87.5% of those who passed the first test also passed the second test.
The given statement in the question is an example of conditional probability rather than supplementary probability. Therefore, the statement is false.
We are given the following information:
- 70% of the class passed both tests.
- 80% of the class passed the first test.
We want to find the percentage of those who passed the first test and also passed the second test.
To do this, we will use the concept of conditional probability.
Let A be the event of passing the first test, and B be the event of passing the second test.
We are asked to find the conditional probability P(B|A), which is the probability of passing the second test given that the student has passed the first test.
Using the formula for conditional probability, we have:
P(B|A) = P(A ∩ B) / P(A)
We know that P(A ∩ B) = 0.7 (since 70% of the class passed both tests) and P(A) = 0.8 (since 80% of the class passed the first test).
Now, we can calculate P(B|A):
P(B|A) = 0.7 / 0.8 = 0.875.
For similar question on conditional probability.
https://brainly.com/question/10739947
#SPJ11
a) Close the following accounts. 9
K. Emmanuel
$
2020
$
640
360
2020
800
Feb. 10 Bank Cash
25
200
Feb. 1 15
Sales Sales
J. Amaze
$
$
2020
2020
260 1090
1350
Mar. 12
Returns inwards
Mar4
Sales
18
Bank
Z. Ventour
2020
$
2020
$
May 13
Cash
518
May 10
Purchases
518
FSampath
2020
$
2020
July 14 22
Returns outwards
Bank
$
220
July 3
Purchases Purchases
8
25
Bank
800
1500
830
350
Answer:
I dont know the answer I dont know what it is I just needed points bye
Step-by-step explanation:
if my circular garden requires 2 cups of water per 10 square feet, how many cups of water do i need when the radius is 3 feet
Please see the attached
the cost of a luna bar is 2 dollars at harmons. what is the cost of 30 luna bars
Answer:
60
Step-by-step explanation:
2$ times 30 luna bars at harmons is $60
wing Lines Parallel
Solve for x to make A||B.
B
3x
A
X = = [?]
7x
Enter
If line A is parallel to line B then the value of x is 18.
Given that a line A is parallel to line B
We have to find the value of x
3x+7x=180
Combine the like terms
10x=180
Divide both sides by 10
value x=18
To learn more on Coordinate Geometry click:
brainly.com/question/27326241
#SPJ1
use synthetic division
PLEASE HELP!!
The quotient using a synthetic method of division is 8x² + 15x + 7/8 and the remainder is 71/64
How to evaluate the quotient using a synthetic methodThe quotient expression is given as
(8x³ + 14x² - 2x + 1) divided by x - 1/8
Using a synthetic method of quotient, we have the following set up
1/8 | 8 14 -2 1
|__________
Bring down the first coefficient, which is 8:
1/8 | 8 14 -2 1
|__________
8
Multiply 8 by 1/8 to get 1, and write it below the next coefficient and repeat the process
1/8 | 8 14 -2 1
|_____1_15/8__7/64_
8 15 7/8 71/64
So, the quotient is 8x² + 15x + 7/8 and the remainder is 71/64
Read more about synthetic method at
brainly.com/question/13820891
#SPJ1
HELP ME PLEASEEEE The matrix below represents a system of equations.
Which matrix represents the solution to this system of equations?
The matrix that represents the solution to this system of equations is
1 0 0 2
0 1 0 -4
0 0 1 3
Therefore option B is correct.
What is a matrix in mathematics?A matrix is described as a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.
We solve a matrix by Arranging the elements of equations in matrices and find the coefficient matrix, variable matrix, and constant matrix.
We then go ahead to write the equations in AX = B form.
we then take the inverse of A by finding the adjoint and determinant of A. Multiply the inverse of A to matrix B, thereby finding the value of variable matrix X.
Learn more about matrix at:
https://brainly.com/question/94574
#SPJ1
18. The volumes of two similar solids are 857.5 mm^3 and 540 mm^3. The surface area of the smaller solid is 108 mm^2. What is the surface area of the larger solid?
Answer:
64.14
Step-by-step explanation:
Reading the passage I see that you have to multiply then divide
The surface area of the larger solid is, 171.7 mm²
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
The volumes of two similar solids are 857.5 mm³ and 540 mm³.
