Answer:
1. sum of term = 465
2. nth term of the AP = 30n - 10
Step-by-step explanation:
1. The sum of all natural number from 1 to 30 can be computed as follows. The first term a = 1 and the common difference d = 1 . Therefore
sum of term = n/2(a + l)
where
a = 1
l = last term = 30
n = number of term
sum of term = 30/2(1 + 30)
sum of term = 15(31)
sum of term = 465
2.The nth term of the sequence can be gotten below. The sequence is 20, 50, 80 ......
The first term which is a is equals to 20. The common difference is 50 - 20 or 80 - 50 = 30. Therefore;
a = 20
d = 30
nth term of an AP = a + (n - 1)d
nth term of an AP = 20 + (n - 1)30
nth term of an AP = 20 + 30n - 30
nth term of the AP = 30n - 10
The nth term formula can be used to find the next term progressively. where n = number of term
The sequence will be 20, 50, 80, 110, 140, 170, 200..............
I NEED HELP PLEASE, THANKS! :)
Answer: b) increasing for x < -4/3 and x > 4/3
decreasing for -4/3 < x < 4/3
Step-by-step explanation:
Graph the equation and the follow the curve from left to right. When you are going up, it is increasing. When you are going down, it is decreasing.
see the image below. Red is increasing. Blue is decreasing.
The vertices occur when x = -4/3 and x = 4/3
5.
The total length of 2 pieces of rope is
108cm. If one piece is 18cm shorter, what is
the length of the longer piece?
Answer:
63 cm
Step-by-step explanation:
piece 1: x
piece 2: x - 18
First you would subtract 2x - 18 = 108
Second you would add 108 + 18 = 2x
Third you would divide 126 divided by 2x = 63
So that would mean x = 63
Answer:
63cm
Step-by-step explanation:
2 pieces of rope, and one is shorter by 18cm.
piece 1: x
piece 2: x-18
Add the equations together, combine both pieces
2x-18
2x-18 = 108
108+18 = 2x
126 = 2x
x = 63
what is the area of the figure below use 3.14 for pie
Answer:
Answer CL 586 cm^2
Step-by-step explanation:
Hello. It's pi, not pie.
The area of the triangle is A1 = (1/2)(base)(height) = (1/2)(18 cm)(7 cm), or
A1 = 63 cm^2.
The area of the rectangle is A2 = (base)(height) = (18 cm)(22 cm) = 396 cm^2.
The area of the semicircle is A3 = (1/2)(pi)(9 cm)^2 = 3.14(81 cm^2)(1/2) = 127 cm^2
Thus, the total area of the figure is A = 127 cm^2 + 396 cm^2 + 63 cm^2, or
586 cm^2 approximately.
please see the attached picture for full solution...
Hope it helps...
Good luck on your assignment....
Sam is baking cakes at her parents' bakery. She gets paid $20 a week in addition to $5 for every cake she bakes. She made $50 this week. Write an equation to show how many cakes Sam baked this week. 20 − 5x = 50 50 + 5x = 20 20 + 5x = 50 50 − 5x = −20
Answer:
20 + 5x = 50
Step-by-step explanation:
Let the number of cakes Sam baked this week be x
Total amount he received this week = $50
Amount he receives each week = $20
Amount he receives for baking one cake = $5
Amount he would receive for baking x cakes = $5x
Equation: 5x + 20 = 50
Answer:
20 + 5x = 50
Step-by-step explanation:
Let x be the number of cakes
Amount paid per cake = $5
Amount paid for "x" cakes = 5*x = 5x
Basic payment per week = $20
Amount paid that week = 20 + 5x
20 + 5x = 50
NEED MATH HELP NOW!!! PLEASE HELP!!!
Answer:
Check the attachment below!
vertex= (0.5,-12.25)y-int= (0,-12)x-int= (-3,0) and (4,0)AOS= x=0.5domain= -∞ to ∞range= -12.25 to ∞What is 12 1/2 - (-4 1/2)
Answer:
the correct answer is
Step-by-step explanation:
= 12 1/2 - (-4 1/2)
=17
hope this helps you!!!!!
Answer:
17
Step-by-step explanation:
12 1/2 - (-4 1/2)
Turn to improper fractions.
25/2 - (-9/2)
Negative times negative is positive.
25/2 + 9/2
Add fractions with common denominators.
34/2
Divide.
= 17
Which of the binomials below is a factor of this trinomial?
X2-16x + 28
O A. x+7
O B. x2 + 7
O c. x+4
O D. X-14
Answer:
x-14
Step-by-step explanation:
The binomial which is a factor of this trinomial is (x- 14).
What is Trinomial?An algebraic expression with three terms is called a trinomial.
Examples of a trinomial expression: x + y + z is a trinomial in three variables x, y and z.
Given:
p(x) = x²-16x + 28
If x+ a is factor of any polynomial p(x) then x= -a satisfy the polynomial.
factorizing p(x)
x²-16x + 28
= x²-14x + 2x + 28
= x( x- 14) + 2 (x+ 14)
= (x- 14)(x+ 2)
Hence, the binomial is (x- 14).
Learn more about Trinomial here:
https://brainly.com/question/16347049
#SPJ2
En comsumo combustible de u camion durante un dia de viaje es el 21,77 litros ,el consumo del siguiente dia es de 15,22 litros¡cuanto combustible consumio el camion en total
Answer:
36.99 litros de combustible.
Step-by-step explanation:
En este problema debemos calcular el combustible total de consumió el camión, para eso debemos sumar el valor que consumió el día 1 más el valor que consumió el día 2, de la siguiente manera:
Consumo total = Consumo día 1 + Consumo día 2
Consumo total = 21.77 + 15.22
Consumo total = 36.99
Es decir que el consumo total del camión es de 36.99 litros de combustible.
please help.. GP is geometric progression
Answer:
unanswerable,don't censore the question
Step-by-step explanation:
sorry pal
Answer:
n is the seventh term=5832
Step-by-step explanation:
a1=8
r=3
a(n)=a1*r^(n-1)=
an=8*3(n-1)
8+24+72+216+648+1944+5832=8744
What is the product?
1
12
64
2
78
30
6
32
78 30
6
64
78 30
6
32
39
15
6
64
39 30
Answer:
9.3526131e+34
Step-by-step explanation:
112*642=71904*4948560=355821258240*7830*664=1.8499574e+18*7830*632=9.1546252e+24*3915*664=6.7577122e+12*3930=2.6557809e+16=9.3526131e+34
Answer:
Answer:
9.3526131e+34
Step-by-step explanation:
112*642=71904*4948560=355821258240*7830*664=1.8499574e+18*7830*632=9.1546252e+24*3915*664=6.7577122e+12*3930=2.6557809e+16=9.3526131e+34
The digits of both the two-digit numbers in the first calculation below have been reversed to give the two-digit numbers in the second calculation. The answers to the two calculations are the same. 62 × 13 = 806 26 × 31 = 806 For which one of the calculations below is the same thing true
Answer:
42x48
Step-by-step explanation:
BRAINLIEST!!!!!!BRAINLIEST!!!!BRAINLIEST!!!!BRAINLIEST!!!BRAINLIEST!!!!!BRAINLIEST!!!!BRAINLIEST!!!!BRAINLIEST !!!!!!!
Answer:
answer D
Step-by-step explanation:
let s estimate the D.
(2x+5) is a common factor so we can write
[tex](2x+5)(3x^2+(-5x)+(-4)) = (2x+5)(3x^2-5x-4)[/tex]
and this is the expression of the question
hope this helps
The correct answer would be D
Hope this helps! :)
Does the table represent a function? why or why not? HELP WANTEDD
Answer:
C no, because one x value corresponds to two different y values
Step-by-step explanation:
The x value of 3 goes to two different y values
This means this cannot be a function
This is not a one to one correspondence
Answer: C
Step-by-step explanation: In order for a table to represent a function each x-value needs to correspond to exactly 1 y-value.
Notice that in the table, the 3 appears twice and it corresponds to a 5 in one case and it corresponds to a 6 in another case.
Since the x-value of 3 corresponds to more than 1 y-value,
no, this table does not represent a function.
A square forms a semi-regular tessellation with which of the following regular polygons?
A. Trapezoid and hexagon
B. Pentagon and hexagon
C.equilateral triangle and hexagon
D. equilateral triangle and trapezoid
Answer:
a:is the answer good luck men
Answer:
Equilateral Triangle and Hexagon
Step-by-step explanation:
Am Supreme Ruler.
PLS ANSWER FOR BRANINETEST
Answer:
3(3/7)
Step-by-step explanation:
Just by doing the math.
The figure shows the dimensions of a wall having a door and window of a room. Write an algebraic expression for the area of the wall to be painted. PLEASE FAST
Answer:
Area of the wall to be painted = (11x² + 12x) square units
Step-by-step explanation:
The figure that should be attached to this question is missing. The figure was obtained and is attached to this solution provided.
From the image attached, it is given that the dimension of the rectangular wall to be painted is (4x+3) by (4x), the dimensions of the window is (2x) by (x) and the dimensions of the door is (x) by (3x).
Since, the window space and the door space cannot be painted along with the wall, the Area of the rectangular wall that will be painted will be given by the expression
(Total Area of the rectangular wall) - [(Area of window space) + (Area of door space)]
Area of a rectangular figure = Length × Breadth
Total area of rectangular wall = (4x+3) × 4x = (16x² + 12x) square units
Area of window space = (2x) × (x) = (2x²) square units
Area of door space = (x) × (3x) = (3x²) square units
Area of the wall to be painted = (16x² + 12x) - (2x² + 3x²)
= 16x² + 12x - 5x²
= (11x² + 12x) square units
Hope this Helps!!!
Very buys a basket of mangoes that is priced $14 before tax. The sales tax is 6%. What is the total price Avery pays for the basket of mangoes
Answer:
Avery needs to pay $14.84
Step-by-step explanation:
When there's a tax we need to sum the original value of the product with the tax's value. To find the amount of money Avery needs to pay in taxes we can apply a rule of three as shown below:
[tex]\frac{14}{x} = \frac{100}{6} \frac{\%}{\%}[/tex]
Where "x" is the tax value, and $14 represents 100%, since it's the value used to calculate the tax. We have:
[tex]x = \frac{14*6}{100}\\x = \frac{84}{100}\\x = 0.84[/tex]
The value to be paid is the product value plus the tax, therefore:
[tex]\text{paid} = 14 + 0.84 = 14.84[/tex]
Avery needs to pay $14.84
At a certain high school, 35 students play only stringed instruments, 10 students play only brass instruments, and 5 students play both. There are also 5 students who play neither stringed nor brass instruments. what is the probability that a randomly selected student plays both a string and a brass instrument?
Answer:
0.09
Step-by-step explanation:
Total = 35+5+10+5 = 55
P(string&brass) = 5/55
= 1/11 = 0.09090909
The sequence -11, -5, 1...... is an arithmetic
progression. State the three consecutive terms of
this arithmetic progression where the sum of
these three terms is 93.
Answer:
25, 31, 37
Step-by-step explanation:
1 2 3 4 5 6 7 8 9 10
-11 -5 1 7 13 19 25 31 37 43
6 6 6 6 6 6 6 6 6
25 + 31 + 37 = 93
The surface area of a sphere with a diameter of 12 units is:
Answer:
Surface area of sphere = 4πr²
r = radius
radius = diameter /2
= 12/2
= 6units
Surface area = 4π×6²
= 144π
= 452.4 square units
Hope this helps.
I KEE asking so many questions lol I just don’t understand!
Answer:
Perimeter = 20
Step-by-step explanation:
Perimeter = 9 + 5 + 6
Best Regards!
A school crossing sign is shown. Find the measures of angle A and angle C
Answer:
m∠A = 135°
m∠C = 135°
Step-by-step explanation:
There are 540° in a pentagon.
You are given 3 90° angles
540-90(3) = 270
∠A and ∠C are congruent
270/2 = 135° each
A girl was born 35 years after her mother what fraction of the mother's age would the girl be at age 15
Answer: 3/10
Step-by-step explanation:
Equations:
m = d + 35
When girl is 15, mom is 35+15 = 50
Ans: girl = (15/50) = 3/10 of the mother's age.
Please solve it the answer is (a+b-2) (a-b+2) should be take out question a^2-b^2+4b-4
Answer:
see explanation
Step-by-step explanation:
Given
(a + b - 2)(a - b + 2)
Each term in the second factor is multiplied by each term in the first factor, that is
a(a - b + 2) + b(a - b + 2) - 2(a - b + 2) ← distribute the parenthesis
= a² - ab + 2a + ab - b² + 2b - 2a + 2b - 4 ← collect like terms
= a² - b² +4b - 4
Answer:
this may help uh to get answer..
Problem 10.084 An article in Knee Surgery, Sports Traumatology, Arthroscopy (2005, Vol. 13, pp. 273-279), considered arthroscopic meniscal repair with an absorbable screw. Results showed that for tears greater than 25 millimeters, 14 of 17 repairs were successful while for shorter tears, 22 of 31 repairs were successful. (a) Is there evidence that the success rate is greater for longer tears? Use alpha equals 0.05 . What is the Upper P -value?
Answer:
The p-value = 0.181186
The p-value is greater than the significance level at which the test was performed, hence, we fail to reject the null hypothesis & say that there isn't enough evidence to suggest that the success rate of repair of longer tears is greater than the success rate of repair of shorter tears.
Step-by-step explanation:
This is a two-sample hypothesis test as we want to test the whether the success rate for one group of tears is more than the other
For hypothesis testing, the first thing to define is the null and alternative hypothesis.
In hypothesis testing, especially one comparing two sets of data, the null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test. It usually maintains that, with random chance responsible for the outcome or results of any experimental study/hypothesis testing, its statement is true.
The alternative hypothesis usually confirms the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test. It usually maintains that significant factors other than random chance, affect the outcome or results of the experimental study/hypothesis testing and result in its own statement.
For this question where we are testing if the success rate of longer tears is greater than the success rate of shorter tears,
The null hypothesis is that there is no significant difference in the success rate for the two types of tears. That is, there isn't enough evidence to suggest that the success rate of longer tears is greater than the success rate of shorter tears.
The alternative hypothesis is that there is enough evidence to suggest that the success rate of longer tears is greater than the success rate of shorter tears.
Mathematically, if the success rate of longer tears is p₁, success rate of repair of shorter tears is p₂. And the difference between the two success rates is μ = p₁ - p₂,
The null hypothesis is represented as
H₀: μ = 0 or p₁ = p₂
The alternative hypothesis is represented as
Hₐ: μ > 0 or p₁ > p₂
We then calculate the test statistic
The test statistic for two samples test is given as
t = (p₁ - p₂)/σ
σ = √{[p₁(1-p₁)/n₁] + [p₂(1-p₂)/n₂]}
p₁ = success rate of repair of longer tears = (14/17) = 0.8235
n₁ = 17
p₂ = success rate of repair of shorter tears = (22/31) = 0.7097
n₂ = 31
σ =
√{[0.8235(1-0.8235)/17] + [0.7097(1-0.7097)/31]}
σ = √[(0.8235×0.1765/17) + (0.7097×0.2903/31)]
= √(0.0085498676 + 0.0066459971)
= √0.0151958647 = 0.1232715081 = 0.1233
t = (p₁ - p₂)/σ
t = (0.8235 - 0.7097)/0.1233
t = 0.92
checking the tables for the p-value of this t-statistic
Degree of freedom = df = n₁ + n₂ - 2 = 17 + 31 - 2 = 46
Significance level = 0.05
The hypothesis test uses a one-tailed condition because we're testing only in one direction.
p-value (for t = 0.92, at 0.05 significance level, df = 46, with a one tailed condition) = 0.181186
The interpretation of p-values is that
When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.
So, for this question, significance level = 0.05
p-value = 0.181186
0.181186 > 0.05
Hence,
p-value > significance level
This means that we fail to reject the null hypothesis & say that there isn't enough evidence to suggest that the success rate of repair of longer tears is greater than the success rate of repair of shorter tears.
Hope this Helps!!!
The volume of a cube is 8cm3, find the length of one of it's sides
Answer:
The side length is 2 cm
Step-by-step explanation:
The volume of a cube is s^3
V = s^3
8 = s^3
Take the cube root of each side
8 ^ 1/3 = s^3 ^ 1/3
2 = s
The side length is 2 cm
Answer:
2 cm
Step-by-step explanation:
The volume of a cube can be found using the following formula:
V=s^3
where s is the length of one side. We know the volume is 8 cm^3, therefore we can substitute that value in for V.
8 cm^3=s^3
We want to find what the side length is. The side length is being cubed. The inverse of a cube is the cube root. Therefore, we must take the cube root of both sides, or raise both sides to the power of 1/3.
(8 cm^3)^1/3=(s^3)^1/3
(8 cm^3)^1/3=s
2 cm=s
The length of one side is 2 centimeters.
What is the contrapositive of the conditional statement? If two variables are directly proportional, then their graph is a linear function. If two variables are directly proportional, then their graph is not a linear function. If two variables are not directly proportional, then their graph is not a linear function. If the graph of two variables is a linear function, then the two variables are directly proportional. If the graph of two variables is not a linear function, then the two variables are not directly proportional
Answer:
D. "If the graph of two variables is not a linear function, then the two variables are not directly proportional"
Step-by-step explanation:
The contrapositive of a statement is basically you changing the conditional part of the statement with its result and then finding the negative of both. This is called Contraposition.
So, for the statement given:
"If two variables are directly proportional, then their graph is a linear function."
The contrapositive will be:
"If the graph of two variables is not a linear function, then the two variables are not directly proportional"
Answer:
d
Step-by-step explanation:
Find the of this circle in terms of pi
Answer: π / 4
Step-by-step explanation:
Area of a circle = π x r^2
= π x 0.5^2
= π / 4
Answer:
A = 0.25 π m²
Step-by-step explanation:
Area = [tex]\pi r^2[/tex]
Where r = 0.5 m
A = (0.5)^2 × π
A = 0.25 π m²
WILL GIVE BRAINLIEST AND 20 POINTS IF ANSWERED FULLY AND CORRECTLY. Two bikers meet at a park. Biker A needs to stop at the store that is 12 miles east of the park. Biker B heads southeast at a 61° angle at the same time for 24 miles. Once biker A leaves the store he heads southwest at an angle of 89° for 21 miles. Do NOT use the law of cosines, use your knowledge from the content of this course(geometry). a. Use your knowledge of triangles to figure out if the two bikers will be able to meet up if each biker travels the distance given. b. If they do not meet up, how much farther would one of the bikers have to travel to meet the other? c. What is the measure of the angle between the bikers? d. What is the relationship between the measure of the angles and the paths the bikers took? e. Classify the triangle the paths created. f. How many miles did they travel together?
Answer:
See below
Step-by-step explanation:
See attached for reference
The path has been created by bikers is almost a right triangle with sides of 12, 21 and 24 miles and angles of 61, 89 and 30 deg
a) Biker A travels a straight line (hypotenuse of triangle)
It is likely the bikers meet at the bottom point of the triangle
They make almost same displacement from the start point:
24 miles ≈ √12²+21² miles
b) they meet each other
c) 30 deg
d) e) as per picture attached, it is almost right triangle
f) Together they traveled 12+21+24= 57 miles
Sylvie finds the solution to the system of equations by graphing.
y =2/3x + 1 and y = -2/3x-1. Which graph shows the solution to Sylvie's system of equations?
Answer:
The third graph is your answer.
Step-by-step explanation:
I included a graph below with the correct graphing.