need help with these two questions when anyone can do so, thanks.

The inverse of a function is the relation that is formed when the function is transformed over the line [tex]y=x[/tex]

Explanation:

The inverse can be found algebraically by switching x for y and y for x in the equation. You must then isolate y.

[tex]f(x)= 5x + 10[/tex]

[tex]y= 5x + 10[/tex]

[tex]x= 5x + 10[/tex]

[tex]x-10=5y[/tex]

[tex]\dfrac{x-10}{5}=y[/tex]

So, [tex]f^{-1}(x)=\dfrac{x-10}{5}[/tex]

The probability of drawing two yellow marbles without replacement is approximately 0.412 or 41.2%.

What is probability ?

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. Probability is used to make predictions, analyze risks, and make decisions in various fields such as science, economics, and finance.

The probability of drawing a yellow marble on the first draw is 9/14, since there are 9 yellow marbles out of a total of 14 marbles in the bag. Since the first marble is not replaced before the second draw, there will be 8 yellow marbles left in the bag out of a total of 13 marbles.

So, the probability of drawing a yellow marble on the second draw, given that the first marble was yellow, is 8/13.

To find the probability of both marbles being yellow, we need to multiply the probability of drawing a yellow marble on the first draw by the probability of drawing a yellow marble on the second draw, given that the first marble was yellow:

P(both yellow) = P(first yellow) x P(second yellow | first yellow)

= 9/14 x 8/13

= 0.412

Therefore, the probability of drawing two yellow marbles without replacement is approximately 0.412 or 41.2%.

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The dimensions of the bookmark  length = (-18 + 2sqrt(117))/9 cm

A quadratic equation is an equation of the form:

ax² + bx + c = 0

where x is the variable, and a, b, and c are constants, with a ≠ 0.

The term "quadratic" comes from the fact that the highest power of x in the equation is 2 (i.e., x is raised to the second power).

Quadratic equations can be solved using a variety of methods, including factoring, completing the square, and using the quadratic formula.

Let's assume the length of the bookmark to be 'l' and the width to be 'w'.

We know that the perimeter of a rectangle is given by:

Perimeter = 2(length + width)

Substituting the values, we get:

18 = 2(l + w) --- (1)

We also know that the area of a rectangle is given by:

Area = length x width

Substituting the values, we get:

18 = l x w --- (2)

We can use equation (2) to solve for one variable in terms of the other:

l = 18/w

Substituting this in equation (1), we get:

18 = 2(18/w + w)

Simplifying, we get:

9 = 9/w + w

Multiplying both sides by 'w', we get:

w² + 9w - 18 = 0

Using the quadratic formula, we get:

w = (-9 + √(117))/2 or w = (-9 - √(117))/2

Since the width of the bookmark can't be negative, we discard the second solution.

Therefore, the width of the bookmark is:

w = (-9 + √(117))/2

We can use equation (2) to find the length of the bookmark:

l = 18/w

Substituting the value of w, we get:

l = 18/(-9 + √(117))

Simplifying, we get:

l = (-18 + 2√(117))/9

Therefore, the dimensions of the bookmark are:

length = (-18 + 2√(117))/9 cm

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Answer:

Step-by-step explanation:

14 - 9x ≥ 50

-9x ≥ 50 - 14

-9x ≥ 36

x ≤ -4

Therefore, the solution to the inequality is x ≤ -4.

Answer: 3.5

Step-by-step explanation:

Graphing calculator

You can also solve for the vertex by doing -b/2a (x value of vertex) and then plug that in for t to get the y value.

Answer:

Step-by-step explanation:

We know the the total of angles for a triangle is 180 degrees.

So in this case we'd want to set up adding all of our angles and setting them equal to 180

17 + 126 + b = 180

then solve for b

143 + b = 180

b = 37 degrees

So the answer would be 37 degrees for angle b

Max's plan gives a larger revenue, so it is the better plan.

