Answer:
Below
Step-by-step explanation:
The two given expressions are:
● √(2p-7) = 3
● 7√(3q-1) = 2
We are told to evaluate p+q^2
To do that let's find the values of p and q^2
■■■■■■■■■■■■■■■■■■■■■■■■■■
Let's start with p.
● √(2p-7) = 3
Square both sides
● (2p-7) = 3^2
● 2p-7 = 9
Add 7 to both sides
● 2p-7+7 = 9+7
● 2p = 16
Divide both sides by 2
● 2p/2 = 16/2
● p = 8
So the value of p is 8
■■■■■■■■■■■■■■■■■■■■■■■■■■
Let's find the value of q^2
● 7√(3q-1) = 2
Square both sides
● 7^2 × (3q-1) = 2^2
● 49 × (3q-1) = 4
● 49 × 3q - 49 × 1 = 4
● 147q - 49 = 4
Add 49 to both sides
● 147q -49 +49 = 4+49
● 147q = 53
Divide both sides by 147
● 147q/147 = 53/147
● q = 53/ 147
Square both sides
● q^2 = 53^2 / 147^2
● q^2 = 2809/21609
■■■■■■■■■■■■■■■■■■■■■■■■■
● p+q^2 = 8 +(2809/21609)
● p+q^2 = (2809 + 8×21609)/21609
● p+q^2 = 175681 / 21609
● p + q^2 = 8.129
Round it to the nearest unit
● p+ q^2 = 8
solve the equation 7*2=?
Answer:
7*2=14
Step-by-step explanation:
7*2=14 because is multiplication
Answer:
14 because it is multiplication
Write the equation of the line that passes through (−2, 6) and (2, 14) in slope-intercept form. (2 points)
Answer:
[tex]y = 4x + 14[/tex]
Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation we must first find the slope of the line
Slope of the line using points (−2, 6) and (2, 14) is
[tex]m = \frac{14 - 6}{2 + 2} = \frac{8}{2} = 4[/tex]
Now we use the slope and any of the points to find the equation of the line.
Equation of the line using point ( - 2, 6) and slope 4 is
[tex]y - 6 = 4(x + 2) \\ y - 6 = 4x + 8 \\ y = 4x + 8 + 6[/tex]
We have the final answer as
[tex]y = 4x + 14[/tex]
Hope this helps you
Tierra's THR zone is 135-185 bpm (beats per minute). What might Tierra's heart rate be to
indicate that she was working too hard?
A. 145 bpm
B. 195 bpm
C. 175 bpm
D. 130 bpm
The correct answer is B. 195 bpm
Explanation:
In health and related areas, THR or Target Heart Rate zone refers to the range of heart rate an individual should have including the maximum heart rate. In the case of Tierra, her THR zone indicates her maximum heart rate should be 185 beats per minute.
In this context, a heart rate above this number shows Tierra is working too hard or that his heart is doing too much effort, which is dangerous for her health. Thus, the heart rate that shows she is doing too hard is 195 bmp as this is the only one that is above the ideal rate.
Which of the following is a solution of y> Ix| - 5?
O (-4,1)
O (-1,-4)
O (4, -1)
Hurry plz
Answer:
O (-4,1)
I hope I helped you^_^
A vending machine company wants to check three of its machines to determine if they are properly dispensing 12 ounces of coffee. Their data is given below α = 0.01.
Row Machine A Machine B Machine C
1 11.5 10.3 11.1
2 12.1 9.7 11.3
3 11.6 10.4 11.9
4 12.0 10.7 11.5
5 11.1 9.9 11.7
6 12.2 10.1 11.3
H0: μA = μB = μC
Ha: Not all means are equal
One-way ANOVA: Machine A, Machine B, Machine C
Source DF SS MS F P
Factor 2 8.363 4.182 31.73 0.000
Error 15 1.977 0.132
Total 17 10.340
P-value: _____
Decision: _____
Is there a significant difference between the vending machines A, B, and C? Use α=0.05.
A. No, there is no significant difference between the means.
B. Yes, there is a significant difference between the means.
C. The F-test cannot be used to answer whether or not there is a significant difference between the means.
Answer:
The correct option is B.
Step-by-step explanation:
The hypothesis to determine whether the vending machines are properly dispensing 12 ounces of coffee is:
H₀: [tex]\mu_{A}=\mu_{B}=\mu_{C}[/tex]
Hₐ: Not all means are equal.
The ANOVA output is as follows:
One-way ANOVA: Machine A, Machine B, Machine C
Source DF SS MS F P
Factor 2 8.363 4.182 31.73 0.000
Error 15 1.977 0.132
Total 17 10.340
The significance level is α = 0.05.
The p-value of the model is:
p-value = 0.000
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected.
p-value = 0.000 < α = 0.05
The null hypothesis will be rejected.
Conclusion:
There is a significant difference between the means.
Thus, the correct option is B.
accountancy
So i have to make trial balance and im kinda confused with 'interest'. So which side did it go to? Credit or debit? It didn't state the interest as received or expense/paid. someone told me to look at the bank but hey i need more explanation T^T
what are the like terms of the expression.
3x+8x+y+x+8
Answer:
the like terms are:
3x+8x+x+y+8
12x+y+8
Answer:
The like terms are
3x, 8x, x
Step-by-step explanation:
3x+8x+y+x+8
The like terms are
3x, 8x, x
They are the terms that are in terms of the first power of x
1. The mean performance score on a physical fitness test for Division I student athletes is 947 with a population standard deviation of 205. Select a random sample of 64 of these students. Hint: we have a sample so use the standard error. What is the probability the mean of the sample is below 900
Answer:
0.033316
Step-by-step explanation:
We use the z score formula to solve for this question.
Since we are given the number of samples in the question, our z score formula is given as:
z = (x-μ)/ S.E
where x is the raw score
μ is the sample mean
S.E is the Standard error.
x is the raw score = 900
μ is the sample mean = Population mean = 947
Standard error =
This is calculated as Population standard deviation/ √No of samples
= 205/√64.
= 205/8
= 25.625
We proceed to calculate the z score
z = (x-μ)/ S.E
z = 900 - 947/25.625
= -1.83415
Using the z score table for normal distribution,
P(x≤ z) = P(z ≤ -1.83) = P(x ≤ 900)
P(x<900) = 0.033316
Therefore, the probability the mean of the sample is below 900 is 0.033316
Consider the function f(x) = x2. Which of the following functions shifts f(x)
downward 5 units and to the right 3 units?
A)f(x) = (x + 3)2 - 5
B) f(x) = (x - 3)2 - 5
C) f(x) = (x - 5)2 - 3
D) f(x) = (x - 5)2 + 3
Answer:
f(x) = (x - 3)² - 5
Step-by-step explanation:
equate equation to 0
(x - 3)² = 0
take the square root on both sides
x - 3 = 0
add 3
x = 3
If x = 3 then you are moving to 3 units to the right.
- 5 means you are going downward 5 units.
Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x) = x , [0, 16]
Answer:
C = 4
Step-by-step explanation:
solution:
f(x) can be differentiated on (0,16)
By mean value theorem
= f(16) = 4
= f(0) = 0
= f(b) - f(a)/b - a
= f(4) - f(0)/ f(16) - f(0)
= f'(c) = 1/2√C
= 1/2√C = 4/16
= 1/2√C = 1/4
= 4 = 2√C
= √C = 4/2
we make c the subject of the formula and also eliminate the square root
= √C = 2
= C = 2²
= C = 4
Tính tích phân sau bằng cách dùng tọa độ cực I=∫∫ [tex]\frac{1}{\sqrt{x^{2} +y^{2} } }[/tex]dxdy R là miền nằm trọg góc phần tư thứ nhất thỏa mãn 4[tex]\leq x^{2} +y^{2} \leq 9[/tex]
It sounds like R is the region (in polar coordinates)
R = {(r, θ) : 2 ≤ r ≤ 3 and 0 ≤ θ ≤ π/2}
Then the integral is
[tex]\displaystyle \iint_R\frac{\mathrm dx\,\mathrm dy}{\sqrt{x^2+y^2}} = \int_0^{\pi/2}\int_2^3 \frac{r\,\mathrm dr\,\mathrm d\theta}{\sqrt{r^2}} \\\\ = \int_0^{\pi/2}\int_2^3 \mathrm dr\,\mathrm d\theta \\\\ = \frac\pi2\int_2^3 \mathrm dr \\\\ = \frac\pi2r\bigg|_2^3 = \frac\pi2 (3-2) = \boxed{\frac\pi2}[/tex]
3)
Write an inequality for the graph below. If necessary, use
<= for < or >= for.
Kinda stuck and running out of time
Answer:
Step-by-step explanation:
Evaluate the following expressions: 2(−1 + 3) − 7
Answer:
-3 is the answer.
Step-by-step explanation:
=2(-1+3)-7
=2(2)-7
=4-7
=-3
Hope it will help you :)
Grandma baked 969696 cookies and gave them to her grandchildren. One of the grandchildren, Cindy, received ccc fewer cookies than she would have received had all of the cookies been evenly divided among the 888 grandchildren.
Answer:
Answer:
96/8 - c
Step-by-step explanation:
96/8 = 12
The average amount of cookies each grandchild would get is 12. However, Cindy gets c less than the average amount. So, it would be 12 - c.
But, it's asking for the original expression. Therefore, the answer would be 96/8 - c.
Which of the following graphs shows a parabola with a vertex of (1,-9) and solutions of (-2,0) and (4,0)?
Answer:
Hello,
Step-by-step explanation:
Roots are -2 and 4
y=k*(x+2)(x-4)
Vertex = (1,-9) is a point of the parabola
-9=k*(1+2)(1-4) ==> k=1
Equation of the parabola is y=(x+2)(x-4)
But you don' t have given the graphs !!!!
The graph show a parabola with a vertex that has Roots are -2 and 4.
What is Parabola?A parabola is a U-shaped curve this is drawn for a quadratic function,
f(x) = ax² + b x + c. The graph of the parabola is downward (or opens down), when the price of a is much less than 0, a < 0. The graph of the parabola is upward (or opens up) when the value of a is more than 0, a > 0.
Given that,
The vertex of (1,-9) and solutions of (-2,0) and (4,0).
y = k*(x+2)(x-4)
Vertex = (1,-9) is a point of the parabola
-9 = k*(1+2)(1-4)
Substitute the value of k = 1 in the equation,
The equation of the parabola is y = (x+2)(x-4).
The graph show a parabola with a vertex that has Roots are -2 and 4.
Learn more about the parabola here:
brainly.com/question/4074088
#SPJ2
1) Santhosh packed 240 oranges and 288 apples in boxes. He packed oranges and apples in separate boxes. He put equal number of fruits in each box. What is the maximum number of fruits that can be put in each box?
The maximum no of fruits that could be put in each box is 48
For determining the maximum no of fruits, we have to find out the highest common factor i.e. HCf between two numbers i.e. 240 and 288
So,
For 240 = [tex]2 \times 2 \times 2 \times 2 \times 3 \times 5[/tex]
And, for 288, it is = [tex]2 \times 2 \times 2 \times 2 \times 2 \times3 \times 3[/tex]
So, the highest common factor between two numbers is
= [tex]2\times 2\times 2\times 2\times 3[/tex]
= 48
So we can conclude that the maximum no of fruits that could be put in each box is 48
Learn more about numbers here: brainly.com/question/17429689?
Answer:
the maximum number of fruits that can be put in each box=48
Given :
Total number of oranges = 240
Total number of apples = 288
we find maximum number of fruits by finding highest common factor HCF
Step-by-step explanation:
Lets find out HCF of 240 and 288
Write the prime factors for 240 and 288
[tex]288=2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3\\240=2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5[/tex]
Now write the common factor for both numbers
[tex]2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 =48[/tex]
So, GCF is 48
We have to put 48 fruits in each box.
Learn more :
brainly.in/question/8084599
In the following equation, when x=3, what is the value of y? -4x + 3y = 12 A. 9 B. 3 C. 0 D. 8 PLZ HURRY IM TIMED WILL MARK BRAINLIEST
Answer:
[tex]\huge\boxed{y = 8}[/tex]
Step-by-step explanation:
-4x + 3y = 12
Given that x = 3
-4 (3) + 3y = 12
-12 + 3y = 12
Adding 12 to both sides
3y = 12+12
3y = 24
Dividing both sides by 3
y = 8
Answer:
y =8
Step-by-step explanation:
-4x + 3y = 12
Let x = 3
-4(3) +3y = 12
-12+3y = 12
Add 12 to each side
-12+12+3y =12+12
3y =24
Divide each side by 3
3y/3 = 24/3
y =8
A race car is traveling at a rate of 36 yards per second. What is the car's speed in miles per hour?
Answer: The car is traveling at 73.63638 Mph
Step-by-step explanation:
1 yard per second is the same as 3 feet per second.
there are 5280ft per mile
So, at 36 yards per second, the car is traveling at 108/5280th (0.02045455) of a mile per second
0.02045455 * 60 (seconds) * 60 (minutes) = 73.63638 Mph
The value of y varies jointly with x and z. If y = 7 when z = 196 and x = 2, find the value of y when x = 3 and z = 336. I will rate you brainliest
Answer:
18
Step-by-step explanation:
Given that:
y∞ xz
y=kxz. Where k is constant
When z=196 and x= 2 then y= 7
7=(196)(2)k
7=392k
k=1/56
There fore y=(1/56)xz
When x=3 and z =336
y=(1/56)xz
y=(1/56)(336)(3)
y=18
if value of y varies jointly with x and z. If y = 7 when z = 196 and x = 2 then the value of y when x = 3 and z = 336 is 18.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Value of y varies jointly with x and z.
y ∞ xz
y=kxz.
Where k is constant
When z=196 and x= 2 then y= 7
Let us find the value of k
7=(196)(2)k
7=392k
Divide both sides by 7
k=1/56
y=(1/56)xz
When x=3 and z =336
y=(1/56)xz
y=(1/56)(336)(3)
y=18
Hence, the value of y when x = 3 and z = 336 is 18.
To learn more on Ratios click:
https://brainly.com/question/13419413
#SPJ2
Rational equation of 3/x+1=2/x-3
Answer:
x = 11
Step-by-step explanation:
3/x+1=2/x-3
Solve by using cross products
2 (x+1) = 3 (x-3)
Distribute
2x+2 = 3x-9
Subtract 2x
2x+2-2x = 3x-2x-9
2 = x-9
Add 9 to each side
2+9 =x-9+9
11 =c
What is the length of the diagonal of a rectangle with the base of 4 and an altitude of 3
Answer:
5
Step-by-step explanation:
Use the Pythagorean Theorem
C^2=a^2 + b^2
c^2= 3^2 + 4^2
c^2= 9+16
c^2= 25
The take the square root
c= √25
c = 5
[2 ÷ (4 - 2) + 8^2] - [2 - (-1) ] ^2
A. 62
B.60
C.56
Answer:
56
Step-by-step explanation:
[2 ÷ (4 - 2) + 8^2] - [2 - (-1) ] ^2
Brackets first
Then parentheses in the brackets
[2 ÷ 2 + 8^2] - [2 - (-1) ] ^2
Exponents in the brackets
[2 ÷ 2 + 64] - [2 - (-1) ] ^2
Divide
[1+64] - [2 - (-1) ] ^2
Add and subtract in the brackets
[65] - [3 ] ^2
Exponents
[65] - [9 ]
Subtract
56
14. Solve for p. Assume that none of the denominators are equal to 0
Plz help me
Answer:
Step-by-step explanation:
Divide by y
kl/y = f/(p + n) + r/u Subtract r/u from both sides
kl/y - r/u = f/(p + n) Multiply both sides by (p + n)
(kl/y - r/u ) (p + n) = f Divide by (kl/y - r/u)
p + n = f / (kl/y - r/u) Subtract n from both sides
p = f / (kl/y - r/u) - n
I think I'd leave this as the answer. I don't think you are expected to make it a 2 tier fraction.
I need help with this question please
Answer:
Step-by-step explanation:
30t - 5t² = 10
5t² - 30t + 10 = 0
t = [30 ± √(30² - 4 ⋅ 5 ⋅ 10)] / [2 ⋅ 5]
= [30 ± √700] / 10
= [30 ± 10√7] / 10
= 3 ± √7
≈ 0.35 seconds and 5.65 seconds
Simplify and give the answer in standard form: (3/8+5/12) ÷ (8/-15 x 27/16)
Find the value of f (x)=x²-4 and g(x)=3x+2 Find the value of f (-1)g(-1)
Answer:
3
Step-by-step explanation:
[tex]f(-1)g(-1) \text{ is the same thing as } f(-1)\cdot g(-1). \\\text{Therefore, find f(-1) and g(-1)}[/tex]
[tex]f(-1)=(-1)^2-4\\f(-1)=1-4\\f(-1)=-3[/tex]
[tex]g(-1)=3(-1)+2\\g(-1)=-3+2\\g(-1)=-1[/tex]
Therefore:
[tex]f(-1)\cdot g(-1)\\=(-3)(-1)=3[/tex]
The data represent the membership of a group of politicians. If we randomly select one politician, what is the probability of getting given that a was selected?
Complete Question
The data represent the membership of a group of politicians. If we randomly select one politician, what is the probability of getting a Republican given that a male was selected?
Republican Democrat Independent
Male 11 6 0
Female 70 17 7
The probability is approximately_____?
Answer:
The probability is [tex]P(k) = 0.647[/tex]
Step-by-step explanation:
From the question we are told that
The sample size of male is [tex]n_m = 11 + 6 =17[/tex]
The number of male Republican is [tex]k = 11[/tex]
Generally the probability of getting a Republican given that a male was selected is
[tex]P(k) = \frac{k}{n_m}[/tex]
substituting values
[tex]P(k) = \frac{ 11}{17}[/tex]
[tex]P(k) = 0.647[/tex]
A covered wagon on the Oregon
Trail could travel about 2.5 miles
per hour on flat terrain. About how
many miles could it travel in
9 hours?
Answer:
3.6miles
Step-by-step explanation:
9/2.5=3.6
1-What is the sum of the series? ∑j=152j Enter your answer in the box.
2-What is the sum of the series? ∑k=14(2k2−4) Enter your answer in the box.
3-What is the sum of the series? ∑k=36(2k−10)
4-Which answer represents the series in sigma notation? 1+12+14+18+116+132+164 ∑j=1712(j+1) ∑j=172j−1 ∑j=1712j+1 ∑j=17(12)j−1
5-Which answer represents the series in sigma notation? −3+(−1)+1+3+5 ∑j=155j−1 ∑j=15(3j−6) ∑j=15(2j−5) ∑j=15−3(13)j−1
Answer:
Please see the Step-by-step explanation for the answers
Step-by-step explanation:
1)
∑[tex]\left \ {{5} \atop {j=1}} \right.[/tex] 2j
The sum of series from j=1 to j=5 is:
∑ = 2(1) + 2(2) + 2(3) + 2(4) + 2(5)
= 2 + 4 + 6 + 8 + 10
∑ = 30
2)
This question is not given clearly so i assume the following series that will give you an idea how to solve this:
∑[tex]\left \ {{4} \atop {k=1}} \right.[/tex] 2k²
The sum of series from k=1 to j=4 is:
∑ = 2(1)² + 2(2)² + 2(3)² + 2(4)²
= 2(1) + 2(4) + 2(9) + 2(16)
= 2 + 8 + 18 + 32
∑ = 60
∑[tex]\left \ {{4} \atop {k=1}} \right.[/tex] (2k)²
∑ = (2*1)² + (2*2)² + (2*3)² + (2*4)²
= (2)² + (4)² + (6)² + (8)²
= 4 + 16 + 36 + 64
∑ = 120
∑[tex]\left \ {{4} \atop {k=1}} \right.[/tex] (2k)²- 4
∑ = (2*1)²-4 + (2*2)²-4 + (2*3)²-4 + (2*4)²-4
= (2)²-4 + (4)²-4 + (6)²-4 + (8)²-4
= (4-4) + (16-4) + (36-4) + (64-4)
= 0 + 12 + 32 + 60
∑ = 104
∑[tex]\left \ {{4} \atop {k=1}} \right.[/tex] 2k²- 4
∑ = 2(1)²-4 + 2(2)²-4 + 2(3)²-4 + 2(4)²-4
= 2(1)-4 + 2(4)-4 + 2(9)-4 + 2(16)-4
= (2-4) + (8-4) + (18-4) + (32-4)
= -2 + 4 + 14 + 28
∑ = 44
3)
∑[tex]\left \ {{6} \atop {k=3}} \right.[/tex] (2k-10)
∑ = (2×3−10) + (2×4−10) + (2×5−10) + (2×6−10)
= (6-10) + (8-10) + (10-10) + (12-10)
= -4 + -2 + 0 + 2
∑ = -4
4)
1+1/2+1/4+1/8+1/16+1/32+1/64
This is a geometric sequence where first term is 1 and the common ratio is 1/2 So
a = 1
This can be derived as
1/2/1 = 1/2 * 1 = 1/2
1/4/1/2 = 1/4 * 2/1 = 1/2
1/8/1/4 = 1/8 * 4/1 = 1/2
1/16/1/8 = 1/16 * 8/1 = 1/2
1/32/1/16 = 1/32 * 16/1 = 1/2
1/64/1/32 = 1/64 * 32/1 = 1/2
Hence the common ratio is r = 1/2
So n-th term is:
[tex]ar^{n-1}[/tex] = [tex]1(\frac{1}{2})^{n-1}[/tex]
So the answer that represents the series in sigma notation is:
∑[tex]\left \ {{7} \atop {j=1}} \right.[/tex] [tex](\frac{1}{2})^{j-1}[/tex]
5)
−3+(−1)+1+3+5
This is an arithmetic sequence where the first term is -3 and the common difference is 2. So
a = 1
This can be derived as
-1 - (-3) = -1 + 3 = 2
1 - (-1) = 1 + 1 = 2
3 - 1 = 2
5 - 3 = 2
Hence the common difference d = 2
The nth term is:
a + (n - 1) d
= -3 + (n−1)2
= -3 + 2(n−1)
= -3 + 2n - 2
= 2n - 5
So the answer that represents the series in sigma notation is:
∑[tex]\left \ {{5} \atop {j=1}} \right.[/tex] (2j−5)
For (1) the sum is 30, for (2) the sum is 90, for (3) the sum is -4, for(4) the sigma notation is [tex]\rm \sum j = 1(\frac{1}{2})^{j-1}\\[/tex] where j = 1 to j = 7, and for (5) the sigma notation is [tex]\rm\sum j = (2j-5)[/tex] where j = 1 to j = 5.
We have different series in the question.
It is required to find the sum of all series.
What is a series?In mathematics, a series can be defined as a group of data that followed certain rules of arithmetic.
1) We have:
[tex]\rm \sum j=2j[/tex] where j = 1 to j = 5
After expanding the series, we get:
= 2(1)+2(2)+2(3)+2(4)+2(5)
=2(1+2+3+4+5)
= 2(15)
=30
2) We have:
[tex]\rm \sum k=(2k^2-4)[/tex] where k = 1 to k = 4
After expanding the series, we get:
[tex]\rm = (2(1)^2-4)+(2(2)^2-4)+(2(3)^2-4)+(2(4)^2-4)+(2(5)^2-4)\\[/tex]
[tex]\rm = 2[1^2+2^2+3^2+4^2+5^2]-4\times5\\\\\rm=2[55]-20\\\\\rm = 90[/tex]
3) We have:
[tex]\rm \sum k= (2k-10)[/tex] where k = 3 to k = 6
After expanding the series, we get:
[tex]= (2(3)-10)+(2(4)-10)+(2(5)-10)+(2(6)-10)\\\\=2[3+4+5+6] - 10\times4\\\\=2[18] - 40\\\\= -4[/tex]
4) The series given below:
[tex]1, \frac{1}{2} ,\frac{1}{4},\frac{1}{8},\frac{1}{16},\frac{1}{32},\frac{1}{64}[/tex]
It is a geometric progression:
[tex]\rm n^t^h[/tex] for the geometric progression is given by:
[tex]\rm a_n = ar^{n-1}[/tex]
[tex]\rm a_n = 1(\frac{1}{2})^{n-1}\\\\\rm a_n = (\frac{1}{2})^{n-1}\\[/tex]
In sigma notation we can write:
[tex]\rm \sum j = 1(\frac{1}{2})^{j-1}\\[/tex] where j = 1 to j = 7
5) The given series:
−3+(−1)+1+3+5, it is arithmetic series.
[tex]\rm n^t^h[/tex] for the arithmetic progression is given by:
[tex]\rm a_n = a+(n-1)d[/tex]
[tex]\rm a_n = -3+(n-1)(2)\\\\\rm a_n = 2n-5[/tex]
In sigma notation we can write:
[tex]\rm\sum j = (2j-5)[/tex] where j = 1 to j = 5
Thus, for (1) the sum is 30, for (2) the sum is 90, for (3) the sum is -4, for(4) the sigma notation is [tex]\rm \sum j = 1(\frac{1}{2})^{j-1}\\[/tex] where j = 1 to j = 7, and for (5) the sigma notation is [tex]\rm\sum j = (2j-5)[/tex] where j = 1 to j = 5.
Learn more about the series here:
https://brainly.com/question/10813422
Find the polynomial for the area.
The area is
Answer: ¹/₂( x² - 10y² + 10xy - xy )
Step-by-step explanation:
From the diagram area of the triangle = ¹/₂ ˣ base ˣ height
where the base = x + 10y and the height = x - y
Therefore putting these into the formula above
Area = ¹/₂ [( x + 10y )( x -y )]
= ¹/₂( x² - xy + 10xy - 10y²)units²
= ¹/₂( x² - 10y² + 10xy - xy )