Answer:
0.0069
Step-by-step explanation:
According to the Question,
Given That, X is a normally distributed random variable with a mean of 22 and a standard deviation of 5. The probability that x is less than 9.7We have, μ=22 , σ= 5 , P(X<9.7)=Area to the left of 9.7.
Z = (x-μ)/σ
Z = (9.7-22) / 5 ⇒ -2.46
Thus,
P(X<9.7)=P(Z < -2.46) ⇒ 0.0069 (From z-table)62. A chemist mixes 15 liters of 40 percent acid solution and 25 liters of 20 percent acid solution.
What percent of the mixture is acid?
40% of 15 L = 6 L of acid
20% of 25 L = 5 L of acid
This means the mixture contains a total of 11 L of acid, and with a total volume of 15 L + 25 L = 40 L, that means the mixture is at a concentration of
(11 L acid) / (40 L solution) = 0.275 = 27.5%
How is solving for speed similar to solving for time?
O They both require that two numbers be added.
O They both require that two numbers be subtracted
O They both involve writing a rate.
O They both use the same units of measure.
Answer:
third one
Step-by-step explanation:
At noon, ship A is 150 km west of ship B. Ship A is sailing east at 30 km/h and ship B is sailing north at 25 km/h. How fast is the distance between the ships changing at 4:00 PM?
Answer:
At 4:00 PM the distance between the two ships is 104.40 kilometers.
Step-by-step explanation:
Given that at noon, ship A is 150 km west of ship B, and ship A is sailing east at 30 km / h and ship B is sailing north at 25 km / h, to determine how fast is the distance between the ships changing at 4:00 PM the following calculation must be performed:
150 - (30 x 4) = 150 - 120 = 30
0 + (25 x 4) = 0 + 100 = 100
30 ^ 2 + 100 ^ 2 = X ^ 2
√ (900 + 10,000) = X
√10,900 = X
104.40 = X
Therefore, at 4:00 PM the distance between the two ships is 104.40 kilometers.
Can someone solve this for me and a couple more questions ?
Answer:
C. -4
Step-by-step explanation:
Answer:
(c) - 4
is your right answer
If f(x) = 4x ^ 2 - 4x - 8 and g(x) = 2x ^ 2 + 3x - 6 then f(x) - g(x) * i * s
Answer:
[tex]4 {x}^{2} - 4x - 8 - (2 {x}^{2} + 3x - 6) = 4 {x}^{2} - 4x - 8 - 2 {x}^{2} - 3x + 6 = 2 {x}^{2} - 7x - 2[/tex]
which of the following function shows the absolute value parent function FX=lxl shifted up
Answer:
The answer is C.
as for C . the value of f(x) increases by 7 and so the graph goes up by units 7.
OR
g(x) = |x| + 7
we know that |x| is f(x), so :-
g(x) = f(x) + 7
and since f(x) is plot on y- axis the graph climbs the y axis by 7 units
*The graph shifts right or left for the other functions*
The amount of snowfall falling in a certain mountain range is normally distributed with a average of 170 inches, and a standard deviation of 20 inches. What is the probability a randomly selected year will have an average snofall above 200 inches
Answer:
0.0668 = 6.68% probability a randomly selected year will have an average snowfall above 200 inches.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normally distributed with a average of 170 inches, and a standard deviation of 20 inches.
This means that [tex]\mu = 170, \sigma = 20[/tex]
What is the probability a randomly selected year will have an average snowfall above 200 inches?
This is 1 subtracted by the p-value of Z when X = 200. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{200 - 170}{20}[/tex]
[tex]Z = 1.5[/tex]
[tex]Z = 1.5[/tex] has a p-value of 0.9332.
1 - 0.9332 = 0.0668
0.0668 = 6.68% probability a randomly selected year will have an average snowfall above 200 inches.
help me plz----------------------------
9514 1404 393
Answer:
A. 5 should have been subtracted in step 4
Step-by-step explanation:
No question is stated, so there is no "answer."
__
If we assume the question is, "What error did Keith make?" then choice A properly describes it.
Step 4 should look like ...
x -5 = 7y . . . . . . . 5 should be subtracted from both sides
and the final result should be ...
g(x) = (x -5)/7
Find the equation of the line tangent to y = sin(x) going through х = pi/4
Answer:
[tex]\displaystyle y - \frac{\sqrt{2}}{2} = \frac{\sqrt{2}}{2} \bigg( x - \frac{\pi}{4} \bigg)[/tex]
General Formulas and Concepts:
Algebra I
Coordinates (x, y)
Functions
Function Notation
Point-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinate y₁ - y coordinate m - slopePre-Calculus
Unit CircleCalculus
Derivatives
The definition of a derivative is the slope of the tangent lineDerivative Notation
Trig Derivative: [tex]\displaystyle \frac{d}{dx}[sin(u)] = u'cos(u)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = sin(x)[/tex]
[tex]\displaystyle x = \frac{\pi}{4}[/tex]
Step 2: Differentiate
Trig Derivative: [tex]\displaystyle y' = cos(x)[/tex]Step 3: Find Tangent Slope
Substitute in x [Derivative]: [tex]\displaystyle y' \bigg( \frac{\pi}{4} \bigg) = cos \bigg( \frac{\pi}{4} \bigg)[/tex]Evaluate [Unit Circle]: [tex]\displaystyle y' \bigg( \frac{\pi}{4} \bigg) = \frac{\sqrt{2}}{2}[/tex]Step 4: Find Tangent Equation
Substitute in x [Function y]: [tex]\displaystyle y \bigg( \frac{\pi}{4} \bigg) = sin \bigg( \frac{\pi}{4} \bigg)[/tex]Evaluate [Unit Circle]: [tex]\displaystyle y \bigg( \frac{\pi}{4} \bigg) = \frac{\sqrt{2}}{2}[/tex]Substitute in variables [Point-Slope Form]: [tex]\displaystyle y - \frac{\sqrt{2}}{2} = \frac{\sqrt{2}}{2} \bigg( x - \frac{\pi}{4} \bigg)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
You are doing research on balance and fitness. To complete this research you will need a watch with a second hand. Identify a random sample of n = 12 men and n = 8 women. You must answer this question: How do you establish that this sample is truly random? STEP 2: Have each subject perform the following task: a) Have the subjects stand with their hands at their side, raise one knee, cross their ankle over the other knee, squat and bring their hands palms together in front of their chest. Time the subject until they put their foot back down on the floor. b) Ask the following questions: i) How many days per week do they exercise? ii) What is their favorite exercise? STEP 3: You will analyze your data and compute the following statistics for each group: 1) The Mean and standard deviation of the number of seconds the subject stayed balanced 2) The Median number of days per week exercised 3) The Mode of the favorite exercise 4) The 90% confidence interval of the mean STEP 4: Construct a complete hypothesis test and determine if the two groups have significantly different balance using α = 0.05. STEP 5: Write a one page introduction to your research, discuss how you selected your sample (is it a random sample?) and write a one page conclusion. Present your data in an organized manner.
Answer:
It should be a 2 sample t-test for the sample mean mu 1 - mu 2 at alpha = 0.05.
Step-by-step explanation:
To solve, you can just insert the data values into a graphing calculator and it should work. Remember to check the conditions and write out the null and alternate hypotheses.
Null: mu 1 - mu 2 = 0 There is no difference
Alternate: mu 1 - mu 2 =/= 0 There is a difference
Conditions:
-Random sample? Yes b/c assume that it is from a simple random sample.
-10%? Assume that there are more than 120 men and 80 women in the population"
-Normal Distribution? If the data for each respective sample is approx normal, assume they come from a normally distributed population. Large counts and the central limit theorem do not work here.
After this, insert ur data values into the graphing calculator n solve for p.
Once you get p, make a conclusion based on alpha = 0.05. If p is less than alpha, you can reject the null and conclude that you have significant evidence that the alternate is true. If p is greater than alpha, you cannot reject the null and conclude that you do not have significant evidence that the alternate is true.
ABCD-EFGH what does y=?
Answer:
y = 3
Step-by-step explanation:
Given that the shapes are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{AB}{EF}[/tex] = [tex]\frac{CD}{GH}[/tex] , substitute values
[tex]\frac{3}{2}[/tex] = [tex]\frac{4.5}{y}[/tex] ( cross- multiply )
3y = 9 ( divide both sides by 3 )
y = 3
Which statement about y=x^2-14x+45 is true
Question 1 of 10
One advantage of a long-term loan compared to a short-term loan is that a
long-term loan:
A. does not require the borrower to have a good credit score.
O
B. can be paid off in full without the borrower paying any interest.
C. does not force the borrower to make payments every month.
D. allows a person to borrow more money at a lower interest rate.
Answer:
D. allows a person to borrow more money at a lower interest rate
The data represent the results for a test for a certain disease. Assume one individual from the group is randomly selected. Find the probability of getting someone who tests negative, given that he or she did not have the disease.
The individual actually had the disease
Yes No
Positive 135 11
Negative 99 145
Answer:
0.9295 = 92.95% probability of getting someone who tests negative, given that he or she did not have the disease.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question:
11 + 145 = 156 people did not have the disease.
Out of those, 145 tested positive. So
[tex]p = \frac{145}{156} = 0.9295[/tex]
0.9295 = 92.95% probability of getting someone who tests negative, given that he or she did not have the disease.
find the sum and difference between the place value and face value of 5 in the number 3508 6941
Answer:
Sum= 5000005
Difference= 4999995
Step-by-step explanation:
The place value of 5 in the number 35086941 is 5000000
The face value is 5
The sum between the face value and place value can be calculated as follows
°= 5000000+5
= 5000005
The difference can be calculated as follows
= 5000000-5
= 4999995
jenny has 3 cherry candies and 3 orange candies. She takes out 2 candies without looking.What is the probability in fractions that both are cherry?
Determine the degree of the polynomial:
7m^6n^5
9514 1404 393
Answer:
11
Step-by-step explanation:
The degree of the given monomial is the sum of the exponents of the variables.
m has degree 6
n has degree 5
The degree of the monomial is 6+5 = 11.
I need help with this word problem.
Answer:
$3.22 per square feet
Step-by-step explanation:
To solve, I usually set up an equation:
sq ft = 12 1/2 = 1
$ 40.21 x
Then, use cross multiplication.
(12 1/2)x=40.21
Divide both sides by 12 1/2 or 12.5
x = 3.2168
Round to the hundredths place [because we're dealing with money]
$3.22
I hope this helps!
Answer:
3.22 per sq ft
Step-by-step explanation:
Take the total cost and divide by the amount of tiles
40.21 / 12.5
3.2168 per sq ft
Rounding to the nearest cent
3.22 per sq ft
Angela’s average for six math tests is 87. on her first four tests she had scores of 93, 87, 82, and 86. on her last tests she scored 4 points lower than she did on her fifth test what scores did Angela receive on her firth and sixth tests?
Answer:
the scores on her last test is x (x > 0)
because on her last tests she scored 4 points lower than she did on her fifth test
=> the scores in the 5th test is x + 4
because Angela’s average for six math tests is 87, we have:
[tex] \frac{93 + 87 + 82 + 86 + x + x + 4}{6} = 87 \\ \\ < = > \frac{352 + 2x}{6} = 87 \\ \\ < = > 352 + 2x = 522 \\ \\ < = > 2x = 170 \\ \\ < = > x = 85[/tex]
=> on her last test, she had 85
=> on her 5th test, she had 85 + 4 = 89
What is division story problem where the dividend is a three-digit number and the divisor is a single digit.
Answer:
dddddddddv
Step-by-step explanation:
Question 1 of 12, Step 1 of 1
0/17
Correct
Two planes, which are 2800 miles apart, fly toward each other. Their speeds differ by 50 mph. If they pass each other in 4 hours, what is the sspeed of each?
Keypad
Answer:
325 and 375 mph
Step-by-step explanation:
Given :
Distance between plane A and B = 2800
Recall :
Distance = speed * time
Let speed of A = v1
Speed of B = v2
v1 = v2 + 50
Time taken = 4 hours
Distance = speed * time
Total distance = 2800
2800 = v1 * 4 + v2 * 4
2800 = (4v1) + (4v2)
2800 = 4(v2+50) + 4v2
2800 = 4v2 + 200 + 4v2
2800 = 8v2 + 200
2800 - 200 = 8v2
2600 = 8v2
v2 = 2600/8
v2 = 325 mph
v1 = v2 + 50
v1 = 325 + 50
v1 = 375 mph
The probability that a tennis set will go to a tiebreaker is 13%. In 120 randomly selected tennis sets, what is the mean and the standard deviation of the number of tiebreakers
Answer:
[tex]\mu = 15.6[/tex]
[tex]\sigma =3.684[/tex]
Step-by-step explanation:
Given
[tex]p =13\%[/tex]
[tex]n = 120[/tex]
Solving (a): The mean
This is calculated as:
[tex]\mu = np[/tex]
So, we have:
[tex]\mu = 13\% * 120[/tex]
[tex]\mu = 15.6[/tex]
Solving (b): The standard deviation
This is calculated as:
[tex]\sigma = \sqrt{\mu * (1 - p)[/tex]
So, we have:
[tex]\sigma = \sqrt{15.6 * (1 - 13\%)[/tex]
[tex]\sigma = \sqrt{15.6 * 0.87[/tex]
[tex]\sigma =\sqrt{ 13.572[/tex]
[tex]\sigma =3.684[/tex]
2.6.58
The lot in the figure shown, except for the house, shed, and driveway, is lawn. One bag of lawn fertilizer
costs $15.00 and covers 3,000 square feet.
Please help :)
Answer:
50 bags ;
£750
Step-by-step explanation:
The dimension of the rectangular lawn is 500ft by 300 ft
The area of the lawn an e obtained thus :
Area of rectangle = Length * width
Area of rectangle = 500 ft * 300 ft
Area of rectangle = 150000 feets
1 bag of fertilizer covers 3000 feets
The minimum bags of fertilizer required :
Area of rectangle / Area covered by 1 bag of fertilizer
Minimum bags of fertilizer required :
(150,000 / 3000) = 50 bags
50 bags of fertilizer
Cost per bag = 15
Total cost = 15 * 50 = £750
4/5×1 1/9÷2 2/3. please help me
Answer:
1/3
Step-by-step explanation:
when you change the mixed numbers to improper fractions, you get 4/5 * 10/9 ÷ 8/3. you can flip the 8/3 to 3/8 and change the division sign to multiplication, because dividing by a fraction is the same as multiplying by its reciprocal. you can cancel some things and ultimately you get 1/3
Solve the inequality. |X-15|>9
Answer:
X<6 or X>24
Step-by-step explanation:
Help someone please
A car uses 3/4% of a tank of gasoline to go 600 kilometers. What must one know to be able to determine how many kilometers the car gets per liter?
(1) the number of liters the tank holds
(2) the cost of gasoline per liter
(3) the average daily mileage of the driver (4) the relative age of the car
(5) the ratio of the mass to volume of the car
Answer:
(1) the number of liters the tank holds
Step-by-step explanation:
4. Cindy purchased a pair of boots which had a sticker price of $85. Cindy paid $5.95 in sales tax. What was the tax rate on Cindy's purchase?
calculate limits x>-infinity
-2x^5-3x+1
Given:
The limit problem is:
[tex]\lim_{x\to -\infty}(-2x^5-3x+1)[/tex]
To find:
The value of the given limit problem.
Solution:
We have,
[tex]\lim_{x\to -\infty}(-2x^5-3x+1)[/tex]
In the function [tex]-2x^5-3x+1[/tex], the degree of the polynomial is 5, which is an odd number and the leading coefficient is -2, which is a negative number.
So, the function approaches to positive infinity as x approaches to negative infinity.
[tex]\lim_{x\to -\infty}(-2x^5-3x+1)=\infty[/tex]
Therefore, [tex]\lim_{x\to -\infty}(-2x^5-3x+1)=\infty[/tex].
The marked price of a bicycle is Rs 2000. If the shopkeeper allows some discount and a customer
bought it for Rs 1921 including 13% VAT, how much amount was given as the discount?
Answer:
Discount amount = $328.73
Step-by-step explanation:
Below is the calculation for the discount amount:
The marked price of bicycle = 2000
Purchase price = Rs 1921
VAT = 13%
First find the purchase price excluding VAT = 1921 - (13% of 1921) = 1671.27
Discount amount = 2000 - 1671.27
Discount amount = $328.73
The edge of a cube was found to be 30 cm with a possible error in measurement of 0.5 cm. Use differentials to estimate the maximum possible error, relative error, and percentage error in computing the volume of the cube and the surface area of the cube. (Round your answers to four decimal places.) My Notes Ask Your Teacher
(a) the volume of the cube maximum possible error relative error percentage error cm
(b) the surface area of the cube maximum possible error relative error percentage error cm Need Help? ReadTalk to Tuter
Answer with Step-by-step explanation:
We are given that
Side of cube, x=30 cm
Error in measurement of edge,[tex]\delta x=0.5[/tex] cm
(a)
Volume of cube, [tex]V=x^3[/tex]
Using differential
[tex]dV=3x^2dx[/tex]
Substitute the values
[tex]dV=3(30)^2(0.5)[/tex]
[tex]dV=1350 cm^3[/tex]
Hence, the maximum possible error in computing the volume of the cube
=[tex]1350 cm^3[/tex]
Volume of cube, [tex]V=(30)^3=27000 cm^3[/tex]
Relative error=[tex]\frac{dV}{V}=\frac{1350}{2700}[/tex]
Relative error=0.05
Percentage error=[tex]0.05\times 100=5[/tex]%
Hence, relative error in computing the volume of the cube=0.05 and
percentage error in computing the volume of the cube=5%
(b)
Surface area of cube,[tex]A=6x^2[/tex]
[tex]dA=12xdx[/tex]
[tex]dA=12(30)(0.5)[/tex]
[tex]dA=180cm^2[/tex]
The maximum possible error in computing the volume of the cube=[tex]180cm^2[/tex]
[tex]A=6(30)^2=5400cm^2[/tex]
Relative error=[tex]\frac{dA}{A}=\frac{180}{5400}[/tex]
Relative error in computing the volume of the cube=0.033
The percentage error in computing the volume of the cube=[tex]0.033\times 100=3.3[/tex]%
