determine the 2nd and 3rd terms of a geometric sequence of which T1 =5 and T4=40
Answers
Answer:
Second term of this sequence: [tex]10[/tex].
Third term of this sequence: [tex]20[/tex].
Step-by-step explanation:
The first step is to find the common ratio of this sequence.
In a geometric sequence, multiply one term by the common ratio to find an expression for the next term. Let [tex]r[/tex] denote the common ratio of this sequence. For this sequence:
The first term of this sequence is [tex]5[/tex]. Multiply the first term by the common ratio to find an expression for the third term: [tex]5\, r[/tex].Multiply the second term by the common ratio to find an expression for the fourth term: [tex]5\, r^{2}[/tex].Similarly, an expression for the the fourth term would be: [tex]5\, r^{3}[/tex].However, the question states that the value of the fourth term is [tex]40[/tex]. In other words, [tex]5\, r^{3} = 40[/tex].
Solve this equation for [tex]r[/tex]:
[tex]r^{3} = 8[/tex].
[tex]r = 2[/tex].
(Since the power of [tex]r[/tex] is non-even in the equation, there's no need to consider the sign of [tex]r\![/tex] when taking the cube root.)
Substitute [tex]r = 2[/tex] into the expression for the second term and the third term to find their values:
Second term: [tex]5\, r = 10[/tex].Third term: [tex]5\, r^{2} = 20[/tex].Related Questions
At the 6th grade school dance, there are 132 boys, 89 girls, and 14 adults. What is the ratio of adults to boys at the school dance?
Answers
Answer:
14 to 132
Step-by-step explanation:
We are given that there are 132 boys and 14 adults. Since the question is only asking for the ratio of adults to boys, we don't have to worry about the number of girls in this question. From here, we see that the question is asking for the ratio of adults to boys, so we put it in that exact order. Our answer is 14 to 132. I hope this helps and please don't hesitate to reach out with more questions!
Factor 2x2+25x+50. Rewrite the trinomial with the x-term expanded, using the two factors.
Answers
9514 1404 393
Answer:
rewrite: 2x^2 +5x +20x +50factored: (x +10)(2x +5)Step-by-step explanation:
I find this approach the most straightforward of the various ways that trinomial factoring is explained or diagramed.
You want two factors of "ac" that have a total of "b". Here, that means you want factors of 2·50 = 100 that have a total of 25. It is helpful to know your times tables.
100 = 1·100 = 2·50 = 4·25 = 5·20 = 10·10
The sums of these factor pairs are 101, 52, 29, 25, and 20. We want the pair with a sum of 25, so that's 5 and 20.
The trinomial can be rewritten using these factors as ...
2x^2 +5x +20x +50
Then it can be factored by grouping consecutive pairs:
(2x^2 +5x) +(20x +50) = x(2x +5) +10(2x +5) = (x +10)(2x +5)
_____
Additional comment
It doesn't matter which of the factors of the pair you write first. If our rewrite were ...
2x^2 +20x +5x +50
Then the grouping and factoring would be (2x^2 +20x) +(5x +50)
= 2x(x +10) +5(x +10) = (2x +5)(x +10) . . . . . same factoring
Will give brainliest answer
Answers
Answer:
1. log3 81 = 4
2. 4 3/2=8
Step-by-step explanation:
1. Convert the exponential equation to a logarithmic equation using the logarithm base (3)(3) of the right side (81)(81) equals the exponent (4)(4).
log3(81)=4
or
you can remember this
loga Y= X
so, a^x =y
2. Use the definition of a logarithm,
log
b
(
x
)
=
y
⟹
b
y
=
x
, to convert from the logarithmic form to the exponential form.
