help!!!
.............​

Answer:

The answer is 60

Step-by-step explanation:

all you have to do is reverse the operation, you have to do 9 x 5 then add 15 to that result and you will get the answer :)

hope this helps!

Answer:

1 +1 = 2

Step-by-step explanation:

The statement that is true about the cost of haircuts is "On Average, the cost of a man's haircut is $16 less than the cost of a women's haircut".

A mean is an arithmetic average of a set of observations. it is given by the formula,

Mean = (Sum of observations)/Number of observations

Given that the mean cost of a haircut for a man is $28 and the mean cost of a haircut for a woman is $44. Therefore, the statement that is true about the cost of haircuts is "On Average, the cost of a man's haircut is $16 less than the cost of a women's haircut".

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Answer:

The number of weeks required = 216 weeks

Step-by-step explanation:

Given that:

Margin of Error E = 200

Confidence interval = 95% = 0.95

Level of SIgnificance  = 1 - C.I

= 1 - 0.95

= 0.05

Standard deviation = 1500

The Critical value for Z :

\(Z_{\alpha/2} =Z_{0.05/2} \\ \\ = Z_{0.025} = 1.96\)

The number of weeks( i.e the sample size (n) ) required is :

\(n = (\dfrac{Z_{\alpha/2} \times \sigma}{E})^2\)

\(n = (\dfrac{1.96 \times 1500}{200})^2\)

\(n = (14.7)^2\)

n = 216.09

n ≅ 216 weeks

Answer:

Step-by-step explanation:

Let's simplify this further to get our answer.

Looking at the options, we can say that Option C and B are correct.

\(\\ \sf\longmapsto \dfrac{-5}{6}(12-6x+18y)\)

\(\\ \sf\longmapsto \dfrac{-5}{6}(12)-\dfrac{(-5)}{6}(6x)+\dfrac{-5}{6}(18y)\)

\(\\ \sf\longmapsto -5(2)-(-5x)+(-5)(3y)\)

\(\\ \sf\longmapsto -10+5x-15y\)

An order-preserving function is one where x < y implies f(x) < f(y). An isomorphism is a one-to-one order-preserving function between two partially ordered sets, while an automorphism is an isomorphism of a set to itself.

In the given excerpt, it explains the concepts of order-preserving functions, isomorphisms, and automorphisms in the context of partially ordered sets.

Order-Preserving Function:

A function f: P -> Q, where P and Q are partially ordered sets, is said to be order-preserving if for any elements x and y in P, if x < y, then f(x) < f(y). In other words, the function preserves the order relation between elements in P when mapped to elements in Q.

Increasing Function:

If P and Q are linearly ordered sets, then an order-preserving function is also referred to as an increasing function. It means that for any elements x and y in P, if x < y, then f(x) < f(y).

Isomorphism:

A one-to-one function f: P -> Q is called an isomorphism of P and Q if it satisfies two conditions:

a. f is order-preserving: For any elements x and y in P, if x < y, then f(x) < f(y).

b. f is onto (surjective): Every element in Q has a pre-image in P.

When an isomorphism exists between (P, <) and (Q, <), it means that the two partially ordered sets have a structure that is preserved under the isomorphism. In other words, they have the same ordering relationships.

Automorphism:

An automorphism of a partially ordered set (P, <) is an isomorphism from P to itself. It means that the function f: P -> P is both order-preserving and bijective (one-to-one and onto). Essentially, an automorphism preserves the structure and order relationships within the same partially ordered set.

These concepts are fundamental in understanding the relationships and mappings between partially ordered sets, particularly in terms of preserving order, finding correspondences, and exploring the symmetry within a set.

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Step-by-step explanation:

Hassan is incorrect because √0.15  is less than 0.4, and the value of  √0.15 is 0.3872 option third is correct.

Iteration is the process of repeating a procedure in order to produce a series of results.

We have:

= √0.15

\(= \rm \sqrt{{\dfrac{15}{100}}}\)

\(= \rm \sqrt{{\dfrac{3}{20}}}\)

= (1.732)/(4.472)

= 0.3872

√0.15 is less than 0.4.

Thus, Hassan is incorrect because √0.15  is less than 0.4, and the value of  √0.15 is 0.3872 option third is correct.

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Answer:

C

Step-by-step explanation:

14 because 14+28=42.

a) The probability that the computer will be fixed by either A or B is 58%.

b) The probability that it was fixed by B is 57.14%

Given data:

a)

To find the probability that the computer will be fixed by either A or B, we can use the principle of addition for probabilities.

The probability that A can fix the computer is 30% or 0.30, and the probability that B can fix the computer if A cannot is 40% or 0.40.

