For the value of L = 144.48, the probability of having L greater than the mean glucose level of Shelia is 0.02.
Here it is given that Sheila's glucose level follows a normal distribution with a mean of 128 mg/dl and a standard deviation of 8 mg/dl
L is the patient's blood test level.
It is given that the probability that the mean glucose level i.e 128 mg/dl is above L is 0.02.
We need to find L
We know
P(128>L) = 0.02
or, 1 - P(128 ≤ L) = 0.02
or, P(128 ≤ L) = 0.98
We know that for any Normal distribution we find the probability by converting it to standard form and then checking the p-value.
P(X < x) = Φ[(x - μ)/σ]
where,
μ = mean
σ = standard deviation
Therefore,
Φ[(L - 128)/8] = 0.98
we see that for a Z score of 2.06,
Therefore we get
(L - 128)/8 = 2.06
or, L - 128 = 16.48
or, L = 128 + 16.48
= 144.48
Therefore, the value of L would be 144.48
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Complete Question
Shelia's doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy). There is variation both in the actual glucose level and in the blood test that measures the level. A patient is classified as having gestational diabetes if the glucose level is above 140 milligrams per deciliter one hour after a sugary drink is ingested. Shelia's measured glucose level one hour after ingesting the sugary drink varies according to the Normal distribution with a mean of 128 mg/dl and a standard deviation of 8 mg/dl. Let L denote a patient's glucose level.
If measurements are made on four different days, find level L such that there is a probability of only 0.02 that the mean glucose level of four test results falls above L for Shelia's glucose level distribution. What is the value of L?
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2 is a factor of 81. Show how you know
Jimmy i eating andwiche at a contant rate the number of andwiche y that he can eat in a hour x i repreented by the linear equation y = 8x how many andwiche doe jimmy eat in 1 hour? 2 hour? 3 hour?
Jimmy ate 8 , 16 , 24 sandwiches in 1 , 2 and 3 hours respectively .
To find : the no . of sandwiches Jimmy eat in 1 hour , 2 hour and 3 hours .
Given : y = the no . of sandwiches Jimmy can eat
x = no . of hours he take in eating
Relation : y = 8 x
( i ) No . of sandwiches eaten by Jimmy in 1 hour
x = 1
y = ( 8 * 1 )
y = 8
( ii ) No . of sandwiches eaten by Jimmy in 2 hours
x = 2
y = ( 8 * 2 )
y = 16
( iii ) No . of sandwiches eaten by Jimmy in 3 hours
x = 3
y = ( 8 * 3 )
y = 24
Hence , Jimmy ate 8 , 16 , 24 sandwiches in 1 , 2 and 3 hours respectively .
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help
If f(1) = 3 and f(n) = f(n − 1) – 3 then find the value of f(4).
If f(1) = 3 and f(n) = f(n − 1) – 3 then the value of f(4) is -6.
Define function.A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). A function is a type of rule that produces one output for a single input. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.
Given,
Function:
f(1) = 3
f(n) = f(n - 1) -3
Let n = 2
f(2) = f(2-1) - 3
f(2) = 3 - 3
Relation:
f(2) = 0
Let n = 3
f(3) = f(3 -1) - 3
f(3) = 0 -3
f(3) = -3
Let n = 4
f(4) = f( 4 -1) - 3
f(4) = -3 -3
Value:
f(4) = -6
If f(1) = 3 and f(n) = f(n − 1) – 3 then the value of f(4) is -6.
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if records indicate that 2 houses out of 1000 are expected to be damaged by fire in any year, what is the probability that a woman who owns 14 houses will have fire damage in 1 of them in a year? (round your answer to five decimal places.)
Given that there will be 14 fires in a year, there will be an expected number of fires. There are more than 1000 points available in this question. We must determine the probability that a woman owned.
In a year, a fire will harm one in 12 homes. That is, given if n is equal to 12 and that the value of x is equal to 1, the probability of x being equal to 1 is also equal to 1. Hence, due to fire damage. We discovered that the probability value p equals 0.014, and we are aware that, in general, binomial probability, or the probability that x equals x, is equal to c x, p to the power of x times q to the power of n minus x. Substituting all of these values into the formula, where q = 1 - p, gives us the value of 12 c 1, or 0.014. The total power of 1 for q is 1 minus p, or 1 minus 0.014. 11 points is the power of 12 as a whole less 1. The result of simplification is 0.143865, so Therefore, we have determined that the likelihood of one out of every twelve homes experiencing fire damage is 0.143865 percent.
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what is 5.37 divied by 3 equals explain your answer
The answer is 1.79.
What is division?Division is breaking a number up into an equal number of parts.
Given that, 5.37 divided by 3
5.37÷3 = 1.79
Hence, 5.37 divided by 3 equals to 1.79.
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Ben and Katy throw darts at a target.
Ben's ratio of hits to misses is
5:1
Katy's ratio of hits to misses is 3:1
Ben says,
"5 is bigger than 3, so I must have more hits than Katy."
Give an example to show that this might not be true
In the given ratio, the statement "5 is bigger than 3, so I must have more hits than Katy." is false. Because this one refer the missing rate.
Ratio:
The relationship between two things when it is expressed in numbers or amounts is known as ratio.
Given,
Ben and Katy throw darts at a target. Ben's ratio of hits to misses is
5:1 Katy's ratio of hits to misses is 3:1
Ben says, "5 is bigger than 3, so I must have more hits than Katy."
Here we need to show that this might not be true.
Here we have the following missing ratios,
Ben's missing ratio = 5 : 1
Katy's missing Ratio = 3 : 1
Here Ben says "5 is bigger than 3, so I must have more hits than Katy."
While we carefully, looking into the given question, we have identified that the given ratios are represents the loosed dart.
So, the given statement is wrong.
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When collecting data, what is a sample?
Thank you for helping.
Answer:
Step-by-step explanation:
Artista , it's the 3rd answer, a random set from the group being studied
Which equation is the standard form of -8x + 3x² = -19?
8r 32² 19 0
The standard form of the equation -8x + 3x² = -19 is 3x² - 8x + 19 = 0.
How to write equation in standard form?The standard form of quadratic equation is ax² + bx + c = 0, where 'a' is the leading coefficient and it is a non-zero real number.
The standard form of quadratic equation with a variable x is of the form ax² + bx + c = 0, where a ≠ 0, and a, b, and c are real numbers.
Therefore, a, b and c are constant and x are the variables.
Let's represent the quadratic equation in standard form.
-8x + 3x² = -19
using the format ax² + bx + c = 0,
3x² - 8x + 19 = 0
where
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Lou and Jacob sold 200 pieces of jewelry. If 20% of Lou's sales were rings, and Jacob sold 35 rings, who sold more rings? How many more?
A. Jacob sold 5 more rings than Lou
B. Lou sold 5% more rings than Jacob
C. Jacob sold 5% more rings than Lou
D. Lou sold 5 more rings than Jacob
Show workk!!
Answer:
below
Step-by-step explanation
If they EACH sold 200 pieces
then Lou sold 200 x 20% = 200 x .20 = 40 rings which is 5 more than Jacob
Which ordered pair is a solution to the linear equation: 2x+3y=6?
2x-3y=6
Intercepts
x= 3
y= 2
ordered pairs: (6,2) (1.2,-1.2)
6 people carry the weight 216kg at a time. How many people are needed to carry the weight of 360kg
The number of people needed to carry the weight of 360 kg is 10 people.
The number of people are needed to carry the weight of 360kg can be calculated as follows ?
The first step is to put the demanded weight and the known weight of the required number of people into a formula which demanded weight is placed on numerator side and the known weight of the required number of people is placed on denominator side.
Formula
= [tex]\frac{360}{216}[/tex]
The next step is to multiply the number that has been entered into the fractional formula by the number of people who are known to be able to carry 216 kg
= [tex]\frac{360}{216}[/tex] × 6
= 10
Hence, the number of people needed to carry the weight of 360 kg is 10 people.
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You would need 10 people to carry a weight of 360 kg.
To find out how many people are needed to carry a weight of 360 kg, we can set up a proportion based on the information provided.
Let's assume that x represents the number of people needed to carry the weight of 360 kg.
The proportion can be set up as follows:
6 people / 216 kg = x people / 360 kg
We can solve this proportion by cross-multiplying:
216 kg · x people = 6 people · 360 kg
216x = 2,160
Dividing both sides of the equation by 216:
x = 2,160 / 216
x = 10
Therefore, you would need 10 people to carry a weight of 360 kg.
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Look at this set of ordered pairs:
(0, 0)
(0, -19)
(-8, 0)
Is this relation a function?
yes
no
What is 2+2 - 5 + 42 - 64 (5 x 5) - 32 x 1/2 + 6/5 * 2^5
Answer:
-1536.6 if not the answer den sorry
Step-by-step explanation:
Answer:
its -39363/25, -1574.32, and -1574 13/25 (hopefully this helps, sorry if its wrong)
The equation of line s is y=1/3x-3. The equation of line t is y=-x+5. The equations of line s and t form a system of equations. The solution to the system of equations is located at point P. Which graph correctly shows line s, line t, and point P?
The graph A is correctly shows for the line s, line t, and point P.
What is linear expression?
A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Given that;
The equation of line for s,
⇒ y = 1/3x - 3
And, The equation of line for t,
⇒ y = - x + 5
Now,
Solve the both equation of line for the solution as;
Since, The equation of line for s,
⇒ y = 1/3x - 3
And, The equation of line for t,
⇒ y = - x + 5
Equate both equation, we get;
⇒ 1/3x - 3 = - x + 5
⇒ 1/3x + x = 5 + 3
⇒ 4/3x = 8
⇒ x = 8 × 3 / 4
⇒ x = 2 × 3
⇒ x = 6
And, ⇒ y = - x + 5
⇒ y = - 6 + 5
⇒ y = - 1
Thus, The solution of the lines is;
Point P = (6, - 1)
Clearly, The graph A is correctly shows for the line s, line t, and point P.
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Geometry B
Spheres
The volume of a sphere is given by the following formula:
V =
4
3
V = = πr³
3
Page #6
Example Cros
What is the volume of the sphere in the diagram?
Find the volume of the sphere by entering the given radius into
the volume formula for a sphere.
4
V=X π X 3³
V = __________π cubic units
PEH
13
The volume of sphere in the diagram by entering the given radius into the volume formula is 36π cubic units.
Given that the volume of sphere is (4/3)×π×r³ and the radius is 3 units.
We want to the find the volume of sphere.
As we are given that the radius is 3 units and the volume of the sphere is (4/3)πr³.
So, firstly, we will substitute the value r=3 in the above formula, we get
V=(4/3)×π×(3)³
Now, we will simplify the above expression, we get
V=4π×9
V=36π cubic units
Hence, the volume of the sphere by entering the given radius into the volume formula for a sphere is 36π cubic units.
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I Need help wit this one
The area of the shaded region is 422.16 cm sq.
Given,
In the question:
Radius of the circle is 12 cm.
The length of rectangle is 10cm
and, Breadth of the rectangle is 3cm.
A rectangle sits inside a circle.
To find the Area of the shaded region.
Now, According to the question;
we know that:
Area of a circle is = [tex]\pi r^2[/tex]
Radius = 12cm
Area of a circle is = 144[tex]\pi[/tex]
Using [tex]\pi[/tex] = 3.14
Area of a circle is = 144 x 3.14 = 452.16 cm sq.
The area of rectangle = 3 x 10 = 30cm sq.
So, The area of the shaded region:
452.16 - 30 = 422.16cm sq.
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
A. 7.8
B. 9.8
Step-by-step explanation:
A. 2006 = 3 years
y = 7.1(1.03)ˣ
y = 7.1(1.03)⁽³⁾
y = 7.1(1.092727)
y = 7.7511907
y = 7.8
----------------------------------------------------------------------------------------------------------
B. 2014 = 11 years
y = 7.1(1.03)ˣ
y = 7.1(1.03)⁽¹¹⁾
y = 7.1(1.38423387)
y = 9.82806047
y = 9.8
If it says, "Round to the nearest tenth," the answer is 9.8. If the answer says, "Round to the nearest whole number," the answer is 10
I hope this helps!
can you please answer this? its timed so dont take too long!
2g³-5g²+6 is the equivalent expression of (5g⁴+5g³-17g²+6g)-(3g⁴+6g³-7g²-12)/g+2
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is (5g⁴+5g³-17g²+6g)-(3g⁴+6g³-7g²-12)/g+2
5g⁴+5g³-17g²+6g-3g⁴-6g³+7g²+12/g+2
2g⁴-g³-10g²+6g+12/g+2
Factorize the numerator
(g+2)(2g³-5g²+6)/g+2
g+2 in numerator and denominator will be cancelled.
2g³-5g²+6
Hence, 2g³-5g²+6 is the equivalent expression of (5g⁴+5g³-17g²+6g)-(3g⁴+6g³-7g²-12)/g+2
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Write an equation in standard form of the line that passes through (4, -1) and has the slope m = 3.
An equation in standard form is __ = -13
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{-1})\hspace{10em} \stackrel{slope}{m} ~=~ 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{ 3}(x-\stackrel{x_1}{4}) \implies y +1= 3 (x -4) \\\\\\ y+1=3x-12\implies y=3x-13\implies \underline{-3x+y=-13}\implies 3x-y=13[/tex]
now, notice, the equation should have a positivized "x" term, however the material is suggesting "incorrectly" the one that's underlined.
What value of x is in the solution set of the inequality 9 2x 1 9x 18?.
The value of x in the solution set of the inequality 9(2x+1) < 9x-18 is
x <-3.
Given inequality:
9(2x+1) < 9x-18
simplifying
9*2x + 9*1 < 9x - 18
18*x + 9 < 9x - 18
18x + 9 < 9x - 18
combining the like terms
18x - 9x + 9 < -18
9x + 9 < -18
combining the constants
9x < -18-9
9x < -27
divide by 9 on both sides
9x/9 < -27/9
x < -27/9
x < -3
Therefore the value of x in the solution set of the inequality 9(2x+1) < 9x-18 is x <-3.
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a survey of athletes at a high school is conducted, and the following facts are discovered: 51% of the athletes are football players, 43% are basketball players, and 1% of the athletes play both football and basketball. an athlete is chosen at random from the high school: what is the probability that the athlete is either a football player or a basketball player?
The probability that the athlete is either a football player or a basketball player is 93%.
What is probability?
The likelihood that something will occur is the foundation of it. The justification for probability serves as the basic foundation for theoretical probability. A coin is tossed, for instance, and the theoretical likelihood of receiving a head is 1 in 2.Football players= 51%
Basketball players= 43%
Both football and basketball= 1%
Probability = Football players + Basketball players
- Both football and basketball
Probability= 51% + 43% - 1%
Probability= 93%
Inconclusion The probability that the athlete is either a football player or a basketball player is 93%.
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Whiskers the cat weights 2 2/3 kg piglio weighs 4 kg how many times as heavyas whiskers is piglio
The weight of Piglio is 3/2 times of weight of Whishkers.
Fraction is comparison between two mathematical numbers or quantities.
Given that, Whisker weights 2 2/3 kg
Piglio weights 4 kg
Weight of Piglio is fraction of weight of Whisker = 4/(2 2/3) = 4/(8/3) = (4*3)/8 = 3/2 times
The weight of Piglio is 3/2 times of weight of Whishkers.
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Determine the y-intercept of the line
11x - 8y = 22
Answer:
- 2.75 or - 2 [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Put in zero for x to solve for y
11x -8y = 22
11(0) -8y = 22
-8y = 22 Divide both sides by -8
y = -2.75
(0, -2.75)
Answer:
[tex]-\frac{22}{8}[/tex] or [tex]- \frac{11}{4}[/tex] in mixed number form, [tex]-2\frac{3}{4}[/tex] simplified
Step-by-step explanation:
Minus 11x from 11x and 22.
You will then get -8y=11x+22.
Divide all the numbers by -8y.
You will get y=-11/8x-22/8
So the y-intercept is -22/8 or -11/4
I hope I got this right
HELP ME: Rewrite _____ using a common factor. (Screenshot with question and answers below)
Rewritten equation using a common factor is (1) [tex]\frac{1}{4}xy(x^{2} +3y)[/tex].
Given equation,
[tex]\frac{1}{4}x^{3}y+\frac{3}{4}xy^{2}[/tex]
Taking [tex]\frac{1}{4}xy[/tex] common,
[tex]\frac{1}{4}xy(x^{2} +3y)[/tex]
Hence, the equation.
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Write the following expressions in correct algebraic notation:
a) 7 x p
b) p x p
The Algebraic Notation of the expression is :
a) 7 x p
7 is multiplied to the p
b) p x p
p is multiplied itself.
Given,
In the question:
a) ) 7 x p
b) p x p
To write the above expressions in correct algebraic notation.
What are the algebraic notations and operations?
The algebraic expressions are used to solve mathematical equations. There are 3 types of algebraic expressions namely, monomial, binomial, and polynomial expressions. The basic algebraic operations are addition, subtraction, multiplication, and division.
Come to the question:
a) 7 x p
7 is multiplied to the p
b) p x p
p is multiplied itself.
Hence, The Algebraic Notation of the expression is :
a) 7 x p
7 is multiplied to the p
b) p x p
p is multiplied itself.
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Nine lemons cost $4.
Use the table to determine how many lemons can be bought for $20
Lemons 9 18 27 36 ?
Cost $4 $8 $12 $16 $20
Answer:
45 lemons can be bought with $20
Step-by-step explanation:
+9 +9 +9 +9 +9
Lemons 9 18 27 36 x
Cost $4 $8 $12 $16 $20
+4 +4 +4 +4 +4
Hynix is comparing two numbers.He knows the larger number is twice the value of 4 more than the smaller number X. He also knows their difference is 11. Which equation can he use to find the value of the smaller number X
The equation that he can use to find the value of the smaller is 8+2x = y and y-x = 11 where y is the larger number.
According to the question,
We have the following information:
Hynix is comparing two numbers. He knows the larger number is twice the value of 4 more than the smaller number X. He also knows their difference is 11.
Now, let's take the larger number to be y.
So, we have:
y = 2(4+x)
y = 8+2x
y-x = 11 ....(2)
Putting the value of y from above equation:
8+2x-x = 11
8+x = 11
x = 11-8
x = 3
Now, putting the value of x in equation 2:
y-3 = 11
y = 11+3
y = 14
Hence, the equation that he can use to find the value of the smaller is 8+2x = y and y-x = 11 where y is the larger number and the value of x is 3 and that of y is 14.
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David bought 5 of the ame ize pumpkin at the pumpkin patch for $33. 75. How much money would it be for David to buy 2 more of the ame pumpkin?
David requires $13.5 to buy 2 more pumpkins.
Firstly calculating the cost of one pumpkin and then calculating the desired answer.
Cost of one pumpkin = total cost ÷ number of pumpkins
Keep the values in formula to find the cost of one pumpkin
Cost of one pumpkin = 33.75 ÷ 5
Performing division on Right Hand Side of the equation
Cost of one pumpkin = $6.75
Now, the amount required to buy 2 more pumpkins = 2 × 6.75
Performing multiplication on Right Hand Side of the equation
The amount required = $13.5
Thus, the amount required by David is $13.5.
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Find the equation of the straight line passing through each of the following pairs of points.
( 11, 13) and ( 14, 19)
The equation of the line is, y = 2x - 9.
What is the point slope form of the equation of line?
The general form of a linear equation is y-y1=m(x-x1). It draws attention to the line's slope and one of the line's points (that is not the y-intercept).
Consider, the given two points, (11, 13) and (14, 19).
First to find the slope of the line, using the given two points,
[tex]m = \frac{y_2-y_1}{x_2 -x_1}[/tex]
[tex]m = \frac{19-13}{14-11} = \frac{6}{2} =2[/tex]
Therefore, the slope of the line is, 2.
Now to find the equation of line.
Consider, the point - slope form of the line,
[tex]y-y_1=m(x-x_1)[/tex] ..(1)
where, [tex](x_1, y_1)[/tex] is one of the given point and m is the slope of the line.
Here, [tex](x_1, y_1) = (11, 13), m = 2[/tex]
Substitute the values in the equation (1).
[tex]y-13=2(x-11)\\y-13=2x-22\\y=2x-22+13\\y=2x-9[/tex]
Therefore, the equation of line is, [tex]y=2x-9[/tex].
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Are the lines perpendicular? y=x+3 and x+y=6
A. Yes, their slopes are negative reciprocals
B. No, their slopes are not negative reciprocals
