A scatter plot would best display the relationship between the number of hours a student spent studying for several tests and the student's grade on each test.
A scatter plot is a graph that displays the relationship between two continuous variables. In this case, the number of hours a student spent studying is the independent variable, which would be plotted on the x-axis. The student's grade on each test is the dependent variable, which would be plotted on the y-axis. Each data point would represent a single test, with the x-coordinate indicating the number of hours studied for that test and the y-coordinate indicating the grade received.
By using a scatter plot, you can easily identify any patterns or relationships between the number of hours studied and the student's grades on each test. It can also help to identify any outliers or anomalies in the data.
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at noon, a ship leaves a harbor and sails south at 20 knots. four hours later, a second ship leaves the harbor and sails east at 15 knots. when will the ships be 100 nautical miles apart? round to the nearest minute. note that 1 knot = 1 nautical mile per hour.
Rounding to the nearest minute, we get that the ships will be 100 nautical miles apart at 8 hours and 10 minutes after the first ship left the harbor.
What is Pythagorean theorem?
The Pythagorean theorem is a fundamental concept in geometry that relates to the three sides of a right-angled triangle. It states that the square of the length of the hypotenuse (the longest side of the triangle) is equal to the sum of the squares of the lengths of the other two sides. In mathematical terms, it can be expressed as:
[tex]a^2 + b^2 = c^2[/tex]
We can use the Pythagorean theorem to find the distance between the two ships at any given time:
d² = (20t)² + (15(t-4))²
Simplifying this equation, we get:
d² = 400t² + 225(t² - 8t + 16)
d² = 625t² - 1800t + 3600
d = √(625t²- 1800t + 3600)
We want to find the value of t when d = 100 nautical miles, so we can set up the following equation:
100 = √(625t² - 1800t + 3600)
Squaring both sides, we get:
10000 = 625t² - 1800t + 3600
Rearranging, we get:
625t² - 1800t - 6400 = 0
Using the quadratic formula, we get:
t = (1800 ± √(1800² + 46256400)) / (2*625)
t = (1800 ± 3900) / 1250
t = 3.84 or t = 8.16
So the time elapsed for the second ship is:
t2 = t + 4
t2 = 7.84 or t2 = 12.16
We can see that the only solution that works is when t = 8.16 and t2 = 12.16. At that time, the first ship will have sailed for 8.16 hours at 20 knots, or 163.2 nautical miles, and the second ship will have sailed for 8.16 - 4 = 4.16 hours at 15 knots, or 62.4 nautical miles. The distance between the two ships will be:
d = √((163.2)² + (62.4)²) = 174.9 nautical miles
Rounding to the nearest minute, we get that the ships will be 100 nautical miles apart at 8 hours and 10 minutes after the first ship left the harbor.
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a game involves a two-sided coin, as well a six-sided die. to play the game, each player flips the coin once and rolls the die once. what is the number of individual outcomes from flipping and rolling one time? a.) 6 b.) 2 c.) 12 d.) 8
Option C : The number of individual outcomes from flipping and rolling one time is 12.
A permutation is a selection of items from a set where the order of the items does matter. In this case, a permutation would be an ordered pair of a heads or tails outcome from flipping a coin followed by a 1, 2, 3, 4, 5, or 6 outcome from rolling a die.
The number of possible combinations is found by multiplying the number of possible outcomes for each event. In this case, there are two possible outcomes from flipping a coin (heads or tails) and six possible outcomes from rolling a die (1, 2, 3, 4, 5, or 6), so the number of combinations is:
2 (outcomes from coin flip) * 6 (outcomes from die roll) = 12
The number of permutations is equal to the number of combinations because the order of the items in each combination does not matter. So, there are 12 individual outcomes from flipping and rolling one time.
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Suppose that a particular nba player makes of his free throws. assume that late in a basketball game, this player is fouled and is awarded two free throws.a. What is the probability that he will make both free throws? (to decimals) b. What is the probability that he will make at least one free throw? (to decimals) c. What is the probability that he will miss both free throws? (to decimals) d. Late in basketball game; team often intentionally fouls an opposing player in order to stop the game clock: The usual strategy is t0 intentionally foul the other team's worst free-throw shooter: Assume the team' worst free throw shooter makes 58% of his free throws Calculate the probabilities for this player as shown in parts (2), (b), and (c) and show that intentionally fouling this player who makes 58% of his free throws is better strategy than intentionally fouling the player who makes 89% of his free throws. Assume as in parts (a), (b), and (c) that two free throws will be awarded.1. What is the probability that this player will make both throws? (to 4 decimals) 2. What is the probability that will make at least one tlrow? (to decimals) 3. What is the probability that thils player wIll mlss bolhi Urows? (to decimals)"
The probability of both free throws is 0.7921, at least one free throw is 0.9889, missing both free throws is 0.0121. 58% of his free throws is a better strategy as it results in a higher probability of missing at least one free throw.
The probability of making one free throw is 0.89. Therefore, the probability of making both free throws is: 0.89 * 0.89 = 0.7921 (rounded to 2 decimals).
The probability of missing one free throw is 1 - 0.89 = 0.11. Therefore, the probability of making at least one free throw is: 1 - 0.11 * 0.11 = 0.9889 (rounded to 2 decimals).
The probability of missing one free throw is 0.11. Therefore, the probability of missing both free throws is: 0.11 * 0.11 = 0.0121 (rounded to 2 decimals).
For the worst free-throw shooter who makes 58% of his free throws:
The probability of making both free throws is: 0.58 * 0.58 = 0.3364 (rounded to 4 decimals).
The probability of making at least one free throw is: 1 - 0.42 * 0.42 = 0.8236 (rounded to 2 decimals).
The probability of missing both free throws is: 0.42 * 0.42 = 0.1764 (rounded to 4 decimals).
For the player who makes 89% of his free throws:
The probability of making both free throws is: 0.89 * 0.89 = 0.7921 (rounded to 4 decimals).
The probability of making at least one free throw is: 1 - 0.11 * 0.11 = 0.9889 (rounded to 2 decimals).
The probability of missing both free throws is: 0.11 * 0.11 = 0.0121 (rounded to 4 decimals).
Therefore, intentionally fouling the player who makes 58% of his free throws is a better strategy as it results in a higher probability of missing at least one free throw.
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lights of america claims that the life length of one of its light bulbs, the twister 7 years bulb2, is normally distributed with a mean of 10,000 hours and a standard deviation of 1000 hours. lang selects one of these light bulbs at random and places it on accelerated life test. (i) what is the probability that the bulb that lang selects will last exactly 9950 hours? (ii) what is the probability that the bulb that lang selects will last at most 9950 hours? (iii) what is the probability that the bulb that lang selects will last at least 9950 hours? (iv) what is the probability that the bulb that lang selects will last less than 9000 hours or more than 11,500 hours? (v) what is the probability that the bulb that lang selected will last between 9000 hours and 11,000 hours, inclusively? (vi) what lifelength represents the 95th percentile?
(i) The probability that the bulb that lang selects will last exactly 9950 hours is 0.3085.
(ii) The probability that the bulb that lang selects will last at most 9950 hours is 0.5
(iii) The probability that the bulb that lang selects will last at least 9950 hours is 0.6915.
(iv) The probability that the bulb that lang selects will last less than 9000 hours or more than 11,500 hours is 0.0668
(v) The probability that the bulb that lang selected will last between 9000 hours and 11,000 hours, inclusively is 0.6826.
(vi) The life length represents the 95th percentile is 11,645
The lifespan of the Lights of America light bulb is normally distributed, with a mean of 10,000 hours and a standard deviation of 1000 hours. This means that the majority of bulbs will last around 10,000 hours, but there will be some that last longer or shorter than this.
(i) To find the probability that the bulb selected by Lang will last exactly 9950 hours, we need to use the normal distribution formula. We know that the mean is 10,000 hours and the standard deviation is 1000 hours. Using these values, we can calculate the z-score (standardized value) for 9950 hours.
z = (9950 - 10000) / 1000 = -0.5
Using a standard normal distribution table or calculator, we can find the probability of a z-score of -0.5, which is 0.3085. Therefore, the probability that the bulb will last exactly 9950 hours is 0.3085.
