The probabilities of the given events are:
A. P(even) = P(A) = 7/15
B. P(multiple) = P(B) = 3/15
C. P(prime) = 6/15
D. P(B|A) = 3/7
What is probability?Probability is defined as the ratio of the number of favorable outcomes of an event to the total number of possible outcomes.
P(E) = n(E)/n(S)
Calculation:The given sample space is S = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}
So, n(S) = 15
A. The selected number is even:
Consider the event as A.
The set of even numbers in the given sample is {2,4,6,8,10,12,14}
So, n(A) = 7
Then, the required probability is
P(A) = n(A)/n(S)
= 7/15
B. The selected number is a multiple of 4:
Consider the event as B.
The set of multiples of 4 in the given sample is {4,8,12}
So, n(B) = 3
Then, the required probability is
P(B) = n(B)/n(S)
= 3/15
C. The selected number is prime:
Consider the event as C.
The set of prime numbers in the given sample is {2,3,5,7,11,13}
So, n(C) = 6
Then, the required probability is
P(C) = n(C)/n(S)
= 6/15
D. calculate P(B|A):
Since events B and A are dependent events of the same sample,
n(A∩B) = 3 and the set is {4,8,12}. Then, P(B|A) is
P(B|A) = n(A∩B)/n(A)
⇒ P(B|A) = 3/7
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The probability of buying a movie ticket with a popcorn coupon is 0.629 and without a popcorn coupon is 0.371. If you buy 29 movie tickets, we want to know the probability that more than 16 of the tickets have popcorn coupons.
Consider tickets with popcorn coupons as successes in the binomial distribution. Do not include p= in your answer.
Answer:
Step-by-step explanation:
The probability and the parameter
Step-by-step explanation:
The formula for probability in a binomial distribution is where p is the probability of success (ticket with popcorn coupon), n is the number of trials (tickets bought) and x the number of successes desired. In this case p=0.629 (probability of buying a movie ticket with coupon), n=29, and x=17,18,19, ...29.
The probability of more than 16 is equal to the sum of the probability of x=17, 17,18,19, ...29.
A botanist secures a 30-year mortgage for $513,000 at an annual interest rate of 4.175% with 1.4 points. The loan origination fee is 0.65 points of the loan amount. Calculate the APR (in percent) for the loan. (Round your answer to the nearest thousandth of a percent.)
Answer:
4.346%
Step-by-step explanation:
The points and origination fee are assumed to be capitalized, so the loan payment amount is based on the total of the original loan amount and those fees. The APR is calculated as the rate that would be charged on the original loan value to produce that payment.
Loaned amountThe loaned amount is the sum of the original loan value and the added points.
P = $513,000×(1 +1.4% +0.65%) = $523,516.50
PaymentThe monthly payment on this amount is given by the amortization formula ...
A = P(r/12)/(1 -(1 +r/12)^(-12t))
where r=0.04175, the annual interest rate, t=30, the period in years
A = $523,516.50(0.04175/12)/(1 -(1 +0.04175/12)^-360)) ≈ $2552.45
APRThere is no formula for calculating the APR. It must be developed iteratively or graphically. The attached calculator images show a couple of different ways the value can be found.
The payment of $2552.45 on a loan value of $513,000 represents an APR of 4.346%.
Solve for the Unknown B:5(B + 4) = 3(B-1) +B
Answer:
B = - 23
Step-by-step explanation:
5(B + 4) = 3(B - 1) + B ← distribute parenthesis on both sides
5B + 20 = 3B - 3 + B
5B + 20 = 4B - 3 ( subtract 4B from both sides )
B + 20 = - 3 ( subtract 20 from both sides )
B = - 23
On November 1, the company rented space to another tenant. A check in the amount of $9,000, representing three months rent in advance, was received from tenant on that date. The payment was recorded with a credit to the
The adjusting entry to registering the Rent revenue shall be as pursues:
Unearned Rent Revenue Debit $6,000
Rent Revenue Credit $6,000
(being the adjustment made for Rent Revenue earned)
How to complete the necessary adjusting entry for December 31 by selecting the account names and dollar amounts?Adjusting entry to record the Rent Revenue are as follows:
It exists shown that on November 1, the company rented space to another tenant. A check in the amount of $9,000, symbolizing three months' rent in advance, stood obtained from the tenant on that date. The payment stood registered with a credit to the unearned rent revenue account.
