The probability that a student's mark is more than 75 is 0.0947 and in a class of 50 students, 5 students should have a mark of more than 75.
In the given question,
The Mathematics marks of all the students in the class are normally distributed with mean mark 54 and standard deviation 16.
We have to find the probability that a student's mark is more than 75.
In a class of 50 students, we also have to find how many students should have a mark of more than 75.
From the question the mean = 54
Standard Deviation = 16
So the probability that a student's mark is more than 75.
Using the normal distribution
z = (x−mean)/Standard Deviation
P(x>75) = P(z>(x−mean)/Standard Deviation)
P(x>75) = 1−P(z<(75−54)/16)
Simplifying
P(x>75) = 1−P(z<21/16)
P(x>75) = 1−P(z<1.3125)
From the standard z table value
P(x>75) = 1−0.9053
P(x>75) = 0.0947
Hence, the probability that a student's mark is more than 75 is 0.0947.
Now finding in a class of 50 students, how many students should have a mark of more than 75.
Total student = 50
So the student having mark of more than 75 = Total student * probability that a student's mark is more than 75
The student having mark of more than 75 = 50 * 0.0947
The student having mark of more than 75 = 4.735
The student having mark of more than 75 ≈ 5
Hence, in a class of 50 students, 5 students should have a mark of more than 75.
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A rectangular box is 12 in. x 14 in. x 18 in. What is the surface area of the largest size sphere that could fit in this box? Leave your answer in
terms of pi.
The surface area of the largest sphere that could fit into the rectangular box of dimensions 12 in x 14 in x 18 in is 324π inches²
The surface area of sphere = 324π inches²
What is a Sphere?
A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center. It has surface area and volume based on its radius. It does not have any faces, corners or edges.
The Surface Area of a Sphere = 4πr²
The Volume of a Sphere = ( 4/3 ) πr³
where r is the radius of the sphere
Given data ,
Let the surface area of the Sphere be = S
Let the dimensions of the rectangular box be L x W x H
12 inches x 14 inches x 18 inches
Now , for the surface area of the sphere to have the largest surface area , the radius should be maximum
From the rectangular box , we can see that the height of the rectangle is best suited as the diameter of the sphere
So , Height of the Box = Diameter of the Sphere
And , Radius of the sphere = Height of the Box / 2
= 18 / 2
Radius of the sphere = 9 inches
Now ,
Surface Area of a Sphere = 4πr²
r = 9 inches
Substituting the values in the equation , we get
Surface Area of a Sphere S = 4 x π x ( 9 )²
= 4 x π x 81
= 324π inches²
Therefore , the value of S is 324π inches²
Hence , The surface area of sphere = 324π inches²
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This is just a question but. if I had a power of ten that was let's say.... 10 3 would i write it like 10000 or 1000?
Answer:
10^3 = 1000
Step-by-step explanation:
10 * 10 * 10 = 1000
Answer:
1000
Step-by-step explanation:
it is ten to the third power so 10*10*10 and then you get the answer of:
1000
I hope this helped!
Give the answer and an explanation
A triangle is said to be right angle if one of the angles is 90 degrees, the value of the side x for the given right angle triangle is 50.51.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° .
The given right-angle triangle has the following sides,
AC = Base
BC = Perpendicular
AB = Hyp.
By tan function,
Since,tanθ = Perp/Base
tan29° = 28/x
x = 50.51
Hence, "A triangle is said to be right angle if one of the angles is 90 degrees, the value of the side x for the given right angle triangle is 50.51".
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NO LINKS!! Please help me with these graphs Part 2a
Answer:
Left graph.
Domain: all real numbers.
Range: y ≤ 4
Middle graph.
Domain: all real numbers
Range: y ≥ 3
Right graph.
Domain: x ≥ -2
Range: y ≥ -3
Answer:
1. Domain: (-∞, ∞) Range: (-∞, 4]
2. Domain: (-∞, ∞) Range: [3, ∞)
3. Domain: [-2, ∞) Range: [-3, ∞)
Step-by-step explanation:
Definitions
Domain: The set of all possible input values (x-values).Range: The set of all possible output values (y-values).Open circle: The value is not included in the interval.Closed circle: The value is included in the interval.Arrow: The function continues indefinitely in that direction.Note: Assume that each square on the given graphs is 1 unit.
Question 1As there are arrows at both endpoints of the curve, the domain of the function is unrestricted.
Domain: (-∞, ∞)The curve has a maximum point at (2, 4) and continues indefinitely towards negative infinity at both endpoints.
Therefore, the range of the function is restricted.
Range: (-∞, 4]Question 2As there are arrows at both endpoints of the function, the domain is unrestricted.
Domain: (-∞, ∞)The function has a minimum point at y = 3.
When x > -2, the line continues indefinitely at y = 3.
When x < -2, the line continues indefinitely towards infinity.
Therefore, the range of the function is restricted.
Range: [3, ∞)Question 3The domain of the function is restricted since there is a closed circle at one endpoint: (-2, -3). When x > -2, the line continues indefinitely towards infinity.
Domain: [-2, ∞)The function has a minimum point at (-2, -3). As x continues towards infinity, so does y.
Therefore, the range of the function is restricted.
Range: [-3, ∞)HELP WILL GIVE BRAINLYEST!!!!!!! 30 POONTS Which of the following is the fourth vertex needed to create a rectangle with vertices located at (−4, −25), (−4, −12), and (−7, −12)?
(−12, 7)
(−7, −25)
(−7, 12)
(−25, 7)
Answer: I believe the answer is (-7, 12)
Step-by-step explanation:
Answer:
-7,12
Step-by-step explanation:
Ethan repairs household appliances like dishwashers and refrigerators. For each visit, he charges 25 plus 22 per hour of work. A linear equation that expresses the total amount of money Ethan earns per visit is y=25+22x .
The independent variable x is the hour of work.
The dependent variable y is the total money Ethan earn per visit.
The y-intercept is 25.
The slope is 22.
Ethan charges a one time fee of 25 dollars. For each visit Ethan earns 22 dollars for each hour of work.
How to solve linear equations?Ethan repairs household appliances like dishwashers and refrigerators. For each visit, he charges 25 plus 22 per hour of work.
A linear equation that expresses the total amount of money Ethan earns per visit is y = 25 + 22x.
Using slope intercept equation,
y = mx + b
where
m = slopeb = y-intercepty = 25 + 22x
The independent variable x is the hour of work.
The dependent variable y is the total money Ethan earn per visit.
The y-intercept is the value of y when x = 0. Therefore, the y-intercept is 25.
The slope is the change in the dependent variable with respect to the change in the independent variable. The slope is 22.
Ethan charges a one time fee of 25 dollars. For each visit Ethan earns 22 dollars for each hour of work.
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What is the asymptote of the exponential function graph below?
y=1
y=5
y=2
y=0
Answer: y=5 is the asymptote answer
Parallel lines l, m, and n are shown. If line l is mapped to line m and line m is mapped to line n, what is true for the transformation that took place?
Line m was translated down 4 units.
Line m was translated up 4 units.
Line n was translated up 8 units.
Line l was translated down 8 units.
Line l was translated down 8 units, is true for the transformation that took place.
What is transformation?A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.
Given that, parallel lines l, m, and n are shown. If line l is mapped to line m and line m is mapped to line n,
We can see line is the original line is l which is first mapped into line m then into line n, so, we can say line is mapped to n.
Hence, Line l was translated down 8 units, is true for the transformation that took place.
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If f(x) is an exponential function where f(-3) = 11 and ƒ(4) = 55, then find the
value of f(-1), to the nearest hundredth.
The value of the exponential function (-1) will be equal to f(-1) = -0.02.
What is an exponential function?The mathematical expression f(x)=exp or e^x denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to complex numbers or adapted to other mathematical objects.
Given that f(x) is an exponential function where f(-3) = 11 and ƒ(4) = 55. The value of the exponential function will be calculated as,
[tex]y=ax^b[/tex]
[tex]11=a(-3)^b\\55=a(4)^b[/tex]
Calculate the value of constants,
log5 = blog(4 / 3)
b = 0.7 / 0.125
b = 5.6
The value of 'a' will be,
11 = a(-3)⁵°⁶
a = -0.02
The exponential function f(-1) will be calculated as,
f(-1) = -0.02(-1)⁵°⁶
f(-1) = -0.02
Therefore, the value of the exponential function (-1) will be equal to f(-1) = -0.02.
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Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
The equation have the same solution as 2.3p – 10.1 = 6.49p – 4 and 230p – 1010 = 650p – 400 – p
How to determine the equations that have the same solution?Given: 2.3p – 10.1 = 6.5p – 4 – 0.01p.
Using this given property, let's write the equation
We can subtract like terms (6.5p– 0.01p = 6.49p) to get:
2.3p – 10.1 = 6.5p – 0.01p – 4
2.3p – 10.1 = 6.49p – 4
Also, we can multiply both sides of the algebraic equation by 100:
(2.3p – 10.1) x 100 = (6.5p – 4 – 0.01p) x 100
230p – 1010 = 650p – 400 – p
Therefore, the equations have the same solution as 2.3p – 10.1 = 6.49p – 4 and 230p – 1010 = 650p – 400 – p. The 2nd and 3rd options are the answers
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Lee Holmes deposited $17,000 in a new savings account at 9% interest compounded semiannually. At the beginning of year 4, Lee deposits an additional $42,000 at 9% interest compounded semiannually.
At the end of 6 years, what is the balance in Lee’s account? (Use the Table provided.)
The balance in Lee's account at the end of 6 years is $384,830.53.
What is the balance?The first step is to determine the future value of the initial amount deposited in the savings account.
The formula for calculating future value:
FV = P (1 + r)^nm
Where:
FV = Future value P = Present value R = interest rate = 9% / 2 = 4.50%m = number of compoundingN = number of yearsBalance at the end of 3 years: $17,000 x (1.045)^(3 x2) = $22,138.42
The total value of the account after $42,000 is deposited is:
$42,000 + $22,138.42 = $64,138.42
The future value of $64,138.42 at the end of 6 years is:
Balance at the end of 6 years: $64,138.42 x (1.045)^(3 x2) = $384,830.53
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Find the rate if a principal of $1,100 earned $1,089 interest in 12 years.
Answer:
8.25
Step-by-step explanation:
Gotta answer this quick this is timed please
Answer:
Step 1:subtract 5 from both sides
step 2: divide both sides by two
final answer: c= p-5/2
Answer:
Step 1: Subtract 5 from both sides.
Step 2: Divide 2 from both sides.
Final answer: C= p-5 / 2
Step-by-step explanation:
ERROR ANALYSIS Describe and correct the error in finding m<1
Answer:
m∠1 = 26°
Step-by-step explanation:
Interior angles of a triangle sum to 180°, not 360°.
Therefore, the correct calculations to find the measure of angle 1 are:
[tex]\boxed{\begin{aligned}115^{\circ}+39^{\circ}+m \angle 1 &=180^{\circ}\\\\154^{\circ}+m \angle1 & = 180^{\circ}\\\\m \angle1 & = 26^{\circ}\end{aligned}}[/tex]
Please help ASAP
See Attached!!
When you add polynomials of different degrees, it is not adding up the degrees, in special cases this may end up with smaller degree polynomials.
When you multiply polynomials of different degrees, it adds up the degrees, and the final polynomial is off the higher degree.
The answers:
a) False, degrees not added,b) False, degrees added but not multiplied.bag has 5 red beads 3 Blue, 4 green random probability a single picked bead is blue
Answer:
1/4
Step-by-step explanation:
add all of them to get the sum which is 12. Since he asked for the blue which are 3. You put the 3/total which is 3/12. Then simplify. Which is equal to 1/4
PLEASE HELP!!!
Dianelys accepted a new job at a company with a contract guaranteeing annual raises. In the first year, Dianelys' salary will be $40000, and she will get a raise of $2500 every year. Make a table of values and then write an equation for S,S, in terms of n,n, representing Dianelys' salary after working nn years for the company.
Number of Years at the Company Dianelys' Salary (Dollars)
00 40000\hspace{3px}\color{green}{\checkmark}40000
11 42500\hspace{3px}\color{green}{\checkmark}42500✓42500
22 45000\hspace{3px}\color{green}{\checkmark}45000✓45000
33 47500\hspace{3px}\color{green}{\checkmark}47500✓
1. The table of values for Dianely's salary can be represented for 4 years as follows:
Year Salary
1 $40,000
2 $42,500
3 $45,000
4 $47,500
2. The equation that models Dianely's salary after n years is S = 40,000 + 2,500n.
What is an equation?An equation is a mathematical statement stating that two mathematical expressions are equivalent or equal.
For instance, given the number of years, one can claim that Dianely's salary will be a given amount based on the above equation.
Equations involve variables, numbers, and the use of the equation sign (=) with some mathematical operands.
Initial salary = $40,000
Salary raise per year = $2,500
Disney's salary after n years in equation form, S = 40,000 + 2,500n.
Table of Values for Dianely's Salary:
Year Salary
1 $40,000
2 $42,500 (40,000 + 2,500)
3 $45,000 (42,500 + 2,500)
4 $47,500 (45,000 + 2,500)
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What is 9.65+0.4, 16.058- 1.2
Answer:
Step-by-step explanation:
9.65+0.4=10.05
16.058-1.2=14.858
Help pls I need a fraction answer
7 4/10 + 2/10 =
Answer: 7 4/10 + 2/10 = 38/5 = 7 3/5 = 7.6
Answer Overall : 38/5
Step-by-step explanation: Conversion a mixed number 7 4/10 to a improper fraction: 7 4/10 = 7 4/10 = 7 · 10 + 4/10= 70 + 4/10= 74/10
To find a new numerator:
a) Multiply the whole number 7 by the denominator 10. Whole number 7 equally 7 * 10/10 = 70/10
b) Add the answer from previous step 70 to the numerator 4. New numerator is 70 + 4 = 74
c) Write a previous answer (new numerator 74) over the denominator 10.
Seven and four tenths is seventy-four tenths
Add: 74/10 + 2/10 = 74 + 2/10 = 76/10 = 2 · 38/2 · 5 = 38/5
The common denominator you can calculate as the least common multiple of both denominators - LCM(10, 10) = 10. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 10 × 10 = 100. In the following intermediate step, cancel by a common factor of 2 gives 38/5.
In other words - seventy-four tenths plus two tenths is thirty-eight fifths.
First convert the mixed number to a fraction by multiplying 7 by 10 and adding 4
74/10+2/10add them together but DONT add the denominators
76/10These numbers can be simplified by 2 so the final answer is:
38/5please answer 25 points
The number of miles (m) between the two cities as represented in the equation given 2[(4m * 3.5) / 400] = 171.5 is 2450 miles
EquationsThe definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an ‘equal’ sign. The most basic and simple algebraic equations consist of one or more variables in math.
In the equation given;
2[(4m * 3.5) / 400] = 171.5
Using changing the subject of formula to find the miles travelled;
2[(4m * 3.5) / 400] = 171.5
28m / 400 = 171.5
28m = 400 * 171.5
28m = 68600
m = 68600 / 28
m = 2450
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The expression 43πr3 represents the volume of a sphere, with radius r. Why is this expression a monomial?
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
It is the product of a number, represented by Response area, and a variable with a whole number exponent, represented by Response area.
Question 2
What is the degree of the monomial?
The degree is
.
Degree of a polynomial is the highest power that its terms contain which is 3 in the given monomial.
What is a polynomial?They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.
WE have been given an expression as 43πr³ represents the volume of a sphere, with radius r.
Terms can be added or subtracted to make a polynomial. They are composed of variables and constants all in multiplication.
So we know that if there is one term, then the polynomial will be called monomial.
Therefore, this expression is a monomial which have inly one term as 43πr³ .
Degree of a polynomial is the highest power that its terms contain which is 3 in the given monomial.
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A house was valued at $254,000. Over several years, the value increased by 16%, giving the house a new value.
Answer:
289560
Step-by-step explanation:
If WX equals to XY , what is the length of WZ?
Answer:
the length of WZ is 10
Step-by-step explanation:
What is the expression 9-z when z=8
Laura and Kirk are comparing how much they have been running. Laura has already
run 36 miles and Kirk has run 64. Laura begins running 21 miles per week and Kirk runs 17 miles
per week. How many additional weeks, w, will it take for their total distance run to be equal?
The additional weeks, w, will it take for their total distance run to be equal is 7 weeks.
How to calculate the number of weeks?From the information, Laura has already
run 36 miles and begins running 21 miles per week. This will be 36 + 21w.
Kirk has run 64 miles and runs 17 miles per week. This will be 64 + 17w
where w = number of weeks
This will be equated as:
36 + 21w = 64 + 17w
Collect like terms
21w - 17w = 64 - 36
4w = 28
Divide
w = 28/4
w = 7
It'll take 7 weeks.
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Suppose that the number of cars manufactured at an automobile plant varies jointly as the number of workers and the time they work. If 160 workers can produce 32 cars in 2 hours, find the number of workers that can produce 66 cars in 3 hours.
If 160 workers can produce 32 cars in 2 hours, The number of workers that can produce 66 cars in 3 hours is 220 .
How to find the number of workers?Using this formula
W = kC/H
160 = k(32 )/2= 17k
k = 160 /16
Hence,
W = (160 /16)C/H
W = (160 /16) (66/3)
W= 220 workers
Therefore we can conclude that 220 workers can produce the cars in 3 hours.
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1.25x10^-3/1.25x10^3
By solving the given fraction equation we get the answer is 1.
What is an exponent?
Exponent is the process of expressing large numbers in terms of powers. In other words, the exponent describes how many times a number has been multiplied by itself.
According to the zero exponent rule, any base with a zero exponent is equal to one. For instance, [tex]x^{0} = 1[/tex].
We have,
[tex]= \frac{1.25\\ * \\ 10^{-3}}{1.25 \\ * \\ 10^{-3}}[/tex]
[tex]= \frac{1.25\\ * \\ 10^{-3}}{1.25 \\} * 10^{3}[/tex]
Using the multiplication rule of fraction [tex]a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}[/tex]
[tex]= \frac{1.25 \ * \ 10^{-3} \ * \ 10^{3}}{1.25 \\}[/tex]
= [tex]= 10^{-3} * 10^{3}[/tex]
By applying the exponent rule [tex]\:a^b\cdot \:a^c=a^{b+c}[/tex] we get,
Add or subtract the numbers = 3 + 3 = 0
[tex]= 10^{0}[/tex]
By applying the rule [tex]a^{0} = 1[/tex], [tex]a \neq e^{0}[/tex]
= 1
Hence, by solving the above fraction equation we get the answer is 1.
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i need some help on these, can anybody help me?
A restaurant manager recorded the number of people in different age groups who attended their food festival. They created the following histogram:
Histogram with title Food Festival Participants, horizontal axis labeled Age Group (year) with bins 0 to 19, 20 to 39, 40 to 59, and 60 to 79, and vertical axis labeled Number of People with values from 0 to 60 at intervals of 10. The first bin goes to 20, the second goes to 40, the third goes to 60, and the last goes to 50.
What percentage of the participants are ages 40 to 59? Round to the nearest whole percent.
20%
35%
60%
100%
According to the histogram, the percentage of participants aged 40 to 59, who attended the restaurant's food festival, is 35%.
What is a histogram?A histogram approximately represents a distribution of grouped data with numerical values.
A histogram uses rectangular bars to show the frequency of data items in successive numerical intervals of equal sizes.
Age Group (year) Number of People
0 to 19 20
20 to 39 40
40 to 59 60
60 to 79 50
Total 170
Percentage of ages 40 to 59 = 60/170 x 100 = 35.29%
Thus, using the histogram, we can assure the restaurant manager that 35% of the festival participants are between 40 and 59 years old.
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Mr.Marx has been in the journalism industry for 24 years. She has worked at her current job 8 of those years. What fraction of her career has she been at her current job? What is this fraction as a decimal?
Fraction of her career has she been at her current job is 1/3 or 0.333.
Given:
Mr.Marx has been in the journalism industry for 24 years.
She has worked at her current job 8 of those years.
Fraction = number of year in current job/number of years in journalism industry.
= 8 years/24 years
= 8/24
= 1/3 ≈ 0.333.
Therefore fraction of her career has she been at her current job is 1/3 or 0.333.
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