this data shows the amount of rainfall in mm that fell on an island during a 12-day period in June
a. work out the range of the rainfall and comment on this value as a measure of the spread of the data

The evaluation of the equation by expressing the terms as improper fractions indicates that the value of y is 14 2/3

A fraction is an expression of a part of a whole, using two numbers, one located in the numerator, and the other in the denominator in the expression of the fraction separated by a line, known as the fraction bar.

The equation can be expressed as follows;

4 2/9 + (16 5/9 - y) = 15 1/9 - 8 7/9

The above equation comprising of fractions can be expressed using improper fractions as follows;

4 2/9 + (16 5/9 - y) = 15 1/9 - 8 7/9

38/9 + (149/9 - y) = 136/9 - 79/9 = 57/9

38/9 + 149/9 - 57/9 = y

130/9 = y

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The delineation of A as a subset of B, and also the differentiation in assertion that A is not equivalent to B, can be attributed to A containing merely three elements (a, b, along with c) as opposed to B's countenance of five elements (including a, b, c, d, subsequently e).

As all components of A coincidentally exist within B, one may ascertrain that A is indeed a subset of B.

However, due to B enclosing two additional elements (d, then e) which are not replete within A, we can conclusively deny that A is comparable to B.

Symbolically:

A ⊆ B (A constitutes a subset of B)

A ≠ B (A isn't analogous to B)

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The total number of subsets is 128 and the total number of proper subsets is 127 and this can be determined by using the given data.

Given :

The set of days of the week.

The following steps can be used in order to determine the number of subsets and the number of proper subsets:

Step 1 - According to the given data, the set is given below:

S = {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}

Step 2 - Now, the total number of subsets is given by the formula  where 'n' is the number of elements of the set.

The total number of subsets is 128.

Step 3 - Now, the total number of proper subsets is given by the formula  where 'n' is the number of elements of the set.

The total number of proper subsets is 127.

a) The total number of subsets is 128.

b) The total number of proper subsets is 127.

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complete question:

Find (a) the number of subsets and (b) the number of proper subsets of the set.

The set of days of the week.

(a) The number of subsets is

(b) The number of proper subsets is

Answer:
79.95 yards.

Step-by-step explanation:

Each board is 16 feet long and there are 3 feet in 1 yard. So, each board is 16/3 = 5.33 yards long (rounded to two decimal places).

If Steven has 15 yards of these boards, the combined length of the boards in yards is 15 times the length of each board, which is 15 x 5.33 = 79.95 yards (rounded to two decimal places).

Therefore, the combined length of the boards in yards is approximately 79.95 yards.

The account will have $7240 after the last deposit.

Given that, $2960 is being deposited at the beginning of every six months for 13 years. The fund earns 7% annual interest, compounded biannually,

So,

When the amount is compounded biannually,

[tex]A = P(1+r/2)^{2t[/tex]

A = final amount, P = initial amount, r = rate and t = time,

[tex]A = 2960(1+0.07/2)^{2(13)[/tex]

[tex]A = 2960(1.035)^{26[/tex]

[tex]A = 7240[/tex]

Hence, the account will have $7240 after the last deposit.

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Answer:

Arc length = (147/360) x (2π x 7)

Arc length = (0.40833) x (2 x 3.14159 x 7)

Arc length = 0.40833 x 43.9823

Arc length = 17.9955

If at the soccer game, Sue bought a pack of gum for 25¢ and a candy bar for $1.00, the average cost of the items Sue and her brother bought is 67 cents.

To find the average cost of the items, we need to add up the total cost and divide by the number of items. In this case, there are three items: gum, candy bar, and hot dog.

The total cost is 25¢ + $1.00 + 75¢ = $2.00

The number of items is 3.

So, the average cost is $2.00 / 3 = $0.67 (rounded to the nearest penny).

This means that on average, each item costs 67 cents.

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The scale factor of the dilation is k = 5/4

Given data ,

A figure with an area of 25 square units is dilated from a figure with an area of 16 square units

Let the dilation scale factor be k

Now , Given that the original area (A) is 16 square units and the target area (B) is 25 square units, we can write the equation as:

B = k² A

k² = 25/16

Taking square roots on both sides , we get

k = 5/4

Hence , the dilation factor is 5/4

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Answer:

In the explanation

Hope this helps!

Step-by-step explanation:

1. 20: 1.3010

2. 25: 1.3979

3. 300: 2.4771

4. 500: 2.690 ( 2.6989700 )

5. 8000: 3.9031

6. 0.7: -0.1549

7. 0.04: -1.3979

( The blank for the question on the bottom is pq, refer to the product property in logarithms :) )

Answer:

Step-by-step explanation:

I explain 1 through 10 that should give you an idea of how this goes.

See image for explan

Sally can solve minimum of 35 calculus problem and maximum of 50 calculus problem.

We know,

Calculus is a branch of mathematics that focuses on rates of change, to put it simply. For instance, you might want to determine how quickly a car will slow down as it approaches a stop sign. Calculus can assist you in calculating that change. Calculus introduces movement into math, that's correct!

Calculus is useful in many different fields, including engineering, medicine, biological research, economics, architecture, space science, electronics, statistics, and pharmacology.

minimum = 35

maximum=50

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complete question:

Sally completely solves at least 7 calculus problems per hour and at most 10 calculus problems per hour. Based on this information, what is a possible number of calculus problems that Sally can completely solve in five hours?

The predicted distance the puck will travel at a speed of 50 miles per hour is 3054.12 yards

Given data ,

The equation for the line of fit is given as y = 3.12 + 61.02s, where y represents the predicted distance (in yards) the puck will travel and s represents the speed of the puck (in miles per hour).

So , y = 3.12 + 61.02s

Now , when the speed of the hockey player is s = 50 miles per hour

On simplifying , we get

y = 3.12 + 61.02 ( 50 )

y = 3.12 + 3051

y = 3,054.12 yards

Hence , the distance traveled by the puck is 3,054.12 yards

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The fish tank requires 7900 square cm of glass.

First, choose three fish for our tank. Let's choose a neon tetra, a guppy, and a corydoras catfish.

According to the guideline given, each fish requires 4,000 cubic centimeters of water for every inch of a fish's length. Determine the total length of the three fish to calculate the required water volume.

Assuming the neon tetra is 1 inch long, the guppy is 2 inches long, and the corydoras catfish is 3 inches long, the total length of the fish is 1+2+3=6 inches.

To accommodate these three fish, we need 6 inches x 4,000 cubic centimeters of water per inch = 24,000 cubic centimeters of water.

To design the fish tank. Make it a rectangular prism shape with the dimensions of 50 cm x 30 cm x 40 cm (length x width x height).

To calculate the amount of glass necessary to build the tank, to find the surface area of the glass required. There are five sides to the tank (four sides and the base), find the area of each and add them up.

The front and back sides each have an area of 50 cm x 40 cm = 2000 square cm.

The two side walls each have an area of 30 cm x 40 cm = 1200 square cm.

The base has an area of 50 cm x 30 cm = 1500 square cm.

So, the total surface area of glass required is:

2(2000 square cm) + 2(1200 square cm) + 1500 square cm = 7900 square cm.

Therefore, 7900 square cm of glass is needed to build our fish tank.

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The requried larger number x is 80 and the smaller number y is 27.

Let's use the given variables:

x be the larger number

y be the smaller number

According to question

The sum of two numbers is 107 is represented by x + y = 107

The difference between the two numbers is 53 is represented by x - y = 53.

Solving the system of equations:

(x + y) + (z - y) = 107 + 53

2x = 160

x = 80

Now, z = 80, substitute this value into one of the original equations to solve for y.

x + y = 107

80 + y = 107

y = 27

Therefore, the requried larger number x is 80 and the smaller number y is 27.

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Answer:

830.53 in²

Step-by-step explanation:

Find the area of the full circle and divide it by 2:Use the circle area formula, A = r²Plug in 3.14 as pi, and plug in the radius:A = r²A = 3.14(23²)A = 1661.06Divide this by 2:1661.06 / 2= 830.53So, the area of one semicircle is 830.53 in²

Answer: The area of one semicircle is approximately 830.53 square inches.

Step-by-step explanation:

The area of a circle is given by the formula:

A = πr²

where A is the area of the circle and r is its radius.

The radius of the circle cut out of the piece of wood is about 23 inches. Therefore, its area is:

A = πr²

A = π(23)²

A = π(529)

A ≈ 1661.06 square inches

The carpenter cuts the circle into two semicircles. Therefore, the area of one semicircle is:

A/2 ≈ 830.53 square inches

Therefore, the area of one semicircle is approximately 830.53 square inches.

I hope this helps! Let me know if you have any other questions.

Answer: $6,320.25

Step-by-step explanation:

Mrs. Cowley's broker fee is calculated by multiplying the purchase price by the broker fee percentage: $32,000 x 0.0075 = $240. Her total cost for the purchase is then $32,000 + $240 = $32,240. When she sells the stock for $25,100, she incurs another fee of $17 for using the discount broker. To calculate her net loss, we subtract her total cost from her selling price and subtract the two broker fees: $25,100 - $32,240 - $17 - $17 = -$6,320.25, which is rounded to $6,320.25 as a net loss.

The coordinates of B'(6, 3) and C'(4, 4).

We have,

The point A (6, 8) is translated to A' (2, 5).

So, here the points are translated as

(x₁ - x₂ , y₁ - y₂)

= (6 -2, 8-5)

= (4, 3)

So, the coordinates of B'

= (8 -2, 8-5)

= (6, 3)

and, the coordinate of C'

= (6-2, 9-5)

= (4, 4)

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A Euler Circuit in the graph is ADGFACFIECBEHDBA.

When we describe an Euler circuit, we are describing a path in a diagram known as a graph that starts and ends at the same vertex.

While you can visit a vertex a number of time, you can only visits every edge of the graph once. This means that you cannot walk the path to a vertex more than once.

For the graph in the picture, ADGFACFIECBEHDBA is the Euler circuit. You can see that vertex like A was repeated three time, E, C and F, were repeated twice.

Can this graph be called Eulerian? No, because it does not fulfill the condition.

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The equations that are true for x = -2 and x = 2 are x² + 4 = 0 and 4x² = 16. So, the correct option is A) and D).

To determine which equations are true for x = -2 and x = 2, we simply substitute these values into each equation and check if the equation is true or not. Here are the results

x² - 4 = 0

Substituting x = -2 gives (-2)² - 4 = 0, which is true. Substituting x = 2 gives 2² - 4 = 0, which is also true. Therefore, this equation is true for both x = -2 and x = 2.

x² = -4

Substituting x = -2 gives (-2)² = -4, which is not true. Substituting x = 2 gives 2² = -4, which is also not true. Therefore, this equation is not true for either x = -2 or x = 2.

3x² + 12 = 0

Substituting x = -2 gives 3(-2)² + 12 = 0, which is true. Substituting x = 2 gives 3(2)² + 12 = 24, which is not equal to zero. Therefore, this equation is true for x = -2 but not for x = 2.

4x² = 16

Substituting x = -2 gives 4(-2)² = 16, which is true. Substituting x = 2 gives 4(2)² = 16, which is also true. Therefore, this equation is true for both x = -2 and x = 2.

2(x - 2)² = 0

Substituting x = -2 gives 2(-2 - 2)² = 0, which is true. Substituting x = 2 gives 2(2 - 2)² = 0, which is also true. Therefore, this equation is true for both x = -2 and x = 2.

Therefore, the two equations that are true for both x = -2 and x = 2 are x² - 4 = 0 and 4x² = 16. So, the correct answer is A) and D).

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[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-8})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{5}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-8)}=\stackrel{m}{- \cfrac{5}{4}}(x-\stackrel{x_1}{(-4)}) \implies y +8 = - \cfrac{5}{4} ( x +4)[/tex]

The company should invest in 69.06 units of labor and 67.47 units of capital to maximize production output given the budget constraint.

We have,

We want to maximize the production output

P = L^0.8 K^0.2

subject to the constraint 10L + 20K = 2700.

We can solve for K in terms of L from the constraint equation:

10L + 20K = 2700

20K = 2700 - 10L

K = (2700 - 10L) / 20

K = 135 - 0.5L

Substitute this expression for K into the production function:

P = L^0.8 K^0.2

P = L^0.8 (135 - 0.5L)^0.2

We want to maximize P with respect to L.

Taking the derivative of P with respect to L:

dP/dL = 0.8L^-0.2 (135 - 0.5L)^0.2 + 0.2L^0.8 (135 - 0.5L)^-0.8 (-0.5)

dP/dL = 0.16(135 - 0.5L)^0.2 L^-0.2 - 0.1(135 - 0.5L)^-0.8 L^0.8

Setting dP/dL equal to zero and solving for L:

[tex]0.16 (135 - 0.5L)^{0.2} L^{-0.2} - 0.1 (135 - 0.5L)^{-0.8} L^{0.8} = 0[/tex]

0.16(135 - 0.5L)^0.2 = 0.1(135 - 0.5L)^-0.8 L^1

1.6(135 - 0.5L) = (135 - 0.5L)^-0.8 L

1.6 = (135 - 0.5L)^-1.8 L^-1

1.6L = (135 - 0.5L)^1.8

1.6L = (135^1.8 - 0.5L)^1.8

1.6L = 2.24474e+15 - 4.52222e+14 L + 1.22313e+13 L^1.8

1.22313e+13 L^1.8 - 4.52222e+14 L + 2.24474e+15 - 1.6L = 0

This equation can be solved numerically using a solver or a graphing calculator.

The solution is L = 69.06 units of labor.

To find the corresponding value of K, we can use the constraint equation:

10L + 20K = 2700

20K = 2700 - 10L

K = (2700 - 10(69.06)) / 20

K = 67.47 units of capital

Therefore,

The company should invest in 69.06 units of labor and 67.47 units of capital to maximize production output given the budget constraint.

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The mass of the trunk of the sequoia tree is 141443.1 kg.

The volume of a cylinder, using the formula:

V = πr²h

π is pi (approximately 3.14)

r is the radius of the trunk (which is half the diameter)

h is the height of the trunk

1 meter = 3.28084 feet

we can convert the given measurements from feet to meters to ensure consistent units.

The base diameter of the tree is 12.2 meters / 3.28084 = 3.719 meters,

so the radius is 3.719 / 2 = 1.8595 meters.

The height of the tree is 95 meters / 3.28084 = 28.9568 meters.

Therefore, the volume of the trunk is:

V = π(1.8595)²(28.9568) = 314.318 cubic meters

Now calculate the mass of the trunk by multiplying the volume by the density of the wood:

M = V × ρ

=  314.318  × 450

= 141443.1 kg

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Answer:

the missing value is y = 48.

Step-by-step explanation:

In a direct variation, the ratio of the two variables remains constant. We can use this fact to find the missing value y:

y / 18 = 8 / 3

To solve for y, we can cross-multiply:

y = 18 * 8 / 3

y = 48

Therefore, the missing value is y = 48.

a) The confidence level of 99% means that we are 99% sure that the interval contains the true population proportion.

b) The 99% confidence interval for the population proportion is given as follows: (0.3145, 0.4055). It means that we are 99% sure that the true population proportion is between 0.3145 and 0.4055.

c) The 95% confidence interval would be narrower, as it would have a lower critical value, thus the margin of error would also be lower.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.

The parameters for this problem are given as follows:

[tex]\pi = 0.36, n = 739[/tex]

The lower bound of the interval is given as follows:

0.36 - 2.575 x sqrt(0.36 x 0.64/739) = 0.3145.

The upper bound of the interval is given as follows:

0.36 + 2.575 x sqrt(0.36 x 0.64/739) = 0.4055.

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Answer:

We don't know the initial value of the principal but we do know that the accumulated value is double (twice) the principal. It takes 9.9 years for money to double if invested at 7% continuous investment

Answer:

(x-1, y) = (x-1, 1/2x + 1/2).

Step-by-step explanation:

To find the point one unit to the left of the given point, we need to subtract 1 from the x-coordinate of the given point.

Let's start with the given point: y = [1/2x - 2] + 3

We can simplify this by combining the constants: y = 1/2x + 1

Now we need to find the point one unit to the left. This means we subtract 1 from the x-coordinate:

y = 1/2(x-1) + 1

Simplifying this expression:

y = 1/2x - 1/2 + 1

y = 1/2x + 1/2

So the point one unit to the left of the original point is (x-1, y) = (x-1, 1/2x + 1/2)

Part(a),

The exponential function that models the total spent on food and drinks as a function of the number of years since 1990 is:

[tex]T(x) = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13}))^x[/tex]

Part(b),

The predicted amount spent in 2000 is 964 billion dollars (rounded to the nearest integer).

Part(c),

The predicted total sales of food and drink in 2018 is 1756 billion dollars

Part(d),

If the exponential trend continues, the total sales will reach 2 trillion dollars approximately 32.72 years after 1990, which is around the year 2022.

(a) To model the total spent on food and drinks as an exponential function of the number of years since 1990, we can use the general form of an exponential function:

[tex]T = a \times b^t[/tex]

where T is the total spent in billions of dollars, t is the number of years since 1990, a is the initial amount spent in 1990, and b is the growth factor or base of the exponential function.

Using the given information, we can set up two equations:

T(0) = 641 (total spent in 1990)

T(13) = 1016 (total spent in 2003, which is 13 years after 1990)

Substituting these values into the exponential function, we get:

[tex]641 = a \timrd b^0[/tex] => a = 641

[tex]1016 = a b^{13[/tex] => [tex]b = (\dfrac{1016}{641})^{\frac{1}{13}[/tex]

Therefore, the exponential function that models the total spent on food and drinks as a function of the number of years since 1990 is:

[tex]T(x) = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13})^x[/tex]

(b) To predict the amount spent in 2000, we need to substitute t = 10 (since 2000 is 10 years after 1990) into the exponential function:

[tex]T(10) = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13}))^{10[/tex] ≈ 964

Therefore, the predicted amount spent in 2000 is 964 billion dollars (rounded to the nearest integer).

(c) To predict the total sales of food and drink in 2018, we need to substitute t = 28 (since 2018 is 28 years after 1990) into the exponential function:

[tex]T(28) = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13}))^{28[/tex] ≈ 1756

Therefore, the predicted total sales of food and drink in 2018 is 1756 billion dollars (rounded to the nearest integer).

(d) To estimate when the total sales will reach 2 trillion dollars, we need to solve for t in the exponential function when T(t) = 2000 (since 2 trillion dollars is equivalent to 2000 billion dollars):

[tex]2000 = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13}))^t[/tex]

[tex]ln(\dfrac{2000}{641}) = t \times ln((\dfrac{1016}{641})^{(\frac{1}{13})[/tex]

[tex]t = \dfrac{ln(\dfrac{2000}{641})} { ln((\dfrac{1016}{641})^{(\frac{1}{13})) }}[/tex]

t = 32.72

Therefore, if the exponential trend continues, the total sales will reach 2 trillion dollars approximately 32.72 years after 1990, which is around the year 2022.

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Answer: (Maybe) B

Step-by-step explanation:

The answer for this problem would be 42. However, if you take 630 and divide it by 15 (630/15) you'll get 42 as well. I'm not sure if you accidentally typed the hyphen in there (choice B) or if it's supposed to represent a negative sign. But, I believe B would be correct.

Step-by-step explanation:

Given the circ , you can find the diameter....then the radius

circ = pi * d

17.584 = pi * d

d = 5.597 in     then radius =   1/2 d = 2.798

AREA = pi r^2 =  pi * 2.798^2 = 24.6 in^2