Step-by-step explanation:
that question is fundamentally wrong.
"appropriate" completely depends on the situation and circumstances.
if we are dealing with a weight that a human can feel, lift and distinguish from other weights without any special tool, then we are usually using kg. because then we humans can "connect" with the case, and deal with every day numbers.
if we are dealing with tiny little quantities like dosages of substances in a pill or other medication, then milligram is more than "appropriate".
because then, as humans, we are still dealing with numbers we can understand. like tens or hundreds.
if we kept kg in such situations, we would have to deal with numbers like 0.000008 kg vs. 0.000021 kg, where we could not see the magnitude of difference right away.
Using a spreadsheet program, create an amortization schedule for a 30-year mortgage of $500,000 at an annual interest rate of 4.23%.
(a)
In which month does the amount of principal in a monthly payment first exceed the amount of interest?
(b)
How much interest is repaid for the term of the loan? (Round your answer to the nearest cent.)
$
(c)
If the loan amount was $750,000 instead of $500,000, would the month in which the amount of principal in a monthly payment first exceeded the amount of interest change?
Yes
No
This exercise requires the ability to create Amortization Schedules Using a Spreadsheet program. Based on the information given about the Amortization of the loan, the principal payable per month became greater than the interest payable per month on the 159th month (given that the loan amount is $500,000.
In which month does the amount of principal in a monthly payment first exceed the amount of interest?The amount of principal in a monthly payment first exceeds the interest payment In 159th Month. The interest on this month is $1, 248.39 while the principal on this month is $1, 205.46.
It is to be noted that when a loan is taken, the constituents of the amounts being paid back is the Principal and part of the interest on the loan.
How do you Calculate Amortization of Loans?The yearly interest rate must be divided by 12.
Your monthly interest rate, for instance, will be 0.3525 percent if your annual interest rate is 4.23 percent (0.0423 annual interest rate x 12 months).
Additionally, you'll add 12 to the number of years remaining on your loan term.
How much interest is repaid for the term of the loan?The total amount of interest that is paid for the term loan is $383,385.54
If the loan amount was $750,000 instead of $500,000, would the month in which the amount of principal in a monthly payment first exceeded the amount of interest change?Yes it would change. It would change to the 165th month. In this month, the interest paid is $1, 834.00 while the principal paid back is $1,846.77. See the attached image for answer C.
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Sahil has a fish tank in the shape of a cuboid, as The tank is 3 cm shown in the diagram. water 55 cm 33 cm 28 cm Diagram M accurately 55 cm long 28 cm wide 33 cm high The surface of the water in the tank is 3 cm below the top of the tank. Sahil is going to put some neon tetra fish in his tank. He must allow 4 litres of water for each of the neon tetra fish he puts in the ta What is the greatest number of neon tetra fish Sahil can put in his tank?
Answer:
9 Sahil has a fish tank in the shape of a cuboid, as shown in the diagram-- Diagram is NOT accurately drawn The tank is
55 cm long
28cm wide
cm 33 high The surface of the water in the tank is 3 cm below the top of the tank. Sahil is going to put some neon tetra fish in his tank. He must allow 4 litres of water for each of the neon tetra fish he puts in the tank. What is the greatest number of neon tetra fish Sahil can put in his tank?
Step-by-step explanation:
Find the value of z such that 0.8664 of the area lies between −z and z. Round your answer to two decimal places.
Using the normal distribution, the value of z is of z = 1.5.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.For this problem, considering the symmetry of the normal distribution, the area above the mean is given by:
0.8664/2 = 0.4332.
Hence z has a p-value of 0.5 + 0.4332 = 0.9332, hence the value of z is z = 1.5.
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18. What is the probability that the student plays football?
(a) 35 /66 (b) 20 /33 (c) 13 /33 (d) 3 /22
The probability that the student plays football is 20/33.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.
The probability that the student plays football = total number of students who play football / total number of students
total number of students who play football = 26 + 3 + 5 + 6 = 40 total number of students = 26 + 3 + 5 + 6 + 9 + 7 + 10= 66The probability that the student plays football = 40/66 = 20/33
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Find an equation of a degree 3 polynomial (in factored form) with the given zeros of f(x): − 3 , 4 , − 3 . Assume the leading coefficient is 1.
f(x) = x³ + 2x² - 15x - 36 is the equation of a degree 3 polynomial (in factored form) with the given zeros of f(x) are − 3 , 4 , − 3 assuming that the leading coefficient is 1. This can be obtained by formula of polynomial function.
Find the required equation:The zeroes or roots of a polynomial function are x values for which f(x) = 0If the zeroes or roots are r₁, r₂, r₃,... then possible polynomial function is⇒ f(x) = a(x - r₁)(x - r₂)(x - r₃)
where a is the leading coefficient
Here in the question it is given that,
Polynomial should be with degree 3zeros of f(x) are − 3 , 4 , − 3By using the formula of polynomial function we get,
⇒ f(x) = a(x - r₁)(x - r₂)(x - r₃)
⇒ f(x) = 1(x - (-3))(x - (4))(x - (-3))
⇒ f(x) = 1(x + 3)(x - 4)(x + 3)
⇒ f(x) = (x + 3)(x² - x - 12)
⇒ f(x) = x³ - x² - 12x + 3x² - 3x - 36
⇒ f(x) = x³ + 2x² - 15x - 36
Hence f(x) = x³ + 2x² - 15x - 36 is the equation of a degree 3 polynomial (in factored form) with the given zeros of f(x): − 3 , 4 , − 3 assuming that the leading coefficient is 1.
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STATISTICS:
Using the research question, "Do certain musical genres impact the task performance of those high in neuroticism?" determine the:
1. Dependent and Independent Variable:
2. Moderator OR Mediator:
The dependent variable here is task performance. The independent variable in the question is musical genres.
What is a dependent variable?This is the term that is used to refer tp the variable that is of interest. It is the variable that one is trying to determine.
The independent variable is the x variable. It is the variable that helps us check the impact that it has on the dependent variable.
The task performance is what we want to know here. To do so we want to use the genre of music.
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Which polygon does not belong with the others?
Question 26: [4 points]
1% of a population have a certain disease and the remaining 99% are free from this disease. A test is used to detect this disease. This test is positive in 95% of the people with the disease and is also (falsely) positive in 2% of the people free from the disease.
If a person, selected at random from this population, has tested positive, what is the probability that she/he has the disease?
Let D be the event "have the disease" and FD be the event "free from the disease" Let the event TP be the event that the "test is positive".
A diagram with all the above information is shown.
[tex]P(D/TP) = \frac{P(D \: n \: TP)}{P(TP)} [/tex]
[tex]P(TP) = P(TP \: n \: D)+P(TP \: n \: FD) \\ P(TP) = 0.95×0.99 + 0.02×0.01 = 0.9407[/tex]
[tex]P(D/TP) = \frac{0.9405}{0.9407} = \frac{9405}{9407} [/tex]≈0.999787
Show that the function f(x)=sin3x + cos5x is periodic and it’s period.
The period of [tex]f(x)[/tex] is [tex]\boxed{2\pi}[/tex].
Recall that [tex]\sin(x)[/tex] and [tex]\cos(x)[/tex] both have periods of [tex]2\pi[/tex]. This means
[tex]\sin(x + 2\pi) = \sin(x)[/tex]
[tex]\cos(x + 2\pi) = \cos(x)[/tex]
Replacing [tex]x[/tex] with [tex]3x[/tex], we have
[tex]\sin(3x + 2\pi) = \sin\left(3 \left(x + \dfrac{2\pi}3\right)\right) = \sin(3x)[/tex]
In other words, if we change [tex]x[/tex] by some multiple of [tex]\frac{2\pi}3[/tex], we end up with the same output. So [tex]\sin(3x)[/tex] has period [tex]\frac{2\pi}3[/tex].
