A triangle with side lengths 8, 15, and 17 is a right triangle by the converse of the
Pythagorean Theorem. What are the measures of the other 2 angles?

The factored form of the given expression is (8x + 4)(2x - 3).

So, the expression is:

Now, evaluate to get the factors as follows:

Factors: (8x + 4)(2x - 3)

Therefore, the factored form of the given expression is (8x + 4)(2x - 3).

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For the given triangle ABC, Measures of given angles are m∠A=30 , m∠C=90 , m∠B=60 and side AC = 28 then the measure of side                   AB = 56√3/3 , BC =28√3/3.

As given in the question,

In the triangle ABC,

Measures of given angles are :

m∠A=30 , m∠C=90 , m∠B=60

And Measure of side AC = 28

As ABC is right angled triangle with m∠C=90,

If we take ∠A,

AC = Base

AB = Hypotenuse

BC = perpendicular side

Using trigonometric ratios,

tan A = BC/AC

⇒tan 30° = BC / 28

⇒1/√3 = BC /28

⇒ BC = 28/√3

⇒BC = 28√3/3

Now,

cos A = AC/AB

⇒ cos 30° = 28/AB

⇒ √3/2 = 28 /AB

⇒ AB = (28 × 2)/√3

⇒ AB = 56√3/3

Therefore, for the given triangle ABC, Measures of given angles are m∠A=30 , m∠C=90 , m∠B=60 and side AC = 28 then the measure of side AB = 56√3/3 , BC =28√3/3.

The complete question is:

What are AB and BC? AC=28 , m∠A=30 , m∠C=90 , m∠B=60.

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The number of elements of event E n(E) is 70.

The selecting of r items out of n items is done by using Combination. The formula for combination is as follows,

[tex]C(n,r)=\frac{n!}{r!(n-r)!}[/tex]

Where n is the total number of elements and out of which r is selected and ! is factorial sign and n is greater than or equal to r.

Now, Finding the number of elements in the event E that at least two 5-dollar bills are drawn from the bag.

Here, three bills are drawn out of which at least two 5-dollar bills must be drawn, so

[tex]n(E)=C(5,2)\times C(6,1)+C(5,3)\\\\=\frac{5!}{2!(5-2)!} \times \frac{6!}{1!(6-1)!} +\frac{5!}{3!(5-3)!}\\\\=10\times6+10\\=70[/tex]

Therefore, the number of elements n(E) in event E is 70.

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Answer:

4.5 i think

Step-by-step explanation:

Answer: -$250.00

Step-by-step explanation:

[tex][(5000)(0.09)+150000(0.0040)]-1300 =-\$250[/tex]

The expected value of the policy to the insurance company is  -$ 250

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the value of probability owners of hours of worth between $120,000 to $170,000 making a claim of $ 5000 = 0.09

Let the value of probability of the house and contents being totally destroyed = 0.0040

Now , the tragedy happens and the company pays = $ 150,000

The amount the insurance company charges = $ 1300

So , the equation will be

The expected value of this policy to the insurance company =
( probability owners of hours of worth between $120,000 to $170,000 making a claim of $ 5000 x $ 5000 ) + ( the amount company pays x 0.0040) - amount the insurance company charges

So , the equation will be

The expected value of this policy to the insurance company =
( ( 0.09 x 5000 ) + ( 150000 x 0.0040 ) - 1300 )

The expected value of this policy to the insurance company =
( ( $ 450 + $ 600 - $ 1300 )

The expected value of this policy to the insurance company = - $ 250

Hence , The expected value of policy to the insurance company is -$ 250

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The value of mean is 158 and the value of standard deviation is 190.99

Let m be mean

Mean= sum/ n

Mean= (1730+1689+1326+1614+1460+1867+1430) / 7

m= 11116 / 7

M= 1588

Mean= 158

Standard deviation sample formula is :

S.D=sqrt((|x-m|^2)/ n-1)

So let start find |x-m|^2

For 1st: |1730-1588|^2=20164

For 2nd: |1689-1588|^2=10201

For 3rd: |1326-1588|^2=68644

For 4th: |1614-1588|^2=676

For 5th: |1460-1588|^2=16384

For 6th: |1867-1588|^2=77841

For 7th: |1430-1588|^2=24964

Summation of |x-m|^2 = 218874

Standard deviation formula is:

