Answer:
0.3694
Step-by-step explanation:
In this question, we are asked to calculate the probability that a golfer scored at least 74 if she played on a particular day.
Given that ,
mean = µ = 73
standard deviation = σ = 3
P(x > 74) = 1 - P(x<74 )
= 1 - P[(x -µ) / σ < (74 -73) /3 ]
= 1 - P(z <0.3333 )
Using z table
= 1 - 0.6305
= 0.3694
probability= 0.3694
To find the probability of a golfer scoring at least 74 on a course with a mean score of 73 and a standard deviation of 3, we calculate the z-score for 74, find the corresponding probability in the z-table, and subtract this from 1 to get the upper tail probability. The probability is approximately 37%.
Explanation:The score of golfers for a particular course follows a normal distribution that has a mean of 73 and a standard deviation of 3. We want to find the probability that a golfer scores at least 74. This is a question of statistics and specifically involves the concept of the normal distribution and calculating z-scores.
Firstly, we need to calculate the z-score for the score of 74. The z-score is calculated as (X-μ)/σ, where X is the score we are interested, μ is the mean, and σ is the standard deviation. Substituting the given values, (74 - 73) / 3 gives a z-score of approximately 0.33.
Then, to find the probability that a score is at least 74, we need to find the proportion of data to the right of this z-score in a standard normal distribution. This is known as the 'upper tail'. We subtract the z-score from 1 because the total probability under the normal curve is 1. If we look up 0.33 in the z-table, we get a value of 0.6293. Subtracting this value from 1 gives us 0.3707.
Therefore, the probability that a golfer scores at least 74 on this course is approximately 0.37 or 37%.
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If the area of a right triangle is 6.22 square inches and its base is 3.11 inches, write an equation that relates the area to the height, h, and the base. Solve the equation to determine the height.
Answer: (a) 12.44 - 3.11h = 0
(b) 4in²
Step-by-step explanation:
Area of a triangle = (1/2)bh, where b is the base and h is the height.
Now from the question, Area = 6.22in² and the base is 3.11inches.
Therefore, the equation that relates the area to the height and the base wiil be
Area = (3.11)h/2
6.22 x 2 = 3.11 x h
12.44 = 3.11h
12.44 - 3.11h = 0
(b) to find the value of h from the equation, make h the subject of the formula by solving for h
12.44 = 3.11h
h = 12.44/3.11
= 4in²
Which is a perfect square? 5, 8, 44, 36
Answer:
The answer is 36.
Step-by-step explanation:
36
/\
6 6
/\ /\
3 2 3 2
Given that 10% of the nails made using a certain manufacturing process have a length less than 2.48 inches, while 5% have a length greater than 2.54 inches, what are the mean and standard deviation of the lengths of the nails? Assume that the lengths have a normal distribution.
Answer:
The mean, μ is 2.5063 and
The standard deviation, σ = 2.0499 × 10⁻²
Step-by-step explanation:
Here we have
[tex]z = \frac{x- \mu}{\sigma}[/tex]
[tex]z \sigma ={x- \mu}{}[/tex] and
10% have length < 2.48 in while
5% have length > 2.54 in
and
From the z score table
Critical z at 10% to the left = -1.282
Critical z at 5% to the right = 1.645
Therefore, the equations become
-1.282σ = 2.48 - μ → μ -1.282σ = 2.48
1.645σ = 2.54 - μ → μ + 1.645σ = 2.54
Solving the above equations gives
The mean, μ = 2.5063 and
The standard deviation, σ = 2.0499 × 10⁻².
Final answer:
Using the Z-score method and the percentages provided, two equations are set up and solved simultaneously to determine the mean and standard deviation of the lengths of the nails.
Explanation:
Given the information that 10% of the nails produced are shorter than 2.48 inches and that 5% are longer than 2.54 inches, and assuming the lengths are normally distributed, we can determine the mean (μ) and standard deviation (σ) of the lengths of the nails. We can use the Z-score formula which is (X - μ) / σ, where X is the value of the length, μ is the mean, and σ is the standard deviation.
Here, we have two Z-scores corresponding to the given percentages. For 10%, the Z-score is approximately -1.28, and for 5%, the Z-score is approximately 1.645. Now, setting up two equations,
(2.48 - μ) / σ = -1.28
(2.54 - μ) / σ = 1.645
we have a system of equations with two unknowns. Solving these equations simultaneously gives us the values for the mean and standard deviation of nail lengths.
To solve the system, multiply the first equation by σ to get μ = σ * -1.28 + 2.48 and the second equation by σ to get μ = σ * 1.645 + 2.54. By setting these two equations for μ equal to each other, you can solve for σ and afterwards find μ.
To solve the given system of equations:
1. (2.48 - μ) / σ = -1.28
2. (2.54 - μ) / σ = 1.645
We can use the method of substitution or elimination. Let's use the substitution method.
From equation 1, we can isolate μ :
(2.48 - μ) / σ = -1.28
2.48 - μ = -1.28σ
μ = 2.48 + 1.28σ
Now, we substitute this expression for μ into equation 2:
(2.54 - (2.48 + 1.28σ)) / σ = 1.645
(2.54 - 2.48 - 1.28σ) / σ = 1.645
(0.06 - 1.28σ) / σ = 1.645
0.06 - 1.28σ = 1.645σ
0.06 = 1.645σ + 1.28σ
0.06 = 2.925σ
Now, we solve for σ :
σ = [tex]\frac{0.06}{2.925}[/tex]
σ ≈ 0.0205
Now that we have found the value of \( σ \), we can substitute it back into the expression we found for \( μ \) to find its value:
μ = 2.48 + 1.28σ
μ = 2.48 + 1.28(0.0205)
μ ≈ 2.48 + 0.02628
μ ≈ 2.50628
So, the solution is approximately μ ≈ 2.50628 and σ ≈ 0.0205 .
Two of the angles in a triangle measure 90° and 16°. What is the measure of the third angle?
Answer:
74°
Step-by-step explanation:
All interior angles of a triangle add up to 180°, so to find the measure of the third angle here, we can use this:
180 - (90+16)
180 - 106
= 74°
Hope this helps!
Stephen spent $4 on milk, $6 on eggs, and $11 on cereal. He wrote the ratio 6
11
to describe some of his purchases. Explain why the ratio is not a fraction.
Answer:
Mass is a measure of the amount of matter in an object. Mass is usually measured in grams (g) or kilograms (kg). ... An object's mass is constant in all circumstances; contrast this with its weight, a force that depends on gravity. Your mass on the earth and the moon are identical.
Answer:
Step-by-step explanation:
The ratio of 6
11
compares money spent on eggs to money spent on cereal. This is a part-to-part comparison, not a part-to-whole comparison.
A tent originally sold for $260 and has been marked down to $208. What
is the percent of discount?
The percent discount of the tent is 20%.
A discount reduces the price of an item. After a discount, the price of an item is reduced.
In order to determine the percent discount, the difference in price of the tents have to determined.
$260 - $208 = $52
The percent discount = ($52 / $260) x 100 = 20%
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The area of a rectangular garden is 18z+24 square feet. What are the possible dimensions of the garden?
Given:
The area of the rectangular garden is 18z+24 sq ft.
To find the possible dimensions of the garden.
Formula
The area of the rectangular garden is
[tex]A = lb[/tex]
where,
l be the length of the rectangle
b be the width.
Let us take l and b be the length and width of the given rectangular park respectively.
Now,
According to the problem,
[tex]lb = 18z+24[/tex]
or, [tex]lb = 6(3z+4)[/tex]
We can determine that,
l = 6 and b = 3z+4 or vice versa.
Hence,
The possible length and width of the rectangular garden is 6 and (3z+4) respectively.
During her lunch hour, Shawna asked 40 students how many after-school clubs they joneu. THICH WIVE
of clubs that the students joined.
2,2,3,0, 3, 2, 4, 2, 1, 4, 3, 2, 4, 1, 0, 2, 1, 3, 2, 0,
1, 1, 2, 1,0,3,0, 1, 4, 1, 1, 0, 2, 3, 2, 0, 3, 2, 0, 1
If this sample is representative of the student population of 360 students, about how many students in the school joi
clubs?
15 students
63 students
109 students
189 students
O
Answer:
maybe 15 students or 63 students and if not I am sorry of that's wrong
rolls
Which reaction shows that the enthalpy of formation of C2H4 IS A Hp = 52.5
kJ/mol?
A. 2C(s) + 2H₂(g) + 52.5 kJ → C₂H₄ shows that the enthalpy of formation of C₂H₄ is 52.5 kJ/mol.
Step-by-step explanation:
Enthalpy of formation of C₂H₄ is given as 52.5 kJ/mol.
There are 4 options given and they are:
A. 2C(s) + 2H₂(g) + 52.5 kJ → C₂H₄
B. 2C(s) + 4H(g) + 52.5 kJ → C₂H₄
C. 2C(s) + 2H₂(g) → C₂H₄ + 52.5 kJ
D. 2C(s) + 4H(g) → C₂H₄ + 52.5 kJ
Here the reactants absorb some energy from the surroundings and gives the product and it is an endothermic reaction.
So A and B is taken into account, but in B there are 4 H atoms involved in the reaction. So in the reaction A hydrogen molecules are involved and also energy is absorbed by the reactants.
So option A is the answer.
Answer: 2C(s) + 2H₂(g) + 52.5 kJ → C₂H₄
which is a name for the angle shown? Select two answers
Answer:
I'm not sure how to answer is but i think its called < CDE or < EDC or it is an acute angle.
Step-by-step explanation:
The two ways of naming the given angle are:
1) D or ∠D2) EDC or ∠EDCHow to name an angle?
There are two general ways of naming an angle.
First, we just call the angle as the vertex. For example, in this case the vertex is D, then the name of the angle would be D or ∠D, where the symbol ∠ is used for angles.
Now, there are another way of naming an angle, and it depends on the arms of the angle (in cases where a point is a common vertex for many angles, we need to specify the arms).
So the name would be:
EDC or ∠EDC
Where the vertex goes always in the middle.
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Answer:
Last one: 5x - 3√y + 1
Step-by-step explanation:
8x + √1 - √9y - √9x^2
8x + 1 - 3√y - 3x
5x + 1 - 3√y
5x - 3√y + 1
CAN YOU PLEASE MARK MY ANSWER BRANLIEST
Solve this system of equations using substitution
y = - 4
x + 2y = 10
Step 1: Substitute for y in the second equation. Which is
the resulting equation?
Answer:
x + 2(-4) = 10
x - 8 = 10
x = -18
y = -4
(-18, -4)
Step-by-step explanation:
Answer:
x + 2(-4) = 10
Step-by-step explanation:
Substituting -4 for y in the second equation results in x + 2(-4) = 10. This simplifies to x - 8 = 10 and then x = 18.
Please, when the problem statement includes possible answer choices, share them.
6.7 is 10% of what number
Answer:
the answer is 67
Step-by-step explanation:
hope it's helpful
if Lydia buys 1/2 pound of the Breakfast Tea and 2 pounds of the Dark Roast coffee, how many 1- pound bags of Pumpkin Spice coffee can she buy?
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
Lydia is at a coffee shop and knows she can spend no more than $65
before tax. She sees this price list in the coffee shop.
Dark Roast Coffee $7.50
Pumpkin Spice Coffee $10.50
Breakfast Tea $23.50
if Lydia buys 1/2 pound of the Breakfast Tea and 2 pounds of the Dark Roast coffee, how many 1- pound bags of Pumpkin Spice coffee can she buy?
Given Information:
Shopping Budge = $65
Price of Dark Roast Coffee = $7.50
Price of Pumpkin Spice Coffee = $10.50
Price of Breakfast Tea = $23.50
Amount of Breakfast Tea required = 1/2 pound
Amount of Dark Roast coffee required = 2 pounds
Required Information:
How many 1-pound Pumpkin Spice Coffee can she buy = ?
Answer:
n = 3 bags of 1-pound Pumpkin Spice Coffee
Step-by-step explanation:
We are given that the amount of Breakfast Tea required is 1/2 pound so the cost of Breakfast Tea is
Cost of Breakfast Tea = 1/2*23.50 = $11.75
We are also given that the amount of Dark Roast coffee required is 2 pounds so the cost of Dark Roast coffee is
Cost of Dark Roast coffee = 2*7.50
Cost of Dark Roast coffee = $15
We know that total Lydia's total budget is $65
11.75 + 15 + 10.50x = 65
Where x represents the amount of Pumpkin Spice coffee required
10.50x = 65 - 11.75 - 15
10.50x = 38.75
x = 3.64 pounds
That means Lydia can buy 3.64 pounds of Pumpkin Spice coffee.
Now assuming that the Pumpkin Spice coffee is sold only in 1-pound bags then the required number of bags that Lydia can buy is
n = 3.64 pound/1-pound
n = 3.64
Since bags cannot be in fraction so
n = 3 bags
Note: we can not round off to 4 bags since that would surpass the given budged.
Plz HELP
.........../....
Answer:
The answer to your question is below
Step-by-step explanation:
Data
4 red marbles
3 blue marbles
3 yellow marbles
a) Total number of marbles = 4 + 3 + 3 = 10 marbles
b) Number of red marbles = 4 marbles
c) Number of blue marbles = 3 marbles
d) P(blue) = number of blue marbles/ total number = 3/10
e) P(red) = number of red marbles/total number = 4/10 = 2/5
Humans usually have 20 baby teeth, which are replaced by 32 adult teeth. Raul said he has lost 6 of his baby teeth. Write two fractions equivalent to this number. Explain your answer.
The question is not very clear, since the most logical thing is to think that the fraction is with respect to the number of baby teeth, if so:
6/20 and 3/10, these would be the two fractions.
But the literal question is to express the number 6, as a fraction.
We can do it by multiplying and dividing by the same number, for example:
6 * 2/2 = 12/2
6 * 10/10 = 60/10
This would be the two fractions.
ms. smith bought a camera that cost $450 in addition she had to pay 4% sales tax how much did ms. smith pay for the camera
Answer:
$468
Step-by-step explanation:
450 + (450*0.04) = $468
Answer:
18
Step-by-step explanation:
In the early 1900's, the deer population of the Kaibab Plateau in Arizona increased rapidly because hunters had reduced the number of predators. However, the food supply was not great enough to support the increased population and the population eventually began to decline. The deer population for the years 1905 to 1930 can be approximated by the polynomial where x is the number of years from 1900. Evaluate the polynomial to find the deer population in 1920.
Answer:
The deer population in 1920 is 104000
Step-by-step explanation:
Here we have the deer population is given approximately by the following equation;
Population of deer = -0.125·x⁵ + 3.125·x⁴ + 4000
Where x = number of years from 1900
Therefore, in 1920, we have x = 20
Hence, the deer population in 1920 is then
-0.125·20⁵ + 3.125·20⁴ + 4000
Which gives
-400000 + 500000 + 4000 = 104000
The deer population in 1920 is therefore, 104000.
Nathan read 2 books in 10 months. What was his rate of reading in books per month
Step-by-step explanation:
Nathan read 2 books in 10 months.
The time taken to complete 1 book = [tex]\frac{10}{2}[/tex] = 5 months
To complete 1 book it takes 5 months.
The rate of reading a book per month = [tex]\frac{1}{5}[/tex] = 20%
What is the area of the following circle?
Answer:
A=153.938 or 154
Step-by-step explanation:
A= pi r^2
A=pi(7)^2
A=pi(49)
A=153.938 or 154
Answer:
49π or 153.86
Step-by-step explanation:
Hi there,
The formula for area of a cirlcle is A = [tex]\pi[/tex][tex]r^{2}[/tex]
So, to find the area, simply plug in the radius into the equation.
A = π * [tex]7^{2}[/tex]
A = 49π
The area is either 49π or if you use 3.14 for pi, it's 153.86.
Hope this helps!
- Emily
The cost of buying a small piece of land in a remote village since the year 1990 is represented by the following table . Which model c(t) the cost of the piece of land t years since 1990, best fits the data?
Answer:
C(t)=30+3.5t
Step-by-step explanation:
Yeah this is the answer
Answer:
C(t)=30+3.5t
Step-by-step explanation:
Time increases by 2, the average difference in the cost is approximately 7.
So if d is the common difference of the function modeling this relationship, then 2d≈72.
Therefore, d≈ 7/2 = 3.5
Since the initial cost of the land is 30 thousand dollars, the function that best models its cost t years since 1990 is C(t)=30+3.5t
If there are 2.2 pounds in 1 kilogram how many pounds are there in x kilograms?
Answer:
P=x/2.2
Step-by-step explanation:
We can create an equation to solve this.
Let the number of pounds be P
Let the number of kilograms be X
Now, we know that for 1 kilogram, there is 2.2 pounds.
Therefore if we have 1 kilogram (X) then we will have 2.2 pounds (P).
X=2.2P
All you have to do now is rearrange the equation to find the number of pounds in x kilograms. To do this divide both sides by 2.
Therefore you will get P=x/2.2
The number of pounds in X kilograms can be obtained by using the proportional relationship, Hence, the number of pounds in X kilograms is 2.2X pounds
Given the Parameters :
Number of pounds in 1 kilograms = 2.2 poundsCreating the proportional expression thus :
1 kilogram = 2.2 pounds
X kilograms =?
Cross multiply :
Number of pounds = 2.2X
Therefore, there will be 2.2X pounds in 1 kilogram.
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A balloon is 23 feet below a tree limb. The balloon floats up 19 feet. What is it’s position relative to the tree limb
Answer:
It is 4 feet below the tree limb now
step by step
it starts at -23 or 23 below and rises 19 or adds 19 to the -23
so -23+19=-4. or 4 feet below the tree limb
Final answer:
After floating up 19 feet from its initial position of 23 feet below the tree limb, the balloon is 4 feet below the limb.
Explanation:
The student's question pertains to finding out the position of a balloon relative to a tree limb if the balloon starts 23 feet below the tree limb and then floats up 19 feet. We begin by acknowledging that the balloon's initial position is -23 feet (since it is below the limb, we consider this as negative). Upon floating up 19 feet, we perform the arithmetic operation of adding +19 feet to the initial position.
The calculation is as follows: -23 feet + 19 feet = -4 feet.
Therefore, the balloon's final position relative to the tree limb is 4 feet below it, since the result is still negative, indicating that the balloon did not reach or surpass the height of the limb.
To use the two sample t procedure to perform a significance test on the difference of two means, we assume: a) The populations' standard deviation are known. b) The samples from each population are independent. c) The sample sizes are large. d) The distributions are exactly normal in each population.
Answer:
The option which is an exception is;
c) The sample sizes are large
Step-by-step explanation:
Here the requirement to perform a two sample t procedure are as follows;
1. The two samples have equal variance, hence the variance should be known
2. The samples for which the two sample t procedure is performed must be independent
3. The data are in alignment with the normal distribution probability
4. The samples are random samples taken from the different respective population
Since the sample size is known, we do not assume that the sample size are large.
Therefore options a), b) and d) are all correct except option c).
help with properties of rhombus,rectangles and squares
Answer:
a = 3
b = 4
c = 5
Step-by-step explanation:
This is a rhombus. A property of a rhombus is that their diagonals perpendicularly bisect each other. In other words, if the point in the center is A, then HA = MA and EA = OA. So: 3 = a and 4 = b.
Since angle HAO forms a right angle, we can use the Pythagorean Theorem to say that HA^2 + AO^2 = OH^2: 3^2 + 4^2 = 9 + 16 = 25.
OH^2 = 25
OH = 5
Hope this helps!
Answer:
a = 3
b = 4
c = 5
Step-by-step explanation:
Rhombus has all sides equal
c = EH = sqrt(4² + 3²) = 5
Diagonals are Perpendicular bisectors of each other
b = 4
a = 3
Two consecutive whole numbers total 17. Find the larger.
Answer:
9
Step-by-step explanation:
Consecutive means in a row
x = 1st number
x+1 = 2nd number
x+x+1 = 17
Combine like terms
2x+1 = 17
Subtract 1 from each side
2x+1-1=17-1
2x = 16
Divide each side by 2
2x/2 =16/2
x=8
x+1 = 9
The larger number is 9
NEED HELP ASAP!!
Which of the following is the correct expanded form for the series below?
a. 0 + 1 + 4 + 9 + 3
b. (0 + 3) +(1 + 3) + (4 + 3) + (9 + 3)
c. 1 + 3 + 9 + 27 + 3
d. (0 +3) + (2 + 3) + (4 + 3) + (6 + 3)
Answer: A
Step-by-step explanation:
The expanded form for the series is 0 + 1+ 4 + 9 +3
What are Arithmetic operations?
Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
[tex]_3\\\sum{n^2}+3\\n=0[/tex]
⇒(0)² + (1)² + (2)² + (3)² +3
⇒0 +1+ 4 + 9 +3
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A baby gains 11 pounds in its firat year of life. The baby gained 4 pounds during the first four months and
second four months. How much did the baby gain in the last four months?
3 1/4 pounds
3 1/2 pounds
4 pounds
5 pounds
Answer:
I think it's 3.5
Step-by-step explanation:
Is the following function exponential? *
3) y=7x-3
Answer:
Step-by-step explanation:
Both x and y have the exponent 1, and therefore this is a LINEAR equation. NO, it is not an exponential function.
Final answer:
The function y=7x-3 is not an exponential function; it is a linear function with a slope of 7 and a y-intercept of -3.
Explanation:
The function given is y=7x-3. To determine whether this function is exponential, we should look at the form of the function. An exponential function has the form y = abˣ, where a is a constant, b is the base of the exponential (which is a positive real number other than 1), and x is the exponent. The given function, however, is a linear function because it can be rewritten in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, m (the slope) is 7, and b (the y-intercept) is -3. Therefore, y=7x-3 is not an exponential function; it is linear.
Express the square root 75 in
simplest radical form.
The square root 75 in simplest radical form will be [tex]5\sqrt{3}[/tex].
We have to Express the square root 75 in simplest radical form.
We know that An expression that uses a root, such as a square root, cube root is known as a radical notation.
First find the factors of 75.
The factors of 75 will be,
[tex]3\times5\times5[/tex].
Now,
[tex]\sqrt{75} =\sqrt{3\times5\times5}[/tex]
since 5 is in pair under the root so it will come out from the root,
[tex]\sqrt{75}=5\sqrt{3}[/tex]
Thus the simplified radical form is [tex]5\sqrt{3}[/tex].
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