The Eco Pulse survey from the marketing communications firm Shelton Group asked individuals to indicate things they do that make them feel guilty (Los Angeles Times, August 15, 2012). Based on the survey results, there is a 0.39 probability that a randomly selected person will feel guilty about wasting food and a 0.27 probability that a randomly selected person will feel guilty about leaving lights on when not in a room. Moreover, there is a 0.12 probability that a randomly selected person will feel guilty for both of these reasons.
Required:
a. What is the probability that a randomly selected person will feel guilty for either wasting food or leaving lights on when not in a room or both (to 2 decimals)?
b. What is the probability that a randomly selected person will not feel guilty for either of these reasons (to 2 decimals)?
Answers
Answer:
a) 0.54 = 54% probability that a randomly selected person will feel guilty for either wasting food or leaving lights on when not in a room or both.
b) 0.46 = 46% probability that a randomly selected person will not feel guilty for either of these reasons
Step-by-step explanation:
We use Venn's Equations for probabilities.
I am going to say that:
P(A) is the probability that a randomly selected person will feel guilty about wasting food.
P(B) is the probability that a randomly selected person will feel guilty about leaving lights on when not in a room.
0.12 probability that a randomly selected person will feel guilty for both of these reasons.
This means that \(P(A \cap B) = 0.12\)
0.27 probability that a randomly selected person will feel guilty about leaving lights on when not in a room.
This means that \(P(B) = 0.27\)
0.39 probability that a randomly selected person will feel guilty about wasting food
This means that \(P(A) = 0.39\)
a. What is the probability that a randomly selected person will feel guilty for either wasting food or leaving lights on when not in a room or both (to 2 decimals)?
\(P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.39 + 0.27 - 0.12 = 0.54\)
0.54 = 54% probability that a randomly selected person will feel guilty for either wasting food or leaving lights on when not in a room or both.
b. What is the probability that a randomly selected person will not feel guilty for either of these reasons (to 2 decimals)?
\(p = 1 - P(A \cup B) = 1 - 0.54 = 0.46\)
0.46 = 46% probability that a randomly selected person will not feel guilty for either of these reasons
Related Questions
(a)Find the scale factor from △ABC to △JKL.Enter the scale factor as a simplified ratio.(b)List all pairs of congruent angles
Answers
Answer:
a) 3/4
Explanation:
Part A
If triangles ABC and JKL are similar, then the ratio of the corresponding sides is:
\(\frac{AB}{JK}=\frac{BC}{KL}=\frac{AC}{JL}\)Substitute the given values:
\(\begin{gathered} \frac{AB}{JK}=\frac{27}{36}=\frac{3}{4} \\ \frac{BC}{KL}=\frac{36}{48}=\frac{3}{4} \\ \frac{AC}{JL}=\frac{21}{28}=\frac{3}{4} \end{gathered}\)Thus, the scale factor from △ABC to △JKL is 3/4.
Part B
Given that ABC and JKL are congruent, then:
\(\begin{gathered} \angle A\cong\angle J \\ \angle B\cong\angle K \\ \angle C\cong\angle L \end{gathered}\)
\( log_{3}(x) + log_{9}(x) = 12\)
solve for x
Answers
Answer:
x = 3⁸
Step-by-step explanation:
Step(i):-
Given that
\(log _{3} (x)+ log_{9} (x) =12\)
\(log _{3} (x)+ log_{3^{2} } (x) =12\)
we know that
\(log^{a} _{b} = \frac{loga}{logb}\)
\(log _{3} (x)+ \frac{logx}{log3^{2} } =12\)
Step(ii):-
Apply log xⁿ = nlogx
\(log _{3} (x)+\frac{1}{2} \frac{logx}{log3 } =12\)
\(log _{3} (x)+ \frac{1}{2} log_{3 } (x) =12\)
\(log _{3} (x)+ log_{3 } (x)^{\frac{1}{2} } =12\) ( ∵ log xⁿ = nlogx)
Apply log(ab) = loga+logb
\(log _{3} (x (x^{\frac{1}{2} }) =12\)
\(log _{3} ( (x^{\frac{3}{2} }) =12\)
\(\frac{3}{2} log _{3} ( x) =12\)
\(\frac{1}{2} log _{3} ( x) = 4\)
\(log _{3} ( x) = 8\)
we know that \(log _{b} ( x) = a\) ⇒ x = bᵃ
∴ x = 3⁸
Find the Constant of proportionality of Henderson Toll Road Cost
Answers
The constant of proportionality is equal to 3/10.
What is a proportional relationship?In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:
y = kx
Where:
y represents the miles traveled.x represents the cost ($).k is the constant of proportionality.Next, we would determine the constant of proportionality (k) by using various data points as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 3/10 = 6/20 = 9/30
Constant of proportionality, k = 3/10.
Therefore, the required linear equation is given by;
y = kx
y = 3/10(x)
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total area of 3 figures
Answers
Given dimensions:
x=31 feet, y= 24 feet and z= 95 feet
We can split the shape above into 3 components: A, B, and C
To find the total area, we will find the sum of the areas of each component
For A
The shape of A is that of a semi-circle.
The area of a semi-circle is given to be
\(\text{Area}=\text{ }\frac{1}{2}\text{ x }\pi r^2\)The radius will be the diameter divided by 2
y= diameter
r= radius = y/2
r=24/2 =12 feet
pi=3.14
\(\begin{gathered} \text{Area}=\frac{1}{2}\text{ x 3.14 x 12 x 12} \\ \text{Area}=226.08\text{ ft}^2 \end{gathered}\)For B
The shape is a rectangle
The area of a rectangle is given by
A = l x b
where l = 31 and b = 24
Area = 31 x 24
Area = 744 square feet
For C
The shape is a triangle
The area of the triangle is given by
\(A=\frac{1}{2}\text{ x base x height}\)base = 64 feet, height = 24 feet
\(\text{Area}=\frac{1}{2}\text{ x }64\text{ x 24 =768 ft}^2\)The total area is
22
Divide.
636-3
The quotient is
and the remainder is
Answers
Answer:
212
Step-by-step explanation:
3 goes into 6 = 2 times
3 goes into 3 = 1 time
3 goes into 6 = 2 times
2 → 1 → 2 = 212
P. S pls mark as brainliest
Suppose the diameter of a circle is 16, What is its circumference?
Answers
Answer:
Step-by-step explanation:
Circumference = πd
= 3.14 * 16
= 50.24
How much will be charged in prepaid interest on a $250,000 loan with an APR of 5.25% that was closed on April 12th
Answers
The amount that will be charged in prepaid interest on a $250,000 loan with an APR of 5.25% closed on April 12th is $9,457.19.
What is the APR?The APR represents the annual percentage rate.
The annual percentage rate is the interest rate for the year, including other finance charges.
To compute the interest, the annual percentage rate is multiplied by the loan amount and the period divided by 365 days.
Loan amount = $250,000
Annual percentage rate (APR) = 5.25%
Loan closing date = April 12th
April 12th to December 31st = 263 days
Interest for the year = $9,457.19 ($250,000 x 5.25% x 263/365)
Thus, for the year, the interest is $9,457.19.
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80% of salmon pass through a single dam unharmed. By what percent does the number of salmon decrease when passing through a single dam?
Answers
Answer:20%
Step-by-step explanation:
Answer: 20%
Step-by-step explanation:
0.02 X 100 = 0.02 X_____=_____
Answers
Answer:
0.02 × 100 = 2
Step-by-step explanation:
move the decimal 2 steps backward according to the numbers of zeros behind the multiplier(100).
0.02 × 100 = 2
please mark brainliest
Simplify: 10(-5x+4)
Jejdjejehhe
Answers
Answer:
-50x + 40
Step-by-step explanation:
10(-5x+4)
-50x + 40
The slope of a line is ¾. A different line passes through the points (6, 3) & (-1, 5). Are the lines parallel? Why or why not?
Answers
Answer:
B. They are not parallel because their slopes are not equal.
Step-by-step explanation:
Find the slope of the line that runs through points (6, 3) and (-1, 5):
\( slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 3}{-1 - 6} \)
\( slope (m) = \frac{2}{-7} = -\frac{2}{7} \)
Since the slope of the line that passes through points (6, 3) and (-1, 5) is not the same with line that has a slope of ¾, therefore, both lines cannot be parallel.
The answer is "B. They are not parallel because their slopes are not equal."
Calculate the volume, in cubic centimeters, of a box which is 125 cm long, 37 cm wide, and 68 cm high. Report your answer with correct significant figures in cubic centimeters.
Answers
Answer:
\(Volume = 314500cm^3\)
Step-by-step explanation:
Given
\(Length = 125cm\)
\(Width = 37cm\)
\(Height = 68cm\)
Required
Determine the volume
Volume is calculated as:
\(Volume = Length * Width * Height\)
Substitute values for Length, Width and Height
\(Volume = 125cm * 37cm * 68cm\)
\(Volume = 314500cm^3\)
Hence, the volume of the box is \(314500cm^3\)
5/8p−3/4=4
A) p=95/32
B) p=26/5
C) p=38/5
Answers
\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p-\frac{3}{4}=4 } \end{gathered}$}}\)
Add 3/4 to both sides.
\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p=4+\frac{3}{4} } \end{gathered}$}}\)
Convert 4 to the fraction 16/4.
\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p=\frac{16}{4} +\frac{3}{4} } \end{gathered}$}}\)
Since 16/4 and 3/4 have the same denominator, add their numerators to add them together.
\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p=\frac{16+3}{4} \longmapsto \ \ Add } \end{gathered}$}}\)
\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p=\frac{19}{4} } \end{gathered}$}}\)
Multiply both sides by 8/5, the reciprocal of 5/8.
\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=\frac{19}{4}\times\left(\frac{5}{8}\right) } \end{gathered}$} }\)
Multiply 19/4 by 8/5 (to do this, multiply the numerator by the numerator and the denominator by the denominator).
\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=\frac{19\times8}{4\times5 }\longmapsto \ Multiply } \end{gathered}$}}\)
\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=\frac{152}{20} } \end{gathered}$}}\)
We reduce the fraction 152/20 to its minimum expression by extracting and canceling 4.
\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=\frac{152}{20} \ \ \longmapsto \ p=\frac{152\div4}{20\div4}=\frac{38}{5} } \end{gathered}$}}\)
Therefore, the answer is option C.5/8 p= 19/4
P= 19/4 / 5/8
P= 19/4 x 8/5
P= 38/5
The answer is C
What is the color blue
Answers
Answer:
Blue is one of the three primary colours of pigments in painting and traditional colour theory, as well as in the RGB colour model. It lies between violet and green on the spectrum of visible light. The eye perceives blue when observing light with a dominant wavelength between approximately 450 and 495 nanometres
Step-by-step explanation:
what do I say
SASAGEYO
Based on the average predictions of 50 economists, the U.S. gross domestic product (GDP) will expand by 2.5% this year. Suppose the sample standard deviation of their predictions was 2%. At the 10% significance level, test if the mean forecast GDP of all economists is less than 3%.
a. Select the null and the alternative hypotheses.
multiple choice 1
H0: μ = 3; HA: μ ≠ 3
H0: μ ≤ 3; HA: μ > 3
H0: μ ≥ 3; HA: μ < 3
b. Calculate the value of test statistic. (Round final answer to 4 decimal places.)
c. Find the p-value.
multiple choice 2
p-value 0.10
p-value < 0.01
0.01 p-value < 0.025
0.025 p-value < 0.05
0.05 p-value < 0.10
d. At the 10% significance level, can we conclude that the mean forecast GDP of all economists is less than 3%?
multiple choice 3
No, since we do not reject H0.
No, since we reject H0.
Yes, since we do not reject H0.
Yes, since we reject H0.
rev: 10_13_2020_QC_CS-234700, 11_27_2020_Q
Answers
The null and hypothesis test; test statistic and the conclusion of the hypothesis are :
\( H_{0} : \mu\geq 3 ; H_{1} : \mu < 3\) Test statistic = -1.7678Pvalue < 0.05Yes, since we reject H0The hypothesis :
\( H_{0} : \mu \geq 3 \) \( H_{1} : \mu < 3 \)The test statistic :
\(\frac{\bar{x} - \mu}{\frac{σ}{\sqrt{n}}}\)
Substituting the values into the equation :
\(\frac{2.5 - 3.0}{\frac{2}{\sqrt{50}}} = -1.7678\)
The Pvalue, using a Pvalue calculator ; 1 - tailed ; 10% level of significance (0.10) = 0.038
Hence, Pvalue < 0.05
3.) At 10% level of significance ;
We compare the Pvalue and the α
α = 10% = 0.10
Since, Pvalue < α (0.038 < 0.10) ; then the result is significant.
Therefore, the result is significant at α = 0.10
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General form of
Y= 1/3x +3 and has an x intercept of 3
Answers
Answer:
Step-by-step explanation:
y
=
1
3
x
−
3
Use the slope-intercept form to find the slope and y-intercept
Slope:
1
3
y-intercept:
(
0
,
−
3
)
Any line can be graphed using two points. Select two
x
values, and plug them into the equation to find the corresponding
y
values.
x
y
0
−
3
3
−
2
Graph the line using the slope and the y-intercept, or the points.
Slope:
1
3
y-intercept:
(
0
,
−
3
)
x
y
0
−
3
3
−
2
image of graph
Kevin made a business trip of 312.5 miles. He averages 60 mph for the first part of the trip and 55 mph for the second part. If the trip took a 5.5 hours how long did he travel at each rate
Answers
Answer:
Kevin travels for 2 hours at 60 mph and 3.5 hours at 55 mph
Step-by-step explanation:
Let's say that Kevin spends x hours going 60 mph and y hours going 55 mph. We can say that the sum of the two parts is 5.5, so x+y = 5.5 . Next, he goes 60 miles per hour for the first part of the trip, so for each hour he goes 60 mph, he travels 60 miles. We can then denote 60 * x as the distance traveled during the first part of his trip as he goes 60 mph for x hours. Similarly, 55 * y denotes the distance Kevin travels during the second part of his trip. His total distance is thus 60 * x + 55 * y = 312.5 miles
We have
x + y = 5.5
60 * x + 55 * y = 312.5
One way we can solve this is to solve for y in the first equation and plug that into the second. Subtracting x from both sides in the first equation, we get
y = 5.5 - x
Plugging that into the second equation, we get
60 * x + 55 * (5.5-x) = 312.5
60 * x + 55 * 5.5 - 55x = 312.5
5x +302.5 = 312.5
subtract 302.5 from both sides to isolate the x and its coefficient
5x = 10
divide both sides by 5 to solve for x
x = 2
y = 5.5 - x = 5.5 - 2 = 3.5
Therefore, Kevin travels for 2 hours at 60 mph and 3.5 hours at 55 mph
If an animal is a giraffe, then it has four legs. Counterexample
Answers
Answer:
If an animal is a dog, it has four legs?
Step-by-step explanation:
HOW DO YOU DO 12/60 PLZ IF YOU CAN CAN YOU GO STEP BY STEP THAT I CAN DO I HAVE TO SIMPLIFY AND IM IN 6TH GRADE HELP PLZ ASAP
Answers
Answer:
i need help with that to
Step-by-step explanation:
Answer:
12/60 simplified is 1/5
Step-by-step explanation:
The most common way to simplify is to divide, as the / is a sign to divide, meaning 12/60 translates to 60 divided by 12. Hope you understand :)
find the equation of the line. a line that is perpendicular to the graph 3x+2y=6 and contains the point (6,-3)
Answers
Answer:
Slope: −32
y-intercept: (0,3)
y=-32x+3
start using online calculators
Answer:
2x-3y=21
Step-by-step explanation:
PLEASE HELP ON QUESTION ASAP! 30PTS!
I WILL ALSO GIVE YOU A THANKS RATE YOU FIVE STARS AND MAYBE EVEN BRAINLIEST any silly answeres will be reported / deleted
Hiba needs 40g sugar to make 15 biscuits. she also needs three times as much flour as sugar . Hiba is going to make 60 biscuits . work out the amount of flour she needs .
Answers
40.3=120g flour➡️15 biscuits
60 biscuits = 16.4➡️120.4 = 480g flour
She needs 480g flour to make 60 biscuits
(05.05)The coordinates below are the three vertices of a rectangle. Identify the fourth coordinate and the area of the rectangle.
(2, 7), 28 units squared
(2, 7), 45 units squared
(7, 2), 28 units squared
(7, 2), 45 units squared
Answers
Answer:
D. (7,2) 45 units squared
Step-by-step explanation:
fourth coordinate would be (7, 2)
area = 9 x 5 = 45
so the answer is (7,2) 45 units squared
Answer:
D
Step-by-step explanation:
Also give the other guy brainist
A 2-column table with 4 rows. Column 1 is labeled x with entries 1, 2, 3, 4. Column 2 is labeled y with entries 11, 22, 33, 44. What relationship between the quantities is shown in the table? The relationship between quantities is +10. The relationship between quantities is ×11. The relationship between quantities is – 30. The relationship between quantities is + 20. A 2-column table with 4 rows. Column 1 is labeled x with entries 1, 2, 3, 4. Column 2 is labeled y with entries 11, 22, 33, 44. What relationship between the quantities is shown in the table? The relationship between quantities is +10. The relationship between quantities is ×11. The relationship between quantities is – 30. The relationship between quantities is + 20. A 2-column table with 4 rows. Column 1 is labeled x with entries 1, 2, 3, 4. Column 2 is labeled y with entries 11, 22, 33, 44. What relationship between the quantities is shown in the table? The relationship between quantities is +10. The relationship between quantities is ×11. The relationship between quantities is – 30. The relationship between quantities is + 20. A 2-column table with 4 rows. Column 1 is labeled x with entries 1, 2, 3, 4. Column 2 is labeled y with entries 11, 22, 33, 44. What relationship between the quantities is shown in the table? The relationship between quantities is +10. The relationship between quantities is ×11. The relationship between quantities is – 30. The relationship between quantities is + 20.
Answers
The relationship between the quantities shown in the table is +10. The values in column 2 (y) are obtained by adding 10 to the corresponding values in column 1 (x).
How to explain the relationshipIn the given table, the values in column 1 (labeled "x") are 1, 2, 3, and 4. The values in column 2 (labeled "y") are 11, 22, 33, and 44.
To determine the relationship between the quantities in the table, we can compare the values in column 2 (y) with the corresponding values in column 1 (x).
If we subtract each value in column 1 from the corresponding value in column 2, we find that:
11 - 1 = 10
22 - 2 = 20
33 - 3 = 30
44 - 4 = 40
By observing these results, we can see that the difference between each value in column 2 and its corresponding value in column 1 is always 10.
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Alex is flying from Boston to Denver with a connection in Chicago. The probability her first flight leaves on time is 0.25 . If the flight is on time, the probability that her luggage will make the connecting flight is 0.95 , but if the flight is delayed, the probability that the luggage will make it is only 0.55 . Suppose you pick her up at the Denver airport and her luggage is not there. What is the probability that 's first flight was delayed?
P(delayed)
(Do not round until the final answer. Then round to three decimal places as needed.)
Answers
Answer: the probability that Alex's first flight was delayed given that her luggage did not make it to Denver is approximately 0.934 (rounded to three decimal places).
Step-by-step explanation:
Let D denote the event that the first flight is delayed, and L denote the event that Alex's luggage makes the connecting flight. We want to find P(D|~L), the probability that the first flight was delayed given that her luggage did not make it to Denver.
We can use Bayes' theorem to calculate this probability:
P(D|~L) = P(~L|D) * P(D) / P(~L)
We are given that P(D) = 1 - P(first flight leaves on time) = 1 - 0.25 = 0.75, and that P(L|D) = 0.55 and P(L|~D) = 0.95. Therefore, we can calculate P(~L) using the law of total probability:
P(~L) = P(~L|D) * P(D) + P(~L|~D) * P(~D)
= (1 - P(L|D)) * 0.75 + (1 - P(L|~D)) * 0.25
= 0.3625
Substituting these values into Bayes' theorem, we get:
P(D|~L) = P(~L|D) * P(D) / P(~L)
= 0.45 * 0.75 / 0.3625
= 0.934
Therefore, the probability that Alex's first flight was delayed given that her luggage did not make it to Denver is approximately 0.934 (rounded to three decimal places).
Is 3times4 the same as 4 times 3
Answers
Answer:
Yes, 3x4=12 and 4x3=12
Step-by-step explanation:
Answer:
Yes
Step-by-step explanation:
3 × 4 = 12
4 × 3 = 12
Probability that student was male or got an “B”
Answers
Answer:
3/23 = .13 = 13%
Step-by-step explanation:
A) Find an equation for the line perpendicular to the tangent line to the curve y=x^3-4x+6 at the point (2,6)
-The equation is y=
b) What is the smallest slope on the curve? At what point on the curve does the curve have this slope?
-The smallest slope on the curve is
-The curve has the smallest slope at the point
c) Find equations for the tangent lines to the curve at the points where the slope of the curve is 8.
Answers
Answer:
f(x) = x³ - 4x + 6
f'(x) = 3x² - 4
a) f'(2) = 3(2²) - 4 = 12 - 4 = 8
6 = 8(2) + b
6 = 16 + b
b = -10
y = 8x - 10
b) 3x² - 4 = 0
3x² = 4, so x = ±2/√3 = ±(2/3)√3
= ±1.1547
f(-(2/3)√3) = 9.0792
f((2/3)√3) = 2.9208
c) 3x² - 4 = 8
3x² = 12
x² = 4, so x = ±2
f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6
6 = -2(8) + b
6 = -16 + b
b = 22
y = 8x + 22
f(2) = 6
y = 8x - 10
The equation perpendicular to the tangent is y = -1/8x + 25/4
-The smallest slope on the curve is 2.92
The curve has the smallest slope at the point (1.15, 2.92)
The equations at tangent points are y = 8x + 16 and y = 8x - 16
Finding the equation perpendicular to the tangentFrom the question, we have the following parameters that can be used in our computation:
y = x³ - 4x + 6
Differentiate
So, we have
f'(x) = 3x² - 4
The point is (2, 6)
So, we have
f'(2) = 3(2)² - 4
f'(2) = 8
The slope of the perpendicular line is
Slope = -1/8
So, we have
y = -1/8(x - 2) + 6
y = -1/8x + 25/4
The smallest slope on the curveWe have
f'(x) = 3x² - 4
Set to 0
3x² - 4 = 0
Solve for x
x = √[4/3]
x = 1.15
So, we have
Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6
Smallest slope = 2.92
So, the smallest slope is 2.92 at (1.15, 2.92)
The equation of the tangent lineHere, we set f'(x) to 8
3x² - 4 = 8
Solve for x
x = ±2
Calculate y at x = ±2
y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)
y = (2)³ - 4(2) + 6 = 6: (2, 0)
The equations at these points are
y = 8x + 16
y = 8x - 16
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Write a quadratic function to model the vertical motion for each situation, given h(t) equals negative 16t squared plus v0t+h0. Find the maximum height. Initial velocity 152
Answers
The maximum height reached by the ball is 908.5 feet.
Using the given values, we can substitute v0 = 152 and h0 = 6 into the equation:
\(h(t) = -16t^2 + 152t + 6\)
This quadratic function models the height of the ball at any time t after it is thrown.
To find the maximum height of the ball, we need to find the vertex of the parabolic curve described by the quadratic function. The vertex can be found using the formula:
t = -b / 2a
where a = -16 and b = 152 are the coefficients of the quadratic function.
t = -152 / 2(-16) = 4.75
So the maximum height is reached after 4.75 seconds. To find the maximum height, we can substitute this value back into the equation:
\(h(4.75) = -16(4.75)^2 + 152(4.75) + 6 = 908.5\)feet
Therefore, the maximum height reached by the ball is 908.5 feet.
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Question
A ball is thrown vertically upward from a height of 6 feet with an initial velocity of 152 feet per second. Write a quadratic function to model the vertical motion of the ball, given that the height of the ball at time t is given by: h(t) = -16t^2 + v0t + h0
Allison bought jelly beans to share with her friends. She bought pounds of blueberry jelly beans and pounds of lemon jelly beans. If she gave pounds of jelly beans away to her friends, how many pounds of jelly beans does Allison have left?
Answers
Answer: \(1\dfrac{11}{12}\text{ pounds}\)
Step-by-step explanation:
The complete question is provided in the attachment.
Given, Amount blueberry jelly beans= \(1\dfrac{1}{4}\) pounds
\(=\dfrac{5}{4}\) pounds.
Amount lemon jelly beans = \(2\dfrac{1}{3}\)pounds
\(=\dfrac{7}{2}\) pounds
Total jelly beans she bought = Amount blueberry jelly beans + Amount lemon jelly beans
\(=(\dfrac{5}{4}+\dfrac{7}{3})\) pounds
\(=\frac{15+28}{12}\text{ pounds}\\\\=\dfrac{43}{12}\text{ pounds}\)
Amount of jelly beans she gave away = \(1\dfrac{2}{3}=\dfrac{5}{3}\text{ pounds}\)
Amount of jelly beans she has left= Total jelly beans - Amount of jelly beans she gave away
=\(\dfrac{43}{12}-\dfrac{5}{3}\\\\=\dfrac{43-20}{12}\\\\=\dfrac{23}{12}\\\\=1\dfrac{11}{12}\text{ pounds}\)
She has left \(1\dfrac{11}{12}\text{ pounds}\) of jelly beans.
Graph the equation −3x+5y=7 by plotting points using the line tool.
Answers
A graph of the linear equation -3x + 5y = 7 in slope-intercept form is shown in the image attached below.
What is a graph?In Mathematics, a graph is a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate respectively.
Next, we would rearrange and simplify the given given linear equation in slope-intercept form in order to enable us plot it on a graph:
-3x + 5y = 7
5y = 3x + 7
y = 3x/5 + 7/5
Lastly, we would use an online graphing calculator to plot the given function as shown in the graph attached below.
In conclusion, the slope of this linear equation is equal to 3/5 and it does not represent a proportional relationship.
Read more on a graph here: brainly.com/question/4546414
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