An ice block in the form of rectangular prism with a square base is melting at a rate of 550cm^3/min. The base length is decreasing at a rate of 1cm/min. How fast is the surface area of the ice block changning when the base length is 10cm, and height is 20cm?

Using rules for logarithms we can see that the statement is false.

Here we have the equation:

logₐ(x^3 + y^3) = 3logₐ(x) + 3logₐ(y)

And we want to see if it is true.

First, remember two rules:

logₐ(x^n) = n*logₐ(x)

and:

logₐ(x) + logₐ(y) = logₐ(x*y)

Then, the right side of the statement can be rewritten as:

3logₐ(x) + 3logₐ(y)

3(logₐ(x) + logₐ(y)) = 3*logₐ(x*y) = logₐ((x*y)^3)

And that is different to what we got in the statement, so the statement is false.

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The coordinate of the point after transformation is: (3, -4)

The coordinate initially is given as (0, -4).

Moving one unit to the left means a deduction of 1 unit from the x coordinate to get:

(0 - 1, -4)

= (-1, -4)

Moving by 4 units to the right means an addition of 4 units to x coordinate to get:

(-1 + 4, -4)

= (3, -4)

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Answer:

K5.60.

Step-by-step explanation:

The exact value of x is 24

To determine the value, we need to that the different trigonometric identities are;

From the information given, we need to determine the value of the opposite side.

The hypotenuse side = 16√3

The opposite side = x

Using the sine identity;

sin θ = opposite/hypotenuse

substitute the values

sin 60 =x/16√3

cross multiply the values

x = 16√3 × √3/2

Divide the values, then multiply the square roots of the values

x = 8×3

x = 24

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Answer:

x = 99

Step-by-step explanation:

Since x is on a straight line the adjacent angle and x must equal 180. We will call this adjacent angle B. The angle to the right of B also is on a straight line.

So,

180 - 123 = the inside angle             Simplify

57

The addition of a triangles interior angles equals 180

180 = 42 + 57 + B                              Move variables to one side

180 - (42 + 57) = B                             Simplify

81 = B

Now we can solve for X

180 - 81 = x                                        Simplify

99

The length of the hypotenuse is 7m.

Let the side opposite to 30° be the shortest leg.

The side opposite to 60° is the longest leg.

So, the side opposite to 90° is hypotenuse.

Length of the shortest side is x.

Length of longest side is [tex]\sqrt{3}x[/tex]

Length of the hypotenuse is 2x.

We know x = 7

So, [tex]\sqrt{3}(x)=\sqrt{3}(7)[/tex]

Thus, the length of the longer leg is [tex]\sqrt{3}(7)[/tex] m

Length of hypotenuse = 2x = 2(7) = 14m

[tex]x^{2} +(\sqrt{3} x)^2 =(2x)^2\\\\(7)^2+(\sqrt{3} (7))^2=(2x)^2\\\\49 + (3(49)) = (2x)^2\\\\49 + 147= (2x)^2\\\\(2x)^2=196[/tex]

Taking square root on both sides:

[tex]2x = \sqrt{196}[/tex]

2x = 14

x = 7

Therefore, the length of the hypotenuse is 7m.

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The increase in Fahrenheit temperature  is of 12.6 degrees.

The formula to have a change of units is:

To convert Celsius to Fahrenheit, you can use the formula:

°F = (°C x 1.8) + 32

(So you are correct, the rate is 9/5 = 1.8)

The increase of 7°C wold be given by the difference:

increase = ((°C + 7°) x 1.8) + 32 - (°C x 1.8) + 32

Solving that equation we can see that

increase =  12.6°F

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Answer:

he increase in Fahrenheit temperature  is of 12.6 degrees.

What is the increases in Fahrenheit temperature?

The formula to have a change of units is:

To convert Celsius to Fahrenheit, you can use the formula:

°F = (°C x 1.8) + 32

(So you are correct, the rate is 9/5 = 1.8)

The increase of 7°C wold be given by the difference:

increase = ((°C + 7°) x 1.8) + 32 - (°C x 1.8) + 32

Solving that equation we can see that

increase =  12.6°F

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Step-by-step explanation:

For given function function f(x)=-x+3-2, the domain is x > -3 and the range is y ≤ 2. So, correct option is D.

The function f(x)=-x+3-2 is a linear function in the form y=mx+b, where m is the slope and b is the y-intercept. In this case, the slope is -1 and the y-intercept is 1. Therefore, the graph of the function is a straight line that intersects the y-axis at (0,1) and has a slope of -1, meaning that it decreases by 1 for every 1 unit increase in x.

The domain of the function is the set of all possible values of x for which the function is defined. Since there are no restrictions on the value of x in the equation f(x)=-x+3-2, the domain is all real numbers, or (-∞, ∞).

The range of the function is the set of all possible values of y that the function can output. In this case, the lowest possible value of y occurs when x approaches positive infinity, and the highest possible value of y occurs when x approaches negative infinity. Therefore, the range is all real numbers less than or equal to 2, or y ≤ 2.

So, the domain is x ∈ (-∞, ∞) and the range is y ≤ 2. Alternatively, the domain can also be expressed as x > -3, since that is the minimum value of x at which the function is defined.

Correct option is D.

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Complete question is:

What are the domain and range of the function f(x)=-x+3-2?

A) domain: -3 -2

B) domain: -3 -3 range: y<-2

C) domain: x>-3 range:y>-2

D) domain : x>-3 range: y ≤ 2

The equation of the line in the slope-intercept form will be y = (-2/3)x - 2.

Given that:

Points, (-3, -4) and (6, -10)

The equation of the line in slope-intercept form is written as,
y = mx + b

The slope of the line is calculated as,

m = (y2 - y1) / (x2 - x1)

m = (-10 - (-4)) / (6 - (-3))

m = -6 / 9

m = -2/3

Now, to find the y-intercept, we can use the point-slope form of a line:

y - y1 = m(x - x1)

y - (-4) = (-2/3)(x - (-3))

y = (-2/3)x - 2

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Answer:

Step-by-step explanation:

just do how tall times the diamiter divided by the

The number of weeks that Vanessa ran for the number of miles given would be = 24 weeks

The amount of distance that Vanessa covers for a week = 4 miles

The amount of weeks it will take for her to cover 96 moles would be = ?

That is;

1 week = 4 miles

X weeks = 96 miles

Make X the subject of formula;

X = 96× 1/4

= 24 weeks

Therefore Vanessa will be able to cover 96 miles in only 24 weeks.

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Answer:

(2,1)

Step-by-step explanation:

The line 4y - 2x = 0 can be written in slope-intercept form as y = 1/2x.

So any point that satisfies this equation will lie on the line. For example, the point (2,1) satisfies the equation:

4(1) - 2(2) = 0

So the point (2,1) is on the line.

The vector v can be decomposed into v₁ = -2i - 2j and v₂ = -6i + 6j.

The decomposition of the vectors is calculated as follows;

v₁ = (v · w / |w|²) w

v₂ = v - v₁

The dot product of v and w is calculated as;

v · w = (-8)(1) + (4)(1)

v · w = -4

The magnitude of w is calculated as;

|w| = √1² + 1²)

|w|= √2

|w|² = 2

The value of v₁ is calculated as;

v₁ = (-4 / 2) (i + j)

v₁  = -2i - 2j

The value of v₂ is calculated as follows;

v₂ = v - v₁

v₂  = (-8i + 4j) - (-2i - 2j)

v₂ = -6i + 6j

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The function f(x) = 12/x + 1/2 is given. To find f(3), we substitute x=3 in the function expression and simplify: f(3) = 12/3 + 1/2 = 4 + 0.5 = 4.5. Therefore, the value of the function f at x=3 is 4.5.

To find f(3) for the function f(x) = 12/x + 1/2. Start with the given function f(x) = 12/x + 1/2. Replace x with 3: f(3) = 12/3 + 1/2. Simplify the first term: 12/3 = 4

Add the two terms: f(3) = 4 + 1/2

Convert the mixed number to an improper fraction: 4 + 1/2 = 8/2 + 1/2 = 9/2

Simplify the fraction: 9/2 = 4 1/2

So, f(3) = 4 1/2 or 9/2, depending on the desired form of the answer.

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Answer:

AB = 90° , AC = BC = 135°

Step-by-step explanation:

the arc AB is equal to the measure of the central angle it subtends, then

AB = 90°

the sum of the arcs in a circle = 360° , then since AC and BC are congruent

AB + AC + BC = 360° ( since AC = BC ), then

90° + 2AC = 360° ( subtract 90° from both sides )

subtract 90° from both sides

2AC = 270° ( divide both sides by 2 )

AC = 135°

since AC = BC , then

AC = BC = 135°

Answer: 2,001.57

Step-by-step explanation:

there ya go!

The solution to all parts from a to f is shown below.

A) Matrix A:

[ 2  -3 ]

[ 4   3 ]

B) The determinant of matrix A is:

det(A) = (2*3) - (-3*4) = 6 + 12 = 18

C) Matrix X:

[ -8  -3 ]

[ -34  3 ]

D) The determinant of matrix X is:

det(X) = (-8*3) - (-3*-34) = -24 - 102 = -126

E) Matrix Y:

[ 2  -8 ]

[ 4  -34 ]

F) The determinant of matrix Y is:

det(Y) = 2(-34) - (-8) (4) = -68 + 32 = -36

G) Using Cramer's rule, we can solve for x and y as follows:

x = det(X) / det(A) = -126 / 18 = -7

y = det(Y) / det(A) = -36 / 18 = -2

Therefore, the solution to the system is (-7, -2).

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For the function f(x) = -2x² + 5x + 7 the slope of the secant line between x = -3 and x = 5 is -4

Consider the function f(x) = -2x² + 5x + 7

We need to find the slope of the secant line between x = -3 and x = 5

We know that the slope of secant line for the function f(x) on the interval [a, b] is given by the formula,

m = [f(b) - f(a)] / (b - a)

Let [a, b] = [-3, 5]

For x = -3 the value of the function would be,

f(-3) = -2(-3)² + 5(-3) + 7

      = -2(9) - 15 + 7

      = -18 - 15 + 7

      = -26

And the value of the function for x = 5 would be,

f(5) = -2(5)² + 5(5) + 7

      = -2(25) - 25 + 7

      = -50 - 15 + 7

      = -58

Using above formula the slope would be,

m = [f(5) - f(-3)] / (5 - (-3))

m = [-58 - (-26)] / 8

m = (-58 + 26) / 8

m = -4

Thus, the required slope is -4

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Answer:

Slope = 1

Step-by-step explanation:

A secant line is a straight line that intersects a curve at two or more points.

Given a curve represented by a function f(x), a secant line is determined by choosing two distinct points on the curve, (x₁, f(x₁)) and (x₂, f(x₂)).

The secant line passes through these two points and can be represented by a linear equation in the form y = mx + b, where m is the slope of the secant line and b is the y-intercept.

The slope of the secant line between the points (x₁, f(x₁)) and (x₂, f(x₂)) is given by the formula:

[tex]m = \dfrac{f(x_2) - f(x_1)}{x_2 - x_1}[/tex]

To find the slope of the secant line between x = -3 and x = 5 for the function f(x) = -2x² + 5x + 7, first find f(-3) and f(5).

[tex]\begin{aligned}f(-3)&=-2(-3)^2+5(-3)+7\\&=-2(9)-15+7\\&=-18-15+7\\&=-26\end{aligned}[/tex]

[tex]\begin{aligned}f(5)&=-2(5)^2+5(5)+7\\&=-2(25)+25+7\\&=-50+25+7\\&=-18\end{aligned}[/tex]

Input the values into the slope formula:

[tex]m = \dfrac{f(5) - f(-3)}{5 - (-3)}=\dfrac{-18-(-26)}{5+3}=\dfrac{8}{8}=1[/tex]

Therefore, the slope of the secant line between x = -3 and x = 5 is 1.

Answer:

Step-by-step explanation:

Answer:

D. It is a two-dimensional object.

The statement D is true about the figure above. The figure is a circle, which is a two-dimensional object.

Statement A is not true. A point is a location in space, but a circle is a shape that takes up space and has a defined area.

Statement B is not true either. A circle has only one measurement, which is its radius or diameter. The radius is the distance from the center of the circle to any point on its circumference, while the diameter is the distance across the circle through its center.

Statement C is also not true. A circle cannot "grow" into a three-dimensional object because it is a two-dimensional object that exists in a flat plane. However, multiple circles can be stacked on top of each other to form a cylinder, which is a three-dimensional object.

Answer:

G^-1(t)=t/7+4

Step-by-step explanation:

G(t) = 7(t - 4)

y = 7(x - 4)

x = 7(y - 4)

x/7 = y - 4

y = x/7 + 4

G^-1(t) = t/7 + 4

Answer: G^-1(t)=t/7+4

The best method to describe data is use median value for how number of daily downloads varies, and mean value or interquartile range for number of daily downloads. So, correct options are A, D and E.

The median value is a measure of central tendency that represents the middle value of a set of data. It is useful to describe how the number of daily downloads varies, as it gives an idea of the typical value of the dataset.

However, mean absolute deviation is a measure of dispersion that describes how far the data values are from the mean. It is not an appropriate method to describe how the number of daily downloads varies, as it does not give information about the distribution of the data.

The maximum value is a measure of the largest value in a dataset, which can provide information on the upper limit of the number of daily downloads. However, it is not an appropriate method to describe how the number of daily downloads varies, as it does not give information on the spread or distribution of the data.

The mean value is a measure of central tendency that summarizes the data with a single number, but it may not be the best choice if the data is skewed or has outliers.

The interquartile range is a measure of dispersion that summarizes the spread of the middle 50% of the data. It can be used to summarize the number of daily downloads with a single number, but it does not give information on the typical or extreme values of the dataset.

The minimum value is a measure of the smallest value in a dataset, which can provide information on the lower limit of the number of daily downloads. However, it is not an appropriate method to summarize the number of daily downloads with a single number, as it does not give information on the spread or distribution of the data.

So, correct options are A, D and E.

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Answer:

1. The slope of the line is 3. The line goes up 3, over 1, and since slope is rise/run, the slope is 3.

2. The slope of the line is 4. The line goes up 4, over 1, and since slope is rise/run, the slope is 4.

3. The slope of the line is 2. The line goes up 2, over 1, and since slope is rise/run, the slope is 2.

4. The slope of the line is -4. The line goes down 4, over 1, and since slope is rise/run, the slope is -4.

The gradients of line equations are listed below:

In this question we have four cases of line equations shown on Cartesian plane, whose gradients must be found. The gradient of each line can be computed by means of secant line formula and two points:

m = Δy / Δx

Where:

Case 1: (x₁, y₁) = (- 1, - 4), (x₂, y₂) = (1, 2)

m = [2 - (- 4)] / [1 - (- 1)]

m = 3

Case 2: (x₁, y₁) = (- 1, - 1), (x₂, y₂) = (0, 3)

m = [3 - (- 1)] / [0 - (- 1)]

m = 4

Case 3: (x₁, y₁) = (- 1, - 1), (x₂, y₂) = (1, 3)

m = [3 - (- 1)] / [1 - (- 1)]

m = 2

Case 4: (x₁, y₁) = (0, 4), (x₂, y₂) = (2, - 2)

m = (- 2 - 4) / (2 - 0)

m = - 3

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If Olivia followed either of those two methods, then she is correct. Both Angelica and Michael have incorrect methods.

Problem 1

One method Olivia could have used is to reflect over the x axis and then translate 10 units to the right.

Let's apply this set of steps to point C.

C = (-2,-4)

C' = (-2,4) after reflecting over the x axis; y coordinate flips in sign

C'' = (8,4) after shifting to the right 10 units; add 10 to the x coordinate

Point C(-2,-4) moves to C''(8,4) which is shown in the diagram. I'll let you check the other four points.

-----------

Another method Olivia could have used is to shift to the right 10 units first, then reflect over the x axis. In this case, the order doesn't matter. Though for some other combinations of transformations, order does matter.

============================================================

Problem 2

Reflecting over the y axis will have the point (x,y) turn into (-x,y). Only the x coordinate changes, and we flip the sign here. The y coordinate stays the same.

A point like C(-2,-4) becomes C'(2,-4) after the y axis reflection. Shifting up 8 units means we add 8 to the y coordinate to arrive at C''(2,4) but this does not match what the diagram shows. Therefore, Angelica's method is incorrect.

You should find other inconsistencies for the other four points as well.

============================================================

Problem 3

Michael's method isn't correct either. He does not apply an x axis reflection and instead relies entirely on translations to move ABCDE to A''B''C''D''E''

At a quick glance, it looks like Michael may be correct. But upon a much closer look, you'll see that things don't line up perfectly.

Instead of point C, we'll pick on point D this time.

D is located at (-6,-2). If we shift up 8 units, then we add 8 to the y coordinate to get to D'(-6,6). Then add 10 to the x coordinate to shift 10 units to the right. This leads us to D''(4,6).

However, the diagram shows D'' is actually at (4,2)

Feel free to examine the remaining points. It will become apparent that merely C and E are accurately plotted; however, the others are not. This is, once again, due to Michael's failure in implementing an x-axis reflection.

The A''B''C''D''E'' diagram he produced is essentially inverted compared to its intended form.

============================================================

To summarize, the methods described in problem 1 are the correct way to get ABCDE to move to A''B''C''D''E''.

If Olivia followed either of those two methods, then she is correct. Both Angelica and Michael have incorrect methods.

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[tex]\frac{5}{25} = \frac{9}{x +4}[/tex] when simplified, the value of x = 41

Equation is  a mathematical statement that is made up of two expressions connected by an equal value.It says that two things are equal and it expresses equality of two mathematical expressions.

How to determine this

[tex]\frac{5}{25} = \frac{9}{x +4}[/tex]

To find the value of x,

By cross multiplying

5(x+4) = 9(25)

Open bracket

5x + 20 = 225

Collect like terms

5x = 225 - 20

5x = 205

Divides through by 5

5x/5 = 205/5

x = 205/5

x = 41

Therefore, the value of x = 41

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1. Daily cost of keeping the bulb lit for 5 hours is 5 cents.

2. Switching to an LED bulb could save $13.50 in a year.

Power consumed by the 100-watt bulb in 5 hours is:

= 100 watts x 5 hours

= 500 watt-hours

= 0.5 kilowatt-hours

The cost of electricity for 0.5 kilowatt-hours at a rate of 10 cents per kilowatt-hour is:

= 0.5 kWh x 10 cents/kWh

= 5 cents

b. The power consumed by the 26-watt LED bulb over 5 hours is:

= 26 watts x 5 hours

= 130 watt-hours

= 0.13 kilowatt-hours

The cost of electricity for 0.13 kilowatt-hours at a rate of 10 cents per kilowatt-hour is:

= 0.13 kWh x 10 cents/kWh

= 1.3 cents

Annual savings is:

= (Daily cost 100-watt bulb - Daily cost LED bulb) * 365 days

= (5 cents - 1.3 cents) x 365 days

= $13.50.

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At the 0.05 significance level, the degree of freedom is 1. So, correct option is B.

To test the hypothesis that the proportion of wins is the same for teams wearing suits as for teams wearing jeans, we can use the chi-square test for independence. The null hypothesis is that the proportion of wins is the same for both groups, and the alternative hypothesis is that they are different.

Using the given data, we can calculate the expected frequencies under the assumption of equal proportions of wins for both groups. The expected frequency for each cell is given by (row total x column total) / grand total.

The calculated chi-square statistic is 2.667, and the degrees of freedom are (r-1)(c-1) = (2-1)(2-1) = 1.

Using a chi-square distribution table with 1 degree of freedom and a significance level of 0.05, the critical value is 3.84. Since the calculated chi-square value is less than the critical value, we fail to reject the null hypothesis.

Therefore, we can conclude that there is not enough evidence to suggest that the proportion of wins is different for teams wearing suits versus jeans and t-shirts at the 0.05 significance level.

The answer choice that corresponds to 1 degree of freedom is B

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Sure, I'd be happy to help you with this problem!

Given that the ratio of boys to girls in the school is 4:3, we can say that for every 4 boys, there are 3 girls.

Let's start by finding the total number of students in the school, using the information that there are 18 girls.

If 3 girls represent a part of the whole, then we can find the total number of parts by dividing the total number of girls by 3:

18 girls ÷ 3 = 6 parts

So, there are 6 parts in the whole.

Now, since there are 4 boys for every 3 girls, we know that for every 7 parts (4 boys + 3 girls), there are 4 boys.

To find the total number of boys, we need to figure out how many groups of 7 parts there are in the whole.

6 parts ÷ 7 = 0 with a remainder of 6

This tells us that there are 0 groups of 7 parts in the whole, with 6 parts left over.

Since we know that for every 7 parts there are 4 boys, we can find the number of boys in the remaining 6 parts by multiplying 4 by the fraction of 6/7:

4 boys × 6/7 = 24/7 boys

This tells us that there are 24/7 boys in the remaining 6 parts.

To find the total number of boys in the school, we need to add the number of boys in the groups of 7 parts and the number of boys in the remaining 6 parts:

0 groups of 7 parts × 4 boys per group = 0 boys

6 parts × 4 boys per 7 parts = 24/7 boys

Total number of boys = 0 boys + 24/7 boys = 24/7 boys

So, there are 24/7 boys in the school. We can simplify this fraction by dividing both the numerator and the denominator by 3:

24/7 ÷ 3/3 = 8/7 boys

Therefore, there are 8/7 boys in the school, which is approximately 1.14 boys.

However, since we cannot have a fraction of a person, we can round this number to the nearest whole number, which is 1.

Therefore, there is 1 boy in the school for every 3 girls, making a total of:

1 boy × 18 girls = 18 boys

So, there are 18 boys in the school.