Answer:
316
Step-by-step explanation:
The question has a little problem:
"the probability that they chose the same book is m n for relatively prime positive integers m and n. Compute 100m + n."
The correct sentence:
the probability that they chose the same book is "m/n" for relatively prime positive integers m and n.
Total number of books = 4
We have:
Number of 200page book = 1
Number of 400page book = 1
Number of 600page book = 1
Number of 800page book = 1
Probability of picking same book:
Velma read page 122 of her book Daphne read page 304 of her book
If it is same book, it must contain atleast 400page.
Therefore, 400page, 600page and 800 page would be considered in the probability.
Pr(one 400page) = 1/4
Pr(picking two 400page) = 1/4 * 1/4 = 1/16
Pr(one 600page) = 1/4
Pr(picking two 600page) = 1/4 * 1/4 = 1/16
Pr(one 800page) = 1/4
Pr(picking two 800page) = 1/4 * 1/4 = 1/16
Pr(picking same book page)=
Pr(picking two 400page) or Pr(picking two 600page) or Pr(picking two 800page)
= Pr(picking two 400page) + Pr(picking two 600page) + Pr(picking two 800page) = 1/16+ 1/16+ 1/16
Pr(picking same book page)= 3/16
This answer satisfies the probability as m/n for relatively prime positive integers m and n.
Two numbers are said to be relatively prime integers if the only positive integer that divides both of them is 1. It means the numerator and denominator of the fraction have been reduced to the lowest form.
m/n = 3/16
m = 3, n= 16
100m + n = 100(3) + 16
= 316
Answer:
100m+n = 6425
Step-by-step explanation:
Let X be the book Velma picks and Y the book that Daphne picks. Note that X and Y are independent and identically distributed, so for computations, i will just focus on X for now.
Lets denote with A, B, C and D the books with 200, 400, 600 and 800 pages respectively.
Note that, without any restriction P(X=A) = P(X=B) = P(X=C) = P(X=D) = 1/4. However, if we also add the condition that R = 122, where R is the page picked, we will need to apply the Bayes formula. For example,[tex]P(X=A|R=122) = \frac{P(R = 122|X=A)*P(X=A)}{P(R=122)}[/tex]
P(X=A) is 1/4 as we know, and the probability P(R=122|X=A) is basically the probability of pick a specific page from the book of 200 pages long, which is 1/200 (Note however, that if he had that R were greater than 200, then the result would be 0).
We still need to compute P(R=122), which will be needed in every conditional probability we will calcultate. In order to compute P(R=122) we will use the Theorem of Total Probability, in other words, we will divide the event R=122 in disjoint conditions cover all possible putcomes. In this case, we will divide on wheather X=A, X=B, X=C or X=D.
[tex]P(R=122) = P(R=122 | X=A)*P(X=A) + P(R=122|X=B)*P(X=B)+P(R=122|X=C)*P(X=C)+P(R=122|X=D)*P(X=D) = 1/200 * 1/4 + 1/400*1/4 + 1/600*1/4+1/800*1/4 = 1/4*(12/2400 + 6/2400 + 4/2400 + 3/2400) = 1/384[/tex]
Thus, P(R=122) = 1/396
With this in mind, we obtain that
[tex]P(X=A|R=122) = \frac{\frac{1}{200}*\frac{1}{4}}{\frac{1}{396}} = \frac{384}{800} = \frac{12}{25}[/tex]
In a similar way, we can calculate the different values that X can take given that R = 122. The computation is exactly the same except that for example P(R=122|X=B), is 1/400 and not 1/200 because B has 400 pages.
[tex]P(X=B|R=122) = \frac{\frac{1}{400}*\frac{1}{4}}{\frac{1}{384}} = \frac{384}{1600} = \frac{6}{25}[/tex]
[tex]P(X=C|R=122) = \frac{\frac{1}{600}*\frac{1}{4}}{\frac{1}{384}} = \frac{384}{2400} = \frac{4}{25}[/tex]
[tex]P(X=D|R=122) = \frac{\frac{1}{800}*\frac{1}{4}}{\frac{1}{384}} = \frac{384}{3200} = \frac{3}{25}[/tex]
We can make the same computations to calculate the probability of Y = A,B,C or D, given that R=304. However, P(Y=A|R=304) will be 0 because A only has 200 pages (similarly, P(R=304|Y=A) = 0, R=304 and Y=A are not compatible events). First, lets compute the probability that R is 304.