Now on December 31, we must organize the adjusting access to record the Rent Revenue for the period (Nov. 1 to Dec. 31) which exists for two months. The Rent Revenue for two months shall be
9000 [tex]*[/tex] 2/3 = $6,000
Therefore the adjusting entry to registering the Rent revenue shall be as pursues:
Unearned Rent Revenue Debit $6,000
Rent Revenue Credit $6,000
(being the adjustment made for Rent Revenue earned)
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The complete question is:
On November 1, the company rented space to another tenant. A check for $9,000, representing three months' rent in advance, was received from the tenant on that date. The payment was recorded with a credit to the unearned rent revenue account. Complete the necessary adjusting entry for December 31 by selecting the account names and dollar amounts from the drop-down menus.
One positive integer is 5 less than twice another. The sum of their squares is 130. Find the integers.
Answer:
7, 9
Step-by-step explanation:
Let x and y represent the two positive integers.
We can write x in terms of y. The question states "one positive integer is 5 less than twice another". Let "one positive integer" represent x.
Therefore:
[tex]x=2y-5[/tex]
We also know that the sum of the squares of the two positive integers is 130. Using this information, we can write another equation.
[tex]x^2+y^2=130[/tex]
These two equations form a system of equations.
[tex]x=2y-5[/tex]
[tex]x^2+y^2=130[/tex]
We can solve this system of equations by the substitution method. Using this method, we substitute [tex]2y-5[/tex] for [tex]x[/tex].
[tex](2y-5)^2+y^2=130[/tex]
Expand [tex](2y-5)^2[/tex] . Notice that [tex](a-b)^2=a^2-2ab+b^2[/tex] :
[tex](2y-5)^2=4y^2-20y+25[/tex]
[tex]4y^2+y^2-20y+25=130[/tex]
Subtract 25 from both sides
[tex]4y^2+y^2-20y=105[/tex]
Add like terms
[tex]5y^2-20y=105[/tex]
Divide both sides by 5
[tex]y^2-4y=21[/tex]
Subtract 21 from both sides
[tex]y^2-4y-21 = 0[/tex]
Factor the equation
[tex]y^2-7y+3y-21=0\\y(y-7)+3(y-7)=0\\(y-7)(y+3)=0\\y=7\text{ or} \ -3[/tex]
Since the question states that the two integers are positive, one of the integers is 7.
We can use this information to find the other integer.
[tex]x=2y-5\\x=2(7)-5\\x=14-5\\x=9[/tex]
[tex]CHECK:\\x^2+y^2=7^2+9^2=49+81=130 \Rightarrow Correct![/tex]
Therefore the two integers are 7 and 9.
PLEASE HELP ALOT OF POINTS
Answer: B
Step-by-step explanation:
What number is six and four hundredths larger than two and five tenths?
Answer:
eight and thirty-seven fiftyths
Step-by-step explanation:
6 and 4/100 + 2 and 5/10
6 and 1/25 + 2 and 1/2
156 / 25 + 5 / 2
312 / 50 + 125 / 50
437 / 50
400 / 50 = 8
8 and 37 / 50
Solve for n:
(n+4)/10 = (n-8)/2
Answer:
n=11
Step-by-step explanation:
(n+4)/10 = (n-8)/2
We can solve using cross products
(n+4) * 2 = 10 * ( n-8)
Distribute
2n+8 = 10n -80
Subtract 2n from each side
2n+8-2n = 10n-80-2n
8 = 8n-80
Add 80 to each side
8+80= 8n-80+80
88 = 8n
Divide each side by 8
88/8 = 8n/8
11 = n
Answer: n=11
Step-by-step explanation:
(n+4)/10 = (n-8)/2
multiply both sides by 10
n+4 = (n-8)/2*10
cancel
n+4=(n-8)*5
n+4=5(n-8)
multiply
n+4=5n-40
subtract both sides by 5n
n-5n+4=-40
subtract both sides by 4
n-5n=-40-4
subtract the like terms
-4n=-44
cancel the negatives
4n=44
divide each side by 4
n=11
Which of these tables represent a function
Answer: W
Step-by-step explanation: I remember learning this in school> you can tell it’s a function because no numbers repeat themselves etc .
Using the principle of
mathematical induction show that 10^(2n-1 ) + 1 is divisible by 11 for all z
When [tex]n=1[/tex],
[tex]10^{2\cdot1 - 1} + 1 = 10^1 + 1 = 11[/tex]
which is of course divisible by 11.
Assume this holds for [tex]n=k[/tex], that
[tex]11 \mid 10^{2k - 1} + 1[/tex]
In other words,
[tex]10^{2k - 1} + 1 = 11\ell[/tex]
for some integer [tex]\ell[/tex].
Use this to show the claim is true for [tex]n=k+1[/tex].
[tex]10^{2(k+1) - 1} + 1 = 10^{2k + 1} + 1 \\\\ ~~~~~~~~~~~~~~~~~~~~ = 10^{2k+1} + \left(10^{2k-1} + 10^{2k-1}\right) + 1 \\\\ ~~~~~~~~~~~~~~~~~~~~ = \left(10^{2k+1} - 10^{2k-1}\right) + \left(10^{2k-1} + 1\right) \\\\ ~~~~~~~~~~~~~~~~~~~~ = 10^{2k-1} \left(10^2 - 1\right) + 11\ell \\\\ ~~~~~~~~~~~~~~~~~~~~ = 99\times10^{2k-1} + 11\ell \\\\ ~~~~~~~~~~~~~~~~~~~~ = 11\left(9\times10^{2k-1} + \ell\right)[/tex]
which is indeed divisible by 11. QED
On the off-chance you meant [tex]10^{2^n-1}+1[/tex], notice that [tex]2n-1[/tex] is odd for any integer [tex]n[/tex]. Similarly [tex]2^n-1[/tex] is odd for all [tex]n[/tex], so the above proof actually proves this automatically.
imageGiven: a = 2, b = 3, and c = 4. What is m measured angle C degree to the nearest tenth?
Given the measure of side a, b and c of the triangle, the measure of angle C to the nearest tenth is 104.5°.
What is the measured angle C?From the law of cosines;
cosC = ( a² + b² - c² ) / 2ab
Where C is the angle C and a, b, and c are the three sides of the triangle.
Given the data in the question;
Side a = 2Side b = 3Side c = 4Angle C = ?Using law of cosine;
cosC = ( a² + b² - c² ) / 2ab
We substitute the values into the equation.
cosC = ( 2² + 3² - 4² ) / ( 2 × 2 × 3 )
cosC = ( 4 + 9 - 16 ) / ( 12 )
cosC = -3 / 12
cosC = -0.25
We find the inverse of cosine.
C = cos⁻¹( -0.25 )
C = 104.477°
C = 104.5°
Given the measure of side a, b and c of the triangle, the measure of angle C to the nearest tenth is 104.5°.
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Subtract: 3x to the power 2 - 6x - 4 from 5 + x - 2xto the power 2.
Answer:
[tex]-8x^2 - 4x + 29 \\[/tex]
Step-by-step explanation:
Second expression evaluates to:
[tex](5 + x -2x)^2 = (5 -x)^2 = (-x+5)^2 = x^2 + 2(-x)(5) +5^2 = x^2 -10x + 25[/tex] (1)
For (1) We are using the rule [tex](a+b)^2 = a^2 +2ab + b^2\\\\[/tex]
Here [tex]a = -x, b = 5\\\\[/tex]
First expression evaluates to
[tex](3x)^2 -6x - 4 = 9x^2 -6x -4[/tex] (2)
Subtract (2) from (1)
[tex]x^2 - 10x +25 - (9x^2 -6x -4) = x^2-9x^2 -10x - (-6x) +25 -(-4)\\\\= -8x^2 - 4x + 29 \\[/tex]
9/16+7/8=
A.)1-3/16inches
B.)1-7/16inches
C.)1-11/16inches
D.)1/-13/16inches
Answer:
hey can you show me the pic because the question doesn't make any sense
What is ZT?
