Answer:
Carlita's Speed or distance over time
Step-by-step explanation:
The rate of change of the data (her distance) is her speed.
Speed is the rate of change of distance, distance covered overtime.
Speed = distance/time
Unit = meter/seconds or miles per hour
Therefore, the rate of change for that data represent Carlita's Speed or distance over time
A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes 6 hours and 24 minutes, but when there is a wind blowing from Penthaven to Jackson at 50 miles per hour, the trip takes 6 hours and 40 minutes. How many miles is the distance from Penthaven to Jackson?
(Assume that the plane flies at a constant speed, and that the turnaround time is negligible.)
Answer:800 miles
Step-by-step explanation:
Given
Round trip for Penthaven to Jackson takes 6 hr and 24 minutes in absence of wind
[tex]t_1=6+\frac{24}{60}=6.4\ hr[/tex]
When Wind blows from Penthaven to Jackson it takes 6 hr and 40 min i.e.
[tex]t_2=6+\frac{40}{60}=\frac{20}{3}\ hr[/tex]
Speed of wind [tex]v=50\ mph[/tex]
Suppose x be the distance between Penthaven and Jackson and u be the speed of plane
So initially
[tex]6.4=\frac{x}{u}+\frac{x}{u}[/tex]
[tex]6.4=\frac{2x}{u}[/tex]
[tex]x=3.2u \quad \ldots(i)[/tex]
When wind is blowing then,
[tex]\Rightarrow \frac{20}{3}=\frac{x}{u+v}+\frac{x}{u-v}[/tex]
[tex]\Rightarrow \frac{20}{3}=x[\frac{1}{u+50}+\frac{1}{u-50}][/tex]
[tex]\Rightarrow \frac{20}{3}=x[\frac{2u}{u^2-50^2}]\quad \ldots(ii)[/tex]
Substitute the value of x in [tex](ii)[/tex]
[tex]\Rightarrow \frac{20}{3}=\frac{2u[3.2u]}{u^2-50^2}[/tex]
[tex]\Rightarrow 10[u^2-50^2]=9.6u^2[/tex]
[tex]\Rightarrow 0.4u^2=50^2\times 10[/tex]
[tex]\Rightarrow u^2=\frac{50^2\times 10^2}{4}[/tex]
[tex]\Rightarrow u=250\ mph[/tex]
Thus [tex]x=3.2\times 250=800\ miles[/tex]
Kim spent 40/100 of a dollar on a snack write as a money amount she has left.
[tex]\frac{60}{100}[/tex] of a dollar
A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters.
Kim spent [tex]\frac{40}{100}[/tex] of a dollar on a snack.
So, she has been left with [tex]1-\frac{40}{100}=\frac{60}{100}[/tex] of a dollar on a snack.
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Final answer:
Kim spent 40/100 of a dollar (40 cents) on a snack, so she has 60 cents left.
Explanation:
The question requires converting a fraction of a dollar into a money amount. Kim spent 40/100 of a dollar on a snack. A dollar is equivalent to 100 cents, so Kim spent 40 cents on her snack. To find out how much she has left, we subtract her spending from the total amount of one dollar.
To perform the calculation: 100 cents - 40 cents = 60 cents.
Therefore, Kim has 60 cents left after purchasing the snack.
Divide the school into classes and then randomly select students from each class is an example of:
Answer:
Stratified sampling
Step-by-step explanation:
Members of the population are divided into two or more subgroups called strata, that share similar characteristics like age, gender, or ethnicity. A random sample from each stratum is then drawn. For instance, if we divide the population of college students into strata based on the number of years in school, then our strata would be freshmen, sophomores, juniors, and seniors. We would then select our sample by choosing a random sample of freshmen, a random sample of sophomores, and so on.
This technique is used when it is necessary to ensure that particular subsets of a population are represented in the sample. Since a random sample cannot guarantee that sophomores would be chosen, we would used a stratified sample if it were important that sophomores be included in our sample. Furthermore, my using stratified sampling you can preserve certain characteristics of the population. For example, if freshmen make up 40% of our population, then we can choose 40% of our sample from the freshmen stratum. Stratified sampling is one of the best ways to enforce "representativeness" on a sample.
If the original quantity is 20 and the new quantity is 18, what is the percent decrease?
Answer:
10%
Step-by-step explanation:
There are many different ways but I did 18 divided by 20 and got 0.9. I did 1 - 0.9 to get 0.1, which is 10%
Gina and Stewart are surf-fishing on the Atlantic coast, where both bluefish and pompano are common catches. The mean length of a bluefish is 264 millimeters with a standard deviation of 57mm. For pompano, the mean is 157mm with a standard deviation of 28mm.
Stewart caught a bluefish that was 283mm long, and Gina caught a pompano that was 152mm long. Who caught the longer fish, relative to fish of the same species?
Answer:
Due to the higher z-score, Stewart caught the longer fish, relative to fish of the same species
Step-by-step explanation:
Problems of normally distributed samples are solved using 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.
Who caught the longer fish, relative to fish of the same species?
Whosoever fish's had the higher z-score.
Stewart caught a bluefish that was 283mm
The mean length of a bluefish is 264 millimeters with a standard deviation of 57mm.
So we have to find Z when [tex]X = 283, \mu = 264, \sigma = 57[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{283 - 264}{57}[/tex]
[tex]Z = 0.33[/tex]
Gina caught a pompano that was 152mm long.
For pompano, the mean is 157mm with a standard deviation of 28mm.
So we have to find Z when [tex]X = 152, \mu = 157, \sigma = 28[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{152 - 157}{28}[/tex]
[tex]Z = -0.18[/tex]
Due to the higher z-score, Stewart caught the longer fish, relative to fish of the same species
The correct answer is Stewart caught the longer fish relative to fish of the same species.
To determine who caught the longer fish relative to the average length of their respective species, we need to calculate the z-scores for both Stewart's bluefish and Gina's pompano. The z-score is a measure of how many standard deviations an observation is above or below the mean.
For Stewart's bluefish:
The mean length of a bluefish is 264 mm, and the standard deviation is 57 mm. Stewart's bluefish is 283 mm long. To find the z-score for Stewart's bluefish, we use the formula:
[tex]\[ z = \frac{X - \mu}{\sigma} \][/tex]
where X is the observed value, [tex]\( \mu \)[/tex] is the mean, and [tex]\( \sigma \)[/tex] is the standard deviation. Plugging in the values for Stewart's bluefish:
[tex]\[ z_{Stewart} = \frac{283 - 264}{57} \] \[ z_{Stewart} = \frac{19}{57} \] \[ z_{Stewart} \approx 0.333 \][/tex]
For Gina's pompano:
The mean length of a pompano is 157 mm, and the standard deviation is 28 mm. Gina's pompano is 152 mm long. To find the z-score for Gina's pompano:
[tex]\[ z = \frac{X - \mu}{\sigma} \] \[ z_{Gina} = \frac{152 - 157}{28} \] \[ z_{Gina} = \frac{-5}{28} \] \[ z_{Gina} \approx -0.179 \][/tex]
Comparing the z-scores:
Stewart's z-score is approximately 0.333, which means his bluefish is 0.333 standard deviations longer than the average bluefish. Gina's z-score is approximately -0.179, which means her pompano is 0.179 standard deviations shorter than the average pompano.
Since Stewart's z-score is positive and larger in magnitude than Gina's negative z-score, Stewart's bluefish is longer relative to its species than Gina's pompano is relative to its species. Therefore, Stewart caught the longer fish relative to fish of the same species.
7. There are seven clarinet players in the concert band. In how
many ways can they be seated in seven chairs at a concert?
Use the Fundamental Counting Principle.
A. 5,040
C. 840
B. 2,520
D. 210
Answer:
Step-by-step explanation:
The number of people in the cabinet is 7.
n = 7.
Fundamental Counting Principle states that if there are m ways of doing a thing and there are n ways of doing other thing then there are total m*n ways of doing both things.
now using fundamental Counting Principle.
since 7 players can sit on chair in
7 , 6, 5 , 4, 3 , 2, 1 ways then together they can be seated in
7 * 6 * 5 * 4 * 3 * 2 * 1 ways = 5,040 ways.
To arrange this seven people in a straight cabinet, the number of way to arrange them is n!
Then,
n! = 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040.
There are 5040 ways of arranging them.
Option A is correct.
help me find the function pls
Answer:
see below
Step-by-step explanation:
The tangent function has been shifted upward by 2 units, but there has been no horizontal scaling. Any horizontal offset must be equal to some number of whole periods.
Choices A and B show tan( )+2, the correct vertical offset. However, choice A has a horizontal scale factor of 2. The correct choice is B, which has no horizontal scaling (the coefficient of x is 1) and a horizontal offset of π, one full period.
_____
Comment on horizontal scaling
Horizontal scaling is different from vertical scaling in that using k·x in place of x compresses the graph horizontally by a factor of k. On the other hand, using k·f(x) in place of f(x) expands the graph vertically by a factor of k.
How many treaspoons are in 20mls
There are 4 teaspoons in 20 mils. I just learned this in class.
-Dhruva;)
Answer:
4.05768 or 4
Step-by-step explanation:
There are 0.202884 teaspoon in a millilitre. If you multiply 0.202884 by 20, you 4.05768.
I am 100% sure (:
Can i pls have brainliest?
-ME
Determine the approximate value of x.
a.
b.
2.13
3.53
c. 4.39
d. 7.52
We have been given a right triangle. We are asked to find the value of x.
We can see that x is opposite side to angle that measures 62 degrees and adjacent side to angle is 4 units.
We know that tangent relates adjacent and opposite side of right triangle.
[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]
[tex]\text{tan}(62^{\circ})=\frac{x}{4}[/tex]
[tex]4\cdot \text{tan}(62^{\circ})=\frac{x}{4}\cdot 4[/tex]
[tex]4\cdot (1.880726465346)=x[/tex]
[tex]7.522905861384=x[/tex]
[tex]x=7.522905861384[/tex]
[tex]x\approx 7.52[/tex]
Therefore, the value of x is approximately 7.52 units and option 'd' is the correct choice.
On a coordinate plane, two parabolas open up. The solid-line parabola, labeled f of x, goes through (negative 2, 4), has a vertex at (0, 0), and goes through (2, 4). The dashed-line parabola, labeled g of x, goes through (negative 6, 10), has a vertex at (negative 4, 6), and goes through (negative 2, 10).
What is the equation of the translated function, g(x), if
f(x) = x2?
g(x) = (x – 4)2 + 6
g(x) = (x + 6)2 – 4
g(x) = (x – 6)2 – 4
g(x) = (x + 4)2 + 6
Answer:
[tex]y = (x+4)^{2}+6[/tex]
Step-by-step explanation:
The parabola with vertex at point (h,k) is described by the following model:
[tex]y - k = C\cdot (x-h)^{2}[/tex]
The equation which satisfies the conditions described above:
[tex]y - 6 = (x+4)^{2}[/tex]
[tex]y = (x+4)^{2}+6[/tex]
The two points are evaluated herein:
x = -6
[tex]y =(-6+4)^{2}+6[/tex]
[tex]y = (-2)^{2}+6[/tex]
[tex]y = 4 + 6[/tex]
[tex]y = 10[/tex]
x = -2
[tex]y = (-2+4)^{2}+6[/tex]
[tex]y = 2^{2} + 6[/tex]
[tex]y = 4 + 6[/tex]
[tex]y = 10[/tex]
The equation of the translated function is [tex]y = (x+4)^{2}+6[/tex].
