Solve: Show your work

0.321 x 50

Answer:

y=2x-2

Step-by-step explanation:

Slope intercept Formula: y=mx+b

y= Y coordinate

m = slope

x = x coordinate

b = y intercept

Point Slope Formula: y-y1=m(x-x1)

Slope Formula: m= y2-y1 / x2-x1

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

y- (-2) = 2 (x - 0) = y+2=2x-0

y=2x-2

The integral to find the volume V is then:

V = ∫[0 to L] 144 dx

What is volume of the solid?

The volume of a solid is a measure of how much area of ​​space an object occupies. It is measured by the number of unit cubes needed to fill the body. It is decided by counting the unit cubes in the solid.

To find the volume of a solid, we need to consider parallel cross-sections perpendicular to the x-axis. Since these cross-sections are square, each square cross-section will have the same area throughout the body.

Consider a representative square cross-section at a given x-coordinate. The length of each side of this square will be equal to the diameter of the corresponding circular disc at this x-coordinate. Since the radius of a circular disk is given as 6, the diameter will be twice the radius, which is 12.

Therefore, the area of ​​a square cross-section at any coordinate is x (12)^2 = 144 square units.

To find the volume of a body, we must integrate the areas of all these square cross-sections over the range of values ​​of x that the body occupies. Since no specific range is mentioned in the information provided, I will assume that the body extends from x = 0 to x = L, where L is the length of the body along the x-axis.

The integral to find the volume V is then:

V = ∫[0 to L] 144 dx

Note: dx represents an infinitesimal change in x.

Note that this integral is just a setup and the actual evaluation of the integral is not required in the question.

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Answer:

Step-by-step explanation:

C

rule 1 pattern: 10, 20, 40, 80, etc.

rule 2 pattern:24,20,16,12,etc.

20 is in both patterns (:

Answer:

C

Step-by-step explanation:

Given:

\(\cos \theta =\dfrac{3}{5}\)

\(\sin \theta <0\)

To find:

The quadrant of the terminal side of \(\theta\) and find the value of \(\sin\theta\).

Solution:

We know that,

In Quadrant I, all trigonometric ratios are positive.

In Quadrant II: Only sin and cosec are positive.

In Quadrant III: Only tan and cot are positive.

In Quadrant IV: Only cos and sec are positive.

It is given that,

\(\cos \theta =\dfrac{3}{5}\)

\(\sin \theta <0\)

Here cos is positive and sine is negative. So, \(\theta \) must be lies in Quadrant IV.

We know that,

\(\sin^2\theta +\cos^2\theta =1\)

\(\sin^2\theta=1-\cos^2\theta\)

\(\sin \theta=\pm \sqrt{1-\cos^2\theta}\)

It is only negative because \(\theta \) lies in Quadrant IV. So,

\(\sin \theta=-\sqrt{1-\cos^2\theta}\)

After substituting \(\cos \theta =\dfrac{3}{5}\), we get

\(\sin \theta=-\sqrt{1-(\dfrac{3}{5})^2}\)

\(\sin \theta=-\sqrt{1-\dfrac{9}{25}}\)

\(\sin \theta=-\sqrt{\dfrac{25-9}{25}}\)

\(\sin \theta=-\sqrt{\dfrac{16}{25}}\)

\(\sin \theta=-\dfrac{4}{5}\)

Therefore, the correct option is B.

Answer:

x = -2

Step-by-step explanation:

3/2 (x-5) - 3/2 = 9x/2

3x/2 - 15/2 - 3/2 = 9x/2 ... alldenominator

are 2 so we can multiply all term by 2

2(3x/2 - 15/2 - 3/2 = 9x/2)

3x - 15 - 3 = 9x ... simplify it

3x - 12 = 9x

-12 = 9x - 3x ... take 3x to the left

-12 = 6x ... simplify

6x/6 = -12/6 ... dividing both side by 6

x = -2 ... simplify and solve x

If an investigator is getting responses very close to each other when assessing skinfold thickness 5 consecutive times, it is a sign that the measurements are precise or reliable.

Measurements refer to the process of quantifying physical quantities or properties such as length, mass, time, temperature, and more. The aim of measurements is to obtain accurate and reliable data that can be used for various purposes, such as scientific research, industrial applications, engineering, and construction.

Measurement involves comparing an unknown quantity with a known standard or unit of measurement. For example, length can be measured using a ruler, mass can be measured using a scale, and time can be measured using a clock. The units of measurement used can vary depending on the system of measurement used, such as the metric system or the imperial system.

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Sarah's charges per hour for working during the week will be $9.5.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

Sarah is a nanny who bills clients at various prices depending on whether she is working during the week or on the weekend. She worked 45 hours in a single week for a salary of $902.50, of which 5 hours were on the weekend. She worked 50 hours the next week, 10 of which were on the weekend, and made 1045 dollars.

Let x be the charge per working hour and y be the number of charges per hour during the weekend. Then the equation will be

45x + 5y = 902.5           ...1

50x + 10y = 1045

25x + 5y = 522.5          ...2

Subtract equation 2 from equation 1, then we have

45x - 25x = 902.5 - 522.5

20x = 380

x = 19

And the value of y will be

25 (19) + 5y = 522.5

475 + 5y = 522.5

5y = 47.5

y = 9.5

Sarah's charges per hour for working during the week will be $9.5.

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To find the 4th order Newton's divided-difference interpolating polynomial for f(x)=ln(x) with x=1,4,5,6,8, we first need to calculate the divided differences:

A. (a) The 4th order Newton's divided-difference interpolating polynomial for the function f(x) = ln(x) using the given data points is:

P(x) = ln(1) + (x - 1)[(ln(4) - ln(1))/(4 - 1)] + (x - 1)(x - 4)[(ln(5) - ln(4))/(5 - 4)(5 - 1)] + (x - 1)(x - 4)(x - 5)[(ln(6) - ln(5))/(6 - 5)(6 - 1)] + (x - 1)(x - 4)(x - 5)(x - 6)[(ln(8) - ln(6))/(8 - 6)(8 - 1)]

B. (a) To find f(x) at x = 7 and x = 9 using the interpolating polynomial, substitute the respective values into the polynomial expression P(x) obtained in the previous part.

Explanation:

A. (a) The 4th order Newton's divided-difference interpolating polynomial can be constructed using the divided-difference formula and the given data points. In this case, we have five data points: (1, ln(1)), (4, ln(4)), (5, ln(5)), (6, ln(6)), and (8, ln(8)). We apply the formula to calculate the polynomial.

B. (a) To find the value of f(x) at x = 7 and x = 9, we substitute these values into the polynomial P(x) obtained in the previous part. For x = 7, substitute 7 into P(x) and evaluate the expression. Similarly, for x = 9, substitute 9 into P(x) and evaluate the expression.

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Answer:

Option (1)

Step-by-step explanation:

Diameter of a bolt can measure anywhere from 0.2 cm less than 1.5 to 0.2 cm greater than 1.5 cm.

Let the diameter of the bolt = x cm

Then the value of x will be,

(1.5 - 0.2) cm < x < (1.5 + 0.2) cm

When we plot the possible measures of the diameter of the bolt on a number line,

Measures of x will be between 1.3 cm to 1.7 cm

Option (1) will be the answer.

Answer:

A

Step-by-step explanation:

Its pretty self explainatory, it tells you that the line has to be anywhere from 0.2 cm less than 1.5 cm to 0.2 cm greater than 1.5 cm, so if you look at the graphs A is the only one that maches with what the question in asking.

a) It is a vertical dilation of scale factor of 5.

b) It is a translation up of 10 units.

Here we have the line:

S(d) = 5d + 10

That represents the cost for renting the surboard for d days.

Remember that the parent linear function is y =x

A) 5 in this case is the slope, it says how much the cost for the rental increases for each day that passes. The effect on the linear parent function is a dilation of scale factor of 5.

B) 10 is the y-intercept, so this will represent a translation up of 10 units.

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The product of the given irrational number  ∛5 × √2 is equal to

option b. \(\sqrt[6]{200}\)

As given in the question,

Given irrational numbers are:

∛5 × √2

Take the least common multiple of 3 and 2

Least common multiple of 3 and 2 is 6.

∛5 = \(5^{2 \times\frac{1}{2}\times \frac{1}{3} }\)

    = \(\sqrt[6]{5^2}\)

    = \(\sqrt[6]{25}\)

√2 = \(2^{3 \times\frac{1}{3}\times \frac{1}{2} }\)

    =\(\sqrt[6]{2^3}\)

    = \(\sqrt[6]{8}\)

Product of ∛5 × √2 is given by:

∛5 × √2 = \(\sqrt[6]{25} \times \sqrt[6]{8}\)

             = \(\sqrt[6]{25 \times 8}\)

             = \(\sqrt[6]{200}\)

Therefore, the product of the given irrational number is equal to \(\sqrt[6]{200}\) .

The complete question is:

What is the following product?

∛5 × √2

a. \(\sqrt[6]{10}\)

b. \(\sqrt[6]{200}\)

c. \(\sqrt[6]{500}\)

d. \(\sqrt[6]{10000}\)

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Check the picture below.

Given,

7p-11p+3>3-4p

-4p+3>3-4p

-4p>-4p

which is absured.

So there is no solution of the inequality.

Answer:

1. radius = 8.4 cm

2. diameter = 9 m

Step-by-step explanation:

Hope it helps!         :3

plz mark as brainliest!

Answer:

1. the radius is 8.4  2. the diameter is 9

Step-by-step explanation:

Radius is half of diameter

So you would do 16.8 / 2 = 8.4

2. Diameter is radius times 2

4.5 ( 2 ) = 9

Hope this helps dude

Answer:

\( \sf \: 6 + 3b + 8 = 32\)

Step-by-step explanation:

Given expression,

→ 6 + 3b + 8

Now we have to use,

→ b = 6

Let's solve the expression,

→ 6 + 3b + 8

→ 6 + 3(6) + 8

→ 6 + 18 + 8

→ 24 + 8

→ 32 => final value

Hence, the answer is 32.

the fixed amount that Daria earns for each television is $60.

Why it is?

Let's assume that the fixed amount that Daria earns for each television is x dollars.

If Daria sells 18 televisions with extended warranties, she earns an additional $20 for each one, so her total earnings from those sales would be 20*18 = $360.

Her total earnings from all 18 televisions would then be the sum of her earnings from the sales without extended warranties (18x dollars) and her earnings from the sales with extended warranties ($360). This can be represented by the equation:

18x + 360 = 1440

Solving for x, we get:

18x = 1080

x = 60

Therefore, the fixed amount that Daria earns for each television is $60.

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The bottleneck time is 10. This is the longest time it takes to complete any task in the assembly line, and all the other tasks must be completed within this time frame.

The bottleneck time is the longest time it takes to complete any task in the assembly line. In this case, the longest time needed is 10, which is the last station. This means that all the other tasks must be completed within 10 seconds in order for the entire assembly line to proceed.

The bottleneck time is 10. This is the longest time it takes to complete any task in the assembly line, and all the other tasks must be completed within this time frame.

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The yy-component of vector a a is -y-direction, which is equal to 0 m/s2.the product of the second term of the vector with unit vector j^j^, which is in the direction of the y-axis.

Given a vector, a⃗ a→ = (5.0 m/s2, −y−direction)Find the yy -component of the given vector a⃗ a→.Solution: The yy-component of the given vector a⃗ a→ = -y-directionTo find the yy-component of the given vector a⃗ a→, we have to take the product of the second term of the vector with unit vector j^j^, which is in the direction of the y-axis.Therefore, the yy-component of vector a⃗ a→ is :a_yy = -y-direction = (-1)(0) = 0 m/s²  Answer: 0 m/s².

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The yy-component of vector a⃗ a→ is -y-direction.

The yy-component of a vector represents the magnitude of the vector in the y-direction.

In this case, the vector a⃗ a→ is given as (5.0 m/s2, −y-direction).

Since the yy-component is the magnitude in the y-direction, the yy-component of the vector a⃗ a→ is -y-direction.

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Answer:

-3x^3+8x-6

step

p-q=5x^4+4x-3-(5x^4+3x^3-4x+3)=5x^4+4x-3-5x^4-3x^3+4x-3

=5x^4-5x^4-3x^3+4x+4x-3-3

=-3x^3+8x-6

Answer:

your your question is wrong please make sure

Answer:

2

Step-by-step explanation:

p/2-5

You can use PEMDAS to help:

Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

So, first we have to substitute 14 for p to get:

14/2-5

Next, comes division before subtraction, so we can rewrite the equation as this:

(14/2)-5

7-5

=2

Answer:

$66.20=1.25x+50

Step-by-step explanation:

Be sure about the question. This problem is exactly the same to another one I did. So this should help.

Answer:

If the question is to reveal how many movies Lynn has watched, then...:

13 movies

Step-by-step explanation:

$50 is the monthly bill

$66.2 - $50 = $16.2 for movies

$16.2 / $1.25 = 12.96 movies .( or 13 movies)

By using normal distribution of probability, it is obtained that

Percentile rank of a turtle whose length is 21 inches is 22%

What is probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probality of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

Here, Normal Distribution of probability is used

Mean = 25.9 inches

Standard deviation = 6.3 inches

P(X \(\leq\) 21) = P(z \(\leq\) \(\frac{21 -25.9}{6.3}\))

               = P(z \(\leq\) -0.78)

               = 0.22

               = 22%

Percentile rank of a turtle whose length is 21 inches is 22%.

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i need the answer i need  help plz give the answear and the work hot to do it plz

To find the lower quartile of a set of numbers, we need to determine the value that separates the lowest 25% of the data from the rest. In the given set of numbers, the lower quartile can be found by arranging the data in ascending order and identifying the value at the 25th percentile.

First, let's arrange the data in ascending order: 1 5 6 6 7 7 8 8 8 8 9 9 18 20 20 20 20 20 24 32 50 50 68 100.

To find the lower quartile, we need to determine the position of the 25th percentile. Since there are 23 data points, the 25th percentile corresponds to the value at the (25/100) * 23 = 5.75th position.

Since the position is not a whole number, we need to find the value between the fifth and sixth data points. The fifth data point is 7, and the sixth data point is also 7. Therefore, the lower quartile is 7.

The lower quartile represents the value below which 25% of the data lies. In this case, 25% of the data points are less than or equal to 7. It indicates that a quarter of the values in the dataset are smaller than or equal to 7, while the remaining 75% are larger.

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The number of jobs that he could he do if the cost was $four thousand, one hundred twenty five will be 25.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

When a man does job at the rate of $165 per job, the number of jobs that he could he do if the cost was $four thousand, one hundred twenty five will be:

= Amount / Rate

= $4125 / $165

= 25

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A man does job at the rate of $165 per job. How many jobs could he do if the cost was $four thousand, one hundred twenty five?

The y-intercept of the equation 2x - y = -3 is 3 and in ordered pair form is (0,3).

The slope-intercept formula is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the equation in the question

2x - y = -3

First, we solve form for y and reorder in slope intercept form.

2x - y = -3

Subtract 2x from both sides

2x - 2x- y = -3 - 2x

- y = -3 - 2x

Divide each term by -1

y = 3 + 2x

Reorder in slope intercept form

y = 2x + 3

To find the y-intercept, replace x with zero and solve for y

y = 2(0) + 3

y = 3

Therefore, the y-intercept is 3.

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The total number of eigenvectors for an n x n matrix is equal to the sum of the multiplicities of its distinct eigenvalues,

which is at most n.

The reason why a 2x2 matrix can have at most two distinct eigenvalues is because the characteristic equation for a

2x2 matrix is quadratic. This means that there can be at most two distinct solutions for the eigenvalues.

As for an n x n matrix, the reason why it can have at most n distinct eigenvalues is because the characteristic equation

for an n x n matrix is of degree n.

This means that there can be at most n distinct solutions for the eigenvalues. Additionally, the maximum number of

eigenvectors that can be associated with each distinct eigenvalue is equal to the multiplicity of the eigenvalue.

Therefore, the total number of eigenvectors for an n x n matrix is equal to the sum of the multiplicities of its distinct

eigenvalues, which is at most n.

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