To find dy/dx, we need to take the derivative of y with respect to x. On evaluating the value of dy/dx is [tex]-9t^{8/9}[/tex]
However, we are given x in terms of t. So first, we need to use the chain rule to find dx/dt:
x = [tex]t^{1/9}[/tex]
dx/dt = (1/9) * [tex]t^{-8/9}[/tex]
Now, we can use the chain rule again to find dy/dt:
y = 9 - t
dy/dt = -1
Finally, we can use the formula for the chain rule to find dy/dx:
dy/dx = (dy/dt) / (dx/dt)
dy/dx = (-1) / ((1/9) * [tex]t^{-8/9}[/tex]
dy/dx = [tex]-9t^{8/9}[/tex]
So, the final answer is dy/dx = [tex]-9t^{8/9}[/tex]
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The coordinates of the vertices of △ABC are A(3,0), B(2,−3), and C(0,3). The coordinates of the vertices of △XYZ are X(1,0), Y(0,3), and Z(−2,−3). Which series of transformations correctly shows that △ABC≅△XYZ?
A: a translation 2 units down and a reflection over the x-axis
B: a translation 2 units up and a reflection over the y-axis
C: a translation 2 units right and a reflection over the y-axis
D: a translation 2 units left and a reflection over the x-axis
The series of transformations correctly shows that △ABC≅△XYZ is D
a translation 2 units left and a reflection over the x-axis.
How do you solve for the transformation?if a translation happens to each point of △ABC horizontally to the left by 2 units, which means subtracting 2 from the x-coordinate of each vertex, we notice that a transformation of ABC to coordinates that are almost identical to XYZ but let it be called it A'B'C'
A(3, 0) ⇒ A'(1, 0)
B(2, -3) ⇒ B'(0, -3)
C(0, 3) ⇒ C'(-2, 3)
Secondly, if a reflection happens to A'B'C' at the x axis the transformation becomes identical to △XYZ
A'(1, 0) ⇒ X(1, 0)
B'(0, -3) ⇒ Y(0, 3)
C'(-2, 3) ⇒ Z(-2, -3)
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Write an inequality and a word sentence that represent the graph. Let x represent the unknown number.
A number line. The number line is shaded left of an open circle at 1.
Inequality:
The word sentence for the given number line represents the X is greater than zero. The inequality is the X is not less than or equal to zero.
In the given number line the values are from negative infinity to positive infinity. Though the number line is having all values, there is some part that is shaded only on certain parts of the number line. The part is from number 1 to positive infinity marking zero as a circle.
The circle represents the value starts counting from the next step. In the given number line circle is shaded at number zero and the value started from the next value which is number 1 onwards to positive infinity.
So, the given number line represents X is greater than zero and X is not less than or equal to zero.
In mathematical words,
X < 0 and X≠0
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Given question is not having enough information to solve, for better understanding attaching the number line image below.
compute (7 4/9 -8)*3.6-1.6*(1/3-3/4)+ 1 2/5 ÷(0.35)
The value of (7 4/9 -8)*3.6-1.6*(1/3-3/4)+ 1 2/5 ÷(0.35) is given as 241/54.
How to solve for the value(7 4/9 -8) = -5/9.
3.6-1.6 = 2.0
1/3-3/4 = 1/3 - 3/4
= 4/12 - 9/12
= -5/12
we will have -5/9 * 2 = -10/9.
-10/9 * -5/12
10/9 * -5/12 = (10 * 5) / (9 * 12) = 50/108
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 2:
50/108 = 25/54
we will have
25/54 + 1 2/5 ÷(0.35)
1 2/5 ÷ 0.35 = (7/5) ÷ (35/100) = (7/5) * (100/35) = 4
Now, we can substitute this value into the expression:
25/54 + 4 = (25/54) + (216/54) = 241/54
Therefore, the value of the expression 25/54 + 1 2/5 ÷(0.35) is 241/54.
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Caroline works in a department store selling clothing. She makes a guaranteed salary
of $200 per week, but is paid a commision on top of her base salary equal to 25% of
her total sales for the week. How much would Caroline make in a week in which she
made $1575 in sales? How much would Caroline make in a week if she made a dollars
in sales?
The amount made by Caroline is $593.75 and 200 + 0.25x when she made $1574 and $x in sales respectively.
The total amount will be given by the formula using percentage -
Total amount = Base salary + 25% × her total sales
Keep the value in equation when she made $1575
Total amount = 200 + 25% × 1575
Total amount = 200 + 393.75
Total amount = $593.75
Keep the value in equation when she made $x
Total amount = 200 + 25% × x
Total amount = 200 + 0.25x
Hence, the earned amount is $593.75 and 200 + 0.25x.
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The complete question is -
Caroline works in a department store selling clothing. She makes a guaranteed salary of $200 per week, but is paid a commision on top of her base salary equal to 25% ofher total sales for the week. How much would Caroline make in a week in which she made $1575 in sales? How much would Caroline make in a week if she made x dollars in sales?
Eratosthenes was born 276 BC. Abraham Lincoln died in 1865. How many years apart were these two events. Answer choices: 276 1865 1589 -1589
The number of years apart between Eratosthenes was born in 276 BC (Before Christ) Abraham Lincoln died in 1865 is 2140 years.
Eratosthenes was born in 276 BC
Abraham Lincoln died in 1865 AD
BC = Before Christ
AD = anno dominie
The difference between the born date of Eratosthenes and the death date of Abraham Lincoln is to be calculated by
Year difference = BC year + AD year - 1
Year difference = 276 + 1865 - 1
Year difference = 2140
hence the difference between the born date of Eratosthenes and the death date of Abraham Lincoln is 2140
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Question 10(Multiple Choice Worth 2 points)
(Comparing Data MC)
The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.
Which drive-thru typically has more wait time, and why?
Burger Quick, because it has a larger median
Burger Quick, because it has a larger mean
Super Fast Food, because it has a larger median
Super Fast Food, because it has a larger mean
Question 11(Multiple Choice Worth 2 points)
(Creating Graphical Representations MC)
The number of carbohydrates from 10 different tortilla sandwich wraps sold in a grocery store was collected.
Which graphical representation would be most appropriate for the data, and why?
Circle chart, because the data is categorical
Line plot, because there is a large set of data
Histogram, because you can see each individual data point
Stem-and-leaf plot, because you can see each individual data point
Question 12(Multiple Choice Worth 2 points)
(Comparing Data MC)
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 10, 16, 20, and 28. There are two dots above 8 and 14. There are three dots above 18. There are four dots above 12. The graph is titled Bus 14 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9, 18, 20, and 22. There are two dots above 6, 10, 12, 14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.
Bus 14, with a median of 14
Bus 18, with a mean of 12
Bus 14, with a mean of 14
Bus 18, with a median of 12
Question 13(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 1 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 1 and 2. There are two dots above 8. There are three dots above 6, 7, and 9.
Which of the following is the best measure of variability for the data, and what is its value?
The range is the best measure of variability, and it equals 8.
The range is the best measure of variability, and it equals 2.5.
The IQR is the best measure of variability, and it equals 8.
The IQR is the best measure of variability, and it equals 2.5
The drive-thru is able to estimate their wait time more consistently will be A. Burger Quick, because it has a smaller IQR.
What is the IQR?The interquartile range (IQR) is a measure of variability that represents the range of values in the middle 50% of scores in a distribution. It is used when the data is skewed and the median is a better measure of central tendency than the mean.
In this scenario, Burger Quick has an IQR of 14.5, while Fast Chicken has an IQR of 4.5.
The IQR is calculated by subtracting the first quartile (Q1) from the third quartile (Q3).
For Burger Quick, Q1 is 9.5 and Q3 is 24, so the IQR is 24 - 9.5 = 14.5. For
Fast Chicken, Q1 is 10 and Q3 is 14.5, so the IQR is 14.5 - 10 = 4.5.
Therefore, Burger Quick has a larger IQR than Fast Chicken, indicating that its data is more consistent and less spread out. This means that Burger Quick is better able to estimate its wait time consistently.
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From monday through friday, earl works in the bookstore on 1 and in the athletic center on another 2 days. on saturday and sunday, earl cooks food 50% of the days. how many days does earl work in a week? what percent of monday through friday does earl work?
Earl works a total of 3 days in a week. From Monday through Friday, he works in the bookstore on 1 day and in the athletic center on 2 days. On Saturday and Sunday, he cooks food on 50% of the days, which would be a total of 1 day. Therefore, he works a total of 3 days in a week.
To calculate the percentage of Monday through Friday that Earl works, we need to first calculate the total number of days in a week, which is 7. Then, we need to subtract the weekend days, which are Saturday and Sunday, leaving us with 5 days.
Finally, we can calculate the percentage by dividing the number of days Earl works from Monday through Friday (which is 1) by the total number of weekdays (which is 5), and multiplying by 100. So, Earl works 20% of Monday through Friday.
In summary, Earl works 3 days in a week, 1 day in the bookstore and 2 days in the athletic center. He also cooks food on 1 day during the weekend. Earl works 20% of Monday through Friday.
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Sally has seen four movies. The ticket prices were: $13, $8, $10, $10 The next movie she plans to see in is 3D and the ticket price is $34. Circle one of the following that will not change after Sally sees the next movie
The prices of the four movies that Sally has already seen will not change after she sees the next movie.
The ticket prices of the four movies that Sally has already seen are fixed and do not depend on whether she sees another movie or not. Therefore, these prices will remain the same even after she sees the next movie. The price of the next movie that Sally plans to see is $34, which is independent of the ticket prices of the previous movies.
Thus, the cost of the previous movies that Sally has seen will not change after she sees the next movie. In other words, the previous expenses are sunk costs and are irrelevant to future decisions.
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Which expression represents the surface area of the prism?
Choose 1 answer:
2.3+3.8
2.6+12+8+8
3+3+12+8+8
12+12+12+3+3
The answer of the given question based on the right triangular prism is , the surface area of the prism is,
(D) 2.6 + 12 + 8 + 8 = 30.
Since, A right triangular prism is a three-dimensional solid that has two congruent, parallel triangular faces (also known as bases) and three rectangular faces that connect the bases at right angles. The perpendicular distance between the two bases is called the height of the prism.
To find the surface area of the prism, we need to calculate the area of each of its faces and then add them up.
The prism has two congruent triangular faces and three rectangular faces.
The area of each triangular face is equal to one-half the product of the base and height, which gives:
1/2 x 3 x 12 = 18
The area of each rectangular face is equal to the product of its length and width, which gives:
8 x 3 = 24 (two of these faces)
12 x 8 = 96 (one of these faces)
Therefore, total surface area of prism is given by:
2 x 18 + 2 x 24 + 96 = 60 + 96 = 156
So, the correct expression that represents the surface area of the prism is option,
(D) 2.6 + 12 + 8 + 8 = 30.
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7) Roy buys pizza for his friends. A whole pizza costs P 190. 00 and P 40. 00 for every
additional topping. If he spent P 1070 for pizza with 3 sets of additional toppings, how
many whole pizzas did he buy?
8) There are 4 large gifts. Inside each large gift are 2 medium-sized gifts and inside each
medium-sized gift are 3 small gifts. How many gifts are there altogether?
9) Mang Cardo has cows and chickens in his farm. If he counted 13 heads and 36 feet,
how many cows and chickens does he have?
10) Alexander travelled at 6:00 a. M. And started driving at an average speed of 70 km per
hour. After two hours of driving, he stopped for 30 minutes for a rest. He continued
driving and reach his hometown at 9:30 a. M. How far did he travel?
7) Roy buys 5 whole pizzas.
8) There are 36 gifts altogether.
9) There is 5 cows and 8 chickens.
10) He travel 210 km.
We have the four parts of question:
Now, We have the information:
7) A whole pizza costs P 190.00 and P 40. 00 for every additional topping.
If he spent P 1070 for pizza with 3 sets of additional toppings.
So, The formation of equation is:
=> (1070 - 3 × 40) ÷ 190
=> 5
8) Total gifts are : 4
and Inside each large gift are 2 medium-sized gifts and inside each
medium-sized gift are 3 small gifts.
So, the formation of equation;
=> 4 × 2 = 8
=> 8 × 3 = 24
The total is:
8 + 24 + 4 = 36
9) There are 13 heads and 36 feet .
We know:
Cows have (C) 4 legs
Chickens have (c) 2 legs
So, The equation will be:
C + c=13 ....eq.(1)
Multiply by 4, we get:
4C+2c=36
Then,
4C+4c=52
4C+2c=36
--------------- (-)
2c=16
c = 8 chickens
We put the value of c in eq.(1), we get
C=13 - 8
C = 5 cows
Hence, There is 5 cows and 8 chickens.
10) Alexander travelled at 6:00 a.m.
and, average speed is 70 km per hour.
So, He travelled 140 km in 2 hours.
After two hours of driving, he stopped for 30 minutes for a rest.
He continued driving and reach his hometown at 9:30 a.m.
So, therefore he continues driving at 8:30
then he arrived at his destination at 9:30
So after his break for driving he travels 1 more hour
So in total he travelled 3 hours to arrive at his destination
3 × 70 = 210.
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Pls get this done fast, tysm if u get it. emanuel surveyed a random sample of 50 subscribers to auto wheel magazine about the number of cars that they own. of the subscribers surveyed, 15 own fewer than 2 vehicles. there are 340 subscribers to auto wheel magazine.based on the data, what is the most reasonable estimate for the number of auto wheel magazine subscribers who own fewer than 2 vehicles?
The most reasonable estimate for the number of Auto Wheel Magazine subscribers who own fewer than 2 vehicles is 102.
To estimate the number of Auto Wheel Magazine subscribers who own fewer than 2 vehicles, we can use the proportion of subscribers in the sample who reported owning fewer than 2 vehicles. We can assume that this proportion is representative of the proportion of all subscribers who own fewer than 2 vehicles.
The proportion of subscribers in the sample who own fewer than 2 vehicles is:
15/50 = 0.3
This means that 30% of the sample subscribers own fewer than 2 vehicles. To estimate the number of all subscribers who own fewer than 2 vehicles, we can multiply this proportion by the total number of subscribers:
0.3 x 340 = 102
Hence, the most reasonable estimate = 102.
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Josh needs to save at least $100 to buy new shoes he wants. He makes $13 an hour working at Target and has already saved $35. How many hours does he need to work to have enough money to buy his shoes? Write an equation and solve the problem
Answer:
13×X + 35= 100 (equation)
X=(100-35)/13 = 5 hours
Answer:
13x+35=100
5 hours
Step-by-step explanation:
New shoes= $100
Hours he makes= $13
Hours he worked= unknown so its "x"
Now it's 5
He already has= $35
13 x 5 = 65) + 35 = 100
Sally is 21 years old and has a resting heart rate of 72 beats per minute. what is her estimated maximum heart rate (mhr)
Sally's estimated maximum heart rate (MHR) is 199 beats per minute.
To estimate Sally's maximum heart rate (MHR), we will use the following formula:
MHR = 220 - age
1. First, note Sally's age, which is 21 years old.
2. Then, apply the formula: MHR = 220 - 21.
3. Calculate the result: MHR = 199 beats per minute.
Sally's estimated maximum heart rate (MHR) is 199 beats per minute.
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What is the horizontal distance between the solutions of y= -5x^2 +12x
The horizontal distance between the solutions is -12/5.
What is function?
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Here the given function is y = [tex]-5x^2+12x[/tex].
Now take y=0 then,
=> [tex]-5x^2+12x[/tex] = 0
=> x(-5x+12) = 0
=> x = 0 and -5x = 12
=> [tex]x_1[/tex] = 0 and [tex]x_2[/tex] = -12/5
Then horizontal distance = [tex]x_2-x_1[/tex]
=> [tex]\frac{-12}{5}-0[/tex] = -12/5
Hence the horizontal distance between the solutions is -12/5.
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GEOMETRY URGENT HELP: SINE, COSINE TANGENT
please help me i have no idea what i am doing
in the given triangle, using SOH CAH TOA, the value of x is 16.48
Trigonometry: Calculating the value of xFrom the question, we are to determine the value of x in the given diagram
In the given diagram,
We are given a right triangle.
70° is the included angle
6 is the adjacent
and x is the opposite
Using SOH CAH TOA,
sin (angle) = Opposite / Hypotenuse
cos (angle) = Adjacent / Hypotenuse
tan (angle) = Opposite / Adjacent
Then, we can write that
tan (angle) = Opposite / Adjacent
Then,
tan (70°) = x/6
x = 6 × tan(70°)
x = 16.48
Hence, the value of x is 16.48
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22. Katie is 6 feet tall and casts a shadow that is 2. 5 feet. If the palm tree next to her casts a shadow of 8. 75 feet at the
same time of day, how tall is the palm tree?
Please help me this due today
No links or I will report you
The palm tree is 21 feet tall.
To find the height of the palm tree, we can use the concept of similar triangles, where the ratio of corresponding sides is equal. In this case, the terms we need are Katie's height, her shadow length, the palm tree's shadow length, and the palm tree's height.
Step 1: Set up the proportion using the given information.
(Katie's Height / Katie's Shadow Length) = (Palm Tree Height / Palm Tree Shadow Length)
Step 2: Plug in the given values.
(6 ft / 2.5 ft) = (Palm Tree Height / 8.75 ft)
Step 3: Solve for Palm Tree Height.
(6 ft / 2.5 ft) * 8.75 ft = Palm Tree Height
2.4 * 8.75 ft = Palm Tree Height
Step 4: Calculate the height.
21 ft = Palm Tree Height
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HERE IS A HARD QUESTION , COULD U PLEASE ANSWER B PLEASE? I DID A ! 1ST ANSWER WOULD BE MARKED BRAINLIEST AND GET 5/5 WITH A THANKS! ILL ALSO COMMENT ON YOUR ANSWER ! BUT IF IT ISNT CORRECT , I WONT MARK BRAINLIEST! Thank you for your answers!!!!
Step-by-step explanation:
The coordinates of point B: (0,6)
Coordinates of point C: (3,8)
A kite has 4 sides, of which we have 2 equal pairs, thus the coordinates of point D must be (6,6)
Answer:
(6,6)
Step-by-step explanation:
The question is asking us to complete the half figure, and make it a kite. We can see that the 2 lines AB and BC are half of the shape. In the attachment, I drew a line of symmetry down the middle of the shape.
I also created a point, Y, down the red line, AC, to represent the perpendicular bisector of the 2 diagonals. We can see that line segment BY is the radius of the entire line BD.
This radius is 3 units, so we now know that the diameter horizontally is 6 units. We can draw this on the other side to create point D.
This means that point D is at (6,6).
See attachment for more information, hope this helps!
Part D
The rectangular bases of the treasure box will be cut from wooden planks
4 1/8 feet long and 4 1/8 feet wide. How many planks will Mr. Penny need for his
18 students to each
make one treasure box?
Answer:
Step-by-step explanation:
The base radius and height of a right circular cone are measured as 10 cm and 25 cm, respectively, with a possible error in measurement of as much as 0.1 cm in each dimension. Use differentials to estimate the maximum error in the calculated volume of the cone. (Hint: V = 1/3 πr²h)
The estimated maximum error in the calculated volume of the cone is 20π cubic centimeters.
How to estimate the maximum error in the calculated volume of the cone?Let V = (1/3)πr²h be the volume of the cone, where r and h are the base radius and height of the cone, respectively.
Let dr and dh be the possible errors in the measurements of r and h, respectively.
Then, the actual dimensions of the cone are (r+dr) cm and (h+dh) cm, respectively.
The differential of V is given by:
dV = (∂V/∂r)dr + (∂V/∂h)dh
We have:
∂V/∂r = (2/3)πrh and ∂V/∂h = (1/3)πr²
Substituting the given values, we get:
∂V/∂r = (2/3)π(10 cm)(25 cm) = 500π/3
∂V/∂h = (1/3)π(10 cm)² = 100π/3
Substituting into the differential equation, we get:
dV = (500π/3)dr + (100π/3)dh
Using the given maximum error of 0.1 cm for both r and h, we have:
|dr| ≤ 0.1 cm and |dh| ≤ 0.1 cm
Therefore, the maximum possible error in V is given by:
|dV| = |(500π/3)(0.1 cm) + (100π/3)(0.1 cm)|
|dV| = 50π/3 + 10π/3
|dV| = 60π/3
|dV| = 20π cm³
Therefore, the estimated maximum error in the calculated volume of the cone is 20π cubic centimeters.
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Given the circle below with tangent GH and secant JIH. If GH = 8 and
12, find the length of IH. Round to the nearest tenth if necessary.
JH
=
H
The value of the segment IH for the circle with secant through H which intersect the circle at points I and J is (6 + 2i√7) or (6 - 2i√7)
What are circle theoremsCircle theorems are a set of rules that apply to circles and their constituent parts, such as chords, tangents, secants, and arcs. These rules describe the relationships between the different parts of a circle and can be used to solve problems involving circles.
GH² = IH × JI {secant tangent segments}
JI = 12 - IH, we shall represent IH with x so that;
8² = x(12 - x)
64 = 12x - x²
x² - 12x + 64 = 0 {rearrange to get a quadratic equation}
with the quadratic formula;
x = [12 + √(-112)]/2 or x = = [12 - √(-112)]/2
√(-112) = 4i√7 {where i = √(-1)}
so;
x = (6 + 2i√7) or x = (6 - 2i√7)
Therefore, the value of the segment IH for the circle with secant through H which intersect the circle at points I and J is (6 + 2i√7) or (6 - 2i√7)
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please solve these 4 and show the work for it
The length, slope and midpoints of the segment in the drawing, obtained using the distance and midpoint formula are;
The length of [tex]\overline{AB}[/tex] = √(29)
The midpoint of [tex]\overline{AB}[/tex] is (3, -0.5)
The slope of segment [tex]\overline{CD}[/tex] = 2/5
The midpoint of segment [tex]\overline{CD}[/tex] = (-1.5, 2)
What is the slope of a segment?The slope of a segment on the coordinate plane is the ratio of the rise to the run of the segment.
The coordinates of the required points in the figure are; A(2, 2), B(4, -3), C(1, 3), and D(-4, 1)
The distance formula that can be used in finding the distance between points on the coordinate plane can be presented as follows;
d = √((x₂ - x₁)² + (y₂ - y₁)²)
The distance formula indicates that the length of [tex]\overline{AB}[/tex] can be found as follows;
[tex]\overline{AB}[/tex] = √((4 - 2)² + (-3 - 2)²) = √(29)
The midpoint formula indicates tha midpoint of the segment [tex]\overline {AB}[/tex] can be found as follows
The midpoint of [tex]\overline{AB}[/tex] = ((2 + 4)/2, (2 + -3)/2) = (3, -0.5)
The slope of [tex]\overline{CD}[/tex] = ((3 - 1)/(1 - (-4)) = 2/5
The midpoint of [tex]\overline{CD}[/tex] = ((1 + (-4))/2, (3 + 1)/2 = (-1.5, 2)
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What is a way you can find the vaule of x
Answer:To find the value of x, bring the all the variable to the left side and bring all of the remaining values to the right side. You then simplify the values to find the answer.
Step-by-step explanation:
Answer:
im not sure bud because i don't know what is the full question?
Step-by-step explanation:
Royce has a collection of trading cards. 16 of his cards are baseball cards, 21 are football cards and 13 are basketball cards. He chooses half of this collection and gives them to his friend. Which of the following represent possible outcomes of this selection?
If 16 of his cards are baseball cards, 21 are football cards and 13 are basketball cards, the possible outcome is (10, 10, 5). So, correct option is B.
One possible method to approach this problem is to first find the total number of trading cards Royce has in his collection, which is the sum of baseball cards, football cards, and basketball cards:
Total number of cards = 16 + 21 + 13 = 50
Then, we can find half of the total number of cards, which is the number of cards Royce gives to his friend:
Half of total number of cards = 1/2 x 50 = 25
To find possible outcomes of this selection, we can start by considering how many baseball cards Royce can give to his friend. Since he has 16 baseball cards in total, he can give any number of them from 0 to 16, but he cannot give more than 25 cards in total.
Similarly, he can give any number of football cards from 0 to 21 and any number of basketball cards from 0 to 13.
Therefore, possible outcomes of this selection can be represented by the set of triples (x, y, z) where x is the number of baseball cards, y is the number of football cards, and z is the number of basketball cards, such that x + y + z = 25 and 0 ≤ x ≤ 16, 0 ≤ y ≤ 21, and 0 ≤ z ≤ 13.
The possible outcome is (10, 10, 5), which means Royce gives 10 baseball cards, 10 football cards, and 5 basketball cards to his friend.
So, correct option is B.
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Complete question is:
Royce has a collection of trading cards. 16 of his cards are baseball cards, 21 are football cards and 13 are basketball cards. He chooses half of this collection and gives them to his friend. Which of the following represent possible outcomes of this selection?
A) (10.20,20)
B) (10, 10, 5)
C) (20, 10, 5)
D) (10, 10, 25)
According to the AAA Foundation for Traffic Safety's American Driving Survey, U. S. Drivers spend,
on average, 51 minutes behind the wheel each day. A researcher believes this is an overstatement.
To investigate, a random sample of 75 drivers were selected. The study revealed that the mean
time behind the wheel for the sample of 75 drivers was 46. 4 minutes with a standard deviation of
18. 8 minutes. Is there convincing evidence that the mean time behind the wheel for all U. S. Drivers
is less than 51 minutes? Use a = 0. 1.
The p-value of the test is 0.017 > 0.01, which means that there is not convincing evidence that the mean time behind the whell for all U.S drivers is less than 51 minutes.
How to test the hypotheses?We are told that:
Time spent by U.S. drivers on average each day = 51 minutes behind the wheel
Thus, the null hypothesis is:
H₀: μ = 51
The alternate hypothesis is:
Hₐ: μ < 51
The formula for the test statistic is:
z = (x' - μ)/(σ/√n)
where:
x' is sample mean
n is sample size
μ is population mean
σ is standard deviation
Thus:
z = (46.4 - 51)/(18.8/√75)
z = -2.12
From online p-value from z-score calculator, we have:
The p-value of the test is referred to as the probability of finding a sample mean that is less than 46.4, which is the p-value of z when X = 46.4.
Looking at the z-table, z = -2.12 has a p-value of 0.017.
Decision:
The p-value of the hypotheses test is seen to be0.017 > 0.01.
Thus, this tells us that we don't have convincing evidence that the mean time spent behind the wheel for all U.S drivers is less than 51 minutes.
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Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) g(v) v³ - 48v + 6
The critical numbers are 4, -4.
To find the critical numbers of the function g(v) = v³ - 48v + 6, follow these steps:
1. Find the derivative of the function, g'(v).
2. Set g'(v) equal to 0 and solve for v.
3. List the critical numbers as a comma-separated list.
Step 1: Find the derivative of the function.
g(v) = v³ - 48v + 6
Using the power rule, the derivative is:
g'(v) = 3v² - 48
Step 2: Set g'(v) equal to 0 and solve for v.
3v² - 48 = 0
Divide both sides by 3:
v² - 16 = 0
Factor the equation:
(v - 4)(v + 4) = 0
Solve for v:
v = 4, -4
Step 3: List the critical numbers.
The critical numbers of the function g(v) = v³ - 48v + 6 are v = 4, -4.
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how to convert from kg to m
Answer:
divide by 100
Step-by-step explanation:
hope it helps
Convert 1 Kilograms to Meters (kg to m) with our conversion calculator and conversion tables. To convert 1 kg to m use direct conversion formula below.
Convert 1 Kilograms to Meters (kg to m) with our conversion calculator and conversion tables. To convert 1 kg to m use direct conversion formula below.1 kg = 1 m.
Convert 1 Kilograms to Meters (kg to m) with our conversion calculator and conversion tables. To convert 1 kg to m use direct conversion formula below.1 kg = 1 m.You also can convert 1 Kilograms to other Weight (popular) units.
[tex]Direct \: \: conversion \: \: formula: 1 Kilograms * 1 = 1 Meters[/tex]
(15 POINTS) Zachary is an American traveling with a tour group in Southeast Asia.
During a stop in Malaysia, he purchases a souvenir that is priced at 58 Malaysian riggits using his credit card. If the exchange rate that day is USD to MYR = 3. 04, which is the best estimate of the charge Zachary will later find on his credit card statement? (3 points)
$20
$55
$61
$180
The best estimate of the charge Zachary will later find on his credit card statement is $20
The formula to be used is -
Amount in USD = Amount of MYR/Value of one MYR
As, 3.04 MYR is 1 USD performing money conversion of 58 MYR
So, 58 MYR will be = 58/3.04
Divide the values in Right Hand Side of the equation to find the value of MYR in USD
Value in USD = $19.07
Hence, the credit card statement will reflect usage of $20 (since it is the closes correct option and we have been asked the best estimate).
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The box-and-whisker plot below represents some data set. What percentage of the data values are between 25 and 45?
Thus, approximately 33.33% of the data values are between 25 and 45.
What is box-and-whisker plot?A box-and-whisker plot, also known as a box plot, is a graphical representation of a set of data that shows the distribution of the data along a number line. The plot is composed of a box that represents the middle 50% of the data, along with two "whiskers" that represent the lowest and highest values in the data set. The box is drawn between the first and third quartiles of the data, with a line inside the box representing the median value. The distance between the first and third quartiles is known as the interquartile range (IQR), which can be used to identify outliers in the data. Box-and-whisker plots are useful for comparing the distribution of data between different groups or data sets.
Here,
To find the percentage of the data values that are between 25 and 45 on the given box-and-whisker plot, we need to find the area of the box that is between the lower quartile (Q1) and the median (Q2). From the plot, we can see that the lower quartile (Q1) is at 30, and the median (Q2) is at 40. The interquartile range (IQR), which is the distance between Q1 and Q3, is 20.
Therefore, the box extends from 30 to 40, which is a distance of 10. The total length of the plot is 30 (from 25 to 55), so the percentage of data values between 25 and 45 is:
10/30 * 100% = 33.33%
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Complete question:
The box-and-whisker plot below represents some data set. What percentage of the data values are between 25 and 45?
dy/dx = e√x/y, y(1) = 4
The solution to the differential equation is:
[tex]y = e^{(2\sqrt{y} - 0.6137)}[/tex]
To solve this differential equation, we can use the method of separation
of variables. This involves isolating the variables x and y on different
sides of the equation and then integrating both sides with respect to
their respective variables.
Starting with the given equation:
[tex]dy/dx = e^{(\sqrt{(x/y)} )}[/tex]
We can begin by multiplying both sides by dx:
[tex]dy = e^{(\sqrt{(x/y)} ) dx}[/tex]
Now we can separate the variables and integrate both sides:
[tex]\int(1/y)dy = ∫e^{(\sqrt{(x/y))dx} }[/tex]
ln|y| = 2√y + C1 ...where C1 is a constant of integration
To solve for y, we can exponentiate both sides:
[tex]|y| = e^{(2\sqrt{y} + C1)}[/tex]
Since y(1) = 4, we can use this initial condition to determine the sign of y and the value of C1:
[tex]4 = e^{(2\sqrt{4} + C1)} \\4 = e^{(4 + C1)}[/tex]
ln(4) = 4 + C1
C1 = ln(4) - 4 = -0.6137
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Given that f(x) = (h(x))10 = h(-1) = 3 h'(-1) = 6 Calculate f'(-1).
The final value is f'(-1) = 16,777,2160.
We can use the chain rule and the power rule of differentiation to find f'(-1).
Recall that the chain rule states that if f(x) = g(h(x)), then f'(x) = g'(h(x)) h'(x). Applying this rule to f(x) = (h(x))^10, we get:
f'(x) = 10(h(x))^9 h'(x)
Now, we can substitute x = -1 into the above equation, since we are asked to find f'(-1). Thus, we have:
f'(-1) = 10(h(-1))^9 h'(-1)
We are given that h(-1) = 3 and h'(-1) = 6, so we can substitute these values to get:
f'(-1) = 10(3)^9 (6)
Simplifying, we get:
f'(-1) = 16,777,2160
Therefore, f'(-1) = 16,777,2160
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