Algebra - Make x the subject of the equation

Can someone please show me step by step how to solve this equation please. The correct order of operations.

Answer:

40 people are currently planning to attend the reunion.

Step-by-step explanation:

If we don't know how many people are coming, we can call that number x.

If those people split the cost ($200) it will be 200/x.

If 10 more people come, the head count is now x+10.

So the cost becomes 200/(x+10)

The cost when more people pitch in is less money per person. If fewer people split the cost its more per person. They are saying the difference here is $1.

So we can write an equation.

200/x = 200/(x+10) + 1

OR

200/x - 1 = 200/(x+10)

Cross multiply. This gives you a quadratic equation so factor to solve or use Quadratic Formula. See image. It shows how to solve by factoring.

see images. There are 2 images.

True, there exists a function f such that f(x) > 0, f'(x) < 0, and f"(x) > 0 for all x.

An example of such a function is[tex]f(x) = e^(-x)[/tex], where e is the base of the natural logarithm (approximately 2.718).

Let's verify the given conditions:

f(x) > 0:

Since e^(ax) is always positive for any real value of x and any constant a, [tex]e^(-x)[/tex]is also always positive for any real value of x.

f'(x) < 0:

To find the first derivative, apply the chain rule: [tex]f'(x) = -e^(-x). As e^(-x)[/tex] is always positive, the derivative

[tex]f'(x) = -e^(-x)[/tex] is  always negative for all x.

f"(x) > 0:

To find the second derivative, apply the chain rule again:

[tex]f"(x) = e^(-x). As e^(-x)[/tex]is always positive, the second derivative[tex]f"(x) = e^(-x)[/tex] is always positive for all x.

Thus, it is true that there exists a function f with the given conditions.

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The function [tex]f(x) = e^(-x)[/tex] meets all the given conditions.

True. There exists a function f such that [tex]f(x) > 0, f'(x) < 0, and f"(x) > 0[/tex] for all x. One example of such a function is [tex]f(x) = e^(-x)[/tex].
True. There exists a function f(x) that satisfies the given conditions: f(x) > 0, f'(x) < 0, and f''(x) > 0 for all x.

Consider the function [tex]f(x) = e^(-x)[/tex]. This function has the following properties:

1. f(x) > 0 for all x because the exponential function is always positive.
2. [tex]f'(x) = -e^(-x)[/tex]which is always negative because e^(-x) is always positive, and the negative sign in front makes the derivative negative.
3. [tex]f''(x) = e^(-x)[/tex]which is always positive.

Thus, the function [tex]f(x) = e^(-x)[/tex]meets all the given conditions.

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Answer: If you want me to evaluate its 18x - 2

Hope it helped :D

Answer:

We can calculate the difference between Lori's and Melissa's purse masses by subtracting Melissa's purse mass from Lori's purse mass:

Lori's purse mass = 16 ounces

Melissa's purse mass = 11 ounces

Difference = Lori's purse mass - Melissa's purse mass

Difference = 16 ounces - 11 ounces

Difference = 5 ounces

Therefore, the difference between Lori's and Melissa's purse masses is 5 ounces.

Thus, the values of x,y, and z for the similar triangles are obtained:

Part A: y = 6.70; z = 13.41 and x = 6.

Part B: z = 17.88 ; y = 35.77 and x = 32.

Congruent triangles and similar triangles are two distinct but closely related concepts. There are two different kinds of similar triangle problems: those that ask you to determine whether a set of triangles is similar and those that ask you to determine the angles and side length of similar triangles that are missing.

Part A: using similarity of the triangle, taking the ratios of corresponding side.

y/15 = x/z = 3/y

Consider

y/15 = 3/y

y² = 15*3

y² = 45

y = 6.70

Now,

applying Pythagorean theorem:

y² = 3² + x²

x² = y² - 3²

x² = 45 - 9

x² = 36

x = 6

And,

z² = 12² + x²

z² = 144 + 36

z² = 180

z = 13.41

Part B:using similarity of the triangle, taking the ratios of corresponding side.

z/(x + 8) = 16/y = 8/x  ... eq 1

applying Pythagorean theorem:

z² = 16² + 8²

z² = 256 + 64

z² = 320

z = 17.88

Now, from eq 1

z² = 8(8 +x)

320 = 64 + 8x

8x = 320 - 64

x = 256/8

x = 32

Now,

applying Pythagorean theorem:

y² = 16² + x²

y² = 256 + 32²

y² = 1280

y = 35.77

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Answer:

29 cm

Step-by-step explanation:

We Know

Pinocchio’s nose is 9cm long.

His nose grows by 6cm if he lies.

His nose shortens by 2cm if he tells the truth.

He lies 4 times and truth 2 times.

We Take

9 + (6 x 4) - (2 x 2) = 29 cm

So, Pinocchio's nose now is 29 cm.

Answer:

29 cm

Step-by-step explanation:

(6x4) + 9

(6x4) = 24 cm

24 + 9 = 33 cm

(2x2) - 33

(2x2) = 4 cm

4 - 33 = 29 cm

I hope this helps!

The sine ratio of for angle A is 4/5 and the right option is B. 4/5.

Sine ratio is the ratio of the length of the opposite side divided by the length of the hypotenuse.

The formula for the sine ratio of angle A is given in the formula below

Formula:

From the diagram.

Given:

Substitute these values into equation 1

Hence, the right option is B. 4/5.

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$682.50

Simple interest only builds on the initial deposit.

Interest Formula

Unlike compound interest, the change per time period is constant for simple interest. This means that simple interest can be calculated through the formula:

In this formula, I represents the amount of interest earned. P is the principle, which is the initial deposit. r is the rate of interest expressed as a decimal. t is the time in years.

Solving For Interest

Now, we can use the information we were given to solve for the amount of interest earned. The question states that the principle is $7,000. From the table, we can tell that the rate is 0.0325. Finally, t is 3 years because 36 months = 3 years. Then, plug these values into the formula.

This means that the account at Victory Bank would earn $682.50 over the course of 3 years.

If a 36-oz bottle of water costs $2. 88, then the cost per ounce is $0.08

Unitary method is a mathematical method used to find the value of a single unit of a quantity, by dividing the total value of the quantity by the number of units.

To find the cost per ounce, we can use the unitary method which involves dividing the total cost by the total number of ounces:

Cost per ounce = Total cost ÷ Total ounces

Total cost of a 36-oz bottle of water = $2.88

Total ounces in a 36-oz bottle of water = 36 oz

Therefore, the cost per ounce of water can be calculated as

Cost per ounce = $2.88 ÷ 36 oz

Cost per ounce = $0.08 per ounce

So the cost per ounce of water is $0.08

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Answer:

≈ $26

Step-by-step explanation:

13% = 0.13

199.99 x 0.13 = $25.9987

So, 13% markup is ≈ $26

Tyler will need to score an 85 on Test 6 to finish the year with an average score of 75.

To calculate the score that Tyler needs to get on Test 6 to achieve an average score of 75, we need to use the following formula

(average score) = (total points earned / total number of tests)

Let's assume that Tyler has taken five tests so far, and his total points earned are X. Also, let's assume that Test 6 is worth Y points.

Therefore, the equation becomes:

75 = (X + Y) / 6

Multiplying both sides by 6, we get:

X + Y = 450

Now, let's say Tyler's scores on his first five tests are as follows

Test 1: 65, Test 2: 72, Test 3: 70, Test 4: 78 and Test 5: 80

To find out how many points Tyler has earned so far (X), we simply add up his scores on the first five tests

X = 65 + 72 + 70 + 78 + 80

X = 365

Substituting this value of X in the equation we derived earlier, we get

365 + Y = 450

Solving for Y, we get:

Y = 85

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Answer:

p < -2

Step-by-step explanation:

Answer:

The answer is -2

Step-by-step explanation:

4/5-1/2p>9/5

C.L.T

-1/2p>9/5-4/5

-1/2p>5/5

-1/2p=1

-p/2>1

-p=2

p= -2

The total number of oranges used in Bertha's pyramid is 24 + 6 + 2 + 1 = 33 oranges.