Therefore, the probability that either A or B can fix the computer is the sum of these probabilities:

P(A or B) = P(A) + P(B if A cannot) = 0.30 + (0.70 * 0.40) = 0.30 + 0.28 = 0.58

Therefore, there is a 58% probability that the computer will be fixed by either A or B.

b)

Let's denote event A as A fixing the computer and event B as B fixing the computer.

P(A) = 0.30 (probability A can fix the computer)

P(B|A') = 0.40 (probability B can fix the computer given that A cannot)

To find P(B|A), the probability that B fixes the computer given that it was fixed, use Bayes' theorem:

P(B|A) = (P(A|B) * P(B)) / P(A)

Since the computer is fixed, P(A) + P(A') = 1, so P(A) = 1 - P(A') = 1 - 0.30 = 0.70

P(B|A) = (P(A|B) * P(B)) / P(A)

P(B|A) = (1 * 0.40) / 0.70

P(B|A) = 0.40 / 0.70

P(B|A) ≈ 0.5714

Hence, if the computer is fixed, there is a 57.14% probability that it was fixed by B.

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In right-angled triangle (ΔABC), the value of cos(B) is equal to 12/13.

A right angle can be defined as a type of angle that is formed by the intersection of two (2) straight lines at 90 degrees. This ultimately implies that, a right angle has a measure of 90 degrees.

In order to determine the magnitude of cos θ, we would apply the law of cosine because the given side lengths represent the adjacent side and hypotenuse of a right-angled triangle.

cos(θ) = Adj/Hyp

Where:

Substituting the parameters into the formula, we have;

cos(B) = 12/13

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The evaluation of the given Boolean expressions are:

a) A && !B =  false              b) B∥C = true

c) B==C = false                   d) A&&!C = true

e) (B∥C)&&(!A) =  false        f) (A!=B)∥(B!=C)  = true

Information available in the problem:

A = true

B = true

C = true

a) Since A and B are both true, !B (which means "not B") is false. Therefore, A && !B evaluates to false, because the logical AND operator returns true only if both of its operands are true.

Hence,

A && !B = true && false = false

b) Since B is true, the result of B∥C will be true, regardless of the value of C. This is because the logical OR operator returns true if at least one of its operands is true.

Hence,

B∥C = true ∥ false = true

c) Since B is true and C is false, B and C have different values, and therefore B==C will evaluate to false. This is because the equality operator returns true only if its operands have the same value.

Hence,

B==C = true == false = false

d) Since A is true and !C (which means "not C") is true, A&&!C evaluates to true. This is because the logical AND operator returns true only if both of its operands are true.

Hence,

A&&!C = true && !false = true && true = true

e) Since B is true, the result of B∥C will be true, regardless of the value of C. This is because the logical OR operator returns true if at least one of its operands is true. Therefore, B∥C evaluates to true.

Since A is true and !A (which means "not A") is false, !A evaluates to false.

Therefore, (B∥C)&&(!A) evaluates to false, because the logical AND operator returns true only if both of its operands are true.

Hence,

(B∥C)&&(!A) = true && false = false

f) Since A is true and B is true, A!=B (which means "A is not equal to B") is false, because A and B have the same value.

Since B is true and C is false, B!=C (which means "B is not equal to C") is true, because B and C have different values.

Therefore, (A!=B)∥(B!=C) evaluates to true, because the logical OR operator returns true if at least one of its operands is true.

Hence,

(A!=B)∥(B!=C) = false ∥ true = true

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Answer:

  4 minutes

Step-by-step explanation:

You want to know how long it takes to drain a cylindrical tank 1.8 ft in diameter and 3 ft long at the rate of 1.7 ft³/minute. (π = 3.14)

The volume of a cylinder can be found using the formula ...

  V = (π/4)d²h . . . . . . . diameter d, height h

Then the volume of the oil tank is ...

  V = 3.14/4(1.8 ft)²(3 fft) = 7.6302 ft³

The time it takes to empty the tank is found by dividing the volume by the rate:

  (7.6302 ft³)/(1.7 ft³/min) ≈ 4.49 min ≈ 4 min

It will take about 4 minutes to empty the tank.

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The values of the expression are;

1. bd/a + c = 6

2.  ac/b - (a + d) = 14

3. d³/a² - (c + b) = 63/4

4. pr/n + m = - 48

5.  p²/m - (np + r) = 10

6. p³/r² - (m + np) = 16

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The values are,

a = - 2, b = 3, c = - 12 and d = - 4

m = - 32, n = 2, p = - 8 and r = 4

Now,

Find the values of the expressions as;

1. bd/a + c

Substitute all the values, we get;

bd/a + c = (3 x - 4)/(-2) + (-12)

             = - 12/- 2 - 12

             = 6 - 12

             = - 6

2. ac/b - (a + d)

Substitute all the values, we get;

⇒ ac/b - (a + d) = - 2 x - 12 /3 - (- 2 - 4)

