Find the probability that a point chosen randomly inside the rectangle is in each given shape. Round to the nearest tenth.

The volume of the cone is (5/3)π(9²) cubic units ≈ 381.7 cubic units.

The formula for the volume of a cone is V = (1/3)πr²h, where r is the radius of the circular base and h is the height of the cone. However, we are given the base area B instead of the radius, so we need to find the radius first.

We know that the area of a circle is A = πr², so if the base area of the cone is B = 5π square units, then πr² = 5π, which means r² = 5. Solving for r, we get r = √5.

Now that we have the height h = 9 units and the radius r = √5 units,

we can use the formula for the volume of a cone:

V = (1/3)πr²h.

Substituting the values, we get

V = (1/3)π(√5)²(9) = (5/3)π(9²) cubic units, which simplifies to ≈ 381.7 cubic units.

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When the pretax financial income is negative (indicating a loss), the taxable income will also be negative. This means that the company can use the loss to offset future profits and reduce its tax liability.

To calculate the taxable income (loss) for each year, we need to apply the corresponding tax rate to the pretax financial income (or loss) figures. Here's the breakdown:

2017:

Taxable income = Pretax financial income * Tax rate

Taxable income = $77,000 * 0.25

Taxable income = $19,250

2018:

Taxable income = Pretax financial income * Tax rate

Taxable income = ($38,000) * 0.20

Taxable income = ($7,600)

2019:

Taxable income = Pretax financial income * Tax rate

Taxable income = ($33,000) * 0.20

Taxable income = ($6,600)

2020:

Taxable income = Pretax financial income * Tax rate

Taxable income = $122,000 * 0.20

Taxable income = $24,400

2021:

Taxable income = Pretax financial income * Tax rate

Taxable income = $90,000 * 0.20

Taxable income = $18,000

Please note that when the pretax financial income is negative (indicating a loss), the taxable income will also be negative. This means that the company can use the loss to offset future profits and reduce its tax liability.

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To solve the given question, we need to use the distributive property and collect like terms. In summary, the distributive property is a useful tool in simplifying expressions.

First, we need to distribute the fraction 4/5 to the expression inside the parenthesis, which gives us 4/5 x 1/4c - 4/5 x 5. Then, we can simplify the expression by multiplying the two fractions and combining the terms. This gives us (1/5)c - 4.

Therefore, the simplified expression is (1/5)c - 4. We can use this expression to evaluate the given expression for any value of c. For example, if c = 15, then the expression becomes (1/5) x 15 - 4 = 3 - 4 = -1.

In summary, the distributive property is a useful tool in simplifying expressions.

By distributing a term to each term inside a set of parentheses, we can collect like terms and simplify the expression. In this case, we used the distributive property to simplify a fraction and a constant and then combined the like terms to obtain the final answer.

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The actual length of the truck is 15.6 meters and the actual width is 3.24 meters.

The actual length of the truck can be calculated by multiplying the length of the model by the scale factor:

Similarly, the actual width of the truck can be calculated as:

Therefore, the actual length of the truck is 15.6 meters and the actual width is 3.24 meters.

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To find the absolute value of the difference between theoretical and experimental probabilities, you need to follow these steps:

1. Calculate the theoretical probability: This is the probability of an event occurring based on the total number of possible outcomes. It can be found by dividing the number of successful outcomes by the total number of possible outcomes.

2. Calculate the experimental probability: This is the probability of an event occurring based on actual experiments or trials. It can be found by dividing the number of successful outcomes by the total number of trials conducted.

3. Find the difference: Subtract the experimental probability from the theoretical probability.

4. Take the absolute value: The absolute value is the non-negative value of a number, disregarding its sign. To find the absolute value of the difference, simply remove the negative sign if the result is negative.

By following these steps, you'll find the absolute value of the difference between theoretical and experimental probabilities, which is an important measure to assess the accuracy of experiments and predictions.

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Answer:

x's will eliminate because they have opposite coefficients

Step-by-step explanation:

Because the x's have opposite coefficients, they will eliminate when the given system of linear equations (2-var) are summed up

Answer:

x's will eliminate because they have opposite coefficients.

Step-by-step explanation:

Why the other choices are incorrect:

y's will eliminate because they have opposite coefficients - not true, they don't have opposite coefficients.

x's will eliminate because you always have to solve for x first - you can solve for y too.

y's will eliminate because why not - isn't a good explanation.

The sale's person commission from the sale of $37,000 worth of furnaces is $2,220. If this is doubled, he would have $4,440.

If the salesperson's commission from the sale of $37,000 is at the rate of 6%, then we will do the following:

6/100 × $37,000 = $2,220

If sales, double, we will now record the amount, 74,000. Now 6% of 74,000 will be $4,440. So, the resultant amount, if the salesperson was to increase his sales to double the original, will be $4,440.

This follows a simple logic. When you have a number and are told to double it, you simply multiply by 2. In the same manner, we multiply the salesperson's commission by 2.

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The number of cones that can be filled with the ice cream from the container is 10.

Let's start with the container. We are given that it is a right circular cylinder with a diameter of 12 cm and a height of 15 cm. To find the volume of this cylinder, we use the formula:

Volume of cylinder = πr²h

where r is the radius of the cylinder (which is half of the diameter), and h is the height. Substituting the given values, we get:

Volume of cylinder = π(6 cm)²(15 cm) = 540π cubic cm

So the container has a volume of 540π cubic cm.

Now, let's move on to the cones. We are given that the cones have a height of 12 cm and a diameter of 6 cm. The cones have a hemispherical shape on the top, so we can consider them as a combination of a cone and a hemisphere. The formula for the volume of a cone is:

Volume of cone = (1/3)πr²h

where r is the radius of the base of the cone, and h is the height. Substituting the given values, we get:

Volume of cone = (1/3)π(3 cm)²(12 cm) = 36π cubic cm

The formula for the volume of a hemisphere is:

Volume of hemisphere = (2/3)πr³

where r is the radius of the hemisphere. Substituting the given values (the radius is half the diameter of the cone, which is 3 cm), we get:

Volume of hemisphere = (2/3)π(3 cm)³ = 18π cubic cm

So the total volume of each cone is:

Volume of cone + hemisphere = 36π + 18π = 54π cubic cm

To find out how many cones can be filled with the ice cream from the container, we divide the volume of the container by the volume of each cone:

Number of cones = Volume of container / Volume of each cone Number of cones

=> (540π cubic cm) / (54π cubic cm) Number of cones = 10

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Complete Question:

A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.

The radius of the lake is approximately 17.89 feet.

To find the radius of the lake, we can use the information given and apply the properties of tangents to circles.

Since point B is the point of tangency, the line segment AB is tangent to the circle. A radius drawn to the point of tangency, in this case from the center of the lake (point O) to point B, will be perpendicular to the tangent line (line AB).

Now, let's use the given measurements. The distance from the duck (point C) to the point of tangency (point B) is 16 feet, and the distance from the duck (point C) to the edge of the lake in the direction of A (line AC) is 8 feet. We can form a right-angled triangle OBC with the given information.

Since OB is perpendicular to AB, we have a right-angled triangle with legs CB and OC. Using the Pythagorean theorem, we can find the length of the hypotenuse, which is the radius of the lake:

OC^2 + CB^2 = OB^2
(8 feet)^2 + (16 feet)^2 = OB^2
64 + 256 = OB^2
320 = OB^2
OB = √320
OB ≈ 17.89 feet

So, the radius of the lake is approximately 17.89 feet.

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The completed equation is:

2 + 7 = a - 2

a = 11.

We are given the following equation:

2 + b = a - 2

We need to select the correct number from the drop-down menu to complete the equation.

From the first drop-down menu, we select 7.

2 + 7 = 9

From the second drop-down menu, we select 2.

2 + b = 9 - 2

2 + b = 7

Subtracting 2 from both sides, we get:

b = 5

Therefore, from the third drop-down menu, we select 5.

So, the completed equation is:

2 + 7 = 5 - 2

9 = 3

This is not a true statement, so there must be an error in one of our selections. Upon closer inspection, we can see that the correct number to select from the first drop-down menu is 5, not 7.

2 + 5 = 7

Now, substituting 5 for b in the original equation, we get:

2 + 5 = a - 2

7 + 2 = a

a = 9

Therefore, from the third drop-down menu, we select 9.

So, the completed equation is:

2 + 5 = 9 - 2

7 = 7

This is a true statement, so we have selected the correct numbers to complete the equation.

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Therefore, the equation in the form of y = mx + b that represents this linear function is: y = -3.2x + 0.1

To write an equation in the form of y = mx + b for a linear function, we need to find the slope (m) and the y-intercept (b).

We can use any two points from the given set of points to find the slope:

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

Let's use the first and second points:

m = (-5.5 - 2.5) / (1.75 - (-0.25))

m = -8 / 2.5

m = -3.2

Now, we can use the slope and one of the points to find the y-intercept:

y = mx + b

-5.5 = (-3.2)(1.75) + b

b = -5.5 + 5.6

b = 0.1

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The minimum value of 9y – 45x^2 is 0, which occurs when y = 5x^2/3, so the range of V is all non-negative real numbers:

Range of V: [0, ∞)

To find the domain and range of the function V(x, y) = 9√(9y – 45x^2), we need to consider the values of x and y that make the expression under the square root non-negative, since we cannot take the square root of a negative number.

So, we have:

9y – 45x^2 >= 0

Dividing both sides by 9 and rearranging, we get:

y >= 5x^2/3

This means that the domain of V is all points (x, y) such that y is greater than or equal to 5x^2/3:

Domain of V: {(x, y) | y >= 5x^2/3}

To find the range of V, we note that the square root is always non-negative, so V(x, y) will be non-negative whenever 9y – 45x^2 is non-negative. The minimum value of 9y – 45x^2 is 0, which occurs when y = 5x^2/3, so the range of V is all non-negative real numbers:

Range of V: [0, ∞)

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Answer:

(-∞, 1) ∪ (1, ∞)

Step-by-step explanation:

1 - x = 0

-x = -1

x = 1

In interval notation, the domain is (-∞, 1) U (1, ∞)

-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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Answer:  B   g(x)=1/4f(x)    odd

Step-by-step explanation:

First Page:

Points from the graph

Points from f(x)                         points from g(x)

(1,2)                                                (1, 1/2)

(4, 16)                                             (4, 4)

f(x) was multiplied by 1/4 to get to g(x)

Second Page:

Even functions are symmetrical about the y-axis: . Odd functions are symmetrical about the x- and y-axis: f(x)=-f(-x).

lets test for even:  does f(x)=f(-x)   =>    f(1)=f(-1)  no   -2[tex]\neq[/tex]2

see image for plotted points

lets test for odd:  does f(x)= -f(-x)   =>    f(1) = -f(-1)  yes  -2 = -2

Answer:

[tex]\textsf{B)} \quad g(x)=\dfrac{1}{4}f(x)[/tex]

[tex]\textsf{B)} \quad \textsf{odd}[/tex]

Step-by-step explanation:

Functions f(x) and g(x) are exponential functions.

From inspection of the given points on both graphs:

When x = 4, the y-value of function f(x) is four times the y-value of function g(x). Therefore, function g(x) is ¹/₄ of function f(x):

[tex]g(x)=\dfrac{1}{4}f(x)[/tex]

[tex]\hrulefill[/tex]

And even function is symmetric about the y-axis:

According to the table, f(3) = -4 and f(-3) = 4.

Therefore, as f(x) ≠ f(-x), the function is not even.

An odd function is symmetric about the origin:

According to the table, f(-3) = 4 and f(3) = -4. So -f(3) = -(-4) = 4.

Therefore, as f(-3) = -f(3), the function is odd.

[tex]\hrulefill[/tex]

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Start with the base graph: y = |x|

Translate the graph one unit to the right: y = |x - 1|

---We use a minus/negative/subtraction sign when dealing with horizontal translations because it is the opposite of the way we want to go. If the translation occurs within parenthesis/absolute value bars, we always do the opposite of what we think we should.

Translate the graph one unit down: y = |x - 1| - 1

---If the translation occurs to the y-value/vertically, we use the expected operation/sign. If the translation occurs outside of parenthesis, we use the same operation/sign as the translation (+ for up, - for down).

Answer: y = |x - 1| - 1

Hope this helps!

Answer:

y=|x-1|-1

Step-by-step explanation:

The function for a v shaped graph is an absolute value function: y=|x|

Subtracting 1 from the absolute value y=|x|, we move the graph 1 unit right of the x axis

Subtracting 1 from the whole equation, y=|x-1|, we move the graph 1 unit down the y axis

So, the equation would be y=|x-1|-1

The best prediction possible for the number of times you will roll a one number when a 6-sided die is rolled 12 times = (0.167)¹²

Events occur as the outcome of an experiment. But one cannot be satisfied with these events until a degree of measurement of the likeliness of its occurrence is not provided. Probability is a statistical tool used widely to obtain predictive value.

Here, 6-sided die rolled 12 times.

If a 6-sided die is rolled, possible outcomes are {1, 2, 3, 4, 5, 6}

So, total number of outcomes = 6

So, number of favorable outcomes = 1

Probability of getting 1 is 1/6 = 0.167

The best prediction possible for the number of times you will roll a one number when a 6-sided die is rolled 12 times = (0.167)¹²

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Answer:

Step-by-step explanation:

tried my best as the first two got me stuck

wouldn't recommend trying my answer and Id wait for another answer

The ratios are: surface area 9:121, volume 27:1331, width 3:11.

(a) The ratio of the surface area of the model to the surface area of the original can be found by using the scale factor to find the ratio of the corresponding side lengths. Since surface area is proportional to the square of the side length, we can use this ratio squared to find the ratio of the surface areas.
The ratio of the corresponding side lengths is 3:11, so the ratio of the surface areas is (3/11)^2, which simplifies to 9/121.
Therefore, the ratio of the surface area of the model to the surface area of the original is 9:121.
(b) The ratio of the volume of the model to the volume of the original can be found using the same method as above, but with volume instead of surface area. Since volume is proportional to the cube of the side length, we can use this ratio cubed to find the ratio of the volumes.
The ratio of the corresponding side lengths is 3:11, so the ratio of the volumes is (3/11)^3, which simplifies to 27/1331.
Therefore, the ratio of the volume of the model to the volume of the original is 27:1331.
(c) The ratio of the width of the model to the width of the original can be found directly from the scale factor, since width is one of the corresponding side lengths.
The ratio of the corresponding side lengths is 3:11, so the ratio of the widths is 3:11.
Therefore, the ratio of the width of the model to the width of the original is 3:11.
Overall, the ratios are: surface area  9:121, volume  27:1331, width 3:11.

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a) To verify that the points A(14, 9) and B(7, 16) are on the circle with center C(2, 4) and radius 13, we can use the distance formula:

Distance between point A and C:

d_AC = sqrt[(x_A - x_C)^2 + (y_A - y_C)^2]

    = sqrt[(14 - 2)^2 + (9 - 4)^2]

    = sqrt[144 + 25]

    = sqrt(169)

    = 13

Since the distance between point A and C is equal to the radius of the circle, point A is on the circle.

Distance between point B and C:

d_BC = sqrt[(x_B - x_C)^2 + (y_B - y_C)^2]

    = sqrt[(7 - 2)^2 + (16 - 4)^2]

    = sqrt[25 + 144]

    = sqrt(169)

    = 13

Since the distance between point B and C is equal to the radius of the circle, point B is also on the circle.

Therefore, points A and B are on the circle with center C(2, 4) and radius 13.

b) The midpoint of line segment AB can be found using the midpoint formula:

M = [(x_A + x_B)/2, (y_A + y_B)/2]

 = [(14 + 7)/2, (9 + 16)/2]

 = [10.5, 12.5]

The slope of line segment AB can be found using the slope formula:

m_AB = (y_B - y_A)/(x_B - x_A)

    = (16 - 9)/(7 - 14)

    = -7/-7

    = 1

The slope of a line perpendicular to AB will be the negative reciprocal of m_AB:

m_CM = -1/m_AB

    = -1/1

    = -1

The equation of the line passing through points C(2, 4) and M(10.5, 12.5) can be found using the point-slope form:

y - y_C = m_CM(x - x_C)

y - 4 = -1(x - 2)

y = -x + 6

The slope of line CM is -1, which is the negative reciprocal of the slope of line AB. Therefore, line CM is perpendicular to line AB.

Hence, we have shown that line segment CM is perpendicular to line segment AB.

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The mean monthly rainfall amount for City A is approximately 338.3 inches, and for City B, it is 6 inches.

The mean absolute deviation for City A is approximately 92.8 inches, and for City B, it is 0.5 inches.

The median for City A is 5.5 inches, and for City B, it is 6 inches.

(a) To find the mean monthly rainfall amount for each city, we sum up the rainfall amounts for each city and divide by the number of months.

For City A:

Mean = (5 + 2.5 + 6 + 2008.5 + 5 + 3) / 6 = 2030 / 6 ≈ 338.3 inches per month

For City B:

Mean = (7 + 6 + 5.5 + 6.5 + 5 + 6) / 6 = 36 / 6 = 6 inches per month

So, the mean monthly rainfall amount for City A is approximately 338.3 inches, and for City B, it is 6 inches.

(b) The mean absolute deviation (MAD) is a measure of the average distance between each data point and the mean. To calculate the MAD, we first find the absolute difference between each data point and the mean, sum them up, and then divide by the number of data points.

For City A:

Absolute differences from the mean: |5 - 338.3|, |2.5 - 338.3|, |6 - 338.3|, |2008.5 - 338.3|, |5 - 338.3|, |3 - 338.3|

MAD = (333.3 + 335.8 + 332.3 + 1670.2 + 333.3 + 335.3) / 6 ≈ 557.0 / 6 ≈ 92.8

For City B:

Absolute differences from the mean: |7 - 6|, |6 - 6|, |5.5 - 6|, |6.5 - 6|, |5 - 6|, |6 - 6|

MAD = (1 + 0 + 0.5 + 0.5 + 1 + 0) / 6 ≈ 3 / 6 = 0.5

So, the mean absolute deviation for City A is approximately 92.8 inches, and for City B, it is 0.5 inches.

(c) To find the median, we arrange the rainfall amounts in ascending order and find the middle value. If there are an even number of data points, we take the average of the two middle values.

For City A: {2.5, 3, 5, 5, 6, 2008.5}

Median = (5 + 6) / 2 = 11 / 2 = 5.5 inches

For City B: {5, 5.5, 6, 6, 6.5, 7}

Median = 6 inches

So, the median for City A is 5.5 inches, and for City B, it is 6 inches.

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Loss on disposal of plant assets = $46400 - $32550

Loss on disposal of plant assets = $13850

Date Account titles and Explanation Debit Credit

Jan. 01 Accumulated depreciation-Equipment $81000

Equipment  $81000

June 30 Depreciation expense (1) $4000

Accumulated depreciation-Equipment  $4000

(To record depreciation expense on forklift)  

June 30 Cash $13000

Accumulated depreciation-Equipment (2) $28000

Equipment  $40000

Gain on disposal of plant assets (3)  $1000

(To record sale of forklift)  

Dec. 31 Depreciation expense (4) $5425

Accumulated depreciation-Equipment  $5425

(To record depreciation expense on truck)  

Dec. 31 Accumulated depreciation-Equipment (5) $32550

Loss on disposal of plant assets (6) $13850

Equipment  $46400

(To record sale of truck)  

Calculations :

(1)

Depreciation expense = (Book value - Salvage value) / Useful life

Depreciation expense = ($40000 - $0) / 5 = $8000 per year

So, for half year = $8000 * 6/12 = $4000

(2)

From Jan. 1, 2019 to June 30, 2022 i.e 3.5 years.

Accumulated depreciation = $8000 * 3.5 years = $28000

(3)

Gain on disposal of plant assets = Sale value + Accumulated depreciation - Book value

Gain on disposal of plant assets = $13000 + $28000 - $40000

Gain on disposal of plant assets = $1000

(4)

Depreciation expense = (Book value - Salvage value) / Useful life

Depreciation expense = ($46400 - $3000) / 8

Depreciation expense = $5425 per year

(5)

From Jan. 1, 2017 to Dec. 31, 2022 i.e 6 years.

Accumulated depreciation = $5425 * 6 years = $32550

(6)

Loss on disposal of plant assets = Book value - Accumulated depreciation

Loss on disposal of plant assets = $46400 - $32550

Loss on disposal of plant assets = $13850

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The container could hold an additional 870 mL of broth if it is already holding the 90 mL of broth from the beaker.

To figure out if the chicken broth in the beaker will fit into the rectangular food storage container, we need to compare the volume of the beaker to the volume of the container.

The volume of the beaker can be calculated by multiplying its base area (which is the same as the area of the circle at the bottom of the beaker) by its height. The volume of the container can be calculated by multiplying its length, width, and height.

If the volume of the beaker is less than or equal to the volume of the container, then the chicken broth will fit. If it is greater, then the chicken broth will not fit.

To find out how much more broth the container could hold if it fits, we can subtract the volume of the beaker from the volume of the container.

For example, if the beaker has a diameter of 6 cm and a height of 10 cm, then its volume would be:

V_beaker = πr^2h = π(3^2)(10) = 90π cm^3 = 90 mL

If the rectangular food storage container has dimensions of 12 cm x 8 cm x 10 cm, then its volume would be:

V_container = lwh = 12(8)(10) = 960 cm^3 = 960 mL

Since 90 mL (the volume of the beaker) is less than 960 mL (the volume of the container), the chicken broth will fit in the container. The amount of broth the container can hold in addition to the beaker's contents would be:       960 mL - 90 mL = 870 mL

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The value of f(4) rounded to the nearest tenth is approximately 194.9.

The value of f(4) can be found by substituting x=4 in the given function f(x) = [tex]4e^x[/tex], so we get:

f(4) = [tex]4e^4[/tex]

Using a calculator, we can evaluate this expression as:

f(4) ≈ 194.92

Rounding this to the nearest tenth gives:

f(4) ≈ 194.9

Therefore, the value of f(4) rounded to the nearest tenth is approximately 194.9.

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The inequality which is used to represent normal "temperature-range" for  "human-body", is (d) |t − 98.6| ≤ 1.8.

The "average-temperature" of body is = 98.6° F, and it can vary by 1.8°F.

The inequality |t − 98.6| ≤ 1.8 indicates that the absolute difference between the body temperature and the average temperature is less than or equal to 1.8° F.

This means that the body temperature t can vary within a range of 1.8° F from the average temperature of 98.6° F.

Which means, the temperature cam range from :

⇒ 98.6-1.8 ≤ t ≤ 98.6+1.8,

⇒ 96.8 ≤ t ≤ 100.4;

Therefore, the correct inequality is (d) |t − 98.6| ≤ 1.8.

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The given question is incomplete, the complete question is

The average human body temperature is 98.6° F, but it can vary by as much as 1.8° F. Write an inequality to represent the normal temperature range of the human body, where t represents body temperature.

(a) |t − 1.8| ≥ 98.6

(b) |t − 1.8| ≤ 98.6

(c) |t − 98.6| ≥ 1.8

(d) |t − 98.6| ≤ 1.8

Answer: |t − 98.6| ≤ 1.8

Step-by-step explanation: If takes then takes then takes then takes then takes.

The numbers that are less than 3/7 are 1/8 and 3/10, while the numbers that are greater than 3/7 are 1/2 and 2/3. The decimal 0.102, which is equivalent to 51/500 as a fraction, is also less than 3/7.

To determine which of the given numbers are less than 3/7, we can convert them to fractions and compare them to 3/7.

12.5% is equivalent to 0.125 as a decimal or 1/8 as a fraction. To compare 1/8 and 3/7, we can convert them to a common denominator. The least common multiple of 8 and 7 is 56, so we can rewrite 1/8 as 7/56 and 3/7 as 24/56. Therefore, 1/8 is less than 3/7.

0.3 is equivalent to 3/10 as a fraction. To compare 3/10 and 3/7, we can also convert them to a common denominator. The least common multiple of 10 and 7 is 70, so we can rewrite 3/10 as 21/70 and 3/7 as 30/70. Therefore, 3/10 is less than 3/7.

50% is equivalent to 0.5 as a decimal or 1/2 as a fraction. To compare 1/2 and 3/7, we can convert 3/7 to a fraction with a denominator of 2. Multiplying the numerator and denominator of 3/7 by 2 gives us 6/14. Therefore, 1/2 is greater than 3/7.

2/3 is already a fraction, and we can compare it directly to 3/7. Multiplying the numerator and denominator of 3/7 by 3 gives us 9/21, and we can see that 2/3 is greater than 3/7.

0.102 is a decimal that is less than 1, but it can also be written as a fraction. To do so, we can place the decimal over 1 followed by the appropriate number of zeros. This gives us 102/1000, which can be simplified to 51/500. To compare 51/500 and 3/7, we can convert them to a common denominator. The least common multiple of 500 and 7 is 3500, so we can rewrite 51/500 as 357/3500 and 3/7 as 1500/3500. Therefore, 51/500 is less than 3/7.

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The equation of line passing through the points (8, 6) and (-3, 6) is y = 6. Since the y-coordinate is the same for both points, the line is a horizontal line at y = 6.

To find the equation of the line passing through the points (8, 6) and (-3, 6), we can use the slope-intercept form of a linear equation:

y = mx + b

where m is the slope of the line and b is the y-intercept.

First, we need to find the slope, which is given by

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

where (x1, y1) = (8, 6) and (x2, y2) = (-3, 6)

m = (6 - 6) / (-3 - 8)

m = 0 / -11

m = 0

Since the slope is zero, the line is a horizontal line. We can see from the given points that the line passes through y = 6. Therefore, the equation of the line is

y = 6

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Since t > 0, the time when the particle has a velocity of 20 m/s is approximately t ≈ 4.27 seconds.

A particle has a position function s(t) = t^3 - 4t^2 - 20t + 2 + 20t, t > 0. To find the time when the particle has a velocity of 20 m/s, we first need to find the velocity function by taking the derivative of the position function with respect to time:

v(t) = ds/dt = 3t^2 - 8t - 20.

Now set v(t) equal to 20 and solve for t:

20 = 3t^2 - 8t - 20.

40 = 3t^2 - 8t.

Now solve the quadratic equation for t:

t ≈ 4.27, -3.10.

To find the time when the acceleration is 0, we need to find the acceleration function by taking the derivative of the velocity function with respect to time:

a(t) = dv/dt = 6t - 8.

Now set a(t) equal to 0 and solve for t:

0 = 6t - 8.

t = 8/6 = 4/3.

So, the acceleration is 0 at t = 4/3 seconds.

The variance in acceleration signifies a change in the motion dynamics of the particle. When the acceleration is 0, it indicates that the particle is neither speeding up nor slowing down at that moment, resulting in a constant velocity.

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The results of the survey suggest that the student's claim of three-quarters of 17-year-olds having their driver's licenses may be accurate, but further research would be necessary to confirm this with a larger and more representative sample.

Based on the computer output, there is no convincing evidence that the true proportion of 17-year-olds at this high school with driver's licenses is not 0.75. This is because the P-value of 0.9315 is very large, indicating that the results of the survey are not statistically significant. Additionally, the 95% confidence interval for the sample proportion of 0.755556 includes 0.75, further supporting the claim that the true proportion may be close to 0.75.

It is important to note that the correct significance test was performed, testing the null hypothesis that p = 0.75 against the alternative hypothesis that p ≠ 0.75. This is the appropriate test when the claim being tested is about a specific value of the proportion, as in this case. The alternative hypothesis being p > 0.75 or p < 0.75 would be incorrect, as it assumes a one-sided test rather than a two-sided test.

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