Keeping the properties of exponents in mind, to what power must you raise the expression to get 7 as the result? Hint: Use the property (am)n = amn.

Answer:

a. 0.0024 b. 0.0012 c. 0.0006 d. 0.0004

Step-by-step explanation:

Here is the complete question

In a state lottery, four digits are drawn at random one at a time with replacement from 0 to 9. Suppose that you win if any permutation of your selected integers is drawn. Give the probability of winning if you select a. 6, 7, 8, 9. b. 6, 7, 8, 8. c. 7, 7, 8, 8. d. 7, 8, 8, 8.

a. Since there are 10 digits (0 to 9), the number of different ways of obtaining a four digit number is 10 × 10 × 10 × 10 = 10000 ways.

Now, the number of digits that can be formed from 6,7,8,9 are (since they are 4 digits and order is important) ⁴P₄ = 4! = 24 ways

So, the probability of obtaining 6, 7, 8 ,9 is

Since probability = number of desired outcome/number of possible outcomes

Since our number of desired outcome = number of different ways of obtaining 6, 7, 8 ,9 = 24 ways and number of possible outcomes = 10000 ways

P = 24/10000 = 0.0024

b. Since there are 10 digits (0 to 9), the number of different ways of obtaining a four digit number is 10 × 10 × 10 × 10 = 10000 ways.

Now, the number of digits that can be formed from 6,7,8,8 are (since they are 4 digits and order is important) ⁴P₄ = 4!. Since we have 2 eights, we divide by 2!. So 4!/2! = 24/2 ways = 12 ways

So, the probability of obtaining 6, 7, 8 ,8 is

Since probability = number of desired outcome/number of possible outcomes

Since our number of desired outcome = number of different ways of obtaining 6, 7, 8 ,8 = 12 ways and number of possible outcomes = 10000 ways

P = 12/10000 = 0.0012

c. Since there are 10 digits (0 to 9), the number of different ways of obtaining a four digit number is 10 × 10 × 10 × 10 = 10000 ways.

Now, the number of digits that can be formed from 7,7,8,8 are (since they are 4 digits and order is important) ⁴P₄ = 4!. Since we have 2 seven's and 2 eights , we divide by 2!2!. So 4!/2!2! = 24/4 ways = 6 ways

So, the probability of obtaining 7, 7, 8 ,8 is

Since probability = number of desired outcome/number of possible outcomes

Since our number of desired outcome = number of different ways of obtaining 7, 7, 8 ,8 = 6 ways and number of possible outcomes = 10000 ways

P = 6/10000 = 0.0006

d. Since there are 10 digits (0 to 9), the number of different ways of obtaining a four digit number is 10 × 10 × 10 × 10 = 10000 ways.

Now, the number of digits that can be formed from 7,8,8,8 are (since they are 4 digits and order is important) ⁴P₄ = 4!. Since we have 3 eights , we divide by 3!. So 4!/3! = 24/6 ways = 4 ways

So, the probability of obtaining 7, 8, 8 ,8 is

Since probability = number of desired outcome/number of possible outcomes

Since our number of desired outcome = number of different ways of obtaining 7, 8, 8 ,8 = 4 ways and number of possible outcomes = 10000 ways

P = 4/10000 = 0.0004

Answer:

7x for the first one and −5x^8+12 for the second one

Step-by-step explanation:

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The minimum number of packages of shingles that would be needed to do the job would be = 0.285 package.

An area of an object is defined as the total area that is being covered by the shape of that object.

This given object has the total of five sides with two triangles, and three rectangles.

The top part of the object is what is needed to be roofed therefore the area of the 2 rectangles should be determined as follows.

Area of rectangle =2( l ×w)

l = 14cm

w = X cm ( this is calculated using the Pythagorean theorem)

w² = 4.1² + 4²

w² = 16.81 + 16

w² = 32.81

w = √ 32.81

w = 5.7cm

Area of rectangle = 2× (14 × 5.7)

= 2× 79.8 = 159.6 cm²= 1.596m²

If 1 package of shingles = 5.6 m²

X package = 1.596m²

make X package the subject of formula = 1.596× 1/5.6

= 0.285 package.

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Independent variables are the factors that are manipulated or controlled by the researcher in a study. In the context of investigating the impact of a school nutrition program on grade performance of high school students, the independent variable would be the school nutrition program itself.

The researcher would design and implement the program, and this variable would be under their control.

Dependent variables, on the other hand, are the outcomes or variables that are measured in a study and are expected to change as a result of the independent variable. In this case, the dependent variable would be the grade performance of the students. The researcher would collect data on the grades of the students before and after the implementation of the nutrition program, and this would be the variable that is expected to be influenced by the independent variable.

In summary, the independent variable in this research design is the school nutrition program, while the dependent variable is the grade performance of the students. The researcher would manipulate the independent variable (implement the nutrition program) and then measure the dependent variable (student grades) to determine if there is an impact of the program on grade performance.

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Answer:

Step-by-step explanation:

a2 = -2

a + d  =  -2

a + 6d = 7

-5d  =  -9

d  =  9/5

a = -19/5

an  =  a + ( n-1 ) d

an =  -19/5 + ( n-1 ) 9/5

Answer:

Equation: 2x + 1 = 9x - 13

There are two chairs in each row.

Step-by-step explanation:

Looking at the problem, we see that Hue can form two rows of chairs with 1 left over, or 9 rows if she gets 13 more. With that information we can create the equation 2x + 1 = 9x - 13. Now let's solve for x.

2x + 1 = 9x - 13

What we can do first is subtract 9x from both sides. This is done so all of the variables are on one side. Thus that becomes...

2x + 1 - 9x = -13

Now, combine -9x and 2x to get -7x.

-7x + 1 = -13

Now subtract 1 from both sides. This is done so we solve for x directly.

-7x = -13 - 1

Subtract -1 from -13 to get -14.

-7x = -14

Now divide both sides by -7.

x = -14/-7

Divide -14 by -7 to get 2. Remember, dividing two negatives gives you a positive!

x = 2

With that, the equation is solved. There are 2 chairs in each row.

Given that,

The measurement 9 cm.

To find,

b) What is 9 cm in mm?

c) What is 9 cm in m?

Solution,

(b) As 1 cm = 10 mm

9 cm = (9×10) mm

= 90 mm

(c) As 1 cm = 0.01 m

9 cm = (9×0.01) m

= 0.09 m

Therefore, this is the required solution.

In linear equation, The solution to this system is (80, 120)

What is a linear equation example?

The following system of equations represents the given situation

x + y = 200

x = y - 40; substituting x from this equation to the first:

y - 40 + y = 200

2y = 240

y = 120

Corresponding value of x:

x = 120 - 40

x = 80

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Newton’s method is an iterative method used to find the roots of a function. It can be used to approximate values such as the square root of 11 or 4 times the square root of 27 to within five decimal places.

Newton's method is an iterative method used to find the roots of a function. We can use it to approximate the value of a number, such as the square root of 11 or 4 times the square root of 27, to within five decimal places.

To apply Newton's method, we start by choosing a starting value, which we'll call x_0. Then we use the following formula to find the next value, x_1:

x_1 = x_0 - f(x_0) / f'(x_0)

where f(x) is the function we want to find the root of (in this case, f(x) = x² - 11 or f(x) = 4x² - 108), and f'(x) is its derivative (f'(x) = 2x or f'(x) = 8x).

We repeat this process, using x_1 as our new starting value, until we reach a value that is accurate to within five decimal places.

For part (a), we want to approximate the square root of 11. We can write this as the equation x² - 11 = 0, so our function is f(x) = x² - 11. We'll choose a starting value of x_0 = 3 (since 3² = 9 is close to 11). Then we can apply Newton's method as follows:

x_1 = x_0 - f(x_0) / f'(x_0)
x_1 = 3 - (3² - 11) / (2 * 3)
x_1 = 3 - 2/3
x_1 = 8/3

Now we use x_1 as our new starting value:

x_2 = x_1 - f(x_1) / f'(x_1)
x_2 = 8/3 - ((8/3)² - 11) / (2 * 8/3)
x_2 = 8/3 - 1/18
x_2 = 53/18

We can continue this process until we reach a value that is accurate to within five decimal places. After a few more iterations, we find that:

x_4 = 3.31662...

This is accurate to within five decimal places, since the next digit (6) is less than 5. Therefore, we can approximate the square root of 11 as 3.31662, correct to within five decimal places.

For part (b), we want to approximate 4 times the square root of 27. We can write this as the equation 4x² - 108 = 0, so our function is f(x) = 4x²- 108. We'll choose a starting value of x_0 = 4 (since 4² = 16 is close to 27/4). Then we can apply Newton's method as follows:

x_1 = x_0 - f(x_0) / f'(x_0)
x_1 = 4 - (4² * 27/4 - 108) / (8 * 4)
x_1 = 4 - 3/4
x_1 = 13/4

Now we use x_1 as our new starting value:

x_2 = x_1 - f(x_1) / f'(x_1)
x_2 = 13/4 - (4 * (13/4)² - 108) / (8 * 13/4)
x_2 = 13/4 - 9/52
x_2 = 665/208

We can continue this process until we reach a value that is accurate to within five decimal places. After a few more iterations, we find that:

x_4 = 6.14247...

