Willy has compounded monthly to invest his summer earnings of $4259 in the
Rock Solid Bank. The bank is offering 6%. Willy plans to use the money to go to
college in 5 years. How much will he have in 5 years?

Answer:

Ernie has a greater range

The statement "the medians are equal" is true for the given table of data about playing a game by Ernie and Lori. This is obtained by calculating the mean, median, mode, and range of the data elements of each.

Given data sets for Ernie and Lori as follows:

Ernie: {18, 24, 17, 19, 17} and Lori: {16, 22, 18, 14, 18}

The number of elements in both the data sets is equal and it is 5

Calculating Mean:

For Ernie: {18, 24, 17, 19, 17}

Mean=(18+24+17+19+17)/2

        =19

For Lori: {16, 22, 18, 14, 18}

Mean=(16+22+18+14+18)/2

        =17.6

Thus, their "means are not equal". (3rd statement is false)

Calculating Median:

For Ernie: {18, 24, 17, 19, 17}

Re-arranging the data - 17, 17, 18, 19, 24

Since n=5 (odd), then the median is at (5+1)/2 th term i.e., 3rd term

So, the median is 18

For Lori: {16, 22, 18, 14, 18}

Re-arranging the data - 14, 16, 18, 18, 22

Since n=5 (odd), then the median is at (5+1)/2 th term i.e., 3rd term

So, the median is 18

Thus, their "medians are equal". (first statement is true)

Calculating Mode:

The most occurring number in Ernie: {18, 24, 17, 19, 17} is 17 and

The most occurring number in Lori: {16, 22, 18, 14, 18} is 18

Thus, their modes are not equal, and "Lori has the greater mode".

(4th statement is false)

Calculating Range:

The range for Ernie's data set is 24 - 17=7

The range for Lori's data set is 22 - 14=8

Thus, their ranges are also not equal but "Lori has the greater range".

(2nd statement is false).

Therefore, 1st statement - " the medians are equal" is true.

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Answer:

6

Step-by-step explanation:

We can use the geometric mean theorem:

The altitude on the hypotenuse is the geometric mean of the two segments it creates.

In your triangle, the altitude is the radius CM and the segments are AC and BC.

[tex]CM = \sqrt{AC \times BC} = \sqrt{ 9 \times 4} = \sqrt{36} = \mathbf{6}\\\text{The radius of the circle M is $\large \boxed{\mathbf{6}}$}[/tex]

The length of the radius of the circle is 6 units

The given parameters are:

AC = 9

BC = 4

To calculate the radius (r), we make use of the following equation:

[tex]r = \sqrt{AC * BC}[/tex]

Substitute known values

[tex]r = \sqrt{9 * 4}[/tex]

Evaluate the product

[tex]r = \sqrt{36}[/tex]

Evaluate the square root

[tex]r = 6[/tex]

Hence, the length of the radius of the circle is 6 units

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Answer:

second option

Step-by-step explanation:

Given

x² - 6x - 33 = 0 ( add 33 to both sides )

x² - 6x = 33

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 3)x + 9 = 33 + 9

(x - 3)² = 42 → second option

Answer:

D. more than 102

E. between 90 and 102 messages

F. less than 78

Step-by-step explanation:

The median number of texts is 90, with approximately 25 students sending fewer than 78 texts (Q1) and 25 sending more than 102 texts (Q3) per day.

For a sample of 100 students, the median number of text messages sent per day is 90, the first quartile (Q1) is 78, and the third quartile (Q3) is 102. This implies that approximately 25 students in the sample send fewer than 78 text messages per day (since Q1 marks the 25th percentile) and approximately another 25 students send more than 102 text messages per day (since Q3 marks the 75th percentile). Hence, the interquartile range (IQR), which measures the middle 50% of the data, is the difference between the third and first quartiles, which is 102 - 78 = 24 messages.

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Answer:

d

Step-by-step explanation:

Answer:

Step 4

Step-by-step explanation:

Tasha was correct in all the steps leading up to the fourth one. However, in the fourth step was where she messed up.

She said that: [tex]\frac{1}{256} =-\frac{1}{4^{-4}}=4^{-4}[/tex]

However, when we have a negative exponent, in order to get rid of the negative, we simply take the reciprocal of the number and then make the exponent positive. Here, the answer should be:

[tex]\frac{1}{256} =\frac{1}{4^{4}}=4^{-4}[/tex]

Answer:

Step 4

Step-by-step explanation:

1/256 = 4^-4 or 1/4⁴

Answer:

7.38

Step-by-step explanation:

Answer:

The radius of a cone is the radius of its circular base. You can find a radius through its volume and height. Multiply the volume by 3.

Step-by-step explanation:

Answer:

Below.

Step-by-step explanation:

The y-intercept of the graph is at (0, 8)

Plugging in x = 0 we get  y = -4/3 * 0 + 8 = 8.

So we can mark 2 points on the graph paper.

One is at (0, 8).

If we let x = 3 then y = -4/3 * 3 + 8

y = -4 + 8

y = 4.

So our second point is at (3, 4)

We draw a line through these 2 points to get our graph.

Final answer:

To rearrange the equation so x is the independent variable, add 4y to both sides and then divide by -5 to solve for x.

Explanation:

To rearrange the equation so x is the independent variable, we need to isolate x on one side of the equation. Let's start by adding 4y to both sides of the equation:

-5x - 4y + 4y = -8 + 4y

-5x = 4y - 8

Next, divide both sides of the equation by -5 to solve for x:

x = (4y - 8) / -5

So, the rearranged equation with x as the independent variable is:

x = (-4y + 8) / 5

Therefore, as per the explaination above,  the answer to the required question is x = (-4y + 8) / 5

Answer:

A) Median: 7

Mode: 8

Range: 5

B) Tyler is wrong, the greater the MAD value, the greater the variability

Step-by-step explanation:

A) Given the data set: 4,6,6,7,7,8,8,8,9

The median is 7 (the middle point in the ordered list)

The mode is 8 (the most repeated number)

The range is 5 (the difference between the highest and lowest values)

Answer: Tanyia lives 18 miles away from the airport.

Step-by-step explanation: First, I took $3.25(initial fee) away from $25.40(starting amount) which equals $22.15. Then, I subtracted -$9.35(How much money Tanyia had after the taxi ride)from $22.15 which came out to $31.50. Lastly, I divided $31.50 by $1.75(cost per mile) which came out to 18.

Hope this helps!

Answer:

x = -1

y = -9

Step-by-step explanation:

7x - 3y = 20

7x - 3(5х – 4) = 20

7x - 15x + 12 = 20

-8x = 20 - 12

x = 8/-8

x = -1

7x - 3y = 20

7(-1) - 3y = 20

-7 - 3y = 20

-3y = 20 + 7

-3y = 27

y = 27/-3

y = -9

Answer:

9

Step-by-step explanation:

Composite Numbers before 10: 4, 6, 8, and 9

The only one of those 4 that is NOT a multiple of 2: 9

The number being referred to in the question is 9. It is less than 10, not a multiple of 2, and is a composite number, as it has factors other than 1 and itself.

The question is asking for a number which is less than 10 and is not a multiple of 2, but is a composite number. In mathematics, a composite number is a positive integer that has at least one positive integer divisor other than one or itself. If we look at the numbers less than 10 which are not multiples of 2, we are left with the numbers 1, 3, 5, 7, and 9. Out of these, the only composite number is 9, because it could be divided evenly by 3 and 1 apart from itself. Therefore, the number you are referring to is 9.

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Answer:

[tex]0\leq x\leq 15[/tex]

Step-by-step explanation:

I think your question missed key information, allow me to add in and hope it will fit the orginal one

For the graph below, what should the domain be so that the function is at least 200?   graph of y equals minus 2 times the square of x plus 30 times x plus 200

My answer:

Given the above information, we have:

[tex]y=-2x^2+30x+200[/tex]

To make  the function is at least 200, it means that:

[tex]y=-2x^2+30x+200[/tex] ≥ 200

<=> [tex]-2x^2+30x[/tex] ≥ 0

<=> x(-2x+30) ≥ 0

This is the product of two numbers hence would be positive only if either both are positive or both are negative

x ≥ 0 and  (-2x+30) ≥ 0

<=> 0 ≤ x ≤ 15

Then we get

[tex]x\leq 0 and -2x+30\leq 0\\\\x\leq 0 and x\geq 15[/tex]

This is inconsistent as a value cannot be less than 0 and greater than 15

=> our correct answer is[tex]0\leq x\leq 15[/tex]

Hope it will find you well.

Answer:

y = f(x + 90)

Step-by-step explanation:

f(x)=Acos(Bx+C)+D,

A is the amplitude: A = 1

B is the 360/period: 360/360 = 1

D is the mean line: y = 0

f(-270) = 0

sin(x + C) = 0

-270 + C = -180

C = 90

y = f(x + 90)

In order to find the area of composite figures and trapezoids, you should decompose the figure into simple shapes, calculate each of their areas, and then sum these areas up. For trapezoids, use the formula 1/2 (sum of the bases) x height.

The question provides a complex description of a figure, but it seems this is a mathematical problem dealing with areas of trapezoids and composite figures. It can be inferred that you need to maneuver pieces to cover the shaded area of a figure. Here's a general way to approach it:

For the trapezoids, remember that the area of a trapezoid is given by 1/2 (sum of the bases) x (height).

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Answer:

b

Step-by-step explanation:

bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

Answer:

Event

Step-by-step explanation:

I got the question right ._.

An outcome is a possible result of some event occurring.

The probability is defined as the possibility of an event is equal to the ratio of the number of outcomes and the total number of outcomes.

An outcome is a possible result of some event occurring.

For example, when you flip a coin, “heads” is one outcome; tails is a second outcome.

Total outcomes are computed simply by counting all possible outcomes.

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Answer: 16384

Step-by-step explanation:

The 15th term of the geometric sequence 4,-8, 16, -32, 64... is 131072. The term is obtained by using the formula for the nth term of a geometric sequence.

The sequence given is a geometric sequence. This means every term is obtained by multiplying the previous term by a constant. In this case, the constant is -2 (since -8 = 4*-2, 16 = -8*-2, -32 = 16*-2, etc).

The formula for the nth term of a geometric sequence is a*r^(n-1), where a is the first term, r is the ratio (constant), and n is the position of the term in the sequence. In this case, the first term a is 4 and the ratio r is -2. Substituting these values and n=15 into the formula, we get the 15th term as 4*(-2)^(15-1) = 131072.

Therefore, the 15th term of the sequence 4,-8, 16, -32, 64... is 131072. This can be found by applying the formula for the nth term of a geometric sequence and substituting the given values.

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Answer:

A) 39.6 divided by 8.25 is true.

Answer:

D

Step-by-step explanation:

Got it right on test

Answer:

3.8 meters

Step-by-step explanation:

Answer:

The probability that [tex] \\ P(x<85)[/tex] is, approximately, 0.3594 or about 35.94% (or simply 36%).

Step-by-step explanation:

Firstly, we have to know that the random variable, in this case, is normally distributed. A normal distribution is completely determined by its two parameters,  namely, the population mean and the population standard deviation. For the case in question, we have a mean of [tex] \\ \mu = 89[/tex], and a standard deviation of [tex] \\ \sigma = 11[/tex].

To find the probability in question, we can use the standard normal distribution, a special case of a normal distribution with mean equals 0 and a standard deviation that equals 1.

All we have to do is "transform" the value of the raw score (x in this case) into its equivalent z-score. In other words, we first standardize the value x, and then we can find the corresponding probability.

With this value, we can consult the cumulative standard normal table, available in most Statistics textbooks or on the Internet. We can also make use of technology and find this probability using statistical packages, spreadsheets, and even calculators.

The corresponding z-score for a raw score is given by the formula:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]

And it tells us the distance of the raw score from the mean in standard deviations units. A positive value of the z-score indicates that the raw value is above the mean. Conversely, a negative value tells us that the raw score is below the mean.

With all this information, we are prepared to answer the question.

The corresponding z-score

According to formula [1], the z-score, or standardized value, is as follows:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]

From the question, we already know that

x = 85

[tex] \\ \mu = 89[/tex]

[tex] \\ \sigma = 11[/tex]

Thus

[tex] \\ z = \frac{85 - 89}{11}[/tex]

[tex] \\ z = \frac{-4}{11}[/tex]

[tex] \\ z = -0.3636 \approx -0.36[/tex]

Consult the probability using the cumulative standard normal table

With this value for z = -0.36, we can consult the cumulative standard normal table. The entry for use it is this z-score with two decimals. This z-score tells us that the raw value of 85 is 0.36 standard deviations below from the population mean.

For z = -0.36, we can see, in the table, an initial entry of -0.3 at the first column of it. We then need to find, in the first line (or row) of the table, the corresponding 0.06 decimal value remaining. With this two values, we can determine that the cumulative probability is, approximately:

[tex] \\ P(x<85) = P(z<-0.36) = 0.3594[/tex]

Then, [tex] \\ P(x<85) = 0.3594[/tex] or, in words, the probability that [tex] \\ P(x<85)[/tex] is, approximately, 0.3594 or about 35.94% (or simply 36%).

Remember that this probability is approximated since we have to round the value of z to two decimal places (z = -0.36), and not (z = -0.3636), because of the restrictions to two decimals places for z of the standard normal table. A more precise result is [tex] \\ P(x<85) = 0.3581[/tex] using technology, shown in the graph below.

Notice that, in the case that the cumulative standard normal table does not present negative values for z, we can use the next property of the normal distributions, mainly because of the symmetry of this family of distributions.

[tex] \\ P(z<-a) = 1 - P(z<a) = P(z>a)[/tex]

For the case presented here, we have

[tex] \\ P(z<-0.36) = 1 - P(z<0.36) = P(z>0.36)[/tex]

[tex] \\ P(z<-0.36) = 1 - 0.6406 = P(z>0.36)[/tex]

[tex] \\ P(z<-0.36) = 0.3594 = P(z>0.36)[/tex]

Which is the same probability obtained in the previous step.

The graph below shows the shaded area for the probability of  [tex] \\ P(x<85)[/tex] finally obtained.  

Final answer:

To find P(x<85), calculate the z-score and use the standard normal distribution to find the cumulative probability. Susan's z-score for her final exam is 2, meaning her performance was significantly above the average. The central limit theorem helps to analyze the mean of large sample sizes, while binomial distributions apply to scenarios such as analyzing a basketball player's field goal completion rate.

Explanation:

Finding Probability in a Normal Distribution

To find the probability P(x<85) when the number of points scored by each team in the NHL at the end of the season is normally distributed with a mean (μ) of 89 and a standard deviation (σ) of 11, we use the standard normal distribution. First, we calculate the z-score for x=85, which is the value for which we want to find the cumulative probability. The z-score is calculated using the formula z = (x - μ) / σ. Substituting the given values, we get z = (85 - 89) / 11 = -0.3636. Then we look up this z-score in the standard normal distribution table or use a calculator or software to find the cumulative probability associated with this z-score.

To express the number 13.7 in terms of the mean and standard deviation of the given data, you would use the formula for the z-score again.

If Susan's biology class has a mean final exam score of 85 and a standard deviation of 5, and Susan scored a 95 on her final exam, her z-score would be z = (95 - 85) / 5 = 2. This means Susan's score is 2 standard deviations above the mean, indicating she performed significantly better than the average student.

When dealing with sample sizes larger than one, the central limit theorem tells us that the sampling distribution of the sample mean will tend to be normal regardless of the shape of the population distribution, especially as the sample size increases (typically n > 30 is considered large enough). This is reflected in the examples involving the estimation of mean final exam scores and calculating probabilities with a sample size of 55.

The probability distribution question for the basketball player's shots would involve the binomial distribution, where the probability of success is given by the player's field goal completion rate. The mean and standard deviation for this binomial distribution can be calculated using the formulas for a binomial distribution.

Answer:

A = 3

B = -7

C = -12

Step-by-step explanation:

3x^2−7x=12.

The standard form for a quadratic equation is

Ax^2 +Bx +C =0

Subtract 12 from each side

3x^2−7x-12=12-12

3x^2−7x-12=0

A = 3

B = -7

C = -12

Answer:

a = 3

b = -7

c = -12

Step-by-step explanation:

General form of a quadratic:

ax² + bx + c

Given:

3x² − 7x = 12

3x² - 7x - 12 = 0

Comparing the two:

a = 3

b = -7

c = -12

Answer:  (3,4)

This is what I had wrote, sorry if I'm wrong.

Answer:

J'(2, 1)

K'(0, 3)

Step-by-step explanation:

On a coordinate plane, coordinates of the points J, K and L are (-2, 1), (0, 3) and (2, -1) respectively.

If we reflect these points over the line x = 0 or y-axis, rule to be followed is

(x, y) → (-x, y)

Only sign of x coordinates get changed while y coordinates remain the same.

Following this rule coordinates of the images of J' and K' will be

J(-2, 1) → J'(2, 1)

and K(0, 3) → K'(0, 3)

Answer:

j = 2, 1

k = 0, 3

Step-by-step explanation:

i got it right on edg

Answer:

B and C

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

A= very light

B= heavy

C= REALLY HEAVY

Answer:

m<A = 20

Step-by-step explanation:

6y plus 3y = 9y

180 divided by 9 = 20

20x6=120

20x2=40

120+40=160

a triangle is equal to 180 so..

180-160=20

i did 6y + 3y because that line is 180 degrees ( half of a circle)

Answer:

1/4

Step-by-step explanation:

(0,1) (4,2)

m=(y2-y1)/(x2-x1)

m=(2-1)/(4-0)

m=1/4