Since spring started, Kareem has been surveying the growth of leaves on his neighborhood trees. He goes out every day and computes the average number of leaves on a sample of trees. He created a scatter plot where the y-axis represents the average number of leaves on the trees, and the x-axis represents the number of weeks since spring started. Use the 2 given points to write a linear equation that can be used to approximate the data distribution.

A. Y=3x+2000
B. Y=4700x+1500
C. Y=x+1700
D. Y=1566. 67x+1716. 67

Based on the equation you created, what would be the expected average number of leaves on a tree 8 weeks after spring has started?​

The equation of the straight line would be -

y = 2x.

Given is that a straight line passes through the points (2, 4) and (3, 6).

We can write the slope as -

m = (6 - 4)/(3 - 2)

m = 2/1

m = 2

For the point (2, 4), we can write -

y = 2x + c

c = 4 - 4

c = 0

Therefore, the equation of the straight line would be -

y = 2x.

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Answer:

1/4

Step-by-step explanation:

3/4 x 2/4 = 6/24

6/24 simplified is 1/4

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Answer:

6/12 or 1/2

Step-by-step explanation:

Start by multiplying the numerators

3 x 2 = 6

Then multiply the denominators

4 x 3 = 12

Then you get your answer of 6/12

But if you want it simplified then divide both the denominator and numerator by 6 and you will get your final answer of

1/2

Hope this helped

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To know more about dividing fractions and checking equations:

No, the statement that 3/5 ÷ 415 equals 9/4 is not true. When dividing fractions, you multiply the first fraction by the reciprocal of the second fraction. In this case, the reciprocal of 415 is 1/415. Therefore, the equation becomes (3/5) × (1/415). Multiplying the numerators gives 3, and multiplying the denominators gives 2075. So, the simplified result is 3/2075, not 9/4.

To check the equation, students can perform the division operation manually and verify if the result matches the given equation. They can divide 3/5 by 415 and simplify the resulting fraction. If the simplified fraction is indeed 9/4, then the statement would be true. However, since the simplified fraction is 3/2075, the statement is false. Students can use this method to double-check their work and ensure the accuracy of their calculations.

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Answer:

Step-by-step explanation:

The cost of the new car is $20,000.

We would apply the periodic interest rate formula which is expressed as

P = a/[{(1+r)^n]-1}/{r(1+r)^n}]

Where

P represents the monthly payments.

a represents the amount of the loan

r represents the annual rate.

n represents number of monthly payments. Therefore

a = $20000

r = 0.05/12 = 0.0042

n = 12 × 5 = 60

Therefore,

P = 20000/[{(1+0.0042)^60]-1}/{0.0042(1+0.0042)^60}]

20000/[{(1.0042)^60]-1}/{0.0042(1.0042)^60}]

P = 20000/{1.286 -1}/[0.0042(1.286)]

P = 20000/(0.286/0.0054012)

P = 20000/52.95

P = $378

Ahmed will pay $378 each month

The total payment is

378 × 60 = $22680

The amount that Ahmed will pay in interest is

22680 - 20000 = $2680

Answer:

2/9

Step-by-step explanation:

Answer: 2/9

Step-by-step explanation:

First write as an improper fraction.

2 5/8 is equal to 21/8

Then re-write

7/12 divided by 21/8

Then multiply 7/12 by the reciprocal of 21/8 which is 8/21

The answer is 56/252

Simplify

The answer is 2/9

F is concave downward on the interval [-3, 1].

The solution can be found by observing the graph of f and determining where it is concave downward. From the graph, we can see that f is concave downward on the interval [-3, 1]. To find where F is concave downward, we need to take the integral of the real part of f over this interval. A function is concave downward if its second derivative is negative. In other words, if the rate of change of the slope of the function is decreasing.Since the integral of f is the area under the curve, we can see that the area under f is decreasing on this interval, which means that F is concave downward.

Therefore, we can conclude that F is concave downward on the interval [-3, 1].

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Answer:

Choice 4

Step-by-step explanation:

#4   because the graph does not intersect the x-axis

The graph that represents a quadratic function with a negative discriminant is graph 4.

The part in the formula of a quadratic equation that helps us to know the nature of the roots of a quadratic equation is known as a discriminant.

D = b2 - 4ac,

Since for the value of the discriminant to be negative, the roots of the quadratic equation should be imaginary. Also, imaginary never intersects the x-axis of the graph.

Now, in the group of the graphs the only graph that does not intersect the x-axis of the graph or have imaginary roots is graph 4.

Hence, the correct option is graph4 (Bottom Right).

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Answer:

\(m=0.02\)

Step-by-step explanation:

\(4.3m=0.086\\m=\frac{0.086}{4.3} \\m=0.02\)

we have established a bijective function between the elements of \(\( D_3 \) and \( S_3 \)\) that preserves their group operations, proving that \(\( D_3 \cong S_3 \).\)

To prove that the dihedral group \(\( D_3 \)\) is isomorphic to the symmetric group \(\( S_3 \)\), we need to show that there exists a bijective function (a one-to-one and onto mapping) between the elements of the two groups that preserves their group operations.

First, let's define the dihedral group \(\( D_3 \)\) and the symmetric group \(\( S_3 \)\):

- The dihedral group \(\( D_3 \)\)is the group of symmetries of an equilateral triangle. It has six elements: the identity element, three reflections (corresponding to reflections across the three axes of symmetry of the triangle), and two rotations (corresponding to 120° and 240° rotations in the clockwise direction).

- The symmetric group \(\( S_3 \)\) is the group of all permutations of three objects. It has six elements as well: the identity element, three 2-cycles (swapping two elements), and two 3-cycles (cyclic permutations of three elements).

To prove that\(\( D_3 \cong S_3 \)\), we need to find a bijective function between the two groups that preserves their group operations. We can construct such a function by considering the correspondence between the elements of the two groups:

- The identity element in both groups maps to each other.

- The three reflections in \(\( D_3 \)\) can be mapped to the three 2-cycles in \(\( S_3 \)\). For example, the reflection across one axis of symmetry can be mapped to the 2-cycle that swaps the corresponding two elements.

- The two rotations in \(\( D_3 \)\) can be mapped to the two 3-cycles in \(\( S_3 \)\). For example, the 120° rotation can be mapped to the 3-cycle that cyclically permutes the corresponding three elements.

This mapping is bijective since each element in\(\( D_3 \\)) is uniquely mapped to an element in \(\( S_3 \),\) and each element in\(\( S_3 \)\) is uniquely mapped to an element in\(\( D_3 \)\). Moreover, this mapping preserves the group operations because the composition of symmetries in \(\( D_3 \)\) corresponds to the composition of permutations in \(\( S_3 \)\).

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Answer:

answer is D from what I got

Jelly beans are $1.5/lb and trail mix is $2.063/lb, according to the data.

A heterogeneous mixture would be a trail mix. When the components of a combination are dispersed unevenly across the mixture, the mixture is said to be heterogeneous. As a mixture of nuts, raisins, and other seeds, trail mix cannot have an evenly distributed dispersion of its ingredients.

t = trail mix, j = jelly beans

3t + 8j = 21

5t + 2j = 18

Solving the first for t

2t = 6j - 3

t = (6j - 3)/2

Substituting

5(6j - 3)/2 + 2j = 18

j = 51/34

j = 1.5, Jelly beans cost $1.5/lb

now,

8t + 3(1.5) = 21

8t = 16.5

t = 2.0625, trailmix costs $2.063 dollars/lb

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The slope is 0.6

The answer is taken by solving from the graph

We need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit which is compounded semi-annually.

To solve this problem, we can use the formula for the future value of an annuity:

\(FV = P * ((1 + r)^n - 1) / r\)

Where:

FV is the future value of the annuity

P is the periodic payment or deposit amount

r is the interest rate per period

n is the number of periods

In this case, the deposit amount is $726.56, the interest rate is 6.45% compounded semi-annually, and the future value is $31,300. We need to find the number of deposits (n).

We can rearrange the formula and solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Substituting the given values:

n = log((31,300 * 0.03225) / (726.56 * 0.03225 + 31,300)) / log(1 + 0.03225)

Using a calculator or software, we find that n ≈ 9.989.

Therefore, we need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit.

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Answer:

D.

Step-by-step explanation:

The correct answer is D because it is equivalent to the original expression. Instead of distributing the 6 twice, it is placed in parenthesis. The other choices are wrong, I tried them, did not yield the same answer.

Answer:

x = 5 or -5

Step-by-step explanation:

if a = b, c^a = c^b

make each side the exponent of 4

4^[log base4 (x+3)(x-3)] = 4^2

since a^(log basea b) = b, (think of the definition of logs as the inverse of exponents here)

(x+3)((x-3) = 16

x^2 -9 = 16x^2 = 25

x = 5 or -5

The value of sin(u+v) given tan u = 15/8 is -9/221

Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the their angles.

A right-angled triangle has 3 sides, hypotenuse, opposite and adjacent. The following should be noted:

Sin = Opposite / Hypothenuse

Tan = Opposite / Adjacent

Cos = Adjacent / Hypothenuse

When tan u = 15/8

Opposite = 15

Adjacent = 8

Hypothenuse will be:

= ✓(15² + 8²)

= ✓(225 + 64)

= ✓289

= 17

Therefore sin u = 15/17

When cos v = -5/13, it should be noted that sin v will be -12/13.

Therefore, sin(u + v) will be:

= 15/17 + (-12/13)

= 15/17 - 12/13

= 195/221 - 204/221

= -9/221

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The number of sales a promoter can expect if he spends $10,000 in advertising is $80,000 that is option B.

While going through a word problem like this, read it a few times to comprehend the context without focusing too much on the numbers..... Something along the lines of....

"If a promoter spends money on advertising, he will get more customers."

Short sentences should be used to summarise the content.

$10,000 is spent by the promoter.

"For every $100 spent, 20 new customers are drawn."

"Tickets are $40."

In one calculation this would be:

Using ratio of,

income/expenditure = 800/100 = income/10,000

= 10000 x 20 x 40 / 100

= 80,000

Therefore, the value of sale increase should be $80,000.

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The Z score that is equivalent to the raw score 92.5 is B. -1.25.

A Z score represents the number of standard deviations a raw score is from the mean in a normal distribution. To calculate the Z score, we use the formula: Z = (X - μ) / σ, where X is the raw score, μ is the mean, and σ is the standard deviation.

Given that the mean score is 100 and the standard deviation is 15, we can calculate the Z score for the raw score 92.5 as follows:

Z = (92.5 - 100) / 15

Z = -7.5 / 15

Z = -0.5

Therefore, the Z score that is equivalent to the raw score 92.5 is -0.5.

The Z score is a useful measure in statistics that allows us to standardize and compare data points across different distributions. It helps us understand the relative position of a data point within a distribution and determine how unusual or typical that data point is compared to others. By calculating the Z score, we can easily determine the percentage of data points that fall below or above a particular value in a normal distribution, which aids in making statistical inferences and drawing conclusions.

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Answer:

No, it does not form a right triangle. 

Step-by-step explanation:

A + B + C = 250

100^2 + 50^2 doesn't equal 100^2

Neither does 100^2 + 100^2 equal 50^2 

The sides are 100, 100, and 50 but these do not make a right triangle

To produce `samplematrix = [1, 4, 7, 5, 8, 3, 6, 9]` with the command `samplematrix([n]) = [ ]`, the value of `n` should be 2.

To produce `samplematrix = [1, 4, 7, 5, 8, 3, 6, 9]` with the command `samplematrix([n]) = [ ]`, the value of `n` should be 2. Here's the explanation: Given `samplematrix=[1, 2, 3; 4, 5, 6; 7, 8, 9]`, the command `samplematrix([n]) = [ ]` would remove the nth row from the matrix and leave an empty row in its place.

For example, if `n = 2`, then the command `samplematrix([n]) = [ ]` would remove the second row and leave an empty row in its place.

The resulting matrix would be:`samplematrix = [1, 2, 3; ; 7, 8, 9]`

Notice that there is an empty row in the middle because the second row was removed.

Next, to produce the desired matrix `samplematrix = [1, 4, 7, 5, 8, 3, 6, 9]`, we need to concatenate the rows of the modified `samplematrix` matrix in a specific order. The order is the first row, then the third row, and finally the second row. So, we can use the following code to achieve this:

result = [samplematrix(1,:); samplematrix(3,:); samplematrix(2,:)]

The resulting `result` matrix would be:`result = [1, 2, 3; 7, 8, 9; 4, 5, 6]`

We can then use the colon operator to reshape the matrix into a row vector, like this:`samplematrix = result(:)'`The resulting `samplematrix` vector would be:`samplematrix = [1, 4, 7, 5, 8, 3, 6, 9]`

Therefore, to produce `samplematrix = [1, 4, 7, 5, 8, 3, 6, 9]` with the command `samplematrix([n]) = [ ]`, the value of `n` should be 2.

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Answer:

$987.50

Step-by-step explanation:

To calculate Joan Smith's tax, we need to follow these steps:

Step 1: Determine the taxable income

Taxable Income = Joan Smith's earnings - Federal exemption

Taxable Income = $42,500.00 - $3,000.00 = $39,500.00

Step 2: Calculate the tax amount

Tax amount = Taxable Income * Tax rate

Tax amount = $39,500.00 * 2.5% = $987.50

Therefore, Joan Smith's tax amount is $987.50.

Statistical conclusion validity is the extent to which inferences and conclusions drawn from statistical data are valid.

The main threat to statistical conclusion validity discussed in class is the potential for spurious correlations. This is when two variables appear to be related when in fact they are not.

Statistical conclusion validity is a measure of how valid the conclusions drawn from statistical data are. This is important because it allows us to draw valid inferences from the data. The main threat to statistical conclusion validity discussed in class is the potential for spurious correlations. This is when two variables appear to be related when in fact they are not. For example, a study may show that there is a correlation between ice cream sales and crime rate, when in fact it is merely a coincidence that both variables increase during the summer months. By controlling for other variables and using appropriate statistical tests, it is possible to identify and avoid spurious correlations.

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The solutions are x = 1/9, x = 25/8, and x = 1. Substituting these values back into either equation will give the corresponding values of y.

We can solve this system of equations by using elimination or substitution method.

Elimination Method:

From the second equation, we can isolate x or y in terms of the other variable:

5xy - 2(x + y) = 20

5xy - 2x - 2y = 20

5xy - 2x - 2y + 4 = 24

5xy - 2(x + 2y) + 4 = 24

5xy - 2(2 - y + 2y) + 4 = 24 (using x + y = a)

5xy - 2(2 + y) + 4 = 24

5xy - 2y = 22

y(5x - 2) = 22

y = 22/(5x - 2)

Substituting this expression for y into the first equation, we get:

2(x² + (22/(5x-2))²) - 5(x + 22/(5x-2)) = 1

Multiplying through by (5x - 2)², we get:

2(5x - 2)²(x² + 22²) - 5(5x - 2)(x(5x - 2) + 22) = (5x - 2)²

Simplifying and rearranging, we get:

9x⁴ - 100x³ + 328x² - 100x + 4 = 0

This is a quartic equation which can be solved using various methods, such as factoring, graphing, or numerical methods.

Substitution Method:

From the first equation, we can solve for y in terms of x:

2(x²+y²)-5(x+y)=1

2x² + 2y² - 5x - 5y = 1

2y² - 5y = 1 - 2x² + 5x

Using the quadratic formula, we get:

y = (5 ± sqrt(25 - 8(1-2x²+5x)))/4

y = (5 ± sqrt(8x² - 25x + 24))/4

Substituting this expression for y into the second equation, we get:

5x(5 ± sqrt(8x² - 25x + 24))/4 - 2(x + (5 ± sqrt(8x² - 25x + 24))/4) = 20

Simplifying and rearranging, we get:

(9x - 4)(8x - 25)(x - 1) = 0

Thus, the solutions are x = 1/9, x = 25/8, and x = 1. Substituting these values back into either equation will give the corresponding values of y.

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The F ratio in a completely randomized ANOVA is a) MSTR/MSE.

The F ratio in ANOVA is a measure of the variability between groups compared to the variability within groups. MSTR (mean square treatment) represents the variability between groups, while MSE (mean square error) represents the variability within groups.

The F ratio is the ratio of MSTR to MSE. A high F ratio indicates that the variability between groups is larger than the variability within groups, suggesting that there is a significant difference between at least two of the group means.

In contrast, a low F ratio suggests that there is little difference between group means, and any observed differences may be due to chance. Therefore, the F ratio is an essential statistic in ANOVA for determining the significance of the observed differences between groups.

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Answer:

D IS THE CORRECT ANSWERRR

Step-by-step explanation:

IN DIAGRAM D

G = Q

I = R

H = S

SO, THEY ARE SIMILAR

The foil was approximately 3.4 × 10⁷ atoms thick.

Rutherford's foil was made of gold and was used in his famous alpha particle scattering experiment. The thickness of the foil can be calculated by dividing its actual thickness by the diameter of a single gold atom.

Let's assume that the gold atoms in the foil are arranged in a simple cubic lattice. In this case, the actual thickness of the foil can be calculated as the number of gold atoms along one edge of the cube times the diameter of a single gold atom:

actual thickness = number of atoms × diameter of a single atom

To calculate the number of gold atoms, we need to know the density of gold and the mass of the foil. Let's assume that the density of gold is 19.3 g/cm³ and the mass of the foil is 0.6 mg = 6.0 × 10⁻⁷ kg.

The volume of the foil can be calculated as its mass divided by its density:

volume = mass / density = 6.0 × 10⁻⁷ kg / (19.3 × 10³ kg/m³) = 3.11 × 10⁻¹⁰ m³

The volume of the foil is also equal to the product of its actual thickness, the area of one face of the cube (which is the square of the number of atoms along one edge), and the volume of a single gold atom (which is (4/3)πr³, where r is the radius of the atom):

volume = actual thickness × (number of atoms)² × (4/3)πr³

Substituting the diameter of a single gold atom (2.9 × 10⁻¹⁰ m) for 2r, we get:

volume = actual thickness × (number of atoms)² × (4/3)π(1.45 × 10⁻¹⁰ m)³

Equating the two expressions for the volume of the foil, we get:

actual thickness × (number of atoms)² × (4/3)π(1.45 × 10⁻¹⁰ m)³ = 3.11 × 10⁻¹⁰ m³

Solving for the number of atoms, we get:

number of atoms = √(3.11 × 10⁻¹⁰ m³ / [(4/3)π(1.45 × 10⁻¹⁰ m)³]) ≈ 3.4 × 10⁷

So the foil was approximately 3.4 × 10⁷ atoms thick.

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Answer:

x = 73°

Step-by-step explanation:

I added a photo of my notes

An inscribed angle is equal to half the arc on which it rests

So, according to the photo I've added (knowing that a full circle forms 360 degrees) we can write an equation:

2x + 214° = 360°

2x = 360° - 214°

2x = 146° / : 2

x = 73°

I not sure if this is the right answer, though...

Given that the box contains 46 red marbles, 58 white marbles, and 51 blue marbles, you know that the total number of marbles the box contains is:

In this case, let be A the event in which the randomly selected marble from the box is white, and B the event in which the randomly selected marble from the box is blue.

Since those events are independent, you can set up that the probability of randomly selecting a white marble or blue marble from the box is:

Knowing that there are 58 white marbles, you can determine that:

And knowing that there are 51 blue marbles, you can determine that:

Therefore:

Hence, the answer is:

Answer:

D 100cm

Step-by-step explanation: