the cost of two brands of a household is given. Find the unit price and tell which is better to buy. A) $6.15 for 24 fl oz of dishwashing liquid B: $9.60 for 42fl oz of dishwashing liquid A: $4.29 for 4 oz of shoe polish B: $6.33 for 6 oz of shoe polish

The utility company will have to increase its generating capacity by approximately 185.3% to meet the expected increase in electricity consumption over the next decade.

The problem involves the use of the exponential growth formula in mathematics, where we are given the current consumption of electricity in a city and we are asked to find the expected consumption of electricity after a certain period of time, assuming a fixed annual growth rate.

We can use the formula:

Here we have

A utility company in a western city in the United States expects the consumption of electricity to increase by 11%/year during the next decade, due mainly to the expected increase in population.

Let C₀ be the current consumption of electricity in the western city of the United States, and let C₁₀ be the expected consumption of electricity at the end of the decade.

We can use the following formula to calculate C₁₀:

C₁₀ = C₀ × (1 + r)ⁿ

Where r is the annual growth rate, n is the number of years

The amount by which the utility company will have to increase its generating capacity in order to meet the needs of the area at the end of the decade is given by the difference between C₁₀ and C₀

That is:

Amount of increase = C₁₀ - C₀

Substituting the values given in the problem, we get:

C₁₀ = C₀ (1 + 0.11)¹⁰

C₁₀/C₀ = (1.11)¹⁰

C₁₀/C₀ = (1.11)¹⁰

C₁₀ = C₀ × 2.84

Therefore, the amount by which the utility company will have to increase its generating capacity in order to meet the needs of the area at the end of the decade is:

Amount of increase =C₁₀ - C₀ = 2.853 × C₀ - C₀ = 1.853 × C₀

Therefore,

The utility company will have to increase its generating capacity by approximately 185.3% to meet the expected increase in electricity consumption over the next decade.

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The probability of drawing a prime is 40%.

To calculate the probability of drawing a prime number, use the formula

P(E) = Number of favorable outcomes / Total number of outcomes

Where P(E) is the probability of event E, and we determine the number of favorable outcomes and total possible outcomes based on the given conditions.

Here we have

Ten cards numbered 1 to 10 are placed in a box.  

The total number of outcomes will get in a random experiment = 10

Here set of prime numbers from 1 to 10 = {2, 3, 5, 7}

Number of favorable outcomes that are getting prime number = 4

Hence, the probability of getting a prime number

= 4/10 = 2/5 = 0.4 = 40%    [ Multiplied by 100 ]

Therefore,

The probability of drawing a prime is 40%.

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If a family chose to opt out of paying the $210 monthly premium for health insurance, they would not have coverage under the health insurance plan. This means that they would be responsible for paying for any medical expenses out of pocket.

Without health insurance, the cost of medical care can be quite high, and a family could potentially face financial ruin if they experienced a serious illness or injury. They may also be unable to afford routine check-ups or preventative care, which could lead to undiagnosed health issues.

It's important for individuals and families to carefully consider the costs and benefits of health insurance coverage, and to choose a plan that best fits their needs and budget. While the monthly premium may seem like a significant expense, the cost of not having coverage can be much higher in the long run.

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Answer:

the correct answer is option B.

Step-by-step explanation:

We can use the formula for the margin of error for a confidence interval for a population mean with a known population standard deviation:

Margin of error = z*σ/√n

where z is the critical value from the standard normal distribution for the desired confidence level (95% in this case), σ is the population standard deviation, and n is the sample size.

We are given that the margin of error is $135 and σ is $538. We need to find the sample size, n. To do this, we first need to find the appropriate value of z for a 95% confidence level. Using a standard normal distribution table or calculator, we can find that z = 1.96.

Substituting the values into the margin of error formula and solving for n, we have:

$135 = 1.96*($538)/√n

Squaring both sides and solving for n, we get:

n = [1.96*($538)/$135]^2 ≈ 62

Therefore, a sample size of 62 business students must be randomly selected to estimate the mean monthly earnings of business students at one college with 95% confidence that the sample mean is within $135 of the population mean, assuming the population standard deviation is known to be $538.

So the correct answer is option B.

Step-by-step explanation:

what "normal" trigonometric function did this remind us of ?

it starts at "high" for x = 0.

"high" signs mean "1" for the standard functions.

the trigonometric function that starts with 1 at x = 0 is cosine.

so, this is a cosine function that we need to scale properly.

original value : 1

graph : 15

original value : -1

graph : 12

original value : 0

graph : (15+12)/2 = 27/2 = 13.5

so, we need to add this to the cosine function result.

the distance from the 0 level (13.5) to high or low is 1.5 (instead of originally 1).

Du, we need to stretch the cosine function result to go from -1.5 to +1.5 (12 to 15).

and for the x-axis :

12 hours = 180° or pi (the interval for cosine to go from +1 to -1).

1 hour = 180/12 = 15° or pi/12.

so, for cosine to react to the hour value as for the curdling degrees we need to multiply x by 180/12 or by pi/12.

so, our temperature function temp(x) is then

temp(x) = 1.5×cos(x×180/12) + 13.5

or

temp(x) = 1.5×cos(x×pi/12) + 13.5

Answer:

The probability of not getting a blue marble is the probability of getting either a red or a green marble. P(not blue) = P(red or green) P(red or green) = P(red) + P(green) P(red or green) = 8/12 + 1/12 P(red or green) = 9/12 P(not blue) = 3/4 Therefore, the answer is D. three-fourths.

So, the answer in its simplest form is 1/200.a) Here's the completed frequency tree: Drink tea.

So, the number of people who drink at least 3 cups of tea each day is:[tex]10 * 0.2 = 2[/tex]Therefore, the fraction of the 400 people who drink at least 3 cups of tea each day is: 2 / 400This fraction can be simplified by dividing both the numerator and the denominator by their greatest common factor, which is 2:1 / 200So, the answer in its simplest form is 1/200.

A fraction is a numerical quantity representing a part of a whole or a ratio between two quantities. It is expressed as one number (the numerator) divided by another number (the denominator), separated by a horizontal line. The numerator represents the number of parts being considered, while the denominator represents the total number of equal parts that make up the whole. For example, in the fraction 3/4, the numerator is 3, which represents three parts out of a total of four equal parts. Fractions can be used to represent many different types of quantities, such as parts of a whole, ratios, percentages, and probabilities.

b) Out of the 400 people, 10 said yes to drinking tea, and 20% of those (or 0.20*10 = 2) said they drink at least 3 cups each day. Therefore, the fraction of people who drink at least 3 cups of tea each day is 2/400, which simplifies to 1/200.

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The solutions are explained below.

Given that, Jeremy and Leslie are each flying their own drones in a flat field with their drones hovering between the two of them. The figure is attached.

Height of Jeremy's drone = 30 m

Height of Leslie's drone = x m

h / 70 = sin 53°

h = 70 × sin 53°

h = 57.34

Therefore, Leslie's drone is higher than Jeremy's drone.

Difference of height = 57.34 - 30 = 27.34 m

27.34 / x = tan25°

x = 58.63 m

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Answer:

Step-by-step explanation:

$499.99 - 15% will give your answers

Answer:

424.99

Step-by-step explanation:

Answer: 63,932

Step-by-step explanation:

September: 11,724

October: 14,380 + 11,724 = 26,104

November: 14,380 + 11,724 = 26,104

Combine all 3 months to get your answer= 63,932

Answer:

6xy^2/(x-y)(x+y)(2x+y)(2x-y)

Step-by-step explanation:

1      - 2          +   1          - 2

x-y     2x+y         x+y        2x-y

= take LCM

Then simplify.

Answer:

-2x+2/x

Step-by-step explanation:

If the number of students who walk is represented by x, then the number of students who ride the school bus is 110% of x, which can be written as:

1.10x

This is because 110% can be written as 1.10 (since 110% means 110 out of 100).

So, if we know the value of x, we can multiply it by 1.10 to find the number of students who ride the school bus.

However, we don't know the value of x in this problem. Therefore, we cannot find the exact number of students who ride the school bus.

Answer:If the number of students who walk is represented by x, then the number of students who ride the school bus is 110% of x, which can be written as:

1.10x

This is because 110% can be written as 1.10 (since 110% means 110 out of 100).

So, if we know the value of x, we can multiply it by 1.10 to find the number of students who ride the school bus.

However, we don't know the value of x in this problem. Therefore, we cannot find the exact number of students who ride the school bus.

Step-by-step explanation:

Answer:

145°

Step-by-step explanation:

The exterior angle 3 is equal to the sum of angle 1 and 2.

Using substitution we can say that:

5x + 4x + 10 = 10x -5

9x + 10 = 10x -5

10x-9x=10+5

x= 15

We have just found that the value of x is equal to 15.

By substituting this back to the angle 3 expression, 10x-5, we get

10(15) - 5

150 - 5

145°

A)The volume of cat food in the can is 9.62 cubic inches .

B) A ratio to show cubic inches to ounces is 4.83.

What is a cylinder?

A cylinder is a three-dimensional geometric shape that has two congruent circular bases connected by a curved surface.

The volume of a cylinder can be calculated using the formula

=> [tex]V = \pi r^2h,[/tex]

where r is the radius of the circular base, h is the height of the cylinder, and π is the mathematical constant pi (approximately equal to 3.14).

To find the volume of the cat food in the can, we need to use the formula for the volume of a cylinder,

Since the diameter is 3.5 inches, the radius is half of that, which is 1.75 inches. The height is 1 inch.

So,[tex]V=3.14\times(1.75)^2\times1[/tex] = 9.62 cubic inches (rounded to the nearest hundredth).

Therefore, the volume of cat food in the can is approximately 9.62 cubic inches.

Now ,To find the ratio of cubic inches to ounces,

Since the can holds 5.8 ounces of cat food, we can find the volume of cat food in cubic inches by dividing the weight by the density:

=> 5.8 ounces / 1.2 ounces per cubic inch

= 4.83 cubic inches (rounded to the nearest hundredth).

Therefore,  a ratio to show cubic inches to ounces is 4.83.

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The correct answer for this would be: Triangles BCA and DAC are congruent according to the Angle-Side-Angle (ASA) Theorem.

A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.

According to the ASA theorem, if the included side of one triangle and its two angles are comparable to the parts of another triangle, then the triangles are said to be congruent.

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Answer: 234 are sophomores

Step-by-step explanation:

You would take 26% of 900 to get 234

It's simple, don't overthink it :)

Have a nice day.

Step-by-step explanation:

Sophomores are 26 % of 900 students

26 %  * 900 = the number of sophomores

26% * 900 =  .26 * 900 = 234 sophomores

So, (f o h)(-3) = 3. This is the value of the composite function (f o h) at -3. Please note that (f o h)(-3) is equivalent to f(h(-3))

An input and an output are connected by a function. It functions similarly to a machine with an input and an output. Additionally, the input and output are somehow connected. The traditional format for writing a function is f(x) "f(x) =... "

To find (f o h)(-3), we need to first evaluate h(-3), and then plug that result into the function f(x).

Given:

f(x) = -2x - 1

h(x) = -x - 5

First, we evaluate h(-3):

h(-3) = -(-3) - 5

h(-3) = 3 - 5

h(-3) = -2

Now, we plug the result of h(-3) into the function f(x):

f(h(-3)) = f(-2)

f(h(-3)) = -2(-2) - 1

f(h(-3)) = 4 - 1

f(h(-3)) = 3

So, (f o h)(-3) = 3. This is the value of the composite function (f o h) at -3. Please note that (f o h)(-3) is equivalent to f(h(-3)), which means we first evaluate h(-3) and then plug that result into f(x). I hope this helps! Let me know if you have any further questions. :)

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Answer:

2 [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

1 1/9 x 2 2/5 = ?

1 1/9 = 10/9

2 2/5 = 12/5

[tex]\frac{10}{9}[/tex] x [tex]\frac{12}{5}[/tex] = [tex]\frac{120}{45}[/tex] = [tex]\frac{8}{3}[/tex] = 2 [tex]\frac{2}{3}[/tex]

So, the answer is 2 [tex]\frac{2}{3}[/tex]

[tex]yx=5[/tex]

Explanation:

If [tex]y[/tex] varies inversely as [tex]x[/tex] then

         [tex]y\times x=k[/tex] for some constant [tex]k[/tex]

Since [tex]y = \frac{1}{8}[/tex] when [tex]x=40[/tex]

          [tex]\huge \text(\dfrac{1}{8}\huge \text)\times(40)=k[/tex]

          [tex]\longrightarrow k=5[/tex]

Both the lines are parallel hence, they cannot intersect each other and value of H= (0,0).

A mathematical statement known as an equation consists of two algebraic expressions separated by equal signs (=) on either side.

It demonstrates the equality of the relationship between the printed statements on the left and right.

Left side equals right side in all formulas.

To find the values of unknowable variables, which stand in for unknowable quantities, you can solve equations.

A statement is not an equation if it lacks the equals sign.

When two expressions have the same value, a mathematical statement known as an equation will include the symbol "equal to" between them.

Hence, Both the lines are parallel hence, they cannot intersect each other and value of H= (0,0).

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The GPA corresponding to the 70th percentile at the college is approximately 3.246 based on standard deviation.

We can use the conventional normal distribution table or a calculator with a normal distribution function to determine the 70th percentile of GPAs at a college, which are normally distributed with a mean of 2.9 and a standard deviation of 0.6.

The inverse normal distribution function with a mean of 2.9, a standard deviation of 0.6, and a percentile of 70 can be used on a calculator. This results in:

[tex]3.246 for invNorm(0.7, 2.9, 0.6).[/tex]

As a result, the GPA that represents the 70th percentile is roughly 3.246.

We can determine the z-score corresponding to the 70th percentile, which is 0.5244, by using a common normal distribution table. Thus, we may apply the equation z = (x - ) /, where x is the GPA that corresponds to the 70%ile, is the mean, and is the standard deviation, and all three variables have values of 2.9. After finding x, we obtain:

0.5244 = (x - 2.9) / 0.6

x = 3.246

Once more, doing so yields the same outcome as using a calculator.

In conclusion, the GPA at the college that represents the 70th percentile is roughly 3.246.

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Answer: 18 students

Step-by-step explanation: 43+27+48=118 118-100=18

Step-by-step explanation:

It is not clear from the given information which angles and sides are being referred to as "107⁰", "-x-8", "-42-7", and "3y-1". However, we can use some properties of rhombuses to solve for x, y, and z.

Opposite angles in a rhombus are equal. Therefore, if one angle is 107⁰, then the opposite angle is also 107⁰.

The diagonals of a rhombus are perpendicular bisectors of each other. This means that they intersect at a right angle and divide each other into two equal parts.

The diagonals of a rhombus bisect each other's angles. This means that the angles formed by each diagonal with the sides of the rhombus are equal.

Using these properties, we can set up some equations to solve for x, y, and z:

Let's assume that "-x-8" and "-42-7" are the lengths of the diagonals of the rhombus, and that "3y-1" is the length of one of the sides.

Since the diagonals bisect each other's angles, we know that the angles formed by each diagonal with the side of the rhombus are equal. Let's call each of these angles "z":

-z + 107⁰ + z = 180⁰ (sum of angles in a triangle)

107⁰ = 180⁰ - 2z

2z = 73⁰

z = 36.5⁰

Now let's use the fact that the diagonals are perpendicular bisectors of each other:

(-x-8)/2 = (-42-7)/2

-x-8 = -49

-x = -41

x = 41

Finally, let's use the fact that the sides of a rhombus are equal:

-x-8 = 3y-1

41-8 = 3y-1

33 = 3y

y = 11

Therefore, the values of x, y, and z in the rhombus are:

x = 41

y = 11

z = 36.5⁰

The total amount that he will pay for the car will be $17,093.40, assuming a loan amount of $15,000, a down payment of $4,300, a 5-year loan term, and a 5.25% APR.

Assuming that Dean has used the $4,300 as a down payment, his loan amount would be the total cost of the car minus the down payment, which is not given in the question.

However, assuming that the loan amount is $15,000 (which would be the case if the total cost of the car was $19,300), the monthly payment would be $284.89.

To calculate the total amount that Dean pays for the car over the course of the loan, we can multiply the monthly payment by the number of payments (60 payments over 5 years) and add the down payment:

Total amount = (Monthly payment x Number of payments) + Down payment

Total amount = ($284.89 x 60) + $4,300

Total amount = $17,093.40

Therefore, if Dean gets the loan and pays it off as scheduled, the total amount that he will pay for the car will be $17,093.40.

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The answer choice which is not a true statement include the following: C. the solution set of |3k + 3| ≤ -9 is {k|-4 ≥ k ≥ 2}.

In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;

In order to determine the solution set to the given inequality, we would write out the absolute value function (inequality) as shown below.

|3k + 3| ≤ -9

Since |3k + 3| would always be positive and negative nine (-9) is negative,  |3k + 3| will always be greater than negative nine (-9), and as such, the inequality cannot be true and has no solution set.

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Let's add the fractions first and then we can estimate the sum.

[tex]= \dfrac{2}{3} +\dfrac{3}{4}[/tex]

change to common denominators

[tex]= \dfrac{8}{12} +\dfrac{9}{12}[/tex]

add numerators only

[tex]\dfrac{17}{12}[/tex] or [tex]1\dfrac{5}{12}[/tex] or [tex]1.42[/tex]

ANSWER: 13 is the best estimate of the answer. Normally we round up to 1.4 with a number like 1.42, but since that is not a choice, we can estimate 1 as the answer.

Answer:

Step-by-step explanation:

To find the direction of minimum rate of change for the function f(x, y) = x² + xy + y² at the point (5, 2), we need to find the gradient vector (also known as the gradient or the vector of partial derivatives) and then find the direction orthogonal to the gradient vector, as this direction will have the minimum rate of change.

First, let's find the gradient vector by computing the partial derivatives of f(x, y) with respect to x and y:

∂f/∂x = 2x + y

∂f/∂y = x + 2y

Now, evaluate the gradient vector at the point (5, 2):

∇f(5, 2) = (2(5) + 2, 5 + 2(2)) = (12, 9)

The gradient vector is (12, 9). To find the direction orthogonal to the gradient vector, we can swap the x and y components and negate one of them. Since the question asks for a vector with an x-component of 1, 0, or -1, we'll negate the x-component:

Orthogonal vector = (-1, 12)

So, the direction of minimum rate of change at point (5, 2) is given by the vector [-1, 12].