The explicit formula for the geometric sequence is,
⇒ tn = 7 (2ⁿ - 1)
What is Geometric sequence?An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.
Given that;
The geometric sequence is,
⇒ 7,14,28,56,112,…
Here, First term = 7
And, Common ratio = 14 / 7 = 2
We know that;
The explicit formula for the geometric sequence is,
⇒ tn = t₁ (rⁿ - 1) / (r - 1)
Substitute all the values we get;
The explicit formula for the geometric sequence is,
⇒ tn = 7 (2ⁿ - 1) / (2 - 1)
⇒ tn = 7 (2ⁿ - 1)
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partition
5 over 7
into fourths and double shade
1 over 4
of
5 over 7.
.
The number of 1/4 that can be found in 5/7 will be 2 6/7
How to calculate the valueIt is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.
The number of 1/4 that can be found on 5/7 will be:
= 5/7 ÷ 1/4
= 5/7 × 4
= 20/7
= 2 6/7
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I need help with both of these can someone please help me
After the shutdown, the hospital will maintain 126 acute hospital beds available for usage.
Which categories and what is a hospital?Hospitals are classified as general, specialist, or government facilities by the source of their funding. In a medical center, nursing education and patient care are both integrated. A care facility which is smaller than a hospital is called a clinic.
If 28% of the hospital's acute card beds are going to ever be closed, that leaves 100% - 28% = 72% of such beds available for utilization.
72% of 175 beds = 0.72 x 175 = 126 beds
As a result, following the shutdown, the hospital will still have 126 basic card beds available for usage.
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binomial theorem
[tex](2x - 3y)^{7} [/tex]
The value of [tex]$(2 x-3 y)^7$$[/tex] be
[tex]$=128x^7-1344 x^6 y+6048 x^5 y^2-15120 x^4 y^3+22680 x^3 y^4-20412 x^2 y^5+10206 x y^6-2187 y^7$[/tex]
What is meant by binomial theorem?The binomial theorem states that the nth power of the sum of two numbers a and b may be written as the sum of n + 1 terms of the form for every positive integer n. Starting with n, the powers on a decrease until the final term, when the power is 0.
Statistical and probability analyses make extensive use of the binomial theorem. Because statistical and probability analyses are so important to our economy, it is quite helpful. The Binomial Theorem is used to locate equations' roots in higher powers in advanced mathematics and computation.
Let the equation be [tex]$(2 x-3 y)^7$$[/tex]
Apply binomial theorem: [tex]$(a+b)^n=\sum_{i=0}^n\left(\begin{array}{c}n \\ i\end{array}\right) a^{(n-i)} b^i$[/tex].
[tex]$$\begin{aligned}& a=2 x, b=-3 y \\& =\sum_{i=0}^7\left(\begin{array}{l}7 \\i\end{array}\right)(2 x)^{(7-i)}(-3 y)^i\end{aligned}[/tex]
substitute the values in the above equation, we get
[tex]$=\frac{7 !}{0 !(7-0) !}(2 x)^7(-3 y)^0+\frac{7 !}{1 !(7-1) !}(2 x)^6(-3 y)^1+\frac{7 !}{2 !(7-2) !}(2 x)^5(-3 y)^2+$[/tex][tex]$\frac{7 !}{3 !(7-3) !}(2 x)^4(-3 y)^3+\frac{7 !}{4 !(7-4) !}(2 x)^3(-3 y)^4+\frac{7 !}{5 !(7-5) !}(2 x)^2(-3 y)^5+$[/tex][tex]$\frac{7 !}{6 !(7-6) !}(2 x)^1(-3 y)^6+\frac{7}{7 !(7-7) !}(2 x)^0(-3 y)^7$[/tex]
simplifying the above equation, we get
[tex]$\begin{array}{ll}\frac{7 !}{0 !(7-0) !}(2 x)^7(-3 y)^0= & 128 x^7 \\ \\ \frac{7 !}{1 !(7-1) !}(2 x)^6(-3 y)^1= & -1344 x^6 y \\ \\ \frac{7 !}{2 !(7-2) !}(2 x)^5(-3 y)^2 = & 6048 x^5 y^2 \\ \\ \frac{7 !}{3 !(7-3) !}(2 x)^4(-3 y)^3= & -15120 x^4 y^3 \\ \\ \frac{7 !}{4 !(7-4) !}(2 x)^3(-3 y)^4= & 22680 x^3 y^4 \\ \\ \frac{7 !}{5 !(7-5) !}(2 x)^2(-3 y)^5= & -20412 x^2 y^5 \\ \\ \frac{7 !}{6 !(7-6) !}(2 x)^1(-3 y)^6 = & 10206 x y^6 \\ \\ \frac{7 !}{7 !(7-7) !}(2 x)^0(-3 y)^7 = & -2187 y^7\end{array}$[/tex]
Therefore, the value of [tex]$(2 x-3 y)^7$$[/tex] be
[tex]$=128x^7-1344 x^6 y+6048 x^5 y^2-15120 x^4 y^3+22680 x^3 y^4-20412 x^2 y^5+10206 x y^6-2187 y^7$[/tex]
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Zoey needs to order some new supplies for the restaurant where she works. The restaurant needs at least 711 glasses. There are currently 281 glasses. If each set on sale contains 10 glasses, use the drop-down menu below to write an inequality representing s, the number of sets of glasses Zoey
PLEASE HELP PLEASE AND THANK YOU HAVE A BLESSED DAY
the fractions with the same denominator will be 14/16 and 13/16.
What is a fraction?
If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.
Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.
The given fraction is given are 7/8 and 13/16.
Taking lcm of the denominator will be 16
So the fraction will be 7*2 = 14
So the fractions will be 14/16 and 13/16.
Hence the fractions with the same denominator will be 14/16 and 13/16.
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Use the function B(t) = 45422 + 34.26t find the inverse of the linear model; write your function using function notation
Answer: A linear function is one whose graph is a straight line. Given the linear function B(t) = 45422 + 34.26t, its inverse function can be found by switching the places of x and y and then solving for y.
The inverse function, written in function notation, can be represented as:
B^(-1)(t) = (1/34.26)(t - 45422)
So the inverse of the linear model B(t) = 45422 + 34.26t can be written as B^(-1)(t) = (1/34.26)(t - 45422) in function notation.
Step-by-step explanation:
Find the principal value of Arctan (1.5) to the nearest minute.
Answer: You will find tan 56 degrees 18 minutes (approx) = 1.5 ... It's generally agreed that the principal value of tan inverse should lie between -90 and +90 ...
Step-by-step explanation:
George took home a net pay of $1, 300on their paycheck this week. They worked 60 hours during this specific pay period and had deductions that totaled $200, what is their hourly rate of pay?
$25 per hour, is their hourly rate of pay.
What is division?Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
Net pay= $1300
Deductions= $200
Hours worked= 60
then,
Total pay=$1300+ $200
= $1500.
Since her net pay is the money left after deductions, so we add the netpay and deductions to get her total pay.
Therefore, to find her hourly pay, we simply divide the total pay by the hours worked,
so we have 1500/60= $25/hour
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6. Given f(x)=3x² - 2x+4, find a. ƒ(-2)= b. f(k+1)=
Answer: a. To find f(-2), substitute -2 for x in the function f(x):
f(-2) = 3(-2)² - 2(-2) + 4 = 3(4) - 2(-2) + 4 = 12 - (-4) + 4 = 16
So, f(-2) = 16.
b. To find f(k+1), substitute (k+1) for x in the function f(x):
f(k+1) = 3(k+1)² - 2(k+1) + 4 = 3k² + 6k + 3 - 2k - 2 + 4 = 3k² + 4k + 5
So, f(k+1) = 3k² + 4k + 5.
Step-by-step explanation:
(4)/(9)((3)/(2)z^(2)y^(3))^(5)
???
how do i do this ??
Answer:
The expression can be solved using algebraic methods. The result is -(2^7)z^2y^3.
Step-by-step explanation:
The solution to the equation 4/(9)((3/2)z^2y^3)^5 is y^15z^10. This can be solved by using the steps of algebraic manipulation. First, the parentheses can be simplified by multiplying the numerator and denominator together, resulting in 4/27z^2y^3. Then, the exponent can be applied to both terms, resulting in y^15z^10. Finally, this answer can be checked by substituting it into the original equation and verifying that it is true.
Math triangle word problem:
The height of the mountain above the level plain is 4465.2 feet
What is an equation?An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either be linear, quadratic, cubic, depending of the degree of the variable.
Trigonometric ratio is used to show the relationship between the sides and angles of a right triangle.
Let h represent the height of the mountain. Let d represent the distance from the plain to the mountain base
Using trigonometric ratio:
tan(32) = h/d
h = d * tan(32)
Also:
tan(36) = h / (d - 1000)
h = (d - 1000) * tan(36)
Equating:
d * tan(32) = (d - 1000) * tan(36)
d = 7145.9 feet
h = d * tan(32) = 7145.9 * tan(32) = 4465.2 feet
The height of the mountain is 4465.2 feet
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an important component of measurements is using the right/appropriate unit for what is being measured! what unit would you use to measure the length of our classroom (assume any classroom).
The required unit would you use to measure the length of our classroom are meters or feet.
What are measurement tools?The usual measurement equipment is composed of thermometers, rulers, yardsticks, scales, beakers, protractors, clocks, and measuring tape. Knowing how to use each instrument properly can make measuring more accurate and enjoyable. Each tool has a unique purpose.
According to question:To measure the length of a classroom, you would use the unit of meters or feet.
These are commonly used units for measuring length or distance. For example, you might say "The length of the classroom is 10 meters" or "The classroom is 30 feet long". The specific unit used might depend on the location and the system of units (metric or imperial) that is commonly used in that area.
It's important to choose a unit that is appropriate for the task at hand, and to be consistent in using that unit throughout the measurement process.
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nitially, suppose that only adventurous citizens buy tickets at 7 flags. each adventurous citizen has an individual demand given by qa
The number of possible combinations for this scenario is 35
A combination is a way of selecting items from a set, where the order of the items does not matter.
Let's assume that each adventurous citizen has a demand for visiting three flags. This means that each citizen wants to visit three flags out of the seven available flags. To find the number of possible combinations, we can use the formula for combinations, which is:
C(n, r) = n! / (r! * (n - r)!)
Where n is the total number of flags available (7), and r is the number of flags that each citizen wants to visit (3). So, the number of possible combinations is:
C(7, 3) = 7! / (3! * (7 - 3)!) = 35
This means that there are 35 different combinations of flags that an adventurous citizen can choose from at 7 flags amusement park.
Complete Question:
Initially, suppose that only adventurous citizens buy tickets at 7 flags. each adventurous citizen has an individual demand given by those 3 flags. Find the number of possible combinations for this one.
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find the sample standard deviation forfind the sample standard deviation for the weights for the offensive linemen 359,297,350,254,312,250,359,253,254,326,254,331
The required standard deviation of the given data is 54.6.
How to find Standard deviation?To find the sample standard deviation for the weights of the offensive linemen, we first need to calculate the mean of the sample and then use that to find the variance and standard deviation.
Mean:
The mean (μ) is the sum of all the values in the sample divided by the number of values in the sample. In this case, the mean is:
(359 + 297 + 350 + 254 + 312 + 250 + 359 + 253 + 254 + 326 + 254 + 331) / 12 = 298.75
Variance:
The variance (σ²) is a measure of the spread of the data. It is calculated as the sum of the squared deviations of each value from the mean divided by the sample size minus one. In this case, the variance is:
( (359 - 298.75)² + (297 - 298.75)² + (350 - 298.75)² + (254 - 298.75)² + (312 - 298.75)² + (250 - 298.75)² + (359 - 298.75)² + (253 - 298.75)² + (254 - 298.75)² + (326 - 298.75)² + (254 - 298.75)² + (331 - 298.75)² ) / (12 - 1) = 2987.5
Standard Deviation:
The standard deviation (σ) is the square root of the variance. In this case, the standard deviation is:
√2987.5 = 54.59
Therefore, the sample standard deviation of the weights of the offensive linemen is 54.59 pounds.
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Answer 27 and 28 please!!
Answer:
27
a 43.56 inches
b 287.496 inches
28
1 1 4 8 9 27 16 64 25 125 36 216 49 343 64 512 81 729 100 1000 121 1331 144 1728Select the equation represented by the fraction strips below. 1 whole fraction strip is shown with a 1 indicated on it. Below it and to the left are 6 smaller fraction strips that are each one-twelfth the width of the whole. Another 6 fraction strips of the same size are shown further down below the image. These 6 one-twelfth-inch strips have an arrow that points from the location directly beside the first 6 one-twelfth strips. A. 6 12 − 6 12 = 0 12 B. 12 12 − 1 12 = 11 12 C. 12 12 − 2 12 = 6 12 D. 12 12 − 6 12 = 6 12 1 / 3 I NEED AN ANSWER ASAP PLEASE
The equation can be represented by 6¹/₁₂ - 6¹/₁₂ = 0. The correct option is A.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that 1 whole fraction strip is shown with a 1 indicated on it. Below it and to the left are 6 smaller fraction strips that are each one-twelfth the width of the whole.
Another 6 fraction strips of the same size are shown further down below the image. These 6 one-twelfth-inch strips have an arrow that points from the location directly beside the first 6 one-twelfth strips.
The equation for the strip can be written as:-
6¹/₁₂ - 6¹/₁₂ = 0
The correct option would be A.
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For triangle XYZ, m∠X = (2g + 16)° and the exterior angle to ∠X measures (4g + 38)°. Find the measure of ∠X and its exterior angle. Interior angle = 122°; exterior angle = 58° Interior angle = 58°; exterior angle = 122° Interior angle = 82°; exterior angle = 38° Interior angle = 38°; exterior angle = 82°
Answer:
Step-by-step explanation:
the sum of the interior and the exterior angle must be 180°.
7g + 12 + 2g + 60 = 180
9g + 72 = 180
9g = 108
g = 12
interior angle = 7×12 + 12 = 96°
exterior angle = 2×12 + 60 = 84°
2.4 divided by 0.75
The answer is 3.2
But I don’t know how to get there I only get 3 with a remainder of 15
I need to see the work please help.
Hi There! Here's your answer:
To make it easier, let's write this in fraction form:
[tex]\frac{2.4}{0.75}[/tex]
Now, multiply the numerator and denominator by 100 to remove the decimal point.
[tex]\frac{2.4}{0.75}[/tex] × [tex]\frac{100}{100}[/tex] = [tex]\frac{240}{75}[/tex]
Now, you can either divide using long division, or you can take out common factors and simplify the fraction that way.
Upon common factor simplification, we get the final fraction to be:
[tex]\frac{240}{75}[/tex] = [tex]\frac{48}{15}[/tex] (Common factor 5) = [tex]\frac{16}{5}[/tex] (Common factor 3)
Therefore, we get the final fraction as [tex]\frac{16}{5}[/tex] which is 3.2.
HOPE IT HELPS!
The recommended daily amount of sodium is 2550 mg. One can of wild rice soup contains 535.5 mg of sodium. What percent of the total recommended daily amount of sodium is in this can of soup?
Round your answer to the nearest tenth of a percent, if necessary.
21% of the total recommended daily amount of sodium is in this can of soup?
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.
The recommended daily amount of sodium is 2550 mg. One can of wild rice soup contains 535.5 mg of sodium. Hence:
Percentage of sodium in can = (535.5/2550) * 100% = 21%
There is 21% of sodium in can
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Write at least three different inequalities the solution is x greater than -10. Find one with x on the left side that uses a less than sign
The following inequalities are,
x > -10-10 < xx ≥ -9.999...What are inequalities?Inequalities are the comparison of mathematical expressions, whether one quantity is greater or smaller in comparison to another quantity.
We use these symbols to represent inequalities, '>' , '<', '≥', '≤'
Given that,
We have to write three different inequalities,
In which, the solution is x greater than -10
1. It can be represented as,
x > -10
2. One on left hand side, so it is further modified as,
-10 < x
3. writing with greater equal to sign, but that x can never be equal to -10, only be greater than it
So, it can be written as
x ≥ -9.999...
Thus, three inequalities are respectively, x > -10, -10 < x, x ≥ -9.999...
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please help!! it’s due in today and i have no idea what u do ahha!!!
Answer:
90000000000
Step-by-step explanation:
3*1 plus 8 zeros
*
3*1 plus 2 zeros
so 300000000 * 300=
90000000000
Which of the following sentences show correct verb tense usage? Check all that apply. When the facilitator announced a bathroom break, the seminar participants took out their iPhones and begun checking their messages a The overall outlook is favorable, so I wrote to the board chair to inform him. She has wrote him an e-mail
The sentence which show correct verb tense usage is The overall outlook is favorable.
Verbs are a necessary component of communication in every language, including English, without which it would be difficult to convey what the subject is doing. All acts, including those motivated by sentiments and emotions, are included.
Verbs exist in a variety of forms and kinds so they can function in many ways to convey the whole meaning. Let's have a look at how different dictionaries define the word "verb" before we examine the many kinds of verbs and their forms.
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Express the following numbers without using words.
a) China had a population of more than 1,3 billion people in 2011.
The expression of the given word phrase 1.3 billion using numbers is; 1,300,000,000.
What if the representation of the given word phrase using numbers?It follows from the task content that the concept described in the given word phrase is to be represented by a number.
On this note, since the number in discuss is; 1.3 billion where a billion represents; 1 × 10⁹.
Hence, 1.3 billion represents; 1.3 × 10⁹.
= 1,300,000,000.
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Please answer the attached picture
Answer:
25
Step-by-step explanation:
(f+g)(x) also stated as f(x)+g(x)
2x²+3x-2
where x=3
2(3)²+3(3)-2
2(9)+9-2
18+7
25
Find parametric equations of the curve given by the intersection of the surfaces:
The cylinder: x2+y2=81
The surface: z=6xy
x(t) = ?
y(t) = ?
z(t) = ?
Correct Answer:
x(t) = 9cos(t)
y(t) = 9sin(t)
z(t) = 54sin(t)cos(t)
What is the parametric equation?
The parametric equation of a curve is a representation of the curve in terms of one or more independent variables (known as parameters), usually represented as t. Each parameter value t corresponds to a unique point (x, y, z) on the curve.
For the given curve, the intersection of the cylinder x² + y² = 81 and the surface z = 6xy can be found by setting the equation of the cylinder equal to the equation of the surface and solving for x, y, and z in terms of a single parameter t.
Starting with the cylinder: x² + y² = 81, we can parameterize x and y as follows:
x(t) = 9cos(t)
y(t) = 9sin(t)
Substituting these expressions into the equation of the surface:
z(t) = 6x(t)y(t) = 6 * 9cos(t) * 9sin(t) = 54sin(t)cos(t)
So, the parametric equations of the curve given by the intersection of the cylinder x² + y² = 81 and the surface z = 6xy are:
x(t) = 9cos(t)
y(t) = 9sin(t)
z(t) = 54sin(t)cos(t)
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A student drink 32 oz energy drink containing 90 calories per 12 oz. How many calories did the student drink?
Answer:
187.5 Calories
Step-by-step explanation:
We start by multiplying 12 x 2 to get 24 which is equal to a total of 180 calories, therefore we have to subtract 32-24 to get 8oz left, we then divide 90 by 12 to get 7.5 calories which we add to the 180 from before to get a total of 187.5 Calories.
I need and 3-4 minute explanation that’s it
Answer:
Step-by-step explanation:
Just plug in the x-intercept to find the y-intercepts. Slope is y2-y1/x2-x1, so just take any 2 y-intercepts and any 2 x intercepts to find the slope.
admission to a carnival costs $15 each games costs $2 to play. Which statements about the function modeling the cost to attend the carnival are True? Select all that apply
A. The slope is positive
B. The initial value is $15
C. The rate of change is $15
D. The graph has a y-intercept of 2
E. The Graph passes through the origin
Answer:
you have find if its proportianal for e thats all I know tho sorry
The equation y equals 4 times 6 to the power of t shows the number of infected people from an outbreak of the measles. The variable y represents the number of infected people, and t represents time in weeks. In how many weeks will the number of infected people reach 568?
Step-by-step explanation:
By the question,
y = 4×6^t
So let y be 568,
568 = 4× 6^t
or, 6^t = 142
t =
[tex] log_{6}(142) [/tex]
Approximately,
[tex] log_{6}(142) [/tex]
weeks it takes for the infected people to be 568.
What is the period of this graph?
Answer:
4π
Step-by-step explanation:
The Period, as measured from crest-to-crest (or from trough-to-trough), is 4π, as read directly from the graph