Is the function y =|x – 7| a one-to-one function? Justify your answer.

(a) False. If the random variable X is constant, the expectation of X will be equal to that constant value, not necessarily zero.

(b) True. If the random variable X is constant, it has no variation in its values, and hence its variance will be zero.

(c) True. If two random variables X and Y are independent, their covariance will always be zero.

(d) False. Although having zero covariance implies independence for some cases,

(a) False. If the random variable X is constant, the expectation of X will be equal to that constant value, not necessarily zero. The expectation represents the average value of a random variable, so if X is constant, its expectation will be equal to that constant.

(b) True. If the random variable X is constant, it has no variation in its values, and hence its variance will be zero. Variance measures the spread or dispersion of a random variable's values around its mean. Since X is constant, there is no spread, resulting in a variance of zero.

(c) True. If two random variables X and Y are independent, their covariance will always be zero. Covariance measures the linear relationship between two random variables. When variables are independent, there is no linear relationship between them, and thus their covariance is zero.

(d) False. Although having zero covariance implies independence for some cases, it does not hold universally. Zero covariance only guarantees independence if the variables are jointly normally distributed. There can be cases where variables have zero covariance but are still dependent. Independence requires more than just zero covariance; it implies that the variables are completely unrelated to each other.

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Answer:

585

Step-by-step explanation:

divide 780 by 12

780/12=65

The answer you get is her speed, so 65miles/hour

So if she did this for nine hours, multiply 65 by 9

65*9=585

Answer:

-0.17

Step-by-step explanation:

a. The expression for the surface area of a dilated cube is 6k², where k is the scale factor.

b. The expression for the volume of a dilated cube is k³, where k is the scale factor.

c. The expressions for surface area and volume differ in terms of the power of the scale factor: surface area is proportional to k², while volume is proportional to k³.

a. When a unit cube is dilated by a scale factor k, all sides of the cube are multiplied by k. Since a cube has six faces, the surface area of the dilated cube can be calculated by multiplying the area of one face (which is k²) by 6. Therefore, the expression for the surface area of the dilated cube is 6k².

b. The volume of a cube is calculated by multiplying the length, width, and height of the cube. In this case, each side of the unit cube is scaled by a factor of k, so the expression for the volume of the dilated cube is k³.

c. Comparing the expressions for surface area and volume, we observe that the power of the scale factor differs. The surface area is proportional to k², indicating that the surface expands in two dimensions (length and width) when the scale factor increases. On the other hand, the volume is proportional to k³, demonstrating that the space inside the cube expands in three dimensions (length, width, and height) as the scale factor increases. This means that the volume of the dilated cube increases faster than its surface area as the scale factor grows, resulting in a greater change in volume compared to the change in surface area.

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[tex]f(x)=\frac{x}{2}+8[/tex]

Given y = f(x)

Substitute x = 10.

[tex]f(10)=\frac{10}{2} +8\\f(10)=5+8\\f(10)=13[/tex]

Therefore f(x) = 13 when x = 10

35-9/45 = 26/45

The answer is 26/45.

Answer:

26/45

Step-by-step explanation:

35/45-9/45=26/45

scientific notation to standard notation is true

8.05 times 10 Superscript 5 Baseline = 805,000

7.09 times 10 Superscript negative 6 Baseline = 0.00000709

8 times 10 Superscript 7 Baseline = 80,000,000

1.03 times 10 Superscript negative 4 Baseline = 0.000103

The right format for scientific notation is an x 10^b wherein a is no. or decimal quantity such that absolutely the cost of a is extra than or same to 1 and much less than ten or, 1 ≤ |a| < 10. b is the energy of 10 required so that the clinical notation is mathematically equal to the unique quantity.

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Answer:

C. 80 times 10 Superscript 3 baseline

Step-by-step explanation:

Answer:

Clara

Step-by-step explanation:

Very very easy:

Amount Of people Clara reached: 4

4 multiplied by 10 is 40! ^^

Answer:

11:7

Hope this helps

Answer:

[tex]\dfrac{4}{3}x[/tex]

Step-by-step explanation:

Given that:

Rate of bottle filling for Machine B = [tex]x[/tex]

Rate of filling of Machine B is 1.5 times the rate of Machine A.

Let the rate of bottle filling for Machine A = [tex]y[/tex]

As per question statement:

[tex]x=1.5y\\\Rightarrow y=\dfrac{2}{3}x[/tex]

Now, combined rate of both the machines, i.e. A and B = [tex]x+y[/tex]

[tex]\Rightarrow x+\dfrac{2}{3}x\\\Rightarrow \dfrac{5}{3}x[/tex]

Bottle filling Rate of new Machine = [tex]3x[/tex]

It is given that both the machines are replaced by the new machine.

Now, increase in the rate can be calculated by subtracting the combined rate of both the machines from the bottle filling rate of new machine.

i.e.

[tex]3x-\dfrac{5x}3\\\Rightarrow \dfrac{9x-5x}{3}\\\Rightarrow \bold{\dfrac{4x}{3}}[/tex]

So, the following expression shows the increase in rate:

[tex]\dfrac{4}{3}x[/tex]

Answer:

2 acute and 1 right angle (the right angle is a 90 degree angle)

Step-by-step explanation:

Dime Thickness = 0.135 cm. Dollar Thickness = 1.0992 x 10^-2 cm. To calculate the thickness of a dime is times greater than the thickness of a dollar bill, we need to divide the thickness of a dime by the thickness of a dollar bill:0.135 cm / 1.0992 x 10^-2 cm = 12.3 times.

Therefore, the thickness of a dime is 12 times greater than the thickness of a dollar bill. Round off the answer to the nearest whole number is 12.

To calculate the thickness of a dime is times greater than the thickness of a dollar bill, we need to divide the thickness of a dime by the thickness of a dollar bill. To do that, let's use the given values to find out the ratio of the thicknesses of a dime and a dollar bill.

Thickness of a dime = 0.135 cmThickness of a dollar bill = 1.0992 x 10^-2 cmLet us divide the thickness of a dime by the thickness of a dollar bill to find the ratio of thicknesses.0.135 cm / 1.0992 x 10^-2 cm= 12.3 timesTherefore, the thickness of a dime is 12 times greater than the thickness of a dollar bill.

The answer should be rounded off to the nearest whole number, which is 12. So, it can be concluded that the thickness of a dime is 12 times greater than the thickness of a dollar bill.

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To create a system of constraints that defines a parallelogram, we need to establish conditions that satisfy the properties of a parallelogram: opposite sides are parallel and equal in length, and opposite angles are congruent.

Here's an example of a system of constraints that represents a parallelogram:

Let's consider a parallelogram with vertices (x, y):

1. Constraint 1: Opposite sides are parallel.

  This can be represented by the equation: y = ax + b, where a is the slope and b is the y-intercept.

2. Constraint 2: Opposite sides are equal in length.

  This can be represented by the equation: [tex](x - x_1)^2 + (y - y_1)^2 = (x - x_2)^2 + (y - y_2)^2[/tex] are the coordinates of two opposite vertices.

3. Constraint 3: Opposite angles are congruent.

  This can be represented by the equation: [tex]m_1 = m_2[/tex], where [tex]m_1[/tex] and [tex]m_2[/tex] are the slopes of two adjacent sides.

By combining these three constraints, we can define a system of equations that represents a parallelogram. The specific values of a, b, ([tex]x_1, y_1[/tex]), and ([tex]x_2, y_2[/tex]) will determine the properties and shape of the parallelogram.

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Answer:

x= 16

i send you a picture how to do it

(a) | Masses (kg) | Frequency | Cumulative Frequency |

|-------------|-----------|---------------------|

| 15-24       | 14        | 14                  |

| 25-34       | 54        | 68                  |

| 35-44       | 24        | 92                  |

| 45-54       | 26        | 118                 |

| 55-64       | 2         | 120                 |

(b) The cumulative frequency curve starts from the origin (0, 0) and moves upward and to the right, indicating that the mass of logs is increasing as we move right on the x-axis.

To construct the cumulative frequency table for the distribution of masses of 120 logs of wood, we need to add up the frequencies of each class and all the classes before it.

(b) To draw a cumulative frequency curve, we plot the cumulative frequency values against the upper class limits. The plot shows how the cumulative frequency increases with the increase in the mass of the log.

We use the same class intervals as in part (a):

- x-axis = Masses (kg)

- y-axis = Cumulative frequency

To plot the cumulative frequency curve, we mark the upper limit of each class on the x-axis, and its corresponding cumulative frequency on the y-axis. Then, we join the plotted points with a smooth curve, as shown in the graph.

The steeper the curve, the more rapid the increase in cumulative frequency, indicating that a larger number of logs fall in higher mass categories.

In the given distribution, the plot of the cumulative frequency curve shows that the majority of logs fall in the mass range of 25-34 kg, closely followed by the range of 45-54 kg.

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To find the final location of the ant after it has walked counterclockwise a distance of 2 units around the unit circle, we need to calculate the coordinates (x, y) of the point.

Since the ant starts at the point (1, 0) on the unit circle, we can think of this point as being at an angle of 0 degrees or 0 radians.

To find the coordinates after walking a distance of 2 units counterclockwise, we can calculate the new angle using the arc length formula:

s = rθ

where s is the arc length, r is the radius of the circle (which is 1 in this case), and θ is the angle in radians.

In this case, the arc length is 2 units and the radius is 1, so we have:

2 = 1θ

Solving for θ, we find:

θ = 2 radians

Now, we can use this angle to find the coordinates (x, y) of the final location on the unit circle:

x = cos(θ)

y = sin(θ)

Plugging in θ = 2, we get:

x = cos(2) ≈ -0.42

y = sin(2) ≈ 0.91

Therefore, the approximate coordinates of the final location of the ant are (-0.42, 0.91).

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Answer:

Adults cost $4, and Students $2.

Step-by-step explanation:

I have adults be x, and Students y, and convert the two groups to equations.

1x + 4y = 12, and 3x + 3y = 18. I divide the last equation by 3, to get x + y = 6.

Then I subtract y, to get x = 6 - y, then we use substitution.

6 - y + 4y = 12

6 +3y = 12, then subtract 6 from both sides, 3y = 6. divide by 3, and get y = 2. we can plug this into our x + y = 6, to get x + 2 = 6. i.e x = 4.

So Adults cost 4 dollars, and Students cost 2 dollars.

Just lots of simple math, take your time with these questions.

Answer:

The expression represents the price you paid per gallon is:

Step-by-step explanation:

To identify the expression is right, I'll show you with an example: suppose that you paid $56 buying 7 gallons of gas, now you can replace those values in the expression I gave you:

And you can check this value by multiplying the price paid by the gallon and the number of gallons, which you obtain the number of dollars you spent:

Answer:

45000000000

Step-by-step explanation:

when multiplying exponents, you multiply base numbers with no exponent (9 and five in this case) and numbers with exponents (10 in this case). 9 X 5 is 45 and 10 to the power of 7 times 10 to the power of 2 is 10 to the power of 9 or 1000000000. 45 X 1000000000 is 45000000000.

The standard form of (5 x 10³) x (9 x [tex]10^7[/tex]) is 450000000000.

The standard form of (7 x [tex]10^5[/tex]) ÷ (2 x 10²) is 3500.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

(5 x 10³) x (9 x [tex]10^7[/tex])

= 5 x 9 x [tex]10^{3 + 7}[/tex]

= 45 x [tex]10^{10}[/tex]

= 450000000000

(7 x [tex]10^5[/tex]) ÷ (2 x 10²)

= (7 x [tex]10^5[/tex])/(2 x 10²)

= 7/2 x [tex]10^{5 -2}[/tex]

= 3.5 x 10³

= 35/10 x 1000

= 3500

Thus,

The standard values are 450000000000 and 3500.

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Answer:

2(2) + 1   =  5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

2*2=4+1=5

The average value of the position function from t = 2 seconds to t = 5 seconds is approximately: Average value ≈ [tex](1 / 3) * [(-2 cos(5) + 215/6) - (-2 cos(2) + 20/6)][/tex]

To find the equation of the velocity function, we need to find the antiderivative of the acceleration function. The antiderivative of 2 sin(t) is -2 cos(t), and the antiderivative of 1 is t.

So, the velocity function v(t) is given by integrating the acceleration function:

v(t) = INT(2 sin(t) + 1) dt

[tex]= -2 cos(t) + t + C[/tex]

Since the initial velocity is v(0) = 0, we can substitute this value into the equation to find the constant C:

[tex]0 = -2 cos(0) + 0 + C\\0 = -2(1) + C\\C = 2[/tex]

Therefore, the equation of the velocity function is:

[tex]v(t) = -2 cos(t) + t + 2[/tex]

To find the position function, we integrate the velocity function:

[tex]s(t) = INT(-2 cos(t) + t + 2) dt\\= -2 sin(t) + 0.5t^2 + 2t + D[/tex]

Since the initial position is s(0) = 3, we substitute this value into the equation to find the constant D:

[tex]3 = -2 sin(0) + 0 + 0 + D\\3 = 0 + 0 + D\\D = 3[/tex]

Therefore, the position function is:

[tex]s(t) = -2 sin(t) + 0.5t^2 + 2t + 3[/tex]

To find the average value of the position function from t = 2 seconds to t = 5 seconds, we use the formula for the average value of a function over an interval:

Average value =[tex](1 / (b - a)) * INT(a, b) f(t) dt[/tex]

In this case, the interval is from t = 2 seconds to t = 5 seconds, so we have:

Average value =[tex](1 / (5 - 2)) * INT(2, 5) (-2 sin(t) + 0.5t^2 + 2t + 3) dt[/tex]

Evaluating the definite integral:

Average value = [tex](1 / 3) * [(-2 cos(t) + (1/6)t^3 + t^2 + 3t) EVAL(2, 5)][/tex]

Average value =[tex](1 / 3) * [(-2 cos(5) + (1/6)(5^3) + 5^2 + 3(5)) - (-2 cos(2) + (1/6)(2^3) + 2^2 + 3(2))][/tex]

Calculating the values:

Average value ≈[tex](1 / 3) * [(-2 cos(5) + 125/6 + 25 + 15) - (-2 cos(2) + 8/6 + 4 + 6)][/tex]

Average value ≈ [tex](1 / 3) * [(-2 cos(5) + 215/6) - (-2 cos(2) + 20/6)][/tex]

Therefore, the average value of the position function from t = 2 seconds to t = 5 seconds is approximately:

Average value ≈ [tex](1 / 3) * [(-2 cos(5) + 215/6) - (-2 cos(2) + 20/6)][/tex]

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The scatter plot shows the relationship between the number of smoothies sold and the high Temperature on that day. The graph displays a pattern of upward trend, indicating that as the temperature increases, the number of smoothies sold also increases.

A concession stand sells smoothies. The scatter plot shows the relationship between the number of smoothies sold and the high temperature on that day. The graph indicates a positive correlation between the two variables. The scatter plot displays a pattern of upward trend, suggesting that as the temperature increases, the number of smoothies sold also increases. Let's understand what scatter plots are and how they are useful in depicting data in detail.Scatter Plots:

Scatter plots are a graphical representation that displays data as a collection of points in a two-dimensional coordinate system. In simple terms, they use dots to show the relationship between two variables. They are useful in identifying patterns, trends, and correlation between variables. In the case of a concession stand selling smoothies, a scatter plot can be used to show the relationship between the number of smoothies sold and the temperature on that day.Positive Correlation:

Positive correlation indicates that as one variable increases, the other variable also increases. In the case of the concession stand selling smoothies, the scatter plot shows a pattern of upward trend, suggesting that as the temperature increases, the number of smoothies sold also increases. This means that the variables have a positive correlation, and an increase in one variable causes an increase in the other variable.

Therefore, we can conclude that the scatter plot shows the relationship between the number of smoothies sold and the high temperature on that day. The graph displays a pattern of upward trend, indicating that as the temperature increases, the number of smoothies sold also increases. The variables have a positive correlation, which means that an increase in one variable causes an increase in the other variable. Scatter plots are useful in identifying trends and patterns and can be used to depict data graphically.

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Answer:

6 and -6

Step-by-step explanation:

Since they're 12 units apart that means one of them is 6 and the fact they're opposites means the other is -12

Answer:

same,different

Step-by-step explanation:

Answer:

positive; negative

Step-by-step explanation:

If a student is multiplying two positive numbers, the answer will always be positive.

  EX: 3 x 4 = 12

The same applies for two negatives. If two negatives are multiplied it will make a positive answer. This is where the phrase "two negatives make a positive" come from.

 EX: -3 x -4 = 12

However, if one number is positive and one is negative, then the answer will always be negative.

  EX 1: -3 x 4 = -12

  EX 2: 3 x -4 = -12

Answer:

she can feed 2,220 people with 555555 pancakes.

Step-by-step explanation:

Answer:20 people

Step-by-step explanation:

we can solve the problem by setting a simple proportion.

We know that 22 pancakes can feed 8 people, so we have to find the number x which corresponds to the number of people that can be feeded with 55 pancakes:

Solving the proportion, we find

So, 55 pancakes can feed 20 people.

Answer:

(113^6*37^3*54^12)

hope it helps you