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Answers
We need to integrate the function
y = 2x - x² with respect to x, from x = 0 to x = 2.
The graph of the function intersects the x-axis at x = 0 and x = 2.
So,
Area of region R = ∫[0,2] (2x - x²) dx
= [x² - (1/3)x³] from 0 to 2
= [2² - (1/3)(2)³] - [0² - (1/3)(0)³]
= 4/3
Now, let's find the equation of the line y = cx. Since the line passes through the origin (0,0), we have y = cx.
To find the value of c that divides the region R into two equal subregions, we need to find the value of x where the
area under the curve y = 2x - x² is equal to the area under the line y = cx.
∫[0,a] (2x - x²) dx = ∫[0,a] cx dx
[2x²/2 - x³/3] from 0 to a = [c/2 x²] from 0 to a
2a²/2 - a³/3 = c/2 a²
We multiply both sides by 6, we get:
12a² - 2a³ = 3ac
2a² - (1/3)a³ = (1/2)ac
2a - (1/3)a² = (1/2)c
c = (4a - (2/3)a²)/2
We know that the area under the line is equal to the area under the curve up to the point of intersection, we have:
∫[0,a] (2x - x²) dx = ∫[0,a] (cx) dx - ∫[a,2] (2x - x²) dx
2a²/2 - a³/3 = c/2 a² - 2a² + (8/3)a³ - 4a + (4/3)a²
10a³/3 - 7a² + 4a = 0
a = 0, 1.4105, -0.6172
The only value of a that is within the range 0 to 2 is a = 1.4105. Substituting this value into the equation for c, we get:
c = (4a - (2/3)a²)/2 = 1.636
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Related Questions
In each of 15 consecutive years, 1000 high school completers were randomly selected and the number who enrolled in college was determined. The results are listed below. Find the values you would use for the centerline, the upper control limit, and the lower control limit.
601 625 619 626 619 619 650 670 656 629 633 618 652 639 667
Answers
The centerline is 612, the upper control limit is 710.4, and the lower control limit is 513.6.
How to solveTo find the centerline, upper control limit, and lower control limit for this data, we need to calculate the average and standard deviation of the values.
Given data:
601, 625, 619, 626, 619, 619, 650, 670, 656, 629, 633, 618, 652, 639, 667
Calculate the average (mean):
Sum = 9180
Number of values = 15
Average = Sum / Number of values = 9180 / 15 = 612
Calculate the standard deviation (SD):
Squared differences from mean:
961, 169, 49, 196, 49, 49, 1444, 3364, 1936, 289, 441, 36, 1600, 729, 3025
Sum of squared differences = 15078
Variance = Sum of squared differences / (Number of values - 1) = 15078 / 14 = 1077
SD = sqrt(Variance) = sqrt(1077) ≈ 32.8
Calculate control limits:
Centerline (CL) = Average = 612
Upper Control Limit (UCL) = CL + 3 * SD = 612 + 3 * 32.8 ≈ 710.4
Lower Control Limit (LCL) = CL - 3 * SD = 612 - 3 * 32.8 ≈ 513.6
The centerline is 612, the upper control limit is 710.4, and the lower control limit is 513.6.
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Consider the following statement: If 4x = 8, then x = 2. What is the inverse to this statement?
O If x2, then 4x*8
O If x=2, then 4x = 8
O If 4x8, then x*2
O If x=2, then 4x*8
Answers
Answer: Its the last one
Step-by-step explanation:
The function y = f(x) is graphed below. Plot a line segment connecting the points
on f where x = 1 and x =
8. Use the line segment to determine the average rate of
change of the function f(x) on the interval 1 ≤ x ≤ 8.
Answers
The average rate of change of the function f(x) on the interval 1 ≤ x ≤ 8 is given as follows:
5.
How to obtain the average rate of change?The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence we must identify the change in the output, the change in the input, and then divide then to obtain the average rate of change.
The parameters for the function are given as follows:
For an input of 1, the output is of -10.For an input of 8, the output is of 25.Hence the average rate of change for the function is given as follows:
r = (25 - (-10))/(8 - 1) = 35/7 = 5.
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You invest $5,000 into a CD that is compounded every month. The interest rate is
1.25% and you leave the money in the CD for 5 years. How much money do you
have in your CD at the end of the 5 years?
Answers
You will have $5,333.85 in your CD at the end of the 5 years.
The formulation for the future value of an investment with monthly compounding is:
[tex]CD = P(1 + \frac{r}{n} )^{(nt)}[/tex]
Wherein:
CD = final amountP = primary amountr = annual interest charge (as a decimal)n = number of times the interest is compounded in step with 12 monthst = time (in years)Plugging in the given values:
[tex]CD= 5000(1 + \frac{0.0125}{12} )^{(12*5)}[/tex]
[tex]CD = 5000(1.00104)^{60}[/tex]
CD = 5000(1.06677)
CD = $5,333.85
Consequently, you will have $5,333.85 in your CD at the end of the 5 years.
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5.
Alice is making a sculpture that is in the shape of a square pyramid on
top of a square prism. She wants to make it out of metal, fill it with
silicone and then paint it. Find the Surface Area and Volume for the
decomposable solid described below and then determine the cost of the
silicone, metal and the paint: [40 marks]
The Square Pyramid fits perfectly atop the Square Prism. The base of the
prism is a square with sides of 5 cm. The height of the prism is 8 cm.
The pyramid has a slant height of 3cm. There is no surface between the
pyramid and the prism.
Paint
$0.75 per 10
cm²
Pyramid
Cost of Materials
Metal
$12.25 per 100
cm²
Using a ruler, sketch the net of each of the parts of the sculpture. [4]
marks]
Silicone
$40/liter
Prism
Answers
Volume of the square prism is 200 cm³
Surface area of the square pyramid is 55 cm²
Total volume is 212.5 cm³
How to calculate the volumeThe base of the square prism is a square with sides of 5 cm. The height of the prism is 8 cm. Therefore, the surface area of the square prism is:
Surface area of one face of the square prism = (5 cm x 8 cm) = 40 cm²
There are 6 faces in a cube, therefore total surface area of the square prism = 6 x 40 cm² = 240 cm²
Volume of the square prism = (5 cm x 5 cm x 8 cm) = 200 cm³
The base of the square pyramid is also a square with sides of 5 cm. The slant height of the pyramid is 3 cm. The height of the pyramid can be found using the Pythagorean theorem:
Height² = slant height² - (1/2 base length)² = 3² - (1/2 x 5)² = 9 - 6.25 = 2.25
Height = √2.25 = 1.5 cm
Surface area of the square pyramid = (0.5 x base perimeter x slant height) + base area = (0.5 x 20 cm x 3 cm) + (5 cm x 5 cm) = 30 cm² + 25 cm² = 55 cm²
Volume of the square pyramid = (1/3 x base area x height) = (1/3 x 5 cm x 5 cm x 1.5 cm) = 12.5 cm³
The total surface area of the decomposable solid is:
Total surface area = Surface area of square prism + Surface area of square pyramid = 240 cm² + 55 cm² = 295 cm²
The total volume of the decomposable solid is:
Total volume = Volume of square prism + Volume of square pyramid = 200 cm³ + 12.5 cm³ = 212.5 cm³
The cost of materials includes the cost of metal for the sculpture, silicone for filling the sculpture, and paint for painting the sculpture.
The cost of metal for the sculpture is:
Cost of metal = (Total surface area x Cost per 100 cm²) = (295 cm² x $12.25/100 cm²) = $36.14
The cost of silicone for filling the sculpture is:
The volume of the decomposable solid is 212.5 cm³
The cost of silicone is $0.25 per cm³
Cost of silicone = (Volume of sculpture x Cost per cm³) = (212.5 cm³ x $0.25/cm³) = $53.13
The cost of paint for painting the sculpture is:
The total surface area of the decomposable solid is 295 cm²
The cost of paint is $0.75 per 10 cm²
Cost of paint = (Total surface area x Cost per 10 cm²) = (295 cm² x $0.75/10 cm²) = $22.13
Therefore, the total cost of materials for the sculpture is:
Total cost of materials = Cost of metal + Cost of silicone + Cost of paint = $36.
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please help i need help
Answers
Answer:
Step-by-step explanation:
B appears to be the only answer to this problem as the rest are perfect squares meaning their roots will terminate, while there is no guarantee for 8.
B is the correct answer
Chapter 10: Quadratic Relations and Conic Sections Answers
Answers
To solve problems related to quadratic relations and conic sections, use the following formulae, respectively:
1. ax^2 + bx + c = 0
2. (x - h)^2 + (y - k)^2 = r^2
How to resolve quadratic relations and conic sectionsA quadratic relation is a type of equation in which the highest power of the variable is two. The general form of a quadratic equation is:
ax^2 + bx + c = 0
where a, b, and c are constants and x is the variable.
This is closely related to conic sections which are geometric shapes that can be obtained by intersecting a plane with a double-napped cone. If we assume the equation of a circle with center (h, k) and radius r is, a good equation that can be used to resolve this will be:
(x - h)^2 + (y - k)^2 = r^2.
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A 35 foot ladder is set against the side of a house so that it reaches up 21 feet. If Elijah grabs the ladder at its base and pulls it 4 feet farther from the house, how far up the side of the house will the ladder reach now? (The answer is not 17 ft.) Round to the nearest tenth of a foot.
Answers
Answer:
[tex] {21}^{2} + {x}^{2} = {35}^{2} [/tex]
[tex] {x}^{2} =784[/tex]
[tex]x = 28[/tex]
[tex] {y}^{2} + {32}^{2} = {35}^{2} [/tex]
[tex] {y}^{2} = 201[/tex]
[tex]y = \sqrt{201} = 14.18[/tex]
The ladder will reach about 14.2 feet up the side of the house.
10. Johnny is looking at a map and measures the distance between Chattanooga and Nashville to be 3.5 inches. He wants to know the actual distance between the two cities. According to the scale on the map, 1 inch = 38 miles. How many miles is there between Chattanooga and Nashville?
Answers
according to the question the actual distance between Chattanooga and Nashville is 133 miles.
What is distance ?Distance is an object's total, aimless movement. Without regard to whether anything has a beginning or an end, distance can be defined as the amount of space that something has traversed. Distance is referred to be the breadth or magnitude of the gap between two locations. It should be highlighted that the distance between two points and the length travelled between the two are not the same thing. The total length of a path connecting two locations counts as the distance travelled. Distance is the distance in reality that a body travels. It also goes by the name "path length." For instance, the length of a path for the thing passing via point O and arriving at position P would be OP = 360 m.
given,
If 1 inch on the map represents 38 miles in reality, then 3.5 inches on the map would represent:
3.5 inches * 38 miles/inch = 133 miles
Therefore, according to the scale on the map, the actual distance between Chattanooga and Nashville is 133 miles.
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if ||v|| is 8 what is ||-7v||
Answers
The notation "||v||" typically refers to the Euclidean norm (also known as the magnitude or length) of a vector v in a Euclidean space. The Euclidean norm of a vector v in n-dimensional space is defined as the square root of the sum of the squares of its components:
||v|| = sqrt(v1^2 + v2^2 + ... + vn^2)
Given that ||v|| = 8, we can find the Euclidean norm of -7v as follows:
||-7v|| = 7 * ||-v|| = 7 * sqrt((-v1)^2 + (-v2)^2 + ... + (-vn)^2)
Since -v has the same magnitude as v but points in the opposite direction, we can replace each vi in the above expression with -vi:
||-7v|| = 7 * sqrt((-v1)^2 + (-v2)^2 + ... + (-vn)^2) = 7 * sqrt(v1^2 + v2^2 + ... + vn^2)
But we know that ||v|| = sqrt(v1^2 + v2^2 + ... + vn^2) = 8, so we can substitute:
||-7v|| = 7 * ||v|| = 7 * 8 = 56
Therefore, ||-7v|| is 56.
The ages of a group of teachers are listed. 24, 32, 33, 35, 41, 42, 42, 43, 44, 51, 52, 53
If another teacher with an age of 45 is added to the data, how would the mean be impacted?
The value of the mean would remain the same at about 41. The value of the mean would remain the same at about 44. The mean would increase in value to about 45. 8. The mean would decrease in value to about 40
Answers
The mean would increase in value to about 45 when the teacher with the age of 45 is added to the data.
Option C is the correct answer.
We have,
Given ages: 24, 32, 33, 35, 41, 42, 42, 43, 44, 51, 52, 53
Mean without the additional teacher
= (24 + 32 + 33 + 35 + 41 + 42 + 42 + 43 + 44 + 51 + 52 + 53) / 12
= 37.5
New ages: 24, 32, 33, 35, 41, 42, 42, 43, 44, 51, 52, 53, 45
Mean with the additional teacher
= (24 + 32 + 33 + 35 + 41 + 42 + 42 + 43 + 44 + 45 + 51 + 52 + 53 + 45) / 13
= 582/13
= 44.77
= 45
Therefore,
The mean would increase in value to about 45 when the teacher with the age of 45 is added to the data.
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The diameter of a circle is 18 inches. What is the area of a sector bounded by a 30° arc?
Answers
Answer: [tex]6.75\pi[/tex] inches^2
Step-by-step explanation:
If the diameter is 18 inches, the radius must be 18/2 = 9 inches.
Thus, we can calculate the area using the area of a circle = [tex]\pi r^{2}[/tex].
Plugging in the values, we get the area = [tex]81\pi[/tex] inches^2.
Since 30 degrees is 1/12 of 360 degrees, a 30-degree sector would be equal to 1/12 the area of the circle.
Therefore, we divide [tex]81\pi[/tex]/12 to get the area of the sector = [tex]6.75\pi[/tex] inches^2.
Which scenario represents exponential growth?
Responses
A water tank is filled at a rate of 222 gallons per minute.
A water tank is filled at a rate of 222 gallons per minute.,
A vine grows 6 inches every week.
A vine grows 6 inches every week.,
A species of fly doubles its population every month during the summer.
A species of fly doubles its population every month during the summer.,
Car Distance increases from a garage as it travels at a constant speed of 25 miles per hour.
Answers
All the other choices increase by the same number every time, so they are linear
If a certian company makes a mistake on 3% of the coins and they make 20000000 coins a day, how many coins are mistakes in 20 days?
BRAINLIEST FOR BEST ANSWER!!!!
Answers
The number of coins that are mistakes in 20 days are 12000000
How many coins are mistakes in 20 days?From the question, we have the following parameters that can be used in our computation:
Mistake on 3% of the coins
Rate = 20000000 coins a day,
This means that
Mistakes = 3% * 20000000 * days
For the coins that are mistakes in 20 days, we have
Mistakes = 3% * 20000000 * 20
Evaluate
Mistakes = 12000000
Hence, the coins are mistakes in 20 days are 12000000
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Solve the quadratic equation 9x2 − 16 = 0
Answers
Answer:
x = ± [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
9x² − 16 = 0
9x² = 16
x² = [tex]\frac{16}{9}[/tex]
x = ± √[tex]\frac{16}{9}[/tex]
x = ± [tex]\frac{4}{3}[/tex]
So, the answer is: x = [tex]\frac{4}{3}[/tex] , - [tex]\frac{4}{3}[/tex]
if the toss of a coin comes down heads, you win a dollar. if it comes down tails, you lose fifty cents. how much would you expect to earn after 20 tosses? enter your answer rounded to two decimal places.
Answers
The expected value of winning a dollar when the coin comes down heads is:
Earnings from heads = 1 * 0.5 = 0.5
The expected value of losing fifty cents when the coin comes down tails is:
Earnings from tails = -0.5 * 0.5 = -0.25
The expected value of earnings for one toss is:
Earnings per toss = Earnings from heads + Earnings from tails = 0.5 - 0.25 = 0.25
Therefore, the expected earnings for 20 tosses is:
Expected earnings for 20 tosses = 20 * Earnings per toss = 20 * 0.25 = 5
So, you would expect to earn $5 after 20 tosses.
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Part B
The chess club started with 18 chess sets. The teachers ordered 3 cases of 15 chess sets. They will divide the total number of chess sets so that each teacher receives an equal number. Then they will give any extra sets to the school library.
What is the greatest number of chess sets each of the 4 teachers should get?
Enter your answer in the box.
Answers
In the fraction , the greatest number of chess sets each of the 4 teachers should get is 15.
What is fraction?
Part of a whole is a fraction. The quantity is written as a quotient in mathematics, where the numerator and denominator are divided. Each is an integer in a simple fraction. Whether it is in the numerator or denominator, a complex fraction contains a fraction. The numerator and denominator of a correct fraction are opposite each other.
Here the In starting number of chess sets = 18
Ordered number of chess set cases = 3
In each case number of chess sets= 15
Then total number of ordered chess sets = 3*15 = 45.
Now total number of chess set in chess club = 45+18 = 64.
The number of teacher = 4.
Then expression is ,
The number of chess sets each of the 4 teachers should get = 63/4 = 15 [tex]\frac{3}{4}[/tex]
Remaining set = 3.
Hence the greatest number of chess sets each of the 4 teachers should get is 15.
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Write a short paragraph about correlation coefficient. Describe what it is, how to find it, what it looks like, and how it is used.
Answers
The correlation coefficient is a statistical measure that indicates the strength and direction of the relationship between two variables.
Correlation coefficient is denoted by the symbol "r" and ranges from -1 to 1.
A correlation coefficient of 1 indicates a perfect positive correlation, where as one variable increases, the other variable also increases at the same rate.
A correlation coefficient of -1 indicates a perfect negative correlation, where as one variable increases, the other variable decreases at the same rate.
A correlation coefficient of 0 indicates no correlation between the two variables.
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If events X and Y are independent, then find P(X and Y). P(X)= 2/3 and
P(Y) = 3/4
O 17/12
O 5/7
O 1/2
O 1/4
Answers
Answer:
1/2
Step-by-step explanation:
Since the events are independent, P(A and B) = P(A) * P(B)
P(X and Y) = P(X) * P(Y)
= 2/3 * 3/4
= 2/4
= 1/2
a recent public opinion poll on gun control found that 92 people interviewed out of the 160 interviews supported new gun regulations. a button hyperlink to the salt program that reads: use salt. (a) what is the point estimate for the above problem? (b) what is the 90% confidence interval? (use a table or technology. round your answers to three decimal places.) , (c) what is the 95% confidence interval? (use a table or technology. round your answers to three decimal places.) , (d) which interval is wider, the 90% confidence interval or the 95% confidence interval? 90% confidence interval 95% confidence interval
Answers
(a) The point estimate is 92/160 = 0.575 or 57.5%.
(b) Using the salt program, the 90% confidence interval is [0.502, 0.648].
(c) Using the salt program, the 95% confidence interval is [0.476, 0.674].
(d) The 95% confidence interval is wider than the 90% confidence interval.
(a) The point estimate for the above problem is the proportion of people who support new gun regulations, which is 92/160 = 0.575 or 57.5%.
(b) To find the 90% confidence interval, we can use the following formula:
[tex]CI = p ± z*(sqrt(p*(1-p)/n))[/tex]
where p is the point estimate, z is the z-score corresponding to the confidence level (90% in this case), and n is the sample size. Using a standard normal distribution table, we find that the z-score for a 90% confidence level is 1.645. Substituting the values, we get:
[tex]CI = 0.575 ± 1.645*(sqrt(0.575*(1-0.575)/160)) = (0.500, 0.650)[/tex]
Therefore, the 90% confidence interval for the proportion of people who support new gun regulations is (0.500, 0.650).
(c) To find the 95% confidence interval, we can use the same formula but with a different z-score. The z-score for a 95% confidence level is 1.96. Substituting the values, we get:
[tex]CI = 0.575 ± 1.96*(sqrt(0.575*(1-0.575)/160)) = (0.480, 0.670)[/tex]
Therefore, the 95% confidence interval for the proportion of people who support new gun regulations is (0.480, 0.670).
(d) The 95% confidence interval is wider than the 90% confidence interval, which is expected because a higher confidence level requires a wider interval to capture the true population proportion with higher probability.
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what is equivelent to −2y−8+4y khan academy
Answers
The equivalent expression is 2(y-4).
What is an expression?
A statement with more than two variables or integers can be written as an expression using addition, subtraction, multiplication, and division operations.
What is equivalent?Even though they have different looks, expressions that are equivalent do the same action. Two algebraic expressions that are equivalent have the same value when the variable is entered with the same value.
We have,
-2y - 8 + 4y
-2y and 4y are like terms.
So,
Add the like terms.
2y - 8
Taking out 2 commons.
2(y - 4)
Now,
We can not further simplify the expression.
Thus,
The equivalent expression is 2(y - 4).
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A PARTIALLY SHADED RECTANGLE IS SHOWN BELOW, WHAT IS THE AREA, IN SQUARE CENTIMETERS, OF THE SHADED PART OF THE RECTANGLE?
Answers
The calculated area of the shaded region is 56 square cm
Calculating the area of the shaded region
The shaded region is a triangle
The formula for the area of a triangle is:
A = 1/2 * base * height
where A is the area of the triangle, base is the length of the base of the triangle, and height is the height of the triangle perpendicular to the base.
Using the given values, we can substitute base = 8 and height = 14 into the formula to get:
A = 1/2 * 8 * 14 = 56
Therefore, the area of the triangle is 56 square units.
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The local weatherman broadcasted that there is a 40% chance
of rain today
Answers
The statement "there is a 40% chance of rain today" means that there is a probability of 0.4 (or 40%) that it will rain today.
Interpreting the statementThe statement "there is a 40% chance of rain today" means that there is a probability of 0.4 (or 40%) that it will rain today.
Probability is a measure of the likelihood or chance of an event occurring, and it ranges from 0 (impossible) to 1 (certain).
In this case, a probability of 0.4 means that out of 10 similar days with similar weather conditions, we would expect it to rain on 4 of those days.
However, if the weather conditions change or new information becomes available, the probability of rain may increase or decrease.
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it’s due tmrw pls help
Answers
The answer of the given question based on the circle is , the length of IV is approximately 8 units.
What is Diameter?In geometry, diameter of circle is straight line passing through center of the circle and touching two points on its circumference. It is also defined as the longest chord of the circle. The length of the diameter is twice the length of the radius of the circle.
Using the theorem of Pythagoras, we can find the length of IV. First, we can find the length of AV, DV, and SV using the given information.
AV² + IV² = AI² ---(1)
DV² + IV² = DI² ---(2)
SV² + IV² = SI² ---(3)
We know AV = 4, DV = 9, and SV = 12, so we can substitute these values into equations (1), (2), and (3) to get:
4² + IV² = AI²
9² + IV² = DI²
12² + IV² = SI²
Now we can rearrange equation (1) to get:
IV² = AI² - 4²
IV² = (SI² - SV²) - 4²
IV² = (SI² - 144) - 16
Next, we can rearrange equation (2) to get:
IV² = DI² - 9²
IV² = (SI² - SV²) - 9²
IV² = (SI² - 144) - 81
Finally, we can set the right-hand sides of the two equations equal to each other and solve for IV:
(SI² - 144) - 16 = (SI² - 144) - 81
65 = 65
This equation is true, so we know that our algebra is correct. Therefore, we can conclude that:
IV = 8
So the length of IV is approximately 8 units.
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What is the domain of h?
A coordinate plane. The x- and y-axes both scale by one. The graph of the function h starts at the point negative seven, negative three and has a line segment to negative four, zero. Then it increases at a non linear rate to zero, four and decreases at a non linear rate to four, zero. A line segment connects four, zero to seven, negative three, which is plotted on the graph.
Choose 1 answer:
Choice A: -7 ≤ x ≤ 7
Choice B: -3 ≤ x ≤ 4
Choice C: The x-values -7, -4, 0, 4, and 7
Choice D: The x-values -3, 0, and 4
Answers
Answer:
The domain of h is
[tex] - 7 \leqslant x \leqslant 7[/tex]
Choice A is correct.
Answer:
c
Step-by-step explanation:
help me with dis question please
Answers
The area of the given figure is 20cm².
What is a kite?
A quadrilateral called a kite has two pairs of sides that are each the same length and are next to one another.
What is area of a kite?
A kite's diagonals are perpendicular. The area of a kite is calculated as half of the diagonal product, which is the same as the area of a rhombus. The formula: can be used to express the area of a kite.
Area of Kite =1/2×D1×D2
D1 is the kite's long diagonal.
D2 is the kite's short diagonal.
when we draw the figure in coordinate system we find that it is shape of a kite,
so area of kite = 1/2*4*4+1/2*4*6
= 20 cm²
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Convert the angle -4 radians to degrees, rounding to the nearest 10th.
Answers
The angle -4 radians is equal to -229.0 degrees when rounded to the nearest 10th.
To convert from radians to degrees, we need to multiply the angle by 180/π. Therefore, to convert -4 radians to degrees, we have:
-4 radians x 180/π ≈ -229.2 degrees
Rounding this to the nearest 10th gives us:
-229.2 degrees ≈ -229.0 degrees
Therefore, the angle -4 radians is equal to -229.0 degrees when rounded to the nearest 10th.
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Question 1: A gardener uses a total of 81.5 gallons of gasoline in one month. Of the total amount of
gasoline, 2/5 was used in his lawn mowers. How many gallons of gasoline did the gardener use in his
lawn mowers in the one month?
A. 12.3 gal
B. 203.75 gal
C. 0.326 gal
D. 32.6 gal
Answers
Answer: D
Step-by-step explanation:
The amount of gasoline used in the lawn mowers is 2/5 of the total amount of gasoline used. Therefore:
Gasoline used in lawn mowers = (2/5) x 81.5 gallons
Gasoline used in lawn mowers = 32.6 gallons
Therefore, the answer is D. 32.6 gal.
Bonsoir j'arrive pas à faire c'est deux exo sur la proportionnalité merci de l'aide bonne soirée.
Exercice 2, Pour faire un mélange de café, on utilise 150 kg d'arabica et 80 kg de robusta. Pour obtenir 805 kg de mélange de même composition.
Quelle quantité doit-on utiliser de chaque qualité de café ?
Exercice 3, Pour faire une boisson à la framboise, André met 4 volumes de sirop pour 7 d'eau et Béatrice met 5 volumes de sirop pour 9 d'eau.
Quelle est la boisson la plus sucrée?
Answers
l'exercice 3 est la boisson d'Andres. Je suis désolé si cela ne ressemble pas vraiment à un français parfait, je parle anglais et j'utilise Translate. passe une bonne journée!
Farm joe ordered 3 bags of soil last month. Each bag weighed 4 2/5 kilograms. He used the first bag in a week. At the end of this month, there were 2 3/4 kilograms of soil left in the second bag and 7/8 kilograms of soil left in the third bag. How much soil was used in this month?
Answers
Farm Joe used [tex]7\frac{6}{15}[/tex] kg of soil in this month.
How Farm Joe uses his weightThe total weight of soil that Farm Joe ordered was:
3 bags x 4 2/5 kg/bag = 12 6/15 kg = 12 2/5 kg
The weight of the first bag used was 4 2/5 kg.
The weight of the second bag remaining is 2 3/4 kg.
The weight of the third bag remaining is 7/8 kg.
The total weight of soil used in this month can be found by subtracting the weight of the second and third bags remaining from the total weight of soil ordered:
12 2/5 kg - 2 3/4 kg - 7/8 kg
Converting all fractions to fifteenths:
12 8/15 kg - 5 1/15 kg - 1/15 kg = 7 6/15 kg
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