We need to mix 3.2 units of the 25% orange juice with 0.8 Units of the 100% orange juice to get a 4-unit mixture with a 25% concentration of pure orange juice.
The first thing we need to do is figure out how much of each type of orange juice we need to mix together to get the desired 25% concentration. Let's call the amount of the 25% orange juice "x" and the amount of the 100% orange juice "y".
We know that the total amount of juice we want to end up with is "4" (since the function f(x) is equal to 4 + 2). So we can write an equation based on that:
x + y = 4
We also know that we want the final concentration to be 25%, which means that the amount of pure orange juice in the mixture should be 25% of the total volume. To calculate that, we can use the formula:
0.25 = (0.25x + y) / 4
Simplifying that equation, we get:
0.25x + y = 1
Now we have two equations with two unknowns (x and y), which we can solve using substitution or elimination. I'll use substitution here:
x = 4 - y (from the first equation)
0.25(4 - y) + y = 1 (substituting for x in the second equation)
1 - 0.25y + y = 1
0.75y = 0
y = 0
Uh-oh, that's not good. It looks like we can't use any of the 100% orange juice, or we'll end up with a concentration greater than 25%. Let's double-check our equations and see if there's a mistake.
x + y = 4
0.25x + y = 1
Hmm, it looks like we made a mistake in the second equation. The 0.25x term should be multiplied by the concentration of the 25% orange juice, which is 0.25 (or 25% as a fraction). So the correct equation should be:
0.25(0.25x) + y = 1
Now let's solve for y:
0.0625x + y = 1
y = 1 - 0.0625x
Substituting that into the first equation, we get:
x + (1 - 0.0625x) = 4
0.9375x = 3
x = 3.2
So we need to mix 3.2 units of the 25% orange juice with 0.8 units of the 100% orange juice to get a 4-unit mixture with a 25% concentration of pure orange juice.
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5. Counting problems, leave answers as expressions, e.g., 10 npr 4, 8 nCr 3 or 35 [5 pts each part]
a) A club elects a steering committee of 5. Among these 5, a chair and secretary are chosen. How many different sets of committees (including officer selection) are possible if club has 15 members? Officers are not the same as the non-officer members, so this is hybrid permutation/combination problem.
b) At an event that drew 100 people where each attendee gets one raffle ticket, there are 6 raffle prizes worth $200, $100, $50, $25, $25, $25. How many different raffle ticket winner selections are possible? Be careful, the $25 prizes are equivalent, so this is hybrid permutation and combination problem.
c)If repeats are allowed but a code cannot begin with 0, how many six-digit PIN codes can be made?
Answer:
Step-by-step explanation:
a) The steering committee of 5 can be chosen from 15 members in 15 nCr 5 ways. Once the committee is chosen, the chair can be selected in 5 ways and the secretary can be selected in 4 ways (since the chair cannot also be the secretary). Therefore, the total number of different sets of committees (including officer selection) is:
15 nCr 5 * 5 * 4 = 3,003,600
b) Each of the 6 raffle prizes can be awarded to any of the 100 people, so there are 100 choices for the first prize, 99 choices for the second prize, and so on, down to 95 choices for the sixth prize. However, since the three $25 prizes are equivalent, we need to divide by 3! to account for the ways in which the $25 prizes can be arranged. Therefore, the total number of different raffle ticket winner selections is:
(100 * 99 * 98 * 97 * 96 * 95) / (3!) = 903,450,240,000
c) Since repeats are allowed and the code cannot begin with 0, there are 9 choices for the first digit and 10 choices for each of the remaining digits. Therefore, the total number of six-digit PIN codes that can be made is:
9 * 10^5 = 9,000,000
Jaime runs 8 miles every 3 days.
At this rate how long will it take
Jaime to run 96 miles?
Answer:
It will take Jaime 36 days to run 96 miles.
Step-by-step explanation:
The formula for rate is:
[tex]\boxed{\sf Rate=\dfrac{Distance}{Time}}[/tex]
Therefore, Jaime's run rate is:
[tex]\implies \sf Rate=\dfrac{8\;miles}{3\;days}=\dfrac{8}{3} \;miles\;per\;day[/tex]
Rearrange the rate formula to isolate time:
[tex]\implies \sf Time=\dfrac{Distance}{Rate}[/tex]
To find how long it will take for Jaime to run 96 miles, substitute the distance and rate into the formula and solve for time:
[tex]\implies \sf Time=\dfrac{96\;miles}{\frac{8 \;miles}{3\;days}}[/tex]
[tex]\implies \sf Time=96\;miles \times \dfrac{3\;days}{8\;miles}[/tex]
[tex]\implies \sf Time= \dfrac{288}{8}\;days[/tex]
[tex]\implies \sf Time= 36\;days[/tex]
Therefore, it will take Jaime 36 days to run 96 miles.
. Translate parallelogram ABCD 2 units down and plot it. 2. Translate rhombus EFGH 2 units to the left, 4 units down, and plot it. 3. If the coordinates of the vertices of a square LMNO are L(-5,-5), M(-5,-2), N(-2,-2). What are the coordinates for O? 4. If the coordinates of the vertices of a triangle XYZ are X (2,1), Y(4,4) and Z(5,2). Translate the triangle XYZ 4 units down. What are the new coordinates? 5. Write the coordinates down for the following points: Please Write The answers
To translate a shape, all of its vertices must be moved in the same direction and by the same amount. The responses to the five sections of the question are as follows:
What are coordinates?Coordinates are used to identify the position of an object on a two-dimensional grid or in three-dimensional space. They are usually written as pairs of numbers, separated by a comma.
1. We must deduct 2 from all of the y-coordinates of the vertices of the parallelogram ABCD in order to translate it two units down. Let's assume that the vertices' initial coordinates are A(a,b), B(c,d), C(e,f), and D. (g,h). The vertices will then have the new coordinates A'(a,b-2), B'(c,d-2), C'(e,f-2), and D' (g,h-2). To obtain the translated parallelogram, plot these new vertex points.
2. To move the rhombus EFGH 2 units to the left and 4 units down, we must deduct 2 from all of its vertices' x-coordinates and 4 from all of its y-coordinates. Let's assume that the vertices' initial coordinates are E(a,b), F(c,d), G(e,f), and H. (g,h). The vertices will then have the new coordinates E'(a-2,b-4), F'(c-2,d-4), G'(e-2,f-4), and H' (g-2,h-4). To obtain the translated rhombus, plot these additional vertices.
3. If we want to translate a square with coordinates L(-5,5), M(-5,5), N(5,5), and O(5,5) 3 units to the right and 2 units up, we must add 3 to all of its x-coordinates and subtract 2 from all of its y-coordinates. The vertices' new coordinates are L'(-2,-7), M'(-2,3), N'(8,3), and O' (8,-7). To obtain the translated square, plot these new vertex points.
4. The new coordinates of triangle XYZ after translating 4 units down will be X' (2,-3), Y' (4,1) and Z' (5,-2). This is happening because when a triangle is translated 4 units down, the y-coordinate of each vertex is decreased by 4 units, while the x-coordinate remains the same.
5. I (4,-2) P (-4,-2) G (5,2) Q (6,-4) R (-2,2)
S (6,4) J (1,-1) U (-5,0) H (3,-1) K (-6,-5)
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i need help asap i have to finish
Answer: (D) 12 to 4
Step-by-step explanation:
First, we will find the number of people waiting in line for each activity.
➜ Bumper cars is 12
➜ Slingshot is 4
Next, we will create our ratio. This is asking for Bumper cars to Slingshot, so Bumper cars is first with Slingshot second.
➜ 12 to 4
Mailani saves some money in a box under her bed. She deposits an additional amount into a savings account where it earns interest compounded annually. This situation can be modeled by the function . Which statement is true? Select all that apply.
The correct statements are:
Mailani saves $200 in a box under her bed.The y-intercept of the function is (0, 700).Explanation:
The function f(x) represents the total amount of money that Mailani has saved after x years. The first term 500 represents the initial amount she saved in the box under her bed, and the second term (1+0.04)^x represents the amount she deposited into the savings account, which earns an interest rate of 4% compounded annually. The third term +200 represents the additional amount she deposited every year into the savings account.
The range of the function is y>=500, since the initial amount saved is 500, and the function is increasing with time.The y-intercept of the function is (0, 700), not (0, 200), because the initial amount saved in the box is 500, and the additional amount deposited into the savings account is 200 per year, so after 0 years, the total saved amount is 500+200=700.The function does not have an asymptote at y=200. An asymptote is a line that a graph approaches but never touches. In this case, the function is increasing with time, so it does not approach any line as x gets larger.Learn more about asymptote here brainly.com/question/4084552
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Full question:
Mailani saves some money in a box under her bed. She deposits an additional amount into a savings account where it earns interest compounded annually. . This situation can be modeled by the function
[tex]f(x)= 500(1+0.04)^x+200[/tex]
Which statements are true? Select all that apply.
The range of the function is y>=0Mailani saves $200 in a box under her bed.The y-intercept of the function is (0, 200).The function has an asymptote at y = 200.Fond the sum 2/5 + 3/6
To add 2/5 and 3/6, we need to find a common denominator for the two fractions. The smallest number that both 5 and 6 divide into evenly is 30. So, we can convert the two fractions to have a denominator of 30:
2/5 = 12/30 3/6 = 15/30
Now, we can add the two fractions by simply adding their numerators (since they have the same denominator):
12/30 + 15/30 = 27/30
We can simplify the fraction by reducing it to the lowest terms. Both the numerator and denominator have 3 as a factor, so we can divide them both by 3:
27/30 = (3 x 9) / (3 x 10) = 9/10
Therefore, the sum 2/5 + 3/6 is equal to 9/10.
Uma pessoa decide fazer uma reforma na sala de
sua casa e, para não provocar problemas estruturais,
resolve analisar a planta da construção primeiro. Ela
nota que a planta da casa está em uma escala de 1:200
e mostra que a área da sala é de 21 cm².
Qual é a área real da sala, em m²?
A 19
B 38
C42
D 84
E168
Use the slope of 5/3 and the point (−3, –4) to graph the line
The equation of the line is 3y-5x=3 and the graph is attached.
Geometrically speaking, a line is a one-dimensional figure because it has length but no width. A group of points can be extended endlessly in opposing directions to form a line. Two points in a two-dimensional plane determine it. There are, however, additional ways to formulate the equation of a line in a two-dimensional coordinate system. The three most popular methods are the point-slope form, slope-intercept form, and general or standard form of the equation of a line. As its name suggests, the point-slope form combines a line point and a straight-line slope. The equations of infinite lines with a particular slope can be expressed, however when we specify that the line passes through a particular point, we get a singularity.
the equation of a line is
y-y'=m(x-x')
[tex]y+4=\frac{5}{3}(x+3)\\\\3y+12=5x+15\\3y-5x=3[/tex]
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At a dog show, the mean weight of the Norfolk Terriers is
11.5 pounds with a MAD of 2. The mean weight of the
Cairn Terriers is 13 pounds with a MAD of 1.8. Express the
difference in mean weights as a multiple of the MAD for
both dog breeds. Show your work.
Answer:
Step-by-step explanation:
To express the difference in mean weights as a multiple of the MAD for both dog breeds, we can use the formula:
(difference in means) / (mean absolute deviation)
Let's plug in the values given in the problem:
(difference in means) = 13 - 11.5 = 1.5
(mean absolute deviation) = 2 + 1.8 / 2 = 1.9 (taking the average of the two MADs)
Now we can calculate:
(difference in means) / (mean absolute deviation) = 1.5 / 1.9 ≈ 0.7895
Therefore, the difference in mean weights between the two breeds is approximately 0.7895 times the average MAD for both breeds.
if 4,a,16 are in geometric sequence find the value of a .
Answer:
a = 8
Step-by-step explanation:
4 x 2 = 8
8 x 2 = 16
Helping in the name of Jesus.
Please help with this equation I’ll give brainliest.
Step-by-step explanation:
a) Since the temperature of the oven is decreasing by a percentage of its current temperature each minute, the function that best represents this situation is an exponential function.
b) Let T be the temperature of the oven in degrees Fahrenheit at time x minutes after it was turned off. The initial temperature of the oven was 450° F, and the temperature decreases by 10% each minute. This can be expressed as:
T = 450(0.9)^x
Therefore, the function that models the situation is:
f(x) = 450(0.9)^x
where f(x) is the temperature of the oven in degrees Fahrenheit x minutes after it was turned off.
The graph of the function y= x^2 is shown. How will the graph change if the equation is changed to y = (1/4) x^2
If the equation is changed from y = x^2 to y = (1/4)x^2, the parabola will become wider.
What is the value of x?
Answer:
x = 20
Step-by-step explanation:
using the cosine ratio in the right triangle and the exact value
cos45° = [tex]\frac{\sqrt{2} }{2}[/tex] , then
cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{10\sqrt{2} }{x}[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ( cross- multiply )
x × [tex]\sqrt{2}[/tex] = 20[tex]\sqrt{2}[/tex] ( divide both sides by [tex]\sqrt{2}[/tex] )
x = 20
Identify the local, maximum and minimum for the function given
The function f(x) = 2x³-3x² - 12x + 1 does not have any local maximum or minimum values over the interval [2, 3].
EquationsTo find the local maximum and minimum of a function over a given interval, we need to find the critical points of the function within that interval and then apply the second derivative test to classify those critical points as local maximum or minimum.
To find the critical points, we first take the derivative of the given function:
f'(x) = 6x² - 6x - 12 = 6(x² - x - 2)
x = -1 or x = 2
Both of these critical points fall outside the given interval [2, 3]. Therefore, there are no critical points of the function within the interval [2, 3], and so there are no local maximum or minimum values of the function over this interval.
In other words, the function f(x) = 2x³-3x² - 12x + 1 does not have any local maximum or minimum values over the interval [2, 3].
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if log x of y=2 and xy=27 find the values of x and y
When we enter x = 3 into the first equation, we obtain: y = 2 log 3 y = 32 y = 9 .Hence, x=3 and y=9.
how can we describe logarithm ?A log is a mathematical function used to calculate how many times the base, or initial value, must be increased by itself to produce the target value. In other terms, a logarithm is an exponent's negative action.
The base-10 logarithm is the most widely used type of logarithm, though there are other types as well. Some many mathematical and scientific tasks include the usage of logarithms, such as estimating the pH of a solution, gauging the volume of sound, and estimating population growth rates.
given
As we are aware that log x of y = 2, x2 = y.
We also understand that xy = 27.
When we change y in the second equation to x2, we obtain:
[tex]xx^{2} =7^{2} \\x^{3} = 27\\[/tex]
x = 3
When we enter x = 3 into the first equation, we obtain: y = 2 log 3 y = 32 y = 9 .Hence, x=3 and y=9.
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Ivan Ukhov, the 2012 Olympics high jump gold medallist jumps 2.4 metres. This is 4% lower than the best height he can jump. What is the best height he can jump?
How do I work this out?
The best height he can jump is 2.5 meters. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?
It is believed that the four fundamental operations, often known as "arithmetic operations," adequately explain all real numbers. Division, multiplication, addition, and subtraction are the mathematical operations that come before quotient, product, sum, and difference.
We are given that Ivan Ukhov jumps 2.4 metres which is 4% lower than the best height he can jump.
Let the best height be 'x'.
So, from the above information, we get
⇒ x - 0.04x = 2.4
⇒ 0.96x = 2.4 (Using subtraction)
⇒ x = 2.5 (Using division)
Hence, the best height he can jump is 2.5 meters.
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Estimate each project draw a diagram if necessary 2/3 x 26
Each product of the fractions are
Part1. =17.33
Part2.= 0.73
Part3.=45.93
Define multiplicationMultiplication is a mathematical operation that involves combining two or more numbers to obtain a product or result. Multiplication is a fundamental arithmetic operation that is used in a wide range of mathematical applications, from simple calculations such as calculating the area of a rectangle, to more complex problems in algebra, geometry, and calculus.
Part1.⅔×26
Multiplying 2 and 26, we get
52/3
Now, dividing it with3, we get
17.33
Part2.⅞×5/6
Multiplying 7 and 5 and 8 and 6, we get
35/48
Now, dividing 35 and 48, we get
.73
Part3.5 ⅕× 8 ×⅚
Solving the improper fractions;
26/5×53/6
Multiplying 26 and 53 and 5 and 6, we get
1378/30
Now, dividing 35 and 48, we get
45.93.
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Cost of Production Report
Bavarian Chocolate Company processes chocolate into candy bars. The process begins by placing direct materials (raw chocolate, milk, and sugar) into the Blending Department. All materials are placed into production at the beginning of the blending process. After blending, the milk chocolate is then transferred to the Molding Department, where the milk chocolate is formed into candy bars. The following is a partial work in process account of the Blending Department at October 31:
ACCOUNT Work in Process—Blending Department ACCOUNT NO.
Date Item Debit Credit Balance
Debit Balance
Credit
October 1 Bal., 2,300 units, 3/5 completed 46,368
31 Direct materials, 26,000 units 429,000 475,368
31 Direct labor 100,560 575,928
31 Factory overhead 48,480 624,408
31 Goods transferred, 25,700 units ?
31 Bal., ? units, 1/5 completed ?
Required:
1. Prepare a cost of production report, and identify the missing amounts for Work in Process—Blending Department. If an amount is zero enter "0". If required, round your cost per equivalent unit answers to the nearest cent.
Bavarian Chocolate Company
Cost of Production Report—Blending Department
For the Month Ended March 31
The missing amounts for Work in Process - Blending Department are: 25,700 units, and $70,944 for direct materials.
Cost of Production Report
Bavarian Chocolate Company processes chocolate into candy bars.
The process begins by placing direct materials (raw chocolate, milk, and sugar) into the Blending Department.
All materials are placed into production at the beginning of the blending process.
After blending, the milk chocolate is then transferred to the Molding Department, where the milk chocolate is formed into candy bars.
The following is a partial work in process account of the Blending Department at October 31:
ACCOUNT Work in Process—Blending Department ACCOUNT NO.
Date Item Debit Credit Balance
Debit Balance
Credit
October 1 Bal., 2,300 units, 3/5 completed 46,368
31 Direct materials, 26,000 units 429,000 475,368
31 Direct labor 100,560 575,928
31 Factory overhead 48,480 624,408
31 Goods transferred, 25,700 units.
1. Prepare a cost of production report, and identify the missing amounts for Work in Process—Blending Department. If an amount is zero enter "0". If required, round your cost per equivalent unit answers to the nearest cent.
Bavarian Chocolate Company
Cost of Production Report—Blending Department
For the Month Ended March 31
Bavarian Chocolate Company
Cost of Production Report—Blending Department
For the Month Ended October 31
Equivalent Units Schedule
Direct Materials Conversion Costs
Units to be accounted for:
Work in process, October 1 (3/5 completed) 2,300 2,300
Units started in October 26,000 26,000
Total units to be accounted for 28,300 28,300
Units accounted for:
Goods transferred to the Molding Department (25,700 units × 100%) 25,700 25,700
Work in process, October 31 (1/5 completed):
Total units accounted for:
Costs to be accounted for:
Direct materials cost $429,000
Direct labor cost $100,560
Factory overhead cost $48,480
Total costs to be accounted for $578,040
Costs accounted for:
Direct materials cost (26,000 units × $15 per unit) $390,000
Direct labor cost (2,300 units × $44 per unit) 101,200
Factory overhead cost (2,300 units × $21.12 per unit) 48,576
Total costs accounted for $539,776
Cost per Equivalent Unit:
Direct materials cost ($429,000 ÷ 28,300 units) $15.16
Direct labor cost ($100,560 ÷ 2,300 units) $43.74
Factory overhead cost ($48,480 ÷ 2,300 units) $21.12
Total cost per equivalent unit $80.02
Work in Process—Blending Department
Direct Materials Conversion Costs Total
Balance, October 1 $27,820 $18,548 $46,368
Current costs $352,380 $222,548 $574,928
Total cost $380,200 $241,096 $621,296
Less: Goods transferred to the Molding Department (25,700 units × $80.02 per unit) (2) $2,048 $2,048
Balance, October 31 (2) $378,152 (2) $239,048 (2) $617,200
(1) Equivalent units of direct materials and conversion costs have been calculated based on the weighted-average method.
(2) The missing amounts for Work in Process—Blending Department are:
Units, October 31: 2,600 units (28,300 total units – 25,700 transferred units).
Direct Materials, October 31: $352,380 (current costs) - $390,000 (costs accounted for) = -$37,620 (overallocated)
Conversion Costs, October 31: $222,548 (current costs) - $241,096 (costs accounted for) = -$18,548 (overallocated).
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Keisha is playing a game using a wheel divided into 8 equal sectors, as shown in the diagram below. Each time the spinner lands on blue, she will win a prize.
If Keisha spins this wheel twice, what is the probability that she will win a prize on both spins?
show all steps
Answer:
4/64
Step-by-step explanation:
The spinner is independent (the total won't be effected)
we know there is 2 whites with 8 coloured option.
we want the probability of getting two whites.
2/8 x 2/8 = 4/64
there is 3 ways to work out probability, fraction, decimal and percentage (i'd personally say fraction is the most easiest)
The foci for the hyperbola (x-1)^2/25 - (y+3)^2/9=1 are (1 + square root 34, -3) and (1 - square root 34, -3)
A. True
B. False
The assertion is accurate. This mean option that is selected should be true
The formula c = √(a 2 + b 2), where a and b are the lengths of the semi-major and semi-minor axes, respectively, yields the foci of a hyperbola.
What exactly is hyperbola?. A hyperbola is a particular kind of conic section that resembles two slightly mirrored parabolic curves. It is described as the collection of all points in a plane where the difference between the locations of two fixed points (referred to as foci) is always constant.
Each of the two branches of a hyperbola resembles a parabola. In relation to the hyperbola's centre, the branches are symmetric. The semi-major axis is the distance between the centre and each vertex, whereas the semi-minor axis is the distance between the centre and each terminal of the transverse axis.
When a² = 25 and b² = 9,
the hyperbola (x-1)2/25 - (y+3)2/9=1 can be calculated.
In light of this, c = √(25 + 9) = √ (34).
The hyperbola's center is located at (1, -3).
The foci are at (1 + √(34), -3) and (1 - √(34), -3), respectively.
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Use the rules for multiplication and/or division of measurements. According to climatologists, the carbon dioxide (CO₂) levels in the atmosphere in 2012 were the highest levels in 650,000 years, standing at 396 parts per million (ppm). The safe upper limit is 350 ppm. The current rate of increase is 2.10 ppm per year. If that rate of increase remains constant from 2012 until 2030, what would be the expected CO₂ level (in ppm) in our atmosphere by the end of the year 2030? (Round your answer to the same number of significant digits as the measurement that has the least number of significant digits.) ppm
Rounding to the same number of significant digits as the measurement with the least number of significant digits (which is "350 ppm"), the expected CO₂ level by the end of 2030 would be 430 ppm.
Describe Significant digits?Significant digits, also known as significant figures or sig figs, are the digits in a number that are considered to be accurate or meaningful. They represent the precision or reliability of a measurement or calculation.
In a number, all digits except for leading zeros are considered to be significant. For example, in the number 0.00456, there are three significant digits (4, 5, and 6), while the zeros before the 4 are not significant.
The rules for determining the number of significant digits in a number are:
All non-zero digits are significant.
Zeros between non-zero digits are significant.
Leading zeros are not significant.
To find the expected CO₂ level in the atmosphere by the end of 2030, we need to calculate the total increase in CO₂ levels from 2012 to 2030 and then add it to the 2012 CO₂ level of 396 ppm.
To calculate the total increase in CO₂ levels, we can use the following formula:
Total increase in CO₂ levels = rate of increase × time
where the rate of increase is 2.10 ppm per year and the time is the number of years from 2012 to 2030, which is 18 years.
Total increase in CO₂ levels = 2.10 ppm/year × 18 years = 37.8 ppm
Therefore, the expected CO₂ level in the atmosphere by the end of 2030 would be:
Expected CO₂ level = 2012 CO₂ level + total increase in CO₂ levels
Expected CO₂ level = 396 ppm + 37.8 ppm
Expected CO₂ level = 433.8 ppm
Rounding to the same number of significant digits as the measurement with the least number of significant digits (which is "350 ppm"), the expected CO₂ level by the end of 2030 would be 430 ppm.
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A and B are two mathematically similar containers.
Container A has surface area of 1550mm2 and container B has surface area of 10478mm2 Given that
volume of container B − volume of container A = 62 160mm3
calculate the volume, in mm3 , of container A.
Answer: Let's call the scale factor between the two containers "k". Then, we know that the ratio of their surface areas is equal to the square of the scale factor:
(surface area of B) / (surface area of A) = k^2
We also know that the ratio of their volumes is equal to the cube of the scale factor:
(volume of B) / (volume of A) = k^3
We can rearrange the first equation to solve for k:
k^2 = (surface area of B) / (surface area of A) = 10478 mm^2 / 1550 mm^2 = 6.75
Taking the square root of both sides, we get:
k = sqrt(6.75) = 2.6 (rounded to one decimal place)
Now we can use the second equation to find the volume of container A:
(volume of B) - (volume of A) = 62160 mm^3
(k^3)(volume of A) - (volume of A) = 62160 mm^3
Simplifying and solving for the volume of A, we get:
volume of A = 62160 mm^3 / (k^3 - 1) = 62160 mm^3 / (2.6^3 - 1) ≈ 4477 mm^3
Therefore, the volume of container A is approximately 4477 mm^3.
Step-by-step explanation:
Need help! (For 50 points)
Answer:
168°------------------------------
Supplementary angles add up to 180°:
m∠A + m∠B = 180°Substitute and solve for x:
x - 9 + 7x + 21 = 1808x + 12 = 1808x = 168x = 21Find the measure of ∠B:
m∠B = (7*21 + 21)° = 168°A TV cable company has 9600 subscribers who are each paying $36 per month. It can get 160 more subscribers for each $0.50 decrease in the monthly fee. What rate will yield maximum revenue, and what will this revenue be?
The function has the maximum revenue of $348,480 with the increasing rate of $33.
Explain about the maxima of function:The highest and smallest values of a function, respectively, can either be found inside a specific range or distributed throughout the entire domain. They are also sometimes referred to collectively as the function's extrema. The plural forms of a function's maximum and minimum are called maxima and minima, accordingly.
Given data:
We are aware that monthly subscription fees are $36.The corporation can increase its subscription count for a $0.50 drop.We also know that the business has 9600 subscribers and has the capacity to add 160 more.The overall revenue is thus:
y = (36 - 0.50x)(9600 + 160x)
Differentiate with respect to x.
y ' = (-0.50)(9600 + 160x) + 160(36 - 0.50x)
y' = -4800 - 80x + 5760 - 80x
y' = 960 - 160x
To find x, put y' = 0
960 - 160x = 0
x = 960/160 = 6 (critical point)
Function is decreasing in interval - [6, +∞)
Increasing Function in interval - (-∞, 6]
Thus, the function has the maximum value at x = 6.
maximum revenue f(6):
f(6) = (36 - 0.50x)(9600 + 160x)
f(6) = (36 - 0.50(6))(9600 + 160(6))
f(6) = $348,480
Rate : 36 - 0.50(6) = $33
The function has the maximum revenue of $348,480 with the increasing rate of $33.
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Find angle ABD please help fast i will mark brainiest
Answer:
I think its 75 degrees and brainliest would be greatly appreciated
Krysti is ordering T-shirts for 25 classmates. She knows that 80% of her class wants a small size she mistakingly ordered 12 small size t shirts
As 80 percentage of 25 classmates is equal to 20. Krysti should have ordered 20 small t-shirts for her 25 classmates
What is error?Error is when a mistake is made while solving a mathematical problem.
Krysti's error in finding the number of small t-shirts is that she forgot to multiply the percentage by the total number of classmates.
If Krysti wanted to find the number of small t-shirts she should have ordered, she should have multiplied
80% * 25.
=0.8 * 25
= 20.
To explain it in another way, Krysti could have also 100/25 and then 80 divided by the answer that is 4. This would also give the same result of 20.
Krysti's error was that she did not correctly use percentages to find the number of small t-shirts she should have ordered.
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PLEASE HELP!!! MIDDLE SCHOOL MATH!!!!!!!!!!!!!!!!!!!!!
Which of the following represent angle measures in the figure shown? select all that apply
PLEASE LOOK AT PICTURE BELOW!!!!!! MUST SHOW WORK!!!!!!!!!!!!!!
Answer:
55°90°145°Step-by-step explanation:
For the 90°/right angle part, we can subtract 35° from 90° to get the degree of that area.
90° - 35° = 55°
We can check off the "55°" box
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Now, for the other half of the straight angle including the right angle, we can subtract 90° from 180°.
Getting 90°
We can check off the "90°" box
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To find the degree of the "(7x + 5°)" -- assuming that that angle is vertical to the "other" -- we can make an equation of
⇒ 7x + 5° = 90° + 55°
Solve:
Add together 90 and 55 which is 145°
New equation:
7x + 5° = 145°
Subtract 5° from both sides, getting the equation
7x = 140°
Isolate x by dividing both sides by 7
x = 20°
Substitute what we have for x into the equation "7x + 5°"
7(20°) + 5
= 145°
We can check off the "145°" box
------------------------------------------
All the boxes checked off:
55°90°145°Hopefully this helps! -- mark me brainliest if you want ofc
how do i plug 3x^2 - 13x + 4 = 0 into a calculator?
the question is asking to factor and solve
Answer:
x=1/3
≈ 0.333333333
x=4
Step-by-step explanation:
The total for which two pet sales is 731
Answer: 363+368=731
Step-by-step explanation:
The net shown represents a square pyramid. 20 ft 32 ft • Determine the area, in square feet, of one triangular face of the square pyramid • Determine the total surface area, in square feet, of the square pyramid.
The total surface area must be calculated by adding the areas of all five faces, the four triangular faces, and the square base.
What is a square pyramid known as?The term "square pyramid" refers to a three-dimensional geometric form with a square base and four triangular faces or sides that meet at a single point (known as a vertex). Because it has five faces, it is referred to as a pentahedron.
Given :
Let s represent the square base's side length and h represent the slant height of each triangle face. The area of a single triangle is then determined by:
A = (1/2) * s * h
The areas of all five face the four triangular faces and the square base must be added up in order to determine the overall surface area of the pyramid.
The overall surface area is: since the square base has a simple area of s2.
When we replace A with the expression, we obtain:
We require further details regarding the pyramid in order to determine the values of s and h.
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