Write 30% as 30100Since, finding the fraction of a number is same as multiplying the fraction with the number, we have
30100 of 84 = 30100 × 84Therefore, the answer is 25.2
If you are using a calculator, simply enter 30÷100×84 which will give you 25.2 as the answer.
The probability that a student studied is 0.85. The probability that a student will not pass, given that the student studied is 0.10.
a) Find the probability that a student will study and will pass.
b) Suppose that the probability that a student will either study or pass is 0.8. Find the probability that a student will pass.
a) The probability that a student will study and will pass is 0.765.
b) The probability that a student will pass is 0.715.
What is probability?
Simply put, probability is the likelihood that something will occur. When how an event will turn out is not known, one can discuss the likelihood of several outcomes.
Define some events -
A: A student studies.
B: A student will pass.
Given that P(A)=0.85 and
P(B|A)=1-P([tex]\bar{B}[/tex]|A)
=1-0.10
=0.90
a) P(a student will study and will Pass)= P(A∩B)
= P(A)·P(B|A)
= 0.85×0.90
= 0.765
b) Given that P( student will either study or pass), the probability is -
=P(A∪B)= 0.8 then P(a student will pass)
=P(B)
It is known that P(A∪B)= P(A)+P(B)-P(A∩B)
Then P(B)=P(A∪B) -P(A) +P(A∩B)
=0.8-0.85 + 0.765
=0.715
Therefore, the probabilities are 0.765 and 0.715.
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The 44 members of the glee club are trying to raise at least $6,000 so they can compete in the state championship. They already have $1,220. What inequality can you enter to find the amount each member must raise, on average, to meet the goal?
The inequality that represents the situation is
The inequality that represents the situation is 45x + 1240 ≥ 6000
There are 45 members overall.
If one individual contributes $x, then
The sum that 45 individuals together raised is then equal to 45x.
$6000 is the bare minimum necessary to enter the competition.
$1240 is the amount they already have.
Therefore, the amount they need to raise is $6000 minus $1240.
Inequality can be displayed as:
45x ≥ 6000 - 1240
This demonstrates that the total amount raised by 45 individuals (45x) should be equal to or more than the sum they need to raise ($6,000 - $1240).
change the equation's order;
45x + 1240 ≥ 6000
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Animal House Rescue is holding a fundraiser raffle. They sell 2,980 tickets for $1 each for a prize telescope valued at $425. What is the expected gain or loss to a participant purchasing ten tickets?
Answer:
Gain: $415
Loss: $10
Step-by-step explanation:
money earned - money spent = gain/loss
The gain is when the participant wins the telescope:
telescope = $425 ==> money earned
10 tickets * $1 = $10 for tickets ==> money spent
$425 - $10 = $415
Loss is when the participant doesn't get the telescope:
$0 ==> money earned (No money earned)
10 tickets * $1 = $10 for tickets ==> money spent
$0 - $10 = -$10 gained
-$10 gained ==> $10 lost
In the figure below, N is between M and O, and O is between N and P. If NO=6, NP=8, and MP=16, find MO.
P
A line segment is merely a portion of a line, one with definite ends and a finite length.
What is a line?A line segment is merely a portion of a line, one with definite ends and a finite length. An object with only one dimension, a line has length but no width. A line is made up of several points that are endlessly stretched in the opposing directions. In a two-dimensional plane, it is specified by two points. Collinear points are described as two points that are on the same line.
An endlessly long, two-directional line is referred to as a line. It just has one, and that is length. Collinear points are those that are situated along the same path. Two points make up a line, which is written as follows with an arrowhead: AB.
O is between M and P, and N is the midpoint of MO. IF NO=3 and MP = 10, find OP.
Given the following details as:
N is between M and O.
O is between N and P .
NO=6 and NP = 8.
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URGENT!!
Which of the following lists is in order from least to greatest?
Answer:
It's B, -2, v/5 4, and 3².
30PTS 30PTS don’t explain just answer.
Answer:
y = 90°
Step-by-step explanation:
What’s the slope of the line going though the points (12,0) and (12,9)
Answer:
infinity/undefined (both are acceptable)
Undefined is actually the best answer in college but your answer key might put it as infinity.
Step-by-step explanation:
Observe that the x coordinates of the two points are exactly the same at 12.
This reduces the possibility of the line being a horizontal or a vertical line.
Imagine, if x coordinates is always the same, it means that you are only varying y and that happens when you move up and down the graph.
Hence, the line is a straight vertical line. (Line equation: x = 12)
Gradient/Slope of a vertical line = infinity/undefined.
The slope of the given line is Undefined
The slope of the line when two points in the line is given is given by
m=(y₂-y₁)/(x₂-x₁)
The points are (12,0) and (12,9)
m=(9-0)/(12-12)
= 9/0
=Undefined
The slope of the line is Undefined
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Julius is allowed to surf the internet for only 3 hours a week. He has already been online for 1 2/3 hours this week. Write and solve an inequality to find how much more time Julius can spend online this week.
The number of hours that Julius can spend online this week is 1 1/3 hours.
How to illustrate the inequality?Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.
Since Julius is allowed to surf the internet for only 3 hours a week. He has already been online for 1 2/3 hours this week.
This will be Illustrated as x.
x + 1 2/3 ≤ 3.
x ≤ 3 - 1 2/3
x ≤ 1 1/3.
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Can you help me with this
The graph of the given equation y=2x+1 is attached below.
How to find the function which was used to make graph?There are many tools we can use to find the information of the relation which was used to form the graph.
A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it.
For example, when the graph of a function is rising upwards after a certain value of x, then the function must be having increasingly output for inputs greater than that value of x.
If we know that the function crosses x axis at some point, then for some polynomial functions, we have those as roots of the polynomial.
The equation y=2x+1 gives the following information:
The slope is 2
The line intercepts is 1 on the y axis
First, we would put a point or a dot on (0,1) on the y axis. Then start making 2 points above and below my original point. IT would do this by using the slope 2/1.
By using my slope we know that (1,3) and (-1,-1).
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Approximately 297 million guests visit the 400 American amusement parks annually, and take 1.7 billion safe rides. The National Safety Council publishes a report titled "Fixed-Site Amusement Ride Injury Survey" for the International Association of Amusement Parks and Attractions. The number of injuries per million patron-rides, X, has a Poisson distribution with parameter 0.8. In one million patron-rides, what is the probability that there are
a) No injuries?
b). More than TWO injuries?
The probabilities are given as follows:
a) No injuries: 0.4493 = 44.93%.
b) More than two injuries: 0.0474 = 4.74%.
What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following equation:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
x is the number of successes that we want to find the probability of.e = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval or range of values of the input parameter.The mean for this problem is of:
[tex]\mu = 0.8[/tex]
The probability of no injuries is of P(X = 0), hence:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-0.8}(0.8)^{0}}{(0)!} = 0.4493[/tex]
The probability of more than two injuries is of:
P(X > 2) = 1 - P(X <= 2)
In which:
P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2)
Hence:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-0.8}(0.8)^{0}}{(0)!} = 0.4493[/tex]
[tex]P(X = 1) = \frac{e^{-0.8}(0.8)^{1}}{(1)!} = 0.3595[/tex]
[tex]P(X = 2) = \frac{e^{-0.8}(0.8)^{2}}{(2)!} = 0.1438[/tex]
Then:
P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.4493 + 0.3595 + 0.1438 = 0.9526.P(X > 2) = 1 - P(X <= 2) = 1 - 0.9526 = 0.0474.More can be learned about the Poisson distribution at https://brainly.com/question/7879375
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You have 3 3/4 cups of nuts to divide evenly among 5 people. How many cups of nuts will each person get
Each will get 3/5 cups of nuts by ratio and proportion concepts.
What does ratio explain mean?A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a bowl of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).
We have to divide total nuts within 5 people.
so,
3 3/5 : 5
but first convert,
3 3/5 = 15/4
substitute,
15/4 : 5 = 15/20cups of nuts
simplify,
3/5 cups
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Solve the simultaneous equations
xy=-16
y=x+8
Answer:
x = 4, y = 12
Step-by-step explanation:
xy = -16
y = x + 8
substitute y = x + 8 into xy = -16
x(x + 8) = -16
x^2 +8x + 16 = 0
x = 4
sub x = 4 into y = x + 8
y = 4 + 8
y = 12
73. Angle of elevation: In 2001, the tallest building in the world was the Petronas Tower
in Kuala Lumpur, Malaysia. For a person standing 25.9 ft from the base of the tower.
the angle of elevation to the top of the tower is 89°. How tall is the Petronas tower?
Analo
The Petronas tower is 1483.811 feet tall.
What is tangent function?One of the six fundamental functions in trigonometry is the tangent function. As stated, Tan A = Opposite Side/Adjacent Side is the Tangent Formula. Tangent may be modeled using sine and cosine as follows: Tan A = Sin A / Cos A.
Given:
Angle of elevation: In 2001, the tallest building in the world was the Petronas Tower in Kuala Lumpur, Malaysia.
For a person standing 25.9 ft from the base of the tower.
The angle of elevation to the top of the tower is 89°.
Let c = height of the tower,
and a = distance from the base of the tower to x.
a = 25.9 feet.
The formula:
Tangent (angle) = opposite side / adjacent side.
tan89° = c / a
57.29 = c / 25.9
c = 57.29 x 25.9
c = 1483.811 feet
Therefore, 1483.811 feet is the height of the Petronas tower.
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He starts by running 3 miles during every training session. Each week he plans to increase the distance of his run by 1/4 mile
The arithmetic expression may be used to get the formula T = (11 + w)/4, which is the distance Kane runs in a training session after w weeks.
Every training session, Kane begins out by running 3 miles, and he has a plan to improve that distance by 1/4 mile each week.
The number of weeks is w.
The arithmetic progression may be used to calculate an expression that displays the distance Kane runs during a training session after w weeks.
T = A + (n-1)d is the formula for the nth term in an arithmetic operation, where an is the first term, which is 3, d is the difference between two consecutive terms, which is, is the last term, and n is the total number of terms.
We get, T = (11+w)/4
This is the expression to show the distance Kane runs in a training session after w weeks.
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Complete question - Kane is training for a marathon. He starts by running 3 miles during every training session each week plans to increase the distance of his runs by 1/4 mile. Let w be the number of weeks. Write and expression to show the distance Kane runs in a training session after w weeks
Solve x=[tex]\sqrt{x} b^2-4ac\frac{x}{y} 2a[/tex]
The solutions to the quadratic function y = x² + 4x + 3, using the quadratic formula, are given as follows:
x = -1 and x = -3.
How to solve a quadratic function?The standard definition of a quadratic function is given as follows:
y = ax² + bx + c.
In which the leading coefficient a must assume a value different of zero.
The solutions to the quadratic function ax² + bx + c = 0 are obtained using the quadratic formula, as follows:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
The quadratic function for this problem is defined as follows:
x² + 4x + 3 = 0.
Hence the coefficients are:
a = 1, b = 4, c = 3.
The first solution is:
[tex]x = \frac{-4 - \sqrt{4^2 - 4(1)(3)}}{2} = -3[/tex]
The second solution is:
[tex]x = \frac{-4 + \sqrt{4^2 - 4(1)(3)}}{2} = -1[/tex]
Missing InformationThis problem was incomplete, hence the quadratic formula is used to solve y = x² + 4x + 3, as an example.
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Interest earned- $25
principal- $500
interest rate -???
time- 2 years
what is the interest rate
The interest rate is 2.5 %.
Simple interest is the form of interest used for short term loans, such as one receives at pawnshops or from loan sharks. It is governed by the formula:
I = Prt
where I is the amount of interest, P is the principal (amount of money borrowed), r is the interest rate (per year), and t is the time (expressed in years).
Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.
I = $25, P = $500, r = ?, t = 2 years
∴ I = Prt
∴ r = I / Pt
∴ r = 25 / ( 500 * 2)
∴ r = 25 / 1000
∴ r = 0.025
∴ r = 0.025 * 100 %
∴ r = 2.5 %
Therefore, the interest rate is 2.5 %.
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11. One side of a kite is 2 cm less than 2 times the length of another. If the perimeter is 38 cm, find the length of each side of the kite. (show work)
Answer:
Step-by-step explanation:
good
Given that,
Perimeter of kite - 38 cm
Let "x" be the one side of kite
Both of the top sides are equal
Therefore, other side = x
One side of a kite is 2 cm less than 2 times the length of another
Therefore,
One of bottom side = 2x - 2
Bottom sides are also equal
Thus, other bottom side = 2x - 5
We know that,
Perimeter = sum of all sides
38 = x + x + 2x - 2 + 2x - 2
38 = 6x - 4
6x = 38 + 4
6x = 42
x = [tex]\frac{42}{6}[/tex]
x = 7
Thus length of each side of kite is:
x = 7
2x - 2 = 2(7) - 2 = 14 - 2 = 12
Thus length of each side of kite is 7 cm , 7 cm , 12cm , 12cm
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A family buy a new minivan for $45,000 and makes a down payment of $12,000. The monthly payment factor is 0.202764. Calculate the monthly payment
The family's monthly payment for their new minivan is $6,664.52
How to calculate the monthly payment?To calculate the monthly payment, we first need to find the total amount that the family is financing by subtracting the down payment from the total cost of the minivan: $45,000 - $12,000 = $33,000.
Then, we can use the monthly payment factor to calculate the monthly payment. The formula to do this is:
Monthly Payment = Financed Amount * Monthly Payment Factor
So in this case:
Monthly Payment = $33,000 * 0.202764 = $6,664.52
Therefore, the family's monthly payment for their new minivan is $6,664.52
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HELP !!!
write days in May and days in a year as a ratio
The ratio of days in May and days in a year is 31 to 365 or 31:365
What is the ratio?It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
We need to find the days in May and days in a year as a ratio
Therefore, Days in may = 31
Days in a year = 365
Thus, the expected ratio = 31/365
Or
31:365
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Ava bought 6 packages of tulip bulbs and 12 bags of daffodil bulbs for a total of $198. Grace spent $254 buying 14 packages of tulip bulbs and 12 bags of daffodil bulbs. Use elimination to solve the system of linear equations and determine how much one package of tulips bulbs costs, x, and how much one bag of daffodil bulbs costs, y. Enter your answer as an ordered pair (x,y).
When Ava purchased six packages of tulip bulbs and twelve bags of daffodil bulbs, the price per tulip bulb was $7 and the price each daffodil bulb was $13.
what is linear equations ?The algebraic equation y=mx+b is known as a linear equation. M serves as the y-intercept, and B serves as the slope. The previous clause has two variables, y and x, and is sometimes referred to as a "linear equation with two variables". Bivariate linear equations are those with two independent variables. The following are a few examples of system of equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation takes the form y=mx+b, with m denoting the slope and b denoting the y-intercept, it is referred to as being linear. The term "linear" refers to an equation having the form y=mx+b, where m stands for the slope and b for the y-intercept.
given
Let x be the price of a single tulip bag.
Y should equal the price of one bag of daffodil bulbs.
Grace = 14x + 12y = 254
ava = 6x + 12y = 198
- 8x = - 56
x = - 56/-8
x = 7.
Equation 1 becomes
6* 7 + 12y = 198
42 + 12y = 198 when x = 7 is substituted.
12y = 198 - 42
12y = 156
y = 156/12
y = 13
When Ava purchased six packages of tulip bulbs and twelve bags of daffodil bulbs, the price per tulip bulb was $7 and the price each daffodil bulb was $13.
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a) What type of triangle is triangle ABC? b) Give reasons for your answer. I need the correct answer for B with Reasons Not "ab and ac are the same" any word other than the same
Answer:
Isosceles triangle
Step-by-step explanation:
Thorough explanation: Through the angles in the triangle ABC.
First, observe that angle ACD = 50 degrees (given)
Since lines AB and DE are parallel to each other,
angle BAC = angle ACD = 50 degrees (by the property of alternate angles)
It is also given that angle ABC = 80 degrees.
Since ABC is a triangle, the sum of the three angles must add up to 180 degrees.
Angle BAC + Angle ABC + Angle ACB = 180 degrees
50 + 80 + Angle ACB = 180
Angle ACB = 180 - 50 - 80
= 50 degrees
Since two of the angles, angles ACB and BAC are the same at 50 degrees, triangle ABC is an isosceles triangle. (With sides AB and BC equal)
What type of data collection might be best to study how voters might decide an upcoming ballot issue
Observational data collection might be best to study how voters might decide an upcoming ballot issue.
What kinds of information is observed?The majority of big data is observational data, such as bank transaction records, user viewing patterns on video streaming services, or social media posts. Observational data, however, can also be sparse data (based on just a few people).
The observational study method is what?In observational research, participants and phenomena are observed in their most natural environments. Instead of using structured environments like research labs or focus groups, this allows researchers to observe how their subjects make decisions and respond to situations in their everyday lives.
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Vanessa will sell yogurt for $2.50 a cup. Fill in the table to show how much money Vanessa will make if she sells 19 cups of vanilla yogurt.
Answer:
2.50 × 19 = 47.5
Therefore, she would get $47.5 if she sold 19 cups.
sqrt{2x-1}-x=-8
solve for x
The values of x are 5 or 13.
What are equations?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given is an equation, [tex]\sqrt{2x-1}[/tex] - x = -8
[tex]\sqrt{2x-1}[/tex] - x = -8
[tex]\sqrt{2x-1}[/tex] = -8+x
Squaring both sides,
2x-1 = x²+64-16x
x²-16x-2x+1+64 = 0
x²-18x+65 = 0
Factorizing the equation,
x²-18x+65 = 0
x²-13x-5x+65 = 0
x(x-13)-5(x-13) = 0
(x-5)(x-13) = 0
x = 5 or 13
Hence, the values of x are 5 or 13.
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Solve for 2 |v+2|-41=-9
If there is more than one solution, separate them with commas. If there is no solution, click on "No solution"
Answer:
[tex]v=-18,14[/tex]
Step-by-step explanation:
[tex]2|v+2|-41=-9\\2|v+2|=32\\|v+2|=16\\\\v+2=16\\v=14\\\\v+2=-16\\v=-18[/tex]
in a right triangle, the two sides adjacent to the right angle are known as the
Answer:legs
Step-by-step explanation: I cannot give a explanation since it is simply math, anything adjacent to a right angle is called a leg.
Answer: the legs? or opposite and hypotenuse.
Step-by-step explanation:
Which of the following lists of ordered pairs is a function?
Answer:
C is a function
Step-by-step explanation:
for a relation to be a function each value of x must map to exactly one unique value of y
A
2 → 5 and 2 → 2 ← not a function
B
- 1 → 6 and - 1 → 7 ← not a function
C
all values of x map to exactly one unique y ← function
D
3 → 1 and 3 → 2 ← not a function
Graph the system on equation . Y-2x+5=0 and y+ 4x-1=0
The graph of the system of equations y - 2x + 5 = 0 and y + 4x + 1 = 0 intersect at (0.667, - 3.667)
What is a graph?The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.
These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.
Given, A system of equations y - 2x + 5 = 0 and y + 4x + 1 = 0.
Let's write the terms in the order x, y therefore,
y - 2x + 5 = 0
- 2x + y = - 5.
2x - y = 5.
And
y + 4x + 1 = 0.
4x + y = - 1.
The graph of the system of equations is attached in the image.
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What is the value of a if 2 is a zero of the polynomial 4x² 2x 5a?
The value of a is [tex]-\frac{12}{5}[/tex] if 2 is a zero of the polynomial [tex]$4 x^2-2 x+5 a$[/tex].
As per the given data, the polynomial is p(x) = [tex]$4 x^2-2 x+5 a$[/tex]
The polynomial is zero polynomial if x is 2
The places where a polynomial becomes zero overall are known as the zeros of the polynomial. The term "zero polynomial" refers to a polynomial with a value of zero (0).
Replace x with 2 we get
Therefore [tex]4(2)^2-2(2)+5 \mathrm{a}=0[/tex]
[tex]\Rightarrow[/tex] 4 (4) - 2 (2)+5 (a) = 0
[tex]& \Rightarrow[/tex] 16 - 4 + 5 (a) = 0
[tex]& \Rightarrow[/tex] 12 + 5 (a) = 0
Add -12 on both sides we get
12 + 5 (a) - 12 = 0 - 12
5 (a) = -12
Divided by 5 into both sides we get
a = [tex]-\frac{12}{5}[/tex]
Therefore the value of a is [tex]-\frac{12}{5}[/tex]
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There were 9 pieces of paper. Some of them were cut into 3 pieces. As a result, there
are now 15 pieces of paper. How many pieces of paper were cut?
6=3
6÷3
2 is the required answer for this question