Similarly, [tex]\cos(5x)[/tex] has a period of [tex]\frac{2\pi}5[/tex],
[tex]\cos(5x + 2\pi) = \cos\left(5 \left(x + \dfrac{2\pi}5\right)\right) = \cos(5x)[/tex]
We want to find the period [tex]p[/tex] of [tex]f(x)[/tex], such that
[tex]f(x + p) = f(x)[/tex]
[tex] \implies \sin(3x + p) + \cos(5x + p) = \sin(3x) + \cos(5x)[/tex]
On the left side, we have
[tex]\sin(3x + p) = \sin(3x + 2\pi + p - 2\pi) \\\\ ~~~~~~~~ = \sin(3x+2\pi) \cos(p-2\pi) + \cos(3x+2\pi) \sin(p-2\pi) \\\\ ~~~~~~~~ = \sin(3x) \cos(p-2\pi) + \cos(3x) \sin(p - 2\pi)[/tex]
and
[tex]\cos(5x + p) = \cos(5x + 2\pi + p - 2\pi) \\\\ ~~~~~~~~ = \cos(5x+2\pi) \cos(p-2\pi) - \sin(5x+2\pi) \sin(p-2\pi) \\\\ ~~~~~~~~ = \cos(5x) \cos(p-2\pi) - \sin(5x) \sin(p-2\pi)[/tex]
So, in terms of its period, we have
[tex]f(x) = \sin(3x) \cos(p - 2\pi) + \cos(3x) \sin(p - 2\pi) \\\\ ~~~~~~~~ ~~~~+ \cos(5x) \cos(p - 2\pi) - \sin(5x) \sin(p - 2\pi)[/tex]
and we need to find the smallest positive [tex]p[/tex] such that
[tex]\begin{cases} \cos(p - 2\pi) = 1 \\ \sin(p - 2\pi) = 0 \end{cases}[/tex]
which points to [tex]p=2\pi[/tex], since
[tex]\cos(2\pi-2\pi) = \cos(0) = 1[/tex]
[tex]\sin(2\pi - 2\pi) = \sin(0) = 0[/tex]
An office has 7 male employees and 8 female employees. The manager randomly chooses 2 employees to
attend a football game. What is the probability that the manager chooses 2 femaleemployees?
From the 2 selected employees, the probability that they will both be females is; C: 4/15
How to find the Probability?We are given;
Number of male employees = 7
Number of female employees = 8
Total number of employees = 8 + 7 = 15
Now, 2 random employees are chosen and so the number of ways of selecting this is; 15C2
Now, out of the 2 selected employees, the probability that they will be female = 8C2/15C2 = 28/105 = 4/15
Thus, we can conclude that from the 2 selected employees, the probability that they will both be females is; C: 4/15
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1. What is the measure of angle x?
Answer: 60
Step-by-step explanation:
Almost everything in this picture is irrelevant to finding the measure of x.
x = 180 - 90 - 30 = 60
f(x)=4x+1 and g(x)=2x2+1, find (f∘g)(x) and (g∘f)(x)
The value of the composite functions (g∘f)(x) and (f∘g)(x) are 32x^2 + 16x + 3 and 8x^2 + 5 respectively
Composite functionsComposite function is also known as function of a function. They are determined by representing x with the other function.
Given the following functions
f(x)=4x+1
g(x)=2x^2+1
(f∘g)(x) = f(g(x))
(f∘g)(x) = f(2x^2+1)
(f∘g)(x) = 4(2x^2+1) + 1
(f∘g)(x) =8x^2 + 5
For the composite function (g∘f)(x)
(g∘f)(x) = g(f(x))
(g∘f)(x) = g(4x+1)
Replace x wit 4x+1 to have:
(g∘f)(x) = 2(4x+1)^2 + 1
(g∘f)(x)= 2(16x^2+8x+1) + 1
(g∘f)(x) = 32x^2 + 16x + 3
Hence the value of the composite functions (g∘f)(x) and (f∘g)(x) are 32x^2 + 16x + 3 and 8x^2 + 5 respectively
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How can 25 e42 n=1 be rewritten?
Answer:
The 'n = 1' below sigma represents the lower bound. meaning the number from which you start adding.
'25' above sigma is the upper bound.
In general it means adding 42 from 1 to 25 times.
so 42(25).
Answer:
C. 42(25)
Step-by-step explanation:
Took the unit test review and this was the correct option choice.
Goodluck on your unit test, I am sure that you will do good :)
The Tortoise and the Hare is a fable about a race with the
moral, “Slow and steady wins the race.” The Tortoise and the
Hare decide to “race” across the United States from
Washington D.C. to Los Angeles.
a. Charles Darwin studied the tortoises when he was on
the Galapagos in 1835. He thought they moved relatively quickly. “One large one, I found by pacing, walked at the rate of 60 yards in 10 minutes” he wrote in Zoology Notes.
i How many inches per minute does the Galapagos tortoise walk?
ii. How long would it take a Galapagos tortoise to walk across the U.S.? Use the most
appropriate unit for time.
b. The Hare can run up to 30mph.
i. How many inches per minute does the Hare run?
ii. How long would it take the Hare to complete the race across the U.S.? Use the
most appropriate unit for time.
c. In the fable, the Hare, confident that he is so far head, relaxes and takes a nap. How long would the Hare need to nap for the Tortoise to pass him and win the race?
a.i) The number of inches per minute that the Galapagos tortoise walks are 216 inches (6 x 36).
a.ii) The time it would take a Galapagos tortoise to walk across the U.S. in hours is 2,933 hours (1,056,000/(6 x 60).
b.i) The Hare runs 31,680 inches per minute (1,900,800/60).
b.ii) The time it would take the Hare to complete the race across the U.S. in hours is 20 hours (600/30).
c.) For the Tortoise to pass the Hare, the Hare needs to sleep for 2,913 hours (2,933 - 20) or 121.4 days (2,933/24).
What are the equivalent values for calculating distance?In this exercise, the following equivalent values are used for computing the distance and speed:
1 mile = 1,760 yards1 yard = 36 inches1 hour = 60 minutesDistance from Galapagos to the U.S. = 600 miles600 miles = 1,056,000 yards (600 x 1,760).Data and Calculations:Speed of Galapagos Tortoise per minute = 6 yards/ min (60 yards in 10 minutes)
Speed of Hare = 30mph
30 miles = 52,800 yards (30 x 1,760)
52,800 yards = 1,900,800 inches (52,800 x 36)
= 880 yards per minute (52,800/60)
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5:
will give brainliest
The focal length of the given ellipse is given as (±6, 0)
Equation of an ellipseAn ellipse is defined as a regular oval shape, traced by a point moving in a plane so that the sum of its distances from two other points (the foci) is constant or when a cone is cut by an oblique plane which does not intersect the base.
The standard equation of an ellipse is expressed as;
x^2/a^2 + y^2/b^2 = 1
The formula for calculating the focus of the ellipse is given as:
c^2 = b^2 - a^2
Given the equation of an ellipse
(x-7)^2/64 + (y-5)^2/100 = 1
This can also be expressed as:
(x-7)^2/8^2 + (y-5)^2/10^2 = 1
Comparing with the general equation
a = 8 and b = 10
Substitute
c^2 = 10^2 - 8^2
c^2 = 100 - 64
c^2 = 36
c = 6
Hence the focal length of the given ellipse is given as (±6, 0)
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Find the height (in meters) of a storage tank in the shape of a right circular cylinder that has a circumference measuring 4 m and a volume measuring 36 m3.
Answer:
[tex]h = \bf 28.3 \space\ m[/tex]
Step-by-step explanation:
• We are given:
○ Volume = 36 m³,
○ Circumference = 4 m
• Let's find the radius of the cylinder first:
[tex]\mathrm{Circumference} = 2 \pi r[/tex]
Solving for [tex]r[/tex] :
⇒ [tex]4 = 2 \pi r[/tex]
⇒ [tex]r = \frac{4}{2\pi}[/tex]
⇒ [tex]r = \bf \frac{2}{\pi}[/tex]
• Now we can calculate the height using the formula for volume of a cylinder:
[tex]\mathrm{Volume} = \boxed{\pi r^2 h}[/tex]
Solving for [tex]h[/tex] :
⇒ [tex]36 = \pi \cdot (\frac{2}{\pi}) ^2 \cdot h[/tex]
⇒ [tex]h = \frac{36 \pi^2}{4 \pi}[/tex]
⇒ [tex]h = 9 \pi[/tex]
⇒ [tex]h = \bf 28.3 \space\ m[/tex]
Answer:
9π m ≈ 28.27m
Step-by-step explanation:
The volume of a right cylinder is given by the formula
πr²h where r is the radius of the base of the cylinder(which is a circle), h is the height of the cylinder
Circumference of base of cylinder is given by the formula 2πr
Given,
2πr = 4m
r = 2/π m
Volume given as 36 m³
So πr²h = 36
π (2/π)² h = 36
π x 4/π² h = 36
(4/π) h = 36
h = 36π/4 = 9π ≈ 28.27m
Please hurry quick I need an answer
Answer:
slope is 4
Step-by-step explanation:
Slope is rise/run
for every 4 units it rises it runs 1 unit
4/1=4
Find the simple interest.
$2000 at 6% for 6 months
The simple interest is $____
(Round to the nearest cent as needed.)
Answer:
I think it's 120 dollars sorry if i get it wrong but I am sure it is right tell me when you get the right answer byeeee.
P: 2,012
1) El volumen de un cubo de arista 1 es Vc = 1³ y el
Volumen de una esfera de radior es
JE
V₁ = πr ²³ Entonces si en un cubo de arista 4cm
3
y se introduce una pelota de diametro 4 cm, al Calcular
aproximación con cuatro cifras decimales, por exceso.
Calcular el volumen que queda entre la esfera y el cubo.
(toma π =
3,141592654)
El volumen que queda entre la esfera y el cubo es: 30.49cm^3
¿Como calcular el volume sobrante?
El volumen sobrante será simplemente la diferencia entre el volumen del cubo y el volumen de la esfera.
Para el cubo que tiene una arista de 4cm, el volumen es:
V = (4cm)^3 = 64 cm^3
Para la esfera con un diametro de 4cm, el radio es:
R = 4cm/2 = 2cm
Y el volumen será:
V' = (4/3)*3.141592654*(2cm)^3 = 33.51 cm^3
El volumen que queda entre la esfera y el cubo es:
V - V' = 64 cm^3 - 33.51 cm^3 = 30.49cm^3
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Use the drop-down menus to complete each equation so the statement about its solution is true.
No Solutions 2x+5+2x+3x= x +
One Solution 2x+5+2x+3x= x +
Infinitely Many Solutions 2x+5+2x+3x= x +
Since there is only one value of x, hence the equation given has only one solution
Equations and expressionsEquations are expressions separated using mathematical operations. Given the equation below;
2x+5+2x+3x = x
Collect the like terms
2x+2x+3x -x = -2
7x -x = -2
Simplify
6x = -2
x = -2/6
x = -1/3
Since there is only one value of x, hence the equation given has only one solution
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In the diagram, angle ADE ≈ angle ABC the ratios blank and blank are equal.
Based on the angle-angle similarity theorem (AA), the pair of ratios that are equal is: AE/EC = AD/DB.
What is the Angle-angle Similarity Theorem (AA)?The angle-angle similarity theorem (AA) states that two triangles are similar to each other if they have two corresponding congruent angles, and therefore, the ratios of their corresponding side lengths are equal. This means their corresponding side lengths are proportional in measure.
Given that angle ADE ≅ angle ABC, we also know that:
Angle EAD ≅ CAB.
Thus, this implies that triangle EAD is similar to triangle CAB based on the angle-angle similarity theorem (AA). Therefore, the ratios of their corresponding side lengths are equal.
Thus, the ratios that are equal to each other would be:
AE/EC = AD/DB.
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Find y'' y = 3 cot x/8
If y = 3 cot x/8, the double differentiation of y gives,
y'' = (3/32) (cosec x/8)(cot x/8)
Given value of y is,
y = 3 cot x/8
Differentiation of the above equation will give us the following,
y' = d(3 cot x/8) / dx
y' = 3d(cot x/8) / dx ........... (1)
Now, we know that the differentiation of cot x is -cosec²x
Therefore, d(cot x/8) / dx = -(cosec²x/8)/8
Thus, equation (1) transforms as follows,
y' = -3(cosec²x/8)/8
Taking differentiation of the above equation, we get,
y'' = -3d((cosec²x/8)/ 8dx
y'' = -6d(cosec x/8) / 8dx [Using chain rule] .......... (2)
As we know, the differentiation of cosec x is -(cosec x)(cot x),
d(cosec x/8) / dx = -(cosec x/8)(cot x/8) / 8 [Using chain rule]
Therefore, equation (2) can be written as,
y'' = -(-6(cosec x/8)(cot x/8) / (8×8)
∴ y '' = 3(cosec x/8)(cot x/8) / 32
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Attached as an image. Please help.
The general solution of the logistic equation is y = 14 / [1 - C · tⁿ], where a = - 14² / 3 and C is an integration constant. The particular solution for y(0) = 10 is y = 14 / [1 - (4 / 10) · tⁿ], where n = - 14² / 3.
How to find the solution of an ordinary differential equation with separable variablesHerein we have a kind of ordinary differential equation with separable variables, that is, that variables t and y can be separated at each side of the expression prior solving the expression:
dy / dt = 3 · y · (1 - y / 14)
dy / [3 · y · (1 - y / 14)] = dt
dy / [- (3 / 14) · y · (y - 14)] = dt
By partial fractions we find the following expression:
- (1 / 14) ∫ dy / y + (1 / 14) ∫ dy / (y - 14) = - (14 / 3) ∫ dt
- (1 / 14) · ln |y| + (1 / 14) · ln |y - 14| = - (14 / 3) · ln |t| + C, where C is the integration constant.
y = 14 / [1 - C · tⁿ], where n = - 14² / 3.
If y(0) = 10, then the particular solution is:
y = 14 / [1 - (4 / 10) · tⁿ], where n = - 14² / 3.
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Which of the following equations has a minimum value of (3,-10)? y = 2x2 + 40x + 203 y = x2 + 6x + 19 y = 2x2 − 12x + 8 y = -2x2 + 12x − 8
Answer:
y = 2x² − 12x + 8
Step-by-step explanation:
FIRST METHOD :
y = 2x² − 12x + 8
= (2x² − 12x) + 8
= 2 (x² − 6x) + 8
= 2 (x² − 6x + 9 − 9 ) + 8
= 2 (x² − 6x + 9) − 2×9 + 8
= 2 (x² − 6x + 9) − 18 + 8
= 2 (x² − 6x + 9) − 10
= 2 (x − 3)² − 10
Then ,the equation has a extremum value of (3,-10)
Since the number 2 in the equation y = = 2 (x − 3)² − 10 is greater than 0
(2 > 0) , the graph (parabola) opens upward
Therefore ,the extremum (3,-10) is a minimum.
SECOND METHOD :
the graph of a function of the form f(x) = ax² + bx + c
has an extremum at the point :
[tex]\left( -\frac{b}{2a} ,f\left( -\frac{b}{2a} \right) \right)[/tex]
in the equation : f(x) = 2x² − 12x + 8
a = 2 ; b = -12 ; c = 8
Then
[tex]-\frac{b}{2a} = -\frac{-12}{2 \times 2} = 3[/tex]
Then
[tex]f\left( -\frac{b}{2a} \right) = f(3) = 2(3)^2- 12(3) + 8 = 18 - 36 + 8 = -18 + 8 = -10[/tex]
the graph of a function f(x) = 2x² − 12x + 8
has an extremum at the point (3 , -10)
Since the parabola opens up ,then the extremum (3,-10) is a minimum.
50 POINTS PLEASE HELP I NEED ANWSER NOW what would the reflection look like
Answer:
Point C will be at (3,1), Point B will be at (7,1) and Point A will be at (7,5)
Step-by-step explanation:
A certain insecticide kills 60% of all insects in laboratory experiments. A sample of 7 insects is exposed to the insecticide in a particular experiment. What is the probability that exactly 4 insects will survive? Round your answer to four decimal places.
Step-by-step explanation:
the probability of 1 tested insect is killed is 60% or 0.6.
the probability that it is not killed is then 1-0.6 = 0.4.
when we test 7 insects and exactly 4 survive is the event that
3 insects are killed, 4 insects survive.
the probability for one such case is
0.6×0.6×0.6 × 0.4×0.4×0.4×0.4
how many such cases do we have ?
as many as ways we can select 4 insects out of the given 7.
these are 7 over 4 combinations :
7! / (4! × (7-4)!) = 7! / (4! × 3!) = 7×6×5/(3×2) = 7×5 = 35
so, the probability that exactly 4 out of 7 tested insects survive is
35 × 0.6³ × 0.4⁴ = 0.193536 ≈ 0.1935
DETAILS BASSELEMMATH7 9.PP1.035. 0/1 Submissions Used The measure of the smallest angle of a right triangle is 10° less than the measure of the other small angle. Find the measures of all three angles in degrees. smallest angle largest angle.
Answer:
40°, 50°, and 90°
Step-by-step explanation:
Let the smallest angle be x.
Then, the other small angle is x+10.
The acute angles of a right triangle are complementary, so x+x+10=90, and thus x=40.
So, the acute angles measure 40° and 50°.
Therefore, the three angles are 40°, 50°, and 90°.
For a certain company, the cost function for producing x items is C(x)=40x+200 and the revenue function for selling x items is R(x)=−0.5(x−80)2+3,200 . The maximum capacity of the company is 100 items.
Based on the cost and revenue functions to the company for selling x items, the domain of C(x) is [0, 100].
The range of C(x) is (200, 4,200).
What is the domain and range of C(x)?The domain would be the lowest capacity and the maximum capacity. As these are physical units to sell, the lowest unit would be 0 units as units can't be negative.
The maximum capacity is given as 100 items so the domain is:
= [0, 100]
The range is:
When x is 0, the function gives C(x) as:
= 40(0) + 200
= 200
When x is the maximum of 100, the C(x) is:
= 40(100) + 200
= 4,200
Range is:
(200, 4,200)
Full question is:
What is the domain and range of C(x)?
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A store is having a sale on trail mix and jelly beans. For 3 pounds of trail mix and 8 pounds of jelly beans, the total cost is $29. For 5 pounds of trail mix and 2 pounds of jelly beans, the total cost is $20. Find the cost for each pound of trail mix and each pound of jelly beans.
Answer:
the price of one pound of trail mix is $3
the price of one pound of jelly beans is $2.5
Step-by-step explanation :
let t be the price of one pound of trail mix.
and b be the price of one pound of jelly beans.
This statement:
“For 3 pounds of trail mix and 8 pounds of jelly beans,
the total cost is $29”
Can be translated mathematically like this :
3t + 8b = 29
This statement:
“For 5 pounds of trail mix and 2 pounds of jelly beans,
the total cost is $20”
Can be translated mathematically like this :
5t + 2b = 20
We obtain a system of two equations :
3t + 8b = 29
5t + 2b = 20
Solving the system:
3t + 8b = 29 (equation 1)
5t + 2b = 20. (equation 2)
3t + 8b = 29
20t + 8b = 80 [4×(equation 2)]
3t + 8b = 29
17t = 51 [4×(equation 2) - equation 1]
3t + 8b = 29
t = 51/17 = 3
9 + 8b = 29
t = 3
8b = 20
t = 3
b = 20/8 = 5/2
t = 3
b = 5/2
t = 3
Therefore ,the solution to our system is (3 , 2.5)
a man borrowed GHC 1200 at the bank for 4 months at the rate of 5%.Calculate a. his simple interest
there are 12 months in a year, so then 4 months is really 4/12 of a year.
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & 1200\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=\to \frac{4}{12}years\dotfill &\frac{1}{3} \end{cases} \\\\\\ I = (1200)(0.05)(\frac{1}{3})\implies I=20~GHC[/tex]
