What is the perimeter of triangle top

The compound amount for the deposit is $57,700 and the amount of interest earned is $41,700

We are given that the principal amount deposited is $16,000. The rate of interest on this amount will be 7% which will be compounded monthly for 19 years. Therefore, the values that we know are;

P (Principal amount) = $ 16,000

r(rate of interest) = 7%

t = 19 years

Now, in order to calculate the compound amount for the deposit, we will apply the formula of the compound amount and substitute the values that we know;

Amount = P( 1 + \(\frac{r}{100}\) \()^t\)

After substituting, the equation becomes;

Amount = 16000( 1 + \(\frac{7}{100}\) \()^{19}\)

Amount = 16000 (107/100\()^{19}\)

Amount = 16000 * 3.61

Amount = 57,700

This is the compound amount for the deposit. Now, to find out the amount of interest earned, we will subtract the principal amount from this amount.

So, compound Interest = 57,700 - 16,000

C.I = $41,700

Therefore, the compound amount for the deposit is $57,700 and the amount of interest earned is $41,700.

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Answer:

value of x +×+= - so 2 ¥ is an

The total number of different combinations Sam can make is 120.

The number of different ways that Sam can order the parts is given by the product of the number of choices he has for each part:

Chips: 2 options

Hard Drive: 4 options

Memory: 3 options

Accessory Bundle: 5 options

Therefore, the total number of different combinations Sam can make is 2 x 4 x 3 x 5 = 120.

This is about a person named Sam who is assembling a computer and has a choice of parts from different brands and stores. The problem is to calculate the number of different combinations of parts he can choose from. The solution involves finding the number of options he has for each part (chips, hard drive, memory, and accessory bundle) and then multiplying these numbers to get the total number of combinations.

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Among the given options, an R-squared value of 0.5 is the most satisfactory as it indicates a moderate level of relationship between the variables. So, the correct option is b.

R-squared is a statistical measure that represents the proportion of the variance in the dependent variable that can be explained by the independent variable(s). It ranges from 0 to 1, with 1 indicating a perfect fit and 0 indicating no relationship between the variables.
In this case, an R-squared value of 0.5 means that 50% of the variance in the dependent variable can be explained by the independent variable(s). This is considered a moderate level of explanatory power.

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With the applicatiοn οf Distributive Prοperty οf Multiplicatiοn, the fοllοwing equatiοn 3 (x + 2) + 5 can be written as

3*x + 3*2 + 5

The distributive prοperty οf multiplicatiοn is a mathematical rule that states that the prοduct οf a number and a sum can be οbtained by adding the prοducts οf the number and each term in the sum. In οther wοrds, a(b+c) = ab + ac. This prοperty can be used tο simplify expressiοns by breaking them dοwn intο smaller parts.

It is an impοrtant cοncept in algebra and is οften used tο sοlve equatiοns and simplify expressiοns. The distributive prοperty can alsο be applied tο variables and expοnents, and is a fundamental principle in the study οf algebraic structures such as rings and fields.

With the applicatiοn οf Distributive Prοperty οf Multiplicatiοn, the fοllοwing equatiοn 3 (x + 2) + 5 can be written as

3*x + 3*2 + 5

further simplified will give 3x + 6 + 5 = 3x + 11

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The mapping diagram above is a function since every element in set A is mapped to exactly one element in set B. There is no element in set A where there are two or more arrows pointing to different elements in set B.

We are given that;

Two sets table

Now,

A mapping from set A to set B represents a function if every element in set A is mapped to exactly one element in set B. That is, there should be no repeated elements in set A and no element in set A should have more than one arrow pointing to set B.

Looking at the mapping diagram, we can see that every element in set A is mapped to exactly one element in set B. There are no repeated elements in set A and no element in set A has more than one arrow pointing to set B.

Therefore, by the set  answer will be function.

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Answer:

3 student.

Step-by-step explanation:

From the first statement:

Let the total score be T

Let the total number of student be x

The average of the score = 72

Average = Tota score / number of student

72 = T/x

Cross multiply

T = 72x ..... (1)

Second statement:

One more student took the test and the average becomes 76 with the student having a score of 88.

Therefore,

Overall score = T + 88

Total student = x + 1

Average = 76

Average = overall score / total number of student

76 = (T + 88) /(x + 1)

Cross multiply

76(x + 1) = T + 88

Clear bracket

76x + 76 = T + 88

From equation 1

T = 72x

76x + 76 = 72x + 88

Collect like terms

76x – 72x = 88 – 76

4x = 12

Divide both side by the coefficient of x i.e 4

x = 12/4

x = 3

Therefore, the initial number of the student were 3.

