The cross section of a regular pyramid contains the altitude of the pyramid. The shape of this cross section is a 1. circle 2. square 3. triangle 4. rectangle

Same age

See explanation below

Let the age of Jasmine = y

Multiplying Jasmine age by 3 and adding 6:

= (y × 3) + 6

= 3y + 6

Multiplyng the sum by 2:

2 × the sum = 2 × (3y + 6)

= 6y + 12

Let James age = z

Multiplying the age by 2 and adding 4:

James age × 2 = z × 2 = 2z

adding 4 = 2z + 4

Multiplying the sum y 3:

3 × the sum = 3 × (2z + 4)

= 6z + 12

Now since they are twins, they ae most likely same age

This means:

6y + 12 = 6z + 12

subtracting 12 from both sides:

6y = 6z

dividing both sides by 6:

y = z

Hence, Jasmine age is the same as James age

B) The expression for Jasmine = 2(3y + 6) = 6y + 12

The expression for James = 3(2z + 4) = 6z + 12

let the twin's age = 2, 3, 4, 5

when twin's age = 2

6y + 12 = 6(2) + 12 = 12 + 12 = 24

6z + 12 = 6(2) + 12 = 12 + 12 = 24

when twin's age = 3

6y + 12 = 6(3) + 12 = 18 + 12 = 30

6z + 12 = 6(3) + 12 = 18 + 12 = 30

when twin's age = 4

6y + 12 = 6(4) + 12 = 24 + 12 = 36

6z + 12 = 6(4) + 12 = 24 + 12 = 36

when twin's age = 5

6y + 12 = 6(5) + 12 = 30 + 12 = 42

6z + 12 = 6(5) + 12 = 30 + 12 = 42

Plotting the table:

Answer:

536.9

Step-by-step explanation:

Answer:

Down Here ↓↓↓↓↓

Step-by-step explanation:

Hello!

The vertical line test is a method to test if a graph is a function or not.

Given a graph, we can draw a vertical line anywhere on the graph. If the line intersects two or more points on the graph, it is not a function.

If the line passes through 2 or more points, it means that there are multiple values for the same x-value.

When you have a function, you can substitute a value for x to get a unique y-value. Having two intersections means that there are two values for one x-value.

A sample containing 2/3 oz. of liquid is approximately 19.72 milliliters (mL).

To convert 2/3 oz. of liquid to milliliters (mL):
1. Identify the conversion factor: There are approximately 29.5735 mL in 1 ounce (oz).
2. Set up a proportion: To convert 2/3 oz. to mL, we need to multiply the given amount by the conversion factor.
  (2/3 oz.) x (29.5735 mL/1 oz.)
3. Cancel out the units: The "oz" units will cancel out, leaving us with mL.
  (2/3) x (29.5735 mL)

4. Multiply the fraction by the conversion factor: Now, multiply 2/3 by 29.5735.
  (2/3) x 29.5735 = 19.7157
5. Round the result: We'll round the result to two decimal places to make it easier to understand.
  19.7157 mL = 19.72 mL
So, a sample containing 2/3 oz. of liquid is approximately 19.72 milliliters.

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Answer:

Answer and Explanation: The symmetric bell shape of the normal curve implies that the skewness of the distribution of the data is 0, and most of the observation is located at the middle of the distribution. The shape of the normal distribution is not positive and negative skewed, the shape seems to be bell-shaped.

HOPE THIS HELPS!

The t-percentile defines the boundaries of the confidence interval and is equal to the critical value of t with a positive or negative sign, depending on whether the confidence interval is one-sided or two-sided.

A t-distribution table determines the t-percentile required to construct two-sided confidence intervals. The first step in determining the t-percentile is to know the degrees of freedom and confidence level. The next step is to find the critical value of t from a t-distribution table. The t-distribution table lists values for the probability density function, cumulative distribution function, and percentile points of the t-distribution.

The table is arranged in rows and columns, with the rows corresponding to the degrees of freedom and the columns corresponding to the significance level. The critical value of t is the value that separates the central area of the t-distribution from the tails of the distribution. It is used to define the boundaries of the confidence interval. The t-value is the same as the critical value of t, but it has a positive or negative sign depending on whether the confidence interval is one-sided or two-sided. The t-percentile that is required to construct two-sided confidence intervals is given by the following steps:

Step 1: To determine the t-percentile, the degrees of freedom and confidence level are needed.

Step 2: Find the critical value of t from a t-distribution table.

(a) 95% confidence level, 15 degrees of freedom.

Using the T-Distribution Calculator with degrees of freedom (df) = 15, a 95% confidence level, the value of t is found to be 2.1318. Therefore, to construct the confidence interval, the t-value is ± 2.1318.

(b) 95% confidence level, 24 degrees of freedom.

