Answer:
21.5
Step-by-step explanation:
geometric progression formula: [tex]A_{n}[/tex]=A*[tex]r^{n-1}[/tex]
where An is nth term
A is first term
r is common ratio
given [tex]A_{99}[/tex] = 48
A=12
we find r
48=12 *[tex]r^{99-1}[/tex]
48/12=[tex]r^{98}[/tex]
[tex]\sqrt[98]{4}[/tex]=r
r=1.014
so to find 50th term
[tex]A_{50}[/tex]=12*[tex]1.012^{50-1}[/tex]
[tex]A_{50}[/tex]=21.53
A chemist weighs samples obtained from a production run. The weights of the samples are 13 g, 14 g, 23 g, 11 g, 15 g, 14 g, 14 g, 12 g, 13 g, 15 g, 14 g, and 12 g. Are there any outliers?
The outlier of the data is 14.16 gram
What is Outlier?An outlier is a data point in statistics that dramatically deviates from other observations. An outlier may reflect measurement variability or it may point to an experimental error; the latter is occasionally removed from the data set. In statistical analyses, an outlier can result in significant issues.
Given:
Weights of the samples are 13 g, 14 g, 23 g, 11 g, 15 g, 14 g, 14 g, 12 g, 13 g, 15 g, 14 g, and 12 g.
So, the outlier is
= 13 x 2 + 14 x 4 + 12 x 2 + 11 + 15 x 2+ 13 / 12
= 170 gram /12
= 14.16 gram.
Hence, the outlier of the data is 14.16 gram
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If tan(t)=3/4 what’s cos(t)
well, let's notice our tangent is positive, that only happens on the 1st and 3rd Quadrants
[tex]tan(t )=\cfrac{\stackrel{opposite}{3}}{\underset{adjacent}{4}}\hspace{5em} \textit{now let's find the hypotenuse} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{4^2 + 3^2}\implies c=5\hspace{5em} \stackrel{I~Quadrant}{cos(t)= \cfrac{\stackrel{adjacent}{4}}{\underset{hypotenuse}{5}}}\qquad \stackrel{III~Quadrant}{cos(t)=-\cfrac{4}{5}}[/tex]
A dog breeder is planning to buy more dog food. He makes a table showing how
many pounds of food he will have after shopping. The table is based on how much he
spends and how much food he already has. Which equation generates the table?
Money Spent (x) $0 $20 $40 $60
Pounds of Food (v) 4 12 20 28
x=y-4
y=8x-4
x=8y +4
y=x+4
The equation that generates the table is
y = (2/5)x + 4.
What is an equation of a line?
The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
Money Spent (x) $0 $20 $40 $60
Pounds of Food (v) 4 12 20 28
We can have the following points from the table.
(0, 4), (20, 12), (40, 20), and (60, 28).
Now,
Choose two points:
(0, 4) and (20, 12)
m = (12 - 4) / (20 - 0)
m = 8 / 20
m = 2/5
Now,
(0, 4) = (x, y)
y = mx + c
4 = (2/5) x 0 + c
4 = c
c = 4
Now,
The equation is given as,
y = mx + c
y = (2/5)x + 4
The equation that generates the table is
y = (2/5)x + 4.
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Consider the relationship 9r+2t=9 .
a. Write the relationship as a function r=f(t) .
Enter the exact answer.
f(t)=
b. Evaluate f(−9) .
f(−9)=
c. Solve f(t)=5 .
t=
1. The relationship as a function r = f(t) is: r = (9 - 2t)/9.
2. The numeric value at t = -9 is: f(-9) = 3.
3. The value of t for which f(t) = 5 is t = -18.
What are the desired measures?The relationship is given as follows:
9r + 2t = 9.
To write the relationship as a function of t, we have to isolate the variable r as a function of the variable t, hence:
9r = 9 - 2t
r = (9 - 2t)/9.
To find the numeric value at t = -9, we replace the lone instance of t in the relationship by -9, hence:
r = (9 - 2(-9))/9 = 27/9 = 3.
To find when f(t) = 5, we have to find t for which f(t) = 5, hence:
9r = 9 - 2t
2t = 9 - 9r
2t = 9 - 9(5)
2t = -36
t = -36/2
t = -18.
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See question in screenshot below:
The value of P is $2,000.
The value of r is 2.8%
The value of n is 4.
The amount of money that Allision will have in 8 years is $2,500.19.
How much will he have in 8 years?When the account is compounded quarterly, it means that the amount invested and the interest that has already been earned would increase in value four times in a year. A compound growth rate can be modelled as an exponential equation.
The equation that can be used to determine the future value with quarterly compounding is:
S(t) = P( 1 + r /n)^(n x t)
Where:
P = amount deposited r = interest rate n = number of compounding t = number of yearsS(t) = 2,000 x ( 1 + 0.028 / 4)^(4 x 8)
S(t) = 2,000 x 1.007^32 = $2,500.19
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Rewrite the equation in vertex form. (Include fractions in final answer).
y=-3x^2 -7x+4
For the given equation y = 3x² -7x + 4 the vertex form is given by
( 7/6, -1/12).
As given in the question,
Equation is given by :
y = 3x² -7x + 4
Standard form of the equation to get the vertex form is given by :
y = a ( x - h )² + k
Where ( h, k ) represents the vertex of the equation,
Now,
Simplify the given equation y = 3x² -7x + 4 into standard form to get vertex form,
y = 3x² -7x + 4
⇒ y = 3 [x² -2×(7/6)] + 4
⇒ y = 3 [ x² - 2×(7/6) + (49/36) - (49/36) ] + 4
⇒ y = 3 [ x² - 2×(7/6) + (49/36) ] - 3(49/36) + 4
⇒ y = 3 [x - (7/6)]² - (49/12) + 4
⇒ y = 3[x - (7/6)]² - (1/12)
Compare it with standard form ,
a = 3, h = (7/6) , k = -(1 /12)
Vertex form ( h, k) = ( 7/6 , -1/12 )
Therefore, for the given equation y = 3x² -7x + 4 the vertex form is given by ( 7/6, -1/12).
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The scatter plot shows the winning times, in seconds, in a 50-meter race over eight consecutive years.
Scatter plot with x axis labeled Time in Years and y axis labeled Winning Time with points at 1 comma 5 and 4 tenths, 2 comma 5, 3 comma 4 and 6 tenths, 4 comma 4 and 9 tenths, 5 comma 4 and 1 tenth, 6 comma 3 and 9 tenths, 7 comma 3 and 6 tenths, and 8 comma 3 and 3 tenths.
Which of the following is an appropriate line of best fit?
y hat equals negative 29 hundredths times x plus 5 and 67 hundredths.
y hat equals 29 hundredths times x plus 5 and 67 hundredths.
y hat equals negative 45 hundredths times x plus 7 and 69 hundredths.
y hat equals 45 hundredths times x plus 7 and 69 hundredths.
Answer:
[tex]\hat{y}=-0.29x+5.67[/tex]
Step-by-step explanation:
Given points on the scatter plot:
(1, 5.4)(2, 5)(3, 4.6)(4, 4.9)(5, 4.1)(6, 3.9)(7, 3.6)(8, 3.3)Plot the given points and draw a line of best fit (see attachment).
As the y-values decrease as the x-values increase, the slope of the line of best fit is negative.
From inspection of the plotted line of best fit, we can see that the y-intercept is approximately 5.7.
Therefore, the equation that is appropriate for the line of best fit is:
[tex]\boxed{\hat{y}=-0.29x+5.67}[/tex]
Answer:
y hat equals negative 29 hundredths times x plus 5 and 67 hundredths.
Step-by-step explanation:
i took the test :)
- Jacob Elementary School had a book drive. On
Monday, the students collected 95 books. They
collected 78 more books on Tuesday. How many
books did the students collect?
The students collected
books.
The Grover family went on a spring vacation. Th
cabin is 305 miles away. If they drive 98 miles
first day, how many more miles do they have to
Step-by-step explanation:
1. 95+78 as its asking how many bools all together. 173 books
2. 305-98 ita asking how many miles LEFT.
PLEASE HELP SOLVE!!!
Answer:
positive, positive, zero, zero, negative, negative, positive
Step-by-step explanation:
The derivative is positive when a function is increasing.
The derivative is zero when a function is neither increasing nor decreasing.
The derivative is negative when the function is decreasing.
The black graph is the graph of
= f(x). Choose the equation for the
red graph.
a.
y = f(2x)
b. y=f(2)
C.
2y = f(x)
d.
½ = f(x)
Enter
The equation for the red graph is y = f(x/2).
We are given a graph. The graph shows two functions. A function connects an input to an output. It is similar to a machine with input and output. And the result is somehow connected to the input in some way. One of the functions is depicted by black lines. We need to find the equation of the function represented by the red lines.
We can see that the function represented by the red lines can be formed if the black lines are stretched horizontally. The black lines can be stretched horizontally by a factor of 2 to form the red lines. A function y = f(x) can be stretched horizontally by a factor of "k" as given below.
y = f(x/k)
Hence, the equation for the red graph is y = f(x/2).
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Karen, a 52-year-old female, bought a $75,000, 20-year life insurance policy through her employer. Karen is paid weekly.
How much is deducted from her paycheck for life insurance? (Use the table.)
ABC Term Life Insurance Company
Annual premium
Age at issue
Male Female 10-year
per $1000 of coverage
20-24 23-27 $2.50
25-29 28-32 $3.25
30-34 33-37 $3.82
35-39 38-42 $4.55
40-44 43-47 $5.78
45-49 48-52 $7.53
20-year
$3.80
$5.84
$7.93
$10.33
$13.68
$17.56
As Karen age is 52- year old and she is a female and her life insurance policy is for 20- years , then amount to be deducted from her life insurance paycheck is equal to $1317.
As given in the question,
Information given about Karen,
Age = 52- year old
Gender = female
Policy = 20 -year life insurance policy
Annual premium given per $1000 for coverage
Karen policy amount = $75,000
From the table it is given that,
Amount deducted per $1000 for 20year policy in the age limit of 48 -52
= $17.56
⇒ $1000 = $17.56
⇒ $75,000 = $( 17.56 × 75,000)/ 1000
= $1317.
Therefore, as Karen age is 52- year old and she is a female and her life insurance policy is for 20- years , then amount to be deducted from her life insurance paycheck is equal to $1317.
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Mara's age is 5 less than four times Brandy's age. Let x represent Brandy's age, and let y represent Mara's age. Which ordered pair (x, y) makes the equation y = 4x − 5 true?
The ordered pair that made the equation, y = 4x - 5 correct is (5, 15).
How to find ordered pair from a linear equation?Mara's age is 5 less than four times Brandy's age. Let x represent Brandy's age, and let y represent Mara's age.
Therefore, the ages can be represented linearly as follows:
y = 4x - 5
where
x = Brandy's agey = Mara's ageTherefore, the ordered pair (x, y) that makes the equation correct can be computed as follows:
y = 4x - 5
y = 4(5) - 5
y = 20 - 5
y = 15
The ordered pair is (5, 15)
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Question content area top
Part 1
Arrivals to a bank automated teller machine (ATM) are distributed according to a Poisson distribution with a mean equal to per minutes. Complete parts a and b below.
The probabilities, using the Poisson distribution, are given as follows:
a) Three customers in five minutes: 0.1805 = 18.05%.
b) Fewer than two customers in ten minutes: 0.0916 = 9.16%.
What is the Poisson distribution?The probability mass function of the Poisson distribution is presented as follows:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters of the Poisson distribution are:
x is the number of successes that we want to find the probability of.e = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval or range of values of the input parameter.The mean is of two arrivals per five minutes, hence:
[tex]\mu = 2[/tex]
The probability of exactly three arrivals in five minutes is:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 3) = \frac{e^{-2}2^{3}}{(3)!} = 0.1805[/tex]
For ten minutes, the mean is given as follows:
[tex]\mu = 2 \times 2 = 4[/tex]
The probability of fewer than two arrivals is:
P(X < 2) = P(X = 0) + P(X = 1).
In which:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-4}4^{0}}{(0)!} = 0.0183[/tex]
[tex]P(X = 1) = \frac{e^{-4}4^{1}}{(1)!} = 0.0733[/tex]
Then:
P(X < 2) = P(X = 0) + P(X = 1) = 0.0183 + 0.0733 = 0.0916 = 9.16%.
Missing InformationThe complete problem is given by the image shown at the end of the answer.
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During one hour of running, Jeff can run 5.5 miles. The number of miles Jeff runs and the number of hours are in a proportional relationship. This is represented by y=5.5x .
The slope of the graph is 5.5.
Given:
During one hour of running, Jeff can run 5.5 miles. The number of miles Jeff runs and the number of hours are in a proportional relationship. This is represented by y=5.5x .
slope:
Slope is the steepness of a line as it moves from LEFT to RIGHT. Slope is the ratio of the rise, the vertical change, to the run, the horizontal change of a line. The slope of a line is always constant .
compare the y = 5.5x with standard equation y = mx + c
m = 5.5 and c =0
m is nothing but slope:
so slope m = 5.5
= 11/2.
Therefore The slope of the graph is 5.5.
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Find the savings plan balance after 2 years with an APR of 3% and monthly payments of $300.
The balance is $
(Do not round until the final answer. Then round to the nearest cent as needed.)
Answer:
Step-by-step explanation:
The balance of the savings plan after 2 years will be=$7,410.85 at 3% compounded monthly.
The balance of the savings plan after 2 years will be=$7,407.95 at 3% compounded annually.
The formula you use to calculate this is:FV=P{[1 + R]^N - 1/ R}=FV OF $1 PER PERIOD, Where R=Interest rate per period, N=number of periods, P=periodic payment, FV=Future value.
PLS HELP GUYS LIKE FR I NEED HELP THIS IS MY LAST PROBLEM FOR MY SHEET. SHOW THE DRAWING PLS
Answer/Step-by-step explanation:
Use the given drawing and scale to find out how big the building is in real life. See image. Then use the scale they asked for to make the new drawing. See image.
What number is halfway between 8.34 and 8.35?
Answer:
The correct answer is 8.345
Step-by-step explanation:
To find the midpoint of any two numbers, add the two numbers together and then divide the sum by two.
Addition:
8.34 + 8.35 = ?
= 16.69
Divide sum by 2:
16.69 ÷ 2 = ?
= 8.345
Hope this helps! Have an amazing rest of your day! Brainliest welcome! :)
helppp pls <233 i’ll make brainliest !!!
The congruent angle of Q is T
t is the solution to the linear equation?
x – StartFraction 2 Over 3 EndFraction x minus StartFraction one-half EndFraction equals StartFraction 1 Over 3 EndFraction plus StartFraction 5 Over 6 EndFraction x. = + x
The solution for the linear equation:
x - (2/3)*x - (1/2) = (1/3) + (5/6)*x
Is x = -5/3
How to solve the linear equation?Is hard to understand what you wanted to write, but I assume that the linear equation that we need to solve is:
x - (2/3)*x - (1/2) = (1/3) + (5/6)*x
To solve this linear equation, we need to isolate the variable x in one of the sides of the equation
To do so, we move all the terms with "x" to the left side and the terms without to the right side:
x - (2/3)*x - (5/6)*x = 1/3 + 1/2
Now we solve this:
x - (4/6)x - (5/6)x = 2/6 + 3/6
x - (9/6)*x = 5/6
We can write the "1" in the first term as 6/6
(6/6)*x - (9/6)*x = 5/6
(-3/6)*x = 5/6
-3x = 5
x = 5/-3
x = -5/3
That is the solution of the linear equation.
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Solve for x: 5x + one third(3x + 6) > 14
The value of x for 5x + 1/3(3x+6) > 14 is x > 2
What are inequality equations in algebra ?
When you first begin learning algebra, the equals sign is used to denote that two items are, in fact, equal to one another. As an illustration, consider the equations 3 = 3, 5 = 3 + 2, apple = apple, pear = pear, etc. When compared, an inequality reveals two things: first, that the objects being compared are not equal, or at the very least, they are not always equal; and second, how they are uneven.
Consider the provided inequality.
5x + 1/3(3x+6) > 14
Distributive property:
a (b +c)= ab + ac
By the distributive property.
5x + 1/3 * 3x + 1/3 * 6 > 14
5x + x + 2 > 14
Add the like terms
6x + 2 > 14
Subtract 2 from both sides.
6x > 12
Divide both sides by 6.
6x/6 > 12/6
x > 2
Hence, value of x for the given inequality equation will be greater than 2 i.e, x > 2.
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Answer:
Nikita Knight
Nikita Knight
Step-by-step explanation:
Nikita Knight
Nikita Knight
Nikita Knight
Nikita Knight
69420
friendly and kind personality and likes to help people but like Hyde, he becomes mysterious and violent
7. For the piecewise defined function {f(x)=1 x<3
{1/2x+7 x_>3
(1) 7
(2) 10
3x-1 x<3
[//x+7 _x23²)
(3) 17
(4) 27
which of the following is the value of f(6)?
Answer:
I think it's 10 idek I just search it
Can you help on 7-9
Please this is due tomorrow
Answer:
The answer for no 7 is A. 24 in, for no 8 is C. 10 in, for no 9 is D. similar
Step-by-step explanation:
The answer for no 7 can be calculation as follows
Since both rectangles are similar, then the corresponding side are proportional, and it follows
[tex]\frac{\overline{KJ}}{\overline{AB}}=\frac{x}{\overline{AD}}[/tex]
[tex]\frac{48}{144}=\frac{x}{72}[/tex]
Where [tex]x[/tex] is the line segment [tex]\overline{MJ}[/tex]
Multiply both sides by [tex]72[/tex] to isolate [tex]x[/tex]
[tex]\frac{48}{144}\times 72=\frac{x}{72}\times 72[/tex]
[tex]\frac{48\times 72}{144}=x[/tex]
[tex]\frac{3456}{144}=x[/tex]
[tex]24=x[/tex]
Since the value of [tex]x[/tex] is [tex]24[/tex], then the length of [tex]\overline{MJ}[/tex] is [tex]24[/tex] in
The answer for no 8 can be calculation as follows
Since both rectangular frames are similar, then the corresponding side are proportional, and it follows
[tex]\frac{w_2}{w_1}=\frac{x}{h_1}[/tex]
Where [tex]w_2[/tex] is the width of frame [tex]2[/tex], [tex]w_1[/tex] is the width of frame [tex]1[/tex], [tex]x[/tex] is the height of frame [tex]2[/tex], [tex]h_1[/tex] is the height of frame 1
Substitute [tex]8[/tex] for [tex]w_2[/tex], [tex]12[/tex] for [tex]w_1[/tex], [tex]15[/tex] for [tex]h_1[/tex]
[tex]\frac{8}{12}=\frac{x}{15}[/tex]
Multiply both sides by [tex]15[/tex] to isolate [tex]x[/tex]
[tex]\frac{8}{12}\times 15=\frac{x}{15}\times 15[/tex]
[tex]\frac{8\times 15}{12}=x[/tex]
[tex]\frac{120}{12}=x[/tex]
[tex]10=x[/tex]
Since the value of [tex]x[/tex] is [tex]10[/tex], then the height of the second rectangular frame is [tex]10[/tex] in
The answer for no 9 can be evaluated as follows
Since two polygons are similar if and only if two conditions are satisfied
All pairs of corresponding angles are congruentAll pairs of corresponding side are proportionalThen the two polygons are similar
what is the greatest comman facter of 2 and 3
Brad wants to have $14832 available as a down payment for a house in 3 years. How much must he deposit now at
9.3% compounded monthly to reach that goal?
Round final answer to the nearest cent (2 decimal places)
Answer:
P = $11233.08
Step-by-step explanation:
Another word for deposit is the principal and the compounded monthly indicates we're working with compound interest.
The formula for compound interest is:
[tex]A(t)=P(1+\frac{r}{n} )^{rt}[/tex], where P is the principal ("deposit"), r is the rate, n is the number of compounding periods, and t is the time.
Before solving, we will need to convert the percentage to a decimal (9.3% to 0.093) and remember that n = 12, since there are 12 months in a year.
Thus, we will need to solve for P to find Brad's deposit:
[tex]14832=P(\frac{0.093}{12})(^{12*3})\\14832=P(1.00775)^{36} \\14832=1.32038641P\\11233.07532=11233.08=P[/tex]
Graph g(x) = |x − 3|.
Answer: x+3
Step-by-step explanation:
since it has the absolute value, it will be x+3 and you can graph that in your calculator!
Which graph represents the function f(x) = -x] -2?
The third graph or option 3 represents the function f(x) = - l x l - 2.
Given:
f(x) = - l x l - 2
Table
x y = - l x l - 2
0 -2
1 -3
2 -4
3 -5
-1 -3
-2 -4
-3 -5
On plotting above points or the above points shown in figure 3 or third graph.
Therefore the third graph or option 3 represents the function f(x) = - l x l - 2.
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Read the problem below on the picture. It's Geometry by the way. Also if u can answer my other one its in my profile.
Answer:
x = 18. y = 54
Step-by-step explanation:
first we we figure out the degrees of the spot where N is.
(I know N references the line but ill be using it to call the spot)
72 + N = 90
subtract 72 from both sides
N = 18
So since opposite angles are the same
2x + N = 3x
2x + 18 = 3x
subtract 2x from both sides
18 = 1x
divide by 1 both sides
18 = x
______
now we add all the angles from the left sides to make 180
2x + N + 72 + y = 180
we know x is equal to 18 and N is also 18
2(18) + 18 + 72 + y = 180
simplify
36 + 18 + 72 + y = 180
add
126 + y = 180
subtract both sides by 126
y = 54
1.e a jupiter day is about 3/8 of an earth day. about how many hours are there is jupiter their in jupiter day
1.f on the moon a person weight is about 1/6 of their weight on earth about how many kilograms would a person weigh on the moon if their weight on earth is 54kg
The number of hours that are there in Jupiter is 9 hours.
The kilograms that a person weigh on the moon is 9kg.
How to calculate the days?It is important to note that there are 24 hours in a day. Therefore, when Jupiter day is about 3/8 of an earth day. The number of hours will be:
= 3/8 × 24
= 9 hours
Also, a person weight is about 1/6 of their weight on Earth. The kilograms that a person weigh on the moon if their weight on earth is 54kg will be:
1/6 × 54
= 9kg
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What’s the correct answer answer asap for brainlist
Answer:
B
Step-by-step explanation:
Answer:
A.
Step-by-step explanation: