Given:
[tex]\begin{gathered} D_{is\tan ace\text{ travelled during tail wind}}=889miles \\ T_{\text{ime taken during tail wind}}=3.5hours \\ D_{is\tan ce\text{ travelled during headwind}}=651miles \\ T_{\text{ime taken during headwind}}=3.5hours \end{gathered}[/tex]To Determine: The speed of the jet in still air and the speed of the wind
Represent the speed of the jet in still air and the speed of the wind with unknowns
[tex]\begin{gathered} T_{he\text{ sp}eed\text{ of the jet in still air}}=x \\ T_{he\text{ sp}ed\text{ of the wind}}=y \end{gathered}[/tex]Note that the speed, distance, and time is related by the formula below
[tex]S_{\text{peed}}=\frac{D_{is\tan ce}}{T_{\text{ime}}}[/tex]Calculate the speed during the tailwind and the headwind
[tex]S_{\text{peed during tail wind}}=\frac{889}{3.5}=254milesperhour[/tex][tex]S_{\text{peed during headwind}}=\frac{651}{3.5}=186milesperhour[/tex]Note that during the tailwild, the speed of the wind and the speed of the jet in still air are in the same direction. Also during the headwind, the speed of the wind and the speed of the jet in still air are in opposite direction. Therefore average speed during the tailwind and the headwind would be
[tex]\begin{gathered} equation1\colon x+y=254 \\ equation2\colon x-y=186 \end{gathered}[/tex]Combine the two equations: Add equation 1 and equation 2 to eliminate y as shown below
[tex]\begin{gathered} x+x-y+y=254+186 \\ 2x=440 \\ x=\frac{440}{2} \\ x=220\text{ miles per hour} \end{gathered}[/tex]Substitute x = 220 in equation 1
[tex]\begin{gathered} x+y=254 \\ 220+y=254 \\ y=254-220 \\ y=34\text{ miles per hour} \end{gathered}[/tex]Hence:
The speed of the jet in still air is 220 miles per hour
The speed of the wind is 34 miles per hour
2,047÷41=sloveadd expression
The given expression is,
[tex]\frac{2047}{41}[/tex]On solving, we have,
[tex]\frac{2047}{41}=49\frac{38}{41}=49.93[/tex]Thus, 2,047÷41=49.93.
In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 44 and a standard deviation of 4. Using the empirical rule, what is the approximate percentage of daily phone calls numbering between 36 and 52?
The empirical rule is an approximation that can be used sometimes if we have data in a normal distribution. If we know the mean and standard deviation, we can use the rule to approximate the percentage of the data that is 1, 2, and 3 standard deviations from the mean. The rules is:
In this case, the mean is 44. The receptionist who answered less than 44 phone calls are to the left of the mean, and to the right are the ones who answered more. Since we want to know the percentage of phone calls numbering between 36 and 52, we know that:
[tex]\begin{gathered} 44+4=48 \\ . \\ 48+4=52 \end{gathered}[/tex][tex]\begin{gathered} 44-4=40 \\ . \\ 40-4=36 \end{gathered}[/tex]Thus, the lower bound is two standard deviations from the mean, and the upper bond is also 2 standard deviations from the mean.
Using the chart above, we can see that this corresponds to approximately 95% of the data.
The answer is approximately 95% of the data is numbering between 36 and 52
..Sam works 40 hours in one week and is paid $610. How much does Samearn per hour?
Answer:
Sam earns $15.25 per hour.
Explanation:
Sam works 40 hours in one week, and is paid $610
To know how much Sam earns per hour, we divide the amount earned by the number of hours worked.
This is:
[tex]\frac{610}{40}=15.25[/tex]Therefore, Sam earns $15.25 per hour.
If there are six servings in a 2/3 pound package of peanut which fraction of a pound is in each serving.
We will have the following:
If there are 6 servings in a 2/3 pound package, we will divide the pounds by the number of servings, that is:
[tex]\frac{(\frac{2}{3})}{6}=\frac{(\frac{2}{3})}{(\frac{6}{1})}=\frac{2\cdot1}{3\cdot6}=\frac{2}{18}[/tex][tex]=\frac{1}{9}[/tex]So, each serving has 1/9 of a pound.
***Explanation***
Since we have 6 servings and then the total value of pounds the package represents we will have that the weigth (in pounds) for each serving is given to us by dividing the total weight by the number of servings.
Now, in order to apply the division of a fraction by another fraction we rewrite the integer 6 as a fraction, and we know that 6 / 1 = 6 so, that is the fraction from for this number (At least the less complicated one) and we proceed with the "ear" opeation.
Suzie has cards in numbers 9-21 in a bag. What is the probability she will pull a card lower than 17?
She has cards that go from 9 to 21.
We assume she has one card with each number that goes from 9 to 21:
9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21.
If we want to calculate the probability she pulls a card lower than 17, we have to count how many cards are lower than 17 and then divide this number by the total amount of cards.
NOTE: each card is a possible event. We will calculate the probability as the quotient between the number of successful events (cards lower than 17) and the total possible events (number of cards available).
We have 17-9 = 8 cards that are lower than 17.
The total number is 22-9 = 13 cards (all the cards lower than 22).
Then, we can calculate the probability as:
[tex]P(C<17)=\frac{8}{13}[/tex]Answer: The probabilty she pull a card lower than 17 is P=8/13
Yolanda has a rectangular poster that is 16 cm long and 10 cm wide what is the area of the poster in square meters do not round your answer is sure to include the correct unit in your answer
The area of a rectangle can be calculated as the height times the wide.
But be careful, the problem asks it in square meters! So let's use meters instead of centimeters.
Remember that : 1 m = 100 cm ----> 1 cm = 0.01 m
[tex]\begin{gathered} A=b\cdot h \\ \\ A=0.16\cdot0.10 \end{gathered}[/tex]Doing the multiplication
[tex]A=0.016\text{ m}^2[/tex]Therefore the area of the poster is 0.016 square meters
a new car is purchased for 24800. the value of the car depreciates at 12% per year what is the Y intercept of starting value
EXPLANATION
Let's see the facts:
Purchase Price = $24,800
Depretiation = 12%/year
We should apply the formula for exponential decay wich is expressed as:
A = P(1-r)^t
A= value of the car after t years
t= number of years
P = Initial Value
r= rate of decay in decimal form
We have that A=unknown t=? P=24,800 r=0.12
Replacing terms:
A=24,800(1-0.12)^t
Now, the y-intercept is the value obtained when t=0, so substituting this on the equation give us the following result:
A=24,800(1-0.12)^0 = 24,800(0.88)^0= 24,800*1=24,800
The starting value is $24,800
For the following line, name the slope and y-intercept. Then write the equation of the line in slope-interceptform.Slope= y - intercept = (0,_ ) Equation: y =
Given:
A line that passes the through the points (4, 0) and (0,-3).
Required:
Slope, y-intercept, and the equation of the given line.
Explanation:
As the line passes through the points (4, 0) and (0,-3), the slope is calculated as,
[tex]\begin{gathered} Slope\text{ = }\frac{y_2-y_1}{x_2-\text{ x}_1} \\ Slope\text{ = }\frac{-3\text{ - 0}}{0\text{ - 4}} \\ Slope\text{ = }\frac{-3\text{ }}{-4} \\ Slope\text{ = }\frac{3}{4} \end{gathered}[/tex]The y-intercept of the given line is the point through which the given line passes on the y-axis which is -3. Therefore the intercept of the given line is -3.
The equation of line in slope point form is given as,
[tex]y\text{ = mx + c}[/tex]Where m is the slope and c is the y-intercept. Therefore the equation of the line is given as,
[tex]y\text{ = }\frac{3}{4}x\text{ - 3}[/tex]Answer:
Thus the required equation of line is
[tex]y\text{ }=\text{ }\frac{3}{4}\text{x{\text{ - 3}}}[/tex]The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is a divisor of 8". Find P(A). Outcome Probability 1 0.01 2 0.04 3 0.4 4 0.01 5 0.08 6 0.07 7 0.21 8 0.07 9 0.11
For divisor of 8:
A be the event "the outcome is a divisor of 8".
Then P(A):
[tex]\begin{gathered} P(A)=P(1)+P(2)+P(4)+P(8) \\ P(A)=0.01+0.04+0.01+0.07 \\ P(A)=0.13 \end{gathered}[/tex]During a coffee house's grand opening.350 out of the first 500 customers who visited ordered only one single item while the rest ordered multiple items. Among the 150 customs who left a tip 60 of them ordered multiple items?
We are given a two-way frequency table with some missing joint frequencies.
The frequencies in the total row and column are called "marginal frequencies"
The frequencies in the other rows and columns are called "joint frequencies"
Let us first find the joint frequency "Single Item and Tip"
[tex]\begin{gathered} x+60=150 \\ x=150-60 \\ x=90 \end{gathered}[/tex]So, the joint frequency "Single Item and Tip" is 90 (option B)
Now, let us find the joint frequency "Single Item and No Tip"
[tex]\begin{gathered} 90+x=360 \\ x=360-90 \\ x=270 \end{gathered}[/tex]So, the joint frequency "Single Item and No Tip" is 270 (option D)
Now first we need to find the marginal frequency as below
[tex]\begin{gathered} 360+x=500 \\ x=500-360 \\ x=140 \end{gathered}[/tex]Finally, now we can find the joint frequency "Multiple Items and No Tip"
[tex]\begin{gathered} 60+x=140 \\ x=140-60 \\ x=80 \end{gathered}[/tex]So, the joint frequency "Multiple Items and No Tip" is 80 (option A)
Therefore, the missing joint frequencies are
Option A
Option B
Option D
what is the y- intercept in the following equationy=-4x-5
What is 6 hundred thousand in hundreds
600,000 (Six hundred thousand)
1) If we divide 600,000 by 100 we'll have 6000
So 600,000 is equal to 6000 hundreds.
Consider the following measures shown in the diagram with the circle centered at point A. Determine the arc length of CB.
Answer:
[tex]\frac{4}{3}\pi\; cm[/tex]Explanation:
If an arc of a circle radius, r is subtended by a central angle, θ, then:
[tex]\text{Arc Length}=\frac{\theta}{360\degree}\times2\pi r[/tex]In Circle A:
• The central angle, θ = 40 degrees
,• Radius = 6cm
Therefore, the length of arc CB:
[tex]\begin{gathered} =\frac{40}{360}\times2\times6\times\pi \\ =\frac{4}{3}\pi\; cm \end{gathered}[/tex]The correct choice is C.
Complete the tables using the formula. Then, identify the starting amount and the amount you change by. These are linear, so the table should go up or go down by a constant amount.Y = 5x + 8
Part A
x= 0 y=8
x=1 y=13
x=2 y=18
x=3 y=23
y=4 y=28
x=5 y=33
y=6 y=28
y=7 y=43
Part B
Starting point (y-intercept) = 8
Part C.
slope is 5.
STEP - BY - STEP EXPLANATION
What to find?
• The values of y at x=0,1,2,3,4,5, 6 and 7
,• Slope
,• Y- intercept.
Given:
y=5x + 8
To determine the values of y at each point of x, substitute into the formula given and simplify.
That is;
At x = 0
[tex]\begin{gathered} y=5(0)\text{ +8} \\ y=0+8 \\ y=8 \end{gathered}[/tex]At x = 1
[tex]\begin{gathered} y=5(1)+8 \\ =5+8 \\ =13 \end{gathered}[/tex]At x = 2
[tex]\begin{gathered} y=5(2)+8 \\ =10+8 \\ =18 \end{gathered}[/tex]At x = 3
[tex]\begin{gathered} y=5(3)+8 \\ =15+8 \\ =23 \end{gathered}[/tex]At x = 4
[tex]\begin{gathered} y=5(4)+8 \\ =20+8 \\ =28 \end{gathered}[/tex]At x = 5
[tex]\begin{gathered} y=5(5)+8 \\ =25+8 \\ =33 \end{gathered}[/tex]At x = 6
[tex]\begin{gathered} y=5(6)+8 \\ =30+8 \\ =38 \end{gathered}[/tex]At x=7
[tex]\begin{gathered} y=5(7)+8 \\ =43 \end{gathered}[/tex]Hence,
x= 0 y=8
x=1 y=13
x=2 y=18
x=3 y=23
y=4 y=28
x=5 y=33
y=6 y=28
y=7 y=43
Part B
Starting point( y-intercept).
The y-intercept is the point at which x =0
Hence, from the values above, at x=0, y=8
Hence, the starting point (y-intercept) = 8
Part C
The changes in slope.
The slope is the changes in y-intercept, the y -values kept increasing by 5.
Hence, the slope is 5.
For each of the following pairs of rational numbers, place a greater than symbol, >, a less than symbol, <, or an equality symbol, =, in the square to make the statement true.
I chow you how to solve for (d) and (i) and you could do the rest by yourself:
The best way to solve this operations is convert the numbers to a one form and then compare.
For (d)
[tex]\begin{gathered} \frac{7}{3}=\frac{6+1}{3}=\frac{6}{3}+\frac{1}{3}=2+\frac{1}{3}=2\frac{1}{3}=2.333 \\ \frac{13}{5}=\frac{10+3}{5}=\frac{10}{5}+\frac{3}{5}=2+\frac{3}{5}=2\frac{3}{5}=2.6 \\ So, \\ \frac{7}{3}<\frac{13}{5} \end{gathered}[/tex]Now for (i), take into account that this numbers are negative:
[tex]\begin{gathered} -11.5=-11.5\cdot\frac{4}{4}=-\frac{11.5\cdot4}{4}=-\frac{46}{4} \\ So,\text{ } \\ -\frac{46}{4}<-\frac{31}{4} \end{gathered}[/tex]Note that 46/4 is greater than 31/4, but -46/4 is lower than -31/4.
Also note that in this example I find to equalize the denominator of the numbers adn then you can compare the numerators.
11) -3(1 + 6r) = 14 - r
Distributing over parentheses,
[tex]\begin{gathered} -3\cdot1+(-3)\cdot6r=14-r \\ -3-18r=14-r \end{gathered}[/tex]Adding r at both sides,
[tex]\begin{gathered} -3-18r+r=14-r+r \\ -3-17r=14 \end{gathered}[/tex]Adding 3 at both sides,
[tex]\begin{gathered} -3-17r+3=14+3 \\ -17r=17 \end{gathered}[/tex]Dividing by -17 at both sides,
[tex]\begin{gathered} \frac{-17r}{-17}=\frac{17}{-17} \\ r=-1 \end{gathered}[/tex]Match each solid cone to it’s surface area. Answers are rounded to the nearest square unit
The surface area of a cone is given by the formula below:
[tex]S=\pi r^2+\pi rs[/tex]Where r is the base radius and s is the slant height.
So, calculating the surface area of first cone, we have:
[tex]\begin{gathered} s^2=21^2+6^2\\ \\ s^2=441+36\\ \\ s^2=477\\ \\ s=21.84\\ \\ S=\pi\cdot6^2+\pi\cdot6\cdot21.84\\ \\ S=525 \end{gathered}[/tex]The surface area of the second cone is:
[tex]\begin{gathered} s^2=8^2+12^2\\ \\ s^2=64+144\\ \\ s^2=208\\ \\ s=14.42\\ \\ S=\pi\cdot12^2+\pi\cdot12\cdot14.42\\ \\ S=996 \end{gathered}[/tex]The surface area of the third cone is:
[tex]\begin{gathered} s^2=15^2+8^2\\ \\ s^2=225+64\\ \\ s^2=289\\ \\ s=17\\ \\ S=\pi\cdot8^2+\pi\cdot8\cdot17\\ \\ S=628 \end{gathered}[/tex]And the surface area of the fourth cone is:
[tex]\begin{gathered} s^2=10^2+10^2\\ \\ s^2=100+100\\ \\ s^2=200\\ \\ s=14.14\\ \\ S=\pi\cdot10^2+\pi\cdot10\cdot14.14\\ \\ S=758 \end{gathered}[/tex]A paper is sold for Php60.00, which is 150% of the cost. How much is the store's cost?
The store's cost is php40
Let's call the store Cost = C
This means that this cost is elevated a 150% in order to get the price of php60
In an mathematical expression, this is:
C · 150% = php60
Then, let's convert the percentage to decimal. To do this, we just divide the percentage by 100:
150% ÷ 100 = 1.5
Now we can solve:
[tex]\begin{gathered} C\cdot1.5=60 \\ C=\frac{60}{1.5}=40 \end{gathered}[/tex]Then the store cost is C = php40
Which statement is true?123.466 > 132.4659.07 > 9.00850.1 < 5.013.37 < 3.368
In the given decimal inequality statements we can infer that only
9.07 > 9.008 is true.
The given statements are :
123.466 > 132.465
9.07 > 9.008
50.1 < 5.01
3.37 < 3.368
Let us take each statement and find out if it is true or false.
Statement 1: 123.466 > 132.465
Using the properties of decimals we see that 231<132 hence the statement is false.
Statement 2:
9.07 > 9.008
Here the second digit after decimal are 7 and 0. Since the first two significant digits are same , and 7>0 therefore 9.07>9.008 so it is true.
Statement 3:
50.1 < 5.01
Here 50 > 5 so the statement is false
Statement 4:
3.37 < 3.368
Here the first two significant digits are same. Again the digit in the hundredths place are 7 and 6, as 7>6, hence the statement is false.
to learn more about decimal visit:
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Dilate f (x) = (x+4)(x+2) by x
Given:
[tex]f(x)=(x+4)(x+2)[/tex]Dilate of function is:
[tex]\begin{gathered} f(x)=(x+4)(x+2) \\ =x(x+2)+4(x+2) \\ =x^2+2x+4x+8 \\ =x^2+6x+8 \end{gathered}[/tex]Sondra is going rock climbing. She starts at 12.25 yards above sea level. She ascends 38.381yards before lunch. She then descends 15.25 yards after lunch. What is Sondra's finalheight relative to sea level?
What we need to do is follow up with Sondra.
Starts at 12.15 yd
Ascendes 38.281, therefore:
[tex]12.15+38.5=50.65[/tex]A total 50.65 yd
Then, descends 15.25, therefore:
[tex]50.65-12.25=38.5[/tex]This means that the relative 38.5 - (15.25 - 12.25) = 38.5 - 3 = 35.5, it is means 35 1/2
The answer is 35 1/2
Which expression is equivalent to sin(71(1) cos (72) - cos () sin (77.)?1?O cos (5)O sin (5)COS2012sin
Let:
[tex]\begin{gathered} A=\frac{\pi}{12} \\ B=\frac{7\pi}{12} \end{gathered}[/tex]Using the sine difference identity:
[tex]\begin{gathered} \sin (A)\cos (B)-\cos (A)\sin (B)=\sin (A-B) \\ so\colon \\ \sin (\frac{\pi}{12})\cos (\frac{7\pi}{12})-\cos (\frac{\pi}{12})\sin (\frac{7\pi}{12})=\sin (\frac{\pi}{12}-\frac{7\pi}{12}) \\ \sin (\frac{\pi}{12}-\frac{7\pi}{12})=\sin (-\frac{6\pi}{12}) \\ \sin (-\frac{\pi}{2}) \end{gathered}[/tex]Answer:
[tex]\sin (-\frac{\pi}{2})[/tex]If the number 659, 983 is rounded to the nearest hundred, how many zeros does the rounded number have?The solution is
We will have the following:
*For 569:
For this number we would round to 600, thus the number of zeros the rounded number would be 2.
*For 983:
For this number, we would round to 1000, thus the number of zeros the rounded number would be 3.
Ava solved the compound inequality +7
Tell me if the inequalities are correct
x/4 + 7 < -1 2x - 1 >= 9
x/4 < -1 - 7 2x >= 9 + 1
x/4 < -8 2x >= 10
x < -32 x >= 10/2
x >= 5
The second option is the correct one
In the diagram below the larger angle is four times bigger than the smaller angle find the larger angle
Answer:
Given that,
In the diagram below the larger angle is four times bigger than the smaller angle
To find the larger angle.
Let x be smaller angle.
Then we get,
Larger angle is,
[tex]4x[/tex]Larger angle and smaller angle are a linear pair.
Therefore we get,
[tex]x+4x=180[/tex][tex]5x=180[/tex][tex]x=36\degree[/tex]Larger angle is,
[tex]4x=4\times36=144[/tex]The larger angle is 144 degrees.
Compute the common and natural logarithms using the properties of logarithms and a calculator.Type the correct answer in each box. Round your answers to two decimal places.
(b)
[tex]\log _{}3.26[/tex]Using the calculator to compute the logarithm, we have;
[tex]\begin{gathered} \log \text{ 3.26 = 0.5132} \\ \log \text{ 3.26 = 0.51 (Round to two decimal places)} \end{gathered}[/tex](c)
[tex]\begin{gathered} \log \text{ 10000} \\ =\log _{10}10^4 \\ =4\log _{10}10 \\ =4\times1 \\ \log \text{ 10000}=4.00\text{ (Round to two decimal places)} \end{gathered}[/tex](d)
[tex]\begin{gathered} \ln 22=3.0910 \\ \ln 22=3.09\text{ (Round to two decimal places)} \end{gathered}[/tex]During a snowstorm, Grayson tracked the amount of snow on the ground. When the storm began, there were 4 inches of snow on the ground. For the first 3 hours of the storm, snow fell at a constant rate of 1 inch per hour. The storm then stopped for 5 hours and then started again at a constant rate of 3 inches per hour for the next 2 hours. As soon as the storm stopped again, the sun came out and melted the snow for the next 2 hours at a constant rate of 4 inches per hour. Make a graph showing the inches of snow on the ground over time using the data that Grayson collected.
We can plot all that happened in the next graph:
This is the graph showing the inches of the snow on the ground over time using the data that Grayson collected.
If ABCD is dilated by a factor of 1/2coordinate of d' would be
On a map, the scale shown is1 inch : 5 miles. If a park is75 square miles, what is thearea of the park on the map?The park's area issquarelinches on the map.
We have the relationship between inches and miles is:
1 inch to 5 miles.
The park has an actual area of:
[tex]75mi^2[/tex]Now, to make the conversion to inches, we need to consider that 1 inch represent 5 miles. Thus:
[tex]\begin{gathered} 1in=5mi \\ 1in^2=25mi^2 \end{gathered}[/tex]We squared this amounts, if 1 inch is 5 miles, 1 inch squared will be equal to 5 squared which is 25.
Now we divide 75 miles squared by 25, to know how many inches squared will the park represent on the map:
[tex]\frac{75}{25}=3in^2[/tex]Answer: the area of the park on the map will be 3 inches squared.
Given:• AJKL is an equilateral triangle.• N is the midpoint of JK.• JL 24.What is the length of NL?L24JKNO 12O 8V3O 12V2O 1213
Answer:
12√3
Explanation:
First, we know that JL = 24.
Then, the triangle JKL is equilateral. It means that all the sides are equal, so JK is also equal to 24.
Finally, N is the midpoint of segment JK, so it divides the segment JK into two equal parts. Therefore, JN = 12.
Now, we have a right triangle JLN, where JL = 24 and JN = 12.
Then, we can use the Pythagorean theorem to find the third side of the triangle, so NL is equal to:
[tex]\begin{gathered} NL=\sqrt[]{(JL)^2-(JN)^2} \\ NL=\sqrt[]{24^2-12^2} \end{gathered}[/tex]Because JL is the hypotenuse of the triangle and JN and NL are the legs.
So, solving for NL, we get:
[tex]\begin{gathered} NL=\sqrt[]{576-144} \\ NL=\sqrt[]{432} \\ NL=\sqrt[]{144(3)} \\ NL=\sqrt[]{144}\cdot\sqrt[]{3} \\ NL=12\sqrt[]{3} \end{gathered}[/tex]Therefore, the length of NL is 12√3