Answer:
a) [tex]P(53<X<62)=P(\frac{53-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{62-\mu}{\sigma})=P(\frac{53-59}{3}<Z<\frac{62-59}{3})=P(-2<z<2)[/tex]
[tex]P(-2<z<2)=P(z<2)-P(z<-2)[/tex]
[tex]P(-2<z<2)=P(z<2)-P(z<-2)=0.97725-0.02275=0.9545[/tex]
b) [tex]a=59 +1.96*3=64.88[/tex]
And for the other limit we have:
[tex]a=59 -1.96*3=53.12[/tex]
And we will have 95% of the values between (53.12, 64.88)
Step-by-step explanation:
Part a
Let X the random variable of interest of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(59,3)[/tex]
Where [tex]\mu=59[/tex] and [tex]\sigma=3[/tex]
We are interested on this probability :
[tex]P(53<X<62)[/tex]
And we can solve this using the z score:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using the last formula we got:
[tex]P(53<X<62)=P(\frac{53-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{62-\mu}{\sigma})=P(\frac{53-59}{3}<Z<\frac{62-59}{3})=P(-2<z<2)[/tex]
And we can find this probability with this difference:
[tex]P(-2<z<2)=P(z<2)-P(z<-2)[/tex]
And uing the normal standard distribution or excel we got:
[tex]P(-2<z<2)=P(z<2)-P(z<-2)=0.97725-0.02275=0.9545[/tex]
Part b
For this part we want to find a value a, such that we satisfy this condition:
[tex]P(X>a)=0.025[/tex] (a)
[tex]P(X<a)=0.975[/tex] (b)
As we can see on the figure attached the z value that satisfy the condition with 0.95 of the area on the left and 0.05 of the area on the right it's z=1.96.
If we use condition (b) from previous we have this:
[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.975[/tex]
[tex]P(z<\frac{a-\mu}{\sigma})=0.975[/tex]
But we know which value of z satisfy the previous equation so then we can do this:
[tex]z=1.96<\frac{a-59}{3}[/tex]
And if we solve for a we got
[tex]a=59 +1.96*3=64.88[/tex]
And for the other limit we have:
[tex]a=59 -1.96*3=53.12[/tex]
And we will have 95% of the values between (53.12, 64.88)
In a normal distribution with mean 59 and standard deviation 3, approximately 81.85% of the data lie between 53 and 62. And about 95% of the data lie between 53 and 65, which is two standard deviations from the mean.
Explanation:In a normal distribution, about 68% of the data lie within one standard deviation of the mean, about 95% lie within two standard deviations, and about 99.7% within three standard deviations.
Part A:
The range from 53 to 62 in this case is from -2 standard deviations from the mean (56) to +1 standard deviation (62). Looking at the empirical rule, we find that about 34.13% of data fall between the mean and -1 standard deviation, and 13.59% fall between -1 and -2 standard deviations. Similarly, about 34.13% of the data fall between the mean and +1 standard deviation. Therefore, the total percentage of data lying between 53 and 62 would be
34.13% + 13.59% + 34.13% = 81.85%, so option B is the closest.
Part B:
About 95% of the data lie between two standard deviations from the mean. Therefore, you would add and subtract two times the standard deviation from the mean, which would yield 59 - 2(3) = 53 and 59 + 2(3) = 65. Thus, about 95% of the data lie between 53 and 65.
Learn more about Normal Distribution here:https://brainly.com/question/34741155
#SPJ12
Find the area of the shaded regions:
Answer:
41 Degrees
Step-by-step explanation:
So basically you add the 72 and the other 72 to get 148.You obviously know the angle in between 72 and 72 is a right angle or 90 degrees.Then you add 148 and 90 to get 238.Then 360 - 238 is 122.Now you know all the angles.So we have to ask ourselves what is 148/360 simplified.It is 37/90.Now that we know that and we know that the radius is 10.We have to find the regular area which is 10 times 10 which is 100.Finally we need to figure out what part of 100 is 37/90 and it is 41.111111111111.Rounded it is 41.
Simon is considering buying a home priced at $104,000. If the current market
is a seller's market, which of the following is most likely not the price Simon
will end up paying for the house?
A. 106,000
B. 109,000
C. 107,000
D. 103,000
Answer:
The answer is actually 103,000
Answer:103,000
Step-by-step explanation:
The steps in solving 5b-6=24 are
A. Add 6 to both sides and divide both sides by 5
B. Add 6 to both sides and multiply both sides by 5
C. Subtract 6 from both sides then multiply both sides by 5
D. Subtract 6 from both sides then divide both sides by 5
I need the answer
Answer:
the answer is A.
Step-by-step explanation:
5b-6=24
add 6 to both sides
5b=30
divide 5 to both sides
b=6
hope this helps
(mark as brainliest)
The steps in solving 5b-6=24 are adding 6 to both sides and dividing both sides by 5, the value of b is 6.
What is the linear equation?The standard form or the general form of linear equations in one variable is written as, Ax + B = 0; where A and B are real numbers, and x is the single variable.
The given equation is;
5b-6=24
The steps are used to solve the problem given below.
Add 6 to both sides
5b-6=24
5b - 6+6 = 24 +6
5b =30
Divide both sides by 5
5b/5 = 30/5
b= 6
Hence, the steps in solving 5b-6=24 are adding 6 to both sides and dividing both sides by 5, the value of b is 6.
Learn more about linear equations here;
https://brainly.com/question/11897796
#SPJ2
Please help me with this :(
Answer:
One less than 25, 24, times five is 120, and that is 4 times as much as 30 so you already know it is wrong.
Step-by-step explanation:
A circle with a radius of 8 centimeters. Use the diagram to complete each statement. Use 3.14 for π, when necessary. The radius of the circle is cm. The circumference of the circle is about cm. The area of the circle is about cm2.
Answer: 200.96 cm area
Step-by-step explanation:
Area=3.14(r^2)
Area=3.14(64)
Area=200.96
Answer:
8
50.24
200.96
Step-by-step explanation:
A bag contains 140 marbles, some white some blue. The ratio of white marbles to blue ones is 5:2. How many blue marbles are there?
Answer:
40
Step-by-step explanation:
5 + 2 = 7
140 div by 7 = 20
2 times 20 = 40
Last night the temperature in New York City went down t 4 degrees F. In Antarctica, the temperature went down to -20 degrees F. What is the difference between the two temperatures?
Answer:
The answer is -16
Step-by-step explanation:
Find the sum. Enter your answer in lowest terms in the box below as a
fraction, using the slash mark ( 7 ) for the fraction bar.
7/20
3/9
Answer here
Answer:
41/60
Step-by-step explanation:
7
20
+
3
9
Cancel the common factor of
3
and
9
.
Tap for more steps...
7
20
+
1
3
To write
7
20
as a fraction with a common denominator, multiply by
3
3
.
7
20
⋅
3
3
+
1
3
To write
1
3
as a fraction with a common denominator, multiply by
20
20
.
7
20
⋅
3
3
+
1
3
⋅
20
20
Write each expression with a common denominator of
60
, by multiplying each by an appropriate factor of
1
.
Tap for more steps...
7
⋅
3
60
+
20
60
Combine the numerators over the common denominator.
7
⋅
3
+
20
60
Simplify the numerator.
Tap for more steps...
41
60
The result can be shown in multiple forms.
Exact Form:
41
60
Decimal Form:
0.68
¯
3
Work out the perimiter of a semi circle with radius of 3
Give your answer in term of pi
Answer:
15.425 cm is it without terms of pie
Step-by-step explanation:
you need to put it into terms of pie
Answer:
3pi + 6 units.
Step-by-step explanation:
The perimeter = the diameter + curved part.
Radius = 3 so the diameter = 2*3 = 6.
Length of the curved part = 1/2 * circumference of the circle = 1/2 * pi * diameter.
Perimeter = 6 + 1/2 pi * 6
= 3pi + 6 units.
3(c+5) = 12
so what does c= ?
Answer: 4
Step-by-step explanation:
12 - 5 = 7,
7 - 3 = 4.
The answer to this is 4.
Which of the following theorems verifies that DEF - XZY?
Answer:
AA
Step-by-step explanation:
The question is about the congruency of two triangles DEF and XZY. A Congruence Theorem (SSS, SAS, ASA, or AAS) would demonstrate their congruence, but without specific measurements, we can't identify which theorem applies.
Explanation:The subject area of this question is Geometry, more specifically, the concepts concerning triangles. The given notation, DEF - XZY, suggests that the student wants to establish the congruency between the two triangles DEF and XZY.
Based on the information provided, the student is likely referring to a Congruence Theorem, which is one of the primary methods to determine if two given triangles are congruent. The main Congruence Theorems are: SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), and AAS (Angle-Angle-Side).
Without any additional specification, it's impossible to definitively say which theorem supports DEF - XZY. The student would need to provide specific measurements related to the triangles DEF and XZY, such as the lengths of the sides or the measures of the angles, to determine which Congruence Theorem applies.
Learn more about Congruence Theorem here:https://brainly.com/question/34422889
#SPJ2
The most popular pizza at Pizza Parlor is a large pizza with a 12- inch radius. which of the following best represents the circumference of this pizza?
Answer:
75.3982236862
Step-by-step explanation:
Answer:
I believe the answer is 75.36
2x^2-19x+9=0 quadratic formula or zero product property. Which ever is easier?
Answer:
9
Step-by-step explanation:
x=9
What does it mean for an equation to be a radical equation?
Answer:
In mathematics, a radical expression is defined as any expression containing a radical (√) symbol. Many people mistakenly call this a 'square root' symbol, and many times it is used to determine the square root of a number. However, it can also be used to describe a cube root, a fourth root, or higher.
Step-by-step explanation:
Based on the data set shown, which of the following is a true statement?
-1, -1, 0, 1, 1, 1, 1, 2, 2, 2, 3
mean = mode
mean < median
mode < median
Answer:
mean = mode
Step-by-step explanation:
To make this easier, let's find the mean, median, and mode.
Mean: Sum of a set of numbers divided by number of terms
Median: Middle number of data when data is in numerical order
Mode: Number that occurs most often in data
To find the mean, add all the values together. -1 - 1 + 0 + 1 + 1 + 1 + 1 + 2 + 2 + 2 + 3 = 11. Now, divide by the number of terms, which is 11. 11/11 = 1. The mean is 1.
To find the median, look at the number in the middle of the data. -1, -1, 0, 1, 1, 1, 1, 2, 2, 2, 3. The median is 1.
To find the mode, look at the number that occurs most often. There are 4 1's, so the mode is 1.
Since all numbers are equal, the only possible answer is the first option.
The mean, median, and mode are all equal; thus, a.) mean = mode is true.
Sum of all values: (-1) + (-1) + 0 + 1 + 1 + 1 + 1 + 2 + 2 + 2 + 3 = 11
Number of values: 11
Mean = Total sum / Number of values = 11 / 11 = 1
Arrange the values in ascending order: -1, -1, 0, 1, 1, 1, 1, 2, 2, 2, 3
The middle value (6th value) is 1
Median = 1
The value that appears most frequently is 1 (occurs 4 times)
Mode = 1
Comparing these values:
Mean = 1
Median = 1
Mode = 1
Select the correct answer.
Which relation does not represent a function?
A. {(3, 0), (0, 3)}
B. {(6, -2), (5, -2)}
C. {(3, 4), (3, 5)}
D. {(5, 5), (-5, -5)}
E. {(1, -2), (-2, 1)}
Relation C: {(3,4), (3,5)} does not represent a function because it has the same first component with different outputs.
Explanation:In Mathematics, a relation is defined as a set of ordered pairs. A relation is considered as a function if for each input (x value), there is exactly one output (y value). In other words, no two distinct ordered pairs in the function have the same first component. Looking at the options given:
A. {(3, 0), (0, 3)}B. {(6, -2), (5, -2)}C. {(3, 4), (3, 5)}D. {(5, 5), (-5, -5)}E. {(1, -2), (-2, 1)}The relation C. {(3,4), (3,5)} does not represent a function because there are two distinct ordered pairs with the same first component (or x-value) which is 3, but with two different y-values which are 4 and 5. Therefore, this relation violates the definition of a function.
Learn more about Function here:https://brainly.com/question/35114770
#SPJ2
Final answer:
The relation that does not represent a function is Option C: {(3, 4), (3, 5)} because the number 3 in the domain is paired with two different values in the range, contradicting the definition of a function.
Explanation:
The relation that does not represent a function is Option C: {(3, 4), (3, 5)}. This is because a function is defined as a set of ordered pairs where each element of the domain (the first value in each pair) must correspond to exactly one element in the range (the second value in each pair). Option C depicts the number 3 in the domain being paired with both 4 and 5 in the range, which violates this rule. Therefore, Option C does not satisfy the definition of a function.
Option A, B, D, and E each show that every element of the domain is matched with only one unique value in the range, indicating they are all functions.
The product of 2 and the sqrt of 3 and 3 and the sqrt of 12 in simplified form is _______? (your supposed to answer the stupid question yourself. your meant to simplify 2 and the sqrt of 3 and 3 and the sqrt of 12 to get your answer so don't report it for being incomplete)
Answer:
[tex](2 \sqrt{3} )(3 \sqrt{12}) = 6 \sqrt{36} = 6(6) = 36[/tex]
The diagram below shows a 20-foot ladder leaning against a wall. The bottom of the ladder is 10 feet from the
base of the wall.
20 ft.
Wall
2-
101. -
Based on the dimensions in the diagram, what is the value of x?
The value of ∠x is 30⁰. Option B is correct.
How to determine the ratio value of ∠x in the figure.
From the given figure,
The triangle formed by ladder is right angled triangle
∠x⁰ is opposite to the horizontal distance between the foot of the and the point where the ladder touches the ground.
The ladder form the hypotenuse of the triangle.
Therefore,
sinθ = opposite/hypotenuse
θ is the angle opposite to distance between the wall foot and the ladder.
θ = x⁰
opposite = 10 ft
hypotenuse = 20 ft
so,
Sin(x) = 10/20
sin(x) = 1/2
find the sine inverse of (0.5)
x = sin⁻¹(0.5)
x = 30⁰
The value of ∠x is 30⁰. Option B is correct.
The first side of a triangle measures 5 in. less than the second side, the third side is 3 in, more than the first side, and the
perimeter is 17 in. How long is the third side?
If s represents the length of the second side, which of the following represents the length of the third side?
A. s - 5
B. s-2
C. s+3
Final answer:
The third side of the triangle is determined by the expression 's - 2 inches', where s represents the length of the second side of the triangle.
Explanation:
To find the length of the third side of the triangle, we can first define the lengths of the other two sides in terms of s, the length of the second side. The first side is s - 5 inches, according to the problem statement. Since the third side is 3 inches more than the first side, its length would be (s - 5) + 3, which simplifies to s - 2 inches.
Now, knowing that the perimeter of the triangle is 17 inches, we can set up an equation to include all three sides: s + (s - 5) + (s - 2) = 17 inches. Solving this equation for s will give us the length of the second side and consequently the length of the third side using s - 2 inches.
PLEASE ANSWER QUICKLY!
Frank is 6 inches taller than his young brother, Pete. Pete's height is p . Write an algebraic expression to represent Frank's height.
Answer:
P + 6
Step-by-step explanation:
plzzz help I need help with this question will give you brainliest!!!!!
Zero softballs with a diameter of 3.8 inches will fit into the container as length of the container is less the diameter of the softball.
Zero softballs can fit in length and zero softballs will fit in width.
Why-
Length of the square base in rectangular pyramid = s
Breadth of the square base in rectangular pyramid = s
Height of the square base in rectangular pyramid, l = 11 inches
Volume of the square base in rectangular pyramid, V=
Volume of the cuboid = l × b × w
V= s × s × l
s = 3 inches
Softballs with a diameter of 3.8 inches.
20 BRAINLY POINTS!!!!!!!!!!!!!!!
Answer:
is A , D , C
maybe b not sure
You have $90 in your bank account. Each week you plan to deposit $8 from your allowance and $15 from your paycheck. The equation bequals90plus(15plus8)w gives the amount b in your account after w weeks. How many weeks from now will you have $200 in your bank account?
Plz plzplzplzplz help me plz
Answer:
ok
Step-by-step explanation:
Which table represents a function?
Answer:
first one
Step-by-step explanation:
same x value can't have more than one y value
Emery bought 3 cans of beans that had a total weight of 2.4 pounds. If each can of beans weighed the same amount, which model correctly illustrates the relationship? Check all that apply
Answer:
Figure 2 and 3
Step-by-step explanation:
This question is incomplete, please find the figures in the attachment.
Number of cans of beans bought by Emery = 3
Total weight of cans = 2.4 pounds
weight of each can = [tex]\frac{2.4}{3}[/tex] = 0.8 pounds
If x be the number of cans and y represents the total weight then the model for this situation will be
y = 0.8x
Figure 1 :
From this graph weight of each can = [tex]\frac{20}{16}=1.25[/tex] pounds
so this graph is not the correct choice.
Figure 2:
From this graph weight of each can = [tex]\frac{8}{10}[/tex] = 0.8 pounds
So this graph is the correct choice.
Figure 3 :
From the given table, weight of each can = [tex]\frac{4}{5}=0.8[/tex] pounds
So the table shows the relationship.
Figure 4 :
From the given table, weight of each can = [tex]\frac{5}{4}[/tex] = 1.25 pounds
so this table is not the correct choice.
Therefore, figure 2 and 3 is illustrate the relationship.
Answer:
if you do not want to read the thing above me the answer is 2 and 3
Step-by-step explanation:
What number completes the sequence below? Enter your answer in the input
box at the bottom
35 ——- 7
50 ——- 10
65—— 13
80—— ?
Answer:
The answer is 5
Step-by-step explanation:
if you see, the start of table starts at 35 and then goes goes to 7
Answer:
Step-by-step explanation:
It’s 16
Please help! i couldnt copy and paste it into here so i decided to just screenshot it :)
The diameter of a circle measures 17 mm. What is the measure of its radius ?
Answer:
the radius is 8.5 mm
Which rays form the sides of WXY?
ロロロロロロ
D. XW
E. Ws
Answer:
XY and XW
Step-by-step explanation: