Answer:
a) 105
b) 110.25
c) Increase of 10.25%. It is not 100% because the second increase of 5% is over the first increased value, not over the initial value.
Step-by-step explanation:
Increase and multipliers:
Suppose we have a value of a, and want a increse of x%. The multiplier of a increase of x% is given by 1 + (x/100). So the increased value is (1 + (x/100))a.
(a) Increase 100 by 5%
The multiplier is 1 + (5/100) = 1 + 0.05 = 1.05
1.05*100 = 105
(b) Increase your result form (a) by 5%.
1.05*105 = 110.25
(C) What was the overall percent increase of the number 100? Why is it not 10%?
110.25/100 = 1.1025
1.1025 - 1 = 0.1025
Increase of 10.25%. It is not 100% because the second increase of 5% is over the first increased value, not over the initial value.
Decompose the fraction 11 /12 towingtwo ways
Given:-
[tex]\frac{11}{12}[/tex]To find:-
Decompose the fraction in two ways.
Way one,
[tex]\frac{11}{12}=\frac{5}{12}+\frac{6}{12}[/tex]Way two,
[tex]\frac{11}{12}=\frac{10}{24}+\frac{12}{24}[/tex]The area of Bryce is 71.5 sq units.what is the area of abcd?
Solution
Step 1:
Area of BXYC = 71.5 square units
Step 2:
The area of ABCD is twice the area of BXYC
Step 3:
[tex]\begin{gathered} \text{Area of ABCD = 2 }\times\text{ Area of BXYC} \\ Area\text{ of ABCD = 2 }\times\text{ 71.5} \\ Area\text{ of ABCD = 143 square units} \end{gathered}[/tex]I need to find the equation of a circle I will include picture
Given,
The center of the circle is (6, -3).
The coordinates of the point, circle is passing through (6,6).
The general equation of the circle is,
[tex](x-h)^2+(y-k)^2=r^2[/tex]Here, x, y are the coordinates of the point.
h and k are the center of the circle.
r is the radius of the circle.
Substituting the value of h, k , x and y in the equation of circle then,
[tex]\begin{gathered} (6-6)^2+(6-(-3))^2=r^2 \\ 0+9^2=r^2 \\ r=9 \end{gathered}[/tex]So, the radius of the circle is 9.
Substituting the value of h, k and r in the general equation of circle.
[tex]\begin{gathered} (x-6)^2+(y-(-3))^2=9^2 \\ x^2+36-12x+y^2+9+6y=81 \\ x^2+y^2-12x+6y-36=0 \end{gathered}[/tex]Hence, the equation of circle is x^2+y^2-12x+6y-36=0
|x|=-5 why is there no solution?
Absolute value is the distance a number is from zero.
Because distance cannot be negative, an absolute value can never be a negative.
Therefore,
|x| = -5 has no solutions
can you please solve this for me I'll make sure to give the best review
-9 is an integer
the location of -9 is with 41
6.3 is a repeating decimal
the location is with 5.86666...
-4/5 is a fraction
the location is with 11/12
a1. The amount of milk in a one-gallon milk container has a normal distribution with a meanof 1.07 gallons and a standard deviation of 0.12 gallons.Calculate and interpret the z-score for exactly one gallon of milk.
The z-score formula is given to be:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where
[tex]\begin{gathered} x=score \\ \mu=mean \\ \sigma=standard\text{ }deviation \end{gathered}[/tex]From the question given, the mean and standard deviations are provided as:
[tex]\begin{gathered} \mu=1.07 \\ \sigma=0.12 \end{gathered}[/tex]Therefore, the z-score of exactly 1 gallon is calculated to be:
[tex]\begin{gathered} x=1 \\ \therefore \\ z=\frac{1-1.07}{0.12}=\frac{-0.07}{0.12} \\ z=-0.583 \end{gathered}[/tex]Therefore, the z-score is -0.583.
This tells us that a container with exactly one gallon of milk lies 0.583 standard deviations below the mean.
David’s watch broke. He decides to get it fixed instead of replacing it. Since David is a loyal customer, he received a coupon in the mail for a discount. The total cost to repair the watch can be represented by 0.07r + (r – 20), where r represents the original cost of the repair. Explain what each part of the expression represents in the context of the problem.
→ r represents the original cost of the repair.
→ 0.07r represents the tax.
→ (r – 20) represents the discount
Given,
The total cost to repair the watch can be represented by 0.07r + (r – 20), where r represents the original cost of the repair.
Explain what each part of the expression represents in the context of the problem.
Now, According to the question:
Given the following algebraic expression:
0.07r + (r – 20)
In the context of fixing David’s broken watch, the variable r represents the original cost of the repair while 0.07r most likely represents the amount of money charged as tax. Lastly the expression (r – 20) represents the discount on fixing David’s broken watch.
What each part of the expression represents in the context of the problem include the following:
→ r represents the original cost of the repair.
→ 0.07r represents the tax.
→ (r – 20) represents the discount
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Jo started a business selling fishing supplies. He spent $5200 to obtain his initial supplies, and it costs him $350 per week for general expenses. He earns $750 per week in sales.
Create the linear function, in slope-intercept form, that represents the scenario.
The linear function is given by 5200+350x = 750x
What is linear function?
A linear function is a function which forms a straight line in a graph. It is generally a polynomial function whose degree is utmost 1 or 0.
Amount spent to obtain merchandise = $5,200
Cost of general expenses = $350
Earnings from sales per week = $750
Now,
Let 'x' be the number of weeks taken to make profit
thus,
Total cost involved = $5,200 + ( $350 × x )
Total profit from sales = $750 × x
Now, the number of weeks after that the cost and earning will be equal, will be given by
5200+350x = 750x
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Convert 255 to base 2
We can count the number of zeros and ones to see how many bits are used to represent 255 in binary i.e. 11111111. Therefore, we have used 8 bits to represent 255 in binary.
Convert 255 to base 2?
255 = 8 bits
255 in Binary: 255₁₀ = 11111111₂
Binary is a system used in mathematics and computer science where values and numbers are stated as 0 or 1.Binary is base-2, which means that there are just two digits or bits used.For computers, 1 denotes truth or "on," while 0 denotes falsehood or "off." Computers communicate and represent information using binary code.Everything you see on a computer, including letters, numbers, and pictures—basically everything—is made up of multiple 0s and 1s combinations. One of the four different kinds of number systems is the binary number system.When used in computer programs, binary numbers are solely represented by the digits 0 (zero) and 1. (one).Here, the base-2 numeral system is used to represent the binary numbers.One binary number is (101)2, for instance. The modern binary number system was first suggested and refined by Gottfried Leibniz in the 17th century in his article Explication de l'Arithmétique Binaire [1].The system was created by Leibniz about 1679, although it wasn't published until 1703.He had already used 0 and 1.To learn more about binary refer
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A company has 10 software engineers and 6 civil engineers. In how many ways can they be seated around a round table so that no two of the civil engineers will sit together? [ 9! × 10!/4!)]
The software engineers can be seated on a round table with no two civil engineers sitting together is 9!×10!/4!
Given, a company has 10 software engineers and 6 civil engineers.
we need to determine in how many ways can they be seated around a round table so that no two civil engineers will sit together.
10 software engineers can be arranged around a round table in :
=(10-1)!
= 9! ways .... eq(A)
Now, we must arrange the civil engineers so that no two can sit next to one another. In other words, we can place 6 civil engineers in any of the 10 *-designated roles listed below.
This can be done in ¹⁰P₆ ways ...(B)
From A and B,
required number of ways = 9!×¹⁰P₆
= 9! × 10!/4!
Hence the number of ways the engineers can be seated is 9! × 10!/4!.
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13. Use the appropriate percent growth todetermine how much money Lyra will have incach ofthe following situations:(a) How much money will Lyra have after 10years if she invests $5,000 at 4% interestcom-poundcl annually?(1) Suppose that Lyra is saving for retirement,and has saved up $20,000. If her retirementaccount earns 3% interest each year, howmuch will she save in 25 years?(o) How much mowy will yra have after 20years if she $5,000 33.5% interestcompoundedannully?(d) How much money will yr hawwur 10 yearsit she is $6,000 AL 15% interestcompounded quarterly?(E) how much money will lyra have after 10years if she invests $5,000 at 0.8% interestcompounded continuously?(F) compare your answer to (a) and (c). Whichone made more money?
Given:
(a) P = $5000
t = 10 years
r = 4%
(b) P = $20,000
t = 25 years
r = 3%
(c) P = $5000
t = 20 years
r = 3.5%
(d) P = $5000
t = 10 years
r = 1.5%
(e) P = $5000
t = 10 years
r = 0.8%
(f) Compare the result of (a) and (c).
Required:
(a) Find the amount when interest is compound annually.
(b) To find the total amount after 25 years.
(c) Find the amount when interest is compound annually.
(d) Find the amount when interest is compound quarterly.
(e) Find the amount when interest is compound continuously.
Explanation:
The compound interest formula is given as:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where p =principal amount
r = rate of interest
n = compound frequency
t = time period in years
(a)
[tex]undefined[/tex]Solve for u.u + 8 = 16
In this case the answer is very simple. .
We must apply algebraic rules to find the solution.
u + 8 = 16
u = 16 - 8
u = 8
The answer is:
u = 8
What happens to F(x) when x is negative but approaches zero for the functionF(x) = 1/x, whose graph is shown below?
Given: The graph of the function below
[tex]F(x)=\frac{1}{x}[/tex]To Determine: What happens to F(x) when x is negative but approaches zero
Solution:
It can be observed from the given graph that when x is negative but approaches zero, F(x) approaches negative infinity
This is as shown below
From the options provided, the best answer is F(x) is a negative number, OPTION C
Assume the hold time of callers to a cable company is normally distributed with a mean of 4.0 minutes and a standard deviation of 0.4 minute. Determine the percent of callers who are on hold between 3.4 minutes and 4.5 minutes. % (Round to two decimal places as needed.)
According to the problem, we have
[tex]\begin{gathered} \mu=4.0\min \\ \sigma=0.4\min \end{gathered}[/tex]We have to find the percent of callers who are on hold between 3.4 minutes and 4.5 minutes.
First, we find the z-score
[tex]z=\frac{x-\mu}{\sigma}[/tex]For x = 3.4
[tex]z=\frac{3.4-4.0}{0.4}=\frac{-0.6}{0.4}=-1.5[/tex]For x = 4.5
[tex]z=\frac{4.5-4.0}{0.4}=\frac{0.5}{0.4}=1.25[/tex]The probability we have to find is
[tex]P=(3.4Using a z-table, we have[tex]\begin{gathered} P(3.4Then, we multiply by 100 to express it in percetange.[tex]0.2351\cdot100=23.51[/tex]Hence, the probability is 23.51%.Write an equation of the line that passes through (4, 3) and is parallel to the line defined by 5x-2y-3. Write the answer in slope-intercept form (if possible)
and in standard form (Ax+By-C) with smallest integer coefficients. Use the "Cannot be written" button, if applicable.
The final answer to the question is highlighted in the box
write an algebraic model for the statement then solve the model the sum of a number and -9 is -21
Answer:
[tex]x + ( - 9) = - 21[/tex]
[tex]x - 9 = - 21[/tex]
[tex]x = - 12[/tex]
Given ABC below, with m B=25°, a = 9, and c = 16, find the area of the triangle.
It is given that the sides of the triangle are a =9 and c=16 . The angle is given mB=25 degree.
The area of triangle is determined as
[tex]A=\frac{1}{2}a\times c\times\sin B[/tex][tex]A=\frac{1}{2}\times9\times16\times\sin 25=72\sin 25^{\circ}[/tex][tex]A=30.428sq\mathrm{}\text{unit}[/tex]Thus the area of triangle is 30.428 sq.unit.
Deter mine the intervals for which the function shown below is increasing
Answer:
The interval at which the function is increasing is from x = -2 to x = 0. In interval notation, it is (-2, 0).
Explanation:
See the graph below for the pattern of the function.
As you can see above, from x = -∞ until x = -2, the value of the function decreases from y = +∞ to y = -7.
Then, starting at x = -2 to x = 0, the value of the function increases from y = -7 to y = -3.
Lastly, starting at x = 0 to +∞, the value of the function decreases again from y = -3 to -∞.
Hence, the interval at which the function is increasing is at (-2, 0).
log(x) + log(x + 3) = 7
Answer:
[tex]x=3160.778016...[/tex]
Step-by-step explanation:
Given logarithmic equation:
[tex]\log(x)+\log(x+3)=7[/tex]
[tex]\textsf{Apply the product log law}: \quad \log_axy=\log_ax + \log_ay[/tex]
[tex]\implies \log(x(x+3))=7[/tex]
[tex]\implies \log(x^2+3x)=7[/tex]
[tex]\textsf{Apply the log law}: \quad \log_ab=c \iff a^c=b[/tex]
[tex]\implies x^2+3x=10^7[/tex]
[tex]\implies x^2+3x-10000000=0[/tex]
Solve the quadratic equation by using the quadratic formula.
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Therefore:
[tex]a=1, \quad b=3,\quad c=-10000000[/tex]
Substitute the values of a, b and c into the quadratic formula:
[tex]\implies x=\dfrac{-3 \pm \sqrt{3^2-4(1)(-10000000)}}{2(1)}[/tex]
[tex]\implies x=\dfrac{-3 \pm \sqrt{9+40000000}}{2}[/tex]
[tex]\implies x=\dfrac{-3 \pm \sqrt{40000009}}{2}[/tex]
[tex]\implies x=3160.778016..., \quad x=-3163.778016...[/tex]
As logs of negative numbers cannot be taken, the only valid solution is:
[tex]\boxed{x=3160.778016...}[/tex]
Which of the following statements must be true based on the diagram below!(Diagram is not to scale)O JL is a segment bisector.JL is a perpendicular bisector.OJT is an angle bisectora Lis the vertex of a right angle,Jis the midpoint of a segment in the diagramNone of the above.
From the diagram, we notice that the line JL bisects the angle J into two equal angles. Hence, we can conclude that the correct statement is this:
JL is an angle bisector
An angle bisector are
The drama club is selling tickets to their play to raise money foe the show's expenses. They are selling both adult tickets and student tickets. The auditorium can hold no more than 109 people. Write an inequality that could represent the possible values for the number of student tickets sold,s, and the number of adult tickets sold,a, that would satisfy the constraint
Adult (A)
student (S)
Total people= 109
the maximum number of tickets is 109, in this case is possible 109.
than means
A + S ≤ 109
or
109 ≥ A + S
15. x=m<1=I'll upload a picture of my HW
Opposite angles are the same
Then:
[tex]\begin{gathered} 6x+4=8x\text{ - }18 \\ 18+4=8x\text{ -}6x \\ 22=\text{ 2x} \\ x=\text{ 22/2} \\ x=11 \end{gathered}[/tex]So: (Remember the line has a 180º degrees
Send me Answers for Questions A, B, and C
Answer: A) 4 B) 30 C) 6
Step-by-step explanation:
For question A, you subtract the highest number and the lowest number (10-6)
For question B, you add all the frequency numbers together
For question C, you use your answer on B and divide it by 5
tristan asked his coworkers about how much time they spent commuting each morning Find the median
SOLUTION
In a box and whisker plot, the firt dot on the box is Q1
The second dot on the box is Q2
The third dot on the box is Q3
Q2 is the median
From what we see,
[tex]Q2=25[/tex]Hence the answer is 25, option D
Chen is opening a new account with a $1,200 deposit. She will be keeping money in the account, compounded monthly for no more than 3 years. the formula gives the value, V, of the account as a function of time, t. Which is a reasonable domain of this function?V(t)= 1,200(1 + 0.02)^t/12A) 0< or equal to t < or equal to 36B) 0C) 0 < or equal to t < or equal to 1,273.45D) 1,200 < or equal to t < or equal to 1,273.45
The Solution:
Given the function:
[tex]V(t)=1200(1+0.02)^{\frac{t}{12}}[/tex]We are required to find a reasonable domain for the given function.
The domain of the function V(t) is the range of values for t.
The question says Chen is will continue to keep money in the account for not more than 3 years, but the interest will be compound monthly.
Recall:
1 year = 12 months
So,
3 years will be
[tex]12\times3=36\text{ months}[/tex]This means that the range of values for t is:
[tex]0\leq t\leq36[/tex]Therefore, the correct answer is [option A]
WILL GIVE BRIANLYEST 100 POINTS ACULLY 200 BC IM GIVING EXTRA POINTS
Answer:
the mean would increase to a value to about 24.6
Q2: median is 7.
