Find all geometric sequences such that the sum of the first two terms is 24 and the sum of the first three terms is 26.

Answer:x=8

Step-by-step explanation:

3x/2-5=7

Move all terms not containing x to the right side of the equation by adding 5 to both sides

3x/2-5+5=7+5

3x/2=12

Multiply both sides of the equation by 2/3 to isolate x.

3x/2*2/3=12*2/3

x=24/3

x=8

Answer: x= 8

Step-by-step explanation:

3x/2-5=7

3x/2 = 12

3x = 24

x= 8

If you can, please give me a Brainliest, thank you!

The minimum distance that Malia needs on her last throw to win the game is less than 2.12 meters.

In this target game, Malia needs to have the lowest mean distance of all throws to win. The mean distance is calculated by adding up all the distances and dividing by the number of throws.

First, we need to calculate the mean distance of Malia's first 7 throws.

Mean distance = (2 + 3 + 4 + 2 + 5 + 3 + 4) / 7 = 3.14

Now, we know that Malia's mean distance must be less than 3.14 to win the game. Let's call the distance of her last throw x.

The mean distance of all 8 throws will be: (2 + 3 + 4 + 2 + 5 + 3 + 4 + x) / 8

To find the minimum distance that Malia needs on her last throw to win the game, we can set up an inequality:

(2 + 3 + 4 + 2 + 5 + 3 + 4 + x) / 8 < 3.14

Multiplying both sides by 8 gives us:

2 + 3 + 4 + 2 + 5 + 3 + 4 + x < 25.12

Simplifying gives us:

x < 25.12 - 23

x < 2.12

Therefore, the minimum distance that Malia needs on her last throw to win the game is less than 2.12 meters.

Learn more about distance at https://brainly.com/question/15172156

#SPJ11

Answer:

Vertical distance = 410.7

Mean = 520.25

Step-by-step explanation:

When a rectangle is rotated about the y-axis, it creates a solid shape known as a cylindrical shell or a hollow cylinder.

When a rectangle is rotated about the y-axis, each point on the rectangle traces a circular path.  

The resulting shape is a solid formed by the collection of these circular paths, creating a cylindrical shell or a hollow cylinder.

The height of the cylinder corresponds to the length of the rectangle, while the circumference of the cylinder corresponds to the width of the rectangle. The rotation about the y-axis gives the shape a cylindrical appearance, with the y-axis running through the center.

This shape is often used in calculus and geometry to calculate volumes and solve related problems. It is important to note that the rotation about the y-axis assumes that the longer side of the rectangle is aligned parallel to the y-axis.

Learn more about y-axis: brainly.com/question/31223168

#SPJ11

When a rectangle is rotated about the y-axis, it creates a solid shape known as a cylindrical shell or a hollow cylinder.

When a rectangle is rotated about the y-axis, each point on the rectangle traces a circular path.  

The resulting shape is a solid formed by the collection of these circular paths, creating a cylindrical shell or a hollow cylinder.

The height of the cylinder corresponds to the length of the rectangle, while the circumference of the cylinder corresponds to the width of the rectangle. The rotation about the y-axis gives the shape a cylindrical appearance, with the y-axis running through the center.

This shape is often used in calculus and geometry to calculate volumes and solve related problems. It is important to note that the rotation about the y-axis assumes that the longer side of the rectangle is aligned parallel to the y-axis.

Learn more about y-axis: brainly.com/question/31223168

#SPJ11

Answer:

4.9%

But I guess you may round to 5%, just be sure to say that you rounded from 4.9%.

However, there is still a 5% chance that the true value falls outside this range.

Therefore, it is important to keep in mind the margin of error and the level of confidence when interpreting the results of a survey or experiment.

A Harris poll of a random sample of 2,113 adults in the United States in October 2010 reported the proportion of people who believe that stem cell research has merit. The confidence interval represented on the number line below is used to answer the following questions.

As per the given number line, the confidence interval is between 60% and 66%.The confidence interval represents the range of values within which the true population parameter (in this case, the proportion of people who believe in stem cell research) is likely to fall. The level of confidence is the degree of certainty that the true value falls within that range, and it is usually expressed as a percentage.In this case, the confidence interval represents a range of values between 60% and 66%, with a 95% level of confidence.

This means that we can be 95% confident that the true proportion of people who believe in stem cell research falls within this range.In other words, the sample results are a good estimate of the true population proportion, and we can be reasonably certain that the true value falls within the confidence interval.

for such more questions on random sample

https://brainly.com/question/24466382

#SPJ11

Answer:

-8 and 3, or -3 and 8

Step-by-step explanation:

xy = -24

x - y = 11

x = y + 11

y(y + 11) = -24

y^2 + 11x + 24 = 0

(y + 8)(y + 3) = 0

y = -8 or y = -3

x = 3 or x = 8

the numbers are -8 and 3, or -3 and 8

Answer:

michin babo-e daehae museun mal-eulhaneungeoya

Answer:

9

Step-by-step explanation:

the range is the difference between the greatest value and the smallest one. The greatest value in the data set is 33, and the smallest is 24.

So u just subtract 24 from 33:

33 – 24 = 9

and that's your range! hope this helps!

Answer:

7x7=49, so 7

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

because 7 cm as the side length is always the square root of the area in a square.

The 87% confidence interval for the size of the candles is (3.503 ounces, 3.937 ounces).

To calculate the 87% confidence interval, follow these steps:

1. Identify the sample size (n=15), sample mean (3.72 ounces), and standard deviation (0.963 ounces).

2. Determine the critical value (z) for an 87% confidence interval using a standard normal distribution table or calculator. For an 87% CI, the critical value is approximately 1.534.

3. Calculate the standard error (SE) using the formula SE = standard deviation / sqrt(n). In this case, SE = 0.963 / sqrt(15) ≈ 0.248.

4. Multiply the critical value (z) by the standard error (SE) to find the margin of error (MOE): MOE = 1.534 * 0.248 ≈ 0.380.

5. Find the lower limit of the confidence interval by subtracting the MOE from the sample mean: 3.72 - 0.380 = 3.503 ounces.

6. Find the upper limit of the confidence interval by adding the MOE to the sample mean: 3.72 + 0.380 = 3.937 ounces.

So, the 87% confidence interval for the size of the candles is (3.503 ounces, 3.937 ounces).

To know more about confidence interval click on below link:

https://brainly.com/question/13067956#

#SPJ11

The domain of the function y = 2 - √(-3x+2) is (-∞ , 2/3] and the range of the function is (-∞ , 2]  .

In the question ,

it is given that , the function is ⇒ y = 2- √(-3x+2) .

For Domain ,

we know that the square root function is defined only when the number inside the root is non negative .

that means ,

-3x \(+\) 2 ≥ 0

Subtracting 2 from both the sides ,

we get ,

-3x ≥ -2

x ≤ 2/3

the Domain is (-∞ , 2/3] .

For range , we know that the root function value in always non negative .

√(-3x + 2) ≥ 0

Multiply by -1 on both sides

we get ,

-√(-3x + 2) ≤ 0

Adding 2 to both the sides

2 - √(-3x + 2) ≤ 2

y ≤ 2

the range is (-∞ , 2] .

Therefore , the domain is (-∞ , 2/3]   and the range is (-∞ , 2] .

How do we find the domain and range of the function y = 2- √(-3x+2) ?

Learn more about Domain and Range here

https://brainly.com/question/17107121

#SPJ4

Answer: $130

Step-by-step explanation:

Simple interest is calculated as:

= PRT/100

where P = principal = $5200

R = Rate = 5%

T = Time = 2 years

S.I = (PRT)/100

= (5200 × 5 × 2)/100

= 52000/100

= $520

Assuming the loan was obtained for 2 1/2 years, the simple Interest will be:

= (5200 × 5 × 2.5)/100

= 65000/100

= $650

This means he'll have saved:

= $650 - $520

= $130

Answer:

Step-by-step explanation:

question doesnt make sense

Answer:

Step-by-step explanation:

first we are told that side and ae and a f are the same

so that means one side of each triangle is the same

next we are told that that the lines coming off of those sides are both right angles. so we know these are both right triangles

and b/c both of those angle are right angles... the sides ab and ac have to also be the same length.. or the angle could not be a right angle

therefore since two sides are the same length then all 3 must be the same lengths

and b/c all three are the same these two triangles are the same .. congruent

Answer:

It is the first one I am pretty sure about it gl for the results of this exam

Answer:

turn them into equivalent fractions with a common denominator.

2/9 and 5/6 common denominator that we can use is 18.

what you do to the denominator must be done to the numerator.

so to get from 9 to 18 we multiply by 2. this needs to be done to the numerator.

2 X 2 = 4 the fraction should now be 4/18

to get from 6 to 18 we multiply by 3 again do same to numerator. should now be 15/18

now compare the two

4/18 and 15/18. now we know that 5/6 is bigger than 2/9.

Hello !

Answer:

\(\Large \boxed{\sf r=\frac{3}{2} }\)

Step-by-step explanation:

Let's remember :

We know that the volume of the sphere is equal to half its surface area.

\(\sf V_{sphere}=\frac{1}{2} A_{sphere}\\\\\sf \frac{4}{3}\pi r^3=\frac{1}{2} 4\pi r^2\\\\\sf \frac{4}{3}\pi r^3=2\pi r^2\)

Let's solve this equation for r.

First, substract \(\sf 2\pi r^2\)  from both sides :

\(\sf \frac{4}{3} \pi r^3-2\pi r^2=0\)

We can now factorize by taking out the highest common factor: 2r²

\(\sf 2r^2(\frac{2}{3} \pi r-\pi )=0\)

We can use the zero-product property.

There are two solutions :

The first solution is absurd : The radius of a sphere cannot be 0.

We conclude that we must keep the second solution.

Have a nice day ;)

after 14 years, there will be approximately 1.97g of the radioactive substance remaining.

To solve this problem, we can use the concept of exponential decay for radioactive substances. The decay of a radioactive substance can be modeled by the equation:

N(t) = N₀ * e^(-kt),

where N(t) is the amount of substance at time t, N₀ is the initial amount of substance, e is the base of the natural logarithm, k is the decay constant, and t is the time elapsed.

In this case, we are given that the initial amount N₀ is 10g and the amount after 9 years N(9) is 5g. We can use this information to find the value of k.

5 = 10 * e^(-9k).

Divide both sides of the equation by 10:

0.5 = e^(-9k).

Take the natural logarithm of both sides:

ln(0.5) = -9k.

Solve for k:

k = ln(0.5) / -9.

Now that we have the value of k, we can use it to find the amount of substance after 14 years, N(14):

N(14) = N₀ * e^(-kt).

N(14) = 10 * e^(-ln(0.5) / -9 * 14).

N(14) = 10 * e^(14 * ln(0.5) / 9).

N(14) ≈ 10 * 0.197 = 1.97.

Therefore, after 14 years, there will be approximately 1.97g of the radioactive substance remaining.

To know more about Exponential Decay related question visit:

https://brainly.com/question/2193799

#SPJ11

Answer:

g = 5c

5*c = g

g/5 = c

Step-by-step explanation:

g = grandfather

c = carl

Answer:

The age of Carl's grandfather is a composite number.

Carl's age is a factor of the age of his grandfather.

The number 5 is a factor of the age of Carl's grandfather.

The correct option b. 0.004629 for  the probability of observing a 1 three times in a row.

Probability of an event = (Number of favorable events) /   (total number of event).

P(B) = (Event B) / (total number of event).

The number of times the dice are rolled has no bearing on the outcome of the roll.

The likelihood of receiving 1 is 1/6.

The likelihood of obtaining 1 three times in a row is equal to the likelihood of getting 1 the first time, the second time, and the third time.

Receiving 1 three times in succession has a probability;

= 1/6 x 1/6 x 1/6

= 1/216.

As a result, there is a 0.463% chance that you'll get 1 three times in a row.

To know more about the probability, here

https://brainly.com/question/13604758

#SPJ4

Answer:

There are no questions below .

The slope (m) and y-intercepts are:

2. (m) is -1 and m = 4;       3. m = 2 and the b = 1.     5. m = 1 and m = -2;

6. m = -3 and b = -5.       8. m = 3 and b = -1.          9. m = -1 and b = 3.

The value of the slope in an equation is represented as m while the y-intercept is represented as b, where the equation is in the form of y = mx + b, in slope-intercept form.

In the equation y = -x + 4, the slope (m) is -1 and the y-intercept is 4.

In the equation y = 2x + 1, m = 2 and the b = 1.

In y = x - 2, the m = 1 and the y-intercept is -2.

In y = -3x - 5, m = -3 and b = -5.

In y = 3x - 1, m = 3 and b = -1.

In y = -x + 3, m = -1 and b = 3.

The graph of y = -x + 4 is in figure 1, while that of y = 2x + 1 is in figure 2.

The graph of y = x - 2 is in figure 3, while that of y = -3x - 5 is in figure 4.

Learn more about Slope and Y-intercept of an Equation on:

https://brainly.com/question/29863316

#SPJ1

Answer:

I

Step-by-step explanation:

I am not sure but I will tell if u would like me to say

Answer:

d

Step-by-step explanation:

i think i helped. have a nice day

1) Probability of drawing a six or club:

  a. Count the number of favorable outcomes (sixes and clubs) and the total number of possible outcomes (cards in the deck).

  b. Divide the favorable outcomes by the total outcomes to calculate the probability.

2) Probability of being dealt 5 non-face cards:

  a. Count the number of favorable outcomes (non-face cards) and the total number of possible outcomes (cards in the deck).

  b. Calculate the combinations of choosing 5 non-face cards and divide it by the combinations of choosing 5 cards to find the probability.

1) Probability of drawing a six or club:

a. Determine the total number of favorable outcomes:

  i. There are 4 sixes in a deck and 13 clubs.

  ii. However, one of the clubs (the 6 of clubs) has already been counted as a six.

  iii. So, we have a total of 4 + 13 - 1 = 16 favorable outcomes.

b. Determine the total number of possible outcomes:

  i. There are 52 cards in a standard deck.

c. Calculate the probability:

  i. Probability = Favorable outcomes / Total outcomes

  ii. Probability = 16 / 52

  iii. Probability = 4 / 13

  iv. Therefore, the probability of drawing a six or club is 4/13.

2) Probability of being dealt 5 nonface cards:

a. Determine the total number of favorable outcomes:

  i. There are 40 non-face cards in a deck (52 cards - 12 face cards).

  ii. We need to choose 5 non-face cards, so we have to calculate the combination: C(40, 5).

b. Determine the total number of possible outcomes:

  i. There are 52 cards in a standard deck.

  ii. We need to choose 5 cards, so we have to calculate the combination: C(52, 5).

c. Calculate the probability:

  i. Probability = Favorable outcomes / Total outcomes

  ii. Probability = C(40, 5) / C(52, 5)

  iii. Use the combination formula to calculate the probabilities.

  iv. Simplify the expression if possible.

Therefore, the steps involve determining the favorable and total outcomes, calculating the combinations, and then dividing the favorable outcomes by the total outcomes to find the probability.

Learn more about card deck visit

brainly.com/question/32862003

#SPJ11

The volume of a sphere with a radius of 7 cm (or diameter of 12 cm) is 904.32 cubic centimeters.

To find the volume of a sphere with a radius of 7 cm, we can use the formula:

V = (4/3) * π * r^3

where V represents the volume and r represents the radius. However, you mentioned that the diameter of the sphere is 12 cm, so we need to adjust the radius accordingly.

The diameter of a sphere is twice the radius, so the radius of this sphere is 12 cm / 2 = 6 cm. Now we can calculate the volume using the formula:

V = (4/3) * π * (6 cm)^3

V = (4/3) * 3.14 * (6 cm)^3

V = (4/3) * 3.14 * 216 cm^3

V = 904.32 cm^3

For more such questions on volume

https://brainly.com/question/463363

#SPJ8

The equation of the line which is perpendicular to this line would be 3x - 2y = 13.

The equation of a parallel line to the line would be 2x + 3y = 0

The slope of the line perpendicular to this would be the negative reciprocal of -2/3, which is 3/2.

So the equation of the perpendicular line is:

y - ( -2 ) = 3/2 (x - 3)

y + 2 = 3/2x - 9/2

2y + 4 = 3x - 9

3x - 2y = 13

The slope of the line parallel to the given line would be equal to the slope of the given line, which is -2/3.

So the equation of the parallel line is:

y - (-2) = -2/3 (x - 3)

y + 2 = -2/3x + 2

y = -2/3x

2x + 3y = 0

Find out more on perpendicular lines at https://brainly.com/question/30011380

#SPJ1

The perimeter of the figure is 53.7.

Perimeter can be defined as the total distance around a object.

To calculate the perimeter of the the figure below, we use the formula below.

Formula:

From the diagram,

Given:

Substitute these values into equation 1

Hence, the perimeter of the figure is 53.7

Learn more about perimeter here: https://brainly.com/question/19819849

#SPJ1