Answer:
-7
Step-by-step explanation:
(6^9)(6^x) = 6^2
Taking logarithms to the base 6, we have ...
9 + x = 2
x = -7 . . . . . subtract 9
Answer:
-7
Step-by-step explanation:
1) Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Let x be a random variable that represents the number of milligrams of porphyrin per deciliter of blood. In healthy circles, x is approximately normally distributed with mean μ = 43 and standard deviation σ = 9. Find the following probabilities.
a) x is less than 60
b) x is greater than 16
c) x is between 16 and 60
d) x is more than 60
2)Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of 4.5 millimeters (mm) and a standard deviation of 1.0 mm. For a randomly found shard, find the following probabilities. a) the thickness is less than 3.0 mm
b) the thickness is more than 7.0 mm
c) the thickness is between 3.0 mm and 7.0 mm.
Answer:
1)
a) 0.9706 = 97.06% probability that x is less than 60.
b) 0.9987 = 99.87% probability that x is greater than 16.
c) 0.9693 = 96.93% probability that x is between 16 and 60.
d) 0.0294 = 2.94% probability that x is more than 60.
2)
a) 0.0668 = 6.68% probability that the thickness is less than 3.0 mm.
b) 0.0062 = 0.62% probability that the thickness is more than 7.0 mm
c) 0.9270 = 92.70% probability that the thickness is between 3.0 mm and 7.0 mm.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
1)
We have that [tex]\mu = 43, \sigma = 9[/tex]
a) x is less than 60
This is the pvalue of Z when X = 60.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{60 - 43}{9}[/tex]
[tex]Z = 1.89[/tex]
[tex]Z = 1.89[/tex] has a pvalue of 0.9706
0.9706 = 97.06% probability that x is less than 60.
b) x is greater than 16
This is 1 subtracted by the pvalue of Z when X = 16.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{16 - 43}{9}[/tex]
[tex]Z = -3[/tex]
[tex]Z = -3[/tex] has a pvalue of 0.0013.
1 - 0.0013 = 0.9987
0.9987 = 99.87% probability that x is greater than 16.
c) x is between 16 and 60
This is the pvalue of Z when X = 60 subtracted by the pvalue of Z when X = 16.
From a), Z when X = 60 has a pvalue of 0.9706.
From b), Z when X = 16 has a pvalue of 0.0013
0.9706 - 0.0013 = 0.9693
0.9693 = 96.93% probability that x is between 16 and 60.
d) x is more than 60
This is 1 subtracted by the pvalue of Z when X = 60.
From a), Z when X = 60 has a pvalue of 0.9706.
1 - 0.9706 = 0.0294
0.0294 = 2.94% probability that x is more than 60.
2)
Now [tex]\mu = 4.5, \sigma = 1[/tex]
a) the thickness is less than 3.0 mm
This is the pvalue of Z when X = 3.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3 - 4.5}{1}[/tex]
[tex]Z = -1.5[/tex]
[tex]Z = -1.5[/tex] has a pvalue of 0.0668
0.0668 = 6.68% probability that the thickness is less than 3.0 mm.
b) the thickness is more than 7.0 mm
This is 1 subtracted by the pvalue of Z when X = 7.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{7 - 4.5}{1}[/tex]
[tex]Z = 2.5[/tex]
[tex]Z = 2.5[/tex] has a pvalue of 0.9938.
1 - 0.9938 = 0.0062
0.0062 = 0.62% probability that the thickness is more than 7.0 mm
c) the thickness is between 3.0 mm and 7.0 mm.
This is the pvalue of Z when X = 7 subtracted by the pvalue of Z when X = 3.
From b), Z when X = 7 has a pvalue of 0.9938.
From a), Z when X = 3 has a pvalue of 0.0668
0.9938 - 0.0668 = 0.9270
0.9270 = 92.70% probability that the thickness is between 3.0 mm and 7.0 mm.
The ages of Rohit and James are in the ratio 2 : 5. In 9 years, the ratio of their ages will be 5 : 8. Find their present ages.
Answer:
Step-by-step explanation:
I don't say you have to mark my ans as brainliest but if you think it has really helped you then plz don't forget to thank me...
Answer:
Rohit is 6 years old
James is 15 years old
Step-by-step explanation:
Rohit : James 2 : 5
the difference between their units is 3
Now we add the 9 years
5 : 8the difference between their units should be 3 because they both age every year. the question was nice enough to give to same amount of units
Now we subtract James's original 'unit age' from his new one
8u - 5u = 3 uWe also need to make sure the difference between Rohit's original 'unit age' is 3
5u - 2u = 3uthis 3 units represent the 9 years that have passed
3 units = 9 yearsTo find James's age all we ahve to find is their original unit number
James (5 units) -> 3 × 5 = 15same for Rohit
Rohit (3 units) -> 3×3 = 9hence, Rohit's and James's ages are 9 and 15 respectivelyA television is 28.5 inches wide and 16 inches long.
Using the Pythagorean Theorem, what is the length of the diagonal of the television, rounded to the nearest inch?
Answer:
33 in
Step-by-step explanation:
The Pythagorean theorem tells you ...
diagonal² = length² +width²
diagonal² = (16 in)² +(28.5 in)² = 1068.25 in²
diagonal = √(1068.25 in²) ≈ 32.684 in
The diagonal of the television is about 33 inches.
find the slope of the line passing through the points (6,9) and (6, -1)
Answer:
Undefined
Step-by-step explanation:
M=undefined
Slope = y2-y1 /x2- x1
=9 -(-1). / 6-6
= 10/0 = infinity ; undefined
PLEASE ANSWER ASAP!!!!!!!!! WILL GIVE BRAINLIEST ANSWER!
Rewrite the expression in the form 9^n.
9 . 9^2 =
Answer:
9^3
Step-by-step explanation:
9* 9^2
9*9(9) = 9^3
We could also look at it as
9^1 * 9^2
We know that a^b * a^c = a^(b+c)
9^(1+2) = 9^3
avier is considering two options for college. Option A: Complete the first two years of schooling at a community college and then transfer to a university. Option B: Complete all four years of schooling at the university.
Answer:
kok
Step-by-step explanation:
Write a division word problem for 31 divided by 4 that requires to round up
Answer:
31/4 is 7.75 so you could round up to 7.8 or 4/31 which is. 0.129... and you could round up to 0.13
Word problem:
Mark has 31 Starburst and wants to give them all to his 4 friends. About how many starburst will each friend have. Be sure to round your answer.
Answer:
This is just going to be a word problem so Imma just give you one you can use.
Step-by-step explanation:
Stacy has 31 cookies that she wants to divide for herself and her three other siblings. About how much cookies did each person get?
in the year 2005 a company made $6.6 million in profit for each consecutive year after that their profit increase by 9% how much would a companies profit be in the year 2009 to the nearest 10th of $1 million
Answer:
$9.3 million
Step-by-step explanation:
Given that the company profit increases by 9% yearly from 2005.
