evaluate begin inline style sum from n equals 3 to 7 of end style left parenthesis n squared plus 2 n right parenthesis .

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.

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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This is a translation of 2 units to the left and 5 units up, so the correct option is the first one.,

Remember that a vertical translation of N units is:

g(x) = f(x) + N

if N < 0 the translation is down.

if N > 0 the translation is up.

And a horizontal translation of N units is:

g(x) = f(x + N)

If N > 0 the translation is to the right.

if N < 0 the translation is to the left.

Here we have the transformation:

f(x) = x²

g(x) = (x + 2)² + 5

So this is a translation of 2 units to the left and 5 units up.

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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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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.

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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Answer:

6 cups

Step-by-step explanation:

When two things are directly proportional (e.g. y and x), we can model the relationship with the direct variation equation, which is

y = kx, where

Step 1:  To find k, we can allow y to represent Jackie's total revenue from selling lemonade ($9) and x to represent the quantity of cups of lemonade sold ($3):

9 = 3k

k = 3

Step 2:  Now that we've found the constant of proportionality, we can plug in 18 for y and 3 for k, allowing us to solve for x:

18 = 3x

6 = x

Thus, in order for Jackie to earn $18, she must sell 6 cups in all.

The angular velocity of the connecting rod is w = 1.939 rad/s

Given data ,

To determine the angular velocity of the connecting rod CD at the instant angle θ = 30 degrees, we need to consider the relationship between the angular velocities of different components in a mechanism. In this case, we can use the concept of relative velocity

The angular velocity of the connecting rod CD can be found using the following equation

ω_CD = ω_AB + ω_BC

angular velocity of CD = angular velocity of AB x (AB/CD) x sin(u) x (1/cos(u))

angular velocity of CD = 4 rad/s x (10/20) x sin(30) x (1/0.825)

Therefore , the angular velocity is CD = 1.939 rad/s

Hence , the angular velocity is w = 1.939 rad/s

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Gaurav bought 500 mangoes for Rs. 1000, which means that he bought each mango for Rs. 2.

He packed the mangoes into small boxes with 25 in each, so he made a total of 500/25 = 20 boxes.

He sells each box for Rs. 60, so he makes a total of 20 x Rs. 60 = Rs. 1200 from selling all the boxes.

To find the profit, we need to subtract the cost of the mangoes from the total revenue.

The cost of 500 mangoes was Rs. 1000, so the profit is:

Profit = Rs. 1200 - Rs. 1000 = Rs. 200

Therefore, Gaurav made a profit of Rs. 200 by selling the mangoes.

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Answer: 6

Step-by-step explanation:

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

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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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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Answer:

To find the perimeter of a scale drawing, we need to use the same scale factor that was used to create the drawing. In this case, the scale factor is 7 inches: 28 feet, or 1 inch: 4 feet. This means that every inch in the drawing represents 4 feet in the actual floor.

To find the perimeter of the floor in the scale drawing, we need to add up the lengths of all the sides. Since the floor is rectangular, it has two pairs of equal sides. The length of the floor is 28 feet, so the length of the scale drawing is 28 / 4 = 7 inches. The width of the floor is 24 feet, so the width of the scale drawing is 24 / 4 = 6 inches.

The perimeter of the scale drawing is then:

7 + 6 + 7 + 6 = 26 inches

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The numbers that are elements of both the subset of odd numbers and the subset of multiples of 3 are 3 and 9.

The odd numbers in the set are {1, 3, 5, 7, 9} and the multiples of 3 in the set are {3, 6, 9}.

The elements that are in both subsets are the ones that appear in both sets, which are only 3 and 9.

Therefore, the numbers 3 and 9 are the elements that are in both the subset of odd numbers and the subset of multiples of 3.

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The percentage of Mr. Reyes total compensation that was withheld for federal taxes is given as follows:

14.2%.

From the table, we have that the parameters for this problem are given as follows:

Hence the proportion of Mr. Reyes total compensation that was withheld for federal taxes is given as follows:

8802.26/61987.5 = 0.142.

Then the percentage is given as follows:

0.142 x 100% = 14.2%.

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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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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:

Use the quotient property of logarithms, logb(x)−logb(y)=logb(xy) log b ( x ) - log b ( y ) = log b ( x y ) . log3(4010) log 3 ( 40 10 ). Step 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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Answer: 90

Step-by-step explanation:

The exponential function has a horizontal asymptote at y = –3 will be; f (x) = –3^x – 3.

We get a horizontal asymptote for a function;

Note that the x-axis (y=0) is the horizontal asymptote.

Since the question asked for a function with asymptotic behaviors of y = -3,

we can shift the function 3 units above by changing Q to +3.

The exponential function has a horizontal asymptote at y = –3 will be;

f (x) = –3^x – 3.

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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 pairs of simultaneous equations have their x and y values to be (a) x+y=5 and xy=x+3: (1, 4) and (2, 3) & (b) 2x+y=5 and x² + y² =10: (x, y) = (1, 3) and (3, -1)

From the question, we have the following parameters that can be used in our computation:

The pairs of simultaneous equations can be solved using a graphical method

Using the above as a guide, we have the following:

(a) x+y=5 and xy=x+3

x and y values:

(x, y) = (1, 4) and (2, 3)

(b) 2x+y=5 and x² + y² =10

x and y values:

(x, y) = (1, 3) and (3, -1)

See attachment for graphs

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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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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:

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 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

The graph that correctly represents the data in the table for this problem is given as follows:

Top right graph.

On the definition of a function, the y-intercept is given by the value of y for which the input assumes a value of zero.

Hence, on the graph of a function, the y-intercept is the value of y for which the graph touches or crosses the y-axis.

From the table, we have that when x = 0, y = 4, hence the graph should cross the y-axis at y = 4, hence the top right graph is the correct option in the context of this problem.

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Nakeisha sold 8 lollipops and 5 fruit snacks yesterday to earn a total of $18.25.

Let's use a system of equations to solve this problem. Let x be the number of lollipops sold and y be the number of fruit snacks sold. From the problem, we know that:
- The price of each lollipop is $1.50, so the total amount of money earned from selling x lollipops is 1.5x.
- The price of each fruit snack is $1.25, so the total amount of money earned from selling y fruit snacks is 1.25y.
- Yesterday, Nakeisha made $18.25 from selling a total of 13 lollipops and fruit snacks, so we can write the equation:
1.5x + 1.25y = 18.25
We also know that Nakeisha sold a total of 13 lollipops and fruit snacks, so we can write the equation:
x + y = 13
Now we have two equations with two variables, which we can solve using substitution or elimination. Let's use substitution:
- Rearrange the second equation to solve for one variable in terms of the other:
x + y = 13
y = 13 - x
- Substitute y = 13 - x into the first equation:
1.5x + 1.25y = 18.25
1.5x + 1.25(13 - x) = 18.25
- Simplify and solve for x:
1.5x + 16.25 - 1.25x = 18.25
0.25x = 2
x = 8
- Substitute x = 8 back into y = 13 - x to find y:
y = 13 - x
y = 13 - 8
y = 5
Therefore, Nakeisha sold 8 lollipops and 5 fruit snacks yesterday to earn a total of $18.25.

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