Using the normal distribution, it is found that:
a) 95.99% of Tiger's drives travel at least 290 yards.
b) 44.40% of Tiger's drives travel between 305 and 325 yards.
c) If the z-scores do not show on table A, they represent too low or too high values, with probabilities very close to either 0 or 1.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the following rule:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X.If the z-score does not show on the z-table, they represent too low or too high values, with probabilities very close to either 0 or 1.The mean and the standard deviation for the length of Tiger Woods's swings are given as follows:
[tex]\mu = 304, \sigma = 8[/tex]
The proportion of golf swings that are at least 290 years is one subtracted by the p-value of Z when X = 290, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (290 - 304)/8
Z = -1.75
Z = -1.75 has a p-value of 0.0401.
1 - 0.0401 = 0.9599.
Hence the percentage is of 95.99%.
The proportion of golf swings that are between 325 yards and 305 yards is the p-value of Z when X = 325 subtracted by the p-value of Z when X = 305, hence:
X = 325:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (325 - 304)/8
Z = 2.63
Z = 2.63 has a p-value of 0.9957.
X = 305:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (305 - 304)/8
Z = 0.13
Z = 0.13 has a p-value of 0.5517.
0.9957 - 0.5517 = 0.4440.
Hence the percentage is of 44.40%.
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Write a polynomial of least degree with roots 5 and – 9.
Answer: x^2+4x-45
Step-by-step explanation:
Multiply (x-5)(x+9)
Using the FOIL Method.
Multiply
x and x
x and -5
x and 9
-5 and 9
You should get x^2-5x+9x-45
Subtract -5x and 9 and you get your answer
x^2+4x-45
Write a polynomial that could be represented by the graph.
(Which one is correct and why)
Answer:
your answer is C
Step-by-step explanation:
by elimination B is not possible as the graph shows a cubic shape B has no cubic terms, D is not possible because the graph shows a translation on X axis and D represents a translation in Y axis, and A is not possible because when X=0 the value of Y must be -64 and A doesn't comply to that.
Answer:
C
Step-by-step explanation:
the graph has 3 zero solutions (values of x with y = 0).
therefore it has to be of 3rd degree (3 is the max. exponent of x).
that eliminates B, because it is only of 2nd degree.
when x = 0, y is a little bit below -60 but above -80.
but y is negative.
that eliminates A, because when x = 0, y = +64.
for x = -8, y has to be 0 too.
that eliminates D, because for x = -8, y = -8³ - 64 = -512 - 64 = -576
and not 0.
so, C must be correct.
for x = 0, y = -64
for x = -8, y = -8³ + 6×-8² - 24×-8 - 64 =
= -512 + 6×64 + 192 - 64 =
= -512 + 384 + 192 - 64 = 0
for x = -2, y = -2³ + 6×-2² - 24×-2 - 64 =
= -8 + 6×4 + 48 - 64 =
= -8 + 24 + 48 - 64 = 0
for x = 4, y = 4³ + 6×4² - 24×4 - 64 =
= 64 + 6×16 - 96 - 64 =
= 64 + 96 - 96 - 64 = 0
all fits.
Each Friday, the school prints 400 copies of the school newsletter. The equation c = 400w models the relationshipbetween the number of weeks and the total number of copies of the newsletters printed. What is true of the graph ofthis scenario?A viable point on the graph isThe values of w must be
Since:
[tex]\begin{gathered} (w,c)=(8,3200) \\ 3200=400(8) \\ 3200=3200 \\ True \end{gathered}[/tex](8,3200) is a viable point
---------------------------
Since w is the number of copies of the school newsletter, the values of w must be whole numbers
4.There are 30 students in the classroom competing for classroom prizes. Only the first two students whose name is drawn will win a prize. The first student wins 5 bonus points and the second student wins 2 bonus points, both on the upcoming test. If you are one of the 30 students, what is the probability you will win the top prize and your best friend wins the second prize?
Out of 30 students, the probability of one student winning the top prize is 1/30.
Since the student who won the top prize cannot be the student who wins the second prize, then the probability of a student winning the second prize is 1/29.
So, the probability that you will win the top prize and your best friend wins the second prize is:
[tex]P=\frac{1}{30}\times\frac{1}{29}=\frac{1}{870}[/tex]Answer:
The probability that you will win the top prize and your best friend wins the second prize is 1/870.
In decimal form, this is 0.001149.
In percent form, this is approximately 0.11%.
How do I solve for 10?It says to leave in the simplest radical form
the length of th diagonal is 10√2
Explanation:side length = 10 inches
We need an illustration to solve the question:
Using pythagoras' theorem:
Hypotenuse² = opposite² + adjacent²
hypotenuse = diagonal
opposite = 10 in, adjacent = 10 in
diagonal² = 10² + 10²
diagonal² = 100 + 100
diagonal² = 200
diagonal = √200
diagonal = 10√2
Hence, the length of th diagonal is 10√2
Find a formula for the exponential function that satisfies f(0) = 6 and f(1) = 42. f(x) =
F(x) = K• (b)^x
then find K, and b
6 = K• (b^0) = K
also
42= K•(b^1) = K• b
then
b= 42/K= 42/6= 7
Then answer formula is
F (x) = K• (b)^x
. = 6• (7^x)
solve the equation for x. 4^5 square root (2x-4)^2=16
The value of x in the equation is 4
What are algebraic expressions?Algebraic expressions are seen as expressions that consist of factors, variables, terms, coefficients, and certain constants.
These expressions are also known to be composed of some arithmetic operations, which includes;
SubtractionAdditionDivisionMultiplicationParenthesesBracket, etcGiven the expression;
(2x-4)^2=16
√(2x-4)^2 = 16
Find the square root of the expression, we have;
√(2x -4)^2= √16
Find the values
2x - 4 = 4
collect like terms
2x = 4 + 4
Add like terms
2x = 8
Make 'x' the subject of formula
x = 8/2
x = 4
Hence, the value is 4
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A bus use 40 litres of fuel to travel 100km.How much fuel will be used on a journey of 68km
If a bus use 40 litres of fuel to travel 100km 27.2 liters fuel will be used on a journey of 68km.
How to calculate fuel efficiency ?The calculation is simple. Divide the number of kilometers by the number of liters consumed.If you have covered 100km on the run and at refill, the vehicle has taken in five litres of fuel, your efficiency is 20kmpl.If you drove 335 miles before refueling, and you filled your car up with 12 gallons of gas, your fuel consumption was 27.9 miles per gallon, or mpg (335 miles / 12 gallon = 27.9 mpg).You have to start from a full tank and return to a full tank to know exactly how much gas your car consumed.Fuel Consumption = (Final Mileage - Starting Mileage) / Fuel Usage.Fuel cost = (Distance / 100 × Consumption) × Cost per gallon.simplification to the amount of fuel needed-
Amount of fuel bus use to travel 100km = 40 liters
How much distance will travel with 1Liter of fuel =
To find that divide 100 by 40
That is total distance travelled by 40 liters of fuel
= 100/40 = 2.5
Bus will travel 2.5 km with 1L fuel.
The amount of fuel for 68KM = 68km /2.5km = 27.2 Liter
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Lines a and b are parallel and t is the transversal. If m<1 = 80 degrees. What isthe sum of <6 and <7? JUST TYPE THE NUMBER]
Since the lines a and b are parallel, the corresponding angles <1 and <5 are congruent, therefore angle <5 measures 80°.
Angles <6 and <7 are supplementary angles to angle <5, so we have:
[tex]\begin{gathered} <5+<6=180\\ \\ 80+<6=180\\ \\ <6=100°\\ \\ <7=<6=100° \end{gathered}[/tex]So the sum of <6 and <7 is:
[tex]<6+<7=100+100=200°[/tex]Therefore the answer is 200.
use transformation of the parent graph of the m(x)=sqrt(x) to sketch the graph of p(x) = -sqrt(x)-3
First we need to look at the change of signal of the function (it changes from √x to -√x).
This change of signal means the function was reflected over the x-axis.
Then, the value of -3 was added to the function.
An addition of -3 in the function means a translation of 3 units down.
So the transformations from m(x) to p(x) are:
A reflection over the x-axis followed by a translation of 3 units down.
The value of y varies jointly with the values of x and z. When x=4 and z=9, the value of y is 360. What is the value of y when x=4 and z=9?
When z = 9 and x = 4, and y = 360. then, with x = 4 and z = 9, we obtain the value of y = 600.
According to question, given that
x = 4, z = 9 , y = 360
The value of y varies jointly with the values of x and z then
Joint variation ⇒ y = k. x. z , where k is constant. In all cases when k ≠ 0
360 = k (4) (9)
360 = 36 k
k = 360/36
k = 10
y = k. x. z
y = 10 .x . z
when x = 5 and z = 12 then
y = 10 .x . z
y = 10 (5) (12)
y = 600
Therefore, When x=4 and z=9, and the value of y is 360. then we get the value of y = 600, when x=4 and z=9 using joint variation.
Any number of issues involving rates, times, and work can be resolved rationally. Rational formulas include direct, inverse, and joint variation equations. In direct variation, the variables are directly related to one another; as one quantity rises, the other will as well.
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Solve for v in terms of w, x, and y.
w = 1/v yx
v =
Answer:
Step-by-step explanation:
g
u
Find the distance between the points
(5 7/8, -1/2) and (9 3/4, -1/2
ANSWER QUICKLY PLEASE!!!!!!!!!!!
The distance between the points where the points are given as [tex](5\frac 78, -\frac 12)[/tex] and [tex](9\frac 34, -\frac 12)[/tex] is 3.875 units
How to determine the distance between the points?The points are given as
[tex](5\frac 78, -\frac 12)[/tex] and [tex](9\frac 34, -\frac 12)[/tex]
The distance between the points is calculated as
d = √(x₁ - x₂)² + (y₁ - y₂)²
Where x and y are the coordinate points and d is the distance
Substitute the known values in the above equation
So, we have
[tex]d = \sqrt{(5\frac 78 - 9\frac 34)\² + (-1/2 + 1/2)\²[/tex]
Evaluate the sum in the above equation
So, we have
[tex]d = \sqrt{(5\frac 78 - 9\frac 34)\²[/tex]
Evaluate the exponents in the above equation
So, we have
[tex]d = (-5\frac 78 + 9\frac 34)[/tex]
Evaluate the difference in the above equation
So, we have
d = 3.875
Hence, the distance between the points is 3.875 units
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Need more explanation to this review question. Not understanding what it wants me to find.
We need to write an equation relating x (leg CD) to the given data.
The image shows the right triangle ACD, with legs, in ft, given by:
[tex]\begin{gathered} AC=1600 \\ \\ CD=x \end{gathered}[/tex]Also, angle DAC is 25.4º. Since CD is the opposite leg, and AC is the adjacent leg to this angle, we have:
[tex]\begin{gathered} \tan 25.4\degree=\frac{CD}{AC} \\ \\ \tan 25.4\degree=\frac{x}{1600} \end{gathered}[/tex]Thus, option A is correct.
Also, we can multiply both sides of the above equation by 1600, to find the equivalent equation:
[tex]\begin{gathered} 1600\cdot\tan 25.4\degree=\frac{x}{1600}\cdot1600 \\ \\ 1600\cdot\tan 25.4\degree=x \\ \\ x=1600\cdot\tan 25.4\degree \end{gathered}[/tex]Thus, option C is also correct.
Notice that:
[tex]\begin{gathered} \cos 25.4\degree=\frac{AC}{AD} \\ \\ \cos 25.4\degree=\frac{1600^2^{}+x^2}{1600} \end{gathered}[/tex]Therefore, only options A and C are correct.
HI CAN SOMEONE PLEASE ACTUALLY HELP ME. I’ll give brainliest :)
Answer:
the answer to your question is that of 17 1/4
help mee pleasee!!
thank you <3
The linear equation that passes through (-2, 11) and (1, -4) is:
y = -5*x + 1
How to get the linear equation?The general linear equation is:
y = a*x +b
Where a is the slope and b is the y-intercept.
If the line passes through points (x₁, y₁) and (x₂, y₂) then the slope is:
a = (y₂ - y₁)/(x₂ - x₁)
Here we know that the line passes through the points (-2, 11) and (1, -4), then the slope is:
a = (-4 - 11)/(1 + 2) = -15/3 = -5
y = -5*x + b
To find the value of b, we use one of the two given points, here i will use (1, -4), it gives:
-4 = -5*1 + b
-4 + 5 = b
1 = b
So the linear equation is:
y = -5*x + 1
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Leticia is studying the stock market in her social studies class. Her teacher had each student pick a stock to track over eight days. Leticia picked a stock from a company that makes her smartphone. Leticia created the table tracking the amount of the price of the stock gain or loss each of the eight days of tracking trading. Time Tracking Stocks Gain/Loss -$2.25 -$1.50 $1.25 Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 -$1.75 $3.75 -$2.50. After the first five days of tracking the stock how much in total did the stock gain or lose in value
To find how much di the stock gain or lose in value after 5 days, we just have to sum the values of the Gain/Loss column from the first row to the fifth one, like this:
Total gain or loss = -2.25 + (-1.5) + 1.25 + (-0.75) + 2.25 = -1
Then, the stock lose $1 in value ($-1)
a) Let U = {1,2, ., 9} be the universal set, and letA = {1,2,3,4,5),C= {5, 6, 7, 8, 9), E= {2,4,6,8),B = {4, 5, 6, 7),D= {1, 3, 5, 7, 9), F = {1,5,9}.Find: AUC'
Given:
U = {1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {1,2,3,4,5}
B = {4, 5, 6, 7}
C = {5, 6, 7, 8, 9}
D= {1, 3, 5, 7, 9}
E= {2, 4, 6, 8}
F = {1, 5, 9}
What is the question: Find AUC'.
Recall the following:
A ∩ C (read as A intersection C) - are members that are common to both set A and set C.
A ∪ C (read as A union C) - are members that are in set A or set C or both, combining the members of all sets.
C' (read as C complement) - are members that are not in the universal set.
Since what we are about to find is A ∪ C', let's first determine the members of C'.
We get,
C' = {1, 2, 3, 4}
A = {1,2,3,4,5}
Therefore, AUC' = {1,2,3,4,5}.
marc hs 45 CDs in his collection and Corrina has 61. if marc buys 4 new CDs each month and Corrina buys 2 new CDs each month after how many months will marc and Corrina have the same number of CDs
Answer: bot eleum got it right
Step-by-step explanation:
thanks for the help!!!!
The value of cos (A - B) will be 33/65.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The values are;
cos A = 24/25
And, sin B = 63/65
Now,
cos (A - B) = cos A cos B + sin A sin B
Since, cos A = 24/25
So, sin A = 7/25
And, sin B = 63/65
So, cos B = 16/65
Substitute all the values, we get;
cos (A - B) = cos A cos B + sin A sin B
= 24/25 x 16/65 + 7/25 x 63/65
= 384/1625 + 441 / 1625
= 825 / 1625
= 33/65
Thus, The value of cos (A - B) will be 33/65.
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[tex]7 \times 9 - 7 - 3 \times 5[/tex]A: 20B: 60C: 41
Therefore the answer is C.
solve the given system of equations2x+8y=524x-4y=-15
The equations given are,
[tex]\begin{bmatrix}2x+8y=5..........1 \\ 24x-4y=-15......2\end{bmatrix}[/tex]Isolate 'x' in equation 1
[tex]\begin{gathered} 2x+8y=5 \\ 2x=5-8y \\ x=\frac{5-8y}{2}...........3 \end{gathered}[/tex]Substitute 'x' is equal to (5-8y)/2 into equation 2
[tex]\begin{gathered} 24\cdot \frac{5-8y}{2}-4y=-15 \\ -100y+60=-15 \\ -100y=-15-60 \\ -100y=-75 \\ \frac{-100y}{-100}=\frac{-75}{-100} \\ y=\frac{3}{4} \end{gathered}[/tex]Substitute y = 3/4 into equation 3 and solve for x
[tex]\begin{gathered} x=\frac{5-8\cdot \frac{3}{4}}{2} \\ x=\frac{5-6}{2} \\ x=-\frac{1}{2} \end{gathered}[/tex]Hence,
[tex]x=-\frac{1}{2},\:y=\frac{3}{4}[/tex]Adoncia nakes a scale drawing of the front of the Lincoln memorial. She used a scale of 15 ft in the monument to 1 in. I’m the drawing. The front of the monument is about 80 ft high and 200 ft long. Will adoncia’s drawing fit on an 8 1/2 in.-by-11 in. Sheet of paper? Explain
Given:
The scale is 15 ft = 1 in
Height = 80 ft
Length = 200 ft
Find-:
The required dimensions of the paper
Explanation-:
The scale is:
[tex]15\text{ ft }=1\text{ in}[/tex]The required dimension of paper is:
[tex]\begin{gathered} \text{ Height }=80\text{ feet} \\ \\ \text{ Height }=\frac{80}{15}\text{ in} \\ \\ \text{ Height }=\frac{16}{3}\text{ in} \\ \\ \text{ Height }=5.33\text{ in} \end{gathered}[/tex]The length is:
[tex]\begin{gathered} \text{ Length }=200\text{ ft} \\ \\ \text{ Length }=\frac{200}{15}\text{ in} \\ \\ \text{ Length }=13.33\text{ in.} \end{gathered}[/tex]So the demission is height 5.33 in and length 13.33 in
The sheet demission is
[tex]\begin{gathered} =8\frac{1}{2}\text{ in and }11\text{ in} \\ \\ =\frac{17}{2}\text{ in and }11\text{ in } \\ \\ =8.5\text{ in and 11 in} \end{gathered}[/tex]So, Adoncia's drawing will not fit on the sheet of paper.
28 ✕ 0 = 20 ✕ y.
If 0 is 140, the value of y is what?
Answer:
196 = y
Step-by-step explanation:
If o is 140, the value of y is what? 28 ✕ o = 20 ✕ y
28 ✕ o = 20 ✕ y
28 ✕ 140 = 20 ✕ y
3,920 = 20✕ y
right side: 20 is multiplied by y and can be written back to back:
3,920 = 20y
divide both sides by 20:
3,920/20 = 20y/20
196 = y
9. Last month, the balance in Tisha's checkbook was $1219.17. Since then she has
deposited her latest paycheck of $2425.66 and written checks for $850.00 (rent),
$235.89 (car payment), and $418.37 (credit card payment). What is the current
balance in Tisha's checking account?
The total amount of security deposits and other deposits received by or on behalf of the Obligors and retained by their originators and affiliates as of any date is referred to as the Deposit Balance (or any agent thereof on their behalf).
What is the balance of your checking account right now?The written checks would be deducted from the balance and the paycheck would be added to it. Hand-doing the math for the realistic quantities in the question would take a lot of time, but the values may be typed into the calculator in a single continuous string as they are shown in the equation.
New Balance Deposited = Old Balance + Paycheck deposited - Check written
New Balance = 1219.17 + 2425.66 + 235.89 - 418.37.
New Balance = 2140.57 .
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Carl attempted 70 free throws and made 37. Find Carl's average of free throws made. Round your answer to 3 decimal places, if necessary.
ANSWER :
0.529
EXPLANATION :
From the problem, Carl made 37 out of 70 free throws attempt.
Divide the number of free throws made by the total number of free throws attempt
[tex]\frac{37}{70}=0.52857\sim0.529[/tex]hi hope your doing great. can you please show me the quick easiest way to solve math problem (work the problem with numbers)thank you kindly
Given:
The graph shows the XY plane where x shows the number of T shirts bought and Y shows the number of stickers received.
The plotted points on the graph have the coordinates:
[tex](1,2),(2,4)\text{ , (3,6) ,(4,8) , (5,10)}[/tex]Clearly, we can see the y coordinate is double of x coordinate here, so the equation of graph shown will be : y = 2x
Now we will check the points given in tables in the options if they satisfy this equation or not.
Check option (F),we get:
[tex](6,6)\text{ ,(7,7) , ( 8,8), (9,9)}[/tex]Which doesnot satisfy the equation y=2x hence, option F is wrong.
Now chcek option G ,
[tex](6,12)\text{ , (7,14), (8,16), (9,18).}[/tex]These points clearly satisfy y= 2x, hence,
Option (G) is correct.
Similarly, if we check option (H) and (I) they will not satisfy the equation, Hence , option (G) is only correct.
the policy at a certain buffet is to have 19 desserts for every 16 people. if they plan for 320 people, how many desserts should they have?
Given that the buffet is to have 19 desserts for every 16 people.
Let's find the number of desserts they should have if they plan for 320 people.
19 desserts = 16 people
x desserts = 320 people
Therefore, we have:
[tex]\begin{gathered} \frac{19}{16}=\frac{x}{320} \\ \\ \text{Cross multiply:} \\ \\ 16x\text{ = 320 }\ast\text{ 19} \\ \\ 16x\text{ = }6080 \end{gathered}[/tex]Divide both sides by 16:
[tex]\begin{gathered} \frac{16x}{16}=\frac{6080}{16} \\ \\ x\text{ = }380 \end{gathered}[/tex]Thereore, they should have 380 desserts if they plan for 320 people.
ANSWER:
380 desserts
On Saturday, a local hamburger shop sold a combined total of 316 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the
number of hamburgers sold. How many hamburgers were sold on Saturda
The number of cheeseburgers sold was three times the number of hamburgers sold then 79 hamburgers and 237 cheeseburgers were sold on Sunday.
How to find the number of hamburgers were sold on Sunday?Let h be the number of hamburgers
c be the number of cheeseburgers
A local hamburger shop sold a combined total of 316 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold.
h + c = 316
c = 3h
h + 3h = 316
simplifying the above equation, we get
⇒ 4h = 316
Dividing both sides of the equation by 4, we get
⇒ 4h / 4 = 316 / 4
⇒ h = 79
Therefore, hamburgers were sold on Saturday is 79.
The number of cheeseburgers sold was three times the number of hamburgers sold then
c = 3h
substitute the value of h in the above equation, we get
⇒ c = 237
Therefore, 79 hamburgers and 237 cheeseburgers were sold on Sunday.
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ZA and B are vertical angles. If m_A = (3x + 13) and mZB = (5x + 9), then find the measure of ZA.
Answer
Angle A = 19°
Explanation
Vertical angles are angles that are directly opposite each other at a point where two lines intersect or cross each other. Vertical angles are known to be equal to each other.
So, Angle A = Angle B
Angle A = 3x + 13
Angle B = 5x + 9
3x + 13 = 5x + 9
We can rewrite this as
5x + 9 = 3x + 13
5x - 3x = 13 - 9
2x = 4
Divide both sides by 2
(2x/2) = (4/2)
x = 2
Angle A = 3x + 13 = 3(2) + 13 = 6 + 13 = 19°
Hope this Helps!!!
