[tex]\textit{sum of a finite arithmetic sequence} \\\\ S_n=\cfrac{n(a_1+a_n)}{2}\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\[-0.5em] \hrulefill\\ a_1=3\\ n=5\\ S_5=75 \end{cases} \implies \begin{array}{llll} S_5=\cfrac{5(a_1+a_5)}{2} \\\\\\ 75=\cfrac{5(3+a_5)}{2} \end{array} \\\\\\ 150=5(3+a_5)\implies \cfrac{150}{5}=3+a_5\implies 30=3+a_5\implies \boxed{27=a_5} \\\\[-0.35em] ~\dotfill[/tex]
[tex]n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ n=5\\ a_5=27\\ a_1=3 \end{cases}\implies 27=3+(5-1)d \\\\\\ 24=(5-1)d\implies 24=4d\implies \cfrac{24}{4}=d\implies \boxed{6=d} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{\LARGE Terms}}{3~~,~~\stackrel{3+6}{9}~~,~~\stackrel{9+6}{15}~~,~~\stackrel{15+6}{21}}~\hfill[/tex]
-2a(-5d-4c) answer this
Answer:
10ad+8ac
Step-by-step explanation:
I know trust me.
Find an equation of the circle that has center (-3, -6) and passes through (0, 1).
Answer:
Step-by-step explanation:
General equation for a circle (x - a)² + (y - b)² = r² with (a,b) represents the center, (x,y) represents one of the points lie on the circle, and r represents the radius Determine r² by substituting the points into the general equation (x - a)² + (y - b)² = r² (5 - (-1))² + (-4 - 2)² = r² (5 + 1)² + (-6)² = r² 6² + 36 = r² 36 + 36 = r² 72 = r² Determine the equation of the circle (x - a)² + (y - b)² = r² (x - (-1))² + (y - 2)² = 72 (x + 1)² + (y - 2)² = 72 (This is the equation of the circle)
The volume of a sphere is
[tex]125\pi[/tex] cm3. What is the radius?
Last question.
Hi!!
Answer:
I'm not 100% sure, but I think it's 3.1.
Step-by-step explanation:
I took your volume, which is 125[tex]\pi[/tex], then a formula, which is
V=[tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex], then I just plugged in the 125 and I got 3.1. I'm so sorry if it's wrong! <3
round 2.577681 to 4 decimal places
Answer:
2.5777
Step-by-step explanation:
Answer: 2.5777
Step-by-step explanation:
Given:
2.577681
Find the fourth decimal place:
2.577681
Round:
2.5777
Rounding:
Is the place to the right greater than or less than 5?
If greater than or equal to, round up. If less than, it stays the same.
In this case, 8 > 5
Interest = $821.25, time = 1 year, rate = 12.42%. Find the principal
Step-by-step explanation:
P = l.100/t.r = $821.25×100/12.42×1 = $6612.318
hope this helps you.
What is the distance between the y-intercept of the function f(x)=2(3)^x and the y-intercept of the function g(x) represented by the table below?
Answer:
A. 1
Step-by-step explanation:
y-intercept of f(x)
f(x) = 2(3)°f(x) = 2(0, 2)y-intercept of g(x)
g(x) = (0, 3)Distance
⇒ 3 - 2
⇒ A. 1
What is the value of x?
Answer:
9
Step-by-step explanation:
x is 9 assuming they are identical triangles.
-4+2(3m+7)
Explain please
Answer:
6m + 10
Step-by-step explanation:
Distributive Property
a(b + c) = ab + acSolving
-4 + 2(3m + 7)-4 + 2(3m) + 2(7)-4 + 6m + 146m + 10ade and ola share a sum of 400 naira in the ratio 3:5. find the amount ade received.
Answer:
150 Naira
Step-by-step explanation:
3 + 5 = 8
Since Ade receives in a 3 to 5 ratio, Ade receives 3/8 of the total.
3/8 × 400 = 150
Answer: 150 Naira
Please help me I really need help
Alex buys 30 shares of Walmart at the close price if $48.80. His broker charges him 3% of each share. How much did Alex spend in total to buy this stock?
Alex spend $1507.92 in total to buy this stock at 3% charges on each shares.
What is shares?
Shares represent equity ownership in a corporation or financial asset, owned by investors who exchange capital in return for these units.
Alex buys 30 shares of Walmart at the close price of $48.80.
His broker charges him 3% of each share.
Purchasing of 30 shares =48.80 *30
=$1464
Now we have to find the 3% of total purchasing of shares.
So,
Broker's fees =[tex]\frac{3}{100}*1464[/tex]
= 0.03 * 1464
= 43.92
So, total cost of stock= 1464+43.92
= 1507.92
Hence, Alex spend $1507.92 in total to buy this stock.
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Dont answer unless your sure will mark brainliest
Answer:
199.5
Step-by-step explanation:
Solve for r.
r= __ ?
r= \frac{q^{2} }{p^{3}} +1
HELP ASAP!!!
The black graph is the graph of y = f(x).
Choose the equation for the red graph.
Answer:
B
Step-by-step explanation:
We shift the black graph about the x axis, to do that we divide y by -1,
We then shift over to the left 5 units, to do that's we add 5 to the x value.
So the answer here is B
dummy forgot his pin code. 20% of his pin code was 246.8 what was his pin code
Answer:
1234
Step-by-step explanation:
If 20% of his pin code was 246.8, we have to multiply 246.8 by 5 to get his pin code, which is 1234 (not safe btw.)
would really appreciate it if you hearted this answer
A smoothie recipe calls for 2 and 1 4th cups of frozen mango if the recipe serves two how many cups of frozen mango is needed to serve one
Answer:
The required number of cups of frozen mango is 1.125.
Step-by-step explanation: Given that a smoothie recipe calls for cups of frozen mango and the recipe serves two.
We are to find the number of cups of frozen mango that is needed to serve one.
We will be using the UNITARY method to solve the problem.
We have
The number of cups of frozen mango that needs to serve two is
Therefore, the number of frozen mango that needs to serve one is given by
Thus, the required number of cups of frozen mango is 1.125.
Step-by-step explanation:
These are confusing can anyone help with this?
Answer:
3. B
Step-by-step explanation:
The sum of two consecutive odd integers is 680 what are the integers
Answer:
let the first number and second number be x+1 and x+3 respectively
Patrick and Brooklyn are making decisions about their bank accounts. Patrick wants to deposit $300 as a principal amount, with an interest of 3% compounded quarterly. Brooklyn wants to deposit $300 as the principal amount, with an interest of 5% compounded monthly. Explain which method results in more money after 2 years. Show all work.
Answer:
Brooklyn's method results in more money after 2 years
Step-by-step explanation:
Compound Interest Formula
[tex]\large \text{$ \sf A=P(1+\frac{r}{n})^{nt} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedPatrick's Method
Given:
P = $300r = 3% = 0.03n = 4t = 2Substituting the given values into the formula and solving for A:
[tex]\implies \sf A=300\left(1+\dfrac{0.03}{4}\right)^{4 \times 2}[/tex]
[tex]\implies \sf A=300\left(1.0075\right)^{8}[/tex]
[tex]\implies \sf A=318.4796543...[/tex]
Therefore, using Patrick's method, there would be $318.48 in the account after 2 years.
Brooklyn's Method
Given:
P = $300r = 5% = 0.05n = 12t = 2Substituting the given values into the formula and solving for A:
[tex]\implies \sf A=300\left(1+\dfrac{0.05}{12}\right)^{12 \times 2}[/tex]
[tex]\implies \sf A=331.4824007...[/tex]
Therefore, using Brooklyn's method, there would be $331.48 in the account after 2 years.
As $331.48 > $318.48 then Brooklyn's method results in more money after 2 years.
Let X1, Xn be i.i.d. random variables with probability density function,
fx (x) = { 1/0 0 0 < x < 0 otherwise.
(a) Let X₁, X denote a bootstrap sample and let X = n
Find: E(XX1, , Xn), V(XX1, , Xn), E(X), V(X₂).
Hint: Law of total expectation: E(X)= E(E(XY)).
Law of total variance: V(X) = E(V(XY))+ (E(X|Y)).
Sample variance, i.e. s² = (X; - X)2 is an unbiased estimator of population variance.
The expected value of the assumed probability density function is 3/4 and the variance is 3/80
How to solve for E(x) and V(x)?The probability density function is not properly stated.
So, I will provide a general explanation on how to determine E(x) and V(x) of a probability density function
Assume that the probability density function is given as:
[tex]f(x)= \left[\begin{array}{ccc}3x^2 &0 \le x \le 1\\0&Otherwise\end{array}\right[/tex]
The expression E(x) is calculated using:
[tex]E(x) = \int\limits^a_b {x \cdot f(x)} \, dx[/tex]
So, we have:
[tex]E(x) = \int\limits^1_0 {x \cdot 3x^2 \ d(x)[/tex]
Evaluate the product
[tex]E(x) = \int\limits^1_0 { 3x^3 \ d(x)[/tex]
Integrate
[tex]E(x) = \frac34x^4 |\limits^1_0[/tex]
Expand
[tex]E(x) = \frac34(1-0)^4[/tex]
Evaluate
[tex]E(x) = \frac34[/tex]
The variance is then calculated using:
[tex]Var(x) = E(x^2) - (E(x))^2[/tex]
Calculate [tex]E(x^2)[/tex] using:
[tex]E(x^2) = \int\limits^a_b {x^2 \cdot f(x)} \, dx[/tex]
This gives
[tex]E(x^2) = \int\limits^1_0 {x^2 \cdot 3x^2} \, dx[/tex]
Expand
[tex]E(x^2) = \int\limits^1_0 {3x^4} \, dx[/tex]
Integrate
[tex]E(x^2) = \frac{3}{5}x^5|\limits^1_0[/tex]
Expand
[tex]E(x^2) = \frac{3}{5}(1 - 0)^5[/tex]
Evaluate
[tex]E(x^2) = \frac{3}{5}[/tex]
Substitute [tex]E(x^2) = \frac{3}{5}[/tex] and [tex]E(x) = \frac34[/tex] in [tex]Var(x) = E(x^2) - (E(x))^2[/tex]
[tex]Var(x) = \frac 35 - (\frac{3}{4})^2[/tex]
Evaluate the exponent
[tex]Var(x) = \frac 35 - \frac{9}{16}[/tex]
Evaluate the difference
[tex]Var(x) = \frac{3}{80}[/tex]
Hence, the variance of the probability density function is 3/80
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What is an element NOT found in creative writing?
A. conflict
B. plot
C. works cited
D. description
Answer:
it should be c
Step-by-step explanation:
find the value of y and x
Answer:
in my wisdom i think x=60 and y=60
Determine the measure of the missing angle.
1 point
65°
?
57°
57 degrees
O 48 degrees
65 degrees
O 58 degrees
Solve for
Step-by-step explanation:
65° + 57° + x = 180° ( the sum of angle of triangle is 180° )
122° + x = 180°
x = 180° - 122°
x = 58°
hence the answer is 58°....
Answer:
58 degrees
Step-by-step explanation:
Sum of angles in a triangle is 180 degrees
180 = 65 + 57 + x
180 = 122 +x
x =180 -122
x = 58
Which expression is the result of solving the equation ar – b = cy for ? (For a 70).
cy
cy + b
+ b
Don
Answer:
4th option, (cy+b)/a
Step-by-step explanation:
By algebraic manipulation, we add b to both sides, then divide by a to isolate x.
HELP PLS A rectangle has vertices at these coordinates.
(0, 8), (5, 8), (5, 0)
What are the coordinates of the fourth vertex of the rectangle?
Enter the coordinates in the boxes
Answer:
(0, 0).
Step-by-step explanation:
The 2 points with y = 8 is a horizontal side with (5, 8) 5 units to the right and the point (5, 0) lies vertically down from (5, 8) so the fourth point is 5 to the left of (5, 0) which is (0, 0)
Identify the coordinates of Point B after it is reflected across the y-axis.
(4, -3)
(4, 3)
(-4, 3)
(-4, -3)
Answer:
(-4,3)
Step-by-step explanation:
the coordinate (4,-3) is just at the 4th quadrant in which the value of x is positive and the value of y is negative
the quadrant (4,3) is on the first quadrant and the value expressed with the letter A
the coordinate (-4,-3) is a coordinate on the quadrant in which both values are negative
Suppose that the average bill for the drive through of 24 customers at Burger Palace is $14.30. It is known that the population standard deviation is σ=2.30. Estimate the true mean bill for a customer at Burger Palace with 95% confidence.
The standard deviation is a measure of a collection of values' variance or dispersion. The true mean bill for a customer at Burger Palace with 95% confidence is $13.38.
What is a standard deviation?The standard deviation is a measure of a collection of values' variance or dispersion. A low standard deviation implies that the values are close to the set's mean, whereas a high standard deviation shows that the values are spread out over a larger range.
Given that the Sample mean ([tex]\overline x[/tex]) is $14.30, the Sample size(n) is 24 customers, the Standard deviation(σ) is 2.30, while for a 95% confidence interval the Z-score is 1.960. Therefore, the true mean can be written as,
[tex]Z = \dfrac{\overline x- \mu}{\frac{\sigma}{\sqrt n}}\\\\\\1.960 = \dfrac{14.30-\mu}{\frac{2.30}{\sqrt{24}}}\\\\\\1.960 = \dfrac{14.3-\mu}{0.47}[/tex]
μ = 13.3788 ≈ 13.38
Hence, the true mean bill for a customer at Burger Palace with 95% confidence is $13.38.
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Verify the Identity!!
Answer:
Check the proof below
Step-by-step explanation:
try to verify from RHS to LHS
(Tan a + tan b) / (tan a - tan b)
= (sin a / cos a + sin b /cos b) / ( sin a/ cos a - sin b/ cos b)
= (sin a cos b + cos a sin b)/ (sin a cos b - cos a sin b)
= sin (a+b) / sin (a-b)
Fyi
sin(A+B) = sinAcosB+cosAsinB
sin(A-B) = sinAcosB-cosAsinB
Since the beginning of the month a local reservoir has been losing water at a constant rate. On the 10th of the month, the reservoir held 300million gallons of water and on the 18th it held only 262 million gallons. A. Write an equation that will give the amount of water in the reservoir at any time B. Hov, much water was in the reservoir on the 14th of the month? C. When will the reservoir get empty?
Total amount in the reservoir = amount of water in the 10th month - (rate of decline x number of months from the 10th month)
Rate of decline = (300 262) / (18 - 10) = 4.75
y = 300 million = 4.75x
Where x is the time of the month.
What will be the quantity of water in the reservoir on the 14th of the month?Total amount in the reservoir = amount of water in the 10th month - (rate of decline x number of months from the 10th month)
300 million - (4.75 x 4) = 281 million
When will the reservoir be empty?
0 = 300 - (4.75x)
x = 300 / 4.75
x = 63.16 days
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Please solve with explanation (high points)
8.1. If x is the distance from P to the flagpole and h is the height of the flagpole, then
tan(53°) = h/x
tan(28°) = h/(x + 20)
Solve for the first equation for h in terms of x :
h = x tan(53°)
Substitute this into the second equation and solve for x :
tan(28°) = x tan(53°) / (x + 20)
(x + 20) tan(28°) = x tan(53°)
x tan(28°) + 20 tan(28°) = x tan(53°)
x (tan(28°) - tan(53°)) = -20 tan(28°)
x = 20 tan(28°) / (tan(53°) - tan(28°))
x ≈ 13.4 m
8.2. By the law of cosines,
BD² = 7² + 11² - 2 • 7 • 11 cos(110°)
⇒ BD = √(170 - 154 cos(110°))
⇒ BD ≈ 14.9 cm
and
BC² = BD² + 16² - 2 • BD • 16 cos(40°)
⇒ BC = √(426 - 154 cos(110°) - 32 cos(40°) √(170 - 154 cos(110°)))
⇒ BC ≈ 10.6 cm
Now use Heron's formula. If S is the semiperimeter of ∆ABD and S' is the semiperimeter of ∆BCD, i.e.
S = (AB + BD + AD)/2 ≈ 16.5 cm
S' = (BC + CD + BD)/2 ≈ 20.7 cm
then
area ∆ABD = √(S (S - AB) (S - BD) (S - AD)) ≈ 36.2 cm²
and
area ∆BCD = √(S' (S' - BC) (S' - CD) (S' - BD)) ≈ 76.7 cm²
so that the total area of ABCD is approximately 112.9 cm².