Clarissa is cutting construction paper into rectangles for a project. She needs to cut one rectangle that is 10 inches × 14 1/2

inches. She needs to cut another rectangle that is 10 1/4

inches by 10 1/2 inches. How many total square inches of construction paper does Clarissa need for her project?

The correct answer is 100.48 degrees = 628π/1125 radians

Here is how to calculate 100.48 degrees to radians. The math to convert 100.48 degrees to radians, is as follows:

degrees in radians, we multiply degrees by π and divide by 180. The formula for conversion of degrees in radians: (degrees × π) ÷ 180 = radians. 100.48 degrees in our formula, we get 100.48 degrees in radians as follows:

(degrees × π) ÷ 180 = radians

(100.48 × π) ÷ 180 = 64251 0/4.4.

48 degrees = 628π/1125 radial

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Answer: 90

Step-by-step explanation:

Find the difference between coordinates:

(x2-x1) = (33 - 33) = 0

(y2-y1) = (-72 - 18) = -90

Square the results and sum them up:

(0)2 + (-90)2 = 0 + 8100 = 8100

Now Find the square root and that's your result:

Exact solution: √8100 = 45√4

Approximate solution: 90

Answer:

The third graph has the bit fit.

Step-by-step explanation:

The attached worksheet explains the selection of the third graph.  The top two graphs are linear, but the line has no relationship to the data points.  The bottom two graphs have line slopes that match the data trend. but the bottom right graph has a line that is too far above the points.  It will predict differences well, but it will miss the actual value since the y-intercept is too high.  The bottom left graph has an accurate slope, and is centered around the points to minimize individual erros.

We are asked that how could we determine the number of feet per second a squirrel can run?

Recall that rate (also known as speed) is given by

Where d is the distance in feet.

t is

The solutions to \((x+5)^(3/2) = (x-1)^3\)are x ≈ -4.65 and x ≈ 0.51, obtained by graphing the functions in Desmos.

To solve \((x+5)^(3/2) = (x-1)^3\) by graphing, we can plot both sides of the equation on the same graph using a tool like Desmos. The solution will be where the two curves intersect.

First, we can simplify the equation by cubing both sides:

\((x+5)^3 = (x-1)^6\)

Next, we can plot \(y1 = (x+5)^3 and y2 = (x-1)^6\) on the same graph in Desmos. The intersection of the two curves will give us the solutions to the equation.

By examining the graph, we can see that there are two real solutions: x ≈ -4.65 and x ≈ 0.51.

Therefore, the solutions to the equation \((x+5)^(3/2) = (x-1)^3\) are x ≈ -4.65 and x ≈ 0.51.

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The functions whose graphs consist only of lines are-

A function is a relationship between a set of inputs (referred to as the domain) and a set of permissible outputs (referred to as the codomain), in which each input is connected to exactly one output. A function on one variable is frequently denoted by f.

Linear functions: A straight line just on coordinate plane is represented by a linear function. For instance, y = 3x - 2 symbolizes a straight line on the a coordinate plane and thus a linear function.

Constant functions: A constant function is employed to portray a quantity that remains constant over time and is considered the simplest type of real-valued function.

Linear absolute value functions: The Absolute Value Function is a two-linear function piecewise defined function.

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The coordinate matrix of a set of matrices with respect to a given basis. The final coordinate matrix is a matrix that represents the given matrix in the given basis and can be used for various calculations.

Given a vector space V with a basis B = {b1, b2, ..., bn} and an element v ∈ V. The coordinate matrix of v with respect to the basis B is the n × 1 matrix [v]B = (a1, a2, ..., an) where v = a1b1 + a2b2 + ... + anbn. This is also referred to as the coordinate vector of v with respect to B.Exercise 11:Let A = {[1 0], [0 1]} be a matrix and B = {[3 1], [2 4]} be a basis of R2. We are to find the coordinate matrix of A with respect to B. We are looking for the solution to the equation AX = B. Rearranging, we have X = A⁻¹B. We can then get the coordinate matrix of A with respect to B by taking the transpose of X. Solving, we haveA⁻¹ = {[1 0], [0 1]}B = {[3 1], [2 4]}Hence,X = A⁻¹B = {[1 0], [0 1]}{[3 1], [2 4]}= {[3 1], [2 4]}Coordinate matrix of A with respect to B is Xᵀ = {[3 2], [1 4]}Exercise 12:Let A = {[2 -1], [3 1]} be a matrix and B = {[1 1], [2 1]} be a basis of R2. We are to find the coordinate matrix of A with respect to B. We are looking for the solution to the equation AX = B. Rearranging, we have X = A⁻¹B. We can then get the coordinate matrix of A with respect to B by taking the transpose of X. Solving, we haveA⁻¹ = 1/(ad - bc) [d -b, -c a] = [1 1, -2 2]B = {[1 1], [2 1]}Hence,X = A⁻¹B = [1 1; -2 2][1 1; 2 1]= [3 2; -4 1]Coordinate matrix of A with respect to B is Xᵀ = {[3 -4], [2 1]}Exercise 13:Let A = {[1 1 1], [0 1 1], [0 0 1]} be a matrix and B = {[1 0 0], [1 1 0], [1 1 1]} be a basis of R3. We are to find the coordinate matrix of A with respect to B. We are looking for the solution to the equation AX = B. Rearranging, we have X = A⁻¹B. We can then get the coordinate matrix of A with respect to B by taking the transpose of X. Solving, we haveA⁻¹ = {[1 -1 0], [0 1 -1], [0 0 1]}B = {[1 0 0], [1 1 0], [1 1 1]}Hence,X = A⁻¹B = {[1 0 0], [0 1 0], [0 0 1]}Coordinate matrix of A with respect to B is Xᵀ = {[1 0 0], [0 1 0], [0 0 1]}Exercise 14:Let A = {[1 2], [3 4]} be a matrix and B = {[1 -1], [1 1]} be a basis of R2. We are to find the coordinate matrix of A with respect to B. We are looking for the solution to the equation AX = B. Rearranging, we have X = A⁻¹B. We can then get the coordinate matrix of A with respect to B by taking the transpose of X. Solving, we haveA⁻¹ = -1/2 [4 -2, -3 1] = [-2 3/2, 1/2 -1/2]B = {[1 -1], [1 1]}Hence,X = A⁻¹B = [-2 3/2; 1/2 -1/2][1 -1; 1 1]= [3/2 1/2; 5/2 3/2]Coordinate matrix of A with respect to B is Xᵀ = {[3/2 5/2], [1/2 3/2]}Exercise 15:Let A = {[1 2 3], [4 5 6], [7 8 9]} be a matrix and B = {[1 0 0], [0 1 0], [0 0 1]} be a basis of R3. We are to find the coordinate matrix of A with respect to B. We are looking for the solution to the equation AX = B.

Rearranging, we have X = A⁻¹B. We can then get the coordinate matrix of A with respect to B by taking the transpose of X. Solving, we haveA⁻¹ = [(-2/3) 0 (1/3); (-2/3) (1/3) (4/3); (1/3) (-2/3) (1/3)]B = {[1 0 0], [0 1 0], [0 0 1]}Hence,X = A⁻¹B = [(-2/3) 0 (1/3); (-2/3) (1/3) (4/3); (1/3) (-2/3) (1/3)][1 0 0; 0 1 0; 0 0 1]= [(-2/3) 0 (1/3); (-2/3) (1/3) (4/3); (1/3) (-2/3) (1/3)]Coordinate matrix of A with respect to B is Xᵀ = {[(-2/3) -2/3 1/3], [0 1/3 -2/3], [(1/3) (4/3) (1/3)]}Exercise 16:Let A = {[1 -1], [2 -2]} be a matrix and B = {[1 1], [1 0]} be a basis of R2. We are to find the coordinate matrix of A with respect to B. We are looking for the solution to the equation AX = B. Rearranging, we have X = A⁻¹B. We can then get the coordinate matrix of A with respect to B by taking the transpose of X. Solving, we haveA⁻¹ = 1/2 [2 1, -2 -1] = [1 -1/2, -1 1/2]B = {[1 1], [1 0]}Hence,X = A⁻¹B = [1 -1/2; -1 1/2][1 1; 1 0]= [0.5 1; -0.5 1]Coordinate matrix of A with respect to B is Xᵀ = {[0.5 -0.5], [1 1]}.

so each main answer consists of finding the inverse of the given matrix, multiplying it by the given basis matrix, and transposing the result to obtain the coordinate matrix.

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Answer:

\(Number\ of\ bags = 3{\frac{3}{8}\)

Step-by-step explanation:

Given

Size of Flower Pot = 9 cubic-inch

Size of filling bag = \(2\frac{2}{3}\) cubic-inch

Required

Determine the number of bags needed to fill the pot

To solve this, we simply divide the volume of the flower pot by the volume of the filling bags;

This is shown as follows:

\(Number\ of\ bags = \frac{Volume\ of\ Pot}{Volume\ of\ filling\ bags}\)

Substitute 9 for Volume of Pot and \(2\frac{2}{3}\) for Volume of filling bags

\(Number\ of\ bags = \frac{9}{2\frac{2}{3}}\)

Convert denominator to improper fraction

\(Number\ of\ bags = \frac{9}{\frac{8}{3}}\)

Rewrite Expression

\(Number\ of\ bags = 9 / {\frac{8}{3}\)

\(Number\ of\ bags = 9 * {\frac{3}{8}\)

\(Number\ of\ bags = {\frac{9 * 3}{8}\)

\(Number\ of\ bags = {\frac{27}{8}\)

Convert to Mixed Fraction

\(Number\ of\ bags = 3{\frac{3}{8}\)

Hence, the number of bags needed to fill the flower pot is \(3{\frac{3}{8}\)

Answer:

a

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

B, C, and D, have straight up and down lines, which is not a function.

Find the inverse of each of the given functions. f(x) = 4x − 12 f−1(x) = x +

first one is 1/4

second one is 3

Answer:

first box is 1/4
second box is 3

for the next question on the page ( h(x) = (2x-4)/3 ) the answer is C (h^-1(x) = (3x+4)/2 )

Step-by-step explanation:

Answer:

2:5 is the answer

Step-by-step explanation:

Why is because it says What is the ratio of the distance Shawn ran to the distance he biked shawn ran 2 miles the ratio is 2:  and comparing how he rode 5 miles is 2:5

Answer:

2:5

Step-by-step explanation:

im in k12 LOL

Answer:

See explanation

Step-by-step explanation:

Mass of  samarium-151  originally present (No) = 5 g

Mass of  samarium-151 discovered (N) = 0.625 grams

time taken = ?

half life of samarium-151 (t1/2) = 96.6 years

From

N/No = (1/2)^t/t1/2

0.625/5 = (1/2)^t/96

0.125 = (1/2)^t/96

1/8 = (1/2)^t/96

(1/2)^3 = (1/2)^t/96

3 = t/96

t = 3 * 96

t = 288 years

The mass of europium-151 when the rock was discovered is obtained from;

Fraction of  samarium-151  left = 1/8

Fraction of  europium-151 formed = 1 - 1/8 = 7/8

Mass of  europium-151 = 7/8 * 5 = 4.375 g

A p-value is a measure of the strength of evidence against the null hypothesis in a statistical hypothesis test. It represents the probability of obtaining the observed data or more extreme results, assuming that the null hypothesis is true.

In general, a smaller p-value provides stronger evidence against the null hypothesis. Therefore, in the given scenario, a p-value of 0.02 would provide stronger evidence against the null hypothesis compared to a p-value of 0.03.

A p-value of 0.02 indicates that there is a 2% chance of obtaining the observed data or more extreme results if the null hypothesis is true. This suggests that the observed data is relatively unlikely under the assumption of the null hypothesis, providing stronger evidence against it.

On the other hand, a p-value of 0.03 indicates that there is a 3% chance of obtaining the observed data or more extreme results if the null hypothesis is true. Although this still suggests that the observed data is unlikely under the null hypothesis, it is not as strong evidence as a p-value of 0.02.

In summary, a lower p-value indicates that the observed data is less likely to occur under the null hypothesis, providing stronger evidence against it. Therefore, a p-value of 0.02 would provide stronger evidence against the null hypothesis compared to a p-value of 0.03.

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Answer:

(2,-3)

Step-by-step explanation:

I thought you'd actually have to calculate it but I guess they just wanted to give you guys a graph lol

Answer:

9

Step-by-step explanation:

(5-2)*3

5-2=3

3*3=9

Answer:

3(5-2) = 9

Step-by-step explanation:

PEMDAS

Answer: 2

Step-by-step explanation:

Answer: £3.38

Step-by-step explanation:

In the first year, the pocket money goes up by:

= 1 + (1 * 50%)

= £1.50

In the second year:

= 1.50 + (1.50 * 50%)

= £2.25

In the third year:

= 2.25 * ( 2.25 * 50%)

= £3.38

Given the triangle with an angle α of 53° and two sides of length b = 15 and c = 16, we can use the Law of Cosines to determine the remaining side a and one of the other angles β.The remaining side a is approximately 9.96 and the angle β is approximately 34.58°

The Law of Cosines states that for any triangle with sides of lengths a, b, and c, and an angle α opposite the side of length a, the following equation holds: c²= a² + b² - 2abcos(α).

