Sally found that out of 750 cans stamped in the ½ hour trial run, 150 were not stamped. About how many were not stamped in 3 hours?

Answer:

13) 57.6 units²

14) 285.6 units²

15) 114.2 units²

(All answers rounded off to the nearest tenth)

Step-by-step explanation:

Please see the attached picture for the full solution.

The turning points of the function y = x³ - 3x² - 9x + 4 are (3, -23) and (-1, 9).

To determine the turning points of the given function y = x³ - 3x² - 9x + 4, we need to find the critical points where the derivative of the function is equal to zero.

1. Find the derivative of the function:

  y' = 3x² - 6x - 9

2. Set the derivative equal to zero and solve for x:

  3x² - 6x - 9 = 0

3. Factorize the quadratic equation:

  3(x² - 2x - 3) = 0

4. Solve the quadratic equation by factoring or using the quadratic formula:

  (x - 3)(x + 1) = 0

  This gives us two possible values for x: x = 3 and x = -1.

5. Substitute these critical points back into the original function to find the corresponding y-values:

  For x = 3:

  y = (3)³ - 3(3)² - 9(3) + 4

    = 27 - 27 - 27 + 4

    = -23

  For x = -1:

  y = (-1)³ - 3(-1)² - 9(-1) + 4

    = -1 - 3 + 9 + 4

    = 9

6. Therefore, the turning points are (3, -23) and (-1, 9).

Note: It appears that there was a typo in the original equation, where the term "-9x" should have been "-3x²". The above solution assumes the corrected equation.

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Using the Empirical Rule, it is found that:

It states that, for a normally distributed random variable:

Hence, the middle 95% of values is within 2 standard deviations of the mean, with bounds given as follows:

The middle 95% of the distribution of moonsoon rainfall amount: (688 mm, 1016 mm).

For the driest 2.5% of years, considering the symmetry of the normal distribution, we have to look at 2 standard deviations below the mean, as 5/2 = 2.5%, hence:

The driest 2.5% of monsoon rainfall amount are less than: 688 mm.

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Answer: W(x) = 3.4 L - (25/1000)(L/s)*x

Step-by-step explanation:

The maximum of the jug is 4 L.

now, the jug is 85% filled, then the amount of water in the jug is:

(85%/100%)*4L = 0.85*4L = 3.4L

Now, we pour 25 mL each second, so we could write a linear equation as:

W(x) = 3.4L - (25ml/s)*x

where x is the number of seconds that passed since the beginning,

But we want to write this in Liters, we have that:

1L = 1000mL.

Then 1mL = (1/1000) L

then we can write 25 mL as:

25m L = 25*(1/1000) L = (25/1000) L.

Then we can write the equation as

W(x) = 3.4 L - (25/1000)(L/s)*x

which is the amount of water remaining in the jug after x seconds.

\(\rightarrow\) Side(a) of the cube = \(\sf{\frac{1}{3}ft}\).

\(\rightarrow\) Surface Area of the cube with side \(\sf{\frac{1}{3}ft.}\)

\(\rightarrow\) Surface area of cube = \(\sf{6a^2}\)

\(\rightarrow\) Surface area of cube = \(\sf{6a^2}\) (putting the value of a from the above given)

\(\rightarrow\) \(\sf{=\:6×(\frac{1}{3})^2}\)

\(\rightarrow\) \(\sf{=\:6×\frac{1}{9}}\)

\(\rightarrow\) \(\sf{=\:\frac{6}{9}}\)

\(\rightarrow\) \(\sf{=\:\frac{2}{3}ft^2}\)

Therefore, surface area of the given square = \(\sf{=\:\frac{2}{3}ft^2}\)

__________________________________

Hope it helps you:)

Answer:

Step-by-step explanation:

there are 6 square faces of a cube.

if side=x

surface area=6x²

=6(1/3)²

=6/9

=2/3 square foot

The graph given can be expressed as piecewise function as,

f(x) = 2x + 10, for [-6, -3)

     = -x + 1, for (-3, 2)

A piecewise function is a function which has different definitions of values for different intervals.

Given is a graph of a function.

The graph consists of two lines.

In the interval [-6, -3), the graph is a line with positive slope.

In the interval (-3, 2), the graph is a line with negative slope.

Now we have to find the equation of two lines.

The positive line passes through (-6, -2) and (-5, 0).

Slope of the line = (0 - -2) / (-5 - -6) = 2 / 1 = 2

Slope intercept form of the line is y = mx + c, where m is slope and c is y intercept.

y = 2x + c

Substitute a point (-5, 0), in the equation.

0 = (2 × -5) + c ⇒ c = 10

Equation is y = 2x + 10

The negative line passes through (0, 1) and (1, 0).

Slope = (0 - 1) / (1 - 0) = -1

y intercept = 1, since the line passes touches the Y axis at the point (0, 1).

Equation of line is y = -x + 1

So the function is, f(x) = 2x + 10, for [-6, -3)

                                    = -x + 1, for (-3, 2)

Hence the piecewise function is found.

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Answer:

y = 2x + 10 for -6 <= x < -3

y = -x + 1 for -3 < x < 2

Step-by-step explanation:

(a) To compute the experimental probability of rolling a 1 or 6 from Latoya's results, we need to determine the number of times a 1 or 6 was rolled and divide it by the total number of rolls Latoya made.

Let's assume that Latoya rolled the dice 100 times and obtained 20 1's and 10 6's. The total number of successful outcomes (rolling a 1 or 6) is 20 + 10 = 30.

Therefore, the experimental probability of rolling a 1 or 6 is 30/100 = 0.3 or 30%.

(b) Assuming the cube is fair, the theoretical probability of rolling a 1 or 6 can be determined by considering the favorable outcomes (rolling a 1 or 6) divided by the total possible outcomes (rolling any number from 1 to 6).

Since there are two favorable outcomes (1 and 6) out of six possible outcomes (1, 2, 3, 4, 5, 6), the theoretical probability is 2/6 = 1/3 or approximately 0.3333.

(c) The correct statement is B. As the number of rolls increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal. This is due to the law of large numbers, which states that as more trials are conducted, the experimental probability tends to converge towards the theoretical probability. However, it is not necessary for them to be exactly equal. Random variations can cause some discrepancy, but with a larger number of rolls, the experimental probability should approach the theoretical probability more closely.

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Answer:

-48

Step-by-step explanation:

we can see each number is getting doubled but flipped from negative and positive and vise versa. aka getting multiple by negative 2

we can also double check our work by multiplying each number in the sequence we have by -2 and make sure it follows the sequence.

Answer:

True

Step-by-step explanation:

Answer:

\(C = 25.1 \text{ cm}\)

Step-by-step explanation:

We can find the circumference of the circle by plugging the given radius value 8 cm into the formula:

\(C = \pi d\)

Note: This formula can also be written as \(C = 2\pi r\) because \(2r = d\).

↓ plugging in the given radius

\(C = 8\pi \text{ cm}\)

↓ rounding to the nearest tenth

\(\boxed{C = 25.1 \text{ cm}}\)

Answer:

8^6 is your answer

Step-by-step explanation:

since you are dividing the exponents you subtract the exponents

Answer:

C

Step-by-step explanation:

So we have a cylinder with a hole the shape of a rectangular prism through it.

Therefore, our total volume would be the cylinder minus the volume of the rectangular prism.

The volume of a cylinder is given by the formula:

\(V=\pi r^2h\)

Use 3.14 for π, 10 for radius, and 15 for the height. Thus:

\(V=(3.14)(10)^2(15)\\V=4710\)

So the volume of the cylinder is 4710 cubic feet.

Now, find the volume of the rectangular prism.

The formula for the volume of a rectangular prism is given by:

\(V=lwh\)

The length is 5, width is 3, and height is 15. Thus:

\(V=(5)(3)(15)\\V=225\)

So, the total volume is:

\(V_{\text{Total}}=V_{\text{Cylinder}}-V_{\text{Rectangle}}\\V_{\text{Total}}=4710-225=4485\text{ feet}^3\)

Our answer is C

Answer:

The value of a₅ is 1875.

Step-by-step explanation:

Given:

a₁ = 3

aₙ = 5aₙ₋₁

To find the value of a₅, we can apply the recursive formula to compute each term successively:

Step 1: Compute a₂

a₂ = 5a₁ = 5(3) = 15

Step 2: Compute a₃

a₃ = 5a₂ = 5(15) = 75

Step 3: Compute a₄

a₄ = 5a₃ = 5(75) = 375

Step 4: Compute a₅

a₅ = 5a₄ = 5(375) = 1875

Damien earns $7.25 at his after school job.

To find a linear equation's solution is to solve a linear equation. Here, the techniques for solving the three primary forms of linear equations—linear equations with one variable, linear equations with two variables, and linear equations with three variables—are described.

There are six main methods to solve linear equations. Some methods for determining the solution to linear equations are:

Graphical Approach

Substitution Method Elimination Method

Method of Cross Multiplication

Matrix Method \sDeterminants Method

Let us suppose the after-school job = x.

Let us suppose the weekend job = y.

Given that, he worked 8 hours at his after-school job and 6 hours at his weekend job, earning a total of $118.

8x + 6y = 118.........(1)

He worked 4 hours at his after-school job and 9 hours at his weekend job, earning a total of $119.

4x + 9y = 119.........(2)

Multiply the second equation with 2 and subtract equation 1 from it:

8x + 18y = 238

- (8x + 6y = 118)

12y = 120

y = 10

Substitute the value of y in equation 2:

4x + 9(10) = 119

4x + 90 = 119

4x = 29

x = 7.25

Damien earns $7.25 at his after school job.

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Answer:

scalene

Step-by-step explanation:

no sides are the same

The average rate of change of the function over the interval is 1

From the question, we have the following parameters that can be used in our computation:

f(x) = x

The interval is given as

From x = 4 to x = 9

The function is a linear function

This means that it has a constant average rate of change

So, we have

f(4) = 4

f(9) = 9

Next, we have

Rate = (9 - 4)/(9 - 4)

Evaluate

Rate = 1

Hence, the rate is 12

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a) -32.06 (To the nearest hundredth)

b) -37.7 (To the nearest tenth)

c) 3.1 (To the nearest tenth)

d) 5.86  (To the nearest hundredth)

f) -4.33  (To the nearest hundredth)

g) 11.44  (To the nearest hundredth)

h) 62x + 45 = 38x + 79

i) 46y - 18 = -37y

An equation is a mathematical statement that asserts the equality of two expressions. It consists of two expressions separated by an equal sign (=), and shows the relationship between the variables present in the equation. Equations are used to model real-world problems and find solutions to various mathematical problems.

They can be solved for a specific variable by using various mathematical methods and techniques.

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Answer:

(B). 90 degree

Step-by-step explanation:

it's not a or c or D it's only B

Plot twist:

The answer is actually is 16

Step-by-step explanation:

15/10 = 1.5)       24/1.5 = 16

The answer is 16

If leg a is the missing side, then transform the equation to the form where a is on one side and take a square root: a = √(c² - b²)

If leg b is unknown, then: b = √(c² - a²)

For hypotenuse c missing, the formula is: c = √(a² + b²)

Answer:

A. by adding an identical classroom and allowing students t use electric ans in it

Step-by-step explanation:

Because Fans are opposite to natural Air

Answer: X=16

Step-by-step explanation:

m<ABF + m<FBC = m<ABC

7x + 20 + 2x - 5=159     by substitution

9x + 15=159     by combining like terms

9x=144      by subtracting 15 from 159

x=16               by division

Answer:

A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

Pythagorean Theorem Formula: a² + b² = hypotenuse²

x² + 5² = 13²

x² + 25 = 169

x² + 25 - 25 = 169 - 25 (subtract 25 in both sides)

x² = 169 - 25

√x² = √144

x = 12

An example of a one-to-one function that is an isomorphism between sets P and Q is the function f: P -> Q defined as f(x) = 2x, where P and Q are the sets of integers.

An example of a one-to-one function that is an isomorphism between sets P and Q is the function f: P -> Q defined as f(x) = 2x, where P and Q are the sets of integers.

This function is one-to-one because for every element x in P, there is a unique element 2x in Q. It is onto because every element y in Q has a preimage x in P such that f(x) = y (e.g., y/2 = x).

Furthermore, this function preserves the group structure between P and Q, as it satisfies the properties of an isomorphism. In this case, the group structure is addition, and the function f preserves addition: f(x + y) = 2(x + y) = 2x + 2y = f(x) + f(y) for all x, y in P.

Therefore, the function f: P -> Q defined as f(x) = 2x is an example of a one-to-one function that is an isomorphism between sets P and Q.

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Answer:

A = 530.929158457

Answer:

Area = 706.8583471

Explanation:

The used law to measure the surface area of the sphere is

\(area \: = 4\pi \: {r}^{2} \)

Where (r) is the radius. The radius is half the diameter, so it will be half 13 which is equal to 7.5. By using this law:

\(4\pi \: {7.5}^{2} = 706.8583471\)

About 90% of the fluctuation in the winning long jump distances may be attributed to the year.

So, option d is correct.

The link between a scalar answer and one or more explanatory variables is modelled linearly in statistics using linear regression. When there is just one explanatory variable, the method is known as simple linear regression; when there are numerous explanatory variables, it is known as multiple linear regression. When an explanatory variable x changes, a straight line called a regression line shows how the response variable y changes. To forecast the value of y given a value for x, a regression line can be utilized. In the 19th century, Francis Galton used the word "regression" to designate a biological phenomena.

R² is a measure of how much of the data's variation the model can account for.

So, r²=90

Therefore, About 90% of the fluctuation in the winning long jump distances may be attributed to the year.

Hence, option d is correct.

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After answering the provided question, we can conclude that  To circle complete the copied triangle, draw a polygon through points D, E, and F.

A circle appears to be a two-dimensional component that is defined as the collection of all points in a jet that are equidistant from the hub. A circle is typically depicted with a capital "O" for the centre and a lower section "r" for the radius, which is the distance from the origin to any point on the circle. The formula 2r gives the girth (the distance from the centre of the circle), where (pi) is a proportionality constant roughly equal to 3.14159. The formula r2 computes the circumference of a circle, which refers to the amount of space inside the circle.

Follow these steps to duplicate the original triangle using only two of its sides and the included angle:

Find the point where the ray and the circle intersect. Place the tip of the compass at point E and draw an arc that intersects the circle twice. Label the point that is on the same side of side AC as point B as point F.

To complete the copied triangle, draw a polygon through points D, E, and F.

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