Step-by-step explanation:
given the geometric sequence 2, -4, 8, -16, ...
a1 = 2
r = -4/2 = -2
find : a9 and a15
solutions:
an = a1. r^(n-1)
=> a9 = 2. (-2)^(9-1)
= 2. (-2)^8
= 2. 2^8
= 2^9
= 512.
=> a15 = 2. (-2)^(15-1)
= 2. (-2)^14
= 2. 2^14
= 2^15
= 32,768
Step-by-step explanation:
Hey there!
The given geometric sequence is: 2, -4, 8, -16.
The;
a1 = 2
Common ratio (r) = T2/T1
= -4/2
= -2
Now;
Use general formula of geometric sequence;
[tex]tn = {a1.r}^{n - 1} [/tex]
Where, "a1" is first term, "n" is no.of terms and "r" is common ratio.
Then;
[tex]t9 = 2 \times { (- 2)}^{9 - 1} [/tex]
or, t9 = 2*256
Therefore, t9 = 512.
Again;
[tex]t15 = 2. { (- 2)}^{15 - 1} [/tex]
or, t15= 2*16384
Therefore, t15 = 32768.
Hope it helps!
Use the Law of Cosines to find the missing angle.
Step-by-step explanation:
180-68=112
112÷293=3.8620
68÷3.87
18
Consider the function f(x) = -2x2 +3x-8. Determine f(k+4). Fully simplify your answer.
Answer:
f(k + 4) = -2k² - 13k - 28
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Terms/CoefficientsExpand by FOILFunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
f(x) = -2x² + 3x - 8
Step 2: Evaluate
Substitute in x [Function f(x)]: f(k + 4) = -2(k + 4)² + 3(k + 4) - 8Expand [FOIL]: f(k + 4) = -2(k² + 8k + 16) + 3(k + 4) - 8[Distributive Property] Distribute: f(k + 4) = -2k² - 16k - 32 + 3k + 12 - 8Combine like terms: f(k + 4) = -2k² - 13k - 28como se lee el número decimal 0.3
Joe wants to add cucumbers to his garden and knows the rectangular area is represented by x^2 - 4x - 21 square units. What expressions would represent the length and width of the cucumber field?
Given:
The area of rectangular garden is [tex]x^2-4x-21[/tex] square units.
To find:
The length and width of the cucumber field.
Solution:
The area of a rectangle is:
[tex]A=l\times w[/tex]
Where l is length and w is width of the rectangle.
The area of rectangular garden is [tex]x^2-4x-21[/tex] square units.
We need to find the factors of [tex]x^2-4x-21[/tex] to get the length and width.
[tex]A=x^2-4x-21[/tex]
Splitting the middle term, we get
[tex]A=x^2-7x+3x-21[/tex]
[tex]A=x(x-7)+3(x-7)[/tex]
[tex]A=(x-7)(x+3)[/tex]
Area of a rectangle is the product of length and width.
Therefore, the length and width of the rectangle are [tex](x-7)[/tex] units and [tex](x+3)[/tex] units.
Maths assignment
a^4-16
Answer:
[tex]a^4-16[/tex]
[tex]\left(a^2\right)^2-4^2[/tex]
[tex]\left(a^2+4\right)\left(a^2-4\right)[/tex]
[tex]=\left(a^2+4\right)\left(a+2\right)\left(a-2\right)[/tex]
------------------------
Hope it helps...
Have a great day!!
Step-by-step explanation:
The difference of squares: a² - b² factors to (a - b) (a + b)
Let x⁴ = (x²)²
Let 16 = 4²
Now by difference of squares x⁴ - 16 factors as (x² - 4)(x² + 4)
The front factor, (x² - 4), can factor by difference of squares again as (x - 2)(x + 2)
t=29pi/6
1. find the reference number
2. find the point on the unit circle
3. 6 trig functiond
What is the center of the circle: .22 + y2 = 4
Let f(x) = 4x - 5 and g(x) = 3x + 7. Find f(x) + g(x) and state its domain.
7x - 12; all real numbers
7x + 2; all real numbers
x + 2; all real numbers
X - 12; all real numbers
Answer:
2nd option
Step-by-step explanation:
f(x) + g(x)
= 4x - 5 + 3x + 7 ← collect like terms
= 7x + 2
domain is all real numbers
(1 + sin x)(1 – sin x) = cos^2x
Answer:
(1 + sin x)(1 – sin x) = cos^2x
1 - sin^2x = cos^2x
cos^2x = cos^2x
Step-by-step explanation:
Simplify the left hand side:
(1 + sin x)(1 – sin x) = cos^2x
1 - sin^2x = cos^2x
Using the Pythagorean Identity, we can see that the two sides are equivalent if you subtract sin^2x from both sides:
sin^2x + cos^2x = 1
cos^2x = 1 - sin^2x
Lastly, write it out:
(1 + sin x)(1 – sin x) = cos^2x
1 - sin^2x = cos^2x
cos^2x = cos^2x
Which of the following are square root of the number below? Check all that apply.
81
Answer:
A, B, D, E
Step-by-step explanation:
[tex]\sqrt{81}[/tex] = ± 9 → D and E
Since 9 × 9 = 81 and - 9 × - 9 = 81
[tex]81^{\frac{1}{2} }[/tex] = [tex]\sqrt{81}[/tex] = 9 → B
- [tex]81^{\frac{1}{2} }[/tex] = - [tex]\sqrt{81}[/tex] = - 9 → A
Suppose that a department contains 10 men and 12 women. How many ways are there to form a committee with six members if it must have the same number of men and women
Answer:
The number of ways is 26,400 ways
Step-by-step explanation:
Given;
total number of men, M = 10
total number of women, W = 12
number of committees to be formed = 6
If there must be equal gender, then it must consist of 3 men and 3 women.
[tex]The \ number \ of \ ways = 10C_3 \times 12C_3\\\\The \ number \ of \ ways =\frac{10!}{3!7!} \times \frac{12!}{3!9!} \\\\T he \ number \ of \ ways = 120 \times 220 = 26,400 \ ways[/tex]
Therefore, the number of ways is 26,400 ways
What's the answer for m⁶ - 25
Step-by-step explanation:
[tex] {m}^{6} - 25 \\ { {m}^{3} }^{2} - {5}^{2} \\ x = {m}^{3} b = 5 \\ ( {m}^{3} - 5)( {m}^{3} + 5)[/tex]
which choice is equivalent to the expression below when x less than or equal to 0
Answer:
b
Step-by-step explanation:
PLEASE HELP ME <3!!!
Answer:
Wasim has enough money.
Step-by-step explanation:
1. find the area of the garden path:
600 cm x 120 cm = 72,000 sq. cm
2. find the area of each stone:
it is a square of 30 cm by 30 cm, so:
30 cm x 30 cm = 900 sq. cm
3. find how many stones can fit in the path:
72,000 / 900 = 80 stones
4. multiply that by the price of each stone:
80 stones x $2.50 = $200
Wasim's budget is $220 and the stones will only cost $200, so it is within the budget
In an English test, the mean is 60 and the standard deviation is 6. Assuming the scores are normally distributed, answer the following question.
a. what is the percentile rank of the score 65?
b. what is the percentile of the score less than 70?
c. what is percent of the scores is greater than 65?
d. what percent of scores is less than 70?
e. what percent of the score is between 50 and 60?
Answer:
a) A score of 65 is in the 79.67th percentile.
b) A score less than 70 is below the 95.25th percentile.
c) 20.33% of the scores are greater than 65.
d) 95.25% of scores are less than 70.
e) 45.25% of the scores are between 50 and 60.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The mean is 60 and the standard deviation is 6.
This means that [tex]\mu = 60, \sigma = 6[/tex]
a. what is the percentile rank of the score 65?
This is the p-value of Z when X = 65.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{65 - 60}{6}[/tex]
[tex]Z = 0.83[/tex]
[tex]Z = 0.83[/tex] has a p-value of 0.7967.
Thus: A score of 65 is in the 79.67th percentile.
b. what is the percentile of the score less than 70?
Below the p-value of Z when X = 70. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{70 - 60}{6}[/tex]
[tex]Z = 1.67[/tex]
[tex]Z = 1.67[/tex] has a p-value of 0.9525.
Thus: A score less than 70 is below the 95.25th percentile.
c. what is percent of the scores is greater than 65?
The proportion is 1 subtracted by the p-value of Z when X = 65.
From item a, when X = 65, Z has a p-value of 0.7967
1 - 0.7967 = 0.2033
0.2033*100% = 20.33%
20.33% of the scores are greater than 65.
d. what percent of scores is less than 70?
The proportion is the p-value of Z when X = 70, which, from item b, is of 0.9525.
0.9525*100% = 95.25%
95.25% of scores are less than 70.
e. what percent of the score is between 50 and 60?
The proportion is the p-value of Z when X = 60 subtracted by the p-value of Z when X = 50.
X = 60
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{60 - 60}{6}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a p-value of 0.5.
X = 50
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{50 - 60}{6}[/tex]
[tex]Z = -1.67[/tex]
[tex]Z = -1.67[/tex] has a p-value of 0.0475.
0.5 - 0.0475 = 0.4525
0.4525*100% = 45.25%
45.25% of the scores are between 50 and 60.
Al sumar y/o restar números decimales, siempre se debe aplicar la norma de los signos. * 1 punto FALSO VERDADERO
Answer:
La norma de los signos es para el producto de números reales, y la norma es la siguiente.
(+)*(+) = (+)
(+)*(-) = (-)
(-)*(+) = (-)
(-)*(-) = (+)
Es decir, el producto de dos números de mismo signo es siempre positivo
El producto de dos números de distinto signo es siempre negativo.
Particularmente, para la suma esta norma no funciona (pues no está definida para la suma)
Pero en casos como:
5 - (-4)
(esto sería: "la diferencia entre cinco y menos cuatro")
notar que podemos reescribir esto como:
5 + (-1)*(-4)
Ahora podemos aplicar la norma de los signos:
5 + 4 = 9
Donde aplicamos la norma de los signos,
Podemos concluir que, si bien es una regla que aplica al producto, siempre la tenemos que tener en cuenta en cualquier operación que hagamos.
Por lo podemos concluir que la respuesta correcta es verdadero.
Part 1- Make sure to show all work. Write both the (i) recursive formula and the (ii) explicit formula for the sequences
A) {-23,-15,-7,1,...}.
B) {5, 5.25, 5.50, 5.75,...}
Part 2- Calculate the 15th term in each of the above sequences, Use the Recursive method for one sequence and the Explicit formula for the other sequence. (make sure to label your work & show each step).
Answer:
A) The sequence is {-23, -15, -7, 1,...}
The common difference of the sequence above, d = 8
The first term, a = -23
The number of terms, n = 15
The recursive formula is, aₙ = aₙ₋₁ + d
Using the recursive method gives;
a₅ = a₍₅₋₁₎ + d
Where;
a₍₅₋₁₎ = 1
Therefore, a₅ = 1 + 8 = 9, a₆ = 9 + 8 = 17, a₇ = 17 + 8 = 25, a₈ = 25 + 8 = 33, a₉ = 33 + 8 = 41, a₁₀ = 41 + 8 = 49, a₁₁ = 49 + 8 = 57, a₁₂ = 57 + 8 = 65 a₁₃ = 65 + 8 = 73, a₁₄ = 73 + 8 = 81, a₁₅ = 81 + 8 = 89
The 15th term of the sequence, {-23, -15, -7, 1,...}, a₁₅ = 89
We check by using explicit formula to get, aₙ = a + (n - 1)·d
Therefore
a₁₅ = -23 + (15 - 1)×8 = 89
B) The given sequence is B) {5 5.25, 5.50, 5.75,...}
The common difference, d = 0.25
The first term, a = 5
The required number of terms, n = 15
Using the recursive method gives;
a₅ = a₍₅₋₁₎ + d
Where;
a₍₅₋₁₎ = a₄ = 5.75
Therefore, a₅ = 5.75 + 0.25 = 6
a₆ = 6 + 0.25 = 6.25, a₇ = 6.25 + 0.25 = 6.5, a₈ = 6.5 + 0.25 = 6.75, a₉ = 6.75 + 0.25 = 7, a₁₀ = 7 + 0.25 = 7.25, a₁₁ = 7.25 + 0.25 = 7.5, a₁₂ = 7.5 + 0.25 = 7.75, a₁₃ = 7.75 + 0.25 = 8, a₁₄ = 8 + 0.25 = 8.25, a₁₅ = 8.25 + 0.25 = 8.5
The 15th term, of the sequence, {5 5.25, 5.50, 5.75,...}, a₁₅ = 8.5
We check by explicit formula to get, aₙ = a + (n - 1)·d
Therefore
a₁₅ = 5 + (15 - 1)×0.25 = 8.5
Step-by-step explanation:
Andre found an old mustang car that can fix.he bought the car of 65⁰/0 of the original $7200 price.what did andrew pay for the car?
Answer:
Step-by-step explanation:
Thinking of this in terms of words, we are looking to solve the equation:
"The price Andre paid for the car is 65% of the original $7200 price" which in algebra-speak is
p = .65(7200) where p is the price Andre paid (our unknown), the word "is" indicates an equals sign, .65 is 65% as a decimal, the word "of" indicates multiplication, and the original price is...well, the original price.
