Jack is ten years older than Anna. Seven years from now Jack will be twice as old as Anna. How old is Jack now?

To simplify the expression (5 + 3i)(7 – 4i), two important processes to remember are to use the distributive property to multiply the real parts and imaginary parts separately and simplify the resulting expression by combining any like terms.

Use the distributive property:

For the expression (5 + 3i)(7 – 4i),

(5 + 3i)(7 – 4i) = 5(7) + 5(-4i) + 3i(7) + 3i(-4i)

= 35 - 20i + 21i - 12i^2

Note that i^2 = -1,

35 + i(21 - 20) - 12(-1) = 47 + i(41)

Simplify the resulting expression:

After using the distributive property to expand the expression, we can simplify the resulting expression by combining any like terms. In this case, there are no like terms to combine, so our final answer is:

(5 + 3i)(7 – 4i) = 47 + 41i

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Answer:

$81

Step-by-step explanation:

36/4 = 9

We can deduce that each shirt costs $9 so...

9x9 = 81

A labour economist aims to estimate the variance of unemployed workers' mathematic test scores. Assume that a random sample of 18 scores had a sample standard deviation of 10.4. To form a 90% confidence interval for the population varianceis The confidence interval is exactly between 46.64 and 202.07. The correct answer is option (a)



Find the degrees of freedom (df) by subtracting 1 from the sample size:
df = n - 1 = 18 - 1 = 17

Find the chi-square values for the 90% confidence interval using a chi-square table or calculator. The lower value corresponds to the 5th percentile (0.05) and the upper value corresponds to the 95th percentile (0.95):
χ² lower = 27.488
χ² upper = 8.672

Calculate the lower and upper limits of the confidence interval using the formula:
CI lower = (df * s²) / χ²_upper
CI upper = (df * s²) / χ²_lower

Where s² is the sample variance (the square of the sample standard deviation):
s² = 10.4² = 108.16

Plugging in the values:
CI lower = (17 * 108.16) / 27.488 = 46.64
CI upper = (17 * 108.16) / 8.672 = 202.07

The 90% confidence interval for the population variance is between the lower and upper limits:
CI = (46.64, 202.07)

Therefore, the correct answer is option (a) The confidence interval is exactly between 46.64 and 202.07.

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Answer:

21.6 feet?

Step-by-step explanation:

8 percent of 3 is 0.24

0.24 x 90 is 21.6

Answer:

56%, 4/5, 1.07, 5/4

Step-by-step explanation:

5/4=1.25

56%=0.56

1.07

4/5=0.8

so the order is

56%, 4/5, 1.07, 5/4

The expression cannot be factored over integers since the roots are not integers.

The error in Sarah's thought process is that she is assuming that the factoring of a quadratic equation can always be done by finding two numbers that add up to the coefficient of the middle term (in this case, -4) and multiply to the coefficient of the quadratic term (in this case, 5). However, this method only works when the quadratic expression is factorable over the integers, which is not always the case.

In fact, the expression [tex]5x^2-4x-9[/tex] cannot be factored over the integers, which means that there are no two integers whose product is [tex]5*(-9)=-45[/tex] and whose sum is -4. To confirm this, we can use the quadratic formula (-b ± \sqrt{(b^2-4ac)} )/2a, which gives the roots of the quadratic equation [tex]ax^2+bx+c=0[/tex]. For this expression, [tex]a=5, b=-4[/tex], and c=-9, so the roots are:

[tex]x=[-(-4)±sqrt{(-4)^2-45(-9)}]/(2*5\leq)[/tex]

[tex]x=(4±sqrt(196))/10\\x=(4±14)/10\\x=1 or x=-9/5[/tex]

Since the roots are not integers, the expression cannot be factored over the integers.

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a) f(x) = x^3 -x^2 + 3x +7 is the correct answer

Answer:

perfect square therefore rational

non perfect square therefore irrational

cuberoot

5

Step-by-step explanation:

the topic is about perfect squares and rationality of numbers

There are 6 people in a group. Their names are selected randomly and they act independently. The probability that the first person arriving has the same name as 1 or more people is 0. The probability that there are people in the group with the same name is 98.46%.

The probability that the initial arrival shares a name with one or more others is 0 percent. This is because the first person arriving has no one to compare their name with, so there is no chance that they will have the same name as someone else.

The probability that there are people in the group with the same name can be calculated using the formula

P(same name) = 1 - P(different names).

The probability of everyone having different names is calculated by multiplying the probabilities of each person having a different name from the previous person. This can be represented as

(6/6) * (5/6) * (4/6) * (3/6) * (2/6) * (1/6) = 0.0154.

Therefore, the probability of there being people in the group with the same name is 1 - 0.0154 = 0.9846 or 98.46%.

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There will be 4 small boxes and 2 large boxes of granola bars.

A variable is an attribute or a phenomenon that can be measured and has a changing value over time.

Given,

Number of granola bars in the small box = 10

Number of granola bars in the large box = 30

The number of small boxes = three times the number of a large boxes

To Find,

The number of small boxes purchased =?

The number of large boxed purchased =?

Let the number of large boxes be y

The number of small boxes be x

Total number of boxes, x + y = 6         ..... equation i

Total number of granola bars in small box = 10x

Total number of granola bars in large box = 30x

So, 10x + 30x = 100

After dividing by 10 we get

x + 3y = 10                                               ..... equation ii

Subtracting equation ii from equation i

We get,   2y = 4

y = 2

Putting the value of y in equation i we get x = 4

So, there will be 4 small boxes and 2 large boxes of granola bars.

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Answer:

θ = 78.69°

Step-by-step explanation:

As this is a right angle triangle we use trigonometric ratios/

The perpendicular i.e the height of the mast = 50 ft

The base i.e the shadow = 10 ft

tanθ = perpendicular / base

tanθ = 50/10

θ = [tex]tan^{-1}[/tex] (50/10)

θ = 78.69°

An equation that best represents the relationship between x and y in the graph is: A. y = -3x/4 - 3.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

At point (-4, 0), an equation of this line can be calculated by using the point-slope form:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 0 = (-3 - 0)/(0 + 4)(x + 4)

y - 0 = -3/4(x + 4)

y = -3x/4 - 3.

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The first monthly charge has about $78.78 allotted in the direction of reducing the principal.

The total buy charge of the house is $96,400 and the Spinoses made a 25% down payment, because of this they paid $96,400 x 0.25 = $24,100 in advance.

Therefore, the final quantity that they financed is $96,400 - $24,100 = $72,300.

They financed this amount at 5.50% for 30 years, which gives us the following method for calculating the monthly payment (P):

P = (r * PV) / (1 - (1 + r)^(-n))

in which:

Substituting the values, we get:

P = (0.00458 * 72,300) / (1 - (1 + 0.00458)^(-360))

P ≈ $410.66

We recognise that the monthly payment is $410.66 and we will calculate the interest portion of the primary monthly price as follows:

interest = balance * monthly interest price

interest = $72,300 * (5.50% / 12) ≈ $331.88

To calculate the amount of the primary monthly charge this is used to lessen the fundamental, we subtract the interest component from the total monthly payment:

$410.66 - $331.88 ≈ $78.78

Thus, the first monthly charge has about $78.78 allotted in the direction of reducing the principal.

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We can write tanz in terms of secz using the Pythagorean Identity as:
tanz = -sqrt(sec^2z - 1)

Part 1 of 2:
The Pythagorean Identity states that sin^2z + cos^2z = 1. We can use this identity to write tan^2z in terms of sec^2z.

First, let's rearrange the Pythagorean Identity to isolate cos^2z:
cos^2z = 1 - sin^2z

Next, we can divide both sides of the equation by cos^2z to get:
1 = sec^2z - (sin^2z)/(cos^2z)

Since tan^2z = (sin^2z)/(cos^2z), we can substitute this into the equation:
1 = sec^2z - tan^2z

Finally, we can rearrange the equation to isolate tan^2z:
tan^2z = sec^2z - 1

Now, let's consider the case when z is in Quadrant II. In this quadrant, tanz is negative and secz is negative. Therefore, we can write:
tanz = -sqrt(sec^2z - 1)

Part 2 of 2:
In the case when z is in Quadrant IV, tanz is negative and secz is positive. Therefore, we can write:
tanz = -sqrt(sec^2z - 1)

So, in both cases, we can write tanz in terms of secz using the Pythagorean Identity as:
tanz = -sqrt(sec^2z - 1)

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Answer:

The width of the window is 122 inches

Step-by-step explanation:

654- known two sides(410) =244

divide 244/2, to get both unknown sides of the rectangular window, 122 inches

The scale factor of dilation is 3.

What is Dilation of a circle?

Dilation is the process of altering an object's or shape's size by reducing or enlarging its dimensions by a certain amount of scale. A circle with a radius of 10 units, for instance, is reduced to a circle with a radius of 5 units. This technique is applied in art and craft, photography, and logo design, among other fields.

Given : Radius of original circle A = 3

            Radius of Dilation circle B = 9

We know that, Scale factor of dilation =

Dimension of Dilation shape / Dimension of original shape

So, Scale factor of given dilation = Radius of Circle B / Radius of Circle A

                                                      = 9/3

                                                      = 3.

Hence, Scale factor of dilation of circle B on Circle A is 3.

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11. The area of the floor is 24. 62 m²

12. The area of the enclosed string is 3, 853. 09cm²

13. The circumference of the circular mat is  4.39m

The formula for the area of a circle is expressed with the equation;

A = πr²

Where;

Also, circumference of a circle is 2πr

For a circumference of 17. 6m, we have

17. 6 = 2×3.14r

r = 2. 80

Substitute the value

Area = 3.14 × (2. 80)²

Area = 24. 62 m²

For the string, circumference = 220cm

220 = 2× 31.4r

r = 35. 03 cm

Area of the enclosed string = 3.14 × (35. 03)²

Area = 3, 853. 09cm²

For the circular mat

1.54 = 3.14r²

r² = 0. 49

Take the square root

r = 0. 7m

Circumference = 2× 3.14 × 0. 7 = 4.39m

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By solving the given equation, we can plot these two points on a coordinate plane, and then connect the points with a line. The formed line is the graph of the linear equation 3y=2x-7.

The coordinate plane is made up of two perpendicular lines called the x-axis and the y-axis. The x-axis, which is horizontal, is used to measure the distance of a point from the left and right side of the plane. The y-axis, which is vertical, is used to measure the distance of a point from the top and bottom of the plane.

To graph the equation 3y=2x-7, we first need to identify two points that satisfy the equation. We can do this by plugging in different values for x and solving for y. For example, when x=0, the equation becomes 3y=-7. Thus, one point that satisfies the equation is (0,-7). We can find a second point by plugging in a different value for x. For example, when x=2, the equation becomes 3y=-3. Thus, the second point that satisfies the equation is (2,-3).

Now, we can plot these two points on a coordinate plane, and then connect the points with a line. The formed line is the graph of the linear equation 3y=2x-7.

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Answer:This free number sequence calculator can determine the terms (as well as the sum of all terms) of the arithmetic, geometric, or Fibonacci sequence.

Step-by-step explanation:

You should invest $26,100 in Stock Boll and $12,900 in Stock Coff to maximize your annual interest earned, and the maximum annual interest is $2,337.

To maximize your annual interest earned, you should invest as much money as possible in the stock with the higher interest rate, which is Stock Coff. However, there are two constraints that you need to consider: the buying limit on Stock Coff and the requirement to spend at least twice as much money on Stock Boll as Stock Coff.

Let's use algebra to solve this problem. Let x be the amount of money you invest in Stock Boll and y be the amount of money you invest in Stock Coff. Then we have the following equations:

x + y = $39,000 (the total amount of money you have to invest)
y <= $12,900 (the buying limit on Stock Coff)
x >= 2y (the requirement to spend at least twice as much money on Stock Boll as Stock Coff)

To maximize your annual interest earned, you want to maximize the expression 0.05x + 0.08y (the sum of the interest earned from Stock Boll and Stock Coff).

If you invest the maximum amount of money in Stock Coff ($12,900), then you have $39,000 - $12,900 = $26,100 left to invest in Stock Boll. This satisfies the requirement to spend at least twice as much money on Stock Boll as Stock Coff ($26,100 >= 2 * $12,900).

So the optimal solution is to invest $26,100 in Stock Boll and $12,900 in Stock Coff. The maximum annual interest earned is 0.05 * $26,100 + 0.08 * $12,900 = $1,305 + $1,032 = $2,337.

Therefore, you should invest $26,100 in Stock Boll and $12,900 in Stock Coff to maximize your annual interest earned, and the maximum annual interest is $2,337.

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As one loaf of bread weighs about 1 pound, the metric measures that are less than 1 pound are:

The pound means the unit of measurement used in the U. S. customary system and the British imperial system to measure weight. One familiar use of pounds is measuring how much a person weighs.

A pound is approximately 0.4535 kilogrammes, so 453.5 grammes. With this information, we can determine that answers 450 grammes and 100 grammes are the only correct ones because they are lesser than 453.5 grammes.

Full question "A loaf of bread weighs about 1pound. Chose all of the metric measures that are less than 1pound. 1kg 0.5kg 500g 450g 100g"

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After solving the given equation In [tex]e^{lnx} +[/tex] in [tex]e ^{lnx2}[/tex] = 2 in 8, we know that the value of x is (B) 4.

The equals sign is a mathematical symbol that indicates that two expressions in a formula are equal.

A mathematical statement known as an equation is one that uses the word "equal to" between two expressions with the same value.

As in 3x + 5 = 15, for example.

Equations can be of many different types, such as linear, quadratic, cubic, and others.

So, we have the equation:

[tex]Ine^{inx} + Ine^{Inx2}[/tex] [tex]= 2In8,[/tex]

Now, solve the following equation as follows:

[tex]Inx * Ine +Inx^2 * Ine = 2In8[/tex]

[tex]e^{Inx}+Ine^{Inx2} = 2in8[/tex]

[tex]Inx+Inx^2 = In8^2[/tex]

[tex]In* (x*x^2) In64[/tex]

[tex]x^2 = 64 =4^3[/tex]

[tex]x=4[/tex]

Therefore, after solving the given equation In [tex]e^{lnx }[/tex] + in[tex]e ^{lnx2}[/tex] = 2in8, we know that the value of x is (B) 4.

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Correct question:

What is the true solution to the equation below? In [tex]e^{lnx}[/tex]+ in [tex]e ^{lnx2}[/tex] = 2 in 8

a x = 2

b x = 4

c x = 8

d x = 64

Answer:

Step-by-step explanation:multiply x by y to the power of 67000 and then you will get 730000000.

The new points after the translation are (0, -4), (0, 0), (5, -5) and (5, 0) and the image is added as attachment

Translation is the movement of a point either up, left, right or down on the coordinate plane.

If a point A(x, y) is translated a units left and b units down, the new point is A'(x - a, y - b)

From the question, the vertices of the rectangle are (2, 3), (2, 7), (7, 2) and (7, 7).

The translation T<-2, -7>; is a translation of 2 units left and 7 units down.

This means that

The new points are (0, -4), (0, 0), (5, -5) and (5, 0).

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We deduced the following from the given phrase:

1) The supplied expression is a sum with the four terms a, b, l, and c.

2) 2c is the result of the factors 2 and c on its own.

A function is a relationship between a number of inputs and outputs. Simply described, a function is an association between inputs in which each input is coupled to exactly one output. For each function, there is a corresponding range, codomain, and domain.

What follows is:

A + (b+1) + 2c is the function that has been discovered and written in the question.

As we can see, three distinct terms—a, b+1, and 2c—have been demonstrated to be a part of this function.

As a result, we deduced the following from the above formula:

1) With the four terms a, b, 1 and 2c, the complete equation is a sum.

2) 2c is the result of the factors 2 and c on its own.

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The complete question is:

On its own 2c is a product with

If more than 400 sheets are duplicated, this equation will provide us with the overall expense, t.

A method that describes how two lines along both side of a sign connect each other. It typically contains an equal symbol and one variable. Similarly, 2x - 4 = 2. The variable x is present in the particular circumstance.

The equation that could be used to calculate the total cost, t, to copy p pages when p is greater than 400 is:

t = $5,000 + ($0.01 × (p - 400))

The base cost for copying the first 400 pages is $5,000. For each additional page above 400, the customer is charged $0.01 per page. Therefore, to calculate the total cost for copying p pages, we need to subtract 400 from p to determine the number of pages that are being charged at the additional rate, and then multiply that by $0.01 to determine the additional cost. This gives us:

Additional cost = $0.01 × (p - 400)

The total cost is then the sum of the base cost and the additional cost:

t = $5,000 + ($0.01 × (p - 400))

This equation will give us the total cost, t, for any number of pages greater than 400 that are copied.

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Option (c) has the same equation as above after simplification, so the answer is (c):y-8=-0.2(x+10).

Simplification involves reducing an expression, equation, or problem to a simpler form. This can involve performing operations such as combining like terms, factoring, or canceling out common factors.

Point-slope form is a way of writing the equation of a straight line in two-dimensional space, using a given point on the line and the line's slope.

The point-slope form equation for a line passing through a point (x1, y1) with slope m is:y - y1 = m(x - x1).

In the given question,

To write the equation of a line in point-slope form, we need to use the formula:

y - y1 = m(x - x1)

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

We are given two points on the line: (-10, 8) and (10, 4). We can use these points to find the slope of the line:

m = (y2 - y1) / (x2 - x1)

= (4 - 8) / (10 - (-10))

= -0.15

Now we can use the point-slope form with the point (-10, 8) and slope -0.15:

y - 8 = -0.15(x - (-10))

Simplifying this equation, we get:

y - 8 = -0.15(x + 10)

Option (c) has the same equation as above after simplification, so the answer is (c):

y-8=-0.2(x+10).

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There is a trade-off between stability and speed when it comes to the slope of a train's wheels.

What is slope ?

Slope is a measure of the steepness of a line or a surface. In mathematics, slope is often represented by the letter "m" and is calculated as the change in the vertical direction (y-axis) divided by the change in the horizontal direction (x-axis) between two points on the line or surface.

Changing the slope of a train's wheels can have both positive and negative effects on the train's overall performance.

On the positive side, increasing the slope of the wheels can improve the train's stability and safety as it goes around curves. This is because the inward slope of the wheels helps to counteract the centrifugal force that pushes the train outward as it goes around curves. By increasing the slope of the wheels, this counteracting force can be increased, which can help prevent derailments and improve the overall safety of the train.

On the negative side, increasing the slope of the wheels can decrease the train's efficiency at producing speed. This is because the slope of the wheels creates additional friction between the wheels and the track, which can slow the train down and require more energy to maintain speed. As the slope of the wheels increases, this friction also increases, which can make the train less efficient at producing speed and more costly to operate.

Therefore, there is a trade-off between stability and speed when it comes to the slope of a train's wheels. Train designers must find the optimal balance between these two factors to ensure that the train is both stable and efficient.

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Step-by-step explanation:

Since the new poison kills half the population every 2 months, we can say that the remaining half will survive for another 2 months. Therefore, after 2 months, the rodent population will be half of 1,000,000, which is 500,000.

After another 2 months, the remaining half of the 500,000 will survive, which is 250,000.

After another 2 months, the remaining half of the 250,000 will survive, which is 125,000.

After 6 months, the rodent population will be 125,000.

Since 12 months is six 2-month periods, we can repeat this process again. After another 2 months, the rodent population will be 62,500.

After another 2 months, the rodent population will be 31,250.

After another 2 months, the rodent population will be 15,625.

Therefore, after 12 months, the rodent population will be 15,625.

815 ÷ 8 = 101.875 ≈ 102

∴ The cafeteria should buy 102 bags.

Answer:

102 bags.

Step-by-step explanation:

You divided 815 by 8. The answer is 101.875 and you can't have half a bag so you round it up to the nearest whole number.