Answer:
The simplest way to prove that triangles are congruent is to prove that all three sides of the triangle are congruent. When all the sides of two triangles are congruent, the angles of those triangles must also be congruent. This method is called side-side-side, or SSS for short.
Suppose you have a litter of mice which consists of 5 males and 3 females. If you randomly grab two of them without replacement.
1. what is the probability that they are both male?
2. what is the probability that you get at least one female
3. what is the probability that one is male and one is female
Problem 1
Answer: 5/14-----------------------
Explanation:
We have 5 males and 3 females, so there are 5+3 = 8 mice total. The probability of selecting a male is 5/8. After that male is chosen, there are 5-1 = 4 of them left out of 8-1 = 7 total. This subtraction happens because the first mouse selected is not replaced. The probability of picking another male is 4/7.
Multiplying these fractions leads to the answer
(5/8)*(4/7) = (5*4)/(8*7) = 20/56 = 5/14
Note: to reduce 20/56 into 5/14, you divide both parts by the GCF 4.
====================================================
Problem 2
Answer: 9/14-----------------------
Explanation:
The events "selecting two males" and "selecting at least one female" are complementary events. One or the other, but not both, must happen.
If we let
A = event of selecting two malesB = event of selecting at least one female (ie one or more females)then we can say
P(A) + P(B) = 1
P(B) = 1 - P(A)
P(B) = 1 - (5/14)
P(B) = (14/14) - (5/14)
P(B) = (14-5)/14
P(B) = 9/14
Note how P(A) = 5/14 is the result from problem 1.
====================================================
Problem 3
Answer: 15/28-----------------------
Explanation:
The probability of selecting a male is 5/8. After the male is chosen, there are 8-1 = 7 mice left. The probability the second mouse is female is 3/7 since there are 3 female mice out of 7 left total.
We get this result after multiplying the values: (5/8)*(3/7) = 15/56
Now consider that the first mouse is female. The probability of this is 3/8. The probability that the second mouse is male is 5/7.
The fractions multiply to (3/8)*(5/7) = 15/56. We get the same result as before due to the numerators swapping places, but not much else happens. So we have a sort of symmetry going on here.
The last step is to add the two results we got:
(15/56)+(15/56) = (15+15)/56 = 30/56 = 15/28
Or you could compute it like this
2*(15/56) = (2*15)/56 = 30/56 = 15/28
The '2' is to signify there are two ways to select exactly one male and exactly one female, where the order doesn't matter.
--------------------------
Here's another way we can get the answer.
The probability we get both males is 5/14 found back in problem 1.
The probability we get both females will follow the same idea as problem 1, and we would compute (3/8)*(2/7) = 6/56 = 3/28
Add those fractions: (5/14) + (3/28) = (10/28) + (3/28) = 13/28
Now consider the events
C = event of selecting two mice of the same gender (both are male OR both are female; pick 1 scenario only)D = event of selecting two mice of different genders (the first is male, the other is female, or vice versa)Events C and D are complementary events.
We calculated that P(C) = 13/28, which means
P(D) = 1 - P(C)
P(D) = 1 - (13/28)
P(D) = (28/28) - (13/28)
P(D) = (28-13)/28
P(D) = 15/28
A community organization wants to determine area support for the construction of a new skate park in the center of town. The organization decides to survey 500 people to see whether they are willing to have their taxes increased for one year to fund the construction of the skate park. What is the best way to randomly choose these 500 people? O Select the first 500 taxpayers listed at the town hall. O Survey the first 500 people who visit the existing skate park. O Assign each taxpayer in town a number and then randomly select 500 of these numbers. O Choose 100 taxpayers from 5 different age groups in town.
PLEASE HELP!!!!
Answer: I just took the test, and the answer is 'Assign each taxpayer in town a number and then randomly select 500 of these numbers.'
Step-by-step explanation: Happy Pride Month!!
In a circle of radius 10 cm, a sector has an area of 40 (pi) sq. cm. What is the degree measure of the arc of the sector?
72
144
180°
Answer:
144°
Step-by-step explanation:
First, find the area of the circle, with the formula A = [tex]\pi[/tex]r²
Plug in 10 as the radius, and solve
A = [tex]\pi[/tex]r²
A = [tex]\pi[/tex](10²)
A = 100[tex]\pi[/tex]
Using this, create a proportion that relates the area of the sector to the degree measure of the arc.
Let x represent the degree measure of the arc of the sector:
[tex]\frac{40\pi }{100\pi }[/tex] = [tex]\frac{x}{360}[/tex]
Cross multiply and solve for x:
100[tex]\pi[/tex]x = 14400[tex]\pi[/tex]
x = 144
So, the degree measure of the sector arc is 144°
Answer:
Solution :-We know that
Area = πr²
Area = 3.14 × (10)²
Area = 314/100 × 100
Area = 314 cm²
Now
40π/314 = x/360
40 × 3.14/314 = x/360
125.6/314 = x/360
0.4 = x/360
0.4 × 360 = x
144 = x
[tex] \\ [/tex]
The pentagons JKLMN and PQRST are similar.
Find the length x of PQ.
Answer:
[tex]x = 9[/tex]
Step-by-step explanation:
Given
The similar pentagons
Required
Find x
To do this, we make use of any equivalent ratios.
In this case, we use:
[tex]KL : QR = KJ : QP[/tex]
Replace each of the above with the side lengths
[tex]4 : 7.2 = 5 : x[/tex]
Express as fractions
[tex]\frac{4 }{ 7.2} = \frac{5 }{ x}[/tex]
Cross multiply
[tex]4 * x = 5 * 7.2[/tex]
[tex]4x = 36[/tex]
Divide by 4
[tex]x = 9[/tex]
PLEASE HELP!!!
Identify the axis of symmetry and the vertex on the graph given. Type your answer in the boxes provided.
RJ's teacher gave a pop quiz in math class yesterday. The scores on the quizzes ranged from 60% to 100%. What grade did most students earn on the pop quiz?
Answer:
Grade's of most student = 80% (Approx.)
Step-by-step explanation:
Given range:
Range of quiz = 60% to 100%
Find;
Grade's of most student
Computation:
⇒ Grade's of most student = Average grade
⇒ Average mean = Sum of observation / number of observation
⇒ Grade's of most student = [60 + 100] / 2
⇒ Grade's of most student = 160 / 2
Grade's of most student = 80% (Approx.)
Ben rented a car. It cost $30.00 plus $0.25 per mile. If Ben paid $85.00 for the car rental, how many miles did he drive the car? Write an equation and then use your equation to find your answer.
Answer:
220 miles
Step-by-step explanation:
85-30=55
55/.25=220
220 = miles
Answer:
Equation:
30 + 0.25x = 85
Work:
30 + 0.25x = 85
85 - 30 = 55
55 / 0.25 = 220
Final answer:
200 miles
Step-by-step explanation:
Hope this helped and have a nice day!!!
Zoe is starting her own snow plowing business. Zoe thinks she will do a better job than her competitors, so she thinks she can charge $11 per hour. If she knows she will only be able to work 40.25 hours per week, how much money will she earn each week
Answer:
$442.75
Step-by-step explanation:
$11/hour x 40.25 hours/week=$442.75
What is the domain for √(3x-3)? *
all real numbers except x=1
all real numbers for x≥1
all real numbers for x≥0
all real numbers except x=0
A politician claims that 20% of the millions of votes cast for his opponent are fraudulent. To test this claim, an investigator collects a random sample of 90 ballots and contacts the voters whose names appear on the ballots to determine if each ballot is in fact fraudulent. Use a normal approximation to find the probability that less than 10 of the selected ballots turn out to be fraudulent, assuming the politician's claim is correct.
Answer:
"0.0125" is the right solution.
Step-by-step explanation:
The given values are:
Random sample,
n = 90
Claims,
p = 20%
or,
= 0.20
By using normal approximation, we get
⇒ [tex]\mu = np[/tex]
On substituting the values, we get
⇒ [tex]=90\times 0.20[/tex]
⇒ [tex]=18[/tex]
Now,
The standard deviation will be:
⇒ [tex]\sigma=\sqrt{np(1-p)}[/tex]
On putting the above given values, we get
⇒ [tex]=\sqrt{90\times 0.20\times (1-0.20)}[/tex]
⇒ [tex]=\sqrt{18\times 0.8}[/tex]
⇒ [tex]=\sqrt{14.4}[/tex]
⇒ [tex]=3.7947[/tex]
hence,
By using the continuity correction or the z-table, we get
⇒ [tex]P(x < 10) = P(x < 9.5)[/tex]
⇒ [tex]P(x < 10) = P(\frac{x-\mu}{\sigma} -\frac{9.5-18}{3.7947} )[/tex]
⇒ [tex]P(x < 10) = P(Z < -2.24)[/tex]
From table,
⇒ [tex]P(x < 10) = 0.0125[/tex]
find the value of x in each case. will be posting more questions soon.
Consider the three points (-7, -7), (21, 14), (49, 35). Part A: Which of the following points are on the same line that passes through the (-7, -7), (21, 14), (49, 35)? Select all that apply. A. (5, 9) B. (5, 2) C. (17, 11) D. (4, 3) E.) (33, 23) Part B: Show or explain how you determined which points were on the line and which were not on the line.
Answer:
A. (5, 9)
Step-by-step explanation:
35 Type the correct answer in each box. Day Amount 1 $26 2 $23 3 $31 4 $26 5 $34 The table shows the amount Bill spent on 5 days last week. The mean of the amount he spent is $ The mean absolute deviation is $ Reset Next
Answer:
The answer is 23 I just took this test and got it right
Step-by-step explanation:
Answer: 23
Step-by-step explanation:
1/4 carton of ice cream divided wvenly by 3
Answer:
Hello There!!
Step-by-step explanation:
You multiply the reciprocal which is 4 by 3 and that is 12.
Another method: 1/4 ÷3 (use KFC) so it is keep 3,flip the fraction so it is 4/1 them change the sign ÷ into multiplication so it is 3×4/1=12. Therefore,the answer is 12.
hope this helps,have a great day!!
~Pinky~
Helpp me please!!
I need it knowwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww
Answer:
8yd×10yd=80yd
80yd÷2=40yd²
Step-by-step explanation:
Hope it helps :)
state of the given functions are inverses. Part 3. NO LINKS!!!!
Answer:
9.
h(x)=-x-1
let y =-x-1
interchanging role of x & y
x=-y-1
y=-x-1
h-¹(x)=-x-1
again
f(x)=(2-3x)/2
let
y=(2-3x)/2
interchanging role of x & y
x=(2-3y)/2
2x-2=-3y
y=(2-2x)/3
f-¹(x)=(2-2x)/3
Given function are not inverse of each other.
10.
f(x)=-x+3
let y=-x+3
interchanging role of x & y
x=-y+3
y=3-x
f-¹(x)=-x+3
equal to g(x)=-x+3
Given function are inverse of each other.
Answer:
Step-by-step explanation:
Call h(x) = y (It's easier to see).
y = -x - 1
The first step is always to interchange x and y
y = -x - 1
-x = y - 1
Solve for y
-x + 1 = y
If I understand the question, these two (f(x) and h(x)) are not inverses.
10 is a bit tricky. An inverse can invert into itself: This is called an involution. But if they are differently labeled, I'm not sure. I don't think that this is exactly what is men by an involution. Something like y = x would be. But you have 2 different inverses. I'm not sure that this qualifies.
y = x + 3
g = x + 3
x = y + 3
x - 3 = y
the sum of a number and its inverse is 3 29/52 . Find the number?
I want the working out and the answers please
Answer:
x1=
104
329+
329
2
−10816
x2=\frac{329-\sqrt{329^{2} -10816} }{104}x2=
104
329−
329
2
−10816
The sum of a number and its inverse is 3 29/52. Find the number?
x+1/x=329/52
x+1/x-329/52=0
solve the fraction
(\frac{(52x^{2} +52-329x)}{52x} =0
52x
(52x
2
+52−329x)
=0
52x^{2} +52-329x=052x
2
+52−329x=0
52x^{2} -329x+52=052x
2
−329x+52=0
using the quadratic formular
(-b+-√b^2-4ac) / 2a(−b+−√b
2
−4ac)/2a
x=\frac{329+-\sqrt{(329)^{2} -4*52*52} }{2*52}x=
2∗52
329+−
(329)
2
−4∗52∗52
x1=\frac{329+\sqrt{329^{2}-10816 } }{104}x1=
104
329+
329
2
−10816
x2=\frac{329-\sqrt{329^{2} -10816} }{104}x2=
104
329−
329
2
−10816
A new laundry detergent is supposed to be equally superior to the leading brand in both hot and cold water. If the new detergent works as predicted, then there should be an interaction between the brand of detergent and the temperature of the water.
a. True
b. False
Answer: false
Step-by-step explanation: because you set the temp not the liquids.
what is the volume of the prism 2m x 3m x 5m
Answer:
30 m³
Step-by-step explanation:
2 m x 3 m x 5 m= 30 m³
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
find the measure of the missing angle
Answer:
61
Step-by-step explanation:
The Home Depot has two special lawnmowers for sale this year. The electric mower costs $300 each, and the gas-powered mower costs $450 each. The store has room for 25 total mowers, and the store has to order at least $6000 worth of mowers to start the sale.
Answer:
300a + 450b ≤ 6000
Step-by-step explanation:
Given:
Cost of electric mower = $300
Cost of gas mower = $450
Total number of mower = 25
Cost of total mower is at least = $6,000
Find:
Number of each mower equation
Computation:
Number of electric mower = a
Number of gas mower = b
So,
Equations
a + b ≤ 25 ........ Equation 1
300a + 450b ≤ 6000 ....... Equation 1
HELP ME PLEASE, I can't figure out this puzzle :(
Geometry i need help with this geometry question
Answer:
RS/XY = ST/YZ
Step-by-step explanation:
They need to follow the same direction and same length in comparision to the rest. From what I can see, that seems to be the one that does that best.
The Scenario: Your manager has asked you to help plan your company's participation at a local trade show. You have $3000 to spend on the booth space and product brochures. Use what you know about solving inequalities to prepare a proposal that meets the budget.
Answer:
[tex]x + y\le 3000[/tex]
Step-by-step explanation:
Given
[tex]x \to booth[/tex]
[tex]y \to brochures[/tex]
[tex]Total = 3000[/tex]
Required
The inequality for this scenario
The total spending will not exceed the amount they have to spend; So, the inequality is:
[tex]x + y\le 3000[/tex]
Un aserradero adquiere maquinaria y equipo para el corte de madera, que va perdiendo valor conforme transcurren los años, hasta que su valor contable es cero, como indica la gráfica de la función D(x)=(-x^3+2x^2+20x+20)/(x^2+4x+4) que modela esta depreciación en el eje y cada unidad son 20 000 pesos y en el eje x cada unidad es de 3 años.
a) ¿Cuál es el valor inicial del equipo y herramienta? ¿cuánto se ha depreciado al cabo de 12 años?
b) ¿existe un modelo lineal que aproxime los mismos valores que la función D(x)?
c) ¿En cuánto difieren los valores de ambas funciones al cabo de 9 años?
Answer:
-1 5
Step-by-step explanation:
88.128 x 0.5 Multiplication question
Answer: 44.064
Step-by-step explanation:
Answer:
44.064
thats the answer
3,984,896 rounded to the nearest hundred
Answer:
3,984,896 rounded to the nearest hundred is 3,984,900
Jill says that 1 2/3 equals 3:5 is Jill correct
Answer:
Not true. Actually, 1 2/3 equals 5/3.
Answer: No
Step-by-step explanation:
If we were to change 1 2/3 into an improper fraction, it would be 5/3. This is expressed as 5:3, not 3:5. These two ratios are not the same. Therefore, Jill is not correct.
Hope this helped :)
(no links) Please Help!
9514 1404 393
Answer:
D, B
Step-by-step explanation:
Price per pound is found by dividing dollars by pounds.
Store A: $9/(3 lb) = $3.00 /lb
Store B: $9.75/(3 lb) = $3.25 /lb
Store C: $12.40/(4 lb) = $3.10 /lb
Store D: $14.50/(5 lb) = $2.90 /lb
Part A: The lowest price per pound is $2.90 per pound at store D.
Part B: The highest price per pound is $3.25 per pound at store B.
what is the first step to solving this equation?
-5+6=4
a. subtract 6 from both sides
b. multiply both sides by 5
c. divide both sides by -5
d. add 6 to both sides
Answer:
a. subtract 6 from both sides
Step-by-step explanation:
Given the algebraic expression;
-5c + 6 = 4
First of all, we would subtract 6 from both sides. This would eliminate the "6" on the left side.
-6 - 5c + 6 = 4 - 6
-5c = -2
5c = 2
Dividing both sides by 5, we have;
c = 2/5