In choosing what music to play at a charity fund raising event, Cory needs to have an equal number of piano sonatas from Haydn, Mozart, and Schubert. If he is setting up a schedule of the 15 piano sonatas to be played, and he has 52 Haydn, 18 Mozart, and 21 Schubert piano sonatas from which to choose, how many different schedules are possible? Express your answer in scientific notation rounding to the hundredths place.

Micro middle sold the least no of different types of consoles.

Matrices represent data in the form of rows and columns together as an array form.

From matrix A we get the data as follows,

A row represents shops and columns represents types of console.

Games Go sold (53 + 21 + 48) = 122 different types of consoles.

Better Buy sold (65 + 34 + 70) = 169 different types of consoles.

Micro middle sold (18 + 11 + 15) = 34 different types of consoles.

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Answer:

176.6

Step-by-step explanation:

You can use sine, cosine, or tangent to find x (the trick is determining which to use).

Looking at the 63° angle, its adjacent side is GH, which has a length of 90. The opposite side of the 63° angle is side FG, which has a length of x. You're going to need a ratio that will give you the opposite side knowing the adjacent.

You can use the... acronym?... SOH-CAH-TOA.

SOH - When using sine (S), you get the ratio of the opposite (O) side to the hypotenuse (H).

CAH - When using cosine (C), you get the ratio of the adjacent (A) side to the hypotenuse (H).

TOA - When using tangent (T), you get the ratio of the opposite (O) side to the adjacent (A) side.

Since we're not using the hypotenuse at all, we need to use tangent, which is the ratio of opposite to adjacent. You can set up the equation:

tan(63°) = x/90

Type this into your calculator (make sure it's in degrees and not radians!) and you get:

1.9626 * 90 = x

x = 176.6

The relation between a and r is 2r

According to the given information

a varies directly with r

a = 8

r = 4

a is directly proportional to r

a ∝ r

a = k r

where k is constant of proportionality

k =  [tex]\frac{a}{r}[/tex]

k = [tex]\frac{8}{4}[/tex]

k = 2

so,

a = k r

putting the value of k in the above equation

we get

a = 2r

The relation between a and r is 2r

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Answer: 1

Let's solve your equation step-by-step.

3x+2=5

Step 1: Subtract 2 from both sides.

3x+2−2=5−2

3x=3

Step 2: Divide both sides by 3.

3x/3 = 3/3

(3x divided by 3 cancels the 3 in 3x making it just x)

x=1

Therefore demand is "decreased by 100 units".

What is predicted value in regression?

Given the values of X, we can predict the values of Y using the regression line. We go directly up to the line for any given value of X, then move horizontally to the left to get the value of Y. The expected value of Y is abbreviated Y' and is known as the predicted value of Y.

[tex]$$\begin{aligned}& \hat{y}=130-20 x \\& \hat{y}=\text { demand of product } \\& x=\text { price of product }\end{aligned}$$[/tex]

Given [tex]$x$[/tex], increased by 5 units

[tex]$$\begin{aligned}& \hat{y}=130-20(x+5)=130-20 x-100 \\& \hat{y}=30-20 x\end{aligned}$$[/tex]

Therefore demand is "decreased by 100 units"

Complete question: Regression analysis was applied between demand for a product (y) and the price of the product (x), and the following estimated regression equation was obtained. ŷ = 130 − 20x Based on the above estimated regression equation, if price is increased by 5 units, then demand is expected to: increase by 100 units. decrease by 20 units. increase by 130 units. decrease by 100 units.

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The height of the new building in the zoo is calculated to be 6.375 m

The problem is solved by using the scale factor to increase or decrease the model.

When the scale factor is less than it leads to decrease but when above  it leads to increasing.

The case in the problem is increasing.

First, they made a model that was 1.7 meters tall

the height of the model = 1.7 m

a more detailed model that was 1.5 times as tall as the first model

the height of the detailed model = 1.7 * 1.5 = 2.55 m

The building will be 2.5 times as tall as the height of the detailed model

= 2.5 * height of the detailed model

= 2.5 * 2.55

= 6.375 m

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The part (a) is not correct i.e. The slope is 3, which indicates that a mouse's weight should increase by about 3 grams for each additional millimeter of tail length.

What is Regression analysis ?

Regression analysis is the process of determining how one or more variables and the outcome variable relate to one another. Risk factors, co-founders, and the outcome variable are all referred to as predictors or independent variables. The result variable is sometimes referred to as the dependent or response variable. Regression analysis displays the dependent variable as "y" and the independent variables as "x".

Given, tail length = (3 × weight) + 20

(a) Here, The slope is 3 which indicates that a mouse's length is the sum of 3 times the weight and 20. So, the statement is not correct.

(b) If weight is 38 gm, then

    tail length = 38 × 3 + 20

                     = 114 + 20 = 134mm.

So, the statement is correct.

(c) We've  tail length = (3 × weight) + 20

we can see that the relationship between the two is positive because when the weight is increased, the tail length also increases.

So, the given statement is correct.

(d) The slope is 3 when the tail length is being measured in millimeters.

Now, If we measure it in centimeter = 3/10 = 0.3 cm

∵ 1 mm = 1/10 cm.

So, the given statement is correct.

(e) when a mouse has weight of 29 grams and tail length of 100 mm.

    When the weight is 29 grams, it should have tail length as :

             tail length = 29 × 3 + 20

                              = 107 mm.

  but, tail length is given as 100 mm.

So, the residual for the mouse is -7 i.e. (100 - 107)

Hence, The given statement is correct.

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(a) The probability that the individual's pressure will be between 120 and 121.8 mm Hg is 0.1255.

(b) The probability that the sample mean will be between 120 and 121.8 mm Hg is 0.4608.

(c) The probability in part a is so much smaller than the probability in part b since, in part a, the probability is calculated for an individual's pressure whereas, in part b, the probability is calculated for a sample of adults.

The z-score formula in a normal distribution is given by

z = (X - μ)/σ

Here, the mean (μ), standard deviation (σ), and random variable (X) are used for finding the z-score.

With this z-score, from the normal distribution table, we can find the probability of the required random variable.

It is given that,

The mean of the pressure of normal adults is μ = 120 mm of Hg

The standard deviation is σ = 5.6

Consider X is a normally distributed variable.

(a) Then, the probability that the individual's pressure will be between 120 and 121.8 mm Hg is calculated by P(120 < X < 121.8).

Here, the z-scores for the given means are:

z-score for the random variable 120 mm Hg is

z = (X - μ)/σ

⇒ z = (120 - 120)/5.6 = 0

z - score for the random variable 121.8 mm Hg is

z = (X - μ)/σ

⇒ z = (121.8 - 120)/5.6 = 0.32

So, the required probability is

P(120 < X < 121.8) = P(0 < z < 0.32)

⇒ P(z < 3.2) - P(z < 0)

From the normal distribution table, we get P(z < 3.2) = 0.6255 and P(z < 0) = 0.5000.

Then, the probability is

P(z < 3.2) - P(z < 0) = 0.625 - 0.5000 = 0.1255

(b) The sample size n = 30 and the random variables are 120 and 121.8 mm Hg.

Since the distribution is for a sample of adults, the sample mean value is

μₓ = μ = 120 and the sample standard deviation is

σₓ = σ/√n = 5.6/√30 = 1.022

Then, the z-scores for the given random variables are:

z-score for the random variable 120 mm Hg is

z = (X - μₓ)/σₓ = (120 - 120)/1.022 = 0

z-score for the random variable 121.8 mm Hg is

z = (X - μₓ)/σₓ = (121.8 - 120)/1.022 = 1.76

So, the required probability is

P(120 < X < 121.8) = P(0 < z < 1.76)

⇒ P(z < 1.76) - P(z < 0)

From the normal distribution table, we get P(z < 1.76) = 0.9608 and P(z < 0) = 0.5000.

Then, the probability is

P(z < 1.76) - P(z < 0) = 0.9608 - 0.5000 = 0.4608.

(c) The answer to part a is so much smaller than the answer to part b. This is because part a is the distribution for an individual and part b is the distribution for a sample of adults.

So, the sample mean and sample standard deviation will get changed in part b.

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The complete statement will be;

⇒ The product of 7 and 5/8 is 35 / 8 because ​5/8​ is less than 1.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The statement is;

''The product of 7 and 5/8 is Choose... because ​5/8​ is less than 1.''

Now,

Since, The statement is;

''The product of 7 and 5/8 is Choose... because ​5/8​ is less than 1.''

Hence, We get;

⇒ 7 × 5/8 = 35 / 8

Thus, The complete statement will be;

⇒ The product of 7 and 5/8 is 35 / 8 because ​5/8​ is less than 1.

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Answer:

-------------------

It is assumed you need to add 5 and square root of 4:

The amount invested in Sock Y is - $126,000 and the Beta of the portfolio is 1.636.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Data provided in the question:

Total amount to be invested = $140000

Stock                          X       Y

Expected return       14%     10%

Beta                          1.42     1.18

Expected return of portfolio = 17.6%

Now,

let the weight invested n stock X be W

therefore,

Weight of Stock Y = 1 - W

thus,

( W × 14% ) + (1 - w) × 10% = 17.6 %

14W + 10% - 10W = 17.6%

4W = 7.6

W = 1.9

Therefore,

weight of Y = 1 - 1.9 = -0.9

Amount investment in Sock Y = Total amount to be invested × Weight

= 140,000 × ( - 0.9 )

= - $126,000 i.e short Y

Beta of portfolio = ∑ (Beta × Weight)

Beta of portfolio= [ 1.42 × 1.9 ] + [ 1.18 × (-0.9) ]

Beta of portfolio= 2.698 - 1.062

Beta of portfolio= 1.636

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The value of f ( 5 ) in the equation f(x) = 3x² + 2x - 1 is f ( 5 ) = 84

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

f(x) = 3x² + 2x - 1

Now , to calculate the value of f ( 5 ) , substitute the value of x as 5

So , when x = 5 , the equation will be

f(x) = 3x² + 2x - 1

f ( 5 ) = 3 ( 5 )² + 2 ( 5 ) - 1

On simplifying the equation , we get

The value of f ( 5 ) = 3 x 25 + 10 - 1

The value of f ( 5 ) = 75 + 10 - 1

The value of f ( 5 ) = 85 - 1

The value of f ( 5 ) = 84

Therefore , the value of f ( 5 ) is 84

Hence , The value of f ( 5 ) in the equation f(x) = 3x² + 2x - 1 is f ( 5 ) = 84

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The inequality that represent each situations are:

a. 6(n + 3) ≥ 42.

b. 6(n + 3) ≤ 42

c. 6(n + 3) < 42

d. 6(n+3) > 42.

To write the inequality for each of the situations, translate each statement into algebraic expressions and use the appropriate inequality sign where necessary.

Thus, let the unknown number be represented as n.

a. The statement, "at least 42" means not less 42, which is the same as "greater than or equal to 42".

Therefore, the first statement is represented by the inequality, 6(n + 3) ≥ 42.

b. "6 times n and 3 is at most 42" is written as, 6(n + 3) ≤ 42

c. "6 times n and 3 is less than 42" would be translated as: 6(n + 3) < 42

d. "6 times n and 3 is more than 42" would be, 6(n+3) > 42.

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Step-by-step explanation:

6(n+3)>42

this is your answer

arlynn

4 is the constant of proportionality of given graph.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given,

The graph of the relationships ( dogs,cost) is a line that contains the points(0,0) (3,12) and (6,24).

We need to find the constant of proportionality

The constant of proportionality is the ratio that relates two given values in what is known as a proportional relationship.

To find the constant of proportionality, we have to divide the value of y by x.

12/3=4

24/6=4

Hence, 4 is the constant of proportionality of given graph.

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Answer:

2/27 or 0.074 or 7.4%

Step-by-step explanation:

Step 1: Roll a fair 6-sided die 27 times. The following outcomes are obtained. 

roll-

1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27

outcome-

2,2,2,5,6,4,5,3,4,3,2,1,2,1,3,6,6,1,4,3,2,6,3,5,4,2,5

Step 2: Make a table for the frequency of each distinct outcome. 

Outcome-

1,2,3,4,5,6

Frequency:

3,7,5,4,4,4

Step 3:  The probability of rolling a two on the die is obtained using the classical probability formula as follows,

P(X=2)= factorable cases/total cases

from the frequency distribution table,

P(X=2)= 2/27= 0.074=7.4%

The dependent variable, y from the given situation is 15

The total number of exercises the individual needs, y = 3x/3

Where,

So,

y = 3x/3

substitute the value of x into the equation

y = 3(15) / 3

open parenthesis

y = 45 /3

y = 15

In conclusion, the value of the dependent variable is 15

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Answer: 12 symmetries

Step-by-step explanation:

just draw the lines on the star.

The value of the function (f⋅g)(3) = 1

The characteristic that every input is associated with exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. It is denoted by the letter f or f(x).  

Here we have

f(x) = − 3x − 2  

g(x) = − x + 2

=> (f · g) = f(g(x))

Now Take x = − x + 2 in f(x)

=> f(g(x)) =  − 3(− x + 2)x − 2  

=  3x − 6 − 2      

=  3x − 8  

From the above calculations,

(f⋅g)(x) =  3x − 8    

Now we need to calculate the value of (f⋅g)(3) as given below

=> (f⋅g)(3) =  3(3) − 8 = 9 − 8 = 1

Therefore,

The value of the function  (f⋅g)(3) = 1

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By using the concept of compounded interest, it can be calculated that

$9549.02 has to be invested  at 4.3% interest compounded continuously to have $19,000 after 16 years

First option is correct

What is compound interest?

If the interest on a certain principal at a certain rate over a certain period of time increases exponentially rather than linearly, the interest earned is called compound interest.

Let the principal be $p

Rate= 4.3 %

Time = 16 years

[tex]19000 = pe^{\frac{4.3}{100} \times 16}\\19000 = pe^{0.688}\\19000 = p \times 1.989732\\p = \frac{19000}{1.989732}\\[/tex]

p = $9549.02

First option is correct

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Answer:

10

Step-by-step explanation:

Because if you line up the numbers 10 is the least common factor of 110,40,120

Answer: b 10

Step-by-step explanation:

the prime factorization of 110: 2 * 5 * 11

the prime factorization of 40: 2^3 * 5

the prime factorization of 120: 2^3 * 3 * 5

the factor they all share is only 2, and they all share 5 but they dont all share 11 and 3. Multiply 2 * 5 = 10. SO 10 is the GCF (Greatest Common Factor) of 110, 40, and 120.

hope this helps!

$1,556.72 is required to deposit in the account each month.

72% of interest is earned.

a)

It is a classic Ordinary Annuity saving plan. The general formula is

FV = P((1+r)^n-1)/r)--------(1)

where  

FV is the future value of the account.  

P is the monthly payment (deposit).

r is the monthly percentage yield presented as a decimal.

n is the number of deposits (= the number of years multiplied by 12, in this case).

From this formula, you get the monthly payment:

P=FV(r/(1+r)^-1)----------(2)

Under the given conditions,

FV = $800,000

r = 0.04/12

n = 25*12.  

So, according to formula (2), the monthly payment is

P=800000(0.04/12(1+0.04/12)^25*12-1)

P=800000(0.003/1.713)

P=$1.556.72

Note that of the projected $800,000 the total you deposit will be only  25*12 times $1.556.72 i.e. about 25*12*1.556.72 = 467016 dollars.                    

The rest is what the account will earn/accumulate over the 25 years.

b)

You will earn:  

(8000000-467016/467016)*100

72% of interest is earned.

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Comparing the number of same-size bottles drank to the amount of ounces of water consumed. So, option c is correct.

When the ratio of the output to the input stays constant at every given point along the function, the rate of change is said to be constant. A linear function's change will occur at a steady rate.

Comparing the number of same-size bottles drank to the amount of ounces of water consumed.

We say there is a constant rate of change when a quantity varies uniformly in relation to the change of another quantity.

Therefore, there is a constant rate of change if one quantity is directly proportionate to the other.

The number of identical-sized bottles drank is directly proportionate to the number of ounces of water consumed. As a result, the rate of change in water ounces in relation to the quantity of identical-sized bottles is constant. The quantity of the remaining alternatives are not directly proportionate to one another.

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The cost for the sheet is $22.60 and a discount of 30% is given.

It is important to note that a percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

From the information, the brand of sheets is on sale 30% off with a regular price of $18.00 per sheet.

Therefore, the cost for the sheet will be:

= $18 - (30% × $18)

= $18 - $5.40

= $12.60

The cost for the brand of sheet is $22.60.

Note that the information was incomplete and the calculation was based on the information given.

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Answer:

24 degree increase

Step-by-step explanation:

If the temperature rises 3 degrees steadily over an eight hour period, the total temperature increase after eight hours would be 3 * 8 = 24 degrees.

How would you express the area of he rectangle using the Distributive Property?

area = length * width

area using Distributive Property: 3 (x + 5)

Answer:

x = 12/5

Step-by-step explanation:

3 (3x − 1) − 3 (5x − 3) = − (x + 6)

9x − 3 − 15x + 9 = − x − 6

9x − 15x + x = 3 − 9 − 6

− 5x = − 12

5x = 12

x = 12/5

Answer:

[tex]x=\dfrac{12}{5}[/tex]

Step-by-step explanation:

Given equation:

[tex]3(3x-1)-3(5x-3)=-(x+6)[/tex]

Distribute:

[tex]\implies 3 \cdot 3x + 3 \cdot (-1) - 3 \cdot 5x - 3 \cdot (-3)=-x-6[/tex]

[tex]\implies 9x-3-15x+9=-x-6[/tex]

Collect and combine like terms on the left side of the equation:

[tex]\implies 9x-15x+9-3=-x-6[/tex]

[tex]\implies -6x+6=-x-6[/tex]

Add 6x to both sides:

[tex]\implies -6x+6+6x=-x-6+6x[/tex]

[tex]\implies 6=5x-6[/tex]

Add 6 to both sides:

[tex]\implies 6+6=5x-6+6[/tex]

[tex]\implies 12=5x[/tex]

[tex]\implies 5x=12[/tex]

Divide both sides by 5:

[tex]\implies \dfrac{5x}{5}=\dfrac{12}{5}[/tex]

[tex]\implies x=\dfrac{12}{5}[/tex]

The value of the W would be 1.9 kg.

What is the mean of numbers?

The mean (aka the arithmetic mean, different from the geometric mean) of a dataset is the sum of all values divided by the total number of values. It's the most commonly used measure of central tendency and is often referred to as the “average.”

Larry has to deliver 7 parcels.

The mean weight of the 7 parcels is 2.7 kg.

So

           mean = sum of all weights of 7 parcels/7

            2.7 * 7 = sum of all weights of 7 parcels

              Sum of all weights of 7 parcels = 18.9 kg

Now Larry delivers 3 of the parcels each of weight 'W'

now the new weight will be = 18.9 - 3W

Remaining parcels = 7 - 3 = 4

New mean = 3.3

               Now again by using the formula of mean, we get

                          3.3  = (18.9 - 3W)/4

                          18.9 - 3W = 13.2

                           3W = 5.7

                              W = 1.9 kg.

Hence, the value of the W would be 1.9 kg.

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