Find the surface area of this prism.

A prism, all dimensions centimeters. The base of the prism is a 6 by 6 rectangle with a 3 by 3 square removed from the corner. The prism is 9 centimeters high.

What is the surface area???

Answer:

34

Step-by-step explanation:

the equation is 2(lw+lh+wh)

2( 1.5 x 2 + 1.5 x 4 + 2 x 4)

Answer:

Step-by-step explanation:

surface area=2lb+2(l+b)h

=2×1.5×2+2(1.5+2)×4

=6+2×3.5×4

=6+28

=34 sq. m

It will take approximately 11.5 years for the balance to grow from $3,000 to $8,000 in a savings account earning 3.4% interest compounding daily.

To determine how long it will take for the balance to grow to $8,000, we can use the formula for compound interest:

A = P * (1 + r/n)^(n*t)

Where:

A = Final amount ($8,000)

P = Principal amount ($3,000)

r = Annual interest rate (3.4% or 0.034)

n = Number of times interest is compounded per year (365, since it's compounded daily)

t = Time in years (unknown)

Substituting the given values into the formula:

$8,000 = $3,000 * (1 + 0.034/365)^(365*t)

Simplifying the equation:

8/3 = (1 + 0.034/365)^(365*t)

Taking the natural logarithm of both sides:

ln(8/3) = ln[(1 + 0.034/365)^(365*t)]

Using the logarithmic property:

ln(8/3) = 365*t * ln(1 + 0.034/365)

Solving for t:

t = ln(8/3) / (365 * ln(1 + 0.034/365))

Using a calculator:

t ≈ 11.5

Therefore, it will take approximately 11.5 years for the balance to grow from $3,000 to $8,000 in a savings account earning 3.4% interest compounding daily.

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For a function to be continuous at a point, it must be defined at that point, its limit must exist at the point, and the value of the function at that point must equal the value of the limit at that point. Discontinuities may be classified as removable, jump, or infinite.

A function is called piecewise continuous on an interval if the interval can be broken into a finite number of subintervals on which the function is continuous on each open subinterval (i.e. the subinterval without its endpoints) and has a finite limit at the endpoints of each subinterval.

A piecewise function is a function built from pieces of different functions over different intervals. For example, we can make a piecewise function f(x) where f(x) = -9 when -9 < x ≤ -5, f(x) = 6 when -5 < x ≤ -1, and f(x) = -7 when -1.

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The surface area of a cylinder depends on two parameters: the radius of the base and the height of the cylinder. Without any of these measurements, it is impossible to calculate the surface area of the cylinder.

In order to find the surface area of a cylinder, we use the formula:

Surface area = 2πr² + 2πrh

where r is the radius of the base and h is the height of the cylinder. If we know both r and h, we can substitute these values into the formula to calculate the surface area.

Without additional information, we cannot calculate the surface area of the cylinder.

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Answer: 4/5

Step-by-step explanation:

Answer:

Below in bold.

Step-by-step explanation:

4.   y = x^5 - 7x

Finding the derivative:

y' = 5x^4 - 7

This is the formula for the slope at any point on the curve.

At (1, -6) the slope = 5(1)^4 - 7= 5 - 7 = -2.

5.  y = 4x - 1/x

y = 4x - x^-1

y' = 4 - (-1x^-2)

y' = 4 + 1/x^2

The slope at (-1,-3)

=  4 + 1/ (-1)^2

= 4 + 1

= 5.

The correct statement is that the value of n that make the relationship a function are any value except 1, 3, or 2

A function is a relationship that maps the elements of a set A to the elements of a set B, such that each element of A is mapped to exactly one element of the set B.

The ordered pair of known values are a function as the elements of the input variable are all different and the element of the output variable are also different, which indicates a 1 to 1 relationship.

The known elements of the set A in the question are; 2, 6, and 4

The elements of the set A are known as the domain of the function.

