Question 13 of 50
In the diagram below, C is the midpoint of AB. If AC is 4 centimeters, what is
the length of CB?
B
A. 6 cm
B. 4 cm
C. 2 cm
D. 8 cm

Answer:

A) 12 and 15

The answer to 3 644 mod 645 is 3.

To solve this problem, we need to find the remainder when 3644 is divided by 645.

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The answer to 3 644 mod 645 is 3.

To solve this problem, we need to find the remainder when 3644 is divided by 645.

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Answer:

x=5

Step-by-step explanation:

An isosceles trapezoid has two pairs of congruent base angles. This means angle F has to equal angle E. So we have 2x^2+21=3x^2-4. Move the variables to one side and we get 25=x^2. Square root both sides and we get two values x=5 and x=-5. Since angles cannot necessarily be negative, we only want the positive value. In this case x=5.  

Answer:

The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.

Answer:

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 and 360, making a total of 24 divisors. 360 is a highly composite number.

Step-by-step explanation:

23 × 32 × 5

Answer:

the 1st one is: 2

the 2nd one is: 3

To create opposite like terms of x variables, the first equation can be multiplied by 2 and the second equation by 3

A system of equation is the set of equation in which the finite set of equation is present for which the common solution is sought.

Given that, the system of equation given in the problem is,

-3x+2y = 20......(i)

2x+11y = -1.....(ii)

As the coefficient of x is 2 in eq(ii) equation by 3 to make the opposite term as,

6x+33y = -3.......(iii)

As the coefficient of y is -3, thus multiply the above eq(i) by 2 to make opposite wise term as,

-6x+4y = 40....(iv)

Compare the equation 3 and 4, we get that both the equation has the equivalent system of equations with opposite like terms of x variables.

Hence, to create opposite like terms of x variables, the first equation can be multiplied by 2 and the second equation by 3

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The length of f-c is 23 units.

From the diagram we know that e-f = 4, b-c = 18, and a-f = 21. We need to  set up and solve an equation to the length of f-c. To set up and solve an equation to the length of f-c let's assign variables to the lengths of the segments:

Let e-f = x, b-c = y, and a-f = z.

From the given information, we have:

x = 4, y = 18, and z = 21.

We need to find the length of f-c, which is the sum of b-c and a-f:

f-c = y + z.

Substituting the given values, we get:

f-c = 18 + 21 = 39.

Therefore, the length of f-c is 39 units.

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Answer:

so 14 can go into 28, 2 times and 19 can go into 38 2 times so the techaer can make 2 group with 14 girls and 19 boys in each group.

Step-by-step explanation:

This is the process of building a model that can be modified before the actual system is installed is B. Prototyping

The answer to the question is B. prototyping. Prototyping is the process of building a preliminary model of a system, which can be modified and improved upon before the final system is installed. This allows for errors to be identified and corrected early on in the process, reducing the risk of costly mistakes later. Prototyping is often used in software development and other types of system design, where it can be difficult to predict exactly how the system will function until it is actually built and tested. Systems analysis is a related process that involves studying existing systems to identify areas for improvement, while systems maintenance involves maintaining and updating existing systems to ensure that they continue to function properly. Overall, prototyping is an important tool for ensuring that complex systems are built correctly and meet the needs of their users.

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Answer:

4

Step-by-step explanation:

a+2a=12

3a=12

3a/3=12/3

a=4

(a) 1, 2, 3, 4, 5, 6; equally likely

(b)Outcome Probability:

1/6, 1/6 , 1/6, 1/6, 1/6, 1/6

Yes, because these values cover the entire sample space.

In probability theory, the sample space of an experiment or random trial is the set of all possible outcomes or outcomes of that experiment.

Probability:

Probability is the branch of mathematics that deals with numerical descriptions of how likely an event or how likely a statement is to be true. The probability of an event is a number between 0 and 1, with 0 representing an impossibility and 1 representing certainty, roughly speaking. The higher the probability of an event, the higher the probability of an event occurring. A simple example is a fair (unbiased) coin toss. Since the coin is fair, both outcomes are equally likely. The probability of an "eagle" is equal to the probability of a "tail". And since no other outcome is possible, the probability of getting heads or tails is 1/2.

According to the Question:

Since, the 5 dice is thrown equally  at a same time then   the probability that all the dice are same is 1/6

Therefore, total Number of cases = n(s) = 6× 5 = 30

On the first roll you may get a number that has not been drawn before. The probability of throwing a new number on the second roll is 5/6. You only have a chance of 4/6 on the third roll, 3/6 on the fourth, then 2/6, and 1/6 on the last roll.

Therefore,

The probability of throwing a different number each time is the product of all these probabilities: 5!/6⁵ or about 1.5% .

Complete Question:

(a) If you roll a single die and count the number of dots on top, what is the sample space of all possible outcomes? Are the outcomes equally likely?

(b) Assign probabilities to the outcomes of the sample space of part (a). (Enter your answers as fractions.)

Do the probabilities add up to 1? Should they add up to 1? Explain.

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The ordered pair (2, 2) and (3,1) is in the solution set of the inequality 12x - 28y < 56.

Let's consider the ordered pair (3, 1). To check whether this ordered pair is in the solution set of the inequality, we need to substitute x = 3 and y = 1 into the inequality as follows:

12(3) - 28(1) < 56

Simplifying this expression, we get:

36 - 28 < 56

8 < 56

This is a true statement, which means that the ordered pair (3, 1) is in the solution set of the inequality 12x - 28y < 56.

Now, let's consider another ordered pair, say (2, 2). To check whether this ordered pair is in the solution set of the inequality, we need to substitute x = 2 and y = 2 into the inequality as follows:

12(2) - 28(2) < 56

Simplifying this expression, we get:

24 - 56 < 56

-32 < 56

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Answer:

8.5 ft (nearest tenth)

Step-by-step explanation:

To find the depth of the pool at the deep end, we need to find the height of the right triangle with angle 16.5° and add it to 4.5 ft

Base of the triangle = 35 - 9 - 12.5 = 13.5 ft

Use the tan trig ratio:

\(\tan(x)=\dfrac{O}{A}\)

where x is the angle, O is the side opposite and angle and A is the side adjacent to the angle in a right triangle.

Given:

\(\implies\tan(16.5)=\dfrac{h}{13.5}\\\\\implies h= 13.5\tan(16.5)\\\\\implies h = 4.0 \textsf{ ft (nearest tenth)}\)

Therefore, the depth of the pool at the deepest end = 4 + 4.5 = 8.5 ft (nearest tenth)

Now

\(\\ \rm\Rrightarrow tan\theta=\dfrac{P}{B}\)

\(\\ \rm\Rrightarrow tan16.5=\dfrac{P}{13.5}\)

\(\\ \rm\Rrightarrow P=13.5tan16.5\)

\(\\ \rm\Rrightarrow P=13.5(0.3)\)

\(\\ \rm\Rrightarrow P\approx 4ft\)

The two positive numbers are 36 and 72 which gives a sum equal to 108 and the product of 36 and the square of 72 is a maximum.

Any integer greater than zero is considered a positive number. A positive number can either be written as a number or with the "+" symbol in front of it.

Let us consider the two positive real numbers as x and y. Then, their sum is written as,

x+y=108

Then, y=108-x

And the product is written as,

P=xy²

Substitute value of y in the above equation, we get,

\(\begin{aligned}P&=x(108-x)^2\\&=x(11664-216x+x^2)\\&=11664x-216x^2+x^3\\&=x^3-216x^2+11664x\end{aligned}\)

Now, differentiate P with respect to x, and we get,

\(\begin{aligned}\frac{dP}{dx}&=3x^2-432x+11664\\&=x^2-144x+3888\end{aligned}\)

Solving the above equation to zero, we get,

\(\begin{aligned}x^2-144x+3888&=0\\x^2-36x-108x+3888&=0\\x(x-36)-108(x-36)&=0\\(x-108)(x-36)&=0\\x&=\text{108 or 36}\end{aligned}\)

Substitute values of x in y=108-x, to get values of y.

If we substitute x=108, we get the y value as zero which doesn't give the required solution.

But, if we substitute x=36, we get,

\(\begin{aligned}y&=108-36\\y&=72\end{aligned}\)

Thus, the two positive numbers are 36 and 72.

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Let x be the number of hours at the fair and y be the number of hours at a beach.

x + y < 7

{ at most 7 hours at a beach and the fair }

x > 2

{ at least 2 hours at the fair }

y > 4

{ more than 3 hours at a beach }

Graph the system accordingly

Answer:

y=-2x+5

Step-by-step explanation:

hope i helped

Answer:

Y=2x+5

Step-by-step explanation:

Move the variable (x) to the right

2y= 10-4x

divide both sides of the equation by 2

y=5-2x

and then reorder the terms

y=-2x+5

:)

Answer: C

The denominator is just the number on the bottom. In this case its \(2\sqrt{2}\)

Answer:

Option A.

Step-by-step explanation:

y + 1 = -3x + 15

y = -3x + 14

A line perpendicular would have a slope of 1/3.

y = 1/3x + c

-6 = 1/3 * 4 + c

4/3 + c = -6

c = -18/3 - 4/3

c = -22/3

So, we have y = 1/3x - 22/3.

y + 6 = 1/3(x - 4)

y + 6 = 1/3x - 4/3

y = 1/3x - 4/3 - 18/3

y = 1/3x - 22/3

So, the correct answer is Option A.

Hope this helps!

The probability that the sample mean will be between 181 and 185 is 0.3039.

Given,

The mean of a population, μ = 180

Standard deviation, σ = 36

Number of sample observations, n = 84

We have to find the probability that the sample mean will be between 181 and 185;

Lets convert 181 and 185 into z scores;

z = (x - μ) / (σ/√n)

z = (181 - 180) / (36/√84)

z = 1/3.93

z = 0.25

z = (185 - 180) / (36/√84)

z = 5 / 3.93

z = 1.27

Lets look z score table;

The area to the left of z = 0.25 is 0.5987

The area to the left of z = 1.27 is 0.8980

The probability that the z is between 0.25 and 1.27 would be 0.8980 – 0.5887 = 0.3039.

That is,

The probability that the sample mean will be between 181 and 185 is 0.3039.

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To calculate the position, velocity, and acceleration of the particle at a specific time, we need to integrate the velocity function. Let's calculate each of them step by step.

(a) Position:

To find the position, we need to integrate the velocity function with respect to time. The position function is obtained by integrating the velocity function:

x(t) = ∫v(t) dt

Given v(t) = 2t^2 m/s, we can integrate it:

∫2t^2 dt = 2 * (t^3/3) + C

Since the initial position x₀ = 1 m is given at t₀ = 0 s, we can substitute these values into the equation:

x(1) = 2 * (1^3/3) + C

To find the value of C, we use the initial condition x₀ = 1:

1 = 2 * (0^3/3) + C

1 = 0 + C

C = 1

Now we can substitute this value back into the equation to find the position at t = 1 s:

x(1) = 2 * (1^3/3) + 1

x(1) = 2/3 + 1

x(1) = 2/3 + 3/3

x(1) = 5/3 m

Therefore, the particle's position at t = 1 s is 5/3 m.

(b) Velocity:

The velocity of the particle is given by the function v(t) = 2t^2 m/s. To find the velocity at t = 1 s, we simply substitute t = 1 into the velocity function:

v(1) = 2 * (1^2)

v(1) = 2 m/s

Therefore, the particle's velocity at t = 1 s is 2 m/s.

(c) Acceleration:

The acceleration of the particle is the derivative of the velocity function with respect to time. Let's differentiate the velocity function to find the acceleration:

a(t) = d/dt (v(t))

= d/dt (2t^2)

= 4t

To find the acceleration at t = 1 s, we substitute t = 1 into the acceleration function:

a(1) = 4 * 1

a(1) = 4 m/s^2

Therefore, the particle's acceleration at t = 1 s is 4 m/s^2.

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Answer:

  A = C²/(4π)

Step-by-step explanation:

You want a formula for the area of a circle, given its circumference.

Relevant relations for a circle are ...

  A = πr² . . . . . . . . A = area, r = radius

  C = 2πr . . . . . . . . C = circumference

Solving the circumference equation for r, we find ...

  r = C/(2π)

Substituting that into the area equation, we have ...

