Negative Exponents
If Xand a are counting numbers, is *** less than or greater than 1?

Answer:

A 5(0.5)^x

B 3(2)^x

C 5(3)^x

D 8(1.25)^x

E 8(0.75)^x

F 10(0.5)^x

Step-by-step explanation:

A 5(0.5)^x

(-1,10) goes by 1/2

B 3(2)^x doubles

C 5(3)^x triples

D 8(1.25)^x * 1 1/4

E 8(0.75)^x by 3/4

F 10(0.5)^x x 1/2

Answer:

The number of pounds of:

Decaffeinated coffee = x = 5 pounds

Regular coffee = y = 9 pounds

Step-by-step explanation:

A 14 ​-pound mixture of coffee that contains both decaffeinated and regular coffee costs ​$37. The decaffeinated coffee costs ​$2 per​ pound, and the regular coffee costs ​$3 per pound.

Let the number of pounds of:

Decaffeinated coffee = x

Regular coffee = y

Hence, our system of equations =

x + y = 14..... Equation

x = 14 - y

2x + 3y = 37....... Equation 2

We substitute 14 - y for x in Equation 2

= 2(14 - y) + 3y = 37

= 28 - 2y + 3y = 37

= - 2y + 3y = 37 - 28

= y = 9 pounds

Solving for x

x = 14 - y

x = 14 - 9

x = 5 pounds

Therefore,

The number of pounds of:

Decaffeinated coffee = x = 5 pounds

Regular coffee = y = 9 pounds

h = 11.9 cm

cos = adjacent/ hypotenuse

therefore:

cos(24) = h/ 13

rearrange:

h = 13cos(24)

put into calculator:

h = 11.8760...

rounded to one decimal point:

h = 11.9cm

The number of sets that Mrs Bowlin created would be = 63 sets.

Sets of an object is defined as the arrangement of an object into various distinct groups in such a way that each group contains the same amount of the object.

The total number of markers organized by Mrs Bowlin = 567.

The number of markers per set = 6

The total number of sets created with respect to the number of markers available = 567/6 = 63 sets.

Learn more about division here:

https://brainly.com/question/25289437

#SPJ1

Complete question:

Mrs. Bowlin organized the markers into sets. If there were 9 markers

in each set, how many sets of markers did Mrs. Bowlin create? there are 567 markers

The number of diagonal in convex polygon with 20 sides is equal to 170.

Number of sides in convex polygon = 20

Interior angle in convex polygon is less than 180 degrees

To find the number of diagonals in a convex polygon with 20 sides,

we can use the formula,

Number of diagonals  = n(n-3)/2

where n is the number of sides.

Substituting the value of number of sides n=20, we get,

⇒ Number of diagonals  = 20(20-3)/2

⇒ Number of diagonals  = 17 x 20 / 2

⇒ Number of diagonals  = 170

Therefore, a convex polygon with 20 sides has 170 diagonals.

learn more about convex polygon here

brainly.com/question/22056240

#SPJ4

60

random stuff because the answer has to be 20 characters long

Answer:

y= 160°

Step-by-step explanation:

as we can see, the corresponding angles are both 20°

a straight line is 180°

180-20= 160

that's you're answer

Applying exponential properties, we have that the solution to the given expression is:

\(-\frac{125}{343}\)

When a fraction is elevated to the exponent, we apply the exponent to both the numerator and the denominator.

In this problem, we have that:

Negative base with odd exponent, hence the solution is negative and given as follows:

\(-\frac{125}{343}\)

More can be learned about exponential properties at https://brainly.com/question/25263760

#SPJ1

The student covers a total distance of 22.05 kilometers in a week's time, walking between the park and the house each day.

To find the total distance covered by the student in a week's time, we need to calculate the distance covered in one round trip (from the house to the park and back) and then multiply it by the number of round trips in a week.

Given that the difference between the park and house is 1 kilometer and 575 meters, we can convert it to a total distance of 1.575 kilometers.

In a round trip, the student covers twice the distance between the park and the house, which is 1.575 kilometers * 2 = 3.15 kilometers.

Now, we need to determine how many round trips the student makes in a week. Let's assume the student makes one round trip each day.

Since there are 7 days in a week, the total distance covered by the student in a week's time is 3.15 kilometers * 7 = 22.05 kilometers.

for similar questions on distance.

https://brainly.com/question/26046491

#SPJ8

Answer:

165 in³

Step-by-step explanation:

volume of rect prism - volume of cylinder

Vol (prism) = 8²×12 = 768

Vol (cyl) = 4²π×12 = 16×12π ≈ 603

768 - 603 = 168

The value of the given integral is: v = [(4√(3) - 5)π/3]

To evaluate the given integral, let's calculate it step by step:

First, let's integrate with respect to z from 1 to √(4 - x² - y²):

∫[1, √(4 - x² - y²)] dz = √(4 - x² - y²) - 1

Next, let's integrate the above expression with respect to y from -√(3 - x²) to √(3 - x²):

∫[-√(3 - x²), √(3 - x²)] (√(4 - x² - y²) - 1) dy

To simplify the integration, let's convert to polar coordinates:

x = r cosθ

y = r sinθ

The bounds of integration in polar coordinates will be:

r: 0 to √(3)

θ: 0 to 2π

Now, we can rewrite the integral in terms of polar coordinates:

∫[0, 2π] ∫[0, √(3)] (√(4 - r²) - 1) r dr dθ

Evaluating the inner integral with respect to r:

∫[0, 2π] [(-1/3) (4 - r²)\(^{3/2}\) - (1/2) r²] | [0, √(3)] dθ

∫[0, 2π] [(2√(3)/3) - (1/3)(4 - 3)\(^{3/2}\) - (1/2)(√(3))²] dθ

Simplifying further:

∫[0, 2π] [(2√(3)/3) - (1/3) - (3/2)] dθ

∫[0, 2π] [(2√(3)/3) - (5/6)] dθ

Now, integrating with respect to θ:

[(2√(3)/3)θ - (5/6)θ] | [0, 2π]

[(2√(3)/3)(2π) - (5/6)(2π)] - [(2√(3)/3)(0) - (5/6)(0)]

[(4√(3)/3)π - (5/3)π] = [(4√(3) - 5)π/3]

Therefore, the value of the given integral is: v = [(4√(3) - 5)π/3]

Complete Question:

Evaluate the integral:

v = ∫∫∫ [−√3, √3] [−√(3−x²), √(3−x²)] [1, √(4−x²−y²)] dz dy dx

To know more about integral, refer here:

https://brainly.com/question/31059545

#SPJ4

Thus, the equation of plane that passes through the point (7, 8, −9) and is perpendicular to the line v = (0, −7, 3) t(1, −2, 3) is −7x − y = 57.

To find the equation of a plane, we need a point on the plane and a normal vector.

We are given a point on the plane as (7, 8, −9).

To find the normal vector, we need to find the cross product of two vectors that are on the plane. We are given a line, which lies on the plane, and we can find two vectors on the line: (1, −2, 3) and (0, −7, 3). We can take their cross product to get a normal vector:
(1, −2, 3) × (0, −7, 3) = (−21, −3, 0)

Note that the cross product is perpendicular to both vectors, so it is perpendicular to the plane.

Now we have a point on the plane and a normal vector, so we can write the equation of the plane in the form Ax + By + Cz = D, where (A, B, C) is the normal vector and D is a constant.

Substituting the values we have, we get:
−21x − 3y + 0z = D

To find D, we plug in the point (7, 8, −9) that lies on the plane:
−21(7) − 3(8) + 0(−9) = D
−147 − 24 = D
D = −171

So the equation of the plane is:
−21x − 3y = 171 + 0z
or
21x + 3y = −171.

Note that we can divide both sides by −3 to get a simpler equation:
−7x − y = 57.

Therefore, the equation of the plane that passes through the point (7, 8, −9) and is perpendicular to the line v = (0, −7, 3) t(1, −2, 3) is −7x − y = 57.

Know more about the equation of plane

https://brainly.com/question/10524369

#SPJ11

Answer: Chicken nuggets in zip loc bag?

Step-by-step explanation:

The expected value of buying one ticket in this charity raffle is $0.42. This means that, on average, a person can expect to win approximately $0.42 if they purchase a single ticket.

To calculate the expected value, we need to consider the probability of winning each prize multiplied by the value of the prize. Let's break it down:

- There is a 1/5000 chance of winning the $600 prize, so the expected value contribution from this prize is (1/5000) * $600 = $0.12.

- There are 3/5000 chances of winning the $300 prize, so the expected value contribution from these prizes is (3/5000) * $300 = $0.18.

- There are 5/5000 chances of winning the $40 prize, so the expected value contribution from these prizes is (5/5000) * $40 = $0.04.

- Finally, there are 20/5000 chances of winning the $5 prize, so the expected value contribution from these prizes is (20/5000) * $5 = $0.08.

Summing up all the expected value contributions, we get $0.12 + $0.18 + $0.04 + $0.08 = $0.42.

Therefore, if you buy one ticket in this raffle, the expected value of your winnings is $0.42.

Learn more about expected value here:

https://brainly.com/question/13749480

#SPJ11

1,814,400 different 10-letter words can be formed from the given letters.

To determine how many different 10-letter words (real or imaginary) can be formed from the letters T, S, O, Y, M, H, S, F, C, and B, we need to calculate the number of unique permutations.

Since there are 10 letters, with the letter "S" appearing twice, we can use the following formula:

Number of permutations = 10! / (2!)

1. Calculate the factorial of 10 (10!): 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3,628,800
2. Calculate the factorial of 2 (2!): 2 × 1 = 2
3. Divide the factorial of 10 by the factorial of 2: 3,628,800 / 2 = 1,814,400

So, 1,814,400 different 10-letter words can be formed from the given letters.

Learn more about "permutation":

https://brainly.com/question/1216161

#SPJ11

Answer:

Your answers are 12.75 an Hour for both!

Step-by-step explanation:

Really Simple!

459 Dollars / 36 Hours of Labor

= $12.75/ 1 Hour

535.5 Dollars / 42 Hours of Labor

= $12.75/ 1 Hour

The solution to the inequality -4 ≤ 2(x-1) < 10 in interval notation is [-1, 6).

To solve the inequality -4 ≤ 2(x-1) < 10, we can start by isolating the expression (x-1) in the middle.

-4 ≤ 2(x-1) < 10

Divide each part of the inequality by 2:

\(-4/2 \leq (x-1) < 10/2-2 \leq (x-1) < 5\)

Next, we add 1 to each part of the inequality:

\(-2 + 1 \leq (x-1) + 1 < 5 + 1-1 \leq x < 6\)

The solution to the inequality -4 ≤ 2(x-1) < 10 in interval notation is [-1, 6).

In interval notation, we use brackets [ ] for inclusive bounds and parentheses ( ) for exclusive bounds.

The interval [-1, 6) represents all real numbers x such that -1 is included, but 6 is not included. This means that x can be any value from -1 up to, but not including, 6. The inequality is satisfied when x lies between -1 and 6, inclusive of -1 but excluding 6.

To summarize, the solution to the inequality -4 ≤ 2(x-1) < 10 in interval notation is [-1, 6).

For more such questions on inequality.

https://brainly.com/question/25944814

#SPJ8

Step-by-step explanation:

it looks like this is a regular (right) triangular prism with 3 equal side areas and one bottom area.

the surface area of the pyramid is the sum of all 4 of these areas.

all these areas are triangles.

the area of a triangle is

baseline × height / 2

in our case

1 side area is 6×8.2/2 = 3×8.2 = 24.6 yd²

all 3 side areas together are 24.6×3 = 73.8 yd²

the bottom triangle is

6×5.2/2 = 3×5.2 = 15.6 yd²

so, the total surface area is

73.8 + 15.6 = 89.4 yd²

Answer:

Answers are below.