The known element of the set B are 8, 0, and 2

The fourth ordered pair (2·n, n), has a value similar to the pair (4, 2)

To prevent the presence of the elements 2,. 6, and 4, being assigned to other elements apart from 8, 0, and 2, the value of 2·n can be any value except 2, 6, 4

Therefore;

n can be any value except 2/2 = 1, 6/2 = 3, or 4/2 = 2

The correct statement is therefore;

n can be any value except 1, 3, or 2

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Answer:13 on each team but there wouldn’t be the Same amount

Step-by-step explanation:

Because you would divid 110 dived by 8 equals 13.75

The volume enclosed by the two curves when revolved about the x-axis is \(\(\frac{6\pi}{5} \ln 3 - \frac{3\pi}{2} \cdot 3^{\frac{4}{5}}\).\) To find the volume when the area enclosed by the graphs of \(\(y = x^2\)\)and \(\(y = \frac{3}{x^3}\)\) is revolved about the x-axis, we can use the method of cylindrical shells.

First, let's find the points of intersection between the two curves by setting them equal to each other:

\(\[x^2 = \frac{3}{x^3}\]\)

To simplify this equation, we can multiply both sides by \(\(x^3\)\):

\(\[x^5 = 3\]\)

Now, taking the fifth root of both sides:

\(\[x = \sqrt[5]{3}\]\)

So the two curves intersect at \(\(x = \sqrt[5]{3}\)\).

To calculate the volume area enclosed by the graphs of \(\(y = x^2\)\)and \(\(y = \frac{3}{x^3}\)\) is revolved about the x-axis, we need to integrate the circumference of each cylindrical shell multiplied by its height. The height of each shell is the difference in the y-values of the two curves, and the circumference is\(\(2\pi x\)\).

Let's integrate from \(\(x = 0\)\) to \(\(x = \sqrt[5]{3}\)\):

\(\[V = \int_0^{\sqrt[5]{3}} 2\pi x \left(\frac{3}{x^3} - x^2\right) \, dx\]\)

Simplifying this expression:

\(\[V = 2\pi \int_0^{\sqrt[5]{3}} \left(\frac{3}{x} - x^3\right) \, dx\]\)

Integrating each term separately:

\(\[V = 2\pi \left[3 \ln|x| - \frac{x^4}{4}\right]_0^{\sqrt[5]{3}}\]\)

Plugging in the limits of integration:

\(\[V = 2\pi \left[3 \ln|\sqrt[5]{3}| - \frac{\sqrt[5]{3}^4}{4}\right] - 2\pi \left[3 \ln|0| - \frac{0^4}{4}\right]\]\)

Since \(\(\ln|0|\)\)is undefined, the second term on the right side is zero:

\(\[V = 2\pi \left[3 \ln|\sqrt[5]{3}| - \frac{\sqrt[5]{3}^4}{4}\right]\]\)

Simplifying further:

\(\[V = 2\pi \left[3 \ln 3^{\frac{1}{5}} - \frac{3}{4} \cdot 3^{\frac{4}{5}}\right]\]\)

Using the properties of logarithms, we can simplify the first term:

\(\[V = 2\pi \left[3 \cdot \frac{1}{5} \ln 3 - \frac{3}{4} \cdot 3^{\frac{4}{5}}\right]\]\)

\(\[V = \frac{6\pi}{5} \ln 3 - \frac{3\pi}{2} \cdot 3^{\frac{4}{5}}\]\)

So the volume enclosed by the two curves when revolved about the x-axis is \(\(\frac{6\pi}{5} \ln 3 - \frac{3\pi}{2} \cdot 3^{\frac{4}{5}}\).\)

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Answer:

\(\frac{2A}{h}\) = b

Step-by-step explanation:

A = \(\frac{1}{2}\) bh   Multiply both sides by \(\frac{2}{h}\)

\(\frac{2}{h}\)  x \(\frac{A}{1}\) = \(\frac{2}{h}\) x  \(\frac{h}{2}\) x b

\(\frac{2A}{h}\) = b

The empirical formula of the uranium chloride is UCl₁.

To determine the empirical formula of the uranium chloride, we need to calculate the mole ratio of uranium to chloride in the compound.