And, The surface area of the smaller solid is 108 mm².l
Now, Let us assume that;
The surface area of the larger solid is, x
Hence, We get;
857.5 / x = 540 / 108
Solve for x as;
857.5 x 108 = 540 x
92,718 = 540x
x = 171.7 mm²
Thus, The surface area of the larger solid is, 171.7 mm²
Learn more about the proportion visit:
https://brainly.com/question/1496357
#SPJ2
HELP ASAP!!!
(Appropriate Measures MC)
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
10, 10, 10, 10, 15,15,15,19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55
A graph titled Donations to Charity in Dollars. The x-axis is labeled 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Frequency. There is a shaded bar up to 8 above 10 to 19, up to 6 above 20 to 29, up to 2 above 30 to 39, and up to 2 above 50 to 59. There is no shaded bar above 40 to 49.
Which measure of variability should the charity use to accurately represent the data? Explain your answer.
The IQR of 10 is the most accurate to use, since the data is skewed.
The range of 10 is the most accurate to use, since the data is skewed.
The IQR of 45 is the most accurate to use to show that they need more money.
The range of 45 is the most accurate to use to show that they have plenty of money.
A measure of variability which the charity should use to accurately represent the data include the following: D. The range of 45 is the most accurate to use to show that they have plenty of money.
What is a box-and-whisker plot?In Mathematics and Statistics, a box plot is a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.
Based on the information provided about the data set, the five-number summary for the given data set include the following:
Minimum (Min) = 10.
First quartile (Q₁) = 13.75.
Median (Med) = 20.
Third quartile (Q₃) = 26.25.
Maximum (Max) = 55.
For the IQR, we have:
IQR = Third quartile (Q₃) - First quartile (Q₁)
IQR = 26.25 - 13.75
IQR = 12.50
For the range, we have;
Range = maximum - minimum
Range = 55 - 10
Range = 45.
Read more on range here: https://brainly.com/question/31352873
#SPJ1
Question is done below. Just multiple sqrts inside of each other.
The solution to the prompt of multiple square roots is 5.
How to solve for the sum of the multiple square rootsTo obtain the sum of the multiple square roots, we need to first find the square of 30, sum it up in four places and find the square root of the last figure we obtained.
So this gives
√30 =5.47
5.47 + 5.47 + 5.47 + 5.47
= 21.88
=4.67 approximately 5
So. option 5 is the solution.
Learn more about square roots here:
https://brainly.com/question/428672
#SPJ1
36 is 15% of what number
Which statement concerning the equation x² - 1 = x is true?
1. Its discriminant is 0, so it has no solution.
2. Its discriminant is 5, so it has two real solutions.
3. Its discriminant is 0, so it has one real solution.
4. Its discriminant is -3, so it has two complex solutions.
Answer:
The equation x² - 1 = x can be rewritten as x² - x - 1 = 0. We can use the quadratic formula to find the solutions:
x = (-b ± sqrt(b² - 4ac)) / 2a
In this case, a = 1, b = -1, and c = -1. So:
x = (1 ± sqrt(1 - 4(1)(-1))) / 2(1)
x = (1 ± sqrt(5)) / 2
Therefore, the equation has two real solutions, and the discriminant is positive. The answer is 2. Its discriminant is 5, so it has two real solutions.
Please help !!!!!!!!!
Find m/_U. Write your answer as an integer or as a decimal rounded to the nearest tenth.
The measure of angle U = 41.83 degree.
In the given right angle triangle
VW = 6
UV = 9
Since sinΘ = (opposite side)/(hypotenuse)
Therefore,
sin U = VW/UV
= 6/9
= 0.667
Take inverse of sin both sides
∠U = arcsin(0.667)
= 41.83
Hence ∠U = 41.83 degree
To learn more about triangle visit:
brainly.com/question/1058720
#SPJ1
Justin mowed 45% of her garden in 18 minutes.how many minutes will it take him to mow all of his garden at this rate? Explain
If Justin mowed 45% of her garden in 18 minutes, then we can set up a proportion to find how long it would take him to mow 100% of the garden:
45/100 = 18/x
where "x" is the unknown number of minutes it would take to mow 100% of the garden.
