Which of the following is the graph of (x + 1)2 + (y − 6)2 = 36?

Answer:

C. HL

Step-by-step explanation:

The Hypotenuse-Leg Theorem is the only viable way to determine congruency between 2 right triangles.

Step-by-step explanation:

x - y = 34

x + y = 212

2x = 246

x = 123

123 + y = 212

y = 89

(123, 89)

Answer:

a. P ( X > 12 ) = 0.5254

b. P ( X < 15 ) = 0.7172

c. P ( 9 < X < 13 ) =  0.3179

d. Not unusual

Step-by-step explanation:

Solution:-

- We will define our random variable X as follows:

       X: The weights of the male babies less than 2 month old in USA ( lb )

- The distribution given for the random variable ( X ) is defined to follow normal distribution.

- The normal distribution is identified by two parameters mean ( u ) and standard deviation ( σ ). The distribution is mathematically stated or expressed as:

                               X ~ Norm ( u , σ^2 )

- The parameters for the normal distribution followed by the random variable ( X ) are given. Hence,

                              X ~Norm ( 12.3 , 4.7^2 )

- We will use standard normal tables to determine the following probabilities:

a) What proportion of babies weigh more than 12 pounds?

- To use the standard normal tables we need to standardized our limiting value of the required probability by finding the corresponding Z-score value.

- The formula used to compute the Z-score value is given below:

                                [tex]Z-score = \frac{x - u}{sigma}[/tex]

- We are requested to compute the probability p ( X > 12 ). the limiting value is 12 pounds. We will use the conversion formula and compute the Z-score:

                               [tex]Z-score = \frac{12 - 12.3}{4.7} \\\\Z-score = -0.06382[/tex]

- The standard normal table gives the probabilities of Z-score values in "less than ". So to determine the required probability we look-up:

                            P ( X > 12 ) = P ( Z > -0.06382 ) = ...

                            P ( Z > -0.06382 ) = 1 - P ( Z < -0.06382 )  

Use standard normal look-up table:

                            P ( X > 12 ) =  1 - 0.4746

                            P ( X > 12 ) = 0.5254  ... Answer

Answer: The proportion of babies that weigh more than 12 pounds is the probability of finding babies weighing more than 12 pounds among the total normally distributed population. The proportion is 0.5254

b) What proportion of babies weigh less than 15 pounds?

- We are requested to compute the probability p ( X < 15 ). the limiting value is 12 pounds. We will use the conversion formula and compute the Z-score:

                             [tex]Z-score = \frac{15-12.3}{4.7} \\\\Z-score = 0.57446[/tex]

- The standard normal table gives the probabilities of Z-score values in "less than ". So to determine the required probability we look-up:

                            P ( X < 15 ) = P ( Z < 0.57446 )

                            P ( X < 15 ) = 0.7172

Answer: The proportion of babies that weigh less than 15 pounds is the probability of finding babies weighing less than 15 pounds among the total normally distributed population. The proportion is 0.7172

c) What proportion of babies weigh between 9 and 13 pounds?

- We are requested to compute the probability p ( 9 < X < 13 ). the limiting value are 9 and 13 pounds. We will use the conversion formula and compute the Z-score:

                           [tex]Z_1 = \frac{9-12.3}{4.7} = -0.70212\\\\Z_2 = \frac{13-12.3}{4.7} = 0.14893\\[/tex]

- The standard normal table gives the probabilities of Z-score values in "less than ". So to determine the required probability we look-up:

                          P ( 9 < X < 13 ) = P ( -0.70212 < X < 0.14893 )

        P ( -0.70212 < X < 0.14893 ) = P ( X < 0.14893 ) - P ( X < -0.70212 )  

Use standard normal look-up table:

                            P ( 9 < X < 13 ) =  0.5592 - 0.2413

                            P ( 9 < X < 13 ) =  0.3179  ... Answer

Answer: The proportion of babies that weigh less than 13 pounds but greater than 9 pounds is the probability of finding babies weighing less than 13 pounds and more than 9 pounds among the total normally distributed population. The proportion is 0.3179

d)

Is it unusual for a baby to weigh more than 18.1 pounds?

- We are requested to compute the probability p (  X > 18.1 ). the limiting value is 18.1 pounds. We will use the conversion formula and compute the Z-score:

                             [tex]Z-score = \frac{18.1-12.3}{4.7} \\\\Z-score = 1.23404[/tex]

The standard normal table gives the probabilities of Z-score values in "less than ". So to determine the required probability we look-up:

                            P ( X > 18.1 ) = P ( Z > 1.23404 )

                            P ( X > 18.1 ) =  0.1086

Answer: The proportion of babies that weight more than 18.1 pounds are 0.1086 of the total babies population. We can say that the proportion of babies that weigh more than 18.1 pounds are significant because the proportion lies is significant. Not enough statistical evidence to be classified as "unusual".

Answer:

it should be -4=x.

Answer: -4

Step-by-step explanation:

Answer:

33.333333%

Step-by-step explanation:

If 6/9 (66.66666666%) of the jeans are blue it means that 3/9 of the jeans are not blue. 3/9 as a percentage is 33.333333%

Answer:

33.3%

Step-by-step explanation:

6 ÷ 9 = 66.66666667%

100% - 66.66666667% = 33.3% (Or you can put 33.33333333)

Hope this helped! :)

Answer:

Option D

Step-by-step explanation:

We are given the following equations -

[tex]\begin{bmatrix}-5x-12y-43z=-136\\ -4x-14y-52z=-146\\ 21x+72y+267z=756\end{bmatrix}[/tex]

It would be best to solve this equation in matrix form. Write down the coefficients of each terms, and reduce to " row echelon form " -

[tex]\begin{bmatrix}-5&-12&-43&-136\\ -4&-14&-52&-146\\ 21&72&267&756\end{bmatrix}[/tex]  First, I swapped the first and third rows.

[tex]\begin{bmatrix}21&72&267&756\\ -4&-14&-52&-146\\ -5&-12&-43&-136\end{bmatrix}[/tex]  Leading coefficient of row 2 canceled.  

[tex]\begin{bmatrix}21&72&267&756\\ 0&-\frac{2}{7}&-\frac{8}{7}&-2\\ -5&-12&-43&-136\end{bmatrix}[/tex]  The start value of row 3 was canceled.

[tex]\begin{bmatrix}21&72&267&756\\ 0&-\frac{2}{7}&-\frac{8}{7}&-2\\ 0&\frac{36}{7}&\frac{144}{7}&44\end{bmatrix}[/tex]       Matrix rows 2 and 3 were swapped.

[tex]\begin{bmatrix}21&72&267&756\\ 0&\frac{36}{7}&\frac{144}{7}&44\\ 0&-\frac{2}{7}&-\frac{8}{7}&-2\end{bmatrix}[/tex]      Leading coefficient in row 3 was canceled.

[tex]\begin{bmatrix}21&72&267&756\\ 0&\frac{36}{7}&\frac{144}{7}&44\\ 0&0&0&\frac{4}{9}\end{bmatrix}[/tex]

And at this point, I came to the conclusion that this system of equations had no solutions, considering it reduced to this -

[tex]\begin{bmatrix}1&0&-1&0\\ 0&1&4&0\\ 0&0&0&1\end{bmatrix}[/tex]

The positioning of the zeros indicated that there was no solution!

Hope that helps!

Answer:

It's the third Answer: It is the portion of internal energy that can be transferred from one substance to another.

Hope this helps

Answer:

c

Step-by-step explanation:

Answer:

The null hypothesis failed to be rejected.

At a significance level of 0.05, there is not enough evidence to support the claim that the mean bad debt ratio for Ohio banks is different than the Midwestern average (3.5%).

Test statistic t = 1.431

Critical values tc = ±2.447

P-value = 0.203

Step-by-step explanation:

This is a hypothesis t-test for the population mean.

The claim is that the mean bad debt ratio for Ohio banks is different than the Midwestern average (3.5%).

Then, the null and alternative hypothesis are:

H_0: \mu=3.5\\\\H_a:\mu\neq 3.5

The significance level is 0.05.

The sample has a size n=7.

We calculate  the sample mean and standard deviation as:

[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{7}(7+4+6+3+5+4+2)\\\\\\M=\dfrac{31}{7}\\\\\\M=4.43\\\\\\[/tex]

[tex]s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{6}((7-4.43)^2+(4-4.43)^2+(6-4.43)^2+. . . +(2-4.43)^2)}\\\\\\s=\sqrt{\dfrac{17.71}{6}}\\\\\\s=\sqrt{2.95}=1.72\\\\\\[/tex]

The sample mean is M=4.43.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=1.72.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{1.72}{\sqrt{7}}=0.65[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{4.43-3.5}{0.65}=\dfrac{0.93}{0.65}=1.431[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=7-1=6[/tex]

This test is a two-tailed test, with 6 degrees of freedom and t=1.431, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=2\cdot P(t>1.431)=0.203[/tex]

As the P-value (0.203) is bigger than the significance level (0.05), the effect is not significant.

If we use the critical value approach, for this level of confidence, the critical values are tc = ±2.447. The test statistic is within the bounds of the critical values and falls within the acceptance region.

The null hypothesis failed to be rejected.

At a significance level of 0.05, there is not enough evidence to support the claim that the mean bad debt ratio for Ohio banks is different than the Midwestern average (3.5%).

Answer:

20 tests

Step-by-step explanation:

There are six different wires, and for each test the author picks three, this means that each test is a combination of three out of six wires (₆C₃) . The number of total combinations possible is given by:

[tex]_6C_3=\frac{6!}{(6-3)!3!}\\_6C_3=\frac{6*5*4}{3*2*1}\\_6C_3=20[/tex]

20 tests are required to verify every possible pairing of three wires.

Answer:

C) (-2, 4), (6,8) is the correct answer.

Step-by-step explanation:

Given that line segment AB:

A (-3, 6) and B (9, 12) is dilated with a scale  factor 2/3 about the origin.

First of all, let us calculate the distance AB using the distance formula:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Here,

[tex]x_2=9\\x_1=-3\\y_2=12\\y_1=6[/tex]

Putting all the values and finding AB:

[tex]AB = \sqrt{(9-(-3))^2+(12-6)^2}\\\Rightarrow AB = \sqrt{(12)^2+(6)^2}\\\Rightarrow AB = \sqrt{144+36}\\\Rightarrow AB = \sqrt{180}\\\Rightarrow AB = 6\sqrt{5}\ units[/tex]

It is given that AB is dilated with a scale factor of [tex]\frac{2}{3}[/tex].

[tex]x_2'=\dfrac{2}{3}\times x_2=\dfrac{2}{3}\times9=6\\x_1'=\dfrac{2}{3}\times x_1=\dfrac{2}{3}\times-3=-2\\y_2'=\dfrac{2}{3}\times y_2=\dfrac{2}{3}\times 12=8\\y_1'=\dfrac{2}{3}\times y_1=\dfrac{2}{3}\times 6=4[/tex]

So, the new coordinates are A'(-2,4) and B'(6,8).

Verifying this by calculating the distance A'B':

[tex]A'B' = \sqrt{(6-(-2))^2+(8-4)^2}\\\Rightarrow A'B' = \sqrt{(8)^2+(4)^2}\\\Rightarrow A'B' = \sqrt{64+16}\\\Rightarrow A'B' = \sqrt{80}\\\Rightarrow A'B' = 4\sqrt{5}\ units = \dfrac{2}{3}\times AB[/tex]

So, option C) (-2, 4), (6,8) is the correct answer.

Answer: $5,000

Step-by-step explanation: First begin with the interest formula.

Interest = Principal × Rate × Time

In this problem, we're solving for the interest.

The principal is the amount invested or $2,500.

The rate is 8% which we can write as .08.

The time is 25 years.

So we have I = (2,500)(.08)(25).

Now we multiply.

(2,500)(.08) is equal to 200.

Now, multiply 200(25) to get 5,000.

This means that the interest earned is $5,000.

Answer:

0

Step-by-step explanation:

The probability of picking a even number is 1/3

If u don’t replace it then the probability of picking an even number is 0/3

Multiply and u get 0/9 or 0

Hope this helps

Answer:

0

Step-by-step explanation:

The number 2 is even.

The probability of picking an even number is 1/3.

You don't put the first card back.

1 and 3 are odd.

1/3 × 0 = 0

Answer:

Step-by-step explanation:

The spread of the height of each person in the group depends on the standard deviation. A low standard deviation means that the heights are closer to the mean than that of a high standard deviation. If an individual is picked, the probability of picking one who is more than 68 inches tall is small as this depends on the number of individuals in this category. The probability of picking a sample of four people who average more than 68 inches tall would be higher since average would be taken. Therefore, it is more likely to pick a sample of four people who average more than 68 inches tall

Answer: n=2

Step-by-step explanation: 4n-2n=4

4(2)-2(2)=

8-4=4

Answer:

n=2

Step-by-step explanation:

Step by Step Solution:

More Icon

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    4*n-2*n-(4)=0  

Step by step solution :

STEP

1

:

Pulling out like terms

1.1     Pull out like factors :

  2n - 4  =   2 • (n - 2)  

Equation at the end of step

1

:

STEP

2

:

Equations which are never true

2.1      Solve :    2   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

2.2      Solve  :    n-2 = 0  

Add  2  to both sides of the equation :  

                     n = 2

Answer:

26,400 N

Step-by-step explanation:

PLEASE CHECK ATTACHMENT FOR COMPLETE SOLUTION

Answer:

92

Step-by-step explanation:

We will list out the numbers which are factors of 12. They include:

1, 2, 3, 4, 6, 12.

We need to get the highest number that has its greatest factor to be 4. It means that 6 and 12 cannot divide it.

To do this, we will write out the multiples of 4. They include:

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88,92,96.

We will have to choose the highest number which only 4  can divide and  6 and 12 cannot divide.

Since we are looking for the largest, We can try dividing all the numbers by 4, 6, and 12 starting from 96.

We will quickly see that 4 can divide 92 but 6 and 12 cannot.

This gives us 92 as the answer.

Answer:

92

Step-by-step explanation:

Answer:

Step-by-step explanation:

x is a random variable. Since we are assuming that x has a normal distribution, then we would apply the formula,

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = standard deviation

From the information given,

µ = 24

σ = 4.2

The indicated probability to be determined is P(x ≥ 30)

P(x ≥ 30) = 1 - P(x < 30)

For P(x < 30),

z = (30 - 24)/4.2 = 1.43

Looking at the normal distribution table, the probability corresponding to the z score is 0.9236

Therefore,

P(x ≥ 30) = 1 - 0.9236 = 0.0764

Answer:

If r = 6 cm, the the circumference is c = 2π(6) = 12π cm

HOPE THIS HELPS AND PLS MARK AS BRAINLIEST

THNXX :)

Answer:

Step-by-step explanation:

Try this:

    1 wall                           1                   288

------------------------ =  ---------------  =  --------------- min  =  8 min

1 wall        1 wall         24 + 12                 36

(---------) + (---------)      ------------

12 min      24 min           288

it would be possible because if it's 6 it's even if it 4 it's even if it's 2 it's even so you okay so it is certain and possible babes

Answer:

Step-by-step explanation:

this triangle is regular one

Answer:

obtuse scalene triangle

Answer:

tan =-1

Step-by-step explanation:

tan(θ)=sen(θ)/cos(θ)

so

[tex]tan(angle)=\frac{\frac{-\sqrt{2} }{2} }{\frac{\sqrt{2} }{2} } }\\\\tan(angle)=-1[/tex]

Answer:

Step-by-step explanation:

[tex]cos \: \: theta \: = \frac{ \sqrt{2} }{2} = \frac{1}{ \sqrt{2} } = cos \: \frac{\pi}{4 } [/tex]

[tex]cos \: (2\pi \: - \frac{\pi}{4} ) \: \: ( \frac{3\pi}{2} < theta < 2\pi)[/tex]

[tex] = cos \: \frac{7\pi}{4} [/tex]

Theta = 7π / 4

[tex]sin \: theta = sin \: \frac{7\pi}{4} [/tex]

[tex] = sin \: (2\pi \: - \frac{\pi}{4} )[/tex]

[tex] - sin \: \frac{\pi}{4} [/tex]

[tex] = \frac{ - 1}{ \sqrt{2} } [/tex]

[tex] = - \frac{ \sqrt{2} }{2} [/tex]

Finding tan theta:

[tex]tan \: theta = tan \: \frac{7\pi}{4} [/tex]

[tex] =tan \: (2\pi - \frac{\pi}{4} )[/tex]

[tex] = - tan \: \frac{\pi}{4} [/tex]

[tex] = - 1[/tex]

Hope this helps...

Good luck on your assignment...

Answer:

It will take 9 years

Step-by-step explanation:

use formula A=P(1+ r/n)^nt

37,500= 25,475(1+.046/1)^1*x

37,500/25,475=1.046^x

1.47203= 1.046^x

try out different numbers for x and use whole number since it asks for the nearest year

1.046^8 = 1.43302 and 1.046^9 = 1.4989

so we know its inbetween

8 and 9 to figure out one is the closest whole number try raising it to the power of 8.5 and if it passes 1.47203 then its 9, if it doesnt then its 8

1.046^8.5 = 1.46561

1.46561< 1.47203

since 1.046561 is lower than 1.47203 its safe to assume that the year is between 8.5-8.99 thus we can round up to 9

Answer:

120,960 ways

Step-by-step explanation:

Assuming that each piece is unique, then the order of each piece matters.

There are 9 pieces in total, there are 3 options for the first piece (3 piano pieces), and the remaining 8 pieces can be permuted. The number of possible arrangements is:

[tex]n=3*\frac{8!}{(8-8)!}\\ n=3*8*7*6*5*4*3*2*1\\n=120,960\ ways[/tex]

The program can be arranged in 120,960 ways.

Answer:

The equation for a parabola with vertex at the origin and a directrix at x = 1/48 is [tex]x= \frac{1}{12}\cdot y^{2}[/tex].

Step-by-step explanation:

As directrix is a vertical line, the parabola must "horizontal" and increasing in the -x direction. Then, the standard equation for such geometric construction centered at (h, k) is:

[tex]x - h = 4\cdot p \cdot (y-k)^{2}[/tex]

Where:

[tex]h[/tex], [tex]k[/tex] - Horizontal and vertical components of the location of vertex with respect to origin, dimensionless.

[tex]p[/tex] - Least distance of directrix with respect to vertex, dimensionless.

Since vertex is located at the origin and horizontal coordinate of the directrix, least distance of directrix is positive. That is:

[tex]p = x_{D} - x_{V}[/tex]

[tex]p = \frac{1}{48}-0[/tex]

[tex]p = \frac{1}{48}[/tex]

Now, the equation for a parabola with vertex at the origin and a directrix at x = 1/48 is [tex]x= \frac{1}{12}\cdot y^{2}[/tex].

Answer:

A translation; (x,y) --> (x-4,y-5)

Step-by-step explanation:

This is because the figures are congruent and in the same orientation but just in different locations on the coordinate plane.

A(0,3) --> A'(-4,-2)

So, the rule is (x,y) --> (x-4,y-5)

Answer:

Step-by-step explanation:

We know that'

GCF × LCM = Product of given number

1. Two numbers have a GCF of 2

= 2 × LCM = Product of given number

LCM = Product of given number / 2

LCM is half of given product.

2. Two numbers have an LCM of 2

= GCF × 2 = Product of given number

GCF = Product of given number / 2

GCF is half of given product.

3. Two numbers have a GCF of 3

= 3 × LCM = Product of given number

LCM = Product of given number / 3

LCM is one-third of given product.

4. Two numbers have an LCM of 10

= GCF × 10 = Product of given number

GCF = Product of given number / 10

GCF is one-tenth of given product.

Answer:

The description is provided following.

Step-by-step explanation:

The given question is incomplete. The complete question will be:

                                     Brain tumors                      No Brain tumors

Cell Phones                          63                                          185

No Cell Phones                    96                                          292                  

The further explanation is given below.

a...

Subjects with these symptoms/diseases are recognized as "cases." Consequently, the majority of the instances would be as follows:

⇒  [tex]63+96[/tex]

⇒  [tex]159[/tex]  

b...

Subjects who might not have the disorder or infection are classified as "controls." Therefore, the amount of controls is as follows:

⇒  [tex]185+292[/tex]

⇒  [tex]477[/tex]

c...

The proportion of control and monitoring of instances:

⇒  [tex]\frac{478}{159}[/tex]

⇒  [tex]3.006[/tex]

Answer: C

Step-by-step explanation:

We can automatically eliminate D because since both matrices are 2x2, the product exists.

[tex]\left[\begin{array}{ccc}1&5\\-3&4\end{array}\right] \left[\begin{array}{ccc}2&6\\6&-1\end{array}\right] =\left[\begin{array}{ccc}1*2+5*6&1*6+5*(-1)\\(-3)*2+4*6&(-3)*6+4*(-1)\end{array}\right]=\left[\begin{array}{ccc}32&1\\18&-22\end{array}\right][/tex]