a) To evaluate loga 15, we can use the property of logarithms that states logab = loga + logb. Since 15 = 3 * 5, we can use this property to find that loga 15 = loga 3 + loga 5. Since loga 3 = 0.56 and loga 5 = 0.83, we can add these values to find that loga 15 = 0.56 + 0.83 = 1.39.
The power to which a number must be increased in order to obtain additional values is referred to as a logarithm. The easiest approach to express enormous numbers is this manner.
Numerous significant characteristics of a logarithm demonstrate that addition and subtraction logarithms may also be represented as multiplication and division of logarithms.
b) To evaluate loga(2/5), we can use the property of logarithms that states log(a/b) = loga - logb. Since 2/5 = 2*(1/5) we can use this property to find that loga(2/5) = loga2 - loga(1/5). Since loga2 = 0.36 and loga(1/5) = -loga5, we can subtract these values to find that loga(2/5) = 0.36 - 0.83 = -0.47
c) To evaluate loga (8a^4), we can use the property of logarithms that states log (a^n) = nloga. We get, loga (8a^4)=loga 8 + log (a^4)
=> loga 8 + loga (a^4)
=>3loga 2 + 4 loga a
=>3loga 2 + 4
=>3 * 0.36 + 4
=5.08
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If the expression 4[tex]\frac{4\sqrt{81x^4y^2}}{x^-1/2y^-1}[/tex] is written in form ax^by^c, then what is the product of a b c?
The product of a, b and c is equal to 18.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is are the expression as -
[tex]$\frac{\sqrt[4]{81x^{4} y^{2} } }{x^{-1} 2y^{-1} }[/tex]
The given expression is -
[tex]$\frac{\sqrt[4]{81x^{4} y^{2} } }{x^{-1} 2y^{-1} }[/tex]
We can rewrite it as -
[tex]$\frac{(81x^{4} y^{2}) ^{\frac{1}{4} } }{x^{-1} (2y)^{-1} } = \frac{(3^{4} x^{4} y^{2})^{\frac{1}{4} } }{x^{-1} (2y)^{-1} } = 6xy^{\frac{1}{2} } xy[/tex]
Now, we can write -
[tex]6xy^{\frac{1}{2} } xy = 6x^{2} y^{(\frac{1}{2} + 1) } = 6x^{2} y^{(\frac{3}{2}) }[/tex]
On comparing, we get -
a = 6
b = 2
c = 3/2
So -
a x b x c = 6 x 2 x 3/2 = 18
a x b x c = 18
Therefore, the product of a, b and c is equal to 18.
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For a science project,3/4 of the students chose to make a poster and 0.25 of the students wrote a report. Rosa said that more students made a poster than wrote a report.Do you agree with Rosa? Use numbers and words to support your answer.
Yes , i agree with Rosa in linear equation.
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 "linear equation of two variables," where x and y are the variables.Linear equations are equations having variables with power 1. ax+b = 0 is an example with one variable where x is the variable, a and b are real numbers.
3/4 is equal to 0.75 and 0.75 > 0.25
Or 0.25 is equal to 1/4,
and 1/4 < 3/4
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Ronald carved 3/3/8 of a totem pole. he says that the totem pole is 3/4 completed.
Part A if h represents the height in feet of the finished totem pole ,then 3/4h=3/3/8 represents this situation. Which equations show the use of the reciprocal to write an equivalent equation that can be used to solve for h?
The height of the totem tree after solving the equation is 1/6 units
What is an equation?An equation is an expression that shows how numbers and variables relate with each other.
Mathematical operations include addition, subtraction, division and multiplication. Mathematical operations are used in equations
Let h represent the height of the totem pole.
Ronald carved 3/3/8 of a totem pole. he says that the totem pole is 3/4 completed. Hence:
(3/4)h = 3÷3÷8
(3/4)h = 3 * (1/3) * (1/8)
(3/4)h = 1/8
Cross multiplying gives:
h = (4 * 1)/(3 * 8)
h = 1/6
The height of the tree is 1/6 units
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Two angles are complementary to each other. One angle measures 18°, and the other angle measures (8x − 28)°. Determine the value of x.
Since one angle measures 18°, and the other angle measures (8x − 28)°, the value of x is equal to 12.5.
What is a complementary angle?In Mathematics, a complementary angle can be defined as two (2) angles or arc whose sum is equal to 90 degrees (90°).
Mathematically, a complementary angle can be calculated by using this mathematical expression:
Q + R = 90°
Where:
Q and R are measure of the angles subtended.
Substituting the given parameters into the complementary angle formula, the sum of the angles is given by;
(8x - 28)° + 18° = 90°
8x - 10 = 90
8x = 90 + 10
8x = 100
x = 100/8
x = 12.5
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In the diagram below, PQ is parallel to MN. If PQ is 2 more than MP,
PO = 12, and MN = 12, find the length of MP. Figures are not necessarily
drawn to scale. State your answer in simplest radical form, if necessary.
Therefore , the solution of the given problem of parallel line comes out to be MP =22.
Parallel lines are what?Geometry refers to parallel lines as beams, straight lines that never overlap. Parallel planes are those that never cross each other while occupying the same three-dimensional space. Curves which are equal with each other and keep a predetermined minimum separation from one another must not overlap or intersect. Parallel lines on a plane are those that always have the same distance between them. A parallel line cannot be crossed. Perpendicular lines are those that intersect directly at a 90 degree angle.
Here,
Given : PQ || MN
=> PQ =MP+2
=> PO = 12 , MN = 12
So,
=> PO + MN = 12 + 12
=> PQ = 24
=> PQ = MP +2
=>24 = MP +2
=> MP =22
Therefore , the solution of the given problem of parallel line comes out to be MP =22.
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Guys i need help with this it's really hard!
Answer: c is correct
Answer:
c
Step-by-step explanation:
factoriser
A=(2x-3)(2x-3)-(x-2)(x-2)
Which of the following gives the area, A
, of a circle with a diameter of 6?
A
A=π(3)
B
A=π×2(3)
C
A=π(3)2
D
A=π×2(3)2
The area of a circle with a diameter of 6 is A=π(3)². Option C
How to determine the area of the circleIt is important to note that the area of a circle is expressed with the formula;
A = πr² or πd²/4
Where;
A is the area of a circleπ takes the value 3. 14 or 22/7r is the radius of the circled is the diameter of the circleFrom the information given, we have that the diameter is 6
Radius = diameter/2 = 6/ 2 = 3
Substitute the value into the formula for area
Area, A = π(3)²
Hence, the area of the circle is π(3)²
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Deon made 2 identical necklaces, each having beads and a pendant. The total cost of the beads and pendants for both necklaces was 13.40. If the beads cost
3.60 for each necklace, how much did each pendant cost?
Answer:
$7.40
Step-by-step explanation:
Would this be SSS, ASA, SAS, or AAS?
Which of the following rational functions is graphed below?
The rational function f(x)= x/x+3 is graphed in the figure.
What is rational function?
A rational function is the function which can be expressed in terms of the ratio of p and q.
f(x)= p(x)/q(x)
From the given graph , the vertical asymptote is at x=-3
Now, let's find out the vertical asymptote of each function
In order to find out vertical asymptote, we set the denominator =0
a. f(x)= x/(x+3)
x+3=0
x=-3
b. f(x)= x-3/x
x=0
c. f(x)= x/3
3≠0
d. f(x)= 3/x
x=0
The first function has vertical asymptote at x=-3.
Hence, the first option f(x)= x/x+3 is graphed in the figure.
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The midpoint of the segment joining points (a, b) and (j, k) is:
The midpoint of the segment joining points (a,b) and (j,k) is, (a+j)/2, (b+k)/2)
The midpoint of the segment joining two points (x1, y1) and (x2, y2) is given by the point ((x1 + x2)/2, (y1 + y2)/2).
So, to find the midpoint of the segment joining the points (a, b) and (j, k), we need to take the average of the x-coordinates and the average of the y-coordinates:
((a + j)/2, (b + k)/2)
So the midpoint of the segment joining points (a,b) and (j,k) is (a+j)/2, (b+k)/2).
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Tickets to the aquarium cost $27 per person. Write an expression to represent the total cost of tickets for a group of people.? (Helping middle schoolers)
it is 57 understand the way is down there
Step-by-step explanation:
j
k
h
a
h
a
HELP QUICK PLS
For males in a certain town, the systolic blood pressure is normally distributed with a
mean of 105 and a standard deviation of 10. What is the probability that a randomly
selected male's systolic blood pressure will be less than 129, to the nearest
thousandth?
Therefore, the solution of given problem of probability is there is a 0.397 percent chance that a randomly chosen male will have a systolic blood pressure below 100.
How does probability work?A branch of mathematics called probability theory determines the likelihood that an event will occur or that a statement is true. A possibility is a number from 0 and 1, where 1 denotes certainty and about 0 denotes how probable an event is to occur. The possibility or chance that a specific event will occur is expressed numerically as a probability. Probabilities can also be expressed as percentages ranging from 0% to 100% and from 0 to 1.
Here,
Considering the query
In a particular municipality, men's systolic blood pressure has a median of 105 as well as a standard deviation = 9, which is considered to be regularly distributed.
Probability that the systolic blood pressure of a man chosen at random will be less than 100
P(x < 100)
Through the use of normalized normal distribution
=> N(100 -105)/9 \s=> N (-5/9)
We have a>0 and N(-a) = 1 - N(a).
=> 1 - N (-5/9)
=> 1 - N(0.556) (0.556)
=>1 - 0.6026
=> 0.3979
≈ 0.397 (nearest hundredths) (nearest thousandth)
Therefore, there is a 0.397 percent chance that a randomly chosen male will have a systolic blood pressure below 100.
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This graph shows a proportional relationship.
What is the constant of proportionality?
Enter your answer in the box.
A
Replanted trees
500
450
400
350
300
250
200
150
100
50
(5,225)
(3, 135)
1 2 3 4 5 6 7 8 9 10
Area (acres)
What is Constant of Proportionality?
The ratio between two proportional quantities' constant values is known as the constant of proportionality.
The formula for calculating slope is expressed as:
m = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
Given: the coordinate points (5,225) and (3, 135). The constant of proportionality is expressed as:
m = [tex]\frac{135-225}{3-5}[/tex]
m = [tex]\frac{-90}{-2}[/tex]
m = 45
Hence, Constant of Proportionality is 45.
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Pls help please easy
Answer: 204
Step-by-step explanation:
2 goes into 12 six times. 34x6=204
hence, your answer.
Roman and Sienna are comparing the number of pages they’ve each read over the Winter Break. Roman said he read 40% of his book, which has a total of 200 pages. Sienna’s book has a total of 400 pages, and she read of it. Without calculating, who do you predict has read more pages of their book? Explain 1/5 your reasoning.
In linear equation, 53% is predict has read more pages of their book .
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 "linear equation of two variables," where x and y are the variables.
Total pages = 400
Remaining pages to be read after Monday = 400 - 200 = 200
40% of 200 = 200 × 40/100 = 80
Remaining pages to be read after Tuesday = 400 - 80 = 320
600 × x/100 = 320
Let the remaining percentage of pages remain to be read be x,
so, 600 × x/100 = 320
x = 320/6 = 53.33333% = 53%
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The radius of a cylindrical construction pipe is 2 ft, and its length is 19 ft. Answer the parts below. Make sure you're using the correct units in your answer.
a. Find the exact volume of the pipe. Write your answer in terms of pi.
The volume of the cylindrical pipe in terms of π is 76π ft³.
The volume of the cylindrical pipe using ALEKS calculator is 238.76 ft³.
How to find the volume of a cylinder?The radius of a cylindrical construction pipe is 2 ft, and its length is 19 ft. The exact volume of the cylindrical pipe can be found as follows:
The answer is in terms of π.
Therefore,
volume of a cylinder = πr²h
where
r = radiush = heightTherefore,
volume of the cylindrical pipe = πr²h
where
r = 2 fth = 19 ftvolume of the cylindrical pipe = π × 2² × 19
volume of the cylindrical pipe = π × 4 × 19
volume of the cylindrical pipe = 76π ft³
Hence, let's approximate the volume of the cylindrical pipe using π in an ALEKS calculator.
Therefore,
volume of the cylindrical pipe = 76 × π = 238.761041673 = 238.76 ft³
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Please help!!! I am so confused and this is due tomorrow!!
The simplified expressions for (A), (B) and (C) are:
(A) [tex]f(x+h) = 4x + 4h - 6[/tex]
(B) [tex]f(x+h) * f(x) = 16x^2 + 4xh - 24x + 4h^2 - 24h + 36[/tex]
(C) [tex]f(x+h) - f(x) / h = 4[/tex]
How to simplify the equation?To simplify we use the given method.
A)
[tex]f(x+h) = 4(x+h) - 6 = 4x + 4h - 6[/tex]
B) [tex]f(x+h) * f(x) = (4x + 4h - 6) * (4x - 6) = 16x^2 + 4xh - 24x + 4h^2 - 24h + 36[/tex]
C)
[tex]f(x+h) - f(x) / h = (4x + 4h - 6) - (4x - 6) / h = 4h / h = 4[/tex]
So the simplified expressions for (A), (B) and (C) are:
(A) [tex]f(x+h) = 4x + 4h - 6[/tex]
(B) [tex]f(x+h) * f(x) = 16x^2 + 4xh - 24x + 4h^2 - 24h + 36[/tex]
(C) [tex]f(x+h) - f(x) / h = 4[/tex]
Please note that in (C) the difference of the functions is divided by h, not multiplied.
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Given that 1 inch = 2.54 cm, how many centimeters are there in 7 feet? Answers may be written using decimal form and should be rounded to the nearest hundredth when necessary. (12 inches = 1 foot)
Answer: 30.48
Step-by-step explanation:
2.54x12=30.48
The number of students, in a class of 35 , who improve their score from the first midterm to the second midterm
Note that the number of students, in a dass of 35, who improve their score from the first midterm to the second midterm is a discrete variable.
What is a discrete variable?A discrete variable is one that can only have particular, unique values and cannot have any other values in between. The number of students who increase their score is a whole number that can only take on specific values (e.g., 0, 1, 2, etc.), indicating that it is a discrete variable.
A quantitative variable in mathematics and statistics can be continuous or discrete depending on whether it is normally obtained by measuring or counting. The variable is continuous in that interval if it can take on two specific real values while simultaneously taking on all real values between them.
Thus, it is correct to state that the number of students, in a dass of 35, who improve their score from the first midterm to the second midterm is a discrete variable.
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Full Question:
Is the following variable best thought of as discrete or continuous?
The number of students, in a class of 35 , who improve their score from the first midterm to the second midterm
The registration fee for a used car is 0.8% of the sale price of $5,900. How much is the fee? (Simplify your answer.)
y = 4/5x + 1 A. slope: 4/5; y - intercept: -1 B. slope: 4/5; y - intercept: 1 C. slope: 5/4; y - intercept: 1 D. slope: 5/4; y - intercept: -1
Answer:
B
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{4}{5}[/tex] x + 1 ← is in slope- intercept form
with slope m = [tex]\frac{4}{5}[/tex] and y- intercept c = 1
You randomly select a letter from the letters A, B, C, D, E and flip a coin. The table represents the sample space, where H represents the coin landing heads up and T represents landing tails up. What is the probability of selecting the letter “C” or the coin landing tails up?
The probability of selecting the letter C or the coin landing tails up is given by the following option:
3/5.
How to obtain a probability?A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
From the table representing the sample space, the number of total outcomes is given as follows:
10.
The desired outcomes are given as follows:
5 outcomes in which the coin lands tails up.A sixth outcome in which the coin lands heads up, however with the letter c.(as the or statement means that at least one of the conditions have to be satisfied, that is, one is enough).
Hence the probability is obtained as follows:
p = 6/10
p = 3/5. (dividing both the numerator and the denominator by 2).
Meaning that the last option is the correct option.
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What type of graph or graphs would you plan to make in a study of each of the following issues?
(a) What makes of cars do students drive? (Select all that apply.)
bar graph
pie chart
histogram
stemplot
boxplot
timeplot
normal quantile plot
none of the above
(B) How old are their cars? (Select all that apply.)
bar graph
pie chart
histogram
stemplot
boxplot
timeplot
normal quantile plot
none of the above
(c) How many hours per week do students study? (Select all that apply.)
bar graph
pie chart
histogram
stemplot
boxplot
timeplot
normal quantile plo
tnone of the above
(d) How does the number of study hours change during a semester? (Select all that apply.)
bar graph
pie chart
histogram
stemplot
boxplot
timeplot
normal quantile plot
none of the above
(e) Which radio stations are most popular with students? (Select all that apply.)
bar graph
pie chart
histogram
stemplot
boxplot
timeplot
normal quantile plot
none of the above
(f) When many students measure the concentration of the same solution for a chemistry course laboratory assignment, do their measurements follow a normal distribution? (Select all that apply.)
bar graph
pie chart
histogram
stemplot
boxplot
timeplot
normal quantile plot
none of the above
The concept given is Graphs. A graph is a chart showing the relationship between magnitudes of variables, usually two variables, each measured along a pair of orthogonal axes.
Charts and tables are powerful visual tools because they present information quickly and easily. that graphics are commonly used in print and electronic media.
Sometimes data is easier to understand in a chart than in a table because a chart can show a trend or comparison.
A) bar graph and pie chart.
B) histogram, stem plot, and box plot.
C) histogram, stem plot, and box plot.
D) time plot.
E) bar graph and pie chart.
F) normal quantile plot.
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Toby draws an array that has 8 columns with 3 counters in each row. Bai draws an array that has 3 columns with 8 counters. How many counters are there in all
Answer:48 counters
Step-by-step explanation:8x3=2, 3x8=24, 24+24+48
A shopkeeper bought 30 pairs of jeans and 10 T-shirts for $2170. Each of jeans cost twice as much as each T-shirt. If he had sold them more than 20% than the price he paid for them, what would the selling price of a T-shirt be?
Answer: The selling price of a T-shirt would be $107.
Step-by-step explanation: The amount paid by the shopkeeper for the Tshirts would be $2170 ÷ 10 = $217
Since the jeans cost twice as much as the T-shirts, we can multiply the cost of the T-shirts by 2 to find the cost of a pair of jeans: $217 x 2 = $434.
We know that the shopkeeper sold the clothes for more than 20% more than he paid for, i.ee, 100 - 20 = 80.
To find the selling price of a T-shirt, we'll divide the cost of the T-shirts by the markup percentage as a decimal: $217 / (80/100) = $107.
Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x) = –3 2(x2 + 6x) = 3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x + 9) = –3 + 9
(2x + 3)(x - 1) = 0
x = (-b ± √(b^2 - 4ac))/ 2a, where a = 2, b = 12, and c = -3.
2x^2 + 12x = 3
(6/2)^2 = 9
2x^2 + 12x + 9 - 9 = 3 - 9
factor out the 2x^2 + 12x + 9 = 0
Given a standard deviation of sigma equals 15 and a sample size of n equals 16, calculate the standard deviation of the sampling distribution.
3.750
1.067
0.938
4.131
The standard deviation of the sampling distribution is; Option A: 3.750
How to calculate the sample standard deviation?Standard deviation is defined as a measure of how spread out numbers usually are. It is further said to be the square root of the Variance, and then the variance is the average of the squared differences from the Mean.
Now, we are given;
Population standard deviation; σ = 15
Sample size; n = 16
Formula for sample standard deviation in this regards is;
s = σ/√n
Plugging in the relevant values gives;
s = 15/√16
s = 15/4
s = 3.750
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Write the coordinates of the vertices after a reflection over the x-axis.
Answer:
J: -5,10
K: -5,5
L: -2,1
M: -2,6
Hope I helped<3