Find the domain and the range of the function. (Enter your answers using interval notation.)
h(x) = −√x+6

The equation of the tangent line to the quadratic function y = 3 · x² at the point (x, y) = (1, 3) is y = 6 · x - 3.

Herein we must determine a line tangent to the quadratic equation y = 3 · x² at the point P(x, y) = (1, 3) by algebraic means. The slope of the line can be found by using the secant line formula and simplify the resulting expression:

m = [3 · (x + Δx)² - 3 · x²] / [(x + Δx) - x]

m = 3 · [(x + Δx)² - x²] / Δx

m = 3 · (x² + 2 · x · Δx + Δx ² -  x²) / Δx

m = 3 · (2 · x + Δ x)

If Δx = 0, then the equation of the slope of the tangent line is:

m = 6 · x

If we know that x = 1, then the slope of the tangent line is:

m = 6 · 1

m = 6

Lastly, we find the intercept of the equation of the line: (x, y) = (1, 3), m = 6

b = y - m · x

b = 3 - 6 · 1

b = - 3

The equation of the tangent line to the quadratic function y = 3 · x² at the point (x, y) = (1, 3) is y = 6 · x - 3.

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Using the normal distribution, it is found that 63.18% of the area under the curve of the standard normal distribution is between z = − 0.9 z = - 0.9.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The area within 0.9 standard deviations of the mean is the p-value of Z = 0.9(0.8159) subtracted by the p-value of Z = -0.9(0.1841), hence:

0.8159 - 0.1841 = 0.6318 = 63.18%.

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95% men are between 165 cm and 186 cm.

What is the empirical rule?

The empirical rule is also referred to as the Three Sigma Rule or the 68-95-99.7 Rule.

z-score = (raw-score minus mean) / standard deviation.

z1 = (165-176)/5 = -2.2

z2 = (186-176)/5 = 2

The empirical rule tells us that about 95% of all values are within standard deviations of the mean,

so, 95% men are between 165 cm and 186 cm.

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95% of men are between 165 cm and 186 cm.

Given:

Find:

Solution:

The empirical rule is also referred to as the three sigma rule or the 68-95-99.7

Rule:

z - score = (raw - score minus mean) / standard deviation.

z1 = (165-176)/5 = -2.2

z2 = (186-176)/5 = 2

The empirical rule tells us that about 95% of all values are within standard deviations of the mean.

So, 95% of men are between 165 cm and 186 cm.

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the table complete is:

x      y

1       4

2      8

3      12

4      16

Where x is the ribbon length in yards and y is the number of bows she can make.

We know that Marina needs 1/4 yards of ribbon for each bow.

Then, with one yard of ribbon, she can make 4 bows, then the relation between y, the number of bows she can make, and x, the yards of ribbon that she has, is:

y = 4*x

Now we want to complete the table:

x           y

1

2

3

4

To do so, we just need to evaluate the above function.

when x = 1.

y = 4*1 = 4

When x = 2:

y = 4*2 = 8

when x = 3

y = 4*3 = 12

when x = 4

y = 4*4 = 16

Then the table complete is:

x      y

1       4

2      8

3      12

4      16

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The decimals would be ordered as:

72.1, 72.5, 73.77, 73.943

42.1, 42.59, 43.2, 43.219

28.23, 38.4, 38.507, 38.507, 39.5

71.3, 71.3, 71.743, 72.43, 72.5

To order decimals from the least to the greatest, first state the lowest value, then progress to the highest taking account of the figures that come immediately after each decimal point.

The decimals will be ordered as shown below:

72.1, 72.5, 73.77, 73.943

42.1, 42.59, 43.2, 43.219

28.23, 38.4, 38.507, 38.507, 39.5

71.3, 71.3, 71.743, 72.43, 72.5

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Considering the situation described, the null hypothesis is given as follows:

[tex]H_0: \mu = 64,000[/tex].

At the null hypothesis, it is tested if the mean is the same as in the Census, of $64,000, hence:

[tex]H_0: \mu = 64,000[/tex].

At the alternative hypothesis, it is tested if the mean is different from the Census, hence:

[tex]H_1: \mu \neq 64,000[/tex].

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Answer:

f(x) = 2 for x < -2

f(x) = -2x + 11 for x > 3

Based on the information provided, the cost function, C(x) is given by 80x + 6000 while the demand function, P(x) is given by -1/20(x) + 920.

Mathematically, the revenue can be calculated by using the following expression:

R(x) = x × P(x)

Revenue, R(x) = x(-1/20(x) + 920)

Revenue, R(x) = x(-x/20 + 920)

Revenue, R(x) = -x²/20 + 920x.

Expressing the profit as a function of x, we have:

Profit = Revenue - Cost

P(x) = R(x) - C(x)

P(x) = -x²/20 + 920x - (80x + 6000)

P(x) = -x²/20 + 840x - 6000.

For the value of x which maximizes profit, we would differentiate the profit function with respect to x:

P(x) = -x²/20 + 840x - 6000

P'(x) = -x/10 + 840

x/10 = 840

x = 840 × 10

x = 8,400.

For the maximum profit, we have:

P(x) = -x²/20 + 840x - 6000

P(8400) = -(8400)²/20 + 840(8400) - 6000

P(8400) = -3,528,000 + 7,056,000 - 6000

P(8400) = $3,522,000.

Lastly, we would calculate the price to be charged in order to maximize profit is given by:

P(x) = -1/20(x) + 920

P(x) = -1/20(8400) + 920

P(x) = -420 + 920

P(x) = $500.

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The values of the probabilities are

The image that completes the question is added as an attachment

From the attached graph, we have:

P(x) = 0.109 when x = 4

Hence, the probability is 0.109

From the attached graph, we have:

P(x) = 0.109 when x = 4

P(x) = 0.093 when x = 5

So, we have:

P(4 or 5) = 0.109 + 0.093

Evaluate

P(4 or 5) = 0.202

Hence, the probability is 0.202

This is represented as:

P(x >= 6)

From the attached graph, we have:

P(x) = 0.022 when x = 6

P(x) = 0.036 when x = 7

P(x) = 0.048 when x = 8

So, we have:

P(x >= 6) = 0.022 + 0.036 + 0.048

Evaluate

P(x >= 6) = 0.106

Hence, the probability is 0.106

This is calculated as:

[tex]E(x) = \sum x * P(x)[/tex]

So, we have:

E(x) = 0.234 * 1 + 0.291 * 2 + 0.167 * 3 + 0.109 * 4 + 0.093 * 5 + 0.022 * 6 + 0.036 * 7 + 0.048 * 8

Evaluate

E(x) = 2.986

Approximate

E(x) = 3

Hence, the expected number of births is 3

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please send a picture of it

the equation seems a lil bit complicated

Using proportions, it is found that:

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The heights are measured in units, hence the ratio is:

[tex]r = \frac{5}{25} = \frac{1}{5}[/tex]

The surface areas are measured in units squared, hence the ratio is:

(1:5)² = 1:25.

The volumes are measured in cubic units, hence the ratio is:

(1:5)³ = 1:125.

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The linear function y = 3 · w - 1 represents the number of sea shells found in each week.

The speed of the driven gear is 180 rounds per minute.

In the first problem we have an example of linear progression, in which the number of sea shells is increased linearly every week. After a quick analysis, we conclude that the linear function y = 3 · w - 1, a kind of direct relationship.

In the second problem, we must an inverse relationship to determine the speed of the driven gear. Please notice that the speed of the gear is inversely proportional to the number of teeths. Then, we proceed to calculate the speed:

[tex]\frac{v_{1}}{v_{2}} = \frac{N_{2}}{N_{1}}[/tex]

If we know that [tex]v_{2} = 60\,rpm[/tex], [tex]N_{2} = 60[/tex] and [tex]N_{1} = 20[/tex], then the speed of the driven gear is:

[tex]v_{1} = v_{2}\times \frac{N_{2}}{N_{1}}[/tex]

[tex]v_{1} = 60\,rpm \times \frac{60}{20}[/tex]

[tex]v_{1} = 180\,rpm[/tex]

The speed of the driven gear is 180 rounds per minute.

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Answer:  x= -3 11/20 Decimal form: x=-3.55

Step-by-step explanation:

Answer:

Your answer is -24.

Step-by-step explanation:

Given information.

The graph of f(x) and g(x)

Solving for

-6 * f(3) - 6 * g(-1) = ?

think of f(x) = y as x is the input and y is the output.

Input a value of x into f(x) or g(x) gets us a y value.

Looking at the graph of f(3) = -2 and the graph of g(-1) = 6

Now substitute that and solve.

-6 * -2 -6 * 6 = 12 - 36 = -24

Answer: -24

Step-by-step explanation:

We should first find the outputs to the functions f and g with inputs 3 and -1 respectively. We can do this by looking at the graph and finding the y value for each desired x value.

Thus, we can see that f(3) = -2 and g(-1) is 6.

We can replace these into the expression to get

[tex]-6*-2-6*6[/tex]

We should first multiply, so we get

[tex]12 -36[/tex]

[tex]-24[/tex]

Hence, the answer is -24.

The magnitude of an earthquake releasing 2.5 * 10¹⁵ Joules of energy is 7.33

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that:

M = (2/3) * log (E/E₀)

Where M is the magnitude, E is the amount of energy and E₀ = 10^4..4

For E = 2.5 * 10¹⁵:

M = (2/3) * log (2.5 * 10¹⁵/10^4.4)

M = 7.33

The magnitude of an earthquake releasing 2.5 * 10¹⁵ Joules of energy is 7.33

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Answer:

Step-by-step explanation:

Steps

1] On the right, put brackets around the 1st 2 terms.

y = (x^2 + 2x) - 6

2] Divide the second term's coefficient by 2 and square the result.

2/2 = 1

3] Square the result

1^2 = 1

4] Add that inside the brackets

y = (x^2 + 2x + 1) - 6

5] Subtract 1 outside the brackets. The original equation is still there.

y = (x^2 + 2x + 1) - 6 - 1

y = (x^2 + 2x + 1) - 7

6] What is inside the brackets is a perfect square.

y = (x + 1)^2 - 7

Answer D

Answer:

Step-by-step explanation:

2x+3y=15

multiply by 2

4x+6y=30   ...(1)

6y=-4x+12

4x+6y=12    ...(2)

(1) and (2) represent parallel lines.

Hence no solution.

Answer:

a

Step-by-step explanation:

The missing number is 20.

Subtraction is the mathematical operation that is used to find the difference between two or more numbers.

In order to find the missing number, subtract the total number of people who like science and mathematics from the total number of people who like science

38 - 18 = 20

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Answer:

Step-by-step explanation:

The definition of a Domain in math is all the possible input values that go into the function, so we will have to find all the valid values that can go into the function

The function given is [tex]F(x, y)=\frac{1}{\sqrt{x^2-y} }[/tex] , the denominator cannot be 0.
So we set up the equation
[tex]\sqrt{x^2-y} \neq 0[/tex]
[tex]\sqrt{x^2-y}^{2} \neq 0x^2-y\neq 0x^2\neq y[/tex]

And that the the square root needs to be more than 0.
[tex]\sqrt{x^2-y}\geq 0[/tex]
[tex]x^2-y\geq 0[/tex]
[tex]x^2\geq y[/tex]

So we can conclude that all values of [tex]x^{2}[/tex] must be greater y

That means that our domain is all X values greater than[tex]\sqrt{y}[/tex]

Answer:  [tex]\displaystyle \boldsymbol{-\frac{1}{2}}[/tex]

================================================

Work Shown:

[tex]\displaystyle L = \lim_{\text{x}\to 1^{+}} \frac{1-\text{x}}{\text{x}^2-1}\\\\\\\displaystyle L = \lim_{\text{x}\to 1^{+}} \frac{-(\text{x}-1)}{(\text{x}-1)(\text{x}+1)}\\\\\\\displaystyle L = \lim_{\text{x}\to 1^{+}} \frac{-1}{\text{x}+1}\\\\\\\displaystyle L = \frac{-1}{1+1}\\\\\\\displaystyle L = -\frac{1}{2}\\\\\\[/tex]

In the second step, I used the difference of squares rule to factor.

The (x-1) terms cancel which allows us to plug in x = 1. We plug this value in because x is approaching 1 from the right side.

The endpoints of the sides of the quadrilateral are; (1, 4), (2, 1), (5, 1), (4, 4)

To get the endpoints of the quadrilateral that has 2 sides with negative slope, we will use the formula for slope;

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

Option A; Coordinates are (–4, –4), (–4, –1), (–1, –4), (–1, –1). Slopes are;

m1 = (-1 + 4)/(-4 + 4) = undefined

m2 = (-4 + 1)/(-1 + 4) = -1

m3 = (-1 + 4)/(-1 + 1) = undefined

m4 = (-4 + 1)/(-4 + 1) = 1

No two slopes are negative and this is not correct.

Option B; Coordinates are (–2, –4), (–1, –1), (1, –1), (2, –4). Slopes are;

m1 = (-1 + 4)/(-1 + 2) = 3

m2 = (-1 + 1)/(1 + 1) = 0

m3 = (-4 + 1)/(2 - 1) = -3

m4 = (-4 + 4)/(-2 - 2) = 0

No two slopes are negative and this is not correct.

Option C; Coordinates are (1, 1), (2, 4), (5, 4), (4, 1). Slopes are;

m1 = (4 - 1)/(2 - 1) = 3

m2 = (4 - 4)/(5 - 2) = 0

m3 = (1 - 4)/(4 - 5) = 3

m4 = (1 - 1)/(1 - 4) = 0

No two slopes are negative and this is not correct.

Option D; Coordinates are (1, 4), (2, 1), (5, 1), (4, 4). Slopes are;

m1 = (1 - 4)/(2 - 1) = -3

m2 = (1 - 1)/(5 - 2) = -0

m3 = (4 - 1)/(4 - 5) = -3

m4 = (4 - 4)/(1 - 4) = -0

Two slopes are negative and this is correct.

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QUE :

75 - [5 + 3 of (25 - 2 × 10)]

= 75 - [5 + 3 of ( 25 - 20)]

= 75 - [5 + 3 of 5]

= 75 - [5 + 15]

= 75 - 20

= 55

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Distributive Property :

[tex]\boxed {a(bx + c) = a(bx) + a(c)}[/tex] or

[tex]\boxed {(ax + b)(cx + d) = acx^{2} + bcx + adx + bd}[/tex]

Question 1 :

Question 2 :

Question 3 :

Question 4 :

Answer:

All the correct statements are,

The vertex of the graph is (5, -37).

The parabola has a minimum.

The parabola opens up.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The function g(x) = 10x² - 100x + 213 written in vertex form is,

⇒ g(x) = 10(x – 5)² – 37.

Since, General equation is,

y = a (x - h)² + k

Where, (h, k) is vertex of parabola.

Hence, We get;

The vertex of the graph is (5, -37)

Since, the coefficient of x² is positive

Hence, The parabola has a minimum

And, The parabola opens up.

Thus, All the correct statements are,

The vertex of the graph is (5, -37).

The parabola has a minimum.

The parabola opens up.

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Answer:

firstly,need to know domain and range

The amount invested in the account that yields 7% interest is $4000.

The amount invested in the account that yields 12% interest is $1000.

a + b = 5000 equation 1

0.07a + 0.12b = 400 equation 2

Where:

a = amount invested in the account that yields 7% interest.

b =  amount invested in the account that yields 12% interest.

Multiply equation 1 by 0.07

0.07a + 0.07b = 350 equation 3

Subtract equation 3 from equation 2

0.05b = 50

b = 50 / 0.05

b = 1000

Subtract 1000 from 5000: 5000 - 1000 = 4000

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