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The number of calories per ounce of soda is 10

The given parameters are:

Calories = 50

Ounces = 5

Let the number of calories be y and the ounces be x.

So, we have:

y = kx

Substitute y = 50 and x = 5

50 = 5k

Divide by 5

k = 10

Substitute k = 10 in y = kx

y = 10x

See attachment for the graph of the relationship between the number of calories and the number of ounces

In (a), we have:

k = 10

This means that the number of calories per ounce of soda is 10

The unit rate and the slope represent the same and they have the same value

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The difference between Alok and Prabir share exists 8000.

Given: Invested by Alok = Rs 90, 000

Invested by Prabir = Rs 1,20000

The time period of Alok = 3 months

The time period of Prabir = 2 years

They earn a profit = Rs 96,000.

Profit exists directly proportional to the product of the amount invested and the time period of investment.

8000 = 90000 [tex]*[/tex] 24/120000 [tex]*[/tex] 21

= 5/7

5x + 7x = 96000

x = 8000

first = 40000

second = 48000

so the difference exists at 8000.

The difference between Alok and Prabir share exists 8000.

Therefore, the correct answer is 8000.

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The second number line best shows how to solve –4 – (–8). This can be obtained by finding the value of –4 – (–8) and checking which number line has the required arrow mark.

The value of  –4 – (–8) is obtained.

–4 – (–8) =  –4 + 8

–4 – (–8) = 4

The arrow should move from zero to - 4 and the second arrow should move from - 4 to 4.

From the question given the number lines,

The first arrow is moving from zero to - 4.

First condition is satisfied.

The second arrow is moving from - 4 to  8.

Second condition is not satisfied.

The first arrow is moving from zero to - 4.

First condition is satisfied.

The second arrow is moving from - 4 to  4.

Second condition is satisfied.

Hence the second number line best shows how to solve –4 – (–8).

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Comparing g(x) with f(x), you can see that the function f(x) is translated to the right by 6 units to produce g(x) which is equivalent to (x-6)²

Transformation is a techniques use to change the position of an object on an xy-plane.

Given the parent function f(x) = x² and the function g(x) = x²-12x +36

Factorize g(x);

g(x) = x²-6x-6x+36

g(x)=x(x-6)-6(x-6)

Group the terms to have;

g(x) = (x-6)²

Comparing g(x) with f(x), you can see that the function f(x) is translated to the right by 6 units to produce g(x) which is equivalent to (x-6)²

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Answer:

  x = 3

Step-by-step explanation:

Maybe you want the value of x such that ...

  4(6^x) = 864

Dividing by 4 gives ...

  6^x = 216

You may know that 216 = 6^3. Using that, we can equate exponents:

  6^x = 6^3

  x = 3

Alternatively, we can use logarithms to find x. Taking logs gives ...

  x·log(6) = log(216)

  x = log(216)/log(6) = 3

The equation of parabola is a [tex]\frac{-(x+ 3)^{2}}{64} + \frac{ (y-1)^{2}}{4} = 1[/tex] and the coordinates of center is (0,0) And asymptote is become 16.

According to the statement

we have to find the centers, foci, vertices and asymptotes of the hyperbola from the given equations.

So, For this purpose,

Hyperbola is a a plane curve generated by a point so moving that the difference of the distances from two fixed points is a constant.

So, The given equation is:

16y²-x² - 6x - 32y = 57

So, rearrange it then

-x² - 6x - 32y + 16y² = 57

-(x² + 6x) + (16y² - 32y ) = 57

-(x² + 6x) + 16(y² - 2y ) = 57

-(x² + 6x + 9) + 16(y² - 2y +1 ) = 57 +1(16) + 9(-1)

-(x+ 3)²  + 16 (y-1)²  = 64

-(x+ 3)²  + 16 (y-1)²  = 64

divide whole equation by 64 then

[tex]\frac{-(x+ 3)^{2}}{64} + \frac{16 (y-1)^{2}}{64} =\frac{64}{64}[/tex]

then equation become

[tex]\frac{-(x+ 3)^{2}}{64} + \frac{ (y-1)^{2}}{4} = 1[/tex]

This become the equation of hyperbola.

So,

here coordinates of center is (0,0)

And asymptote is become 16.

So, The equation of parabola is a [tex]\frac{-(x+ 3)^{2}}{64} + \frac{ (y-1)^{2}}{4} = 1[/tex] and the coordinates of center is (0,0) And asymptote is become 16.

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Answer:

x₁ = -4

x₂ = 3

Step-by-step explanation:

x²+ x + 12 = 0

x = {-1±√((1²)-(4*1*-12))} / (2*1)

x = {-1±√(1+48)} / 2

x = {-1±√49} / 2

x = {-1±7} / 2

x₁ = {-1-7} / 2 = -8/2 = -4

x₂ = {-1+7} / 2 = 6/2 = 3

Check:

x₁

-4² + (-4) - 12 = 0

16 - 4 - 12 = 0

x₂

3² + 3 - 12 = 0

9 + 3 - 12 = 0

Answer:

f(x) = -3x + 3

Step-by-step explanation:

The surface area of the figure illustrated will be 286 yards²

The surface area of a solid object simply implies the measure of the total area which the surface of an object occupies. This is typically done by adding all the areas on the surface of the object.

It should be noted that the surface area of a cuboid will be:

= 2(lw + lh + wh)

w = width = 7

l = length = 9

h = height = 5

Surface area = 2(lw + lh + wh)

= 2(7 × 9) + 2(9 × 5) + 2(7 × 5)

= 126 + 90 + 70

= 286 yards²

Therefore, the surface area of the solid will be 286 yards².

Complete question:

Find the surface area of the solid given that the length is 9 yards, the width is 7 yards, and the height is 5 yards.

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Answer:

Step-by-step explanation:

[tex]2x > 30+\frac{5}{4x} \\2x-\frac{5}{4x} > 30\\\frac{8x^2-5}{4x} > 30\\case~1\\if~x > 0\\8x^2-5 > 120x\\8x^2-120x > 5\\x^2-15x > \frac{5}{8} \\adding~(-\frac{15}{2} )^2~to~both~sides\\(x-\frac{15}{2} )^2 > \frac{5}{8}+\frac{225}{4} \\(x-\frac{15}{2} )^2 > \frac{455}{8} \\x-\frac{15}{2} < -\sqrt{\frac{455}{8} } \\x < \frac{15}{2}-\sqrt{\frac{455}{8} } \\or~x < 0\\rejected~as~x > 0[/tex]

[tex]x-\frac{15}{2} > \sqrt{\frac{455}{8} } \\x > \frac{15}{2} +\sqrt{\frac{455}{8} }[/tex]

case~2

[tex]if~x < 0\\8x^2-5 < 120x\\8x^2-120x < 5\\x^2-15x < \frac{5}{8} \\adding~(-\frac{15}{2} )^2\\(x-\frac{15}{2} )^2 < \frac{5}{8} +(-\frac{15}{2} )^2\\|x-\frac{15}{2} | < \frac{5+450}{8} \\-\sqrt{\frac{455}{8} } < x-\frac{15}{2} < \sqrt{\frac{455}{8} } \\\frac{15}{2} -\sqrt{\frac{455}{8} } < x < \frac{15}{2} +\sqrt{\frac{455}{8} } \\but~x < 0\\7.5-\sqrt{\frac{455}{8} } < x < 0[/tex]

The surface area of the given two rectangular prism is given as follows:

498 cm².

The surface area of a rectangular prism of length l, width w and height h is given as follows:

S = 2(lw + wh + hl).

For this problem, there are two prisms, with dimensions given as follows:

Hence the surface area of the figure is the combined surface area of each figure, hence:

S = 2(7 x 7 + 12 x 7 + 12 x 7) + 2(2 x 7 + 2 x 2 + 7 x 2) = 498 cm².

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The value of k such that the graph of f and the graph of g only intersect one is equal to 2.

The value of k such that the graph of f and the graph of g only intersect one is equal to 2. According to the image attached below, functions f(x) and g(x) intersect at point (x, y) = (0, 4) for k = 2.

Herein we have a system formed by two nonlinear equations, a quadratic equation and a cubic equation. Given the constraint that both function must only intersect once, we have the following expression:

f(x) - x² - k · x = 4       (1)

g(x) - x² - k · x = x³ + 2 · k        (2)

x³ + 2 · k = 4

x³ + 2 · (k - 2) = 0

If f and g must intersect once, then the roots must of the form:

(x - r)³ = x³ + 2 · (k - 2)

x³ - 3 · r · x² + 3 · r² · x - r³ = x³ + 2 · (k - 2)

Then, the following conditions must be met: - 3 · r · x² = 0, 3 · r² · x = 0. If x may be any real number, then r must be zero and the value of k must be:

2 · (k - 2) = 0

k - 2 = 0

k = 2

Therefore, the value of k such that the graph of f and the graph of g only intersect one is equal to 2. According to the image attached below, functions f(x) and g(x) intersect at point (x, y) = (0, 4) for k = 2.

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Answer: 28

Step-by-step explanation:

[tex]8+(7+1)2+4\\\\8+(8)2+4\\\\8+16+4\\\\24+4\\\\28[/tex]

The ODE is separable.

