The probability of P(B and C) is 1/6
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty. It is more likely that an event will occur if its probability is higher.
For e.g., A straightforward illustration is tossing a fair (impartial) coin.
Given that, the probabilities, P(A) = 1/8, P(C) = 1/4, and P(A and B) = 1/12
P(A and B) = P(A)×P(B)
Therefore,
1/12 = 1/8 × P(B)
P(B) = 8/12 = 2/3
Now,
P(B and C) = P(C)×P(B)
P(B and C) = 1/4×2/3
P(B and C) = 1/6
Hence, P(B and C) = 1/6
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Tyler is 30 years younger than Naeste 9years ago
Answer:
i dont understand this question but i think maybe 21
Step-by-step explanation:
30-9 =21
Answer:
21
Step-by-step explanation:
if a tree is 105 metres tall in real life what would be the height of the diagram of the tree if the scale was 1: 1000
Answer:
1.05
Step-by-step explanation:
it is 105 divided by 1000
Answer:
0.105 metres
Step-by-step explanation:
105 divided by 1000
4a. Find the 120th term of the sequence: a1 = 5, d = 0.5 (3 marks) b. Find the sum of the first 120 terms of that sequence. (3 marks)
Answer:
a₁₂₀ = 64.5 , S₁₂₀ = 4170
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 5 and d = 0.5 , then
a₁₂₀ = 5 + (119 × 0.5) = 5 + 59.5 = 64.5
---------------------------------------------------------
the sum to n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ] , then
S₁₂₀ = [tex]\frac{120}{2}[/tex] [ (2 × 5) + (119 × 0.5) ]
= 60(10 + 59.5)
= 60 × 69.5
= 4170
A recipe calls for 6 liters of oj, 3 liters of grape juice and 9.5 liters of ice water. How much grape juice and water will be used with 2 liters of Jo?
If we use 2 liters of OJ, you will need to change the recipe and use:
1 liter of grape juice.3.2 liters of water.How much grape juice and water it will need?We know that a recipe calls for 6 liters of OJ, 3 liters of grape juice and 9.5 liters of ice cream.
If instead we use 2 liters of OJ, then the ratio of the recipe that we use is given by the quotient below:
2L/6L = 1/3
So we will just use 1/3 of each of the amounts that the recipe calls, we will se:
(1/3)*3 liters of grape juice = 1 liter of grape juice.
(1/3)*9.5 liters of water = 3.2 liters of water.
These are the amounts that you need to use.
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Give the following number
in Base 10.
F16 = [? ]10
The next decimal number should be changed to hexadecimal. Your final response may contain up to six fractional digits. In decimal 386210, subscript 10 to F16.
How do you write a number in base 10?F16 is 001000011000.1111. 218. F716 is 001000011000.111101112. 710 = (h0)16 = 716 is how the hexadecimal number is represented. It is necessary to add a 1 to the left and modify the number for both to 0. In base-2, the numeral 15 is represented as 1111, and the number 16 is represented as 10000. The greatest value in base-16 is the letter F, in a similar vein. such that 10 is the new value.
Binary 10 equals 1010, thus. Dividing 10 by 2 successively until the quotient equals 0 will yield the decimal to binary equivalent. By writing the remainder in each division step from bottom to top, it is possible to determine the binary equivalent.Base-16 is the definition given to hexadecimal. There are many powers of 16 in each place value in the number. The hexadecimal numbers are: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F. 10 through 15 are represented, accordingly, by the letters A through F.
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Combine the like terms
-n + (-4) - (-4n) + 6
the simplest form of the given expression is 3n+2.
What is polynomials?
Using variables and coefficients, polynomials are algebraic expressions. The term "indeterminates" is sometimes used to describe variables. The terms Poly and Nominal, which together signify "many" and "terms," make up the word polynomial. When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable). The expression is categorized as a monomial, binomial, or trinomial based on the number of terms it contains.
-n + (-4) - (-4n) + 6
= -n + (-4) + 4n + 6
= 3n -4 +6
= 3n+2
Hence the simplest form of the given expression is 3n+2.
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a simple l cell organism divides in to 3 identical cells every 20 minutes, how many organisms will there be after 8 hours.
Step-by-step explanation:
Let’s see … one division every 20 minutes? That would be like <grinding noise> three binary doublings per hour, right? Now for the tough part … three doublings per hour, for eight straight hours? <more grinding noises> … Is that even mathematically possible? After much thinking, I decide that the total number of binary doublings has to be in the neighborhood of no less than eight times three!
Would you believe that 224=16777216 ? While mathematically true, it is not the answer to the posted question… Since we started at 0 minutes, there are only 23 buddings inside eight hours … so the answer has to be 223=8388608 , right?
Wrong again, this time forgetting all about the newlybud bacteria generations, that all go on budding side by side of their ancestors …
Now that you’ve caught on to the basic idea, I leave it to you to figure out the real answer! Keep in mind that after 20 minutes, you have two budding bacteria to reckon with, for 440 minutes … after 40 minutes another two (for 420 minutes), and so on, down the line.
Hint: the answer still is not 16777216 …
Answer:
after 1 division,there is 3 cell
after 2 divisions,there is 9 cell.
after 3 divisions,there is 27 cell
The above data takes the form of Geometric sequence.
3,9,27......,last term
here,Common ratio(r)=9/3=27/9=3
and,first term(a)=3
Let, n be the no.of divisions.
then, n=8 hrs/20 min=480 min/20min=24
Now,from the G.S,
last term=ar^n-1
=3×3^24-1
=9²³
Hence,9²³ organisms will there be after 8 hours
It can be written as 8.86293812×10²¹ as well
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how do you get 3/8 from 13/8
You can get 3/8 from 13/8 by subtraction. The solution is 10 / 8
How to get 3/8 from 13/8In order to get 3/8 from 13/8 we would have to carry out a subtraction of fractions.
That is we would have: 13/8 - 3/8
take the lcm of the denominator
[tex]\frac{13 - 3}{8}[/tex]
= 10 / 8
Hence when we take 3 / 8 from 13 / 8, the solution that we would have would be from subtraction. This is 10 / 8
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how many inscribed circle can exist inside a triangle ?
Answer:
1 circle
Step-by-step explanation:
Angle bisectors will meet at one specific point. Radius taken from centre to one side of triangle is the radius of the incircle. There can be no other configuration to form an incircle so only one incircle can be inscribed in a triangle.
the ratio of boys to girls in the sixth grade is 3 to 5 if there are 45 girls how many students are there in the 6th grade
Answer: 27 boys
Step-by-step explanation:
There is a rule in math, what you do to one side, you do to the other.
So in this case the ration is 3:5
?:45
As you can see, they multiplied 5 by 9 to get 45, remember the rule, so we do the same.
3 times 9 is 27, so 27 boys
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PLEASE HELP!!
The equation of a circle is (x+10)2+(y−4)2=100.
What is the center and radius of the circle?
Responses
center: (10, −4); radius: 10,000
center: , begin ordered pair 10 comma negative 4 end ordered pair, ; radius: 10,000
center: (−10, 4); radius: 10,000
center: , begin ordered pair negative 10 comma 4 end ordered pair, ; radius: 10,000
center: (10, −4); radius: 10
center: , begin ordered pair 10 comma negative 4 end ordered pair, ; radius: 10
center: (−10, 4); radius: 10
The center of the circle is (-10,4) and the radius is 10.
What is a circle?The circle is defined as the locus of the point traces around a fixed point called as the center and is equidistant from the outer trace.
All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
The equation of the circle is,
( x - h )² + ( y - k )² = r²
(x+10)² + (y−4)² = 100
(x+10)² + (y−4)² = 10²
Compare the equations and find the center and radius,
Center = ( h,k) = ( -10,4)
Radius = r = 10
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I need help on questions 9 and 12 pls help:(
The graphs as per the transformations are given below.
What are transformation of graphs?
There are four transformations that happens in a graph -
When a figure is translated, it is moved in any direction.
Flipping a figure over a line is called reflection.
Rotation is the process of turning a figure a specific amount around a point.
When we dilate a figure, we increase or decrease its size.
The triangle CHV have points C(-4,5), H(-3,3) and V(-3,5). When it is reflected across x=-3. The image gets mirrored in the negative y-axis with the points C(-4,-2), H(-3,0) and V(-3,-2).
The parallelogram CJWY have points C(-3,-1), J(-2,-1), W(-2,-4), Y(-1,-4). It needs to be translated by (x,y)->(x+2,y+0)
C=(-3+2,-1+0)=(-1,-1)
J=(-2+2,-1+0)=(0,-1)
W=(-2+2,-4+0)=(0,-4)
Y=(-1+2,-4+0)=(1,-4)
The parallelogram TSCH have points T(-1,3), S(1,4), C(1,-1), H(3,0). It needs to be translated by (x,y)->(x+0,y-1)
T=(-1+0,3-1)=(-1,2)
S=(1+0,4-1)=(1,3)
C=(1+0,-1-1)=(1,0)
H=(3+0,0-1)=(3,-1)
The triangle RDP have points R(0,0), D(-2,-2) and P(3,-3). On rotation of 180 degrees graph (x,y) becomes (-x,-y).
R=(0,0)
D=[-(-2),-(-2)]=(2,2)
P=[-(3).-(-3)]=(-3,3)
Therefore, the transformations are made.
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If a man works for 8 hours a day, he can finish a job in 12 days. How many hours per day must he work to complete it in 10 days?
Answer:
9.6 hours
Step-by-step explanation:
12×8 would equal the amount of hours it takes to complete the job in 12 days so you simply divide that number by 10 which will give you 9.6h
Answer:
6.67 hour per day
Step-by-step explanation:
If
=8 hours a day = 12 days
then
= ? = 10 days
= 10/12 × 8hours per
= 6.67 hours per day.
How much did the population change between 1970 and 1980? population change between 1990 and 1995? What was the average annual change for that period?
Hint: Calculate the changes, then calculate the mean, or average, by dividing by the number of years. State the units clearly. The units are listed on the chart.
The population change for each period is given as follows:
1970 to 1980: 0.748 billion.1990 to 1995: 0.407 billion.Hence the average annual change for the period between 1970 and 1995 is given as follows:
7,932,000 people a year.
How to obtain the population change?The population change over a period is given by the subtraction of the population at the end of the period by the population at the beginning of the period.
The population data for each year is given by the table on the image presented at the end of the answer.
Hence the changes are obtained as follows:
1970 to 1980: 4.456 - 3.708 = 0.748 billion.1990 to 1995: 5.691 - 5.284 = 0.407 billion.The change between 1970 and 1995 is of:
5.691 - 3.708 = 1.983 billion.
This period is composed by 25 years, hence the average annual change is of:
1.983/25 = 0.07932 billion people a year = 7,932,000 people a year.
Missing InformationThe chart is given by the image presented at the end of the answer.
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The number of views for a video on a social media website doubles every day. You begin observing the
number of views 8 days after the video was introduced. The number y of views x days after the video is introduced is
represented by the function = 22(2^x-8). When will there be one million views?
The total number of times social media browsers have been showed your content.
How is social media value calculated?A general, but simplified earned media value formula is: EMV = impressions x cost per 1000 impressions x adjustable variable. The adjustable variable can be anything you are looking to track like engagement or impressions.
Simplifying
22 = 2(x + 8)
Reorder the terms:
22 = 2(8 + x)
22 = (8 * 2 + x * 2)
22 = (16 + 2x)
Solving
22 = 16 + 2x
Solving for variable ‘x’.
Move all terms containing x to the left, all other terms to the right.
Add ‘-2x’ to each side of the equation.
22 + -2x = 16 + 2x + -2x
Combine like terms: 2x + -2x = 0
22 + -2x = 16 + 0
22 + -2x = 16
Add ‘-22’ to each side of the equation.
22 + -22 + -2x = 16 + -22
Combine like terms: 22 + -22 = 0
0 + -2x = 16 + -22
-2x = 16 + -22
Combine like terms: 16 + -22 = -6
-2x = -6
Divide each side by ‘-2’.
X = 3
Simplifying
X = 3
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Question 1-1
Barrett earns $15 per hour cutting grass and $10 per hour tutoring reading. In one month, Barrett needs to save at least $400 for a
new lawnmower but does not want to work more than 35 hours.
Part A: Let z represent the hours cutting grass and y represent the hours tutoring. Given z 20 and y ≥ 0, select all the inequalities
that represent the situation.
On solving the inequality we know, Barrett should work 25 hours tutoring and 10 hours cutting grass to make $400.
What exactly does inequality mean?In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality results from a lack of balance.
Solution:-
given,
z=hours of cutting grass
y=hours of tutoring
Two equation can be made using given condition
15z+10y=400
and
z+y=35
Solving both equation simultaneously,
we get
y=25
z=10
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could u please help me
Answer:
there is not enough info but i think it would be (5,11)
Step-by-step explanation:
divide
Answer:
[tex]y=\dfrac{11}{4}x[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]
Choose two (x, y) points from the given table:
Let (x₁, y₁) = (4, 11)Let (x₂, y₂) = (8, 22)Substitute them into the slope formula:
[tex]\implies \dfrac{22-11}{8-4}=\dfrac{11}{4}[/tex]
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]
Substitute point (4, 11) and the found slope into the point-slope formula and rearrange to slope-intercept form:
[tex]\implies y-11=\dfrac{11}{4}(x-4)[/tex]
[tex]\implies y-11=\dfrac{11}{4}x-11[/tex]
[tex]\implies y=\dfrac{11}{4}x[/tex]
12 Aftab wants a patio in his garden. He is going to use concrete slabs to make the patio. Each concrete slab is a square with sides of length 0.5 m. A sketch of the planned patio is shown below. 3 m Patio 3 m 2
(a) What is the area of Aftab's patio? Give units with your answer.
Aftab pays £3.10 per concrete slab. (b) How much will it cost Aftab to buy enough concrete slabs to make the patio?
Answer:
5-3=2m
3x2=6m^2
Step-by-step explanation:
I can’t explain
LETTER B I DON’T KNOW THE ANSWER
100 POINTS!!!!! PLEASE HELP!
Answer:
[tex]a^{12} b^{4}[/tex]
Step-by-step explanation:
To simplify we will have to use the negative exponent rule and the power rule along with some algebra.
Negative Exponent Rule
[tex]a^{-b} =\frac{1}{a^b}[/tex]
Power Rule
[tex](a^b)^{c} =a^{bc}[/tex]
Given
[tex](a^{-4}b^{-1}c )^{2} (a^2bc)^{2}[/tex]
Rewrite [tex]a^{-4}[/tex] using negative exponent rule.
[tex](\frac{1}{a^{4}}* b^{-1}c )^{2} (a^2bc)^{2}[/tex]
Rewrite [tex]b^{-1}[/tex] using negative exponent rule.
[tex](\frac{1}{a^{4}}* \frac{1}{b}*c )^{2} (a^2bc)^{2}[/tex]
Simplify
[tex](\frac{c}{a^4b} )^{2} (a^2bc)^{2}[/tex]
Rewrite the base as its reciprocal.
[tex](\frac{a^4b}{c} )^{2} (a^2bc)^{2}[/tex]
Apply the power rule.
[tex]\frac{a^8b^2}{c^2} *(a^2bc)^{2}[/tex]
Apply the power rule.
[tex]\frac{a^8b^2}{c^2} *a^4b^2c^2[/tex]
Cancel the common factor of [tex]c^2[/tex].
[tex]a^8b^2 a^4b^2[/tex]
Apply the power rule.
[tex]a^{12} b^{4}[/tex]
Answer:
[tex]a^{12}\:b^{4}[/tex]
Step-by-step explanation:
Given expression:
[tex]\left(a^{-4}\:b^{-1}\:c\right)^{-2}\left(a^2\:b\:c\right)^2[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies a^{(-4 \times -2)}\:b^{(-1 \times -2)}\:c^{-2}\:a^{(2 \times 2)}\:b^2\:c^2[/tex]
Simplify:
[tex]\implies a^{8}\:b^{2}\:c^{-2}\:a^{4}\:b^2\:c^2[/tex]
Collect like terms:
[tex]\implies a^{8}a^{4}\:b^{2}b^2\:c^{-2}c^2[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies a^{(8+4)}\:b^{(2+2)}\:c^{(-2+2)}[/tex]
Simplify:
[tex]\implies a^{12}\:b^{4}\:c^{0}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^0=1:[/tex]
[tex]\implies a^{12}\:b^{4}(1)[/tex]
[tex]\implies a^{12}\:b^{4}[/tex]
***** 6. A certain movie is 105 minutes long. It started at 6:15 pm. During the movie, there were two commercial breaks, one lasting 9 minutes and one lasting 6 minutes. At what what time did the movie finish
According to the given conditions in the question, the movie did finish at 8:15pm exactly.
What is the average movie length in hollywood?The average movie length of movies in hollywood is around 120 -130 mins per movie. However this fact can vary as per the genre and type of the film.
How are movies helping to improve world economy?The movie business, usually referred to as the film industry, has a big influence on the economy. For those involved in the industry, such as performers, directors, camera operators, sound technicians, special effects designers, and theater owners, the creation and distribution of films can result in jobs and financial gain.
The local economy can benefit from the tourists that movies can bring to an area where a movie is being made or is located. The money made by persons employed in the film business is likely to be spent on other goods and services, stimulating extra economic activity. As a result, the film industry may also have a "multiplier impact" on the economy.
So according to the question, the movie itself started at 6:15 pm, and it lasted for 105 mins , also adding the time for commercials of 9 mins and 6 mins , which ultimately added 15 more mins, the total screen time would be ,
105 + 15 = 120 mins
Which is equal to 2 hrs, so the movie finished at 8:15 pm.
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Given A(0, a) and B(b, 0) , find coordinates of C so that the orthocenter of triangle ABC lies on the triangle.
The coordinate of the point C is (0, a)
How to determine the coordinates of point CFrom the question, we have the following parameters that can be used in our computation:
A = (0, a)
B = (b, 0)
As a general rule, the orthocenter of a triangle is a point located at the intersection of the lines containing the altitudes of the triangle.
This means that we start by calculating the equation of the altitude from B to line AC.
A linear equation is represented as
y = mx + c
Where
slope = m
y-intercept = c
Using the above as a guide, we have the following:
slope = (y₂ - y₁)/(x₂ - x₁)
This gives
m(BC) = (0 - 0)/(b - 0) = 0
y-intercept (c) = a
So the equation of the line BC is
y = 0 * x + a
y = a
For line AC, we have
m(AC) = (a - 0)/(0 - 0) = a/0 = undefined.
This means that the equation of the line AC is
x = 0
The equation x = 0 implies that the x-coordinate is always 0, irrespective of the y-coordinate e.g. (0, a)
At this stage, we have the coordinates of the points from lines AC and BC to be
(0, a) and (0, a)
Next, we calculate the C as follows
C = Midpoints of (0, a) and (0, a)
This gives
C = 1/2 * (0 + 0, a + a)
Evaluate
C = (0, a)
Hence, the coordinate of C is (0, a)
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Solve the following quadratic equation for all values of x in simplest form.
4(x 2−5)−1=3
The solutions to the equation 4(x² − 5) − 1 = 3 are ±√6
How to determine the solutions to the equation?From the question, we have the following parameters that can be used in our computation:
4(x 2−5)−1=3
Express properly
This gives
4(x² − 5) − 1 = 3
Subtract -1 from both sides of the equation
So, we have the following representation
4(x² − 5) = 4
Divide both sides by 4
This gives
x² − 5 = 1
Subtract -5 from both sides of the equation
So, we have the following representation
x² = 6
Take the square root of both sides
x = ±√6
Hence, the solution is ±√6
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In ΔUVW, w = 1.4 cm, m m∠W=63° and m m∠U=29°. Find the length of v, to the nearest 10th of a centimeter.
In order to find the length of v in ΔUVW, we can use the Law of Sines.
The Law of Sines states that the ratio of the length of a side of a triangle to the sine of the opposite angle is the same for all sides and angles in the triangle. This can be expressed as:
a/sin A = b/sin B = c/sin C
Where a, b, and c are the lengths of the sides of the triangle and A, B, and C are the angles opposite those sides.
In ΔUVW, we are given the lengths of two sides (w and v) and the measure of the angles opposite those sides (m∠W and m∠U). We can use the Law of Sines to find the length of v:
v/sin U = w/sin W
v = (w/sin W) * sin U
Substituting the given values, we get:
v = (1.4 cm / sin 63°) * sin 29°
Using a calculator, we find that v = 2.72 cm to the nearest hundredth of a centimeter. Rounding to the nearest 10th of a centimeter, we get v = 2.7 cm.
Therefore, the length of v in ΔUVW is approximately 2.7 cm to the nearest 10th of a centimeter.
Ross walked 7 miles in 2 hours. What is his unit rate of miles per hour?
Answer:
3.5 miles per hours
Step-by-step explanation:
7/2 =3.5
24.
-2
2
NO
2
y-int=
slope =
equation:
y
2
X
On solving the provided question we can say that from data provided by the graph, we have a straight line, which means that the coordinates are equal. so the equation will be x = y = > x-y = 0
What is graphs?Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle.
from data provided by the graphs,
we have a straight line,
which means that the coordinates are equal.
so the equation will be x = y
x-y = 0
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What is a quadratic function (f) whose zeros are -2 and -11
Hence the required quadratic equation is +13x+22.we can find by multiplying of given factor.
What are quadratic equations explain?Quadratics equation is a polynomial equation of a second degree which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations. The general form of the quadratic equation is: ax² + bx + c = 0. where x is an unknown variable and a, b, c are numerical coefficients.
What are the ways to solve a quadratic equation?The four methods of solving a quadratic equation are factoring, using the square roots, completing the square and the quadratic formula. Quadratic equations have many applications in everyday life. Quadratic equations must be used directly or indirectly in every field that involves calculating speed.
Now we have [tex]x1[/tex]=2 [tex]x2[/tex]=-11
then quadratic function will be
(x+2) (x+11)
[tex]x^2+2x+11x+22[/tex]
[tex]x^2+13x +22[/tex]
this is our required quadratic equation.
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Complete question is: Write a quadratic function f whose zeros are 2 and -13.
Hence the required quadratic equation is +13x+22.we can find by multiplying of given factor.
What are quadratic equations explain?Quadratics equation is a polynomial equation of a second degree which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations. The general form of the quadratic equation is: ax² + bx + c = 0. where x is an unknown variable and a, b, c are numerical coefficients.
What are the ways to solve a quadratic equation?The four methods of solving a quadratic equation are factoring, using the square roots, completing the square and the quadratic formula. Quadratic equations have many applications in everyday life. Quadratic equations must be used directly or indirectly in every field that involves calculating speed.
Now we have x¹ = 2 x² = -11
then quadratic function will be
(x+2) (x+11)
x² + 2x + 11x + 22
x² + 13x + 22
This is our required quadratic equation.
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The complete question is-
Write a quadratic function f whose zeros are 2 and -13.
What value for the
constant, h, in the equation
shown below will result in an infinite number of
solutions?
6t + 18 = h(3x + 9)
Therefore , As a result, h = 2 is the answer to the equation in the given question.
Explain equation.An equation is a mathematical representation of two equal variables, one on each side of a "equals" sign. Everyday issues can be resolved with equations. We commonly look for pre algebra help to deal with problems in real life. Pre-algebra is the fundamental foundation of mathematics.
Here,
The formula is as follows: 6x + 18 = h(3x + 9)
To ensure that the expression has an unlimited number of answers, h's value must be determined.
Take the expression now and continue solving it.
=> 6x + 18 = h(3x + 9)
=>3hx + 9h= 6x +8
The expression will have an endless number of solutions if the coefficients of the left-hand side and the right-hand side are equal.
Therefore, 3h = 6 and h = 2
As a result, h = 2 is the answer to the equation in the given question.
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In a survey, 13 out of 20 teachers respond yesto a proposal for a new after-school club. In the same survey, 37 out of 50 students respond yes. a.Which group is more in favor of the new after-school club, teachersor students? Show your work
Answer: To compare the level of support for the new after-school club between teachers and students, we can calculate the percentage of individuals in each group that responded "yes" to the proposal.
For teachers: 13 out of 20 is equivalent to 13/20 = 0.65 or 65%
For students: 37 out of 50 is equivalent to 37/50 = 0.74 or 74%
Based on the percentage of individuals in each group that responded "yes," we can see that students are more in favor of the new after-school club than teachers. 74% of students responded "yes" to the proposal, while only 65% of teachers responded "yes."
It's worth mentioning that it's important to keep in mind that this comparison is based on the sample size of teachers and students that responded to the survey and not the whole population, also if the sample size isn't representative of the population and not randomly selected it can't be generalized.
Step-by-step explanation:
Two alien spaceships start traveling toward each other from space stations that are 710,000 km apart. The first spaceship started an hour before the second spaceship and is traveling at 110,000 km/hr. In how many hours will the two spaceships meet if the second spaceship is traveling at 90,000 km/hr?
The spaceship will meet in how many hours?
The time that it will take for the spaceships to meet is given as follows:
3 hours.
How to model the situation?Each of the spaceships is traveling at a constant rate, hence linear functions are used to model the situation.
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which the parameters are given as follows:
The slope m represents the velocity.The intercept b represents the initial position.The positive direction is considered from the first spaceship towards the second spaceship.
The first spaceship started an hour before the second spaceship and is traveling at 110,000 km/hr, hence the difference when the second spaceship starts traveling is given as follows:
710,000 - 110,000 = 600,000 km.
Then the functions are given as follows:
x1(t) = 110t.x2(t) = 600 - 90t. (negative as they travel in opposite direction).They will meet when:
x1(t) = x2(t).
Hence:
110t = 600 - 90t
200t = 600
t = 600/200
t = 3 hours.
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The time that it will take for the spaceships to meet is given as follows:
3 hours.
How to model the situation?
Each of the spaceships is traveling at a constant rate, hence linear functions are used to model the situation.
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which the parameters are given as follows:
The slope m represents the velocity.
The intercept b represents the initial position.
The positive direction is considered from the first spaceship towards the second spaceship.
The first spaceship started an hour before the second spaceship and is traveling at 110,000 km/hr, hence the difference when the second spaceship starts traveling is given as follows:
710,000 - 110,000 = 600,000 km.
Then the functions are given as follows:
x1(t) = 110t.
x2(t) = 600 - 90t. (negative as they travel in opposite direction).
They will meet when:
x1(t) = x2(t).
Hence:
110t = 600 - 90t
200t = 600
t = 600/200
t = 3 hours.
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