The mean clotting time of blood is 7.45 seconds with a standard deviation of 3.6 seconds. What is the probability that an individual's clotting time will be less than 6 seconds or greater than 11 seconds? Assume a normal distribution. The probability is nothing.
The probability that an individual's clotting time will be less than 6 seconds or greater than 11 seconds, under a normal distribution with a mean of 7.45 and a standard deviation of 3.6, is approximately 50.9%.
Explanation:The subject in question pertains to the calculation of probabilities using the Normal Distribution. Given that the mean clotting time is 7.45 seconds with a standard deviation of 3.6 seconds, we need to find the probability that the clotting time will be either less than 6 seconds or more than 11 seconds.
First, we convert the clotting times to z-scores (the number of standard deviations away from the mean). The z-score for 6 seconds is (6-7.45)/3.6 = -0.40, and the z-score for 11 seconds is (11-7.45)/3.6 = 0.98. We can look these z-scores up in a Z-table to find the corresponding probabilities.
From the Z-table, we find that the probability of a z-score less than -0.40 is 0.345. The probability of a z-score less than 0.98 is about 0.836. Because we're asked to calculate the probability that the clotting time is either less than 6 seconds or greater than 11 seconds, we need to calculate the probabilities at the tails of the distribution. So we subtract the probability for 0.98 (0.836) from 1 to find the probability that clotting time is greater than 11 seconds, which is 0.164.
The probability of the clotting time being either less than 6 seconds or more than 11 seconds would be the sum of the two probabilities: 0.345 + 0.164 = 0.509 or 50.9%.
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The probability that an individual's blood clotting time is less than 6 seconds or greater than 11 seconds is approximately 0.5057, calculated using the Z-scores and the standard normal distribution.
The mean clotting time of blood is 7.45 seconds, with a standard deviation of 3.6 seconds. To find the probability that an individual's clotting time will be less than 6 seconds or greater than 11 seconds under normal distribution, we will use the Z-score formula:
Z = (X - mean) / standard deviation
For X = 6 seconds:For X = 11 seconds:Using Z-tables or standard normal distribution calculators:
P(Z < -0.40) ≈ 0.3446P(Z > 0.99) ≈ 0.1611Therefore, the total probability is:
P(X < 6 or X > 11) = P(Z < -0.40) + P(Z > 0.99) ≈ 0.3446 + 0.1611 = 0.5057
The height of a rocket a given number of seconds after it is released is modeled by h (t) = negative 16 t squared + 32 t + 10. What does t represent?
Answer:
t represents the number of seconds after the rocket is released
Answer:
A
Step-by-step explanation:
answer is the number of seconds after the rocket is released
Finding the Area of a Regular Polygon
The apothem of a regular hexagon measures
8 cm.
Which are true of the regular hexagon? Check all that
apply.
The perimeter of the hexagon is 48 cm.
The measure of the angle formed by the radius and
the apothem is 30°.
The side length of the hexagon is about 4.6 cm.
In a regular hexagon, the radius and side length are
equal in length.
The area of the hexagon is about 221.7 square cm.
8 cm
Intro
Done
Answer:
B, D and E.
just trust me
The angle made by the apothem and the radius would be; 30 degrees. Then the correct option is B.
What is a polygon?The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.
The apothem of a regular hexagon = 8 cm.
Then the side length of the hexagon will be
[tex]\rm x = \dfrac{8}{\sin 60^o}= 9.24\ cm[/tex]
The perimeter of the hexagon;
Perimeter = 6 × 9.24 = 55.43 cm
The area of the hexagon;
Area = 0.5 × 8 × 9.24 = 36.95 cm².
The angle made by the apothem and the radius = 30 degrees.
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Two parallel lines are crossed by a transversal.
What is the value of d?
d = 55
d = 75
d = 125
d = 155
Answer:
Incomplete question check attachment for diagram
Step-by-step explanation:
Two parallel lines, cross by a transversal
The angle between one of the line and the transfer is 125° and this angle is opposite to angle d, so it is vertical opposite angle
Vertically Opposite Angles are the angles opposite each other when two lines cross, so it was the transversal line that cross the parallel lines
and we know that, vertical opposite angle is equal.
Then, d = 125°
Answer:
(C) d=125
Step-by-step explanation:
Solve the equation 3x = 2x + 5.
What can you do to isolate the variable on one side of the equation?
What is the solution?
Answer:
x = 5
Step-by-step explanation:
To solve this equation for x, subtract 2x from both sides, obtaining:
x = 5.
Find the rate of change of total revenue, cost, and profit with respect to time. Assume that R(x) and C(x) are in dollars.
R(x)= 2x, C(x)= 0.01x² + 0.4x + 30, when x=25 and dx/dt=7 units per day.
1. Find the rate of change of total revenue per day.
2. Find the rate of change of total cost per day.
3. Find the rate of change of total profit per day.
Answer:
1.- dR/dt = 14 $/day
2.- dC/dt = 4.55 $/day
3.- dP/dt = 7,7 $/day
Step-by-step explanation:
By definition Profit is equal to Revenue minus total costs then.
We have
R(x) = 2*x
C(x) = 0,01*x² + 0,4*x + 30
Then Profit P(x) = 2*x - 0,01*x² - 0,4*x - 30
P(x) = - 0.01*x² + 1.6*x - 30
1.- Find rate of change total revenue per day, when
x = 25 and dx/dt = 7 u/day
R(x) = 2*x
dR/dt = 2*dx/dt ⇒ dR/dt = 2* 7
dR/dt = 14 $/day
2.-
C(x) = 0,01*x² + 0,4*x + 30
dC/dt = 0,01*x* dx/dt + 0,4*dx/dt
dC/dt = 0,01*25*7 + 0.4*7
dC/dt = 1.75 + 2.8
dC/dt = 4.55 $/day
3.-
P(x) = - 0.01*x² + 1.6*x - 30
dP/dt = - 2*0,01*x*dx/dt + 1.6*dx/dt
dP/dt = - 2*0,01*25*7 + 1.6*7
dP/dt = - 3,5 + 11.2
dP/dt = 7,7 $/day
Answer:
The rate of change of total Revenue is $14 per day.The rate of change of total Cost is $4.55 per day.The rate of change of total Profit is $7.7 per day.Step-by-step explanation:
Given information
[tex]R(x)=2x\\C(x)=0.01x^2+0.4x+30[/tex]
When,
[tex]x=25\\dx/dt=7[/tex] units per day
As we know that
Profit = Revenue - Cost
Then, the Profit,
[tex]P(x)=2x-0.01x^2+0.4x-30\\P(x)=-0.01x^2+1.6x-30[/tex]
Now, The total Revenue per day
[tex]R(x)=2*x[/tex]
By differentiating both side with respect to [tex]t[/tex]
[tex]\\dR/dt=2*dx/dt\\dR/dt=2*7\\dR/dt=14[/tex]
Hence the rate of change of total revenue is $14 per day.
Similarly,
The total cost per day
[tex]C(x)=0.01x^2+0.4x+30[/tex]
By differentiating both side with respect to [tex]t[/tex]
[tex]dC/dT=0.01*x*dx/dt+0.4*dx/dt\\dC/dt=0.01*25*7+0.4*7\\dC/dt=1.75+2.8\\dC/dt=4.55[/tex]
Hence the rate of change of total cost is $4.55 per day
And the total Profit per day
[tex]P(x)=-0.01x^2+1.6x-30\\[/tex]
By differentiating both side with respect to [tex]t[/tex]
[tex]dP/dt=2*(-0.01)*x*dx/dt+1.6*dx/dt\\dP/dt=-2*(-001)*25*7+1.6*7\\dP/dt=-3.5+11.2\\dP/dt=7.7[/tex]
Hence the rate of change of total Profit is $7.7 per day
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Sarina has two pieces of square paper. Each piece of paper has a side length of 7 inches. Both pieces of paper are cut along a diagonal, and the resulting triangles are arranged to form a new square, as shown below. What is the area of the new square?
Answer: 49
Step-by-step explanation:
If iTs half of each square its the same
Haley scored 3, 13, 15, 16, and 19 on five homework assignments. Her scores were based on a perfect score of 20. Which measure would be the most accurate to use to measure Haley's overall grade?
A) mean
B) median
C) mode
D) range
Answer:
median
Step-by-step explanation:
which one of these numbers is not like the others?
21,15,6,16,27
Answer:
16
Step-by-step explanation:
It's hard to tell what the what the problem means by "not like the others", but here's a guess.
16 is a perfect square. 16 = 4^2
None of the other numbers are perfect squares.
Also, 16 is not divisible by 3. All other numbers are divisible by 3.
The cylinder above has a radius of 5 inches and a height of 12 inches. What is the surface of the cylinder above?
Answer:
I think its b
Step-by-step explanation:
A=2πrh+2πr2=2·π·5·12+2·π·52≈534
2/3 - 1/2 =? please answer quick
Answer:
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
[tex]\frac{2}{3} - \frac{1}{2} =\frac{2x2}{3x3} -\frac{1x3}{2x3} =\frac{4}{6} -\frac{3}{6} =\frac{4-3}{6} =\frac{1}{6}[/tex]
Answer:
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
[tex]\frac{2}{3}-\frac{1}{2}=\\ \\=\frac{2*2-1*3}{6}\\ \\=\frac{4-3}{6}\\ \\=\frac{1}{6}[/tex]
If I have 10
cups of cake batter to split amongst 18 cupcakes. How many cups of bafter will use for each cupcake?
⁵/₉ of bafter a cup would go per cupcake .
To determine how many cups of cake batter to use for each of the 18 cupcakes when you have 10 cups of batter, you need to divide the total amount of batter by the number of cupcakes.
Divide the total cups of batter (10 cups) by the number of cupcakes (18):
= 10 ÷ 18
≈ 10 / 18
Divide both sides by 2 to simplify and get:
= 5 / 9
How is multiplying exponents (x² ⋅ x⁴) different from raising a power to a power ((x²)⁴)?
Answer:
When you are "multiplying" exponents, you're really just adding them together. So in the case of (x² ⋅ x⁴), you add the exponents:
2 + 4 = 6
[tex]x^{6}[/tex] would be the answer.
On the other hand, raising a power to a power, is actually multiplying them. So it would just be:
2 ⋅ 4 = 8
[tex]x^{8}[/tex] would be the answer.
Keith's Catering charges a $100 setup fee and $25 per
person served. Zoey's Catering uses the table below to
calculate catering charges.
Number of
People Served
Total Cost
(y)
10
$325
20
$525
30
$725
Which Caterer charges the most per person, and how much more?
Answer:
Keith charges more per person
Step-by-step explanation:
10 = 325
20 = 525
30 = 725
Zoey's price goes up 200 for every 10 people making her setup fee 125 (325-200=125). 200 per 10 people is 20 per person
Kyle drove his car 250 miles on 20 gallons of gas. How many miles per gallon did Kyle average?
Answer:
Step-by-step explanation:
250 divided by 20= 12.5
So 12.5 miles per gallon.
12.5. The answer ask for how many miles in 1 gallon. So, you do 250 divided by 20. 250 divided by 20 is 12.5, so he will drive 12.5 or 12 1/2 miles using each gallon of gas.
ANSWER : 12.5 or 12 1/2
Name 5 decimals whose sum is between 2 and 3.
Answer:
BET! 0.3 + 0.6 + 0.9 + 0.2 + 0.4 = 2.4
I hope this is what you mean I was kind of confused
Step-by-step explanation:
Solve: 3m - 2.4 = 6.6
Answer:
m=3
Step-by-step explanation:
i hope today brings you joy and happiness :)))
Answer:
The answer is 3
Step-by-step explanation:
This is how you solve it
3m-2.4=6.6
+2.4 . +2.4
3m=9
/3 . /3
m=3
At a football game 100 students were surveyed about their food and drink purchases. Out of the 100 students surveyed, 70 bought a drink, 60 bought a food item, and 50 bought both a drink and a food item.
A student is chosen at random from the 70 students that bought a drink. What is the probability that the student also bought a food item?
Answer:
The probability is 5/7
Step-by-step explanation:
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Pablo is training for a marathon. He ran 5 4/8 miles on Friday, 6 5/8 miles on Saturday, and 7 4/8 miles on Sunday. How many miles did he run on all three days?
Answer:
19 5/8 miles
Step-by-step explanation:
First you convert all fractions into improper fraction which are
5 4/8 = 44/8
7 4/8 = 60/8
6 5/8 = 53/8
Then add just the numerators together as the denominator stays the same which looks like 157/8
Then see how many times 157 goes into 8 which is 19 with 5 left over
So you rewrite the answer as 19 5/8 miles
what is a diagonal matrix
Answer:
, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero
Step-by-step explanation:
a large data sample of heights of US women is normally distributed with a mean height of 64.2 inches and a standard deviation of 2.6 inches. What is the approximate probability that a randomly selected person in this sample is shorter than 61.6 inches? (I need this by Tuesday the 22nd)
To find the probability that a randomly selected person is shorter than 61.6 inches, calculate the z-score and use a standard normal distribution table or calculator to find the corresponding probability.
Explanation:To find the approximate probability that a randomly selected person in the sample is shorter than 61.6 inches, we can use the standard normal distribution.
First, we need to calculate the z-score for 61.6 inches using the formula:
z = (x - mean) / standard deviation
z = (61.6 - 64.2) / 2.6 = -1.0
We can then use a standard normal distribution table or a calculator to find the area to the left of z = -1.0, which represents the probability that a randomly selected person is shorter than 61.6 inches. The probability is approximately 0.1587, or 15.87%.
A baker uses a coffee mug with a diameter of 8 cm8\text{ cm}8 cm8, start text, space, c, m, end text to cut out circular cookies from a big sheet of cookie dough. What is the area of each cookie?
Answer:
16 pi cm^2 or 50.27 cm^2
Step-by-step explanation:
In this question, we are told that by using a particular mug of coffee with a certain diameter, a baker was able to circular cookies from a big sheet of cookie dough so we need to know the area of each of the cookie.
Now this is pretty much straightforward. since we do know the diameter of the mug, finding the area of the cookie is simple!
How do we do this?
what to do simply is to apply the formula of a circle to find the area of a circle of diameter 8cm
mathematically, the area of a circle A = pi * r^2
Since we are given D in the question, we know quite well that we need r from the equation. Mathematically, d = 2r or more specifically r = d/2 = 8/2 = 4cm
now let’s find the area of a circle of radius 4cm
A = pi * 4^2 = 16 pi cm^2 or simply 50.27 cm^2
A car dealer raised the price of car form $10.500 to 11.000. what was the percent of change.
Answer:
4.5% (1dp)
Step-by-step explanation:
10500/11000x100=95.4545454545%
100-95.4545454545= 4.5454545455%
=4.5% (1dp)
I hope this helps!
Answer:
4.762%
Step-by-step explanation:
Change:
11,000 - 10,500 = 500
% change:
500/10500 × 100
100/21
4.761904762%
The Martins plan for a garden is shown in the diagram. They need to figure out how much they will spend on topsoil for the garden. What is the area of the garden? The area of the garden is ft2. If topsoil costs $0.15 per square foot, how much will they spend to cover the area with topsoil? They will spend $.
answer 1 is : 144
Answer2:21.60
Answer:
144 and 21.60
Step-by-step explanation:
14 is what percent of 25?
Answer:
56%
Step-by-step explanation:
U reported me and the answer got deleted so
14:25*100 =
( 14*100):25 =
1400:25 = 56
here's your step by step explanation
and pls mark me brainliest
bye
Answer:
56%
Step-by-step explanation:
Is means equals and of means multiply. Let P be the percent
14 = P * 25
Divide each side by 25
14/25 = 25P/25
.56 = P
Change to percent form
56% =P
PLEASE HELP ME !!!
the expression 49x² - 36 is equivalent to :
(A) (7x - 6 )²
(B) (7x - 6 ) ( 7x + 6)
(C) (24.5x - 18 )²
(D) (24.5x - 18) (24.5x + 18 )
Answer:
(B) (7x - 6 ) ( 7x + 6)
Step-by-step explanation:
49x^2 - 36
This is the difference of squares
(7x)^2 - 6^2
We can factor this as
(a^2 -b^2) =(a-b) (a+b)
(7x)^2 - 6^2 = (7x-6) (7x+6)
Consider the square spinner shown and assume all sections are the same size.
17
3
11
N
An experiment consists of spinning the spinner one time.
a. How many possible outcomes are there in the experiment?
b. What are the possible outcomes of the experiment?
c. List the sample space for the experiment.
d. Calculate P(z).
Answer:
a. 4 possible outcomes.
b. Possible outcomes - the spinner will fall on a 17, 3, 11 or N.
c. {17, 3, 11, N}
d. P(z) = 1/4.
Step-by-step explanation:
The probability of a specific value on one spin P(z) = 1/4.
a) There are four possible outcomes in the experiment.
b) The possible outcomes are 17, 3, 11, and N.
c) The sample space for the experiment is {17, 2, 11, N}.
d) P(z) = 1/4.
What is sample space?It is the total number of possible outcomes from a given set.
We have,
The square spinner has the following sections.
17, 3, 11, N.
Now,
a)
The number of possible outcomes.
= 17, 3, 11, N
= 4
b)
The possible outcomes are:
= 17, 3, 11, and N
c)
The sample space.
= {17, 3, 11, N}
d)
The probability of getting one specific outcome.
P(z) = 1/4
Thus,
The answers for a), b), c), and d) are given above.
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A coffee business sells a pound of coffee for $ 9.75. Monthly expenses are $ 4,500 plus $ 4.25 for every pound of coffee sold. a. Write an IT function for total monthly income as a function of the number of pounds of coffee sold. b. Write a GT function for total monthly expenses as a function of the number of pounds of coffee sold. c. Write a function G for monthly profitability (profit) as a function of the number of pounds of coffee sold.
Answer:
a. IT = 9.75 * X
b. GT = 4500 + 4.25 * X
c. G = 9.75 * X - 4500 - 4.25 * X
Step-by-step explanation:
With the data of the statement we can get a function. Let X be the number of pounds sold.
to. Monthly income
IT = 9.75 * X
b. Monthly expenses
GT = 4500 + 4.25 * X
c. Monthly Earnings (Monthly Income - Monthly Expenses)
G = 9.75 * X - (4500 + 4.25 * X)
G = 9.75 * X - 4500 - 4.25 * X
a. The IT function should be = [tex]9.75 \times X[/tex]
b. The GT function is = [tex]4500 + 4.25 \times X[/tex]
c. The function G is = [tex]9.75 \times X - 4500 - 4.25 \times X[/tex]
Calculation of the functions:here we assume X be the number of pounds sold.
Since A coffee business should sell the coffee for $ 9.75. Monthly expenses are $ 4,500 along with $ 4.25 for each pound of coffee.
So,
a. The IT function is [tex]9.75 \times X[/tex]
b. The GT function should be [tex]4500 + 4.25 \times X[/tex]
c. The function G should be [tex]G = 9.75 \times X - (4500 + 4.25 \times X)[/tex]
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Find the discriminant
9x^2+14x+13=8x^2
Answer:
The discrimant of this equation is 144.
Step-by-step explanation:
First you have to move all the variables to one side to make the equation/expression into 0 by substracting 8x² to both sides :
9x² + 14x + 13 = 8x²
9x² + 14x + 13 - 8x² = 8x² - 8x²
x² + 14x + 13 = 0
It is given that the formula of discriminant is, D = b² - 4ac where a&b&c represent the number of the equation, ax²+bx+c = 0 :
x² + 14x + 13 = 0
D = b² - 4ac
= 14² - 4(1)(13)
= 196 - 52
= 144
Final answer:
The discriminant of the quadratic equation 9x²+14x+13=8x² is found by simplifying to x²+14x+13=0 and using the formula b² - 4ac, yielding a result of 144.
Explanation:
The student's question involves finding the discriminant of the quadratic equation 9x² + 14x + 13 = 8x². We simplify this equation by subtracting 8x² from both sides, resulting in x² + 14x + 13 = 0.
The discriminant of a quadratic equation ax² + bx + c = 0 is given by b² - 4ac. For this equation, a = 1, b = 14, and c = 13. Substituting these into the discriminant formula gives (14)² - 4(1)(13) = 196 - 52 = 144.
Since the discriminant is positive, there are two distinct real roots to the equation. This could be relevant if we were to graph the equation, indicating where it crosses the x-axis, or if further solving for x was required.
At 5 feet tall, Emily casts a shadow that is 8 feet long. She is standing near a tree that casts a shadow that is 28 feet long. How tall is the tree?
Answer:
The tree is 17.5 ft tall
Step-by-step explanation:
We can use proportions to solve this.
Notice that Emily (5 feet tall) and her shadow (8 feet long) constitute the two legs of a right angle triangle (see attached image).
The nearby tree (unknown height H), will also cast a shadow (28 ft long) with the same inclination as Emily does due to the unique position of the sun relative to them.
Then we can use the proportion associated with the sides of similar triangles:
[tex]\frac{5\,ft}{8\,ft} =\frac{H}{28\,ft}[/tex]
Then, we can solve for H in the equation:
[tex]\frac{5\,ft}{8\,ft} =\frac{H}{28\,ft} \\H=\frac{28*5}{8} \,ft\\H=17.5 \.ft[/tex]