Answer:
15√3
Step-by-step explanation:
after grouping and adding them to get 15√9
then you apply Surds
1. If A = {a, b, c, d}, B={c, d, e, f}, C={x, y, z} find (A-B)
Answer
here
A={a,b,c,d}
B={c,d,e,f}
C={x,y,z}
A-B={e,f}
Graph the line y+3x=-3
Answer: y = -3x-3 (Choose values for x)
Step-by-step explanation:
1st change the equation to y = mx+b form
In order to change the equation to y = mx+b form subtract the 3x to both sides.
The equation now becomes y = -3x-3
2nd we can either choose values for x such has (-2,-1,0,1,2) and plug in those values into our equation y = -3x-3
For example, if we plug in x= -2 we get y= -3(-2)-3 which becomes y =3. We then plot the point (-2,3) because -2 is our x coordinate and 3 is our y coordinate.
Or we can plug the equation into a calculator that will graph the equation for you.
5=logb(32) what does b equal
Answer: 2
Step-by-step explanation:
When a^b = c, loga(c) = b
So b^5 = 32 and b is 2
Karin has 13 coins (2 quarters, 6 dimes, 4 nickels, and 1 penny) in a piggy bank. She turns the bank
upside down and shakes the bank until a coin falls out, puts it aside, and the shakes until another coin
falls out.
What is the probability that the first coin is a nickel and the second coin is a quarter?
Select one:
a. 2/30
b. 6/13
c. 2/13
d. 1/8
Using it's concept, the probability that the first coin is a nickel and the second coin is a quarter is:
2/39.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that:
For the first coin, 4 out of 13 will be nickels.For the second coin, considering a nickel was taken with the first coin, 2 out of 12 will be quarters.Hence the probability will be given as follows:
p = 4/13 x 2/12 = 4/13 x 1/6 = 2/13 x 1/3 = 2/39.
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Classify each number below as an integer or not.
Using it's concept, the integer numbers in the data-set are given as follows:
6/1, -14, 56/7.
The other numbers, -74.48 and 3/17, are not integers.
What are integer numbers?Integer numbers are numbers that have no decimal part. They can be represented by pure numbers, either negative or positive, or also fractions that result in an exact division.
In this problem, we have that:
The division of 6 by 1 has a exact result of 6, hence 6/1 is an integer.The division of 56 by 7 has a exact result of 8, hence 56/7 is an integer.-14 is a pure number with no decimal part, hence it is an integer.-74.48 has a decimal part, hence it is not an integer.3/17 is not an exact division, hence it is not an integer.More can be learned about integer numbers at https://brainly.com/question/17405059
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USH financial is a small bank that is examining its customers use of its website.the number of online transactions made per day during the past 9 days are as follows
The mean, median, and mode are;
median=77
Mean=73.33
Mode= 78, 67
This is further explained below.
What is median?Generally, The middle number in a list that is arranged from smallest to greatest is referred to as the median. On the list, the value that occurs most often is known as the mode. Therefore
median=77
Generally, In mathematics, particularly statistics, the term "mean" may refer to a number of different concepts. The purpose of each mean is to summarize a certain collection of data, often for the purpose of gaining a better understanding of the overall value of a specific data set.
A dataset's mean (also known as the arithmetic mean, which is distinct from the geometric mean) is calculated by dividing the sum of all of the values in the dataset by the total number of values in the dataset. It is the measure of central tendency that is used the most often, and it is sometimes referred to as the "average."
[tex]mean=\frac{\sum x}{n}\\\\Mean=\frac{78+67+98+50+67+78+67+77+78}{9}[/tex]
Mean=73.33
Mean=73.3 in one dp
What exactly is the mode in math?In conclusion, The mode is the number that appears the most often, or the number that stands out as having the most occurrences overall. The number 2 is the mode of the sequence 4, 2, 4, 3, 2, 2 because it appears three times, which is more than any other number in the sequence.
The mode of 78, 67, 98, 50, 67, 78, 67, 77, 78 is
Mode= 78, 67
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The GCF of 15 and 27 is _____.
Answer:
The answer is 3
Step-by-step explanation:
List all prime factors
15:1,3,5,
27:1,3,
Biggest one is 3
Answer:
the answer is 3
Step-by-step explanation:
cuz the prime factors of 27 is 1,3,and 27
while 15 is 1, 3 ,5 and 15
I hope this helps
120 high school seniors were asked,
"Are you going to the graduation
party?" Of those 120 students, 75 said yes. Estimate the population mean
that a senior will say they are going to the graduation party.
Using proportions, the estimate of the population percentage of seniors that will say they are going to the graduation party is of 62.5%.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
The estimate of a population proportion is the sample proportion. In this problem, the sample proportion is of 75 out of 120 students, hence:
p = 75/120 = 0.625 = 62.5%.
The estimate of the population percentage of seniors that will say they are going to the graduation party is of 62.5%.
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Please help! I am trying to do my homework but I am have trouble with these problems
The interpretation based on the confidence interval given is that the population mean will fall within the interval.
How to illustrate the information?Number of observations = 10
Sample mean = 2.60
Standard deviation = 1.07
The degree of freedom will be:
= n - 1
= 10 - 1 = 9
Confidence level = 95% = 0.95
Level of significance = 1 - 0.95 = 0.05
The value of the t critical from the t table will be 2.262.
The margin of error will be:
= 2.262 × 1.07/✓10
= 0.765
We get the 95% confidence interval for the population mean. This will be:
(2.60 - 0.765( <= U =(2.60 + 0.765)
1.83 <= 3.37
Therefore, the interpretation is that the population mean will fall within the interval.
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If Lonnie has 40 plants and half of his plants die...how many plants does that
equal?
A 20
B 15
C 25
Answer:
20
Step-by-step explanation:
We know that she initially had 40 plants. The half of 40 is 20. That is also the number of plants that died.
Answer: A. 20
Step-by-step explanation:
Given Information:
Original = 40 Plants
New = Half Died
Find the number of plants that died:
40 × (1 / 2) = 40 / 2 = 20 Plants
or
40 ÷ 2 = 20 Plants
Therefore, it equals to [tex]\boxed{20 \:Plants}[/tex]
Hope this help!! :)
Please let me know if you have any questions
graph f(x)=(1/4)^x step 4: Plot the points (1, 1/4) and (-1, 4)
The graph of the function, f(x) = (1/4)ˣ, can be seen in the attached graph, following the given steps.
In the question, we are given the function, f(x) = (1/4)ˣ.
Step 1, has asked us to find the initial value of the graph, f(0).
This can be calculated by substituting x = 0, in the given function, which gives us:
f(0) = (1/4)⁰ = 1.
Step 2, has asked us to plot the initial value of the function at (0, 1). This is plotted using the graphing tools.
Step 3, has asked us to evaluate f(1) and f(-1). By substituting x = 1, and x = -1, we get:
f(-1) = (1/4)⁻¹ = 4,
f(1) = (1/4)¹ = 1/4.
Step 4, has asked us to plot the points (1, 1/4), and (-1, 4). This is plotted using the graphing tools.
Step 5, has made us identify the asymptote y = 0.
Step 6, gives us the final curve for the function, f(x) = (1/4)ˣ.
The provided question is incomplete. The complete question is:
"Graph: f(x) = (1/4)ˣ
Step 1: Calculate the initial value of the function. f(0) =
Step 2: Plot the initial value of the function at (0, 1).
Step 3: Evaluate the function at two more points. f(1) = 1/4, f(-1) = 4
Step 4: Plot the points (1, 1/4) and (-1, 4)
Step 5: Identify the horizontal asymptote of the function. The asymptote is the line y = 0
Step 6: The smooth curve that includes these points and approaches to the asymptote shows the graph of the function"
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Tanya is a car saleswoman. Below are the number of cars that she sold in each of the last six months. 23, 21, 21, 20, 21, 20 Using this data, create a dot plot where each dot represents a month. 19, 20 ,21 Number of cars sold 22 ,23 pls
Answer: so there would be 1
23
3 21
2 20
Step-by-step explanation:
What are the x- and y- coordinates of point E, which partitions the directed line segment from J to K into a ratio of 1:4?
The x- and y- coordinates of point E, which partitions the directed line segment from J to K into a ratio of 1:4 is (17, 11)
Midpoint of coordinate pointsThe midpoint of a line is the point that bisects or divides the line into two equal parts
If the line JK is partitioned into the ratio 1:4 with the following coordinates
J(-15, -5) and K(25, 15)
Using the expression below;
M(x, y) =[mx1+nx2/m+n, my1+ny2/m+n]
Substitute the ratio and the coordinates
M(x, y) =[1(-15)+4(25)/4+1, 1(-5)+4(15)/1+4]
M(x, y) = [(85)/5, 55/5]
M(x, y) = (17, 11)
Hence the x- and y- coordinates of point E, which partitions the directed line segment from J to K into a ratio of 1:4 is ((17, 11)
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Perdue Company purchased equipment on October 1 for $36,100. The equipment was expected to have a useful life of three years, or 4,900 operating hours, and a residual value of $1,800. The equipment was used for 900 hours during Year 1, 1,700 hours in Year 2, 1,500 hours in Year 3, and 800 hours in Year 4.
Required: Round up all final values
Straight line Method
Under the straight-line depreciation method, the depreciation expenses for the years ended December 31, Year 1, Year 2, Year 3, and Year 4, for Perdue Company, are as follows:
Year Amount
Year 1 $2,858.33 ($11,4333.33 x 3/12)
Year 2 $11,433.33
Year 3 $11,433.33
Year 4 $8,575.01 ($11,433.34 - $2,858.33)
What is the straight-line depreciation method?The straight-line method is one of the depreciation methods in use by companies to allocate the cost of plants and equipment over their useful lives.
Under the straight-line method, the depreciable amount (cost less residual value) is divided by the estimated useful life.
Other depreciation methods include the unit-of-production, double-declining-balance, and the sum-of-the-years-digit methods.
Data and Calculations:Equipment cost = $36,100
Residual value = $1,800
Depreciable amount = $34,300 ($36,100 - $1,800)
Estimated useful life = 3 years
Annual depreciation = $11,433.33 ($34,300/3)
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Question Completion:Determine the amount of depreciation expense for the years ended December 31, Year 1, Year 2, Year 3, and Year 4, by the straight-line method.
Find a formula for the nth term in this
arithmetic sequence:
a₁ = 7, a2 = 4, a3 = 1, a4 = -2, ...
an
=
[?]n +
Answer:
[tex]a_{n} = -3n + 10[/tex]
Step-by-step explanation:
The arithmentic function formula is:
[tex]a_{n} = a_{1} + d(n-1)[/tex]
Let's plug in what we know. [tex]a_{1}[/tex] (the first term in our sequence) is 7. d (the common difference) is -3. This means we are subtracting 3 every time.
Plugging that in to the formula, we get
[tex]a_{n} = 7 -3(n-1)[/tex]
Now we distribute and combine like terms.
[tex]a_{n} = 7 - 3n +3[/tex]
[tex]a_{n} = 10 - 3n[/tex]
Change the order to fit the format and you get
[tex]a_{n} = -3n + 10[/tex]
What is the center and radius of the circle?
The population of a rabbit colony triples every 3 days. The population starts at 10 rabbits. Write an exponential function that will model the population of the colony after, t, days have passed.
Answer:
DO not working in you
Step-by-step explanation:
PLEASE help me in answering
Answer:
Step-by-step explanation:
The population at various days is as follows since population triples every 3 days
Day Population
0 10
3 30
6 90
9 270
.... ......
This can be modeled by the general equation
[tex]n_{t} = n_{0}(r)^{t/k}[/tex]
where
[tex]n_{t}[/tex] is the population after t days
[tex]n_{0}[/tex] is the population at start (10)
[tex]r[/tex] is the rate at which population changes ie 3
[tex]t[/tex] is the number days from start
[tex]k[/tex] is the number of days at which the population triples(here k =3 days)
We can check this by plugging in values for each of the variables
At day 0, population = 10(3)⁰ = 10. 1 = 10
Similarly populations for days 3, 6, 9 are:
[tex]\\\\10.3^{3/3} = 10. 3^1 = 10.3 = 30\\10.3^{6/3} = 10. 3^2 = 10.9 = 90\\\\10.3^{9/3} = 10. 3^3 = 10.27 = 270[/tex]
value of 10 in A/B
value of letter
The value of the expression (a - b)² from the given equations is; 16
How to solve simultaneous equations?
We are given the two equations as;
a + b = 10 -----(eq 1)
ab = 21 ------(eq 2)
From eq 1, square both sides;
(a + b)² = 10²
a² + 2ab + b² = 100
a² + b² = 100 - 2ab
We are given ab = 21. Thus;
a² + b² = 100 - 2(21)
a² + b² = 58
Now, we know that (a - b)² = a² - 2ab + b²
Thus;
(a - b)² = 58 - 2(21)
(a - b)² = 16
Complete question is;
If a + b = 10 and ab = 21, then the value of (a - b)² is?
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Database A contains 40 data items and is made up with an equal number of the values of 0 and 100 and has a mean of 50. Database B also has 40 entries made up equally of the values 49 and51 and also has a mean of 50. Which database will have the smaller value for its standard deviation?
Set A: 1 2 3 23 24 25
Set B: 9 10 11 14 16 18
If we compare the given values then we can find that the database B is more likely to have smaller standard deviation.
