Answer:
r=2,n=7
Step-by-step explanation:
The formula for the sum of the nth term of a Geometric Progression is given as:
Sn = a(1-r^n)/(1-r)
Where n = Number of terms
r = Common ratio
From the above question, we are told that:
The sum of the 1st nth term gp is 127.
Hence:
127 = 1(1-r^n)/(1-r)
We are also told that:
The sum of the reciprocal is 127/64
This means the inverse, the formula is given as:
Sn = 1/a(1-r^n)/(1-r)
127/64 = 1(1-1/r^n)/(1-1/r)
= r^(1-n)(1-r^n)/(1-r)
Solving the above, we obtain:
r^(n-1) = 64
r^(n-1) = 2⁶
Hence:
r = 2
Solving for n
n - 1 = 6
n = 6 + 1
n = 7
Therefore:
r=2,n=7
What is the solution of the system of equations below?
y + 2x = 2
y + 4x = 0
F. (1, -4) G. (-1,-4) H. (-1, 4) I. (1, 4)
G
Solution:
Here,
y+2x=2
y=2-2x
Now,
Putting the value of y
y+4x=0
2-2x+4x=0
2+2x=0
2(1+x)=0
1+x=0
x=-1
Then,
Putting the value of x
y=2x-2
=2×-1-2
=-2-2
=-4
Hence,the solution is (-1,-4)
help will give brainliest if right
BTW the last answer choice is D. 1
What is the solution to the equation 2(x + 3)2 = 98?
Answer: if you're solving by x it would be x=43/2
Step-by-step explanation:
Maria’s phone bills were $95, $67, $43, and $115. What was the mean, or average, of her phone bills?
Answer:
the mean is $80
Step-by-step explanation:
Answer:
80
Step-by-step explanation:
Mean of Phone Bills =
[tex] \frac{phone \: bills \: total}{number \: of \: phone \: bills} \\ = \frac{95 + 67 + 43 + 115}{4} \\ = \frac{320}{4} \\ = 80[/tex]
Felicia got a designer job with a company that pay $55,000/year. What is Felicia's gross monthly income
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Answer: 4583.33$
Explanation:
55000 / 12
I hope this helped!
<!> Brainliest is appreciated! <!>
- Zack Slocum
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
A study in which conditions are under the direct control of the investigator.
Answer:
Experimental study
Step-by-step explanation:
A wooden building has the shape of a
rectangular pyramid. The building's
base is 100 meters long and 50
meters wide. The height of each
triangular face is 40 meters. How
much wood was used to make the
entire building?
A 33,000 m²
B 13,000 m2
C 11,000 m2
D 6,000 m2
Answer:
B: 13000 m²
Step-by-step explanation:
To find how much wood is used, we will have to find the surface area of the wooden building.
Formula for surface area of a rectangular pyramid is;
SA = lw + l√(h² + w²/4) + w√(h² + l²/4)
We are given;
l = 100 m
w = 50 m
h = 40 m
Thus;
SA = (100 × 50) + 100√(40² + 50²/4) + 50√(40² + 100²/4)
SA = 5000 + 4717 + 3201.56
SA = 12918.56
Approximating to 2 significant figures gives;
SA = 13000 m²
Xochitl bought 5 shirts all for the same price.
After using a coupon that took $10 off the
total price, her total before tax was $35. What
was the cost of each shirt?
Answer:
Each shirt costed 9 dollars.
Step-by-step explanation:
35+10=45 (initial price)
45/5=9 dollars per shirt
Find the lateral surface 14ft area of the 2ft cylinder. Round your answer to the nearest tenth if necessary.
Answer:
616 square feet
Step-by-step explanation:
Lateral surface area of a cylinder can be determined by;
Lateral surface area = 2[tex]\pi[/tex]rh
where: r is its radius, and h is its height.
Given in the question that the height of the cylinder is 14 feet and of radius 2 feet, then;
Lateral surface area = 2[tex]\pi[/tex]rh
= 2 x [tex]\frac{22}{7}[/tex] x 2 x 14
= 2 x 22 x 2 x 7
= 616
Lateral surface area = 616 square feet
Thus, the lateral surface area of the cylinder is 616 square feet.
A regular hexagonal prism has a base area of 84.3ft^2 and a Volume of 337.2ft^3. What is the height of the prism?
Answer:
Height = 4 ft
Step-by-step explanation:
Base are : 84.3 ft square
Volume : 337.2 square cuboid
Find the product: (6x+5)(2x−7)
Ayuda por favor, es de calculo diferencial Tema: optimización.
Se desea construir una caja sin tapa que contenga el máximo volumen a partir de una lámina cuadrada de 10 m de lado. Determina las dimensiones de la caja.
Answer:
dots dots tods jajtikalaj majc kala mo meroonnn anoo asa ka
(-12)+(-18)+(-30) simplify this question
Answer:
-60
Step-by-step explanation:
Well just follow the equation from left to right
Add it all up.
2x+4y=8
x+2y=4
Which of the following statements is true about the ordered pair (-2,3) is TRUE?
1. It is one of many solutions to the system
2. It is not a solution to either equation
3. It is the only solution to the system of equations
4. It is a solution to the first equation but not the second equation
Answer:
(-2, 3) is one of many solutions to the system
Step-by-step explanation:
Let's actually solve the system so that we can compare the result with the given pair (-2, 3):
Multiplying the second equation by -2 results in:
2x + 4y = 8
-2x - 4y = -8
We see that these equations are identical. Thus, there are infinitely many solutions.
1. is true: (-2, 3) is one of many solutions to the system
The other three possible answers are incorrect.
Evaluate the function
Answer:
92
Step-by-step explanation:
plug -4 into the function
3(-4)²-10(-4)+4
48+40+4
92
Answer:
92
Step-by-step explanation:
f(-4)=3(-4)^2-10(-4)+4
=3(16)-10(-4)+4
=48+40+4
=92
Two people start biking from the same point. One heads east at 13 mph, the other south at 18 mph. What is the rate at which the distance between the two people is changing after 25 minutes and after 35 minutes? What is the rate at which the distance between the two people is changing after 25 minutes?
Answer:
[tex]22.21\ \text{mph}[/tex]
[tex]22.2\ \text{mph}[/tex]
Step-by-step explanation:
[tex]\dfrac{da}{dt}=13\ \text{mph}[/tex]
[tex]\dfrac{db}{dt}=18\ \text{mph}[/tex]
[tex]\dfrac{dc}{dt}[/tex] = Rate at which the distance between the two people is changing
At 25 minutes
[tex]a=13\times \dfrac{25}{60}=5.417\ \text{miles}[/tex]
[tex]b=18\times \dfrac{25}{60}=7.5\ \text{miles}[/tex]
[tex]c=\sqrt{5.417^2+7.5^2}\\\Rightarrow c=9.25\ \text{miles}[/tex]
Distance between the two people is
[tex]c^2=a^2+b^2[/tex]
Differentiating with respect to time we get
[tex]c\dfrac{dc}{dt}=a\dfrac{da}{dt}+b\dfrac{db}{dt}\\\Rightarrow \dfrac{dc}{dt}=\dfrac{a\dfrac{da}{dt}+b\dfrac{db}{dt}}{c}\\\Rightarrow \dfrac{dc}{dt}=\dfrac{5.417\times 13+7.5\times 18}{9.25}\\\Rightarrow \dfrac{dc}{dt}=22.21\ \text{mph}[/tex]
Distance between the two people is changing at a rate of [tex]22.21\ \text{mph}[/tex].
At 35 minutes
[tex]a=13\times \dfrac{35}{60}=7.583\ \text{miles}[/tex]
[tex]b=18\times \dfrac{35}{60}=10.5\ \text{miles}[/tex]
[tex]c=\sqrt{7.583^2+10.5^2}\\\Rightarrow c=12.95\ \text{miles}[/tex]
Distance between the two people is
[tex]c^2=a^2+b^2[/tex]
Differentiating with respect to time we get
[tex]c\dfrac{dc}{dt}=a\dfrac{da}{dt}+b\dfrac{db}{dt}\\\Rightarrow \dfrac{dc}{dt}=\dfrac{a\dfrac{da}{dt}+b\dfrac{db}{dt}}{c}\\\Rightarrow \dfrac{dc}{dt}=\dfrac{7.583\times 13+10.5\times 18}{12.95}\\\Rightarrow \dfrac{dc}{dt}=22.2\ \text{mph}[/tex]
Distance between the two people is changing at a rate of [tex]22.2\ \text{mph}[/tex].
The radius of a circle is 6 m. Find its area in terms of π.
Answer:
A=πr^2
22/7×6×6
=113 1/7
Find the mean of 9,5,10 graphically will mark Brainliest if correct ( no files or links)
Answer:
the answer to the question is 8
Which quantity makes the equation true?
x + 3x + _______ = 7x
Answer:
Step-by-step explanation:
C) 3X
Answer: C. 3x
Step-by-step explanation:
Since x and 3x both have x, you can add them together to get 4x (if there is x by itself, it really means that there is one of it, so it would be 1x.)
Then, you subtract 7x by 4x, which gives you the answer, 3x. You could also solving it by asking yourself: What number plus 4x equals 7x, which would give you 3x.
A jet ski depreciates at 11% of its original value each year. If the jet ski was $8,000 at its time of purchase, what is the value of the jet ski after 5 years?
Answer: $4467.25
Step-by-step explanation:
Exponential decay problem. 8000(0.89)^5.
100-11 = 89
89/100= 0.89, that is how we got the decimal.
Then, solve.
0.89 * 0.89 * 0.89 * 0.89 * 0.89 = 0.5584059449
0.5584059449 * 8000 = 4467.2475592
Round the decimal part to the nearest hundredth, which is $4467.25.
Pls pls pls answer I need this done before 10;50
Answer:
1/12
Step-by-step explanation:
BRAINIEST TO WHIVER RIGHT HELP
Write a linear function f with f(2)=-2 and f(1)=1
Answer:
y = -3x + 4
Step-by-step explanation:
x y
0 4
1 1
2 -2
Going down 3 for every increase of x by 1, when x = 0, y = 4
. Government Waste In a Gallup poll 513 national adults aged 18 years or older who consider themselves to be Republican were asked, "Of every tax dollar that goes to the federal government in Washington, D.C., how many cents of each dollar would you say are wasted?" The mean wasted was found to be 54 cents with a standard deviation of 2.9 cents. The same question was asked of 513 national adults aged 18 years or older who consider themselves to be Democrat. The mean wasted was found to be 41 cents with a standard deviation of 2.6 cents. Construct a 95% confidence interval for the mean difference in government waste, mR - mD. Interpret the interval.
Answer:
Part A
The 95% confidence interval is approximately 12.66 ≤ [tex]m_R[/tex] - [tex]m_D[/tex] ≤ 13.34
Part B
We are 95% confident that the true difference in the mean amount of waste per dollar stated by the two categories of adults is larger than zero and it is approximately between 12.66 and 13.34
Step-by-step explanation:
Part A
The given parameters are;
The mean amount adults that consider themselves Republican say is wasted for every dollar, [tex]m_R[/tex] = 54 cents
The standard deviation of the statistics, s₁ = 2.9 cents
The number of respondents in the group, n₁ = 513
The mean amount adults that consider themselves Democrats say is wasted for every dollar, [tex]m_D[/tex] = 41 cents
The standard deviation of the statistics, s₂ = 2.6 cents
The number of respondents in the group, n₂ = 513
The F-test, F = s₁²/s₂² = 2.9²/2.6² = 1.244
The critical-t, t* = 1.962
F ≤ t*, therefore, we pool the data
[tex]s_p =\sqrt{\dfrac{\left ( n_{1}-1 \right )\cdot s_{1}^{2} +\left ( n_{2}-1 \right )\cdot s_{2}^{2}}{n_{1}+n_{2}-2}}[/tex]
[tex]s_p =\sqrt{\dfrac{\left ( 513-1 \right )\cdot 2.9^{2} +\left ( 513-1 \right )\cdot 2.6^{2}}{513+513-2}} = \sqrt{7.585}[/tex]
The 95% confidence interval is given by the following formula;
[tex]\left (m_R- m_D \right )\pm t^* \cdot s_p \cdot\sqrt{\dfrac{1}{n_{1}}+\dfrac{1}{n_{2}}}[/tex]
The test statistic, is given as follows;
[tex]t = \dfrac{m_R - m_D}{s_p \times\sqrt{ \dfrac{1}{n_1} + \dfrac{1}{n_2}} }[/tex]
Therefore;
[tex]t = \dfrac{54 - 41}{\sqrt{7.585} \times\sqrt{ \dfrac{1}{513} + \dfrac{1}{513}} } \approx 75.598[/tex]
Given that the test statistic, t = 75.598 > The critical-t, t* = 1.962, we reject the null hypothesis, therefore, there is significant statistical evidence to suggest that there is a difference in the mean stated by the two sets
[tex]s_p =\sqrt{\dfrac{\left ( 513-1 \right )\cdot 2.9^{2} +\left ( 513-1 \right )\cdot 2.6^{2}}{513+513-2}} = \sqrt{7.585}[/tex]
[tex]C. I. = \left (54- 41 \right )\pm 1.962 \times \sqrt{7.585} \times \sqrt{\dfrac{1}{513}+\dfrac{1}{513}}[/tex]
The 95% confidence interval, C.I. ≈ 12.66 ≤ [tex]m_R[/tex] - [tex]m_D[/tex] ≤ 13.34
Part B
From the 95% confidence interval, we are 95% confident that the true difference in the mean amount adult who consider themselves Republicans say politicians waste and the true difference in the mean amount adult who consider themselves Democrats say politicians waste is between 12.66 and 13.34
Given that there is no '0' in the range of values in the 95% confidence for the difference in mean from the two groups, difference in the mean amount of waste per dollar observed by the two categories of adults.
Find the value of x.
Answer:
x=90°
Step-by-step explanation:
The inside angles in a triangle always add up to 180°.
So:
53°+37°=90°
180°-90°=90°
x=90°
Answer:
see below
Step-by-step explanation:
since the sum of angles in a triangle is 180 degrees
x + 53 + 37 = 180
x = 180 - 53 - 37
x = 90 degrees
hope this helps, please mark it brainliest
help me please. Very much appreciated
Answer:
A = 23.2 mm²
Step-by-step explanation:
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
Here b = 8 and h = 5.8 , then
A = 0.5 × 8 × 5.8 = 4 × 5.8 = 23.2 mm²
The square root of 17 is between the what two whole numbers? (just list them with a comma in between them.)
Answer:
17 lies between 16 and 25. So√17 lies between √16 and √25. The prime factorization method is used to write a square root of a non-perfect square number in the simplest radical form.
Answer:
The answer is 16,25
Identify the transformation from figure A to figure B in the image below.
glide reflection
reflection
translation
dilation
Answer:
Reflection
Step-by-step explanation:
Here, we want to get the transformation that yielded figure B from figure A
Looking at the plot, we can see that we have the origin as the center of transformation
The kind of transformation however is reflection
The shape A was reflected about the origin or the point (0,0) to give shape B
Answer:
glide reflection
Step-by-step explanation:
got it right on a quiz
Asking this again because the person who answered the last one gave the incorrect answer. If 7 iced cupcakes cost $21, then how much would 5 iced cupcakes cost?
Answer:
$15 for 5 cupcakes
In ARST, the measure of ZT=90°, the measure of ZR=39°, and TR = 55 feet.
Find the length of ST to the nearest tenth of a foot.
Answer:
ST = 44.5 feet
Step-by-step explanation:
sing SOH CAH TOA to solve the problem;
Given
m<T = 90
m<R = 39 degrees
TR = 55feet
Required
ST = opposite to m<R
TR is the adjacent
tan theta = opp/adj
tan m<R = ST/TR
tan 39 = ST/55
ST = 55tan39
ST = 55*0.8098
ST = 44.5 feet