The probability that he hits the hare within his first 4 shots is 0.8789.
Probability of success for the first shot = P1 = 12 Probability of missing the first shot = 1 – P1 = 1 – 12 = 12 Probability of
success for the second shot, given that the first shot missed = P2 = 14Hence, the probability that he hits the hare within
his first 2 shots is:P1 + (1 – P1)P2= 12+(12)×(14)= 12+16= 38(2) The probability that he hits the hare within his first 3 shots is
most nearly (a) 1 (b) 0.9 (c) 0.8 (d) 0.7We have to find the probability of hitting the hare within his first 3 shots. Probability
of success for the first shot = P1 = 12Probability of missing the first shot = 1 – P1 = 1 – 12 = 12Probability of success for the
second shot, given that the first shot missed = P2 = 14Probability of success for the third shot, given that the first two
shots missed = P3 = 18Hence, the probability that he hits the hare within his first 3 shots is:P1 + (1 – P1)P2 + (1 – P1)(1 –
P2)P3= 12+(12)×(14)+(12)×(34)×(18)= 12+16+18×(12)= 1316= 0.8125(3) The probability that he hits the hare within his first 4
shots is most nearly (a) 0.9 (b) 0.7 (c)1 (d) 0.8We have to find the probability of hitting the hare within his first 4
shots. Probability of success for the first shot = P1 = 12Probability of missing the first shot = 1 – P1 = 1 – 12 = 12Probability
of success for the second shot, given that the first shot missed = P2 = 14Probability of success for the third shot, given
that the first two shots missed = P3 = 18 Probability of success for the fourth shot, given that the first three shots missed
= P4 = 116Hence, the probability that he hits the hare within his first 4 shots is:P1 + (1 – P1)P2 + (1 – P1)(1 – P2)P3 + (1 – P1)
(1 – P2)(1 – P3)P4= 12+(12)×(14)+(12)×(34)×(18)+(12)×(34)×(78)×(116)= 12+16+18×(12)+18×(78)×(116)= 7892= 0.8789
Therefore, the answer is (d) 0.8.
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Use the Extended Euclidean Algorithm to show that the inverse of 177 in mod 901 is 56 by hand calculations ?
The inverse of 177 in mod 901 is indeed 56, as determined through the Extended Euclidean Algorithm by hand calculations.
Given that the inverse of 177 in mod 901 is 56.
To find the inverse of 177 modulo 901 using the Extended Euclidean Algorithm, perform the calculations step by step.
Step 1: Initialize the algorithm with the given values:
a = 901 (modulus)
b = 177 (number for which to find the inverse)
Introduce two variables:
[tex]x_0 = 1, y_0 = 0[/tex]
[tex]x_1 = 0, y_1 = 1[/tex]
Step 2: Perform the iterations of the Extended Euclidean Algorithm:
While b is not zero, repeat the following steps:
Calculate the quotient and remainder of a divided by b:
q = a / b
r = a % b (modulus operator)
Update the values of a and b:
[tex]a = b[/tex]
[tex]b = r[/tex]
Update the values of x and y:
[tex]x = x_0 - q * x_1[/tex]
[tex]y = y_0 - q * y_1[/tex]
Update the values of [tex]x_0, y_0, x_1, y_1[/tex]:
[tex]x_0 = x_1[/tex]
[tex]y_0 = y_1[/tex]
[tex]x_1 = x[/tex]
[tex]y_1 = y[/tex]
Step 3: Once the loop ends and b becomes zero, and obtain the [tex]gcd(a, b) = gcd(901, 177) = 1[/tex], indicating that 177 has an inverse modulo 901.
Step 4: The inverse of 177 modulo 901 is given by [tex]y_0[/tex], which is 56.
Therefore, the inverse of 177 in mod 901 is indeed 56, as determined through the Extended Euclidean Algorithm by hand calculations.
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how do I solve sin(4x)=sin(2x)?
Answer:
sin(4x) = sin(2x) is unsolvable.
Step-by-step explanation:
The two sides are not equal.
You spend £41.01 on groceries, £49.54 on fuel, and £12.50 on lottery tickets, how much do you have left from £105?
Answer:
£1.95
Step-by-step explanation:
£41.01 + £49.54 + £12.50 = £103.05
£105 - £103.05 = £1.95
x is 40% of 60
x=?
please help!!
Answer:
x = 24
Step-by-step explanation:
x = .4(60)
x = 24
40% of 60 can be found by converting 40% to a decimal and multiplying it by 60.
40% = 0.4
60x0.4=2.4
Now move the decimal point right one.
So x is 24.
---
hope it helps
Interest earned in the first year was $75 . If the total interest for the next 10 years is $750 ,
then the investment must be receiving simple interest .
True
False
Interest earned in the first year was $75. If the total interest for the next 10 years is $750, then the investment must be receiving simple interest. False.
If the total interest for the next 10 years is $750, it indicates that the investment is receiving compound interest, not simple interest. In compound interest, the interest earned in each period is added to the principal, resulting in an increasing base for calculating subsequent interest. Simple interest, on the other hand, is calculated solely based on the initial principal amount and does not incorporate any interest earned over time.
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find the range of f(x)=2/5x + 5 for the domain (-4, -2, 0 3)
my answer is 3.4, 4.2, 5, 6.2 but im not fully sure
Answer:
Your answers are correct
Step-by-step explanation:
the top of a swimming pool is at ground level. if the pool is 2.50 m deep, how far below ground level does the bottom of the pool appear to be located for the following conditions?
Given a swimming pool that is 2.50 m deep, we need to determine how far below ground level the bottom of the pool appears to be located.
The apparent depth of an object submerged in a medium, such as water, can be calculated using the concept of refraction. Refraction occurs when light travels from one medium to another, and its speed changes. According to Snell's law, the apparent depth (d') of an object in a medium is related to its actual depth (d) and the refractive index (n) of the medium.
The formula for calculating the apparent depth is:
d' = d / n.
In this case, the actual depth of the pool is 2.50 m, and the pool is filled with water, which has a refractive index of approximately 1.33.
Substituting the values into the formula, we have:
d' = 2.50 m / 1.33 ≈ 1.88 m.
Therefore, the bottom of the pool appears to be located approximately 1.88 meters below ground level. This means that when observing the pool from above, it would appear as if the bottom of the pool is situated 1.88 meters below the surface of the ground.
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Prove that for a normal matrix A, eigenvectors corresponding to different eigenvalues are necessarily orthogonal.
Eigenvalues and eigenvectors play a crucial role in the study of linear transformations and matrices. For a normal matrix A, it can be proven that eigenvectors corresponding to different eigenvalues are necessarily orthogonal.
To understand why eigenvectors corresponding to different eigenvalues are orthogonal for a normal matrix, we need to consider the properties of normal matrices. A matrix A is normal if it commutes with its conjugate transpose A* (i.e., A * A* = A* A).
Now, let's consider two eigenvectors v₁ and v₂ corresponding to different eigenvalues λ₁ and λ₂, respectively. We want to show that v₁ and v₂ are orthogonal, meaning their dot product is zero (v₁ · v₂ = 0).
Let's denote the conjugate transpose of A as A*, and the eigenvalues and eigenvectors as follows:
A * A = A * A* (1)
Multiplying both sides of equation (1) by v₂* (the conjugate transpose of v₂) from the left gives:
v₂* A * A = v₂* A * A* (2)
Since v₂ is an eigenvector of A, we can express it as:
A * v₂ = λ₂ v₂ (3)
Substituting equation (3) into equation (2) gives:
v₂* λ₂ A = v₂* A * A* (4)
Now, let's multiply equation (4) by v₁ from the right:
v₂* λ₂ A v₁ = v₂* A * A* v₁ (5)
Since v₁ is an eigenvector of A, we can express it as:
A * v₁ = λ₁ v₁ (6)
Substituting equation (6) into equation (5) gives:
v₂* λ₂ λ₁ v₁ = v₂* λ₁ A* v₁ (7)
Notice that λ₁ and λ₂ are scalars, so we can move them around. Taking the conjugate transpose of equation (7), we get:
(λ₂ λ₁) v₁* v₂ = (λ₁ v₁)* A v₂ (8)
Now, we have v₁* v₂ on the left-hand side and (λ₁ v₁)* A v₂ on the right-hand side. If v₁ and v₂ are not orthogonal (v₁ · v₂ ≠ 0), then v₁* v₂ ≠ 0. However, the right-hand side of equation (8) is proportional to (λ₁ v₁)* A v₂, which is proportional to A v₂. This implies that A v₂ is a scalar multiple of v₁, which contradicts the assumption that v₁ and v₂ correspond to different eigenvalues.
Therefore, we conclude that eigenvectors corresponding to different eigenvalues for a normal matrix are necessarily orthogonal.
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A mint milk shake contains 1.25 fluid ounces of milk for every 4 ounces of ice cream. A strawberry milk shake contains 1.75 fluid ounces of milk for every 5 ounces of ice cream. Which milk shake is thicker?
Answer:
1.25/4 = 5/16
1.75/5 = 7/20
Determine which one of these fractions is bigger.
Both milkshakes have the same thickness.
Given that,
A mint milkshake contains 1.25 fluid ounces of milk for every 4 ounces of ice cream. A strawberry milkshake contains 1.75 fluid ounces of milk for every 5 ounces of ice cream. Which milkshake is thicker is to be determined.
The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
Here,
According to the question,
A mint milkshake contains 1.25 fluid ounces of milk for every 4 ounces of ice cream.
Ratio of the milk = 1.25 / 4 = 0.35
A strawberry milkshake contains 1.75 fluid ounces of milk for every 5 ounces of ice cream.
Ratio of the milke = 1.75 / 5 = 0.35
comparing the ratio both are equal,
Thus, Both milkshakes have the same thickness.
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HHEEEEEELLLLPPPPPP ANSWER THIS QUICKLYYYYY
Answer: 27
Step-by-step explanation:
[tex]a_{1}=6\\a_{2}=a_{n-1}+7=a_{2-1} +7=a_{1} +7=6+7=13\\a_{3}=a_{n-1}+7=a_{3-1} +7=a_{2} +7=13+7=20\\a_{4}=a_{n-1}+7=a_{4-1} +7=a_{3} +7=20+7=27[/tex]
find the value of X such that the data set has a mean of 118. 101, 119, 104, 115, 109, x
Answer:
160
Step-by-step explanation:
101+119+104+115+109+x=548+x
there are 6 terms including x so divide the sum by 6
(548+x)/6=118
multiply both sides by 6
548+x=708
subtract 548
x=160
hope that helps :)
Answer:
160
Step-by-step explanation:
There are 6 numbers in the set
101 + 119 + 104 + 115 + 109 + x = 6(118)
101 + 119 + 104 + 115 + 109 + x = 708
548 + x = 708
-548 -548
x = 160
Assume that women's heights are normally distributed with a mean given by = 62.5 in, and a standard deviation given by a = 2.1 in. (a) If 1 woman is randomly selected, find the probability that her height is less than 63 in. (b) If 33 women are randomly selected, find the probability that they have a mean height less than 63 in.
(a) The probability is approximately __________ (Round to four decimal places as needed.)
(b) The probability is approximately_______________
(a) The probability is approximately 0.6915. (Round to four decimal places as needed.)
(b) The probability is approximately 0.9999.
(a) The probability that a randomly selected woman's height is less than 63 inches is approximately 0.6915.
To find this probability, we can use the standard normal distribution and z-scores. The z-score is calculated using the formula z = (x - μ) / σ, where x is the value we are interested in, μ is the mean, and σ is the standard deviation. In this case, x = 63 inches, μ = 62.5 inches, and σ = 2.1 inches.
Substituting these values into the formula, we get z = (63 - 62.5) / 2.1 = 0.2381. To find the probability corresponding to this z-score, we can look it up in the standard normal distribution table or use a statistical calculator. The probability associated with a z-score of 0.2381 is approximately 0.5915.
However, since we want to find the probability that the height is less than 63 inches, we need to find the area to the left of the z-score. Since the standard normal distribution is symmetrical, the area to the left of a positive z-score is equal to 1 minus the area to the right. Therefore, the probability that a randomly selected woman's height is less than 63 inches is approximately 1 - 0.5915 = 0.6915.
(b) The probability that a sample of 33 randomly selected women has a mean height less than 63 inches is approximately 0.9999.
When we have a sample of multiple individuals, the distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution. This phenomenon is known as the Central Limit Theorem.
For this problem, we can assume that the mean height of the sample of 33 women follows a normal distribution with the same mean as the population (62.5 inches) but with a standard deviation equal to the population standard deviation divided by the square root of the sample size. In this case, the sample standard deviation would be 2.1 inches divided by the square root of 33, which is approximately 0.3669 inches.
To find the probability that the sample mean height is less than 63 inches, we can again use z-scores. The z-score is calculated using the formula z = (x - μ) / (σ / √n), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
Substituting the values into the formula, we get z = (63 - 62.5) / (0.3669) = 1.3662. The probability corresponding to this z-score can be found using a standard normal distribution table or a statistical calculator. The probability associated with a z-score of 1.3662 is approximately 0.9082.
However, since we want to find the probability that the sample mean height is less than 63 inches, we need to find the area to the left of the z-score. Thus, the probability that a sample of 33 randomly selected women has a mean height less than 63 inches is approximately 0.9999.
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Plssss help me out I really need a 87 and don’t get this wrong ❤️
Answer:
73 degrees
Step-by-step explanation:
The total number of all of the angles in a triangle added together should be 180 degrees. You know that one of the angles is 17. The other angle is 90 because it is a right triangle.
90 + 17 = 107
180 - 107 = 73
So, the other angle is 73 degrees. If this is wrong I am so sorry. Hope this helps you, let me know if it is right!
Answer:
73°
Step-by-step explanation:
A right triangle has one right angle and two acute angles.
A right angle is 90° and the question says that one of the angle are 17°.
We need to add both angles together which = 107°.
A triangle internal total angles will always add up to 180°.
So we need to do 180° - 107° to find the missing angle which = 73°.
Also, the question said that the missing angles was acute and 73° is acute.
hope this helps :)
PLSSSSS HELPPP PLSSSSSSSSS PLS I NEED HELPP
Jorge takes his friends out for smoothies. He buys 5 smoothies and leaves a $3 tip,
paying a total of $23. He wants to know the price of one smoothie.
• price of 5 smoothies: 23 – 3 = 20
1) Which equation shows how to find the price of one smoothie?
20 – 5 = 15
20 : 5 = 4
23 : 5 = 4.60
23 - 5 = 18
Answer:
Each smoothie was $4
Step-by-step explanation:
Tbh you can guess for the fractions
Answer:
4:1 ratio
Sugar: 1 cup
Butter: 3/4 cups
Eggs: 2
Baking powder: 3/8 tsp
Flour: 5/8 tsp (you need way more flour for cookies)
Salt: 1/8 tsp (original # was hard to make out but I think it was 1/2 tsp)
Expert Help me plssss. I dont understand how to do it
Answer:
V=301.44ft^3
Step-by-step explanation:
l^2°r^2r^2+h^2
10^2=6^2+h^2
100=36+h^2
100-36=h^3
h^2=64
h=8
Volume of cone:
1/3πr^2h
1/3(π)(6)^2(8)
301.44ft^3
Hope it helps....
2( 5/3 + 3/4 ) − 4/3
Answer: = 42/12 Or simply = 7/2
Step-by-step explanation:
2(5/3 + 3/4 ) − 4/3
= 2(5/3) + 2(3/4) − 4/3
= 10/3 + 6/4 - 4/3
= 6/3 + 6/4
= 24/12 + 18/12
= 42/12
Or simply = 7/2
For the quadratic function show below the coordinates of its vertex are
Answer: 0,2
Step-by-step explanation:
What is the solution to the following graph? Write it as an ordered pair to get credit.
Answer:
(2,6)
Step-by-step explanation:
A rectangle is 29 feet long and 7 feet long. What is the area of this rectangle? 203 ft² 143 ft² 107 ft² 72 ft²
Answer:
203 ft²
Step-by-step explanation:
We need to use multiplication for the answer of this.
29 × 7 = 203
so that means that the answer in feet is 203 ft²
good luck hope this helped
-cheesetoasty
OMG HELP PLS IM PANICKING OMG OMG I GOT A F IN MATH AND I ONLY HAVE 1 DAY TO CHANGE MY GRADE BECAUSE TOMORROW IS THE FINAL REPORT CARD RESULTS AND I DONT WANNA FAIL PLS HELP-
AND CAN ANYONE PLS DRAW ME THE ANSWERS I CANT UNDERSTAND ANYTHING PLS I BEG U ILL GIVE U BRAINLEST
Answer:
here, i can help you out!
Step-by-step explanation:
Answer:
For 1. 2/5 is less full then 1/2
EASY POINTS!!
INCLUDE A DISC
Answer:
I don't know what you mean by disc but the answer is 80 degrees.
Step by Step explanation:
A triangle is made up of 180 deg
65+35=100
180-100=80
Answer:
F. 80°
Step-by-step explanation:
Because a triangle measues 180°
35+65= 100
180-100=80
So the remaining angle must measure an exact 80°
Vera exercised for 60% of the time that Noah exercised. Vera exercised for 78 minutes. How long did Noah exercise
The time spent by Noah exercising is 130 minutes
How to determine how long did Noah exerciseFrom the question, we have the following parameters that can be used in our computation:
Vera exercised for 60% of the time that Noah exercised. Vera exercised for 78 minutes.using the above as a guide, we have the following:
Vera = 60% * Noah
So, we have
60% * Noah = 78
Divide both sides by 60%
Noah = 130
Hence, Noah exercised for 130 minutes
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a triangle with an area of 23 cm² is dilated by a factor of 6. what is the area of the dilated triangle?
When a triangle is dilated by a scale factor, the area of the dilated triangle is equal to the scale factor squared times the area of the original triangle. The area of the dilated triangle is 828 cm².
In this case, the original triangle has an area of 23 cm². The triangle is dilated by a factor of 6, so the scale factor is 6.
To find the area of the dilated triangle, we use the formula:
Area of Dilated Triangle = (Scale Factor)^2 * Area of Original Triangle
Plugging in the values:
Area of Dilated Triangle = 6^2 * 23 cm²
= 36 * 23 cm²
= 828 cm²
Therefore, the area of the dilated triangle is 828 cm².
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What is the surface area 3yd 3yd 3yd
Answer:
12
Step-by-step explanation:
your welcome :)
pls pls pls, I beg you to answer this question only if you know the correct answer please please please I beg you
Answer:
Median is the middle line of the box, Lower quartile is the number of the lower end of the box, Upper quartile is the line at the larger end of the box, Maximum is the largest number in the box plot (end of right whisker), Minimum is the lowest number (end of left whisker).
Step-by-step explanation:
32.
Median: 88
Maximum (largest number): 102
Minimum (lowest number): 38
Interquartile range:
96 - 72 = 24
b.
25 % higher
75 % lower?
c.
You can see the range is more towards the right of the box meaning they have higher scores, and that the median or middle is a higher number so it means that most of the students understood and did well on the test.
???.
First quartile: 16
Second: 19
Third: 20
Range: 4
34. Since they are already in least to greatest order, all we have to do is graph it!
85 - 99 is 2
100 - 114 is 1
115 - 129 is 5
130 - 144 is 6
Show your work please
Answer:
B 2208cm squared
you follow this formula
A=2(wl+hl+hw)
w means width
l means length
h means height
input the numbers and you got your answer.
Hope this helped ;)
Answer:5760 cm2
Step-by-step explanation:length times width times height 12 times 12 is 144 and 144 times 40 is 5770 cm2
Solve -72 = 8 (y - 3) pls
Step-by-step explanation:
Given
- 72 = 8 ( y - 3 )
or - 72 / 8 = y - 3
or, - 9 = y - 3
y = - 9 + 3
Therefore X = - 6
Hope it will help :)❤
Answer:
Step-by-step explanation:
-72=8y-24
-72+24=8y
-48=8y
-48/8=y
-6=y
help pls Evaluate.
169−−−√
Enter your answer in the box.
Answer:
square root is 13
Step-by-step explanation:
Answer:
13!
Step-by-step explanation:
i used my calculator and did the test k-12! its right!
divide 54 books between A and B in the ratio 13:14
Answer:
hi
Step-by-step explanation:
i think,
13:14=54
13k+14k=54
27k=54
k=54/27
k=2
13×2=26 and 14×2=28
to verify the correctness of the answer-26+28=56
have a nice day
hope it helps
The ratio of the divide is mathematically given as
26:28
What is the ratio of the divide?Question Parameters:
divide 54 books between A and B in the ratio 13:14
Generally, ratios are mathematically given as
X=13/27*54
X=26
Y=14/27*54
Y=28
In conclusion, the ratio of the divide would be
26:28
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