Answer:
Approximately $594.38
Step-by-step explanation:
Use the formula: y = a(1 + r)^t
a is the initial amount
r is the percent of interest in decimal form
t is the time in years
y is the money after t years
Substitute the values given in the problem into the equation:
400(1+0.02)^20
Use a calculator or solve manually
Around 594.38
Bret is planning a long hike. He figures that he will need at least 0.75 liters of water for each hour on the trail. He also wants to have 1.8 liters of water in reserve at all times. If he can only carry 9 liters of water maximum, how many hours can he hike?
The number of hours that Bret can hike with 9 liters of water is 9.6 hours.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
As per the given,
Water needed = 0.75 liters per hour
For x number of hours = 0.75x liters
Reserved water = 1.8 liters.
Total water needs for x hours = (0.75x + 1.8)
The number of hours that can be hiked with 9 liters will be as,
(0.75x + 1.8) = 9
x = 9.6 hours.
Hence "The number of hours that Bret can hike with 9 liters of water is 9.6 hours".
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Pls answer quickly, make sure to answer all parts
Find the area of the region bounded by the line y =3x -6 and line y=-2x+8 and
a) the x-axis. b) the y-axis. c) the line y=6. d) the line x=5.
The area of the region bounded by the line y =3x -6 and line y=-2x+8 is 12/5 units
How to find the area?y = 3x - 6
y = -2x + 8
Set these two equations equal to each other.
3x - 6 = -2x + 8
Add 2x to both sides of the equation.
5x - 6 = 8
Add 6 to both sides of the equation.
5x = 14
Divide both sides of the equation by 5.
x = 14/5
Find the y-value where these points intersect by plugging this x-value back into either equation.
y = 3(14/5) - 6
Multiply and simplify.
y = 42/5 - 6
Multiply 6 by (5/5) to get common denominators.
y = 42/5 - 30/5
Subtract and simplify.
y = 12/5
These two lines intersect at the point 12/5. This is the height of the triangle formed by these two lines and the x-axis.
Now let's find the roots of these equations (where they touch the x-axis) so we can determine the base of the triangle.
Set both equations equal to 0.
(I) 0 = 3x - 6
Add 6 both sides of the equation.
6 = 3x
Divide both sides of the equation by 3.
x = 2
Set the second equation equal to 0.
(II) 0 = -2x + 8
2x = 8
x = 4
The base of the triangle is from (2,0) to (4,0), making it a length of 2 units.
The height of the triangle is 12/5 units.
A = 1/2bh
Substitute 2 for b and 14/5 for h.
A = (1/2) · (2) · (12/5)
A = 12/5
The area of the region bounded by the lines y = 3x - 6 and y = -2x + 8 between the x-axis is 12/5 units.
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The number of wrecks at a certain intersection varies directly as the number of cars that travel through the intersection. If there are 31 wrecks when 1,085 cars have traveled through the intersection, how many cars have passed through the intersection after 7 wrecks?
The number of cars that have passed through the intersection is 245.
How many cars passed through the intersection?Direct variation is when two variables move in the same direction. If one variable increases, the other variable increases.
The equation that represents direct variation is; c = wk
Where:
c = number of carsw = number of wrecks k = constant of proportionality1085 = k31
k = 1085 / 31
k = 35
c = 7 x 35
c = 245
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What is the best estimate of the perimeter of the figure on the grid if each square has side lengths of 1 mm?
Answer:
4mm
Step-by-step explanation:
you have to add both sides after substituting each of the 4 sides by 1mm
which gives you the total of 4
Let f(x)=(3)^x−3. What is f(0) in fraction form?
Answer:
1/27
Step-by-step explanation:
We can substitute x=0 into the function to get:
f(0) = 3^(0-3)f(0) = 3^(-3)f(0) = 1/27A building casts a shadow of 40 feet on the ground. A wooden figure of a man is placed on the building and casts a shadow an additional 10 feet beyond the building's shadow. What is the height of the man?\
The height of the man from the given question is; 37.5 ft
How to solve trigonometric ratios?This question will form a triangle where;
Height of building = 30 ft
Height of man = h ft
Initial height of shadow = 40 ft
Additional height of shadow = 10 ft
Using similarity theorem, we have;
h/30 = (40 + 10)/40
h/30 = 5/4
h = (30 * 5)/4
h = 37.5 ft
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What is the following answer to 2+2
Answer:
well the answer is 4 have a good day
Which numbers are irrational???
Answer:
√2/4, √3/4, and √5/4.
Step-by-step explanation:
A rational number is any integer, fraction, terminating decimal, or repeating decimal.
what is the value of the rational expression below when is equal to 5?
15-(5)/5-10=10/-5=-2 hope it helps!
a and b are positive integers and 7a+ 5b= 49. Find the values of a and b.
3.1 What is a?
2 What is b?
Answer:
B = 49/5 - 7a/5
A = = -5b/7 + 7
Step-by-step explanation:
Given that,
7a+ 5b= 49
Solution:
Solving for a:
Add -5b to both sides:
[tex]7a+5b - 5b=49 - 5b[/tex][tex]7a = - 5b + 49[/tex]Divide both sides by 7:
[tex] \cfrac{7a}{7} = \cfrac{ - 5b + 49}{7} [/tex][tex]a = \cfrac{ - 5b}{7} + 7[/tex]Hence,a = -5b/7 + 7.
Solving for b:
Add -7a to both sides:
[tex]7a+5b+( - 7a)=49+(−7a)[/tex][tex]7a + 5b - 7a = 49 - 7a[/tex][tex]5b = 49 - 7a[/tex]Divide both sides by 5:
[tex] \cfrac{5b}{5} = \cfrac{49 - 7a}{5} [/tex][tex]b = \cfrac{49}{5} - \cfrac{7a}{5} [/tex]Hence,b = 49/5 - 7a/5.
if the figure forms the base of a right solid 110 centimeters high, find the surface area
Answer:
60200 cm^2
Step-by-step explanation:
I believe I've answered this question on another post: https://brainly.com/question/27987703
please help! due very soon!
Answer:
{x | x = -6, -1, 0, 3}
(first option listed)
Step-by-step explanation:
The domain of a function is all possible x-values for that function
So, we can see (from the x-value portion of our table) that the possible x-values are:
-6 , -1, 0, and 3
We write domain and range in lowest - highest number value order, so we write our domain as such:
{x | x = -6, -1, 0, 3}
{range is all possible y-values, and this would include -7 , 1, 9, and -2}
hope this helps!!
find the area for this pls
Answer:
Area = 3.36 in²
Step-by-step explanation:
[tex]Area\space\ of \space\ trapezium = \frac{a \space\ + \space\ b}{2} h[/tex] ,
where a and b are the two parallel sides, and h is the height.
[tex]Area = \frac{1.3 \space\ + \space\ 3.5}{2} (1.4)\\\\Area = 3.36 \space\ in^{2}[/tex]
how many lines of symmetry does the following figure have ?
Answer:
1
Step-by-step explanation:
It has only 1 line of symmetry. The line is a vertical line that passes through the top vertex.
Answer: 1
The function below has at least one rational zero.
Use this fact to find all zeros of the function.
f(x)=7x³ +9x²-12x-4
Answer:
Using the rational root theorem, we know to divide the function by (x - 1).
(7x³ + 9x² - 12x - 4) / (x - 1) = 7x^2 + 16x + 4
Now we can further factorize 7x^2 + 16x + 4 into (7x + 2) and (x + 2).
Therefore, the original function can be rewritten as (x - 1) (7x + 2) (x + 2).
Using the factorized form above, the zeros of the function are 1, -2/7, and -2.
A cone has a volume of 350 cubic meters. The area of the base is 70 square meters. What is the height of the cone? Show work
Answer: The height is 15
Step-by-step explanation:
Vcone = pi * r^2 * h / 3
Area of the base = pi*r^2 = 70 so...
350 = 70 * h / 3
350 = (70/3) * h multiply both sides by 3/70
350 (3/70) = h = 15 m
A camper lights an oil lantern at 12 noon and lets it burn continuously. Once the lantern is lit, the lantern burns oil at a constant rate each hour. At 2 p.m., the amount of oil left in
the lantern is 63 ounces. At 5 p.m., the amount of oil left in the lantern is 61 ounces.
Based on the average rate of oil burning per hour, how much oil, in ounces, was in the
lantern at 12 noon?
SHOW WORK!
Answer:
09
Step-by-step explanation:
09
Unit rate is the quantity of an amount of something at a rate of one of another quantity.
The rate at which the oil burns.
1 hour = 2/3 ounce
At 12 noon = 193/3 = 64.33 ounces
At 2 pm = 63 ounces
At 5 pm = 61 ounces
The amount of oil at 12 noon is 64.33 ounces.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
A camper lights an oil lantern at 12 noon and lets it burn continuously. Once the lantern is lit, the lantern burns oil at a constant rate each hour.
At 2 p.m., the amount of oil left in the lantern is 63 ounces.
At 5 p.m., the amount of oil left in the lantern is 61 ounces.
This means,
Amount of oil burnt in the lantern from 2 pm to 5 pm.
= 63 ounces - 61 ounces
= 2 ounces
Now,
3 hours = 2 ounces
2 hours = 1.33 ounces
1 hour = 0.67 ounces
Now,
The number of hours from 12 noon to 2 pm.
= 2 hours
So,
The amount of oil at 12 noon.
= 63 + 4/3
= (189 + 4) / 3
= 193/3 ounces
Thus,
The amount of oil at 12 noon is 65 ounces.
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the answer to this asap please!
The required work done is 62400 J.
work done to lift a 1500 N object from the ground to the top of a 40 m building if the cable weighs 3 N per m
work done, is define as the product of force and displacement.
since,
work done to lift 1500N to height of 40 m is:
W= FS
= 1500 x 40 = 60000J
now work done for rope
is given by
w = mgΔx(40-x)
w= [tex]\int _0^{40}\left mg(40-x\right)dx[/tex]
w=[tex]3\int _0^{40}\left(40-x\right)dx[/tex]
w= 3[tex][40x-x^2/2]\left \{ {{40} \atop {0}} \right.[/tex]
w= 3[1600-800]
w = 2400
Total work done for lifting 1500N to 40m height
= 6000+2400=62400J
Thus the required work done to lift 1500N weight to 40m is 62400J.
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Which of the following is the graph of y = -2√x-3+2?
I presume you meant [tex]y=-2\sqrt{x-3}+2[/tex].
The graph is shown in the attached image.
16 Let f(x) and g ) are function such that f () = x+5 and g(x) x+4, what is domain of f(x)+g(x)?
Answer: all real numbers
Step-by-step explanation:
I assume you meant to write:
Let f(x) and g(x) be functions such that f(x) = x+5 and g(x) = x+4. What is domain of f(x)+g(x)?[tex]f(x)+g(x)=(x+5)+(x+4)=2x+9[/tex]
Since this is a linear function, the domain is all real numbers.
If a participant skips hard to answer questions in a survey, it causes
A.nonadherent bias
B.sampling bias
C.response bias
D.nonresponse bias
E.researcher bias
Answer:
I think non response bias because response bias includes answering incorrectly on a survey to get it over with so that is my answer
Step-by-step explanation:
Assume that a procedure yeilds a binomial with n trial and the probability of success for one trial is p. Use the given values of n and p to find the mean and standard deviation. Also, use the range rule of thumb to find the minimum usual value mean -2standard deviation and the maximum usual value mean + 2 standard deviation n=1490,p=2/5
The value of minimum usual value is, [tex]\mu-2\sigma=-119.2[/tex]
The value of maximum usual value is, [tex]\mu+2\sigma=1311.2[/tex]
Given the values of the parameters of Binomial Distribution are,
Total number of trials (n) = 1490
probability of success in one trial is (p) = 2/5
The probability of failure in on trial is given by,
[tex]q=1-p=1-\frac{2}{5}=\frac{5-2}{5}=\frac{3}{5}[/tex]
For Binomial distribution we know that,
Mean [tex](\mu)=np=1490\times\frac{2}{5}=596[/tex]
and Standard Deviation [tex](\sigma)=\sqrt{npq}=\sqrt{1490\times\frac{2}{5}\times\frac{3}{5}}=357.6[/tex]
Now, calculating the required measurement we get,
The minimum usual value is given by,
Mean -2 Standard Deviation [tex]=\mu-2\sigma=596-2\times357.6=-119.2[/tex]
The maximum usual value is given by,
Mean + 2 Standard Deviation [tex]=\mu+2\sigma=596+2\times357.6=1311.2[/tex]
Hence the minimum and maximum usual values are -119.2 and 1311.2 respectively.
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Larry Mitchell invested part of his $36,000 advance at 7% annual simple interest and the rest at 2% annual simple interest. If his total yearly interest from both
accounts was $1,970, find the amount invested at each rate.
The amount invested at 7% is $
The amount invested at 2% is $
The amount invested at each rate
Investment at 7% = $25000
Investment at 2% = $11,000
What is investment?Investment definition is an asset acquired or invested in to build wealth and save money from the hard earned income or appreciation.
Given:
Larry Mitchell invested = $36,000 at 7% annual simple interest
the rest at 2% annual simple interest.
Total investment = 36000
let the investment at 7% is x
then, invested at 2% = 36000 - x
Total interest earned = $1,970
Simple interest = principal * rate * time
Investment at 4%:
(x * 0.07) + [(36000 - x) * 0.02] = 1970
0.07x + 720 - 0.02x= 1970
0.05x = 1970-720
0.05x = 1250
x= 25000
Hence,
Investment at 7% = $25000
Investment at 2% = $36,000 - $25000 = $11,000
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the table shows the length of time in hours ,some children spent watching tv last week
The histogram of the distribution plotted on the y - axis and the interval for the length of time on the x - axis is attached below.
How to denote the histogram?The first bar denotes the length of time between 0 and 10 having a frequency of 8. The second bar denoted the interval between 10 and 15 with a frequency of 15
The third bar denoted the interval between 15 and 20 with a frequency of 10. The fourth bar denoted the interval between 20 and 30 with a frequency of 11
Therefore, the histogram of the distribution is attached below.
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Evaluate.
-|a+b| 2-c when a=1 2/3 b=-1 ,and c= -3 Enter your answer as a simplified fraction in the box.
Step-by-step explanation:
-| 12/3 - 1| 2-(-3)
-|12-3/3|5
-5|9/3|
-5|3|
-5×3 & -5×-3
-15 & 15
I think it is the answer
John is buying a new car. The value of one car he is considering is $20,000. The value of the car as it ages can be modeled by the function V = 20 , 000 ( 0 . 84 ) t , where t is the number of years from the time of purchase. One of the factors John is using to make his decision is the value of the car over time until it reaches half its original value. What values of domain are reasonable for the given function in this context?
A. all real numbers greater than or equal to 0 and less than 2.8
B. all real numbers greater than or equal to 10,000 and less than or equal to 20,000
C. all real numbers greater than or equal to 0
D. all real numbers greater than or equal to 0 and less than 4
Option D is the correct answer.
All real numbers greater than or equal to 0 and less than 4.
What is Domain?The domain of a function is the set of its possible inputs, i.e., the set of input values where for which the function is defined.
Here, The function of the car value is given as:
V(x) = 20000 X (0.84)ˣ
When the car reaches half its value, we have:
V(x) = 10000
Substitute V(x) = 10000 in V(x) = 20000 * (0.84)ˣ
10000 = 20000 X (0.84)ˣ
Divide both sides by 20000
0.84ˣ = 0.5
Take the logarithm of both sides
x log(0.84) = log(0.5)
Divide both sides by log(0.84)
x = 4
This means that the maximum value of x is 4.
Thus, all real numbers greater than or equal to 0 and less than 4.
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Which of the following equations would correspond to a conic section formed when a plane intersects a cone parallel to the base?
x2 + y2 = 32
x squared over 2 squared plus y squared over 3 squared equals 1
x2 = 8y
x squared over 2 squared minus y squared over 3 squared equals 1
The equation of the circle, ellipse, and hyperbola will be x² + y² = 3², x² + y² / 3² = 1, and x² / 2² - y² / 3² = 1, respectively.
What is the conic section?The curve that is derived from the section of the cone is known as conic section.
The following equations are given below.
x² + y² = 3², this is the equation of the circle.
x² + y² / 3² = 1, this is the equation of the ellipse.
x² / 2² - y² / 3² = 1, this is the equation of the hyperbola.
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Find domain and range of
f(x) = -x2 - 4x + 2
Answer:
domain is all reals
Step-by-step explanation:
sorry I couldn't find the range
1) Suppose the heights of 18-year-old men are approximately normally distributed, with mean 71 inches and standard deviation 5 inches.
a)
What is the probability that an 18-year-old man selected at random is between 70 and 72 inches tall? (Round your answer to four decimal places.)
b)
If a random sample of twenty-six 18-year-old men is selected, what is the probability that the mean height x is between 70 and 72 inches? (Round your answer to four decimal places.)
c)
Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this?
!) The probability in part (b) is much higher because the mean is larger for the x distribution.
!!) The probability in part (b) is much lower because the standard deviation is smaller for the x distribution.
!!!) The probability in part (b) is much higher because the standard deviation is smaller for the x distribution.
!!!!) The probability in part (b) is much higher because the mean is smaller for the x distribution.
!!!!!) The probability in part (b) is much higher because the standard deviation is larger for the x distribution.
2) Let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12 hour fast. Assume that for people under 50 years old, x has a distribution that is approximately normal, with mean = 66 and estimated standard deviation = 45. A test result x < 40 is an indication of severe excess insulin, and medication is usually prescribed.
a)
What is the probability that, on a single test, x < 40? (Round your answer to four decimal places.)
b)
Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x? Hint: See Theorem 6.1.
!) The probability distribution of x is approximately normal with x = 66 and x = 45.
!!) The probability distribution of x is approximately normal with x = 66 and x = 22.50.
!!!) The probability distribution of x is approximately normal with x = 66 and x = 31.82.
!!!!) The probability distribution of x is not normal.
c) What is the probability that x < 40? (Round your answer to four decimal places.)
d) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)
e) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.)
f) Compare your answers to parts (a), (b), (c), and (d). Did the probabilities decrease as n increased?
Yes
NO
g) Explain what this might imply if you were a doctor or a nurse.
!) The more tests a patient completes, the weaker is the evidence for lack of insulin.
!!) The more tests a patient completes, the stronger is the evidence for lack of insulin.
!!!) The more tests a patient completes, the weaker is the evidence for excess insulin.
!!!!) The more tests a patient completes, the stronger is the evidence for excess insulin.
Answer:
Suppose the heights of 18-year-old men are approximately normally distributed, with mean 71 inches and standard deviation 4 inches.
(a) What is the probability that an 18-year-old man selected at random is between 70 and 72 inches tall? (Round your answer to four decimal places.)
z1 = (70-71)/4 = -0.25
z2 = (72-71/4 = 0.25
P(70<X<72) = p(-0.25<z<0.25) = 0.1974
Answer: 0.1974
(b) If a random sample of thirteen 18-year-old men is selected, what is the probability that the mean height x is between 70 and 72 inches? (Round your answer to four decimal places.)
z1 = (70-71)/(4/sqrt(13)) = -0.9014
z2 = (72-71/(4/sqrt(13)) = 0.9014
P(70<X<72) = p(-0.9014<z<0.9014) = 0.6326
Answer: 0.6326
please mark me the brainiest
Help me please, geometry
Answer:
x = 19.5 (nearest tenth)
Step-by-step explanation:
Trigonometric ratios
[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angle
O is the side opposite the angleA is the side adjacent the angleH is the hypotenuse (the side opposite the right angle)Use the cos ratio to find the measure of the altitude (the perpendicular drawn from the vertex of the triangle to the opposite side):
[tex]\implies \cos(47^{\circ})=\dfrac{a}{18}[/tex]
[tex]\implies a=18\cos(47^{\circ})[/tex]
Now use the sin ratio to the the measure of side x:
[tex]\implies \sin(39^{\circ})=\dfrac{a}{x}[/tex]
[tex]\implies x=\dfrac{a}{\sin(39^{\circ})}[/tex]
[tex]\implies x=\dfrac{18\cos(47^{\circ})}{\sin(39^{\circ})}[/tex]
[tex]\implies x=19.50671018[/tex]
Therefore, x = 19.5 (nearest tenth)
