The accompanying data represent women's median earnings as a percentage of men's median earnings for recent years beginning with 1989. Is there a trend? How does it appear to affect women? Construct a time-series graph. Median Earnings Year Median Earnings 1989 1990 1991 1992 1993 1994 1995 1996 1997 59.2 60.1 62.3 61.7 62.5 61.7 61.7 65.0 67.0 Year 1998 1999 2000 2001 2002 2003 2004 2005 Median Earnings 65.6 62.9 63.3 61.5 65.2 63.9 66.7 68.8 Full data set 0 www X C. Median Earnings 70- 64- 584 1989 1997 Year 2005 Clear all Final check
Answers
Time Series Graph: Plot A
Based on the above plot, earnings first rise till 1997, and then start falling till 2001. After 2001, earnings start rising again. So overall there is an upward trend.
Why is option A the answer?Based on these observations, the answer is Option A, which says:
Option A: There is a general upward trend though there have benn some down years. An upward trend would be helpful to women so that their earnings become equal to those of men.
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Related Questions
Graph the equation y=-x^2+12x−35 on the accompanying set of axes. You must plot 5 points including the roots and the vertex.
Answers
Answer:
To graph the equation y=-x^2+12x-35, we need to find the vertex and the roots of the equation.
The equation can be written in vertex form as y=-(x-6)^2+1, where the vertex is (6,1).
To find the roots, we need to set y=0 and solve for x:
0=-x^2+12x-35
x^2-12x+35=0
(x-5)(x-7)=0
x=5 or x=7
So the roots are (5,0) and (7,0).
The vertex is at (6,1) and the roots are at (5,0) and (7,0). The curve is a downward-facing parabola.
HELP PLEASE
Solve by graphing g(x)=lx-4l+3
Answers
Please refer to the attachment
It is possible to select 3 restraunts in how many different ways?
Answers
There are 1140 different possible ways to select 3 restaurants out of 20 for the promotional program.
In mathematics, what are a permutation and combination?Combination and permutation are two alternative strategies in mathematics to divide up a collection of components into subsets. The subset's components can be listed in any order when combined. The components of the subset are listed in a permutation in a certain order.The combination formula, which is: can be used to resolve this issue.
n C r = r! * (n-r)!
where r is the number of restaurants to be chosen, and n is the total number of restaurants (20 in this case). (3 in this case).
By replacing these values, we obtain:
20 C 3 = 20! / (3! * (20-3)!) = 20! / (3! * 17!) = (20 * 19 * 18) / (3 * 2 * 1) = 1140
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,Kofi, Adoma and Esenam are three siblings, Kofi is x years older than Adoma and Adoma is y years older than Esenam. a. How much older than Esenam is Kofi ? b. If Esenam is 5 years old, how old is (i) Adoma (ii)Kofi
Answers
a. K = E + (x + y). This implies that Kofi is (x + y) older than Esenam.
b. (i) Adoma = (5 + y) years
(ii) Kofi = (5 + (x+y)) years
What is a word problem?Word problem is a topic that requires the transformation of a mathematical statement into an equation, such that the variable is to be determined.
In the given question, we have;
Let the age of Kofi, Adoma, and Esenam be represented by K, A and E respectively. So that;
K = A + x ...... i
A = E + y........ ii
substitute i into ii
K = (E + y) + x
= E + (x + y)
K = E + (x + y) ........ iii
Thus,
a. From equation iii, we can deduce that Kofi is (x + y) years older than Esenam.
b. The age of Adoma = 5 + y years
ii. The age of Kofi = 5 + (x + y) years
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PLEASE HELP ME!!! Unit 10 Circles Homework Inscribed Angles questions 15 and 17
Answers
Applying the inscribed angle theorem, we have the missing measures as: 15. m<DEF = 127° 16. m(PL) = 62°
How to Apply the Inscribed Angle Theorem?15. Angle DEF is an inscribed angle while arc FGD is the intercepted arc. Thus, according to the inscribed angle theorem, we have:
m<DEF = 1/2(m(FGD)
Plug in the values:
6x + 37 = 1/2(19x - 31)
2(6x + 37) = 19x - 31
12x + 74 = 19x - 31
12x - 19x = -74 - 31
-7x = -105
x = 15
m<DEF = 6x + 37 = 6(15) + 37 = 127°
16. m<LMP = m<LNP
Plug in the values:
5x - 19 = 2x + 11
5x - 2x = 19 + 11
3x = 30
x = 10
m(PL) = 2(LMP) [based on the inscribed angle theorem]
Plug in the values:
m(PL) = 2(5x - 19)
Plug in the value of x:
m(PL) = 2(5(10) - 19)
m(PL) = 62°
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answers
Answer:
The y-intercept represents Adam's base salary
Step-by-step explanation:
Since it's y = 0.28x + 38,000, when x is 0, the salary is 38,000 without commission.
