Using the normal distribution, it is found that there is a 0.4038 = 40.38% probability that the person has an IQ score between 92 and 108.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 100, \sigma = 15[/tex].
The probability that the person has an IQ score between 92 and 108 is the p-value of Z when X = 108 subtracted by the p-value of Z when X = 92, hence:
X = 108:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{108 - 100}{15}[/tex]
Z = 0.53
Z = 0.53 has a p-value of 0.7019.
X = 92:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{92 - 100}{15}[/tex]
Z = -0.53
Z = -0.53 has a p-value of 0.2981.
0.7019 - 0.2981 = 0.4038.
0.4038 = 40.38% probability that the person has an IQ score between 92 and 108.
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two siblings are 55 years old combined the youngest sibling is 9 years younger than the oldest sibling how old is the youngest sibling
To solve systems of equations word problems, we can delegate certain variables to subjects mentioned in the word problem. From there, we can form equations based on the given values.
Solving the QuestionLet a be the older sibling's age and b be the younger sibling's age.
We're given:
a + b = 55 years oldb + 9 years = aAll we've done so far is translate the given sentences into equations. Now, we have to solve for b, which is the age of the youngest sibling. Solve using substitution:
[tex]a+b=55\\(b+9)+b=55\\b+9+b=55\\2b+9=55\\2b=46\\b=23[/tex]
Therefore, the younger sibling is 23 years old.
Answer23 years old.
A pizza place has pizzas in 2 different sizes, with 8 different flavors for the crust, and 8 different toppings.
How many one-topping pizzas can be ordered?
Use multiplication:
[tex]2\text{ sizes}*8\text{ flavors}*8\text{ toppings}=\large\boxed{128\text{ pizzas}}[/tex]
This question is basically the same as the other question of yours that I answered, so the explanation is very similar:
You can imagine the possibilities as leaves on a tree. Your tree has 2 large branches to represent the two possible sizes. Each of those branch off into 8 smaller branches, each representing a crust flavor. Each one of the smaller branches has 8 leaves to represent a different topping. Each leaf is a combination of a size, a crust flavor, and a topping, so it represents a complete pizza. Your job is to calculate the number of leaves.
HELP ME ANSWER THIS PLEASE
The table does not represent a function.
What is a function?
A function is a relationship that maps elements of the domain into elements of the range. Such that each element of the domain can be mapped into only one element of the range.
Here we have a table.
If you look at the table, you can see that the element of the domain:
x = -18
Is being mapped into two different values in the range.
Into y = -10 and y = 21.
From that, we conclude that this table does not represent a function.
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New topic please help
Answer:
2262.9cm squared
Step-by-step explanation:
That's all I could do.Hope it helps.
2y + 5 =
solve for the correct answer
let the value of y be 2
Now,
2y+5
2x2+5
4+5
9
Hence,proved
Part B: In complete sentences, explain how a circle can be used to find the circumcenter of the triangle graphed below.
Part C: Use a circle to locate the circumcenter of the triangle. Provide the location of the circumcenter.
Answer:
Step-by-step explanation:
Part B:
The center of the circumscribed circle around a triangle is equidistant from vertices of that triangle. To find the circumcenter need to draw at least two perpendicular bisectors to the sides of the given triangle. Point of intersect of them is center of the circumscribed circle.
Part C:
Coordinates of the midpoint of line BC ( y = - 1 ) are
( [tex]\frac{-6+2}{2}[/tex] , [tex]\frac{-1-1}{2}[/tex] ) = ( - 2 , - 1 ) and the equation of the line ⊥ to BC is x = - 2
Because BC is ║ to x-axis and m∠A is 90° , the center of the circle is midpoint of BC and r = [tex]\frac{BC}{2}[/tex] = 4
Schweser Satellites Inc. produces satellite earth stations that sell for $115,000 each. The firm's fixed costs, F, are $3 million, 50 earth stations are produced and sold each year, profits total $600,000, and the firm's assets (all equity financed) are $4 million. The firm estimates that it can change its production process, adding $3 million to assets and $500,000 to fixed operating costs. This change will reduce variable costs per unit by $12,000 and increase output by 15 units. However, the sales price on all units must be lowered to $110,000 to permit sales of the additional output. The firm has tax loss carryforwards that render its tax rate zero, its cost of equity is 13%, and it uses no debt.
What is the incremental profit? Enter your answer in dollars. For example, an answer of $4 million should be entered as 4,000,000, not 4. Round your answer to the nearest dollar.
$
To get a rough idea of the project's profitability, what is the project's expected rate of return for the next year (defined as the incremental profit divided by the investment)? Round your answer to two decimal places.
%
Should the firm make the investment?
-Select-
Would the firm's break-even point increase or decrease if it made the change?
The change would
-Select-
the break-even point.
Would the new situation expose the firm to more or less business risk than the old one?
I. The new situation would obviously have more business risk than the old one.
II. The new situation would obviously have less business risk than the old one.
III. It is impossible to state unequivocally whether the new situation would have more or less business risk than the old one.
-Select-
The incremental profit is $175,000 and the new situation would obviously have less business risk than the old one.
Incremental profitFirst step
Profit $600,000
Add Fixed cost $3,000,000
Contribution $3,600,000
Variable Cost=Total Sales−Contribution
Variable Cost=$115,000×50-$3,600,000
Variable Cost=$2,150,000
Second step
Profit at revised cost
Sales $8,625,000
(75x $115,000)
Less: Variable cost $4,350,000
[75×($3,000,000+$500,000/50-$12,000)]
Contribution $4,275,000
Less Fixed cost $3,500,000
($3,000,000+$500,000)
Profit $775,000
Incremental profit=Profit at revised cost-Existing profit
Incremental profit=$775,000-$600,000
Incremental profit=$175,000
Expected rate of return=Incremental profit/Investment
Expected rate of return=$175,000/$4,000,000×100
Expected rate of return=$4.375%
2. Break-even point
Existing
Break-even point=Fixed cost/Contribution
Break-even point=$3,000,000/[($115,000-($3,000,000+$500,000/50)]
Break-even point=$3,000,000/[($115,000-$70,000)
Break-even point= 66.67
Revised
Break-even point=Fixed cost/Contribution
Break-even point=$3,500,000/[($110,000-($3,000,000/50)]
Break-even point=$3,000,000/[($110,000-$60,000)
Break-even point=60
II. The new situation would obviously have less business risk than the old one.
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Which two points are on the graph of y=x - 4?
(4.0), (1, 3)
(0.-4). (4.1)
(1.5), (0, -4)
(1.-3), (-1,-5)
Answer: (1.-3), (-1,-5)
Step-by-step explanation:
Substituting the x coordinates into the equation, we get that the result is equal to the y coordinate of the points.
Thus, the points lie on the line.
The diameter of a proton is about 1.9 cross times 10 to the power of short dash 15 end exponent meters. A hydrogen atom has an overall length of 100,000 times (or 1 cross times 10 to the power of 5 times) the diameter of a proton.
What is the length of the hydrogen atom, in meters, if it were written in scientific notation?
A. 1.9 x 10 (15 exponent)
B. 1.9 x 10 (-15 exponent)
C. 1.9 x 10 (-8 exponent)
D. 1.9 x 10 (-12 exponent)
Using scientific notation, the measure is given as follows:
[tex]1.9 \times 10^{-10}[/tex]
What is scientific notation?A number in scientific notation is given by:
[tex]a \times 10^b[/tex]
With the base being [tex]a \in [1, 10)[/tex].
The diameter of a proton, in scientific notation, is given by:
[tex]1.9 \times 10^{-15}[/tex].
The hydrogen atom has an overall length of 100,000 = 10^5 times the diameter of the proton, hence the length is given by:
[tex]L = 100000 \times 1.9 \times 10^{-15} = 10^5 \times 1.9 \times 10^{-15} = 1.9 \times 10^{5 - 15} = 1.9 \times 10^{-10}[/tex]
For the above length, I applied the multiplication of factors with the same base and different exponents, where we keep the base and add the exponents.
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If....................
Answer:
C - 22
Step-by-step explanation:
Put in '3 ' for 'x' in both of the equations....then multiply the results together
f(3) = 3 (3)^2 - 5 = 22
g(3) = -1
22 * -1 = -22
To solve for f(3)g(3):
* We know fg(x) means we need to multiply f with g replacing all x's with the x-value given
Replace all x's with 3Solve for f(3)g(3)[tex](3(3)^{2}-5)(-2(3)+5)\\(3(9)-5)(-6+5)\\22 * -1\\-22[/tex]-22 is the answer
Hope it helps!
Isn't the series here divergent? doesn't that mean it cannot be represented as a riemann sum
No issues with convergence here. If you actually expand the summand you can use the well-known Faulhaber formulas to compute the sum.
[tex]\displaystyle \sum_{i=1}^n 1 = n[/tex]
[tex]\displaystyle \sum_{i=1}^n i = \frac{n(n+1)}2[/tex]
[tex]\displaystyle \sum_{i=1}^n i^2 = \frac{n(n+1)(2n+1)}6[/tex]
[tex]\displaystyle \sum_{i=1}^n i^3 = \frac{n^2(n+1)^2}4[/tex]
and so on. You would end up with
[tex]\displaystyle L_n = \frac2n \times \frac{96-8796n^2+40283n^3-49458n^4}{n^3}[/tex]
As [tex]n\to\infty[/tex], we have [tex]L_n\to-98916[/tex].
Now, when [tex]i=1[/tex], the first term of the sum is
[tex]7(5+0)^3 - 6(5+0)^5[/tex]
so the left endpoint of the first subinterval is [tex]a=5[/tex].
At the other end, when [tex]i=n[/tex], the last term of the sum is
[tex]7\left(5+\dfrac{2(n-1)}n\right)^3 - 6\left(5+\dfrac{2(n-1)}n\right)^5[/tex]
which converges to
[tex]7(5+2)^3 - 6(5+2)^5[/tex]
so the left endpoint of the last subinterval converges to [tex]b=5 + 2 = 7[/tex].
From here it's quite clear that [tex]f(x)=7x^3-6x^5[/tex]. So, the Riemann sum converges to the definite integral
[tex]\boxed{\displaystyle \int_5^7 (7x^3 - 6x^5) \, dx}[/tex]
If 5 cups of flour are needed to make 40 biscuits how much flour is needed to make 18 cups of the same kind of biscuit express your answer in mixed fraction
Answer:
[tex]2\frac14[/tex]
Step-by-step explanation:
Note: 18 cups of biscuit?
Anyway:
Since 5 cups of flour = 40 biscuits, 1 biscuit = [tex]\frac{1}8[/tex] cups of flour
18 biscuits = [tex]\frac{18}{8}=\frac94=2\frac14[/tex]
Aamir wants to add 894 and 76. He first adds 890 and 80. What should he do next to get the correct answer?
O add 4
O add 8
O subtract 4
O He has already calculated the correct answer in the first step
21. Find the measure of angle A.
40
20
80
160
160°
Answer:
m<A = 20°
Step-by-step explanation:
360 160 = 200
m<A = (1/2)(200° - 160°)
m<A = 20°
Which function is a quadratic function?
y - 3x² = 3(x² + 5) + 1
y²-7x = 2(x² + 6) + 7
y-2x² = 6(x3 + 5)-4
y - 5x = 4(x + 5) + 9
Answer:
y – 3x2 = 3(x2 5) 1 is correct
Step-by-step explanation:
hope this helps this may be wrong
For the data that are shown on the graph below, which best describes within which range of x-values extrapolation occurs?
On a graph, points are at (0, 15), (1, 17), (3, 18), (4, 20) and (6, 22).
A) x greater-than 6
B) x less-than 0 and x greater-than 6
C) x less-than 0 and x greater-than 10
D) x greater-than-or-equal-to 0 and x less-than-or-equal-to 6
The range of x-values extrapolation occurs in between x < 0 and x > 6
We have given that,
On a graph, points are at (0, 15), (1, 17), (3, 18), (4, 20) and (6, 22).
What is the range?
The Range is the difference between the lowest and highest values.
Therefore we can conclude that the,
range of x-values extrapolation occurs in between x < 0 and x > 6.
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Find the value of x for which the lines I and m are parallel.
5x+13
11x-73
14.3
15
16.6
10
Answer:
15
Step-by-step explanation:
5x+13+11x-73=180°( co-interior angles sum is 180)
5x+11x+13-73=180°
16x-60=180
16x=180+60
16x=240
x=15
What is the solution, if any, to the inequality |3x|≥0?
all real numbers
A.all real numbers
B.no solution
C.x20
D.x≤0
The inequality is all real numbers.
What is inequality?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Given:
|3x|≥0
3x = 0
Divide both sides of the equation by the coefficient of variable
x= 0/3
x=0 = RHS
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Use a truth table to decide whether each argument is valid or invalid If a person is on this reality show, they must be self-absorbed. Laura is notself-absorbed. Therefore, Laura cannot be on this reality show.
The arguments are valid therefore F F →T
What is a truth table?A truth table is a mathematical table which shows the truth values for a given set of arguments and tells if the argument is valid or invalid.
Analysis:
Argument 1( P)= if a person is on this reality show(true) T
Argument 2(Q) = the person is self absorbed true(T)
Laura is not self absorbed = False(≈Q)
Laura wont be on the reality show = False(≈P)
So she can only be on the reality show if she is self absorbed else she cannot.
so F F → T
Which means that the argument is valid.
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her the
Use the figure for exercises 13-14. Rewrite each sum using a single angle.
13. mLLMN + mLNMP
14. mLNMP
mLOMP
Given that x = 3 + y and that -2y + 3 < -1, provide
reasons for each step in the following solution for x.
STATEMENTS
15. x = 3 + y and -2y + 3 < -1
16. x > y
17. -2y<-4
18. y> 2
19. x > 2
15.
16.
17.
18.
19.
REASONS
M
Answer:
13. m∠MN + m∠NMP = m∠MP.
14. m∠NMP - m∠OMP = m∠NMO.
~
15. x = 3 + y and -2y + 3 < -1 : Given
16. x > y : x = 3 + y
17. -2y < -4 : -2y < -4
18. y > 2 : y > 2
19. x > 2 : x = 3 + y and y > 2
------------------------------------------
line segment SU is a diameter at Circle V what is the measure of arc ST?
The measure of ST based on the diagram regarding the circle is 56°.
How to calculate the value?Fron the information given, angle S is equal to 34°. Also, the triangle is inscribed in a circle.
Therefore, the measure of the angle will be:
= 180 - 90 - 34
= 56°
Therefore, the measure of angle ST is 56°.
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Find the value of 5y-3 given that -3y-8=7. Simplify your answer as much as possible. Find the value of 5y - 3 given that -3y - 8 = 7 . Simplify your answer as much as possible .
Answer:
-28
Step-by-step explanation:
Find 5y-3 , given -3y - 8 = 7.
First, we will multiply -3y - 8 = 7 by [tex]-\frac{5}{3}[/tex] to get 5y first.
[tex]-\frac{5}{3} (-3y-8)=-\frac{5}{3} (7)\\5y+\frac{40}{3} =-\frac{35}{3} \\[/tex]
Now we will get the constant on the left side of the equation to 3.
[tex]5y+\frac{40}{3} -\frac{40}{3} =-\frac{35}{3} -\frac{40}{3} \\5y=-25\\5y-3=-25-3\\5y-3=-28[/tex]
tommy starts walking from school to home at the same time that his dad starts walking home to school the both depart at 300pm tommy is walking at a speed of 1.35meters pr second and his dad is walking at a speed of 1.65 meters per second. the distance between home and school is 720 meters at what time wil they meet
Tommy and his father will meet after 2400 seconds or 40 minutes. So they will meet at 3:40 pm.
What is speed?Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance.
Given that:-
Tommy starts walking from school to home at the same time that his dad starts walking home to school they both depart at 300pm Tommy is walking at a speed of 1.35meters per second and his dad is walking at a speed of 1.65 meters per second. the distance between home and school is 720 meters at what time will they meetThe time will be calculated by using the relative speed concept.
Relative speed = Speed of father - Speed of Tommy
Relative speed = 1.65 - 1.35
Relative speed = 0.3 meter per second
Relative speed = Distance / Time
0.3 = 720 / Time
Time = 720 / 0.3
Time = 2400 seconds = 2400/ 60 = 40 minutes
We know that both departed at 3 pm they will meet at 3:40 pm.
Therefore Tommy and his father will meet after 2400 seconds or 40 minutes. So they will meet at 3:40 pm.
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Answer:
They will meet at 3:04 p.m
Step-by-step explanation:
Since they are walking toward each other, that means we should add their speed together:
speed = 1.35 m/s + 1.65 m/s
= 3 m/s
Now that we have found the speed, we can calculate the time:
time = 720 meters / 3 m/s
= 240 seconds
= 4 minutes ( 240 seconds is 4 minutes)
What is the length of the unknown leg in the right triangle? a right triangle has a side with length 20 meters, hypotenuse with length 25 meters, and side labeled b.
The length of the unknown leg of the triangle is 15 m.
Length of one leg = 20 m
Length of the hypotenuse= 25m
As it is a right angled triangle we can use pythogoras theorem.
Let the unknown length be y
(20) (20) + y(y) = (25) (25)
400 + y(y) = 625
[tex]y^{2}[/tex]= 225
y = √225
y = 15
The length of the unknown leg is 15 m.
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If $200 is put in the bank and each year the account earns 5% simple interest,
then how much interest will be earned in two years?
$10
$20
$30
$100
Work Shown:
i = P*r*t
i = 200*0.05*2
i = 20
A quick mental shortcut is to double the 5% interest to get 10%, since this occurs over 2 years. Then taking 10% of something is the same as moving the decimal point one spot to the left. So we go from 200 to 20
A, B & C form the vertices of a triangle.
CAB = 90°, ABC = 30° and AC = 9.3.
Calculate the length of AB rounded to 3 SF.
The length of AB = 18.6 .
What is a Triangle ?A triangle is a polygon with three sides , angles and vertices.
It is given that ABC is a triangle such that
CAB = 90°
ABC = 30° and
AC = 9.3.
AB = ?
As the triangle is a right angled triangle
Trigonometric ratios can be used.
sin x = Perpendicular / base
sin 30 = AC / AB
(1/2) = 9.3 / AB
AB = 9.3 /0.5
AB = 18.6
Therefore the length of AB = 18.6 .
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how many solutions does equation 6x + y = -1 and -6x - 4y =4 have
Answer:
There are no solutions.
Step-by-step explanation:
When you solve for x in the first equation, you get x = (-1-y)/6. Plugging this value for x into the second equation gives you -4y = 4 + y, which has no solutions.
Edgar records the time that it takes his school bus to take him from the bus stop
to school each day. This is a
______ random variable.
A. continuous
B. infinite
C. discrete
D. intervalled
Answer: I'm pretty sure it is D. intervalled
explanation: Because it can never be exact each and every time
System A
−10x−4y=0
−2x+7y=8
System B
−10x−4y=8
−2x+7y=0
1) How can we get System B from System A?
(Choice C, Checked, Correct)
CORRECT (SELECTED)
Swap only the right-hand sides of both equations
2) Based on the previous answer, are the systems equivalent? In other words, do they have the same solution?
CORRECT (SELECTED)
No
For the given systems we have:
1) Swap the right sides of both equations in system A.
2) No, the systems are not equivalent systems.
How can we get System B from System A?
The two systems are:
A:
-10x - 4y = 0
-2x + 7y = 8
B:
-10x - 4y = 8
-2x + 7y = 0
Notice that the only different thing between the systems is that the right sides are inverted. So, if we invert the right side of A, we will get system B.
2) Are the systems equivalent?
No, the systems are not equivalent because to go from system A to system B we only modified the right side of system A, the systems would be equivalent only if modifying both sides of A gave system B, but this is not the case.
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Which the most accurate statement about progress monitoring?
a. Progress monitoring is a useful way to ensure children are participating in targeted, purposeful, and meaningful math instruction and allows for the teacher to identify the skills children may need additional support in.
b. Incorporating children's individual differences into lesson planning is not necessary since the curriculum includes all the skills children need to learn in the order they need to learn them.
c. Progress monitoring is about administering formal assessments at the beginning and end of the year.
Answer:
progress monitoring is used to access students academic and social emotional behaviour as EB progress examine rate of improvement and evaluate effectiveness of introduction are invention it is typical use with both individual students and small groups