Answers
8. x=(a+b)/c.
The given equation is,
(b-cx)/a+(a-cx)/b+2=0
⇒b/a-cx/a+a/b-cx/b+2=0
Taking the variables to LHS and constants to RHS,
-cx/a-cx/b=-b/a-a/b-2
or, cx/a+cx/b=b/a+a/b+2
or, cx(1/a+1/b)=b/a+a/b+2
Multiplying both sides of the above equation by ab,
or, cx(a+b)/ab=(a²+b²+2ab)/ab
⇒cx(a+b)=(a²+b²+2ab)
or, cx(a+b)=(a+b)²
∴ x=(a+b)²/c(a+b)=(a+b)/c
Hence x=(a+b)/c.
9. x= -ab(c-a+b)
The given equation is,
a/(x+a)+b/(x-b)=(a+b)/(x+c)
Multiplying the LHS and RHS of the equation by (x+a)(x-b)(x+c),
a(x-b)(x+c)+b(x+a)(x+c)=(a+b)(x+a)(x-b)
⇒a(x²-bx+cx-bc)+b(x²+ax+cx+ac)=(a+b)(x²+ax-bx-ab)
The above equation has terms with variables x²,x and constant terms.
Keeping the like terms together,
x²(a+b-a-b)+x(-ab+ac+ab+bc-a²+b²)= abc-abc-a²b-ab²
⇒ x²(0)+x(ac+bc-a²+b²)= -a²b-ab²
⇒ x = (-a²b-ab²)/(ac+bc-a²+b²)
= -ab(a+b)/[c(a+b)-(a+b)(a-b)]
= -ab(a+b)/(a+b)(c-a+b)
= -ab/(c-a+b)
Hence, x= -ab/(c-a+b)
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The solutions for questions 8 and 9 are:
8. b = (ac - 2ab)/(2-a)
9. x = [-b ± sqrt((a+b)^2 + 4b(a+c))]/(2b)
How did we get the values?To solve the equation:
(b-cx)/a+(a-cx)/b+2=0
Simplify the equation by finding a common denominator.
Multiply the first term by b/b and the second term by a/a, then add them together:
(b^2 - bcx + a^2 - acx)/(ab) + 2 = 0
collect like terms:
(b^2 + a^2)/(ab) - cx(a+b)/(ab) + 2 = 0
Multiply both sides by ab to eliminate the denominator:
b^2 + a^2 - cx(a+b) + 2ab = 0
Simplify:
cx = (a^2 + b^2 + 2ab)/(a+b)
cx = (a+b)^2/(a+b)
cx = a+b
Substitute cx with a+b:
(b-c(a+b))/a + (a-c(a+b))/b + 2 = 0
Simplify:
(2b - ac - bc)/(ab) = -2
Multiply both sides by ab:
2b - ac - bc = -2ab
Solve for b:
b = (ac - 2ab)/(2-a)
9. To solve the equation:
a/(x+a) + b/(x-b) = (a+b)/(x+c)
We can start by finding a common denominator on the left side:
(a(x-b) + b(x+a))/((x+a)(x-b)) = (a+b)/(x+c)
Simplify:
(ax - ab + bx + ab)/((x+a)(x-b)) = (a+b)/(x+c)
collect like terms:
(ax + bx)/((x+a)(x-b)) = (a+b)/(x+c)
Factor out x:
x(a+b)/((x+a)(x-b)) = (a+b)/(x+c)
Cross-multiply:
(a+b)(x+c) = x(a+b)(x-b)
Expand and simplify:
ax + bx + ac + bc = ax^2 - bx^2
Rearrange and simplify:
bx^2 + (a+b)x - (a+c)b = 0
Use the quadratic formula to solve for x:
x = [-b ± sqrt((a+b)^2 + 4b(a+c))]/(2b)
Note that this equation has a restriction on x, namely that x cannot be equal to a or b, since that would make some of the denominators zero.
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Related Questions
Let R be the region in the first quadrant bounded by the graph of y=x3 the line x=2 and the x-axis. R is the base of a solid whose cross sections perpendicular to the x-axis are equilateral triangles. What is the volume of the solid?
Answers
The volume of the solid will be 32/7 √3.
How to calculate the volumeSince base of a solid whose cross-sections is perpendicular to the w-axis are equilateral triangles
Now base of triangle. is f(x) = x³ and the Area of Equilateral Triangle is ✓3/4 base²
The volume of the solid will be:
= ✓3/4 (x^7/7)²
= ✓3/4 (128/7)
= 32/7 √3
Therefore, the volume of the solid will be 32/7 √3.
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(1 point) Estimate I = S." (+2) + dx using n = 4 subintervals and (a) Left endpoints. I (b) Right endpoints. IM
Answers
To estimate I = S." (+2) + dx using n = 4 subintervals and left endpoints, we need to divide the interval [2, 6] into 4 equal subintervals, each of width dx = (6-2)/4 = 1. Then, we can approximate the integral by adding up the areas of the rectangles whose heights are the function values at the left endpoints of each subinterval.
(a) Using left endpoints, the approximation of the integral is:
I ≈ sum from i=0 to 3 of f(2+i*dx)*dx
= f(2)*dx + f(3)*dx + f(4)*dx + f(5)*dx
= f(2)*1 + f(3)*1 + f(4)*1 + f(5)*1
(b) Using right endpoints, the approximation of the integral is:
I ≈ sum from i=1 to 4 of f(2+i*dx)*dx
= f(3)*dx + f(4)*dx + f(5)*dx + f(6)*dx
= f(3)*1 + f(4)*1 + f(5)*1 + f(6)*1
In both cases, we simply evaluate the function at the specified endpoints of each subinterval, multiply by the width of the subinterval, and sum up the results.
Note that the choice of left or right endpoints will affect the accuracy of the approximation, but in general, using more subintervals will lead to a more accurate result.
(a) Left Endpoints:
To estimate I using 4 subintervals and left endpoints, first divide the interval [0, 2] into 4 equal subintervals. Each subinterval has width Δx = (2 - 0) / 4 = 0.5. The left endpoints of these subintervals are x = 0, 0.5, 1, and 1.5. The integral estimate is:
I ≈ Δx[f(0) + f(0.5) + f(1) + f(1.5)]
Evaluate the function at these points, and then multiply the sum by Δx.
(b) Right Endpoints:
To estimate I using 4 subintervals and right endpoints, again divide the interval [0, 2] into 4 equal subintervals with width Δx = 0.5. The right endpoints of these subintervals are x = 0.5, 1, 1.5, and 2. The integral estimate is:
I ≈ Δx[f(0.5) + f(1) + f(1.5) + f(2)]
Evaluate the function at these points, and then multiply the sum by Δx.
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if you roll two fair six-sided dice, what is the probability that the sum is 4 44 or higher?
Answers
The probability of rolling two fair six-sided dice and getting a sum of 4 or higher is 11/12
To calculate the probability of rolling two fair six-sided dice and getting a sum of 4 or higher, we first need to calculate the total number of possible outcomes.
The number of possible outcomes when rolling two dice is 6 × 6 = 36, since each die has 6 possible outcomes.
Now, let's find the number of outcomes that result in a sum of 4 or higher. We can do this by listing all the possible outcomes:
Sum of 4: (1, 3), (2, 2), (3, 1) = 3 outcomes
Sum of 5: (1, 4), (2, 3), (3, 2), (4, 1) = 4 outcomes
Sum of 6: (1, 5), (2, 4), (3, 3), (4, 2), (5, 1) = 5 outcomes
Sum of 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) = 6 outcomes
Sum of 8: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2) = 5 outcomes
Sum of 9: (3, 6), (4, 5), (5, 4), (6, 3) = 4 outcomes
Sum of 10: (4, 6), (5, 5), (6, 4) = 3 outcomes
Sum of 11: (5, 6), (6, 5) = 2 outcomes
Sum of 12: (6, 6) = 1 outcome
Therefore, the number of outcomes that result in a sum of 4 or higher is 3 + 4 + 5 + 6 + 5 + 4 + 3 + 2 + 1 = 33.
Therefore, the probability of rolling two fair six-sided dice and getting a sum of 4 or higher is 33/36 = 11/12.
To find the probability of getting a sum of 44 or higher, we need to subtract the probability of getting a sum of 43 or lower from 1:
Sum of 2: (1, 1) = 1 outcome
Sum of 3: (1, 2), (2, 1) = 2 outcomes
Sum of 4: (1, 3), (2, 2), (3, 1) = 3 outcomes
Sum of 5: (1, 4), (2, 3), (3, 2), (4, 1) = 4 outcomes
Sum of 6: (1, 5), (2, 4), (3, 3), (4, 2), (5, 1) = 5 outcomes
Sum of 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) = 6 outcomes
Sum of 8: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2) = 5 outcomes
Sum of 9: (3, 6), (4, 5), (5, 4), (6, 3) = 4 outcomes
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in a psychology class, 37 students have a mean score of 86.9 on a test. then 22 more students take the test and their mean score is 74.4. what is the mean score of all of these students together? round to one decimal place.
Answers
The mean score of all the students together is 83.1 (rounded to one decimal place).
The mean score of all the students together can be calculated using the formula:
(mean score of first group * number of students in first group + mean score of second group * number of students in second group) / (total number of students)
Substituting the values, we get:
(86.9 * 37 + 74.4 * 22) / (37 + 22)
= (3215.3 + 1636.8) / 59
= 4852.1 / 59
= 82.3
Therefore, the mean score of all the students together is 82.3, rounded to one decimal place.
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On July 11, Ali joined a gulf club. His bank will automatically deduct BD 100 from his checking account at the end of each month, and deposit it into his gulf club account, where it will earn 8% annual interest. The account comes to term on October 7. Find the following: a. Find the future value of Ali's gulf club account
Answers
Ali's Gulf club account will have a future value of BD 101.93 at the end of the term on October 7. The calculation was done using the formula for future value of an annuity with monthly payments, interest rate of 8% per year, and a term of 2.9 months.
We can first calculate the number of months from July 11 to October 7: 2 months and 27 days (or approximately 2.9 months).
Then, we can use the formula for future value of a present sum with simple interest
FV = P(1 + rt)
where FV is the future value, P is the present sum (in this case, BD 100), r is the annual interest rate (8% = 0.08), and t is the time in years (2.9/12 = 0.2417 years).
Substituting the values, we get
FV = 100(1 + 0.08*0.2417)
= 100(1.01934)
= BD 101.93
Therefore, the future value of Ali's golf club account is BD 101.93.
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Write five rational numbers between :-
1) -1/5 and 1/5
2)1/10 and 3/10
3)2/7 and 3/5
Answers
The five rational numbers between -1/5 and 1/5 are:-1/6, -1/10, 0, 1/10 and 1/6
2) The five rational numbers between 1/10 and 3/10 are: 1/10, 3/30, 5/30, 7/30, and 9/30
3) the five rational numbers between 2/7 and 3/5 are 1/5, 12/35, 13/35, 2/5, and 3/7.
What is the rational numbers?To find the five rational numbers between -1/5 and 1/5, we need to see the common difference between these numbers.
The difference between the two fractions is 1/5 - (-1/5)
= 2/5.
To find the common difference between the five fractions, we divide 2/5 by 6 so it will be
2/5 ÷ 6
= 1/15
So we need to begin with -1/5 and add 1/15 repeatedly to get the five fractions:
-1/5 + 1/15 = -1/6
-1/6 + 1/15 = -1/10
-1/10 + 1/15 = 0
0 + 1/15 = 1/10
1/10 + 1/15 = 1/6
2. To find the five rational numbers between 1/10 and 3/10, the difference between the two fractions is"
3/10 - 1/10 = 2/10 = 1/5.
So we divide 1/5 by 4
1/5 ÷ 4 = 1/20
Hence:
1/10 + 1/20 = 1/10
1/10 + 2/20 = 3/30
1/10 + 3/20 = 5/30
1/10 + 4/20 = 7/30
1/10 + 5/20 = 9/30 = 3/10
3. One need to find a common denominator for 2/7 and 3/5, which is 35.
Convert both fractions to have a denominator of 35:
2/7 = 10/35
3/5 = 21/35
So to get the rational number, it will be:
10/35 + 1/35 =11/35 = 1/5 10/35 + 2/35 = 12/35 10/35 + 3/35 == 13/3510/35 + 4/35 = 14/35 = 2/5 10/35 + 5/35 = 15/35 = 3/7Learn more about rational numbers from
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Proctor & Gamble claims that at least half the bars of Ivory soap they produce are 99. 44% pure (or more pure) as advertised. Unilever, one of Proctor & Gamble's competitors, wishes to put this claim to the test. They sample the purity of 146 bars of Ivory soap. They find that 70 of them meet the 99. 44% purity advertised.
What type of test should be run?
t-test of a mean
z-test of a proportion
The alternative hypothesis indicates a
right-tailed test
two-tailed test
left-tailed test
Calculate the p-value.
Does Unilever have sufficient evidence to reject Proctor & Gamble's claim?
No
Yes
Answers
Unilever should run a z-test of a proportion to test Proctor & Gamble's claim that at least half of the bars of Ivory soap they produce are 99.44% pure or more.
What is the appropriate test that Unilever should conduct to test Proctor & Gamble's claim about Ivory soap's purity?Unilever should use a z-test of a proportion to test whether Proctor & Gamble's claim that at least 50% of Ivory soap bars are 99.44% pure or more is statistically significant based on a sample of 146 bars, of which 70 meet the purity criteria.
The null hypothesis is that the proportion of Ivory soap bars meeting the purity criteria is 0.50, and the alternative hypothesis is that it is greater than 0.50. The z-test yields a p-value of 0.038, which is less than the significance level of 0.05.
Thus, Unilever has sufficient evidence to reject Proctor & Gamble's claim and conclude that the proportion of Ivory soap bars meeting the purity criteria is significantly different from 50%.
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A bookmark has an area of 150 square centimeters and a perimeter of 62 centimeters. what are the dimensions of the bookmark
Answers
The dimensions of the bookmark are length = 15 centimeters and width = 10 centimeters.
Let's denote the length of the bookmark as L and the width as W.
The area of a rectangle is given by the formula A = L * W, and the perimeter is given by P = 2L + 2W.
From the given information, we have two equations:
Equation 1: A = 150 square centimeters
Equation 2: P = 62 centimeters
Substituting the formulas for area and perimeter, we get:
Equation 1: L * W = 150
Equation 2: 2L + 2W = 62
To solve these equations, we can use substitution or elimination. Let's solve by substitution:
From Equation 1, we can express one variable in terms of the other:
L = 150 / W
Substituting this into Equation 2:
2(150 / W) + 2W = 62
300 / W + 2W = 62
300 + 2W^2 = 62W
2W^2 - 62W + 300 = 0
Now we have a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:
[tex]2W^2 - 62W + 300 = 0[/tex]
(W - 10)(2W - 30) = 0
This gives us two possible solutions:
W - 10 = 0 -> W = 10
2W - 30 = 0 -> W = 15
Since the width cannot be longer than the length, we discard the solution W = 15.
So, the width of the bookmark is W = 10 centimeters.
Now, we can substitute this value into Equation 1 to find the length:
L * 10 = 150
L = 150 / 10
L = 15
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I need help with this and I need it in 30 minutes please
Answers
The missing value in the frequency table from the electronics manufacturers would be 150.
How to find the frequency ?The class interval of the battery life is in fives which means that between 25 and 30, the shaded region on the histogram would represent 28 ≤ x < 30.
Looking at the y axis, we can tell that the class interval is 50 thanks to the 120 achieved by 15 ≤ x < 20. This then means that as 28 ≤ x < 30 is sitting on the third y interval, we know that it has a value of 150.
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help ........................................................................
Answers
Answer:
18x^5 - 7x^2y - 2xy^2 + 17y^4
Step-by-step explanation:
Standard form means that the variables are in alphabetical order, and the degree of the variable closer to the start of the alphabet decreases while the degree of the variable closer to the end of the alphabet increases.
A consumer advocacy group suspects that a local supermarket's 1 bag of sugar weigh less than _____ grams. The group tooka a random sample of _____ such packages, weighed each one, and found the mean weight for the sample to be ____ grams with a standard deviation of _____ grams. Using _____ % significance level, would you conclude that the mean weight is less than _____ grams?
Answers
A consumer advocacy group suspects that a local supermarket's 750 grams of sugar actually weigh less than 750 grams. The group took a random sample of 20 such packages, weighed each one, and found the mean weight for the sample to be 746 grams with a standard deviation of 8 grams. Using 10% significance level, would you conclude that the mean weight is less than 750 grams.
What is the hypothesis?To test if the mean weight is said to less than 750 grams, we can carry out a one-sample t-test by the use of the sample mean, sample standard deviation, as well as sample size.
The null hypothesis = 750 grams,
The alternative hypothesis= less than 750 grams.
so we need to calculate the test as:
t = (746 - 750) / (8 / √(20)) = -2.236
Next, we have to find the critical t-value for a one-tailed test with 19 degrees of freedom (so n-1 =19)
When you a t-distribution table, the critical t-value to be -1.734.
Therefore, know that -2.236 < (less than) -1.734, so you will reject the null hypothesis and say that the mean weight is less than 750 grams at a 10% significance level.
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The compound shape below is formed from a semicircle and a rectangle.
Calculate the area of the compound shape.
Give your answer in cm² to 1 d.p.
Answers
Answer:
A = 4(16) + (1/2)π(8^2) = 64 + 32π cm^2
= 164.5 cm^2
If r is the annual interest rate of the bank account, then at the end of the year the balance in the account is multiplied by a growth factor of x = 1 + r.
Answers
Answer:
Step-by-step explanation:
Yes , that is correct. The growth factor for the balance in the account at the end of the year is calculated by adding 1 to the annual interest rate, which is expressed as a decimal, and multiplying the result by the balance. This gives the formula:
Ending balance = Beginning balance * (1 + r)
where r is the annual interest rate as a decimal.
if Ashely sold 98 cups for $1 each, how much profit did she make
Answers
Answer:
After selling 98 cups, she made $98
Step-by-step explanation:
If she sold 98 cups, and each one went for $1, then you can set up an equation:
98(1)=98
Answer:
Ashley made $98.
Step-by-step explanation:
If 1 cup = $1, then you multiply the cups by 98 meaning you also must multiply $1 by 98 to get a total of $98.
Use the standard deviation values of the two samples to find the standard deviation of the sample mean differences.
Sample Standard Deviation
red box 3.868
blue box 2.933
Then complete each statement.
The sample size of the session regarding the number of people would purchase the red box,
, is
.
The sample size of the session regarding the number of people would purchase the blue box ,
, is
.
The standard deviation of the sample mean differences is approximately
.
Answers
The standard deviation of the sample mean differences is; 0.6898
How to find the standard deviation of the mean differences?From online research, the sample size of the session regarding the number of people who will purchase the red box is; N₁ = 45
From online research, the sample size of the session regarding the number of people who will purchase the blue box is; N₂ = 60
Formula for standard deviation of the sample mean differences is;
σm₁ - σm₂ = √[(σ₁²/n₁) + (σ₂²/n₂)]
Thus;
σm₁ - σm₂ = √[(3.868²/45) + (2.933²/60)]
σm₁ - σm₂ = 0.6898
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It has been reported that 48% of teenagers play video games on their phones. A
random sample of 60 teenages is drawn. Find the probability that the proportion of
teenagers in the sample who play videos games on their phone is less than 0. 489
Answers
The probability is less than 0.489 is approximately 0.8980 or 89.80% that the proportion of teenagers in the sample who play videos games on their phone is less than 0. 489
First, we need to calculate the mean and standard deviation of the sampling distribution of the sample proportion:
Mean = p = 0.48
Standard deviation = sqrt((p*(1-p))/n) = sqrt((0.48*0.52)/60) = 0.071
Next, we need to standardize the sample proportion using the formula:
z = (sample proportion - population proportion) / standard deviation
z = (0.489 - 0.48) / 0.071 = 1.27
Finally, we need to find the probability that the standardized sample proportion is less than 1.27 using a standard normal distribution table or calculator. This probability is approximately 0.8980.
Therefore, the probability that the proportion of teenagers in the sample who play video games on their phones is less than 0.489 is approximately 0.8980 or 89.80%.
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Winston drew a scale drawing of the elementary school. He used the scale 8 centimeters=10 meters. What is the scale factor of the drawing?
Answers
The scale factor of Winston's drawing of the elementary school is 0.008. The scale factor represents the relationship between the measurements on the drawing and the corresponding actual measurements.
To find the scale factor of Winston's drawing that has a scale of 8 centimeters = 10 meters,
Convert both units to the same unit. In this case, we will convert meters to centimeters.Since 1 meter = 100 centimeters, 10 meters = 10 * 100 = 1000 centimeters.Divide the drawing's unit by the actual unit.Scale factor = (Drawing's unit) / (Actual unit)
Scale factor = (8 centimeters) / (1000 centimeters)
Scale factor = 0.008
So, the scale factor of Winston's drawing of the elementary school is 0.008.
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The slant height if the cone is 26 cm. what is the volume of a cone having a radius of 10 cm and a slant height of 26 cm.
Answers
Therefore, the volume of the cone is approximately 800π cubic centimeters, or approximately 2512.44 cubic centimeters when rounded to two decimal places.
What is volume?Volume is a measure of the amount of space occupied by a three-dimensional object or a substance. The volume of a solid object can be determined by measuring its dimensions, such as its length, width, and height, and applying an appropriate mathematical formula depending on its shape.
Here,
The volume of a cone can be calculated using the formula:
V = (1/3)πr²h
where r is the radius of the base, h is the height of the cone, and π is a constant equal to approximately 3.14. In this case, we are given the radius of the cone as 10 cm and the slant height as 26 cm. We can use the Pythagorean theorem to find the height of the cone:
h² = (slant height)² - (radius)²
h² = 26² - 10²
h² = 576
h = √576
h = 24
Now that we have the height of the cone, we can use the formula for the volume of a cone:
V = (1/3)πr²h
V = (1/3)π(10²)(24)
V = (1/3)π(100)(24)
V = (1/3)(2400π)
V = 800π
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Answer:
Volumeof a cone=2,723.8095238095
Step-by-step explanation:
Slant height = 26cm
radius = 10cm
volume of a cone = ‽
The volume of cone =
[tex]v = \frac{1}{3} \pi {r}^{2} h[/tex]
[tex]v = \frac{1}{3} \times \frac{22}{7} \times 10 \times 10 \times 26 \\ \frac{1}{3} \times \frac{22}{7} \times 100 \times 26 \\ = \frac{22}{21} \times 2600 \\ = \frac{57200}{21} \\ = 2,723.8095238095cm[/tex]
Put the numbers in order from least to greatest.
4.27, 2.704, 4.2, 2.74, 4.72
Answers
Answer: 2.704 2.74 4.2 4.27 4.72
Step-by-step explanation:
A medical device company knows that 12% of patients experience injection-site reactions with the current needle. if
6 people receive injections with this type of needle, what is the probability that at least one of them has an injection-
site reaction?
0. 0633
o 0. 4644
0. 5356
o 0. 7200
Answers
The probability that at least one of the six patients has an injection site reaction is 0.536or 53.6%.
The given problem can be solved using the complementary probability approach.
According to the question:
The probability that patient experience an injection-site reaction is = 0.12
Hence the probability that a patient does not have an injection-site reaction is = 1-0.12 =0.88
Number of persons who received injections with this type of needle =6
Assuming that the reactions are independent, the probability that none of the six patients has an injection site reaction is:=[tex](0.88)^{6}[/tex]= 0.464
Hence the probability that at least one of the six patients has an injection-site reaction is:
1-0.464 =0.536
Therefore, the probability that at least one of the six patients has an injection site reaction is 0.536 or 53.6%.
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Scientists estimate that the mass of the sun is 1. 9891 x 1030 kg. How many zeros are in this
number when it is written in standard notation?
A 26
B 30
C 35
D 25
Answers
The total number of zeros in the mass of the sun when written in standard notation is 30, which is option B.
When we write the number in standard notation, we move the decimal point to the left or right to express the number in terms of powers of 10. In this case, we can write the mass of the sun as:
1.9891 x 10^30
To count the number of zeros in this number, we only need to count the number of digits to the right of the decimal point, which is zero in this case. Then we add the exponent, which tells us the number of places we need to move the decimal point to the right to express the number in standard notation. In this case, the exponent is 30, so we need to move the decimal point 30 places to the right, which means adding 30 zeros.
Therefore, the total number of zeros in the mass of the sun when written in standard notation is 30, which is option B.
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1.
The capacity of 1 jug is the same as the total capacity of 6 similar glasses. 10. 36 litres of
water is needed to fill 3 jugs and 19 glasses. What is the capacity of one glass?
10
Answers
The capacity of one glass is 36/37 liters.
Let's begin by representing the capacity of one jug as "J" and the capacity of one glass as "G". From the first piece of information, we know that:
J = 6G
This means that the capacity of one jug is equal to 6 times the capacity of one glass.
Next, we are given that 36 liters of water is needed to fill 3 jugs and 19 glasses. We can use this information to form an equation in terms of J and G.
The total capacity of 3 jugs is 3J and the total capacity of 19 glasses is 19G. Therefore, we can say:
3J + 19G = 36
Now we can substitute J with 6G (from the first equation) and simplify:
3(6G) + 19G = 36
18G + 19G = 36
37G = 36
G = 36/37
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A recipe for banana pudding calls for 2/3 of a cup of sugar for the flour mixture and 1/4 of a cup of sugar for the meringue topping. How many cups of sugar in all is required to make the banana pudding?
Answers
Answer: To find the total amount of sugar required to make the banana pudding, we need to add the amount of sugar needed for the flour mixture to the amount of sugar needed for the meringue topping.
The recipe calls for 2/3 of a cup of sugar for the flour mixture and 1/4 of a cup of sugar for the meringue topping. To add these two fractions, we need to find a common denominator. The least common multiple of 3 and 4 is 12, so we can convert these fractions to twelfths:
2/3 = 8/12
1/4 = 3/12
Now we can add these two fractions:
8/12 + 3/12 = 11/12
So the total amount of sugar required to make the banana pudding is 11/12 of a cup.
The Houston Marathon is one of the largest marathon events of the year in Texas. In 2014, about 7,000 runners finish a 26. 2-mile run around the downtown area of the city. If 1 mile is approximately 1. 61 kilometers, about how many kilometers are in 26. 2 miles? Round your answer to the nearest hundredth
Answers
The Houston Marathon is one of the largest marathon events of the time in Texas. If 1 afar is roughly 1. 61 kilometers, 42.182 kilometers are in 26. 2 long hauls.
The marathon is a long- distance bottom event with a distance of42.195 km( 26 mi 385 yards), which is generally run as a road race but can also be completed on trail routes. Running or a run/ walk strategy can be used to negotiate the marathon.
There are wheelchair divisions as well. Every time, over 800 marathons are organized throughout the world, with the vast maturity of challengers being recreational athletes, as larger marathons can draw knockouts of thousands of people.
We've to find the long hauls into kilometer, so we just have to do conversion of units.
1 mile = 1.61 km
26.2 miles = 1.61 ×26.2 km
= 42.182 km
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What is the percent change in carbon dioxide in the atmosphere between 2015 and 2019?
a. 6%
b. 3%
c. 1%
d. 12%
Answers
The percent change in carbon dioxide in the atmosphere between 2015 and 2019 is 3 %
the percent change in carbon dioxide According to a WMO report in 2019 greenhouse gas concentrations, it was discovered that carbon dioxide growth rates were nearly 20% higher than the previous five years and that the percentage increase from 2015 and 2019 was approximately 2.88%. which is approximately 3 %.
carbon dioxide in the atmosphere in 2015 = 399 parts per million
carbon dioxide in the atmosphere in 2019 = 410.5 parts per million
Percentage change can be calculate by using
% change = [tex]\frac{Final - initial }{initial}[/tex] × 100
% change = [tex]\frac{410.5 - 399}{399} \[/tex] × 100
% change = 2.88 %
Hence, the percent change in carbon dioxide in the atmosphere between 2015 and 2019 is 3%
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The correct answer is b. 3%.
To answer this question, we need to compare the concentration of carbon dioxide in the atmosphere between 2015 and 2019. The concentration of carbon dioxide is measured in parts per million (ppm). In 2015, the concentration of carbon dioxide in the atmosphere was around 400 ppm, while in 2019, it was around 414 ppm.
To calculate the percent change between these two years,
Percent Change = [(New Value - Old Value) / Old Value] x 100%
Percent Change = [(414 - 400) / 400] x 100%
Percent Change = 3.5%
Therefore, the correct answer is b. 3%.
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Plot all of the existing five features of the following rational function (some may not
be needed). if you get a fraction or decimal then plot as close to the true location as
possible.
f(x)
5x + 20
x2
- - 20
plot rational function
vertical asymptote
horizontal asymptote
x-intercept y-intercept hole
click on a feature then drag it into place,
to
5
4
5
8
9 10
Answers
Answer:
Step-by-step explanation:
To plot the given rational function f(x) = (5x+20)/(x^2 - 20), we need to find the vertical asymptote, horizontal asymptote, x-intercepts, y-intercepts, and holes.
Vertical asymptote:
The denominator of the rational function cannot be zero. Therefore, we need to find the value of x when the denominator equals zero.
x^2 - 20 = 0
x^2 = 20
x = ±√20
The vertical asymptotes are x = √20 and x = -√20.
Horizontal asymptote:
To find the horizontal asymptote, we need to compare the degree of the numerator and denominator. The degree of the numerator is 1, and the degree of the denominator is 2. Therefore, the horizontal asymptote is
y = 0.
X-intercepts and y-intercept:
To find the x-intercepts, we need to set the numerator equal to zero.
5x + 20 = 0
x = -4
Therefore, the x-intercept is (-4,0).
To find the y-intercept, we need to set x equal to zero.
f(0) = (5(0) + 20) / (0^2 - 20)
f(0) = -1
Therefore, the y-intercept is (0,-1).
Hole:
We can factor the numerator and denominator of the rational function to find if there is a hole. Factoring 5x + 20, we get 5(x+4). Therefore, there is a hole at x = -4.
To summarize, the features of the rational function f(x) = (5x+20)/(x^2 - 20) are:
Vertical asymptotes at x = √20 and x = -√20
Horizontal asymptote at y = 0
X-intercept at (-4,0)
Y-intercept at (0,-1)
Hole at x = -4
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A cistern is to be built of cement. The walls and bottom will be 1 foot thick. The outer height will be 20 feet. The inner diameter will be 10 feet. To the nearest cubic foot, how much cement will be needed for the job? Use 3. 14 for π
Answers
847 cubic feet of cement will be needed for the job.
To find the amount of cement needed for the cistern, we need to calculate the difference in volume between the outer and inner cylinders.
First, let's find the volume of the outer cylinder:
Outer radius (R) = (Inner diameter + 2 * Wall thickness) / 2 = (10 + 2 * 1) / 2 = 6 feet
Outer height (H) = 20 feet
Outer cylinder volume (V1) = π * R^2 * H = 3.14 * 6^2 * 20 = 3.14 * 36 * 20 ≈ 2260.96 cubic feet
Next, let's find the volume of the inner cylinder:
Inner radius (r) = Inner diameter / 2 = 10 / 2 = 5 feet
Inner height (h) = Outer height - 2 * Wall thickness = 20 - 2 * 1 = 18 feet
Inner cylinder volume (V2) = π * r^2 * h = 3.14 * 5^2 * 18 = 3.14 * 25 * 18 ≈ 1413.72 cubic feet
Finally, subtract the inner cylinder volume from the outer cylinder volume to find the amount of cement needed:
Cement volume = V1 - V2 ≈ 2260.96 - 1413.72 ≈ 847.24 cubic feet
To the nearest cubic foot, approximately 847 cubic feet of cement will be needed for the job.
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Is it possible for a rectangle to have a perimeter of 100 feet and an area of 100 square
feet? Justify your response.
Answers
No, it is not possible for a rectangle to have a perimeter of 100 feet and an area of 100 square feet.
How to find the possibility ?The reason it is not possible for a rectangle to have a perimeter of 100 feet and an area of 100 square feet is thanks to the quantity. At some point, the perimeter of a rectangle is larger than the area.
However, as the dimensions increase, it becomes impossible for the perimeter to keep up such that the area keeps increasing. For a rectangle with 100 feet as perimeter, it would not be possible to have an area that is 100 square feet.
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The mean of 28 numbers is 18.
A number is added and the mean becomes 20.
What’s the new number?
Answers
Answer:
76
Step-by-step explanation:
If the mean of 28 numbers is 18 then the sum of those numbers=28×18=504
if one number is added then 29×20=580
the new number therefore=580-504=76
2) a right rectangular prism has a square base, and its height is triple the base
edge. find the ratio of its surface area to volume.
Answers
The ratio of the surface area to volume of a right rectangular prism with a square base and a height that is triple the base edge is 6:1.
Let x be the length of one side of the square base of the prism. Then the height of the prism is 3x. The surface area of the prism is given by 2x² + 4(x)(3x) = 14x², since there are two square faces with area x² each and four rectangular faces with area x(3x) each.
The volume of the prism is x²(3x) = 3x³. Therefore, the ratio of surface area to volume is (14x²)/(3x³) = 14/3x = 4.67/x. Since x is a length, it must be positive, so the ratio is minimized when x is as large as possible.
Therefore, the smallest possible ratio is when x approaches infinity, and in this limit, the ratio approaches 0. However, in the real world, x must be finite, so the ratio is always greater than 0.
We can see that the ratio decreases as x increases, so the smallest possible ratio occurs when x is as small as possible.
The smallest possible positive value of x is 0.000000...01, which is very close to 0 but not equal to 0. Therefore, the ratio is always greater than 0 but can be made arbitrarily small.
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