Given that the values in database A are 0 from 100 and has mean of 50 and Database B has entries from 49 to 51 and also has mean of 50.
We are required to find the database whose standard deviation is lower.
Standard deviation measures the variation of values. It is calculated after finding mean. The square of a standard deviation is known as variance.
Database A has values from 0 to 100 and has mean of 50. Because the values are somewhat very larger than 50 and in database B has values from 49 to 51,there are more chances that the standard deviation of database B will have smaller value than from standard deviation of database A.
Hence if we compare the given values then we can find that the database B is more likely to have smaller standard deviation.
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You need a 75 % alcohol solution. On hand, you have a 260 mL of a 30% alcohol mixture. You also have 95 % alcohol mixture . How much of the 95% mixture will you need to add to obtain the desired solution? You will need mL of the 95% solution
[tex]30 \: percent \: alcohol \: in \: 260 \: ml \\ alcohol = 0.3 \times 26 0= 78 \: ml[/tex]
[tex]c( \gamma ) = \frac{78 + 0.95\gamma }{260 + \gamma } \times 100[/tex]
[tex]c( \gamma ) = 75[/tex]
[tex] \frac{78 + 0.95\gamma }{260 + \gamma } = 0.75[/tex]
[tex]78 + 0.95\gamma = 0.75 \gamma + 195 \\ 0.2 \gamma = 117 \\ \gamma = 585[/tex]
[tex]we \: need \: 585 \: ml \: of \: 95% \: alcohol[/tex]
Answer:
You will need 585 mL of the 95% solution.
Step-by-step explanation:
What are the rational roots for the polynomial shown below?
x³ + 5x²-8r-20=0
[tex]x ^{3} + 5x {}^{2} - 8 r - 20 = 0 \\ x { }^{3} + 5x {}^{2} - 8r - 20(x {}^{3} + 5x {}^{2} ) = 0 - (x {}^{3} + 5x {}^{2} ) \\ - 8r - 20 = - (x {}^{3} + 5x {}^{2} ) \\ \\ - 8r - 20 + 20 = - (x {}^{3 } + 5x {}^{2} ) + 20 \\ \\ - 8r = x {}^{3} - 5x {}^{2} + 20 \\ \\ [/tex]
hope it is helpful
find the x-intercept of the graph of the equation y=(x+2)(x-1)
Answer:-2,0 & 1,0
Step-by-step explanation:
Substitute them in with zero product property
If $6,000 principal plus $132.90 of simple interest was withdrawn on August 14, 2011, from an investment earning 5.5% interest, on what day was the money invested?
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$132.90\\ P=\textit{original amount deposited}\dotfill & \$6000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ t=years \end{cases} \\\\\\ 132.90 = (6000)(0.055)(t)\implies \cfrac{132.90}{(6000)(0.055)}=t\implies \cfrac{443}{1100}=t \\\\\\ \stackrel{\textit{converting that to days}}{\cfrac{443}{1100}\cdot 365} ~~ \approx ~~ 147~days[/tex]
now, if we move back from August 14th by 147 days backwards, that'd put us on March 20th.
mary is making a batch of chocolate chip cookies the recipe calls for 9 cups of flour and 2 4/7 cups of sugar she isshort on flour cuts the recipe down to 7 cups if flour how much sugar should she add
Mary added [tex]$24 \frac{1}{2}[/tex] cups of sugar.
How to estimate how much sugar should Mary add?The ratio of flour to sugar exists at 9 cups: 2 4/7 cups
Utilizing equivalent ratios, given that 7 cups of sugar was utilized,
Let cups of flour needed = x such that our equation becomes
flour/sugar[tex]$ =\frac{9}{2\frac{4}{7} }=\frac{x}{7}[/tex]
[tex]$ \frac{9}{2\frac{4}{7} }=\frac{x}{7}[/tex]
Convert mixed numbers into improper fractions
[tex]$2 \frac{4}{7}= \frac{18}{7}[/tex]
simplifying the above equation, we get
[tex]$\frac{9}{\frac{18}{7} } = \frac{x}{7}[/tex]
= [tex]$24 \frac{1}{2}[/tex]
x = 24.5
The value of x = 24.5.
Therefore, [tex]$24 \frac{1}{2}[/tex] cups of sugar exist required.
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Use the following information collected in a town of fast food restaurants. 13 served hamburgers, 8 served roast beef sandwiches, 10 served pizza, 5 served hamburgers and roast beef sandwiches 3 served hamburgers and pizza, 2 served roast beef sandwiches and pizza, 1 served hamburgers, roast beef sandwiches and pizza, 5 served none of the three foods
a) Construct a Venn Diagram and put the correct numbers in the Venn diagram.
b) Find the Probabilities. P(pizza)= ___________
c) P (roast beef and pizza)=___________
d) P ( hamburgers, but not roast beef) =______________
e) P (only hamburgers) = ____________
Answer:
I don't know what are you saying bro
THE NICHOLS ARE BUYING A HOUSE SELLING FOR $245,000. THEY PAY A DOWN
PAYMENT OF $45,000 FROM THE SALE OF THEIR CURRENT HOUSE. TO OBTAIN A 15-
YEAR MORTGAGE AT 4.5% INTEREST, THEY MUST PAY 1.5 POINTS AT THE TIME OF
CLOSING. WHAT IS THE AMOUNT OF THE MORTGAGE, AND WHAT IS THE COST OF
THE 1.5 POINTS
The amount of the mortgage on this house is given as $300000, while the 1.5 points on the house is given as 3000 dollars
How to solve for the mortgage that is on this houseThe data from the questions says that the cost of the house = $245000
The down payment amount amount is 45000
Given that they already paid 45000 from the cost of the house, the mortgage would be 245000 - 45000
= $200000
The cost of 1.5 points is the same as the cost of 1.5% of the mortgage of this house.
This is calculated as 0.015 x 200000
= $3000
The conclusion is that the amount of the mortgage on this house is given as $300000, while the 1.5 points on the house is given as 3000 dollars
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If
m ≤ f(x) ≤ M
for
a ≤ x ≤ b,
where m is the absolute minimum and M is the absolute maximum of f on the interval [a, b], then
m(b − a) ≤
b
a
f(x) dx ≤ M(b − a).
Use this property to estimate the value of the integral.
⁄12 7 tan(4x) dx
It's easy to show that [tex]7\tan(4x)[/tex] is strictly increasing on [tex]x\in\left[0,\frac\pi8\right][/tex]. This means
[tex]M = \max \left\{7\tan(4x) \mid \dfrac\pi{16} \le x \le \dfrac\pi{12}\right\} = 7\tan(4x) \bigg|_{x=\pi/12} = 7\sqrt3[/tex]
and
[tex]m = \min \left\{7\tan(4x) \mid \dfrac\pi{16} \le x \le \dfrac\pi{12}\right\} = 7\tan(4x) \bigg|_{x=\pi/16} = 7[/tex]
Then the integral is bounded by
[tex]\displaystyle 7\left(\frac\pi{12} - \frac\pi{16}\right) \le \int_{\pi/16}^{\pi/12} 7\tan(4x) \, dx \le 7\sqrt3 \left(\frac\pi{12} - \frac\pi{16}\right)[/tex]
[tex]\implies \displaystyle \boxed{\frac{7\pi}{48}} \le \int_{\pi/16}^{\pi/12} 7\tan(4x) \, dx \le \boxed{\frac{7\sqrt3\,\pi}{48}}[/tex]
what is 23,995 rounded to the nearest ten
Answer: 24,000
Step-by-step explanation:
Decimals from greatest to least
.750
.475
-0.123
.675
.253
Answer:
0.75, 0.675, 0.475, 0.253, -0.123
Step-by-step explanation:
Positive Numbers will always be greater than negative numbers, so you know -0.123 comes at the end.
Example
0.ABC
The tenth's place (A in the number above) holds the most weight. 0The hundreth's place (B in the number above) holds the second most weight. The thousandth's place (C in the number above) holds the third most weight.
Comparing 0.75 and 0.675 is the same as comparing 75 and 67.5. When in doubt, you can multiply the decimals by 100 to determine their order of value.
A metallurgist has one alloy containing 26% copper and another containing 69% copper. How many pounds of each alloy must he use to make 53 pounds of a third alloy containing 50% copper?
The pounds of alloy that contains 26% copper that would be used is 23.42 pounds.
The pounds of alloy that contains 69% copper that would be used is 29.58 pounds.
What are the linear equations that represent the question0.26a + 0.69b = (53 x 0.5)
0.26a + 0.69b = 26.50 equation 1
a + b = 53 equation 2
Where:
a =pounds of alloy that contains 26% copperb = pounds of alloy that contains 69% copperHow many pounds of each alloy should be in the third alloy?Multiply equation 2 by 0.26
0.26a + 0.26b = 13.78 equation 3
Subtract equation 3 from equation 2
12.72 = 0.43b
b = 12.72 / 0.43
b = 29.58 pounds
a = 53 - 29.58 = 23.42 pounds
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