Answer:
The value of x^3 + 1/x^3 is 47/x + 1/x^3 - 1/x^5
Step-by-step explanation:
x^4 + 1/x^4 = 47
x^4 = 47 - 1/x^4
x^3 + 1/x^3 = 1/x(x^4 + 1/x^2)
x^4 = 47 - 1/x^4
x^3 + 1/x^3 = 1/x(47 - 1/x^4 + 1/x^2) = 47/x - 1/x^5 + 1/x^3 = 47/x + 1/x^3 - 1/x^5
Mai deposited $4000 into an account with 4.8% interest, compounded quarterly. Assuming that no withdrawals are made, how much will she have in the
account after 7 years?
Do not round any intermediate computations, and round your answer to the nearest cent.
Answer:
5,586.17
Step-by-step explanation:
A = $ 5,586.17
A = P + I where
P (principal) = $ 4,000.00
I (interest) = $ 1,586.17
Compound Interest Equation
A = P(1 + r/n)^nt
Where:
A = Accrued Amount (principal + interest)
P = Principal Amount
I = Interest Amount
R = Annual Nominal Interest Rate in percent
r = Annual Nominal Interest Rate as a decimal
r = R/100
t = Time Involved in years, 0.5 years is calculated as 6 months, etc.
n = number of compounding periods per unit t; at the END of each period
1. The mean of the data set{9,5,y,2,x} is twice the data set {8,x,4,1,3}. What is (y-x) squared.
2. How many alcohol must be added to480 grams of hand sanitizer that is 24% alcohol to make it a hand sanitizer that is 40% alcohol?
Answer:
1. (y - x)² = 256
2. 128g needed to be added
Step-by-step explanation:
1.
9 + 5 + 2 + y + x = 2(8 + 4 + 1 + 3 + x)
16 + y + x = 32 + 2x
y - x = 16
∴ (y - x)² = 256
2.
x = mass of alcohol to add
480 × 0.24 = 115.2 ← current mass of alcohol
0.4(480 + x) = 115.2 + x (×5)
2(480 + x) = 576 + 5x
960 + 2x = 576 + 5x
3x = 384
x = 128g
Help asap giving branlist!!!
Answer:
B
Step-by-step explanation:
Let's arrange it into slope-intercept form.
2x - y = 4
y = 2x - 4
We are looking for a line with slope of 2 and y-intercept -4. This line is Line B.
A fluctuating electric current II may be considered a uniformly distributed random variable over the interval (9, 11)(9,11). If this current flows through a 2-ohm resistor, find the probability density function of the power P = 2I^2P=2I 2 .
Answer:
Step-by-step explanation:
A fluctuating electric current II may be considered a uniformly distributed random variable over the interval (9, 11)
[tex]p_1=\{^{\frac{1}{2}:9\leq i\leq 11}_{0:otherwise[/tex]
Now define
[tex]p = 2I^2[/tex]
[tex]\Rightarrow I^2=(\frac{p}{2} )\\\\\Rightarrow I=(\frac{p}{2} )^{\frac{1}{2} }\\\\\Rightarrow h^{-1}(p)=(\frac{p}{2} )^{\frac{1}{2}}[/tex]
[tex]\frac{dh^{-1}}{dp} =\frac{d[h^{-1}(p)]}{dp} \\\\=\frac{d(p/2)^{\frac{1}{2} }}{dp}[/tex]
[tex]=\frac{1}{2} \times \frac{1}{2} (\frac{p}{2} )^{{\frac{1}{2}-1} }\\\\=\frac{1}{4}(\frac{p}{2} )^{{\frac{1}{2}-1} }\\\\=\frac{1}{2}(\frac{2}{p} )^{{\frac{1}{2}} }[/tex]
using the transformation method, we get
[tex]f_p(p)=f_1(h^{-1}(p))|\frac{d[h^{-1}(p)]}{dp} |\\\\=\frac{1}{2} \times \frac{1}{4} (\frac{2}{p} )^{\frac{1}{2} }\\\\=\frac{1}{8} (\frac{2}{p} )^{\frac{1}{2} }[/tex]
[tex]f_p(p)=\{^{\frac{1}{8} (\frac{2}{p} )^{\frac{1}{2} },162\leqp\leq 242} }_{0,otherwise}[/tex]
A(x) = -0.015x^3+1.05xA ( x ) = − 0.015 x 3 + 1.05 x gives the alcohol level in an average person's blood x hrs after drinking 8 oz of 100-proof whiskey. If the level exceeds 1.5 units, a person is legally drunk.
Would an average person be legally drunk after 4 hours?
Answer:
Yes
Step-by-step explanation:
the function that gives the alcohol level is:
[tex]A ( x ) = - 0.015 x^3 + 1.05 x[/tex]
where x is the number of hours.
we need to know if after 4 hours an average person is legally drunk, thus:
[tex]x=4[/tex]
and we substitute this in the function:
[tex]A ( 4 ) = - 0.015 (4)^ 3 + 1.05(4)[/tex]
solving these operations we obtain:
[tex]A(4)=-0.015(64)+4.2\\A(4)=-0.96+4.2[/tex]
[tex]A(4)=3.24[/tex]
the alcohol level after 4 hours is 3.24.
Since a person is considered to be legally drunk if the level exceeds 1.5, and we obtained 3.24 which is greater than 1.5, a person who has been drinking for 4 hours under the conditions indicated by the problem would be considered legally drunk.
You are writing music for a movie and you have to synchronize the music to the amount of frames per click in it. It's a battle scene so you want fast, energetic and exciting music. You choose a Presto tempo marking of 200 beats per minute. How many picture frames are there per each tempo click? (Round to the nearest whole number and write only the number.)
Answer: 7.2 frames per bit.
Step-by-step explanation:
Our teempo is 200 bpm.
in one minute we have 60 seconds, so here we have:
200b/60s = 3.33 bits per second.
For movies, the standar is 24 frames per second
now, we can take the quotient between the frames per second and the bits per second and get the frames per bit.
24fps/3.33bps = 7.2 frames per bit.
WILL GIVE BRAINLIEST! HURRY
Answer:
4
Step-by-step explanation:
2(6x+4)-6+2x=3(4x+3)+1
=14x+2=12x+10
=14x+2-2=12x+10-2
=14x=12x+8
=14x-12x=12x+8-12x
=2x=8
=2x/2=8/2
x=4
Find the circumference of each circle, use 3.14 for . Include units and round to the nearest tenth. Show work
7. The circumference of a circle is 34.54 cm. What is the diameter and radius of the circle? (Show work)
8. What is the circumference of a circle in terms of , if it has a radius of 3.5 in?
(in terms of means do not substitute 3.14 for pi, leave the symbol in the final answer)
Answer:
Answer:-
a) The circumference of the circle C = 21.98 m
b) The circumference of the circle C = 37.68 ft
c) The circumference of the circle C = 40.82 km
d) The radius of the circle = r = 11 c.m
The Diameter of the circle 'd' = 2(r) = 2(11) =22 c.m
e) The circumference of the circle = 21.98 inches
Step-by-step explanation:
a) In First diagram
Given radius of the circle 'r' = 7.1 m
The circumference of the circle C = 2πr
C = 2 (3.14) (7.1)
C = 21.98 m
The circumference of the circle C = 21.98 m
b) In second diagram
Given diameter of the circle 'd' = 12 ft
The circumference of the circle C = 2πr
C = π(2 r)
Diameter = 2 X radius
d = 2 r
The circumference of the circle C = πd
C = 3.14 ×12
The circumference of the circle C = 37.68 ft
c)
Given diameter of the circle 'd' = 13 km
The circumference of the circle C = 2πr
C = π(2 r)
Diameter = 2 X radius
d = 2 r
The circumference of the circle C = πd
C = 3.14 ×13
The circumference of the circle C = 40.82 km
7) The circumference of the circle C = 2πr
Given The circumference of a circle is 34.54 cm
Now 2πr = 34.54
2(3.14) r = 34.54
[tex]r = \frac{34.54}{3.14} = 11[/tex]
The radius of the circle = r = 11 c.m
The Diameter of the circle 'd' = 2(r) = 2(11) =22 c.m
8) Given radius of the circle 'r' = 3.5 inches
The circumference of the circle C = 2πr
C = 2 (3.14) (3.5)
C = 21.98
The circumference of the circle = 21.98 inches
What is the y-intercept of a line that has a slope of -3 and passes through point (0, -7)?
