The sides of the base of this square right prism are 16 centimeters each and the height of the prism is 10 centimeters. What is the surface area of the prism?

a)964 cm^2

b)1000 cm^2

c)1152 cm^2

d)1232 cm^2

Answer:

5/8

Step-by-step explanation:

1 whole race (8/8) - 3/8 = 5/8

The equation of the regression line for the sample data (1, 1), (3, 2), (2, 4) is y = (1/2) × x + 4/3.

To find the equation of the regression line for the given sample data, we can use the method of linear regression.

The regression line represents the best-fitting line that minimizes the sum of the squared differences between the observed data points and the predicted values on the line.

Let's denote the independent variable as x and the dependent variable as y.

We have three data points: (1, 1), (3, 2), and (2, 4).

Calculate the mean of x and y:

Mean of x (\($\bar{x}$\)) = (1 + 3 + 2) / 3 = 2

Mean of y (\($\bar{y}$\)) = (1 + 2 + 4) / 3 = 7/3

Calculate the deviations from the means for x and y:

Deviations from the mean of x (x - \($\bar{x}$\)): (-1, 1, 0)

Deviations from the mean of y (y - \($\bar{y}$\)): (-4/3, -1/3, 5/3)

Calculate the product of the deviations for x and y:

Product of deviations (x - \($\bar{x}$\))(y - \($\bar{y}$\)): (4/3, -1/3, 0)

Calculate the sum of the product of deviations:

Sum of (x - \($\bar{x}$\))(y - \($\bar{y}$\)) = (4/3) + (-1/3) + 0 = 1

Calculate the squared deviations for x:

Squared deviations for x \((x - \bar{x} )^2\): (1, 1, 0)

Calculate the sum of the squared deviations for x:

Sum of \((x - \bar{x} )^2\) = 2

Calculate the slope of the regression line (b):

b = sum of (x - \($\bar{x}$\))(y - \($\bar{y}$\)) / sum of \((x - \bar{x} )^2\) = 1 / 2 = 1/2

Calculate the y-intercept of the regression line (a):

a = \($\bar{y}$\) - b × \($\bar{x}$\) = 7/3 - (1/2) * 2 = 7/3 - 1 = 4/3

Therefore, the equation of the regression line for the given sample data is: y = (1/2) × x + 4/3

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Answer:

\((x+2)(2x-1)(2x+3)\)

Start by multiplying the first two terms:

\((2x^2+3x-2)(2x+3)\)

Now multiply these two terms to prove:

\((4x^3+6x^2+6x^2+9x-4x-6)\)

Simplify:

\((4x^3+12x^2+5x-6)\)

To show that the total charge contained in the charge distribution is Q, we integrate the charge density over the entire volume. The charge density is given by:

ρ(r) = ρ₀(1 - r/R) for r ≤ R,

ρ(r) = 0 for r > R,

where ρ₀ = 3Q/πR³.

To find the total charge, we integrate ρ(r) over the volume:

Q = ∫ρ(r) dV,

where dV represents the volume element.

Since the charge density is spherically symmetric, we can express dV as dV = 4πr² dr, where r is the radial distance.

The integral becomes:

Q = ∫₀ᴿ ρ₀(1 - r/R) * 4πr² dr.

Evaluating this integral gives:

Q = ρ₀ * 4π * [r³/3 - r⁴/(4R)] from 0 to R.

Simplifying further, we get:

Q = ρ₀ * 4π * [(R³/3) - (R⁴/4R)].

Simplifying the expression inside the parentheses:

Q = ρ₀ * 4π * [(4R³/12) - (R³/4)].

Simplifying once more:

Q = ρ₀ * π * (R³ - R³/3),

Q = ρ₀ * π * (2R³/3),

Q = (3Q/πR³) * π * (2R³/3),

Q = 2Q.

Therefore, the total charge contained in the charge distribution is Q.

To show that the electric field in the region r > R is identical to that created by a point charge Q at r = 0, we can use Gauss's law. Since the charge distribution is spherically symmetric, the electric field outside the distribution can be obtained by considering a Gaussian surface of radius r > R.

