During the past year, Mrs. Singh purchased 29 books at a wholesale club store. She purchased softcover books for $3.50 each and hardcover books for $11.50
each. The total cost of the books was $205.50. How many of each type of book did she purchase?

Part 1 of 2
Mrs. Singh purchased (blank) softcover books

Part 2 of 2
Mrs. Singh purchased (blank) hardcover books.

Answer:

[tex]\sqrt{\frac{P}{R} }[/tex]

Step-by-step explanation:

[tex]P=I^2*R\\[/tex]

Divide both sides by R

[tex]\frac{P}{R} =I^2[/tex]

Remove the exponent by finding the square root of each side

[tex]\frac{\sqrt{P} }{\sqrt{R} } = I[/tex]

[tex]I=\sqrt{\frac{P}{R} }[/tex]

Answer:

A. No, because (-1) and (-1, -2) have the same input value.

Step-by-step explanation:

So what exactly is a function? It's very similar to a relation where there is input and for each input we have some output and sometimes multiple. The difference is in a function there is only one output for each input. Now the outputs of two different inputs can be the same, such that the input 2 and 3 will both output 4 or any value, but we cannot have an input such as 2 outputting 3 and 4 since we can only have one output for each input.

In the table given, the input "-1" outputs "2" and -2" which means the table  does not represent a function.

This makes "A" the correct answer to whether it's a function or not and explanation.

1.14 kg  is the total weight of the rocks, in kilograms.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

2 such rocks weigh 20 ounces each.

i.e. weight of 2 rocks = 20*2

                                  =40 ounces

now,

a kilogram is 35.2 ounces

the total weight of the rocks, in kilograms = 40/35.2

                                                                       =1.14 kg.

Hence, 1.14 kg  is the total weight of the rocks, in kilograms.

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Let A and B be two countable sets. Then there exists a bijective function f from A to B.

Since f is onto, for every element b in B, there exists a unique element a in A such that f(a)=b. This implies that the number of elements in B is equal to the number of elements in A, i.e. B is also countable.

Formally, if A = {a1, a2, ..., an}, then B = {f(a1), f(a2), ..., f(an)}. Since f is onto, B has n elements, which implies that B is countable.

Let A be a countable set and let B be a set with an onto function f from A to B. Since A is countable, it can be written as an infinite sequence of distinct elements an, where n is a natural number. To show that B is also countable, we can construct a one-to-one correspondence between the elements of A and B. We can do this by assigning bi to the element ai in A, for each i. Thus, we can write B as an infinite sequence of distinct elements bn, where n is a natural number. Therefore, B is countable.

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The probability of selecting one solid chocolate and 2 cherries is given as follows:

0.1544 = 15.44%.

A probability is obtained by the division of the number of desired outcomes by the number of total outcomes.

The outcomes resulting in one chocolate and two cherries being taken are given as follows:

Hence the probability is obtained as follows:

p = 7/17 x 6/16 x 5/15 + 6/17 x 7/16 x 5/15 + 6/17 x 5/16 x 7/15

p = 0.1544 = 15.44%.

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Displacement is the difference between the initial position and the final position of an object.

We can determine the displacement with the following formula:

Displacement = Final position - Initial position

In this case, the initial position is 0 m and the time is 6 seconds. We can find the displacement using the equation of motion:

Displacement = Initial Velocity × Time + ½ × Acceleration × Time2

Given that the acceleration of the object is 4 m/s2, the equation of motion becomes:

Displacement = 0 + ½ × 4 × 62

Therefore, the displacement of the object after 6 seconds is 72 m.

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The scale factor for 7 millimeters to 5 meters is 0.0014.

The scale factor is the ratio between the scale of an original object, drawing, map, model, or blueprint compared to its representation as a larger or smaller object.

We can compute the scale factor (scaled-down) using the following formula:

Scale factor = Dimension of the new shape ÷ Dimension of the original shape

1 meter = 1,000 millimeters

5 meters = 5,000 millimeters (1,000 x 5)

The scale-down factor of 7 millimeters to 5,000 millimeters = 0.0014 (7/5,000)

The scale-up factor of 7 millimeters to 5,000 millimeters = 714.286 (5,000/7)

Thus, the scale factor is 0.0014.

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What is the scale factor?

Answer:

First find a number you can take out of both numbers.

In this case 3.

You get left with 2+3y

So the answer is 3(2+3y).

The discount of the purchase price results in the buyer making the identical monthly payment under either purchase option, $4064.76.

Financing is the process of providing funds for business activities, making purchases, or investing. Financial institutions, such as banks, are in the business of providing capital to businesses, consumers, and investors to help them achieve their goals. The use of financing is vital in any economic system, as it allows companies to purchase products out of their immediate reach.

the PV=FV÷(1+r)^N,

here, PV is present value, FV is future value and r is the rate of discount or interst.

According to the given conditions,

if car financing at 0% ,

then car price=$36,000.

time period =48 months.

so, monthly payment =36000÷48

                                   =$750.

if financing at regular rate then, monthly interest rate is 0.5%

time=48 month.

monthly payment, if we consider same payment=$750

the discount of the purchase price will be $4064.76.

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Statements A and C are correct.

We have to select the true statements from the given four statements in options.

step 1:

I think the statements A and C are true from the mathematical point of view.

If the original function is y=[tex]\sqrt{x}[/tex] and then by reflecting it about the x-axis

the equation will become y= - [tex]\sqrt{x}[/tex] and then shrinking it vertically by a

factor of 1/2 the function will finally become y= 1/2 [tex]\sqrt{x}[/tex]

Hence, statement A is true.

step2:

Again, the original function y= [tex]\sqrt{x}[/tex] has domain x ≥ 0 and range y ≥ 0, but in the transformed equation  y=-1/2 [tex]\sqrt{x}[/tex] has domain same as original equation i.e. x ≥ 0 but the range is different i.e. y ≤ 0.

Hence, statement C is also true.

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We graph points A(0,3) and B(1,2) to find the solution.

What is the intercept?

An intercept in mathematics is a location on the y-axis through which the line's slope passes. It is a place on the y-axis where a straight line or a curve crosses.

Here, we have

Given: f(x) = 3(2/3)ˣ

We first find the y-intercept

The y-intercept is the value of f(x) when the value of x is equal to zero

For x = 0

f(0) = 3(2/3)⁰ = 3

Point A(0,3)

Now, we find the value of f(x) when x = 1

f(1) = 3(2/3)¹ = 2

Point B(1,2)

Hence, we graph points A(0,3) and B(1,2) to find the solution.

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The volume of the fish tank is 633,957.5 cubic cm or 0.634 cubic meter.

The formula for calculating the volume of a cuboid is

=  length  × breadth ×height

Given :

the length of fish tank = 105 cm

The width of fish tank= 75 cm

The height of fish tank= 80.5 cm

So, the volume of the fish tank =105×75 ×80.5

                                                =633,957.5 [tex]cm^{3}[/tex]

In metric units ;

1 meter = 100 cm

So, converting all the dimensions into metric units.

length of fish tank = 1.05 m

width of fish tank = 0.75 m

height of fish tank = 0.805 m

So, the volume of fish tank = 1.05 x 0.75 x 0.805

                                         = 0.6339575 [tex]m^{3}[/tex] or

                                         = 0.634 [tex]m^{3}[/tex]

Answer: The building is in the form of a cylinder surmounted by a cone. To find the outer surface area of the building, we need to find the total surface area of the cylinder and the cone and add them together.

The total surface area of the cylinder = 2πr^2 + 2πrh = 2π(7^2) + 2π(7)(24) = 2π(49) + 2π(168) = 98π + 336π = 434π square meters

The total surface area of the cone = πr^2 + πr√(r^2 + h^2) = π(7^2) + π(7)(√(7^2 + 24^2)) = 49π + 49π(√(625)) = 49π + 49π(25) = 49π + 1225π = 1274π square meters

The outer surface area of the building is the sum of the total surface area of the cylinder and the cone, which is 434π + 1274π = 1708π square meters.

Step-by-step explanation:

A convex pentagon has five exterior angles, and the sum of the measures of these angles is equal to 360 degrees.

We know that the measures of the exterior angles of a convex pentagon are 75°, 62°, 68°, and 101°, we need to find the measure of the last exterior angle.

To find the measure of the last exterior angle, we can use the formula:

Sum of all exterior angles = (n-2) x 180

where n is the number of sides in the polygon.

For a pentagon, n = 5, so the sum of all exterior angles is (5-2) x 180 = 540 degrees

So we can use this information to find the measure of the last exterior angle:

75 + 62 + 68 + 101 + x = 540

x = 244

Therefore, the measure of the last exterior angle is 244 degrees.

Answer:282.6 cm²

Step-by-step explanation:

The formula for the surface area of a cylinder is 2πr(r+h) where r is the radius and h is the height.

Since the diameter is given, we can find the radius by dividing the diameter by 2, so r = 6/2 = 3 cm.

Then we can plug in the values into the formula:

2πr(r+h) = 2π(3)(3+12) = 2π(3)(15) = 90π cm²

To round the answer to the nearest tenth, we can use the following method:

If the digit in the thousandths place is less than 5, we keep the hundredths digit as is.

If the digit in the thousandths place is greater than 5, we round up the hundredths digit.

Since π is an irrational number it can't be rounded to the nearest tenth. But an approximation for π is 3.14 and 90π is approximately 282.6 cm².

We can be 90% confident that the interval [76.4, 79.3] contains the true mean monthly percentage of on-time departures. This means that we are highly confident that the true mean monthly percentage of on-time departures lies within this interval.

To find the 90% confidence interval, we first need to calculate the margin of error. To calculate this, we need to use the standard error, which is calculated by dividing the standard deviation by the square root of the sample size. The standard deviation for the given data is 2.2 and the sample size is 72 (6 years × 12 months). So, the standard error is calculated as 2.2/√72 = 0.44. The margin of error is then calculated by multiplying the standard error by the critical value for 90% confidence, which is 1.645. The margin of error is therefore 0.44 × 1.645 = 0.72. The confidence interval is then calculated by adding and subtracting the margin of error from the sample mean. The sample mean is 77.8, so the 90% confidence interval is 77.8 ± 0.72, or [76.4, 79.3]. This means that we are highly confident that the true mean monthly percentage of on-time departures lies within this interval.

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A dependent variable is precisely what it sounds like, just like an independent variable. It is something on which other elements depend.

A test score, for instance, may be a dependent variable because it could vary based on a number of variables, including how much you studied, how much sleep you got the night before the test, and even how hungry you were. Typically, when attempting to establish a connection between two variables, the goal is to determine what causes the dependant variable to vary in the manner that it does.

Many people struggle to recall which variable is the independent variable and which variable is the dependent variable.

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Total number of monthly payments, not including the final balloon payment is $1,195.77

The monthly payment is the sum that must be paid each month for the duration of the loan to cover the principal balance. When a loan is taken out, not only the principal—the amount that was initially loaned out—but also the interest—which accrues—must be repaid.

Step1

M = 350,000(0.071/12)(1+0.071/12)² /(1+0.071/12)¹² =3,618.02

M = P(r/12) (1+r/12)¹²×n/(1+r/12)¹²×n -1

Step2:

3,618.02 × 12 × 12 = 520,994.88

The total paid is the product of the monthly payment and the number of payments.

520,994.88 - 350,000 = 170,994.88

= 170,994.88÷143

= 1,195.77

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1. The value of x is 1.35

2. The value of x is 0.25

The first step in finding the value of x in an equation is to isolate the variable. To do this, you will need to use the appropriate rules of algebra to rearrange the equation so that x is on one side of the equation and all other terms are on the other side. Then, you can solve the equation by using the appropriate method (e.g. factoring, quadratic formula, etc.) to solve for x.

1) 13 - 5x- 4/6 = 10x - 8

13+  8- 4/6 = 10x + 5x

21-4/6 = 15x

20.3 = 15x

x = 1.35

2) 6(14x-21) = 14(18x - 6)

84x - 126 = 252x - 84

-126 + 84 = 252x - 84x

-42 = 168x

x = 0.25

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The operations of functions results in another function which are shown as below.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

There are two functions given.

f(x) = x² + 7

g(x) = 2x + 1

7. Addition of functions

   (f + g)(x) = f(x) + g(x)

                 = x² + 7 + 2x + 1

                 = x² + 2x + 8

8. Subtraction of functions

    (f - g)(x) = f(x) - g(x)

                 = (x² + 7) - (2x + 1)

                 = x² - 2x + 6

9. (g - f)(x) = g(x) - f(x)

                 = (2x + 1) - (x² + 7)

                 = -x² + 2x - 6

10. Multiplication of Functions

     (f . g)(x) = f(x) . g(x)

                  = (x² + 7) . (2x + 1)

                  = 2x³ + 14x + x² + 7

                  = 2x³ + x² + 14x + 7

11. Division of functions

   [tex]\frac{f}{g}[/tex](x) = [tex]\frac{f(x)}{g(x)}[/tex]

          = (x² + 7) / (2x + 1)

12.  [tex]\frac{g}{f}[/tex](x) = [tex]\frac{g(x)}{f(x)}[/tex]

            = (2x + 1) / (x² + 7)

Hence the operations of the functions are done.

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The total volume of both storages will be 76 cubic ft.

A volume is defined as the amount of space occupied by a three-dimensional solid shape. It is difficult to visualize in any shape, but it can be compared between shapes.

A compass box, for example, has a larger volume than an eraser placed inside it. We divide any two-dimensional shape into equal square units to calculate its area.

The volume of the larger box will be calculated as:-

Volume = side³

Volume = (4)³

Volume = 64 cubic ft

The volume of the smaller box = 12 cubic ft

Total volume = 64 + 12 = 76 cubic ft

Hence, the total volume of the boxes is 76 cubic ft.

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Answer:

1) x² + 4x +1 = 1 (You have to put in +1)

2) True

Step-by-step explanation:

1)

2) A range is a representation of values between two points. When you're calculating the range of a parabola, you only know one of those points to start with. Your parabola will go on forever either up or down, so the end value of your range is always going to be ∞ (or −∞ if your parabola faces down.)

Answer: the answer is true

Step-by-step explanation: There are an infinite amount of numbers the parabola can hit, and there is no limit

hence the statement is true

A approach to geometrically represent complex numbers is by using the complex plane, commonly known as the Argand plane or the Gauss plane.

A approach to geometrically represent complex numbers is by using the complex plane, commonly known as the Argand plane or the Gauss plane. The real and imaginary halves of a complex number are represented by displacements along the x and y axes, respectively, in what is essentially a modified Cartesian plane.

Similar to how we may represent the set of real numbers on a number line, we can represent the set of complex numbers on a complex plane. At the coordinates (0,0)left parenthesis, 0 comma, 0 right parenthesis, two number lines that make up the complex plane cross at a right angle.

You may think of the y-axis as the hypothetical axis.

The actual axes are on the x-axis.

In light of this, we can say:

A: (-2, 3i) (-2, 3i)

B: (-1, -i) (-1, -i)

C: (3, -4i) (3, -4i)

D: (4, I (4, i)

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How the transformations below affect length, angles or both?

A) n = 50, Since the sample size is small, it is more likely that a higher value is selected as the median, and the sample would be skewed to the right tail.

What is the median value?

The median value of a set of data is the middle value when the data is arranged in order. It is the value that separates the higher half of the data from the lower half. In other words, it's the value that has half the observations below it and half the observations above it.

In a residential neighborhood, the median value of a house is $200,000, which means that half the houses in the neighborhood are worth more than $200,000 and half are worth less.

For a sample median most likely to be above $250.000, the sample size would have to be small and skewed to the right tail, where the higher values are. In this case, the answer would be

Hence, A) n = 50, Since the sample size is small, it is more likely that a higher value is selected as the median, and the sample would be skewed to the right tail.

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The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.

When referring to a function, "end behaviour" refers to the character of the value as the function parameter becomes closer to +∞ and -∞.

In the given table for f(x), we see that for every value of x, function f(x) is decreasing.

f(-2) = 48

f(0) = 12

f(2) = 3

f(3) = 1.5

In other words as the value of x increases, f(x) is approaching towards 0.

Now we take another function g(x) =

Now we plug in the values of x to get the values of g(x)

g(-1) =2^-1-5  

    = 1-10/2

    = -9/2

    = -4.5

g(0) =  2^0-5

     = 1 - 5 = -4

g(2) = 2^2-5

     = 4 - 5 = -1

g(3) = 2^3-5

     = 8 - 5= 3

Now we find that g(x) is increasing with the values of x.

Now we take third function h(x).

By analyzing the given graph we find

h(-4) = 2

h(0) = 3

h(1) = 5

So when we are increasing the value of x function h(x) is increasing.

Finally we conclude by the options given that f(x) is the only function which tends to 0 with the increase in the values of x.

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Answer:

False, if this is not what you mean comment and tell me

Step-by-step explanation:

The estimate errors in the adjacent side and the hypothenuse are ≅ ±0.29 cm and ≅ ±0.145 cm respectively. The percentage errors in the adjacent side and hypothenuse are 2.009% & 0.502%.

Hypothenuse y₁ = 25/sin x = 25cosec x

Adjacent y₂ = 25/tan x = 25cot x

Opposite angle is 60° = π/3

Possible error, dx ≅ ±0.5° = 0.5 × π/180 = ±π/360

Differentiating y₁ = 25cosec x

dy₁ = -25(cosec x · cot x)dx

dy₁ = -25(cosec (π/3) · cot (π/3))×±π/360

= -25(2/√3)(1/√3)(±π/360)

= ≅ ±0.145 cm

Similarly

dy₂ = -25 cosec²x .dx

dy₂ = -25 cosec²(π/3) .×±π/360

= -25(2/√3)²×±π/360

≅ ±0.29 cm

So the errors in the hypothenuse = ±0.145 cm

Error in the adjacent side = ±0.29 cm

Percentage error in the adjacent side = 0.29/(25/√3) = 2.009 %

Percentage error in the hypothenuse = 0.145/(25/sin60) = 0.502%

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