Explain the error in the solution below. What additional step needs to be completed?
log x – log53 = 2log53
log x = 3log53
log x = log533
x = 27

Ahlam needs to give the shopkeeper $15 more to get a balance of $25.

Word problems in Mathematics are mathematical approaches we make use of in our ongoing day to day activities. Algebra leading to word problems usually consist of numbers, variables, and its arithmetic operations.

Ahlam bought goods worth = $90, If she gave the shopkeeper $100, then she will collect $100 - $90 = $10 back.

But if the shopkeeper did not have an exact balance and Ahlam decided to give the shopkeeper $x to get a balance of $25.

Then we can write the expression as:

10 + x = 25

x = 25 - 10

x = 15

Therefore, we can conclude that Ahlam needs to give the shopkeeper $15 more to get a balance of $25.

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Answer:

y = 2 and x = 6

Step-by-step explanation:

Let y = x - 4 be  equation a

Let 4x + y = 26 be equation b

Substitute a into b:

4x + (x-4) = 26

5x - 4 = 26

5x = 30

x = 6

Substitute the value of x into a:

y = x - 4

y = 6 - 4

y = 2

CHECK:

4x + y = 26

4*6 + 2 = 26

24 + 2 = 26

26 = 26

LHS = RHS

Therefore, y = 2 and x = 6

Paul records data that the number of hot chocolates sold increases as temperature outside decreases. The depiction of the finding is "There is a correlation between two variables". So, the correct option is A.

Specifically, the data suggest that there is a relationship between two variables - the number of hot chocolates sold and the temperature outside.

When the temperature outside decreases, more hot chocolates are sold, and when the temperature increases, fewer hot chocolates are sold. This indicates that there is a correlation between the two variables, as they appear to be related.

However, we cannot determine from this information alone whether the correlation is strong or weak, or whether it is positive or negative.

The strength of the correlation would depend on how much the sales of hot chocolate increase or decrease as the temperature changes, while the direction of the correlation (positive or negative) would depend on whether the increase or decrease in hot chocolate sales is associated with an increase or decrease in temperature, respectively.

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Complete question is:

Paul records data that indicate that the number of hot chocolates sold at a concession stand increases as temperature outside decreases. (for example, more hot chocolates are purchased during late fall than late spring) which statement is the most accurate depiction of this finding?

a) There is a correlation between two variables

b) There is a strong , positive correlation between two variables

c) There is a weak , positive correlation between two variables

d) There is a negative correlation between two variables

The standard form of the quadratic function that represents the area of the garden is: G(x) = - 2x² + 20x

Mrs Miller has 20 ft of fencing to put around three sides of the garden.

Let us assume that l represents the length of the garden.

Here x represents the width of the rectangular garden.

So, l = 20 - 2x

We know that the formula for the area of rectangle is:

A = length × width

Let G(x) be a function that represents the area of the garden.

Using above formula,

G(x) = x × l

G(x) = x(20 - 2x)

G(x) = 20x - 2x²

G(x) = - 2x² + 20x

Therefore, the required quadratic function is: G(x) = - 2x² + 20x

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Find dthe complete question below.

Answer:

100

Step-by-step explanation:

100x2=200

200-100=100!

Answer:

100

Step-by-step explanation:

First do 100 multiplied by 2 you will then get 200

Next step is to do 200 subtracted by 100 which will give you 100.

The most likely option (b) to be possible is making a grouped frequency table from an ordinary frequency table.

A frequency table is a way of organizing data into classes or categories based on the number of times a particular observation or value occurs.

Now, let's examine the options provided. Making a grouped frequency table from an ordinary frequency table is possible, as we can simply group the values into intervals and calculate the frequencies for each interval. This allows us to better visualize and understand the distribution of the data.

Making a normal curve from a bimodal distribution is not possible, as a bimodal distribution has two distinct peaks or modes, while a normal distribution has only one. A normal curve is symmetrical and bell-shaped, and represents a continuous distribution of values.

Making an ordinary frequency table from a grouped frequency table is also possible, as we can simply list the intervals or classes and their corresponding frequencies, without the need to group them into intervals.

Finally, making a bimodal distribution from a normal curve is possible, as we can add two normal distributions with different means and standard deviations to create a bimodal distribution. However, it is important to note that a bimodal distribution may not always be appropriate for the given data.

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Answer: look at the image for the answer and solution

Step-by-step explanation:

The exponential equation after solving gives -26.

Exponential equations are equations where the independent variable, x is in the exponent.

The given equation is,

[tex]5^{7x+5}[/tex] = [tex]125^{2x-7}[/tex]

We know that 125 = 5³

[tex]5^{7x+5}[/tex] = [tex]5^{3(2x-7)}[/tex]

The base in the both sides of the equation is 5.

So,

7x + 5 = 3(2x - 7)

7x + 5 = 6x - 21

7x - 6x = -21 - 5

x = -26

Hence the value of x is -26.

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Answer: B

Step-by-step explanation:

if r is close to 1 (or -1) it means the relationship is strong, -0.2041 is really close to 0 so the data is most likely scattered and the association is weak

Answer:

Strong

Step-by-step explanation:

edge 2023

In all three cases, the height of the cone is proportional to the volume and inversely proportional to the square of the radius. So, if we know the volume and radius of a cone, we can use the formula for h to find its height.

[tex]\text{Height } = h = \frac{3V}{\pi r^2} = \frac{3V}{\pi (2^2)} = \frac{3V}{4\pi}[/tex]

The volume of a cone is given by the formula V = (1/3)πr²h, where V is the volume, r is the radius, and h is the height of the cone.

If we rearrange this formula to solve for h, we get h = 3V / (πr²). This means that the height of a cone is directly proportional to the volume and inversely proportional to the square of the radius.

a. If the radius of a cone is 2 inches and its volume is given, we can find its height by plugging in the values of V and r into the formula for h.

[tex]h = \frac{3V}{\pi r^2} = \frac{3V}{\pi (2^2)} = \frac{3V}{4\pi}[/tex]

b. Similarly, if the radius is 3 inches, the height would be:

[tex]h = \frac{3V}{\pi r^2} = \frac{3V}{\pi (3^2)} = \frac{3V}{9\pi}[/tex]

c. If the radius is 6 inches, the height would be:

[tex]h = \frac{3V}{\pi r^2} = \frac{3V}{\pi (6^2)} = \frac{3V}{36\pi}[/tex]

In all three cases, the height of the cone is proportional to the volume and inversely proportional to the square of the radius. So, if we know the volume and radius of a cone, we can use the formula for h to find its height.

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Answer:

To substitute x = 2 and y = 1 into the expression 4x^-3 y^-2, we simply replace x with 2 and y with 1:

4 * (2)^-3 * (1)^-2 = 4 * (1/8) * (1) = 4/8 = 0.5

So the expression 4x^-3 y^-2 evaluated at x = 2 and y = 1 is equal to 0.5.

Step-by-step explanation:

The solution to the inequality are the region in the shaded area and the graph is attached

From the question, we have the following parameters that can be used in our computation:

y ≥3(0.8)^x

y ≥ x² - 5

Represent properly

y ≥ 3(0.8)^x

y ≥ x² - 5

Next, we make a plot of the system to determine the solution

The shaded area in the plot represent the solution to the inequality

In this case, one of the coordinates in the shaded area has a coordinate of (0, 5)

None of the options represent the shaded area (see attachment)

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Answer:

12.2 pints

Step-by-step explanation:

In all means add.  Add the two decimals together.

4.8 + 7.4

12.2 pints

Answer:  -2 ±√6
                    2

Step-by-step explanation:
Use the quadratic formula - its better to separate it into two parts
Δ = b²-4ac
   = 4² -4(2*-1)
   = 16 + 8

∴ Δ = 24
Then
x = (-b ± √Δ) ÷ 2a
  = (-4 ± √24) ÷ 4
  = (-4 ± 2√6) ÷ 4 (simplify the surd form)
∴ x = -2 ±√6   (simplify by crossing out the 2's)
             2

There is no mode of the number of girl in the three classes.

The value that appears the most frequently in a data collection when it is unique is known as the mode, and like the median and mean, it can be used to measure central tendency. However, occasionally there is either no mode or more than one mode.

Given:

The data for boys: 15, 12, 12

The data for Girls: 14, 12, 16

As, mode is the most repeating data.

We can see that the data repeats in boys but not for the Girls.

So, number of boys have the mode but the number of girls do not have the mode.

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If the slope of a staircase is 0. 95 and rises with 210, then the run is:

221.05 units.

In this problem, we can use the formula for the slope of a staircase, which is given by:

where "rise" is the vertical height of the staircase and "run" is the horizontal distance of the staircase.

We are given the slope of the staircase as 0.95 and the rise as 210. We can substitute these values in the formula and solve for the run:

Multiplying both sides by run, we get:

Dividing both sides by 0.95, we get:

Simplifying the expression, we get:

Therefore, the run of the staircase is approximately 221.05 units.

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Answer:

true

the t-value does change depending on the number of data points collected.

It is true that the t-value can change depending on the number of data points collected.

The t-value is a statistic used in hypothesis testing to determine whether a sample mean is significantly different from a population mean.

The formula for calculating the t-value includes the sample size (n) in the denominator, which means that as the sample size increases, the t-value decreases (assuming all other factors remain constant).

In other words, a larger sample size will generally result in a smaller t-value, which in turn may affect the interpretation of the results of a hypothesis test. Therefore, the t-value can change depending on the number of data points collected.

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The solution of x in the triangle is 11.5

From the question, we have the following parameters that can be used in our computation:

The triangle

Using the Pythagoras theorem, we have the following equation

x^2 = 13^2 - 6^2

Evaluate the expression

x^2 = 133

Take the square roots of both sides

x = 11.5

Hence, the solution is 11.5

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The recipe requires two-thirds of a cup of milk, and Sam needs 1/3 cup of milk to make 5 banana pancakes.

What is the proportion?

A proportion is two ratios that have been set equal to each other; a proportion is an equation that can be solved. When I say that a proportion is two ratios that are equal to each other, I mean this in the sense of two fractions being equal to each other. For instance, 5/10 equals 1/2.

The recipe for 20 banana pancakes requires 2/3 cup of milk.

To find out how much milk is needed for 5 pancakes, we can use proportion. We can set up a proportion that relates the amount of milk needed to the number of pancakes:

(milk needed) / 2/3 cup = 5 pancakes / 20 pancakes

Simplifying the right side of the equation, we get:

(milk needed) / 2/3 cup = 1/4

To solve for the milk needed, we can cross-multiply:

milk needed = (2/3 cup) * (1/4) = 1/3 cup

Therefore, Sam needs 1/3 cup of milk to make 5 banana pancakes.

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Answer:

could write 21 + 38 + 75 = 134

Step-by-step explanation:

Answer: A, B, F

Step-by-step explanation:

For convenience sake, let's establish early on that 1/2 is equal to 0.5 or 50% in their decimal and percentage forms respectively.

- A as a decimal is 0.25, which is not only smaller than 1/2, but it is exactly half of the value, so A works.

- B is also smaller than the decimal of 0.5, therefore it counts.

- 3/5 as a decimal is 0.5, which is greater, so doesn't count.

- 67% is bigger than 50%, so doesn't count.

- 0.74 is bigger than 0.5, so doesn't count.

- 40% is smaller than 50%, so it counts.

Answer:

A, B, and F

Step-by-step explanation:

A. 1/4 = 25%

B. .26 = 26%

F. 40%

Answer:

Step-by-step explanation:

The slope of a line between two points (x1, y1) and (x2, y2) is given by:

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

In this case, we are given that m = -1/2, so substituting in the two points we have:

-1/2 = (9 - 12) / (x - 8)

Expanding and simplifying the equation:

-1/2 = -3 / (x - 8)

Multiplying both sides by -2:

1 = 3 / (x - 8)

Multiplying both sides by (x - 8):

x - 8 = 3

Adding 8 to both sides:

x = 11

So the x-coordinate of the second point is x = 11.

Answer:

Each one-inch binder costs $2.67 and each two-inch binder costs $6.

Step-by-step explanation:

Let's call the cost of a one-inch binder "x" and the cost of a two-inch binder "y".

From Hansen's purchase, we know that 3x + 2y = $20.

From Pam's purchase, we know that 3x + 5y = $32.

We can use these two equations to solve for the cost of each size of binder. If we subtract the first equation from the second, we get:

2y = $32 - $20 = $12

So, y = $6, which is the cost of a two-inch binder.

Next, we can plug this value back into either of the original equations to find the cost of a one-inch binder:

3x + 2($6) = $20

Expanding the right side, we get:

3x + $12 = $20

Subtracting $12 from both sides, we get:

3x = $8

Finally, dividing both sides by 3, we find that:

x = $2.67

So, each one-inch binder costs $2.67 and each two-inch binder costs $6.

The answer is (b) The margin of error will be about 2 times larger.

The margin of error in a confidence interval is affected by the sample size, so decreasing the sample size will generally increase the margin of error. Specifically, the margin of error is inversely proportional to the square root of the sample size.

That is, if we reduce the sample size by a factor of k, then the margin of error will increase by a factor of sqrt(k).

In this case, the original sample size was 1000, and the proposed sample size is 250, which is 1/4 of the original size. Therefore, the margin of error for the smaller sample will be:

sqrt(1000/250) times the original margin of error.

Simplifying this expression, we get:

sqrt(4) times the original margin of error.

So the margin of error for the smaller sample will be about 2 times the original margin of error.

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The inequality is c ≤ 187, where c is the number of 130-kg crates that can be added to the shipping container

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the number of 130-kg crates that can be added to the shipping container be c

The greatest weight the shipping container can hold = 27,500 kg

The weight that is already loaded = 3,100 kg

So , the total number of 130kg weights = 130c

Substituting the values in the equation , we get

27500 - 3100 ≥ 130c

130c ≤ 24,400

Divide by 130 on both sides of the equation , we get

c ≤ 187.69

So , the value of c is 187 crates

Hence , the inequality is c ≤ 187

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Answer: 78.39 thousand, (78,390)

Step-by-step explanation:

Using the quadratic formula with this gives us two answers, 78.39 and -65.39. Since a negative answer doesnt make sense in this context, we will go with 78.39 thousand pens, (78,390 pens). The limit on x however doesn't seem to make sense as it says x </= 25 and x>/= 0. The only two answers are both above and below this limit.

An objective tally of the results of a probability experiment is called a random variable. It gives a number to each potential result of the experiment, and its values are decided by chance.

How something is to Happen is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics defines series of events subject to probability.

Always between 0 and 1 are the possible outcomes. Probability = Number of favourable outcomes / Total number of outcomes is how the general probability formula is written. Alternatively, P(A) = f / N.

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