a car is to be placed on a metal incline for display. if only friction is to be used to keep the car at rest on the incline, what is the maximum angle theta of the incline if, for the car on the incline, the coefficient of static friction is 0.8 and the coefficient of kinetic friction is 0.6?

We can write the coordinates after reflection as -

A (x₁, y₁) → A" (x₁, - y₁)

B (x₂, y₂) → B" (x₂, - y₂)

C (x₃, y₃) → C" (x₃, - y₃)

Given is that to describe a sequence of transformation that maps triangle ΔABC onto triangle ΔA”B”C” a student starts with a reflection over x - axis.

Assume the coordinates of a triangle are -

A (x₁, y₁)

B (x₂, y₂)

C (x₃, y₃)

So after the reflection over the {x} axis, we can write the coordinates as -

A" (x₁, - y₁)

B" (x₂, - y₂)

C" (x₃, - y₃)

Therefore, we can write the coordinates after reflection as -

A (x₁, y₁) → A" (x₁, - y₁)

B (x₂, y₂) → B" (x₂, - y₂)

C (x₃, y₃) → C" (x₃, - y₃)

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To achieve a margin of error of about 2% at a 95% confidence level, the recommended sample size would depend on several factors, including the population size and the desired level of confidence.

Determining the sample size requires considering the formula for sample size calculation, which takes into account the population size, desired margin of error, and desired level of confidence. However, without specific information on the population size, it is not possible to provide an exact sample size recommendation.

In general, a larger sample size tends to decrease the margin of error and increase the precision of the estimate. However, it is important to strike a balance between the desired margin of error and practical considerations, such as time and cost constraints.

To estimate an appropriate sample size, statistical software or online calculators can be used, which consider the desired margin of error, confidence level, and other relevant factors. These tools can provide an approximate sample size recommendation based on standard statistical formulas.

In conclusion, to achieve a margin of error of about 2% at a 95% confidence level, it is recommended to calculate the sample size using appropriate statistical methods considering the population size and other relevant factors.

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Answer:

Justin did not eat 7/12 of the pizza

Step-by-step explanation:

Marc eats 1/6 × 24 = 4, 24 - 4 = 20 left over

Claudine eats 1/4 × 20= 5, 20 - 5 = 15 left over

Sylvia eats 1/3 × 15 = 5, 15 - 5 = 10 left over

Justin eats 10.

24 - 10 = 14

Justin did not eat 14/24 = 7/12

Answer:

C

Step-by-step explanation:

Hopefully

C

I did it on edge hopefully this helps you and don't think i copied the other person

The equation in the slope-intercept form is:

y = (1/2)*x + 3

A general linear equation is:

y = a*x + b

Where a is the slope and b is the y-intercept.

To get the slope, we need two points on the line, by using the graph we can identify the points: (0, 3) and (2,4)

Then the slope is:

\(a = \frac{4 - 3}{2 - 0} = 1/2\)

And we also can see that the y-intercept is y = 3, because of the point (0,3)

Then the line is:

y = (1/2)*x + 3

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F = quantity of five dollar bills

S = quantity of single dollar bills

so she deposited 62 bills, that means that whatever F and S are, we know that F + S = 62.

we also know that all those amount to $218, so the fives are really 5*F or 5F from those $218, and the singles are just 1*S of the same $218, so we can also say that 5F + S = 218.

\(F+S=62\implies F=62-S \\\\\\ 5F+S=218\implies \stackrel{\textit{substituting from above}}{5(62-S) +S=218}\implies 310-5S+S=218 \\\\\\ 310-4S=218\implies 310=4S+218\implies 92=4S\implies \cfrac{92}{4}=S\implies 23=S\)

(a). The above context-free grammar (CFG) generates the language that has at least five "a's" and any combination of "b's".

(b). The above CFG generates the language {a¹b³c¹|i, j, k ≥ 0 and i =jor i = k}.

(c).  it is ambiguous.

(a). Context-free grammar for L₁ = {w = {a, b}*w contains at least five as}:

S → aaaaaA | aaaaS | bS | aA | bA | ε

A → aA | bAb → bB | ε

B → bB | aB | ε

The above CFG generates the language that has at least five "a's" and any combination of "b's".

(b). Context-free grammar for L₂ = {a¹b³c¹|i, j, k ≥ 0 and i =jor i = k}:

S → AbC | AcB | BCa | CBa

A → aA | ε

B → bBb

B → bBbBbBb

C → cC | ε

C → cC | ε

The above CFG generates the language {a¹b³c¹|i, j, k ≥ 0 and i =jor i = k}.

(c). Yes, the language for b) is inherently ambiguous. It is because there are two variables A and B in the grammar, so the string can be generated in two ways. Thus, it is ambiguous.

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The y intercept is 0 and rate of change is 0.25 of the given function.

The function tells the relation between a collection of inputs, each having an output.

Given that, the late fees for a school library are represented by the function c = 0.25d, where c is the total cost and d is the number of days a book is late.

The slope intercept form of an equation is given by,

y = mx + c

Where, m is the slope and c is the constant,

The given equation is,

c = 0.25d

On comparison with slope intercept form, we get,

m = 0.25,

c = 0

We know that, the rate of change is given by the slope of the line and y intercept is given the constant.

Hence, rate of change is 0.25 and y intercept is 0

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Uncle Makhosi needs approximately 1.56 kilograms of butter.

To determine the amount of butter in kilograms, we'll use the conversion rate of 1 kg = 2.25 pounds.

First, we need to convert 3 and a half pounds to a decimal form. Since half a pound is equal to 0.5 pounds, we can express 3 and a half pounds as 3.5 pounds.

Next, we'll use the conversion rate to calculate the equivalent weight of 3.5 pounds in kilograms:

3.5 pounds * (1 kg / 2.25 pounds) = 1.56 kilograms (rounded to two decimal places).

To summarize, based on the given conversion rate of 1 kg = 2.25 pounds, Uncle Makhosi requires approximately 1.56 kilograms of butter to fulfill his 3 and a half pound requirement. This conversion can be useful when dealing with different units of measurement, allowing us to easily switch between kilograms and pounds.

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Answer:

1.4

Step-by-step explanation:

We need to convert 103/7497 into a percentage.

All we have to do is multiply the fraction by 100:

103/7497 * 100 = 1.37

To one decimal place, the equivalent fraction is 1.4

Answer: 15-4x

Step-by-step explanation: 15 is being subtracted by 4 multiplied by x (4x).

Answer:

see below

Step-by-step explanation:

Complements add to 90 degrees

x+40 = 90

x = 90-40

x = 50

Supplements add to 180

y+63 =180

y = 180-63

y = 117

If the sum of the measures of two angles is 90° they are known as complementary angles.

According to the question

⇨x + 40° = 90°

⇨x = 90° - 40° [Subtract]

⇨x = 50°

Complement angle is 50°

If the sum of the measures of two angles is 180° they are known as supplementary angles.

According to the question

⇛x + 63° = 180°

⇛x = 180° - 63° [Subtract]

⇛x = 117°

Supplement angle is 117°

If the sum of the measures of two angles is 90° they are known as complementary angles.

According to the question

⇛x + 40° = 90°

⇛x = 90° - 40° [Subtract]

⇛x = 50°

Complement angle is 50°

If the sum of the measures of two angles is 180° they are known as supplementary angles.

According to the question

⇨x + 63° = 180°

⇨x = 180° - 63° [Subtract]

⇨x = 117°

Supplement angle is 117°

Answer:

see explanation

Step-by-step explanation:

cos C = \(\frac{adjacent}{hypotenuse}\) = \(\frac{BC}{AC}\) = \(\frac{24}{51}\) = \(\frac{8}{17}\)

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

tan Z = \(\frac{opposite}{adjacent}\) = \(\frac{XY}{ZY}\) = \(\frac{15}{20}\) = \(\frac{3}{4}\)

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

sin C = \(\frac{opposite}{hypotenuse}\) = \(\frac{AB}{AC}\) = \(\frac{60}{65}\) = \(\frac{12}{13}\)

Answer:

cube

Step-by-step explanation:

prisms are 3d figures just like cubes are

the other options are just 2d figures

\(\huge\tt\pink{Answer}\)

C. Cube or Cuboid

A cuboid is a solid that has six rectangular faces--think of a typical box. All faces are either parallel or perpendicular to each other. Further, a cuboid is a right rectangular prism. A cuboid with six square faces is a cube, whereas a cuboid with at least two square faces is known as a square cuboid.

The number of ways prizes can be distributed is 30240. The probability of getting a all four green balls is 0.0038

a. Seven prizes are distributed to a group of 9 people. So the total number of combinations will be

ₙCr = n!/ r!(n-r)!

₉C₇ =9!/ 7! (9-7)1 = 36

Total permutations between the chosen 7. Each will get either first, second, third or fourth. So the total permutation can be

nPr = n!/(n-r)!

₇P₄ = 7!/(7-4)! = 840

So the total ways the prize can be distributed = 36× 840 = 30240

b. Number of white balls = 5

Number of red balls = 10

Number of green balls = 6

Total number of balls = 5+10+6 =19

The combination of choosing 4 balls from 19 = ₁₉C₄ = 3876

The combination for all four balls to be green = ₆C₄ = 15.

Probability = number of likely events/ Total number of events = 15/3876 = 0.0038

So the answer for question a is 30240 and for b is 0.0038.

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We need to find the Least Common Multiple between 4x² - 9 and 4x² + 12x +9.

First, we need to factorize each expression:

4x² - 9 can be factorized using the difference of squares given by:

Then:

Now, for 4x² + 12x +9

Can be factorized using:

Then:

Now, we need to find the LCM between (2x+3)(2x-3) and (2x+3)².

Then, the LCM is (2x+3)²(2x-3).

The correct answer is the third option.

Statistical power is a measure of the ability to reject the null hypothesis when it is false. It represents the probability of correctly identifying a true effect or relationship in a statistical hypothesis test.

A high statistical power indicates a greater likelihood of detecting a significant result if the null hypothesis is indeed incorrect. The power of a statistical test depends on several factors, including the sample size, the effect size (the magnitude of the true effect or difference), the chosen significance level (often denoted as α), and the variability or noise in the data. Increasing the sample size or effect size generally increases the statistical power, while a lower significance level or higher variability decreases it.

Power analysis is commonly used to determine an appropriate sample size for a study, ensuring that it is adequately powered to detect the desired effect. A higher power is desirable as it reduces the chances of a Type II error (failing to reject the null hypothesis when it is false) and increases the chances of correctly detecting real effects or relationships.

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The total amount of balls there are is : 8 + 2 + 1 + 3 + 5 = 19 (balls)

There are 5 footballs in the bag, so the probability of you selecting a football is 5 : 19 = 5/19

Given:

sample size = 73

mean = 29.4

standard deviation = 21.3

To find:

98% confidence interval for the sample size and mean

To get the confidence interval, we'll apply the formula:

a. To complete the recursive formula for the number of cars sold, we need to determine the growth pattern between weeks.

Since the number of cars is growing linearly, we can calculate the difference between consecutive weeks and use that as the increment for each subsequent week.

In this case, the difference between week 1 and week 0 is P1 - P0 = 9 - 4 = 5.

Therefore, the recursive formula for the number of cars sold, P, n weeks later is:

P = P(n-1) + 5

b. To find the number of cars that will be sold 7 weeks later (n = 7), we can use the recursive formula and iterate it until we reach the desired week.

Let's start with the given information: P0 = 4 and P1 = 9.

Using the recursive formula, we can calculate:

P2 = P1 + 5 = 9 + 5 = 14

P3 = P2 + 5 = 14 + 5 = 19

P4 = P3 + 5 = 19 + 5 = 24

P5 = P4 + 5 = 24 + 5 = 29

P6 = P5 + 5 = 29 + 5 = 34

P7 = P6 + 5 = 34 + 5 = 39

Therefore, if the trend continues, 39 cars will be sold 7 weeks later (n = 7).

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Answer:

It's in Quadrant IV.

..............

Answer:

It should be C

Step-by-step explanation:

Substituting in a value of x,

4 * ( 1/2 )^x               4 * ( 1/2 )^x

= 4 * ( 1/2 )^ 2         = 4 * ( 1/2 )^ -2

= 4 * 1/4                  = 4 * 4

= 1                           = 16

C checks out, and all the other options don't equal to the values on the table.

Answer:

s /2 pi r  - r = h

Step-by-step explanation:

s = 2 pi r ( r+h)

Divide each side by 2 pi r

s /2 pi r = 2 pi r ( r+h) / 2 pi r

s /2 pi r =  ( r+h)

Subtract r from each side

s /2 pi r  - r = ( r+h)  -r

s /2 pi r  - r = h

Answer:

\( h = \frac{s}{2\pi \: r} - r \\ \)

Step-by-step explanation:

\(s = 2\pi \: r(r + h) \\ \frac{s}{2\pi \: r} = \frac{2\pi \: r(r + h)}{2\pi \: r} \\ \frac{s}{2\pi \: r} = r + h \\ \frac{s}{2\pi \: r} - r = h\)

hope this helps

brainliest appreciated

good luck! have a nice day!

Step-by-step explanation:

11/5−7/4+2/1

=49/20(Decimal: 2.45)

The value of the determinant of matrix(2A^2B^T) - 1 cannot be determined with the given information. None of the options can be concluded.

The determinant of a matrix is not directly related to the determinant of its transpose. Therefore, we cannot determine the value of det(2A^2B^T) - 1 without additional information about matrices A and B.

Given that det(A) = 1, we know the determinant of matrix A. However, the determinant of matrix B being singular does not provide enough information about the individual elements or properties of B to determine the value of det(2A^2B^T) - 1.

Therefore, based on the given information, we cannot conclude any of the options provided: None of the mentioned (a) would be the correct answer. To determine the value of det(2A^2B^T) - 1, we would need additional information about the matrices A and B, such as their specific values or properties.

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Question:

What is the measure of an interior angle of a 21-gon?

Concept:

Define a 21-gon

A 21-gon is a 21 sided polygon also know as An icosikaihenagon

In the case of this polygon, the value of n is

We will then calculate the sum of interior angles of a 21-gon and then divide the sum by the number of sides n...

Therefore,

The formula we will use to calculate the measure of an interior angle of a 21-gon is given below as

The formula for the sum of interior angles is given below as

Hence,

We will have

Step 2:

Substitute the value of n=21 in the formula above, we will have

Hence,

The final answer = 162.86°

Answer:

The answer would be 87^2

Step-by-step explanation:

The solution is, Area of a sector is 138.23 cm².

Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

here, we have,

The formula for the area of a sector is given as:

θ/360 × πr²

θ = 110°

Radius = r = 12 cm

Hence

Area of a sector = 110/360 × π × 12²

= 138.23007676 cm²

Approximately, Area of a sector = 138.23 cm²

Hence, The solution is, Area of a sector is 138.23 cm².

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The mean of the data sets of Restaurants A and B which Walt collected is 17.3 and 15.8 respectively. Degree of overlap of two data set is 1.5.

The mean of the data is the average value of the given data. The mean of the data is the ratio of sum of all the values of data to the total number of values of data.

Walt collected random samples of data on the number of people who eat at who restaurants daily. He created two dot plots to represent his data.  

Mean of Restaurants A is,

\(X_A=\dfrac{10+15+16+18+18+18+19+19+20+20}{10}\\X_A=\dfrac{173}{10}\\X_A=17.3\)

Mean of Restaurants B is,

\(X_A=\dfrac{ 10+13+15+15+15+16+17+18+19+20}{10}\\X_A=\dfrac{158}{10}\\X_A=15.8\)

Degree of overlap is the difference of both the means.

\(DO=X_A-X_B\\DO=1.5\)

Thus, the mean of the data sets of Restaurants A and B which Walt collected is 17.3 and 15.8 respectively. Degree of overlap of two data set is 1.5.

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Answer:

Step-by-step explanation: