True or false? The graph represents a function.

Step-by-step explanation:

credits are also on there

There are 23.33 pounds of defective nails should the manager expect the 350-pound delivery to contain.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The manager of a hardware store took a random sample of 4.5 pounds of nails from a delivery of 350 pounds of nails.

And, The manager found that 0.3 pounds of nails in the sample were defective.

Since, The manager found that 0.3 pounds of nails in the sample were defective.

Hence, Amount of pounds of defective nails should the manager expect the 350-pound delivery to contain is,

⇒ 350 × 0.3 / 4.5

⇒ 23.33 pounds

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Sample Parameter: The population's weight and the average weight of the cereal box The grain on the line's average weight is the parameter.

The value that consistently appears in a given set is known as the mode in statistics. The mode or modal value is the value or number that appears most frequently in a data set and has a high frequency. Along with mean and median, there are three other ways to measure central tendency. The mode can be calculated quite easily. After sorting the numbers in a set according to their order—lowest to highest or highest to lowest—count how many times each number appears in the group.

given

Example: 50th box of cereal

All cereal boxes are lined up in the population

Example Parameter: The cereal box's average weight

Population metric: The cereal on the line's average weight

Sample Parameter: The population's weight and the average weight of the cereal box The grain on the line's average weight is the parameter.

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Therefore the correct answer is A. Adam earns $5.25 more per hour than Kim.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

Adam earns $186 for 8 hours of work, so his hourly rate is $186/8 = $23.25 per hour

Kim earns $54 for 3 hours of work, so her hourly rate is $54/3 = $18.00 per hour

Kim earns $125 for 7 hours of work, so her hourly rate is $125/7 = $17.86 per hour

Kim earns $216 for 12 hours of work, so her hourly rate is $216/12 = $18.00 per hour

Adam earns $23.25 per hour and Kim earns $18.00 per hour on average.

Adam earns $23.25 - $18.00 = $5.25 more per hour than Kim.

Therefore the correct answer is A. Adam earns $5.25 more per hour than Kim.

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Jasmine can buy a average of 4 binders because the cost of the binders, multiplied by the number of binders she wants to buy, plus the cost of the pens, must not exceed her total budget of $26.

Step 1: Define the variable. Let x represent the number of binders Jasmine can buy.

Step 2: Write the inequality. 5x + 4.75 ≤ 26

Step 3: Solve the inequality. 5x ≤ 21.25

Step 4: Isolate the variable. x ≤ 4.25

Step 5: The maximum number of binders Jasmine can buy is 4.

Let x represent the number of binders Jasmine can buy

5x + 4.75 ≤ 26

5x ≤ 21.25

x ≤ 4.25

Jasmine has a total of $26 to spend on binders and one pack of pens. The cost of the pens is $4.75, and each binder costs $5. To determine the maximum number of binders she can buy. The inequality we need to solve is 5x + 4.75 ≤ 26. We can solve this inequality by first multiplying both sides of the equation by 5, which gives us 5x ≤ 21.25. We can then isolate the variable by dividing both sides of the equation by 5, which gives us x ≤ 4.25. This means that the maximum number of binders Jasmine can buy is 4.

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The options that shows expressions which are functions in the ranges they are defined are;

Option A: f(x) = 2x + 5

Option B:  f(x) = x² + 1

Real numbers are defined as the combination of rational and irrational numbers, in the number system. This means that, all the arithmetic operations can be performed on real numbers and they can be represented in the number line.

Now, integers are defined as whole numbers that can be positive, negative or zero.

a) We are told that the input of real numbers must yield only real numbers. Yes this is true because any real number we put in for x in f(x) = 2x + 5 will yield an output that is also a real number.

b) We are told that the input of real numbers must yield only real numbers. Yes this is true because any real number we put in for x in f(x) = x² + 1 will yield an output that is also a real number.

c) We are told that the input of real numbers must yield only real numbers. No this is not true because if we put -1 which is a real number for x in the denominator, we will get an undefined function.

d) We are told that the input of integers must yield only integers. No this is not true because if we put 1 for x which is an integer, we will get a fraction which is not an integer.

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The x-intercept and the y intercept of the graph of 6x - 3y = 36 are x = 6 and y = -12

How to determine the x-intercept and the y intercept of the graph?

From the question, we have the following parameters that can be used in our computation:

6x - 3y = 36

Set y to 0 to determine the x-intercept

So, we have the following representation

6x = 36

Divide by 6

x = 6

Set x to 0 to determine the y-intercept

-3y = 36

Divide by -3

y = -12

hence, the intercepts are x = 6 and y = -12

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The parabola is open upward direction. The vertex is the minimum value of the parabola.

What is a parabola?

A parabola is a planar curve that is mirror-symmetrical and roughly U-shaped in mathematics. It fits various seemingly disparate mathematical descriptions, all of which can be shown to define the same curves. A point and a line are two ways to describe a parabola.

Given quadratic function is

f(x) = 5x² -3x

The leading term of the given function is 5x².

The sign of the leading term is positive, thus it is open upward direction.

Rewrite the given function in the form f(x) = a(x - h)² + k

f(x) = 5x² -3x

f(x) = 5( x² - 3/5 x)

f(x) = 5( x² - 3/5 x + 9/100 - 9/100)

f(x) = 5( x² - 3/5 x + 9/100) - 5 × 9/100

f(x) = 5( x -  3/10)² - 9/20

f(x) = 5( x -  3/10)² + (-9/20)

The vertex of the parabola is (3/10, -9/20).

Since the parabola opens upward direction, thus the vertex of the parabole is a minimum value.

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The necessary probabilities are 3/8, 1/3, 9/64, and 37/64.

The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.

Here,

S = { G1, G2, G3, Y1, Y2, Y3, Y4, Y5 }

G = { G1, G2, G3 }

P(G) = 3/8

E = { G2, Y2, Y4 }

P(G|E) = 1/3

P(G and E) = P(G)*P(E) = (3/8)*(3/8) = 9/64

P(G or E) = P(G) + P(E) - P(G and E) = (3/8) + (3/8) - (9/64) = (6/8) - (9/64) = (48/64) - (9/64) = 37/64

The required probability is 3/8, 1/3, 9/64 and 37/64.

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Answer:

√28 and √11

Step-by-step explanation:

Note : -

Irrational number is any real number that cannot be expressed as the quotient of two integers.

Here,

√28 = 5.291.......

5.291.... is an infinite number, it keeps going, it cannot be expressed in terms of a fraction.

Similarly,

√11 = 3.316......

Hence,

√28 and √11 are irrational numbers.

Answers:

=============================================

Explanation:

We have a function since the curve passes the vertical line test. Recall that this test is where we try to draw a single vertical line through more than on point on the curve. Such a task isn't possible in this case.

-----------

On the other hand, the curve does not pass the horizontal line test. It is possible to draw a single horizontal line through more than one point on the curve.

This function is not one-to-one since it does not pass the horizontal line test.

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

Because the graph isn't one-to-one, the inverse won't be a function. The process of finding the inverse involves swapping x and y; which means we swap from "horizontal line test" to "vertical line test".

The original function failing the horizontal line test would mean the inverse fails the vertical line test.

Answer: No, -0.0022 is not less that -0.022

Step-by-step explanation:

1. We know that the bigger the negative number the lesser it is ( 0.022 is a bigger number than 0.0022) but since it's a negative number it's less in value.

Answer: Choice 2

Step-by-step explanation:

Answer:

Answer:

Foci: (±5, 0)

Vertex: ( ±4 , 0)

Eccentricity: e = 5/4

Step-by-step explanation:

Hyperbola:

Write the equation of hyperbola in the form,

\boxed{\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1}

a

2

x

2

−

b

2

y

2

=1

9x² - 16y² = 144

Divide the entire equation by 144,

\begin{gathered}\sf \dfrac{9x^2}{144}-\dfrac{16y^2}{144}=\dfrac{144}{144}\\\\\\ \dfrac{x^2}{16}-\dfrac{y^2}{9}=1\\\\\\\dfrac{x^2}{4^2}-\dfrac{y^2}{3^2}=1\end{gathered}

144

9x

2

−

144

16y

2

=

144

144

16

x

2

−

9

y

2

=1

4

2

x

2

−

3

2

y

2

=1

a = 4 and b =3

Eccentricity: e

\boxed{e=\sqrt{1+\dfrac{b^2}{a^2}}}

e=

1+

a

2

b

2

\begin{gathered}\sf = \sqrt{1+\dfrac{9}{16}}\\\\=\sqrt{\dfrac{16}{16}+\dfrac{9}{16}}\\\\=\sqrt{\dfrac{25}{16}}=\sqrt{\dfrac{5*5}{4*4}}\\\\\\=\dfrac{5}{4}\end{gathered}

=

1+

16

9

=

16

16

+

16

9

=

16

25

=

4∗4

5∗5

=

4

5

Foci:

(ae, 0) & (-ae , 0)

\begin{gathered}\sf \left(4*\dfrac{5}{4},0 \right) \ ; \ \left( -4*\dfrac{5}{4},0 \right)\\\\\\(5, 0) \ ; \ (-5,0)\end{gathered}

(4∗

4

5

,0) ; (−4∗

4

5

,0)

(5,0) ; (−5,0)

Vertex of hyperbola:

The vertex of the hyperbola is a point where the hyperbola cuts the axis. (-a , 0) ; (a , 0)

Vertex : (-4 , 0) ; (4 , 0)

Answer:

Step-by-step explanation:

To find the y-intercept, we can use the slope-intercept form of a linear equation which is y = mx + b, where m is the slope of the line, and b is the y-intercept.

Since the line passes through the points (2, -2.5) and (4, -2), we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.

To find the slope(m) we can use the rise over the run formula ,

m = (y2 - y1) / (x2 - x1) = (-2 - (-2.5)) / (4 - 2) = -0.5

then we can substitute the values in point-slope form

y - (-2.5) = -0.5 (x - 2)

And now we can use x = 0,

y = -0.5(0-2) -2.5 = 1.5

so the y-intercept of the line is 1.5

The value of k⁻¹(8) in for k(x) = 4 ÷ 5x - 6 is 2/35.

First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.

We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.

Given, k(x) = 4 ÷ 5x - 6.

k(x) = (4/5x) - 6.

Let, y = k(x).

y =  (4/5x) - 6.

(4/5x) = y + 6.

1/x = 5(y + 6)/4.

x = 4/{5(y + 6)}.

y = 4/{5(x + 6)}.

k⁻¹(x) = 4/{5(x + 6)}.

k⁻¹(8) = 4/{5(8 + 6)}.

k⁻¹(8) = 4/{5(14)}.

k⁻¹(8) = 4/70.

k⁻¹(8) = 2/35.

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Therefore , In the instance of an equilateral triangle, each side's length (3 sides are equal) is equivalent to 28 cm.

What is triangle?

Triangular polygons in geometry are those with right side and three vertices. There are three straight sides to this two-dimensional shape. Three-sided polygons include triangles. A triangle's three angles add up to a whole 180 degrees. A single plane contains the triangle.

A polygon is a closed two-dimensional geometric shape that has three or more straight sides. The sides of a polygon are called edges and the points where the edges meet are called vertices.

Here,

We must apply the mathematical procedure for computing an equilateral triangle's area.

An equilateral triangle's area is equal to 3/4 of each side; assume that each side is x cm long.

[3/4 (a)2] cm2 is the equilateral triangle's surface area.

In light of the information mentioned in the query,

√3/4 × (a)² = 196√3

a²/4 = 196√3/√3

a²/4 = 196

a² = 196×4

a² = 784

a = √784

a = 28

In the instance of an equilateral triangle, each side's length (3 sides are equal) is equivalent to 28 cm.

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Answer:

2/3 + 1/6 + 2/8

=(2×8+1×4+2×3)/24

=(16+4+6)/24

=26/24

=13/12

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In a double number line diagram, equal ratios are represented by two parallel number lines. On both number lines, the tick marks are in the same places. Though the other numbers are frequently varied, the tick marks labeled with 0 always line up.

According to question:-

How much more garlic powder than salt is in the triple batch?

Answer: 6 teaspoons of garlic powder - 15 teaspoons of salt = -9 teaspoons. So there is 9 teaspoons less garlic powder than salt in the triple batch.

How much spice mix is in the triple batch?

Answer: 6 teaspoons of garlic powder + 15 teaspoons of salt = 21 teaspoons of spice mix.

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Answer:

b and c

Step-by-step explanation:

b is basically saying flip it up and turning the whole thing left which will put it on top of pnms and c is saying rotate it where line sr and sm would be side by side then flip it right

The conclusion on if there is convincing evidence that the one detergent is better than the other is; Option D: No, because a difference in mean rating of 1.5 or more occurred 23 out of 200 times, meaning the difference is not statistically significant and there is not convincing evidence that one brand is better than the other.

We are told that, 25 pieces are randomly assigned to be cleaned with detergent A, while the remaining 25 pieces are cleaned with detergent B.

Therefore, we can say that the sample size for both detergent A and detergent B is same. We can also say that the sample is distributed randomly which means that the sample is unbiased (fair).

We are also told that the mean rating for detergent B is found to be significantly less than the mean rating for detergent A.  Since we know that the mean is the average of a set of given numbers, then we can conclude that there is No evidence that the one detergent is better than the other because a difference in mean rating of 1.5 or more occurred 23 out of 200 times, meaning the difference is not statistically significant and there is not convincing evidence that one brand is better than the other.

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Writing the whole number in the numerator and 1 in the denominator. Fraction in simplest form is 8

How to Find the Most Basic Form

Determine the GCF of the fraction’s numerator and denominator.

Divide the created GCF by the numerator and denominator.

Fill in the blanks with the simplified fraction of the supplied fraction.

The most basic form, If the top and bottom have no common components other than 1, the fraction is in its simplest form. In other words, the top and bottom cannot be divided any further and still remain full numbers. You may sometimes hear the phrase “lowest terms” when referring to the simplest form.

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Using the distributive property to rewrite the expression, gives (14 x 10) + ( 14 x 2). When evaluated, the result would be 168.

According to the distributive property, it is necessary to multiply each of the two numbers by the factor before performing the addition operation when a factor is multiplied by the sum or addition of two terms.

This means that with the formula given, 14 (10 + 2):, the distributive property makes it:

= 14 (10 + 2)

= (14 x 10) + ( 14 x 2)

The evaluation gives :

= (14 x 10) + ( 14 x 2)

= 140 + 28

= 168

In conclusion, using the distributive property gives (14 x 10) + ( 14 x 2).

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Yara's mother was 32n-5 years old 5 years ago in terms of n.

Yara's mother is 4n times older than Yara, and Yara is 8 years old, so we can set up the equation:

Mother's age = 4n * 8 years

We are also told that Yara's mother is 5 years older than she is now, so we can add 5 to the equation above:

Mother's age 5 years ago = 4n * 8 years - 5 years

Now we can simplify this equation:

Mother's age 5 years ago = 32n - 5 years

Now we can substitute the value of n to find the mother's age in terms of n.

To find the age of Yara's mother 5 years ago in terms of n, we need to know the value of n. But we don't have the value of n so we can't find the exact age but we can find it in terms of n which is 32n-5 years.

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Answer:

44.8

Step-by-step explanation:

44.4 - (-0.4) = 44.8

Answer:

Step-by-step explanation:

Find the prime factorization of 144

144 = 2 × 2 × 2 × 2 × 3 × 3

Find the prime factorization of 405

405 = 3 × 3 × 3 × 3 × 5

To find the GCF, multiply all the prime factors common to both numbers:

Therefore, GCF = 3 × 3

Answer = 9

There is no upper limit if the ratio raises x to a higher power. The limit is 0 if the ratio causes the power of x to be reduced to zero.

A ratio is an expression for an ordered pair of numbers, a and b, where b is not equal to zero and the expression is written as a/b. A ratio is created by combining two ratios. Assuming a ratio of one boy to three girls, this would suggest that 3/4 of the population is female and only 1/4 is male. A part can be an amount, a percentage, or the difference between two or more objects.

Here,

The ratio of, say, the highest-degree words serves as the upper bound as x grows.

There is no upper bound on how much the ratio can raise the power of x. The limit is 0 if the ratio causes the power of x to be reduced to zero.

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Answer:

20, yes

Step-by-step explanation:

11+9=20

If he is charged $9 for each guest then it will make a huge impact to the number of guests.

The greatest possible quotient of any two distinct members of the set; { 2 / 5, 1 / 2, 5, 10 } as required to be determined is; 25.

It is evident from the task content that the set from which the two numbers whose quotient is to be maximised is; { 2 / 5, 1 / 2, 5, 10 }.

On this note, since the quotient which is to be maximised is hypothetically; x / y;

Therefore, in a bid to maximize the result of the quotient; it follows that the numerator, x must be as great as possible and the denominator, y must be as less as possible.

On this note, since the maximum number in the set is 10 and the minimum is 2 / 5; we have that;

10 / (2 / 5)

= ( 10 × 5 ) / 2

= 25.

Ultimately, it can be inferred that the greatest possible quotient as required is; 25.

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Answer:

2.50 × 19 = 47.5

Therefore, she would get $47.5 if she sold 19 cups.