if p and n are positive integers and p > n, what is the remainder when p2 – n2 is divided by 15 ?

To draw a table of values for the first 6 natural numbers, draw the rows and columns and input the numbers 1, 2, 3, 4, 5, and 6 against the variables being compared.

A table is a visual representation that is used to compare two or more variables. To draw this sort of table for natural numbers, you need to insert 6 rows to contain all of the numbers.

The number of columns that will e drawn depends on the variable or variables that you are checking. The first 6 natural numbers are numbers 1 to 6.

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90π m² is the combined surface area of the top and sides of the sail to determine the amount of paint needed for the job note there is no need to paint the bottom of the silo

We know that t = 12m

t= 2×diameter

12=2×diameter

6=diameter

Radius = 3m

Combined surface area = 2πrt+1/2×4πr²

=2π(3)(12)+1/2×4π(9)

=72π+18π

=90π m²

Hence, 90π m² is the combined surface area of the top and sides of the sail to determine the amount of paint needed for the job note there is no need to paint the bottom of the silo

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Answer:

The surface area of the right triangular prism is 168 cm².

Step-by-step explanation:

The formula for the surface area of a right triangular prism is SA=bh+pl, where p=b+h+c

P=b+h+c

P=4+3+5

=12

SA=bh+pl

SA=(4)(3)+(12)(13)

SA= 12+156

SA=168 cm²

For more information on how to find the surface are of right triangular prisms, check out "Triangular Prism - Volume, Surface Area, Base and Lateral Area Formula, Basic Geometry" by the Organic Chemistry Tutor.

Hope this helps!

The value of x in the chord intersection is 16 units.

The intersecting chord theorem  states that the products of the lengths of the line segments on each chord are equal. In other words, If two chords intersect in a circle , then the products of the measures of the segments of the chords are equal.

Therefore, lets find the value of x in the intersecting chords as follows:

15 × x = 24 × 10

15x = 240

divide both sides of the equation by 15

x = 240 / 15

x = 16

Therefore,

x = 16 units

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True.

The expression c(n,r), also known as "n choose r" or the binomial coefficient, represents the number of ways that r elements can be selected from a set of n elements without regard to order. It is commonly used in combinatorics, probability, and statistics. The formula for c(n,r) is c(n,r) = n!/r!(n-r)!, which can be calculated using factorials.

For example, c(5,2) = 10, which represents the number of ways to choose 2 elements from a set of 5 elements (i.e., {1,2}, {1,3}, {1,4}, {1,5}, {2,3}, {2,4}, {2,5}, {3,4}, {3,5}, {4,5}).

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The first five terms in the recursive sequence are: 2, 3, 6, 18, 108.

First five terms of the recursive sequence defined by a1 = 2, a2 = 3, and an = an-2 * an-1.
1. First term (a1): Given as 2.
2. Second term (a2): Given as 3.
3. Third term (a3): To find a3, use the formula an = an-2 * an-1. In this case, n = 3, so a3 = a1 * a2 = 2 * 3 = 6.
4. Fourth term (a4): Similarly, to find a4, use the formula with n = 4. So a4 = a2 * a3 = 3 * 6 = 18.
5. Fifth term (a5): Finally, to find a5, use the formula with n = 5. So a5 = a3 * a4 = 6 * 18 = 108.
The first five terms in the recursive sequence are: 2, 3, 6, 18, 108.

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Answer: 90

Step-by-step explanation:

Answer: 6

Step-by-step explanation:

If you divide both sides by 63 it isolates the t and leaves you with 6=t.

The method used to determine the probability of a family having six girls, based on a survey of 1000 families with six children, is the classical method.

The classical method involves calculating probabilities based on the assumption of equally likely outcomes and known sample spaces. In this case, the sample space consists of all possible combinations of genders for six children, and the probability of a family having six girls is calculated as the ratio of the favorable outcome (one specific combination) to the total number of outcomes (all possible combinations).

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There are several formulas for finding the area, volume, and perimeter of different shapes. Some examples are: [tex]P = 2(l + w)[/tex], [tex]A = lw[/tex], and [tex]V = lwh[/tex]

Perimeter:

Area:

Volume:

Note: This question is incomplete. Here is the complete question:

What is the formula of perimeter, area and volumen of rectangle, square, and circle

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If the coach was to pick the player based on the best average, the coach would choose Jessie.

If the coach is picking based on who has been the most consistent, they would pick Sam.

The average for Jessie is :

= ( 150 + 145 + 181 + 235 + 196 + 211 + 204 + 221 + 185 ) / 9

= 192 points

The average for Sam :

= ( 186 + 187 + 192 + 195 + 194 + 157 + 157 + 162 + 200 ) / 9

= 181 points

The coach would pick Jessie based on average.

For consistency, we can use the measure of variability of range. The range for Jessie is:

= 235 - 145

= 90 points

The range for Sam would be:

= 200 - 157

= 43 points

This shows that Sam is more consistent and so would be picked based on consistency.

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The measure of I'J' is 18 units.

We have,

Scale factor= 2

length of IJ = 9

Now, If the segment IJ is dilated by a scale factor of 2, the length of I'J' will be:

I'J' = 2 x IJ

I'J' = 2 x 9

I'J' = 18

Therefore, the measure of I'J' is 18 units.

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Answer:

Step-by-step explanation:

Given that vector (g, h) moves a shape g squares right and h squares up, you want the description for the vector (7, 9).

As with a numerical expression, you can substitute the values for the letters in the English description. When (g, h) = (7, 9), it means "g" can be replaced by "7" and "h" can be replaced by "9". The sentence with these replacements is ...

  vector (7, 9) moves a shape 7 squares right and 9 squares up

__

Additional comment

It's not math. It's reading comprehension.

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Answer:

option 2

Step-by-step explanation:

They both travel x miles per week

option 1: SUV (15 + 1)mpg + hybrid (65)mpg = 81combined mpg

option 2: SUV (15)mpg + hybrid (80) mpg = 95 combined mpg

getting 95mpg is better than 81mpg.

so they should choose option 2

As the project progresses, the actual finish times (AFs) of completed activities play a crucial role in determining various aspects of the project schedule.

The AFs are used to calculate the earliest start and earliest finish times for the remaining activities in the network diagram. These calculations are based on the dependencies between activities and the actual durations of completed activities.

By considering the AFs, the project team can determine the earliest possible start and finish times for the remaining activities, taking into account the sequence of activities and any imposed constraints. This information helps in managing the project schedule and identifying any potential delays or critical paths.

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Ivan has created 9 sculptures.

We know, ratio is a comparison between two quantities or numbers. It expresses how many times one quantity is contained in another or how the two quantities relate to each other.

To find the number of sculptures he has created, we need to divide the number of paintings by the ratio of paintings to sculptures.

Number of paintings: 54

Ratio of paintings to sculptures: 6 paintings : 1 sculpture

Number of sculptures

= Number of paintings / Ratio of paintings to sculptures

= 54 / (6/1)

= 54 / 6

= 9

Therefore, Ivan has created 9 sculptures.

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The probability that the number is in set B is 20 %.

The probability that the number is in the set A ∪ B is 30 %.

If a number is chosen at random from the universal set, the probability that the number is in set B is calculated as follows;

The total number of outcome = {1, 2, 3, 4, 5, 6, 7, 8, 9 , 10} = 10 numbers

The numbers in set B = { 3, 7}

The probability = 2/10 = 1/5 = 20%

The probability that the number is in the set A ∪ B is calculated as follows;

A ∪ B = { 2, 3, 7 }

The probability = 3/10  = 30%

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The solution is: 90, 86, 92 and 89 could be Brooke’s sixth quiz score

Here, we have,

step 1

Find the mean

To do this, add all the numbers, then divide by the number of numbers there are.

so

mean = 85.60

step 2

if after taking the sixth quiz, Brooke’s mean score increased

then

the sixth score of Brooke's quiz must be higher than the mean obtained in the first 5 quizzes

case a)

85 < 85.60------> is not a solution

case b)

90 > 85.60------> is a solution

case c)

83< 85.60------> is not a solution

case d)

86 > 85.60------> is a solution

case e)

92 > 85.60------> is a solution

case f)

89 > 85.60------> is a solution

so, we get,

the answers are

90, 86, 92 and 89

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the complete question is

Brooke has scores of 84, 72, 90, 95, and 87 on her first five quizzes. After taking the sixth quiz, Brooke’s mean score increased.

Which could be Brooke’s sixth quiz score? Check all that apply.

85

90

83

86

92

89

Answer:

9

Step-by-step explanation:

Answer:

x = 9

Step-by-step explanation:

58 = 7x -5

Add + 5 to both sides

58+5 = 7x - 5 + 5

63 = 7x + 0

63 = 7x

Divide both sides by 7 to isolate the variable x.

63/7 = 7x/7

9 = x

So x = 9.

Check your answer:

7(9) - 5 = 63-5 = 58 so it works!

Step-by-step explanation:

To evaluate y when x = 2 in the equation y = -1/2x² + 6x + 5, we simply substitute x = 2 into the equation and solve for y:

y = -1/2(2)² + 6(2) + 5

y = -1/2(4) + 12 + 5

y = -2 + 12 + 5

y = 15

Therefore, when x = 2, y = 15 in the equation y = -1/2x² + 6x + 5.

We need to use the fact that the percentages of all three categories must add up to 100%. Therefore, the percentage of independent voters can be found by subtracting the percentages of democrat and republican voters from 100%.
Percentage of independent voters = 100% - 35% - 40% = 25%
So, 25% of the registered voters are independent.
In conclusion, the percentage of independent voters is 25%. This is because the percentages of democrat, republican, and independent voters must add up to 100%. The percentages of democrat and republican voters are given, so we can find the percentage of independent voters by subtracting those from 100%.
Based on the given information, 35% of registered voters are classified as Democrats, and 40% are classified as Republicans. To find the percentage of registered voters who are independent, we need to subtract the total percentage of Democrats and Republicans from 100%.
100% - (35% + 40%) = 100% - 75% = 25%
Therefore, 25% of the registered voters are classified as independent.

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There is only one triangle with sides measuring 3, 4, and 5.

When no side is specified, an infinite number of triangles are created.

If side lengths are not given, the three angles will result in an infinite number of triangles that are unique.

In this case the three sides of the triangle are specified and condition like this leads to formation of one unique triangle which a right triangle

This is a well known right triangle, the sides given is also known as a Pythagorean triple.

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Answer:

16 years

Step-by-step explanation:

We can use the formula for compound interest to solve this problem:

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

where A is the final amount, P is the principal (initial amount), r is the annual interest rate (as a decimal), n is the number of times per year the interest is compounded, and t is the number of years.

In this case, P = $5000, r = 0.05 (since the annual interest rate is 5%), n = 12 (since the interest is compounded monthly), and we need to solve for t when A = $6,568.52.

Plugging in the values, we get:

$6,568.52 = $5000(1 + 0.05/12)^(12t)

Dividing both sides by $5000 and taking the natural logarithm of both sides, we get:

ln(1.313704) = ln(1 + 0.05/12)^(12t)

Using the logarithmic identity ln(a^b) = b ln(a), we can simplify the right side:

ln(1.313704) = 12t ln(1 + 0.05/12)

Dividing both sides by 12 ln(1 + 0.05/12), we get:

t = ln(1.313704) / (12 ln(1 + 0.05/12)) = 16.0

Therefore, it will take Mr. Sanchez 16 years to have $6,568.52 in the college fund, if he does not make any deposits or withdrawals. The answer is 16 years.

Note that the  input value for which the statement f(x) = g(x) is true are

3.5 and 10/3

In this question , we have a graph given, and we have to find the x coordinate of the intersection point .

From the graph , the input value is approximately 3.3 .

In the graph, f(x) = 3

And for g(x), we need the slope and y intercept .

Slope is the ratio of rise and run .

Here rise equals 3 units and run equals 2 units. And the graph touch the y axis at -2 .

So the equation of g(x) = (3/2)x - 2

Since we need to factor f(x) = g(x)

Substituting the values of the two functions, we will get

3 =  (3/2)x - 2

Adding 2 to both sides

5 =  (3/2)x

Cross multiply and you have

10 = 3x

x = 10/3

So  the  input value for which the statement f(x) = g(x) is true are

3.5 and 10/3

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We can use the equation for the angle of the bright fringes in a double-slit experiment. The answer is D. 15.1o.

where θ is the angle of the bright fringe, m is the order of the fringe (in this case, m=3), λ is the wavelength of the incident light, and d is the distance between the slits.

Plugging in the given values, we get:

sinθ = (3)(5.04x10^-7m)/(5.82x10^-5m) = 0.260

Taking the inverse sine of both sides, we get:

θ = sin^-1(0.260) = 15.1o

Therefore, the answer is D. 15.1o.

To find the angle of the 3rd order bright fringe, we can use the formula for the double-slit interference pattern:

mλ = d * sinθ

where m is the order number (3 in this case), λ is the wavelength of the incident light (5.04x10^-7 m), d is the distance between the slits (5.82x10^-5 m), and θ is the angle we want to find.

First, rearrange the formula to solve for the angle:

sinθ = (mλ) / d

Now, plug in the given values:

sinθ = (3 * 5.04x10^-7 m) / 5.82x10^-5 m

Calculate the result:

sinθ = 0.02594

Now, find the inverse sine (arcsin) of the result to get the angle:

θ = arcsin(0.02594) ≈ 1.49°

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Answer:

Sure. Here are the steps on how to construct a confidence interval at a 95% confidence level for the mean amount spent on a child's last birthday gift:

Identify the sample size, n. In this case, n=13.

Identify the sample mean,  

x

ˉ

. In this case, $\bar{x} = $36.

Identify the sample standard deviation, s. In this case, $s = $15.

Identify the t-critical value, t. The t-critical value is the value that cuts off 2.5% of the distribution in each tail, leaving 95% of the distribution in the middle. To find the t-critical value, we need to know the degrees of freedom, df. The degrees of freedom are calculated as df=n−1. In this case, df=13−1=12.

We can find the t-critical value using a t-distribution table. The t-distribution table shows the t-critical values for different degrees of freedom and different confidence levels. For a 95% confidence level and 12 degrees of freedom, the t-critical value is 2.179.

Calculate the confidence interval. The confidence interval is calculated as follows:

$\bar{x} \pm t \cdot \frac{s}{\sqrt{n}}$

In this case, the confidence interval is:

$36 \pm 2.179 \cdot \frac{15}{\sqrt{13}} = (27.28, 44.72)$

Therefore, a 95% confidence interval for the mean amount spent on a child's last birthday gift is $27.28 to $44.72.

Step-by-step explanation:

The sum of the 4th and 6th square numbers is 52.

The formula for the nth square number is as below

n²

Using this formula we can find the 4th and 6th square numbers

4th square number = 4² = 16

6th square number = 6² = 36

The sum of the 4th and 6th square numbers is solved by addition

16 + 36 = 52

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(a) The probability of a random high school student having an IQ score between 60 and 75 points is approximately 0.186. (b) About 6.5% of high school students will require special attention based on IQ scores below 55 or above 100 points. (c) The cutoff IQ score to be a member of Mensa International is approximately 105.

To solve these problems, we will use the standard normal distribution, also known as the Z-distribution. We'll need to calculate z-scores and use the z-table or technology to find probabilities.

(a) To find the probability that a high school student chosen at random has an IQ score between 60 and 75 points, inclusive, we need to calculate the area under the normal curve between these two values.

First, we convert the IQ scores to z-scores using the formula:

z = (x - μ) / σ

where x is the value we want to convert, μ is the mean, and σ is the standard deviation.

For 60 points:

z1 = (60 - 80) / 12 = -1.6667

For 75 points:

z2 = (75 - 80) / 12 = -0.4167

Next, we use technology or a z-table to find the probabilities associated with these z-scores:

P(-1.6667 ≤ Z ≤ -0.4167)

Using technology or a z-table, the probability comes out to be approximately 0.186.

Therefore, the probability that a high school student chosen at random has an IQ score between 60 and 75 points, inclusive, is 0.186.

(b) To find the proportion of high school students who will need special attention, we need to calculate the area under the normal curve below 55 points (z ≤ (55 - 80) / 12) and above 100 points (z ≥ (100 - 80) / 12).

P(Z ≤ -2.0833) + P(Z ≥ 1.6667)

Using technology or a z-table, we find the probabilities:

P(Z ≤ -2.0833) ≈ 0.018

P(Z ≥ 1.6667) ≈ 0.047

Adding these probabilities, the proportion of high school students who will need special attention is approximately 0.018 + 0.047 = 0.065.

Therefore, about 6.5% of high school students will need special attention.

(c) To determine the cutoff IQ score to be a member of Mensa International, we need to find the value corresponding to the 98th percentile of the standard normal distribution.

We want to find the IQ score x such that P(Z ≤ z) = 0.98.

Using technology or a z-table, we find the z-score corresponding to a cumulative probability of 0.98 is approximately 2.055.

Now, we solve for x in the z-score formula:

2.055 = (x - 80) / 12

Simplifying and solving for x:

24.66 = x - 80

x = 24.66 + 80

x ≈ 104.66

Therefore, the cutoff IQ score to be a member of Mensa International would be 105 (rounded to the nearest whole number).

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When point O is between points M and N on line segment MN. O is the midpoint of line segment MN if

O ON + OM = MN

In geometry the midpoint is the point that divides a line segment into two equal parts

It is the point that is equal distance from both endpoints of the segment.

In this case the endpoints are M and N, the midpoint is point O, which is the point that is halfway between M and N, so that ON = OM. and adding the points returns the original line MN

Therefore, we have that ON + OM = MN

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Step-by-step explanation:

Decimal interset per period (day) = .05/365

# periods = 365 *6 = 2190

FV = 15800 ( 1 + .05/365)^2190  = 21327.33 Euros