Step-by-step explanation:

From smallest to largest:-

Domain: {0, 3, 5, -4, -6, -9}

Range: {0}

Answer:

The domain is the set of all the values of x

The range is the set of all the values of y.

Domain:

{0,1,2,4,5,6,7,8}Range: {5,4,9,6,0}

Step-by-step explanation:

To determine the maximum and minimum of a function, you need to find the critical points and endpoints, evaluate the function at these points, and compare the values.

The highest value represents the maximum, while the lowest value represents the minimum.

To determine the maximum and minimum of a function, follow these steps:

Find the critical points of the function by finding where its derivative equals zero or is undefined.

Determine the endpoints of the interval you are considering, if applicable.

Analyze the function at its starting and ending locations.

The highest value represents the maximum, and the lowest value represents the minimum.

Let's consider an example using the function f(x) = x^2 - 4x + 3 over the interval [0, 5].

Find the critical points:

Take the derivative of the function: f'(x) = 2x - 4.

Set the derivative equal to zero: 2x - 4 = 0.

Solve for x: 2x = 4,

x = 2.

The critical point is x = 2.

Determine the endpoints:

In this case, the endpoints of the interval are x = 0 and x = 5.

Evaluate the function:

Calculate f(0) = (0)^2 - 4(0) + 3

= 3.

Calculate f(2) = (2)^2 - 4(2) + 3

= -1.

Calculate f(5) = (5)^2 - 4(5) + 3

= -7.

Determine the maximum and minimum:

The highest value is 3, which occurs at x = 0. Therefore, the maximum value is 3.

The lowest value is -7, which occurs at x = 5. Therefore, the minimum value is -7.

To determine the maximum and minimum of a function, you need to find the critical points and endpoints, evaluate the function at these points, and compare the values. The highest value represents the maximum, while the lowest value represents the minimum. It is important to consider the given interval to ensure that the maximum and minimum values are within the specified range.

To know more about Maximum, visit

brainly.com/question/30236354

#SPJ11

Answer:

-8 > 8

Step-by-step explanation:

You find one that is less and one that is greater

Answer:

Step-by-step explanation:

Slope- intercept form:

Given

As per given point, y-intercept is b = 10

So the equation is:

Answer:

9x - 7

Step-by-step explanation:

6x - 9 + 3x + 2

= (6x + 3x) (- 9 + 2)

= 9x - 7

Answer: 58

Step-by-step explanation:

From 10 AM to 1 PM the numbers are 161, 368, 842, and 1918

So now we find the difference between the numbers.

368 - 161 = 207

842 - 368 = 474

1918 - 842 = 1076

now it asked for the average so you add them together then divide by 3

which is (207+474+1076)/3 = 585.66666666....

Then it says to round to the nearest integer which is 586

Hey why not mark me as brainliest

The average increase between 10 AM and 1 PM is 586.

An average is a single number taken as representative of a list of numbers.

Given that, a microbiologist is studying A bacterial culture. Every hour, she counts the number of bacteria.

From 10 AM to 1 PM the numbers are 161, 368, 842, and 1918

The difference between the numbers.

368 - 161 = 207

842 - 368 = 474

1918 - 842 = 1076

Now it asked for the average, so you add them together then divide by 3

Which is (207+474+1076)/3 = 585.66666666....

Rounding to the nearest integer, we get 586

For more references on average, click;

https://brainly.com/question/24057012

#SPJ2

There is not sufficient evidence to reject the claim that the mean weight of the cereal packets is at least 14 oz.

Η0 : μ = 14 (Null hypothesis)

H1 : μ < 14 (Alternative hypothesis)

At least sign is ≥ therefore, it should be in null hypothesis. Null Hypothesis, the mean weight of the individual serving boxes of the cereal company is 14 oz or less.

But, we can consider = sign instead of ≥ : Alternative Hypothesis, the mean weight of the individual serving boxes of the cereal company is greater than 14 oz.

Therefore, There is not sufficient evidence to reject the claim that the mean weight of the cereal packets is at least 14 oz.

To know more about hypothesis check below link:

https://brainly.com/question/25263462

#SPJ4

Complete question:

A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz. Express the null and alternative hypotheses in symbolic form.

the binary representation of 63.25 as 111111.01.

To convert the decimal number 63.25 to binary, we need to convert the integer part (63) and the fractional part (0.25) separately.

1. Converting the integer part (63):

  Divide 63 by 2, and keep track of the remainders:

  63 ÷ 2 = 31 (remainder 1)

  31 ÷ 2 = 15 (remainder 1)

  15 ÷ 2 = 7 (remainder 1)

  7 ÷ 2 = 3 (remainder 1)

  3 ÷ 2 = 1 (remainder 1)

  1 ÷ 2 = 0 (remainder 1)

  The remainders in reverse order give us the binary representation of the integer part: 111111.

2. Converting the fractional part (0.25):

  Multiply 0.25 by 2 and record the whole number part:

  0.25 × 2 = 0.5 (0)

  0.5 × 2 = 1.0 (1)

  The whole number parts give us the binary representation of the fractional part: 01.

Putting the integer and fractional parts together, we have the binary representation of 63.25 as 111111.01.

Learn more about binary representation here

https://brainly.com/question/30871458

#SPJ4

The binary representation of the decimal number 63.25 is 111111.01.

To convert the decimal number 63.25 to binary, we need to separate the whole number part and the fractional part.

Whole Number Part:

Divide the whole number part (63) by 2:

Divide the quotient (31) by 2:

Divide the quotient (15) by 2:

Divide the quotient (7) by 2:

Divide the quotient (3) by 2:

Divide the quotient (1) by 2:

Reading the remainders in reverse order, the binary representation of the whole number part is 111111.

Fractional Part:

To convert the fractional part (0.25) to binary, we multiply the fractional part by 2 and note the whole number part of the result. Repeat this process until the fractional part becomes 0 or until the desired precision is achieved.

Multiply the fractional part (0.25) by 2:

Multiply the fractional part (0.5) by 2:

Since the fractional part becomes 0, we stop the process.

Reading the whole number parts in order, the binary representation of the fractional part is 01.

Combining the binary representation of the whole number part and the fractional part, the binary representation of the decimal number 63.25 is 111111.01.

About binary representation here:

https://brainly.com/question/29220229

#SPJ11

Step-by-step explanation:

the easiest way (at least for me) is to stay with the point-slope form and then transform it to get the slope-intercept form.

the general slope-intercept form is

y = ax + b

a being the slope, and b the y-intercept (the y-value when x = 0).

the general point-slope form is

y - y1 = a(x - x1)

a is again the slope, and (x1, y1) is a point on the line.

so,

1.

y - 1 = 2(x - 4)

y = 2(x - 4) + 1 = 2x - 8 + 1 = 2x - 7

y = 2x - 7

2.

y - 4 = 1/2 × (x - 2)

y = 1/2 × (x - 2) + 4 = x/2 - 1 + 4 = x/2 + 3

y = 1/2 × x + 3 or x/2 + 3

3.

y - 0 = 2/3 × (x - -6)

y = 2/3 × x + 4 or 2x/3 + 4

4.

y - -1 = -3/4 × (x - -8)

y + 1 = -3/4 × x - 6

y = -3/4 × x - 7 or -3x/4 - 7

5.

y - -3 = -1×(x - 4)

y + 3 = -x + 4

y = -x + 1

6.

y - -9 = 4(x - 0)

y + 9 = 4x

y = 4x - 9

Answer:

i got 16.25=2

Step-by-step explanation:

Answer:

X = - 12.8

Step-by-step explanation: