Answer:
2700 years
Step-by-step explanation:
The exponential function for the fraction remaining is ...
r(t) = (1/2)^(t/5730)
where r is the remaining fraction and t is the time in years. We can solve for t to get ...
log(r) = (t/5730)log(1/2)
t = 5730·log(r)/log(1/2)
For the given r=0.72, the age of the artifact is estimated to be ...
t = 5730·log(0.72)/log(0.5) ≈ 2700 . . . years
point estimate A sample of 81 observations is taken from a normal population with a standard deviation of 5. The sample mean is 40. Determine the 95% confidence interval for the population mean
Answer:
The 95 percent Confidence Interval is for the population is (38.911 , 41.089)
Step-by-step explanation:
To solve the above question, we would be making use of the confidence interval formula:
Confidence Interval = Mean ± z score × σ/√n
In the above question,
Mean = 40
σ = Standard deviation = 5
n = number of samples = 81
Confidence Interval = 95%
The z score for a 95% confidence interval = 1.96
Therefore, the confidence interval =
= 40 ± 1.96 (5/√81)
= 40 ± 1.96(5/9)
= 40 ± 1.0888888889
Confidence Interval
a)40 + 1.0888888889
= 41.0888888889
Approximately = 41.089
b ) 40 - 1.0888888889
= 38.911111111
Approximately = 38.911
Therefore, the 95 percent Confidence Interval is for the population is (38.911 , 41.089)
What's the simplified expression of -2a-3 bº?
Answer:
-2a - 3
Step-by-step explanation:
bº equals 1 due to the zero exponent.
Thus, -2a-3 bº simplifies to -2a - 3.
Answer:
−2/a^3
Step-by-step explanation:
The average person lives for about 78 years. Does the average person live for at least 1,000,000, minutes? (Hint: There are 365 days in each year, hours in 24 each day, and 6o minutes in each hour.)
Answer:
YES
Step-by-step explanation:
1 million minutes = 1.9 years
An average man can live upto 78 years.
So, an average man can easily live upto 1,000,000.
Answer:
There will be (365 x 24 x 60) minutes each year.
and that is 525600.
and 525600 x 78 is 40,996,800.
so, It is definitely more than 1 million minutes.
Hop it helps!
Bye!
A population culture begins with 20 strands of bacteria and then doubles every 4 hours. This can be modeled by , where t is time in hours. How many strands of bacteria are present at 20 hours?
Question 13 options:
A)
425 strands of bacteria
B)
567 strands of bacteria
C)
640 strands of bacteria
D)
375 strands of bacteria
Answer:
C) 640 strands of bacteria
Step-by-step explanation:
We are told in the question that the population doubles every 4 hours
Hence, formula to solve this question =
P(t) = Po × 2^t/k
From the question, we have the following information:
Beginning amount (Po) = 20 strands of bacteria
Rate(k) = 4 hours
Time(t) = 20 hours
Ending time (P(t)) = unknown
Ending amount = 20 × 2^20/4
= 20 × 2^5
= 20 × 320
= 640 strands of bacteria.
Therefore, the number of strands left after 20 hours is 640 strands of bacteria.
For an experiment with 3 groups of 10 participants in each group. Fcrit for alpha 0.05=_________
a. 3.35
b. 2.35
c. 5
d. 12
Answer:
a. 3.35
Step-by-step explanation:
Given that :
an experiment with 3 groups consist of 10 participant in each group.
This implies that:
number of group k = 3
number of participants n = 10
N = nk
N = 10 × 3 = 30
The degree of freedom within can be calculate as:
dfw = N - k
dfw = 30 - 3
dfw = 27
The degree of freedom for the critical value
dfc = n- 1
dfc = 3 - 1
dfc = 2
At the level of significance ∝ = 0.05
The F critical value from the standard normal F table
i.e
[tex]F_{critical { (2, 27)}=[/tex] 3.35
The given line segment has a midpoint at (-1, -2).
What is the equation, in slope-intercept form, of the
perpendicular bisector of the given line segment?
ch
4
3
O y=-4x - 4
O y = -4x - 6
O y=x-4
2
1
х
5 4 -3 -2 -11
61,-2)
Oy=+x-6
234
(3.-1).
-3
(-5, 3)
w5
Answer:
y = -4x -6
Step-by-step explanation:
The given segment has a rise if 1 for a run of 4, so a slope of ...
m = rise/run = 1/4
The desired perpendicular has a slope that is the negative reciprocal of this:
m = -1/(1/4) = -4
A point that has a rise of -4 for a run of 1 from the given midpoint is ...
(-1, -2) +(1, -4) = (0, -6) . . . . . . . the y-intercept of the bisector
So, our perpendicular bisector has a slope of m=-4 and a y-intercept of b=-6. Putting these in the slope-intercept form equation, we find the line to be ...
y = mx +b
y = -4x -6
The equation of the line in slope intercept form is y = -4x -6
What is a linear equation?A linear equation is in the form:
y = mx + b
Where y,x are variables, m is the rate of change and b is the y intercept.
Two lines are perpendicular of the product of the slope is -1
The line passes through the point (-5, -3) and (3, -1). Hence:
Slope = (-1 - (-3)) / (3 - (-5)) = 1/4
The slope of the line perpendicular to this line is -4 (-4 * 1/4 = -1).
The line passes through (-1, -2), hence:
y - (-2) = -4(x - (-1))
y + 2 = -4(x + 1)
y = -4x -6
The equation of the line in slope intercept form is y = -4x -6
Find out more on linear equation at: https://brainly.com/question/14323743
* 2. Use digits and other symbols to write "One hundred one thousand is
greater than one thousand, one hundred."
Answer:
101,000>1,100
Step-by-step explanation:
101,000>1,100
Answer:
101,000>1,100
Step-by-step explanation:
What is the volume of a cube with side lengths that measure 8 cm?
Answer: 512 cm³
Explanation: Since the length, width, and height of a cube are all equal,
we can find the volume of a cube by multiplying side × side × side.
So we can find the volume of a cube using the formula v = s³.
In the cube in this problem, we have a side length of 8 cm.
So plugging into the formula, we have (8 cm)³
or (8 cm)(8 cm)(8 cm), which is 512 cm³.
So the volume of the cube is 512 cm³.
Answer:512[tex]cm^{3}[/tex]
Step-by-step explanation:
All sides are equal. Hence, volume =[tex]l^{3} = 8^{3} =512cm^{3}[/tex]
How does the multiplicity of a zero affect the graph of the polynomial function?
Select answers from the drop-down menus to correctly complete the statements
The zeros of a ninth degree polynomial function are 1 (multiplicity of 3), 2, 4, and 6 (multiplicity of 4).
The graph of the function will cross through the x-axis at only
The graph
will only touch (be tangent to) the x-us at
the x-axis
At the zero of 2, the graph of the function will choose...
Answer:
Step-by-step explanation:
Let the equation of a polynomial is,
[tex]y=(x-a)^2(x-b)^1(x-c)^3[/tex]
Zeroes of this polynomial are x = a, b and c.
For the root x = a, multiplicity of the root 'a' is 2 [given as the power of (x - a)]
Similarly, multiplicity of the roots b and c are 1 and 3.
Effect of multiplicity on the graph,
If the multiplicity of a root is even then the graph will touch the x-axis and if it is odd, graph will cross the x-axis.
Therefore, graph will cross x -axis at x = b and c while it will touch the x-axis for x = a.
In this question,
The given polynomial is,
[tex]y=(x-1)^3(x-2)^1(x-4)^1(x-6)^4[/tex]
Degree of the polynomial = 3 + 1 + 1 + 4 = 9
The graph of the function will cross through the x-axis at x = 1, 2, 4 only, The graph will touch to the x-axis at 6 only.
At the zero of 2 , the graph of the function will CROSS the x-axis.
Which expression is the factored form of x2-7x+10
Answer:
[tex]\boxed{ (x - 2)(x - 7)}[/tex]
Step-by-step explanation:
Hey there!
To factor,
[tex]x^2-7x+10[/tex]
We need 2 numbers that multiply to get 10 and add to get -7 which is,
-2 and -5.
-2*-5 = 10
-2x + -5x = -7x
x*x=x^2
Factored - (x - 2)(x - 7)
Hope this helps :)
Please help me. What is the y intercept of the graph shown below?
Answer:
(0,2)
Step-by-step explanation:
the point where Oy intercepts the graph has x=0 and y= f(0)
so this is (0,2)
Find the missing side or angle.
Round to the nearest tenth.
Answer:
[tex] b = 2.7 [/tex]
Step-by-step explanation:
Given:
< C = 53°
< B = 80°
a = 2
Required:
Find b
Solution:
The question given suggests we are given measures for a ∆.
To find side b, which corresponds to angle B, first, we'd find angle A, which corresponds to side a, then apply the Law of sines to find side b.