To calculate how many oranges are used in Bertha's pyramid, we first need to find out how many oranges are in each

layer of the pyramid. Since the base of the pyramid is a rectangle that is 4 oranges by 6 oranges, there are a total of 4 x 6 = 24 oranges in the base layer.

For the second layer of the pyramid, each orange rests on 4 oranges below it.

Since the base layer has 24 oranges, there will be 24 / 4 = 6 oranges in the second layer.

For the third layer, each orange again rests on 4 oranges below it.

So there will be 6 / 4 = 1.5 oranges in the third layer.

Since we cannot have half an orange, we round up to 2 oranges.

Finally, the top layer of the pyramid will consist of a single orange.

Therefore, the total number of oranges used in Bertha's pyramid is 24 + 6 + 2 + 1 = 33 oranges.

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The angle G is (1/18) th {or (20/360)th } fraction of complete circle.

The angle G is measured to be 20°.

We know, the total angle of a complete circle is 360°.

Thus, by simple fraction we can say,

The angle G fraction of complete circle is = 20° / 360°

Simplifying we get, the angle G fraction of complete circle is = 1/18

Hence the angle G is (1/18 )th fraction of a complete circle.

In mathematical term, fractions are defined as a part of the whole. In other words, fraction is referred to the ratio of the value observing to the whole set of values.

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Step-by-step explanation:

let's first sort the data points from low to high :

42, 68, 70, 72, 74, 75, 79, 80, 82, 83, 84, 85, 86, 87, 91, 92, 94, 95, 97, 98

67.

the mean score is the sum of all data points divided by the number of data points :

1634/20 = 81.7

=> BC is correct

68.

the median is the number in the sorted list, what half of the data points are lower, and the other half higher.

in case of an even number of data points, it is the mean value of the 2 central data points.

in our case these are 83 and 84. the mean value between these two numbers is 83.5.

=> BE is correct

69.

the mode is the most frequent number among the data points.

but all scores appear only once.

so, some say, the mode is the set of all data points.

or, others say, there is no mode (like your teacher, apparently)..

=> ABC is correct.

70.

mean absolute deviation (MAD) of a data set is the average distance between each data value and the mean.

so, now we are creating a new data set : the individual distances of the original data points to their mean value :

39.7, 13.7, 11.7, 9.7, 7.7, 6.7, 2.7, 1.7, 0.3, 1.3, 2.3, 3.3, 4.3, 5.3, 9.3, 10.3, 12.3, 13.3, 15.3, 16.3

the man value for these is the MAD of the original data points :

187.2/20 = 9.36

=> B is correct

71.

the range is the difference between the highest and lowest values in a set of numbers.

so, in our case that is

98 - 42 = 56

=> AD is correct

72.

quartiles are the values that divide a list of numbers into quarters (4 equally long parts).

we have here 20 numbers, so all Qs are between 2 numbers.

Q1 is between the 5th and the 6th number (and again, the mean value between these two numbers is the result) :

Q1 = (74 + 75)/2 = 74.5

=> AE is correct

73.

as above, just for Q3 it is between the 15th and 16th number :

Q3 = (91 + 92)/2 = 91.5

=> DE is correct

74.

the interquartile range (IQR) contains the second and third quartiles, or the middle half of your data set.

while the range gives you the spread of the whole data set, the interquartile range gives you the range of the middle half of a data set - so, between Q1 and Q3 :

91.5 - 74.5 = 17

=> E is correct

75.

outliers are extreme values that differ from most other data points in a dataset (much lower or higher than the others).

outliers are therefore values at the extreme ends of a dataset.

often we see at least some of them right away, like 42 in our set.

but are there any others ?

there are some guidelines like building an upper and lower "fence" (or limit), and any value beyond these limits are great candidates for being outliers.

upper fence = Q3 + 1.5 × IQR = 91.5 + 1.5×17 = 117

we have no values higher than 117.

lower fence = Q1 - 1.5 × IQR = 74.5 - 1.5×17 = 49

we have one value (as expected) lower than that (42), which makes this a confirmed outlier.

=> AB is correct.

If we shuffle a deck of cards ,turn over first card, then

(a) "Sample-Space" of this experiment is set of all 52 cards.

(b) Number of outcomes in event that the first card is a heart is 13 .

Part (a) : The "Sample-Space" of this experiment refers to all possible outcomes that occur when "first-card" from a shuffled deck of cards is turned over.

In a "standard-deck" of 52 playing cards, the sample space consist of all 52 cards, which includes 4 suits (hearts, diamonds, clubs, spades) each with 13 cards (Ace - 10, Jack, Queen, King).

So, the sample space of this experiment will be set of all 52 possible cards that could be turned over as "first-card".

Part (b) : The event that "first-card" is a heart will consist of all outcomes where the first card turned over is a heart.

In a "standard-deck" of 52 "playing-cards", there are 13 hearts (Ace of Hearts, 2 of Hearts, 3 of Hearts, ..., 10 of Hearts, Jack of Hearts, Queen of Hearts, and King of Hearts).

Therefore, there are 13 outcomes in the event .

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The given question is incomplete, the complete question is

Shuffle a deck of cards and turn over the first card.

(a) What is the sample space of this experiment?

(b) How many outcomes are in the event that the first card is a heart?

Answer:

2.36 miles

Step-by-step explanation:

radius, r = 3 miles∅ = 45°Length of an arc = ∅/360 * 2πr= 45/360 * 2 * 3.14 * 3= 2.36 miles

Answer:

B

B

A

B

D

C

Step-by-step explanation:

5. B

65 = teachers

15 = principal

65/80 = 81.25

If there's is a total of 900 people, find 81.25 (number of teachers)

=731.25

=731

6. B

The best graphical representation for the teacher's data would be a histogram. A histogram is a graph that displays the distribution of continuous data, such as the number of students who prefer a particular subject. It shows the frequency of each interval, or bin, of values.

A stem-and-leaf plot is typically used for small datasets and displays each data point. A circle graph, also known as a pie chart, is used to show how different parts make up a whole and is not appropriate for showing the distribution of preferences among the students. A box plot, also known as a box-and-whisker plot, is used to display the distribution of data, but it may not be as useful for showing the specific frequencies of each preference as a histogram would be.

7) A

There's an image for it I attached

8) B

The correct circle graph that represents the data in the table is option B) circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent.

In the given table, the number of visitors for each type of transportation is given. To create a circle graph, we need to convert the given numbers to percentages. Then, we can use these percentages to determine the angle of each section in the circle graph.

Using the given numbers, we can calculate the percentage of visitors for each transportation type as follows:

Walk: (120/300) x 100 = 40%

Bicycle: (24/300) x 100 = 8%

Car Service: (45/300) x 100 = 15%

Bus: (30/300) x 100 = 10%

Subway: (81/300) x 100 = 27%

Option B) correctly represents these percentages in a circle graph.

9) D

The best prediction about the scoops of ice cream the college will need is option D) The college will have about 1,440 students who prefer ice cream.

To make this prediction, we need to use the information given in the table and assume that the entire student body has the same preferences as the sample of 225 students.

According to the table, 81 out of 225 students prefer ice cream.

To estimate the number of students who prefer ice cream in the entire student body of 4,000 students, we can use proportions.

81/225 = x/4000

Multiplying both sides by 4000, we get:x = 81/225 x 4000 = 1,440

Therefore, the college will have about 1,440 students who prefer ice cream, and they will need to prepare that many scoops.

10) C

The drive-thru that typically has more wait time is option C) Super Fast Food, because it has a larger median.

The median is the middle value when a set of data is arranged in order. In this case, the median wait time for Super Fast Food is 12 minutes, and the median wait time for Burger Quick is 15.5 minutes.

This means that half of the customers at Super Fast Food waited less than 12 minutes, while half of the customers at Burger Quick waited less than 15.5 minutes.

Therefore, the wait time at Super Fast Food is typically shorter than at Burger Quick.

The mean, on the other hand, is influenced by outliers or extreme values, and it is not as robust a measure of central tendency as the median. Therefore, we cannot determine which drive-thru typically has more wait time based on the mean alone.

The means of a stock that has a beta measure of 2.5 is 2.5%.

A beta measure of 2.5 indicates that the stock is 2.5 times as volatile as the market.

This means that if the market goes up by 1%, the stock is expected to go up by 2.5%.

The beta measure is a measure of the volatility of a stock relative to the market.

If the market goes down by 1%, the stock is expected to go down by 2.5%.

Therefore,

The stock is considered to be more risky than the average stock in the market.

A beta measure of 2.5 indicates that the stock is 2.5 times as volatile as the market.

This means that if the market goes up by 1%, the stock is expected to go up by 2.5%.

Conversely, if the market goes down by 1%, the stock is expected to go down by 2.5%.

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The value of the given expression -0.4( -6g - 9h ) - 2h - 0.2( -5h + 3g ) in the simplest form  is equal to  1.8g + 2.6h.

The expression is equal to,

-0.4( -6g - 9h ) - 2h - 0.2( -5h + 3g )

Apply distributive law multiplication over addition.

A ( B + C ) = A × B + A × C

Simplify the expression by first distributing the -0.4 and -0.2 coefficients to the terms inside the parentheses,

= (-0.4 × -6g  + 0.4 × 9h ) -2h - ( 0.2 × -5h  + 0.2 × 3g )

= 2.4g + 3.6h - 2h + h - 0.6g

Combine like terms,

= (2.4g - 0.6g) + (3.6h - 2h + h)

= 1.8g + 2.6h

Therefore, the simplest form of the expression is 1.8g + 2.6h.

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The above question is incomplete, the complete question is:

Rewrite in simplest terms:

− 0. 4 ( − 6 g − 9 h ) − 2 h − 0. 2 ( − 5 h + 3 g )

Answer: question#7 is 7/12

question#8 is 1  3/8

question#5 is 1/2

question#6 is 12

question#9 is 1  1/6

question#10 is 31/40

question#11 is 3/4

Step-by-step explanation: give brainliest

Question #5: Option A, [tex]\frac{1}{2}[/tex]

Question #6: Option A, 12

Question #7: Option A, [tex]\frac{7}{12}[/tex]

Question #8: Option D, [tex]1\frac{3}{8}[/tex]

Question #9: Option D, [tex]1\frac{1}{6}[/tex]

Question #10: [tex]\frac{31}{40}[/tex]

Question #11: [tex]\frac{3}{4}[/tex]

Pls mark brainliest

Step-by-step explanation:

Each term goes UP by 4 from the one before it

 common difference,   d = 4

Answer:

-2

Step-by-step explanation:

The explanation is in the picture

Answer:

Jar 2 has the greatest unit price. B is correct.

Step-by-step explanation:

Jar 1: $1.60/16 oz = 10¢/ounce

Jar 2: $2.40/20 oz = 12¢/ounce

Jar 3: $2.64/24 oz = 11¢/ounce

Jar 4: $2.88/32 oz = 9¢/ounce

Jar 2 has the greatest unit price, so the correct answer is B.

The value of x in the expression is 3 / 2.

The value of x in the expression can be found as follows:

Therefore, the quotient rule can be used to find the value of quotient x in the expression as follows:

q⁵ × q²ˣ = q¹⁰ ×  q⁶ / q⁸

Using the quotient rule

[tex]A^{x} X A^{y} = A^{x + y}[/tex]

Therefore,

q⁵ × q²ˣ = q¹⁰ ×  q⁶ / q⁸

q⁵⁺²ˣ = q¹⁶ / q⁸

q⁵⁺²ˣ = q⁸

cancel the base

5 + 2x = 8

2x = 8 - 5

2x = 3

divide both sides of the equation by 2

x = 3 / 2

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Systematic sampling is a type of probability sampling method where every nth item in a population is selected for inclusion in the sample.

For example, if a researcher wanted to select a systematic sample of 100 students from a school population of 1,000 students, they would randomly select one of the first 10 students (1/10th of the population) and then select every 10th student thereafter until they reach 100. Systematic sampling is often used when the population is too large to enumerate and it is more efficient than simple random sampling. However, it is important to ensure that the sampling interval is not biased in any way, otherwise the sample may not be representative of the population.

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Systematic sampling is a relatively easy and quick method of sampling, as it requires less effort and time than other methods such as stratified or cluster sampling.

The starting point is truly random, and that the interval selected does not create any bias in the sample.

Systematic sampling is a method of selecting a sample from a population using a system or a pattern.

It involves selecting every nth item or person from the population after a random starting point has been determined.

To perform systematic sampling, the first item or individual in the sample is randomly selected from the population.

Then, the remaining items or individuals are selected at regular intervals, such as every 10th or 20th item or individual.

The interval is calculated by dividing the population size by the desired sample size.

A researcher wants to select a sample of 100 from a population of 1000, the interval would be. [tex]1000/100 = 10.[/tex]

The researcher would randomly select the first item or individual from the population, and then select every 10th item or individual thereafter until the desired sample size is reached.

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Welch's two-sample t-test indicates that the average of Load Return's population is significantly greater than the average of No Load Return's population, with a large effect size.

The null hypothesis (H0) that the two population means are equal is rejected as the p-value (0.005) is less than the chosen significance level (α=0.05). This indicates that the chance of a Type 1 error is small, and the alternative hypothesis (H1) that the average of Load Return's population is greater than the average of No Load Return's population is supported.

The test statistic (T=-2.646) falls outside the 95% critical value accepted range, which further supports the rejection of H0. The effect size (0.68) is considered large, indicating that the difference between the two population means is substantial.

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Complete Question:

use the 60 mutual funds in the table below to conduct the hypothesis test. what is the p value? p value is (to 4 decimals)

The type of sampling the principal can use is systematic sampling.

Sampling means selecting the group that you will actually collect data from in your research. For example, if you are researching the opinions of students in a university, you could survey a sample of 50 students.

Systematic sampling is a probability sampling method where researchers select members of the population at a regular interval.

Therefore , with the definition of systematic sampling, it is best for the principal to use a method of systematic sampling for the procedure.

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The standard deviation of the ACT scores is approximately 4.2.

Standard deviation is a measure of the amount of variation or dispersion in a set of data values. It indicates how much the data values deviate, on average, from the mean (or average) of the data set. A higher standard deviation indicates greater variability or spread in the data, while a lower standard deviation indicates less variability or spread.

According to the given information:

To find the standard deviation of ACT scores, we can use the given information about the mean and the percentage of scores above a certain threshold.

Given:

Mean (μ) = 21.4

Percentage of scores above 26 = 15%

Since the distribution is approximately normal, we can use the Z-score formula to find the Z-score corresponding to the given percentage. The Z-score is the number of standard deviations a particular value is from the mean in a normal distribution.

Z-score formula:

Z = (X - μ) / σ

Where:

Z = Z-score

X = Value (in this case, 26)

μ = Mean (21.4)

σ = Standard deviation (to be found)

We can rearrange the formula to solve for σ:

σ = (X - μ) / Z

Substituting the given values:

X = 26

μ = 21.4

Z = Z-score corresponding to 15% (which can be found using a standard normal distribution table or a Z-score calculator)

Assuming a standard normal distribution table or calculator gives us a Z-score of approximately 1.04 for a percentage of 15%, we can plug in the values:

σ = (26 - 21.4) / 1.04

σ = 4.4 / 1.04

σ ≈ 4.2 (rounded to the nearest tenth)

So, the standard deviation of the ACT scores is approximately 4.2.

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