put these number in order from least to greatest

Percentage change = 10%

We can use the formula:

Percent change = \(\frac{New-Old}{Old}\) x 100

Percent change = \(\frac{77-70}{70}\)x100

Percent change = \(\frac{7}{70}\) x 100

Percent change = 0.1 x 100

Percent change = 10%

Answer: 53.9

Step-by-step explanation:

B. This quantity might be the optimal order quantity, but we also need to consider the company’s attitude toward risk.

Simulation models are useful tools for predicting the outcomes of different scenarios, but they are not always accurate representations of reality. Running a simulation model several times with different order quantities can give an indication of the order quantity that maximizes the output, but it does not guarantee that this is the optimal order quantity.

There are many factors that can affect the outcome of a simulation model, such as the model's assumptions, limitations, and inputs. Additionally, simulation models are subject to randomness and variability, so the results of different runs may vary.

For this reason, it is important to consider other factors, such as the company's attitude toward risk, when making decisions based on the results of a simulation model. The company's attitude toward risk can influence the choice of order quantity and affect the overall outcome of the simulation.

Therefore, while the order quantity that maximizes the output in a simulation model might be a good starting point, it is not necessarily the optimal order quantity. Further analysis and consideration of other factors is necessary to determine the best order quantity for the company.

A ratio is a mathematical expression that compares the relative size of two or more values. It is a way of expressing the relationship between two or more quantities in terms of their relative size.

A ratio can be expressed in different ways, such as a fraction, decimal, or percentage. For example, the ratio of 2 to 4 can be expressed as 2/4, 0.5, or 50%.

Ratios are used in many areas of mathematics and science, such as finance, economics, engineering, and physics, to describe and analyze relationships between quantities. For example, in finance, ratios are used to measure a company's financial performance, such as its profitability, liquidity, and debt-to-equity ratios. In engineering, ratios are used to describe the relationship between the size and power of a machine, such as the gear ratio in a car's transmission.

In general, ratios are useful for comparing quantities and understanding the relationships between them, and they play a key role in many aspects of mathematics and science.

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Answer:

Long solution

Step-by-step explanation:

(a) Let the height of the cone be h cm. The volume of the hemisphere is given by (1/2)(4/3)πr³ = (2/3)πr³. The volume of the solid is the sum of the volumes of the hemisphere and the cone, which is (2/3)πr³ + (1/3)πr²h. Since the volume of the hemisphere is one third of the volume of the solid, we have:

(2/3)πr³ = (1/3)πr²h

Simplifying, we get:

2r = h

Therefore, h is expressed in terms of r as h = 2r.

(b) The slant height of the cone can be found using the Pythagorean theorem. Let l be the slant height, then we have:

l² = r² + h²

Substituting h = 2r, we get:

l² = r² + (2r)² = 5r²

Taking the square root of both sides, we get:

l = r√5

Since k is an integer, we can write:

l = Vk cm, where k is an integer

Comparing the two expressions, we get:

Vk = r√5

Therefore, the value of k is k = ⌊r√5⌋, where ⌊x⌋ denotes the largest integer less than or equal to x.

(c) The total surface area of the solid is the sum of the curved surface area of the cone, the curved surface area of the hemisphere, and the area of the circular base of the cone. We have:

Curved surface area of the cone = πr l = πr(r√5) = πr²√5

Curved surface area of the hemisphere = 2πr²

Area of the circular base of the cone = πr²

Therefore, the total surface area of the solid, in cm², is given by:

πr²√5 + 2πr² + πr² = (πr²)(√5 + 3)

Step-by-step explanation:

5.

\(y = \frac{2}{3} x - 1\)

6.

\(y = - x + 8\)

7.

given two points

(-4,2) and (0,-4)

slope is (-4-2)÷(0-(-4))=-6÷4=-1.5

\(y = - 1.5x - 4\)

8.

given two points

(0,0) and (5,0)

slope is 5

\(y = 5x\)

9.

\(2x + 8y = 16 \\ x + 4y = 8 \\ 4y = - x + 8 \\ y = - \frac{1}{4} x + 2\)

10.

\(3x - y = 5 \\ y = 3x - 5\)

Answer:

i think its a or d

Step-by-step explanation:

Answer:

\(\bold{\dfrac{11}{2 }}\)

Step-by-step explanation:

Given the geometric series:

\(\{\dfrac{1}2, -1, 2, -4, ..... \}\)

To find:

Sum of series upto 5 terms using the geometric series formula = ?

Solution:

Formula for sum of a n terms of a geometric series is given as:

\(S_n=\dfrac{a(1-r^n)}{1-r} \ \{r<1 \}\)

\(a\) is the first term of the geometric series

\(r\) is the common ratio between each term (2nd term divided by 1st term or 3rd term divided by 2nd term ..... ).

Here:

\(a = \dfrac{1}{2}\)

\(r = \dfrac{-1}{\dfrac{1}{2}} = -2\)

\(n=5\)

So, applying the formula for given values:

\(S_5=\dfrac{\dfrac{1}2(1-(-2)^5)}{1-(-2)} \\\Rightarrow S_5=\dfrac{1-(-32)}{2 \times 3} \\\Rightarrow S_5=\dfrac{1+32}{6} \\\Rightarrow S_5=\dfrac{33}{6} \\\Rightarrow \bold{S_5=\dfrac{11}{2}}\)

So, the answer is

\(\bold{\dfrac{11}{2 }}\)

By using the concept of LCM, it can be concluded that

It is necessary to find the LCM of polynomials to divide polynomials

What is LCM ?

LCM means least common  multiple. LCM of two numbers a and b is the least number which is divisible by both a and b.

LCM means least common multiple

As there is a question of multiple here, so there will be a concept of division into question

So it is necessary to find the LCM of polynomials to divide polynomials

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Value falls within the 90% confidence interval for a sample size of 45 is 3.28. The correct option is C.

To determine which value falls within the 90% confidence interval for a sample size of 45, we need to calculate the margin of error and then find the range of values within that interval.

The margin of error (E) can be calculated using the formula:

E = (Z * σ) / √n

Where:

Z is the critical value corresponding to the desired confidence level (in this case, for a 90% confidence level),

σ is the standard deviation, and

n is the sample size.

The critical value for a 90% confidence level can be obtained from a standard normal distribution table, and it is approximately 1.645.

Substituting the given values into the formula, we have:

E = (1.645 * 0.98) / √45

E ≈ 0.309

The confidence interval is then calculated as the sample mean ± the margin of error.

Lower Limit = Sample Mean - E

Lower Limit = 3.56 - 0.309

Lower Limit ≈ 3.251

Upper Limit = Sample Mean + E

Upper Limit = 3.56 + 0.309

Upper Limit ≈ 3.869

From the given answer choices, the value that falls within the 90% confidence interval is:

C. 3.28

Therefore, the correct option is C. 3.28.

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Answer: (3x+4)^2

Step-by-step explanation: X is the unknown numerical value.

Answer:

(3x+4)^2

Step-by-step explanation:

Answer: -6.3 lb after 3.5 hours

Step-by-step explanation:

-1 (4)/(5) = -9/5 = -1.8

0.5hr = -0.9

1hr = -1.8

2hr=-3.6

3hr=-5.4

3.5hr = -6.3

Answer:

21.4 miles (Answer A)

Step-by-step explanation:

17 miles west and then 13 miles south can be represented by a triangle whose leg lengths are 17 miles and 13 miles respectively.  We use the Pythagorean Theorem to find the length of the hypotenuse of this triangle; the hypotenuse length is the straight line distance between starting and end points:

d = √(13² + 17²) miles, or d = 21.4 miles

The matrices A and B that were defined are the integer matrices:

A = [1 0 0; 0 1 0]

B = [1 1 0; 0 0 0]

Both A and B are integer matrices, and they have the same null space and column space but are not multiples of each other. Therefore, they satisfy the requirements " Integer matrices A,B not multiples of each other such that Nul(A)=Nul(B) and Col(A)=Col(B)."

Let A and B be 3x3 matrices given by:

A = [1 0 0; 0 1 0]

B = [1 1 0; 0 0 0]

We can see that A and B have the same null space and column space, but they are not multiples of each other. To show that A and B have the same null space, we need to find the null space of both matrices.

For A, we need to solve the equation Ax = 0:

[1 0 0; 0 1 0] [x1; x2; x3] = [0; 0]

This Equations has the unique solution x = [0; 0; 0], so null space of A is the trivial subspace {0}.

For B, first solve the equation Bx = 0:

[1 1 0; 0 0 0] [x1; x2; x3] = [0; 0]

This equations has the general solution x = [-x2; x2; x3], where x2 and x3 are arbitrary integers, so null space of B is the subspace spanned by the vector [-1; 1; 0].

Show that A and B have the same column space, we have to show the columns of A and B span the same subspace. The columns of A are [1; 0] and [0; 1], which span the entire 2-dimensional space. The columns of B are [1; 0] and [1; 0], which span the 1-dimensional subspace { [x; x] : x is an integer }. But, the column space of A is also the subspace { [x; y] : x and y are integers }, which is the same as the column space of B.

Therefore, A and B have the same column space.

Since A and B have the same null space and column space but are not multiples of each other, they satisfy the conditions " integer matrices A,B not multiples of each other such that Nul(A)=Nul(B) and Col(A)=Col(B)."

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The number of portion with each having 12 fruits is at most 6 portions.

To divide the fruits into 12 portions

Total number of fruits = 80

Number of fruits per portion = 12

Number of fruits per portion = (Total number of fruits / Number of fruits per portion )

Number of fruits per portion = 80/12 = 6.67

Therefore, to divide the fruits into 12 fruits , There would be at most 6 portions.

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To determine the p-value corresponding to a z-test statistic of 1.47 in a right-tailed test, we need to find the probability of obtaining a z-value equal to or greater than 1.47.

The p-value is the probability of observing a test statistic as extreme as, or more extreme than, the one calculated under the null hypothesis.

Using a standard normal distribution table or calculator, we can find the area to the right of 1.47. This area represents the probability of obtaining a z-value greater than 1.47.

Looking up the z-score of 1.47 in a standard normal distribution table, we find that the corresponding area is approximately 0.9292.

Since this is a right-tailed test, the p-value is equal to the area to the right of the test statistic. Therefore, the p-value is approximately 0.9292.

Thus, the p-value is approximately 0.9292 or 92.92%.

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Explanation:

The "given the customer ordered a cold drink" means we only focus on the bottom row of values. There are B = 8+12+5 = 25 people who ordered a cold drink. Of that total, A = 5 people ordered a cold large drink.

The probability we want is A/B = 5/25 = 1/5 = 0.20 = 20%

a. triangle XYZ

b. Locus of a point equidistant from Y and Z:

c. Construct point Q on this locus, equidistant from YX and YZ:

To construct a line, we have to;

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Answer:

Step-by-step explanation:

    a) Diameter = 2.1 m

                      r = 2.1 ÷ 2 = 1.05 m

            Area   = πr²

                       = 3.14 * 1.05 * 1.05

                      = 3.46 = 3.5 m²

    b) To find the number of paint tins, divide the area of table top by 1.75 m²

     Number of tins =  3.5 ÷ 1.75

                               = 2 tins

c) Cost of 1 tin = $ 5.50

   Cost of 2 tin = 2 *5.50

                        = $ 11

\(\sf d) Cost\ of \ labour = \dfrac{2}{3} * 11\)

                         = $ 7.30

Answer:

a=3.46 (2dp)   b(ii)=2  

Step-by-step explanation:

a)

πr²=area

2.1/2 = 1.05 as the radius

1.05² x π= 3.46 (2dp)

b)

3.46/1.75= 1.98

1.98 can be changed into two

∴ 2 tins will be needed

To conduct a hypothesis test to determine if the population proportion of good parts is the same for all three shifts, we can use a chi-square test for independence.

The null hypothesis states that the proportions of good parts in each shift are equal, while the alternative hypothesis states that they are not equal.
Assuming a significance level of .05, we can calculate the p-value of the test. If the p-value is less than .05, we reject the null hypothesis, indicating that there is evidence to suggest that the population proportions are not equal. On the other hand, if the p-value is greater than .05, we fail to reject the null hypothesis, indicating that there is not enough evidence to suggest that the population proportions are not equal.
After performing the test, we obtain a p-value of .02. Since this value is less than .05, we reject the null hypothesis and conclude that there is evidence to suggest that the population proportions of good parts are not equal for all three shifts. Therefore, we can conclude that there is a significant difference in the proportion of good parts produced by each shift.

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Answer:

1

Step-by-step explanation:

Answer: 1

Step-by-step explanation:

     We can find the slope by using the slope formula.

           \(\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }\)

           \(\displaystyle \frac{4-0}{4-0}\)

           \(\displaystyle \frac{4}{4}\)

           1

The five-number summary would therefore be 0, 0.5, 7.5, 44, and 63.

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The chi-square goodness-of-fit test can provide important information about whether the observed data significantly deviates from the expected distribution, which categories or bins contribute to the deviation, and the overall goodness-of-fit of the data to the expected distribution.

The chi-square goodness-of-fit test is a statistical test used to determine if a sample of data comes from a population with a specific distribution. Specifically, the test compares the observed frequencies of data in different categories or bins with the expected frequencies of data in those categories based on a hypothesized distribution.

It can determine whether the observed data significantly deviates from the expected distribution. If the test results in a p-value less than the chosen level of significance, it indicates that the observed data significantly deviates from the expected distribution, and the null hypothesis (that the data follows the expected distribution) can be rejected.

It can identify which categories or bins contribute the most to any significant deviation. The test statistic and associated p-value can help to identify which categories or bins show significant differences between the observed and expected frequencies.

It can provide information on the overall goodness-of-fit of the data to the expected distribution. The test statistic provides a measure of the overall goodness-of-fit, with higher values indicating greater deviation from the expected distribution.

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The system of equations that models the given situation are;

y = 10x + 35

y = 5x + 35

Let x denote the number of years since 2010

Let y denote the total members

The linear equation in slope intercept form is expressed as;

y = mx + b

where;

m is the slope or unit rate

b is the y-intercept or initial value

For the swim team, since  the team increased by an average of 10 members per year, then;

Slope = 10

In 2010, they had 5 members and so; y-intercept = 35

Thus, the equation is; y = 10x + 35

For the chorus team, we can deduce that;

Slope = 5 members per year

In 2010, they had 35 members and so; y-intercept = 35

Thus, the equation is; y = 5x + 35

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Complete question is;

Central High School had five members on their swim team in 2010. Over the next several years, the team increased by an average of 10 members per year. The same school had 35 members in their chorus in 2010. The chorus saw an increase of 5 members per year. Write a system of equations to model this situation, where x represents the number of years since 2010.

The 95% confidence interval for the mean gas mileage for this car model is (26.26, 28.74) mi/gallon.

The confidence interval for a statistical data is written as-

(x+ zr/√n, x- zr/√n)

Here, we are given that-

Mean ⇒ x = 27.5 mi/gallon.

Standard deviation ⇒ r = 4 mi/gallon

Number of samples ⇒ n = 49

and Confidence interval = 95%

z-score at 95% confidence level = 2.17

Substituting the values we have;

= [27.5 - 2.17(4.0) /(√49),  27.5 + 2.17(4.0) /(√49)]

= (27.5 - 8.68 / 7,  27.5 + 8.68 / 7)

= (27.5 - 1.24,  27.5 + 1.24)

= ( 26.26, 28.74)

Therefore, the 95% confidence interval for the mean gas mileage for this car model is (26.26, 28.74) mi/gallon.

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The second boxplot is correct representation of the number of customers at each Slurpee Sam's Spaghetti Shop.

Given the data set is,

24, 25, 29, 30, 31, 31, 32, 34, 34

Hence, Minimum value = 24

Maximum value = 34

And, First quartile (Q1) = 1/4(n+1)th term

Q1 = 1/4 x 10 = 10/4 = 2.5th term = (25+29)/2 = 27

Q2 = 1/2(n+1)th term = 1/2(10) = 5th = 31

Q3 = 3/4(n+1)th term = 3/4(10) = 30/4 = 7.5th term = (7th +8th) term = (32 + 34) / 2 = 66/2 = 33

Hence, correct boxplot should have :

Minimum value = 24

Q1 = 27

Q2 = 31

Q3 = 33

Maximum value = 34

Thus, The second boxplot is correct.

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Answer:

The answer is true

Step-by-step explanation:

14(-9)-17(-8)=10

11(-9)-14(-8)=13

Answer:

Hello!!

Yes, (-9,-8) is a solution to the system of equations.

\(14x-17y=10\\11x-14y=13\)

Step-by-step explanation:

Solve for the first variable in either one of the equations and then substitute the result for the other equation.

Hope this helps and let me know if you need any other help!

Answer:

\(y=\dfrac{1}{625}\)

Step-by-step explanation:

Given equation:

\(y=\left(\dfrac{1}{5}\right)^x\)

Substitute x = 4 into the given equation:

\(\implies y=\left(\dfrac{1}{5}\right)^4\)

\(\textsf{Apply exponent rule} \quad \left(\dfrac{a}{b}\right)^c=\dfrac{a^c}{b^c}:\)

\(\implies y=\dfrac{1^4}{5^4}\)

Simplify:

\(\implies y=\dfrac{1\times1\times1\times1}{5\times5\times5\times5}\)

\(\implies y=\dfrac{1}{25\times5\times5}\)

\(\implies y=\dfrac{1}{125\times5}\)

\(\implies y=\dfrac{1}{625}\)

After 15 more years of contributions of $4,000 at the end of each quarter, the retirement account will be worth approximately $760,514.47.

To calculate this, we need to use the formula for the future value of a lump sum. A lump sum is a one-time payment made at the beginning or end of a specific period. In this case, we're looking at the future value of the retirement account after 15 more years of contributions.

Using the given information, we can plug in the values and solve for FV:

PV = $150,000

Pmt = $4,000

r = 10%

n = 4 (since interest is compounded quarterly)

t = 15 years

First, we need to calculate the future value of the current investment of $150,000:

FV1 = $150,000 x (1 + 0.1/4)⁴ ˣ ¹⁵ = $548,534.24

Then, we can calculate the future value of the quarterly contributions of $4,000 over 15 years:

FV2 = $4,000 x [(1 + 0.1/4)⁶⁰ - 1] / (0.1/4) = $211,980.23

Finally, we can add FV1 and FV2 to get the total future value of the retirement account after 15 more years:

Total FV = FV1 + FV2 = $548,534.24 + $211,980.23 = $760,514.47

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