We know that they have a total of 360 tangerines, Holly says that they should put 24 tangerines in each bag and sell each bag for $1.50

If they put 24 per bag, the number of bags will be given by the quotient:

360/24 = 15

And if they sell each bag for $1.50, the revenue is:

R = 15*$1.50 = $22.50

Max says that is better to divide the tangerines in 24 bags and sell each for $1.50, so there are more bags, this time the revenue is:

R = 24*$1.50 = $36.

We can see that with Max's plan the revenue is larger.

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Answer:

per hour he earns 416/8= 52$

in 2.8 hours he will earn = 52×2.8= 145.6$

Step-by-step explanation:

i hope you find it helpful, have a nice day

The first thing we must know is how much David earns per hour.

$416 ÷ 8 hrs = $52/hr

$52/hr  x 2.8hrs = $145.6

David earns $145.6 in 2.8 hours.

The Pigeonhole Principle is a counting principle that states that if n items are put into m containers, with n > m, then at least one container should give  more than one item.

This principle is often used in counting problems to find the minimum number of items or containers needed to guarantee a certain outcome.

1. The smallest number of people in a group needed to guarantee that at least two were born in the same month is 13. This is because there are 12 months in a year, so if there are 12 people in the group, it is possible that each person was born in a different month. However, if there are 13 people in the group, by the Pigeonhole Principle, at least two people must have been born in the same month.

2. The smallest number of people are  needed to guarantee that at least two have the same first and last initials is 53. There are 26 letters in the given alphabet, so there are

possible two-letter combinations for initials. If there are 52 people in the group, it is possible that each person has a unique pair of initials. However, if there are 53 people in the group, at least two people must have the same initials by the Pigeonhole Principle.

3. The smallest number of people in a group needed to guarantee that at least two have the same first initial and were born on the same day of the week is 8. There are 7 days in a week, so if there are 7 people in the group, it is possible that each person was born on a different day of the week with a different first initial. However, if there are 8 people in the group, by the Pigeonhole Principle, at least two people must have been born on the same day of the week with the same first initial.

4. The smallest number of people in a group needed to guarantee that at least two were born on the same day of the year, assuming that nobody in the group was born on February 29 in a leap year, is 367. There are 366 possible days of the year (excluding February 29), so if there are 366 people in the group, it is possible that each person was born on a different day of the year. However, if there are 367 people in the group, by the Pigeonhole Principle, at least two people must have been born on the same day of the year.

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1.  The probability that the mean salary of the sample is less than $60,000 is 0.0150.

2. Interpretation: There is a 1.50% probability that a random sample of 37 environmental compliance specialists will have a mean salary of less than $60,000,

To solve for the probability, we use the equation

(Sample mean - population mean)

    standard deviation / sqrt (n)

Therefore it becomes;

z = 60,000 - 62, 0000

5600/ sqrt (37)

z = -2000

      919.26

Using a standard normal distribution table or a calculator, we can find the probability that a z-score is less than -2.17.

The probability is approximately 0.0150 (rounded to four decimal places).

Therefore, the probability that the mean salary of the sample is less than $60,000 is 0.0150.

The above answer is based on the question below;

Find the probability and interpret the result. If convenient, use technology to find the probability.

The population mean annual salary for environmental compliance specialist is about $62, 000. A random sample of 37 specialists is drawn from the population. what is the probability that the mean salary of the sample is less than $60, 000? Assume б = $5,600

The probabiility that the mean salary is less than $60,000 is ................ Round to 4 decimal places is necessary.

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The required residual for Dianna's iguana is $0.05.

To find the residual for Dianna's iguana, we need to first calculate the predicted value of weekly food cost for the iguana using the given regression equation:

[tex]$\hat{y} = 0.4 + 0.15x$[/tex]

where x is the weight of the iguana in pounds.

Substituting x = 11 into the equation, we get:

[tex]$\hat{y} = 0.4 + 0.15(11) = 2.05$[/tex]

So the predicted weekly feed cost for Dianna's iguana is $2.05.

To find the residual, we subtract the predicted value from the actual value:

[tex]$residual = actual\ value - predicted\ value = 2.10 - 2.05 = 0.05$[/tex]

Therefore, the residual for Dianna's iguana is $0.05.

