(b)In the sequence the sum of the third and fourth term is -12, the sum of the third and fifth term is 60 and the sum of the fourth and fifth term is 24. Show that the term form geometric progression. Find the sum of the first ten terms of the sequence. ​

The number of different possible outcomes if you spin a spinner labeled Red, Blue, Yellow five times (excluding outcomes where the same color is spun five times) is 243 x 1/10 = 24.3, which we can round down to 24.

If you spin a spinner labeled Red, Blue, Yellow five times, there are a total of 3^5 (three raised to the power of five) different possible outcomes.

This is because each spin has three possible outcomes and the number of possible outcomes is calculated by multiplying the number of outcomes for each spin together.

Therefore, 3 x 3 x 3 x 3 x 3 = 243. However, this includes outcomes where the same color is spun five times, which we want to exclude.

To calculate this, we can use the formula for combinations: nCr = n! / (r! * (n-r)!). In this case, we want to find the number of combinations of 3 colors taken 5 at a time, which is 3C5 = 3! / (5! * (3-5)!) = 3! / (-2! * 5!) = 1/10.

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The distributive property allows the formula (-128 x 46) + (128 x -36) to be simplified to -10496.

We may use the distributive property of multiplication over addition/subtraction, which asserts that an x (b + c) = an x b + an x c, to simplify the above calculation (-128 x 46) + (128 x -36).

Let's dissect the expression in detail:

(-128 x 46) + (128 x -36)Let's first assess the goods:

-128 x 46 = -5888

128 x -36 = -4608

Reintroduce these values into the phrase now:

(-5888) + (-4608)

We simply add the absolute values of the two negative numbers while maintaining the sign of the negative:

-5888 + (-4608) = -10496

Consequently, -10496 is the reduced expression.

Last but not least, the phrase (-128 x 46) + (128 x -36) becomes -10496. .By applying the distributive property and carrying out the required multiplication, addition, and subtraction, the result is -10496.

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Answer:

[tex]3n = 57[/tex]

[tex]n = 19[/tex]

D is the correct answer.

The Kruskal-Wallis test is a non-parametric test used to compare three or more independent groups to determine if there is a significant difference between the medians of the groups. The test statistic used in this test is denoted by the letter "H," which is calculated based on the ranks of the data.

True. The test statistic calculated in the Kruskal-Wallis test is denoted by the symbol H, not to be confused with the Shapiro-Wilk test statistic denoted by W. The Kruskal-Wallis test is a non-parametric test used to compare the median ranks of three or more independent groups. The test statistic H is calculated by comparing the between-group sum of squares to the total sum of squares. H follows a chi-squared distribution with degrees of freedom equal to the number of groups minus one. The p-value obtained from the chi-squared distribution is used to determine whether to reject or fail to reject the null hypothesis that there is no significant difference between the groups.

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Answer: Put this in your own words:

Convenience sampling is like staying in a certain area of a mall and giving samples to  people as the come by you stay there at that one place because it is convenient  because you don't want to move from that spot so you stay at that spot and only that spot. Convenience sampling is also like ordering food because it is convenient and you don't want to cook.

Step-by-step explanation:

The required, age of Trisha is 15 years old.

Let's represent Trisha's age as "T." Then we can use this variable to represent the ages of her brothers and father as well.

According to the problem, Trisha's first brother is three years older than her, so his age would be T + 3. Her second brother is three years younger than her, so his age would be T - 3. Trisha's third brother is one-third of her age, so his age would be T/3. Trisha's father is three times her age, so his age would be 3T.

The sum of all their ages is 95, so we can create the equation:

T + (T + 3) + (T - 3) + (T/3) + 3T = 95

T = 15

Thus, the required age of the Trisha is 15 years.

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The value of x in the parallel lines is 15.

Option C is the correct answer.

We have,

The concept being used here is the concept of alternate exterior angles and the parallel lines property.

Alternate exterior angles are pairs of angles that lie on opposite sides of a transversal and are located outside the two parallel lines.

According to the property of alternate exterior angles, when two parallel lines are intersected by a transversal, the alternate exterior angles are congruent or equal in measure.

Since lines s and t are parallel lines,

8x + 7 and 127 are alternate exterior angles.

So,

8x + 7 = 127

Now,

Solve for x.

8x + 7 = 127

8x = 127 - 7

8x = 120

x = 120/8

x = 15

Thus,

The value of x in the parallel lines is 15.

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The length of the model when the scale given is used would be = 240 yards.

To calculate the length of the model, the formula for scale factor should be used. That is;

Scale factor = Actual length/Model length

The scale factor = 1/4

Actual length = 60 yards

Model length = ?

That is;

1/4 = 60/?

Model length = 60×4

= 240 yards

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Answer: D

Step-by-step explanation: Got it right on test

Answer:

First take the difference between the squares of the semi-major axis and the semi-minor axis: (13 cm)² - (5 cm)² = 144 cm².

Then, take the square root of their difference to obtain the distance of the foci from the ellipse's center along the major diameter to be √144 = 12 cm.

Step-by-step explanation:

Your welcome

To convert r10,000 to Thai Baht using the exchange rate R0.448 = 1 Thai Baht, we can set up a proportion to find the equivalent amount in Thai Baht.

R0.448 (Thai Baht)   R10,000 (Rand)

------------------ = --------------

       1                         x

Cross-multiplying, we have:

R0.448 * x = R10,000

Dividing both sides by R0.448:

x = R10,000 / R0.448

Calculating the division, we find:

x ≈ 22,321.43

Therefore, r10,000 is approximately equivalent to 22,321.43 Thai Baht, using the given exchange rate.

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There are 250,000 different completed answer sheets possible using counting principle.

For part a, there are 2 choices for each of the 5 questions, so there are a total of 2^5 = 32 ways to complete part a.

For part b, there are 5 choices for each of the 4 questions, so there are a total of 5^4 = 625 ways to complete part b.

For part c, there are 6 choices for the first question, 5 choices for the second question (since one of the answers has already been used), 4 choices for the third question, and so on. So there are a total of 6 x 5 x 4 x 3 x 2 x 1 = 720 ways to complete part c.

To find the total number of possible completed answer sheets, we need to multiply the number of choices for each part. However, since part b and part c are mutually exclusive (you can only choose one of them), we need to add their totals together. Therefore, the total number of possible completed answer sheets is:

32 x (625 + 720) = 70,240

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The work required to pump the sludge is approximately 21449.6 ft-lbs.

To calculate the work required to pump the sludge, we need to determine the volume of the sludge and then multiply it by the weight of the sludge.

First, let's find the volume of the sludge in the tank. Since the tank is formed by rotating the segment between (2, 0) and (4, 4) around the y-axis, it forms a frustum of a cone. The formula for the volume of a frustum of a cone is:

V = (1/3) * π * h * (R^2 + r^2 + R*r),

where h is the height of the frustum, R is the radius of the larger base, and r is the radius of the smaller base.

In this case, the height of the frustum is the difference in y-coordinates between the two points: h = 4 - 0 = 4 ft.

The radius of the larger base, R, is the y-coordinate of the point (4, 4): R = 4 ft.

The radius of the smaller base, r, is the y-coordinate of the point (2, 0): r = 0 ft.

Substituting these values into the volume formula, we have:

V = (1/3) * π * 4 * (16 + 0 + 0) = (4/3) * π * 16 = 67.03 ft^3 (approximately).

Next, we need to calculate the weight of the sludge, which is the volume multiplied by the density:

Weight = Volume * Density = 67.03 ft^3 * 80 lbs/ft^3 = 5362.4 lbs (approximately).

Finally, we can calculate the work required to pump the sludge 4 feet upwards. The work is given by the formula:

Work = Force * Distance,

where Force is the weight of the sludge and Distance is the vertical distance it is pumped.

Work = Weight * Distance = 5362.4 lbs * 4 ft = 21449.6 ft-lbs (approximately).

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The statements that are true, according to the histogram include

A histogram is a graphical depiction of data points arranged into ranges that the user specifies.

The histogram, which resembles a bar graph in appearance, condenses a data series into an easily read visual by grouping many data points into logical ranges or bins.

Looking at the diagram, a total of 50 sharks were measured and most of the sharks that were measured were over 16 feet long.

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The time taken for the stone to hit the surface of the water is T = 2 seconds

Given data ,

Let the function be represented as h ( t )

where h = -16t² - 64t + 192

On simplifying , we get

The time taken for the stone to hit the water surface is when h = 0

So , when h = 0

16t² + 64t - 192 = 0

On solving the quadratic equation , we get

t = (-64 ± √(64² - 4 * 16 * -192)) / (2 * 16)

Simplifying further:

t = (-64 ± √(4096 + 12288)) / 32

t = (-64 ± √(16384)) / 32

t = (-64 ± 128) / 32

Now, we have two possible solutions:

t = (-64 + 128) / 32 = 64 / 32 = 2

t = (-64 - 128) / 32 = -192 / 32 = -6

Hence , the time taken is t = 2 seconds

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Answer:

He can make a maximum of 60 shortcakes

Step-by-step explanation:

With the sugar alone he has enough to make:

500/50=10×12=120 shortcakes

Taking the butter into account he can make a maximum of:

1000/200=5×12=60 shortcakes

Now taking the flour into account he can still make a maximum of 60 shortcakes before running out of supply.

However, with the milk alone, he can make up to

500/10=50×12=600 shortcakes

All we need to do is find the minimum number of shortcakes he can make before running out of supply.

In this case he would make 60 shortcakes

Hope this helps!

Answer:Therefore, the answer is D. 16.

Step-by-step explanation:

The expression 4 + (f + 7) simplifies to 11 + f. When f = 5, the value of the expression is:

11 + 5 = 16

Therefore, the answer is D. 16.

Answer:

Step-by-step explanation:

You can find the hieght from slant height and side edge using this formula:

[tex]\sqrt{s^{2} - \frac{a}{2}^{2} }[/tex]    where s is the slant height and a is the base length of one edge.

[tex]\sqrt{92.5^{2} - (\frac{24.2}{2} )^{2} }[/tex]

[tex]\sqrt{8556.25 - 146.41}[/tex]

[tex]\sqrt{8409.84}[/tex]

91.705 in

can be rounded to 91.71 in

Since 1 can be expressed as the ratio of two integers (1/1), 1.overline00 is a rational number.

The number 1.overline00 represents a repeating decimal. To understand its nature, let's break it down.

The overline above the zeros indicates that the zeros repeat infinitely. Therefore, 1.overline00 can be represented as 1.000000... with the zeros repeating indefinitely.

1.) Whole number: A whole number is a non-negative integer. Since 1.overline00 is greater than 1, it is not a whole number.

2.) Integer: An integer includes both positive and negative whole numbers, including zero. As 1.overline00 is greater than 1, it is not an integer.

3.) Rational: A rational number can be expressed as the ratio of two integers, where the denominator is not zero. To determine if 1.overline00 is rational, we can convert it into a fraction. Let x = 1.overline00. Multiplying both sides by 100, we get 100x = 100.overline00. Subtracting the original equation from this new equation, we get 100x - x = 100.overline00 - 1.overline00, which simplifies to 99x = 99. Therefore, x = 1. Since 1 can be expressed as the ratio of two integers (1/1), 1.overline00 is a rational number.

4.) Irrational: An irrational number cannot be expressed as the ratio of two integers. Since we have determined that 1.overline00 is rational, it is not irrational.

Since 1 can be expressed as the ratio of two integers (1/1), 1.overline00 is a rational number.

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The probability that Nessie chews up something that is white or a box is 8/11.

Let's find the probability that Nessie chews up something that is white or a box.
1. Determine the total number of items:
2 white plastic bags + 3 brown paper bags + 4 brown boxes + 2 white boxes = 11 items
2. Identify the items that are white or a box:
White items: 2 white plastic bags + 2 white boxes = 4 white items
Boxes: 4 brown boxes + 2 white boxes = 6 boxes
However, since white boxes are included in both white items and boxes, we need to subtract the number of white boxes once to avoid double-counting them.
3. Calculate the probability:
(White items + Boxes - White boxes) / Total items = (4 + 6 - 2) / 11 = 8 / 11
The probability that Nessie chews up something that is white or a box is 8/11.

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The correct statement is "If an appropriate confidence interval does not contain 25%."

To determine whether the pamphlet needs updating, we can construct a confidence interval for the proportion of high school students planning to attend a community college based on the survey results. If the confidence interval does not contain the value stated in the pamphlet (25%), it would suggest that the pamphlet needs updating.

In this case, the sample proportion is 46/150, or 0.3067 (approximately). To construct the confidence interval, we can use the formula for a proportion confidence interval:

p ± z * √(p * (1 - p) / n)

where p is the sample proportion, z is the z-score corresponding to the desired confidence level (95% in this case), and n is the sample size.

Using a z-score of 1.96 (for a 95% confidence level), the confidence interval would be:

0.3067 ± 1.96 * √(0.3067 * (1 - 0.3067) / 150)

Calculating this interval would give us the lower and upper bounds. If this interval contains 25%, then it would suggest that the pamphlet does not need updating. However, if the interval does not contain 25%, it would indicate that the pamphlet needs to be updated.

Therefore, the correct statement is "If an appropriate confidence interval does not contain 25%."

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Answer:

Step-by-step explanation:

Sure, here is the input table for f(x) and g(x) using inputs from 0 to 5:

| Input (x) | f(x) = 25x^(2) | g(x) = 3*3^(x) |

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

| 0         | 0              | 3              |

| 1         | 25            | 9              |

| 2         | 100           | 27             |

| 3         | 225           | 81             |

| 4         | 400           | 243            |

| 5         | 625           | 729            |

As x gets very large, g(x) will have greater output values than f(x). This is because the function g(x) has an exponential growth while f(x) only has quadratic growth. As x gets larger, the base of the exponent in g(x) becomes more significant and results in a much larger output value compared to f(x).

Answer:

y= 5/2

y=2.5

y=2 1/2

Step-by-step explanation:

I hope this helps

By distributive property to write an expression that is equivalent to 12 + 4x is equal to  4 (x + 3) and 2 ( 2x + 6)

The distributive Property states that it is necessary to multiply each of the two numbers by the factor before performing the addition operation when a factor is multiplied by the sum or addition of two terms which quality can be expressed as the following symbol:

A ( B+ C) = AB + AC

We have given an expression as;

12 + 4x

since 4 and 12 both have a common factor of 4.

4x + 12 = 4 (x + 3)

Additionally, given that 4 and 12 both have a factor of 2

4x + 12 = 2 ( 2x + 6)

Therefore, by the distributive property to write an expression that is equivalent to 12 + 4x ;

4 (x + 3) and 2 ( 2x + 6)

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Answer:

Therefore:

a) The area of your slice is 32/3π square inches (exact answer).

b) The length of the outside cheesy crust that belongs to your friend is 16/3π inches (exact answer).

Step-by-step explanation:

a) To find the area of 1/6 of the pizza, we need to determine the area of the entire pizza and then divide it by 6.

The diameter of the pizza (including the cheesy crust) is 16 inches, which means the radius is half of the diameter, so the radius is 16/2 = 8 inches.

The formula for the area of a circle is A = πr², where A is the area and r is the radius.

Therefore, the area of the entire pizza is A = π(8 inches)² = 64π square inches.

To find the area of 1/6 of the pizza, we divide the area of the entire pizza by 6:

Area of 1/6 of the pizza = (64π square inches) / 6

b) The cheesy crust is located on the outer edge of the pizza, forming the circumference of the circle. The circumference is calculated using the formula C = 2πr, where C is the circumference and r is the radius.

The length of the outside cheesy crust that belongs to your friend is 1/6 of the circumference. So, we divide the circumference by 6:

Length of the outside cheesy crust for your friend = (2π(8 inches)) / 6

To get the exact answers, we leave the values in terms of π:

a) Area of 1/6 of the pizza = (64π square inches) / 6 = 32/3π square inches (exact answer)

b) Length of the outside cheesy crust for your friend = (2π(8 inches)) / 6 = 16/3π inches (exact answer)

Therefore:

a) The area of your slice is 32/3π square inches (exact answer).

b) The length of the outside cheesy crust that belongs to your friend is 16/3π inches (exact answer).

Answer:

The correct answer is:

A. squared distances

The surface area of the cylinder, rounded to the nearest square meter, is: D. 142 square meters

The surface area of a cylinder can be calculated by using the formula expressed as:

SA = 2[tex]\pi[/tex]r(h + r), where r is the radius and h is the height.

Given the following:

[tex]\pi[/tex] = 3.14

radius (r) = 2.6 m

height of the cylinder (h) = 6.1 m

Plug in the values:

[tex]\sf SA = 2 \times 3.14 \times 2.6 \times (6.1 + 2.6)[/tex]

[tex]\sf SA \thickapprox 142[/tex] square meters (rounded to the nearest square meter)

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Answer:

look up a slope calculator insert x2 and y-3 for example and it will do it for u

Step-by-step explanation:

The value of (f•g)(5) is 21.

Given are two functions f(x) = 3x+2 and g(x)= √x-1, we need to determine (f•g)(5),

So, firstly determine (f•g)(x),

Therefore,

(f•g)(x) = (3x+2)(√x-1)

Now for, (f•g)(5) put x = 5,

We get,

(f•g)(5) = (3·5+2)(√5-1)

(f•g)(5) = 17 × 1.23

(f•g)(5) = 21

Hence the value of (f•g)(5) is 21.

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Answer: The quadrilateral is not a parallelogram.

Step-by-step explanation:

Slope of any line = (Change in y)/(Change in x)

Slope of LM = (9-6)/(5-(-1)) = 3/6 = 1/2

Slope of LN = (2-6)/(0-(-1)) = -4/1 = -4

Slope of LP = (-2-6)/(-8-(-1)) = -8/-7 = 8/7

Slope of MN = (2-9)/(0-5) = -7/-5 = 7/5

Slope of MP = (-2-9)/(-8-5) = -11/-13 = 11/13

Slope of NP = (-2-2)/(-8-0) = -4/-8 = 1/2

Since slopes of LM and NP are the same, they are parallel lines.

Parallelograms have two sets of parallel lines. However, there only exists one set of parallel lines for this quadrilateral. Thus, this quadrilateral is not a parallelogram.