Answer:
The probability that a student earns a grade of A is 1/7.
Let E be an event and S be the sample space. The probability of E, denoted by P(E) could be computed as:
P(E) = n(E) / n(S)
As the total number of students = n(S) = 35
Students getting the grade A = n(E) = 5
So, the probability that a student earns a grade of A:
P(E) = n(E) / n(S)
= 5/35
= 1/7
Hence, the probability that a student earns a grade of A is 1/7.
Keywords: probability, sample space, event
11. Find the amount of interest on $600, if a bank is paying 5.5% interest.
[A] $30 [B] $3.30
[C] $330
[D] $33
[E] $23
Simplify 10√3x +4√3x +5√3x
Add the like terms :
10√3x + 4√3x + 5√3x(10 + 4 + 5)√3x19√3xwhat is 2(5+34-67/45*43)^2 equal to?
The value of the give expression is [tex]\frac{313}{748845}[/tex] OR 4.18 × 10⁻⁴
Evaluating an ExpressionFrom the question, we are to determine the value of
2(5+34-67/45*43)^2
This can be written as
[tex]2 (\frac{5+34-67}{45 \times 43 })^{2}[/tex]
First, we will simplify the bracket
[tex]2 (\frac{-28}{1935 })^{2}[/tex]
Then, we get
[tex]2 \times \frac{-28}{1935 }\times \frac{-28}{1935 }[/tex]
= [tex]\frac{1568}{3744225}[/tex]
= [tex]\frac{313}{748845}[/tex] OR 4.18 × 10⁻⁴
Hence, the value of the give expression is [tex]\frac{313}{748845}[/tex] OR 4.18 × 10⁻⁴
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In triangle PQR, find the measure of angle Q.
P= 64 degrees
Q= X
R= 2x
Answer:
38.667°
Step-by-step explanation:
the total sum of 3 angles in a triangle is 180
in triangle PQR this means:
P+Q+R = 180
so:
64+x+2x=180
64+3x=180
3x=116
x=116/3=38.667
So Q=X=38.667
Choose any set of Pythagorean triplets of your choice and illustrate them using graph sheet.
Example given below:
The required Pythagorean triplets are hypotenuse, perpendicular and base is 13, 12 and 5 respectively.
In a right angled triangle, its side, such as hypotenuse, perpendicular and base is Pythagorean triplets.
We have
Hypohypotenuse = 13
perpendicular = 12
base = 5
Which satisfies the condition of the Pythagorean theorem.
[tex]a^2+b^2=c^2\\12^2+5^2=c^2\\169=c^2[/tex]
and c = 13
Thus, the required value of Pythagorean triplets satisfies the Pythagorean theorem.
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What is the factored form of the following expressions?
x2 – x – 42
Answer:
(x-7)(x+6)
Step-by-step explanation:
Write a system of equations that could be used to solve the situation described below.
You find 12 coins under the couch. Every coin is either a nickel or a penny, and they add up to a total of 32 cents. How many of each type of coin do you have? Let x represent the number of pennies and y represent the number of nickels.
Please select the best answer from the choices provided
A. x+y=12
0.05x+0.01y=0.32
B. x+y=0.32
0.01x+0.05y=12
C. x+y=12
0.01x+0.05y=0.32
D. not enough information
If there are 12 coins under the couch and every coin is either a nickel or a penny and together they are forming 32 cents then the equations which represent the problem will be x+y=12, 0.01x+0.05y=0.32. The correct option is B which is x+y=12, 0.01x+0.05y=0.32.
Given There are 12 coins and total money is 32 cents.
Let the number of pennies be x and the number of nickels be y.
According to question there are 12 coins so the first equation becomes:
x+y=12.
Then we have been told that together they amount to 32 cents.
We know that 1 penny is 1 cent coin and 1 nickel is 5 cent coin so the equation becomes :
1*x+5*x=32
x+5y=32
converting into dollar
0.01x+0.05y=0.32.
Hence the right equations showing the problem of nickel and pennies are x+y=12, 0.01x+0.05y=0.32.
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What is the transformation of C(9, 3) when dilated with a scale factor of 1/3,
using the point (3, 6) as the center of dilation
The transformation of C(9, 3) when dilated with a scale factor of 1/3, using the point (3, 6) as the center of dilation would be an option B: C'(3,1).
What is Dilation transformation?A dilation transformation is a transformation that changes the size of the original figure but the shape remains unchanged.
If any figure is dilated by a scale factor k with the center of dilation as the origin.
Then the change of transformation in each of the vertices of the figure is given:
(x,y) → (kx, ky)
It is given a point C which is located at C(9,3).
Hence, here k=3
We get:
C(9,3) → C'(9×3,3×3)
C(9,3) → C'(27,9) = C'(3,1)
Hence, the transformation of C(9, 3) when dilated with a scale factor of 1/3, using the point (3, 6) as the center of dilation would be an option B: C'(3,1).
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Answer:
(5,5)
Step-by-step explanation:
count from the center
Elaine saw statistics showing that union employees make an average of 30 percent more than nonunion workers, so when she was looking for a new job, she looked for one at a company that was unionized. Elaine was motivated by
Elaine saw statistics showing that union employees make an average of 30 percent more than nonunion workers, so when she was looking for a new job, she looked for one at a company that was unionized. Elaine was motivated by Economic needs.
What do we mean by economic needs?
By economic need Elaine is trying to get a company that would pay her more. Hence the need to go for the Unionized company.
This is given that the Unionized company is said to earn more than the other company. Hence her motivation is due to her economic needs.
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PLEASE ANSWER ASAP!!!!!11
The nth term of a sequence is represented by 2n^3+25n^2+32n−15/ 6n^4+2n^3−11n^2−2n+17.
What is the limit of the the nth term as x becomes increasingly large?
A. 0
B. 1/3
C. 3
D. The limit does not exist
The limit of the nth term of a sequence does not exist option (D) is correct.
What is the limit?A limit is a value at which a function approaches the output for the given values in mathematics. Limits are used to determine integrals, derivatives, and continuity in calculus and mathematics.
We have an expression:
[tex]= \rm \dfrac{2n^5+25n^2+32n-15}{6n^4+2n^3-11n^2-2n+17}[/tex]
Applying limit:
[tex]= \lim_{n \to \infty} \rm \dfrac{2n^5+25n^2+32n-15}{6n^4+2n^3-11n^2-2n+17}[/tex]
[tex]=\lim _{n\to \infty \:} n \left(\dfrac{2+\dfrac{25}{n^3}+\dfrac{32}{n^4}-\dfrac{15}{n^5}}{6+\dfrac{2}{n}-\dfrac{11}{n^2}-\dfrac{2}{n^3}+\dfrac{17}{n^4}}\right)[/tex]
= ∞ = The limit does not exist
Thus, the limit of the nth term of a sequence does not exist option (D) is correct.
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experimental verification
See below for the verification of ∠ACD = ∠ABC + ∠BAC
How to verify the angles?The following proof works for both triangles.
The sum of angles in a triangle is 180 degrees.
So, we have:
∠ABC + ∠BAC + ∠ACB = 180
Make ∠ACB the subject
∠ACB = 180 - ∠ABC - ∠BAC
The sum of angles on a straight line is 180 degrees.
So, we have:
∠ACD + ∠ACB = 180
Make ∠ACB the subject
∠ACB = 180 - ∠ACD
Substitute ∠ACB = 180 - ∠ACD in ∠ACB = 180 - ∠ABC - ∠BAC
180 - ∠ACD = 180 - ∠ABC - ∠BAC
Subtract 180 from both sides
- ∠ACD = - ∠ABC - ∠BAC
Multiply both sides by -1
∠ACD = ∠ABC + ∠BAC
Hence, ∠ACD = ∠ABC + ∠BAC has been verified
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8) Mark ran a mean distance of 13.2 km in five days. The next day, Mark ran 20 km.
Find the mean distance Mark ran in the six days.
Answer:
16.6
Step-by-step explanation:
Add the numbers together.
13.2+20=33.2
Now divide the number by 2.
33.2/2=16.6
Hope this helps!
If not, I am sorry.
If two angles have the same angle measure, then they are said to be____.
A. Complementary
B.adjacent
C.congruent
Answer:
C
Step-by-step explanation:
2 equal angles are said to be congruent
The area of a square is 256cm2. When each side of the square is increased by x cm, its area becomes 324 cm2.Find the value of x.
Answer: x = 2
Step-by-step explanation:
First, let's take the root of 256 to find the length of each side before the addition of x.
[tex]\sqrt{256} = 16[/tex]
This means 16 cm is the length of each side before the addition of x.
Then increase each side by X to get
[tex](16 + x)(16 + x) = 324[/tex]
[tex]256 + 16x + 16x + x^2=324[/tex]
[tex]x^2+32x -68=0[/tex]
[tex]x=2[/tex] or [tex]x=-34[/tex]
The value cannot be negative so x has to be 2
The radius of a circle is 7 metres. What is the length of a 135° arc?
Answer:
16.5 meters
Step-by-step explanation:
The length of an arc of a circle = 2πr(C/360°) ;where:
C is the central angle of the arc,
R is the radius of the arc
Length of the arc = 2π(7)(135/360)
= 16.493
= 16.5 metres (approx.)
Answer:
Arc Length: 5.25π or [tex]\frac{21}{4} \pi[/tex]
Explanation:
An arc is the part of the circumference of a circle.
Formula:
[tex]\sf Arc \ Length = \dfrac{\theta}{360} \ \times \ 2\pi \ \times radius[/tex]
If applied:
[tex]\sf Arc \ Length = \dfrac{135}{360} \ \times \ 2\pi \ \times 7[/tex]
[tex]\sf Arc \ Length = \dfrac{3}{8} \ \times \ 14\pi[/tex]
[tex]\sf Arc \ Length = \dfrac{21}{4} \pi[/tex]
[tex]\sf Arc \ Length = 5.25 \pi[/tex]
What type of relationship is expressed below?
5x = 2x 9
O equation
O function
O inequality
factoris fully 2ab² + 8a²b
Answer:
2ab(b + 4a)
Step-by-step explanation:
2ab² + 8a²b
Factor Out the 2:
2(ab² + 4a²b)
Factor Out the a:
2a(b² + 4ab)
Factor Out the b:
2ab(b + 4a)
the graph of F(x) can be stretched vertically and flipped over the x axis to produce the graph of G(x) if F(x)=x^2 which of the following could be the equation of G(x)
A. G(x)=-1/5x^2
B. G(x)=-5x^2
C. G(x)=5x^2
D. G(x)=1/5x^2
Answer:
g(x) = -5x²
(option B)
Step-by-step explanation:
we know that our original graph, f(x) = x² is a parabola.
So, we can consider what happens when we adjust the function/equation of a parabola.
when we "vertically stretch" a parabola, we are increasing the value of x.
think of it this way: the steepness of a slope is rise over run. If we rise ten, and run one, that's going be a lot more steep than if we rise 1, run 1.
Let's say our x = 5
if f(x)=x²
f(5) = 25
> y value / steepness is 25
f(x) = 3x²
f(5) = 75
> y value / steepness is 75
So, we are looking for an equation with an increase in x present.
When a parabola has been flipped over the x-axis, we know that the original equation now includes a negative
suppose that x = 1
if y = x² ; y = 1² = 1
if y = -(x²) ; y = -(1²) ; y = -1
So, when we set x to be negative, we make our y-values end up as negative also (which makes the graph look as if it has been flipped upside-down)
This means that we are looking for a function with a negative x value.
So, we are looking for a negative x-value that is multiplied by a number >1
The graph that fits our requirements is g(x) = -5x²
hope this helps!!
please place the dot for me(20 points will give brainliest!!!)
Answer:
2,
Step-by-step explanation:
The vertex is the very highest or very lowest point. X coordinates are listed first, then Y.
Find the x-intercept of the rational function.
A (-5,0)
B (0,-5)
C (0, -1)
D (-1, 0)
Answer:
(-5,0)
Step-by-step explanation:
The x intercept is where it crosses the x axis
It crosses the x axis where x = -5
The y value is 0
(-5,0)
Answer:
A
Step-by-step explanation:
The x -intercept is 'shorthand' for x - AXIS intercept
where the graph crosses the x - axis
this will always have a ZERO value for the 'y'- coordinate
looking at the graph this point is -5,0
Figure 1 is similar to figure 2. What is TS?
1 unit
4 units
8 units
2 units
Answer:
8 units
Step-by-step explanation:
ratios
(x-3) /( x+1) = (x-2)/(x+3) cross multiply
x^2 -x -2 = x^2 - 9
-x - 2 + 9 = 0
x = 7
so TS = x + 1 = 8 units
2.865; cut it to the ten thousandths
Answer:
2.865.
Step-by-step explanation:
first get to know the place value of each digit is you move on you will realise that there's no digit for tens of thousands that means that you can add a zero which which will be counted as tens of thousands and since it's not past 5 it can't change the other number. I mean it can't add 1 to 5 so the number remains 2.865 good day.
Identify the equation with an x-intercept of 3 and a y-intercept of -2.
The equation of line is 2x - 3y = 6.
What is intercept?The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.
The x-intercept is 3 and the y-intercept is -2.
So, the line passes through the points (3, 0) and (0, -2)
Now, slope of line is
m= -2-0/ 0-3 = 2/3
Equation of line is
y = 2/3 x - 2
y = 2x-6 /3
3y= 2x -6
2x - 3y = 6
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Currently,nova is 3 times as old as Damon. in 8 years, she will be as only 2 times as old as Damon. How old will Damon be in 8 years?
Answer:
16
Step-by-step explanation:
consider X = Damon's age
3x + 8 = 2x
x = 8
so Damon will be 16 in 8 years ( 8+8)
Answer:
16
Step-by-step explanation:
24/3 8
24+8=32
8+8=16
16/32=1/2
Write the algebraic expression for the following statement.
The sum of a number and 3 is 14.
Answer:
the algebraic expression is; x+3=14
X^2 + y^2 = 81 write down the equations of the two horizontal lines that are tangent to c
Answer:
Step-by-step explanation:
x² + y² = 81
x + y = √81
x + y = 9
x ≥ 9
y ≤ 9
What is the slope-intercept equation of the line below?
Answer:
y= 2x - 3
Step-by-step explanation:
To calculate the slope (or gradient) of a line, take two points on the line whose x and y values are easy to read. Then divide the difference of they y-coordinate values by the difference of their x-coordinate values.
Here I have taken the points p (3, 3) and q (1, -1) to calculate the slope.
• slope = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1}}[/tex]
= [tex]\frac{3 - (-1)}{3 - 1}[/tex]
= [tex]\frac{4}{2}[/tex]
= 2
The intercept is the y-coordinate value of the point at which the line crosses ("intercepts") the y-axis. I've marked the intercept point with a green line.
• intercept = -3
The slope-intercept equation of a line takes the form:
y = mx + c
where 'm' is the slope and 'c' is the y-intercept.
Substituting the values we found into the equation gives us:
y = 2x + (-3)
∴ y = 2x - 3
Quick please!!! Buford, the farm hand, is preparing feed for
the animals. He wants to mix the contents of a
bag containing 50% corn with one containing
90% corn to optain a 30-pound bag containing
80% corn. How many pounds of the 50% bag
should he use? (write your answer as a
decimal.)
Buford should use 7.5 pounds of the 50% corn bag.
How do we solve a system of linear equations from word problems?A system of linear equation is an equation containing two different equations with variables and the coefficient.
From the given information, let:
The weight of the bag containing 50% corn be = xThe weight of the bag containing 90% corn be = ySp, we can a system of a linear equation that says:
x + y = 30
0.5x + 0.9y = 0.8(30)
Using elimination method
x + y = 30
-
x - 1.8y = -48
0 - 0.8y = -18
y = 18/0.8
y = 22.5
From x + y = 30
x = 30 - 22.5
x = 7.5
Therefore, we can conclude that he should use 7.5 pounds of the 50% corn bag.
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In the equation 17x2 = 12x, the value of c is:
17
12
0
Probability of Next Candy
Fill in the chart below with the probability of choosing the next candy.
Answer:
8 is correct.
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