Use like bases and the one-to-one property to solve each exponential equation. using logarithms 4^(-3v-2)=4^(-v)
The solution to the exponential equation [tex]4^-3v-2=4^-v[/tex]is v = -1.
To solve the exponential equation 4^(-3v-2)=4^(-v) using like bases and the one-to-one property,
Identify the like bases on both sides of the equation. In this case, the like base is 4.
Use the one-to-one property of exponential functions, which states that if two exponential functions with the same base are equal, then their exponents must also be equal. So, we can set the exponents equal to each other:
-3v - 2 = -v
Solve for the variable, v. We can do this by isolating the variable on one side of the equation:
-3v + v = 2
-2v = 2
v = -1
Check our answer by plugging it back into the original equation:
4^(-3(-1)-2) = 4^(-(-1))
4^(3-2) = 4^(1)
4^(1) = 4^(1)
4 = 4
So the solution to the exponential equation [tex]4^-3v-2=4^-v[/tex]is v = -1.
To know more about exponential equation refer here:
https://brainly.com/question/29506679#
#SPJ11
A number is equal to the sum of half a sebond number and 3. The first number is also equal to the sum of one-quarter of the second number and 5. The situation can be represented by using the graph below, where x represents the second number.
Hi, can anyone please answers this. I appreciate it very much. I need the answer and solution of (b) only
Answer:
[tex]\frac{\sqrt{x+3} }{x+1}[/tex]
Step-by-step explanation:
nothing further can happen.
If a=6 and b=24 eat is the calculation of b/a
Solution:
[tex]value \: of \: a = 6[/tex][tex]value \: of \: b = 24[/tex][tex] \frac{b}{a} = \frac{24}{6} [/tex][tex] = \frac{4}{1} = 4[/tex]The final value of b/a = 4Helpppppp meeee and thank uuuuuuu
Answer:
look in the comments and have a good day
(2.5 X 10^-2)(4.2 X 10^6)
show work pleaseee
After the multiplication of the given decimal numbers and their power, we got the value as 105,000.
What are decimal numbers?One of the number types in algebra that has a whole integer and a fractional portion separated by a decimal point is a decimal. The decimal point is the dot that appears between the parts of a whole number and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole quantities.
Simply change the decimal place to the right by the number of 0s in the power of 10 when multiplying a decimal by a power of 10. Simply change the decimal place to the left by the number of 0s in the power of 10 when dividing a decimal by a power of 10.
We are asked to solve the question:
(2.5 X 10⁻²)(4.2 X 10⁶)
Now we have to solve this following the PEDMAS rule.
So we have to solve the parentheses first.
2.5 * 10⁻²
Here the exponent has negative power.
10⁻² = 1/10² = 1/100
Then,
2.5 * 10⁻² = 2.5 * 1/100 = 0.0025
This is because when the number is divided by the power of 10, the decimal point moves to the left by the value of the power of 10.
Here the power is 2. So it moved two decimal places to the left.
4.2 * 10⁶
Here the decimal number is multiplied by the power of 10. So the decimal point moves 6 places to the right.
4.2 * 10⁶ = 4200000
Now after solving parentheses, we get
0.0025 * 4200000 = 25 * 10⁻⁴ * 4200000 = 105,000,000 * 10⁻⁴
= 105,000
Therefore after the multiplication of the given decimal numbers and their power, we got the value as 105,000.
To learn more about decimal numbers, follow the link.
https://brainly.com/question/1827193
#SPJ1
Ramon is filling cups with juice. Each cup is shaped like a cylinder and has a diameter of 4.4 inches and a height of 7 inches. How much juice can Ramon pour into 6 cups? Round to the nearest hundredth and approximate using π = 3.14.
A) 2,553.20 cubic inches
B)638.30 cubic inches
C)425.53 cubic inches
D)106.38 cubic inches
Answer:
D) 106.38 cubic inchesStep-by-step explanation:
Info:Diameter is the width of the cup and 7 is the height.
Process of elimination rules out A as it is too big.
The base of the cup is a circle.
Finding the base:Formula for area of a circle is Pi (3.14) times the radius squared.
1. Find radius
Diameter is 2x the radius, so if we have a 4.4 diameter, the radius will be 2.2.
2. Square radius
2.2x2.2=
4.84
3. Times Pi
Multiply 4.84 by 3.14 (Pi) to get
15.1976
Finding area:15.1976 is the area of the base. Now we multiply that by 7!
15.1976 x 7=
106.3832This is our answer, but we need to round it to the nearest hundredth, the question tells us.
106.38 is the final answer.
Which ordered pair is a solution of the equation? y = 3 x + 5
A solution of the equation is an ordered pair where the y-value is equal to the equation when the x-value is plugged in. An example of a solution for the equation y = 3x + 5 is the ordered pair (2, 11), because when 2 is plugged in for x, the y-value is 11 (3 * 2 + 5 = 11).
A solution of the equation y = 3x + 5 is an ordered pair of values that satisfies the equation. In other words, when the x-value of the ordered pair is plugged into the equation, the resulting y-value should be the same as the y-value of the ordered pair. For example, the ordered pair (2, 11) is a solution of the equation because when 2 is plugged into the equation, the result is 11 (3 * 2 + 5 = 11). This is true for any ordered pair that satisfies the equation, as the y-value of the ordered pair should always be equal to the result of the equation when the x-value is plugged in. Solutions of equations can be found by solving for the x-value and then plugging it into the equation to find the corresponding y-value. This is the same for any equation, not just y = 3x + 5.
Learn more about equation here
https://brainly.com/question/29657992
#SPJ4
You work for a company that wants to distribute 1.25 L cylindrical water bottles. Find dimensions of a cylinder that will result in the desired volume if the height must be between 4 to 6 times the radius.
To find the dimensions of a cylinder with a specific volume and height to radius ratio, we can use the formula for the volume of a cylinder, V = πr^2h, where V is the volume, r is the radius, and h is the height. We can also use the given information that the height must be between 4 to 6 times the radius, or 4r ≤ h ≤ 6r.
We can start by plugging in the given volume and the height to radius ratio into the formula:
1.25 L = πr^2(4r)
Dividing both sides by 4π gives us:
r^3 = 1.25 L / (4π)
Taking the cube root of both sides gives us the radius:
r = (1.25 L / (4π))^(1/3)
Now we can use the height to radius ratio to find the height:
h = 4r = 4(1.25 L / (4π))^(1/3)
So the dimensions of the cylinder are:
r = (1.25 L / (4π))^(1/3)
h = 4(1.25 L / (4π))^(1/3)
These dimensions will result in the desired volume of 1.25 L and a height that is between 4 to 6 times the radius.
To know more about dimensions refer here:
https://brainly.com/question/28688567
#SPJ11
for
the function f(x) = x^2 - 2x, what are the intervals for which f(x)
is greater than or equal to zero?
For the function f(x) = x2 - 2x, the intervals for which f(x) is greater than or equal to zero are x ≥ 0 and x ≤ 2.
We can solve this equation by setting f(x) equal to zero and solving for x:
x2 - 2x = 0
x(x - 2) = 0
x = 0 or x = 2
Therefore, the intervals for which f(x) is greater than or equal to zero are x ≥ 0 and x ≤ 2.
Equations are two mathematical expressions that equal each other, separated by an equals sign ("="). In equations, we can find data that may or may not be known.
For more information about function, visit:
https://brainly.com/question/25638609
#SPJ11
In studies looking at the movement patterns of penguins, penguins are often monitored by placing a metal tag on their flipper. A group of scientists were concerned that these metal tags may be negatively affecting the survival of penguins (Saraux et al. 2011, "The Reliability of flipper-banded penguins as indicators of climate change", Nature 469, 203- 206). They conducted a small study with a total of 1983 penguins to determine whether the type of tag (metal or electronic) influenced the 5-year survival of penguins. In total, the study included 957 penguins that wore metal tags, 540 penguins that wore metal tags and survived, and 301 penguins that wore electronic tags and died.
a) Assuming that the type of tag and penguin survival are independent of one another, what 2x2 table do we expect to see? Is the observed data consistent with this assump- tion of independence? Carry out a chi-squared test to address this question. Give all your steps, and state as clearly as you can what hypotheses you are testing, your p-value, and what you conclude.
b) Suppose a condition was specified in the null hypothesis through prior knowledge that the probability of survival is 0.637 and that the probability of a penguin wearing a metal tag is 0.483. Would anything in your analysis in (a) change? Is there any change in your conclusion from (a)?
c) Suppose a separate study had only included 21 penguins in total, 12 penguins that wore electronic tags, 4 penguins that wore metal tags and survived, and 5 penguins that wore electronic tags and died. Explain what reservations (if any) you may have with performing a chi-squared test. Carry out an appropriate test to address the question of independence between survival and tag type for the new data. Give all your steps, and state as clearly as you can what hypotheses you are testing, your p-value, and what you conclude.
We cannot conclude that the type of tag and penguin survival are not independent of one another for this smaller sample size.
a) The expected 2x2 table would look like this:
| | Metal Tag | Electronic Tag |
|------------|-----------|----------------|
| Survived | 483.637 | 456.363 |
| Not Survived | 473.363 | 569.637 |
The observed data is not consistent with the assumption of independence, as the observed values are different from the expected values. To carry out a chi-squared test, we need to calculate the chi-squared statistic:
X^2 = (957-483.637)^2/483.637 + (540-456.363)^2/456.363 + (301-473.363)^2/473.363 + (185-569.637)^2/569.637 = 237.525
The degrees of freedom for this test are (2-1)(2-1) = 1. Using a chi-squared distribution table, we can find the p-value for this test. The p-value is less than 0.001, which is very small. This means that the observed data is very unlikely to have occurred by chance if the assumption of independence is true. Therefore, we can reject the null hypothesis that the type of tag and penguin survival are independent of one another.
b) If the null hypothesis specified the probability of survival and the probability of a penguin wearing a metal tag, then the expected values in the 2x2 table would change. The new expected values would be:
| | Metal Tag | Electronic Tag |
|------------|-----------|----------------|
| Survived | 609.711 | 330.289 |
| Not Survived | 347.289 | 695.711 |
The chi-squared statistic would also change:
X^2 = (957-609.711)^2/609.711 + (540-330.289)^2/330.289 + (301-347.289)^2/347.289 + (185-695.711)^2/695.711 = 444.787
The p-value for this test would still be less than 0.001, so we would still reject the null hypothesis that the type of tag and penguin survival are independent of one another.
c) With a smaller sample size, the chi-squared test may not be appropriate. The expected values in the 2x2 table would be very small, and the chi-squared statistic may not follow a chi-squared distribution. Instead, we could use a Fisher's exact test to address the question of independence between survival and tag type. The null hypothesis for this test is that the type of tag and penguin survival are independent of one another. The alternative hypothesis is that the type of tag and penguin survival are not independent of one another. The p-value for this test is 0.657, which is not small enough to reject the null hypothesis. Therefore, we cannot conclude that the type of tag and penguin survival are not independent of one another for this smaller sample size.
Learn more about movement
brainly.com/question/2856566
#SPJ11
How much of a 12% salt solution must combined with a 26% salt solution to make 2 gallons of a 20% salt solution?
The final answer is 0.857 gallons of the 12% solution and 1.143 gallons of the 26% solution.
To find how much of a 12% salt solution must be combined with a 26% salt solution to make 2 gallons of a 20% salt solution,
We can use the equation:
x(12%) + (2 - x)(26%) = 2(20%)
where x is the amount of the 12% solution needed.
Simplifying the equation gives us:
12x + 52 - 26x = 40
-14x = -12
x = 0.857 gallons
Therefore, we need 0.857 gallons of the 12% salt solution and 1.143 gallons of the 26% salt solution to make 2 gallons of a 20% salt solution.
Answer: 0.857 gallons of the 12% solution and 1.143 gallons of the 26% solution.
To know more about combined solution refer here:
https://brainly.com/question/16122098#
#SPJ11
Math question 11 help
Determine if the function f(x)=x+4 is increasing or decreasing on the interval of 2≤x≤5
. Justify your answer.
The given function, f(x) = x + 4 is increasing on the entire interval of 2≤x≤5
Determining if a function is increasing or decreasing on the intervalFrom the question, we are to determine if the given function is increasing or decreasing over the given interval
The given function is
f(x) = x + 4
To determine if the function f(x)=x+4 is increasing or decreasing on the interval of 2≤x≤5, we need to look at the sign of the first derivative of the function on that interval.
The first derivative of the function is
f'(x) = 1
Which is always positive
This means that the function is increasing on the entire interval of 2≤x≤5.
To justify this, we can also look at the graph of the function, which is a straight line with a positive slope. Any line with a positive slope is always increasing, so this confirms our conclusion that the function is increasing on the given interval.
Learn more on Determining if a function is increasing or decreasing here: https://brainly.com/question/1503051
#SPJ1
17. In right triangle AABC shown below, the given lengths
are in millimeters. What is sin A ?
A.
B.
C.
D.
4√2
9
4√2
7
7√/2
8
779927
E. 2/7
A
4√2
9
B 7
C
The value of sin A in the triangle is 7/9
How to determine the value of sin AThe complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The triangle ABC
Using the sine rule, we have
sin(A) = Opposite/Hypotenuse
Substitute the known values in the above equation, so, we have the following representation
sin(A) = 7/9
Hence, the solution is 7/9
Read more about triangles at
https://brainly.com/question/14285697
#SPJ1
7y−10=−3(5−x)
Step 2 of 2 : Find the equation of the line which passes through the point
(14,−14)(14,−14) and is parallel to the given
line. Express your answer in slope-intercept form. Si
The answer is [tex]y = (3/7)x - 20[/tex]
To find the equation of the line that passes through the point (14,-14) and is parallel to the given line, we will use the slope-intercept form of an equation, which is [tex]y = mx + b[/tex], where m is the slope and b is the y-intercept.
First, we need to find the slope of the given line. To do this, we will rearrange the equation to get it in slope-intercept form:
[tex]7y - 10 = -3(5 - x)[/tex]
[tex]7y - 10 = -15 + 3x[/tex]
[tex]7y = 3x + 5[/tex]
[tex]y = (3/7)x + (5/7)[/tex]
The slope of the given line is 3/7.
Since the new line is parallel to the given line, it will have the same slope. So, the slope of the new line is also 3/7.
Now, we will use the point-slope form of an equation to find the equation of the new line. The point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Plugging in the point (14,-14) and the slope 3/7, we get:
[tex]y - (-14) = (3/7)(x - 14)[/tex]
[tex]y + 14 = (3/7)x - 6[/tex]
[tex]y = (3/7)x - 20[/tex]
This is the equation of the new line in slope-intercept form. The slope is 3/7 and the y-intercept is -20.
So, the final answer is [tex]y = (3/7)x - 20[/tex].
See more about point-slope at: https://brainly.com/question/29955295
#SPJ11
Feb 22, 8:31:06 AM Determine if the expression 6 is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial.
The expression 6 is a polynomial. It is a constant polynomial with a degree of 0.
A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. A constant polynomial is a polynomial with no variables, and only consists of a constant term.
In the expression 6, there are no variables and it only consists of a constant term, which makes it a constant polynomial. The degree of a polynomial is the highest exponent of the variable in the polynomial. Since there are no variables in the expression 6, the degree of the polynomial is 0.
Therefore, the expression 6 is a constant polynomial with a degree of 0.
To know more about polynomial click on below link :
https://brainly.com/question/11536910#
#SPJ11
What mice would be the “fittest” to do the forest environment? Why?
Answer:
The "fittest" mice to survive in a forest environment would depend on various factors such as the specific characteristics of the forest, availability of resources, and the predators and other species present in the area.
Generally, mice that are well adapted to forest environments would possess certain traits such as:
Good sense of smell: Forest environments are often dense and may provide cover for predators. Mice with a good sense of smell are better equipped to navigate and find food in such environments.
Good vision: Some mice species have adapted to have good vision to better navigate through their environment and avoid predators.
Climbing ability: Mice that are able to climb trees and other obstacles can better avoid predators and find food sources.
Ability to burrow: Some mice may dig burrows to escape predators or find shelter, and those that are well adapted to digging will be better equipped to do so in a forest environment.
Based on these criteria, mice such as the white-footed mouse and the deer mouse are well-suited to forest environments. These species possess a good sense of smell and vision, can climb and burrow when necessary, and are able to find food sources such as nuts, seeds, and insects in the forest. However, there may be other mouse species that are better adapted to a specific forest environment, and the "fittest" mice would ultimately depend on the specific characteristics of the forest in question.
find the missing segment in the image below
In the triangle ABC, the value of BD is obtained as 34 units.
What are triangles?
Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.
A triangle ABC is given.
A line segment DE divides the triangle.
The measure of AD is given as 51 units.
The measure of BE is given as 16 units.
The measure of CE is given as 24 units.
According to the indirect measurement -
AD / BD = CE / BE
Substitute the values in the equation -
51 / BD = 24 / 16
24 BD = 51 × 16
BD = 17 × 2
BD = 34
Therefore, the value of BD is obtained as 34 units.
To learn more about triangles from the given link
brainly.com/question/25215131
#SPJ1
Answer: 34
Step-by-step explanation:
Solve the simultaneous equations
5
x
+
2
y
=
3
2
y
=
3
x
−
5
Answer:
Step-by-step explanation:
dvbd
Drag each set of coordinates to the correct location on the table. Calculate the distance between the pairs of coordinates, and classify them according to the distance between them. (3, 4) and (2, 1) (3, 7) and (5, 2) (5, -2) and (3, 3) (-2, 3) and (1, 2) (-4, -2) and (-3, 1) (4, -1) and (-1, 1)
The distances based on their values, we have:
Distances of approximately 1 to 2 units: (-3, 1) and (-4, -2)
Distances of approximately 3 units: (2, 1) and (1, 2)
Distances of approximately 5 units: (3, 7) and (4, -1), (5, -2) and (3, 3), and (-1, 1) and (4, -1).
Coordinates (3, 4) (3, 7) (5, -2) (-2, 3) (-4, -2) (4, -1)
(2, 1) 3.16
(5, 2) 5.39
(3, 3) 5.1
(1, 2) 3.16
(-3, 1) 1.41
(-1, 1) 5.1
We may use the distance formula to determine the separation between each pair of coordinates:
Distance is equal to sqrt((x2 - x1) + (y2 - y1))
Using the values to categorise the distances, we have:
About 1 to 2 unit distances are (-3, 1) and (-4, -2)
Distances roughly 3 units apart: (2, 1) and (1, 2) Distances roughly 5 units apart: (3, 7) and (4, -1), (5, -2) and (3, 3), and (-1, 1) and (4, -1).
To know more about Distance visit:
brainly.com/question/30701405
#SPJ1
You are stranded on a boat in the middle of the ocean with no fresh water on board. However, you are not alone, and some of those with you want to drink the ocean water. You tell them they should not do that but they don’t believe you. Use your understanding of osmosis to convince them WHY drinking salt water is very bad and a potentially deadly idea.
You can't drink salt water as it leads to dehydration and damage to our organs due to the high concentration of salt.
Why it is not recommended to drink salt water?Drinking salt water can be a potentially deadly mistake because of a phenomenon called osmosis. Osmosis is the movement of water molecules across a semi-permeable membrane, from an area of low solute concentration to an area of high solute concentration.
When we drink salt water, we introduce a high concentration of salt into our bodies. This high concentration of salt draws water out of our cells and tissues, causing dehydration. This is because our bodies require water to dilute the salt concentration and maintain a balance of solutes both inside and outside the cells.
The more salt water a person drinks, the greater the concentration of salt in their body becomes, leading to an increased loss of water through osmosis. This can lead to a vicious cycle where the more a person drinks salt water, the more dehydrated they become, thus damaging the organs of the person.
More can be learned about salt water at https://brainly.com/question/16617094
#SPJ1
Use your knowledge about linear function to determine if the two point (-2,-3) and (2,-1) are belong to the same function? If they do, then what is the function? Show your work.
Yes, the two points (-2,-3) and (2,-1) belong to the same linear function.
To determine the function, we can use the slope-intercept form of an linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
First, we need to find the slope of the line using the formula m = (y2 - y1) / (x2 - x1). Plugging in the values of the given points, we get:
m = (-1 - (-3)) / (2 - (-2)) = 2 / 4 = 1/2
Now, we can use one of the given points and the slope to find the y-intercept. Let's use the point (2,-1) and plug in the values into the equation y = mx + b:
-1 = (1/2)(2) + b
Solving for b, we get:
b = -1 - 1 = -2
Therefore, the equation of the linear function is y = (1/2)x - 2.
So, the two points (-2,-3) and (2,-1) belong to the same function, which is y = (1/2)x - 2.
To know more about linear function click on below link:
https://brainly.com/question/21107621#
#SPJ11
may someone help me with this????
Answer:
The answer would be at 11 30 the temperature would be at 3°C
Evaluate The Following Integral ∫[infinity]0e^(−x^2/a)dx
Given That ∫[infinity]0e^(−x^2)dx=1/2√π
And a = 2.1. Round your answers to five decimal places. Answer : _____
∫[infinity]0e^(−x^2/a)dx is 1/2√π/a, rounded to five decimal places is 0.38539.
To evaluate the integral ∫[infinity]0e^(−x^2/a)dx, given that ∫[infinity]0e^(−x^2)dx=1/2√π and a = 2.1, we use the substitution u = x^2/a. We then have du = 2x/a dx and the limits of the integral change to 0 to ∞/a. So, the integral becomes:
∫[∞/a]0 e^(-u) du
By the given information, we know that ∫[∞/a]0 e^(-u) du = 1/2√π/a.
Therefore, the answer to the integral ∫[infinity]0e^(−x^2/a)dx is 1/2√π/a, rounded to five decimal places is 0.38539.
Learn more about integration
brainly.com/question/18125359
#SPJ11
Use the rational zeros theorem to list all possible rational zeros of the following. f(x)=5x^(4)-9x^(3)-7x^(2)+9x-2
The possible rational zeros of [tex]f(x) = 5x^(4) - 9x^(3) - 7x^(2) + 9x - 2[/tex] are [tex]±1, ±2, ±1/5, and ±2/5.[/tex]
According to the Rational Zeros Theorem, the possible rational zeros of a polynomial function are the ratios of the factors of the constant term to the factors of the leading coefficient. In this case, the constant term is -2 and the leading coefficient is 5.
The factors of -2 are ±1 and ±2. The factors of 5 are ±1 and ±5. So, the possible rational zeros are:
[tex]±1/1, ±2/1, ±1/5, ±2/5[/tex]
Simplifying these gives us the following list of possible rational zeros:
[tex]±1, ±2, ±1/5, ±2/5[/tex]
To know more about Rational Zero Theorem refer to-
brainly.com/question/29004642#
#SPJ11
You instructor is considering the installation of a circular dart board with radius 5.1 on the office wall, instead of actually reading your papers, it has been suggested that grades be assigned by chance by dividing the board into three grade sectors and tossing a dart. The area of an "A" sector with central angle 2.781 is ____. The area of a "B" sector with central angle 1.54519 is _____. The area of a "C" sector with central angle 112.128 degree is _____. Assume a dart is randomly thrown at the board and the grade is noted on your paper. List your grade in order of increasing likelihood: ___ ___ ___
If the chance of your receiving a given grade is based upon the size of the sector divided by the size of the whole circle, determine the likelihood that you will receive an "A" ______.
The area of an "A" sector with central angle 2.781 is 36.17 square units. The area of a "B" sector with central angle 1.54519 is 20.10 square units. The area of a "C" sector with central angle 112.128 degree is 49.81 square units. Grade in order of increasing likelihood: B, A, C. Likelihood that you will receive an "A" is 0.4427.
The area of a sector of a circle can be found using the formula A = (1/2)r^2θ, where r is the radius of the circle and θ is the central angle of the sector in radians. To find the area of each sector, we need to convert the central angles from degrees to radians by multiplying by π/180.
The area of an "A" sector with central angle 2.781 radians is A = (1/2)(5.1)^2(2.781) = 36.17 square units.
The area of a "B" sector with central angle 1.54519 radians is A = (1/2)(5.1)^2(1.54519) = 20.10 square units.
The area of a "C" sector with central angle 112.128 degrees is A = (1/2)(5.1)^2(112.128)(π/180) = 49.81 square units.
The total area of the circle is A = πr^2 = π(5.1)^2 = 81.71 square units.
The likelihood of receiving an "A" is the area of the "A" sector divided by the total area of the circle, or 36.17/81.71 = 0.4427.
The likelihood of receiving a "B" is the area of the "B" sector divided by the total area of the circle, or 20.10/81.71 = 0.2460.
The likelihood of receiving a "C" is the area of the "C" sector divided by the total area of the circle, or 49.81/81.71 = 0.6096.
Therefore, the grades in order of increasing likelihood are: B, A, C.
The likelihood that you will receive an "A" is 0.4427.
Learn more about Central angle:
https://brainly.com/question/29545058
#SPJ11
Karen invested her savings in two investment funds. The amount she invested in Fund A was 4 times as much as the amount she invested in Fund B. Fund A returned a 4% profit and Fund B returned a 7% profit. How much did she invest in Fund B, if the total profit from the two funds together was $1380?
Karen invested $6000 in Fund B, and $24000 in Fund A, as the weighted average of the two funds' returns is 5%, yielding a total profit of $1380, and we can use a system of equations to solve for the amounts invested in each fund.
To solve this problem, we can set up a system of equations using the information given.
Let x be the amount invested in Fund B, then the amount invested in Fund A is 4x. The total amount invested is the sum of these two amounts, so we have:
x + 4x = 5x = total amount investedThe total profit from the two funds is given as $1380, which is the sum of the profits from Fund A and Fund B.
We can express these profits using the amounts invested and the respective return rates:
0.04(4x) + 0.07(x) = 0.16x + 0.07x = 0.23x = $1380Solving for x, we find that x = $6000, which is the amount invested in Fund B. Therefore, the amount invested in Fund A is 4x = $24000.
Learn more about investment funds https://brainly.com/question/25300925
#SPJ11
The angle marked a=44 work out the angle marked x
The value of angle x is 134°.
We have:
Angle ABD = 180° (straight line)
Angle ABE = 44° (given)
Angle BCE = 90° (as BC is perpendicular to AB)
Angle AEC = 180° - Angle BCE - Angle BAE = 180° - 90° - 44° = 46° (angle sum of triangle ABE)
Now, we can use the exterior angle property of triangles to find the value of angle x.
Angle AED = Angle AEC + Angle CED = 46° + x (exterior angle property of triangle CED)
Angle AED = Angle ABD = 180° (opposite angles of a cyclic quadrilateral)
Therefore, we have:
46° + x = 180°
x = 180° - 46°
x = 134°
Hence, the value of angle x is 134°.
To learn more about angle property
https://brainly.com/question/7870936
#SPJ4
A food company conducted a survey and found that 4 out of 20 people had french toast for
breakfast yesterday.
What is the probability that a randomly selected person had french toast for breakfast?
The probability that a randomly selected person had French toast for breakfast is 20%.
What is the probability?Probability describes the result of a random event based on the expected successes or outcomes.
Probability is computed as the quotient of the expected outcomes, events, or successes out of many possible outcomes, events, or successes.
Probability values lie between zero and one based on the degree of certainty or otherwise and can be depicted as percentages, decimals, or fractions.
The total number of survey participants = 20
The number of participants found to be having French toast for breakfast = 4
The probability of selecting a person having French toast for breakfast = 20%,or 0.2, or 1/5 (4/20 x 100)
Learn more about probabilities at https://brainly.com/question/25870256.
#SPJ1