(ii) To find the probability that the bulb will last at most 9950 hours, we need to find the area under the normal curve to the left of 9950 hours. We can use the z-score formula to calculate the z-score for 9950 hours as we did in part (i).
z = (9950 - 10000) / 1000 = -0.5
Using a standard normal distribution table or calculator, we can find the probability of a z-score of -0.5, which is 0.3085. However, since we want the probability of the bulb lasting at most 9950 hours, we need to add the area under the normal curve to the left of -0.5, which is 0.3085 + 0.1915 = 0.5. Therefore, the probability that the bulb will last at most 9950 hours is 0.5.
(iii) To find the probability that the bulb will last at least 9950 hours, we need to find the area under the normal curve to the right of 9950 hours. We can use the z-score formula to calculate the z-score for 9950 hours as we did in part (i).
z = (9950 - 10000) / 1000 = -0.5
Using a standard normal distribution table or calculator, we can find the probability of a z-score of -0.5, which is 0.3085. However, since we want the probability of the bulb lasting at least 9950 hours, we need to add the area under the normal curve to the right of -0.5, which is 1 - 0.3085 = 0.6915. Therefore, the probability that the bulb will last at least 9950 hours is 0.6915.
(iv) To find the probability that the bulb will last less than 9000 hours or more than 11,500 hours, we need to find the areas under the normal curve to the left of 9000 hours and to the right of 11,500 hours, and add them together. We can use the z-score formula to calculate the z-scores for 9000 hours and 11,500 hours.
For 11,500 hours: z = (11,500 - 10,000) / 1000 = 1.5
Then the corresponding probability from Z table is written as,
=> 0.0668
(v) To find the probability that the bulb will last between 9000 hours and 11,000 hours, inclusively, we need to find the area under the normal curve between the z-scores for 9000 hours and 11,000 hours. We can use the z-score formula to calculate the z-scores for 9000 hours and 11,000 hours.
For 9000 hours: z = (9000 - 10,000) / 1000 = -1
For 11,000 hours: z = (11,000 - 10,000) / 1000 = 1
Using a standard normal distribution table or calculator, we can find the probability of a z-score of -1 (for 9000 hours), which is 0.1587, and the probability of a z-score of 1 (for 11,000 hours), which is 0.8413. Subtracting the area under the normal curve to the left of -1 from the area under the normal curve to the left of 1, we get the probability of the bulb lasting between 9000 hours and 11,000 hours inclusively, which is 0.8413 - 0.1587 = 0.6826.
(vi) To find the lifelength that represents the 95th percentile, we need to find the z-score that corresponds to the 95th percentile of the normal distribution. We can use a standard normal distribution table or calculator to find this value, which is approximately 1.645.
Using the z-score formula, we can solve for the life length that corresponds to a z-score of 1.645:
1.645 = (x - 10,000) / 1000
Multiplying both sides by 1000 and adding 10,000, we get:
x = 11,645
Therefore, the life length that represents the 95th percentile is 11,645 hours, which means that only 5% of bulbs will last longer than this value.
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A field in the shape of a rectangle has an area of 1/3 square mile. The length of the field is 2/5 mile. What is the width of the field?
If the area of a rectangle 1/3 square mile and length of the field is 2/5 mile then the width of the field is
What is Area of a Rectangle?
The quantity of unit squares that can fit inside a rectangle called its area. In other terms, the area of a rectangle is the area that it occupys. The flat surfaces of laptop monitors, blackboards, painting canvases, etc. are a few instances of rectangular shapes.
Given in the question,
Area of rectangle [tex]= \frac{1}{3} square mile[/tex]
The length of the field [tex]= \frac{2}{5} mile[/tex]
Let breadth be x.
As we know that,
Area of rectangle = [tex]length * breadth[/tex]
Now,
[tex]\frac{1}{3} = \frac{2}{5} *x[/tex]
[tex]x=\frac{1}{3} * \frac{5}{2}[/tex]
[tex]x=\frac{5}{6}[/tex]
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Find X then find angle RB
The value of x is 11 and arc RB = 150°.
What is an angle measure?When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.
