Answers
We have then:
(root (117)) ^ 2 = x ^ 2 + 6 ^ 2
Clearing x we have:
x ^ 2 = (root (117)) ^ 2 - 6 ^ 2
Rewriting:
x = root (117-36)
x = root (81)
x = 9
Answer:
The value of x is given by:
x = 9 cm
Related Questions
Please do not answer unless you are pretty sure. Thanks!
Answers
Population size: 12
Medium: 54
Lowest value: 40
Highest value: 81
First quartile: 43
Third quartile: 76.25
Interquartile range: 33.25
With this information we can infer that the correct option is option 2, since it is the only diagram where the third quartile is greater than 76.
how can you write the expression with a rationalized denominator? √3/√4
Answers
So √3 / √4 would be √3 / 2 so denominator is now rationalized.
Hope this helps.
Kevin rolled two number cubes each numbered 1 to 6.
what is the probability that both number cubes land on 3?
Answers
Juan is spinning a wheel with 4 unequal spaces marked with values of $200, $300, $400, and $600. The probability of landing on $200 is 2/9 . The probability of landing on $300 is 4/9 . The probability of landing on $400 is 2/9. The probability of landing on $600 is 1/9 . The expected value of spinning the wheel once is $, and the expected value of spinning the wheel three times is
Answers
The expected value of spinning the wheel is given by:
E(x)=2/9(200)+4/9(300)+2/9(400)+1/9(600)
E(x)=44 4/9+133 1/3+88 8/9+66 2/3
E(x)=333 1/3
b] The expected value of spinning the wheel thrice will be:
(expected value of spinning once)*(number of spins)
=333 1/3*3
=1000/3*3
=1000
Answer:
333 and 1000
Step-by-step explanation:
What is the area of the region between the graphs of y=x^2 and y=-x from x=0 to x=2?
Answers
_____________
The area between [tex]\( y = x^2 \)[/tex] and [tex]\( y = -x \) from \( x = 0 \) to \( x = 2 \) is \( \frac{14}{3} \)[/tex] square units, found by integrating [tex]\( x^2 + x \)[/tex] from 0 to 2.
Intersection Points: To find the area between [tex]\( y = x^2 \)[/tex] and [tex]\( y = -x \)[/tex] from [tex]\( x = 0 \) to \( x = 2 \)[/tex], first find their intersection points by setting [tex]\( x^2 = -x \)[/tex]. This gives [tex]\( x^2 + x = 0 \)[/tex], which factors to [tex]\( x(x + 1) = 0 \)[/tex], yielding [tex]\( x = 0 \)[/tex] and [tex]\( x = -1 \)[/tex] as the intersection points.
Limits of Integration: We are interested in the area between these curves from [tex]\( x = 0 \) to \( x = 2 \)[/tex]. Since[tex]\( x = -1 \)[/tex] lies outside this interval, we only consider [tex]\( x = 0 \)[/tex].
Integration: The area can be calculated by integrating the difference between the upper curve [tex]\( y = x^2 \)[/tex] and the lower curve [tex]\( y = -x \) from \( x = 0 \) to \( x = 2 \):[/tex]
[tex]\[ \text{Area} = \int_{0}^{2} (x^2 - (-x)) \, dx \][/tex]
Sure, here is the rewritten line:
[tex]\[ \text{The area can be found by integrating} \, x^2 + x \, \text{from} \, x = 0 \, \text{to} \, x = 2: \, \int_{0}^{2} (x^2 + x) \, dx \][/tex]
Integrating term by term:
[tex]\[ = \left[ \frac{x^3}{3} + \frac{x^2}{2} \right]_{0}^{2} \][/tex]
[tex]\[ = \left( \frac{2^3}{3} + \frac{2^2}{2} \right) - \left( \frac{0^3}{3} + \frac{0^2}{2} \right) \][/tex]
[tex]\[ = \left( \frac{8}{3} + 2 \right) - 0 \][/tex]
[tex]\[ = \frac{8}{3} + 2 \][/tex]
[tex]\[ = \frac{14}{3} \][/tex]
Complete question:
What is the area of the region between the graphs of y=x² and y=-x from x=0 to x=2?
Christina goes to the market with $50. She buys one papaya for $20 and spends the rest of the money on bananas. Each banana cost $6. Write an inequality for the number of bananas purchased
Answers
A camera manufacturer spends $2,100 each day for overhead expenses plus $9 per camera for labor and materials. The cameras sell for $14 each. a. How many cameras must the company sell in one day to equal its daily costs? b. If the manufacturer can increase production by 50 cameras per day, what would their daily profit be?
Answers
Here, first we need to find the number of cameras that can be sold, so that total costs are equal to total revenues.
Let the number of cameras that can be sold be "x".
Total revenue = $ 14x
Total costs will be = $ 2100 + $9x
So, the equation that will be formed ⇒
14 x = 2100 + 9x
5x = 2100
x = 420
Thus, in order to make total costs equal to total revenues, 420 cameras are required to be sold.
If instead of 420, 470 cameras are sold, the daily profit will be calculated as under -
Total revenue = $ 14 × 470 cameras = $ 6,580
Total costs = $ 2100 + ( $ 9 × 470 cameras) = $ 6,330
Daily profit = Total revenue - Total costs = $ 6,580 - $ 6,330 = $ 250
Mary has three baking pans. Each pan is 8" × 8" × 3". Which expression will give her the total volume of the pans?
8^2 × 3
8 × 3^2
(8 × 2 × 3) × 3
(8^2 × 3) × 3
Answers
Answer:
D. (8^2 × 3) × 3
Step-by-step explanation:
its d on plato
Assume that the population of the world in 2010 was 6.9 billions and is growing at the rate of 1.1 percent a year. (a) set up a recurrence relation for the population of the world n years after 2010 (b) find an explicit formula for the population of the world n years after 2010. (c) what will the population of the world be in 2030
Answers
a) an=(an-1)(1.1)
b) an=(6.9)(1.1^n-1)
c) 46.419 billion
Answer:
a 1=6.9
a an =
(an-1)(1.1)
b an=
(6.9)
(1.1^n-1)
c
46.419
billion
Step-by-step explanation:
The height of a triangle is increasing at a rate of 2 2 centimeters/minute while the area of the triangle is increasing at a rate of 3.5 3.5 square centimeters per minute. at what rate is the base of the triangle changing when the height is 10 10 centimeters and the area is 80 80 square centimeters?
Answers
A ball is thrown upward from the top of a building. The function below shows the height of the ball in relation to sea level, f(t), in feet, at different times, t, in seconds:
f(t) = −16t2 + 48t + 100
The average rate of change of f(t) from t = 3 seconds to t = 5 seconds is _____ feet per second.
Answers
f(t)=-16t^2+48t+100
the rate of change will be:
f'(t)=-32t+48
thus:
when t=3
f(3)=-32(3)+48=-48
when t=5
f(5)=-32(5)+48=-112
thus the rate of change will be:
[f(5)-f(3)]/(5-3)
=(-112-(-48))/(5-3)
=(-64/2)
=-32 ft/sec
What is the volume of a right circular cylinder with a base diameter of 18yd. And a height of 3yd.
Answers
Answer:
[tex]Volume=254[/tex] to the nearest cubic yard.
Step-by-step explanation:
The volume of a right circular cylinder can be calculated using the formula;
[tex]Volume=\pi r^2h[/tex].
The diameter of the base is given to us. We divide it into two to obtain the radius.
[tex]r=\frac{18}{2}=9yd[/tex] and also the height of the cylinder is [tex]h=3yd[/tex].
We substitute these values into the formula to obtain;
[tex]Volume=9^2\times 3\pi yd^3[/tex]
[tex]Volume=243\pi yd^3[/tex]
[tex]Volume=763.4yd^3[/tex]
Answer:
answer= 254
Step-by-step explanation:
Using a rain gauge, Gerry determined that 1/2 inch of rain fell during 3/4 of an hour. What is the unit rate of rainfall in inches per hour?
Answers
1/2 ÷3/4 =
1/2 ×4/3 = 4/6
4/6 ÷2 = 2/3 is the answer
Final answer:
To calculate the unit rate of rainfall in inches per hour, divide the amount of rainfall (1/2 inch) by the duration (3/4 hour), which gives 2/3 inches per hour.
Explanation:
The student is asking how to find the unit rate of rainfall in inches per hour when given that 1/2 inch of rain fell during 3/4 of an hour. To find the unit rate, divide the total amount of rainfall by the total time to get the amount of rain per one hour.
Step-by-step calculation:
Amount of rainfall: 1/2 inch
Duration of rainfall: 3/4 hour
To find inches per hour, divide the amount of rainfall by the duration:
(1/2 inch) / (3/4 hour) = (1/2) / (3/4) = (1/2) * (4/3) = 4/6 = 2/3 inches per hour.
Therefore, the unit rate of rainfall is 2/3 inches per hour.
Q # 17 please solve the figures
Answers
Angle C is congruent with angle X, angle D is congruent with angle Y, angle A is congruent with angle Z
A triangle has side lengths 4, 7 and 9. What is the measure of the angle across from the longest side?
92 = 42 + 72 − 2g4g7cos(A)
81 = 16 + 49 − 56cos(A)
81 = 9cos(A)
9 = cos(A)
A cannot exist!
Gabe tried to use the law of cosines to find an unknown angle measure in a triangle. His work is shown. What is Gabe’s error?
Gabe reversed the order of the 9 and the 4.
Gabe squared the numbers incorrectly.
Gabe should not have subtracted 56 from
16 + 49.
Gabe incorrectly stated that cos–1(9) is not defined.
Answers
Gabe should not have subtracted 56 from 16+49.
_____
Rather, Gabe should have subtracted 16+49 from 81 to get
16 = -56cos(A)
cos(A) = -16/56 = -2/7
A = arccos(-2/7) ≈ 106.6°
Answer:
Step-by-step explanation:
Given that a triangle has sides 4,7 and 9
A student Gabe tried to use law of cosines to find unknown angle measure
The angle is opposite side 9 because angle across the longest side is given
He used cosine formula for triangles
[tex]a^2=b^2+c^2-2bccosA\\9^2 = 4^2+7^2-2(4)(8) cosA\\81-65 =-56 cosA\\[/tex]
But instead he adjusted -56 with 16 +49 which is wrong
Because -56 has product as cosA it is not like term as other constants
So correct step should be
81 = 65-56 Cos A
Gabe should not have subtracted 56 from
16 + 49.
This is the correct answer
two dice are tossed what is the probability of obtaining a sum greater than 6
Answers
hello can you please help me posted picture of question
Answers
Event A is: {Rolling 1,2 or 3}
Complement of event A will contain all those outcomes in the sample space which are not a part of event A.
So, complement of event A will be: {Rolling a 4,5 or 6}
Thus option A gives the correct answer
Using what you know about angles and triangles, what is the measure of angle 6?
Answers
∠2 = 68 (verticallyopposite)
∠6 = ∠2 + ∠4 (exterior angles = sum of opposite angles)
∠6 = 68 + 90 = 158°
Answer: 158°
Answer:158
Step-by-step explanation:∠6 = 68 + 90 = 158°
Simon has a scale model of the Concorde airplane. The actual length of the Concorde is approximately 200 feet. If the ratio of the actual length in feet to the length of the model in centimeters is 5 : 1, what is the approximate length of Simon's model?
Answers
_________________________________________________________
Note:
_________________________________________________________
[tex] \frac{200 ft }{ (x) cm} = \frac{5}{1} [/tex] ;
Solve for "x" (in "cm" ) ;
→ 5x = 200 * 1 ;
→ 5x = 200 ;
Divide each side of the equation by "5" ;
to isolate "x" on one side of the equation; & to solve for "x" ;
→ 5x / 5 = 200 / 5 ;
to get:
→ x = 40 .
___________________________________________________________
The answer is: " 40 cm " .
___________________________________________________________
Answer:
yur
Step-by-step explanation:
What are the zeros of the polynomial function f(x)=x^2+5x+6
Answers
3*2 = 6
3+2 = 5
x^2 + 5x+6 = (x+3)(x+2) = 0
Set each factor equal to zero.
x+3 = 0 ----> x = -3
x+2 = 0 -----> x = -2
Answer:
There are two zeros at -2 and -3.
A company has a minimum required rate of return of 9% and is considering investing in a project that costs $350,000 and is expected to generate cash inflows of $140,000 at the end of each year for three years. the net present value of this project is
Answers
NPV = - Cost + present value of all cash flows
Cost = $350,000
Present value of all cash flows = C*{[1-(1+r)^-n]/r}
Where C = Yearly cash flows = $140,000, r = discount rate = 9%, n = time of generating cash flows = 3 years.
Therefore,
NPV = -350,000 + 140,000*{[1-(1+0.09)^-3]/0.09} = $4,381.25
Estimate the size of a crowd standing along 1 mile section of parade route that is 10 feet deep on both sides of the street assume that each person occupies 2.5 square feet
A) 21,120
B) 42,240
C) 84,480
D) 168,960
Answers
The correct answer is option B). The size of a crowd standing along 1 mile section of parade route that is 10 feet deep on both sides of the street is 42,240.
To estimate the size of the crowd, we need to calculate the total area occupied by the crowd and then divide by the area occupied by each person.
First, let's calculate the total area available for the crowd on both sides of the street:
The length of the parade route is 1 mile. Since there are 5280 feet in a mile, the length in feet is 5280.
The depth of the crowd on both sides of the street is 10 feet.
Therefore, the total area available for the crowd on both sides is:
Total area = 2 [tex]\times[/tex] (Depth of crowd) [tex]\times[/tex] (Length of parade route)
Total area = 2 [tex]\times[/tex] 10 feet [tex]\times[/tex] 5280 feet
Total area = 105,600 square feet
Next, we need to calculate how many people can fit in this area:
Each person occupies 2.5 square feet.
The number of people that can fit in the total area is:
Number of people = Total area / Area per person
Number of people = 105,600 square feet / 2.5 square feet per person
Number of people = 42,240.
AB is tangent to circle O at B. Find the length of the radius, r, for AB = 5 and AO = 13.
Answers
AO² = AB² + BO²
13² = 5² + r²
169 -25 = r²
r = √144 = 12
The radius (r) is 12.
the radius is twelve
Clabber company has bonds outstanding with a par value of $113,000 and a carrying value of $105,100. if the company calls these bonds at a price of $101,500, the gain or loss on retirement is:
Answers
So, $3600 should be the gain or loss on the retirement.
The first term in a sequence is -2 and the common ratio is 3. What is the sixth term of the sequence?
Answers
The n-th term of a geometric sequence with initial value a and common ratio r is given by:
[tex]a_n=a_1\cdot r^{n-1}\ for\ n\in\mathbb{N^+}[/tex]
We have:
[tex]a_1=-2;\ r=3;\ n=6[/tex]
Substitute:
[tex]a_6=-2\cdot3^{6-1}=-2\cdot3^5=-2\cdot243=-486[/tex]
Answer: The sixth term is equal -486.
Jim picked a card from a standard deck. What is the probability that Jim picked a heart or an ace?
Answers
Answer:
The answer is actually 16/52.
Step-by-step explanation:
There are 13 hearts and 4 aces. However, one of the 4 aces is a heart, so there would only be 3 other aces.
13 hearts + 3 other aces = 16
There are 52 cards in a deck, so the probability would be 16/52.
Paige rides her bike around town. She can ride one half of a mile in 1 30 ith of an hour. If she continues to ride at the same pace, how many miles could she travel in 1 hour?
Answers
We have been given that Paige can ride one half of a mile in 1/30 th of an hour. And we have to found the distance traveled in 1 hour if she continues to ride at the same pace.
Let d be the distance traveled in 1 hour.
In 1/30 th of an hour distance traveled is 0.5 mile
Hence, in 1 hour the distance traveled is given by
[tex]d=\frac{0.3}{1/30} \\ \\ d=0.5\times 30\\ \\ d=15[/tex]
Therefore, she will travel 15 miles.
Solve for x
in the equation x^2-12x+36=90
Answers
(x -6)² = 90 . . . . . the left side is already a perfect square
x -6 = ±√90 . . . . . take the square root
x = 6 ±3√10 . . . . add 6
Answer:
Using the identity rule:
[tex](a-b)^2 = a^2-2ab+b^2[/tex]
Given the equation:
[tex]x^2-12x+36 = 90[/tex]
Rewrite the above equation as:
[tex]x^2-2 \cdot x \cdot 6+6^2 = 90[/tex]
Apply the identity rule:
[tex](x-6)^2 = 90[/tex]
Take square root to both sides we have;
[tex]x-6 = \pm \sqrt{90}[/tex]
Add 6 to both sides we have;
[tex]x = 6\pm \sqrt{90}[/tex]
or
[tex]x = 6 \pm 3\sqrt{10}[/tex]
Therefore, the value of x are:
[tex]6+3\sqrt{10}[/tex] and [tex]6-3\sqrt{10}[/tex]
In 1983, a year-long newspaper subscription cost $12.75. Today, a year-long newspaper subscription costs $28.50. If the CPI is 193, what is the relation of the actual price of a year-long newspaper subscription to the expected price, to the nearest cent? a. The actual price is $14.79 higher than the expected price. b. The actual price is $3.89 higher than the expected price. c. The actual price is $9.20 lower than the expected price. d. The actual price is $11.86 lower than the expected price
Answers
$12.75 * 193/100 = $24.61
The actual price is $28.50 -24.61 = $3.89 more than expected. The appropriate choice is ...
b. The actual price is $3.89 higher than the expected price.
Answer:
Option b - The actual price is $3.89 higher than the expected price.
Step-by-step explanation:
Given : In 1983, a year-long newspaper subscription cost $12.75. Today, a year-long newspaper subscription costs $28.50. If the CPI is 193
To find : What is the relation of the actual price of a year-long newspaper subscription to the expected price, to the nearest cent?
Solution :
CPI is the consumer price index.
The formula of CPI is
[tex]\text{CPI}=\frac{\text{Cost of newspaper subscription in Given Year}}{\text{Cost of newspaper subscription in Base Year}}\times 100[/tex]
We have given CPI = 193
Cost of newspaper subscription in Base Year = $12.75
We have to find cost of newspaper subscription in Given Year
[tex]193=\frac{\text{Cost of newspaper subscription in Given Year}}{12.75}\times 100[/tex]
[tex]\text{Cost of newspaper subscription in Given Year}=\frac{193\times12.75}{100}[/tex]
[tex]\text{Cost of newspaper subscription in Given Year}=\frac{2460.75}{100}[/tex]
[tex]\text{Cost of newspaper subscription in Given Year}=24.61[/tex]
The actual price of newspaper subscription = $28.50
The expected price of newspaper subscription = $24.61
Now, to find how much higher they expected is
$28.50 -$24.61 = $3.89
Therefore, Option b is correct.
The actual price is $3.89 higher than the expected price.
hey can you please help me posted picture of question
Answers
C (t) = 6t - 180
Clearing t we have:
6t = c + 180
t = c / 6 + 180/6
Rewriting:
t (c) = (c + 180) / 6
Answer:
The inverse function for this case is given by:
t (c) = (c + 180) / 6
option A