Thane Company is interested in establishing the relationship between electricity costs and machine hours. Data have been collected and a regression analysis prepared using Excel. The monthly data and the regression output follow:
Month Machine Hours Electricity Costs
January 2,300 $ 19,100
February 2,700 $ 22,400
March 1,700 $ 14,200
April 2,900 $ 24,400
May 3,600 $ 28,950
June 3,100 $ 23,400
July 3,900 $ 25,450
August 3,300 $ 23,450
September 1,800 $ 16,900
October 3,500 $ 27,400
November 4,500 $ 32,400
December 4,000 $ 28,450
Summary Output
Regression Statistics
Multiple R 0.957
R Square 0.917
Adjusted R2 0.908
Standard Error 1,586.26
Observations 12.00
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 5,970.52 1,766.77 3.38 0.01 2,033.90 9,907.13
Machine Hours 5.76 0.55 10.49 0.00 4.54 6.98
The percent of the total variance that can be explained by the regression is:
Answers
Answer:
0.924
Step-by-step explanation:
R² = 0.854
R = √0.854
R = 0.924
Hence, the correlation Coefficient of electricity tarrif is 0.924 ; this correlation Coefficient value, depicts a strong positive correlation between machine hours and cost of electricity. And can he interpreted to mean that ; Electricity tarrif increases as machine hours increases and also decreases as machine hours decreases.
the complement of guessing 5 correct answers on a 5 question true or false examination is
Answers
Answer:
Guessing at least one incorrect answer
Step-by-step explanation:
The complement of guessing 5 correct answers on a 5-question true/false exam is-
Guessing at least one incorrect answer because, when 1 or more questions are incorrectly guessed, the event of 5 correct answers can not occur.
Calculate 20% of 15,998
Answers
Answer:
3,199 approximately
Step-by-step explanation:
to find how much 20% of 15,998 does we multiply 15,998 with 20 and then divide it by 100
15,998 x 20 / 100 = 3,199
a pie chart is divided into four sectors in fig. 12.42. Each sector represents a percentage of the whole. The two larger sectors are equal and each represents x%. What is the angle subtended by one of those larger sectors ?
Answers
Answer:
Angle formed by the sector measuring x% will be 126°.
Step-by-step explanation:
Since, sum of all sectors formed in a circle is 100%.
By adding the measures of all the sectors,
x + x + 21 + 9 = 100
2x + 30 = 100
2x = 70
x = 35%
Now we know sum of all the central angles formed at the center of a circle = 360°
Therefore, angle formed by x% = 360° × 35%
= [tex]\frac{360\times 35}{100}[/tex]
= 126°
A certain list of movies were chosen from lists of recent Academy Award Best Picture winners, highest grossing movies, series movies (e.g. the Harry Potter series, the Spiderman series), and from the Sundance Film Festival and are being analyzed. The mean box office gross was $138.64 million with a standard deviation of $11.2526 million. Given this information, 98.49% of movies grossed greater than how much money (in millions)
Answers
g A. (Points: 7) Compute (without using a calculator) 241^257 mod 12 B. (Points: 3) Compute Z*20 C. (Points: 6) Find the multiplicative inverse of 7 in Z19
Answers
Answer:
[tex]241^{257}\ mod\ 12 =1[/tex]
[tex]7 * 20 = 140[/tex]
[tex]\frac{1}{700}[/tex]
Step-by-step explanation:
Solving (a): 241^257 mod 12
To do this, we simply calculate [tex]241\ mod\ 12[/tex]
Because [tex]a\ mod\ b = a^n\ mod\ b[/tex]
The highest number less than or equal to 241 that is divisible by 12 is 240; So:
[tex]241\ mod\ 12 = 241- 240[/tex]
[tex]241\ mod\ 12 =1[/tex]
Hence:
[tex]241^{257}\ mod\ 12 =1[/tex]
Solving (b): 7 * 20
[tex]7 * 20 = 140[/tex]
Solving (c): Multiplicative inverse of 7 in 719
The position of 7 in 719 is 700
So, the required inverse is 1/700 ---- i.e. we simply divide 1 by the number
What is the slope of the line?
Answers
it's tooooo easy who wants brain list
Answers
Answer:
1) Isosceles
2) Acute
3) Right angled
4( Obtuse
5) Equilateral
2)Acute
3) right angled
4)obtuse
5)Equilateral
Write 0.851 as a fraction in simplest form.
Answers
Answer:
[tex]\frac{851}{1000}[/tex]
Step-by-step explanation:
First, we can simply multiply that number by 1000, and divide again by 1000 to get a base fraction:
[tex].851\\\\= \frac{1000}{1000} \times .851\\\\= \frac{1000 \times .851}{1000}\\\\= \frac{851}{1000}[/tex]
851 is a secondary prime, having only two factors, both of which are prime. Those factors are 23 and 37, neither of which is a factor of 1000, so this is already in simplest form.
If h(x) is the parent function, which equation describes the function song shifted 3 units left and 5 units down?
Answers
Answer:
h(x + 3) - 5Step-by-step explanation:
Given function h(x).
Shift left:
h(x) → h(x + 3)Shift down:
h(x + 3) → h(x + 3) - 5Given function is,
→ h(x)
As we shift left,
→ h(x) = h(x + 3)
As we shift down,
→ h(x + 3) = h(x+3)-5
Then the equation is,
→ h(x+3)-5
It is correct answer.
An economic instructor at UCF is interested in the relationship between hours spent studying and total points earned in a course. Data collected on 11 students who took the course last semester follow:
# of observation(s) n = 30
# of independent variable(s) = 1
SSR = 1,297 SSE= 920
Required:
Find the F test statistic.
Answers
Answer:
[tex]F = 39.47[/tex]
Step-by-step explanation:
Given
[tex]n = 30[/tex] --- observations
[tex]p = 1[/tex] -- variables
[tex]SSR = 1,297[/tex]
[tex]SSE= 920[/tex]
Required
The F statistic
This is calculated using:
[tex]F = \frac{SSR}{p} \div \frac{SSE}{n - p -1}[/tex]
[tex]F = \frac{1297}{1} \div \frac{920}{30 - 1 -1}[/tex]
[tex]F = \frac{1297}{1} \div \frac{920}{28}[/tex]
[tex]F = 1297 \div \frac{920}{28}[/tex]
Rewrite as:
[tex]F = 1297 * \frac{28}{920}[/tex]
[tex]F = \frac{1297 *28}{920}[/tex]
[tex]F = \frac{36316}{920}[/tex]
[tex]F = 39.47[/tex]
g At a certain gas station, 30% of all customers use the restroom. What is the probability that, out of the next 10 customers, (a) exactly 4 will use the restroom
Answers
Answer:
[tex]P(x=4) = 0.200[/tex]
Step-by-step explanation:
Given
[tex]n=10[/tex] --- selected customers
[tex]x = 4[/tex] --- those that are expected to use the restroom
[tex]p =30\% = 0.30[/tex] --- proportion that uses the restroom
Required
[tex]P(x = 4)[/tex]
The question illustrates binomial probability and the formula is:
[tex]P(x) = ^nC_x * p^x * (1 - p)^{n - x}[/tex]
So, we have:
[tex]P(x=4) = ^{10}C_4 * (0.30)^4 * (1 - 0.30)^{10 - 4}[/tex]
[tex]P(x=4) = ^{10}C_4 * (0.30)^4 * (0.70)^6[/tex]
[tex]P(x=4) = 210* (0.30)^4 * (0.70)^6[/tex]
[tex]P(x=4) = 0.200[/tex]
Use the coordinates of the labeled point to find a point-slope equation of the
line.
5
5
(-2,-5) 6.5
>
O A. y- 5 = -2(x - 2)
O B. y + 5 = 2(x + 2)
O C. y + 5 = -2(x + 2)
OD. y- 5 = 2(x - 2)
Answers
Answer:
B. [tex] y + 5 = 2(x + 2) [/tex]
Step-by-step explanation:
Point-slope equation is given as [tex] y - b = m(x - a) [/tex], where,
(a, b) = (-2, -5)
[tex] m = slope = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Using two points on the line (-2, -5) and (0, -1),
Slope (m) = (-1 -(-5))/(0 -(-2)) = 4/2
m = 2
✔️To write the equation in point-slope form, substitute a = -2, b = -5, and m = 2 into [tex] y - b = m(x - a) [/tex]
Thus:
[tex] y - (-5) = 2(x - (-2)) [/tex]
[tex] y + 5 = 2(x + 2) [/tex]
Need help with this one please
Answers
it right answer is Clovis 2.5% it answer
The 2010 GSS provides the following statistics for the average years of education for lower-, working-, middle-, and upper-class respondents and their associated standard deviations. Assume that years of education are normally distributed in the population. Mean Standard Deviation N Lower-class 11.61 2.67 123 Working-class 12.80 2.85 697 Middle-class 14.45 3.08 626 Upper-class 15.45 2.98 38 How many years of education correspond to a Z score of +1.2 for upper-class respondents?
Answers
Answer:
The answer is "18.087 years".
Step-by-step explanation:
For upper class:
[tex]\mu=15.45 \ years\\\\\alpha=2.98 \ years\\\\[/tex]
[tex]P(Z \leq 1.2)[/tex] from the standard normal distribution on the table:
[tex]P(Z \leq 1.2) =0.8849\\\\x=z_{\alpha}+\mu\\\\[/tex]
[tex]=0.8849 \times 2.98 +15.45\\\\ = 2.637002+15.45 \\\\=18.087 \ \ years\\[/tex]
what is answer if 2xyx5
Answers
Answer:
Answer is 3bu2(DeEZ)=1
Step-by-step explanation:
A party supply company makes cone shaped party hats for children using thin cardboard. To the nearest square centimeter, how much cardboard is required to make the party hate use pie = 3.14.
Answers
Answer:
A. 754 cm²
Step-by-step explanation:
Amount of cardboard needed = surface area of the cone
Curved surface area of the cone = πrl
Where,
π = 3.14
r = ½(20) = 10 cm
l = 24 cm
Plug in the values into the formula
Curved surface area = 3.14 × 10 × 24 = 753.6 ≈ 754 cm²
Multiplying 10x² and (2x²)² we get …..
Answers
Hi there!
[tex]\large\boxed{40x^{6}}[/tex]
Begin by simplifying (2x²)²
2² · (x²)² <-- Power rule for exponents, multiply them together:
4 · x⁴ = 4x⁴
Multiply by 10x². ADD exponents when multiplying.
10x² · 4x⁴ = 40 · x²⁺⁴
40x⁶
what is the value of x?
what is the value of y?
type in an integer or decimal
Answers
9514 1404 393
Answer:
x = 5.6y = 65Step-by-step explanation:
There are a couple of relations that are applicable to these questions.
the product of segment lengths of crossed chords is the same for both chordsthe angle formed at crossed chords is the average of the intercepted arc measures__
The segment lengths relation tells us ...
10x = 8×7 . . . . . . products of segment lengths are equal
x = 56/10 = 5.6 . . . . divide by 10
__
The value of y° is the average of the intercepted arcs:
y° = (85° +45°)/2 = 65°
_____
Additional comment
This diagram does not have enough information to allow computation of z. We would need to know the intercepted arc, or the length of the secant that meets tangent z.
Sarah ordered 39 shirts that cost $8 each. She can sell each shirt for $16.19. She sold 32 shirts to customers. She had to return 7 shirts and pay a $1.4 charge for each returned shirt. Find Sarah's profit.
Answers
Answer:
$196.28
Step-by-step explanation:
Original cost: 39 × $8 = $312
Revenue: 32 × $16.19 = $518.08
Return charge: 7 × $1.4 = $9.8
$312 + $9.8 = total cost, which is $321.8
$518.08 - $321.8 = profit
Profit = $196.28
Uma pizzaria oferece em seu cardápio 12 sabores de pizza. Se um cliente pretende pedir 3 pizzas, então o número de maneiras que ele pode realizar esse pedido é;
•364
•220
•440
•1320
Answers
Answer:
Step-by-step explanation:
Partindo do pressuposto de que você pode ter coberturas duplas e triplas do mesmo item, o cálculo é relativamente simples. Para calcular as combinações possíveis; deve-se multiplicar as coberturas disponíveis pelo número total de coberturas permitidas. Este cálculo é semelhante a como olhamos para diferentes sistemas de contagem de base. Normalmente contamos com decimais (base 10), portanto, o número de combinações, se usar 3 dígitos, seria calculado por 10 x 10 x 10.
10x10 = 100
100x10 = 1000 combinações (0 a 999)
Sua pergunta sobre coberturas de pizza é a mesma, mas assumindo um sistema de numeração de base 12, então 12x12x12 ou 12³
Portanto, 1.728 combinações incluindo 0 (sem coberturas?) E também incluindo 12 ocasiões em que todas as 3 coberturas seriam iguais. Se esses cenários de pessoas forem restritos de modo que você só possa ter coberturas duplas máximas, etc., então essas combinações devem ser removidas (subtraídas do total de combinações permitidas).
Espero ter ajudado você a entender os princípios, então você deve ser capaz de trabalhar a partir disso, de muitas outras soluções semelhantes
8. Calculate the Perimeter AND Area of
the RIGHT Triangle below.
17 m
10 m
21 m
Answers
Answer:
[tex]\text{Perimeter: }48\:\mathrm{m},\\\text{Area: }84\:\mathrm{m^2}[/tex]
Step-by-step explanation:
The area of a triangle with side lengths [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] is given by:
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex], where [tex]s=\frac{a+b+c}{2}[/tex]
Substituting [tex]a=21, b=17, c=10[/tex], we have:
[tex]A=\sqrt{24(24-21)(24-17)(24-10)},\\A=\sqrt{24(3)(7)(14)},\\A=\sqrt{7,084},\\A=\boxed{84\:\mathrm{m^2}}[/tex]
The perimeter of a polygon is given by the sum of its sides. Since the triangle has sides 10, 17, and 21, its perimeter is [tex]10+17+21=\boxed{48\:\mathrm{m}}[/tex].
The force F (in pounds) needed on a wrench handle to loosen a certain bolt varies inversely with the length L (in inches) of the handle. A force of 40 pounds is needed when the handle is 7 inches long. If a person needs 20 pounds of force to loosen the bolt, estimate the length of the wrench handle. Round answer to two decimal places if necessary.
in inches
Answers
Answer:
14 inches
Step-by-step explanation:
Since F is inversely proportional to L,
[tex]f = \frac{k}{l} \\ when \: f = 40 \: l \: = 7 \\ \frac{k}{7} = 40 \\ k = 280 \\ when \: f = 20 \\ 20 = \frac{280}{l} \\ l = 14[/tex]
How do I find the missing number?
Answers
Answer:
to find the missing number is all u have to do is understand the problem and silve the problem!
Step-by-step explanation:
paki brainly po
Prove this plzzz help me
Answers
Answer:
Answer is in the picture. have a look
You paid $6.99 for a shirt that was 70% of what was the original price of the shirt?
Answers
Answer:
$23.3
Step-by-step explanation:
you can use ratios to solve this:
$6.99/x=0.30/0.100 then cross multiply to get 0.3x=6.99
So, 6.99 divided by 0.3 = 23.3
so the original price is $23.3
the diagram shows a regular dodecagon. a) work out the size of one interior angle. b) work out the size of one exterior angle.
Answers
Answer: Interior angle: 150 degrees Exterior angle: 30 degrees
Step-by-step explanation:
We use the angle formula to find the value of an interior angle: 180*(12-2)/12 = 150 degrees. Since an exterior angle is the supplement of an interior angle, the measure of an exterior angle is 180 - 150 = 30 degrees
