Answer:
10
Step-by-step explanation:
Use the pythagorean theorem/distance formula.
AB = \sqrt{(4-(-2))^2+(7-(-1))^2} = \sqrt{36+64} = \sqrt{100} = 10
: (17, -12) and (12, 8)
Answer:
What is the question?
Step-by-step explanation:
Suppose that the mean retail price per gallon of regular grade gasoline in the United States is $3.45 with a standard deviation of $0.20 and that the retail price per gallon has a bell-shaped distribution. (a) What percentage of regular grade gasoline sold between $3.25 and $3.65 per gallon? % (b) What percentage of regular grade gasoline sold between $3.25 and $3.85 per gallon? % (c) What percentage of regular grade gasoline sold for more than $3.85 per gallon? %
The required percentage of regular grade gasoline are;
a) 34%
b) 95.5%
c)4.5%
How we determine the percentage of regular grade gasoline?(a) To determine the percentage of regular grade gasoline sold between $3.25 and $3.65 per gallon, we need to find the proportion of the data that falls within this range. Assuming a bell-shaped distribution, we can use the standard deviation and mean to find the z-scores for these two prices, and then look up the cumulative probability in a standard normal table.
$3.25$ is $1$ standard deviation below the mean and $3.65$ is $0.5$ standard deviation above the mean.
Using a standard normal table, we find that approximately 68% of the data falls within one standard deviation of the mean, and approximately 34% falls between $-0.5$ and $0.5$ standard deviations.
Therefore, approximately 34% of regular grade gasoline is sold between $3.25 and 3.65 per gallon.
(b) To find the percentage of regular grade gasoline sold between $3.25 and $3.85 per gallon, we need to find the cumulative probability for the range $3.25$ to $3.85$.
$3.85$ is $1.5$ standard deviations above the mean.
Using a standard normal table, we find that approximately 95.5% of the data falls within $1.5$ standard deviations of the mean.
Therefore, approximately 95.5% of regular grade gasoline is sold between $3.25 and $3.85 per gallon.
(c) To find the percentage of regular grade gasoline sold for more than $3.85 per gallon, we need to find the cumulative probability for values greater than $3.85$.
Using a standard normal table, we find that approximately 100% - 95.5% = 4.5% of the data falls above $1.5$ standard deviations from the mean.
Therefore, approximately 4.5% of regular grade gasoline is sold for more than $3.85 per gallon.
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The following data represent the monthly phone use, in minutes customer enrolled in fraud prevention program for the past 20 months: The phone company decides to use the upper fence as the cutoff point for the number of minutes at which the customer should be contacted_ What is the cutoff point? 339 489 458 480 463 358 458 430 350 388 501 536 The cutoff point is minutes_ (Round to the nearest minute.
This indicates that the cutoff value for the amount of minutes before contacting the consumer is 674 minutes, rounded to the closest minute.
What is quartiles?Quartiles are three numbers that divide sorted data into four equal portions with an equal amount of observations each. A quantile is a sort of quantile. The first quartile is sometimes known as the lower quartile or Q1. Second quartile: Also known as the median or Q2. Third quartile: Also known as the higher quartile or Q3.
Here,
To find the upper fence, we need to calculate the following statistics:
Q1 (first quartile), Q2 (median), and Q3 (third quartile) of the data
Interquartile range (IQR), which is the difference between Q3 and Q1
Upper fence, which is Q3 + 1.5 * IQR
First, we need to order the data in ascending order:
339, 350, 358, 388, 430, 458, 458, 463, 480, 489, 501, 536
Next, we can find the quartiles:
Q1 = 388
Q2 = 458
Q3 = 501
IQR = Q3 - Q1 = 501 - 388 = 113
Finally, we can calculate the upper fence:
Upper fence = Q3 + 1.5 * IQR = 501 + 1.5 * 113 = 674
This means that the cutoff point for the number of minutes at which the customer should be contacted is 674 minutes, rounded to the nearest minute.
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Which equation represents the relationship between the independent
variable, x, and the dependent variable, y, as shown in the table below?
X
(input)
7
8
9
10
y
(output)
14
16
18
20
y = 2x
x = 3y
x = 5y
y
HE
3X
The equation represents the relationship between the independent variable, x, and the dependent variable is y= 2x
How to determine the equationFrom the question, we have the following parameters that can be used in our computation:
The table of values
On the yable of values, we can see that
y is twice of x
When represented as an equation, we have
y = 2x
Hence, the equation is y = 2x
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IF AT bisects LAS prove that LAT=SAT
Answer:
Use SAS postulate
Step-by-step explanation:
In triangles LAT and SAT,
AT = AT (common side)
ang. LAT = ang. SAT (given, as angle is bisected)
SA = LA (from figure)
Hence, the triangles are congruent
a small bus interchange has 2 feeder services that start simultaneously at 9 am. bus number 801 leaves the interchange at 15-min intervals, while bus number 802 leaves at 20- min intervals. on a particular day, how many times did both services leave together from 9 am to 12 noon inclusive?
The number of times both services left the interchange together from 9am to 12 noon is 0.
Let's call the number of 15-minute intervals that have passed since 9 am "t".
So, the time that bus number 801 leaves the interchange after t intervals is 9am + 15t minutes.
Similarly, the time that bus number 802 leaves the interchange after t intervals is 9 am + 20t minutes.
For both services to leave the interchange at the same time, the number of 15-minute intervals that have passed since 9 am must be the same for both buses.
In other words, 15t must equal 20t.
Dividing both sides of this equation by 5, we get 3t = 4t.
This equation has no solution, which means that bus number 801 and bus number 802 never leave the interchange at the same time from 9am to 12 noon.
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Round to the nearest tenth. This is a multi-step problem so do not round until the final answer.
The segment drawn from the apex to the edge of the circular base is ___ units.
The segment drawn from the apex to the edge of the circular base is 24.19 units.
How to determine the slant heightFrom the question, we have the following parameters that can be used in our computation:
Volume = 72π
Diameter = 6
The volume of a cone is
V = 1/3πr^2h
Where
r = 6/2 = 3
So, we have
1/3π * 3^2h = 72π
This gives
3h = 72
Divide by 3
h = 24
The slant height is then calculated as
l = √(h² + r²)
So, we have
l = √(24² + 3²)
Evaluate
l = 24.19
Hence, the slant height is 24.19 units
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Peter says 3/4 of a pizza is always the same as 6/8 of a pizza. Nadia says while 3/4 and 6/8 are equivalent fractions, 3/4 and 6/8 of a pizza could represent different amounts.
PLEASE HELP ASAP I HAVE 3 MINS LEFT!!!
PLEASE ANSWER THE PICTURE I SENT YOU BECAUSE IT HAS TO DO WITH THE QUESTION.
JUST DO NUMBER 2
Peter is right and Nadia is wrong.
What are equivalent fractions?Equivalent fractions are fractions that represent the same value, even though they look different.
Given is that Peter says 3/4 of a pizza is always the same as 6/8 of a pizza. Nadia says while 3/4 and 6/8 are equivalent fractions, 3/4 and 6/8 of a pizza could represent different amounts.
{ 1 } -
3/4 = (3 x 2)/(4 x 2) = 6/8
Peter is right.
Now -
3/4 = 6/8
So it could not represent two different quantities. So, Nadia is wrong.
{ 2 } -
3/4 = 6/8 = 9/12 = 12/15
These all represent the same quantity. Division of all the expressions will result in same value.
Therefore, Peter is right and Nadia is wrong.
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which of the following is true regarding p-values associated with the estimated coefficients in a linear regression model? group of answer choices the larger the p-value, the higher the probability that the variable is statistically significant. the larger the p-value, the more confident we are that we should reject the null hypothesis that the population coefficient is equal to 0. p-values less than 0.01 guarantee both statistical significance and practical significance.
The larger the p-value, the more likely it is that the null hypothesis that the population coefficient is equal to 0 is true regarding p-value.
In a linear regression model, p-values are associated with the estimated coefficients and provide information about the statistical significance of each predictor variable. The null hypothesis for each predictor is that the population coefficient for that predictor is equal to 0, meaning that it has no effect on the response variable.
The p-value is the probability of observing the estimated coefficient given the null hypothesis is true. If the p-value is small, it means that the observed coefficient is unlikely to be due to chance, If the p-value is large, it means that the observed coefficient could easily be due to chance and we cannot reject the null hypothesis.
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total of 900 5, 10 dollar bills
value of all the 5, 10 dollar bills is 5500 dollar bills
how many 5 and 10 do have
There is 700 number of $5 bills and 200 number of $10 bills
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical expressions. Equations are classified based on degree as linear, quadratic, cubic
Let x represent the number of $5 bills and y represent the number of $10 bills.
There is a total of 900 $5, $10 dollar bills, hence:
x + y = 900 (1)
The value of all the bills is $5500, hence:
5x + 10y = 5500 (2)
From both equation, solving simultaneously:
x = 700, y = 200
There are 700 $5 bills and 200 $10 bills
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Kyle is creating a frame for a model car. He begins by piecing two rods together, as shown in the diagram. Justify why ∠AEC is a right angle. Definition of parallel lines Definition of perpendicular bisector Definition of complementary angles Definition of adjacent anglesKyle is creating a frame for a model car. He begins by piecing two rods together, as shown in the diagram. Justify why ∠AEC is a right angle. Definition of parallel lines Definition of perpendicular bisector Definition of complementary angles Definition of adjacent anglesKyle is creating a frame for a model car. He begins by piecing two rods together, as shown in the diagram. Justify why ∠AEC is a right angle. Definition of parallel lines Definition of perpendicular bisector Definition of complementary angles Definition of adjacent angles
The solution is Option B.
The angle ∠AEC is a right angle by definition of perpendicular bisector
What is perpendicular bisector?A perpendicular bisector is defined as a line or a line segment that divides a given line segment into two parts of equal measurement. Lines that cross each side's midpoint and are perpendicular to the specified side are known as a triangle's perpendicular bisectors.
The perpendicular bisector theorem states that any point on the perpendicular bisector is equidistant from both the endpoints of the line segment on which it is drawn
Given data ,
Let the first line be represented as AB
Let the second line be represented as CD
Now , AB is perpendicular to the line CD
where , the measure of ∠CEB = 90°
And , angles on a straight line has a sum of 180°
So , the measure of ∠AEC is a right angle by perpendicular bisector theorem
Hence , the measure of the perpendicular angle ∠AEC is 90°
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Answer: Definition of Perpendicular Bisector
Step-by-step explanation:
Took the test!
What is the range of the function shown in the graph below?
The range of the function shown in the graph below is [-6, ∞].
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
From the graph,
The y-coordinate value is the range of the function.
We see that,
The y-coordinate value is from -6 to ∞.
So,
Range = [-6, ∞].
Thus,
The range of the function is [-6, ∞].
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question 5 mathematics
The quadratic regression equation for the data-set in this problem is given as follows:
y = 0.96x² - 5.77x + 1.38.
How to obtain the regression equation?Regression equations are obtained inserting the points of a data-set into a calculator.
In this problem, we want to find the quadratic regression equation, hence a quadratic regression calculator is used.
The points are given as follows:
(-1,8), (5,-4), (7,8), (2,-6).
Inserting these points into a calculator, the regression equation is given as follows:
y = 0.96x² - 5.77x + 1.38.
Meaning that the second option is the correct option.
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Montana decided to start his ball from the second diamond from the left along the bottom rail. He is planning to aim at the third diamond from the top right. If he hits the ball sufficiently hard, will the ball eventually reach a pocket? If so, show the path of the ball. Explain the steps used to solve the problem and write a concluding statement
Answer:
To determine whether the ball will eventually reach a pocket, we need to determine if the ball will collide with any other balls or obstacles on the way to its target. If there are no obstacles, and the ball has enough force and the correct trajectory, it will reach the target pocket.
To show the path of the ball, we can draw a straight line connecting the starting position and the target pocket. This line represents the trajectory of the ball if it is not obstructed by any other balls or obstacles.
In conclusion, without any obstacles in the way, if Montana hits the ball with enough force and the correct trajectory, the ball will reach the target pocket. It is important to consider any potential obstacles or interference when planning a shot in billiards.
The following data represent the test scores of a math class.
Make a frequency table using six classes.
26 29 37 37 46 62 64 68 71 73 74 80 86 92 94 97 100
The frequency table using the six classes have been done below
How to draw the frequency tableClass interval Frequency
20 - 35 2
36 - 50 0
51 - 65 2
66 - 80 5
81 - 95 5
96 - 110 5
Note: The class intervals were created as follows: 20-35, 36-50, 51-65, 66-80, 81-95, and 96-110. The frequency is the number of data values that fall into each class interval.
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there are 6 balls in a box - 2 white and 4 black. if we select three balls, what is the probability of selecting exactly one white one?
If we select three balls, the probability of selecting exactly one white one is 16.
There are 6 balls in a box.
2 white and 4 black.
If we select three balls, then we have to determine the probability of selecting exactly one white.
First we determine the number of ways of selecting three balls in total of 6 balls. So
[tex]^{6}C_{3} = \frac{6!}{3!(6-3)!}[/tex]
[tex]^{6}C_{3} = \frac{6!}{3!3!}[/tex]
[tex]^{6}C_{3} = \frac{6\times5\times4\times3!}{3\times2\times1\times3!}[/tex]
Simplify
[tex]^{6}C_{3}[/tex] = 5 × 4
[tex]^{6}C_{3}[/tex] = 20
Now determining the probability of selecting the 3 balls out of non white balls.
[tex]^{4}C_{3}=\frac{4!}{3!(4-3)!}[/tex]
[tex]^{4}C_{3}=\frac{4!}{3!1!}[/tex]
Simplify
[tex]^{4}C_{3}=\frac{4\times3!}{3!\times1}[/tex]
[tex]^{4}C_{3}[/tex] = 4
Now, the probability of selecting exactly one white one = The number of ways of selecting three balls in total of 6 balls - The probability of selecting the 3 balls out of non white balls
The probability of selecting exactly one white one = 20 - 4
The probability of selecting exactly one white one = 16
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a loan of $900 at a rate of 11% with paid off in 6 months which equation could be used to determine the amount of interest that was paid
Equation used to represent the amount of interest that was paid is S.I = 900 × 0.11 × 0.5 and the amount is $49.5.
What is Simple Interest?Simple interest is defined as the interest obtained over the principal amount on a certain rate.
Simple interest amount can be calculated using the formula,
S.I = Prt
Here P is the principal amount, r is the rate of interest and t is the time in years.
Given a loan of $900 at a rate of 11% with paid off in 6 months.
P = $900,
r = 11% = 0.11 and
t = 6 months = 0.5 year
S.I = 900 × 0.11 × 0.5
= 49.5
Hence the amount of simple interest is $49.5.
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the blenders produced by a company have a normally distributed life span with a mean of 8.2 years and a standard deviation of 0.8 years. the company is willing to have a warranty that replaces at most 6% of their blenders sold. what is the longest a blender can last and still be in the lowest 6% of life spans?
The longest a blender can last and still be in the lowest 6% of life spans is 7.96 years.
The longest a blender can last and still be in the lowest 6% of life spans is calculated by using the inverse normal distribution formula. This formula is P(X ≤ x) = 1 - P(X > x). The X is the longest a blender can last and P(X ≤ x) is 6%. First, we need to calculate the z-score for 6%. This can be done by P(X ≤ x) = 0.06 and using the z-score formula z = (x - μ) / σ , where μ is the mean and σ is the standard deviation. Substituting the values into the equation, we get z = 0.06 = (x - 8.2) / 0.8. Solving for x gives us x = 7.96. Therefore, the longest a blender can last and still be in the lowest 6% of life spans is 7.96 years.
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which of the following is true regarding trendlines in a scatter chart in excel? group of answer choices excel can add only linear trendlines to data in a scatter chart. excel can output the r square value for a trendline in excel for scatter charts of 3 or more variables. for simple linear regression models, the trendline in excel will give a different equation than the data analysis toolpak regression tool. none of these are true.
Out of the following, the statement Excel can add only linear trendlines to data in a scatter chart is true regarding trendlines in scatter chart in excel.This means that the trendline in Excel will be a straight line that will best fit the data points in the scatter chart.
It will not be able to fit any other type of trendline, such as a polynomial or exponential trendline. Additionally, Excel cannot output the R Square value for a trendline in Excel for scatter charts of 3 or more variables. This is because the R Square value is a statistical measure that can only be calculated for linear regression models.
Finally, for simple linear regression models, the trendline in Excel will give the same equation as the data analysis toolpak regression tool. This means that the equation of the trendline in Excel will be the same as the equation of the regression line calculated by the data analysis.
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a starting lineup in basketball consists of two guards, two forwards, and a center. (a) a certain college team has on its roster three centers, four guards, four forwards, and one individual (x) who can play either guard or forward. how many different starting lineups can be created? [hint: consider lineups without x, then lineups with x as guard, then lineups with x as forward.] lineups
In total, there are 192 + 144 + 144 = 480 different starting lineups that can be created.
There are 3 centers to choose from, and for each center there are 4 choices for each of the two guard positions and 4 choices for each of the two forward positions. So, there are:
3 * 4 * 4 * 4 = 192
different starting lineups without x.
Lineups with x as guard: There are 3 centers, 3 choices for the first guard (since x can play either guard or forward), 4 choices for the second guard, and 4 choices for each forward. So, there are
3 * 3 * 4 * 4 = 144
different lineups with x as guard.
Lineups with x as forward: There are 3 centers, 4 choices for each guard, 3 choices for the first forward (since x can play either guard or forward), and 4 choices for the second forward. So, there are 3 * 4 * 3 * 4 = 144 different lineups with x as forward.
In total, there are 192 + 144 + 144 = 480 different starting lineups that can be created.
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What is the midpoint of 1/3 and 6/11 as a fraction
The midpoint of the 1/3 and 6/11 as a fraction is, 29/33
What is the midpoint of a fraction?The midpoint of two numbers can be found by taking the average of the two numbers. To find the average of two fractions, you need to find a common denominator, add the numerators, and divide the sum by the denominator.
Given that,
Two fractions,
1/3 and 6/11
To find the common denominator for 1/3 and 6/11, you can find the least common multiple (LCM) of the denominators:
LCM(3, 11) = 33
Next, convert each fraction to an equivalent fraction with a denominator of 33:
1/3 = 11/33
6/11 = 18/33
Finally, add the numerators and divide the sum by the denominator to find the average:
(11 + 18) / 33 = 29/33
The midpoint of 1/3 and 6/11 as a fraction is 29/33.
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WILL MARK BRAINLIEST!
A) On a school trip the ratio of adults to students is 1: 10.
All of the students are in year 10 or year 11.
The ratio of year 10 to year 11 is 1: 4.
What fraction of all the people on the trip are year 11 students?
(b)
In a cinema the ratio of adults to children is 2: 3.
The children are either boys or girls.
The ratio of boys to girls is 5: 2.
What fraction of all the people in the cinema are girls?
Answer:
A) 2/5
B) 4/15
Step-by-step explanation:
A)
adults : students
1 : 10
year 10 : year 11
1 : 4
fraction of all the people on the trip are year 11 students =
4 : 10
4 / 10
2 / 5
B)
adults : children
2 : 3 _____________(1)
boys : girls
5 : 2 _____________(2)
multiplying ratio (1) with 5
adults : children
10 : 15
multiplying ratio (2) with 2
boys : girls
10 : 4
fraction of all the people in the cinema are girls
4 : 15
4 / 15
given a normal distribution with mean of 50 and a standard deviation of 4, what is x value for the boundary for the lowest 2.5%?
The X value for the boundary for the lowest 2.5% of a normal distribution with a mean of 50 and a standard deviation of 4 is 43.04.
The lowest 2.5% boundary for a normal distribution with a mean of 50 and standard deviation of 4 can be calculated using the Z-score formula.
Z = (X - mean) / standard deviation
We want to find the X value for which Z = -1.96 since -1.96 represents the boundary for the lowest 2.5% of a standard normal distribution.
Plugging in the mean and standard deviation:
-1.96 = (X - 50) / 4
Solving for X:
X = 50 - 1.96 × 4
X = 43.04
So, the X value for the boundary for the lowest 2.5% of a normal distribution with a mean of 50 and a standard deviation of 4 is 43.04.
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BRAINLIEST MARKED FOR EXPLANATION - HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Figure 1 is vertical, through the cone's topmost point
Figure 2 is horizontal
Figure 3 is diagonal
Explanation:
The easiest way to think about this is that you have a cone-shaped cake and you are cutting it.
Use the graph of y=e^x on a graphing calculator to evaluate the following expression to four decimal places.
y = e^ -4
(Round to four decimal places as needed.)
***
The equation y = e^-4 can be evaluated using a graphing calculator by plugging in -4 for x and finding the corresponding y-value.
On a graphing calculator, this is usually done by setting the calculator to the "y=" mode and entering the equation y = e^x. Then, by entering -4 as the value of x, the corresponding y-value can be found.
The result would be y = e^-4 = 0.0183. To four decimal places, this value is 0.0183.
The time it takes to travel to a location varies inversely to the speed traveled. It takes 4 hours driving at an average speed of 55 miles per hour to reach a location. To the nearest tenth of an hour, how long will it take to reach the same location driving at an average speed of 50 miles per hour?
Time it will take to reach the same location driving at an average speed of 50 miles per hour, 4.4 hour
What is the relation between time, distance & speed ?The distance covered by the object is equal to the product of the speed at which the object is moving and time taken for covering the distance.
Distance = Time × Speed
Given that,
The time it takes to travel to a location varies inversely to the speed traveled,
Time = 4 hours
Average speed = 55 miles per hour
If average speed = 50 miles per hour
then time = ?
First, it is required to calculate distance covered,
Distance = Time × Speed
= 4 x 55
= 220 miles
Now, when average speed is 50 miles per hour,
Distance = Time × Speed
Speed = Distance/Time
= 220/50
= 4.4 hour
Thus, the required time is 4.4 hour
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You and your friend just got new puppies. Your puppy, Max, currently weighs 5 pounds and is expected to gain 1 pound per week. Your friend's puppy, Ruby, currently weighs 8 pounds and is expected to gain 0.5 pounds per week. After how many weeks will the puppies weigh
Two puppy's Max and Ruby will have equal weight after 6 weeks
What is an arithmetic sequence?In the arithmetic sequence the common difference remains constant between any two consecutive terms. In this sequence we can get the next term by adding one fixed value which is known as a common difference. It is also known as arithmetic progression(AP).
Formula for any nth term in AP,
T = a + nd
d = T₂-T₁
Where, a is first term , n is nth term and d is common difference
Given that,
Two puppy's
Max, currently weighs 5 pounds and is expected to gain 1 pound per week,
Ruby, currently weighs 8 pounds and is expected to gain 0.5 pounds per week
The number of weeks when both will have equal weight = ?
Suppose, it number of weeks = n
It can be solved by using concept of arithmetic sequence,
a₁ = 5 pounds
d₁ = 1 pound per week
Tₙ = 5 + 1xn = 5 + n
a₂ = 8 pounds
d₂ = 0.5 pounds per week
Tₙ = 8 + 0.5xn = 8 + 0.5n
Both should be equal,
5 + n = 8 + 0.5n
0.5n = 8 - 5
n = 6
Hence, after 6 weeks they will have same weight
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describe the evidence that allowed scientists to conclude that electrons occupy specific energy levels and are not just randomly distributed outside the nucleus
Scientists can conclude that electrons occupy specific energy levels and are not just randomly distributed outside the nucleus.
The evidence that allowed scientists to conclude that electrons occupy specific energy levels and are not just randomly distributed outside the nucleus comes from the application of the quantum mechanical model. The quantum mechanical model states that the energy of an electron is quantized, meaning it can only occupy discrete energy levels rather than any random energy level in between. This is expressed mathematically through the equation E n = nhf, which states that the energy of an electron is equal to the product of Plank's constant (h) and the frequency (f) of the electron's orbit multiplied by the quantum number (n). This equation demonstrates that electrons can only occupy certain energy levels and not any random energy level. Therefore, scientists can conclude that electrons occupy specific energy levels and are not just randomly distributed outside the nucleus.
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find the scalar and vector projections of b onto a.
a = {-8, 15}
b ={3,5}
The scalar projection of vector b onto vector a is 57/289 and the vector projection of vector b onto vector a is (0.38, 0.92).
What is vector?A quantity or phenomena with independent qualities for both magnitude and direction is called a vector. The term can also refer to a quantity's mathematical or geometrical representation. Velocity, momentum, force, electromagnetic fields, and weight are a few examples of vectors in nature.
According to question:The scalar projection of vector b onto vector a is given by:
(b . a) / ||a||^2
= (3 * -8 + 5 * 15) / ( -8^2 + 15^2)
= 165 / 289
= (57/289)
The vector projection of vector b onto vector a is given by:
proj(b onto a) = (b . a) / ||a||^2 * (a / ||a||)
= (57/289) * (-8/√(-8^2 + 15^2), 15/√(-8^2 + 15^2))
= (0.38, 0.92)
Note: sqrt(-8^2 + 15^2) = sqrt(289) = 17
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Question 1
Does 8! 8 7 • 6? Why or why not?
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The expanded form of 8! is 8×7×6×5×4×3×2×1.
What is a factorial?A whole number's factorial is the result of multiplying the integer by each natural number below it.
The sign '!' can be used to indicate a factorial symbolically.
Therefore, 'n factorial' is denoted by the number n and is the product of n up to whole numbers below n except zero.
Given, A factorial number 8!.
Therefore, 8! = 8×7×6×5×4×3×2×1.
The product of all whole numbers below 8 and except zero.
We use factorials in permutation and combination also.
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