(lesson 4.2.5) Find g(-5) given g(x) = x³ - 2​

Answers

Answer 1

Answer: g (-5)

-127

Step-by-step explanation:

Answer 2

Answer: 125 + 25 = 150 i think is the answer

Step-by-step explanation: To evaluate g(5), substitute x = 5 into g(x)

g

(

5

)

=

5

3

+

(

5

×

5

)

×

x

=

125

+

25

=

150


Related Questions

Write three dollars and 65 cents
as an improper fraction (and then reduce).

Answers

Answer:

300/65

Step-by-step explanation:

Answer:

3 65/100 then the simplified version is 13/20

Step-by-step explanation:

A line has a slope of -2 and passes through the point (-2, -3). Write its equation in slope-
intercept form.

Answers

The slope-intercept form of a line's equation is y = mx + b, where m is the slope of the line and b is the y-intercept. We can use the given slope and point to solve for the y-intercept and write the equation in slope-intercept form.

Given: Slope (m) = -2 and point (-2, -3)

Step 1: Use the point-slope form of a line's equation to find the equation of the line in point-slope form:y - y1 = m(x - x1) (where x1,y1 are the coordinates of the given point)y - (-3) = -2(x - (-2))y + 3 = -2(x + 2)Step 2: Simplify the equation by distributing the -2:y + 3 = -2x - 4Step 3: Solve for y by subtracting 3 from both sides of the equation:y = -2x - 7Therefore, the equation of the line in slope-intercept form is y = -2x - 7.

Knowing that the given sides are congruent, find the perimeter of the
triangle. *Congruent is EQUAL
9x-3
4x+7

Answers

Answer:

Step-by-step explanation:

9x-3=4x+7

             +3

9x=4x+10

-4x=-4x

5x=10

divide the 5 by 10 which equals 2.

x=2

find the values of X and Y

Answers

The values of x and y for the right triangle are 4 and 7.21

How to evaluate for the values of x and y for the triangle

The perpendicular height of the right triangle divides the triangle in two triangles with the same proportions as the original triangle.

by Pythagoras, the hypotenuse for the bigger of the two triangles is calculated as;

√(6² + 9²) = 10.82

the angle opposite the side length 6 for triangle with hypotenuse 10.82 and the angle opposite the side length x for triangle with hypotenuse y are the same by proportion, so:

x/6 = 6/9 {opposite/adjacent}

x = 36/9 {cross multiplication}

x = 4

also;

4/y = 6/10.52 {opposite/hypotenuse}

y = 42.08/6

y = 7.21

Therefore, the values of x and y for the right triangle are 4 and 7.21

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find the products AB and BA to determine whether B is the multiplicative inverse of A.

Answers

B is not the multiplicative inverse of A.

Multiplicative inverse matrix:

The multiplicative inverse matrix, also known as the inverse matrix or simply the inverse, is a matrix that when multiplied by a given matrix, results in the identity matrix. The identity matrix is a square matrix with ones on the diagonal and zeros elsewhere.

Here we have

[tex]A = \left[\begin{array}{cc}3&-2&\\0&-3&\end{array}\right][/tex]    [tex]B = \left[\begin{array}{cc}-1&2&\\0&-4&\end{array}\right][/tex]  

Product of A and B

[tex]AB = \left[\begin{array}{cc}3&-2&\\0&-3&\end{array}\right] \times \left[\begin{array}{cc}-1&2&\\0&-4&\end{array}\right][/tex]

[tex]AB = \left[\begin{array}{cc}3(-1) + (-2)(0) &3(2) + (-2)(-4)&\\0 + 0 &0 +(-3)(-4)&\end{array}\right][/tex]  

[tex]AB = \left[\begin{array}{cc}-3 &14&\\0 &12&\end{array}\right][/tex]  

Product of B and A

[tex]BA = \left[\begin{array}{cc}-1&2&\\0&-4&\end{array}\right] \times \left[\begin{array}{cc}3&-2&\\0&-3&\end{array}\right][/tex]

[tex]BA = \left[\begin{array}{cc}1(3) + 2(0)&-1(-2)+2(-3)\\0(3)+0 &0(-2)+(-4)(-3) \end{array}\right][/tex]

[tex]BA = \left[\begin{array}{cc}-3&-4\\0&12\end{array}\right][/tex]

Here AB ≠ BA ≠ I

Therefore,

B is not the multiplicative inverse of A.

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Complete Question given in the picture

Solve the equation
x^2 + 11x - 26 = 0

Answers

The two solutions of the quadratic equation x² + 11x - 26 = 0 are x = 2 and x = -13

How to solve the quadratic equation?

Here we have the quadratic equation:

x² + 11x - 26 = 0

A quadratic equation is a second-degree polynomial equation in one variable, where the highest power of the variable is two.

To solve it we need to use the quadratic formula, it will give:

[tex]x = \frac{-11 \pm \sqrt{11^2 - 4*1*-26} }{2*1}[/tex]

Now we can simplify that and we will get two solutions, these are:

[tex]x = \frac{-11 \pm \sqrt{11^2 - 4*1*-26} }{2*1}\\\\x = \frac{-11 \pm15}{2}[/tex]

Then the two solutions of the quadratic equation are:

x+ = (-11 + 15)/2 = 4/2 = 2

x- = (-11 - 15)/2 = -26/2 = -13

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Another method of identifying an outlier is to investigate whether there is evidence that a value might have come
from a population with a mean different from the mean of the population of the other values.
Let X and Y represent random variables. X is distributed normally with mean u, and standard deviation o.
and Y is distributed normally with mean u, and standard deviation o. Consider I randomly selected value of Y
and I randomly selected values of X.
-
(b) Consider the difference Y-X.
(i) In terms of μ, and .. what is the mean of the difference Y - X?
(ii) In terms of n and standard deviation . what is the standard deviation of the difference Y - X?

Answers

The standard deviation of the difference Y - X depends on the standard deviations of both X and Y, and is given by the formula below.

(b) (i) The mean of the difference Y - X is μY - μX, which is 0 since both X and Y have the same mean, μ.

(b) (ii) The standard deviation of the difference Y - X is √(σY^2 + σX^2), where σY and σX are the standard deviations of Y and X, respectively. Assuming that the values of X are independent of the value of Y, we can use the formula for the variance of the difference of two random variables to get:

Var(Y - X) = Var(Y) + Var(X) - 2Cov(Y, X)

where Cov(Y, X) is the covariance between Y and X. Since Y and X have the same mean, we have:

Cov(Y, X) = E[(Y - μ)(X - μ)] = E[(Y - μ)X] - μE[X] = E[(Y - μ)X] - μ^2

where E[] denotes the expected value. Since X and Y are independent, we have:

E[(Y - μ)X] = E[Y - μ]E[X] = 0

Therefore, we get:

Var(Y - X) = Var(Y) + Var(X) = σY^2 + σX^2

Taking the square root of both sides gives us the standard deviation of Y - X:

SD(Y - X) = √(σY^2 + σX^2)

Therefore, the standard deviation of the difference Y - X depends on the standard deviations of both X and Y, and is given by the formula above.

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Debbie saves $900 each summer with her summer job. She plans to work the same job for the next four summers. She wants to save money from her summer job to pay for her first year of college. She's thinking of attending a college that costs $8,500 for one year's tuition. Her parents have said that they will pay for half of her tuition. How much more money will Debbie need by her freshman year of college to afford her first year's tuition?

Answers

Step-by-step explanation:

If Debbie saves $900 each summer for four summers, she will have saved a total of:

$900 x 4 = $3600

Her parents have agreed to pay half the tuition, which is $8,500 / 2 = $4250.

Therefore, Debbie will need to come up with the remaining amount:

$8,500 - $4,250 = $4,250

Since Debbie will have saved $3,600 from her summer job, she will need an additional:

$4,250 - $3,600 = $650

Debbie will need $650 more to afford her first year's tuition.

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ΔQRS is an isosceles triangle. What is the length of RT¯¯¯¯¯
R
T
? Round to the nearest hundredth. Enter your answer in the box.

Answers

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{11}\\ a=\stackrel{adjacent}{6}\\ o=\stackrel{opposite}{RT} \end{cases} \\\\\\ RT=\sqrt{ 11^2 - 6^2}\implies RT=\sqrt{ 121 - 36 } \implies RT=\sqrt{ 85 }\implies RT\approx 9.22[/tex]

A central angle of a circle whose radius is 14 centimeters subtends an arc whose length is 7pi/15 centimeters. What is the radian measure of the central angle?

Answers

 π/30 R is the radian measure of the central angle.

What is a circle, exactly?

The collection of all points in the plane that make up a circle are all equally spaced from a certain point known as the "centre," making the form a closed two-dimensional shape.

                       The reflection symmetry line is created by all lines that traverse the circle. Additionally, it is symmetrical in rotation around the centre at all angles.

Total circle circumference would be  π d  =   28 π

this arc is a fraction of the total

7π/15 / 28π  x  2π   =   π/30 R

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A boat is heading towards a lighthouse, where Lamonte is watching from a vertical distance of 141 feet above the water. Lamonte measures an angle of depression to the boat at point � A to be 21 ∘ ∘ . At some later time, Lamonte takes another measurement and finds the angle of depression to the boat (now at point � B) to be 57 ∘ ∘ . Find the distance from point � A to point � B. Round your answer to the nearest foot if necessary.

Answers

The distance from point A to point B is 812 feet.

What is triangle?

A triangle is a form of polygon with three sides; the intersection of the two longest sides is known as the triangle's vertex. There is an angle created between two sides. One of the crucial elements of geometry is this.

Certain fundamental ideas, including the Pythagorean theorem and trigonometry, rely on the characteristics of triangles. The angles and sides of a triangle determine its kind.

Here lines AC and ED are parallel. So alternate angles are equal. Now the corresponding angles in triangle ADC and BDC.

In Δ ADC ,

=> tan 9 = opposite / adjacent = 141/AC

=> AC = 141/ tan9= 890.2389.

Now In ΔBDC,

=> tan 61 = 141/BC

=> BC = 141/tan 61 = 78.1575

Now distance AB = AC - BC = 890.2389 - 78.1575 = 812 feet.

Hence the distance from point A to point B is 812 feet.

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Hurit Imala works 40 hours a week as a clerk in a local store. She earns $8.50 an hour. Assuming she is paid for 52 weeks annually, what is her gross annual pay?

Answers

Answer:

Hurit Imala's gross annual pay is $17,680

Step-by-step explanation:

Hurit Imala works 40 hours a week, so her weekly pay would be:

40 hours/week x $8.50/hour = $340/week

To find her annual pay, we need to multiply her weekly pay by the number of weeks in a year:

$340/week x 52 weeks/year = $17,680/year

Therefore, Hurit Imala's gross annual pay is $17,680.

Task 1abcd: Suppose we have n = 60 puppies (across several litters from these two dogs). For the sample, we have the (previously observed) sample proportion
= 0.3833.

Suppose we wanted to use this sample to determine if there is evidence that p = the population proportion of puppies who are spotted is greater than 0.25.

a. State the hypotheses about the population proportion p.

H0:

H1:

Answers

H0 is the null hypothesis stating with that the population proportion of

puppies who are spotted is less than or equal to 0.25,

H0: p <= 0.25

H1: p > 0.25

Why do you use the term "hypothesis"?

In a scientific setting, a hypothesis (plural: hypotheses) is a tested

claim regarding the causal connection between two or more variables

or a suggested explanation for a phenomenon that has been

observed.

where H0 is the null hypothesis stating that the population proportion

of puppies who are spotted is less than or equal to 0.25, and H1 is the

alternative hypothesis stating that the population proportion of puppies

who are spotted is greater than 0.25.

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Please help me. I need help real bad.

Answers

Answer:

  θ ∈ {π/4, π/2, 3π/4, 5π/4, 3π/2, 7π/4}

Step-by-step explanation:

You want the solutions to sin(2θ)sin(θ)=cos(θ) on [0, 2π).

Factors

We can use the identity for sin(2θ) to write the equation in terms of sine and cosine.

  (2sin(θ)cos(θ))·sin(θ) = cos(θ) . . . . replace sin(2θ)

  2sin(θ)²cos(θ) - cos(θ) = 0 . . . . . . . subtract cos(θ)

  cos(θ)(2 sin(θ)² -1) = 0

Zero product rule

The zero product rule tells you a product will be zero only when one or more factors is zero. The zeros of the factors are ...

  cos(θ) = 0   ⇒   θ = π/2, 3π/2

  2sin(θ)² -1 = 0   ⇒   sin(θ) = ±√(1/2)   ⇒   θ = π/4, 3π/4, 5π/4, 7π/4

The solutions are θ ∈ {π/4, π/2, 3π/4, 5π/4, 3π/2, 7π/4}.

__

Additional comment

The solutions are the x-intercepts of the graph of sin(2θ)sin(θ) -cos(θ), the values of x where this expression is zero. A graphing calculator finds them nicely.

Read the following text from a student essay. How can the writer best improve his or
her organization?
Ponies are a type of horse, but there are significant differences between ponies and
horses. Ponies are generally shorter than horses. Ponies also tend to live longer than
horses. Horses are considered to be over fifty-eight inches tall, and ponies are less
than that. Horses usually live to be twenty-five to thirty years old. Most ponies live
to be thirty-five or even forty.
by adding missing commas
moving the first sentence to the end of the paragraph
by moving the first sentence to the second paragraph
by reordering sentences to keep the related ideas together

Answers

The writer can best improve their organization by reordering sentences to keep related ideas together.

Who is called writer?

Writers are individuals who use written words to communicate ideas, stories, or information to a particular audience. They may work in various fields such as journalism, creative writing, copywriting, technical writing, or academic writing. Writers can be novelists, poets, essayists, screenwriters, playwrights, and more, and their work can take many forms, such as books, articles, blogs, scripts, and speeches. Writing is a skill that can be developed and honed through practice, and good writers are able to engage and captivate their readers with their words.

Here,

The writer can best improve their organization by reordering sentences to keep related ideas together. Here's a possible reorganization of the text:

Ponies and horses have significant differences. Horses are considered to be over fifty-eight inches tall and usually live to be twenty-five to thirty years old. In contrast, ponies are generally shorter than horses, with a height of less than fifty-eight inches, and they tend to live longer, often up to thirty-five or even forty years.

This revision keeps the sentences that relate to each other together, creating a clear and logical progression of ideas. Additionally, it removes the redundant statement of defining ponies as a type of horse, which is already well-known information.

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FREE

Find the Sin, Cos and Tan of the right triangle Round your answers to the nearest tenth.
2. Sin=
3. Cos=
d. Tan=

Answers

Using trigonometric functions, we can find the value of the angles as:

Sinθ = 3/5

Cosθ = 4/5

Tanθ = 3/4

Define trigonometric functions?

Six basic trigonometric operations are used in trigonometry. These operations are described by trigonometric ratios. The six basic trigonometric functions are the sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function. The foundation for trigonometric identities and functions is the ratio of the sides of a right-angled triangle. The sine, cosine, tangent, secant, and cotangent values are computed for the perpendicular side, hypotenuse, and base of a right triangle using trigonometric formulas.

Here as per the question,

Opposite side of the angle = 3 units.

Adjacent side of the angle = 4 units.

Hypotenuse of the triangle = 5 units.

Sinθ = opposite side/ hypotenuse

= 3/5

Cosθ = adjacent side/ hypotenuse

= 4/5

Tanθ = opposite side/adjacent side

= 3/4

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State the amplitude, period, midline and an equation involving the sine function for the
graph shown below using a horizontal shift between 0 and 2pi
Amplitude:
Period:
Midline: y =
f(x) =

Answers

The amplitude is 2 units.

The period is 2π units.

f(x) = 2 sin(x - π/2)

What is sine function?

An oscillation that repeats itself repeatedly in many natural events is described by the sine function, which is a mathematical function. It is described as the proportion of a right triangle's hypotenuse to the side that faces an angle. The typical notation for the sine function is sin(x), where x represents the angle.

Amplitude:

The distance between the graph's midline and its maximum or minimum point is known as the amplitude. The midline in the following graph is located at y=0, midway between the greatest value of 2, and the minimum value of -2. The amplitude is therefore 2 units.

Period:

The distance among two consecutive graph points with the same value and direction is known as the period. The above graph repeats itself every 2π units of x and has one complete cycle between x=0 and x=2π. The duration is therefore 2π units.

Midline:

The midline, also referred to as the average of the highest and minimum values, traverses the graph's centre horizontally. The x-axis or the line y=0 serves as the midline in the presented graph.

It is possible to write the sine function equation for the provided graph with a horizontal shift between 0 and 2 as:

f(x) = 2 sin(x - π/2)

The graph fluctuates up and down near the midline, hence the sine function is utilised. The highest value occurs at x=π/2, which is π/2 units to the right of x=0, and the graph continues every 2π units of x, therefore the horizontal shift is π/2. The sine function multiplies the amplitude of two units.

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find the surface area and volume of this retangular prism 7cm by 6cm by 5cm

Answers

The volume of the rectangular prism is 210cm³.

Define rectangular prism

A rectangular prism is a three-dimensional solid shape that has six rectangular faces. Each face of the prism is a rectangle, and the opposite faces are congruent and parallel. The rectangular prism is also known as a rectangular cuboid or a rectangular parallelepiped. The rectangular prism has eight vertices (corners), twelve edges, and six faces. It is a special case of a parallelepiped, which is a three-dimensional solid with six parallelogram faces.

The surface area of the rectangular prism is:

Surface Area = 2(lw + lh +  wh)

Surface Area = 2(7cm x 6cm) + 2(7cm x 5cm) + 2(6cm x 5cm)

Surface Area = 84cm² + 70cm² + 60cm²

Surface Area = 214cm²

Hence, the rectangular prism has a 214 cm² surface area.

We must multiply the rectangular prism's length, width, and height in order to get its volume.

The volume of the rectangular prism is:

Volume = lwh

Volume = 7cm x 6cm x 5cm

Volume = 210cm³

Hence, the rectangular prism has a 210 cm³ volume.

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Simplify each complex fractions. Assume no denominators are 0

Answers

The complex fractions are simplified to;

60. 3/2062. xy.64. (x² + x + 1)/[2x³(x-1)].

How to calculate complex fractions?

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

To simplify this complex fraction, first simplify the numerator by finding a common denominator:

(1/4 - 1/5) = (5/20 - 4/20) = 1/20

Then, we can divide by the denominator by multiplying by its reciprocal:

1/20 ÷ (1/3) = 1/20 × (3/1) = 3/20

Therefore, the simplified complex fraction is 3/20.

(x-y)/(x⁻¹ - y⁻¹)

To simplify this complex fraction, use the formula for the difference of squares on the denominator:

x⁻¹ - y⁻¹ = (x - y)/(xy)

Then, we can rewrite the complex fraction as a division of two fractions:

(x-y)/(x⁻¹ - y⁻¹) = (x-y) × (xy)/(x - y) = xy

Therefore, the simplified complex fraction is xy.

((2x + 1)/(x- (1/x)) - (1/x))/(2x + (2x)/(1-1/x))

To simplify this complex fraction, first simplify each of the two fractions in the numerator and denominator separately:

(2x + 1)/(x- (1/x)) = [(2x² + x)/x]/[(x² - 1)/x] = (2x² + x)/(x² - 1)

(1/x) = (x⁻¹)

(2x + (2x)/(1-1/x)) = (2x + (2x)/(x-1))

= [(2x(x-1) + 2x)/ (x-1)] / [(x-1)/(x-1)]

= (2x² - 2x + 2x)/(x-1)

= (2x²)/(x-1)

Substituting these simplified fractions back into the original complex fraction:

[(2x² + x)/(x² - 1) - x⁻¹] ÷ [(2x²)/(x-1)]

= [(2x² + x)/(x² - 1) - (1/x)] × [(x-1)/(2x²)]

= [(2x² + x) - (x² - 1)]/[x(x² - 1)] × [(x-1)/(2x²)]

= (x² + x + 1)/[2x³(x-1)]

Therefore, the simplified complex fraction is (x² + x + 1)/[2x³(x-1)].

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Image transcribed:

60. (1/4 -1/5)/(1/3)

62. (x-y)/(x⁻¹ - y⁻¹)

64. ((2x 1)/(x- (1/x)) - (1/x))/(2x + (2x)/(1-1/x)

Answer:

  60. 3/20

  62.  -xy

  64.  (2x³ -x² +1)/(4x⁴ +2x³ -2x²)

Step-by-step explanation:

You want the simplified form of various complex fractions.

Simplification

Fractions are added and divided in the usual ways:

  a +b/c = (ac +b)/c

  a/b +c/d = (ad +bc)/(bd)

  (a/b)/(c/d) = (ad)/(bc)

60.

  (1/4 -1/5)/(1/3) = (5 -4)/(5·4)·(3/1) = 3/20

62.

  (x -y)/(1/x -1/y) = (x -y)/((y -x)/(xy)) = xy(x -y)/(y -x) = -xy

64.

  [tex]\dfrac{\dfrac{2x}{x-\dfrac{1}{x}}-\dfrac{1}{x}}{2x+\dfrac{2x}{1-\dfrac{1}{x}}}=\dfrac{\dfrac{2x^2}{x^2-1}-\dfrac{1}{x}}{2x+\dfrac{2x^2}{x-1}}=\dfrac{(2x^3-x^2+1)(x-1)}{x(x^2-1)(2x^2-2x+2x^2)}\\\\=\dfrac{2x^3-x^2+1}{2x^2(x+1)(2x-1)}=\boxed{\dfrac{2x^3-x^2+1}{4x^4+2x^3-2x^2}}[/tex]

__

Additional comment

The factored form in 64 is useful for many purposes. "Simplified" usually means that factors are multiplied out. Note that we used (x²-1) = (x-1)(x+1).

If you were to describe the domain of the expression in 64, it would exclude x=1 as well as those values of x that make the remaining denominator factors zero.

Given the parent function f(x)=√x and a new function g(x)=√x+6+3.

Select from the drop-down menus to correctly describe the changes on the graph from f(x) to g(x)

1. The graph will shift 6 units ___

UP , DOWN , LEFT , RIGHT

2. and 3 units ____

UP , DOWN , LEFT , RIGHT


Answers

Answer:

up down

Step-by-step explanation:

11. A local grocery store has 7 different kinds of hot sauce that you would love try.
However, you only have enough money to purchase 5 of the different flavors. How
many of the flavors of hot sauce are possible for you to purchase?

Answers

we are selecting 5 flavors out of 7 without regard to order. The number of combinations of 7 things taken 5 at a time is given by: C(7,5)  = 21

what is  combinations ?

Combinations, on the other hand, refer to the selection of objects from a set without considering their order. For example, the combinations of 2 letters from the set "ABC" are "AB", "AC", and "BC". The order of the letters in each combination does not matter, so "AB" and "BA" are considered the same combination.

In the given question,

This is a combination problem, since we are selecting 5 flavors out of 7 without regard to order. The number of combinations of 7 things taken 5 at a time is given by:

C(7,5) = 7! / (5! * 2!) = (76543) / (54321) = 21

Therefore, you can purchase 21 different combinations of 5 flavors of hot sauce

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At West Point School District, enrollment increased from 320 students in 2019 to 225 students in 2020. What is the percent of change in enrollment? Round to the nearest percent.

Answers

Answer:95

Step-by-step explanation: cause 320 - 225 = 95

NEED HELP!! 9.1 Puzzle Time
What Do You Get When You Cross a Computer With a Lifeguard?

Answers

6. Using Pythagoras Theorem the value of x = 99. 7, The value of x is 102.56. 8. The triangle is a right triangle. 9. The triangle is acute. 10. The triangle is acute. 11. The value of x is 32.28. 12. The value of x is 40.

What is Pythagoras Theorem?

The relationship between the sides of a right triangle is explained by the Pythagorean theorem, a fundamental mathematical theorem. The square of the hypotenuse's length, the longest side in a right triangle, is said to be equal to the sum of the squares of the lengths of the other two sides.

6. For a = 20, b = 99 using the Pythagoras Theorem we have:

x² = a² + b²

x² = 20² + 99²

x² = 9801

x = 99

7. For a = 60, b = 91 we have:

x² = 60² + 91²

x² = 10521

x ≈ 102.56

8. To determine whether the triangle is acute, obtuse, or right we check for using the Pythagoras Theorem.

a = 20, b = 21, and c = 29

Here,

20² + 21² = 841

29² = 841

Hence, the triangle is right.

9. For a = 15, b = 19, and c = 24. We have:

15² + 19² = 556

24² = 576

The triangle is acute.

10. For a = 11, b = 23, and c = 26. We have:

11² + 23² = 650

26² = 676

The triangle is acute.

11. Using the Pythagoras Theorem we have:

x² = 53² - 45²

x² = 1044

x ≈ 32.28

The value of x is 32.28

12. x² = 41² - 9²

x² = 1600

x = 40

The value of x is 40.

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Answer:

Step-by-step explanation:

The following are equivalent radicals
3√3 = √27
-
3√6 = √54
3√7 = √63
What would be an equivalent form of 3√11 ? Explain
how you know.

