Answer:
363 = 11223₄
Step-by-step explanation:
You want 363 written in base 4.
Base conversionWe can convert to base 4 by looking at the remainders from repeated division by 4:
363 ÷ 4 = 90 r 3
90 ÷ 4 = 22 r 2
22 ÷ 4 = 5 r 2
5 ÷ 4 = 1 r 1
1 ÷ 4 = 0 r 1
Writing the remainders in reverse order gives the base-4 number:
363 = 11223₄
a kite string is 50 feet long, and you are able to measure the angle of elevation to be 25 degrees. You are holding the kite from 5 feet above the ground.
Show all your work to find the total height (h) of the kite.
9514 1404 393
Answer:
26.1 ft
Step-by-step explanation:
The height of the kite above your position is the opposite side of a right triangle whose hypotenuse is 50 ft. The relevant trig relation is ...
Sin = Opposite/Hypotenuse
Filling in the known values, we have ...
sin(25°) = height/(50 ft)
height = (50 ft)sin(25°) ≈ 21.1 ft
Added to the height at which you are holding the string, this becomes the total height of the kite.
h = 5 ft + 21.1 ft = 26.1 ft . . . . total height of the kite
HELP ME PLEASE I HAVE NO CLUE
Answer:
tan =opposite divided by adjacent
therefore tan j is 11÷60 = 0.1833
tan-1 0.1833= 10.39
so tan j is 10.39
tan l is 60 ÷11 = 5.4545
tan-1 5. 4545= 79.61
hope it made sense
Divide the polynomials. If there is a remainder, enter the remainder in fraction form. x^4+3x^3-x-2/x+1
The polynomial x⁴ + 3x³ - x - 2 will have a remainder of 1 when divided by x + 1 and the result can be written in the form (x³ + 2x² + 2x - 3) + 1/(x + 1).
How to divide the polynomialUsing the long division method will require us to; divide, multiply, subtract, bring down the next number and repeat the process to end at zero or arrive at a remainder
We shall divide the polynomial x⁴ + 3x³ - x - 2 by x + 1. as follows;
x⁴ divided by x equals x³
x + 1 multiplied by x³ equals x⁴ + x³
subtract x⁴ + x³ from x⁴ + 3x³ - x - 2 will result to 2x³ - x - 2
2x³ divided by x equals 2x²
x + 1 multiplied by 2x² equals 2x³ + 2x²
subtract 2x³ + 2x² from 2x³ - x - 2 will result to 2x² - x - 2
2x² divided by x equals 2x
x + 1 multiplied by 2x equals 2x² + 2x
subtract 2x² + 2x from 2x² - x - 2 will result to -3x - 2
-3x divided by x equals -3
x + 1 multiplied by -3 equals -3x - 3
subtract -3x - 3 from -3x - 2 will result to a remainder of 1.
Therefore, the polynomial x⁴ + 3x³ - x - 2 divided by x + 1 gives a quotient x³ + 2x² + 2x - 3 and a remainder of 1 and can be written as (x³ + 2x² + 2x - 3) + 1/(x + 1).
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What is an equation of the line that passes through the points (6, -7) and (-6,3)?
Answer:
y=-5/6x-2
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(3-(-7))/(-6-6)
m=(3+7)/-12
m=10/-12
simplify
m=-5/6
y-y1=m(x-x1)
y-(-7)=-5/6(x-6)
y+7=-5/6x+30/6
y+7=-5/6x+5
y=-5/6x+5-7
y=-5/6x-2
A new ride being built at an amusement park includes a vertical drop of 71.6 meters. Starting from rest, the ride vertically drops that distance before the track curves forward. If the velocity at the bottom of the drop is 10.0 m/s and the mass of the cart and passengers is 3.5 x 104 kg, how much potential energy was converted into thermal energy (heat)? (2 points)
answers:
2.3 x 107 J
2.6 x 107 J
4.3 x 107 J
6.7 x 107 J
Step-by-step explanation:
2.3 x 107 J is your correct AnswerLast school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification. Freshmen 83 Sophomores 68 Juniors 85 Seniors 64 We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. The calculated value for the test statistic equals a. 6.66. b. 1.66. c. .54. d. .65. Icon Key
Answer:
1.66
Step-by-step explanation:
Using the Chi square statistic (χ²) test :
χ² = Σ(Oi - Ei)² / Ei
Expected, Ei :
Freshmen = 30% * 300 = 90
Sophomore =24% * 300 = 72
Junior = 26% * 300 = 78
Senior = 20% * 300 = 60
Observed, Oi :
Freshmen = 83
Sophomore = 68
Junior = 85
Senior = 64
χ² = ((83 - 90)²/90) + ((68 - 72)²/72) + ((85 - 78)²/78) + (64 - 60)²/60)
χ² = 49/90 + 16/72 + 49/78 + 16/60
χ² = 0.544 + 0.222 + 0.628 + 0.267
χ² = 1.661
The test statistic = 1.66
use partial quotients to solve
5,140÷9=
Answer: 571.11111...(Fraction: 9/28)
Step-by-step explanation:
5,140÷9 = 571.11111...
Keenan is buying tires. Keenan has to spend 2 dollars for each tire purchased
Answer:
what's the question? I don't know
50 POINTSSS!!!!!! PLS HURRRYYYYY!!!!!!! A set of data includes 98 data points ranging from 0 – 160. If the data is split into classes with a range of 10 (1 – 10, 11 – 20, etc), and there are no values that fall in the class 81 – 90, what can you say about the data?
1 The mean of the data will not be between 81 – 90.
2 All the data lies below 80.
3 The relative frequency of the class 81 – 90 is 0.
4 The median could be in the range 81 – 90
Answer:
3
Step-by-step explanation:
Customary American Units of Capacity
1 cup = 8 ounces
1 pint = 2 cups or 16 ounces
1 quart = 2 pints, 4 cups, or 32 ounces
1 gallon = 4 quarts, 8 pints, 16 cups, or 128 ounces
5 quarts 4 pints =____ pints
Answer:
14
Step-by-step explanation:
5 quarts = 10 pints
10 pints + 4 pints = 14 pints
The average teaching salary in Georgia is $48,553 per year. The school districts in the metro Atlanta area boast that they pay more. A company that is running a career fair decides to take a random sample of 228 teachers from the metro Atlanta area and record their salaries. The sample mean is $49,021, with a standard deviation of $3,127.
Required:
Do the data provide statistically significant evidence at the 0.06 kevel that the average teaching stay in the metro Atlanta area is greater than the state average?
Answer:
The p-value of the test is 0.0119 < 0.06, which means that the data provides statistically significant evidence at the 0.06 level that the average teaching stay in the metro Atlanta area is greater than the state average.
Step-by-step explanation:
The average teaching salary in Georgia is $48,553 per year. The school districts in the metro Atlanta area boast that they pay more.
At the null hypothesis, we test if they pay the average, that is:
[tex]H_0: \mu = 48553[/tex]
At the alternate hypothesis, we test if they pay more, that is:
[tex]H_1: \mu > 48553[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
48553 is tested at the null hypothesis:
This means that [tex]\mu = 48553[/tex]
Sample of 228 teachers from the metro Atlanta area and record their salaries. The sample mean is $49,021, with a standard deviation of $3,127.
This means that [tex]n = 228, X = 49021, \sigma = 3127[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{49021 - 48553}{\frac{3127}{\sqrt{228}}}[/tex]
[tex]z = 2.26[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample mean above 49021, which is 1 subtracted by the p-value of z = 2.26.
Looking at the z-table, z = 2.26 has a p-value of 0.9881
1 - 0.9881 = 0.0119
The p-value of the test is 0.0119 < 0.06, which means that the data provides statistically significant evidence at the 0.06 level that the average teaching stay in the metro Atlanta area is greater than the state average.
Answer:
it's D
Step-by-step explanation:
Joe earned 2,100$.He spent 1/5 on rent and 1/3 on food.How much money did he have left
Answer:
$980
Step-by-step explanation:
Step 1: Find [tex]\frac{1}{5}[/tex] of 2100 = 420
[tex]\frac{1}{5}\times \:2100[/tex]Convert 2100 to a fraction: [tex]\:2100=\frac{2100}{1}[/tex][tex]=\frac{1}{5}\times \frac{2100}{1}[/tex]Cross Divide[tex]2100 \div 5 = 420[/tex]Step 2: Find [tex]\frac{1}{3}[/tex] of 2100 = 700
[tex]\frac{1}{3}\times \:2100[/tex]Convert 2100 to a fraction: [tex]\:2100=\frac{2100}{1}[/tex][tex]=\frac{1}{3}\times \frac{2100}{1}[/tex]Cross Divide[tex]2100 \div 3 = 700[/tex]Step 3: Add both results together
[tex]420 + 700 = 1120[/tex]
Step 4: Subtract the result from how much joe earns ($2,100)
[tex]2100 - 1120 = 980[/tex]
Joe has $980 left
If Joe earned 2,100$ and He spent 1/5 on rent and 1/3 on food, Joe had $980 left after paying for rent and food.
Joe earned $2,100 and spent 1/5 of it on rent and 1/3 on food. To calculate the amount he spent on rent, we need to find 1/5 of $2,100, which is
(1/5) * $2,100 = $420.
Similarly, the amount he spent on food is found by calculating 1/3 of $2,100, which is (1/3) * $2,100 = $700.
To determine how much money Joe had left, we subtract the total amount he spent from his earnings. Adding the amounts spent on rent and food, we get $420 + $700 = $1,120.
To find the money Joe had left, we subtract the total spent from his earnings: $2,100 - $1,120 = $980.
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A large ice cream cone can hold 143.56 cm of ice cream. The cone is 15 cm tall. What is the radius of the base of the cone? Be sure your answer is in the proper units. Round your answer to the nearest hundredth.
Answer:
r = 3.02 cm
Step-by-step explanation:
V cone = πr²h/3
r = √(3V/πh)
r = √(3(143.56)/π(15))
r = 3.0231297
what is 2/9s of 630
Answer: its 18.27
Step-by-step explanation:
Answer:
140
Step-by-step explanation:
A rectangular prism is shown below. What is the volume of the prism?
1/2yd
1/4yd
5/6yd
Answer:
Option B, 5/48 yd³
Step-by-step explanation:
[tex] \frac{5}{6} \times \frac{1}{4} \times \frac{1}{2} [/tex]
[tex] = \frac{5}{4} [/tex]
Audrey does babysitting on the weekends and receives $15 for 6 hours. At this rate, how much will she get for 8 hours?
Answer:
She makes 2.50 $ a hour and she will make 20 $ at 8 hours
Pls help! Step by step:)
Answer:
x = 15
Step-by-step explanation:
using Pythagoras' identity in the right triangle.
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
x² = 9² + 12² = 81 + 144 = 225 ( take square root of both sides )
x = [tex]\sqrt{225}[/tex] = 15
Answer:
x = 15
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
From inspection of the given right triangle:
a = 9b = 12c = xSubstitute the given values into Pythagoras Theorem and solve for x:
[tex]\implies 9^2+12^2=x^2[/tex]
[tex]\implies 81+144=x^2[/tex]
[tex]\implies 225=x^2[/tex]
[tex]\implies \sqrt{x^2}=\sqrt{225}[/tex]
[tex]\implies x=15[/tex]
help me plss about seasons and stuff
a wall is 500sq. feet a gallon of paint covers 160sq feet. what is an appropriate conversion factor to help determine how many gallons will be needed to paint the wall
Answer:
Given:
-> Area of the wall: 500sq. feet
-> 1 gallon of paint covers 160sq. feet of area
-> By unitary method:
-> 1 ft. square of wall requires 1/160 gallon of paint
Thus,
-> 500 ft. square of wall will require = 500 x 1/160 gallons of paint
= 3.0125 gallons
Hope it helps :)
Though my answer may be wrong :(
Have a great day!
Rhombus LMNO is shown with its diagonals.
Rhombus L M N O is shown. Diagonals are drawn from point M to point O and from point L to point N and intersect at point P. All sides are congruent.
The length of LN is 28 centimeters. What is the length of LP?
7 cm
9 cm
14 cm
21 cm
Answer:
14 cm
Step-by-step explanation:
The length of the line segment, LP is; 14 cm
Diagonals of a RhombusFrom the task content, it follows that the diagonal LN of the Rhombus has length, 28 centimetres.
However, from the task content also, the point P is the point of intersection of the two diagonals.
On this note, it follows that P is the midpoint of line LN and the length of line LP is therefore;
LP = 28/2 = 14 cm.Read more on Diagonals of a Rhombus;
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Goran invested his savings in two investment funds. The amount he invested in Fund A was 7000 less than the amount he invested in Fund B. Fund A returned a 4% profit and Fund B returned a 2% profit. How much did he invest in Fund B, if the total profit from the two funds together was 500?
If Goran invested his savings in two investment funds. The amount that Goran invest in Fund B, if the total profit from the two funds together was 500?
How to find the amount invested?Amount Invested in Fund A = x
Amount invested in Fund B = x+7000
Profit from fund A = 0.04x
Profit from fund B = 0.02(x+7000)
0.04x +0.02(x+7000) = 500
0.04 +0.02x + 140 =500
Combine like terms
0.06 x =360
Divide both side by 0.06x
x = 360 /0.06
x = 6,000
Amount Invested in Fund A = x =6,000
Amount invested in Fund B = x+7000
Amount invested in Fund B = 6,000 + 7,000
Amount invested in Fund B = 13,000
Therefore the amount invested in Fund A 6,000 and the Fund B is 13,000.
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Please help answer question
Answer: x = 9
Step-by-step explanation: To find the value of x, we must understand a few things:
- whatever is in lines like | 2x + 4 | means it's the absolute value or positive value of the number.
Now, with that out of the way, I have one more thing to explain.
- whenever trying to find the value of a variable, you need to do inverse operations, so the opposite of adding is subtracting, and the opposite of multiplication is division. Now, let's solve:
22 - 4 = ?
? = 18
18 / 2 = ?
?(x) = 9
Therefore, x = 9
We can check our answer by doing:
| 2(9) + 4 | = 22
2 x 9 = 18
18 + 4 = 22
22 = 22
So, both answers add up, so x = 9
I hope this helps!
Latonya earns a gross annual salary of 61,870. If she is paid weekly, how much is her weekly gross paycheck?
A) 5,155.83
B) 2,577.92
C) 1 ,189.81
D) 1 ,237.40
Answer: C
Step-by-step explanation: 52 weeks in a year. 61870/52 is 1,189.81.
Does perpendicular lines have something same to intersecting lines
Answer:
They are similar in a way. Perpendicular lines can intersect, but they must make a 90 degree angle to be prerpendicular lines. A cross is an example of this.
Step-by-step explanation:
Find the profit-maximizing price.
80
For a monopolist's product, the demand equation is p = 22 - 2q and the average-cost function is c=2+
q
The profit-maximizing price is $
Answer: [tex]\$11.5[/tex]
Step-by-step explanation:
Given
Demand function is [tex]p=22-2q[/tex]
The average cost function is [tex]c=2+q[/tex]
Total revenue is the product of demand and the price per unit.
[tex]r=\left(22-2q\right)q[/tex]
Profit is given by the difference of the total revenue and the cost
[tex]\Rightarrow P=r-c\\\Rightarrow P=22q-2q^2-2-q\\\Rightarrow P=-2q^2+21q-2[/tex]
Find the derivative of profit to get the maximum profit
[tex]\Rightarrow P'=-4q+21\\\text{Put the derivative equal to 0 to get the maximum profit}\\\\\Rightarrow q=\dfrac{21}{4}[/tex]
Put q in the equation of demand to get the price
[tex]\Rightarrow p=22-2\times \dfrac{21}{4}\\\\\Rightarrow p=22-10.5\\\Rightarrow p=\$11.5[/tex]
Edet took sixth at the end of term test and each test was marked out of 80. If his marks were 48, 52, 46, 46, 44 and 52. What percentage of the total marks did he get?
The percentage of the total marks that Edet gets is 60%
How to calculate the percentage?The percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.
In this situation, the score of Edet will be:
= 48 + 52 + 46 + 46 + 44 + 52
= 288
Total score = 80 × 6
= 480
The percentage will be:
= 288 / 480 × 100
= 60%
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A triangular prism has a height of 6 meters and a triangular base with the following dimensions. What is the value of B ? 54 m 2 48 m 2 96 m 2 30 m 2
Answer:
96m
Step-by-step explanation:
Answer:
The correct answer is 48 m.
Step-by-step explanation:
To find our answer we will first multiply the base times height. 16 is the base and 6 is the height. Therefore, 16 x 6 = 96. Now we are going to multiply 1/2 or 0.5 by 96 and we get 48m.
I also had a quiz on this and I got it correct after I checked my work. Have a good one mate
Find the length of the third side. If necessary, round to the nearest
tenth.
Answer:
7.5
Step-by-step explanation:
Using pythagoras theorem
Sqrt(9^2-5^2)=7.483
WHAT DO I PUT NO LINKS WILL BE REPORTED!! JUST GIVE ME THE NUMBERS AS A RATIO
Answer:
33
Step-by-step explanation:
48 - 15 = 33
Answer:
33??
Step-by-step explanation:
Find the measure of the angle.
The angle turns through
1/10
of the circle.
What measure is the angle?
Answer:
radian
Step-by-step explanation:
1/10 circle or degree The SI derived unit for angle is the radian. 1 radian is equal to 1.591549430919 or 1/10 circle, or 57.295779513082 degree.
36 deg
1/10 of a circle is equal to 36 deg.