Plz I need help this is due at 7:10 and I wasn’t paying attention in class.
Answer:
253cm²
Step-by-step explanation:
Area of the trapezoid = 1/2(b1+b2)*h
Given
h = 22cm
b1 = 10.5cm
b2 = 12.5cm
Substitute
Area of the trapezoid = 1/2(10.5+12.5)*22
Area of the trapezoid = 1/2(23)*22
Area of the trapezoid =11*23
Area of the trapezoid = 253cm²
Hence the area of the trapezoid is 253cm²
The phone lines to an airline reservation system are occupied 61% of the time. Assume that the events that the lines are occupied on successive calls are independent. If 11 calls are placed, what is the probability that the lines are occupied for exactly 5 calls
Answer:
0.1373 = 13.73% probability that the lines are occupied for exactly 5 calls
Step-by-step explanation:
For each call, there are only two possible outcomes. Either the lines are occupied, or they are not. The events that the lines are occupied on successive calls are independent. This means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The phone lines to an airline reservation system are occupied 61% of the time.
This means that [tex]p = 0.61[/tex]
If 11 calls are placed, what is the probability that the lines are occupied for exactly 5 calls
This is P(X = 5) when n = 11. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{11,5}.(0.61)^{5}.(0.39)^{6} = 0.1373[/tex]
0.1373 = 13.73% probability that the lines are occupied for exactly 5 calls
fill 1 ⅕ bottles with 3 liters of water. How many liters of water fill 1 bottle?
Answer: It would be 2 1/2 liters
Step-by-step explanation:
There can be 2 and a half litres of water will be filled in 1 bottle.
What is division?Division is breaking a number up into an equal number of parts.
Given that, 3 litres of water can fill 1 ⅕ bottles,
Since, there are 3 litres in 6/5 bottles
so, 1 litre = 6/5×3 = 2 ¹/₂
Hence, There can be 2 and a half litres of water will be filled in 1 bottle.
For more references on division, click;
https://brainly.com/question/21416852
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a. Define a relation with four ordered pairs
such that the first element is a university
and the second element is its mascot.
Pls help I’ll mark brainliest
Answer:
2=72 4=148 6=222 10=370 15=555 16=592
sorry about the second part i didnt see it
Answer:
148, 3 , 740, 1110, 8.
Step-by-step explanation:
Miles: 148 + 740 + 1,110 = 1,998
Gallons: 2 + 4 + 3 + 10 + 15 + 8 = 42
For the geometric sequence, find the sum of the specified number of terms.
The first 8 terms of 4, -12, 36, ...
S8=
Given:
The geometric sequence is
[tex]4, -12, 36,...[/tex]
To find:
The sum of first 8 terms of the given geometric sequence.
Solution:
We have,
[tex]4, -12, 36,...[/tex]
Here, the first term is 4 and the common ratio is
[tex]r=\dfrac{-12}{4}[/tex]
[tex]r=-3[/tex]
The sum of first n terms of a geometric sequence is
[tex]S_n=\dfrac{a(r^n-1)}{r-1}[/tex]
Where, a is the first term and r is the common ratio.
Putting n=8, a=4 and r=-3, we get
[tex]S_8=\dfrac{4((-3)^8-1)}{-3-1}[/tex]
[tex]S_8=\dfrac{4(6561-1)}{-4}[/tex]
[tex]S_8=-6560[/tex]
Therefore, the sum of first 8 terms is -6560.
A white-tailed deer is running from a black bear at 20 miles per hour. It is 1/3 miles in front of the bear. The bear is running at 30 miles per hour. How many minutes will it take the bear to catch the deer? Assume both continue running at a constant pace.
Answer:
Step-by-step explanation:
d=20t+1/3, b=30t
20t+1/3=30t
10t=1/3
t=1/30 hr
t=(1/30)60=2 min
At Davidson's Bike Rentals, it costs $41 to rent a bike for 8 hours. How many hours of bike use does a customer get per dollar?
Answer:
0.192 hour
Step-by-step explanation:
41$ / 8 = 0.192 hours = 11.703 minutes
How do I evaluate this using trigonometric substitution?
∫dx/(81x^2+4)^2
Answer:
[tex]\displaystyle \frac{1}{144}arctan(\frac{9x}{2}) + \frac{x}{8(81x^2 + 4)} + C[/tex]
General Formulas and Concepts:
Alg I
Terms/CoefficientsFactorExponential Rule [Dividing]: [tex]\displaystyle \frac{b^m}{b^n} = b^{m - n}[/tex]Pre-Calc
[Right Triangle Only] Pythagorean Theorem: a² + b² = c²
a is a legb is a legc is hypotenuseTrigonometric Ratio: [tex]\displaystyle sec(\theta) = \frac{1}{cos(\theta)}[/tex]
Trigonometric Identity: [tex]\displaystyle tan^2\theta + 1 = sec^2\theta[/tex]
TI: [tex]\displaystyle sin(2x) = 2sin(x)cos(x)[/tex]
TI: [tex]\displaystyle cos^2(\theta) = \frac{cos(2x) + 1}{2}[/tex]
Calc
Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
IP [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
U-Substitution
U-Trig Substitution: x² + a² → x = atanθ
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \int {\frac{dx}{(81x^2 + 4)^2}}[/tex]
Step 2: Identify Sub Variables Pt.1
Rewrite integral [factor expression]:
[tex]\displaystyle \int {\frac{dx}{[(9x)^2 + 4]^2}}[/tex]
Identify u-trig sub:
[tex]\displaystyle x = atan\theta\\9x = 2tan\theta \rightarrow x = \frac{2}{9}tan\theta\\dx = \frac{2}{9}sec^2\theta d\theta[/tex]
Later, back-sub θ (integrate w/ respect to x):
[tex]\displaystyle tan\theta = \frac{9x}{2} \rightarrow \theta = arctan(\frac{9x}{2})[/tex]
Step 3: Integrate Pt.1
[Int] Sub u-trig variables: [tex]\displaystyle \int {\frac{\frac{2}{9}sec^2\theta}{[(2tan\theta)^2 + 4]^2}} \ d\theta[/tex][Int] Rewrite [Int Prop - MC]: [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{[(2tan\theta)^2 + 4]^2}} \ d\theta[/tex][Int] Evaluate exponents: [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{[4tan^2\theta + 4]^2}} \ d\theta[/tex][Int] Factor: [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{[4(tan^2\theta + 1)]^2}} \ d\theta[/tex][Int] Rewrite [TI]: [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{[4sec^2\theta]^2}} \ d\theta[/tex][Int] Evaluate exponents: [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{16sec^4\theta} \ d\theta[/tex][Int] Rewrite [Int Prop - MC]: [tex]\displaystyle \frac{1}{72} \int {\frac{sec^2\theta}{sec^4\theta} \ d\theta[/tex][Int] Divide [ER - D]: [tex]\displaystyle \frac{1}{72} \int {\frac{1}{sec^2\theta} \ d\theta[/tex][Int] Rewrite [TR]: [tex]\displaystyle \frac{1}{72} \int {cos^2\theta} \ d\theta[/tex][Int] Rewrite [TI]: [tex]\displaystyle \frac{1}{72} \int {\frac{cos(2\theta) + 1}{2}} \ d\theta[/tex][Int] Rewrite [Int Prop - MC]: [tex]\displaystyle \frac{1}{144} \int {cos(2\theta) + 1} \ d\theta[/tex][Int] Rewrite [Int Prop - A/S]: [tex]\displaystyle \frac{1}{144} [\int {cos(2\theta) \ d\theta + \int {1} \ d\theta][/tex]Step 4: Identify Sub Variables Pt.2
Determine u-sub for trig int:
u = 2θ
du = 2dθ
Step 5: Integrate Pt.2
[Ints] Rewrite [Int Prop - MC]: [tex]\displaystyle \frac{1}{144} [\frac{1}{2} \int {2cos(2\theta) \ d\theta + \int {1 \theta ^0} \ d\theta][/tex][Int] U-Sub: [tex]\displaystyle \frac{1}{144} [\frac{1}{2} \int {cos(u) \ du + \int {1 \theta ^0} \ d\theta][/tex][Ints] Integrate [Trig/Int Rule - RPR]: [tex]\displaystyle \frac{1}{144} [\frac{1}{2} sin(u) + \theta + C][/tex][Expression] Back Sub: [tex]\displaystyle \frac{1}{144} [\frac{1}{2} sin(2 \theta) + arctan(\frac{9x}{2}) + C][/tex][Exp] Rewrite [TI]: [tex]\displaystyle \frac{1}{144} [\frac{1}{2}(2sin(\theta)cos(\theta)) + arctan(\frac{9x}{2}) + C][/tex][Exp] Multiply: [tex]\displaystyle \frac{1}{144} [sin(\theta)cos(\theta) + arctan(\frac{9x}{2}) + C][/tex][Exp] Back Sub: [tex]\displaystyle \frac{1}{144} [sin(arctan(\frac{9x}{2}))cos(arctan(\frac{9x}{2})) + arctan(\frac{9x}{2}) + C][/tex]Step 6: Triangle
Find trig values:
[tex]\displaystyle tan\theta = \frac{9x}{2}[/tex]
[tex]\displaystyle \theta = arctan(\frac{9x}{2})[/tex]
tanθ = opposite / adjacent; solve hypotenuse of right triangle, determine trig ratios:
sinθ = opposite / hypotenuse
cosθ = adjacent / hypotenuse
Leg a = 2
Leg b = 9x
Leg c = ?
