How is a fraction related to its simplified form?
A) The simplified fraction is the square root of the original fraction.
B) The original fraction is larger in value than the simplified one.
C) The simplified fraction is half the value of the original fraction.
D) The simplified fraction and the original fraction have the same value

The zero of the function f(x) = 3x - 9 is x = 3.

The zero of the function f(x) = -x + 4 is x = 4.

The zero of a function is any replacement for the variable that will produce an answer of zero.

Therefore, let's find the zero of the function f(x) = 3x - 9.

0 = 3x - 9

add 9 to both sides of the equation

0 + 9 = 3x - 9 + 9

9 = 3x

divide both sides by 3

x = 9 / 3

x = 3

The zero of the function is x = 3.

Therefore, let's find the zero of the function f(x) = -x + 4.

0 = - x + 4

subtract 4 from both sides of the equation

0 - 4 = -x + 4 - 4

-4 = - x

x = 4

The zero of the function is x = 4.

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The probability that a random sample of 30 smoke detectors will have a mean lifetime between 57 and 62 months is 0.8945.

Let x represent the lifespan of smoke detectors manufactured by a business.

We assume that the lifetime of smoke detectors manufactured by a business is normally distributed.

Given: The average lifetime of a company's smoke detectors is 5 years, or 60 months, with an 8-month standard deviation.

μ = 60, σ = 8 and samle size n = 30

The probability that a random sample of 30 smoke detectors will have a mean lifetime of 57 to 62 months is :

P(57 < P < 62) = P{(57-60)/(8/√30) < ((x-μ)/σ)/(σ/√n) < (62-60)/(8/√30)}

P(57 < P < 62) = P(-1.37 < z < 2.05)

= P(z<2.05) - P(z< -1.37)

= P(<2.05)-(1-P(<1.37)) P(Z) = 1 − P(Z < 2)]

= 0.9798178-(1-0.9146565) [By using p-value table for z]

= 0.8944743≈ 0.8945

Hence, the probability that a random sample of 30 smoke detectors will have a mean lifetime between 57 and 62 months is 0.8945.

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Answer:

We have to prove the triangles ΔXYW and ΔZYW are similar. We can do this by showing that they have two equal/in-ratio corresponding sides with the same angle between them (SAS/side-angle-side), or by showing they have two equal corresponding angles (AA/angel-angle), or by showing their sides are in ratio (SSS).

We are told XY=ZY, so we already know the triangles share an equal side.

Both triangles also share YW as a side.

Because YW bisects <XYZ, we know <XYW = <ZYW, so we know the angle between the triangle's corresponding sides are the same.

Therefore, since the triangles have two equal corresponding sides with the same angle between them (SAS), we can say they are similar.

Hope this helps :)

when y equals zero, x equals -2

or, at y = 0, the function touches the x-axis at -2

Answer:

25%

Step-by-step explanation:

got it right on my quiz .

The value after differentiate will be;

⇒ [tex]\frac{dy}{dx} = 3x^2 3^{x^{3} } log_{e} 3[/tex]

What is an expression?

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

Given that;

The function is,

⇒ [tex]y = 3^{x^{3} }[/tex]

Now,

Differentiate the function with respect to x as;

The function is,

⇒ [tex]y = 3^{x^{3} }[/tex]

⇒ [tex]\frac{dy}{dx} = 3^{x^{3} } log_{e} 3 \frac{d}{dx} (x^3)[/tex]

⇒ [tex]\frac{dy}{dx} = 3^{x^{3} } log_{e} 3 * 3x^2[/tex]

⇒ [tex]\frac{dy}{dx} = 3x^2 3^{x^{3} } log_{e} 3[/tex]

Thus, The value after differentiate will be;

⇒ [tex]\frac{dy}{dx} = 3x^2 3^{x^{3} } log_{e} 3[/tex]

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The cost of each friend's meal in terms of a is 35/a.  

The cost of each friend's meal when the number of friends is 5 is $7.

We are given that;

Total amount that they can spend on food bill = $41 including delivery charge of $6

The equation is given as;

6 + ax = 41

Where;

a is the number of people

x is the cost of each friend's meal.

