At a party, 75% of the people are adults and 25% are children. What is the simplest ratio of adults to children?

The expression can be simplified to a polynomial of degree 2.

[tex]x^2 - 10x + 2[/tex]

Here we have the expression:

[tex](3x^2 -11x - 4) - (2x^2 - x - 6)[/tex]

We can directly simplify this by taking the variable as common factor:

[tex](3 - 2)*x^2 + (-11 + 1)*x + (-4 + 6)\\\\x^2 - 10x + 2[/tex]

This is a polynomial, as you can see, the maximum exponent is 2, so the degree of the polynomial is 2.

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Answer:

Number sets are closed under an operation when you perform the operation and the result is another member of the same number set

Answer:

x = 1

Step-by-step explanation:

Simplifying

7(x + 1) + -2 = 5(x + 1) + 2

Reorder the terms:

7(1 + x) + -2 = 5(x + 1) + 2

(1 * 7 + x * 7) + -2 = 5(x + 1) + 2

(7 + 7x) + -2 = 5(x + 1) + 2

Reorder the terms:

7 + -2 + 7x = 5(x + 1) + 2

Combine like terms: 7 + -2 = 5

5 + 7x = 5(x + 1) + 2

Reorder the terms:

5 + 7x = 5(1 + x) + 2

5 + 7x = (1 * 5 + x * 5) + 2

5 + 7x = (5 + 5x) + 2

Reorder the terms:

5 + 7x = 5 + 2 + 5x

Combine like terms: 5 + 2 = 7

5 + 7x = 7 + 5x

Solving

5 + 7x = 7 + 5x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5x' to each side of the equation.

5 + 7x + -5x = 7 + 5x + -5x

Combine like terms: 7x + -5x = 2x

5 + 2x = 7 + 5x + -5x

Combine like terms: 5x + -5x = 0

5 + 2x = 7 + 0

5 + 2x = 7

Add '-5' to each side of the equation.

5 + -5 + 2x = 7 + -5

Combine like terms: 5 + -5 = 0

0 + 2x = 7 + -5

2x = 7 + -5

Combine like terms: 7 + -5 = 2

2x = 2

Divide each side by '2'.

x = 1

Simplifying

x = 1

Answer:

Hello! The answer is x = 1.

Step-by-step explanation:

To solve this equation, we need to find x.

The first step in approaching this problem would be to use the distributive property:

7(x + 1) - 2 = 5(x + 1) + 2 will turn into:

7x + 7 - 2 = 5x + 5 + 2

Now, you can combine like terms on each side of the equation:

7x + 5 = 5x + 7

Now, you want to get the x's on one side and the whole numbers on the other side. In order to do this, we will subtract 5 from both sides and subtract 5x from both sides:

7x + 5 = 5x + 7

-5x -5   -5x  -5

This will leave us with:

2x = 2

We will have to now divide both sides by 2 to get x by itself:

2x = 2

--     --

2     2

This leaves us with the result: x = 1

Option A is accurate. The points were plotted with the coordinates (x, log) y), and they are (3, 2.097), (4, 2.796), and (5, 3.495).

Exponents can also be written as logarithms. The other number is equal to a logarithm with a number base. It's the exact inverse of the exponent function.

Identity used;

[tex]\rm log_x (y) = z \\\\ z^x=y[/tex]

From the data we obtained;

[tex]\rm log_3(125) = 5 \\\\ 5^3 = 125[/tex]

[tex]\rm log_5 625 = 4 \\\\ 5^4 = 625[/tex]

[tex]\rm log_5 (3125) = 5 \\\\ 5^5 = 3125[/tex]

The points with the coordinates (x, log) y)) were plotted, the points are (3, 2.097), (4, 2.796), (5, 3.495)

Hence, option A is correct.

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The owner  funding that  would make you skeptical of the results is: D. Francesca Xi.

Company A funded the study which will attract potential customer to the company product as the  company product will be more attractive to customers after the study.

Hence, since company A which is  Francesca Xi has the longest-lasting products, he will be the business owner funding that would make you skeptical of the results .

Therefore the correct option is D.

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The value of the expression given the information about the quotient is 8.

From the information given, the equation will be:

= (10/n - 3) + 6

where n = 2

(10/2 - 3) + 6

= (5 - 3) + 6

= 2 + 6

= 8

In conclusion, the correct option is 8.

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Answer:

$9450

Step-by-step explanation:

Answer:

A = $9,450.00

A = P + I where

P (principal) = $9,000.00

I (interest) = $450.00

Calculation Steps:

First, convert R as a percent to r as a decimal

r = R/100

r = 5/100

r = 0.05 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 9,000.00(1 + 0.05/1)(1)(1)

A = 9,000.00(1 + 0.05)(1)

A = $9,450.00

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $9,000.00 at a rate of 5% per year compounded 1 times per year over 1 years is $9,450.00.