[tex]\dfrac{dy}{dx} = xy \iff \dfrac{dy}y = x\,dx[/tex]

Integrate both sides to get

[tex]\displaystyle \int\frac{dy}y = \int x\,dx[/tex]

[tex]\boxed{\ln|y| = \dfrac12 x^2 + C}[/tex]

But notice that replacing the constant [tex]C[/tex] with [tex]-C[/tex] doesn't affect the solution, since its derivative would recover the same ODE as before.

[tex]\ln|y| = \dfrac12 x^2 - C \implies \dfrac1y \dfrac{dy}{dx} = x \implies \dfrac{dy}{dx} = xy[/tex]

so either of the first two answers are technically correct.

(i) The expanded form of (1 / 2 - 2 · x)⁵ in ascending form is 1 / 32 - (5 / 8) · x + 5 · x² - 20 · x³ + 40 · x⁴ - 32 · x⁵.

(ii) The coefficient of x³ from (1 + a · x + 3 · x²) · (1 / 2 - 2 · x)⁵ is - 265 / 8.

In this problem we must apply the concept of Pascal's triangle to expand the power of a binomial of the form (x + y)ⁿ and further algebra properties.

(i) First, we proceed to expand the power binomial (1 / 2 - 2 · x)⁵ in ascending order:

(1 / 2 - 2 · x)⁵ = (1 / 2)⁵ + 5 · (1 / 2)⁴ · (- 2 · x) + 10 · (1 / 2)³ · (- 2 · x)² + 10 · (1 / 2)² · (- 2 · x)³ + 5 · (1 / 2) · (- 2 · x)⁴ + (- 2 · x)⁵

( 1 / 2 - 2 · x)⁵ = 1 / 32 - (5 / 8) · x + 5 · x² - 20 · x³ + 40 · x⁴ - 32 · x⁵

(ii) Second, we proceed to expand the following product of polynomials by algebra properties:

(1 + a · x + 3 · x²) · (1 / 2 - 2 · x)⁵ = (1 + a · x + 3 · x²) · [1 / 32 - (5 / 8) · x + 5 · x² - 20 · x³ + 40 · x⁴ - 32 · x⁵]

(1 + a · x + 3 · x²) · (1 / 2 - 2 · x)⁵ = 1 / 32 + (a / 32 - 5 / 8) · x + (- 5 · a / 8 + 163 / 32) · x² + (- 175 / 8 + 5 · a) · x³ + (65 - 20 · a) · x⁴ + (- 92 + 40 · a) · x⁵ + (120 - 32 · a) · x⁶ - 96 · x⁷

In accordance with the statement, we find that:

- 5 · a / 8 + 163 / 32 = 13 / 2

- 5 · a / 8 = 45 / 32

a = - 9 / 4

Thus, the coefficient of x³ is:

C = - 175 / 8 + 5 · (- 9 / 4)

C = - 265 / 8

The coefficient of x³ from (1 + a · x + 3 · x²) · (1 / 2 - 2 · x)⁵ is - 265 / 8.

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Given the following:

The economic order quantity is 24.

Eoq = √2 * demand * ordering cost / holding cost)

= √(2 * 1050 * 15 / 55)

EOQ = 24

The  Average inventory = EOQ / 2

= 24 / 2

= 12

Expected number of orders = demand / EOQ

= 1050 / 24

= 44

Annual holding cost (AHC) = (EOQ / 2) * Holding cost

= (24 / 2) * 55

= 660

Annual ordering cost (AOC) = (demand / EOQ) * ordering cost

= (1050 / 24) * 15

= 656

Thus,

Total cost of managing = AHC + AOC

= 660 + 656

TCM = 1,316

5. For holding cost of 60

EOQ= √(2 * demand * ordering cost / holding cost)

= √(2 * 1050 * 15 / 60)

= 23

Annual holding cost = (EOQ / 2) * holding cost

this gives us

= (23 / 2) * 60

= 690

Annual ordering cost = (demand / EOQ) * ordering cost

= (1050 / 23) * 15

= 685

Total cost of managing = AHC+ AOC

= 690 + 685

= 1375

Change in total annual cost = new - old

= 1375 - 1316

= 59

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Answer:

simplification of the original equation is below/

Step-by-step explanation:

9+4t=-3(1-2t) can be simplified into

9+4t=-3+6t because of distributing the -3 to both the 1 and -2t.

however, this can simplified to

4t-6t=-3-9

and this can simplify to

-2t=-12

which can simplify to

t = 6

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6 decks of cards = 60 cards

---> 60/8 = 15/2 = 7.5

7.5 cards = 0.75 decks of cards

Therefore, each student will get 0.75 decks of cards.

Answer:

1

Step-by-step explanation:

Everyone gets 1 and there's 2 left over

Answer: Pr(4.19 ≤ X ≤ 4.81)

Step-by-step explanation:

First of all, let's calculate the mean;

x¯ = (4.3 + 5.1 + 3.9 + 4.5 + 4.4 + 4.9 + 5.0 + 4.7 + 4.1 + 4.6 + 4.4 + 4.3 + 4.8 + 4.4 + 4.2 + 4.5 + 4.4)/17

x¯ = 76.5/17

x¯ = 4.5

We are given standard deviation; s = 0.31

Now, z-value for a 68% Confidence interval is 1

Range in which the data falls is;

Range = x¯ ± zs

Range = 4.5 ± (1 × 0.31)

Range is;

Pr[(4.5 - 0.31) ≤ X ≤ (4.5 + 0.31)]

Pr(4.19 ≤ X ≤ 4.81)

Answer:

Pr (3.57 ≤ X ≤ 5.43)

Step-by-step explanation:

Took the quiz.

Answer:

Step-by-step explanation:

The probability that exactly 7 are men out of 10 sports car owners who are randomly selected is 0.215 given that 60% of people who purchase sports cars are men. This can be obtained by using binomial distribution formula.

This question can be solved using binomial distribution formula.

The formula for binomial distribution is the following,

P(X) = ⁿCₓ pˣ qⁿ⁻ˣ

where,

n = number of trials(or the number being sampled)

x = number of success desired

p = probability of getting a success in one trial

q = 1 - p = probability of getting a failure in one trial

Here in the question it is given that,

⇒ 60% of people who purchase sports cars are men

This statements clearly means that probability of men purchase sports cars is 60%.

⇒ P(men purchasers) = p = 60% = 0.6

From this we can find the probability of women who purchase sports cars,

⇒ P(women purchasers) = q = 1 - p = 1 - 0.6 = 0.4

So we can find the probability that exactly 7 are men out of 10 sports car owners who are randomly selected

It is a binomial case with n = 10

By using the  formula for binomial distribution we get,

P(X = 7) = ¹⁰C₇ × 0.6⁷ × 0.4³

P(X = 7) = 120 × 0.0279936 × 0.064

P(X = 7) = 0.21499

P(X = 7) = 0.215

Hence the probability that exactly 7 are men out of 10 sports car owners who are randomly selected is 0.215 given that 60% of people who purchase sports cars are men.

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Answer:

e

Step-by-step explanation:

[tex]volume~of~cone=\frac{1}{3}volume ~of~cylinder\\volume~of~cylinder=3 \times volume ~of~cone=3 \times15=45 \\volume ~of~two~cylinders=2 \times45=90[/tex]

Answer:

57

Step-by-step explanation:

-7a + 4b

Let a = -3  b = 9

Substitute the values in

-7(-3) + 4(9)

Multiply

21 + 36

Add

57

Using the permutation formula, there are 157,410 ways for the medals to be distributed.

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this problem, 3 athletes are chosen from a set of 55, hence the number of ways is given by:

P(55,3) = 55!/52! = 157,410

157,410 ways for the medals to be distributed.

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Answer:

39 pages

Step-by-step explanation:

If 13 pages are read in 1/3 of an hour, we need to multiply 13 by 3 to get the number of pages read in 1 hour. 13*3 = 39 pages

The exponential function that represent the concentration of algae cells per milliliter in d days is [tex]C(d) = 10(2)^d[/tex]

An equation is an expression that shows the relationship between two numbers and variables.

The standard form of an exponential funtion is in the form:

y = abˣ

Where a is the initial value and b is the multiplication factor.

Let C(d) represent the concentration of algae cells per milliliter in d days

At point (1, 20)

20 = ab   (1)

At point (2, 40)

40 = ab²     (2)

From equations 1 and 2:

b = 2, a = 10

The exponential function that represent the concentration of algae cells per milliliter in d days is [tex]C(d) = 10(2)^d[/tex]

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Answer:

f^-1(x)=x-14

Step-by-step explanation:

change f(x) to y :y=x×14

interchange variables :x=y+14

move constant(14) to the left :x-14=f^-1(x)

Answer:

1) 13m, 2) 10ft, 3) 11.4ft, 4) 12.7m

Step-by-step explanation:

Since all of these triangles are right triangles, we can use the Pythagorean Theorem: a^2+b^2 = c^2

1) 5^2+12^2 = c^2 = 25+144 = c^2 = 169 = c^2 = 13 = c

2) 6^2+8^2 = c^2 = 36+64 = c^2 = 100 = c^2 = 10 = c

3) 5^2+10.3^2 = c^2 = 25+106.09 = c^2 = 131.09 = c^2 = 11.4494541 = 11.4 = c

4) 8.6^2+9.4^2 = c^2 = 73.96+88.36 = c^2 = 162.32 = c^2 = 12.7404866 = 12.7 = c