Answer:
-1/32.
Step-by-step explanation:
(-1/2)^3 * (-1/2)^2
= -1/8 * 1/4
= -1/32.
a) 31 c) 30
b) 28 d) 61
Answer:
A) 31
Step-by-step explanation:
The difference of low-end values for successive classes is 31. This is the class width.
The register that holds bit values (flags) that describe comparison operation results, control conditional BRANCH execution, or indicate actual or potential error conditions ____.
Answer:
program status word
Step-by-step explanation:
The acronym for PSW is Program Status Word. The Program Status Word or the PSW consists of status bits which shows the present Central Processing Unit state.
The PSW or Program Status Word is IBM System/360 architecture which means it is an independent model architecture for S/360 series of computers developed by IBM.
The status register contains all the information about the processor.
Thus the answer is program status word.
Simplify the radical expression.
[tex]\mathbb{ANSWER:}[/tex]
Refer to the attachment for the answer.
You are standing 41 meters from the base of a building. You estimate that the angle of elevation to the top of the 86th floor (the observatory) is 82°. If the total height of the building is another 124 meters above the 86th floor, what is the approximate height of the building? (Round your answers to one decimal place.)
Answer:
408.6 meters.
Step-by-step explanation:
Let x be the height from the base of the building to the 86th floor,
∵ the total height of the building is another 124 meters above the 86th floor,
So, the total height of the building = ( x + 124 ) meters,
Now, the angle of elevation from the point on the ground to 86th floor = 82°,
Also, the distance from the point to the base of the building = 41 meters,
Thus, by trigonometric ratio,
[tex]tan 82^{\circ}=\frac{x}{41}[/tex]
[tex]\implies x = 41\times tan 82^{\circ}=284.614788895\approx 284.6\text{ meters}[/tex]
Hence, the height of the building = ( 284.6 + 124 ) = 408.6 meters.
The height of the building in consideration is given approximately as 408.61 meters
What is angle of elevation?You look straight parallel to ground. But when you have to watch something high, then you take your sight up by moving your head up. The angle from horizontal to the point where you stopped your head is called angle of elevation.
Consider the figure attached for the given situation as described in the problem.
The person watching the building's 86th floor is at A.
The 86th floor is at C, the base of the building is at B.
The total height of the building is at D.
Using the tangent ratio to find the height of the building, we get:
[tex]\tan(82^\circ) = \dfrac{x}{41} \\\\x = \tan(82^\circ) \times 41\\x \approx 284.61 \: \rm meters[/tex] (from calculator).
Thus, the height of the building is length of AD
= |AD| = x + 124 ≈ 284.61 + 124 = 408.61 meters
Thus, the height of the building in consideration is given approximately as 408.61 meters
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Suppose the schools pay $2.00 per bottle for the juice and sell it to community members for $2.50 per bottle. What percent markup are they charging?
- the answer is 25% markup
just exlpain how to get the answer
Answer:
The answer to your question is 25%
Step-by-step explanation:
Data
Initial price = $2.00
Final price = $2.50
First we subtract the final price to the inicial price
increment = 2.50 - 2.00
= $0.50 It's the amount that the school increases to the community members
Now we use a rule of three to find the percent
$2.00 ---------------------- 100%
$0.50 --------------------- x
x = 0.50 x 100/2 = 50/2 = 25%
Please help!!!step by step
Answer:
slope = -1/3, y-intercept (0, -3), x-intercept (-9 , 0)
Step-by-step explanation:
3 - x = 3(y + 4)
3 - x = 3y + 12
3y = 3 - x - 12
3y = -x -9
y = -1/3 x - 3
slope = -1/3
when x = 0 (y-intercept)
y = -1/3 × 0 - 3
y = -3
y-intercept (0, -3)
when y = 0 (x-intercept)
0 = -1/3 x - 3
1/3 x = -3
x = -9
x-intercept (-9 , 0)
Write an example of a number with a first non-zero digit six place values away from the decimal point. Then, write this number in scientific notation.
Answer:
The answer to your question is: 7.00 x 10⁶
Step-by-step explanation:
- Write a number with a non-zero digit 7
- Six place values away from the decimal point 7 000 000.00
-Write this number in scientific notation 7.00 x 10⁶
An example of a number with its first non-zero digit six places away from the decimal is 0.000001, which is written in scientific notation as 1 × 10^-6 by moving the decimal six places to the right.
An example of a number with its first non-zero digit six place values away from the decimal point is 0.000001. To write this number in scientific notation, we follow the standard convention: moving the decimal point such that there is only one non-zero digit to the left of the decimal point and counting the number of places the decimal point has moved to determine the power of 10.
In this case, we move the decimal point six places to the right, which gives us 1 × 10^-6. This means that 0.000001 in scientific notation is expressed as 1 × 10^-6 .
City A is due north of City B. Find the distance between City A (37 degrees 2 prime north latitude) and City B (19 degrees 44 prime north latitude). Assume that the radius of Earth is 3960 miles.
Answer:
1196 mi
Step-by-step explanation:
The latitude difference is 17°18', so is about 0.301942 radians. Then the arc length is ...
s = r·θ = (3960 mi)(0.301942) ≈ 1196 mi
The distance between City A and City B, given their latitudes and the radius of the Earth, is found using the arc length formula (length = radius x angle in radians) to be approximately 2011 miles.
Explanation:The subject of this question is Geography and it entails finding the distance between two cities located at different latitudes on Earth. The difference between the two latitudes is used to find the distance. Since the Earth is a sphere, we can use the formula for the length of an arc to find the distance between these two cities. To do so, subtract the latitude of City B (19 degrees 44 prime) from the latitude of City A (37 degrees 2 prime) to get the difference in degrees which is equal to 17 degrees 18 prime. Convert this to decimal form by dividing the prime by 60 (17 + 18/60 = approx. 17.3 degrees).
Then use the formula for the length of an arc: length = radius x angle (in radians). The radius of the Earth is given as 3960 miles and the angle in radians is obtained by multiplying the angle in degrees by π/180. Therefore, the distance is 3960 miles x 17.3 x π/180 = approximately 2011 miles. As such, City A and City B are estimated to be about 2011 miles apart.
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What are significant figures?
A. They are a close approximation of the actual value of what is being measured
B. They are all known digits in a measurement
C. The limit of a measurement
D. The gauge of the accuracy of a measurement
The best option is A: They are a close approximation of the actual value of what is being measured.
Significant figures, also known as significant digits, are a set of rules used to determine the precision or accuracy of a measured or calculated value. They indicate the reliability of the digits in a number and help communicate the level of certainty associated with a measurement or calculation.
The correct definition of significant figures is:
A. They are a close approximation of the actual value of what is being measured.
Significant figures represent the digits in a number that contribute to its precision. They include all the known digits in a measurement, as well as one estimated digit. The estimated digit is the least certain or the first uncertain digit in the measurement. The number of significant figures reflects the level of confidence in the measurement and helps convey the precision of the value.
Option B ("They are all known digits in a measurement") is incorrect because significant figures include both known digits and one estimated digit.
Option C ("The limit of a measurement") is incorrect because significant figures do not define a limit but rather represent the precision of the measurement.
Option D ("The gauge of the accuracy of a measurement") is partially correct, as significant figures can provide an indication of the accuracy, but they primarily convey the precision or reliability of the measurement rather than the overall accuracy.
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Which of the following rational functions is graphed below?
Answer:
A
Step-by-step explanation:
from the graph you can tell that there is a vertical asymp. at -3.
In the anwers A is the only one with vertical asymp. at -3.
Answer:
A f(x)=[tex]\frac{x}{x+3}[/tex]
Step-by-step explanation:
To answer this question, to identify which rational function relates to that graph we must at first look for Rational Function in this form:
[tex]P(x)=\frac{Q(x)}{R(x)}[/tex]
Where P(x)= Polynomial Quotient, Q(x)=Quotient, R(x)=Remainder. Q(x) and R(x) are Polynomial Functions.
So exclude B, then C, for they do not fit as Polynomial Functions.
Then rather than setting the graph, the second step would be looking for the vertical asymptote, given by the equation on the denominator. We must detach it from the original function then solve it.
x+3=0 ∴ x=-3
IF A SUBSCRIPTION IS $499 PLUS 8% TAX FOR 30 DAYS, BUT IS BEING PRORATED FOR 7 DAYS, PLUS THERE IS A $10 OFF COUPON, WHAT'S THE FINAL COST?
Answer:
Your final answer is $528.92
Step-by-step explanation:
[tex]499 + 8\% = 538.92[/tex]
[tex]538.92 - 10 = 528.92[/tex]
Answer:
$519.6048
Step-by-step explanation:
Cost of subscription is $499 + 8% tax for 30 days
Cost of subscription for 30 days = $499
Cost of subscription for 1 days = [tex]\frac{499}{30}[/tex]
So, Cost for (30-7 = 23)days = [tex]\frac{499}{30} \times 23 [/tex]
= [tex]382.56[/tex]
Cost of subscription for 23 days = [tex]382.56[/tex]
Sale tax = 8 %
Sales Tax = [tex]30.6048[/tex]
Cost of subscription = $499+$30.6048 = $529.6048
There is an off of $10
So, Final cost = $529.6048-$10= $519.6048
Hence The final cost is $519.6048
Owens Industries is trying to increase its profile in the community. As part of this effort, Owens sponsors a Little League baseball team. The cost of sponsorship is $850. How should Owens record this transaction in order to maintain a balanced accounting equation (A = L + SE)?
The Owens Industries should credit $850 to their Assets, denoted by A and debit the sum of $850 to the Stockholder's Equity, denoted by SE.
Step-by-step explanation:In the question,
As the Owens industries is trying to increase its profile.
Cost of sponsorship = $850
To maintain the profile he can, by using the transaction accounting balance equation,
A = L + SE
The Owens Industries should credit $850 to their Assets, denoted by A and debit the sum of $850 to the Stockholder's Equity, denoted by SE.
That is,
$850 = L + $850
L = 0
This is how the accounting equation can be balanced.
A student is conducting a research project that involves using a survey. The survey asks subjects about their political affiliation and their favorite politicians. No identifiable information will be collected. This study would be categorized as which type of review?
Answer:
This study will be identified as : exempt review
Step-by-step explanation:
A student is conducting a research project that involves using a survey. The survey asks subjects about their political affiliation and their favorite politicians.
No identifiable information will be collected.
This study will be identified as : exempt review
To qualify for a review at the exempt level, the research should be less than the minimal risk defined.
The minute hand of a clock is 6 inches long and moves from 12 to 4 o'clock. How far does the tip of the minute hand move? Express your answer in terms of pi and then round to 2 decimal places.
Answer: 12.56 inches
Step-by-step explanation: First, when know the following:
A clock is a circle, so the total movement, from 12 to 12 is 360° or 2π.
It is also know that a circle circunference (The total size of the circle on a straight line) is 2π * Radius
The minute hand does a circle on its travel, that circle radius is equal to 6 inches.
The movement from 12 to 4 is a third (4/12 = 1/3). Knowing this:
120° = (1/3) * 360° = (1/3) * 2π = (2/3) * π
So the travel from 12 to 4 is (2/3)π
To know the distance on inches, we multiply the distance on radians per the radius.
Total distance = 6 * (2/3)π
Total distance = 4π inches
Total distance = 12.56 inches
Final Answer:
The tip of the minute hand moves approximately 12.57 inches from 12 o'clock to 4 o'clock.
Explanation:
To solve this problem, we will consider the movement of the minute hand as an arc on a circle. The distance that the tip of the minute hand moves is the length of the arc that it traces as it moves from 12 o'clock to 4 o'clock. Here's how we'll calculate it:
Step 1: Determine the angle of movement in degrees.
The clock is divided into 12 hours, so each hour represents an angle of 360 degrees / 12 = 30 degrees. Since the minute hand moves from 12 o'clock to 4 o'clock, it covers 4 hours. Thus, the angle covered is 4 hours * 30 degrees/hour = 120 degrees.
Step 2: Convert the angle from degrees to radians.
To find the arc length, it is convenient to work with radians rather than degrees. The conversion from degrees to radians is performed using the factor π radians = 180 degrees.
[tex]\( \text{Angle in radians} = \text{Angle in degrees} \times \frac{\pi}{180} \)[/tex]
So, for our angle:
[tex]\( \text{Angle in radians} = 120 \times \frac{\pi}{180} \\\\\( \text{Angle in radians} = \frac{2}{3} \pi \)[/tex]
Step 3: Use the arc length formula.
The arc length (s) on a circle can be calculated using the formula s = r * θ, where r is the radius (length) of the circle (in this case, the length of the minute hand), and θ is the angle in radians.
[tex]\( s = r * \theta \\\\\( s = 6 \text{ inches} * \frac{2}{3} \pi \\\\\( s = 4 \pi \text{ inches} \)[/tex]
So, the distance the tip of the minute hand moves is [tex]\( 4 \pi \)[/tex] inches.
Step 4: Calculate the numerical value of the arc length.
To find the numerical value, we will approximate [tex]\( \pi \)[/tex] to 3.14159.
[tex]\( s \approx 4 * 3.14159 \\\\\( s \approx 12.56636 \text{ inches} \)[/tex]
Step 5: Round the numerical value to two decimal places.
[tex]\( s \approx 12.57 \text{ inches} \)[/tex]
Therefore, the tip of the minute hand moves approximately 12.57 inches from 12 o'clock to 4 o'clock.
A cyclist rides his bike at a speed of 18 miles per hours.what is this speed in kilometers per hour? How many kilometers will the cyclist travel in 2 hours ?
Answer:
about 29 km/h57.94 kmStep-by-step explanation:
The conversion factor cancels units of miles and leaves units of km.
[tex]\dfrac{18\,mi}{h}\cdot\dfrac{1.609344\,km}{1\,mi}=\dfrac{28.968192\,km}{h}[/tex]
The speed rounds to 29 km/h.
Multiplying the distance per hour by the number of hours, we find the distance to be ...
(28.968192 km/h)×(2 h) = 57.936384 km ≈ 57.94 km
To convert a quantity from km/h to m/s, you must a. multiply by 3600 and divide by 1000 b. multiply by 1000 and divide by 60 c. multiply by 60 and divide by 1000 d. multiply by 1000 and divide by 3600e. none of these is correct
Answer:
The correct answer is D
Multiply by 1000 and divide by 3600
Step-by-step explanation:
We know that in 1 km we have 1000 m and in 1 h we have 60 minutes and each minute have 60 seconds, then we multiply 60*60 to know how many seconds are in an hour and we have that 1 h have 3600 s. Using a conversion factor we have:
[tex]\frac{km}{h}(\frac{1000 m}{1km})(\frac{1h}{3600s})[/tex]
With this we can see that to convert a quantity from kn/h to m/s we must multiply by 1000 and divide by 36000
To convert from kilometers per hour to meters per second, you should multiply by 1000 (to convert kilometers to meters) and then divide by 3600 (to convert hours to seconds). An example with a speed of 50 km/h would result in approximately 13.9 m/s after conversion.
Explanation:To convert a quantity from kilometers per hour (km/h) to meters per second (m/s), the correct approach is (a) multiply by 1000 and then divide by 3600. This is because 1 km is equal to 1000 meters, and 1 hour is equal to 3600 seconds. Therefore, to change the unit from km/h to m/s, you need to perform these conversion operations.
Let's consider an example. If you have a speed of 50 km/h and want to convert it into m/s, here's the step-by-step process:
Multiply 50 (km/h) by 1000 to convert kilometers into meters. You'll get 50000 m/h.Next, divide 50000 m/h by 3600 to convert hours into seconds. The result is approximately 13.9 m/s.Learn more about Unit Conversion here:https://brainly.com/question/19420601
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Solve for n.
1/2n+3/4n=1/2
Answer:
n=2/5 or 0.4
Step-by-step explanation:
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A softball team is ordering pizza to eat after their tournament. They plan to order cheese pizzas that cost $6 each and four-topping pizzas that cost $10 each. They order c cheese pizzas and f four-topping pizzas. Which expression represents the total cost of all of the pizzas they order?
The equation would be [tex]6c + 10f[/tex].
The expression which represents the total cost of all of the pizzas they order is 6c + 10f.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .
Now it is given that,
Cost of cheese pizza = $6
Cost of four-topping pizzas = $10
Number of cheese pizza order = c
Number of four-topping pizzas order = f
Hence,
Total cost cheese pizza = Cost of cheese pizza*Number of cheese pizza order
⇒Total cost cheese pizza = 6*c = 6c
Similarly,
Total cost of four-topping pizzas = Cost of four-topping pizzas*Number of four-topping pizzas order
⇒Total cost of four-topping pizzas = 10*f = 10f
Hence, total cost of all of the pizzas they order
= Total cost cheese pizza + Total cost of four-topping pizzas
⇒ total cost of all of the pizzas they order = 6c + 10f
Hence,The expression which represents the total cost of all of the pizzas they order is 6c + 10f.
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Gerry is looking to buy a new car and finds one she likes for $1,000. The dealership is currently offering 15% off. How much money will Gerry save if she buys the car? Select one: A. $15 B. $985 C. $850 D. $150
D 1000 X .15 = 150.
.15 = 15%
Answer:
D) $150.
Step-by-step explanation:
Gerry is looking to buy a new car and finds one she likes for $1000. It means 100% corresponds to $1000.
There is 15% off. It means, she can save 15% of the total value of the car. We need to calcualte the amount of money that she can save taking the 15% off (O)
O = $1000 * (15%)
O = $1000*(15/100)
O = $1000*(0.15)
O = $150.
100% corrsponds to $1000, and 15% corresponds to $150.If she takes 15% off, we can conclude that she can save $150.
Finally, the answer is D) $150.
Which of the following is equivalent to
Answer:
Step-by-step explanation:
To solve this, we need to remember that when you multiplicate two roots you can multiply the numbers inside the two roots and put them inside just one root.
So in this case we have ∛5ab² ·∛25ab
We are going to multiply the numbers inside the roots and we get
∛5ab²·25ab = ∛75a²b³
But 75 = 5³ so we have
∛75a²b³ = ∛5³a²b³
Since we have powers of 3 inside the root, we can take them outside the root with the exponent divided by 3.
∛5³a²b³ = 5b∛a²
Thus, the correct answer is a) 5b∛a²
show that when the measure of an angle is added to three times the angle's complement, the result is equal to the sum of the anle's complment and the angle's supplement.
Answer with Step-by-step explanation:
Let x be the angle
We have to show that when the measure of an angle is added to three times the angle's complement , the result is equal to the sum of the angle;s complement and the angle' s supplement.
Angle's complement =90-x
(by definition of complementary angles)
Therefore, the angle's supplement=180-x ( By definition of supplement angles )
According to question
[tex]x+3(90-x)=270-2x[/tex]
[tex]90-x+180-x=270-2x[/tex]
Hence, when the measure of an angle is added to three times the angle's complement , the result is equal to the sum of the angle's supplement.
Hence, proved
Sophie is buying fabric to make items for a craft fair. The table shows some combinations of how much of each color fabric she might buy. Which equations model the total yards of fabric Sophie will buy? Check all that apply.
A. X+Y=28
B. 28+X=Y
C. X-Y=28
D. 28-X=Y
E. 28-Y=X
Answer:
OPTION A.
OPTION D.
OPTION E.
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
The Standard form of the equation of the line is:
[tex]Ax + By = C[/tex]
Where "A" is a positive integer, and "B" and "C" are integers.
Choose two points from the table and find the slope with this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].
Points:
[tex](1,27)\\\\(4,24)[/tex]
So we get that the slope is:
[tex]m=\frac{24-27}{4-1}=-1[/tex]
Let's substitute the slope and the coordinates of the point (1,27) into [tex]y=mx+b[/tex] and then solve for "b":
[tex]27=(-1)(1)+b\\\\27+1=b\\\\b=28[/tex]
Then, we get that the equation of the line in Slope-Intercept form is:
[tex]y=-x+28[/tex] or [tex]28-x=y[/tex]
In order to write it in Standard form, we can add "x" to both sides of the equation:
[tex]y+x=-x+28+x\\\\x+y=28[/tex]
We can solve for "x" by subtracting "y" from both sides of the equation:
[tex]x+y-y=28-y\\x=28-y\\\\28-y=x[/tex]
Answer:
A,D, and E
Step-by-step explanation:
find the area and circumference.
Answer:
area ≈ 176.7 cm²circumference ≈ 47.1 cmStep-by-step explanation:
The radius is half the diameter, so is ...
r = d/2 = 15 cm/2 = 7.5 cm
The area formula is ...
A = πr²
Filling in the radius, we have ...
A = π·(7.5 cm)² = 56.25π cm² ≈ 176.7 cm² . . . area
__
The circumference formula is ...
C = πd
Filling in the diameter, we have ...
C = π·(15 cm) = 15π cm ≈ 47.1 cm . . . circumference
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The length of a rectangle is 4 inches longer than its width. The area of the rectangle is 12 square inches. What are the length and width?
Which equation models this problem?
w – (4 + w) = 12
w + (4 + w) = 12
w(4 + w) = 12
4 • w = 12
Answer:
w(4 + w) = 12 is the correct answer.
Step-by-step explanation:
You have to think that area is lenght x widht, so the first and second options musn't be correct. (you have + and -)
The last one, it isn't correct because, you have width but don't have lenght.
Length is not 4.
The temperature reading from a thermocouple placed in a constant-temperature medium is normally distributed with mean μ, the actual temperature of the medium, and standard deviation σ. What would the value of σ have to be to ensure that 95% of all readings are within 0.6° of μ?
Answer: 0.3061.
Step-by-step explanation:
Given : The temperature reading from a thermocouple placed in a constant-temperature medium is normally distributed with mean [tex]\mu[/tex], the actual temperature of the medium, and standard deviation [tex]\sigma[/tex].
Let X be the random variable that represents the reading of the thermometer.
Confidence level : [tex]=95\%[/tex]
We know that the z-value for 95% confidence interval is 1.96.
Then, we have
[tex]-1.96<\dfrac{X-\mu}{\sigma}<1.96[/tex] [tex]z=\dfrac{X-\mu}{\sigma}[/tex]
[tex]\Rightarrow\ -1.96\sigma<X-\mu<1.96\sigma[/tex]
But all readings are within 0.6° of [tex]\mu[/tex].
So, [tex]1.96\sigma=0.6[/tex]
[tex]\Rightarrow\ \sigma=\dfrac{0.6}{1.96}=0.30612244898\approx0.3061[/tex]
Hence, the required standard deviation will be
The confidence level is 95% in normal distribution then The value of standard deviation is 0.3061.
What is a normal distribution?It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.
Given
The temperature reading from a thermocouple placed in a constant temperature medium is normally distributed with mean μ, the actual temperature of the medium, and standard deviation σ.
Let x be the random variable that represents the reading of the thermometer.
The confidence level is 95%. Then the z-value for 95% confidence level interval is 1.96.
Then we have
[tex]-\ \ 1.96 \ < \dfrac{x- \mu}{\sigma} < 1.96\\-1.96 \sigma < x- \mu \ < 1.96 \sigma[/tex]
But all the readings are within 0.6° of μ. Then
[tex]1.96 \sigma = 0.6\\[/tex]
On solving
[tex]\sigma = \dfrac{0.6}{1.96}\\\\\sigma = 0.306122 \approx 3061[/tex]
Thus, the standard deviation is 0.3061.
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true or false Linear? y = –5x
True. It is linear because it forms a straight line.
Answer:
TrueStep-by-step explanation:
It is a straight line, which is always linear.
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walt averages 98 miles per hourin 4 races. if each race is 95 miles in lenght, how many miles did walt drive in the race?
Answer: 380
Step-by-step explanation: Did you mean to ask how much time it took him? If he’s doing 4 races each being 95 miles it would simply be 95 x 4 = 380
The total distance driven by Walt is calculated by multiplying the length of each race (95 miles) by the number of races (4), giving a total of 380 miles.
Explanation:Walt averages 98 miles per hour, each race is 95 miles long, and he completed 4 races. To find the total distance driven by Walt, we only need to know how long each race is and how many races Walt completed because the speed at which Walt drives does not affect the total distance he covered in the race. Therefore, to get the total distance, we simply multiply the length of each race by the number of races. In this case, Walt drove 95 miles x 4 = 380 miles in total.
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If each side of a square patio is increased by 4 feet, the area of the patio would be 196 square feet. Solve the equation (s+4)2=196 for s to find the length of a side of the patio.
Answer:
The answer is 10
Step-by-step explanation:
The side length cannot be negative, hence the side length of the patio will be 10 feet
Give the expression that represents the statement given as:
[tex](s+4)^2 = 196[/tex]
We need to get the length of the side of the patio "s"
[tex](s+4)^2 = 196\\s+4 = \pm\sqrt{196}\\s+4=\pm14[/tex]
Subtract 4 from both sides
[tex]s+4-4=14-4\\s=14-4\\s =10ft[/tex]
Since the side length cannot be negative, hence the side length of the patio will be 10 feet
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ABC Auto Insurance classifies drivers as good, medium, or poor risks. Drivers who apply to them for insurance fall into these three groups in the proportions 30 percent, 50 percent, and 20 percent, respectively. The probability a "good" driver will have an accident is .01, the probability a "medium" risk driver will have an accident is .03, and the probability a "poor" driver will have an accident is .10. The company sells Mr. Brophy an insurance policy and he has an accident. What is the probability Mr. Brophy is: a. A "good" driver? b. A "medium" risk driver? c. A "poor" driver?
Answer:
a.[tex]P(E_1/A)=0.0789[/tex]
b.[tex]P(E_2/A)=0.395[/tex]\
c.[tex]P(E_3/A)=0.526[/tex]
Step-by-step explanation:
Let [tex]E_1,E_2,E_3[/tex] are the events that denotes the good drive, medium drive and poor risk driver.
[tex]P(E_1)=0.30,P(E_2)=0.50,P(E_3)=0.20[/tex]
Let A be the event that denotes an accident.
[tex]P(A/E_1)=0.01[/tex]
[tex]P(A/E_2=0.03[/tex]
[tex]P(A/E_3)=0.10[/tex]
The company sells Mr. Brophyan insurance policy and he has an accident.
a.We have to find the probability Mr.Brophy is a good driver
Bayes theorem,[tex]P(E_i/A)=\frac{P(A/E_i)\cdot P(E_1)}{\sum_{i=1}^{i=n}P(A/E_i)\cdot P(E_i)}[/tex]
We have to find [tex]P(E_1/A)[/tex]
Using the Bayes theorem
[tex]P(E_1/A)=\frac{P(A/E_1)\cdot P(E_1)}{P(E_1)\cdot P(A/E_1)+P(E_2)P(A/E_2)+P(E_3)P(A/E_3)}[/tex]
Substitute the values then we get
[tex]P(E_1/A)=\frac{0.30\times 0.01}{0.01\times 0.30+0.50\times 0.03+0.20\times 0.10}[/tex]
[tex]P(E_1/A)=0.0789[/tex]
b.We have to find the probability Mr.Brophy is a medium driver
[tex]P(E_2/A)=\frac{0.03\times 0.50}{0.038}=0.395[/tex]
c.We have to find the probability Mr.Brophy is a poor driver
[tex]P(E_3/A)=\frac{0.20\times 0.10}{0.038}=0.526[/tex]
Final answer:
The probability that Mr. Brophy is a good, medium, and poor risk driver given he has had an accident is approximately 0.079, 0.395, and 0.526 respectively, as calculated using Bayes' theorem.
Explanation:
Using Bayes' theorem, we can find out the probability that Mr. Brophy is a good, medium, or poor risk driver given that he has had an accident:
Let's denote A as the event of having an accident and Gi, Mi, Pi as the events of Mr. Brophy being a good, medium, or poor risk driver respectively.
P(Gi) = 0.30, P(Mi) = 0.50, P(Pi) = 0.20P(A|Gi) = 0.01, P(A|Mi) = 0.03, P(A|Pi) = 0.10The total probability of an accident, P(A), is given by:
P(A) = P(A|Gi)P(Gi) + P(A|Mi)P(Mi) + P(A|Pi)P(Pi)
P(A) = (0.01)(0.30) + (0.03)(0.50) + (0.10)(0.20) = 0.003 + 0.015 + 0.02 = 0.038
The probability of Mr. Brophy being a good driver given he had an accident, P(Gi|A), is:
P(Gi|A) = (P(A|Gi)P(Gi)) / P(A) = (0.01)(0.30) / 0.038 ≈ 0.079
The probability of Mr. Brophy being a medium risk driver given he had an accident, P(Mi|A), is:
P(Mi|A) = (P(A|Mi)P(Mi)) / P(A) = (0.03)(0.50) / 0.038 ≈ 0.395
The probability of Mr. Brophy being a poor risk driver given he had an accident, P(Pi|A), is:
P(Pi|A) = (P(A|Pi)P(Pi)) / P(A) = (0.10)(0.20) / 0.038 ≈ 0.526
Samantha has cut a pastry into four parts. Suppose PS||RQand T is the midpoint of PR. Determine whether SPT = QRT brainly
Answer:
Here's ur answer
Step-by-step explanation: