Answer: D. He made a mistake in his calculations when substituting the ordered pair into the equation 5x -2y =6 and simplifying.
Step-by-step explanation: I got the answer correct on a test. Hope this helps!
Use the drop-down menus to identify the key values of the box plot. The median is . The minimum is . The maximum is . The lower quartile (Q1) is . The upper quartile (Q3) is .
Answer:
The median is - C
The minimum is - A
The maximum is - E
The lower quartile (Q1) is - B
The upper quartile (Q3) is - D
The median is C, the minimum is A, the maximum is E, the lower quartile (Q1) is B and the upper quartile (Q3) is D.
What is median?The value that divides the mathematical numbers or expressions in half is known as the median. The middle data point is known as the median value. Then, organize the data points in ascending order before calculating the median.
As per the given data, whiskers range from A to E.
The middle point of whisker is C.
Hence, the median is given by C.
And the whisker ranges to maximum E.
And range starts from A.
So the minimum is A.
Quartiles are three values that split sorted data into four parts, each with an equal number of observations.
The lower quartile is B and upper quartile is D.
Therefore, the answers of the median is C, the minimum is A, the maximum is E, the lower quartile (Q1) is B and the upper quartile (Q3) is D.
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5. The shaded area is 327, find r.
Answer: 10.2
Step-by-step explanation:
Area of a circle is
A= pixr^2
327= 3.14r^2
Divide by 3.14
= 104.14
Get the sq rat of 104.14
= 10.2
Determine any data values that are missing from the table, assuming that the data represent a linear function.
Answer:
D
Step-by-step explanation:
Kevin is going to purchase sod for his backyard (see diagram below). How many square feet of sod will Kevin need?
Answer:
450 square feet
Step-by-step explanation:
Think of the shape as a complete rectangular
The area of the rectangular shape would be 25×30 = 750 square feet
Now find the area of the missing space and subtract it from 750
it would be 15×20 = 300 square feet
750 - 300 = 450 square feet
In a city school, 70% of students have blue eyes, 45% have dark hair, and 30% have blue eyes and dark hair. What is the probability (rounded to the nearest whole percent) that a randomly selected student has dark hair, given that the student has blue eyes
Answer:
The probability that a randomly selected student has dark hair, given that the student has blue eyes is 43%.
Step-by-step explanation:
Conditional probability:
Let A and B any two events connected to a given random experiment E. The conditional probability of the event A on the hypothesis that the event B has occurred, denoted by P(A|B), is defined as
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]
Given that,
In a city school, 70% of students have blue eyes, 45% have dark eyes and 30% have blue eyes and dark hair.
A= students have blue eyes
B= Students have dark hair.
P(A)= 70% [tex]=\frac{70}{100}[/tex] [tex]=\frac7{10}[/tex]
P(B)=45% [tex]=\frac{45}{100}[/tex] [tex]=\frac9{20}[/tex]
P(A∩B)=30%[tex]=\frac{30}{100}[/tex] [tex]=\frac3{10}[/tex]
∴P(B|A)
[tex]=\frac{P(A\cap B)}{P(A)}[/tex]
[tex]=\frac{0.3}{0.7}[/tex]
[tex]=\frac37[/tex]
=0.429
=0.429×100 %
≈43%
The probability that a randomly selected student has dark hair, given that the student has blue eyes is 43%.
A spotlight on the ground shines a beam of light to the top of a tree that is 12 m tall. The beam of light makes an angle of 40° with the ground. What is the distance from the spotlight to the base of the tree, rounded to the nearest meter? 10 m 14 m 16 m 19 m A right triangle. The perpendicular is labeled 12 meters. The angle made between the base and the hypotenuse is labeled 40 degrees. The angle made between the base and the perpendicular is marked as a right angle.
Answer:
B.14 m
Step-by-step explanation:
We are given that
Height of tree=12 m
[tex]\theta=40^{\circ}[/tex]
We have to find the distance between the spotlight and the base of tree.
In triangle ABC
AB=12 m
[tex]tan\theta=\frac{perpendicular\;side}{base}[/tex]
Using the formula
[tex]tan 40=\frac{AB}{BC}=\frac{12}{BC}[/tex]
[tex]BC=\frac{12}{tan 40}=14.3\approx 14 m[/tex]
Hence, option B is true.
Answer:
14m
Step-by-step explanation:
I took the test
In a probability experiment, Eric flipped a coin 45 times. The coin landed on heads 30 times. What is the ratio of heads to tails in this experiment?
Answer:
30:15 (simplified is 2:1)
Step-by-step explanation:
Out of the 45 times Eric flipped a coin, 30 of them landed on heads. Tails is the the only other probable occurance, so since we know that there are 15 trials left, this means that the coin landed on tails 15 times. This would give a heads to tails ratio of 30:15, but the simplified ratio would be 2:1, because that's the smallest it can be divided evenly.
45-30=15
30:15=2:1
3. Determine whether each event is certain to occur, just as likely to occur as not to occur, or
impossible to occur. Then write the probability
a. A coin is flipped and the coin lands heads up. Express the probability as a fraction
b. Tuesday follows Monday in the week. Express the probability as a percent.
c. You have only white shirts in your closet. Express the probability of reaching into your
closet and choosing a red shirt as a fraction,
d. A box contains 2 green balls and 2 yellow balls. You reach into the box and grab a
yellow ball. Express the probability as a decimal
Answer:
A) 1/2 - there are 2 sides - just as likely to occur as not to occur
B) 0% - it's never going to happen (impossible)
C) 0/0 - it's never going to happen (impossible)
D) 1/2 simplified from 2/4 - that was 2 out of the four balls. - just as likely to occur as not to occur
A investor has an account with stock from two different companies. Last year her stocking company A was worth $4600 in her stocking company B was worth $1000. Stocking company a has decreased 25% since last year in stock and Company B has decreased 22%. What was the total percentage decrease in the investor stock account round your answer to the nearest 10
Answer: 24.5%
Step-by-step explanation:
Last year her stock in company A was worth $4600. If her Stock in company A has decreased by 25% since last year in stock, then the amount by which it decreased is
25/100 × 4600 = $1150
The present worth is
4600 - 1150 = $3450
Also, her stock in company B was worth $1000. If her Stock in company B has decreased by 22% since last year in stock, then the amount by which it decreased is
22/100 × 1000 = $220
The present worth is
1000 - 220 = $780
The total worth of both stocks last year was
4600 + 1000 = $5600
The total worth of both stocks this year was
3450 + 780 = $4230
The amount by which it decreased is
5600 - 4230 = 1370
the total percentage decrease in the investor stock account is
1370/5600 × 100 = 24.5%
A manufacturer of cell phone screens is concerned because 12 percent of the screens manufactured using a previous process were rejected at the final inspection and could not be sold. A new process is introduced that is intended to reduce the proportion of rejected screens. After the process has been in place for several months a random sample of 100 screens is selected and inspection. Of the 100 screens 6 are rejected. What are the appropriate hypotheses to investigate whether the new process reduces the population proportion of screens that will be rejected
In hypothesis testing for this scenario, the null hypothesis (H-0) is that the proportion of rejected screens remains 12 percent (H-0: p = 0.12). The alternative hypothesis (Ha) is that the proportion of rejected screens is less than 12 percent (Ha: p < 0.12). A sample is taken and a significance test (such as a z-test for proportion) is conducted to decide if the null hypothesis can be rejected.
Explanation:The question is looking for you to conduct a hypothesis test to investigate whether a new process in manufacturing cell phone screens has led to a reduced proportion of rejected screens. When conducting such a hypothesis test, you'll need to consider a null hypothesis and an alternative hypothesis.
The null hypothesis (H-0) is often the initial claim about a population proportion. In this case, the null hypothesis would be that 12 percent of the screens (0.12) are still being rejected: H-0: p = 0.12.
The alternative hypothesis (Ha) is what you might believe to be true if the null hypothesis is proven to be incorrect. Here, the alternative hypothesis would be that less than 12 percent of screens are being rejected with the new process: Ha: p < 0.12.
To clarify, if the new process is effective, a lower proportion of screens should be rejected. Thus, the hypotheses to be tested are:
H-0: p = 0.12Ha: p < 0.12Lastly, after selecting the sample, compute the sample proportion. Here a total sample size of 100 screens with only 6 being rejected means the sample proportion (p) = 6/100 = 0.06.
From here, you would proceed to conduct a significance test (possibly a z test for proportion) and determine a p-value to make a decision regarding the null hypothesis.
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Metal Fabrication If an open box is made from a tin sheet 10 in. square by cutting out identical squares from each corner and bending up the resulting flaps, determine the dimensions of the largest box that can be made. (Round your answers to two decimal places.)
Answer:
ength (l) : (10-2*5/3) = 20/3 width(w): (10 - 2*5/3) = 20/3 height(h): 5/3Step-by-step explanation:
Let x is the side of identical squares
By cutting out identical squares from each corner and bending up the resulting flaps, the dimension are:
length (l) : (10-2x)width(w): (10-2x)height(h): xThe volume will be:
V = (10-2x) (10-2x) x
<=> V = (10x-2[tex]x^{2}[/tex]) (10-2x)
<=> V = 100x -20[tex]x^{2}[/tex] - 20[tex]x^{2}[/tex] + 4[tex]x^{3}[/tex]
<=> V = 4[tex]x^{3}[/tex] - 40[tex]x^{2}[/tex] + 100x
To determine the dimensions of the largest box that can be made, we need to use the derivative and and set it to zero for the maximum volume
dV/dx = 12[tex]x^{2}[/tex] -80x + 100
<=> 12[tex]x^{2}[/tex] -80x + 100 =0
<=> x = 5 or x= 5/3
You know 'x' cannot be 5 , because if we cut 5 inch squares out of the original square, the length and the width will be 0. So we take x = 5/3
=>
length (l) : (10-2*5/3) = 20/3 width(w): (10 - 2*5/3) = 20/3 height(h): 5/3To determine the dimensions of the largest box that can be made from a tin sheet, we need to find the side length of the square that will be cut out from each corner of the tin sheet. The dimensions of the largest box that can be made are approximately 6.67 inches by 6.67 inches by 1.67 inches.
Explanation:To determine the dimensions of the largest box that can be made from a tin sheet, we need to find the side length of the square that will be cut out from each corner of the tin sheet. Let's assume the side length of the square to be x inches. The length and width of the resulting box will be 10 - 2x inches and 10 - 2x inches, respectively. The height of the box will be x inches. To find the dimensions of the largest box, we need to find the value of x that maximizes the volume of the box.
The volume of the box is given by V = (10 - 2x)(10 - 2x)(x). We can write this as V = 4x^3 - 40x^2 + 100x. To find the value of x that maximizes the volume, we can take the derivative of V with respect to x and set it equal to 0. Differentiating V, we get dV/dx = 12x^2 - 80x + 100. Setting this equal to 0 and solving for x, we find x = 1.67 inches (rounded to two decimal places). Therefore, the dimensions of the largest box that can be made are approximately 6.67 inches by 6.67 inches by 1.67 inches.
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1. Find g(x), where g(x) is the translation 7 units up of f(x) = x.
2. Find g(x), where g(x) is the translation 5 units left of f(x) = x2.
3. Find g(x), where g(x) is the translation 3 units right and 4 units up of f(x) = x2.
4. Find g(x), where g(x) is the translation 1 unit left and 5 units down of f(x) = |x|.
Translations of functions involve adjusting the graph horizontally by adding or subtracting values within the function's argument, and vertically by adding or subtracting values directly to the function. For the given functions, respective translations have resulted in g(x) expressions that have been adjusted according to these rules.
Explanation:To answer the student's mathematics questions about translations of functions, we will apply the concepts learned from algebra to transform each given function accordingly.
Translation 7 units up of f(x) = x results in g(x) = x + 7.For the translation 5 units left of f(x) = x2, we use g(x) = (x + 5)2.The translation 3 units right and 4 units up of f(x) = x2 gives us g(x) = (x - 3)2 + 4.Translation 1 unit left and 5 units down of f(x) = |x| leads to g(x) = |x + 1| - 5.In these function transformations, we've made use of horizontal and vertical translations, where adding or subtracting values within the function argument adjusts the graph horizontally, and adding or subtracting values outside the function adjusts it vertically.
The score of golfers for a particular course follows a normal distribution that has a mean of 73 and a standard deviation of 3. Suppose a golfer played the course today. Find the probability that her score is at least 74.
Answer:
0.3694
Step-by-step explanation:
In this question, we are asked to calculate the probability that a golfer scored at least 74 if she played on a particular day.
Given that ,
mean = µ = 73
standard deviation = σ = 3
P(x > 74) = 1 - P(x<74 )
= 1 - P[(x -µ) / σ < (74 -73) /3 ]
= 1 - P(z <0.3333 )
Using z table
= 1 - 0.6305
= 0.3694
probability= 0.3694
To find the probability of a golfer scoring at least 74 on a course with a mean score of 73 and a standard deviation of 3, we calculate the z-score for 74, find the corresponding probability in the z-table, and subtract this from 1 to get the upper tail probability. The probability is approximately 37%.
Explanation:The score of golfers for a particular course follows a normal distribution that has a mean of 73 and a standard deviation of 3. We want to find the probability that a golfer scores at least 74. This is a question of statistics and specifically involves the concept of the normal distribution and calculating z-scores.
Firstly, we need to calculate the z-score for the score of 74. The z-score is calculated as (X-μ)/σ, where X is the score we are interested, μ is the mean, and σ is the standard deviation. Substituting the given values, (74 - 73) / 3 gives a z-score of approximately 0.33.
Then, to find the probability that a score is at least 74, we need to find the proportion of data to the right of this z-score in a standard normal distribution. This is known as the 'upper tail'. We subtract the z-score from 1 because the total probability under the normal curve is 1. If we look up 0.33 in the z-table, we get a value of 0.6293. Subtracting this value from 1 gives us 0.3707.
Therefore, the probability that a golfer scores at least 74 on this course is approximately 0.37 or 37%.
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James has an ice cube tray that makes ice in the shape of spheres rather than cubes. Each sphere of ice has a radius of 22 2 2 cm. One tray makes 66 6 6 spheres.
Answer:
James has an ice cube tray that makes ice in the shape of spheres rather than cubes. Each sphere of ice has a radius of 2 cm. One tray makes 6 spheres.What is the total volume of ice the tray can make at one time?
Total volume of the tray James have = 201.06 cm^3
Step-by-step explanation:
Given:
Radius of the spherical ice cube = 2 cm
No. of spheres in the ice cube = 6
We have to find the total volume of the ice tray that can make at one time.
Let the total volume be "V".
Formula to be used:
Volume of sphere = [tex]\frac{4\pi r^3 }{3}[/tex] cubic unit.
Total volume = [tex]n\times \frac{4\pi r^3 }{3}[/tex] cubic unit.
So,
Total volume of the ice tray (V) :
⇒ [tex]V=n\times \frac{4\pi r^3 }{3}[/tex]
⇒ Plugging n = 6 and r = 2
⇒ [tex]V=6\times \frac{4\pi (2)^3 }{3}[/tex]
⇒ [tex]V=6\times \frac{4\pi (8) }{3}[/tex]
⇒ [tex]V=6\times \frac{32\pi }{3}[/tex]
⇒ [tex]V=\frac{32\times 6\pi }{3}[/tex]
⇒ [tex]V=32\times 2\pi[/tex]
⇒ [tex]V=201.06\ cm^3[/tex]
So,
The total volume of ice the tray can make at one time = 201.06 cm^3
which function represents a parabola?
Answer:
b. g(x) only
Step-by-step explanation:
Please can you help me with this question
what is the value of x angel in a pentagon if each interior angel is 117 , 100 , 105 and 115
Answer:
Step-by-step explanation:
Well first you have to find what the total amount of all the interior angles. In Oder to do that you count how many sides the shape has the subtract two from that number. Take the number you get from that and multiply it by 180. That number is total amount of all the interior angles including the angle x. Take the angles you do know and add them together. Take the number you get from that and subtract it from the total amount of all interior angles. The number you get from that is your answer. The answer to this problem is 103.
The value of angle x in a pentagon is 103 degrees.
Explanation:In a pentagon, the sum of the interior angles is always 540 degrees. To find the value of angle x, we can subtract the given angles from 540 degrees and then divide by the number of missing angles.
Given angles: 117, 100, 105, 115
Sum of given angles: 117 + 100 + 105 + 115 = 437 degrees
Sum of missing angles: 540 - 437 = 103 degrees
Since there is only one missing angle x in the pentagon, the value of x must be 103 degrees.
A scientist estimated that a mixture would need 5 millimeters of a chemical to balance. The actual amount d was 7 millimeters. What was the percent error of the scientists estimation?
Answer:
29%
Step-by-step explanation:
If 7 is 100% correct then 5 would only be a portion of it
So you need to divide 5 by 7
So 5 divided by 7 is .714 or .71
this means the error was 29%
A parking lot in the shape of a trapezoid has an area of 12,0521 square meters the length of the other base is 108.6 meters. What is the width of the parking lot
Please consider the complete question.
A parking lot in the shape of a trapezoid has an area of 12,052.1 square meters. The length of one base is 82.4 meters and the length of the base is 108.6 meters. What is the width of the parking lot
We will use area of trapezoid to formula to solve our given problem.
[tex]\text{Area of trapezoid}=\frac{1}{2}(a+b)\times h[/tex], where
a and b represents parallel sides of trapezoid,
h = height of trapezoid.
Width of the trapezoid will be equal to height.
Upon substituting our given values in above formula, we will get:
[tex]12,052.1=\frac{1}{2}(82.4+108.6)\times h[/tex]
[tex]12,052.1\cdot 2=2\cdot \frac{1}{2}(82.4+108.6)\times h[/tex]
[tex]24104.2=(191)\times h[/tex]
[tex]\frac{24104.2}{191}=\frac{(191)\times h}{191}[/tex]
[tex]126.2=h[/tex]
Therefore, the width of the parking lot is 126.2 meters.
Find the 3rd term in the sequence
Step-by-step explanation:
a(n) = a ( n - 1) - 17
a(1) = 20
a(2) = a ( 2 - 1) - 17
= a (1) - 17
= 20 - 17
= 3
Now
a(3) = a ( 3 - 1 ) - 17
= a (2) - 17
= 3 - 17
= - 14
Hope it will help you.
Drag and drop a statement or reason to each box to complete the proof. Given: parallelogram EFGH Prove: EG¯¯¯¯¯ bisects HF¯¯¯¯¯¯ and HF¯¯¯¯¯¯ bisects EG¯¯¯¯¯ . Parallelogram E F G H with diagonals E G and H F intersecting at point K. Statement Reason parallelogram EFGH Given EF¯¯¯¯¯∥HG¯¯¯¯¯¯ When two parallel lines are cut by a transversal, alternate interior angles are congruent. The opposite sides of a parallelogram are congruent. △EKF≅△GKH ASA Congruence Postulate CPCTC EG¯¯¯¯¯ bisects HF¯¯¯¯¯¯ and HF¯¯¯¯¯¯ bisects EG¯¯¯¯¯ .
By proving triangle HKE and triangle GKF congruent, it is proved EG bisects HF and HF bisects EG.
Given that, parallelogram EFGH.
Prove that, EG bisects HF and HF bisects EG.
Parallelogram EFGH with diagonals EG and HF intersecting at point K.
Proof:
Consider, ΔHKE and ΔGKF
∠HKE=∠GKF (Vertically opposite angles are equal)
∠FHE=∠GFH ( Alternate angles between the parallel line EF and HG)
∠GEH=∠FGE ( Alternate angles between the parallel line EF and HG)
By AAA congruency, ΔHKE and ΔGKF are congruent
By CPCT,
KE=GK
JF=HK
So, EG bisects HF and HF bisects EG.
Hence, proved.
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Final answer:
To prove that EG¯¯¯¯¯ bisects HF¯¯¯¯¯¯ and HF¯¯¯¯¯¯ bisects EG¯¯¯¯¯ in parallelogram EFGH, we can use the statements and reasons provided.
Explanation:
To prove that EG¯¯¯¯¯ bisects HF¯¯¯¯¯¯ and HF¯¯¯¯¯¯ bisects EG¯¯¯¯¯ in parallelogram EFGH with diagonals EG and HF intersecting at point K, we can use the following statements and reasons:
Statement: parallelogram EFGHWhat is 3x5 , answer is
Answer:15
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
5=1
10=2
15=3
She paid £40 altogether. She paid £3.25 for each pineapple, £2.75 for each melon 50p for each grapefruit. She bought the same number of pineapple as she did melon. How many of each did mrs Gillespie buy
Answer:
6 pineapple, 6 melons, 8 grapefruits
Step-by-step explanation:
3.25P + 2.75M + 0.5G = 40
P = M
6M + 0.5G = 40
Let M = 6
6(6) + 0.5G = 40
0.5G = 4
G = 8
P = 6
M = 6
G = 8
What is the midpoint of ?
A: (2p – 2t, r)
B: (t + p, r)
C: (p, r)
D: (p – t, r)
The midpoint of a line segment is given by the formula ((x₁ + x₂) / 2, (y₁ + y₂) / 2). After applying this formula to the given options, the correct midpoint is (p, r).
Explanation:The midpoint of a line segment with coordinates (x₁, y₁) and (x₂, y₂) is given by the formula:
Midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
Applying this formula to the given options:
A: Midpoint = (2p - 2t, r)B: Midpoint = (t + p, r)C: Midpoint = (p, r)D: Midpoint = (p - t, r)After substituting the values, we find that the correct answer is Option C: (p, r).
4x + 3y = 6
-4x + 2y = 14
solve the system of equations
Answer:
I believe it is
x = -3/2 (-1.5)
y = 4
Answer:
A) 4x + 3y = 6
B) -4x + 2y = 14
Add the equations
5 y = 20
y = 4
Putting y into A)
A) 4x + 3*4 = 6
A) 4x = -6
x = -1.5
Step-by-step explanation:
What are the differences between pyramids and cones?
Answer:
Pyramids are triangular in shape with a sided shape, whereas cones have circular bases that merely adjoin at a point.
Step-by-step explanation:
Answer:
A pyramid is a cone with a polygonal base ;)
the quoient of 36 and 3 is j
Answer:
j = 12
Step-by-step explanation:
Quotient means the answer when you divide the dividend by the divisor.
In this example, we are dividing 36 by 3, so 36 = dividend, 3 = divisor.
36 / 3 = 12. See the attachment if you need extra help on long division!
Answer:
It is 12
Step-by-step explanation:
So first you divide 36 by 3. So 3 goes into 3 once. Now 3 goes into 6 twice so there you have it
Is (1,1) a function?
Answer:
I don't think it is a function
A function is a set of ordered pairs where a x-value is paired with only one y-value.
As long if the x-value (1) is sharing only one y-value then it makes it a function.
A house has increased in value by 38% since it was purchased. If the current value is $621,000 what was the value when it was purchased.
The original value of the house when it was purchased was $450,000.
Let us assume the original value of the house was x. This means that the house has increased by 38% from x to become $621,000.
In order to find the original value therefore, you can use the formula:
Original value + (Original value x Increase) = Current price
x + (38% × x) = 621,000
1.38x = 621,000
x = 621,000 / 1.38
= $450,000
In conclusion, the original value was $450,000.
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Final answer:
The original purchase price of the house was $450,000.
Explanation:
To find the original value of the house before it increased in value, we must first understand that the current value represents 138% of the original value, since the house has increased in value by 38%. This is because the original value is 100%, and the increase is 38%, making the total 138%. Therefore, the equation to find the original purchase price (which we can call 'P') is:
P * 138% = $621,000
We can rewrite this as:
P * 1.38 = $621,000
To solve for P, we divide both sides of the equation by 1.38:
P = $621,000 / 1.38
Now, doing the division:
P = $450,000
So, the house was originally purchased for $450,000 before it increased by 38% to its current value of $621,000.
PLZ HELP ME!
Directions up above the picture
**MATH (Algebra)
Answer:
The answer to your question is t = 1.3 s
Step-by-step explanation:
Data
Equation h(t) = -4.9t² + v₀t + h₀
v₀ = 0 m/s
h₀ = 8 m
t = ?
h = 0 m
Process
1.- Substitute the values in the formula
0 = -4.9t² + 0t + 8
2.- Simplification
0 = -4.9t² + 8
3.- Solve for t
4.9t² = 8
t² = 8/4.9
t² = 1.63
4.- Result
t = 1.27 ≈ 1.3 s