Answer:
Step-by-step explanation:
line equation: y=mx + C
substitute given values
-7 = -3*0 + C
C=y= -7 ANS
Are You Ready for More?: Two raised to the 12th power is equal to 4,096. How many other
whole numbers can you raise to a power and get 4,096? Explain or show your reasoning.
(1 Point)
2^12 = 4096
Answer:
4, 8, 16,64 and 4096.
Step-by-step explanation:
We are already given: [tex]4096=2^{12}[/tex]
To determine other whole numbers that can be raised to a power to obtain 4096, we apply the product rule of indices.
Product Rule of Indices: [tex]a^{xy}=(a^x)^y[/tex]
Now 12 can be factored in the following ways where one of the terms must be a perfect square:
12=2 X 612 =6 X 212 =3 X 412 =4 X 312=1 X 12[tex]2^{12}=(2^2)^6=4^6\\\\2^{12}=(2^6)^2=64^2\\\\2^{12}=(2^4)^3=16^3\\\\2^{12}=(2^3)^4=(8^2)^2=8^{2*2}=8^4\\\\2^{12}=(2^{12})^1=4096^1 $(This is the trivial case)[/tex]
Therefore, the other whole numbers that can be raised tp a power to obtain 4096 are: 4, 8, 16, 64 and 4096.
5. (03.02 MC)
If f(x) = 2х2 - 30, find f(4). (1 point)
НА
Мен
ка
ООО
Амер
-14
2
o17
Answer:
f(4) =2
Step-by-step explanation:
f(x) = 2х^2 - 30,
Let x=4
f(4) = 2 (4)^2 -30
= 2*16 -30
=32-30
= 2
1. O perímetro de um quadrado é 20 cm. Determine sua diagonal. 1 ponto a) 2 √5 cm b) 20√2 cm c) 5√2 cm d) 2√10 cm
Answer:
c) 5√2 cm
Step-by-step explanation:
A square with side length l has a perimeter given by the following equation:
P = 4l.
In this question:
P = 20
So the side length is:
4l = 20
l = 20/4
l = 5
Diagonal
The diagonal forms a right triangle with two sides, in which the diagonal is the hypothenuse. Applying the pytagoras theorem.
[tex]d^{2} = l^{2} + l^{2}[/tex]
[tex]d^{2} = 5^{2} + 5^{2}[/tex]
[tex]d^{2} = 50[/tex]
[tex]d = \pm \sqrt{50}[/tex]
Lenght is a positive meausre, so
[tex]d = \sqrt{50}[/tex]
[tex]d = \sqrt{2 \times 25}[/tex]
[tex]d = \sqrt{2} \times \sqrt{25}[/tex]
[tex]d = 5\sqrt{2}[/tex]
So the correct answer is:
c) 5√2 cm
4. Dean Pelton wants to perform calculations to impress the accreditation consultants, but upon asking for information about GPAs at Greendale Community College, Chang only tells Pelton that the GPAs are distributed with a probability density function f(x) = D(2 + e −x ), 2 ≤ x ≤ 4 where D was some unknown "Duncan" constant. How many student records have to be retrieved so that the probability that the average GPA is less than 2.3 is less than 4 percent?
Answer:
the minimum records to be retrieved by using Chebysher - one sided inequality is 17.
Step-by-step explanation:
Let assume that n should represent the number of the students
SO, [tex]\bar x[/tex] can now be the sample mean of number of students in GPA's
To obtain n such that [tex]P( \bar x \leq 2.3 ) \leq .04[/tex]
⇒ [tex]P( \bar x \geq 2.3 ) \geq .96[/tex]
However ;
[tex]E(x) = \int\limits^4_2 Dx (2+e^{-x} ) 4x = D \\ \\ = D(e^{-x} (e^xx^2 - x-1 ) ) ^D_2 = 12.314 D[/tex]
[tex]E(x^2) = D\int\limits^4_2 (2+e^{-x})dx \\ \\ = \dfrac{D}{3}[e^{-4} (2e^x x^3 -3x^2 -6x -6)]^4__2}}= 38.21 \ D[/tex]
Similarly;
[tex]D\int\limits^4_2(2+ e^{-x}) dx = 1[/tex]
⇒ [tex]D*(2x-e^{-x} ) |^4_2 = 1[/tex]
⇒ [tex]D*4.117 = 1[/tex]
⇒ [tex]D= \dfrac{1}{4.117}[/tex]
[tex]\mu = E(x) = 2.991013 ; \\ \\ E(x^2) = 9.28103[/tex]
∴ [tex]Var (x) = E(x^2) - E^2(x) \\ \\ = .3348711[/tex]
Now; [tex]P(\bar \geq 2.3) = P( \bar x - 2.991013 \geq 2.3 - 2.991013) \\ \\ = P( \omega \geq .691013) \ \ \ \ \ \ \ \ \ \ (x = E(\bar x ) - \mu)[/tex]
Using Chebysher one sided inequality ; we have:
[tex]P(\omega \geq -.691013) \geq \dfrac{(.691013)^2}{Var ( \omega) +(.691013)^2}[/tex]
So; [tex](\omega = \bar x - \mu)[/tex]
⇒ [tex]E(\omega ) = 0 \\ \\ Var (\omega ) = \dfrac{Var (x_i)}{n}[/tex]
∴ [tex]P(\omega \geq .691013) \geq \dfrac{(.691013)^2}{\frac{.3348711}{n}+(691013)^2}[/tex]
To determine n; such that ;
[tex]\dfrac{(.691013)^2}{\frac{.3348711}{n}+(691013)^2} \geq 0.96 \\ \\ \\ (.691013)^2(1-.96) \geq \dfrac{-3348711*.96}{n}[/tex]
⇒ [tex]n \geq \dfrac{.3348711*.96}{.04*(.691013)^2}[/tex]
[tex]n \geq 16.83125[/tex]
Thus; we can conclude that; the minimum records to be retrieved by using Chebysher - one sided inequality is 17.
the average mark of candidates in an aptitude test was 138.5 with a standard deviation of 10.6. three scores extracted from the test are 178,122,100.what is the average of the extracted scores that are extreme value
Answer:
The average of the extracted scores = 133.33
Step-by-step explanation:
Given data the average mark of candidates in an aptitude test was 138.5 with a standard deviation of 10.6
mean of the aptitude test = 138.5
Standard deviation of the aptitude test = 10.6
Given three scores extracted from the test are 178,122,100
The average of the extracted scores = ∑x / n
The average of the extracted scores
= [tex]\frac{178 +122 +100}{3}[/tex]
= 133.33
Final answer:-
The average of the extracted scores = 133.33
The sum of one and the product of 4 and a number x
Answer:
1 + 4x
Step-by-step explanation:
Let's break this down.
"The sum of one" means that something is being added to the number one:
1 +
"and" whatever comes after the word 'and' will be added to the number one
"the product of 4 and a number x" this means that the number four and the variable x are being multiplied:
4x
Put it together:
1 + 4x
Therefore, the expression is 1 + 4x.
What is the answer to 3ab + 3ac
Answer: 3ab + 3ac
Step-by-step explanation: Although the terms in this problem look like one another, there are no like terms.
Therefore, this problem cannot be simplified.
So the answer is the same as the question.
A foundry has been commissioned to make souvenir coins. The coins are to be made from an alloy that is 40% silver. The foundry has on hand two alloys, one with 50% silver content and one with a 25% silver content. How many kilograms of each alloy should be used to make 10 kilograms of the 40% silver alloy?
Answer:
the amount of 50% silver alloy is 6 kilograms and the amount of 25% silver alloy is (10-6)= 4 kilograms.
Step-by-step explanation:
Suppose, the weight of the alloy with 50% silver content is x kilograms.
As, the weight of the mixed alloy should be 10 kilograms, so the weight of the alloy with 25% silver content will be: kilograms
The percentage of silver content in the mixed alloy is 40%. So the equation will be calculated as
[tex]0.5x+0.25(10-x)=0.4\times10\\0.5x+2.5-0.25x=4\\0.25x=1.5\\\Rightarrow x=\frac{1.5}{0.25} = 6[/tex]
So, the amount of 50% silver alloy is 6 kilograms and the amount of 25% silver alloy is (10-6)= 4 kilograms.
Please answer this correctly
Answer:
698 cm²
Step-by-step explanation:
The volume is given by ...
V = LWH
Filling in the given values, we have ...
1020 = (17)(5)y . . . . . . . using L=17, W=5, H=y
y = 1020/(17·5) = 12
The surface area is given by ...
