Connor's allowance is $2.00 per week. His parents start his piggy bank with $40.00. So, at the beginning of the first week, he has $40.00 in the bank, at the beginning of the second week, he has $42.00 in the bank, and so on. Connor does not spend any of the money. At the beginning of which week will he have $160.00 in his bank?


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According to the given information, the measure of the larger acute angle in the 3-4-5 right triangle is approximately 36.87 degrees.

What is 3-4-5 right angle triangle?

A 3-4-5 right triangle is a right triangle where the lengths of the three sides are in the ratio of 3:4:5. In other words, the length of the longest side (the hypotenuse) is 5 times the length of the shortest side, and the length of the remaining side is 4 times the length of the shortest side. This special right triangle has angles of 30 degrees, 60 degrees, and 90 degrees, which are the angles of a 30-60-90 triangle. The sides of a 3-4-5 right triangle can be scaled up or down by any common factor (e.g. 6-8-10, 9-12-15, etc.) and will still form a right triangle with the same angles.

In a 3-4-5 right triangle, the larger acute angle is opposite to the longer leg, which has a length of 4. To find the measure of this angle, we can use the inverse tangent function:

tan(theta) = opposite / adjacent = 3/4

\(theta = tan^{-1} (3/4)\)

Using a calculator, we can find that:

theta ≈ 36.87 degrees

Therefore, the measure of the larger acute angle in the 3-4-5 right triangle is approximately 36.87 degrees.

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Step-by-step explanation:

-26a-19-35=-84

-26a-19+(19)-35=-84+(19)

-26a-35=-65

-26a-35+(35)=-65+(35)

-26a=-30

-26a/26=-30/26

The expression [3.8×10^6]^(-1/2) can be expressed in scientific notation as 1.9×10^(-5).

To simplify the expression, we can apply the rule of exponentiation which states that \((a^m)^n = a^(^m^*^n^)\). In this case, we have \((3.8\times10^6)^(^-^1^/^2^)\), which is equivalent to  \((3.8\times10^6)^(^-^1^/^2^)\)

Evaluating each part separately, \(3.8^(^-^1^/^2^)\)is approximately 0.5176. And \((10^6)^(^-^1^/^2^)\) is equal to \((10^6)^(^-^1^/^2^)\)= \(10^-^3\), which is 0.001 in decimal notation.

Multiplying these two results, we get 0.5176 × 0.001 = 0.0005176.

Since this result is less than 1, we can express it in scientific notation by moving the decimal point three places to the right, resulting in 5.176 × \(10^-^4\). However, we need to adjust the exponent to maintain the same value. Since we moved the decimal point three places to the right, we decrease the exponent by three, giving us 1.9 × \(10^-^5\\\).

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Answer: each store gets 787 pairs and 1 is left over

Step-by-step explanation:Divide 4723 by 6

The number of lollipops in a container is 206.

These are steps to find the number of lollipops in a container:

1. Let x be the number of lollipops in a packet and 2x be the number of lollipops in a container.

2. According to the given information, we have the equation: 2(2x) + 3x = 721

3. Simplify the equation: 4x + 3x = 721 7x = 721

4. Solve for x: x = 103

5. Substitute x back into the equation to find the number of lollipops in a container: 2x = 2(103) = 206 Therefore, the number of lollipops in a container is 206.

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When measuring wind speed with a cup anemometer on a sailboat trip across the Atlantic Ocean, there are a few situations that may arise, as shown below:1. When the bearing of the axle is old, the type of error that occurs is systematic error. To reduce or overcome this error, you would need to replace the bearing to avoid it.

2. When there is turbulent flow, the type of error that occurs is random error. To overcome this error, you would have to wait for the wind to stabilize or take an average of many measurements.  3. When there is icing on the cups, the type of error that occurs is also random error.

To overcome this error, you would need to remove the ice or wait for it to melt before continuing the measurement.4. When there is strong tumbling of the sailboat, the type of error that occurs is systematic error. To overcome this error, you would need to find a way to stabilize the boat or take measurements when the boat is less unstable.

It is not well posed to use a cup anemometer to measure in-cabin air flow in a quiet environment because the device is not sensitive enough. The device needs a minimum wind speed to provide accurate readings, and it is not designed to measure low wind speeds. Therefore, it may not be the right tool for the job, and a different instrument may be more appropriate.

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Answer:

Box 2

Step-by-step explanation:

length x width x height = volume

Answer:

box  2

Step-by-step explanation:

The linear function is 8.50x + 5.50 and a $5.50 delivery fee would be included in the price of each hoodie purchased.

Part 1

The linear function rule is used in cases with only one shipping charge.

= 8.50x + 5.50, where x is the number of sweatshirts and y is the total cost in dollars.

Part 2

The linear function rule would be y = 8.50x + 5.50x = 14x, where y is the total cost in dollars and x is the number of sweatshirts if the shipping fee is applied to each sweatshirt. This implies that the $5.50 delivery fee would be included in the price of each hoodie purchased.

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Answer:

56° + 40° + x = 180°

96° + x = 180°

x = 84°

Answer:

563.76

here ya go

Answer:

563.76

Step-by-step explanation:

(8.59 x 104) - (3.2 x 103)

893.36 - 329.6

=563.76

Answer:

1923 kg 170 g

Step-by-step explanation:

800 kg 450 g + 50 kg 850 g

= 851 kg 300 g

=> 851 kg 300 g + 1071 kg 870 g

=1923 kg 170 g

Therefore, it is proved that the lengths of opposite and adjacent sides are equal when angle of right triangle is 45 degrees. Property The length of hypotenuse equals to square root of two times of length of either opposite or adjacent side when angle of right triangle is 45 degrees. The length of both opposite and adjacent sides is 4.25 c m.

Answer:

Area of small little rectangle above:

3 x 5 = 15

Let's find the area of the trapezoid now:

5 + 13 = 18

18 x 7( i got 7 from: 10 - 3 = 7) = 126

126 x 1/2 (basically just dividing by 2) = 63

Now let's add all the given areas:

15 + 63 = 78 inches^2 is your answer

To perform scalar multiplication on matrix A and matrix B,  the result of 4A-3B is [[-24, -4, -63]].

The Matrix trilogy makes the argument that each person must decide for himself whether to live in the real world or a simulation.

To calculate 4A-3B, we need to perform scalar multiplication on matrix A and matrix B, and then subtract the corresponding elements. Let's calculate it:

A = [[-6, 2, -9]]

B = [[0, 4, 9]]

Scalar multiplication:

4A = [[4*(-6), 42, 4(-9)]] = [[-24, 8, -36]]

3B = [[30, 34, 3*9]] = [[0, 12, 27]]

Subtract the corresponding elements:

4A - 3B = [[-24-0, 8-12, -36-27]] = [[-24, -4, -63]]

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Answer:

X=-33

Step-by-step explanation:

Answer:

x= -33

Step-by-step explanation:

Subtract 9 from both sides:

2/3x+9-9=-13-9

Simplify the arithmetic:

2/3 · x =-13-9

Simplify the arithmetic:

2/3 · x = -22

Multiply both sides by inverse fraction 3/2:

2/3x ·3/2= -22 ·3/2

Group like terms:

 2/3 ·3/2x= -22 ·3/2

Simplify the fraction:

x=-22 · 2/3

Multiply the fractions:

x= -22·2/3 ÷2

Simplify the arithmetic:

x = -33

The ordered pairs (0, 2), (3, 0), and (-3, 4) are solutions to the linear equation 2x + 3y = 6.

To determine the ordered pairs (x, y) that are solutions to the linear equation 2x + 3y = 6, we can plug in different values for x or y and solve for the other variable. Here are some possible solutions:

(0, 2): If we substitute x = 0 and y = 2 into the equation, we get 2(0) + 3(2) = 6, which is true.

(3, 0): If we substitute x = 3 and y = 0 into the equation, we get 2(3) + 3(0) = 6, which is also true.

(-3, 4): If we substitute x = -3 and y = 4 into the equation, we get 2(-3) + 3(4) = 6, which is again true.

These ordered pairs (0, 2), (3, 0), and (-3, 4) are solutions to the linear equation 2x + 3y = 6.

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Answer:

\(60\pi\)

Step-by-step explanation:

Use this arc length formula,

\(s = r \times x\)

where s is the arc length, r is the radius and x is the radians.

\(30 \times 2\pi = 60\pi\)

Answer:

Step-by-step explanation:

-3x - 8y - 2

Answer:Answer:

D'F' = 28

Step-by-step explanation:

For the vertex D(1, 1)

D'(1 × 7, 1 × 7) = D'(7, 7)

For the vertex E(1, 5)

E'(1 × 7, 5 × 7) = E'(7, 35)

For the vertex F(5, 1)

F'(5 × 7, 1 × 7) = C'(35, 7)

Now to find the D'F':

we do:

y2 - y1 =

and

x2 - x1 =

Here are what the numbers mean

x1 = 7

y1 = 7

x2 = 35

y2 = 7

For the points above (7,7) and (35,7), in which (7,7) is Point 1 and (35,7) is Point 2:

Find the distance along the y-axis.

y2 - y1 = 7 - 7

7 - 7 = 0

Find the distance along the x-axis.

x2 - x1 = 35 - 7

35 - 7 = 28

Now we do: y² and x²

y² = 0² = 0

x² = 28² = 784

Next we add the y and x

0 + 784 = 784

And lastly, we do √x + y

Which is the same as: √0 + 784

√0 + 784 = 28

So the answer is 28

Step-by-step explanation:

The Solution:

Given:

We are asked to find the output when the input is 3.2

That is, find y when x = 3.2

Therefore, the correct answer is 5.4 [option 4]

hi

Step-by-step explanation:

a

Answer:

Because she found it improves division.

Step-by-step explanation:

To find all points on the curve x²y² + xy = 2, we can rewrite the equation in the form of a parametric representation.

Let x = t, and then solve for y in terms of t:
x²y² + xy = 2
t²y² + ty = 2
Now, we can solve for y in terms of t:
y(t^2y + t) = 2
y = 2 / (t^2y + t)
Unfortunately, the equation above cannot be simplified further to provide an explicit equation for y in terms of t. However, we can use this parametric representation to find all points on the curve by varying the value of t. To find specific points on the curve, plug in different values of t into the equation above and solve for the corresponding values of y. The points (x, y) will lie on the curve x²y² + xy = 2.

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Part A: the probability that a cow produces between 2.0 and 2.5 gallons is approximately 0.6826.

Part B: To calculate the probability that the total volume for one milking session for 20 cows exceeds 50 gallons, we need additional information about the correlation or independence of the milk volumes of the 20 cows.

Part A: To calculate the probability that a randomly selected cow produces between 2.0 and 2.5 gallons in a single milking session, we can use the normal distribution. We calculate the z-scores for the lower and upper bounds and then find the area under the curve between these z-scores. Using the mean of 2.3 gallons and standard deviation of 0.96 gallons, we can calculate the z-scores as (2.0 - 2.3) / 0.96 = -0.3125 and (2.5 - 2.3) / 0.96 = 0.2083, respectively. By looking up these z-scores in the standard normal distribution table or using a calculator, we can find the corresponding probabilities.

Part B: To calculate the probability that the total volume for one milking session for 20 cows exceeds 50 gallons, we need to consider the distribution of the sum of 20 independent normally distributed random variables. We can use the properties of the normal distribution to find the mean and standard deviation of the sum of these variables and then calculate the probability using the normal distribution.

Part C: Yes, we needed to know that the population distribution of milk volumes per milking session was normal in order to complete Parts A and B. The calculations in both parts rely on the assumption of a normal distribution to determine the probabilities. If the distribution were not normal, different methods or assumptions would be required to calculate the probabilities accurately.

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To find the derivatives of the given expressions, we can apply the chain rule, which states that the derivative of a composition of functions is equal to the derivative of the outer function multiplied by the derivative of the inner function.

(a) To find the derivative of f(g(x)), we start by differentiating the outer function f with respect to the inner function g(x), and then multiply it by the derivative of the inner function g(x) with respect to x.

df/dx = df/dg * dg/dx

df/dx = cos(g(x)) * (2x)

(b) To find the derivative of g(f(x)), we differentiate the outer function g with respect to the inner function f(x), and then multiply it by the derivative of the inner function f(x) with respect to x.

dg/dx = dg/df * df/dx

dg/dx = 2f(x) * cos(x)

Hence, the derivatives are:

(a) d/dx(f(g(x))) = cos(g(x)) * (2x)

(b) d/dx(g(f(x))) = 2f(x) * cos(x)

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Option A, 3x, is a monomial because it is a single term with a coefficient of 3 and a variable of x.

An expression of the form kxn, where k is a real number and n is a positive integer, is known as a monomial. It is essentially a single-term polynomial. Using multiplication and exponent properties, we can rewrite the product when multiplying two monomials into a single one.

A monomial is a single term in algebraic expressions.

Option A, 3x, is a monomial because it is a single term with a coefficient of 3 and a variable of x.

Option B, \(\sqrt{2}x + 1$\), is not a monomial because it is not a single term. It consists of two terms: \(\sqrt{2}x$\) and 1.

Option C, \($9x^2 + 2x + 4$\), is also not a monomial because it consists of three terms.

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The partial fraction expansion of the rational function

f(s) = 7s²+30s+27s/3+9s is 7s/9 - 164/81s + 27 + 164/27

In math the term partial fraction is defined as a method that is used to split the complicated fraction into a simpler form.

Here we have given the rational function f(s) = 7s²+30s+27s/3+9s.

And we have to find the partial fraction expansion for the function.

While we looking into the given rational function, for the given function we have to perform the partial fraction decomposition of

=>  f(s) = 7s²+30s+27s/3+9s.

And it can be simplified as,

=> f(s) = 7s²+57s/3+9s.

Take s as common on the numerator, then we get

=> f(s) = s(7s + 57) / 3 + 9s

Since the degree of the numerator is not less than degree of the denominator, perform synthetic division, then we get the result as

=> f(s) = 7s/9 + 164/27 + [-164/9]/9s + 3

When we further simplify this expression, then we get,

=> f(s) = 7s/9 + 164/27 - 164/81s + 27

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Answer:

(5,-3)

Step-by-step explanation:

The probability that it will be at least 5 minutes before the next coffee-ordering customer arrives is approximately 0.1889, or 18.89%.

The area of mathematics known as probability deals with the outcomes of random events. Probability refers to a result's chance or potential. It clarifies the likelihood that a specific occurrence will take place. We frequently say things like, "He will probably pass the test," "There is very little chance of receiving a storm tonight," and "Most likely the price of onions will increase once more." We substitute the word probability for every instance of chance, uncertainty, maybe, likely, etc. in these statements. In essence, the probability is the ability to anticipate an outcome based on the variety and quantity of potential possibilities or the analysis of historical data.

The average rate of customers per minute is:

20 customers per hour / 60 minutes per hour = 1/3 customers per minute

Let X be the number of customers that arrive in a 5-minute interval. Then X is a Poisson random variable with parameter λ = (1/3) * 5 = 5/3.

We want to find the probability that there are no customers that arrive in the next 5 minutes, which is equal to P(X = 0).

The probability mass function of a Poisson distribution is given by:

P(X = k) = (e^(-λ) * λ^k) / k!

So, in this case, we have:

P(X = 0) = (e^(-5/3) * (5/3)^0) / 0! = e^(-5/3) ≈ 0.1889

Therefore, the probability that it will be at least 5 minutes before the next coffee-ordering customer arrives is approximately 0.1889, or 18.89%.

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Answer:

ok

Step-by-step explanation:

Answer:

y=-1/2x-1

Step-by-step explanation: