Answer:
the interest earned= 93.401
and the future value of an annuity= 493.401
Step-by-step explanation:
Given Data:
Interest rate= 7%
time,t = 3 years
weekly payment, P= 400
At the end of 3 years, final investment A= ?
n= 52 as it is weekly
As per the interest formula
A= P(1+r/n)^nt
Putting value in above equation
= [tex]400\left(1+\frac{0.07}{52}\right)^{156}[/tex]
= 493.401
Interest earned = A-P
= 493.401-400
= 93.401 !
find the roots of the polynomial equation x3 - 2x2 + 10x + 136 = 0
Answer: x=-4,3+5x; 3,-5x
step-by-step explanation: I just used ,athway. this is what is told me. i hope this helps
PLEASE HELP RIGHT AWAY
ANSWER
The fifth term is 27
EXPLANATION
The explicit rule for the given sequence is
[tex]t_n= {2}^{n} - n[/tex]
To find the fifth term, we substitute n=5 to get,
[tex]t_5= {2}^{5} - 5[/tex]
[tex]t_5= 32 - 5[/tex]
Simplify:
[tex]t_5= 27[/tex]
The fifth term is 27
Stefan’s family rented a rototiller to prepare an area in their backyard for spring planting. The rental company charged an initial fee of $43 with an additional fee per hour. If they paid $64 after renting the rototiller for 7 hours, what was the hourly fee?
Answer:
$3
Step-by-step explanation:
Whenever some type of expenditure is made, there are usually 2 types of costs available: the fixed cost and the variable cost. Former is the constant cost which has to be incurred in order to gain the advantage from the expense. Latter is the cost that varies with the duration of the expense. Therefore, total costs (TC) = fixed costs (FC) + variable costs (VC). VC can be expressed as: VC = price per hour (p) * number of hours (h). So the equation becomes TC = FC + p*h. In this question, FC = $43, TC = $64, h = 7 hours, and p is unknown. So plugging in the values give:
64 = 43 + 7p.
Solving the equation for p gives:
p = 21/7. This implies that p = 3.
Therefore, the hourly fee is $3!!!
Answer:
7h+43=64
$3 the hourly fee for the rototiller
Step-by-step explanation:
help needed! 30 points!!
Answer:76 and 84
Step-by-step explanation:
Answer:
1) 78 and 82
2)76 and 84
3)74 and 86
Step-by-step explanation:
1)
Given
mean, x= 80
standard deviation, sd= 2
given percentage of class= 68%
now as per the properties of normal distribution:
-68% of the scores will lie within one standard deviation, sd of the mean, x
i.e. between x-sd and x+sd
Putting values in above we get:
x-sd= 80-2 = 78
x+sd=80+2= 82
Hence about 68% of the class would score between 78 and 82
2)Given
mean, x= 80
standard deviation, sd= 2
given percentage of class= 95%
now as per the properties of normal distribution:
-95% of the scores will lie within 2 standard deviation, sd of the mean, x
i.e. between x-2sd and x+2sd
Putting values in above we get:
x-sd= 80-2(2) = 80-4 = 76
x+sd=80+2(2)= 80+4 = 84
Hence about 95% of the class would score between 76 and 84
3)Given
mean, x= 80
standard deviation, sd= 2
given percentage of class= 99%
now as per the properties of normal distribution:
-99% of the scores will lie within 3 standard deviation, sd of the mean, x
i.e. between x-sd and x+sd
Putting values in above we get:
x-sd= 80-3(2) = 80-6 = 74
x+sd=80+3(2)= 80+6 = 86
Hence about 99% of the class would score between 74 and 86!
Let f(x)=x2−3x−4 .
What is the average rate of change from x = 7 to x = 10?
Answer:
The average rate of change from x= 7 to x=10 is 14
Step-by-step explanation:
We can use the slope formula to find the average rate of change
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Now, we are given f(x) = x^2-3x-4 and x=7 to x=10
Our formula can be rewritten as:
[tex]m=\frac{f(10)-f(7)}{10-7}[/tex]
finding f(10) = (10)^2 -3(10) -4
= 100 -30 -4
= 66
and f(7) = (7)^2 -3(7) -4
= 49-21-4
= 24
Now finding m:
m= 66 - 24 / 10-7
m= 42/3
m= 14
So, the average rate of change from x= 7 to x=10 is 14.
ANSWER
[tex]14[/tex]
EXPLANATION
The given function is
[tex]f(x) = {x}^{2} - 3x - 4[/tex]
The average rate of change from x=7 to x=10 is given by;
[tex] \frac{f(10) - f(7)}{10 - 7} [/tex]
[tex]f(10) = {(10)}^{2} - 3(10) - 4[/tex]
[tex]f(10) = 100 - 30 - 4[/tex]
[tex]f(10) = 66[/tex]
[tex]f(7) = {7}^{2} - 3(7) - 4[/tex]
[tex]f(7) = 49 - 21- 4 = 24[/tex]
The average rate of change now becomes:
[tex] \frac{26 - 24}{3} = \frac{52}{3} =14[/tex]
What’s 1/6 of 2 I’m learning about this and I still don’t get it
Answer:
it would be in a decimal 2.6
Step-by-step explanation:
Answer:1/3
Step-by-step explanation:
1/6 × 2/1 =1/3
Cross multiply 6÷2 =3
What is the reciprocal of (13xz)/(31zy)?
Answer:
(31zy)/(13xz)
Step-by-step explanation:
A reciprocal is a number that you can multiply the original number by and get a product of 1. To find the reciprocal of a fraction, flip it upside down, putting the numerator in the denominator, and the denominator in the numerator:
[tex]\frac{31zy}{13xz}[/tex]
If we multiply this fraction by the other, we would end up simplifying it to 1 by cross multiplication.
Identify the vertex of y = -1 (x-4)^2 +9 and tell whether it’s a minimum or maximum
please and thanks!
Answer:
maximum at (4, 9)
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
y = - 1(x - 4)² + 9 is in this form
with vertex = (4, 9)
• If a > 1 then vertex is a minimum
• If a < 0 then vertex is a maximum
here a = - 1 , hence vertex (4, 9) is a maximum
ax-bx+y=z which of the following represents the formula that could be used to find x?
Step by step explanation:
You first subtract z on both sides of the equal sign
ax-bx=(z-y)
Since a and b both have a "x" you can subtract them
(a-b)x=(z-y)
then you divide "x" on both sides of the equal sign
[tex]\frac{a - b}{x} = \: \frac{z - y}{x} [/tex]
To find x in the equation ax-bx+y=z, combine like terms, subtract y from both sides, and then divide by (a-b) to get the formula x = (z-y)/(a-b).
To find the value of x in the equation ax - bx + y = z, you can follow these steps:
Combine like terms by factoring out x from the terms ax and -bx, which gives you x(a - b).Subtract y from both sides of the equation to isolate the term with x on one side, resulting in x(a - b) = z - y.Finally, divide both sides by (a - b) to solve for x, assuming that a ≠ b, which gives the formula x = (z - y) / (a - b).This step-by-step process allows you to solve for x in terms of a, b, y, and z.
I need help finding the missing sides using the law of sines
Check the picture below.
By the law of sines,
[tex]\dfrac{\sin\angle A}a=\dfrac{\sin\angle B}b=\dfrac{\sin\angle C}c[/tex]
The interior angles of any triangle sum to 180 degrees in measure, so we know
[tex]m\angle A=(180-85-40)^\circ=55^\circ[/tex]
Then
[tex]\dfrac{\sin55^\circ}a=\dfrac{\sin85^\circ}{26}\implies a\approx21[/tex]
and
[tex]\dfrac{40^\circ}c=\dfrac{\sin85^\circ}{26}\implies c\approx17[/tex]
Use the following matrices, A, B, C and D to perform each operation.
A = |3 1|
|5 7|
B = |4 1|
|6 0|
C = |-2 3 1|
|-1 0 4|
D = |-2 3 4|
|0 -2 1|
|3 4 -1|
40. A + B
41. B - A
42. 3C
43. CD
44. 2D + 3C
Step-by-step explanation:
[tex]\bold{40.}\\\\A+B=\left[\begin{array}{ccc}3&1\\5&7\end{array}\right] +\left[\begin{array}{ccc}4&1\\6&0\end{array}\right] =\left[\begin{array}{ccc}3+4&1+1\\5+6&7+0\end{array}\right]=\left[\begin{array}{ccc}7&1\\11&7\end{array}\right][/tex]
[tex]\bold{41.}\\\\B-A=\left[\begin{array}{ccc}4&1\\6&0\end{array}\right]-\left[\begin{array}{ccc}3&1\\5&7\end{array}\right]=\left[\begin{array}{ccc}4-3&1-1\\6-5&0-7\end{array}\right]=\left[\begin{array}{ccc}1&0\\1&-7\end{array}\right][/tex]
[tex]\bold{42.}\\\\3C=3\left[\begin{array}{ccc}-2&3&1\\-1&0&4\end{array}\right]=\left[\begin{array}{ccc}(3)(-2)&(3)(3)&(3)(1)\\(3)(-1)&(3)(0)&(3)(4)\end{array}\right]=\left[\begin{array}{ccc}-6&9&3\\-3&0&12\end{array}\right][/tex]
[tex]\bold{43.}\\\\CD=\left[\begin{array}{ccc}-2&3&1\\-1&0&4\end{array}\right]\left[\begin{array}{ccc}-2&3&4\\0&-2&1\\3&4&-1\end{array}\right]\\\\=\left[\begin{array}{ccc}(-2)(-2)+(3)(0)+(1)(3)&(-2)(3)+(3)(-2)+(1)(4)&(-2)(4)+(3)(1)+(1)(-1)\\(-1)(-2)+(0)(0)+(4)(3)&(-1)(3)+(0)(-2)+(4)(4)&(-1)(4)+(0)(1)+(4)(-1)\end{array}\right]\\\\=\left[\begin{array}{ccc}4+0+1&-6-6+4&-8+3-1\\2+0+12&-3+0+16&-4+0-4\end{array}\right]\\\\=\left[\begin{array}{ccc}5&-8&-6\\14&13&-8\end{array}\right][/tex]
[tex]\bold{44.}\\\\2D+3C=2\left[\begin{array}{ccc}-2&3&4\\0&-2&1\\3&4&-1\end{array}\right]+3\left[\begin{array}{ccc}-2&3&1\\-1&0&4\end{array}\right]\\\\=\left[\begin{array}{ccc}(2)(-2)&(2)(3)&(2)(4)\\(2)(0)&(2)(-2)&(2)(1)\\(2)(3)&(2)(4)&(2)(-1)\end{array}\right]+\left[\begin{array}{ccc}(3)(-2)&(3)(3)&(3)(1)\\(3)(-1)&(3)(0)&(3)(4)\end{array}\right]\\\\=\left[\begin{array}{ccc}-4&6&8\\0&-4&2\\6&8&-2\end{array}\right]+\left[\begin{array}{ccc}-6&9&3\\-3&0&12\end{array}\right][/tex]
[tex]\large\bold{You\ can\ not\ add\ matrices\ of\ different\ dimensions!!!}[/tex]
What numbers are multiples
of 9 and factors of 36?
Answer:
9,18, and 36
Step-by-step explanation:
9*4=36 and 9*1=9
18*2=36 and 9*2=18
36*1=36 and 9*4=36
Answer:
multiples of 9: 9, 18, 27, 36, 45, 54, 63,72, 81, 90, 99, 108, etc.
factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Step-by-step explanation:
A real estate agent earns 6% commission. If she sells a house for $125,700. What is her commission
Answer:
$7,542
Step-by-step explanation:
Her commission is 6% of $125,700.
To find a percent of a number, multiply the percent by the number. Change the percent to a decimal by dividing the percent by 100.
6% of $125,700 =
= 6% * $125,700
= 0.06 * $125,700
= $7,542
IF IT'S RIGHT I Promise BRAINLIST;5-STARS;THANKS; Beleive me it's simple I promise!!
What would the graph of y=3/4-7/8 look like?
A. A straight line
B. A parabola
C. A curve
D. None of the above
B) a parabola
SHSJDKD
The graph of y = 3/4 - 7/8 will end up being a straight line. The line will be horizontal and cross the y axis at approximately (0,1).
Use algebraic rules of equations to predict the solution type to the system of equations. Include all of your work for full credit.
{x+y=-4
{y=2x-1
Answer:
The solution of the two equations is (-1 , -3)
Step-by-step explanation:
* Lets revise how to solve the system of the linear equations
- We have two ways to do that
# Substitution method
# Elimination method
- Substitution method is to find one variable in terms of the other
variable from one of the two equations, then substitute this value
in the second equation
* Lets solve the problem by the substitution method
∵ x + y = -4 ⇒ (1)
∵ y = 2x - 1 ⇒ (2)
- In equation (2) we have y in terms of x
∴ Substitute (2) in (1)
∴ x + (2x - 1) = -4 ⇒ simplify ir
∴ x + 2x - 1 = -4 ⇒ add the like terms
∴ 3x - 1 = -4 ⇒ add 1 to both sides
∴ 3x = -3 ⇒ divide both sides by 3
∴ x = -1
- Substitute the value of x in equation (2)
∴ y = 2(-1) - 1 = -2 - 1 = -3
∴ The solution of the two equations is (-1 , -3)
* Lets check the answer
- Substitute the value of x-coordinate and y-coordinate in equation (1)
∵ The left hand side = (-1) + (-3) = -4
∵ The right hand side = -4
∴ The two sides equal each other
∴ (-1 , -3) is a solution of the equation x + y = -4
* Lets do the same in the second equation
∵ The left hand side = -3
∵ The right hand side = 2(-1) - 1 = -2 -1 = -3
∴ The two sides equal each other
∴ (-1 , -3) is a solution of the equation y =2x - 1
∴ (-1 , -3) is the solution of the two equations
I have no idea how to do this. Please help.
Answer:
C. 14,871.21
Step-by-step explanation: You take the number 29,742.42 and multiply it by .2 to get how much they spend on food (5,948.48), and you multiply the same number by .3 to get how much they spend on housing (8,922.73). Then, you add them up to get the total. .2 is acctually 20% of what they spend out of the 29,742.42 and the same for the .3. Hope this wasn't too complicated by the way I explained it.
1. Choose the order pair that is a solution for this equation.
X - 3y = -7
A. (2,4)
B. (2,3)
C. (2,-1)
2. Could this order pair be a solution to this equation?
3x - 2y = 10
A. Yes
B. No
3. In which quadrant is point (4,6) located? (Remember to use roman numerals to write the quadrant numbers.)
4. Find the Slope of the line that contains these points.
(3,2) (5,12)
5. Is this ordered pair a solution to the inequality?
(5,1)
2.2x - 4.33y > 0
A. Yes
B. No
6. In which quadrant would these coordinates be located?
(3,-6)
A. Quadrant ll
B. Quadrant lll
C. Quadrant lV
D. Quadrant l
7. Which ordered pair could be a solution to this inequality?
5x + 1 < 3y
A. (-2,3)
B. (2,-3)
C. (-4,-7)
Solve the system by substitution. Check your solution.
a - 1.2b = -3
0.2b + 0.6a = 12
a.
(15, 15)
c.
(13, 12)
b.
(10, 12)
d.
(7, 9)
Answer:
a. (15, 15)
Step-by-step explanation:
We start with those two equations:
1) a - 1.2b = -3
2) 0.2b + 0.6a = 12
We'll begin by modifying equation #1 to isolate a:
a = -3 + 1.2b
Then we'll use this value for a in the second equation:
0.2b + 0.6 (-3 + 1.2b) = 12
0.2b - 1.8 + 0.72b = 12
0.92b = 13.8
b = 15
Then we'll place that value of b in the first equation to find a:
a - 1.2 (15) = -3
a - 18 = -3
a = 15
Answer:
(15,15) is right
Step-by-step explanation:
WILL MARK BRAINLIEST HELP ASAP
Answer:chicken nuggie
Step-by-step explanation:
in a symmetrical distribution the mean, median, and mode are:
A. supplementary
B. equal
C. not equal
D. congruent
Answer:
The correct answer option is B. equal.
Step-by-step explanation:
In a symmetrical distribution the mean, median, and mode are equal.
In any distribution which is symmetric, half of its curve is the mirror image of the other half. The pull remains same on each side and the frequencies are also symmetrically distributed.
Therefore, mean, median and mode all fall at the middle as one side balances the other sides.
Answer:
B) EQUAL
Hope this hels
math im soooooooooooooo baaaaaaaaaaaadddddddddddddd
Answer:
The correct answer is A, 73
Step-by-step explanation:
First we have to arrange the whole numbers in ascending order. i-e from smallest to largest. Showing it as follows:
53 54 59 62 64 65 66 68 70 71 75 78 79 79 83 83 86 90 91 94
Now we would find the median by taking the middle number. But this series consists of even numbers. There are 20 numbers. So we will take the middle two numbers and find their average like follows:
71 + 75 = 146/2 = 73
The answer is 73
Answer:
median =73
Step-by-step explanation:
Given list of data is
{94,79,83,78,70,66,68,75,53,54.79,59,83,91,64,65,71,62,86,90}.
Now we need to find about what is the median for the data listed above.
So first we need to rearrange the given data in increasing order. then we can easily find the middle number as median.
Sorted list of data is:
{53, 54, 59, 62, 64, 65, 66, 68, 70, 71, 75, 78, 79, 79, 83, 83, 86, 90, 91, 94}
there are two numbers at the middle 71 and 75
then median = (71+75)/2=146/2=73
if the side of a regular hexagon is 10 cm then the radius of its circumcircle is?
Answer:
10 cms.
Step-by-step explanation:
The circumcircle passes through each vertex of the hexagon so the radius is equal to one of the 2 equal sides of an isosceles triangle with base = 10 cm and vertex = 60 degrees.
So considering this triangle the base angles are ( 180 - 60) / 2 = 60 degrees. So we have an equilateral triangle with each side = 10 cm.
Therefore the radius is 10 cm. long.
The radius of the circumcircle of the regular hexagon is approximately 5.77 cm.
In a regular hexagon:
- Each side length s = 10 cm.
- The circumcircle passes through all vertices of the hexagon, making it the circle that circumscribes the hexagon.
The radius R of the circumcircle of a regular hexagon can be related to its side length s by the formula:
[tex]\[ R = \frac{s}{\sqrt{3}} \][/tex]
Let's apply this formula:
[tex]\[ R = \frac{10}{\sqrt{3}} \][/tex]
To simplify [tex]\( \frac{10}{\sqrt{3}} \)[/tex], multiply the numerator and the denominator by [tex]\( \sqrt{3} \)[/tex]
[tex]\[ R = \frac{10 \cdot \sqrt{3}}{3} \][/tex]
Therefore, the radius of the circumcircle of the regular hexagon with a side length of 10 cm is [tex]\( \frac{10 \sqrt{3}}{3} \)[/tex] cm. This is the exact value of the radius in terms of [tex]\( \sqrt{3} \)[/tex]. If you need a numerical approximation, you can calculate it as follows:
[tex]\[ R \approx \frac{10 \times 1.732}{3} \approx \frac{17.32}{3} \approx 5.77 \text{ cm} \][/tex]
Part A: Factor x2a2 + 3xa2 + 2a2. Show your work. (4 points)
Hope this is what you need
Answer:
I am not sure of the equation but I interpreted it as x^2a^2+3xa^2+2a^2
Step-by-step explanation:
X^2a^2+3xa^2+2a^2
1. a^2 (x^2+3x+2)
2.a^2(x^2+2x+x+2)
3. a^2(x(x+2)+x+2)
4. a^2(x+2)(x+1)
Y=2/3x-4 and y=-3/2x+1 are perpendicular lines. Jack notices that the product of the two perpendicular slopes is -1. If a line has a slope of a/b, determine the perpendicular slope, and then show that the product is-1.
Answer:
Slope = -b/a.
Step-by-step explanation:
Note that the relation between 2/3 and -3/2 is that their product is -1.
If the slope is a/b then we have a/b * m = -1 where m is the slope of the perpendicular line .
So m = -1 / a/b
= -b/a.
The produce = a/b * -b/a = -1.
Which function corresponds to the table?
x y
0 3
1 1
2 -1
A) y = 3x - 2
B) y = 2x + 3
C) y = -2x + 3
D) y = -3x + 2
Answer:
c
Step-by-step explanation:
according to the synthetic division below which of the following statements is true
Answer:
A, D, and F.
Step-by-step explanation:
A:
The remainder is 0, thereby satisfying the factor theorem.
D: Synthetic division is in the form p(x)/(x-a). Since -4 is the number, the factor must be (x--4) or (x+4)
F: Refer to D.
How many natural numbers are between 45 and 58?
Answer:
12
Step-by-step explanation:
You could actually list the numbers between (but not including) 45 and 58:
{46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57}. I count 12 numbers here.
A number is an arithmetic value that is used to represent a quantity and calculate it. The number of natural numbers between 58 and 45 are 12.
What are Numbers?A number is an arithmetic value that is used to represent a quantity and calculate it. Numericals are written symbols that represent numbers, such as "3."
The number of natural numbers between any two natural numbers is given by the (n₂-n₁-1), where the two of the numbers are not included. Also, n₂ and n₁ represent the two natural numbers.
As it is needed to be found the natural number is between 45 and 58, the value of n₂ is 58, while the value of n₁ is 45. Therefore,
The number of natural numbers = (n₂-n₁-1) = (58-45-1) = 12
Hence, the number of natural numbers between 58 and 45 are 12.
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What is the solution of 9|2x – 1| + 4 < 49?
Answer: [tex]-2<x<3[/tex]
Step-by-step explanation:
You need to set up two cases (Positive case and negative case) and solve for "x".
- POSITIVE CASE IF: [tex]2x-1>0[/tex]
[tex]9(2x -1) + 4 < 49\\18x-9<49-4\\18x<54\\x<3[/tex]
- NEGATIVE CASE IF: [tex]2x-1<0[/tex]
[tex]-9(2x -1) + 4 < 49\\-18x+9<49-4\\-18x<36\\x>-2[/tex]
Therefore, the solution is:
[tex]-2<x<3[/tex]
Answer:
see explanation
Step-by-step explanation:
Given
9 | 2x - 1 | + 4 < 49 ( subtract 4 from both sides )
9 | 2x - 1 | < 45 ( divide both sides by 9 )
| 2x - 1 | < 5
Inequalities of the type | x | < a always have solutions of the form
- a < x < a, thus
- 5 < 2x - 1 < 5 ( add 1 to all 3 intervals )
- 4 < 2x < 6 ( divide all 3 intervals by 2 )
- 2 < x < 3
Which expression is equivalent to cos 120 degrees
Answer:
option b) cos 240 degrees.
Step-by-step explanation:
This means that the expression cos 120 degrees can also be written as cos 240 degrees.
This because cos 240 degrees = -1/2 = cos 120 degrees.
This happens because the second and third quadrants carry the same signs.
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The cos240 degree is equal to cos120 degree because they both have same value which is -1/2
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have a:
= cos120°
The value of the cos120 is -1/2
= cos(90+30)
= -sin30
= -1/2
The value of cos240
cos240 = cos(180+60) = -cos60 = 1/2
cos120° = cos240°
Thus, the cos240 degree is equal to cos120 degree because they both have same value which is -1/2
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Which of these is an equation? A 2y + 7 = 9 B 2x > 3 C 3n + 5 D a2 + 2
Answer:
Option A is correct answer.
Step-by-step explanation:
An equation is having two sides equal. It has an = sign in it.
So, Option A 2y+7 = 9 is an equation as it has = sign in it. So, it is correct option.
All other options do not have = sign in them so, they are not equations.