By Gauss's law, the electric field through a closed surface is given by:

∮E · dA = (1/ε₀) * Qenc,

where ε₀ is the permittivity of free space, Qenc is the enclosed charge, and the integral is taken over the closed surface.

Since the charge distribution is spherically symmetric, the enclosed charge within the Gaussian surface of radius r is Qenc = Q.

For the Gaussian surface outside the distribution, the electric field is radially directed, and its magnitude is constant on the surface. Hence, E · dA = E * 4πr².

Plugging these values into Gauss's law:

E * 4πr² = (1/ε₀) * Q,

Simplifying:

E = Q / (4πε₀r²).

This is the same expression as the electric field created by a point charge Q at the origin (r = 0).

To derive an expression for the electric field in the region r ≤ R, we can again use Gauss's law. This time we consider a Gaussian surface inside the charge distribution, such that the entire charge Q is enclosed.

The enclosed charge within the Gaussian surface of radius r ≤ R is Qenc = Q.

By Gauss's law, we have:

∮E · dA = (1/ε₀) * Qenc.

Since the charge distribution is spherically symmetric, the electric field is radially directed, and its magnitude is constant on the Gaussian surface. Hence, E · dA = E * 4πr².

Plugging these values into Gauss's law:

E * 4πr² = (1/ε₀) * Q.

Simplifying:

E = Q / (4πε₀r²).

This expression represents the electric field inside the charge distribution for r ≤ R.

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The distance, that car will travel in 15 minute, is 28 km.

The formula used to explain the relationship between speed, distance, and time is speed distance time.

That is speed = distance/ time

So, distance = speed * time

Alternatively, you can calculate the time by dividing the distance traveled by the speed. You can figure out the third input if you know two of the inputs.

Given Speed of car = 112 km per hour

Time = 15 minutes = 15/60 hour

Time = 1/4 hour

Distance traveled by car in 15 minute = Speed of car * time

Distance = 112 * 1/4

Distance = 28 km

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Answer

0. Horizontal translation 5 units.

1. Reflection over the x-axis

2. Vertical compression 2 units

3. Vertical translation down 3 units

Explanation

• Writing the function in completed-square form.

As a ≠ 1, where a is the coefficient of the leading term, to write it in the completed-square form we have to make a = 1:

Now we have to take half of the x term and square it and add it to the function as follows:

Finally, we have a Perfect Squared Trinomial in the left side that we can rewrite as follows, obtaining our function g(x):

As our parent function is:

Then, the transformations that suffered were:

• Horizontal translation to the left 5 units

• Reflection over the x-axis

• Vertical compression 2 units

• Vertical translation down 3 units

Answer:

Hopes it helps

Step-by-step explanation:

Len

Simplifying

5(3 + -8x) = 0

(3 * 5 + -8x * 5) = 0

(15 + -40x) = 0

Solving

15 + -40x = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-15' to each side of the equation.

15 + -15 + -40x = 0 + -15

Combine like terms: 15 + -15 = 0

0 + -40x = 0 + -15

-40x = 0 + -15

Combine like terms: 0 + -15 = -15

-40x = -15

Divide each side by '-40'.

x = 0.375

Simplifying

x = 0.375

Monty

Simplifying

7 + -2(-5x) = 0

Remove parenthesis around (-5x)

7 + -2 * -5x = 0

Multiply -2 * -5

7 + 10x = 0

Solving

7 + 10x = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-7' to each side of the equation.

7 + -7 + 10x = 0 + -7

Combine like terms: 7 + -7 = 0

0 + 10x = 0 + -7

10x = 0 + -7

Combine like terms: 0 + -7 = -7

10x = -7

Divide each side by '10'.

x = -0.7

Simplifying

x = -0.7

Nailany

Simplifying

7 + -6 + -16x = 0

Combine like terms: 7 + -6 = 1

1 + -16x = 0

Solving

1 + -16x = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.

1 + -1 + -16x = 0 + -1

Combine like terms: 1 + -1 = 0

0 + -16x = 0 + -1

-16x = 0 + -1

Combine like terms: 0 + -1 = -1

-16x = -1

Divide each side by '-16'.

x = 0.0625

Simplifying

x = 0.0625

Answer:

Step-by-step explanation:

6

The interpretation of this expression is that the partial derivative of TC w.r.t. x is the rate of change of TC with respect to x, considering all other variables constant. It means if we change one unit of labor, TC will increase by 2e2x - 4 units, considering all other variables remain constant.

T C = 1/2 e2x + ey - 4x - 2ywhere x = units of labor and y = units of human capital, x, y > 0.Calculate:We need to calculate dTC/dx.

Interpretation:First, we need to calculate partial derivative of T C w.r.t. x. We know that partial derivative of a function with respect to one of its variable means to find the derivative of that variable with respect to the function, considering the other variables constant. Hence, it is a rate of change of one variable with respect to other variables considered constant. This is used to find the slope of a surface in a given direction.

The partial derivative of T C w.r.t. x is given as:

∂/∂x (T C)

= 2e2x - 4.∂/∂x (T C)

= 2e2x - 4

The interpretation of this expression is that the partial derivative of TC w.r.t. x is the rate of change of TC with respect to x, considering all other variables constant. It means if we change one unit of labor, TC will increase by 2e2x - 4 units, considering all other variables remain constant.

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Answer:

\(y = 0x - 7\)

Step-by-step explanation:

I'm guessing you mean that the slope is 0??

Equation will then look like this

\(y = 0x + b\)

to get b insert the point into the equation so y will be replaced by -7 and x will be replaced by -6

\( - 7 = 0 \times( - 6) + b\)

\(b = - 7\)

Therefore the equation will be

\(y = 0x - 7\)

Answer: 0.0386

Step-by-step explanation:

Given: The probability hat the frozen chickens contain enough salmonella bacteria to cause illness if improperly cooked : p= 0.30

Sample size : n = 12

Let x = Number of contaminated chickens

Here , two outcomes for any chicken (either contaminated or not) , so it follows binomial distribution.

Binomial probability formula:

\(P(X=x) = \ ^nC_x p^x(1-p)^{n-x}\)

The probability that the consumer will have more than 6 contaminated chickens :-

\(P(X>6)=P(X=7)+P(X=8)+P(X=9)+P(X=10)+P(X=11)+P(X=12)\\\\=^{12}C_6(0.3)^6(0.7)^6+^{12}C_7(0.3)^7(0.7)^5+^{12}C_8(0.3)^8(0.7)^4+^{12}C_9(0.3)^9(0.7)^3+^{12}C_{10}(0.3)^{10}(0.7)^2+^{12}C_{11}(0.3)^{11}(0.7)^1+^{12}C_0(0.3)^{12}(0.7)^0\)

\(=0.03860084306\approx0.0386\)  (simplified)

Hence, the required probability = 0.0386

The length of the line segment AB is 11/2 mm.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points.

Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know a line segment parallel to one side of a triangle divides the other two sides in the same ratio.

Therefore, AC/AB = EC/ED.

22/AB = 44/11.

2/AB = 4/11.

4AB = 22.

AB = 11/2.

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Answer:

28 %

Step-by-step explanation:

Percentage of glass cookware items = no. of glass cookware items / total no. of cook wares * 100

= 7 / 25 * 100

= 28 %

Answer:

Step-by-step explanation:

Each term in the sequence is 4 less than the previous term.  That indicates an arithmetic sequence, which has the form a(n) = a(1) + d(n -1), where d is the common difference.  Here the common difference is -4, and so the appropriate sequence is

a(n) = 14 - 4(n - 1)

A rectangle's length is 7 inches longer than its width. the perimeter is 38 inches. the length is 13 inches and the width of the rectangle is 12 inches

width = (38 - 14) / 2 = 12 inches

length = (38 - 12) / 2 = 13 inches

to find the length and width of the rectangle given that the length is 7 inches more than the width, and the perimeter is 38 inches, we can use the formula for perimeter (2 x length + 2 x width = perimeter). Plugging in the values given, we get 2 x length + 2 x width = 38. Solving for width, we get width = (38 - 14) / 2 = 12 inches. Plugging this value into the original equation, we get length = (38 - 12) / 2 = 13 inches. Therefore, the length and width of the rectangle are 13 inches and 12 inches, respectively.

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Answer:

The average rate of change over the interval is 120

Step-by-step explanation:

For a function f(x) the average rate of change over an interval [a,b] is given as;

f(b)-f(a)/b-a

in this case, a is 2 and b is 4

f(b) is 256 and f(a) is 16

Substituting these values in the equation for rate of change, we have;

(256-16)/(4-2) = 240/2 = 120

The link between xn+1 and xn for all n ∈ N is xn+1 = 2xn - xn-1. The link between yn+1 and yn is yn+1 = 2yn - yn-1. The link between xn and x0 is xn = 2x0 - xn-1. The link between yn and y0 is yn = 2yn - yn-1.

The explicit formula for x1n, x2n, and x3n is as follows:

x1n = 2x10 - x1(n-1)

x2n = 2x20 - x2(n-1)

x3n = 2x30 - x3(n-1)

The sheep can jump to infinity in a bounded space of the plane if and only if the initial positions of M1, M2, and M3 form an equilateral triangle.

The link between xn+1 and xn can be found by considering the symmetry of the leapfrog game. When M1 jumps over M2, the new position of M1 is the mirror image of its previous position with respect to M2. This means that the x-coordinate of M1 will be the same as the x-coordinate of M2, but the y-coordinate will be the negative of the y-coordinate of M2.

The link between yn+1 and yn can be found by considering the symmetry of the leapfrog game. When M2 jumps over M3, the new position of M2 is the mirror image of its previous position with respect to M3. This means that the y-coordinate of M2 will be the same as the y-coordinate of M3, but the x-coordinate will be the negative of the x-coordinate of M3.

The explicit formula for x1n, x2n, and x3n can be found by using the recursive formulas for xn+1 and xn.

The condition for the sheep to jump to infinity in a bounded space of the plane can be found by considering the distance between the sheep. If the initial positions of M1, M2, and M3 form an equilateral triangle, then the distance between the sheep will remain constant. This means that the sheep will continue to jump forever, and they will never reach the boundary of the space.

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Answer:

Part A

Here the entire population is the total number of people who live in Scotland and the sample considered in this survey is the randomly chosen 34,572 people.

Part B

The approximations made out of the sample cannot be considered same as that of the entire population. Because here, only a random sample of 34,572 is taken whereas the total population here is the people who live in the Scotland, which can be quite large sample. The patient details recorded are used for survey. So in the sample surveyed we do not have the data about the rest of the population. The approximations made out of the sample become same as that of the entire population only if the entire population number is near to the randomly collected sample.

In the theater, that have 1,464 seats.

1426 seats are in "regular" sections

38 seats are  "premium" front-row section

The seat arrangement is solved by division. In this case the 62 equal spaced is the divisor while the number of seats is the in each row is the quotient

The division is as follows

1464 / 62

= 23 19/31

The number of seats in the regular section is 23 * 62 = 1426

The remainder will be arranged in premium front row

using equivalent fractions

19 / 31 = 38 / 62

the remainder is 38 and this is the seat for the premium front row section

OR 1464 - 1426 = 38 seats

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Answer:

(x,y) -> (5,4)

Step-by-step explanation:

there is a positive slope.

Given:

Right triangle XYZ has right angle Z.

\(\sin(x)=\dfrac{12}{13}\)

To find:

The value of \(\cos x\).

Solution:

We know that,

\(\sin^2(x)+\cos^2(x)=1\)

\(\cos^2(x)=1-\sin^2(x)\)

\(\cos(x)=\pm\sqrt{1-\sin^2x}\)

For a triangle, all trigonometric ratios are positive. So,

\(\cos(x)=\sqrt{1-\sin^2x}\)

It is given that \(\sin(x)=\dfrac{12}{13}\). After substituting this value in the above equation, we get

\(\cos(x)=\sqrt{1-(\dfrac{12}{13})^2}\)

\(\cos(x)=\sqrt{1-\dfrac{144}{169}}\)

\(\cos(x)=\sqrt{\dfrac{169-144}{169}}\)

\(\cos(x)=\sqrt{\dfrac{25}{169}}\)

On further simplification, we get

\(\cos(x)=\dfrac{\sqrt{25}}{\sqrt{169}}\)

\(\cos(x)=\dfrac{5}{13}\)

Therefore, the required value is \(\cos(x)=\dfrac{5}{13}\).

Answer:

Answer:

Lol hi

Whathca tryin to test?

Step-by-step explanation:

Llololoo

Step-by-step explanation:

Answer:

Okok

Step-by-step explanation:

➊➋➌

❃

☟

➜↷↶

≅

lolololololol

Answer: 5π/3 (5,236)

Step-by-step explanation: Length of the whole circle arc is 2πr, in this case it is 12π. 50° is 50/360 = 5/36 part of the arc, so we can multiply 12π by 5/36 to get an answer. 12π * 5/36 = 5π/3.

Let x be the amount of the 30% alcohol and let y be the amount of 5% alcohol.

We want the total amount to by 25 gal, then we have:

We also want the resulting mix to be 25% alcohol, this is 0.25 in decimal form; also we know that the first type of alcohol is 30% and the second is 5%, then we have:

Hence we have the system of equations:

To solve the system we solve the first equation for y:

then we plug this value of y in the second equation:

Once we have the value of x we plug it in the expression we found for y:

Therefore, the mixture will have 20 gallons of 30% alcohol and 5 gallons of 5% alcohol.

Answer:

No, the ladder is not within the safe range because the slope is 5.

Step-by-step explanation:

To solve, find the slope of the ladder using the slope formula and check if the slope is between 6.3 and 9.5.

Slope is how steep a line is. In this case, the line is the ladder. If the ladder is too steep, them it is not safe.

You can calculate slope using the following formula:

\(slope = \frac{rise}{run}\)

Rise means how faraway vertically, or how high up the ladder is.

Run means the how faraway horizontally, or from the wall the ladder is.

Let's calculate slope using the formula.

\(\displaystyle {slope=\frac{rise}{run}}\)

\(\displaystyle {slope=\frac{2\ m}{0.4\ m}}\)           Substitute the values, 2m for rise, 0.4m for run.

\(\displaystyle {slope=5}\)                   Final answer

The question tells us that a safe ladder has a slope of 6.3 to 9.5. The slope, 5, is not between that range. Therefore, the ladder is not safe.

Answer:  \(\frac{28}{27}\) or \(1\frac{1}{27}\)

Step-by-step explanation:

\(\frac{7}{9} /\frac{6}{8} = \frac{7}{9}(\frac{8}{6})\)

\(\frac{7}{9} (\frac{8}{6} ) = \frac{28}{27}\)

\(\frac{28}{27} = 1 \frac{1}{27}\)

Answer:

8 grams

Step-by-step explanation:

a triangle is half a square

Hey love! <3

Answer:

f(x) = 2^x

Step-by-step explanation:

You can see the scatter plot increase by 2^x just by observations of the graph and statistic residuals (if you calculated them!)

Hope this brightens up your day/night! ╰(◡‿◡✿╰) Sincerely, Kelsey from Brainly.

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The function that best fits the data is \(y = 2^x\)

From the graph, we have the following ordered pairs

(0,1) and (1,2)

The graph represents an exponential function.

An exponential function is represented as:

\(y = ab^x\)

At (0,1), we have:

\(ab^0 = 1\)

\(a =1\)

At (1,2), we have:

\(ab^1 = 2\)

\(ab =2\)

Substitute 1 for a

\(1 * b = 2\)

\(b =2\)

Recall that:

\(y = ab^x\)

So, we have:

\(y = 1 * 2^x\)

\(y = 2^x\)

Hence, the function that best fits the data is \(y = 2^x\)

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Answer:

shouldn't it be all the same answer since it looks like a equilateral triangle