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if you rotate cars tires at 10,000 miles, if a car tire has 25,200 rotations per day, how many weeks will it be until you rotate the tires
Answers
It will take 4. 09 weeks for the tires to be rotated at the current rate.
How to find the time till rotation ?When rotating a car's tires every 10,000 miles, each tire must complete this distance before being moved.
25, 200 rotations / day x 7 days / week = 176, 400 rotations per week
To solve this predicament, dividing 10,000 miles by the number of rotations/mile (which equates to the tire's circumference) is necessary. The formula for calculating a tire's circumference can aid in obtaining this number along with the weeks required to perform the rotation process:
C = 2πr
Rotation per mile is:
1 mile / 87.96 inches / rotation = 72.26 rotations / mile
Number of weeks:
10, 000 miles x 72. 26 rotations / mile = 722, 600 rotations
722, 600 rotations / 176, 400 rotations/week = 4.09 weeks
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For what values of x and y are the triangles to the right congruent by HL?
Answers
The values of x and y that make the triangles congruent by HL are:
x = 3 and y = 1
Congruent triangles: Calculating the values of x and yFrom the question, we are to determine the values of x and y that make the triangles congruent by HL.
Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.
Thus,
For the triangles to be right congruent by HL
x = y + 2
and
x + 1 = 4y
Solve the equations simultaneously
Substitute x = y + 2 in the second equation
x + 1 = 4y
y + 2 + 1 = 4y
y + 3 = 4y
3 = 4y - y
3 = 3y
Divide both sides by 3
3/3 = 3y/3
1 = y
Therefore,
y = 1
Substitute the value of y into the first equation
x = y + 2
x = 1 + 2
x = 3
Hence,
The values are:
x = 3 and y = 1
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Tell whether the given side lengths can represent the sides of a right triangle
10, 12, 20
Determine if the segment lengths form an acute, right, or obtuse triangle,
10, 11, 14
26.
Need help with all of these please need this asap. Please show work
Answers
23. By the diagram, the triangle is a [tex]45^\circ - 45^\circ-90^\circ[/tex] triangle. Therefore, the triangle is isosceles, so [tex]x=6.[/tex] And by the Pythagorean theorem, [tex]y^2=x^2+6^2=6^2+6^2=72,[/tex] and taking the square root yields [tex]y = 6\sqrt{2}.[/tex]
24. Notice that by the diagram, the triangle is a [tex]30^\circ-60^\circ-90^\circ[/tex] triangle. It is well known that in these special types of triangles, if [tex]a[/tex] is the side length opposite the [tex]30^\circ[/tex] angle, then the side length opposite the [tex]90^\circ[/tex] angle is [tex]2a,[/tex] and finally the side length opposite the [tex]60^\circ[/tex] is [tex]a\sqrt{3}.[/tex] This is shown in the image I've attached below, and can also be easily proven by the fact that two of these triangles combine to form an equilateral triangle.
So using this fact, we know that [tex]x = \frac{8}{2} = 4,[/tex] and [tex]y = x\sqrt{3} = 4\sqrt{3}.[/tex]
25. Tell whether the given side lengths can represent the sides of a right triangle: 10, 12, 20
For this question, we simply use the converse of the Pythagorean theorem. One part of its statement says that if a triangle has sides of length [tex]a, b, c[/tex] such that [tex]a^2 + b^2 = c^2[/tex], and [tex]c[/tex] is the longest side, then the angle opposite the side of length [tex]c[/tex] is a right angle.
Thus, if the triple [tex](a, b, c)[/tex] does not satisfy the equation, the triangle it forms is not a right triangle. In our case, the corresponding values for [tex](a, b, c)[/tex] are [tex](10, 12, 20),[/tex] because [tex]20[/tex] is the largest number in this triple. But [tex]10^2+12^2=244\neq 400 = 20^2,[/tex] so the triangle with side lengths [tex]10, 12, 20[/tex] is not a right triangle.
26. Another statement of the converse of the Pythagorean theorem is that if a triangle has side lengths [tex]a, b, c[/tex] such that [tex]c^2 > a^2+b^2[/tex] , with [tex]c[/tex] being the longest side, then the triangle is an obtuse triangle. So the corresponding values for [tex]a, b, c[/tex] are [tex]10, 11, 14,[/tex] and because [tex]14^2 = 196 < 221 = 10^2+11^2,[/tex] the triangle is an obtuse triangle.
Find the measure of each indicated side. Round your answer to the nearest tenth.
Answers
Answer:
m∠R = 78.9°------------------------------
We are given three sides and need to find one of angles.
Use the law of cosines:
[tex]cos(A) = \cfrac{ b^2 + c^2 - a^2}{2bc}[/tex]
Here we are given:
R - angle A, a = 59.7, b = 52, c = 41Substitute above values into the given equation:
[tex]cos(R) = \cfrac{ 52^2 + 41^2 - 59.7^2}{2*52*41} =0.1925[/tex]
Find m∠R:
m∠R = arccos (0.1925), use calculatorm∠R = 78.9° (rounded to the nearest tenth)For each SSA case below, i) solve by the law of cosines, (ii) solve by the law of sines; use degrees for angles, and round each answer to its nearest 100th:
Answers
The values of the angles will be 6.67°, 156.78° Be 29.93° and the sides will be 10.01, 34 and 43.
How to explain the angleSSA stands for side side angle postulate. In this postulate of congruence, we say that if two sides and an angle not included between them are respectively equal to two sides and an angle of the other triangle then the two triangles are equal.
By sine rule,
Y = sin156.78 × 44 / 34
= 29
sin Y = 0.499
Y = 29.93°
By the angle sum property. The last angle will be:
180 - 156.78 - 29.93
= 6.67°
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Of the following Z-score values, which one represents the location closest to the mean?
A. Z=+0.5
B. Z=+1,0
C. Z=-1.5
D. Z=-0.3
Answers
Z=+0.5, which has an absolute value of 0.5 and is the closest Z-score to the mean so option A is correct.
What is?In mathematics, the absolute value (also known as modulus) of a real number is its distance from zero on the number line. It is denoted by enclosing the number between two vertical bars, such as |x|.
For example, the absolute value of 5 is 5, because 5 units to the right of zero on the number line is at a distance of 5 units from zero. Similarly, the absolute value of -5 is also 5, because 5 units to the left of zero on the number line is at a distance of 5 units from zero.
According to the given informationTo determine which Z-score represents the location closest to the mean, we need to know the sign of each Z-score, as well as the absolute value of each Z-score.
The sign of the Z-score indicates whether the location is above (+) or below (-) the mean. The absolute value of the Z-score indicates how far away the location is from the mean, measured in standard deviations.
Looking at the options provided, we see that:
A. Z=+0.5 is positive, indicating a location above the mean, and has an absolute value of 0.5.
B. Z=+1.0 is positive, indicating a location above the mean, and has an absolute value of 1.0.
C. Z=-1.5 is negative, indicating a location below the mean, and has an absolute value of 1.5.
D. Z=-0.3 is negative, indicating a location below the mean, and has an absolute value of 0.3.
Since we want to find the Z-score closest to the mean, we should look for the option with the smallest absolute value. Therefore, the answer is A. Z=+0.5, which has an absolute value of 0.5 and is the closest Z-score to the mean.
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which average is the most representative of the data
Answers
The median is the average that is most representative of the data.
How to obtain the median of a data-set?The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than. Hence, the median also represents the 50th percentile of a data-set.
In this problem, we have that smaller values have a higher number of observations, meaning that the data-set is not symmetric.
As the data-set is not symmetric, it means that the median is the average that is most representative of the data.
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Find the sum of the interior angles of the following polygon:
115⁰
4
130⁰
115
95⁰
Sum of interior angles =
Part 2:
Find the measure of x:
degrees.
degrees.
Answers
The Sum of interior angles of the given polygon is: 540°
The value of the angle x is: 85°
What is the interior angle of the polygon?The interior angle-sum formula for an irregular polygon is the same as the sum of interior angle in a regular polygon.
Sum of interior angles in a n-sided polygon is:
Sum = (n - 2)180
where:
n is the number of sides of the irregular polygon.
This is a 5-sided irregular polygon
Thus:
Sum = (5 - 2)180
Sum = 540°
Thus:
x + 115 + 115 + 130 + 95 = 540
x + 455 = 540
x = 540 - 455
x = 85°
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Which parent functions have a domain of all real values of x? Select all that apply.
A. Absolute value
B. Linear
C. Reciprocal
D. Quadratic
E. Cube root
F. Cubic
Answers
Answer:
D. Quadratic
Step-by-step explanation:
The vertex of the parent function y = x2 lies on the origin. It also has a domain of all real numbers and a range of [0, ∞). Observe that this function increases when x is positive and decreases while x is negative
A scatter plot is shown on the coordinate plane. scatter plot with points at 1 comma 8, 2 comma 5, 4 comma 7, 5 comma 2, 7 comma 6, 8 comma 2, 10 comma 1, and 10 comma 4 Which of the following graphs shows a line on the scatter plot that fits the data? scatter plot with points at 1 comma 8, 2 comma 5, 4 comma 7, 5 comma 2, 7 comma 6, 8 comma 2, 10 comma 1, and 10 comma 4, with a line passing through the coordinates 2 comma 5, 8 comma 2, and 10 comma 1 scatter plot with points at 1 comma 8, 2 comma 5, 4 comma 7, 5 comma 2, 7 comma 6, 8 comma 2, 10 comma 1, and 10 comma 4, with a line passing through the coordinates 4 comma 7, and 10 comma 4 scatter plot with points at 1 comma 8, 2 comma 5, 4 comma 7, 5 comma 2, 7 comma 6, 8 comma 2, 10 comma 1, and 10 comma 4, with a line passing through the coordinates 1 comma 8, and 10 comma 1 scatter plot with points at 1 comma 8, 2 comma 5, 4 comma 7, 5 comma 2, 7 comma 6, 8 comma 2, 10 comma 1, and 10 comma 4, with a line passing through the coordinates 4 comma 5.33, and 6 comma 4.33 Question 11(Multiple Choice Worth 5 points) (Scatter Plots MC) A large retailer calculated the average hourly wage of employees over 6 years. The following table shows the years since 2016 and the average hourly wage of an employee at that time. Years (since 2016) 0 1 2 3 4 5 6 Hourly Wage (in dollars) 10 10.5 11 11.5 12 13 14 Which of the following representations is most appropriate for showing the change in the average hourly wage each year? scatter plot with the title average hourly wage and the x axis labeled years since 2016 and the y axis labeled hourly wage in dollars, with points at 0 comma 10, 1 comma 10 and a half, 2 comma 11, 3 comma 11 and a half, 4 comma 12, 5 comma 13, 6 comma 14 scatter plot with the title average hourly wage and the x axis labeled hourly wage in dollars and the y axis labeled years since 2016, with points at 10 comma 0, 10 and a half comma 1, 11 comma 2, 11 and a half comma 3, 12 comma 4, 13 comma 5, and 14 comma 6 line graph with the title average
Answers
For the second question, the most appropriate representation for showing the change in the average hourly wage each year is: scatter plot with the title average hourly wage and the x axis labeled years since 2016 and the y axis labeled hourly wage in dollars, with points at 0 comma 10, 1 comma 10 and a half, 2 comma 11, 3 comma 11 and a half, 4 comma 12, 5 comma 13, 6 comma 14
Rajindri, a physician assistant who works in an emergency room, earns $163 for every two hours that she works.
Which equation represents the relationship between d, the number of dollars Rajindri earns, and t, the amount of time Rajindri works, in hours?
A. d= 163 + t
B. d= 163/2 × t/2
C. d= 163t
D. d= 81.50t
Answers
Answer:
b but I'm not exactly sureb
Richard is saving money for a down payment on a car. He opens a savings account at his local bank and deposits $500. He models his savings plan with the equation y = 200x + 500 based on his current monthly savings rate. What does the y-intercept of linear model represent?
Question 8 options:
The date the savings account was started.
The starting amount in his savings account.
The date when he will have enough money.
The largest amount that he can save.
Answers
In a case whereby Richard is saving money for a down payment on a car He models his savings plan with the equation y = 200x + 500 based on his current monthly savings rate y-intercept of linear model represent B. The starting amount in his savings account.
How can the linear model be interpreted?It should be noted that in a linear equation the y intercept can be seen as one that is starting point whereby x is zero, which implkies that starting balance he had is 1000 in the bank.
Therefore, from the equation y = 200x + 500, the y-intercept of linear model serves as the starting amount in his savings account.
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The solids are similar.
Find the surface area of
solid B to the nearest
hundredth.
Cylinder A
24 mm
S = 594 mm²
Cylinder B
16 mm
The surface area of solid B is
square millimeters.
Answers
Answer:
264π
Step-by-step explanation:
A sidewalk in front of Kathy’s house is in the shape of a rectangle four feet wide by 45 feet long. Find the perimeter and the area
Answers
Answer:
Parameter= 98ft
Area=180ft^2
Step-by-step explanation:
Parameter= Length times 2 plus width times 2 or
L2+W2=P 4(2)+45(2)=8+90=98
Area= LxW=A^2
4x45=180^2
Perimeter = 2(45 + 4)
Perimeter = 2(49)
Perimeter = 98 feet
Area = length x width
Area = 45 x 4
Area = 180 square feet
Can someone actually help me with this!!!! please do A through D, I attached the picture. BRAINLIEST!!!!!
Answers
1. Substitute the smallest possible value for each variable into the inequality and check that the inequality is true.
2. Substitute the largest possible value for each variable into the inequality and check that the inequality is true.
3. Check that the solution set of the inequality contains only whole numbers, since the number of containers must be a whole number.
For example, let's check the compound inequality for the number of containers of cheese popcorn c:
5.65c + 0.4p ≤ 50 and c ≥ 0
1. Substituting c = 0 and p = 125 (the largest possible value) into the inequality, we get:
5.65(0) + 0.4(125) ≤ 50
50 ≤ 50
This is true.
2. Substituting c = 9 (the largest possible value) and p = 0 into the inequality, we get:
5.65(9) + 0.4(0) ≤ 50
50.85 ≤ 50
This is false.
3. The solution set of the inequality is:
0 ≤ c ≤ 8.849...
Since the number of containers must be a whole number, the solution set is:
0 ≤ c ≤ 8
Therefore, the compound inequality for the number of containers of cheese popcorn c is:
0 ≤ c ≤ 8
We can follow the same steps to check the compound inequality for the number of containers of peanut butter popcorn p.
Jen works for a cellular phone company. She earns a salary of $250 per
week plus a bonus of 10% of the value of any phones and accessories
that she sells. In the past four weeks, Jen sold $312 worth of phones
and accessories.
Circle the amount that correctly completes the statement.
In the past four weeks, Jen earned a total income of $
1,031.20
562.00
312.00
281.20
31.20
Answers
Okay, here are the steps to solve this problem:
* Jen earns a weekly salary of $250
* She gets a 10% bonus on any sales
* In the past 4 weeks, she sold $312 worth of phones and accessories
* 10% of $312 is $31.20
* So in 4 weeks, her bonus would be $31.20 * 4 = $124.80
* Her weekly salary is $250
* So in 4 weeks, her salary would be $250 * 4 = $1000
* Her total income over 4 weeks is $1000 + $124.80 = $1124.80
* The choices are:
** $1,031.20 ** $562.00 ** $312.00 ** $281.20 ** $31.20
So the correct choice is $1,031.20.
$550 is deposited in an account with 8.5%
interest rate, compounded continuously.
What is the balance after 6 years?
F = $[?]
Answers
the balance after 6 years is approximately $926.45.
What is Continuous compounding ?
Continuous compounding is the process of calculating interest and reinvesting it into an account's balance over an infinite number of periods.
We can use the formula for continuous compounding to find the balance after 6 years:
[tex]F = Pe^{(rt)}[/tex]
where F is the future value, P is the present value, e is the mathematical constant e (approximately 2.71828), r is the annual interest rate, and t is the time in years.
In this problem, P = $550, r = 8.5% = 0.085 (note that we need to use the decimal form of the interest rate), and t = 6 years.
[tex]F = 550e^{(0.085*6)}[/tex]
F ≈ $926.45
Therefore, the balance after 6 years is approximately $926.45.
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Will give brainliest if you get correctly!
Guessing = Report
Answers
Answer:
Step-by-step explanation:
What is the value of cos(15°)?
StartFraction StartRoot 6 EndRoot minus StartRoot 2 EndRoot Over 2 EndFraction
StartFraction StartRoot 6 EndRoot minus StartRoot 2 EndRoot Over 4 EndFraction
StartFraction StartRoot 6 EndRoot + StartRoot 2 EndRoot Over 4 EndFraction
StartFraction StartRoot 6 EndRoot + StartRoot 2 EndRoot Over 2 EndFraction
Answers
we know that,
[tex] \sf \dashrightarrow \: cos(a - b) = cos a \times cos b + sin a \times sin b[/tex]
Therefore,
[tex] \sf \leadsto \: cos \: 15 \degree[/tex]
[tex] \sf \leadsto \: cos \: (45 \degree - 30 \degree)[/tex]
[tex] \sf \leadsto \: cos \: 45 \degree . \: cos \: 30 \degree + \: sin \: 45 \degree . \: sin \: 30 \degree[/tex]
[tex] \sf \leadsto \: \frac{1}{ \sqrt{2} } \: . \: \frac{ \sqrt{3} }{2} + \: \frac{1}{ \sqrt{2} } \: . \: \: \frac{1}{2} \\ [/tex]
[tex] \sf \leadsto \: \frac{1. \: \sqrt{3} }{ \sqrt{2} \: . \: 2} \: + \: \frac{1 \: .\: 1}{ \sqrt{2} \: .\: 2} \\ [/tex]
[tex] \sf \leadsto \: \frac{ \: \sqrt{3} }{ 2\sqrt{2} \: } \: + \: \frac{1}{ 2\sqrt{2} \: } \\ [/tex]
[tex] \sf \leadsto \: \frac{ \: \sqrt{3} + 1 }{ 2\sqrt{2} \: } \: \\ [/tex]
Therefore Value of cos 15° is [tex] \sf \: \frac{ \: \sqrt{3} + 1 }{ 2\sqrt{2} \: } \: [/tex]
ASAP Scott and Lana booked a cruise that departs from Seward, Alaska, but their flight flew into Anchorage, Alaska. The couple decided to travel from Anchorage to Seward on the Alaska Railroad's non-stop Coastal Classic route to enjoy the 117 miles of beautiful scenery. If the train had traveled 13 miles in 30 minutes, how long, in hours, was the non-stop train ride from Anchorage to Seward?
A. 4.5 hours
B. 18 hours
C. 3 hours
D. 9 hours
Answers
Answer:
A. 4.5 hours
Step-by-step explanation:
We can use a proportion to solve this problem. Let x be the total time in hours for the train ride from Anchorage to Seward. We know that the train traveled 117 miles in x hours, and it traveled 13 miles in 0.5 hours (30 minutes). Therefore:
117 miles / x hours = 13 miles / 0.5 hours
We can cross-multiply to get:
117 miles * 0.5 hours = 13 miles * x hours
Simplifying:
58.5 = 13x
x = 58.5 / 13
x = 4.5 hours
Therefore, the non-stop train ride from Anchorage to Seward took 4.5 hours. Answer: A.
Hope this helps!
Answer:
A. 4.5 hours
Step-by-step explanation:
We can use a proportion to solve this problem. Let x be the total time in hours for the train ride from Anchorage to Seward. We know that the train traveled 117 miles in x hours, and it traveled 13 miles in 0.5 hours (30 minutes). Therefore:
117 miles / x hours = 13 miles / 0.5 hours
We can cross-multiply to get:
117 miles * 0.5 hours = 13 miles * x hours
Simplifying:
58.5 = 13x
x = 58.5 / 13
x = 4.5 hours
Therefore, the non-stop train ride from Anchorage to Seward took 4.5 hours. Answer: A.
Hope this helps!
riangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−9, −9), B(9, 9), C(0, 9). Determine the scale factor used.
6
one sixth
3
Answers
To find the scale factor used to dilate triangle ABC to triangle A'B'C', we need to compare the corresponding side lengths of the two triangles.
The distance formula can be used to find the lengths of the sides of triangle ABC:
AB = sqrt[(3 - (-3))^2 + (3 - (-3))^2] = sqrt[6^2 + 6^2] = 6sqrt(2)
AC = sqrt[(0 - (-3))^2 + (3 - (-3))^2] = sqrt[3^2 + 6^2] = 3sqrt(5)
BC = sqrt[(3 - 0)^2 + (3 - 3)^2] = 3
Similarly, we can use the distance formula to find the lengths of the sides of triangle A'B'C':
A'B' = sqrt[(9 - (-9))^2 + (9 - (-9))^2] = sqrt[18^2 + 18^2] = 18sqrt(2)
A'C' = sqrt[(0 - (-9))^2 + (9 - (-9))^2] = sqrt[9^2 + 18^2] = 9sqrt(5)
B'C' = sqrt[(9 - 0)^2 + (9 - 3)^2] = sqrt[9^2 + 6^2] = 3sqrt(5)
The scale factor is the ratio of the side lengths of the corresponding sides of the two triangles. For example, the scale factor for side AB is:
AB' / AB = (18sqrt(2)) / (6sqrt(2)) = 3
Similarly, we can find the scale factors for sides AC and BC:
A'C' / AC = (9sqrt(5)) / (3sqrt(5)) = 3
B'C' / BC = (3sqrt(5)) / 3 = sqrt(5)
Since the scale factors for all three pairs of corresponding sides are the same, the scale factor used to dilate triangle ABC to triangle A'B'C' is 3.
Therefore, the answer is 3.
In the given diagram find the value of x
a) 1
b) 2
c) 3
d) 4
Answers
Given
ABCΔ is a triangle.
D is a point on [BC]
|BD|=4
|AD|=|CD|
m(CBAˆ)=α=30∘
m(ACBˆ)=β=20∘
To Find
What is |AC|=x?
Solution
Geometric approaches gave me nothing. Letting |AD|=|CD|=a, |AB|=b
and applying law of cosines to all three triangles yields;
x=2acos20∘16=a2+b2+2abcos70∘(a+4)2=b2+x2+2bxcos50∘respectively, from ACDΔ, ABDΔ and ABCΔ. Directly isolating x from these equations gives an expression involves trigonometric function(s), and i cannot find a way to annihilate trigonometric functions in these equations to reach the answer which is x=4
The complete question is -
In the given diagram find the value of x
a) 1
b) 2
c) 3
d) 4
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A person invests 8000 dollars in a bank. The bank pays 4.75% interest compounded daily. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 20400 dollars?
Answers
To the nearest tenth of a year, the person must leave the money in the bank for 15.5 years.
How long must the person leave the money in the bank until it reaches 20400 dollars?We can use the formula for compound interest:
A = P[tex](1 + r/n)^{nt}[/tex]
where A is the final amount, P is the principal (initial investment), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time in years.
We know P = 8000, r = 0.0475, and we want A = 20400. We also know that the interest is compounded daily, so n = 365.
Let's solve for t:
20400 = 8000[tex](1 + 0.0475/365)^{(365t)}[/tex]
2.55 = [tex](1.00013)^{(365t)}[/tex]
Taking the natural logarithm of both sides, we get:
after solving
Using a calculator, we find:
t ≈ 15.5
So, to the nearest tenth of a year, the person must leave the money in the bank for 15.5 years.
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Diane is a camp counselor she did signs in new obstacle course and tested course with three friends the Doppler shows the time it takes to complete the obstacle course. What is the mean absolute deviation(MAD)of the times.
Answers
Therefore, the mean absolute deviation of the times taken to complete the obstacle course is 0.3125 minutes.
What is mean absolute deviation?Mean absolute deviation (MAD) is a statistical measure that calculates the average distance between each data point in a dataset and the mean or median of that dataset. It measures the dispersion or variability of the data points in relation to the central tendency of the dataset.
To calculate the MAD, you first find the mean or median of the dataset, and then you calculate the absolute difference between each data point and the mean or median. The absolute differences are then averaged to give the mean absolute deviation.
MAD is expressed in the same units as the original data and is commonly used in finance, economics, and other fields to measure the variability of financial returns, economic indicators, or other datasets. MAD is a robust measure of dispersion that is less sensitive to extreme values or outliers compared to other measures of dispersion such as standard deviation.
Let's say the times taken by the four people are:
Diane: 2 minutes
Friend 1: 1.5 minutes
Friend 2: 2.5 minutes
Friend 3: 1.75 minutes
The mean of these times is:
Mean = (2 + 1.5 + 2.5 + 1.75) / 4 = 1.9375 minutes
Next, we need to find the absolute deviations of each time from the mean. To do this, we subtract the mean from each time and take the absolute value of the result:
|2 - 1.9375| = 0.0625
|1.5 - 1.9375| = 0.4375
|2.5 - 1.9375| = 0.5625
|1.75 - 1.9375| = 0.1875
Then, we find the mean of these absolute deviations:
MAD = (0.0625 + 0.4375 + 0.5625 + 0.1875) / 4 = 0.3125 minutes
Therefore, the mean absolute deviation of the times taken to complete the obstacle course is 0.3125 minutes.
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