a. 7
b. 14
c. 28
d. 29
Answer:
B
Step-by-step explanation:
• the opposite sides of a parallelogram are congruent , then
ZY = WX , that is
5x - 6 = 4x + 1 ( subtract 4x from both sides )
x - 6 = 1 ( add 6 to both sides )
x = 7
• the diagonals bisect each other , then
ZT = TX = 2x = 2 × 7 = 14
Which of the following best reflects a theme of art influenced by the teachings of Sigmund Freud?
a.
images with antiwar themes
b.
a dream-like image
c.
ready-mades
d.
none of the above
Please select the best answer from the choices provided
A
B
C
D
Answer:
B
Step-by-step explanation:
a dream like imageeeeee
Directions: Find the missing angle in each of the following problems.
1. QR = 36 ; PR = 45 ; PQ = 21, Sin __?___ = 21 / 45
2. QR = 16 ; PR = 2 ; PQ = 8, tan __?__ = 8 / 16
3. QR = 15 ; PR = 28 ; PQ = 15, Cos __?__ = 15 / 28
4. QR = 47 ; PR = 64 ; PQ = 38, tan __?__ = 38 / 47
5. QR = 4 ; PR = 17 ; PQ = 12, Sin __?___ = 12 / 17
6. QR = 36 ; PR = 59 ; PQ = 20, Cos __?___ = 36 / 59
7. QR = 82 ; PR = 63 ; PQ = 29, tan __?__ = 29 / 82
8. QR = 10 ; PR = 28 ; PQ = 8, Sin __?___ = 8 / 28
9. QR = 51 ; PR = 42 ; PQ = 9, tan __?__ = 9 / 51
10. QR = 16 ; PR = 20 ; PQ = 17, Cos __?___ = 16 / 20
11. QR = 12 ; PR = 84 ; PQ = 60, Sin __?_ = 60 / 84
12. QR = 19 ; PR = 32 ; PQ = 45, Cos __? = 19 / 32
13. QR = 76 ; PR = 27 ; PQ = 64, tan __ ?_ = 64 / 76
14. QR = 26 ; PR = 48 ; PQ = 37, Cos __?_ = 37 / 48
15. QR = 19 ; PR = 66 ; PQ = 23, Cos __?__= 23 / 66
The missing angles are listed below:
sin 27.818° = 21 / 45
tan 26.565° = 8 / 16
cos 57.607° = 15 / 28
tan 38.956° = 38 / 47
sin 44.901° = 12 / 17
cos 52.398° = 36 / 59
tan 19.477° = 29 / 82
sin 16.601° = 8 / 28
tan 10.008° = 9 / 51
cos 36.870° = 16 / 20
sin 35.538° = 60 / 84
cos 53.576° = 19 / 32
tan 40.101° = 64 / 76
cos 39.571 = 37 / 48
cos 69.605° = 23 / 66
How to find the measure of missing angles by definition of inverse of trigonometric functions
In this question we must find the measure of the angle associated to the rational numbers seen in the statement. There are two methods to estimate such measures: (i) Drawing an equivalent right triangle and estimate the measure of the angle by definition of trigonometric functions, (ii) Using inverse trigonometric functions and numerical methods since they are trascendent variables.
Herein we decided to use the second method by reasons of rapidness and effectivity:
sin 27.818° = 21 / 45
tan 26.565° = 8 / 16
cos 57.607° = 15 / 28
tan 38.956° = 38 / 47
sin 44.901° = 12 / 17
cos 52.398° = 36 / 59
tan 19.477° = 29 / 82
sin 16.601° = 8 / 28
tan 10.008° = 9 / 51
cos 36.870° = 16 / 20
sin 35.538° = 60 / 84
cos 53.576° = 19 / 32
tan 40.101° = 64 / 76
cos 39.571 = 37 / 48
cos 69.605° = 23 / 66
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Help me with this question asap!
Answer:
false
Step-by-step explanation:
The converse of the statement is
If two angles are not a linear pair of angles, they are not adjacent.This is false by definition.
The function f(x) = x3 – 8x2 + x + 42 has zeros located at 7, –2, 3. Verify the zeros of f(x) and explain how you verified them. Describe the end behavior of the function.
Answer:
zeros are {-2, 3, 7} as verified by graphingend behavior: f(x) tends toward infinity with the same sign as xStep-by-step explanation:
A graphing calculator makes finding or verifying the zeros of a polynomial function as simple as typing the function into the input box.
ZerosThe attachment shows the function zeros to be x ∈ {-2, 3, 7}, as required.
End behaviorThe leading coefficient of this odd-degree polynomial is positive, so the value of f(x) tends toward infinity of the same sign as x when the magnitude of x tends toward infinity.
x → -∞; f(x) → -∞x → ∞; f(x) → ∞__
Additional comment
The function is entered in the graphing calculator input box in "Horner form," which is also a convenient form for hand-evaluation of the function.
We know the x^2 coefficient is the opposite of the sum of the zeros:
-(7 +(-2) +3) = -8 . . . . x^2 coefficient
And we know the constant is the opposite of the product of the zeros:
-(7)(-2)(3) = 42 . . . . . constant
These checks lend further confidence that the zeros are those given.
(The constant is the opposite of the product of zeros only for odd-degree polynomials. For even-degree polynomials. the constant is the product of zeros.)
What are the next three terms in the sequence -27, -19,
-11, -3, 5, ...?
Answer:
13, 21, 29
Step-by-step explanation:
You are adding 8 to each term. -27 + 8 = -19 + 8 = -11 + 8 = -3, etc.
Use the normalcdf function on a calculator to find the probability that battery life is 20 ± 2 hours (between 18 and 22 hours) for each phone.
Prior values (If needed)
.159
.50
The probability that the battery life is 20 ± 2 hours (between 18 and 22 hours) for each of the phones is:
Phone C = 15.9%Phone T = 50%What is the probability of the battery life?Using the normalcdf function on a calculator, the probability that Phone C's battery would last between 18 and 22 hours can be found by inputing the function:
normalcdf (20, IE99, 18, 2)
The result is 0.158655 or 15.9%.
For Phone T, the function is:
normalcdf (20, IE99, 20, 3)
The result is 0.5 or 50%.
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Evaluate (f + g)(x) if f(x) = 2x and g(x) = 3X - 2
when x = 3
Answer:
13
Step-by-step explanation:
→ Substitute 3 into 2x
2 × 3
→ Evaluate
f ( x ) = 6
→ Substitute x = 3 into 3x - 2
3 × 3 - 2
→ Evaluate
7
→ Find the sum of the 2 results
13
When x = 3, the value of (f + g)(x) is 13.
To evaluate (f + g)(x) when f(x) = 2x and g(x) = 3x - 2, we substitute the given functions into the expression (f + g)(x).
(f + g)(x) = f(x) + g(x)
Substituting the given functions:
(f + g)(x) = 2x + (3x - 2)
Simplifying the expression:
(f + g)(x) = 2x + 3x - 2
Combining like terms:
(f + g)(x) = 5x - 2
Now, to find the value of (f + g)(x) when x = 3, we substitute x = 3 into the expression:
(f + g)(3) = 5(3) - 2
Simplifying further:
(f + g)(3) = 15 - 2
(f + g)(3) = 13
Therefore, when x = 3, the value of (f + g)(x) is 13.
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IM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each
In the given figure, the measure of the central angle CAD is 80°, the major arc is arc CBD, and minor arc is arc CD. The measure of arc BEC is 2.27r and that of arc BC is 0.87r.
