Tanika was born in 2003 .According to her most recent Social Security Statement, her monthly benefit at full retirement will be $1,990 per month.
If she delays claiming Social security until age 69, her benefit will increase to

Answer:

210 + -1x

Step-by-step explanation:

Simplifying

X + (x + -30) = 180

Reorder the terms:

X + (-30 + x) = 180

Remove parenthesis around (-30 + x)

X + -30 + x = 180

Reorder the terms:

-30 + X + x = 180

Solving

-30 + X + x = 180

Solving for variable 'X'.

Move all terms containing X to the left, all other terms to the right.

Add '30' to each side of the equation.

-30 + X + 30 + x = 180 + 30

Reorder the terms:

-30 + 30 + X + x = 180 + 30

Combine like terms: -30 + 30 = 0

0 + X + x = 180 + 30

X + x = 180 + 30

Combine like terms: 180 + 30 = 210

X + x = 210

Add '-1x' to each side of the equation.

X + x + -1x = 210 + -1x

Combine like terms: x + -1x = 0

X + 0 = 210 + -1x

X = 210 + -1x

Simplifying

X = 210 + -1x

Answer:

25.12

Step-by-step explanation:

Radius=4

4x2=8

Diameter=8

8x3.14= 25.12

Two different ways to write f dA as an iterated integral for the shaded region R. 1 + R 1, in the order dy dx and dx dy.

To write f dA as an iterated integral in two different ways for the shaded region R. 1 + R 1, we need to first determine the limits of integration for each variable.

If we start with the order dy dx, we can see that the shaded region is bounded by y = 0, y = 2, x = 1 and x = 2. Therefore, we can write the integral as follows:

f dA = ∫∫R f(x,y) dy dx
= ∫1^2 ∫0²-x f(x,y) dy dx + ∫2³ ∫0 f(x,y) dy dx
= ∫1^2 [∫0²-x f(x,y) dy] dx + ∫2³ [∫0 f(x,y) dy] dx
(Note: We split the integral into two parts based on the two different regions.)

Alternatively, if we switch the order to dx dy, we can see that the shaded region is bounded by x = 1, x = 2, y = x-1 and y = 2. Therefore, we can write the integral as follows:

f dA = ∫∫R f(x,y) dx dy
= ∫0 ∫x+1² f(x,y) dy dx + ∫1² ∫1 f(x,y) dx dy
= ∫0 [∫x+1² f(x,y) dy] dx + ∫1² [∫1 f(x,y) dx] dy
(Note: We split the integral into two parts based on the two different regions.)

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Two different ways to write f dA as an iterated integral for the shaded region R. 1 + R 1, in the order dy dx and dx dy.

To write f dA as an iterated integral in two different ways for the shaded region R. 1 + R 1, we need to first determine the limits of integration for each variable.

If we start with the order dy dx, we can see that the shaded region is bounded by y = 0, y = 2, x = 1 and x = 2. Therefore, we can write the integral as follows:

f dA = ∫∫R f(x,y) dy dx
= ∫1^2 ∫0²-x f(x,y) dy dx + ∫2³ ∫0 f(x,y) dy dx
= ∫1^2 [∫0²-x f(x,y) dy] dx + ∫2³ [∫0 f(x,y) dy] dx
(Note: We split the integral into two parts based on the two different regions.)

Alternatively, if we switch the order to dx dy, we can see that the shaded region is bounded by x = 1, x = 2, y = x-1 and y = 2. Therefore, we can write the integral as follows:

f dA = ∫∫R f(x,y) dx dy
= ∫0 ∫x+1² f(x,y) dy dx + ∫1² ∫1 f(x,y) dx dy
= ∫0 [∫x+1² f(x,y) dy] dx + ∫1² [∫1 f(x,y) dx] dy
(Note: We split the integral into two parts based on the two different regions.)

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Answer:

11.92418

Step-by-step explanation:

I hope it's right sorry if it's not.

Answer: 4

Step-by-step explanation:

Given:

To draw the graph:

Let us find the slope as the ratio.

Comparing the given equation with y=mx+c

So, the slope m=4.

In ratio,

Let us take two points, (0,0) and (1,4).

So, the graph is,

The set S = {(6, 7, 1), (−3, 4, 7), (1, −3, 4)} spans  R³

For (x, y, z) ∈ R³, we can find scalars a, b, c for which the equation

(x, y, z) = a(6, 7, 1) + b (−3, 4, 7) + c (1, −3, 4) is true.

We can write above equation (x, y, z) = a(6, 7, 1) + b (−3, 4, 7) + c (1, −3, 4)  as system of equations,

6a - 3b + c = x

7a + 4b - 3c = y

a + 7b + 4c = z

Above system of equations in matrix form as,

\(\begin{bmatrix}6 & -3 & 1 \\7 & 4 & -3 \\1 & 7 & 4\end{bmatrix}\begin{bmatrix}a\\b \\c\end{bmatrix}=\begin{bmatrix}x \\y \\z\end{bmatrix}\)

The determinant of coefficient matrix is,

\(\left|\begin{matrix}6 & -3 & 1 \\7 & 4 & -3 \\1 & 7 & 4\end{matrix}\right|=360\)

Since the determinant of the coefficient matrix is not zero (it equals 360), the coefficient matrix is invertible.

This means, the system of equations must have solution.

Therefore, S = {(6, 7, 1), (−3, 4, 7), (1, −3, 4)} spans  R³

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The correct answer is (b) divide the sum of the cross-products of Z scores by the sample size.

When calculating the correlation coefficient, also known as Pearson's correlation coefficient, the last step involves dividing the sum of the cross-products of Z scores by the sample size. The correlation coefficient measures the strength and direction of the linear relationship between two variables.

To calculate the correlation coefficient, we follow these steps:

Standardize the variables: Convert the raw scores of each variable into Z-scores. The Z-score represents the number of standard deviations a particular score is from the mean. This step is done to put both variables on the same scale and make them comparable.

Calculate the cross-products: Multiply the Z-scores of the corresponding pairs of observations. This step gives us the cross-products of Z-scores for each pair of observations.

Sum the cross-products: Add up all the cross-products of Z-scores.

Divide by the sample size: Divide the sum of the cross-products of Z-scores by the sample size. The sample size represents the number of paired observations used in the analysis.

By dividing the sum of the cross-products by the sample size, we obtain the covariance of the variables. The covariance measures the extent to which the variables vary together. However, the covariance itself is not sufficient to determine the strength and direction of the relationship.

The final step involves dividing the covariance by the product of the standard deviations of the variables. This step normalizes the covariance and results in the correlation coefficient, which is a value between -1 and 1. The correlation coefficient indicates the strength and direction of the linear relationship between the variables. A positive correlation coefficient indicates a positive linear relationship, a negative correlation coefficient indicates a negative linear relationship, and a correlation coefficient close to zero indicates a weak or no linear relationship.

Therefore, the last step in calculating the correlation coefficient is to divide the sum of the cross-products of Z-scores by the sample size.

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Answer:

Jackie cut the cake into ten equal pieces, so each piece is 1/10 of the original cake.

If she had four-tenths of the cake left after dinner, then she had 6/10 of the cake left.

She wrapped a piece that was one-fifth of the original cake for her sister. One-fifth of the original cake is 1/5 x 1 = 1/5.

So, Jackie gave away 1/5 of the cake and had 6/10 - 1/5 = 3/10 of the cake left.

Therefore, the fraction of the cake that was left is 3/10.

Answer:

3/10

Step-by-step explanation:

The value of the mean weigh is,

⇒ 9.1

We have to given that;

A scale is tested by repeatedly weighing a standard 9.0 kg weight. The weights for 10 measurements are

⇒ 9.1,8.9,9.5,9.3,8.9,9.4,9.3,8.9,9.4,8.3

Now, We can find the mean as;

⇒ 9.1 + 8.9 + 9.5 + 9.3 + 8.9 + 9.4 + 9.3 + 8.9 + 9.4 + 8.3 / 10

⇒ 91/10

⇒ 9.1

Thus, The value of the mean weigh is,

⇒ 9.1

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The probability of choosing a 5 and then a 6 is 1/49

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

The tiles

Where we have

Total = 7

The probability of choosing a 5 and then a 6 is

P = P(5) * P(6)

So, we have

P = 1/7 * 1/7

Evaluate

P = 1/49

Hence, the probability of choosing a 5 and then a 6 is 1/49

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Question

You randomly choose one of the tiles. Without replacing the first tile, you choose a second tile. Find the probability of the compound event. Write your answer as a fraction or percent rounded to the nearest tenth. The probability of choosing a 5 and then a 6

Answer:

  C  12.80%

Step-by-step explanation:

You want the interest rate that, convertible monthly, will allow an annuity immediate to pay $600 quarterly for 12 years at a cost of $15,000.

The relationship between the variables of an annuity immediate is ...

  P = A(1 -(1 +i)^-n)(1 +i)/i

where i is the interest rate per payment period, n is the number of payments of amount A, and P is the cost of the annuity.

Since payments are quarterly and interest is converted monthly, the annual rate r relates to the i in the formula by ...

  (1 +i)^4 = (1 +r/12)^12

We need to solve for r that satisfies both of these equations when ...

  P = 15000, A = 600, n = 48

The solution requires iteration. Financial calculators and spreadsheets are capable of this. The result is shown in the attachment.

The nominal interest rate is 12.79%. The closest answer choice is 12.80%.

__

Additional comment

"Converted" in this context apparently means the interest is converted to principal. That is, interest is compounded monthly.

"Annuity immediate" means the payments are made at the beginning of the period, so do not earn interest for the period.

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Answer:

A) 30% of the students are girls.

B) If 60% of the students leave the auditorium, there will be 120 students left.

I hope this helps!

\(\\ \sf\longmapsto \dfrac{BQ}{DQ}=\dfrac{RC}{CD}\)

\(\\ \sf\longmapsto \dfrac{26}{39}=\dfrac{18}{x}\)

\(\\ \sf\longmapsto \dfrac{2}{3}=\dfrac{18}{x}\)

\(\\ \sf\longmapsto 2x=54\)

\(\\ \sf\longmapsto x=27\)

Answer: 18 mega rolls

Step-by-step explanation:                      

Answer:

the second one is a better deal.

Step-by-step explanation:

first deal:

6 rolls for 9.24

9.24/6 = 1.54

1.54$ per roll

second deal:

18 rolls for 27.54

27.54/18 = 1.53

1.53$ per roll

the second one is one cent cheaper

Answer:

She has 3 dresses for sure! But I don't know the percentage!

- The rate of the jet in still air is 615 miles per hour.
- The rate of the Jetstream is -40 miles per hour.

The rate of the jet in still air can be found by averaging the speeds of the jet against and with the Jetstream.

Let's calculate the rate of the jet in still air step-by-step:

1. First, find the average distance traveled against and with the Jetstream:
  - Distance traveled against the Jetstream: 2875 miles
  - Distance traveled with the Jetstream: 3275 miles
  - Average distance: (2875 + 3275) / 2 = 6150 / 2 = 3075 miles

2. Next, find the average time taken against and with the Jetstream:
  - Time taken against the Jetstream: 5 hours
  - Time taken with the Jetstream: 5 hours
  - Average time: (5 + 5) / 2 = 10 / 2 = 5 hours

3. Now, calculate the rate of the jet in still air:
  - Rate = Distance / Time
  - Rate = 3075 miles / 5 hours = 615 miles per hour

The rate of the jet in still air is 615 miles per hour.

To find the rate of the Jetstream, subtract the rate of the jet in still air from the rate of the jet with the Jetstream:
  - Rate of the Jetstream = Rate with Jetstream - Rate in still air
  - Rate of the Jetstream = 615 miles per hour - 3275 miles / 5 hours
  - Rate of the Jetstream = 615 miles per hour - 655 miles per hour
  - Rate of the Jetstream = -40 miles per hour

Therefore, the rate of the Jetstream is -40 miles per hour.

In summary:
- The rate of the jet in still air is 615 miles per hour.
- The rate of the Jetstream is -40 miles per hour.

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The estimated number of times it will land on an odd number is 30times

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event is 1 and the equivalent in percentage is 100%

Probability = sample space / Total outcome

The sample is odd number, odd numbers are numbers that can not be divided by 2

sample space = 3

Therefore probability getting odd number

= 3/5

If it is spinned 50 times

= 3/5 × 50

= 30

Therefore the estimated number of times it will land on a odd number is 30 times.

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Answer:

The believe the function is 3.

Answer:

since there is one value of Y for every value of X its a function

Step-by-step explanation: like all of its a function

The equation of the tangent line to the curve \(y = \frac {(x^2 - 1)}{ (x^2 + x + 1)}\) at the point (1, 0) is y = (2/3)x - 2/3.

To find the equation of the tangent line to the curve at the point (1, 0), we need to find the slope of the tangent line and then use the point-slope form of a linear equation.
Let's differentiate \(y = \frac {(x^2 - 1)}{ (x^2 + x + 1)}\) using the quotient rule:

\(y' = [(2x)(x^2 + x + 1) - (x^2 - 1)(2x + 1)] / (x^2 + x + 1)^2\)
Substituting x = 1 into the derivative expression:

\(y'(1) = [(2(1))(1^2 + 1 + 1) - (1^2 - 1)(2(1) + 1)] / (1^2 + 1 + 1)^2\)

        \(= [2(3) - (0)(3)] / (3)^2\)

        = 6/9

        = 2/3

Using the point-slope form y - y₁ = m(x - x₁), where (x₁, y₁) = (1, 0) and m = 2/3 we get,  
y - 0 = (2/3)(x - 1)

y = (2/3)x - 2/3

The point-slope form of a linear equation is given by y - y₁ = m(x - x₁) where (x₁, y₁) is a point on the line, and m is the slope of the line.

Therefore, the equation of the tangent line to the curve y = (x^2 - 1) / (x^2 + x + 1) at the point (1, 0) is y = (2/3)x - 2/3.

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The complete question is:

Find an equation of the tangent line to the given curve at the specified point, \(y = \frac {(x^2 - 1)}{ (x^2 + x + 1)}\) at (1,0).

Therefore , the solution of the given question of triangle  comes out to be the only true option is A.

Any three points in a plane can be connected to create triangles, which have three sides and three angles. They were one of the very first geometric shapes to be studied. They are particularly important because any polygon, whether it has four, five, six, or n sides, may be split into a triangle.

Here,

Because angles 1 and 2 are close to one another, they are neighboring angles.

A They share a side and are near to each other, making them neighboring angles.

B. The angles are complimentary (add to 90 degrees) False—Angle 2 has a 90 degree angle.

C. They are additional angles. (add to 180) They do not create a straight line, which is untrue.

D. Vertical angles describe them. (Contrary angles) False, they are not created through the intersection of lines.

Therefore , the solution of the given question of triangle  comes out to be the only true option is A.

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Answer: \(f(x) = 200(\frac{1}{2})^{x}\)

Step-by-step explanation:

If you plug in the x value(s) to each equation, you can see that \(f(x) = 200(\frac{1}{2})^{x}\) is the correct answer because each y value matches the y value on the table. Therefore, \(f(x) = 200(\frac{1}{2})^{x}\) is the correct answer.

The nutritionist should perform hypothesis testing followed by Independent T-test to see if coffee and tea differ in mean caffeine content .

We need to Know about Hypothesis testing and independent t test to answer this-

Hypothesis testing is a type of statistical test that is used to comapare data and drawing conclusion from them.

An independent t-test is a statistical test that determines whether the means of two unrelated groups are significantly different from each other.

We can find the difference caffeine content following these steps -

1)H0=Null hypothesis=tea and coffee has same caffeine level

HA=tea and coffee has different caffeine level

2)The independent samples t-test is utilized to determine whether two different sample means come from the same population or whether they come from two distinct populations with different mean values. Two populations can be considered independent when the data in one group is not connected to the data in the other group.

The t value obtained should be then performed under hypothesis testing.

3)And the calculated T value should be comaperd with the desired significance level (generally =0.05) and if the t value comes in between the critical values the nutritionist can assume that both tea and coffee has same caffeine level in this null hypothesis will be accepted.

Whereas if the calculated t value doesn't falls in between the critical value then the nutritionist can assume that tea and coffee has different caffeine level.

Hence null hypothesis will be rejected.

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Answer: It is Exponential

Step-by-step explanation: There is a graph provided below.

The kind of model which describes the given data best is exponential.

An exponential graph is a curve that has a horizontal asymptote and it either has an increasing slope or a decreasing slope. i.e., it starts as a horizontal line and then it first increases/decreases slowly and then the growth/decay becomes rapid. It always cuts the y-axis at some point but it may or may not cut the x-axis. i.e., an exponential graph always has a y-intercept but it may or may not have the x-intercept.

According to the given question.

We have a data set {(-1, 0.5), (0,1), (1, 2), (3, 8), (5, 52)}.

So, if we locate this points on the graph.

We see that, when 'x' varies 'y' varies as \(2^{x}\).

Hence, the kind of model which describes the given data best is exponential.

Thus, option B is correct.

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Answer:

Clockwise

Step-by-step explanation:

Sorry I answered late

Answer:Clockwise

Step-by-step explanation:

The solution to the initial value problem y'' 2y' 3y = h(t − 4) y(0) = y' (0) = 0 is y(t) = (1/3)(t-4) u(t-4).

To solve the given initial value problem, we will use the method of undetermined coefficients. First, we will find the homogeneous solution by solving the characteristic equation:

r^2 + 2r + 3 = 0

Using the quadratic formula, we get:

r = (-2 ± sqrt(4 - 4(1)(3))) / (2(1))

r = (-2 ± sqrt(-8)) / 2

r = -1 ± i sqrt(2)

Therefore, the homogeneous solution is:

y_h(t) = e^(-t) (c1 cos(sqrt(2)t) + c2 sin(sqrt(2)t))

Next, we will find a particular solution to the non-homogeneous equation:

y_p(t) = A (t - 4)

y_p'(t) = A

y_p''(t) = 0

Substituting these into the original equation, we get:

0 + 2A + 3A(t-4) = h(t-4)

Since h(t-4) is zero for t<4 and one for t>=4, we can solve for A separately in each region. For t<4, the equation becomes:

0 + 2A + 3A(t-4) = 0

A = 0

0 + 2A + 3A(t-4) = 1

A = 1/3

Therefore, the particular solution is:

y_p(t) = (1/3)(t-4) u(t-4)

The general solution is then:

y(t) = y_h(t) + y_p(t)

y(t) = e^(-t) (c1 cos(sqrt(2)t) + c2 sin(sqrt(2)t)) + (1/3)(t-4) u(t-4)

Using the initial conditions, we can solve for the constants c1 and c2:

y(0) = 0 = c1

y'(0) = 0 = -c1 + sqrt(2)c2

c1 = 0

c2 = 0

Therefore, the solution to the initial value problem is y(t) = (1/3)(t-4) u(t-4).

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