if 3(2x-4)=-36 ,the value of x is

The value of LM is 8 for the given line segment.

A line section that can connect two places is referred to as a segment.

In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.

The line is here! It extends endlessly in both directions and has no beginning or conclusion.

Given the line segment KM with midpoint L

So,

KL = LM

(KM - LM) = LM

9x + 7 - 8x = 8x

x + 7 = 8x

7x = 7

x = 1

Now,

LM = 8(1) = 8 unit.

Hence "The value of LM is 8 for the given line segment".

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The method that will not give the correct number of inches is that the total length of the plant in a week is 19/4 inches.

Length of the small plant = 2 1/2 = 5/2 inches

Rate of growth = 3/4 inches

Increase in length in 3 weeks will be:

= 3 × 3/4 = 4

Total length = 5/2 + 9/4

= 19/4 inches.

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Answer:38

Step-by-step explanation:

Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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Answer:

FH = 35.64

Step-by-step explanation:

(∠A = 360 so the other angle is 40)

By law of cosines,

FH² = AH² + FA² - 2(AH)(FA) * cos(A)

= 30² + 25² - 2(30)(25) * cos(80)

= 900 + 625 - 1500 * 0.17

= 1525 - 255

FH²  = 1270

FH = √1270

FH = 35.64

Answer:

The campsite would be 65 m by 65 m. 65 x 65 = 4,225. Another way to put it (and the way to figure it out) is that the square root of 4,225 is 65.

Step-by-step explanation:

Answer:

3(12 + 7)

Step-by-step explanation:

To find the GCF of 36 and 21, list out their factors.

36: 1, 2, 3, 4, 6, 9, 12, 18, 36

21: 1, 3, 7, 21

The greatest factor which both numbers share is 3.

Therefore, you can factor 36 + 21 as 3(12 + 7)

Answer:

1) f is the name of the function

2) x is the argument

3) output is (3x + 1)

Step-by-step explanation:

In function notation, The expression "f (x)" simply means that f is a formula that has an input variable known as "x". It should be noted that f(x) does not imply that we multiply f and x. Hence, f is the name of the function.

Now, the term "x" is an input variable known as the argument of the function.

f(x) is the output of the function and is; 3x + 1

Answer:

s= the customer buy a shirt

p= the customer buy pants

\( p(s) = 0.55, p(p) = 0.25 , p(s \cap p) =0.20\)

And we want to find this probability:

\( p(s \cup p) \)

And we can use the definition of total probability and we have:

\( p(s \cup p) = p(s) +p(p) -p(s \cap p)\)

And replacing we got:

\( p(s \cup p) = 0.55+0.25 -0.20 = 0.60\)

And the best answer for this case is:

B. 0.60

Step-by-step explanation:

For this case we can define the following events:

s= the customer buy a shirt

p= the customer buy pants

And we have the following probabilities given:

\( p(s) = 0.55, p(p) = 0.25 , p(s \cap p) =0.20\)

And we want to find this probability:

\( p(s \cup p) \)

And we can use the definition of total probability and we have:

\( p(s \cup p) = p(s) +p(p) -p(s \cap p)\)

And replacing we got:

\( p(s \cup p) = 0.55+0.25 -0.20 = 0.60\)

And the best answer for this case is:

B. 0.60

Siama and Wills used different methods to find the differences between (5x + 6x) and (2x - 1) but they both arrived at the same answer.

I prefer Wills method because it is easier and less complicated.

Wills method:

(5x + 6x) - (2x - 1)

Subtract both 2x and -1

5x + 6x - 2x - - 1

5x + 4x + 1

In conclusion, Wills method is preferred when both methods are compared.

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(-3, 23/2)

the picture i linked shows the step by step

Answer:

0.343, 0.424, 0.443

Step-by-step explanation:

The probability that more than 2 students will attend is 0.9179.

Part (a) List the values that X may take on.

X may take on the values 0, 1, 2, 3, ..., 13.

Part (b) Give the distribution of X.

The distribution of X can be represented as follows: X-0:0, 1:0.23, 2:0.23, 3:0.23, 4:0.23, 5:0.23, 6:0.23, 7:0.23, 8:0.23, 9:0.23, 10:0.23, 11:0.23, 12:0.23, 13:0.23

Part (c) How many of the 13 students do we expect to attend the festivities? (Round your answer to the nearest whole number.)

We can expect 3 students to attend the festivities.

Part (d) Find the probability that at most 3 students will attend. (Round your answer to four decimal places.)

The probability that at most 3 students will attend is 0.6923.

Part (e) Find the probability that more than 2 students will attend. (Round your answer to four decimal places.)

The probability that more than 2 students will attend is 0.9179.

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Answer:

- 7x ² -x +10

Step-by-step explanation:

⇒Given

10-x- 7x ²

⇒We have a polynomial of second degree that has the standard from ax²+bx+c

⇒Rearrange the terms of the polynomial to match the standard form

- 7x ² -x +10

Answer: $75

Step-by-step explanation: If interest earned on an account in 2 years is $15, then after 10 years, the interest would be $75.

We can know this because, if we divide $15 by 2, we get the amount of interest the account makes in 1 year.

15/2 = $7.50. The account makes $7.50 interest pear year.

We want to know how much interest the account will make in 10 years, simply multiply 7.50 by 10.

$7.50 x 10 = $75 in 10 years.

The required of the sidewalk to the nearest square foot is 13.14 ft².

The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth.

A circle's area is the area that it takes up in a two-dimensional plane. It can be simply calculated using the formula A = r2, (Pi r-squared), where r is the circle's radius. The square unit, such as m2, cm2, etc., is the unit of area.

We have,

Length = 5 ft, width = 2 ft, Radius of circle = 2 ft

Now,

Area of sidewalk = area of rectangle + area quadrant

Area of sidewalk = (5×2) + π(2)^2/4

Area of sidewalk = 10 + 3.14

Area of sidewalk = 13.14 ft²

Thus, required area of the sidewalk is 13.14 ft².

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Answer:

-90

Step-by-step explanation:

The percentages of people taking the test who scores between 421 and 645 is: 68 %

The empirical rule, also referred to as the three-sigma rule or the 68-95-99.7 rule, is defined as a statistical rule which states that almost all observed data for a normal distribution will fall within three standard deviations (denoted by σ) of the mean or average (denoted by µ).

We are given:

Sample mean: x' = 553

standard deviation; s = 112

Thus:

x' - ns = 421

x' + ns = 645

Where n is the number of standard deviations from the mean. Thus:

553 - 112s = 421

112s = 553 - 421

112s = 132

s = 132/112

s ≈ 1

So 1 standard deviation from the means indicates a percentage of 68%

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The equation for a vertical line(s) L such that a region bounded by L, the x-axis and the line 2y − 3x = 6 is 3y + 2x = 6

The formula of the line in point-slope form is expressed as:

\(y-y_0=m(x-x_0)\)

m is the slope

(x0, y0) is any point on the line

Given the equation 2y - 3x = 6

2y = 3x + 6

y = 1.5x + 3

mx = 1.5x

m = 1.5

Hence the slope of the vertical line will be -2/3

IIf the point on the line is (3, 0), hence the required equation will be:

\(y - 0 = -2/3 (x - 3)\\3y = -2(x-3)\\3y = -2x + 6\\3y+2x = 6\)

Hence the equation for a vertical line(s) L such that a region bounded by L, the x-axis and the line 2y − 3x = 6 is 3y + 2x = 6

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Answer: i believe it’s 0.28, but tbh i’m on a unit test so i can’t see what’s wrong and what’s right. good luck!

Step-by-step explanation:

Answer:

c- 0.28

Step-by-step explanation:

Answer:

E

Step-by-step explanation:

AP Classroom says so.

The data doesn't provide convincing statistical evidence for considered proportion comparison. We deduce that: Option E: There is not convincing statistical evidence

There are two hypotheses. First one is called null hypothesis and it is chosen such that it predicts nullity or no change in a thing. It is usually the hypothesis against which we do the test. The hypothesis which we put against null hypothesis is alternate hypothesis.

Null hypothesis is the one which researchers try to disprove.

Suppose we have:

Then, we get:

\(Z = \dfrac{\hat{p}_1 - \hat{p}_2}{\sqrt{\hat{p}(1-\hat{p}_1 )(\dfrac{1}{n_1} + \dfrac{1}{n_2}) }}\)

If the level of significance = \(\alpha\)critical value of Z is: \(Z_{\alpha/2}\), and if \(Z > Z_{\alpha/2}\)null hypothesis, else if \(Z_{\alpha/2} > Z\) then we cannot reject it.

For this case, we want to know if  the data provides convincing statistical evidence that the proportion who would be classified as normal after one month of taking cinnamon is greater than the proportion who would be classified as normal after one month of not taking cinnamon.

Thus, we get our hypotheses as:

Null hypotheses: They don't provide convincing evidence (and thus, cinnamon had no improvement on the proportion), and thus:

\(H_0: \hat{p}_1 \leq \hat{p}_2\)

Alternate hypothesis: Data provides convincing evidence (that the use of cinnamon made increment in considered proportion), and thus:

\(H_a: \hat{p}_1 > \hat{p}_2\)

The test is single tailed.

For this case, we have:

Thus, we get:

\(Z = \dfrac{\hat{p}_1 - \hat{p}_2}{\sqrt{\hat{p}(1-\hat{p}_1 )(\dfrac{1}{n_1} + \dfrac{1}{n_2}) }} =\dfrac{0.35 - 0.25}{\sqrt{0.3(0.7 )(\dfrac{1}{40} + \dfrac{1}{40}) }} \approx 0.976\)

At 0.01 level of significance (\(\alpha = 0.01 = 1\%\)), we get the critical value of Z from z-tables as:

\(Z_{\alpha/2} = 2.576\)

Since \(Z_{\alpha/2} > Z\) , we cannot reject the null hypothesis, and thus, deduce that there is not convincing statistical evidence at the level of 0.01

At 0.05 level of significance (\(\alpha = 0.05 = 5\%\)), we get the critical value of Z from z-tables as:

\(Z_{\alpha/2} = 1.96\)

Since \(Z_{\alpha/2} > Z\) , we cannot reject the null hypothesis, and thus, deduce that there is not convincing statistical evidence at the level of 0.05

At 0.10 level of significance (\(\alpha = 0.10 = 10\%\)), we get the critical value of Z from z-tables as:

\(Z_{\alpha/2} = 1.645\)

Since \(Z_{\alpha/2} > Z\) , we cannot reject the null hypothesis, and thus, deduce that there is not convincing statistical evidence at the level of 0.10

Remember that the conclusions can be made even if they were volunteers since that doesn't make it wrong as volunteers are randomly coming out people from real population.

Thus, we deduce that: Option E: There is not convincing statistical evidence

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Answer:18/5

Step-by-step explanation:

Answer:

 \(\dfrac{x^2+8x+8}{2x+4}\\\\\)

Step-by-step explanation:

Simplify:

        \(\dfrac{3x + 4}{x +2}+\dfrac{x^2+2x}{2x+ 4}\)

Multiply the denominator and the numerator of the first term by 2,

                        \(=\dfrac{2*(3x +4)}{2*(x+ 2)}+\dfrac{x^2+2x}{2x+4}\\\\\\=\dfrac{2*3x+2*8}{2*x +2*2}+\dfrac{x^2+2x}{2x+4}\\\\\\=\dfrac{6x+8}{2x+4}+\dfrac{x^2+2x}{2x+4}\)

                       \(\sf = \dfrac{6x+8+x^2+2x}{2x+4}\\\\\text{\bf Combine like terms,}\\\\=\dfrac{x^2+8x+8}{2x+4}\\\\\)

(a) The value of the z-score for the 6.4 fluid ounce orange is -1.64

(b) The value of the z-score for the 3.11 fluid ounce orange is -4.63

From the question, we have the following parameters that can be used in our computation:

Mean = 8.2

Standard deviation = 1.1

The values of the z-scores is calculated as

z = (z - Mean)/Standard deviation

So, we have

z = (z - 8.2)/1.1

When the score is 6.4, we have

z = (6.4 - 8.2)/1.1

Evaluate

z = -1.64

Recall that

z = (z - Mean)/Standard deviation

So when the score is 3.11, we have

z = (3.11 - 8.2)/1.1

Evaluate the expression

z = -4.63

Hence, the values of the z-scores are -1.64 and -4.63

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Answer: The answer is 32.7 i just used a calculator.

The simplified boolean expression for F5 is F5 = P OR (NOT R). In this expression, P represents one boolean variable, and (NOT R) represents the negation of another boolean variable R. The OR operator combines the two variables, resulting in the final boolean expression F5.

To simplify the boolean expression F5 = (P AND Q) OR (R AND NOT P), we can apply Boolean algebra rules to reduce it to its simplest form.

Step 1: Apply De Morgan's laws

NOT (R AND NOT P) can be simplified as (NOT R) OR P.

Step 2: Distributive property

F5 = (P AND Q) OR ((NOT R) OR P)

Step 3: Apply associative property

F5 = (P AND Q) OR (P OR (NOT R))

Step 4: Apply absorption law

F5 = P OR (P OR (NOT R))

Step 5: Apply idempotent law

F5 = P OR (NOT R)

By simplifying the expression, we have reduced it to its simplest form while preserving its logical meaning. The simplified expression can be used to analyze and evaluate logical circuits or systems where the variables P and R are used.

Remember, boolean algebra allows us to manipulate and simplify complex logical expressions by applying various rules and properties. These simplifications help in understanding and analyzing logical operations in digital systems and circuits.

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The question probable may be:

Consider the boolean variables P, Q, and R. Determine the boolean expression for the variable F5 using the given variables:

F5 = (P AND Q) OR (R AND NOT P)

Using the boolean variables P, Q, and R, can you simplify the expression F5 to its simplest form by applying Boolean algebra rules?

What is Function?

Function is the relationship between inputs where each input is related to exactly one output. It is a special relationship among the inputs (i.e. the domain) and their outputs (known as the codomain) where each input has exactly one output, and the output can be traced back to its input.

"y is a function of x" (denoted y = f(x)) means that y varies according to whatever value x takes on.

How to determine

Where F(x) = 2x^4 + x^2 - 10x + 1

So, to calculate f(-10)

f(x) = y

Where x = -10

f(-10) = 2(-10)^4 + (-10)^2 -10(-10) + 1

f(-10) = 2(10000) + 100 + 100 + 1

f(-10) = 20000 + 100 + 100 + 1

f(-10) = 20201

For f(2),

f(x) = y

Where x = 2

f(2) = 2(2)^4 +2^2 -10(2) + 1

f(2) = 2(16) + 4 -20 + 1

f(2) = 32 + 4 -20 + 1

f(2) = 17

For f(3)

f(x) = y

Where x = 3

f(3) = 2(3)^4 + 3^2 -10(3) + 1

f(3) = 2(81) + 9 -30 + 1

f(3) = 162 + 9 - 30 + 1

f(3) = 142

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