Answers

To find an equivalent form of 3√11, we need to simplify the radical expression. We can start by factoring 11 into its prime factors:

11 = 1 x 11

Since there are no perfect squares that divide evenly into 11, we cannot simplify the radical any further. Therefore, an equivalent form of 3√11 is simply 3√11.

We can confirm this by rationalizing the denominator of the radical expression:

3√11 * (√11/√11) = 3√(11*11)/√121 = 3√121/√121 = 3(11)/11 = 3

This shows that 3√11 is in simplest form and cannot be simplified any further

URGENT - A triangle is shown in the imagine below. Answer the questions related to it.

Answers

Answer:

  a) sin(β) = 7/6 is false for any β

  b) angle β is not a real angle

Step-by-step explanation:

You want to use the Sine Law to show that a triangle with sides of lengths 6 and 10 and a smallest angle of 44.5° is impossible.

a) Beta

The Sine Law tells you side lengths are proportional to the sines of their opposite angles.

  sin(β)/10 = sin(44.5°)/6

  sin(β) = 10(0.7)/6

  sin(β) = 7/6

The angle β does not exist. The maximum value of the sine function is 1. There are no angles for which the sine is greater than 1.

b) Impossible

The triangle is impossible because angle β cannot exist.

In effect, the angle 44.5° is too large, or side 10 is too long, or side 6 is too short for the figure to be a triangle.

__

Additional comment

In the realm of complex numbers, β ≈ π/2 -0.569618i radians, about (90 -32.64i)°. You cannot draw this complex angle with your real pencil.

a) For any, sin(β) = 1.17 is false.

b) Angle (β) is not a true angle.

What is trigonometry?

In the branch of mathematics known as trigonometry, the relationships between the sides and angles of triangles are examined.

It involves the study of trigonometric functions like sine, cosine, tangent, cotangent, secant, and cosecant that describe the connections between the sides and angles of a right triangle.

(a) Using the Sine Law, we have:

sin(β)/10 = sin(44.5°)/6

Multiplying both sides by 10, we get:

sin(β) = (10/6)sin(44.5°)

sin(β) = 1.17

However, this is impossible since the sine of an angle can never be greater than 1. Therefore, there is no value of β that satisfies the equation, and we cannot find the value of B.

(b) The fact that the sine of β is greater than 1 means that there is no angle whose sine is equal to that value.

Therefore, there is no possible angle for β that can satisfy the given conditions of the triangle.

This means that the triangle is impossible and cannot exist with the given side lengths and angle measures.

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You made $75 an hour with your commission pay. This month I want to increase that by 20% so that I make

Answers

The increase is $15 dollars so you need to make $90 an hour

the lenghth of a picture frame is 7 inches more than th width. For what values of x is the perimeter of the picture frame greater than 154 inches

Answers

Answer:

x > 35

Step-by-step explanation:

Let's denote the width of the picture frame as "x" inches.

According to the problem, the length of the picture frame is 7 inches more than the width, so it can be expressed as "x + 7" inches.

The perimeter of the picture frame can be found by adding up the lengths of all four sides, which is given by:

Perimeter = 2*(length + width)

Substituting the values of length and width in terms of x, we get:

Perimeter = 2*(x + 7 + x)

Perimeter = 4x + 14

Now we can set up an inequality to find the values of x for which the perimeter is greater than 154 inches:

4x + 14 > 154

Subtracting 14 from both sides, we get:

4x > 140

Dividing both sides by 4, we get:

x > 35

Therefore, the values of x for which the perimeter of the picture frame is greater than 154 inches are x > 35.

Mary is planning to buy a mobile phone that costs $500. She can choose any of five different payment plans with varying simple interest rates and periods:

plan 1: 6% for 10 months
plan 2: 8% for 12 months
plan 3: 10% for 14 months
plan 4: 12% for 18 months
plan 5: 14% for 12 months

Which plan offers the lowest monthly payments?

Answers

As a result, Plan 4's $38.89 monthly premium is the lowest.

How to find the lowest monthly payments ?

The monthly premium you pay for health insurance. You typically have to pay additional fees for your health care in addition to your premium, such as a deductible, copayments, and coinsurance.

(P + Simple Interest) / (500 + 58.33) / 14 = $42.02 is the formula for the monthly payment.

Plan 4: P = $500

t = 18/12 years, and r = 0.12

Simple interest equals $500 * 0.12/* (18/12) = $90.

(P + Simple Interest) / t = ($500 + $90) / 18 = $38.89 is the monthly payment.

Plan 5: P = $500

t = 12/12 years, and r = 0.14.

Simple interest is equal to $500 * 0.14 * (12/12) = $70.

(P + Simple Interest) / t = ($500 + $70) / 12 = $47.50 is the amount due each month.

As a result, Plan 4's $38.89 monthly premium is the lowest.

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The vertices of a rectangle are plotted.

A graph with both the x and y axes starting at negative 8, with tick marks every one unit up to 8. The points negative 5 comma 2, 4 comma 2, negative 5 comma negative 4, and 4 comma negative 4 are each labeled.

What is the area of the rectangle?

15 square units
30 square units
45 square units
54 square units

Answers

The area of the rectangle is d. 54 square units.

What is rectangle?

A rectangle is a closed two-dimensional geometry with four sides, four corners, and four right angles (90°). A rectangle's opposite sides are equal and parallel. Because a rectangle is a 2-D form, it has two dimensions: length and width. The length of the rectangle is the longer side, while the width is the shorter side.

The rectangle has two pairs of parallel sides, so its area can be calculated by multiplying the length of one pair of parallel sides by the length of the other pair of parallel sides.

From the given points, we can see that the length of one pair of parallel sides of the rectangle is:

4 - (-5) = 9 units

And the length of the other pair of parallel sides of the rectangle is:

2 - (-4) = 6 units

Therefore, the area of the rectangle is:

9 units × 6 units = 54 square units.

So the area of the rectangle is d. 54 square units.

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3. The t test for two independent samples - Two-tailed example
“Bullying,” according to noted expert Dan Olweus, “poisons the educational environment and affects the learning of every child.” Bullying and victimization are evident as early as preschool, with the problem peaking in middle school. Suppose you are interested in the emotional well-being of not only the victims but also bystanders, bullies, and those who bully but who are also victims (bully-victims). You decide to measure depression in a group of victims and a group of bully-victims using a 26-item, 3-point depression scale. Assume scores on the depression scale are normally distributed and that the variances of the depression scores are the same among victims and bully-victims.
The group of 30 victims scored an average of 21.5 with a sample standard deviation of 10 on the depression scale. The group of 27 bully-victims scored an average of 25.8 with a sample standard deviation of 9 on the same scale. You do not have any presupposed assumptions about whether victims or bully-victims will be more depressed, so you formulate the null and alternative hypotheses as:
H0
: μvictims
– μbully-victims
= 0
H1
: μvictims
– μbully-victims
≠ 0
You conduct an independent-measures t test. Given your null and alternative hypotheses, this is a test. To use the Distributions tool to find the rejection region, you first need to set the degrees of freedom. The degrees of freedom is .

The critical t-scores that form the boundaries of the rejection region for α = 0.01 are ± .
In order to calculate the t statistic, you first need to calculate the standard error under the assumption that the null hypothesis is true. In order to calculate the standard error, you first need to calculate the pooled variance. The pooled variance is s2p
= . The standard error is s(M1 – M2)
= .
The t statistic is .
The t statistic in the rejection region. Therefore, the null hypothesis is . You conclude that victims have a different mean depression score than bully-victims. Thus, it can be said that these two means are different from one another.

Answers

The test statistics do not lie in the rejection so the null hypothesis does not reject.

How to solve

Here we have the following information:

[tex]\bar{x}_{1}=25.3, n_{1}=25, s_{1}=9, \bar{x}_{2}=20.5, n_{2}=23, s_{2}=8[/tex]

Here degree of feedom will be

[tex]df=n_{1}+n_{2}-2=25+23-2=46[/tex]

The critical values of t are: +/- 2.687

Rejection region:

If t < -2.687 and t > 2.687, reject H0

Pooled variance is :

[tex]s^{2}_{p}=\frac{(n_{1}-1)s_{1}^{2}+\left ( n_{2}-1 \right )s_{2}^{2}}{n_{1}+n_{2}-2}=72.8696[/tex]

The standard error is

[tex]s_{M_{1}-M_{2}}=s_{p}\sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}}}=2.4664[/tex]

and t-statistics will be

[tex]t=\frac{\bar{x}_{1}-\bar{x}_{2}}{s_{p}\sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}}}}=1.946[/tex]

The test statistics do not lie in the rejection so the null hypothesis does not reject.

You cannot conclude...

not

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