The value for the number of red lights that Alice encounters are found.
Mean = 2; Var = 1; PMF = ⁿCˣ0.5ˣ × 0.5 ⁽⁴⁻ˣ⁾What is meant as the independent events?The set of findings from an experiment is thought to as events in probability. There are numerous sorts of events, including independent, dependent, and mutually exclusive ones.X = no of red lights crossed by Alice.
X is Binomial distributed
In which n=4, p=0.5, q = 0.5
Mean value is found by the formula,
Mean = np
Mean = 4×0.5
Mean = 2
And, variance = npq
Var = np(1-p)
Var = 4×0.5×0.5
Var = 1
PMF = ⁿCˣ0.5ˣ × 0.5 ⁽⁴⁻ˣ⁾
Thus, the value for pmf, the mean, and the variance of the number of red lights that Alice encounters are found.
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9. A family ordered 2 large pizzas for lunch. They ate
7
-
8
of one pizza and of the other pizza. What
fraction of a pizza was left for dinner?
118
b. 1/2
d. 12/12
b.
e.
318
334
C.
718
00
10
Answer:
9/16
Step-by-step explanation:
Urgent(Please answer in 2 days):In the figure below, ABCD is a parallelogram, AD=18 and DC=27. Segments overline{EG} and overline{FH} are perpendicular to sides of the parallelogram as shown, and EG=16. What is the area of the parallelogram?
The area of the parallelogram shown in this problem is of:
A = 432 units squared.
What is the area of a parallelogram?The area of a parallelogram of base b and height h is given by the multiplication of these two dimensions, as presented as follows:
A = b x h.
In this problem, these dimensions are given as follows:
Base: AB = DC = 27.Height: EG = 16.(the height is perpendicular to the sides of the parallelogram, forming an angle of 90º, as is the case in this problem).
Hence the area of the parallelogram, applying the multiplication of the obtained base and height, is calculated by the multiplication of the base and of the height given as follows:
A = 27 x 16 = 432 units squared.
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Answer:
432
Step-by-step explanation:
The area of a parallelogram is the product of a side length (the base) and the perpendicular distance between that side and the opposite side (the height). In this case, we can use (line)DC as a base and (line)EG as the matching height, so the area is equal to
(DC) ∙ (EG) = 27 ∙ 16 = 432.
Stacy is one-fourth as old as her mother. If Stacy's mother is 36, how old is Stacy?
Answer: Stacy is 12 years old
Step-by-step explanation:
36/4 = 12
Part A Write a paragraph proof to prove ABC ≌ ABD. Explain in complete sentences each statement and reason. Be sure to give the reason the two triangles are congruent.
Part B Now that you have proven the two triangles are congruent, can you show that ∠CBA ≌ ∠DBA? Explain your reasoning in a complete sentence.
A. Both triangles have two pairs of corresponding sides and a pair of included angles, therefore, ΔABC ≌ ΔABD by SAS.
B. ∠CBA ≌ ∠DBA by CPCTC.
What is the SAS Congruence Theorem?The SAS congruence theorem state that if we have two triangles that we can show that they posses two pairs of corresponding sides that are equal and a pair of included angles that are also equal, then we can state that the two triangles are congruent to each other
When two triangles are proven to be congruent to each other, every corresponding parts of both triangles will be equal to each other based on CPCTC.
Part A:
We are given that AC ≌ AD, and ∠CAB ≌ ∠DAB.
Also, AB ≌ AB based on the reflexive property.
Therefore, both triangles are congruent to each other based on SAS.
ΔABC ≌ ΔABD
Part B:
Since both triangles are congruent, therefore ∠CBA ≌ ∠DBA by CPCTC.
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What would the final cost be
for a trick or treat bucket that
originally costs $3.00 if you
have a coupon for 10% off and
you have to pay tax of 7.5%?
Answer:
4.73
Step-by-step explanation:
10% is 10
so, you have to multiple 3×.10=.30
3-.30=2.70
2.70×.75 because 7.5% is .75
that is 2.0250 and then you have to add 2.0250 with 2.70 that is 4.7250 and if you round it. It is 4.73
Hope that works
the probability that a single radar station will detect an enemy plane is 0.65. (a) how many such stations are required to be 98% certain that an enemy plane flying over will be detected by at least one station? stations (b) if four stations are in use, what is the expected number of stations that will detect an enemy plane? (round your answer to one decimal place.)
If seven stations are in use, the expected number of stations that will detect an enemy plane is 4.55.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.acc to our question-,
(b) If seven stations are in use, what is the expected number of stations that will detect an enemy plane?The expected number of sucesses of a binomial variable is given by:If seven stations are in use, the expected number of stations that will detect an enemy plane is 4.55.learn more about probability click here:
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Jacob distributed a survey to his fellow students asking them how many hours they spent on the Internet in the past day. He also asked them to rate their mood on a scale from 0,10, with ten being the happiest. A line was fit to the data to model the relationship.
Answer:
The answer is B. y = -x + 7.5.
Step-by-step explanation:
The slope is -1 and the y-intercept is 7.5.
PLEASE MARK AS BRAINLIEST!!!last year at a certain high school, 10 students sought the nomination for president of the student body. in how many ways could the voters (student body) rank their first 5 choices? a) 5 b) 50 c) 30,240 d) 3,628,800 e) 252 f) none of the above.
The number of ways voters could rank their first 5 choices out of 10 is 30240.
Given,
Number of students sought the nomination for president of the student body = 10 students
We have to find the number of ways voters could rank their first 5 choices.
Permutation;
An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order.
Here we have to use permutation formula;-
ⁿPr = n! / (n - r)!
Here,
n is the number of students = 10
r is the choices = 5
Then,
ⁿPr = n! / (n - r)!
¹⁰P₅ = 10! / (10 - 5)!
¹⁰P₅ = 10! / 5!
¹⁰P₅ = 10 x 9 x 8 x 7 x 6
¹⁰P₅ = 30240
That is,
The number of ways voters could rank their first 5 choices out of 10 is 30240.
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in a survey, 19 people were asked how much they spent on their child's last birthday gift. the results were roughly bell-shaped with a mean of $40.7 and standard deviation of $9.2. estimate how much a typical parent would spend on their child's birthday gift (use a 80% confidence level). give your answers to 3 decimal places.
The parent spend on their child’s birthday gift is by using 80% confidence level is (43.5, 37.9)
A sample mean is the result of a chance experiment. When we sample a random variable, we get one of its possible values. A sample is a specific value. The random variable's probability distribution determines the possible values and the likelihood of each.
Given that,
Point estimate = sample mean = X = 40.7
sample standard deviation = s = 9.2
sample size = n = 19
Degrees of freedom = df = n - 1 = 19 - 1 = 18
At 80% confidence level
α = 1 - 80%
α =1 - 0.80 =0.2
α/2 = 0.1
t α/2,df = t0.1,18 = 1.330
The margin of error = E = t /2, df x (s/√n)
= 1.330 x (9.2/√19)
= 1.330 x 2.110
= 2.8
Margin of error = E = 2.8
The 80% confidence interval estimate of the population mean is,
X ± E
= 40.7 ± 2.8
= (43.5, 37.9)
Therefore The parent spend on their child’s birthday gift is by using 80% confidence level is (43.5, 37.9)
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help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The function f(x) = [tex]-3x^2[/tex] + 18x + 3 has the maximum value of 30 at x = 3
The quadratic function is
f(x) = [tex]-3x^2[/tex] + 18x + 3
The general form of the quadratic function is
y = [tex]ax^2[/tex] + bx + c
If a < 0, the quadratic function has maximum value
Here the value of a = -3
Therefore the function has maximum value.
Maximum value will be at x = -b / 2a
= -18 / 2(-3)
= -18 / -6
= 3
The maximum value of quadratic function will be (4ac - [tex]b^2[/tex]) /4a
Substitute the value in the equation
(4ac - [tex]b^2[/tex]) /4a = (4×-3×3 - 18×18) / 4×-3
= (-36 - 324 / -12
= -360 / -12
= 30
Hence, the function f(x) = [tex]-3x^2[/tex] + 18x + 3 has the maximum value of 30 at x = 3
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help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The value of function is positive so the function have maximum value 30 at x=3.
In the given question we have to find the maximum or the minimum value of a function.
The given function is
f(x) = -3x^2+18x+3
To find the maximum or minimum value we firstly find the value of f'(x).
f'(x) = -6x+18
Now put f'(x)=0
-6x+18=0
Subtract 18 on both side we get
-6x=-18
Divide by -6 on both side we get
x = 3
Now finding the value of function at x=3
f(3)= -3*(3)^2+18*3+3
f(3)= -3*9+54+3
f(3)= -27+54+3
f(3)= 30
Since the value of function is positive so the function have maximum value 30 at x=3.
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recipe requires 1 cup of sugar for every 6 cups of flour. How many cups of sugar will be required for 18 cups of flour?
