Answer:Given a normal distribution with μ = 62 and σ = 4., calculate the 68-95-99.7 rule, or three-sigma rule, or empirical rule ranges
Calculate Range 1:
Range 1, or the 68% range, states that 68% of the normal distribution values lie within 1 standard deviation of the mean
68% of values are within μ ± σ
μ ± σ = 62 ± 4.
62 - 4. <= 68% of values <= 62 + 4.
58 <= 68% of values <= 66
Calculate Range 2:
Range 2, or the 95% range, states that 95% of the normal distribution values lie within 2 standard deviations of the mean
95% of values are within μ ± 2σ
μ ± 2σ = 62 ± 2(4.)
62 - 2 x 4. <= 95% of values <= 62 + 2 x 4.
62 - 8 <= 95% of values <= 62 + 8
54 <= 95% of values <= 70
Calculate Range 3:
Range 3, or the 99.7% range, states that 99.7% (virtually ALL) of the normal distribution values lie within 3 standard deviations of the mean
99.7% of values are within μ ± 3σ
μ ± 3σ = 62 ± 3(4.)
62 - 3 x 4. <= 99.7% of values <= 62 + 3 x 4.
62 - 12 <= 99.7% of values <= 62 + 12
50 <= 99.7% of values <= 74
Step-by-step explanation:
The probability that a data value is between 56 and 64 is,
= 64.7%
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Given that :
Mean (m) = 62
Standard deviation (s) = 4
Hence, Probability that a data value is between 56 and 64
P(56 < x < 64)
Using the relation :
(x - m) / s
P(x < 56) : (56 - 62) / 4
= - 1.5
P(Z < - 1.5) = 0.10565
( Z probability calculator)
P(x < 64) :
(64 - 62) / 4 = 0.75
P(Z < 0.75) = 0.77337 (Z probability calculator)
Hence, We get;
P(Z < 0.75) - P(Z < - 1.25)
0.77337 - 0.10565
= 0.64772
= 64.7%
Thus, the probability that a data value is between 56 and 64 is,
= 64.7%
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A computer technician charges $37.50 per hour plus a $70 service charge find the total charges if it takes to computer technician 5.5 hours to complete a task
Answer:
276.25
Step-by-step explanation:
37.50 x 5.5 = 206.25
206.25+ 70 = 276.25
Brainliest if correct
Answer:
-6
Step-by-step explanation:
Answer:
-6
Step-by-step explanation:
3(-2)(-1)(-1)= -6
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Garfield had $10 in the bank yesterday. Then, Garfield bought dinner for $14, but didn't realize that he overdrew from his bank. His account balance was negative now and he was in debt! What is the absolute value of his new account balance?
Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle C?
Enter your answer in the box.
___°
Answer:
m<C = 62°
Step-by-step explanation:
[tex]m[tex]m [tex]x+20+3x=180[/tex]
[tex]4x=160,[/tex] [tex]x=40[/tex]
[tex]m [tex]118+m [tex]m [tex]m
Compare.
5 /3
8 /5
A. >
B.<
C. =
Answer:
a
Step-by-step explanation:
5/3 is 1.6666667
8/5 is 1.6
therefore 5/3 > 8/5
If f(x) = x + 1 and g(x) = x^3, the function (fοg)(x) is:
Answer:
x³ + 1
Step-by-step explanation:
to evaluate (f ￮ g)(x) , substitute x = g(x) into f(x)
f(g(x) )
= f(x³)
= x³ + 1
Can someone help with this please
Step-by-step explanation:
[tex]y = \frac{4}{x} + \sqrt{x + 0.2} - 5x[/tex]
[tex]x = \frac{4}{5} [/tex]
[tex]y = \frac{4}{1} \div \frac{4}{5} + \sqrt{ \frac{4}{5} + 0.2} - 5 \times \frac{4}{5} [/tex]
[tex] \frac{4}{1} \times \frac{5}{4} + \sqrt{0.8 + 0.2} - 4[/tex]
[tex]5 + \sqrt{1} - 4[/tex]
[tex]5 + 1 - 4 \\ 6 - 4 = 2[/tex]
james has 202 cookie his friend wanted 132 cookies how much is the amount?
What is the length of this downhill track?
Answer: 10
Step-by-step explanation:
The terminal side contains the point (-5, 12). Find sin θ.
Question 4 options:
-.923
-.385
.923
.385
Answer:
sin theta = .923
Step-by-step explanation:
see image. An angle in standard position has one side glued to the x-axis, and the other side-the terminal side- rotating around the origin. When it gets to (-5, 12) in your problem, it stops there. 5, 12are the legs of a right triangle and they are recognizable as part of a pythagorean triple 5,12,13. So the hypotenuse is 13. Sin is OPP/HYP. So that is 12/13. Its in the 2nd quadrant, so it should be positive. We used the reference angle, bc the actual angle is the >90° angle from the positive x-axis to thru (-5,12). It calcs the same tho.
sin theta = 12/13
= 0.923
Answer:
(c) 0.923
Step-by-step explanation:
The coordinates of a point on the unit circle are (cos(θ), sin(θ)). That is, the y-coordinate of a point on the terminal ray will have the same sign as the sine of the angle. Here, the sign of the sine is positive, eliminating the first two answer choices.
We know that cos(θ) < sin(θ) for reference angles greater than 45°, where both values are √2/2 ≈ 0.707. Since 5 < 12, that means the angle of interest here will have a sine that is more than 0.707. Only one of the positive answer choices is in this range: sin(θ) ≈ 0.923.
_____
Additional comment
The value of sin(θ) is precisely ...
sin(θ) = y/√(x²+y²) = 12/√(25+144) = 12/13
sin(θ) = 0.923076...(6-digit repeat)
Solve these equations
1. 3x^2-16x-10=-15x
2. (3x - 7)(2x + 5) = 0
3. 2x + 5 - 3x = 4x + 17 + x
4. x^2 - 49 = 0
5. x^2 + 8x + 12 = 0
6. 0= (2x^2 - 3x + 5) - (x^2 + x + 37)
7. 12x^2 + 4x - 1
8. x^2 - 7x + 12
9. 6x^2 - 3x - 3
Answer: 1. x=2,-5/3
Step-by-step explanation:
what is [tex]\frac{1}{2} \sqrt{4}[/tex]
Answer:
square root of 4 is 2, 1/2 of 2 is 1
Step-by-step explanation:
Circle O and triangle OQR are shown below. What is the length of OQ?
48
64
O
48
80
R
112
64
Q
The required length of side OQ is given as 80 units, as of the given conditions.
What are Pythagorean triplets?In a right-angled triangle, its sides, such as hypotenuse, perpendicular, and base are Pythagorean triplets.
here,
From the figure,
Applying Pythagoras' theorem,
OQ² = OR² + RQ²
OQ = √[48² + 64²]
OQ = 80 units
Thus, the required length of side OQ is given as 80 units, as of the given conditions.
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A basket of the fruit contains 12 apples, 8 bananas, and 6 oranges. What is the ratio of bananas to apples? (Please simplify)
Answer:
2 : 3
Step-by-step explanation:
bananas to apples = 8 : 12
simplify by dividing both values by highest common factor of 4:
8 ÷ 4 : 12 ÷ 4 = 2 : 3
from the definition of absolute value, |3x|= when x>=0
Explanation:
When x is zero or larger, then |x| = x.
An example: |9| = 9
This applies to |3x| as well, so |3x| = 3x when [tex]x \ge 0[/tex]
Instructions: Use the graph to identify the vertex and then fill in the vertex form of the
quadratic function.
taking a peek at the picture, we can see that the U-turn or vertex occurs at the point (2 , -9), and we can also see that the graph passes through the point say (5 , 0).
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{vertex}{(2~~,~-9)}\qquad y=a(x-2)^2-9\qquad \qquad \textit{we know that} \begin{cases} x=5\\ y=0 \end{cases} \\\\\\ 0=a(5-2)^2-9\implies 9=9a\implies \cfrac{9}{9}=a\implies 1=a~\hfill \\\\\\ y=1(x-2)^2-9\implies \boxed{y=(x-2)^2-9}[/tex]
Mathieu grows specialty tomatoes that are much larger than typical tomatoes. The distribution of their weights is strongly skewed to the left with a mean of 232g and a standard deviation of 12g. Suppose we were to calculate the mean weight from a random sample of 16 of Mathieu's tomatoes. We can assume independence between tomatoes in the sample.
What is the probability that the mean weight from the sample of 16 tomatoes x is within 6g of the population mean?
Answer:
We cannot calculate this probability because the sampling distribution is not normal.
Step-by-step explanation:
Since the parent population is not normally distributed, the small sample size will result in a sampling distribution that isn't normal.
If point A, shown on the coordinate plane below, is reflected over both axes to create A’, what will be the coordinates of A’?
(-6, 3)
(-6, -3)
(6, -3)
(6, 3)
Answer:
(c) (6, -3)
Step-by-step explanation:
Reflection over both axes is the same as reflection across the origin, or rotation 180° about the origin. It has the effect of negating both coordinates:
(x, y) ⇒ (-x, -y) . . . . . reflection over both axes
The coordinates of A are (-6, 3), so the coordinates of A' will be ...
A(-6, 3) ⇒ A'(6, -3)
5.524(2 significant figures)
Answer:
5.524 in 2 significant figures rounding the value to 2 non zero numbers.
5.524 = 5.5 (2 significant figures)
Match the form with each linear Equation. Some matches will be used more than
once:
y - 6 = 10(2x - 1)
y = -9x + 7
y + 2 = 6(x-4)
y = 3x - 2
5x = 3y - 9
5x + 2y = 10 1) Standard Form. 2) Slope Intercept Form. 3) Point Slope Form. 4) None of the Forms.
Answer:
1) slope form
2) standard form
3)slope form
4)standard form
5) none of theese
6)point slope form
Step-by-step explanation:
Please help: Find an equation of a line that is tangent to the graph of f and parallel to the given line.
The equation of a line that is tangent to the graph of f and parallel to the given line is; y = 3x + 2 and y = 3x - 2
How to find the equation of a line in slope intercept formThe given equation of the line is 3x - y + 3 = 0
In slope intercept form, this can be rewritten as;
y = 3x + 3
Therefore, the slope of this line will be 3 since in y = mx + c, m is the slope. Thus, the slope of the parallel line will be 3
We will be looking for the value of x when the derivative of f(x) equals 3.
f(x) = x³ and so f'(x) = 3x²
Thus;
3x² = 3
x² = 3/3
x² = 1
x = 1 or -1
Thus;
y = 1³ or y =-1³
y = 1 or -1
Equation of tangent is;
y - 1 = 3(x - 1)
y - 1 = 3x - 3
y = 3x - 2
or y - (-1) = 3(x - (-1))
y + 1 = 3x + 3
y = 3x + 2
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If 200,000 is saved at simple interest of 5%per annum,calculate the total amount after 4years
Answer:
$240000
Step-by-step explanation:
[tex]p = 200000[/tex]
[tex]t = 4[/tex]
[tex]r = 5 \: percent\: per \: anum[/tex]
[tex]si = \frac{p \times r \times t}{100} [/tex]
[tex] = \frac{200000 \times 5 \times 4}{100} [/tex]
[tex] = 2000 \times 5 \times 4[/tex]
[tex] = 2000 \times 20[/tex]
[tex] = 40000[/tex]
[tex]amount = si + principle[/tex]
[tex] = 200000 + 40000 = 240000[/tex]
HOPE IT HELPS YOU #ITZADMIRERThe total amount after 4 years is $240,000
What is the total amount?Simple interest rate is the interest that is paid only on the principal portion of a the amount that is saved.
Total amount = principal + interest
Interest = principal x time x interest rate
200,000 x 0.05 x 4 = $40,000
Total amount = 200,000 + 40,000 = $240,000
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A bike with an original price of 90$ is discounted 40%. What is he sale price
Answer:
$54
Step-by-step explanation:
Original Price = $90
Discounted = 40%
Percent to decimal 40% = .40
$90 x .40=36 ( 36 is the Discount)
$90 - 36=54
Sale Price = $54
Hence, Sale Price = $54
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Awnser down below!
⬇ ⬇ ⬇
Answer:
1. 103
2. 156
3. 114
4. 115.14
5. 140
6. 123.8
7. 120.28
8. 107
Step-by-step explanation:
Answer:
hope it helps you :)) !
I’ll give you all the points I can give if you help me no links pls pls
Answer:
We cant see the writing it is too small
Step-by-step explanation:
Quadrilateral CAWT is the image of quadrilateral MOPS translated 7 units right and 5 units down. If you know the measure of ∠M, what other angle do you know the measure of?
∠C
∠A
∠W
∠T
i d k
Step-by-step explanation:
Option (A) will be the answer.
Rigid transformation: If the size and shape of a figure after transformation remains unchanged, transformation is called as rigid transformation.
(Example: Translation, Rotation and Reflection)
Given in the question,
Quadrilateral CAWT is the image of quadrilateral MOPS translated by 7 units right and 5 units down. Measure of ∠M is known.Since, image quadrilateral MOPS is formed by the translation of quadrilateral CAWT by 7 units right and 5 units down,
It's a rigid transformation having measures of all interior angles unchanged.
By the definition of rigid transformation → ∠M ≅ ∠C
Therefore, option (A) will be the answer.
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someone please help me
Answer:
a. 2/5; reduction
Step-by-step explanation:
It appears that C is the center of dilation, so C' and C are coincident. The scale factor is ...
P'C'/PC = 4/10 = 2/5 . . . scale factor
The scale factor is less than 1, so the dilation is a reduction in size.
Of students in the AP curriculum at a prep school, 40% take one AP exam, 45% take two AP exams, and the remaining 15% take 3 AP exams. The highly desirable score of 5 is hard to earn, and only 20% of these students will earn a 5 on any given exam they take. Assuming their results on each exam are independent, what is the probability a student in the AP curriculum will earn at least one 5
It should be noted that the probability that a student will earn at least one 5 will be 0.3152.
How to calculate the probabilityTest P(x). P(at least one 5)
1. 0.4. 0.2
2. 0.45. 0.36
3. 0.15. 0.488
Therefore, the probability that a student in the AP curriculum will earn at least one 5 will be:
= (0.4 × 0.2) + (0.45 × 0.36) + (0.15 × 0.488)
= 0.3152
In conclusion, the correct option is 0.3152.
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The terminal side of a 130° angle in standard position lies in the
quadrant.
Answer:
Second quadrant
Step-by-step explanation:
Quadrant I ranges from [tex]0^\circ<\theta<90^\circ[/tex]
Quadrant II ranges from [tex]90^\circ<\theta<180^\circ[/tex]
Quadrant III ranges from [tex]180^\circ<\theta<270^\circ[/tex]
Quadrant IV ranges from [tex]270^\circ<\theta<360^\circ[/tex]
What is the measure of angle UST?
A cannot be determined
B 72 degrees
C 30 degrees
D 150 degrees
Answer:
C 30 degrees
Step-by-step explanation:
Sum of interior angles of a triangle = 180°
⇒ ∠UST + 78 + 72 = 180
⇒ ∠UST = 180 - 78 - 72
⇒ ∠UST = 30°