(i) T-interval
(ii) F. Because I don't have a large number of professors and I don't know the standard deviation of all FSU professors' heights.
What is standard deviation?
Standard deviation is a measure of the amount of variation or dispersion of a set of data values from the mean value.
When constructing a confidence interval for the mean of a population using a sample, we use either a Z-interval or a T-interval based on the sample size and whether we know the population standard deviation.
If the sample size is large (usually taken to be greater than or equal to 30) and/or we know the population standard deviation, then we can use a Z-interval.
However, if the sample size is small (usually less than 30) and/or we don't know the population standard deviation, we should use a T-interval.
In this case, we don't have a large sample size (just the professors the student has this term), and we don't know the standard deviation of all FSU professors' heights, so we would use a T-interval.
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in college basketball games, a player may be afforded the opportunity to shoot two consecutive foul shots (free throws). a. suppose a player who makes (i.e., scores on) 80% of his foul shots has been awarded two free throws. if the two throws are considered independent, what is the probability that the player makes both shots? exactly one? neither shot?
Answer:
Both shots good: .8(.8) = .64 = 64%
Exactly one shot good: 2(.2)(.8) = .32 = 32%
Neither shot good: .2(.2) = .04 = 4%
A distribution is given as X ~ Exp(0. 75). Find P(x < 4)
The probability of P(x < 4) is 0.6922 or approximately 69.22%.
The exponential distribution is often used to model the time between events that occur randomly and independently at a constant rate over time. The probability density function of the exponential distribution with parameter λ is given by f(x) = λe^(-λx) for x ≥ 0.
In this case, X ~ Exp(0.75) means that the parameter λ is 0.75. To find P(x < 4), we need to calculate the area under the curve of the probability density function to the left of 4. This can be done by integrating the function from 0 to 4 as follows
P(x < 4) = ∫₀⁴ λe^(-λx) dx
= [-e^(-λx)]₀⁴
= -e^(-0.75 * 4) + 1
= 0.6922
Therefore, the probability that X is less than 4 is 0.6922 or approximately 69.22%.
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5|8 - 2x|-3 > 27?
solve the inequality
Answer: x<1 or x>7
Step-by-step explanation:
Hope this helps! :)
If you borrow $1,600 for 6 years at an annual interest rate of 10%, what is the total amount of money you will pay back?
Answer:
$2560 is the total amount to be paid back
Step-by-step explanation:
This is Simple interest described in the question
P = Principal amount
= Amount of money borrowed
= $1600
R = Rate of interest
= 10% per year
= 10% per annum
T = Time period
= 6 years
Make sure the base units of R and T are the same:
S.I. = Simple Interest = [tex]\frac{PRT}{100}[/tex]
= [tex]\frac{(1600 Dollars)(10\frac{Percent}{Year})(6Years)}{(100 Percent)}[/tex]
= $960
This means:
Total amount to be paid back = P + S.I.
= $1600 + $960
= $2560
The Blackburn family has a square field where they keep their cattle. The area of the field is 40,000 ft square, and Mr. Blackburn wants to put a fence diagonally through the field. What should the length of the fence be?
If area of cattle's "square-field" is 40000 ft², and Mr. Blackburn is constructing a fence diagonal in the field, then length of cattle field's fence should be 282.84 ft.
The area of the Blackburn's family cattle square-field is 40000 ft²,
So, We First, equate this area with area formula,
On Equating ,We get,
⇒ (side × side) = 40000,,
⇒ side is 200 ft,
Now, we substitute the "side-length" of field as 200 ft, in the formula for diagonal of a square,
we get,
⇒ Length of cattle-field's diagonal is = (side)√2,
⇒ Length of cattle-field's diagonal is = (200)√2,
⇒ Length of cattle-field's diagonal is ≈ 282.84 ft.
Therefore, the length of cattle field's fence is 282.84 ft.
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CAN SOMEONE HELP ME WITH THESE 50 POINTS
A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.
spinner divided evenly into eight sections with three colored blue, one colored orange, two colored purple, and two colored yellow
Determine P(not yellow) if the spinner is spun once.
75%
37.5%
25%
12.5%
Question 2
Spin a spinner with three equal sections colored red, white, and blue. What is P(yellow)?
33%
0%
100%
66%
Question 3
A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.
Number of hours Total number of students
0 1
1 3
2 2
3 5
4 9
5 7
6 3
Determine the probability that a student studied for 1 hour.
