An t-shirt was originally priced at 45, but was placed on sale for 10% off the original price. If a sales tax of 8% was added on to the sale price what did the t-shirt cost at the register, including the tax?

Answer: x 33/5

Step-by-step explanation:

Answer: 9/11

Step-by-step explanation:

Step 1: Cross-multiply.

3/11 = x/3

(3)*(3) = x*(11)

9 = 11x

Step 2: Flip the equation.

11x = 9

Step 3: Divide both sides by 11.

11x/11 = 9/11

x = 9/11

Answer:

We can start solving this problem by finding the two numbers that bound the range of integers we're looking for.

First, we can approximate $\sqrt{5}$ to the nearest integer by finding the square root of 5. We know that 2^2 = 4 and 3^2 = 9, so 2 < $\sqrt{5}$ < 3. Therefore, $\sqrt{5}$ is a little bit more than 2 and a little bit less than 3.

Therefore, there are 6 integers that fall between $\sqrt{5}$ and $\sqrt{50}$ on a number line.

Step-by-step explanation:

Similarly, we can approximate $\sqrt{50}$ to the nearest integer by finding the square root of 50. We know that 7^2 = 49 and 8^2 = 64, so 7 < $\sqrt{50}$ < 8. Therefore, $\sqrt{50}$ is a little bit more than 7 and a little bit less than 8.

Now we know that the range of integers we are looking for is between 2 and 7, inclusive. There are 7-2+1 = 6 integers between 2 and 7: 2, 3, 4, 5, 6, 7.

Therefore, there are 6 integers that fall between $\sqrt{5}$ and $\sqrt{50}$ on a number line.

Answer:

Step-by-step explanation:

The functions

Axis of symmetry is defined by x- value of the vertex which is calculated by a formula -b/2a

Ranking in ascending order is

The probability that all of them get the same number is 1/36.

Given :

Three people are asked to throw a fair die.

Probability :

Probability is a branch of mathematics that deals with the occurrence of a random event.

In one dice probable outcomes 1, 2, 3, 4, 5 and 6

Total out comes in three dice = ( 6 * 6 * 6 = 216 )

Probability of getting 1 = 1/216

Similarly for 2, 3, 4, 5 and 6

Probability of getting same number = 6 * 1/6 * 1/6 * 1/6

= 6*1/6 * 1 * 1 / 6 * 6

= 6/6 * 1/36

= 1 * 1/36

= 1/36

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Answer:

Step-by-step explanation:

y = mx + b  <-- slope intercept form

Looking at the line from point (0,-5) to (3,0)

The slope (mx), rise over run

Rises 5 (in the positive direction, up) and runs 3 (in the positive direction, right)

the slope being 5/3

Then the b being your y-intercept

-5 will be your b because the line crosses the y axis at (0,-5) but the y-intercept is -5

Overall: y = \(\frac{5}{3}\) x + (-5)

or

y = 5/3 x - 5

The equation of the line in slope intercept form is y = 6x + 5

The given parameters are

Slope, m = 6

Points, (x₁, y₁) = (-2, -7)

A linear equation can be represented as

y = slope * x + y-intercept

i.e.

y = m(x - x₁) + y₁

Substitute the known values in the above equation

So, we have the following equation

y = 6(x + 2) - 7

Expand

y = 6x + 12 - 7

Evaluate the like terms

y = 6x + 5

Hence. the linear equation is y = 6x + 5

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The length of the shorter leg is 2.5 feet and the longer leg is 4.5 feet.

It is important to note that the Pythagoras theorem states that the square of the sides are equal to the hypotenuse.

This will be:

a = First leg = x

b = Second leg = x + 4

c = Hypothenuse = 7

This will then be:

a² + b² = c²

x² + (x + 4)² = 7²

x² + x² + 8x + + 16 = 49

Collect like terms

2x² + 8x + 16 - 49

2x² + 8x - 33

Using the quadratic formula, x = 2.5.

Therefore shorter leg = 2.5 feet

Longer leg = 2.5 + 4 = 6.5 feet

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The first step needed to solve the equation of the word sentence, 4 over 7 multiplied by x minus 5 equals negative 13, is to add 5 to both sides.

According to the question,

We have the following information:

4 over 7 multiplied by x minus 5 equals negative 13

Now, we will first convert this word sentence into an expression:

(4/7)x-5 = -13

Or this equation can rewritten as follows:

4x/7-5 = -13

Now, the first step to solve this equation should be to add 5 on both sides of the equation.

(More to know: we can easily solve this equation to find the value of x.)

Hence, the correct option is A.

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Answer: B. 4 × 10⁻⁵

Step-by-step explanation:

0.00003762 = 3.762 × 10⁻⁵ ≈ 4 × 10⁻⁵

Answer:

b

Step-by-step explanation:

\(4 \times {10}^{ - 5} = 4 \times \frac{1}{100000} \)

In the given public good provision game, player 1's expected payoff for contributing and not contributing depends on player 2's cutoff point (C*₂). When player 1 contributes, their payoff is v - C₁ if C₁ < C*₂, and 0 if C₁ ≥ C*₂. When player 1 does not contribute, their payoff is always 0.

In this public good provision game, player 1's decision to contribute or not contribute depends on their private cost, C₁, and player 2's cutoff point, C*₂. If player 1 contributes, they incur a cost of C₁ but gain access to the public good valued at v dollars. However, if C₁ is greater than or equal to C*₂, player 1's expected payoff for contributing would be 0 since player 2 would not contribute.

On the other hand, if player 1 does not contribute, their expected payoff is always 0, as they neither incur any cost nor receive any benefit from the public good. Therefore, player 1's expected payoff for not contributing is constant, irrespective of the cutoff point.

To determine player 1's expected payoff for contributing, we consider the case when C₁ is less than C*₂. In this scenario, player 2 contributes to the public good, allowing both players to consume it. Player 1's payoff would then be v - C₁, which represents the value of the public good minus their cost of contribution. However, if C₁ is greater than or equal to C*₂, player 1's contribution would be futile, as player 2 would not contribute. In this case, player 1's expected payoff for contributing would be 0, as they would not gain access to the public good.

In summary, player 1's expected payoff for contributing is v - C₁ if C₁ < C*₂, and 0 if C₁ ≥ C*₂. On the other hand, player 1's expected payoff for not contributing is always 0. Therefore, when C₁ is low, player 1 would prefer to contribute, as long as the cost of contribution is less than player 2's cutoff point.

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The.maximum number of gigabytes Meena can use while staying within her budget is 5 gigabytes

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal.

They are denoted by the symbols ≥ < > ≤.

Let the maximum gigabytes be x.

The inequality to illustrate the information will be:

38 + 3x < 55

Collect like terms

3x < 55 - 38

3x < 17

Divide

x < 17/3

x < 5 2/3

The maximum gigabytes is 5.

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The probability that there are at least 10 neutrophils in a field of 50 bone marrow cells, given that the probability of a single bone marrow cell being a neutrophil is 0.2, is approximately 0.034.

In this problem, we are given that the number of neutrophils in a field of 50 bone marrow cells follows a binomial distribution with a probability of success, i.e., the probability of a single bone marrow cell being a neutrophil, p=0.2. We need to find the probability that there are at least 10 neutrophils in the field.

To solve this problem, we can use the cumulative distribution function (CDF) of the binomial distribution. The CDF gives the probability of getting up to a certain number of successes in a given number of trials.

Using a binomial distribution calculator or a statistical software package, we can find that the probability of getting 10 or more neutrophils in the field is approximately 0.034. Therefore, the probability that there are at least 10 neutrophils in the field is 0.034.

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Question: In a laboratory biopsy, a field of 50 bone marrow cells is observed under a microscope. A special dye is inserted, which only the neutrophils absorb. Then, the number r of neutrophils in the field is counted. What is the probability that there are at least 10 neutrophils in the field if the probability of a single bone marrow cell being a neutrophil is 0.2? Assume that the number of neutrophils in the field follows a binomial distribution.

Answer:

\(1*2^{24}\)=16777216

Step-by-step explanation:

y=C*2^t is the equation for this type of growth

C is starting population and t is time

C=1 and t=24 (1 day= 24 hours)

Solve

Answer:

D is a correct answer..

Answer:

3/8 unit

Step-by-step explanation:

\( \sqrt[3]{ \frac{27}{64} } = \frac{3}{8} \)

Answer:

The length of the cube is 3/4 units.

Step-by-step explanation:

Answer:

Irrational

Step-by-step explanation:

40 is not a perfect square.

Answer:

irrational

Step-by-step explanation:

40 isnt a perfect square where if you want to know weather it is or not you put the square root of any number on the calculator and if it's the same answer or in the answer there is a square root then it is an irrational number

Answer:

AB = 5.2 cm , ED = 5 cm

Step-by-step explanation:

Δ ABE and Δ ACD are similar by the AA postulate

Then the ratios of corresponding sides are in proportion , that is

(a)

\(\frac{AB}{AC}\) = \(\frac{BE}{CD}\) , substitute values

\(\frac{AB}{11.7}\) = \(\frac{6}{13.5}\) ( cross- multiply )

13.5 × AB = 70.2 ( divide both sides by 13.5 )

AB = 5.2 cm

-------------------------------------------

(b)

\(\frac{AE}{AD}\) = \(\frac{BE}{CD}\) , substitute values

\(\frac{4}{AD}\) = \(\frac{6}{13.5}\) ( cross- multiply )

6 × AD = 54 ( divide both sides by 6 )

AD = 9

Then

ED = AD - AE = 9 - 4 = 5 cm

It is important to remember that the null hypothesis is only accepted or rejected, not proved or disproved. Therefore, this experiment should be repeated multiple times with different test subjects to get a better sense of the validity of the alternative hypothesis.

The null hypothesis to test your friend's claim is that the average time to walk to class from your dorm is 10 minutes.

This can be tested by having multiple people time themselves walking from the dorm to class and averaging the results. If the average time is greater than 10 minutes, then the null hypothesis is rejected, and the alternative hypothesis is accepted - that the average time is 7 minutes. If the average time is less than 10 minutes, then the null hypothesis is accepted, and the alternative hypothesis is rejected.

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1a. To find out whether the number of eggs consumed is proportional to the population size, we need to calculate the number of eggs per person for both countries. For United States the number of eggs per person would be: 5.070 million/325 million ≈ 0.0156 eggs/person.For Republica the number of eggs per person would be: 902 million/55 million ≈ 16.4 eggs/person.Since the number of eggs consumed per person is significantly different in the two countries, the relationship is not proportional.

1b. Since the number of eggs consumed is NOT proportional to the population size, we can conclude that eggs are a more popular food in Republica, as the number of eggs per person is much higher in that country. If a country of 86 million people consumes eggs proportional to the Republica, we can expect them to consume 86 million × 16.4 eggs/person = 1.41 billion eggs.2a. The population of the U.S. is 325 million − 55 million = 270 million more than the population of Republica.2b. The population of the U.S. is 325 million/55 million × 100% − 100% = 490.91% more than the population of Republica, which is rounded to 1 decimal place.2c.

The population of Republica is 55 million/325 million ≈ 0.169 times the size of the population of the U.S., which is rounded to 3 decimal places.2d. The population of Republica is 55 million/325 million × 100% ≈ 16.92% of the population of the United States, which is rounded to 1 decimal place.3. To calculate the density of cattle (number of cattle per square mile), we need to divide the number of cattle by the area of the country.3a. The density of cattle in the United States would be: 75.9 million/3.797 million sq mi ≈ 19.99 cattle/sq mi, which is rounded to the nearest whole number.3b. The density of cattle in Republica would be: 47.3 million/1.077 million sq mi ≈ 43.89 cattle/sq mi, which is rounded to the nearest whole number.3c. There are more cattle per square mile in Republica than in the United States. The density of cattle in Republica is 43.89/19.99 ≈ 2.195 times the density of cattle in the United States.3d. The density of cattle in Republica is 43.89/19.99 × 100% ≈ 219.61% of the density of cattle in the United States.

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The number of eggs consumed is not proportional to the population size. Eggs are a more popular food in Republica. The population of the U.S. is 270 million more than Republica's population. The population of Republica is 16.9% of the population of the United States. The density of cattle in Republica is higher than in the United States.

To determine if the number of eggs consumed is proportional to the population size, we need to calculate the ratio between the two for both countries:
For the United States: 5.070 million eggs / 325 million population = 0.0156 eggs/person
For Republica: 902 million eggs / 55 million population = 16.4 eggs/person
Since the ratios are not equal, the number of eggs consumed is not proportional to the population size.

Since the number of eggs consumed is not proportional to the population size, we can conclude that eggs are a more popular food in Republica because their ratio of eggs consumed to population size is significantly higher compared to the United States.

The population of the U.S. is 325 million - 55 million = 270 million people more than the population of Republica.

The population of the U.S. is approximately 490.9% more than the population of Republica.

The population of Republica is 55 million / 325 million = 0.169 times the size of the population of the U.S.

The population of Republica is approximately 16.9% of the population of the United States.

The density of cattle in the United States is 75.9 million cattle / 3.797 million square miles = 20 cattle per square mile.

The density of cattle in Republica is 47.3 million cattle / 1.077 million square miles = 43.9 cattle per square mile.

The absolute comparison of cattle density shows that there are more cattle per square mile in Republica because the density is higher (43.9 cattle per square mile) compared to the United States (20 cattle per square mile).

The relative comparison of cattle density shows that cattle are more concentrated in Republica because the density in Republica (43.9 cattle per square mile) is higher than in the United States (20 cattle per square mile).

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Answer:

Step-by-step explanation:

C

the equation would be y=2x+4

The solution is Option C.

The linear equation is given as y = 2x + 4

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the x values be = { -4 , -2 , 0 , 2 }

Let the y values be = { -4 , 0 , 4 , 8 }

The slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 0 - ( -4 ) / ( -2 - ( - 4 ) )

On simplifying the equation , we get

Slope m = 4/2 = 2

Now , the equation of line is

y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 0 = 2 ( x - ( -2 ) )

On simplifying the equation , we get

y = 2x + 4

Hence , the linear equation is y = 2x + 4

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The maximum rectangular area that can be fenced can be

2499 sq meters.

We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.

We know for a quadrilateral, A square has the maximum area.

We also know That the product of two numbers is maximum when the difference between them is minimum.

Given, A farmer has 2,000 meters of fencing and wants to use it to create a rectangular area for grazing.

So, 2(l + b) = 2000.

l + b = 1000.

For a square, it would be 500 and 500, But to be a rectangle it can be 49 and 51.

Therefore, The maximum area would be,

= (51×49) sq meters.

= 2499 sq meters.

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The sum of the first 200 multiples of 3 is 60,300(B).

To find the sum of the first 200 multiples of 3, we need to calculate the arithmetic series. The formula for the sum of an arithmetic series is Sn = (n/2)(a + l), where Sn is the sum, n is the number of terms, a is the first term, and l is the last term. In this case, the first term (a) is 3, and the last term (l) is 3 * 200 = 600.

Plugging these values into the formula, we get Sn = (200/2)(3 + 600) = 100 * 603 = 60,300. Thus, the sum of the first 200 multiples of 3 is 60,300(C).

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Answer:

6565 = 1010(4) + 2525

Step-by-step explanation:

so the equation would be

6565 = 1010x + 2525

x = 4 because

1010 (4) = 4040

and 4040 + 2525 = 6565, so

6565 = 1010(4) + 2525

Answer: x=35

Step-by-step explanation: hi! i’m happy to help. subtract the three from both sides, multiply the entire problem by 5 to even out the x, and there’s your answer :)

The speed of the scooter is 1/2 miles per minute.

The time traveled by an object or person in any direction in a particular period of time is called speed. Speed is a scalar quantity that has no direction, it has only magnitude.

Uniform speed, variable speed, average speed, and instantaneous speed are the four kinds of speed.

To find the required speed of a scooter, you can use the following formula:

Speed= Distance/Time

Here given that, the scooter traveled 1/4 miles in 1/2 minute.

By applying the formula,

speed=(1/4)miles/(1/2)minutes

=1/2 miles/minute

Therefore, the speed of the scooter is 1/2 mile/minute.

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Half a mile per minute is the speed at which the scooter moves.

Speed is the amount of time it takes for a person or object to move in any direction over a predetermined amount of time. Speed is a scalar quantity with only magnitude and no direction.

Uniform, variable, average, and instantaneous speeds are the four different types of speed.

Apply the following formula to determine the required speed for a scooter:

Time/Distance = Speed

As a result, the scooter traveled a quarter mile in just over a minute.

Using the equation,

speed=(1/4)miles/(1/2)minutes

50/60 miles per hour

The scooter moves at a speed of half a mile per minute as a result.

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a. The MRS is constant (not diminishing) at 1/3.

U(x,y) = 3x + y

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = 1 / 3

The MRS is constant (not diminishing) at 1/3.

b. The MRS is diminishing because as y increases, the MRS decreases.

U(x,y) = x * y

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = 1 / y

The MRS is diminishing because as y increases, the MRS decreases.

c. The MRS is diminishing because as y increases, the MRS decreases.

U(x,y) = x * y

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = 1 / y

Similar to the previous case, the MRS is diminishing because as y increases, the MRS decreases.

d. The MRS depends on the ratio of y to x and can vary.

U(x,y) = x^2 - y^2

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = -2y / 2x = -y / x

The MRS depends on the ratio of y to x and can vary. It is not necessarily diminishing.

e. The MRS depends on the values of x and y and can vary.

U(x,y) = x + y / (x * y)

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = -1 / (y^2) + 1 / (x^2 * y)

The MRS depends on the values of x and y and can vary. It is not necessarily diminishing.

Now let's move on to the second part of the question:

For parts a, b, and c, we need more specific information about the utility functions, such as the values of α and β, to calculate the demand curves for x and y, the indirect utility function, and the expenditure function.

To show that the demand curve is homogeneous in degree zero in terms of income and prices, we need the specific functional form of the utility functions and information about the prices of x and y. Please provide the necessary details for parts A, b, and c to continue the analysis.

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Answer:

2/45

Step-by-step explanation:

If the radius is quadrupled, then the area of the new area to the old area will be 4:1

You should be aware that the quadrupled of a circle is four times the area of the old one.

In this case the area of the circle is denoted by

Area = πr²

Where r= radius=6 cm

The area of the old circle is 22/7 * 6 * 6

Area of the circle is = 113.1cm²

To this effect, the area of the new circle is 4(area of the old one)

Area = 4*22/7 * 6 * 6

Area = 3167/7

Area is = 452.6

This implies that 4(113.2) =452.6

In conclusion, you will discover that four times the area of the new circle is the old circle

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hello

we are requested to perform a basic arithmetic of 51 * 37

we can easily solve this by using the multiplication operator in our calculator or following through the basic method manually.

the answer to this question is 1887