most people can roll their tongues, but many can't. the ability to roll the tongue is genetically determined. suppose we are interested in determining what proportion of students can roll their tongues. we test a timple random sample of 400 studens and find that 317 can roll their tongues. the margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is closest to

Answer:

a 0.05x = t

Step-by-step explanation:

5% = 0.05

0.05 * x = her discounted price

0.05x = t

Answer: -3x + 4

Step-by-step explanation:

To convert standard form:

3x + y = 4

to slope intercept form all we have to do is bring the x to the other side.

When we take the x to the other side we get

y = -3x + 4

Therefore when rewritten in slope-intercept form, the answer is:

y = -3x + 4

Answer: x = 0, Y = 2    

              x = 1, Y = 5

Step-by-step explanation:

Y = −3x^2 + 6x + 2

Y = 3x + 2

We can set the two equations equal to each other, since they both equal Y:

−3x^2 + 6x + 2 = 3x + 2

−3x^2 + 3x = 0

 3x(-x + 1) = 0

This gives us two possible solutions:

x = 0

x = 1

When x = 0, Y = 3(0) + 2 = 2

When x = 1, Y = 3(1) + 2 = 5

Therefore, the solutions to the system of equations are:

x = 0, Y = 2

x = 1, Y = 5

Given:

The point is A(-1,3).

To find:

The coordinates of the final image. If the given point reflected in

(a) x-axis

(b) line y=4.

Solution:

(a)

If a figure reflected across the x-axis, then

\((x,y)\to (x,-y)\)

Using this rule, we get

\(A(-1,3)\to A'(-1,-3)\)

Therefore, the coordinates of the final image are A'(-1,-3).

(b)

If a figure reflected across the line y=4, then

\((x,y)\to (x,-(y-4)+4)\)

\((x,y)\to (x,-y+4+4)\)

\((x,y)\to (x,-y+8)\)

Using this rule, we get

\(A(-1,3)\to A'(-1,-3+8)\)

\(A(-1,3)\to A'(-1,5)\)

Therefore, the coordinates of the final image are A'(-1,5).

To determine whether the geometric series ∑(n=0 to ∞) (√(1/7))^n is convergent or divergent, we can examine the common ratio (r) of the series.

The given series has a common ratio of (√(1/7)). For a geometric series to be convergent, the absolute value of the common ratio (|r|) must be less than 1.

In this case, |√(1/7)| = √(1/7) ≈ 0.377, which is less than 1. Therefore, the geometric series is convergent.

To find the sum of the geometric series, we can use the formula for the sum of an infinite geometric series:

Sum = a / (1 - r),

where 'a' is the first term and 'r' is the common ratio.

In this case, the first term 'a' is (√(1/7))^0 = 1, and the common ratio 'r' is √(1/7).

Substituting these values into the formula, we have:

Sum = 1 / (1 - √(1/7)).

To simplify this expression, we can rationalize the denominator:

Sum = 1 / (1 - √(1/7)) * (1 + √(1/7)) / (1 + √(1/7)).

Multiplying the numerators and the denominators, we get:

Sum = (1 + √(1/7)) / (1 - (1/7)).

Simplifying further:

Sum = (1 + √(1/7)) / (6/7).

Finally, multiplying the numerator by 7, we obtain the sum of the geometric series:

Sum = 7(1 + √(1/7)) / 6.

Therefore, the sum of the given geometric series is 7(1 + √(1/7)) / 6.

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a. In the event that Jada uses 15 cups of apple juice, 10 cups of sparkling water will she require.

b. If Jada uses 6 glasses of sparkling water, 9 cups of apple juice will she need.

c. The equation that shows s and j are s=2/3 j

Given that,

Using 2 cups of sparkling water for every 3 cups of apple juice, Jada creates sparkling juice.

We have to find

a. In the event that Jada uses 15 cups of apple juice, how much sparkling water will she require is

It need 2 cups of sparking water for every 3 cups of apple juice.

So, for 15 = 5×3 cups of apple juice, Jade needs 5×2 = 10 cups of sparking water.

b. If Jada uses 6 glasses of sparkling water, how much apple juice will she need is

We need 3×2 cups of sparking water

So, she needs 3×3 =9 cups of apple juice.

c. Assume that s stands for the volume of sparkling water and j for the volume of apple juice. Describe the relationship between s and j are using an equation.

We know that

s=kj

Where

k = 2/3

So,

s=2/3 j

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Answer:

3x + 10 < 3

=> 3x < -7

=> x < -7/3

2x - 5 ≥ 5

=> 2x  ≥  10

=> x  ≥  5

Answer:

x < -7/3 or x > 5

The five values for a data set are: minimum = 0 lower quartile = 2 median = 3. 5 upper quartile = 5 maximum = 10 Bruno created the box plot using the five values. Bruno made error. The left whisker should go from 0 to 2.

Quartiles is a type of quartile that divides data into four parts with approximately the same number. The first quartile or lower quartile (Q1) is the middle value between the smallest value and the median of the data group. The first quartile is a marker that the data in that quartile is 25% below the data group.

The second quartile (Q2) is the median data which marks 50% of the data (dividing the data in half). The third or upper quartile (Q3) is the middle value between the median and the highest value of the data set. The third quartile is a marker that the data in that quartile is 75% below the data group. Quartiles are a form of an ordered statistic because to determine quartiles, data needs to be sorted from smallest to largest value first.

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Answer:

C. The function shown on the graph has a greater rate of change and a higher starting point.

Step-by-step explanation:

I don't have an explanation but I had got it wrong on and it said C  was the answer.

Answer:

 113097.33552923 yards3

Step-by-step explanation:

Answer:

The expression for the perimeter of the rectangle is:

P = 2*(12 cm) + 2*(7 cm)

And the perimeter is:

P = 38cm

Step-by-step explanation:

We know that for a rectangle of length L and width W, the perimeter is given by:

P = 2*L + 2*W

So, if we have a rectangle that is 12 cm long,  we have L = 12cm

and if the rectangle is 7cm wide, we have W = 7cm

Now we can replace these in the perimeter equation to get:

P = 2*(12 cm) + 2*(7 cm)

P = 24cm + 14cm

P = 38cm

The function which is in format f(x) =aˣ where x is variable and a is constant,  the domain of this exponential function lies   (-∞, ∞).

Given, a function  Y=500(1.067)^x

For calculating the y-intercept x will be 0

Thus  y-intercept of the given exponential function  = 500 (1.067)^0 = 500

As we can show in the attached graph the function is exponential growth.

In the attached image an equation is given that is \(\frac{(3g^3m^4)^{-3}}{(g^5 m^{-5})^ {-2}}\)

When we will simplify this using the only condition if the base is the same then power can be equal.

Thus the simplified version of the given function is \(\frac{g}{3 m^{22} }\).

In the third question,

A certain car depreciates at a rate of 15% a year,

The price is $26,000,

Expression of the depreciating price is given as,

= 26000(1 - 0.15)⁶

= 26000(0.85)⁶

= $9805.88

Thus, the required depreciated cost of the car is $9805.88 in 6 years.

Given a line  2x+y=6 that has another parallel line passing through the point (0, -1).

The equation of the parallel Line is 2x + y = c

Since, it goes through the point (0, -1)

value of c = 2*0 -1 = -1

Thus, the equation of the line parallel to 2x+y=6 and passing through the point (0,-1) is 2x +y  + 1 = 0

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Complement of set A is the set of all elements in the universal set that are not in the set .

If there is a subset of the universal set (U) called A, then the complement of set A, denoted by the symbol A', is different from the elements of set A and contains the elements of the universal set but not the elements of set A.

In this case, A' = x U: x A.

In other words, the complement of a set A is the difference between the universal set and set A.

For example: U = {1, 2, 3, 5, 7, 9, 15 ,14, 13}, A = {1, 2, 3, 5,7,9}, find the complement of A.

A' = U - A = {1, 2, 3, 5, 7, 9, 15,14,13} - {1, 2, 3, 5,7,9} = {15,14, 13}

A set that contains items from all related sets, without any repetition of elements, is known as a universal set (often symbolised by the letter U). If A and B are two sets, for example, A = 1, 2, 3 and B = 1, a, b, c, then U = 1, 2, 3, a, b, c is the universal set that these two sets belong to.

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Answer:

518

Step-by-step explanation:

solution:

=8^2^×1^+1+6^2^×1^-1

=8^3+6^1

=8^3+6

=8×8×8+6

=512+6

=518

Answer:

-66

Step-by-step explanation:

-4n+6

-72+6

-66

might not be right thk

Answer:

- 66

Step-by-step explanation:

The n th term of an arithmetic sequence is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 2 and d = a₂ - a₁ = - 2 - 2 = - 4, thus

\(a_{18}\) = 2 + (17 × - 4) = 2 - 68 = - 66

A positive credit history is crucial for accessing credit, securing favorable terms, expanding financial opportunities, and building a solid foundation for future financial endeavors.

Having a positive credit history is important for several reasons. First and foremost, it allows individuals to access credit and loans at favorable terms.

Lenders use credit history as a measure of an individual's creditworthiness and ability to repay borrowed money.

A positive credit history demonstrates responsible financial behavior, such as making payments on time and managing debt effectively, making lenders more likely to approve credit applications and offer lower interest rates.

Additionally, a positive credit history can enhance one's financial opportunities. It can make it easier to secure housing by demonstrating reliability in meeting financial obligations.

Landlords often review credit histories to assess the likelihood of timely rent payments. Similarly, employers, especially those in the financial sector, may consider credit history when making hiring decisions, as it can be indicative of an individual's level of responsibility and integrity.

Furthermore, a positive credit history enables individuals to build a solid foundation for future financial goals. It establishes a track record of responsible financial management, making it easier to qualify for larger loans, such as mortgages or business loans when needed.

Good credit can also lead to higher credit limits, which can provide flexibility in managing unexpected expenses or seizing investment opportunities.

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Check the picture below.

\(\textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh~~ \begin{cases} b=base\\ h=height\\[-0.5em] \hrulefill\\ b=8\\ h=10 \end{cases}\implies A=\cfrac{1}{2}(8)(10)\implies A=40\)

The area of a vertical cross-section through the centre of the base of the party hat is 40 square inches.

It is defined as the three-dimensional shape in which the base is a circular shape and if we go from circular base to top the diameter of the circle reduces and at the vertex, it becomes almost zero.

Clyde has a cone-shaped party hat.

The height of the hat = 10 inches

The radius of the base of the hat = 4 inches.

The diameter of the base of the hat = 2×4 ⇒8 inches

The vertical cross-section of the cone exactly looks like a triangle.

In this scenario, the vertical cross-section of the hat is a triangle with a height of 10 inches, and base length of 8 inches.

We know the formula for the area of a triangle is given by:

\(\rm A = \frac{1}{2} (b\times h)\)

Here b = 8 inches, and h = 10 inches

\(\rm A = \frac{1}{2} (8\times 10)\)

A = 40 square inches

Thus, the area of a vertical cross-section through the centre of the base of the party hat is 40 square inches.

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Answer:

(d) -15

Step-by-step explanation:

Given system of equations are:

\( \begin{cases}kx-5y=2\\\\6x+2y=7\end{cases}\)

Since, given system of equations have no solution.

\( \therefore \frac{k}{6}=\frac{-5}{2} \neq\frac{2}{7}\)

\( \implies \frac{k}{6}=\frac{-5}{2} \)

\( \implies k=\frac{6(-5)}{2} \)

\( \implies k=\frac{-30}{2} \)

\( \implies k=-15\)

The table which shows the input and output values of g (x) is,

f (x)              g(x)

  2                 4

  1                  2

  0                 0

  1                  2

  2                 4

A relation between a set of inputs having one output each is called a function.

Given that;

The input and output values of a function f (x) are shown in the table.

     X                          f (x)

     -4                           2

     -3                           1

     -2                           0

     -1                            1

     0                            2

Here, We have;

⇒ g (x) = 2f (x),

Hence, The table which shows the input and output values of g (x) is,

f (x)              g(x)

  2                2×2 = 4

  1                 1×2 = 2

  0               0×2 = 0

  1                 2×1 = 2

  2                2×2 = 4

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The true population mean is (222.52, 227.48) with a 95% confidence interval.

The critical factor for a 90% confidence interval for the true population mean is given by;

Critical factor = (x-μ)/(s/√n)

where, x = sample mean repair cost

s =  standard deviation of a sample

n = sample of stereos

μ  = critical value

⇒ P(-1.96< (x-μ)/(s/√n) < 1.96) = 0.95

⇒ P(-1.96×(s/√n) < (x-μ) < 1.96×(s/√n)) = 0.95

⇒ P(x - 1.96×(s/√n) < μ < x + 1.96×(s/√n)) = 0.95

95% confidence interval for

⇒ μ = (x - 1.96×(s/√n) , x + 1.96×(s/√n))

Here, x = 225, s  = 8.5, and n = 45

⇒ μ = (225- 1.96×(10.81/√13) , 225+ 1.96×(10.81/√13))

⇒ μ = (222.52, 227.48)

Hence, the true population mean is (222.52, 227.48) with a 95% confidence interval.

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The question seems to be incomplete the correct question would be

Calculate the 95% confidence interval for the true population mean based on a sample with x=225, s=8.5, and n=45.

238.20 cubic inches of cotton is needed if the remaining space is to be filled with cotton for padding. The volume of cotton needed is obtained by subtracting the volume of four glass balls from the volume of the box.

The radius of a glass ball = 2.5 inches.

The volume of a ball = \(\frac{4}{3}\pi r^3\)

                                   = \(\frac{4}{3}\times 3.14\times (2.5)^3\)

                                   = 65.42 cubic inches.

The volume of 4 balls = 4 × 65.42 cubic inches

                                    = 261.67 cubic inches.

Length of the box = 4 × 2.5 × 2 = 20 inches,

Width of the box = 2.5 × 2 = 5 inches,

Height of the box = 2.5 × 2 = 5 inches.

So,

the volume of the box = Length × Width × Height

                                     = 20 × 5 × 5

                                     = 500 cubic inches.

Now,

The volume of cotton needed = the volume of the box - the volume of 4 balls.

= 500 - 261.67

= 238.20 cubic inches.

Thus, if the remaining space is to be filled with cotton for padding, 238.20 cubic inches of cotton is needed.

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The trigonometric ratios for angle θ are given as follows:

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the formulas presented as follows:

Applying the Pythagorean Theorem, the missing side length is given as follows:

x² + 3² = 4²

x² = 7

\(x = \sqrt{7}\)

For the angle θ in this problem, we have that:

Hence the trigonometric ratios are given as follows:

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Answer:

I would tell you

Step-by-step explanation:

you need to put 2 y and 2 x and that you need to divide

Answer:

An 11 inch tall roll of paper towels has an inner cardboard tube with a diameter of 1.5 inches.

Step-by-step explanation:

Answer: each pencil would cost 0.36¢

Step-by-step explanation: first, divide 12.82 by 36 to get the unit rate. The answer should be 0.356111111. Now round that to the nearest cent. 0.356111111~0.36

Answer:

Each pencil is worth 36 cents

Step-by-step explanation:

To do the problem we have to find the unit price which is \(Total Price/Total Units\)

Once you have that round the answer then the answer is 0.36

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option a-0.2816. To find the probability that Judy will answer exactly 3 questions correctly, we can use the binomial probability formula. In this case, the number of trials is 10 (since there are 10 questions), the probability of success is 1/4 (since there is only one correct answer out of 4 possible choices), and we want to find the probability of getting exactly 3 successes.

The binomial probability formula is:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

Where:
- P(X=k) is the probability of getting exactly k successes
- (n choose k) represents the number of ways to choose k items out of n items
- p is the probability of success on a single trial
- k is the number of successes
- n is the number of trials

Using this formula, we can calculate the probability as follows:

P(X=3) = (10 choose 3) * (1/4)^3 * (3/4)^(10-3)

(10 choose 3) = 10! / (3! * (10-3)!)
= 10! / (3! * 7!)
= (10 * 9 * 8) / (3 * 2 * 1)
= 120

Now we can substitute the values into the formula:

P(X=3) = 120 * (1/4)^3 * (3/4)^(10-3)
= 120 * (1/64) * (3/4)^7
= 120 * (1/64) * (2187/16384)
= 0.2816

Therefore, the probability that Judy will answer exactly 3 questions correctly is 0.2816.

The correct answer is option a-0.2816.

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The means and standard deviation of the length of time that four randomly selected transistors will last are 3200 hours and 5 hours, respectively.

mean = 4 * 800 hours = 3200 hours.

The standard deviation of the length of time that four randomly selected transistors will last is equal to the standard deviation of a single transistor's lifetime divided by the square root of the sample size (which is 4), which is:

standard deviation = \(\frac{10}{\sqrt{4} }\) = 5 hours.

Standard deviation is a measure of the amount of variation or dispersion of a set of data values around the mean. It is a statistical concept used in probability theory and statistics to measure the amount of spread or dispersion of a data set. The standard deviation is expressed in the same units as the original data and provides a measure of how tightly the data is clustered around the mean.

To calculate the standard deviation, you first find the mean of the data set. Then, for each data point, you find the difference between the data point and the mean. You square these differences, sum them up, and then divide by the number of data points minus one. The resulting value is the variance of the data set. The standard deviation is then calculated by taking the square root of the variance.

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To find the correct equations for the missing boxes, we need more information about the relationships between the different activities in Jake's Gems. However, based on the given context, we can make some assumptions and suggest potential equations:

Mining and Cutting activities produce diamonds, rubies, and other gems. Let's assume that the production of each gem type is represented by a variable: D (diamonds), R (rubies), and G (other gems).

Maintenance supports the Mining and Cutting activities. We can assume that the maintenance effort required for each activity is represented by the variable M (maintenance).Since the question mentions five missing boxes, we can suggest additional equations to represent relationships between these variables, such as:

Mining + Cutting = D + R + G (the sum of all gem types produced equals the total production from Mining and Cutting activities).

Maintenance = M (maintenance effort required).

The relationships between these variables might include equations like D = f(M), R = g(M), G = h(M), where f, g, and h represent some functions or formulas that relate gem production to maintenance effort.

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