What is the Domain of f(x) = -x^3 + 6x^2 -10x + 4

Answer:

a = 3√2;

b = 3

Step-by-step explanation:

Use trigonometry:

[tex] \tan(45°) = \frac{b}{3} [/tex]

Cross-multiply to find b:

[tex]b = 3 \times \tan(45°) = 3 \times 1 = 3[/tex]

Use the Pythagorean theorem to find a:

[tex] {a}^{2} = {3}^{2} + {b}^{2} [/tex]

[tex] {a}^{2} = {3}^{2} + {3}^{2} = 9 + 9 = 18[/tex]

[tex]a > 0[/tex]

[tex]a = \sqrt{18} = \sqrt{9 \times 2} = 3 \sqrt{2} [/tex]

0.2342 is the probability that the number of women that would prefer to drink tea over coffee is within 1 standard deviation of the mean

Let's start by finding the mean and standard deviation of the number of women who prefer to drink tea over coffee in a sample of 7 women.

The mean is given by:

μ = np

where n is the sample size and p is the probability of success (the proportion of women who prefer tea over coffee).

So, for this problem, μ = 7 * 0.31 = 2.17

The standard deviation is given by:

σ = sqrt(np(1-p))

where sqrt denotes the square root.

So, for this problem, σ = sqrt(7 * 0.31 * (1 - 0.31)) = 1.22

2.17 - 1.22, 2.17 + 1.22

= 0.95, 3.39

using binomial probability

p^x * 1 - p

= 0.31 * 7 x 0.108

= 0.2342

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Based on the given information, Yelena jumped the highest with a jump of 74 inches (6.17 feet).

Measurement is the process of assigning a numerical value to a physical quantity, such as length, mass, time, temperature, or volume. It is a fundamental aspect of science, engineering, and everyday life. In order to measure something, we need a unit of measurement, which is a standard reference quantity that is used to express the measurement. For example, meters or feet are commonly used units for length, while grams or pounds are used for mass.

To compare the high jumps of the four athletes, we need to convert all the measurements to the same unit.

Anna: 2.1 yards = 6.3 feet

Javier: 72 inches = 6 feet

Charles: 5 feet 11 inches = 71 inches = 5.92 feet

Yelena: 74 inches = 6.17 feet

So, Yelena jumped the highest with a jump of 74 inches (6.17 feet).

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The function f(x) will be after shifting is g(x)= (x – 1)² + 1

The function f is used to move the graph of a function f(x) to the right by h units (x-h). This is because when we substitute x with x-h in f(x), we obtain f(x-h), meaning that we are substituting x with x+h in the initial function f. (x). Hence, if we wish to move the graph of f(x) = (x + 2)² + 1 three units to the right, we may do it by using the function f(x-3) to move the graph three units to the right.

g(x)=(x-3+2)²+1

g(x)= (x – 1)² + 1

The complete question is

Consider the function f(x) = (x + 2)2 + 1. Which of the following functions shifts the graph of f(x) to the right three units?

g(x) = (x + 5)2 + 1

g(x) = (x + 2)2 + 3

g(x) = (x – 1)2 + 1

g(x) = (x + 2)2 – 2

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The solution to the problem is that the number "x" must be less than or equal to -3.9 in order for the sum of "a number times 10 and 20" to be at most -19.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can contain variables, constants, and operators (such as addition, subtraction, multiplication, and division) that are used to represent quantities and their relationships.

Let's use algebra to solve this problem.

Let's call the number we're trying to find "x".

The sum of "a number times 10 and 20" can be written as "10x + 20".

So, we can translate the statement "the sum of a number times 10 and 20 is at most -19" into an equation:

10x + 20 ≤ -19

Now we can solve for x:

10x + 20 ≤ -19

Subtract 20 from both sides:

10x ≤ -39

Divide both sides by 10:

x ≤ -3.9

Therefore, the solution to the problem is that the number "x" must be less than or equal to -3.9 in order for the sum of "a number times 10 and 20" to be at most -19.

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Answer:

(4x - 5) years old

Step-by-step explanation:

Nick = x years old

Matt = (3 x X)

=3x years old

Oscar = (x - 5) years old

total age = x + 3x + (x - 5)

= (4x - 5) years old

A) Let X be the amount of time it takes Capt. Rigg to land a plane from announcement to touch down. We know that X has a uniform distribution from 0 to 25 minutes. The probability that it takes at least 5 minutes to land the plane is equal to the probability that X is greater than or equal to 5:

P(X ≥ 5) = (25-5)/(25-0) = 20/25 = 0.8

So the probability that, for a randomly selected flight, it takes Capt. Rigg at least 5 minutes to land the plane after the announcement is 0.8.

b) Since X has a continuous uniform distribution, the probability that it takes exactly 15 minutes to land a plane is 0.

Answer:

The circumcenter of the triangle with vertices (-7, -1), (-1, -1), and (-7, -9) is (-4, -8).

Step-by-step explanation:

To find the coordinates of the circumcenter of the triangle with vertices (-7, -1), (-1, -1), and (-7, -9), we can use the following steps:

Step 1: Find the midpoint of two sides

We first find the midpoint of two sides of the triangle. Let's take sides AB and BC:

Midpoint of AB: ((-7 + (-1))/2, (-1 + (-1))/2) = (-4, -1)

Midpoint of BC: ((-1 + (-7))/2, (-1 + (-9))/2) = (-4, -5)

Step 2: Find the slope of two sides

Next, we find the slope of the two sides AB and BC:

Slope of AB: (-1 - (-1))/(-1 - (-7)) = 0/6 = 0

Slope of BC: (-9 - (-1))/(-7 - (-1)) = -8/(-6) = 4/3

Step 3: Find the perpendicular bisectors of two sides

We can now find the equations of the perpendicular bisectors of the two sides AB and BC. Since the slope of the perpendicular bisector is the negative reciprocal of the slope of the side, we have:

Equation of perpendicular bisector of AB:

y - (-1) = (1/0)[x - (-4)]

x = -4

Equation of perpendicular bisector of BC:

y - (-5) = (-3/4)[x - (-4)]

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

y = (-3/4)x - 8

Step 4: Find the intersection of perpendicular bisectors

We now find the point of intersection of the two perpendicular bisectors. Solving for x and y from the two equations, we get:

(-4, -8)

Therefore, the circumcenter of the triangle with vertices (-7, -1), (-1, -1), and (-7, -9) is (-4, -8).

Answer:

54 degrees

Step-by-step explanation:

Any angle subtended by the angle is twice the angle subtended by the same angle.

Or m<LMP =2m<LNM.

So m<LNM = 108/2 = 54 degrees.

a) The percentage of residents who liked the local parks out of those surveyed is 30%.

b) The percentage of the residents who liked the school system out of those surveyed is 60%.

The percentage refers to a portion of a whole value or quantity, expressed in percentage terms.

The percentage is a ratio, which compares a value of interest with the whole, and is computed by multiplying the quotient of the division operation between the particular value and the whole value by 100.

The total number of Plana residents surveyed = 240

The number of residents who responded that they liked the local parks = 72

The percentage of residents who liked the local parks = 30% (72 ÷ 240 x 100)

The number of residents who responded that they liked the school system = 144

The percentage of residents who liked the school system = 60% (144 ÷ 240 x 100).

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Answer:

To calculate the monthly payment for each option, we can use the loan formula:

Payment = (P * r) / (1 - (1 + r)^(-n))

where P is the principal amount, r is the monthly interest rate, and n is the total number of payments.

For Option A, the principal amount is $60,000, the interest rate is 4% per year, and the loan term is 10 years. We first need to convert the annual interest rate to a monthly interest rate:

r = 4% / 12 = 0.00333333 (rounded to 8 decimal places)

n = 10 years * 12 months/year = 120 months

Using the loan formula, we get:

Payment = (60000 * 0.00333333) / (1 - (1 + 0.00333333)^(-120)) = $630.55

Therefore, the monthly payment for Option A is $630.55.

For Option B, the principal amount is also $60,000, the interest rate is 3% per year, and the loan term is 20 years. We convert the annual interest rate to a monthly interest rate:

r = 3% / 12 = 0.0025 (rounded to 4 decimal places)

n = 20 years * 12 months/year = 240 months

Using the loan formula, we get:

Payment = (60000 * 0.0025) / (1 - (1 + 0.0025)^(-240)) = $342.61

Therefore, the monthly payment for Option B is $342.61.

To calculate the total amount paid over the life of the loan for each option, we simply multiply the monthly payment by the total number of payments:

For Option A, the total amount paid = $630.55 * 120 months = $75,665.92

For Option B, the total amount paid = $342.61 * 240 months = $82,226.40

To calculate the total interest paid over the life of the loan for each option, we subtract the principal amount from the total amount paid:

For Option A, the total interest paid = $75,665.92 - $60,000 = $15,665.92

For Option B, the total interest paid = $82,226.40 - $60,000 = $22,226.40

Therefore, Option A has a lower monthly payment and total amount paid over the life of the loan, but Option B has a longer loan term and a lower interest rate, resulting in a higher total interest paid over the life of the loan

Answer:

Certainly, here's an illustration:

       ----------------------

       |                    |

 2cm   |                    |

       |                    |  12cm

       |                    |

       ----------------------

           <---- ¾ of 12cm --->

             (9cm - 2cm)

               = 7cm

In this illustration, the rectangle is represented by a box with a length of 12cm and a width of 7cm. The width is calculated by taking ¾ of the length (which is 9cm) and subtracting 2cm from it. The dimensions of the rectangle are shown inside the box, with the length indicated by the vertical line and the width indicated by the horizontal line.

About 25% of students ride the bus for less than 13 minutes.

About 75% of students ride the bus for less than 27 minutes.

Median is a measure of central tendency that represents the middle value in a dataset when the values are arranged in order of magnitude.

In this case, the median is 21 minutes. This means that half of the students ride the bus for less than 21 minutes and half of the students ride the bus for more than 21 minutes.

The lower quartile (Q1) is the value that separates the lowest 25% of the data from the other 75%. In this case, the lower quartile is 13 minutes. This means that 25% of the students ride the bus for less than 13 minutes and 75% ride the bus for more than 13 minutes.

The upper quartile (Q3) is the value that separates the highest 25% of the data from the other 75%. In this case, the upper quartile is 27 minutes. This means that 75% of the students ride the bus for less than 27 minutes and 25% ride the bus for more than 27 minutes.

So, to answer the statement about the data set:

About 25% of students ride the bus for less than 13 minutes. (this is because the lower quartile separates the lowest 25% of the data from the other 75%)

About 75% of students ride the bus for less than 27 minutes. (this is because the upper quartile separates the highest 25% of the data from the other 75%)

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Answer:

that's the slope of the y intercept

Answer:

To find the slope of a line perpendicular to another line, we need to first find the slope of the given line. The equation of the given line is x + y = 3. We can rewrite this equation in slope-intercept form (y = mx + b) by solving for y: y = -x + 3 So the slope of the given line is -1. To find the slope of a line perpendicular to this line, we know that it will have a slope that is the negative reciprocal of -1, which is 1. Therefore, the slope of a line perpendicular to the line whose equation is x + y = 3 is 1.

Answer: 1

Step-by-step explanation:

The given equation x + y = 3 can be rearranged to slope-intercept form, which is y = -x + 3.

To find the slope of this line, we can see that the coefficient of x is -1. Therefore, the slope of the line is -1.

To find the slope of a line perpendicular to this line, we need to take the negative reciprocal of the slope of the given line.

The negative reciprocal of -1 is 1/1 or simply 1. Therefore, the slope of a line perpendicular to the line x + y = 3 is 1.

Answer: [tex]-6x^3+23x^2+59x-120[/tex]

Step-by-step explanation:

(2x – 3)(8 + 3x)( 5 - x)

To multiply this polynomial we can break it down into two steps.

First, lets multiply (2x – 3)(8 + 3x) from the polynomial (2x – 3)(8 + 3x)(5 - x).

Its best to rearrange the x in the parenthesis, so it can look and be much easier: (2x – 3)(8 + 3x)  ->  (2x – 3)(3x + 8)

Now lets multiply it out: (2x – 3)(3x + 8)

[tex]6x^2+16x-9x-24[/tex]

After multiplying it out, combine like terms:

[tex]6x^2+7x-24[/tex]

Now take this polynomial and multiply the remaining factor, (5 - x)

[tex](-x + 5)(6x^2+7x-24)\\\\-6x^3+-7x^2+24x+30x^2+35x-120[/tex]

Now lets combine like terms!

[tex]-6x^3+23x^2+59x-120[/tex]

So the answer is: [tex]-6x^3+23x^2+59x-120[/tex]

The identity 1/csc x+1 - 1/csc x-1 = [tex]-2tan^2 x[/tex] is verified and correct.

To verify the identity:

[tex]\\\frac{1}{csc x+1} - \frac{1}{csc x-1} = -2tan^2 x[/tex]

Starting with the reciprocal identity, we can say:

csc x = [tex]\frac{1}{sin x}[/tex]

So we have:

[tex]1/(1/sin x + 1) - 1/(1/sin x - 1) = -2tan^2 x[/tex]

We need to identify a common denominator in order to simplify the left side of the equation. The common denominator is:

[tex](1/sin x + 1)(1/sin x - 1) = (1 - sin x)/(sin x)^2[/tex]

As a result, we can change the left side of the equation to read:

[tex][(1 - sin x)/(sin x)^2] [(sin x - 1)/(sin x + 1)] - [(1 - sin x)/(sin x)^2] [(sin x + 1)/(sin x - 1)][/tex]

Simplifying this expression by multiplying the numerators and denominators, we get:

[tex](1 - sin x)(sin x - 1) - (1 - sin x)(sin x + 1) / (sin x + 1)(sin x - 1)(sin x)^2[/tex]

Expanding the brackets and simplifying, we get:

[tex]-(2sin^2 x - 2sin x) / (sin x + 1)(sin x - 1)(sin x)^2[/tex]

Factor out -2sin x from the numerator:

[tex]-2sin x(sin x - 1) / (sin x + 1)(sin x - 1)(sin x)^2[/tex]

Simplifying, we get:

[tex]-2sin x / (sin x + 1)(sin x)^2[/tex]

Now, we can use the identity:

[tex]tan^2 x = sec^2 x - 1 = (1/cos^2 x) - 1 = sin^2 x / (1 - sin^2 x)[/tex]

Simplifying, we get:

[tex]sin^2 x = tan^2 x (1 - tan^2 x)[/tex]

When we add this to the initial equation, we obtain:

[tex]-2sin x / (sin x + 1)(sin x)^2 = -2tan^2 x(sin x)/(sin x + 1)[/tex]

Now, we can use the identity:

sin x / (sin x + 1) = 1 - 1/(sin x + 1)

Simplifying, we get:

[tex]-2tan^2 x(sin x)/(sin x + 1) = -2tan^2 x + 2tan^2 x / (sin x + 1)[/tex]

When we add this to the initial equation, we obtain:[tex]-2tan^2 x + 2tan^2 x / (sin x + 1) = -2tan^2 x[/tex]

Simplifying, we get:

[tex]-2tan^2 x = -2tan^2 x[/tex]

Therefore, the identity is verified.

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Answer:

14°

Step-by-step explanation:

Let a be the angle of depression.

Set your calculator to degree mode.

[tex]tan(a) = \frac{2000}{8020} [/tex]

[tex] a = {tan}^{ - 1} \frac{2000}{8020} = 14[/tex]

So a = 14°

Answer: 14°

Step-by-step explanation:

tan(x) = 8020/2000

x = tan^-1 (8020/2000)

x = 75.99 ≈ 76°

Angle of Dep = 90 - 76

Angle of Dep = 14°

Answer: 20

Step-by-step explanation:

Therefore, the distance between the pilot and the home is roughly 5,348.2 feet.

The height of the balloon divided by the neighboring side yields the tangent of the angle of depression (the distance from the balloon to the house).

Tan(32°) is therefore equal to 2828/x,

where x is the distance between the balloon and the home.

The answer to the x equation is

x = 2828/tan(32°)

Value of tan 32° = 0.6610060414

x=  5,348.2 feet.

The height of the balloon divided by the neighboring side yields the tangent of the angle of depression (the distance from the balloon to the house).

Tan(45°) is therefore equal to 2828/x, where x is the distance between the balloon and the home.

The answer to the x-problem is x = 2828/tan(45°) 2828 feet.

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Answer: -4x(x-1)

Step-by-step explanation:

Since both are perfect squares just factor.

Answer:

(D) 8 units to the left

Step-by-step explanation:

Took the test, got it right. FLVS

After answering the presented question, we can conclude that inequality therefore, the solution for z is z < -7.

In mathematics, an inequality is a non-equal connection between two expressions or values. As a result, imbalance leads to inequity. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal symbol is typically used (). Various disparities, no matter how little or huge, are utilised to contrast values. Many simple inequalities can be solved by altering the two sides until just the variables remain. Yet, a lot of factors contribute to inequality: Negative values are divided or added on both sides. Exchange left and right.

[tex]15 - 3(2 - z) < -12\\15 - 6 + 3z < -12 \\9 + 3z < -12 \\3z < -21 \\z < -7 \\[/tex]

Therefore, the solution for z is z < -7.

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After answering the presented question, we can conclude that  area of Circle M, [tex]C = 2\pi [(17/\pi )^0.5] km\\[/tex]

A circle appears to be a two-dimensional component that is defined as the collection of all places in a jet that are equidistant from the hub. A circle is typically depicted with a capital "O" for the centre and a lower portion "r" for the radius, which represents the distance from the origin to any point on the circle. The formula 2r gives the girth (the distance from the centre of the circle), where (pi) is a proportionality constant about equal to 3.14159. The formula r2 computes the circumference of a circle, which relates to the amount of space inside the circle.

area of Circle M,

[tex]289 = \PI(x + 6)^2\\289/\PI = (x + 6)^2\\\sqrt(289/\pi ) = x + 6\\(17/\pi )^0.5 - 6 = x\\x = (17/\pi )^0.5 - 6 km\\C = \pi (2x + 12) km\\C = 2\pi (x + 6) km\\[/tex]

[tex]C = 2\pi [(17/\pi )^0.5] km\\[/tex]

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The domain of fog is: Domain of fog = {x ∈ R | 3 ≤ g(x) ≤ 9}

The range of fog is:  Range of fog = {1, 2, 5}

The domain of a function is the set of all possible input values (usually denoted by x) for which the function is defined.

The range of a function is the set of all possible output values (usually denoted by y) that the function can produce for its corresponding inputs in the domain.

(a) Domain of fog:

The domain of fog is the set of all inputs for which the composition is defined. Since g is defined for all values in its domain, and f is defined for all values in the range of g, the domain of fog is the set of all values in the domain of g for which g(x) is in the domain of f.

(b) Range of fog:

The range of fog is the set of all possible outputs of the composition. Since g is defined for all values in its domain, and f is defined for all values in the range of g, the range of fog is the set of all possible outputs of f when its input is an output of g.

Range of fog = {f(g(x)) | x ∈ R, 3 ≤ g(x) ≤ 9}

To determine the values in the range of fog, we need to evaluate f(g(x)) for each x in the domain of fog. We can do this by first determining the outputs of g for each value in its domain, and then evaluating f at those outputs.

The outputs of g for x = 4, 5, 7 are:

g(4) = 6

g(5) = 8

g(7) = 9

Since f is defined for all values in the range of g, we can evaluate f at each of these outputs to get:

f(g(4)) = f(6) = 5

f(g(5)) = f(8) = 2

f(g(7)) = f(9) = 1

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According to the quadrilaterals, the proof perpendicularity and congruence are stated below.

Proof #7:

Statement | Reasons

XY | ZW | Given

XW bisects ZY | Given

ZR ≅ RY | Definition of segment bisector

∠XRY ≅ ∠RW | Alternate interior angles theorem

ΔXRY ≅ ΔWRZ | AAS ≅ theorem

∠XYR ≅ ∠WZR | Definition of segment bisector and corresponding parts of congruent triangles

Proof #8:

Statements | Reasons

EF ≅ HL | Given

∠PER ≅ ∠PHE | Given

∠EPF and ∠HPL are right angles | Definition of perpendicular lines

EP ≅ PH | Definition of perpendicular bisector

AEFP ≅ AHLP | SAS ≅ theorem

ΔEFP ≅ ΔHLP | Base angles converse theorem

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Image transcribed:

A Proof #7

Given: XY || ZW

XW bisects ZY

Prove: ΔXRY ≅ ΔWRZ

Statements | Reasons

1.                | 1.

2.                | 2.

3.                | 3.

4.                | 4.

5.                | 5.

6.                | 6.

XY || ZW,   Alternate Int. ∠ Theorem,   AAS ≅ Theorem

∠XRY ≅ ∠RW,    Def. of Segment Bisector,   ZR ≅ RY

ΔXRY ≅ ΔWRZ,    ∠XYR ≅ ∠WZR,    XW bisects ZY

ASA ≅ Theorem,   Given,     Vertical Angles ≅ Theorem

A Proof # 8

Given: EL ⊥ FH, ∠PEH ≅ ∠PHE

EF ≅ HL

Prove: ΔEFP ≅ ΔHLP

Statements | Reasons

1.                | 1.

2.                | 2.

3.                | 3.

4.                | 4.

5.                | 5.

6.                | 6.

EF ≅ HL,    AEFP ≅ AHLP,    EP ≅ PH,    ∠PER ≅ ∠PHE

HL ≅ Theorem,      SAS ≅ Theorem,      Base Angles Converse Theorem

Definition of ⊥ Lines,     ∠EPF and ∠HPL are right angles

EL ⊥ FH,        Given

Answer:

D

Step-by-step explanation:

-6 is constant because it has a degree of 0

3x is linear because it has a degree of 1

[tex]4x^{2}[/tex] is quadratic because it has a degree of 2

So the answer is D

The net profit can be calculated by subtracting the production costs from the total revenue generated by selling tickets. Since each ticket was sold for a fixed price, we can assume that the relationship between the net profit and the number of tickets sold is linear.

We know that when 200 tickets were sold, the net profit was $12,000, which means that the slope of the linear function is:

[tex]\text{slope = (net profit at 200 tickets - net profit at 0 tickets)} \div (200 - 0)[/tex]

[tex]\text{slope} = (\$12,000 - \$1,200) \div 200[/tex]

[tex]\text{slope} = \$55[/tex]

The y-intercept of the linear function represents the net profit when no tickets have been sold, which is equal to the negative of the production costs:

[tex]\text{y-intercept} = -\$1,200[/tex]

Therefore, the equation of the linear function is:

[tex]\text{y} = \$55x - \$1,200[/tex]

where x is the number of tickets sold and y is the net profit in dollars.

The graph of this function is an increasing linear function in quadrant 1 with a positive y-intercept, which is choice A. Therefore, the answer is choice A: graph of an increasing linear function in quadrant 1 with a positive y-intercept.

Answer: it makes 74 degree

Step-by-step explanation: This forms a right triangle. The 25-ft ladder is the hypotenuse of the right triangle. and the 7ft bottom of the ladder is the base of a triangle

For the angle where the ladder meets the ground, the

ground is the adjacent leg. The ladder is the hypotenuse.

Call the angle between the ladder and the ground angle A.

The trig ratio that relates the adjacent leg and the hypotenuse is cosine.

Answer: Let the total number of students in the class be x.

Then the number of boys in the class is 60% of x, or 0.6x.

And the number of girls in the class is 16.

We can write an equation based on the information given:

0.6x + 16 = x

Solving for x:

0.4x = 16

x = 40

Therefore, there are 0.6x = 24 boys in the class.

Step-by-step explanation: