Answer:
d=8 and a=7
Step-by-step explanation:
The sum of a arithmetic sequence is given by (n/2)*(2a+(n-1)d). Comparing coefficients with the given Sn, we have; a-d/2=3 and d/2=4, d=8 and a=7. The sequence is 7, 15, 23, 31, 39
If my final is worth 15% of my mark and I'm at 70% right now what would I need to get on my final to get at least 75% overall
Answer:
Step-by-step explanation:
70*85/100 = 59.5 This is what you have right now.
You need 15.5 gross marks to get up to 75
As you can see, I'm sorry to say, you cannot do it.
Mind you, you would not miss by much. You could get about 74.5 if you got a hundred % on your final. This is just an estimate. I'm just trying to show you what you have to do to get near your goal. The 59.5 is accurate. So is the 15.5. Only your possible final grade is an estimate.
4. Solve the system of equations. (6 points) Part I: Explain the steps you would take to solve the system by eliminating the x-terms. (1 point) Part II: Explain the steps you would take to solve the system by eliminating the y-terms. (2 points) Part III: Choose either of the methods described in parts I or II to solve the system of equations. Write your answer as an ordered pair. Show your work. (3 points)
Answer:
The system of equations you want to be solved is not given. I would however give an example with which the method of elimination will be shown, and can be used in solving problems of the nature.
Step-by-step explanation:
Consider the system of equations:
x + y = 7 ................................(1)
2x - y = 8 ..............................(2)
To eliminate x:
First multiply (1) by 2 to have
2x + 2y = 14 ...........................(3)
Next, subtract (2) from (3) to have
3y = 6
y = 6/3 = 2
To eliminate y:
Add (1) and (2) to have
3x = 15
x = 15/3 = 5
Therefore, (x, y) = (5, 2).
10 points plssssss!!!
Answer:
A. rectangle
B. any of triangle, quadrilateral, pentagon, hexagon
Step-by-step explanation:
A. A plane perpendicular to the base will intersect 2 adjacent or 2 opposite lateral faces, as well as the two bases. Each plane intersected will result in an edge of the cross sectional figure. The figure will have two pairs of parallel edges, so is a rectangle.
__
B. If the intersecting plane is not constrained to be perpendicular to the base(s), it can intersect 3, 4, 5, or all 6 faces of the prism. Hence, the shape of the cross section can be any of ...
trianglequadrilateralpentagonhexagonthe x coordinates of the point 2y-x=10 intersect the line yaxis
Answer:
Point has co-ordinates, (0, 5)
Step-by-step explanation:
If they cut y-axis, then x = 0
[tex]2y - x = 10 \\ 2y - 0 = 10 \\ 2y = 10 \\ y = 5[/tex]
A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly. When he started his diet, he weighed 79.5 kilograms. He gained weight at a rate of 5.5 kilograms per month. Let y represent the sumo wrestler's weight (in kilograms) after x months. Which of the following could be the graph of the relationship? graph of an increasing linear function in quadrant 1 with a positive y-intercept (Choice B) B graph of an increasing linear function in quadrants 1 and 4 with a positive x-intercept and negative y-intercept (Choice C) C graph of a decreasing linear function in quadrants 1 and 4 with a positive x-intercept and positive y-intercept (Choice D) D graph of a decreasing linear function in quadrant 4 with a negative y-intercept
Answer:
(Choice A) A graph of an increasing linear function in quadrant 1 with a positive y-intercept.
Step-by-step explanation:
The weight of the sumo wrestler starts at a positive value of 79.5 kilograms, and we are given that the sumo wrestler gains a linear amount of weight per month at 5.5 kilograms per month.
If we were to graph this relationship, the sumo wrestler's weight would be represented on the y-axis, and the amount of time on the x-axis.
So the initial weight would occur at (0, 79.5) which is the positive y-intercept.
And since his weight is increasing at 5.5 kilograms per month, the slope of the linear function is positive.
Hence, the graph of the linear increasing function in quadrant 1 with a positive y-intercept.
Cheers.
Plz answer quickkkk help will give 5 star rate if answer is right nd will say thx
Answer:
To find the x-intercept, substitute in 0 for y and solve for x.
To find the y-intercept, substitute in 0 for x and solve for y.
x-intercept(s):
(−6,0)
y-intercept(s):
(0,3)
So I would say -6 and 0 and 2 are in domain
Answer:
-6, 0 ,2 are in the domain
Step-by-step explanation:
The domain is what values that x can take
There are no restrictions on the values that x can take
All real numbers are in the domain
-6, 0 ,2 are in the domain
5 STARS IF CORRECT! In general, Can you translate a phrase or sentence into symbols? Explain the answer.
Answer:
Step-by-step explanation:
I answered this already a few minutes ago.
Answer:
yes you can
Step-by-step explanation:
you can write algebraic expressions and use variables for the unknown
A class with n kids lines up for recess. The order in which the kids line up is random with eachordering being equally likely. There are three kids in the class named John, Betty, and Mary. The useof the word "or" in the description of the events, should be interpreted as the inclusive or. That is"A or B" means thatAis true,Bis true, or bothAandBare true.Give an expression for each of the probabilities below as a function ofn. Simplify your final expressionas much as possible so that your answer does not include any expressions of the form (a/b).Requried:a. What is the probability that Betty is first in line or Mary is last in line? b. Explain the method used to calculate probability.
Answer:
A) P(Betty is first in line and mary is last) = P(B₁) + P(Mₙ) - (P(B₁) × P(Mₙ/B₁))
B) The method used is Relative frequency approach.
Step-by-step explanation:
From the question, we are told a sample of n kids line up for recess.
Now, the order in which they line up is random with each ordering being equally likely. Thus, this means that the probability of each kid to take a position is n(total of kids/positions).
Since we are being asked about 3 kids from the class, let's assign a letter to each kid:
J: John
B: Betty
M: Mary
A) Now, we want to find the probability that Betty is first in line or Mary is last in line.
In this case, the events are not mutually exclusive, since it's possible that "Betty is first but Mary is not last" or "Mary is last but Betty is not first" or "Betty is the first in line and Mary is last". Thus, there is an intersection between them and the probability is symbolized as;
P(B₁ ∪ Mₙ) = P(B₁) + P (Mₙ) - P(B₁ ∩ Mₙ) = P(B₁) + P(Mₙ) - (P(B₁) × P(Mₙ/B₁))
Where;
The suffix 1 refers to the first position while the suffix n refers to the last position.
Also, P(B₁ ∩ Mₙ) = P(B₁) × P(Mₙ/B₁)
This is because the events "Betty" and "Mary" are not independent since every time a kid takes his place the probability of the next one is affected.
B) The method used is Relative frequency approach.
In this method, the probabilities are usually assigned on the basis of experimentation or historical data.
For example, If A is an event we are considering, and we assume that we have performed the same experiment n times so that n is the number of times A could have occurred.
Also, let n_A be the number of times that A did occur.
Now, the relative frequency would be written as (n_A)/n.
Thus, in this method, we will define P(A) as:
P(A) = lim:n→∞[(n_A)/n]
Given this pair of probabilities, the probability that Mary is the first is n(A) = n-1!, while the probability that Betty is last is n(A) = n-1!
There are n! ways of making this arrangement
We have probability of A: Betty is the first person in this line
Probability of B: Mary is the last person
A U B = p(A) + p(B) - p(A ∩ B)
n(A) = n-1 that is given that Betty is the first person on the line.
then n(A) = n-1!
As the last person on the line P(B) = n-1!
Probability of (A∩B) =( n-2)! this has Mary as the first and Betty as the last person.
Remaining students that would have to be on this line are n-2
Prob(A∪B) = n(A ∪ B)/n!
= 2(n-2)/n(n-1)
What is the probability theory in Mathematics?This is the theory that talks about the chances or the likelihood of an event occuring in a pair of events.
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22/25of a number is what percentage of that number?
Answer:
88%.
Step-by-step explanation:
Multiply the fraction by 100:
(22/25) * 100
= 22 * 4
= 88%.
10
[tex] {10}^{4} = [/tex]
whats the answer..
Answer:
10,000
Step-by-step explanation:
The answer is 10*10*10*10 = 10,000
When the power is positive and in the numerator, the number of places moved or zeros added = the power. This has a power of 4. You add 4 zeros to 1 to get the answer.
For the lengths AB, BC, and AC to equal 7,6, and 13 respectively, what is the
value of x?
Answer:
x = 5
Step-by-step explanation:
We know that AB = 2x - 3 and AB = 7, therefore:
2x - 3 = 7
2x - 3 + 3 = 7 + 3
2x = 10
2x / 2 = 10 / 2
x = 5
When trying to find the best deals for items, you should what?
Answer:
Try to find the unit rate for bulk items that you have for these and then compare all of the prices together.
a ball is dropped from a height of 512 inches onto a level floor. after the fourth bounce it is still 2 inches off the ground. presuming that the height the ball bounces is always the same fraction of the height reached on the previous bounce. what is that fraction? A) 1/4 B) 3/7 C) 5/9 D)4/7 E)3/5
Answer:
A. 1/4
Step-by-step explanation:
We know that before the 1st bounce, the height of the ball is 512 inches.
Say the fraction is x.
Then, after the first bounce, the height of the ball is 512 * x = 512x.
After the second bounce, the height is now x * 512x = 512x².
By similar reasoning, the height after the third bounce is 512x³ and after the fourth bounce, it is [tex]512x^4[/tex].
We also know that after the fourth bounce, the height is 2 inches. So, set 2 equal to [tex]512x^4[/tex]:
2 = [tex]512x^4[/tex]
Divide both sides by 512:
[tex]x^4=2/512[/tex][tex]x^4=2/512=1/256[/tex]
Take the fourth root of both sides:
[tex]x=\sqrt[4]{1/256} =1/4[/tex]
Hence, the answer is A.
~ an aesthetics lover
Answer:
A. 1/4.
Step-by-step explanation:
This is exponential decay so we have , where x = the fraction:
512(x)^4 = 2
x^4 = 1/256
x= 1 / (256)^0.25
= 1/4
Randy is walking home from school. According to the diagram above, what is his total distance from school to home? Show your work and include units. If he had a jet pack, would you use distance or displacement? Why?
Answer:
if he needs to walk, we can see that between the street and his house he must walk 4 times a distance of 0.5km, so this is a total of 4¨*0.5km = 2km.
Now he has a jet-pack, he can ignore the buildings and just travel in the shorter path, so we can draw a triangle rectangle, in such a way that the hypotenuse of this triangle is the distance between the home and the school.
One of the cathetus is the vertical distance, in this case, is 1km, and the other one is the horizontal distance, also 1km.
So the actual distance is given by the Pythagorean's theorem:
A^2 + B^2 = H^2
Where A and B are the cathetus, and H is the hypotenuse, then:
H^2 = 1km^2 + 1km^2
H = (√2)km = 1.41km.
Now, in the case that he has a jet-pack, he can actually go to the school using this hypotenuse line as his path, so in this case the distance and the displacement would be the same.
Distance: "how much ground an object has covered"
Displacement: "Difference between the final position and the initial position"
When he walks, the distance is 2km, but the displacement is 1.41km
When he uses the jet-pack, both the distance and the displacement are 1.41km
Answer and Step-by-step explanation:
The first thing is we can see in the image, when he walks, that between the house and his school he has to walk four times a distance of 0.5 km. The result of this is a total of 4¨*0.5 km = 2 km. The second thing is that he must walk 2 kilometers. On the other hand, if he has a jetpack, he can simply take the shorter path by ignoring all the buildings. This idea is where we can draw a triangular rectangle on the map in a way so that the hypotenuse of the triangle is the distance between the school and the home. As for the Catheti, it is a vertical distance which in this case is two blocks of 0.5 km. The result is that these catheti have a length of 2*0.5 km = 1 km. The other is the distance of the horizontal line, which is 1 km. The absolute distance of this path is given by Pythagorean's theorem, which is A^2 + B^2 = H^2. Here, A and B are the cathetus, and H is the hypotenuse, then, H^2 = 1 km^2 + 1 km^2. As well, H = (√2)km = 1.41 km. Currently, in the situation where he has a jetpack, he can literally fly to the school utilizing this hypotenuse line for the path he would need to follow. For this specific situation, the displacement, and the distance would be the exact same. The reason for this is that the definitions of displacement and distance are displacement is the difference between the final position and the initial position and distance is how much area an item has covered. Also, when he walks, the distance is 2 km and the displacement is 1.41 km. Also, when he utilizes the jet pack, the distance is equal to the displacement. Both of these are 1.41 km.
Andrea is told that the means of two groups in a study were statistically significant. She knows the means and standard deviations of the two groups and is interested in calculating an estimate of effect size. Given this information, which effect size estimate should she calculate
Answer:
Cohen's D
Step-by-step explanation:
Cohen's D is a statistic that measures effect size. It shows standardised difference between 2 means.
Effect size is defined as how large the effect of a something is or its magnitude.
Cohen's D works effectively when the sample is >50 (that is for large samples). However a correction factor can be used to make results from small samples more accurate
The formular for Cohen's D is:
D = (mean1 - mean2) ÷ (√({standard deviation1}^2 + {standard deviation 2}^2)/2)
This is the most appropriate method in the given scenario
Let f(x)=x+8 and g(x)= x2-6x-7 find f(g2)
Answer:
-7.
Step-by-step explanation:
g(x) = x^2 - 6x - 7
g(2) = 2^2 - 6(2) - 7
= 4 - 12 - 7
= -8 - 7
= -15
f(x) = x + 8
f(-15) = (-15) + 8
= 8 - 15
= -7
Hope this helps!
A market vendor sells pawpaws and guavas. In a week the number of pawpaws sold and the number of guavas sold were in the ratio 3:5 respectively. The total number of pawpaws and guavas sold in a week was 328. (a) How many pawpaws were sold in a week? (1 ma (b) How many guavas were sold in a week? (1 ma Yoon Dohored a prize money of $400.00 in
Total awpaws and guavas sold in a week = 328
Let the number of pawpas and guavas be x
ATQ
3x + 5x = 328
8x = 328
x = 328/8
x = 41
Pawapas in a week = 123
Guavas in a week = 205
Must click thanks and mark brainliest
You earned $100, plus 15% of your sales (commission), less $32 withholding (taxes), for a total net of
$250. What were your sales?
At a baby shower, 15 guests are in attendance and 4 of them are randomly selected to receive a door prize. If all 4 prizes are identical, in how many ways can the prizes be awarded?
Answer:
1365
Step-by-step explanation:
We figure out combinations using this formula: n!
r!(n-r)!
n=15
r=4
So n!= 15x14x13x12x11x0x9x8x7x6x5x4x3x2x1
r! = 4x3x2x1 times 15-4!, which is 11! = 11x10x9x8x7x6x5x4x3x2x1
Put this together and you have 15x14x13x12/4x3x2x1=
There are 1365 different ways to award the 4 door prizes to 4 guests from a group of 15 guests.
What are the Combinations?Combinations are the procedures used in mathematics to pick k things from n different items without replacement.
The following formula computes the combinations of k items from n:
(n, k) = n! / k!×(n-k)!
The number of ways to award the 4 door prizes to 4 guests out of a group of 15 guests is a combinatorial problem that can be calculated using the formula.
Here, n = 15 (the total number of guests) and k = 4 (the number of prizes to be awarded).
So, the number of ways to award the prizes is:
C(15, 4) = 15! / (4! (15 - 4)!)
= 15! / (4! 11!)
= 15 x 14 x 13 x 12 / (4 x 3 x 2 x 1)
= 1365.
Therefore, there are 1365 different ways to award the 4 door prizes to 4 guests from a group of 15 guests.
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How do we solve this?
Answer:
[tex] = - \frac{1}{36(6x + 1) ^{6} } + c[/tex]
I hope I helped you^_^Answer:
[tex]-\frac{1}{36\left(6x+1\right)^6} +C[/tex]
Step-by-step explanation:
we're going to us u substitution
[tex]\int (6x+1)^-7 dx[/tex]
[tex]u=6x+1[/tex]
[tex]\int\frac{1}{6u^7} du[/tex]
take out the constant, [tex]\frac{1}{6}[/tex]
[tex]\frac{1}{6}[/tex] · [tex]\int u^-7du[/tex]
next use the power rule, [tex]\int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1[/tex]
[tex]\frac{1}{6}\cdot \frac{u^{-7+1}}{-7+1}[/tex]
simplify by substituting [tex]6x+1[/tex] for [tex]u[/tex]
[tex]\frac{1}{6}\cdot \frac{(6x+1)^{-7+1}}{-7+1} = -\frac{1}{36\left(6x+1\right)^6}[/tex]
add a constant, [tex]C[/tex]
[tex]-\frac{1}{36\left(6x+1\right)^6} +C[/tex]
If 1/2 of a loaf of brown bread costs R6,how much will 2 halves cost
Answer:
wdym R6
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
6*2
How would A = L + O be rewritten to solve for O?
Answer:
A - L = O
Step-by-step explanation:
A = L + O
Subtract L from each side
A-L = L + O - L
A - L = O
The way that the given formula A = L + O can be rewritten to solve for O is; O = A - L
How to change subject of formula?We are given the formula to find A as;
A = L + O
Now, to make O the subject of the formula, let us use subtraction property of equality to subtract L from both sides to get;
A - L = L + O - L
O = A - L
Thus, the way the formula can be rewritten to solve for O is;
O = A - L
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Determine whether the statement (p∧(p⟶q))⟶q is a tautology one time by using truth table and the other time without using truth table
It is.........................................................
One way to prove this without a truth table is to use a conditional proof. We assume the portion p ^ (p --> q). If that's true, then so is p and p-->q
Using p and p-->q, the modus ponens rule allows us to derive q. It says that if p is true and p --> q, then q must be true as well.
Since we arrive at q, we have found the conclusion we're after. The assumption (p ^ (p-->q)) leads to q, and therefore the entire statement (p ^ (p-->q)) --> q is true for any combination of p,q.
Use the point-slope formula to determine the equation of the line that has a slope of 1⁄2 and passes through point (0, 0).
Answer:
y-0 = 1/2(x-0)
y = 1/2(x)
Step-by-step explanation:
Point slope form is
y-y1 = m(x-x1)
where m is the slope and (x1,y1) is a point on the line
y-0 = 1/2(x-0)
y = 1/2(x)
state if the triangles in each pair are similar. If so State how you know they are similar and complete the similarity statement
Answer:
fourth option
Step-by-step explanation:
∠ FTC = ∠ MTL ( vertical angles )
Since FC and ML are parallel, then
∠ FCT = ∠ TML (corresponding angles )
Thus
Δ TCF ~ Δ TML by the AA postulate
Answer:
[tex]\large \boxed{\mathrm{similar, \ AA \ similarity}, \ \Delta TML}[/tex]
Step-by-step explanation:
The two triangles are similar.
We can prove by angle-angle similarity, in [tex]\mathrm{AA}[/tex] similarity, there are two pairs of congruent corresponding angles in two triangles, this proves the two triangles are similar.
[tex]\angle U[/tex] and [tex]\angle M[/tex] are a pair of congruent corresponding angles.
[tex]\angle V[/tex] and [tex]\angle L[/tex] are a pair of congruent corresponding angles.
Therefore,
[tex]\Delta TUV \sim \Delta TML[/tex]
3.85∙47.3+52.7∙3.85 PLSSSSS HELP
Answer:
385
Step-by-step explanation:
A computer parts company wants to make a rectangular memory board that has a perimeter of 14 cm and a diagonal of length 5 cm. What are the dimensions of the board?
Answer:
A computer parts company wants to make a rectangular memory board that has a perimeter of 28 centimeters and a diagonal length of 10 centimeters. Find the dimensions of the board. Consider the length to be the longer side.: Call the two sides L & W: the perimeter 2L + 2W = 28 Simplify, divide by 2 L + W = 14 L = (14-W); use this form for substitution
Step-by-step explanation:
==========================================================
Explanation:
x = width
y = length
both x and y are positive real numbers, and the units of which are in cm.
The perimeter of any rectangle is found by saying
P = 2*(length+width)
P = 2*(x+y)
Plugging in P = 14 leads us to
P = 2*(x+y)
14 = 2*(x+y)
14/2 = x+y
7 = x+y
Solve for one of the variables. Let's say we solve for y. That should get us y = 7-x which we'll use a bit later.
--------------
Notice how the diagonal forms two identical right triangles. The legs of which are x and y as defined earlier. The hypotenuse is 5, which is the diagonal length.
Use the pythagorean theorem to help solve for x
a^2 + b^2 = c^2
x^2 + y^2 = 5^2
x^2 + (7-x)^2 = 25 ... plug in y = 7-x
x^2 + 49 - 14x + x^2 = 25 ... use FOIL rule
2x^2-14x+49 = 25
2x^2-14x+49-25 = 0
2x^2-14x+24 = 0
2(x^2-7x+12) = 0
x^2-7x+12 = 0
(x-3)(x-4) = 0
x-3 = 0 or x-4 = 0
x = 3 or x = 4
If x = 3, then y = 7-x = 7-3 = 4
If x = 4, then y = 7-x = 7-4 = 3
We have this symmetry going on. If x is one of 3 or 4, then y is the other of those values. Because x = 3 and y = 4, or vice versa, this means we have a 3-4-5 right triangle (well to be fair we have two identical copies of such a triangle to form the rectangle).
Therefore, the dimensions of the rectangular board is 3 cm by 4 cm. The order doesn't matter so you could easily say "4 cm by 3 cm" to mean the same thing.
--------------
Check:
P = perimeter
P = 2*(length+width)
P = 2*(x+y)
P = 2*(3+4)
P = 2*7
P = 14
That helps confirm the answer.
802.4 divided 1.7
Thankkkk u
The answer to this equation is 472.
Answer:
472
Step-by-step explanation:
First we make both numbers into wholes by moving the decimal point one place behind.Then divide normally.
8024 ÷ 17 = 472
I hope this helps :)
Problem E2 Moving points B and C are on circle x² + y2 = 25. Let A be (2,0) and M be mid-point of BC. If BAC is a straight line, what is the locus of M?
Answer:
Step-by-step explanation:
The perpendicular bisector of any chord is a diameter and therefore passes through the center of the given circle.
The triangle OMA is thus rectangle.
The locus of M is the circle of diameter OA with center (1,0) and radius 1.
. Round off the numbers to the nearest ten.
28 , 188 , 250 , 101 , 122 ?
Rounding to the nearest ten:
28 → 30
188 → 190
250 → 250
101 → 100
122 → 120