=> A = 180 - (53 + 80) = 47°
Law of Sines: [tex] \frac{a}{sin(A} = \frac{b}{sin(B} [/tex]
Plug in the values into the formula
[tex] \frac{2}{sin(47} = \frac{b}{sin(80} [/tex]
Cross multiply
[tex] 2*sin(80) = b*sin(47) [/tex]
Divide both sides by sin(47) to make b the subject of formula
[tex] \frac{2*sin(80)}{sin(47} = b [/tex]
[tex] 2.69 = b [/tex]
[tex] b = 2.7 [/tex] (nearest tenth)
Solve for 2 in the diagram below.
120°
32°
T=
Step-by-step explanation:
Hello, there!!!
It's so simple here,
Here,
we have is 1 angle is 120°and other is 3x°.
now,
3x°=120° {because when two st.line intersects eachother then the opposite angle formed are equal}
so, 3x°=120
or, x=120°/3
=40°
Therefore, the value of x is 40°.
Hope it helps....
Geometry pls help !!! Find the value of AB.
AB = [?]
Answer:
AB = 16 Units
Step-by-step explanation:
In the given figure, CD is the diameter and AB is the chord of the circle.
Since, diameter of the circle bisects the chord at right angle.
Therefore, AE = 1/2 AB
Or AB = 2AE...(1)
Let the center of the circle be given by O. Join OA.
OA = OD = 10 (Radii of same circle)
Triangle OAE is right triangle.
Now, by Pythagoras theorem:
[tex] OA^2 = AE^2 + OE^2 \\
10^2 = AE^2 + 6^2 \\
100= AE^2 + 36\\
100-36 = AE^2 \\
64= AE^2 \\
AE = \sqrt{64}\\
AE = 8 \\
\because AB = 2AE..[From \: equation\: (1)] \\
\therefore AB = 2\times 8\\
\huge \purple {\boxed {AB = 16 \: Units}} [/tex]
Simplify cube root of 7 over fifth root of 7. 7 to the power of one fifth 7 to the power of eight fifteenths 7 to the power of five thirds 7 to the power of two fifteenths
Answer:
[tex]\huge\boxed{7^{\frac{2}{15}}}[/tex]
Step-by-step explanation:
[tex]\dfrac{\sqrt[3]7}{\sqrt[5]7}\qquad\text{use}\ a^\frac{1}{n}=\sqrt[n]{a}\\\\=\dfrac{7^\frac{1}{3}}{7^\frac{1}{5}}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\=7^{\frac{1}{3}-\frac{1}{5}}\qquad\text{find the common denominator (15)}\\\\=7^{\frac{(1)(5)}{(3)(5)}-\frac{(1)(3)}{(5)(3)}}=7^{\frac{5-3}{15}}=7^{\frac{2}{15}}[/tex]
Answer:
D. 7 to the power of two fifteenths
Step-by-step explanation:
Which of the following could be the equation of the line passing through (8, 3) parallel to y = -2.
Answer:
y = 3 passes through (8, 3) and is therefore parallel to y = -2
Step-by-step explanation:
Any line parallel to y = -2 is a horizontal one, and it has the same slope (zero) as does y = -2.
We could invent the horizontal line y = 3 (which comes from the point (8, 3) and surmise that it is parallel to the given line y = -2.
Thus, y = 3 passes through (8, 3) and is therefore parallel to y = -2.
In the future, please share any answer choices that are give you. Thank you.
A certain animal's body temperature has a mean of F and a standard deviation of F. Convert the given temperatures to z scores.
A certain animal's body temperature has a mean of 94.72° F and a standard deviation of 0.57°F. Convert the given temperatures to z scores.
a. 93.52 °F b. 95.22 °F c. 94.72 °F
Answer:
a. z = - 2.1053
b. z = 0.87719
c. z = 0
Step-by-step explanation:
Given that :
The population mean μ = 94.72
The standard deviation σ = 0.57
the formula for calculating the standard normal z score, which can be represented as:
[tex]z= \dfrac{\overline x - \mu}{\sigma}[/tex]
For a.
The sample mean [tex]\bar x[/tex] = 93.52
The z score can be computed as follows:
[tex]z= \dfrac{\overline x - \mu}{\sigma}[/tex]
[tex]z= \dfrac{93.52 - 94.72}{0.57}[/tex]
[tex]z= \dfrac{-1.2}{0.57}[/tex]
z = - 2.1053
For b.
The sample mean [tex]\bar x[/tex] = 95.22
[tex]z= \dfrac{\overline x - \mu}{\sigma}[/tex]
[tex]z= \dfrac{95.22 - 94.72}{0.57}[/tex]
[tex]z= \dfrac{0.5}{0.57}[/tex]
z = 0.87719
For c.
The sample mean [tex]\bar x[/tex] = 94.72
[tex]z= \dfrac{\overline x - \mu}{\sigma}[/tex]
[tex]z= \dfrac{94.72 - 94.72}{0.57}[/tex]
[tex]z= \dfrac{0}{0.57}[/tex]
z = 0
Find the solution of the system of equations.
2x – 10y = -28
-10x + 10y = -20
GbA
Answer:
(6, 4 )
Step-by-step explanation:
Given the 2 equations
2x - 10y = - 28 → (1)
- 10x + 10y = - 20 → (2)
Adding (1) and (2) term by term eliminates the term in y, that is
- 8x = - 48 ( divide both sides by - 8 )
x = 6
Substitute x = 6 into either of the 2 equations and evaluate for y
Substituting into (1)
2(6) - 10y = - 28
12 - 10y = - 28 ( subtract 12 from both sides )
- 10y = - 40 ( divide both sides by - 10 )
y = 4
Solution is (6, 4 )
A spinner has five congruent sections, one each of blue, green, red, orange, and yellow. Yuri spins the spinner 10 times and records his results in the table. A 2-column table has 5 rows. The first column is labeled Color with entries blue, green, red, orange, yellow. The second column is labeled Number with entries 1, 2, 0, 4, 3. Which statements are true about Yuri’s experiment? Select three options. The theoretical probability of spinning any one of the five colors is 20%. The experimental probability of spinning blue is One-fifth. The theoretical probability of spinning green is equal to the experimental probability of spinning green. The experimental probability of spinning yellow is less than the theoretical probability of spinning yellow. If Yuri spins the spinner 600 more times and records results, the experimental probability of spinning orange will get closer to the theoretical probability of spinning orange.
Answer:
A. The theoretical probability of spinning any one of the five colors is 20%.
C. The theoretical probability of spinning green is equal to the experimental probability of spinning green.
E. If Yuri spins the spinner 600 more times and records results, the experimental probability of spinning orange will get closer to the theoretical probability of spinning orange.
These are the answers on edg 2020, just took the test.
Step-by-step explanation:
Answer:
a, c, e,
Step-by-step explanation:
:)
Write down the name of the shape for question D. Please help!
Step-by-step explanation:
thats shape is a delta
:)
Answer:
arrow head
Step-by-step explanation:
What is the equation of the line of best fit for the following data? Round the
slope and y-intercept of the line to three decimal places.
Answer:
the line of best fit can be approximated to:
y = -1.560 x + 22.105
Step-by-step explanation:
You are most likely expected to use a graphing tool are statistical program to calculate this. So enter the list of x-values separate from the list of y values and run the tool in linear regression mode.
Look at the attached image with the actual results including the line of best fit.
The equation can be written (rounding slope and y-intercept to 3 decimals) as:
y = -1.560 x + 22.105
Given a right triangle with a hypotenuse of 6 cm and a leg of 4cm, what is the measure of the other leg of the triangle rounded to the tenths?
Answer:
4.5 cm
Step-by-step explanation:
a^2+b^2=c^2
A represents the leg we already know, which has a length of 4 cm. C represents the hypotenuse with a length of 6 cm:
4^2+b^2=6^2, simplified: 16+b^2=36
subtract 16 from both sides:
b^2=20
now find the square root of both sides and that is the length of the other leg.
sqrt20= 4.4721, which can be rounded to 4.5
Answer:
4.5 cm
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean Theorem.
[tex]a^2+b^2=c^2[/tex]
where a and b are the legs and c is the hypotenuse.
One leg is unknown and the other is 4 cm. The hypotenuse is 6 cm.
[tex]a=a\\b=4\\c=6[/tex]
Substitute the values into the theorem.
[tex]a^2+4^2=6^2[/tex]
Evaluate the exponents first.
4^2= 4*4= 16
[tex]a^2+16=6^2[/tex]
6^2=6*6=36
[tex]a^2+16=36[/tex]
We want to find a, therefore we must get a by itself.
16 is being added on to a^2. The inverse of addition is subtraction. Subtract 16 from both sides of the equation.
[tex]a^2+16-16=36-16\\\\a^2=36-16\\\\a^2=20[/tex]
a is being squared. The inverse of a square is a square root. Take the square root of both sides.
[tex]\sqrt{a^2}=\sqrt{20} \\\\a=\sqrt{20} \\\\a=4.47213595[/tex]
Round to the nearest tenth. The 7 in the hundredth place tells us to round the 4 in the tenth place to a 5.
[tex]a=4.5[/tex]
Add appropriate units. In this case, centimeters.
a= 4.5 cm
The length of the other leg is about 4.5 centimeters.
What are two solutions of x
Answer:
Answer is attached below :)
How many dozen (dz) eggs are needed to make 12 muffins ? What about 15.5
muffins? (hint cross out units first)
12muffins
6eggs
lbatch
18muffin
200blueberrie
3batch
x
ldz
X
70blueberries 12eggs
1
Answer:
1 dz to make 12 muffins
1 7/24 dz to make 15.5 muffins
Step-by-step explanation:
How many dozen (dz) eggs are needed to make 12 muffins?
See answer options, we are looking for an option with dz indicated along with the number:
12 muffins 6 eggs 1 batch 18 muffin 200 blueberries s3 batch x 1 dz X 70 blueberries 12 eggs 1The correct option is:
1 dz which is the only one with required unitSo 1 dozen of eggs required for 12 muffins, that is 12 eggs for 12 muffins or 1 egg for 1 muffin or 1/12 dz per muffin
To get 15.5 muffins:
Eggs required 15.5Or in dozens:
15.5*1/12 = 31/24 = 1 7/24 dz(II) Time intervals measured with a stopwatch typically have an uncertainty of about 0.2 s, due to human reaction time at the start and stop moments.What is the percent uncertainty of a hand-timed measurement of (a) 5.5 s, (b) 55 s, (c) 5.5 min?
Answer:
(a) 36.36%
(b) 0.36%
(c) 0.06%
Step-by-step explanation:
Given that the time intervals measured with a stopwatch have an uncertainty of about 0.2 s.
We want to know what is the percent uncertainty of a hand-timed measurement of:
(a) 5.5 s
Percentage = (0.2/5.5) × 100
≈ 36.36%
(b) 55 s
Percentage = (0.2/55)×100
≈ 0.36%
(c) 5.5 min
5.5 min = 5.5 × 60 s
= 330 s
Percentage = (0.2/330)×100
≈ 0.06%
Which cross-sectional shapes do you find the most surprising? Which shapes do you find the least surprising? Explain why.
Answer:
I was surprised that a plane parallel to the vertical axis creates a rectangular cross-section. I guess I was expecting to always see a circle or a circular shape in the cross-section, not purely straight edges as seen in a rectangle.
Step-by-step explanation:
edmentum answer
Answer:
The circles were the least surprising because the base of the cone is a circle. The curves that look like bent rods were the most surprising because I have not seen geometric figures like those before.
Step-by-step explanation:
Simplify 6m^2-5m-3+3m+4+9m^2
Answer: 15m²-2m+1
Step-by-step explanation:
To simplify, you want to combine like terms.
15m²-2m+1
Answer:
[tex]\huge\boxed{15m^2-2m+1}[/tex]
Step-by-step explanation:
[tex]6m^2-5m-3+3m+4+9m^2\\\\\text{combine like terms}\\\\=(6m^2+9m^2)+(-5m+3m)+(-3+4)\\\\=(6+9)m^2+(-5+3)m+1\\\\=15m^2-2m+1[/tex]
BRAINLIEST
Given that 104 = 10,000, write this in logarithm form.
Answer:
[tex]log_{10}[/tex] 10000 = 4
Step-by-step explanation:
Using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]
Here b = 10, n = 4 and x = 10000, thus
[tex]log_{10}[/tex] 10000 = 4 ← in logarithmic form
that is [tex]10^{4}[/tex] = 10000 ← in exponential form
I need help ASAP THANK YOU
Answer:
174 cm²
Step-by-step explanation:
The figure given is a prism with isosceles trapezoid as base.
Its surface area can be calculating the area of each face that makes up the prism, and summing all together.
There are 6 faces. Their dimensions and areas can be calculated as follows:
2 isosceles trapezium:
It has 2 parallel bases, (a and b), of 4cm and 6cm,
Height (h) = 2.8cm
Area = ½(a+b)*h
Area = ½(4+6)*2.8
Area = ½(10)*2.8 = 5*2.8 = 14 cm²
4 rectangles of different dimensions:
Rectangle 1 (down face): l = 10cm, b = 4cm
Area = 10*4 = 40 cm²
Rectangle 2 and 3 (side faces): l = 10cm, b = 3cm
Area = 2(l*b) = 2(10*3) = 60cm²
Rectangle 4 (top face) = l = 10cm, b = 6cm
Area = 10*6 = 60cm²
Surface area of the figure = 14 + 40 + 60 + 60 = 174 cm²
PLEASE HELP ! (3/5) - 50 POINTS -
Answer:
5
Step-by-step explanation:
Answer:
B
Step-by-step explanation: