Andrea wanted to buyy some grapes. If she bought 8kg of grapes, she would be $3 short. If she bought 6kg of grapes, she would have $5 extra. What was the cost of 1kg of grapes?
(steps pls)

The commission is calculated as 12% of the portion of the weekly revenue that is over $1000. So, to calculate the commission, we subtract $1000 from the weekly revenue r, and then multiply the result by 0.12. The fixed salary of $500 is then added to the commission to get the total weekly salary.

Step-by-step explanation:

The formula that describes how the salesman's weekly salary s depends on his weekly revenue r is:

s = $500 + 0.12(r - $1000)

In this formula, s represents the salesman's total weekly salary, which includes both the fixed salary of $500 and the commission based on his weekly revenue. r represents the salesman's weekly revenue.

The commission is calculated as 12% of the portion of the weekly revenue that is over $1000. So, to calculate the commission, we subtract $1000 from the weekly revenue r, and then multiply the result by 0.12. The fixed salary of $500 is then added to the commission to get the total weekly salary.

To learn more about weekly visit:

https://brainly.com/question/4281863

#SPJ11

Answer:

The second one is your answer!!

Step-by-step explanation:

The total area of all six faces of the tunnel is \(614.197\pi\) square centimeters.

The surface area of the solid (\(A\)) used to represent the tunnel for a toy train is the sum of its six faces (two semicircular sections, inner semicircular arc section, outer semicircular arc section, two rectangles).

We calculate the surface area as following:

\(A = 2\cdot \frac{\pi}{2} \cdot [(10\,cm)^{2}-(8\,cm)^{2}] + \pi\cdot (8\,cm)\cdot (30\,cm) + \pi\cdot (10\,cm)\cdot (30\,cm) + 2\cdot (2\,cm)\cdot (30\,cm)\)

\(A = 614.197\pi\,cm^{2}\)

The total area of all six faces of the tunnel is \(614.197\pi\) square centimeters. \(\blacksquare\)

To learn more on surface areas, we kindly invite to check this verified question: https://brainly.com/question/2835293

Answer:

\(\dfrac{1}{729}\)

Step-by-step explanation:

\(\left(\dfrac{}{}(-3)^2\dfrac{}{}\right)^{-3}\)

First, we should evaluate inside the large parentheses:

\((-3)^2 = (-3)\cdot (-3) = 9\)

We know that a number to a positive exponent is equal to the base number multiplied by itself as many times as the exponent. For example,

\(4^3 = 4 \, \cdot\, 4\, \cdot \,4\)

       ↑1 ↑2 ↑3 times because the exponent is 3

Next, we can put the value 9 into where \((-3)^2\) was originally:

\((9)^{-3}\)

We know that a number to a negative power is equal to 1 divided by that number to the absolute value of that negative power. For example,

\(3^{-2} = \dfrac{1}{3^2} = \dfrac{1}{3\cdot 3} = \dfrac{1}{9}\)

Finally, we can apply this principle to the \(9^{-3}\):

\(9^{-3} = \dfrac{1}{9^3} = \boxed{\dfrac{1}{729}}\)

Answer:

30⁰ , 60⁰ , 90⁰

Step-by-step explanation:

Let the angles x , 2x , 3x

By angle sum property:

x + 2x + 3x = 180⁰

6x = 180⁰

x = 30⁰

Angles are : 30⁰ , 60⁰ , 90⁰

Let one angle be x, the second 2x and the third 3x.

x + 2x + 3x = 180 degrees (angle sum property of a triangle)

6x = 180 degrees

x = 180/6

x = 30 degrees

So one angle is 30°, the second is 60°, and the third is 90°.

Answer:

-15

Step-by-step explanation:

they are opposite angles so they are congruent

x+70=55

x=55-70

x=-15

The probability of both selected room air conditioners are defective is equal to 0.0952 rounded to four decimal places.

Total number of room air conditioners in shipment = 15

Number of defective room air conditioners = 5

The probability of the first air conditioner being defective is 5/15.

Since there are 5 defective air conditioners out of a total of 15.

After one air conditioner has been inspected,

There will be 4 defective air conditioners left out of a total of 14.

The probability of the second air conditioner also being defective, given that the first one was defective, is 4/14.

Probability of both air conditioners being defective.

Multiply probability of first air conditioner being defective by probability of second air conditioner being defective.

Given by first one was defective,

P(both defective) = (5/15) x (4/14)

Simplifying this expression ,

P(both defective) = 2/21

Therefore, the probability that the selected two air conditioners are both defective is 0.0952 rounded to four decimal places.

learn more about probability here

brainly.com/question/30613202

#SPJ4

The total number of possible combinations of numbers and letters on the license plates: 10 * 9 * 8 * 26 * 26 * 26

For the first number on the license plate, there are 10 options (0-9). For the second number, there are 10 options again, but since the numbers cannot be repeated, only 9 options are available. Similarly, for the third number, there are 10 options initially, but since the numbers cannot be repeated, only 8 options remain.

For the letters, there are 26 options for each position (first letter, second letter, and third letter) since all 26 letters of the alphabet can be used. The letters can be repeated, so there are no restrictions on the number of options for each letter.

To calculate the total number of different license plates, we multiply the number of options for each position together: 10 * 9 * 8 * 26 * 26 * 26. This gives us the total number of possible combinations of numbers and letters on the license plates.

Learn more about combinations of numbers here:

https://brainly.com/question/1380218

#SPJ11

Answer:

  (d)  1 mile = 10 blocks

Step-by-step explanation:

The ballpark is 8 blocks west and 15 blocks north of Jeff's home. The Pythagorean theorem tells us the straight-line distance is ...

  d² = 8² +15² = 64 +225 = 289

  d = √289 = 17 . . . blocks

The problem tells us this represents 1.7 miles, so the proportion is ...

  blocks/miles = 17 blocks/(1.7 miles) = 10 blocks/mile

The map scale is 1 mile = 10 blocks.

The data provide convincing evidence at the level that the mean salary for the baseball players on the east coast is different from $3.2 million.

To determine whether the data provide convincing evidence at the level that the mean salary for the baseball players on the east coast is different from $3.2 million, we need to conduct a hypothesis test.

The null hypothesis (H0) is that the mean salary for baseball players on the east coast is equal to $3.2 million, while the alternative hypothesis (Ha) is that the mean salary is different from $3.2 million.

H0: µ = $3.2 million

Ha: µ ≠ $3.2 million

Here, µ represents the population mean salary for baseball players on the east coast.

To conduct a significance test, we can use a t-test since the population standard deviation is not known and the sample size is less than 30.

The test statistic for this hypothesis test is:

t = (X - µ) / (s / √n)

where X is the sample mean, µ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Substituting the given values, we get:

t = (3.9 - 3.2) / (2.1 / √30)

t = 2.98

Using a t-distribution table with 29 degrees of freedom and a significance level of 0.05, we find the critical values to be ±2.045.

Since the calculated t-value of 2.98 is greater than the critical value of 2.045, we reject the null hypothesis (H0) and conclude that there is sufficient evidence to suggest that the mean salary for baseball players on the east coast is different from $3.2 million.

Therefore, the data provide convincing evidence at the level that the mean salary for the baseball players on the east coast is different from $3.2 million.

To know more about standard mean refer here:

https://brainly.com/question/31298828?#

#SPJ11

Given:

Fabric required for each chair = 10 yards

Fabric required for each sofa = 20 yards.

Total available fabric = 300 yards.

The number of sofas must be at least twice the number of chairs.

Profit on each chair = $50

Profit on each sofa = $80.

To find:

The function that represents the manufacturer's profit, P.

Solution:

Let P represents the manufacturer's profit, x represent the number of chairs and y represent the number of sofas.

Profit on 1 chair = $50

Profit on x chairs = $50x

Profit on 1 sofa = $80

Profit on y sofas = $80y

Total profit = Profit on x chairs + Profit on y sofas

\(P=50x+80y\)

Therefore, the required profit function is \(P=50x+80y\).

Answer:

B on edge

Step-by-step explanation:

Answer: 6. z<14 7. d≥18

Step-by-step explanation:

Standard error with equal n = S(m1 - m2 ) = √S₁²/n₁ + S₂²/n₂

and Standard error with unequal n = S(m1 - m2 ) = √Sp²/n₁ + Sp²/n₂

What is the standard deviation?

When comparing a population mean to a sample mean, the standard error of the mean, or simply standard error, shows how dissimilar the two are likely to be. It informs you of the degree to which the sample mean would fluctuate if the research were to be repeated with fresh samples drawn from the same population.

Standard error with equal n = S(m1 - m2 ) = √S₁²/n₁ + S₂²/n₂

Standard error with unequal n = S(m1 - m2 ) = √Sp²/n₁ + Sp²/n₂

Learn more about Standard error

brainly.com/question/13179711

#SPJ1

The complete question is -

In calculating the _____________(estimated standard error M1 - M2, pooled variance), you typically first need to calculate the ____________(estimated standard error M1 - M2, pooled variance). The ________________(estimated standard error M1 - M2, pooled variance) is the value used in the denominator of the t statistic for the independent-measures t tests.

Answer:

34

Step-by-step explanation:

Find h(-2) for h(r)= r^2 - 7r + 2

Simply put in -2   for 'r'

(-2)^2 - 7(-2) + 2 =

 4 -   - 28   + 2 =

 4+ 28 + 2 = 34

Answer:

11.2 and 78.8

Step-by-step explanation:

x + x + 67.6 = 90

2x = 22.4

x= 11.2 (first angle)

11.2 + 67.6 = 78.8 (second angle)

EXPLANATION:

Given;

We are given the revenue and cost function of a car wash facility as follows;

Also, we are told that in this function, x represents the number of cars washed.

Required;

We are required to calculate the profit when 10 cars are washed.

Step-by-step solution;

To begin, we will take note that the profit function is given as;

Therefore, to determine the profit at any level of input x, we would have;

We now substitute the values given;

Notice how the negative sign is distributed among the two values in the right parenthesis.

We can now determine the profit when 10 cars are washed, that is, when x = 10.

ANSWER:

The profit from washing 10 cars therefore will be $31.5

Answer:what

Step-by-step explanation:what does this mean

The closest integers to 44 are 43 and 45.

To complete the statement using the integers closest to the number in the middle, we need to determine the middle number in a sequence or set of numbers. However, the given prompt only provides the number "44" without any context or additional information.

If we assume that the number "44" is part of a sequence or set, we would need more information to determine the middle number and complete the statement accurately.

Without additional context or information, it is not possible to provide a specific answer or complete the statement. Please provide more details or clarify the question to assist further.

Learn more about integers

brainly.com/question/15276410

#SPJ11

Answer:reflects over y- axis, reflects over x- axis, 180

Step-by-step explanation:

Step-by-step explanation:

\(y = {2.5}^{2} - 2(2.5) - 3 \)

-1.75

Here we need to learn how to read a graph.

In a normal graph we have the inputs (the values of x) in the horizontal axis and the outputs in the vertical axis.

Here we want to see what is the value of y for the blue graph when x = 2.5

We will find y = -1.5

(the blue graph is the one that corresponds to: y = x^2 - 2x - 3)

To find this:

The first thing we need to do is find x = 2.5 in the horizontal axis.

Now that we found it, we need to draw a vertical line, and see at which point of the blue graph this vertical line intersects the curve. At that point we draw an horizontal line that intercepts the vertical axis.

At that point we have the y-value

You can see an example of this, a good estimation by only looking at the graph is y = -1.5

For the other point, the value of x when y = 1.

We do exactly the same thing but in the inverse order, we first find y = 1

Then we draw an horizontal line that intercepts the graph

Then we draw a vertical line that intercepts the x-axis and we find the value.

We can see that for y = 1 we have x = 3.2 aprox.

If you want to learn more you can read:

https://brainly.com/question/16781210

Answer:

68.8 square inches

Step-by-step explanation:

The total cost to produce a thousand pens can be calculated by substituting x = 1 into the cost function C(x) = x^2 - 4x + 28. The calculation yields C(1) = 1^2 - 4(1) + 28 = $25.

To find the total cost of producing 4810 pens, we substitute x = 4.81 into the cost function. The calculation gives C(4.81) = (4.81)^2 - 4(4.81) + 28 ≈ $4.89.

To minimize the cost, we need to find the production level at which the cost function is at its minimum. This can be determined by finding the x-coordinate of the vertex of the quadratic function C(x) = x^2 - 4x + 28. The x-coordinate of the vertex is given by x = -b/2a, where a and b are the coefficients of the quadratic function.

