What is the solution to the equation 10^x=23? a) x = log 33 b) x = log 23 c) x = log 13 d) x = log 130​

x = 108 is 3.10 standard deviations to the left of the mean.

The standard deviation (SD, also written as the Greek symbol sigma or the Latin letter s) is a statistic that is used to express how much a group of data values vary from one another.

The z-score when x = 108 is:

z = (108 - 153) / 14.5

z = -3.10

This tells us that x = 108 is 3.10 standard deviations to the left of the mean.

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Answer:

2.15g + 0.75w = 20.35

Step-by-step explanation:

(no explanation needed)

There are 813 minutes in between 17:53 to 7.26 .

Time can be represented in two formats, that is in a twelve - hour format and in a twenty four - hour format.

Here the time 17:53 and 7:26 is represented in twenty four - hour format where the day is divided in twenty four hours and time runs from midnight and ends at midnight.

(If the time 17:53 and 7:26 was represented in twelve - hour format then it would have AM and PM to denote if the time is from midnight till noon or noon till midnight, which is clearly not the case.)

Thus, from 17:53 to 7.26 there is 13 hours and 33 minutes.

We know one hour has 60 minutes. Therefore by method of conversion of hours to minutes we get,

Number of minutes between 17:53 to 7.26 = {(13*60) + 33} = 780+33 = 813

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Since the center of this semicircle is at the origin, O (0, 0), the radius of the semicircle is 5 units.

Since the center of this semicircle is at the point A (3, 4) and point B (-4, 5), the radius of the semicircle is 5√2 units.

In Mathematics and Geometry, the distance between two (2) points that are on a coordinate plane can be calculated by using the following mathematical equation (formula):

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represents the data points (coordinates) on a cartesian coordinate.

By substituting the given points into the distance formula, we have the following;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(3 - 0)² + (4 - 0)²]

Distance = √[(3)² + (4)²]

Distance = √(9 + 16)

Distance = √25

Distance = 5 units.

At point A (3, 4) and point B (-4, 5), the radius is given by;

Distance = √[(-4 - 3)² + (5 - 4)²]

Distance = √[(-7)² + (1)²]

Distance = √(49 + 1)

Distance = √50 = 5√2 units.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer: To find the proportion of students who performed worse than Aaron, we need to find the area to the left of his score of 989 on the normal distribution curve.

First, we need to standardize Aaron's score using the formula:

z = (x - mu) / sigma

where x is the score, mu is the mean, and sigma is the standard deviation.

Plugging in the values, we get:

z = (989 - 1100) / 200 = -0.55

Next, we look up the area to the left of z = -0.55 on the standard normal distribution table, or use a calculator to find:

P(Z < -0.55) = 0.2912

Therefore, the proportion of students who performed worse than Aaron is approximately 0.2912, or 29.12% (rounded to 2 decimal places).

Step-by-step explanation:

Answer:

24 slices

Step-by-step explanation:

There are 3 whole pizzas. He cuts each of them into eighths. That means eight slices. 3 times 8 is 24. There are a total of 24 slices. This can also look like this: 24/8   or 24 over 8.  Which also equals to 3.

When the temperature increases and the water vapor content in the air stays the same, the relative humidity decreases. This is because warmer air can hold more moisture than colder air, and therefore the ratio of the actual amount of water vapor in the air to the maximum amount of water vapor that the air can hold decreases as the air temperature increases.

Relative humidity depends on two factors: the amount of water vapor present in the air and the maximum amount of water vapor that the air can hold at a given temperature. As the temperature rises, so does the amount of water vapor that the air can hold, since warm air has more energy to hold the water molecules in vapor form. This reduces the ratio of the actual amount of water vapor in the air to the maximum amount of water vapor the air can hold, resulting in lower relative humidity.

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A value of 0.25 for p(1-p) in the sample size formula when the true value of p is unknown.

This is because the value of p(1-p) is maximum when p=0.5, and since we do not have any information about the true value of p, assuming p=0.5 is the most conservative approach. Therefore, to calculate the sample size required to estimate a proportion using a confidence interval with a margin of error e, we can use the formula:

[tex]n = [z^2 * p(1-p)] / e^2[/tex]

where z is the z-score corresponding to the desired level of confidence (e.g., 1.96 for 95% confidence), and e is the desired margin of error. We can use p=0.5 and solve for n to get a conservative estimate of the sample size required for the given confidence level and margin of error.

