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Round decimals - FOR
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The market price of shrimp, to be bought in bulk, is $9.123 per pound. Round 9.123 to the nearest hundredth.
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The angle between lines b and s and the angle between lines b and t can only be equal, like showed in the picture, if the angles are corresponding angles, in which case s and t must be parallel.

Similarly, the angle between lines b and s and the angle between lines a and s can only be equal if the angles are corresponding angles, in which case lines a and b must be parallel.

So the first two statements are correct and the last one is not.

====================================================

Explanation:

s = 32 = sample standard deviation

n = 40 = sample size

Despite not knowing the population standard deviation (sigma), we can still use the Z distribution because n > 30. When n is this large, the student T distribution is approximately the same (more or less) compared to the standard Z distribution. The Z distribution is nicer to work with.

At 90% confidence, the z critical value is roughly z = 1.645. This can be found using either a Z table or a calculator.

------------------

We have these values:

Plug these values into the margin of error formula.

\(E = z*\frac{s}{\sqrt{n}}\\\\E \approx 1.645*\frac{32}{\sqrt{40}}\\\\E \approx 8.32311480156318\\\\E \approx 8.323\\\\\)

The margin of error is roughly 8.323

I rounded to 3 decimal places because z = 1.645 is rounded to 3 decimal places. If your teacher wants some other level of precision, then be sure to follow those instructions.

Answer:

None

Step-by-step explanation:

Answer is isn't there

the gcf = 2

the LCM = 20

Answer:

13.5

hope it helpeddddd

:P

Step-by-step explanation:

Answer: 13.5

Step-by-step explanation: Just divide

The roots of the quadratic equation \(3x^2 - 14x - 5 = 0\), in exact square root form, are x = 5 and x = -1/3.

Using the quadratic formula to solve the quadratic equation \(3x^2 - 14x - 5 = 0\),we have

\(x = (-(-14) ± sqrt((-14)^2 - 4(3)(-5))) / (2(3))\\x = (14 ± sqrt(14^2 + 4(3)(5))) / (2(3))\\x = (14 ± sqrt(196 + 60)) / 6\\x = (14 ± sqrt(256)) / 6\\x = (14 ± 16) / 6\\\)

Therefore, the two roots of the quadratic equation in exact square root form are:

\(x = (14 + 16) / 6 = 5\\x = (14 - 16) / 6 = -1/3\\\)

Thus, the roots of the quadratic equation \(3x^2 - 14x - 5 = 0\), in exact square root form, are x = 5 and x = -1/3.

A quadratic equation is a second-degree polynomial equation in one variable of the form:

\(ax^2 + bx + c = 0\)

where x is the variable, and a, b, and c are constants. In this equation, the highest power of x is 2, and it is called the coefficient of x^2. The coefficient of x is b, and the constant term is c.

The quadratic equation is called "quadratic" because the highest power of x is a square (i.e., x^2), and the graph of the equation is a parabola.

The quadratic equation can have zero, one, or two real solutions, depending on the values of a, b, and c. The solutions can be found by using the quadratic formula:

\(x = (-b ± √(b^2 - 4ac)) / 2a\)

where the symbol ± means "plus or minus" and the square root is of the discriminant (b^2 - 4ac).

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Answer:

Base rate: $120

Rate: $2 per person

Equation: f(x)=2x+120

Step-by-step explanation:

If 30 people cost $180 and 50 people cost $220, the charge for 20 extra people is $40.  This means, \(\frac{220-180dollars}{50-30people}=\frac{40dollars}{20people}=2\frac{dollars}{person}\).

These values correspond to a base rate for the bus of $120.

The function for the cost per bus with x number of people on it would be:

\(f(x)=2x+100\)

This can be checked by using the values given in the problem:

\(f(30)=2(30)+120=180\\f(50)=2(50)+120=220\)

The base rate of $120 and $2 per person satisfies the given equation and established values.

This means that after two years since the purchase, the boat was worth $24.57.

In general, worth refers to the value or monetary equivalent of something. It can be used to describe the financial value of assets such as property, stocks, or commodities, or to describe the value of something in terms of its usefulness, importance, or significance.

Michael tracked the value of his boat each year after he purchased it. Determine whether the data are linear, quadratic, or exponential. Use regression to find the function that models the data.

16.75

19.5

4

3

22.9

27.25

2

1

32

0

Years Since Purchase

To better understand the exponential function that models the data, let's break it down:

y = 10.92 * 1.50ˣ

The constant "10.92" represents the initial value of the boat when it was purchased. This means that the boat was worth $10.92 when Michael first bought it.

The constant "1.50" represents the growth factor of the boat's value. This means that each year, the value of the boat increases by a factor of 1.50.

The variable "x" represents the number of years since the boat was purchased. The function takes this input and returns the value of the boat at that time.

For example, if we plug in x=1 into the function, we get:

y = 10.92 * 1.50¹

y = 16.38

This means that after one year since the purchase, the boat was worth $16.38. Similarly, if we plug in x=2 into the function, we get:

y = 10.92 * 1.50²

y = 24.57

This means that after two years since the purchase, the boat was worth $24.57.

It's important to note that the exponential function assumes that the growth rate remains constant over time. In reality, the value of the boat may be affected by other factors such as wear and tear, maintenance, and market fluctuations. Nevertheless, the exponential function provides a useful model for understanding the trend in the data and making predictions about the future value of the boat.

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Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.

How to Interpret a Box-and-whisker Plot?

In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.

The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.

Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.

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Step-by-step explanation:

a) k(x) = (x - 2)² - 4 → x = (y - 2)² - 4 → (y - 2)² = x + 4 → y - 2 = ±√( x + 4) → y = 2 ±√( x + 4) → k-¹(x) = 2 ±√( x + 4)

b) f(x) = ½(x + 2)² - 3 → x = ½(y + 2)² - 3 → ½(y + 2)² = x + 3 → (y + 2)² = 2x + 6 → y + 2 = ±√(2x + 6) → y = -2 ±√(2x + 6) → f-¹(x) = - 2 ±√(2x + 6)

Based on the analysis, the only absolute value equation or inequality that has a solution set that is not the empty set is |2x - 1| - 7 < -6.

Option  A is the correct answer.

We have,

To determine which absolute value equation or inequality has a non-empty solution set, we can analyze each option:

|2x - 1| - 7 < -6:

Subtracting 7 from both sides, we get |2x - 1| < 1.

The absolute value of any real number is always non-negative, so the left-hand side is non-negative.

Since the right-hand side is also non-negative, the absolute value inequality is always true.

Therefore, this inequality has a solution set that is not the empty set.

|4x + 5| - 4 = -5:

Adding 4 to both sides, we get |4x + 5| = -1.

The absolute value of any real number is always non-negative, so the left-hand side is non-negative.

However, the right-hand side is negative, which is not possible.

Therefore, this equation does not have a solution, and the solution set is the empty set.

3|x + 2| - 2 = -3:

Adding 2 to both sides, we get 3|x + 2| = -1.

The absolute value of any real number is always non-negative, so the left-hand side is non-negative.

However, the right-hand side is negative, which is not possible.

Therefore, this equation does not have a solution, and the solution set is the empty set.

2|x - 5| - 4 < -8:

Adding 4 to both sides, we get 2|x - 5| < -4.

The absolute value of any real number is always non-negative, so the left-hand side is non-negative.

However, the right-hand side is negative, which is not possible.

Therefore, this inequality does not have a solution, and the solution set is the empty set.

Thus,

Based on the analysis, the only absolute value equation or inequality that has a solution set that is not the empty set is |2x - 1| - 7 < -6.

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relationship between v and x is C:Consecutive interior angles

Answer:

Not sure but I think the answer is 129

Step-by-step explanation:

first, substitute the value of x in the expression like this

18(3*2+1)+3

after substituting, our work has made easier

18(6+1)+3

18(7)+3 or simply 18*7+3

126+3

129

The length of the diameter of the sphere is 30 cm.

The surface area of a sphere is given by the formula:

\(A = 4\pi r^2\)

where A is the surface area and r is the radius of the sphere.

We are given that the surface area of the sphere is 900π cubic cm. Therefore:

\(A = 4\pi r^2 = 900\pi\)

Dividing both sides by 4π, we get:

\(r^2 = 225\)

Taking the square root of both sides, we get:

r = 15

The diameter of the sphere is twice the radius, so:

d = 2r = 30

Therefore, the length of the diameter of the sphere is 30 cm.

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The value of the function operation f - g(x) is 3x² + x

Function operations refer to mathematical operations that can be performed on functions, such as addition, subtraction, multiplication, and composition.

Addition and subtraction of functions:

A function can be added or subtracted with another function if both of them have the same domain. The result is a new function with the same domain as the original functions.

Multiplication of functions:

Two functions can be multiplied together to create a new function. The result is a new function whose value at each point in the domain is the product of the original functions' values at that point.

Composition of functions:

Function composition is the application of one function to the result of another function. The result is a new function that is the composition of the original functions. It is represented by (f ∘ g) (x) = f(g(x)) where f and g are the functions being composed.

In this problem, we have two functions which are;

The value of (f - g)(x) = 3x² + x

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Answer:

$2600

Step-by-step explanation:

Given that:

the employee earns $50,000 in  a year

The amount of money on wages paid by the employee towards social security = 5.2% of their gross wage

= \(\dfrac{ 5.2 \times 50000}{100}\)

= $2600

if an employee makes $50,000 in  the year, he will pay $2600 towards social security.

The other employees that paid 7.3% of their gross wages will not be regarded since they're paying it from their own fund.

Answer:

A

Step-by-step explanation:

f(-2)=3(4)+1

      =13

Answer: A

Step-by-step explanation:

Do it step by step : f(-2)= 13, f(1)= 4

Answer:

d² - 24d + c = (d - 12)² - 144 + c

Answer:

  B.  A point

Step-by-step explanation:

You want a description of the intersection between a plane and a cone given that the plane is parallel to the base and passes through the vertex of the cone.

The vertex of a cone is a single point. If a plane passes through that, but does not intersect the base of the cone, it will not intersect anywhere else.

The intersection is one point.

__

Additional comment

Figure f in the attachment illustrates this case.

A. The total value of the loan with quarterly compounded interest is $52,400.

B. The total value of the loan with monthly compounded interest is $52,010.04

Part A: Total value of the loan with the quarterly compounded interest

To find the total value of the loan, we'll use the formula for compound interest:

A = P * (1 + r/n)^(nt)

Where:

A = final amount (loan + interest)

P = principal amount (initial loan) = $20,000

r = interest rate = 7% = 0.07

n = number of times compounded per year = 4 (quarterly)

t = number of years = 10

Plugging in the values, we get:

A = $20,000 * (1 + 0.07/4)^(4 * 10)

A = $20,000 * (1.0175)^40

A = $20,000 * 2.620075

A = $52,401.51

Rounding to the nearest hundred, the total value of the loan with quarterly compounded interest is $52,400.

Part B: Total value of the loan with the monthly compounded interest

To find the total value of the loan with monthly compounded interest, we'll use the same formula with a different value of n:

A = P * (1 + r/n)^(nt)

Where:

n = number of times compounded per year = 12 (monthly)

Plugging in the values, we get:

A = $20,000 * (1 + 0.07/12)^(12 * 10)

A = $20,000 * (1.005833)^120

A = $20,000 * 2.600502

A = $52,010.04

Rounding to the nearest hundredth, the total value of the loan with monthly compounded interest is $52,010.04

The difference between the two loans is $52,401.51 - $52,010.04 = $391.47

The difference between the two loans is due to the higher frequency of compounding in the monthly compounded interest loan. The interest is compounded more times per year, so the interest is accumulating on the interest more quickly, leading to a higher overall interest charge.

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Answer:

Five times the quantity x plus four equals x minus y.

Step-by-step explanation:

Probably the most confusing part is that parenthesis are pronounced "the quantity"

Answer:

y = 8x + 0 or y = 8x

Step-by-step explanation:

Given the graph of a positive-sloped line passing through the point of origin:

In order to determine the linear equation in slope-intercept form, y = mx + b, we must solve for the slope of the line.

Let's use the following points on the graph:

(x₁, y₁) = (0, 0)

(x₂, y₂) = (2, 16)

Substitute these values into the following slope formula:

m = (y₂ - y₁)/(x₂ - x₁)

m = (16 - 0)/(2 - 0)

m = 16/2

m = 8

Thus, the slope of the line is m = 8.

Next, we must determine the y-intercept, which is the point on the graph where it crosses the y-axis.

The line crosses at the point of origin, (0, 0), which means that the y-intercept, b = 0.

Therefore, the linear equation in slope-intercept form is: y = 8x + 0 or y = 8x.

Answer:

\(\displaystyle y = 8x\)

Step-by-step explanation:

Start from the y-intercept of \(\displaystyle [0, 0]\)and move eight units south over one unit west. They both are negative integers, so when divided, you get a positive integer:

\(\displaystyle 8 = \frac{-8}{-1}\)

Moreover, this function is what is considered direct variation because the graph intersects the origin.

Well, there you have it. I am joyous to assist you at any time.

Answer:

-22

Step-by-step explanation:

You have to add -32+10

and you will get the answer -22

Answer:

-22

Step-by-step explanation:

On a number line, negative numbers go left and posative numbers go right. So on a numberline, if you find -32 and jump ten spaces to the right, you land on -22

Answer:

Step-by-step explanation:

2000≤20x +475

x = 76.25  so 76 people may attend

graph a number line from 0 to 76 . include the end points

1) no more 76 may attend

2)less than 77 may attend

3) between 0 and 76 may attend  

Answer:

18

Step-by-step explanation:

hope this helps you out

Answer:

the answer is 1 because any expression divide itself equals tp 1

\(\sf \frac{3}{4} \div \frac{3}{4} \)

\(\sf \longmapsto \frac{3}{4} \times \frac{4}{3} \)

\(\sf \longmapsto \frac{3 \times 4}{4 \times 3} \)

\(\sf \longmapsto \frac{12}{12} \)

\(\sf \longmapsto \cancel{ \frac{12}{12}{ } }\)

\(\sf \longmapsto1\)

OR the last 2 steps can also be written as,

\(\sf \longmapsto \frac{12 \div 12}{12 \div 12} \)

\(\sf \longmapsto1\)

Check the picture below.

\(\sin( \theta )=\cfrac{\stackrel{opposite}{0.5}}{\underset{hypotenuse}{0.64}} \implies \sin^{-1}(~~\sin( \theta )~~) =\sin^{-1}\left( \cfrac{0.5}{0.64} \right) \\\\\\ \theta =\sin^{-1}\left( \cfrac{0.5}{0.64} \right)\implies \theta \approx 51.4^o\)

Make sure your calculator is in Degree mode.