A four side sandbox has exactly two right angles, two side leghts 5 ft, and two side leghts 6 ft. What geometric shape best describes the shape of the sandbox?

Answers and Step-by-step explanations

13. Square both sides: x^2 + 4x + 4 = 16(x - 2) = 16x - 32

Move all the terms to one side: x^2 - 12x + 36 = 0

Factorize: (x - 6)^2 = 0  ⇒  x = 6

14. Move one of the roots to one side: [tex]-\sqrt{2x-1} =\sqrt{3x-12}[/tex]

Square both sides: 2x - 1 = 3x - 12

Solve for x: x = 11

15. Subtract 4 from both sides: x - 4 = [tex]2\sqrt{x-4}[/tex]

Square both sides: x^2 - 8x + 16 = 4(x - 4) = 4x - 16

Move all the terms to one side: x^2 - 12x + 32 = 0

Factorize: (x - 4)(x - 8) = 0  ⇒  x = 4 or x = 8

16. Square both sides: x^2 - 4x + 4 = 9x - 36

Move all the terms to one side: x^2 - 13x + 40 = 0

Factorize: (x - 5)(x - 8) = 0  ⇒  x = 5 or x = 8

Hope this helps!

Answer:

13. x = 6

14. No real solutions

15. x = 4, 8

16. x = 5, 8

Step-by-step explanation:

13. Square both sides

(x + 2)² = 4²(x - 2)

x² + 4x + 4 = 16x - 32

x² - 12x + 36 = 0

x² - 6x - 6x + 36 = 0

x(x - 6) - 6(x - 6) = 0

(x - 6)(x - 6) = 0

x = 6

14. sqrt(2x - 1) = -sqrt(3x - 12)

No real solutions because a positive square root can not be equal to a negative square root

15. x - 4 = 2sqrt(x - 4)

(x - 4)² = 4(x - 4)

(x - 4)² - 4(x - 4) = 0

(x - 4)(x - 4 - 4) = 0

(x - 4)(x - 8) = 0

x = 4, 8

16. x - 2 = sqrt(9x - 36)

(x - 2)² = (9x - 36)

x² - 4x + 4 - 9x + 36 = 0

x² - 13x + 40 = 0

x² - 5x - 8x + 40 = 0

x(x - 5) - 8(x - 5) = 0

(x - 8)(x - 5) = 0

x = 5, 8

Answer:

the anser is c

Step-by-step explanation:

just did the quiz and got 100 percent :)

Correct answer is C)

sorry this may not be helpful but the other answer is (A)

Answer:

a) 5180

Step-by-step explanation:

We must calculate with respect to each of the options:

a)  5180

We have that the mean (m) is equal to 5850, the standard deviation (sd) 1125 and the sample size (n) = 20

They ask us for P (x <5180)

For this, the first thing is to calculate z, which is given by the following equation:

z = (x - m) / (sd / (n ^ 1/2))

We have all these values, replacing we have:

z = (5180 - 5850) / (1125 / (20 ^ 1/2))

z = -2.66

With the normal distribution table (attached), we have that at that value, the probability is:

P (z <-2.66) = 0.0039

Which means that the probability is 0.39%, which is a very low probability, which is not necessary to calculate the other options, we already know that this data is very unusual.

The mean expense of (a) 5180 is considered unusual because its z-score is approximately -2.67, which is beyond the usual ±2 range for a normal distribution.

To determine which of the given mean expenses would be considered unusual, we will use the concept of the Standard Error of the Mean (SEM) and the properties of a normal distribution.

The SEM can be calculated as:

[tex]SEM = \frac{\sigma}{\sqrt{n}}[/tex]

Where:

So,
[tex]SEM = \frac{1125}{\sqrt{20}} = 251.21[/tex]

We then determine the z-scores for the given mean expenses to see how many standard errors away from the population mean they are. The population mean is $5850.

A z-score beyond ±2 is generally considered unusual. Therefore, the mean expense of 5180 would be considered unusual as its z-score is approximately -2.67.

Answer:

-1.6 m/s

Step-by-step explanation:

According to the equations of motion, the height in meters (s) after t seconds is:

[tex]s(t) = s_0+v_0t+a\frac{t^2}{2}[/tex]

If the initial position is 10 m and the initial velocity is 10 m/s:

[tex]s(t) = 100+10+a\frac{t^2}{2}[/tex]

When comparing it with the given height equation, it is possible to obtain the acceleration as follows:

[tex]100+10+a\frac{t^2}{2} =100+10t-0.8t^2\\\frac{a}{2}=-0.8\\ a=-1.6\ m/s[/tex]

Acceleration is -1.6 m/s.

Answer:

7

Step-by-step explanation:

We need to isolate the variable:

-2c + 6 = -8

-2c + 6 - 6 = -8 - 6

-2c = -14

-2c/-2 = -14/-2

c = 7

Thus, c = 7.

Hope this helps!

Method:

-2c+6=-8

     -6  -6

-2c=-14

/-2   /-2

c=7

[tex]c=6, e=2; so\\6\times6+2\times2=40[/tex]

Answer:

Riko is wrong

Step-by-step explanation:

To find the distance of two point, we use the following formula:

A (x1, y1)

B (x1, y2)

AB = [tex]\sqrt{(x2-x1)^{2} + (y2-y1)^{2} }[/tex]

In this situation, we have:

A (-2,-3)

B  (2,-5)

So the distance is: [tex]\sqrt{(2 - (-2))^{2} + (-5 - (-3))^{2} }[/tex] = [tex]\sqrt{4^{2} + 8^{2} }[/tex] = [tex]\sqrt{80} = 4\sqrt{5}[/tex]

Hope it will find you well.

Sample Response: No, Riko is not correct. The points do not have the same x-coordinates. If you connect the points, they do not form a horizontal or vertical line, so you cannot count spaces or use absolute value to find the distance.

Answer:

18 Houseboats

Step-by-step explanation:

Given the set of numbers

12 18 23 26 29

Minimum = 12

First Quartile, Q₁ = 18

Median, Q₂ = 23

Third Quartile, Q₃ = 26

Maximum = 29

The first 25% of lakes have less than or equal to 18 houseboats.

Therefore, the 5-Number Summary suggests that about 75% of lakes in Minessotta have more than 18 Houseboats.

Answer:

18

YEET

Step-by-step explanation:

Answer:

Longer: 17 ft and Shorter: 8 ft

Step-by-step explanation:

Here is what we know:

a = longer part

b = shorter part

a + b = 25

2b + 1 = a

Let's rearrange the equation

b = 25 - a

Now we can plug this into the other equation.

2(25 - a) + 1 = a

50 - 2a + 1 = a

51 - 2a = a

51 = 3a

a = 17 ft

To find b, plug a into one of the equations.

17 + b = 25

b = 8 ft

I hope this helped! :)

Answer:

[tex]8\sqrt{3}[/tex]

Step-by-step explanation:

2/3 pi radians =   2/3 * 180 =  2  * 60 =  120 degrees

split triangle in half:

30, 60, 90  triangle

1/2 PR= 4 root   3

Answer:

A≈54300

Step-by-step explanation:

To calculate the final amount in the bank account, we can use the formula A = P(e(rt)), where A is the final amount, P is the principal amount, e is the base of natural logarithms, r is the interest rate, and t is the time in years. In this case, Lucy invested $30,000 at an interest rate of 6.6% compounded continuously for 9 years. By substituting these values into the formula and evaluating the expression, the final amount in the account after 9 years is approximately $53,509.79.

To calculate the final amount in the bank account, we can use the formula: A = P(e(rt)), where A is the final amount, P is the principal amount, e is the base of natural logarithms, r is the interest rate, and t is the time in years. In this case, Lucy invested $30,000 at an interest rate of 6.6% compounded continuously for 9 years.

