Select the correct answer. Given the equations `9x + (3)/(4)y = 6` and `2x + (1)/(2)y = 9`, by what factor would you multiply the second equation to eliminate y and solve the system through linear combinations? A. `-4/3` B. `-3/4` C. `-3/2` D. `-7/2`

Answer:

$72

Step-by-step explanation:

100 - 10% = 90

90 - 20% = 72

Answer:

x > 0

Step-by-step explanation:

The domain of the graph are all the possible values of x. Since the graph never touches the negative part of the graph, x will always be greater than 0. Thus, x > 0 meaning x will be greater (not equal to) 0.

Answer:

75%

Step-by-step explanation:

390/520 = 0.75 =75

hope that helps ;)

Answer:

75%

Step-by-step explanation:

390/520×100%

0.75×100%

75%

Using the combination formula, it is found that:

1. A. 7 combinations are possible.

B. 21 combinations are possible.

C. 1 combination is possible.

2. There are 245 ways to group them.

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by:

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

Exercise 1, item a:

One letter from a set of 7, hence:

\(C_{7,1} = \frac{7!}{1!6!} = 7\)

7 combinations are possible.

Item b:

Two letters from a set of 7, hence:

\(C_{7,2} = \frac{7!}{2!5!} = 21\)

21 combinations are possible.

Item c:

7 letters from a set of 7, hence:

\(C_{7,7} = \frac{7!}{0!7!} = 1\)

1 combination is possible.

Question 2:

Three singers are taken from a set of 7, and four dances from a set of 10, hence:

\(T = C_{7,3}C_{10,4} = \frac{7!}{3!4!} \times \frac{10!}{4!6!} = 245\)

There are 245 ways to group them.

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a

Step-by-step explanation:

Answer:

A. $52.50

Step-by-step explanation:

$50 x .05 (5% as a decimal)

This gives you $2.50, add this to the cost of the dress.

Answer:

52.50

Step-by-step explanation:

Find the tax

50 * 5%

50 * .05

2.5

Add the tax to the price of the dress

50 +2.5

52.50

The greatest number of groups that can be formed with equal numbers of each type of voice in the choir is 12 groups.

To determine the greatest number of groups that can be formed, we need to find the greatest common divisor (GCD) of the number of sopranos, altos, and tenors. The GCD represents the largest number that can divide each of the given numbers without leaving a remainder.

The prime factorization of 24 is 2 * 2 * 2 * 3, the prime factorization of 60 is 2 * 2 * 3 * 5, and the prime factorization of 36 is 2 * 2 * 3 * 3. By considering the highest power of each prime factor that appears in all three numbers, we find the GCD to be 2 * 2 * 3 = 12.

Since we want to divide the choir into smaller groups with equal numbers of sopranos, altos, and tenors, each group should have 24/12 = 2 sopranos, 60/12 = 5 altos, and 36/12 = 3 tenors. Therefore, the greatest number of groups that can be formed is the number of sopranos in each group, which is 2.

In conclusion, the greatest number of groups that can be formed with equal numbers of sopranos, altos, and tenors in the choir is 12 groups.

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Answer:

x=8 y=2

Step-by-step explanation:

the ratio is 9:6 so it'll be 3:2

complete one by one, pair by pair

\( \frac{4 + x}{3} = \frac{x}{2} \)

then complete for y

\( \frac{4 + y}{3} = \frac{4}{2} \)

The correct argument in support of the team that should be awarded the prize is; Team A because their distribution of total call times is skewed to the right, which shows the majority of total call times are less than the mean.

A skewed distribution is a distribution which is non-symmetric and also it has no mirror-imaging.

One common characteristic of skewed distributions, is that one tail of the distribution will be quite longer or drawn out relative to the other tail.

A distribution is said to be skewed right when one of the tail is on the right side.

A distribution is said to be skewed left when one of the tail is on the left side.

Now, we want to find the correct argument in support of the team that should be awarded the prize.

Looking at the two graphs of team A and B, we see that team A has a distribution that is skewed to the right which means majority of total call times are less than the mean.

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To calculate the annual payment required to pay off a five-year, $25,000 loan at an interest rate of 3.50 percent EAR, we can use the formula for calculating the equal annual payment for an amortizing loan.

The formula is: A = (P * r) / (1 - (1 + r)^(-n))

Where: A is the annual payment,

P is the loan principal ($25,000 in this case),

r is the annual interest rate in decimal form (0.035),

n is the number of years (5 in this case).

Substituting the given values into the formula, we have:

A = (25,000 * 0.035) / (1 - (1 + 0.035)^(-5))

Simplifying the equation, we can calculate the annual payment:

A = 6,208.61

Therefore, the annual payment required to pay off the five-year, $25,000 loan at an interest rate of 3.50 percent EAR is $6,208.61.

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Answer: For every apple you sell, you earn 4 bucks. y is the number of apples, 4 is the constant price.

Answer:

0.42846931021

Step-by-step explanation:

-5x - 5 = 3x + 19

---Move the x's to one side

-5x - 3x - 5 = 3x - 3x + 19

-8x - 5 = 19

---Isolate the -8x by removing the -5 from the left side

-8x - 5 + 5 = 19 + 5

-8x = 24

---Divide both sides by -8 to get x by itself

x = -3

Hope this helps!

-5x-5= 3x+19

= > -5x-3x= 19+5

= > -8x= 24

= >-x=24/8

= >x= -3

Answer: Answer Bellow

Step-by-step explanation: To check yourself, multiply 6.0 x 105 times 4.0 x 103 on your calculator. Your answer should be 2.4 x ...

The value of 'x' in the given equation is 0.1058 and this can be determined by using the arithmetic operations.

Given :

Equation  --  (2.4 × 103) × (3 × 10x) = 7.2 × 109

The following steps can be used in order to determine the value of x in the given equation:

Step 1 - The arithmetic operations can be used in order to determine the value of x in the given equation.

Step 2 - Write the given equation.

(2.4 × 103) × (3 × 10x) = 7.2 × 109

Step 3 - Simplify the above equation.

(247.2) \(\times\) (30x) = 784.8

Step 4 - Further simplify the above expression in order to determine the value of 'x'.

7416x = 784.8

x = 0.1058

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a) The magnitude of Pˉ is P.  b) The direction cosine of Pˉ with respect to the x-axis is 110/P.  c) The directional angle of Pˉ with respect to the z-axis is arctan(60/√(110^2+(-0.58P)^2)).

a) To find the magnitude of vector Pˉ, we use the formula for the magnitude of a vector in three dimensions, which is the square root of the sum of the squares of its components.

b) The direction cosine of a vector with respect to a specific axis is the ratio of the component of the vector along that axis to its magnitude. In this case, the x-component of Pˉ is 110, so the direction cosine with respect to the x-axis is 110 / P.

c) The directional angle of a vector with respect to a specific axis can be found using the arctan function. In this case, we use the y-component and z-component of Pˉ to find the angle between Pˉ and the z-axis.

Therefore, the magnitude of Pˉ is given by P, the direction cosine with respect to the x-axis is cos(θ_x), and the directional angle with respect to the z-axis is θ_z.

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Answer:

It will take Shanti 150 square inches of paper to wrap the gifts

Step-by-step explanation:

Shanti wraps the gift she is taking to a friend's birthday party. She doesn't have very much paper, so she does not overlap any of the edges. The side lengths of the cube are all 5in.

How much paper did it take to cover the gift?

Solution

To solve this, you will find the surface area of a cube

Surface area of a cube = 6a^2

Where,

a=side length of the cube

a= 5 in

a^2=a × a

=5 × 5

=25 in^2

a^2=25 in^2

Surface area of a cube = 6a^2

=6 × 25 in^2

=150 in^2

It will take Shanti 150 square inches of paper to wrap the gifts

Answer:

1014

Step-by-step explanation:

I took the test i know

The calculated value of 9.76 should be rounded to 10 for use in the table.

In a two sample test of means with unknown and unequal population variances, the degrees of freedom is calculated as 9.76. When using the t-distribution table, it is important to note that the table only lists integer values for degrees of freedom.  

Therefore, we must round the calculated degrees of freedom to the nearest integer value.

In this case, the nearest integer to 9.76 is 10. Therefore, when using the t-distribution table for this two sample test of means, we should use 10 as the degrees of freedom value.

It is important to note that rounding the degrees of freedom can have a small effect on the accuracy of the results, particularly if the calculated value is close to an integer value. However, in most cases, rounding to the nearest integer is a reasonable approximation.

In summary, when calculating degrees of freedom for a two sample test of means with unknown and unequal population variances, it is important to round to the nearest integer value when using the t-distribution table. In this case, the calculated value of 9.76 should be rounded to 10 for use in the table.

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Answer:

1 ≤ y ≤ 4

Step-by-step explanation:

Range is all possible y values

a point is written as (x, y)

The line starts at point (0, 1) and ends at (3, 4)

so the range of the y values is 1 to 4

According to the given information, the sample period should be from 2010-2020.

a) Model specification

The model specification based on the scenario above is as follows:

SDF= f(T, TI, NL)

Where: SDF= Sustainable Development Framework

T= Tourism

TI= Technological innovation

NL= National leadership

b) Justification for the selection of the dependent and independent variables model:

Dependent variable: The dependent variable in this model is Sustainable Development Framework (SDF). The model seeks to develop a framework for sustainable development that would facilitate growth, environmental and socio-cultural sustainability.

Independent variables:

The independent variables are tourism sustainability, technological innovation, and quality of leadership. These variables drive economic development. The inclusion of tourism sustainability reflects its importance in the global economy and its potential to drive growth.

The inclusion of technological innovation reflects its potential to enhance productivity and create new industries. The inclusion of national leadership reflects the role of governance in promoting sustainable development and managing negative externalities.

c) Justification for the selection of the sample period:

The sample period should be selected based on the availability of data for the variables of interest. Ideally, the period should be long enough to capture trends and patterns in the data. However, it should not be too long that the data becomes obsolete or no longer relevant.

Additionally, the period should also reflect the context and relevance of the research question. Therefore, the sample period for this study should cover the last decade to capture the trends and patterns in the data and reflect the relevance of the research question.

The sample period should be from 2010-2020.

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Answer: 360 unoccupied rooms on Saturday night

=========================================

Explanation:

There are 432 occupied rooms on Sunday.

The ratio of occupied to unoccupied on Sunday is 6:1. This means there are 6 times as many filled rooms as empty ones.

Divide 432 by 6 to get 72. So there are 72 empty rooms on Sunday.

In total, there are 432+72 = 504 rooms

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

On Saturday night, the filled room to empty room ratio is 2:5. This means for every 2 rooms taken, 5 are empty.

Let x be some integer such that 2x and 5x represent the filled and empty room counts.

2x = number of filled rooms

5x = number of empty rooms

Since we found earlier there are 504 rooms total, this means

2x+5x = 504

because we're simply adding the filled room count (2x) and the empty room count (5x) to get the total number of rooms (504).

Solve for x

2x+5x = 504

7x = 504

x = 504/7

x = 72

Now use this to find the following data for Saturday night

As a check, 144+360 = 504, which confirms we have the right answer.

Answer:

X = 105

Step-by-step explanation:

2x = 42

5

Multiply both sides by 5

5 × 2x = 5×42

5

5 cancle 5

2x = 5 × 42

2x = 210

Divide both sides by 2

2x = 210

2 2

x = 105

Answer:

x=2; the extraneous root x=42.

All the details are in the attached picture, the answer is marked with red colour.

The radical equation 2 + 2x - 3. √(x + 7) has a solution set z = 2 and an extraneous root = -7.

To solve the equation, we can start by simplifying the radical. We get:

2 + 2x - 3√(x + 7) = 0

We can then move the constant term to the other side of the equation. We get:

2x - 3√(x + 7) = -2

We can then multiply both sides of the equation by -1. We get:

3√(x + 7) - 2x = 2

We can then square both sides of the equation. We get:

9(x + 7) - 12x * √(x + 7) + 4x² = 4

We can then rearrange the terms on the left-hand side of the equation. We get:

4x² - 12x * √(x + 7) + 5 = 0

We can then factor the expression on the left-hand side of the equation. We get:

(2x - 1)(2x - 5) = 0

This gives us two solutions, x = 1/2 and x = 5.

The solution x = 1/2 is a valid solution because it does not make the radical expression undefined. However, the solution x = 5 is an extraneous root because it does make the radical expression undefined.

Therefore, the solution set z = 2 and the extraneous root = -7.

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For a bacteria population which become doubles in every 10 hours and the initial 20 bacteria number. Then the bacteria population after two and half days is equal to the 113.14.

There is a certain type of bacteria. The favorable growth medium, doubles in population every 10 hours. Initial bacteria population, a₀ = 20

We have to determine number of bacterias will there be in two and a half days, x = 2 + 1/2

= 5/2 days

The exponencial growth function that makes this work is written as

\(y = a_02^x\), where

Since they double every 10 hours. So, the equation is written by,

\(y = 20 × 2^{5/2} \)

= 113.14

Hence, required value is 113.14.

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Answer:

7.82

Step-by-step explanation:

I solved it

The random variables that are discrete from this set are:

A discrete random variable is a variable that can only take on a finite or countable number of values, meaning that it cannot take on all values within a given interval. The number of people riding on a bus and the number of concert tickets sold are both examples of variables that can only take on a countable number of values. For example, the number of people riding on a bus can only take on values of 0, 1, 2, 3, and so on, while the number of concert tickets sold can only take on values of 0, 1, 2, 3, and so on.

On the other hand, the life span of a parakeet and the height of a person from a class of eight are continuous random variables, meaning that they can take on any value within a given interval. For example, the life span of a parakeet can be any positive number, while the height of a person can be any real number within a certain range.

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The expression represents the amount of tip, that Nina will give, when she has a positive experience eating a meal that cost n dollars is \(0.18n\). Hence the option A is the correct option.

Algebraic expression are the expression which consist the variables, coefficients of variables and constants.

The  algebraic expression are used represent the general problem in the mathematical way to solve them.

Steps to write down the simple algebraic expression-

Given information-

The tip given by the the Nina is 18 percent.

The cost of food is \(n\) dollars.

Here the Nina gave the tip of 18 percent. This 18 percent is the percentage of total cost of the food.

Let \(f(n)\) is the required expression.

As the the cost of food is \(n\) dollars. Thus the 18 percent of \(n\) dollars is,

\(f(n)=\dfrac{18}{100} \times n\\f(n)=0.18n\)

Thus the expression represents the amount of tip, that Nina will give, when she has a positive experience eating a meal that cost n dollars is \(0.18n\). Hence the option A is the correct option.

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The amount of money that in the interest will the bank put Henry's account is $1000

If Henry keeps at least $5,000 in his savings account, the bank will put a 20% interest on it annually.

To find out how much interest Henry will earn, we can use the formula:

Interest = Principal x Rate

Where the,

Principal is the amount of money , Henry keeps in his savings account, which is $5,000 or more.

Rate is the interest rate, which is 20% or 0.20 in decimal form.

So, the interest Henry will earn is:

Interest = $5,000 x 0.20

Interest = $1,000

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The range of the square footage values for the given mean , standard deviation and  95% confidence interval is equal to (1257.26 , 508.74).

As given in the question,

Sample size 'n' = 2

Sample mean '\(\bar{x}\)' = 883 sq ft

Standard deviation 'σ' = 270 sq ft

95% confidence interval.

95% confidence interval = 1 - 0.95

                                        = 0.05

Critical value for 95% is \(Z_{0.05}\) = 1.96

Population mean for the given confidence interval is given by :

= \(\bar{x}\) ± \(Z_{0.05}\) (σ / √n)

= 883 ± 1.96 ( 270 / √2)

= 883 ± 374.26

= ( 1257.26 , 508.74 )

Therefore , the range of the square footage values for the 95% confidence interval is equal to ( 1257.26 , 508.74 ).

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Answer:B

Step-by-step explanation: