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If x is between two consecutive integers such that n ≤ x < n + 1, then the greatest integer function [x] maps x to the largest integer smaller than x so that [x] = n.

(i) If x is approaching -2 from above, that means x > -2. As x gets closer to -2, we essentially have -2 < x < -1, so that [x] will approach

[tex]\displaystyle \lim_{x\to-2^+} [x] = \boxed{-2}[/tex]

(ii) However, if x is approaching -2 from below, then x < -2, so that [x] = -3. In other words

[tex]\displaystyle \lim_{x\to-2^-} [x] = -3 \neq -2[/tex]

Because the one-sided limits do not match, the two-sided limit

[tex]\displaystyle \lim_{x\to-2} [x] ~~\boxed{\text{does not exist}}[/tex]

(iii) -2.4 lies between -3 and -2, so

[tex]\displaystyle \lim_{x\to-2.4} [x] = \boxed{-3}[/tex]

Explanation:

There are 8 red marbles out of 22 total

8/22 = 4/11 is the probablity of randomly selecting red.

If the first marble is put back, then that probability will not change.

The probability of two red marbles in a row is (4/11)*(4/11) = 16/121

Side note: 16/121 = 0.1322 = 13.22% approximately

The probability of exactly 3 of the containers being defective is given as 0.1468

We have to set p as the  probability of container being non- defective

We have p as the  probability of container being defective 50 - 10 = 40

p = 40/50

= 0.8

q = 10/50

= 0.2

P(3) = 8c3 * 0.2² * 0.8⁵

= 0.1468

Hence the probability that the container has exactly 3 defective containers is 0.1468

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Answer:

P(not A) = 8/9

Step-by-step explanation:

To write a simple probability, write a fraction. The bottom is all the possibilities, here there are 9. So put a 9 on the bottom. Then on top write how many ways the event can happen. There are 8 ways you can land on "Not A" (that is: B, C, D, E, F, G, H, I) So 8 goes on top. Simplify if possible. 8/9 cannot be simplified.

P(not A) = 8/9

As per the probability of an event, the value of P(not A) is 8/9.

The probability of an event is the chance of happening that particular event.

Given, total number of events in the sample space = 9.

Number of favorable events in that sample space is = 1.

Therefore, the probability P(A) = 1/9.

Now,  P(not A)

= 1 - P(A)

= 1 - 1/9

= 8/9

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Answer:

shippng charge = 60 dollars

Step-by-step explanation:

5%   is .05 in decimal form

.05 x 1200 = 60 dollars

The amount of money Sarah have left written as an expression is 55 - 3m

The amount of money Sarah have left = Amount Sarah received for her birthday - (Number of shirts bought × Cost of each shirt)

= 55 - (3 × m)

= 55 - 3m

The complete question:

Sarah received $55 dollar sign,for her birthday. She used some of that money to buy 3 shirts priced at m dollars each. How much money does Sarah have left? Write your answer as an expression.

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Answer:

Negative correlation

Step-by-step explanation:

You can draw a line of best fit the would go downhill from left to right which would be a negative slope. This means it has a negative correlation.

Answer:

1) Arithmetic since it decreases by 3 so, -3n + 38.

2) Arithmetic since it decreases by 20 each time, so -20n+17

Step-by-step explanation:

Answer:

[tex]A=41\pi\: \text{units}^2\approxA\approx128.8053\:\text{units}^2[/tex]

Step-by-step explanation:

I assume you mean [tex]r=3+8\sin\theta[/tex]:

Use the formula [tex]\displaystyle A=\int\limits^a_b \frac{1}{2} {r(\theta)^2} \, d\theta[/tex] where [tex]a[/tex] and [tex]b[/tex] are the lower and upper bounds and [tex]r(\theta)[/tex] is the equation of the polar curve.

Since the graph is symmetrical about the line [tex]\displaystyle \theta=\frac{\pi}{2}[/tex], let the bounds of integration be [tex]\displaystyle \biggr(-\frac{\pi}{2},\frac{\pi}{2}\biggr)[/tex] to find half the area of the curve, and then find twice of that area:

[tex]\displaystyle A=\int\limits^a_b \frac{1}{2} {r(\theta)^2} \, d\theta\\\\A=2\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \frac{1}{2} {(3+8\sin\theta)^2} \, d\theta\\\\A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} 9+48\sin\theta+64\sin^2\theta \, d\theta\\\\A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} 9+48\sin\theta+64\biggr(\frac{1-\cos2\theta}{2} \biggr) \, d\theta\\\\\\A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} (9+48\sin\theta+32-32\cos2\theta) \, d\theta[/tex]

[tex]\displaystyle A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} (41+48\sin\theta-32\cos2\theta) \, d\theta\\\\A=41\theta-48\cos\theta-16\sin2\theta\biggr|^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\\\\[/tex]

[tex]A=\biggr[41\biggr(\frac{\pi}{2}\biggr)-48\cos\biggr(\frac{\pi}{2}\biggr)-16\sin2\biggr(\frac{\pi}{2}\biggr)\biggr]-\biggr[41\biggr(-\frac{\pi}{2}\biggr)-48\cos\biggr(-\frac{\pi}{2}\biggr)-16\sin2\biggr(-\frac{\pi}{2}\biggr)\biggr]\\\\A=\biggr[\frac{41\pi}{2}-24\sqrt{2}\biggr]-\biggr[-\frac{41\pi}{2}+24\sqrt{2}\biggr]\\ \\A=41\pi\\\\A\approx128.8053[/tex]

Thus, the area of the curve is 41π square units. See below for a graph of the curve and its shaded area.

Answer:

30

Step-by-step explanation:

gave 15 to his friend 30-15=15 his mom bought mom 60 candies so 30

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

Explanation:

The point (9,8) is in the original set of ordered pairs.

We cannot include (9,-8) since x = 9 is already listed. We can't have repeated x values. If x repeats, then we don't have a function.

This rules out choice A.

Choices B and D are eliminated for similar reasoning.

Choice C can be included because x = -9 hasn't been mentioned yet.

Note: A function is when any given x value leads to exactly one y value.

Answer:

6.42 %

Step-by-step explanation:

Formula    FV = PV ( 1 + i)^n        i = periodic interest in decimal

                                                 FV = future value    PV = present value

                                                    n = periods ( years in this case)

3412.23 = 2500 ( 1 + i)^5

3412.23/2500  = (1+i)^5

1.364892 = (1+i)^5

1.0641 = 1+ i

i = .0642      or    6.42 %

Answer:

please write question with full info

Answer:

78 sq. units

Step-by-step explanation:

1/2 × (7+19) × 6 = 78

The probability that both I and my best friend get the 100 classroom credits is 0.06%.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Since Mr Q's class is having a give-away where his students can receive 100 classroom credits, he will pull names out of a hat and select two winners, and once a student wins, they are not eligible to win a second time, if there are 40 total people in the class, including me and my best friend, to determine what is the probability that both I and my best friend get the 100 classroom credits, the following calculation must be performed:

I = 1/40 = 0.025

my best friend = 1/39 = 0.02564

0.02564 x 0.025 = X

0.0006410 = X

X x 100 = 0.064

Therefore, the probability that both I and my best friends get the 100 classroom credits is 0.06%.

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Answer:

$ 10 021 . 65

Step-by-step explanation:

The equation for continuous compounding is   e^(i * t)

   where i = decimal yearly  interest      t = years

   FV  = 5500 e^(.12 * 5) = 10 021 .65

Answer:

[tex]3\times8=24[/tex]

Step-by-step explanation:

Notice that the shaded figure has a width of 3 cm and a length of 8 cm. The area of the rectangle is equal to the product of the width and length, so [tex]8\:\text{cm}\times3\:\text{cm}=24\:\text{cm}^2[/tex] would be the area of the shaded figure.

The arc length of the circle will be equal to 5.89 units.

The length of the curve on the circumference of the circle making an angle with the centre is called the length of the arc of the circle.

Given that:-

The length of the arc will be calculated as:-

Arc  =  Angle  x  radius

Arc  =  ( 3π / 4  )  x  2.5

Arc  =   5.89 units.

Therefore the arc length of the circle will be equal to 5.89 units.

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Answer:

290 in^2.

Step-by-step explanation:

Adding all the areas of rectangles:

= 11*8 + 11*3 + 11*8 + 11*3 + 3*8 + 3*8

= 290 in^2.

Answer:

B)  290 in²

Step-by-step explanation:

Area of a rectangle = length × width

⇒ SA of the net = 2(11 × 8) + 2(11 × 3) + 2(8 ×3)

                           = 176 + 66 + 48

                           = 290 in²

Answer:

radius r = 1.41047396 m

base circumference C = 8.86226925 m

volume V = 5.87697483 m^3

curved surface area A = 12.5 m^2

base surface area B = 6.25 m^2

total surface area K = 18.75 m^2

base circumference C = 2.82094792 π m

volume V = 1.87069919 π m3

curved surface area A = 3.97887358 π m^2

base surface area B = 1.98943679 π m^2

total surface area K = 5.96831037 π m

Step-by-step explanation:

V = (2/3)πr^3

C = 2πr

A = 2πr^2

B = πr^2

K = (2πr^2) + (πr^2) = 3πr^2

Answer:

Approximately 6.4 ft³

Step-by-step explanation:

A *hemisphere* is half of a sphere. As far as surface area goes, we not only need to account for the curved area, but also the area of the circular disc at the bottom. The area of the curved region is going to be half the area of the whole sphere. Since a sphere with radius r has a surface area of 4πr², the curved part of the hemisphere must have half that, or 2πr². Add in the area of the circular disc, πr², and we have a total area of 3πr². Setting this equal to the given area of 12.5 ft², we can solve for r:

[tex]3\pi r^2=12.5\\r^2=12.5/3\pi\\\\r=\sqrt{12.5/3\pi}[/tex]

Now, using the formula for the volume of a sphere, [tex]V=(4/3)\pi r^3[/tex], we can substitute our new value for r and solve:

[tex]V=(4/3)\pi r^3\\=(4/3)\pi(\sqrt{12.5/3\pi})^3\\\approx 6.4[/tex]

Answer:

46,145 yards

Step-by-step explanation:

convert miles to yards then add

Answer:

False

Ab is not perpendicular bisector to bc

Answer:

[tex]volume \: of \: triangular \: prism = \frac{1}{2} \times b \times h \times h \\ = \frac{1}{2} \times 8 \times 12 \times 9 \\ = 432m {}^{3} [/tex]

Answer:

(c) x = 15.26

Step-by-step explanation:

a² + b² = c²

8² + 13² = c²

64 + 169 = c²

c² = 233

c = 233 ½

c = 15.26

Answer:

87.36 ft.

Step-by-step explanation:

Angle of depression : 41°

Length of shadow : 76 ft.

Taking the tan ratio (let the height of the tree be 'h') :

tan 41° = 76/h

0.87 = 76/h

h = 76/0.87

h = 87.36 ft.

Answer:

the height of the tree = 87.4 ft (Rounded to the tenths place)

Step-by-step explanation:

the tree form a right angle with the ground

Then , we have a right triangle .

let H be the height of the tree.

[tex]\tan 41=\frac{76}{H}[/tex]

[tex]\Longrightarrow H = \frac{76}{\tan(41)} = 87.427998948797[/tex]