Identify the lateral area and the surface area of a cube with edge length 15 in.

Answer:

When \(x=0\), the value of f(x) is 1.

Each time x increases by 1, f(x) is multiplied by 4.

Equation of function: \(f(x)=1\cdot 4^x\)

Step-by-step explanation:

The detailed explanation is attached below.

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Answer: x=11

Explanation: See below!

I hope this helped!

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Answer:

Step-by-step explanation:

\(\sqrt{x - 2} + 8 = x\\ \sqrt{x - 2} = x - 8\\x - 2 = (x - 8)^2\\x - 2 = x^2 - 16x + 64\\x^2 - 17x + 66 = 0\\(x^2 - 11x) - (6x - 66) = 0\\x(x - 11) - 6(x - 11) = 0\\(x - 6)(x - 11) = 0\\x - 6 = 6 >> x = 6\\x - 11 = 0 >> x = 11\)

Answer:

its the thrid one i think i might be wrong srry

Step-by-step explanation:

Answer:

20/53

Answer number 4

Step-by-step explanation:

There are 20 brown, 16 orange, 4 navy, and 13 purple marbles. A marble is drawn at random. What is the probability the marble is brown?

Let's first add the marbles together.

20+16+4+13=53

there are 53 marbles altogether.

20 of the marbles are brown.

So the probability of drawing a brown marble is 20/53

Using the Green's Theorem, the one along which the work done by the force is 11π/16.

In the given question we have to find the one along which the work done by the force is the greatest.

The given closed curves in the plane is

\(F(x,y)=\left(\frac{x^{2}y}{4} + \frac{y^3}{3}\right)\hat{i}+x\hat{j}\)

Suppose C be a simple smooth closed curve in the plane. It is also oriented counterclockwise.

Let S be the interior of C.

Let P = \(\frac{x^{2}y}{4} + \frac{y^3}{3}\) and Q = x

So the partial differentiation is

\(\frac{\partial P}{\partial y}=\frac{x^2}{4}+y^2\) and  \(\frac{\partial Q}{\partial x}\) = 1

By the Green's Theorem, work done by F is given as

W= \(\oint \vec{F}d\vec{r}\)

W= \(\iint_{S}\left ( \frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y} \right )dxdy\)

W= \(\iint_{S}\left ( 1-\frac{x^2}{y}-y^2 \right )dxdy\)

Let C = x^2+y^2 = 1 and

x = rcosθ, y = rsinθ

0≤r≤1; 0≤θ≤2π

There;

W = \(\int_{r=0}^{1}\int_{\theta=0}^{2\pi}\left ( 1-\frac{r^2\cos^2\theta}{4}-r^2\sin^2\theta \right )\left|\frac{\partial(x,y)}{\partial{r,\theta}}\right|d\theta dr\)

and \(\frac{\partial (x,y)}{\partial(r, \theta)}=\left|\begin{matrix}\cos\theta &-r\sin\theta \\ \sin\theta & r\cos\theta\end{matrix} \right |\) = r

Thus;

W = \(\int_{r=0}^{1}\int_{\theta=0}^{2\pi}\left ( 1-\frac{r^2\cos^2\theta}{4}-r^2\sin^2\theta \right )rd\theta dr\)

After solving

W = 11π/16

Hence, the one along which the work done by the force is 11π/16.

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The right question is:

Among all simple smooth closed curves in the plane, oriented counterclockwise, find the one along which the work done by the force:

\(F(x,y)=\left(\frac{x^{2}y}{4} + \frac{y^3}{3}\right)\hat{i}+x\hat{j}\)

is the greatest. (Hint: First, use Green’s theorem to obtain an area integral—you will get partial credit if you only manage to complete this step.)

Using it's concept, it is found that the mode of the given data set of science test scores is of 94, hence option C is correct.

The mode is the value that appears the most times in the data-set.

Considering the key of the stem-and-leaf plot, the scores are given as follows:

68, 74, 78, 82, 85, 87, 89, 90, 92, 94, 94, 95.

The only score that appears twice is 94, hence it is the mode and option C is correct.

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Designing an easy do-it-yourself compost bin:

Drawing and Description:

The compost bin can be a simple structure made of wood or wire mesh. It consists of four sides, a bottom, and a removable lid. The sides and bottom are connected securely to form a rectangular shape, while the lid allows for easy access to the contents inside.

The bin can be placed directly on the ground or on a solid surface, depending on personal preference.

Materials Used:

Wood or wire mesh (depending on preference)

Nails or screws to assemble the structure

Size of the Bin:

The size of the bin can vary based on the available space and the amount of compostable materials you generate. A suitable size for a home compost bin could be approximately 3 feet wide, 3 feet deep, and 3 feet tall.

Substances Used to Fill It:

To fill the compost bin, you would need a mix of "green" and "brown" materials. "Green" materials include fruit and vegetable scraps, coffee grounds, tea leaves, grass clippings, and plant trimmings. "Brown" materials consist of dry leaves, shredded newspaper, cardboard, and small twigs.

Household Items That Can Go in It:

You can add a variety of household items to the compost bin, such as fruit and vegetable peels, eggshells, coffee grounds, tea bags, yard waste (leaves, grass clippings, plant trimmings), shredded paper, cardboard, and natural fibers (like cotton or wool scraps).

Time for Compost to Be Ready:

The time it takes for the compost to be ready varies depending on factors like temperature, moisture, and the type of materials used. Generally, it takes about 2 to 6 months for compost to fully decompose and become ready to use.

Using the Compost:

Once the compost has broken down into a dark, crumbly, and earthy material, it is ready to use. You can spread it in your garden beds or pots as a nutrient-rich soil amendment. It improves soil structure, retains moisture, and provides essential nutrients for plants' growth.

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Answer:

x=17

Divide both sides by the numeric factor on the left side, then solve.

Answer:

x = 17

Step-by-step explanation:

-5 ( x - 10) = -35

-5x + 50 = -35

-5x + 50-50 = -35-50

-5x = -85

-5x ÷ -5

-85 ÷ -5

x = 17

Answer:This problem involves using the concept of probability. We can use the formula for probability:

Probability = (number of desired outcomes) / (total number of possible outcomes)

First, let's calculate the total number of possible outcomes. Since there are 27 doors and each door can only have one piece of artwork, there are a total of 27 possible outcomes.

Next, let's calculate the number of desired outcomes. The teacher wants to display 8 sculptures, 9 sketches, and 10 oil paintings. We can choose 8 sculptures from the 11 available in C(11,8) ways (using the combination formula), 9 sketches from the 10 available in C(10,9) ways, and 10 oil paintings from the 12 available in C(12,10) ways. To find the total number of desired outcomes, we can multiply these together:

number of desired outcomes = C(11,8) * C(10,9) * C(12,10)

= (165) * (10) * (66)

= 108,900

Finally, we can plug these values into the formula for probability:

Probability = (number of desired outcomes) / (total number of possible outcomes)

= 108,900 / 27

= 4,033.3 (rounded to one decimal place)

However, probabilities cannot be greater than 1. Therefore, the probability of displaying 8 sculptures, 9 sketches, and 10 oil paintings is 1.

Answer: -3

Step-by-step explanation:

Answer:

y= -3x+1

Step-by-step explanation:

x1= -2 x2=2 y1=7 y2=-5

using the formula

(y-y1)/(x-x1)=(y2-y1)/(x2-x1)

(y-7)/(x-(-2))=(-5-7)/(2-(-2))

(y-7)/(x+2)=(-5-7)/(2+2)

(y-7)/(x+2)=(-12)/4

(y-7)/(x+2)=-3

cross multiply

y-7=-3(x+2)

y-7=-3x-6

y=-3x-6+7

y=-3x+1

Answer:

Step-by-step explanation:

→ If includes the point (0,2) first mark that point on the graph

→From point (0,2) go up 5 and to the right 1 and mark that point

Slope = rise / run = 5/ 1 so go 5 up and 1 to the right (because 5 is a positive number and a positive slope will give un a line that goes up from left to right)

→Draw a line trough the points (0.2) and (1,7)

D) 3 x 3/5 = 9 x 1/5 represents the LHS as a multiple of the unit fraction.

A) the fraction 2/5 s not a unit fraction

B) 3 x 3/5 \(\neq\) 3 x 1/5

C) 3 x 3/5 \(\neq\) 6 x 1/5

D) 3 x 3/5 = 9 x 1/5

A unit in measurement, is the smallest fundamental measure, in terms of which all other measurements are given. By a unit fraction, we mean a simple fraction, such that every other fraction in a certain class of fractions can be represented as an integer multiple of that fraction. The point to note is that every other fraction in the group should be an integer multiple of the unit fraction.

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Required equation represents

3 × 3/5 as a multiple of a unit fraction is 9 x 1/5.

To multiply a whole number by a fraction, you can convert the whole number to a fraction with a denominator of 1. So, 3 can be written as 3/1.

Now, to multiply 3/1 by 3/5, you can multiply the numerators (top numbers) together and the denominators (bottom numbers) together separately:

3/1 × 3/5 = (3 × 3) / (1 × 5)

Simplifying the numerator and denominator gives 9/5

To write this as a multiple of a unit fraction (a fraction with a numerator of 1), you need to rewrite 5 as a product of 1 and another number (in other words, find a denominator that is a multiple of 5):

5 = 1 × 5

Then, you can write 9/5 as:

9/5 = (9/1) × (1/5)

So, the equation that represents 3 × 3/5 as a multiple of a unit fraction is:

3 × 3/5 = 9 x 1/5

So, the correct option is D) 9 x 1/5.

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x = 85

sum of all the angles must be 540,

105 + 120 + 3x + 35 + 25 = 540

3x = 255

x is 85

Answer:

Step-by-step explanation:

simply  70×100÷140, which will give you the answer.

Answer:

50

Step-by-step explanation:

mental math look at my profile if you want to trust me or not

The new goal time for the promotion should be 3 minutes and 42 seconds in order to ensure that only about 5% of the orders will be free.

We can use the inverse of the cumulative distribution function of a normal distribution with a mean of the goal time and a standard deviation of 2 minutes and 15 seconds to find the new goal time.

Specifically, we want to find the time t such that the area under the normal distribution curve to the left of t is 0.95 (since we want 95% of orders to be within the goal time frame).

Using a standard normal distribution table or calculator, we find that the z-score corresponding to an area of 0.95 to the left is approximately 1.645.

We know that the standard normal distribution has a mean of 0 and a standard deviation of 1, so we can set up the following equation:

1.645 = (t - goal time) / (2 minutes + 15 seconds expressed in decimal minutes)

Solving for t, we get:

t = goal time + 1.645 * (2.25 minutes)

Since we want the answer in minutes and seconds, we can convert the decimal minutes back to minutes and seconds:

2.25 minutes = 2 minutes + 0.25 minutes

= 2 minutes + 0.25 * 60 seconds

= 2 minutes + 15 seconds

Substituting this back into the equation for t, we get:

t = goal time + 1.645 * (2 minutes + 15 seconds)

= goal time + 3.70725

To solve for the new goal time, we need to round to the nearest second:

t ≈ goal time + 3.707 ≈ goal time + 3.71

Since we want about 5% of orders to be free, the goal time should be set at 3 minutes and 42 seconds.

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The mean of the test is 20.

To determine the mean of the test, we need to use the information provided about the scores falling above the mean in terms of standard deviations.

Let's denote the mean of the test as μ, and the standard deviation as σ.

We are given that a score of 29 falls three standard deviations above the mean, so we can write this as:

29 = μ + 3σ

Similarly, we are told that a score of 23 falls one standard deviation above the mean, which can be expressed as:

23 = μ + σ

Now we have a system of two equations with two variables (μ and σ). We can solve this system of equations to find the values of μ and σ.

From the second equation, we can isolate μ:

μ = 23 - σ

Substituting this value into the first equation, we have:

29 = (23 - σ) + 3σ

Simplifying the equation, we get:

29 = 23 + 2σ

2σ = 29 - 23

2σ = 6

σ = 3

Substituting the value of σ back into the second equation, we find:

μ = 23 - 3

μ = 20

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Answer:

y = 2

Step-by-step explanation:

We are given the value of x (second equation). Let's substitute the value of x into the first equation to find y.

\(\rightarrow \dfrac{x}{y} = 6\)

\(\rightarrow \dfrac{4(y + 1)}{y} = 6 \ \ \ \ \ \ \ \ \ \ \ \ \ \text{\large{[}x = 4(y + 1)]}\)

Use cross multiplication.

\(\rightarrow 4(y + 1) = 6 \times y\)

\(\rightarrow 4(y + 1) = 6 y\)

Simplify the distributive property.

\(\rightarrow 4(y + 1) = 6 y\)

\(\rightarrow 4y + 4 = 6 y\)

Subtract 4y both sides.

\(\rightarrow 4y - 4y + 4 = 6 y - 4y\)

\(\rightarrow 4 = 2y\)

Divide both sides by 2.

\(\rightarrow \dfrac{4}{2} = \dfrac{2y}{2}\)

\(\rightarrow 2 = y\)

Thus, the value of y is 2.

Answer:

estimate, 3000. exact answer 3256

Step-by-step explanation:

hope this helps

Answer:

1) 9

2) 27

3) Read explanation below!

Step-by-step explanation:

1) Use the Pythagorean theorem to find AD. Show your working

To find '?' we first have to expand the indices...

Now work out '?'

2) Find AC. Show your working

We have found out that AD is 9 and to find AC we have to add 18!

3) Is ΔABC a right triangle? Explain

We can that ΔABC is not a right angle as none of the angles in the triangle are 90°!  If it was a right angled triangle we would see the ∟sign on one of the angles. Even though there are two of those in the middle it does not count as the question is asking about ΔABC!!

Have a lovely day :)

Line EG ≈ 22.4

We are told that;

Line FG is parallel to CD

FC = 16.9

GD = 13.5

EF = 28.1

EF/FC = EG/GD

Plugging in the relevant values, we have;

28.1/16.9 = EG/13.5

Making EG the subject, we have;

EG = (28.1 × 13.5)/16.9

EG ≈ 22.4

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Answer:

Step-by-step explanation:

Delilah needs to buy 8 reams of paper which cost $5.89 each, $5.89 x 8 = $47.12

Delilah needs to buy 6 cartridges of ink which cost $38.40 each, $38.40 x 6 = $230.4

We then add $230.4 and $47.12

$230.4 + $47.12 = $277.52.

Delilah needs to bring $277.52 to cover the cost of her supplies.

Answer:

t = 6.8 years

Step-by-step explanation:

The formula for compound interest is

\(A(t)=P(1+r/n)^n^t\), where P is the principal/amount invested, r is the interest rate, n is the number of compound periods per year (4 for quarterly), and t in the time in years.

We know that A = $5900, P = $4000, and r = 0.0575 (we must convert the percentage to a decimal).  We must solve for t and round to the nearest tenth:

\(5900=4000(1+0.0575/4)^(^4^t^)\\\\59/40=(1623/1600)^4^t\\\\log(59/40)=log(1623/1600^4^t)\\\\log(59/40)=4t*log(1623/1600)\\\\log(59/40)/log(1623/1600)=4t\\\\1/4(log(59/40)/log(1623/1600))=t\\\\6.80773607=t\\\\6.8=t\)

Answer:

(1, 0.5)

Step-by-step explanation:

i just used order of operations calculator

Solving the equation with elimination method, I got x=1, y= 1/2

Pair (1.00, 0.50)

Answer:

B

Step-by-step explanation:

Answer:

BC = 21 cm

Step-by-step explanation:

In similar triangles the corresponding sides are in same proportion.

Its given in the sum that AC = 12 cm; DF = 20 cm and EF = 35 cm.

      \(\sf \dfrac{AB}{DE}=\dfrac{BC}{EF}=\dfrac{AC}{DF}\\\\\\\dfrac{AC}{DF}=\dfrac{BC}{EF}\\\\\dfrac{12}{20}=\dfrac{BC}{35}\)

     \(\sf \dfrac{12}{20}*35=BC\\\\\\\dfrac{12}{4}*7=BC\\\\\\3*7=BC\\\\ \boxed{BC = 21 cm}\)

The perimeter of the rectangle is equal to 2(√90 + √40).

A coordinate plane is a 2D plane which is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

The perimeter is defined as the sum of all the sides of the rectangle.

Given coordinates of the rectangle are (4, −3), (2, 3), (11, 6), and (13, 0). The length and width of the rectangle are calculated by the distance formula.

D = √ [ ( y₂ - y₁ )² + ( x₂ - x₁ )² ]

Here, D is the distance, and the  y₂ and y₁ are the coordinates.

L = √(13-4)² + 3² = √90

W = √ ( 4-2)² + (3 + 3)² = √40

The perimeter is,

P = 2(L + W)

Here, P is the perimeter and L is the length, and W is the width.

P = 2 (√90 +√ 40)

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