The value of f(8) is 3.
What is logarithm?
The opposite of exponentiation in mathematics is the logarithm. The exponent to which b must be raised in order to obtain a number x is hence the logarithm of a number x to the base b. For instance, since 1000 = 103, log10 of 1000 is 3, or [tex]log_1_0=3[/tex].
Let, [tex]f(x) = log_2(x)[/tex]
We have to find the value of f(8).
Plug x = 8 in the above equation.
[tex]f(8) =log_2(8)[/tex]
Here 8 = 2 x 2 x 2 = 2^3
So, replace 8 with 2^3 in the above equation.
[tex]f(8) = log_2(2^3)[/tex]
Using the log rule: [tex]log_a(a^b) = b[/tex]
Here a = 2, b = 3
So, [tex]log_2(2^3) = 3[/tex]
Hence, f(8) = 3.
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the freshman class of 63 students conducted a survey to compare how many students took spanish as opposed to french as a foreign language. the results are shown in the venn diagram. how many students studied neither spanish nor french?
With the help of sets we can conclude our answer.
What are sets?Simply put, a set in mathematics is a grouping of different items. Any group of objects, such as a collection of numbers, days of the week, different kinds of cars, etc., can be included in a set. An element of the set is any component of the set. When writing a set, curly brackets are utilized. An extremely basic set would look somewhat like this. Set A = {1,2,3,4,5}. The components of a set can be represented using a variety of notations. set is a well-defined collection of objects. Sets are named and represented using a capital letteracc to our qusetion-
Total students = 50Students taking french = 31Remaining Students= 50 - 31 = 19Students taking none = 10So remaining students have taken only spanish i.e. 19-10 = 9But total no of students taken spanish are 17So the students who had taken both are 17-9 = 8.Leran more about sets click here:
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Please Help
Takayla looked at a scale drawing of a piece of land she was interested in buying. The drawing used a scale of 1 in ft. = 200 ft. She was told that the actual length of the land was 588 ft. How long should the land be on the map?
A. 3.33 in
B. 2.98 in
C. 2.90 in
D. 2.94 in
Given the equation 6x + 18 = 72:
Part A: Write a short word problem about a purchase made to illustrate the equation. (6 points)
Part B: Solve the equation showing all work. (4 points)
Part C: Explain what the value of the variable represents. (2 points)
The short word problem that illustrates the given equation is seen below. The value of the variable is 9.
Expression of the algebraic equation into word problems:Linear algebra equations are equations that can be expressed in word problems and these equations can be used to solve real-life scenarios. These algebraic equations are designed by the application of the desired set of variables with its arithmetic operations.
A.
In a food factory, Eighteen fried chickens are added to the six times the number of food plates is seventy-two. How much-fried chicken goes into each food plate?
B.
6x + 18 = 72
Subtract 18 from both sides;
6x + 18 - 18 = 72 - 18
6x = 54
Divide both sides by 6.
6x/6 = 54/6
x = 9
C.
The value of the variable is 9, and according to the example we used, it represents the number of chickens that goes into each plate of food.
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K(15) = ?
Please find what k(15) is of the following graph below
Evaluate Each expression show your work
1. Evaluate 3 + 4x if x = 5
Answer:
23
Step-by-step explanation:
3+4x
3+4(5)
3+20
23
Hopes this helps please mark brainliest
EASY POINTS WILL GIVE BRAINLIST TO BEST ASWER!!
write the point slope form of the equation of the line through the given point with the given slope
(-2, -3) slope = 2
Answer:
y+3=2x+4
Step-by-step explanation:
Could someone help quick
The constant of proportionality is 1/7
What is constant of proportionality?The ratio between two proportional quantities' constant values is known as the constant of proportionality. When either their ratio or their product gives a constant, two changing values are said to be in a proportionate relationship. The Direct Variation and Inverse Variation types of proportions between the two provided quantities determine the proportionality constant's value.Direct Variation: The direct proportionality equation is y = kx, which demonstrates that as x rises, y rises at the same pace. Example: y x represents the cost per item(y), which is directly proportional to the number of items(x) purchased.Inverse Variation: The indirect proportionality equation, y = k/x, demonstrates that when y rises, x falls, and vice versa. As shown by the formula y 1/x, the speed of a moving object (y) inversely varies with the amount of time (x) needed to travel a distance.K is constant in both circumstances. The coefficient of proportionality is the name given to this constant's value. The unit rate is another name for the proportionality constant.To learn more about constant of proportionality, refer to https://brainly.com/question/26171814
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on average, the number of students that choose to study application development subjects at brock university is 18 each year. (hint: use poisson distribution formula). what is the probability that exactly 13 students will take up application development in the coming year? a. 0.06585 b. 0.05093 c. 0.14260 d. 0.08795
0.05093 is the probability that exactly 13 students will take up application development in the coming year .
Describe probability using an example?
It is based on the probabilities that something could happen. The theory of probability primarily relies on the justification for probability. A coin is tossed, for instance, and the theoretical likelihood of receiving a head is 1 in 2.Average rate (number) of students who chose to study Application Development (λ)= 18
Poisson random variable(number of students taking up Application Development in the coming year)(x)=13
Poisson distribution = P(X = x) = e^−λ (λ)^x/ x!
Here, probability of 13 students choosing application development next year= P(X=13)
= ^(−18 ) 18^13/ 13!
P(X=13) = 0.0509286= 0.05093
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The top of a 15-foot ladder is 3 feet farther up a wall than the foot of the ladder is from the bottom of the wall. How far up is the foot of the ladder from the bottom of the wall?
The answer is 9 but I don’t know how to get there.
Check the picture below.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2 \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}\implies 15^2=x^2+(x+3)^2 \\\\\\ 225=x^2+(x^2+6x+9)\implies \implies 225=2x^2+6x+9 \\\\\\ 0=2x^2+6x-216\implies 0=2(x^2+3x-108) \\\\\\ 0= x^2+3x-108\implies 0=(x-9)(x+12)\implies x= \begin{cases} 9 ~~ \checkmark\\\\ -12 \end{cases}[/tex]
let's notice that "x" does have two valid values, however for this scenario 'x" cannot be negative, so we don't use that one.
charlie has 2 fair coins. he repeatedly tosses the pair of coins simultaneously (i.e., two tosses at a time), until he has seen both sides of both coins. in expectation, how many total tosses does this take?
By using the trial method we get a total number of trials taken by Charlie to see both sides of both the coins is 4.
What is probability?Probability is the name of the area of mathematics that deals with the examination of random events. The ratio of favorable occurrences to the total number of events is used to calculate an event's probability.
P(E) = F(E)/T (E)P(E)
It stands for the probability that an event will occur.
F(E) = Amount of favorable occurrences
Total number of trials (T(E))
Given that Charlie has 2 fair coins.
If he tosses the pair of coins simultaneously, then the number of samples can be HH, HT, TH, TT.
So to see both sides of both the coins he should toss the coin four times.
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A hiking guide recommends that a person wear snowshoes when the accumulated snow has a depth of at least 6 inches. At 8:00 a.m., the depth of snow in a certain area is 4 inches. The predicted average rates of change of the depth of snow for different time intervals are shown in the table. For which of the following time periods between 8:00 a.m. and 8:00 p.m. would the guide recommend wearing snowshoes?
A. 8:00 a.m.-10:00 a.m. and 1:00 p.m.-3:00 p.m.
B. 8:00 a.m.-11:00 a.m. and 3:00 p.m.-4:00 p.m.
C. 10:00 a.m.-12:00 p.m. and 5:00 p.m.-8:00 p.m.
D. 9:00 a.m.-11:00 a.m. and 2:00 p.m.-4:00 p.m.
Considering the average rate of change, the time periods in which snowshoes are recommended are given as follows:
C. 10:00 a.m.-12:00 p.m. and 5:00 p.m.-8:00 p.m.
What is the average rate of change of a function?The average rate of change of a function is given by the change in the output of the function (change in the numeric value) divided by the change in the input of the function. Hence, over an interval [a,b], the rate is given by the fraction presented as follows:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
The initial amount is of 4 inches, hence, considering the rates, the amounts of snow on the ground are given as follows:
11 am: 4 + 3 x 0.75 = 6.25 inches. (>6 at 10 am).3 pm: 6.25 - 4 x 0.25 = 5.25 inches.8 pm: 5.25 + 5 x 0.50 = 7.75 inches. (>6 at 5 pm).Hence the intervals are given by option c.
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A plumber has a 36-inch pipe that he has to cut into two
pieces so that one piece is 8 in. longer than the other. Find
the length of each piece.
A plumber has a 36-inch pipe that he needs to cut into two pieces, one 8 inches longer than the other. Each piece's length is x = 14, while the other piece's length is 22.
What is meant by length?The measurement or extent of something from end to end is defined as length. In other words, it is the larger of the two or the highest of three geometrical shapes or objects' dimensions. A rectangle, for example, has length and breadth dimensions.Centimeters, meters, kilometers, inches, feet, yards, and other standard units of length measurement are some examples.A segment's length or the dimensions of a room are examples of length measurements. Distance is the distance between two objects, such as two cities or two points. There will never be a negative value for length or distance.Therefore,
let x = the first piece and x+14 is the second.
2x + 8 = 36
2x = 28
x = 14, the other piece is 22
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for sample size n, the margin of error is 3. how many more samples do we need to make the margin of error 0.3?
We will need 100 more samples to make the margin error of 0.3 .
What are sample errors?When the statistical characteristics of a population are estimated from a subset, or sample, of that population, sampling errors are made in statistics. Statistics of the sample (commonly referred to as estimators), such as means and quartiles, usually diverge from those of the total population because the sample does not include all individuals of the population (known as parameters). The sampling error is defined as the discrepancy between the sample statistic and the population parameter. For example, if one measures the height of a thousand individuals from a population of one million, the average height of the thousand is typically not the same as the average height of all one million persons in the country.acc to our question-
Margin error is 3Margin error tobe 0.3 SAMPLE size ?0.3 =3/10Ratio =3/3/10=10n^2=10×10=100Samples in size of 100Hence, We will need 100 more samples to make the margin error of 0.3 .
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angela is following this recipe to make biscuits. angela uses 3.3 litres of syrup. how much sugar is needed in kg
The quantity of sugar that is needed in kg would be = 1.8kg
What is recipe?Recipe is defined as the list of components of ingredients that makes up a food product.
From the recipe given by Angela, the quantity of syrup that is used to make up to 14 biscuits= 275 ml.
The quantity of sugar that is used to make up to 14 biscuits= 150g
Therefore the quantity of sugar that would be used for syrup of 3.3 liters would be= X
That is;
275ml = 150g
3.3L = X
Convert 3.3L to ml = 3,300ml , then make x the subject of formula;
X = 3300×150/275
X = 495000/275
X= 1,800g
Then convert 1,800g to kg by dividing through with 1000;
1800/1000 = 1.8 kg
Therefore, the quantity of sugar that would be used for 3.3L of syrup would be 1.8kg.
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Complete question:
Angela is following this recipe to make biscuits.Angela uses 3.3 litres of syrup.
How much margarine is needed in kg?
Recipe: Makes 14 biscuits
120 g margarine
150 g sugar
275 ml syrup
200 g oats
60 g sultanas
How much sugar is needed in kg?
What is the domain of the function?
A XER
B x≤5
C y≤ 5
D y≥5
Answer:
A
Step-by-step explanation:
Domain is the set of x values, so we can cross off C and D as answer choices as those would be possible answer choices for range. Looking at the graph, you can see the graph continues infinitely. The domain of the function is all real numbers, or A.
I GIVE you 20 points if you answer ASP PLS
The function graphed shows the total cost of a gym membership for x months.
Select from the drop-down menus to correctly identify the gym membership information provided by the graph.
The Slope is
The Slope Represents
Answer: Y=mx+b
Step-by-step explanation:
If you use the formula you can figure it out.
Answer:
the slope is 10
The slope represents the cost of gym membership per month.
In quadrilateral BADC, AB=AD and BC=DC. Which of the following contains only true statements?
Answer:
abad
Step-by-step explanation:
11. √1156
12. √1024
13. √1225
14. √1764
15. √1936
please ahh little help please
The evaluation of the square roots of the numbers using prime factorization gives;
11. √1156 = 32
12. √1024 = 32
13. √1225 = 35
14. √1764 = 42
15. √1936 = 44
What are prime factors?Prime factors are the factors of a number that are also prime numbers.
The square roots of the numbers found using prime factorization are as follows;
11. √1156
1156 ÷ 2 = 578
578 ÷ 2 = 289
289 ÷ 17 = 17
17 ÷ 17 = 1
√1156 = √(2 × 2 × 17 × 17) = √(2² × 17²)
√1156 = √(2² × 17²) = 2 × 17 = 34
√1156 = 34
12. √1024
1024 ÷ 2 = 512
512 ÷ 2 = 256
256 ÷ 2 = 128
128 ÷ 2 = 64
64 ÷ 2 = 32
32 ÷ 2 = 16
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
Therefore; √(1024) = √(2×2×2×2 ×2×2×2×2×2×2) = √(2¹⁰) = 2⁵ = 32
√1024 = 32
13. √1225
1225 ÷ 5 = 245
245 ÷ 5 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1
Therefore;
√(1225) = √(5 × 5 × 7 × 7) = √(5² + 7²) = 5 × 7 = 35
14. √1764
1764 ÷ 2 = 882
882 ÷ 2 = 441
441 ÷ 3 = 147
147 ÷ 3 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1
√1764 = √(2 × 2 × 3 × 3 × 7 × 7) = √(2² × 3² × 7² = 2 × 3 × 7 = 42
15. √1936
1936 ÷ 2 = 968
968 ÷ 2 = 484
484 ÷ 2 = 242
242 ÷ 2 = 121
121 ÷ 11 = 11
11 ÷ 11 = 1
Therefore; √(1936) = √(2 × 2 × 2 × 2 × 11 × 11) = √(2⁴ × 11²) = 2² × 11
√(1936) = 2² × 11 = 44
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Match the vocabulary word with the correct definition.
Base
Exponent
Scientific Notation
a.
The number that is going to be raised to a power.
b.
The number that tells you how many times you will multiply the base number.
c.
A way of writing VERY large or VERY small numbers so the numbers are easier to compare or calculate.
Answer:
Exponent: B
Base: A
Scientific Notation: C
Step-by-step explanation:
vocabulary
Answer:
Exponent and A
Base and B
Scientific Notation and C
Step-by-step explanation:
Because the Exponent is the number that is going to raise the Base and that Base is the number that you are going to multiply by.
Calculate the length of the unknown side of this right-angled triangle.
9 cm
8 cm
Determine the value of y for the inequality 2 times the quantity y plus one third end quantity is greater than two thirds. Y is greater than negative 1 over 36 y is less than negative 1 over 36 y > 0 y < 0
The solution to the inequality is y < -12 ( y less than negative 12).
Given inequality is;
y + 15 less-than 3
y+15<3
For solving the inequality, we will subtract 15 from both sides in order to find y.
Subtracting 15 from both sides of inequality
The solution to the inequality is y < -12 ( y less than negative 12).
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Considering a circle whose equation is x² + y² – 2x – 8 = 0. The statements that are true about it is as follows
The radius of the circle is 3 unitsThe center of the circle lies on the y-axisThe standard form of the equation is (x – 1)² + y² = 3How to determine the equation the circleInformation given in the question
a circle whose equation is x² + y² – 2x – 8 = 0
Equation of a circle is given as
(x - h)² (y - k)² = r²
The equation of the circle is written in standard form by completing the square of each of the quadratic equation involved
x² + y² – 2x – 8 = 0
x² - 2x + 1 + y² + 0 = 8 + 1
(x – 1)² + (y - 0)² = 3²
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Britney is buying a shirt and a hat at the mall. The shirt costs $30.70, and the hat costs $20.79. If Britney gives the sales clerk $100.00, how much change should she receive? (Ignore sales tax.)
Answer:
$48.51
Step-by-step explanation:
30.70+20.79 = 51.49
100-51.94 = $48.51
your welcome :)
Answer: $48.51
Step-by-step explanation:
If you add both $30.70 and $20.79, you would get $51.49. Then you subtract it from the $100 & you get a total of $48.51. So Britney is going to receive $48.51.
when 1515 is appended to a list of integers, the mean is increased by 22. when 11 is appended to the enlarged list, the mean of the enlarged list is decreased by 11. how many integers were in the original list?
In the initial list, there were 4 integers.
We have the following system if the mean is m, x is the list's initial sum, and n is the number of integers in the list:
m = x/n , m + 2 = (x + 15) / (n + 1) and m + 1 = (x + 16) / (n + 2).
The initial equation is x = mn.
Therefore, changing x in the other two equations:
m + 2 = (mn + 15) / (n + 1) ..............(1)
m + 1 = (mn + 16) / (n + 2)...............(2)
Based on equation (1):
(m + 2)(n + 1) = mn + 15
mn + m + 2n + 2 = mn + 15
m + 2n + 2 = 15
m + 2n = 13
m = 13 - 2n.
Now change m in equation (2) to:
13 - 2n + 1 = ( n(13 - 2n) + 16) / (n + 2)
14 - 2n = (13n - 2n^2 + 16) / (n + 2) Through-multiplication by n + 2:
(14 - 2n)(n + 2) = 13n - 2n^2 + 16
14n + 28 - 2n^2 - 4n = 13n - 2n^2 + 16
10n + 28 = 13n + 16
12 = 3n
n = 4.
Hence, there were 4 integers in the original list.
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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.
A boy scout troop is selling Christmas trees at a local tree lot. In the morning, they sold 6 Douglas Fir trees and 16 Noble Fir trees, earning a total of $986. In the afternoon, they sold 6 Douglas Fir trees and 24 Noble Fir trees, earning a total of $1,386. How much does each type of tree cost?
A Douglas Fir costs $_____
and a Noble Fir costs $_______
Solving the system of equations we can see that:
A Douglas Fir costs $33.50_and a Noble Fir costs $47.75__How to write and solve the system of equations?
We can define the variables:
x = price of a Douglas Fir trees
y = price of a Noble Fir trees.
By using the given information we can write:
6x + 16y = 986
6x + 24y = 1368
That is our system of equations
If we take the second equation and we subtract the first one we get.
(6x + 24y) - (6x + 16y) = 1368 - 986
8y = 382
y = 382/8 = 47.75
now that we know the value of y, we can find the value of x using the first equation.
6x + 16y = 986
6x = 965 - 16y
x = (965 - 16y)/6
x = (965 - 16*47.75)/6 = 33.5
So:
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16. Points X, Y, and Z are collinear, and Y is
the midpoint of XZ. Find the value of b.
Answer:
b=11
Step-by-step explanation:
lets set up the equation. we know that both sides equal each other so the equation is
2b+7=3b-4 let's move the 2b to the other side so we get
7=b-4 now add the 4 to the other side
11=b
Answer:
B is 11
Step-by-step explanation:
Consider the circle represented by this equation.
x² + 4x + y2² - 2y - 4 = 0
Which features are features of the circle?
000
radius of 1
center at (-2, 1)
center at (-4, 2)
radius of 3
radius of 9
center at (2,-1)
Reset
Next
The given circle equation [tex]x^2+4x+y^2-2y-4[/tex]=0 has center(-2,1) and radius r=3.
What is circle equation?
For all values of g, f, and c, the general equation of any type of circle is written as x2 + y2 + 2gx + 2fy + c = 0. The collection of all points in a plane that maintain a fixed, finite distance r from a fixed point is known as a circle. O = (a,b). The definition of a circle on the coordinate plane can be expressed using the equation of a circle. The equation is where r is the radius and if the centre of the circle is at the origin of the coordinate plane.
Here the given circle equation is,
=> [tex]x^2+4x+y^2-2y-4[/tex]=0
=>[tex]x^2+4x+y^2-2y =4[/tex]
[tex]= > x^2+4x+4+y^2-2y+1=4+4+1\\= > (x+2)^2+(y-1)^2=9[/tex]
we know that equation of circle is [tex](x-a)^2+(y-b)^2=r^2[/tex]
Here (a,b)= center and r is radius.
=> [tex](x+2)^2+(y-1)^2=3^2[/tex]
Then the Center (a,b)=(-2,1) and radius r=3.
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3. One batch of pancakes needs 1½ cups of pancake mix. One box has 9 cups of pancake mix.
How many batches of pancakes can be made with one box of pancake mix?
In linear equation, 27/2 pancakes are in the box .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a " of two variables," where x and y are the variables.Number of b pancake mix to be need = 1½ cups
Number of box has pancake mix = 9 cups
Therefore, in order to get the total number of batches of pancakes needed for the batches will be calculated thus
= 1½ * 9
= 3/2 * 9
= 27/2
therefore 27/2 pancakes are in the box .
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I need help I’m thinking its D but I’m not sure
3. Martin finishes a swim race in 78.934 seconds. His teammate, Abby finishes the race in 83.978 seconds and their last teammate finishes the race in 84.765 seconds.
If the teammates were to have a combined time of less than 250 seconds to qualify to the next round, did they qualify or not? How do you know?
help me please i really need help!
