Simplify these expressions
5×x
6×x×y
2×x×3×y​

The null hypothesis is formulated as a statement of equality to represent the assumption of no effect, no difference, or no relationship between variables in hypothesis testing.

The null hypothesis is typically formulated as a statement of equality because it represents the assumption or claim of no effect, no difference, or no relationship between variables in the context of statistical hypothesis testing.

When conducting hypothesis tests, we start with the assumption that there is no significant difference or relationship between variables, and any observed differences or relationships are merely due to random chance or sampling variability. The null hypothesis serves as a benchmark or reference point against which we compare the observed data.

Formulating the null hypothesis as a statement of equality allows for a clear and specific claim to be tested statistically. It sets the baseline or default position that is assumed to be true unless there is sufficient evidence to reject it in favor of an alternative hypothesis.

For example, in a study comparing the mean scores of two groups, the null hypothesis might state that the population means are equal (μ1 = μ2). This implies that any observed difference in sample means is due to chance, rather than a true difference in the population means.

By specifying the null hypothesis as a statement of equality, statistical tests provide a framework to assess the likelihood of observing the obtained data under the assumption of no effect or no difference, allowing us to make inference and draw conclusions about the population parameters based on the evidence from the sample.

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The volume of the cylinder given the radius and the height is 562.2 cubic units

Volume of a cylinder = πr²h

= 3.14 × 2² × 5

= 3.14 × 4 × 5

= 562.2 cubic units

Therefore, the volume of the cylinder is 562.2 cubic units.

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Answer:62.8

Step-by-step explanation:

just took the test

Answer:

D. <15/√346>

Have a nice day! :)

Answer:

Angle k is 34.5 degrees

Step-by-step explanation:

a circle makes 360 degrees total.  okay so u have to consider the angles given. m arc go= 127

m<0 = 54.5

54.5 times 2 = 109

109 is arc gk

109 + 127+ 55= 291

360-291=69= arc OU

69 divided by 2 is 34.5

Angle k is 34.5 degrees

The charge q is ±7.46 × 10⁻⁷C.

Give:

Take a look at the charge on the left. The following forces are at work in response to this charge:

(Refer to the diagram below)

Because the charge is in equilibrium, the charge's vertical and horizontal forces must be zero.

We have the following in the vertical direction:

\(\begin{aligned}T \cos 20^{\circ} &=W \\\Rightarrow T &=\frac{m g}{\cos 20^{\circ}} \\&=\frac{3.0 \times 10^{-3} \mathrm{~kg} \times 9.8 \mathrm{~m} / \mathrm{s}^2}{\cos 20^{\circ}} \\&=3.13 \times 10^{-2} \mathrm{~N}\end{aligned}\)

Coulomb's Law states that the electrostatic force between two point charges, q₁, and q₂, separated by r is given by the equation:

\(\begin{aligned}F &=\frac{q_1 q_2}{4 \pi \epsilon_0 r^2} \\&=\frac{K q_1 q_2}{r^2}\end{aligned}\)

Here,

Using trigonometric personalities, the distance between any two charges is:

\(\begin{aligned}r &=2 l \sin 20^{\circ} \\&=2 \times 1.0 \mathrm{~m} \times 0.342 \\&=0.684 \mathrm{~m}\end{aligned}\)

We have the following in the vertical direction:

\(\begin{aligned}F_e &=T \sin 20^{\circ} \\\Rightarrow \frac{K q_1 q_2}{r^2} &=T \sin 20^{\circ} \\\Rightarrow \frac{K q^2}{r^2} &=T \sin 20^{\circ} \\\Rightarrow q^2 &=\frac{r^2 T \sin 20^{\circ}}{K} \\&=\frac{(0.684 \mathrm{~m})^2 \times 3.13 \times 10^{-2} \mathrm{~N} \times \sin 20^{\circ}}{9 \times 10^9 \mathrm{~N} \cdot \mathrm{m}^2 / \mathrm{C}^2} \\&=55.65 \times 10^{-14} \mathrm{C}^2 \\\Rightarrow q &=\pm 7.46 \times 10^{-7} \mathrm{C}\end{aligned}\)

Therefore, the charge q is ±7.46 × 10⁻⁷C.

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The correct question is given below:
Two 3.0g point charges on 1.0m - long threads repel each other after being equally charged, as shown in the figure. What is the charge q?

Answer:

From largest to smallest: FG, FH, GH

Step-by-step explanation:

Given

\(FG = 6x + 7\)

\(GH = 8x - 5\)

\(FH = 10x - 11\)

\(Perimeter = 87\)

Required

Order the sides in descending order

First, we need to solve for x.

Perimeter of FGH is calculated as thus:

\(Perimeter = FG + GH + FH\)

Substitute values for FG, GH, FH and Perimeter

\(87 = 6x + 7 + 8x - 5 + 10x - 11\)

Collect Like Terms

\(87 - 7 + 5 + 11= 6x + 8x + 10x\)

\(96= 24x\)

Reorder

\(24x = 96\)

Divide through by 24

\(x = 96/24\)

\(x = 4\)

Substitute 4 for x in FG, GH and FH

\(FG = 6x + 7\)

\(FG = 6 * 4 + 7\)

\(FG = 24 + 7\)

\(FG =31\)

\(GH = 8x - 5\)

\(GH = 8 * 4 - 5\)

\(GH = 32 - 5\)

\(GH = 27\)

\(FH = 10x - 11\)

\(FH = 10*4 - 11\)

\(FH = 40 - 11\)

\(FH = 29\)

In order of arrangement in descending order, we have:

\(FG =31\)    \(FH = 29\)     \(GH = 27\)

Answer:

96.00 increased by 86% is 178.56

Step-by-step explanation:

The domain and range of the inverse relation are {2, 3, 5, 7, 8} for both.

The given relation consists of the points 2, 3, 5, 7, and 8. To find the domain and range of the inverse relation, we need to swap the x-values with the y-values. The resulting set of values will represent the domain and range of the inverse relation.

In the given relation, the x-values are 2, 3, 5, 7, and 8, and the corresponding y-values are not provided. To find the inverse relation, we swap the x-values with the y-values.
After swapping the values, we obtain the following set of points: (2, 2), (3, 3), (5, 5), (7, 7), and (8, 8). These points represent the inverse relation.
The domain of the inverse relation is the set of x-values from the swapped points, which is {2, 3, 5, 7, 8}. This means that these are the values for which there exist corresponding y-values in the original relation.
Similarly, the range of the inverse relation is the set of y-values from the swapped points, which is also {2, 3, 5, 7, 8}. These are the values that correspond to the x-values in the original relation.
Therefore, the domain and range of the inverse relation are {2, 3, 5, 7, 8} for both.

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sin(t) = -sqrt(61) / 30, cos(t) = sqrt(61) / 15, and tan(t) = -5/3.

To find sin(t), cos(t), and tan(t) we need to use the coordinates of the terminal point p(x,y) determined by the real number t.
Given that the terminal point is (1/5, -2/6), we can find the values of sin(t), cos(t), and tan(t) using the following formulas:
sin(t) = y / r
cos(t) = x / r
tan(t) = y / x
where r is the distance from the origin to the point p(x,y), which can be calculated using the Pythagorean theorem:
r = sqrt(x^2 + y^2)
Plugging in the values for the coordinates of p(x,y), we get:
r = sqrt((1/5)^2 + (-2/6)^2) = sqrt(1/25 + 4/36) = sqrt(36/900 + 25/900) = sqrt(61/900)
sin(t) = (-2/6) / (sqrt(61/900)) = -sqrt(61) / 30
cos(t) = (1/5) / (sqrt(61/900)) = sqrt(61) / 15
tan(t) = (-2/6) / (1/5) = -5/3
Therefore, sin(t) = -sqrt(61) / 30, cos(t) = sqrt(61) / 15, and tan(t) = -5/3.

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Step-by-step explanation:

To find the X value corresponding to z = -0.25, we can use the formula:

z = (X - M) / s

where z is the standardized score, X is the raw score we want to find, M is the population mean, and s is the population standard deviation.

Rearranging this formula, we get:

X = z * s + M

Substituting the given values, we get:

X = -0.25 * 12 + 50

X = 47

Therefore, the X value corresponding to z = -0.25 is 47.

Hence, the answer is option B.

The X value corresponding to z = -0.25 is 47 (option b).

To answer this question, we need to use the formula for calculating z-scores, which is:
z = (X - M) / (s)
where z is the z-score, X is the raw score, M is the population mean, and s is the population standard deviation.
In this case, we are given the population mean (M = 50) and the z-score (z = -0.25). We also know that the population standard deviation (s) is 12.
We can rearrange the formula to solve for X:
X = z * s + M
Plugging in the values we have:
X = -0.25 * 12 + 50
X = 47
Therefore, the X value corresponding to z = -0.25 is 47. The answer is (b).
It's important to note that z-scores are a way of standardizing data so that we can compare different sets of data that may have different scales or units. In this case, we are using the z-score to find the corresponding raw score.

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Answer:

If \(p\) is people and \(h\) is hot dogs, the equation is \(3h=4p\).

The  relation among people who attend and hot dog sold is 4x = 3y.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

At the Football game they expect that for every 4 people that attend 3 hot dogs will be sold.

let the are total x people and y number of hot dogs will be sold.

So, the relation among people who attend and hot dog sold is

4x = 3y

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7x-5=6x+4

first take like terms,

7x-6x=4+5

from the above, when a term moves to the other side, the sign automatically changes. therefore, we +6x becomes -6x and -5 becomes +5

7x-6x=4+5

1x= 9

x= 9/1

x=9

answer is 9.

Answer:

Simplifying

9x + 7 = 5x + -3

Reorder the terms:

7 + 9x = 5x + -3

Reorder the terms:

7 + 9x = -3 + 5x

Solving

7 + 9x = -3 + 5x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5x' to each side of the equation.

7 + 9x + -5x = -3 + 5x + -5x

Combine like terms: 9x + -5x = 4x

7 + 4x = -3 + 5x + -5x

Combine like terms: 5x + -5x = 0

7 + 4x = -3 + 0

7 + 4x = -3

Add '-7' to each side of the equation.

7 + -7 + 4x = -3 + -7

Combine like terms: 7 + -7 = 0

0 + 4x = -3 + -7

4x = -3 + -7

Combine like terms: -3 + -7 = -10

4x = -10

Divide each side by '4'.

x = -2.5

Simplifying

x = -2.5

make me brainiest plz!!!

Step-by-step explanation:

Answer:

x=3

Step-by-step explanation:

-43 - 9x = -7 - 15x - 18

-43 - 9x = -15x - 25

15x -9x = 43 -25

6x = 18

x = 3

Answer:

Forma exacta:

x= −37/30

Forma decimal:

x=−1.23

Forma numérica mixta:

x=−17/30

The Fountain's theoretical breadth is 190 feet if the length is longer, or 60 feet if the length is shorter.

A perimeter is a closed path that covers, surrounds, or outlines a two-dimensional shape or length in one dimension. A circle's or an ellipse's circumference is its perimeter.

There are various applications for calculating the perimeter. A wheel's or circle's perimeter describes how far it may roll in one revolution. Similarly, the amount of string coiled around a spool is proportional to the perimeter of the spool; if the length of the string were precise, it would equal the perimeter.

Given, the perimeter of a rectangular fountain=500 feet

And an area is at least 11400 feet

Perimeter =2L+2W

Perimeter =2(L+W)

500=2(L+W)

Therefore L + W = 250

Area = L×W =11400

Where L= Length

W = Width

We have to find the multiples of 11400 which can sum up to 500

The answer is 190 feet and 60 feet

Now, by checking we get

190×60=11400

2(190+60)=2(250)=500

Therefore, The Fountain's theoretical breadth is 190 feet if the length is longer, or 60 feet if the length is shorter.

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Answer:

7 - 2m can be translated to "7 minus two times m" or "the difference between 7 and twice m".

3(m + 2) = 15 can be translated to "three times the sum of m and 2 is equal to 15" or "the product of 3 and the sum of m and 2 is 15".

To solve the equation, we can start by distributing the 3 on the left side:

3(m + 2) = 15

3m + 6 = 15

Then, we can subtract 6 from both sides:

3m + 6 - 6 = 15 - 6

3m = 9

Finally, we can divide both sides by 3:

3m/3 = 9/3

m = 3

Therefore, the solution to the equation 3(m + 2) = 15 is m = 3.

5m - m(2 - m) can be translated to "5m minus the product of m and the difference between 2 and m" or "the difference between 5m and m times the quantity 2 minus m".

To simplify the expression, we can use the distributive property to expand the second term:

5m - m(2 - m) = 5m - 2m + m^2 = m^2 + 3m

Therefore, the simplified expression is m^2 + 3m.

Answer:

John sold 8 funnel cakes in 1 hour

Step-by-step explanation:

Hope I helped

Answer:

An average of 8 funnel cakes an hour

Step-by-step explanation:

40/5=8 but we don't know if he sold the same amount every hour.

\({ \red{ \boxed{ \sf{ \sqrt{344} \: units}}}}\)

Step-by-step explanation:

Let, (9, 3) = (x1, y1) and (21, 23) = (x2, y2)

By using distance formula, we can find the answer. Let us use the formula and get answer fast.

\({ \sf{d = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } }}\)

Substitute all the values in this above formula.

\({ \sf{d = \sqrt{ {(21 - 9)}^{2} + {(23 - 3)}^{2} }}} \)

\({ \sf{d = \sqrt{ {(12)}^{2} + {(20)}^{2} }}} \)

\({ \sf{d = \sqrt{144 + 200}}} \)

\({ \sf{d = \sqrt{344} \: units}} \)

Answer:

D

Step-by-step explanation:

D

Answer:

3.14

Step-by-step explanation:

Answer:

7g + 3n - 2

Step-by-step explanation:

(7g - 6) - (-3n - 4)

7g - 6 + 3n + 4

7g + 3n - 2

I hope this helps!

The Taylor polynomials P1, P2, P3, and P4 centered at a0 for f(x) are given as:P1(x) = 1P2(x) = 1 - x²/2!P3(x) = 1 - x²/2! + x⁴/4!P4(x) = 1 - x²/2! + x⁴/4! - x⁶/6!

We will apply the Taylor's theorem formula, which is supplied as follows, to determine the Taylor polynomials P1, P2, P3, and P4 centred at a0 for f(x) in the given question:f'(a)(x-a)/1 = f(x) = f(a) + f'(a)! + f''(a)(x-a)²/2! + ... + fⁿ(a)(x-a)ⁿ/n!We have f(0) = 1f'(0) = 0f''(0) = -1f'''(0) = 0f4(0) = 1 for f(x) = cos(x) at x = 0.We can get the following polynomial expressions by using these values in the Taylor's theorem formula:P1(x) = 1P2(x) = 1 - x²/2!P3(x) = 1 - x²/2! + x⁴/4!P4(x) = 1 - x²/2! + x⁴/4! - x⁶/6!Consequently, the Taylor polynomials P1, P2, P3, and P4 for f(x) are provided as follows:P1(x) = 1P2(x) = 1 - x²/2!P3(x) = 1 - x²/2! + x⁴/4!P4(x) = 1 - x²/2! + x⁴/4! - x⁶/6!

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The probability to obtain the sum of two rolled dice as a multiple of 6 or a multiple of 4 is 13/36.

When comparing the likelihood of an outcome to all other possible outcomes, we use a sort of ratio known as probability.

Given that a dice is rolled twice. Sum of the two rolls has following possibilities,

2,3,4,5,6,7,8,9,10,11,12

A multiple of 6 is obtained when the sum is either 6 or 12.

Sum of 6 is obtained when the two rolls are (1,5) , (2,4) , (3,3), (4,2) , (5,1)

Probability for each is 1/36. Therefore total probability to obtain sum of 6 is 5/36.

Sum of 12 is obtained only when the two rolls (6,6).

Probability to obtain sum of 12 is therefore 1/36.

Similarly for a sum of 4, the probability is 3/36.

For a sum of 8, the probability is 4/36.

Therefore the required probability is the sum of above calculated probabilities,

Required probability = 5/36 + 1/36 + 3/36 + 4/36 = 13/36

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She has 4 babies, which is the required solution to the given problem.

Mother Rabbit woke up one morning and looked for her babies to see if they were all safe. Since her burrow was so cramped, she could only count their ears and legs. There were ten more legs than ears.

Let's use algebra to solve this. Let's assume that she had x babies. Since each bunny has 4 legs and 2 ears, the equation is:

4x + 2x = 20

Simplify the equation.

6x = 20

Divide each side by 6.

x = 20/6

Round up to the nearest whole number, because she can't have a fraction of a bunny.

x = 4

Therefore, Mother Rabbit has four babies.

Therefore, she has 4 babies, which is the required solution to the given problem.

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The set of integers that are divisible by 7 or divisible by 10 can be determined to be countably infinite.

To exhibit a one-to-one correspondence between this set and the set of positive integers, we can list them as follows:

-7
7
-14
14
-21
. 21
-28
...
Thus, we can see that for every positive integer n, we have a corresponding element in the set of integers that are divisible by 7 or divisible by 10.

The set of integers less than 100 is finite since there are a limited number of integers between negative infinity and 100. We can count them one by one: -99, -98, -97, ..., 99. In this case, we have a finite number of elements in the set.

The set of real numbers between 1 and 2 is uncountable. This is because there are an infinite number of real numbers between any two distinct real numbers, and the set of real numbers is uncountable. We cannot establish a one-to-one correspondence between this set and the set of positive integers.

The set of prime numbers is countably infinite. To exhibit a one-to-one correspondence between this set and the set of positive integers, we can list them as follows:
2
3
5
7
11
13
17
...
Thus, for every positive integer n, we have a corresponding prime number in the set.

The set of integers that are divisible by 3 but not by 6 is countably infinite. To exhibit a one-to-one correspondence between this set and the set of positive integers, we can list them as follows:
3
-3
9
-9
15
-15
21

Thus, for every positive integer n, we have a corresponding element in the set of integers that are divisible by 3 but not by 6.

The sets can be classified as follows:
A. Countably infinite.
B. Finite.
C. Uncountable.
D. Countably infinite.
E. Countably infinite.

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The length of the  Boca Grand Causeway is  126,000 feet

Multiplication is the continual addition of two or more numbers of equal sizes. The value gotten after multiplication is the product. Multiplication is one of the basic mathematical operations. The sign used to denote multiplication is x. Other basic mathematical operations include addition, subtraction and division.

Length of the Boca Grand Causeway = length of the golden gate bridge x 14

9,000 x 14 = 126,000 feet

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Answer:

exterior angle

Step-by-step explanation:

Answer:

42.6cm

Step-by-step explanation:

The sum total of all the sides of the shape is the perimeter of the shape. Hence;

Perimeter = x+3 + 4 + x+9 + 2x+5

Perimeter = 4x + 21

Given

Area of the figure = 75cm^2

Area = (x+3)(2x+5) + (2x+1)(6)

75 = 2x²+5x+6x+15+12x+6

75 =  2x²+23x+21

2x²+23x+21-75 = 0

2x²+23x-54 = 0

x = -23±√23²-4(2)(-75)/4

x = -23±√529+600/4

x = -12±√1129/4

x = -12+33.6/4

x = 21.6/4

x = 5.4

Recall that;

Perimeter = 4x+21

Perimeter = 4(5.4) + 21

Perimeter = 21.6+21

Perimeter = 42.6cm

Hence the perimeter is 42.6cm