Express each ratio as a fraction in the simplest form 1) 21 dimes to 30 dimes

Answer:

B. Dependent samples

Step-by-step explanation:

Dependent samples occur when you have two samples that do affect one another. Dependent samples are paired measurements for one set of items.

While independent samples occur when you have two samples that do not affect one another.

Independent samples are measurements made on two different sets of items.

The ordered pairs that represent the linear function is Option A, B and C.

A linear function in mathematics is one that has either one or two variables and no exponents. It is a function with a straight line as its graph. If the function has more variables, they should all be constants or known variables in order for the function to continue to function as a linear function.

To determine which ordered pairs represent a linear function we use the equation of slope.

The slope is given as:

m = (y2 - y1) / (x2 - x1)

Option A:

m = (5 - 8) / (-4 + 8) = -3 / 4

m = (2 - 5) / (0 + 4) = -3/ 4

The slopes between the consecutive points are same hence option A represents a linear equation.

Similarly, for option B:

m = (1 + 2) / (2 + 1) = 1

m = (4 - 1) / (5 - 2) = 1

Option B is correct.

Option C:

m = (5 - 8) / (1 + 2) = -3 / 3 = -1

m = (2 - 5)/ (4 - 1) = -1

Option C is correct.

Option D:

m = (1- 0)/ (1 + 1) = 1/2

m = (5 - 1) / (7 - 1) = 4 / 6 = 2/3

Option D is incorrect.

Hence, the ordered pairs that represent the linear function is Option A, B and C.

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Here are the correct matches to the expressions to their solutions.

The GCF of 28 and 60 is 4.

(-3/8)+(-5/8) = -4/4 = -1.

-1/6 DIVIDED BY 1/2 = -1/6 X 2 = -1/3.

The solution of 0.5 x = -1 is x = -2.

The solution of 1/2 m = 0 is m = 0.

-4 + 5/3 = -11/3.

-2 1/3 - 4 2/3 = -10/3.

4 is not a solution of -4 < x.

1. The GCF of 28 and 60 is 4.

The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. To find the GCF of 28 and 60, we can factor each number completely:

28 = 2 x 2 x 7

60 = 2 x 2 x 3 x 5

The factors that are common to both numbers are 2 and 2. The GCF of 28 and 60 is 2 x 2 = 4.

2. (-3/8)+(-5/8) = -1.

To add two fractions, we need to have a common denominator. The common denominator of 8/8 and 5/8 is 8. So, (-3/8)+(-5/8) = (-3 + (-5))/8 = -8/8 = -1.

3. -1/6 DIVIDED BY 1/2 = -1/3.

To divide by a fraction, we can multiply by the reciprocal of the fraction. The reciprocal of 1/2 is 2/1. So, -1/6 DIVIDED BY 1/2 = -1/6 x 2/1 = -2/6 = -1/3.

4. The solution of 0.5 x = -1 is x = -2.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate x by dividing both sides of the equation by 0.5. This gives us x = -1 / 0.5 = -2.

5. The solution of 1 m = 0 is m = 0.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate m by dividing both sides of the equation by 1. This gives us m = 0 / 1 = 0.

6. -4 + 5/3 = -11/3.

To add a fraction and a whole number, we can convert the whole number to a fraction with the same denominator as the fraction. In this case, we can convert -4 to -4/3. So, -4 + 5/3 = -4/3 + 5/3 = -11/3.

7. -2 1/3 - 4 2/3 = -10/3.

To subtract two fractions, we need to have a common denominator. The common denominator of 1/3 and 2/3 is 3. So, -2 1/3 - 4 2/3 = (-2 + (-4))/3 = -6/3 = -10/3.

8. 4 is not a solution of -4 < x.

The inequality -4 < x means that x must be greater than -4. The number 4 is not greater than -4, so it is not a solution of the inequality.

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Step-by-step explanation:

Range if third side is in between 10-22

Reason:

For the lowest value of third side 16-6= 10

For the highest value if third side 16+6= 22

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Answer:

10

Step-by-step explanation:

big brain B)

The absolute value of the Rational number -474/513 is 474/513.

To find the sum of the rational numbers -8/9 and -2/57, you need to have a common denominator. The least common multiple (LCM) of 9 and 57 is 513. So, you can rewrite the fractions with a common denominator:

-8/9 = (-8/9) * (57/57) = -456/513

-2/57 = (-2/57) * (9/9) = -18/513

Now, you can add the fractions:

-456/513 + (-18/513) = (-456 - 18)/513 = -474/513

To find the absolute value of the rational number -474/513, you simply ignore the negative sign and take the value as positive:

| -474/513 | = 474/513

Therefore, the absolute value of the rational number -474/513 is 474/513.

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The method of proof required to prove the statements are are as follows:(a) proof by contradiction. (b)  proof by construction. and (c) proof by contrapositive.

a) To prove the statement "there are no integers x and y such that x is a prime greater than 5 and x 6y 3", we can use proof by contradiction.

The proof starts by assuming that there exist integers x and y such that x is a prime greater than 5 and x 6y 3. We then show that this assumption leads to a contradiction, i.e., a statement that cannot be true.

Suppose that x is a prime greater than 5 and x 6y 3 for some integers x and y. Then, we can write x as x = 6y + 3 = 3(2y + 1). This means that x is divisible by 3 and hence cannot be a prime greater than 5, contradicting our initial assumption. Therefore, our assumption that there exist integers x and y such that x is a prime greater than 5 and x 6y 3 is false, and the statement is proven.

b) To prove the statement "for all integers n, if n is a multiple of 3, then n can be written as the sum of consecutive integers", we can use proof by construction.

The proof starts by taking an arbitrary integer n that is a multiple of 3. We then construct a sequence of consecutive integers whose sum is equal to n.

Let k = n/3 be an integer. Then, we can write n as n = 3k. We can now construct a sequence of consecutive integers starting from k - (k-1) = 1 and ending at k + (k-1), such that their sum is n. For example, if k = 4, then the sequence is 1, 2, 3, 4, 5, 6, 7, and their sum is 3k = 12 = 1+2+3+4+5-6-7. Since we can construct such a sequence for any integer n that is a multiple of 3, the statement is proven.

c) To prove the statement "for all integers a and b, if a 2 b 2 is odd, then a or b is odd", we can use proof by contrapositive.

The contrapositive of the statement is: "if both a and b are even, then a 2 b 2 is even". To prove this, we can use the properties of even numbers, which can be written in the form 2k for some integer k.

Suppose that both a and b are even. Then, we can write a = 2m and b = 2n for some integers m and n. Substituting these values into the expression a 2 b 2, we get:

a 2 b 2 = (2m)2 (2n)2 = 4m2n2 = 2(2m2n2).

Since 2m2n2 is an integer, we have shown that a 2 b 2 is even. Therefore, the contrapositive statement is true.

Since the contrapositive statement is true, the original statement "for all integers a and b, if a 2 b 2 is odd, then a or b is odd" must also be true, because it is the logical equivalent of the contrapositive.  

Therefore, the mentioned statements are proved with the methods of contradiction, construction, and contrapositive.

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Using double angle identity, we are able to prove tan(x)(1 + cos(2x)) = sin(2x).

To prove the identity tan(x)(1 + cos(2x)) = sin(2x), we can start by using trigonometric identities to simplify both sides of the equation.

Starting with the left-hand side (LHS):

tan(x)(1 + cos(2x))

We know that tan(x) = sin(x) / cos(x) and that cos(2x) = cos²(x) - sin²(x). Substituting these values, we get:

LHS = (sin(x) / cos(x))(1 + cos²(x) - sin²(x))

Next, we can simplify the expression by expanding and combining like terms:

LHS = sin(x) / cos(x) + sin(x)cos²(x) / cos(x) - sin³(x) / cos(x)

Simplifying further:

LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)

Now, let's work on the right-hand side (RHS):

sin(2x)

Using the double angle identity for sine, sin(2x) = 2sin(x)cos(x).

Now, let's compare the LHS and RHS expressions:

LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)

RHS = 2sin(x)cos(x)

To prove the identity, we need to show that the LHS expression is equal to the RHS expression. We can combine the terms on the LHS to get a common denominator:

LHS = [sin(x) - sin³(x) + sin(x)cos²(x)] / cos(x)

Now, using the identity sin²(x) = 1 - cos²(x), we can rewrite the numerator:

LHS = [sin(x) - sin³(x) + sin(x)(1 - sin²(x))] / cos(x)

    = [sin(x) - sin³(x) + sin(x) - sin³(x)] / cos(x)

    = 2sin(x) - 2sin³(x) / cos(x)

Now, using the identity 2sin(x) = sin(2x), we can simplify further:

LHS = sin(2x) - 2sin³(x) / cos(x)

Comparing this with the RHS expression, we see that LHS = RHS, proving the identity.

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The area of the enclosed shape is about 14.47 km^2.

We are given that;

056° for 9.8km and  3.5 km on a bearing of 112°

Now,

We can see that the enclosed shape is a triangle with sides 9.8 km, 3.5 km, and z km, and angles 56°, 112°, and y°. We can use the fact that the sum of angles in a triangle is 180° to find y:

y = 180° - 56° - 112°

y = 12°

Now we can use the cosine rule to find z:

z^2 = 9.8^2 + 3.5^2 - 2(9.8)(3.5)cos(12°)

z^2 ≈ 101.87

z ≈ 10.09

Therefore, Fred is about 10.09 km away from his start point.

To find the area of the enclosed triangle, we can use the sine rule to find x, the height of the triangle:

sin(56°) = x/9.8

x = 9.8 sin(56°)

x ≈ 8.27

The area of a triangle is given by half the base times the height, so:

A = (1/2)(3.5)(8.27)

A ≈ 14.47

Therefore, by trigonometric ratios the answer will be 14.47 km^2.

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Answer:

The answer should be b. (0,2) because that the order pair for y

Answer:

(2,3) makes the equation false.

Step-by-step explanation:

a. -1 = 1/2(0)-1

-1 = -1

b. 0 = 1/2(2) - 1

0 = 1 - 1

0 = 0

c. 2 = 1/2 (3)-1

2 = 3/2 - 1

2 = .5

d. 1=1/2(4)-1

1=2-1

1=1

The cost per cookie, in dollars, for a sugar cookie is A; $0.54.

The mean is the average value which can be calculated by dividing the sum of observations by the number of observations

Mean = Sum of observations/the number of observations

WE know that Chocolate chip = $0.73

Double chocolate = $0.82

Oatmeal raisin = $0.70

Sugar = X

Butter pecan = $0.86

We need to find the  cost per cookie, in dollars, for a sugar cookie.

So, Mean = $0.73

Mean = 0.73 + 0.82 + 0.70+ X + 0.86 / 5

0.73 (5) =0.73 + 0.82 + 0.70+ X + 0.86

x = 0.54

Therefore, The cost per cookie, in dollars, for a sugar cookie is A; $0.54.

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Answer:

-17

Step-by-step explanation:

A linear equation is given and we need to solve out and find the value of x. So ,

⇒ x+5/ 3+11 = -1

⇒ x + 5 = 14 (-1)

⇒ x + 5 = -14

⇒ x = -5-14

⇒ x = -17

The correct statement regarding the measure of variability used to represent the data is given as follows:

The IQR of 10 is the most accurate to use, as the data is skewed.

The interquartile range of a data-set is given by the difference of the third quartile by the first quartile of the data-set.

It is the measure of variability to be used when a data-set contains outliers, or is skewed, as is the case for this problem.

The charity received 18 donations, hence the quartiles are given as follows:

Hence the IQR is given as follows:

IQR = 22.5 - 12.5

IQR = 10.

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Answer:

Evaluate each expression:

Answer:

5 = 10

6 = 13

7 = 5

8 = 17

Step-by-step explanation:

5.

1: simplify

\(\sqrt{8^2+6^2}\)

2: take both to power

\(\sqrt{64+36}\)

3: sqrt

\(\sqrt{100} = 10\)

6.

1: simplify

\(\sqrt{5^2+12^2}\)

2: take both to power

\(\sqrt{25+144}\)

3: sqrt

\(\sqrt{169} = 13\)

7.

1: simplify

\(\sqrt{4^2+3^2}\)

2: take both to power

\(\sqrt{16+9}\)

3: sqrt

\(\sqrt{25} = 5\)

8.

1: simplify

\(\sqrt{15^2+8^2}\)

2: take both to power

\(\sqrt{225+64}\)

3: sqrt

\(\sqrt{289} = 17\)

Answer:

Thus, the equation of line for point (-1, 2)  is y = x + 3.

Step-by-step explanation:

Answer:

The equation of the line is y = x + 3.

Step-by-step explanation:

A line that is parallel to y=x+4 and passes through the point (-1,2) will have the same slope as y=x+4. The slope of y=x+4 is 1, so the equation of the line will be in the form y = mx + b, where m=1. To find b, we can plug in x = -1 and y = 2 into the equation and solve for b.

y = mx + b

y = 1 * -1 + b

y = -1 + b

b = y + 1

b = 2 + 1

b = 3

Answer:

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

Use the formula for z-score

Substituting the given values, we get:

Solve it for mean μ:

Therefore, the mean of the normal distribution is 8.79.

Answer:

19

Step-by-step explanation:

There are 38 points total, each field goal is 2 points.

If we do 38/2 we get 19.

Image has work...

\(\frac{38}{2}\)

Answer:

Step-by-step explanation:

Put the equation into vertex form.

y = 2x² + 10x + 8

= 2(x² + 5x) + 8

= 2(x² + 5x + 2.5²) - 2·2.5² + 8

= 2(x+2.5)² - 4.5

vertex (-2.5, -4.5)

Answer:

y= -3x+1

Step-by-step explanation:

x1= -2 x2=2 y1=7 y2=-5

using the formula

(y-y1)/(x-x1)=(y2-y1)/(x2-x1)

(y-7)/(x-(-2))=(-5-7)/(2-(-2))

(y-7)/(x+2)=(-5-7)/(2+2)

(y-7)/(x+2)=(-12)/4

(y-7)/(x+2)=-3

cross multiply

y-7=-3(x+2)

y-7=-3x-6

y=-3x-6+7

y=-3x+1

To determine if the equation is true we multiply the expression on the right side by the denominator on the left; if the result is the numerator on the left then the equation is true:

Since the result is the numerator on the left side we conclude that the equation is true.

Answer:she will have 96,600

Step-by-step explanation:

Hope this helps

After 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

The amount of a radioactive isotope remaining after a certain number of half-lives can be calculated using the formula:

Amount remaining = Initial amount × (1/2)^(number of half-lives)

In this case, we are given the initial amount as "grams" and we want to find out the amount remaining after 4 half-lives.

So, the equation becomes:

Amount remaining = Initial amount × (1/2)^4

Since each half-life reduces the quantity to half, (1/2)^4 represents the fraction of the initial amount that will remain after 4 half-lives.

Simplifying the equation:

Amount remaining = Initial amount × (1/16)

Therefore, after 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

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Given

To find

we know that

Inserting the value of radius

In the given triangle, we have a right triangle where one angle is 90 degrees (marked as a square symbol). To find the value of x, we can use the trigonometric ratios sine, cosine, or tangent.

Looking at the triangle, we can see that the side adjacent to the angle x is 8 cm, and the hypotenuse of the triangle is 10 cm.

Using the cosine ratio, which is defined as the adjacent side divided by the hypotenuse, we can set up the equation:

cos(x) = adjacent/hypotenuse

cos(x) = 8/10

To find the value of x, we can take the inverse cosine (arccos) of both sides:

x = arccos(8/10)

Using a calculator, we can determine the approximate value of x:

x ≈ 36.87 degrees

Therefore, the value of x in the given triangle is approximately 36.87 degrees.

The volume of the given cylinder in terms of pi as required to be determined in the task content is; 5000 pi.

It follows from the task content that the volume of the cylinder which is as represented is to be determined.

Since the volume of a cylinder is;

V = 2πr²h

where r = 10 and h = 25.

V = 2π × 10² × 25.

V = 5000π.

Ultimately, the volume of the given cylinder as required to be determined is; V = 5000 pi.

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The equation z = 30x represents a direct variation the two variables, z and x, are directly proportional to each other. a.

Direct variation can be defined as a relationship between two variables where their values increase or decrease at the same rate.

In the case of the given equation, as x increases, z also increases proportionally.

Similarly, if x decreases, z will also decrease proportionally.

Direct variation can be represented as y = kx, where y and x are the variables, and k is the constant of variation.

In the given equation, we can see that z is the dependent variable, and x is the independent variable.

We can rewrite the equation as z = kx, where k = 30.

To understand how direct variation works, let's consider an example. Suppose we have an equation y = 5x, where y represents the cost of buying x apples at $5 per apple.

Here, the cost of buying apples is directly proportional to the number of apples purchased.

For instance, if we buy 10 apples, the total cost will be 10 × $5 = $50.

Similarly, if we buy 20 apples, the total cost will be 20 × $5 = $100.

Thus, we can see that the cost increases as the number of apples purchased increases, and vice versa.

The given equation z = 30x represents a direct variation is a type of relationship between two variables where their values increase or decrease proportionally.

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Answer: C. For every 2 rectangles there are 4 triangles.

Step-by-step explanation: I just did it on Edge :)

Answer:

D

Step-by-step explanation:

Just came back from the quiz

Answer:

what was the question I dont get it pls

Step-by-step explanation:

u can tell me

The total cost of the installation units that was purchased is calculated as: $288.

To calculate the total cost when given the unit price, the formula to use is:

Total cost = number of units × cost of each unit (unit price).

We are given the following information:

Cost of each unit that is on sale (unit price) = $18

Number of unit that was purchased 16 units.

To calculate the total cost of the solar lighting units that you purchased for installation along the driveway for your house, multiply the cost of each unit by the number of units to be bought.

Total cost = 16 units × $18.

Total cost = $288

Therefore, the total cost of the installation units that was purchased is calculated as: $288.

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