Using the exponential growth formula;
A = P(1+r)^(t) .....1
Where;
A = final amount/value of profit
P = initial amount/value = $6.6 million
r = growth rate yearly = 9% = 0.09
t = time of growth in years = 2009 - 2005 = 4 years
Substituting the values;
A = 6.6(1+0.09)^(4)
A = 6.6(1.09)^(4)
A = 9.3164386 million
A = $9.3 million
The companies profit in the year 2009 to the nearest 10th of $1 million is $9.3 million
Carlo buys $14.40 worth of grapefruit. Each grapefruit costs 0.80. (PLz help and yeett) with steps plz
Answer:
a) 18 grapefruits
b) 6 grapefruits
Step-by-step explanation:
a) n = 14.4 / 0.80 = 18 grapefruits
b) n = (14.4 / 3) / 0.8 = 6 grapefruits
The percent markup on a video game is known to be 108% based on cost. If the seller paid $35 for one, then what would be the corresponding percent markup based on the sale price? (Round to the nearest tenth percent)
Answer: 48.1%
Step-by-step explanation:
The percent markup is defined as:
PM = (gross benefit/cost per unit.)*100%
We know that the cost per unit is $35
then we have:
108% = (gross benefit/$35)*100%
gross benefit = (108%/100%)*$35 = $37.8
This means that a game is selled by $35 + $37.8 = $72.8
Now we have:
Markup percent = (gross benefit/selling price)*100% = ($35/$72.8)*100% = 48.1%
What is the value of 4p − 2, when p = 8? 16 24 30 34
Answer:
30
Step-by-step explanation:
Substitute 8 for p.
4(8)-2=
32-2=
30
Answer: 30
Step-by-step explanation: 4p-2
4(8)- 2
32-2
= 30
The amplitude of y= – sin is
b 0
C2
d 1
Answer:
d. 1
Step-by-step explanation:
The amplitude of such a function is the magnitude of the coefficient of the sine function.
|-1| = 1 . . . . the amplitude . . . matches choice D
Please Help With problem 1
Answer:
60
Step-by-step explanation:
To find the volume of a rectangular prism you need to use the formula Base times height or in this case length times-width times height so multiply 5 x 4 x 3 to get your answer
What is the volume, in cubic cm, of a rectangular prism with a height of 19cm, a
width of 16cm, and a length of 8cm?
Answer: 2432
19 x 16 x 8 = 2432
Answer: 2,432 cm³
Step-by-step explanation: To find the volume of a rectangular prism or a prism whose base is a rectangle, we use the formula below.
Volume = length × width × height
Since the rectangular prism has a length of 8 centimeters, a width of 16 centimeters, and a height of 19 centimeters,
we can plug this information into the formula to get
(8 cm)(16 cm)(19 cm).
This gives us 2,432 cm³.
So the volume is 2,432 cm³.
Please help.
Best answer will get brainliest.
Answer:
59.1 for the mean
Step-by-step explanation:
You add all the numbers together and divde it by the amount of numbers there are.
Answer:
Mean= 59.1
Median= 58
Range= 11
Step-by-step explanation:
Mean= Total data/Number of given datas
= 60+58+54+56+63+65+62+59+56+58/10
Mean = 591/10= 59.1
Median= Middle value
= 65, 63, 62, 60, 59, 58, 58, 56, 56, 54
Median= 58
Range= Highest value- Lowest value
= 65-54
Range= 11
ASAP! GIVING BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answer:
x > 5
Step-by-step explanation:
Subtract 7 from both sides, like so:
x + 7 > 12
- 7 - 7
________
x > 5
The diagram above shows
circle ABCD
with Centre E Quadrilateral EADC is a rhombus.
<BAE =<ECB=n and <ABC=m.
find
i) m
ii) n
Answer:
m = 60°n = 30°Step-by-step explanation:
Opposite angles D and E in the rhombus are congruent. The measure of arc ADC is the same as the measure of central angle AEC. The measure of arc ABC is twice the measure of angle AEC, so the measure of arc ABC is twice the measure of arc ADC.
This means that short arcs AB, BC and CA are all 120°. Inscribed angle ABC (angle m) is half that value, or 60°.
Likewise, the angle BAC is 60°. We know that angle EAD is supplementary to angle AEC, so is 180° -120° = 60°. Segment AC bisects this angle, so angle n is 60°/2 = 30° less than angle BAC.
angle m is 60°, angle n is 30°
In Prof. Smith's class, the 11 students had the following scores on the last midterm.
73, 77, 78, 82, 83, 85, 86, 89, 95, 95, 188
Identify all values that are outliers.
If there is more than one outlier, separate them with commas.
If there are no outliers, click on "None".
Answer:
There are no values that are outliers.
The mean temperature for the first 7 days in January was 4 °C.
The temperature on the 8th day was 4 °C.
What is the mean temperature for the first 8 days in January?
Answer:
4 degrees Celsius
Step-by-step explanation:
Since the mean is (total/amount), we can remake this to get That mean*amount=total. For the first 7 days, 4*7=28 for our total, and add that to the 8th day to get 32 for our total. 32/8=4 for our mean for the first 8 days of january
Answer:
Answer:
4 degrees Celsius
Step-by-step explanation:
Since the mean is (total/amount), we can remake this to get That mean*amount=total. For the first 7 days, 4*7=28 for our total, and add that to the 8th day to get 32 for our total. 32/8=4 for our mean for the first 8 days of january
which algebraic expression represents the phrase 14 increased by a number
Answer:
The answer is 14 plus y
Step-by-step explanation:
Number A is correct
I need help on this problem please
Step-by-step explanation:
side ratio = big/small = 28/4 = 7
perimeter ratio = side ratio = 7
-> perimeter ratio = big / small = big/34 = 7
-> big perimeter= 7*34 = 238
"Eat For 10 Hours. Fast For 14. This Daily Habit Prompts Weight Loss, Study Finds"
This is the title of an NPR article about a 2019 study that recruited 19 overweight adults diagnosed with metabolic syndrome (elevated blood sugar, elevated cholesterol levels, high blood pressure). Participants were asked to restrict any eating to a period of just 10 hours each day. The study found a statistically significant reduction in body weight after 12 weeks of this eating pattern.
1. To be able to conclude that a time-restricted eating pattern causes a weight loss in this population on average, we would need to ___________.
O use a much larger sample than what this study used
O collect weight-loss data on all adults, not just adults with metabolic syndrome
O find a significant weight-loss difference for participants that would be randomly assigned to time-restricted eating or regular eating
O collect weight-loss data on the entire population of adults with metabolic syndrome
O make sure that the study found a very small P-value and check that the conditions for inference were all met
Answer:
Option A
Step-by-step explanation:
To conclude that a time-restricted eating pattern causes a weight loss in this population on average, we would need to use a much larger sample than the 19 actually used in the study to get an unbiased conclusion and to also ensure that the sample itself and whatever result produced is a true representation of this particular population itself.
A seabird rescue center has a special habitat for birds that will be released soon. The habitat is shaped like a rectangular prism. The habitat has a ground area of 2,000 square meters that is covered in grass and sand. The height of the habitat is 9 meters. What is the volume of the bird habitat? This is not collage level.
Answer:
18,000 Cubic meters
Step-by-step explanation:
Since volume is lwh and the area of the ground is lw and it gives you the height, You just multiply The area of the ground, 2,000 m, and the height, 9, to find the volume. 9 x 2,000= 18,000.
a cartographer used a scale of 1 inch :300 meters for the heights of different mountains if the actual height of one of those mountains is 3700 meters high. what is the height on the map?
Answer:
[tex]12\frac{1}{3}[/tex] inches
Step-by-step explanation:
So to go from 300 to 3700 you have to multiply by [tex]12\frac{1}{3}[/tex]
An above-ground swimming pool is 5 feet long, 4 feet wide, and 3 feet deep and is shaped like a rectangular prism. A rectangular prism has a length of 5 feet, height of 3 feet, and width of feet. If you use a net to find the amount of material used to make the pool, what faces are included in the calculation?
Answer:
the faces representing the sides and bottom of the pool are included
Step-by-step explanation:
Obviously, there is no pool material covering the top of the pool. Rather, it is "an open-top box", so the area of the faces of the box does not include the area of the top. The five faces other than the top face are included.
Answer:
First answer is 1
Second is 2
Third is 2
Jamie spent $12 dollars a day on food for 6 days. What was Jamie’s overall change in her bank account for food over the 6days?
Answer:
-72
Step-by-step explanation:
12 * 6 = 72
Jaime spent 72 dollars for the 12 days
It went down because the money was spent
-72
what is the number that has the same value as l6l
Answer:6
Step-by-step explanation: Moving two bars to the edge of 6 will result in 6.
A fenced enclosure consists of a rectangle (length L and width 2R) attached to a semicircle with a radius R as pictured below. Note: there is fencing between the rectangular and semi-circular portions. The enclosure is to be built to have a total area (the entire shaded region), A, of 2000 ft2. The cost of the fence is $20/ft for curved sections and $30/ft for straight sections. Analytically (show all of your steps using algebra and calculus in the write up), find the minimum cost to build the fence and the dimensions of the enclosure. Show all equations that you derive and use. This part should be done entirely in the write-up: no coding. It is fine to do this by hand and include a high-resolution picture in the writeup rather than using Equation Editor. Hint: you will need to use two equations in order to find the cost as a function of only R or L. Construct a plot to graphically determine the values of R and L (x-axis) that minimize the total cost (y-axis) of the fence. Using the MIN function, determine the R and L that minimize cost and what that cost is Do your answers in A, B and C all agree? Why or why not?
Answer:
A. $ 6053.44
B. From the graph, R = 21.027 ft and C = $ 5700.005, L = 31.043 ft
The values in A and B do not all agree. This could be due to error in approximations. Their values are close though.
Step-by-step explanation:
A. The area A of the enclosure equals, A = 2RL + πR²/2.
The total cost C = 20 × length of curved section + 30 × length of straight section
C = 20πR + 30[2(L + 2R)]
= 20πR + 60L + 120R
Making L subject of the formula from A,
L = A/2R - πR/4
Substituting L into C, we have
C = 20πR + 60(A/2R - πR/4) + 120R
= 20πR + 30A/R - 15πR + 120R
= 5πR + 30A/R + 120R
We now differentiate C with respect to R to find the value of R for minimum cost
dC/dR = 5π - 60A/R² +120
Equating dC/dR to zero, we have
5π - 60A/R² + 120 = 0
So, R = ±√[60A/(5π + 120)]
substituting A = 2000 ft²
R = ±√[60 × 2000/(5π + 120)] = ±29.74 ft
We take the positive answer, R = 29.74 ft since R cannot be negative.
To determine if this is a minimum point, we differentiate dC/dR with respect to R.
So d²C/dR² = 120A/R³
Since d²C/dR² = 120A/R³ > 0 for positive R, it is a minimum point.
Substituting the value of R into C we have
C = 5πR + 30A/R + 120R
= 5π(29.74) + 30 × 2000/29.74 + 120(29.74)
= 467.155 + 2017.485 + 3568.8
= $ 6053.44
and L = A/2R - πR/4
= 2000/2(29.74) - π(29.74)/4
= 33.625 - 23.356
= 10.269
≅ 10.27 ft
B. From the graph, R = 21.027 ft and C = $ 5700.005, L = 31.043 ft
The values in A and B do not all agree. This could be due to error in approximations. Their values are close though.
5lb 7oz -11oz need help quick
Answer:
76 ounces
Step-by-step explanation:
I'm assuming you meant:
5lb+7oz-11oz=
16 ounces in a pound
5lb+7oz-11oz=
80+7-11=
87-11=
76 ounces
Function f is an increasing exponential function that is negative on the interval (-∞, 2) and positive on the interval (2, ∞). Which could be the graph of function f?
Answer:
An exponential function is a function in the form of f(x) = bx or y = bx (if we wish to express the function in terms of y instead of f(x)), where b > 0, b ≠ 1 and x is a ... the interval (-∞, ∞) is because any real number can be put in for x the function f(x) ... zero and negative numbers are not part of the range is because any positive
Step-by-step explanation: