For each sequence, find the first 4 terms of a sequence:
a) n²+3
b) 2n²
Answers
Answer:
a) 4, 7, 12, 19
b) 2, 8, 18, 32
Step-by-step explanation:
Sequence is just number line sir, so to begin with you get n=1, then n=2, then n=3, then n=4, these are the first 4 terms
Answer:
a) 4, 7, 12, 19
b) 2, 8, 18, 32
Step-by-step explanation:
In order to find the first 4 terms, you have to substitute 1 to 4 into n for both expressions :
\(a) {n}^{2} + 3\)
\(1st \: term \\ {1}^{2} + 3 = 4\)
\(2nd \: term \\ {2}^{2} + 3 = 7\)
\(3rd \: term \\ {3}^{2} + 3 = 12\)
\(4th \: term \\ {4}^{2} + 3 = 19\)
\(b)2 {n}^{2} \)
\(1st \: term \\ 2( {1}^{2} ) = 2\)
\(2nd \: term \\ 2( {2}^{2} ) = 2(4) = 8\)
\(3rd \: term \\ 2( {3}^{2} ) = 2(9) = 18\)
\(4th \: term \\ 2( {4}^{2} ) = 2(16) = 32\)
Related Questions
find dy/dx. x = t sin(t), y = t2 + 8t
Answers
find dy/dx
x= t sin(t); (Given in the question)
y= t²+8t; (Given in the question)
then, x= t sin(t)
dx/dt = sin t + t cos t ;
y= t²+8t
dy/dt = 2t + 8;
then, dy/dx = dy/dt x dx/dt
dy/dx = (2t+8)/(sin t + t cos t)
dy/dx = 2(t+4)/(sin t + t cos t)
Learn more about derivative at:
brainly.com/question/23847661
#SPJ4
find the domain of each function.
f(x)=1/(x-3)
Answers
The domain of the function f(x)=1/(x-3) will be all the real numbers except 3.
What is a domain?The domain of the function is defined as the set of all the possible values of the function. The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x).
A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
Given function is f(x)=1/(x-3). The domain of the function will be all the real numbers. But at x = 3 the value of the function does not exist.
Therefore, the domain of the function f(x)=1/(x-3) will be all the real numbers except 3.
To know more about the domain follow
https://brainly.com/question/26098895
#SPJ1
find [t]-1 given that cos sin sin cos and show that [t]21 5[t]t and hence that [t] is an orthogonal matrix.
Answers
TT is equal to T-1, so the given matrix is an orthogonal matrix.
What is an orthogonal matrix?
A matrix is said to be orthogonal if its antipode is also its transpose and if its relationship to the inner product is established. A real square matrix with orthonormal vectors in its columns and rows is known as an orthogonal matrix or orthonormal matrix in direct algebra. Where QT is the transpose of Q and I is the identity matrix is one system to put this into words. However, the matrix is said to be orthogonal, If the transpose of a square matrix with real figures or values is equal to the inverse matrix of the matrix. In other words, an identity matrix will always be affected by the product of a square orthogonal matrix and its transpose.Here, the determinant of T,
|T| = cos²∅ + sin²∅
= 1
Now, its cofactors,
\(T_{11}\) = cos ∅
\(T_{12\) = sin ∅
\(T_{21\)= -sin ∅
\(T_{22\) = cos ∅
Now, the adjoint matrix of cofactors matrix transpose \(T^T\) is equal to \(T^{-1.\)
Hence, the given matrix is an orthogonal matrix.
Learn more about orthogonal matrix here: https://brainly.com/question/13258857
#SPJ4
what is good for your health
Answers
Answer:
Exercise, 8 hrs of sleep, healthy diet with lots of fruits and vegetables are all good for your health
Step-by-step explanation:
You work at Dave's Donut Shop. Dave has asked you to determine how much each box of a dozen donuts should cost. There are 12 donuts in one dozen. You determine that it costs $0.27 to make each donut. Each box costs $0.16 per square foot of cardboard. There are 144 square inches in 1 square foot.
Answers
Using mathematical operations, each box of a dozen donuts should cost $3.40.
What are the mathematical operations?The basic mathematical operations used to determine the cost of a dozen donuts include multiplication and addition.
Firstly, the total cost of 12 donuts is computed by multiplication, while the total cost of the donuts per box (including the cost of the box) is obtained by addition.
1 dozen = 12 donuts
The cost unit of a donut = $0.27
The total cost of donuts = $3.24 ($0.27 x 12)
The cost per square foot of cardboard = $0.16
The total cost of a dozen donuts and the box = $3.40 ($3.24 + $0.16)
Learn more about mathematical operations at https://brainly.com/question/28398580.
#SPJ1
The answer is 3,4 what is the question
Answers
Answer:
What is the x and y coordinate of (3,4)
What is the maximum width on a stair before another stringer is
required?
A.12
B.16
C.24
D.30
Answers
Answer:
A.12
Step-by-step explanation:
20 points!!! please help
Answers
Answer:
1/8
Step-by-step explanation:
1 of the 8 branches of the tree is TTH in that order. If all branches are equally likely, the probability is 1/8, or 0.125, or 12.5%.
PLEASE HELP AND EXPLAIN
Answers
See below for the interpretation of the graph
How to interpret the graph?From the graph, the initial values of x and y are 0
As x increases, y decreases.
This means that the first statement is
Initially, as x increases, y decreases.Slope is calculated as:
\(m = \frac{y_2 - y_1}{x_2 -x_1}\)
Using the graph values at the interval x =0 to x = 3, we have:
\(m = \frac{-3 - 0}{3 - 0}\)
m = -1
This means that the second statement is
The slope of the graph is equal to -1 for all x between x = 0 and x = 3From the graph, y = -3, when x = 3
As x increases at this point, y increases.
This means that the third statement is
Starting at x = 3, the function value y increases as x increasesUsing the graph values at the interval x = 3 to x = 5, we have:
\(m = \frac{3 + 3}{5 - 3}\)
m = 3
This means that the fourth statement is
The slope of the graph is equal to 3 for x between x = 3 and x = 5All y values at x = 0 to x = 4 are less than 0, while all y values at x = 4 to x = 8 are greater than 0
So, the last two statements are
For x between x = 0 and x = 4, the function value y is less than 0For x between x = 4 and x = 8, the function value y is greater than 0Read more about functions at:
https://brainly.com/question/27831985
#SPJ1
three circles are drawn, so that each circle is externally tangent to the other two circles. each circle has a radius of a triangle is then constructed such that each side of the triangle is tangent to two circles, as shown below. find the perimeter of the triangle.
Answers
To find the perimeter of triangle formed by the tangents to the circles, find radii of circles and side lengths of triangle. The perimeter of triangle formed by the tangents to the circles is 12 times the radius of each circle.
Let's denote the radius of each circle as r. Since the circles are externally tangent to each other, the distance between their centers is equal to the sum of their radii, which is 2r.
When a triangle is formed by connecting the points of tangency on each circle, it creates three isosceles triangles. Each of these isosceles triangles has two congruent sides, which are the radii of the circles.By drawing the triangle, we can observe that the base of each isosceles triangle is equal to 2r, which corresponds to the diameter of one of the circles. The height of each isosceles triangle is equal to r, which is the radius of the circle.
Therefore, each side of the triangle formed by the tangents has a length of 4r.Since the triangle has three equal sides, its perimeter is given by 3 times the length of one side, which is 3 * 4r = 12r.The perimeter of the triangle formed by the tangents to the circles is 12 times the radius of each circle.
To learn more about tangents click here : brainly.com/question/10053881
#SPJ11
Need Help! Please Due later tonight at 11:59 :))
Answers
B) 34
C) 36
D) √25
E) 34
F) 36
G) 6
#5
CONNECTING CONCEPTS You use 94 inches of plastic to frame the perimeter of a kite. One side of the kite has a
length of 18 inches. Find the length of each of the three remaining sides in order from least to greatest.
Length: in.,in., in
Answers
The length of each of the three remaining sides, in order from least to greatest, is x = 8, y = 18 and z = 3.
