Answer:
The best option is the first one. It provides a higher present value.
Step-by-step explanation:
Giving the following information:
Option 1:
Receive $15,000,000 today.
Option 2:
Receive $1,000,000 for 30 years.
Discount rate= 7% compounded annually
To compare both options, we need to calculate the present value of Option 2. The option with the higher present value is the most convenient.
Option 2:
First, we need to determine future value:
FV= {A*[(1+i)^n-1]}/i
A= annual cash flow
FV= {1,000,000*[(1.07^30) - 1]} / 0.07
FV= $94,460,786.32
Now, the present value:
PV= FV/(1+i)^n
PV= 94,460,786.32 / (1.07^30)
PV= $12,409,041.18
The best option is the first one. It provides a higher present value.
How do I write 3x3x3x3 in exponential form
Answer:
3 with the exponent of four.
Step-by-step explanation:
You would count the number of of three's. Since there are four three's, then you would write the 4 right by the three on the top right hand corner.
The exponential expression is [tex]3^4[/tex].
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
3 x 3 x 3 x 3
The form to write an exponential expression.
= [tex]Base^{Exponents}[/tex]
Now,
There are four 3's and we can write it as an exponent form where the base is 3 and the exponent is 4.
So,
= [tex]3^4[/tex]
Thus,
The exponential expression is [tex]3^4[/tex].
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The number of adult tickets sold at a school talent show, a, is 5 less than 3 times the number c of children’s tickets sold. Which equation represents the number of adult tickets sold?
Answer:
3c - 5
steps: A=3c+5
Six classes from a school in Indiana collected a total of 2,166 pounds of paper to recycle. if each class collected the same amount, how much did each class collect?
During a science experiment, Daniel noted the starting temperature of a At the end of the experiment, the change in temperature was What was the final temperature?
Complete question :
During a science experiment, Daniel noted the starting temperature of a -4°F. At the end of the experiment, the change in temperature was -5°F. What was the final temperature?
A.-1 B.1 C.9 D.-9
Answer:
D.) - 9
Step-by-step explanation:
Given the following :
Temperature at the start of experiment = - 4°F
At the end of experiment, change in temperature = - 5°F
This means between the temperature at the start of the experiment was - 4°F and during the cause of the experiment, there was a change in temperature of - 5°F.
Hence, the final temperature is the sum of the initial temperature and and the temperature change recorded.
Initial temperature + temperature change
-4°F + (-5°F)
- 4°F - 5°F = - 9°F
Hence, final temperature = - 9°F
Answer:
The answer is 9
Given the following :
Temperature at the start of experiment = - 4°F
At the end of experiment, change in temperature = - 5°F
This means between the temperature at the start of the experiment was - 4°F and during the cause of the experiment, there was a change in temperature of - 5°F.
Hence, the final temperature is the sum of the initial temperature and and the temperature change recorded.
Initial temperature + temperature change
-4°F + (-5°F)
- 4°F - 5°F = - 9°F
Hence, final temperature = - 9°F
Ecuacion, porfa ayuda.
x - 8 = x/2 - x-6/3
Answer:
x=4
Step-by-step explanation:
x-8= x/2 -x-6/3
x-8=x/2-x-2
x-8=-x/2-2
1.5x-8=-2
1.5x=6
x=4
Ms. Gantt has a $15 gift card to Starbucks. She buys 2 muffins for $2.65 each, 2 hot chocolates for $1.79 each, and a juice for $3.05. How much remains on her gift card?
PLEASE HELP ME I WILL MARK YOU BRAINLIEST
Answer:
Remains on her gift card:
$3.07
Step-by-step explanation:
15 - ((2*2.65) + (2*1.79) + (1*3.05))
= 15 - (5.3 + 3.58 + 3.05)
= 15 - 11.93
= 3.07
Answer:
$3.07
Step-by-step explanation:
Ms. Gantt has a $15 gift card to Starbucks.
She buys 2 muffins for $2.65 each, = 2 × 2.65 = $5.3
2 hot chocolates for $1.79 each, = 2 × 1.79 = $3.58
and a juice for $3.05. = 1 × 3.05 = $3.05
Now,
$15 - $5.3 - $3.58 - $3.05 = $3.07
Thus, $3.07 remains on her gift card
A rectangular barn door needs to be painted. The door is 74 inches high and
50 inches wide. What is the area of the front of the door?
Answer:
2700 square inches
Step-by-step explanation:
Area of a rectangle is A = lw, where l= lenght, w = widthGiven a rectangular barn door with dimensions:
Height = 74 inWidth = 50 inThe area of front side of the door is:
A = 74 in * 50 in = 2700 square inchesThe steps below show the solution to the equation LaTeX: 3\left(x-2\right)=2\left(x-3\right)3 ( x − 2 ) = 2 ( x − 3 ). Order the reasons for the steps.
LaTeX: 3\left(x-2\right)=2\left(x-3\right)3 ( x − 2 ) = 2 ( x − 3 )
LaTeX: 3\left(x\right)+3\left(-2\right)=2\left(x\right)+2\left(-3\right)3 ( x ) + 3 ( − 2 ) = 2 ( x ) + 2 ( − 3 )
[ Select ]
LaTeX: 3x-6=2x-63 x − 6 = 2 x − 6
[ Select ]
LaTeX: 3x-2x=-6+63 x − 2 x = − 6 + 6
[ Select ]
LaTeX: x=0x = 0
Answer:
See Bold Texts
Step-by-step explanation:
Given
The steps to solve:
[tex]3( x - 2 ) = 2( x - 3 ).[/tex]
Required
Order the steps with reasons
[tex]3( x - 2 ) = 2( x - 3 ).[/tex]
Open Brackets
[tex]3(x) + 3(-2)= 2(x)+ 2(-3)[/tex]
Open Brackets
[tex]3x - 6 = 2x -6[/tex]
Collect Like Terms
[tex]3x - 2x = -6 + 6[/tex]
[tex]x =0[/tex]
Answer:
i believe X=4? sorry math is not my strong suit and probably didn't get the answer right!
Jayla gets the right
shade of pink paint by
mixing 1/4 cup of white
paint with 1/3 cup of red
paint. How many cups
of white and red paint
does Jayla need to
make 18 cups of this
shade of pink paint?
Answer: actually I'm a 13 year old child but still I will answer right. so lets start okay. first step for me is to add 1/4+1/3 = lcm of 1/4+1/3is 12 so then total will be 7/12 then we will. 7/12of18 maybe and answer is 21/2
Exponents does what to the same number continuously?
Answer:
Exponents multiply a base number by itself continuously
Step-by-step explanation:
Exponents create repeated multiplication, where the base number will be continuously multiplied by itself.
The number of times it will be multiplied depends on the exponent.
For example, 2³ will be the number 2 multiplied by itself 3 times.
Find the equation of an ellipse centered at the origin with foci at the points( 0 , 3 ) and ( 0 , − 3 ). Additionally, the major axis of this ellipse has a length of 10. 15 POINTS, DUE IN 2 HOURS, will give BRAINLIEST!
Answer:
[tex]\frac{x^2}{25}+\frac{y^2}{16}=1[/tex]
Step-by-step explanation:
We know that the foci lies on the major axis, so it should lie on the x - axis. Additionally the center is the midpoint of the line joining the foci, at (0,0).
Now remember we have our foci at the point (0, ± 3). Our major axis length is 10, so if covers 5 units on either side of the x - axis. Therefore, c = 3, and a = 5. But remember that c is not part of an ellipse equation. Take a look at the formula below,
(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1
However we can solve for " b " instead, using c. Take a look at another major formula below,
c^2 = a^2 - b^2,
(3)^2 = (5)^2 - b^2,
9 = 25 - b^2,
- b^2 = 16,
b = 4 = - 4
Whether b = - 4 or b = 4, or equation will be the same.
(x - 0)^2 / (5)^2 + (y - 0)^2 / (4 or - 4)^2 = 1,
x^2 / 25 + y^2 / 16 = 1
Our solution is hence option number 1 : [tex]\frac{x^2}{25}+\frac{y^2}{16}=1[/tex]
Solve for s.
(6s - 5)(s - 3) = 0
Write your answers as integers or as proper or improper fractions in simplest form.
S = or s =
Answer:
s = 5/6, s = 3
Step-by-step explanation:
(6s - 5)(s - 3) = 0
Solving for s:
1. ...........
6s - 5 =06s = 5s = 5/62. ...........
s - 3 = 0s =3Find the coordinates of point A, if point M(-1, 2) is the midpoint of segment AB and B has coordinates of (3, -5) A. ( -5, 9) B. ( 1, -1 ) C. ( 4, 3) D. ( -2 , 4)
Answer:
A. (-5,9)
Step-by-step explanation:
hard to explain but i found the distance of M and B which is (4,7). using this i added that with M which equals (-5,9)
(sorry for bad explanation)
If a is directly proportional to b/2 and a=1 when b=10, then what is the value of a when b=35
Answer:
3.5
Step-by-step explanation:
b divided by 10 is A
35 divided by 10 is 3.5
A ball flies through the air. Right before it hits the ground, its speed is 10 meters/second and it has 500 joules of kinetic energy. The mass of the ball is kilograms.
Answer:
10 kg
Step-by-step explanation
Explanation:
Kinetic Energy = 1/2 * M (V square )
M is mass and V is velocity of the ball
500J = 1/2 *M *( 10)*(10)
M = 10 kg
Answer:
10 kg
Step-by-step explanation:
Formula for the kinetic energy:
½mv²
Find the mass:
= ½ × m × 10² = 500 joules
= 50 × m
m = 500 ÷ 50
m = 10 kg
The answer is 10 kg.
Mia is making fruit punch for her birthday party. She puts 120 milliliters of cherry juice into a pitcher. Then she adds 250 milliliters of raspberry juice. She tops it off with sparkling water. How many milliliters of juice does she use?
Answer: She used 370 milliliters of juice
Step-by-step explanation:
Solve 25n=2×25 for n. You can use a related equation. n = [tex]\frac{2*25}{25}[/tex]
Answer:
n=2
Step-by-step explanation:
25n=2×25
Divide each side by 25
25n/25=2×25/25
n = 2 * 25/25
n =2
Please Hurry!!! THANKS!!
Answer:
first one is A. I have no idea what the second is. good luck, it might be D.
Answer:
1) 3x³ - x² - 15x + 5
2) x² - 4
3) (5, 3)
4) f⁻¹(x) = 1/3x - 4
Step-by-step explanation:
1......................
Givenf(x) = 3x - 1g(x) = x² - 5f(x) · g(x) =?Solution f(x) · g(x) = (3x - 1)(x² - 5) =3x·x² - 3x·5 - x² + 5 =3x³ - x² - 15x + 5Correct option is A.
2......................
Givenf(x) = x²g(x) = x - 4g(f(x)) =?Solutiong(f(x)) = g(x²) = x² - 4Correct option is D.
3......................
Point (5, 3) is the inverse of point (3,5)
Correct option is C
4......................
Givenf(x) = 3x - 12Inverse of function = ?SolutionTo get the inverse of the function, switch over domain and range:
x = 3f⁻¹(x) - 123f⁻¹(x) = x - 12f⁻¹(x) = 1/3x - 4Correct option is D.
Which two ordered pairs represent a proportional relationship?
OA. (2, 2) and (4, 4)
ОВ.
(4, 3) and (4,4)
OC. (3, 2) and (4, 4)
OD. (2, 2) and (4, 6)
I need the answer ASAP
Answer:
Hey there!
(2, 2) and (4, 4) represent a proportional relationship.
Let me know if this helps :)
Sonya, who is paid time and a half for hours worked in excess of 40 hours, had gross weekly wages of $345 for 44 hours worked. What is her regular hourly rate?
Answer:
$7.5/hour
Step-by-step explanation:
Sonya is paid time and half for hours worked in excess of 40 hours
She has a gross weekly wages of $345 for 44 hours
Let y represent sonya's hourly rate
Since she is paid one and half then it can be represented as 1.5y
Sonya is suppose to work for a period of 40 hours, this means that she has 4 overtime hours
Therefore Sonya regular hourly rate can be calculated as follows
40y + 4(1.5y) = 345
40y + 6y = 345
46y= 345
y = 345/46
y= 7.5
Hence Sonya's regular hourly rate is $7.5/hour
the product of 5 and g
Answer:
5g
Step-by-step explanation:
Check the functions whose inverses are also functions.
a. On a coordinate plane, an absolute value function opens down.
b. On a coordinate plane, an exponential functions increases from quadrant 2 into quadrant 1.
c. On a coordinate plane, a cubic function has an x-intercept of (0, 0).
Answer: B and C.
Step-by-step explanation:
A function will have an inverse, only and only if every value of y can be linked to only one value x.
A) Here we have an absolute value:
We know that for example:
I5I = 5 and I-5I = 5.
Then an absolute value function can not have an inverse function.
B) one way of having a function that is invertible or not, is see if the function is increasing or decreasing.
If a function is, for example, increasing, then as the value of x increases, also does the value of y.
Then we will never see that a single value of y is related to two or more different values of x.
Then an exponential function, which is an increasing function, will have an inverse that is also a function.
C) A cubic function that has a root in (0,0)
The cubic function that has only one root at x = 0 is the function:
f(x) = a*x^3 + b*x
where a and b are real numbers of the same sign.
Now, we can see at the first derivate of f(x) to see if it is strictly increasing or strictly decreasing.
f'(x) = 3*a*x^2 + b
Ok, as x^2 is always positive, we can know that the sign of f'(x) will always be the same, so this function is strictly increasing or strictly decreasing (it depends on the signs of a and b).
Then this function has an inverse that is also a function.
Answer:
b and c
Step-by-step explanation:
got a 100 on edge2020. I hope this helped!
Need help stuck with this
Answer:
2 is scalene
3 is obtuse
4 is isosceles
Step-by-step explanation:
Your neighborhood deli kept track of the wraps it sold for three months. The deli sold, 13d+25of the Turkey Waldorf Wraps and 16d+14of the Triple-Decker Chicken Wraps. Write and simplify a polynomial expression that represents the total amount of wraps sold.
Answer: 29 d + 39
Step-by-step explanation:
Given : The deli sold, 13d+25 of the Turkey Waldorf Wraps and 16d+14 of the Triple-Decker Chicken Wraps.
Then, the total amount of wraps sold will be
13d+25 + 16d+14
Simplify
13d+16d+25+14 [add like terms]
= 29 d + 39
Hence, the polynomial expression that represents the total amount of wraps sold is 29 d + 39.
In a mathematics class, half of the students scored 42 on an achievement test. With the
exception of a few students who scored 78, the remaining students scored 53. Which of the
following statements is true about the distribution of scores?
Answer:
If half the students scored 42 and some scored 53, the median must be (53 + 42)/2 = 47.5.
If the other half all scored 53, the mean would be the same, but the few 78s is going to raise the mean.
The mode is 42.
i hope it helps you
The mean is greater than the median. Then the correct option is B.
What are statistics?Statistics is the study of collection, analysis, interpretation, and presentation of data or to discipline to collect, and summarise the data.
In a mathematics class, half of the students scored 42 on an achievement test.
With the exception of a few students who scored 78, the remaining students scored 53.
We know that if the half of data is the same and the remaining data is greater than that data.
Then the mean is greater than the median.
Then the correct option is B.
The complete options of the question is attached below.
More about the statistics link is given below.
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Find the value(s) of k such that 4x² + kx + 4 = 0 has 1 rational solution
Answer:
If you mean only one rational solution, the answer is
[tex]k_1 = 8, k_2 = -8[/tex]
If you mean at least 1 rational solution, the answer is
[tex]k\in (-\infty, -8]\cup[8, \infty)[/tex]
Step-by-step explanation:
[tex]4x^2 + kx + 4 = 0[/tex]
Let's calculate the discriminant.
[tex]\Delta = b^2 - 4ac[/tex]
[tex]\Delta = k^2 -4 \cdot 4 \cdot 4[/tex]
[tex]\Delta = k^2 -64[/tex]
Now, remember that:
[tex]\text{If } \Delta > 0 : \text{2 Real solutions}[/tex]
[tex]\text{If } \Delta = 0 : \text{1 Real solution}[/tex]
[tex]\text{If } \Delta < 0 : \text{No Real solution}[/tex]
Therefore, I will just consider the first two cases.
[tex]k^2 - 64 > 0[/tex]
and
[tex]k^2 -64 = 0[/tex]
[tex]\boxed{\text{For } k^2 - 64 > 0}[/tex]
[tex]k^2 > 64 \Longleftrightarrow k>\pm\sqrt{64} \Longleftrightarrow k\in (-\infty, -8)\cup(8, \infty)[/tex]
[tex]\boxed{\text{For } k^2 - 64 = 0}[/tex]
[tex]k^2 = 64 \Longleftrightarrow k=\pm\sqrt{64} \implies k_1 = 8, k_2 = -8[/tex]
Write the prime factors of 15. Separate each number with a comma.
Answer:
21
Step-by-step explanation:
21_++_+_+
Answer:
21
Step-by-step explanation:
Solve the equation for x. 3/4(x + 21) = 10 1/2
Answer:
x=7
Step-by-step explanation:
3/4(x+21)=10 1/2
3/4x+63/4 = 21/2
3/4x= 21/2-63/4
3/4x= -21/4
x= (-21/4)/(3/4)
x= (-21/4)x(4/3)
x= -84/12
x=-7
The equation for x is -7 .
To find the equation for x.
What is algebra?A part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.
Given that:
The equation are
3/4(x+21)=10 1/2
3/4x+63/4 = 21/2
3/4x= 21/2-63/4
3/4x= -21/4
By cross multiplication
x= (-21/4)/(3/4)
Reverse the numerator and denominator
x= (-21/4)x(4/3)
x= -84/12
x=-7
So, the equation for x is -7 .
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Which inequality matches the number line ? Help!!
What is the value of x?
Answer:
x = 24
Step-by-step explanation:
Pythagorean Theorem: a² + b² = c²
a = a leg
b = another leg
c = hypotenuse
Step 1: Plug in known variables
x² + 10² = 26²
Step 2: Evaluate
x² + 100 = 676
Step 3: Isolate x term
x² = 576
Step 4: Isolate x
√x² = √576
x = 24
Answer:
[tex]x=24[/tex]
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean Theorem.
The Pythagorean Theorem is:
[tex]a^2+b^2=c^2[/tex]
The hypotenuse is c, and the legs are a and b.
Plug in 26 for c since 26 is the hypotenuse, and let 10 for a and x be b. Therefore:
[tex]x^2+10^2=26^2[/tex]
Square:
[tex]x^2+100=676[/tex]
Subtract 100 from both sides:
[tex]x^2=576[/tex]
Take the square root of both sides:
[tex]\sqrt{x^2}=\sqrt{576}\\x=\sqrt{576}=24[/tex]
The answer is 24.