Consider the triangle.
Which statement is true about the lengths of the sides?
45°
Each side has a different length.
Two sides have the same length, which is less than the
length of the third side.
D. The three sides have the same length.
D. The sum of the lengths of two sides is equal to the
length of the third side.
45°

Work Shown:

In the numerator, we have 2^2*x^2, which is really just 4x^2. Replace x with 3 and we get 4*x^2 = 4*3^2 = 36.

For the denominator, xy^2, we get

x*y^2 = 3*2^2 = 12

So far we have,

[tex]\frac{2^2x^2}{xy^2} = \frac{4x^2}{xy^2} = \frac{36}{12} = 3\\\\\text{ or simply} \\\\\frac{2^2x^2}{xy^2} = 3[/tex]

when x = 3 and y = 2.

Square both sides to end up with...

[tex]\frac{2^2x^2}{xy^2} = 3\\\\\left(\frac{2^2x^2}{xy^2}\right)^2 = 3^2\\\\\left(\frac{2^2x^2}{xy^2}\right)^2 = 9[/tex]

Answer:

Mode: 11

Median: 13

Answer:

(23, 13, 17, 11, 11):

Median: 13

Arithmetic mean: 15

Geometric mean: 14.380735416546

Harmonic mean: 13.848764056076

Mode: 11

Standard deviation: 4.5607017003966

Variance: 20.8

Mean Absolute Deviation: 4

Range: 12

Interquartile range: 9

Lower quartile: 11

Upper quartile: 20

Quartile deviation: 4.5

Population size:5

Answer:

A. X=6 only

Step-by-step explanation:

Answer:

2 divided

Step-by-step explanation:

Answer

I believe C considering cubic mass

Answer:

D

Step-by-step explanation:

Answer:

  A number line going from negative 1 to positive 7. An open circle is at 3. Everything to the right of the circle is shaded.

Step-by-step explanation:

The area of a parallelogram is given by the formula ...

  A = bh

So, we have the condition that ...

  A > 42

  bh > 42 . . . . . substitute the expression for area

  14h > 42 . . . . fill in the given base

  h > 3 . . . . . . . divide by 14

Numbers greater than 3 are to the right of 3 on the number line.

_____

The relation is > rather than ≥, so the "or equal to" case is not included. That is why the circle is open, rather than solid.

Answer:

a).

Step-by-step explanation:

Answer:

The average of the extracted scores that are extreme values (outliers) = 102

Step-by-step explanation:

With the logical assumption that the population size is large enough, for a normal distribution,

68% of the data lies within 1 standard deviation of the mean.

95% of the data lies between 2 standard deviations of the mean.

99.7% of the data lies within 3 standard deviations of the mean.

So, the outliers for a normal distribution are usually beyond 3 standard deviations of the mean.

The mean = 128.5

Standard deviation = 8.2

The range of scores within 3 standard deviations of the mean is obtainable thus

(Mean ± 3standard deviations)

3 × standard deviations = 3 × 8.2 = 24.6

(128.5 ± 24.6) = (103.9, 153.1)

The 3 extracted scores are 148, 102 and 152. The only extreme value of these 3 extracted scores is 102. The two other scores are within the range of 3 standard deviations of the mean.

Hence, the average of the extracted scores that are extreme values (outliers) = 102

Hope this Helps!!!

Answer:

Hence, Stacy will spin 6,  8.33 times out of her n = 50 attempts.

Step-by-step explanation:

Let us consider a success to get a 6. In this case, note that the probability of having a 6 in one spin is 1/6. We can consider the number of 6's in 50 spins to be a binomial random variable. Then, let X to be the number of trials we get a 6 out of 50 trials. Then, we have the following model.

We will estimate the number of times that she spins a 6 as the expected value of this random variable.

Recall that if we have X as a binomial random variable of n trials with a probability of success of p, then it's expected value is np.

Then , in this case, with n=50 and p=1/6 we expect to have  number of times of having a 6, which is 8.33.

Answer:

3/90

Step-by-step explanation:

1 slot  is 1/30

2 slot is 1/30

3 slot is 1/30

this gives you that 3/90 when you had them

Answer:

D)  1/(30×30×30) = 1/27000 = 0.00003 or 0.003%

Step-by-step explanation:

Answer:

3 1/4

Step-by-step explanation:

3/4 + (1/3 ÷1/6) - (-1/2)

Subtracting a negative is adding

3/4 + (1/3 ÷1/6) +1/2

Parentheses first

Copy dot flip

3/4 + (1/3 * 6/1) +1/2

3/4 + 2 + 1/2

Get a common denominator

3/4 + 2 + 2/4

2 + 5/4

2 + 4/4 +1/4

2+1 + 1/4

3 1/4

Answer:

C

Step-by-step explanation:

Answer:

e = d + 5

Step-by-step explanation:

e = d + 5

f = d - 7

Solve for e means write as e = ...d

and this is already there...

You can not write it more compact then this.

If you try, you will notice you finally end with the initial equation which you started with, or you endup with something which is obviously very true like

e = e or d = d.

Answer:

21

Step-by-step explanation:

Answer:

6.7

Step-by-step explanation:

Answer:

[tex]B(t) = 1150*(2)^{t}[/tex]

After 10 hours: 1,177,600

Step-by-step explanation:

The number of bacteria after b hours is given by the following equation:

[tex]B(t) = B(0)(1+r)^{t}[/tex]

In which B(0) is the initial number of bacteria and r is the rate that it increases.

The initial number of bacteria in the dish was 1,150. The amount of bacteria doubles at the end of each hour.

This means that [tex]B(0) = 1150, B(1) = 2*1150[/tex]

So

[tex]B(t) = B(0)(1+r)^{t}[/tex]

[tex]2*1150 = 1150(1+r)^{1}[/tex]

[tex]1 + r = 2[/tex]

[tex]r = 1[/tex]

So

[tex]B(t) = 1150*(2)^{t}[/tex]

After 10 hours:

[tex]B(10) = 1150*(2)^{10} = 1177600[/tex]

1,177,600 bacteria after 10 hours.

Answer: 1050 people.

Step-by-step explanation: It's a rule of three question.

15/50 as x/3500

Then you have that 50x = 52500

x = 1050

There you have it.

Answer:

D. 96

F. 32

Step-by-step explanation:

The inequality 3x ≥ 96, means that x and 3 must be multiplied to get a product that is greater than 96.  So to figure this out, you must plug in the numbers given for x, like so:

3x ≥ 96

A. 3(31) ≥ 96

     93 ≥ 96                            This is incorrect since 93 is not greater than 96

A tip that makes this easier is that, you can see that 31 multiplied by 3 is 93, which is only a couple numbers off 96, so all numbers after 31 will result in a product greater than 96. For example:

D. 3(96) ≥ 96

    288 ≥ 96                             This inequality is correct

F. 3(32) ≥ 96

   96 ≥ 96                        

The inequality sign states that the number must be either greater or equal to 96, which it is.

Answer:

A. 1/2

Step-by-step explanation:

20x=10

Divide 20 on both sides of the equation to get x by itself

20x=10

___.  __

20.     20

x =1/2

Answer:

A) x= 1/2

Step-by-step explanation:

20x= 10 we then divide 10 by 20 to get x= 10/20 or if we simplify x= 1/2. Thus answer choice A) is correct!

Answer:

x=26

Step-by-step explanation:

(x+6)2=64

x+6=32

x=26

Answer:

Here is the solution. Mark as brainlist please.

Answer:4.6

Step-by-step explanation:

Percentage decrease=(65-62)/65 x 100

Percentage decrease=3/65 x 100

Percentage decrease=(3x100)/65

Percentage decrease=300/65

percentage decrease=4.6

Answer:

B. -3(4x + 1) (x - 4)

Step-by-step explanation:

Out of the other answer choices, "B," is the only that factorizes correctly and ends up with the correct factorization (It already gives you the break-down of the trinomial).

However, if you're unsure about the answer, you can always take the end result: -3(4x + 1) (x - 4), and multiply it together to see if you can end up with the original trinomial: [tex]-12x^2 + 45x + 12[/tex]

Answer:

E 39

Step-by-step explanation:

x+6 = 45

Subtract 6 from each side

x+6-6 = 45-6

x = 39

Answer:

6

Step-by-step explanation:

The ratio would be 3:65, so to get it to ?:130 you would multiply by 2 (65•2=130). So all you have to do is do 3•2=6 to get the correct ratio which is 6:130. So that answer would be 6.

Answer:

300

Step-by-step explanation:

5x60=5x6 tens it equal to 30 tens. 30 tens equals 300

Answer:

see below

Step-by-step explanation:

there are 6 tens in 60!

5x60 = 5 x 6 tens

= 30 tens

= 300

Answer:

MC = 4.5cm

Step-by-step explanation:

Question:

Let the isosceles triangle ABC with AB = AC = 3 cm. if the mediator of the sides AC intersects with the side BC in M ​​and the perimeter of the triangle AMC = 12 cm. Calculate MC.

Solution:

Find attached the diagram used in solving the question.

Given:

∆ABC is an isosceles triangle (two sides and angles are equal)

AB = BC = 3cm

Perimeter of ∆AMC = 12cm

From the diagram, M cuts AC at the the middle.

AD = CD = AC/2 = 3/2

Perimeter of Right angled ∆AMD = AM + AD + MD

= 3/2 + AM +MD

Perimeter of Right angled ∆CMD =CM + CD + MD

= 3/2 + CM +MD

Right angled ∆AMD = Right angled ∆CMD

CM = AM

Therefore ∆AMC is an isosceles triangle

CM = AM (two sides of an isosceles triangle are equal)

Let CM = AM = x

Perimeter of ∆AMC = AM + CM + AC

12 = x + x + 3

12 = 2x + 3

2x = 12-3

2x = 9

x = 9/2 = 4.5

CM = AM = 4.5cm

MC = CM = 4.5cm

The answer is 4.55

When you divide 5 by 11 you will get  0.45454545454 than when you multiply these numbers by 10 you will get 4.54545454545 and then the rounded answer is 4.55.

Answer: 4.54

Step-by-step explanation:

Answer:

x=10

Step-by-step explanation:

9x-3=87

add 3 to both sides

9x=90

divide by 9 on both sides

x=10

Answer:

x=10

Step-by-step explanation:

9x-3=87

you add 3 to both sides

9x-3(+3)=87(+3)

which equals

9x=90

90/9= 10

answer:

x =10

I hope this helped!

Answer:

Basically it's asking for the sum of 212 + 216 + 220 + ..... 586

Each number is 22 more than the previous one.

Therefore the sum will be 212 + (212+22) + (212+22*2) + (212+22*3)

the amount of numbers from 212 through 586 is 18.

Therefore we will need 212 plus 212 * 17 = 3,816 *******************

We will also need all those 22's.

We must add 22 *1 plus 22*2 plus 22*3 ..... plus 22*17

Which equals 22 + 44 + 66 + 88 ... 374

Which totals 3,366 *****************

So, we total 3,816 + 3,366 which equals 7,182

Step-by-step explanation:

[tex]\displaystyle\bf\\Sum=586+564+542+...+212\\\\Sum=212+234+256+...+586\\\\\textbf{We calculate the number of terms (n):}\\\\n=\frac{586-212}{22}+1=\frac{374}{22}+1=17+1=18\\\\\boxed{\bf~n=18~terms}\\\\Sum=\frac{n(586+212)}{2}\\\\Sum=\frac{18\times 798}{2}\\\\Sum=9\times798\\\\\boxed{\bf~Sum=7182}[/tex]

Answer:

  116.82 square inches

Step-by-step explanation:

The overall shape is that of a 10-inch square with four triangles attached. Each of those is an isosceles right triangle with leg lengths of 2.9 inches.

The area of the four triangles is ...

  total triangle area = 4(1/2)(2.9 in)(2.9 in) = 16.82 in²

The area of the 10-inch square is ...

  square area = (10 in)² = 100 in²

Then the total window area is ...

  window area = 16.82 in² +100 in²

  window area = 116.82 in²

Answer:

78.88% probability that this sample proportion is within 0.05 of the population proportion

Step-by-step explanation:

We need to understand the normal probability distribution and the central limit theorem to solve this question.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For proportion p in a sample of size n, we have that [tex]\mu = p, s = \sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In this question:

[tex]p = 0.8, n = 100[/tex]

So

[tex]\mu = 0.8, s = \sqrt{\frac{0.8*0.2}{100}} = 0.04[/tex]

What is the probability that this sample proportion is within 0.05 of the population proportion.

This is the pvalue of Z when X = 0.8 + 0.05 = 0.85 subtracted by the pvalue of Z when X = 0.8 - 0.05 = 0.75.

X = 0.85

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.85 - 0.8}{0.04}[/tex]

[tex]Z = 1.25[/tex]

[tex]Z = 1.25[/tex] has a pvalue of 0.8944.

X = 0.75

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.75 - 0.8}{0.04}[/tex]

[tex]Z = -1.25[/tex]

[tex]Z = -1.25[/tex] has a pvalue of 0.1056.

0.8944 - 0.1056 = 0.7888

78.88% probability that this sample proportion is within 0.05 of the population proportion

Answer:

⅓ m/s

Step-by-step explanation:

Area of a square is:

A = s²

Take derivative of both sides with respect to time:

dA/dt = 2s ds/dt

Given that dA/dt = 6 m²/s and s = 9 m:

6 m²/s = 2 (9 m) ds/dt

ds/dt = ⅓ m/s

The Formula of the area of a square: A = bh or A = s^2

Solution:

~Take derivative of both sides

da/dt = 2s * ds/dt

~Use given values (6m^2/s and 9m)

6 = 2(9) * ds/dt

~Simplify

1/3m/s = ds/dt

Best of Luck!

Answer:

b.69.08

Step-by-step explanation:

formula:

c=2(pi)r

c=2(pi)11

Answer:b

Step-by-step explanation:

radius=r=11

π=3.14

Circumference=2 x π x r

Circumference=2 x 3.14 x 11

Circumference=69.08