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Assuming the rate is constant, 125,000,000 years agο the cοasts were tοuching.

It is a term that basically defines the change in sοme quantity with respect tο anοther quantity. In mathematics it alsο defines ratiο where the numeratοr is οne physical quantity and denοminatοr is anοther quantity.

Given that, the twο cοast are separated by 5,000km.

Alsο given that Africa and Sοuth America are mοving away frοm each οther at a rate οf 4 centimetres per year.

The rate is cοnstant.

Nοw 5000km= 500,000,000 cm

distance = rate × time

distance/rate = time

sο, 500,000,000/4 = 125,000,000

Hence, the cοasts were tοuching  125,000,000 years agο.

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Answer:80384

Step-by-step explanation: Uh you multiply the radius squared to get the answer:)

The total amount the electrician will need in retirement savings to meet their retirement income goal is option D,  $1,560,000.

The electrician wants to have an annual retirement income of 80% of their current annual gross wage, which is $78,000. So, the retirement income goal is the following, per year:

0.8 x $78,000 = $62,400  

The electrician plans to draw 4% of their retirement savings in the first year. So, the total amount the electrician needs in retirement savings is as follows:

$62,400 / 0.04 = $1,560,000.

Therefore, the answer is option D $1,560,000. We can conclude we have correctly answered this question.

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Answer:

Step-by-step explanation:

To find the total number of text messages sent per month by the 23 million people aged 13-17 in the United States, we can multiply the average number of text messages per person (800) by the number of people (23,000,000):

Total number of text messages = 800 text messages/person/month x 23,000,000 people

Total number of text messages = 18,400,000,000 text messages/month

To express this number in scientific notation, we can move the decimal point 10 places to the left, since there are 10 digits to the right of the decimal point:

Total number of text messages = 1.84 x 10^10 text messages/month

Therefore, the total number of text messages sent per month by the 23 million people aged 13-17 in the United States is approximately 1.84 x 10^10 text messages.

If we substitute pi as 3.14 we would be doing -

56.52 / 3.14 = 18

18 / 2 = 9.

So the circle's radius would be 9.

BUT if you want it with PI. . .

The answer would be 8.995437385

Answer:

254.19

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Since C is the largest half, then C is part of the largest whole.

Answer: C

Applying equations, the number of each type of pancake are originally: 81 blueberry pancakes, 27 plain pancakes, and 42 chocolate chip pancakes.

Let's use the following variables to represent the number of each type of pancake:

From the problem statement, we know that:

x + y + z = 150 (total number of pancakes)

1/3 x blueberry pancakes are left

4/5 y plain pancakes are left

1/2 z chocolate chip pancakes are left

There are now an equal number of each type of pancake

From the last statement, we can set up the following equations:

1/3 x = y = 1/2 z

Multiplying all sides of each equation by the least common multiple of the denominators, we get:

2x = 6y = 3z

Dividing all sides of each equation by 2, we get:

x = 3y = 3/2 z

Now we can use the equation x + y + z = 150 to substitute for x in terms of y and z:

3y + y + 2/3(3/2z) = 150

Simplifying and solving for z, we get:

5z = 270

z = 54

Substituting z = 54 into x = 3/2 z, we get:

x = 81

Substituting z = 54 into y = x/3, we get:

y = 27

Therefore, there were originally 81 blueberry pancakes, 27 plain pancakes, and 42 chocolate chip pancakes.

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Answer:

[tex]2x-7 \geq -29[/tex]

Step-by-step explanation:

the difference means subtract, at least means  [tex]\geq[/tex], and a number can be represented by x. So twice a number is 2x, a difference of that is - 7, and at least 29 is [tex]\geq 29[/tex]

Therefore, the recursive formula for the population growth model is:

[tex]P_n = 0*P_n-1[/tex] And the explicit formula for [tex]P_n[/tex] is:

[tex]P_n = 80*(1+0) n\\P_n=80[/tex]

The exponential growth model is a mathematical function that describes the growth of a population or system over time, assuming that the rate of growth is proportional to the size of the population or system. In other words, the model assumes that the growth rate of the population or system increases as the population or system grows larger.

by the question.

To find the recursive formula for the population growth model, we need to use the equation:

[tex]P_n = r*Pn-1[/tex]

where [tex]P_n[/tex] represents the population size at time n, Pn-1 represents the population size at the previous time step (n-1), and r represents the growth rate.

Given that the population grows exponentially with Po = 80, we can use the formula:

[tex]P_n = Po *(1 + r)n[/tex]

where Po is the initial population size and n is the number of time steps.

Using the fact that [tex]P_1 = 80[/tex], we can solve for the growth rate r:

[tex]Pq = Po * (1 + r)1\\80 = 80* (1 + r)1\\1 + r = (80/80)^(1/1)\\1 + r = 1^(1/1)\\1 + r = 1\\r = 0[/tex]

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Answer:

4 5/8

Step-by-step explanation:

7 7/8= 63/8

3 1/4= 13/4= 26/8

63/8 - 26/8= 37/8

37/8= 4 5/8

Answer: 113.09734

Step-by-step explanation:

Answer:

Step-by-step explanation:

5

Answer:

249.60

Step-by-step explanation:

there 4 triangles

bh1/2

(12)(10.4)1/2= 62.4 (one triangle)

62.4(4)=249.60 (all 4)

Answer:

249.6 cm

Step-by-step explanation:

Ok so the formula for a triangle is (base*height)1/2

Base: 12

Height = 10.4

12 * 10.4 * 1/2 = 62.4

We have 4 triangles

62.4 * 4 = 249.6

Based on the dot plots, it can be concluded the students in the second period had higher scores with a typical score of 3 on the essay.

The dot plots show the scores Ms. Munoz students got on their essays for two different periods. In these plots, we can observe that in the first period the scores were between 1 and 4, while in the second period, the scores were between 2 and 5.

This shows the scores were higher in the second period, moreover, the typical or the most common score was 3.

Note: This question is incomplete; below I attach the missing information.

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If a triangle has one side length of 9cm and another side of .12cm . The 3 possible answers for the third side​ are:  17, 20, and 21.

To determine the possible lengths for the third side of the triangle, we can use the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side.

Using this theorem, the possible lengths for the third side can be found by checking which of the following inequalities hold:

   9 + 12 > x

   9 + x > 12

   12 + x > 9

Simplifying these inequalities, we get:

   x > -3 (always true)

   x > -9 (always true)

   x > -3 (always true)

Therefore, the possible lengths for the third side of the triangle must satisfy x > -9, which eliminates the answer 3 (which is less than 9 - 12 = -3).

The possible lengths for the third side are:

   9 + 12 > x, so x < 21

   9 + x > 12, so x > -3

   12 + x > 9, so x > -3

Therefore, the possible lengths for the third side of the triangle are:

   17 (9 + 12 = 21, which is greater than 17)

   20 (9 + 12 = 21, which is greater than 20)

   21 (9 + 12 = 21, which is equal to 21)

So, the three possible lengths for the third side of the triangle are 17, 20, and 21.

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The complete question is:

A triangle has one side length of 9

centimeters (cm) and another side length of 12

cm.

Which answers are possible lengths for the third side?

Select three that apply

17

22

9

21

20

3

(a) Desipramine appears to be the most effective treatment for cocaine addiction among the three treatments compared, with a success rate of 58.3%. Lithium has a success rate of 25.0% and Placebo has a success rate of 16.7%.

b) A two-way table that shows the relationship between treatment and success in staying off cocaine has constructed

(a) The effectiveness of the three treatments can be compared by looking at the percentage of subjects who succeeded in staying off cocaine during the study. From the given data, it can be observed that the highest percentage of success was in the Desipramine group (58.3%), followed by the Lithium group (25.0%) and the Placebo group (16.7%). Therefore, Desipramine appears to be the most effective treatment for cocaine addiction among the three treatments compared.

(b) The two-way table showing the relationship between treatment and success in staying off cocaine can be constructed as follows

The table shows the number of subjects in each treatment group who succeeded or failed in staying off cocaine during the study. It also shows the total number of subjects in each treatment group.

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