First, we need to find the moles of uranium and chloride in the given sample.

Mass of uranium (U) = 0.176 g

Atomic mass of uranium (U) = 238.03 g/mol

Moles of uranium (U) = mass / atomic mass = 0.176 g / 238.03 g/mol ≈ 0.0007387 mol

Since the molar ratio between uranium and chloride is 1:1 in the empirical formula, the moles of chloride will also be approximately 0.0007387 mol.

Next, we can convert the moles of chloride to grams using the molar mass of chloride.

Mass of chloride (Cl) = 0.255 g - 0.176 g = 0.079 g

Now, we can calculate the molar mass of chloride (Cl).

Molar mass of chloride (Cl) = mass / moles = 0.079 g / 0.0007387 mol ≈ 107 g/mol

The empirical formula of the uranium chloride can be determined by dividing the subscripts of each element by their greatest common divisor (GCD). In this case, the GCD of 1 and 1 is 1.

Therefore, the empirical formula of the uranium chloride is UCl₁.

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Based on the calculation below, the amount that can be withdrawn each month for 10 years is a. $769.27.

First, we calculate the future value (FV) of the amount after 20 years using the formula for calculating the Future Value (FV) of an Ordinary Annuity as follows:

FV = A * (((1 + r)^n – 1) / r) ................................. (1)

Where,

FV = Future value of the amount after 20 years =?

A = Monthly deposit = $235.15

r = Monthly interest rate = 3.2% / 12 = 0.00266666666666667

n = number of months = 20 * 12 = 240

Substituting the values into equation (1), we have:

FV = $235.15 * (((1 + 0.00266666666666667)^240 – 1) / 0.00266666666666667) = $78,910.41

The amount planned to be withdrawn on monthly basis can be calculated using the formula for calculating the present value (PV) of an ordinary annuity as follows:

P = PV / ((1 - (1 / (1 + r))^n) / r) …………………………………. (2)

Where;

P = Monthly withdrawal or payment = ?

PV = Present value = FV calculated above = $78,910.41

r = Monthly interest rate = 3.2% / 12 = 0.00266666666666667

n = number of months = 10 * 12 = 120

Substitute the values into equation (2), we have:

P = $78,910.41PV / ((1 - (1 / (1 + 0.00266666666666667))^120) / 0.00266666666666667) = $769.27

Therefore, the amount that can be withdrawn each month for 10 years is $769.27.

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The answer is A: $769.27

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Have a great day and God bless! :D

Answer:

If you are finding the equation using two points then the answer is

y = −2 x + 1

If this does not help, just ignore honestly.

Part A: least-squares regression line' equation: Test score = 85.706 - 1.1171 (row).

Part B:  slope of the least-squares regression line. Slope = 1.1171.

A least-squares regression line, typically minimises the vertical distance between the data points and the regression line, is the line that best fits a linear connection among two variables when the data indicates such a relationship. Since it represents the smallest total squared of errors, also known as the "variance," the phrase "least squares" is used to describe it.

Part A:  least-squares regression line' equation:

Take the values for test score from the attached table for Coef:

Test score = constant - row

Test score = 85.706 - 1.1171

Part B:  slope of the least-squares regression line.

As there is increase of 1 row,  the predicted test core reduced by the value 1.1171.

Slope = 1.1171.

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Complete question:

Does seat location matter? Many people believe that students learn better if they sit closer to the front of the classroom Does sitting closer cause higher achievement; or do better students simply choose sit in the front? To investigate, AP Statistics teacher randomly assigned 30 students seat locations in his classroom for particular chapter and recorded the test score for each student at the end of the chapter: The explanatory variable in this experiment is which row the students were assigned (row is closest to the front and row 7 is the farthest away).

Part A: state the equation of  least-squares regression line?

Part B: Interpret the slope of the least-squares regression line in this context.

The data is shown in table:

Answer:

-3

Step-by-step explanation:

f(1)=x-4

x=1

=1-4

=-3

Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

Triangle ABC has angles A = 43.17°, B = 36.93°, and C = 112°, with sides a ≈ 5.88, b ≈ 9.18, and c = 17.

To solve triangle ABC, we used the given angle measures and side lengths to find the remaining angle and sides.

We found angle C by subtracting angles A and B from 180°, resulting in C ≈ 112°.

Using the Law of Sines, we determined the lengths of sides a and b.

Side a was approximately 5.88, calculated by (Sin(25°) * 17) / Sin(112°).

Side b was approximately 9.18, calculated by (Sin(43°) * 17) / Sin(112°).

Using the Law of Cosines, we found angles A and B.

Angle A was approximately 43.17°, obtained from arccos((9.18² + 17² - 5.88²) / (2 * 9.18 * 17)).

Angle B was approximately 36.93°, obtained from arccos((5.88² + 17² - 9.18²) / (2 * 5.88 * 17)).

The solved triangle ABC has angles A ≈ 43.17°, B ≈ 36.93°, and C ≈ 112°, with sides a ≈ 5.88, b ≈ 9.18, and c = 17 (rounded to the nearest hundredth).

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The method of documentation that describes the setting up of squares of known dimension over the entire pattern is known as grid method.

Grid method is a method of documentation that involves the setting up of squares of known dimensions over the entire pattern to document a site. This method is commonly used in archaeological surveys and historical preservation.

Therefore, grid method is a simple and effective way of recording data, and it is still widely used in the field of archaeology today.

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About 11.90% of students scored 59.99 or lower on the exam and failed the course (since this is a proportion, we can multiply it by 100 to get the percentage).

To determine the percentage of students who failed the course, we need to find the proportion of students who scored 59.99 or lower on the exam, and then convert this proportion to a percentage.
First, we need to standardize the cutoff score of 59.99 using the formula:
z = (x - μ) / σ
where x is the cutoff score, μ is the mean, and σ is the standard deviation.
Plugging in the values given in the question, we get:
z = (59.99 - 73) / 11 = -1.18
Next, we look up the proportion of scores below a z-score of -1.18 in a standard normal distribution table (or use a calculator or software). This proportion is approximately 0.1190.
Therefore, about 11.90% of students scored 59.99 or lower on the exam and failed the course (since this is a proportion, we can multiply it by 100 to get the percentage).
In other words, roughly 12% of the students failed the course based on the given criteria.

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The equation of the parabola is (y + 1)^2 = 4(x + 4).For a parabola, the distance from any point on the parabola to the focus is equal to the perpendicular distance to the directrix.

The focus is given as (-4, -1), and the directrix is y = -5. The standard form of the equation for a parabola with a vertical axis is (y - k)^2 = 4a(x - h), where (h, k) is the vertex and "a" is the distance from the vertex to the focus or directrix. The vertex is halfway between the focus and directrix, so it's (-4, (-1 + -5)/2) = (-4, -3). Since the focus is closer to the vertex than the directrix, "a" is positive. Substituting "a" and the vertex coordinates, the equation simplifies to (y + 1)^2 = 4(x + 4).

Now we can substitute the values into the equation: (y + 3)^2 = 4a(x + 4). To find "a," we use the distance formula: a = distance from vertex to focus = |-1 - (-3)|/2 = 2/2 = 1.

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Answer:

r < 6

Step-by-step explanation:

\( \implies \dfrac{1}{2}r + 3 < 6\)

\( \implies \dfrac{r}{2} < 6 - 3\)

\( \implies \dfrac{r}{2} < 3\)

\( \implies r < 3 \: \cdot \: 2\)

\( \implies \underline{ r < 6}\)

Answer:

i really dont know but yeh

Answer:

7

Step-by-step explanation:

Answer:

Give me a question to answer

The number for this equation is 5.

What is equation?

In arithmetic, Associate in Nursing equation could be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.

Main body:

let the number be x.

So , according to question =

3(x+2) = x+16

Now solving this equation , we will get the answer

⇒ 3x +6 = x+16

now moving x to left side and taking the constant to right,

⇒ 3x-x = 16 -6

⇒ 2x = 10

⇒ x=5

Hence the number is 5.

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(-4 , 2 ) so x1 = -4 and y1 = 2. The slope is still 1/2 so m = 1/2. y = 1/2 x +4 final answer

Answer:

B. (x+4)(x-4)

Step-by-step explanation:

We are given:

\(y=\frac{2x}{x^2-16}\)

And asked to factor the denominator.

When factoring, you have a^2 + bx + c, and when wanting to turn it into a binomial, you have to find two numbers that multiply to c and add up to b.

In this case, we see that c is equal to -16. List out the factor of -16:

±1 , ±16

±2 , ±8

-4 , 4

Now we see that b is not present, therefore being 0. Our goal is to find two factors of -16 that will equal to 0 when added.

1 and 16 will never make 0

2 and 8 cannot make 0 either

4 and 4 can make 0, and since 16 is a negative number, one 4 needs to be negative while the other is a positive.

Basically stating, our factor of the denominator is:

[(x + 4)(x - 4)]

Answer:

70/2

Step-by-step explanation:

We have a population of 200 people

Growth rate = 2%

How long it will take for the population to double

Double the population = 2× 200 = 400

The formula for Exponential growth =

y = a(1 + r)^t

y = Value at time t = 400

a = Initial value = 200

r = 2% = 0.02

t = ?

Hence:

400 = 200 ( 1 + 0.02)^t

Divide both sides by 200

400/200 = 200 ( 1 + 0.02)^t/200

2 = (1.02)^t

Take logarithm of both sides

log 2 = log(1.02)^t

log 2 = t log 1.02

t = log 2/log 1.02

t = 35.003417942

Approximately t = 35

We have so many formula to calculate doubling time

t = 70/Growth rate

From the above question

Growth rate = 70/2%

= 35

Therefore, the equation that we use to calculate how long it will take for the population to double to 400 people is 70/2

Answer:

The value of the missing coordinate 'r' is -10

Step-by-step explanation:

The two points have the following given parameters;

The point coordinates = (4, -17) and (8, r)

The line on which the two points rests has a slope of, m = 3/4

To find the value of 'r', we use the slope formula as follows;

\(Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

Plugging in the values gives;

\(m = \dfrac{3}{4} = \dfrac{-1-r}{11-(-1)} =\dfrac{-1-r}{11 + 1} = \dfrac{-1 - r}{12}\)

\(\dfrac{3}{4} =\dfrac{-1 - r}{12}\)

∴ 3 × 12 = 4 × (-1 - r)

36 = -4 - 4·r

36 + 4 = -4·r

r = 40/(-4) = -10

r = -10

Answer:

D. 4.5​

Step-by-step explanation:

The unit tangent vector of the parameterized curve r(t) = ⟨28t, 2, t^7⟩ at t = -2 does not exist.

To find the unit tangent vector, we need to differentiate the given vector function r(t) with respect to t. The unit tangent vector is obtained by normalizing the resulting derivative.

The derivative of r(t) with respect to t is:

r'(t) = ⟨28, 0, 7t^6⟩

To find the unit tangent vector at t = -2, we substitute the value into the derivative:

r'(-2) = ⟨28, 0, 7(-2)^6⟩ = ⟨28, 0, 7(64)⟩ = ⟨28, 0, 448⟩

Next, we calculate the magnitude of the tangent vector:

| r'(-2) | = √(28^2 + 0^2 + 448^2) = √(784 + 200704) = √201488 = 449.08

Finally, we divide the derivative vector by its magnitude to obtain the unit tangent vector:

T(-2) = r'(-2) / | r'(-2) | = ⟨28/449.08, 0/449.08, 448/449.08⟩ ≈ ⟨0.0623, 0, 0.9978⟩

At t = -2, the unit tangent vector of the parameterized curve r(t) = ⟨28t, 2, t^7⟩ does not exist. This is because the derivative vector, when normalized, yields a magnitude of 449.08, which is not zero. Thus, we can conclude that there is no unit tangent vector at t = -2.

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