Answer with Step-by-step explanation:
We are given that
Radius of circular disk=r=25 cm
Maximal error in measurement of radius =[tex]\Delta r=[/tex]0.3
We know that
Surface area of circle =A=[tex]\pi r^2[/tex]
Differentiate w.r.t r
a.Maximum error=[tex]dA=2\pi rdr[/tex]
Substitute the values then we get
[tex]dA=2\times 3.14\times 25\times 0.3=47.1 cm^2[/tex]
Hence, the maximum error in area of disk=[tex]47.1 cm^2[/tex]
b.
Relative error in A: [tex]\frac{\Delta A}{A}=\frac{2\pi r\Delta r}{\pi r^2}[/tex]
Substitute the value in the formula
Then ,we get
Relative maximal error in area of disk=[tex]\frac{2\cdot 25}{(25)^2}(0.3)=0.024[/tex]
Hence, the relative maximum error in area of disk=0.024
c.Relative error percentage in area of disk=[tex]\frac{\Delta A}{A}\times 100[/tex]
Substitute the values then we get
Relative error percentage in area of disk=[tex]0.024\times 100=2.4[/tex]%
Hence, the percentage error in area of disk=2.4%
To estimate the maximum error in the calculated area of a disk, use differentials. The maximum error in the area is approximately 15π cm². The relative maximum error is 0.24 and the percentage error is 24%.
Explanation:To estimate the maximum error in the calculated area of the disk, we can use differentials. The formula for the area of a disk is A = πr², where r is the radius. Taking the differential of this equation gives dA = 2πr dr. Since the maximum error in the radius is 0.3 cm, we substitute dr = 0.3 cm into the equation to find the maximum error in the area. Thus, the maximum error in the calculated area of the disk is approximately 2π(25 cm)(0.3 cm) = 15π cm².
The relative maximum error is the ratio of the maximum error in the area to the actual area. Therefore, the relative maximum error can be calculated as (15π cm²) / (π(25 cm)²) = 15 / 25² = 0.24.
To calculate the percentage error, we multiply the relative maximum error by 100%.
Thus, the percentage error is 0.24 * 100% = 24%.
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In a calculus class, Jack Hartig scored 4 on a quiz for which the class mean and standard deviation were 2.9 and 2.1, respectively. Norm Alpina scored 8 on another quiz for which the class mean and standard deviation were 6.5 and 1.9, respectively. Relatively speaking, which student did better? Make use of z-scores.
Answer: Norm Alpina did better with z-score 0.79
Step-by-step explanation:
Z score formula = (raw score - mean) / standard deviation
For Jack Hartig,
score = 4; mean = 2.9; standard deviation = 2.1
Hence, Z score = (4 - 2.9) /2.1
= 1.1/2.1
= 0.52
For Norm Alpina,
score = 8; mean = 6.5; standard deviation = 1.9
Hence, Z score = (8 - 6.5) /1.9
= 1.5/1.9
= 0.79
Relatively, Norm Alpina did better for having Z score 0.79
By calculating z-scores for both students, which represent the number of standard deviations their scores are from the mean, Norm Alpina has a higher z-score and hence performed relatively better compared to Jack Hartig on their respective quizzes.
In order to determine which student did relatively better on their quizzes, we need to calculate the z-scores for each student. A z-score indicates how many standard deviations an observation is above or below the mean. The formula for a z-score is Z = (X - μ) / σ, where X is the score, μ(mu) is the mean, and σ(sigma) is the standard deviation.
For Jack Hartig:
Z = (4 - 2.9) / 2.1
= 1.1 / 2.1
= 0.524
For Norm Alpina:
Z = (8 - 6.5) / 1.9
= 1.5 / 1.9
= 0.789
Norm Alpina's z-score is higher, indicating that, relatively speaking, he performed better than Jack Hartig on the quiz based on how their scores relate to their respective class means and standard deviations.
The perpendicular bisector of side AB of triangle ABC intersects the extension of side AC at D. Find the measure of angle ABC if measurement of angle CBD=16 degrees and measurement of angle ACB=118 degrees
Answer:
23°
Step-by-step explanation:
Let the interior angles of ΔABC be referenced by A, B, and C. The definition of point D means that ΔDAB is an isosceles triangle, so we have the relations ...
A + B + 118 = 180 . . . . interior angles of ΔABC
A = B +16 . . . . . . . . . . base angles of ΔDAB
Using the expression for A in the second equation to substitute into the first equation, we get ...