  A = π(C/(2π))²

  A = C²/(4π)

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The function that models the area A of a circle in terms of its circumference C is A = C²/(4π).

The formula for the circumference of a circle is C = 2πr or C = πd, where r is the radius and d is the diameter. To find a function that models the area A of a circle in terms of its circumference C, we can rearrange the formula for the circumference to solve for the radius: r = C/(2π). Substituting this value of r into the formula for the area, we get A = π(C/(2π))² = C²/(4π).

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The length of string will be used to hang each pennant is 3.9 meters.

The term length in math is defined as the measurement or extent of something from end to end and it is used to identifying the size of an object or distance from one point to the other.

Here we have given that Ingrid has 14. 4 meters of string to hang 5 pennants and a banner at her school.

And here we have also know that she needs 0. 65 meter of string for the banner and the same length string for each pennant.

the length of the string needed for 5 pennants is calculated as,

=> 0.65 x (5 + 1)

=> 3.9 meter.

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Answer:  The cost of the 7.5 lbs of walnuts be $2.16 . It costs $3.45 to buy lb of chopped walnuts.

Answer:

$34.50

Step-by-step explanation:

First, find how much 1 lb costs.

To do this divide 3.45 by 3 to get 1/4 lb and then multiply by 4 to get the cost of 1 lb.

3.45/3 = 1.15      1.15 x 4 = 4.60

So 1 lb is $4.60

Multiply the cost of 1 lb by 7.5 to find the cost for 7.5 lbs

$4.60 x 7.5 = $34.50

Hope this helps!

Answer:

6x-48=4x-10

2x=38

x=19

Step-by-step explanation:

Let x and y be the numbers;

We have x + 2y = 9 and 2x + y = 21;

Then, x = 9 - 2y;

Finally, 2(9-2y) + y = 21 ;

18 - 4y + y = 21;

18 - 3y = 21;

-3y = 3;

y = - 1;

x = 9 - 2× (-1);

x = 9 + 2 ;

x = 11;

The length of AB in simplest radical form is 8.06.

We can find the length of AB using the principle of similar triangles on the triangles ABD and ABC.

Considering triangle ABD, given that AD = 5 then

Cos A = AD/AB

Also,

Cos A = AB/AC

Given that AD = 5, AC = 13, AB = x

therefore,

x/13 = 5/x

x² = 65

x = √65

= 8.06

Hence, the length of AB in simplest radical form is 8.06.

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Answer:

B. ½

Step-by-step explanation:

____________________

Answer:

-69

Step-by-step explanation:

inches:-69

-5 9/12 (-5 3/4 clearer) feet

Explanation in detail:

Write the equation down and distribute it.

3x - 1 = 2(x + 34)

3x - 1 = 2x + 68

Remove the variable on one side first (it makes solving the equation less complicated.)

3x - 1 = 2x + 68

-3x -3x

-1 = -x + 68

On all sides, subtract 68.

-1 = -x + 68

-68 -68

-69 = x

I'm guessing the answer in feet and inches is...

inches:-69

-5 9/12 (-5 3/4 simplified) feet

Answer:

XW in the first blank

Z in the second blank

Given:

Consider the equations are

\(3x+4y=7\)

\(4x+3y=9\)

To find:

The value of x-y.

Solution:

We have,

\(3x+4y=7\)        ...(i)

\(4x+3y=9\)        ...(ii)

Subtracting (i) from (ii), we get

\(4x+3y-(3x+4y)=9-7\)  

\(4x+3y-3x-4y=2\)  

\((4x-3x)+(3y-4y)=2\)  

\(x-y=2\)

Therefore, the value of x-y is 2.

The area of the triangle is mathematically given as

A=20.8cm

This is further explained below.

The region that is surrounded by the perimeter of the triangle, also known as the three sides of the triangle, is referred to as the area of the triangle.

The space that is encompassed by all three of a triangle's sides is referred to as the triangle's area.

It is computed with the assistance of a variety of formulae that differ according to the kind of triangle, and the results are represented in square units such as centimeters squared, inches squared, and so on.

Generally, the equation for Area the is mathematically given as

A = 1/2 * base * height

Therefore

A= 1/2 * 8 * 5.2

A=20.8cm

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