Step-by-step explanation:
Answer:
Q1) the mean would increase in value to about 24.6
Q2) 7
a loaf of sandwich bread contains 24 slices. which of these tables correctly shows the ratios of different of loaves of bread to the number of total slices they contain
We have that a loaf of sandwich bread contains 24 slices, then we have that the ratio must be constant between the loaves and the slices. If we have 1 loaf: 24 slices, this ratio must be equal in the table.
Therefore, we have that the only table that follows this is the table that has:
If we have:
2/48 = 1/24
3/72 = 1/24
4/96 = 1/24
The ratio of loaves to slices is the same, that is, 1 / 24.
On a particular day, the amount of untreated water coming into the plant can be modeled by f(t) = 100 + 30cos(t/6) where t is in hours since midnight and f(t) represents thousands of gallons of water. The amount of treated water at any given time, t, can be modeled by g(t) = 30e^cos(t/2)a) Define a new function, a′(t), that would represent the amount of untreated water inside the plant, at any given time, t.b) Find a′ (t).c) Determine the critical values of this function over the interval [0, 24).
a)The amount of untreated water inside the plant will be the difference between the difference f(t) - g(t), then, a(t) can be defined as follows:
[tex]a(t)=100+30cos(\frac{t}{6})-30e^{cos(\frac{t}{2})}[/tex]b) the derivative of a(t) is the following:
[tex]a^{\prime}(t)=-5sin(\frac{t}{6})+15sin(\frac{t}{2})e^{cos(\frac{t}{2})}[/tex]c) the critical values of a(t) over the interval [0, 24) are:
[tex]\begin{gathered} t=0 \\ t=6\pi \end{gathered}[/tex]Find the volume of each prism. Round your answers to the nearest tenth, if necessary. Do not include units (i.e. ft, in, cm, etc.). (FR)
EXPLANATION:
Given;
We are given the picture of an isosceles trapezoidal prism.
The dimensions are as follows;
[tex]\begin{gathered} Top\text{ }base=4 \\ Bottom\text{ }base=9 \\ Vertical\text{ }height=4.3 \\ Height\text{ }between\text{ }bases=6 \end{gathered}[/tex]Required;
We are required to find the volume of this trapezoidal prism.
Step-by-step solution;
The area of the base of a trapezium is given as;
[tex]Area=\frac{1}{2}(a+b)\times h[/tex]For the trapezium given and the values provided, we now have;
[tex]\begin{gathered} a=top\text{ }base \\ b=bottom\text{ }base \\ h=height \\ Therefore: \\ Area=\frac{1}{2}(4+9)\times4.3 \\ Area=\frac{1}{2}(13)\times4.3 \\ Area=6.5\times4.3 \\ Area=27.95 \end{gathered}[/tex]The volume is now given as the base area multiplied by the length between both bases and we now have;
[tex]\begin{gathered} Volume=Area\times height\text{ }between\text{ }trapezoid\text{ }ends \\ Volume=27.95\times6 \\ Volume=167.7 \end{gathered}[/tex]ANSWER:
The volume of the prism is 167.7
There are 39 chocolates In a box call identically sheet dear 16 off filled with nuts 13 with caramel and 10 are solid chocolate you randomly select one piece eat it and then select a second piece find the probability of selecting to solid in a row
The probability of selecting two solid chocolates in a row is 0.0607 .
In the question ,
it is given that
there are total 39 chocolates in the box .
number of chocolates filled with nuts = 16
number of chocolates filled with caramel = 13
number of chocolates filled with solid = 10
Probability of selecting first chocolate as a solid is 10/39.
Now , there are 38 chocolates , with 9 solid chocolates ,
hence the probability of selecting second chocolate as a nut is = 9/38
So, the probability of selecting two solid chocolates in a row = 10/39×9/38
= 90/1482
= 0.0607
Therefore , the probability of selecting two solid chocolates in a row is 0.0607 .
The given question is incomplete , the complete question is
There are 39 chocolates in a box, all identically shaped. There 16 are filled with nuts, 13 with caramel, and 10 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the probability of selecting 2 solid chocolates in a row.
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