Please answer this correctly

The top left graph represents the weight of the radioactive isotope over time.

An exponential function has the definition presented according to the equation as follows:

\(y = ab^x\)

In which the parameters are given as follows:

The parameter values for the function in this problem are given as follows:

a = 96, b = 0.5.

Hence the function is given as follows:

\(y = 96(0.5)^x\)

Two points on the graph of the function are given as follows:

(1,48) and (2, 24).

Hence the top left graph represents the weight of the radioactive isotope over time.

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Answer:

Graph W

Step-by-step explanation:

The given information describes a radioactive decay process, where the weight of the isotope decreases by half at regular intervals. This type of decay is characteristic of exponential decay.

Based on the description, the graph that represents the weight of the radioactive isotope over time would be a decreasing exponential curve, where the y-axis represents the weight of the isotope (in grams), and the x-axis represents time (in hours).

The initial weight of the isotope is 96 grams, and after each subsequent hour, the weight becomes half of what it was in the previous hour. Therefore, the correct graph would start at 96 grams (the initial weight when x = 0) and then decrease by half every hour. It would be a curve that gets closer and closer to zero but never quite reaches it.

Initial weight: 96 grams

After 1 hour: 96 / 2 = 48 grams

After 2 hours: 48 / 2 = 24 grams

After 3 hours: 24 / 2 = 12 grams

After 4 hours: 12 / 2 = 6 grams

After 5 hours: 6 / 2 = 3 grams

So, the points on the graph would be:

Therefore, the graph that represents the weight of the radioactive isotope over time is Graph W.

Using thie model ,The answer is D. 27.

To calculate 9÷1/3 using the model below, we can imagine dividing the green rectangle into thirds vertically. Each third would contain 3 cells.

Then, we can see that there are a total of 9 cells in the rectangle. Since we are dividing by 1/3, we need to find out how many sets of 1/3 are in 9.

We can see that there are 3 sets of 1/3 in each row (since each row contains 3 cells, which are thirds). So, in total, there are 3 rows of 3 sets of 1/3, which gives us:

9÷1/3 = 3 rows x 3 sets of 1/3 = 9 sets of 1/3 = 27

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The new area would be 40 square inches. When a scale factor dilates a polygon, the area is multiplied by the square of the scale factor. If the original area is 10 square inches and the scale factor is 4, the new area would be 10 x 4^2 = 10 x 16 = 40 square inches.

h = how old the house is right now

so right now Mark and Lynne are paying the house off, the house as we speak is "h" years old, it happens that Mark and Lynne are going to be paying the whole house in 18 years from now, so by then the house will be whatever years is now, or "h", plus 18 years, so when Mark and Lynne are done paying for it, the house will be "h + 18" years old.

Now, if the house in 18 years is going to be 4 times as old as it's right now, well, hell right now is "h" years old, 4 times that much is just "4h" years, so we can say

\(\stackrel{\textit{18 years from now}}{h+18}~~ = ~~\stackrel{\textit{18 years from now}}{4h}\implies 18=3h\implies \cfrac{18}{3}=h\implies 6=h\)

Answer:

70%

Step-by-step explanation:

50/10 is 5 (which is 10%). 5 x 7 is 35 (or 70%)

Answer:

3x=12

Step-by-step explanation:

3 times X with x being 4 making it 12 so X=4 and 3x=12

The graph that represents the given piecewise function has a range of

R: (-∞, 0) ∪ (0,2] ∪ (4, ∞).

A piecewise function is a combination of subfunctions that are defined with different intervals in the domain.

The range of the piecewise function is the union of all the ranges of the subfunctions.

The given piecewise function is

g(x) = x², x < 0

      = 1/2 x, 0 < x ≤ 4

      = x, x > 4

The domain and range for the subfunctions in the given piecewise function are:

for g(x) = x²; Domain is {x < 0} and Range is (-∞, 0)

for g(x) = 1/2 x; Domain is {0 < x ≤ 4} and Range is (0, 2]

for g(x) = x; Domain is {x > 4} and Range is (4, ∞)

Then, the range of the given piecewise function is

Range: (-∞, 0) ∪ (0, 2] ∪ (4, ∞)

Thus, the graph shown in the question is the correct one.

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Answer: c, its da 3rd graph

Step-by-step explanation:

Answer:

The standard form of the equation of y = -1/4x - 2 is x + 4y = -8 which is C

Answer:

c.57

Step-by-step explanation:

Note that the notation   "∪C = {x : x ∈ for some S ∈ C} = ∪ { S:S ∈ C}" represents a mathematical statement involving sets.

∪C : This represents the  union (∪) of the sets in C.

{x : x ∈ for some S ∈ C}: This is the description or definition of the elements in the set formed by the union of sets in C.

It states that an element x belongs to the union of   sets in C if and only if x belongs to at least one set S that is an   element of the set C.

= ∪{ S:S ∈ C}   : This means that the union (∪) of sets in C is equal to the union of all sets S that belong to the set C.

In summary,  the statement is saying that the union of sets in C consists of all elements that belong to at least one set in C. It is the combined collection of elements from all sets in C.

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Answer:

Whole number —> X

Twice the square of the number —> 2X²

X + 2X² = 10

2X²+X –10 =0

(2x + 5) ( x–2) =0

2x +5=0 —> 2x= – 5 —> x= – 5/2 = —> x= - 2.5 (rejected)

x–2=0 —> x= 2

So Ans ; X= 2 ( the number )

I hope I helped you^_^

The circumference of the given circle is approximately 47.3 inches.

Since the length of the arc KL and the measure of the central angle ∠KOL are known, we can use the formula for arc length to find the circumference of the circle:

arc length = (central angle / 360°) x circumference

Plugging in the known values, we have:

4.6 in = (35° / 360°) x circumference

Solving for the circumference, we get:

circumference = 4.6 in / (35° / 360°)

circumference = 4.6 in x (360° / 35°)

circumference ≈ 47.3 in (rounded to the nearest tenth)

Therefore, the circumference of the circle is approximately 47.3 inches.

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Answer:

To solve this problem, we need to use the concept of distance, rate and time (D = R x T)

We know that the distance is 49 miles and the rate is 14 miles per hour.

We want to find the time T.

We can use the formula D = R x T, to find the time T:

T = D/R = 49 miles / 14 miles/hour = 3.5 hours

So it takes Nena 3.5 hours to ride from the city park to the nearby lake.

Now we know that she needs to arrive at the lake at 1:00 PM, so we have to work out what time she needs to leave the park. We can subtract the time T from the arrival time to find the departure time:

1:00 PM - 3.5 hours = 9:30 AM

Therefore, the latest Nena can leave the park in order to arrive at the lake at 1:00 PM is 9:30 AM

Considering the definition of perpendicular line, the equation of the perpendicular line that passes through the point (x, y) = (3, 1) and is perpendicular to the line 2x + 3y = 12 is y= 3/2x -7/2.

A linear equation o line can be expressed in the form y = mx + b

where

Perpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.

In this case, the line is 2x+3y= 12. Expressed in the form y = mx + b, you get:

3y= 12 - 2x

y= (-2x +12)÷ 3

y= -2/3x +4

Since multiplying the slopes of two perpendicular lines, you get -1, and the line has a slope of -2/3, you get:

-2/3× slope perpendicular line= -1

slope perpendicular line= (-1)÷ (-2/3)

slope perpendicular line= 3/2

The line passes through the point (3, 1). Replacing in the expression for parallel line:

1= 3/2× (3) + b

1= 9/2 + b

1- 9/2 = b

-7/2= b

Finally, the equation of of perpendicular line is y= 3/2x -7/2.

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The central angles for the categories with the numbers 40, 100, 50, and 50 are 60 degrees, 150 degrees, 75 degrees, and 75 degrees, respectively.

To calculate the central angles for each category based on the given numbers 40, 100, 50, and 50, we need to find the proportion of each value to the total sum of all the values. Let's proceed with the following steps:

Step 1: Calculate the total sum of the given numbers: 40 + 100 + 50 + 50 = 240.

Step 2: Find the proportion of each value by dividing it by the total sum and multiplying it by 360 (since a full circle has 360 degrees).

Central angle for the first category: (40/240) * 360 = 60 degrees.

Central angle for the second category: (100/240) * 360 = 150 degrees.

Central angle for the third category: (50/240) * 360 = 75 degrees.

Central angle for the fourth category: (50/240) * 360 = 75 degrees.

The central angles for each category based on the given numbers are 60 degrees, 150 degrees, 75 degrees, and 75 degrees, respectively.

These central angles represent the relative proportions of each category's spending in relation to the total spending. They can be used to create a pie chart or visualize the distribution of expenses in a circular graph.

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Note the search engine cannot find the complete question

Answer: $1652.17

Step-by-step explanation:

First, let's calculate the hire purchase cost of the video game set.

The hire purchase cost is the initial deposit plus the total cost of the monthly installments.

The total cost of the monthly installments is $171 * 12 = $2052.

So, the total hire purchase cost is $190 (deposit) + $2052 (total monthly payments) = $2242.

Now, let's calculate the selling price of the video game set if no sales tax is included.

If the marked price of $1900 includes a 15% sales tax, we can calculate the pre-tax price (the selling price without the tax) by dividing the marked price by 1 plus the tax rate.

The tax rate in decimal form is 15% = 0.15.

So, the selling price without the tax would be $1900 / (1 + 0.15) = $1900 / 1.15 = approximately $1652.17.

Answer:

4.77*10^5<7.47*10^5

Step-by-step explanation:

4.77*10^5=477000

7.47*10^5=747000

The measures of angle 4 (m<4) and angle 7 (m<7) are 42° and 96°, respectively.

To find the measures of angles 4 and 7, we need to apply some geometric principles. Since the top and bottom pieces of the crib are parallel to each other, we can use the property of alternate interior angles.

Angle 4 (m<4) is formed by a transversal (the line connecting the top and bottom pieces of the crib) intersecting two parallel lines. Given that angle m<2 is 42°, we know that angle 4 is congruent to angle 2. Therefore, m<4 = m<2 = 42°.

Angle 7 (m<7) is formed by a transversal intersecting two parallel lines as well. However, in this case, angle 7 is an exterior angle, which is equal to the sum of the two remote interior angles. The remote interior angles are angles 2 and 4. We know that m<2 = 42° (as given) and m<4 = m<2 = 42° (as explained above). Therefore, the sum of angles 2 and 4 is 42° + 42° = 84°. Since angle 7 is an exterior angle, it is equal to 180° minus the sum of the remote interior angles. Thus, m<7 = 180° - 84° = 96°.

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Answer:

\(a^{2}(24a^{2}+36a+12)\)

Step-by-step explanation:

Area of rectangle= Length*Width

so \((6a^{2}+9a+3)*4a^{2}\)   multiply each coefficient of a times 4a^2

\(24a^{4}+36a^{3}+12a^{2}\)  then take a^2 common factor so it will be

\(a^{2}(24a^{2}+36a+12)\)=area

You need 5 gallon of the 45% acid solution 35 gallon of the 85% solution to get 40  gallon at 80%.

Let x represent the number of liters

0.45x+0.85(40-x) = 0.8(40)

0.45x+34-0.85x = 32

-0.4x = -2

Divide both sides by -0.4

x = -2/-0.4

x = 5

You need 5 gallon of the 45% acid solution

Gallon of the 85% solution to get 40  gallon at 80% = 40-5 = 35 gallon

Therefore 5 gallon and 35 gallon are needed.

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Answer: \($m=-\frac{1}{22}$\)   \($b=\frac{15}{22}$\)

Step-by-step explanation:

To find the equation of the tangent line to the curve \($xy^3+xy= 14$\) at the point \($(7,1)$\) we need to first find the derivative of the equation with respect to x using implicit differentiation.

Taking the derivative of both sides with respect to x:

\($\frac{d}{dx}(xy^3+xy)=\frac{d}{dx}(14)$\)

Using the product rule and chain rule:

\($y^3+x(3y^2\frac{dy}{dx}+y)=0$\)

Simplifying and solving for \($\frac{dy}{dx}$\)

\($\frac{dy}{dx}=-\frac{y}{3y^2+1}$\)

Now we can substitute x=7 and y=1 into this equation to find the slope of the tangent line at the point (7,1):

\($m=\left.-\frac{y}{3y^2+1}\right|_{(7,1)}=-\frac{1}{22}$\)

So the slope of the tangent line is \($-\frac{1}{22}$\)

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

\($y-1 = m(x-7)$\)

\($y=mx+(1-7m)$\)

Therefore, the equation of the tangent line to the curve \($xy^3+xy=14$\) at the point (7,1) can be written as:

\($y=-\frac{1}{22}x+\frac{15}{22}$\)

So \($m=-\frac{1}{22}$\) and \($b=\frac{15}{22}$\)

Answer:

\(m=\frac{1}{2}\)

Step-by-step explanation:

Slope Formula: \(m=\frac{y_2-y_1}{x_2-x_1}\)

Simply plug in 2 coordinates into the slope formula to find slope m:

(0, 2)

(-4, 0)

\(m=\frac{2-0}{0-(-4)}\)

\(m=\frac{2}{0+4}\)

\(m=\frac{2}{4}\)

\(m=\frac{1}{2}\)

Answer:

The answer is C

Step-by-step explanation:

The derivative of the function is f'(s) = 9s^2 + 2 and the values are 146 and 11

From the question, we have the following parameters that can be used in our computation:

f(s) = 3s^3 + 2s

Differentiate the function

So, we have

f'(s) = 9s^2 + 2

When the values are evaluated, we have

f(-4) = 9(-4)^2 + 2 = 146

f(-1) = 9(-1)^2 + 2 = 11

Hence, the values are 146 and 11

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The monthly cell phone bill when shared data equals zero is given as follows:

$26.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The intercept of the line in this problem is given as follows:

b = 26.

Hence $26 is the monthly cell phone bill when shared data equals zero.

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The quantity that is multiplied by pi in the formula for the area of a circle is the square of the radius

From the question, we have the following parameters that can be used in our computation:

Area of a circle

The formula for the area of a circle is represented as

A = πr²

Express the formula as a product

So, we have the following representation

A = π * r²

In the above formula, we can see that the square of r is multiplied by pi

Hence, the required quantity is the square of the radius of the circle

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The volume of the family value box increases by approximately 44% compared to the regular box.

The volume of a rectangular box can be calculated as the product of its length, width, and height.

Let's assume the dimensions of the regular box are L, W, and H, and the dimensions of the family value box are 1.25L, W, and 1.15H, respectively.

The volume of the regular box is LWH, and the volume of the family value box is

(1.25L)(W)(1.15H) = 1.4375LWH.

To find the percentage increase in volume from the regular box to the family value box, we can use the following formula:

Percentage increase = (New value - Old value) ÷ Old value x 100%

In this case, the old value is the volume of the regular box, and the new value is the volume of the family value box. Therefore, the percentage increase in volume is:

(1.4375LWH - LWH) ÷ LWH x 100% ≈ 44%

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The correct question is:

A food company sells its cornflakes in boxes of two different sizes: the regular box and the family value box. For the family value box, the length of the box has been increased by 25% the height has been increased by 15% and the width remains the same. By what percentage does the volume of the box increase from the regular box to the value box? Round your answer to the nearest percent.

Answer:

Step-by-step explanation:

To dilate the square by a factor of 1111 from the origin, we need to multiply each coordinate by 1111.

The coordinates of point C are (8,8). So, to find the coordinates of point C' after dilation, we can simply multiply each coordinate by 1111:

x-coordinate of C' = 1111 * 8 = 8888

y-coordinate of C' = 1111 * 8 = 8888

Therefore, the coordinates of point C' are (8888, 8888).