To stock your school store, you buy a total of 25 sweatshirts and hats for $172.50. You pay $8.00 per sweatshirt and $2.50 per hat. How many of each item do you buy?

Answer:

i think the green line would be the horizontal asymptote cause its like horizontal amd it goes across the graph.

Step-by-step explanation:

The 90% confidence interval for the mean height of students at UH is (5.885,5.915) feet.

We have given that, an srs of 28 students at UH gave an average height of 5.9 feet and a standard deviation  of 0.1 feet.

i.e n = 28

x = 5.9 feet

s = 0.1 feet

and we have to construct a 90% confidence interval for the mean height of students at UH.

The level of significance, α = 1 - 0.9 = 0.1

The value of 0.9 in z-table is 0.816.

The formula for confidence interval is,

CI = x ± z* (s/\(\sqrt{n}\))

Substituting the values,

CI = 5.9 ± (0.816) (0.1/√28 )

   = 5.9 ± (0.816)(0.1/5.291)

   = 5.9 ± (0.816)(0.0189)

CI = 5.9 ± 0.015

CI = 5.9 + 0.015 = 5.915

CI = 5.9 - 0.015 = 5.885

Therefore 90% confidence interval for the mean height of students at UH is 5.885 feet to 5.915 feet.

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Answer:

You should buy 3 packages of beads that come in packages of 4 and 1 package of beads that come in packages of 12 to have an equal number of each of the different kinds of beads.

Step-by-step explanation:

Since the different kinds of beads Jen is using to make purses come in packages of 4 and 12, to determine what is the least number of each kind of bead Jen can buy to have an equal number of each of the different kinds of beads the following calculation must be performed:

12/4 = 3

4 x 3 = 12

Thus, you should buy 3 packages of beads that come in packages of 4 and 1 package of beads that come in packages of 12 to have an equal number of each of the different kinds of beads.

Answer:

  (C)  2

Step-by-step explanation:

Given equations 2a + 7b+2c=16 and 2a + 3b +2c= 8, you want to know the value of b.

The coefficients of 'a' and 'c' are the same in the two equations, so we can eliminate those variables by subtracting one equation from the other. We can keep the resulting coefficient of 'b' positive if we subtract the second equation from the first.

  (2a +7b +2c) -(2a +3b +2c) = (16) -(8)

  4b = 8 . . . . . . . simplify

  b = 2 . . . . . . . divide by 4

Answer:

can u add a picture please?

Step-by-step explanation:

multiply Start Fraction 5 Over 7 End Fraction by 3.

What do math fractions mean?

An element of a whole is a fraction. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction.

                                Whether it is in the numerator or denominator, a complex fraction contains a fraction.

                             The numerator and denominator of a correct fraction are opposite each other.

What is basic fraction theory?

Every fraction has two components: the numerator, which is the actual number of parts, and the denominator, which is the total number of parts.

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Answer:

c is the answer i took the test

Step-by-step explanation:

The least preferable and reliable method of selecting people to participate in a research study is convenience sampling.

Convenience sampling is a type of sampling in which you include people who are easy to reach. Convenience sampling is included in non-probability sampling because it doesn't include a random selection of the participants. Convenience sampling can be used when you need to conduct a study quickly or when you are on a shoestring budget as it is inexpensive compared to other methods of sampling.

It is the least preferable method because of the inability to generalize the result of the survey to the population as a whole. In addition to this, there is a possibility of under or over-representation of the population as a whole. The biggest problem with convenience sampling is dependence as the sample items are connected to each another in some way. This dependency interferes with statistical analysis.

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The triangles ∆ABC and ∆ADC are similar triangles, and:

m∠BAC = m∠DAC = 70°

m∠ACB = 20°

CB = CD = 12

AB = DA = 7

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

Considering the angles of the right triangle ACD;

m∠DAC = 180° - (90 + 20)°

m∠DAC = 70°

The angle m∠BAC corresponds to m∠DAC so;

m∠BAC = m∠DAC = 70°

The angle m∠ACB corresponds to m∠ACD so;

m∠ACB = m∠ACD = 20°

The side AB corresponds to side DA hence;

5x - 3 = 3x + 1

5x - 3x = 1 + 3 {collect like terms}

2x = 4

x = 4/2

x = 2

AB = 5(2) - 3 = 7

AB = DA = 7

In conclusion, since the triangles ∆ABC and ∆ADC are similar triangles, then:

m∠BAC = m∠DAC = 70°

m∠ACB = 20°

CB = CD = 12

AB = DA = 7

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Answer: 11 pieces of candy

Step-by-step explanation: First we would have to do 64 ÷ 8 which gives us 8. Then since Mrs. Fry adds 3 lollipops to each bag we would do 8 + 3 which gives us 11.

The formula for allocation deviation is as follows:σA = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)σB = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)

Here,

σ1 = 15%

σ2 = 10%

w1 = 50%,

w2 = 50%

Substituting the values in the above formula:

σA = (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158 = 1.58%σB

= (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158

= 1.58%

Hence, the correct option is

D. σ(A) = 14.14%;

σ(B) = 16.33%.

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There are 11,390,625 license plates that differ from Megan's at exactly one position.

To do this, we will use the following formula:

Number of license plates that differ at exactly one position = Number of different options for the first position × Number of different options for the second position × Number of different options for the third position × Number of different options for the fourth position × Number of different options for the fifth position × Number of different options for the sixth position

For the first position, there are 25 different options (26 letters in the alphabet - 1 for the letter "u" that is already in Megan's license plate).

For the second position, there are 25 different options (26 letters in the alphabet - 1 for the letter "w" that is already in Megan's license plate).

For the third position, there are 25 different options (26 letters in the alphabet - 1 for the letter "u" that is already in Megan's license plate).

For the fourth position, there are 9 different options (10 digits - 1 for the digit "1" that is already in Megan's license plate).

For the fifth position, there are 9 different options (10 digits - 1 for the digit "4" that is already in Megan's license plate).

For the sixth position, there are 9 different options (10 digits - 1 for the digit "4" that is already in Megan's license plate).

So, the total number of license plates that differ from Megan's at exactly one position is:

25 × 25 × 25 × 9 × 9 × 9 = 11,390,625.

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We fail to reject the null hypothesis that the temperature level has no effect on the mean yield process.

Summary of Result:

Source | SS | df | MS | F | p-value

Treatment | 118.2 | 2 | 59.1 | 2.94 | 0.095

Error | 241.0 | 12 | 20.1 | |

Total | 359.2 | 14 | | |

To construct an analysis of variance (ANOVA) table and test whether the temperature level has an effect on the mean yield process, we need to perform the following steps:

Step 1: Calculate the total sum of squares (SST), the treatment sum of squares (SSTR), and the error sum of squares (SSE).

SST = ΣΣ(yij - ȳ)^2 = 359.2

where yij is the yield of the ith batch at the jth temperature level and ȳ is the overall mean yield.

SSTR = Σ(nj(ȳj - ȳ)^2) = 118.2

where nj is the number of batches produced at the jth temperature level, ȳj is the mean yield at the jth temperature level, and ȳ is the overall mean yield.

SSE = SST - SSTR = 241.0

Step 2: Calculate the degrees of freedom (df) for SST, SSTR, and SSE.

df(Total) = N - 1 = 14

where N is the total number of observations.

df(Treatment) = k - 1 = 2

where k is the number of treatment levels.

df(Error) = df(Total) - df(Treatment) = 12

Step 3: Calculate the mean square (MS) for SSTR and SSE.

MS(Treatment) = SSTR / df(Treatment) = 59.1

MS(Error) = SSE / df(Error) = 20.1

Step 4: Calculate the F-statistic.

F = MS(Treatment) / MS(Error) = 2.94

Step 5: Determine the critical value of F for a 0.05 level of significance with df(Treatment) = 2 and df(Error) = 12.

From a table of F-distributions, the critical value of F is 3.89.

Step 6: Compare the F-statistic to the critical value of F and make a decision.

Since 2.94 < 3.89, we fail to reject the null hypothesis that the temperature level has no effect on the mean yield process. In other words, we do not have sufficient evidence to conclude that there is a difference in mean yield among the three temperature levels.

Step 7: Summarize the results in an ANOVA table.

Source | SS | df | MS | F | p-value

Treatment | 118.2 | 2 | 59.1 | 2.94 | 0.095

Error | 241.0 | 12 | 20.1 | |

Total | 359.2 | 14 | | |

Note: The p-value is calculated as P(F > 2.94) = 0.095, which is greater than the significance level of 0.05. Therefore, we do not reject the null hypothesis.

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Answer:

Step-by-step explanation:

42.6 divided by 0.07 is 608.571428

Regular division.

The value of x in the given equation is 24.

Given equation:

(2/3)x + 4 = (5/6)x

We have to find the value of x by eliminating the fraction.

Fraction

Fraction is  termed as a portion or section of any quantity. It is denoted by using ‘/’ symbol, such as a/b. For example, in 2/4 is a fraction where the upper part denotes the numerator and the lower part is the denominator.

LCM (3,6) = 6

Multiplying the whole equation by 6, we get:-

(2/3)x*6 + 4*6 = (5/6)x*6

4x + 24 = 5x

5x - 4x = 24

x = 24

Hence, the value of x is 24.

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The variables on the horizontal and vertical axes of a scatter plot are always continuous.Corresponding: When two sets of data are plotted on a scatter plot, each data point in the two sets has a corresponding point in the other set.

When you plot two sets of data on a scatter plot, you should use different colors or symbols for the data points from each set.The horizontal axis represents one variable while the vertical axis represents the other. Each point on the graph represents one set of data that corresponds to both variables, with the x-value and y-value corresponding to the respective data points being plotted.Scatterplot versus: A scatter plot has two axes that correspond to two variables. In a scatter plot, we can determine how one variable changes as the other variable changes. The variables on the horizontal and vertical axes of a scatter plot are always continuous.Corresponding: When two sets of data are plotted on a scatter plot, each data point in the two sets has a corresponding point in the other set. When you plot two sets of data on a scatter plot, you should use different colors or symbols for the data points from each set.

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Step-by-step explanation:

When 508,000,000 is written in scientific notation, it will be represented as:

5.08 x 10^8

Therefore, the value of the exponent is 8.

Answer: Distance of  flower from the base of the tree = 0.4 meters

Step-by-step explanation:

Given: A hummingbird lives in a nest that is 9 meters high in a tree. The hummingbird flies 9.4 meters to get from its nest to a flower on the ground.

Distance of  flower from the base of the tree = 9.4 meters - 9 meters

= 0.4 meters

Hence, Distance of  flower from the base of the tree = 0.4 meters

Answer:

Step-by-step explanation:

410 ft i think

Answer: 75.6

rounded= 76 ft

Step-by-step explanation:

Tan60= x/400 = 692.8

tan62.5= 4/400 =  768.4

x= 75.6ft

Main Answer:The recurrence relation for the power series solution of the given differential equation is:   a_(n+2) = a_n / (n+2)

Supporting Question and Answer:

How can we find the recurrence relation for the power series solution of a differential equation?

To find the recurrence relation for the power series solution of a differential equation, we can assume the solution can be expressed as a power series and substitute it into the differential equation. By equating the coefficients of like powers of x to zero, we can derive the recurrence relation for the coefficients of the power series. This recurrence relation allows us to express the coefficients in terms of previous coefficients, providing a systematic way to compute the coefficients of the power series solution.

Body of the Solution: To find the recurrence relation for the power series solution of the differential equation y′′(1 - x)y = 0, we can assume that the solution can be expressed as a power series:

y(x) = ∑(n=0)^(∞) a_n x^n

First, to find the first and second derivatives of y(x):

y'(x) = ∑(n=1)^(∞) na_nx^(n-1)

=∑(n=0)^(∞) (n+1)×a_(n+1)×(x)^n

y''(x) =∑(n=2)^(∞) n(n-1)a_nx^(n-2)

= ∑(n=0)^(∞) (n+2)(n+1)×a_(n+2)×(x)^n

Now, substitute these expressions into the differential equation:

∑(n=0)^(∞) (n+2)(n+1)×a_(n+2)×(x)^n× (1 - x) × ∑(n=0)^(∞) a_n x^n = 0

Expand and collect terms:

∑(n=0)^(∞) [(n+2)(n+1)×a_(n+2) - (n+1)×a_n] ×( x)^n - ∑(n=0)^(∞) (n+2)(n+1)×a_(n+2)×(x)^(n+1) = 0

Now, equating the coefficients of like powers of x to zero:

For n = 0:

[(2)(1)×a_2 - (1)×a_0] = 0

a_2 = a_0

For n ≥ 1:

[(n+2)(n+1)×a_(n+2) - (n+1)×a_n] - (n+2)(n+1)×a_(n+2) = 0

a_(n+2) = (n+1)×a_n / ((n+2)(n+1)) = a_n / (n+2)

Final Answer: Hence, the recurrence relation for the power series solution of the given differential equation is:

a_(n+2) = a_n / (n+2);where a_0 is a constant representing the coefficient of x^0 in the power series solution.

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Answer:

2

Step-by-step explanation:

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

= (22-10)/(2--4)

= 12/(2+4)

= 12/6

=2

The future value of the $10,000 investment after 7 years, at an interest rate of 6% per year, compounded annually, is approximately $14,185.10.

To calculate the future value (FV) of an investment of $10,000 at an interest rate of 6% per year, compounded annually, after 7 years, we can use the formula:

FV = P(1 + r)^n

Where:

P is the principal amount (initial investment) = $10,000

r is the interest rate per period = 6% = 0.06

n is the number of periods = 7

Plugging in the values, we have:

FV = $10,000(1 + 0.06)^7

Calculating the expression inside the parentheses first:

(1 + 0.06)^7 ≈ 1.41851

Now, multiply the principal amount by the calculated expression:

FV ≈ $10,000 * 1.41851 ≈ $14,185.10

Therefore, the future value of the $10,000 investment after 7 years, at an interest rate of 6% per year, compounded annually, is approximately $14,185.10.

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Answer:

3343621.39918 or rounding would be 3343621.40

Step-by-step explanation:

this is because taking 260,000 divided by .6 then dividing that answer by .6 so on till you done that five times

Applying the rules of exponents, the letter answers that form the code are: MATH IS NOT JUST ANOTHER FOUR LETTER WORD.

Some of the rules of exponents to be applied are as follows:

\(x^0 = 1\\\\x^m \times x^n = x^{(m + n)}\\\\x^{-m} = \frac{1}{x^m} \\\\x^m \div x^n = x^{(m - n)}\\\\\)

If two expressions have the same value, both are said to be equivalent expressions.

1. \(3^2 \times 3^{-5} = 3^{2 - 5}\\\\\)

\(3^-3 = \frac{1}{3^3} = \frac{1}{27}\)

Answer: H

2. 3³/6² = 27/36 = 3/4

Answer: R

3. \(\frac{3^2}{3^5} = 3^{2 - 5} = 3^{-3]} = \frac{1}{3^3} = \frac{1}{27}\)

Answer: M

4. 7²/7² = 49/49 = 7° = 1

Answer: J

5. 8^-2 = 1/8² = 1/64

Answer: A

6. (4²)(4³) = 4^(2 + 3) = \(4^5\)

Answer: L

7. (3²)³ = 3²*³ = \(3^6\)

8. 4° × 4^-1 = 1 × 1/4 = 1/4

Answer: E

9. \(\frac{(2^4)^3}{(2^7)(2^5)} = \frac{2^{12}}{2^{12}}\) = 1

Answer: U

10. \((3^2)^{-1} = 3^{-2}\)

Answer: I

11. \(1^{98}\) = 1

Answer: D

12. \(y^{10} \div y^5 = y^{10 - 5} = y^5\)

Answer: F

13. \(8^{-2} \times 8^4 = 8^{(-2 + 4)}\) = 8² = 64

Answer: S

14. \(2^{-3} \times 3^{-2} =\) 1/2³ × 1/3² = 1/8 × 1/9 = 1/72

Answer: O

15. \(\frac{3^2}{3^2} = 3^{2-2} = 3^0 = 1\)

Answer: N

16. \((\frac{1}{2} )^{-1} = (2^{-1})^{-1}\) = 2

Answer: T

Thus, applying the rules of exponents, the letter answers that form the code are: MATH IS NOT JUST ANOTHER FOUR LETTER WORD.

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Answer:

a cycle is a sequence of non-repeated vertices and the degree of a graph is the number of neighbors the vertex has.

The total number of adult tickets sold is 250.

x / y  = 2/5

Cross multiply :5x = 2y

y = 5/2

y = 2.5x

(x + 70) / (y + 300) = 1/3

Cross multiply :210 + 3x = 300 + y

Substitute for y

210 + 3x = 300 + 2.5x

300 - 210 = 3x - 2.5x

90 = 0.5x

x = 90 / 0.5

x = 180

Total tickets sold = 180 + 70 = 250

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Answer:

Step-by-step explanation:

She collected 2/6 gallon of orange juice from two trees and 2/3 from the last tree.  To add these two fractions, both must have common denominators.

Multiply both the numerator and denominator of 2/3 by 2.  This results in 4/6.

Now you have 4/6 + 2/6 which equals 8/6.  This can be converted to 1 and 2/6, further simplified to 1 and 1/3.  Therefore, Sue collected a total of 1 and 1/3 gallons of orange juice.

Answer:

7 (b - 5) (b- 4)