Answers
[tex]\text{Area of the trapezoid}= \left(\dfrac{AD+BC}2\right)CK\\\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=\left( \dfrac{10+8}2\right) \times 30 \\\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=\dfrac{18}2 \times 30\\\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=9 \times 30\\\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=270~~ \text{sq units.}[/tex]
Related Questions
A professor has learned that three students in his class of 20 will cheat on the final exam. He decides to focus his attention on four randomly chosen students during the exam. What is the probability that he finds at least one of the students cheating
Answers
Answer:
6%
Step-by-step explanation:
3/20=4/x
It is a indirect proportion so we reciprocal,
Then,
3/20=x/40
3×40=20×x
120=20x
x=120/20
x=6
The required probability for the given case is 0.4779.
How to find probability using binomial distribution?The binomial distribution is based on the binomial theorem which can be written as (a + b)ⁿ = ⁿC₀aⁿb⁰ + ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b²+ ....+ ⁿCₙa₀bⁿ.
In order to use in the probability, there should be events independent of each other and the sum of there probabilities is 1.
Given that,
The total number of students are 20.
And, the probability that a student cheats is 3/20 = 0.15.
The number of students chosen by the teacher is 4.
Thus, the probability that at least one student cheats can be found by binomial distribution as,
P(at least one student cheats) = ⁴C₁(0.15)¹(0.85)³ + ⁴C₂(0.15)²(0.85)² + ⁴C₃(0.15)³(0.85)¹ + ⁴C₄(0.15)⁴(0.85)⁰
= 4 × 0.15 × 0.6141 + 6 × 0.0225 × 0.7225 + 4 × 0.003375 × 0.85 + 1 × 0.00050625
= 0.4779
Hence, the probability that at least one student selected by the teacher does cheating is 0.4779.
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Twenty years ago a small town in Texas had a population of 10,000. The population has increased 8% each year
since then. Predict what the population of the town will be in 10 more years.
a. In 10 more years the population of this town will be approximately 21,589
b.
In 10 more years the population of this town will be approximately 100,626
c. In 10 more years the population of this town will be approximately 123,794
d. In 10 more years the population of this town will be approximately 81,966
Please select the best answer from the choices provided
Answers
Answer:
A
Step-by-step explanation:
8% = .08 in decimal form
10 000 ( 1 + .08)^10 =
Solve for x. Your answer must be simplified
x/7 ≥ -6??
Answers
X>_42
Explanation:
When an oil tank is full, it contains 5¼ gallons. How many gallons does it hold when full?
Answers
What is the missing angle
Answers
[tex]Answer ☘️[/tex]
★ Important points to know
[tex] {\boxed{ \bold{Exterior \: Angle \: Theorem : - }}}[/tex]
The exterior angle of a triangle is equal to the sum of the two opposite interior angles.[tex] \pink{ ↪ \sf \angle \: C + \angle \: D = \angle \: B}[/tex]★ Let's solve :-
[tex] \sf ↪\angle \: 65 \degree + \angle \: 30 \degree =\angle \:B\\ \\ \sf ↪\angle \: 95 \degree = \angle \:B[/tex]
Hence option A 95⁰ is the right ans ✓
[tex]\sf{\:мѕнαcкεя\: ♪...}[/tex]
[tex]\sf\large \green{\underbrace{\red{Answer⋆}}}:[/tex]
To find :-
The angle ∠ABC = ?
Given :-
∠BCD = 65°
∠BDC = 30°
Solution :-
Firstly we have to find ∠CBD, with the help of ∠CBD, we will able to find ∠ABC.
To find ∠CBD, we will use angle sum formula
(=> The sum of angles of all 3 sides of triangle is equal to 180°).
∠CBD + ∠BCD + ∠BDC = 180° (angle sum property)
∠CBD + 65° + 30° = 180°
∠CBD + 95° = 180°
∠CBD = 180° - 95°
∠CBD = 85°
Now we have ∠CBD, and in the diagram ∠CBD and ∠ABD lies on the same line but it is seperated by line BC, it means they are linear pair and the sum of both angles (∠CBD and ∠ABC) is equal to 180°.
∠ABC + ∠CBD = 180° (linear pair)
∠ABC + 85° = 180°
∠ABC = 180° - 85°
∠ABC = 95°
Result :-
The ∠ABC is 95° by using the above method.
Choose the first option
(A) 95°
Solve each exponential equation. round your answer to two decimal places.