A = 2(LW +H(L+W))
A = 2(17·5 +12(17+5)) = 2(85 +264) . . . . . . . using L=17, W=5, H=y=12
A = 698 . . . . square centimeters
if a-2= (2^2/3+2^1/3) find a^3-6a^2+12a-14
Answer:
Step-by-step explanation:
7. 1, for r = 0 - 1, for r = 1 Hence, determine alo. Using characteristic root ... find the solution of the recurrence relation y, + 9 y, 2 = 6y, 1, subjected to the ... Solve a, -5a, 1 + 6a, 2 = 0 , given initial conditions ao = 2 and a1 = 5. ... Solve the recurrence relation a, – 7a, 1 + 16a, 2 – 12a, 3 = 0 for n > 3 with ... 2"; 3. a = (2)” – n.
Answer:
2
Step-by-step explanation:
I solved in the picture
Hope this helps ^-^
A humanities professor assigns letter grades on a test according to the following scheme. A: Top 12% of scores B: Scores below the top 12% and above the bottom 61% C: Scores below the top 39% and above the bottom 21% D: Scores below the top 79% and above the bottom 6% F: Bottom 6% of scores Scores on the test are normally distributed with a mean of 67.7 and a standard deviation of 7.8. Find the minimum score required for an A grade. Round your answer to the nearest whole number, if necessary.
Answer:
The minimum score required for an A grade is 77.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 67.7, \sigma = 7.8[/tex]
Find the minimum score required for an A grade.
Top 12% of scores get an A.
100-12 = 88th percentile.
The 88th percentile of scores is the minimum required for an A grade. This score is X when Z has a pvalue of 0.88. So X when Z = 1.175.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.175 = \frac{X - 67.7}{7.8}[/tex]
[tex]X - 67.7 = 7.8*1.175[/tex]
[tex]X = 76.865[/tex]
Rounding to the nearest whole number:
The minimum score required for an A grade is 77.
Company A makes a large shipment to Company B. Company B can reject the shipment if they can conclude that the proportion of defective items in the shipment is larger than 0.1. In a sample of 400 items from the shipment, Company B finds that 59 are defective. Conduct the appropriate hypothesis test for Company B using a 0.05 level of significance.
Answer:
[tex]z=\frac{0.1475-0.1}{\sqrt{\frac{0.1(1-0.1)}{400}}}=3.17[/tex]
The p value for this case would be given by:
[tex]p_v =P(z>3.17)=0.00076[/tex]
For this case the p value is lower than the significance level so then we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 0.1 and then Company B can reject the shipment
Step-by-step explanation:
Information provided
n=400 represent the random sample taken
X=59 represent number of defectives from the company B
[tex]\hat p=\frac{59}{400}=0.1475[/tex] estimated proportion of defectives from the company B
[tex]p_o=0.1[/tex] is the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to verify if the true proportion of defectives is higher than 0.1 then the system of hypothesis are.:
Null hypothesis:[tex]p \leq 0.1[/tex]
Alternative hypothesis:[tex]p > 0.1[/tex]
The statistic would be given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.1475-0.1}{\sqrt{\frac{0.1(1-0.1)}{400}}}=3.17[/tex]
The p value for this case would be given by:
[tex]p_v =P(z>3.17)=0.00076[/tex]
For this case the p value is lower than the significance level so then we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 0.1 and then Company B can reject the shipment
Assuming that $3u + 12v\neq0$, simplify $\dfrac{12u^3 + 48u^2v}{3u+12v}$.
Answer:
4u²
Step-by-step explanation:
[tex]\dfrac{12u^3 + 48u^2v}{3u+12v}=\dfrac{12u^2(u+4v)}{3(u+4v)}=\boxed{4u^2}[/tex]
Common factors cancel from numerator and denominator. The one factor that might make the expression undefined is given as non-zero, so no additional restrictions apply.
Statistics show that about 42% of Americans voted in the previous national election. If three Americans are randomly selected, what is the probability that none of them voted in the last election
Answer:
19.51% probability that none of them voted in the last election
Step-by-step explanation:
For each American, there are only two possible outcomes. Either they voted in the previous national election, or they did not. The probability of an American voting in the previous election is independent of other Americans. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
42% of Americans voted in the previous national election.
This means that [tex]p = 0.42[/tex]
Three Americans are randomly selected
This means that [tex]n = 3[/tex]
What is the probability that none of them voted in the last election
This is P(X = 0).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{3,0}.(0.42)^{0}.(0.58)^{3} = 0.1951[/tex]
19.51% probability that none of them voted in the last election
the sum of two rational numbers is 8 if one of the numbers is -5/6 find the other
Answer:53/6
Step-by-step explanation:
Let X be the other rational number
-5/6+X=8
Add 5/6 to both sides
-5/6+5/6+X=8+5/6
0+X= 53/6 (inverse property)
X=53/6. (Identity property)
For the given equation, find the values of a, b, and c, determine the direction in which the parabola opens, and determine the y-intercept. Decide which table best illustrates these values for the equation: y = x squared minus 6 x Table A a b c up or down y-intercept 1 -6 0 up (0,0) Table B a b c up or down y-intercept 1 0 0 up (0,-6) Table C a b c up or down y-intercept 1 6 0 up (0,0) Table D a b c up or down y-intercept 1 -6 0 down (0,0) a. Table A c. Table C b. Table B d. Table D Please select the best answer from the choices provided
Answer:
The table that illustrates this equation is table A:
1 -6 0 up (0,0)
Step-by-step explanation:
The values of the parameters a, b, and c have to agree with the values for the general quadratic equation in standard form:
[tex]y = a\,x^2+b\,x+c[/tex]
compared to:
[tex]y=x^2-6\,x[/tex]
So the coefficient "a" of the quadratic term in our case is: "1"
the coefficient "b" of the linear term is : "-6"
the coefficient "c" for the constant term s : "0" (zero)
since the coefficient "a" is a positive number, we know that the parabola's branches must be opening "UP".
The y intercept can be found by evaluating the expression for x = 0:
[tex]y=x^2-6x\\y=(0)^2-6\,(0)\\y=0[/tex]
Therefore the y-intercept is at (0, 0)
These results agree with those of Table "A"
Answer:
Table A.)
Step-by-step explanation:
a 1, b -6, c 0, up, (0, 0), Table A.
Which numbers are solutions of the inequality below? (Select all that apply.)
x − 2 < −8
a) 6
b) −6
c) 4
d) −8
Answer:
d) −8
Step-by-step explanation:
x − 2+2 < −8+2
x < -6
The only number less than -6 is -8
What is the image of R for a dilation with center (0,0) and a scale factor of 1 1/2?
Answer: The image is (6,-3)
Step-by-step explanation:
The coordinates of R is ( 4,-2) and to find the image using the scale factor 1.5 you will multiply the x coordinates by 1.5 and the y coordinate also by 1.5 to have the new image of R.
4 * 1.5 = 6
-2 * 1.5 = -3
The new coordinates care (6, -3)
Determine the magnitude of the resultant force by adding the rectangular components of the three forces.
a) R = 29.7 N
b) R = 54.2 N
c) R = 90.8 N
d) R = 24.0 N
A marine biologist is preparing a deep-sea submersible for a dive. The sub stores breathing air under high pressure in a spherical air tank that measures wide. The biologist estimates she will need of air for the dive. Calculate the pressure to which this volume of air must be compressed in order to fit into the air tank. Write your answer in atmospheres. Round your answer to significant digits.
The complete question is;
A marine biologist is preparing a deep-sea submersible for a dive. The sub stores breathing air under high pressure in a spherical air tank that measures 78.0 cm wide. The biologist estimates she will need 2600 L of air for the dive. Calculate the pressure to which this volume of air must be compressed in order to fit in to the air tank. Write you answer in atmospheres
Answer:
10.5 atm
Step-by-step explanation:
Formula for Volume of a sphere is;
V = (4/3)πr³
r = 78/2 = 39 cm
V = (4/3)π(39)³
V = (4/3)*π*59319
V = 248475 cm³
Now, from conversions, 1000 cm³ = 1L
So,
V = 248475/1000
V = 248.5 L
This is the volume of the storage tank
If we assume that the 2600 L of air is measured at 1 atmosphere pressure, then we will obtain the following relationship:
From Boyles law,
P1 × V1 = P2 × V2
Thus;
(1 atm) × (2600 L) = (P2) × (248.5 L)
P2 = 2600/248.5
P2 = 10.463 atmospheres
Approximating to 3 significant figures is; P2 = 10.5 atm
Need help ASAP please!!
Answer:
AOB = 73
BOC = 107
Step-by-step explanation:
So make an equation.
9x + 27 = 180
9x = 153
x = 17
AOB = 73
BOC = 107
