Answer:
A) 0.2253, 0.0153; B) 0.4925, 0.0017
Step-by-step explanation:
This is a binomial distribution. This is because there are only two outcomes; each trial is independent of each other; and the outcomes are independent.
This means we use the formula
[tex]_nC_r\times p^r\times (1-p)^{n-r}[/tex]
For part A,
There are 12 wolves selected; this means n = 12. We want the probability that 9 or more are male; this makes r = 9, 10, 11 or 12. We will find each probability and add them together.
p, the probability of success, is 0.6 for the first question (males). This makes 1-p = 1-0.6 = 0.4. Together this gives us
[tex]_{12}C_9(0.6)^9(0.4)^3+_{12}C_{10}(0.6)^{10}(0.4)^2+_{12}C_{11}(0.6)^{11}(0.4)^1+_{12}C_{12}(0.6)^{12}(0.4)^0\\\\=220(0.6)^9(0.4)^3+66(0.6)^{10}(0.4)^2+12(0.6)^{11}(0.4)+1(0.6)^{12}(1)\\\\\\= 0.2253[/tex]
We now want the probability that 9 or more are female; this makes r = 9, 10, 11 or 12. p is now 0.4; this makes 1-p = 1-0.4 = 0.6. This gives us
[tex]_{12}C_9(0.4)^9(0.6)^3+_{12}C_{10}(0.4)^{10}(0.6)^2+_{12}C_{11}(0.4)^{11}(0.6)^1+_{12}C_{12}(0.4)^{12}(0.6)^0\\\\=220(0.4)^9(0.6)^3+66(0.4)^{10}(0.6)^2+12(0.4)^{11}(0.6)^1+1(0.4)^{12}(1)\\\\=0.0153[/tex]
For part B,
There are again 12 wolves selected, so n = 12. We want the probability in the first question that 9 or more are male; this makes r = 9, 10, 11 or 12. The probability of success is now 0.7, so 1-p = 1-0.7 = 0.3[tex]_{12}C_9(0.7)^9(0.3)^3+_{12}C_{10}(0.7)^{10}(0.3)^2+_{12}C_{11}(0.7)^{11}(0.3)^1+_{12}C_{12}(0.7)^{12}(0.3)^0\\\\=220(0.7)^9(0.3)^3+66(0.7)^{10}(0.3)^2+12(0.7)^{11}(0.3)^1+1(0.7)^{12}(0.3)^0\\\\= 0.4925[/tex]
For the second question, the probability of success is now 0.3 and 1-p = 1-0.3 = 0.7:
[tex]220(0.3)^9(0.7)^3+66(0.3)^{10}(0.7)^2+12(0.3)^{11}(0.7)^1+1(0.3)^{12}(0.7)^0\\\\=0.0017[/tex]
Probabilities are used to determine the outcomes of events.
Before 1918,
The probability of selecting 9 or more male wolves is 0.225The probability of selecting 9 or more female wolves is 0.015The probability of selecting lesser than 6 female wolves is 0.665Since 1918,
The probability of selecting 9 or more male wolves is 0.493The probability of selecting 9 or more female wolves is 0.002The probability of selecting lesser than 6 female wolves is 0.516The question is an illustration of binomial probability, where:
[tex]\mathbf{P(x) = ^nC_x \times p^x \times (1 - p)^{n -x}}[/tex]
(a i) Probability of selecting 9 or more wolves out of 12, before 1918
The given parameters are:
[tex]\mathbf{p = 0.60}[/tex] --- the probability of selecting a male wolf
So, we have:
[tex]\mathbf{P(x \ge 9) = P(9) + P(10) + P(11) + P(12)}[/tex]
Using [tex]\mathbf{P(x) = ^nC_x \times p^x \times (1 - p)^{n -x}}[/tex], we have:
[tex]\mathbf{P(x \ge 9) = ^{12}C_9 \times 0.6^9 \times (1 - 0.6)^{12-9} +..............+^{12}C_{12} \times 0.6^{12} \times (1 - 0.6)^{12-12} }[/tex]
[tex]\mathbf{P(x \ge 9) = 220 \times 0.00064497254 +..........+1 \times 0.00217678233}[/tex]
[tex]\mathbf{P(x \ge 9) =0.225 }[/tex]
(a ii) Probability of selecting 9 or more female wolves
The given parameters are:
[tex]\mathbf{p = 0.40}[/tex] --- the probability of selecting a female wolf
So, we have:
[tex]\mathbf{P(x \ge 9) = P(9) + P(10) + P(11) + P(12)}[/tex]
Using [tex]\mathbf{P(x) = ^nC_x \times p^x \times (1 - p)^{n -x}}[/tex], we have:
[tex]\mathbf{P(x \ge 9) = ^{12}C_9 \times 0.4^9 \times (1 - 0.4)^{12-9} +..............+^{12}C_{12} \times 0.4^{12} \times (1 - 0.4)^{12-12} }[/tex]
[tex]\mathbf{P(x \ge 9) = 220 \times 0.0000566231+..........+1 \times 0.00001677721}[/tex]
[tex]\mathbf{P(x \ge 9) =0.015 }[/tex]
(a ii) Probability of selecting fewer than 6 female wolves
The given parameters are:
[tex]\mathbf{p = 0.40}[/tex] --- the probability of selecting a female wolf
Using the complement rule, we have:
[tex]\mathbf{P(x < 6) = 1 - P(x \ge 6)}[/tex]
So, we have:
[tex]\mathbf{P(x < 6) = 1 - [P(6) + P(7) + P(8) + P(x \ge 9)]}[/tex]
Using [tex]\mathbf{P(x) = ^nC_x \times p^x \times (1 - p)^{n -x}}[/tex], we have:
[tex]\mathbf{P(x < 6) = 1 - [^{12}C_6 \times 0.4^6 \times 0.6^6 + ^{12}C_7 \times 0.4^7 \times 0.6^5 + ^{12}C_8 \times 0.4^8 \times 0.6^4 + P(x \ge 9)}[/tex][tex]\mathbf{P(x < 6) = 1 - [924 \times 0.00019110297 +........ + 0.0153]}[/tex]
[tex]\mathbf{P(x < 6) = 1 - [0.335]}[/tex]
[tex]\mathbf{P(x < 6) = 0.665}[/tex]
(b i) Probability of selecting 9 or more wolves out of 12, since 1918
The given parameters are:
[tex]\mathbf{p = 0.70}[/tex] --- the probability of selecting a male wolf
So, we have:
[tex]\mathbf{P(x \ge 9) = P(9) + P(10) + P(11) + P(12)}[/tex]
Using [tex]\mathbf{P(x) = ^nC_x \times p^x \times (1 - p)^{n -x}}[/tex], we have:
[tex]\mathbf{P(x \ge 9) = ^{12}C_9 \times 0.7^9 \times (1 - 0.7)^{12-9} +..............+^{12}C_{12} \times 0.7^{12} \times (1 - 0.7)^{12-12} }[/tex]
[tex]\mathbf{P(x \ge 9) = 220 \times 0.00108954738+..........+1 \times 0.0138412872}[/tex]
[tex]\mathbf{P(x \ge 9) =0.493 }[/tex]
(b ii) Probability of selecting 9 or more female wolves
The given parameters are:
[tex]\mathbf{p = 0.30}[/tex] --- the probability of selecting a female wolf
So, we have:
[tex]\mathbf{P(x \ge 9) = P(9) + P(10) + P(11) + P(12)}[/tex]
Using [tex]\mathbf{P(x) = ^nC_x \times p^x \times (1 - p)^{n -x}}[/tex], we have:
[tex]\mathbf{P(x \ge 9) = ^{12}C_9 \times 0.3^9 \times (1 - 0.3)^{12-9} +..............+^{12}C_{12} \times 0.3^{12} \times (1 - 0.3)^{12-12} }[/tex]
[tex]\mathbf{P(x \ge 9) = 220 \times 0.00000675126+..........+1 \times 5.31441e-7}[/tex]
[tex]\mathbf{P(x \ge 9) =0.002 }[/tex]
(b iii) Probability of selecting fewer than 6 female wolves
The given parameters are:
[tex]\mathbf{p = 0.40}[/tex] --- the probability of selecting a female wolf
Using the complement rule, we have:
[tex]\mathbf{P(x < 6) = 1 - P(x \ge 6)}[/tex]
So, we have:
[tex]\mathbf{P(x < 6) = 1 - [P(6) + P(7) + P(8) + P(x \ge 9)]}[/tex]
Using [tex]\mathbf{P(x) = ^nC_x \times p^x \times (1 - p)^{n -x}}[/tex], we have:
[tex]\mathbf{P(x < 6) = 1 - [^{12}C_6 \times 0.3^6 \times 0.7^6 + ^{12}C_7 \times 0.3^7 \times 0.7^5 + ^{12}C_8 \times 0.3^8 \times 0.7^4 + P(x \ge 9)}[/tex]
[tex]\mathbf{P(x < 6) = 1 - [924 \times 0.4^6 \times 0.7^6 + 792 \times 0.3^7 \times 0.7^5 + 495 \times 0.3^8 \times 0.7^4 + 0.002}[/tex]
[tex]\mathbf{P(x < 6) = 1 - [0.484]}[/tex]
[tex]\mathbf{P(x < 6) = 0.516}[/tex]
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An amusement park ride has cars that move around a circular track at the rate of 16 revolutions in 20 seconds. To the nearest hundredth, the angular velocity of the cars is radians per second.
Answer:
[tex]5.03\frac{rad}{sec}[/tex]
Step-by-step explanation:
To find the angular velocity divide the revolutions by the time
so
[tex]\frac{16}{20}=0.8\frac{rev}{sec}[/tex]
Remember that
[tex]1\ rev=2\pi \ rad[/tex]
Convert rev/sec to rad/sec
[tex]0.8\frac{rev}{sec}=0.8*(2\pi)=1.6 \pi\frac{rad}{sec}[/tex]
assume [tex]\pi=3.1416[/tex]
[tex]1.6(3.1416)=5.03\frac{rad}{sec}[/tex]
Answer:
5.03
Step-by-step explanation:
If the outside temperature ranges from -5 degrees c to 40 degrees c, find the range in degrees fahrenheit.
Answer: -109
Step-by-step explanation:
if you make celcius into fahrenheit,
-5 degrees becomes 23 degrees
40 degrees becomes 104 degrees
-5 + 104 = -109
Answer:
Step-by-step explanation:
Which expression is equivalent to sqr 400i8j4k6
I have attached the correct answer. Brainliest will be much appreciated!
Which equation can be used to find the volume of the right rectangular prisms
A) V = (10)(5)
B) V = (10)(2)
C) V = (10)(5)(2)
D) V = 10(5 + 2)2
The answer is C because it’s length x width x height
Answer:
C) V = (10)(5)(2)
Step-by-step explanation:
V = (10)(5)(2) To find the volume of a right rectangular prisms, multiply the length times the width times the height. -- V = lwh.
James thought of a number and divided it by 9.
What can he do to get back his original number?
A) multiply by 9.
B) add 9.
C) divide by 9 again.
D) subtract 9.
The correct answer is A.
Example: 36 divided by 9= 4 and 4 x 9 = 36
Example: 72 divided by 9= 8 and 8 x 9 = 72
Hope this helps.
To get back the original number after dividing by 9, one should multiply the result by 9, because multiplication and division are inverse operations.
The student's question asks: James thought of a number and divided it by 9. What can he do to get back his original number? The correct answer is (A) multiply by 9. When a number is divided by 9 to undo this operation one must multiply it by 9. This is because multiplication is the inverse operation of division. Therefore, if James wants to obtain his original number back, he should take the result he got after dividing by 9 and multiply it by 9.
True or false (Picture provided)
The answer is: True.
Why?A counterexample is a way that we can prove that something is not true about a mathematical expression or equation, it could be considered as an exception to a rule, so to check if the answer is true or false, we must prove that a counterexample of the given expression is 0°, so:
The given expression is:
[tex]sinytany=cosy[/tex]
Then,
[tex]sin(0)*\frac{sin(0)}{cos(0)}=cos(0)\\\\0*\frac{0}{1}=1\\\\0*0=1\\0=1[/tex]
We can see that the equation is not fulfilled, so 0° is a counterexample of [tex]sinytany=cosy[/tex] and the answer is true.
Have a nice day!
A recent survey by the cancer society has shown that the probability that someone is a smoker is P(S)=0.19. They have also determined that the probability that someone has lung cancer, given that they are a smoker is P(LC|S)=0.158. What is the probability (rounded to the nearest hundredth) that a random person is a smoker and has lung cancer P(S∩LC) ?
0.35
0.03
0.02
0.83
Answer:
P (S∩LC) = 0.03
Step-by-step explanation:
We are given that the probability that someone is a smoker is P(S)=0.19 and the probability that someone has lung cancer, given that they are a smoker is P(LC|S)=0.158.
Given the above information, we are to find the probability hat a random person is a smoker and has lung cancer P(S∩LC).
P (LC|S) = P (S∩LC) / P (S)
Substituting the given values to get:
0.158 = P(S∩LC) / 0.19
P (S∩LC) = 0.158 × 0.19 = 0.03
What is the least common multiple (LCM) of 3 and 7?
it is 21 :)))))))))))))))
let's find the least common multiple (LCM) of 3 and 7 is 21.
List the multiples of each number.
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, ...
Multiples of 7: 7, 14, 21, 28, 35, 42, ...
identify the common multiples.
The common multiples of 3 and 7 are the numbers that appear in both lists. In this case, the number 21 is the smallest positive integer that appears in both lists Determine the LCM.
the LCM of 3 and 7 is 21.
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If the radius of a circle is 14 ft, then the diameter of the circle is _____.
7 ft
28 ft
42 ft
87.92 ft
Answer:
The answer is 28ft.
Step-by-step explanation:
A radius will always be exactly half of the diameter: meaning, the diameter is double the length of the radius.
12 decreased by twice a number is the same as 8 times the sum of the number and four. What is the number?
Fill in the blank to make the the equation true
__________ x 9/5 = -27
Answer:
-15
Step-by-step explanation:
Multiply the whole equation by the inverse of the multiplier of the blank. Then you get ...
___ × 1 = (-27)×(5/9) = -15
The blank filled with -15 will make the equation true.
HELP PLEASE!
Find the exact values of cos and sin for the angle measure. 180 degrees
Answer:
[tex]\large\boxed{\sin180^o=0\ and\ \cos180^o=-1}[/tex]
Step-by-step explanation:
[tex]\text{Use}\\sin(2\theta)=2\sin\theta\cos\theta\\\\\cos(2\theta)=\cos^2\theta-\sin^2\theta\\\\180^o=2(90^o)\\\\\sin90^o=1\\\\\cos90^o=0\\===================\\\\\sin180^o=\sin(2\cdot90^o)=2\sin90^o\cos90^o=2(1)(0)=0\\\\\cos180^o=\cos(2\cdot90^o)=\cos^290^o-\sin^290^o=0^2-1^2=-1[/tex]
Find the surface area of the figure
Answer:
[tex]\large\boxed{S.A.=1,119\ in^2}[/tex]
Step-by-step explanation:
We have:
two triangles with base b = 17in and height h = 7in
two rectangles with length l = 17in and width w = 10in
two rectangles with length l =11in and width w = 10in
one rectangle with length l = 8in and width w = 11in
one rectangle with length l = 15in and width w = 11in
one rectangle with length l = 17in and width w = 11in
The formula of an area of a triangle:
[tex]A_\triangle=\dfrac{bh}{2}[/tex]
b - base
h - height
The formula of an area of a rectangle:
[tex]A_{\boxed{\ }}=lw[/tex]
l - length
w - width
Calculate:
[tex]A_\triangle=\dfrac{(17)(7)}{2}=59.5\ in^2\\\\A_1=(17)(10)=170\ in^2\\\\A_2=(11)(10)=110\ in^2\\\\A_3=(8)(11)=88\ in^2\\\\A_4=(15)(11)=165\ in^2\\\\A_5=(17)(11)=187\ in^2[/tex]
The Surface Area:
[tex]S.A.=2A_triangle+2A_1+2A_2+A_3+A_4+A_5[/tex]
Substitute:
[tex]S.A.=2(59.5)+2(170)+2(110)+88+165+187=1,119\ in^2[/tex]
Need help with Geometry
Answer:
Answer: 56*pi
Step-by-step explanation:
The easiest way is to find the area of the circle and subtract the area of the sector.
Area of the circle
d = 16 cm given
d = 2*r definition
16 = 2*r divide by 2
16/2 = 2r/2
r = 8
Area of the circle = pi * r^2
Area of the circle = pi * 8^2
Area of the circle = 64 pi
Area of the sector
Area of sector = (theta/360) * pi * r^2
Area of sector = 45/360 * pi * 64
Area of sector = 1/8 * pi * 64
Area of sector = 8 * pi
Area of the shaded area
Area of the shaded area = 64 * pi - 8*pi = 56*pi
Note: There is a shorter way, but one can never be confident of getting an angle greater than 180 correct.
360 - 45 = 315
Area of the sector = 315/360 * pi * r2
Area of the sector = 7/8 * pi * 64
Area of the sector = 7 * pi * 8
Area of the sector = 56*pi
Conrad paid $52.26 for a pair of shoes. Michelle paid $3.89 more for a pair of shoes than Conrad paid for his. How much did Michelle pay for her shoes
Answer:Michelle paid $56.15 for her shoes
Step-by-step explanation:
Since Michelle paid $3.89 more for her shoes compared to Conrad, who paid $52.26. This means you have to add $3.89 to $52.26.
$3.89+$52.25= $56.15
Final answer:
Michelle paid $56.15 for her shoes, which is $3.89 more than the $52.26 that Conrad paid for his.
Explanation:
The question involves a simple arithmetic calculation to determine how much Michelle paid for her shoes. To find the answer, we will add $3.89, which is the additional amount Michelle paid, to $52.26, which is the amount Conrad paid for his shoes.
Step-by-step calculation:
Conrad's shoe price: $52.26Additional amount paid by Michelle: $3.89Michelle's shoe price: $52.26 (Conrad's price) + $3.89 = $56.15Therefore, Michelle paid $56.15 for her shoes.
Use the x-intercept method to find all real solutions of the equation.
x^3-11x^2+31x-21=0
Answer:
c. [tex]x=1,3,\:or\:7[/tex]
Step-by-step explanation:
The given equation is
[tex]x^3-11x^2+31x-21=0[/tex]
To find all real solutions using the x-intercept method, we to graph the corresponding function using a graphing tool.
The corresponding function is;
[tex]f(x)=x^3-11x^2+31x-21[/tex]
From the graph the x-intercepts are
(1,0),(3,0) and (7,0).
Therefore the real solutions are
[tex]x=1,3,\:or\:7[/tex]
Answer:
C. is the answer
Step-by-step explanation:
the starting salary at a company is $38000 per year.the company automatically gives a raise of 3.5% per year.write the explicit and recursive frmulas for the geometric sequence formed by the salary increase.
Final answer:
The explicit formula for the salary increases represented as a geometric sequence is a_n= 38,000(1.035)^(n-1), and the recursive formula is a_1= $38,000 and a_n= a_(n-1) × 1.035 for n > 1, reflecting an annual raise of 3.5%.
Explanation:
The starting salary at a company is $38,000 per year with an annual raise of 3.5%. To represent the salary increases as a geometric sequence, we need both explicit and recursive formulas.
The explicit formula for a geometric sequence is an= a1 × r(n-1), where a1 is the first term, r is the common ratio, and n is the term number. In this case, a1= $38,000 and r = 1.035 (since the salary increase is 3.5%, or 0.035 in decimal form, plus the original amount, hence 1 + 0.035). Therefore, the explicit formula is an= 38,000(1.035)(n-1).
The recursive formula defines each term based on the previous term. It can be written as a1= $38,000, an= a(n-1) × 1.035, for n > 1. This means that starting from the second year (when n > 1), the salary is obtained by multiplying the previous year's salary by 1.035.
A. concave dodecagon
B. Concave hexagon
C. Convex hexagon
D. Convex dodecagon
Answer:
bro whats the question
Step-by-step explanation:
HELP CHECK MY ANSWERS, TY!
The graph shows the vertical position of a ball attached to a spring oscillating between a low point and a high point as a function of time.
Select all statements that describe the graph.
Answer:
That is correct
Step-by-step explanation:
When doing the math you can find that b and d are correct
Answer:
Step-by-step explanation:
Here all the statement describing the graph.
1- the cycle of the graph is 2 second.
2- mid-line of the graph is at y=0
3- amplitude is 24 i.e 12 unit + 12 unit
4- ball is traveling 24 cm in 1 sec. I.e. 12 unit in 0.5 sec and another 12 units in 0.5 sec.
What is the mean absolute deviation of Dean's homework scores? 70, 95, 35, 90, 85
Answer:
18.
Step-by-step explanation:
Mean of the values = (70+95+35+90+85) / 5
= 75.
Mean absolute deviation :-
70 - 75 = |-5| = 5 (absolute value is taken
95 - 75 = 20
35-75 = 40
90-75 = 15
85-75 = 10
Mean Absolute Deviation = (5 + 20 + 40 + 15 + 10) / 5
= 18.
Answer: 18
Step-by-step explanation: it was correct on ttm
(1CQ) Write the repeating decimal as a fraction .51
Answer: Your answer is 17/33! Hope this helps. If you need anymore help let me know!
For this case we must indicate the representation in the form of a fraction of the following decimal number:
0.51 periodic number
Option A:
[tex]\frac {17} {100} = 0.17[/tex]
Option B:
[tex]\frac {51} {100} = 0.51[/tex]
Option C:
[tex]\frac {17} {33} = 0.51515151[/tex]
Option D:
[tex]\frac {51} {33} = 1.5454[/tex]
So, the correct option is C
Answer:
Option C
Before she went on a diet, Jenna's waist measured 32.45 inches.After the diet, it measured 26.97 inches.How many inches did Jenna lose?
Answer:
5.48
Step-by-step explanation:
32.45 - 26.97 = 5.48
Answer:
Jenna lost 5,48
Step-by-step explanation:
Before the diet Jenna's waist measured 32.45 inches.
After the diet Jenna's waist measured 26.97 inches.
To get the difference between the two measures, we have to discount the new measure from the previous one.
So, difference is 26.97 inches-32.45 inches= -5,48. It is negative because she lost inches.
Please help me out.............
Since the sides are equal the angels have to be equal too
5x-20=2x+37
3x=57
X=19
Simplifying the expression results in what binomial expression?
The answer is 2x−5
Step-by-step explanation:see the image
Which of the following shows the correct order of the numbers below?
First who answers will get brainlyest
Answer:
c)
Step-by-step explanation:
if you look at option c it would be correct because 0.75 (3/4) is bigger than 0.7. Then 11/12 is a bigger proportion then 0.75. there for your answer is correct.
The correct order of the numbers given when converted to decimals for easy comparison is 0.7, 3/4 and 11/12, which corresponds to option b: 0.7 < 3/4 < 11/12.
Explanation:This is a question about comparing and ordering fractions and decimals. To answer this, we first need to convert all the numbers into the same format. We can convert the fractions 11/12 and 3/4 into decimals for easier comparison.
First, to convert 11/12 to a decimal, you'll do the division to find approximately 0.9167. Secondly, 3/4 can be converted to a decimal by performing 3 divided by 4, which equals 0.75. Now, we can easily compare these decimals to 0.7.
From this, we can see that 0.7 is less than 0.75 (3/4) and both 0.7 and 0.75 are less than 0.9167 (11/12). So the correct order of the numbers from least to greatest would be 0.7 < 3/4 < 11/12.
So the correct option is b. 0.7 < 3/4 < 11/12.
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David and Tonya each cut a cylinder in half. The cross-section that results from David's cut is a rectangle. The cross-section that results from Tonya's cut is a circle.
Answer:
Tonya cut the cylinder vertically and David cut it diagonally.
David’s cut along the length of his cylinder resulted in a rectangular cross-section, while Tonya’s perpendicular cut resulted in a circular cross-section. This illustrates principles of geometric cross-sections and plane intersections with solids.
Explanation:In the problem described, David and Tonya are each cutting a cylinder, a geometric shape. The cuts they make, and the cross-sections they create, depend on the orientation of their cuts in relation to the shape of the cylinder.
When David cuts the cylinder, his cross-section result is a rectangle. This implies that he made a longitudinal cut along the length of the cylinder, essentially splitting it from top to bottom.
When Tonya cuts her cylinder, the cross-section is a circle. This means she made a cross-sectional cut perpendicular to the length of the cylinder, slicing it into two equal half cylinders.
This problem illustrates the principles of geometric cross-sections and plane intersections with solids, which are part of the broader field of study in geometry.
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Which system of linear inequalities is graphed?
Both lines are dotted so no equation should include equal to in it.
The shaded area is on the left side .
The correct answer would be y>2x+1 and x+y = -2
The 3rd answer is correct.
Answer:
y>2x+1 and x+y < -2 represent the graph line.
Step-by-step explanation:
Given : graph .
To find : Which system of linear inequalities is graphed
Solution : We have given graph with two line both lines are dotted line and shaded down.
Equation of line form : y = mx + b.
Where, m = slope , b= y intercept.
Line x+y < -2 less than sign for shaded down and y intercept -2.
and y>2x+1.
Therefore, y>2x+1 and x+y < -2 represent the graph line.
Please help!!!
The area of the green square is 9 ft2. The area of the yellow square is 25 ft2.
What is the area of the red square (labelled "b" in the diagram)?
Answer:
the answer is 16Ft^2
Step-by-step explanation:
Square A's area is 9 so take its square root =3
then do the same for Square c =5
then use pythagram theory which is
3^2 + 5^2 = 4^2 = 16
Answer:
area = 16 ft²
Step-by-step explanation:
The area of the green square = 9 ft²
area of the yellow square = 25 ft²
Area of the red square can be computed as follows:
area of a square = L²
Since one side of each triangle forms a part of the triangle knowing the length of sides of the green and yellow triangle can be use to get the sides of the red square and invariably the area.
Green square
L² = 9
square both sides
√L² = √9
L = 3 ft
Yellow square
L² = 25
square both sides
√L² = √25
L = 5 ft
use Pythagoras theorem to get the third side of the triangle which is the b
c² = a² + b²
b² = c² - a²
a = 3 ft
c = 5 ft
b² = 5² - 3²
b² = 25 - 9
b² = 16
square both sides
√b² = √16
b = 4
Red square
area = L²
area = 4²
area = 16 ft²
A father who is 42 years old has a son and a daughter. The daughter is three times as old as the son. In 10 years, the sum of all their ages will be 100 years. How old are the two siblings at present? PLEASE HELP!!!!!!!!!!!!!!!!
Answer:
The daughter is 36 years old and the son is 12 years old.
A college football stadium holds 45,000 fans. In a random sample of 30 fans, 26 were wearing the colors of the home team. Predict the number of fans who are wearing the colors of the home team.
Answer:
38,999
Step-by-step explanation:
In your sample you have 26 out of 30. I like to get that number into a percentage, so you do 26 divided by 30
26/30 = .8666
Then you take your total amount of fans, 45,000 and multiply it by your percentage wearing team colors.
45,000 x .8666 = 38,999.97
Since you can't have .97 of a person, your round it down to 38,999.