About the Central Angle:
An angle formed by two radii of a circle is known as a central angle. Thus, arc BC and arc CD both subtends central angles at the center.
Since BD is the diameter of the circle,
∠BAC + CAD = 180°
It is given that ∠BAC = 100°
⇒ ∠CAD = 180° - 100°
⇒ ∠CAD = 80°
About Major Arc:
The arc which subtends an angle greater than 180° at the center, is called a major arc.
Angle subtended by arc BEC = 360° - m(arc CD)
= 360° - 80°
= 280° > 180°
∴ Arc BEC is the major arc
About Minor Arc:
The arc which subtends an angle less than 180° at the center, is called a minor arc.
⇒ Arc CD is the minor arc.
Calculating arc BEC and arc BC:
Let us assume the radius of the circle is r.
Then, the formula of the measure of an arc is given by,
θ × (π/180) × r
Here, θ is the angle ( in degrees) subtended by the arc at the center.
Arc BEC = 260 × (π/180)r ......... [Put π = 3.14]
= 2.27r
Similarly, arc BC = 100 ×(π/180) × r .......... [Put π = 3.14]
= 0.87r
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The quadratic functions shown are written in factored form. The roots of a quadratic function will make the factors equal to 0.
Drag each function to show whether it has roots at x=−2 and x=3, roots at x=2 and x=−3, or neither.
The following classification of quadratic equations is presented below:
x = - 2 and x = 3: h(x) = (x + 2) · (x - 3), k(x) = - 3 · (x + 2) · (x - 3). x = 2 and x = - 3: g(x) = 8 · (x + 3) · (x - 2), m(x) = (x + 3) · (x - 2). Neither: j(x) = (x - 2) · (x - 3)How to classify quadratic equations in terms of its roots
In this problem we have quadratic equations in factored form, whose form is presented below:
y = a · (x - r₁) · (x - r₂) (1)
Where r₁ and r₂ are the roots of the equation and a is the leading coefficient. A value of x is a root if and only if y is zero. Besides, we must located all the quadratic equations according to their roots.
x = - 2 and x = 3
h(x) = (x + 2) · (x - 3)
k(x) = - 3 · (x + 2) · (x - 3)
x = 2 and x = - 3
g(x) = 8 · (x + 3) · (x - 2)
m(x) = (x + 3) · (x - 2)
Neither
f(x) = 3 · (x - 1) · (x + 2)
j(x) = (x - 2) · (x - 3)
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Let f= {(-5,-4),(6,-5),(2, -3)}.
Find f(-5).
Answer:
f(–5)=–4
Step-by-step explanation:
as it is defined
* Let S = Span {(2,-1, 1), (3, 1, 1), (1, 2, 0)}. (i) Calculate the dimension of S.
1
2
3
9
The span of 3 vectors can have dimension at most 3, so 9 is certainly not correct.
Check whether the 3 vectors are linearly independent. If they are not, then there is some choice of scalars [tex]c_1,c_2,c_3[/tex] (not all zero) such that
[tex]c_1 (2,-1,1) + c_2 (3,1,1) + c_3 (1,2,0) = (0,0,0)[/tex]
which leads to the system of linear equations,
[tex]\begin{cases} 2c_1 + 3c_2 + c_3 = 0 \\ -c_1 + c_2 + 2c_3 = 0 \\ c_1 + c_2 = 0 \end{cases}[/tex]
From the third equation, we have [tex]c_1=-c_2[/tex], and substituting this into the second equation gives
[tex]-c_1 + c_2 + 2c_3 = 2c_2 + 2c_3 = 0 \implies c_2 + c_3 = 0 \implies c_2 = -c_3[/tex]
and in turn, [tex]c_1=c_3[/tex]. Substituting these into the first equation gives
[tex]2c_1 + 3c_2 + c_3 = 2c_3 - 3c_3 + c_3 = 0 \implies 0=0[/tex]
which tells us that any value of [tex]c_3[/tex] will work. If [tex]c_3 = t[/tex], then [tex]c_1=t[/tex] and [tex]c_2 = -t[/tex]. Therefore the 3 vectors are not linearly independent, so their span cannot have dimension 3.
