The following figures are not drawn to scale but AB and CD are straight lines.
Find x.

To determine if the LCM of two numbers is the product of the two numbers using their prime factorization, you need to check if the numbers are coprime.

Coprime numbers have no common prime factors except for 1. If the numbers are coprime, their LCM will be equal to the product of the two numbers.

To tell if the LCM of two numbers is the product of the two numbers, you need to compare the prime factorization of the two numbers. If the prime factors of both numbers are unique (meaning they do not share any common factors), then the LCM will be the product of the two numbers. However, if the two numbers share some common prime factors, then the LCM will have to include those factors at their highest power. So, to find the LCM of the two numbers, you need to take the highest power of each prime factor that appears in either number and multiply them together. If the product of these highest powers matches the product of the two numbers, then the LCM is equal to the product of the two numbers.

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The formula V = (1/12)πd^2h is the derived formula for calculating the volume of a cone using the given diameter and height.

The formula to calculate the volume of a cone is V = (1/12)πd^2h, where V represents the volume, d is the diameter of the cone, and h is the height of the cone.

To understand how this formula is derived, let's break it down step by step.

The volume of a cone is derived from the formula for the volume of a cylinder, which is V = πr^2h, where r represents the radius of the base of the cylinder.

In the case of a cone, the base is a circle, and the radius is half the diameter. So we can substitute r = d/2 in the formula for the volume of a cylinder to get the volume of a cone.

V = π(d/2)^2h

= π(d^2/4)h

Now, let's simplify the equation further. To get rid of the fraction, we can multiply both sides of the equation by 4:

4V = πd^2h

Finally, to match the given formula, we divide both sides of the equation by 12:

(1/12)(4V) = (1/12)(πd^2h)

V = (1/12)πd^2h

Therefore, the formula V = (1/12)πd^2h is the derived formula for calculating the volume of a cone using the given diameter and height.

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By probability, 5  different choices are possible .

Describe probability using an example?

A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

                          The likelihood of an event occurring increases as its probability increases. The flip of a fair (impartial) coin serves as a straightforward illustration.

According to the situation, The probabilities for each one is given below

As there are 20 families

So the probabilities for each one is

For four families have one child is

     = 1/20  

For eight families have two children is

       = 2/20 = 1/10

For five families have three children is

           = 3/20

For two families have four children is

            = 4/20  = 1/5

For one family have five children is

           = 5/20 = 1/4

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Answer:

6/6 or one foot.

Step-by-step explanation:

If one of the fish tanks is 5/6 of a foot wide, and the other is 1/6, add them together.

5/6+1/6=6/6 or 1 foot wide. 6/6 means a whole number.

The total width of the two fish tanks as per the given relation is equal to 1 foot.

To find the total width of the two fish tanks when placed next to each other, add their widths.

The widths are given as fractions of a foot, so add them directly:

Width of the first fish tank = 1/6 foot

Width of the second fish tank = 5/6 foot

Total width of the two fish tanks = (1/6) + (5/6)

To add fractions, they need to have the same denominator.

Here, both fractions already have the same denominator (6),

So, simply add their numerators:

Total width = (1 + 5)/6

Total width = 6/6

Now, 6/6 is equal to 1.

Therefore, the total width of the two fish tanks is 1 foot.

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The correct representation of the sentence 15 is what percent of 40 is 15 is 37.5% of 40.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

The algebraic representation of the statement 15 is what percent of 40 is:

40 (x/100) = 15

40x / 100 = 15

40x = 1500

x = 1500/40

x = 37.5

Hence, the correct representation of the sentence 15 is what percent of 40 is 15 is 37.5% of 40.

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Answer:

OK what is the rest of the question i cant answer it as of right now the question is a statement.

Step-by-step explanation:

So sorry.

Answer:

9.5 decimal

espero y te ayude

9514 1404 393

Answer:

  (b)  a trapezoid

Step-by-step explanation:

A graph of the points reveals one pair of parallel sides: a trapezoid.

Step-by-step explanation:

20. x^2+8x+12

x^2 + 6x +2x + 12

X(X+6) + 2(X+6)

(X+2) (X+6)

18. 5x^4 - 25x

5x(x^3-5)

19. 4x^2 - 9

4x^2/4 -9/4 = 0/4

x^2 = 9/4

X=√9/4

Answer: To solve -x²-2x=0 by factoring, we can factor out x from the left-hand side:

x(-x-2) = 0

This equation is true if either x = 0 or -x-2 = 0. Solving for x in the second equation:

-x-2 = 0

-x = 2

x = -2

Therefore, the solutions to the equation -x²-2x=0 are x = 0 and x = -2.

To solve x²-4x-8--6x by factoring, we can simplify it first by combining like terms:

x²-10x-8 = 0

To factor this quadratic, we need to find two numbers that multiply to -8 and add to -10. These numbers are -2 and -8, so we can write:

x²-2x-8x-8 = 0

(x²-2x) - (8x+8) = 0

x(x-2) - 8(x+1) = 0

(x-8)(x-2) = 0

Therefore, the solutions to the equation x²-4x-8--6x are x = 8 and x = 2.

To solve 3x² +12=-21x-24 by completing the square, we first need to move all the terms to one side:

3x² + 21x + 36 = 0

Next, we divide both sides by 3 to simplify the coefficient of x²:

x² + 7x + 12 = 0

To complete the square, we need to add and subtract (7/2)² = 49/4 inside the parentheses:

x² + 7x + 49/4 - 49/4 + 12 = 0

(x + 7/2)² = 1/4

Taking the square root of both sides and solving for x, we get:

x + 7/2 = ±1/2

x = -7/2 ± 1/2

Therefore, the solutions to the equation 3x² +12=-21x-24 by completing the square are x = -4 and x = -3.

To solve -x²-3x-13 = -2x² by using the quadratic formula, we first need to move all the terms to one side:

-x² + x - 13 = 0

Next, we identify the coefficients a, b, and c:

a = -1, b = 1, c = -13

Substituting these values into the quadratic formula:

x = (-b ± sqrt(b² - 4ac)) / 2a

x = (-1 ± sqrt(1² - 4(-1)(-13))) / 2(-1)

x = (-1 ± sqrt(1 + 52)) / (-2)

x = (-1 ± sqrt(53)) / (-2)

Therefore, the solutions to the equation -x²-3x-13 = -2x² by using the quadratic formula are approximately x = -3.25 and x = 4.25.

Step-by-step explanation:

Answer:

(x - 5)(x + 9)

Step-by-step explanation:

the velocity vector is v(t) = (2t + 1)i + 3t²j + 4t³k, and the position vector is r(t) = (t² + t)i + t³j + t⁴k + 7j - 4k

To find the velocity and position vectors of a particle given its acceleration, initial velocity, and initial position, we can integrate the acceleration to obtain the velocity vector and then integrate the velocity to obtain the position vector.

Given:

Acceleration: a(t) = 2i + 6tj + 12t²k

Initial velocity: v(0) = i

Initial position: r(0) = 7j - 4k

1. Velocity vector:

To find the velocity vector, we integrate the acceleration with respect to time:

v(t) = ∫ a(t) dt

    = ∫(2i + 6tj + 12t²k)dt

    = 2ti + (6t²/2)j + (12t³/3)k + c

    = 2ti + 3t²j + 4t³k + c

Applying the initial condition v(0) = i:

v(0) = i

i = 0i + 0j + 0k + c

c = i

v(t) = 2ti + 3t²j + 4t³k + i

Therefore, the velocity vector is given by:

v(t) = (2t + 1)i + 3t²j + 4t³k

2. Position vector:

To find the position vector, we integrate the velocity with respect to time:

r(t) = ∫ v(t) dt

Integrating each component of the velocity separately:

   = i ∫ (2t + 1)dt + 3j ∫ t²dt + 4k ∫ t³dt

   = i (2t²/2 + t) + 3j(t³/3) + 4k(t⁴/4) + d

   = i (t² + t) + jt³ + t⁴k + d

Applying the initial condition r(0) = 7j - 4k:

0i + 0j + 0k + d = 7j - 4k

d = 7j - 4k

r(t) = (t² + t)i + t³j + t⁴k + 7j - 4k

Therefore, the position vector is given by:

r(t) = (t² + t)i + t³j + t⁴k + 7j - 4k

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Complete question is below

Find the velocity and position vectors of a particle that has the given acceleration and the given initial velocity and position. a(t) = 2 i + 6t j + 12t² k, v(0) = i, r(0) = 7 j − 4 k

Answer:

0 ≤ t ≤ 18

Step-by-step explanation:

The cost of renting the boat without any discount is $8 per hour. However, Leila has a discount coupon for $3 off, so the effective cost per hour would be $8 - $3 = $5.

Let's assume Leila rents the boat for t hours. The total cost of renting the boat for t hours would be $5 multiplied by t, which is 5t.

According to the problem, Leila wants to spend at most $93. Therefore, we can set up the following inequality:

5t ≤ 93

This inequality represents the condition that the total cost of renting the boat (5t) should be less than or equal to $93.

Simplifying the inequality:

5t ≤ 93

Dividing both sides by 5 (since the coefficient of t is 5):

t ≤ 93/5

t ≤ 18.6

Since we cannot rent the boat for a fraction of an hour, we can round down the decimal value to the nearest whole number:

t ≤ 18

0 ≤ t ≤ 18

Answer: 0≤t≤12

Step-by-step explanation:

(I’m not sure if it’s 5 dollars off per hour, or total, but here’s what I did!)

If Leila has a $3 coupon, than she can spend +$3 because when you get a coupon, you can spend more, so 93+3 is equal to 96, now we just divide by 8 (because a boat costs $8 per hour) and we get 96/8=12.

Then, in inequality form it’s t≤12, because she can rent the boat for at most 12 hours, you could also do 0≤t≤12, because you can’t rent it for a negative amount of time, but either works.

Remember that the general formula of an arithmetic sequence is:

Where:

• An is the n-term

• d is the common difference

• n is the number of the step

Using the given data,

Therefore, the 13th term of the arithmetic sequence is 73

(a) When performing an ANOVA with the data the alternative hypothesis is at least two of the restaurants have different mean delivery times.

(b)75.8

Analysis of variance. or ANOVA, is a statistical method that separate observed variance data into different components to use for additional tests. A one way ANOVA is used for three or more groups of data, to gain information about the relationship between the dependent and independent variables.

The ANOVA table shows how the sum of squares are distributed according to source of variation, and hence the mean sum of squares.

It is given that a pizza lover wants to compare the average delivery times.

Therefore the null hypothesis and alternate hypothesis implies that,

H₀ =  all restaurants have equal mean delivery time

Hₐ = at least two restaurants have different two deliveries

Hence the alternate hypothesis for performing an ANOVA with the data is at least two of the restaurants have different mean delivery times.

The alternate hypothesis (Hₐ) defines that there is a statistically important relationship between two variables. Whereas null hypothesis states that is no statistical relationship between the two variables.

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Answer:

12

Step-by-step explanation:

5 + 7 = 12

just follow the rule in the equation and further simplify

that's why you should get 12

hope this helps :)

Answer:

12

Step-by-step explanation:

5 - (-7) = 5 + 7 = 12

To evaluate the integral ∫(5x^2/(196+x^2)^2) dx using trigonometric substitution, the substitution x = 14tanθ will be the most helpful. Let's rewrite the given integral using this substitution. First, we need to find the derivative of x with respect to θ:

dx/dθ = 14sec^2θ.

Next, we substitute x = 14tanθ and dx = 14sec^2θ dθ into the integral:

∫(5x^2/(196+x^2)^2) dx = ∫(5(14tanθ)^2/(196+(14tanθ)^2)^2) (14sec^2θ) dθ

= ∫(5(196tan^2θ)/(196+196tan^2θ)^2) (14sec^2θ) dθ.

Simplifying the expression, we have:

∫(980tan^2θ)/(196(1+tan^2θ)^2) (14sec^2θ) dθ

= ∫(980tan^2θ)/(196(1+tan^2θ)^2) (14sec^2θ) dθ

= 13720∫tan^2θ/(1+tan^2θ)^2 dθ.

Now, we can integrate the expression with respect to θ. This involves using trigonometric identities and integration techniques for rational functions The result of the integral will depend on the specific limits of integration or if it is an indefinite integral.

Therefore, the rewritten integral is ∫(980tan^2θ)/(196(1+tan^2θ)^2) (14sec^2θ) dθ, and the evaluation of the integral requires further calculations using trigonometric identities and integration techniques.

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Answer:

Hi! -5/3 :)

Step-by-step explanation:

Hope this helps!

Best of luck! ♥

Answer: This is my opinion but I think it’s D ;)

Step-by-step explanation:

I just took the quiz it’s right !

Answer:

10^2+24^2

Step-by-step explanation:

got 100% on the quiz

Answer:

Slope = -6/8

Step-by-step explanation:

(-20, -4)

(-12, -10)

Slope = (Y2 - Y1)/(X2 - X1)

Plug in the x and Y coordinates:

-10 - (-4)/-12 - (-20)

-10 + 4/-12 + 20

-6/8

Slope = -6/8

Please let me know if I'm incorrect :)

The completely factored expression of 5n²(2n − 3) + 10x(2n − 3) is (5n²+ 10x)(2n − 3)

The expression is given as:

10n³ − 15n² + 20xn² − 30xn

Factor out 5n² and 10xn in the expression

5n²(2n − 3) + 10x(2n − 3)

In (a), we have:

5n²(2n − 3) + 10x(2n − 3)

Factor out 2n - 3

(5n²+ 10x)(2n − 3)

Hence, the completely factored expression of 5n²(2n − 3) + 10x(2n − 3) is (5n²+ 10x)(2n − 3)

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You must use the t-distribution table when working problems when the population standard deviation (σ) is not known and the sample size is small (n<30). General Correct Rule: If σ is not known, then using t-distribution is correct. If σ is known, then using the normal distribution is correct.

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

In graphical form, the normal distribution appears as a "bell curve".

The normal distribution is the proper term for a probability bell curve.

In a normal distribution the mean is zero and the standard deviation is1. It has zero skew and a kurtosis of 3.

Normal distributions are symmetrical, but not all symmetrical distributions are normal.

The t-distribution describes the standardized distances of sample means to the population mean when the population standard deviation is not known, and the observations come from a normally distributed population.

Therefore,

You must use the t-distribution table when working problems when the population standard deviation (σ) is not known and the sample size is small (n<30). General Correct Rule: If σ is not known, then using t-distribution is correct. If σ is known, then using the normal distribution is correct.

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This is Single-Blinded Randomized Controlled trial type of study because the recipient is unaware that they are receiving a treatment, only the researchers are aware of who is receiving which treatment. So the option d is correct.

One of the most rigorous research designs is experimental research, which is frequently referred to as the "gold standard" in research designs.

This design involves the researcher manipulating one or more independent variables (as treatments), randomly assigning individuals to various treatment levels (random assignment), and observing the effects of the treatments on outcomes (dependent variables).

Experimental research has a distinct advantage in that it may link cause and effect through treatment manipulation while controlling for the erroneous effect of unrelated variables, which is known as internal validity (causality).

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The complete question is:

A team of researchers randomly separates their study's participants into two groups, giving one group a placebo and the other a new treatment to be tested. As the treatment is somewhat experimental, participants do not know whether they receive the placebo but researchers do know whether a specific participant receives the placebo. What type of study is this?

a. Standard Deviation Study

b. Type 1 Study

c. Case-Control Study

d. Non-Blinded Randomized Controlled Trial

e. Single-Blinded Randomized Controlled trial

To find -r - 2x + 3 given that x-1, we substitute x-1 for x:
-r - 2(x-1) + 3 = -r - 2x + 1
Now we can simplify by combining like terms:
-r - 2x + 1


It seems like there are multiple parts to this question, and some of the information is unclear. However, I will answer each part as best as I can, based on the information provided.

a) To find the simplest form of the given expression "-r - 2x + 3", there are no like terms to combine, so the expression is already in its simplest form: -r - 2x + 3.

b) To find dy/dx given that y = x'/x + dy, it seems like there might be a typo. However, if the equation is y = x'/x, then to find the derivative, we can use the quotient rule:
dy/dx = (x'(1) - x'(0))/x^2 = x'/x^2

c) It seems like there is not enough information for this part of the question.

d) To find dy/dx given that y = *( *+2), there might be a typo in the given equation. Please provide the correct equation for me to find the derivative.

e) To find dy/dx given that y = ∫sin(x)(sin(x) + cos(x))dx, first, we need to differentiate the integral with respect to x. The Fundamental Theorem of Calculus states that the derivative of an integral is the original function. Therefore,
dy/dx = sin(x)(sin(x) + cos(x))

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The probability that someone does not have this​ belief is (1-x%)

If, x % of people believe that it is morally wrong to not report all income on tax returns.

A research center poll showed that ​% of people believe that it is morally wrong to not report all income on tax returns.

let, x % of people believe that it is morally wrong to not report all income on tax returns.

then, the probability that someone does not have this​ belief-->

the sum of the probability of all events equal to 1.

so, probability(believe it morally wrong to not report ) + probability(does not believe this )=1;

so, the probability that someone does not have this​ belief = 1-x%

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A deck of 52 cards is shuffled thoroughly, and n cards are turned up. The probability that one face card turns up is (1/4) × (n/52).

The probability of one face card turning up when n cards are turned up from a shuffled deck of 52 cards is determined by the following formula:
Probability of 1 face card = (number of face cards/number of total cards) × (n/52)

Therefore, the probability of one face card turning up when n cards are turned up is (12/52) × (n/52), or (1/4) × (n/52).

For example, if 10 cards are turned up, the probability of one face card turning up would be (1/4) × (10/52) = 0.2, or 20%.

In general, the more cards are turned up, the higher the probability that one face card turns up. This is because there is a higher chance of drawing at least one face card from the larger sample.

Therefore, The probability that one face card turns up in a shuffled deck is (1/4) × (n/52).

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Answer:

Step-by-step explanation:

See attached image