Oliver saves 10% of his weekly earnings for living expenses. He usually makes $520 each week. This
week he made 10% more. Oliver incorrectly claims that he has $520 left for spending money this
week. Calculate the amount of spending money Oliver has left for this week. What error did Oliver
likely make?
Oliver has $
left for spending money this week.

The value that remains unchanged when the four values (mean, median, range, and standard deviation) are reported using the corrected weight is the median.

When the horse with the lowest reported weight is found to actually weigh 101010 pounds less than its reported weight, it means that the reported weight was higher by 101010 pounds. This correction affects the mean, range, and standard deviation, but not the median.

The mean is the average of all the weights in the data set. By subtracting 101010 pounds from the weight of the horse with the lowest reported weight, the sum of all the weights will decrease by that amount. As a result, the mean will also decrease by an amount proportional to the size of the data set.

The range is the difference between the highest and lowest values in the data set. Since the correction only affects the lowest reported weight, the range will decrease by 101010 pounds.

The standard deviation measures the spread or dispersion of the data set. It takes into account the differences between each weight and the mean. Since the correction affects one weight, it will impact the standard deviation, making it slightly smaller.

However, the median is the middle value when the weights are arranged in ascending or descending order. The correction does not affect the order or position of the other weights relative to the median, so the median remains unchanged.

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Answer:

1 2 3 6

Step-by-step explanation:

1x6=6

2x3=6

3x2=6

6x1=6

The greatest common divisor of each of these pairs of integers are

a) 1    b)  1    c) 12   d)  1     e)  3   g)  1     h)  2    i) 1  

f) 0 is not a positive integer, so it doesn't have a prime factorization.

The greatest common divisor (GCD), also known as the highest common factor (HCF), of two or more integers is the largest positive integer that divides each of the integers without a remainder.

To find the GCD we need to write each number as a product of prime factorization and then we need to find out the common factors which is greatest among them.

a) 10 = 2 × 5,

11 is prime

GCD(10, 11) = 1 (no common factors)

b) 21 = 3 × 7,

44 = 2 × 2 × 11

GCD(21, 44) = 1 (no common factors)

c) 36 = 2 × 2× 3 × 3

48 = 2 × 2 × 2 × 2 × 3

GCD(36, 48) = 2 × 2 × 3 = 12

d) 34 = 2  × 17,

55 = 5 × 11

GCD(34, 55) = 1 (no common factors)

e) 117 = 3 × 3 × 13,

213 = 3 × 71

GCD(117, 213) = 3

f) 0 is not a positive integer, so it doesn't have a prime factorization.

g) 123 = 3 × 41, 2347 is prime

GCD(123, 2347) = 1 (no common factors)

h) 3454 = 2 × 1727,

4666 = 2 × 2333

GCD(3454, 4666) = 2

i) 9999 = 3 × 3 × 11 × 101,

11111 = 41 × 271

GCD(9999, 11111) = 1 (no common factors)

Therefore,

The greatest common divisor of each of these pairs of integers are

a) 1    b)  1    c) 12   d)  1     e)  3   g)  1     h)  2    i) 1  

f) 0 is not a positive integer, so it doesn't have a prime factorization.

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Answer:

Ratios are proportional if both serve the identical tie. A method to detect if a pair of ratios remain equivalent is to rewrite them being fractions, then decrease them. If the decreased fractions are equal, the ratios are comparative.

Step-by-step explanation:

Answer:

still need help?

Step-by-step explanation:

Answer:

n + q = 20

5n + 25q = 300 or 0.05n + 0.25q = 3

Step-by-step explanation:

You know that you have some nickels and some quarters, and together there are 20 coins. So if n represents the number of nickels, and q represents the number of quarters, you can use this equation:

n + q = 20

You also know that together the coins total three dollars. We know that a nickel is worth 5 cents and a quarter is worth 25. So if n and q still represent the number of each type of coin, we can use this equation:

5n + 25q = 300

or

0.05n + 0.25q = 3

The reason I said 300 in the first equation is because you are counting the number of cents. There are 300 cents in 3 dollars.

a. Approximately 84.13% of the boxes weigh more than 22.4 ounces.

b. Approximately 4.78% of the boxes weigh less than 21.3 ounces.

a. To find the percentage of boxes weighing more than 22.4 ounces, we need to calculate the area under the normal distribution curve to the right of 22.4. We can use the z-score formula to standardize the value. The z-score is calculated as (x - μ) / σ, where x is the given value, μ is the mean, and σ is the standard deviation. In this case, the z-score is (22.4 - 23.5) / 1.1 ≈ -1. The corresponding area to the right of the z-score -1 can be looked up in the standard normal distribution table or calculated using software, which is approximately 0.8413. Therefore, approximately 84.13% of the boxes weigh more than 22.4 ounces.

b. Similarly, to find the percentage of boxes weighing less than 21.3 ounces, we calculate the area under the normal distribution curve to the left of 21.3. The z-score is (21.3 - 23.5) / 1.1 ≈ -2. The corresponding area to the left of the z-score -2 can be looked up in the standard normal distribution table or calculated using software, which is approximately 0.0228. However, since we want the percentage of boxes weighing less than 21.3 ounces, we subtract this value from 1 to get approximately 0.9772 or 97.72%. Therefore, approximately 4.78% of the boxes weigh less than 21.3 ounces.

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The fee charged for the R 2, 500 withdrawal from TownBank would be R 33. 30.

To find the total fee charged to withdraw the sum of R 2, 500 from TownBank, the formula is :

= 3. 30 + R 1, 20 per R 100

The amount withdrawn was R 2, 500 so the total fee charged would be :

= 3. 30 + 1, 20 x ( 2, 500 / 100 )

= 3. 30 + 1. 20 x 25

= 3. 30 + 30

= 33. 30

= R 33. 30

In conclusion, the total fee charged was R 33. 30.

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First part of the question :

The TownBank current account charges R3,30 plus R1,20 per R100 or part thereof for a cash withdrawal from a TownBank ATM. The first five withdrawals in a month are free. Determine the bank charges for a withdrawal of:

Answer: Than did not use 0.06 for 6 percent.

Step-by-step explanation:

From the question, we are informed that Than computed 6 percent of 38 as 6 percent of 38 = 0.6 times 38 = 22.8.

His above solution is wrong. We should note that:

6% × 38

= 6/100 × 38.

= 0.06 × 38

= 2.28

The mistake that he made was that Than did not use 0.06 for 6 percent.

Answer:

b

Step-by-step explanation:

edge

We need to integrate

\(\\ \tt\Rrightarrow {\displaystyle{\int}_{-3}^{-2}}3x^2-x-1\)

\(\\ \tt\Rrightarrow \left[\dfrac{3}{4}x^4-\dfrac{x^2}{2}-x\right]_{-3}^{-2}\)

\(\\ \tt\Rrightarrow \dfrac{3}{4}(-2)^4-\dfrac{(-2)^2}{2}-(-2)-\left(\dfrac{3}{4}(-3)^4-\dfrac{(-3)^2}{2}+3\right)\)

\(\\ \tt\Rrightarrow 12-2+2-(\dfrac{243}{4}-\dfrac{9}{2}+2)\)

\(\\ \tt\Rrightarrow 12-(\dfrac{225}{4}+2)\)

\(\\ \tt\Rrightarrow 12-\dfrac{233}{4}\)

\(\\ \tt\Rrightarrow \dfrac{48-233}{4}\)

\(\\ \tt\Rrightarrow \dfrac{-185}{4}\)

\(\\ \tt\Rrightarrow 46(approx)\neq 0\)

It has a zero in between-3 and -2

Answer:

see explanation

Step-by-step explanation:

Evaluate f(x) for x = - 3 and - 2

f(- 3) = 3(- 3)² - 10(- 3) + 9 = 3(- 27) + 30 + 9 = - 81 + 39 = - 42

Then (- 3, - 42 ) is below the x- axis

f(- 2) = 3(- 2)³ - 10(- 2) + 9 = 3(- 8) + 20 + 9 = - 24 + 29 = 5

Then (- 2, 5 ) is above the x- axis

Since f(x) is below the x- axis at x = - 3 and above the x- axis at x = - 2

Then it must cross the x- axis between x = - 3 and x = - 2

Indicating there is a real zero between - 3 and - 2

9514 1404 393

Answer:

  x = -2 or 3

Step-by-step explanation:

Let z = 2^x. Then the equation becomes ...

  \(2^{2x+2}+8=33(2^x)\\\\(2^2)(2^x)^2+8=33(2^x)\\\\4z^2+8=33z \qquad\text{substitute $z$ for $2^x$}\\\\4z^2-33z+8=0 \qquad\text{put the quadratic in standard form}\\\\(4z-1)(z-8)=0 \qquad\text{factor}\\\\z=\dfrac{1}{4}\text{ or }z=8\qquad\text{values of z that make the factors 0}\\\\x=\log_2{z}=\{-2,\ 3\}\)

The values of x that satisfy the equation are -2 and 3.

_____

For the graph, we rewrite the equation to the form ...

  f(x) = 0

where

  f(x) = 2^(2x+2) +8 -33(2^x)

Then the x-intercepts of the function are the solution values for x.

Option 1 is correct, The point will be on 10 for the cost $240.

=> 0—————————-10—————————-20

By multiplying the data οbtained with such a nanοsectiοn variable whilst alsο twο that used the unitary methοd , the jοb can be finished. In essence, this mean that whenever a desired item appears, the specified entity is set οr the cοlοur space οf bοth prοductiοn runs is skipped. A varying fee οf Inr ($1.01) might have been necessary fοr fοrty pens.

Here,

Greg wants tο cοllect enοugh cash tο spend $210 οn a new bicycle. He needs tο make an extra $150 because he already has $60. He needs tο mοw the fοllοwing lawns in οrder tο make his $15 per lawn:

=> 150 ÷ 15 = 10 acres

Greg must mοw at least 10 yards in οrder tο accοmplish his οbjective. The number line shοwing hοw many fields he can mοw is as fοllοws:

=> 0—————————-10—————————-20

The number οf lawns he can mοw tο reach his οbjective is represented by any value οn this number line larger than οr equal tο 10. He will, fοr instance, be cοmpensated:

=> 12 × $15 = $180

He already has $60, sο after adding this, he will have:

=> $60 + $180 = $240

which will cοver the cοst οf the new mοtοrbike.

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Statistically significant means that the relationship between two variables is likely to be real and not due to chance. If the p-value is lower than the predetermined threshold, usually 0.05, then the correlation is said to be statistically significant.

When a correlation between two variables is said to be statistically significant, it means that the relationship between the two variables is not due to chance or random error. In other words, the relationship is likely to be a real one and not just a coincidence.

Statistical significance is often determined by calculating a p-value, which is the probability of observing a relationship as strong as the one observed if there was no actual relationship between the variables. If the p-value is less than a predetermined threshold, usually 0.05, the relationship is considered to be statistically significant. This means that there is less than a 5% chance that the relationship observed is due to random error.

Therefore, It is usually determined by calculating a p-value, which measures the probability that the relationship between two variables is due to random chance.

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A) The decimal 2.256 in expanded form and word form are respectively;  2 + 0.2 + 0.05 + 0.006;  Two and three hundred fifty six one - thousandths

B) The decimal 24.09 in expanded form  and word form are respectively; 20 + 4 + 0 + 0.09; Twenty four and 9 one - hundredths.

The expanded form used when writing decimals is the mathematical expression that shows the sum of the values of each digit in the given number.