To solve for "x," we can use cross-multiplication:
45x = 100 * 18
Simplifying the right-hand side:
45x = 1800
Dividing both sides by 45:
x = 40
Therefore, it would take Justin 40 minutes to mow all of his garden at the same rate of 45% in 18 minutes.
To explain this, we used the fact that the amount of work done (mowing a certain percentage of the garden) is directly proportional to the time it takes to do that work. This means that if Justin mowed 45% of the garden in 18 minutes, he would take proportionally longer to mow the entire garden. The proportion we set up allows us to find the unknown amount of time it would take to mow the entire garden. Solving the proportion, we found that it would take Justin 40 minutes to mow all of his garden at the same rate he mowed the 45%.
Enter the endpoints as ordered pairs (x, y).
Provide your answer below:
The endpoints of the latus rectum are and
(y + 3)² = (x - 2)
The endpoints of the latus rectum of the parabola are (3, -2) and (3, -4)
Given data ,
Let the equation of the parabola be (y + 3)² = (x - 2)
Now , y² + 6y + 9 = x - 2
y² + 6y = x - 11
Now we can see that the vertex of the parabola is (2, -3), and the axis of symmetry is parallel to the y-axis. This means that the focus and directrix will also be parallel to the y-axis.
x = h - p
where (h, k) is the vertex and "p" is the distance between the vertex and the focus. In this case, (h, k) = (2, -3) and p = 1, so
x = 2 - 1
x = 1
Therefore, the equation of the directrix is x = 1
And , the axis of symmetry of the parabola is parallel to the y-axis, the latus rectum will be parallel to the directrix, and its endpoints will be equidistant from the focus and the directrix
The distance between the focus and the directrix is 1 unit, so the distance between the endpoints of the latus rectum will also be 1 unit
Therefore, the endpoints of the latus rectum will be at the points where the perpendiculars drawn from the focus to the directrix intersect the parabola
To find the points of intersection between this line and the parabola, we can substitute x = 3 into the equation of the parabola and solve for y
(y + 3)² = (x - 2)
(y + 3)² = (3 - 2)
(y + 3)² = 1
y + 3 = ±1
y = -2 or y = -4
Hence , the points of intersection between the perpendicular and the parabola are (3, -2) and (3, -4)
To learn more about parabola click :
https://brainly.com/question/24042022
#SPJ1
The height y(in feet) of a ball thrown by a child isy=−114x2+2x+3
where x is the horizontal distance in feet from the point at which the ball is thrown.
(a) How high is the ball when it leaves the child's hand? (Hint: Find y
when x=0)
Your answer is y=____
(b) What is the maximum height of the ball? _____
(c) How far from the child does the ball strike the ground?_____
In a coordinate plane, what is the distance between the points (6,−10)
and (6,−7)
?
The distance between the points (6,−10) and (6,−7) is 3 units
What is the distance between the points (6,−10) and (6,−7)?From the question, we have the following parameters that can be used in our computation:
Points (6,−10) and (6,−7)
Because the points have the same x coordinate, the distance between the points (6,−10) and (6,−7) is the difference between the y coordinates
Using the above as a guide, we have the following:
Distance = -7 - -10
Evaluate
Distance = 3
Hence, the distance between the points (6,−10) and (6,−7) is 3 units
Read more about distance at
https://brainly.com/question/28551043
#SPJ1
which fraction is greater than the fraction by the model if the fraction is 3/8
The calculated value of the fraction that is greater than the fraction by the model is 1/2
Which fraction is greater than the fraction by the modelFrom the question, we have the following parameters that can be used in our computation:
Model fraction = 3/8
A fraction that is greater than the fraction by the model is represented as
Fraction > Model fraction
Substitute the known values in the above equation, so, we have the following representation
Fraction > 3/8
Add 1 to the numerator
So, we have
Fraction = 4/8
Simplify
Fraction = 1/2
Hence, the fraction that is greater than the fraction by the model is 1/2
Read more about fraction at
https://brainly.com/question/17220365
#SPJ1
Jim bought a pair of shoes for $50 and laces for $1. If the sales tax is 7%, how much tax must he pay?
(a) $3.57
(c) $0.36
(b) $350
(d) $35.70
Jim must pay tax $3.57.
The correct answer is (a) $3.57.
To calculate the sales tax that Jim must pay, we need to find 7% of the total cost of the shoes and laces.
The total cost of the shoes and laces is $50 (shoes) + $1 (laces) = $51.
To calculate the sales tax, we multiply the total cost by the tax rate:
Sales tax = 7% of $51
[tex]= 0.07 \times $51[/tex]
= $3.57.
Therefore, Jim must pay $3.57 in sales tax.
The correct answer is (a) $3.57.
For similar question on sales.
https://brainly.com/question/25743891
#SPJ11
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
The equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis are:
A. x² + (y - 3)² = 36.
D. x² + (y + 8)² = 36.
What is the equation of a circle?In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.Note: A center that lies on the y-axis simply means the value of h on the x-axis is equal to 0.
Based on the information provided above, we have the following parameters:
Radius, r = diameter/2 = 12/2 = 6 units.
Center, (h, k) = (0, 3).
By substituting the given parameters into the equation of a circle formula, we have the following;
(x - h)² + (y - k)² = r²
(x - 0)² + (y - 3)² = 6²
x² + (y - 3)² = 36.
Read more on equation of a circle here: brainly.com/question/15626679
#SPJ1
Write the equation of a line parallel to 2y = x – 3 and that passes through point (-4,3) in slope intercept form.
Answer:
The equation of the line parallel to 2y = x – 3 and passing through point (-4,3) in slope-intercept form is y = (1/2)x + 5.
Step-by-step explanation:
To find the equation of a line that is parallel to 2y = x – 3, we need to determine the slope of the given line.
2y = x - 3 can be written in slope-intercept form y = (1/2)x - 3/2.
The slope of this line is 1/2.
Since we want a line parallel to this line, the slope of the new line will also be 1/2.
Next, we can use the point-slope form of a line to write the equation of the new line.
Point-slope form: y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope of the line.
Substituting the values, we get:
y - 3 = (1/2)(x - (-4))
Simplifying, we get:
y - 3 = (1/2)x + 2
Adding 3 to both sides, we get the final equation in slope-intercept form:
y = (1/2)x + 5
Therefore, the equation of the line parallel to 2y = x – 3 and passing through point (-4,3) in slope-intercept form is y = (1/2)x + 5.
john want to buy a new bike that costs 337and he already has save 103 estimates to find about how much more john needs to save to buy the bike
To find the estimated amount John needs to save to buy the bike, we can subtract the amount he already has saved from the cost of the bike:
Estimated amount = Cost of bike - Amount already saved
Estimated amount = $337 - $103
Estimated amount = $234
Therefore, John needs to save an estimated $234 more to buy the bike.
Answer:
John needs to save about $234 more to buy the bike. Note that this is an estimate, as we do not know if John will need to pay any taxes or additional fees when purchasing the bike.
Step-by-step explanation:
To find out how much more John needs to save to buy the bike, we can subtract the amount he has already saved from the cost of the bike:
337 - 103 = 234
Therefore, John needs to save about $234 more to buy the bike. Note that this is an estimate, as we do not know if John will need to pay any taxes or additional fees when purchasing the bike.
Find the value of x.
The value of x in the circle is 4.2
Calculating the value of x in the circleFrom the question, we have the following parameters that can be used in our computation:
The circle
Using the intersecting chords equation, we have
(5x - 8) * 4 = (x + 1) * 10
When solved for x, we have
x = 4.2
Hence. the value of x is 4.2
Read more about circle at
https://brainly.com/question/12823137
#SPJ1
Can someone help me please
The resulting matrix will be in the form :
5 9 -4
0 -14 15
What is a matrix in mathematics ?A matrix is described as a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.
To get a 1 in row 1, column 1, we perform the following elementary row operation:
R2 - 2R1 -> R2
This will subtract 2 times the first row from the second row and give us the result:
5 9 -4
0 -14 15
Matrices are useful for describing systems of linear or differential equations, as well as representing a linear application.
In conclusion, in a matrix function, the input and the output values are matrices.
Learn more about matrices at:
brainly.com/question/94574
#SPJ1
Solve for x. Round to the nearest tenth, if necessary.
Using the sine ratio, the value of x in the right triangle shown is calculated to the nearest tenth as: 2.6 units.
How to Find the Value of x Using the Sine Ratio?The sine ratio is part of the trigonometry ratios that can be applied to solve a right triangle, and it is written as:
sin ∅ = length of the opposite side / length of the hypotenuse of the right triangle
We are given the following information from the image above:
Reference angle (∅) = 75 degrees
length of the opposite side = x
length of the hypotenuse = 9
Plug in the values:
sin 75 = x/9
9 * sin 75 = x
x = 8.7 [to the nearest tenth]
Learn more about the sine ratio on:
https://brainly.com/question/2920412
#SPJ1
A solution has a total mass of 400 g. If the solvent has a mass of 236 g of the total mass, what is the strength of the drug?
In a case whereby A solution has a total mass of 400 g. If the solvent has a mass of 236 g of the total mass, the strength of the drug can be expressed as 41%.
How can the strength of the drug be calculated?From the question, the total mass =400 g
The solvent mass = 236 g
Then the mass of the drug = 400-236
= 164
Then the mass percentage of the drug can be calculated as 164/400 * 100
= 41%
Therefore, the strenght of the drug can be expressed as 41%
Learn more about total mass at:
https://brainly.com/question/29644807
#SPJ1
20x^2-7x-6=0 by factoring
Answer:
x = -2/5
x = 3/4
Step-by-step explanation:
Factoring:
20x²-7x-6=0
20x²+8x - 15x - 6 = 0
4x * (5x + 2) - 3 * (5x + 2) = 0
(5x + 2) * (4x - 3) = 0
Cases:
5x + 2 = 0
4x - 3 = 0
x = -2/5
x = 3/4
Answer:
20x^2 -x(15-8)-6=0 here 6×20=120an by subtracting 15-8 we got seven where the 15×8 is also 120
Step-by-step explanation:
now,
20x^2 -15x+8x -6 =0 (here -×-is equal to +thus we write +8)
5x(4x-3) +2(4x-3)=0
(5x+2) (4x-3)=0
Either 5x=-2
X=-2/5
Or
4x=3
X=3/4
It’s due tomorrow I really need help
Answer:
B.
Step-by-step explanation:
As the steps imply,
Step 1 is to first convert the 3.5% (0.035) and then multiply it by 16 to find out by how many grams the amount should decrease (0.035 * 16 = 0.56). Step 2 is to subtract this amount from 16 to find the amount remaining after one hour (16 - 0.56 = 15.44). Step 3 is to convert 4.25% to a decimal (0.0425) and multiply it by the amount remaining at the end of one hour to find out by how many grams this amount should decrease after two hours (0.0425 * 15.44 = 0.6562)Step 4 finally is to subtract this amount from 15.44 to find the amount remaining after two hours (15.44 - 0.6562 = 14.7838)100 Points! Algebra question. Please show as much work as possible. Photo attached. Thank you!
The value of the constant term k in the exponential model of the bacteria population is k ≈ 0.0972
What is an exponential function?An exponential function is one in which the input variable is part of the exponent of the expression for the function.
The function for the population of the bacteria indicates;
[tex]P(t) = \frac{22,000 }{1 + 1.2\cdot e^{(-k\cdot t)}}[/tex]
The population of the bacteria after t = 1 hour is P(1) = 10,532
Therefore;
[tex]P(1) = \frac{22,000 }{1 + 1.2\cdot e^{(-k\times 1)}} = 10,532[/tex]
[tex]1 + 1.2\cdot e^{(-k\times 1)} = \frac{22,000}{10,532}[/tex]
[tex]1.2\cdot e^{(-k\times 1)} = \frac{22,000}{10,532} - 1[/tex]
[tex]e^{(-k\times 1)} = \frac{\frac{22,000}{10,532} - 1}{1.2}[/tex]
Taking the natural logarithm of both sides, we get;
[tex]\ln (e^{(-k\times 1)}) = \ln (\frac{\frac{22,000}{10,532} - 1}{1.2})[/tex]
[tex]\ln (e^{(-k)}) = \ln (\frac{\frac{22,000}{10,532} - 1}{1.2})[/tex]
[tex]\ln (e^{(-k)}) = -k = \ln (\frac{\frac{22,000}{10,532} - 1}{1.2})[/tex] ≈ -0.0972 (rounded to 4 decimal places)
-k ≈ -0.0972
k ≈ 0.0972Learn more on exponential functions here: https://brainly.com/question/15662160
#SPJ1