Repeating the calculations above while taking only 2 of the given vectors at a time, we see that they are pairwise linearly independent, so the span of each pair has dimension 2. This means the span of all 3 vectors taken at once must be 2.
Find the volume of a grain storage building that has
a cylinder bottom that is 20 meters in diameter and
10 meters in height. It has a cone-shaped top as a
roof that has the same diameter as the bottom and a
height of 6 meters. Find the volume of the building
in cubic meters if it was full of grain from the
bottom to the top of the roof. All measures noted in
the diagram below are in meters. Use = 3.14 in
your calculations. Enter only the number.
m
10 m
The solution is
10 m
The volume of the grain storage building is 3770. 4 m³
How to determine the volume
From the given question, it can be deduced that the grain storage is a combination of a cylinder and a cone
The volume of the grain storage = volume of the cone + the volume of the cone
The formula for finding the volume of a cylinder is given as;
Volume of cylinder = πr²h
But we know that radius is the diameter divided by 2
radius = 20/2
radius = 10 meters
height = 10 meters
Substitute the values in the formula
Volume of cylinder = 3. 142 × 10 × 10 × 10
Volume = 3. 142 × 1000
Volume = 3142 m³
The formula for finding the volume of a cone is given as;
Volume of cone = [tex]\pi r^2\frac{h}{3}[/tex]
If the cone has the same diameter, then the radius is 10 meters and the height is 6 meters
Substitute the values into the formula
Volume of the cone = 3. 142 × 10 × 10 × 6/ 3
Volume = 3. 142 × 100 × 2
Volume = 628. 4 m³
The volume of the grain storage building = 3142 + 628. 4
The volume of the grain storage building = 3770. 4 m³
Thus, the volume of the grain storage building is 3770. 4 m³
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Answer:
3770. 4 m³
Step-by-step explanation:
i took the test
Solve the inequality and enter your solution as an inequality comparing the
variable to a number.
x+11 >12
Answer:x>1
Step-by-step explanation:
Subract 11 from both sides
find r^-1 (x)
r(x) = 2/3 (4x -5)
Answer:
Step-by-step explanation:
Let r(y)=x.
[tex]x=\frac{2}{3}(4y-5)\\\\\frac{3}[2}x=4y-5\\\\\frac{3}{2}x+5=4y\\\\y=\frac{3}{8}x+\frac{5}{4}\\\\r^{-1}(x)=\frac{3}{8}x+\frac{5}{4}[/tex]
A student bought a truck for 4000 down with payments of 250 for 4yrs what’s the total cost
The total cost of the truck is $16,000
What is the total cost?
We know that first, we have a down payment of $4000.
And then we have a monthly payment of $250 for 4 years. In each year there are 12 months, then in 4 years there are:
4*12 = 48 months.
Then the student needs to pay $250 48 times, this is:
$250*48 = $12,000
Then the total cost is:
$12,000 + $4,000 = $16,000
The total cost of the truck is $16,000
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BUYING A TOWNHOUSE SELLING FOR $175,000. THE BANK IS
OFFERING A 30-YEAR FIXED RATE MORTGAGE AT 5.5% WITH A MINIMUM 20% DOWN
PAYMENT. DETERMINE THE AMOUNT OF THE DOWN PAYMENT AND THE MONTHLY PAYMENT
Using the monthly payment formula, we have that:
The down payment is $35,000.The monthly payment is of $795.87.What is the monthly payment formula?It is given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which:
P is the initial amount.r is the interest rate.n is the number of payments.The down payment is 20% of $175,000, hence:
D = 0.2 x 175,000 = $35,000.
Hence the parameters are:
P = 175,000 - 35,000 = 140,000, r/12 = 0.055/12 = 0.004583, n = 30 x 12 = 360.
Then the monthly payment is found as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 140,000\frac{0.004583(1.004583)^{360}}{(1.004583)^{360} - 1}[/tex]
A = $795.87.
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