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the and dec in a ratio
Q2- Dividing in a ratio
Miss Penny inherits $960.
She decides to save some of the
money and spend the rest.
This reduces the amount she has
to save in the ratio 7: 12
How much does she save and how
much does she spend?
Savings
$
Spending money $
[2]
[2]

Answer:

9x-7

Step-by-step explanation:

AB =3x-2

BC= 6x-5

AC=AB+AC

AC=(3X-2)+(6X-5)

AC=3X-2+6X-5

AC=3X+6X-2-5

AC=9X-7

Answer:

I believe it's

Step-by-step explanation:

A

however I could be wrong

Answer:

16

Step-by-step explanation:

I explained every step in the picture, I hope you understand it.

Answer:

B. making an inference.

Step-by-step explanation:

The drama teacher's decision to add another performance time on Saturday is a result of making an inference based on the information that 80% of last year's sold-out plays occurred during weekend performances. By observing this pattern, the drama teacher infers that adding another performance on Saturday will likely attract a larger audience and increase the chances of having a sold-out show.

Answer:

10, 5+5=10

correct answer would be 10

Answer:

  2.  $19,547.04

  3.  $10,276.54

  4.  $16,758.38

Step-by-step explanation:

You have three problems in compound interest with different initial payments, interest rates, and compounding intervals. You want the relationship between the initial payment and the future value.

The multiplier of a single payment earning annual interest rate r compounded n times per year for t years is ...

  k = (1 +r/n)^(nt)

For this problem, r=0.09, n=1, t=9. The multiplier of the payment is ...

  k = (1 +0.09/1)^(1·9) = 1.09^9 = 2.17189328

Then the future value of $9000 will be ...

  FV = $9000 × 2.17189328 ≈ $19,547.04

For this problem, r=0.10, n=12, t=4. The multiplier of the payment is ...

  k = (1 +0.10/12)^(12·4) = 1.08333...^48 = 1.48935410

Then the future value of $6900 will be ...

  FV = $6900 × 1.48935410 ≈ $10,276.54

For this problem, r=0.13, n=12, t=13. The multiplier of the payment is ...

  k = (1 +0.13/12)^(12·13) = 1.0108333...^156 = 5.3704484

Then the payment that gives a future value of $90,000 will be ...

  P = $90,000/5.3704484 = $16,758.38

__

Additional comment

For the spreadsheet calculation, we used the "Goal Seek" capability to adjust the value of cell F4 to 90000 by changing the value in cell B4.

We could have calculated the multiplier as above, then used it different ways for the different problems. Instead, we used one FV( ) function for all of the problems.

The estimate of the average height of all the trees having a trunk diameter of 7 inches is y = 18.1 feet. This is obtained by using the LSRL equation. Option A is the correct value.

The LSRL equation is defined as the Least squares regression line. This is the line that minimizes the variance. So, it is the best line of fit for a set of data points.

The equation is in the form of Y = a + bX

Here a is the intercept and b is the slope.

It is given that,

X is given as the diameter of a tree trunk in inches

Y is given as the tree height in feet

The given data points are:

X: 4, 2, 8, 6, 10, 6

Y: 8, 4, 18, 22, 30, 8

For these data points, the least squares regression line is given by the equation Y = - 3.6 + 3.1X

So, the estimate of the average height of all trees having a trunk diameter of 7 inches is

Y = - 3.6 + 3.1X ⇒ Y = -3.6 + 3.1 × 7

⇒ Y = -3.6 + 21.7

∴ Y = 18.1 feet

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Answer:

(a) 0
(b) 0
(c) 1
The function is not continous at x = 9

Step-by-step explanation:

To the left and right of the point x = 9, the graph would seem to continue at  f(x) = 0, however on the exact point x = 9 there is a hole in the graph allowing it to be equal to 1. Due to the hole in the graph, it is not continuous

Apologies if this is wrong its been a bit since I did calculus

Answer:

20

Step-by-step explanation:

just a substitute 3 in x so 3x3=9

11+9=20

Answer:

84%

Step-by-step explanation:

I solved it, and I took the test.

Answer:

32 red cars.

Step-by-step explanation:

Let the red cars be denoted by R

Let the green cars be denoted by G

Translating the word expression into an algebraic equation;

\( R + G = 36\) ...........equation 1

\( R = 8G\) ...........equation 2

Substituting equation 2 into equation 1;

\( 8G + G = 36\)

\( 9G = 36\)

\( G = \frac{36}{9}\)

G = 4

The number of green cars are 4.

From, \( R = 8G\)

\( R = 8*4\)

R = 32

Therefore, the number of red cars that Susan counted are 32.

Answer:

no solutions

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

equation of blue line is y = x + 2 , in slope- intercept form

with slope m = 1

equation of red line is y = x - 3 , in slope- intercept form

with slope m = 1

• Parallel lines have equal slopes

then the blue and red lines are parallel.

the solution to the system is at the point of intersection of the 2 lines

since the lines are parallel then they do not intersect each other.

thus the system shown has no solution.

Answer:

(6x) + 9 = 4

Step-by-step explanation:

Times means 'The answer when you multiply' So we are working in multiplication. ( x )

6x is the multiplication.

It says 'more than' which means adding to our answer. So we add 9. So far our equation is: (6x) + 9 (Brackets are needed as we are multiplying 6 by x and not multiplying 6 by x+9)

Lastly, it says the answer must be 4 so we add that at the end. So the answer is:

(6x) + 9 = 4

Answer:

9yx

Step-by-step explanation:

product means multiply.

nine, y and x

9yx

Answer:

a. The angles in the picture are: a, 2a, 2a, 3a, 3a, 4a, 4a, 5a.

Step-by-step explanation:

The cruise ship's resultant velocity is approximately 22.67 mph, and its direction is approximately 10.2 degrees south of east.

To find the resultant direction, we can use vector addition. Let's represent the southward velocity of the cruise ship as vector A and the eastward velocity of the Gulf Stream as vector B.

Given:

Magnitude of vector A (southward velocity of the cruise ship) = 22 mph

Magnitude of vector B (eastward velocity of the Gulf Stream) = 4 mph

To find the resultant velocity, we add the two vectors together. Since the vectors are perpendicular to each other, we can use the Pythagorean theorem to find the magnitude of the resultant vector:

Resultant velocity = √(A^2 + B^2) = √(22^2 + 4^2) ≈ 22.67 mph

Now, to find the direction of the resultant vector, we can use trigonometry. The angle between the resultant vector and the south direction can be calculated as:

θ = arctan(B / A) = arctan(4 / 22) ≈ 10.17 degrees

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Answer:

B).

Step-by-step explanation:

Add 8 to half the difference of 6 and 2 then subtract 1.

Answer:

I apologize but I haven't worked for an answer. but my mind is, what is the point of this question? everyone is familiar with the "when am I ever going to use this in life and why do I need to learn this?" but this is a whole new level of w t f.

Answer:

$15.69

Step-by-step explanation:

multiply the retail price by 1.06 to get the price after taxes.

find the discounted price by multiplying the price after taxes(19.61) by 0.8 since it is 20% off to get the answer

part a.

There is  a 49.1% chance that HRC finds a sample mean between $477 and $527.

part b.

There is a 20.9% chance that the sample mean falls between $492 and $512.

The standard error (SE) of the sample mean.

SE = σ / √(n)

σ = $80 and n = 68.

SE = 80 / √(68)

z1 = (X1 - μ) / SE

z2 = (X2 - μ) / SE

for first scenario:

X1 = $477, X2 = $527, and μ = $499.

z1 = (477 - 499) / SE

z2 = (527 - 499) / SE

For the range $477 to $527:

z1 = (477 - 499) / SE

z2 = (527 - 499) / SE

z1 = -0.275

z2 = 0.35

Probability 1 =  0.4909 = 49.1%

We have a 49.1% chance that HRC finds a sample mean between $477 and $527.

For the second scenario

X1 = $492, X2 = $512, and μ = $499.

z1 = (492 - 499) / Standard Error

z2 = (512 - 499) / SE

We have a 20.9% chance that the sample mean falls between $492 and $512.

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Based on the net present value profile, Project H has a higher NPV than Project E.

To compare the net present value (NPV) of Project E and Project H, we need to calculate the present value of cash flows for each project and determine which one has a higher NPV. The cash flow patterns for the two projects are as follows:

Project E:

Initial investment: -$100,000

Cash flows for Year 1: $40,000

Cash flows for Year 2: $50,000

Cash flows for Year 3: $60,000

Project H:

Initial investment: -$120,000

Cash flows for Year 1: $60,000

Cash flows for Year 2: $50,000

Cash flows for Year 3: $40,000

To calculate the present value of cash flows, we need to discount them using an appropriate discount rate. The discount rate represents the required rate of return or the cost of capital for the company. Let's assume a discount rate of 10%.

Using the formula method, we can calculate the present value (PV) of each cash flow and sum them up to obtain the NPV for each project:

For Project E:

PV = $40,000/(1 + 0.10)^1 + $50,000/(1 + 0.10)^2 + $60,000/(1 + 0.10)^3

PV = $36,363.64 + $41,322.31 + $45,454.55

PV = $123,140.50

For Project H:

PV = $60,000/(1 + 0.10)^1 + $50,000/(1 + 0.10)^2 + $40,000/(1 + 0.10)^3

PV = $54,545.45 + $41,322.31 + $30,251.14

PV = $126,118.90

Using the financial calculator method, we can input the cash flows and the discount rate to calculate the NPV directly. By entering the cash flows for each project and the discount rate of 10%, we find that the NPV for Project E is approximately $123,140.50 and the NPV for Project H is approximately $126,118.90.

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Answer:

The midpoint is ( 7,5)

Step-by-step explanation:

To find the x coordinate of the midpoint, add the x coordinate of the endpoints and divide by 2

( 4+10)/2 = 14/2 = 7

To find the y coordinate of the midpoint, add the y coordinate of the endpoints and divide by 2

(8+2)/2 = 10/2 = 5

The midpoint is ( 7,5)

Using the given zero . The three zeros of the polynomial function are 1 + i, 1 - i, 1/2, and 2.

If 1 + i is a zero of the polynomial function P(x), then its conjugate, 1 - i, must also be a zero of the polynomial, since complex zeros of polynomial functions with real coefficients always come in conjugate pairs.

To find the remaining zero, we can use polynomial division or synthetic division to divide P(x) by (x - 1 - i)(x - 1 + i), which is the quadratic factor corresponding to the two known zeros:

      2x^2 - 3x + 2

P(x) = --------------

       (x - 1 - i)(x - 1 + i)

Now we need to solve for the roots of the quadratic factor 2x^2 - 3x + 2. We can use the quadratic formula:

x = [3 ± sqrt(9 - 4*2*2)] / (2*2)

 = [3 ± sqrt(1)] / 4

 = 1/2 or 2

Therefore, the remaining zeros of P(x) are 1/2 and 2. The three zeros of the polynomial function are 1 + i, 1 - i, 1/2, and 2.

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The factored form of the equation  P(x) = x³ + 3x² + x + 3  is P(x) = (x+1)(x² + 2x + 3).

An equation is a mathematical expression that shows that two things are equal.

One common method for finding the factored form of a polynomial equation is to use the Rational Root Theorem, which states that if a rational number a/b is a root of the polynomial equation, then (x-a/b) is a factor of the polynomial equation.

We can then use long division to divide the polynomial by the linear factor, repeat the process with the remaining polynomial, and continue this process until the polynomial is fully factored.

The polynomial equation

=> P(x) = x³ + 3x² + x + 3

can be factored as

=> (x+1)(x² + 2x + 3).

The equation P(x) = (x+1)(x² + 2x + 3) is now written as a product of two linear factors, (x + 1) and (x² + 2x + 3).

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There were 5 1/4 bags of popcorn left after eating 4 bags.

To find out how much popcorn was left after eating 4 bags, we need to subtract the amount eaten from the total amount Brianna made.

Brianna made 9 1/4 bags of popcorn, which can be represented as a mixed number. To perform calculations, let's convert it to an improper fraction:

9 1/4 = (4 * 9 + 1) / 4 = 37/4

Now, let's subtract the 4 bags eaten from the total:

37/4 - 4

To subtract fractions, we need a common denominator. The common denominator of 4 and 1 is 4. Therefore, we can rewrite the expression as:

37/4 - 4/1

Now, let's find a common denominator and subtract the fractions:

37/4 - 16/4 = (37 - 16) / 4 = 21/4

The result is 21/4, which is an improper fraction. Let's convert it back to a mixed number:

21/4 = 5 1/4

Therefore, there were 5 1/4 bags of popcorn left after eating 4 bags.

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a) The joint probability density function is \(f(y_1,y_2) = f(y_1) * f(y_2) = (1/3e^{(-y1/3)})(1/3e^{-y2/3})\)

b) The total effective length of life of the two fuses is less than or equal to one.

The exponential distribution is a probability distribution that models the length of life of fuses, and its probability density function can be used to find the joint probability density function for the lengths of two independent fuses.

a) To find the joint probability density function for the lengths of two independent fuses, we simply multiply the probability density functions of each individual fuse. In this case, we have

\(= > f(y_1,y_2) = f(y_1) * f(y_2) = (1/3e^{(-y1/3)})(1/3e^{-y2/3})\)

for y₁, y₂ > 0. This is a function that gives the probability of a given pair of lengths (y₁,y₂) occurring.

b) To find P(Y₁ + Y₂ ≤ 1), we must first determine the cumulative distribution function for the sum of the lengths of the two fuses. This is given by

=> F(y) = P(Y₁ + Y₂ ≤ y) = ∫∫f(x,y)dxdy,

where the integral is taken over the region x+y ≤ y. We can simplify this by changing the order of integration:

=> \(F(y) = \int0^y\int0^{y-x}f(x,y)dxdy.\)

Using the probability density function given in part (a), we have

=> \(F(y) = \int0^y\int0^{y-x}(1/9)e^{-(x+y)/3}dxdy\)

This can be solved using integration by parts or by using the fact that the exponential function integrates to itself, giving

=> \(F(y) = 1 - e^{-y/3)(y+3)}\)

Finally, we can find P(Y₁ + Y₂ ≤ 1) by evaluating F(1) - F(0), which gives

=> \(P(Y_1 + Y_2 ≤ 1) = 1 - e^{(-1/3)(4/3)}\).

This is a function that gives the probability that the total effective length of life of two fuses is less than or equal to one.

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Complete Question:

The length of life Y1 AND Y2 for fuses of a certain type is modeled by the exponential distribution, with

\(f(y) = \left \{ {1/3e^{-y/3} y > 0,} \atop {0, else where }} \right.\)

(The measurements are in hundreds of hours.)

a) If two such fuses have independent lengths of life Y1 and Y2, find the joint probability density function for Y1 and Y2.

b) One fuse in part (a) is in a primary system, and the other is in a backup system that comes into use only if the primary system fails. The total effective length of life of the two fuses is then Y1 + Y2. Find P(Y1 + Y2 ≤ 1).