Using the normal distribution and the central limit theorem, the probability that the mean of a month's reviews will take Yoonie from 3.5 to 4.25 hrs is:
[tex]P(3.5 \leq \bar{X} \leq 4.25) = 0.7482[/tex]
Normal Probability DistributionThe z-score of a measure X of a variable that has mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The mean and the standard deviation of each review are given as follows:
[tex]\mu = 4, \sigma = 1.2[/tex]
For the sampling distribution of sample means of size 16, the standard error is given as follows:
[tex]s = \frac{1.2}{\sqrt{16}} = 0.3[/tex]
The probability that the mean of a month's reviews will take Yoonie from 3.5 to 4.25 hrs is the p-value of Z when X = 4.25 subtracted by the p-value of Z when X = 3.5, hence:
X = 4.25:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (4.25 - 4)/0.3
Z = 0.83.
Z = 0.83 has a p-value of 0.7967.
X = 3.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (3.5 - 4)/0.3
Z = -1.67.
Z = -1.67 has a p-value of 0.0475.
Hence the probability is:
0.7967 - 0.0485 = 0.7482.
The statement is:
[tex]P(3.5 \leq \bar{X} \leq 4.25)[/tex]
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1: 9 11. The cost for a group of people to go to the movies is given by the expression 9a + 5b, where a is the number of adults and b is the number of children. What are the variables of this expression? of of A. 9 and 5 B. a and b C. 9a and 5b D. + and x
the variables are
a and bwhere
a -----> is the number of adults
b-------> is the number of children.
answer is option B
3. Trigonometric Function a. Describe two real-world situations that could be modelled by a trigonometric function. Cannot be Ferris Wheel ride, tides, hours of daylight. Cite any Internet source you may have used for reference. b. Clearly define all variables in the relationship. c. Clearly justify why this model fits the real applications with specific reference to key features of the function. d. Your justification should also include reference to the graphical and algebraic models. e. Accurately describe what changes to the base function y = sin x would be necessary to fit both real applications.
For this problem, we need to describe a real-life situation where trigonometric functions can be used to model the problem.
Let's assume that a certain vehicle's position is controlled by the speeds of the wheels on each side of the car. Whenever the speeds on the left wheels and right wheels are equal, then the car moves forward, if the speed on the left side is greater than the one on the right side the car goes right, and if the speed on the right side is greater, then the vehicle goes to the left side. This type of car is called a differential drive car, and it's very common on remote-controlled (RC) vehicles.
If we want to model the speed of the car in a two dimensional grid, such as below:
We need to assume that the vehicle will have two components of velocity, one that is parallel to the x-axis and one that is parallel to the y-axis. These will form the linear velocity for the vehicle. We also need an angular velocity, which is the rate at which the angle of the vehicle changes.
If we assume that the wheels of the vehicles are at a distance of "L" apart from each other, then we can model the angular velocity of the vehicle as:
[tex]\omega=\frac{v_r-v_l}{L}[/tex]Where "vr" is the speed on the right wheel, and "vl" is the speed on the left wheel. The movement will happen with the center of the car as the center of the movement, with this we can assume that the velocity of the vehicle on the two axes should be:
[tex]\begin{gathered} v_x=\frac{1}{2}(v_r+v_l)\cdot cos(\theta)\\ \\ v_y=\frac{1}{2}(v_r+v_l)\cdot sin(\theta) \end{gathered}[/tex]Therefore we can describe the vehicle speed with the following equations:
[tex]\begin{gathered} \omega=\frac{v_{r}-v_{l}}{L}\\ \\ v_x=\frac{1}{2}(v_r+v_l)cos(\theta)\\ \\ v_y=\frac{1}{2}(v_r+v_l)s\imaginaryI n(\theta) \end{gathered}[/tex]The input variables are "vr" and "vl" which are the speeds of each wheel and the angle of the vehicle "theta", the output is the speed at the x coordinate and the speed at the y coordinate, and the angular speed.
This works very well because if the vehicle is moving parallel to the x-axis, the angle will be 0, the cosine of 0 is 1, therefore the speed on the y axis will be 0 and the speed on the x-axis will be given by 0.5(vr+vl). The opposite happens when the vehicle is moving parallel to the y-axis.
Philip departed from town A with coordinates (1,6) towards town B with coordinates (7 ,6). At the same time Bruce headed from town B to town A. What are the coordinates of Point C where they will meet if the ration of Phillip's to Bruce's rates is 7:5 respectively ?
if there was no ratio they were in the middle (4,6)
but in this case we must multiply by the ratio
so
[tex]4\times\frac{7}{5}=\frac{28}{5}\approx5.6[/tex]so the C point is
[tex](5.6,6)[/tex]
There are 2 liters of soda left after a class party. Laura, Gavin, Anita, Emmett, and Rebecca are on the clean-up crew, and decide to split the soda equally.
How much soda does each student get?
Write your answer as a proper fraction or mixed number.
0.4 liters or 2/5
Step-by-step explanation:
Dividing the soda equally, Each student would get 0.4 liters or 2/5
Consider the circle x ^ 2 + y ^ 2 = 100 and the line x + 3y = 10 and their points of intersection (10, 0) and B = (- 8, 6) . Find coordinates for a point C on the circle that makes chords AB and AC have equal length . Be sure to justify your answer.
The equation of circle is given by,
[tex]x^2+y^2=100\text{ ---(1)}[/tex]The equation of line is given by,
[tex]x+3y=10\text{ ---(2)}[/tex]The points of intersection of the circle and line is,
A=(Xa, Ya)=(10, 0)
B=(Xb, Yb)=(-8, 6)
The length of chord AB can be calculated using distance formula as,
[tex]\begin{gathered} AB=\sqrt[]{(X_b-X_a)^2+(Y_b-Y_a)^2} \\ =\sqrt[]{(-8-10)^2+(6-0)^2} \\ =\sqrt[]{(-18)^2+6^2} \\ =\sqrt[]{324+36} \\ =\sqrt[]{360} \\ =6\sqrt[]{10} \end{gathered}[/tex]Let (Xc, Yc) be the coordinates of point C on the circle. Hence, using equation (1), we can write
[tex]X^2_c+Y^2_c=100\text{ ---(3)}[/tex]Using distance formula, the expression for the length of chord AC is given by,
[tex]AC=\sqrt[]{(X_c^{}-X_a)^2+(Y_c-Y_a)^2_{}}[/tex]Since (Xa, Ya)=(10, 0),
[tex]\begin{gathered} AC=\sqrt[]{(X^{}_c-10_{})^2+(Y_c-0_{})^2_{}} \\ AC=\sqrt[]{(X^{}_c-10_{})^2+Y^2_c} \end{gathered}[/tex]It is given that chords AB and AC have equal length. Hence, we can write
[tex]\begin{gathered} AB=AC \\ 6\sqrt[]{10}=\sqrt[]{(X^{}_c-10_{})^2+Y^2_c} \end{gathered}[/tex]Squaring both sides of above equation,
[tex]\begin{gathered} 360=(X^{}_c-10_{})^2+Y^2_c\text{ } \\ (X^{}_c-10_{})^2+Y^2_c=360\text{ ----(4)} \end{gathered}[/tex]Subtract equation (4) from (3) and solve for Xc.
[tex]\begin{gathered} (X^{}_c-10_{})^2-X^2_c=360-100 \\ X^2_c-2\times X_c\times10+100-X^2_c=260 \\ -20X_c=260-100 \\ -20X_c=160 \\ X_c=\frac{160}{-20} \\ X_c=-8 \end{gathered}[/tex]Put Xc=-8 in equation (3) to find Yc.
[tex]\begin{gathered} (-8)^2+Y^2_c=100 \\ 64+Y^2_c=100 \\ Y^2_c=100-64 \\ Y^2_c=36 \\ Y^{}_c=\pm6 \\ Y^{}_c=6\text{ or }Y_c=-6 \end{gathered}[/tex]So, the coordinates of point C can be (Xc, Yc)=(-8, 6) or (Xc, Yc)=(-8, -6).
Since (-8, 6) are the coordinates of point B, the coordinates of point C can be chosen as (-8, -6).
Therefore, the coordinates of point C is (-8, -6) if chords AB and AC have equal length.
(Combining Equations)What is the result of subtracting the second equation from the first ? -4x - 2y = -2x - 2y = 9
Subtract the second equation from the first,
[tex]\begin{gathered} -4x-2y=-2 \\ - \\ x-2y=9 \\ (-4x-x)-(2y-\lbrack-2y\rbrack)=-2-9 \\ -5x-2y+2y=-11 \\ -5x+0=-11 \\ -5x=-11 \\ \text{Divide both sides by -5} \\ \frac{-5x}{-5}=\frac{-11}{-5} \\ x=\frac{11}{5} \end{gathered}[/tex]A straight driveway is 87.0 ft long, and the top is 11.0 ft above the bottom. What angle does it make with the horizontal? ( Round to the nearest tenth
Let us begin by illustrating the problem using a diagram:
Here we have represented the angle that the driveway makes with the horizontal to be x
Step 1: Label the sides as shown:
Step 2: Using the sides given, find the required angle
The formula that relates the angle, opposite side and hypothenuse side is:
[tex]sin\theta\text{ = }\frac{opposite}{hypothenuse}[/tex]Applying the formula:
[tex]\begin{gathered} sinx\text{ = }\frac{11}{87} \\ sin\text{ x = 0.126437} \\ x\text{ }\approx\text{ 7.3}^0 \end{gathered}[/tex]Hence, it makes an angle of 7.3 degrees with the horizontal
find the greatest common factor for 8n^3 6n^3
We determine the greatest common factor as follows:
[tex]8n^3+6n^3[/tex]So, we factor:
[tex]2n^3(4+3)[/tex]So, the greatest common factor is 2n^3.
solve for rv=r+at, for r
Since we need to solve for r we have to leave that variable alone in one side of the equation. We notice that at is adding in the right side, then it goes to the left side substracting, that is:
[tex]v-at=r[/tex]Therefore:
[tex]r=v-at[/tex]in the last part we only switch the sides of the equation.
Solve for xX/250 = 3/500
Answer:
x = 3/2 = 1.5
Explanation:
The initial equation is:
[tex]\frac{x}{250}=\frac{3}{500}[/tex]To solve the equation, we need to multiply both sides by 250 as:
[tex]\begin{gathered} \frac{x}{250}\cdot250=\frac{3}{500}\cdot250 \\ x=\frac{3\cdot250}{500} \\ x=\frac{750}{500} \end{gathered}[/tex]This fraction can be simplified as:
[tex]x=\frac{750}{500}=\frac{750\div250}{750\div250}=\frac{3}{2}=1.5[/tex]Therefore, the value of x is 3/2 as a fraction or it is 1.5 as a decimal.
Carmen has 12 loaves of pumpkin bread. She cuts each loaf into 1/8 pieces and gives one piece to each of her friends. How many friends can Carmen give a piece of pumpkin bread?
12 loaves of pumpkin bread.
Each loave is cut into 1/8 pieces.
So, there are 8 pieces per loaf:
8 pieces per loaf x 12 loaves = 96 pieces
If she gives one piece to each friend she can give it to 96 friends:
96 pieces / x friends = 1 per friend
96/x =1
96 = x(1)
96= x
How many different committees can be formed from 12 teachers and 32 students if the committee consists of 3 teachers and 2 students?
Answer: 4 committees
Step-by-step explanation:
12 divided by 3 = 4 (this equation represents the teachers)
2 x 4 = 8 (this equation represents the students)
There can only be 4 committees because there are only 12 teachers. There are some students that will not be in a committee. 24 students will be committee-less to be exact.
The figure shows the measures of various angles of a roof and it supports. Find the measure of angle 1, the angle between an eave and a horizontal support beam.
Answer:
35 degrees.
Explanation:
The figure shown is an isosceles triangle. An isosceles triangle has two of its sides and base angles to be equal.
Since the sum of the angles in a triangle is 180 degrees, hence:
110 + (base angles) = 180
110 + (<1 + <1) = 180 (since base angles are the same)
110 + 2<1 = 180
2<1 = 180-110
2<1 = 70
Divide both sides by 2
2<1/2 = 70/2
<1 = 35 degrees
Hence the angle between an eave and the horizontal support beam is 35 degrees.
All lines that cross the x-axis are vertical lines.A. TrueB. False
Given:
All lines that cross the x-axis are vertical line.
Required:
To find whether the given statement is true or false.
Explanation:
A vertical line is one the goes straight up and down, parallel to the y-axis of the coordinate plane.
The x-intercept is the point at which the graph crosses the x-axis.
Here all lines are not vertical lines.
Therefore the given statement is false.
Final answer:
False.
Convert the binary number ( 365.24 ) into decimal number.
Given:
The given deciaml number is 365.24.
Required:
We need to convert the given decimal number into a binary number.
Explanation:
Consider the integer part of the given number.
[tex]365[/tex]Divide the number 365.
Consider the fraction part of the given number.
[tex]0.24[/tex]Multiply the number 0.24 by 2.
The binary number of the decimal number is
[tex]365.24_{10}=101101101.0011110101_2[/tex]Final answer:
[tex]101101101.0011110101[/tex]The number of books he collects, n, is defined by n = 140 + 21 where d is the number of days he spends collectingRobert is collecting books to donate to the library.books.What does 14 represent in the context of Robert's book collecting?A represents the number of books per day that are collected,® represents the number of books per week that are collected.represents the number of books per month that are collected.o represents the number of books per year that are collected.
The equation for number of books collected by Robert is given as;
n= 14 d + 21
where d is the number of days he spent collecting .
Answer A. represents the number of books per day that are collected
30-28-25-21-16 next number
Answer:
10
Step-by-step explanation:
30 -2
28 -3
25 -4
21 -5
16 -6
= 10
Answer:
10
Step-by-step explanation:
Given the sequence 30, 28, 25, 21, 16, you want to know the next number.
DifferencesFirst differences between successive terms are ...
28 -30 = -2
25 -28 = -3
21 -25 = -4
16 -21 = -5
These are not constant, so this is not an arithmetic sequence. However, we notice the second differences are constant:
-3 -(-2) = -1
-4 -(-3) = -1
-5 -(-4) = -1
ApplicationThis observation tells us the next second difference is ...
-5 +(-1) = -6
And the next number in sequence is ...
16 +(-6) = 10
The next number is 10.
__
Additional comment
When a sequence of numbers is described by a polynomial or exponential, looking at differences (and their differences) can help determine the degree of the polynomial, or the common ratio of the exponential.
Here, the second differences are constant, so a second-degree (quadratic) polynomial will describe the sequence. The polynomial describing this sequence is ...
a(n) = 31 -(n)(n+1)/2
The figure shown represents a triangular window design. If ΔIKL ≅ ΔJOP, which of the following statements must be true?
The most appropriate choice for congruency of triangles will be given by
[tex]\bar{IL} \cong \bar{JP}[/tex]
Third option is correct.
What are congruent triangles?
Two triangles are said to be congruent if their corrosponding sides and corrosponding angles are equal.
There are five axioms of congruency. They are
SSS axiom, SAS axiom, ASA axiom, AAS axiom, RHS axiom.
Here,
ΔIKL ≅ ΔJOP [Given]
[tex]\bar{IL} \cong \bar{JP}[/tex] [Corrosponding parts of congruent triangles are congruent]
Third option is correct.
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Complete Question
The diagram with the question has been attached below
Can someone help me with this please? If the painting is 18 inches high, how wide would it be?
The ratio of width to height is :
[tex]\frac{w}{h}=\frac{1+\sqrt[]{5}}{2}[/tex]If h = 18 inches, the value of w will be :
[tex]\begin{gathered} \frac{w}{18}=\frac{1+\sqrt[]{5}}{2} \\ \text{Cross multiply :} \\ 2w=18(1+\sqrt[]{5}) \\ w=\frac{18(1+\sqrt[]{5})}{2} \\ w=9(1+\sqrt[]{5}) \\ w=9+9\sqrt[]{5}\quad or\quad 29.12 \end{gathered}[/tex]The answer is w = 29.12 inches
? Question
Refer to section 1.3.2, Credit scores, beginning on page 22 of the report.
Arrange the five tiers of credit scores in order, starting with the lowest tier of credit scores.
The five credit score tiers are listed in ascending order, starting with the lowest tier:
Deep Subprime < Subprime < near prime < prime < superprime
The ability of a consumer to get credit may be significantly influenced by their credit score. These interactive graphs demonstrate how lending behavior has changed for different credit score profiles of borrowers.
We concentrate on the following five commercially available credit score levels:
Subprime's credit scores is between 580 to 619.
Prime's credit score level is between 660 to 719.
The credit score level of deep subprime is below 580.
The credit score level of near prime is 620 - 659.
The credit score level of superprime is 720 or above.
Therefore, the five tires of credit scores from lowest to highest are:
Deep Subprime < Subprime < near prime < prime < superprime
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Find the absolute change and the percentage change for the given situation 150 increased to 861
Given that 150 is increased to 861
The absolute change formula is
[tex]\text{Absolute Change}=New\text{ value - Old value}[/tex]Where
The new value = 861
The old value = 150
The absolute change is
[tex]\text{Absolute Change}=861-150=711[/tex]Hence, the absolute change is 711
The formula for percentage is
[tex]Percentage\text{ change}=\frac{New\text{ value-Old value}}{Old\text{ value}}\times100\text{\%}[/tex]Substitute the values into the percentage change formula
[tex]\begin{gathered} Percentage\text{ change}=\frac{New\text{ value-Old value}}{Old\text{ value}}\times100\text{\%} \\ Percentage\text{ change}=\frac{861-150}{150}\times100\text{\%} \\ Percentage\text{ change}=\frac{711}{150}\times100\text{\%}=4.74\times100\times=474\text{\%} \\ Percentage\text{ change}=474\text{\%} \end{gathered}[/tex]Hence, the percentage change is 474% increase
determine the sample space of all the possible outcomes of choosing a card number 1 2 3 or 4 and a blue green or yellow marble how many outcomes involves choosing a Blue Marble
There are a total of 4 outcomes that involve choosing a blue marble
Here, we want to write a sample space for the selection
For us to have the sample space, we will have to write out the possible outcomes
We shall be representing the blue marble by b, the green by g and the yellow by y
We have the sample space as follows;
{1B,1G,1Y,2B,2G,2Y,3B,3G,3Y,4B,4G,4Y}
From the sample space, we can see that there are actually 12 possible results
Now, to get the outcomes involving blue marbles, we simply select the members of the sample space having B at the back
We have these as 1B, 2B, 3B and 4B
This is a total of 4 outcomes
A snail starts crawling toward a flower 7 feet away. The snail crawls 2 feet every hour for 3 hours. What graph represents the distance of the snail to the flower over that time period? Use the graphing tool to graph your answer
y represents the distance of the snail to the flower, in ft
x represents time, in hours
In the beginning, the distance of the snail to the flower is 7 feet. Then, the point (0, 7) is on the graph
After the first hour, the snail crawls 2 feet, then its distance to the flower is 7 - 2 = 5 ft. Then, the point (1, 5) is on the graph.
After the second hour, the snail crawls another 2 feet, then its distance to the flower is 5 - 2 = 3 ft. Then, the point (2, 3) is on the graph.
After the third hour, the snail crawls another 2 feet, then its distance to the flower is 3 - 2 = 1 ft. Then, the point (3, 1) is on the graph.
The graph is
Between what two consecutive integers must solution 2^x=7 lie?
Answer:
2 and 3
Explanation:
Given the equation:
[tex]2^x=7[/tex]Now, observe the following:
[tex]\begin{gathered} 2^2=4 \\ 2^3=8 \\ 4<7<8 \\ \implies2^2<2^x<2^3 \end{gathered}[/tex]Taking the indices:
[tex]2Therefore, the solution of 2^x=7 lies between the consecutive integers 2 and 3.in a regular polygon a exterior angle 15° how many sides does the polygon have
Sum of the exterior angles of a polygon = 360°
For a regular polygon, all the angles are equal:
mn = 360
where n = the number of sides
m = the size of an exterior angle
For m = 15°
15n = 360
n = 360/15
n = 24
Therefore, the polygon
find an ordered pair for 5x+y=1
An ordered pair for the equation 5x + y = 1 is (0, 1)
How to determine the ordered pair?The equation of the function is given as
5x + y = 1
To determine the ordered pair, we simply set the value of x to any value.
And then calculate the value of y
Using the above parameters as a guide, we can assume that
x = 0
Substitute x = 0 in 5x + y = 1
5(0) + y = 1
Evaluate the product
0 + y = 1
So, we have
y = 1
Express as ordered pairs
(x, y) = (0, 1)
Hence, the ordered pair in the solution is (0, 1)
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An ordered pair of the equation 5x + y = 1 is (1, - 4).
What is an ordered pair?An ordered pair (a,b) is a set of values for x and y coordinates.
As the name suggests (a, b) and (b, a) are two different ordered pairs.
Given, 5x + y = 1.
Or,
y = 1 - 5x.
Now we can choose any arbitrary value of x that corresponds to a value
of y.
At x = 1,
y = 1 - 5(1).
y = 1 - 5,
y = - 4.
∴ An ordered pair o the given equation 5x + y = 1 is (1, - 4).
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Finding Angles with JustificationIn the diagram below BC = EC and m
Answer:
Angle Reason
m∠ECD = 140 Given
m∠ECB = 40 Supplementary angles
m∠EBC = 70 Isosceles triangle
m∠ABE = 110 Supplementary angles
Explanation:
Angle ECB and CED are supplementary because they form a straight line and their sum is 180 degrees. So, we can calculate the measure of ∠ECB as
m∠ECB = 180 - 140
m∠ECB = 40
Then, the interior sum of the angles of a triangle is equal to 180 degrees, so
m∠ECB + m∠EBC + m∠BEC = 180
40 + m∠EBC + m∠BEC = 180
However, m∠EBC = m∠BEC because triangle ABC is an isosceles triangle where 2 sides have the same length BC and EC. So, we can find m∠EBC as follows
40 + m∠EBC + m∠EBC = 180
40 + 2m∠EBC = 180
40 + 2m∠EBC - 40 = 180 - 40
2m∠EBC = 140
m∠EBC = 140/2
m∠EBC = 70
Then, the measure of ∠ABE is equal to
∠ABE = 180 - m∠EBC
∠ABE = 180 - 70
∠ABE = 110
Therefore, we can answer it as follows
Angle Reason
m∠ECD = 140 Given
m∠ECB = 40 Supplementary angles
m∠EBC = 70 Isosceles triangle
m∠ABE = 110 Supplementary angles
Write each ratio using the given figure. If necessary, find the missing side.Tan P = ___________Answer?
Hello!
First, let's analyze the figure and write each side:
Analyzing it, we don't have enough information yet to calculate the tangent (because we don't know the measurement of P).
So, let's calculate the opposite side (by Pithagoras):
[tex]\begin{gathered} a^2=b^2+c^2 \\ 41^2=40^2+c^2 \\ 1681=1600+c^2 \\ 1681-1600=c^2 \\ c^2=81 \\ c=\sqrt{81} \\ c=9 \end{gathered}[/tex]As we know the opposite side, we can calculate the tangent of P, look:
[tex]\begin{gathered} \tan(P)=\frac{\text{ opposite}}{\text{ adjacent}} \\ \\ \tan(P)=\frac{9}{40} \\ \\ \tan(P)=0.225 \end{gathered}[/tex]Curiosity: using the trigonometric table, this value corresponds to approximately 13º.
Answer:The tangent of P is 0.225.
If each quadrilateral below is a square, find the missing measure
ANSWER
[tex]x=11[/tex]EXPLANATION
The figure given is a square.
Each angle in a square is 90 degrees and the diagonals bisect each angle.
This means that :
[tex]\begin{gathered} 6x-21=45 \\ \text{Collect like terms:} \\ 6x=45+21 \\ 6x=66 \\ \text{Divide through by 6:} \\ x=\frac{66}{6} \\ x=11 \end{gathered}[/tex]That is the value of x.
A union voted on whether to go on strike 120 people vote the ratio of yes and no votes is 2:3 how many people vote no
Answer:
80
Step-by-step explanation:
This is a ratio and we can set it up as follows and solve for x:
[tex]\frac{2}{3} = \frac{x}{120}[/tex]
Multiply both sides by 120
80 = x