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Triangle A"B"C" is formed using the translation (x +0, y+ 2) and the dilation by a scale factor of 2 from the origin. Which equation explains the relationship between line
AC and line A"C"?

A. Line AC
——————- = 2
A"C"

B. Line A" C" 1
————— = —
AC 2

C. Line A"C"
Line AC = —————-
2



D. Line AC
Line A"C" = —————
2

a. You would expect 3.5 of those in the sample to name chocolate.

b. The probability exactly four of those in the sample name chocolate is 0.2438.

c. The probability four or more name chocolate is 0.5829..

a. If 35% of people in the general population indicate that chocolate is their favorite flavor of ice cream, then we would expect 35% × 10 = 3.5 people in a sample of 10 to name chocolate as their favorite flavor. Since we cannot have a fractional number of people, we can round this down to 3 people.

b. The probability that exactly 4 people in a sample of 10 name chocolate as their favorite flavor can be calculated using the binomial distribution. The probability of each individual event (i.e., a person naming chocolate as their favorite flavor) is 0.35, and there are 10 total events. The probability of exactly 4 successes (people naming chocolate as their favorite flavor) is given by the formula:

(10 choose 4) × (\(0.35^4\)) × (\(0.65^6\))

Where "choose" denotes the binomial coefficient, and the exponent indicates the number of times each event occurs. Plugging in the values, we get:

(210) × (0.0036125) × (0.274625) = 0.2438

So the probability that exactly 4 people in the sample name chocolate as their favorite flavor is approximately 0.2438.

c. To calculate the probability that 4 or more people in the sample name chocolate as their favorite flavor, we can use the same formula as above, but sum the probabilities for each possible number of successes greater than or equal to 4. For example, the probability of 4 successes is given by:

(10 choose 4) × (\(0.35^4\)) × (\(0.65^6\))

The probability of 5 successes is given by:

(10 choose 5) × (\(0.35^5\)) × (\(0.65^5\))

And so on. Summing the probabilities for each possible number of successes greater than or equal to 4, we get:

0.2438 + 0.1933 + 0.1047 + 0.0380 + 0.0081 = 0.5829

So the probability that 4 or more people in the sample name chocolate as their favorite flavor is approximately 0.5829.

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The statements that are true are B and D.

Given are some statements we need to check which is true.

Let's analyze each statement:

A. 4 is a perfect cube.

False. 4 is not a perfect cube because there is no integer that can be cubed to give 4.

B. 16 is a perfect square.

True. 16 is a perfect square because it can be expressed as 4^2, where 4 is an integer.

C. 2,197 is both a perfect square and a perfect cube.

False. 2,197 is not a perfect square because there is no integer that can be squared to give 2,197.

However, it is a perfect cube because 13³ equals 2,197.

D. 8 is a perfect cube.

True. 8 is a perfect cube because it can be expressed as 2³, where 2 is an integer.

E. 18 is neither a perfect square nor a perfect cube.

True. 18 is neither a perfect square nor a perfect cube because there is no integer that can be squared or cubed to give 18.

Therefore, the statements that are true are B and D.

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The total amount that the person with base salary 42000; total sales 175000; commission 4% gets is $51000.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. In this case, the percentage of commission is given as 4%.

The commission will be:

= Percentage × Amount

= 4% × 175000

= 7000

Therefore, the total amount that the person gets will be:

= Salary + Commission

= 42000 + 7000

= $51000

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Answer:

f(g(x)) = -1

Step-by-step explanation:

\(f(x) = \frac{1}{x} \\ \\ g(x) = x - 2 \\ \\ \implies \: f(g(x)) = \frac{1}{x - 2} \\ \\ \implies \: f(g(1)) = \frac{1}{1 - 2} \\ \\ \implies \: f(g(1)) = \frac{1}{ - 1} \\ \\ \implies \: f(g(1)) = - 1\)

Rounding to the nearest hundredth, the area is approximately 151.976 cm².

The formula for the area of a sector is:

A = (θ/360) x πr²

where θ is the central angle in degrees, r is the radius, and π is pi (3.14).

Plugging in the given values, we get:

A = (144/360) x 3.14 x 11^2

A = 0.4 x 3.14 x 121

A = 151.976

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Answer:

432000/135×100

Step-by-step explanation:

current house value is an increase of 35% oner the original value,

so if current value is 100% plus 35% or 135% of original value,

then original value is $432,000 / 135 x 100

Answer:

2,5

Step-by-step explanation:

The cost per ounce of the premium walnut is $0. 23

To determine the value of the cost, we need to note that proportion is simply described as the comparison of numbers such  that they are made equal to another.

From the information given, we have that;

54 ounces of premium walnuts costs $12.95

This is represented as;

54 ounces = $12. 95

Then 1 = x

cross multiply the values, we get;

x = $12.95/54

Divide the values, we get;

x = $0. 23

Hence, the value is $0. 23 per premium walnut

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3√2 and 3 are the values of x and y respectively from the figure.

The given diagram is a right triangle with an acute angle of 45 degrees

We need to determine the values of variables x and y.

Applying the trigonometry identity, we will have:

sin 45 = opposite/hypotenuse
sin45 = 3/x

x = 3/sin45

x = 3/(1/√2)
x = 3√2

Similarly:

tan 45 = opposite/adjacent
tan 45 = 3/y

1 = 3/y

y = 3

Hence the values of x and y from the figure is 3√2 and 3 respectively

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Answer: 12

Step-by-step explanation: Plug in and use pythagorean theorem

The number of codes that can be made using the 5 letters given is 120 as calculated using permutation and combination.

Now when no letters are repeated:

5 letter codes to be made.

Possible options for each space = 5

so first digit has 5 options, second digit has 4 options , third digit has 3 options , fourth digit has 2 options and the final digit will have only 1 option left.

So total number of codes = 5 × 4 × 3 × 2 × 1 = 120 codes

if letters can be repeated

5 letter codes to be made.

Possible options for each space = 5

so first digit has 5 options, second digit has 5 options , third digit has 5options , fourth digit has 5 options and the final digit will have only 5 options also.

So total number of codes = 5 × 5 × 5× 5× 5= 3125 codes

if adjacent letters cannot be repeated

5 letter codes to be made.

Possible options for each space = 5

so first digit has 5 options, second digit has 4 options , third digit has 4 options , fourth digit has 4 options and the final digit will have only 4 options also.

So total number of codes = 5 × 4 × 4× 4× 4 = 1280 codes

Hence the total number of codes as calculated by permutation and combination is 1280.

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The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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Answer:

C) angle 7

Step-by-step explanation:

angle 7

To solve this problem one must be aware of the concepts of standard deviation and variance of raw data.

There is a direct formulae to calculate the variance of the data,

Variance = \(σ^{2} =\frac{Sigma(xi-m)^{2}}{n}\)

Now here we need to verify ∑x and ∑\(x^{2}\).

∑x = 21+19+15+32+27

     = 114

and ∑\(x^{2}\) = \(21^{2} +19^{2} +15^{2} +32^{2} +27^{2}\)

             = 441+361+225+1024+729

             = 2780

So, the given relation is true.

Now the variance of the given data by putting the values in the formulae is  equal to 45.2.

And Standard deviation=\(\sqrt{Variance}\)

                                     = \(\sqrt{45.2}\)

                                      = 6.72

And for population α²=36.16 and deviation=6.01.

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Answer:

5m-n

Step-by-step explanation:

Answer:

Yes.

Explanation:

3/4 is 75% of a whole, 3/5 is 60%.

The missing number in the sequence is 39 .

A sequence is a collection of objects where repeats are allowed and the order is important in mathematics.

From the given figure we can see that the vertically opposite numbers are three times one another.

For example:

11 × 3 = 33

12 × 3 = 36

8 × 3 = 24

hence the last unknown number of the sequence will be

13 × 3 = 39

Hence the unknown number of the sequence is 39.

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Answer:

the son is 2

man is 26

+10 yrs

son=12

man=36

Step-by-step explanation:

Let the son's age be x.

Then the father's age is 13x.

In ten years their ages will be (x+10) and (13x+10).

(13x+10)=3(x+10)

13x+10=3x+30

10x=20

x=2

The son is 2 years old.

Answer:

c)  C

 \(y = A e^{\frac{(x-b)^{2} }{c} }\)  

Step-by-step explanation:

Explanation:-

Normal distribution

A random variable 'x' is said to have a normal distribution. if its identity function or probability is given by

f( x,μ,σ) = \(\frac{1}{\alpha \sqrt{2\pi } } e^{\frac{(x-b)^{2} }{c} }\)   ...(i)

Here 'b' be the mean of the normal distribution

And σ be the standard deviation

and C = 2σ²

Now, the equation (i) changes to

          \(y = A e^{\frac{(x-b)^{2} }{c} }\)      this represents the normal graph

where A = \(\frac{1}{\alpha \sqrt{2\pi } }\)   and  C = 2σ²

When asking the value of '9' ⇒ in another number

  ⇒ means that it asking for the name of the position of that number in

      the other number

Let's examine the name of the positions in the number:

  ⇒ look at the image attached

Based on the image:

 ⇒ 9 is the hundreds position of 2,448,901

Answer: hundreds

Hope that helps!

Answer:

Hundreds

Step-by-step explanation:

1=units

0=tens

9=hundreds

it doesn't make sense kay

Answer:

0.5² + (3/5)²=0.5²+0.6²=0.25+0.36=0.71

Answer:

0.61

Step-by-step explanation:

0.5 squared is equal to 0.25

3/5 squared is equal to 9/25

9/25=0.36

0.36+0.25=0.61

welcome

Answer:

Step-by-step explanation:

a relation that is not a function

Answer:

the value of x is 3

Step-by-step explanation:

Hope this helps!!!! :)

Answer:

one is a

two is c

three is b

Step-by-step explanation:

Answer:

Yes he is correct because -12 and 12 are the opposite.

Step-by-step explanation:

Answer:

He is correct because the numbers are in opposite directions on the number line, and their distances from 0 on the vertical number line are equal

cos(x) (tan(x) + cot(x))

Recall that tan(x) = sin(x)/cos(x) and cot(x) = 1/tan(x) = cos(x)/sin(x). Then

cos(x) (sin(x)/cos(x) + cos(x)/sin(x)) = sin(x) + cos²(x)/sin(x)

Write both terms with a common denominator and combine the fractions:

sin²(x)/sin(x) + cos²(x)/sin(x) = (sin²(x) + cos²(x))/sin(x)

Recall the Pythagorean identity,

sin²(x) + cos²(x) = 1

so our expression reduces to

1/sin(x)

Finally, recall that csc(x) = 1/sin(x) and we're done. So

cos(x) (tan(x) + cot(x)) = csc(x)

Answer:

A) At α = 0.05, reject the null hypothesis.

Step-by-step explanation:

Given a p-test value of 0.0436 ;

P-value = 0.0436

Recall :

Decision region :

Reject Null if p value < α

Testing the options :

A) At α = 0.05,

0.0436 < 0.05 (true)

Since p value < α ; Reject the null hypothesis.

B) At α = 0.10,

0.0436 < 0.1

True conclusion is to reject the Null Hypothesis

Hence, option B is incorrect.

C) At α = 0.025, reject the null hypothesis.

0.0436 > 0.025

True conclusion is ; Fail to reject the Null ;

Hence, option C is incorrect

D) At α = 0.05, accept the null hypothesis.

0.0436 < 0.05

True conclusion is ; reject the Null

Hence, option D is incorrect