The function machine at right
follows the equation h(x) = 5x + 2.

a. If the crank is turned backwards, what number should be pulled up into the machine in order to have a 4 come out of the top?

b. Keiko wants to build a new machine that will undo what h(x) does to an input. What must Keiko's machine do to 17 to undo it
and return a value of 3?

c. An "undo" function is called an inverse and has the notation h¹(a). Note that the -1 is not a negative exponent. It is the
mathematical symbol that indicates the inverse function of h(x). Write an equation for h ¹(x), the "undo" function machine.

d. Choose a value for z. Then find a strategy to show that your equation, h¹(x), undoes the effects of the function machine h(x).

Answer: Perimeter: [tex]10mn^2+4m^2[/tex]; Area : [tex]6m^3n^2[/tex]

Step-by-step explanation: For Perimeter add like terms 7mn^2 and 3mn^2 add but 4 m^2 isolates. For area multiply 3 mn^2 and 4m^2 to get 12 m^3n^2 and then divide by 2 because it is right triangle.

The missing length of the triangle is the hypotenuse which is given by 12.08

Pythagorean theorem states that the sum of the square of the opposite and adjacent sides of a triangle is equal to the square of the hypotenuse.

a² + b² = c²

c = √a² + b²

a = 11

b = 5

c = √a² + b²

= √11² + 5²

= √121 + 25

= √146

c = 12.08304597359

Approximately,

c = 12.08

Consequently, the hypotenuse of the triangle is approximately 12.08

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Answer:

the answer according to your question is that " b" is = -0.3

The probability of a person dying of renal failure if neither of their parents had renal failure is 0.056 or about 5.6%.

To solve this problem, we can use Bayes' theorem, which states that:

P(A|B) = P(B|A) * P(A) / P(B)

where P(A|B) is the probability of event A given that event B has occurred, P(B|A) is the probability of event B given that event A has occurred, P(A) is the prior probability of event A, and P(B) is the prior probability of event B.

In this case, we want to find the probability of a person dying of renal failure given that neither of their parents had renal failure. Let's define the following events:

R: death due to renal failure

P: at least one parent with renal failure

NP: neither parent has renal failure

We are given the following information:

Total deaths = 1000

Deaths due to renal failure (R) = 321

People with at least one parent with renal failure (P) = 460

Deaths due to renal failure among people with at least one parent with renal failure = 115

Using this information, we can calculate the probabilities as follows:

P(R) = 321/1000

P(P) = 460/1000

P(R|P) = 115/460

To find the probability of a person dying of renal failure given that neither of their parents had renal failure (i.e., P(R|NP)), we need to use Bayes' theorem. We can start by finding the probability of neither parent having renal failure (i.e., P(NP)):

P(NP) = 1 - P(P) = 1 - 0.46 = 0.54

Next, we can use the law of total probability to find the probability of dying of renal failure among people with neither parent having renal failure:

P(R|NP) = P(R) * P(NP|R) / P(NP)

We can find P(NP|R) using the formula:

P(NP|R) = P(NP ∩ R) / P(R)

To find P(NP ∩ R), we can use the formula:

P(NP ∩ R) = P(R|NP) * P(NP)

Substituting the values, we get:

P(R|NP) = P(R) * P(NP|R) / P(NP)

= 321/1000 * (1 - 115/460) / 0.54

= 0.056

This calculation shows how conditional probabilities can be calculated using Bayes' theorem and the law of total probability.

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Answer:

Part A: If (26)x = 1, the value of x is approximately 0.03846.

Part B: If (50)x = 1, the possible value of x is approximately 0.02.

Step-by-step explanation:

Part A: To find the value of x in the equation (26)x = 1, we need to find the value that, when raised to the power of 26, will equal 1. This value can be found by taking the reciprocal (or multiplicative inverse) of 26 and taking the natural logarithm of both sides.

Using the formula x = 1/26, we get:

x = 1/26 = 0.03846

So, the value of x in the equation (26)x = 1 is approximately 0.03846.

Part B: To find the possible values of x in the equation (50)x = 1, we need to find the values that, when raised to the power of 50, will equal 1. This value can be found by taking the reciprocal (or multiplicative inverse) of 50 and taking the natural logarithm of both sides.

Using the formula x = 1/50, we get:

x = 1/50 = 0.02

So, the possible value of x in the equation (50)x = 1 is approximately 0.02.

Understand the strengths and weaknesses of the tools, eliminate the outliers, critically analyze the correlations, and look at the context are all methods that help to consider any limitations of the data.

When preparing for a question-and-answer session after a presentation, it is important to consider any limitations of the data used. To do this, it is important to understand the strengths and weaknesses of the tools used to collect and analyze the data. Eliminating outliers from the data can help to ensure accuracy, as outliers can skew the results. It is also important to critically analyze any correlations that may be present in the data, as these could be indicative of a limitation in the data. Additionally, looking at the wider context of the data can help to identify any potential limitations, as certain factors may not have been taken into account when collecting the data. All of these methods can help to ensure accuracy and validity of the data used in the presentation.

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Answer:

x=10

Step-by-step explanation:

Answer:

x=10

Step-by-step explanation:

The function g(x) = 5x²models the number of bulbs she will plant is  if the garden has a side length of 8 feet, Cindy will plant 320 tulip bulbs.

What is Function?

A function is a mathematical rule that assigns a unique output value for every input value. In other words, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output.

Functions are often denoted using function notation, such as f(x), where "f" is the name of the function and "x" is the input. The output of the function is denoted by f(x), which is read as "f of x" and represents the value of the function at the input value x.

To find the number of bulbs Cindy will plant if the garden has a side length of 8 feet, we need to evaluate the function g(8) = 5(8)²

Using the order of operations, we first need to square the side length, which gives us 8² = 64.

Then, we multiply 64 by 5 to get the total number of bulbs:

g(8) = 5(64) = 320

Therefore, if the garden has a side length of 8 feet, Cindy will plant 320 tulip bulbs.

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At 12 noon the count in a bacteria culture was 400, at 3:00 pm the count was 1200. The bacteria count at 9 am, rounded off to the nearest bacterium, was 255.

The problem involves finding the bacteria count at 9 am, given the counts at 12 noon and 3 pm, and assuming that the bacteria culture obeys the population growth law.

To solve the problem, we use the population growth law, which states that the rate of growth of a population is proportional to the size of the population at any given time. This can be expressed as a differential equation, and its solution gives the population as a function of time.

Assuming the bacteria culture grows exponentially between 9 am and 3 pm, we can use the population growth law to find the bacteria count at 9 am. Let the initial count at 9 am be denoted by P, and let the growth rate be denoted by r.

Then we have:

P * (1 + r)^3 = 1200

Solving for P, we get:

P = 1200 / (1 + r)^3

Similarly, assuming the bacteria culture grows exponentially between 12 noon and 3 pm, we have:

400 * (1 + r)^3 = 1200

Solving for r, we get:

r = (1200/400)^(1/3) - 1

Plugging this value of r into the equation for P, we get:

P = 1200 / (1 + (1200/400)^(1/3) - 1)^3

Using a calculator, we get:

P ≈ 255

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Answer:

4x * -16

Step-by-step explanation:

You use the distributive property and multiply 4 by everything in the parentheses. The 16 is negative because you keep the minus sign with the number behind it.

"3 added to 5 is the same as 3 more than 5",  this statement is true. The statement "3 added to 5 is the same as 3 more than 5" means that the expression "3 added to 5" is equal to the expression "3 more than 5".

Another way to express the equality of two mathematical expressions is "3 added to 5 is the same as 3 more than 5".

"3 added to 5" is equivalent to the sum "3 + 5", which equals 8.

"3 more than 5" can be written as "5 + 3," which equals 8 as well.

Because both expressions have the same value of 8, the statement "3 plus 5 equals 3 more than 5" is correct.

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The area of the composite figure is equal to 99 mm² square milimetresmetres.

The composite figure can be observed to be made up of two horizontal rectangle, and a vertical rectangle, so we shall calculate for the areas of the three figures and then add the result to get the total area of the composite figure as follows:

area of the bigger horizontal rectangle = 11 mm × 3 mm

area of the bigger horizontal rectangle = 33 mm²

area of the smaller horizontal rectangle = 5 mm × 2 mm

area of the smaller horizontal rectangle = 10 mm

area of the vertical rectangle = 14 mm × 4 mm

area of the vertical rectangle = 56 mm²

total area of the composite figure = 33 mm² + 10 mm² + 56 mm²

total area of the composite figure = 99 mm²

Therefore, the area of the composite figure is equal to 99 mm² square milimetres.

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Answer:

Step-by-step explanation:

This question of of Trigonometry

Tan means the ratio of sides which are opposite to the given angle divided by the adjacent side to the angle (NOT THE HYPOTENUSE)

So Tan(Unknown angle) = 5/14
Unknown angle = 19.6 Degrees

Answer:

Yes, because 50x20= 5x10x2x10= (5x2)x(10x10)

So you can multiply 5x2 first and than add the zeros

Answer:

no answer

soory

Step-by-step explanation:

The ratio used to find the measurement of angle x is given as follows:

cos(x) = 40/68.

The three trigonometric ratios are defined as follows:

For angle x, we have that:

Hence the ratio is given as follows:

cos(x) = 40/68.

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a. 1 hour and 45 minutes for the bacteria population to double.

To find out how long it takes for the bacteria population to double, we need to solve the equation:

2p(0) = p(h)

where p(0) is the initial population and h is the time it takes for the population to double.

Since p(h) = [tex]1000e^{(0.4h)}[/tex], we can write:

2p(0) = [tex]1000e^{(0.4h)}[/tex]

Dividing both sides by 1000, we get:

2p(0)/1000 = [tex]e^{(0.4h)}[/tex]

Taking the natural logarithm of both sides, we get:

ln(2p(0)/1000) = 0.4h

Solving for h, we get:

h = ln(2p(0)/1000) / 0.4

We know that p(0) = 1, since the initial population is given as 1,000. Substituting this value, we get:

h = ln(2) / 0.4

h ≈ 1.73

So it takes approximately 1.73 hours for the bacteria population to double.

Rounding to the nearest quarter of an hour.

we get:

h ≈ 1.75 hours

h ≈ 1 hour and 45 minutes

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The given proof follows the symmetric property of angle congruence. Therefore, option C is the correct answer.

Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.

Given that,

       Statements            Reasons

1. ∠ABC≅∠DEF           1. Given

2. m∠ABC=m∠DEF     2. Definition of congruent angles

3. m∠DEF=m∠ABC     3. Symmetric property of equality

4. ∠DEF≅∠ABC          4. Definition of congruent angles

The symmetric property says that if one geometric shape is congruent to another, than the second shape is also congruent to the first. The symmetric property of congruence says that for any angles A and B, if ∠A≅∠B then ∠B≅∠A.

Therefore, option C is the correct answer.

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The range of the data set is, 28

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

The data set is,

74, 64, 90, 74, 92, 68, 71

Now, We know that;

Range of data set is calculating by subtracting the lowest value from highest value.

Hence, The range is,

⇒ Highest value - Lowest value

⇒ 92 - 64

⇒ 28

Thus, The value of range = 28

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Answer:

give the diagram please

The slope of the line through each pair of points (11, 8), (- 13, 11) is -1/8.

The slope of a line is defined as the change in y- coordinate with respect to x - coordinate. The slope of a line represents the direction and steepness of a line. The formula for the slope of a line that passes through the points (x₁, y₁) and (x₂, y₂) is given by

Here we have

The pair of points (11, 8), (- 13, 11)  

By the given formula,

Slope (m) = [ y₂ - y₁]/ [x₂ - x₁]

The slope from (11, 8) to (- 13, 11) can be calculated as follows

Slope = [ 11 - 8 ]/ [ -13 -11 ] = 3/-24 = -1/8

Therefore,

The slope of the line through each pair of points (11, 8), (- 13, 11) is -1/8.    

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If there are 8 men and 5 women , then the number of ways of selecting a 4 people committee is 715 ways  .

The number of ways to select a committee of 4 people from a group of 13 people, where 5 are women and 8 are men, is calculated by Combination ;

where , "n" is = total number of people, "r" is = number of people to be selected,

In this case, we have:

the total number of people is = 8 + 5 ⇒ n = 13 ;

the number of committee member to be selected is "r" = 4 ;

So, the number of ways to select a committee of 4 people from a group of 13 people is  :  ¹³C₄ = 715 ways ;

Therefore, there are 715 ways to select a committee of 4 people from a group of 5 women and 8 men.

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The given question is incomplete , the complete question is

There are 5 women and 8 men is a department . Find the Number of ways can a committee of 4 people be selected ?

The standard deviation is used more frequently then the variance because  standard deviation is more stable and less sensitive to outliers.

The Standard Deviation and Variance are defined as two closely related measures of the spread or dispersion of a set of data.

The Variance is defined as average of squared differences from mean, while Standard Deviation is square root of variance.

The reason why the standard deviation is used more frequently than  variance is because the standard deviation is expressed in same units as the original data, whereas  the variance is expressed in squared units.

For Example, if we measure  heights of a group of people in inches, the standard deviation will be expressed in inches, whereas variance will be expressed in square inches.

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Step-by-step explanation:

= 9>x or. = 11<x.

Here is the answer

4214.7 is the balance in the account after 2 months .

What does compound and simple interest mean?

A fixed proportion of the principal amount borrowed or lent is what is known as simple interest and is paid or received over a given period of time.

                                Borrowers are required to pay interest on interest in addition to principal because compound interest accrues and is added to the total amount of interest from earlier periods.

P = $4200

R = 2.1% = 2.1/100 = 0.021  =

     T = 2 month = 2/12 = 1/6

    I = PRT

     = 4200 * 0.021 * 1/6 = 14.7

 Amount = P + I = 4200 + 14.7  = 4214.7

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The orthocenter of ▲ABC is the point (27/4, 17/4)

What is Orthocenter in coordinate geometry?

Any triangle's three altitudes are contemporaneous line segments (they intersect in a single point), and this point is known as the triangle's orthocenter.

To find the orthocenter of ▲ABC, we need to first find the altitude lines of the triangle, which are the perpendicular lines from each vertex to the opposite side. The point where these three lines intersect is the orthocenter.

The slope of this line is:

BC = (-1 - (-4)) / (-1 - 5)

BC = 3/2

Using point-slope form, the equation of the line BC is:

[tex]y -y_{b} = m_{BC} (x - x_{b} )[/tex]

y - (-4) = (3/2)(x - 5)

y = (3/2)x - 17/2

To find the altitude from vertex A to BC, we need to find the equation of the line passing through A and perpendicular to BC. The slope of this line is the negative reciprocal of the slope of BC:

[tex]m\ altitude_A = -2/3[/tex]

The point-slope form of the equation of the altitude from A is:

[tex]y -y_{A} = m_{BC} (x - x_{A} )[/tex]

y - 5 = (-2/3)(x - 5)

y = (-2/3)x + 25/3

Similarly, we can find the equations of the altitudes from vertices B and C to the opposite sides AC and AB, respectively:

Altitude from B to AC:

[tex]m_{AC} = \frac{(y_{C} -y_{A})}{(x_{C} -x_{A})} \\\\m_{AC} = \frac{-3}{2}[/tex]

AC = 2/3

y - (-4) = (2/3)(x - 5)

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

Altitude from C to AB:

[tex]m_{AB} =\frac{(y_{B}- y_{A})}{(x_{B}- x_{A})} \\[/tex]

= (-4 - 5) / (5 - 5)

= undefined

x = -1

Now, we need to find the point of intersection of these three altitudes, which is the orthocenter. To do this, we can solve the system of equations formed by the three altitude lines:

y = (3/2)x - 17/2

y = (-2/3)x + 25/3

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

Substituting the third equation into the first two equations, we get:

(2/3)x - 2/3 = (-2/3)x + 25/3

(4/3)x = 9

x = 27/4

Substituting x = 27/4 into any of the three equations, we get:

y = (2/3)(27/4) - 2/3 = 17/4

Therefore, the orthocenter of ▲ABC is the point (27/4, 17/4).

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Answer:

0.75y + 0.5x = 8.00

Step-by-step explanation:

Answer: I assume you are trying to find how many jars the beekeeper has produced per week.

The answer is: 53

Step-by-step explanation:

We know that he produced 636 jars of honey over 12 weeks.

Therefore, to find out the number of jars he made each week, we divide the amount by the time.

So 636/12

Answer 53.