Find the length of a segment in the coordinate plane with endpoints (-4,-5) and (8, 1).

Answer:

120°

Step-by-step explanation:

Angles in a quadrilateral add to 360°, so

90+90+x+2x=360

180+3x=360

3x=180

x=60

So, angle R measures 120°.

Answer:

B

Step-by-step explanation:

because at origin they are both positive and when it rotates about 270 both will change to negative

The binomial expansion of the [tex](x-4)^5[/tex] is  [tex]x^5+20x^4+160x^3+640x^2+1280x+1024[/tex]

According to the statement

we have given that a equation and we have to expand it by use of the binomial theorem.

So, For this purpose we know that the

A binomial theorem, statement that for any positive integer n, the nth power of the sum of two numbers a and b may be expressed as the sum of n + 1 terms of the form.

And the general formula is

[tex](x+y)^n= ^nC_0x^ny^0+^nC_1x^(n-1)y^1+^nC_2x^(n-2)y^2+...+^nC_nx^0y^n[/tex]

And we have to solve it with the given equation (x-4)^5.

Then

[tex](x-4)^5=x^5+20x^4+(20)/(2)x^3(4^2)+(60)/(6)x^2(4)^3+(120)/(24)x^1(4)^4+(120)/(120)x^0(4)^5[/tex]

Now after solving the equation become

[tex](x-4)^5=x^5+20x^4+160x^3+640x^2+1280x+1024[/tex]

So, The after expanding the given statement with the binomial theorem the result output is

[tex](x-4)^5=x^5+20x^4+160x^3+640x^2+1280x+1024[/tex]

So, The binomial expansion of the [tex](x-4)^5[/tex] is  [tex]x^5+20x^4+160x^3+640x^2+1280x+1024[/tex]

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Answer:

x = -3

Step-by-step explanation:

Axis of symmetry is the vertical line that divides the parabola into two equal halves and it passes through the vertex of the parabola.

From the graph, Vertex (-3, 4)

Axis of symmetry:  x = -3

Answer:

Cinthia studied 2/3 of her time on Tuesday

Using the t-distribution, the 96% confidence interval is given as follows:

(18.96, 21.04).

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which:

The critical value, using a t-distribution calculator, for a two-tailed 96% confidence interval, with 100 - 1 = 99 df, is t = 2.0812.

The parameters are given as follows:

[tex]\overline{x} = 20, s = 5, n = 100[/tex]

Hence the bounds of the interval are:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 20 - 2.0812\frac{5}{\sqrt{100}} = 18.96[/tex]

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 20 + 2.0812\frac{5}{\sqrt{100}} = 21.04[/tex]

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Answer:

45°

Step-by-step explanation:

Angles in a triangle add to 180 degrees, so

So, the measure of angle X is 2(14)+17=45°

The number of people who how many most likely purchased crunchy-flakes cereal is 1000 customers.

Ratio expresses the relationship between two or more numbers. It shows the number of times that one value is contained within other value(s).

The first step is to determine the ratio of people who preferred crunchy-flakes cereal:

Ratio of people who preferred crunchy-flakes cereal : 5 - 3 = 2

Now, multiply the ratio of those who prefer crunchy-flakes cereal by the total number of customers: (2/5) x 2500 = 1000  customers.

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Answer:

[tex]\frac{169}{49}[/tex]

Step-by-step explanation:

Square the top and bottom numbers in the fraction

13^2 = 169

7^2 = 49

169/49

The values of x and y that can represent the equation is illustrated.

The equation given us 32 = xy + 16

The table will be:

x. y

4. 4

16. 1

2. 8

32. 0.5

For example, when x and y are 4. This will be:

= xy + 16

= (4 × 4) + 16

= 32

Other values of x and y will also give 32.

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Andy needs to subtract cost from the service revenue.

Revenue is the total income earned before any deductions are made. Net income is the total revenue less total expenses or cost.

Net income = total revenue - cost

For example, if a company sold 100 loaves of bread for $100 dollars. The cost of making the bread is $50. The revenue is $100 and the net income is $50 (100 - 50).

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The test statistic based on the probability illustrated is -2.57.

The basic training is given as 103 hours. The variance is also given as 9.

The test statistic will be:

= (102 - 104/3/✓60)

= -1/(3/7.7)

= -2.57.

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On average, the height of a plant varies 3.2 inches from the mean of 6 inches.

An outlier is a number that is way smaller or way larger than that of other numbers in a data set. The outlier is 22.

Mean absolute deviation =  (1/n) x ∑ l x - m(x) l

Mean without the outlier : (9 + 4 +  10 + 9 + 5+  2 +  10 + 3 + 3+  5) / 10 = 6

(1/10) x ∑ l (9 - 6) + (4 - 6) +  (10 - 6)  + (9 - 6)  + (5 - 6) +  (2 - 6) +  (10 - 6)  + (3 - 6)  + (3 - 6) + ( 5 - 6) = 3.2

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The explicit formula that can be used to determine the number of wolves is w = 210 (1.0692^t) .

The first step is to determine the growth rate of the wolf species.

Growth rate = [(future population / present population)^(1/number of years)] - 1

[(410 / 210)^(1/10)] - 1 = 6.92

The exponential function would have the form:

FV = P (1 + r)^t

w = 210 (1.0692^t)

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Answer:

x = 15 & y = 35

Step-by-step explanation:

[tex]y = x + 20[/tex]

[tex]x + y = 50 \\ x + (x + 20) = 50 \\ 2x + 20 = 50 \\ 2x = 50 - 20 \\ 2x = 30 \\ x = \frac{30}{2} = 15[/tex]

[tex]y = x + 20 = (15) + 20 = 35[/tex]

The function is increasing on the intervals:

(-∞, 3] and [5, ∞)

Then the correct options are a and c.

The function is increasing when, reading from left to right, we can see that the curve goes upwards.

By looking at the graph, we can see that the function increases between -∞ and 3, and also increases between 5 and ∞, then the correct options are a and c-

(-∞, 3] and [5, ∞)

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The probability that all 3 books would be nonfiction is 0.1846.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that all 3 books would be nonfiction = (number of non fiction books / total number of books) x (number of non fiction books - 1 / total number of books - 1) x (number of non fiction books - 2 / total number of books - 2)

9 /15 x 8/14 x 7/13 = 0.1846

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20 x (-5) + 10x (-3) + (-5) × (-6)-(3x5) = -115

Answer:

The simplified form of the above expressions solution is -115.

Step-by-step explanation:

Answer: 5

Step-by-step explanation:

[tex]\sqrt{(-4-0)^2 + (1-(-2))^2}=5[/tex]

The equation of the median in standard form is; 9y - 38x = 179.

It follows from the task content that the point D is the midpoint of segment BC; Hence, the coordinates of point D given the coordinates of B and C above are given as; D(-13, -35).

The equation of the median which is the line joining points A and D is therefore determined as follows;

Slope = (-35-3)/(-13-(-4)) = 38/9

38/9 = (y-3)/(x+4)

9y -27 = 38x + 152

9y - 38x = 179.

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Answer:

0

Step-by-step explanation:

On a graph, any line that is horizontal has a slope of zero. Try any points and and plug them into the slope formula equation

(Y2-Y1/X2-X1).

The answer will always be zero.

The value of the expression for the given values of the variables is 1/9

From the question, we are to determine the value of the expression for the given values of the variables

The given expression is

[tex](\frac{4x^{3} -2y-2z^{3} }{4y^{2}-16x^{2} }) ^{2}[/tex]

From the given information,

x = 2

y = -5

z = 3

Putting the values of the variables into the expression

[tex](\frac{4(2)^{3} -2(-5)-2(3)^{3} }{4(-5)^{2}-16(2)^{2} }) ^{2}[/tex]

[tex](\frac{4(8) +10-2(27) }{4(25)-16(4) }) ^{2}[/tex]

[tex](\frac{32 +10-54 }{100-64 }) ^{2}[/tex]

[tex](\frac{-12 }{36 }) ^{2}[/tex]

[tex](\frac{-1 }{3 }) ^{2}[/tex]

[tex]= \frac{1}{9}[/tex]

Hence, the value of the expression for the given values of the variables is 1/9

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The total interest is $107,270

What is monthly payment formula?

The formula for monthly payment is:

[tex]M = \frac{P(\frac{r}{12})( 1+\frac{r}{12})}{( 1+\frac{r}{12})^n-1}[/tex]

We can find total interest as shown below:

Value of property = $475,000

Money available as a deposit = $80,000

P = 475,000-80,000

= 395000

t = 25 year

r = 2% = 0.02

n = 25*12 = 300

[tex]M = \frac{P(\frac{r}{12})( 1+\frac{r}{12})}{( 1+\frac{r}{12})^n-1}[/tex]

Putting the value of P, t, r, and n in the above formula

[tex]=\frac{395000(\frac{0.02}{12} )(1+\frac{0.02}{12}) }{(1+\frac{0.02}{12})^{300}-1}[/tex]

after solving the above expression

M = $1674.22

Interest = M*n-P

Putting the value of P, n and M

= 1674.22*300-395000

= 502266-395000

= 107,266

Rounding to nearest ten dollar

= $107,270

Hence, the total interest is $107,270.

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Answer:

Step-by-step explanation:

Using the Poisson distribution, it is found that:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

In this problem, the mean is:

[tex]\mu = 3.2[/tex]

The probability that the company will find 2 or fewer defective products in this batch is:

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

In which:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-3.2}3.2^{0}}{(0)!} = 0.0408[/tex]

[tex]P(X = 1) = \frac{e^{-3.2}3.2^{1}}{(1)!} = 0.1304[/tex]

[tex]P(X = 2) = \frac{e^{-3.2}3.2^{2}}{(2)!} = 0.2087[/tex]

Then:

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0408 + 0.1304 + 0.2087 = 0.3799[/tex]

There is a 0.3799 = 37.99% probability that the company will find 2 or fewer defective products in this batch.

The probability that 4 or more defective products are found in this batch is:

[tex]P(X \geq 4) = 1 - P(X < 4)[/tex]

In which:

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3).

Then:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-3.2}3.2^{0}}{(0)!} = 0.0408[/tex]

[tex]P(X = 1) = \frac{e^{-3.2}3.2^{1}}{(1)!} = 0.1304[/tex]

[tex]P(X = 2) = \frac{e^{-3.2}3.2^{2}}{(2)!} = 0.2087[/tex]

[tex]P(X = 3) = \frac{e^{-3.2}3.2^{3}}{(3)!} = 0.2226[/tex]

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0408 + 0.1304 + 0.2087 + 0.2226 = 0.6025

[tex]P(X \geq 4) = 1 - P(X < 4) = 1 - 0.6025 = 0.3975[/tex]

There is a 0.3975 = 39.75% probability that 4 or more defective products are found in this batch.

For 5 or more, the probability is:

[tex]P(X \geq 5) = 1 - P(X < 5)[/tex]

In which:

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4).

Then:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-3.2}3.2^{0}}{(0)!} = 0.0408[/tex]

[tex]P(X = 1) = \frac{e^{-3.2}3.2^{1}}{(1)!} = 0.1304[/tex]

[tex]P(X = 2) = \frac{e^{-3.2}3.2^{2}}{(2)!} = 0.2087[/tex]

[tex]P(X = 3) = \frac{e^{-3.2}3.2^{3}}{(3)!} = 0.2226[/tex]

[tex]P(X = 4) = \frac{e^{-3.2}3.2^{4}}{(4)!} = 0.1781[/tex]

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0408 + 0.1304 + 0.2087 + 0.2226 + 0.1781 = 0.7806

[tex]P(X \geq 5) = 1 - P(X < 5) = 1 - 0.7806 = 0.2194[/tex]

Since [tex]P(X \geq 5) > 0.05[/tex], the company should not stop production it there are 5 defectives in a batch.

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Answer:

x = 15, UV = 12, SV = 31

Step-by-step explanation:

13 + 6 + (2x - 18) = 4x - 29

2x + 1 = 4x - 29

2x = 30

x = 15

UV = 2x - 18 = 2*15 - 18 = 30 - 18 = 12

SV = 4x - 29 = 4*15 - 29 = 60 - 29 = 31

Answer:

The product would be: -22/3 = 16/3, if true or false: false the left side -7.3 does not equal to the right side 5.3 which means the given statement is false, if it is evaluated -22/3 = 16/3, if multiplied it would still be -22/3 = 16/3 (you never said how to solve it so here are ways)

The pattern of 324, 256, 196, 144 is the square of the even numbers in a descending order starting from 18.

A sequence is a set of things next to each other in a set order. It is also referred to as a series.

According to this question, the following sequence is given: 324, 256, 196, 144. A careful observation of these numbers shows that each is the square of even numbers.

18² = 324

16² = 256

14² = 196

12² = 144

Therefore, the pattern of 324, 256, 196, 144 is the square of the even numbers in a descending order starting from 18.

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Answer:

3/2y-5

Step-by-step explanation:

Answer: -x² + 4x + 6

Given:

f(x) = 4x + 1

g(x) = x² - 5

Solve:

= (f - g)(x)

= f(x) - g(x)

= 4x + 1 - (x² - 5)

= 4x + 1 - x² + 5

= -x² + 4x + 6

Answer:

(f-g) (x) = 4x+1 - x² + 5 = -x² + 4x + 6

Step-by-step explanation:

Explanation can be given if needed in the comments (ㅅ´ ˘ `)