To find the remaining side a, we can substitute the given values into the equation: 16² = a² + 15² - 2(15)(a)cos(53°).

Simplifying the equation gives: 256 = a² + 225 - 30acos(53°).

Rearranging the terms, we have: a²- 30acos(53°) + 31 = 0.

Solving this quadratic equation yields two possible values for a: a ≈ 9.96 and a ≈ 39.04 (rounded to two decimal places).

To find the angle β, we can use the Law of Sines: sin(β)/15 = sin(53°)/a.

Substituting the known values, we get: sin(β)/15 = sin(53°)/9.96 (using the approximate value of a).

Solving for sin(β) and then finding the inverse sine gives us β ≈ 34.58° (rounded to two decimal places).

Therefore, the remaining side a is approximately 9.96 and the angle β is approximately 34.58°.

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a. The cross-section taken through the vertex and perpendicular to the base of a right circular cone is a triangle.

Specifically, it is an isosceles triangle with two equal sides that are radii of the base and the third side being the slant height of the cone. The dimensions of this slice depend on the size of the cone, specifically the radius of the base and the height of the cone.

b. The cross-section taken parallel to the base and closer to the vertex than the base plane is also a triangle. However, this triangle is smaller than the one in part a and is also an isosceles triangle with two equal sides that are segments of the slant height of the cone. The third side is a chord of the base circle that is parallel to the base of the cone. The dimensions of this slice also depend on the size of the cone, specifically the radius of the base, the height of the cone, and the distance from the base plane to the cross-section.

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Answer:

B, D, and E

Step-by-step explanation:

Edge 2020

The sets of vectors are orthogonal and will be c-d,g-h, and v-w.

A vector is a quantity with a magnitude, and direction that follows the law of vector addition.

Fo the orthogonal vector their dot product is equal to zero.

The dot product for the set are as follows;

a.b)〈–1, 0〉〈1, 0〉 = -1

c.d)〈1, 0〉  〈0, –1〉=0

e.f) 〈–4, –6〉 〈12, 8〉=-96

g.h)〈4, –6〉〈12, 8〉=0

v.w) 〈10, –5〉〈–10, –20〉=0

x.y)〈10, –5〉 〈–10, –2〉=-90

The sets of vectors are orthogonal are;

c-d ,g-h,v-w

Sets B, D, and E of vectors are orthogonal.

Hence the sets of vectors are orthogonal and will be c-d,g-h, and v-w.

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Answer:

B. RZ =R BZ

Step-by-step explanation:

Since point Z is equidistant from the sides of ARST, it lies on the perpendicular bisectors of both sides. Therefore, CZ and SZ are perpendicular bisectors of AB and ST, respectively.

Option B is true because point R lies on the perpendicular bisector of AB, and therefore RZ = RB.

Answer: vv

Step-by-step explanation:

Since point Z is equidistant from the sides of ARST, it lies on the perpendicular bisector of the sides ST and AR.

Therefore, we can draw perpendiculars from point Z to the sides ST and AR, which intersect them at points T' and R', respectively.

Now, let's examine the options:

A. SZ & TZ: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of ST, and the distance from Z to S and T could be different.

B. RZ = RB: This is true, as point Z lies on the perpendicular bisector of AR, and is therefore equidistant from R and B.

C. CTZ = ASZ: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of AR, and the distances from Z to C and A could be different.

D. ASZ = ZSB: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of ST, and the distances from Z to A and B could be different.

Therefore, the only statement that must be true is option B: RZ = RB.

Answer

how much is like saying time the this

Step-by-step explanation:

60,000 time 9.35%= 56100

The volume flow rate of the air supply required is 533 CFM and the relative humidity of the air supply should be 60% and the dew point temperature of the air supply should be 55.2°F.

The quantity of air required is calculated using the formula:

CFM = Q/(1.08 x ΔT x 1.1) where,

Q = Sensible Heat Load in Btu/hr

ΔT = Temperature Difference between Room Air and Outdoor Air

CFM = Cubic Feet per Minute of Air Supply 1.08 = Specific Heat of Air at Constant Pressure 1.1 = Density of Standard Air at 70°F and 29.92" Hg Absolute.

According to the problem statement,

Q = 42,000 Btu/hr

ΔT = (86 - 15)°F = 71°F

CFM = 42,000/(1.08 x 71 x 1.1)

= 532.9

~ 533 CFM

Thus, we can say that the volume flow rate of the air supply required is 533 CFM and the relative humidity of the air supply should be 60%, and the dew point temperature of the air supply should be 55.2°F.

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For the total purchase, vera has been overcharged by $3. 50 for her purchase.

We have information that

3 orders at 0.89$

\(=3\times 0.89=2.67\)$

12 orders for 0.15$

\(=12\times0.15=1.8\)$

for 1 order 2.99$

\(=1\times 2.99=2.99\)$

and also 8.69$ for a photo album

so total amount = 2.67+1.8+2.99+8.69= 16.15$

Now 7% of the tax =\(16.15\times1.07=17.2805\)

Thus the difference of the amount =20.78-17.2805=3.5$

Thus the total purchase, vera has been overcharged by $3. 50 for her purchase.

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Answer:

D. Vera has been over charged by $3.50 for her purchase.

Step-by-step explanation:

I just did the assignment!

The answer is option (C), that is, the events of rolling a fair die two times are independent. The events are neither disjoint nor exclusive.

When rolling a fair die two times, one can get any one of the 36 possible outcomes equally likely. Let A be the event of obtaining an even number on the first roll and let B be the event of getting a number greater than 3 on the second roll. Let’s see how the outcomes of A and B are related:

There are three even numbers on the die, i.e. A={2, 4, 6}. There are four numbers greater than 3 on the die, i.e. B={4, 5, 6}. So the intersection of A and B is the set {4, 6}, which is not empty. Thus, the events A and B are not disjoint. So option (A) is incorrect.

There is only one outcome that belongs to both A and B, i.e. the outcome of 6. Since there are 36 equally likely outcomes, the probability of the outcome 6 is 1/36. Now, if we know that the outcome of the first roll is an even number, does it affect the probability of getting a number greater than 3 on the second roll? Clearly not, since A∩B = {4, 6} and P(B|A) = P(A∩B)/P(A) = (2/36)/(18/36) = 1/9 = P(B). So the events A and B are independent. Thus, option (C) is correct. Neither option (A) nor option (C) can be correct, so we can eliminate options (D) and (E).

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The probability of leaving it in any given class is 1/4, the probability of leaving it in the 5th class is 1/4, or\(0.250 (25.0%).\)

The probability that the student left her iClicker device in the 5th class is 0.250 (25.0%). This is because the probability of leaving it in any given class is 1/4, and as she attends 5 different classes,

there is 5/4 or 1.25 chances of her leaving it in the 5th class.

To explain further, the probability of an event can be calculated by dividing the number of ways the event can occur by the total number of possible outcomes. In this case, the event is leaving the iClicker device in the 5th class, and the total number of possible outcomes is 5 (for the 5 classes).

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It takes approximately 52.7 hours for the activity of a sample of gallium-67 to fall to 6.73 percent of its original value.

The decay of radioactive substances is governed by the following equation:

\(N(t) = N_{0} e^{(-\lambda t)\)

where:

N(t) is the amount of the substance at time t

N₀ is the initial amount of the substance

λ is the decay constant

t is time

The half-life of gallium-67 is 78.2 hours, which means that:

λ = ln(2)/t₁/₂ = ln(2)/78.2 = 0.00887 h⁻¹

Let N be the amount of gallium-67 remaining after time t, and N₀ be the initial amount. Then, we can use the above equation to find the time t required for the activity of the sample to fall to 6.73 percent of its original value:

N/N₀ = 0.0673

\(0.0673 = e^{(-\lambda t)}\)

Taking the natural logarithm of both sides:

ln(0.0673) = -λt

t = ln(1/0.0673)/λ

t = ln(14.84)/0.00887

t ≈ 52.7 hours

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The symmetry of the distribution depends on the probability of success and the number of trials, as it can be skewed when the probability of success is not equal to 0.5.

A binomial experiment is characterized by certain features, and among the statements provided, the two that accurately describe these features are:
1. Trials are independent: In a binomial experiment, each trial is conducted independently of one another, meaning the outcome of one trial does not affect the outcome of any other trial. This independence ensures that the probability of success remains constant across all trials.
2. The outcome of a trial can be classified as either a success or a failure: In a binomial experiment, there are only two possible outcomes for each trial - success or failure. This simplifies the experiment's setup and makes it easier to calculate probabilities, as it focuses on the number of successful outcomes out of a fixed number of trials.
The other two statements are not accurate descriptions of a binomial experiment. The trials do not represent selection without replacement, and the distribution is not always symmetrical.

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Answer:

This shape is a hexagon. Angles in a hexagon add to 720 degrees.

2(y) + 4(2y-20) =  720

2y + 8y-80 = 720

10y-80=720

10y=800

y=80

Let me know if this helps!