7 students failed the examination out of 28 students who appeared for the examination.
What is the Proportion?
A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as 1 : 3 (for every one boy there are 3 girls)
When we say that a proportion is two ratios that are equal to each other, it means this in the sense of two fractions being equal to each other.
For instance, 5/10 equals 1/2.
If 3/4 of the students passed the exam, this means that 1 - 3/4 = 1/4 of the students failed the exam.
We can use this information to find the number of students who failed the exam by multiplying the total number of students who appeared for the exam by the proportion of students who failed:
Number of students who failed = Total number of students * Proportion of students who failed
Number of students who failed = 28 students * 1/4 = 28 students * 0.25 = 7 students
Hence, 7 students failed the examination out of 28 students who appeared for the examination.
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Adella wants to have $10,000. 00 saved in 5 years. Her local bank offers an account at 4% APR
compounding monthly. How much would she need to deposit to reach her goal?
$8000. 33
$8191. 67
$8189. 67
$8219. 29
The deposit to be made to save $10,000 in 5 years is $8189.67 when compounded monthly.
What is compound interest?Compound interest is interest on a loan or deposit that is calculated on both the principal amount and the interest accumulated in previous periods. It differs from simple interest, which is calculated on the principal only. Compound interest can be more favorable to the lender and more expensive to the borrower. The frequency of compounding (annual, quarterly, monthly, etc.) also affects the total amount of interest earned or paid.
Given that:
A = $10,000
r = 4% = 0.04
t = 5 years
n = 12 (since the compounding is monthly)
P = ?
The compound interest is given as follows:
[tex]A= P(1+\frac{r}{n} )^{nt}[/tex]
Substituting the values in the formula we have:
[tex]10000= P(1+\frac{0.04}{12} )^{(12)(5)}\\\\10000= P(1+0.0033 )^{(60)}\\\\10000= P(1.0033 )^{(60)}\\\\10000= P(1.2185)\\\\P= \frac{10000}{1.2185} \\\\P=8189.67[/tex]
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Select the correct answer. what is the equation of a parabola whose vertex is (0, 5) and whose directrix is x = 2?
a. y2 = 8(x − 5)
b. 8(y − 5) = x2
c. (y − 5)2 = 8x
d. (y − 5)2 = -8x
Check the picture below, so the parabola looks more or less like so, with a vertex at (0 , 5) and a "p" distance of negative 2 units, since it's opening to the left, so
[tex]\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{p~is~negative}{op ens~\supset}\qquad \stackrel{p~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=0\\ k=5\\ p=-2 \end{cases}\implies 4(-2)(~~x-0~~) = (~~y-5~~)^2\implies {\Large \begin{array}{llll} -8x=(y-5)^2 \end{array}}[/tex]
John and Wesley both work for telephone companies installing internet connections into new homes, but they do not work for the same company. John's paycheck at the end of the month includes his base pay of $2,000 and his commission of $65. 25 for each installation he makes that month. Wesley is paid $380 plus a commission of $105. 75 for each installation he makes each month. In September of last year, they both made the same number of installations and they both earned the same amount of money
The number of installations in September were forty that lead to John and Wesley earning same amount of money.
Let the number of installations be x. The equation of be formed for each paycheck will be -
Total paycheck = base pay + number of installations × comission on each installation
The total paycheck and number of installations is same. So equating the equations by keeping x.
2000 + 65.25x = 380 + 105.75x
Rewriting the equation -
105.75x - 65.25x = 2000 - 380
Performing subtraction on each side of the equation
40.5x = 1620
x = 1620/40.5
Performing division on Right Hand Side of the equation
x = 40
There were 40 installations.
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Aquarium one contains 4. 6 gallons of water Luis Will begin filling aquarium one at a rate of 1. 2 gallons per minute aquarium to contains 54. 6 gallons of water Isaac will begin draining aquarium two at a rate of 0. 8 gallons per minute
The Filling time is After 25 minutes, both Aquariums will contain same amount of water.
What is filling time?you've fully prepared the aquarium, all you need to do is follow these quick and easy steps and safely fill your aquarium with water.
Calculate the Filling Time of the aquarium Explanation
Given,
Water in Aquarium A = 4.6 gallons
Water in Aquarium B = 54.6 gallons
Filling rate = 1.2 gallons per minute.
Draining rate = 0.8 gallons per minute.
Let,
x represents the minutes.