What is Perimeter?
Perimeter is the total length of the boundary of a two-dimensional shape or figure. It is the distance around the outside of a closed shape, such as a rectangle, triangle, circle, or any other polygon. To find the perimeter of a shape, you add up the lengths of all its sides. Perimeter is usually measured in units of length, such as centimeters, meters, feet, or inches. Perimeter is an important concept in geometry, and it is used to calculate the amount of material needed to surround a shape or to measure the distance around a path or track.
Let's denote the lengths of the three remaining sides of the kite as x, y, and z, where x is the shortest side.
The perimeter of the kite is the sum of the lengths of all four sides:
P = x + y + z + 18
We also know that the total length of plastic used to frame the perimeter is 94 inches:
94 = 2x + 2y + 2z + 36
Simplifying the equations by dividing both sides of the second equation by 2, we get:
47 = x + y + z + 18
47 = x + y + z + 18
Substituting the first equation into the second equation, we get:
x + y + z + 18 = 2x + 2y + 2z + 36
Simplifying this equation, we get:
x = 8
Substituting x = 8 into the first equation, we get:
y + z + 26 = 47
Simplifying this equation, we get:
y + z = 21
We want to find the values of y and z. Since we don't have enough information to solve for each of them individually, we'll use a bit of logic to determine their relative values.
The only combination that satisfies these conditions is:
y = 18
z = 3
Therefore, the length of each of the three remaining sides, in order from least to greatest, is:
x = 8
y = 18
z = 3
Learn more about Perimeter click here:
https://brainly.com/question/19819849
#SPJ1
Evaluate-+61
Enter your answer in the box.
- 7 when x = 18
Answers
The expression 61+x when x = 18 evaluates to 79.
What is expression?Expression is a combination of numbers, symbols and operators that represent a mathematical quantity or operation.
To find the value of the expression, we must first substitute 18 in for x. To evaluate this expression, we must add 61 and 18. 61+18 = 79. Therefore, the expression 61+x when x = 18 evaluates to 79.
To verify the answer, we can use the distributive property of multiplication to expand the expression. 61+x is equivalent to 61+18, which can be written as
61+18 = 61+1*18.
We can now distribute the 1 to the 18,
so 61+1*18 = 61+18 = 79.
Therefore, the expression 61+x when x = 18 evaluates to 79.
For more questions related to distributive property
https://brainly.com/question/4077386
#SPJ1
Question: Evaluate-61+x
Enter your answer in the box.
Find the value of equation, when x = 18.
The registration fee for a used car is 0.6% of the sale price of $5,400. How much is the fee?
Answers
The registration fee for a used car is 0.6% of the sale price of $5,400, so the fee is $32.4
What is sale price?A consumer must pay the selling price in order to acquire a good or a commodity. It is a price that is higher than the cost price and contains a proportion of profit. The cost price is the amount paid by the seller for the product or commodity. Then follows that by adding a portion of income or profits.
Given that,
Registration fee = 0.6%
Sale price = $5,400
Let, the fee = x
Now, the fee is:
x = $5,400 × 0.6%
x = $5,400 × (0.6 ÷100)
x = $32.4
So, the fee is $32.4.
To know more about sale price refer to:
https://brainly.com/question/7459025
#SPJ1
a+b/c=5. Solve for b
Answers
Answer:
b = c(5 - a)
Step-by-step explanation:
Given
a + \(\frac{b}{c}\) = 5 ( subtract a from both sides )
\(\frac{b}{c}\) = 5 - a ( multiply both sides by c to clear the fraction )
b = c(5 - a)
The value of b form the equation a + b/c = 5 will be b = c(5 - a)
How to evaluate a given mathematical expression with variables if values of the variables are known?We can simply replace those variables with the value you know of them and then operate on those values to get a final value. This is the result of that expression at those values of the considered variables.
Given;
a + b/c = 5
subtract a from both sides;
b/c = 5 - a
multiply both sides by c to clear the fraction;
b = c(5 - a)
Hence, The value of b form the equation a + b/c = 5 will be b = c(5 - a)
Learn more about evaluating a function at a value here:
https://brainly.com/question/2753269
#SPJ2
Please Answer The Question Correctly!!!!!!!!!!!!!!!!
Answers
Answer:
a is not a function and the rise over run of b is 1/1Step-by-step explanation:
3 has two outputs in a
Carrie Ann has a penny bank with 812 pennies in it. She gave her little sister 10 pennies to start her own penny bank savings. She gave 68 pennies to her brother in exchange for taking her turn at doing the dishes. How many pennies does Carrie Ann have in her penny bank? Explain how you got your answer.
Answers
Answer:
Just do 812-78 that equals 734.
Answer:
734 pennies
Step-by-step explanation:
10 +68 =78 pennies that she gave to her sister and her brother
812 - 78 =734 pennies has
Find the solution on the MATLAB
Develop a function M-file to compute \( v \) as a function of \( t \) \[ v(t)=\left\{\begin{array}{cc} 10 t^{2}-5 t & 0 \leq t \leq 8 \\ 624-3 t & 8 \leq t \leq 16 \\ 36 t+12(t-16)^{2} & 16 \leq t \le
Answers
The solution to compute the function is coded below.
function v = compute_v(t)
if t >= 0 && t <= 8
v = 10 * t^2 - 5 * t;
elseif t > 8 && t <= 16
v = 624 - 3 * t;
elseif t > 16 && t <= 24
v = 36 * t + 12 * (t - 16)^2;
else
error('Invalid value of t. t should be between 0 and 24.');
end
end
To use this function, you can call it with a specific value of t, and it will return the corresponding value of v. For example:
t = 5;
v = compute_v(t);
disp(v);
This will compute the value of v at t = 5 and display the result.
Learn more about Array here:
https://brainly.com/question/33609476
#SPJ4
(HELP ASAPPP)
The Wilson’s new pool shed is shown (in the image).Mrs Wilson wants to paint it a turquoise color to match the pools tile.Find the area that needs to be painted, not including the door which is 1.0 m wide.
Answers
Answer:
2.9
Step-by-step explanation:
You first find the area of the shed, including the door. You can split the shed into 2 parts, first the triangle, then the rectangle. You find the area of both, add it together, and then subtract the area of the door. (I might have caluculated incorrectly. If you are not sure you can double check.)
The number of chocolate chips in an 18-ounce bag of Chips Ahoy! chocolate chip cookies is approximately normally distributedwith a mean of 1262 chips and a standard deviation of 118 chips, according to a study by cadets of the US Air Force Academy.
(a) Determine the 29th percentile for the number of chocolate chips in an 18-ounce bag of Chips Ahoy! cookies.
(b) Determine the number of chocolate chips in a bag of Chips Ahoy! that make up the middle 97% of bags.
(c) What is the interquartile range of the number of chips in Chips Ahoy! cookies?
Answers
Answer: (a) To determine the 29th percentile for the number of chocolate chips in an 18-ounce bag of Chips Ahoy! cookies, we need to find the value of x such that 29% of the bags have a smaller number of chocolate chips than x. We can use the standard normal distribution and the z-score formula to do this:
z = (x - μ) / σ
where μ is the mean, σ is the standard deviation, and z is the z-score corresponding to the desired percentile. We want to find the z-score for the 29th percentile, which we can look up in a standard normal distribution table or use a calculator to find as -0.87. Plugging in the values we have, we get:
-0.87 = (x - 1262) / 118
Solving for x, we get:
x = -0.87 * 118 + 1262 ≈ 1153
Therefore, the 29th percentile for the number of chocolate chips in an 18-ounce bag of Chips Ahoy! cookies is approximately 1153 chips.
(b) To determine the number of chocolate chips in a bag of Chips Ahoy! that make up the middle 97% of bags, we need to find the range of values that includes the middle 97% of the distribution. This corresponds to the range between the 1st and 97th percentiles, which we can find using the z-score formula and a standard normal distribution table or calculator.
The z-score corresponding to the 1st percentile is -2.05, and the z-score corresponding to the 97th percentile is 1.88. Using the same formula as before, we can find the values of x that correspond to these z-scores:
-2.05 = (x - 1262) / 118
x = -2.05 * 118 + 1262 ≈ 994
and
1.88 = (x - 1262) / 118
x = 1.88 * 118 + 1262 ≈ 1536
Therefore, the number of chocolate chips in a bag of Chips Ahoy! that make up the middle 97% of bags is between approximately 994 and 1536 chips.
(c) The interquartile range (IQR) is a measure of the spread of a distribution that represents the range between the 25th and 75th percentiles. We can find the values of x that correspond to these percentiles using the z-score formula and a standard normal distribution table or calculator:
-0.67 = (x - 1262) / 118
x = -0.67 * 118 + 1262 ≈ 1176
and
0.67 = (x - 1262) / 118
x = 0.67 * 118 + 1262 ≈ 1350
Therefore, the values that represent the interquartile range for the number of chocolate chips in an 18-ounce bag of Chips Ahoy! cookies are approximately 1176 and 1350 chips. The IQR is the range between these values, which is approximately 174 chips.
Step-by-step explanation:
3.If a kilogram of pork cost Php 105.75,how much is the cost of 5.5 kilogram?
Answers
Answer:
581.625 php
Step-by-step explanation:
If 1 kilo of pork is 105.75, just multiply it by 5.5 to get the answer
Answer:
=5.5×105.75
=581.62
hope it helps
what is 7 divided by -14
Answers
a local bank reviewed its credit card policy with the intention of recalling some of its credit cards. in the past approximately 3% of cardholders defaulted, leaving the bank unable to collect the outstanding balance. hence, management established a probability of 0.03 that any particular cardholder will default. the bank also found that the probability of missing a monthly payment is 0.21 for customers who do not default. of course, the probability of missing a monthly payment for those who default is 1. (a) given that a customer misses a monthly payment, compute the probability that the customer will default. (round your answer to 2 decimal places.) 0 changed: your submitted answer was incorrect. your current answer has not been submitted. (b) the bank plans to recall its card from customers who miss a monthly payment, if the probability those customers will default is greater than 0.20. should the bank recall its card from a customer who has missed a monthly payment? why or why not? the bank ---select--- recall its card because the probability of default for these customers is ---select--- than 0.20.
Answers
The probability that the customer will default. is 0.2337.
How to calculate the probabilityProbability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.
P(missing one month payment | not default) = 0.21
P(missing one month payment | default) = 1
P(missing one month payment) = P(missing one month payment | default) * P(default) + P(missing one month payment | not default) * P(not default)
= 1 * 0.03 + 0.21 * 0.97
= 0.2337
Learn more about probability on:
https://brainly.com/question/24756209
#SPJ1
4.(01.02 MC) 8° 8.4.2 8.7 х x 78 Which value is equivalent to ? (1 point) 64 49 8 49 016 7 512 7
Sorry for quality btw :( ill give brainliest!!!
Answers
In anova, by dividing the mean square between groups by the mean square within groups, a(n) _____ statistic is computed.group of answer choices
Answers
In anova, by dividing the mean square between groups by the mean square within groups, a(n) Analysis of variance statistic is computed.
What is Analysis of variance ?
With the help of the statistical analysis approach known as ANOVA, apparent aggregate variability within a data set is explained by separating systematic components from random factors. Systematic influences, but not random ones, statistically affect the data set that is being presented.What are some instances where ANOVA has been applied?
An ANOVA demonstrates the link between the dependent variable and the level of the independent variable. For illustration: In order to determine whether there is a difference in the number of hours of sleep each night as your independent variable, you divide the groups into low, medium, and high social media use categories.Learn more about Analysis of variance
brainly.com/question/28274784
#SPJ4
The scale factor from rectangle you UVWX two rectangle STQR is
Answers
Answer:
The scale factor is 1/3
Step-by-step explanation:
Compare side length XW with RQ, the side length decreases from 15 to 5, which is a shrinking by a factor of 1/3, since 5 is 1/3 of 15. You can check this by comparing the sides WV with RS, and since 8 is 1/3 of 24, the scale factor is 1/3 going from UVWX to STQR.
If I helped, a brainliest would be greatly appreciated!
denise measured a community college and made a scale drawing. in real life, a building at the college is 122 meters long. it is 183 centimeters long in the drawing. what scale did denise use?
Answers
The scale Denise used is as follows:
3 centimetres: 2 metres
How to find the scale of a drawing?Denise measured a community college and made a scale drawing. In real life, at the college is 122 meters long. it is 183 centimetres long in the drawing.
The scale of Denise use can be calculated as follows:
Using the proportional relationship,
3 / x = 183 / 122
cross multiply
122(3) = 183x
366 = 183x
divide both sides by 183
x = 366 / 183
x = 2 metres.
learn more on scale here: https://brainly.com/question/32042187
#SPJ4
Rectangular prism B is the image of rectangular prism A after dilation by a scale factor of 1/3. If the surface area of rectangular prism B is 14^2 find the surface area of rectangular prism A, the preimage.
Answers
.\(SA_A = 2LW + 2LH + 2WH = 2(LW + LH + WH) = 2(882) = 1764\) The surface area of rectangular prism A is 1764 square units.
What are rectangular prism?A three-dimensional object called a rectangular prism has six rectangular faces, each of which has four right angles and the two opposing faces are congruent and parallel. It is sometimes referred to as a rectangular box or a parallelepiped.
Let's start by defining some variables. Let the length, width, and height of rectangular prism A be denoted by L, W, and H, respectively. Similarly, let the length, width, and height of rectangular prism B be denoted by l, w, and h, respectively.
Since rectangular prism B is a dilation of rectangular prism A by a scale factor of 1/3, we have:
\(l = (1/3)L\)
\(w = (1/3)W\)
\(h = (1/3)H\)
The surface area of a rectangular prism is given by the formula:
SA = 2lw + 2lh + 2wh
Therefore, the surface area of rectangular prism B is:
\(SA_B = 2lw + 2lh + 2wh\)
\(= 2((1/3)L(1/3)W) + 2((1/3)L(1/3)H) + 2((1/3)W(1/3)H)\)
\(= (2/9)LW + (2/9)LH + (2/9)WH\)
\(= (2/9)(LW + LH + WH)\)
We are given that the surface area of rectangular prism B is 14^2, so we have:
\(SA_B = (2/9)(LW + LH + WH) = 14^2\)
Simplifying this equation, we get:
\(LW + LH + WH = (9/2)14^2 = 882\)
Therefore, the surface area of rectangular prism A is:
\(SA_A = 2LW + 2LH + 2WH = 2(LW + LH + WH) = 2(882) = 1764\)
Therefore, the surface area of rectangular prism A is 1764 square units.
Learn more about prism here:
https://brainly.com/question/27812749
#SPJ1
once she completes a wall, sabrina notices that the number of squares along each side of the wall equal to the number of square centimeters in each tiles area. write an equation for the number of squares on the wall, SW, in terms of c. Then solve for the number on the wall
Answers
Answer:
width of each tile are equal to x cm.
SW = (number of squares on one side)^2
SW = x^2
But we also know that the area of each tile is equal to x^2 square cm. Therefore, the area of the wall can be expressed as:
SW = A/x^2
Where A is the total area of the wall.
SW × x^2 = A
SW = A/x^2
So the equation for the number of squares on the wall, SW, in terms of c, is:
SW = A/c^2
where c is the length and width of each tile in centimeters.
To find the actual number of squares on the wall, we would need to know the value of A and c.
3. Find the midpoint between the following points. (-2,-5) and (-3,1)
Answers
Answer:
Step-by-step explanation:
(x₁, y₁) = (-2 , -5) & (x₂ , y₂) = (-3 , 1)
Midpoint = \((\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})\)
\(=(\frac{-2 + [-3]}{2} ,\frac{-5 + 1}{2})\\\\\\=(\frac{-5}{2} , \frac{-4}{2})\\\\=(-2.5, -2)\)