Answer:

Not really sure but i i think it is not

Step-by-step explanation:

Answer:

x = 15

Step-by-step explanation:

the opposite angle of a cyclic quadrilateral sum to 180° , then

6x + 20 + 3x + 25 = 180

9x + 45 = 180 ( subtract 45 from both sides )

9x = 135 ( divide both sides by 9 )

x = 15

Answer:

x=15º

Step-by-step explanation:

Sum of quadrilateral interior angles;

(4x + 25) + (3x + 25) + (6x + 20) + 180-(4x + 25)=360

3x + 25 + 6x + 20 + 180 =360

9x = 360 - 225

9x = 135

   x = 15º

Answer:

5,8 or 8,5

Step-by-step explanation:

A arcade game gives 8 tickets this = y

For every 5 game played this = x

so we can make the assumption that every 5 games played he gets 8 tickets you can write this as 5,8 or. Every 5 game played is 8 tickets.

Answer:

f(-3) = 4

Domain: (-infinity, 4), Range: (-infinity, 4]

Step By Step Solution:

Value of f(-3):

Looking at the graph, at x = -3, there is a jump discontinuity, and there appears to be two values that f(-3) can equal.

At x = -3, from the left side, there is a closed circle at y = 4, and from the right side, there is an open circle at y = 3.

A closed circle denotes that the point IS included in the function, while an open circle denotes the point is NOT included in the function and that point is undefined.

Therefore, the value of f(-3) is 4, because (-3, 4) is included in the function.

Domain and range:

The domain represents the set of all x-values that exist for the function.

In this case, we can see that the function continues off the graph on the left side, meaning it continues on to -infinity. We see a jump discontinuity at x = -3, however, because f(-3) is defined, this will not affect the domain. The function continues to the right until x = 4, where there is an open circle.

An open circle denotes undefined, x = 4 is not included in the domain.

Putting everything together, the domain is:

D: (-infinity, 4)

* Note we used a parenthesis after 4. Parenthesis denote that 4 is not included in the answer, whereas a bracket denotes that 4 would be included. Parenthesis are used for infinity and -infinity due to there not being a defined answer for what infinity is, so we would not use a bracket for infinity.

The range represents the set of all y-values that exist for the function.

In this case, we can see on the left side that the function continues downwards, and approaches negative infinity. We can see there is a jump discontinuity when x = -3, and that there is an undefined point at y = 3. We can, however, see that at around x = -4, that y = 3 IS defined there, so this will not affect our range. We can see the highest point is y = 4, which has a closed circle, meaning it is included in the range.

Putting everything together, the range is:

R: (-infinity, 4]

* Note that this time, a bracket IS used. This is because y = 4 IS defined and included in the function's range

Answer:

3 pizzas

Step-by-step explanation:

First, we can calculate how many slices are necessary. Each person wants two slices, so for each person, we must add 2 slices. We can add 2 15 times, or multiply 2 by 15 to get 2 * 15 = 30

We now know that we need 30 slices of pizza. Next, we need to figure out how many pizzas we need given this information.

For each pizza, we can add 10 slices, as there are 10 slices of pizza.

For the first pizza, we have 10 slices

For the second, we have 10+10 = 20 slices

For the third, we have 10+10+10 = 10 * 3 = 30 slices. Perfect!

Another way of figuring out the number of pizzas we need would be to divide 30 by 10, and 30/10=3 would equal the number of pizzas. We need to figure out how many pizzas we need to have 30 slices, so we can divide here.

Answer:

3054.024cm^3

Step-by-step explanation:

Given data

Diameter= 18cm

Radius= 9cm

The expression for the volume of a sphere is given as

Volume = 4/3πr^3

Volume= 4/3*3.142*9^3

Volume= 4/3*3.142*729

Volume= 9162.072/3

Volume= 3054.024 cm^3

Hence the volume is 3054.024cm^3

Both methods, definition of surface integrals and evaluating the triple integral, yield the same result of zero, indicating that the surface integral of the vector field F over the unit sphere is zero.

The surface integral of the given vector field over the unit sphere can be computed using the definition of surface integrals or by evaluating the triple integral of an appropriate function.

a. Using the definition of surface integrals:

The outward normal at any point (x, y, z) on the unit sphere is a multiple of (x, y, z), which can be written as n = k(x, y, z), where k is a constant.

The surface integral is then given by:

∬S F · dS = ∬S (x(y² - 2² + 1)i + y(2² - x² + 1)j + z(x² - y² + 1)k) · (k(x, y, z) dS)

Since the unit sphere has radius 1, we can write dS = dA, where dA represents the area element on the sphere's surface.

The dot product between the vector field F and the outward normal k(x, y, z) simplifies to:

F · n = (x(y² - 2² + 1) + y(2² - x² + 1) + z(x² - y² + 1))k

By substituting dS = dA and integrating over the surface of the unit sphere, we have:

∬S F · dS = k ∬S (x(y² - 2² + 1) + y(2² - x² + 1) + z(x² - y² + 1)) dA

Integrating this expression over the unit sphere will result in zero since the integrand is an odd function with respect to each variable (x, y, z) and the sphere is symmetric.

b. Evaluating the triple integral:

Alternatively, we can compute the surface integral by evaluating the triple integral of an appropriate function over the region enclosed by the unit sphere.

Let's consider the function g(x, y, z) = x(y² - 2² + 1) + y(2² - x² + 1) + z(x² - y² + 1).

By using the divergence theorem, the triple integral of g(x, y, z) over the region enclosed by the unit sphere is equal to the surface integral of F over the unit sphere.

Applying the divergence theorem, we have:

∬S F · dS = ∭V ∇ · F dV

Since the divergence of F is zero (∇ · F = 0), the triple integral evaluates to zero.

Therefore, both methods yield the same result of zero, indicating that the surface integral of the vector field F over the unit sphere is zero.

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From the universal set; N = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17}

Probability of drawing an even or prime number will be 15/17.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event. The probability of all the events in a sample space adds up to 1.

N = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17}

Prime = {1,2,5,7,11,13,17}

Even = {2,4,6,8,10,12,14,16}

Pr(Prime) = 7/17

Pr(Even) = 8/17

Pr(Prime or even) = 7/17 + 8/17

Pr(Prime or even) = 15/17

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The probability that a randomly selected loan application takes longer than 13 days to process is 2/5 or 0.4.

Given that the time to process a loan application follows a uniform distribution over the range 7 to 17 days.

The standard uniform distribution is a special case of the beta distribution, with parameters (1,1).

We need to find the probability that a randomly selected loan application takes longer than 13 days to process.

Now, we need to calculate the probability using the formula of the uniform distribution:

P(X > 13) = (17 - 13) / (17 - 7) = 4/10 = 2/5

Therefore, the probability that a randomly selected loan application takes longer than 13 days to process is 2/5 or 0.4.

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The mean is 1.25. The median is 3 and the mode is purple.

a) It is possible to find the mean of the given colors.

b) It is possible to find the median of the given colors.

c) It is possible to find the mode of the given colors.

To calculate the mean, you would assign numerical values to each color and find the average. For example, purple = 1, red = 2, blue = 3, green = 4. Then, you would add up the numerical values and divide by the total number of colors.

To find the median, you would arrange the colors in order and find the middle value. If there is an even number of colors, you would take the average of the two middle values.

To find the mode, you would determine which color appears most frequently in the list. In this case, "purple" appears three times, which makes it the mode.

So, the mean is 1.25. The median is 3 and the mode is purple.

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a=6

c=6

d=6sqrt(3)

b=12

Hope this helped! :)

The quantity of substance remains after 850 years is 8.98g if the half life of radioactive radium is 1,599 years.

The time taken by substance to reduce to its half of its initial concentration is called half life period.

We will use the half- life equation N(t)

N e^{(-0.693t) /t½}

Where,

N is the initial sample

t½ is the half life time period of the substance

t2 is the time in years.

N(t) is the reminder quantity after t years .

Given

N = 13g

t = 350 years

t½ = 1599 years

By substituting all the value, we get

N(t) = 13e^(0.693 × 50) / (1599)

= 13e^(- 0.368386)

= 13 × 0.691

= 8.98

Thus, we calculated that the quantity of substance remains after 850 years is 8.98g if the half life of radioactive radium is 1,599 years.

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Fixed-Width is data format does each column start and end at the same place in every row.

What do statisticians mean by nominal data?

Nominal data have a quality?

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To find the optimal dimensions of the cylindrical metal can with a capacity of 1078 cm³ and minimize the surface area, we can use the concepts of calculus and optimization.

Let's denote the height of the can as h and the radius of the base as r. The volume V of the cylindrical can is given by V = πr²h, and the surface area A is given by A = 2πrh + πr².

We want to minimize A subject to the constraint V = 1078 cm³. We can express the surface area A in terms of a single variable by eliminating h using the volume constraint.

Substituting the volume constraint into the surface area equation, we have A = 2πr(1078/πr²) + πr².

Simplifying further, A = 2156/r + πr².

To find the optimal dimensions, we need to minimize A. We can do this by taking the derivative of A with respect to r, setting it equal to zero, and solving for r.

Differentiating A with respect to r, we get dA/dr = -2156/r² + 2πr.

Setting dA/dr = 0, we have -2156/r² + 2πr = 0.

Solving this equation, we find r = √(2156/2π) ≈ 9.86 cm.

Substituting this value of r back into the volume constraint, we can solve for h: h = V/(πr²) = 1078/(π(9.86)²) ≈ 3.46 cm.

Therefore, the optimal dimensions of the can for minimizing the surface area while having a capacity of 1078 cm³ are approximately a radius of 9.86 cm and a height of 3.46 cm.

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Answer:

4.104

Step-by-step explanation:

Volume of any prism = Area of cross section x height.

so, volume = 0.6 x 1.9 x 3.6 = 4.104

The functions are p(x) = b² - 16b +32 and q(x) = -32b-32 the x value when the functions are equivalent to each other is 8.

Given that,

The functions are p(x) = b² - 16b +32 and q(x) = -32b-32

We have to find the x value when the functions are equivalent to each other.

We know that,

Take the functions

p(x) = b² - 16b +32 and q(x) = -32b-32

When the function are equivalent

p(x) = q(x)

b² - 16b +32 = -32b-32

b² - 16b +32 +32b+32=0

b² + 16b +64 = 0

Now find the factors for 64

64 =  8×8

b² + 8b + 8b +64 = 0

Taking common terms

b(b + 8) + 8(b + 8)=0

(b + 8)(b + 8)=0

b=8

Therefore, The functions are p(x) = b² - 16b +32 and q(x) = -32b-32 the x value when the functions are equivalent to each other is 8.

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Answer:

(5x+49)

Step-by-step explanation:

hope that helps

The best conclusion for her to come to: D. this could easily happen with a fair coin after only 3 flips.

A fair coin can be defined as an idealized type of coin that has an equal probability of revealing both heads and tails when randomly tossed.

This ultimately implies that, the best conclusion for her to come to is that this could easily happen with a fair coin after only 3 flips considering 2 of the three coins come up tails.

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The value of n in the equation 1/2(n-4) - 3 = 3 - (2n+3) is 2.

To find the value of n in the equation 1/2(n-4) - 3 = 3 - (2n+3), we can solve the equation step by step.

Distribute the 1/2 and -3 on the left side of the equation:

\(1/2 \times n - 1/2 \times4 - 3 = 3 - (2n+3)\)

This simplifies to:

1/2n - 2 - 3 = 3 - 2n - 3

Combine like terms on both sides of the equation:

1/2n - 5 = -2n

Add 2n to both sides of the equation to isolate the n terms:

1/2n + 2n - 5 = -2n + 2n

This simplifies to:

2.5n - 5 = 0

Add 5 to both sides of the equation to isolate the n terms:

2.5n - 5 + 5 = 0 + 5

This simplifies to:

2.5n = 5

Divide both sides of the equation by 2.5 to solve for n:

(2.5n)/2.5 = 5/2.5

This simplifies to:

n = 2.

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Answer:

  (c)  the converse of the original conditional statement

Step-by-step explanation:

If a conditional statement is described by p→q, you want to know what is represented by q→p.

For the conditional p→q, the variations are ...

As you can see from this list, ...

  the converse of the original conditional statement is represented by q→p, matching choice C.

__

Additional comment

If the conditional statement is true, the contrapositive is always true. The inverse and converse may or may not be true.

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The critical point (0,0) is a stable node

The Jacobian matrix for the given system

J = | ∂dx/∂x  ∂dx/∂y | | ∂dy/∂x  ∂dy/∂y |

Here are the partial derivatives of the system equations

dx = - 4x- 10y - x² - y² dt and dy = 10x + 16y - 3xy dt

∂dx/∂x = -4 - 2x

∂dx/∂y = -10 - 2y

∂dy/∂x = 10 - 3y

∂dy/∂y = 16 - 3x

Now, let's evaluate the Jacobian matrix at (0,0)

J(0,0) = | -4 -10 | | 10 16 |

To find the eigenvalues, we need to compute the characteristic equation

det(J(0,0) - λI) = 0,

where λ represents the eigenvalue and I is the identity matrix.

Substituting the values from the Jacobian matrix, we get

| -4-λ -10 | | -4-λ -10 | = (λ+4) (λ+16) + 100

λ² + 20λ + 84 = 0

Now we solve this quadratic equation for λ

λ² + 20λ + 84 = 0.

Using the quadratic formula, we have

λ = (- b ± √b²-4ac)/2a

b = 20 , a = 1 , c = 84

λ = (-20 ± √(20² - 4×84×1)) / (2×1)

λ = (-20 ± √(400 - 336)) / 2

λ = (-20 ± √64) / 2

λ = (-20 ± 8) / 2

λ = -10 ± 4.

So the eigenvalues are λ₁ = -10 + 4 = -6 and λ₂ = -10 - 4 = -14.

Both eigenvalues have negative real parts (-6 and -14). Therefore, the critical point (0,0) is a stable node.

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