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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a television program director has 14 shows available for monday night but can choose only 5 shows. how many different possible combinations are there?
There are 240240 possible permutations of choosing 5 shows from 14 available shows. It can be obtained by applying the formula of permutation.
What is permutation?
In mathematics, it is the number of ways in which given number of items can be arranged in different orders.
Here, we need to select 5 iteams from the given 14 iteams.
[tex]P(14,5)=\frac{14!}{(14-5)!}\\=\frac{14!}{(9!)}\\=\frac{(14)(13)(12)(11)(10)(9!)}{(9!)}\\=(14)(13)(12)(11)(10)\\=240240[/tex]
Hence, there are 240240 possible permutations of choosing 5 shows from 14 available shows.
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Find the area of the figure. Use 3.14 for pi.
what are the appropriate measures of central location for interval data? mean and median median and mode mean, median, and mode what are the appropriate measures of variability for interval data? range, interquartile range, variance, standard deviation, and coefficient of variation variance coefficient of variation what are the appropriate measures of relative standing for interval data? interquartile range percentiles and quartiles none
The appropriate measures of central location for interval data are Mode, median, and average
The measure of a data set's most valuable position is its core location. Basically, they are mean, median, and mode.
Mean: The mean is the data set's average value. It is the total number of data divided by the sum of the data set.
The data point in the middle of the data collection is known as the median.
It can be obtained by halving the data set, which will show where the median is located.
Simply put, mode refers to the data that occurs most frequently.
Each of these provides positional information on the data, as can be seen from the definition.
The one value that other values in the data center around is given by the mean.
Therefore, the correct options are Mode, median, and average
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-6 = -2/9w solve for w and simplify your answer as much as possible
Answer:
w = 27
Step-by-step explanation:
Solve for w: -6 = -2/9w
-6 = -2/9w
divide both sides by -2/9:
-6/(-2/9) = -2/9w/(-2/9)
27 = w
Do the interior angles of a quadrilteral always add up to the same thing? Explain why you think so.
A scientist was in a submarine below sea level, studying ocean life. Over the next ten minutes, she ascended 61.9 feet. How many feet had she been below sea level, if she was 21.6 feet below sea level after she ascended?
The scientist was 83.5 feet below sea level while studying ocean life.
Given that:-
Distance the scientist ascended after studying the ocean life = 61.9 feet
Distance below sea level the scientist is after ascending = 21.6 feet
We have to find the distance by which the scientist was below sea level while studying the ocean life.
We know that,
Distance by which the scientist was below sea level while studying the ocean life = Distance the scientist ascended after studying the ocean life + Distance below sea level the scientist is after ascending
Hence, we can write,
Distance by which the scientist was below sea level while studying the ocean life = 61.9 + 21.6 = 83.5 feet.
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Ryan Pick 6 1/2 cups of berries from his garden he use 3 3/8 cups of to make fruit salad if he needs 3 cups of berries to make a pie does Ryan have enough very stuff to also make a pie?
We will simply subtract 3 3/8 from 6 1/2
That is;
6 1/2 - 3 3/8
= 3 4-3/8
=3 1/8
The amount of berry left is more than 3 cups, hence Ryan have enough very stuff to also make a pie
Write an equation in slope-intercept form of the line that passes through the given points.
The equation of the line is y = -2.5x - 1
How to determine the line equation?The table represents the given parameter
On the table, we have the following points
Point, (x, y) = (0, -1) and (2, -6)
So, we start by calculating the slope of the line using the following slope equation
Slope = (y₂ - y₁)/(x₂ - x₁)
Where x and y are defined above
So, we have
Slope = (-6 + 1)/(2 - 0)
Evaluate
Slope = -2.5
The equation of the line is then calculated as
y = m(x - x₁) +y₁
Where
Slope, m = -2.5
(x₁, y₁) = (0, -1)
So, we have
y = -2.5(x + 0) - 1
Open the brackets and evaluate
y = -2.5x - 1
Hence, the line has an equation of y = -2.5x - 1
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Lexi and Raymond are hosting events that are catered by the same company. Lexi plans to have 63 adults and 59 children attend, so the total projected cost of her meals is $2,582. Raymond has 63 adults and 93 children on her guest list, so he will pay the caterer $3,126. How much does the caterer charge for each meal?
Every adult's meal costs $
, and every child's meal costs $
.
The cost for children meal is $16 and the.cost for adult meal is $26.
How to calculate the value?Let cost of adult meal = a
Let cost of child meal = c
Lexi plans to have 63 adults and 59 children attend, so the total projected cost of her meals is $2,582.This will be:
63a + 59c = 2582 ...... i
Raymond has 63 adults and 93 children on her guest list, so he will pay the caterer $3,126. This will be;
63a + 93c = 3126 ...... ii
Collect both equations
63a + 59c = 2582 ...... i
63a + 93c = 3126 ...... ii
Subtract i from ii
34c = 544
Divide
c = 544 / 34
c = 16
The cost of children meal is $16.
From equation i, 63a + 59c = 2582
63a + 59(16) = 2582
63a + 944 = 2582
Collect like terms
63a = 2582 - 944
63a = 1638
a = 1638/63
a = 26
Adult meals is $26.
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8. Find the area of the kite.
Answer:
A=16, the formula to find the area of a kite is A=pq/2
Step-by-step explanation:
A=pq/2 = 4×8/2=16
Write the sum of 7√28x6 + 4√7x6 in simplest form, if x # 0
The sum equivalent to 7√28x⁶+4√7x⁶ is :
18√7x⁶ .
Solution:Remove parentheses and combine like terms to simplify each side of the equation.To isolate the variable term on one side of the equation, use addition or subtraction.To find the variable, use multiplication or division.Given ,7√28x⁶+4√7x⁶,
To find sum in simplest form ;
7√28x⁶+4√7x⁶
By splitting to factors,
= 7√(7*4)x⁶+4√7x⁶
= 7*2√7x⁶+4√7x⁶
= 14√7x⁶+4√7x⁶
By factoring out like terms,
= 2√7x⁶(7+2)
= 2√7x⁶(9)
= 18√7x⁶
Therefore sum is = 18√7x⁶.
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Karl drove 40 miles in 50 minutes. Teresa drove 35 miles in 42 minutes. Who had a higher average speed?
The person that has the higher average speed is Teresa.
How to calculate average speed?The average speed is the total distance travelled by the object in a particular time interval.
Average speed measures the average rate of speed over the extent of a trip.
Therefore,
average speed = distance / time
Hence, Karl drove 40 miles in 50 minutes.
Therefore,
average speed of Karl = 40 / 50
average speed of Karl = 4 / 5 miles per minute
Teresa drove 35 miles in 42 minutes.
Therefore,
average speed of Teresa = 35 / 42
average speed of Teresa = 5 / 6 miles per minutes
Therefore, Teresa had the higher average speed.
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according to multiple studies, including those by the american association of university women and the pew research center, on average, women are paid approximately which percent of what men are paid? select one: a. 80 b. 100 c. 90 d. 70
Women are paid approximately 80 percent of what men are paid.
Multiple studies have been carried out to discuss the income inequality prevailing in United States. Pay inequity has been found as a corollary of the income inequality.
The women and men has different pay levels for the same work at certain work places. Income inequality is considered as an injustice and to put forward this issue may organizations are trying.
Hence according to multiple studies, including those by the American association of university women and the pew research center, on average, women are paid approximately 80 percent of what men are paid.
We can see the appreciable difference in the pay levels of women and men prevailing.
As a result several laws has been passed recently to have a solution for this injustice.
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assuming that the population size is 1,000 people, the prevalence of smoking in epiland is 60% and the percentage of people drinking water with a high concentration of heavy metals is 30%, calculate the total number of cases of cancer x that could be prevented if each one of the exposures were eliminated. what would be your suggestion to the public health agencies if they asked you which one of the exposures would have a greater impact on reducing the prevalence of the disease if it was eliminated?
1. The total number of cases of cancer x that could be prevented if each one of the exposures were eliminated is 900.
2. The suggestion to the public health agencies if they requested the one exposure that would have a greater impact on reducing the prevalence of cancer x if eliminated is smoking.
What is the prevalence rate?The prevalence rate refers to the proportion of the population who have a particular disease or attribute or can be exposed to risks at a specified time or over a specified period.
The assumed population size in Epiland = 1,000
Prevalence of smoking in Epiland = 60%
The number of Epiland smokers = 600 persons (1,000 x 60%)
Percentage of people drinking water with a high concentration of heavy metals = 30%
The number of people drinking the water = 300 (1,000 x 30%)
The total number of people exposed to cancer x = 900 (600 + 300).
Thus, 90% of the population in Epiland is exposed to cancer x based on the prevalence rate of smoking and the high concentration of heavy metals in their drinking water.
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27. A table and five chairs cost $3500. The cost of three chairs is $1050. What is the cost of a table if all the chairs cost the same price?
8. Find the polynomial function of degree 3 for the given conditions I.f(1) = 32 and x-2, x-3,x+1 are factors of the polynomial II.f(3) = -24 and 5,2,4 are zeros of the polynomial
Part I
In factored form, [tex]f(x)=a(x-2)(x-3)(x+1)[/tex]. Substituting x=1,
[tex]f(1)=32=a(1-2)(1-3)(1+1)\\\\\implies 32=4a\\\\a=8\\\\\therefore f(x)=8(x-2)(x-3)(x+1)[/tex]
Part II
In factored form, [tex]f(x)=a(x-5)(x-2)(x-4)[/tex]. Substituting x=3,
[tex]f(3)=-24=a(3-5)(3-2)(3-4)\\\\\implies 24=2a\\\\a=12\\\\\therefore f(x)=12(x-5)(x-2)(x-4)[/tex]
overbooking flights is a common practice of most airlines. a particular airline, believing that 4% of passengers fail to show for flights, overbooks (sells more tickets than there are seats). suppose that for a particular flight involving a jumbo-jet with 267 seats, the airline sells 278 tickets. question 1. what is the expected number of ticket holders that will fail to show for the flight? (use 2 decimal place in your answer.) question 2. what is the probability that the airline will not have enough seats for all the ticket holders who show for the flight? (use 3 decimal places.)
1. 3.2673 is the expected number of ticket holders that will fail to show for the flight.
2. 0.425 is the probability that the airline will not have enough seats for all the ticket holders who show for the flight.
P(airline will not have enough seats for all the ticket holders who show for the flight) = P(more than 267 people show up for the flight)
p = P(will show for flight) = 1 - 0.04 = 0.96
n = 278
µ = n * p = 278 * 0.96 = 266.88
σ = [tex]\sqrt{ n*p* (1 - p)} = \sqrt{278 * 0.96 * 0.04} = 3.2673[/tex]
P(X > 267) = P(X > 267.5)
p(x- µ) / σ > 267.5- µ /σ
= P(Z> 267.5 – 266.88/ 3.2673 )
= P(Z > 0.19)
= 0.425.
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. To 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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an engineer is going to redesign an ejection seat for an airplane. the seat was designed for pilots weighing between 140 lbs. and 190lb. the new population of pilots has normally distributed weights with a mean of 158 lbs. and a standard deviation of 27.2 lb. find the probability that a pilot weight is between 140 lbs. and 190 lbs. the probability that the pilot weighs between 140 and 190 pounds is
The probability that the pilot weighs between 140 and 190 pounds is 0.6262.
When provided,
µ = 158
σ = 27.2
We must determine P(140 x 190).
P(140< x < 190) = P(x< 190) - P(x<140)
Locate P(x 190).
Z = (x - µ)/σ
Z = (190 - 158)/27.2
Z = 1.176471
P(Z<1.176471) = P(x<190) = 0.880297
[This probability can be determined using a z-table, Excel, Ti-83/84 calculator, software, etc. Z-table is less accurate than other methods in terms of value.]
Find P(x>140) now.
Z = (x - µ)/σ
Z = (140 - 158)/27.2
Z = -0.66176
P(Z<-0.66176) = P(x<140 ) = 0.254061
P(140< x < 190) = P(x< 190) - P(x<140)
P(140< x < 190) = 0.880297 - 0.254061
P(140< x < 190) = 0.626236
The necessary probability is 0.6262.
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Answer:
Step-by-step explanation:
0.626 is the probability that the pilot weighs between 140 and 190 pounds.
Mean (µ ) = 158
S.D(σ ) = 27.2
P(140 x 190)=?
P(140< x < 190) = P(x< 190) - P(x<140)
Find P(x 190).
Probability determined using Z-table.
Z = (x - µ)/σ
= (190 - 158)/27.2=1.176471
P(Z<1.176471) = P(x<190) = 0.88
Find P(x>140)
Z = (140 - 158)/27.2= -0.66176
P(Z<-0.66176) = P(x<140 ) = 0.254
P(140< x < 190) = 0.88 - 0.254
= 0.626
Therefore probability is 0.626.
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A person has lost a card game and is counting the points left in his hand. He announces that he has five fours and five sevens. Write this statement as a number expression.
The statement as number expression is given by the total number of points are 55.
What is Mathematical expression?
An expression is a finite combination of symbol and numbers depending on the context
We are given that A person has lost a card game and he is counting the points left in his hand.
His cards were five fours and five sevens
And we have to write this statement as number expression
Now there are five fours that is [tex]5*4=20 points[/tex]
And five sevens that is [tex]5*7=35 points[/tex]
Hence the total number of points are 20+35=55 points.
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Dwayne puts $200.00 into an account to use for school expenses. The account earns 9% interest, compounded quarterly. How much will be in the account after 4 years? nt 1 Use the formula A = P 1 + where A is the balance (final amount), P is the principal (starting n amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years. Round your answer to the nearest cent.
Solution
For this case we can use the following formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where:
P= 200
r= 0.09
n = 4
t= 4
And solving we got:
[tex]A=200(1+\frac{0.09}{4})^{4\cdot4}=285.52[/tex]A car, initially traveling east with a speed of 15 meters per second , is accelerated uniformly at 4 meters per second 2 east for 10 seconds along a straight line. what is the total distance the car travels during this 10 second interval?
Answer:
350m
Step-by-step explanation:
Vi = 15 m/s
A = 4 m/s^2
delta t = 10s
delta x = ?
delta x = (Vi)(delta t) + 1/2(A)(delta t)^2
delta x = (15m/s)(10s) + 1/2(4m/s^2)(10s)^2
delta x = 350 m
A z-score of z = −2.00 indicates a position in a distribution __________.
A- above the mean by a distance equal to 2 standard deviations
B- below the mean by 2 points
C- below the mean by a distance equal to 2 standard deviations
D- above the mean by 2 points
Answer:
C- below the mean by a distance equal to 2 standard deviations
Step-by-step explanation:
The Z-score, or standard score, is the number of standard deviations a given data point lies above or below the mean.The z-score is positive if the value lies above the mean, and negative if it lies below the mean.So, a z-score of z = −2.00 indicates a position in a distribution below the mean by a distance equal to 2 standard deviations.Christina is doing an obstacle course in gym class. First, she runs 100 feet and jumps over a hurdle. Then, she crawls through a 20-foot tunnel. Finally, she dribbles a soccer ball 60 feet to the finish line. How many yards long is the obstacle course?
Answer:
60 yards
Step-by-step explanation:
100 feet + 20 feet + 60 feet = 180 feet
180 feet = 60 yards (there are 3 feet in 1 yard)
Claire scheduled a taxi to pick her up at her house. The taxi service says it will take 15 minutes to get to her house based on normal traffic routines. However, due to either no traffic or more traffic than normal, the time could vary by as much as 4 minutes. Which inequality and solution show the range of possible minutes, t, it will take for the taxi to get to Claire's house?
The inequality would be 15 ≤ t ≤ 19 showing the range of possible minutes it will take for the taxi to get to Claire's house.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
The time could vary by as much as 4 minutes.
Let t be the range of possible minutes
The taxi service says it will take 15 minutes to get to her house based on normal traffic routines.
So the inequality as 15 ≤ t
The time could vary by as much as 4 minutes.
So the inequality as 15 ≤ t ≤ 15 + 4
⇒ 15 ≤ t ≤ 19
Therefore, the inequality would be 15 ≤ t ≤ 19 showing the range of possible minutes.
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Only 20 percent of the spectators left the contest discontented. If 6000 spectators left the contest contented,
how many left discontented?
There are 24000 spectators left the contest discontented.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
We have been given that Only 20 percent of the spectators left the contest discontented.
If 6000 spectators left the contest contented, then the contest left discontented are;
The spectators left the contest contented = 6000
20/ 100 x D = 6000
D = 6000 x 100/20
D = 30000
Now the contest left discontented are;
80 percent = 80/100 x 30000
= 24000
Hence, 24000 spectators left the contest discontented.
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If M is between G and T, MG = 2x + 1, MT = 3x + 3, and GT = 19, Then X = ___.MG = ___.MT = __.
We are given the following information
M is between G and T
MG = 2x + 1
MT = 3x + 3
GT = 19
Let us draw a sketch to better understand the problem
As you can see, the sum of MG and MT must be equal to the GT
Mathematically,
[tex]\begin{gathered} GT=MG+MT \\ 19=(2x+1)+(3x+3) \end{gathered}[/tex]Let us solve the above equation or x
[tex]\begin{gathered} 19=2x+1+3x+3 \\ 19=2x+3x+1+3 \\ 19=5x+4 \\ 19-4=5x \\ 15=5x \\ \frac{15}{5}=x \\ 3=x \\ x=3 \end{gathered}[/tex]So, the value of x is 3
[tex]\begin{gathered} MG=2x+1 \\ MG=2(3)+1 \\ MG=6+1 \\ MG=7 \end{gathered}[/tex][tex]\begin{gathered} MT=3x+3 \\ MT=3(3)+3 \\ MT=9+3 \\ MT=12 \end{gathered}[/tex]Therefore, the required values are
x = 3
MG = 7
MT = 12
brainly 100!!! Which of the following functions is graphed below?
The function that is represented on the graph is (a) y = x^2 + 4, x < 2 and y = x + 4, x ≥ 2
How to determine the graphed function?The graph represents the given parameter
From the graph, we have the following function types
Whole graph: Piecewise functionQuadratic function to the leftLinear function to the rightUsing the options as a guide, we have the equations to be
Quadratic function: y = x^2 + 4Linear function: y = x + 4Next, we calculate the domain
The quadratic function stops at x = 2 with an open circle
So, the domain is x < 2
The linear function starts at x = 2 with a closed circle
So, the domain is x ≥ 2
Hence, the graphed function is (a)
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What is the absolute value of the number plotted on the number line?.
A. -1.75
B. -1.25
C. 1.25
D. 1.75
Answer:
D. 1.75
Step-by-step explanation:
Absolute value cannot be negative, so that gets rid of A & B. The point is at -1.75 so it has to be D.
Kamal invest $6130 at a rate of r% per year compound interest the value of his investment at the end of 5 years is $6669
The rate which the investment is compounded annually is 1.7%
Compound InterestCompound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest.
Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
Compound interest is when you earn interest on both the money you've saved and the interest you earn.
The formula to calculate compound interest is given as
[tex]A = p(1 + \frac{r}{n})^n^t[/tex]
A = final amountp = principalr = rate n = number of times compoundedt = timesubstituting the values into the equation and solve for rate at which the investment is compounded
[tex]A = p(1 + \frac{r}{n})^n^t\\6669 = 6130(1+ \frac{r}{1})^1^*^5\\ r = 1.7[/tex]
The rate of the investment is 1.7%
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Which of the following service providers may use credit reports and/or credit scores to decide whether a person can buy a service and/or what price he or she will pay?Group of answer choicesLandlordMortgage lenderCell phone companyAll of the aboveCredit card issuer
Answer:
All of the above
Explanation:
All the given options make use of credit scores and/or credit reports to decide whether a person can buy a service and/or to decide what price he or she will pay. landlords may use credit scores to decide if they will require a security deposit and, if so, how much it should be. Also, other service providers like Mortgage lender, Cell phone company and Credit card issuer makes use of credit scores and/or credit reports in making certain decisions.