Answer:
a. k = -0.01014 s⁻¹
b. [tex]\mathbf{\dfrac{dy}{dt} = - \dfrac{In(\dfrac{3}{2})}{40}(y-60)}[/tex]
c. [tex]\mathbf{y(t) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} \ e^{\dfrac{-In(\dfrac{3}{2})\ t}{40}}}[/tex]
d. y(t) = 130.485°F
Step-by-step explanation:
A hot metal bar is submerged in a large reservoir of water whose temperature is 60°F. The temperature of the bar 20 s after submersion is 120°F. After 1 min submerged, the temperature has cooled to 100°F.
(Let y be measured in degrees Fahrenheit, and t be measured in seconds.)
We are to determine :
a. Determine the cooling constant k. k = s−1
By applying the new law of cooling
[tex]\dfrac{dT}{dt} = k \Delta T[/tex]
[tex]\dfrac{dT}{dt} = k(T_1-T_2)[/tex]
[tex]\dfrac{dT}{dt} = k (T - 60)[/tex]
Taking the integral.
[tex]\int \dfrac{dT}{T-60} = \int kdt[/tex]
㏑ (T -60) = kt + C
T - 60 = [tex]e^{kt+C}[/tex]
[tex]T = 60+ C_1 e^{kt} ---- (1)[/tex]
After 20 seconds, the temperature of the bar submersion is 120°F
T(20) = 120
From equation (1) ,replace t = 20s and T = 120
[tex]120 = 60 + C_1 e^{20 \ k}[/tex]
[tex]120 - 60 = C_1 e^{20 \ k}[/tex]
[tex]60 = C_1 e^{20 \ k} --- (2)[/tex]
After 1 min i.e 60 sec , the temperature = 100
T(60) = 100
From equation (1) ; replace t = 60 s and T = 100
[tex]100 = 60 + c_1 e^{60 \ t}[/tex]
[tex]100 - 60 =c_1 e^{60 \ t}[/tex]
[tex]40 =c_1 e^{60 \ t} --- (3)[/tex]
Dividing equation (2) by (3) , we have:
[tex]\dfrac{60}{40} = \dfrac{C_1e^{20 \ k } }{C_1 e^{60 \ k}}[/tex]
[tex]\dfrac{3}{2} = e^{-40 \ k}[/tex]
[tex]-40 \ k = In (\dfrac{3}{2})[/tex]
- 40 k = 0.4054651
[tex]k = - \dfrac{0.4054651}{ 40}[/tex]
k = -0.01014 s⁻¹
b. What is the differential equation satisfied by the temperature y(t)?
Recall that :
[tex]\dfrac{dT}{dt} = k \Delta T[/tex]
[tex]\dfrac{dT}{dt} = \dfrac{- In (\dfrac{3}{2})}{40}(T-60)[/tex]
Since y is the temperature of the body , then :
[tex]\mathbf{\dfrac{dy}{dt} = - \dfrac{In(\dfrac{3}{2})}{40}(y-60)}[/tex]
(c) What is the formula for y(t)?
From equation (1) ;
where;
[tex]T = 60+ C_1 e^{kt} ---- (1)[/tex]
Let y be measured in degrees Fahrenheit
[tex]y(t) = 60 + C_1 e^{-\dfrac{In (\dfrac{3}{2})}{40}t}[/tex]
From equation (2)
[tex]C_1 = \dfrac{60}{e^{20 \times \dfrac{-In(\dfrac{3}{2})}{40}}}[/tex]
[tex]C_1 = \dfrac{60}{e^{-\dfrac{1}{2} {In(\dfrac{3}{2})}}}[/tex]
[tex]C_1 = \dfrac{60}{e^ {In(\dfrac{3}{2})^{-1/2}}}}[/tex]
[tex]C_1 = \dfrac{60}{\sqrt{\dfrac{2}{3}}}[/tex]
[tex]C_1 = \dfrac{60 \times \sqrt{3}}{\sqrt{2}}}[/tex]
[tex]\mathbf{y(t) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} \ e^{\dfrac{-In(\dfrac{3}{2})\ t}{40}}}[/tex]
(d) Determine the temperature of the bar at the moment it is submerged.
At the moment it is submerged t = 0
[tex]\mathbf{y(0) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} \ e^{\dfrac{-In(\dfrac{3}{2})\ 0}{40}}}[/tex]
[tex]\mathbf{y(t) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} }[/tex]
y(t) = 60 + 70.485
y(t) = 130.485°F
A report states that the mean yearly salary offer for students graduating with a degree in accounting is $48,722. Suppose that a random sample of 50 accounting graduates at a large university who received job offers resulted in a mean offer of $49,870 and a standard deviation of $3900. Do the sample data provide strong support for the claim that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722? Test the relevant hypotheses using α = 0.05. State your conclusion.A. Reject H0. We do not have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.B. Do not reject H0. We do not have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.C. Reject H0. We have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.D. Do not reject H0. We have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.
Answer:
Option C - Reject H0. We have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.
Step-by-step explanation:
First of all let's define the hypothesis;
Null hypothesis;H0; μ = $48,722
Alternative hypothesis;Ha; μ > $48,722
Now, let's find the test statistic for the z-score. Formula is;
z = (x' - μ)/(σ/√n)
We are given;
x' = 48,722
μ = 49,870
σ = 3900
n = 50
Thus;
z = (49870- 48722)/(3900/√50)
z = 2.08
So from online p-value calculator as attached, using z = 2.08 and α = 0.05 ,we have p = 0.037526
This p-value of 0.037526 is less than the significance value of 0.05,thus, we reject the claim that that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722
What are the solutions of the system 7x + 3y=-3 and y= -2*?
Answer:
opt 4
Step-by-step explanation:
when x=0, 0+3y= -3, so y=-1 (0,-1) is solution
when x=3 , 21+3y=-3, 3y= -3-21= -24
y= -8 (3,-8) is also solution
In a mathematics class, half of the students scored 86 on an achievement test. With the exception of a few students who scored 46, the remaining students scored 77. Which of the following statements is true about the distribution of scores
Answer:
B. The mean is less than the median.
Step-by-step explanation:
Say there was 20 kids: 10 kids(half) scored 86's, 3 kids(a few) scored 45's, and 7 kids(the remaining) scored 77's.
The median would be- 81.5 (chronological order, find the middle number)
The mean would be- 76.85 (sum of all the scores divided by the number of scores)
The mode would be- 86 (most frequent number)
The mean(76.85) is less than(<) the median(81.5)
Geometry pls help !!! Find the value of AB.
AB = [?]
Answer:
AB = 16 Units
Step-by-step explanation:
In the given figure, CD is the diameter and AB is the chord of the circle.
Since, diameter of the circle bisects the chord at right angle.
Therefore, AE = 1/2 AB
Or AB = 2AE...(1)
Let the center of the circle be given by O. Join OA.
OA = OD = 10 (Radii of same circle)
Triangle OAE is right triangle.
Now, by Pythagoras theorem:
[tex] OA^2 = AE^2 + OE^2 \\
10^2 = AE^2 + 6^2 \\
100= AE^2 + 36\\
100-36 = AE^2 \\
64= AE^2 \\
AE = \sqrt{64}\\
AE = 8 \\
\because AB = 2AE..[From \: equation\: (1)] \\
\therefore AB = 2\times 8\\
\huge \purple {\boxed {AB = 16 \: Units}} [/tex]
What is the approximate area of the unshaded region under the standard normal curve below? Use the portion of the standard normal table given to help answer the question.
A normal curve with a peak at 0 is shown. The area under the curve shaded is 1 to 2.
z
Probability
0.00
0.5000
1.00
0.8413
2.00
0.9772
3.00
0.9987
0.14
0.16
0.86
0.98
Answer:
0.14
Step-by-step explanation:
The z score is a score used in statistics to determine by how many standard deviations ti the raw score above or below the mean. If the raw score is above the mean then the z score is positive while If the raw score is below the mean then the z score is negative, It is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
From the normal distribution table, The area under the curve shaded is 1 to 2 = P(1 < z < 2) = P(z < 2) - P(z < 1) = 0.9772 - 0.8413 = 0.1359 ≈ 0.14
The area under the curve shaded is 1 to 2 is 0.14
What are probabilities?Probabilities are used to determine the chances of an event
The shaded region represents the probability of the z-scores
The shaded region 1 to 2 is represented as:
P(1 < z < 2) =
Using the probability of z-score, we have the formula
P(1 < z < 2) = P(z < 2) - P(z < 1)
From the given standard normal table:
P(z < 2) = 0.9772
P(z < 1) = 0.8413
So, we have:
P(1 < z < 2) = 0.9772 - 0.8413
P(1 < z < 2) = 0.1359
Approximate
P(1 < z < 2) = 0.14
Hence, the area under the curve shaded is 1 to 2 is 0.14
Read more about normal distribution at:
https://brainly.com/question/4079902
Choose two statements that are true for this expression.
5x3 – 6x2
25
y
+ 18
25
O A. The term
is a ratio.
B. There are three terms.
C. The entire expression is a difference.
O D. There are four terms.
Answer:
Step-by-step explanation:
I'm having difficulty reading your input: 25, y, + 18, 25. Please clarify your meaning.
5x3 – 6x2 is a polynomial expression with two terms.
The term is a ratio. False. See above.
The entire expression is a difference. True.
There are four terms. False. See above.
Two statements B and C are true for the expression 5x3 – 6x2 25y+ 18
How many options are correct for given expressio?
A. The term is a ratio. False
B. There are three terms.terms. True
C. The entire expression is a difference. True
D. There are four terms. False
Learn more about linear equation here: brainly.com/question/1884491
#SPJ2
find the area of this figure to the nearest hundredth. Use 3.14 to approximate pi.
Answer:
86.28 ft²
Step-by-step explanation:
The figure given consists of a rectangle and a semicircle.
The area of the figure = area of rectangle + area of semicircle
Area of rectangle = [tex] l*w [/tex]
Where,
l = 10 ft
w = 8 ft
[tex] area = l*w = 10*8 = 80 ft^2 [/tex]
Area of semicircle:
Area of semicircle = ½ of area of a circle = ½(πr²)
Where,
π = 3.14
r = ½ of 8 = 4 ft
Area of semi-circle = ½(3.14*4) = 6.28 ft²
Area of the figure = area of rectangle + area of semi-circle = 80 + 6.28 = 86.28 ft² (nearest hundredth)
Answer:
the area of the figrue is 105.12
Step-by-step explanation:
area of rectangle A= l · w10 x 8= 80area of simi-circle= 1/2(3.14 x r²)1/2 x 3.14 x 4²=25.1280+25.12=105.12 (nearest Hundredth)If you draw one card at random, what is the probability that card is a (n) Heart?
Answer:
1/13
Step-by-step explanation:
There are 52 cards in a deck of cards and 13 of them are hears
P(heart) = hearts / total
= 13/52 = 1/13
Choose the correct simplification of the expression (a^3/b^7)^2
Answer:
(a^3/b^7)^2 = (a^6/b^14)
The research group asked the following question of individuals who earned in excess of $100,000 per year and those who earned less than $100,000 per year: "Do you believe that it is morally wrong for unwed women to have children?" Of the individuals who earned in excess of $100,000 per year, said yes; of the individuals who earned less than $100,000 per year, said yes. Construct a 95% confidence interval to determine if there is a difference in the proportion of individuals who believe it is morally wrong for unwed women to have children.
Complete Question
The complete question is shown on the first uploaded image
Answer:
The lower bound is [tex]0.0234[/tex]
The upper bound is [tex]0.100[/tex]
So from the value obtained the solution to the question are
1 Does not include
2 sufficient
3 not different
Step-by-step explanation:
From the question we are told that
The sample size of individuals who earned in excess of $100,000 per year is [tex]n_ 1 = 1205[/tex]
The number of individuals who earned in excess of $100,000 per year that said yes is
[tex]w = 712[/tex]
The sample size individuals who earned less than $100,000 per year is [tex]n_2 = 1310[/tex]
The number of individuals who earned less than $100,000 per year that said yes is
[tex]v= 693[/tex]
The sample proportion of individuals who earned in excess of $100,000 per year that said yes is
[tex]\r p _ 1 = \frac{w}{n_1 }[/tex]
substituting values
[tex]\r p _ 1 = \frac{712}{1205}[/tex]
[tex]\r p _ 1 =0.5909[/tex]
The sample proportion of individuals who earned less than $100,000 per year that said yes is
[tex]\r p _ 1 = \frac{v}{n_2 }[/tex]
substituting values
[tex]\r p _ 1 = \frac{693 }{1310}[/tex]
[tex]\r p _ 1 = 0.529[/tex]
Given that the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha = 1 -0.95[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table the value is [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{ \r p _1 (1- \r p_1 )}{n_1} + \frac{ \r p _2 (1- \r p_2 )}{n_2} } }[/tex]
substituting values
[tex]E = 1.96 * \sqrt{ \frac{ 0.5909 (1- 0.5909 )}{1205} + \frac{ 0.592 (1- 0.6592 )}{1310} } }[/tex]
[tex]E =0.03846[/tex]
Generally the 95% confidence interval is
[tex](\r p_1 - \r p_2) - E < p_1 - p_2 <( \r p_1 - \r p_2 ) + E[/tex]
substituting values
[tex](0.5909 - 0.529 ) - 0.03846 < p_1 - p_2 < (0.5909 - 0.529 ) + 0.03846[/tex]
[tex]0.02344 < p_1 - p_2 < 0.10036[/tex]
The lower bound is [tex]0.0234[/tex]
The upper bound is [tex]0.100[/tex]
So from the value obtained the solution to the question are
1 Does not include
2 sufficient
3 not different
The lower bound is 0.0234 and the upper bound is 0.100. Then the 95% confidence interval is (0.0234, 0.100)
What is the margin of error?The probability or the chances of error while choosing or calculating a sample in a survey is called the margin of error.
The research group asked the following question of individuals who earned in excess of $100,000 per year and those who earned less than $100,000 per year.
The sample size of individuals who earned in excess of $100,000 per year will be
[tex]\rm n_1 =1205[/tex]
The sample size of individuals who earned less than $100,000 per year will be
[tex]\rm n_1 =1205[/tex]
The number of individuals who earn an excess of $100,000 per year that said yes will be
[tex]\rm w = 712[/tex]
The number of individuals who earn less than $100,000 per year that said yes will be
[tex]\rm v= 693[/tex]
Then the sample proportion of individuals who earned in excess of $100,000 per year that said yes will be
[tex]\rm \hat{p}_1=\dfrac{w}{n_1}\\\\\hat{p}_1=\dfrac{712}{1205}\\\\\hat{p}_1= 0.5909[/tex]
Then the sample proportion of individuals who earned less than $100,000 per year that said yes will be
[tex]\rm \hat{p}_2=\dfrac{v}{n_2}\\\\\hat{p}_2=\dfrac{693}{1310}\\\\\hat{p}_2= 0.529[/tex]
The confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha =1-0.95\\\\\alpha =0.05[/tex]
Then the critical value of α/2 from the normal distribution table. Then the value of z is 1.96, then the error of margin will be
[tex]E = z_{\alpha /2} \times \sqrt{\dfrac{\hat{p}_1(1-\hat{p}_1)}{n_1} + \dfrac{\hat{p}_2(1-\hat{p}_2)}{n_2}}\\\\E = 1.96 \times \sqrt{\dfrac{05909(1-0.5909)}{1205} + \dfrac{0.529(1-0529)}{1310}}\\\\E = 0.03846[/tex]
The 95% confidence interval will be
[tex]\begin{aligned} (\hat{p}_1-\hat{p}_2)-E & < p_1-p_2 < (\hat{p}_1-\hat{p}_2) + E\\\\(0.5909 - 0.529) - 0.03846 & < p_1-p_2 < (0.5909 - 0.529) + 0.03846\\\\0.02344 & < p_1-p_2 < 0.10036 \end{aligned}[/tex]
More about the margin of error link is given below.
https://brainly.com/question/6979326
You are an urban planner assessing the growth of a city. Ten years ago, the city's population was 250,823. Its current population is 325,823. By about what percentage has the city grown over the past ten years? Round to the nearest percent.
Answer:
Here is the answer i got-
Step-by-step explanation:
325823-250823=75000
325823’s 244367250percent is 75000
A car dealership is advertising a car for $16,299.99. If the sales tax rate is 6.5 percent, what
is the total tax paid for the car?
A. S993 34
B. $1.000.00
CS1.059 50
DS1.359.19
Answer:
C. 1059.50
Step-by-step explanation:
Sales price x sales tax rate = sales tax
16299.99 x .065 (6.5%) = 1059.50
A graphics designer is designing an advertising brochure for an art show. Each page of the brochure is rectangular with an area of 52 in^2 and a perimeter of 30in. Find the dimensions of the brochure. The longer side is _____in. The shorter side is ______ in.
9514 1404 393
Answer:
9.562 in5.438 inStep-by-step explanation:
The sum of side lengths of a rectangle is half the perimeter, so is 15 inches for this brochure. If x is one of the side lengths, then (15 -x) is the other one, and the area is ...
x(15 -x) = 52
x^2 -15x = -52 . . . . multiply by -1 and expand
(x -7.5)^2 = -52 +56.25 = 4.25 . . . complete the square
x = 7.5 ±√4.25 ≈ {5.438, 9.562} . . . inches
The longer side is 7+√4.25 ≈ 9.562 inches; the shorter side is 7-√4.25 ≈ 5.438 inches.
Convert the following:
4 quarts is equivalent to
ao liters (rounded to the hundredth)
Answer: 3.79 litres
Step-by-step explanation:
1 litre is equivalent to about 1.05668821 American quarts.
4 quarts would therefore be;
= 4/1.05668821
= 3.78541178
= 3.79 litres
An athletic club charges a monthly membership
fee of $65. Members can also take classes for an
additional $15 per class. For this month only, the
club has a special that includes two free classes for
all new members. Which of the following functions
expresses the cost for the month for new members
who take x classes this month, where x > 2?
(A) C(x) = 2x + 65
(B) C(x) = 15x + 65
(C) C(x) = 2(x - 15) + 65
(D) C(x) = 15(x - 2) + 65
A helicopter is at a cruising height of 1,200 feet. Suppose the angle of depression to the landing pad is 15°, which is located on top of a building that is 64 feet high. If the helicopter continues at the current cruising height, how far does the helicopter need to travel to be directly above the landing pad? Include a sketch that shows all known information and clearly shows what you need to find. Show all work and give the answer rounded to the nearest foot.
Answer:
we have a right triangle and to get the internal angle of the right triangle formed at the helicopter we subtract 62 degrees from 90 which equals 28 degrees
we now use the cosine to find the distance (d) from the helicopter
cosine 28 = 85/d
d = 85 / cosine 28 = 85 / 0.8829 = 96.2736 = 96 feet
Determine whether Rolle's Theorem can be applied to f on the closed interval
[a, b].
f(x) = −x2 + 3x, [0, 3]
Yes, Rolle's Theorem can be applied.No, because f is not continuous on the closed interval [a, b].No, because f is not differentiable in the open interval (a, b).No, because f(a) ≠ f(b).
If Rolle's Theorem can be applied, find all values of c in the open interval
(a, b)
such that
f '(c) = 0.
(Enter your answers as a comma-separated list. If Rolle's Theorem cannot be applied, enter NA.)
c =
Answer:
Yes, Rolle's theorem can be applied
There is only one value of c such that f'(c) = 0, and this is c = 1.5 (or 3/2 in fraction form)
Step-by-step explanation:
Yes, Rolle's theorem can be applied on this function because the function is continuous in the closed interval (it is a polynomial function) and differentiable in the open interval, and f(a) = f(b) given that:
[tex]f(0)=-0^2+3\,(0)=0\\f(3)=-3^2+3\,(3)=-9+9=0[/tex]
Then there must be a c in the open interval for which f'(c) =0
In order to find "c", we derive the function and evaluate it at "c", making the derivative equal zero, to solve for c:
[tex]f(x)=-x^2+3\,x\\f'(x)=-2\,x+3\\f'(c)=-2\,c+3\\0=-2\,c+3\\2\,c=3\\c=\frac{3}{2} =1.5[/tex]
There is a unique answer for c, and that is c = 1.5
Rolle's theorem is applicable if [tex]f(a)=f(b)[/tex] and $f$ is differentiable in $(a,b)$
since it's polynomial function, it's always continuous and differentiable..
and you can easily check that $f(0)=f(-3)=0$
so it is applicable.
now, $f'(x)=-2x+3=0 \implies x=\frac32$
there is only once value (as you can imagine, the graph will be downward parabola)
somebody please help
Which of the fractions below are less than 2/5? Select two.
Answer:
1/8 is less than
Step-by-step explanation:
i dont see any fractions below gona have to edit your answer
Write six hundred twelve thousand, three hundred in the place-value chart. Then write the number in expanded
Answer:
612,300
600,000
10,000
2,000
300
00
0
(3.5x10^8)x(4.0x10^-12)=
Answer:
Below
Step-by-step explanation:
● (3.5× 10^8) × (4×10^(-12))
● (3.5×4) × (10^8 × 10^(-12) )
● 14 × 10^ (-12+8)
● 14 × 10^(-4)
● 14/10^4
In triangle ABC, ∠ABC=70° and ∠ACB=50°. Points M and N lie on sides AB and AC respectively such that ∠MCB=40° and ∠NBC=50°. Find m∠NMC.
Answer:
∠NMC = 50°
Step-by-step explanation:
The interpretation of the information given in the question can be seen in the attached images below.
In ΔABC;
∠ A + ∠ B + ∠ C = 180° (sum of angles in a triangle)
∠ A + 70° + 50° = 180°
∠ A = 180° - 70° - 50°
∠ A = 180° - 120°
∠ A = 60°
In ΔAMN ; the base angle are equal , let the base angles be x and y
So; x = y (base angle of an equilateral triangle)
Then;
x + x + 60° = 180°
2x + 60° = 180°
2x = 180° - 60°
2x = 120°
x = 120°/2
x = 60°
∴ x = 60° , y = 60°
In ΔBQC
∠a + ∠e + ∠b = 180°
50° + ∠e + 40° = 180°
∠e = 180° - 50° - 40°
∠e = 180° - 90°
∠e = 90°
At point Q , ∠e = ∠f = ∠g = ∠h = 90° (angles at a point)
∠i = 50° - 40° = 10°
In ΔNQC
∠f + ∠i + ∠j = 180°
90° + 10° + ∠j = 180°
∠j = 180° - 90°-10°
∠j = 180° - 100°
∠j = 80°
From line AC , at point N , ∠y + ∠c + ∠j = 180° (sum of angles on a straight line)
60° + ∠c + ∠80° = 180°
∠c = 180° - 60°-80°
∠c = 180° - 140°
∠c = 40°
Recall that :
At point Q , ∠e = ∠f = ∠g = ∠h = 90° (angles at a point)
Then In Δ NMC ;
∠d + ∠h + ∠c = 180° (sum of angles in a triangle)
∠d + 90° + 40° = 180°
∠d = 180° - 90° -40°
∠d = 180° - 130°
∠d = 50°
Therefore, ∠NMC = ∠d = 50°
What is the true solution to the equation below? 2 in e in2×-in e in 10×= in 30 A x=30 B x=75 C x=150 D x=300
Answer:
Option B.
Step-by-step explanation:
Let as consider the given equation:
[tex]2\ln e^{\ln 2x}-\ln e^{\ln 10x}=\ln 30[/tex]
It can be written as
[tex]2(\ln 2x)-(\ln 10x)=\ln 30[/tex] [tex][\because \ln e^a=a][/tex]
[tex]\ln (2x)^2-(\ln 10x)=\ln 30[/tex] [tex][\because \ln a^b=b\ln a][/tex]
[tex]\ln \dfrac{4x^2}{10x}=\ln 30[/tex] [tex][\because \ln \dfrac{a}{b}=\ln a-\ln b][/tex]
[tex]\ln \dfrac{2x}{5}=\ln 30[/tex]
On comparing both sides, we get
[tex]\dfrac{2x}{5}=30[/tex]
Multiply both sides by 5.
[tex]2x=150[/tex]
Divide both sides by 2.
[tex]x=75[/tex]
Therefore, the correct option is B.
Answer:
b x=75
Step-by-step explanation:
The cost in dollars y of producing x computer
desks is given by y = 20x + 3000
х
100
200
300
a. Complete the table
y
b. Find the number of computer desks that can be produced for $4300. (HintFind x when y = 4300)
a. Complete the table.
х
100
200
300
y
b. For $4300, computer desks can be produced.
Answer:
Step-by-step explanation:
a. table
x = 100,y = 20*100+3000 = 2000+3000 = 5000
x = 200,y = 20*200+3000 = 4000+3000 = 7000
x = 300,y = 20*300+3000 = 6000+3000 = 9000
b：
y = 4300
4300 = 20x+3000
20x = 4300-3000
20x = 1300
x = 1300/20
x = 65
so 65 computer desks can be produced.
Amira starts an exercise programme on the 3rd of March. She decides she will swim every
3 days and cycle every 4 days. On which dates in March will she swim and cycle on the
same day?
Answer:
12 days
Step-by-step explanation:
The answer of the problem is the LCM of 3 and 4=12. Hence the answer is 12 days
On 12 March she will swim and cycle on the same day if Amira starts an exercise program on the 3rd of March.
What is LCM?It is defined as the common number of two integers, which is the lowest number that is a multiple of two or more numbers. The full name of LCM is the least common multiple.
We have:
Amira starts an exercise program on the 3rd of March.
She will swim every 3 days and cycle every 4 days.
Total days =3 + 4 = 7 days = 1 week
The day she swims and cycles on the same day = LCM of 3 and 4
= 3, 6, 9, 12, 15
= 4, 8, 12, 16
= 12
Thus, on 12 March she will swim and cycle on the same day if Amira starts an exercise program on the 3rd of March.
Learn more about the LCM here:
brainly.com/question/20739723
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Solve 5x + 3 = -7x + 21
If sin2 x + cos2 y = 2 sec2 z, then general solution of triplets (x, y, z) is
Answer:
x=(n+12)π, y=mπ∴x=n+12π, y=mπ and z = rπ where n∈I, m∈I, r∈I
Step-by-step explanation:
∴ LHS ≤ 2 and RHS ≥ 2
So, sin2 x = 1, cos2 y = 1 and sec2 z = 1
∴x=(n+12)π, y=mπ∴x=n+12π, y=mπ and z = rπ where n∈I, m∈I, r∈I
help asap!!
Find the length of AB
A. 2.89
B. 33.13
C. 378.63
D. 377.19
Answer:
C
Step-by-step explanation:
[tex] \sin( 5 ^{o} ) = \frac{33}{ab} \\ ab = 378.63[/tex]
Assume the triangular prism has a base area of 49cm^2 and a volume of 588cm^3. What side length does the rectangular prism need to have the same volume?
Answer:
Length = Width = 7 cm
Step-by-step explanation:
Volume of a triangular prism is represented by the formula,
Volume = (Area of the triangular base) × height
588 = 49 × h
h = [tex]\frac{588}{49}[/tex]
h = 12 cm
We have to find the side length of a rectangular prism having same volume.
Volume = Area of the rectangular base × height
588 = (l × b) × h [l = length and b = width ]
588 = (l × b) × 12
l × b = 49 = 7 × 7
Therefore, length = width = 7 cm may be the side lengths of the rectangular prism to have the same volume.
In a study of 100 new cars, 29 are white. Find and g, where
is the proportion of new cars that are white.
Question
In a study of 100 new cars, 29 are white. Find p and q , where p is the proportion of new cars that are white.
Answer:
p = 0.29 and q = 0.71
Step-by-step explanation:
Given
Total new cars = 100
White new cars = 29
Required
Determine p and q
From the question;
p represents white new cars
Hence;
[tex]p = 29[/tex]
Note that;
[tex]p + q = 100[/tex]
Substitute 29 for p
[tex]29 + q = 100[/tex]
[tex]29 - 29 + q = 100 - 29[/tex]
[tex]q = 100 - 29[/tex]
[tex]q = 71[/tex]
The proportion of p is calculate by dividing p by the total number of new cars (Same process is done for q)
For proportion of p
[tex]Proportion,\ p = \frac{p}{new\ cars}[/tex]
[tex]Proportion,\ p = \frac{29}{100}[/tex]
[tex]Proportion,\ p = 0.29[/tex]
For proportion of q
[tex]Proportion,\ q = \frac{q}{new\ cars}[/tex]
[tex]Proportion,\ q = \frac{71}{100}[/tex]
[tex]Proportion,\ q = 0.71[/tex]