A die is rolled. find the probability of the given event. (a) the number showing is a 3;

We can say with 95% confidence that the true mean amount that women in the population spend dining out per week lies within the range of $91.74 to $108.26.

Based on the given information, we can calculate a 95% confidence interval for the mean amount that women in the population spend dining out per week. With a sample size of 25 and a standard error of $4, we can use the formula:

95% CI = sample mean +/- (critical value x standard error)

To find the critical value, we need to look up the t-distribution with degrees of freedom (df) = n-1 = 24 and a significance level of alpha = 0.05/2 = 0.025 (since we are interested in a two-tailed test). From a t-table or calculator, we find that the critical t-value is approximately 2.064.

Plugging in the values, we get:

95% CI = $100 +/- (2.064 x $4)
95% CI = $100 +/- $8.26
95% CI = ($91.74, $108.26)

Therefore, we can say with 95% confidence that the true mean amount that women in the population spend dining out per week lies within the range of $91.74 to $108.26. This means that if we were to repeatedly take random samples of 25 women and calculate their mean amount spent dining out, about 95% of the intervals we construct using this method would contain the true population mean.

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The equivalent expression for -4/7-8/9+4/7+9/8 is given by option C. -8/9 + 9/8 and option D. - (4/7+ 8/9 ) + 4/7 + 9/8.

The expression is equals to,

-4/7-8/9+4/7+9/8

Verify  all attached options using property of addition.

-4/7- (8/9+4/7 )+9/8

Open the parenthesis as plus minus is minus we get,

- 4/7 - 8/9 - 4 /7 + 9/8

It is not equivalent to -4/7-8/9+4/7+9/8.

Incorrect option.

- ( 4/7-8/9+4/7 ) + 9/8

Open the parenthesis as (+)( - )is minus  and ( - ) ( - ) is plus we get,

- 4/7  + 8/9 - 4 /7 + 9/8

It is not equivalent to -4/7-8/9+4/7+9/8.

Incorrect option.

-8/9 + 9/8

= 0 -8/9 + 9/8

= -4/7 + 4/7  -8/9 + 9/8

Rearrange terms we get,

-4/7-8/9+4/7+9/8

It is equivalent to -4/7-8/9+4/7+9/8

Correct option.

- (4/7+ 8/9 ) + 4/7 + 9/8

Open the parenthesis as plus minus is minus we get,

-4/7 -8/9 + 4/7 + 9/8

It is equivalent to -4/7-8/9+4/7+9/8

Correct option.

0

Incorrect option.

Therefore, for the given expression equivalent terms are option C. -8/9 + 9/8 and option D. - (4/7+ 8/9 ) + 4/7 + 9/8.

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The above question is incomplete, the complete question is:

-4/7-8/9+4/7+9/8

Which of the following expressions are equivalent to

Attached options.

Q3. Integrate by using partial fraction, \( \int \frac{2 x^{2}+9 x-35}{(x+1)(x-2)(x+3)} d x \).The given integral can be solved using partial fraction as follows:\[\frac{2x^2+9x-35}{(x+1)(x-2)(x+3)}=\frac{A}{x+1}+\frac{B}{x-2}+\frac{C}{x+3}\]Multiplying both sides by the product of the denominators we get:\[2x^2+9x-35=A(x-2)(x+3)+B(x+1)(x+3)+C(x+1)(x-2)\]Substituting values of x and solving for A, B and C we get,\[A=3\] \[B=-2\] \[C=2\]Thus, the integral can be written as:\[\begin{aligned}\int \frac{2 x^{2}+9 x-35}{(x+1)(x-2)(x+3)} d x&=\int \frac{3}{x+1} d x-\int \frac{2}{x-2} d x+\int \frac{2}{x+3} d x\\&=3 \ln|x+1|-2 \ln|x-2|+2 \ln|x+3|+C\end{aligned}\]where C is the constant of integration.Q4. Find the area of the region bounded by the curves \( y=x^{2}+4 \) lines \( y=x, x=0 \) and \( x=3 \)We are required to find the area of the region bounded by the curves \( y=x^{2}+4 \) lines \( y=x, x=0 \) and \( x=3 \)The given curves can be plotted as shown below:Since the function \( y=x^{2}+4 \) lies above the line y = x in the interval [0, 3] the area can be computed as:\[\begin{aligned}Area&=\int_{0}^{3}(x^{2}+4-x)dx\\&=\left[\frac{x^{3}}{3}+4x-\frac{x^{2}}{2}\right]_{0}^{3}\\&=\frac{9}{2}+6-\frac{9}{2}-0\\&=6\end{aligned}\]Hence, the area of the region bounded by the curves \( y=x^{2}+4 \) lines \( y=x, x=0 \) and \( x=3 \) is 6 square units.

Q.3

To integrate the given function using partial fractions, we need to decompose the rational function into simpler fractions. Let's proceed step by step:

1. Factorize the denominator:

(x+1)(x-2)(x+3)

2. Write the partial fraction decomposition:

\(\frac{2x^{2}+9x-35}{(x+1)(x-2)(x+3)} = \frac{A}{x+1} + \frac{B}{x-2} + \frac{C}{x+3}\)

3. Multiply both sides by the denominator to clear the fractions:

2x^2 + 9x - 35 = A(x-2)(x+3) + B(x+1)(x+3) + C(x+1)(x-2)

4. Expand and simplify the right-hand side:

2x^2 + 9x - 35 = A(x^2 + x - 6) + B(x^2 + 4x + 3) + C(x^2 - x - 2)

Expanding further:

2x^2 + 9x - 35 = (A + B + C)x^2 + (A + 4B - C)x + (-6A + 3B - 2C)

5. Equate the coefficients of corresponding powers of x:

For x^2: A + B + C = 2

For x: A + 4B - C = 9

For constant term: -6A + 3B - 2C = -35

Solving these equations simultaneously will give us the values of A, B, and C.

6. Solve the system of equations:

From the first equation, we can express C in terms of A and B:

C = 2 - A - B

Substituting this into the second equation:

A + 4B - (2 - A - B) = 9

2A + 3B = 11

From the third equation, we can express B in terms of A:

B = (35 + 6A - 2C)/3

B = (35 + 6A - 2(2 - A - B))/3

B = (35 + 6A - 4 + 2A + 2B)/3

3B - 2B = 6A + 35 - 4 - 2A

B = 4A + 31

Substituting B = 4A + 31 into the equation 2A + 3B = 11:

2A + 3(4A + 31) = 11

2A + 12A + 93 = 11

14A = -82

A = -82/14

A = -41/7

Substituting A = -41/7 into B = 4A + 31:

B = 4(-41/7) + 31

B = -164/7 + 217/7

B = 53/7

Now, substituting the values of A, B, and C into the partial fraction decomposition, we get:

\(\frac{2x^{2}+9x-35}{(x+1)(x-2)(x+3)} = \frac{-41/7}{x+1} + \frac{53/7}{x-2} + \frac{2-(-41/7)-(53/7)}{x+3}\)

7. Integrate each term separately:

∫\(\frac{2x^{2}+9x-35}{(x+

1)(x-2)(x+3)} dx = \frac{-41}{7} \int \frac{1}{x+1} dx + \frac{53}{7} \int \frac{1}{x-2} dx + \frac{64}{7} \int \frac{1}{x+3} dx\)

Simplifying the integrals:

∫\(\frac{-41}{7} \frac{1}{x+1} dx + \frac{53}{7} \frac{1}{x-2} dx + \frac{64}{7} \frac{1}{x+3} dx = -\frac{41}{7} \ln|x+1| + \frac{53}{7} \ln|x-2| + \frac{64}{7} \ln|x+3| + C\)

Therefore, the integral of the given function is:

∫\(\frac{2x^{2}+9x-35}{(x+1)(x-2)(x+3)} dx = -\frac{41}{7} \ln|x+1| + \frac{53}{7} \ln|x-2| + \frac{64}{7} \ln|x+3| + C\)

Now, let's move on to the next question.

Q4.

To find the area, we need to calculate the definite integral of the difference between the curves \(y = x^{2} + 4\) and \(y = x\) over the given interval [0, 3]:

Area = ∫[0, 3] (x^2 + 4 - x) dx

Simplifying:

Area = ∫[0, 3] (x^2 - x + 4) dx

Integrating each term separately:

Area = ∫[0, 3] x^2 dx - ∫[0, 3] x dx + ∫[0, 3] 4 dx

Calculating the integrals:

Area = [(1/3)x^3] [0, 3] - [(1/2)x^2] [0, 3] + [4x] [0, 3]

Substituting the limits:

Area = [(1/3)(3)^3 - (1/3)(0)^3] - [(1/2)(3)^2 - (1/2)(0)^2] + [4(3) - 4(0)]

Simplifying:

Area = [(1/3)(27 - 0)] - [(1/2)(9 - 0)] + [12 - 0]

Area = 9 - 4.5 + 12

Area = 16.5

Therefore, the area of the region bounded by the curves \(y = x^{2} + 4\), \(y = x\), \(x = 0\), and \(x = 3\) is 16.5 square units.

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Answer:

Peter started with 21 cards

Step-by-step explanation:

half of his card that gave to bobby =9

so the other half is 9

9+9=18

18+3 cards that he lost at the beginning=21

Answer:

Substitute 21 for X in the original equation YES

Substitute any number for X in the original equation NO

Bobby’s claims that x=21 is correct YES

The result of verifying Bobby's work is 9=9 YES

The result of verifying Bobby's work is 21=21 NO

Step-by-step explanation:

got right on edg

Answer:

5/4 (In terms of fours)

Step-by-step explanation:

1/4+1/2+1/2

5/4

Answer:

Jeremy is 10

Adam is 5

Step-by-step explanation:

Let Adam age be x

Todd is 3x

Jeremy is x + 5

If Todd is 15 years old, Adam will be 5 coz Todd's age is 3 times that if Adam

So Jeremy will be 5+5 = 10

Answer:

Jeremy is 10

Adam is 5

The quotient of two integers can be positive, negative, or zero depending on the signs of the dividend and divisor.

When dividing two integers, the quotient can be positive, negative, or zero. The sign of the quotient depends on the signs of the dividend and the divisor. If both the dividend and divisor have the same sign (both positive or both negative), the quotient will be positive.

If they have opposite signs, the quotient will be negative. If the dividend is zero, the quotient is zero regardless of the divisor.

For example, when we divide 12 by 4, we get a quotient of 3, which is positive because both 12 and 4 are positive integers. However, when we divide -12 by 4, we get a quotient of -3, which is negative because the dividend (-12) is negative and the divisor (4) is positive.

Finally, if we divide 0 by any integer, the quotient is always 0.

Therefore, the quotient of two integers can be positive, negative, or zero depending on the signs of the dividend and divisor.

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The sample will remain after 5000 years is 1.14mg and it will take 0.7 years will only 18 mg of the sample remain

Look for a function that describes the mass that is left after t years.

Using the radioactive decay model mt = m0e^-rt:

m0 = 23mg, r=(ln2/1600) = -0.00043

A rate cannot be negative.

You probably mean r=0.00043

m(t) = 23e^-0.00043t

a) After 5000 years, how much of the sample will still be there?

t = 4000

m(4000) = 23e^(-0.00043)(5000) = 1.14 mg

(b) How long will it be till only 18 mg of the sample are left?

m(t) = 23e^-0.00043t

18 = 23e^-0.00043t

18/23 = e^-0.00043t

0.78/0.99 = t

t = 0.7 years

Hence, Only 1.14 mg of the sample will be left after 5000 years, and it will take 0.7 years for only 18 mg to be left.

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Answer: availability heuristic

Step-by-step explanation:

The letter on the number line that represents the given number is B.

A number line is a straight line which extends from -∞ to -∞, on which the position or location of all directed numbers can be identified.

Directed numbers are numbers which have either a negative or positive sign. Examples include; -4, -1 2/3. 9 etc. Therefore all numbers can be located on a number line.

Considering the given question, to locate the position of 1 85/100. The whole number make us to understand that its position falls between 1 and 2. And the fraction part shows that the number is closer to 2 more than 1.

Therefore, the letter on the number line that represents 1 85/100 is B.

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The transverse axis and foci of the hyperbola are on the x-axis.

To determine whether the transverse axis and foci of the hyperbola are on the x-axis or the y-axis, we need to look at the equation of the hyperbola:

(y²)/10 - (x²)/16 = 1

We can rewrite this equation as:

(x²)/16 - (y²)/10 = -1

Compare this equation with standard form

(x²/a²) - (y²/b²) = 1

The transverse axis of the hyperbola is along the x-axis, since the term with x² is positive and the term with y² is negative.

This means that the hyperbola opens horizontally.

To find the foci of the hyperbola, we need to use the formula:

c = √a² + b²

c =  √16 + 10) =  √26

The foci of the hyperbola are located along the transverse axis, so they are on the x-axis.

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Answer:

12.

Step-by-step explanation:

Area = base * perpendicular height

= 6 * 2 = 12.

Answer:

12 square units

Step-by-step explanation:

6 x 2 = 12

The ends of the parallelogram are triangles, so you can just multiply the base times height.

Answer:

4

Step-by-step explanation:

One way to do it: The y-axis is the vertical axis. The point is at 4 on the y-axis.

Another way to do: Coordinates of the point = (2,4)

The y-coordinate is the second number.

We can write the {y} - coordinate of the given point as 4 because the general form of the coordinate in 2 - D plane is (x, y).

Given is to find the value of the {y} coordinate of the plotted point

The given point is (2, 4). We can write the {y} - coordinate of the given point as 4. This is because we know that the general form of the coordinate in 2 - D plane is (x, y).

Therefore, we can write the {y} - coordinate of the given point as 4 because the general form of the coordinate in 2 - D plane is (x, y).

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Attached figure shows the triangle pairs which can be mapped to each other using a single translation.

What are Transformation and Reflection?

Single or multiple changes in a geometrical shape or figure are called Geometrical Transformation.

A geometrical transformation in which a geometrical figure changes his position to his mirror image about some point or line or axis is called Reflection.

The translation is a rigid transformation that creates a congruent image as that of the original figure such that the distance between the each point of the original figure and the image is fixed and the same.

The translation mapping is given by (x,y)→(x+h,y+k), where h is the distance of the x coordinate of the each point of the original figure to the image and k is the distance of the y coordinate of each point of the original figure to the image.

In the attached figure we can see that the distance between each point of ΔCED is equal to the distance between each point of ΔMPN. Thus it shows the triangle pairs which can be mapped to each other using a single translation.

Attached figure shows the triangle pairs which can be mapped to each other using a single translation.

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Complete Question:

'Which of these triangle pairs can be mapped to each other using a single translation? pls help need it fast '

Notice that

(x - 1)²/4 + (y + 2)²/9 = (2 sin(θ))²/4 + (3 cos(θ))²/9

… = sin²(θ) + cos²(θ)

… = 1

Solve for y in terms of x :

(x - 1)²/4 + (y + 2)²/9 = 1

(y + 2)²/9 = 1 - (x - 1)²/4

(y + 2)² = 9 - 9/4 (x - 1)²

y + 2 = ± √(9 - 9/4 (x - 1)²)

y + 2 = ± 3/2 √(4 - (x - 1)²)

y = -2 ± 3/2 √(4 - (x - 1)²)

In order for the square root to be defined, one needs

4 - (x - 1)² ≥ 0

(x - 1)² ≤ 4

-2 ≤ x - 1 ≤ 2

-1 ≤ x ≤ 3

so x must belong to the interval [-1, 3].

Answer: apple lol hope i made your day byee

Step-by-step explanation:

Answer:

1: 41

2: 85

3: 95

4: 85

5: 36

6: 49

7: 106

Based on the number of names of winners that can be drawn, and the number of names in the basket, the number of different ways they can be drawn is 190 different ways

There are 20 names that you can draw from, in the raffle. There are however, only 2 names that can be picked for the same prize. This means that this is a combination problem.

The number of ways to pick the two winners can be modelled as:

= ₂₀C₂

= 20! / ( 2 ! ( 20 - 2) ! )

= 190 different ways

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Answer: Choice C

We can rotate the figure 180 degrees so that it lines up with its original image perfectly. In other words, the before and after would be identical images.

The rotational symmetry of a form explains why an item has the same shape when rotated on its own axis. The correct option is C.

The rotational symmetry of a form explains why an item has the same shape when rotated on its own axis. When turned 180 degrees or with specific angles, clockwise or anticlockwise, many geometrical forms appear to be symmetrical. Examples include squares, circles, hexagons, and more.

The shape that has a rotational symmetry is option C, which is a parallelogram.

Hence, the correct option is C.

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0.29 km is equal to 290,000 mm when rounded to two significant figures.

Convert kilometers to millimeters, you need to multiply the given value by a conversion factor. In this case, since there are 1,000 meters in a kilometer and 1,000 millimeters in a meter, the conversion factor is 1,000,000 (1,000 x 1,000).

Step 1: Multiply 0.29 km by the conversion factor:

0.29 km x 1,000,000 = 290,000,000 mm

Step 2: Round the result to two significant figures:

Since the original value, 0.29 km, has two significant figures, we round the result to match.

290,000,000 mm becomes 290,000 mm.

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(f- g)(x) = 2x²-3x -8 , Option B is the correct answer.

A function is a mathematical statement that derives relation between two variables.

Two functions are given in the question

f(x) = 2x² - 5

g(x) = 3x + 3

(f- g)(x) = ?

(f- g)(x) = (2x² - 5 - (3x + 3))

(f- g)(x) = 2x²-3x -8

Therefore Option B is the correct answer.

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The inverse of a relation R is obtained by swapping the positions of the elements in each ordered pair of R. In other words, if (a, b) is in R, then (b, a) will be in the inverse relation R⁻¹.

Given the relation R = {(n, m) | n, m ∈ ℤ, n ≥ m}, the inverse relation R⁻¹ will have pairs where the second element is less than the first element.

Therefore, the correct inverse relation for R is:

R⁻¹ = {(n, m) | n, m ∈ ℤ, n > m}

Option (a) R⁻¹ = {(n, m) | n, m ∈ ℤ, n < m} is incorrect because it reverses the inequality sign incorrectly.

Option (b) R⁻¹ = {(n, m) | n, m ∈ ℤ, n ≠ m} is also incorrect because it includes pairs where n and m can be equal, which is not consistent with the given relation R.

Hence, the correct answer is R⁻¹ = {(n, m) | n, m ∈ ℤ, n > m}.

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The difference between the compound interest and simple interest for 7 years is $3,944.72 or approximately $3,944.73.

We have to calculate the difference between the compound interest and simple interest for 7 years. The principal amount is $3,000, and the interest rate is 9%. The formula for simple interest can be represented as,

I = Prt

where I is the simple interest, P is the principal amount, r is the rate of interest, and t is the time taken.

The interest for one year using simple interest will be,

I = Prt = $3,000 × 0.09 × 1 = $270

So, the interest for 7 years using simple interest will be $270 × 7 = $1,890.

The formula for compound interest can be represented as,

A = P(1 + r/n)^nt

where A is the amount, P is the principal amount, r is the rate of interest, t is the time taken, and n is the number of compounding periods.

The interest for 7 years using compound interest will be,

A = $3,000(1 + 0.09/1)^(1 × 7) = $5,834.72

The interest Lori will receive in the 7th year with compound interest can be calculated as follows:

Amount for 6 years = $3,000(1 + 0.09/1)^(1 × 6) = $5,178.38

Amount for 7 years = $3,000(1 + 0.09/1)^(1 × 7) = $5,834.72

Interest for 7th year with compound interest = $5,834.72 - $5,178.38 = $656.34

The interest for 7 years using simple interest is $1,890.

The interest for 7 years using compound interest is $656.34 + interest for the first 6 years.

Interest for 6 years using compound interest,

A = $3,000(1 + 0.09/1)^(1 × 6) = $5,178.38

The total interest for 7 years using compound interest is $5,178.38 + $656.34 = $5,834.72.

The difference between the compound interest and simple interest for 7 years is $5,834.72 - $1,890 = $3,944.72, which is the answer.

However, it is not one of the options. So, we need to round it off to the nearest cent.

The difference rounded to the nearest cent is $3,944.73 - $3,944.72 = $0.01

Hence, the difference between the compound interest and simple interest for 7 years is $3,944.72 or approximately $3,944.73.

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Answer:

5($2.50)+3($1.50)=17

Step-by-step explanation:

you you just need to put up quantity by side of the bar pound it goes in the brackets that will give you the answer when you multiply that or something fruits value.

Answer:

Step-by-step explanation:

The FSA can be defined as follows:

Q: set of states {q0, q1, q2, q3}

∑: set of input symbols {0, 1}

q0: initial state

F: set of final states {q1, q2, q3}

δ: transition function

δ(q0, 0) = q0

δ(q0, 1) = q1

δ(q1, 0) = q2

δ(q1, 1) = q1

δ(q2, 0) = q3

δ(q2, 1) = q1

δ(q3, 0) = q3

δ(q3, 1) = q3

The FSA (Finite State Automaton) that recognizes binary strings with two or more Os anywhere in the string can be constructed using four states: q0, q1, q2, and q3. The initial state is q0 and the set of final states is {q1, q2, q3}. At state q0, the machine reads input symbol 0 and remains in state q0, while reading input symbol 1 transition to state q1.

At state q1, the machine reads input symbol 0 and transitions to state q2, while reading input symbol 1 remains in state q1. At state q2, the machine reads input symbol 0 and transitions to state q3, while reading input symbol 1 transition to state q1.

At state q3, the machine reads either input symbol 0 or 1 and remains in state q3. If the machine reaches any of the final states, it accepts the input string.

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Outliers have a significant impact on a sample's parameters, errors, variance, and standard deviation. Instead of being regarded as outliers, Z-scores between -1.96 and +1.96 represent values that fall within the expected range.

Outliers can have a significant impact on the parameters, errors, variance, and standard deviation of a sample. Parameters, such as the mean and standard deviation, are influenced by outliers because they are sensitive to extreme values. Outliers can pull the mean towards their value, resulting in a biased estimate.

Similarly, outliers can inflate the variance and standard deviation, making them less representative of the majority of the data. Z-scores are a measure of how many standard deviations a data point is away from the mean. Z-scores falling between -1.96 and +1.96 (corresponding to approximately the 95% confidence interval) are not considered outliers.

These z-scores represent data points within a range that is expected and common for normally distributed data. Outliers are typically defined as data points that fall beyond a certain threshold, often defined as three standard deviations from the mean. When calculating z-scores for skewness and kurtosis, we use standard error instead of standard deviation.

This is because standard error takes into account the sample size and provides an estimate of the variability of the statistic being calculated. Since skewness and kurtosis are sample statistics, the standard error is used to assess the precision of these statistics in representing the corresponding population parameters.

In conclusion, outliers can greatly affect the parameters, errors, variance, and standard deviation of a sample. Z-scores falling between -1.96 and +1.96 are not considered outliers but rather represent values within the expected range.

Standard error is used when calculating z-scores for skewness and kurtosis to account for the sample size and provide a measure of precision for these statistics.

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Answer:

LOL i don't even know

Step-by-step explanation: