question in pic. please help!

An equation of line that passes through the point (-3, -7) and is parallel to the line 2x-3y = 24 is 3y = 2x - 15.

The equation of line is 2x - 3y = 24.

The general equation of line is  y = mx + c, where m is the slope of line and c is the y intercept.

We first express the equation of line in the general form of equation.

First isolate the y term.

Add 3y on both side, we get

2x = 3y + 24

Subtract 24 on both side, we get

3y = 2x - 24

Divide by 3 on both side, we get

y = 2/3 x - 8

On comparing with y = mx + c

m = 2/3

The points are (-3, -7); \(x_{1}\) = -3 and \(y_{1}\) = -7.

The equation of line passes through the points are

y - \(y_{1}\) = m(x - \(x_{1}\))

y - (-7) = 2/3(x - (-3))

Simplify

y + 7 = 2/3 (x + 3)

Multiply by 3 on both side, we get

3y + 21 = 2x + 6

Subtract 21 on both side, we get

3y = 2x - 15

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Answer:

Step-by-step explanation:

A=number Adult tickets;S=A+74= number Student tickets

Total tickets=adult tickets + student tickets

724=A+(A+74)

724=2A+74 Subtract 74 from each side

650=2A divide each side by 2

325=A ANSWER 1: There were 325 Adult tickets sold

Answer: a

Step-by-step explanation:

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

Work Shown:

area = 0.5*side1*side2*sin(angle)

area = 0.5*13*7.5*sin(94)

area = 48.6312474501664

area = 48.6 square inches

Notes:

Answer: 48.6

Step-by-step explanation:

i took the test

Answer:

Step-by-step explanation:

Product of slope of perpendicular lines = -1

6x + 5y = 30

Write this equation in y = mx + b  form

        5y = -6x + 30

          y = \(\frac{-6}{5}x+\frac{30}{5}\)

          \(y=\frac{-6}{5}x + 6\)

Slope of this line m₁ = -6/5

m₁ * m₂ = -1

      m₂ = -1÷m₁ = -1 * \(\frac{5}{-6}\)  

\(m_{2}=\frac{5}{6}\)     & (-6 , -7)

Equation of the required line: y - y₁ = m (x - x₁)

\(y - (-7) = \frac{5}{6}(x - [-6])\\\\y + 7 = \frac{5}{6}x + 6 *\frac{5}{6}\\\\y = \frac{5}{6}x +5-7\\\\y=\frac{5}{6}x-2\)

The given statement "The misuse of statistics is sometimes intentional." is True, because there are instances where people intentionally misuse statistics to manipulate or deceive others.

The misuse of statistics can be an intentional act by individuals or organizations to manipulate or deceive others. This is often done by selectively choosing data or statistics that support a particular argument or position, while ignoring or downplaying information that does not support it.

One way this can be achieved is by distorting graphs or charts. For example, a bar chart can be designed to visually exaggerate the differences between data points, making the differences appear more significant than they actually are. This can be done by adjusting the scale of the chart or by changing the width of the bars.

Another way that statistics can be misused is by making false claims based on the data. For example, someone may use a correlation between two variables to imply a causal relationship, even though there may not be any evidence to support this claim.

Similarly, statistics can be used to mislead people by presenting them in a way that is misleading. For example, a statistic may be presented without any context or compared to an irrelevant baseline, making it appear more significant or less significant than it actually is.

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Answer:

y(t) = 720e^0.3466t

y = 2036.6288

Step-by-step explanation:

The exponential relation :

y = Ae^kt

A = initial value ; y = final value ; r ; k = exponential rate, t = time

At t = 0

y = 720e^0 ; y = 720

At t = 2 ; y = 720e^2k

1440 = 720e^2k

1440/720 = e^2k

2 = e^2k

Take the In of both sides

0.6931471 = 2k

k = 0.6931471 / 2

k = 0.3466

Hence, equation becomes :

y = 720e^0.3466t

After 3 hours ;

t = 3

y = 720e^0.3466*3

y = 720e^1.0398

y = 720 * 2.8286512

y = 2036.6288

The vector w = |u|v + |v|u bisects the angle between vectors u and v. The sum of the lengths of the sides AB, BC, and CA of a triangle is equal to the perimeter of the triangle.

To show that w = |u|v + |v|u bisects the angle between u and v, we need to prove that the angle between w and u is equal to the angle between w and v.

Let's calculate the dot product between w and u:

w · u = (|u|v + |v|u) · u

= |u|v · u + |v|u · u

= |u|v · u + |v|u · u (since v · u = u · v)

= |u|v · u + |v|u²

= |u||v|u · u + |v|u²

= |u||v|(u · u) + |v|u²

= |u||v||u|² + |v|u²

= |u|²|v| + |v|u²

= |u|²|v| + |v||u|² (since |u|² = u²)

= (|u|² + |v||u|) |v|

= |u|(u · u) + |v|(u · u) (since |u|² + |v||u| = |u|(u · u) + |v|(u · u))

= (|u| + |v|) (u · u)

= (|u| + |v|) ||u||²

= (|u| + |v|) ||u||²

= (|u| + |v|) ||u||

= (|u| + |v|) |u|

Similarly, we can calculate the dot product between w and v:

w · v = (|u|v + |v|u) · v

= |u|v · v + |v|u · v

= |u||v|v · v + |v|u · v

= (|u|v · v + |v|u · v) (since v · v = ||v||²)

= (|u| + |v|) (v · v)

= (|u| + |v|) ||v||²

= (|u| + |v|) ||v||

= (|u| + |v|) |v|

From the above calculations, we can see that w · u = (|u| + |v|) |u| and w · v = (|u| + |v|) |v|.

Since u · u and v · v are both positive (as they are dot products with themselves), we can conclude that w · u = w · v if and only if |u| + |v| ≠ 0. Therefore, when |u| + |v| ≠ 0, the vector w bisects the angle between u and v.

Moving on to the second question, the sum of the lengths of the sides AB, BC, and CA of a triangle is equal to the perimeter of the triangle. Therefore, AB + BC + CA represents the perimeter of the triangle.

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Answer:

(3,7) (4,4) (1,2)

Step-by-step explanation:

180 degrees: (x, y) —> (-x, -y)

Answer:

54 minutes

Step-by-step explanation:

1) There are 60 minutes in an hour. So, you can do 60-36 to find the first value. (24)

2) Add 24 minutes to 30 and get 54 minutes.

Answer:

x<30

Step-by-step explanation:

3/6x-1/6x<10

1/3x<10

x<30

Step-by-step explanation:

the middle one has to be the same for both part ratios.

the best here is to bring the ratio element of B in the first part ratio to 10. we need to double the B element there

for that (as a ratio is a fraction) we also have to adapt the A element in the same way.

so, we get

4×2 : 5×2 : 9 =

= 8 : 10 : 9

and that is also shown in the graphic.

Answer:

X:Y:Z= 8:10:9

Step-by-step explanation:

Let x be the number of students in class A

Let y be the number of students in class B

Let z be the number of students in class C

x:y = 4:5

y:z= 10: 9

x:y:z = ?

Find the LCM of the y terms (5 and 10 ) which is 10

Divide 10 by the first y term (5) = 2

Divide 10 by the second y term(10) = 1

X: y = (4 x 2) :(5 x 2)= 8:10

y:z =(10 x 1) : (9:1)= 10:9

x:y:z= 8:10:9

a) About 4.16% of test takers earn a score less than 500 on the GRE Chemistry test.

b) About 96.64% of test takers earn a score greater than or equal to 900 on the GRE Chemistry test.

c) The estimated score at the 99th percentile on the GRE Chemistry test is approximately 954.512.

To answer these questions, we'll use the properties of the normal distribution and the given mean and standard deviation.

(a) To find the percentage of test takers who earn a score less than 500 on the GRE Chemistry test, we need to calculate the cumulative probability up to the score 500.

z-score = (X - mean) / standard deviation

where X is the score we are interested in.

z-score = (500 - 694) / 112

z-score ≈ -1.732

Now, we look up the cumulative probability for a z-score of -1.732 in the standard normal distribution table or use a calculator to find that the cumulative probability is approximately 0.0416 or 4.16%.

So, about 4.16% of test takers earn a score less than 500 on the GRE Chemistry test.

(b) To find the proportion of test takers who earn a score greater than or equal to 900, we need to calculate the cumulative probability from 900 to positive infinity.

z-score = (X - mean) / standard deviation

where X is the score we are interested in.

z-score = (900 - 694) / 112

z-score ≈ 1.839

Now, we look up the cumulative probability for a z-score of 1.839 in the standard normal distribution table or use a calculator to find that the cumulative probability is approximately 0.9664 or 96.64%.

So, about 96.64% of test takers earn a score greater than or equal to 900 on the GRE Chemistry test.

(c) To estimate the score at the 99th percentile on the GRE Chemistry test, we need to find the value that separates the lowest 99% of the scores from the highest 1%.

We use the z-score formula to find the z-score corresponding to the 99th percentile:

z-score = invNorm(0.99)

z-score ≈ 2.326

Now, we use the z-score to find the score corresponding to the 99th percentile:

X = mean + (z-score * standard deviation)

X = 694 + (2.326 * 112)

X ≈ 694 + 260.512

X ≈ 954.512

So, the estimated score at the 99th percentile on the GRE Chemistry test is approximately 954.512.

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We have been given the following values:Radius of cylindrical tank, r = 1.02 mHeight to which the tank is filled, h = 3.13 mAmount of industrial solvent, V = 14100 kgWe need to calculate the density of the liquid industrial solvent.

We know that the formula for volume of a cylinder is given by :

Volume of a cylinder = πr²hSubstituting the values of r and h, we get:Volume of cylindrical tank = π(1.02)²(3.13)Volume of cylindrical tank = 10.150 m³.

Since we know the amount of solvent, we can use the formula for density of a substance to find its density:

Density = Mass / Volume.

Substituting the values of mass and volume, we get:

Density of industrial solvent = 14100 / 10.150.

Density of industrial solvent = 1391.13 kg/m³Hence, the density of the liquid industrial solvent is 1391.13 kg/m³.

To calculate the density of the industrial solvent, we use the formula:

Density = Mass / Volume.

We have been given the mass of the solvent as 14100 kg. We can find the volume of the cylindrical tank by using the formula for the volume of a cylinder, which is given by:

Volume of a cylinder = πr²hWe have been given the radius of the cylindrical tank as 1.02 m and the height to which it is filled as 3.13 m. We substitute these values in the formula to get the volume of the tank.Volume of cylindrical tank = π(1.02)²(3.13)Volume of cylindrical tank = 10.150 m³.

Substituting the values of mass and volume in the formula for density of a substance, we get:Density of industrial solvent = 14100 / 10.150Density of industrial solvent = 1391.13 kg/m³Therefore, the density of the liquid industrial solvent is 1391.13 kg/m³.

The density of the industrial solvent is 1391.13 kg/m³.

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Step-by-step explanation:

(e) = number of erasers she had originally.

now she has 38.

so,

A

38 = (e) + 10

B

38 - 10 = (e) + 10 - 10

28 = (e)

she had originally 28 erasers.

This is a translation of 2 units to the left and 5 units up, so the correct option is the first one.,

Remember that a vertical translation of N units is:

g(x) = f(x) + N

if N < 0 the translation is down.

if N > 0 the translation is up.

And a horizontal translation of N units is:

g(x) = f(x + N)

If N > 0 the translation is to the right.

if N < 0 the translation is to the left.

Here we have the transformation:

f(x) = x²

g(x) = (x + 2)² + 5

So this is a translation of 2 units to the left and 5 units up.

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Answer:

let number be x

30=5% of X

3000=5x

X=600

so,5% of 600 is 30

The average tax rate for a firm with taxable income of $311,360 is approximately 33.61%.

To find the average tax rate for a firm with taxable income of $311,360, we need to calculate the total tax paid and then divide it by the taxable income. Here's a step-by-step explanation:

1. Determine the tax brackets applicable to the taxable income: The firm's taxable income falls into the first four tax brackets.

2. Calculate the tax for each bracket:
  a. For the first bracket ($0-$50,000): 15% of $50,000 = $7,500
  b. For the second bracket ($50,001-$75,000): 25% of $25,000= $6250    
  c. For the third bracket ($75,001-$100,000): 34% of $25,000 = $8,500
  d. For the fourth bracket ($100,001-$335,000):

The firm's taxable income falls within this bracket at $311,360. So, we calculate the tax for the income in this bracket, which is $311,360 - $100,000 = $211,360.

Thus, 39% of $211,360 = $82,430.40

3. Calculate the total tax paid:

$7,500 + $6,250 + $8,500 + $82,430.40 = $104,680.40

4. Calculate the average tax rate: Total tax paid divided by taxable income = $104,680.40 / $311,360 ≈ 0.3361 or 33.61%

The average tax rate for a firm with taxable income of $311,360 is approximately 33.61%.

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Answer:

(-6,2)

Step-by-step explanation:

\(x = - 6 \\ x - y = - 8\)

Substitution

Substitute x = -6 from the first equation in the second equation.

\( - 6 - y = - 8 \\ - 6 + 8 = y \\ 2 = y\)

Normally, we have to substitute either x-term or y-term in one of the equation to get another term. For this situation, we already know the value of x so It is not necessary to substitute the y-value.

Answer Check

We have to check the answer to make sure that we have got the right answer.

We can check the answer by substituting both x-value and y-value in the equation.

\(x - y = - 8\)

Substitute x = -6 and y = 2 in the equation.

\( - 6 - 2 = - 8 \\ - 8 = - 8\)

The equation is true. Therefore, our answer is (-6,2)

The distance of the comet from the laser rangefinder after x days, denoted as g(x), is given by the equation:

g(x) = 250,000csc(π36x)

where x represents the number of days and g(x) is the distance in kilometers.

In this equation, the function csc represents the cosecant function, which is the reciprocal of the sine function. The π/36 factor in the argument of the csc function ensures that the period of the comet's distance is 36 days.

To find the distance of the comet at a specific number of days, substitute the value of x into the equation g(x). For example, to find the distance after 10 days, substitute x = 10 into the equation:

g(10) = 250,000csc(π36(10))

To calculate the distance, evaluate the cosecant function using the appropriate mathematical tools or software.

The given equation provides a mathematical model for the distance of the comet as it approaches Earth over a period of 36 days.

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Answer: 5 pints

Step-by-step explanation: So, to find the conversion of cups and ozs to pints, we should know the formula. So, It would be

Cups ÷ 2.

So, using that 8 ÷ 2 is 4, so we now know that 8 cups is equivalent to 4 pints. And we all know that 16 cups = 1 pint (hopefully), we add 4 + 1 pint to get 5 pints. I hope this helps!

The equation of the line tangent to the graph of y = sin^(-1)(x^2/4) at x = 2 is x = 2.

To find the equation of the line tangent to the graph of y = sin^(-1)(x^2/4) at the point where x = 2, we need to find the slope of the tangent line and the coordinates of the point of tangency.

First, let's find the derivative of y with respect to x. The derivative of sin^(-1)(x^2/4) can be found using the chain rule:

dy/dx = d/dx[sin^(-1)(x^2/4)]

= (1/sqrt(1 - (x^2/4))) * (2x/4)

= (2x)/(4 * sqrt(1 - (x^2/4)))

= x / (2 * sqrt(1 - (x^2/4)))

Now, let's substitute x = 2 into the derivative to find the slope at x = 2:

slope = 2 / (2 * sqrt(1 - (2^2/4)))

= 2 / (2 * sqrt(1 - 1))

= 2 / (2 * sqrt(0))

= 2 / (2 * 0)

= Undefined

The slope is undefined because the derivative becomes infinite at x = 2.

Next, let's find the y-coordinate of the point of tangency by substituting x = 2 into the original equation:

y = sin^(-1)((2^2)/4)

= sin^(-1)(1)

= π/2

So, the point of tangency is (2, π/2).

Since the slope is undefined, the line tangent to the graph at x = 2 is a vertical line. The equation of a vertical line passing through the point (2, π/2) is given by:

x = 2

Therefore, the equation of the line tangent to the graph of y = sin^(-1)(x^2/4) at x = 2 is x = 2.

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The probability of rolling the same number on all three dice can be found by multiplying the probabilities of rolling the same number on each individual die. The probability of rolling the same number on the 6-sided die is 1/6, the probability of rolling the same number on the 8-sided die is 1/8, and the probability of rolling the same number on the 12-sided die is 1/12. Multiplying these probabilities together gives us the probability of rolling the same number on all three dice: (1/6) * (1/8) * (1/12) = 1/576.

The probability of rolling a "4" on one of the dice and it being the 6-sided die can be found by multiplying the probability of rolling a "4" on the 6-sided die (1/6) by the probability of picking the 6-sided die at random (1/3). This gives us a probability of (1/6) * (1/3) = 1/18.

The probability of the smallest number rolled being at least 3 can be found by subtracting the probability of the smallest number being less than 3 from 1. The probability of the smallest number being less than 3 is the probability of rolling a 1 or a 2 on each of the dice: (2/6) * (2/8) * (2/12) = 1/72. Therefore, the probability of the smallest number being at least 3 is 1 - (1/72) = 71/72.

The probability of the product of the three numbers rolled being even can be found by subtracting the probability of the product being odd from 1. The probability of the product being odd is the probability of rolling an odd number on each of the dice: (3/6) * (4/8) * (6/12) = 1/8. Therefore, the probability of the product being even is 1 - (1/8) = 7/8.

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Answer:

- the pressure will decrease

(volume is doubled ,the pressure reduced by half).

Step-by-step explanation:

P_1 V_1=P_2 V_2

This equation shows that, as volume increases, the pressure of the gas decreases in proportion.

Similarly, as volume decreases, the pressure of the gas increases.

Experiment was conducted to study tensile strength of Portland cement using four different mixing techniques. Data was collected to compare performance of these techniques in terms of tensile strength.

In a completely randomized experiment, the four different mixing techniques for Portland cement were randomly assigned to different samples. The tensile strength of each sample was then measured, resulting in a dataset that allows for comparisons between the mixing techniques.

The collected data can be analyzed to determine if there are any significant differences in tensile strength among the mixing techniques. Statistical methods such as analysis of variance (ANOVA) can be applied to assess whether there is a statistically significant variation in tensile strength between the techniques.

The analysis of the data will provide insights into which mixing technique yields the highest tensile strength for Portland cement. It will help identify the most effective method for producing cement with desirable tensile properties. By conducting a completely randomized experiment, researchers aim to eliminate potential biases and confounding factors, ensuring a fair comparison between the different mixing techniques.

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Answer:

The slope is 1

Step-by-step explanation:

the equation y=mx+b represents slope intercept form, and "mx" represents the slope.

the equation can also be written as: y = 1x + 5

\(A=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right]\)

We can find the A as shown below:

Given A^2=I

We know that A^2=A×A

And \(I=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]\)

So, \(A^2=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]\)

Let \(A=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right]\)

\(A^2=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right] \left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right]\)

\(A^2=\left[\begin{array}{ccc}9-8&-6+6\\12-12&-8+9\end{array}\right]\)

\(A^2=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]\)

Hence, \(A=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right]\)

Hence, option C is correct

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