[tex]P(R=304) = P(R=304|Y=A)*P(Y=A)+P(R=304|Y=B)*P(Y=B)+P(R=304|Y=C)*P(Y=C)+P(R=304|Y=D)*P(Y=D) = 0+1/400*1/4+1/600*1/4+1/800*1/4 = 13/9600[/tex]
Thus, P(R=304) = 13/9600. Now, lets compute each of the conditional probabilities
[tex] P(Y=A|R=304) = 0[/tex] (as we stated before)
[tex]P(Y=B|R=304) = \frac{\frac{1}{400}*\frac{1}{4}}{\frac{13}{9600}} = \frac{9600}{1600*13} = \frac{6}{13}[/tex]
[tex]P(Y=C|R=304) = \frac{\frac{1}{600}*\frac{1}{4}}{\frac{13}{9600}} = \frac{9600}{2400*13} = \frac{4}{13}[/tex]
[tex]P(Y=D|R=304) = \frac{\frac{1}{800}*\frac{1}{4}}{\frac{13}{9600}} = \frac{9600}{3200*13} = \frac{3}{13}[/tex]
We want P(X=Y) given that [tex] R_x = 122 [/tex] and [tex] R_y = 304 [/tex] (we put a subindex to specify which R goes to each variable). We will remove the conditionals to ease computations, but keep in mind that we are using them. For X to be equal to Y there are 3 possibilities: X=Y=B, X=Y=C and X=Y=D (remember that Y cant be A given that [tex] R_y = 304). Using independence, we can split the probability into a multiplication.
[tex] P(X=Y=B) = P(X=B|R=122)*P(Y=B|R=304) = \frac{6}{25} * \frac{6}{13} = \frac{36}{325} [/tex]
[tex] P(X=Y=C) = P(X=C|R=122)*P(Y=C|R=304) = \frac{4}{25}*\frac{4}{13} = \frac{16}{325} [/tex]
[tex] P(X=Y=D) = P(X=D|R=122)*P(Y=D|R=304) = \frac{3}{25}*\frac{3}{13} = \frac{9}{325} [/tex]
Therefore
[tex] P(X=Y) = \frac{36}{325} + \frac{16}{325} + \frac{9}{325} = \frac{61}{325} [/tex]
61 is prime and 325 = 25*13, thus, they are coprime. Therefore, we conclude that m = 61, n = 325, and thus, 100m+n = 6425.
7. A travel website wants to gauge the perceived quality of a major airport. The maximum possible rating is 10, and the results of a random sample of 50 travelers can be found in the Airport.xlsx file. Develop a 95% confidence interval estimate of the population mean rating for the airport based upon this data.
Answer:
The 95% confidence interval has Minimum = 6.053 and Maximum = 7.467
Step-by-step explanation:
Here we have
Data as
1 5 6 7 8 8 8 9 9 9 9 10 3 4 5 5 7 6 8 9 10 5 4 6 5 7 3 1 9 8 8 9 9 10 7 6 4 8 10 2 5 1 8 6 9 6 8 8 10 10
The sum is 338
∴ Mean, [tex]\bar x[/tex] = 6.76, Standard Deviation, s = 2.55
Sample size, n = 50
For a 95% confidence interval, we have
[tex]CI=\bar{x}\pm z\frac{s}{\sqrt{n}}[/tex]
Where z is;
z at 95% z = [tex]\pm[/tex]1.96
Therefore, we have
95% confidence interval as Minimum = 6.053 to Maximum = 7.467.
The scale drawing represents an existing barn. The shortest side of the barn measures 150 meters. If a new barn that is 2/3 its size replaces the existing barn, what will be the scale of this drawing to the new barn?
The scale of the drawing to the new barn is 1:1.5.
Explanation:To find the scale of the new barn compared to the existing barn, we can use the ratio of their sides. Let's call the shortest side of the new barn x meters. The ratio of the lengths of the shortest sides of the new and existing barns is given as 2/3. Setting up the proportion, we have 2/3 = x/150. Cross-multiplying, we find x = (2/3) * 150 = 100 meters. Therefore, the shortest side of the new barn measures 100 meters. The scale of the drawing to the new barn can be determined by dividing the length of the shortest side of the drawing by the length of the shortest side of the new barn. Let's call the scale factor y. We have y = 150/100 = 1.5. Therefore, the scale of the drawing to the new barn is 1:1.5.
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A dot plot titled seventh grade test score. There are 0 dots above 5, 6, 7, 8 and 9, 1 dot above 10, 1 dot above 11, 2 dots above 12, 1 dot above 13, 1 dot above 14, 2 dots above 15, 3 dots above 16, 3 dots above 17, 2 dots above 18, 2 dots above 19, 3 dots above 20. A dot plot titled 5th grade test score. There are 0 dots above 5, 6, and 7, 1 dot above 8, 2 dots above 9, 10, 11, 12, and 13, 1 dot above 14, 3 dots above 15, 2 dots above 16, 1 dot above 17, 2 dots above 18, 1 dot above 19, and 1 dot above 20.
Students in 7th grade took a standardized math test that they also had taken in 5th grade. The results are shown on the dot plot, with the most recent data shown first.
Which statement is true?
Both data sets have a gap.
Both data sets have the same median.
Both plots have the same mode.
Both data sets have the same number of data points.
Answer:
D. Both data sets have the same number of data points.
Step-by-step explanation:
Answer:
itd d on egeunity
Step-by-step explanation:
A researcher is investigating whether a new fertilizer affects the yield of tomato plants. As part of an experiment, 20 plants will be randomly assigned the new fertilizer and 20 will be assigned the current fertilizer. The mean number of tomatoes produced per plant will be recorded for each fertilizer, and the difference in the sample means will be calculated. Which of the following is the appropriate inference procedure for analyzing the results of the experiment?a)A matched-pairs t-interval for a mean differenceb)A two-sample t-interval for a difference between sample meansc)A two-sample t-interval for a difference between population meansd)A one-sample t-interval for a sample meane)A one-sample t-interval for a population mean
Answer:
Correct option is (c).
Step-by-step explanation:
The experiment is conducted to determine whether a new fertilizer affects the yield of tomato plants.
The procedure involves randomly assigning the new fertilizer to 20 plants and the other 20 will be assigned the current fertilizer.
Then the mean number of tomatoes produced per plant will be recorded for each fertilizer, and the difference in the sample means will be calculated.
The collected sample data will then be used to make conclusion about the population.
The researchers main aim is to determine whether the new fertilizer is effective or not, i.e. if on using the new fertilizer the yield of tomatoes increases or not.
So, the parameter under study id the difference between tow population means.
To make inferences about the experiment the researcher can construct a two-sample t-interval for a difference between population means. The confidence interval has a certain specific probability of including the true parameter value.
Thus, the correct option is (c).
The correct answer is (c) option.
The following information should be considered:
The experiment is conducted for measuring whether a new fertilizer impacts the yield of tomato plants or not After this, the mean number of tomatoes produced per plant will be recorded for each fertilizer, and the difference in the sample means will be determined. The researchers main focus is to measured whether the new fertilizer is effective or not. Thus, the parameter under study is the difference between two population means. For make inferences related to the experiment the researcher can construct a two-sample t-interval for a difference between population means. The confidence interval has a specific probability of involving the true parameter value.
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Convert 30 to radians. Leave answer as a reduced fraction in terms of pi
Answer:
[tex]\frac{\pi }{6}[/tex]
Step-by-step explanation:
[tex]\frac{\pi}{180}[/tex] = [tex]\frac{x}{30}[/tex]
180x = 30π
x = [tex]\frac{30\pi }{180}[/tex]
x = [tex]\frac{3\pi }{18}[/tex]
x= [tex]\frac{\pi}{6}[/tex]
READ CAREFULLY! :)
John is putting a fence around his garden that is shaped like a half circle and a rectangle
Answer:
46 feet
Step-by-step explanation:
Perimeter of rectangle needed =
[tex]14+14+7= 35\\[/tex]
Half of the circumference of a circle needed =
[tex]\frac{1}{2} \pi d = \frac{1}{2} * \frac{22}{7} * 7= 11[/tex]
Total perimeter needed =
[tex]35 + 11=46[/tex]
Answer:
46 ft
Step-by-step explanation:
John will need to put a fence along 3 sides of the rectangle: 14 ft, 7 ft, 14 ft
He also needs to put a fence along the half circle:
C (circumference) = 2×π×r = π×d
⇒C÷2 = π×d÷2 = 22/7×7÷2 = 22÷2 = 11 ft
Together: 14 + 7 + 14 + 11 = 46 ft
One hundred and 50 people were asked whether they like to see comedies or dramas and whether or not I buy popcorn from for the movie out of 90 people that like comedies they bought popcorn day or 40 people that said they do not buy popcorn
Answer: a) 0.6, b) [tex]\dfrac{4}{15}[/tex]
Step-by-step explanation:
Since we have given that
Total number of people were surveyed = 150
Number of people that like comedies they bought popcorn that day = 90
Number of people that said they do not buy popcorn = 40
So, Probability of getting who like comedies and bought popcorn = [tex]\dfrac{90}{150}=\dfrac{3}{5}=0.6[/tex]
Probability of getting who said they do not buy popcorn = [tex]\dfrac{40}{150}=\dfrac{4}{15}[/tex]
Hence, a) 0.6, b) [tex]\dfrac{4}{15}[/tex]
I will give you all my points and mark you the brainliest! Please help
Answer and Step-by-step explanation:
Since this is a quadrilateral, we know that all the angles will add up to 360 degrees (by definition). We are given that angle A is 90 degrees and that the ratio of A to B is 5 to 3. This means that we can set up a proportion and solve for B:
A/B = 5/3 ⇒ 90/B = 5/3 ⇒ 5B = 270 ⇒ B = 54
So, we know that angle B is 54 degrees.
Now that we know angle B is 54 and A is 90, we can find the sum of the remaining two angles X and Y because A + B + X + Y = 360:
90 + 54 + X + Y = 360
X + Y = 216 degrees
We also know that the ratio of X to Y is 1 to 3, so we can set up another proportion:
X/Y = 1/3 ⇒ Y = 3X
Substitute 3X in for Y in X + Y = 216:
X + 3X = 216
4X = 216
X = 54
Thus, we see that both angles B and X equal 54, so B = X.
Hope this helps!
Answer:
[tex]\frac{a}{b}=\frac{5}{3}=>b=\frac{3a}{5}=\frac{270}{5}=54 \\\\x+y=360-(90+54)=360-144=216\\\\\frac{x}{y}=\frac{1}{3}=>y=3x\\ \\x+3x=216\\\\4x=216\\\\x=216:4\\\\x=54\\\\x=b\\[/tex]
Consider the graph below.
Which of the following is the function represented
by the graph?
y=(x+3)-5
2
*5
*
x
+
5
DONE
ONANODOTTI
Answer:
y=−259x+8
Step-by-step explanation:
i think this might be the answer but not sure
Answer:D
Step-by-step explanation:
Triangle R has an area of 40 square units. Salome drew a scaled version of triangle R and labeled it triangle T what scale factor did salome use to go from triangle R to triangle T
Answer:
Scale factor = 1/2
Ratio R:T = 2:1
Attached is the missing image;
Step-by-step explanation:
From the image attached;
The height of the triangle T is = 5 units
Base of triangle T = 4 units
Since the two triangles are scaled versions;
Area of a triangle = 1/2 × h × b
For triangle R;
Area = 40 = 1/2 × h × b
hb = 80
And, h : b = 5:4
h= 5/4 b
5/4 ×b × b = 80
b^2 = 64
b = 8
h = 5/4 × 8 = 10
The height of the triangle R = 10 units
Base of triangle R = 8 units
Scale factor = h2/h1 = 5/10 = 1/2
Scale factor = 1/2
In a recent survey of monetary donations made by 489 college graduates, the following information was obtained. 95 has donated to a political campaign, 76 had donated to assist medical research, 133 had donated to preserve the environment, 25 had donated to all three, 38 had donated to a political campaign and to medical research, 46 had donated to medical research and to preserve the environment, and 54 donated to a political campaign and to preserve the environment.
(a) How many college graduates donated to none of the listed causes?
(b) What percent of the college graduates donated to exactly one of the three listed causes?
Answer:
Step-by-step explanation:
The Venn diagram representing this situation is shown in the attached photo.
P represents the set of college graduates that donated to a political campaign.
M represents the set of college graduates that donated to assist medical research.
E represents the set of college graduates that donated to preserve the environment.
From the diagram,
The number of college graduates that donated to all three is 25
The number of college graduates that donated to a political campaign and medical research only is
38 - 25 = 13
The number of college graduates that donated to a political campaign and preserve the environment only is
54 - 25 = 29
The number of college graduates that donated to medical research and to preserve the environment only is 46 - 25 = 21
The number of college graduates that donated to a political campaign only is
95 - (29 + 25 + 13) = 28
The number of college graduates that donated to medical research only is
76 - (13 + 25 + 21) = 17
The number of college graduates that donated to preserve the environment only is
133 - (29 + 25 + 21) = 58
a) the number of college graduates that donated to none is
489 - (28 + 17 + 58 + 13 + 21 + 29 + 25)
= 298 college graduates
b) the number of college graduates that donated to exactly one of the three listed causes is
28 + 17 + 58 = 103
The percentage would be
103/489 × 100 = 21.1%
the probability of not rolling on a 2 on a 6-sided number cube is _____.
A.1/2 - B.1/3 -C.1/6 - D.5/6
Answer:
C.1/6
Step-by-step explanation:
What is the next term of the geometric sequence?
72,36, 18,
Answer:
9
Step-by-step explanation:
To find the common ratio, take the second term and divide by the first
36/72 = 1/2
To find the next term, take the last term and multiply by the common ratio
18*1/2 = 9
Answer:
9.
Step-by-step explanation:
The common ratio = 36/72 = 18/36 = 1/2.
So the next term is 18 * 1/2 = 9.
Two cards are selected from a deck of cards numbered from 1 to 10. Once a card is selected, it is not replaced. What is P(two even numbers)? Write the answer as a fraction in simplest form.
Include Explanation please
10 cards would have 5 even cards.
First pick would be 5/10 = 1/2 probability of getting an even card.
Without replacing there are 9 cards left with 4 even ones. The probability of picking an even card would be 4/9
The probability of both happening would be Found by multiplying the two probability’s together:
1/2 x 4/9 = 4/18 = 2/9
Two cards are selected from a deck of cards numbered from [tex]1[/tex] to [tex]10[/tex] and once a card is selected, it is not replaced, then Probability of two even numbers is [tex]\frac{2}{9}[/tex] .
What is Probability ?Probability is a ratio of the number of favorable outcomes to the number of possible outcomes of the experiment.
Probability[tex](E)[/tex] [tex]=\frac{Number \ of \ favorable \ outcomes}{Number \ of \ possible \ outcomes \ of \ the \ experiment}[/tex]
We have,
Let [tex]E[/tex] be event of drawing cards.
A deck of cards numbered from [tex]1[/tex] to [tex]10[/tex] .
i.e. total number of possible outcomes [tex]=10[/tex]
And,
Even numbers from [tex]1[/tex] to [tex]10[/tex] are [tex]2,4,6,8,10[/tex]
[tex]=10[/tex]
Total even numbers are [tex]5[/tex].
So,
Probability[tex](E)[/tex] [tex]=\frac{Number \ of \ favorable \ outcomes}{Number \ of \ possible \ outcomes \ of \ the \ experiment}[/tex]
Probability[tex](E)[/tex] [tex]=\frac{5}{10}*\frac{4}{9}[/tex]
[tex]=\frac{2}{9}[/tex]
So, the Probability of two even numbers is [tex]\frac{2}{9}[/tex] , as there are total [tex]10[/tex] cards and it is said that once a card is selected, it is not replaced, so when one card is selected there remains only [tex]9[/tex] cards, so when next time we select a card then Probability will be from those [tex]9[/tex] cards.
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vlad a economiit o suma de bani.A cheltuit 20 lei pentru felicitari apoi tatal i-a dublat suma. A cheltuit 40 lei pe martioare apoi bunicul i-a mai dat 50 lei. A cumparat un buchet de flori pentru mama lui pe care a dat 30 lei apoi tatal i-a dublat suma.La final, vlad a contatat ca mai are 280 lei
He had saved 320 initially
Step-by-step explanation:
Let the amount he saved be 'a'
Amount spent = 20 + 40 + 30
= 90
His grand father gave 50
At the end he has 280
280 = a - 90 +50
a = 280 -50 +90
= 320
He had saved 320 initially
An isosceles triangle has an angle that measures 70°. Which other angles could be in that isosceles triangle? Choose all that apply. 40 55 70 1-
Answer:
This depends on the way the triangle
Step-by-step explanation:
Anyway angles that apply includes: 55 and 70
Write in slope-intercept form an equation of the line that passes through the given points.
(6,8),(3,−9)
Slope-intercept form: [tex]y=mx+b[/tex]
m = slopeb = y-interceptSlope formula: [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are two points that fall on the lineSolving the Question
We're given:
The line passes through (6,8), (3,-9)1) First, find the slope using the slope formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{8-(-9)}{6-3}\\\\m=\dfrac{8+9}{6-3}\\\\m=\dfrac{17}{3}[/tex]
Therefore, the slope of this line (m) is [tex]\dfrac{17}{3}[/tex]. Plug this into slope-intercept form:
[tex]y=\dfrac{17}{3}x+b[/tex]
2) Now, find the y-intercept by using one of the given points:
[tex]y=\dfrac{17}{3}x+b[/tex]
Plug in one of the given points as (x,y):
[tex]8=\dfrac{17}{3}(6)+b\\\\8=34+b\\b=8-34\\b=-26[/tex]
Therefore, the y-intercept of the line is -26. Plug this into our original equation:
[tex]y=\dfrac{17}{3}x+b\\\\y=\dfrac{17}{3}x-26[/tex]
Answer[tex]y=\dfrac{17}{3}x-26[/tex]
To write the equation of the line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept, we need to determine the slope first and then use one of the points to find the y-intercept.
Step 1: Find the slope (m)
The slope of a line passing through two points, (x1, y1) and (x2, y2), can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Given our points (6, 8) and (3, -9), we can substitute them into our formula:
x1 = 6, y1 = 8
x2 = 3, y2 = -9
m = (-9 - 8) / (3 - 6)
m = (-17) / (-3)
m = 17/3
m = 5.666666666666667 (rounded to 5.67 for simplicity)
Step 2: Find the y-intercept (b) using one of the points
Next, we can use the point-slope form of a line equation, which is:
y - y1 = m(x - x1)
We will use the first point (6, 8) and the slope m = 5.67 that we calculated.
Substitute the point and the slope into the point-slope form equation:
8 - y1 = 5.67(6 - x1)
Since we know that (x1, y1) is (6, 8), this simplifies to:
8 - 8 = 5.67(6 - 6)
b = 8 - 5.67(6)
Now, we do the multiplication and subtraction:
b = 8 - 34.02
b = -26
So now we have our y-intercept, which is b = -26.
Step 3: Write the equation in slope-intercept form
Now that we have both m and b, we can write the equation of the line:
y = mx + b
Substitute m and b into the equation:
y = 5.67x - 26
This is the equation of the line in slope-intercept form that passes through the points (6, 8) and (3, -9). For exact calculations, you may want to use the more precise value of the slope (5.666666666666667) in the equation:
y = 5.666666666666667x - 26
By doing so, we obtain a more accurate representation of the line's equation.
Brian pays £475.29 a year on his car insurance. The insurance company reduces the price by 2.1%. How much does the insurance cost now? Give your answer rounded to 2 DP.
Answer:
[tex]\£465.31[/tex]
Step-by-step explanation:
we know that
The insurance company reduces the price by 2.1%
Remember that
The actual cost of £475.29 a year represent the 100%
so
[tex]100\%-2.1\%=97.9\%=97.9/100=0.979[/tex]
To find out the new insurance cost, multiply the original cost by the factor 0.979
[tex]\£475.29(0.979)=\£465.31[/tex]
Brian's car insurance, after a 2.1% reduction from the original cost of £475.29, is now £465.31 when rounded to two decimal places.
Explanation:Brian's original car insurance cost is £475.29, and the company is offering a reduction of 2.1% on this cost. To calculate the reduced cost, we first find the discount amount by multiplying the original cost by the reduction percentage:
Discount = Original Cost x Reduction Percentage
Discount = £475.29 x 0.021
Discount = £9.98109
Now, we subtract the discount from the original cost to find the new cost of the insurance:
New Cost = Original Cost - Discount
New Cost = £475.29 - £9.98109
New Cost = £465.30891
When rounding to two decimal places, Brian's new cost for car insurance is:
New Cost = £465.31
A circle is shown. Points Q, U, A, D are on the circle. Lines connect the points to form a quadrilateral. Angle Q U A is 111 degrees. Arc Q U is 88 degrees. What is the measure of Arc A U? 44° 50° 64° 92
The angle subtended by an arc [tex]\widehat{AU}[/tex] is given by the angle ∠UOA.
Response:
[tex]\widehat{AU}[/tex] is 50°Which methods can be used to find [tex]\widehat{AU}[/tex] ?According to circle theorem, we have;
Angle at the center = 2 × Angle at the circumference∠QUA = 111°
Therefore;
[tex]m\widehat{QDA}[/tex] = 2 × ∠QUA
[tex]m\widehat{QDA}[/tex] = 2 × 111° = 222°
Which gives;
Angle ∠QOA = [tex]m\widehat{QUA}[/tex] = 360° - 222° = 138°
∠QOA = ∠QOU + ∠UOA by angle addition property
Which gives;
∠QOA = 138° = 88° + ∠UOA
∠UOA = 138° - 88° = 50°
[tex]\widehat{AU}[/tex] = ∠UOA = 50°Learn more about more circle theorems here:
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Cape Hatteras Lighthouse was built in 1870 and rises 208 feet above sea level. From the top of the lighthouse, the lighthouse keeper observes two ships along the same line of sight. The angle of depression to ship 1 is 20 and the angle of depression to ship 2 is 12.5 . For safety purposes, the keeper thinks the two ships should be at least 300 feet apart. If they are less than 300 feet apart, she will sound a warning. How far apart are the vessels? Will she sound the warning?
Answer:
The distance between them is 366.75 feet.
She doesn't need to sound a warning yet.
Step-by-step explanation:
Please see the attached files for explanation.
To find the Distance between ships, we can use trigonometry. The distance between the ships is the absolute difference between their heights above the horizontal.
To find the distance between the two ships, we can use trigonometry. Let's consider the triangle formed by the lighthouse, ship 1, and ship 2. The angle of depression to ship 1 is 20°, so the angle between the line of sight and the horizontal is also 20°. Similarly, the angle of depression to ship 2 is 12.5°, so the angle between the line of sight and the horizontal is also 12.5°.
We can use the tangent function to find the height of ship 1 and ship 2 above the horizontal. Using the formula tan(angle) = opposite/adjacent, we have: tan(20°) = height of ship 1/208 and tan(12.5°) = height of ship 2/208. Rearranging these equations, we get the heights: height of ship 1 = 208 * tan(20°) and height of ship 2 = 208 * tan(12.5°).
Now, to find the distance between the ships, we need to subtract the heights of the ships from each other. If the distance is less than 300 feet, the keeper will sound a warning. So, the distance between the ships is: distance = |height of ship 1 - height of ship 2|. If this distance is less than 300 feet, she will sound the warning.
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The table displays the scores of students on a recent exam. Find
the mean of the scores to the nearest 10th.
Score Number of Students
80
85
6
90
95
100
6
8
Summary:
pls I need a summary asap
The mean is 59
Add all the scores together, then divide by the number of test scores
The mean of the scores to the nearest 10th Score Number of Students is 59.
We have given a data,
80,85,6,90,95,100,6,8
What is the meaning of mean?
Mean is the adding all the scores together, then divide by the number of test scores.
So we have given a data,
80,85,6,90,95,100,6,8
80+85+6+90+95+100+6+8=470
The number of of test scores=8
[tex]mean=\frac{470}{8}=58.75[/tex]
Mean≈59
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how old am i if 500 reduced by 4 times my age is 184
Answer:
79 years old
Step-by-step explanation:
Let's say your age is x.
The problem says "500 reduced by 4 times my age is 184", so we convert this to math:
- "4 times my age" ⇒ 4 * x = 4x
- "500 reduced by" ⇒ 500 - (something)
- "500 reduced by 4 times my age" ⇒ 500 - 4x
- "is 184" ⇒ = 184
- "500 reduced by 4 times my age is 184" ⇒ 500 - 4x = 184
Now, we simply solve for x:
500 - 4x = 184
4x = 500 - 184 = 316
x = 79
Thus, you are 79 years old.
Hope this helps!
Toby wants a paintbrush that costs $2.70, a set of paints that costs $15.45, and an easel that costs $22.90. Toby already has $1.00. How much more money does Toby need?
Answer:
$40.05
Step-by-step explanation:
You would add up 2.70+15.45+22.90 then, subtract the total by 1.00
Answer:
40.05
Step-by-step explanation:
you basically add up all the prices then subtract the 1 dollar the he has and u get ur answer
what's 1.12 as a fraction.
Answer:
1.12 = 28 / 25
Step-by-step explanation:
28 over 25
28
---
25
BRAINLIST please have a great day
Answer:
28/25
Step-by-step explanation:
hope this helps.
Select the expression that represents the additive inverse of 6. A. 1/6 B. -1/6 C. -(-6) D. -6
Answer:
D. -6.
Step-by-step explanation:
The inverse is the number when added to 6 results in 0.
So it is 0 - 6 = -6. (6 + -6 = 0)
Answer:
C
Step-by-step explanation: I big brain
please help me with this question, I am kinda desperate :( I honestly have no idea what i am doing...
if logb2=1 and logb3=1.58, evaluate the following:
logb8
Answer:
3
Step-by-step explanation:
logb(8)
logb(2³)
3 × logb(2)
3 × 1
3
molly has $45 in her wallet, which is 3 times as much as her brother has
Answer:$15
Step-by-step explanation:
45 divided by 3 =15
Answer:
her brother has $15
Step-by-step explanation:
m= molly
b= brother
m=45
b= 45÷3
b=15
Need help ASAP please!
Answer:
so f(0) = g(0) and f(2) = g(2)
Step-by-step explanation:
f(x) = g(x) where the two graphs intersect
The graphs cross at the x coordinate 0 and x coordinate 2
so f(0) = g(0) and f(2) = g(2)
Answer:
First one
Step-by-step explanation:
f(x) = g(x)
Is the point of intersection of the two graphs
(0,4) and (2,0)
Solutions are: x = 0 and x = 2
(x - 17.7) + 19.6 = 27.8 and an explanation
[tex](x - 17.7) + 19.6 = 27.8 \\ x - 17.7 = 27.8 - 19.6 \\ x - 17.7 = 8.2 \\ x = 17.7 + 8.2 \\ x = 25.9[/tex]
A basketball player made the following number of free throws in 8 successive games: 6, 18, 15, 14, 19, 12, 19, and 15. What is the median number of successful free throws?
Answer:
15
Step-by-step explanation:
Hello!
To find the median, all you have to do is order the number of terms in ascending order and then count to the middlemost number(s).
Arranging in ascending order:
[tex]6,\:12,\:14,\:15,\:15,\:18,\:19,\:19[/tex]
Since this is an even number, our two medians are 15 and 15.
(15 + 15) / 2 = 15.
Thus, the median of successful free throws is [tex]\boxed{15}[/tex].