The half life period is the time in which only half of the given population remains. It can be represented through this equation:
[tex]f(t)=a\times(1/2)^{\frac{t}{h}}[/tex]
t = time passeda = y-intercepth = half lifeSolving the QuestionWe're given:
h = 28 million yearsa = 184 grams (this is the initial mass, after 0 time has passed)For most questions like this, we would have to plug these values into the equation mentioned above. However, this question asks for the time elapsed after 3 half-lives.
This can be calculated simply by multiplying the given half-life by 3:
28 million years x 3
= 84 million years
Answer84 million years
Find the 14th term of the arthmetic sequence x-1, 7x -7 , 13x-13,....
Since they're in arithmetic progression, there is a constant difference between consecutive terms of
[tex](7x - 7) - (x - 1) = 6x - 6[/tex]
Recursively, the sequence is given by
[tex]\begin{cases} a_1 = x-1 \\ a_n = a_{n-1} + 6x - 6 & \text{for }n\ge2\end{cases}[/tex]
By substitution, we have
[tex]a_2 = a_1 + 6x-6[/tex]
[tex]a_3 = a_2 + 6x-6 = a_1 + 2(6x-6)[/tex]
[tex]a_4 = a_3 + 6x-6 = a_1 + 3(6x-6)[/tex]
and so on, up to the 14th term
[tex]a_{14} = a_1 + 13(6x-6)[/tex]
[tex]a_{14} = (x-1) + 78 (x - 1)[/tex]
[tex]a_{17} = 79 (x - 1) = \boxed{79x-79}[/tex]
Margo borrows $800 agreeing to pay it back with 8% annual interest after 8 months. how much interest will she pay?
Answer:
43
Step-by-step explanation:
800 × 8% × (8/12)
The data below shows the number of people visiting a local clinic per day to be vaccinated against Measles.
5 12 19 29 35 23 15 33 37 21 26 18 23 18 13 21 18 22 20
1.1 Determine the mean of the given data. (2)
1.2 Calculate the standard deviation of the data.(2)
1.3 Determine the number of people vaccinated against Measles that lies within ONE standard deviation of the mean.(2)
1.4 Determine the interquartile range for the data.(3)
1.5 Draw a box and whiskers diagram to represent the data.(3)
1.6 Identify any outliers in the data set. Substantiate your answer.(2)
Answer:
1.3
2.5
3.7
4.95.0
5.38
6.67
Step-by-step explanation:
Answer:
Step-by-step explanation:
34
45
11
9
78
56
(4x+1)(4x+1)
im so confused
Answer:
16x² + 8x + 1
Step-by-step explanation:
(4x + 1)(4x + 1)
each term in the second factor is multiplied by each term in the first factor, that is
4x(4x + 1) + 1(4x + 1) ← distribute both parenthesis
= 16x² + 4x + 4x + 1 ← collect like terms
= 16x² + 8x + 1
Answer:
16 x 2 + 8x + 1
Step-by-step explanation:
Using the foil method we expanded the polynomial.
need help with this! show work please!
Answer:
(a) 1/2
(b) $1,080,000
(c) 72°
Step-by-step explanation:
We have to find the ratio in which the money is being distributed
To do this first add up the individual values in the ratio 5:3:2 which represents the ratio C:D:E for apportioning savings
5 + 3 + 2 = 10
Chris's share = 5/10 = 1/2
Danny's share = 3/10
Evelyn's share = 2/10 = 1/5
Answers
(a) Fraction of Danny's share = 1/2
(b) If Danny is to receive $540,000 and his share is 1/2 of total savings then the total savings = 2 x 540,000 = $1,080,000
(c) The ratio of the angles in a pie chart will be the same as the ratio of the division. A pie chart shows the relative shares as part of a circle. Since a circle contains 360° , the angle of the sector that represents Evelyn's share will be 1/5 x 360 = 72°
An angle is defined as the space between two rays that emanate from a common point. True or false
True, there are some undefined terms like line, point angle, distance between two points .
Which definition of angle is the best?
The figure in which two rays intersect at the vertex, or common point, is referred to as an angle. The symbol "∠" is used to represent the angle.How does Euclid define angle?
A plane angle is the inclination toward one another of two intersecting, non-straight lines in the plane.
True, there are some undefined terms like line, point angle, distance between two points .
we intuitively know about the angle but can not give mathematical definition .
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What is an equation of the line, in point-slope form, that passes through the point (9, -9) and has a slope of 4?
Please explain how to do this : )
[tex](\stackrel{x_1}{9}~,~\stackrel{y_1}{-9})\hspace{10em} \stackrel{slope}{m} ~=~ 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-9)}=\stackrel{m}{ 4}(x-\stackrel{x_1}{9}) \implies y +9= 4 (x -9)[/tex]
Answer:
m = 4
Step-by-step explanation:
slope = 4
Triangle PQR is transformed to triangle P′Q′R′. Triangle PQR has vertices P(3, −6), Q(0, 9), and R(−3, 0). Triangle P′Q′R′ has vertices P′(1, −2), Q′(0, 3), and R′(−1, 0).
Plot triangles PQR and P′Q′R′ on your own coordinate grid.
Part A: What is the scale factor of the dilation that transforms triangle PQR to triangle P′Q′R′? Explain your answer. (4 points)
Part B: Write the coordinates of triangle P′′Q′′R′′ obtained after P′Q′R′ is reflected about the y-axis. (4 points)
Part C: Are the two triangles PQR and P′'Q′'R′' congruent? Explain your answer. (2 points)
Answer:
A: sf 2 or 1/2
Step-by-step explanation:
Answer:
Part A: The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' is 1/4
Part B:
P''(-1, 0)
Q''(0, -1)
R''(2, -1)
Part C:
The two Triangles PQR and P''Q''R'' are not congruent.
Step-by-step explanation:
please help please help this is easy but hard for me lol
Answer:
To make AEH(triangle) do a vertical cut from A to H
Step-by-step explanation:
Help please what is the slope of this
Answer:
1/2
Step-by-step explanation:
Rise over run. The rise is 4 the run is 8. Simplify.
In a certain school, there were 180 students in year 7. 110 study french, 88 study german, 65 study indonesian, 40 study both french and german while 38 study german and german only. find the number of students who study all the three languages. also, find the number of students who study indonesian only
The number of students who study Indonesian only = 10
Total pupils= 110
Study French = 88
Study Indonesian = 65
Study French and German = 40
Study German and Indonesian = 38
Study French and Indonesian = 26
Study German only = 19
Students who study German only = G - F∩G - G∩I + F∩G∩I
19= 88-40-38 + F∩G∩I
F∩G∩I = 9
Students who study all three languages = 9
So the students who study only Indonesian = I - F∩I - G∩I + F∩G∩I
= 65- 38-26+ 9
= 10
Therefore the number of students studying Indonesian only = 10.
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The complete question is:
In a certain school, there are 180 pupils in Year 7. One hundred and
ten pupils study French, 88 study German and 65 study Indonesian.
Forty pupils study both French and German, 38 study German and
Indonesian, and 26 study both French and Indonesian, while 19 study
German only. Find the number of pupils who study Indonesian only.
98÷13=
I need help please...
Answer:
7.538461538
Step-by-step explanation:
Simplify: A , B , C , D?
Answer:
7 5/6
Step-by-step explanation:
Reverse the operation
[tex]-2\frac{1}{3} - -10\frac{1}{6} = 2\frac{1}{3} + 10\frac{1}{6}\\= 2-\frac{1}{3} + 10+\frac{1}{6}\\-2 + 10 = 8(2 - 10)\\-\frac{1}{3} +\frac{1}{6}\\-\frac{2}{6}(x2) +\frac{1}{6}\\= -\frac{1}{6}\\8-\frac{1}{6}\\= 7\frac{5}{6}[/tex]
Noah is trying to bisect angle BAC. He draws circles of the same radius with centers B and C and then uses one of the points of intersection for his ray. What mistake has Noah made in his construction
The mistake done by Noah in his construction is that; length of the line segment AB and AC should be equal.
How to bisect an angle?
The steps in bisecting an angle say PQR is as follows;
Start with angle PQR that we will bisect.
1. Place the compasses' point on the angle's vertex Q.
2. Adjust the compasses to a medium wide setting. The exact width is not important.
3. Without changing the compasses' width, draw an arc across each leg of the angle.
4. The compasses' width can be changed here if desired. Recommended: leave it the same.
5. Place the compasses on the point where one arc crosses a leg and draw an arc in the interior of the angle.
6. Without changing the compasses setting repeat for the other leg so that the two arcs cross.
7. Using a straightedge or ruler, draw a line from the vertex to the point where the arcs cross.
8. This is the bisector of the angle ∠PQR.
Therefore, the mistake done by Noah is that length of the line segment AB and AC should be equal in order to bisect it.
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solve the equation. (find only the real solutions. enter your answers as a comma-separated list.) 5x2 10x 4
After changing the form the equation becomes 5x (x + 2) = 4.
What is an equation?An is a mathematical statement composed of two expressions joined by an equal sign. An equation is 3x - 5 = 16. By solving this equation, we obtain the value of the variable x as x = 7.We cannot solve the equation as the value of x is not given but we can change its form.
Given equation is 5x² + 10x - 4.
Then,
5x² + 10x - 4 = 05x² + 10x = 45x (x + 2) = 4 (Take 5x as common)Therefore, after changing the form the equation becomes 5x (x + 2) = 4.
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The correct question is given below:
solve the equation. (find only the real solutions. enter your answers as a comma-separated list.)
5x² + 10x - 4
3(8-3)+2(4-1)
9(6-2)-11(5-2)
the solution for it ..
solving the bracket is important
To hire an accountant to prepare taxes costs a flat fee and an additional hourly rate. The amount the accountant costs can be modeled by the function A(x) = 140 + 25x, where x represents the number of hours the accountant works to prepare the taxes and 140 represents the flat fee. What is the value of A(215) and its interpretation?
A(215) = 3; If the accountant takes 215 hours to prepare the taxes, the cost will be $2.
A(215) = 3; If the account takes 3 hours to prepare the taxes, the cost will be $215.
A(215) = 5515; If the accountant takes 215 hours to prepare the taxes, the cost will be $5,515.
A(215) = 5515; If the accountant takes 5,515 hours to prepare the taxes, the cost will be $215.
The value of A(215) and its interpretation are captured thus:
A(215) = 5515; If the accountant takes 215 hours to prepare the taxes, the cost will be $5,515
What does the function represents?
The function given as A(x) = 140 + 25x, represents the total cost of using the services of the accountants for tax computation and preparation, bearing in mind that the 140 means $140 which is the fixed charged irrespective of the number of hours it takes to prepare the tax returns whereas the 25x means that $25 is charged as variable fee for every hour the accountant works on the tax computation
A(x) = 140 + 25x
In this case, A(215) means that 215 hours were made use of by the accountants, hence, to determine the total fees, we simply substitute for x
A(215) = 140+(25*215)
A(215) = 140+5375
A(215)=$5,515
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The salary for a groun of executives was listed as follows: 18 at $50,000; 10 at $60,000; 8 at $75,000; 2 at $90,000; and 2 at $10,000. What is the average salary?
Answer:
The average salary is $57,500
Step-by-step explanation:
You would find the total salaries and divide that by 40 because there were 40 people: 18 + 10 +8 + 2 + 2
To find the total salaries"
18(50,000) + 10(60,000) + 8(75000) + 2(90,000) + 2(10000) = 2300000
2300000/40 = 57,500
compute 9600 divided by 30
Answer:
9600 divided by 30 is 320
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13. There are 4,585 students who
rode the bus to school today.
There were 3,369 students who
came to school another way.
How many students were there
in all at the school?
The number of students in all at the school is 7,954 students.
How many students are in school?In order to determine the number of students in all at the school, you would add the number of students that rode the bus with the number of students that came to school another way.
Addition is the mathematical operation that is used to determine the sum of two or more numbers. The sign used to denote addition is +. Other mathematical operations are subtraction, division and multiplication.
Number of students in school = number of students that rode the bus + number of students that came another way
4,585 + 3,369 = 7,954 students
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Peter signed up for a program that cost $10.50 per month to stream movies to his computer. He decided to cancel the service after 5/6 month, he only has to pay for the amount of time he use the service. What number represents the total change in what amount of money Peter has after paying for the service.
In linear equation, $1.75 is amount of money Peter has after paying for the service.
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.Peter signed up for a program that costs $10.50 per month to stream movies to his computer.
He decided to cancel his service after 5/6 month.
So, has to pay for the amount of time he used the service
$10.50 . 5/6 = $175.5 = $8.75
The amount of money Peter has after paying for the service is
$10.50 - $8.75 = $1.75
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2 1/2 x 1/3 x 3 find the sum.
Answer:
2 1/2 x 1/3 x 3 = 5/2 or 2 1/2
In+a+recent+poll,+64%+of+the+respondents+supported+stricter+gun+laws.+is+this+an+example+of+statistic+or+a+parameter?
In a recent poll, 64% of the respondents supported stricter gun laws is statistic.
What is an example of a parameter?
To describe the entire population under study, a parameter is utilized. For instance, we are interested in learning the typical length of a butterfly. This information about the total butterfly population makes it a parameter.What is an example of a population parameter?
A parameter is a descriptive measure applied to a whole population. Numerous population parameters exist. For instance, the population size (N) is one parameter, while other parameters that relate to continuous variables are the population's mean diastolic blood pressure or mean body weight.Learn more about population parameter
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Simplify completely:
(c^-6 d^4)^1/2
Answer:
d^2/c^3
Step-by-step explanation:
write problem with negative exponent rule
(1/c^6 d^4)^1/2
combine 1/c^6 & d^4
(d^4/c^6)^1/2
use exponent rules to finish simplifying
d^2/c^3
|2x-5| < 7
How to solve for x?
Answer:
-1 < x < 6
Step-by-step explanation:
|2x - 5| < 7
-7 < 2x - 5 < 7
-2 < 2x < 12
-1 < x < 6
A recipe uses both carrots and onions. The recipe uses 4 times more carrots than onions. If the recipe uses a total of 25 ounces of chopped carrots and onions, how many ounces of onions does the recipe use?
The ounces of onions is 5 ounces.
How to calculate the value?Let the onions be represented by x.
The recipe uses 4 times more carrots than onions. The carrots will be 4 × x = 4x.
Therefore, the equation will be:
4x + x = 25
5x = 25
Divide by 5
x = 25/5
x = 5
Therefore, the ounces of onions is 5 ounces.
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Answer:
Step-by-step explanation:
The ounces of onions is 5 ounces.
The recipe uses 4 times more carrots than onions. The carrots will be 4 × x = 4x.
Therefore, the equation will be:
4x + x = 25
5x = 25
Divide by 5
x = 25/5
x = 5
Therefore, the ounces of onions are 5 ounces.
The number has 2 digits the number has 13 as a factor the sum of the digits is 11
Answer:
65
Step-by-step explanation:
- 2 digits ✅
- Has 13 as a factor ✅
- Sum of digits is 11 ✅
Use the equation of the least-squares regression line and the residual plot to estimate the actual mean weight of the infants when they were 1 month old
The actual mean weight of the infants when they were 1 month old is 4.297
The residual plot doesn't show any obvious leftover pattern, confirming that a linear model is appropriate.
the equation of this line as ˆy=12x−1 with an accent on the y to indicate that the y-values computed using this equation
y = 4.88 + 0.267(1)
y = 5.147
residual = -0.85 = A - 5.147 + 5.147
residual = 4.297
the actual mean weight of the infants when they were 1 month old is 4.297
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Problem B: Mr. Zoetz placed red, blue, and yellow gumballs in his gumball machine. • He placed 253 yellow gumballs in the gumball machine. He placed 98 more yellow gumballs than red gumballs in the gumball machine • He placed 27 fewer blue gumballs than red gumballs in the gumball machine. How many gumballs did Mr. Zoetz place in the gumball machine?
He placed 479 gumballs in the gumball machine.
We are given that Zoetz placed red, blue, and yellow gumballs in his gumball machine.
Now in the gumball machine, we are given that he:
He has placed 253 yellow gumballs.
Now, we are given an expression that the number of red gumballs is 98 less than the yellow ones.
Number of red gumballs = 253 - 98 = 155 gumballs.
Also, another expression says that blue gumballs are 27 less than the red ones.
Number of blue gumballs = 155 - 27 = 128 gumballs.
Total gumballs = 253 + 98 + 128 = 479 gumballs.
Therefore, he placed 479 gumballs in the gumball machine.
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The diagram shows five touching semicircles, each with radius 2. What is the length of the perimeter of the shaded shape? Give your answer in terms of π
The Length of perimeter of the shaded shape is; 24 - 8π
What is the Perimeter of the shaded area?
Let us first find the rectangle measurements that contains the shaded portions.
Width of rectangle = 2 * 4 = 8
Length of rectangle = 2 + 2 = 4
Perimeter of rectangle = 2(8 + 4) = 24 units
Now, let us find the perimeter of all semi circles and quarter circles that fall into into this rectangle region;
Perimeter of semi circles = πr + πr + πr + πr/2 + πr/2 = 4πr
Perimeter of semi circles inside the rectangle = 4π * 2 = 8π
Thus;
Length of perimeter of shaded shape = 24 - 8π
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