Answer:
just practice alot . .. ...........
Answer:
you could do all your work and try to ask the teacher for help
Step-by-step explanation:
A spinner contains four sections: red, blue, green, and yellow. Joaquin spins the spinner twice. The set of outcomes is given as S = {RB, RG, RY, RR, BR, BG, BY, BB, GR, GB, GY, GG, YR, YB, YG, YY}. If the random variable is "yellow (Y)," which of the following is the correct probability distribution? A 2-column table has 3 rows. The first column is labeled Yellow: x with entries 0, 1, 2. The second column is labeled Probability with entries 0. 5625, 0. 375, 0. 625. A 2-column table has 3 rows. The first column is labeled Yellow: x with entries 0, 1, 2. The second column is labeled Probability with entries 0. 75, 0. 25, 0. A 2-column table has 3 rows. The first column is labeled Yellow: x with entries 0, 1, 2. The second column is labeled Probability with entries 0. 5, 0. 375, 0. 125. A 2-column table has 3 rows. The first column is labeled Yellow: x with entries 0, 1, 2. The second column is labeled Probability with entries 0. 5, 0. 25, 0. 25.
The correct probability distribution of the random variable tracking "yellow (Y)" color is given by: Option A:
Yellow:x Probability
0 9/16 = 0.5625
1 6/16 = 0.375
2 1/16 = 0.0625
What is probability distribution?Probability distribution of a random variable is the collection of value and its probability pair for values of that considered random variable.
It might be a function, a table etc.
How to calculate the probability of an event?Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.
Then, suppose we want to find the probability of an event E.
Then, its probability is given as
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]
where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.
For this case, the experiment consists of a spinner with four color sections, and is spun twice.
The sample space is:
S = {RB, RG, RY, RR, BR, BG, BY, BB, GR, GB, GY, GG, YR, YB, YG, YY}
Let we take:
X = the number of times out of two spins the color yellow occurs in a pair of spin of the considered spinner.
Then, as there are only two spin going to happen, so the values X can take are:
X = 0 (no yellow color in both spin)X = 1 (one of the spin ended up yellow, and other doesn't)X = 2 (both the spins resulted in yellow color).Let we take:
A = event that in first spin of the considered spinner, color yellow occurs.B = event that in second spin of the considered spinner, color yellow occurs.Then, as there are four colors equally likely, so we get:
P(A) = 1/4 (yellow color can occur in 1 way in one spin, and total number of colors that can occur = 4).
Similarly, we get P(B) = 1/4
Also, as first and second spins are independent of each other's result, so both A and B are independent events.
Getting the probabilities for each value of X:
Case 1: X = 0[tex]P(X = 0) = P(A' \cap B') = P(A')P(B') = (1-P(A))(1-P(B)) \\P(X = 0) = \dfrac{3}{4} \times \dfrac{3}{4}\\\\P(X = 0) = \dfrac{9}{16}[/tex]
(where A' and B' are complement of A and B, and as (A and B) are independent, so as (A' and B') and (A' and B) and (A and B') )
Case 2: X = 1So either first spin had yellow color, or second, so we get:
[tex]P(X = 1) = P((A' \cap B) \cup (A \cap B'))\\ P(X=1) = P(A' \cap B) + P(A \cap B') - P((A' \cap B) \cap (A \cap B'))\\P(X=1) = P(A')P(B) + P(A)P(B') -0\\P(X=1) = \dfrac{3}{4} \times \dfrac{1}{4} + \dfrac{1}{4} \times \dfrac{3}{4} - 0\\\\P(X = 1) = \dfrac{6}{16}[/tex]
Case 3: X = 2Both event A and B occured this time, so we get:
[tex]P(X = 2) = P(A \cap B) = P(A)P(B) \\P(X = 0) = \dfrac{1}{4} \times \dfrac{1}{4}\\\\P(X = 0) = \dfrac{1}{16}[/tex]
Thus, the probability distribution of X is:
X=x P(X = x)
0 9/16 = 0.5625
1 6/16 = 0.375
2 1/16 = 0.0625
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please help me
To build a pizza, customers choose stuffed (S) or thin (T) crust, red (R) or white (W) sauce, and a topping. The choices for toppings are pepperoni (P), sausage (S), or vegetables (V).
The following list shows the possible pizzas that can be made. The first letter represents the crust, the second letter represents the sauce, and the third letter represents the topping. For example, a stuffed-crust pizza with red sauce and pepperoni is listed as SRP, and a stuffed-crust pizza with white sauce and sausage is listed as SWS.
SRP, SRS, SRV, SWP, SWS, SWV, TRP, TRS, TRV, TWP, TWS, TWV
How many outcomes include red sauce or sausage?
Enter you answer as a number, like this: 42
Answer:
8
Step-by-step explanation:
I bolded what I think is important to know.
To build a pizza, customers choose stuffed (S) or thin (T) crust, red (R) or white (W) sauce, and a topping. The choices for toppings are pepperoni (P), sausage (S), or vegetables (V).
The following list shows the possible pizzas that can be made. The first letter represents the crust, the second letter represents the sauce, and the third letter represents the topping. For example, a stuffed-crust pizza with red sauce and pepperoni is listed as SRP, and a stuffed-crust pizza with white sauce and sausage is listed as SWS.
SRP, SRS, SRV, SWP, SWS, SWV, TRP, TRS, TRV, TWP, TWS, TWV
How many outcomes include red sauce or sausage?
How can you best describe a stop sign using polygons? The sign has sides, so it is. It appears to be because the sides and angles appear to be congruent.
The stop sign is an octagon or regular polygon.
It is given that a stop sign has 8 sides.
It is required to describe the sign using a polygon.
What is a polygon?It is defined as the flat planner geometry in two dimensions with a closed shape there are two types of polygon one is irregular in which the angle and sides are not equal and the second one is a regular polygon in which sides and angles are equal called regular polygon.
We have a stop sign that has 8 sides.
As we know the definition of a polygon they are planner geometry and in a regular polygon, the sides and angles are equal called regular polygon.
The stop sign has 8 if we assume they are all equal sides and angles then we can say that the stop sign is an octagon(in which the number of sides is 8) or a regular polygon.
Thus, the stop sign is an octagon or regular polygon.
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Answer:
8, octagon, & regular
Step-by-step explanation:
I did it
what ratios are equivalent to 4/11
Answer:
Here!!
Step-by-step explanation:
Here are a few ratios that are equivalent to 4 : 11 . . . . .
8 : 22
12 : 33
20 : 55
400 : 1100
308 : 847
4 billion : 11 billion
please explain how you got your answer because i cant grasp this :/
Answer:
39 sq inches
Area of sector = [tex]\frac{θ}{360}*\pi r^{2}[/tex]
Given: θ = 70°, radius (r) = 8 inches
Area of sector = [tex]\frac{70}{360} * \pi *8^{2}[/tex]
= 39.095
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One of the logo meets the building requirements. Explain which logo meets the biulding requirements and why.
The logo that meets the building requirement must be:
Aesthetically appealingVisually accurate at all sizesMust be memorableRelated to the value being delivered.What are logos in art?A Logo in art is a visual symbol, that an organization selects as one of the primary visual identifiers of its brand.
They are first conceptualized, then built or created after much consultation with graphic and marketing professionals.
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Dean Halverson recently read that full-time college students study 20 hours each week. She decides to do a study at her university to see if there is evidence that students study an average of less than 20 hours each week. A random sample of 33 students were asked to keep a diary of their activities over a period of several weeks. It was found that he average number of hours that the 33 students studied each week was 17. 7 hours. The sample standard deviation of 3. 9 hours. Find the p -value. The p -value should be rounded to 4-decimal places
Using the t-distribution, as we have the standard deviation for the sample, it is found that the p-value is of 0.0009.
What are the hypotheses tested?At the null hypothesis, it is tested if the students study 20 hours, that is:
[tex]H_0: \mu = 20[/tex].
At the alternative hypothesis, it is tested if they study less than 20 hours, that is:
[tex]H_1: \mu < 20[/tex].
What is the test statistic?The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.In this problem, the values of the parameters are given as:
[tex]\overline{x} = 17.7, \mu = 20, s = 3.9, n = 33[/tex].
Hence, the value of the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{17.7 - 20}{\frac{3.9}{\sqrt{33}}}[/tex]
[tex]t = -3.39[/tex]
What is the p-value?Using a t-distribution calculator, considering a left-tailed test, as we are testing if the mean is less than value, the p-value is of 0.0009.
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Solve for x if 2(5x + 2)^2 = 48
This figure represents the base of an fish tank that is 6 inches high.
What is the volume of the fish tank?
390 in³
330 in³
270 in³
240 in³
Answer:
270
Step-by-step explanation:
5 x 7 x 6= 210
2 x 5 x 6= 60
210 + 60= 270
The required volume of the fish tank is 240 cubic inches. option D is correct.
What is volume?Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
Here,
The requried volume of the figure is given as,
Volume = height [area of the plot]
Since the area of the plot is given as,
area = area of the left rectangle + area of the right triangle.
area = 5 × 7 + 1/2 × [12-7]×[5-3]
area = 35 + 5
area = 40 square inches.
Volume = 6 [40]
Volume = 240 in³
Thus, the required volume of the fish tank is 240 cubic inches. option D is correct.
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What is the value of 6(2b-4) when b=5?
Answer:
Step-by-step explanation:
What is the value of 6(2b-4) when b =5 2. The value of is 36. Step-by-step explanation: Given expression: To find the value of at b= 5, we need to substitute the b=5 in the expression, we get.
can i have brainly please :) thanks bro
Answer: 36
Step-by-step explanation:
please help me answer the question in the image
Answer:
2x/x+2
Step-by-step explanation:
Factor out 2x in the numerator
Then you get: 2x(x+4)
Factor the denominator
Two numbers that multiply to 8 and add to 6(2 and 4)
So you get: (x+2)(x+4)
Now you have: (2x(x+4))/(x+2)(x+4)
Simplify by cancelling the x+4
2x/x+2
Hey there!
Answer: [tex] \Rightarrow \boxed {\sf{\frac{2x}{(x+2)}}}[/tex]
Solving steps:-
[tex] \rightarrow\sf{\frac{ {2x}^{2} + 8x}{ {x}^{2} + 6x + 8} }[/tex]
[tex] \rightarrow\sf{\frac{ 2x(x + 4)}{ {x}^{2} + 4x +2x + 8} }[/tex]
[tex] \rightarrow\sf{\frac{ 2x(x + 4)}{ x (x + 4) +2(x + 4)} }[/tex]
[tex] \rightarrow\sf{\frac{ 2x\sout{(x + 4)}}{ \sout{(x + 4)} (x + 2)} }[/tex]
[tex] \rightarrow\sf{\frac{ 2x}{ (x + 2)} }[/tex]
~Done~
If both zeroes of quadratic polynomial (k+2)x^2-(k-2)x-5 are equal in magnitude but opposite in sign find k
Answer:
k=2
Step-by-step explanation:
[tex](k + 2) {}^{2} - (k - 2)x - 5 = 0[/tex]
If we have two zeroes that are equal in size, but different signs then we have a different of squares,
[tex](a + b)(a - b) = {a}^{2} - b {}^{2} [/tex]
So in order to do this we must make the middle term, x 0 so
[tex]k - 2 = 0[/tex]
[tex]k = 2[/tex]
please help it’s for my homework
Answer:
1st option
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - [tex]\frac{4}{5}[/tex] , then
y = - [tex]\frac{4}{5}[/tex] x + c
to find c substitute (5, 1 ) into the equation
1 = - 4 + c ⇒ c = 1 + 4 = 5
y = - [tex]\frac{4}{5}[/tex] x + 5 ( multiply through by 5 to clear the fraction )
5y = - 4x + 25 ( add 4x to both sides )
4x + 5y = 25 ← in standard form
What is the value of x? If necessary express your answer in simplest radical form.
A. 18
B. 20
C.4✔️2
D. 4✔️3
Answer:
B, 20
Step-by-step explanation:
The Pythagorean Theorem states that the two shortest lengths in a right triangle (in our case, 12 and 16), is equal to the longest length in a right triangle (c). So,
a²+b²=c²
Substitute 12 and 16 for a and b, our side lengths
12²+16²=c²
144+256=400
400=c²
Square root both c and 400, which gives us...
20=c
So, the value of x is 20.
Use the diagram to find the distances. Then write the distances to complete the equations.
Triangle P Q R in a coordinate plane. Point P is 1, 2. Point Q is sixteen, ten. Point R is twenty-two, 2. Point S is between P and R, at sixteen, 2. A vertical line segment connects points S and Q.
(A) QS =
(B) PS =
(C) SR =
(D) PQ =
(E) QR =
Answer:
(A) QS = 8
(B) PS = 15
(C) SR = 6
(D) PQ = 17
(E) QR = 10
Step-by-step explanation:
i did it and got it correct! :D
All the distances are;
(A) QS = 8
(B) PS = 15
(C) SR = 6
(D) PQ = 17
(E) QR = 10
What is the distance between two points?The length of the line segment bridging two points on a plane is known as the distance between the points.
The formula to find the distance between the two points is usually given by d=√{(x₂-x₁)² + (y₂-y₁)²}
Given:
The three points P(1,2), Q(16,10), and R(22,2) are on the coordinate plane.
To find the lengths of the different line segments in the given figure, we can use the distance formula:
Distance = √[(x2 - x1)² + (y2 - y1)²]
(A) To find the length of QS, we need to find the difference between the y-coordinates of Q and S:
QS = |10 - 2| = 8
Therefore, QS has a length of 8 units.
(B) To find the length of PS, we need to find the difference between the x-coordinates of P and S:
PS = |16 - 1| = 15
Therefore, PS has a length of 15 units.
(C) To find the length of SR, we need to find the difference between the x-coordinates of S and R:
SR = |22 - 16| = 6
Therefore, SR has a length of 6 units.
(D) To find the length of PQ, we need to find the difference between the x-coordinates of P and Q:
PQ = √[1 - 16)² + (2 - 10)²]
Therefore, PQ has a length of 17 units.
(E) To find the length of QR, we need to use the distance formula:
QR = √[(22 - 16)² + (2 - 10)²]
= √[36 + 64]
= √100
= 10
Therefore, QR has a length of 10 units.
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Use the explicit rule to find a12. an=-2n+8
The explicit rule formula an = -2n + 8 is an arithmetic progression
The value of a11 is -14
How to evaluate the explicit rule?The explicit rule formula is given as:
an = -2n + 8
Substitute 11 for n to calculate a11
a11 = -2 * 11 + 8
Evaluate the product
a11 = -22 + 8
Evaluate the sum
a11 = -14
Hence, the value of a11 is -14
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Isolate the variable to find the solution of the equation. 6. 2w = 18. 6 w = 3 w = 12. 4 w = 24. 8 w = 115. 32.
An equation is formed of two equal expressions. The solution of the equation is w=3.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
In order to solve the equation, we need to isolate the variable in the following manner, therefore, the solution of the equation can be written as,
[tex]6.2w=18.6[/tex]
Divide both sides of the equation by 6.2,
[tex]6.2w=18.6\\\\\dfrac{6.2w}{6.2}=\dfrac{18.6}{6.2}\\\\w = 3[/tex]
Hence, the solution of the equation is w=3.
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why are the cars values modeled by exponential functions and not linear function?
NEED HELP ASAP!!! GIVING BRAINLIEST+30 POINTS FOR FASTEST, BEST ANSWER FOR THESE TWO QUESTIONS!!!!!
Solve nine times two thirds.
Leave your answer as an improper fraction.
eleven twenty sevenths
eighteen twenty sevenths
eleven thirds
eighteen thirds
eighteen thirds
two thirds refers to : [tex]\sf \sf \dfrac{2}{3}[/tex]
[tex]\sf \rightarrow 9 * \dfrac{2}{3}[/tex]
[tex]\sf \rightarrow \dfrac{9*2}{3}[/tex]
[tex]\sf \rightarrow \dfrac{18}{3}[/tex] [ also refereed as eighteen thirds ]
Answer:
[tex]6\\six~is~2/3~of~9\\this~can~also~be~looked~at~as\\2 * 3 = 6\\[/tex]
↓ Second problem
[tex]11/27\\18/27\\11/3\\18/3[/tex]
Hope it helps, be great!
Find the value of x. Round to the nearest tenth.
I’m going to Mcshoot myself pls help
Answer:
x = 10.8
Explanation:
[tex]\sf \sf cos(x)= \dfrac{adjacent}{hypotensue}[/tex]
using cosine rule:
[tex]\rightarrow \sf cos(26)= \dfrac{x}{12}[/tex]
[tex]\rightarrow \sf x = cos(26) *12[/tex]
[tex]\rightarrow \sf x =10.8[/tex]
Answer:
The answer is rounded 10.8
Step-by-step explanation:
Cosine is the adjacent side over the hypotenuse, or a/h. So, cos 26=x/12. To solve for x, isolation of the variable is necessary. If both sides are multiplied by 12, the equation becomes 12 (cos 26)=x. The cosine of 26 is 0.8988, which multiplied by 12 is 10.8.
Hope this helps!
Benito made a small pitcher of fruit punch. He mixed together lemonade and cherry juice. Use the picture to find the amount of juice Benito made. A 9 liters В 100 milliliters C 900 milliliters D2 liters 900 milliliters
The amount of juice by Benito is an illustration of volumes
The amount of juice made is 900 milliliters
How to determine the amount of juice made?The question is incomplete, as the figure and the dimensions are not given.
So, I will give a general solution
Assume the following parameters
Shape of the punch = CylinderRadius = 4Height = 18The amount of juice would be:
V = πr^2h
This gives
V = 3.14 * 4^2 * 18
Evaluate
V = 904.32
Approximate
V = 900
Hence, the amount of juice made is 900 milliliters
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NEED HELP! I JUST NEED HELP ON 31 PLEASSEE HELP
Answer:
A
Step-by-step explanation:
the quartiles are illustrated as 55 and 59. The average is 57.5 so 58? These are the key points on this type of graph.
The diameter of a cylindrical construction pipe is7ft. If the pipe is 36ft long, what is its volume?
Use the value 3.14 for, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
Question:
The diameter of a construction pipe is 7ft. If the pipe is 35ft long, what is the volume. (Use 3.14 for pie and round your answer to the nearest cubic foot.)
Answer: V=pir^2h V=3.14*3.5^2*35 V=1346 cu ft
Not fully sure....
But it should be right...
use the muliplier method to increase 88 pound by 14% show your working
Answer:
100.32
Step-by-step explanation:
Since the question is asking to INCREASE, you want to multiply 88 by 1.14
This is because a percent is a number multiplied by 100 (For example 0.1 is 10%)
Whenever you want to increase by a percent, you add 100% to the number.
So:
88 * 1.14 =
100.32
calculate the perimeter of a rectangle that is 5.5 c by 3.5 cm?
P = 2 x (5,5 + 3,5) = 18 cm
P = is the circumference of the figure
Answer:
the answer should be 18 cm
you can either do 2 × (length + width)
2 × (5.5 + 3.5)
2 × 9 = 18
or
5.5 + 5.5 = 11
3.5 + 3.5 = 7
11 + 7 = 18
either way it's 18, I hope this helps
A car used 1/81 of a gallon of gas to drive 1/4 of a mile. At this rate, how many miles can the car travel using 1 gallon of gas? ??????????
Step-by-step explanation:
1/81 gallon for 1/4 mile.
what do I need to multiply 1/81 with to get 1 gallon ?
it is simple, right ? i need to multiply it by 81 to get 1 gallon.
in order to keep the relationship (ratio) unchanged, I need to multiply the other part (1/4 mile) with the same factor :
1/4 × 81 = 81/4 = 80/4 + 1/4 = 20 1/4 miles
so, at this rate, that car can travel 20 1/4 miles using 1 gallon of gas.
6 workers can build a wall in 30 days. If after 6 days 3 more workers join, find the number of days to build the same wall?
The wall can be built in 22 days by 6 workers in first 6 days and 9 workers in the rest of time.
How to use inverse proportionality to determine building time of a wallIn this question we must use the definition of inverse proportionality, in which the number of workers ([tex]n[/tex]), no unit, is inversely proportional to the building time ([tex]t[/tex]), in days.
According to the statement, 6 workers spent 6 days building a wall and there are 24 days left for completion, but 3 more workers entered to reduce building time, which can be represented by the following expression:
[tex]x = 24\,days \times \frac{6}{9}[/tex]
[tex]x = 16\,days[/tex]
In this scenario, the wall can be built in 22 days. [tex]\blacksquare[/tex]
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Helen wrote and solved the equation.
x minus 17 = 56. x minus 17 + 17 = 56 minus 17. x = 39.
What was Helen’s error?
Helen only needed to add 17 to the left side of the equation.
Helen should have added 17 to both sides of the equation.
Helen’s work is correct.
Helen made a subtraction error when subtracting 17 from 56.
Answer:
x-17=56
x-17+17=56+17
x=56+17
x=73
Step-by-step explanation:
Do mark BRAINLIEST
Answer:
d
Step-by-step explanation:
3/4 plus 4/5 subtract 7/10
Hey There! Happy to Help! Your answer is below.
Answer:
17/20 = 0.85000
Step 1:
Simplify 7/10⇒ (3/4 + 4/5) - 7/10
Step 2:
Simplify 4/5⇒ (3/4 + 4/5) - 7/10
Step 3:
Simplify 3/4⇒(3/4 + 4/5) - 7/10
Step 4:
Calculating the Least Common Multiple⇒ Find the Least Common Multiple
The left denominator is : 4 The right denominator is : 5Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
2 2 0 2
5 0 1 1
Product of all
Prime Factors 4 5 20
Least Common Multiple:
20
Calculating Multipliers⇒ Calculate multipliers for the two fractions
⇒ Denote the Least Common Multiple by L.C.M
⇒ Denote the Left Multiplier by Left_M
⇒ Denote the Right Multiplier by Right_M
⇒ Denote the Left Deniminator by L_Deno
⇒ Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 5 Right_M = L.C.M / R_Deno = 4Making Equivalent Fractions⇒ Rewrite the two fractions into equivalent fractions
⇒ Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. • L. Num. 3 • 5
----------------------------- = ------------
L.C.M 20
R. Mult. • R. Num. 4 • 4
----------------------------- = -------
L.C.M 20
Adding fractions that have a common denominatorAdding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
3 • 5 + 4 • 4 31
------------------ = ---
20 20
Equation at the end of step 4:
31 7
---- - ----
20 10
Step 5:
Calculating the Least Common Multiple :Find the Least Common Multiple
The left denominator is : 20
The right denominator is : 10
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
2 2 1 2
5 1 1 1
Product of all
Prime Factors 20 10 20
Least Common Multiple:
20
Calculating Multipliers :
Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 1
Right_M = L.C.M / R_Deno = 2
Making Equivalent Fractions :
Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. 31
------------------------- = ----
L.C.M 20
R. Mult. • R. Num. 7 • 2
---------------------------- = -----
L.C.M 20
Adding fractions that have a common denominator :
Adding up the two equivalent fractions
31 - (7 • 2) 17'
-------------- = ---
20 20
17
—— = 0.85000
20
1. liola drives 130 m up a hill that has a slope of 7°. what horizontal distance, to the nearest hundredth of a
meter, has she covered?
o 129. 03 m
o 15. 84 m
o 15. 96 m
o 130. 97 m
The horizontal distance to the nearest hundredth of a meter, that Liola covered is 129.03 m (option A)
How to determine the horizontal distance?The following data were obtained from the question:
Hypotenuse = 130 mAngle (θ) = 7°Horizontal distance = Adjacent =?The horizontal distance Liola covered as she drives 130 m up the hill can be obtained as follow:
Cos θ = Adjacent / Hypotenuse
Cos 7 = Horizontal distance / 130
Cross multiply
Horizontal distance = 130 × Cos 7
= 130 × 0.9925
= 129.03 m
Thus, the horizontal distance Liola covered is 129.03 m (option A)
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