4a. 4²x +3=1
4b. ex-1 -5 = 5
Answers
4a.4²x +3=1
Slotuion:
4²x + 3=1 : x= -⅛ (Decimal:x= -0.125)
Steps
4² x +3=1
4²=16
16x + 3=1
Subract 3 from borh sides
16x +3-3=1-3
Simplify
16x=-2
Divides both sides by 16
[tex] \frac{16 \times }{16} =
[tex] \frac{ - 2}{16} [/tex]
[/tex]
Simplitfy
[tex] \frac{16 \times }{16} : x[/tex]
Simplify
[tex] \frac{ - 2}{16}: -⅛ [/tex]
x = -⅛
therefore the answer is x= -⅛
4b.ex-1 -5 =5
x~=3.30258
explanation:
e^(x-1)-5=5
e^(x-1)=10
x-1=ln 10
x-1~=2.30258
x~=3.30258
[tex] \large \pink{ \overbrace{ \underbrace{ \tt{ \color{red}{ \: \: \: \: \: \: \: hope \: it \: help \: you \: \: \: \: \: \: \: \: }}}}}[/tex]
You have writing errors may be
[tex]\\ \rm\Rrightarrow 4x²+3=1[/tex]
[tex]\\ \rm\Rrightarrow 4x²=1-3[/tex]
[tex]\\ \rm\Rrightarrow 4x²=-2[/tex]
[tex]\\ \rm\Rrightarrow x^2=-1/2[/tex]
[tex]\\ \rm\Rrightarrow logx²=-log0.5[/tex]
[tex]\\ \rm\Rrightarrow 2logx=-log0.5[/tex]
[tex]\\ \rm\Rrightarrow logx=0.15[/tex]
[tex]\\ \rm\Rrightarrow x=10^{0.15}[/tex]
[tex]\\ \rm\Rrightarrow x=1.412[/tex]
#2
[tex]\\ \rm\Rrightarrow e^{x-1}-5=5[/tex]
[tex]\\ \rm\Rrightarrow e^{x-1}=10[/tex]
[tex]\\ \rm\Rrightarrow x-1=ln10[/tex]
[tex]\\ \rm\Rrightarrow x-1=2.3[/tex]
[tex]\\ \rm\Rrightarrow x=2.3+1[/tex]
[tex]\\ \rm\Rrightarrow x=3.3[/tex]
Identify the type of circuit that has one path for electricity to travel through.
A:single circuit
B:parallel circuit
C:complex circuit
D:series circuit
Answers
Describe the transformation that maps the pre-image (ΔA) to the image (ΔA').
Answers
Step-by-step explanation:
90 degrees rotation, clockwise
Alogger runs 1 1/2 miles 3
times each week and 2 1/2
miles 4 dimes each week
What is the total distance
run by the Jogger each
week?
Answers
Answer: 14.5
Step-by-step explanation: (1½ ×3 ) + (2½ ×4)² = 4.5 + 10
A ball is thrown from the top of a seaside cliff. Its height, h, in meters, above the sea after t seconds can be modelled by h= -5t² +21t + 120
Answers
Using the vertex of the quadratic equation, it is found that the ball reaches it's maximum height after 2.1 seconds.
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex]
[tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]
Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.In this problem, the equation is given by:
h(t) = -5t² + 21t + 120.
Meaning that the coefficients are a = -5, b = 21, c = 120.
Hence, the time at which the maximum height is reached is given by:
[tex]t_v = -\frac{b}{2a} = -\frac{21}{-10} = 2.1[/tex]
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HELP will give brainliest
complete the worksheet 2-18
Answers
Answer: 1/10, 1/7, 2/9, 2/5, 7/11, 1/4, 1/10, 1/7, 1/9, 1/2 , 1/8, 1/12, 0/1, 0/0
1/13, 1/3, 1/4
Step-by-step explanation: i think i know all the answers
Help! I will give brainliest!!!!
Answers
Answer:
3.14 (or pi ) feet
Step-by-step explanation:
Entire circle circumference = pi *d = 8 pi feet
45 degrees is a fraction of the entire 360 degrees of the circle
45 / 360 * 8 pi = pi = 3.14 ft
How do you solve this?
Answers
Answer: a= -18
b= -28 inches c=30 pounds
Step-by-step explanation:
The quantity q varies inversely with the square of m and directly with the product of r and x. when m is 4 and the product of r and x is 8, q is 2.5. what is the constant of variation? five-eighths five-fourths 5 10
Answers
The proportionality shows the relation between two values. The value of the constant of variation is 5.
What is proportionality?The proportionality shows the relation between two values.
As given in the question the quantity q varies inversely with the square of m and directly with the product of r and x. Therefore, the proportionality can be written as,
[tex]q \propto \dfrac{rx}{m^2}[/tex]
Now to remove the proportionality add a constant to the equation which is the constant of variation.
[tex]q =k\dfrac{rx}{m^2}[/tex]
When m is 4 and the product of r and x is 8 then the value of q is 2.5. Therefore, the value of k can be written as,
[tex]q =k\dfrac{rx}{m^2}\\\\2.5 = k\dfrac{8}{4^2}\\\\\dfrac{2.5 \times 16}{8}=k\\\\k=5[/tex]
Thus, the value of the constant of variation is 5.
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The process of grouping and assigning values to various responses from the survey instrument is called
Answers
The term used to describe the process of assigning values to responses in a research instrument and grouping them is called: coding.
What is Coding in Research Analysis?In data analysis, before raw data can be processed, the researcher groups and assigns values to each response in the research instrument for easy collation and analysis.
This is referred to as coding, in research analysis.
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11 divided by 15?
Help me
Answers
Answer:
0.733 repeating
Step-by-step explanation:
use your calculator
()
Which of the following fractions is the
largest? A.5/81 B.75/81 C.10/9 D.11/9
Answers
Answer:
D. 11/9
Step-by-step explanation:
Which of the following fractions is the largest?
A. 5/81
B. 75/81
C. 10/9
D. 11/9
To make things easier, convert the fractions to decimals:
A. 5/81 = 0.062
B. 75/81 = 0.93
C. 10/9 = 1.11
D. 11/9 = 1.22
As we can see, 11/9 or 1.22, is the largest of all the values.
Hope this helps!
To make the denominators of the given fractions equivalent, we need to determine the LCM of the denominators. Clearly, the denominators of the set of fractions are 81, 81, 9, and 9 respectively.
81 ⇔ 81, 162, 243...9 ⇔ 9, 18, 27, 36, 45, 54, 63, 72, 81, 90....LCM = 81 (81 × 1 = 81 and 9 × 9 = 81)
Multiply the denominators such that the denominator is equivalent to 81. Keep in mind that if we are multiplying a number (x), the numerator must be multiplied by the same number (x) .
⇒ 5/81, 75/81, 10/9, 11/9
⇒ (5 × 1)/(81 × 1), (75 × 1)/(81 × 1), (10 × 9)/(9 × 9), (11 × 9)/(9 × 9)
⇒ (5)/(81), (75)/(81), (90)/(81), (99)/(81)
⇒ 5/81, 75/81, 90/81, 99/81
Step 2. Compare the fractions in the given set:Since 99 > 90 > 75 > 5, we can tell that 99/81 is the largest as:
5/81 (5/81) < 75/81 (75/81) < 90/81 (10/9) < 99/81 (11/9)Therefore, 11/9 is the largest fraction in the set.
If the line that passes through the points below
5
has a slope of Find the value of k.
2
(-2, k) and (6. - 11)
Answers
Answer:
the value of k is 27.
Step-by-step explanation:
find by using formula y2-y1/x2-x1
4. Ashley claims that if she triples the side length of a square (s), the area of the square will also be tripled. Do you agree? Explain your thinking.
Answers
Answer :-
Let the side of the square measure a cm, thus, according to the question,
New length = 3(a cm)We know that,
➭ Area ( Square ) = a²
Thus, the area of the square with normal length i.e. a cm, will be,
⤳ Area = a x a
⤳ Area = a²
Now, by taking the new length, the area will become,
⤳Area = 3a x 3a
⤳ Area = 9a²
Now,
We observe that, if we divide these, we get,
➤ 9a²/a²
( a² will get canceled since its common )
Thus, the ratio becomes,
➭ 9 : 1 = Area square with tripled length : Area of square
Thus, the area will increase by 9 times, and not 3.
Hence, Ashley's assumptions are wrong.
Find the missing side. Round to the nearest tenth
Answers
Answer:
x=11.1
Step-by-step explanation:
we can use the sine function: (opposite/hypotenuse)
sin(46)=8/x
x=8/(sin46)
11.1
Stephanie has a homeowners insurance policy for her $355,000 home with an annual premium of $0.42 per $100 of value and a deductible of $500. under this policy, in the event of a major mishap, stephanie would have a total annual out-of-pocket expense of left-bracket (355,000 dollars divided by 100) times 42 cents right-bracket 500 dollars = 1,991 dollars. stephanie would like to lower her premium by increasing her deductible. if stephanie wants to increase her deductible to $1000, what annual premium would result in an annual out-of-pocket expense that is about the same as her current plan? a. $0.16 per $100 of value b. $0.28 per $100 of value c. $0.35 per $100 of value d. $0.46 per $100 of value
Answers
The annual premium result in an annual out-of-pocket expense that is about the same as her current plan is $0.28 per $100 of value.
What is an insurance premium?Insurance premiums are paid for policies that cover all the basic needs such as healthcare, home, and life insurance.
We are given Amount of insurance policy for Stephanie = $ 355,000
Annual premium = $ 0.42 per $100
Deductible amount = $ 500
Total Annual out of pocket expense
= [($355,000/100) x $0.42] + $500
= $1,991
Now, the New Deductible amount that Stephanie wants is $ 1000
So, Let the annual premium be x
To find the annual premium in an annual out-of-pocket expense that is about the same as her current plan when the deductible amount increases to $1000
355,000x / 100 + 1000 = 1991
3550x + 1000 = 1991
3550x = 1991 - 1000
3550x = 991
x = 991/3550
x = 0.279≈0.28
Hence the annual premium result in an annual out-of-pocket expense that is about the same as her current plan is $0.28 per $100 of value.
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Please HELP Me with this problem!
Answers
Answer:
B
Step-by-step explanation:
because 30÷3=10
Answer:
Your answer is B
Step-by-step explanation:
Sale! 50% OFF of the original price! Zane buys a suitcase during the sale. If the original price was $60, how much does Zane pay?
Answers
Answer:
$30
Step-by-step explanation:
if something is 50% off that is the same as saying half off.
so you simply do 60 divided by 2 and you get 30
Answer:
$30
Step-by-step explanation:
You get this anaswer by multiplying 60 (the cost of the suitcase) by 0.50 (50 percent as a decimal) and get 30 then subtract 30 by 30 to get the total cost.
Find the range from the following date 50,75,65,35,85,55,95,70,25,45
Answers
Answer:
range: 70
Step-by-step explanation:
range is the difference between the highest and lowest values.
Rearrange the equation below to highlight the variable Y.
3x+1/2y=-4
Answers
Answer:
OPTION D
Step-by-step explanation:
[tex]3x + \frac{1}{2} y = - 4[/tex]
[tex]6x + y = - 8[/tex]
[tex]y = - 6x - 8[/tex]
I hope it helped you
Last week, Ken ran 10 laps around the lake. Heather ran 2/3 as many laps around the lake as Ken did. How many laps around the lake did Heather run? Write your answer as a fraction or as a whole or mixed number
Answers
The number of laps around the lake did Heather run last week when the Ken ran 10 laps around the lake is 20/3.
What is the fraction number?Fraction number is the number which is a part of a whole number. It is written with a numerator and denominator. Fraction number are written as,
[tex]\dfrac{a}{b}[/tex]
Here (a) is the numerator and (b) is the denominator.
Last week, Ken ran 10 laps around the lake. Heather ran 2/3 as many laps around the lake as Ken did. Thus, the number of laps heather ran is,
[tex]x=\dfrac{2}{3}\times10\\x=\dfrac{20}{3}[/tex]
Hence, the number of laps around the lake did Heather run last week when the Ken ran 10 laps around the lake is 20/3.
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-13)
1) Look for any properties used in each equation. Choose ALL equations that correctly apply properties of operations.
A) 5(3 + b) = 8 + 3b
B) 3(4 + x) = 12 + 3x
+
C) 20a + 12b = 4(5a + 3b)
D) y+ y + y = y
E) 9+9+9+9=49
Answers
A) no property
B) distributive property of multiplication
C) no property
D) no property
E) no property
Step-by-step explanation:A) [tex]Identify\ the\ property\ used:[/tex][tex]\downarrow[/tex]
[tex]no\ property[/tex]
____________________________________
B) [tex]Identify\ the\ property\ used:[/tex][tex]\downarrow[/tex]
[tex]distributive\ property\ of\ multiplication[/tex]
____________________________________
C) [tex]Identify\ the\ property\ used:[/tex][tex]\downarrow[/tex]
[tex]no\ property[/tex]
____________________________________
D) [tex]Identify\ the\ property\ used:[/tex][tex]\downarrow[/tex]
[tex]no\ property[/tex]
____________________________________
E) [tex]Identify\ the\ property\ used:[/tex][tex]\downarrow[/tex]
[tex]no\ property[/tex]
I hope this helps you
:)
Answer:
D and E
Step-by-step explanation:
i took the quiz on usa test prep
Substitution. Please help answer.
Answers
Answer:
A and C
Step-by-step explanation:
1) -5(4x-6)-14=-4x+16
-20x+30-14+4x-16=0
-16x=0
x=16
3)4x-8(x-2)=-4x+16
-4x+16=-4x+16
There are 15 jelly beans left in a bag. The table shows the frequency of each color.
Number
Color
In Bag
Blue 3
Pink 1
Green 4
Yellow 3
Orange 4
Which of the following BEST describes the probability of choosing a particular color of jelly bean?
Answers
Answer:
Pink is the least likely to be chosen because it has the lowest frequency.
Step-by-step explanation:
Given the equation , then m =
Answers
Answer:
v=3,m=2
Step-by-step explanation:
You can find the complete solution in given attachment
I hope it helped you
Hence, m= (m+1)(2/3)
m= 2/3(m) + 2/3