Six people are running for class president. Assuming there are no ties, in how
many different ways can first and second places be awarded?

Final answer:

To solve for A and B, we translated the word problem into two algebraic equations and then solved the system of equations step-by-step to find that A equals 200 and B equals 250.

Explanation:

We are given two equations based on the relationship between 30% of number A and 20% of number B, and vice versa. Let's translate the words into algebraic expressions where A and B represent the numbers we need to find:

0.30A = 0.20B + 10 (Equation 1)

0.30B = 0.20A + 35 (Equation 2)

Now let's solve this system of equations step-by-step:

Multiply both sides of Equation 1 by 10 to clear out decimals: 3A = 2B + 100.

Multiply both sides of Equation 2 by 10 as well: 3B = 2A + 350.

Rearrange Equation 1 to get A on its own: A = (2B + 100) / 3.

Substitute the expression for A from step 3 into Equation 2: 3B = 2((2B + 100) / 3) + 350.

Multiply through by 3 to clear the fraction: 9B = 4B + 200 + 1050.

Simplify to find B: 5B = 1250, so B = 250.

Substitute B back into the equation from step 3 to find A: A = (2(250) + 100) / 3, so A = 200.

Therefore, the numbers we are looking for are A = 200 and B = 250.

Answer:

4

Step-by-step explanation:

Sample size: 4

Mean: 19

MAD: 4

Area of the figure is 71.13

Step-by-step explanation:

Find the area of the semicircle. Here, radius = 3.

Area = 1/2 πr² = 1/2 × 3.14 × 3² = 14.13

Area = length × width = 8 × 6 = 48

Area = 1/2 × base × height = 1/2 × 3 × 6 = 9

Area of the figure = 14.13 + 48 + 9 = 71.13

Answer:

7 + q/2

Step-by-step explanation:

"seven more than half of a number"?

There are two sides to the phrase

1) let the number be "q"

2) Seven (7) more: Adding seven (7 +)

3) Half of a number: dividing the number by '2'

Equation = 7 + q/2

Answer:

x>-4

Step-by-step explanation:

-6x + 5 – 4x < 45

Combine like terms

-10x + 5 < 45

Subtract 5 from each side

-10x + 5 – 5 < 45-5

-10x< 40

Divide each side by -10, remembering to flip the inequality

-10x/-10 >40/-10

x >-4

Question 1

The given system of equations is:

[tex]y = {x}^{2} + 5x + 6 \\ y = 3x + 6[/tex]

Equate the two equations:

[tex] {x}^{2} + 5x + 6 = 3x + 6[/tex]

Rewrite in standard form:

[tex] {x}^{2} + 5x - 3x + 6 - 6 = 0[/tex]

[tex] {x}^{2} + 2x = 0[/tex]

[tex]x(x + 2) = 0[/tex]

[tex]x = 0 \: or \: x = - 2[/tex]

When we put x=0, in y=3x +6, we get:

[tex]y = 3(0) + 6 = 6[/tex]

One solution is (0,6)

When we put x=-2, into y=3x+6, we get:

[tex]y = 3( - 2) + 6 = 0[/tex]

Another solution is (-2,0)

The solutions are; (0,6) and (-2,0)

Question 2:

The function is

[tex]f(x) = {x}^{6} - {x}^{4} [/tex]

Let us put x=-x,

[tex]f( - x) = {( - x)}^{6} - {( - x)}^{4} [/tex]

This gives:

[tex]f( - x) = {x}^{6} - {x}^{4} [/tex]

We can observe that:

[tex]f(x) = f( - x)[/tex]

This is the property of an even function.

Question 3:

The given function is

[tex]f(x) = {x}^{2} + 3x - 2[/tex]

The average rate of change of f(x) from x=a to x=b is given as:

[tex] \frac{f(b) - f(a)}{b - a} [/tex]

This is the slope of the secant line connecting the two points on f(x)

From x=2 to x=6, the average rate of change

[tex] = \frac{f(6) - f(2)}{6 - 2} \\ = \frac{ {6}^{2} + 3 \times 6 - 2 - {2}^{2} - 3 \times 2 + 2 }{4} \\ = \frac{36 + 18 - 4 - 6}{4} \\ = \frac{44}{4} \\ = 11[/tex]

The average rate of change is 11

The factory will make 350.56 liters of apple juice in 7.2 minutes.

To find out how many liters of apple juice the factory will make in 7.2 minutes, we can set up a proportion. If the factory makes 48.8 liters of apple juice per minute, then the amount of apple juice made in 7.2 minutes would be:

48.8 liters of apple juice / 1 minute = x liters of apple juice / 7.2 minute

Cross multiplying, we get:

x = (48.8 liters of apple juice / 1 minute) * (7.2 minutes)

Simplifying the expression, we find that the factory will make 350.56 liters of apple juice in 7.2 minutes.

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Final answer:

The model diameter of the bicycle wheel is found using the scale factor of 1:5 and the actual diameter of 24 inches (2 feet). By setting up a proportion and solving for the model diameter, we find it to be 4.8 inches.

Explanation:

To find the missing diameter of the bicycle wheel model when given the actual diameter and a scale factor, we use a proportion:

The scale is given as 1:5, which means 1 unit on the model represents 5 units in reality. First, we need to convert the actual diameter of 2 feet into inches because the model's diameter will be given in inches. There are 12 inches in 1 foot, so 2 feet is 24 inches.

After calculating, the model diameter is 4.8 inches.

Answer: 1096cm^2

Step-by-step explanation: 2(17x14+ 17x10+ 10x14)

Step-by-step explanation:

[tex]x + 15 \degree = 102 \degree \: \\ (corresponding \: \angle s) \\ \therefore \: x = 102 \degree - 15 \degree \\ \huge \red { \boxed{\therefore \: x = 87 \degree}}[/tex]

The value of x according to the relationship between the angles is; x= 87°

By mathematical convention, Corresponding angles (otherwise called F-angles) are equal.

On this note; the angle 102° and x +15° are equal.

Therefore,

x = 87°.

Read more on corresponding angles;

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Answer:

54 or as an expression (3 * 13) + (3 * 5)

Step-by-step explanation:

Step 1:  Distribute

To distribute means to break the parenthesis apart.  To make two different combinations.

3(13 + 5)

(3 * 13) + (3 * 5)

Step 2:  Multiply it out

(3 * 13) + (3 * 5)

39 + 15

54

Answer:  54 or as an expression (3 * 13) + (3 * 5)

Answer: 39 + 15

Step-by-step explanation: 3(13 + 5) can be simplified by distributing the 3 through both terms that are inside the parentheses.

So we have 3(13) + 3(5) which simplifies to 39 + 15 or 54.

So 3(13) + 3(5) is an equivalent.

Answer:

X=5m-6

Step-by-step explanation:

Step-by-step explanation:

[tex] \sqrt[8]{ {x}^{2} {y}^{6} } \\ \\ = ( {x}^{2} {y}^{6} )^{ \frac{1}{8} } \\ \\ = {x}^{2 \times \frac{1}{8}} {y}^{6\times \frac{1}{8}} \\ \\ = x^{\frac{1}{4}} {y}^{3\times \frac{1}{4}} \\ \\ = x^{\frac{1}{4}} {y}^{\frac{3}{4}} \\ \\ = \sqrt[4]{x {y}^{3} } \\ [/tex]

Final answer:

[tex]\(\sqrt[8]{x^2 y^6} = x^{\frac{1}{4}} y^{\frac{3}{4}}\)[/tex] This is the expression in its simplest radical form.

Explanation:

To simplify the given expression [tex]\sqrt[8]{x^2 y^6}[/tex], we must consider the rules for radicals and exponents.

Recall that [tex]\(\sqrt[n]{a^m} = a^{\frac{m}{n}}\)[/tex], assuming [tex]\(a\geq0\)[/tex] when n is even. Breaking down the radicals, we can rewrite the expression as:

Since both terms are under the same radical, we can multiply them together:

[tex]\(\sqrt[8]{x^2 y^6} = x^{\frac{1}{4}} y^{\frac{3}{4}}\)[/tex]

This is the expression in its simplest radical form.

Answer:

0.7=7/10

this is the fraction in the simplest form

Step-by-step explanation:

Answer:

Step-by-step explanation: 288

Answer:

Bayes' theorem, was named after a  British mathematician from the 18th-century named Thomas Bayes. The Bayes´ theorem is a mathematical formula for determining conditional probability. The theorem provides a way to revise any existing predictions or theories, and given new or additional evidence. It updates probabilities.

Hope it helps answer the question:)

Final answer:

Bayes' Theorem is a principle in statistics used to update the probability of a hypothesis in light of new evidence. It combines prior knowledge with observed data to estimate probabilities, and is widely applicable in different fields for making informed decisions.

Explanation:

Understanding Bayes' Theorem

Bayes' Theorem is a fundamental concept in the field of probability and statistics. It offers a way to revise existing predictions or theories in light of new evidence. Bayes' theorem states that the probability of A occurring given that B has occurred is P(A|B) = P(A and B) / P(B). In Bayesian analysis, this is often expressed as the probability of a hypothesis given observed data. The formula can be expanded to include prior knowledge by considering the probability of the hypothesis before observing the data, P(A), and the likelihood of observing the data given the hypothesis, P(B|A).

The theorem has extensive applications across various fields, including science, engineering, and even history. For instance, it can be utilized for the estimation of probabilities of unobserved traits, such as determining the age of individuals based on skeletal indicators. By considering prior knowledge and observed data, Bayes' theorem provides a powerful tool for updating beliefs and making informed decisions.

In practice, Bayesian approaches can incorporate prior information that quantifies existing knowledge about a parameter, which can lead to greater certainty in parameter estimates. The use of Bayesian models is often facilitated by software like WinBUGS, which helps in applying complex Bayesian methods to practical problems

Answer:

13/52

Step-by-step explanation:

i think that because in one deck of cards there are 52 cards in total and you divide 52 ÷ 4 it will give you 13 and you divide by four because there are 4 suits in total.

Answer: there both equal

Step-by-step explanation: first we have to find the unit rate of both. Francisco unit rate for his recipe is 12/18=6/9=2/3 so the unit rate is 2/3

Nia uses 8/12=4/6=2/3 so the both will have the same if they use 6 ounces

Final answer:

Both Francisco and Nia use a proportional amount of milk in their smoothies; thus, they would both use 4 ounces of milk for 6 ounces of fruit.

Explanation:

To determine who would use more milk if they each use 6 ounces of fruit, we need to compare Francisco's and Nia's milk-to-fruit ratios. Francisco uses 12 ounces of milk for every 18 ounces of fruit, and Nia uses 8 ounces of milk for every 12 ounces of fruit. To find how much milk they would use for 6 ounces of fruit, we can set up a proportion for each and solve for the amount of milk.

For Francisco:
12 ounces of milk / 18 ounces of fruit = x ounces of milk / 6 ounces of fruit.
Using cross-multiplication, we get:
18x = 12 × 6.
Dividing both sides by 18 gives us:
x = (12 × 6) / 18 = 4 ounces of milk.

For Nia:
8 ounces of milk / 12 ounces of fruit = y ounces of milk / 6 ounces of fruit.
Using cross-multiplication, we get:
12y = 8 × 6.
Dividing both sides by 12 gives us:
y = (8 × 6) / 12 = 4 ounces of milk.

Therefore, both Francisco and Nia would use 4 ounces of milk for 6 ounces of fruit in their smoothie recipes.

Answer: The last option

Step-by-step explanation:

3/4÷1/8=6

This is the answer because this is the only equation that gives a true answer all the others give an incorrect answer.

Answer:

Set 1: 43 ft3 + 21 ft3 = 64ft3

Red prism in set 2: 16ft3

Step-by-step explanation:

When you add the first one together you get 64. So what plus 48 = 64? Your answer is 16.

Answer:

6 * [tex]10^{3}[/tex] larger

Step-by-step explanation:

divide [tex]\frac{6*10^{8}}{1*10^{5} }[/tex]

[tex]\frac{6*10^{8}}{1*10^{5} }[/tex] = 6 * [tex]10^{3}[/tex]

Answer:

6000

Step-by-step explanation:

aka 6*10^3

Answer:

[tex]y =8x+9[/tex]

Step-by-step explanation:

The points are (6,39) and (-5,-49)

We need to find the equation of this line.

The slope is given by:

[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]

[tex]m = \frac{ - 49 - 39}{ - 5 - 6} [/tex]

[tex]m = \frac{ - 88}{ - 11} [/tex]

[tex]m = 8[/tex]

We use the formula:

[tex]y-y_1=m(x-x_1)[/tex]

We substitute the point (6,39) and m=8 to get:

[tex]y - 39 = 8(x - 6)[/tex]

We expand to obtain:

[tex]y - 39=8x-48[/tex]

[tex]y =8x-48 + 39[/tex]

[tex]y =8x + 9[/tex]

To find the equation of the line passing through two points, we can use the point-slope form of a linear equation:

[tex]\[y - y_1 = m(x - x_1)\][/tex]

Where:

- [tex]\( (x_1, y_1) \)[/tex] is one point on the line.

- [tex]\( m \)[/tex] is the slope of the line.

First, let's find the slope (\(m\)) using the two given points:

[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

Given points:

[tex]\( (x_1, y_1) = (6, 39) \)\( (x_2, y_2) = (-5, -49) \)\[ m = \frac{-49 - 39}{-5 - 6} \]\[ m = \frac{-88}{-11} \]\[ m = 8 \][/tex]

Now, we have the slope (\(m\)). We can choose either of the two given points and plug them into the point-slope form. Let's use \( (6, 39) \):

[tex]\[ y - 39 = 8(x - 6) \][/tex]

Now, we can simplify this equation to get it into slope-intercept form (\(y = mx + b\)):

[tex]\[ y - 39 = 8x - 48 \]\[ y = 8x - 48 + 39 \]\[ y = 8x - 9 \][/tex]

So, the equation of the line passing through the points (6, 39) and (-5, -49) is [tex]\( y = 8x - 9 \).[/tex]

The area of the shaded region is 0.7257.

The area of the shaded region represents the probability that a standard normal variable will be less than 0.74.

Since the standard normal distribution is symmetrical, the area less than -0.74 is equal to the area greater than 0.74, which can be found using the standard normal table or a calculator.

Using the standard normal table, we find that the area less than -0.74 is 0.2743.

Therefore, the area greater than 0.74 is also 0.2743.

The total area under the curve is 1, so the area less than 0.74 is 1 - 0.2743 = 0.7257.

Complete Question:

Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation.

Answer:

a. Every integer is a __________ number.  

A.  

rational < this onee

B.  

whole  

C.  

natural  

D.  

negative

Step-by-step explanation:

Answer:

[tex]x \: < \: 3\: and \: x\: > \: 2[/tex]

Step-by-step explanation:

The given inequality is

[tex]4x - 4 \: < \: 8 \: and \: 9x + 5 \: > \: 23[/tex]

Add 4 to both sides of the first inequality and subtract 5 from both sides of the second inequality.

[tex]4x \: < \: 8 + 4 \: and \: 9x\: > \: 23 - 5[/tex]

We simplify to get:

[tex]4x \: < \: 12 \: and \: 9x\: > \: 18[/tex]

Divide through the first inequality by 4 and the second by 9.

[tex]x \: < \: 3\: and \: x\: > \: 2[/tex]

Answer:

13.89 Dollars

Step-by-step explanation:

Add 47.72 and 3.39

51.11

Subtract that answer from 65

13.89

Answer:

($13.39 mistype) $13.89

Step-by-step explanation:

65 - 47.72 = 17.28

17.28 - 3.39 = 13.89

The answer is $13.89. Don't feel ashamed you don't know the answer. Have you considered tutoring?

Answer:

153 units^2

Step-by-step explanation:

Formula for area of a trapezoid is: A=(b1+b2)*1/2*h

b1=10

b2=24

h=9

Thus:

A=(10+24)*1/2*9

A=34*1/2*9

A=17*9

A=153

So the area of the trapezoid is 153 units^2

Answer: 153

step by step Explanation

Answer:

Step-by-step explanation:

rational number

Answer: 11/3 is a fraction that cannot be written as a whole number

Step-by-step explanation:

11/3 is a fraction that can only be reduced to 3 2/3