Look at the picture below

The answer double will be of 8 is 16, by multiplication.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

The fundamental concept of repeatedly adding the same number is embodied in the process of multiplication. The outcome of multiplying two or more numbers is known as the product of those numbers, and the factors that are multiplied are referred to as the factors. The process of repeatedly adding the same number is made easier by multiplication.

So the double of 8 means adding 2 two times. Or multiplying 8 with 2

8*2 = 16

Hence, double will be of 8 is 16

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Answer:

The solution of such a system is the ordered pair that is a solution to both equations. To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.

Step-by-step explanation:

Answer:

x = 24

Step-by-step explanation:

\(\frac{6+x}{3}\)  = \(\frac{x}{4}\) + 4  Multiply though by 12 to clear the fraction

4(6 + x) = 3x + 48  Distribute the 4)

24 + 4x = 3x + 48  Subtract 3x from both sides of the equation

24 + x = 48  Subtract 24 from both sides.

x = 24

From the situation described in the problem, we have that:

a) The system of inequalities is given by: s + a ≤ 800, 4s + 7a ≥ 3400.

b) The solution is graphed at the end of the answer.

c) Yes, the club could meet it's goal.

A system of inequalities is when multiple variables are related in a described situation, and then inequalities are built to find the interval ranges of each variable, according to the relations built.

In the context of this problem, the variables are given as follows:

The auditorium has 800 seats, hence:

s + a ≤ 800.

They have a goal of making at least $3400, hence, considering the price of the tickets, we have that:

4s + 7a ≥ 3400.

The graphical solution of the inequality is given by the painted region on the graph, and since point (200, 475) is inside the region, the club could meet it's goal.

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The endpoints of the directed line segment QR are Q(8, 4) and R. (-2, -1).The x-coordinates of P is 6.2 and y-coordinates of P is 1.4.

Given that,

The endpoints of the directed line segment QR are Q(8, 4) and R. (-2, -1).

We have to find the coordinates of the QR line segment aimed at point P along that QP to PR is a 1 to 4 ratio.

QR has the endpoints Q(8, 4) and R. (-2, -1).

Line segment QR divides at point P in ratio 1:4.

Using section formula:

The section formula provides the coordinates of a point that, either internally or externally, divides the line connecting two locations in a ratio.

P(x,y)=\((\frac{mx_{2} +nx_{1} }{m+n},\frac{my_{2} +ny_{1} }{m+n},)\)

Where m is 1 and n is 4. x₁=8,y₁=4 and x₂=-2,y₂=-1.

Substitute in the formulae we get,

P(x,y)=((1×-1+4×8)/1+4,(1×-1+4×4/1+4))

P(x,y)=((-1+32)/5,(-1+8)/5)

P(x,y)=(31/5,7/5)

P(x,y)=(6.2, 1.4)

Therefore, the x-coordinates of P is 6.2 and y-coordinates of P is 1.4

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Answer:

y = -1/12 x + 11/3

Step-by-step explanation:

do you need one?

Answer:

y=-1/12x+11/3

Step-by-step explanation:

When a line is perpendicular, the slope is going to be the negative reciprocal

negative reciprocal ex: 3----> -1/3

since the slope of line you are given is 12, the slope of the perpendicular line is -1/12

so you now know your equation so far is y= -1/12x+b

to find b, replace x and y with the coordinates.

4= -1/12(-4)+b

4=1/3+b

11/3=b

the equation is y=-1/12x+11/3

Answer:

√{99×33×3}=√{33×3×33×3}=√(33²×3²)=±33×3=±99

Answer:

99

Step-by-step explanation:

Cause 33×3=99 ,and the function of the root is to get the number that we multiply it ti itself

For example \(\sqrt{4}\) =2 cause 2×2=4 ,so\(\sqrt{2*2}\) =\(\sqrt{4}\) which is =2

so \(\sqrt{99^{2} }\) =99

Answer:

The equation of the line is:

\(y = -3x+10\)

The graph is attached below.

Step-by-step explanation:

Given that the line has a slope of -3, so

m = -3

As the point contains the point (4, -2), so we can use the point-slope form of the line equation to determine the line.

Point slope form:

\(y-y_1=m\left(x-x_1\right)\)

where m is the slope of the line and (x₁, y₁) is the point

so substituting the values m = -3 and the point (4, -2)

\(y-y_1=m\left(x-x_1\right)\)

\(y - (-2) = -3(x-4)\)

\(y+2 = -3x+12\)

\(y = -3x+12-2\)

\(y = -3x+10\)

Therefore, the equation of the line is:

\(y = -3x+10\)

The graph is attached below.

There are 6 possible outcomes when rolling a single standard six-sided number cube: 1, 2, 3, 4, 5, or 6. When rolling two number cubes, the possible sums range from 2 (1+1) to 12 (6+6).

To find the number of ways to roll a sum of 7, we need to look at all the possible combinations of numbers on the two cubes that add up to 7. These are: 1+6, 2+5, 3+4, 4+3, 5+2, and 6+1. Therefore, there are 6 ways to roll a sum of 7 when rolling two standard six-sided number cubes.

To determine how many ways Tre can roll a sum of 7 using two standard six-sided number cubes, we'll consider the possible outcomes:

1. First cube shows 1, second cube shows 6 (1+6=7)
2. First cube shows 2, second cube shows 5 (2+5=7)
3. First cube shows 3, second cube shows 4 (3+4=7)
4. First cube shows 4, second cube shows 3 (4+3=7)
5. First cube shows 5, second cube shows 2 (5+2=7)
6. First cube shows 6, second cube shows 1 (6+1=7)

There are 6 different ways Tre can roll a sum of 7 using two standard six-sided number cubes.

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Answer:

the answer is B

Step-by-step explanation:

8 + 14 = 2(4 + 7)

Answer:

A history

Step-by-step explanation:

Answer:

a=7

Step-by-step explanation:

The image is rendered and attached below.

Triangle WXY is an Isosceles right triangle, since WX=XY.

First, we determine the length of WY using Pythagoras Theorem.

\(WY=\sqrt{4^2+4^2}\\WY=\sqrt{32}\)

Since triangle WXY is Isosceles, \(\angle XYW=45^\circ\)

\(\angle XYZ=\angle XYW+\angle WYZ\\135^\circ=45^\circ+\angle WYZ\\\angle WYZ=135^\circ-45^\circ=90^\circ\)

Therefore:

Triangle WYZ is a right triangle with WZ as the hypothenuse.

Applying Pythagoras Theorem

\(WZ^2=WY^2+YZ^2\\9^2=(\sqrt{32})^2+a^2\\a^2=81-32\\a^2=49\\a^2=7^2\\$Therefore: a=7\)

The value of a in the triangle illustrated is 7.

From the information, the length of WY will be:

WY = ✓4² + ✓4²

WY = ✓32

Therefore, angle WYZ will be:

= 135° - 45°

= 90°

Therefore, the value of a will be calculated thus:

a² = 9² - (✓32)²

a² = 81- 32

a = ✓49

a = 7

In conclusion, the value of a is 7.

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The approximation for the function g(4.2) is 12.44

From the table, we know that g'(4) = 2.2

g (4) = 12

Using the line tangent to the graph of g at x=4 ,

g (4.2)  = g (4 ) + (4.2 -4 )2.2

           = 12 + 0.44

           = 12.44

The approximation for the function g(4.2) is 12.44. So ,option A is correct.

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To calculate the weight of the lead cylinder, we need to determine its volume first. The volume of a cylinder can be calculated using the formula: Volume = π * r^2 * h

Given that the diameter of the cylinder is 2 inches, the radius (r) is 1 inch. The height (h) is 4 inches.

Substituting these values into the formula, we get:

Volume = 3.14159 * 1^2 * 4

Volume = 12.56636 cubic inches

Now, to calculate the weight, we multiply the volume by the weight per cubic inch of lead:

Weight = Volume * Weight per cubic inch

Weight = 12.56636 * 0.04

Weight = 0.5026544 pounds

Therefore, the weight of the lead cylinder is approximately 0.5027 pounds.

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The antiderivative of sin is -cos(x) + C.

The antiderivative of a function is the inverse operation of differentiation which is is also known as its indefinite integral.

So, the integral of sin

                 ∫sin(x) = -cos(x) + C

where C = constant of integration.

This can be verified by differentiating -cos(x) + C with respect to x, which gives sin(x).

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Answer:

\( \purple { \bold{ \frac{ (x - 3)}{3x - 18} }}\)

Step-by-step explanation:

\( \frac{x + 3}{ {x}^{2} + 7x + 12 } . \frac{ {x}^{2} + x - 12}{3x - 18} \\ \\ = \frac{x + 3}{ {x}^{2} + 4x + 3x + 12 } . \frac{ {x}^{2} + 4x - 3x - 12}{3(x - 6)} \\ \\ = \frac{x + 3}{ {x}(x + 4) + 3(x + 4) } . \frac{ {x}(x + 4) - 3(x + 4)}{3(x - 6)} \\ \\ = \frac{ \cancel{(x + 3)}}{ (x + 4) \cancel{(x + 3)} } . \frac{ (x + 4) (x - 3)}{3(x - 6)} \\ \\ = \frac{1}{ \cancel{ (x + 4)} } . \frac{ \cancel{ (x + 4)} (x - 3)}{3(x - 6)} \\ \\ \red{ \bold{= \frac{ (x - 3)}{3x - 18} }}\\ \\ \)

The best first step in calculating an inferential statistic for the given scenario would be to calculate the mean for older siblings.

To compare the motivation to succeed between older and younger siblings, the first step is to compute descriptive statistics for each group separately. In this case, we are interested in determining if older siblings have greater motivation.

Calculating the mean for older siblings will provide an initial understanding of the central tendency of their motivation scores. By taking the average of their responses on the 1-7 scale, we can obtain a measure of their typical motivation level.

Further statistical analysis, such as hypothesis testing or calculating effect sizes, can be performed using the mean values of both older and younger siblings. However, the initial step is to calculate the mean for older siblings to establish a baseline understanding of their motivation level.

In the given scenario, the best first step in calculating an inferential statistic is to calculate the mean for older siblings. This provides a starting point to compare their motivation to succeed with that of their younger siblings.

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complete question- When should you calculate and use a "weighted average" for pooled variance in an inferential t-test? When sample sizes are equal. When sample sizes are unequal: When data is invalid. When data is unreliable: Question 17 1 pts A researcher wants to know if older siblings have greater motivation to succeed than their younger siblings. The researcher asks a group of 50 sibling pairs how motivated they are to succeed on a scale of 1-7. As discussed in lecture, what would be the best first step in calculating an inferential statistic? Calculate the standard deviation for older siblings. Calculate the mean for younger siblings. Calculate the mean for older siblings. Subtract the motivation of younger sibling from the other (older sibling).

The number of regular sodas served is 12.

Percentage is the fraction of an amount that is expressed as a number out of hundred. The sign that is used to represent percentage is %. Percentage is a measure of frequency.

Number of regular sodas served = percentage of regular sodas served x number of sodas served

= 25% x 48

= 25/100 x 48 = 12

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The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input.

The collection of all potential inputs for a function is its domain. For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.

Think about the function y = f. (x). The range of the function is the range of all the y values, from least to maximum. Substitute all possible values of x into the provided expression of y to see whether it is positive, negative, or equal to other values.

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The velocity of the top of the ladder is 20.62 feet per second.

We can use the Pythagorean theorem to relate the distance between the wall and the base of the ladder to the height of the ladder. Let h be the height of the ladder, then we have:

h² + 7² = 25²

h² = 576

h = 24 feet

We can then use the chain rule to find the velocity of the top of the ladder. Let v be the velocity of the base of the ladder, then we have:

h² + (dx/dt)² = 25²

2h (dh/dt) + 2(dx/dt)(d²x/dt²) = 0

Simplifying and plugging in h = 24 and dx/dt = -2, we get:

(24)(dh/dt) - 2(d²x/dt²) = 0

Solving for (d²x/dt²), we get:

(d²x/dt²) = (12)(dh/dt)

We can find (dh/dt) using the Pythagorean theorem and the fact that the ladder is sliding down the wall at a rate of 2 feet per second:

h² + (dx/dt)² = 25²

2h(dh/dt) + 2(dx/dt)(d²x/dt²) = 0

Substituting h = 24, dx/dt = -2, and solving for (dh/dt), we get:

(dh/dt) = -15/8

Finally, we can find (d²x/dt²) by plugging in (dh/dt) and solving:

(d²x/dt²) = (12)(dh/dt) = (12)(-15/8) = -45/2

Therefore, the velocity of the top of the ladder is 20.62 feet per second.

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Answer:

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

Where:

A = the final amount

P = the initial balance

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

We know that P = $3500, A = $4390.40, r = unknown, n = 1 (compounded annually), and t = 2. Plugging in these values and solving for r:

$4390.40 = $3500(1 + r/1)^(1*2)

$4390.40/$3500 = (1 + r)^2

1.2544 = (1 + r)^2

√1.2544 = 1 + r

1.12 = 1 + r

r = 0.12 or 12%

Therefore, the annual interest rate is 12%.

To find the percentage, we can use the following formula:

Percentage = (Part / Whole) * 100

So, $131,701.32 is approximately 16.67% of $790,207.91.

In this case, the part is $131,701.32 and the whole is $790,207.91.

Percentage = ($131,701.32 / $790,207.91) * 100

Calculating the value:

Percentage ≈ 0.1667 * 100

Percentage ≈ 16.67%

Therefore, $131,701.32 is approximately 16.67% of $790,207.91.

Alternatively, we can calculate the percentage by dividing the part by the whole and multiplying by 100:

Percentage = ($131,701.32 / $790,207.91) * 100 ≈ 0.1667 * 100 ≈ 16.67%

So, $131,701.32 is approximately 16.67% of $790,207.91.

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b) It will take approximately 24.6 years to save $3,000 for your vacation by saving $100 each month with a 3% nominal interest rate compounded monthly.

c) equivalent effective interest rates are:

i. Semi-annually: 5.06%

ii. Quarterly: 5.11%

iii. Daily: 5.13%

iv. Continuously: 5.13%

EXPLANATION:

To calculate the time it will take for you to save $3,000 for your vacation, we can use the future value formula for monthly compounding:

\(Future Value = Principal * (1 + rate/n)^(n*time)\)

Where:

- Principal is the amount you save each month ($100)

- Rate is the nominal interest rate (3% or 0.03)

- n is the number of compounding periods per year (12 for monthly compounding)

- Time is the number of years we want to calculate

We need to solve for time. Let's substitute the given values into the formula:

\($3,000 = $100 * (1 + 0.03/12)^(12*time)Dividing both sides of the equation by $100:30 = (1.0025)^(12*time)\)

Taking the natural logarithm (ln) of both sides:

\(ln(30) = ln((1.0025)^(12*time))Using logarithmic properties (ln(a^b) = b * ln(a)):ln(30) = 12*time * ln(1.0025)\)

Solving for time:

\(time = ln(30) / (12 * ln(1.0025))\)

Using a calculator:

time ≈ 24.6

c)To calculate the equivalent effective interest rate for a nominal rate of 5% compounded at different intervals:

i. Semi-annually:

The effective interest rate for semi-annual compounding is calculated using the formula:

Effective Interest Rate = (1 + (nominal rate / number of compounding periods))^number of compounding periods - 1

For semi-annual compounding:

\(Effective Interest Rate = (1 + (0.05 / 2))^2 - 1\)

Calculating:

Effective Interest Rate ≈ 0.050625 or 5.06%

ii. Quarterly:

The effective interest rate for quarterly compounding is calculated similarly:

\(Effective Interest Rate = (1 + (0.05 / 4))^4 - 1\)

Calculating:

Effective Interest Rate ≈ 0.051136 or 5.11%

iii. Daily:

The effective interest rate for daily compounding is calculated using the formula:

Effective Interest Rate = (1 + (nominal rate / number of compounding periods))^number of compounding periods - 1

Since there are approximately 365 days in a year:

\(Effective Interest Rate = (1 + (0.05 / 365))^365 - 1\)

Calculating:

Effective Interest Rate ≈ 0.051267 or 5.13%

iv. Continuously:

The effective interest rate for continuous compounding is calculated using the formula:

\(Effective Interest Rate = e^(nominal rate) - 1\)

For a nominal rate of 5%:

\(Effective Interest Rate = e^(0.05) - 1\)

Calculating:

Effective Interest Rate ≈ 0.05127 or 5.13%

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The product in scientific notation is 1.36 x 10^22

The product expression is given as:

3.2 x 1012 and 4.25 x 109

Express the product, properly

3.2 x 10^12 x 4.25 x 10^9

Regroup the factors

3.2  x 4.25 x 10^12 x 10^9

Evaluate the product

13.6 x 10^21

Rewrite as:

1.36 x 10^22

Hence, the product in scientific notation is 1.36 x 10^22

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Answer:

c 1.36 x 1012

explanation:

Answer:

x- intercept=6/2=3

y-intercept=6/3=2

Step-by-step explanation:

Given:

The general equation of tangent line is:

Where,

Solpe of line is:

slope of tangent line is -6

then equation of tengent line is: