Consider the following ratios and state that whether these ratios forms a proportion?
​Case1 - 20 friends to 15 strangers
Case 2 - ​ 4 friends to 3 strangers​
A. Yes
B. No

Part B
Find the ratio of the number of friends in Case 1 to the number of friends in Case 2.
​ Answer:_____________

​Note: Type the answer as shown. Ex: (3:8)

Answer:

mode=most common answer

Step-by-step explanation:

1.12

2.9

3.1.8

4.56

5.5.9

Answer:

2k

Step-by-step explanation:

-k + 3k = 2k

Answer: f(0)= -4, f(5)= 15, f(-3)= -7

Step-by-step explanation:

0 < 1, so plug into x-4. 0-4=-4

5> 1, so plug into 3(x). 3*5=15

-3<1, so plug into x-4. -3-4=-3+(-4)= -7

The perimeter of one square tile is 40 cm.

A square is a type of rectangle whose adjacent sides are equal.

The diagonals of a square are equal and divide it into two cngruent triangles.

Given that,

Total area of three square tiles is 300cm².

Suppose the side of each of the square tiles is x.

The area of a square is given by  A = (side)².

As per the question the following expression can be written,

3x² = 300

⇒ x² = 100

⇒ x = √100

      = 10

Since perimeter of a square is given as 4 × side, the perimeter of the given square can be calculated as,

4 × 10 = 40 cm.

Hence, the perimeter of one of the square tiles is 40 cm.

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The equation of the line passing through the point (-6, 4) and (-2, 2) is y = -(1/2)x + 1

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

The standard form of a linear equation is:

y = mx + b

Where m is the slope and b is the y intercept.

The equation of a line passing through the point (-6, 4) and (-2, 2) is:

y - 4 = [(2 - 4)/(-2 - (-6))](x - (-6))

y - 4 = -(1/2)(x + 6)

y - 4 = -(1/2)x - 3

y = -(1/2)x + 1

The equation of the line is y = -(1/2)x + 1

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To find the expected value of a category, we need to multiply the value of the correct choice by the probability of making that choice and subtract the sum of the penalties for all incorrect choices from the value of the correct choice.

For Category A:

Expected value of Category A = 1500x0.05−1000 = 75

For Category B:

Expected value of Category B = 1000x0.15−500 = 75

For Category C:

Expected value of Category C = 500x0.25−0 = 62.50

Therefore, Category B has the highest expected value, with an expected value of 75 compared to 62.50 for Category C and 75 for Category A.

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The correct phrase commonly used to word conditional probabilities is "given that." This phrase explicitly indicates the condition or event on which the probability calculation is based and emphasizes the dependence between events in the probability calculation.

Let's discuss each option in detail to understand why the correct phrase is "given that" when wording conditional probabilities.

"Dependent": The term "dependent" refers to the relationship between events, indicating that the occurrence of one event affects the probability of another event. While dependence is a characteristic of conditional probabilities, it is not the specific wording used to express the conditionality.

"Given that": This phrase explicitly states that the probability is being calculated based on a specific condition or event being true. It is commonly used to introduce the condition in conditional probabilities. For example, "What is the probability of event A given that event B has already occurred?" The phrase "given that" emphasizes that the probability of event A is being evaluated with the assumption that event B has already happened.

"Either/or": The phrase "either/or" generally refers to situations where only one of the two events can occur, but it does not convey the conditional nature of probabilities. It is often used to express mutually exclusive events, where the occurrence of one event excludes the possibility of the other. However, it does not provide the specific condition on which the probability calculation is based.

"Mutually exclusive": "Mutually exclusive" refers to events that cannot occur simultaneously. While mutually exclusive events are important in probability theory, they do not capture the conditionality aspect of conditional probabilities. The term implies that if one event happens, the other cannot occur, but it does not explicitly indicate the specific condition on which the probability calculation is based.

In summary, the correct phrase commonly used to word conditional probabilities is "given that." It effectively introduces the condition or event on which the probability calculation is based and highlights the dependency between events in the probability calculation.

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The degrees of freedom is determined by the number of categories in your data minus 1.

The step after calculating your test statistic chi-squared is to calculate the degrees of freedom (df) and the critical value. The degrees of freedom is determined by the number of categories in your data minus 1. The critical value is found using a chi-squared distribution table and is based on your chosen significance level and degrees of freedom. Once these values are calculated, you can compare your test statistic to the critical value to determine if your results are statistically significant. This step is necessary to ensure that your hypothesis testing is valid and reliable.
This will help you determine whether to reject or accept the null hypothesis based on your data.

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Answer:

"one tail, alpha"

and

"negative"

The tax rate given as a percentage, can be used to find out the amount

to be paid as tax.

Correct response:

The given parameters are;

Susan Wong's taxable income last year = $52,915

The income tax rate = 2%

Required:

Susan Wong's tax last year

Solution:

The tax rate is given as a percentage of the taxable income.

The amount payable as tax = The tax rate × The taxable income

Therefore;

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Answer:

substitute value of x and y as 2 and 4

y=5x-6

4= 5*2-6

4=4 so yes

Step-by-step explanation:

The point (2, 4) lie on the line y = 5x-6

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

For example, 3x + 5 = 15.

Given that, we need to check whether the point 2,4 lie on the line y=5x-6 or not,

So, the verification of the same, we will simply put the value of x (2) in the equation and see whether we are getting 4 or not, if not then points do not lie on the line, if yes, the point lies on the line.

So, the equation is

y = 5x-6

Put x = 2,

y = 5(2) - 6

y = 10-6

y = 4

Since, we get the value of y = 4, therefore, the point lies on the line.

Hence, the point (2, 4) lie on the line y = 5x-6

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two thirds of a number b which is no more than 12, is b ≤ 18

What is inequality ?

In mathematics, an inequality represents the connection between two values in an imbalanced algebraic statement. A sign of inequality can be used to show that one of the two variables is larger than, greater than or equal to, less than, or equal to another value.

According to question

two thirds of a number b = (2/3)b

Given two thirds of number b is no more than 12

⇒   (2/3)b ≤ 12

⇒   2b ≤ 12*3

⇒   b ≤ (12*3)/2

⇒   b ≤ 36/2

⇒   b ≤ 18

hence the number b whose 2/3 is no more than 12 is, b ≤ 18

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g(x) = x^2 - 3

f(x) = x^3+7x^2-x

Start with the g(x) function. Replace every x with f(x)

g(x) = x^2 - 3

g(f(x)) = ( f(x) )^2 - 3

Then replace the f(x) on the right side with x^3+7x^2-x

g(f(x)) = (x^3+7x^2-x)^2 - 3

The highest term inside the parenthesis is x^3. Squaring this leads to (x^3)^2 = x^(3*2) = x^6

So the highest exponent found in g(f(x)) is 6, meaning the degree of is 6

Cara has consumed 139/425 of her 212 1/2 liter water goal.

To find the fraction of her 212 1/2 liter goal that Cara has consumed, we can divide the amount she has consumed by her total goal

Fraction consumed = amount consumed / total goal

Fraction consumed = 34 3/4 / 212 1/2

To make it easier to work with, we can convert the mixed numbers to improper fractions

Fraction consumed = (434 + 3) / (2212 + 1)

Fraction consumed = 139 / 425

Therefore, water consumed 139/425 of cara is 212 1/2 liter goal.

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--The given question is incomplete, the complete question is given

" Cara is trying to drink more water. She wants to drink 212 1/2 liters of water today. So far, she has consumed 34 3/4 of a liter of water.

What fraction of her 212 1/2 liter goal has Cara consumed thus far? "--

Complete Question

The diagram for this question is shown on the first uploaded image

Answer:

The length of a training track running around the field is  \(Z = 377.54 \ m\)

Step-by-step explanation:

From the question we are told that

      The length of the field is  \(L= 93 \ m\)

       The width of the field is  \(W = 61 \ m\)

The length of the two semicircle is mathematically evaluated as

          \(A = 2 * \pi * \frac{W}{2}\)

substituting values

          \(A = 2 *3.142 * \frac{61}{2}\)

         \(A = 191.54 \ m\)

Now the length of a training track running around the field is

       \(Z = A + 2 L\)

  substituting values

       \(Z = 191.54 + 2 (93)\)

       \(Z = 377.54 \ m\)

In ANOVA (Analysis of Variance), treatments refer to different levels of a factor. A factor is a variable that is controlled or manipulated in an experiment to study its effect on the dependent variable, which is the variable that is being measured. The different levels of a factor correspond to different values or settings of that factor.

For example, in a study comparing the effectiveness of three different drugs for treating a particular condition, the factor would be the drug treatment, and the three different drugs would be the levels of that factor (i.e., the treatments). The dependent variable in this case might be the patient's symptom improvement.

So, in summary, treatments in ANOVA refer to different levels of a factor that are manipulated to study their effect on the dependent variable.

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Answer:

Step-by-step explanation:

prime factors of 20 = 2 * 2 * 5

\(\frac{7}{20}=\frac{7}{2*2*5}\)

Answer:

Hello,

p=0.1024

Step-by-step explanation:

The probability is the ratio of the areas of the 2 circles:

\(p=\dfrac{\pi*8^2}{\pi*25^2} =\dfrac{64}{625} =0.1024\)

Answer:

64/625.

Step-by-step explanation:

Probability = area of small circle / area of the large one

= 8^2 / 25^2

= 64/625

Answer:

w = \(\frac{13}{23}\)

Step-by-step explanation:

Change the mixed numbers to improper fractions , that is

\(\frac{13}{8}\) = \(\frac{23}{8}\) w ( multiply both sides by 8 to clear the fractions )

13 = 23w ( divide both sides by 13 )

\(\frac{13}{23}\) = w

Answer:

w = 13/23

Step-by-step explanation:

Yes, quadrilateral ABCD is a parallelogram.

What are the properties of parallelogram?

A parallelogram is a particular sort of polygon. It is a quadrilateral in which the opposite side pairs are parallel to one another.

Properties:

1. Opposite sides are congruent.

2. Opposite angels are congruent.

3. Consecutive angles are supplementary.

4. If one angle is right, then all angles are right.

5. The diagonals of a parallelogram bisect each other.

6. Each diagonal of a parallelogram separates it into two congruent

It is given that the coordinates of the vertices of quadrilateral ABCD are A (8, -3), B(-2, 1), C (-4,-4), and D(6, -8).

According to distance formula,

If A(a,b) and B(x,y) are two coordinates then

AB = \(\sqrt{(x-a)^{2}+(y-b)^{2}}\)

Now, using this distance formula in quadrilateral ABCD

AB = \(\sqrt{(-2-8)^{2}+(1+3)^{2}}= \sqrt{(-10)^{2}+(4)^{2}}=\sqrt{100+16}=\sqrt{116}\)

CD = \(\sqrt{(6+4)^{2}+(-8+4)^{2}}=\sqrt{10^2+(-4)^2}=\sqrt{100+16}=\sqrt{116}\)

Now, If we have two coordinates A(a,b) and B(x,y) then

Slope of AB = \(\frac{y-b}{x-a}\)

Using this formula , finding slope of AB and CD of quadrilateral ABCD we get ,

Slope of AB = \(\frac{1+3}{-2-8}=\frac{4}{-10}=\frac{2}{-5}\)

Slope of CD = \(\frac{-8+4}{6+4}=\frac{-4}{10}=\frac{-2}{5}\)

As slope of both AB and CD is equal therefore, we can say that AB and CD are parallel.

As AB = CD and AB is parallel to Cd Therefore, ABCD is a parallelogram as opposite sides of parallelogram are equal and parallel.

Hence, quadrilateral ABCD is a parallelogram.

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Answer:

17.6

Step-by-step explanation:

To multiply radical expressions with the same index, we use the product rule for radicals. \(\sqrt[n]{A}.\sqrt[n]{B} = \sqrt[n]{A.B}\)

To divide radical expressions with the same index, we use the quotient rule for radicals. \(\frac{\sqrt[n]{A} }{\sqrt[n]{B} } =\sqrt[n]{\frac{A}{B} }\)

Multiplying Radical Expressions :

Example,

given:  Multiply: \(\sqrt[3]{12} .\sqrt[3]{6}\)

Apply the product rule for radicals, and then simplify.

\(\sqrt[3]{12}.\sqrt[3]{6}=\sqrt[3]{12.6}\)

            \(=\sqrt[3]{72}\\=\sqrt[3]{2^{3} .3^{2} } \\=2\sqrt[3]{3^{2} } \\=2\sqrt[3]{9}\)

Dividing Radical Expressions

Example,

given: Divide: \(\frac{\sqrt[3]{96} }{\sqrt[3]{6} }\)

In this case, we can see that 6 and 96 have common factors. If we apply the quotient rule for radicals and write it as a single cube root, we will be able to reduce the fractional radicand.

\(\frac{\sqrt[3]{96} }{\sqrt[3]{6} } =\sqrt[3]{\frac{96}{6} }\)

      \(=\sqrt[3]{16} \\=\sqrt[3]{8.2} \\=2\sqrt[3]{2}\)

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Answer:

c

Step-by-step explanation:

Temperament is to do with the personality of someone.

Thus the dog's temperament would relate to its physical and mental character.

c

Temperament is to do with the personality of someone.

Thus the dog's temperament would relate to its physical and mental character.

Answer:

hey so you know they the fractions arent there

Answer:

Option B: Target.

Step-by-step explanation:

Kohl's sale

1/3 × 100= 33.3% off

While,

Target sale

1/2 × 100 = 50% off

Answer:

Target (option b/second option)

Step-by-step explanation:

We have to first convert the fraction rates into percentage rates. To change a fraction to a percentage, you can divide the numerator by the denominator then multiply the result by 100. Alternatively, you can multiply the numerator by 100 first then divide the result by the denominator of the fraction.

1/2 = 50%

1/3 = 33.33%

Now reviewing this data, we see that a 50% decrease of a price is more than a 33.33% decrease.

Answer:

Sugar for 1 cake = 7.4 g

Sugar for 7 cakes = 7.4 × 7 = 51.8 g.

In a case whereby you can buy 5 small pizzas for the same price as 3 small pizzas and 10 one dollar drinks. price that each of the pizza cost  can be expressed as $5.

The concept that will be used here is simplification.

We were to to compute the cost of each small pizza

Let represent the cost of each small pizza = x

The we can compute the equation as:

5x = (3x + 10)

(5x - 3x) = 10

2x = 10

x= 5

Hence, the cost of each small pizza = $5

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The function used to represents the time spend by Jasmine in biking for a distance of d miles is given by f(d) = d / 18.

The time Jasmine spends biking is indeed a function of the distance she bikes.

The formula to calculate the time Jasmine takes to bike a certain distance is equal to,

time = distance / speed __(1)

Here the speed is the rate at which Jasmine bikes = 18 miles per hour.

Let us consider 'd' be the distance representing the number of miles Jasmine bikes.

This implies,

The function that represents the time Jasmine spends biking in terms of the distance .

Function f(d)  representing the time Jasmine spends biking for a distance of d miles

Substitute all the values in the formula (1) we get,

⇒ f(d) = d / 18

Therefore, the function representing the time spend by Jasmine for distance d is equal to f(d) = d / 18.

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The above question is incomplete , the complete question is:

The time Jasmine spends biking is a function of the distance she bikes. Jasmine bikes 18 miles per hour. Assume she bikes at a constant rate.

Write the function representing the time Jasmine spends biking in terms of the distance?

The first digit must be 1. The remaining seven ones must be either 0 or 1.

Therefore, there can be formed \(2^7=128\) different numbers.