Write the equation in standard form using integers
(no fractions or decimals): = −
2
3
− 1

The indeterminant form to which the L'Hopital's Rule can be applied are 0/0 and ∞/∞ , the correct options are (d) and (f) .

L'Hopital's Rule in calculus is used to evaluate weird limits that result in indeterminate forms that are 0/0, ∞/∞ .  These types of limits

(a) cannot be calculated by direct substitution of limit and/or

(b) can be evaluated but using a very long procedure .

that means if [tex]\lim_{x \to a} \frac{f(x)}{g(x)}[/tex] = 0/0  or ∞/∞ ,

then [tex]\lim_{x \to a} \frac{f(x)}{g(x)} = \lim_{x \to a} \frac{f'(x)}{g'(x)}[/tex]

In the question ,

there are several indeterminant forms given which are  0.∞ ,  [tex]0^{0}[/tex] , [tex]1^{\infty}[/tex] , 0/0 ,  ∞ - ∞ , ∞/∞ ,  ∞⁰  .

By the definition of L'Hopital's Rule , the option that matches with the definition is 0/0 and ∞/∞ ,

So , the correct option is (d) 0/0 and (f) ∞/∞   .

Therefore , The indeterminant form to which the L'Hopital's Rule can be applied are 0/0 and ∞/∞ , the correct options are (d) and (f) .

The given question is incomplete , the complete question is

Select EVERY indeterminate form to which L'Hopital's Rule can be directly applied to (there may be more than one).

(a) 0.∞

(b) [tex]0^{0}[/tex]

(c) [tex]1^{\infty}[/tex]

(d) 0/0

(e) ∞ - ∞

(f) ∞/∞

(g) ∞⁰

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The area of the circular table is 1075.21 square inches.

Jada has a table. The table is circular in shape. She paints the table. The diameter of the circular table is 37 inches. We need to find out the area of the table. We will, first of all, find the radius of the circular table. Let the radius and the area of the table be represented by the variables "r" and "A", respectively.

The radius of a circle is equal to half its diameter.

r = 37/2

r = 18.5 inches

To find the area of the table, we will use the formula for the area of a circle.

A = πr²

A = π(18.5)²

A = 1075.21

Hence, the area of the circular table is 1075.21 square inches.

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As per the given function, the local minimum is 1 and the local maximum is 9 and it can be written as (1, 9)

Local Minimum and maximum

The term Local maxima and minima are the maxima and minima of the function that arises in a particular interval.

Here the Local maxima would be the point in the particular interval for which the values of the function near that point are always less than the value of the function at that point.

Whereas the local minima would be defined as the point where the values of the function near that point are greater than the value of the function at that point.

Given,

Here we have the function f is increasing on the interval (1, 4) and decreasing on the interval (4, 9).

Here we need to determine and explain whether there is a local maximum or local minimum on the interval (1, 9).

According to the definition of the local minimum and local maximum,

While we looking into the given point,

We have identified that the resulting point is

=> (1, 4) => 1 (minimum)

=> (4, 9) => 9 (maximum)

Therefore, the minimum and maximum is (1, 9).

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Using the subtraction, the number of member who only like caava is 12.

In the given question we have to find how many member like caava.

Total member of family = 48

Member who like caava=24

Member who like potato=36

Member who like both caava and potato=12

In the given number of member who like caava having a member who also like potato and some are who only like caava.

So the number of member who only like caava = Total number of member who like caava−Total number of member who like both caava and potato

The number of member who only like caava =24−12

The number of member who only like caava =12

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The length of the side CD of the triangle is 12.686 cm up to 3 significant figures.

We know from the information that

AB = 6cm AC = 12cm

Now we have to calculate the length of DC

From given figure, we have,

In Δ ACB,

CA² = BA² + BC² (By using Pythagoras theorem)

12² = CB²+ 6²

CB² = 12² - 6²

CB² = 144 - 36

CB² = 108

∴ BC = √( 108) cm.

Now consider, in Δ CBD,

as, we know that from trigonometric ratios , sin x = opposite side / hypotenuse

sin 55° = BC / DC

0.81915 = √108 / DC

DC = 10.392 / 0.81915

⇒ DC = 12.68632...

∴ DC ≈ 12.686 cm

Therefore the length of the side DC is approximately 12.686 cm up to 3 significant figures.

Disclaimer: The missing image of the triangle is attached below.

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You could stand at 7 feet and still be completely in the shadow of the tree.

What is the property of a similar triangle?

Two triangles are similar if their corresponding angles are equal and their corresponding sides are within the same ratio (or proportion).

Given

You are standing such that a 63-foot tree is directly between you and the sun.

If you are standing 240 feet away from the tree and the tree casts a 270-foot shadow.

BC to be the height of the tree and DE to be the height of how tall you could be and still be completely in the shadow of the tree.

∠D = ∠B = 90 degrees

Therefore,

By the similar triangle property;

DE/BC = AD/AC

x/63 = (270-240)/270

x/63=30/270=0.11

x=63*0.11 = 7

Hence, you could stand at 7 feet and still be completely in the shadow of the tree.

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Answer: 43/5

Step-by-step explanation: I multiplied the 5 and 8, which gave me 40. Then I added 3 and got 43/5.

The length of the line is 18 units.

If there are two point P( a, b) and Q (c, d) then the distance between P and Q is

d= √ ( c- a)² + ( d- b)²

Given points: ( -10 ,9 ) and ( 5, -1)

So, the distance between these two points

Using Distance formula

d= √ ( c- a)² + ( d- b)²

d = √(5 - (-10))² + (- 1- 9)²

d= √15² + (-10)²

d= √225+ 100

d= 18. 027 units

Hence, the length of the line is 18 units.

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Answer:

The solution to this problem is option (B) - 18 units

Step-by-step explanation:

I took the test and the test told me the answer is 18 so hence, choose option (B) as your answer.

Hope this helped:)

The solid has an estimated volume of 1510.8 cubic yards

The volume of a cylinder is the density of the cylinder which signifies the amount of material it can carry or how much amount of any material can be immersed in it. Cylinder’s volume is given by the formula, πr²h , where r is the radius of the circular base and h is the height of the cylinder.

The volume of the cylinder can be calculated as

v = πr²h

v = π* 10² * 5

v = 500π yd³

Let's calculate the volume of the rectangular figure

v = l * w * h

v = 3 * 4 * 5

v = 60 yd³

We should subtract the volume of the rectangular figure from the volume of cylinder to determine the volume of the solid.

V = 500π - 60

v = 1510.8 yd³

The volume of the solid is calculated as 1510.8 yd³

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Answer:

1,510

Step-by-step explanation:

Answer:

A 0

Step-by-step explanation:

Answer:

36/5

Step-by-step explanation:

32.55

Step-by-step explanation:

21/4×31/5

651/20

Answer:

Albert drove further.

He drove 5 miles further.

Step-by-step explanation:

The formula d = r x t is used to determine distance.

D is distance. R is rate ( in this case miles per hour). T is time.

Tom: D= 50 x 2.5

50 multiplied by 2.5 hours = 125

Tom drove 125 miles.

Albert: D= 65 multiplied by 2 hours = 130

Albert drove 130 miles.

Answer:

16

Step-by-step explanation:

=6(4)-(8)

=24-8

=16

The value of the expression -13+√70 to the nearest tenth is -4.6

Arithmetic operations involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.

The expression -13+√70 comprises of addition of -13 and √70

The value of √70 is 8.4(to the nearest tenth).

Therefore the value of -13+√70

=-13+8.4

= -4.6( nearest tenth)

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The probability of a type I error in the case of the new blood test is 0.022.

Given;

It is not always possible to identify rare diseases by screening. A blood test that has been created by researchers is thought to be reasonably dependable. In 97% of those who suffer from a sickness, it produces a favorable response. However, 5% of those tested who do not have the condition received an incorrectly positive response. Take into account the null hypothesis that "the person does not have the disease."

A: The individual does not have the disease

B: The individual does have the disease

We know that,

Type I Error is rejecting the true null hypothesis

P (Type I Error) = P(Positive reaction to an individual who does not have the disease)

                         =0.022

Hence, the probability of a type I error is 0.022.

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Answer:

h(x) = -1/3 x - 1

Step-by-step explanation:

Solution

h(x) = - f(x)                               This is a given

f(x) = (1/3) x + 1                         Put h(x) on the left. Use a minus sign for f(x)

h(x) =-1((1/3)x + 1)                      Remove the outside brackets.

h(x) = -(1/3) x - 1

The outside brackets make 1/3 x and 1 = to a minus when a minus is put in front of f(x)

Answer:

58 miles

Step-by-step explanation:

              One truck                           second truck

rate               85                                          60

time                t                                              t

Distance      d + 10                                     d -10

d + 10 = 85t                                                d - 10 = 60t

d = 85= -10                                                  d = 60t +10

Set the two equations equal to each other and solve

85t -10 = 60t + 10  Subtract 60t from each side

25t - 10 = 10  Add 10 to each side

25 t = 20  Divide both sides by 25

t = [tex]\frac{4}{5}[/tex]

Each were driving 4/5 of an hour.  Plug into the one of the equaions

d + 10 = 85t

d + 10 = 85([tex]\frac{4}{5}[/tex])

d +10 = 68  Subtract 10 from both sides

d = 58

Answer:

Step-by-step explanation:

Givens

Truck = 85 km/hr

Van = 65 km/hr

t is the time they meet

Note

Truck A is travelling faster, so the place where they meet is closest to Town B.

Solution

Let the distance travelled by the truck be

d/2 + 10

Let the distance travelled by the van be

-d/2 + 10

Let t be the time they meet

85* (d/2 + 10) /t = -60*(d/2 + 10)/t            multiply both sides by t

85*(d/2 + 10)*t/t = -60*(d/2 + 10)*t/t         Combine

85*(d/2 + 10) = -60(d/2 + 10)                    Remove the brackets.

42.5 d + 850 = -30d - 600                      Add 30 d to both sides

72.5d+ 850 = - 600                                 Subtract 850 from both sides.

72.5d = - 600 - 850                                 Combine

72.5d = -1450                                           Divide by 72.5  

d = -1450 / 72.5

d = -20

The minus means that you are looking at it from the van's point of view.

y= -3(-1)+3[slope intercept form]

The value of x in the given figure is x = 71° , the correct option is (c) .

In the question ,

a triangle ABC is given ,

the measure of angle A = 38°

we can see that length of the sides AB and AC is 21 , and we know when the length of two sides of the triangle is equal , it is called as isosceles triangle .

In isosceles triangle , the two angles corresponding to the two equal sides are equal , that means

angle B = angle C = x

In triangle ABC ,

By Angle Sum Property , we get

angle A + angle B + angle C = 180°

38 + x + x = 180

38 + 2x = 180

subtracting 38 from both the sides , we get

2x = 180 - 38

2x = 142

Dividing both sides by 2 , we get

x = 142/2

x = 71

Therefore , The value of x in the given figure is x = 71° .

The given question is incomplete , the complete question is

What is the value of x  ,in the figure given below ? Drawing not to scale

(a) 21°

(b) 42°

(c) 71°

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The percent markup is 11.11%.

There is a department store. The total number of shirts bought by the department store is 400. The total cost of the shirts bought by the department store is $10,800. The department store sells all the shirts for $30 each. We need to find the percent markup.

We first need to find out the cost of each shirt. The cost price of each shirt is the total cost of all the shirts divided by the total number of shirts bought by the department store.

C = $10,800/400

C = $27

Hence, each shirt was purchased for a price equal to $27. To find the markup percentage, we need to find the percentage difference between the cost price and the selling price of the shirt.

M = [(30 - 27)/27]*100%

M = (3/27)*100%

M = 100/9%

M = 11.11%

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The ratio between the fruit and vegetable is 1:3

Ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six. Similarly, the ratio of lemons to oranges is 6:8 and the ratio of oranges to the total amount of fruit is 8:14. The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. Ratios can be classified into two types. One is part to part ratio and the other is part to whole ratio.

We can simply say that a ratio is a fraction of one quantity over another quantity

In this case, we just have to figure the ratio between fruit and vegetables.

In the first column, we have fruit to vegetable as 2:6 = 1:3

In the second column, we have fruit missing. We can make that x.

Using the ratio between fruit and vegetable, when vegetable is 12, the fruit will be 12/3 = 4

The value of fruit in the second column will be 4.

In the third column, we have fruit as 6 and vegetable as y.

We can apply same ratio to get the vegetable which will be 6 * 3 = 18

In the third column, the vegetable is 18

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Answer:

A

Step-by-step explanation:

1. calculate discount

30/100 × 58 = 17.4

2. calculate sell price

58 - 17.4 = 40.6

3. calculate sales tax

7/100 × 40.6 = 2.842

4. calculate total price

sell price + sales tax = 40.6 + 2.842 = 43.442

Answer: 70 dollars in profit

Step-by-step explanation: 20 x 13.50 = 270 20 - 3 = 17 20 x 17 = 340 340 - 270 = 70

Answer:

~201.1[tex]u^2[/tex]

Step-by-step explanation:

Formula for area of a circle:

[tex]\pi r^2[/tex]

The diameter is any straight line that passes through the circle and endpoints lie on the perimeter of the circle.

We are given the diameter: 16. The diameter is twice the radius (for all circles) Divide the diameter, 16 by 2 to get the radius. If the problem gives you the radius, which is a line from the center of the circle, do not divide by 2 and directly plug into formula.

16/2 = 8

Plug into formula.

[tex]\pi r^2[/tex]

[tex]\pi 8^2[/tex]

Using PEMDAS, the standard order of operations order for math, we firsty do 8^2 before multiplying by pi.

8^2 = 8 x 8 = 64

[tex]64*\pi[/tex] = ~201.1

The equation of the blue line in the given graph is y = -x/2 + 2   .

In the question ,

a line graph is given,

we have to find the equation of the blue line .

to find the equation of line , we need at least two points ,

So , from the graph we can see that the two points from where the blue line passes the graph are (4,0)  and (0,2) .

the slope = (2-0)/(0-4)

m = 2/(-4)

m = -1/2

So , the equation of the line passing from the points (4,0) with slope -1/2 , is

(y - y₁) = m(x - x₁)

y - 0 = (-1/2)(x - 4)

y = -x/2 + 2

Therefore , The equation of the blue line in the given graph is y = -x/2 + 2   .

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Z score of a 3rd grader who is 47 inches tall with mean of 52 inches and standard deviation of 2.5 inches is  2

Z- Score give an idea how far a data point is from mean .

z = x- μ / σ where numerator is difference between the random variable and the actual mean dividing by the standard deviation .

Given , x = 47 inches

standard deviation = 2.5 inches

mean = 52 inches

z-score = x- μ / σ

putting all the values ,

z-score = 47 - 52 / 2.5

= -5 / 2.5

= -2

|Z| = 2

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