A(x) = 4.6 + 1.2x
(Because Luis is adding water in the tank.)
B(x) = 54.6 - 0.8x
(Isacc is draining water from the tank.)
For same amount of water;
A(x) = B(x)
4.6+1.2x=54.6-0.8x
1.2x+0.8x=54.6-4.6
2x=50
Dividing both sides by 2
2x/2=50/2
x=25
Therefore, After 25 minutes, both Aquariums will contain same amount of water.
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Simplify the expression below:
20-10y-7y + 9
A) Зу — 29
B) 3y + 11
C) 3y + 29
D) -17y + 11
E) -17y + 29
To simplify the expression 20-10y-7y + 9, we can combine like terms.
Like terms are terms that have the same variables raised to the same exponents. For example, 10y and -7y are like terms because they both have the variable y raised to the exponent 1.
We can start by combining the like terms:
20 - 10y - 7y + 9
= 20 + (-10y - 7y) + 9
= 20 + (-17y) + 9
Next, we can combine the constants:
20 + (-17y) + 9
= (20 + 9) + (-17y)
= 29 + (-17y)
The simplified expression is: 29 + (-17y)
[tex]20-10y-7y + 9[/tex]
Combine Like Terms:
[tex](-10y+-7y)+(20+9)[/tex]
[tex]-17y+29[/tex]
[tex]\fbox{Option E}[/tex]
In ΔXYZ, x = 5. 2 inches, y = 9. 8 inches and z=7. 1 inches. Find the measure of ∠Z to the nearest degree
The measure of ∠Z is 165 degrees to the nearest degree.
In a triangle, the measure of each angle is equal to the sum of the measures of the other two angles subtracted from 180 degrees. This is known as the Triangle Sum Theorem.
Given that x = 5.2 inches, y = 9.8 inches, and z = 7.1 inches in triangle XYZ, we can use the theorem to find the measure of angle Z.
∠Z = 180 - (x+y)
∠Z = 180 - (5.2+9.8)
∠Z = 180 - 15
∠Z = 165
So the measure of ∠Z is 165 degrees to the nearest degree.
Therefore, The measure of ∠Z is 165 degrees to the nearest degree.
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A child pushes a toy car with a force of 5. 25 N a distance of 6. 5 m. The car rolls for a total distance of 32 m. How much work is done on the toy car? Need formula and the way the work is done, ASAP
The work done on the toy car is 164.4 J.
The formula for work is:
Work = force * distance
In this case, given that:
Force = 5.2 N
Distance = 32 m
So, the work is:
Work = force * distance
Work = 5.2 * 32
Work = 166.4 J
Hence, the work done is 164.4 J.
What is work vs force?Force is described as the rate of change of momentum with respect to time, in which momentum is mass multiplied by velocity. Work is the product of displacement and the component of force in the direction of displacement. When work is done, then the kinetic energy of an object changes.
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10 POINTS. Answer please.
The two sets A and B triangle must have identical items, but this does not require that they be put in the same order for the sets to be equal.
Describe the triangle.A triangle is a 2D shape with three vertices, three straight edges, and three straight edges. A key feature of these shapes is that each type of triangle has three inner angles that add up to 180° in these designs. during their math lectures about these angles and how to use this quality to spot missing values.
Here,
Triangle 1 in this instance has two angles, one of 34 degrees and the other of 48 degrees.
The third angle is therefore 180-34- 48=98.
The angles in Triangle 2 are 34 and a, where an is 48, respectively.
In other words, the third angle is 180−34−a=146−a≠146−48=98.
Jennifer claims that given the information at hand, triangles 1 and 2 cannot be compared.
If 34,98,48=34,a,146a., they are equivalent.
How many degrees will Jennifer's claim be ruled untrue? To compare the triangles, use the formula a.
It is crucial to understand that while components in two sets A and B must match, the sets are not always equal if they are not listed in the same order.
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Simplify by using order of operations:
4+(9 x 2) divided by (4 - 1) -4
Which milk product will have approximately 15.36 grams of milk fat in an 80-gram serving? (Milk products and percent milk fat: Heavy Cream(36.7%), Light Cream(19.2%), Whole Milk(3.5%), Low-Fat Milk(1.5%), Skim Milk(0.05%)
The light cream milk product have approximately 15.36 grams of milk fat in an 80-gram serving.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
Let n be the percentage of milk product to have approximately 15.36 grams of milk fat in an 80-gram serving.
Using percentage formula,
15.36 = n x 80 / 100
n = 1536 / 80
n = 19.2%
Therefore, the product is light cream milk.
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the length breadth and height of a cuboid are in the ratio 7:5:2 its volume is 35840cm³
The length of the cuboid is 56 cm.
The breadth of the cuboid is 40 cm.
The height of the cuboid is 16 cm.
What is a cuboid?A cuboid is a three-dimensional shape where the volume is given by
Length x width x height.
We have,
Volume of a cuboid = 35840 cm³
The ratio of length, breadth, and height of the cuboid = 7:5:2
This means,
Length = 7x
Breadth = 5x
Height = 2x
Now,
(7x)(5x)(2x) = 35840
70x³ = 35840
x³ = 512
x = ∛512
x = 8
Now,
Length = 7x = 7 x 8 = 56 cm
Breadth = 5x = 5 x 8 = 40 cm
Height = 2x = 2 x 8 = 16 cm
Thus,
The length, breadth, and height of the cuboid are 56cm, 40cm, and 16 cm.
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PLEASE HELP ME ASAP!!!!!!!!!
In a school, 10% of students have 7 ball pens, 30% of students have 3 ball pens, 40% of students have 2 ball pens and 20% of students have 1 ball pens. What is the expected number of ball pens of a student?
The expected number of ball pens of a student is 2.4.
What is the expected number?
In statistics and probability analysis, the expected value is calculated by multiplying each of the possible outcomes by the likelihood that each outcome will occur and then summing all of those values.
The expected number of ball pens of a student can be calculated by taking a weighted average of the number of ball pens that each group of students has.
The weight for each group is the percentage of students that are in that group.
So, we can calculate the expected number of ball pens of a student by:
(10% * 7) + (30% * 3) + (40% * 2) + (20% * 1)
0.7 + 0.9 + 0.8 + 0.2
The expected value is also known as the population means and it can be calculated by summing the product of each outcome’s probability and its corresponding value.
Here, the outcome is the number of ball pens.
Hence, the expected number of ball pens of a student is 2.4.
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What is the x-coordinate of the solution to the system shown?
3x - y = 6
3x + y = 34
The x-coordinate of the solution of the system of equations is x = 20/3
What is the x-coordinate of the solution?Here we have a system of equations below:
3x - y = 6
3x + y = 34
And we want to find the x-cordinate of the solution, so we need to solve this for x.
We can use the elimination method, you can see that if we add both equations we will get:
(3x - y) + (3x + y) = 6 + 34
6x = 40
x = 40/6
We can simplify that fraction to get:
x = 20/3
That is the x-coordinate of the solution.
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what is m for y = 7x - 17
On solving the provided question, we can say that - the linear equation y = 7x - 17 at x= 0; y = -17 and m = -17
What is a linear equation?The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
y = 7x - 17
at x= 0
y = -17
and m = -17
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What is the gradient of 2x 3y 6?
The gradient of the linear equation 2x + 3y + 6 is (3/2).
The gradient of a linear equation in the form of y = mx + c is m, which represents the slope of the line. The slope is defined as the ratio of the change in y to the change in x. It represents the steepness of the line.
The equation 2x + 3y + 6 is not in the form of y = mx + c. It is in the form of Ax + By + C = 0, which is the general form of a linear equation. To find the gradient of such an equation we need to divide -A/B. In this case, the gradient of the line is -2/3.
The gradient of a line gives us the direction of the line, it is the slope of the line. It tells us how steep the line is and if it is going up or down. A positive gradient means the line is going up and a negative gradient means the line is going down.
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3.5 x 4 + 11 x 2.2 = 115.5
i know what the answer is i used a calculator i just need to explain how i got the answer its the last question then im done it i might give the brain thing if i can
Answer:
3.5. 2.2.
x 4. x 1 1
------ -----------
14.0. 22
220
24.2
Step-by-step explanation:
answer for me is 38.2
are you sure ur math is right?
Mr. Wú needs to buy new carpet for his
office. The length of the office is 12 feet
and the width is 10 feet. If each square
foot of carpet costs $3, how much will it
cost Mr. Wú to buy carpet for his office? NEED HELP PLS!!!
Answer:
A - $360
Step-by-step explanation:
Length times width equals area.
12 × 10 = 120
His office has 120 sq ft of space. If each sq ft costs $3
120 × 3 = $360
A
Answer:
A ($360)
Step-by-step explanation:
imagine a rectangle with one side 12ft and one side 10ft
multiply the length and the width to find the square footage:
12*10=120ft^2
each square foot is $3 so multiply 3 by 120
$3*120ft^2= $360
oops didn't realize someone already answered sorry
Sue ate one sweetie one day, and each day afterward she ate one sweetie more than she did the day before. How many sweeties did she eat during her first week?
Answer:
28
Step-by-step explanation:
1 + 2 + 3 + 4 + 5 + 6 + 7
Ritu had 6 time a number of tamp and Raj took twice the number from Ritu o that he ha a total of 24. Write the algebraic equation and find the root of the equation
The equation to find the root of the statement given in the question is , 12x = 2x - 24.
Let the number of tamp which Ritu have be x
Then the number of tamp which Raj have be 2x = 24
Now as Ritu has 6 times more than Raj , 6( 2x) = 24 x 6
Therefore, the required equation becomes,
12x = 2x - 24
=> 10x = 24
=> x = 2.4 answer.
An equation is a mathematical statement which is made up of constants , variables and operators. There are two parts of an equation which are equated using the equal sign . The right hand and the left hand side of the equation.
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At what point does the graph of the linear equation 2x 3y =- 15?
The graph of the linear equation 2x - 3y = -15 is a line that passes through the point (-5, 5), and has a slope of 2/3.
The linear equation
2x - 3y = -15
can be written in the form
y = mx + b,
where m is the slope and b is the y-intercept. To find the slope of this equation, we can rearrange the equation to be in the form y = mx + b, which gives us
y = (2/3)x - 5.
This means that the slope of the line is 2/3. To find the y-intercept, we can plug in 0 for x and solve for y. This gives us
y = -5.
Therefore, the graph of this equation is a line that passes through the point (-5, 5) and has a slope of 2/3.
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Could you help me solve this
Answer: The middle number is 15
Step-by-step explanation:
45/3= 15 so the three numbers will be around there.
14+15+16= 45
Which of the following are possible examples of sampling distributions? (Select all that apply.) O all mean trout lengths in a sampled lake O mean trout lengths based on samples of size 5 O heights of college students at a sampled university O average SAT score of a sample of high school students
O average male height based on samples of size 30 X
The potential instances of sample distribution are options C and E.
Option E. Average male height based on samples of size 30.
Option C. Mean trout lengths based on samples of size 5.
The sampling distribution of the mean is the distribution of the variable x (all feasible sample means of size n) for a variable x and a given sample size n.
The mean is the most typical kind of sample distribution. Plotting the data points and computing the means of each sample group drawn from the population are its main goals.
This idea, which is a form of the probability distribution, is frequently used to gather precise data from a sizable population that is divided into a number of randomly chosen samples. This idea is further divided into three categories: T-Sampling, proportional sampling, and the sampling distribution of the mean.
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The correct questions should be like this:
Which of the following are possible examples of sampling distributions? (Select all that apply.) average SAT score of a sample of high school students
all mean trout lengths in a sampled lake
mean trout lengths based on samples of size 5
heights of college students at a sampled university
average male height based on samples of size 30
if you shift the linear parent function, f(x)=x, left 14 units, what is the equation of the new function
Answer: This is a horizontal translation so, the equation is f(x) = (x + 5). Whenever you translate to the right it is negative
Step-by-step explanation:
Let the random variable h represent the height of a woman in the population. P(h<60) represents the probability of randomly selecting a woman with height less than 60 inches. Based on the information given, the probability can be found using either the discrete model or the normal model. 1. Give an example of a probability h that can be found using the discrete model but not the normal model
The probability of h that can be found using the discrete model but not the normal model is 0.03.
A discrete probability distribution or DPD (also known as a discrete probability model) records all possible values of a discrete random variable and gives their probabilities.
The normal probability model involves when the distribution of the continuous outcome conforms reasonably well to a normal or Gaussian distribution, which resembles a bell-shaped curve.
H represents the height of women
Determine P ( H < 60 ) using either a discrete or normal model
using discrete model
P ( H < 60 ) = ∑ relative frequencies of the women with height < 60 inches
P ( H < 60 ) = 0.01 + 0.02 = 0.03
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Two sides of a triangle have lengths 15 and 20. The length of the third side can be any number greater than A and less than
The third side of the triangle will be less than 35.
What is a triangle?A polygon with three angles, sides and angles is called a triangle.
Given that, Two sides of a triangle have lengths 15 and 20. The length of the third side can be any number greater than A and less than
We know that, triangle inequality theorem states that the sum of any two sides of a triangle is greater than or equal to the third side.
Therefore, length of the third side < 15+20 < 35
Hence, the third side of the triangle will be less than 35.
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Based on these data, how many students received a score higher than 95?
A. At least 15
B. More than 25
C. 6 or fewer
D. Exactly 10
Bar charts display categorical variables, whereas histograms display numerical or quantitative data.
What is mean by histogram?The frequency distribution of a few data points for one variable is represented graphically by a histogram. Heterogeneous "bins" or "range groups" are frequently used in histograms in order to categorize data and count the number of data points that are part of each bin.
Among graphing tools, the histogram is widely used. It is utilized to encapsulate discrete or continuous data that is measured on an interval scale. It is frequently employed as a convenient way to highlight the key characteristics of the data distribution.
Histograms show numerical or quantitative data, whereas bar charts show categorical factors. The numerical data in a histogram will typically be continuous in most cases (having infinite values). It would be ridiculous to attempt to plot an axis that included every potential value for a continuous variable.
Therefore, the correct answer is option C. 6 or fewer.
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May someone please help me
The positive value of the distance between the two objects
is [tex]r = + \sqrt\frac{GM_1M_2}{F_g}[/tex]
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Considering the equation for determining the gravitational pull between two items [tex]F_g = \frac{GM_1M_2}{r^2}[/tex], where r is the distance between the objects M is the individual masses and G is the gravitational constant.
The answer to the r in the problem has two values. Since distance cannot be negative, there can only be one positive value, hence we want the positive value.
[tex]F_g = \frac{GM_1M_2}{r^2}[/tex]
[tex]r^2 = \frac{GM_1M_2}{F_g}[/tex].
[tex]r = \pm\sqrt\frac{GM_1M_2}{F_g}[/tex]
[tex]r = +\sqrt\frac{GM_1M_2}{F_g}[/tex].
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solve for x, Give your answer as a fraction or decimal rounded to the nearest hundredth.
Using the fact that the triangles are similar, we will see that:
x = 5.626
How to find the value of x?On the image we can see two triangles, such that one is inscribed on the other.
Just because of that, it is obvious that the two triangles are similar.
And because the triangles are similar, the quotients between correspondent sides must be equal, that allows us to write the equation:
3/x = 8/15
The quotient is "left side over the bottom side"
We can solve that equation for x:
3/x = 8/15
3 = (8/15)*x
(15/8)*3 = x
45/8 = x
5.625 = x
That is the value of x.
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What is the product 4y 3 )( 2y^2 3y 5?
The product for the given polynomial is [tex]8y^5 + 6y^4 + 20y^3.[/tex]
When multiplying two polynomials, it is important to keep track of the exponents of each term. The exponents will determine the degree of the resulting polynomial. To find the product, you multiply each term of the first polynomial by each term of the second polynomial, then combine like terms.
In this case, the first polynomial is 4y^3 and the second polynomial is 2y^2 3y 5. To find the product, you would multiply 4y^3 by 2y^2, 4y^3 by 3y, and 4y^3 by 5. This would give you 8y^5, 12y^4, and 20y^3. Since these are the only terms in the product, you simply add them together to get the final answer of [tex]8y^5 + 6y^4 + 20y^3.[/tex]
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In a particular country, the average adult is spending even more time on a mobile device than watching television. From 2014 to 2021, the function y=-9.11x+280x can be used to estimate the average number of minutes per day that an adult spends watching television, and the function y=12.34x + 169.9 can be used to estimate the average number of minutes per day that an adult spends on a mobile device. For both functions, x is the number of years after 2014. a. Based on this information, determine the year in which the time spent watching television is the same as the time spent on a mobile device. b. Use these functions to predict how much time the average adult spends per day watching television and on a mobile device for the year 2021..
After 0.6412 years the average for mobile device and television usage will coincide.
What are functions?
Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given here the equations as y=-9.11x+280x and y=12.34x + 169.9 the period for which the averages are equal will be given by
9.11x+280x=12.34x + 169.9
x = 0.6412 years
Again, after 7 years in 2021 the respective averages will be 9.11 ×7+280×7 = 2023.77 and similarly for mobile device the time spent would be 256.28 minutes
Hence, the answers are After 0.6412 years the average for mobile device and television usage will coincide.
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