A) We are given the decimal 2.256

Thus, in expanded form, the given decimal can be expressed as;

2 + (2/10) + (5/100) + (6/1000)

= 2 + 0.2 + 0.05 + 0.006

In word form, we can write the decimal as;

Two and three hundred fifty six one - thousandths

B) We are given the decimal 24.09

Thus, in expanded form, the given decimal can be expressed as;

20 + 4 + (0/10) + (9/100)

= 20 + 4 + 0 + 0.09

In word form, we can write the decimal as;

Twenty four and 9 one - hundredths.

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Answer:

The original cost of the product was $35.68.

Step-by-step explanation:

As Sasha has a discount coupon of 35%, the final amount that he will pay is 65% of the initial value of the product (100 - 35). Thus, 65% of the value is $ 23. Therefore, to determine the initial cost of the product, it is necessary to perform the following calculation:

65 = 23

100 = X

((100 x 23) / 65) = X

2,300 / 65 = X

35.68 = X

Therefore, the initial value of the product was $ 35.68.

Answer:a. 1.5 kg of tuna, 1 kg of onion, 0.75 kg of red pepper and 2.4 kg of tomatoes

b. 16 empanadas

Step-by-step explanation:Since each of these ingredients is needed and the recipe is for a single empanada, each ingredient in the recipe must be multiplied by 6 since they are 6 empanadas, like this:

1/4 kg tuna * 6 = 6/4 = 3/2 kg tuna

1/6 kg of onion * 6 = 6/6 = 1 kg of onion

1/8 kg of red pepper * 6 = 6/8 = 3/4 kg of red pepper

2/5 kg of tomatoes * 6 = 12/5 kg of tomatoes

Therefore 1.5 kg of tuna, 1 kg of onion, 0.75 kg of red pepper and 2.4 kg of tomatoes need it.

Now, with 2 kg of red pepper, what we should do is divide this quantity by the quantity for a recipe, like this:

2 / (1/8) = 16

that is to say that with 2 kg of red pepper, a total of 16 empanadas would be made

Answer:

negative 1 over 27

Step-by-step explanation:

81 * negative 1 over 27 = -3

Answer:

\( \dfrac{1}{27} \)

Step-by-step explanation:

\( 81^{-\frac{3}{4}} = \)

\( = \dfrac{1}{81^{\frac{3}{4}}} \)

\( = \dfrac{1}{(\sqrt[4]{81})^3} \)

\( = \dfrac{1}{(3)^3} \)

\( = \dfrac{1}{27} \)

Answer:

I might be wrong, but if I did this right it would be D.

Step-by-step explanation:

I'm sincerely sorry if I got this wrong.

Answer:

B. 3.72 x \(10^{7}\)

Step-by-step explanation:

The distance between the sun and Mercury is approximately 36,000,000 miles.

Move the decimal point 7 positions to the left so that there is only one digit to the left of it.

Multiply that number by 10 raised to the power of 7

7 is the number of positions that the decimal point was moved.

I do not know this subject too well but hopefully this helps.

The conditions for a sampling distribution of a sample mean, when you know the true involve random sampling, independence, and a large enough sample size.

The conditions for a sampling distribution of a sample mean, when you know the true mean, are as follows:

1. Random Sampling:

The samples should be selected randomly from the population to ensure that they are representative of the entire population.

2. Independence:

Each sample should be independent of the others.

This means that the outcome of one sample should not influence the outcome of another sample.

3. Sample Size:

The sample size should be large enough to ensure that the sampling distribution approximates a normal distribution.

In general, a sample size greater than 30 is considered sufficient.

Random sampling is important because it helps to minimize bias and ensure that the sample is representative of the population.

Independence is necessary to avoid any potential confounding factors that may influence the results.

Lastly, a sufficiently large sample size is needed to satisfy the central limit theorem, which states that as the sample size increases, the sampling distribution of the sample mean approaches a normal distribution.

These conditions are important to ensure the validity and reliability of the statistical analysis.

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Step-by-step explanation:

The line representing the equation 7x1 + 4x2 = 28 goes through the points (4,0) and (0,7).

Eliminating y right away is easiest. Add -3(equation 1) to equation 2, and add 3(equation 3) to equation 2:

-3(2x + y + 3z) + (-3x + 3y - 2z) = -3(3) + (-8)

-6x - 3y - 9z - 3x + 3y - 2z = -9 - 8

-9x - 11z = -17

9x + 11z = 17   [equation 1]

3(5x - y + 5z) + (-3x + 3y - 2z) = 3(13) + (-8)

15x - 3y + 15z - 3x + 3y - 2z = 39 - 8

12x + 13z = 31   [equation 2]

Eliminating x next is easier than eliminating z. Add -4(equation 1) to 3(equation 2):

-4(9x + 11z) + 3(12x + 13z) = -4(17) + 3(31)

-36x - 44z + 36x + 39z = -68 + 93

-5z = 25

z = 25/(-5)

z = -5

Plug this into either of the previous equations and solve for x :

9x + 11z = 17

9x + 11(-5) = 17

9x - 55 = 17

9x = 72

x = 72/9

x = 8

Plug x and z into any of the 3 original equations and solve for y :

2x + y + 3z = 3

2(8) + y + 3(-5) = 3

16 + y - 15 = 3

1 + y = 3

y = 2

Given statement solution is :- When the weight of apples is increased by a factor of 4, the total cost also increases by a factor of 4. The correct answer is 4, not 8.

To determine the factor by which the total cost increases when the weight of apples is increased by a factor of 4, let's examine the relationship between the weight and total cost in the given ratio table.

Weight (lb) | Total cost (S)

1 | 2

4 | 8

6 | 12

10 | 20

To find the factor by which the total cost increases, we need to compare the change in total cost to the change in weight. Let's consider the first and last entries in the table:

Initial weight: 1 lb

Initial total cost: 2 S

Final weight (increased by a factor of 4): 4 * 1 lb = 4 lb

Final total cost: 8 S

The change in weight is from 1 lb to 4 lb, which is a factor of 4. The change in total cost is from 2 S to 8 S, which is also a factor of 4.

Therefore, when the weight of apples is increased by a factor of 4, the total cost also increases by a factor of 4. The correct answer is 4, not 8.

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Answer:

To write an inequality to describe the situation where students receive a pizza, we need to use the concept of average.

The average of a set of numbers is equal to the sum of the numbers divided by the number of numbers. So, if the class has an average of at least 85 out of 100 correct questions on the mid term exam, we can write an inequality as:

(number of correct questions) / (number of students) ≥ 85/100

or

(number of correct questions) ≥ (85/100) * (number of students)

So the inequality that describes the situation where students receive a pizza is:

(number of correct questions) ≥ (85/100) * (number of students)

This inequality states that the number of correct questions must be greater than or equal to 85/100 multiplied by the number of students in order for them to receive a pizza.

The problem can be solved using the simplex method, and the solution can be verified using the graphical method. The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

The problem can be solved using the simplex method, and verified using the graphical method. Here are the steps:

Convert the problem to standard form by introducing slack variables:
Min Z = -2X1 - 4X2 - 3X3 + 0S1 + 0S2 + 0S3
St. X1 + 3X2 + 2X3 + S1 = 30
X1 + X2 + X3 + S2 = 24
3X1 + 5X2 + 3X3 + S3 = 60
Xi, Si >= 0

Set up the initial simplex tableau:
| 1 3 2 1 0 0 30 |
| 1 1 1 0 1 0 24 |
| 3 5 3 0 0 1 60 |
| 2 4 3 0 0 0 0 |

Identify the entering variable (most negative coefficient in the objective row): X2

Identify the leaving variable (smallest ratio of RHS to coefficient of entering variable): S1

Pivot around the intersection of the entering and leaving variables to create a new tableau:
| 0 2 1 1 -1 0 6 |
| 1 0 0 -1 2 0 18 |
| 0 0 0 5 -5 1 30 |
| 2 0 1 -2 4 0 36 |

Repeat steps 3-5 until there are no more negative coefficients in the objective row. The final tableau is:
| 0 0 0 7/5 -3/5 0 18 |
| 1 0 0 -1/5 2/5 0 6 |
| 0 0 1 1/5 -1/5 0 6 |
| 0 0 0 -2 4 0 24 |

The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

To verify the solution using the graphical method, plot the constraints on a graph and find the feasible region. The optimal solution will be at one of the corner points of the feasible region. By checking the values of the objective function at each corner point, we can verify that the optimal solution found using the simplex method is correct.

In conclusion, the problem can be solved using the simplex method, and the solution can be verified using the graphical method. The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

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Answer:

68

Step-by-step explanation:

Ok might be wrong but

0.5 in. = 6

there is 6 0.5 in 3 in. so 6 + 6 + 6 + 6 + 6 + 6 = 68

Answer:

6/5

Step-by-step explanation:

We can use the slope formula to find the slope

Slope formula: \(m = \frac{y_2-y_1}{x_2-x_1}\), where the x and y values are derived from know points

The points chosen can vary as there are many given but the ones I chose were (6,9) and (11,15)

Now that we chose two points we want to define the variable ( the variables are x2, x1, y2 and y1 )

Define Variables

x1 = x value of first point which would be 6

x2 = x value of second point which would be 11

y1 = y value of first point which would be 9

y2 = y value of second point which would be 15

Now that we have defined our variables the next step is to plug in the variables into the slope formula

slope formula: \(m = \frac{y_2-y_1}{x_2-x_1}\)

y2 = 15, y1 = 9, x2 = 11 and x1 = 6

* plug in values *

\(m=\frac{15-9}{11-6}\)

subtract top numbers

\(m=\frac{6}{11-6}\)

subtract bottom numbers

\(m = \frac{6}{5}\)

there is no simplification needed meaning that the slope in simplest form is 6/5

The unit which is used to measure the attribute under investigation is inches.

Given a histogram which shows the height of the adults in male.

Here in the X axis, the height in inches are marked starting from 66 to 74.

In the Y axis, the number of people who have a specified height is given.

Here we have to find the unit which is used to measure the attribute under investigation.

For that, first we have to find the attribute under investigation.

Here the point of graphing this is to find the height of the people.

So attribute under investigation is the height of the people.

So the unit is that of the unit used to measure the height.

Here the unit is inches.

Hence the unit used is inches.

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Answer:

To multiply decimals, first multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor. Finally, put the same number of digits behind the decimal in the product.

To divide a decimal by another decimal: Move the decimal point in the divisor to the right until it is a whole number. Move the decimal point in the dividend to the right by the same number of places as the decimal point was moved to make the divisor a whole number. Then divide the new dividend by the new divisor.

Answer:

Step-by-step explanation:

Okay, first multiplying decimals:

If you want to multiply decimals first you have to put the 2 decimals one on top of each other

for example:

  2.27

x 4.89

Then multiply it just like if you were multiplying a regular number without the decimals

  227

x 489

This equals 111,003 now to figure out the answer we can count that there are 4 numbers after the decimal point so you move the decimal point 4 to the left so the answer would be 11.1003

Answer:

A

Step-by-step explanation:

11.4-15.7 = -4.3

Answer:

A. -4.3 F

Step-by-step explanation:

Originally you started with 11.4 F, and the question said it decreased by 15.7 F so that basically means you subtract the final condition from initial,

11.4 F - 15.7 = -4.3 F, so at night it was -4.3 F cold.

If you think about this question in terms of apples. Originally I gave you 12 apples to keep for a day. When I returned home at 7pm the numbers of apples decreased by 8. So bascially my final apples will be 12- 8 = 4 apples remaining.