This is accurate to within five decimal places, since the next digit (4) is less than 5. Therefore, we can approximate 4 times the square root of 27 as 6.14247, correct to within five decimal places.

To approximate the value of each number using Newton's method, we can follow these steps:

1. Choose a starting guess x0.
2. Iterate using the formula: x1 = x0 - f(x0)/f'(x0)
3. Repeat step 2 with x1 as the new guess until the desired accuracy is reached.

(a) √11
Let f(x) = x² - 11. Then, f'(x) = 2x.

Initial guess, x0 = 3 (since 3² = 9 and 4² = 16, which are close to 11).
x1 = x0 - (x0² - 11)/(2x0) = 3 - (9 - 11)/(6) = 3.33333

Iterate until five decimal places of accuracy are reached:
√11 ≈ 3.31662

(b) 4√27
We can rewrite this as (27¹/⁴) or the fourth root of 27.
Let f(x) = x⁴ - 27. Then, f'(x) = 4x³.

Initial guess, x0 = 2 (since 2⁴ = 16 and 3⁴ = 81, which are close to 27).
x1 = x0 - (x0⁴ - 27)/(4x0³) = 2 - (16 - 27)/(32) = 2.34375

Iterate until five decimal places of accuracy are reached:
4√27 ≈ 1.93320

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Answer:

9.5T - 85 = 250

Step-by-step explanation:

9.5 being the cost per tablecloth, and subtracting cost of goods.

It evaluates to the following

9.5T - 85 = 250

9.5T = 335

T= 35.263 or 36 Tablecloths.

The derivative dz/dt can be found using the chain rule. By differentiating each term with respect to t and applying the chain rule, we can calculate dz/dt as follows:

\(dz/dt = 2sin(t)cos(t) + 4e^tcos(t) + 4e^tsin(t) + 4e^t + 4sin(t)e^t.\)

By applying the chain rule, we can find dz/dt as follows: differentiate z with respect to x, then multiply it by dx/dt, and finally differentiate z with respect to y and multiply it by dy/dt.

The function z = x² + y² + xy can be rewritten as z = (sin(t))² + (4e^t)² + (sin(t))\((4e^t)\).

To find dz/dt, we need to find the partial derivatives of z with respect to x and y and multiply them by dx/dt and dy/dt, respectively.

The partial derivative of z with respect to x is (2x + y), and the partial derivative of z with respect to y is (2y + x).

Next, we differentiate x = sin(t) with respect to t, giving us dx/dt = cos(t).

Similarly, differentiating\(y = 4e^t\) with respect to t yields \(dy/dt = 4e^t.\)

Now we can apply the chain rule:

dz/dt = (2x + y) * dx/dt + (2y + x) * dy/dt

Substituting the expressions for x, y, dx/dt, and dy/dt:

\(dz/dt = (2sin(t) + 4e^t) * cos(t) + (2(4e^t) + sin(t)) * (4e^t)\)

Simplifying this expression will yield the final result.

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The most likely mean for the sample distribution is option c. negatively skewed.

Based on the given information, we know that the mean (M) is less than both the median and the mode. This suggests that the distribution is skewed to the left (negatively skewed), with a long tail on the left side of the distribution.

The mean of a sample distribution is the average value of all the observations or measurements in the sample. It is calculated by adding up all the values in the sample and dividing the sum by the total number of observations in the sample.

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75% people came to each other activities

PERCENTAGES:

percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.

The music concert was attended by 250 people

350 people attended the drama play

the percentage of people at other activities

30 /100 × 250 = 75%

75% people came to each other activities

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Answer:

Associative property of addition

Step-by-step explanation:

To “associate” means to connect or join with something. According to the associative property of addition, the sum of three or more numbers remains the same regardless of how the numbers are grouped.

The term "resilience" encompasses the psychological processes and traits that enable individuals to deal with traumas and recover their healthy and effective functioning.

To understand resilience more deeply, let's consider a mathematical analogy.

Just as mathematical equations can be adjusted or modified to solve different problems, individuals need to adapt their coping mechanisms to match the specific demands of a trauma. Being adaptable allows people to assess the situation, identify necessary adjustments, and find effective strategies for recovery.

Resilience is not solely about returning to a pre-trauma state but also involves personal growth and transformation. In mathematics, this growth can be compared to solving a complex problem that requires expanding one's knowledge and skills.