Thus;

ax = 41 - 6

ax = 35\

x = 35/a

So it will be the cost of each friend's meal in terms of a.

Now,

If the number of friends = 5

Then,

a = 5

Thus;

x = 35/5 = $7

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Complete question is;

A group of friends are ordering food. The total amount that they can spend on their food bill is $41, including the delivery charge of $6. The equation below represents the situation, where x is the cost of each friend's meal.

The cost of each friend's meal in terms of a is

.

The cost of each friend's meal when the number of friends is 5 is $

Answer:

252

Step-by-step explanation:

The second and third smallest factors must add to 5. The only possibility is that these factors are 2 and 3.

The second and third largest factors must add to [tex]462-N[/tex]. These factors are [tex]N/2[/tex] and [tex]N/3[/tex].

[tex]462-N=\frac{N}{2}+\frac{N}{3} \\ \\ 462-N=\frac{5N}{6} \\ \\ 462=\frac{11N}{6} \\ \\ N=252[/tex]

Answer: Though there is not enough information to be sure, a table to complete this ratio could be one include the sets of numbers (5,3) (10,6) and (15, 9)

Step-by-step explanation:

The probability of randomly choosing a green marble after you have chosen red is 4.4%

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

Given

A jar has 20 marbles: 3 green, 12 blue, 5 red.

Probability;

In probability theory, an event is a set of outcomes of an experiment or a subset of the sample space.

The total number of marbles = 20

The number of green marbles= 3

The number of blue marbles = 12

The number of red marbles = 5

The probability of choosing a red marble = Number of red marbles / Total number of marbles

= 5/20

The probability of choosing a green marble is =  Number of green marbles / New total number of marbles

= 3/19

Therefore,

The probability of randomly choosing a green marble after you have chosen red is;

= 5/20 * 3/19

= 3/68

percentage = 3/68 * 100 = 4.4%

Hence, the probability of randomly choosing a green marble after you have chosen red is 4.4%

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The values can be 4, 25 and -4, -25.

What is a Linear Equation in Two Variable?

A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Solution:

Let,

The first number be x and second number be y

Equation 1: x*y = 100

Equation 2: x - y = 21

From equation 2 we can write x = 21 + y

Substituting the value of x in equation 1

(21 + y)*y = 100

21y + y^2 - 100 = 0

y = 4, -25

this implies that x = 25, -4

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The inverse element of the binary operation is given by  (20-7a)/9 .

The binary operation is defined by a * b = 2a + 3b - 5

Now let us first find the identity element of the operation.

let e be the identity element.

Hence we know that a * e = a

Therefore a * e = 2a + 3e - 5

or, a = 2a + 3e - 5

or, a - 2a = 3e - 5

or, -a = 3e - 5

or, e = (5-a) / 3

Now we know that the inverse of the operation will be such that

a * a⁻¹ = e

or,  a⁻¹ = (20-7a) / 9

Therefore the inverse of the operation is given by (20-7a) / 9  .

A binary operation or dyadic operation is a rule that combines two elements (referred to as operands) to produce a third element. Formally, a binary operation is a two-arity operation.

An internally binary operation on a set is a binary action with the same set as its two domains or codomain. Examples include addition, multiplication, and other basic mathematical operations.

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Answer:

576482670576482670576482670576482670576482670576482670576482670576482670576482670576482670

Step-by-step explanation:

Answer:

[tex]g(x)=(x+4)^2-5[/tex]

Step-by-step explanation:

The graph of [tex]f[/tex] was shifted 4 units left and 5 units down,

Answer:

C

Step-by-step explanation:

FUNCTION A

21 : 7 = 3

FUNCTION B

8: 4 = 2

3 is greater than 2

The distance around the given triangle is [tex]\cfrac{13x}{12}[/tex].

We are asked to calculate the distance around the triangle, commonly known as the perimeter.

The perimeter is the sum of all side lengths in any shape. For a triangle, you add up all the side lengths and that is your perimeter.

Now we need to add up all these side lengths.

[tex]\cfrac{x}{2} +\cfrac{x}{3} +\cfrac{x}{4}[/tex]

We have fractions with unlike denominators. We need to get common denominators in order to solve. To do this, we need to obtain the GCF (Greatest Common Factor) of the numbers 2, 3, and 4.

This number is 12.

By changing the fractions so they all have denominators of 12, we retrieve our new equation:

[tex]\cfrac{6x}{12} +\cfrac{4x}{12} +\cfrac{3x}{12}[/tex]

Now we add them:

[tex]\cfrac{6x+4x+3x}{12}=\cfrac{13x}{12}[/tex]

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When the population standard deviation, is unknown, a hypothesis test for the population mean is conducted the same way as if the population standard deviation were known. The t-distribution is used instead of the conventional normal distribution, which is the only distinction (z-distribution).

As per the given population function, the growth function is written as, P = 13000(1.05)ˣ

Population function:

Population function refers the positive change in a particular population as a function of time. And this growth is not linear, but exponential, and so the formula for population growth can be found by starting with the premise that P (population) multiplies by a rate r over time.

Given,

A population numbers 13,000 organisms initially and grows by 5% each year. Suppose P represents population and t represents the number of years of growth. An exponential model for the population can be written in the form P = abˣ

Now, we have to find the population growth function for this situation.

From the given question, 'we have the following details,

Population numbers = 13,000

So, the value of a in the population function is 13,000

And it grows every year as 5%.

So, in decimal form in can be 0.05.

So, the value of b is calculated as,

=> b = 1 + 0.05

=> b = 1.05

Now, we have to apply these values on the function,

Then we get,

=> P = 13000(1.05)ˣ

Therefore, the population growth function is been identified

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All the missing lengths and missing angles of the given right angle triangle are as calculated below

We are given a right angle triangle and as such we can use the trigonometric ratios as;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

a) A = 30°, Thus;

B = 180 - (90 + 30)

B = 60°

Using sine rule;

a/sin A = b/sin B

a/sin 30 = 6/sin 60

a = 3.464

c/sin 90 = 6/sin 60

c = 6.928

b) a = 13 and b = 13

Using Pythagoras theorem;

c = √(13² + 13²)

c = 18.385

Since a = b, it means it is an isosceles triangle and so;

A = B = 45°

c) B = 30°, c = 10

A = 180 - (30 + 90)

A = 60°

10/sin 90 = b/sin 30

b = 5

10/sin 90 = a/sin 60

a = 8.66

d) A = 45°, c = 12

B = 45°

c/sin 90 = b/sin 45 = a/sin 45

b = a = 12 * sin 45 = 8.485

e) c = 1, b = 1/√2

c/sin 90 = b/sin B

1/sin 90 = (1/√2)/ sin B

B = 45° = A

a = √(1² - (1/√2)²)

a = 0.7071

f) c = 4 and b = 4;

a = √(4² - (4)²)

a = 0

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The number of ways  that five out of seven patients are called to remind them of their appointment is 21 ways

Total number of patients = 7

Number of patients that called to remind them of their appointments = 5

To find the total number of ways we have to use the combination methods

The combination is the method of selection of elements from the collection. In the combination order of the selection does not matters

Total number of ways = [tex]7C_5[/tex]

= 7! / (5!(7 - 5)!)

Subtract the terms

= 7! / 5! × 2!

= (7×6×5!) /  (5!×2!)

= 7 × 6 / 2 × 1

= 42 / 2

= 21 ways

Hence, the number of ways  that five out of seven patients are called to remind them of their appointment is 21 ways

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According to the solving the value of the Quadratic equation are as follows:

x = 0

x = 2

We can answer any quadratic equation using the quadratic formula. The first step is to change the equation's form to ax2+bx+c=0, where a, b, but instead c are the coefficients. The formula (-b(b2-4ac))/(2a) is then used to enter these coefficients. View instances of the formula being used to solve various equations.

Make a video of the pupils utilizing one technique to solve a quadratic equation. Allowing pupils to pick is an option, but you can also direct them to utilize the quadratic equation, factoring, or square-rooting.

f(x) = 2x² – 3x

x- (2x² – 3x) = 0

x - 2x² + 3x = 0

4x - 2x²= 0

x = 0

x = 2

According to the solving the value of the Quadratic equation are as follows:

x = 0

x = 2

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The statement that would be true if the data in the data in the stem-and-leaf plot is shown in a line plot is: D. We could calculate the range and median.

A line plot is a graph that shows individual data in a data set with the use of dots. Each dot represents a data plot.

In a line plot, we can easily find the middle of the data distribution which is the median of the data and also we can determine the highest and lowest value which enables us to find the range of the data.

Thus, using the stem-and-leaf plot in the diagram, below, write out each data points given, which are:

68, 70, 80, 86, 88, 88, 96, 96, 97, 97, 98, 98, 99, 100, 100, 100, 100, 100

The line plot for these data would have the following frequency for each data point:

68 - 1 dot

70 - 1 dot

80 - 1 dot

86 1 dot

88 - 2 dots

96 - 2 dots

97 - 2 dots

98 - 2 dots

99 - 1 dot

100 - 5 dots

The line plot is shown in the diagram below.

Range = 100 - 68 = 32

Median = 97

Therefore, the answer is: D. We could calculate the range and median.

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Answer:

[tex]3^{7/2}[/tex]

Step-by-step explanation:

[tex]3^3 \sqrt{3} \\ \\ =3^3 \cdot 3^{1/2} \\ \\ =3^{3+\frac{1}{2}} \\ \\ =3^{7/2}[/tex]

The kilograms of sugar that were used for cherry jam is 9kg.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

Since there are 40 kg of sugar in the bag. Strawberry jam was used which was 4 kg. The remaining kilograms will be:

= 40kg - 4kg

= 36 kg

Since 1/4 of the remaining sugar was used, the amount used will be:

= Fraction × Total amount

= 1/4 × 36

= 9kg.

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Answer:

0 hundreds

0 tens

7 ones

.

4 tenths

0 hundredths

8 thousandths

Standard form=7.408

Step-by-step explanation:

Lets first solve (7x1)+(4x1/10)+(8x1/1000)

7+0.4+0.008

Simplify:

7.408

The standard errors for the sample sizes of 440, 230, and 1200 are 1.2, 1.65, and 0.72, respectively.

The mean of the population is μ = 90. The standard deviation of the population is σ = 25. We are given three sample sizes. We need to compute the standard error for each sample size.

The standard error is computed by dividing the standard deviation by the square root of the sample size. It calculates the accuracy of a sample mean by factoring in sample-to-sample variability.

Let S1, S2, and S3 represent the standard errors for the sample sizes of 440, 230, and 1200, respectively.

S1 = σ/√n

S1 = 25/√440

S1 = 1.2

S2 = σ/√n

S2 = 25/√230

S2 = 1.65

S3 = σ/√n

S3 = 25/√1200

S3 = 0.72

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The triangle has a hypothenuse 9.21 units and the graph it's attached below

The distance between any two points is the length of the line segment joining the points. There is only one line passing through two points. So, the distance between two points can be calculated by finding the length of this line segment connecting the two points.

The formula of distance between two points is given as

d = √(y₂ - y₁)² + (x₂ - x₁)²

The two points are

Substituting the values into the formula above;

d = √(2 -(-7))² + (-6-(-8))²

d = √85

d = 9.21 units

The hypothenuse of the triangle is 9.21 units

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Step-by-step explanation:

g(7)=

[tex] {7}^{2} + n[/tex]

[tex]49 + n[/tex]

f(g(7))=n

[tex]f(g(7)) = \sqrt{49 + n + 1} [/tex]

[tex]f(g(7)) = \sqrt{n + 50} [/tex]

[tex]9 = \sqrt{n + 50} [/tex]

[tex]81 = n + 50[/tex]

[tex]n = 31[/tex]

So

[tex]g(31) = 31 {}^{2} + 31[/tex]

[tex] = 992[/tex]