∇ f (0, 3, 0) = (-3, 0, 1)

This vector is orthogonal to the surface z = f(x, y). Then the equation of the tangent plane is

∇ f (0, 3, 0) • (x, y - 3, z) = 0

(-3, 0, 1) • (x, y - 3, z) = 0

-3x + z = 0

z = 3x

On solving the provided question, we can say that the trigonometry sin3θcos2θ+cos3θsin2θ = 4sin3(1−2cos2θ)+sinθ

The area of mathematics knοwn as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, arοund the third century BC. frοm the use of geometry in astronοmical study.

The area of mathematics knοwn as exact methods deals with specific trigonometric functions and hοw they might be used in calculations. There are six popular trigonοmetric functions in trigonometry. Sine, cosine, tangent, cοtangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics οf triangles, particularly right triangles, is called trigonοmetry. The study of geοmetry, however, is the characteristics of all geοmetric figures.

the trigonometry

sin3θcos2θ+cοs3θsin2θ=4sin3(1−2cos2θ)+sinθ

Use the variation cοs2θ=1−sin2θ to express sin(5θ) in terms of sinθ

sin5θ=4sin3θ(1−2(1−sin2θ))+sinθ(8(1−sin2θ}

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The length of the zip wire, with a 10-degree angle to the horizontal and a distance of 25 meters between the posts, is approximately 25.35 meters.

To calculate the length of the zip wire, we can use trigonometry. Let's consider the triangle formed by the zip wire, where the horizontal distance between the two posts is 25 meters and the angle between the zip wire and the horizontal is 10 degrees.

Using trigonometric functions, we can determine the length of the zip wire. In this case, we'll use the sine function because we have the opposite side (the vertical distance) and we want to find the hypotenuse (the length of the zip wire).

The formula for sine is:

sin(angle) = opposite / hypotenuse

Rearranging the formula, we have:

hypotenuse = opposite / sin(angle)

In this case, the opposite side is the vertical distance, which is h.

So, the formula becomes:

hypotenuse = h / sin(angle)

To find h, we can use the formula for the length of the zip wire:

h = 25 * tan(angle)

Substituting this into the previous formula, we get:

hypotenuse = (25 * tan(angle)) / sin(angle)

Calculating the value, we have:

hypotenuse = (25 * tan(10°)) / sin(10°)

Using a calculator, we find:

tan(10°) ≈ 0.1763

sin(10°) ≈ 0.1736

Substituting these values, we can calculate the length of the zip wire:

hypotenuse ≈ (25 * 0.1763) / 0.1736 ≈ 25.35 meters

Therefore, the length of the zip wire is approximately 25.35 meters.

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1. Find the graph of the parabola attached below

2. Vertex (-4, 2)   Focus (-7/2, 2)  Directrix (x = -9/2)  Endpoints (-7/2, 1) (-7/2, 3)

For the parabola,  x = 1/2(y-2)² - 4 we will use the equation x = 4p(y-k)² + h,

Vertex → (h, k)

In our given equation, (y - 2) → (y - k), so k = 2. The term on the rightmost side of our equation (-4) → h in the form, so we know h = -4. ∴  vertex (-4, 2).

focus → (h, k) = (-4, 2); P = 1/2

Parabola is symmetric around the x axis and so the focus lies a distance P, from the center, along the x axis.

∴  Focus is (-4 + p, 2)

(-4 + 1/2, 2) ⇒ (-7/2, 2)

directrix → x = d

Parabola is symmetric around the x axis and therefore the directrix is a line paralled to the y axis a distance away from the ceter (-4, 2) x coordinate.

∴ x = -4 - p   ⇒ x = -4 - 1/2

x = 9/2

focal chord endpoints →

The focus of the parabola is (-7/2, 2).

The y-coordinate of the focus is 2, so the y-coordinates of the endpoints of the focal chord are 2 + 1 and 2 - 1, → 3 and 1.

Therefore, the endpoints of the focal chord are:

(-7/2, 3) and (-7/2, 1).

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Answer:

20π [in].

Step-by-step explanation:

1. formula is:

C=π*2r;

2. the circumference according to the formula is:

C=π*10*2=20π.

The zeros of the function f(x) = 2x⁴ + 11x³ + 16x² + x - 6 are x = -3, x = -2,

x = -1 and x = 1/2 respectively

The zero of a real-, complex-, or generally vector-valued function f, is a member x of the domain of f such that f(x) vanishes at x; that is, the function f attains the value of 0 at x, or equivalently, x is the solution to the equation f(x) = 0. Graphically, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.

In the given problem, the zero of the function;

f(x) = 2x⁴ + 11x³ + 16x² + x - 6; -3 are

f(-3) = 2(-3)⁴ + 11(-3)³ + 16(-3)² -3 - 6 = 0

f(-2) = 2(-2)⁴ + 11(-2)³ + 16(-2)² - 2 - 6 = 0

f(-1) = 2(-1)⁴ + 11(-1)³ + 16(-1)² - 1 - 6 = 0

f(1/2) = 2(1/2)⁴ + 11(1/2)³ + 16(1/2)² - 1/2 - 6 = 0

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We need to make a box plot (also known as box-and-whisker) with the following data:

84, 68, 80, 52, 64, 68, 58, 83, 70, 54, 59, 73, 56, 72, 53, 57, 73, 51, 82.

Answer:

The answer is C

Step-by-step explanation:

c.  8√(2^4 )

given 2^(4/8)  can be written as 2^(4×1/8)  

eg: 2^(1/2) is √2 hence same rule we can apply here and since 2^(1/8) we can write as 8√2 and given 2^4

further knowledge: so if asked to expand more we can write it as 8√16 simplifying this further we get 2^(1/2) which is actually √2

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Answer:

adventure

Step-by-step explanation:

Answer:

adventure

Step-by-step explanation:

Answer:

Step-by-step explanation:

2(3x + 12y - 5 - 17x - 16y +4)

the 2 outside the bracket means we need to multiply everything by 2

=

6x+24y-10-34x-32y+8

now put all the like-terms together

6x-34x+24y-32y+8-10

now add them together

=-28x-8y-2

now find the HCF

2

put 2 outside the bracket and then divide every number by 2

2(-14x-4y-1)

this is as simplified it can get

Complete Question

A random sample of 114 observations produced a sample mean of 30. Find the critical and observed values of z for the following test of hypothesis using α=0.01. The population standard deviation is known to be 5 and the population distribution is normal.

\(H_o: \mu =28\)  versus H1: μ>28.

Round your answers to two decimal places.

\(z_{critical} =\)

Answer:

 \(z_{critical} = 2.33\)

The observed value  is   \( z = 4.27  \)

Step-by-step explanation:

From the question we are told that

   The sample size is  n  =  114

   The sample mean  is  \(\= x   =  30\)

   The  significance level is  \(\alpha = 0.01\)

   The population standard deviation is  \(\sigma = 5\)

The null hypothesis is  \(H_o: \mu =28\)  

 The alternative hypothesis is   H1: μ>28.

 Generally the test statistics (observed value ) is mathematically represented as

      \( z = \frac{ \= x - \mu }{ \frac{\sigma }{\sqrt{n} } } \)

=>     \( z = \frac{ 30- 28 }{ \frac{5}{\sqrt{114} } }  \)

=>     \( z = 4.27  \)

From the normal distribution table the critical value  of  \(\alpha = 0.01\) is  

     \(z_{critical} = 2.33\)

The cost price of the shorts is K22.50.

To find the cost price of the shorts, we need to reverse calculate the original price before the markup and taxes were applied.

Let's assume the cost price of the shorts is represented by C.

The markup of 17% is applied to the cost price, which means the selling price (including the markup) is 117% of the cost price.

117% of the cost price C can be calculated as (117/100) * C.

GST (Goods and Services Tax) is also included in the selling price. GST is typically calculated as a percentage of the selling price. In this case, the selling price of the shorts including GST is K29.25.

Since the GST is included in the selling price, we can subtract it from the selling price to obtain the selling price before GST.

Let's assume the GST rate is R% (as a decimal), then the selling price before GST can be calculated as:

Selling price before GST = Selling price - (Selling price × R)

In this case, the selling price before GST is K29.25, and the GST rate is 17% (0.17 as a decimal). Substituting these values into the equation, we have:

K29.25 = Selling price - (Selling price × 0.17)

Simplifying the equation

K29.25 = Selling price × (1 - 0.17)

K29.25 = Selling price × 0.83

Selling price = K29.25 / 0.83

Now we can substitute the selling price in terms of the cost price:

K29.25 / 0.83 = (117/100) × C

Simplifying the equation:

C = (K29.25 / 0.83) × (100/117)

Calculating the cost price C:

C = K22.50

Therefore, the cost price of the shorts is K22.50.

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The polynomial simplifies to -x² + 8x + 1 with a highest degree of 2.

To simplify a mathematical expression is to represent it in the least complicated form possible.

In general the simplest form is one that has used the fundamental properties of numbers, exponents, algebraic rules, etc. to remove any duplication or redundancy from the expression.

The given expression;

= (3x²- x - 7) - (5x² - 4x - 2) + (x + 3)(x + 2)

The simplified form of the given expression is calculated as follows;

= 3x² - x - 7 - 5x² + 4x + 2 + x² + 2x + 3x + 6

= -x² + 8x + 1

Thus, the polynomial simplifies to -x² + 8x + 1 with a highest degree of 2.

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Answer:

\( \boxed{ \bold{{ \boxed{ \sf8 {x}^{7} + 3 {x}^{6} + {x}^{5} + 5 {x}^{4} - 2 {x}^{3} }}}}\)

Step-by-step explanation:

Here, we have to arrange the polynomial from higher power to lower power.

So, Option C is the correct option

Hope I helped!

Best regards! :D

The net force on the cart is 62N

and the vertical component =36.64 N

the horizontal component= 50N

What is revolution of vector?

The process of splitting a vector into its components is called resolution of the vector. We resolve a vector into two components which are. component along the x-axis called horizontal component. component along the y-axis called vertical component

30N tension on the cart is westward which mean the vertical component will be 0 and the horizontal component will be 30N.

40N tension isN 30° E which means

the vertical component= 40 sin60=36.64N

Horizontal component= 40 cos 60= 20N

sum of vertical = 36.64N +0= 36.64N

sum of horizontal= 30N+20N= 50N

60° was used for tension 40N because the angle of vector must always lie on the horizontal axis

therefore the net force F is obtained by using Pythagoras theorem

F= √(50^2+36.64^2)

= 62N to the nearest whole number.

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The slope of the line is 2.

Slope is a measure of the steepness of a line or a surface. In geometry and mathematics, slope refers to the rate at which a line rises or falls as it moves horizontally. It is calculated as the ratio of the vertical change between two points on a line (the rise) to the horizontal change between those same two points (the run).

The slope of a line can be expressed as a fraction or a decimal. A positive slope indicates that the line is increasing as it moves from left to right, while a negative slope indicates that the line is decreasing as it moves from left to right. A slope of zero indicates a horizontal line, and a slope that is undefined indicates a vertical line.

In real-world applications, slope is used in a variety of fields, such as physics, engineering, and architecture. For example, slope is used to calculate the angle of a roof or a ramp, the rate of change in the value of a stock or a commodity, or the rate of change of a moving object. Understanding slope is an important concept in mathematics and has many practical applications in the real world.

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:

m = (y2 - y1) / (x2 - x1)

Here, the given two points are (0, 2) and (-1, 0). Substituting these values into the slope formula, we get:

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

Therefore, the slope of the line is 2.

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Answer:

For the first city, the 95% confidence interval would be:

28,900 +/- 2300 x 3 = 28,900 +/-6900$

For the second city, the 95% confidence interval would be:

30,300 +/- 2100 x 3 = 30,300 +/- 6300$

Answer:

B.) 21.2 units

Step-by-step explanation:

Radius = Diameter divided by 2

So

Diameter = radius multiple by 2

Answer:

150 percent

Step-by-step explanation:

30/20. Multiply both sides by 5. 150/100. 30 is %150 of 20

Answer:

150

Step-by-step explanation: from goog  .le

Okay, here we have this:

Considering the provided table, we are going to analize if the table shows direct variation, so we obtain the following:

To identify if there is direct variation then we will calculate the ratios between the points, and if they are all the same then the table does show direct variation, then we have:

y=kx

k=y/x

5/2=2.5

45/18=2.5

80/30=2.66

Since the ratios between the points are not the same, then it does not represent a direct variation.

Answer:

62.16

Step-by-step explanation:

994.01 - 200.00 / 12

Answer:

53\(x_{123}\) == 134 cf

Step-by-step explanation:

A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a​

The height of the building is approximately 78.63 meters.

The following is a step-by-step explanation of how to solve the problem. We'll need to use some trigonometric concepts and formulas to find the solution.

Therefore, the height of the building is approximately 78.63 meters.

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Answer:

15.66 cm

Step-by-step explanation:

180-66.4=113.6°

113.6÷360=0.315555555, which equals 31.55555% of the circumference

2x3.14x7.9=49.612 would be the entire circumference.

So...

31.5555555% of 49.612=15.6554 cm