Using the T-Distribution Calculator with degrees of freedom (df) = 24, a 95% confidence level, the value of t is 2.064. Therefore, to construct the confidence interval, the t-value is ± 2.064.

(c) 99% confidence level, 13 degrees of freedom.

Using the T-Distribution Calculator with degrees of freedom (df) = 13, a 99% confidence level, the value of t is 3.012. Therefore, to construct the confidence interval, the t-value is ± 3.012.

(d) 99.9% confidence level, 15 degrees of freedom.

Using the T-Distribution Calculator with degrees of freedom (df) = 15, a 99.9% confidence level, the value of t is found to be 3.579. Therefore, to construct the confidence interval, the t-value is ± 3.579.

The t-percentile can be found using a t-distribution table, which lists the critical value of t for different degrees of freedom and significance levels. The t-percentile defines the boundaries of the confidence interval and is equal to the critical value of t with a positive or negative sign, depending on whether the confidence interval is one-sided or two-sided.

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Answer:

Step-by-step explanation:

Given That,

Earth's mass is 6 × 10^24 kg.

Mass of the Sun = 330,000 times the mass of Earth.

I also present this data as scientific notation.

Mass of the Sun = 3.3 × 10^5 times the mass of the Earth.

From the data and conditions,

Mass of the Sun

\(= 3.3 \times 10^5 \times (6 \times 10^{24} kg)\\\\ = 19.8 \times 10^{29} kg \\\\= 1.98 \times 10 ^{30} kg.\)

The Sun's mass is said to be 330,000 larger than Earth; This in scientific notation represents:

330 * 10³ times.

The mass of the earth is known to be equal to:

6 * 10²⁴ kg

Knowing this, then the mass of the sun is equal to:

Mass of the Sun = 330 * 10³ * mass of the Earth

Mass of the Sun = 330 * 10³ * 6 * 10²⁴ kg

Mass of the Sun = 1.98 * 10³⁰ kg

Answer:

128 miles

Step-by-step explanation:

If 48 miles equals 12 minutes ,and every 4 minutes equals 12 miles,then 32 minutes equals 128 miles

The claim that the diamond cone indenter was probably dull is not a valid claim without further investigation and evidence

Here a statistical sampling of Rockwell c hardness tests is conducted on a material. The claim that the diamond cone indenter was probably dull is not a valid claim without further investigation and evidence. While a dull diamond cone indenter could potentially result in inaccurate hardness measurements, it is not necessarily the only factor that could have led to insufficient hardness readings. Other factors, such as improper preparation of the sample or incorrect testing conditions, could also contribute to inaccurate hardness measurements. Therefore, it is essential to thoroughly investigate all possible sources of error before concluding that the tests were flawed due to a dull diamond cone indenter.

Additionally, if the supplier is making this claim, they should provide evidence to support it, such as records of when the diamond cone indenter was last sharpened or a comparison of the results from the defective material and other samples tested using the same diamond cone indenter.

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if at 10:15 the bus has not yet arrived, The conditional probability p(x > 25 | x > 15) that you will have to wait longer than 10 additional minutes is given below

p(x > 25 | x > 15)= P(X > 25)/ P(X > 15)= 1/3

What is probability?

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.

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If function g is a quadratic function that contains the points (-3, 5) and (0, 14), the statement which is true over the interval [-3, 0] is: B. The average rate of change of f is less than the average rate of change of g.

An average rate of change is also referred to as slope and it can be defined as a type of function that describes the average rate at which a quantity changes (decreases or increases) with respect to another quantity, over a given interval.

In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this formula:

Average rate of change = [f(b) - f(a)]/(b - a)

Next, we would determine the average rate of change of function f over the interval [-3, 0]:

a = -3; f(a) = -4.5

b = 0; f(b) = 0

Substituting the given parameters into the formula, we have;

Average rate of change = (0 - (-4.5))/(0 - (-3))

Average rate of change = 4.5/3

Average rate of change = 1.5.

Also, we would determine the average rate of change of function g over the interval [-3, 0]:

a = -3; f(a) = 5

b = 0; f(b) = 14

Substituting the given parameters into the formula, we have;

Average rate of change = (14 - 5)/(0 - (-3))

Average rate of change = 9/3

Average rate of change = 3.

In conclusion, the average rate of change of function f is less than the average rate of change of function g.

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Answer:

The average rate of change of f is less than the average rate of change of g.

Step-by-step explanation:

Plato/Edmentum

Answer:

Step-by-step explanation:

dived the figure into 3 areas (see attached image)

1. area of a triangle = 1/2 b h   where b=6 , h=3

A1 = 1/2 (6) 3 = 9

2. area of  trapezoid = a + b * (h/2)  here a = 4, b = 6, h = 5

A2 = (4 + 6 ) * 5/2  =  25

3. area of a triangle = 1/2 b h   where b=8 , h=6

A3 = 1/2 (8) 6  =  24

total  area = 9 + 25 + 24

                 = 58 in²

The answer to this question is  the test statistic is a. option a. 100.75.

To arrive at this answer, we need to use the chi-square distribution to test the null hypothesis that the population variance (σ2) is equal to 20. The test statistic for this hypothesis test is given by:

χ2 = (n - 1) * s²  / σ2

where n is the sample size, s is the sample standard deviation, and σ is the population standard deviation (which is assumed to be equal to the hypothesized value of 20).

Substituting the given values, we get:

χ2 = (41 - 1) * 5² / 20
χ2 = 40 * 25 / 20
χ2 = 50

Therefore, the test statistic is 50.

However, to determine the p-value (i.e. the probability of obtaining a test statistic as extreme or more extreme than the observed one, assuming the null hypothesis is true), we need to consult a chi-square distribution table with (n - 1) degrees of freedom. For this problem, the degrees of freedom is 40 (i.e. 41 - 1).

Using the chi-square distribution table, we find that the p-value for a test statistic of 50 with 40 degrees of freedom is less than 0.001. This means that the probability of obtaining a sample with a variance as extreme or more extreme than 20 (assuming the null hypothesis is true) is less than 0.001.

Therefore, we can reject the null hypothesis at a significance level of 0.001 or lower. This leads us to the conclusion that the population variance is unlikely to be 20, based on the given sample of 41 observations with a sample standard deviation of 5.

finding the p-value using a chi-square distribution table, and making a conclusion based on the significance level. The main answer is option a. 100.75, which corresponds to the test statistic calculated using the formula χ2 = (n - 1) * s²  / σ2.

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The mean score of the given three scores is approximately 26.6, which is not the mean score for all ninth graders in the city.

To find the mean score for all ninth graders in the city, we need more information than just three scores. Without additional data, we cannot accurately determine the mean score for all ninth graders in the city.

However, we can calculate the mean of the given scores to verify that it is not 79.7 as claimed by the PR manager:

Mean = (77 + 91 + 71) / 3 = 79.7/3 = 79.7 ÷ 3 ≈ 79.7/3 ≈ 26.6

So the mean score of the given three scores is approximately 26.6, which is not the mean score for all ninth graders in the city.

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Answer:

x = 5

Step-by-step explanation:

X+3(2×-4)=-19

x + 3(-8) = -19

x - 24 = -19

x = 5

Answer:

x=-2

Step-by-step explanation:

-5(x-1)-x+1=-18

subtraction and addition is left to right so ...

-5x+5-x+1=-18

-6x+6=18

divide both sides by 6...

-x+1=3

x=-2

Answer:

See below ~

Step-by-step explanation:

Finding the x-intercepts :

Finding the vertex :

Answer:

2.B

Step-by-step explanation:

2.

Henry's container holds milk=200*7/8=175 ml

Answer:

-739

Step-by-step explanation:

i used Calculator, np :)

The sum of −3 1/4 + (−4 2/5) is 7.65

Mixed fractions are type of a fraction which includes a whole number and a fraction.

Any improper fraction can be written as a mixed fraction. Quotient will be the whole number and in the fractional part, numerator is the remainder and denominator will be the divisor.

[−(3 1/4)] + [−(4 2/5)] = [-(13/4)] + [-(22/5)]

Cross multiplying, we get

-(13/4 + 22/5) = -(65 + 88)/20 = -153/20 = 7.65

Hence, sum of −3 1/4 + (−4 2/5) is 7.65.

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Answer:

\(option \: (b) \: is \: ur \: answer \: to \: the \: question \: \)

\(to \: know \: the \: answer \: with \: proof\)

\(refer \: to \: the \: above \: attatchment\)

\(f = \frac{rn}{1 - r} \)

\(\huge \tt༆ Answer ༄\)

The required expression is ~ B

\( \boxed{ \sf \: F = \dfrac{ RN }{ 1 - R} }\)

Refer to the attachment for Solution ~

we conclude that the correct option is A, the slope is:

"the average number of pounds per foot tall"

The linear equation:

y = 48.3*x - 127

Relates the height, x, and the weight, y of an adult.

Then the slope, which is 48.3, should have units of mass over height.

Now, if x is in feet and y is in pounds, then the slope has units of pounds/feet.

Then it represents the mean number of pounds per feet. So we conclude that the correct option is A:

"the average number of pounds per foot tall"

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The c is equal to half of the definite integral of the function over the interval [0, 2].

To determine c such that f(c) is the average value of the function on the interval [0, 2], we can use the formula for the average value of a function:

avg = 1/(b-a) * ∫(a to b) f(x) dx

In this case, a = 0 and b = 2, so the formula becomes:

avg = 1/2 * ∫(0 to 2) f(x) dx

We want to find the value of c such that f(c) = avg, so we can set these two expressions equal to each other and solve for c:

f(c) = avg
f(c) = 1/2 * ∫(0 to 2) f(x) dx

We can then use calculus to solve for c by finding the derivative of both sides with respect to c and setting them equal to each other:

f'(c) = 1/2 * (f(2) - f(0))

Solving for c gives us:

c = (1/2) * ∫(0 to 2) f(x) dx

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Answer:

-112

Step-by-step explanation:

just remove the parentheses and solve if no sign its a mutiplication

-16x7=-112

The area of the composite figure from the image attached is 112.5 units²

The area of a composite figure refers to the sum total of all the areas of the shapes in that composite figure. This can be done by first identifying the shapes in that composite figure, then finding each area, followed by the addition of all the areas to determine the area of the composite figure.

From the given figure; we can break it down into:

The area of a parallelogram = b × h

where;

The area of a parallelogram =  9 × 6

The area of a parallelogram = 54 units²

The area of a rectangle = Length × breadth

The area of a rectangle = (9 × 3) units²

The area of a rectangle = 27 units²

The area of the triangle \(\mathbf{=\dfrac{1}{2}\times b \times h}\)

where;

The area of the triangle \(\mathbf{=\dfrac{1}{2}\times b \times h}\)

The area of the triangle \(\mathbf{=\dfrac{1}{2}\times 9 \times 7}\)

The area of the triangle \(\mathbf{= 31.5 units^2}\)

Therefore, the area of the composite figure is:

= 54 + 27 + 31.5

= 112.5 units²

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A car travel 20kph faster than a truck. the car cover 350 km in two hours less than the time. The speed of the car is 50 km/h. The speed of truck is 70 km/h.

You can determine an object's speed if you know how far it moves in a given amount of time. For instance, an automobile is moving at a pace of 70 miles per hour if it covers 70 miles in an hour (miles per hour).

Given,

A car travel 20kph faster than a truck. the car cover 350 km in two hours less than the time.

Let s represent the truck's speed and (s+20) represent the car's speed.

to determine each vehicle's time

Time = Speed / Distance

truck time = 350/s

Time in an automobile is 350/(s+20)

Truck time - car time = 2 hours

So,

(350/s) - [350/(s+20)] = 2

LCM is s(s+20)

[350(s+20) - 350s]/s(s+20) = 2

Cross multiplying,

350(s+20) - 350s = 2s(s+20)

Simplifying the equation,

350s + 7000 - 350s = 2s² + 40s

Now, we have quadratic equation to simplify,

2s² + 40s - 7000 = 0

Dividing the equation by 2

s² + 20s - 3500 = 0

Factorizing,

s= 50

s= -70 (impossible because of the sign)

Hence the truck's speed is s = 50 km/h.

The speed of the car is s + 20 = 70 km/h.

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Answer:

y = - x + 2

Step-by-step explanation:

the slope is negative, so eliminate choice 2 and 3.

the y intercept is 2 and the slope is -1, hence the answer is choice 4

1) If the couple must sit together, there are 240 ways that they can be seated.

2) If the couple must not be together, there are 720 ways that they can be seated.

1) If the couple must sit together, we can think of them as one unit. So, there are 5 units to be seated around the table. We can choose any one of these units to be the starting point, and then arrange the other units clockwise around the table.

The couple can be arranged in two different ways within their unit. So, the total number of ways they can be seated is: 5! × 2 = 240.

2) If the couple must not sit together, we can think of them as separate units. So, there are 6 units to be seated around the table. We can choose any one of these units to be the starting point, and then arrange the other units clockwise around the table.

The couple cannot be seated next to each other, so there are 3 possible units where they cannot be seated next to each other. Once we have chosen one of these units for the starting point, there are 2 ways to arrange the couple within their unit. Therefore, the total number of ways they can be seated is: 5! × 2 × 3 = 720.

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Answer:

26.25 questions

Step-by-step explanation:

75% of 35 is 26.25

To clean the office building's 200-gallon aquarium It will take Candice 20 minutes to drain the entire 200-gallon aquarium.

To clean the office building's 200-gallon aquarium, Candice needs to remove the fish and drain the water. The water drains at a constant rate of 10 gallons per minute.
So, the time it takes to drain the entire 200-gallon aquarium can be calculated by dividing the total volume of water by the drain rate.
200 gallons / 10 gallons per minute = 20 minutes
Therefore, it will take Candice 20 minutes to drain the entire 200-gallon aquarium.

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Answer:

600

Step-by-step explanation:

? = 1000 x .03 x 20

the 1000 is the original amount

the .03 is the percent/interest

the 20 is the time