Sub variables [PT]: [tex]\displaystyle 2^2 + (9x)^2 = c^2[/tex]Evaluate exponents: [tex]\displaystyle 4 + 81x^2 = c^2[/tex][Equality Property] Square root both sides: [tex]\displaystyle \sqrt{4 + 81x^2} = c[/tex]Rewrite: [tex]c = \sqrt{81x^2 + 4}[/tex]Substitute into trig ratios:
[tex]\displaystyle sin\theta = \frac{9x}{\sqrt{81x^2 + 4}}[/tex]
[tex]\displaystyle cos\theta = \frac{2}{\sqrt{81x^2 + 4}}[/tex]
Step 7: Integrate Pt.3
[Exp] Sub variables [TR]: [tex]\displaystyle \frac{1}{144} [\frac{9x}{\sqrt{81x^2 + 4}} \cdot \frac{2}{\sqrt{81x^2 + 4}} + arctan(\frac{9x}{2}) + C][/tex][Exp] Multiply: [tex]\displaystyle \frac{1}{144} [\frac{18x}{81x^2 + 4} + arctan(\frac{9x}{2}) + C][/tex][Exp] Distribute: [tex]\displaystyle \frac{1}{144}arctan(\frac{9x}{2}) + \frac{x}{8(81x^2 + 4)} + C[/tex]PLS HELP!!!! :))) BDHDHSJWJDJD
Answer:
Your answer is "H"
Step-by-step explanation:
A submarine descended 3/4 of a kilometer in 1/4 of an hour. What was the submarine's rate of descent?
GEOMETRY PLZZZZZ HELPPPPP
Answer:
(x,y) becomes (-y,x) so (3,2) would become (-2,3)
78.84 is what percent of 292?
Pleasee
Answer:
230.2128. Im pretty sure
Step-by-step explanation:
Answer:
27%
Step-by-step explanation:
Please answer ASAP!
Which proportional relationship has the greatest rate of change?
Answer:
Option (1) ; y = 7x
Step-by-step explanation:
(1) reads y = 7x, a line with slope 7, therefore the rate of change in this is 7
(2) says that y increases 12 units every time that x increases 4 Then the rate of change is: (increase in y / increase in x = 12/4 =3
(3) shows a table from which we can see that an increase of y in 8 corresponds to an increase of x in 2: rate of change = (8 - 0) , (2 - 0) = 4
(4) shos a line with slope (rate of change) given by: (12 - 0) / (2 - 0) = 12/2 = 6
Therefore, the greatest rate of change is shown by the first expression
y = 7 x
I Need Help Giving Out 10 points! Plz Help
Answer:
b and d
Step-by-step explanation:
5×2 to the power of five
Answer:
5x2^5 is 160
Step-by-step explanation:
Answer:
160
Step-by-step explanation:
2^5 is 32. 32 x 5 is 260.
Hope it helps!
Multiplying by which number is equivalent to a decrease of 8.2%?
Tyler has $125.00 to spend on books and CDs. He buys one book for $30.00. He wants to spend the rest on CDs that are on sale for $9.00 each. Which of these statements is true?
Group of answer choices
He can't buy any CDs.
He can buy 11 CDs.
He can buy 10 CDs.
He can buy more than 11 CDs.
Answer:
He can buy 10 cds
Step-by-step explanation:
125-30=95
95 divided by 9 = 10.5555555556
An order of tissues was shipped in 20 cube shaped boxes, each in the shape of a cube, measuring 4 inches in each dimension. How many cubic inches of tissues are in a shipment?
Answer:
1,280in cubes
Step-by-step explanation:
For one box it would be 4 x 4 x 4=64. Then for 20 boxes it would be 64 x 20= 1,280 cubic inches.
The value, y, in dollars of an autographed basketball after x years can be represented by the function y=4000(1.05)x.
What is the value of the basketball after 5 years to the nearest dollar?
Answer:
I took the test!!
Step-by-step explanation:
Pit this in your calculator exactly like this 4,000(1.05)^5 and you get the answer 5,105.12625. So round your answer to the nearest dollar, which is 5,105.
I ate water by drinking it how?
Answer:
There's no concern that water will dilute the digestive juices or interfere with digestion. In fact, drinking water during or after a meal actually aids digestion. Water is essential for good health. Water and other liquids help break down food so that your body can absorb the nutrients.
Answer:
chewing on it or by ice
Step-by-step explanation:
Find c.
Round to the nearest tenth:
a
10 cm
1509
12°
с
c = [? ]cm
Law of Sines: sin A
sin B.
b
sin C
С
a
Enter
9514 1404 393
Answer:
14.9 cm
Step-by-step explanation:
To find c using the Law of Sines, you must know angle C. That is found from ...
C = 180° -A -B = 180° -150° -12° = 18°
Then the law of sines tells you ...
c/sin(C) = b/sin(B)
c = b·sin(C)/sin(B) = (10 cm)·sin(18°)/sin(12°)
c ≈ 14.9 cm
How many grams of aluminum hydroxide are produced when 8 moles of aluminum sulfite react in excess sodium hydroxide ?
Answer:
Number of moles Aluminium sulfide
1 mole of sulfide contains 150 g
Therefore; 16.2/150
= 0.108 moles
The mole ratio of Al2S3 : Al(OH)3 is 1:2
Therefore; moles of Aluminium hydroxide will be;
= (0.108 × 2)
= 0.216 moles
But, 1 mole of Al(OH)3 contains 77 g
Therefore, the mass of aluminium hydroxide is
0.216 moles × 77
= 16.632 g
Step-by-step explanation:
Two points are given from each of two lines L1 and L2. Without graphing the points, determine if the lines are perpendicular, Parallel, or neither.
Answer:
the lines are neither
Step-by-step explanation:
Math please help ASAP
Answer:
11
Step-by-step explanation:
i don't know
Nellie's office had already recycled 1 kilogram this year before starting the new recycling
plan, and the new plan will have the office recycling 1 kilogram of paper each week. How
many weeks will it take Nellie's office to recycle a total of 50 kilograms of paper?
weeks
Submit
+
Answer:
50/1= 50 weeks
Step-by-step explanation:
Please hurry; Rajiv bought a rare stamp for $125. A function that models the value of Rajiv’s after t years is v(t) = 125 (1.05)t . What is the value of Rajiv’s stamp after 20 years?
a $131.25
b $331.66
c $2,625.00
d $3316.62
Answer:
C.
Step-by-step explanation:
5 × 3/2, but the answer as a fraction
Answer:
15/2
Step-by-step explanation:
5/1 * 3/2 = 15/2
Find the absolute value of each of the following numbers.
2.54
17.65
14.2
90.44
12
A model maker wants to make a model of a
ship
He will use a scale of 1:50
The ship was 100ft long
1 foot = 0.3 m
How long will the ship be in cm?
9514 1404 393
Answer:
60 cm
Step-by-step explanation:
The model ship will be x feet long, where ...
x/100 = 1/50
x = 100/50 = 2
In meters, that is ...
2(0.3 m) = 0.6 m
A meter is 100 cm, so the length in centimeters is ...
(0.6)(100 cm) = 60 cm