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If prior knowledge or data suggests that the proportion is significantly different from 0.5, then a more accurate estimate of p should be used in the formula.

To calculate the sample size formula for estimating a proportion using a confidence interval with a margin of error e, we

use the following formula:

[tex]n = (Z^2 × p × (1-p)) / e^2[/tex]

where n is the required sample size, Z is the Z-score corresponding to the desired level of confidence,

p is the estimated proportion, and

e is the margin of error.

Since the product p(1-p) is not known, a conservative approach is to use p = 0.5, which is the value that maximizes the

product p(1-p) for any given proportion.

This approach ensures that the sample size will be large enough to obtain a reliable estimate of the proportion, even if

the true proportion is close to 0 or 1. However, if prior knowledge or data suggests that the proportion is significantly

different from 0.5, then a more accurate estimate of p should be used in the formula.

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An F test is used to test the hypothesis that the values of the regression parameters β1, β2, . . . , βq are all zero. So the correct option is A.

The F test is based on the ratio of the mean square of the regression to the mean square of the error, and it is used to test the overall significance of the regression model. It tests whether there is a linear relationship between the independent variables and the dependent variable, and whether the model is statistically significant. In contrast, a t test is used to test the significance of individual regression coefficients, and the least squares method is a technique used to estimate the parameters of a linear regression model. Extrapolation is the process of estimating values of a dependent variable outside the range of the independent variables based on the regression model.

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The F test is used to test the hypothesis that the values of the regression parameters β1, β2, . . . , βq are all zero. therefore, option a. an F text is correct.

This test is commonly used in regression analysis to determine whether there is a significant relationship between the

dependent variable and the independent variables.

The F test compares the variance explained by the regression model to the residual variance, and the null hypothesis

assumes that all regression coefficients are equal to zero, indicating no relationship between the dependent variable

and the independent variables.

If the calculated F-statistic is larger than the critical value, we reject the null hypothesis and conclude that there is a

significant relationship between the dependent variable and the independent variables.

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It will take approximately 1.59 hours to fill the hot tub with a hose that has a filling rate of 4.6 gallons per minute

Assuming that the filling rate of the hose is constant, we can use the formula:

time = volume / rate

where time is the time taken to fill the hot tub, volume is the volume of the hot tub (440 gallons), and rate is the filling rate of the hose (4.6 gallons per minute).

Substituting the values, we get:

time = 440 / 4.6

which simplifies to:

time = 95.65 minutes

To convert minutes to hours, we divide by 60 (since there are 60 minutes in an hour):

time = 95.65 / 60

which simplifies to:

time = 1.59 hours

Therefore, it will take approximately 1.59 hours to fill the hot tub with a hose that has a filling rate of 4.6 gallons per minute.

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It will take approximately 1.594 hours to fill a 440-gallon hot tub with a hose that fills at a rate of 4.6 gallons per minute.

To determine how many hours follow these steps:

First, we need to find out how many minutes it takes to fill the hot tub.

Divide the total volume of the hot tub (440 gallons) by the rate at which the hose fills (4.6 gallons per minute):

440 gallons ÷ 4.6 gallons/minute = 95.65 minutes

Now, we need to convert the minutes into hours.

Since there are 60 minutes in an hour, divide the minutes by 60:

95.65 minutes ÷ 60 minutes/hour = 1.594 hours

It will take approximately 1.594 hours to fill a 440-gallon hot tub with a hose that fills at a rate of 4.6 gallons per minute.

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According to the function, the 10th term of the sequence is 2.038.

