Answer:
Infinite because it keeps going
ANSWER
EXPLANATION
The given series is
5 + 10 + 15 + 20 + . . . + 5n + . . .
The first term of this series 5
The constant difference is:
d=10-5=5
The +... at the end of the series means it does continue to infinity.
The series is infinite
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!
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
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
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.
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]
PLEASE HELP ME!!!!!!
Answer:
Sample size is 6, event of rolling an even number is 3/6 (or 1/2)
Step-by-step explanation: When you roll a dice it could be 1, 2, 3, 4, 5, or 6. Count those up and you'll have the sample size. Odds of rolling a 2, 4, or 6 (even number) is 3/6 or 1/2, or 50%
WILL MARK BRAINLIEST HELP ASAP
Answer:chicken nuggie
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
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:
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:
68 is 85% of what number
Hello! Based on this problem, 68 is part of a whole. To solve it, we can write and solve a proportion. Set it up like this:
68/x = 85/100
Cross multiply the sections. 68 * 100 is 6,800 and 85 * x is 85x. So you get 6,800 = 85x. Now, divide each side by 85 to isolate the x. 85x/85 cancels out. 6,800/85 is 80. We can check this answer by multiplying 80 by 85%. 80 * 85% (0.85) is 68. There's our answer. 68 is 85% of 80.
The number whose 85 percent gives 68 is 8000.
What is the number whose 85 percent gives 68?Given the parameters in the question:
Given Value = 68
Percentage = 85%
To find the number whose 85 percent gives 68, we can use the following formula:
Number = (Given Value / Percentage) × 100
First, convert 85% from percent to decimal:
85% = 85/100 = 0.85
Now, plug these values into the above formula:
Number = (Given Value / Percentage) × 100
Number = ( 68 / 0.85 ) × 100
Number = 80 × 100
Number = 8,000
Therefore, 68 is 85% of the number 8000.
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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:
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.
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.
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.
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]
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
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
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
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:
what is the constant term of -3x^4-7x+2
Answer:
The equation written in the standard form is written as
ax^4 + bx+c
where a and b are the coefficients of the second-order and first-order term, while c is the constant term.
The equation we have in this problem is
By comparing (1) with (2), we immediately see that
A = -3x^4
B = 7x
C = 2
Step-by-step explanation:
Hope this helps :)
Final answer:
The constant term in the polynomial [tex]-3x^4 - 7x + 2[/tex] is 2, as it is the term without any variables.
Explanation:
The constant term in the polynomial [tex]-3x^4 - 7x + 2[/tex] is the term that does not contain any variables. In this polynomial, the terms are classified based on their variable's degree. In this case, -3x^4 is the term with the variable raised to the fourth power, -7x is the term with the variable to the first power, and 2 is the term with no variable, which makes it the constant term. Therefore, the constant term is 2.
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]
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
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]
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).
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
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)
5 yards 2 feet × 2=
Answer:
11 and 1/3 yards
Step-by-step explanation:
5 yards and 2 feet = 5 and 2/3 yards = 17/3 yards
(17/3 yards)(2) = 34/3 yards = 11 and 1/3 yards
The equivalent value of 5 yards 2 feet × 2 is 11 and 1/3 yards.
Given,
5 yards 2 feet × 2
Here,
Firstly convert feet to yard,
1 yard = 1/3 feet
So,
2 feet = 2/3 yard
So,
5 yards and 2 feet = 5 and 2/3 yards
= 17/3 yards
Now,
(17/3 yards)(2) = 34/3 yards
= 11 and 1/3 yards
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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.
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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