Step-by-step explanation:

Answer:

B)  0.5

Step-by-step explanation:

The given formula is:

          Height = Constant * Width

You may now choose any point on the graph (the horizontal line represents a point for width, and the vertical line represents a point for height) and put it into the specified formula. Let's test the two supplied points (2, 1):

Now, 2 is on the horizontal line, so we put it in for width, and 1 is on the vertical line, so we plug that in for height. When we do it, we get:

1 = C * 2

(In the expression above we need to solve for C, and we can do that by dividing both sides by 2)

C= 1/2 = 0.5

So, the answer is 0.5 or option B.

The equation has 2 real roots

The equation is given as:

[tex]y = 3x^2 + 12x - 12[/tex]

Calculate the determinant using

d = b^2 - 4ac

So, we have:

d = 12^2 - 4 * 3 * (-12)

Evaluate

d = 288

Because d > 0

i.e. 288 is greater than 0

Then it means that the equation has 2 real roots

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Answer:

13/40

Step-by-step explanation:

Rewrite a percentage as a decimal: [tex]\frac{32.5}{100}[/tex]

Convert decimals to integers: [tex]\frac{325}{100}[/tex]

Reduce the fraction: [tex]\frac{13}{40}[/tex]

Answer: [tex]\frac{13}{40}[/tex]

32.5% as a fraction in simplest form is 13/40.

Here we have to find fractional form of 35 percent

Since we knw that,

A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

To convert a percentage to a fraction,

we can simply write it as a fraction with a denominator of 100.

Then,

we simplify the resulting fraction to its simplest form.

For 32.5%,

we can write this as,

⇒ 32.5/100

Now, we can simplify this fraction by dividing both the numerator and denominator by their greatest common factor (GCF).

The GCF of 32.5 and 100 is 12.5,

so we can divide both by 12.5,

⇒ 32.5/100 = (32.5 ÷ 12.5) / (100 ÷ 12.5)

                   = 13/40

Therefore, 32.5% as a fraction in simplest form is 13/40.

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Final answer:

The required distance is 3728.372 miles.

Step-by-step explanation:

Step 1

The distance flown is t hours given by:

2193.16t

Step 2

Let distance be represented by d, thus:

d = 2193.16t

Step 3

d = 2193.16t

Substitute t = 1.7 in the relation:

d = 2193.16 x 1.7

Step 4

Solve for d:

d = 2193.16 x 1.7

d = 3728,372

Answer:

d is correct answer

The correct option is C which is The z-statistic is 3.32, so the null hypothesis should be rejected. One can reject the null hypothesis.

When there are two possibilities then we calculate the null hypothesis if the hypothesis is true hypothesis is accepted if it is

To conduct a hypothesis test for the above situation. We define the null hypothesis and the alternative hypothesis.

The null hypothesis is the claim that the average commute time to downtown is 20 minutes while the alternative hypothesis is a contradiction of the null hypothesis which is that the average commute time to downtown is not 20 minutes.

i.e. H0: μ = 20 and H1:  μ ≠ 20.

The z-statistics is given by (sample mean - hypothesized mean) divided by (standard deviation divided by the square root of the sample size).

i.e.

[tex]z= \dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

x = 26,  [tex]\mu[/tex] = 20, [tex]\sigma[/tex] = 7 and n = 15 putting the values in the question we will get the z-score value.

[tex]z = \dfrac{26-20}{\dfrac{7}{\sqrt15}}[/tex]

z = 6 / 1.807

z = 3.32

Therefore, the z-statistic is 3.32, so the null hypothesis should be rejected. Because the calculated value of z (3.32) is greater than the table value of z (1.96).

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The values of x that makes the inequality true are all values less than -5

Given the inequalities below expressed as;

4x-1 < 6x+9

Collect the like terms

4x-6x < 9+1

-2x < 10

x <-10/2

Hence the values of x that makes the inequality true are all values less than -5

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Step-by-step explanation:

location

of the distribution.

Work is attached. Hope it helped!

Step-by-step explanation:

x = 11

is a vertical line going through x = 11.

a parallel line going through (9,5) has to be a vertical line too and use x = 9.

so, that is the equation :

x = 9.

Answer:

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

Explanation:

[tex]\dfrac{1}{4} + \dfrac{1}{6}[/tex]

The least common multiple of 4 and 6 is 12

So, make the denominator's same

[tex]\dfrac{3(1)}{12} + \dfrac{2(1)}{12}[/tex]

multiply numbers

[tex]\dfrac{3}{12} + \dfrac{2}{12}[/tex]

Join both fractions

[tex]\dfrac{3+ 2}{12}[/tex]

simplify following

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

Domain: All real numbers

Range: All real numbers

Since the function is linear it is a continuous straight line meaning that the domain and range are all real numbers.

The volatile acid/alkalinity relationship in a digester is volatile acid/alkalinity = 3/80

An equation is an expression that shows the relationship between two or more variables and numbers.

Ratio of volatile acid to alkalinity = 90 mg/L ÷ 2400 mg/L = 3/80

The volatile acid/alkalinity relationship in a digester is volatile acid/alkalinity = 3/80

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The rational expression written using the least common denominator  [tex]\frac{x+1}{4x^{2} }+\frac{x+1}{x^{2} }\\[/tex] is [tex]\frac{x+1}{4x^{2} }+\frac{4(x+1)}{4x^{2} }[/tex].

The ratio of two polynomials is displayed in rational expressions. It indicates that the denominator and numerator are polynomials. It is an algebraic expression that has a ratio and an unknown variable, just like a fraction. Although we can simplify this kind of equation with the aid of a calculator.

Because one is divided by the other, just like a ratio, it is a "rational expression."

The polynomial that we divide by cannot be zero, as a reminder.

The least common denominator for [tex]4x^{2}[/tex] and [tex]x^{2}[/tex] is calculated to be [tex]4x^{2}[/tex].

Thus, the required rational expression is [tex]\frac{x+1}{4x^{2} }+\frac{4(x+1)}{4x^{2} }[/tex].

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Answer:

no solution

Step-by-step explanation:

2x²+ x + 6 = 0

Use quadratic formula

x = (-b±√(b²-4ac))/2a

x = (-1±√(1²-4(2)(6)))/2(2)

x = (-1±√(-47))/2(2)

Answer:

Last graph that slopes upwards from left to right and that has an y-intercept of -1

Step-by-step explanation:

let us pick some points!(you can chose any two)

when x =3 , y = 14 : helps us get points (3,14)

when x =1 , y = 4 : helps us get points (1,4)

so we find the gradient using the two points:

[tex]gradient \ =\frac{14-4}{3-1} =\frac{10}{2} \\[/tex]

we now use gradient 10/2 and point (1,4) to find the equation  of the line:

[tex]\frac{10}{2} =\frac{y-4}{x-1} \\2(y-4)=10(x-1)\\2y-8=10x-10\\2y=10x-10+8\\2y=10x-2\\y=5x-1[/tex]

from the equation of the line found we are able to find the y- intercept of the line is -1 and that the line has a positive gradient thus should slope upwards from left to right.

From the pictures you posted, we pick the last graph as it seem to slope upwards from left to right and has the line cutting y axis at around -1

Answer:

it is A

Step-by-step explanation:

Answer:

[tex]\{-\frac{1}{2} \} \cup \{\frac{2}{5}\}[/tex]

Step-by-step explanation:

[tex]10x^2 + x - 2 = 0; \\ a = 10, b = 1, c = -2; \\ D = b^2 - 4ac = 1^2 - 4 * 10 * (-2) = 1 + 80 = 81 = 9^2, > 0; \\ x_{1, 2} = \frac{-b \pm \sqrt{D}}{2a} = \frac{-1 \pm \sqrt{9^2}}{2 * 10} = \frac{-1 \pm 9}{20} = \left \ [ {{\frac{-1 - 9}{20} = -\frac{10}{20} = -\frac{1}{2} } \atop {\frac{-1 + 9}{20} = \frac{8}{20} = \frac{2}{5}}} \right.[/tex]

Answer:

D.

Step-by-step explanation:

D. is the binomial since it has 2 terms.

Answer:

A) Yes, because the sum of any two side lengths is greater than the third side length.

Step-by-step explanation:

All triangles have a property that the sum of two side lengths is greater than the remaining side length.

4 + 8 = 12 > 10, making it a triangle

Answer:

the ratio of total sales or revenue to average assets

Step-by-step explanation:

djjcjdm.x....

Answer:

Days of Asset Turnover The Enterprise Accounting System specifies that the net revenue from main business of an enterprise should be the amount of revenue from main business after deducting sales discounts and sales discounts, which is called net revenue from main business. Total asset turnover ratio = total sales revenue / average total assets x 100%.

Step-by-step explanation:

Answers:

(a) x = 0.5

(b) Given Below.

Explanation:

(a)

[tex]4^x = 2[/tex]

apply ln both sides

[tex]ln(4^x) = ln(2)[/tex]

simplify

[tex]xln(4) = ln(2)[/tex]

divide both sides by ln(4)

[tex]x = 0.5[/tex]

(b)

Recall that rational numbers can be expressed in fractions a/b

[tex]4^x = 5[/tex]

apply ln on both sides

[tex]ln( 4^x) = ln(5)[/tex]

simplify

[tex]xln( 4) = ln(5)[/tex]

divide both sides by ln(4)

[tex]x =\frac{ ln(5)}{ln(4)}[/tex]

simplify

[tex]x =1.160964047...[/tex]  The value is endless and continues.

The following cannot be expressed as a fraction or whole number.

Hence, the following value of x is irrational.