We can now use the values of A1, A4, A2, and A3 to find the value of d. Substituting A2 and A3 into the expression for A4 - A3, we get:

A4 - A3 = d

2.86 - (A1 + 2d) = d

Solving for d, we get:

d = -0.12

Now that we know the common difference between consecutive terms, we can write the function rule for the nth term of the sequence as:

An = A1 + (n - 1)d

Substituting A1 = 3.1 and d = -0.12, we get:

An = 3.1 - 0.12(n - 1)

To find the 10th term of the sequence, we simply plug in n = 10 into the formula:

A10 = 3.1 - 0.12(10 - 1) = 2.038

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Answer:

Step-by-step explanation:

720

The equation with the fewest symbols is 30x - 18, which represents the simplified form of the given expression.

An equation is a mathematical statement that shows the equality between two expressions. The given expression is not an equation since there is no equality sign present. However, we can simplify the expression to get an equivalent equation with the fewest symbols.

To simplify the expression, we use the distributive property of multiplication over addition/subtraction. We multiply 6 with each term inside the parentheses, i.e., 5x and -3. This gives us:

6(5x - 3) = 6(5x) - 6(3) = 30x - 18

This simplified expression is an equation that shows the equality between the left-hand side (LHS) and the right-hand side (RHS). The LHS is 30x - 18, and the RHS is also 30x - 18, which means that they are equal.

Therefore, the equation with the fewest symbols is 30x - 18, which represents the simplified form of the given expression.

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Since the gravitational force is directly proportional to the mass, we can see that Satellite D has the greatest mass and therefore the greatest gravitational force with Earth. Therefore, the correct option is D.

To determine which satellite has the greatest gravitational force with Earth, we need to use the formula for gravitational force, which is:

force = (G x m1 x m2) / r^2

where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between the centers of the objects.

Since the mass of Earth is much greater than any of the satellites, we can assume that the distance between Earth and each satellite is the same. Therefore, we can compare the gravitational force of each satellite with Earth by calculating:

force = (G x Earth's mass x satellite's mass) / distance^2

Using this formula and plugging in the given values, we get:

For Satellite A: force = (G x Earth's mass x 375 kg) / (320 km)^2

For Satellite B: force = (G x Earth's mass x 250 kg) / (320 km)^2

For Satellite C: force = (G x Earth's mass x 50 kg) / (320 km)^2

For Satellite D: force = (G x Earth's mass x 500 kg) / (320 km)^2

Therefore, the correct option is D.

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A) The correct features is,

⇒ a = 9000

⇒ r = 15%

B) The equation correctly models the context of the problem is,

⇒ y = 9000 (0.85)ˣ

We have to given that;

Tiffany’s mother bought a car for $9000 five years ago.

And, She wants to sell it to Tiffany based on a 15% annual rate of depreciation.

Now, We have;

the exponential growth formula is,

⇒ y = a(1 − r)ˣ

Here, We have;

⇒ a = 9000

⇒ r = 15%

Thus, We get;

The equation correctly models the context of the problem is,

⇒ y = a(1 − r)ˣ

⇒ y = 9000 (1 - 0.15)ˣ

⇒ y = 9000 (0.85)ˣ

Therefore, We get;

A) The correct features is,

⇒ a = 9000

⇒ r = 15%

B) The equation correctly models the context of the problem is,

⇒ y = 9000 (0.85)ˣ

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The surface area of the given pyramid is 203 in²

From the question, we are to calculate the surface area of the given square pyramid

From the given information, the base of the pyramid is 7 in

and

The slant height of the pyramid is 11 in

The surface area of a pyramid can be calculated by using the formula

A = a² + 2al

Where A is the area of the pyramid

a is the side base

and l is the slant height

From the given information,

a = 7 in

and

l = 11 in

Thus,

Surface area = 7² + 2(7)(11)

Surface area = 49 + 154

Surface area = 203 in²

Hence,

The surface area is 203 in²

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The answer of the given question based on the cylinder is ,  the volume of the solid = 929.44  inch³ . , the mistake is student may have only calculated the volume of the inner cylinder.

What is Volume?

Volume is amount of three-dimensional space occupied by object or substance. It is  physical quantity that is measured in cubic units, like cubic meters (m³), cubic centimeters (cm³), or cubic inches (in³). The volume of  object can be calculated by measuring its dimensions and using  mathematical formula specific to its shape.

To find volume of  solid, we need to subtract  volume of  inner cylinder from  volume of outer cylinder.

Volume of the outer cylinder = πr²h

where r = radius of the outer cylinder = 4 inches (diameter is given as 8 inches)

h = height of the outer cylinder = 23 inches

Volume of the outer cylinder = π(4)²(23) = 368π in³

Volume of the inner cylinder = πr²h

where r = radius of the inner cylinder = 2 inches

h = height of the inner cylinder = 18 inches

Volume of the inner cylinder = π(2)²(18) = 72π in³

So, the volume of the solid = Volume of the outer cylinder - Volume of the inner cylinder

= 368π - 72π

= 296π

= 929.44  inch³

The student's answer of 988.05 in³ is significantly higher than the correct answer, suggesting that the student may have only calculated the volume of the inner cylinder instead of subtracting it from the volume of the outer cylinder. This mistake may have arisen due to misreading the problem or misunderstanding the instructions.

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Answer:

x=2

Step-by-step explanation:

This is a system of equations that we can solve by using substitution.

We know that y=7. We know that y is also equal to 8x-9.

Since y is equal to both 7 and 8x-9, this must mean that 7 is also equal to 8x-9.

Let's set them equal and solve for x, like so:

[tex]y=8x-9=\\7=8x-9=\\16=8x=\\2=x[/tex]

So, x=2.

Marilyn has $75 to spend on two Series EE savings bonds as graduation gifts. The face values of the bonds she can buy are $50, $75, and $100. Therefore, she could buy two $50 bonds.

Since Marilyn has $75 to spend and she needs to buy two bonds, the total face value of the bonds she can purchase must be equal to $75.

Let x be the face value of the first bond, then the face value of the second bond must be 75 - x.

The face values of the bonds are $50, $75, and $100, so we can set up the following three equations

x + (75 - x) = 75 (since the total face value must be $75)

x = 50 (since the face value must be $50, $75, or $100)

x = 100 (since the face value must be $50, $75, or $100)

Solving these equations, we find that the possible face values for each bond are $50 and $25, $75 and $0, or $100 and $-25 (which is not a valid option).

Therefore, Marilyn could buy two bonds with face values of $50 each, or one bond with a face value of $75 and the other with a face value of $0 (which essentially means she would only be buying one bond).

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Answer:

4800

Step-by-step explanation:

15 x 20 = 300 x 16 = 4800

The answer of the given question based on the cylinder is ,  the volume of the solid = 929.44  inch³ . , the mistake is student may have only calculated the volume of the inner cylinder.

Volume is amount of three-dimensional space occupied by object or substance. It is a physical quantity that is measured in cubic units, such as cubic meters (m³), cubic centimeters (cm³), or cubic inches (in³). The volume of an object can be calculated by measuring its dimensions and using a mathematical formula specific to its shape.

To find volume of  solid, we need to subtract  volume of  inner cylinder from  volume of outer cylinder.

Volume of the outer cylinder = πr²h

where r = radius of the outer cylinder = 4 inches (diameter is given as 8 inches)

h = height of the outer cylinder = 23 inches

Volume of the outer cylinder = π(4)²(23) = 368π in³

Volume of the inner cylinder = πr²h

where r = radius of the inner cylinder = 2 inches

h = height of the inner cylinder = 18 inches

Volume of the inner cylinder = π(2)²(18) = 72π in³

So, the volume of the solid = Volume of the outer cylinder - Volume of the inner cylinder

= 368π - 72π

= 296π

= 929.44  inch³

The student's answer of 988.05 in³ is significantly higher than the correct answer, suggesting that the student may have only calculated the volume of the inner cylinder instead of subtracting it from the volume of the outer cylinder. This mistake may have arisen due to misreading the problem or misunderstanding the instructions.

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If the cabinets are 34 inches tall, 24 inches deep, and 16 inches wide, the volume of the kitchen cabinets is 16,384 cubic inches.

To find the volume of the rectangular prisms-shaped kitchen cabinets, we need to multiply the three dimensions: height, depth, and width. We are given the following measurements:

Height = 34 inches

Depth = 24 inches

Width = 16 inches

So the formula for the volume is:

Volume = Height x Depth x Width

Substituting the given values, we get:

Volume = 34 x 24 x 16

Volume = 16,384 cubic inches

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The exponential function that represents the data in the table is given as follows:

y = 3(2)^x.

The standard definition of an exponential function is given as follows:

y = a(b)^x.

In which the parameters are given as follows:

From the table, when x = 0, y = 3, hence the parameter a is given as follows:

a = 3.

When x is increased by one, y is multiplied by 2, hence this is an exponential function and the parameter b is given as follows:

b = 2.

Hence the function is defined as follows:

y = 3(2)^x.

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Based on the medians, we can conclude that Bus 47 typically has a faster travel time than Bus 18. The median travel time for Bus 47 is 16 minutes, which is 3 minutes faster than the median travel time for Bus 18, which is 13 minutes.

To determine which bus typically has the faster travel time, we need to compare the measures of center for each data set. Since the data sets are relatively small and appear to have some outliers, the median is the more appropriate measure of center to use in this case, as it is less affected by extreme values than the mean.

For Bus 47, the median is 16, which means that half of the students take less than 16 minutes to travel to school on that bus, and half take more than 16 minutes.

For Bus 18, the median is 13, which means that half of the students take less than 13 minutes to travel to school on that bus, and half take more than 13 minutes.

Therefore, based on the medians, we can conclude that Bus 47 typically has a faster travel time than Bus 18. The median travel time for Bus 47 is 16 minutes, which is 3 minutes faster than the median travel time for Bus 18, which is 13 minutes.

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The solutions to the equation x² + 10x + 22 = 13 are: x = -5 ± 4

To rewrite the equation by completing the square, we need to isolate the constant term on one side and group the x-terms together. Starting with:

x² + 10x + 22 = 13

Subtracting 13 from both sides:

x² + 10x + 9 = 0

Next, we add and subtract the square of half of the coefficient of x (which is 5 in this case) to complete the square:

x² + 10x + 25 - 25 + 9 = 0

x² + 10x + 25  - 16 = 0

Factor the perfect square trinomial:

(x + 5)² - 16 = 0

Now that we have rewritten the equation in the form (x + c)² = d, we can solve for x by taking the square root of both sides:

(x + 5)² - 16 = 0

Taking the square root of both sides and solving for x, we get:

x + 5 = ±4

So, we have

x = -5 ± 4

So the solutions to the equation are:

x = -5 + 4 = -1

x = -5 - 4 = -9

Therefore, the answer is x = -5 ± 4.

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The relative minimum of the function include the following: -2.

In this exercise, you are required to determine the relative minimum of the function with respect to the vertex form of a quadratic function h(x) that is written in standard form. Mathematically, the vertex form of a quadratic equation is given by this formula:

y = a(x - h)² + k

Where:

Based on the information provided about this quadratic function, we can reasonably infer and logically deduce that that its vertex is at x equals negative three and y equals negative two.;

Vertex (h, k) = (-3, -2)

Therefore, the relative minimum is equal to -2.

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To find the margin of error, we use the formula:

Margin of Error (ME) = Z * [tex]\sqrt{(p * (1-p) / n)}[/tex]

Z = 1.96 (for a 95% confidence level)

p = 0.33 (proportion of adults who said skim milk is a good calcium source)

(1-p) = 1 - 0.33 = 0.67 (complement of the estimated proportion)

n = 2406 (sample size)

ME = 1.96 * [tex]\sqrt{(0.33 * 0.67 / 2406)}[/tex] = 0.0185 (rounded to four decimal places)

This means that we can estimate, with 95% confidence, that the true proportion of adults who believe skim milk is a good calcium source falls within a range that is 1.85% above or below the reported proportion of 33% based on the survey results.

In other words, the actual proportion of adults who believe skim milk is a good calcium source could be as low as 31.15% or as high as 34.85% based on the margin of error.

The 1st and the 3rd are the distributions where the median the best measure of center

The median represents the central value in a dataset that is organized in ascending or descending order. If there are an even number of data points, the median can be calculated as the mean of the two middle values.

This method is much less prone to influence by extreme values when compared to other methods such as the mean. Hence, it is considered a more reliable measure of center particularly for datasets with outliers.

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