The value of 3log2 +log20 - log 1.6 is 2.
What is logarithm?
A logarithm is defined as the power to which a number must be raised to get some other values. It is the most convenient way to express large numbers. or
logarithm is the exponent or power to which the base must be raised to be raised to yield a given number.
Given,
3log2 +log20 - log 1.6
we can write it as
log[tex]2^{3}[/tex]+log20 - (log 1.6)
= log 8+ log20 - (log 1.6) (property of logarithm)
= log (8×20/1.6)
=log 100
=2
Hence, the value of 3log2 +log20 - log 1.6 = 2
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What is -2=-1+n/8? I’ve been stuck on it for a while
Answer: n= -8
Step-by-step explanation:
1. -2 = -1 + [tex]\frac{n}{8}[/tex]
2. -1 = [tex]\frac{n}{8}[/tex]
3. -8 = n
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Step-by-step explanation:
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What is the value of x?
Answer:
15
Step-by-step explanation:
Divide $180 in the ratio of 2 : 3 : 4
Answer:
40,60,80
Step-by-step explanation:
let 2x 3x and 4x
9x=180
x=20
2x=40
3x=60
4x= 80
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A number has 3, 4, and 8 as some of its factors. Which number could this be?
The number with 3,4 and 8 as its factors is 24
What is Lowest Common Multiples?The least common multiple(LCM) can be defined as the smallest multiple that two or more numbers have in common
The Lowest Common Multiples of 3 are:3, 6, 9, 12, 15, 18, 21, 24, 27 and 30
The Lowest Common Multiples of 4 are: 4, 8, 12, 26, 20, 24, 28, 32, ...
The Lowest Common Multiples of 8 are: 8, 16, 24, 32, 40, 48, ...
From the Lowest Common Multiples above, 24 is the only number that is common among the multiples of 3,4 and 8
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2x-4<6
what is the solution to this inequlity
Answer:
x < 5
Step-by-step explanation:
[tex]2x - 4 < 6[/tex]
[tex]2x < 10[/tex]
[tex]x < 5[/tex]
.........................................................
2. Evaluate the expression
4 (-1.2-4-4.75) +1+(-3)².
Answer:
-29.8
Step-by-step explanation:
4 (-1.2-4-4.75) +1+(-3)²
4 (-1.2-4-4.75) +1+(-3)²
4 (-9.95) +1+9
4 (-9.95) +1+9
-39.8 +1+9 = -29.8
Assume that each circle shown below represents one unit. Express the shaded amount as a single fraction and as a mixed number. One Fraction: Mixed Number: Submit Answer attempt
The shaded amount can be express as a single fraction and mixed fraction below
[tex]\begin{gathered} \text{each circle=1 unit} \\ 2\text{ circle= 2 unit} \\ \text{each circle was divided into 12 parts} \\ \text{the shaded parts in the 24 parts =14} \\ Therefore, \\ 1\frac{2}{12}=\frac{14}{12}=1\frac{1}{6} \end{gathered}[/tex]This data can best be modeled withwhich type of function?ху018,250118,730a. Linearb. QuadraticC. Exponential219,210319,690420,170
A linear function is a function in which we add multiple of a constant.
Given data:
We have
[tex]\begin{gathered} y=18,250+480(1)\text{ at x=0} \\ y=18,730=18,250+480(1)\text{ at x=1} \\ y=19,210=18,250+480(2)\text{ at x=2} \\ y=19,690=18,250+480(3)\text{ at x=3} \\ y=20,170=18,250+480(4)\text{ at x=4} \end{gathered}[/tex]Clearly, we have add multiples of 480 to 18,250.
So, the given function represents a linear function.
So, the correct option is (a).
31. a statistics class has 26 students. the instructor would like to select a random sample of 3 students to work together on a group project. a. how many different samples are possible? b. if 13 of the 26 students in class are freshmen, what is the probability that all 3 of the selected students are freshmen?
a. 2600 ways different samples are possible.
b. 0.11 is the probability that all 3 of the selected students are freshmen.
total student = 26
3 students are randomly selected on group project
a. the possible different sample are
[tex]26 C_{3}[/tex] = [tex]\frac{26}{3 (26-3)}[/tex]
= [tex]\frac{26}{3 (23)}[/tex]
= 2600 ways.
b. 13 students are freshmen
Pr ( 3 selected students is freshman)
[tex]\frac{13C_{3} }{26C_{3} }[/tex] = [tex]\frac{286}{2600}[/tex] = 0.11
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
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C)
to make the total value equal to 2. Re-write the statement 19 + 7 + 2 x 6 + 1 by including two pairs
of brackets
If you place brackets or parenthesis around the numbers 19+7 and 2*6+1. It would appear as follows: (19+7)/(2*6+1) = 26/13 = 2. It takes special parenthetical treatment to express the mathematical expression 19+7/26+1 to get a result of 2.
What is expression?An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being similar to phrases. A phrase in language may contain an action on its own, but it does not constitute a complete sentence.
Here,
y=19+7/2×6+1
becomes
y=(19+7)/(2×6+1)
y=26/(12+1)
y=26/13
y=2
If you enclose the numbers 19+7 and 2*6+1 in parenthesis or brackets. It would look like this: (19+7)/(2*6+1) = 26/13 = 2. The mathematical expression 19+7/26+1 must be expressed with special parenthetical treatment to yield the number 2.
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The set of ordered pairs shown below is a relation that is
a function of x.
{(-5, 1), (-4, 1), (−3, 1), (−2, 1)}
Which ordered pairs could be included in the set so that
the relation remains a function of x?
O (-3,0), (-1, 1)
O (-6, 1), (-5, 1)
O (-6, 1), (-1, 1)
O (-2, 2), (-1, 1)
The ordered pairs that could be included in the set so that the relation remains a function of x is (-6, 1), (-1, 1).
What is defined as the relation of function?A function is a relation that states that there must be only one output for each input (or) we can say that a function is a special type of relation (a set of ordered pairs) that follows a rule, i.e., every X-value should be related with only one y-value.The Cartesian product is a subset of it. Alternatively, a slew of points (ordered pairs). In other words, the relationship between the two sets is described as a collection of a ordered pair, where the ordered pair is formed by an object from each set.For the given relation that is a function of x.
{(-5, 1), (-4, 1), (−3, 1), (−2, 1)}
As, from the definition of the function, the domain of the function will not repeat in the set.
Thus, (-6, 1), (-1, 1) is the ordered pairs that could be included in the set so that the relation remains a function of x.
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Alysa buys 23 boxes of toothpicks. There are 255 toothpicks in each box. Which equation and solution show the number toothpicks, t, in all the boxes?
Answer:
255 ^t because the amount if toothpicks depend on the number of boxes she/he gets.
do blood-building drugs help brain development in babies born prematurely? researchers randomly assigned 53 babies, born more than a month premature and weighing less than 3 pounds, to one of three groups. babies either received injections of erythropoietin (epo) three times a week, darbepoetin once a week for several weeks, or no treatment. results? babies who got the medicines scored much better by age 4 on measures of intelligence, language, and memory than the babies who received no treatment.how many different treatments were there and what principle of experimental design does that address?
There were three different treatments: erythropoietin, darbepoetin, and no treatment. This selection exemplifies the principle of randomization principle.
What is a treatment?In experiments, the word treatment refers to the use of a specific medicine, therapy, or condition that is controlled by the research to test the effect of the treatment on subjects. For example, if the researcher wants to find out the ideal amount of water for a plant to grow, the treatment would be the amount of water.
In the case presented, there are three treatments:
Erythropoietin (epo) three times a week.Darbepoetin once a week for several weeks.No treatment.What principle of experimental design does that address?Randomization is the principle applied because the subjects are selected randomly for each of the groups and this reduces bias.
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note: this is a multi-part question. once an answer is submitted, you will be unable to return to this part. 7 women and 7 men are on the faculty in the mathematics department at a school. how many ways are there to select a committee of five members of the department if at least one woman must be on the committee?
No. of ways of selecting the 5 member committee by combination= 1981
What are the number of ways of selecting the 5 member committee ?
No. of women faculty in the mathematics department = 7
No. of men faculty in the mathematics department = 7
Total number of faculty members = 14
Condition - at least one woman must be on the committee
No. of ways of selection = C (14, 5) - C (7, 5)
We know that combination C(n , r) = [tex]\frac{n!}{(n-r)!r!}[/tex]
Consider the total combination C (14, 5),
[tex]C (14, 5)=\frac{14!}{9!5!} \\\\=\frac{14 *13* 12 *11 *10 *9!}{9!* 5!} \\\\=\frac{14 *13* 12 *11 *10}{120} \\\\= \frac{240240}{120} \\\\= 2002[/tex]
Consider the combination of men C (7, 5) ,
[tex]C (7, 5)=\frac{7!}{2!5!} \\\\=\frac{7*6*5!}{2!* 5!} \\\\=\frac{7*6}{2} \\\\= 7*3\\\\=21[/tex]
No. of ways of selection = C (14, 5) - C (7, 5)
= 2002 - 21
=1981
No. of ways of selecting the 5 member committee of the department with least one woman by combination= 1981
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x + m = p - n + yx Solve for x
Answer:
[tex]x=\frac{-m-n+p}{-y+1}[/tex]
Step-by-step explanation:
Jeremiah keeps a record of how many pages he reads each day. He read 40% fewer pages today than yesterday. If he read 90 pages today, how many pages did he read yesterday?
Answer: 126
Step-by-step explanation:: 90 ÷ 10 = 9 (10%) 9 × 4 = 36 (40%) 90 + 36 = 126
a 13-ft ladder rests against a vertical wall. if the bottom of the ladder slides away at 1 ft/s, at what rate is the top of the ladder sliding down the wall when the bottom of the ladder is 5 ft from the wall? g
The given situation can be solved using the differential equation and the top of the ladder slides downward at 0.417 ft/s.
Let:
x be the distance from the bottom of the ladder to the base of the wall
y be the distance from the top of the ladder to the bottom of the wall
When the ladder is still, apply the Pythagorean Theorem,
x² + y² = 13²
5² + y² = 13²
y² = 169 - 25 = 144
y = 12 ft
When the ladder slides, apply the differential equation:
x² + y² = 13²
2x . dx/dt + 2y . dy/dt = 0
Substitute x = 5, dx/dt = 1, y = 12
2 . 5 . 1 + 2 . 12 . dy/dt = 0
24 dy/dt = -10
dy/dt = -5/12 = - 0.417 ft/s
The minus sign indicates that the ladder is sliding downward.
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Consider the line y = = 8 x-4. Find the equation of the line that is parallel to this line and passes through the point (7, -2). Find the equation of the line that is perpendicular to this line and passes through the point (7, -2).
Answer: y=8x-58
Step-by-step explanation:
1. find the slope
Since the new line is parallel to the first one that means the slope of 8x will remain the same.
2. plug it into the point slope formula y-y1=m(x-x1)
which would look like
y-(-2)=8(x-7)
3. solve for y
y-(-2)=8(x-7)
y+2=8x-56
y=8x-58
A pottery studio has 11 pounds of clay. It takes 7/8 of clay to make a coffee mug find 11 divided by 7/8.Then interpret the question.
The number of coffee mugs that can be made is 12.
How to calculate the fraction?From the information, the pottery studio has 11 pounds of clay and it It takes 7/8 of clay to make a coffee mug.
The number of coffee mugs that can be made will be:
= Number of pounds of clay / Fraction used for each mug
= 11 / 7/8
= 11 × 8/7
= 88 / 7
= 12
There'll be 12 coffee mugs.
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Students in a fitness class each completed a one-mile
Which statements are true about a histogram with one-
walk or run. The list shows the time it took each person
minute increments representing the data? Select three
to complete the mile. Each time is rounded to the
options.
nearest half-minute.
5.5, 6, 7, 10, 7.5, 8, 9.5, 9, 8.5, 8, 7, 7.5, 6, 6.5, 5.5
O A histogram will show that the mean time iS
approximately equal to the median time of 7.5
minutes.
O The histogram will have a shape that is left-skewed.
O The histogram will show that the mean time is greater iS
than the median time of 7.4 minutes.
O The shape of the histogram can be approximated with
a normal curve.
0 The histogram will show that most of the data is
centered between 6 minutes and 9 minutes.
In linear equation, The histogram will show that most of the data is centered between 6 minutes and 9 minutes.
What in mathematics is a linear equation?
An x-y linear relationship, or two variables in which the value of one of them (often y) relies on the value of the other one, is what is known as a linear equation in two variables (usually x).The dependent variable in this scenario is y since it depends on the independent variable, x.5.5+6+7+10+7.5+8+9.5+9+8.5+8+7+7.5+6+6.5+5.5=111.5
Since there are 15 values,
their mean is 111.5/15=7.43 which is very close to the mean.
A)A histogram will show that the mean time is approximately equal to the median time of 7.5 minutes
D)The shape of the histogram can be approximated with a normal curve.
E)The histogram will show that most of the data is centered between 6 minutes and 9 minutes.
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What is the value of the the 9 in 194.6
The place value of 9 in 194.6 is tens or 90.
According to the question,
We have the following expression:
194.6
Now, we know that place value of any digit can be found easily. The place value of the digit at the right most corner (of a number without any decimal point) is unit, left to this digit we have place value of tens, then we have hundred, then thousand, ten thousand, etc.
Now, in this case, we have a decimal point. So, we will look at the last digit before the decimal point because it's place value is unit place. And the next left digit to this is tens.
Hence, the place value of 9 in 194.6 is tens.
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In the community of Greendale, a local restaurant donates 15% of the total sales to student-based clubs on certain funding nights.
A- Write an equation to represent the relationship between the dinner sales (d) and the amount (a) the organization will receive.
B- What is the constant of proportionality? Interpret the constant proportionally for the problem situation.
C- How much will the organization receive if dinner sales are $3600?
NEED BY 2:35 CENTRAL TIME!!! OFFERING 35 POINTS! MIDDLE SCHOOL MATH!
The equation that represents the relationship between dinner sales and the amount the organisation would receive is a = 0.15d
The constant of proportionality is 0.15.
Th amount the organisation will receive if dinner sales is $3600 is $540
What is the relationship between dinner sales and the amount the organisation would receive?The equation that would be used to represent the relationship between dinner sales and the amount the organisation would receive is a linear equation.
A linear equation is an equation that has one variable that is raised to the power of one. A linear equation can either be either be a positive function or a negative equation. When a linear equation is drawn on a graph, the graph is a straight line.
The form of the linear equation would be:
total amount received by the organisation = percentage x amount the restaurant receives.
a = 0.15d
0.15 is the constant of proportionality. It is the value that relates the amount the organisation would receive and the amount the restaurant would receive.
a = 0.15 x 3600
a = $540
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2. Write three decimals that
have a sum of 114.056.
Three decimal that sum of 114.056 is 52.2+34.15+28.5.
What is decimal?
decimal is a term that describes the base-10 number system, probably of the most commonly used the number system. The decimal number system of consists of ten single-digit numbers.
We will represent this as 1.5 pizzas in decimal form. In this case, the dot stands in for the decimal point, the number before the dot, in this case "1," represents one whole pizza, and the number after the decimal point, or the fractional part, represents the other half of the pizza. You may have seen decimal numbers similar to these while grocery shopping, on a scale, or even during a baseball game.
Sol- we have to add three decimal that have a sum of 114.056 no parts are given here.
Let's take
X+Y+Z = 114.056
We need to add any particular number here
Let's put 52+34+28
Still we need .056 extra
So we have to add points here
52.2+34.15+28.5
So these are 3 decimal point.
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Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth. tan 26° = ___
Answer:
0.49
Explanation:
Given the expression:
tan 26°
Evaluating using calculator
tan 26° = 0.4877
Hence the decimal rounded to the nearest hundredth is 0.49
Answer:
0.49 to nearest hundredth
Step-by-step explanation:
tan 26⁰ = 0.48773
Given segments AB and CD intersect at E.
A(1, 2), B(4, 5), C(2, 4), D(2, 1), E(2, 3)
What is the midpoint of cd?
Answer: (2, 5/2)
Step-by-step explanation:
CD=(2, 4),(2, 1)
((2+2)/2, (4+1)/2)=
(4/2, 5/2)=(2, 5/2)
Consider the density curve plotted below:1.63.24.86.480.050.10.150.20.25XPDF(X)Density CurveFind P(X<1.6) : Find P(X>4.8) :
Given:
There is a density curve given in the question
Required:
We need to find for
[tex]\begin{gathered} P(X<1.6) \\ P(X>4.8) \end{gathered}[/tex]Explanation:
Part a
We want to find P(X<1.6)
For this we just need to find the area below the curve until x=1.6, since we have a triangle we can do this:
[tex]P(X<1.6)=\frac{1}{2}*1.6*0.05=0.04[/tex]Part b
For this case we want to find this probability:
P(X>4.8)
and we can complement rule and we got
[tex]P(X>4.8)=1-P(X<4.8)=1-\frac{1}{2}*4.8*0.15=0.64[/tex]Final answer:
0.04
0.64
A baker has four containers. Three of the containers contain 3/4 pounds of sugar. The fourth container has 1/3 pound of sugar. How many total pounds of sugar does the baker have?
The baker has 13/3 pounds of sugar.
Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
We have been given two fractions.
The three containers have 3/4 pounds of sugar and fourth one have 1/2 pounds of sugar.
To find the total sugar, we have to add both the fractions
Total pounds of sugar = Sugar in three containers + sugar in fourth container
= 3/4 + 1/3
= (9 + 4)/3
= 13/3 pounds
So, the total sugar the baker has is 13/3 pounds.
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− 5/7 . (−3) can someone write this in the simplest form
Adam plans to choose a video game from a section of the store where everything is 75% off. He writes the expression d−0.75d to find the sale price of the game if the original price is d dollars.
Rena correctly writes another expression, 0.25d, that will also find the sale price of the game if the original price is d dollars.
Drag each description to explain each part of both expressions.
Both Adam and Rena re both correct regarding the expression.
What is an expression?An expression simply means an illustration that can be used to represent a scenario or situation.
From the information, Adam writes the expression d−0.75d to find the sale price of the game if the original price is d dollars.
Rena correctly writes another expression, 0.25d, that will also find the sale price of the game if the original price is d dollars.
In this case, they are both correct. This can be illustrated as:
= 1 - 0.75d
= 0.25d
Note that the information was answered based on the information given.
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