Answer:
Independent measures, or repeated measures,
Step-by-step explanation:
I would use those experimental designs because it is used to compare different participants over a length of time.
How many x-intercepts does the graph of y = 2x2 + 4x - 3 have?
Answer:
3
Step-by-step explanation:
Given
y
=
2
x
2
−
4
x
+
3
The y-intercept is the value of
y
when
x
=
0
XXX
y
=
2
(
0
)
2
−
4
(
0
)
+
3
=
3
For a quadratic in the general form:
XXX
y
=
a
x
2
+
b
x
+
c
the determinant
Δ
=
b
2
−
4
a
c
indicates the number of zeros.
Δ
⎧
⎪
⎨
⎪
⎩
<
0
==⇒
no solutions
=
0
==⇒
one solution
>
0
==⇒
two solutions
In this case
XXX
Δ
=
(
−
4
)
2
−
4
(
2
)
(
3
)
<
0
so there are no solutions (i.e. no values for which the expression is equal to zero).
This can also be seen from a graph of this equation:
graph{2x^2-4x+3 [-6.66, 13.34, -0.64, 9.36]}
Answer link
Vinícius Ferraz
Nov 13, 2015
(
0
,
3
)
Explanation:
x
=
0
⇒
y
=
0
−
0
+
3
y
=
0
⇒
x
=
−
b
±
√
b
2
−
4
a
c
2
a
a
=
2
,
b
=
−
4
,
c
=
3
But
Δ
< 0, then there is no real root
(
x
0
,
0
)
.
Answer:
it has 2
Step-by-step explanation:
I hope this helps!
Mexican currency is the peso. One Mexican peso is currently equal to 0.055 U.S. dollars. If a traveler exchanges $400 for Mexican pesos, how many pesos will he receive? Round to the nearest peso.
Answer:
7,273 Pesos
Step-by-step explanation:
1 Peso = $0.055
The formula below converts pesos to dollars:
1 Peso x 0.055 = $1
The formula below converts dollars to pesos:
$1/0.055= 1 Pesos
We use the second formula because we are coverting
from dollars to pesos.
$400/0.055=7,273 Pesos
Answer:
22
Step-by-step explanation:
If one Mexican peso is .055 U.S dollars that means it has a greater value than the dollar so we can make the following ratio 1:.055. But if the .055 is a 400 1:400 we just multiply to get 22.
3/7 of which is 2 1/14
Answer:
Let the number be x
The statement is written as
[tex] \frac{3}{7}x = \frac{29}{14} [/tex]
Multiply through by 14
That's
[tex] 14 \times \frac{3}{7} x = \frac{29}{14} \times 14[/tex]
We get
2 × 3x = 29
6x = 29
Divide both sides by 6
That's
[tex] \frac{6x}{6} = \frac{29}{6} [/tex]
[tex]x \: = \frac{29}{6} \: \: or \\ 4 \frac{5}{6} [/tex]
Hope this helps you
You spend $3.50 on fruit. Apples cost $0.20 each while oranges cost $0.30 each. The equation models the situation, where x is the number of apples and y is the number of oranges. Which of the following is not a possible solution in the context of the problem?
a. 1 apple; 11 oranges
b. 11 apples; 1 orange
c. 7 apples; 7 oranges
d. 4 apples; 9 oranges
Answer:
b. 11 apples; 1 orange
Step-by-step explanation:
We test each option, and see if the total is $3.50(what you spend). If the result is different, it is not a possible solution.
a. 1 apple; 11 oranges
1 apple for $0.20
11 oranges for $0.30 each
0.20 + 11*0.30 = $3.50
Possible solution
b. 11 apples; 1 orange
11 apples for $0.20 each
1 orange for $0.30
11*0.2 + 0.3 = 2.5
Not $3.5, so this is not a possible solution.
This is the answer
c. 7 apples; 7 oranges
7*0.2 + 7*0.3 = $3.5
Possible
d. 4 apples; 9 oranges
4*0.2 + 9*0.3 = $3.5
Possible
Reflections over the X-Axis
Answer:
Domain : (-∞, ∞)
Range : (-∞, ∞)
Step-by-step explanation:
Parent function (y = [tex]\sqrt[3]{x}[/tex] ) of the given function y = -[tex]\sqrt[3]{x}[/tex] has been shown as the dotted line on the graph.
Solid curve represents the function,
y = [tex]-\sqrt[3]{x}[/tex]
Therefore, Domain of this function will be (-∞, ∞) Or x ∈ set of all real numbers.
And Range of the function will be (-∞, ∞) Or y ∈ set of all real numbers
Can someone help me do this? Me and my son are stuck
Hey there! :)
Answer:
Last option. (-1, 0) and (0, 6).
Step-by-step explanation:
Solve this system by setting the two equations equal to each other:
6x + 6 = -x² + 5x + 6
Rearrange the equation:
x² + 6x + 6 - 5x - 6 = 0
Combine like terms:
x² + x = 0
Factor out x:
x(x + 1) = 0
Set each factor equal to 0:
x = 0
x + 1 = 0
x = -1
These are the x values of the solutions. Plug these into an equation to solve for y:
y = 6(0) + 6
y = 6
-------
y = 6(-1) + 6
y = -6 + 6
y = 0
Therefore, the solutions to the equation are (-1, 0) and (0, 6).
What is the surface area of this right prism?
Answer: C - 600cm^2
Step-by-step explanation:
Area of one triangle:
(12)(5) ÷ 2 = 30
Area of two triangles:
30 x 2 = 60
Area of top rectangle:
Step 1: Figure out side length of triangle by using pythagorean:
√a^2 + b^2 = c
√(5)^2 + (12)^2 = c
√25 + 144 = c
√ 169 = c
13 = c
Step 2: Find area of top rectangle:
(18) x (13)
234
Find area of bottom rectangle:
(18) x (12)
216
Find area of back rectangle:
(18) x (5)
90
Add all the underlined numbers:
Area of two triangles + Area of top rectangle + Area of bottom rectangle + Area of back rectangle
60 + 234 + 216 + 90 = 600cm^2
Of 41 bank customers depositing a check, 22 received some cash back. Construct a 90 percent confidence interval for the proportion of all depositors who ask for cash back. (Round your answers to 4 decimal places.)
Answer:
CI: {0.4085; 0.6647}
Step-by-step explanation:
The confidence interval for a proportion (p) is given by:
[tex]p \pm z*\sqrt{\frac{(1-p)*p}{n} }[/tex]
Where n is the sample size, and z is the z-score for the desired confidence interval. The score for a 90% confidence interval is 1.645. The proportion of depositors who ask for cash back is:
[tex]p=\frac{22}{41}=0.536585[/tex]
Thus the confidence interval is:
[tex]0.536585 \pm 1.645*\sqrt{\frac{(1-0.536585)*0.536585}{41}}\\0.536585 \pm 0.128109\\L=0.4085\\U=0.6647[/tex]
The confidence interval for the proportion of all depositors who ask for cash back is CI: {0.4085; 0.6647}
I have no idea what this is
Answer:
B. -1.
Step-by-step explanation:
[tex]i^1[/tex] = i
[tex]i^2 = -1[/tex]
[tex]i^3 = -i[/tex]
[tex]i^4 = 1[/tex]
...And it keeps going in a pattern, from i to -1 to -i to 1. And so, we have four values.
34 / 4 = 8 with a remainder of 2. That means that the value of [tex]i^{34}[/tex] is the same thing as [tex]i^2\\[/tex], so it is B. -1.
Hope this helps!
Someone please answer this emergency pleaseee
Answer:
7). y = 140
8). x = 9
Step-by-step explanation:
Question (7).
All-right pencil factory will produce the graphite pencils, table formed will represent a linear graph.
Three points on the graph are (12, 42) and (18, 63), (40, y)
Slope of the line passing through these points = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m = [tex]\frac{63-42}{18-12}[/tex] = [tex]\frac{y-42}{40-12}[/tex]
[tex]\frac{21}{6}[/tex] = [tex]\frac{y-42}{40-12}[/tex]
3.5 = [tex]\frac{y-42}{40-12}[/tex]
98 = y - 42
y = 140
Question (8),
If a bicyclist rides at a constant rate, table formed will represent a linear graph.
Slope of a line passing through three points (2, 25), (5, 62.5) and (x, 112.5) given in the table,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\frac{62.5-25}{5-2}=\frac{112.5-62.5}{x-5}[/tex]
[tex]\frac{37.5}{3}=\frac{50}{x-5}[/tex]
37.5x - 187.5 = 150
37.5x = 337.5
x = 9
Rectangle LMNO has vertices L(–4,6), M(–1,6), N(–1,2), and O(–4,2). Suppose you first reflect this rectangle across the y-axis. Then, translate it down four units and to the left one unit. Where are the corresponding vertices L′M′N′O′ located?