Answer: 3 cups of sugar will be required for 18 cups of flour.
Step-by-step explanation:
1 cup of sugar - 6 cups of flour
2 cups of sugar - 12 cups of flour
3 cups of sugar - 18 cups of flour
I hope this make sense.
Determine which of the lines, if any, are parallel or perpendicular. explain. line a passes through (2, 10) and (4, 13). line b passes through (4, 9) and (6, 12) . line c passes through (2, 10) and (4, 9) .
Line a and line b are parallel to each other, and c is neither parallel nor perpendicular.
Line a passes through (2, 10) and (4, 13).
Line b passes through (4, 9) and (6, 12).
Line c passes through (2, 10) and (4, 9).
If a line passes through two points, then the slope of the line is
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Line a passes through (2, 10) and (4, 13). So, the slope of this line is
[tex]m_{a}=\frac{13-10}{4-2}=\frac{3}{2}[/tex]
Line b passes through (4, 9) and (6, 12). So, the slope of this line is
[tex]m_{b}=\frac{12-9}{6-4}=\frac{3}{2}[/tex]
Line c passes through (2, 10) and (4,9). So, the slope of this line is
[tex]m_{c}=\frac{9-10}{4-2}=\frac{1}{2}[/tex]
The product of slopes of perpendicular lines is -1.
and if the slope of 2 lines is equal then those lines are parallel
so, line a and line b are parallel to each other, and c is neither parallel nor perpendicular.
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Can anyone write the equation of the graph?
The absolute equation in the graph is f(x) = |x - 3| + 5
How to find the equation of the graph line?From the question, we can see that the lines on the graph has a sharp v-shape
Graphs that have this form are absolute value graphs
The general form of an absolute value equation is expressed as
y = |x - h| + k
From the above form, we have
Vertex = (h, k)
By definition, the vertex of a function is either the maximum point or the minimum point
On the given graph, the minimum point is (3, 5)
So, we have the following representation
(h, k) = (3, 5)
Substitute (h, k) = (3, 5) in the above equation
So, we have:
y = |x - 3| + 5
Hence, the function represented by the graph has an equation of f(x) = |x - 3| + 5
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ABC is and isosceles triangle. ACDE is a parallelogram. Find BCD
angle bcd is 140. see explanation in image
Pls help/ The y-intercept of f(x)=(1.6)x is ______________________ the y-intercept of the function in the graph:
The y-intercept of f(x) = (1.6)x is (a) less than the y-intercept of the function in the graph
How to complete the blank?The equation of the function is given as
f(x) = (1.6)x
To determine the y-intercept, we set x = 0
So, we have
f(0) = 1.6 * 0
Evaluate
f(0) = 0
For the graph, we have
When x = 0, the function has a value of 1
This means that
y-intercept is 1
0 is less than 1
Hence, the y-intercept of f(x) = (1.6)x is (a) less
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Find the equation of the line that is parallel to another line whose equation is x+2y+8=0 and passes though the point(-2,-3)
There is no line parallel to the line x + 2 · y + 8 = 0, as point (x, y) = (- 2, - 3) lies on the original line.
How to determine the equation of a line parallel to another line and that passes through a given point.
In this problem we need to determine the equation of line based on its slope relationship respect to another line and a given point. Two lines are parallel if and only if they have the same slope (m) and two distinct intercepts (b). First, transform the given equation of the line into slope-intercept form:
x + 2 · y + 8 = 0
2 · y = - x - 8
y = - (1 / 2) · x - 4
Then, the resulting line has a slope of - 1 / 2.
Second, determine the intercept of the resulting line:
y = m · x + b
b = y - m · x
b = - 3 - (- 1 / 2) · (- 2)
b = - 3 - 1
b = - 4
The intercept of the resulting line is - 4.
Third, transform the equation of the resulting line into standard form:
y = - (1 / 2) · x - 4
- 2 · y = x + 8
x + 2 · y + 8 = 0
There is no parallel line for the point (x, y) = (- 2, 3).
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Point B is graphed on the coordinate plane. Which ordered pair represents point B?
Sophie has bought some plants 36 violas 54 sweet peas and 72 fuchsias she wants to plant them in pots so that there is one type of plant in each pot and each pot has the same number of plants in it what is the maximum number of plants she could have in each pot
The maximum number of plants Sophie can have in each pot is 18.
Highest Common factor:
The greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.
Here it is given that Sophie plants 36 violas, 54 sweet peas, and 72 fuchsias. She wants to plant them in pots.