Solving for p:
p = $4680
given that cos θ = 8/17 and sin θ = -15/17 what is the value of tan θ
Answer:
- 1.875
Step-by-step explanation:
tan = sin ÷ cos
tan = 8/17 ÷ - 15/17
tan= - 1.875
Answer:
-8/15
Step-by-step explanation:
see image
someone help me please with this algebra homework
find all two digit numbers with the following property:the difference between the number and the number with the same digits in reverse order is 54
answer
71-17=54
82-28=54
93-39=54
60-06=54
Step-by-step explanation:
What is the domain of the following function ?
Answer:
{-6, 1, 5, 8}
Step-by-step explanation:
The domain is the set of x-coordinates or inputs.
{-6, 1, 5, 8}
The metric system has several advantages that include all of the following except _____.
only need to move the decimal point for conversions
prefixes are the same throughout
based on the numeral ten
only 10 base units to learn
Answer:
Only 10 base units to learn
Step-by-step explanation:
The metric system is a decimal based system developed to be universally acceptable by making use of base units from obtained from nature and the use of prefixes for multiples and submultiples of the base units, decimal ratios, which allows easy representation of quantities, as well as having a coherent structure of base and derived units which are obtained from the base units
During conversion in the metric system, which is decimal based, it is only required to move the decimal point
The prefixes which are used to specify multiples and submultiples are the same through out
The decimal system is based on the powers of ten
The number of base units to learn are 7 including; 1. Meter (m), 2. Kilogram (kg), 3. Second (s), 4. Ampere (A), 5. Kelvin (k), 6. Candela (cd), and 7. mole (mol)
Therefore the metric system has several advantages that include all of the following except; Only 10 base units to learn
n a certain exam of grade ten, 75% students got high score in mathematics, 65%students got high score in English. If 6% of them did not get high score in both mathematics and English, then calculate: i. the percent of students who got high score in both the subjects. ii. the total number of students who got high score either in mathematics or in English if 300 students had attended the exam.
Answer:
thank you for the points
Step-by-step explanation:
What is the value of this expression?
Answer:
-3
Step-by-step explanation:
Step 1: Solve (-2+(-1))^2/3 3
1. -2+(-1) = -3
2. (-3)^2 = 9
3. 9/3 = 3
Step 2: Solve (-4)^2-17 -1
1. 3/-1
Step 3: Simplify 3/-1 = -3. I hope this helped and please don't hesitate to reach out with more questions!
If a semi circle has a diameter of 5 m what is the area?
Answer:
Exact answer = 10.41666666666666666666666666666pi
Estimated answer = 32.70938
Step-by-step explanation:
Semi circle formula: 1/2 * 4/3 * pi * r^3
r = 2.5
1/2 * 4/3 * pi * 2.5^3
2/3 * pi * 2.5^3
2/3 * pi * 15.625
10.416..... * pi
Exact answer = 10.417pi
We can estimate pi as 3.14
So, 10.417 * 3.14 = 32.70938
Exact answer = 10.41666666666666666666666666666pi
Estimated answer = 32.70938
When 7 times a number is decreased by 8, the answer is the same as when 3 times the number is increased by 4. Find the number.
Answer:
x=3
Step-by-step explanation:
Equation: 7x-8=3x+4
4x=12
x=3
Marlene earns $12,800 per year. 15% is taken from her earnings for taxes. how much money is paid in taxes? how much money is left for Marlene to spend???
Answer:
$1,920
$10,880
Step-by-step explanation:
Amount marlene earns per year = $12,800
Percentage of taxes = 15%
how much money is paid in taxes?
Amount of tax Marlene pays = 15% of $12,800
= 15/100 × $12,800
= 0.15 × $12,800
= $1,920
how much money is left for Marlene to spend?
Amount left for Marlene to spend = Amount marlene earns per year - Amount of tax Marlene pays
= $12,800 - $1,920
= $10,880
Write the ratio 5/36 as a fraction in simplest form.
Use the slash key (/) to indicate a fraction.
9514 1404 393
Answer:
5/36
Step-by-step explanation:
5 and 36 have no common factors, so the fraction 5/36 is already in simplest form.
Answer:
[tex] \frac{5}{36} [/tex]Step-by-step explanation:
#CARRYONLEARNINGSolve for x. Round to the nearest tenth of a degree, if necessary.
Step-by-step explanation:
[tex] \tan(x \degree) = \frac{54}{32} \\ = \frac{3}{4} \\ x \degree = { \tan}^{ - 1} ( \frac{3}{2} ) \\ = 56.3 \degree[/tex]