Trigonometry: Question 2
In triangle ABC with right angle C, the measure of angle A is 37
degrees, and the length of the hypotenuse is 10. What is the length of
AC?
Select one:
12,5
7.9
Answer:
b = 7.9
Step-by-step explanation:
A = 37 a =
B = 53 b =
C = 90 c = 10
B = 180 - 90 -37 = 53
[tex]\frac{sinB}{b} = \frac{sinC}{c}\\ \frac{sin(53)}{b} = \frac{sin(90)}{10}\\ b = \frac{10 sin(53)}{sin(90)} \\b = 7.9[/tex]
To find the length of side AC in a right-angled triangle ABC with angle A of 37 degrees and hypotenuse 10, we use the cosine function. AC equals the hypotenuse multiplied by the cosine of angle A, resulting in AC being approximately 7.9 units long.
Explanation:The student wants to know the length of side AC in a right-angled triangle ABC, where angle C is a right angle, angle A is 37 degrees, and the hypotenuse (side BC) is 10. To find the length of side AC, we will use trigonometric functions. Specifically, we will use the cosine function, which relates the adjacent side to the hypotenuse in a right-angled triangle. The cosine of angle A (cos 37°) is equal to the adjacent side (AC) divided by the hypotenuse (BC).
The formula is: Cosine of angle A = AC / BC
This can be rewritten as: AC = BC * Cosine of angle A
By substituting the given values (BC = 10 and angle A = 37°), we get:
AC = 10 * cos(37°)
To find cos(37°), we can use a calculator set to degree mode. The calculation gives us:
AC = 10 * 0.7986 (approximately)
Therefore, AC ≈ 10 * 0.7986 = 7.986
AC is approximately 7.9 units long.
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Giving brainliest for CORRECT awnser.
Answer:
C. F(x) = x²
Step-by-step explanation:
"Quadratic" means "second degree". The only function with an exponent of 2 is choice C.
what is the simplest form of this expression? m(m+4)+m(m-2)
Answer:
First by expansion,
mxm +mx4 + mxm + mx(-2)
=m^2 +4m + m^2 - 2m
= 2m^2 + 2m
Note: ^2 means square
Step-by-step explanation:
Lauren makes bracelets using small beads. She uses
60 beads for each bracelet. How many beads does
Lauren need to make 7 bracelets?
A 42 beads
C 420 beads
B 67 beads
D 670 beads
Answer:
420
Step-by-step explanation:
She uses 60 beads per bracelet and is making 7 bracelets
7*60 = 420 beads total
PLEASE HELP ASAP
Jessica brings her friends to a party. There are 40 people attending. Jessica brings 2 friends there. How many people are at the party without Jessica and her friends?
a. 37
b. 38
c. 40
d. 3
Answer:
a. 37
Step-by-step explanation:
"Jessica brings her friends to a party. There are 40 people attending. Jessica brings 2 friends there. How many people are at the party without Jessica and her friends?
"
40 total minus Jessica and her friends = 37
Hope this helps!
Answer:
C.) 37 I think
Step-by-step explanation:
SoRrY i'M nOt sMaRt. But i think it's 37 and then minus her and her 2 friends means:
[tex]40-3=37:)[/tex]
An ice cream cone has a radius of 2 in. How much melted ice cream will the cone hold if it has a height of 6 inches?
Answer:
it will hold 25.13 cubic inches of melted ice cream
Step-by-step explanation:
first we get the cone formula because a melted ice cream cone will have a flat top, making it a cone
the cone formula is π*r^2 * h /3
so we input radius and height
π*2^2 * 6 /3
then we simplfy
π * 4 * 6 /3
12.56 *6/3
75.398/3
25.13
If u = <-7, 6> and v = <-4, 17>, which vector can be added to u + 3v to get the unit vector <1, 0> as the resultant vector?
With u = <-7, 6> and v = <-4, 17>, we have
u + 3v = <-7, 6> + 3 <-4, 17> = <-7, 6> + <-12, 51> = <-19, 57>
We want to find a vector w such that
u + 3v + w = <1, 0>
Subtract u + 3v from both sides to get
w = <1, 0> - (u + 3v) = <1, 0> - <-19, 57>
w = <20, -57>
To get the required vector, subtract u + 3v from the unit vector <1, 0>. The required vector is <20, -57>.
Explanation:To find the vector that can be added to u + 3v to get the unit vector <1, 0>, we need to subtract u + 3v from the unit vector. This will give us the required vector. Let's calculate:
Unit vector: <1, 0>
u + 3v: <-7, 6> + 3<-4, 17> = <-7, 6> + <-12, 51> = <-19, 57>
Required vector = Unit vector - (u + 3v) = <1, 0> - <-19, 57> = <1 + 19, 0 - 57> = <20, -57>
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There are 3 feet in 1 yard. This is equivalent to 12 feet in 4 yards. Which proportion can be used to represent this? StartFraction 12 over 1 EndFraction = StartFraction 4 over 12 EndFraction One-third = StartFraction 12 over 4 EndFraction StartFraction 3 over 1 EndFraction = StartFraction 4 over 12 EndFraction StartFraction 3 over 1 EndFraction = StartFraction 12 over 4 EndFraction
Answer:
[tex]\dfrac{3}{1}=\dfrac{12}{4}[/tex]
Step-by-step explanation:
If you write the proportion as ratios of feet to yards, you have ...
[tex]\dfrac{3\,\text{ft}}{1\,\text{yd}}=\dfrac{12\,\text{ft}}{4\,\text{yd}}\\\\\boxed{\dfrac{3}{1}=\dfrac{12}{4}}\qquad\text{without the units}[/tex]
__
Please note that a proportion is a true statement. Here, you need only pick the true statement from those offered. For example, here's the first choice written in more readable form:
[tex]\dfrac{12}{1}=\dfrac{4}{12}\qquad\text{FALSE statement}[/tex]
Answer:
d: 3/1 12/4
Step-by-step explanation:
One study estimated that bears populate the Kenai Peninsula of Alaska at a rate of 424242 bears per 1,000 \text { km}^21,000 km 2 1, comma, 000, start text, space, k, m, end text, squared of available habitat. According to this study, about how many bears would you expect to find in a habitable region of this peninsula 8,500 \text { km}^28,500 km 2 8, comma, 500, start text, space, k, m, end text, squared in size?
Answer:
357 bears
Step-by-step explanation:
Given;
Population density of bears in the Kenai Peninsula of Alaska = 42 bears per 1000km^2
Area of habitable region of this peninsula = 8500 km^2
how many bears would you expect to find in a habitable region of this peninsula N;
N = population density × area
N = 42/1000 × 8500
N = 357 bears
A Ferris wheel has a diameter of 40 feet. What is its circumference?
Round to the nearest tenth. Use 3.14 for .
Answer:125.6 feet
Step-by-step explanation:
diameter=40 feet
π=3.14
Circumference= π x diameter
Circumference=3.14 x 40
Circumference=125.6
In order to estimate the difference between the average hourly wages of employees of two branches of a department store, the following data have been gathered. Downtown Store North Mall Store Sample size 25 20 Sample mean $9 $8 Sample standard deviation $2 $1 Refer to Exhibit 10-7. A 95% interval estimate for the difference between the two population means is
Answer:
[tex] (9-8) -2.02 \sqrt{\frac{2^2}{25} +\frac{1^2}{20}}= 0.0743[/tex]
[tex] (9-8) +2.02 \sqrt{\frac{2^2}{25} +\frac{1^2}{20}}= 1.926[/tex]
And we are 9% confidence that the true mean for the difference of the population means is given by:
[tex] 0.0743 \leq \mu_1 -\mu_2 \leq 1.926[/tex]
Step-by-step explanation:
For this problem we have the following data given:
[tex]\bar X_1 = 9[/tex] represent the sample mean for one of the departments
[tex]\bar X_2 = 8[/tex] represent the sample mean for the other department
[tex]n_1 = 25[/tex] represent the sample size for the first group
[tex]n_2 = 20[/tex] represent the sample size for the second group
[tex]s_1 = 2[/tex] represent the deviation for the first group
[tex]s_2 =1[/tex] represent the deviation for the second group
Confidence interval
The confidence interval for the difference in the true means is given by:
[tex] (\bar X_1 -\bar X_2) \pm t_{\alpha/2} \sqrt{\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}[/tex]
The confidence given is 95% or 9.5, then the significance level is [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. The degrees of freedom are given by:
[tex] df=n_1 +n_2 -2= 20+25-2= 43[/tex]
And the critical value for this case is [tex] t_{\alpha/2}=2.02[/tex]
And replacing we got:
[tex] (9-8) -2.02 \sqrt{\frac{2^2}{25} +\frac{1^2}{20}}= 0.0743[/tex]
[tex] (9-8) +2.02 \sqrt{\frac{2^2}{25} +\frac{1^2}{20}}= 1.926[/tex]
And we are 9% confidence that the true mean for the difference of the population means is given by:
[tex] 0.0743 \leq \mu_1 -\mu_2 \leq 1.926[/tex]
Each costume for a dance group in a talent show requires 2 yards of black material and 3 yards of red material. The dance group has 30 yards of black material and 60 yards of red material. What is the greatest number of costumes they can make? Please explain the steps
Answer:
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
30 / 2 = 15
60 / 3 = 20
if we try both numbers to see if the limit is ever crossed, that is the case only with 20
15 is the maximum amount of costumes
What do dinosaurs use to run their cars?
Answer:
Probably the engine from their helicopter
Step-by-step explanation:
If y varies directly as x and y=8 when x=3 what is the value of y when x=9?
A 8/3
B 27/8
C 14
D 24
Answer:
24
Step-by-step explanation:
y=24 when x=3 because you * 3*3=9 so you do 8*3=24 which you your answer
The value of y when x = 9 such that the y varies directly with respect to x is 24 therefore, option (D) will be correct.
What are the ratio and proportion?Proportion is the relation of a variable with another. It could be direct or inverse.
The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
As per the given question,
y varies directly as x
y ∝ x
Removing proportion y = kx
Given that,y=8 when x=3
So, k = 8/3
Therefore, relation converts as, y = (8/3)x
At x = 9 → y = (8/3)9 = 24
Hence "The value of y when x = 9 such that the y varies directly with respect to x is 24".
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Helpppppppppppppppppp
Answer:
4*4*4*4*4
Step-by-step explanation:
Exponents are written as
b^x
where b is the base, and x is the number of times the base is being multiplied
We have
4^5
Therefore, 4 is the base, and it is being multiplied 5 times.
If we are to write it out, we have:
4*4*4*4*4
Therefore, the correct choice is B
Select the graph that represent the equation (x-6)^2+(y+7)^2=16
Answer:
This is a circle with centre (6,-7) and radius 4.
Step-by-step explanation:
The equation of a circle has the following format:
[tex](x - x_{0})^{2} + (y - y_{0})^{2} = r^{2}[/tex]
In which r is the radius(half the diameter) and the centre is the point [tex](x_{0}, y_{0})[/tex]
In this question:
[tex](x-6)^{2} + (y+7)^{2} = 16[/tex]
So
[tex]x_{0} = 6, y_{0} = -7[/tex]
[tex]r^{2} = 16[/tex]
[tex]r = \pm \sqrt{16}[/tex]
The radius is the positive value.
[tex]r = 4[/tex]
So this is a circle with centre (6,-7) and radius 4.
Answer:
Given equation
(x-6)^2+(y+7)^2=16
centre (6,-7) and radius 4.
Step-by-step explanation:
The equation of a circle is (x - a)² + (y - b)² = r²
the radius is r
the centre is (a, b)
Given equation
(x-6)^2+(y+7)^2=16
so ,
a = 6
b = - 7
r² = 16
[tex]r = \pm \sqrt{16}[/tex]
r = 4
Therefore, the circle with centre (6,-7) and radius 4.
What is the area of a square with side length of 4 and one-fourth m?
Answer:18.0625m^2
Step-by-step explanation:
Length =4 1/4 m
Area= length x length
Area=4 1/4 x 4 1/4
Area=(4x4+1)/4 x (4x4+1)/4
Area=17/4 x 17/4
Area=(17x17)/(4x4)
Area=289/16
Area=18.0625m^2
when oxygen reacts with hydrogen it has the capacity to release 29 kilojoules of energy. Inside a fuel cell, oxygen reacts with hydrogen to produce 23 kilojoules of useful energy. The rest of the energy is lost as heat. Whats the efficiency percent of the fuel cell?
Answer:
79
Step-by-step explanation:
A clownfish costs $3.60 to buy. An angelfish costs $5.80 to buy. Joy spends $42.00 on some clownfish and some angelfish. She buys at least one of each. How many of each type does she buy? What if she had $52 to spend on fish? How many of each type did she buy?
Answer:
a) 6 angelfish, 2 clownfish
b) 4 angelfish, 8 clownfish
Step-by-step explanation:
There are at least a couple of different algorithms for finding integer solutions to problems like this. However, it is easiest to describe a trial-and-error solution.
Here, we have defined a function that tells us the number of clownfish we will get if we purchase some number of angelfish. When the function value is an integer, we have found a solution. We compute the value of the function for all reasonable numbers of angelfish.
a) The problem statement tells us the total purchase amount for "c" clownfish and "a" angelfish will be ...
3.60c +5.80a = 42.00
We are told that we must buy at least 1 of each kind of fish, so the most clownfish we can buy will be ...
3.60c +5.80×1 = 42.00
c = (42.00 -5.80)/3.60 = 10 1/18
And the most angelfish we can buy will be ...
3.60×1 +5.80a = 42.00
a = (42.00 -3.60)/5.80 = 6 18/29
Since we can buy fewer angelfish, a trial-and-error solution will look a the number of clownfish we can buy for each different purchase of angelfish.
We can write a function, similar to the equation for "c" above, that tells us the number of clownfish for x angelfish:
f(x) = (42 -5.80x)/3.60
We want to find the value of x that results in an integer number of clownfish. The attached table shows us that purchase of 6 angelfish will allow purchase of 2 clownfish for $42.
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b) Using the same idea, we can repeat the process for a total purchase of $52. The attached table tells us the solution is a purchase of 4 angelfish and 8 clownfish for $52.
Beth writes a number that shows 60 parts out of 100. Select all that could be Beth's number
Beth's number, which indicates 60 parts out of 100, can be expressed as 60%, 0.60, 60/100, or in simplest form, 3/5. These representations are commonly used in mathematics to show percentages and their equivalent values.
Beth writes a number that shows 60 parts out of 100. In mathematics, expressing a part out of 100 is essentially describing a percentage. So, Beth's number could be expressed in several ways that all represent 60 out of 100. The simplest form would be 60%, which directly translates to 60 per 100. Another possible representation could be 0.60, which is the decimal form equivalent to 60%. If we were to convert this percentage into a fraction, it would be
60/100, which can also be simplified to
3/5. It cannot be a number such as N(60, 5.477) which suggests a normal distribution with a mean of 60 and a standard deviation of 5.477, nor can it be .9990 which is not equivalent to 60 parts out of 100 in any common mathematical representation.