The proportionality constant is 1/2 (0.5) and the equation of the line will be given as y = 0.5x.
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
On a coordinate plane, a graph has a number of hours on the x-axis and a number of haircuts on the y-axis. A line goes through points (2, 1), (4, 2), and (6, 3).
We know that the equation of the line passing through the two-point is given as
[tex]\rm (y-y_1)=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Then we have
[tex]\rm y-1 = \dfrac{2-1}{4-2} \times (x-2)\\\\y = \dfrac{1}{2}\ x - 1+1 \\\\y = \dfrac{1}{2}\ x[/tex]
The proportionality constant is 1/2 (0.5) and the equation of the line will be given as y = 0.5x.
More about the linear system link is given below.
https://brainly.com/question/20379472
Answer:
first one is 1/2 second one is y = 1/2 x
Hope it helps!!!
©
Sara is 3 years older than Fiona. Paul is 3 years younger than Fiona. If the total of their ages is
60, how old is the youngest of them?
Answer:
Paul is the youngest at 17 years old. Fiona is 20 years old, Sara is 23 years old
Step-by-step explanation:
Assign variables to the ages.
S = sara's age
F = Fiona's age
P = Paul's age.
S + F + P = 60
S = 3 + F
P = F - 3
(3 + F) + F + (F - 3) = 60
3 + 3F - 3 = 60
3F = 60
F = 20
S = 23
P = 17
I need of help ASAP please
plzzzzzz hellpppp !!!!!!!!!!!!
listen yeah
plot the points on the graph and join up dots
then draw a line x = 4 so 4 on x axis draw a vertical line as its line of symmetry
then reflect the shape
for the x co ordinates, say that they are different because the x values are not the same
for the y co ordinates, say thay they are the same because the y values did not change
plot points on 2nd graph and join up dots
then draw a line y = 2 so 2 on y axis draw a horizontal line as its line of symmetry
then reflect shape
for the x co ordinates, say that they are the same because the x values did not change
for the y co ordinates, say that they are different because the y values are not the same
θ is an acute angle. Find the value of θ in radians.
sin(θ)=1
Write your answer as an integer or as a decimal rounded to the nearest hundredth.
The value of θ in radians when sin(θ) = 1 is π/2, approximately equal to 1.57 rounded to the nearest hundredth.
To find the value of θ in radians when sin(θ) = 1, we know that sine is the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle.
Since the sine of an acute angle cannot exceed 1, and sin(θ) = 1, this indicates that θ must be a 90-degree angle, or π/2 radians.
In radians, π represents the ratio of the circumference of a circle to its diameter, and π/2 corresponds to one-fourth of the circumference, which equals a right angle.
Therefore, the value of θ in radians is π/2, or approximately 1.57 rounded to the nearest hundredth.
After getting trounced by your little brother in a children's game, you suspect the die he gave you to roll may be unfair. To check, you roll it 60 times, recording the number of times each face appears. Do these results cast doubt on the die's fairness? Full data set Face Count Face Count 1 14 4 15 2 5 5 14 3 11 6 1 a) If the die is fair, how many times would you expect each face to show? nothing b) To see if these results are unusual, will you test goodness-of-fit, homogeneity, or independence? A. Independence B. Homogeneity C. Goodness-of-fit c) State your hypotheses. A. Upper H 0: The die is unfair. Upper H Subscript Upper A: The die is fair. B. Upper H 0: The die is fair. Upper H Subscript Upper A: The die produces outcomes that are less than the expected value. C. Upper H 0: The die is fair. Upper H Subscript Upper A: The die is unfair. D. Upper H 0: The die is fair. Upper H Subscript Upper A: The die produces outcomes that are greater than the expected value. d) Check the conditions. Is the counted data condition met? No Yes Is the randomization condition met? Yes No Is the expected cell frequency condition met? Yes No e) How many degrees of freedom are there? nothing
Answer:
Given:
Face ____________Count
1_________________14
4_________________15
2_________________5
5_________________14
3_________________11
6_________________1
a) I rolled the die 60 times and my values are recorded.
Assuming the die is fair, each face is expected to show 10 times.
[tex] 60* \frac{1}{6} = 10 [/tex]
b) To check if my results are unusual hypothesis test is used to address this. In this case the test is called goodness of fit.
c) For the null and alternative hypothesis :
The null hypothesis states , the die is fair (the number of times each face appear is equal)
The alternative hypothesis states the die is not fair.
H0 : p = 0.6
H1 : p ≠ 0.6
d)
The number of times the die is rolled is recorded.
The number of times the die is rolled is independent because the outcomes are independent.
Here the expected value of observation is more than five because the null hypothesis expects each die roll to be 10. Thus, the condition is satisfied.
e) Number of degrees of freedom for this test is n-1.
n = 6 (total faces in a die)
Therefore, degrees of freedom =
6-1 = 5
A box with a square base and open top must have a volume of 48668 cm3. We wish to find the dimensions of the box that minimize the amount of material used.First, find a formula for the surface area of the box in terms of only x, the length of one side of the square base.[Hint: use the volume formula to express the height of the box in terms of x.]Simplify your formula as much as possible.
Answer:
x=46 gives us the minimum value
Step-by-step explanation:
Let us have the height of the box to be y. Since the box has a square base, let us call the side of the base as x. So, the volume of the box is given by
[tex]x^2\cdot y = 48668[/tex]. From here, we know that [tex]y=\frac{48668}{x^2}[/tex]
Now, we will find the area of the box. Since the box has an open top, then we only have the 4 sides of the box and the base. The base is a square of side x, so its area is [tex]x^2[/tex]. Recall that each side is a rectangle of base x and height y. So, the are of one side is [tex]x\cdot y[/tex]. Then, the area of the box is given by the function
[tex]A(x,y) = x^2+4xy[/tex]. Since we can relate y to x through the volume, this can be a function of one variable. Namely
[tex]A(x) = x^2+4x\cdot \frac{48668}{x^2}= x^2+4\cdot \frac{48668}{x} = x^2+48668x^{-1}[/tex]
If we want to find the mininum value, we should derive the function A and find the value of x for which A'(x) is zero. REcall that the derivative of a function of the form [tex]x^n[/tex] is [tex]nx^{n-1}[/tex]. Then, applying the properties of derivatives, we have
[tex] A'(x) = 2x-4\cdot \frac{48668}{x^2} = \frac{2x^3-4\cdot 48668}{x^2}[/tex]
So, we want to solve the following equation
[tex]2x^3-4\cdot 48668 =0[/tex]
which implies [tex]x^3 = 97336[/tex]. Using a calculator we get the value [tex] x= 46[/tex]
REcall that to check if the point is a minimum, we use the second derivative criteri. It states that the point x is a mininimum if f'(x) =0 and f''(x)>0
Note that [tex]A''(x) = 2+8\cdot\cdot 48668}{x^3}[/tex], note that A''(46) = 6>0, so x=46 is the minimum value of the area.
To find the formula for the surface area of the box in terms of only the length of one side of the square base, express the height of the box in terms of x. The formula for the surface area is S = 194672 / x + x².
Explanation:To find the formula for the surface area of the box in terms of only the length of one side of the square base, we need to express the height of the box in terms of x. The volume of the box is given as 48668 cm³, which is equal to the base area (x²) multiplied by the height (h). So, we have the equation x² * h = 48668. Solving for h, we get h = 48668 / x².
The surface area of the box consists of the area of the four sides of the box (4 * x * h) and the area of the square base (x²). We can substitute the value of h in terms of x into this expression to get the simplified formula for the surface area: S = 4 * x * (48668 / x²) + x². Simplifying further, we get S = 194672 / x + x².
Learn more about Formula for surface area of a box here:https://brainly.com/question/32052445
#SPJ6
The graph of a hyperbola is shown. What are the coordinates of a focus of the hyperbola?
(−12, 0)
(0, −5)
(0, 0)
(13, 0)
The answer is D.) (13,0)
I remember seeing this question somewhere before... Along with the graph.
Additionally, make sure to add the graph to the question next time!
The coordinates of focus are ( 13, 0)
What is Hyperbola?The hyperbola can be defined as the difference of distances between a set of points, which are present in a plane to two fixed points is a positive constant.
A hyperbola is a set of points whose difference of distances from two foci is a constant value. This difference is taken from the distance from the farther focus and then the distance from the nearer focus. For a point P(x, y) on the hyperbola and for two foci F, F', the locus of the hyperbola is PF - PF' = 2a.
We know,
Foci for hyperbola is : (c,0) and (−c,0)
As, from the attached graph below the focus is:
Focus : ( 13, 0)
Hence, the Focus is: ( 13, 0).
Learn more about hyperbola here:
https://brainly.com/question/11307750
#SPJ2
What is the volume of the following rectangular prism?"
8 units
5- 1/4units
Volume =
Answer: 42
Step-by-step explanation:
convert 5 1/4 to an improper fraction=21/4
then multiply 21/4 • 8 = 42!
hope this helps (:
The volume of the rectangular prism is, 42 units³
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
For a rectangular prism,
Base area = 5 1/4 units
Height = 8 units
We know that;
The volume of the rectangular prism = Base area x Height
Substitute given values, we get;
The volume of the rectangular prism = Base area x Height
The volume of the rectangular prism = 5 1/4 x 8
The volume of the rectangular prism = 21/4 x 8
The volume of the rectangular prism = 42 units³
Thus, The volume of the rectangular prism is, 42 units³
Learn more about the multiplication visit:
https://brainly.com/question/10873737
#SPJ7
A truck that can carry no more than 7200 lb is being used to transport refrigerators and upright pianos. Each refrigerator weighs 250 lb and each piano weighs 525 lb. Write and graph an inequality to show how many refrigerators and how many pianos the truck could carry. Will 14 refrigerators and 9 pianos overload the truck? Explain. Let x be the number of refrigerators in the truck and y be the number of pianos in the truck. Write an inequality to show how many refrigerators and how many pianos the truck could carry.
Answer:
x250+y525=7200 the answer is no
Step-by-step explanation:
Identify the domain and range of each function.
y = 3.52
The domain of this function is
The range of this function is
DONE
The domain and range of each function y = 3.52 is All real numbers and {3.52}.
What is the domain and range of the function?The domain of a function is defined as the set of all the possible input values that are valid for the given function.
The range of a function is defined as the set of all the possible output values that are valid for the given function.
We are given that;
The function y=3.52
Now,
For the function y = 3.52, the output (y-value) is always the same, regardless of the input (x-value). Therefore, the domain of this function is all real numbers, and the range of this function is the single value 3.52.
Therefore, the domain and range will be All real numbers and {3.52}
Learn more about the domain and range of the function:
brainly.com/question/2264373
#SPJ7
What are the most bags Mrs. Dupree can make? Will choose brainliest and will report absurd answers
Answer:
B. 4 bags
Step-by-step explanation:
The number of bags that will have the same quantities of the different gifts is the Greatest Common Divisor of the numbers of gifts.
GCD(24, 32, 44) = 4
Mrs. Dupree can make at most 4 identical bags.
___
How to find the GCD
The GCD can be found by looking at factors:
24 = 4·632 = 4·844 = 4·114 is the largest common factor of these numbers.
__
The GCD can also be found using Euclid's algorithm. In that algorithm, the larger number is divided by the smaller, with the remainder replacing the larger number after each step. If the remainder is zero, the smaller number is the GCD.
The GCD of several numbers can be found by finding the GCD of a pair, then of that value and the next number:
GCD(24, 32, 44) = GCD(GCD(24, 32), 44) = GCD(8, 44) = 4
_
32/24 = 1 r 8 . . . . first step in Euclid's algorithm for GCD(24, 32)
24/8 = 3 r 0 ⇒ GCD(24, 32) = 8
Then
44/8 = 5 r 4
8/4 = 2 r 0 ⇒ GCD(8, 44) = 4 = GCD(24, 32, 44)
Steve order plaster cases for storing his baseball cards. Each case has a length of 12 centmeters a width of 6.5 centmeters and a height of 1.25 centmeters. What is the volume in cubic centmeters of one baseball card?
what shape would you get if you cut off one of the corners of a rectangular prism
Cutting off one corner of a rectangular prism creates a bicapped trigonal prismatic shape.
When you cut off one of the corners of a rectangular prism, you would get a shape known as a bicapped trigonal prismatic. This shape is formed by twisting one face of a cube relative to another, folding opposing faces towards one another, and distorting the original rectangular prism.
Find the error in the student’s calculation.
a. The student should have simplified the exponent first.
b. The student did not subtract 3 and 8 correctly.
c. The student should not have multiplied 8 and -2.
d. The student did not make an error.
Answer:
The answer is A
Step-by-step explanation:
When doing an equation you always have to follow this order: exponents, parentheses, multiply/divide, then addtion/subtraction
At a high school, the cafeteria staff provides optional comment cards to students eating in the cafeteria. Students who wish to make a comment can obtain and fill out a comment card and return it to a drop box in the front office. At the end of the semester, the staff analyzes the responses and finds that 72% of the students who filled out a comment card recommend major changes to the food selection. What conclusions can the cafeteria staff draw from these responses?A) Since all of the students had an opportunity to respond, this is evidence that a majority of all the students supports major changes. B) The cafeteria staff should not use the results to draw any conclusions since some students may not have filled out a comment card, which is non-response. C) If the students recorded their grade level with their response, the staff could make the original sample a stratified sample and use the responses to learn what proportion of each grade recommends major changes to food selection. D) The responses were from a voluntary response sample, so the cafeteria staff should not use the results to draw any conclusions. E) The opportunity to fill out comment cards should be offered to students at all high schools in the school district to get a larger sample size, which will make the results more reliable,
Answer:
A) Since all of the students had an opportunity to respond, this is evidence that a majority of all the students supports major changes.
Step-by-step explanation:
Since all the students were given equal opportunity then the response suggest that a major change is required by the students.
Answer: d
Step-by-step explanation: the responses were from voluntary response sample, so the cafeteria staff should not use the results to draw any conclusions
Someone pls pls pls help me!!
In 2002, there were 972 students enrolled at Oakview High School. Since then, the number of students has increased by 1.5% each year. Write an exponential function to model the situation, then find the number of students enrolled in 2014. Is this considered growth or decay?
Answer:
n(t) = 972×1.015^t1162 studentsgrowthStep-by-step explanation:
The growth factor is 1 added to the growth rate of 1.5%, so is 1.015. This factor is applied each year. So the number of students will be the original number multiplied by this factor as many times as there are years (after 2002).
Repeated multiplication is signified using an exponent. The function can be written as ...
n(t) = 972×1.015^t
In 12 years after 2002, the number of students is modeled as ...
n(12) = 972×1.015^12 ≈ 1162 . . . students in 2014
__
When the change is described as "increased by ...", it means the function is modeling growth. If the population were to decrease, it would be considered decay. That is, the "growth factor" is greater than 1 for growth, and less than 1 for decay. 1.015 is greater than 1, so this is considered growth.
A research company desires to know the mean consumption of milk per week among males over age 25. A sample of 650 males over age 25 was drawn and the mean milk consumption was 3.4 liters. Assume that the population standard deviation is known to be 1.3 liters. Construct the 95% confidence interval for the mean consumption of milk among males over age 25. Round your answers to one decimal place.
Answer:
[tex]3.3\leq x\leq 3.5[/tex]
Step-by-step explanation:
The 95% confidence interval can be calculated as:
[tex]x'-z_{\alpha/2}\frac{s}{\sqrt{n}} \leq x\leq x'+z_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]
Where [tex]x[/tex] is the mean consumption of milk, [tex]x'[/tex] is the sample mean, [tex]s[/tex] is the population standard deviation, [tex]n[/tex] is the size of the sample, [tex]\alpha[/tex] is 5% and [tex]z_{\alpha /2}[/tex] is the z-value that let a probability of [tex]\alpha /2[/tex] on the right tail.
So, replacing [tex]x'[/tex] by 3.4 liters, [tex]s[/tex] by 1.3 liters, n by 650 and [tex]z_{\alpha /2}[/tex] by 1.96, we get that the 95% confidence interval is equal to:
[tex]3.4-(1.96*\frac{1.3}{\sqrt{650}})\leq x\leq 3.4+(1.96*\frac{1.3}{\sqrt{650}}) \\3.4-0.1\leq x\leq 3.4+0.1\\3.3\leq x\leq 3.5[/tex]
Answer:
Step-by-step explanation:
Confidence interval is written in the form,
(Sample mean - margin of error, sample mean + margin of error)
The sample mean, x is the point estimate for the population mean.
Since the sample size is large and the population standard deviation is known, we would use the following formula and determine the z score from the normal distribution table.
Margin of error = z × σ/√n
Where
σ = population standard Deviation
n = number of samples
From the information given
x = 3.4
σ = 1.3
n = 650
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.025 = 0.975
The z score corresponding to the area on the z table is 1.96. Thus, confidence level of 95% is 1.96
Margin of error = 1.96 × 1.3/√650 = 0.1
Confidence interval = 3.4 ± 0.1
The lower end of the confidence interval is
3.4 - 0.1 = 3.3 litres
The upper end of the confidence interval is
3.4 + 0.1 = 3.5 litres
The following represent statistics of weekly salaries at the Harper Publishing Company.
Mean = $470 Median = $475 Mode = $460 Standard deviation = $30
First Quartile = $450 Third Quartile = $485 79th Percentile = $545 P67 = $483
Answer:
1) The most common salary is $460.
2) The salary that half of the employees surpassed is $475
3) The percentage of employees with salaries below $485 is 75%
4) 75% of the employees have a salary above $450.
5) The salary that stands 3 standard deviations below the mean is $380
6) 33% of the employees have a salary above $483.
7) The salary that stands 2 standard deviations above the mean is $530
Step-by-step explanation:
Hello!
1. What is the most common salary?______________
The measure that allows you to know which one is the most common value (i.e. the most frequent/observed number) in a data set is the mode. According to the given statistics, the most common salary is $460.
2. What salary did half the employees surpass?_________________
The measure that divides the sample in exactly a half (bottom 50% from the top 50%) is the median. In this example the salary that half of the employees surpassed is $475.
3. About what percent of employee's salaries is below $485?__________________
As you can see in the descriptive statistics, the third quartile (Q₃) is $485.
The Q₃ is the value that divides the bottom 75% of the sample from the top 25%. So the percentage of employees with salaries below $485 is 75%
4. What percent of the employees are above $450?___________________
The first quartile (Q₁) is the value that separates the bottom 25% of the sample from the top 75%. In this case Q₁= $450, which means that 75% of the employees have a salary above $450.
5. What salary is 3 standard deviations below the mean?____________________
The mean is $ 470 and the standard deviation is $30, the salary that stands 3 standard deviations below the mean is
X[bar]-3S= $470-3*$30= $380
6. About what percent of employee's salaries is above $483?__________________
P₆₇= $483, this value is the 67th percentile and means that 67% of the employees have a salary below $483.
If 67% are below $483, then 100 - 67= 33% of the employees have a salary above $483.
7. What salary is 2 standard deviations above the mean?______________________
The mean is $ 470 and the standard deviation is $30, the salary that stands 2 standard deviations above the mean is
X[bar]+2S= $470+2*$30= $530
I hope you have a SUPER day!
The Louvre Pyramid, designed by the architect I. M. Pei, is a landmark in the city of Paris. The right pyramid has a vertical height of 21.621.621, point, 6 meters (\text{m})(m)(, start text, m, end text, )and a square base with side length 35\,\text{m}35m35, start text, m, end text. The Inverted Pyramid is a skylight in the shape of an upside-down right pyramid located on the ceiling of a mall below the Louvre Pyramid. The Inverted Pyramid has a vertical height of 7and a square top with side length 16. Approximately how much greater is the volume of the Louvre Pyramid than the volume of the Inverted Pyramid, to the nearest cubic meter t, cubed,
Answer:
8223 cubic meter
Step-by-step explanation:
Louvre Pyramid
Vertical Height =21.6 meters
Side Length of Square Base =35 m
Volume of a Pyramid [tex]=\frac{1}{3}*$Base Area X Height[/tex]
Therefore, Volume of Louvre Pyramid[tex]=\frac{1}{3}*35^2 X 21.6[/tex]
=8820 cubic meter.
Inverted Pyramid
Vertical Height =7 meters
Side Length of Square Base =16 m
Volume of a Pyramid [tex]=\frac{1}{3}*$Base Area X Height[/tex]
Therefore, Volume of Louvre Pyramid[tex]=\frac{1}{3}*16^2 X 7[/tex]
=597.33 cubic meter.
Difference in Volume
Difference=Volume of Louvre Pyramid-Volume of Inverted Pyramid
=8820-597.33
=8222.67
=8223 cubic meter (to the nearest cubic meter)
On circle OOO below, \overline{SE} SE start overline, S, E, end overline is a diameter. What is the measure of \angle ISE∠ISEangle, I, S, E?
Answer:
Step-by-step explanation:
34
What is the value of the expression below?
(121/4)4
Answer:
121
Step-by-step explanation:
Answer:
if the 1/4 is supposed to be small and above the 12, the answer should be 12
Step-by-step explanation:
test
A major traffic problem in the Greater Cincinnati area involves traffic attempting to cross the Ohio River from Cincinnati to Kentucky using Interstate 75. Let us assume that the probability of no traffic delay in one period, given no traffic delay in the preceding period, is 0.85 and that the probability of finding a traffic delay in one period, given a delay in the preceding period, is 0.75. Traffic is classified as having either a delay or a no-delay state, and the period considered is 30 minutes.
a. Assume that you are a motorist entering the traffic system and receive a radio report of a traffic delay. What is the probability that for the next 60 minutes (two time periods) the system will be in the delay state? Note that this result is the probability of being in the delay state for two consecutive periods.
b. What is the probability that in the long run the traffic will not be in the delay state?
c. An important assumption of the Markov process models presented in this chapter has been the constant or stationary transition probabilities as the system operates in the future. Do you believe this assumption should be questioned for this traffic problem? Explain.
Answer:
Check the explanation
Step-by-step explanation:
First define the below events
Delayt : Traffic delay in current period
Delayt-1 : Traffic delay in preceding period
No-Delayt : No traffic delay in current period
No-Delayt-1 : No traffic delay in preceding period
Based on above definitions, define below given probabilities
P(No-Delayt/No-Delayt-1) = Probability of "no delay" in current period given that "no delay" in preceding period
= 0.85
P(Delayt/Delayt-1) = Probability of "delay" in current period given that "delay" in preceding period
= 0.75
and given that one period = 30 minutes
a) Given that motorist already knows that there is a traffic delay, probability of delay in next 60 minutes will be possible if both the consecutive periods is in "delay" state.
Period A Period B
---------------- -----------------
Delay -------> Delay ------> Delay
Since both the delay events should occur together(consecutive) to get the required probability, hence
Probability that next 60 minutes(two consecutive periods) will be in delay state
= P(Delayt/Delayt-1) * P(Delayt/Delayt-1)
= 0.75 * 0.75
= 0.5625 [ANSWER]
b) probability that in the long run the traffic will not be in the delay state is equivalent to proability that all the time in No-delay state.
First calculate the probability of currren period in delay state given that preceding period in No-delay state
P(Delayt/No-Delayt-1) = 1 - P(No-Delayt/No-Delayt-1)
= 1 - 0.85
= 0.15
Now the required probability,
P(All the time No-Delay state) = 1 - P( one period in delay state)
= 1 - ( P(Delayt/Delayt-1) + P(Delayt/No-Delayt-1) )
= 1 - (0.75 + 0.15)
= 0.10 [ANSWER]
c) Yes. Because this assumption assumes that for the 30 minutes traffic will be in delay state and just after 30 minutes, there will be No-delay state which is a hypothetical situation. In general scenario, traffic doesn't behave like this. To make the model more realistic, the probabilities might have been modeled as a function of time, instead of being constant for 30 minutes.
Please help 6th grade math ! :)
Answer:
2.50 per two bottles of sprite
Step-by-step explanation:
It's too short. Write at least 20 characters to get a great answer.It's too short. Write at least 20 characters to get a great answer.
Answer:
143°
Step-by-step explanation:
We know that the two lines are parallel, which means that since ∠A and ∠B are same-side angles, they are equal. That means we can set the expressions equal:
7x + 24 = 3x + 92
4x = 68
x = 17
Plug this into the expression for A:
∠A = 7x + 24 = 7 * 17 + 24 = 143
The answer is 143°.
Since both lines are parallel, both equations are equal.
7x + 24 = 3x + 92
Solve for x.
~Subtract 24 to both sides
7x + 24 - 24 = 3x + 92 - 24
~Simplify
7x = 3x + 68
~Subtract 3x to both sides
7x - 3x = 3x - 3x + 68
~Simplify
4x = 68
~Divide 4 to both sides
4x/4 = 68/4
~Simplify
x = 17
Substitute 17 with x in ∠A
∠A = 7x + 24
∠A = 7(17) + 24
∠A = 119 + 24
∠A = 143
Best of Luck!
What is the volume of a hemisphere with a radius of 61.9 m, rounded to the nearest
tenth of a cubic meter?
Answer:
The volume of the hemisphere is 496741.6 m³
Step-by-step explanation:
The volume of an sphere is given by:
[tex]V_{s} = \frac{4\pi r^{3}}{3}[/tex]
In which [tex]\pi = 3.14[/tex] and r is the radius.
An hemisphere is half of an sphere, so it's volume is half the sphere's volume. So
[tex]V_{h} = \frac{V_{s}}{2} = \frac{2\pi r^{3}}{3}[/tex]
In this question:
[tex]r = 61.9[/tex]. So
[tex]V_{h} = \frac{2\pi (61.9)^{3}}{3} = 496741.6[/tex]
The volume of the hemisphere is 496741.6 m³
Answer:
The volume of the hemisphere = 496741.6 m³
Step-by-step explanation:
Volume of a sphere is= (4/3) × π × r³
r is the radius
π is 22/7
hemisphere is half of an sphere,
so the volume of henisphere is (2/3) × π × r³
Given that ;
r = 61.9 m
[tex]V = \frac{2\pi (61.9)^{3}}{3} = 496741.6[/tex]
therefore, the volume of the hemisphere is 496741.6 m³
Write this number
7 ones, 2, tens, 3 hundreds
Answer:
327
Step-by-step explanation:
7 ones = 7*1 = 7
2 tens = 2*10 = 20
3 hundreds = 3 * 100 = 300
300 +20 +7 = 327
A bag contains red and blue marbles, such that the probability of drawing a blue marble is 3/8. An experiment consists of drawing a marble, replacing it, and drawing another marble. The two draws are independent. A random variable assigns the number of blue marbles to each outcome. What is the probability that the random variable has an outcome of 3?
The correct answer is that the probability of the random variable having an outcome of 3 is 0.
To solve this problem, we need to understand that the random variable assigns the number of blue marbles drawn to each outcome of the experiment. Since the experiment consists of two independent draws with replacement, there are four possible outcomes:
1. Draw a blue marble, then draw another blue marble.
2. Draw a blue marble, then draw a red marble.
3. Draw a red marble, then draw a blue marble.
4. Draw a red marble, then draw another red marble.
The probability of drawing a blue marble in a single draw is given as 3/8. Therefore, the probability of drawing a red marble is the complement of this, which is 1 - 3/8 = 5/8.
Now, let's calculate the probability of each of the four outcomes:
1. The probability of drawing two blue marbles (BB) is (3/8) * (3/8), because the draws are independent.
2. The probability of drawing a blue marble followed by a red marble (BR) is (3/8) * (5/8).
3. The probability of drawing a red marble followed by a blue marble (RB) is (5/8) * (3/8).
4. The probability of drawing two red marbles (RR) is (5/8) * (5/8).
Since the random variable assigns the number of blue marbles to each outcome, the only way to have an outcome of 3 is to draw a blue marble, then draw another blue marble. This is the first outcome listed above.
The probability of drawing two blue marbles (BB) is (3/8) * (3/8) = 9/64.
However, the question asks for the probability of the random variable having an outcome of 3. Since the maximum number of blue marbles that can be drawn in two draws is 2, it is impossible to have an outcome of 3. Therefore, the probability of the random variable having an outcome of 3 is 0.
In conclusion, the probability that the random variable has an outcome of 3 is 0, because it is not possible to draw more than 2 blue marbles in two independent draws with replacement from a bag where the probability of drawing a blue marble is 3/8.
Q2
Solve for the height (h) of this
triangular prism if the volume is 1080.
The volume of a triangular prism is V =
(B)(h), where B is the area of the
triangle. Remember the area of a
triangle is 1/2(b)(h). BE CAREFUL
BECAUSE THERE ARE TWO HEIGHTS,
ONE FOR THE TRIANGLE AND ONE
FOR THE TRIANGULAR PRISM. *
A
Answer:
(C)18 Units
Step-by-step explanation:
Volume of a Triangular Prism =Base Area X Height
The base is a right triangle of base 8 Units and Height 15 Units.
Area of the Triangle =0.5 x 8 x 15 =60 Square Units
Base Area, B=60 Square Units
Since Volume of the Triangular Prism=1080
1080=60h
Divide both sides by 60
Height of the Prism=18 Units
Drag the numbers to the correct locations on the table. Not all numbers will be used.
Alexis performed an experiment by drawing equal-sized colored balls from a box. She randomly drew a ball 50 times and recorded the color in the frequency table.
Answer:
Red-5-0.1
Blue-0.26
White-10
Green-22
Step-by-step explanation:
In the experiment, Alexis drew colored balls and you need to organize the results in a frequency table. The numbers given represent frequency counts for each color. Keep in mind that the total draws were 50, so no frequency count should exceed this number.
The question is about Alexis' experiment involving drawing colored balls from a box. The results of the 50 trials are recorded in a frequency table. As the student, you are expected to correctly assign certain numbers to their respective places in this table. These numbers represent the total counts per color across the 50 trials.
To accomplish this, you must first understand what a frequency table is. A frequency table is a method of organizing raw data in a compact form by displaying a series of data values in ascending order, along with their corresponding frequencies.
In this scenario, the frequencies are the number of times Alexis drew a ball of a specific color. For example, if she drew a red ball 15 times, we would put 'Red' in the color column and '15' in the frequency column.
Please note that not all the provided numbers will be used, and there should be no number in the table higher than 50 since that was the maximum number of trials Alexis performed.
For more such questions on frequency table, click on:
https://brainly.com/question/31660971
#SPJ2
g For a specific location in a particularly rainy city, the time a new thunderstorm begins to produce rain (first drop time) is uniformly distributed throughout the day and independent of this first drop time for the surrounding days. Given that it will rain at some point both of the next two days, what is the probability that the first drop of rain will be felt between 9:10 AM and 3:30 PM on at least one of the next two days
Answer:
The probability that the first drop of rain will be felt between 9:10 AM and 3:30 PM on at least one of the next two days is 0.2639.
Step-by-step explanation:
The random variable X is defined as the time a new thunderstorm begins to produce rain.
The random variable X is uniformly distributed throughout the day, i.e. between the 24 hours a day or 1440 minutes.
[tex]X\sim Uniform\ [0, 1440][/tex]
The probability density function of X is:
[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b,\ a<b[/tex]
It is provided that it will rain at some point both of the next two days.
Compute the probability that the first drop of rain will be felt between 9:10 AM and 3:30 PM as follows:
9:10 AM = (9 × 60) + 10 = 550 minutes.
3:30 PM = 15:30 = (15 × 60) + 30 = 930 minutes.
Compute the value of P (550 < X < 930) as follows:
[tex]P(550<X<930)=\int\limits^{930}_{550}{\frac{1}{1440-0}}\, dx\\\\=\frac{1}{1440}\times \int\limits^{930}_{550}{1}\, dx\\\\=\frac{1}{1440}\times [x]^{930}_{550}\\\\=\frac{930-550}{1440}\\\\=0.2639[/tex]
The probability that the first drop of rain will be felt between 9:10 AM and 3:30 PM is 0.2639.
Then the complement of this event is:
The probability that the first drop of rain will not be felt between 9:10 AM and 3:30 PM is:
P (Not between 9:10 AM and 3:30 PM) = 1 - 0.2639 = 0.7361
Compute the probability that the first drop of rain will be felt between 9:10 AM and 3:30 PM on at least one of the next two days as follows:
P (At least 1) = 1 - P (Less than 1)
= 1 - P (None)
= 1 - P (Not between 9:10 AM and 3:30 PM)
= 1 - 0.7361
= 0.2639
Thus, the probability that the first drop of rain will be felt between 9:10 AM and 3:30 PM on at least one of the next two days is 0.2639.