1.0
0.9
0.3
0.1
Question 4
When tossing a two-sided, fair coin with one side colored yellow and the other side colored green, determine P(yellow).
yellow over green
green over yellow
2
one half
Question 5
When given a set of cards laying face down that spell M, A, T, H, I, S, F, U, N, determine the probability of randomly drawing a consonant.
six thirds
six tenths
two thirds
two ninths
Question 6
When rolling a fair, eight-sided number cube, determine P(number greater than 2).
0.25
0.50
0.66
0.75
Question 7
Joseph has a bag filled with 2 red, 4 green, 10 yellow, and 9 purple marbles. Determine P(not purple) when choosing one marble from the bag.
64%
36%
24%
8%
Answer:
1. 75%
2. 0%
3. 0.1
4. one half
5. six tenths
6. 0.75
7. 64%
Step-by-step explanation:Answer 1:
The spinner has a total of 8 sections, out of which there are 2 yellow sections. Therefore, the probability of not getting a yellow section when the spinner is spun once is 6/8 or 3/4, which is equal to 75%.
Answer 2:
The spinner has only three sections and none of them is colored yellow. Therefore, the probability of getting a yellow section when the spinner is spun once is 0%.
Answer 3:
The total number of students surveyed is:
1 + 3 + 2 + 5 + 9 + 7 + 3 = 30
The number of students who studied for 1 hour is 3. Therefore, the probability of a student studying for 1 hour is 3/30, which simplifies to 1/10 or 0.1.
Answer 4:
Since the coin is fair and has one side colored yellow and the other side colored green, the probability of getting a yellow side when the coin is tossed is 1/2 or one half.
Answer 5:
The set of cards has 10 letters, out of which 4 are vowels (A, I, U). Therefore, the number of consonants in the set is 10 - 4 = 6. The probability of drawing a consonant is therefore 6/10, which simplifies to 3/5 or 0.6.
Answer 6:
The number cube has 8 sides, numbered 1 through 8. The probability of getting a number greater than 2 is the same as the probability of getting any number from 3 to 8. There are 6 such numbers out of 8 total numbers, so the probability is 6/8 or 3/4, which is equal to 0.75.
Answer 7:
The total number of marbles in the bag is:
2 + 4 + 10 + 9 = 25
The number of marbles that are not purple is:
2 + 4 + 10 = 16
Therefore, the probability of not getting a purple marble when one marble is chosen from the bag is 16/25, which is equal to 64%.
Given the ______ of the z-distribution, the p-value for a two-tailed test is twice that of the p-value for a one-tailed test.
Answer:
the answer is symmetry.
What points lie on u'?
The points that belong to the image of the equation of a line are (4, - 8) and U' = (1, 4).
How to find the image of a line by rigid transformation
In this question we find the definition of the equation of a line, whose image must be found by a kind of rigid transformation known as dilation:
U'(x, y) = O(x, y) + k · [U(x, y) - O(x, y)]
Where:
O(x, y) - Center of dilation.k - Dilation factor.U(x, y) - Original point.U'(x, y) - Resulting point.If we know that O(x, y) = (5, - 8), k = 1 / 4 and y = - 4 · x - 4, then the image of the point:
U'(x, y) = (5, - 8) + (1 / 4) · [(x, - 4 · x - 4) - (5, - 8)]
U'(x, y) = (5, - 8) + (1 / 4) · (x - 5, - 4 · x + 4)
U'(x, y) = (5, - 8) + (x / 4 - 5 / 4, - x + 1)
U'(x, y) = (x / 4 + 15 / 4, - x - 7)
Now we evaluate the expression at each x-value:
x = 1
U' = (1 / 4 + 15 / 4, - 1 - 7)
U' = (4, - 8) (YES)
x = - 11
U' = (- 11 / 4 + 15 / 4, - (- 11) - 7)
U' = (1, 4) (YES)
x = - 23
U' = (- 23 / 4 + 15 / 4, - (- 23) - 7)
U' = (- 2, 16) (NO)
x = 17
U' = (17 / 4 + 15 / 4, - 17 - 7)
U' = (8, - 24) (NO)
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This is more trig i need
Awnsers
The length of the sides are
AC = 5.4
BC = 10.5
How to determine the valueTo determine the value, we need to know the different trigonometric identities.
They include;
secantcosecantsinetangentcotangentcosineThese identities also have their ratios;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
From the information given, we have;
tan 31 = AC/9
cross multiply the values
AC = 5. 4
sin 59 = 9/BC
cross multiply the values
BC = 10. 5
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5√17− 4
is rationalized by multiplying the numerator and denominator by what?
To rationalize the expression,5√17− 4, we multiply the numerator and denominator by √17
What are surds?Surds are simply defined as those values found in square root and which cannot be further simplified into whole numbers or integers alike.
Examples of surds are;
√3, √5, √7
In rationalizing surds, we want to achieve that no surd forms are found as the denominator of a fraction.
Thus, we have that;
Example;
3/√3
To rationalize, we have;
3√3/√3 × √3
Multiply the values, we get;
3√3/3
Divide the values, we get;
√3
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a group of observations measured at successive time intervals is known as a(n) . a. trend component b. forecast c. additive time series model d. time series
The answer is d. time series, a time series is a collection of observations that are measured at successive time intervals.
These observations are usually recorded at equal time intervals and are used to study patterns and trends over time. Time series data is used in a wide range of applications such as economics, finance, weather forecasting, and sales forecasting.
Time series analysis is the statistical method used to analyze time series data. It involves identifying patterns and trends over time, as well as forecasting future values based on past trends.
Time series models can be classified as either additive or multiplicative, depending on whether the components of the model are added or multiplied together. Trend, seasonal, and cyclical components are the main components of a time series model, and they help to explain the underlying patterns and trends in the data.
The goal of time series analysis is to use these components to develop a model that accurately describes the underlying patterns and trends in the data and to use that model to make forecasts of future values.
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(L3) The orthocenter will lie in the exterior of a(n) _____ triangle.
(L3) The orthocenter will lie in the exterior of a(n) obtuse triangle. Contrary to an acute triangle, the orthocenter of an obtuse triangle will lie in the exterior of the triangle.
The orthocenter is the point of intersection of the altitudes of the triangle, which are perpendicular lines drawn from each vertex to the opposite side. In an obtuse triangle, one of the angles measures more than 90 degrees, so when an altitude is drawn from this vertex to the opposite side, it will lie outside of the triangle. Therefore, the three altitudes will intersect outside of the triangle, forming the orthocenter in the exterior. This is in contrast to an acute triangle, where all three altitudes intersect inside the triangle.
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Subtract
�
4
+
4
�
2
�
2
−
2
�
4
a
4
+4a
2
b
2
−2b
4
a, start superscript, 4, end superscript, plus, 4, a, squared, b, squared, minus, 2, b, start superscript, 4, end superscript from
−
3
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4
+
5
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2
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2
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−3a
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minus, 3, a, start superscript, 4, end superscript, plus, 5, a, squared, b, squared, plus, 2, b, start superscript, 4, end superscript.
Your answer should be a polynomial in standard form.
The expressions are subtracted to give -a⁴ + a²b² + 4b⁴
What are algebraic expressions?It is important to note that algebraic expressions are described as expressions that are made up of terms, variables, constants, coefficients and factors.
These expressions are also identified with arithmetic operations. These operations are;
SubtractionBracketParenthesesDivisionMultiplicationAdditionFrom the information given, we have that;
4a⁴ + 4a²b² - 2b⁴
3a⁴ + 5a²b² + 2b⁴
Now, subtract the expressions;
3a⁴ + 5a²b² + 2b⁴ - (4a⁴ + 4a²b² - 2b⁴)
expand the bracket
3a⁴ + 5a²b² + 2b⁴ - 4a⁴ - 4a²b² + 2b⁴
add the values
-a⁴ + a²b² + 4b⁴
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A survey of 50 college students was conducted to determine how much weekly income they earned from employment. Given the data set in Applications folder for this experience complete the following. Refer to the model/methodology for the desired format.a. Find the 5 number summary of the data set.Min=Q1=Median=Q3=Max=
The 5 number summary of the data set. Min=Q1=Median=Q3=Max is calculated as below.
To help you find the 5 number summary of the data set for the survey of 50 college students' weekly income. I'll provide a step-by-step explanation on how to calculate the 5 number summary.
1. First, arrange the data set in ascending order (from smallest to largest).
2. To find the minimum value (Min), simply identify the smallest number in the data set.
3. To find the maximum value (Max), identify the largest number in the data set.
4. To find the median (the middle value), follow these steps:
a. If the data set has an odd number of values, the median is the middle value.
b. If the data set has an even number of values, find the average of the two middle values.
5. To find the first quartile (Q1), you'll calculate the median of the lower half of the data set (excluding the overall median if the data set has an odd number of values).
6. To find the third quartile (Q3), calculate the median of the upper half of the data set (again, excluding the overall median if the data set has an odd number of values).
Once you've completed these steps, you'll have the 5 number summary for the data set:
Min, Q1, Median, Q3, Max.
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What is 0. 81818181818 as a fraction in its simplest form?
‹
0. 81818181818 as a fraction in its simplest form is 9/11
How to find the fraction in simplest formConverting the decimal to fraction we have
x = 81818181818/100000000000
Using a calculator we san reduce the fraction to 9/11
Therefore, 0.81818181818... as a fraction in its simplest form is 9/11.
This is a recurrence fraction and a recurring fraction, also called a recurring decimal, is a decimal number with repeating digits after the decimal point. The repeatability of the lines is indicated by a horizontal line or a line above the repetition line.
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(L1) What statement in the Converse of the Angle Bisector Theorem tells you that the point must be in the same plane as the angle?
The Converse of the Angle Bisector Theorem states that if a point is in the same plane as an angle and divides the angle into two congruent angles, then it lies on the angle's bisector.
The fact that the converse states that the point must be in the same plane as the angle implies that if the point is not in the same plane as the angle, then it cannot divide the angle into two congruent angles, and thus cannot lie on the angle's bisector.
The Angle Bisector Theorem states that if a ray bisects an angle of a triangle, then it divides the opposite side into segments that are proportional to the other two sides of the triangle. The converse of this theorem states that if a point on the interior of a triangle divides one side of the triangle into two segments that are proportional to the other two sides, then the point lies on the bisector of the angle opposite the divided side.
To understand why this implies that the point must be in the same plane as the angle, we need to consider the definition of a plane. A plane is a flat, two-dimensional surface that extends infinitely in all directions.
It is determined by any three non-collinear points in space. In the context of a triangle, the three vertices of the triangle are non-collinear points that determine a plane.
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SIMPLIFY THIS EXPRESSION!
Answer:
The answer is 3x-5y
Step-by-step explanation:
13x+2y-10x-7y
C.L.T.
13x-10x-7y+2y
3x-5y
Answer:
3x - 5y
Step-by-step explanation:
you 1st have to collect like terms which has the same variable
13x + 2y - 10x - 7y
(13x - 10x) + (2y - 7y)
3x - 5y .... is the simplified form of the equation.
Kellys new snowboard is 115% longer than her old snowboard. If the new snowboard is 130 cm, how many cm long is her old snowboard? (Round to the nearest tenth)
Answer:
The answer to your problem is, 149.5
Step-by-step explanation:
How to find our number from the problem, 115% of 130.
Calculate:
[tex]\frac{115}{100}[/tex] of 130 = [tex]\frac{115}{300}[/tex] × 130
= 149.5
The new snowboard is 149.5 centimeters now.
Thus the answer to your problem is, 149.5
A researcher was interested in the relationship between a swimmer’s hand length and corresponding time to complete the 100-meter freestyle. The researcher selected a random sample of twenty swimmers from all participants in a swim competition. Assuming all conditions for inference are met, which of the following significance tests should be used to investigate whether there is convincing evidence, at a 5 percent level of significance, that a longer hand length is associated with a decrease in the time to complete the 100-meter freestyle?.
To investigate whether there is convincing evidence, at a 5 percent level of significance,
that a longer hand length is associated with a decrease in the time to complete the 100-meter freestyle, the researcher should use a two-sample t-test.
The independent variable is hand length, and the dependent variable is time to complete the 100-meter freestyle.
The t-test compares the mean time to complete the 100-meter freestyle for swimmers with longer hand lengths to the mean time for swimmers with shorter hand lengths.
The t-test is appropriate because the sample size is small, and the researcher is comparing two groups.
By conducting a two-sample t-test, the researcher can determine whether the observed difference in mean times is statistically significant or due to chance.
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use spherical coordinates.evaluate x2 dv,e where e is bounded by the xz-plane and the hemispheres y
∫∫∫ x² dv over the region e is (3/40) a⁵ π².
What is volume?
A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.
To use spherical coordinates, we need to express the volume element dv in terms of ρ, θ, and φ, where ρ is the radial distance from the origin, θ is the angle in the xy-plane measured from the positive x-axis, and φ is the angle measured from the positive z-axis.
We have x² = ρ² sin²(φ) cos²(θ). The volume element dv can be expressed as dv = ρ² sin(φ) dρ dφ dθ.
The region e is bounded by the xz-plane and the hemispheres y = ±√(a² - x²), where a > 0.
Since we're only interested in the part of e that lies in the first octant, we can restrict θ to the range [0, π/2] and φ to the range [0, π/2].
Note that since y is always positive in the first octant, we don't need to consider the negative hemisphere.
So, the integral we need to evaluate is:
∫∫∫ x² dv
= ∫[0,π/2]∫[0,π/2]∫[0,a] (ρ² sin³(φ) cos²(θ)) ρ² sin(φ) dρ dφ dθ
= ∫[0,π/2]∫[0,π/2]∫[0,a] ρ⁴ sin⁴(φ) cos²(θ) dρ dφ dθ
= ∫[0,π/2]∫[0,π/2] [(1/5)ρ⁵ sin⁴(φ) cos²(θ)]|[0,a] dφ dθ
= (1/5) a⁵ ∫[0,π/2] cos²(θ) dθ ∫[0,π/2] sin₄(φ) dφ
= (1/5) a⁵ [(1/2)π] [(3/4)(π/2)] = (3/40) a⁵ π².
Therefore, ∫∫∫ x² dv over the region e is (3/40) a⁵ π².
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the side length of a rectangle is 5 more than three times the width. the side length has a measure of 65cm. what is the length of the width
Answer:
the width is 20cm
Step-by-step explanation:
According to the question the length is 5 more than three times the width which is 3 times the width plus 5 so you have to minus five from the length and divide your answer by three
Answer:
The width is 20 cm.
Step-by-step explanation:
Let w represent the measure of the width.
5 + 3w = 65
-5 -5
___________
3w = 60
÷ 3 ÷3
_______
w = 20 cm
On a game show, a contestant randomly chooses a chip from a bag that contains numbers and strikes. The theoretical probability of choosing a strike is 15. The bag contains 8 strikes. How many chips are in the bag?
There are approximately 53 chips in the bag.
How to determine many chips are in the bagThe theoretical probability of choosing a strike is given as 15, which can be written as 15/100 or 0.15 as a decimal.
Let's represent the number of chips in the bag with the variable "x". Since there are 8 strikes in the bag, the probability of choosing a strike can be expressed as 8/x.
we can write the equation: 8/x = 0.15
To solve for x, we can cross-multiply and simplify:
8 = 0.15x
x = 8/0.15
x = 53.33
Therefore, there are approximately 53 chips in the bag.
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7.03 Inscribed Quadrilaterals
pls help
The value of angles in inscribed quadrilateral are μ(∠zyx) is 92⁰ and μ(∠yxw) is 65⁰.
An inscribed quadrilateral is a quadrilateral that can be inscribed in a circle, meaning that its vertices all lie on the circumference of a circle. In other words, the four vertices of an inscribed quadrilateral are concyclic.
The opposite angles of an inscribed quadrilateral are supplementary, which means that they add up to 180 degrees. This property is known as the "interior angle sum" of a quadrilateral.
μ(∠zyx) + μ(∠xwz) = 180⁰ (opposite angle of cyclic quadrilateral are supplementary)
μ(∠xwz) = 88⁰
μ(∠zyx) = 180⁰ - 88⁰ = 92⁰
μ(∠yzw) is an inscribed angle that intercepts the arc 112⁰ and 118⁰. Therefore,
μ(∠yzw)
= (112⁰ + 118⁰)/2
= 230⁰/2
= 115⁰
μ(∠yxw) + μ(∠yzw) = 180⁰ (opposite angle of cyclic quadrilateral are supplementary)
μ(∠yxw) = 180⁰ - 115⁰ = 65⁰
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an article about search engine optimization states that, on average, the number of keywords that should be targeted when creating a website is 5 keywords. a website developer, who is looking to increase traffic on their websites, believes the average number of keywords targeted for a website is different than the number stated by the article. after completing a study, the website developer found that the average number of keywords targeted in a website is is 5.6 keywords, on average. as the website developer sets up a hypothesis test to determine if their belief is correct, what is their claim? select the correct answer below: the average number of keywords targeted in a website is different than 5 keywords. the average number of keywords targeted in a website is different than 5.6 keywords. websites should contain more keywords. the average number of keywords targeted in a website is 5 keywords.
The right response is "the average number of targeted keywords in a website is different than 5 keywords." The website developer asserts that the value of 5 in the article does not accurately reflect the genuine population mean of the number of keywords targeted in a website.
This claim may be one-tailed (if the website developer thinks the true mean is larger or less than 5) or two-tailed (if the website developer thinks the true mean is merely different from 5) in nature. The website developer feels the true mean is different from the value given in the article, without stating whether it is larger or less than 5. As a result, the claim is two-tailed in this instance.
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Find the radius of convergence, r, of the following series. [infinity] n!(6x − 1)n n = 1 r = find the interval, i, of convergence of the series. I = 1 i = − 1 6 , 0 ∪ 1 6i = − 1 6 , 1 6 i = 0 i = 1 6
The radius of convergence is given as [tex]i = {x | 0 \leq x < \frac{1}{3} }[/tex]
How to find the radius of convergenceTo find the radius of convergence, we can use the ratio test:
[tex]\frac{lim |(n+1)!(6x-1)^n^+^1|}{|n!(6x-1)^n|} \\\\[/tex]
[tex]= lim |6x-1| \\=|6x-1|[/tex]
The series will converge if this limit is less than 1. So we solve the inequality:
[tex]|6x-1| < 1[/tex]
which gives us:
-1 < 6x - 1 < 1
0 < 6x < 2
[tex]0 < x < \frac{1}{3}[/tex]
Therefore, the radius of convergence is [tex]\frac{1}{6}[/tex]
To find the interval of convergence, we check the endpoints of the interval [0, [tex]\frac{1}{3}[/tex]]:
When x = 0, the series becomes:
∑(n=1 to infinity) n!(6x-1)^n = ∑(n=1 to infinity) n!(-1)^n
which diverges by the test for divergence.
When x = 1/3, the series converges by the ratio test. Therefore, the interval of convergence is:
i = [0, 1/3)
or in set-builder notation:
[tex]i = {x | 0 \leq x < 1/3}[/tex]
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Sphere A is similar to Sphere B. The scale factor of the lengths of the radii of Sphere A to Sphere B is 4. Sphere A has the radius of 6 units and a volume of 288pi cubic units. Find the volume of Sphere B
The volume of the sphere B is 14.13 cubic units.
Given that the two similar spheres, the scale factor of the lengths of the radii of Sphere A to Sphere B is 4.
So, we need to find the volume of the sphere B,
So,
Radius A / Radius B = 4/1
6 / Radius B = 4
Radius B = 1.5
Now we know that the volume of a sphere = 4/3 × πr³
= 4/3 × 3.14 × 1.5³
= 42.39/3
= 14.13
Alternatively, you can calculate by =
We know that the ratio of the volumes of two similar solids is equal to the cube of their scale factor, so here, the scale factor is 4/1.
Therefore,
Volume A / Volume B = (4/1)³
288π / Volume B = 64
Volume B = 4.5π
Volume B = 14.13
Hence, the volume of the sphere B is 14.13 cubic units.
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(Q1) Given: ΔABC; ray DB→ is the perpendicular bisector of AC¯;AB=12 inWhat is the length of CB¯ ?By what Theorem?
The length of CB is 4√(3), and we used the Pythagorean theorem and the perpendicular bisector theorem to solve for it.
By the perpendicular bisector theorem, if a point lies on the perpendicular bisector of a line segment, then it is equidistant from the endpoints of the segment. Therefore, in triangle ABC, since ray DB is the perpendicular bisector of AC, it follows that BD = DC.
Let x be the length of CB. Then, by the Pythagorean theorem in triangle ABC, we have:
[tex]AB^2 + BC^2 = AC^2[/tex]
Substituting AB = 12 and BD = DC = x/2, we get:
[tex]12^2 + x^2 = (2x)^2[/tex]
[tex]144 + x^2 = 4x^2[/tex]
[tex]3x^2 = 144[/tex]
[tex]x^2[/tex]= 48
x = √(48) = 4√(3)
Therefore, the length of CB is 4√(3), and we used the Pythagorean theorem and the perpendicular bisector theorem to solve for it.
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A point S is 54 km due east of point T. The bearings of an electricity pole from S and Tare N28°W and N70°E, respectively. Calculate the distance of the electricity pole from T.
The distance of the electricity pole from T is 53 km
Given that;
The ST is 54 kilometer long
(180 - 28) + (180 - 70) = 262 degree is the angle PST,
which is the product of the angles at S and T.
S has a 62 degree angle.
The law of sines can be written as:
sin(62)/SP = sin(262/ST)
To find SP, we can rearrange this equation as follows:
SP = sin(62)/sin(262)x(ST)
When we enter the values we are aware of, we obtain:
SP = sin(62)/sin(262)*54 km
We can evaluate this expression to determine that:
SP ≈ 53.5 km Consequently, 53.5 kilometer or so separate T from the electricity pole.
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Sky View School Riverside School0 5, 6, 99, 7, 2, 0 1 0, 2, 4, 5, 6, 78, 7, 6, 5, 5, 5, 4, 3, 1, 0 2 0, 0, 2, 3, 50 34 2Key: 2 | 1 | 0 means 12 for Sky View and 10 for RiversidePart A: Calculate the measures of center. Show all work. (5 points)Part B: Calculate the measures of variability. Show all work. (5 points)Part C: If you are interested in a larger class size, which school is a better choice for you? Explain your reasoning.
Part A: Sky View - median = 5.5, Riverside - median = 5.5
Part B: Sky View - range = 99, Riverside - range = 78
Part C: Sky View has a larger class size on average (12 vs 10), so it may be a better choice if a larger class size is desired.
Part A: Measures of Center
For Sky View School:
Mean: sum of values / number of values [tex]= (5 + 6 + 99 + 7 + 2 + 0) / 6 = 119 / 6 = 19.83[/tex]
Median: arrange the values in ascending order: 0, 2, 5, 6, 7, 99. The median is 6.5.
Mode: there is no mode as all values occur only once.
For Riverside School:
Mean: sum of values / number of values [tex]= (1 + 0 + 2 + 4 + 5 + 6 + 78 + 7 + 6 + 5 + 5 + 5 + 4 + 3 + 1 + 0) / 16 = 133 / 16 = 8.31[/tex]Median: The median is equal to the average of each of the middle values [tex](5 + 5 / 2 = 5)[/tex], which is 5.
Mode: the mode is 5 as it occurs most frequently.
Part B: Measures of Variability
For Sky View School:
Range: maximum value - minimum value = 99 - 0 = 99
Variance: [tex]((5-19.83)^2 + (6-19.83)^2 + (99-19.83)^2 + (7-19.83)^2 + (2-19.83)^2 + (0-19.83)^2) / (6-1) = 2134.4[/tex].
Standard deviation: approximately 46.2.
For Riverside School:
Range: maximum value - minimum value = 78 - 0 = 78
Variance: [tex]((1-8.31)^2 + (0-8.31)^2 + (2-8.31)^2 + (4-8.31)^2 + (5-8.31)^2 + (6-8.31)^2 + (78-8.31)^2 + (7-8.31)^2 + (6-8.31)^2 + (5-8.31)^2 + (5-8.31)^2 + (5-8.31)^2 + (4-8.31)^2 + (3-8.31)^2 + (1-8.31)^2 + (0-8.31)^2) / (16-1) = 422.3.[/tex]
Standard deviation: approximately 20.55.
Part C: Answer with Explanation
If you are interested in a larger class size, Riverside School may be a better choice. This is because the mean and median class sizes at Riverside School are both smaller than those at Sky View School, indicating that the typical class size is smaller at Riverside. Additionally, the range and standard deviation of class sizes at Riverside School are smaller than those
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Joan wants to jog 13 miles on a circular track
1
4
mile in diameter.
How many miles is one circle of the track? (Round your answer to two decimal places.)
mi
How many times must she circle the track? Round to the nearest lap.
times
Joan should run 13 times around the park to complete her goal.
Given that, Joan wants to jog in a circular track which 1/4 mile in diameter.
We need to find the circumference of the track and the number of rounds she needs run to complete her goal.
So,
Circumference = π × diameter
= 3.14 × 1/4 = 0.785 miles
Let she runs x rounds to complete her goal,
So,
0.785x = 10
x = 12.73
x ≈ 13
Hence, Joan should run 13 times around the park to complete her goal.
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