can someone please help me on this problem

solve (round to two decimal places)

a) The volume V of the solid is (112/3) π r² h.

b) The volume V of the solid is 9.333π.

a) To find the volume V of the right circular cone, we can use the formula:

V = (1/3) π (base radius)² height

Given that the base radius is 4r and the height is 7h,

V = (1/3)  π (4r)²  7h

V = (1/3) π 16r² 7h

V = (112/3) π r² h

Therefore, the volume V of the solid is (112/3) π r² h.

b) To find the volume V of the solid obtained by rotating the region bounded by the curves about the line y = 2, we can use the disk method. The volume of each disk is given by the formula:

dV = π (outer radius)² dx

The outer radius is the distance from the curve y = 2 to the axis of rotation y = 2.

In this case, the curve y = 2x intersects y = 2 at x = 1. So the outer radius is 1 - x.

To find the limits of integration, we set the two curves equal to each other:

2x = 2

x = 1

Therefore, the limits of integration are x = 1 and x = 3.

Now, V = ∫[1, 3] π  (1 - x)² dx

On solving the integration we get

V = π * (9 + 1/3)

V = π * (27/3 + 1/3)

V = π * (28/3)

V ≈ 9.333π

So, the volume V of the solid is approximately 9.333π.

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Answer:

The probability of drawing exactly one blue marble is 15 over 32

Step-by-step explanation:

did test

How can you find the first digit in the quotient: Divide 54 by 13. The first digit goes in the 4 place.

In Mathematics, a quotient can be defined as a mathematical expression that is simply used to represent the division of a number (numerator) by another number (denominator).

By writing the given mathematical expression as a division of a number (numerator) by another number (denominator), we have the following quotient:

Quotient = 54/13 = 4 R 0

Quotient = (54 - 52)|6/13 = 26/13 = 2 R 0

Note: The variable R represent the the number of remainder after the quotient is computed.

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Becky conducted a one-proportion hypothesis test at the 5% significance level, to test whether the true proportion of heads is different from 50%.

Her null hypothesis was that the proportion of heads is equal to 50%, and her alternative hypothesis was that the proportion of heads is different from 50%. Using the z-test for a proportion, with a sample size of 30, Becky calculated a test statistic of z=1.05 and a p-value of 0.295. Since the p-value is greater than 0.05, she fails to reject the null hypothesis and concludes that there is not enough evidence to suggest that the true proportion of heads is different from 50%. Therefore, she cannot claim that the coin is biased towards heads or tails.

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the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

so in this case we have the provided ones (2005 , 12000) and (2010 , 12250)

\((\stackrel{x_1}{2005}~,~\stackrel{y_1}{12000})\qquad (\stackrel{x_2}{2010}~,~\stackrel{y_2}{12250}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{12250}-\stackrel{y1}{12000}}}{\underset{run} {\underset{x_2}{2010}-\underset{x_1}{2005}}} \implies \cfrac{12250 -12000}{2010 -2005}\implies \cfrac{250}{5}\implies \underset{\textit{rate of change}}{50}\)

Answer:

can i have life orientation project memo for term 2

The equation that can be used to find the value of y, the total amount of flour that Otto used in the recipe is D. y=x+5.5; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 5.5

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, Otto used 5.5 cups of whole wheat flour and x cups of white flour in the recipe.

The equation will be:

y = 5.5 + x

where y = total wheat

The option that correctly reflects this is D.

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Answer:

The answer is D

Step-by-step explanation:

Answer:

x = 7

Step-by-step explanation:

To find the value of x

Transpose

3x-4=17

3x = 17 +4

3x = 21

x = 21/3

x = 7

We can even cross check by replacing the value of x by 7

3 (7) - 4 = 17

21 - 4 =17

17 = 17

CROSS-CHECKED

To get the minimum value of f(x), we need to get the critical points of the function.

First, we need to set f'(x) equal to zero: e^-xcos(x^2) = 0
The exponential term e^-x can never be zero, so we can ignore it. This means that cos(x^2) = 0.
The solutions to this equation are x = sqrt((2n+1)pi/2) or x = sqrt(npi), where n is any integer. However, we are only interested in the solutions that lie between -1 and 1, since that is the domain of the function.
The only solution in this range is x = sqrt(pi/2), which is approximately 1.2533.
Next, we need to check whether this critical point is a minimum or a maximum. To do this, we can use the second derivative test. f''(x) = -e^-x(cos(x^2) + 2x^2sin(x^2))
At x = sqrt(pi/2), f''(x) is negative, which means that the critical point is a local maximum. Since there are no other critical points in the domain of the function, this is also the global maximum.
Therefore, there is no minimum value of f(x) for -1

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The length of the shorter leg will be 2.5 feet and the length of the longer leg is 4.5 feet.

The Pythagoras theorem will be used in calculating the lengths.

This will be:

a = First leg = x

b = Second leg = x + 4

c = Hypothenuse = 7

In this case, the values will be substituted into the formula given below:

a² + b² = c²

x² + (x + 4)² = 7²

x² + x² + 8x + + 16 = 49

Collect like terms

2x² + 8x + 16 - 49

2x² + 8x - 33

By using the quadratic formula, the value of x will be 2.5. This is the shorter leg. The Longer leg will be: 2.5 + 4 = 6.5 feet

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The Jupiter is 6.93 times farther  from the Sun than Venus

The Saturn is 6.29 times farther from the Sun than Mars

Distance between the sun and Jupiter = 748.02 million km

Distance between the sun and venus = 108.01 million km

Ratio of the distance between the sun and Jupiter to the distance between the sun and Venus = 748.02/108.01

Ratio of the distance between the sun and Jupiter to the distance between the sun and Venus = 6.93

Therefore, the Jupiter is 6.93 times farther  from the Sun than Venus

Distance between the Sun and Saturn = 1.4823 billion km = 1482.3 million km

Distance between the Sun and Mars = 235.66 million km

Ratio of the distance between the Sun and Saturn to the distance between the Sun and Mars = 1482.3/235.66

Ratio of the distance between the Sun and Saturn to the distance between the Sun and Mars = 6.29

Therefore, the Saturn is 6.29 times farther from the Sun than Mars

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The noun names in decimal and binary equivalents represent the same numeric value but in different positional numeral systems.

There is a significant difference between the two systems.

While the decimal number system uses ten digits (0 through 9), the binary number system employs only two digits: 0 and 1.

Furthermore, in decimal numbers, the weight of each digit is a multiple of ten, whereas in binary numbers, the weight of each digit is a multiple of two.

The weight of each digit in a binary number is always a power of 2. As the digit moves from the right to the left, the weight of the digit increases.

The weight of the first digit on the right-hand side is 20. The weight of the second digit from the right is 21, and the weight of the third digit from the right is 22.

Similarly, the weight of the fourth digit from the right is 23, and so on.

In the decimal system, the weight of the first digit from the right is 100. The weight of the second digit from the right is 101, and the weight of the third digit from the right is 102, and so on.

So, this is how the noun names relate between the decimal and binary equivalents.

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Answer:

39.

Step-by-step explanation:

78% of 50 is 39. To calculate x% of a number y, we use the following rule: x% of y = (x / 100) × y.

Answer:

This function is increasing.

Step-by-step explanation:

This function passes the right hand test when graphed, if it was decreasing, it would be a negative slope, and pass the left hand test.

Answer: 4

NOTE: ONLY REFER FIRST METHOD IF YOU ARE FROM CLASSES BELOW 5TH GRADE AND IF YOU KNOW THEM BOTH ITS OK.

First we list factors of both 28 & 78

28: 1,2,4,7,14,28

78: 1,2,3,4,6,8,9,12,18,24,36,72

Now the common factors are, 1,2,4

And we know that 1<2<4

And thus 4 is the highest common factor

Another way is prime factorisation:

In this method, we need to find the prime factors of both the given numbers and find out the common factors and mutiply them.

So, 28: 2*2*7 and 72: 2*2*2*3*3

In now we see that, 2*2 is common in  both common prime factors of both 28&72, Thus we get  2*2, And after solving it we get the highest common factor as 4

Step-by-step explanation:

in 3 hours the truck used 17 - 3 = 14 gallons.

that means it used

14 gallons / 3 hours = 14/3 gallons / hour

and that means it is using

14/3 × x gallons in x hours

y = 17 - (14/3 × x)

the gas left in the tank is decreasing by 14/3 gallons per hour.

Answer:

The correct answer is B. 20,000

Step-by-step explanation:

To determine the man's total monthly salary, we can set up a simple equation using the given information. Let's denote the total monthly salary as "x."

According to the information provided, 33% of the man's monthly salary is equal to Birr 6600. We can express this relationship mathematically as:

0.33x = 6600

To solve for "x," we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 0.33:

x = 6600 / 0.33

Evaluating the right side of the equation gives:

x ≈ 20,000

Therefore, the man's total monthly salary is approximately Birr 20,000.

Hence, the correct answer is B. 20,000.

Interval (-4, 2) and (2, [infinity]) provide complete solution.

The correct set of points that can be tested to find a complete solution to the rational inequality with critical points x = -4 and x = 2 is option c. (-4, 2) and (2, [infinity]).

Critical points are the values of x where the rational inequality may change its sign or behavior. In this case, the critical points are x = -4 and x = 2. To determine the complete solution, we need to test intervals on the number line to see where the inequality is true or false.

The interval (-[infinity], -4) does not include x = -4, so it does not provide information about the inequality's behavior at x = -4. Similarly, the interval (-4, 2) does not include x = 2, so it does not provide information about the inequality's behavior at x = 2.

However, the interval (2, [infinity]) includes x = 2, which allows us to test the behavior of the inequality after x = 2. By testing a value greater than 2 in the inequality, we can determine if the inequality is true or false in this interval.

Therefore, the correct set of points to find a complete solution to the rational inequality is option c. (-4, 2) and (2, [infinity]).

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Answer:

step two

Step-by-step explanation:

All three equations are satisfied when x = 3 and y = 2, which means that the lines intersect at the point (3, 2).

To find the coordinates of point P where the three lines intersect, we need to solve the system of equations formed by the three lines:

x = 3 (equation 1)

y - 2.5 = -(x - 0.5) (equation 2)

y - 2.5 = x - 3.5 (equation 3)

From equation 1, we know that x = 3. substituting this into equations 2 and 3, we get:

y - 2.5 = -2.5 (from equation 2)

y - 2.5 = -0.5 (from equation 3)

Simplifying these equations, we get:

y = 0 (from equation 2)

y = 2 (from equation 3)

So the coordinates of point P are (3, 2).

To verify that the lines all intersect at this point, we can substitute these coordinates into each of the original equations and check that they hold:

For equation 1: x = 3 holds when x = 3.

For equation 2: y - 2.5 = -(x - 0.5) becomes y - 2.5 = -(3 - 0.5) = -2 holds when x = 3 and y = 2.

For equation 3: y - 2.5 = x - 3.5 becomes y - 2.5 = 3 - 3.5 = -0.5 holds when x = 3 and y = 2.

So all three equations are satisfied when x = 3 and y = 2, which means that the lines intersect at the point (3, 2).

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Answer

linear

nonproportional

Step-by-step explanation:

Since for each equal change in time (1 week), there is an equal change in weight (5 lb), the situation is linear.

At time zero, the first week, the weight was not zero. It was 60 lb, so it is not proportional.

Answer:

linear

nonproportional

The proportional relationship between the price and quantity of ears of corn can be represented using a table or a graph, showing how the price and quantity vary in a consistent manner.

One way to represent the proportional relationship between the price and quantity of ears of corn is by using a table:

Price (in dollars) Quantity (in ears of corn)

             2             5

             4             10

This table shows the corresponding values of the price and quantity.

As we can observe, when the price is $2, the quantity is 5 ears of corn, and when the price is $4, the quantity is 10 ears of corn.

The relationship is proportional because as the price doubles, the quantity also doubles.

Another representation of this proportional relationship is through a graph.

We can plot the points (2, 5) and (4, 10) on a coordinate plane, where the x-axis represents the price and the y-axis represents the quantity.

By connecting these two points with a straight line, we can visualize the proportional relationship.

The line will pass through the origin (0, 0) since zero price corresponds to zero quantity.

The slope of the line will indicate the rate of change between price and quantity.

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Answer:

The variable can be any letter.

Step-by-step explanation:

The value of z is 4.

Given that,

Based on the above information, the calculation is as follows:

4z = 16

z = 4

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Answer:

3(6 - 4) + 7²

3 x 2 + 7²

3 x 2 + 49

6 + 49

= 55

The slope of the line represents the rate of change between the independent variable (number of available staff) and the dependent variable (number of available staff) (wait time).

The slope of the line in this case is -1.62, which means that for every one unit increase in the number of staff available, the wait time decreases by 1.62 units.

In this case, a negative slope indicates that as the number of staff available increases, so does the wait time, indicating a positive relationship between the two variables. In other words, as the number of employees available increases, the wait time decreases.

It is important to remember that the equation models this relationship, and that actual wait times in the real world may not always follow this exact relationship due to other factors that influence wait times.

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Answer:

A. 24x = 192

Step-by-step explanation:

Answer:

A. 24x = 192

Step-by-step explanation:

you would have to multiply 24 x 8 in order to 192!

So yes, the correct answer would be A. 24 x = 192!

Its simple you just have to multiply how many packs x how many crayons he bought! :D

Answer:

-5

Step-by-step explanation:

The leading coefficient means the thing you're multiplying your highest power by. Here, your highest power of x is x^2, and that term's coeff. is -5, so the leading coefficient is -5.

Answer:

What you are looking for is the length of the 'solid diagonal'. First we need to find the length of the base diagonal. That can be done easily using Pythagorean theorem.  52+32−−−−−−√=6. Now this diagonal is a leg of the bigger right triangle whose hypotenuse is the required solid diagonal. You can see this from amd's picture. So apply Pythagorean theorem again.  62+(2.5)2−−−−−−−−−√=37.25−−−−√. You can work that out with a calculator.

In general for a cuboid with dimensions a, b and c(order doesn't matter), the solid diagonal is:  a2+b2+c2−−−−−−−−−−√

Step-by-step explanation:

Answer:

√62+(2.5)2=√37.25.

Step-by-step explanation:

What you are looking for is the length of the 'solid diagonal'. First we need to find the length of the base diagonal. That can be done easily using Pythagorean theorem. &#xA0;52+32=6" role="presentation" style="margin: 0px; padding: 0px; border: 0px; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; line-height: normal; font-family: inherit; font-size: 15px; vertical-align: baseline; box-sizing: inherit; display: inline; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;"> 52+32−−−−−−√=6 52+32=6. Now