Given the expression: 8x2 + 28x - 16
Part A: What is the greatest common factor? Explain how to find it. (3 points)
Part B: Factor the expression completely. Show all necessary steps. (5 points)
Part C: Check your factoring from Part B by multiplying. Show all necessary steps. (2 points)

The measure of angle number 1 is 69°.

We know that ∠1 + ∠2 = 180°

We also know that the sum of the interior angles of a triangle is always equal to 180°.

Then we can write simple linear equations to find the missing angles, for example we can write:

21° + 38° + ∠2 = 180°

∠2 = 180° - 21° - 38°

∠2 = 121°

Now we can replace that in the original equation  ∠1 + ∠2 = 180°:

∠1 + 121° = 180°

∠1 = 180° - 121° = 69°

∠1 = 69°

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Answer:

Step-by-step explanation:

1. Imagine a triangle with base side 36 feet and Kate at the right with the angle of elevation, 24 degrees. We can use tangent:

tan 24 = o/a ; tan(24) = o/36 ; 36(tan(24)) = o ; o = 16 feet

This is how tall the screen is.

2. We do a similar operation:

tan(74) = o/a ; tan(74) = 555/a ; a = 555/tan(74) ; a = 159.1 feet

Hope this helps!

Answer:umm

There are no values of

x

that make the equation true.

No solution

Step-by-step explanation:

Answer: The first improvement cut the time by 32 * 0.08 = 2.56 minutes.

So, the new time after the first improvement is 32 - 2.56 = 29.44 minutes.

The second improvement cut the time by 29.44 * 0.05 = 1.472 minutes.

So, the final time is 29.44 - 1.472 = 27.968 minutes.

Rounding to the nearest minute, it now takes 28 minutes to manufacture the piece.

Step-by-step explanation:

The No Information Rate (NIR) is a measure of the accuracy of a classification model that predicts the most frequent class as the outcome for all cases.

In statistics, the No Information Rate (NIR) is a measure of the accuracy of a classification model that predicts the most frequent class as the outcome for all cases. It represents the accuracy rate that can be achieved by simply guessing the most frequent outcome without using any predictive model or variable.

The NIR is commonly used as a benchmark for evaluating the performance of classification models, as any model that performs worse than the NIR is considered to be poorly performing. Conversely, a model that performs better than the NIR is considered to have some predictive power beyond simply guessing the most frequent outcome.

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1. Answer: The price of Andrea's tacos is $8.

Step-by-step explanation:

Hi, to answer this question we have to write an equation with the information given:

Tip amount: $2.0

Percentage: 25% = 0.25 (decimal form, 25/100=0.25)

So, if we multiply the taco's price (x) by the percentage (0.25) we will obtain the amount of the tip (2).

Mathematically speaking:

x (0.25) = 2

Solving for x

x = 2/0.25

x = 8

The price of Andrea's tacos is $8.

2. To solve this problem what you can do is the following rule of three:

40 iris blooms -----> 100%

x iris blooms -------> 115%

Clearing the value of x we have:

x = (115/100) * (40)

x = 46

Then, comparing with last year we have:

40-46 = 6

Answer:

Savanna had this year 6 more iris blooms than last year.

The length of the guy wire is 20 feet

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We can use the Pythagorean theorem to find the length of the guy wire.

Let's call the length of the guy wire "g".

Then we have a right triangle with hypotenuse g, one leg of length 7 ft, and the other leg of length 19 ft.

Using the Pythagorean theorem, we have:

g² = 7² + 19²

g² = 49 + 361

g² = 410

Take square root on both sides

g = 20.24

Therefore, the length of the guy wire is 20 feet

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Answer:

1800

7800

Step-by-step explanation:

6000x0.06 = 360 x 5 for years since its annual then you get 1800 add that to the additional 6000 add those together and you get 7800.

Answer: The equivalent expression to Sarah's expression is:

6.25(x + y) + 242.78

This expression takes into account the total number of hours worked by James (x) and Sarah (y) and adds it to the sum of their tips, which is $242.78. The expression multiplies the total number of hours worked by 6.25, which is their hourly wage.

Step-by-step explanation:

Answer: $225. If the price of the coat was $250 last year, then the coat costs $225 this year.

Step-by-step explanation:

Since the coat costed $250 last year, it is 100% of its original.

Now that it has decreased 10%, it is 100%-10%=90% of its original price.

The new price of the coat will be (90% ÷ 100%) × $250 = $225

The total surface area of the rectangular prism represented by the net is  174 inch²

A prism is a solid geometric shape with parallelograms for its sides and two comparable, equal, and parallel rectilinear figures for its ends.

Given:

Length of the base = 9 inch

Width of the base = 3inch

Height of the base = 5 inch

Area of the two rectangular base

= 2 x length x width

= 2 x 9 x 3

= 54 inch²

and, Area of lateral surfaces

= 2 lateral surfaces with length 9 inch + 2 lateral surfaces with width 3 inch

= 2 x 9 x 5+ 2 x 3 x 5

= 120 inch²

So, Total surface area = 54+120 = 174 inch²

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The surface area of the rectangular prism is,

⇒ SA = 174 Square units.

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

Given that;

The figure is the net for a rectangular prism.

And, Length = 9 in.

Width = 3 in.

Height = 5 in.

Now, We know that;

The surface area of a rectangular prism is given by,

⇒ SA = 2 (lh +wh + lw ) Square units.

Substitute all the values, we get;

⇒ SA = 2 (lh +wh + lw ) Square units.

⇒ SA = 2 (9×5 + 3×5 + 9×3 ) Square units.

⇒ SA = 2 (45 + 15 + 27) Square units.

⇒ SA = 2 × 87

⇒ SA = 174 Square units.

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The original number in the word problem is 77.

Let's call the original two-digit number "x".

Information from the problem

the sum of the digits in x is 14.

So, we can write the number as x = 10a + b,

where a and b are the tens and ones digit, respectively, and a + b = 14.

Reversing and doubling the original number gives us 2(10b + a)

= 20b + 2a.

Adding the original number, x, and the doubled, reversed number, 2(10b + a),

we have 3x = 222.

Substituting x = 10a + b

3(10a + b) = 222

30a + 3b = 222

30a = 222 - 3b

Since the sum of the digits is 14, a + b = 14, so we can substitute for a in the equation:

30(14 - b) = 222 - 3b

420 - 30b = 222 - 3b

198 = 27b

Dividing both sides by 27, we find:

b = 7

So, the original number is x = 10a + b = 10(14 - 7) + 7 = 77.

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The mean and standard deviation of the sampling distribution of the difference in sample means xF − xM is 1.5 minutes(mean) and 1.533 minutes(std. dev) approx The probability of getting a difference in sample means xF − xM that is less than 0 is 0.0239 approx.

Suppose that a random variable X is formed by n mutually independent and normally distributed random variables such that:

Xi = N(μi, σ²) ; i = 1, 2,......, n

And if

X = X1 + X2 +........+ Xₙ

Then, its distribution is given as:

X ≈ N (μ1 + μ2+........+ μₙ)

For this case, it's given that

Distribution of time taken for distance ran by lady is Normal distribution and had a mean handling time of = 8.8 minutes with standard divagation of = 3.3 minutes.

Distribution of time taken for distance ran by joker is Normal distribution and had a mean handling time of = 7.3 minutes with standard divagation of = 2.9 minutes.

Samples of size n = 8 are taken from both population.

Estimated sample mean = population mean

Estimated sample standard deviation = population std. dev / √n

where n = sample size

For sample of females, the distribution is

For sample of males, the distribution is

Also, if we take distribution of difference between sample means(, then it would be normal with mean = 8.8-7.3 = 1.5 minutes (as mean for  will be -7.3 but same standard deviation) as factor gets squared for affecting standard deviation and variance)

and standard deviation is:

[tex]\sqrt{s^2f + s^2m } = \sqrt{3.3^2/8 + 2.9^2/8}[/tex]

≈ 1.553 minutes.

The distribution of difference between sample means is  approximately

We need [tex]P(Xf - Xm < 0)[/tex]

Thus, the mean and standard deviation of the sampling distribution of the difference in sample means xF − xM is 1.5 minutes(mean) and 1.533 minutes(std. dev) approx The probability of getting a difference in sample means xF − xM that is less than 0 is 0.0239 approx.

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The number that is less than 200 and have the prime factors 3, 5, and 13 is 195.

Prime factors are the prime numbers that divide a given positive integer exactly without leaving any remainder. In other words, prime factors are the building blocks of a number.

For example, the prime factors of the number 24 are 2 and 3, because 24 can be written as the product of these prime numbers: 2 × 2 × 2 × 3.

To find the numbers that have prime factors  3,5, and 13, multiply the prime factors together:

3 * 5 * 13 = 195

This is the only number less than 200 that has prime factors 3,5, and 13.

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Answer:

2 3/7

Step-by-step explanation:

Answer:

2^[tex]\frac{3}{2}[/tex]

Step-by-step explanation:

2^3·1/2 = 2^[tex]\frac{3}{2}[/tex]

the image you posted is very blurry, but it looks like the answer is the last choice

The p-value can be calculated from the Z-score of the observed result using the Z-table, which is a table of values for the standard normal distribution.

The p-value is the probability of getting a result at least as extreme as the one observed, given that the null hypothesis is true. It is calculated from the Z-score of the observed result, which is a measure of how many standard deviations away from the mean the observed result is. To calculate the p-value from a Z-score, you need to use the Z-table, which is a table of values for the standard normal distribution. The Z-table shows the probability of a given Z-score, or the area under the normal distribution curve to the left of the Z-score. To find the p-value associated with a given Z-score, you simply look up the probability in the Z-table, and subtract this probability from 1. This gives you the p-value, which is the probability of getting a result at least as extreme as the one observed, given that the null hypothesis is true.

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The measure of the value of x in the given circle is 27

In geometry, an inscribed angle is the angle formed in the interior of a circle when two chords intersect on the circle.

Given that a circle D, having an inscribed angle ∠ EBC measuring 51° and an arc covered by it is arc EC measuring 5x-33, we are to find the value of x,

We know that,

The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc.

Therefore,

m ∠ EBC = 2 arc EC

5x-33 = 2×51

5x-33 = 102

5x = 135

x = 27

Hence, the measure of the value of x in the given circle is 27

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The figure is not given, the question is solved for the attached figure.

Answer: 1/2(10+x)

Step-by-step explanation:

"Half the sum of 10 and a number" means 1/2(10+x), where x is the unknown number.

From the given information, by using mass conversion, 156 lbs is equal to approximately 70.76 kg.

Mass conversion is the process of converting a given mass from one unit of measurement to another. It involves using a conversion factor to change the numerical value of the mass while keeping the physical quantity constant.

For example, converting a mass from pounds to kilograms involves using a conversion factor of 0.45359237 kg/lb.

To convert pounds to kilograms, you can use the following conversion formula:

1 lb = 0.45359237 kg

So, to convert 156 lbs to kg, you can multiply 156 by 0.45359237:

156 lbs × 0.45359237 kg/lb = 70.76 kg (rounded to two decimal places)

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The rank (m) and the nullity (n) is the Matrix A is 5 and 3 respectively according to the planes given.

The maximum number of its linearly independent columns (or rows ) of a matrix is called the rank of a matrix. And the dimension of the null space of A, also called the kernel of A.

Given null space of [tex]L_{A}[/tex] is a plane in [tex]lR^{3}[/tex] .

So nullity of matrix A is A = 2

Since the dimensions of a plane in [tex]lR^{3}[/tex] is 2.

Also the range is spanned by non-vector V in [tex]R^{5}[/tex].

So rank of matrix A is A = 1

Clearly the linear transformation is from [tex]lR^{5}[/tex] to [tex]lR^{3}[/tex],

Then the Matrix A is a = 5x3 matrix.

Therefore, Rank of the matrix A (m)= 5 and Nullity of the matrix A (n) = 3.

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Note that the cost of wax that is required to cover the floor is given as = $1.677.39

To arrive at the correct answer, we had to deconstruct the complex shape in regular shapes comprising two rectangles and one right-angled triangle.

When disassembled, a composite form (or complex figure), also known as a compound shape, is made up of several separate regular shapes.

Note that the arrive at the correct answer, we need to deconstruct the complex shape in regular shapes comprising two rectangles and one right-angled triangle.

The objective is to add the area of all the shapes which comprise the irregular floor and multiply by the cost of wax per square foot. (See attached Image for Deconstructed Compound Shape.)

Step 1 - Find the area of the Right-Angled Triangle

Recall that the rea of a Right Angled Triangle = 1/2 B*H;

B = 15ft

H = 35ft

Area of Δ = 1/2 * 15 *35

Area of Triangle = 262.5ft

Step 2 - Find the area of the Two Rectangles
Dimensions of Rectangle a are: L = 30ft; B = 15ft

Area = L*B

Area = 30*15

Area of (a) = 450ft

Dimensions of Rectangle b are: L = 25ft: B= 20ft
Area (b) = 25* 20

Area (b) = 500ft


Step 3 - Find the area of the compound shape
Area of the compound shape = Sum of the area of the individual shapes  =

262.5ft + 450ft + 500ft
= 1212.5 ft

Step 4 - Find the cost of waxing the floor (compound shape)
This is given as:

$1.38 * Area of Compound Shape

⇒ 1.38 * 1212.5
= $1.677.39

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See the images attached for the missing part of the question

The vector "p" that represents "a's closest point" on the line "b" spans is the orthogonal projection of vector "a" onto vector "b."

So the vector "p" that represents "a's closest point" on the line "b" spans is the orthogonal projection of vector "a" onto vector "b." The following is the formula for projecting "a" orthogonally onto "b": CSS Copy: p = (dot(a, b) / dot(b, b)) * b, where "dot" stands for the dot product of the two vectors.

The procedures to determine the orthogonal projection of a vector "a" onto a vector "b" are as follows:

Identify the "a" and "b" dot product.

Add "b" to itself and calculate the dot product.

Divide the intersection of "a" and "b" by the intersection of "b" and itself.

Multiply the vector "b" by the step 3 result.

Here is a MATLAB sample that shows the orthogonal projection.

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The expression [tex]\frac{(\sqrt[3]{3})^{3/5} }{(\sqrt[3]{3})^{6/5}}[/tex] is equivalent to the expression [tex]\frac{1}{\sqrt[5]{3} }[/tex]. Then the correct option is B.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

[tex]\rightarrow \dfrac{(\sqrt[3]{3})^{3/5} }{(\sqrt[3]{3})^{6/5}}[/tex]

Simplify the expression, then we have

[tex]\rightarrow \dfrac{(\sqrt[3]{3})^{3/5} }{(\sqrt[3]{3})^{6/5}}\\\\\rightarrow \dfrac{(3)^{1/5 }}{(3)^{2/5}}\\\\\rightarrow \dfrac{(3)^{1/5 }}{(9)^{1/5}}\\\\\rightarrow \dfrac{1}{\sqrt[5]{3} }\\[/tex]

The expression [tex]\frac{(\sqrt[3]{3})^{3/5} }{(\sqrt[3]{3})^{6/5}}[/tex] is equivalent to the expression [tex]\frac{1}{\sqrt[5]{3} }[/tex]. Then the correct option is B.

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The required proportional relationship used to evaluate the measure of segment LM is 9/LM = 6/4.5. Option D is correct.

Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

Here,
Since Triangle HJK is similar to triangle LMN.
The property of similar triangle states that the sides of both the triangle will be proportional to each other.
So,
9/6 = LM/4.5

Or

9/LM = 6/4.5

Thus, the required proportional relationship used to evaluate the measure of segment LM is 9/LM = 6/4.5. Option D is correct.

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Answer:

Daniel is 8 years old now

Step-by-step explanation:

Let Kevin's age now be K and let Daniel's age now be D

"Kevin is 3 times as old as Daniel"

Translation: K = 3D

"4 years ago, Kevin was 5 times as old as Daniel"
4 years ago Kevin's age = K - 4
4 years ago Daniel's age = D - 4
4 years ago, Kevin was 5 times as old as Daniel.

Translation: K - 4 = 5(D - 4)
K - 4 = 5D - 20

Simplify this equation:
Add 4 to both sides:
K - 4 + 4 = 5D - 20 + 4

K = 5D - 16

Substitute K = #D:
3D = 5D - 16

Subtract 5D from both sides:
3D - 5D = - 16
-2D = -16

or

2D = 16   (multiply by - 1)

D = 16/2 = 8

and

K = 3D = 3 x 8 = 24

Now, Kevin is 24 years old and Daniel is 8 years old

Verify
If Kevin is 3x older than Daniel who is 8 now,
Kevin's age now = 3 x 8 = 24  Check

4 years ago, Daniel was 8 - 4 = 4 years
4 years ago, Kevin was 24 - 4 = 20
Kevin's age 4 years ago = 5 x 4 = 20 Check

The critical value for the 0.05 level of significance is k = 21.

To find the critical value, we can use the binomial distribution. The binomial distribution models the number of successes in n independent Bernoulli trials, each with probability p of success. In this case, the number of successes is the number of dog owners who say Woof Chow is their regular brand, and the number of trials is n = 100. The null hypothesis is that the true market share of Woof Chow is 25%, and the alternative hypothesis is that it is not 25%.

We can use the binomial cumulative distribution function (CDF) to find the critical value. The CDF gives the probability of getting k or fewer successes in n trials, given a probability of success p. The critical value is the smallest value of k such that the CDF at k is greater than or equal to 1 - alpha, where alpha is the level of significance. In this case, alpha = 0.05.

So, we want to find the smallest k such that:

P(X <= k) >= 1 - 0.05

where X is a random variable representing the number of dog owners who say Woof Chow is their regular brand. We can use a binomial calculator or a software package to calculate the binomial CDF, or we can use a table of critical values for the binomial distribution.

The critical value for the 0.05 level of significance is k = 21. This means that if the true market share of Woof Chow is 25%, then the probability of getting 23 or more dog owners who say Woof Chow is their regular brand is less than 0.05. Since the observed number of dog owners who say Woof Chow is their regular brand is 23, which is greater than 21, we can reject the null hypothesis that the true market share is 25%.

This means that based on the survey results, we cannot conclude that Woof Chow has a market share of 25%. The survey results suggest that Woof Chow may have a market share that is greater than 25%.

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Answer:

Step-by-step explanation:

The solution is, an equation where y is the subject that represents this proportional relationship is,  y = 4x/9.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

given that,

Edward serves 4 cups of coffee every nine minutes

now, we have to find that,

how many cups of coffee does he serve every minute ,

i.e. we get,

in 9mint. cup = 4

so, in 1 mint cup = 4/9

now, an equation where y is the subject that represents this proportional relationship is,

y = 4x/9

where, x for the amount of minutes .

Hence, The solution is, an equation where y is the subject that represents this proportional relationship is,  y = 4x/9.

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The outcome is three more than the number, which is 9 if five is taken away from it and the difference is tripled.

Whole Numbers: The collection of natural numbers that include the number 0. Integers are whole integers that are next to their counterparts (negative numbers). Real numbers would be any integers that can be stated as fractions. Any number that cannot be expressed as a fraction is irrational.

Many operations, like measuring, counting, and indexing, require the use of numbers. According to their characteristics, there are several sorts of numbers, including natural numbers, whole figures, rational or irrational numbers, integers, actual values, complex numbers, and even odd numbers, etc.

Let the number be y

5 is subtracted from the number. This can be written as:

y – 5

The difference is tripled. This can be written as:

3(y – 5)

The result of the difference tripled is 23 more than the number. This can be written as:

3(y – 5) = 3 + y

Thus, we can obtain the value of y as follow:

3(y – 5) = 3 + y

Clear bracket

3y – 15 = 3 + y

Collect like terms

3y – y = 3 + 15

2y = 18

y = 18 / 2

y = 9

Thus, the number is 9.

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