At a sale, coats were sold for $66 each. If the coats originally cost $120 each,
what percentage of its original price was a coat sold for?

The total amount fundraised after 7 days is 5200 dollars.

The relationship between the number of days a high school sports team spends fundraising per year and the number of dollars is received in donations during that year can be modelled by the equation.

y = 600x + 1000

Where

Hence, let's find the amount fundraised for 7 days.

y = 600x + 1000

y = 600(7) + 1000

y = 4200 + 1000

y = 5200

Therefore,

amount fundraised after 7 days = 5200 dollars

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95% confidence interval for the mean weight of all bags of potatoes is: (20.402, 21.548).

Here, we have,

from the given information we get,

x = 20.975

s = 0.36

DF = 4 - 1 = 3

With 3 df and 95% confidence interval the critical value is

t0.025, 3 = 3.182

The 95% confidence interval is

x +/- t0.025, 3 * s/√(n)

= 20.975 +/- 3.182 * 0.36/√(4)

= 20.975 +/- 0.573

= 20.402, 21.548

Hence, 95% confidence interval for the mean weight of all bags of potatoes is: (20.402, 21.548).

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The minimum amount of money Brad needs in total to distribute his $5 bills into the boxes is $105.

To determine the minimum amount of money Brad needs to distribute his $5 bills into the 6 boxes without any two boxes having the same amount, we can start by analyzing the pattern.

Since each box must have a unique amount, we can distribute the bills in ascending order, starting with one bill in the first box, two bills in the second box, three bills in the third box, and so on. The last box will have six bills.

Adding up the total number of bills in each box, we get 1 + 2 + 3 + 4 + 5 + 6 = 21 bills. Therefore, Brad needs a minimum of $5 x 21 = $105 in total.

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The equation 36.50x + 15.25 = 416.75 can be simplified to solve for x, representing the number of people who can go to the amusement park. By isolating the variable, we find that x is approximately 11, meaning that 11 people can go to the amusement park with the given budget.

The term x(36.50) represents the total cost of admission tickets for x number of people, and 15.25 represents the cost of parking. The sum of these costs must be equal to the total amount of money available, which is $416.75. To solve for x, we can first simplify the equation to 36.50x + 15.25 = 416.75, and then isolate the variable by subtracting 15.25 from both sides, giving 36.50x = 401.50. Finally, we can divide both sides by 36.50 to find that x is approximately 11, meaning that 11 people can go to the amusement park with the given budget.

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The simple linear regression model y = β0 + β1x + ε implies that if x goes up by one unit, we expect y to change by β1, irrespective of the value of x.

The simple linear regression model y = β0 + β1x + ? implies that if x goes up by one unit, we expect y to change by β1, irrespective of the value of x because the model represents a straight line. However, if x goes down by one unit or curves by one unit, the change in y may not necessarily be equal to β1. The simple linear regression model y = β0 + β1x + ε implies that if x goes up by one unit, we expect y to change by β1, irrespective of the value of x.

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An F statistic is “A ratio of two variances”

A test for comparing “variances” or “standard deviations” from two populations is done by F-test statistic.

The "F-statistic" is calculated using the formula,

F-statistic= \(S1^2/S2^2,\)

where the ‘degrees of freedom’ for the denominator are df2 = n2 - 1 and the ‘degrees of freedom’ for the numerator are df1 = n1 - 1.

Therefore, the ‘F-statistic’ is the ratio of two variances.

The F-statistic cannot be “difference between three means”, “A ratio of two means”, and “A population parameter

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\(\huge\text{Hey there!}\)

\(\large\boxed{\mathsf{\dfrac{1}{2}a = 7}}\\\\\large\text{MULTIPLY 2 to BOTH SIDES}\\\\\large\boxed{\mathsf{2\times\dfrac{1}{2}a= 2\times7}}\\\\\large\text{CANCEL out: }\rm{2\times\dfrac{1}{2}}\large\text{ because it gives you 1.}\\\large\text{KEEP: }\rm{2\times7}\large\text{ because it helps you get your a-value}\\\\\large\boxed{\mathsf{a = 2\times7}}\\\\\\\large\text{SIMPLIFY IT!}\\\\\large\boxed{\mathsf{a = 14}}\\\\\\\huge\boxed{\text{Therefore, your answer is: \boxed{\mathsf{a = 14}}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

The probability of selecting an orange marble is 0.33.

Option B is the correct answer.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The number of times each marble is selected.

Green = 4

Black = 6

Orange = 5

Total number of times all marbles are selected.

= 4 + 6 + 5

= 15

Now,

The probability of selecting an orange marble.

= 5/15

= 1/3

= 0.33

Thus,

The probability of selecting an orange marble is 0.33.

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Answer:

The total area is 11x

Step-by-step explanation:

So if you split the model then the left side would be A=2x*3x which would be 6x because the 1 doesn't apply because we don't know what x is, so the area of the left side is 6x. Then the right side would be A=5*x which would just be 5x because again, we don't know the value of x, so the area of the left side is also 5x. Put the two together and BOOM- 11x!

Answer: |t - 15| ≤ 30 ; -30 ≤ t - 15 ≤ 30

Step-by-step explanation:

To set up the equation, we have to find the center, and the tolerance, so that we can use formula "|x - c| ≤ t"

First, we can find the tolerance by adding both number, then dividing by 2 --> -15 + 45 = 30 --> 30/2 = 15, so we now know that the center is 15

Next, we can find the tolerance by finding the distance between the center and one of the number --> 15 - (-15) = 30, so we now know that the tolerance is 30

Now we can set up our equation,

center (c) = 15

tolerance (t) = 30

|t - 15| ≤ 30

Now that we have our equation, we can set up the inequality

|x - c| ≤ t = -t ≤ x - c ≤ t

so,

-30 ≤ t - 15 ≤ 30

Hope this helps!

(sorry it was so long)

The transformation of System A into System B is:

Equation [A2]+ Equation [A 1] → Equation [B 1]"

The correct answer choice is option D

How can we transform System A into System B?

To transform System A into System B as 1 × Equation [A2] + Equation [A1]→ Equation [B1] and 1 × Equation [A2] → Equation [B2].

System A:

-3x + 4y = -23 [A1]

7x - 2y = -5 [A2]

Multiply equation [A2] by 2

14x - 4y = -10

Add the equation to equation [A1]

14x - 4y = -10

-3x + 4y = -23 [A1]

11x = -33 [B1]

Multiply equation [A2] by 1

7x - 2y = -5 ....[B2]

So therefore, it can be deduced from the step-by-step explanation above that System A is ultimately transformed into System B as 1 × Equation [A2] + Equation [A1]→ Equation [B1] and 1 × Equation [A2] → Equation [B2].

The complete image is attached.

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The calculations for the slope-intercept forms of the equations are (1) m=-\(\frac{3}{4}\),B=2  (2)m=1, B=5  (3) m=-1, B=6

How to use the Slope -intercept form?

Slope of a line is a number that describes both the direction and the steepness of the line.

The intercept of a line is defined as the point at which it intersects the y-axis in a graph.

The equation of a line is expressed as follows;

Y=MX+B

Where M=slope and B=intercept

From the equations:

(1) y<\(\frac{-3x}{4}\)+2

Applying the equation of slope-intercept form,

m=\(\frac{-3}{4} , B=2\)

(2) Y\(\leq 5\)

Applying the equation: Y=MX+B

m=1,  B=5

(3) x+y>6

Applying the formula: Y=MX+B

Re-arrange the equation

y>-x+6(1)

⇒ m=-1, B=6

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Sample is a subset of the population used to estimate data about the population without including everyone. It is used in statistics to draw inferences about larger populations or groups and statistical research methods are used to achieve better sample results.

In the given scenario, the population in the study would be Bottles of soda produced in the plant on February 2. While the sample in the study would be The 70 bottles of soda selected in the plant on February 2A population is the complete group of people or things that we are studying. Population is the set of all things under examination, while the sample is a subset of the population, which is used to estimate data about the population.What is Sample?A sample is a subset of the population, and it is a way to investigate the entire population without including everyone. It is used to acquire an estimation of the population, but it is not intended to be an exact representation of the population. Sample data is used in statistics to draw inferences about larger populations or groups. To achieve better sample results, statistical research methods are used.

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Answer:

$2

Step-by-step explanation:

Step-by-step explanation:

Given, John had $30

after riding 5 rides, He had $20

( Let's subtract the balance and the balance he had after ride )

$(30 - 20)

$10

Therefore, Each ride costs = $10 ÷ 5

(dividing 10 and 5, we get 2)= $2

Hence, It took $2 for a ride.

Hope it helps. If it helps don't forget to like and mark me.

The value of x of the triangle is given by the trigonometric relation x = 30°

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the triangle be represented as ΔPQR

Now , the measure of side PQ = 48 cm

The measure of side PQ = 96 cm

The measure of ∠x is calculated by

From the trigonometric relations ,

sin x = opposite side / hypotenuse

On simplifying , we get

sin x = 48 / 96

sin x = 1/2

Taking inverse on both sides , we get

x = sin ⁻¹ ( 1/2 )

x = π/6

x = 30°

Therefore , the value of x is 30°

Hence , the angle of the triangle is 30°

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Explanation:

Plane symmetry only applies to objects in 3D space. So choice A won't apply.

Point symmetry is where we can rotate the object some number of degrees (between 0 and 360 excluding the endpoints) and have it line up with itself. We can't do such a rotation, so this figure has no point symmetry. We rule out choice B.

Choice C works since we can reflect the upper half of the letter over the horizontal midline to have its reflection line up with the lower half, and vice versa. There is only one line of symmetry here.

Choice D is not true since choice C was shown to be true.

Answer: Is c-line

Step-by-step explanation:

The guy above me got it right I just did the quiz

Answer:

The answer is

Converting this into a geometry problem requires us to name the points. Let give the home plate a symbol A, first base will be B, second base will be C, and the third base will be D. Now, we can present a geometrical proof:

STATEMENTS | REASONS

(1) BC = CD | Given

m(2) AC = AC | Reflexive Property

(3) triangle ACD = triangle ACB | SAS Congruence

(4) AD = AB | CPCTC

when  CPCTC means Congruent Parts of Congruent Triangles are Congruent.

Therefore, the distance from first base to home plate, and from home plate to third plate are equal.

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149

4.0

(91 votes)

Answer

3.0/5

Step-by-step explanation:

Answer:

The answer is

Converting this into a geometry problem requires us to name the points. Let give the home plate a symbol A, first base will be B, second base will be C, and the third base will be D. Now, we can present a geometrical proof:

STATEMENTS | REASONS

(1) BC = CD | Given

m(2) AC = AC | Reflexive Property

(3) triangle ACD = triangle ACB | SAS Congruence

(4) AD = AB | CPCTC

when  CPCTC means Congruent Parts of Congruent Triangles are Congruent.

Therefore, the distance from first base to home plate, and from home plate to third plate are equal.Step-by-step explanation:

Answer:

equal to rolling an odd number

Step-by-step explanation:

fair number cube is your average 6 side die

even numbers = 2,4,6

odd numbers = 1,3,5

total sides=6

even number probability = 3/6

odd number probability = 3/6

Answer:

the awnser is:30° yup it is

Answer:

30°

Step-by-step explanation:

We Know

(4x - 2) + (20x - 10) = 180°

4x - 2 + 20x - 10 = 180

24x - 12 = 180

24x = 192

x = 8

Find m∠EBD

∠ABC is a vertical angle to ∠EBD, meaning they will equal it.

4(8) - 2

32 - 2

30°

So, m∠EBD is 30°

The area of the triangle in front of the triangular prism is xy/2.

The triangular prism is a three-dimensional shape with three rectangular and two triangular faces. The triangular faces are parallel to one another and the rectangular faces are perpendicular to the triangular edges.

The area of a shape is determined by the measurement of the surface of the shape.

The area of a triangle is base multiplied by the height of a triangle divided by 2.

We have to find the area of the front triangle which means the area of the one triangle.

Assume that the base of the triangle is x and the height of the triangle is y

So,

Area of triangle= ½ base×height

                          =  ½ x × y

                          = xy/2

Therefore the area of a triangle  is xy/2

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The Cauchy-Schwarz inequality have shown that ΔxΔP ≥ ℏ/2, confirming the uncertainty principle.

To show that the uncertainty principle holds, we need to demonstrate that \(\Delta x \Delta p > h/2\), where \(\Delta x\) and \(\Delta p\) are the uncertainties in position and momentum, respectively, and ℏ is the reduced Planck constant.

Let's start with the uncertainty in position, \(\Delta x\). It is defined as the square root of the expectation value of x squared, \(\delta x^2\), minus the square of the expectation value of x. Mathematically, this can be written as \(\Delta x^2 = \delta x^2 - x^2\)

Similarly, the uncertainty in momentum,\(\Delta p\), is given as \(\Delta p^2 = p_x_^_2 - p_x^2\)

Now, we want to prove that ΔxΔP ≥ ℏ/2.

Substituting the expressions we have \((\delta x^2- x^2) (p_x - p_x^2 )\)

Expanding the left side of the inequality, we get \(\delta x^2 p_x^2 - \delta x^2 p_x - x^2 p_x^2 + x^2p_x^2 \geq h^2/4 + x^2p_x^2- \delta x^2p_x^2\)

Recognizing that the term in parentheses is equal to \(\Delta p^2\), we have \(\delta x^2 p_x^2 - \delta x^2 p_x - x^2 p_x^2 + x^2p_x^2 \geq h^2/4 + x^2p_x^2\)

Applying the Cauchy-Schwarz inequality, we know that \(x^2 \Delta p^2\geq x^2(h/2)^2\), which can be written as ⟨x⟩(ΔP)^2 ≥ ℏ^2/4.\(x \Delta p^2 \geq h^2/4\)

The left side of the inequality is now greater than or equal to \(h^2/4+h^2/4 = h^2/2\)

Therefore, we have shown that ΔxΔP ≥ ℏ/2, confirming the uncertainty principle.

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To evaluate a function with a specific value in the domain you susbtitute in the equation of the function the independient variable (x) for the value in domain.

For x = -1 (a number n powered to a negative number (m) n^-m is equal to 1/n^m

For x=0 (any number powered to 0 is equal to 1)

For x = 1

For x = 2

Answer:

all the  fractions that are equivalent to 2/5 are 4/10, 6/15, 8/20

Step-by-step explanation:

this is all I can rember

Answer:

It is C

Step-by-step explanation:

It cannot be d bc - 7-4=-11 so rejected

Not b bc the first number is - 7

The same w a

See the attached image.

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

Explanation:

The original data set is

162,160,167,170,167,170,160,167,162,165,162,159,161,162,161,170,167,159,159,170,161,159,159,165,165,160,159,170,162,159,167,162

This sorts to

159, 159, 159, 159, 159, 159, 159, 160, 160, 160, 161, 161, 161, 162, 162, 162, 162, 162, 162, 165, 165, 165, 167, 167, 167, 167, 167, 170, 170, 170, 170, 170

Use computer software to make the sorting really fast/easy.

Also, it's beneficial to use spreadsheet software to create the grouped frequency table and histogram. I used LibreOffice Calc spreadsheet which is a free program. There are other free options to pick from as well.

The class interval 159-161 means we are focused on the interval \(159 \le x < 161\). So we include 159 but exclude 161.

The values in this class interval are: {159,159,159,159,159,159,159,160,160,160}

There are 10 items in that subset shown above. Don't toss out any duplicates.

Since there are 10 heights on the interval \(159 \le x < 161\), this means we write "10" as the first frequency in the table.

The other frequencies are handled the same way. The completed table and histogram are shown below. Note the height of each histogram bar is the frequency value for that class (eg: a frequency of 10 means the bar's height is 10 units tall).

Also note that there are no gaps between the bars. The "gap" shown in the diagram below is because of the frequency 0 for the class interval 163-165. If that frequency was something positive, then we wouldn't have any gaps at all. This is to contrast a bar chart where there are gaps.

Price of Jeans = $17

Price of 2 pair = 17 + 17 = $34

There is a 10% discount. Let's find the discount on them and subtract it from the total sale price.

10% means 10/100 = 0.1

Thus, 10% of $34 is:

0.1 * 34 = $3.40

We subtract it:

$34 - $3.40 = $30.60

The 90% confidence interval for the difference in the population means is -2.51 to 0.31

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

xˉ₁ = −17.1

s₁² = 8.4

n₁ = 22

​xˉ₂ = −16.0

s₂² = 8.7

n₂ = 24

Calculate the pooled variance using

P = (df₁ * s₁² + df₂ * s₂²)/df

Where

df₁ = 22 - 1 = 21

df₂ = 24 - 1 = 23

df = 22 + 24 - 2 = 44

So, we have

P = (21 * 8.4 + 23 * 8.7)/44

P = 8.56

Also, we have the standard error to be

SE = √(P/n₁ + P/n₂)

So, we have

SE = √(8.56/22 + 8.56/24)

SE = 0.86

The z score at 90% CI is 1.645, and the CI is calculated as

CI =  (x₁ - x₂) ± z * SE

So, we have

CI = (-17.1 + 16.0) ± 1.645 * 0.86

This gives

CI = -1.1 ± 1.41

Expand and evaluate

CI = (-2.51, 0.31)

Hence, the confidence interval is -2.51 to 0.31

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a.) The limit of  limx→0 ln(1 + x)/x = 1

b.) The limit of limx→[infinity] x^5 + 5x + 10/x^10 + 10e + 5 = 0

c.) The limit of limx→0+ x ln x does not exist

(a) We can use L'Hôpital's rule to evaluate this limit:

lim x→0 ln(1 + x)/x = lim x→0 (1/(1 + x))/1

= 1/1 = 1

Therefore, the limit exists and is equal to 1.

(b) To evaluate this limit, we can use the fact that as x goes to infinity, x^5 + 5x + 10 grows much faster than x^10 + 10e + 5. Therefore, we can approximate the limit as:

\(lim x→[infinity] x^5 + 5x + 10/x^10 + 10e + 5 \\\≈ lim x→[infinity] x^5 / x^10 \\= lim x→[infinity] 1/x^5 = 0\)

Therefore, the limit exists and is equal to 0.

(c) This limit does not exist. To see why, note that as x approaches 0 from the positive side, ln x approaches negative infinity. Therefore, the limit from the positive side does not exist.

Similarly, as x approaches 0 from the negative side, ln x approaches negative infinity as well, so the limit from the negative side also does not exist.

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