4. The figure below is a rectangle. What is the value of x?
Hint: opposite sides of a rectangle are congruent
3(x + 4)
5x-9

The volume of the new cone is 0.507 times the volume of the old cone.

What is meant by volume?

Volume is a measure of the space occupied by a three-dimensional object or substance. It is usually measured in cubic units such as cubic meters, cubic centimeters, or cubic feet and can be calculated using various formulas depending on the shape and size of the object.

What is a cone?

A cone is a three-dimensional geometric shape that tapers smoothly from a flat circular base to a point called the apex. It has one circular base, one curved surface, and a vertex or apex.

According to the given information

Let's start by finding the radius of the original cone using its diameter:

Radius = Diameter/2 = 48/2 = 24

Now, we can use the formula for the volume of a cone:

Volume of original cone = (1/3) * pi * r² * h

= (1/3) * pi * 24² * 18

= 54,432 pi

The new cone has a diameter of 48x and a length of 18x. So, its radius and height are:

Radius = (48x)/2 = 24x

Height = 18x

The volume of the new cone is:

Volume of new cone = (1/3) * pi * (24x)² * (18x)

= 27,648 x³ pi

To compare the volumes, we can divide the volume of the new cone by the volume of the old cone:

Volume of new cone / Volume of old cone = (27,648 x³ pi) / (54,432 pi)

= 0.507 x³

Therefore, the volume of the new cone is 0.507 times the volume of the old cone.

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__________

\( \: \)

\( \sqrt{1,69} = ...\)

\( = {1,69}^{ \frac{1}{2} } \)

\( = \bold{1,3}\)

Soo, asnwer for Question \(\sqrt{1,69} = 1,3\)

Therefore , the solution of the given problem of coordinates comes out to be B' = (-2, 1)  and  C' = (4, 6) .

A coordinate system is a method that employs one or more values or coordinates to accurately locate points or even other mathematical objects on a space, such as Euclidean space. Coordinates, that are pairs of numbers, are used to locate a point or object on a double plane. The y and x vectors are two integers that specify where a point is situated on a two - dimensional plane. a group of numerals designating particular places. Usually, the number has two numbers.

Here,

By adding 1 to the x-coordinate and 3 to the y-coordinate, we can determine that position A is translated to point A'. As a result, we can determine the values of B' and C' using the same translation vector.

We increase the x-coordinate for position B by one

=> (-3 + 1 = -2) and

the y-coordinate by three

=> (-2 + 3 = 1). Consequently, B"s values are (-2, 1).

We increase the x-coordinate for position C by one

=> (3 + 1 = 4) and

the y-coordinate by three

=>(3 + 3 = 6). Consequently, C"s dimensions are (4, 6).

Consequently, the translated locations' coordinates are as follows:

=> B' = (-2, 1)

=> C' = (4, 6)

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The researcher is testing whether the data gives sufficient evidence to support that more than 80% of adults are honest.

The null and alternative hypotheses are as follows;

H0:

P ≤ 0.80H1: P > 0.80

where P is the population proportion of adults who are honest.

The sample proportion is: p = 42/50 = 0.84

where 50 is the sample size.

The sample proportion is the point estimate of the population proportion.To conduct a hypothesis test for a proportion, the sampling distribution of sample proportions is used. The sampling distribution of sample proportions can be approximated to a normal distribution using the central limit theorem. Since the sample size is greater than 30, the sampling distribution of sample proportions is approximately normal.

The mean of the sampling distribution of sample proportions is

equal to the population proportion.μp = P = 0.80

The standard error is the standard deviation of the sampling distribution of sample proportions.

σp = sqrt[(P(1 - P)) / n]σp = sqrt[(0.80(0.20)) / 50]σp = sqrt(0.0016)σp = 0.04

To calculate the test statistic, the sample proportion is compared to the population proportion while taking into consideration the variability in the sampling distribution.

The test statistic for this hypothesis test is a one-sample z-test.z = (p - P) / σpz = (0.84 - 0.80) / 0.04z = 1.00

To calculate the P-value,

the area to the right of the test statistic is found using the standard normal distribution table.

The P-value is the probability of obtaining a test statistic at least as extreme as the calculated value under the null hypothesis.

P(z > 1.00) = 0.1587

The P-value is 0.1587,

which is greater than the level of significance of 0.05.

Since the P-value is greater than the level of significance, the null hypothesis cannot be rejected. Therefore, there is insufficient evidence to support that more than 80% of adults are honest.

The values of the test statistic and P-value for this test are:

z = 1.00 and P-value = 0.1587

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Answer:

8.8 x 10 to the power of 6

Step-by-step explanation:

Answer:

-6, 6

Step-by-step explanation:

I hope this helps :)

When everyone is sitting down, the number of free seats is 26, using arithmetic addition and subtraction.

The two main arithmetic operations that we learn to add and subtract two or more integers or other mathematical values are arithmetic addition and subtraction. The addition symbol is the plus sign (+), and the subtraction symbol is the minus sign (-). (minus sign).

The initial number of passengers on board=29

After 4 people get off at the first stop,

Using arithmetic addition and subtraction, we get,

Number of passengers left=29-4=25

After 11 people get on,

Number of passengers=25+11=36

At the second stop, when 7 people get off,

Number of passengers=36-7=29

When 23 people get on,

Number of passengers=29+23=52

Total number of passenger seats in the bus=78

Number of free seats, when everyone is sitting=78-52

                                                                              =26

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A. Compute the following limits1. `lim [(V1+x2) - x]`: To compute this limit, we will substitute `h = x - V1 - x^2` as `x -> V1 + x^2`.`lim [(V1+(x+h)^2) - (x+h)]`Now, we simplify the numerator and denominator.

`[(V1+x^2) + 2xh + h^2 - x - h] / h`   Rearranging , we get `[(2x + 1)h + (V1 + x^2 - x)] / h`Taking the limit of this expression as `h -> 0`, we get `2V1 + 1`.Hence, `lim  [(V1+x2) - x] = 2V1 + 1`.2. `lim [-19 / (Vx-3)]`: As `x -> 3`, the denominator `Vx-3` approaches `0`. The numerator is constant. Hence, the limit is undefined.3. `lim [(Vx cosx) / (x^2 + 2x)]`: We can simplify the expression to `lim [(Vx cosx) / x(x+2)]`. Now, we need to compute both `lim (Vx cosx)` and `lim (x(x+2))` separately.

Using L'Hopital's rule,`lim (Vx cosx) = lim [cosx / (1/x)] = lim (x cosx) = 0`.Using L'Hopital's rule again, `lim (x(x+2)) = lim [2x+2 / 2x+1] = 2`.Hence, `lim [(Vx cosx) / (x^2 + 2x)] = 0/2 = 0`.B. Compute the following limits1. `lim [(Vx+1) / (1-cosx)]`: We can simplify this expression to `lim [(Vx+1) / 2(sin^2(x/2))]`. Now, we need to compute both `lim (Vx+1)` and `lim [2(sin^2(x/2))]` separately. Using L'Hopital's rule, `lim (Vx+1) = lim [1 / (1/2 Vx)] = 0`. Using the identity `sin^2(x/2) = [1-cosx]/2`, we get `lim [2(sin^2(x/2))] = 1`.Hence, `lim [(Vx+1) / (1-cosx)] = 0/1 = 0`.2. `lim [(sinx) / (2-x^2)]`: As `x -> 0`, the denominator approaches `2`. Using the Squeeze Theorem, we can show that the limit is `0`.3.

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The probability of drawing a 7 followed by a 10 is (4/52) x (4/51) = 0.006 or 0.6%.

To calculate the probability of drawing a 7 first and then a 10 from a standard 52-card deck, you need to consider the number of 7s and 10s in the deck and the total number of cards.

There are 4 sevens and 4 tens in the deck. The probability of drawing a 7 first is 4/52 (since there are 4 sevens and 52 cards in total). After drawing a 7, there are now 51 cards left in the deck. The probability of drawing a 10 next is 4/51 (since there are still 4 tens but now only 51 cards).

To find the overall probability, multiply the probabilities of each event: (4/52) * (4/51) = 16/2652 ≈ 0.006 or 0.6%.

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The probability that a senior takes the bus to school every day, given that he or she has a driver's license, is approximately 17%.

To find the probability that a senior takes the bus to school every day given that he or she has a driver's license, we can use conditional probability.

Let's denote the event that a senior has a driver's license as A and the event that a senior takes the bus to school every day as B. We want to find the probability of event B given event A, denoted as P(B|A).

We are given the following information:

The conditional probability formula states that P(B|A) = P(A ∩ B) / P(A).

Substituting the given values, we have:

P(B|A) = P(A ∩ B) / P(A) = 0.14 / 0.84 ≈ 0.1667

To the nearest whole percent, the probability that a senior takes the bus to school every day, given that he or she has a driver's license, is approximately 17%.

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The probability that a senior takes the bus to school every day, given that he or she has a driver’s license, is 17%.

To find the probability that a senior takes the bus to school every day, given that he or she has a driver’s license, we need to use the concept of conditional probability. Conditional probability is the probability of one event happening given that another event has already occurred. In this case, we want to find the probability of taking the bus to school every day, given that the student has a driver’s license.

We can use the formula:

P(A|B) = P(A and B) / P(B)

where P(A|B) is the probability of event A happening given that event B has happened, P(A and B) is the probability of both events A and B happening, and P(B) is the probability of event B happening.

In the given problem, 84% of the seniors have driver’s licenses, 16% of seniors take the bus every day to school, and 14% of the seniors have driver’s licenses and take the bus to school every day. We want to find the probability of taking the bus every day, given that the student has a driver’s license.

Plugging in the values into the formula:

P(Taking the bus every day | Having a driver’s license) = P(Taking the bus every day and Having a driver’s license) / P(Having a driver’s license)

P(Taking the bus every day | Having a driver’s license) = 0.14 / 0.84 ≈ 0.1667

To the nearest whole percent, the probability that a senior takes the bus to school every day, given that he or she has a driver’s license, is 17%.

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The dividend in the formula P3 = Dx/(R - g) is for period e. three.

In the given formula P3 = Dx/(R - g), the dividend, Dx, refers to the cash flow or payment made during a specific period. The subscript "3" in P3 indicates the period of time for which the dividend is associated.

In the given formula, P3 = Dx/(R - g), the subscript 3 represents the period of time for which we are calculating the dividend.

The dividend, Dx, represents the cashflow or payment made during a specific period. In this case, the dividend is associated with period 3.

Therefore, the dividend in the formula corresponds to period e. three.

The dividend in the formula P3 = Dx/(R - g) is for period e. three

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Answer:

a. 3 5/6

b. 5 1/7

Step-by-step explanation:

Answer:

5.83333333333
5.14285714286

Step-by-step explanation:

Answer:

Lose 12y yards.

Lose 5.2x yards.

What is the net yardage for these four plays?

is the que correct

Answer:

19.8x - 11.1y

Step-by-step explanation:

Given information:

"Gain" means to add the value.

"Lose" means to subtract the value.

Therefore, net yardage is:

⇒ 25x + 0.9y - 12y - 5.2x

Collect like terms:

⇒ 25x - 5.2x + 0.9y - 12y

Factor out the common variables x and y:

⇒ x(25 - 5.2) + y(0.9 - 12)

Carry out the operations in the parentheses:

⇒ x(19.8) + y(-11.1)

Therefore, the net yardage is  19.8x - 11.1y

The general solution to the recurrence relation xₙ = 4xₙ₋₁ - 3nₙ₋₂ with initial conditions x₀ = 0 and x₁ = 1 is xₙ = 2ⁿ⁺¹ - n - 1.

The given recurrence relation xₙ = 4xₙ₋₁ - 3xₙ₋₂, with initial conditions x₀ = 0 and x₁ = 1, can be solved by analyzing the recursive formula. By examining the pattern, we observe that each term xₙ is derived by multiplying the previous term xₙ₋₁ by 4 and subtracting 3 times the term xₙ₋₂.

By solving for xₙ in terms of n using the initial conditions, we find that the general solution is xₙ = 2ⁿ⁺¹ - n - 1.

This solution combines a geometric pattern (2ⁿ⁺¹) with a linear decrement (n + 1) and an offset (-1). It satisfies the initial conditions and represents the sequence for any value of n.

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Answer:

54!

Step-by-step explanation:

300-30

=270×.20

=54

Answer:

I think the midpoint is 5.

Step-by-step explanation:

Answer:

the answer is d.8(/)(w)

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

The volume of the orange traffic cones is 102.63 in³ respectively.

A cone is a recognizable three-dimensional geometric shape with a smooth and curving surface that is directed upward in mathematics. The

Greek word "konos," which denotes a peak or a wedge, is the source of the English word "cone."

The apex is the pointy end, while the base is the level area.

So, the cone volume is:

V=πr²h/3

Now, insert values as follows:

V=πr²h/3

V=π7²2/3

V=102.63

Therefore, the volume of the orange traffic cones is 102.63 in³ respectively.

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The answer is option B: 224 square in.

What is dimensions?

dimensions refer to the measurable physical quantities or characteristics of an object or system. The term can have different meanings depending on the context.

In mathematics, dimensions refer to the number of coordinates needed to specify a point in space. For example, a point in two-dimensional space (such as a piece of paper) can be specified with two coordinates (x,y), while a point in three-dimensional space (such as a cube) requires three coordinates (x,y,z).

we can see that the solid figure has 6 faces, each of which is a rectangle. We can label the dimensions of each face as follows:

Top face: L x W

Bottom face: L x W

Front face: W x H

Back face: W x H

Left face: L x H

Right face: L x H

From the given information, we have L : W = 4 in and H = 12 in.

To find the surface area of the solid figure, we need to calculate the area of each of its faces and then add them up. Using the dimensions above, we can calculate the area of each face as follows:

Area of top face = L x W = (4 in) x (1 in) = 4 in^2

Area of bottom face = L x W = (4 in) x (1 in) = 4 in^2

Area of front face = W x H = (1 in) x (12 in) = 12 in^2

Area of back face = W x H = (1 in) x (12 in) = 12 in^2

Area of left face = L x H = (4 in) x (12 in) = 48 in^2

Area of right face = L x H = (4 in) x (12 in) = 48 in^2

Therefore, the total surface area of the solid figure is:

Total surface area = Area of top + Area of bottom + Area of front + Area of back + Area of left + Area of right

Total surface area = 4 in^2 + 4 in^2 + 12 in^2 + 12 in^2 + 48 in^2 + 48 in^2

Total surface area = 128 in^2

Hence, the answer is option B: 224 square in.

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Answer: 1 month = 500ml

4 month = 500ml × 4 = 2000ml = 2L

you should use the 2L container

Step-by-step explanation:

Answer:

your answer is, -x+5

Step-by-step explanation:

Fοr distributions with a nοrmal shape or symmetry, the mean and standard deviation are emplοyed; for asymmetrical distributiοns, the median and interquartile range are used.

Because it is unaffected by οutliers, the IQR is frequently regarded as a mοre accurate measure of spread than the range. The variance and standard deviatiοn are indicators of hοw widely the data are dispersed from the mean. Each οbserved data value's prοximity to the mean is summarised.

The strοngest indicator of variability in data sets with οutliers or skewed distributions is the interquartile range. It's unlikely to be impacted by οutliers because it's based οn numbers that come frοm the centre half of the distribution.

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Answer:

\( \sqrt{58} \)

Answer:

B

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is

x² = 3² + 7² = 9 + 49 = 58 ( take square root of both sides )

x = \(\sqrt{58}\) → B

Answer:

D

Step-by-step explanation:

The graph in the picture given is obviously a function of f(x) = x^3 which answers whether the graph is a function or not. In addition, the answer the part on why it's a graph, it's because it passes the vertical line test.

To find Paul's monthly salary, we need to add his base salary of $1500 to his commission on sales.Therefore, Paul's monthly salary is $2,740.

Commission is a percentage of the sales that a salesperson earns as a bonus on top of their base salary or hourly wage. It is usually based on the total dollar amount of sales made by the salesperson during a certain period of time.Paul earns 8% commission on anything he sells, so the commission he earns is 0.08 times the sales amount. If he sells $15,500 worth of items, his commission would be:0.08 x 15,500 = $1,240In addition to his commission, he also has a monthly salary of $1,500. So his total monthly income would be:1,500 + 1,240 = $2,740 Therefore, Paul's monthly salary is $2,740.Paul earns a base salary of $1500 per month and an additional 8% commission on anything he sells.

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The speed of Aro's paddling and speed of the river will be 1.56 miles per hour and 0.52 miles respectively.

Aro diagrams his river rafting trip, estimating the time it will take him to paddle upstream against the current, and then back downstream with the current. His campsite destination is 5.2 miles upstream. Determine how fast Aro can paddle and how fast the river water is moving. Round to the nearest hundredth as needed. Upstream: Downstream: Let x be the speed of Aro’s paddling and let y be the speed of the river. Upstream: 1.04 = x – y Downstream: 2.08 = x + y Aro can paddle at a speed of miles per hour. The river’s speed is miles per hour.

Based on the information given, the equations will be:

x + y = 1.04

x + y = 2.08

Add both equations together. This will be:

x = 1.56

Now substitute the value of x into equation ii. This will be:

1.56 + y = 2.08

y = 2.08 - 1.56

y = 0.52

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Answer:

twenty three and 13 hundredths

Answer:

Twenty three point thirteen

Answer:

15 inches

Step-by-step explanation:

As the square cake was cut in two equal pieces, we have that one side of the rectangle is the double of the other side, so we have that:

2*Length + 2*Width = 45

Length = 2*Width

So using the value of length in the first equation, we have:

4*Width + 2*Width = 45

6*Width = 45

Width = 7.5

Length = 2*Width = 15

So each side of the original cake is equal to the length of the rectangle pieces, that is, 15 inches.

Answer:

50.24

Step-by-step explanation:

radius R = 2

SA = 4πR^2 = 4π*2^2 = 16π = 16*3.14 = 50.24