Solve the following proportion for xx/7 = 3/13round your answer to nearest tenth

Answer:

\(y=(x+12)^2\\\)

Step-by-step explanation:

To write a quadratic equation into binomial form we can compare the equation into the completing square form of a quadratic equation like this ,

\(y=a(x-h)^2+k\)

now since,

\(y=x^2+24x+144\)

we can equate both the equations from left hand side to right hand side like this,

\(x^2+24x+144=a(x-h)^2+k\\\)

now we solve,

\(x^2+24x+144=a(x-h)^2+k\\x^2+24x+144=a((x)^2-2(x)(h)+(h)^2)+k\\x^2+24x+144=a(x^2-2hx+h^2)+k\\x^2+24x+144=ax^2-2ahx+ah^2+k\\\)

now we compare the coefficients of x^2:

\(1 = a\\\)

now we compare the coefficients of x :

\(24=-2ah\\24=-2(1)h\\24=-2h\\\frac{24}{-2}=h\\-12=h\\\)

now we compare the constants , (constants are the letters which are not associated with any variable in this case the variable is x)

\(144 = ah^2+k\\144=(1)(-12)^2+k\\144=(1)(144)+k\\144=144+k\\144-144=k\\0=k\\\)

so now the value we got all the values for the completing square form we plug those in , a = 1 , h = -12 , k = 0 ,

\(y=a(x-h)^2+k\\y=1(x-(-12))^2+0\\y=(x+12)^2\\\)

this is the square of a binomial, if you want to verify if we expands this formula by the formula of (a + b)^2 we would get the same result. Thus this is the correct answer.

Answer:

$21.00 / 3 hours = $7.00/hour

($7.00/hour)(10 hours) = $70.00

Answer:

if she probably earns $21.00 per hour.It may be 21.00×10 which is $210.thats my own answer

Answer:

24:26 and 36:39 are two ratios that are equivalent to 12:13.

Step-by-step explanation:

In a unit rate, the denominator is always 1.

let's bear in mind that complex roots never come alone, their conjugate sister is always with her, so if we have the complex root of "i" or namely "0 + i", her conjugate is also coming along, or "0 - i", so we really have four roots, so

\(\begin{cases} x = 0+i &\implies x -i=0\\ x = 0-i &\implies x +i=0\\ x = \sqrt{2} &\implies x -\sqrt{2}=0\\ x = 3 &\implies x -3=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x -i )( x +i )( x -\sqrt{2} )( x -3 ) = \stackrel{0}{y}}\hspace{5em}\stackrel{\textit{we are assuming that}}{a=1} \\\\\\ 1( x -i )( x +i )( x -\sqrt{2} )( x -3 ) = y\implies ( x -i )( x +i )( x -\sqrt{2} )( x -3 ) = y \\\\[-0.35em] ~\dotfill\)

\(\stackrel{ \textit{difference of squares} }{( x -i )( x +i )}\implies x^2 - i^2\implies x^2-(-1)\implies x^2+1 \\\\[-0.35em] ~\dotfill\\\\ (x^2+1)( x -\sqrt{2} )( x -3 )\implies (x^2+1)(x^2-3x-x\sqrt{2}+3\sqrt{2}) \\\\\\ (x^2+1)[x^2-x(3+\sqrt{2})+3\sqrt{2}] \\\\\\ x^4-x^3(3+\sqrt{2})+3x^2\sqrt{2}+x^2-x(3+\sqrt{2})+3\sqrt{2} \\\\\\ \boxed{x^4-x^3(3+\sqrt{2})+x^2(3\sqrt{2}+1)-x(3+\sqrt{2})+3\sqrt{2}~~ = ~~y}\)

The direct labor cost included in the Preble Company's flexible budget for March is $819,000.

To find the direct labor cost included in the company's flexible budget for March, we shall estimate the actual direct labor cost incurred during the period.

Given:

Actual production and sales =n26,600 units

Actual direct labor rate = $13.00 per hour

Actual direct labor hours worked = 63,000 hours

Direct labor cost = Actual direct labor rate × Actual direct labor hours worked

Direct labor cost = $13.00/hour × 63,000 hours

Direct labor cost = $819,000

Hence, the direct labor cost included in the company's flexible budget for March would be $819,000.

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Answer:

x= -6

Step-by-step explanation:

The table can be summarized as follows:

|          | Has a dog | Does not have a dog |

|----------|-----------|---------------------|

| Has a cat     | 2         | 3                   |

| Does not have a cat | 12        | 10                  |

To find the probability that a student chosen randomly from the class has a cat, we need to find the total number of students who have a cat (regardless of whether or not they have a dog), and divide it by the total number of students in the class.

The number of students who have a cat is 2 (those who have a dog and a cat) + 3 (those who have a cat but do not have a dog) = 5.

The total number of students in the class is the sum of all four categories: 2 (has a cat and a dog) + 3 (has a cat, does not have a dog) + 12 (does not have a cat, has a dog) + 10 (does not have a cat, does not have a dog) = 27.

So, the probability that a student chosen randomly from the class has a cat is 5/27.

Answer:

y = 3x + 2

Step-by-step explanation:

The easiest way to do this, would be to substitute a point (e.g., (2,8)) into your equations to find the one that is true.

(2, 8)

y = 3x - 2

8 = 3(2) - 2

8 = 6 - 2

8 = 4

This statement is false

(2, 8)

y = 3x + 2

8 = 3(2) + 2

8 = 6 + 2

8 = 8

This statement is true

(2, 8)

y = 2x - 3

8 = 2(2) - 3

8 = 4 - 3

8 = 1

This statement is false

(2, 8)

y = 2x + 3

8 = 2(2) + 3

8 = 4 + 3

8 = 7

Therefore, b is the correct answer.

Hope this helps!

The relation that represents the pattern in the table of values is given as; y = 3x + 2

Let us first find the slope of the values from;

m = (y₂ - y₁)/(x₂ - x₁)

m = (8 - 5)/(2 - 1)

m = 3

Thus, the y-intercept is;

5 = 3(1) + c

c = 2

Thus, equation is;

y = 3x + 2

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The only equivalent expression is option (a) \(7^x\).

What is expression ?

An expression in mathematics is a group of symbols that represent a statistical correlation or quantity, such as integers, variables, and operators. It may contain exponents, logarithms, and trigonometric functions in addition to mathematical operations like addition, multiplication, multiplication, and division. It may also contain constants, variables, and functions. Expressions can be used in a variety of subjects, including mathematics, calculus, geometry, and statistics, to represent mathematical models, resolve equations, and carry out calculations.

To find equivalent expressions for\(21^x/3^x\), we can try to simplify the expression using exponent rules.

21 can be factored as 7*3, so we can write:

\(21^x/3^x = (7 × 3)^x/3^x = 7^x × 3^x/3^x = 7^x\)

Therefore, we can see that option (a) 7^x is equivalent to the given expression.

To check the other options:

b) \((7/3)^x\) = \((7^x)/(3^x)\) which is not equivalent to the given expression.

c) \(3^(2x+1)\) can be written as \(3^(2x)\) × \(3^1\) = \((3^2)^x\) × 3 = \(9^x\) × 3 which is not equivalent to the given expression.

d) \(7^(x-1)\) can be written as \(7^x/7\) which is not equivalent to the given expression.

e) \((3/7)^x\) is not equivalent to the given expression.

Therefore, the only equivalent expression is option (a) \(7^x\).

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The complete question is:

Which expressions are equivalent to \(21^x/3^x\)? Check all that apply.

a) \(7^x\)

b) \((7/3)^x\)

c) \(3^(2x+1)\)

d) \(7^(x-1)\)

e) \((3/7)^x\)

Answer:

C

Step-by-step explanation:

1/2(1/2)=1/4

Answer:

7.5 cm²

Step-by-step explanation:

Dimensions of the large ∆:

\( base (b) = 3cm, height (h) = 9cm \)

\( Area = 0.5*b*h = 0.5*3*9 = 13.5 cm^2 \)

Dimensions of the small ∆:

\( base (b) = 2cm, height (h) = 6cm \)

\( Area = 0.5*b*h = 0.5*2*6 = 6 cm^2 \)

Difference between the area of the large and the small ∆ = 13.5 - 6 = 7.5 cm²

a) The null hypothesis is that there is no difference in the proportion of homeowners using water filters among the three communities. The alternative hypothesis is that at least one community has a different proportion of homeowners using water filters than the other communities.

b) To calculate the expected count for the bottom right cell, we can use the formula:

Expected count = (row total x column total) / grand total

The row total for Community C and the column total for No are both 100, and the grand total is 300. Therefore:

Expected count = (100 x 100) / 300 = 33.33

The expected count of 33.33 for the bottom right cell means that if there were no difference in the proportions of homeowners using water filters among the three communities, we would expect 33.33 of the 100 homeowners in Community C to answer 'No' to the question about water filters.

c) To determine what we can conclude from the Chi-square statistic of 13.22, we need to compare it to the critical value for a Chi-square distribution with (3-1) x (2-1) = 2 degrees of freedom at the desired level of significance. Let's assume a level of significance of 0.05. From a Chi-square distribution table, the critical value with 2 degrees of freedom at 0.05 level of significance is 5.99.

Since 13.22 is greater than 5.99, we can reject the null hypothesis and conclude that there is a significant difference in the proportion of homeowners using water filters among the three communities. However, we cannot determine from this test alone which communities have different proportions of homeowners using water filters. We would need to conduct further tests, such as post-hoc tests, to investigate the specific differences among the communities.

Answer:

54

Step-by-step explanation:

ratio is 7:9

7=42

9=?

9×42÷7

Answer:

Step-by-step explanation:

Answer:

165 minutes

Step-by-step explanation:

To solve for the number of minutes that Joaquin played for, we can use this expression:

(let 'a' represent how much time passed from the time Joaquin started playing basketball until the time he arrived at home)

Subtracting 1:10 from each side:

1:10 - 1:10 cancels out to 0, while 3:35 - 1:10 is equal to 2:25.

So, the expression is now:

So, 2 hours and 25 minutes passed.

If we know that 1 hour is equivalent to 60 minutes, we can use this expression to solve for however many minutes are in 2 hours:

Now we need to add on the number of minutes and the time it took him to get home:

Therefore, 165 minutes passed from the time Joaquin started playing basketball until the time he arrived at home.

Given:

a² + b² = c²

a² + b² = n²

To find:

Substituting both equation to get a new equation

Steps:

We know,

a² + b² = c²

a² + b² = n²

Now if we substitute a² + b² to equal to c², in equation a² + b² = n² we get,

a² + b² = n²

       c² = n²

         c = n

Therefore we get the new equation as c = n

Happy to help :)

If you need any help, pls feel free to ask

The equation that we get after solving the given equation should be considered as the c = n.

As per the Pythagoras theorem, It defined that the area of the square i.e. hypotenuse is equivalent to the sum of the areas of the squares on the other two sides.

So based on this, we can considered the following equations:

Since

a² + b² = c²

a² + b² = n²

So here  

a² + b² = n²

 c² = n²

c = n

Therefore we get the new equation as c = n

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Answer:

y = 1/3x + 2

Step-by-step explanation:

Rise over run + y intercept

Answer:

1,091,291,533,405,608

Step-by-step explanation:

Even because 8 is an even number

Answer:

the perimeter is : 40

the area is: 10,000

"97.72% of the female students have scores above," seems to be a misinterpretation as the correct statement is that approximately 99.72% of the female students have scores between the lower and upper limits

To calculate the scores that are three standard deviations above and below the mean, we use the formula:

Lower limit = Mean - (Standard Deviation * 3)

Upper limit = Mean + (Standard Deviation * 3)

Given:

Mean = 269

Standard Deviation = 33

Using the formula, we can calculate the limits:

Lower limit = 269 - (33 * 3) = 269 - 99 = 170

Upper limit = 269 + (33 * 3) = 269 + 99 = 368

Therefore, the lower limit is 170 and the upper limit is 368.

To calculate the probability that a female student will have a score between these limits, we need to find the area under the normal distribution curve between the lower and upper limits. This can be calculated using a standard normal distribution table or calculator.

Since the distribution is assumed to be normal, approximately 99.72% of the scores will fall within three standard deviations from the mean. Therefore, the probability that a female student will have a score between these limits is approximately 99.72%.

For a score of 302, which is above the mean of 269, we can calculate the percentage of female students with scores below 302:

Percentage = (1 - Probability) * 100

= (1 - 0.9972) * 100

= 0.0028 * 100

= 0.28%

Therefore, approximately 0.28% of the female students have scores below 302.

It's important to note that the value mentioned, "97.72% of the female students have scores above," seems to be a misinterpretation as the correct statement is that approximately 99.72% of the female students have scores between the lower and upper limits

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Answer:

a.

f(4) = 10•4 -6

f(4) = 40 -6

f(4) = 34

b.

f(-1/2) = 10•(-1/2) -6

f(-1/2) = -5 -6

f(-1/2) = -11

c.

f(0) = 10•0 -6

f(0) = 0 -6

f(0) = -6

Answer:

$677.25

Step-by-step explanation:

Money deposited: $375.45 + 614.20 + $187.60 = $1177.25

Money withdrawn: $500.00

Total deposit: $1177.25 - $500.00 = $677.25

Answer: $677.25

Answer:

5,150 bigger

Step-by-step explanation:

5,500-350= that answer hope this helps

Combining similar terms:

Answer:

The angle D is 64 degrees.

Step-by-step explanation:

This is because they are vertical

Answer:

i think its the yellow square

Step-by-step explanation: