Cassie wants to buy a shirt for $15. 75 and some shoes for $10. 25. If the sales tax is 8. 25%, what is the TOTAL amount Cassie will pay?

5.490490490 can be expressed as the ratio of integers 5485/999. Hi! To express the given number as a ratio of integers, we need to find two integers that represent the given repeating decimal.

The number 5.490490490 can be written as 5.490(490 repeating). To convert the repeating part into a ratio, we can use the following method:

Let x = 0.490490...
Multiply x by 1000 (since there are 3 digits in the repeating part):
1000x = 490.490490...

Subtract the original x from the 1000x equation:
1000x - x = 490.490490... - 0.490490...
999x = 490
Now, divide both sides by 999:
x = 490/999

So, the repeating decimal 0.490490... can be represented as the ratio 490/999. To express the entire number as a ratio of integers, add the non-repeating part (5) to the ratio:

5 + (490/999) = (5 * 999 + 490) / 999 = (4995 + 490) / 999 = 5485/999.

Your answer: 5.490490490 can be expressed as the ratio of integers 5485/999.

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The general solution is then [tex]y(x) = y_c(x) + yp(x) = c1 e^√2x + c2 e^-√2x - 3/2 cot^3 x.[/tex]

To find the general solution for the nonhomogeneous equation [tex]y'' = 2y + 12 cot^3x[/tex] with particular solution

yp(x) = 6 cotx, we can use the method of undetermined coefficients.

First, we need to find the complementary function, which is the general solution to the homogeneous equation y'' = 2y. The characteristic equation is r² - 2 = 0, which has roots r = ±√2.

Therefore, the complementary function is[tex]y_c(x) = c1 e^√2x + c2 e^-√2x.[/tex]

Next, we need to find a particular solution yp(x) to the nonhomogeneous equation. Since the right-hand side is 12 cot^3 x, we can guess a solution of the form [tex]yp(x) = a cot^3 x.[/tex] Taking the first and second derivatives of this, we get

[tex]yp''(x) = -6 cotx - 18 cot^3 x and yp'''(x) = 54 cot^3 x + 54 cotx.[/tex]

Substituting these into the original equation, we get:

[tex](-6 cotx - 18 cot^3 x) = 2(a cot^3 x) + 12 cot^3 x-6 cotx = 2a cot^3 x[/tex]
a = -3/2

Therefore, the particular solution is[tex]yp(x) = -3/2 cot^3 x.[/tex]

The general solution is then [tex]y(x) = y_c(x) + yp(x) = c1 e^√2x + c2 e^-√2x - 3/2 cot^3 x.[/tex]

So the final answer is [tex]y(x) = y_c(x) + yp(x) = c1 e^√2x + c2 e^-√2x - 3/2 cot^3 x.[/tex]

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The value of the function at x = 7, f(7) on the graph is 2, therefore;

f(7) = 2

A function is a rule or defines that maps an input munto an output.

The evaluation of the function using the graph of the function can be performed by drawing a vertical line at the point of the corresponding input or x-value, and reading the point of intersection of the vertical line and the point on the graph, as follows;

f(7) = The value of the function at x = 7

The vertical line at x = 7, intersects the graph at the point f(7) = 2

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None of the given expressions (A, B, C, D, E) are equal to 45 x 67.

To find which expressions are equal to 45 x 67, we simply need to simplify each of the expressions given.

Therefore, none of the expressions are equal to 45 x 67.

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Given the sequence an = n^7/n^4, The sequence is = divergent. So, the answer is that the sequence is divergent.

The sequence an = n^7/n^4 can be simplified by cancelling out the common factor of n^4 in the numerator and denominator. This yields an = n^3.

Therefore, the sequence is simply the cubes of the positive integers, or 1, 8, 27, 64, 125, 216, ... and so on. This sequence grows without bound, as n gets larger, so it does not converge to any finite limit. In other words, the sequence an does not have a limit, and it is divergent.

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The interest rate necessary for an investment to quadruple after 6 years of continuous compound interest is approximately 23.105%.

To find the interest rate necessary for an investment to quadruple after 6 years of continuous compound interest, we will use the formula for continuous compounding:

A = P * e^(rt)

where:
A = final amount (quadruple the initial investment)
P = initial principal amount
r = interest rate (the value we need to find)
t = time (6 years in this case)
e = base of the natural logarithm (approximately 2.718)

Since the investment needs to quadruple, we have A = 4P. Now, we can substitute the values into the formula:

4P = P * e^(r * 6)

Divide both sides by P:

4 = e^(6r)

To solve for r, take the natural logarithm (ln) of both sides:

ln(4) = ln(e^(6r))

Using the property of logarithms, we can rewrite this as:

ln(4) = 6r

Now, divide by 6 to isolate r:

r = ln(4) / 6

Using a calculator, we find:

r ≈ 0.231049 (or 23.105% when expressed as a percentage)

So, the interest rate necessary for an investment to quadruple after 6 years of continuous compound interest is approximately 23.105%.

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The length of UT, to the nearest tenth, is approximately 10.5 inches.

How long is segment UT?

To find the length of UV, we can use the tangent-secant theorem, which states that the square of the length of the tangent segment (UV) is equal to the product of the lengths of the secant segments (RS and ST).

First, we need to find the length of RS + ST:

RS + ST = 8 in + 4 in = 12 in

Next, we can use the formula for the tangent-secant theorem:

[tex]UV^2 = RS * ST[/tex]

[tex]UV^2 = 8 in * 4 in[/tex]

[tex]UV^2 = 32 in^[/tex]

To find the length of UV, we take the square root of both sides:

[tex]UV = √32 in[/tex]

Calculating the square root, we get:

UV ≈ 5.7 in (rounded to the nearest tenth)

Therefore, the length of UV is approximately 5.7 inches.

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a. The correlation between temperature and yield is 0.63, between stirring rate and yield is 0.05, and between temperature and stirring rate is -0.01.

b. The data suggest that increasing temperature causes yield to increase, but confounding variables cannot be ruled out.

c. The data do not provide strong evidence that increasing stirring rate causes yield to increase, and confounding variables cannot be ruled out.

a. To compute the correlation between temperature and yield, stirring rate and yield, and temperature and stirring rate, we can use the Pearson correlation coefficient.

The correlation between temperature and yield is 0.61, indicating a moderate positive correlation. The correlation between stirring rate and yield is 0.02, indicating a weak positive correlation. The correlation between temperature and stirring rate is -0.43, indicating a moderate negative correlation.

b. The correlation between temperature and yield suggests that increasing the temperature may lead to an increase in yield. However, we cannot conclude that this relationship is causal as there may be other factors (e.g., stirring rate) that are confounding the relationship. To establish a causal relationship, we would need to conduct a controlled experiment where we manipulate temperature while keeping other factors constant.

c. The correlation between stirring rate and yield is weak, and it is difficult to draw strong conclusions from this relationship. It is possible that the relationship is due to confounding factors such as temperature or other unmeasured variables. Further experimentation is needed to establish a causal relationship between stirring rate and yield.

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The average depth of the Indian Ocean is 3.7 time greater than that of Arctic Ocean. Therefore, the correct option is A.

To find how many times as great the average depth of the Indian Ocean is compared to the Arctic Ocean, we need to divide the average depth of the Indian Ocean by the average depth of the Arctic Ocean.

1: Divide the average depth of the Indian Ocean by the average depth of the Arctic Ocean:

3900 meters (Indian Ocean) / 1050 meters (Arctic Ocean) = 3.7142857

2: Round the result to the nearest tenth:

3.7

So, the average depth of the Indian Ocean is approximately 3.7 times greater than the average depth of the Arctic Ocean. The correct answer is A. 3.7.

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Answer:

Step-by-step explanation:

33

The values of the sequence defined by the formula aₙ = crⁿ⁻¹ - d are c = 7, r = 2, and d = 7.

A sequence is defined as an arrangement of numbers in a particular order.

Given aₙ = crⁿ⁻¹ - d, then;

c - d = 0...(1)

cr - d = 7...(2)

cr² - d = 21...(3)

from equal (1), c = d so that equation (2) becomes;

cr - c = 7 and;

c = 7/(r - 1)...(4)

put 7/(r - 1) for c and d in equation (3);

7/(r - 1)(r²) - 7/(r - 1) = 21

7r² - 7 = 21(r - 1)

7r² - 21r + 14 = 0

r² - 3r + 2 = 0

by factorization;

r = 1 or r = 2

denominator in equation (4) will be zero if r = 1, so we put 2 for r in equation (4) to get c;

c = 7/(2- 1)

c = 7.

Therefore, values of the sequence defined by the formula aₙ = crⁿ⁻¹ - d are c = 7, r = 2, and d = 7.

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The volume of the soccer ball to the nearest cubic inch is 125 cubic inches.

To find the volume of Sydney's soccer ball, we will use the formula for the volume of a sphere, which is V = (4/3)πr³, where V is the volume, r is the radius, and π is a constant (approximately 3.14).

First, we need to find the radius (r) of the soccer ball. Since the diameter is given as 6.2 inches, we can find the radius by dividing the diameter by 2: r = 6.2 / 2 = 3.1 inches.

Now we can plug the values into the volume formula:
V = (4/3)π(3.1)³
V ≈ (4/3)(3.14)(29.791)

Next, we calculate the volume:
V ≈ 124.72

Finally, we round the volume to the nearest cubic inch, which is approximately 125 cubic inches.

So, the volume of Sydney's soccer ball with a diameter of 6.2 inches is approximately 125 cubic inches when using π = 3.14.

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Answer:

Step-by-step explanation:

The correct answer is:

the initial height of the plant

The y-intercept represents the point where the graph intersects the y-axis. In the context of a relationship between plant growth and time, the y-intercept would represent the initial height of the plant, which is the height of the plant at the start of the experiment, before any growth has occurred.

Answer:

3456 [tex]m^{2}[/tex]

Hope this helps!

Step-by-step explanation:

A square pyramid is comprised of a square and four triangles.

The square has an area of 1296 m ( 36m × 36m ) ( length × width ).

A triangle has an area of 540 m ( [tex]\frac{1}{2}[/tex] × 36m × 30m ) ( [tex]\frac{1}{2}[/tex] × width × ( slant ) height ).

The total surface area would be 1296 m + 4 × ( 540 m ) : ( Multiply 4 because there are 4 triangles ).

The total surface area is 3456 [tex]m^{2}[/tex].

Answer: 3,456 m^2

Step-by-step explanation:

The formula is SA = 2bs + b^2.

SA = 2 (36) (30) + 36^2

= 72 (30) + 1,296

= 2,160 + 1,296

= 3,456 m^2

Answer:

18.84 kilometers

Step-by-step explanation:

Formula for circumference:  C=2πr

1) find radius

r = d / 2

In this case the diameter is 6 so:

r = 6 / 2

r = 3

2. Plug in your values in the formula:

C = 2 (3.14) (3)

3. Solve (multiply)

C = 2 x 3.14 x 3

C = 18.84

So your answer is 18.84 kilometers, and rounded its 19 kilometers.

Hope this helps :D

As a result, the function's absolute maximum and minimum values are 5 and -45, respectively, at x = -5 and x = 2, respectively.

Every element in a set (referred to as the domain) in mathematics is connected by a rule known as a function to exactly one component in some other set (called the range or codomain). In other terms, a role is a connection among 2 sets where every element in the domain matches exactly one member in the range. Using a formula or equation with a variable input, function notation is a common way to represent functions. As an illustration, the formula f(x) = 2x + 1 gives each true figure x the value 2x + 1.

given

We can apply the second derivative test to determine whether this critical point is a maximum or minimum. By taking f'(xderivative, )'s we arrive at:

f''(x) = -4

The critical point at x = 0 is a local maximum since f"(0) = -4 is a negative value.

Secondly, we must determine whether the interval's endpoints of -5 x 2 provide values that are higher or lower than the crucial point. By entering x = -5 and x = 2, we obtain:

[tex]f(-5) = 5-2(-5) (-5)^2 = 5 – 50 = -45[/tex]

[tex]f(2) = 5 - 2(2) (2)^2 = -3[/tex]

As a result, the function's absolute maximum and minimum values are 5 and -45, respectively, at x = -5 and x = 2, respectively.

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The surface area of the rectangular prism with the given dimensions is 540yd².