(B+16) +B +118 = 180
2B + 134 = 180 . . . . . collect terms
2B = 46 . . . . . . . . . . . subtract 134
B = 23 . . . . . . . . . . . . divide by 2
m∠ABC = 23°
Dale graphed the absolute value parent function. Then, he reflected the graph over the x-axis, shifted it four units to the right and three units up. Give the new equation
Answer:
i(x) = - |x - 4| + 3Step-by-step explanation:
Refer to attached graph
Parent function:
f(x) = |x|, solid black on the graphTransformations
1. Reflection over x-axis: f(x) → -f(x)
g(x) = -|x|, dotted blue on the graph2. Horizontal shift 4 units to the right: g(x) → g(x - 4)
h(x) = -|x - 4|, dotted green on the graph3. Vertical shift 3 units up: h(x) → h(x) + 3
i(x) = - |x - 4| + 3, solid red on the graphThis is the final function
Use synthetic division to check that the number k is a lower bound for the real zeros of the function f.
k=-7; f(x)= 5x^3 - 8x^2 + x -5
Answer:
see below
Step-by-step explanation:
The signs on the bottom line alternate, so the value of k is, indeed, a lower bound.
_____
Comment on lower bound for this cubic
The signs of the coefficients alternate, so Descartes' rule of signs will tell you there are zero negative real roots. That is, 0 is a lower bound for real roots. No synthetic division is needed.
The article modeling sediment and water column interactions for hydrophobic pollutants suggests the uniform distribution on the interval (7.5,20) as a model for depth (cm) of the bioturbation layer in sediment in a certain region stats.
1. what is the mean and variance of depth?
2. what is the cdf of depth?
3. what is the probability that observed depth is at most 10? between 10 and 15?
4.what is the probability that the observed depth is within one standard deviation of the mean value? within 2 standard deviations?
Answer:
1)[tex]\mu=\frac{1}{2}(7.5+20) =13.75[/tex]
[tex]\sigma^2 = \frac{1}{12}(20-7.5)^2 =13.02[/tex]
2) [tex]F(x)=\big\{0, x<a[/tex]
[tex]F(x) =\big\{ \frac{x-a}{b-a}=\frac{x-7.5}{20-7.5}, a\leq x<b[/tex]
[tex]F(x)=\big\{1, x\geq b[/tex]
3) [tex]P(X<10)=F(10)=\frac{10-7.5}{20-7.5}=0.2[/tex]
[tex]P(10\leq X \leq 15)=F(15)-F(10)=\frac{15-7.5}{20-7.5} -\frac{10-7.5}{20-7.5}=0.6-0.2=0.4[/tex]
4) [tex]P(10.142\leq X \leq 17.358)=F(17.358)-F(10.142)=\frac{17.358-7.5}{20-7.5} -\frac{10.142-7.5}{20-7.5}=0.789-0.211=0.578[/tex]
[tex]P(6.534\leqX\leq 20.966)=P(6.534\leq X<7.5)+P(7.5\leq X \leq 20)+P(20<X\leq 20.966)=0+1+0=1[/tex]
Step-by-step explanation:
A uniform distribution, sometimes also known as a rectangular distribution, is a distribution that has constant probability.
Part 1
If X is a random variable that follows an uniform distribution [tex]x\sim U(a,b)[/tex]. The mean for an uniform distribution is given by : [tex]\mu=\frac{1}{2}(a+b)[/tex]
On this case a=7.5 and b=20 so if we replace we got:
[tex]\mu=\frac{1}{2}(7.5+20) =13.75[/tex]
The variance for the uniform distribution is given by this formula:
[tex]\sigma^2 = \frac{1}{12}(b-a)^2 [/tex]
And replacing we have:
[tex]\sigma^2 = \frac{1}{12}(20-7.5)^2 =13.02[/tex]
Part 2
The cumulative distribution function is given by:
[tex]F(x)=\big\{0, x<a[/tex]
[tex]F(x) =\big\{ \frac{x-a}{b-a}=\frac{x-7.5}{20-7.5}, a\leq x<b[/tex]
[tex]F(x)=\big\{1, x\geq b[/tex]
Part 3
What is the probability that observed depth is at most 10?
We are interested on this probability:
[tex]P(X<10)=F(10)=\frac{10-7.5}{20-7.5}=0.2[/tex]
What is the probability that observed depth is between 10 and 15?
On this case we want this probability:
[tex]P(10\leq X \leq 15)=F(15)-F(10)=\frac{15-7.5}{20-7.5} -\frac{10-7.5}{20-7.5}=0.6-0.2=0.4[/tex]
Part 4
What is the probability that the observed depth is within one standard deviation of the mean value? within 2 standard deviations?
First we find the limits within one deviation from the mean:
[tex]\mu-\sigma= 13.75-3.608=10.142[/tex]
[tex]\mu-\sigma= 13.75+3.608=17.358[/tex]
And we want this probability:
[tex]P(10.142\leq X \leq 17.358)=F(17.358)-F(10.142)=\frac{17.358-7.5}{20-7.5} -\frac{10.142-7.5}{20-7.5}=0.789-0.211=0.578[/tex]
Now we find the limits within two deviation's from the mean:
[tex]\mu-2*\sigma= 13.75-2*3.608=6.534[/tex]
[tex]\mu-2*\sigma= 13.75+2*3.608=20.966[/tex]
But since the random variable is defined just between (7.5 and 20) so we can find just the probability on these limits.
[tex]P(6.534\leqX\leq 20.966)=P(6.534\leq X<7.5)+P(7.5\leq X \leq 20)+P(20<X\leq 20.966)=0+1+0=1[/tex]
The probability of the observed depth being at most 10 is 0.295 and between 10 and 15 is 0.295. The probability that the observed depth is within one standard deviation of the mean is 0.525.
Explanation:To find the mean and variance of the depth, we use the formula:
Mean = (a + b) / 2 = (7.5 + 20) / 2 = 13.75 cm
To find the variance, we use the formula:
Variance = (b - a)^2 / 12 = (20 - 7.5)^2 / 12 ≈ 12.1875 cm^2
The cumulative distribution function (CDF) of depth can be calculated by finding the probability that the observed depth is less than or equal to a certain value. In this case, since the depth follows a uniform distribution, the CDF is:
CDF(x) = (x - a) / (b - a)
To find the probability that the observed depth is at most 10, we substitute x=10 into the CDF formula:
CDF(10) = (10 - 7.5) / (20 - 7.5) = 0.295
To find the probability that the observed depth is between 10 and 15, we subtract the CDF of 10 from the CDF of 15:
Probability = CDF(15) - CDF(10) = (15 - 7.5) / (20 - 7.5) - (10 - 7.5) / (20 - 7.5) = 0.59 - 0.295 = 0.295
To find the probability that the observed depth is within one standard deviation of the mean value, we need to find the range between Mean - Standard Deviation to Mean + Standard Deviation. Since the variance is the square of the standard deviation, we take the square root of the variance to find the standard deviation:
Standard Deviation = √Variance = √12.1875 ≈ 3.49 cm
Hence, the range is (Mean - Standard Deviation, Mean + Standard Deviation):
Range = (13.75 - 3.49, 13.75 + 3.49) = (10.26, 17.24) cm
To find the probability within this range, we calculate the difference between the CDF of 17.24 and the CDF of 10.26:
Probability = CDF(17.24) - CDF(10.26) = (17.24 - 7.5) / (20 - 7.5) - (10.26 - 7.5) / (20 - 7.5) ≈ 0.82 - 0.295 ≈ 0.525
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Betty measured the diagonal length of a playing card to be 6 inches. The short side of the card is 4 inches. What is the length of the side of the playing card?
Answer:
The length of the longer side is 4.48 inches.
Step-by-step explanation:
Given,
Length of diagonal = 6 in
Length of Short side = 4 in
Solution,
Let the length of long side be x.
Since the card is in the shape of rectangle. On drawing the diagonal the rectangle divides into two equal triangle.
So for find out the length of other side we use the Pythagoras theorem, which states that;
"In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides."
[tex]Hypotenuse^2=(Short\ side)^2+(Long\ side)^2[/tex]
[tex]\therefore 6^2=4^2+x^2\\36=16+x^2\\x^2=36-16=20\\x=\sqrt{20} =2\sqrt{5}[/tex]
[tex]x=2\times2.24=4.48\ in[/tex]
Thus the length of the longer side is 4.48 inches.
A soccer ball is kicked in the air off a 22.0 meter high hill. The equation h(t)=-5t^2+10t+22 gives the approximated height h, in meters, of the ball t seconds after it is kicked. What equation can be used to tell if the ball reaches a height of 35 meters? Does the ball reach a height of 35 meters? How can you tell?
Equation:____
Answer:____
Answer:
Equation: 5t² − 10t + 13 = 0
Answer: No
Step-by-step explanation:
h(t) = -5t² + 10t + 22
When h(t) = 35:
35 = -5t² + 10t + 22
5t² − 10t + 13 = 0
This equation must have at least one real solution if the ball is to reach a height of 35 meters. Which means the discriminant can't be negative.
b² − 4ac
(-10)² − 4(5)(13)
100 − 260
-160
The ball does not reach a height of 35 meters.
Answer:
Equation: 5t² − 10t + 13 = 0
Answer: No
Find the length of the base of a triangle when one side is 2cm shorter than the base and the other side is 3cm longer than the base. The perimeter is greater than 19cm
Answer:
> 6 cm
Step-by-step explanation:
Let b represent the length of the base in cm. Then the perimeter is ...
b + (b -2) + (b +3) > 19
3b +1 > 19 . . . . . . collect terms
3b > 18 . . . . . . . . subtract 1
b > 6 . . . . . . . . . divide by 3
The length of the base is greater than 6 cm.
The length of the base of the triangle is greater than 6 cm.
Explanation:To find the length of the base of the triangle, let's assume that the base is x cm. According to the question, one side is 2 cm shorter than the base, so its length would be (x - 2) cm. The other side is 3 cm longer than the base, so its length would be (x + 3) cm. The perimeter of a triangle is the sum of all its sides, so we can set up an equation: x + (x - 2) + (x + 3) > 19. Solving this inequality will give us the value of x, which is the length of the base.
Start by simplifying the equation: 3x + 1 > 19.Subtract 1 from both sides: 3x > 18.Divide both sides by 3: x > 6.Therefore, the length of the base of the triangle is greater than 6 cm.
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Richard walked around 2 rectangular parks. One measures 450 feet by 167 feet and the other measures 234 feet by 156 feet. Part B Richard's brother walked around a different park that is 254 feet by 56 feet.
What is the question?
Answer:
The answer is in the explanation.
Step-by-step explanation:
450x2=900 167x2=334 Then you add those together and you get 1,234 then you do 234x2=468 156x2=312 then you add those two, and you get 780 then you add 1,234+780= 2014. For his brother you do 254x2=508 and 56x2=112 then you add them and you get 620. Then you subtract 2014-620= 1394. That is the final answer. Hope it helps!
Solve the inequality and graph the solution
|2x - 7| > 1
Answer:
Open circle to the right of 4
x > 4
Step-by-step explanation:
Add 7 to both sides
2x > 8
x > 4
Open circle to the right of 4
Elizabeth brought a box of donuts to share. There are two-dozen (24) donuts in the box, all identical in size, shape, and color. Three are jelly-filled, four are lemon-filled, and seventeen are custard-filled. You randomly select one donut, eat it, and select another donut.
Find the probability of selecting a lemon-filled donut followed by a custard-filled donut.
Answer:
P = 68/552 = 0.123 or 12.3%
Step-by-step explanation:
First, let's calculate the probability of getting a lemon donut. We have only 4 lemon donut among 24 donuts, so probability is:
P(A) = 4/24
Next, as we already ate the lemon donut, we only have 23 donuts now, and among these 23, 17 are custard filled, so probability of choosing one of those is:
P(B) = 17/23
But we want to know the probability that the custard filled donut is choosen after you eat the lemon one so:
P(B|A) = P(A) * P(B)
Replacing:
P(B|A) = 4/24 * 17/23
P(B|A) = 68/552 = 0.123 or 12.3%
Robert's father is 4 times as old as robert. After 5 years, father will be three times as old as robert.What is their present ages of robert and his father respectively
Answer: Robert's present age is 10 years
Robert father's present age is 40 years
Step-by-step explanation:
Let r = Robert's current age
Let y = Robert father's current age
Robert's father is 4 times as old as robert. This means that
y = 4x
After 5 years, Robert's father will be three times as old as Robert. This means that
y + 5 = 3(x+5)
y + 5 = 3x + 15 - - - - - - - ;1
We will substitute y = 4x into equation 1. It becomes
4x + 5 = 3x + 15
Collecting like terms,
4x - 3x = 15 - 5
x = 10
y = 4x
Substituting x = 10,
y = 4× 10 = 40 years
A girl flies a kite at a height 34 m above her hand. If the kite flies horizontally away from the girl at the rate of 3 m/s, at what rate is the string being let out when the length of the string released is 60 m? Assume that the string remains taut.
Answer:
2.47 m/s
Step-by-step explanation:
A girl flies a kite at a height 34 m above her hand.
It is vertical height of kite, 34 m
The horizontal rate of kite, [tex]\dfrac{dx}{dt}=3/ m/s[/tex]
Let the length of string released be s m
In right triangle using pythagoreous theorem
[tex]s^2=34^2+x^2[/tex]
For s = 60 m ,
[tex]60^2=34^2+x^2[/tex]
[tex]x=49.44[/tex] m
Differentiate the equation [tex]s^2=34^2+x^2[/tex] w.r.t t
[tex]2s\dfrac{ds}{dt}=0+2x\dfrac{dx}{dt}[/tex]
[tex]2\cdot 60\cdot \dfrac{ds}{dt}=2\cdot 49.44\cdot 3[/tex]
[tex]\dfrac{ds}{dt}=\dfrac{296.62}{120}[/tex]
[tex]\dfrac{ds}{dt}=2.47[/tex] m/s
Hence, the rate of string letting out 2.47 m/s
What is the solution of the linear-quadratic system of equations?
y=x^2+5 −3
y − x = 2
The answer is (1,-5).
The solution to the linear-quadratic system of equations is found by substituting y from the linear equation into the quadratic equation and solving for x, then back-solving for y. The system has two solutions: (-5, -3) and (1, 3).
Explanation:To solve the linear-quadratic system of equations:
First, let's use substitution. The second equation can be rearranged to y = x + 2. Substituting this into the first equation gives us:
x + 2 = x2 + 5x - 3
Let's move all terms to one side to make it a quadratic equation:
x2 + 5x - x - 3 - 2 = 0
x2 + 4x - 5 = 0
This is a quadratic equation that can be factored into:
(x + 5)(x - 1) = 0
Setting each factor equal to zero gives us the solutions for x:
Now we'll substitute these x-values back into y = x + 2 to find the corresponding y-values:
Therefore, the system has two solutions: (-5, -3) and (1, 3).
If we needed to use the quadratic formula, it would be in the context of an equation that is not easily factorable.
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The sum of an infinite geometric series is 450, while the common ratio of the series is 4/ 5 . What is the first term of the series? A) 22 1 2 B) 45 C) 90 D) 180
Answer:
answer is 90 for first term
Step-by-step explanation:
Let the terms be
First term x
We will use the formula s∞=x/1−r to find the sum of an infinite geometric series, where −1<r<1.
We know the sum and the common ratio, so we'll be solving for x where r =4/5
s∞=x/1−r
450=x/1−4/5
450=x/1/5
450=5x
x=90
this is the first term x1 = 90
we know that common ratio is 4/5, so multiplying the first term by factor 4/5 to get the second term
90 x 4/5= 72 second term
Answer:
C) 90
Step-by-step explanation:
The sum of an infinite geometric series is:
S = a₁ / (1 − r)
where a₁ is the first term and r is the common ratio.
450 = a₁ / (1 − 4/5)
450 = a₁ / (1/5)
450 = 5a₁
a₁ = 90
Please help me with this!!!
Answer:
{A, H, M, O, P, R, S, T} = {1, 7, 5, 0, 8, 6, 4, 9}
or
{O, A, S, M, R, H, P, T} = {0, 1, 4, 5, 6, 7, 8, 9}
Step-by-step explanation:
Starting in the thousands column, we see the sum P+M+A mod 10 = M, so P + A = 10 or 11. That is, there is a carry to the next column of 1, meaning T + 1 = O, and that sum must also create a carry of 1, so S + 1 = M.
In order for T + 1 to generate a carry, we must have T = 9 and O = 0.
Now, consider the 10s column. This has 36 +A +(carry in) mod 10 = 9. So, A+(carry in) = 3.
Considering the 1s column, we have 9+0+2H+S = H+10 or H+20. We know H+S+9 cannot be 10, so it must be 20. That means H+S = 11, and (carry in) to the 10s column must be 2. Since A = 3 - (carry in), we must have A=1.
At this point, we have ... A=1, T=9, O=0, S+H=11, S+1=M.
Now, consider the 100s column. We know the carry in from the 10s column is 3, so we have 3+2A+R=A+10. Since we know A=1, this means 5+R=11, or R=6.
The carry in to the 1000s column is 1, so we have P+A+1 = 10, or P=8.
__
Our assignments so far are ...
0 = O, 1 = A, 6 = R, 8 = P, 9 = T.
and we need to find S, M, and H such that M=S+1 and S+H=11. We know S and H cannot be 2, 3, or 5, because the 11's complement of those digits is already assigned. That leaves 4 and 7 for S and H, but we also need an unassigned value that is 1 more than S. These considerations make it necessary that S=4, M=5, H=7.
Then the addition problem is ...
8197 + 90 + 5197 +491694 +19 = 505197
_____
Final assignments are ...
O = 0, A = 1, S = 4, M = 5, R = 6, H = 7, P = 8, T = 9
Use Euler's formula to derive the identity. (Note that if a, b, c, d are real numbers, a + bi = c + di means that a = c and b = d. Simplify your answer completely.) sin(2θ) = 2 sin(θ) cos(θ) Using Euler's formula, we have ei(2θ) = + i sin(2θ). On the other hand, ei(2θ) = (eiθ)2 = + i sin(θ) 2 = (cos2(θ) − sin2(θ)) + i sin(θ) . Equating Correct: Your answer is correct. parts, we find sin(2θ) = 2 sin(θ) cos(θ).
Answer with Step-by-step explanation:
We have to prove that
[tex]sin 2\theta=2sin\theta cos\theta[/tex] by using Euler's formula
Euler's formula :[tex]e^{i\theta}=cos\theta+isin\theta[/tex]
[tex]e^{i(2\theta)}=(e^{i\theta})^2[/tex]
By using Euler's identity, we get
[tex]cos2\theta+isin2\theta=(cos\theta+isin\theta)^2[/tex]
[tex]cos2\theta+isin2\theta=(cos^2\theta-sin^2\theta+2isin\theta cos\theta)[/tex]
[tex](a+b)^2=a^2+b^2+2ab, i^2=-1[/tex]
[tex]cos2\theta+isin2\theta=cos2\theta+i(2sin\theta cos\theta)[/tex]
[tex]cos2\theta=cos^2\theta-sin^2\theta[/tex]
Comparing imaginary part on both sides
Then, we get
[tex]sin2\theta=2sin\theta cos\theta[/tex]
Hence, proved.
What is the height of the pyramid?
Answer:
Step-by-step explanation:
280 cubit
Answer:
Step-by-step explanation:
The formula for the volume,V of the square base pyramid is
V = 1/3(lwh)
Where
l = length of one side of the base of the pyramid.
w = length of the other side of the base of the pyramid.
h = the perpendicular height of the pyramid. Since the base of the pyramid is a square, l = w
The Volume, V is given as 18069333.3333 cubits^3
l = 440 cubits
w = 440 cubits
18069333.3333 = 1/3 × 440 × 440 × h
18069333.3333 = 64533.33h
h = 18069333.3333/64533.33
h = 280 cubits
The price of the 8 ounce box is $2.48, and the price of the 14 ounce box is $3.36. How much greater is the cost per ounce of cereal in the 8 ounce box than in the 14 ounce box
Answer:
Step-by-step explanation:
The price of the 8 ounce box is $2.48, we will determine the price per ounce for the 8 ounce box
If 8 ounce = $2.48
1 ounce will be 2.48/8 = $0.31
The price of the 14 ounce box is $3.36
we will also determine the price per ounce for the 14 ounce box
If 14 ounce = $3.36
1 ounce will be 3.36/14 = $0.24
To determine how much greater is the cost per ounce of cereal in the 8 ounce box than in the 14 ounce box, we will subtract the unit cost of the 14 ounce box from the 8 ounce box. It becomes
$0.31 - $0.24= $0.07
During one month, a rental agency rented a total of 155 cars, trucks, and vans. Nine times as many cars were rented as vans, and three times as many vans were rented as trucks. Let x represent cars, let y represent vans and let z represent trucks. Write a system of three equations that represent the number of each vehicle rented
The system of equations that represents the number of each vehicle rented is: x + y + z = 155, x = 9y, and y = 3z.
Explanation:The question represents a system of linear equations. With the agreed notations: Let x represent cars, let y represent vans and let z represent trucks. We are given that:
The total number of all vehicles rented was 155. Therefore, the first equation is: x + y + z = 155. It was also given that nine times as many cars were rented as vans. Thus, the second equation is: x = 9y. Finally, three times as many vans were rented as trucks, giving us the third equation: y = 3z.Learn more about Linear Equations here:
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write a proportion and solve for the question.
121.32 croatian kuna is worth US$18. How much in US dollars would you get for 375 croatian kuna?
Answer:
The worth of 375 Croatian Kuna = $ 55.54
Step-by-step explanation:
Here, given:
The worth of 121.32 Croatian Kuna = $18
Now, let us assume the worth of 375 Croatian Kuna = $ m
As, both have same units in conversion at the same rate,
So, by the RATIO OF PROPORTION:
[tex]\frac{18}{121.32 } = \frac{m}{375}[/tex]
Solving for the value of m, we get:
[tex]m = \frac{18}{121.32} \times 375 = 55.64[/tex]
or, m = $55.64
Hence, the worth of 375 Croatian Kuna = $ 55.54
The function f(x) = 2x + 26 represents the distance a flock of birds travels in in miles. The function g(x) = x − 1 represents the time the flock traveled in hours.
Solve f divided by g of 5, and interpret the answer.
Final answer:
The average speed of the flock of birds over 5 hours is 9 miles per hour, calculated by dividing the distance function f(x) by the time function g(x) at x equal to 5.
Explanation:
The student asked to solve f divided by g of 5 for the given functions f(x) = 2x + 26 and g(x) = x − 1. This will give us the average speed of the flock of birds over the time interval when x equals 5.
First, we substitute x with 5 in both functions:
f(5) = 2(5) + 26 = 10 + 26 = 36 miles
g(5) = 5 − 1 = 4 hours
Next, we divide the outcome of function f by the outcome of function g:
\(\frac{f(5)}{g(5)} = \frac{36}{4} = 9 \) miles per hour
This result represents the average speed of the flock of birds over the time interval when x equals 5 hours.
Mae king earns a weekly salary of $305 plus a 7.5% commission on sales at a gift shop.How much would she make in a work week if she sold 4,300 worth of merchandise
Answer:
Step-by-step explanation:
Mae king earns a weekly salary of $305 plus a 7.5% commission on sales at a gift shop. This means that the total amount that she can earn in a week is not fixed. If in a week, she sold 4,300 worth of merchandise, her commission on this amount of sales will be 7.5 % of 4,300
Commission on sales = 7.5/100× 4300 = 0.075×4300= $332.25
Amount of money made for the week will be the sum of her weekly salary and the commission earned on sales. It becomes
305 + 332.25 = $627.5
Mrs.Gonzalez has 36 students in her class and only 9 of them are boys . What percent of the students in Mrs.Gonzalez class are boys? Write a proportion and show your work please
A new pair of wireless earbuds cost $125. You found earbuds online and the website is offering a 20% discount if you buy them this week. But you remember seeing the same earbuds at your local store on sale for $90. Where will you purchases earbuds? Show work to support your answer please
Question #1:
To find the percentage of boy's in the class, divide.
9 / 36 = 0.25
0.25 * 100% = 25% (boys in the class)
We can write this proportion as 9/36 since this is the same as 25%.
_________
Question #2:
We know that the ear buds in both options cost $125.
The earbuds online are on a 20% discount.
The earbuds in store are on a 90$ sale
Lets find the discount for the online pair.
20% = 0.2
125 * 0.2 = 25
125 - 25 = $100 (price after discount)
After solving we can see that the earbuds in store are a better price. So, you will purchase the ear buds in store.
_________
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9. If AXYZ ~ ARST, find the value of x.
Answer:
12
Step-by-step explanation:
5x-3/3x+2 = 60/40
=> x = 12
Hope it's helpful ;)
Suppose that the functions r and a are defined for all real numbers x as follows. r(x)=2x-1 S(x)=5x write the expressions for (r-s)(x)and(r•s)(x)and evaluate(r+s)(-2).
[tex]\boxed{(r-s)(x)=-3x-1} \\ \\ \boxed{(r\cdot s)(x)=10x^2-5x} \\ \\ \boxed{(r+s)(-2)=-15}[/tex]
Explanation:In this exercise, we have the following functions:
[tex]r(x)=2x-1 \\ \\ s(x)=5x[/tex]
And they are defined for all real numbers x. So we have to write the following expressions:
First expression:
[tex](r-s)(x)[/tex]
That is, we subtract s(x) from r(x):
[tex](r-s)(x)=2x-1-5x \\ \\ Combine \ like \ terms: \\ \\ (r-s)(x)=(2x-5x)-1 \\ \\ \boxed{(r-s)(x)=-3x-1}[/tex]
Second expression:
[tex](r\cdot s)(x)[/tex]
That is, we get the product of s(x) and r(x):
[tex](r\cdot s)(x)=(2x-1)(5x) \\ \\ By \ distributive \ property: \\ \\ (r\cdot s)(x)=(2x)(5x)-(1)(5x) \\ \\ \boxed{(r\cdot s)(x)=10x^2-5x}[/tex]
Third expression:
Here we need to evaluate:
[tex](r+s)(-2)[/tex]
First of all, we find the sum of functions r(x) and s(x):
[tex](r+s)(x)=2x-1+5x \\ \\ Combine \ like \ terms: \\ \\ (r+s)(x)=(2x+5x)-1 \\ \\ (r+s)(x)=7x-1[/tex]
Finally, substituting x = -2:
[tex](r+s)(-2)=7(-2)-1 \\ \\ (r+s)(-2)=-14-1 \\ \\ \boxed{(r+s)(-2)=-15}[/tex]
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Machines A and B always operate independently and at their respective constant rates. When working alone, Machine A can fill a production lot in 5 hours, and Machine B can fill the same lot in x hours. When the two machines operate simultaneously to fill the production lot, it takes them 2 hours to complete the job. What is the value of x ?
Answer:
The value of x is [tex]\frac{10}{3}[/tex] hours.
Step-by-step explanation:
Machine A = 5 hours
Machine B = x hours
Machine A and B = 2 hours
Using the formula: [tex]\frac{T}{A} + \frac{T}{B} = 1[/tex]
where:
T is the time spend by both machine
A is the time spend by machine A
B is the time spend by machine B
[tex]\frac{2}{5} + \frac{2}{x} = 1[/tex]
Let multiply the entire problem by the common denominator (5B)
[tex]5x(\frac{2}{5} + \frac{2}{x} = 1)[/tex]
2x + 10 = 5x
Collect the like terms
10 = 5x - 2x
10 = 3x
3x = 10
Divide both side by the coefficient of x (3)
[tex]\frac{3x}{3} = \frac{10}{3}[/tex]
[tex]x = \frac{10}{3}[/tex] hours.
Therefore, Machine B will fill the same lot in [tex]\frac{10}{3}[/tex] hours.
Find the circumference. Leave your answer in terms of pi.
The circumference of circle with radius 18 inches in terms of pi is 36π inches
Solution:From the given figure, radius "r" = 18 inches
We have to find circumference of circle
circumference would be the length of the circle if it were opened up and straightened out to a line segment.
The circumference of circle is given as:
[tex]\text {circumference of circle }=2 \pi r[/tex]
Where "r" is the radius of circle
Substituting the value r = 18 inches in above formula,
[tex]\text {circumference of circle }=2 \times \pi \times 18=36 \pi[/tex]
Thus circumference of circle in terms of pi is 36π inches
Jill planted two flowers in her garden. The first flower is 2 inches tall, and it is growing 2.25 inches each week. The second plant is 5.75 inches tall, and it is growing 1.5 inches each week. How many weeks will it be until the two plants are the same height?
Answer:it will take the two plants 6 weeks before the heights are the same
Step-by-step explanation:
Jill planted two flowers in her garden.
The first flower is 2 inches tall, and it is growing 2.25 inches each week. Since the growth rate is in an arithmetic progression, we will apply the formula for finding the nth term of the series
Tn = a + (n - 1)d
Tn = the nth height of the first flower
a = the initial height of the first flower
d = the common difference in height of the first flower weekly
n = number of weeks
From the information given,
For the first flower,
a = 2
d = 2.25
Tn ?
n ?
Tn = 2 + (n - 1)2.25
For the second flower,
a = 5.75
d = 1.5
Tn ?
n ?
Tn = 5.75 + (n - 1)1.5
To determine the number of weeks that it will take until the two plants are the same height, we would equate Tn for both flowers. It becomes
2 + (n - 1)2.25 = 5.75 + (n - 1)1.5
2 + 2.25n - 2.25 = 5.75 + 1.5n - 1.5
Collecting like terms
2.25n - 1.5n = 5.75 - 1.5 - 2 + 2.25
0.75n = 4.5
n = 4.5/0.75
n = 6 weeks
To find out how many weeks it will be until the two plants are the same height, set up an equation and solve for x. The plants will be the same height after 5 weeks.
Explanation:To find out how many weeks it will be until the two plants are the same height, we need to set up an equation. Let the number of weeks be represented by x. The height of the first plant can be represented as 2 + 2.25x, and the height of the second plant can be represented as 5.75 + 1.5x. Set these two expressions equal to each other: 2 + 2.25x = 5.75 + 1.5x.
To solve for x, subtract 1.5x from both sides: 2 + 0.75x = 5.75.
Then, subtract 2 from both sides: 0.75x = 3.75.
Finally, divide both sides by 0.75 to solve for x: x = 5.
The angle of inclination from the base of skyscraper A to the top of skyscraper B is approximately 10.4degrees. If skyscraper B is 1472 feet tall, how far apart are the two skyscrapers? Assume the bases of the two buildings are at the same elevation.
Answer:
8020 feet
Step-by-step explanation:
The tangent relation can be used to answer this question, since it relates the sides of a right triangle to the acute angle.
tan(elevation angle) = (1472 ft)/(distance between)
Then ...
distance between = (1472 ft)/tan(10.4°) ≈ 8020 ft
The skyscrapers are 8020 feet apart.
Using the tangent of the given angle of inclination and the height of skyscraper B, the horizontal distance between the bases of the two skyscrapers is calculated to be approximately 8077 feet.
Explanation:The question is looking for the horizontal distance between the bases of two skyscrapers, given the height of one skyscraper and the angle of inclination from its base to the top of the other. This scenario forms a right triangle, where the height of skyscraper B is the opposite side, the distance between the skyscrapers is the adjacent side, and the angle of inclination is the given angle. We can use the tangent trigonometric function, which is the ratio of the opposite side to the adjacent side, to solve for the distance.
To calculate the distance (adjacent side) we can rearrange the equation: Tan(angle) = opposite/adjacent, to: Adjacent = opposite/tan(angle). Plugging in our given values we find: Distance = 1472 feet / tan(10.4 degrees) = approximately 8077 feet. Thus, the two skyscrapers are about 8077 feet apart.
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