The sum of the squares of two consecutive positive integers is 340. find the integers. 

Evaluating the function we can see that:

a) f(7) is equal to f(-7)

b) f(-10) is greater than f(3).

Here we have the quadratic function f(x) = x²

A) First we need to evaluate the function in x = 7 and x = -7 to see which one gives a larger value.

f(7) = 7² = 49

f(-7) = (-7)² = 49

Then neither of these two is greater, because are the same value.

B) now we need to evaluate in x = -10 and x = 3

f(-10) = (-10)² = 100

f(3) = 3² = 9

We can see that f(-10) is greater.

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(a) The people that did not own a car are 13

(b) The sentence to describe the problem is "13 of every 20 people do not own a car"

Given that

Number of friends = 20

Percentage that do not own a car = 65%

Using the above as a guide, we have the following:

People = 65% * 20

Evaluate

People = 13

Writing a sentence to describe the problem, we have:

The statement is given as

65% of people do not own a car".

This can be rewritten as

"13 of every 20 people do not own a car"

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The sum of the measures of the angle of a triangle is 180 degrees.

The given triangle is a type of triangle and the type of triangle a scalene triangle.

For a scalene triangle, the measure of the three sides are unequal and the sum of the interior angle of a triangle is 180 degrees.

Hence the measure of the angles <A, <B and <C are all less than 90 degrees since they are all acute angles.

We can therefore conclude that:

m<A + m<B + m<C = 180 degrees

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The sample space has 13 outcomes.

We have to given that;

A player randomly selects a marble from a bag.

And, In the bag which has 5 blue marbles, 6 red, 1 orange, and 1 yellow.

Since, The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Now, We can formulate;

Total number of marbles = 5 + 6 + 1 + 1

Total number of marbles = 13

Hence, there are 13 possible outcomes for the player's selection.

Therefore, We get;

The sample space has 13 outcomes.

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The final expression for the given problem is (f(3+h) - f(3))/h = -h - 3.

To solve this problem, we first need to determine the value of f(3+h) and f(3):

Given [tex]F(x) = 4 + 3x - x^2[/tex], we can find f(3+h) by substituting 3+h for x:

[tex]f(3+h) = 4 + 3(3+h) - (3+h)^2\\f(3+h) = 4 + 9 + 3h - (9 + 6h + h^2)\\f(3+h) = -h^2 - 3h + 4[/tex]

Next, we can find f(3) by substituting 3 for x:

[tex]f(3) = 4 + 3(3) - (3)^2\\f(3) = 4 + 9 - 9\\f(3) = 4[/tex]

Now we can substitute these values into the expression (f(3+h) - f(3))/h:

[tex](f(3+h) - f(3))/h = ((-h^2 - 3h + 4) - 4)/h\\(f(3+h) - f(3))/h = (-h^2 - 3h)/h\\(f(3+h) - f(3))/h = -h - 3[/tex]

Therefore, the final expression for the given problem is:

(f(3+h) - f(3))/h = -h - 3

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Therefore, the dimensions of the rectangular plot are either 20 meters by 11 meters or 11 meters by 20 meters.

Let's assume that the length of the rectangular plot is x meters. Then the width would be (220/x) meters because we know that the area is 220 square meters.

The perimeter of the rectangular plot would be:

2x + 2(220/x) = 62

Simplifying this equation, we get:

2x^2 + 440 = 62

2x^2 - 62x + 440 = 0

x^2 - 31x + 220 = 0

Factoring this equation, we get:

(x - 20)(x - 11) = 0

Therefore, x = 20 or x = 11.

If x = 20, then the width would be 11 and if x = 11, then the width would be 20.

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a.

i. The initial value (IV) is 37.

ii. The percent increase or decrease is 4%.

b.

i. The initial value (IV) of the function is -0.7.

ii. The percent decrease is 40%.

a.

i. The initial value (IV) of the function is 37.

ii. The percent increase or decrease is 4%, because the base of the exponential function is 1.04, which is 1 plus 4% (0.04).

b.

i. The initial value (IV) of the function is -0.7.

ii. The percent decrease is 40%, because the base of the exponential function is 0.6, which is 60% (0.6) of the initial value (-0.7).

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The complete question:

1. For each equation, find the initial value and the percent increase or decrease.

a. f(x) = 37(1.04)ˣ

i. IV:__

ii. % Inc/Dec:_

b. f(x) = (-0.7) (0.6)ˣ

i. IV:

ii. % Inc/Dec:___

the maximum value of the function is y = -1 + 6cos(2π/7(26.75-5)) = 5.

The function y = -1 + 6cos(2π/7(x-5)) is a periodic function with a period of 7. The maximum value of the function occurs when the cosine function reaches its maximum value of 1.

So, we need to find the value of x that makes the argument of the cosine function equal to an odd multiple of π/2, which is when the cosine function is equal to 1.

2π/7(x-5) = (2n + 1)π/2, where n is an integer

Simplifying this equation, we get:

x - 5 = (7/4)(2n + 1)

x = 5 + (7/4)(2n + 1)

Since the function has a period of 7, we can restrict our attention to the interval [5, 12].

For n = 0, we get x = 5 + 7/4 = 23/4

For n = 1, we get x = 5 + (7/4)(3) = 26.75

For n = 2, we get x = 5 + (7/4)(5) = 33.25

For n = -1, we get x = 5 + (7/4)(-1) = 1.75

For n = -2, we get x = 5 + (7/4)(-3) = -4.75

Out of these values of x, the only one that lies in the interval [5, 12] is x = 26.75.

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By probability , Tom can arrange his 5 red and 5 white books in an alternating pattern in 48 ways

There are 5 red books and 5 white books to arrange in an alternating pattern on the shelf.

To do this, Tom can start with either a red or a white book. If he starts with a red book, he can arrange the rest of the books in 4! (4 factorial) ways. Similarly, if he starts with a white book, he can arrange the rest of the books in 4! ways. Therefore, the total number of ways Tom can arrange the books in an alternating pattern is 2 x 4! = 48.

Tom can arrange the 10 books in an alternating pattern by starting with either a red or a white book. If he starts with a red book, he can arrange the rest of the books in 4! ways, and if he starts with a white book, he can also arrange the rest of the books in 4! ways. Therefore, the total number of ways to arrange the books is 2 x 4! = 48.

Tom can arrange his 5 red and 5 white books in an alternating pattern in 48 ways.

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Multivariable calculus in college is generally more challenging than AP Calculus BC due to the additional complexity of working with functions of several variables.

Multivariable calculus in college typically goes beyond the content covered in AP Calculus BC in high school. While both cover calculus concepts, multivariable calculus adds the complexity of working with functions of several variables, including partial derivatives, multiple integrals, and vector calculus. As a result, the difficulty level of multivariable calculus in college can be significantly higher than AP Calculus BC. However, this can vary depending on the individual student and the rigor of their high school AP course.

AP Calculus AB and BC are two levels of Advanced Placement calculus courses typically offered in high school.

AP Calculus AB covers a wide range of calculus topics including limits, derivatives, integrals, applications of derivatives and integrals, and the Fundamental Theorem of Calculus. The focus is on single-variable calculus, meaning students work with functions of one variable.

AP Calculus BC, on the other hand, covers all the topics included in AB as well as additional concepts such as parametric, polar, and vector functions, series, and sequences. The course is designed to be more challenging and covers more advanced topics in calculus, including applications of calculus in physics and engineering.

Overall, AP Calculus BC is considered to be a more rigorous course than AP Calculus AB, but both courses prepare students for college-level calculus.

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complete question:

how does multivariable calculus in college compare with ap calculus bc in high school? is there a significant gap in difficulty?

Answer:

The formula is V = r²h for the volume of a cylinder, we need to first find the radius of the cylinder:

The diameter of the cylinder is 7 feet, so the radius is half of that cylinder, so you have to divide by 2 to get half of the diameter:

r = 7/2

= 3.5 feet.

V = π(3.5)²(12)

V = π(12.25)(12)

V = 147π

Therefore, the volume of the cylinder is 147π cubic feet.

Step-by-step explanation:

1:3    means you need to find 1 /(1+3) = 1/4 th of the way to 5,8 from -2,0

x:   from -2 to +5 is 7 units     1/4th * 7 = 7 /4   added to -2

              is  - 1/4

y: from 0 to 8    is 8 units   1/4 th * 8  = 2 added to 0   is   2

(-1/4 , 2)

A 95% confidence set for two or more coefficients is a set that contains: D) the population values of these coefficients in 95% of randomly drawn samples.

A 95% confidence set for two or more coefficients is a set that contains the same values as the 95% confidence intervals constructed for the coefficients. This means that the set includes all possible values for the coefficients that are consistent with the observed data and the level of uncertainty indicated by the confidence level. It is important to note that the confidence set is not guaranteed to contain the true population values of the coefficients in 95% of randomly drawn samples, as the true values are unknown.

The confidence set provides a range of plausible values that can be used for inference and decision making. The concept of a 95% confidence set.

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Answer:

20

Step-by-step explanation:

4x + 5x = 180

9x = 180

x = 20

Answer:

198 in²

Step-by-step explanation:

triangle (A=1/2)bh [A=1/2(22×8)] b=22 H=8

rectangle (A=bh) [A= 22×5] B=22 H=5

triangle = 88

rectangle = 110

So, 88+110 = 198

ANSWER:

(-4,-4)

EXPLANATION:

Just simply multiply the two points by 2. Since -2*2 is equal to -4, then the answer would be (-4, -4).

Answer:

150 square inches

Step-by-step explanation:

The formula is A=2(wl+hl+hw)

Plug in the values.

2(9+33+33)

Evaluate.

=150

(Assuming both the length and width is 3)

The attributes, measurements used, and observations of the data are listed  below:

Attributes:

- Light bulb

- Wattage (number of watts of electricity used)

Measurements used:

- Watts (units of measurement for the amount of electricity used by a light bulb)

Observations:

- The data shows the wattage for different types of light bulbs.

- The wattage varies widely among different types of light bulbs.

- Incandescent bulbs have the highest wattage, followed by halogen bulbs, fluorescent bulbs, and LED bulbs.

- The wattage for each type of bulb can vary within a certain range, with some bulbs having higher or lower wattage than others within the same category.

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Answer:

Step-by-step explanation:

The test statistic if the sample proportion is 20/50 and the hypothesized proportion was 0.5 is:  -1.414.

Using z-test formula to determine the test statistic

z = (p - P) / [tex]\sqrt[/tex]((P(1-P))/n)

Where:

p = sample proportion = 20/50 = 0.4

P = hypothesized proportion = 0.5

n= sample size = 50

Let plug in the formula

Test statistic  = (0.4 - 0.5) / [tex]\sqrt[/tex]((0.5(1-0.5))/50)

Test statistic = (-0.1) / [tex]\sqrt[/tex]((0.25)/50)

Test statistic = (-0.1) / [tex]\sqrt[/tex](0.005)

Test statistic = (-0.1) / 0.0707

Test statistic = -1.414

Therefore the test statistic  is -1.414.

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The radius of the golf ball is given as follows:

2.1 feet.

The volume of an sphere of radius r is given by the multiplication of 4π by the radius cubed and divided by 3, hence the equation is presented as follows:

[tex]V = \frac{4\pi r^3}{3}[/tex]

The volume of the ball in this problem is given as follows:

V = 38.7 cubic feet.

Hence the radius of the ball is obtained as follows:

r³ = 3 x 38.7/4π

r³ = 9.2389

[tex]r = \sqrt[3]{9.2389}[/tex]

r = 2.1 feet

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Answer:

And solving for the initial amount  we got:

So then the original price for the car would be approximately 18263.539$

Step-by-step explanation:

For this case we can use the exponential model given by:

Where:

represent the initial amount for the car

represent the exponential growth/decay rate

t represent the number of years. With t =0 at the begin

After 6 year we have that t =6, and we know this condition:

So then we can use the exponential model formula and the condition given and we have this:

And solving for the initial amount  we got:

So then the original price for the car would be approximately 18263.539$

Answer:

y=-[tex]\frac{9}{7}[/tex]

Step-by-step explanation:

Answer:

180 cm³

Step-by-step explanation:

split the side (the side facing us) into three rectangles. one rectangle immediately beneath top step, next under middles step and so on.

area under top step = (2 + 2 + 2) X 3 = 18.

area under middle step = (2 + 2) X 3 = 12

area under bottom step = 2 X 3 = 6

total area of this side (cross-section) = 18 + 12 + 6 = 36.

volume = 36 X length

=  36 X 5

= 180 cm³

The answer for (1) is 31, the answer for (2) is 25, and the answer for (3) is 17.

It is given that:

In a secondary school class, 23 pupils study Economics, 6 pupils study both Government and Economics. 48 pupils study either Government or Economics or both.

Based on the information we can draw a Venn diagram:

From the Venn diagram:

A + B = 17 + 6

A + B = 23

B = 6

A + B + C = 48

A = 23 - 6 = 17

C = 48 - 17 - 6

C = 25

The total number of pupils who only study Government = 25

The total number of pupils who study Government = 25 + 6 = 31

The total number of pupils who study Economics only = 17

Thus, the answer for (1) is 31, the answer for (2) is 25, and the answer for (3) is 17.

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The circumference of the given circle is 14π mm.

We have,

The circumference of a circle with radius r is given by the formula:

C = 2πr

In this case,

The radius of the circle is given as 7 mm.

Substituting the value of r in the above formula.

C = 2π(7) mm

Simplifying this expression, we get:

C = 14π mm

Therefore,

The circumference of the given circle is 14π mm.

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To determine the cost of a box spread, you need to calculate the net cost or net debit of the options involved in the spread. In a long box spread, you buy a bull call spread and a bear put spread using the same expiration date and strike prices.

In this case, the investor has a long box spread using the June 50 and 55 options. The bull call spread involves buying the June 50 call option and selling the June 55 call option, while the bear put spread involves buying the June 55 put option and selling the June 50 put option.

To calculate the cost of the box spread, you would add the cost of the bull call spread (net debit) to the cost of the bear put spread (net debit). The net debit is the difference in premiums between the options involved in each spread.

Since the specific premium values for the options are not provided in the question, it is not possible to determine the exact cost of the box spread without that information. You would need the premium values to calculate the net debit for each spread and then sum them to determine the total cost of the box spread.

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The greatest possible mass of the rock to two decimal places is 86.34 g

Since the mass of the piece of rock is 86.3 g, correct to the nearest 0.1 g. Thus, the actual mass of the rock  in 2 decimal places could be between 86.25 g and 86.34 g.

To find the greatest possible mass of the rock, we need to round up to the higher end of the range of the mass of the rock.

Therefore, the greatest possible mass of the rock to two decimal places is 86.34 g

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Answer:

50.85% increase

Step-by-step explanation:

The formula for % change is (new-old)/old.

So (89-59)/59 = 30/59 = 0.5084745763 = 50.85% increase