Write $0.025\%$ as a fraction in lowest terms.

Answer:

D. t(x) = 4x - 1

Step-by-step explanation:

The sequence shows the first four terms. As such, the x coordinates of the graph will be 1, 2, 3, and 4. The y coordinates will be 3, 7, 11, and 15 respectively.

Graphing that, the 4 points all lie on the line 4x - 1, so D is the answer.

The graph I made for this is below.

The given problem involves a parallelogram with vertices P(0,-6), Q(5,-4), R(4,-7), and D(-1,-9). We are required to perform two transformations: a translation along the vector (7,0) and a 90ᵒ counterclockwise rotation about the point (3,-2).

a) Translation along the vector (7,0):

To perform a translation, we add the components of the vector to the coordinates of each vertex. For point P(0,-6), the translation will result in a new point P'(7,-6). Similarly, for points Q(5,-4), R(4,-7), and D(-1,-9), the translation will yield new points Q'(12,-4), R'(11,-7), and D'(6,-9), respectively. The translated parallelogram will have vertices P'(7,-6), Q'(12,-4), R'(11,-7), and D'(6,-9).

b) 90ᵒ counterclockwise rotation about the point (3,-2):

To perform a rotation, we need to determine the new coordinates of each vertex after rotating 90ᵒ counterclockwise about the given point. Using the rotation formula, the new coordinates of point P' will be (-y + 3, x - 2), resulting in P''(2, 3). Similarly, for points Q', R', and D', the rotation will yield new points Q''(3, 8), R''(0, 5), and D''(1, 6), respectively. The rotated parallelogram will have vertices P''(2,3), Q''(3,8), R''(0,5), and D''(1,6).

By performing the translation and rotation, we have transformed the original parallelogram into a translated parallelogram with vertices P'(7,-6), Q'(12,-4), R'(11,-7), and D'(6,-9), and a rotated parallelogram with vertices P''(2,3), Q''(3,8), R''(0,5), and D''(1,6).

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There is only one way to divide the 12 people into committees of sizes 3, 4, and 5, and the probability of this division occurring is 1.

To find the number of divisions possible and the probability, we need to consider the number of ways to divide 12 people into committees of sizes 3, 4, and 5.

First, we determine the number of ways to select the committee members:

For the committee of size 3, we can select 3 people from 12, which is represented by the combination "12 choose 3" or C(12, 3).

For the committee of size 4, we can select 4 people from the remaining 9 (after selecting the first committee), which is represented by C(9, 4).

Finally, for the committee of size 5, we can select 5 people from the remaining 5 (after selecting the first two committees), which is represented by C(5, 5).

To find the total number of divisions, we multiply these combinations together: Total divisions = C(12, 3) * C(9, 4) * C(5, 5)

To calculate the probability, we divide the total number of divisions by the total number of possible outcomes. Since each person can only be in one committee, the total number of possible outcomes is the total number of divisions.

Therefore, the probability is: Probability = Total divisions / Total divisions

Simplifying, we get: Probability = 1

This means that there is only one way to divide the 12 people into committees of sizes 3, 4, and 5, and the probability of this division occurring is 1.

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Factors of 130: 1, 2, 5, 10, 13, 26, 65, 130

GCF of 52 and 130 is 26

I found a similar question here so that's what I can only tell you. I hope it will help you.

The smallest sample size n that provides the desired accuracy is 10.

To find the smallest sample size n that provides the desired accuracy, we can use the formula:

n = (Z-value * standard deviation / margin of error)²

Where:
Z-value = the critical value for the desired confidence level (in this case, 1.96 for 95% confidence)
Standard deviation = the preliminary sample standard deviation (1.5 in this case)
Margin of error = the desired accuracy (0.3 units in this case)

Substituting the values, we get:

n = (1.96 * 1.5 / 0.3)²
n = 9.8

Since we cannot have a fractional sample size, we round up to the nearest whole number, giving us:

n = 10

Therefore, the smallest sample size n that provides the desired accuracy is 10.

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9/16

I think you first add all the ratios then use the answer you got as a dinominator then the ratio of the yellow counter as you nominator

Answer:

Step-by-step explanation:

(x - 5)(x + 2) = 0

x - 5 = 0

x = 5

x + 2 = 0

x = -2

x = 5, -2

Answer:

9

Step-by-step explanation:

Mode: the value that occurs most frequently in a given set of data

9 has the most dots stacked up for the number of hours slept--

(in that particular data set)

Hope this made sense!

The margin of error for the population mean is 5.601

What does the term "margin of error" mean?

Your results will deviate by how many percentage points from the actual population value, according to your margin of error. It is described as a very small percentage that is allowed for error in calculations.

Given c = 0.95

The significance level is obtained as follows:

alpha = 1 - c

alpha = 1 - 0.95

alpha = 0.05

Also, it is given that n = 150 and sigma = 35 .

The critical value of Z distribution at 0.05 level of significance can be computed in MS Excel using + NORMS INV (alpha/2) function as follows:

Thus, \(Z_{0.005/2}=1.96\)

Now, the margin of error can be computed as follows: ME = Critical Value x Standard Error

\(Z_{0.005/2}*\frac{sigma}{\sqrt{n} } \\= 1.96 * \frac{35}{\sqrt{150} } \\= 5.601\)

Thus, the margin of error for the population mean is 5.601

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Answer:

Just add them! The answer is $12.14

(Make sure you line up the decimal points)

Step-by-step explanation:

Answer:

2 feet

Step-by-step explanation:

By solving a quadratic equation, we will see that the width of the walkway must be 2 ft.

Remember that the area of a rectangle of length L and width W is:

A = L*W

In this case, we know that the dimensions are:

Now, if we add a walkway of width x all around the garden, the new dimensions of the garden are:

Now with these dimensions, the area is 192 ft^2, then we can write:

192 ft^2  = (8ft + 2x)*(12ft + 2x)

Now we need to solve that for x:

192 ft^2 = 96ft^2 + 4x^2 + 40ft*x

0 = 96ft^2 - 192ft^2 + 4x^2 + 40ft*x

0 = 4x^2 + 40ft*x - 96ft^2

This is a quadratic equation, the solutions are given by Bhaskara's formula:

\(x = \frac{-(40ft) \pm \sqrt{(40ft)^2 - 4*4*(-96ft^2)} }{2*4} \\\\x = \frac{-(40ft) \pm 56ft }{8}\)

Notice that we have two solutions, but we only care for the positive one, so we take:

x = (-40ft + 56ft)/8 = 2ft

So the width of the walkway must be 2ft.

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The value of n is found as the 6 for the given exponent equation.

For the stated equation.

36 Superscript 12 minus n Baseline = 6 Superscript 2 n

This can be written as;

36¹²⁻ⁿ = 6²ⁿ

Using the adding exponent rule.

36¹².36⁻ⁿ = 6²ⁿ

Simplifying.

(6)²ˣ¹².(6)⁻ⁿˣ² = 6²ⁿ

(6)²⁴.(6)⁻²ⁿ = 6²ⁿ

Thus,

As, the base of number is equal , equating the powers.

24 - 2n = 2n

4n = 24

n = 6

Thus, the value of n is found as the 6 for the given exponent equation.

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The correct question is-

If 36 Superscript 12 minus n Baseline = 6 Superscript 2 n, what is the value of n?

Answer:B

Step-by-step explanation:

edge 2023

The probability that a randomly selected jury of 12 people is all male is 2.1 × 10⁻⁵.

What is the probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

An order does not matter so it is a Combination.

There are 16 men and we are going to choose 12 --> ₁₆C₁₂

There are 30 people and we are going to choose 12  --> ₃₀C₁₂

₁₆C₁₂ / ₃₀C₁₂

\(= \frac{16!}{(16 - 12)!} \div \frac{30!}{(30 - 12)!}\)  

= 0.00002104211

= 2.1 × 10⁻⁵

Hence, the probability that a randomly selected jury of 12 people is all male is 2.1 × 10⁻⁵.

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Step-by-step explanation:

multiply the bottom numbers to get the common denominator quickly

4*5 = 20

20 is the common denominator and answer

The common denominator to both the fractions is 20.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. In a fraction say (x/y), [y] is called denominator.

We have two fractions (3/4) and (3/5).

We have -

3/4 and 3/5

Multiply both the numerator and denominator by 5 in the fraction 3/4, we get -

(3 x 5)/(4 x 5)

15/20

Multiply both the numerator and denominator by 4 in the fraction 3/5, we get -

(3 x 4/5 x 4)

12/20

Therefore, the common denominator to both the fractions is 20.

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Answer:

k^-1= -x/2+4

Step-by-step explanation:

Its should be -x/2+4 instead of -1/2x +4

20+7x

just use the distributive property on 2(5+3x) then add x and 10

Answer:

LALLALA IS

Step-by-step explanation:

The number of passcodes that can be formed from the letters {a, b, c, d} if each letter can only be used once is  24 according to permutations.

ni this problem we are not allowed to repeat the letters, so:  we will be referring to the permutations,  where Permutations are basically for the problems where the order or we can the arrangement matters

the formula for permutation is ⁿPr=n!/(n-r)! where n is the number of given letters and r is the number of letters to be used.here n and r are 4, substituting the values on the above  formula,  we get

⁴P₄=4!/(4-4)! = 4! = 4*3*2*1=  24

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To find the linearizations of the function f(x, y, z) = 8xy + 7yz + xz at the given points, we need to use the formula for the linearization: L(x, y, z) = f(a, b, c) + f_x(a, b, c)(x - a) + f_y(a, b, c)(y - b) + f_z(a, b, c)(z - c)

where f_x, f_y, and f_z represent the partial derivatives of f with respect to x, y, and z, respectively.

a. (1, 1, 1):

The linearization L(x, y, z) at (1, 1, 1) is:

L(x, y, z) = f(1, 1, 1) + f_x(1, 1, 1)(x - 1) + f_y(1, 1, 1)(y - 1) + f_z(1, 1, 1)(z - 1)

Plugging in the values, we get:

L(x, y, z) = 8(1)(1) + 7(1)(1) + (1)(1) + 8(x - 1) + 7(y - 1) + (z - 1)

L(x, y, z) = 8 + 7 + 1 + 8(x - 1) + 7(y - 1) + (z - 1)

L(x, y, z) = 8x + 7y + z

b. (1, 0, 0):

The linearization L(x, y, z) at (1, 0, 0) is:

L(x, y, z) = f(1, 0, 0) + f_x(1, 0, 0)(x - 1) + f_y(1, 0, 0)(y - 0) + f_z(1, 0, 0)(z - 0

Plugging in the values, we get:

L(x, y, z) = 8(1)(0) + 7(0)(0) + (1)(0) + 8(x - 1) + 7(0) + (0)

L(x, y, z) = 0 + 0 + 0 + 8(x - 1) + 0 + 0

L(x, y, z) = 8(x - 1)

c. (0, 0, 0):

The linearization L(x, y, z) at (0, 0, 0) is:

L(x, y, z) = f(0, 0, 0) + f_x(0, 0, 0)(x - 0) + f_y(0, 0, 0)(y - 0) + f_z(0, 0, 0)(z - 0)

Plugging in the values, we get:

L(x, y, z) = 8(0)(0) + 7(0)(0) + (0)(0) + 8(x - 0) + 7(0) + (0)

L(x, y, z) = 0 + 0 + 0 + 8x + 0 + 0

L(x, y, z) = 8x

Therefore, the linearizations of the function f(x, y, z) at the given points are:

a. L(x, y, z) = 8x + 7y + z

b. L(x, y, z) = 8(x - 1)

c. L(x, y, z) = 8x

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The transformation rule that describes the rotation from the original parallelogram ABCD to the image parallelogram A'B'C'D' is (x, y) → (–y, x).

The rule that describes the transformation from the original parallelogram ABCD to the image parallelogram A'B'C'D' is (x, y) → (–y, x).

To understand this, let's apply the transformation rule to each vertex of the original parallelogram ABCD:

Point A (2, 5) becomes A' (-5, 2).

Point B (5, 4) becomes B' (-4, 5).

Point C (5, 2) becomes C' (-2, 5).

Point D (2, 3) becomes D' (-3, 2).

By applying the transformation rule, we observe that the x-coordinate of each point becomes the negative of the original y-coordinate, and the y-coordinate becomes the original x-coordinate.

This transformation is a 90-degree counterclockwise rotation about the origin (0, 0) on the coordinate plane. The image parallelogram A'B'C'D' is obtained by rotating the original parallelogram ABCD by 90 degrees counterclockwise.

Visually, this transformation can be seen as the original parallelogram being rotated around the origin, where the x-axis becomes the y-axis, and the y-axis becomes the negative x-axis.

Therefore, the transformation rule that describes the rotation from the original parallelogram ABCD to the image parallelogram A'B'C'D' is (x, y) → (–y, x).

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The effect of a single independent variable is a main effect.

The independent variable is the cause. Its value is independent of other variables in your study.

The dependent variable is the effect its value depends on changes in the independent variable

A main effect also called a simple effect is the effect of independent variable on a dependent variable

It ignores the effect of any other independent variables . In general, there is one main effect for each dependent variable

When two independent variable work together on the dependent variable in that case the effect are called interaction effects.

Therefore, the effect of one single independent variable is known as main effect.

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The  function f(x)=500\(x^2\) +10,000  can  be  used  to  model  the  food  vendor's  annual  revenue. The  food  vendor  would expect  to  bring  in  $ 60,000  in  annual  revenue by 10 years from now.

To find out when the mobile food vendor should expect to bring in $60,000 in annual revenue using the function f(x) = 500x^2 + 10,000, follow these steps:

1. Set the function equal to 60,000: 500\(x^2\)+ 10,000 = 60,000
2. Subtract 60,000 from both sides of the equation: 500\(x^2\)+ 10,000 - 60,000 = 0
3. Simplify the equation: 500\(x^2\)- 50,000 = 0
4. Divide both sides by 500:\(x^2\) - 100 = 0
5. Add 100 to both sides: \(x^2\) = 100
6. Find the square root of both sides: x = ±10

Since it doesn't make sense to have a negative number of years, the food vendor should expect to bring in $60,000 in annual revenue 10 years from now.

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Answer:

7.5

Step-by-step explanation:

\(a^2+b^2=c^2\\x^2+5^2=9^2\\x^2+25=81\\x^2=56\\\sqrt{x^2} =\sqrt{56} \\x=7.5\)

Answer:

There are 68,640 different ways the runners can finish first, second, and third in the race.

Concept of Permutations

The number of different ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations.

Brief Overview

Since there are 42 runners competing for the top three positions, we have 42 choices for the first-place finisher. Once the first-place finisher is determined, there are 41 remaining runners to choose from for the second-place finisher. Similarly, once the first two positions are determined, there are 40 runners left to choose from for the third-place finisher.

Calculations

To calculate the total number of different ways, we multiply the number of choices for each position:

42 choices for the first-place finisher × 41 choices for the second-place finisher × 40 choices for the third-place finisher = 68,640 different ways.

Concluding Sentence

Therefore, there are 68,640 different ways the runners can finish first, second, and third in the race.

The mathematical comparison of your experimental results to a known value is known as Percentage error.

According to the statement

We have to tell the term about the experimental value and the known value comparison.

So, For this purpose, we know that the

when we compare the known value with the comparison va;ue and by this way we find the percentage error.

So,

Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage.

And by this way we find that the experimental value is correct or not.

Because when the percentage error is increased then experimental value stated as false values.

So, The mathematical comparison of your experimental results to a known value is known as Percentage error.

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Answer:

Step-by-step explanation:

35-27=8

Answer:22.85%

Step-by-step explanation:

27 - 35

|35|

× 100% =

-8

35

× 100 = -22.8571428571% (decrease)

Answer:

D.

Step-by-step explanation:

Answer:

its d

Step-by-step explanation: