Answer:
See below.
Step-by-step explanation:
We are asked to simplify the equation.
First, we should Combine Like Terms.
What is Combining Like Terms?
Combining Like Terms is adding terms that are alike.
For example, 4x and 11x are like terms since there's no differences than the coefficient, which can be different.
Let's combine like terms for this problem now.
Combine Like Terms:
[tex]\frac{2}{5} x+ 7 - \frac{2}{3} x -15\\\\\frac{2}{5} x - \frac{2}{3} x = \frac{6}{15} x - \frac{10}{15} x=-\frac{4}{15} x\\\\7 - 15 = -8[/tex]
We should have;
[tex]- \frac{4}{15} x - 8[/tex]
This will be our final answer.
What is the sum of the first 4 terms of an arithmetic sequence in which the 7th term
is 19 and the 11th term is 29?
Hint: create a system of equations to find d.
A 09
B 31
C 48
D 11.5
E 45
Answer:
it's 48 I think that's the answer for the question.
Can someone answer this just read the picture? Right answers only please!
Answer:
6 + 40 *3 = 126
Step-by-step explanation:
first is 6 and you add 3 in every step
Answer:
126 smileys
Step-by-step explanation:
[tex]a_{1} =[/tex] First term
= 6
[tex]d =[/tex] Common difference
= 3
[tex]n =[/tex] [tex]n^{th} term[/tex]
= Step number
Arithmetic sequence will be applied:
[tex]a_{n} = a_{1} + (n - 1)d[/tex]
For n = 2:
[tex]a_{2} = 6 + (2 - 1)(3)[/tex]
[tex]= 6 + (1)(3)[/tex]
[tex]= 9[/tex]
For n = 3:
[tex]a_{3} = 6 + (3-1)(3)[/tex]
[tex]= 6 + (2)(3)[/tex]
[tex]= 6 + 6[/tex]
[tex]= 12[/tex]
∴For n = 41:
[tex]a_{41} = 6 + (41 - 1)(3)[/tex]
[tex]= 6 + (40)(3)[/tex]
[tex]= 6 + 120[/tex]
[tex]= 126[/tex]
∴There will be 126 smiley faces in Step 41
Imagine you are about to run two laps of an athletics track. You can go at any speed for the first lap. On the second lap, you will have to run faster such that your average speed is twice the speed of the first lap. How fast do you have to run the second lap to make this happen?
Answer:
Let's assume that the length of the athletics track is "L" units, and let "x" be the speed (in units per minute) at which you run the first lap.
Since you're running two laps, the total distance covered is 2L. The time it takes to complete the first lap is L/x, since time = distance ÷ speed. For the second lap, you want your average speed to be twice the speed of the first lap, so your total time for the second lap must be half the time of the first lap:
Total time for second lap = 0.5 * (L/x) = L/2x
The total time for the two laps is the sum of the time for each lap:
Total time = L/x + L/2x = (2L + L)/(2x) = 3L/(2x)
The average speed for the two laps is the total distance (2L) divided by the total time (3L/2x):
Average speed = (2L) / (3L/2x) = 4x/3
Since you want your average speed for the second lap to be twice the speed of the first lap, you can set up the following equation:
2x = (4x/3) - x
Solving for x, we get:
2x = 4x/3 - x
5x/3 = 0
x = 0
This means that you would have to run the first lap at a speed of 0 units per minute, which is impossible. Therefore, it's not possible to run two laps of an athletics track such that the average speed of the second lap is twice the speed of the first lap.
Step-by-step explanation:
Calculate the simple interest and find the new balance on a principal of $575 deposited at 6.5% for a period of 10 years round the the nearest cent
Answer:
Step-by-step explanation:
The simple interest can be calculated using the formula:
I = P * r * t
where:
P = principal amount = $575
r = annual interest rate = 6.5% = 0.065
t = time period = 10 years
I = 575 * 0.065 * 10
I = $373.75
The new balance can be found by adding the interest to the principal:
New balance = Principal + Interest
New balance = $575 + $373.75
New balance = $948.75
Rounded to the nearest cent, the new balance is $948.75.
Bella owns a small business selling ice-cream. She knows that in the last week 50 customers paid cash, 2 customers used a debit card, and 4 customers used a credit card. Based on these results, express the probability that the next customer will pay with cash or a credit card as a decimal to the nearest hundredth.
Answer:
0.96
Step-by-step explanation:
Bella owns a small business selling ice-cream. She knows that in the last week 50 customers paid cash, 2 customers used a debit card, and 4 customers used a credit card.
Based on these results, express the probability that the next customer will pay with cash or a credit card as a decimal to the nearest hundredth.
50 cash, 2 debit card, and 4 credit card.
50+2+4= 56
There were a total of 56 customers. 50+4=54 customers paid with cash or a credit card.
Probability the next customer will pay with cash or a credit card:
54
56
= 0.964285...
≈ 0.96
Round to the nearest hundredth
The probability as a decimal to the nearest hundredth is
0.96
Which system of inequalities is graphed to the right?
The system of inequalities graphed is given as follows:
y > -1.y ≤ -x + 1.How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change.b is the intercept, representing the value of y when x = 0.The lower bound of the graph is a horizontal line at y = -1, hence:
y > -1.
For the upper bound of the graph, we have a linear function with these following parameters:
b = 1, as when x = 0, y = 1.m = -1, as when x increases by 1, y decays by 1.The upper bound is also a closed interval, as the line is solid, hence:
y ≤ -x + 1.
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Write a real-world problem that could be solved using the system of equations below. HELP RIGHT AWAY!!
Answer:
Step-by-step explanation:
y=4x + 10
y=3x + 15
Which statement sentence is true?
A) 0.35 > 0.36
B) 0.3 < 0.04
C) 0.3 > 0.20
D) 0.75 < 0.7
Answer: C
Step-by-step explanation: 0.3 is greater than 0.20
0.3 could be 0.30 or 0.35 or even 0.31, depends.
A young executive is going to purchase a vacation property for investment purposes. She needs to borrow $127,000.00 for 28 years at 4.3% compounded monthly, and will make monthly payments of $650.71. (Round all answers to 2 decimal places.)
What is the unpaid balance after 15 months? $
During this time period, how much interest did she pay? $
4.
A principal estimated that 100 students attended the school's play. Select
all of the statements that could represent this estimate.
65% of 150 students
24% of 394 students
52% of 140 students
78% of 211 students
the jacket is
Answer:
Step-by-step explanation:
The statement "65% of 150 students" could represent the estimate that 100 students attended the school's play.
To see this, we can calculate 65% of 150:
0.65 x 150 = 97.5
Since 97.5 is close to 100, it is possible that the estimate was based on 65% of 150 students.
The other statements do not come close to 100, so they are not likely to represent the estimate that 100 students attended the school's play.
please help me with these problems
The values of the missing sides are;
1. q = 4. 1, p = 11. 3
2. y = 56. 6, x = 35. 6
3. b = 16. 7, a = 9.1
How to determine the valuesUsing the sine and cosine identities, we have;
sin θ = opposite/ hypotenuse
cos θ = adjacent/hypotenuse
We have that;
sin 20 = q/12
find the values
q = 4. 1
Also
cos 20 = p/12
p = 11. 3
For the second triangle
cos 39 = 44/y
cross multiply
y = 44/0. 7777
y = 56. 6
Also,
sin 39 = x/56.6
x = 35. 6
For the third triangle
sin 57 = 14/b
cross multiply
b = 16. 7
Also,
cos 57 = a/16. 7
cross multiply
a = 9. 1
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WILL GIVE 5 STARS
Find the eighth term in the sequence and explain how you arrived at this answer.
4, 16, 36, 64, 100, ...
The eighth term of the sequence is 256.
What is the eighth term in the sequence?To find the eighth term in the sequence 4, 16, 36, 64, 100, ...., we need to first determine the pattern that generates the sequence.
Looking at the sequence, we notice that;
the first term is 4, which is equal to 2^2. the second term is 16, which is equal to 4^2. the third term is 36, which is equal to 6^2. the fourth term is 64, which is equal to 8^2. the fifth term is 100, which is equal to 10^2.Therefore, we can see that the nth term of the sequence is equal to n^2 * 2^0, 2^2, 2^2, 2^2, 2^2, 2^2, ...
So, the eighth term of the sequence would be:
8^2 * 2^2 = 64 * 4 = 256
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Super Scary Circles
This figure is NOT drawn to scale.
a = 90°
b=12°
C=
d=
e=
F=
g=
h=
I=
J=
Need to find the angle for each letter . Will be great if I can get the answer tonight
The measure of the angle for each letter found by finding the variables representing the angles simultaneously using circle theorems are;
a = 90°, b = 12°, c = 64°, d = 52°, e = 52°, f = 48°, g = 66°, h = 32°, i = 36°, j = 20°
What is a simultaneous equation?A simultaneous equation consists of two or more equations that consists of the same variables.
The evaluation of the angles in the circle are presented as follows;
a + a = 180° (linear pair angles)
2·a = 180°
a = 180°/2 = 90°
a = 90°
The 32° angle indicates that the base angle of the large isosceles triangle is 2 × 32° = 64°
Angle c is a base angle of the isosceles triangle, therefore, we get;
c = 64°
Angle b + 90° + 78° = 180° (Angle sum property of a triangle)
b = 180° - (90° + 78°) = 12°
b = 12°
In the isosceles triangle with angle 2·b, and the isosceles triangle formed by the radii to the vertices, we get;
2·b + 2·b = f, therefore;
f = 2·b + 2·b = 4·b
f = 4·b
f = 4 × 12° = 48°
f = 48°
The measure of angle g is equivalent to the measure of a base angle of the isosceles triangle with the angle 2·b, with angle f = 48° being a vertex of the triangle, therefore;
g = (180° - 48°)/2 = 66°
g = 66°
Vertex angle of the cyclic quadrilateral with 5·b can be found as follows;
2·f + The vertex angle = 180°
Vertex angle = 180° - 2 × 48° = 84°
Vertex angle = 84°
5·b + 2·h + i + j = 180°
5 × 12 + 2·h + i + j = 180°
60° + 2·h + i + j = 180°
2·h + i + j = 180° - 60° = 120°
2·h + i + j = 120°...(1)
2 × 2·h + 2 × j = 2 × 84°
2·h + j = 84°...(2)
2·f + 5·b + i + 168° = 360°
i = 360° - 2·f + 5·b + 168°
i = 360 - (96 + 60 + 168) = 36
2·h + i + j - (2·h + j) = 120° - 84° = 36°
i = 36°
5·b + 2·h + 2·f + i + j + 84° = 360°
60° + 2·h + 96° + 36° + j + 84° = 360°
2·h + j = 360° - 84° - 36° - 60° - 96° = 84°
2·h + j = 84°
The two tangent theorem indicates that we get;
90° - 64° = 26°
180° - 2 × 26° = 128°
h = (180° - 128°/2)/2 - 26° = 32°
h = 32°
2·h + j = 84°
j = 84° - 2·h
j = 84° - 2 × 32° = 20°
j = 20°
d = e (Angles subtended by the same chord)
2·c + d = 180°
2 × 64° + d = 180°
d = 180° - 2 × 64° = 52°
d = 52° = e
e = 52°
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Review the table of values for function g(x). x g(x) 32.9 –7 32.99 –6.1 32.999 –6.01 33.001 –15.01 33.01 –15.1 33.1 –16 What are the values of Limit of g (x) as x approaches 33 minus and Limit of g (x) as x approaches 33 plus? Limit of g (x) = negative 16 as x approaches 33 minus and limit of g (x) = negative 7 as x approaches 33 plus Limit of g (x) = negative 15 as x approaches 33 minus and limit of g (x) = negative 6 as x approaches 33 plus Limit of g (x) = negative 7 as x approaches 33 minus and limit of g (x) = negative 16 as x approaches 33 plus Limit of g (x) = negative 6 as x approaches 33 minus and limit of g (x) = negative 15 as x approaches 33 plus
The values of the limits of g(x) as x approaches 33 minus and 33 plus can be determined by examining the table of values and looking for the values of g(x) as x gets closer and closer to 33 from the left and the right sides.
As x approaches 33 from the left (i.e., values of x slightly less than 33), we can see from the table that the values of g(x) decrease from -7 to -16. Therefore, the limit of g(x) as x approaches 33 from the left is -16.
As x approaches 33 from the right (i.e., values of x slightly greater than 33), we can see from the table that the values of g(x) increase from -6.1 to -7. Therefore, the limit of g(x) as x approaches 33 from the right is -7.
Therefore, the correct answer is:
Limit of g(x) = negative 16 as x approaches 33 minus and limit of g(x) = negative 7 as x approaches 33 plus.
Men have XY (or YX) chromosomes and women have XX chromosomes. X-linked recessive genetic diseases (such as juvenile retinoschisis) occur when there is a defective X chromosome that occurs without a paired X chromosome that is not defective. Represent a defective X chromosome with lowercase x, so a child with the xY or Yx pair of chromosomes will have the disease and a child with XX or XY or YX or xX or Xx will not have the disease. Each parent contributes one of the chromosomes to the child. Complete parts a through d below.
Question content area bottom
Part 1
a. If a father has the defective x chromosome and the mother has good XX chromosomes, what is the probability that a son will inherit the disease?
enter your response here
(Type an integer or a decimal. Do not round.)
The probability that a son will inherit the disease would be
P{E} = 1/4.
What is probability?The probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%Given is that men have XY (or YX) chromosomes and women have XX chromosomes. X-linked recessive genetic diseases (such as juvenile retinoschisis) occur when there is a defective X chromosome that occurs without a paired X chromosome that is not defective. Represent a defective X chromosome with lowercase x, so a child with the xY or Yx pair of chromosomes will have the disease and a child with XX or XY or YX or xX or Xx will not have the disease. Each parent contributes one of the chromosomes to the child.
The probability that a son will inherit the disease if a father has the
defective {x} chromosome and the mother has good {XX} chromosomes
as -
P{E} = 4/16
P{E} = 1/4
Therefore, the probability that a son will inherit the disease would be
P{E} = 1/4.
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Tina is getting broadband for her new flat.
She finds this deal.
Broadband deal
router normal price £39.99
15% discount on the normal router price
18 months contract at £56.99 each month
Tina buys the router and the 18 months contract.
Work out the total cost of this deal for Tina.
The total cost of the deal for the router for Tina is given by A = $ 1059.81
What is Percentage?A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.
Percentage change is the difference between the measured value and the true value , as a percentage of the true value
Percentage change =( (| Measured Value - True Value |) / True Value ) x 100
Given data ,
Let the total cost of the deal be represented as A
Let the initial price of the router be = $ 39.99
Now , the percentage of discount for the router = 15 %
So , the final cost of the router = ( 85/100 ) x 39.99
On simplifying , we get
The final cost of the router = $ 33.9915
Now , the number of months = 18 months
The contract rate = $ 56.99 per month
So , the total contract rate for 18 months = 18 x 56.99
The total contract rate for 18 months = $ 1,025.82
Now , total cost of the deal A = final cost of the router + total contract rate for 18 months
On simplifying the equation , we get
The total cost of the deal A = $ 1,025.82 + $ 33.9915
The total cost of the deal A = $ 1059.8115
The total cost of the deal A = $ 1059.81
Hence , the total cost of the deal is $ 1059.81
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The expression −−18−−−−√−−18 can be rewritten as −1⋅−1−−−√⋅9–√⋅2–√−1⋅−1⋅9⋅2. Which expression is equivalent to −1⋅−1−−−√⋅9–√⋅2–√−1⋅−1⋅9⋅2?
The answer of imaginary expression is option a. The value is -3i[tex]\sqrt2[/tex] .
What is Imaginary expression?Imaginary expression is a specific type of algebraic expression which involves the square root of a negative number. For example 2+3i is an Imaginary expression.
Given that,
-1[tex]\sqrt{-1[/tex] [tex]\sqrt9[/tex] [tex]\sqrt{2[/tex]
=-1×i×3×√2 [since [tex]\sqrt-1[/tex]= i and [tex]\sqrt{9[/tex] =3]
[Here [tex]\sqrt-1[/tex] is an imaginary number]
= -3i√2
Hence the answer is -3i√2 .
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A line passes through the point (2, - 3) and has a slope of - 4.
Write an equation in slope-intercept form for this line.
Answer:
y = -4x + 5.
Step-by-step explanation:
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
Given that the line passes through the point (2, -3) and has a slope of -4, we can use the point-slope form of a linear equation to find the y-intercept:
y - y1 = m(x - x1)
where x1 and y1 are the coordinates of the given point, and m is the slope.
Substituting the given values, we get:
y - (-3) = -4(x - 2)
Simplifying and rearranging, we get:
y + 3 = -4x + 8
Subtracting 3 from both sides, we get:
y = -4x + 5
Therefore, the equation in slope-intercept form for the given line is y = -4x + 5.
Question content area top
Part 1
You are certain to get a queen when selecting 49 cards from a shuffled deck. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
Answer:
Step-by-step explanation:
A standard deck of cards has 52 cards, including 4 queens. If you are certain to get a queen when selecting 49 cards from a shuffled deck, it means that one of those 49 cards must be a queen, and the remaining 48 cards can be any of the remaining 48 cards in the deck.
So, the probability of selecting a queen from a shuffled deck of cards is:
probability = number of favorable outcomes / total number of possible outcomes
Since we are certain to get a queen, the number of favorable outcomes is 4 (the number of queens in the deck), and the total number of possible outcomes is 49 (the number of cards selected from the deck).
Therefore, the probability of selecting a queen is:
probability = 4/49
This fraction cannot be simplified any further. Since the probability value is between 0 and 1 inclusive, we can express the indicated degree of likelihood as a probability value of approximately 0.0816.
2
MP Use Tools Cal orders 1 ton of gravel to use in 2 cactus beds.
If he uses the same amount in each bed, how much gravel does
he use in one bed? Write an equation to model the situation.
Then represent the problem on the number line.
According to the information, the equation that expresses this situation is x = 1/4 / 2
How to identify the equation that corresponds to this expression?To identify the equation that corresponds to this expression, we must take into account that the amount of gravel that he used in a single cactus is equal to x.
Additionally, we must take into account that x is equal to half of 1/4. Therefore, we must write the equation as follows:
x = 1/4 / 2If we want to know the result we can develop the operation as shown below:
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How much do we need to invest at 12% simple interest in order to have a total of $12,400 in 2 years?
Answer:
$10,000
Step-by-step explanation:
Let
Principal= x
Rate = 12%
Time = 2 years
Interest = (Final amount with interest placed on it) - Principal
Therefore,
Interest = 12,400 - x
Using
I = (P·r·t) / 100
Making P, subject of formula,
P = (100·I) / (R·T)
x = [100·(12,400 - x)] / (12.2)
x = (1,240,000 - 100x) / 24
Cross multiply,
24x = 1,240,000 -100x
24x + 100x = 1,240,000
124x = 1,240,000
x = 1,240,000 / 124
x = 10,000
Therefore, the principal, amount we need to invest is
$10,000
Please mark brainliest.
Thanks.
60 pounds of cat food in 5 bags
Answer:
12 lbs of food per bag
Step-by-step explanation:
To distribute cat food equally into a certain number of bags, we can divide the amount of cat food by the number of bags to get how much food should go in each bag.
60 lbs of food ÷ 5 bags = 12 lbs of food per bag
Use algebra to show that the product of any two terms in the sequence is also a term in the
sequence.
The product of any two terms in the sequence is also a term in the sequence has been proved.
What is a sequence?
A series is an ordered collection of numbers (or other things like geometric objects), and it typically has a particular structure or function. Sequences can be A series is an ordered collection of numbers (or other things like geometric objects), and it typically has a particular structure or function. Sequences can be either infinite or illimitable in length.either infinite or illimitable in length.
Suppose there is a sequence 3, 9, 27, 81.
Taking product of first two numbers, we get
3 × 9 = 27
We can see that the term 27 is present in the sequence.
This represents that in a sequence, the product of two numbers will be the term in the sequence.
Hence, the product of any two terms in the sequence is also a term in the sequence.
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[tex]P(x) = x^4 - x^3 - 11x^2 + 9x + 18[/tex]. Describe to the CEO what the graph looks like and, in general, how to sketch the graph without using technology. Use complete sentences, and focus on the end behaviours of the graph and where the company will break even (where P(x) = 0)
The graph of the function P(x) = x^4 - x^3 - 11x^2 + 9x + 18 rises on both ends and intersects the x-axis at x = -2, x = -1, and x = 3. The graph intersects the y-axis at the point (0, 18). The company will break even at the points where P(x) = 0, which are x = -2, x = -1, and x = 3.
How did we arrive at this assertion?The function P(x) = x^4 - x^3 - 11x^2 + 9x + 18 is a polynomial function of degree 4.
To sketch the graph of this function without using technology, we can start by analyzing the end behaviors of the function. As x approaches negative infinity, the leading term of the function, x^4, dominates and the function approaches positive infinity. As x approaches positive infinity, the leading term also dominates and the function again approaches positive infinity. This means that the graph will have a shape that rises on both ends.
Next, we can find the x-intercepts of the function, which are the values of x where P(x) = 0. We can use synthetic division or factorization to find that the function has three real roots: x = -2, x = -1, and x = 3. These values represent the points where the graph intersects the x-axis.
Finally, we can find the y-intercept of the function, which is the value of P(0). We can plug in x = 0 into the function to find that P(0) = 18. This means that the graph intersects the y-axis at the point (0, 18).
Putting all of this information together, we can sketch a rough graph of the function. The graph rises on both ends and intersects the x-axis at x = -2, x = -1, and x = 3. The graph intersects the y-axis at the point (0, 18). The function is positive between x = -2 and x = -1, and between x = 3 and positive infinity. The function is negative between x = -1 and x = 3.
To summarize, the graph of the function P(x) = x^4 - x^3 - 11x^2 + 9x + 18 rises on both ends and intersects the x-axis at x = -2, x = -1, and x = 3. The graph intersects the y-axis at the point (0, 18). The company will break even at the points where P(x) = 0, which are x = -2, x = -1, and x = 3.
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if you looked through a spectroscope and saw light with a wavelength of 450nm, what color would you see? How would its energy and frequency compare to red light?
I know I put it under the wrong subject but math is the most looked at and I know I'll get an answer faster
Answer:
The visible spectrum can be broken up into particular ranges of wavelengths; each corresponding to what we call colors: violet and indigo: 380 - 450 nm. blue and aqua: 450 - 500 nm. green: 500 - 570 nm.
Find the slope
y = -5x - 2
Answer: -5
Step-by-step explanation:
from slope-intercept form, y=mx + b, where b is (-2), and the slope/m is (-5).
hope this helps, and please respond if I'm wrong
M = -5
That’s the answer
Express the absolute value function f(x)=7|x| as a piecewise-defined function.
What function type does the graphed data points represent?
A)
Exponential
B)
Can't be determined
C)
Linear
D)
Quadratic
It sure looks like a linear function to me.
You can confirm this by finding the slope of "down 10/right 2" to give you a slope of -5.
Intelligence Quotient (IQ) scores are often reported to be normally distributed with μ=100.0
and σ=15.0
. A random sample of 41
people is taken.
Step 1 of 2 : What is the probability of a random person on the street having an IQ score of less than 98
? Round your answer to 4
decimal places, if necessary.
Answer:
Step-by-step explanation:
To solve this problem, we need to standardize the IQ score using the formula:
z = (x - μ) / σ
where x is the IQ score, μ is the mean IQ score, and σ is the standard deviation of IQ scores.
So, for x = 98, we have:
z = (98 - 100) / 15 = -0.1333
Using a standard normal distribution table or calculator, we can find that the probability of a standard normal variable being less than -0.1333 is approximately 0.4483.
Therefore, the probability of a random person on the street having an IQ score of less than 98 is 0.4483 (or 44.83% rounded to four decimal places).
 Using the graph of the function f, find the following
Here is the other questions that get cut off by the picture
On which intervals is the graph decreasing? A) The graph is decreasing on _ (type ur anseer in interval notation using pi as needed B) There is no interval on which the graph is decreasing
On which intervals is the graph constant? A) the graph is constant on _ (type your answer in interval notation, type an exact answer using pi as needed)
B) There is no interval on which the graph is constant
The function is: A)odd B) even
C) neither even nor odd
The intercepts are (0, 0), (-π, 0) and (π, 0)
The domain is (-∝, ∝)The range is [-2, 2]The graph is increasing on (-π/2, π/2)The graph is decreasing on (-π, -π/2] u [π/2, π)The function is oddHow to determine the key features of the graphThe intercepts
The intercepts of a graph are the points where the graph intersects the x-axis (horizontal axis) and the y-axis (vertical axis).
From the given graph, we have the intercepts to be
(0, 0), (-π, 0) and (π, 0)
The domain and the range
The domain of a graph refers to the set of all possible input values, while the range refers to the set of all possible output values.
Using the above definition as a guide, we have
Domain = (-∝, ∝)
Range = [-2, 2]
The increasing and the decreasing interval
From the graph, we can see that the y values decrease from x = -π till x = -π/2 and also decrease from x = π/2 till x = π
Also, it increase from -π/2 till π/2
These are the increasing and the decreasing intervals
The function type
Based on the appearance of the graph, the function is an odd function
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