To find the surface area (sa) of the rectangular prism with the given dimensions, we need to calculate the area of each face and add them together.

The formula for the area of a rectangle is length multiplied by width (A = l x w).

Face 1 has a length of 5yd and a width of 37yd, so its area is 5 x 37 = 185yd².
Face 2 has a length of 5yd and a width of 20yd, so its area is 5 x 20 = 100yd².
Face 3 has a length of 5yd and a width of 51yd, so its area is 5 x 51 = 255yd².

To find the total surface area, we add the areas of all three faces:

sa = area of face 1 + area of face 2 + area of face 3
sa = 185yd² + 100yd² + 255yd²
sa = 540yd²

Therefore, the numerical value of the surface area of the rectangular prism with the given dimensions is 540yd².

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-3.8 is the slope of the secant line connecting (1, f(1)) and (9, f(9)).

To get the slope of the secant line, we must first compute the values of f(1) and f(9):

f(1)

= 1² - 5(1)

= -4

f(9)

= 9² - 5(9)

= 36 - 45

= -9

The formula for the slope of the secant line running between these two locations is:

slope = (y-change)/(x-change)

= (f(9)-f(1))/(9-1)

Substituting f(1) and f(9) values and simplifying yields slope ,

= (-9-(-4))/(9-1)

= -5/8

= -0.625

When we round this to two decimal places, we get:

slope = -0.63

The slope of the secant line connecting (1, f(1)) and (9, f(9)) is thus -0.63.

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"IF THERE BASES ARE SAME POWER WILL BE ADD"

4^6+2=4^8 THAT IS AN ERROR

Both the chess and checkers group have the same range.

The box plots range for the ages of club members in the chess and checkers group are given. Based on the box plots, it appears that both groups have similar ranges, and it is difficult to determine which group has a greater range.

The range is a measure of variability that indicates the difference between the smallest and largest values in a dataset. In the chess group, the smallest value is 18, and the largest value is 20, which gives a range of 2. In the checkers group, the smallest value is 10, and the largest value is 20, which also gives a range of 10.

Although the difference between the smallest and largest values in the checkers group is greater than that in the chess group, the box plots suggest that the checkers group has more outliers than the chess group. An outlier is a data point that is significantly different from other observations in a dataset. The presence of outliers can increase the range of a dataset.

Therefore, despite the larger difference between the smallest and largest values in the checkers group, the presence of outliers makes it difficult to determine which group has a greater range. Overall, the box plots show that both groups have similar ranges, but the checkers group has more variability in the form of outliers.

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The amount of water that flows out of the tank during the first m minutes is given by the expression 200m - 2m², where m is the number of minutes.

The rate of water flowing from the bottom of the storage tank is given by r(t) = 200 - 4t, where t is the time in minutes. To find the amount of water that flows out of the tank during the first m minutes, we need to integrate the rate function from t = 0 to t = m:

Amount of water = ∫₀ₘ (200 - 4t) dt
Evaluating this integral, we get:
Amount of water = [200t - 2t²] from t = 0 to t = m
Amount of water = (200m - 2m²) - (0 - 0)

Simplifying this expression, we get:
Amount of water = 200m - 2m²

Therefore, the amount of water that flows out of the tank during the first m minutes is given by the expression 200m - 2m², where m is the number of minutes.

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The total cost to transport 12 tons of sugar is $8,600. The equation relating the total cost (c) to the amount of sugar transported (s) is: c = 175s + 6500

To find the total cost to transport 12 tons of sugar, we substitute s = 12 into the equation: c = 175(12) + 6500, c = 2100 + 6500, c = 8600

Therefore, the total cost to transport 12 tons of sugar is $8,600.

The equation shows that the total cost increases by $175 for each additional ton of sugar transported, and there is also a fixed cost of $6,500 for renting the trucks, which is added to the variable cost.

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The conclusion should be made using the Alpha = 0. 05 significance level is because the P-value is greater than Alpha = 0.05, there is not convincing evidence that greater than 75% of puppies are house-trained by the time they are 6 months old. The correct answer is B.

The given null hypothesis is that 75% of puppies are house-trained by the time they are 6 months old. The alternative hypothesis is that greater than 75% of puppies are house-trained by the time they are 6 months old.

The test statistic is a z-score, which is calculated by subtracting the hypothesized proportion (0.75) from the sample proportion (42/50 = 0.84), dividing by the standard error of the sample proportion, and then standardizing with respect to the standard normal distribution. The resulting z-score is 1.47.

The P-value is the probability of observing a test statistic as extreme or more extreme than the calculated z-score, assuming the null hypothesis is true. A P-value of 0.708 means that there is a 70.8% chance of observing a sample proportion as extreme or more extreme than 0.84, assuming that 75% of puppies are house-trained by the time they are 6 months old.

Since the P-value is greater than the significance level (alpha) of 0.05, we fail to reject the null hypothesis. In other words, there is not convincing evidence to suggest that greater than 75% of puppies are house-trained by the time they are 6 months old.

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Answer:

x = 13

Step-by-step explanation:

We Know

(5x - 6) + (8x + 17) must equal 180°

Find the value of x.

Let's solve

5x - 6 + 8x + 17 = 180

13x + 11 = 180

13x = 169

x = 13

So, the value of x is 13.

It sounds like Leo will be using a specific type of random number generator that produces only five possible outcomes: 1, 2, 3, 4, or 555. It seems that the generator produces a repeating pattern of four numbers (1, 2, 3, 4) followed by a fifth number (555).

If Leo uses this generator 400400400 times, then he will get 100100100 repetitions of the pattern. This means that he will get 100100100 x 4 = 400400400 numbers 1, 2, 3, or 4, and 100100100 occurrences of the number 555.

It is important to note that this type of random number generator is not truly random, as it is not generating numbers with equal probability. Instead, it is producing a predetermined sequence of numbers. This means that if Leo knows the pattern, he could predict the next number that will be generated with certainty.

In general, it is important to use truly random number generators for many applications, such as cryptography or scientific simulations, where the results need to be unpredictable and unbiased.

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Alissa's new fish tank should hold 35 gallons of water.

"Gallons" is a unit of measurement for volume, typically used to measure liquids or gases. It is commonly abbreviated as "gal" and is equivalent to 3.785 liters in the metric system.

Alissa's old fish tank holds 20 gallons of water. To find out how many gallons of water her new fish tank should hold, we need to multiply the old tank's capacity by 175% or 1.75 (since 175% = 1.75 as a decimal).

So, the new tank's capacity should be:

20 gallons x 1.75 = 35 gallons

Therefore, Alissa's new fish tank should hold 35 gallons of water.

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Caroline bought approximately 3.70 pounds of chicken breast.

Let's use algebra to solve the problem:

Let x be the number of pounds of chicken breast Caroline bought.

We know that 2.5 pounds of chicken breast cost $23.50, so we can set up the following proportion:

2.5 / $23.50 = x / $34.78

To solve for x, we can cross-multiply and simplify:

2.5 * $34.78 = x * $23.50

$86.95 = $23.50x

x = $86.95 / $23.50

x ≈ 3.70 pounds

Therefore, Caroline bought approximately 3.70 pounds of chicken breast.

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The solution to the differential equation is f(a) = 1/√(12a⁴/125 - 769/5000).

To find f(a), we need to solve the differential equation:

dy/dx = 24yx³

Separating variables, we get:

dy/y³ = 24x³ dx

Integrating both sides, we get:

-1/(2y²) = 6x⁴ + C

where C is the constant of integration.

To find the value of C, we use the fact that the y-intercept of the curve y = f(2) is 5. This means that when x = 2, y = 5. Substituting these values into the equation above, we get:

-1/(2(5)²) = 6(2)⁴ + C

Simplifying and solving for C, we get:

C = -1/(2(5)²) - 6(2)⁴

C = -769/125

So the solution to the differential equation is:

-1/(2y²) = 6x⁴ - 769/125

Solving for y, we get:

y = 1/√(12x⁴/125 - 769/5000)

Therefore, f(a) = 1/√(12a⁴/125 - 769/5000).

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8:10

subtract 20min from 30 min

30-20=10

Answer: He should move at 8:10

Explanation:  10 + 20 = 30  /  30 - 20 = 10

Therefore he should leave at 8:10