The rotated vector is (-2,0). To see why, imagine the original vector (0,2) plotted on the coordinate plane. To rotate it 270° clockwise about the origin, we can first rotate it 90° clockwise to get (2,0), then rotate that 180° clockwise to get (-2,0).
To understand this geometrically, think of the vector (0,2) as pointing straight up on the y-axis. Rotating it 90° clockwise means it now points to the right on the x-axis. Then, rotating it another 180° clockwise means it points straight down on the negative y-axis, which corresponds to the vector (-2,0).
In general, to rotate a vector (x,y) by an angle θ about the origin, we can use the following formulas: x' = x cos θ - y sin θ. y' = x sin θ + y cos θ In this case, θ = 270°, so cos θ = 0 and sin θ = -1.
Plugging in x=0, y=2, we get: x' = 0 - 2(-1) = 2 y' = 0(270) + 2(0) = 0. So the rotated vector is (2,0), which corresponds to (-2,0) because we rotated it clockwise instead of counterclockwise.
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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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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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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:
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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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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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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"The times for the mile run of a large group of male college students are approximately Normal with mean 7. 06 minutes and standard deviation 0. 75 minutes. Use the 68-95-99. 7 rule to answer the following questions. (Start by making a sketch of the density curve you can use to mark areas on. ) (a) What range of times covers the middle 95% of this distribution
According to the 68-95-99.7 rule, approximately 68% of the distribution falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
In this case, the mean is 7.06 minutes and the standard deviation is 0.75 minutes. Therefore, the range of times that covers the middle 95% of the distribution would be from the mean minus two standard deviations (7.06 - 2 x 0.75 = 5.56 minutes) to the mean plus two standard deviations (7.06 + 2 x 0.75 = 8.56 minutes).
In other words, 95% of the male college students' mile run times are expected to fall between 5.56 and 8.56 minutes. This means that most of the students' mile run times will be within this range, and only a small percentage will be outside of it.
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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]
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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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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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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a time capsule has been buried 98m away from the cave at a bearing of 312 degrees how far west of the cave is the time capsule buried? give your answer in 1 decimal places
If a time capsule has been buried 98m away from the cave at a bearing of 312. the time capsule is buried about 82.2 meters west of the cave.
What is the time capsule?To find how far west the time capsule is buried, we need to find the horizontal component of the displacement vector that points from the cave to the location of the time capsule. We can use trigonometry to do this:
cos(312°) = adjacent/hypotenuse
The hypotenuse is the distance between the cave and the time capsule, which is 98m. The adjacent side represents the horizontal distance between the two points, which is what we want to find. Rearranging the equation, we get:
adjacent = cos(312°) x hypotenuse
adjacent = cos(312°) x 98
adjacent ≈ 82.2
Therefore, the time capsule is buried about 82.2 meters west of the cave.
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Find the average x-coordinate of the points in the prism D={(x,y,z):0 ≤ x ≤ 6,0 ≤ y ≤ 18-3x, 0 ≤ z ≤ 4}. The average x-coordinate of the points in the prism is (Simplify your answer.)
The average x-coordinate of the points in the prism is 3.
What is a prism?A prism is a polyhedron that has two parallel and congruent polygonal bases that are linked by parallelogram faces that are lateral. The height of the prism is the perpendicular distance between the bases.
The formula for calculating the average x-coordinate of the points in the prism D = {(x,y,z):0 ≤ x ≤ 6,0 ≤ y ≤ 18-3x, 0 ≤ z ≤ 4} is$$\frac{\text{sum of all x-coordinates}}{\text{number of vertices}}$$
The vertices of a prism are the points where two adjacent edges meet. There are eight vertices in a rectangular prism, and the x-coordinate of each vertex is either 0 or 6. The x-coordinates of the vertices are $$0,0,0,0,6,6,6,6.
$$The sum of all the x-coordinates is 24. Thus, the average x-coordinate of the points in the prism is$$\frac{24}{8}=\boxed{3}.
$$Hence, the average x-coordinate of the points in the prism is 3.
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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?
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:
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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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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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)
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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The height of Mount Rushmore is 5900 feet. What is the height of Mount Rushmore in
centimeters? (1 in = 2. 54 cm)
Answer:
the answer is 14,986 centimetres
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!
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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X-1 if x < 2 Let f(x)=1 if 2sxs6 X+4 if x > 6 a. Find lim f(x). X-+2 b. Find lim f(x). X-6 Select the correct choice and, if necessary, fill in the answer box to complete your choice. O A. lim = X-2 O B. The limit is not - oo or co and does not exist. Select the correct choice and, if necessary, fill in the answer box to complete your choice. O A. lim = X-6 OB. The limit is not - oor oo and does not exist.
a. The limit does not exist.
b. The limit is equal to 4.
a. To find the limit as x approaches 2, we need to evaluate the left-hand and right-hand limits separately and check if they are equal.
Left-hand limit: lim f(x) as x approaches 2 from the left
We have f(x) = x - 1 for x < 2. So, as x approaches 2 from the left, f(x) approaches 1.
Right-hand limit: lim f(x) as x approaches 2 from the right
We have f(x) = 1 for 2 ≤ x ≤ 6 and f(x) = x + 4 for x > 6. So, as x approaches 2 from the right, f(x) approaches 6.
Since the left-hand and right-hand limits are not equal, the limit as x approaches 2 does not exist.
b. To find the limit as x approaches 6, we need to evaluate the left-hand and right-hand limits separately and check if they are equal.
Left-hand limit: lim f(x) as x approaches 6 from the left
We have f(x) = 1 for 2 ≤ x ≤ 6 and f(x) = x + 4 for x > 6. So, as x approaches 6 from the left, f(x) approaches 1.
Right-hand limit: lim f(x) as x approaches 6 from the right
We have f(x) = x + 4 for x > 6. So, as x approaches 6 from the right, f(x) approaches 10.
Since the left-hand and right-hand limits are not equal, the limit as x approaches 6 does not exist.
Therefore, the correct choices are:
a. The limit is not -oo or co and does not exist.
b. lim = 4.
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Complete the proof that △QST≅△QRT.
The congruent triangles is solved and the triangles are congruent by AAS postulate
Given data ,
Let the two triangles be represented as ΔRQT and ΔTQS
And , the side TQ is the common side of both the triangles
Now , the measure of ∠TQR ≅ measure of ∠TQS ( given )
And , the measure of ∠TRQ ≅ measure of ∠TSQ ( given )
So , Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
Hence , the triangles are congruent by ASA postulate
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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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(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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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?
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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The ratio of runners to walkers at the 10k fund-raiser was 5 to 7. if there
were 350 runners, how many walkers were there?
There were 490 walkers at the 10k fund-raiser.
The ratio of runners to walkers is 5:7, that means that the every five runners, there are 7 walkers so therefore we will use ratio formula.
If there have been 350 runners, we can use this ratio to discover what number of walkers there were:
5/7 = 350/x
Where x is the number of walkers.
To solve for x, we will cross-multiply:
5x = 7 * 350
5x = 2450
x = 490
Consequently, there were 490 walkers at the 10k fund-raiser.
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