In this case, a = 1 and b = -4, so x = -(-4)/(2(1)) = 2. Therefore, to minimize the cost, the production level should be 2000 pens.

To find the minimum cost, we substitute x = 2 into the cost function. The calculation gives C(2) = 2^2 - 4(2) + 28 = $24. Hence, the minimum cost is $24.

Learn more about Cost function here :

brainly.com/question/29583181

#SPJ11

Adding a tracking variable to count the number of times a loop executes can be an effective way to measure the answer choice's truthfulness.

Adding a tracking variable to count the number of loop executions can indeed be a useful technique for various purposes. By incrementing the tracking variable within the loop, we can keep track of the number of times the loop body is executed. This information can be valuable in measuring the accuracy or efficiency of the loop and evaluating the truthfulness of an answer choice.

For example, when comparing different algorithms or approaches, counting loop iterations can help determine which solution performs better. It provides a quantitative measure to assess time complexity or resource usage. Additionally, the tracking variable can be used to validate the correctness of a loop by ensuring that the expected number of iterations is reached.

By monitoring the loop execution count, we can gain insights into the behavior of the code, identify potential issues such as infinite loops, and make informed decisions based on the observed results. Hence, adding a tracking variable to count loop executions can be an effective technique to measure the truthfulness or performance of an answer choice in certain scenarios.

Learn more about variable here:

https://brainly.com/question/16906863

#SPJ11

Step-by-step explanation:

Break it up into two trapezoids as shown

area = trap1 + trap2

      = 2 *   (7+3) / 2   + 3 *  ( 7 + 3) / 2 = 10 + 15 = 25 units^2

The value of x is equal to 15°

In Mathematics and Geometry, the sum of the exterior angles of both a regular and irregular polygon is always equal to 360 degrees.

Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.

By substituting the given parameters, we have the following:

3x + 4x + 8 + 5x + 5 + 6x - 1 + 5x + 3 = 360°.

3x + 4x + 5x + 6x + 5x + 8 + 5 - 1 + 3 = 360°.

23x + 15 = 360°.

23x = 360 - 15

23x = 345

x = 345/23

x = 15°.

Read more on sum of interior angles here: brainly.com/question/13293407

#SPJ1

Answer:

the value of x is 17 cm

Step-by-step explanation:

The computation of x is shown below:

Here we applied the pythagoreans theorem

x^2 = a^2 + b^2

x^2 = 15^2 + 8^2

X^2 = 225 + 64

x^2 = 289

x = sqrt(289)

= 17

Hence, the value of x is 17 cm

Answer:

-14

Step-by-step explanation:

2a + 4b

Let a = 5 and b = -6

2*5 +4(-6)

Multiply

10 - 24

Subtract

-14

Answer:

-14

Step-by-step explanation:

2a + 4b

= 2(5) + 4(-6)

= 10 -24

= -14

The solution to the given quadratic equation, x^2 + 5x + 6 = 0, is  x = -3 and x = -2

From the question, we are to solve the given quadratic equation.

The given quadratic equation is

x^2 + 5x + 6 = 0

First, we will write the given equation properly.

The given equation written properly is

x² + 5x + 6 = 0

Solving the equation by factoring

x² + 2x + 3x + 6 = 0

x(x + 2) +3(x + 2) = 0

(x + 3)(x + 2) = 0

x + 3 = 0 and x + 2 = 0

x = -3 and x = -2

Hence, the solution to the equation is x = -3 and x = -2

Learn more on Solving Quadratic equation here: https://brainly.com/question/24334139

#SPJ1

The relationship between a statistic and a parameter is the same as the relationship between , Option(A) a sample and a population

The Population is defied as an entire group of individuals that we are interested in studying, while a sample is a subset of that population that we actually observe and collect data from.

A Parameter is defined as a numerical characteristic of a population, such as its mean or variance, whereas a statistic is a numerical characteristic of a sample, such as its sample mean or sample standard deviation.

The relationship between a sample and a population is similar to the relationship between a statistic and a parameter because a sample is used to estimate  information about the population, and a statistic is used to estimate  information about a parameter.

Learn more about Parameter here

https://brainly.com/question/9192779

#SPJ4