The arithmetic sequence has the 73rd term of 306
How to find the 73rd term for the arithmetic sequence?The sequence is given as:
18,22,26,30,....
The above sequence has the following parameters
First term, a = 18Common difference, d = 4 i.e. 22 - 18 = 4Number of terms , n = 73This means that the sequence is an arithmetic sequence
The nth term of an arithmetic sequence is calculated as
f(n) = a + (n - 1) * d
Substitute the known values in the above equation
So, we have the following equation
f(73) = 18 + (73 - 1) * 4
Evaluate
f(73) = 306
Hence, the 73rd term for the arithmetic sequence is 306
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Katelyn’s older brother borrowed money for school. He took out a loan that charges 6% simple interest. He will end up paying $720 in interest after 6 years. How much did Katelyn’s brother borrow for school?
The amount of money that Katelyn’s brother borrowed for school would be = $ 2,000.
What is interest?Interest in the amount of money that an individual pays in extra with a borrowed amount of money either from an individual or from the bank.
The formula for simple interest= Principal ×Time × Rate/100
Rate of payment= 6%
Time = 6 years
Simple interest = $720
Principal= X
From the formula above, make principal the subject of formula;
Principal = SI × 100/ T× R
= 720 × 100/ 6×6
= 72000/36
=$ 2,000
Therefore, the amount of money that Katelyn’s brother borrowed for school is $2,000.
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In the diagram ray MO bisects the measurement of
An electrician cuts a 50 ft piece of wire into 3 pieces. The first piece is 4 ft longer than the second piece and the third piece is 2 feet shorter than the second piece. How long are the pieces?
The required length of the pieces is given as 20 ft, 16ft, and 14ft.
Given that,
An electrician cuts a 50 ft piece of wire into 3 pieces. The first piece is 4 ft longer than the second piece and the third piece is 2 feet shorter than the second piece. How long are the pieces is to be determined.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
according to the question,
Length of the first, second, and third be x, y and z,
According to the question,
x + y + z = 50 - - - - - - - - (1)
x = y + 4
z = y - 2
put x and z in equation 1
y + 4 + y + y - 2 = 50
3y = 50-2
y = 48/3
y = 16 ft
Now,
x = 16 + 4 = 20 ft
z = 16 - 2 = 14 ft
Thus, the required length of the pieces is given as 20 ft, 16ft, and 14ft.
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Many Texas cities have experienced substantial growth in population over the last 20 years. The growth of Houston, Texas, since 2015 is shown in the scatterplot. A least-squares equation that relates the number of years since 2015 to the population of that year (in millions) is given by Population = 0.025 (year) + 2.01.
Based on the residual plot, is a linear model suitable for modeling the population growth of Houston?
A linear model is suitable because a pattern is evident in the residual plot.
A linear model is not suitable because the residuals do not cluster around zero.
A linear model is not suitable because the residual plot shows a curved pattern.
A linear model is suitable because the residuals seem to be randomly scattered.
Based on the given residual plot, as regards the linear model, we can say that; A linear model is not suitable because the residual plot shows a curved pattern.
What is a residual Plot?
A residual plot is a plot that shows the difference between the observed response and the fitted response values.
The ideal residual plot is usually called the null residual plot, and it shows a random scatter of points that form an approximately constant width band around the identity line.
When it comes to finding out if a linear model will be suitable, we can say that the points will form a pattern when the model function is not correct.
Now, you might be able to transform variables or even add polynomial and interaction terms in order to remove the pattern.
Now, looking at the given graph, we can say that a linear model is not suitable because from the definitions above, we can see that the residual plot shows a curved pattern.
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What is 43+5673+20(1)
Answer:
5736
Step-by-step explanation:
calculator
Answer: 5736
Step-by-step explanation:
Given p(x)=x+7/3, if p(x)=13 find x
x = 32
Step-by-step explanation:
[tex]{ \tt{p(x) = \frac{x + 7}{3} }}[/tex]
If p(x) = 13, then
[tex]{ \tt{13 = \frac{x + 7}{3}}} [/tex]
[tex]{ \tt{13 \times 3 = x + 7}}[/tex]
[tex]{ \tt{39 = x + 7}}[/tex]
[tex]{ \tt{39 - 7 = x}}[/tex]
[tex]{ \red{ \boxed{ \blue{ \sf{x = 32}}}}}[/tex]
3. One batch of pancakes needs 1 1/4 cups of pancake mix. One box has 9 cups of pancake mix How many batches of pancakes can be made with one box of pancake mix?
Find D subscript x y if
y = e^(-1/x^2)
Hint: remember the definition of derivative of natural log and use chain rule
The derivative of the natural log function y = e^(-1/x^2) is
2x^(-3)e^(-1/x^2)How to solve for the derivativeThe given function is
y = e^(-1/x^2)
The given function is rearranged as
y = e^(-1/x^2) = e^u such that u = (-1/x^2)
Applying chain rule
y = e^u
y' with respect to u = e^u
u = (-1/x^2) = -x^(-2)
u' with respect to x = 2x^(-3)
(y' with respect to u) * (u' with respect to x)
= e^u * 2x^(-3)
plugging in the value of u
= e^(-1/x^2) * 2x^(-3)
= 2x^(-3)e^(-1/x^2)
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Wanda walked 43.4 km in 14 days. At this rate, how far would she walk in 40 days?
She would walk__km in 40 days.
Answer:
124 km
Step-by-step explanation:
Wanda walked 43.4 km in 14 days. At this rate, how far would she walk in 40 days? She would walk__km in 40 days.
First, figure km per day:
43.4/14 = 3.1 km per day
3.1 * 40 = 124 km
She would walk 124 km in 40 days.
ABCD is a quadrilateral.
Work out angle x.
Optional working
Answ
4
+
B.
8 cm
A
X
6 cm
D
29%
13 cm
C
The require angle of x is 52.4°
Given is a quadrilateral
The given diagonal divides the quadrilateral in two parts
the first part is a right angled triangle
Thus to find the side BD
we will use the Pythagoras theorem ;
So according to this theorem
AB² + AD² = BD² [ because BD is the hypotenuse ]
Given AB = 8 cm and AD = 6 cm
8² + 6² = BD²
this implies 64 + 36 = BD²
100 = BD which implies BD = 10 cm
To find x
we know that in triangle BCD
BD = 10 cm and CD = 13 cm
tan theta = [tex]\frac{13}{10}[/tex]
this means theta = [tex]tan^{-1}[/tex] [tex]\frac{13}{10}[/tex]
theta = 52.4°
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Answer:
39.07
use pythagros to find bd then use the sine rule substitute in the values
bd=10
beacuse a²+b²=c²
substitute in 8²+6²=c²
15. Graph 6 and 6 on the number line.
A++
-6 5 4 3 2 1 0 +1 +2 +3 +4 +5 +6
Page 6
Wilson says both 6 and 6 have an absolute value of 6. Is
Wilson correct? Use the number line and words to explain why
or why not.
Yes, Wilson is right since "negative numbers" don't exist when you find the absolute value.
How Do You Define Absolute Value?Without taking into account direction, absolute value describes how far a number is from zero on the number line.A number's absolute value can never be negative.A number or phrase is most frequently represented by the absolute value sign, which consists of two vertical straight lines, around it|-6| = 6 denotes that "6 is -6 in absolute terms.""The absolute value of the phrase -2 minus x" is what |-2 - x| denotes.The meaning of -|x| is "the opposite of the absolute value of x."The number line can be used to graph equalities and inequalities that contain expressions with absolute value in addition to displaying the distance from zero.Therefore, Wilson is correct as there is no negative term in absolute value.
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(6, y) and (-8, 4); slope: 1/7
For the given points (6, y) and (-8, 4) having slope = 1/7 the value of y = 10.
What is the slope of a line?
A line's slope, also known as its gradient, is defined as the value of a line's steepness or direction in a coordinate plane. Slope can be calculated using various methods given a line equation or the coordinates of points on a straight line.
If P(a, b) and Q(c, d) are two given points on a coordinate plane, then the slope of line PQ can be computed using the formula
[tex]Slope(m)=\frac{d - b}{ c - a}[/tex]
The given points are (6, y) and (-8, 4).
and the slope of the line is given as m = 7.
By using the slope of a line formula, we get
[tex]m = \frac{8-y}{-8-7}\\\\ \frac{1}{7}= \frac{8-y}{-8-7}\\\\\frac{1}{7}= \frac{8-y}{-14}\\\\\\8-y=-2\\y=8+2\\y=10[/tex]
Hence, the value of y is 10.
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A boy paid $11
for a bottle with a cork.
A bottle costs $10
more than a cork.
How much does a cork cost?
Step-by-step explanation:
A boy paid $11 for a bottle with a cork. A bottle costs $10 more than a cork. How much does a cork cost?
cork: c
bottle: 10c
c + 10c = 11
11c = 11
c = $1
A cork costs $1
33.21 divided by 9
What is the answer? And can you explain pls
Answer:
[tex]33.21 = \frac{3321}{100} \\ \\ \frac{33.21}{9} = \frac{3321}{100 \times 9} = \frac{3321}{900} = \frac{369}{100} = 3.69[/tex]Step-by-step explanation:
Thanks
Ingia went to the farmers market to get ingredients. Determine the price per item of each vegetable.
4.1 6 onions for $1.80
12 mushrooms for $3 4.3 5 peppers for $5.50
4.2
Tina has 5345 beads . She has 3687 fewer beads than her sister . How many beads does her sister have ?
Answer:
Her sister has 9032 beads
Step-by-step explanation:
All you have to do is Tina's beads plus the extra number of beads that her sister has
5345 + 3687 = 9032
a - domain and range
b - intercepts
c - horizontal asymptotes
d - vertical asymptotes
e - oblique asymptotes
From given graph,
a - domain and range: (-∞, 3) ∪ (3, ∞)
b - intercepts: x = 0 and y = 0
c - horizontal asymptotes: y = 3
d - vertical asymptotes: x = 3
e - oblique asymptotes: No
In this question, we have been given a graph of a function.
From given graph we need to answer the following questions.
1) domain of function: (-∞, 3) ∪ (3, ∞)
the range of function : (-∞, 3) ∪ (3, ∞)
2) the intercepts:
x = 0, y = 0
3) horizontal asymptotes
A red dotted line y = 3 is a horizontal asymptotes
4) vertical asymptotes
A red dotted line x = 3 is a vertical asymptotes
5) Oblique asymptotes
The graph of function does not have any Oblique asymptotes
Therefore, from given graph,
a - domain and range: (-∞, 3) ∪ (3, ∞)
b - intercepts: x = 0 and y = 0
c - horizontal asymptotes: y = 3
d - vertical asymptotes: x = 3
e - oblique asymptotes: No
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Differentiate the function with respect to x.
Differentiation of the function [tex]f(x) = (-x^{2} - 4)x^{5}[/tex] with respect to [tex]x[/tex] is [tex]f'(x) = -7x^{6} - 20x^{4}[/tex].
What is the differentiation of the function?
A function differentiation is a method of displaying the rate of change of a function at a given moment. It is the slope of the tangent line at a point on a graph for real-valued functions.
We have,
[tex]f(x) = (-x^{2} - 4)x^{5}[/tex]
By simplifying the given function, we get
[tex]f(x) = -x^{7} - 4x^{5}[/tex]
Now, we will differentiate the given function with respect to [tex]x[/tex].
[tex]\frac{d}{dx} f(x) = \frac{d}{dx} (-x^{7} - 4x^{5})[/tex]
[tex]f'(x) = \frac{d}{dx} (-x^{7}) - \frac{d}{dx} (4x^{5}))[/tex]
[tex]f'(x) = -7x^{6} - 20x^{4}[/tex]
Hence, differentiation of the given function with respect to [tex]x[/tex] is [tex]f'(x) = -7x^{6} - 20x^{4}[/tex].
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Find the side length of x. Round your answer to nearest hundredth
Answer:
9
Step-by-step explanation:
I hope this helps!
HELP PLEASE ASAP 30 POINTS PLUS BRAINLEST Find the sum of (8.7 x 10^6) and (5.5 x 10^5). Write the final answer in scientific notation.
14.2 x 10^11
1.42 x 10^10
9.25 x 10^6
9.25 x 10^5
A cone has a volume of 2411.52 cubic millimeters and a radius of 12 millimeters. What is its height? Use ≈ 3.14 and round your answer to the nearest hundredth.
The height of the cone given the volume of 2411.52 cubic millimeters and a radius of 12 millimeters is 16 millimeters.
How to find height of a cone?Volume of a cone = 2411.52 cubic millimetersRadius of the cone = 12 millimetersVolume of a cone = 1/3πr²h
2411.52 = 1/3 × 3.14 × 12 x 12 × h
2411.52 = 1/3 × 3.14 × 144h
2411.52 = 452.16h / 3
cross product7,234.56 = 452.16h
divide both sides by 452.16h = 7,234.56 / 452.16
h = 16 millimeters
In conclusion, the height of the cone is given by 16 milliliters.
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In a psychology class, 30 students have a mean score of 87.7 on a test. Then 21 more students take the test
and their mean score is 67.7.
What is the mean score of all of these students together? Round to one decimal place.
mean of the scores of all the students.
The mean score of all the students is 79.5 and it is round off into one decimal place.
Mean
Mean refers the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
Given,
In a psychology class, 30 students have a mean score of 87.7 on a test. Then 21 more students take the test and their mean score is 67.7.
Here we need to find the mean score of all students.
In order order to find the mean score, we have to calculate the total score of the students by multiplying the mean score by the number of students then we get,
=> 30 x 87.7 = 2631
Similarly, the total score for 21 students is,
=> 21 x 67.7 = 1421.7
So, the 51 students, cumulative score is
=> 2631 + 1421. 7 = 4052.7
Therefore, the mean score is calculated as,
=> 4052.7/51
=> 79.464
When we round off the value into one decimal place then we get
=> 79.5
Therefore, the mean value of all the students is 79.5.
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The store bought a pair of shoes for $50 and sold them for $80. What percentage was the markup?
Answer: They resold them for $30 more than the original price.
Answer: 37.5%
Step-by-step explanation:
$80 - $50 = $30,
$30/$80 = 0.375 > 37.5%
Solve for r.
r/3 + 16 = 19
Answer:
r = 9
Step-by-step explanation:
Hello!
Solve for r by isolating the variable.
Solve for r[tex]\frac r3 + 16 = 19[/tex] Subtract 16 from both sides[tex]\frac r3 = 3[/tex] Multiply both sides by 3[tex]r = 9[/tex]The value of r is 9.
△MNP≅△QST.
What is m∠S?
Enter your answer in the box.
Answer:
78°
Step-by-step explanation:
∠M=∠Q
∠N=∠S
∠P=∠T
Answer:
m∠S =78°---------------------
Given
Two congruent triangles △MNP≅△QSTWe know that corresponding angles of congruent triangles are congruent (vertices in same order as name of triangle):
∠M ≅ ∠Q, ∠N ≅ ∠S, ∠P ≅ ∠TAngle S corresponds to angle N, hence their values are equal:
m∠S = m∠N = 78°The radius of a circle is 8 ft. Find its area in terms of pi
Answer:
Step-by-step explanation:
201.06ft²
Answer:
Step-by-step explanation:
Step 1: –10 + 8x < 6x – 4
Step 2: –10 < –2x – 4
Step 3: –6 < –2x
Step 4: ________
What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?
x < –3
x > –3
x < 3
x > 3
Answer: x < 3
Explanation: Once you reach step 3, you divide -2 on both sides. -2x cancels out, and -6 divided by -2 is 3
If using the method of completing the square to solve the quadratic equation
x² - 13x +31 = 0, which number would have to be added to "complete the
square"?
To make a square using the method of completing the square.
[ (a + b)² = a² + 2ab + b² ]
[ (a - b)² = a² - 2ab + b² ]
x² - 13x + 31 = 0
(x - 13/2)² + (293/4) = 0
The number added to complete the square is 293/4.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
x² - 13x + 31 = 0
To make a square using the method of completing the square.
[ (a + b)² = a² + 2ab + b² ]
[ (a - b)² = a² - 2ab + b² ]
x² - 2 x (13/2)x + (13/2)² - (13/2)² + 31 = 0
(x - 13/2)² + 169/4 + 31 = 0
(x - 13/2)² + (293/4) = 0
Thus
The number added to complete the square is 293/4.
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What is the range of the given function?
{(-2, 0), (-4, -3), (2, −9), (0, 5), (−5, 7)}
O {x|x = -5, -4, -2, 0, 2)
Oyly = -9, -3, 0, 5, 7)
{x|x = -9, -5, -4, -3, -2, 0, 2, 5, 7}
Oyly = -9, -5, -4, -3, -2, 0, 2, 5, 7}
The range of the given function is:
Range: {-9,-3,0,5,7}
We are given ordered pair of set (x,y)
where, first value of ordered pair shows domain of function and second value of ordered pair shows range.
Range: It is output value of function.
Ordered pair: {(–2, 0), (–4, –3), (2, –9), (0, 5), (–5, 7)}
We can write as:
f(-2)=0, f(-4)=-3, f(2)=-9, f(0)=5, f(-5)=7
The values of f(x) are the range of function.
We will make a set of second value of all ordered pair of given set.
Range: {-9,-3,0,5,7}
Hence we get the required range of the function.
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ching and his 4 brothers set up computers at their family company. how many computers did they set up if they each set up the same number of computers?
There are '5n' computers set up if they each set up the same number of computers.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Ching and his 4 brothers set up computers at their family company.
Now,
Let the number of computers for each person = n
The total number of persons = 5
So, We can formulate;
⇒ The number of computers set up if they each set up the same number of computers = 5n
Thus, There are '5n' computers set up if they each set up the same number of computers.
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