In 2002, the temperature on the first day of summer was 79°F. This is 4°F less than it was on the first day of summer the previous year. What was the temperature on the first day of summer in 2001?
A. In 2001, the temperature was 75°F.
B. In 2001, the temperature was 93°F.
C. In 2001, the temperature was 83°F.
D. In 2001, the temperature was 82°F.

Answer:

it is D

Step-by-step explanation:

Answer: 13y - 55

Step-by-step explanation:

Given

7 (3y - 5) - 2 (10 + 4y)

Expand parentheses and apply the distributive property

=7 · 3y - 7 · 5 - 2 · 10 - 2 · 4y

=21 y - 35 - 20 - 8y

Move like terms together

=21y - 8y - 35 - 20

Combine like terms

=13y - 55

Hope this helps!! :)

Please let me know if you have any questions

Step-by-step explanation: Go.dzilla 2 king of monsters is one of the best movies out there in my opinion, right down to the CGI, the movie makers did a fantastic job of creating an emotional attachment to the family in the movie.  

Basically in the movie it starts in a nuclear power plant, the power plant has a melt down, kil.ling the team that went into the core to see what the issue was, the director of the power plants wife died and he knew that it wasn.t normal for the plant to meltdown the way it did, so he dedicates the rest of his life to trying to figure out what really happened there. He even goes as far as to sneak in to the restricted area with his son, when there they find out that they are digging up something from the wreckage, this is the giant moth (it wont let me say the name), The giant moth was feeding on the nuclear radiation and that was what caused the plant to melt down all those years ago. the giant moth then flies across the country searching for nuclear radiation and in turn waking her mate and destroying the place, this awakens Go.dzilla so that he can reassert himself as the ap.ex predator. He finds both the giant moths and kil.ls them and then returns to the bottom of the ocean.

The ratio of b to a is b/a = 2. This is option B.

We can say that both triangles ABE and BCE are equilateral triangles.

The length of each side of the triangle ABE is a.

So, BE = a ………. (1)

The length of each side of the triangle BCE is 2a.

So, BE = 2a ………. (2)

From equation (1) and (2), we can say that a = 2a or a = a ⇒ a = 2a ⇒ a/2 = a/2

Again, let us consider the triangles ABD and CBD.The length of each side of triangle ABD is a.

So, BD = a ………. (3)

The length of each side of the triangle CBD is a.So, BD = a ………. (4)

From equation (3) and (4), we can say that a = a or a = a ⇒ a = a

Again, let us consider the triangles ADE and CDE.

The length of each side of triangle ADE is b.

So, DE = b ………. (5)

The length of each side of the triangle CDE is 2a.So, DE = 2a ………. (6

)From equation (5) and (6), we can say that b = 2a or b = 2a ⇒ b/2 = a

So, the ratio of b to a is b/a = 2

Hence, the Answer is option (B) 2.

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I apologize, I cannot visually perceive or manipulate colors or lines directly. However, if you provide me with the equations of the lines or any additional information about their slopes, I would be more than happy to help you match the slopes with the corresponding lines.

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To match the lines (l1, l2, l3) with their corresponding slopes, we need to assign letters representing the slopes to each set.

Without specific information about the lines l1, l2, and l3, it is not possible to determine the exact slopes or their corresponding letters. In order to match the lines with their slopes, we would need additional details such as the equations of the lines or the coordinates of points on the lines.

The slope of a line represents the rate at which the line changes vertically (y-axis) with respect to the horizontal (x-axis). It is typically denoted by the letter "m" in mathematical notation.

To accurately match the lines l1, l2, and l3 with their respective slopes, we require more information about the lines themselves. Once the equations or coordinates are provided, we can calculate the slopes using the formula for slope, which is the change in y divided by the change in x.

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If the actual temperature of steam is 99 °C and is assumed to be 100 °C in calculations, the error introduced can be significant depending on the specific calculations being performed.

Similarly, if the actual temperature of steam is 101 °C and is assumed to be 100 °C, the error introduced can also be significant.

The amount of error introduced when assuming the temperature of steam to be 100 °C instead of the actual temperature of 99 °C or 101 °C depends on the specific calculations being performed.

Similarly, in industrial processes, assuming an incorrect temperature of steam could result in inefficiencies or even safety hazards. Therefore, the difference between the actual temperature of steam and the assumed temperature of 100 °C should not be considered negligible in many cases.

In conclusion, the error introduced by assuming a temperature of 100 °C instead of the actual temperature of steam depends on the specific calculations being performed and can be significant in some cases. It is always best to use accurate and precise measurements in scientific and engineering calculations to minimize the potential for error.

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Complete Question:

1. If you use 100 °C for the temperature of steam in your calculations, how much error do you introduce if it is actually 99 °C or 101 °C? Is this difference negligible?

Answer:

Step-by-step explanation:

Supplementary

180-112= 68

alternate exterior

112

Answer:

∡4 and ∡3 are supplementary

∡3 = 68°

∡5 is an alternate-exterior to ∡4

∡5 = 112°

Step-by-step explanation:

Answer: 300

1 year of tution and college fee: $9,500

= $9,500 × 2 = $19,000

2 years of tution and college fee: $19,000

Money already in Account = $5,000

If we deposit $100 every month for 5 years we would get $11,000 that is less than $19,000.

If we deposit $200 every month for 5 years qe would get $17,000 which is still less.

If we deposit $300 every month we would get $23,000 which is not less so the correct answer is $300.

The least square approximation for the function sin x as a quadratic function a bx cx² in the interval [0,π] is [(3 sin(π₀) - π₀ cos(π₀)) / (3π₀)] + [2 (cos(π₀) - sin(π₀) / π₀³)] x².

To find the least square approximation for the function sin x as a quadratic function a bx cx² in the interval [0,π], use the inner product 〈f, g〉= ∫ π₀ f(x)g(x)dx. Now let us break down the given function into a quadratic function. Let a bx cx² be the quadratic function,

The first step is to find the inner product of sin x and x² sin x∫ π₀ sin(x) dx  = [-cos(x)]π₀∫ π₀ x sin(x) dxNow, evaluate ∫ π₀ x sin(x) dx∫ π₀ x sin(x) dx = [x(-cos(x)) - sin(x)] π₀ = (π₀ cos(π₀) + sin(π₀))

This implies that ∫ π₀ sin(x) dx = (π₀ cos(π₀) + sin(π₀)) / π₀= cos(π₀) + sin(π₀) / π₀sin x is a linear combination of 1 and x²,So, let sin x = a + bx²where a, b are constants.∫ π₀ (sin x - a - bx²)² dx is the least square approximation.

In order to minimize this integral, take the partial derivatives with respect to a and b respectively, and set them equal to zero:∂/∂a ∫ π₀ (sin x - a - bx²)² dx = 0∂/∂b ∫ π₀ (sin x - a - bx²)² dx = 0

This gives us the following equations,π₀a + b(π₀³/3 - π₀) - 2 cos(π₀) ∫ π₀ sin(x) dx = 0π₀² a + b(π₀⁴/2 - π₀²/2) - 2∫ π₀ x sin(x) dx = 0

Plug in the values from the earlier calculations.π₀a + b(π₀³/3 - π₀) - 2 cos(π₀) (cos(π₀) + sin(π₀) / π₀) = 0π₀²a + b(π₀⁴/2 - π₀²/2) - (π₀ cos(π₀) + sin(π₀)) = 0Solve these two equations to get the values of a and b:  a = (3 sin(π₀) - π₀ cos(π₀)) / (3π₀)  b = 2 (cos(π₀) - sin(π₀) / π₀³)

Now, substitute the values of a and b in sin x = a + bx²sin x = [(3 sin(π₀) - π₀ cos(π₀)) / (3π₀)] + [2 (cos(π₀) - sin(π₀) / π₀³)] x².

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The easiest way to find the line parallel to 3x -2y =5 through (1,2), we must set 3x - 2y = 5 into slope-intercept form

   \(3x-2y =5\\-2y = -3x+5\\y = \frac{3}{2}x-\frac{5}{2}\)

In slope-intercept form, y = mx + b, m is the slope. For two lines to be parallel, their slopes must be equal.

Thus the new line that is parallel to 3x - 2y = 5 must also have a slope of (3/2)x

    \(y= \frac{3}{2} x+b\)

To find b, we must plug in (1,2)

   \(2 = \frac{3}{2}*1 + b\\b = \frac{1}{2}\)

Thus the equation that is parallel to 3x-2y = 5 and passes through (1,2) is \(y = \frac{3}{2}x+\frac{1}{2}\)

Hope that helps!

Answer:

3/2x+1/2

Step-by-step explanation:

just took on progress learning and was correct:)

To determine if the difference in years at the company between employees with a high school degree and those with an MBA is significant at the 95% confidence level, we can perform a hypothesis test for p-value.

We can run a hypothesis test to see if the difference in years spent at the organization between workers with a high school diploma and those with an MBA is significant at the 95% confidence level.

We must first specify our alternative hypothesis and null hypothesis. Our null hypothesis is that there is no discernible difference in the number of years that personnel with a high school diploma and those with an MBA have worked for the organization. Our alternate theory is that the two groups have significantly different average years of employment.

The probability of witnessing the data if the null hypothesis is correct can then be determined using a t-test. The null hypothesis can be rejected if the p-value is less than 0.05, and the difference in years spent at the company between workers with a high school diploma and those with an MBA is determined to be significant at the 95% level of confidence.

We can use a two-sample t-test to compare the means of the two groups if the data is normally distributed and the variances are identical.

If the t-test yields a p-value of less than 0.05, we can reject the null hypothesis and draw the conclusion that there is a significant difference in the number of years that employees with a high school diploma and those with an MBA have worked for the organisation. In contrast, if the p-value is higher than 0.05, we are unable to rule out the null hypothesis since there is insufficient data to support the existence of a significant difference.

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The domain of the function is a semicircle with a radius of 5 and centered at the origin, where y is non-negative.

The domain of a function is the set of all possible input values for which the function is defined. In this case, the function is defined as:

\(f(x,y) = \sqrt{y} + \sqrt{[25 - x^2 - y^2} ]\)

To find the domain of this function, we need to determine the values of x and y that would result in the function producing a real-valued output.

For the square root of y to be real, y must be non-negative. That is, y ≥ 0.

For the square root of [\(25 - x^2 - y^2\)] to be real, we must have:

\(25 - x^2 - y^2 \geq 0\\x^2 + y^2 \leq 25\)

This is the equation of a circle with radius 5 centered at the origin. Therefore, the domain of the function is the set of all points (x, y) that lie inside or on this circle and have y ≥ 0.

In interval notation, we can write:

Domain: {(x, y) |\(x^2 + y^2 \leq 25, y \geq 0\)}

To sketch the domain, we can plot the circle with radius 5 centered at the origin and shade the region above the x-axis. This represents all the valid input values for the function. The boundary of the domain is the circle, and the domain includes all points inside the circle and on the circle itself, but not outside the circle.

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The expression that is equivalent to the given expression, 4t - 12 + 3 - 5t, is -t - 9 or -(t + 9)

From the question, we are to determine the expression that is equivalent to the given expression.

The given expression is

4t - 12 + 3 - 5t

To determine the expression that is equivalent to the given expression, we will simplify the expression.

Simplifying the expression

4t - 12 + 3 - 5t

Simplify the middle terms

4t - 9 -5t

Collect like terms

4t - 5t - 9

-t - 9

-(t + 9)

Hence, the expression is -t - 9 or -(t + 9)

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"The school sold 8 adult tickets and 5 child tickets for a total of $104", we can express it as follows

"On the second day they sold 4 adult tickets and 6 child tickets for a total of $80", we can express it as follows

These two equations form a linear system of equations, which we can solve by multiply the second equation by -2

Then, we combine the equations

Now, we find x

According to this solution, each adult ticket costs $8 and each child ticket costs $8.

If they sold 10 adult tickets and 4 child tickets on the third day, then they made

If they sold 22 adult tickets and 8 child tickets on the last day, then they made

The rule for independent samples with equal variance is that the quotient of their variances falls between 0.5 and 2 is the correct answer.

The statement that summarizes a general rule about independent samples with equal variance is: "When the variance of one sample is divided by the variance of the other sample, the quotient is between 0.5 and 2."

This statement reflects the common assumption made in statistical analysis that when dealing with independent samples, the variances of the two samples are approximately equal. This assumption allows for certain statistical tests, such as t-tests, to be applied to compare the means of the samples.

If the quotient of dividing one sample's variance by the other sample's variance falls within the range of 0.5 to 2, it suggests that the variances are not significantly different from each other. This assumption of equal variance simplifies the statistical analysis and allows for more reliable and accurate comparisons between the samples.

It's important to note that this assumption may not always hold true, and there are statistical techniques available to handle cases where the assumption of equal variance is violated.

Therefore, as a general rule, assuming equal variance between independent samples within the range of 0.5 to 2 is a common practice in statistical analysis.  

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Answer:

3 days

Step-by-step explanation:

company A would have the equation 50x+40 =y  and company B would be 30x + 100 =y. we're tying to find the days that these cost the same so you would do 50x+40 = 30+100. When you isolate x you get 3

The money left is $296.54

The total number of people in the track team is 25

The total amount that all members will pay for the shirt is $463.50

Only 9 members have purchased the shirt

The change left can be calculated as follows

25= 463.50

1= x

cross multiply

25x= 463.50

x= 463.50/25

x= 18.54

18.54 × 9

= 166.86

463.50-166.86

= 296.54

Hence the change left is $296.54

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The required sign between -12.7a and -12.7b should be greater than sign (>).

If a is less than b, then -12.7a will be greater than -12.7b, because multiplying a smaller number by a negative constant (-12.7 in this case) will result in a larger negative value than multiplying a larger number by the same constant.

To see this, suppose we have two positive numbers x and y such that x < y. Then, multiplying both by a negative constant c will result in two negative numbers with magnitudes that are greater for x:

cx < cy, because c is negative and (x < y)

Therefore, if a is less than b, then:

-12.7a > -12.7b

So the sign between -12.7a and -12.7b should be greater than sign (>).

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The Laplace transform of (e^4t/7 + 7e^t - 7e^(-t)) is (s + 4)/(7s^2 - 7s - 56), where s is the complex variable.

1. Apply the linearity property of the Laplace transform to each term separately.

  - The Laplace transform of e^(4t/7) is 1/(s - 4/7).

  - The Laplace transform of 7e^t is 7/(s - 1).

  - The Laplace transform of 7e^(-t) is 7/(s + 1).

2. Combine the transformed terms using the properties of addition and subtraction.

  - (1/(s - 4/7)) + (7/(s - 1)) - (7/(s + 1))

3. Find the common denominator by multiplying each term by the appropriate factor.

  - [(7(s + 1)) + (7(s - 4/7)(s + 1)) - (7(s - 4/7)(s - 1))]/[(s - 4/7)(s - 1)(s + 1)]

4. Simplify the numerator:

  - [7s + 7 + 7(s^2 + s - 4/7 - 4/7s - 4/7 - 4/7s) - 7(s^2 - s - 4/7s + 4/7s - 1 + 4/7)]/[(s - 4/7)(s - 1)(s + 1)]

  - [7s + 7 + 7(s^2 + s - 8/7) - 7(s^2 - s - 1 + 4/7)]/[(s - 4/7)(s - 1)(s + 1)]

  - [7s + 7 + 7s^2 + 7s - 56/7 - 7s^2 + 7s + 7 - 28/7]/[(s - 4/7)(s - 1)(s + 1)]

  - (14s - 15)/(7s^2 - 7s - 56)

5. Simplify the expression:

  - (14s - 15)/(7s^2 - 7s - 56)

  - (2s - 15/7)/(s^2 - s - 8)

  - (s + 4)/(7s^2 - 7s - 56)

Therefore, the Laplace transform of (e^4t/7 + 7e^t - 7e^(-t)) is (s + 4)/(7s^2 - 7s - 56).

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The explicit solution to the initial value problem is y(t) = -1/(t - 1).

The given differential equation is (y(t))² * y(t) = y(t).

To solve this problem of initial values, we can separate variables and integrate.

Separating variables:

dy/y² = dt

Integrating both sides:

∫(1/y²) dy = ∫dt

This gives us:

-1/y = t + C

Now, we can use the initial condition y(0) = 1 to find the constant C.

When t = 0, y = 1:

-1/1 = 0 + C

C = -1

Substituting the value of C back into the equation, we have:

-1/y = t - 1

To find the explicit solution, we can solve for y:

y = -1/(t - 1)

So, the explicit solution to the initial value problem is:

y(t) = -1/(t - 1)

Note: The given problem has two conflicting initial conditions, y(0) = 1 and y(0) = -1. As a result, there is no unique solution to this problem. The explicit solution provided above is based on the initial condition y(0) = 1.

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The correct answer is option B which is {x | x ≤ 4.5}

A number line is a representation of a graduated straight line used to represent real numbers in introductory mathematics.

Because the arrow is pointing to the left, the answer to the solution set needs to be less than the number the dot is on.

A solid dot on a number means that that number is included in the solution set.

In the picture the solid dot is on 4.5, so the solution set needs to be equal to or less than 4.5.

Therefore the correct answer is option B which is {x | x ≤ 4.5}

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a point on the y-axis at positive 4

for the rest of the points go right 1 down 2

and left 1 up 2

Answer:wait it must be 30 for the product which means the answer is 26

Step-by-step explanation:

The data point "50" represents a quantitative discrete variable in this study. In the given context, the data point "50" represents the number of books owned by individuals in a study of 85 adults.

Based on this information, the type of data represented by "50" is quantitative. Specifically, it is a discrete variable because it represents a countable value that can only take on whole numbers. In this case, "50" represents the minimum number of books owned by most adults in the study. Quantitative data refers to numerical measurements that can be analyzed and manipulated mathematically. It provides a more precise and detailed understanding of the phenomenon under study. By categorizing the number of books owned by individuals, researchers can gather insights into people's reading habits and preferences. Analyzing this data further may reveal trends, pattern, or relationships between book ownership and various factors, such as age, education, or socioeconomic status.

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Answer:

5:3

Step-by-step explanation:

a) True, b) False, c) False, d) True, e) False, f) False, g) True

a) The statement is true. The symbol "∅" represents the empty set, which does not contain any elements. Since 0 is not an element of the empty set, the statement "0 ∈ ∅" is false.

b) The statement is false. The symbol "{0}" represents a set containing the element 0. The empty set, represented by "∅", does not contain any elements. Therefore, the empty set is not an element of the set {0}.

c) The statement is false. The symbol "{0}" represents a set containing the element 0. However, the empty set, represented by "∅", does not contain any elements. Therefore, the set {0} is not a subset of the empty set.

d) The statement is true. The empty set, represented by "∅", does not contain any elements. Every set is a subset of the empty set, including the set {0}.

e) The statement is false. The symbol "{0}" represents a set containing the element 0. In this case, {0} is not an element of itself. Therefore, the statement "{0}∈{0}" is false.

f) The statement is false. The symbol "{0}" represents a set containing the element 0. In this case, {0} is not a proper subset of itself. Therefore, the statement "{0}⊂{0}" is false.

g) The statement is true. The symbol "{∅}" represents a set containing the empty set. In this case, {∅} is a subset of itself because it contains the element ∅. Therefore, the statement "{∅} ⊆ {∅}" is true.

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The value of the given expression is 7.0 × 10⁸

From the question, we are to determine the value of the given expression

The given expression is

(3.5x10⁶)÷(5x10-³)

The expression can be simplified as follows

(3.5x10⁶)÷(5x10⁻³)

= (3.5 ÷ 5) × (10⁶ ÷ 10⁻³)

= (0.7) × (10⁶⁻⁽⁻³⁾)

= 0.7 × (10⁶⁺³)

= 0.7 × (10⁹)

= 7.0 × 10⁸

Hence, the value of the given expression is 7.0 × 10⁸

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Based on the calculation, it appears that Matti had approximately 94 bottles of 0.5 litres and 11 bottles of 0.7 litres in the last patch of moonshine that he sold.

To solve the problem using the determinant method (Cramer's rule), we need to set up a system of equations based on the given information and then solve for the unknowns, which represent the number of 0.5 litre bottles and 0.7 litre bottles.

Let's denote the number of 0.5 litre bottles as x and the number of 0.7 litre bottles as y.

From the given information, we can set up the following equations:

Equation 1: 0.5x + 0.7y = 16.5 (total volume of moonshine)

Equation 2: 8x + 10y = 246 (total earnings from selling moonshine)

We now have a system of linear equations. To solve it using Cramer's rule, we'll find the determinants of various matrices.

Let's calculate the determinants:

D = determinant of the coefficient matrix

Dx = determinant of the matrix obtained by replacing the x column with the constants

Dy = determinant of the matrix obtained by replacing the y column with the constants

Using Cramer's rule, we can find the values of x and y:

x = Dx / D

y = Dy / D

Now, let's calculate the determinants:

D = (0.5)(10) - (0.7)(8) = -1.6

Dx = (16.5)(10) - (0.7)(246) = 150

Dy = (0.5)(246) - (16.5)(8) = -18

Finally, we can calculate the values of x and y:

x = Dx / D = 150 / (-1.6) = -93.75

y = Dy / D = -18 / (-1.6) = 11.25

However, it doesn't make sense to have negative quantities of bottles. So, we can round the values of x and y to the nearest whole number:

x ≈ -94 (rounded to -94)

y ≈ 11 (rounded to 11)

Therefore, based on the calculation, it appears that Matti had approximately 94 bottles of 0.5 litres and 11 bottles of 0.7 litres in the last patch of moonshine that he sold.

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Question

Matti is making moonshine in the woods behind his house. He’s selling the moonshine in two different sized bottles: 0.5 litres and 0.7 litres. The price he asks for a 0.5 litre bottle is 8€, for a 0.7 litre bottle 10€. The last patch of moonshine was 16.5 litres, all of which Matti sold. By doing that, he earned 246 euros. How many 0.5 litre bottles and how many 0.7 litre bottles were there? Solve the problem by using the determinant method (a.k.a. Cramer’s rule).

Answer:

Area=88in squared

Step-by-step explanation:

Answer 128 to the second  power

explanation:

its 128 to the second power because if you multiply 16*8 and you will get 128to the second power