y−10=2(x−8)Write in Standard Form

There is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

To find the probability that a box of cereal is underfilled by 5 g or more, we need to calculate the probability of obtaining a weight measurement below 345 g.

First, we can standardize the problem by using the z-score formula:

z = (x - μ) / σ

Where:

x = the weight value we want to find the probability for (345 g in this case)

μ = the mean weight (350 g)

σ = the standard deviation (4 g)

Substituting the values into the formula:

z = (345 - 350) / 4 = -1.25

Next, we can find the probability associated with this z-score using a standard normal distribution table or a statistical calculator.

The probability of obtaining a z-score less than -1.25 is approximately 0.1056.

However, we are interested in the probability of underfilling by 5 g or more, which means we need to find the complement of this probability.

The probability of underfilling by 5 g or more is 1 - 0.1056 = 0.8944, or approximately 89.44%.

Therefore, there is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

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9514 1404 393

Answer:

  (b)  8

Step-by-step explanation:

We assume that a path must not repeat any node. (So, loops at G are forbidden.)

There are 2 paths through B to A.

There are 2 paths through D to A, so a total of 4 ways to get from C to A.

There is one path from A to H.

There are two paths from H to F, and one path from F to E.

The total number of possible paths is (4)(1)(2)(1) = 8.

Here is a list.

  CBAHFE, CDBAHFE, CBAHGFE, CDBAHGFE,

  CDAHFE, CBDAHFE, CDAHGFE, CBDAHGFE

Answer:

About 1885 sq. ft

Step-by-step explanation:

\(v = \pi \: (10)^{2} (6) \)

Since the radius is 10ft and the height of the cylinder is 6 ft you substitute that into the formula and you receive 1884.96.

Answer:

x = 3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

12x = 36

Step 2: Solve for x

Answer:

a=9

b=9

c=18

Step-by-step explanation:

c(a+b)+a+b=36

2a+2b=36

a+b=18

c=18

Answer:

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

first substitute letters for their numbers in parentesis

-5(-4)+(5)

20+5

25

The expression that is equivalent to (f g) (5) is f (5) times g (5). Option A

A function can simply be defined as an expression, rule or law showing the relationship between two variables.

These variables are namely;

From the information given, we have;

Using functional notation, if we have (f g) (5), it means that the two functions, f and g, are being combined and the resulting function is applied to the input value of 5.

Substituting the function g on the input of 5, we have g(5).

Next, we utilize the function f on the output of g(5), we have;

f(g(5))

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Answer:

4x² + 22x - 12

Step-by-step explanation:

A = bh/2

A = (4x - 2)(2x + 12)/2

A = (8x² + 48x - 4x - 24)/2

A = (8x² + 44x - 24)/2

A = 4x² + 22x - 12

Answer:

919,827.000

Step-by-step explanation:

You basically just move three places forward from the last number which is 7.

Answer:

Step-by-step explanation:

1) a) 15x =  12x + 15          {Alternate interior angles}

b) 15x - 12x = 15             {Subtract 12x from both sides}

       3x  = 15

        x = 15/3

x = 5

c) Alternate interior angles

2) a) 3x + 10 + 3x - 28 = 180  {co- interior angles are supplementary}

b) 6x  - 18 = 180      { Combine like terms}

        6x   = 180 + 18

         6x  = 198

          x = 198/6

         x = 33

c) co- interior angles are supplementary

3) a) 7x + 9 + 5x +3 = 180

  b) 12x + 12 = 180

      12x    = 180 - 12

          12x = 168

             x = 168/12

           x = 14

c) linear pair

4) a) 12x - 18 = 8x + 10

b) 12x - 8x - 18 = 10

           4x - 18  = 10

                   4x = 10 +18

                   4x = 28

                     x = 28/4

x = 7

c) Vertically opposite angles are equal.

Answer:

b + 1.75f

Step-by-step explanation:

1.75 cups are used for every loaf of pumpkin bread.

Answer:

f(4/7)=b

Step-by-step explanation:

3+1/2=7/2

(7/2)x=2

x=4/7

the constant of the equation is 4/7

so take f and b and put f in place for 7/2 cups and b for 2 loaves of bread.

f(4/7)=b

Hope that helps :)

The proposed skyscraper is 172.8 m tall

From the question, we are to determine the how tall the proposed skyscraper is in meters

From the given information,

The scale of the model is

1 in : 7.2 m

and

The model is 2 ft tall

First, convert 2 ft to inches

NOTE: 1 foot = 12 inches

∴ 2 feet = 2 × 12 inches

= 24 inches

Now,

If 1 inch represents 7.2 m

Then,

24 inches will represent 24 × 7.2 m

24 × 7.2 m = 172.8 m

Hence, the proposed skyscraper is 172.8 m tall

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Answer:

Since the order of choice matters, we will permute the values.                       a bit more explanation for this:

If the order of choice did NOT matter, ABC and BCA will be counted as one since order of choice does NOT matter

Since order of choice does matter, ABC , BCA and CAB are all different possibilities for the arrangement of the same 3 letters

Since we have 3 slots:

___  ___ ___

Now, for the first slot. You can out either one if the 4 alphabets in the first slot since no slot has been used as of now

So:

_4_ ___ ___

**Keep in mind that the 4 is the possible number of values this slot can have**

Now that one slot has been used, one of the 4 alphabets has been used and since we are not allowed to repeat the same alphabets, we are left with  3 more alphabets

we can put any one of the 3 alphabets in this second slot, Hence:

_4_ _3_ ___

Now that 2 of the 4 alphabets have been used, we are left with only 2 alphabets, so there are only 2 possible alphabets for slot 3

Therefore:

_4_ _3_ _2_

Now that we know the possible alphabets for all 3 slots, we will multiply them with each other to get the total possible number of 3 - alphabet words we can make with 4 alphabets

Total possible words = 4 * 3 * 2

Total possible words = 24

We could've used the formula for Permutation as well

Step-by-step explanation:

A. To find the profit-maximizing level of price and output, we need to find the equilibrium point where the marginal revenue equals marginal cost.

The marginal cost of production is the derivative of the total cost function: MC = dC/dQ = 3.

The marginal revenue is the derivative of the inverse demand function: MR = dP/dQ = -1.

So at the profit-maximizing level of output, MC = MR.

3 = -1

Q = 6

Then we can substitute Q = 6 back into the inverse demand function to find the price:

P (Q) = 12 - Q

P (6) = 12 - 6

P = 6

So the profit-maximizing level of output is 6 units at a price of $6.

B. To find the maximum profit of the firm, we need to calculate the total revenue and the total cost at the profit-maximizing level of output.

The total revenue is the product of the price and the quantity:

TR = P * Q

TR = 6 * 6

TR = 36

The total cost is given by the total cost function:

TC = C (Q)

TC = 3 * Q

TC = 3 * 6

TC = 18

So the maximum profit is the difference between the total revenue and the total cost:

Profit = TR - TC

Profit = 36 - 18

Profit = 18

The maximum profit of the firm is $18 at an equilibrium price level of $6 and an output level of 6 units.

analyze problem

32% discount of x(original price)=67.80

make equation

original price-discount=final price

x-x*32/100=67.80

\(\frac{17}{25}x=67.8\)

\(x=\frac{1695}{17}\)

simplify

\(99\frac{12}{17}\)

Answer:

Step-by-step explanation:

-1 +2=1

2+2=4

5+1=6

The height of the cylinder with radius of 7 yards and given volume of 2,923.34 cubic yards is calculated as; h = 19 yards

A cylinder is defined as a 3D solid shape that consists of two identical and parallel bases linked by a curved surface.

Now, the formula to find the volume of a cylinder is;

V = πr²h

where;

r is radius

h is height

V is volume

The parameters are;

Radius; r = 7 yards

Volume; V = 2923.34 cubic yards

Thus;

2923.34 = π * 7² * h

h = 2923.34/(49π)

h = 19 yards

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Answer:

The numbers are 10 and 139.

Step-by-step explanation:

Assuming you have two numbers you need to search for, let's label them as x and y.

x is 19 more than 12 times y. We can rearrange this to be x = 19 + 12y. This will be our first equation. It is then stated that their sums, or x + y, is equal to 149. We have two equations now:

Because x is already separated, we can plug equation (1) into equation (2).

(19 + 12y) + y = 149

Because there is nothing in the parentheses that we can combine, we can remove them and begin combining like terms.

19 + 12y + y = 149

19 + 13y = 149

We subtract 19 from both sides to begin to isolate the variable y.

13y = 130

y = 10

Because we have obtained y, we can plug it back into equation (2) to obtain x.

x + y = 149

x + (10) = 149

x = 139

-1 does not equal 0, the equation is not true for any value of "a". This means that there is no value of "a" for which the function f(x) is continuous at x = 1.

To determine the value of "a" for which the function f(x) is continuous at x = 1, we need to check if the left-hand limit and the right-hand limit of f(x) as x approaches 1 are equal, and if the value of f(x) at x = 1 is equal to these limits.

First, let's calculate the left-hand limit of f(x) as x approaches 1. For x < 1, the function is given by f(x) = (ax² - 1). To find the left-hand limit, we substitute x = 1 into this expression:

lim(x→1-) f(x) = lim(x→1-) (ax² - 1) = a(1²) - 1 = a - 1.

Next, let's calculate the right-hand limit of f(x) as x approaches 1. For x > 1, the function is given by f(x) = (a(x² - 2x + 1)). Substituting x = 1 into this expression, we have:

lim(x→1+) f(x) = lim(x→1+) (a(x² - 2x + 1)) = a(1² - 2(1) + 1) = a(1 - 2 + 1) = a.

For the function f(x) to be continuous at x = 1, the left-hand limit and the right-hand limit should be equal. Therefore, we have:

a - 1 = a.

To solve this equation for "a," we subtract "a" from both sides:

-1 = 0.

Since -1 does not equal 0, the equation is not true for any value of "a". This means that there is no value of "a" for which the function f(x) is continuous at x = 1.

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Answer:

<ABC + <CBD =180⁰

<ABC =180⁰ - <CBD

<ABC =180⁰ - 47⁰

<ABC =133⁰

The probability that a gorilla in this particular zoo will live between 14.3 and 19.4 years is 86% (or 0.86)

From the Empirical Rule, for a Normal Distribution, approximately:

68% of the data falls within one standard deviation of the mean

95% of the data falls within two standard deviations of the mean

99.7% of the data falls within three standard deviations of the mean

To estimate the probability of a gorilla living between 14.3 and 19.4 years, we first need to standardize these values by subtracting the mean and dividing by the standard deviation:

For 14.3 years: (14.3 - 16) / 1.7 = -1.18

For 19.4 years: (19.4 - 16) / 1.7 = 2

Now we can use a standard normal distribution table to find the probabilities associated with these z-scores:

The probability of a gorilla living less than 14.3 years is approximately the same as the probability of a standard normal variable being less than -1.18, which is about 0.12.

The probability of a gorilla living less than 19.4 years is approximately the same as the probability of a standard normal variable being less than 2, which is about 0.98.

Therefore, the probability of a gorilla living between 14.3 and 19.4 years is approximately the difference between these two probabilities: 0.98 - 0.12 = 0.86.

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Answer:

-5 and -The zeros of a parabola are the points on the parabola that intersect the line y = 0 (the horizontal x-axis). Since these points occur where y = 0,

Answer:

31.5 units²

Step-by-step explanation:

Area = ½*base*height

Height of the triangle on the grid = 9 units

Base = 7 units

Area = ½*9*7

Area = ½*63

Area = 63/2

Area = 31.5 units²

Answer:

995

Step-by-step explanation:

Because you would have to subtract 5 from 1000 which is 995, hope this helped!

Answer:

100

Step-by-step explanation:

If 4 Cups = 50Lbs, then there will be 200 cups in 40Lbs.

Then if it takes 2 cups of flour to make a cake, 200 / 2 = 100.

The answer is (NOT LISTED): 100

The outputs 1, -5, -14 and 25 is matched to the the inputs f(2), f(0), f(-3) , and f(10) for the relation defined as f(x) = 3x - 5.

If the relation defined by f(x) = 3x - 5, then:

we input the value 2 for x;

f(2) = 3(2) - 5

f(2) = 6 - 5

f(2) = 1 match to a output

we input the value 0 for x;

f(0) = 3(0) - 5

f(0) = -5 match to b output

we input the value -3 for x;

f(-3) = 3(-3) - 5

f(-3) = -9 - 5

f(-3) = -14 match to c output

we input the value 10 for x;

f(10) = 3(10) - 5

f(10) = 30 - 5

f(10) = 25 match to d output of

Therefore, the inputs f(2), f(0), f(-3) , and f(10) is matched to the outputs 1, -5, -14, and 25 respectively.

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Answer:

distance between the points (3,4) and (1,5) = 2.236

Step-by-step explanation:

The distance between two points is the length of the path connecting them. The shortest path distance is a straight line. In a 2 dimensional plane, the distance between points (X1, Y1) and (X2, Y2) is given by the Pythagorean theorem:

\(d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)'

For:

\((X1, Y1) = (3, 4)\\\\(X2, Y2) = (1, 5)\)

\(d = \sqrt {(1 - 3)^2 + (5 - 4)^2}\\\\d = \sqrt {(-2)^2 + (1)^2}\\\\d = \sqrt {{4} + {1}}\\\\d = \sqrt {5}\\\\d = 2.236068\)

Answer:

Exact distance is \(\sqrt{5}\)

Approximate distance is  2.2361

Round the decimal value however your teacher instructs.

====================================================

Work Shown:

I used the distance formula to get the following.

\((x_1,y_1) = (3,4) \text{ and } (x_2, y_2) = (1,5)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-1)^2 + (4-5)^2}\\\\d = \sqrt{(2)^2 + (-1)^2}\\\\d = \sqrt{4 + 1}\\\\d = \sqrt{5}\\\\d \approx 2.2361\\\\\)

----------------

A slight alternative is to plot the points A(3,4) and B(1,5) and C(3,5).

Points A and B are the original points we were given. Point C helps form a right triangle. The hypotenuse is AB and the legs are AC and BC.

Leg AC = 1 unit and leg BC = 2 units

Use the pythagorean theorem \(a^2+b^2 = c^2\) to plug in a = 1 and b = 2 to find that the hypotenuse is exactly \(c = \sqrt{5}\) units long, which is the distance from A to B.

Answer:

The formula for density (ρ) is:

Density (ρ) = Mass (m) / Volume (V)

Step-by-step explanation:

Where:

Answer:

piecewise, continuous.

Step-by-step explanation:

This is piecewise simply because it is in pieces. Thus PIECEwise (Pun intended). This is continuous because, as you can see, there is a filled in dot on the same x coordinate as every empty dot. The empty dots mean that that value is not in that part of the graph. However, since the other parts of the function "fill the gaps," then it is continuous.  I hope this helps!

It's offcourse piecewise

For continuity

Observe the graph

The domain is like

For close ineterval there is an open interval hence it's continuous