Answer:
Step-by-step explanation:
The expression (6)(2)^(n-1) means to multiply 6 by 2 raised to the power of n-1. For example, when n = 3, we have:
(6)(2)^(n-1) = (6)(2)^(3-1)
= (6)(2)^2
= (6)(4)
= 24
On the other hand, the expression 12^(n-1) means to raise 12 to the power of n-1. For example, when n = 3, we have:
12^(n-1) = 12^(3-1)
= 12^2
= 144
5 gallons of gas cost $16.25 the cost per gallon is $3.25
the question what unit rate describes the number of gallons per dollar?
Answer: To find the unit rate that describes the number of gallons per dollar, we need to divide the number of gallons by the cost in dollars. In this case, we have:
Number of gallons = 5
Cost in dollars = $16.25
Dividing the number of gallons by the cost in dollars, we get:
Gallons per dollar = Number of gallons / Cost in dollars
= 5 / $16.25
= 0.3077...
Rounding to two decimal places, we get:
Gallons per dollar = 0.31
Therefore, the unit rate that describes the number of gallons per dollar is 0.31 gallons per dollar.
Step-by-step explanation:
Find the area. Leave your answer in simple radical form.
Therefore, the area of the pentagon is 928 square units.
lengthLength is a measure of the size or extent of an object or a distance between two points. It refers to the longest dimension of an object or the distance between two points in space, typically measured in units such as inches, centimeters, meters, or miles. In mathematics, length is also used to describe the size of a line segment or a curve, which can be measured using various techniques such as Euclidean distance, arc length, or fractal dimension. Length is an important concept in many fields, including physics, engineering, geometry, and statistics.
Find the area.
Pentagon
apothem = 16 side = 23.2
Note: When necessary, enter your answer as a decimal If it is not a terminating decimal, round to the nearest hundredth
For the first question, we need more information to find the area of the triangle. Knowing the apothem and one side is not enough. We also need to know the number of sides of the triangle or the length of another side or the height.
For the second question, the formula to find the area of a regular pentagon is:
Area = (perimeter x apothem)/2
Since we are given the apothem and the side, we can find the perimeter of the pentagon as:
perimeter = 5 x side = 5 x 23.2 = 116
Substituting the values in the formula, we get:
Area = (116 x 16)/2 = 928
Therefore, the area of the pentagon is 928 square units.
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3) a baseball team had 80 players show up for tryouts last year and this year had 96 players show up for tryouts. find the percent increase in players from last year to this year.
The percent increase in players from last year to this year = 20%
We know that the formula for the percentage change a quantity is :
(P) = [Final value - Initial value] / Initial value x 100
Here, a baseball team had 80 players show up for tryouts last year and this year 96 show up for tryouts.
initial number of players = 80
current number of players = 96
So, using above formula the percent increase in players is:
P = [(96 - 80) / (80)] x 100
P = (16 / 80) x 100
P = 0.20 x 100
P = 20%
Therefore, the percentage of increase in players = 20%.
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consider a product with 500 components. each component has a defect probability of 0.015%. what is the defect probability of the final product?
Using the probability multiplication we know that the defect probability of the final product will be 7.5%.
What is probability?Simply put, the probability is the likelihood that something will occur.
When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.
Statistics is the study of events that follow a probability distribution.
The higher the likelihood, the more likely it is that the event will take place.
So, the probability formula is:
P(E) = Favourable events/Total events
So, in the given situation, the number of components integrated:
500
Defect probability of each component:
0.015%
Then, the defect probability of the final product:
= 500 * 0.015
= 7.5%
Therefore, using the probability multiplication we know that the defect probability of the final product will be 7.5%.
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A square table has a side length of 15ft. what is the measure of the diagonal
The measure of the diagonal of the square table is 15 * [tex]\sqrt{2}[/tex] feet (approximately 21.21 feet).
What is the measure of the diagonal?The diagonal of a square is the line segment that links two opposed corners of the square. The Pythagorean theorem asserts that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the diagonal of the square is the hypotenuse of a right triangle with two legs of length 15ft each (since the sides of a square are equal in length). So, we can use the Pythagorean theorem as follows:
[tex]diagonal^2[/tex] = [tex]15^2 + 15^2[/tex]
[tex]diagonal^2[/tex] = 450
diagonal = [tex]\sqrt{450}[/tex]
Using a calculator or simplifying by factoring out perfect squares, we get:
diagonal = [tex]\sqrt{(225 * 2)}[/tex] = 15 * [tex]\sqrt{2}[/tex]
Therefore, the measure of the diagonal of the square table is 15 * [tex]\sqrt{2}[/tex] feet (approximately 21.21 feet).
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Finding Perpendicular Lines. Which line is perpendicular to a line that has a slope of -1/3 ?
Answer:
3
Step-by-step explanation:
you want to flip your slope so the 3 goes over the 1 like this: 3/1
And then flip the sign so the negative turns to a positive
A student is asked to find the vertex of a parabola whose equation is as follows: y = 3 * (x + 4) ^ 2 - 2 The student concludes the vertex is at (4, - 2) . the student correct? If not, what do you think the student did wrong? Explain with as much relevant mathematical detail as possible. Please use at least 3 sentences total in your answer
Step-by-step explanation:
the general equation of a parabola is
y = a(x – h)² + k.
(h, k) is the vertex of the parabola.
comparing it to
y = 3(x + 4)² - 2
we see that (h, k) = (-4, -2).
the student made a sign mistake. it is "- h" in the squared factor. so, "+4" indicates "-4" as "h".
but the student simply used "+4".
Find f(10) for this piecewise-defined function.
f(x) = { -4x + 1 if x < 3
{2/5x -3 if x > 3
Write your answer as an integer or as a fraction in simplest form.
f(10) =
Answer:
-39
Step-by-step explanation:
I cannot provide picture, but plug 10 in for x for both equations
-4(10)+1 = -39 -39 less than 3? yes
2/5(10)-3 = 1 1 is greater than or equal to 3? no
the value of y when f(10) is -39
since when you plug 10 in for x -39 is the result
Robyn, a programmer, had a few important !les saved on her computer. The space occupied by the !les was 84.6 megabytes in all. If each !le used a memory of 21.15 megabytes, how many !les were there
Robyn has 4 important files saved on her computer.
To solve this problem, we can use a simple formula that relates the total space occupied by the files to the size of each file:
Total space occupied = Size of each file x Number of files
In this case, we know the total space occupied (84.6 megabytes) and the size of each file (21.15 megabytes), so we can rearrange the formula to solve for the number of files:
Number of files = Total space occupied ÷ Size of each file
Plugging in the values we know, we get:
Number of files = 84.6 megabytes ÷ 21.15 megabytes per file
Simplifying this expression gives us:
Number of files = 4
Therefore, Robyn has 4 important files saved on her computer.
It's important to note that this problem assumes that each file uses exactly 21.15 megabytes of memory. In reality, file sizes can vary depending on their content, so this may not always be the case. Additionally, it's worth noting that file size can be affected by various factors such as compression and encoding, so the actual size of a file on disk may differ from its theoretical size. Nonetheless, for the purposes of this problem, we can assume that each file uses exactly 21.15 megabytes of memory.
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Alejandra and her family are discussing how to pay for her college education. The cost of tuition at the college that Alejandra wants to attend is $9,000 per year. Alejandra's parents will pay 85% of the tuition cost every year, and she will pay the rest. Alejandra has one year to save enough money to attend her first year of college. What is the minimum amount of money she should save every month in order to reach her goal?
Responses
$637.50
$637.50
$1,350.00
$1,350.00
$112.50
$112.50
$28.12
The correct answer is $112.50. She should save $112.50 as the minimum amount every month in order to reach her goal.
To find the minimum amount of money Alejandra needs to save every month to attend her first year of college, we need to first determine the amount she needs to pay herself.
We know that her parents will pay 85% of the tuition cost, which is:
85% of $9,000 = 0.85 x $9,000 = $7,650
Therefore, Alejandra needs to pay the remaining amount:
$9,000 - $7,650 = $1,350
Since Alejandra has one year to save this amount, we need to divide $1,350 by 12 to find the minimum amount she should save every month:
$1,350 ÷ 12 = $112.50
Therefore, Alejandra should save at least $112.50 every month to reach her goal of attending college for her first year.
The correct answer is $112.50.
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a 6 foot ladder is leaning against a wall. if the top of the ladder slides down the wall at a rate of 2 feet per second, how fast is the bottom moving along the ground when the bottom of the ladder is 2 feet from the wall?
When the bottom of the 6-foot ladder is 2 feet from the wall, the bottom is moving along the ground at 1 foot per second.
To find the rate at which the bottom of the ladder moves along the ground, we can use the Pythagorean theorem and related rates. Let x be the distance from the bottom of the ladder to the wall, and y be the height of the ladder on the wall. The Pythagorean theorem is x² + y² = 36.
Differentiating both sides with respect to time (t) gives 2x(dx/dt) + 2y(dy/dt) = 0. We are given that dy/dt = -2 ft/s, and we need to find dx/dt when x = 2 feet.
To find y, we can use the Pythagorean theorem: 2² + y² = 36, so y² = 32, and y = 4√2. Plugging these values into the differentiated equation, we get 2(2)(dx/dt) + 2(4√2)(-2) = 0. Solving for dx/dt, we find that dx/dt = 1 ft/s.
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1
2
3
4
5
Complete the following sentence.
Government benefit programs have been established for a range of
TIME F
assistance.
15
Government benefit programs have been established for a range of assistance over time.
What is context of above answer?
The answer given was "Government benefit programs have been established for a range of assistance." This sentence is referring to various programs created by the government to provide support or aid to those in need.
These programs may include financial assistance, food assistance, housing assistance, medical assistance, and more. The sentence suggests that the government recognizes the importance of providing help to individuals and families who may be struggling and has taken steps to create programs to address these needs.
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Complete Question:
What types of assistance have government benefit programs been established for?
Select the expression that represents this real-world situation.
Vesi snowboards 4 hours before lunch and 3 hours after lunch each day. How many hours did she snowboard in 2 days?
4 + 3 + 2
(4 + 3) x 2
4 x 3 ÷ 2
(4 x 3) − 2
Answer:
(4 + 3) x 2
Step-by-step explanation:
In one day, Vesi would snowboard 4+3 hours, so in two days, we would multiply this by two and get the expression (4+3) * 2.
a fair coin 1s flipped repeatedly. what ts the probability that the fifth tail occurs before the tenth head?
The probability of having fifth tail occurring before the tenth head if a fair coin is flipped repeatedly is 0.377.
To solve this problem, we need to use the concept of negative binomial probability distribution.
The negative binomial probability distribution is a type of probability distribution that is used to describe the probability of k failures occurring before r successes in a sequence of independent and identical trials.
Let us consider the problem at hand.
We need to find the probability that the fifth tail occurs before the tenth head if a fair coin is flipped repeatedly.
Let X be the number of trials required to obtain the fifth tail. Then, X follows a negative binomial distribution with parameters r = 5 (number of successes we want) and p = 0.5 (the probability of obtaining a tail in a single flip).
The probability of obtaining the fifth tail on the kth trial is given by: P(X = k) = ᵏ-¹C₄(1 - p)ᵏ-ʳ *
where ᵏ-¹C₄ denotes the number of combinations of (k - 1) trials that yield 4 tails before the kth trial.
Since X should occur before the tenth head, k should be less than or equal to 9.
Therefore, we can calculate the required probability as follows:
P(X ≤ 9) = ∑P(X = k) for k = 5 to 9
= (⁴C₄*0.5⁵) + (⁵C₄*0.5⁶) + (⁶C₄*0.5⁷) + (⁷C₄*0.5⁸) + (⁸C₄*0.5⁹)
= (1*0.03125) + (5*0.015625) + (15*0.0078125) + (35*0.00390625) + (70*0.001953125)
= 0.376953125
Therefore, the probability that the fifth tail occurs before the tenth head if a fair coin is flipped repeatedly is 0.377.
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2.2.3 b for which -x²+8x+20=b will have real roots
Answer:
second that -x is the correct answer
A) 142
B) 146
C) 138
D) 132
E) 144
Answer:
it is 146 i no what work your doing i do i
21. A triangle with area 5 cm² is
dilated with a scale factor of 3.
What is the area of the image, in
square centimeters?
The area of the dilated triangle is 45 squared meters
What is the area of the triangle?Dilation is a geometric transformation that involves resizing a shape while maintaining its shape and proportions. The scale factor is the ratio of the size of the image to the size of the original shape.
In this problem, we are given a triangle with an area of 5 cm², and we are asked to find the area of the dilated triangle when it is scaled up by a factor of 3. To find the area of the dilated triangle, we need to use the formula for the area of a triangle, which is 1/2 * base * height.
When a triangle is dilated by a scale factor of k, both its base and height are multiplied by k. This means that the area of the dilated triangle is k^2 times the area of the original triangle. In this case, the scale factor is 3, so the area of the dilated triangle is 3^2 times the area of the original triangle.
Therefore, the area of the dilated triangle is 9 times the area of the original triangle, which is 9 * 5 cm² = 45 cm².
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What is the measure of arc c e d? 106° 108° 148° 212°
The measure of angle CED in a circle is 212°
The measurement of angles is done using basic geometric tools such as protractors and compasses. This tool helps to find precise measurements of angles. A protractor helps provide accurate measurements of angles, while compasses help construct angles. Angles are measured in three ways: degrees, radians, and revolutions.
In the given figure:
∠ EBD = 160°
and ∠ CBE = 52°
We have to tell the measure of arc CED.
Since m( arc EBD) = 160° and m( arc CBE ) = 52°
From the figure:
m( arc CED ) = m( arc CBE ) + m( arc CBE)
= 160° + 52°
= 212°
Therefore, measure of angle CED = 212°.
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A student is selected at random to work a problem on the
board.
What is the probability that the student selected is a female
junior?
0.15
0.25
0.20
0.50
Square and pentagon each have 9 in sides are their perimeters the same
No they wouldn't be the same because, the perimeter is adding all sides.
The square has 4 sides so you would add 9, four times.
9 + 9 + 9 + 9 = 36
And a pentagon has 5 sides so you would add 9, five times.
9 + 9 + 9 + 9 + 9 = 45
So, they are not the same.
m/3 = 4
solve m.
Please show your work
The polygons below are similar. Find the value of x
The value of x is 6m. Polygons can be regular or irregular, depending on whether all their sides and angles are congruent or not.
To find the value of x in the similar polygons shown in the figure, we can use the fact that corresponding sides of similar polygons are proportional. A polygon is a two-dimensional closed shape with three or more straight sides and angles. It is formed by connecting consecutive line segments, which are called sides, at their endpoints. The point where two sides of a figure meets is called a vertex. A polygon can have any number of sides, but it must have at least three. Polygons include triangles, quadrilaterals, pentagons, hexagons, and many more.
Since the polygons are similar so, the ratio of sides will be equal:
[tex]\frac{5}{10} = \frac{x}{12}[/tex]
x = 6 m.
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On Thursday afternoon the temperature fell by 3°C. On Friday it had risen by 5°C.
If Thursday morning
s temperature was - 4°C, what was the temperature on Friday?
Answer:
Thursday morning temperature was -4 degrees Celsius.
Thursday afternoon temperature dropped by 3 degrees.
So Thursday afternoon's temperature was:- -4 - 3 = -7
On Friday, the temperature had risen by 5 degrees Celsius
So -7 + 5 = -2 degrees Celsius
Write the equation that is parallel to y = -3x + 7 and passes through the point (2, -1). Write your answer in slope intercept form.
The equation of the line parallel to y = -3x + 7 and passing through the point (2, -1) is y = -3x + 5, written in slope-intercept form.
How to Write an Equation of a Line in Slope-intercept Form?The given equation is in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
The slope of the given equation is -3, which means any line parallel to it will have the same slope.
Using the point-slope form of a linear equation, we can write the equation of the line passing through the point (2, -1) and having a slope of -3:
y - y1 = m(x - x1) where (x1, y1) = (2, -1) and m = -3
y - (-1) = -3(x - 2)
y + 1 = -3x + 6
y = -3x + 5
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Tell what each of the residual plots to the right indicates about the appropriateness of the linear model that was fit to the data. Choose the best answer for residuals plot (a). O The fanned pattern indicates that the linear model is not appropriate. The model's predicting power decreases as the values of the explanatory variable increases. O The fanned pattern indicates that the linear model is not appropriate. The model's predicting power increases as the values of the explanatory variable increases. O The scattered residuals plot indicates an appropriate linear model.
Each of the residual plots indicates the appropriateness of the linear model that was fit to the data. The appropriate answer for residuals plot (a) is: the fanned pattern indicates that the linear model is not appropriate.
The model's predicting power decreases as the values of the explanatory variable increase.
A residual is the difference between the actual y value and the predicted y value, which is determined by the regression equation or linear model. A scatterplot of residuals is often used to evaluate the appropriateness of a linear model in a regression analysis, as well as to check for other things like non-linear relationships or non-constant variance.
Residuals scatterplots assist in detecting various types of patterns or lack of patterns that may be present in data. Patterns in a residual plot indicate that the linear model does not fit the data well, whereas the lack of pattern in a residual plot indicates that the linear model is appropriate.In this problem, the residual plot (a) has a fanned pattern. This means that the linear model is not appropriate. Furthermore, the model's predicting power decreases as the values of the explanatory variable increase. This means that the model may overestimate or underestimate the response variable as the values of the explanatory variable rise.
Therefore, we can conclude that the fanned pattern on residual plot (a) indicates that the linear model is not appropriate.
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a college entrance test consists of 112 questions. the test contains true/false (7 points each), fill in the blank (9 points each) and multiple choice (13 points each). there are 1172 possible points total on the test. the number of fill in the blank is 34 less than the number of true/false. how many points come from fill in the blank questions?
The test has average 80 true/false questions, 24 fill in the blank questions, and 28 multiple choice questions, with 7, 9 and 13 points respectively, totaling 1172 points.
The college entrance test consists of 112 questions in total, with different types of questions having different point values. There are 80 true/false questions, each worth 7 points, with a total of 560 points from these questions. There are also 24 fill in the blank questions, each worth 9 points, giving a total of 216 points from these questions. Finally, there are 28 multiple choice questions, each worth 13 points, for a total of 364 points from these questions. All together, the test has 1172 points available. The number of fill in the blank questions is 34 less than the number of true/false questions, meaning that there are more true/false questions than fill in the blank questions. The test is designed to assess a student's knowledge and comprehension of the subject they are taking the test for, and is made up of the three different types of questions to give a comprehensive assessment of their understanding.
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The line plot shows the size (in inches) of several different frog species. What is the difference between the shortest and longest species of frog?
The difference between the shortest and longest species of frog is [tex]3^{3\\}[/tex].
A line plot is a graph that shows data as checkmarks or points over a number line, indicating the frequency of each value.
When displaying information that changes over time, a line graph, also referred to as a line chart or a line plot, is frequently used. It can be visualized using a series of points connected by straight lines. The "x-axis" and the "y-axis" are two of its axes.
is a graph where the lines connecting the various data points are used. A line graph shows numerical values over a predetermined period of time. The shortest and longest frog species differ in terms of [tex]3^{3}[/tex].
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a raffle has a grand prize of a european cruise valued at $9000 with a second prize of a rocky point vacation valued at $1300. if each ticket costs $3 and 11200 tickets are sold, what are the expected winnings for a ticket buyer?
The expected winnings for a ticket buyer is $0.8036.
The given details are:
Grand prize = $9000
Second prize = $1300
Cost of each ticket = $3
Total tickets sold = 11200
Expected winnings are calculated by finding the expected value. Expected value is calculated by multiplying each outcome by its probability and then adding the products.
The total amount collected from selling 11200 tickets will be:
Total amount collected = 11200 × $3 = $33,600
Probability of winning grand prize = 1/11200
Probability of winning second prize = 1/11200
Probability of losing = 1 - (1/11200 + 1/11200) = 1 - 2/11200 = 11200/11200 - 2/11200 = 11198/11200
Expected value = probability of winning grand prize × grand prize + probability of winning second prize × second prize + probability of losing × zero
Expected value = (1/11200) × $9000 + (1/11200) × $1300 + (11198/11200) × 0 = $0.8036
The expected winnings for a ticket buyer is $0.8036.
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I'm reallyy confused on whats going on
Answer:82.13
Step-by-step explanation: you break it down into different shapes then add it.
Semi circle-a=pie times radius squared. radius is 3 so 3 squared is 9 and you multiply that by pie which is 28.26 and half is 14.13.
rectangle=6times 6=36
rectangle=14 times 3=32
add that all up and you should get 82.13
Are these triangles similar, congruent, or neither? What theorem supports the answer?
options:
Similar: SSS
Similar: SAS
Similar: AA
Congruent: SAS
Congruent: ASA
Congruent: AAS
Neither
Answer:
Similar: SAS
Step-by-step explanation:
The triangles are not congruent( they're not the equal) but the are similar because they form vertical angles that are congruent and their corresponding side lengths are in proportion