i need help on this question

Answer:

[tex]\frac{69+2\sqrt{2}}{97}[/tex]

Step-by-step explanation:

(10 + √2)÷(14+ √2)= [tex]\frac{10+\sqrt{2} }{14+\sqrt{2} }[/tex]

                             = [tex]\frac{(10+\sqrt{2}) x (14-\sqrt{2})}{(14+\sqrt{2}) x (14-\sqrt{2}) }[/tex]

                             = [tex]\frac{(10+\sqrt{2}) x (14-\sqrt{2})}{14^{2}-(\sqrt{2}^{2})}[/tex]

                             = [tex]\frac{{(10+\sqrt{2}) x (14-\sqrt{2})}}{196-2}[/tex]

                             = [tex]\frac{140-10\sqrt{2}+14\sqrt{2}-2}{194}[/tex]

                             = [tex]\frac{138+4\sqrt{2}}{194}[/tex]

                             = [tex]\frac{2 x (69+2\sqrt{2})}{194}[/tex]

                             = [tex]\frac{69+2\sqrt{2}}{97}[/tex]

∴ the answer is [tex]\frac{69+2\sqrt{2}}{97}[/tex] in the form [tex]\frac{a+b\sqrt{2}}{c}[/tex]

(10 + √2)÷(14+ √2) can be written in the form (69 + 3√2) ÷ 97, where a = 69, b = 3, and c = 97, and all are integers.

A number that includes zero, positive numbers, and negative numbers, is an integer. Integer's can never be a fraction, a decimal, or a percent, it should be noted.

To write (10 + √2)÷(14+ √2) in the form a+b√2/c, we need to rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator, which is 14 - √2.

[(10 + √2) ÷ (14 + √2)] x [(14 - √2) ÷ (14 - √2)]

= [(10 + √2) x (14 - √2)] ÷ [(14 + √2) x (14 - √2)]

= [140 + 8√2 - 2√2 - 2] ÷ [196 - 2]

= (138 + 6√2) ÷ 194

= (69 + 3√2) ÷ 97

Therefore, (10 + √2)÷(14+ √2) can be written in the form (69 + 3√2) ÷ 97, where a = 69, b = 3, and c = 97, and all are integers.

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The number of students are 110 students offer Biology but not Mathematics.

Let's use a Venn diagram to solve this problem. We know that 125 students offer Biology and 110 offer Mathematics, and we want to find out how many offer Biology but not Mathematics.

First, we can fill in the number of students who offer both Biology and Mathematics, which is the overlap between the two circles. We can do this by subtracting the total number of students who offer both from the total number of students who offer either:

220 (total) - (125 + 110) = 220 - 235 = -15

Wait a minute! A negative number of students doesn't make sense in this context. What this tells us is that there must be some double-counting going on - in other words, some students are being counted twice, once in each of the Biology and Mathematics categories.

To correct for this, we need to add back in the number of students who are counted twice, which is the overlap between the two circles. We can calculate this by adding the number of students who offer Biology and Mathematics together:

125 + 110 = 235

Now we can redo the calculation:

220 (total) - 235 (double-counted) = -15

This tells us that there are 15 students who are being counted twice. To find the number of students who offer Biology but not Mathematics, we need to subtract this number from the number of students who offer Biology:

125 - 15 = 110

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Answer: if im correct i think its 95

From the given data, the probability that the pedestrian was not intoxicated or the driver was not intoxicated is 99.7%.

To find the probability that the pedestrian was not intoxicated or the driver was not intoxicated, we can add the probabilities of the two mutually exclusive events:

Pedestrian not intoxicated and driver intoxicated

Pedestrian intoxicated and driver not intoxicated

From the table, we can see that there were 603 pedestrian deaths where the driver was not intoxicated and 54 pedestrian deaths where the driver was intoxicated, for a total of 657 deaths where the driver was not intoxicated. Similarly, there were 246 pedestrian deaths where the pedestrian was not intoxicated and 83 pedestrian deaths where the pedestrian was intoxicated, for a total of 329 deaths where the pedestrian was not intoxicated.

Therefore, probability that pedestrian was not intoxicated or driver was not intoxicated is:

P = (657 + 329) / 986

= 0.9969

Converting to percentage and rounding to one decimal place,

P = 99.7%

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The final result of the expression (6e−3f−4)⋅2 is e3f−8.

The calculation is as follows: (6e−3f−4)⋅2 = (6e-3f-4)*2. In order to calculate this expression, it is necessary to use the Order of Operations. The Order of Operations is a set of rules that determine the order in which operations should be performed when evaluating an expression. First, any parentheses need to be evaluated. In this expression, there are parentheses surrounding 6e−3f−4. This means that any operations within the parentheses should be done first. Inside the parentheses, there is an exponent, e−3f, and a subtraction, 4. Exponents should be done first, so e−3f should be evaluated first. This is equivalent to e multiplied by e multiplied by e, multiplied by f, which is equal to e3f. Then, 4 should be subtracted from e3f, which is equal to e3f−4. After the parentheses have been evaluated, the remaining multiplication should be done. This is equivalent to (e3f−4)*2, which is equal to e3f−8.

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The leading coefficients of a polynomial is the factor of the term with the greatest degree. The largest exponent of a polynomial's variable is its degree. The coefficient for the given polynomial is [tex]4[/tex], and the degree is [tex]5[/tex].

An expression that consists of variables, constants, and exponents that is combined using arithmetic computations like addition, subtraction, multiplication, and division is referred to as a polynomial.

By noticing which formulas only contain the operations of adding, subtract, manipulation, and quasi integer exponents, the polynomials may be located.

In the given polynomial [tex]P(x) = 4x^5 + 9x^4 + 6x^3 - x^2 + 2x - 7[/tex], the highest degree of the polynomial is [tex]5[/tex], which means it is a [tex]5^{0}[/tex] polynomial.

The coefficient of the term with the highest degree, which is [tex]4x^5[/tex], is [tex]4[/tex]. Therefore, the leading coefficient is [tex]4[/tex].

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The answer to given linear equation will be When y = 200, x = 8.82.

The values of x and y utilised will determine the solution to the equation y = 11.7x + 96.7.

You can solve for y by substituting a particular value of x into the equation. For instance, if x equals 2, then:

y = 11.7(2) + 96.7

y = 23.4 + 96.7

y = 120.1

Hence, at x = 2, y = 120.1.

Nevertheless, you might choose a different value of y and solve for x by substituting it into the equation. For instance, if y equals 200, then

200 = 11.7x + 96.7

103.3 = 11.7x

x = 8.82

Hence, x equals 8.82 when y is 200.

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Minimum EOL = 72Best alternative based on expected opportunity loss = d3EVPI = 520

Answer:To solve this problem, we will have to first calculate the regret for each option. We will do that by finding the maximum payoff for each column and subtracting the current payoff from that. That gives us the opportunity loss. We will then multiply the opportunity loss with the probabilities of the events to calculate the expected opportunity loss. We will find the minimum expected opportunity loss by selecting the minimum value in each row. We will then add the minimum expected opportunity loss to the minimum payoff for each option to calculate the maximum regret. Finally, we will calculate the EVPI by subtracting the maximum regret from the maximum payoff. Here are the tables that we need to construct: Regret table: Minimum expected opportunity loss table: Minimum EOL = 72Best alternative based on expected opportunity loss = d3EVPI = 520

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Answer:

3, 9

Step-by-step explanation:

Surface A = 2(wl + hl + hw)

Where in the red prism, l is 12, w is 6, h is 9 and in the red prism l is 4, w is 2, h is 3

Lenght 12/4 =3

Width 6/2 =3

Height 9/3 =3

Calculate surface are of red prism

SA = 2( 6x12 + 9x12 + 9x6)

SA = 2( 72 +108+54)

SA = 2(234) = 468 m²

Calculate surface area of blue prism

SA = 2(2x4 + 3x4 + 3x2)

SA = 2(8 +12+6)

SA = 2(26)

SA =52

Area of red /area of blue = 468/52

Ans =9

Answer:

the answer is A

Step-by-step explanation:

p³-125q³

(p-5q)³

but if expand A

it will give the same p³-125q³

(p-5q)(p²+5pq+25q²)

expanding will give

p3+5p²q+25pq²-5p²q-25pq²-125q³

C.L.T

p³+5p²q-5p²q+25pq²-25pq²-125q³

p³-125q³

Total Earnings = (8 x 1.5 x 8) + (10 x 2) + (10 x 1) + (9 x 1) + (8 x 1) = $136. Once we have all the calculations, we can add them together to find Mary’s total earnings amount for the week. In this case, Mary’s total earnings is $136.

To calculate Mary’s total earnings for the week, we need to take into account the time and a half for hours over 40 and the double time for holidays. First, we multiply the 8 hours worked on Monday (a holiday) by 1.5 to calculate the time and a half earnings for that day. Then we multiply the 10 hours worked on Tuesday and Wednesday by 1 to calculate the regular earnings for those days. We multiply the 9 hours worked on Thursday by 1 to calculate regular earnings for that day. Finally, we multiply the 8 hours worked on Friday by 1 to calculate regular earnings for that day. Once we have all the calculations, we can add them together to find Mary’s total earnings for the week. In this case, Mary’s total earnings is $136 amount.

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a) The number of ways to choose three people from a set of eleven is given as follows: 165.

b) The number of ways to choose three women from a set of five women is given as follows: 10.

c) The probability that the group will consist of all women is given as follows: 0.0606 = 6.06%.

The number of different combinations of x objects from a set of n elements is obtained with the formula presented as follows, using factorials.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The number of ways to choose 3 people from a set of 11 is given as follows:

C(11,3) = 11!/(3! x 8!) = 165.

The number of ways to choose 3 women from a set of 5 is given as follows:

C(5,3) = 5!/(2! x 3!) = 10.

Hence the probability that the group will consist of all women is given as follows:

10/165 = 0.0606 = 6.06%.

a group consists of six men and five women.Three people are selected to attend a conference. a) how many ways can three people be selected from this group of eleven?

In how many ways can three women be selected from the five women?

Find the probability that selected group will consist of all women.

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If a curve passes through the point (0,5) and has the property that the slope of the curve at every point P is twice the y-coordinate of P.  The equation of the curve is  y = 5e^(²x).

Let's assume that the equation of the curve is y = f(x), where f(x) is some unknown function.

We are given that the slope of the curve at every point P is twice the y-coordinate of P. This means that:

f'(x) = 2f(x)

where:

f'(x) is the derivative of f(x) with respect to x.

We can solve this differential equation by separating the variables and integrating:

1/f(x) df/dx = 2

Integrating both sides with respect to x, we get:

ln|f(x)| = 2x + C

where C is a constant of integration.

To find the value of C, we can use the fact that the curve passes through the point (0,5). Substituting x=0 and y=5 into the equation, we get:

ln|f(0)| = C

Since ln|f(0)| is just a constant, we can write it as another constant, say A. Therefore:

ln|f(x)| = 2x + A

Taking the exponential of both sides, we get:

|f(x)| = e^(²x+A)

Since f(x) cannot be negative (otherwise, the slope of the curve would be negative at some points), we can drop the absolute value signs:

f(x) = e^(²x+A)

To find the value of A, we can use the fact that the curve passes through the point (0,5). Substituting x=0 and y=5 into the equation, we get:

f(0) = e^A = 5

Therefore, A = ln(5). Substituting this value into the equation, we get:

f(x) = e^(²x+ln(5)) = 5e^(²x)

So the equation of the curve is y = 5e^(²x).

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Answer:

15×2

Step-by-step explanation:

5×+2/(5× +1) =15×2^

Based on the sample of 37 sandwich cookies, it can be concluded that the average weight of a sandwich cookie is close to 11.3 grams, as the manufacturer claimed. This conclusion is supported by the mean, standard deviation, and range of the sample.

Standard deviation is a measure of how spread out a set of numbers is. It gives us an idea of how much variation there is from the average or expected value. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean.

The manufacturer of a sandwich cookie claims that the average weight of a sandwich cookie is 11.3 grams. To test this claim, a statistics class randomly selected 37 sandwich cookies and weighed them. The sample of 37 sandwich cookies had a mean of 11.2 grams, standard deviation of 0.5 grams, and range of 10.1 to 12.5 grams.

The mean of 11.2 grams is very close to the manufacturer’s claim of 11.3 grams. The standard deviation of 0.5 grams indicates that the sample of sandwich cookies had a very small amount of variance. The range of 10.1 to 12.5 grams indicates that the sample had sandwich cookies with weights that were close to the mean, which further supports the conclusion that the mean is close to 11.3 grams.

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The simple interest has an expression and the total amount after an year at an interest rate of 4.5% is approximately $2478.33. The value of R(x) after 6 years is 275 and the new expression for A(x) is 525x^5 + 450x^4 + 375x^3 + 500x^2 + 300x + 275

1. To find the total amount in the account after 5 years with an interest rate of 4.5%, we can simply plug in x = 1.045 (1 + 0.045) into the expression for A(x):

A(1.045) = 525(1.045)^5 + 450(1.045)^4 + 375(1.045)^3 + 500(1.045)^2 + 300(1.045)

≈ 2478.33

So the total amount in the account after 5 years with an interest rate of 4.5% is approximately $2478.33

2. After 6 years, the expression for A(x) would become:

A(x) + 275

We can find the new expression for R(x) by subtracting the original expression for A(x) from the new expression:

R(x) = A(x) + 275 - A(x)

= 275

So the new expression for R(x) after 6 years is simply R(x) = 275.

3. The original expression for A(x) was:

A(x) = 525x^5 + 450x^4 + 375x^3 + 500x^2 + 300x

To find the new expression for A(x) after 6 years, we can simply plug in x = 1.045 (1 + 0.045) and add 275:

A(1.045) + 275 = 525(1.045)^5 + 450(1.045)^4 + 375(1.045)^3 + 500(1.045)^2 + 300(1.045) + 275

≈ 2923.97

So the new expression for A(x) after 6 years is:

A(x) = 525x^5 + 450x^4 + 375x^3 + 500x^2 + 300x + 275

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The expression 10a - 14c is factorized and then found to be equivalent to 2(5a - 7c)

An equation is an expression containing numbers and variables linked together by mathematical operations such as addition, subtraction, division, multiplication and exponents.

Given the equation:

10a - 14c

We are to solve the equation by factorizing the expression. To factorize the expression, we need to find the term that is common to both 10a and -14c. The common term is 2, hence:

10a - 14c

2(5a - 7c)

The expression 10a - 14c is equivalent to 2(5a - 7c)

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Answer:

17.

Step-by-step explanation:

[tex]a^2+b^2 = c^2[/tex] is the formula used to find the hypotenuse (also known as the Pythagora's Theorem).

Substitute the given values into the equation.

[tex]8^2+15^2=c^2[/tex]

64 + 225 = [tex]c^2[/tex]

289 = [tex]c^2[/tex]

[tex]\sqrt{289}[/tex] = c

c = 17

If the length of one side of the rhombus is 6m and the radius of the rhombus as 4 m then the area of the rhombus is 24 m².

What is the area of the rhombus?

The Area of a Rhombus = A = ½ × d1 × d2,

Where d1 and d2 are the diagonals of the rhombus.

The area of a rhombus can be found using the formula:

Area = (diagonal 1 x diagonal 2) / 2

or

Area = (base x height) / 2

We are given the length of one side of the rhombus as 6 m, which means the length of the other side is also 6 m since all sides of a rhombus are congruent. We are also given the radius of the rhombus as 4 m, which is half the length of the diagonal.

Using the Pythagorean theorem, we can find the length of the other diagonal:

diagonal 2 = 2(radius) = 2(4) = 8 m

Now we can use the formula to find the area of the rhombus:

Area = (diagonal 1 x diagonal 2) / 2

Area = (6 m x 8 m) / 2

Area = 24 m²

Therefore, the area of the rhombus is 24 m².

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Answer:

3. The number of hours you work.

Step-by-step explanation:

Independent variable means that the occurrence of the event is not dependent on another event occurring.

In this case, the independent variable is the amount of hours you work, as you can, assumingly for the question, can work any amount you would like. However, the pay would be on the basis of how much work you do, and is dependent on the amount of hours you do (assuming you are on hourly).

~

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Answer: the circumference of Jill's pie is 31.4 inches.

Step-by-step explanation:

The circumference (C) of a circle is given by the formula C = πd, where d is the diameter of the circle and π (pi) is a constant approximately equal to 3.14.

In this case, the diameter of Jill's pie is 10", so we can use the formula to find the circumference:

C = πd

C = 3.14 x 10

C = 31.4 inches

Therefore, the circumference of Jill's pie is 31.4 inches.

Answer:

10pi or 31.42

Step-by-step explanation:

the formula for circumference of a circle is 2pir (yes, i can't find the symbol for pi... sorry...) (and r = the radius)

since the diameter is 2*r, the radius is 5 inches.

2*5*pi = 10pi, which is about 31.42

The box of Cremora is typically rectangular in shape, with six rectangular faces and twelve edges.

Answer:

1.5 gallons per minute

Step-by-step explanation:

To solve this question we have to figure out how much water there was in every time scale calculated. To do this we simply have to divide both values...

We don't need to figure out the 0 as no time has passed for water to fill up!

We can see that for each one the answer is 1.5, so our average rate would be 1.5 gallons per minute!

Hope this helps, have a lovely day! :)

Answer:

g(x) was shifted 9 units to the left and 5 units down

Step-by-step explanation:

Horizontal shifts take place when the x value is changed within the parentheses, or in this case, absolute value.

The graph is shifted 9 units left because of the + 9.

Vertical shifts happen when the entire equation is added or subtracted to.

The graph is shifted 5 units down because of the - 5.

See the graph for a visualization.

31.f(f-1(6)) = 6

34.f-1(f(1)) = 1

36.f-1(f-1(0)) = 0
37.f(g(x)) = f(x + 6) = x + 6 - 6 = x  g(f(x)) = g(x - 6) = x - 6 + 6 = x

39.f(g(x)) = f(3x) = 3(3x) = x  g(f(x)) = g(3x) = 3(3x) = x

40.f(g(x)) = f(3x - 4) = 3(3x - 4) + 4 = x  g(f(x)) = g(3x + 4) = 3(3x + 4) - 4 = x

41. f(g(x)) = f(5/2 - x) = 2 - 5(5/2 - x) = x  g(f(x)) = g(2 - 5x) = 5/2 - (2 - 5x) = x

42. f(g(x)) = f(x2) = (x2)1/2 = x  g(f(x)) = g(x1/2) = (x1/2)2 = x

43.f(g(x)) = f(x + 9) = (x + 9)2 - 9 = x g(f(x)) = g(x2 - 9) = x2 - 9 + 9 = x

44.f(g(x)) = f((x - 1)1/3) = (x - 1)1/33 + 1 = x  g(f(x)) = g(x3 + 1) = (x3 + 1 - 1)1/3 = x

45.f(g(x)) = f(x1/2 + 1) = x1/2 + 1 - 11 = x  g(f(x)) = g(x - 11) = (x - 11)1/2 + 1 = x

To answer your questions, here is the following information:

1. Finding values of an Inverse Using a Table values: f-1(5) = 0.31

f(f-1(6)) = 6

f-1(f(1)) = 1

f-1(f-1(0)) = 0

2. Inverse Function Property: To show that f and g are inverses of each other, you must use the Inverse Function Property which states that if f and g are two inverse functions, then f(g(x)) = x and g(f(x)) = x.

3. Examples:

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6/23 is the value of x that ensures that the equation 23x + 5 = 11 holds true. The solution to this problem cannot be found in the available selections since none of the answer possibilities match this value.

We must find x in order to determine what value of x results in the equation 23x + 5 = 11 being true.

Initially, we must remove 5 from both sides of the equation to isolate the variable x:

23x + 5 - 5 = 11 - 5

When we combine the left and right sides, we obtain:

23x = 6

Then, by multiplying both sides of the equation by 23, we must find x:

23x/23 = 6/23

When we combine the left and right sides, we obtain:

x = 6/23

As a result, 6/23 is the value of x that ensures that the equation 23x + 5 = 11 holds true.

The solution to this problem cannot be found in the available selections since none of the answer possibilities match this value.

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Answer: A

Week Amount Paid

1 $200

2 $250

3 $300

4 $350

5 $400

6 $450

Option B:

Week Amount Paid

1 $200

2 $220

3 $242

4 $266.20

5 $292.82

6 $322.10

Your welcome stranger. (:

Answer:

B. Make a table of equal ratios to find how long it takes each printer to print 120 photos and find the difference would be an appropriate process to determine how much longer it will take Khalil's printer to print 120 photos than Alex's.

Step-by-step explanation:

To use this process, we can set up a table showing the ratio of photos printed to time taken for each printer. Then we can use these ratios to find how long it would take each printer to print 120 photos, and find the difference between the two times to determine how much longer it would take Khalil's printer.

Answer:

Step-by-step explanation:

B and E

Answer: distributive property

Step-by-step explanation:1 2 times 95 can indeed be rewritten as 12(100-5) and we can use the distributive property IN OUR HEADS, so we get 1200 - 60 = 1140.