                    = 8 + 6

                    = 14

3. d³/a² - (c + b)

Substitute all the values, we get;

d³/a² - (c + b) = 3³/(-2)² - (-12 + 3)

                    = 27/4 + 9

                    = 63/4

4. pr/n + m = - 8 x 4 /2 + (-32)

                 = - 16 - 32

                 = - 48

5. p²/m - (np + r) = (-8)²/- 32 - (2 x - 8 + 4)

                         = - 64/32 - (- 16 + 4)

                          = - 2 + 12

                          = 10

6. p³/r² - (m + np) = (-8)³/4² - (- 32 + 2 x - 8)

                           = - 32 - (- 32 - 16)

                           = - 32 + 48

                           = 16

Thus, The values of the expression are;

1. bd/a + c = 6

2.  ac/b - (a + d) = 14

3. d³/a² - (c + b) = 63/4

4. pr/n + m = - 48

5.  p²/m - (np + r) = 10

6. p³/r² - (m + np) = 16

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The probability distribution of Y = X mod (4) is: 3/10, 3/10, 2/10, 2/10 and the probability distribution of Y = 6 mod (X + 1) is: 1/10, 1/10, 2/10, 1/10, 2/10, 2/10 , 1/10.

The probability distribution of Y = X mod (4) can be found as follows:

Y = 0, when X = 0, 4, 8

Y = 1, when X = 1, 5, 9

Y = 2, when X = 2, 6

Y = 3, when X = 3, 7

So, the probability distribution of Y = X mod (4) is:

Y = 0, P(Y = 0) = 3/10

Y = 1, P(Y = 1) = 3/10

Y = 2, P(Y = 2) = 2/10

Y = 3, P(Y = 3) = 2/10

The probability distribution of Y = 6 mod (X + 1) can be found as follows:

Y = 0, when X = 5

Y = 1, when X = 0

Y = 2, when X = 1, 6

Y = 3, when X = 2

Y = 4, when X = 3, 7

Y = 5, when X = 4, 8

Y = 6, when X = 9

So, the probability distribution of Y = 6 mod (X + 1) is:

Y = 0, P(Y = 0) = 1/10

Y = 1, P(Y = 1) = 1/10

Y = 2, P(Y = 2) = 2/10

Y = 3, P(Y = 3) = 1/10

Y = 4, P(Y = 4) = 2/10

Y = 5, P(Y = 5) = 2/10

Y = 6, P(Y = 6) = 1/10

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Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

Highest speed measured = 71.3 Mbps

Mean speed (x) = 18.29 Mbps

Standard deviation (s) = 20.59

a.) What is the difference between​ carrier's highest data speed and the mean of all 50 data​ speeds?

(71.3 - 18.29) Mbps = 53.01 Mbps

b. How many standard deviations is that​ [the difference found in part​ (a)]?

53.01 / 20.59 = 2.57

c. Convert the​ carrier's highest data speed to a z score.

Zscore = (score - mean) / standard deviation

Zscore = (71.3 - 18.29) / 20.59

Zscore = 2.57

d. If we consider data speeds that convert to z scores between -2 and 2 to be neither significantly low nor significantly​ high, is the​ carrier's highest data speed​ significant?

Yes, this highest speed is significant as it's Zscore is higher than 2 (2.57).

The length of side X in simple radical form with a rational denominator is 10/√3.

In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.

This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):

Adjacent side = 5/√3

Hypotenuse, x = 2 × 5/√3

Hypotenuse, x = 10/√3.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

(1) x² - 2 x - 8 and Option (2) x² + 2 x - 8 are two polynomials which has been factored.

Given are the polynomials,

1) x² - 2 x - 8

Factors = (x+2)(x-4)

2) x² + 2 x - 8

Factors = (x-2)(x+4)

3) x²-2x-4 = There will be no integral root.

4) x²+2x-4 = There will be no integral root.

Hence the (1) x² - 2 x - 8 and Option (2) x² + 2 x - 8 are two polynomials which has been factored.

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Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

The median will be greater than the mean in a left-skewed distribution

We have,

In statistics, skewness is a measure of the asymmetry of a probability distribution around its mean.

A distribution is said to be skewed left if it has a long tail on the left side and the bulk of the data is on the right side.

When the data is skewed left, it means that the distribution is being pulled towards the left side.

This is because there are a few extreme values on the left side that are pulling the mean in that direction.

In contrast, the median is the middle value of the dataset, and it is not influenced by outliers.

For a left-skewed distribution,

The median will be greater than the mean because the mean is being pulled towards the left by the few extreme values.

In a data distribution that is skewed left, the mean will be less than the median.

This is because the mean is sensitive to outliers and is pulled towards the direction of the skewness, while the median is not affected by extreme values and is a more robust measure of central tendency.

Therefore,

The median will be greater than the mean in a left-skewed distribution

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Answer: On a coordinate plane, 2 lines are parallel to each other.

Step-by-step explanation:

The solution of the system of equations of two lines is the intersecting point where both lines intersect.

When two lines intersect at one point then, we say it has a unique solution.

When two lines coincide, then we say it has an infinite number of solutions.

But when two lines are parallel to each other then, we say it has no solution.

Hence, the graph represents a system of equations with no solution:

On a coordinate plane, 2 lines are parallel to each other.

On a coordinate plane, \(2\) lines are parallel to each other.

A graph is a diagram that depicts the relationship between two or more variables measured along one of a pair of axes at right angles.

A coordinate plane is a two-dimensional plane formed by the intersection of a vertical line called \(y-\)axis and a horizontal line called \(x-\)axis.

A system of equations has no solution if the lines are parallel.

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Answer:

A

Step-by-step explanation:

Each domain value (x-value) of a function has exactly one range value (y-value).

A function can have two or more domain (x-value) having the same range (y-value)

Graph A shows the different domain value (x-values) having exactly one range value (y-value). No x-value has two different y-values.

Therefore, graph A is a function.

Step-by-step explanation:

you drew already the right things, you have everything.

so, what is the problem ?

the most common form of line equation is

y = ax + b

a is the slope of the line. it is expressed as the ratio

y coordinate change / x coordinate change

when going from one point to the other.

b is the y-intercept (the y value when x = 0).

once we have the slope, we get b by using the coordinates of one of the given points as x and y in the equation and solve for b.

so, for the 2 marked points you showed correctly the differences :

x changes by +8 (from -4 to 4).

y changes by -2 (from 3 to 1).

so the slope is -2/+8 = -1/4

the y-intercept we also see directly in the chart : +2.

Answer: 450

Step-by-step explanation: 95+115+240=450

Answer:

$ 600

Step-by-step explanation:

From the question given above, the following data were obtained:

Principal (P) = $ 3000

Time (T) = 5 years

Rate (R) = 4%

Interest (I) =?

The total interest he will receive can be obtained as follow:

I = PTR/100

I = 3000 × 5 × 4 / 100

I = 60000 / 100

I = $ 600

Thus, the total interest he will receive is $ 600

The amount of $600 received by Prince Charming on the investment of $3000 for 5 years.

Prince Charming invests $3000, thus the principal amount is $3000.

He invest the same amount for 5 years, thus time we have to paid on this principal is 5 years.

The rate for which the principal amount increase is 4 %.

The formulated way to represent the simple interest (I) after passing t years of time, at a rate of r % and having a principal amount of P is mentioned below.

\(I=\dfrac{P \times r \times t}{100}\)

Substitute the given values in the above formula to calculate simple interest.

\(\begin{aligned}I&=\dfrac{3000 \times 4 \times 5}{100}\\&=600 \end{aligned}\)

Thus, the amount of $600 received by Prince Charming on the investment of $3000 for 5 years.

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Answer:

21.4%

Step-by-step explanation:

You would pay back a 21.4%

The simple interest rate on the loan of $1400 is approximately 21.4% per year.

The simple interest can be expressed as:

A = P( 1 + rt )

Where A is accrued amount, P is the principal, r is the interest rate and t is time.

Given the parameter:

Principal P = $1400

Accrued amount A = $2000

Time t = 2 years

Interest rate r =?

Plug these values into the above formula and solve for the interest rate.

A = P( 1 + rt )

\(r = \frac{1}{t} * ( \frac{A}{P} - 1 ) \\\\r = \frac{1}{2} * ( \frac{2000}{1400} - 1 ) \\\\r = \frac{1}{2} * ( \frac{2000}{1400} - 1 ) \\\\r = 0.21428\)

Convert r decimal to R a percentage

R = 0.214 × 100

R = 21.4% per year

Therefore, the rate is approximately 21.4% per year.

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Explanation:

Let's say the teacher pulls the two boys out of the line, and stands in their place. So we have 5 girls and 1 teacher making 6 people total.

There are 6! = 6*5*4*3*2*1 = 720 different permutations here. Order matters. This involves the teacher, so let's have him/her step out of the line and have the two boys replace the teacher's position. This guarantees the boys stick together. For any permutation, we have 2 different ways to arrange the boys. So we have 2*720 = 1440 different ways to arrange the students so that the two boys are next to each other.

This is out of 7! = 7*6*5*4*3*2*1 = 5040 different permutations overall (we're arranging 5 girls+2 boys = 7 people).

The probability we're after is going to be 1440/5040 = 2/7

--------

Or you could see it like this

1440 = 2*6!

5040 = 7! = 7*6!

So,

1440/5040 = (2*6!)/(7*6!)

1440/5040 = 2/7

Answer:

?

Step-by-step explanation: