In a basketball free-throw shooting contest shots made by Sam and Wil were in the ratio 7:9.Wil made 6 more shots than Sam. Find the number of shots made by each of them.

If we randomly select 62 travel mugs and measure the amount of soft drink dispensed in each mug, the sample mean will be within 0.5 ounces of the population mean with 95% confidence.

To determine the number of travel mugs required for the study, we need to use the formula for sample size determination for means. The formula is:

n = (Z^2 * σ^2) / E^2

Where:

n = sample size

Z = Z-score for the desired confidence level (e.g., 1.96 for 95% confidence level)

σ = standard deviation of the population

E = desired margin of error (i.e., the maximum difference between the sample mean and the population mean)

In this case, we are given that the standard deviation of the soft drink dispensed is 2.0 ounces and we want the sample mean to be within 0.5 ounces of the population mean. Let's assume a 95% confidence level, which corresponds to a Z-score of 1.96. Plugging in the values, we get:

n = (1.96^2 * 2^2) / 0.5^2 = 61.6

We need to round up to the nearest whole number, so the final sample size should be 62 travel mugs. The larger the sample size, the smaller the margin of error will be, but it also means more time and resources required for the study.

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Complete question is:

a baseball parkamount of soft drink dispensed is normally distributed with standard deviation 2.0 ounces. how many travel mugs should be included in a study if it is desiredthat the sample mean soft drink dispensed be within 0.5 ounces of the population mean with 95% confidence.

Answer:

105

Step-by-step explanation:

10² is 100

100+5=105

Answer:

-45

Step-by-step explanation:

To find the probability that at least one of the two cards drawn from a standard deck of 52 playing cards is a spade, we can use the complement rule.

The complement of the event "at least one of the cards is a spade" is "neither of the cards is a spade."

To find the probability that neither of the two cards is a spade, we can multiply the probabilities of drawing a non-spade on the first card and a non-spade on the second card:

P(neither is spade) = (39/52) x (38/51) = 0.4498 (rounded to four decimal places)

P(at least one is spade) = 1 - P(neither is spade)

P(at least one is spade) = 1 - 0.4498

P(at least one is spade) = 0.5502 (rounded to four decimal places)

Therefore, the probability that at least one of the two cards drawn from a standard deck of 52 playing cards is a spade is 0.5502 or approximately 55.02%.

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Let x be the number of $1 bills and y be the number of $5 bills that Hermione had in her purse. Then we can write two equations based on the given information:

x + y = 12 (because Hermione had 12 bills in total)

x + 5y = 40 (because the total value of the bills was $40)

We can solve this system of equations by first solving the first equation for x:

x = 12 - y

Substituting this expression for x into the second equation, we get:

(12 - y) + 5y = 40

Simplifying and solving for y, we get:

4y = 28

y = 7

Therefore, Hermione had 7 $5 bills in her purse. Answer: 7.

Answer:

yes

Step-by-step explanation:

replace r and q with y and x:

y = 4x - 5

It is a line.

To make a table of the two possible payouts on each policy with the probability of each, we can use the following information:

The premium is $280.

The probability of a fire is 0.1% or 0.001.

In the event of a fire, the insured damages will be $270,000.

There are two possible outcomes:

No fire occurs:

The probability of this outcome is 1 - 0.001 = 0.999.

The payout is $0.

Fire occurs:

The probability of this outcome is 0.001.

The payout is $270,000.

Therefore, the table of the two possible payouts on each policy with the probability of each is:

Outcome Probability Payout

No fire           0.999            $0

Fire                   0.001       $270,000

Note that the expected value of the policy can be calculated as the sum of the products of the probabilities and payouts:

Expected value = (0.999 x $0) + (0.001 x $270,000) = $270.

The probability of getting a sum of at least 3 when two different colored dice are rolled simultaneously is 5/6.

To calculate the probability of getting a sum of at least 3 when two different colored dice are rolled simultaneously, we need to list out all possible combinations of the dice and find out how many of them add up to at least 3. Let's begin:

Possible combinations when rolling two dice:

1 + 1, 1 + 2, 1 + 3, 1 + 4, 1 + 5, 1 + 62 + 1, 2 + 2, 2 + 3, 2 + 4, 2 + 5, 2 + 63 + 1, 3 + 2, 3 + 3, 3 + 4, 3 + 54 + 1, 4 + 2, 4 + 3, 4 + 55 + 1, 5 + 2, 5 + 36 + 1, 6 + 2, 6 + 3

Total number of combinations:

6 x 6 = 36.

Now, we need to find out how many of these combinations add up to at least 3.

We can ignore 1+1 because it's less than 3. The rest are as follows:

1 + 2, 2 + 1, 1 + 3, 3 + 1, 2 + 2, 1 + 4, 4 + 1, 2 + 3, 3 + 2, 1 + 5, 5 + 1, 2 + 4, 4 + 2, 3 + 3, 1 + 6, 6 + 1, 2 + 5, 5 + 2, 3 + 4, 4 + 3, 2 + 6, 6 + 2, 3 + 5, 5 + 3, 4 + 4, 3 + 6, 6 + 3, 4 + 5, 5 + 4, 4 + 6, 6 + 4, 5 + 5, 5 + 6, 6 + 5, 6 + 6.

Total: 30.

So, the probability of getting a sum of at least 3 when two different colored dice are rolled simultaneously is 30/36 or 5/6.

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Answer: 900,012

Step-by-step explanation:

Answer: 900,012

this is because, nine hundred thousand is shown as 900,000 in number form

and then you just add 12 to that number, making it 900,012

The solution of the system of equations:

2x+2y+ 6z = 8

5x+6y + 5z = 3

5x + 6y + 3z = 5

Is the one in option a.

(x= 34, y = -27,z = -1)

Here we have the system of equations:

2x+2y+ 6z = 8

5x+6y + 5z = 3

5x + 6y + 3z = 5

If we subtract the third equation from the second one we will get:

(5x + 6y + 5z) - (5x + 6y + 3z) = 3 - 5

5z - 3z = -2

We just removed two of the variables, so we can now solve this linear equation for z so we get:

2z = -2

z = -2/2

z = -1

We know that the value of z is -1, that is enough to identify the correct option because only one of these has z = -1  which is the first one, so that is the correct option.

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The statement is true.

The coefficient of correlation, also known as the Pearson correlation coefficient, is a measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, with a value of -1 indicating a perfect negative correlation, a value of 0 indicating no correlation, and a value of 1 indicating a perfect positive correlation.

The coefficient of correlation is useful in many applications, including research, business, and finance. It allows us to quantify how closely related two variables are, which is important when analyzing data and making predictions.

For example, in finance, the correlation coefficient can be used to measure the degree of correlation between the returns of two assets, which is important when building diversified portfolios. It is important to note, however, that the coefficient of correlation only measures the strength and direction of the linear relationship between two variables.

It does not indicate causation, nor does it capture any non-linear relationships that may exist between the variables. Therefore, it should be used in conjunction with other analytical tools to fully understand the nature of the relationship between the variables.

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The weight of an object varies directly with the mass of the object therefore, the mass of the other object that weighs 15 N is 3 kg.

We can use the formula for direct variation, which states that if y varies directly with x, then y = kx, where k is the constant of variation. In this case, the weight y varies directly with the mass x, so we have:

y = kx

We are given that when x = 5 kg, y = 25 N. Substituting these values into the formula, we get:

25 = k(5)

Solving for k, we have:

k = 5

Now we can use this value of k to find the mass of another object that weighs 15 N. Let's call the mass of this object x2. We know that y2, the weight of the object, is 15 N. So we have:

15 = 5x2

Solving for x2, we have:

x2 = 3 kg

Therefore, the mass of the other object that weighs 15 N is 3 kg.

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Answer:

72 ft

Step-by-step explanation:

Alright so two ways you can solve this, but the easier one (imo) is to find the scale factor by doing 24/2 since its an enlargement, and multiplying 6 by the scale factor (12)

The range of the function is a set of positive values greater than 500 and 60.

Therefore, the range of the function is given by:

Range = {c(t) : c(t) > 500, c(t) > 60t} or {c(t) : c(t) > 500, c(t) > 60}.

The given situation of a cell phone company charges $500 for a new phone and then $60 each month after the purchase.

If c (t) is a rational function that represents the average monthly cost of owning the cell phone, the range of the function is given by:

Range = {c(t) : c(t) > 500, c(t) > 60t} or {c(t) : c(t) > 500, c(t) > 60}

The cell phone company charges a one-time amount of $500 and $60 each month after the purchase.

It is given that c (t) represents the average monthly cost of owning the cell phone.

From this information, it can be inferred that the average monthly cost of owning the cell phone is given by: c(t) = (500 + 60t)/t

The given function is a rational function that represents the average monthly cost of owning the cell phone.

The range of a function is the set of all possible values of the function.

The average monthly cost of owning the cell phone is a positive value.

Hence the range of the function is a set of positive values greater than 500 and 60.

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Answer:

  5. 3 cm × 2 cm × 7 cm

  6. f(x) = x³ -3x² -x +3

Step-by-step explanation:

You want the dimensions of a cuboid with edges marked (x-1), (x-2), and (x+3) and a volume of 42 cm³. You also want the coefficients of a monic cubic f(x) with values f(2) = -3, f(-3) = -48, and f(-1) = f(1).

The volume of the cuboid is the product of its dimensions, so we have ...

  V = LWH

  42 = (x -1)(x -2)(x +3)

The value of x can be found as the solution to this equation. A graphical solution is attached. It shows x=4, so the dimensions are ...

  4 -1 = 3

  4 -2 = 2

  4 +3 = 7

The dimensions of the cuboid are 3 cm by 2 cm by 7 cm.

Note that the prime factors of 42 are 2, 3, 7, which have the required differences. You don't really need a polynomial to guess these are the dimensions.

The expanded polynomial is x³ -7x -36 = 0, so potential rational roots will be from the set {1, 2, 3, 4, 6, 9, 12, 18, 36}. An estimate of the upper bound of the real root puts it at ∛36 +√7 ≈ 5.9. We require x > 2, so the viable choices for testing are 3 and 4. x=4 is the solution.

The remainder theorem tells you that the remainder from dividing f(x) by (x-a) is f(a). To obtain linear equations in b, c, d, we can rearrange the function to ...

  bx² +cx +d = -x³ +f(x)

For x = ±1, we know the remainders f(x) are the same, so we can look at the difference of the equations for these x-values.

  (b(-1)² +c(-1) +d) - (b(1)² +c(1) +d) = (-(-1)³ +f(-1)) - (-(1)³ +f(1))

  b -b -c -c +d -d = 1 -(-1)

  -2c = 2

We can fill in values x=2, x=-3 to get two more equations in b, c, d. The coefficients of the three equations we have for the three unknowns are shown in the second attachment. The third attachment shows the solution of these equations is (b, c, d) = (-3, -1, 3).

The table in the first attachment confirms the remainders using these coefficients.

__

Additional comment

For problem 6, we started out using synthetic division, then realized the resulting equations are the same as those developed using the rearranged form shown above. We like to let calculators and spreadsheets do the tedious arithmetic where possible.

Answer:

5)The dimensions of the rectangular prism are 3 , 7 and 2.

6) f(x) = x³ - 3x² - x + 3

Step-by-step explanation:

5) The volume of rectangular prism = l*w*h.

    l*w*h= 42

(x- 1)(x -2)(x+3) = 42

We can find (x - 2) *(x + 3) using the identity (x + a)(x + b) = x² + (a +b)*x + ab

(x - 2)(x + 3) =x² + (-2 +3)x + (-3)*2

                   = x² + 1x - 6

(x -1)(x + 3)(x - 2) = 42

(x - 1)(x² + x - 6) = 42

x*x² + x*x - 6*x + (-1)*x² + (-1) *x + (-1)(-6) = 42

x³ + x² - 6x - x² - x + 6 - 42 = 0

x³ + x² - x² - 6x - x + 6 -42 = 0

Combine the like terms,

   x³ - 7x - 36 = 0

Find the zeros of the cubic polynomial by synthetic division method.

     4       1       0      -7      -36

                      4       16       36

              1       4       9          0

x - 4 is zero of the polynomial.  

Ignore the quadratic polynomial x² + 4x  + 9 as it will have irrational roots(zeros) and dimensions will be always positive integer.

x - 4 = 0

x = 4

length =  x - 1     =  4 - 1 = 3

Width  =   x + 3 = 4 + 3 = 7

Height =  x - 2 = 4 - 2  = 2

The dimensions of the rectangular prism are 3 , 7 and 2.

6)   f(x) = x³ + bx² + cx + d

It is given that when f(x) is dived by x + 1 and x- 1, the remainders are same.

   x + 1 = 0              ; x - 1 = 0

         x = -1             ;      x = 1

                       f(-1) =  f(1)

         -1 + b -  c + d = 1 + b + c + d

-1 -1 + b - b - c - c + d - d = 0

                -2 - 2c             = 0

                                   -2c = 2

                                      c = 2 ÷ (-2)

                                      [tex]\boxed{c = -1}[/tex]   -------------(I)

It is given that when f(x) divided by ( x - 2) it leaves a remainder (-3)

                         f(2) = -3

     8 + 4b + 2c + d  = -3

   8 + 4b + 2*(-1) + d = -3    {from (I)}

      8 + 4b - 2 + d    = -3

                    4b + d = -3 + 2 - 8

                     4b + d = -9 -------------(II)

It is given that when f(x) divided by ( x + 3) it leaves a remainder (-48).

                             f(-3) = -48

        -27 + 9b - 3c + d = -48

       -27 + 9b - 3*(-1) +d = -48      {From (I)}

           -27 + 9b + 3 + d  = - 48

                       9b + d     = -48 + 27 - 3

                         9b + d   = -24  --------------(III)

Subtract equation (III) from equation (II),

         (II)           4b + d = -9

        (III)            9b + d = -24

                      -        -       +    

                           -5b      = 15

                                 b    = 15 ÷ (-5)

                                [tex]\boxed{b=-3}[/tex]

Plugin b = -3 in equation (II),

             4*(-3) + d = -9

               -12   + d = -9

                          d = -9 + 12

                          [tex]\boxed{d = 3}[/tex]

                 [tex]\boxed{\bf f(x) = x^3 - 3x^2 -x + 3 }[/tex]

Answer:

£164.50

Step-by-step explanation:

If the discount is 6%, then the discounted price is 94% of the original price.

95% of £175 = 0.94 × £175 = £164.50

Answer:

The solutions to the equation x² = 196 are:

x = 14 or x = -14

Therefore, the smallest answer is -14 and the largest answer is 14.

X = -14 or 14

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The sum of the deviations of the individual data elements from their mean is always equal to zero. Correct option is A.

This is because the deviation is defined as the difference between each data point and the mean of all the data points.

Since the mean is calculated as the sum of all the data points divided by the total number of data points, the positive deviations from the mean must be balanced out by the negative deviations from the mean. In other words, for every data point that is above the mean, there is a corresponding data point that is below the mean.

When we add up all the deviations from the mean, the positive deviations will cancel out the negative deviations, resulting in a sum of zero. This property of the sum of deviations from the mean is fundamental to many statistical concepts, such as variance and standard deviation.

Therefore, the correct answer to the question is (a) equal to zero, since the sum of the deviations from the mean is always zero.

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The height of the second cylinder is 7 inches.

The Dreamy Donut Shop is 3 miles away from Cara's starting point.

For the first question, we can use the fact that the ratio of the diameter to the height is the same for both cylinders. The first cylinder has a diameter of 6 inches and a height of 14 inches, so its ratio is 6/14. If the second cylinder has the same ratio, then we can set up the equation

3/x = 6/14,

where x is the height of the second cylinder. Solving for x, we get

x = 7 inches.

Therefore, the height of the second cylinder is 7 inches.

For the second question, we can use the formula distance = rate × time. Since Cara drives at the same rate to both work and the donut shop, we can set up the equation

r × 0.5 = 15 for her commute to work, where r is her rate (in miles per minute). Solving for r, we get r = 30 miles per hour. Using the same formula for her trip to the donut shop, we get

r × 0.1 = d,

where d is the distance to the donut shop (in miles). Solving for d, we get

d = 3 miles.

Therefore, the Dreamy Donut Shop is 3 miles away from Cara's starting point.

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The probability that a patient will relapse after receiving desipramine depends on a variety of factors, such as dosage, duration of treatment, and pre-existing mental health conditions.

Generally speaking, it is estimated that around 50-70% of people who take desipramine as an antidepressant will experience relapse within six months of treatment cessation.

However, this rate can be decreased through longer treatment periods and/or higher doses of medication.

Additionally, patients may also benefit from lifestyle changes, such as increased physical activity, increased social engagement, and improved dietary habits.

Taking all of these factors into consideration, it is difficult to determine the exact probability of relapse in any given case.

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Answer: I think It is 63.64%. If I'm wrong I'm sorry.

Step-by-step explanation:

Ask yourself what is 56% out of 88%. I did it in my head, but I got 63.6363636% then I rounded it to 63.64%.

One possible technique to address heteroscedasticity with group-specific variances is the use of weighted least squares (WLS) estimation, where observations from each group are assigned weights that are inversely proportional to the variance of the error term in that group.

Heteroscedasticity refers to the situation where the variance of the error term in a regression model is not constant across different levels of the independent variable(s). This violates the assumption of homoscedasticity, which can lead to biased and inefficient estimates of the model parameters.

When the heteroscedasticity is related to group-specific variances, a possible solution is to use WLS estimation. This involves calculating weights for each observation based on the inverse of the estimated variance of the error term in its group. By doing so, observations with larger variances are given smaller weights, while observations with smaller variances are given larger weights, which effectively downweighs the influence of more variable observations.

The resulting WLS estimator is more efficient and less biased than the standard OLS estimator, and it can lead to more accurate inferences about the relationship between the independent and dependent variables. However, WLS requires the researcher to specify the appropriate weights for each observation, which can be challenging and subjective in practice.

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Answer: 14x + 14

Step-by-step explanation: To find the perimeter of the room without the door, we need to add up the four sides. Using the simplified expression for the perimeter, which is 2(4x+1) + 2(3x+6), we can simplify further by distributing the 2:

2(4x+1) + 2(3x+6) = 8x + 2 + 6x + 12

Combining like terms, we get:

14x + 14

Therefore, the perimeter of the room without the door in simplest form is 14x+14.

In the following question, among the given options, The statement "In a meta-analysis, there is a manipulation of variables" is false. hence meaning that the rest of them are stated to be true.

In A meta-analysis is a statistical technique for synthesizing the findings of multiple studies. It involves combining the results from multiple studies, analyzing them, and presenting a summary of the overall evidence. It does not involve manipulating variables or performing a random assignment. In a meta-analysis, any amount of studies can be used, and researchers can look for gaps in the research, based on a statistical analysis.

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The rate at which water is being poured into the conical paper cup when the water level is 4 cm is 707.1067 cm3 / 353.5534 seconds = 2 cm/sec.

The rate at which water is being poured into the conical paper cup with a height of 30 cm and a radius of 10 cm when the water level is 4 cm is determined by the volume of water that must be added to the cup in order to raise the water level from 0 cm to 4 cm. The volume of a cone is

V = (1/3)πr2h.

Therefore, the volume of water added to the cone when the water level is 4 cm is

V = (1/3)π × 102 × (30 - 4) = 707.1067 cm3.

Since the water level is rising at a rate of 2 cm/sec, it will take 707.1067 cm3 / 2 cm/sec = 353.5534 seconds to add the necessary water to the cup to raise the water level to 4 cm.

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This means that the algorithm will end after just one step, and the GCD will be equal to the last non-zero remainder, which in this case is 3. Therefore, we can be certain that the Euclidean algorithm will end with a zero remainder in one step, and the lowest number we can be certain of is 3.

In this particular question, the student is asking how many steps are required for the Euclidean algorithm to end with a zero remainder when applying it to two positive integers a and b.Suppose you apply the Euclidean algorithm to two positive integers a, b. You only know that a is a number with 1000 decimal digits. The value of b, on the other hand, is given as 3. We can be certain that the Euclidean algorithm will end with a zero remainder in one step.

In order to understand why this is the case, it is important to know that the Euclidean algorithm is a method for computing the greatest common divisor (GCD) of two positive integers. It is based on the observation that the GCD of two numbers does not change if the smaller number is subtracted from the larger number repeatedly.The Euclidean algorithm begins by dividing the larger number by the smaller number and taking the remainder.

The larger number is then replaced with the smaller number, and the smaller number is replaced with the remainder. This process is repeated until the remainder is zero. At this point, the algorithm ends, and the GCD is equal to the last non-zero remainder that was computed.In the case of the student's question, we know that b=3. Since 3 is relatively prime to any number, including a number with 1000 decimal digits, the remainder of the first step will always be 0.

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From the given information provided, the area of the new hexagon when dilated by scale factor is 675 square inches.

When a polygon is dilated by a scale factor of k, its area is multiplied by k².

A hexagon is a six-sided polygon. It is a flat shape with straight sides, and all six of its angles add up to 720 degrees.

In this case, the hexagon is being dilated by a scale factor of 3, so the area of the new hexagon will be:

Area of new hexagon = (scale factor)² x Area of original hexagon

Area of new hexagon = 3² x 75

Area of new hexagon = 9 x 75

Area of new hexagon = 675 square inches

Therefore, the area of the new hexagon is 675 square inches.

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The area of the piece of art is 448 square inches.

Shiloh made a scale drawing of a triangular piece of art.

Shiloh used a scale factor of 4 when making her drawing.

If the base and the height of Shiloh's drawing are 7 inches and 2 inches respectively,

what is the area of the piece of art?

Shiloh used a scale factor of 4 when making her drawing.

Therefore, the actual dimensions of the original triangular piece are four times the dimensions of the scaled drawing. Thus, the actual dimensions of the base and the height of the triangular piece are, respectively:

4 × 7 = 28 inches and 4 × 2 = 8 inches.

Using the formula for the area of a triangle,

we can find the area of the triangular piece.

The formula is given as A=12bh where b is the base and h is the height.

A = 12 × 28 × 8A = 112 × 4A = 448

Therefore, the area of the piece of art is 448 square inches.

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Answer:

1440000

Step-by-step explanation:

Since for every mile, there are 12 people, we have 120000 miles. If we multiply 12 by 120000, we get 1440000.