type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar(s). find the inverse of the given function. f(x)=2x-4 f^-1(x)= __x+___

A coordinate plane with the x-axis labeled Blueberries (in pints) and the y-axis labeled Cost (in dollars) shows a line going through (0, 0) and (5, 17).

It is defined as the relationship between two quantities as one quantity increases the other quantity also increases and vice versa.

It is given that there is a proportional relationship between cost and pints of blueberries as,

Blueberries (in pints)          2      5

Cost (in dollars)                6.80   17

17/6.80 = 5/2

As we draw the graph and analyze each option one by one we get the graph shown by the statement C following the given proportional relationship.

Thus, a coordinate plane with the x-axis labeled Blueberries (in pints) and the y-axis labeled Cost (in dollars) shows a line going through (0, 0) and (5, 17).

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Answer:

Step-by-step explanation:

I hate algebra personally so here's an easier to understand explanation. A ratio is a percent split.

Your ratio is 5:3. To find the percent you'll add the 2 numbers then put the originals over the sum to find the denominator for your fractions. 5+3 = 8 so for one side it is 5÷8 and the other is 3÷8 ---or--- 62.5%:37.5%

So all you do is multiply 240 on each side to find the new ratio.

For example …

62.5% × 240 ---or--- 0.625×240 = 150

And

32.5% × 240 ---or--- 0.325×240 = 90

Now quick tip for 2 number ratios is they ALWAYS add up to the original number. So you diddnt even have to do the second half. You can just find the difference.

The Greatest concentration of the medication that a patient will have in their body is 8 mg/L, which occurs at t = 2.The maximum concentration of the medication that a patient will have in their body is 8 mg/L.

Part A:

To determine the domain and range of the function C(t) = -2t^2 + 8t, we need to consider the context of the problem.

Domain:

The domain of a function represents the set of all possible input values. In this case, the function represents the concentration of the medication after being injected into a patient. Since time, t, is the independent variable representing hours after injection, it should be a non-negative value.

To find the domain, we need to determine the range of valid values for t. Since time cannot be negative in this context, the domain of the function is t ≥ 0.

Range:

The range of a function represents the set of all possible output values. In this case, the function represents the concentration of the medication, C(t), in mg/L.

To find the range, we can analyze the behavior of the function. The function is a quadratic equation, which opens downward since the coefficient of the t^2 term is negative (-2). This means that the maximum concentration will occur at the vertex of the parabolic curve.

The vertex of a quadratic function can be found using the formula: t = -b / (2a), where a and b are the coefficients of the quadratic equation.

In this case, a = -2 and b = 8. Substituting these values into the formula, we get:

t = -8 / (2(-2))

t = -8 / (-4)

t = 2

Therefore, the vertex occurs at t = 2.

Substituting t = 2 back into the original function, we can find the maximum concentration:

C(2) = -2(2)^2 + 8(2)

C(2) = -2(4) + 16

C(2) = -8 + 16

C(2) = 8

The maximum concentration of the medication that a patient will have in their body is 8 mg/L.

Part B:

To graph the function C(t) = -2t^2 + 8t and determine the greatest concentration, we can plot points and sketch the parabolic curve.

We can choose different values of t and calculate the corresponding values of C(t):

When t = 0, C(0) = -2(0)^2 + 8(0) = 0

When t = 1, C(1) = -2(1)^2 + 8(1) = 6

When t = 2, C(2) = -2(2)^2 + 8(2) = 8

When t = 3, C(3) = -2(3)^2 + 8(3) = 6

Plotting these points on a graph, we can connect them to form a parabolic curve.

The graph will be a downward-opening parabola, and the vertex will be at t = 2, C = 8.

The greatest concentration of the medication that a patient will have in their body is 8 mg/L, which occurs at t = 2.

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Explanation:

p = 0.58 = probability HR rep says to follow up within two weeks

n = 7 = sample size

Let's calculate the binomial P(x) value for x = 0 which will tell us the probability of having a sample with 0 reps recommending the follow up within two weeks.

\(P(x) = (_n C _x)*(p)^{x}*(1-p)^{n-x}\\\\P(0) = (_{7} C _{0})*(0.58)^{0}*(1-0.58)^{7-0}\\\\P(0) = (1)*(0.58)^{0}*(0.42)^{7}\\\\P(0) \approx 0.00230539333249 \\\\P(0) \approx 0.002 305\\\\\)

If we were to randomly select a sample of n = 7 HR managers, then there's roughly a 2.305% chance that x = 0 of that group will say to follow up within two weeks. This is when there's a 58% chance of each individual rep of saying "yes".

Repeat for x = 1 and you should find that P(1) = 0.022285 approximately.

Then we can say this:

\(P(\text{0 or 1})+P(\text{at least 2}) = 1\\\\P(\text{x=0 or x=1})+P(x \ge 2) = 1\\\\P(0)+P(1)+P(x \ge 2) = 1\\\\P(x \ge 2) = 1-P(0)-P(1)\\\\P(x \ge 2) \approx 1-0.002305-0.022285\\\\P(x \ge 2) \approx 0.97541\\\\P(x \ge 2) \approx 0.9754\\\\\)

If we selected a sample of n = 7 HR reps, there's roughly a 97.54% chance that 2 or more reps will recommend following up within 2 weeks.

Answer:

21% or C

Step-by-step explanation:

If 60 students either didn't pass, got Cs or Bs, then 16 out of the 76 got As which is 21 percent.

Answer:

I believe the slope is m = 0.

(Let me know if you need the work)

Hello!

To find the slope, we use the following formula:

m=\(\frac{y2-y1}{x2-x1} \\\frac{4-4}{7-5}\)

m=\(\frac{0}{2} \\0\)

Keep in mind that if the y-coordinates are the same, then the slope is 0.

That's because if the y-coordinates are the same, then the line is horizontal and the rise  (how many units we rise up) is 0 units.

Therefore, the slope is: 0.

Hope this helps you!

~Just a felicitous girlie

#HaveASplendidDay

\(SilentNature :-):-):-):-):-)\)

12 hours will it take to fill the given pool .

we can solve this problem using unitary method ,

10 hours is required to fill the full pool

1 hour is required to fill 1/10th of the pool

30 hours is required to empty the pool

1 hour is required to empty 1/30th of the pool

If two pipes are open then in 1 hour ( 1/10 - 1/30 = 2/30 = 1/15 ) pool will be filled .

The pool is 1/5th filled already as it is mentioned .

So , remaining is ( 1 - 1/5 = 4/5 )

If 1/15th is filled in 1 hour , then 4/5th will be filled in ( 15 × 4/5 ) hours = 12 hours

So, it will take 12 hors to fill the pool .

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The inequality x - 4 ≥ 8 represents the sentence "  the sum of a number and -4 is at least 8" and the solution of the inequality is the value of variable x is x ≥ 12.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

Let's assume that the number would be x

The sum of a number and -4 is at least 8

According to the given question, translate the phrase into an algebraic form :

x - 4 ≥ 8

Add 4 both sides of the above inequality,

x - 4 + 4 ≥ 8 + 4

x ≥ 12

Therefore, the inequality x - 4 ≥ 8 represents the sentence "  the sum of a number and -4 is at least 8" and the solution of the inequality is the value of variable x is x ≥ 12.

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The inequality solved to give a solution of x ≥ 1 and x ≤ -3 is |x + 1| ≥ 2.

b = 1, ≥

From the diagram, the solution to the inequality is x ≥ 1 and x ≤ -3

Hence:

|x + b| ≥ 2

x + b ≥ 2 or -(x + b) ≥ 2

x ≥ 2 - b or x ≤ -2 - b

2 - b = 1 and -2 - b = -3

b = 1

Hence |x + 1| ≥ 2

The inequality solved to give a solution of x ≥ 1 and x ≤ -3 is |x + 1| ≥ 2. b = 1, ≥

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Answer:

Answer:

A) y ≥ -3x + 4

Step-by-step explanation:

Given the graph of an inequality, where it shows that the y-intercept is (0, 4), and the line has a negative slope (as it declines from left to right). To figure out the value of the slope, choose two points from the graph, and substitute its values into the slope equation,

m = (y2 - y1)/(x2 - x1)

Let (x1, y1) = (0, 4)

(x2, y2) = (2, -2)

m = (-2 - 4)/(2 - 0)

m = -6/2

m = -3

Now that we have the value of the slope, m = -3, and the y-intercept, b = 4:

We need to determine which part of the region is shaded. Choose a test point that is not on the graph.  Let's use the point of origin, (0, 0) to see whether it is included as a solution:

Option A: y ≥ -3x + 4

Substitute values of (0, 0) into the inequality statement:

0 ≥ -3(0) + 4

0 ≥ 0 + 4

0 ≥ 4 (False statement). The shaded region must not contain the given test point, (0, 0), which is actually the case in your given graph. The right-half plane is the shaded region.  Hence, y ≥ -3x + 4 is the correct inequality statement that represents the graph.

The answer cannot be y ≤ -3x + 4 because if you plug in the test point into y ≤ -3x + 4, it will provide a true statement.

y ≤ -3x + 4

0 ≤ -3(0) + 4

0 ≤ 0 + 4

0 ≤  4 (True statement, which means that the region where the test point is located should be shaded).

Therefore, the correct answer is Option A) y ≥ -3x + 4

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Therefore, each person will get 12 grams of almonds when 20 people share 2 2/5 kilograms (or 12 grams/person when 20 people share 2.4 kilograms) of almonds.

To determine how much almonds each person will get when 20 people share 2 2/5 kilograms of almonds, we need to divide the total amount of almonds by the number of people.

First, let's convert 2 2/5 kilograms to a single fraction. We can rewrite it as 12/5 kilograms.

Now, we can calculate the amount of almonds per person:

Amount of almonds per person = Total amount of almonds / Number of people

Amount of almonds per person = (12/5) kilograms / 20 people

To simplify the calculation, we can convert kilograms to grams:

Amount of almonds per person = (12/5) * 1000 grams / 20 people

Amount of almonds per person = 240 grams / 20 people

Amount of almonds per person = 12 grams/person

Answer:

The answer is 6

Step-by-step explanation:

42 divided by 7=6

Answer:

Question 6: y = x + 9

Question 7: y = x - 2

Step-by-step explanation:

Well this is a good question. We can take out Y, and X because that is a variable and it isn't defined. Now what we need to figure out is B or the Y - Intercept. Something thats in every Slope - Intercept form type equation:

Y = MX + B

The Y - Intercept is basically the y value when x is 0. A handy tip is that whatever value of y that is on the vertical line in the graph is B. If we look at the graph for Question 6 we find that it is +9. Since Y = X + 9 is the only equation that has +9 as it's B or Y - Intercept we can figure out the first one.

Using our handy tip from above, let's do the same for 7. This time the line intercepts the vertical line in the negative value of -2. So we find that B for this equation is -2. Therefor the only equation with -2 as it's be is Y = X - 2. So that is our answer.

The matrices A and B that were defined are the integer matrices:

A = [1 0 0; 0 1 0]

B = [1 1 0; 0 0 0]

Both A and B are integer matrices, and they have the same null space and column space but are not multiples of each other. Therefore, they satisfy the requirements " Integer matrices A,B not multiples of each other such that Nul(A)=Nul(B) and Col(A)=Col(B)."

Let A and B be 3x3 matrices given by:

A = [1 0 0; 0 1 0]

B = [1 1 0; 0 0 0]

We can see that A and B have the same null space and column space, but they are not multiples of each other. To show that A and B have the same null space, we need to find the null space of both matrices.

For A, we need to solve the equation Ax = 0:

[1 0 0; 0 1 0] [x1; x2; x3] = [0; 0]

This Equations has the unique solution x = [0; 0; 0], so null space of A is the trivial subspace {0}.

For B, first solve the equation Bx = 0:

[1 1 0; 0 0 0] [x1; x2; x3] = [0; 0]

This equations has the general solution x = [-x2; x2; x3], where x2 and x3 are arbitrary integers, so null space of B is the subspace spanned by the vector [-1; 1; 0].

Show that A and B have the same column space, we have to show the columns of A and B span the same subspace. The columns of A are [1; 0] and [0; 1], which span the entire 2-dimensional space. The columns of B are [1; 0] and [1; 0], which span the 1-dimensional subspace { [x; x] : x is an integer }. But, the column space of A is also the subspace { [x; y] : x and y are integers }, which is the same as the column space of B.

Therefore, A and B have the same column space.

Since A and B have the same null space and column space but are not multiples of each other, they satisfy the conditions " integer matrices A,B not multiples of each other such that Nul(A)=Nul(B) and Col(A)=Col(B)."

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Answer:50%

Step-by-step explanation:

Answer:

The answer is 50%

Step-by-step explanation:

He will get £158.43. After paying the agent commission, he will get amount of £154.65 for R2100.

0.075199 x 2100 = 158.43 pound

158.43 - 105 = 53.43 pound

53.43 + 5.343 = 58.78 pound

158.43 - 58.78 = 154.65

First, we need to calculate the amount of pound for R2100. To do this, we need to use the exchange rate of R1 to 0.075199 pound. Thus, R2100 is equal to 0.075199 x 2100 = 158.43 pound.

Second, we need to calculate the amount of pound after paying the agent commission. To do this, we need to subtract the commission which is 5% of R2100. Thus, 5% of R2100 is equal to 0.05 x 2100 = 105. Thus, the amount of pound after paying the commission is equal to 158.43 - 105 = 53.43 pound.

Finally, we need to calculate the amount of pound after increasing the price. To do this, we need to add the increased price which is 10% of 53.43 pound. Thus, 10% of 53.43 is equal to 5.343 pound. Thus, the amount of pound after increasing the price is equal to 53.43 + 5.343 = 58.78 pound.

Therefore, the amount of pound that Brain will get for R2100 after paying the agent commission and increasing the price is equal to 158.43 - 58.78 = 154.65

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Answer:

The inequality is 6x ≥ -24

The solution of this inequality is {x : x ∈ R, x ≥ -4} ⇒ [-4, ∞)

Step-by-step explanation:

Let us solve the question

∵ Six times a number x means 6 × x = 6x

∵ At least means ≥

∴ Six times a number x is at least -24 is 6x ≥ -24

∴ The inequality is 6x ≥ -24

Now we will find the solution of the inequality

∵ 6x ≥ -24

→ Divide both sides by 6

∵ \(\frac{6x}{6}\) ≥ \(\frac{-24}{6}\)

∴ x ≥ -4

∴ The solution of this inequality is {x : x ∈ R, x ≥ -4} ⇒ [-4, ∞)

Answer:

The inequality is 6x ≥ -24

The solution is x ≥ -4

Step-by-step explanation:

To solve this you have to divide both sides by 6, so 6 ÷ 6 cancels out and -24 ÷ 6 = -4

So, the solution is x ≥ -4

Answer:

40

Step-by-step explanation:

first do what is in the parentheses (4*4) which is 16 then rewrite the whole equation. 71-5(3)-16. then you'll want to multiply 5 times 3 because if there is no sign before the parentheses then it is automatically multiplication. 5 times 3 is 15. rewrite the equation again. 71-15-16 then simply subtract.

Hope this helps! :)

Answer:

\({ \tt{circumference \approx\pi \: d}} \\ \approx{ \tt{3.14 \times 15}} \\ \\ \approx47.124 \: inches\)

Answer:

1.00 significant figures

The required, 0.9967 rounded to 2 significant figures is approximately 1.0.

To round 0.9967 to 2 significant figures, we look at the first two non-zero digits: 0.9967

The first two non-zero digits are 99. Since there is no third significant digit, we round according to the following rules:

If the third digit is 5 or greater, round up the second digit.

If the third digit is less than 5, leave the second digit unchanged.

In this case, the third digit is 6, which is greater than 5. So, we round up the second digit:

Thus, 0.9967 rounded to 2 significant figures is approximately 1.0.

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Tukey's procedure, also known as the Tukey-Kramer test, a statistical method used to compare multiple groups and identify significant differences in their means. Tukey's procedure is used to identify differences in the true average bond strengths among the five protocols in Example 10.3.

Tukey's procedure, also known as the Tukey-Kramer test, a statistical method used to compare multiple groups and identify significant differences in their means. In this case, we are applying Tukey's procedure to the data in Example 10.3, which consists of bond strengths measured under five different protocols.

To perform Tukey's procedure, we first calculate the mean bond strength for each protocol. Next, we compute the standard error of the mean for each protocol. Then, we calculate the Tukey's test statistic for pairwise comparisons between the protocols. The test statistic takes into account the means, standard errors, and sample sizes of the groups.

By comparing the Tukey's test statistic to the critical value from the studentized range distribution, we can determine if there are statistically significant differences in the true average bond strengths among the protocols. If the test statistic exceeds the critical value, it indicates that there is a significant difference between the means of the compared protocols.

Using Tukey's procedure on the data in Example 10.3 will allow us to identify which pairs of protocols have significantly different average bond strengths and provide insights into the relative performance of the protocols in terms of bond strength.

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Answer:

∛(3b)^4

Step-by-step explanation:

Note that the square root of 36 is 6; in other words, 6^2 = 36.

So (√36)(5) = 6√5

We are asked to prove the inequality L(f, S) ≤ L(f, P) ≤ U(f, P) ≤ U(f, S) for a bounded function f on an interval [a, b], where S and P are partitions of the interval.

To prove the inequality, we start by considering the lower sums. The lower sum L(f, S) is defined as the sum of the infimum values of f over each subinterval of the partition S. Since the partition P is a refinement of S, each subinterval of S is contained within a subinterval of P. Therefore, the infimum value of f over each subinterval in S will be less than or equal to the infimum value over the corresponding subinterval in P. This implies that L(f, S) ≤ L(f, P).

Next, we consider the upper sums. The upper sum U(f, S) is defined as the sum of the supremum values of f over each subinterval of the partition S. Again, since P is a refinement of S, each subinterval in S is contained within a subinterval in P. Thus, the supremum value of f over each subinterval in S will be greater than or equal to the supremum value over the corresponding subinterval in P. Therefore, U(f, S) ≥ U(f, P).

Combining the results, we have L(f, S) ≤ L(f, P) and U(f, P) ≤ U(f, S). This establishes the desired inequality L(f, S) ≤ L(f, P) ≤ U(f, P) ≤ U(f, S), proving the statement.

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The convolution integral y(t) = x(t) * h(t) for the given pair of signals x(t) and h(t) can be computed as follows:

y(t) = ∫[x(τ) * h(t - τ)] dτ

1) x(t) = δ(t) and h(t) = δ(t - 2) * (t - 1)

The convolution integral becomes:

y(t) = ∫[δ(τ) * δ(t - τ - 2) * (τ - 1)] dτ

To evaluate this integral, we consider the properties of the Dirac delta function. When the argument of the Dirac delta function is not zero, the integral evaluates to zero. Therefore, the integral simplifies to:

y(t) = δ(t - 2) * (t - 1)

The convolution result y(t) is equal to the shifted impulse response h(t - 2) scaled by the factor of (t - 1). This means that the output y(t) will be a shifted and scaled version of the impulse response h(t) at t = 2, delayed by 1 unit.

In summary, for x(t) = δ(t) and h(t) = δ(t - 2) * (t - 1), the convolution integral y(t) = x(t) * h(t) simplifies to y(t) = δ(t - 2) * (t - 1).

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27.32 x 48.97

multiplying this will give 1337.8604

The equivalent expression written in the format ax^2 + bx + cx + d is (b) x^3 - 12x^2 + 41x - 42.

Jennifer is building a post for her mailbox. To find the correct dimensions, she needs to expand this expression: (x-3)(x - 7)(x - 2) Select the equivalent expression written in the format ax^2 + bx+ cx+d. a.) x^3 + 6x^2 + 13x - 42 b.) x^3-12x^2 +41x-42 c.) x^3 - 6x^2–13x +42 d.) x^3 + 12x^2-41x +42 EXPLAIN

To expand the expression (x-3)(x - 7)(x - 2), we can use the distributive property and multiply the first two factors, and then multiply the result by the third factor:

(x-3)(x - 7)(x - 2) = (x^2 - 7x - 3x + 21)(x - 2)

= (x^2 - 10x + 21)(x - 2)

= x^3 - 2x^2 - 10x^2 + 20x + 21x - 42

= x^3 - 12x^2 + 41x - 42

So the expanded form of the expression is x^3 - 12x^2 + 41x - 42.

Therefore, the equivalent expression written in the format ax^2 + bx + cx + d is (b) x^3 - 12x^2 + 41x - 42.

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