First, we need to convert the interest rate to a decimal by dividing it by 100: 6.6% = 0.066. Then, we can substitute the values into the formula: A = 30000(e0.066*9)). Using a calculator, we can evaluate this expression to get the final amount, which is approximately $53,509.79.

Answer:

it takes 1st person 4 hour and second person is 8 hours

Step-by-step explanation:

Let t is the time (t >0)

We have:

<=> 1/3  = 1/t  + 1/t-8  

<=> [tex]t^{2} -14t = -24[/tex]

<=> [tex](t-7)^{2} =25[/tex]

<=> t  - 7 = 5

<=> t = 12

So it takes 1st person 4 hour and second person is 8 hours

Answer:

Person A complete the task in 1.125 hours

Person B complete the task in 9 hours

Step-by-step explanation:

Person A complete a task 8 hours sooner than person B

Working together they perform the task in 3 hours

Let call "x" hours person A  need to do the task alone

Then person B will take 8*x hours to do the job

In 1 hour person A do 1/x  part of the task

In 1 hour person B do 1/8*x  part of the task  

Then A + B in one hour of work will do

1/x + 1/8x   =  [ 8 + 1 ]/8*x    ⇒  9/8*x

And according to problem statement that time is 1/3 (one third of the time)

Then 3* (9/8*x) =  3

9 = 8*x

x = 9/8

x =  1.125 hours

And person B will take  8*1,125  = 9 hours

Answer:

He can process 210 words in 3 minutes

Answer:

C. 8

At 8 seconds the object will hit the ground.

Answer: C. 8

Step-by-step explanation:

just did this

Answer: QP and SR on ed

Step-by-step explanation:

The chords in the circle that are congruent are PQ and SR.

Circle is the locus of a point such that its distance from a fixed point known as the center is constant.

Given from the diagram that:

∠PTQ = ∠STR (Vertical opposite angles are congruent)

Hence:

PQ = SR

The chords in the circle that are congruent are PQ and SR.

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Answer:

a. The slope is incorrect

b. y = 3x, ( 0 , 0 )

c) y = 4 - x

Step-by-step explanation:

Given:-

The slope between two points (1, 3) and (6, -2) is 3.

a. Explain why the information Mary was given cannot be correct.

- The slope between two arbitrary points, ( x1 , y1 ) and  (x2 , y2) is given by the following relationship:

                         slope = ( y2 - y1 ) / ( x2 - x1)

- Use the given points (1, 3) and (6, -2) and determine the slope:

                        slope = ( -2 - 3 ) / ( 6 - 1 )

                        slope = ( -5 ) / ( 5 )

                        slope = -1

- Yes, the given slope is incorrect it should be = -1

b.If the given point (1, 3) and the given slope are correct, what is the equation for the line? Give the  coordinates of another point on the line

- We will assume the point (1,3) lies on line with a slope = 3.

- We will use the slope-intercept equation of line:

                              y = slope*x + c

Where,      m : Slope

                 c : y-intercept

                             y = 3x + c

Using the given correct point to evaluate the y-intercept (c):

                             3 = 3*1 + c

                             c = 0

- The equation of line is,

                            y = 3x

- The origin (0,0) lies on the line y = 3x.

c. If the given points are correct for the line, what is the slope? Write an equation for the line

- We will assume the points (1, 3) and (6, -2) lies on line with a slope calculated in part (a) to be = -1.

- We will use the slope-intercept equation of line:

                              y = slope*x + c

Where,      m : Slope

                 c : y-intercept

                             y = -x + c

Using the given points to evaluate the y-intercept (c):

                             3 = -1 + c

                             c = 4

- The equation of line is,

                            y = -x + 4

Mary's information is incorrect because the slope of the line passing through the points (1, 3) and (6, -2) is -1, not 3. If the slope is actually 3, the line equation is y = 3x and an additional point on the line is (2, 6). If the given points are correct, the line equation is y = -x + 4.

To understand these questions, it's important to know how the slope of a line is defined and how to write the equation of a line.

Given two points (x1, y1) and (x2, y2), the slope of the line is calculated as (y2 - y1) / (x2 - x1). For the points given, (1, 3) and (6, -2), the slope would be (-2 - 3) / (6 - 1) = -5/5 = -1. So, the slope of the line passing through these two points is not 3, which contradicts the information given. Therefore, the information Mary was given cannot be correct.

If the point (1, 3) and the slope 3 are correct, the equation of the line is given by y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point on the line. Substituting these values we get y - 3 = 3(x - 1). This simplifies to y = 3x. A point on this line can be (2, 6).

If the points (1, 3) and (6, -2) are correct, we've already calculated the slope as -1. To find the equation of the line we use the same formula, y - y1 = m(x - x1). Substituting these values we get y - 3 = -1(x - 1), simplifying to y = -x + 4.

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Answer:

D

Step-by-step explanation:

it's In the picture

please like and Mark as brainliest

Answer:

Volume of the cylinder = D) 113.04 cubic cm

Step-by-step explanation:

[tex] \boxed{ \bold{formula = \pi \: {r}^{2} \: h }}[/tex]

= 3.14 × 2 × 2 × 9

= 3.14 × 36

= 113.04 cm³

There are a total of 9 possible schedules that Tycho can choose from.

Thus, option (C) is correct.

Let consider the days of the week as Monday (M), Tuesday (T), Wednesday (W), Thursday (Th), Friday (F), Saturday (Sa), and Sunday (Su).

To create a schedule for exercise, Tycho needs to choose three days of the week to exercise such that no two exercise days are consecutive.

So, the possibilities are:

1. Tycho chooses Monday, Wednesday, and Friday.

The schedule is MW FSu.

2. Tycho chooses Monday, Wednesday, and Saturday.

The schedule is MW SaSu.

3. Tycho chooses Monday, Thursday, and Saturday.

The schedule is MT F SaSu.

4. Tycho chooses Monday, Thursday, and Sunday.

The schedule is MT SaSu.

5. Tycho chooses Tuesday, Thursday, and Saturday.

The schedule is TThSaSu.

6. Tycho chooses Tuesday, Thursday, and Sunday.

The schedule is TTSaSu.

7. Tycho chooses Tuesday, Friday, and Sunday.

The schedule is TFSaSu.

8. Tycho chooses Wednesday, Friday, and Sunday.

The schedule is W F SaSu.

9. Tycho chooses Wednesday, Thursday, and Saturday.

The schedule is W T FSaSu.

Thus, total of 9 possible schedules that Tycho can choose from.

Thus, option (C) is correct.

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Answer:

ok

1) n=27

2) x=5/21

3) no solution

4) x=18

5) x=0

6) a=11

Step-by-step explanation:

hope this helps you..(:

The population of the town in 2007, according to the exponential growth function y = 8.5(1.1)x, would be approximately 16,630 people.

The function given is an exponential growth function, where y = 8.5(1.1)x. Here, the variable y represents the population in thousands and x represents the number of years after 2000. To find the town's population in 2007, we replace x with 7 (since 2007 is 7 years after 2000) and calculate y.

Using the formula, y = 8.5 * (1.1)7. When calculated, we find y to be approximately 16.63. This means that, according to the model, the town's population in 2007 would be approximately 16630 (because the model represents the population in thousands).

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Answer:

4:30

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Answer:

100%

Step-by-step explanation:

Answer: there were not a lot of safe places kids could play

Step-by-step explanation:

i got it right.

The problem led to playgrounds becoming more common in America cities is: Due to unsafe places.

Playgrounds is a safe place that is specifically set aside for children to play.

Playgrounds can tend to contribute to a child social growth when the child plays among is age group or peer group.

Playgrounds is common in America in order to prevent danger and injury because there were not safe places for children to play.

Therefore the problem led to playgrounds becoming more common in America cities is: Due to unsafe places.

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Answer:

The correct option is option [B].

The probability that both girls Selena and Tracey will a next at bat is [tex]\frac{48}{320}[/tex].

Step-by-step explanation:

Independent events:

If A and B are event. The occurrence of one of them does not affect the outcomes of other event. Then A and B are independent events.

P(A and B) =P(A)× P(B)

Dependent events:

If A and B are event. The outcomes of one of them affects the outcomes of other event. Then A and B are called dependent events.

P(A and B) =P(A)× P(B|A)= P(B)×P(A|B)

Given that,

Selena has 8 hits out of 20 times at bat.

The number of hits by Tracey out of 16 is 6 at bat.

A= Selena hits a softball.

B= Tracey hits a softball.

The probability that the Selena his a softball is

=P(A)

[tex]=\frac{8}{20}[/tex]

The probability that the Tracey his a softball is

=P(B)

[tex]=\frac{6}{16}[/tex]

Both event are independent. Sine the events do not affect the outcomes of other event.

The probability that both girls will a next at bat is

=P(A and B)

=P(A)×P(B)

[tex]=\frac{8}{20}\times \frac{6}{16}[/tex]

[tex]=\frac{48}{320}[/tex]

Answer:

Step-by-step explanation:

√20 can be rewritten as the product of two radicals:  √4√5,

and √4 = 2.

Thus, 5√20 = 5(2)√5 = 10√5.  Thus, B:  10 is correct; k = 10.

Answer: The measure of the central angle of the circle is 73°

Step-by-step explanation: Please see the attachments below

Answer: 287 degree

Step-by-step explanation:

Area of a sector = θ/360 x pi r^2

Where pi = 22/7

Given that the

area = 40.8 square inches

radius = 8 inches

40.8 = θ/360 × 3.143 × 8 × 8

θ = (360 × 40.8)/201.06

θ = 73 degree

The measure of the central angle of the circle = 360 - θ

= 360 - 73

= 287 degree

Answer:

(x/3) - 5.

Step-by-step explanation:

Let the number be x.

The quotient of the number and 3 is x/3.

So the expression is:

(x/3) - 5.

Answer:

6

Step-by-step explanation:

22 - 4 = 18

18 / 3 = 6

Answer:

6

Step-by-step explanation:

22-4=18/3=6

start from what you get that use the inverse to get the the original answer

Answer:

The probability that the sum of the numbers rolled will equal 4 is [tex]\frac{1}{12}[/tex]

Step-by-step explanation:

Total possible outcome is 36

The sample space for the dice is shown below

[tex]\left[\begin{array}{cccccc}1,1&1,2&1,3&1,4&1, 5&1,6\\2,1&2,2&2,3&2,4&2, 5&2,6\\3,1&3,2&3,3&3,4&3, 5&3,6\\4,1&4,2&4,3&4,4&4, 5&4,6\\5,1&5,2&5,3&5,4&5, 5&5,6\\6,1&6,2&6,3&6,4&6, 5&6,6\end{array}\right][/tex]

From the above sample, the event of sum equals 4 is:

(1, 3)

(2, 2)

(3, 1)

Number of outcome with sum equals 4 is 3

[tex]Probability = \frac{number of possible outcome}{number of total outcome} \\Probability = \frac{3}{36} = \frac{1}{12}[/tex]

The probability that the sum of the numbers rolled will equal 4 is [tex]\frac{1}{12}[/tex]

Answer:

0.3333

Step-by-step explanation:

Out of 6x6 = 36 different scenarios that could happen when rolling the 2 cubes, there are 3 cases where the sum of the numbers rolled will equal 4:

(1,3) (3,1) and (2,2)

So the probability for these 3 cases to happen out of 36 is

[tex]\frac{3}{36} = \frac{1}{3}[/tex] or 0.3333