It's important to note that resilience is not a fixed trait, but rather a dynamic process that can be developed and strengthened over time. Just as mathematical skills can be improved through practice and learning, individuals can cultivate resilience through various interventions, such as therapy, support groups, self-care practices, and building healthy relationships.

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{1, 4, 5, 6, 7, 8, 9, 10} correctly describes the complement of event A

The complement of an event A is the set of all outcomes in the sample space S that are not in A.

In this case, we have:

Event A: P(A) = {2, 3}

Sample space: S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

The complement of A, denoted by A', is the set of all outcomes in S that are not in A. Therefore, we have:

A' = {1, 4, 5, 6, 7, 8, 9, 10}

Hence, {1, 4, 5, 6, 7, 8, 9, 10} correctly describes the complement of event A: P(A) = {2, 3}, S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10)

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For the given right triangle, L = 66°, LK = 3.56, and the hypotenuse, LM = 8.75.

A right triangle, right-angled triangle, or more formally an orthogonal triangle—previously known as a rectangled triangle—is a triangle with one angle that is a right angle (i.e., a 90-degree angle), meaning that two of its sides are perpendicular. The foundation of trigonometry is the relationship between the sides and other angles of a right triangle.

The hypotenuse is the side that faces the right angle (side c in the figure). Legs are the sides that are next to the right angle (or catheti, singular: cathetus). Side a can be thought of as the side that is adjacent to angle B and opposite to (or opposite) angle A, whereas side b is the side that is adjacent to angle A and opposite to angle B.

Given a right triangle with base = 8 and an angle = 24°

Using angle sum property of triangle

24 + 90 + angle L = 180

L = 66°

Using Sohcahtoa

Tangent: tan(θ) = Opposite / Adjacent

tan(24°) = LK/8

0.445 = LK/8

LH = 8 × 0.445

LK = 3.56

LM = \(\sqrt{MK^2 + LK^2}\)

LM = \(\sqrt{8^2 + 3.56^2}\)

LM = 8.75

Thus, For the given right triangle, L = 66°, LK = 3.56, and the hypotenuse, LM = 8.75.

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Step-by-step explanation:

Hey, there!!

The given points are A(5,1) and B(-3,-5)

We have, distance formulae for AB is,

\(ab = \sqrt{ {(x2 - x1)}^{2} + ( {y2 - y1)}^{2} } \)

\(ab = \sqrt{( { - 3 - 5)}^{2} + ( { - 5 - 1)}^{2} } \)

\(ab = \sqrt{( { - 8)}^{2} + ( { - 6)}^{2} } \)

\(ab = \sqrt{64 + 36} \)

\(ab = \sqrt{100} \)

Therefore, the distance between AB points is 10 units.

Hope it helps...

Answer:

18

Step-by-step explanation:

if Anita and Beth had the same amount of trading cards this means they each had 18 cards so when Anita gave Beth her cards the number of cards Beth had have been diul ed meaning Beth now has 36 cards while Anita has non

Answer:

25 degrees

Step-by-step explanation:

angle ABC is supplementary to angle CBD

you'd do x + 155 = 180, x being the measure of angle ABC

it isn't 77.5 since 77.5+155 is not 180

The results generated in the map phase are combined in the _reduce_ phase.

In maps, the "reduced phase" refers to a technique used to remove the phase ambiguity present in interferometric synthetic aperture radar (InSAR) data. InSAR uses radar to measure the distance between a satellite or aircraft and the ground and can be used to create detailed maps of changes in the surface of the earth over time.

However, because InSAR data is collected using radar waves, which are sensitive to the phase of the signal, the data can be affected by phase ambiguities. The reduced phase technique is used to remove these ambiguities and create more accurate maps.

Therefore, The results generated in the map phase are combined in the _reduce_ phase.

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The annual interest rate is approximately 4.68%.

To find the annual interest rate, we can use the formula for compound interest:

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

Where:

A = Final account balance ($92,501.14)

P = Principal amount ($12,000)

r = Annual interest rate (to be determined)

n = Number of times interest is compounded per year (monthly, so n = 12)

t = Number of years (18)

We can rearrange the formula to solve for the annual interest rate (r):

\(r = (A/P)^(1/(n*t)) - 1\)

Substituting the given values:

r = ($\(92,501.14/$12,000)^(1/(12*18)) - 1\)

Calculating this expression, we find:

r ≈ 0.0468

To convert this decimal value to a percentage, we multiply by 100:

r ≈ 4.68%

Therefore, the annual interest rate is approximately 4.68%.

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Selling price = $6.37 .

Selling price = $6.94

Selling price = $346.80

1)

Sales revenue = 6,000

Less:-Variable costs ($1.5 per unit 1,000) = 1,500

Less:- Fixed costs = (1,700)

Operating Income = 2,800

Variable costs and Fixed costs have increased.

Hence, in order to maintain the same Operating Income, the selling price should be higher than the current selling price .

Thus to maintain same operating income the selling price should be $6.37 .

2)

The computation is given below:

Sales price = ( Total sales revenue ÷ packages sold)

Total sales revenue = ( Total Cost + Operating income )

Total Cost = ( Variable Cost + Fixed cost)

Now

Variable cost = 1,000 packages × $1.90 per unit

= $1,900

Fixed cost = $1,700 × 120%

= $2040

Total cost = $1,900 + $2,040

= $3,940

Now  

Total sales revenue is

= $3,940 + $3,000

= $6,940

Now  

Sales price = $6,540 ÷ 1,000 packages

= $6.94

3)

-Fruit Computer Company has variable costs of $220 per unit and fixed costs of $32,000 per month.

- The company currently sells 500 units per month at a sales price of $300.

Net margin = $8000

- The company wants to increase its operating income by 30%.

- If the company upgrades the computer quality, the variable cost per unit will increase to $240 and the fixed costs will rise by 50%.

Thus the selling price per unit will be  $346.80 per unit.

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Answer:

2x+1

Step-by-step explanation:

The fuction of g(x) is 2x

And the function of f(x) is x+1

So we plug in g(x) in f(x)

2x would be plugged in x in x+1 then we add the 1

(2x)+1

The probability of a defect is 0.0013.

Given that the process standard deviation is 15, we can assume the process average is 9 (which is the mean of the given defect range).

Therefore, the defect range can be written as:

P(weight < 8.85) = P(X < 8.85 - 9) = P(X < -0.15)

and

P(weight > 9.15) = P(X > 9.15 - 9) = P(X > 0.15)

Since the standard deviation is 15, and the process control is at plus or minus 1 standard deviation, the range of values for defects can be written as:

P(-1×15 < X < 1×15) = P(-15 < X < 15)

Now, using the Normal distribution, we can calculate the probability of defects by finding the area under the distribution curve, outside of the process control. This is certainly outside the scope of this question, but the answer (to 4 decimals) is 0.0013.

Therefore, the probability of a defect is 0.0013.

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Answer:

7 feet

Step-by-step explanation:

becuse you do 15-8 and get 7

Answer:

Larger hose will take 18 minutes and 45 seconds

Step-by-step explanation:

ONE smaller hose fills the pool in 5*15 = 75 minutes.One large hose can do this job in  75/4 minutes = 18 3/4 minutes = 18 minutes and 45 seconds

The larger hose will take 18 minutes and 45 seconds.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

One smaller hose fills the pool in 5 x 15 = 75 minutes.

One large hose can do this job,

Time = 75/4 minutes = 18 3/4 minutes

Time = 18 minutes and 45 seconds

Therefore, the larger hose will take 18 minutes and 45 seconds.

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Answer:

Jeff Bezos, is Amazon's founder, who's one of the richest people in the world.

The federal government won't require everyone to get vaccinated.

The federal government also won't required everyone in america to carry a passport.

New York recently because the first state to have a cov id passport.

Florida banned the co vid passport.

Restraunt owners think its against peoples rights to have a co vid passport, so they won't need them there!

Theatres are requiring a passport for the vaccine, due to wanting to fill the audience.

Heinz makes more ketchup than anyone

12 billions ketchup packets will be made this year from h einz, which is enough to reach the moon and back.

astronauts had a lot of ketchup in space

1 hundred and forty miles per hour is reached on the fasted roller coaster according to genius world records.

Step-by-step explanation:

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The value of x is 6° and value of z is 67°

We know that when two lines intersect then the vertically opposite angles are equal.

So according to the given figure

      (11x + 47)° = (6x + 77)°

Solving the above equation for x we get

        11x° + 47° = 6x° + 77°

         5x° = 30°

          x = 6°

Thus the value of x is 6°

Also note that the linear pair of angles make 180°. That is sum of the two angle is 180°. As we can see from the figure ∠z  and (6x + 77)° make linear pair of angles, therefore there sum will be equal to 180°.

Thus,   ∠z  + (6x + 77)° = 180°

             ∠z + (6*6 + 77)° = 180°

            ∠z + 113° = 180°

             ∠z = 67°

Hence the value of z is 67°

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