Identify the constant of proportionality from the table. A:3. B:1/2. C:2. D:6​

Answer: Option C

Step-by-step explanation:

C because 6+1=1+1+1+1+1+1+1

Answer:

C

Step-by-step explanation:

We want to find which model shows two equal expressions. We know that the value of x is 6. That being said, on the left side of each equation, plug in 6 for every "x" you see. Then, add the values on both sides. If they're equal, that's your answer.

For example:

In choice A, we see two x's, so we plug in 6 for them both and add them. That's 12 on the left side. On the other side of the equation, we have 7 "1" boxes, which simply just means add them, so that's 7 on the other side. 12 does not equal 7, therefore A is not the answer. However, for choice C, we are given x, which we know is 6, and a "1" box, which simply means 6 + 1, which is 7. On the other side of this equation, we have 7 "1" boxes, so that's 7. The equation becomes 7 = 7, which is true, so that is our answer.

Answer:

-23/4 =c

Step-by-step explanation:

21+30=-4c+28​

Combine like terms

51 = -4c+28

Subtract 28 from each side

51 = -4c+28

Subtract 28 from each side

51-28 = -4c+28-28

23 = -4c

Divide each side by -4

23/-4 = -4c/-4

-23/4 =c

Answer: \(-\frac{23}{4}\) or 5.75

Step-by-step explanation:

Step 1. Simplify 21 + 30 to 51

51 = −4c + 28

Step 2. Subtract 28 from both sides

51 - 28 = -4c

Step 3. Simplify 51 - 28 to 23

23 = -4c

Step 4. Divide both sides by -4

\(-\frac{23}{4}\) = c

Step 5. Switch sides

c = \(-\frac{23}{4}\)

Decimal Form Answer: -5.75

I hope this helps you out.

Answer:

8 miles

Step-by-step explanation:

:p

1. A) The initial mass, in grams, of the radioactive isotope in the substance when t = 0.

2. C) I and II (Both the mean and the median are the same for both data sets.)

3. D) f(x) = 12(x - 3) + b (where b is a constant)

1. The value 10 in the function A(t) = 10(1)^30 represents the initial mass, in grams, of the radioactive isotope in the substance when t = 0. In the context of exponential decay, the function A(t) represents the remaining mass of the substance after time t. The coefficient 10 indicates the initial mass at t = 0, which is the starting point for the decay process. Therefore, option A is the correct interpretation.

2. The mean and median are two measures of central tendency used in data analysis. The mean is the average value of a dataset, obtained by summing all the values and dividing by the number of data points. The median is the middle value in a dataset when arranged in ascending or descending order.

Since the dot plots for data sets X and Y are not provided, we can only determine the same property based on the given options. Option C, which states that both the mean and median are the same for both data sets, indicates that the average and middle values are identical in both sets. This implies that the distribution of values and the overall central tendency are the same for both sets, regardless of the specific values.

3. The given property states that if point (a, b) is on the graph of the equation y = f(x), then the point (a + 1, b) is also on the graph. This means that for each x-value, the corresponding y-value remains the same when incremented by 1.

Among the given options, option D, f(x) = 12(x - 3) + b, satisfies this property. In this equation, the term (x - 3) represents the x-value, and when incremented by 1, it becomes (x - 3 + 1) = (x - 2). The coefficient 12 ensures that the change in y is 12 times the change in x, maintaining the property that y remains the same when x is increased by 1. The constant term b allows for a vertical shift of the graph.

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The probability that the person participates in at least one school-sponsored activity given that the student works part-time is 0.58.

The possibility of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability.

Assume that events A and B are two independent occurrences with probabilities P(A) and P(B), respectively, such that the probability that event B will occur given that event A is given by: P(B|A) = P(A∩B)/P (A)

Given:

Percentage of the students who have part-time jobs, P(A) = 73%

Percentage of the students who participate in at least one school-sponsored activity, P(B)= 65%

Percentage of the students who work part-time and participate in at least one school-sponsored activity, P(A∩B) = 42%

The probability that the person participates in at least one school-sponsored activity given that the student works part-time is:

P(B|A) = P(A∩B)/P(A)

          = 42/73

          = 0.58

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Answer:

0.575

Step-by-step explanation:

nice job

Answer:

Step-by-step explanation:

(10j – 7)-(-9j + 2)

10j-7+9j-2

19j-9

If you conduct a hypothesis test at a 95% level, it means that you are using a significance level of 0.05. This significance level represents the probability of rejecting the null hypothesis when it is actually true.

In hypothesis testing, the null hypothesis is the assumption that there is no significant difference or relationship between the variables being tested. The alternative hypothesis, on the other hand, suggests that there is a significant difference or relationship.

Now, when you conduct a hypothesis test at a 95% level, you set a threshold for rejecting the null hypothesis. This threshold is determined by the significance level of 0.05. If the p-value (the probability of obtaining the observed data or more extreme values assuming the null hypothesis is true) is less than 0.05, you would reject the null hypothesis in favor of the alternative hypothesis.

However, there is still a chance of making a Type I error, which is rejecting the null hypothesis even though it is actually true. The probability of making a Type I error is equal to the significance level you set, which is 0.05 in this case.

So, if you conduct a hypothesis test every so often at a 95% level, you can expect to reject the null hypothesis about 5% of the time, even though you should not. This means that approximately 5% of your tests will result in a Type I error.

To summarize:
- Conducting a hypothesis test at a 95% level means using a significance level of 0.05.
- The null hypothesis assumes no significant difference or relationship between variables.
- The alternative hypothesis suggests a significant difference or relationship.
- If the p-value is less than 0.05, the null hypothesis is rejected.
- However, there is a chance of making a Type I error, which is rejecting the null hypothesis even though it is true.
- The probability of making a Type I error is equal to the significance level, which is 0.05 in this case.
- Therefore, you can expect to reject the null hypothesis about 5% of the time, even though you should not.

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Las cantidades requeridas de ingredientes para la preparación de alfajores son 3,5 barras de mantequilla, 3,5 bolsas de manjar, 2 tazas de maicena y 9 / 4 tazas de harina.

Sabrina entrega un vuelto de 10,4 soles por el pago de 100 soles por la compra de 7 docenas de 12,80 soles.

En este problema debemos determinar la cantidad requerida de ingredientes para la preparación de alfajores, se tiene como referencia una tabla de preparación, de modo que se puede determinar las cantidades requeridas mediante regla de tres simple:

y' = (p' / p) × y

Where:

A continuación, determinamos los ingredientes requeridos y los faltantes en cada caso:

Barra de mantequilla:

y' = (60 / 24) × 1

y' = 2,5 barras

y'' = 6 barras - 2,5 barras

y'' = 3,5 barras

Bolsas de manjar

y' = (60 / 24) × 1

y' = 2,5 bolsas

y'' = 6 bolsas - 2,5 bolsas

y'' = 3,5 bolsas

Maicena

y' = (60 / 24) × (1 / 2)

y = 5 / 4 tazas

y'' = 5 / 4 tazas - 1 / 4 tazas

y'' = 2 tazas

Tazas de harina

y' = (60 / 24) × (3 / 2)

y' = 15 / 4 tazas

y'' = 15 / 4 tazas - 3 / 2 tazas

y'' = 9 / 4 tazas

Tazas de azúcar en polvo

y' = (60 / 24) × (1 / 2)

y' = 5 / 4 tazas

y'' = 5 / 4 tazas - 10 tazas

y'' = - 35 / 4 tazas (Tiene exceso de azúcar en polvo).

En consecuencia, los faltantes para la preparación de 60 alfajores son los siguientes: 3,5 barras de mantequilla, 3,5 bolsas de manjar, 2 tazas de maicena y 9 / 4 tazas de harina.

Por último, determinamos el vuelto tras el pago de 100 soles peruanos:

C = 100 soles - 7 · 12,80 soles

C = 10,4 soles

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A homogeneous system in parametric vector form:

(x1,x2,x3) = (s,s,-0.25s)

Parametric vector Form:

Any equation expressed as a parameter is a parametric equation. The general equation y = mx + b (where m and b are parameters) of a straight line in the form of a slope intersection is an example of a parametric equation. Example: one of the variables to t(x = t). Then we can rewrite this equation as y = t²+5.

So the set of parametric equations is x = t and y=t²+5.

According to the Question:

We are to solve them in parametric form.

X₁ + 2X₂ + 12X₃ = 0     ----------------------- (1)

2X₁ + X₂ + 12X₃ = 0     ----------------------- (2)

-X₁ + X₂ = 0                  ----------------------- (3)

From equation 3 we get

x₁ = x₂

Substitute in 1 and 2 to get

3x₁ + 12x₃ = 0 and

3x₁ + 12x₃ = 0

Thus, we find these two equations are dependent.  So we can have infinite solutions in parametric form only.

No unique solution is possible

Let x₁ = x₂ = s

Since 3x₁ +12x₃ = 0

x₁ = -4x₃

Or x₃ = -0.25s

So solution in parametric form is

(x1,x2,x3) = (s,s,-0.25s) for all real values.

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Answer:

Step-by-step explanation:

2(x + 3) + 2x

2x + 6 + 2x

4x + 6 and 4x + 3 not equal

3(x + 2) + 4x

3x + 6 + 4x

7x + 6 and 6x + 6 not equal

5x + 2(x + 4)

5x + 2x + 8

7x + 8 and 6x + 8 not equal.

4 + 5(x + 2)

4 + 5x + 10

5x + 14 and 5x + 14 are equal

Answer:

6.84 weeks

Step-by-step explanation:

$719.95 - $178.95 = 541$

541/79 = 6.84 weeks

A person buying a personal computer system has choice of 48 distinct computer systems that can be purchased.

To find the total number of distinct computer systems that can be purchased, we need to multiply the number of choices for each component.

Number of choices for the basic unit = 4 Number of choices for the keyboard = 3 Number of choices for the printer = 4

The total number of distinct computer systems that can be purchased is: 4 (choices for basic unit) x 3 (choices for keyboard) x 4 (choices for printer) = 48 Hence, there are 48 distinct computer systems that can be purchased.

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Answer:

x=8

Step-by-step explanation:

The volume of copper in the pipe according to mentioned dimensions of height and diameter is 1 inch³.

Volume of pipe will be calculated using the below mentioned formula -

V = πh(R² - r²), where V represents the volume of pipe, h is the height of copper pipe, R is the external and r is the internal radius. Also, we know the diameter and radius are related as -

Diameter = 2×radius

So, internal radius = 0.5/2

Internal radius = 0.25 inches

External radius = 0.65/2

External radius = 0.325 inches

V = 3.14 × 8 × (0.325² - 0.25²)

Taking square and performing multiplication outside the bracket on Right Hand Side of the equation

V = 25.12 × (0.1 - 0.06)

Performing subtraction on Right Hand Side of the equation

V = 25.12 × 0.04

Performing multiplication on Right Hand Side of the equation

V = 1 inch³.

Thus, the volume of copper in pipe is 1 inch³.

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Answer:

-60

Step-by-step explanation:

(-3 x \(10^{4}\)) x (2 x \(10^{-3}\))

(-30,000) x (.002) = -60

The required number is 936.

We have,

Since the number has 3 different digits and the hundreds and ones place digits are both divisible by 3, this means that the number must be in the form of ABC, where A and C are divisible by 3 and A ≠ C.

We also know that the hundreds place digit is the third multiple of 3, so it must be 9.

This leaves us with two options for the ones and tens place digits: 3 and 6.

However, since the digits must be different, the one's place digit must be 3, and the tens place digit must be 6.

Therefore,

The number is 936.

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Answer:

64/3

Step-by-step explanation:

8÷3/8

8×8/3

64/3 is the answer..

Answer:

\(\displaystyle{8 \div \frac{3}{8} }\)

\(\displaystyle{ \frac{8}{1} \times \frac{8}{3} }\)

\(\displaystyle{ \frac{64}{3} }\)

\(\displaystyle{}21 \frac{1}{3} \)

Step-by-step explanation:

First thing you need to do is Slope - intercept form of the line going through point A and B.

Slope-intercept form: y = mx + b (m = slope, b = y-intercept)

To get slope: \(\frac{y2 - y1}{x2-x1}\)

Lets set point A as point1 (x1, y1) and point B as point2(x2, y2).

x1 = -4

x2 = 8

y1 = 6

y2 = 3

If you plug these numbers in the slope equations:

\(\frac{3 - 6}{8 - 4}\) = \(\frac{-3}{4}\)

m = \(\frac{-3}{4}\)

So a parallel line is a line that has a different b value but the same slope value.

To get b  for the parallel line : we need to substitute the x and y for a given point (0,-2).

which will make -2 = 0(\(\frac{-3}{4}\) ) + b

now we solve for b:

-2 = 0 +b

b = -2

So the whole Slope-intercept form of the parallel line is: y = \(\frac{-3}{4}\) x -2

For the given equation, the value of x = -21.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

For the given equation,

x ≠ ±3

On taking LHS,

⇒ \(\frac{5}{x+3} - \frac{2}{x-3}\)

Taking LCM,

⇒ \(\frac{5(x-3) - 2(x+3)}{(x+3)(x-3)}\)

⇒ \(\frac{5x - 15 - 2x - 6}{x^2 - 9}\)

⇒ \(\frac{3x - 21}{x^2 - 9}\)

On Comparing both sides,

⇒ \(\frac{3x - 21}{x^2 - 9} = \frac{4x}{x^2 - 9}\)

⇒ 3x - 21 = 4x

⇒ x = -21

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Answer:

B. 642.22 units squared

Step-by-step explanation:

Knowing that QP ║ MN and ∠QLP = ∠MLN, then ΔQLP ~ ΔMLN.

That means corresponding sides and heights have the same ratios.

We know that QP = 25, which corresponds to MN = 34. Also, the height of ΔQLP, LS, corresponds to the height of ΔMLN, LR = LS + SR = LS + 10. Let's say LS = x.

We can now write:

QP / MN = LS / LR

25 / 34 = x / (x + 10)

Cross-multiply:

34 * x = 25 * (x + 10)

34x = 25x + 250

34x - 25x = 250

9x = 250

x = 250/9 ≈ 27.78 units

So, LS = 27.78 units and LR = LS + SR = 27.78 + 10 = 37.78 units.

The area of a triangle is denoted by A = (1/2) * b * h, where b is the base and h is the height.

Here, the base of ΔLMN is MN = 34, and the height is LR = 37.78. Plug these in:

A = (1/2) * b * h

A = (1/2) * 34 * 37.78 ≈ 642.22 units squared

The answer is thus B.

~ an aesthetics lover

The percentage of the figures that are Disney Funko Pops is 18%

From the question, we have the following number of sales that can be used in our computation:

9 Disney Funko Pops,

23 Avengers Funko Pops,

18 Harry Potter Funko Pops

Start by calculating the total number of Funko Pops

This is represented as

Total = Disney Funko Pops +  Avengers Funko Pops + Harry Potter Funko Pops

Substitute the known values in the above equation

So, we have the following equation

Total = 9 + 23 + 18

Evaluate

Total = 50

The percent of the figures that is Disney Funko Pops is calculated as

Percent =Disney Funko Pops/Total * 100%

So, we have

Percent = 9/50* 100%

Evaluate

Percent = 18%

Hence, the percentage is 18%

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Our expression is

Answer:

186 beats per minute

Step-by-step explanation:

The maximum heart rate (r ) in beats per minute is modeled by the equation :

r = 220 - a ...(1)

Where

a is age of the person in years

If Sanchez age is, a = 34 years

Put a = 34 in equation (1)

r = 220 - 34

= 186 beats per minute

Hence, the maximum heart rate is 186 beats per minute.

Answer:

B

Step-by-step explanation:

B has a slope of 7 while A has a slope of 6.

slope of B 14-7/2-1 = 7

A slope is y= mx+b and m is the slope. so 6.

Answer:

b: -5

Step-by-step explanation:

To solve the equation, factor the left hand side by grouping. First, left hand side needs to be rewritten as 3x

2

+ax+bx−5. To find a and b, set up a system to be solved.

a+b=14

ab=3(−5)=−15

Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product −15.

−1,15

−3,5

Calculate the sum for each pair.

−1+15=14

−3+5=2

The solution is the pair that gives sum 14.

a=−1

b=15

Rewrite 3x

2

+14x−5 as (3x

2

−x)+(15x−5).

(3x

2

−x)+(15x−5)

Factor out x in the first and 5 in the second group.

x(3x−1)+5(3x−1)

Factor out common term 3x−1 by using distributive property.

(3x−1)(x+5)

To find equation solutions, solve 3x−1=0 and x+5=0.

x=

3

1

​

x=−5

Answer: B

Step-by-step explanation:

Because it’s the answer lol

The formula for the equation of a circle is (x - h)² + (y - k)² = r²

where (h, k) is the center of the circle and r is the radius.

So we need to find the values of (h, k) in order to find the center of the circle.

If we simply line up the equation of our given circle with our formula,

we can see that -h = 3 or h = -3 and -k = -2 so k = 2.

So now we have our answer.

center ⇒ (-3, 2)

The unit rate of the juice is 0.5 carrot juice per green apple juice

From the question, we have the following parameters that can be used in our computation:

This means that

Carrot juice = 2

Green apple juice = 4

Using the above as a guide, we have the following:

Unit rate = Carrot juice/Green apple juice

Substitute the known values in the above equation, so, we have the following representation

Unit rate = 2/4

Evaluate

Unit rate = 0.5

Hence, the unit rate is 0.5 carrot juice per green apple juice

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