S.D = sqrt((summation of |x-m|^2) / n-1)

S.D=sqrt(218874/6)

S.D=sqrt(36479)

S.D=190.99

Therefore the mean and standard deviation  is 1588 and  190.99

The complete question is : A person's metabolic rate is the rate at which the body consumes energy. Metabolic rate is important in studies of weight gain, dieting, and exercise. Here are the metabolic rates of 7 men who took part in a study of dieting. (The units are calories per 24 hours. These are the same calories used to describe the energy content of foods.) 1730 1689 1326 1614 1460 1867 1430 Calculate the mean and standard deviation of the metabolic rates, showing each step in detail.

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The number of adults is 882 adults.

The number of teenagers is 252 teenagers.

The number of children is 441 children.

From the information, 1575 people visited the amusement park. 56% of the visitors were adults, 16% were teenagers, and 28% were children ages 12 and under.

The number of adults will be:

= 56% × 1575.

= 882 adults

The number of teenagers will be:

= 16% × 1575

= 252 teenager

The number of children will be:

= 28% × 1575

= 441 children

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Answer:

Number of adults

56/100×1575=882

Number of teenagers

16/100×1575=252

Number of children

28/100×1575=441

Answer:

0.00075757575.

Step-by-step explanation:

I looked it up.

Answer:

Y= 20x + 35

Step-by-step explanation: I have the same test.

Answer:

   (-10)  '  (-8)  '  |  '  |  '  |  '  (0)  '  |  '  |  '  |  '  |  '  (10)  

The range of values possible for the length of her garden is 19 ≤ length ≤ 36 .

In the question ,

it is given that ,

the length of the deer resistant fence = 110 ft

let the width of the garden be "x" ,

and let the length of the  garden be "y" .

So , the equation representing the perimeter of the rectangular garden is

2(x + y) = 110

y = 55 - x

and the equation representing the area of the rectangular garden is

xy = 684

Substituting the value of y = 55 - x in xy = 684 ,

we get ,

x*(55 - x) = 684

55x - x² = 684

x² - 55x + 684 = 0

x² - 36x - 19x + 684 = 0

x(x - 36) -19(x - 36) = 0

(x - 19)(x - 36) = 0

x = 19            OR        x = 36 .

Substituting the values of x= 19 we get

the length (y) = 55 - 19 = 36

putting the values of x = 36 , we get

the length (y) = 55 - 36 = 19 .

So , we get the range of length as   19 ≤ y ≤ 36 .

Therefore ,  The range of values possible for the length of her garden is 19 ≤ length ≤ 36 .

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Answer:

  (a) 68.3%

  (b) 764 students

  (c) 49.87%

  (d) 1 student

Step-by-step explanation:

You want to know various percentages and numbers of students in different test score ranges when 800 students have scores normally distributed with a mean of 75 and a standard deviation of 7.

The range 68 to 82 is one standard deviation either side of the mean: 75±7. The "empirical rule" tells you about 68% of students will have a test score in this range. An appropriate calculator gives the fraction as 68.3%.

The range 61 to 89 is 2 standard deviations either side of the mean: 75±2·7. The "empirical rule" tells you about 95% of the 800 students will have a test score in this range. An appropriate calculator puts the number slightly higher than 760 students: 764 students.

The range 54 to 75 is 3 standard deviations below the mean. The empirical rule tells you about 99.7% of the group falls inside 3 standard deviations. Half this number is below the mean, about 49.85% An appropriate calculator puts the number slightly higher: 49.87%.

The scores at 96 and above are more than 3 standard deviations above the mean. As in part (c), the number in that tail are given by the empirical rule as about 0.15%, or 1.2 students. An appropriate calculator puts the number in the tail of the distribution at a slightly lower value. Hence, the estimated number of students with a score at least 96 is 1 student.

__

Additional comment

The numbers in this question seem to be chosen so you can use the empirical rule to find the answers. That rule will make the answers slightly different: 68%, 760 students, 49.85%, 1 student.

a) The percentage of a class has a test score between 68 and 82 is; 68.269%

b) The number of students that will score between 61 and 89 is; 764 students

c) The probability that a student chosen at random has a test score between 54 and 75 is; 0.49865

d) The number of students that have a test score greater than or equal to 96 is; 1

We are given;

Mean; μ = 75

Standard deviation; σ = 7 ;

a) We have to find percentage of a class has a test score between 68 and 82. This is expressed as; P(68 < X < 82)

P(68 < X < 82) = P(X < 82) - P(X < 68)

The formula for z-score is;

z = (x' - μ)/(σ)

Thus;

P(68 < X < 82) = P(Z < (82 - 75)/7) - P(Z < (68 - 75/7)

P(-1<x<1) = 0.68269 = 68.269%

b) The number of students that will score between 61 and 89 is;

P(61 < X < 89)

z -scores;

z = (61 - 75)/7

z = -2

z = (89 - 75)/7

z = 2

p-value between the two z-scores from online calculator is;

p = 0.9545

Number of students here = 0.9545 * 800 ≈ 764 students

c) The probability that a student chosen at random has a test score between 54 and 75;

P(54 < X < 75)

z -scores;

z = (54 - 75)/7

z = 3

z = (75 - 75)/7

z = 0

p-value between the two z-scores from online calculator is;

p = 0.49865

d) We want to find out how many students have a test score greater

than or equal to 96.

z = (96 - 75)/7

z = 3

p-value from z-score calculator gives;

p = 0.00135

Thus;

Number of students in this regards = 0.00135 * 800 ≈ 1

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The measures are:

The opposites sides of a parallelogram are parallel. Here, PQ ‖ RT and PR ‖ QT.

The opposite sides of a parallelogram are equal. Here, PQ = RT and PR = QT

The opposite angles of a parallelogram are equal. Here, ∠P = ∠T and ∠Q = ∠R

The diagonals of a parallelogram bisect each other. Here, RE = EQ and PE = ET

Same-side interior angles supplement each other. Here, ∠PRT + ∠RTQ = 180°, ∠RTQ + ∠TQP = 180°∘, ∠TQP + ∠QPR = 180°, ∠QPR + ∠PRT = 180°

The diagonals divide the parallelogram into two congruent triangles. Here, ΔRPQ is congruent to ΔQTR, and ΔRPT is congruent to ΔQTP

Therefore,

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Answer:

  (x, y) = (1, 2)

Step-by-step explanation:

You want to solve the system of equations x=2y-3, -4x+3y=2 using the substitution method.

The first equation gives you an expression for x that can be substituted into the second equation.

  -4(2y-3) +3y = 2 . . . . . . substitute (2y-3) for x

  -8y +12 +3y = 2 . . . . . simplify

  10 = 5y . . . . . . . . . . add 5y -2 to both sides

  2 = y . . . . . . . . . . divide by 5

Now, the value of x can be found from the first equation:

  x = 2(2)-3 = 1

The solution is (x, y) = (1, 2).

__

Additional comment

The advantage of the substitution method is that once you find the value of the remaining variable, you can use the substitution equation to find the value of the variable that was eliminated. That is, the equation for x made it easy to find x once we solved for y.

Substitution is easiest when there is already an equation for one of the variables. It can also be used fairly easily if one of the variables has a coefficient of 1 or -1.

Using mathematical operations, Joanna needs an additional $2.25 to meet her requirements for the zoo visit.

The additional amount that Joanna requires is calculated with mathematical operations of addition and subtraction.

First, when you add $12.25 to $15.00, the sum is $27.25. This sum is subtracted from $25 or vice versa to get a difference of $2.25, which is the additional amount required to pay for her expenses at the zoo.

Another way to work out the difference is to first subtract the entrance fee of $12.25 from Joanna's amount. The difference becomes the minuend from which the amount of the snacks (the subtrahend) is deducted to obtain the difference as -$2.25.

Thus, with mathematical operations, Joanna's required additional amount is $2.25.

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Joanna has $25 to spend at the zoo. Admission costs $12.25, and she plans to buy snacks worth $15.00.  How much more does she require to meet her needs at the zoo?

The transformations are:

The transformations that appear here are:

Vertical dilation:

For a function f(x), a vertical dilation of scale factor k is written as:

g(x) = k*f(x)

Horizontal translation:

For a general function f(x), a horizontal translation of N units is written as:

g(x) = f(x + N).

If N is positive, the shift is to the left.If N is negative, the shift is to the right.

Vertical translation:

For a general function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N.

If N is positive, the shift is upwards.If N is negative, the shift is downwards.

so:

f(x) + 5.5 is a translation of 5.5 units upwards.

5.5*f(x) is a vertical dilation of scale factor 5.5

f(x + 5.5) is a translation of 5.5 units to the left.

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If interest is paid at the rate of 2%, compounded semiannually, the amount of each deposit is $7,306.27.

Payment amount =x

Future value =80000

Periodic interest: 2% = .02

Number of periods: 5×2 = 10

Hence,

80,000=x [ (1+0.02)^10 -1 ) ÷ 0.02]

80,000=x [ (1.02)^10 -1) ÷ 0.02]

80,000=x [ (1.21899 -1) ÷ 0.02]

80,000=x (0.21899  ÷ 0.02)

80,000= x(10.9495)

x =80,000 /10.9495

x = $7,306.27

Therefore payment amount is $7,306.27.

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The three inequalities will be :

1) 400 + 15x > 520

2) 520 < 400 + 15x

3) 15x > 120

Given,

In the question:

Dan’s dog-walking job pays $15 per hour.

His job as a car-wash attendant pays $400 each week.

Walking dogs to earn more than $520 in a week.

To find the which three inequalities can model this situation?

Now, According to the question:

Car wash = $400 per week

Dog - walking = $15per hour

To earn more than $520 in a week .

Let the hour be = x hour

Based on the given conditions:

Hence, The three inequalities will be :

1) 400 + 15x > 520

2) 520 < 400 + 15x

3) 15x > 120.

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The graph of the  parent function Y = 2²⁻ ˣ +1 is presented below.

The parent function of a function is the simplest form of the function, which satisfies all the conditions of the given function.

The given function is,

Y= 4×2⁻ˣ+1

To find the parent function, simplify the given function,

Y = 2²ˣ2⁻ˣ+1

Y = 2²⁻ ˣ +1

Function Y = 2²⁻ ˣ +1  is the parent form of the given function Y= 4×2⁻ˣ+1.

The graph of the  Y = 2²⁻ ˣ +1 is presented below.

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The answer of 11/3*7/3*5/3 after multiplication is 385/27.

According to the question,

We have the following expression:

11/3*7/3*5/3

We know that when we multiply two more than two fractions then numerator is multiplied into the numerator and the denominator is multiplied into the denominator of another fraction.

So, we have the following expression after multiplying first two fractions:

77/9*5/3

Now, again repeating the above step:

385/27

(This can not be further classified into the simplest form because the numerator and denominator of this fraction can not be divided by one number.)

Hence, the answer of 11/3*7/3*5/3 after multiplication is 385/27.

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The scale Alexander is using for his map is 1 inch : 300 feet

The height of Alexander's triangle in inches is 4 inches

The scale of the map is gotten by comparing the first dimensions Alexander drew

He made 10 inches to represent 3000 feet, this is equivalent to 1 inch to 300 feet hence the scale is 1 inch : 300 feet

Using the scale, a height of 1200 feet would be

1 inch = 300 feet

? inch = 1200 feet

cross multiplying

? * 300 = 1200 * 1

? = 1200 / 300

? = 4 inches

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Answer:

y=-2x

Step-by-step explanation:

2=-2(-1)

2=2

Sorry for late response

The minimum number of trophies that can be ordered so that the total charge at Company P is less than the total charge at Company R is 3

Company P charges $3.50 for each trophy and a one-time engraving fee of 25$

Let the number of trophies he buys be x

Total price at company P = 3.50x + 25

Company R charges $7.50 for each trophy and a one-time engraving fee of 17$.

Total price at company R = 7.50x + 17

minimum number of trophies that can be ordered so that the total charge at Company P is less than the total charge at Company R

3.50x + 25 < 7.50x + 17

- 4x < -8

4x > 8

x > 2

Therefore, minimum number of trophies that can be ordered so that the total charge at Company P is less than the total charge at Company R is 3

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False Credentials: The "grant" was a fake certification rather than something that was given to Irvine.

False Experience: He was serving the president food. The fact that he was simply a line, however, was revealed

False chronology: Five Star Diamon Award for a couple of back-to-back years. However, it was found that it was not consecutive.

Embellished experience:  it was discovered that he had only chosen particular organic ingredients for the cake, didn't handle it

False References: The queen of England personally selected him for knighthood, which was inaccurate since it will never happen.

What is a resume?

A resume is a formal record that a candidate for a job makes to list their qualifications for the position. A personalized cover letter is typically included with a resume, in which the candidate expresses interest in a particular position or business and highlights the key information on the CV.

False Credentials: Robert Irvine misrepresented his education and experience by claiming on his résumé that he had completed a four-year program at the University of Leeds to earn a degree in food and nutrition. The college claimed they were unable to find any concrete connections between Irvine and the college in their records. Additionally, Irvine had to pay to participate in order to receive the "gift," making the American Academy of Hospitality Sciences anything but a licensed group. In this way, the "grant" was a fake certification rather than something that was given to Irvine.

False Experience: Irvine claimed to be a gourmet chef for the White House and implied that he was serving the president food. The fact that he was simply a line, however, was revealed

False chronology: According to Irvine, the American Academy of Hospitality Sciences gave him the Five Star Diamon Award for a couple of back-to-back years. However, it was found that it was not consecutive.

Embellished experience:He claimed on his resume that he had handled the wedding cake for Prince Charles and Princess Diana, although this was an inflated experience. Nevertheless, it was discovered that he had only chosen particular organic ingredients for the cake.

False References: Finally, he claimed that the Queen of England personally selected him for knighthood, which was inaccurate since it will never happen.

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(a) The information remembered by the person in starting is 100%.

(b) The information remembered by the person after 1 week is 66.67%.

(c) The information remembered by the person after 12 weeks is 12.46%.

(d) The information remembered by the person after 52 weeks is 10%

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The given function is,

f(x) = [tex]90e^{-0.3x}+10[/tex]              (1)

(a)

Substitute x=0 in the equation (1)

f(0) = 90 e⁰ +10

Since, e⁰ = 1

f(0) = 90 +10

f(0) = 100

The information remembered by the person is 100.

(b)

Substitute x=1 in the equation (1)

f(1) = 90 [tex]e^{-0.3}[/tex]  +10

f(1) = 66.67 + 10

f(1) = 76.67

The information remembered by the person is 66.67%.

(c)

Substitute x=12 in the equation (1)

f(12) = 90[tex]e^{-3.6}[/tex] +10

f(12) = 2.46 + 10

f(12) = 12.46

The information remembered by the person is 12.46%.

(d)

Substitute x=52 in the equation (1)

f(52) = 90[tex]e^{-15.6}[/tex] +10

f(52) = 0.00015 + 10

f(52) = 10(approx)

The information remembered by the person is 10%.

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a. The two transformations we perform are

b. Find the graph in the attachment

Transformations are mathematical operation sthat are performed to change the shape or orientation of a function or object.

Since we require to transform the function f(x) = (x-3)² + 1 to g(x) = (x² -4), we perform the following transformation operations.

In f(x), first we shift the term (x - 3)² three units to the left. So,  (x - 3 + 3)²  = x²

So, f(x) = x² + 1

To transform f(x) = x² + 1 to g(x) = (x² - 4), we shift f(x) five units down.

So, the transformation is  f(x) = x² + 1

= x² + 1 - 5

= x² - 4

So, the two transformations we perform are

Find the graph in the attachment

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The value of P(8)=0.0039

What is binomial distribution?

The binomial distribution gives out either success or failure as two possible results in an experiment, is the discrete probability distribution used in probability theory and statistics.

In binomial terms, what is PMF?

Since the 17th century, researchers have focused on the binomial probability mass function, a discrete probability mass function that is particularly popular. It applies to numerous experiments with two possible results, such as the heads-or-tails coin toss or the decay-or-no decay radioactive nucleus experiment.

let x ~ Binomial(n=20, p=0.7)

Use following binomial p.m.f:

[tex]P(x)=^{n}C_{x}p^{x}(1-p)^{n-x}[/tex]

[tex]P(x=8)=^{20}C_{8}(0.7)^{8}(0.3)^{20-8}[/tex]

P(x=8)=0.0039

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Answer: The solution set of the system of inequalities is the region above the dashed line (y=-2x-2) and below the solid line (y=x+4).

Answer: 1/60

Step-by-step explanation:

1/4 times1/4  times 1/4 eqauls 1/60

me too. did you know that animals that lay eggs don't have belly buttons?