We know that,
∠RDB = 1/2(RB - EC)
So, substituting the values,
5x - 10 = 1/2(13x + 7 - 60)
10x - 20 = 13x - 53
3x = 33
x = 11
So, arc RB = 13 x 11 + 7 = 150°.
Hence, arc RB = 150°.
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1/2 of 2/3 = 1/2 of ____ third(s) = ____ third(s)
The product of 1/2 and 2/3 is equivalent to one third
Taking the product of fractions
Fractions are expressions written as a ratio of two integers. For instance a/b is a fraction
Given the expression below
1/2 of 2/3
This can also be written as;
1/2 of 2/3 = 1/2 of two thirds
Simplify
1/2 * 2/3 = 2/6
1/2 of 2/3 = 1/3
Hence the resulting value of the expression is one third
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Write an equivalent expression by combining like terms. 8b - 4b b =5
The equivalent expression for 8b-4b is 4b.
What are like terms?In algebra, like terms are the terms that contain the same variable which is raised to the same power. In this only numerical coefficients may vary.
Given 8b-4b. b=5
We have to combine the like terms to get an equivalent expressions.
Like terms containing variables with same power.
When combining like terms, we have to add or subtract their coefficients.
Coefficients are the numbers which are placed with variable.
Then, 8b-4b=4b.
When b=5⇒4*5=20
Hence, the equivalent expression for 8b-4b is 4b.
Complete question:
Write an equivalent expression by combining the like terms 8b-4b. Find the value of expressions when b=5.
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Monday: P.S. 2- Algebraic Expressions
Problem and Effort:
Simplify the following
expression given the
variables m = 4, n = -3,
and p = -3
√e
m+n²-p
Correct Answer:
Answer:
Therefore, the simplified expression with the given values is √e^16.
Step-by-step explanation:
Given the values of the variables m = 4, n = -3, and p = -3, we can simplify the expression √e^(m + n^2 - p) as follows:
m + n^2 - p = 4 + (-3)^2 - (-3) = 4 + 9 + 3 = 16
So the expression becomes: √e^16 = √e^(m + n^2 - p) = √e^16
Therefore, the simplified expression with the given values is √e^16.
What is 2 1/2 doubled
Answer:
5
Step-by-step explanation:
2 1/2
+ 2 1/2
1/2 and 1/2 makes a whole which is 1
so if you have 4 and and a whole which is 5
They can also be turned into decimals. 1/2 as a decimal is .5
so 2.5 plus 2.5 = 5
math question|| geometry
The length TE in the parallelogram is 11 units
How to determine the length TEFrom the question, we have the following parameters that can be used in our computation:
The parallelogram QRST
The diagonals of parallelogram are equal
Using the above as a guide, we have the following:
QE =SE
Substitute the known values in the above equation, so, we have the following representation
3x + 12 = x + 16
So, we have
2x = 4
Divide
x = 2
Recall that
TE = 6x - 1
So, we have
TE = 6 * 2 - 1
Evaluate
TE = 11
Hence, the lentth is 11 units
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A ball is rolling down a slope and continuously picks up speed. Suppose the function f(x)=1.2(1.11) to the power of x describes the speed of the ball in inches per minute. How fast will the ball be rolling in 20 minutes? Round the answer to the nearest whole number.
plug in 20 = x for function f(x)
1.2(1.11)^20 = ?
HELPP!! please!!! asap
Answer:
6 units
Step-by-step explanation:
Since the two angles are equal, this means that the triangle is isosceles. So x+4 = 3x-8. After solving, 2x = 12, x = 6. So AC is 6 units.
Answer: 6 units
Step-by-step explanation:
Since this is an isosceles triangle lines AB and BC are congruent so
x + 4 = 3x - 8 ---- add 8 and subtract x on both sides
12 = 2x ---- divide by 2 to isolate the x
x = 6
What is the area of this compound figure?
Answer:
66mm
Step-by-step explanation:
a cup of soup is left on a countertop to cool. the table below gives the temperatures , in degrees fahrenheit, of the soup recorded over a 10-minute period. write an exponential regression equation for the data, rounding all values to the nearest thousandth.
Y = -0.0063e0.16x + 99.97 is the exponential regression equation for the data, where x is the time in minutes and y is the temperature of the soup.
Calculate the x and y means in step one.
X's average: (0 + 10) / 2 = 5.
(95 + 88.5) / 2 = 91.75 is the mean of y.
Calculate the variance and covariance in step two.
(-5 6.5) + (5 -2.5) = 32.5 is the covariance.
X's variation is (5 0).
2 + (10 − 0)2 = 125
Calculate the regression coefficients in step three.
x = -32.5 / 125 = -0.26 where a = Covariance / Variance of x
Mean of x = 91.75 (-0.26 5) = 99.97 where b = Mean of y a Mean of x
Step 4: Compose the equation for exponential regression.
y = -0.0063e^0.16x + 99.97
Y = -0.0063e0.16x + 99.97 is the exponential regression equation for the data, where x is the time in minutes and y is the temperature of the soup. We must first determine the means of x and y before we can solve the problem. By summing the first and last values of x and dividing by 2, the mean of x is 5 and the mean of y is 91.75. (calculated by adding the first and last y values and then dividing by 2).
Calculating the covariance and variance comes next. The difference between each x and the mean of x is multiplied with the difference between each y and the mean of y to determine the covariance. By squaring the difference between each x and the mean of x, the variance of x is determined. The regression coefficients a and b can be determined when the covariance and variance have been computed.
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Mr. Steiner purchased a car for about $14,000. Assuming his loan was
compounded monthly at an interest rate of 4. 9% for 72 months:
p=
r=
n=
t=
A. How much will he have paid total?
B. How much more did he pay than the price of the car?
Mr. Steiner will need to pay $18774 in total and he paid $4774 more than the actual price of the car.
we know that the amount of money earned, in compound interest after t years is showed as, A(t) = P (1+[tex]\frac{r}{n}[/tex])ⁿ[tex]^{t}[/tex]
here, we know that A(t) is the amount of money after t years.
P is the initial sum of money, know as principal,
r is the interest rate as a decimal value,
n is the number of times that interest is compounded per year,
and
t is the time in years for which the money is invested or borrowed.
now here we know,
P = 14000, r = 0.049, n = 12, t = 6
when we have all values we can find,
A(t) = P(1+[tex]\frac{r}{n}[/tex])ⁿ[tex]^{t}[/tex]
A(6) = 14000 (1+[tex]\frac{0.049}{12}[/tex])¹²ˣ⁶
A(6) = 18774
therefore we know that Mr. Steiner needs to pay $18774 in total.
now,
18774 - 14000 = 4774
therefore we get to know that Mr. Steiner paid $4774 more than the actual price of the car.
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A 13-ft by 27-ft rectangular swimming pool is surrounded by a walkway of uniform width. If the total area of the walkway is 384 ft^2, how wide is the walkway?
Answer:
w = 25 / 4 feet wide.
Step-by-step explanation:
Let's call the width of the walkway "w."
The area of the rectangular pool is 13 * 27 = 351 ft^2.
The area of the walkway can be calculated by adding up the area of four rectangles, one around each side of the pool:
2 * (13 + w) * w + 2 * (27 + w) * w = 384
Expanding the equation:
2 * 13w + 2w^2 + 2 * 27w + 2w^2 = 384
Combining like terms:
2w^2 + 40w = 384
Solving for w^2:
2w^2 + 40w - 384 = 0
Using the quadratic formula:
w = (-40 ± √(40^2 - 4 * 2 * -384)) / (2 * 2)
Simplifying:
w = (-40 ± √(1600 + 3072)) / 4
w = (-40 ± √4272) / 4
w = (-40 ± 65) / 4
w = (25 / 4) or (-105 / 4)
Since w must be a positive value, w = 25 / 4 feet wide.
Answer:look it up frfr
Step-by-step explanation:
Compare the investment below to an investment of the same principal at the same rate compounded annually.
principal: $7,000, annual interest: 3%, interest periods: 6 , number of years: 17
The difference between the investment below and one with the same principal at the same rate compounded yearly is $18123.29.
How would you compare investments?The Payback Period is the most straightforward metric to use when contrasting investment options. Simply defined, this is the minimal amount required for you to recoup your initial investment.
compound interest, which is referred to as
[tex]A = P(1+r/n)^n×t[/tex]
Where
A = amount at the end of t years
r = interest rate.
n = periodic interval
P = principal amount deposited
Considering investment compounded annually
P = 7000
r = 3% = 3/100 = 0.03
n = 1
t = 17 years
[tex]A = 7000(1 + 0.03/1)^1× 12A = 7000(1.03)^12[/tex]
A = $9980.32
For the second investment,
n = 6
[tex]A = 7000(1 + 0.08/6)^6 × 12A = 7000(1 + 0.0133)^72A = 7000(1.0133)^72A = $18123.29[/tex]
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Mrs. Martinez and Ms. Jones' classes are competing for best average homework completion over the course of the semester.
According to the given figure Mrs Martinez data has greater variability than Mrs Jone's data.
How do average and mean differ?The average may be calculated by dividing the total number of values by the sum of all the numbers. The arithmetic average of a group of two or more data variables is referred to as a mean. Typically, average is referred to as mean or arithmetic mean. The word "mean" is only a way of defining the sample's average.
Comparing the median and average.By adding up each value individually and dividing the result by the total number of observations, the average is obtained. The "middle" value, for which half of such observations are greater and half are less, is used to compute the median.
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A new refrigerator comes packaged in a box shaped like a rectangular prism. The base of the box measures 6 feet by 12 feet. The total surface area of the box is 396 square feet. What is the height of the box in feet?
Answer:
7 feet
Step-by-step explanation:
You want the height of a 6' by 12' cuboid box that has a total surface area of 396 square feet.
Surface areaThe formula for the surface area of a cuboid is ...
SA = 2(LW +H(L+W))
ApplicationFor the given box, this is ...
396 = 2(6·12 +H(6+12))
198 = 72 +18H . . . . . . . . . . divide by 2
126 = 18H . . . . . . . . . . . subtract 72
7 = H . . . . . . . . . . . . divide by 18
The height of the box is 7 feet.
Find the Slope of line LM algebraically.
L(-1,-5)M(-4,-2)
Answer:
-2+5/-4+1= -1
Step-by-step explanation:
put y2 minus y1 over x2 minus x1
if a multiple regression dataset has 3 predictors, what is the minimum number of observations needed to meet doane's rule?
Doane's rule is used for choosing the number of histogram bins, not for determining the minimum sample size needed for a multiple regression analysis.
However, a commonly cited rule of thumb is that the sample size should be at least 10 times the number of predictors, so for a multiple regression dataset with 3 predictors, a minimum of 30 observations may be recommended.
Doane's rule is a guideline for choosing the number of histogram bins based on the sample size and skewness of the data. It suggests that the number of bins should be approximately equal to 1 + log2(N) + log2(1 + |g1|/SE(g1)), where N is the sample size and g1 is the sample skewness.
It is important to note that Doane's rule is used for determining the number of bins for a histogram, not for determining the minimum sample size needed for a multiple regression analysis.
That being said, in general, the minimum sample size needed for a multiple regression analysis depends on a variety of factors, including the number of predictors, the strength of the relationships between the predictors and the outcome variable, the desired statistical power, and the level of significance. There is no set minimum sample size that applies to all situations. However, a commonly cited rule of thumb is that the sample size should be at least 10 times the number of predictors, so for a multiple regression dataset with 3 predictors, a minimum of 30 observations may be recommended.
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Find X and y-intercepts for
12x +6y =108
Answer:
y=-2 over 1x+18
Step-by-step explanation:
A recipe calls for 2 cups of water for every 1/3 cups of flour. How much water is needed if you use 7 cups of flour?
On Thursday a theme park sells 627 tickets. Each ticket costs
£54.99. The park has costs of £18,273 on Thursday. What is the
percentage profit that the theme park make on Thursday?
Answer: The theme park made a 46.8% profit on Thursday.
Step-by-step explanation:
Step 1: First, we need to calculate the total revenue from ticket sales:
627 tickets x £54.99 = £34,341.73
Step 2: Subtract the costs from the total revenue:
£34,341.73 - £18,273 = £16,068.73
Step 3: Calculate the percentage profit:
£16,068.73 / £34,341.73 x 100 = 46.8%
The theme park made a 46.8% profit on Thursday.
consider a group of 150 students. out of them suppose 30 are math majors, 40 are engineering majors, and 20 are both math and engineering majors. if a student is selected randomly, a). what is the probability that the student is from other majors? note: round your answer to the nearest second decimal place b) what is the probability that the student majors only math? note: round your answer to the nearest second decimal place c) what is the probability that the student does not major engineering? note: round your answer to the nearest second decimal place
The probability that the student is from other majors is 0.40, the probability that the student majors only math is 0.13, and the probability that the student does not major engineering is 0.73.
a) Probability of a student being from other majors = (150-90) / 150 = 0.40
b) Probability of a student majoring only math = (30 - 20) / 150 = 0.13
c) Probability of a student not majoring engineering = (150 - 40 - 20) / 150 = 0.73
Probability = Number of Favorable Outcomes / Total Number of Outcomes
For part a)
Number of Favorable Outcomes = 150-90 = 60
Total Number of Outcomes = 150
Therefore, Probability = 60 / 150 = 0.40
For part b)
Number of Favorable Outcomes = 30-20 = 10
Total Number of Outcomes = 150
Therefore, Probability = 10 / 150 = 0.13
For part c)
Number of Favorable Outcomes = 150-40-20 = 90
Total Number of Outcomes = 150
Therefore, Probability = 90 / 150 = 0.73
The probability that the student is from other majors is 0.40, the probability that the student majors only math is 0.13, and the probability that the student does not major engineering is 0.73.
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Degree 5. Double zero at x = 1, and triple zero at x = 3. Passes through the point (x, y) = (2, 87). y=
The equation is [tex]y=-87(x-1)^{2} (x-3)^{3}[/tex].
What is meant by zeroes of polynomials?
All the x-values that bring a polynomial, p(x), to zero are referred to as its zeros. They are intriguing to us for a variety of reasons, one of which is that they provide information on the graph's x-intercepts for the polynomial.
It is given that degree of the equation is 5. so the highest power is 5 and there will be 5 zeroes.
It is given that 2 zeroes at x=1 and 3 zeroes at x= 3.
So, the equation is [tex]y=a(x-1)^{2} (x-3)^{3}[/tex].
We will substitute x=2 and y= 87 in the above equation.
[tex]87=a(2-3)^{3} \\a=-87[/tex]
Therefore now the equation will be:
[tex]y=-87(x-1)^{2} (x-3)^{3}[/tex].
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NEED HELP ASAPPP
Find m/TUV.
m/TUV=
Answer: 54 degrees
Step-by-step explanation:
The angle will be half of that arc segment
Cans of soda are packaged in boxes containing the same number of cans.
There are 36 cans in 4 boxes.
a) How many cans are there in 7 boxes?
b) How many boxes are needed to package 99 cans of soda?
a)
63 cans in 7 boxes.
b)
11 boxes are needed for 99 cans.
What is a unit rate?It is a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
36 cans in 4 boxes.
This means,
1 box = 36/4 cans
1 box = 9 cans
Multiply 7 on both sides.
7 box = 63 cans ______(1)
1 box = 9 cans
Multiply 11 on both sides.
11 box = 99 cans ______(2)
Now,
From (1) and (2)
a)
63 cans in 7 boxes.
b)
11 boxes are needed for 99 cans.
Thus,
63 cans in 7 boxes.
11 boxes are needed for 99 cans.
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a cylinder with radius of 5ft has a volume of 314ft. Find its height
3.9979(depends on what place you need to round to
The equation is V=πr2h. First plug in what you know, 314=π5^2h. 5x5=25 and its multiplied with π. It would look like 314=25πh. Divide the 25π by both sides, leaving your h. Plug it into your calculator.
Check answer:
(I rounded the 4 to the nearest whole number) 4*25*π is approximately 314
Answer:
4 ft
---------------
Volume of cylinder formula:
V = πr²hGiven:
r = 5 ft,V = 314 ft³Find h:
314 = 3.14*5²h314 = 3.14*25hh = 314/(3.14*25)h = 4 ft