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The volume of the larger cone is equal to the total volume of the two smaller cones

From the question, we have two equal cylinders.

This means that the cylinders have equal volume.

From the complete question, a large cone is placed in one of the cylinders, while two small cones are placed in the other.

Since the cylinders have equal volumes, then the volume of the large cone equals the sum of the volumes of the smaller cones.

Hence, the volume of the larger cone is equal to the total volume of the two smaller cones

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Answer:

.

Step-by-step explanation:

                            .

If you are paid $8.75 a hour and you work 8 hours, you earn 8.75·8 dollar in one day.

However, you spend $4.00 round trip to get to andfrom work. Then, the net money you earnd in one day is gievn by the following expression:

8.75·8 - 4

The given data represents the number of seats available in different cafes. The data is organized into intervals and their corresponding frequencies are calculated to create a frequency table. The table shows that the majority of cafes have seats between 15-21 and 22-28.

To create the frequency table, we first need to determine the range of the data

Range = maximum value - minimum value

Range = 26 - 1

Range = 25

Next, we need to determine the width of each interval. One common method is to use a width of 7, which means each interval will cover a range of 7 seats.

Width = (Range/Number of Intervals) rounded up

Width = (25/4) rounded up

Width = 7

Now we can create the intervals for the frequency table

Interval 1-7 8-14 15-21 22-28

Next, we can count how many data points fall into each interval

Interval 1-7 8-14 15-21 22-28

Frequency 1 4 2 3

Finally, we can complete the frequency table

CafeSeats  Frequency

1 -7                 1

8 -14              4

15-21              2

22-28             3

This shows that there is 1 cafe with 1-7 seats, 4 cafes with 8-14 seats, 2 cafes with 15-21 seats, and 3 cafes with 22-28 seats.

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--The given question is incomplete, the complete question is given

" 78 10 Ed counted the number of seats available in each cafe in his town. Complete the frequency table. 15, 17, 24, 26, 11, 8, 17, 18, 1, 14 Interval 1-7 8-14 112 3 4 15-21 22-28 Frequency Cafe Seats 56​

"--

The component form of the linear combination of the two vectors is u - 2v = < -5, 20>

Here we have the two vectors: u = <-3, -2> and v = <1, -5> We want to determine the value of the linear combination:

u - 2v

To do that we just add the correspondent components, then we get:

u - 2v = <-3, -2> - 2*<1, -5>          

= <-3, -2> - <2*1, 2*-5>          

= <-3, -2> -  <2, -10>          

= < -3 - 2, -2 -(-10)>          

= < -5, 20>

That is the component form of the linear combination.

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We know

D = RT

D is distance

R is rate

T is time

Upstream rate = x - c

Downstream rate = x + c

note: c is rate of current and x is still water rate (x)

Answer:

A. 1/12

if wrong sorry

hope this helps you ☺️☺️

Answer:

D. \( \frac{3}{20}\)

Step-by-step explanation:

\(l = \frac{ \theta}{360 \degree} \times c \\ \\ l = \frac{54 \degree}{360 \degree} \times c \\ \\ l = \frac{3}{20} \times c \\ \\ \)

Thus, the length of the arc RST is \( \frac{3}{20}\) times of the circumference of the circle with center C.

The appropriate test statistic to test the hypotheses is 2.71. Hence, the correct option is D.

The appropriate test statistic to test the hypotheses is the z value. The z value is calculated using the formula:

z = (x - μ) / (σ / √n)

Where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, x = 6.65, μ = 6, σ = 1.5, and n = 39.

Plugging these values into the formula gives:

z = (6.65 - 6) / (1.5 / √39)
z = 0.65 / (1.5 / 6.24)
z = 0.65 / 0.24
z = 2.71

Therefore, the appropriate test statistic to test the hypotheses is 2.71, which corresponds to option D.

Note: The question is incomplete. The complete question probably is: A mail-order business prides itself in its ability to fill customers' orders in less than six calendar days, on average. Periodically, the operations manager selects a random sample of customer orders and determines the number of days required to fill the orders. On one occasion when a sample of 39 orders was selected, the average number of days was 6.65 with a population standard deviation of 1.5 days. calculate the appropriate test statistic to test the hypotheses. (z value). A) 4.54 B) 4.87 C) 1.76 D) 2.71.

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Answer:1,2,3,5

Step-by-step explanation:

Answer: B) 86°

Step-by-step explanation:

The angles of a triangle always add to equal 180.

So let's call the third angle x and add the other two angles with it.

32+62+x=180

94+x=180

Now we solve for x

Subtract 94 from both sides

94-94+x=180=94

x=86

Answer:

x=5

Step-by-step explanation:

set up the equation:

x-2 = 3

solve

x = 5

Answer:

x=1

Step-by-step explanation:

you put 3 in for x in the equation

There are 2 common factors of 9 and 24, that are 1 and 3. Therefore, the greatest common factor of 9 and 24 is 3.

In mathematics, the greatest common divisor of two or more nonzero integers is the largest positive integer that divides each integer

. The greatest common divisor (GCF) of a set of numbers is the greatest factor of division of all numbers.

GCF by listing factor method :-

Factors of 9: 1, 3, 9

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

There are 2 common factors of 9 and 24, that are 1 and 3. Therefore, the greatest common factor of 9 and 24 is 3.

other two methods are attached below .

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Answer:

21.44 ft

Step-by-step explanation:

(sketch to understand)

use SOH/CAH/TOA rules to solve

sin rule is used

solve for x

(working in the picture attached)

The real GDP for country A in 2004 prices was 260.87 billion.

To calculate the real GDP in 2004 prices, we need to use the formula: real GDP = nominal GDP x Deflator. Given that the nominal GDP in 2005 for country A was 300 billion and the deflator against 2004 prices was 1.15, we can substitute these values into the formula.

Real GDP = 300 billion x 1.15 = 345 billion. However, since we want to find the real GDP in 2004 prices, we need to adjust it. To do that, we divide the calculated real GDP by the deflator: 345 billion / 1.15 = 300 billion.

Therefore, the real GDP for country A in 2004 prices is 260.87 billion.

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The area of triangle BMN is 124.7 square centimeter.

Similar triangles are triangles that their corresponding angles are equal and the ratio of their corresponding lengths are equal. They are often similar When at least Two angles are equal or The ratio of any corresponding lengths are same.

Analysis:

AB = AC = BC = 50cm

AH = AC/2 = 50/2 = 25cm

From Δ ABH, using Pythagoras theorem to find BH.

\((BH)^{2}\) = \((AB)^{2}\) - \((AH)^{2}\)

\((BH)^{2}\) = \(50^{2}\) - \(25^{2}\)

\((BH)^{2}\) = 2500 - 625

\((BH)^{2}\) = 1875

BH = \(\sqrt{1875}\) = 43.3cm

ΔBMN and BHC are similar,

so, BM/BH = MN/HC

BM/43.3 = 12/25

25BM = 12 X 43.3

BM = 519.6/25 = 20.78cm

Area of ΔBMN

= 1/2(MN)(BM) = 1/2 x 12 x 20.78 = 124.7 square centimeter

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Answer:

Median #1: 10.5

Q1 #1: 5.5

Q3 #1: 19

IQR #1: 13.5

Median #2: 14

Q1 #2: 3

Q3 #2: 45

IQR #2: 42

Step-by-step explanation:

Question 1:

First order the data so that they are in order from least to greatest:

2, 5, 6, 8, 13, 16, 22, 24

Now, find the median by crossing out one value on the left and one value on the right until you get to the center value.

2, 5, 6, 8, 13, 16, 22, 24

/2/, /5/, /6/, /8/, /13/, /16/, /22/, /24/

In this case, there were four values crossed off of each side, so you'll need to find the average of the final two crossed out values: 8 and 13.

(8+13)/2 = 10.5

To find the first quartile, find the median of all values below the median.

2, 5, 6, 8

/2/, /5/, /6/, /8/

The median of these values is the average of the center two, so

(5+6)/2 = 5.5

The third quartile is the median of all values above the median.

13, 16, 22, 24

/13/, /16/, /22/, /24/

The median of those values is the average of the center two as well, so

(16 + 22)/2 = 19

The IQR can be found by subtracting Q1 from Q3. (IQR = Q3 - Q1)

Q3 - Q1

19 - 5.5

IQR = 13.5

Question 2:

Arrange the values from least to greatest and cross them out until you find the middle falue, like in problem one.

1, 3, 7, 14, 21, 45, 63

/1/, /3/, /7/, 14, /21/, /45/, /63/

The center value is 14, so the median is 14.

The first quartile can be found by finding the median of all values below the median.

1, 3, 7

/1/, 3, /7/

The first quartile is 3.

The third quartile can be found by finding the median of all values above the median.

21, 45, 63

/21/, 45, /63/

The third quartile is 45.

The interquartile range can be found using the equation from above.

Q3 - Q1

45 - 3

The interquartile range is 42.

The Correct answer is A. (-4,1) ordered pair generated by this model should be discarded because the values are unreasonable.

In algebra, a quadratic equation (from Latin quadratus 'rectangular') is any equation that can be rearranged in well-known form as ax²+bx+c=0 Where x represents an unknown value, and a, b, and c constitute recognized numbers.

One supposes usually that a ≠ zero; the one's equations with a = zero are taken into consideration degenerate because the equation then will become linear or even simpler. The numbers a, b, and c are the coefficients of the equation and can be prominent with the aid of calling them, respectively, the quadratic coefficient, the linear coefficient, and the consistent or loose time period.

The values of x that satisfy the equation are referred to as answers to the equation, and roots or zeros of the expression on its left-hand aspect. A quadratic equation has at most two answers. If there is handiest one solution, one says that it's miles a double root. If all the coefficients are real numbers, there are both actual solutions, a single actual double root, or two complicated answers which can be complicated conjugates of each other.

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Complete Question:

Louis used a quadratic equation to model the height, y, of a falling object x seconds after it is dropped. which ordered pair generated by this model should be discarded because the values are unreasonable?

The sets of transformations that result in the same image when performed in any order are:

Translation, dilation with center (0,0)

Two translations

In mathematics, a transformation refers to a process that changes the size, shape, position, or orientation of a geometric figure or an object in a coordinate plane or space. There are several types of transformations, such as translation, rotation, reflection, and dilation, which are used to alter the original figure to create a new one that is similar or congruent to the original. Transformations are used in geometry, algebra, and other branches of mathematics to study and understand various properties of geometric shapes and objects.

Here,

For the first set, if we perform a translation followed by a dilation with center (0,0), the result will be the same as if we perform the dilation first followed by the translation. This is because the dilation does not change the direction of the translation, and the center of dilation is at the origin, so the translation is unaffected.

For the second set, any two translations can be combined to form a single translation, so the order in which they are performed does not matter.

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Based on the information, Paulo will need to find a larger mailer or use a different method to ship the plaque to the winner of the chess tournament.

The mailer is a triangular prism with 4-inch equilateral triangle bases, which means that each side of the triangle is 4 inches long. Since it is a triangular prism, the height of the mailer is not given, but it doesn't matter for this calculation.

The plaque is 31 inches high. We don't know the width or depth of the plaque, but we only need to worry about the height, since that is what will determine whether it fits through the opening.

The opening of the mailer is the triangular shape formed by the three sides of the triangle that form the base. To calculate the size of this opening, we need to know the length of each side of the triangle. Since it is an equilateral triangle, all sides have the same length of 4 inches.

To see whether the plaque will fit through the opening, we need to compare the height of the plaque (31 inches) to the height of the opening. The height of the opening is the height of an equilateral triangle, which can be calculated using the formula:

height = ✓(3)/2 * length

where "length" is the length of one side of the equilateral triangle. In this case, the length is 4 inches, so we have:

height = ✓(3)/2 * 4 = 2*sqrt(3) inches ≈ 3.5 inches

Therefore, the height of the opening is approximately 3.5 inches. Since the plaque is 31 inches high, it is clearly too large to fit through the opening of the mailer. Therefore, Paulo will need to find a larger mailer or use a different method to ship the plaque to the winner of the chess tournament.

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Answer:

Step-by-step explanation:

its is 192 ft2

The equation for the rate of change of concentration is Δc/Δt, and this is equal to the rate of change of concentration over a given interval, -0.0680 m/s.

To calculate the final concentration, we must use the equation Δc = rate × time, where Δc is the change in concentration, and rate and time are the rate of change of concentration and the interval, respectively. Plugging in our values, Δc = -0.0680 m/s × 3.0 s = -0.204 m. This means that the final concentration of c is 2.700 m - 0.204 m, which is equal to 2.496 m.

To summarize, the rate of change of concentration equation is Δc/Δt = rate of change, and the equation to calculate the final concentration is Δc = rate × time. Plugging in the rate of change and interval, we get Δc = -0.0680 m/s × 3.0 s = -0.204 m, which gives us the final concentration of c at the end of the same interval as 2.496 m.

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Answer: 73.7

5 rounds up so you add 1 to the 6

Answer:

A

Step-by-step explanation:

To determine the convergence of the series \(\sum \frac{(-1)^n}{n(n^2 + 1)}\), we will examine both absolute convergence and conditional convergence.

First, let's check for absolute convergence. To do this, we need to consider the series formed by taking the absolute value of each term:

\(\sum \left| \frac{(-1)^n}{n(n^2 + 1)} \right|\)

Taking the absolute value of \((-1)^n\) simply gives 1 for all n. Therefore, the series becomes:

\(\sum \frac{1}{n(n^2 + 1)}\)

To determine the convergence of this series, we can use the comparison test. Let's compare it to the series \(\sum \frac{1}{n^3}\):

\(\sum \frac{1}{n^3}\)

We know that the series \(\sum \frac{1}{n^3}\) converges since it is a p-series with p = 3, and p > 1. Therefore, if we can show that \(\sum \frac{1}{n(n^2 + 1)}\) is less than or equal to \(\sum \frac{1}{n^3}\), then it will also converge.

Consider the inequality \(\frac{1}{n(n^2 + 1)} \leq \frac{1}{n^3}\). This inequality holds true for all positive integers n. Therefore, we can conclude that \(\sum \frac{1}{n(n^2 + 1)} \leq \sum \frac{1}{n^3}\).

Since \(\sum \frac{1}{n^3}\) converges, the series \(\sum \frac{1}{n(n^2 + 1)}\) converges absolutely.

Next, let's check for conditional convergence. To determine if the series \(\sum \frac{(-1)^n}{n(n^2 + 1)}\) is conditionally convergent, we need to check the convergence of the series formed by taking the absolute value of the terms, but removing the alternating sign:

\(\sum \left| \frac{(-1)^n}{n(n^2 + 1)} \right|\)

This series becomes:

\(\sum \frac{1}{n(n^2 + 1)}\)

We have already determined that this series converges absolutely. Therefore, there is no alternating sign to change the convergence behavior. Thus, the series \(\sum \frac{(-1)^n}{n(n^2 + 1)}\) is not conditionally convergent.

In summary, the series \(\sum \frac{(-1)^n}{n(n^2 + 1)}\) is absolutely convergent.

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The area enclosed by the curve x = t^2 − 3t, y = √t and the y-axis is 2.08 square units.

We have been given parametric equations x = t^2 − 3t, y = √t

We need to find the area enclosed by the curve x = t^2 − 3t, y = √t and the y-axis.

Consider x = 0

So, t^2 − 3t =  0

t(t - 3) = 0

t = 0   or  t = 3

Let f(t) =  t^2 − 3t and g(t) = t

Differentiate the curve f(t) with respect to t.

f'(t) = 2t - 3

NWe know that the formula to find the area under the curve.

A = ∫[a to b] g(t)f'(t) dt

here, a = 0 and b = 3

so, A = ∫[0 to 3] √t (2t - 3) dt

A = ∫[0 to 3] (2t√t - 3√t) dt

A = ∫[0 to 3] (2t^(3/2) - 3t^(1/2)) dt

A = [4/5 t^(5/2) - 2 t^(3/2)]_[t = 0, t = 3]

A = 4/5 3^(5/2) - 2 3^(3/2) - 0 + 0

A = 4/5 3^(5/2) - 2 3^(3/2)

A = 6√3 /5

A = 2.08

Therefore,  the area of the curve is 2.08 square units.

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Answer:

try 17.89 cm..then 18 for answer

The conclusion from the equation |y + 6| = 2 is that it has two solutions , the correct option is (b) .

In the question ,

it is given that ,

the equation is given as |y \(+\) 6| \(=\) 2 ,

after removing the modulus  , we get the two equations , that are

y + 6 = 2 and y + 6 = -2

Solving y + 6 = 2 , we get

y + 6 = 2

Subtracting 6 from both LHS and RHS ,

we get

y = 2 - 6

y = -4

On Solving y + 6 = -2 ,

we get

y + 6 = -2,

Subtracting 6 from both LHS and RHS ,

we get

y = - 2 - 6

y = -8 .

the two solutions are y = -8 and y = -4 .

Therefore , The conclusion from the equation |y + 6| = 2 is that it has two solutions , the correct option is (b) .

The given question is incomplete , the complete question is

Consider this equation. |y + 6| = 2 what can be concluded of the equation? check all that apply.

(a) There will be one solution

(b) There will be two solutions.

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