Answer:
L'(3, 2)
M'(0, 2)
N'(0, -2)
O'(3, -2)
Step-by-step explanation:
Vertices of a rectangle LMNO are L(-4, 6), M(-1, 6), N(-1, 2) and O(-4, 2).
If a point (x, y) is reflected across y-axis, rule to be followed,
(x, y) → (-x, y)
After reflection across y-axis new ordered pairs will be,
L(-4, 6) → L"(4, 6)
M(-1, 6) → M"(1, 6)
N(-1, 2) → N"(1, 2)
O(-4, 2) → O"(4, 2)
Then these points were translated 4 units down and 1 unit left,
Rule to be followed for the translation will be,
(x'', y'') → [(x' - 1), (y' - 4)]
By this rule vertices of the rectangle after translation will be,
L''(4, 6) → L'(3, 2)
M''(1, 6) → M'(0, 2)
N''(1, 2) → N'(0, -2)
O''(4, 2) → O'(3, -2)
Answer:
L'(3, 2)
M'(0, 2)
N'(0, -2)
O'(3, -2)
Step-by-step explanation:
Which expression is equivalent to [tex]4^7*4^{-5}[/tex]? A. [tex]4^{12}[/tex] B. [tex]4^2[/tex] C. [tex]4^{-2}[/tex] D. [tex]4^{-35}[/tex]
Answer:
B. [tex]4^2[/tex]
Step-by-step explanation:
[tex]4^7 \times 4^{-5}[/tex]
Apply rule (if bases are same) : [tex]a^b \times a^c = a^{b + c}[/tex]
[tex]4^{7 + -5}[/tex]
Add exponents.
[tex]=4^2[/tex]
Answer:
[tex] {4}^{2} [/tex]Step by step explanation
[tex] {4}^{7} \times {4}^{ - 5} [/tex]
Use product law of indices
i.e
[tex] {x}^{m} \times {x}^{n} = {x}^{m + n} [/tex]
( powers are added in multiplication of same base)
[tex] = {4}^{7 + ( - 5)} [/tex]
[tex] = {4}^{7 - 5} [/tex]
[tex] = {4}^{2} [/tex]
Hope this helps...
Best regards!
The tens digit in a two digit number is 4 greater than one’s digit. If we interchange the digits in the number, we obtain a new number that, when added to the original number, results in the sum of 88. Find this number
Answer:
The original digit is 62
Step-by-step explanation:
Let the Tens be represented with T
Let the Units be represented with U
Given:
Unknown Two digit number
Required:
Determine the number
Since, it's a two digit number, then the number can be represented as;
[tex]T * 10 + U[/tex]
From the first sentence, we have that;
[tex]T = 4 + U[/tex]
[tex]T = 4+U[/tex]
Interchanging the digit, we have the new digit to be [tex]U * 10 + T[/tex]
So;
[tex](U * 10 + T) + (T * 10+ U) = 88[/tex]
[tex]10U + T + 10T + U= 88[/tex]
Collect Like Terms
[tex]10U + U + T + 10T = 88[/tex]
[tex]11U + 11T = 88[/tex]
Divide through by 11
[tex]U + T = 8[/tex]
Recall that [tex]T = 4+U[/tex]
[tex]U + T = 8[/tex] becomes
[tex]U + 4 + U = 8[/tex]
Collect like terms
[tex]U + U = 8 - 4[/tex]
[tex]2U = 4[/tex]
Divide both sides by 2
[tex]U = 2[/tex]
Substitute 2 for U in [tex]T = 4+U[/tex]
[tex]T = 4 + 2[/tex]
[tex]T = 6[/tex]
Recall that the original digit is [tex]T * 10 + U[/tex]
Substitute 6 for T and 2 for U
[tex]T * 10 + U[/tex]
[tex]6 * 10 + 2[/tex]
[tex]60 + 2[/tex]
[tex]62[/tex]
Hence, the original digit is 62
A cube with 40-cm-long sides is sitting on the bottom of an aquarium in which the water is one meter deep. (Round your answers to the nearest whole number. Use 9.8 m/s^2 for the acceleration due to gravity. Recall that the weight density of water is 1000 kg/m^3.)
Answer:
940.8 N
1254.4 N
Step-by-step explanation:
I would think the questions would be to calculate the forces at the top of the cube and at the sides. Thus:
On the top:
F = pressure * area
P = density * gravity * height
the height would be:
1m - 0.4m = 0.6m
replacing:
P = 1000 * 9.8 * 0.6 = 5880
A = (0.4) ^ 2 = 0.16
F = 5880 * 0.16
F = 940.8 N
On the sides:
dF = d * g * h * dA
dA = 0.4 * dh replacing
dF = 1000 * 9.8 * h * 0.4 * dh
dF = 3920 * h * dh
We integrate both sides and we have:
F = 3920 * (h ^ 2/2), h = 0.6 up to h = 1
F = (3920/2) * (1 ^ 2 - 0.6 ^ 2)
F = 1254.4 N
Simplify 4 + (−3 − 8)
Answer:
-7
Step-by-step explanation:
4 + (−3 − 8)
PEMDAS
Parentheses first
4 + (-11)
Add and subtract next
-7
Answer:
first I'm using BODMAS
4+(-11)
= -7
hope it helps
If a computer depreciates at a rate of 18% per year, what is the monthly depreciation rate? A.6.83% B.1.50% C.5.33% D.8.21%
Answer:
b 150
Step-by-step explanation:
The number of job applications submitted before landing an interview are normally distributed with a population standard deviation of 4 applications and an unknown population mean. A random sample of 19 job seekers is taken and results in a sample mean of 55 applications. The confidence intervalis (52.87.57.14). What is the margin of error? Round to two decimal places.
Answer:
The margin of error = 2.13
Step-by-step explanation:
Explanation:-
Given random sample size 'n' =19
mean of the sample(x⁻) = 55 applicants
Given standard deviation of the Population(S.D) = 4
Given confidence intervals are
((52.87.57.14)
we know that The Margin of error is determined by
[tex]M.E = Z_{\alpha } \frac{S.D}{\sqrt{n} }[/tex]
The confidence intervals are determined by
(x⁻ - M.E , x⁻+ M.E)
Step(ii):-
Given confidence intervals are
((52.87.57.14)
Now equating
(x⁻ - M.E , x⁻+ M.E) = ((52.87 , 57.14)
Given mean of the sample x⁻ = 55
( 55 - M.E , 55 + M.E) =((52.87.57.14)
Equating
55 - M.E = 52.87
M.E = 55 - 52.87
M.E = 2.13
Final answer:-
The margin of error = 2.13
A competition
took place in 1983
takes place every 6 years.
What is the first year after 2045 that it will also take place?
Answer:
2049.
Step-by-step explanation:
2045 - 1983 = 62 years.
So the competition will take place in 1983 + 60 = 2043.
After 2045 the competition takes place in 2049.
Based on data from the Greater New York Blood Program, when blood donors are randomly selected the probability of the having Group O blood is 0.45. Knowing that information, find the probability that AT LEAST ONE of the 5 donors has Group O blood type.
Answer:
The probability that at least one of the 5 donors has Group O blood type is 0.9497.
Step-by-step explanation:
We can model this as a binomial random variable, with n=5 (the sample size) and p=0.45.
The probability that exactly k donors have Group O blood type in the sample can be written as:
[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{5}{k} 0.45^{k} 0.55^{5-k}\\\\\\[/tex]
We have to calculate the probability P(x≥1). In this case it easy to substract from 1 the probabitity that x is exactly 0:
[tex]P(X\geq1)=1-P(x=0)\\\\\\P(x=0) = \dbinom{5}{0} p^{0}(1-p)^{5}=0.55^5=0.0503\\\\\\P(x\geq1)=1-0.0503=0.9497[/tex]
The length of time it takes students to complete a statistics examination is uniformly distributed and varies between 40 and 60 minutes. What is the probability density function for the length of time to complete the exam?
Answer:
[tex]X \sim Unif (a=40, b=60)[/tex]
And for this case we want to find the probability density function and we know that is given by:
[tex] f(x) =\frac{1}{b-a}=\frac{1}{60-40}= \frac{1}{20}, 40\leq X\leq 60[/tex]
Step-by-step explanation:
Let X the random variable who represent the length of time it takes students to complete a statistics examination. And the distribution for x is given by:
[tex]X \sim Unif (a=40, b=60)[/tex]
And for this case we want to find the probability density function and we know that is given by:
[tex] f(x) =\frac{1}{b-a}=\frac{1}{60-40}= \frac{1}{20}, 40\leq X\leq 60[/tex]
Researchers want to determine whether or not there is a difference in systolic blood pressure based on how many hours a person exercises per week. They divide a sample of 72 people into 3 groups based on how many hours they exercise per week. Group 1 exercises less than 2 hours per week, Group 2 exercises between 2 and 5 hours per week, and Group 3 exercises more than 5 hours per week. Researchers measure and record the systolic blood pressure for each participant. They choose α = 0.05 level to test their results. For your convenience, I have prepared an excel file with the data titled: data_homework10_BP groups. Use this data to run a One-way Anova.
1. What is the between groups degrees of freedom for this study?
a. 2
b. 3
c. 72
d. 69
2. This finding is statistically significant.
a. True
b. False
3. Based on this information, the researcher should make the decision to ___________.
a. reject the null hypothesis
b. fail to reject the null hypothesis
Answer:
(1) The between groups degrees of freedom is 2.
(2) TRUE.
(3) The correct option is (a).
Step-by-step explanation:
(1)
The between groups degrees of freedom for the study is:
[tex]\text{df}_{B}=k-1\\=3-1\\=2[/tex]
Thus, the between groups degrees of freedom is 2.
(2)
The hypothesis for he one-way ANOVA is:
H₀: All the means are equal.
Hₐ: At least one of the mean is not equal.
The output of the ANOVA test is attached below.
The p-value of the test is 0.00005.
p-value = 0.00005 < α = 0.05
Thus, the result is statistically significant.
The statement is TRUE.
(3)
As the p-value of the test is less than the significance level, the researcher should make the decision to reject the null hypothesis.
The correct option is (a).
For what value of the constant c is the function f continuous on (−[infinity],[infinity]) ? f(x)={cx2+2xifx<3x3−cxifx≥3
Answer:
c = 6.25
Step-by-step explanation:
We are given the following piecewise function:
[tex]\left \{ {{cx^{2} + 2x, x < 3} \atop {3x^{3} - cx, x \geq 3}} \right[/tex]
Continuous function:
A function f(x) is continuous, at a point a, if:
[tex]\lim_{x \to a} f(x)[/tex] exists and [tex]\lim_{x \to a} f(x) = f(a)[/tex]
In this question:
Piece-wise function, so we have to verify if the limit exists.
The function changes at x = 3. So we verify at a = 3.
It will exist if:
[tex]\lim_{x \to 3^{-}} f(x) = \lim_{x \to 3^{+}} f(x)[/tex]
To the left:
Less than 3.
[tex]\lim_{x \to 3^{-}} f(x) = \lim_{x \to 3^{-}} cx^{2} + 2x = c*(3)^{2} + 2*3 = 9c + 6[/tex]
To the right:
Greater than 3.
[tex]\lim_{x \to 3^{+}} f(x) = \lim_{x \to 3^{+}} 3x^{3} - cx = 3*3^{3} - 3c = 81 - 3c[/tex]
f continuous:
They have to be equal:
[tex]\lim_{x \to 3^{-}} f(x) = \lim_{x \to 3^{+}} f(x)[/tex]
[tex]9c + 6 = 81 - 3c[/tex]
[tex]12c = 75[/tex]
[tex]c = \frac{75}{12}[/tex]
[tex]c = 6.25[/tex]
Bijan has agreed to run a half-marathon to raise money for charity. Each day before school, Bijan runs a 2.4-mile route around his neighborhood. Then, each day after school, he runs on a lakeside trail. After 4 days, Bijan has run a total of 14.8 miles. Suppose you want to find out the length of the lakeside trail, x. What expression would represent how far Bijan runs everyday? What is the equation that represents his total distance after 4 days?
Answer:
First one is (x+2.4)
Second one is 4(x+2.4)=14.8
Step-by-step explanation:
Answer:
What expression would represent how far Bijan runs everyday?
✔ (x + 2.4)
What is the equation that represents his total distance after 4 days?
✔ 4(x + 2.4) = 14.8
Step-by-step explanation: I TOOK THE TEST
Find the domain of the function f(x) = 7x2 + 8x - 15.
Answer:
Domain is all real numbers or (negative infinity, positive infinity)
Step-by-step explanation:
Domain is all values of x (inputs) that will work with the function. Since a parabola has no limits for x, and all numbers work for x, then the domain can be any number. That leaves us with All Real Numbers as our answer.
My computer can download a movie in 5 hours. If I install an extra processor it can download the movie in 4 hours. How long, working alone, would it have taken the new extra processor to download the movie?
Pls try to help within 10-20 min I really need it!!!!!!
=======================================================
Explanation:
We have two workers, more or less. Worker A gets the job done in 5 hours. Worker B comes along to help. If A and B work together, they get the job done in 4 hours. This assumes neither worker hinders the other.
Worker A's rate is 1/5 of a job per hour. In other words, after 1 hour, 1/5 of the job is done.
The combined rate is 1/4 for similar reasoning
Worker B's rate is 1/x where x represents how long it takes worker B to get the job done on its own.
The equation to solve is
1/5 + 1/x = 1/4
Note how 1/5 and 1/x represents the sum of the individual rates to get the combined rate 1/4
To solve this equation, it helps to clear out the fractions. Multiply every term by the LCD 20x
20x(1/5 + 1/x) = 20x(1/4)
20x(1/5) + 20x(1/x) = 20x(1/4)
4x + 20 = 5x
From here you can probably see solving this is relatively easy
4x+20 = 5x
20 = 5x-4x
20 = x
x = 20
Therefore, it will take 20 hours for worker B to get the job done on its own.
Going back to the processing context, it takes 20 hours for the new processor to download the movie. This is where the new processor is working alone without help from the original processor.
----------------
Side note: downloading a movie really depends on internet speed rather than processor speed.
Identifying Additive Inverses
Try it
Match each polynomial expression to its additive inverse.
-6x²-x-2
6x²-x+2
6x2 + x-2
6x2 - X+2
622 - x + 2
622 + x + 2
1-6x²+x-2
6x²+x-2
Intro
Done
Answer:
he additive inverse of:
a) [tex]-6x^2-x-2[/tex] is : [tex]6x^2+x+2[/tex]
b) [tex]6x^2-x+2[/tex] is : [tex]-6x^2+x-2[/tex]
c) [tex]6x^2+x-2[/tex] is : [tex]-6x^2-x+2[/tex]
d) [tex]6x^2+x+2[/tex] is : [tex]-6x^2-x-2[/tex]
Step-by-step explanation:
You need to consider that the additive inverse of a polynomial is that polynomial that consists of the opposite of each term of the polynomial given.
Then, the additive inverse of:
a) [tex]-6x^2-x-2[/tex] is : [tex]6x^2+x+2[/tex]
b) [tex]6x^2-x+2[/tex] is : [tex]-6x^2+x-2[/tex]
c) [tex]6x^2+x-2[/tex] is : [tex]-6x^2-x+2[/tex]
d) [tex]6x^2+x+2[/tex] is : [tex]-6x^2-x-2[/tex]
what value of x is in the solution set of 2(3x–1)>4x–6?
Answer:
x > -2
Step-by-step explanation:
2(3x–1)>4x–6
Divide each side by 2
2/2(3x–1)>4x/2–6/2
3x-1 > 2x-3
Subtract 2x from each side
3x-2x-1 > 2x-3-2x
x-1 > -3
Add 1 to each side
x-1+1 > -3+1
x > -2
HELP!! Im not sure what i did wrong!!
I'm not sure what exactly you did wrong, but I agree with you that the sample size is too small, so the correct answer will probably be the fourth options. Hope that this gives you some confidence, and 'm sorry not to be able to help you any further...
PLEASE HELP!!!! Find the common difference
Answer:
The common difference is 1/2
Step-by-step explanation:
Data obtained from the question include:
3rd term (a3) = 0
Common difference (d) =.?
From the question given, we were told that the 7th term (a7) and the 4th term (a4) are related by the following equation:
a7 – 2a4 = 1
Recall:
a7 = a + 6d
a4 = a + 3d
a3 = a + 2d
Note: 'a' is the first term, 'd' is the common difference. a3, a4 and a7 are the 3rd, 4th and 7th term respectively.
But, a3 = 0
a3 = a + 2d
0 = a + 2d
Rearrange
a = – 2d
Now:
a7 – 2a4 = 1
Substituting the value of a7 and a4, we have
a + 6d – 2(a + 3d) = 1
Sustitute the value of 'a' i.e –2d into the above equation, we have:
–2d + 6d – 2(–2d + 3d) = 1
4d –2(d) = 1
4d –2d = 1
2d = 1
Divide both side by 2
d = 1/2
Therefore, the common difference is 1/2
***Check:
d = 1/2
a = –2d = –2 x 1/2 = –1
a3 = 0
a3 = a + 2d
0 = –1 + 2(1/2)
0 = –1 + 1
0 = 0
a7 = a + 6d = –1 + 6(1/2) = –1 + 3 = 2
a4 = a + 3d = –1 + 3(1/2) = –1 + 3/2
= (–2 + 3)/2 = 1/2
a7 – 2a4 = 1
2 – 2(1/2 = 1
2 – 1 = 1
1 = 1
evaluate the algebraic expression for the given values 6+5(x-6)³ for X=8