Enzo drew Triangle K L N. In Enzo's triangle, Measure of angle K is represented as x degrees. The measure of Angle L is 5 times Measure of angle K. The measure of Angle N is 16 degrees less than 8 times Measure of angle K. Which statements must be true about the angle measures of Enzo's triangle? Check all that apply. Measure of angle K = x degrees Measure of angle L = (5 x) degrees Measure of angle N = (16 minus 8 x) degrees Measure of angle K + measure of angle L = measure of angle N Measure of angle K + measure of angle L + measure of angle N = 180 degrees

Here, we want to graph the line y = 2x-3 using slope and the y-intercept

The value of the slope if positive or negative will tell us the direction of the graph whether rising or falling while the y-intercept will tell us the point at which the graph crosses the y-axis

Mathematically, we can have the equation representing a linear function as;

where m represents the slope and b represents the y-intercept

If the slope is positive as in the case with this question (+2), then the graph is a rising graph.

To complete the graph, we need to identify the y-intercept which is -3 in this case

So to graph the line, we locate the point -3 on the y-axis then we draw a rising line through this point

To get a point on the x-axis, we will need the value of the x-axis

The value on the y-axis is 0 at this point

An overview is shown below;

Answer:

x = -16

Step-by-step explanation:

Answer: X = -16

Step-by-step explanation:

1. -2(2x + 5) - 3 = -3(x - 1)

2. -4x-10-3=-3x+3

3. -13=x+3

4. x=-16

check: -2(-16*2+5)-3=-3(-16-1)

51=51

Hope it helps.

If you have any query, feel free to ask.

Check the picture below.

\(\cfrac{x}{10}=\cfrac{24.5}{14}\implies x=\cfrac{(10)(24.5)}{14}\implies x=\cfrac{245}{14}\implies x=17.5\)

It becomes

\($$\begin{aligned}5: 8: & 6.5: x \\5 \times x & =8 \times 6.5 \\x & =\frac{8 \times 6.5}{5} \\x & =\frac{52}{5} \\x & =10.4\end{aligned}$$\)

Therefore,

5 machines will take $10.4$ hour to produce the same number of parts.

Equivalent interest rates are interest rates that produce the same future value after one year. For example, 10% compounded quarterly and 10.125% compounded semiannually are equivalent nominal interest rates. If you calculate the future value of $100 invested at either rate for one year, you will obtain $110.38.

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The probability of getting 1, 2, 3, 5, or 6 when you roll a standard six-sided die is 5/6

The given parameters are:

Sample space = {1, 2, 3, 4, 5, 6}

So, we have

P(1)  1/6

P(2) = 1/6

P(3) = 1/6

P(5) = 1/6

P(6) = 1/6

The probability of getting 1, 2, 3, 5, or 6 when you roll a standard six-sided die is calculated as:

P = 1/6 + 1/6 + 1/6 + 1/6 + 1/6

So, we have

P =5/6

Hence, the probability of getting 1, 2, 3, 5, or 6 when you roll a standard six-sided die is 5/6

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Answer:

D. $ 36

Step-by-step explanation:

84-48=36

48+36=84

84+36=120

120+36=156

156+36=192

26 out of 130 were marked.

Divide 26 by 130:

26/130 = 0.20

20% of the bass caught were tagged.

Now divide the total amount caught and tagged by that percentage:

258 / 0.20 = 1,290

There are 1,290 bass in the lake.

The diver's velocity during the first 2 sec of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.

Given data: Initial velocity, u = 0 ft/sec

Acceleration, a = g = 32.2 ft/sec²

The maximum rate of fall, vmax = 80 mph

Time, t = 2 seconds

Air resistance constant, Ar = 0.2

We are supposed to determine the sky diver's velocity during the first 2 seconds of fall using the modified Euler method.

The governing equation for the velocity of the skydiver is given by the following:

ma = -m * g + k * v²

where, m = mass of the skydive

r, g = acceleration due to gravity, k = air resistance constant, and v = velocity of the skydiver.

The equation can be written as,

v' = -g + (k / m) * v²

Here, v' = dv/dt = acceleration

Hence, the modified Euler's formula for the velocity can be written as

v1 = v0 + h * v'0.5 * (v'0 + v'1)

where, v0 = 0 ft/sec, h = 2 sec, and v'0 = -g + (k / m) * v0² = -g = -32.2 ft/sec²

As the initial velocity of the skydiver is zero, we can write

v1 = 0 + 2 * (-32.2 + (0.2 / 68.956) * 0²)0.5 * (-32.2 + (-32.2 + (0.2 / 68.956) * 0.5² * (-32.2 + (-32.2 + (0.2 / 68.956) * 0²)))

v1 = 62.732 mph

Therefore, the skydiver's velocity during the first 2 seconds of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.

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The probability that at least 200 out of 215 college graduates under age 25 are employed is 0.29

In this question we have been given  8% of college graduates, under the age of 25 are unemployed.

We need to find the probability that at least 200 out of 215 college graduates under age 25 are employed.

Here, n = 215

8% of college graduates, under the age of 25 are unemployed.

So, p = 0.08

For graduates under age 25 are employed,

Pr = 1 - 0.08

Pr = 0.92

We use Normal probability distribution

The expected value of the binomial distribution is:

E(x) = n * Pr

E(x) = 215 * 0.92

E(x) = 197.8

So, μ = E(x)

        = 197.8

An the standard deviation would be,

σ = √n * Pr * (1 - Pr)

σ = √(215 * 0.92 * 0.08)

σ = 3.98

An expression for the exact probability that at least  200 out of 215 college graduates under age 25 are employed.

P(x ≥ 200)

which is nothing but the pvalue of Z when x = 200

z = x - μ/σ

z = (200 - 197.8)/3.98

z = 0.55 has p value 0.29

Therefore, the required probability is 0.29

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Answer:

algebraic expression. An expression that contains at least one variable, at least one numbers and at least one operation.

Step-by-step explanation:

Answer:

expressions

Step-by-step explanation:

this is how a definition in a textbook would be written. they just put a blank in

Answer:

The answer would be 2.1 so it must be D

Step-by-step explanation: divide them

The length of the rectangle is approximately 41.34 inches.

Let's assume the width of the rectangle is represented by the variable w. According to the given information, the length of the rectangle is four less than twice the width, which can be expressed as 2w - 4.

The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 128 inches. Since a rectangle has two pairs of equal sides, we can set up the equation:

2w + 2(2w - 4) = 128.

Simplifying the equation, we get:

2w + 4w - 8 = 128,

6w - 8 = 128,

6w = 136,

w = 22.67.

So, the width of the rectangle is approximately 22.67 inches. To find the length, we can substitute this value back into the expression 2w - 4:

2(22.67) - 4 = 41.34.

Therefore, the length of the rectangle is approximately 41.34 inches.

In summary, the length of the rectangle is approximately 41.34 inches. This is determined by setting up a system of equations based on the given information: the perimeter of the rectangle being 128 inches and the length being four less than twice the width.

By solving the system of equations, we find that the width is approximately 22.67 inches, and substituting this value back, we obtain the length of approximately 41.34 inches.

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Answer:

x = 15

Step-by-step explanation:

The two angles form a straight line so they add to 180

6x-5+6x+5 = 180

Combine like terms

12x= 180

Divide by 12

12x/12 =180/12

x = 15

Dividing in math is the process of finding the quotient of two numbers.

The formula for dividing two numbers is a/b = c, where a and b are the two numbers being divided and c is the quotient.

Division is a mathematical operation that is used to split a whole number into parts. It is the opposite of multiplication, which combines numbers together. The formula for division is A / B = C, where A is the dividend (the number being divided), B is the divisor (the number dividing the dividend), and C is the quotient (the result of the division). To calculate, you divide the dividend by the divisor and the quotient is the resultTo calculate the quotient, you must divide a by b. For example, if we wanted to divide 8 by 4, we would divide 8 by 4 to get 2. The calculation would look like this: 8/4 = 2. As a result, 8 divided by 4 is equal to 2.

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Answer:

n great than 13.

hope this isn't wrong

The solution to the inequality is n > 13. This means that any value of n greater than 13 will satisfy the inequality.

Given is an inequality n - 8 > 5, we need to solve it,

To solve the inequality "n - 8 > 5," you can follow these steps:

Step 1: Add 8 to both sides of the inequality to isolate the variable n.

(n - 8) + 8 > 5 + 8

n - 8 + 8 > 13

n > 13

Step 2: Simplify the inequality.

n > 13

Hence the simplified inequality is n > 13.

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If an event is likely to occur, the probability that the event will occur is between 3/4 and 1.

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

If the probability lies between 0 and 1/5, it is likely that the event would not occur. If the probability lies between 1/5 and 1, it is likely that the event would occur.

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Answer:

75% and 100%

Step-by-step explanation:

The probability spectrum is (the spaces are supposed to be equal):

|----------------------|--------------------|--------------------|---------------------|

0%                    25%               50%              75%                   100%

impossible   unlikely          equal            likely                  certain

Answer:

6:7

Step-by-step explanation:

=store A:store B

=150:175

=6:7

Answer:

x = -.5

Step-by-step explanation:

x - 2.5 = -3​

Add 2.5 to each side

x - 2.5+2.5 = -3+2.5​

x = -.5

Answer:

its flipped over the y axis and then it goes 6 to the right and 6 up. To find how they are congruent, just use Pythagorean theorem to find the side lengths for each side and say that by using the rule SSS or side side side you know that the triangles are the same.

Step-by-step explanation:

to find the side length with Pythagorean theorem for example for side DE, side DE is basically the hypotenuse of the triangle to just count the height and base using the graph and in this case it would be  h=6 b=3 and then use the Pythagorean theorem to find the actual side length of the line, which would be √45.

Answer:

  -2 ≤ x < 12

Step-by-step explanation:

-15x +4 ≤ 34

Add 15x-34 to both sides

  -30 ≤ 15x

Divide by 15

  -2 ≤ x

__

-6x +70 > -2

Add 6x +2 to both sides

  72 > 6x

Divide by 6

  12 > x

__

The two solution spaces overlap. Since the AND of the two inequalities is involved, the solution of both is just that part of the number line where there is overlap.

The solution is ...

  -2 ≤ x < 12

Using the general addition rule, p(F or G) = 0.667.

What is sample space?

In probability theory, the set of all feasible outcomes or outcomes of an experiment or random trial is referred to as the sample space. The sample points, or potential ordered outcomes, are listed as elements in the set used to represent the sample space.

Let,

S = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}

F = {8, 9, 10, 11, 12, 13}

G = {12, 13, 14, 15}

n(S) = number of elements in set S are 12.

n(F) = 6

n(G) = 4

n(F and G) = common elements in F and G = 2

n(F or G) = n(F) + n(G) - (F and G)

n(F or G) = 6 + 4 - 2

n(F or G) = 8

Now, using the general addition rule,

P(F or G) = P(F) + P(G) - P(F and G)

Here,

P(F) = n(F)/n(S) = 6/12 = 1/2

P(G) = n(G)/n(S) = 4/12 = 1/3

P(F and G) = n(F and G)/n(S) = 2/12 = 1/6

⇒ P(F or G) = 1/2 + 1/3 - 1/6

                   = 5/6 - 1/6

                   = 4/6

⇒ P(F or G) = 0.667

Hence, using the general addition rule, P(F or G) = 0.667.

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The value of a(t) is -1 and b(t) is 55 + \(e^t\)

No, the given equation y' - y = 55 + \(e^t\) is not in the standard form of a first-order linear differential equation.

In the method for solving a first-order linear differential equation, an integrating factor is a function used to transform the equation into a form that can be easily solved.

For an equation in the standard form y' + a(t)y = b(t), the integrating factor is defined as:

μ(t) = e^∫a(t)dt

To solve the equation, you multiply both sides of the equation by the integrating factor μ(t) and then simplify. This multiplication helps to make the left side of the equation integrable and simplifies the process of finding the solution.

To put it in standard form, we need to rewrite it as y' + a(t)y = b(t).

Comparing the given equation with the standard form, we can identify:

a(t) = -1

b(t) = 55 + \(e^t\)

Therefore, The value of a(t) is -1 and b(t) is 55 + \(e^t\)

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Answer:

it is a statistical measure of the relationship between two variables that indicates the extent to which the variables change together in the same or opposite direction. Correlation does not imply causation, meaning that a correlation between two variables does not necessarily mean that one variable causes the other.

Based on this definition, the correct answer is b. Increasing values of X go with either increasing or decreasing values of Y. A correlation exists between two variables when both variables increase or decrease together. This statement captures the idea that correlation can be positive or negative, and that it reflects a linear relationship between two variables.

Step-by-step explanation:

a is wrong because it only describes positive correlation, not negative correlation.

c is wrong because it confuses correlation with consistency. Correlation does not require that higher values of X always go with higher or lower values of Y, only that they tend to do so on average.

d and f are wrong because they assume causation from correlation, which is a logical fallacy.

e is wrong because it contradicts itself. It says that increasing values of X go with increasing values of Y, which is positive correlation, but then it says that a correlation exists when both variables decrease together, which is negative correlation.

If X is correlated with Y, it implies a predictive statistical relationship between X and Y. This correlation can be positive or negative implying respective increase or decrease in values of both variables. But, this correlation doesn't prove causation.

If X is correlated with Y, it indicates a statistical relationship between the two variables, X and Y. This relationship can be positive or negative. If it is a positive correlation, as X increases, Y will also increase and similarly, as X decreases, Y will also decrease. Contrarily, in a negative correlation, as X increases, Y decreases and vice versa. However, it is important to understand that correlation does not imply causation. That is, if X and Y are correlated, it does not necessarily mean that changes in X cause changes in Y or vice versa. It only means that they move in a predictable manner relative to each other.

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Therefore, the standard deviation for the number of people with the genetic mutation in groups of 500 is approximately 6.726.

To find the standard deviation for the number of people with the genetic mutation in groups of 500, we can use the binomial distribution formula.

Given:

Probability of having the genetic mutation (p) = 0.09

Sample size (n) = 500

The standard deviation (σ) of a binomial distribution is calculated using the formula:

σ = √(n * p * (1 - p))

Substituting the given values:

σ = √(500 * 0.09 * (1 - 0.09))

Calculating the standard deviation:

σ ≈ 6.726 (rounded to three decimal places)

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Here are the base five numerals from 1 to 100

1, 2, 3, 4, 10, 11, 12, 13, 14, 20, 21, 22, 23, 24, 30, 31, 32, 33, 34, 40, 41, 42, 43, 44, 100.

With the base five, every number can only take on the values of 0, 1, 2, 3, or 4.

After the number 4, we carry over to the following place value and start again with 0. So, for instance, the number after 4 in base five is 10, because we've carried over to the next place value and started with 0 again.

In this way, we can count all the way up to 100 in base five, using these 25 unique numerals.

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Answer:

48

Step-by-step explanation:

18% of 1500 is 270

270x18% is 48.6 since it increased by 18%

Answer:

B

Step-by-step explanation:

To make it easy

To calculate net amount to be paid, accounts payable officer needs to determine whether cash discount is applicable.Net amount the accounts payable officer will need to pay is $1,296.72 - $51.87 = $1,244.85.

The net amount that the accounts payable officer will need to pay for the invoice is $1,296.72. The terms of the invoice are given as 4/10, n/30, which means that a cash discount of 4% is applicable if the payment is made within 10 days. The "n" in the terms represents the net payment period, which is 30 days in this case.

To calculate the net amount to be paid, the accounts payable officer needs to determine whether the cash discount is applicable based on the payment date. Since the invoice is dated June 10 and the payment is made on June 16, which is within the 10-day discount period, the cash discount is applicable.

The net amount to be paid is calculated by subtracting the cash discount from the net price of the invoice. The cash discount is calculated as 4% of the net price: 0.04 * $1,296.72 = $51.87. Therefore, the net amount the accounts payable officer will need to pay is $1,296.72 - $51.87 = $1,244.85.

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Answer:

C

Step-by-step explanation:

3 \(\frac{1}{8}\) ÷ 1 \(\frac{5}{8}\) ( change mixed numbers to improper fractions )

= \(\frac{25}{8}\) ÷ \(\frac{13}{8}\)

to perform the division

leave first, change ÷ to × , turn second fraction ' upside down '

= \(\frac{25}{8}\) × \(\frac{8}{13}\) ( cancel 8 on numerator/ denominator )

= 25 × \(\frac{1}{13}\)

= \(\frac{25}{13}\)

= 1 \(\frac{12}{13}\)