So we have to find the maximum number of plants she could have in each pot.
For that, we have to find the Highest common factor of the given different-different plant she has.
HCF of 36, 54, 72 = 18
So the maximum number of plants she can pot is 18.
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which is a perfect square 20 13 25 24 14 10 7 11 8
HELPPPP PLSPLSPPSPPPLSPSLPLLSLPSLP
Answer: What do those numbers mean
Step-by-step explanation:
he management of an indoor shopping mall wants to survey its shoppers about the layout of the stores in the mall. at a specified time one day, they send a team of interviewers to survey 2 randomly selected customers in each of the 48 stores in the mall. this scenario describes
The scenario describes the stratified random sampling method .
There are many sampling techniques to collect sample from a given population such as Simple random sampling , Systematic Sampling , Cluster Sampling and so on . All of them vary in reliability , accuracy and efficiency .
Stratified Random Sampling : It is a method of sampling in which division of population is done into smaller subgroups known as strata .The strata are formed based on member's shared attributes or characteristics . It has numerous applications . It is also called proportional random sampling or quota random sampling .
Therefore , the scenario describes the stratified random sampling method .
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help meeeeeeeeeeeeeeeeee please
Answer:
324 ft
Step-by-step explanation:
[tex]v=\sqrt{2gh}[/tex]
[tex]v^2=(\sqrt{2gh})^2[/tex]
[tex]v^2=2gh[/tex]
[tex]\frac{v^2}{2g}=\frac{2gh}{2g}[/tex]
[tex]\frac{v^2}{2g}=h[/tex]
[tex]\frac{144^2}{2(32)}=h[/tex]
[tex]\frac{20736}{64}=h[/tex]
[tex]324=h[/tex]
Write the equation of the line in fully simplified slope-intercept form.
ANSWER ASAP
WILL GIVE BRAINLIEST
The equation of the line in fully simplified slope - intercept form is 5x + 4y = 12 .
In the question ,
a graph of the line is given , we need to find the equation of the given line in the simplified slope - intercept form .
to find the equation , we need minimum two points ,
So , from the given graph ,
we can find that
when x [tex]=[/tex] 0 , the value of y [tex]=[/tex] 3 ,
the first point is (0 [tex],[/tex] 3) .
when x [tex]=[/tex] 4 , the value of y [tex]=[/tex] -2 ,
the second point is (4 [tex],[/tex] -2) .
the slope can be calculated by
slope = (-2-3)/(4-0)
= -5/4
So , the equation of the line passing through point (4,-2) with slope -5/4 , in the slope intercept form is
(y -(-2)) = (-5/4)(x-4)
y + 2 = (-5/4)x + 5
y = (-5/4)x + 5 - 2
y = (-5/4)x + 3
Simplifying further , we get
4y = -5x + 12
5x + 4y = 12
Therefore , The equation line in fully simplified slope - intercept form is 5x + 4y = 12 .
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the p-value is 0.026, so we reject the null hypothesis and accept the alternative hypothesis. we conclude that this year the proportion of americans who support federal spending cuts to medicaid is less than 0.12 what type of error is possible here?
The proportion of Americans who support federal spending cuts to Medicaid is less than 0.12 leads to Type 1 error.
What is Type 1 error and Type 2 error?When we reject a true H₀ it is known as type 1 error. The probability of type 1 errors is inversely proportional to the amount of confidence you choose. There is a 5% possibility of receiving a type 1 error on a test with a 95% confidence level.
When we feel to reject a false H₀ it is known as type 2 error.
H₀:P= 0.12
Hₐ:P= 0.12
The question implies that we actually rejected the null hypothesis, while there is a chance that it is true and we are rejecting a true null hypothesis.
Therefore, it only suggests that there is a possibility that we will make a type 1 error.
Consequently, Type 1 error is the response to our query.
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P and q started a business. the profits earned are divided in the ratio of their capital, 2:3. if p invested capital of $40,000, what was the capital invested by q?
The capital invested by q is $60,000 when p invested capital of $40,000.
According to the question,
We have the following information:
The ratio of the profits earned by by p and q is 2:3.
Amount invested by p = $40,000
Now, let's take the amount invested by p to be $2x and the amount invested by q to be $3x.
So, we have the following expression:
2x = 40000
x = 40000/2
x = $20000
Now, putting the value of x in 3x in order to find the amount invested by q:
3*20,000
$60,000
Hence, the amount invested by q is $60,000 when p invested capital of $40,000.
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heidi's scores on her first 3 tests were 92, 95, and 86. what is the minimum score she mulst earn on her next test to maintain at least a 90 average
The inequality that needs to be solved is:
3t +270/ 6 ≥ 90.
let we consider that Heidi has 6 subjects in her school.
Therefore, She needs to average at least 90 on her three remaining tests to have at least a 90 overall average for all 6 tests.
Now,
To obtain an average first add up all the scores of the tests and then divide by the number of tests.
So far Heidi has taken 3 tests and we know the total number of tests will be 6 so we will be dividing by 6 to get the average of all the score.
If we let each of the three remaining tests each be represent by t, then the sum of all the tests would be:
95 + 92 + 86 + t + t + t
or
273 + 3t
The average of these 6 tests can then be represented by:
3t + 273 / 6
And for her average to be at least 90 then she can get a 90 or more which is the same as ≥ 90
So the inequality that needs to be solved is:
[tex]\frac{3t + 273}{6}[/tex] ≥ 90
or, [tex]\frac{3 ( t + 91)}{6} \geq 90[/tex]
or, [tex]\frac{t + 91}{2} \geq 90[/tex]
Now, Heidi has to score :
t/2 ≥ 91
or, t/2 ≥ 90
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street light is at the top of a 19-ft-tall pole. a 6-ft tall woman walks away from the pole with a speed of 6 ft/sec along a straight path (see figure). how fast is the tip of her shadow moving, in ft/sec, when she is 50 ft from the base of the pole?
8.77 ft/sec is the tip of her shadow moving with a speed of 6 ft/sec .
What is speed, for instance?
Speed is the rate of change in location of an item, expressed in meters per second. If something starts at the origin and moves three meters in three seconds, for instance, its speed is one meter per second. The formula for speed is as straightforward as dividing a distance by a time.Let H = the height of the pole.
h = the height of the woman.
x = the length of the woman's shadow.
s = the distance from the pole to the woman.
By similar triangles, H/h = (s + x)/x or Hx = h(s + x).
Differentiating, H dx/dt = h(ds/dt + dx/dt)
19 dx/dt = 6(6 + dx/dt) = 36 + 6 dx/dt
13 dx/dt = 36
dx/dt = 36/13 ft/sec = 2.77 ft/sec for how fast her shadow is lengthening.
The speed of the tip of her shadow would be this speed added to her traveling speed: 2.77 + 6 = 8.77 ft/sec.
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15÷(3+13)2 i need help
Answer: 47
Step-by-step explanation:
bruce bought two books,one book equal 4 dollals more than three times the other book they both equal 72
what is x
The value of x in the equation is $55 and this represents the cost of the expensive book
How to determine the value of x?The variable x is not defined in the question
So, we represent x as the more expensive book and y to represent the less expensive book
Also, from the question we understand that
One book = $4 more than three times than the other.Both books = $72The above statements can be interpreted to the following equations
x = 4 + 3y
x + y = 72
Substitute x = 4 + 3y in the equation x + y = 72
So, the equation x + y = 72 is represented as
4 + 3y + y = 72
Evaluate the like terms in the above equation
4 + 4y = 72
Collect the like terms in the above equation
4y = 72 - 4
Evaluate
4y = 68
Divide both sides by 4
So, we have
y = 17
Substitute 17 for y in the equation x = 4 + 3y to solve for x
x = 4 + 3 * 17
Evaluate the products
x = 4 + 51
Evaluate the sum
This gives
x = 55
Hence, the cost of the more expensive book is $55
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Which of these strategies would eliminate a variable in the system of equations?
2x + 8y = -3
3x + 6y = -4
A: Multiply the top equation by 333, multiply the bottom equation by -2−2minus, 2, then add the equations.
B: Multiply the top equation by 333, multiply the bottom equation by 444, then subtract the bottom equation from the top equation.
C: Multiply the top equation by -4−4minus, 4, multiply the bottom equation by 333, then add the equations
Option A: Multiply the top equation by 3, multiply the bottom equation by -2, then add the equations will eliminate the variables.
Rewriting the equation -
2x + 8y = -3 : Equation 1
3x + 6y = -4 : Equation 2
Multiplying equation 1 with and equation 2 with -2.
6x + 24y = -9 : Equation 3
-6x - 12y = 24 : Equation 4
Adding the equation 3 and equation 4. This will eliminate the variable x.
12y = 15
y = 5/4
So, option 1 will eliminate the variable x on solving we get the value of y as 5/4.
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