The first five terms in the sequence generated by the explicit formula [tex]y_n[/tex] = -5n - 5 are: -10, -15, -20, -25, -30.
To generate the first five terms in the sequence using the explicit formula [tex]y_n[/tex] = -5n - 5,
we substitute the values of n from 1 to 5 into the formula.
For n = 1:
[tex]y_1[/tex]= -5(1) - 5 = -10
For n = 2:
[tex]y_2[/tex] = -5(2) - 5 = -15
For n = 3:
[tex]y_3[/tex] = -5(3) - 5 = -20
For n = 4:
[tex]y_4[/tex] = -5(4) - 5 = -25
For n = 5:
[tex]y_5[/tex] = -5(5) - 5 = -30
Therefore, the first five terms in the sequence generated by the explicit formula [tex]y_n[/tex] = -5n - 5 are:
-10, -15, -20, -25, -30.
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Assume the availability of a function is_prime. Assume a variable n has been associated with positive integer. Write the statements needed to compute the sum of the first n prime numbers. The sum should be associated with the variable total.
Note: is_prime takes an integer as a parameter and returns True if and only if that integer is prime.
To find the sum of the first n prime numbers, use a while loop to add each prime number to a total. Use a function is prime to check if each integer is prime. Continue the loop until you've added n primes.
Explanation:To compute the sum of the first n prime numbers, you would first initialize the total and the count of primes to 0. Then, for each integer starting from 2, you would check if it is prime using the is prime function. If it is prime, you would add it to the total and increment the count of primes. This loop would continue until the count of primes reaches n.
Here is how the code might look in Python:
total = 0This code uses a while loop to continue adding prime numbers to the total until it has added the first n primes. The total of the prime numbers is updated inside an if statement that checks whether the current integer i is prime.
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Select the term that best describes the statement.
If a polygon has six sides, then it is a hexagon.
A. conjunction
B. disjunction
C. negation
D. conditional
Answer:
D. Conditional
Step-by-step explanation:
The statement is a conditional statement.
A science teacher has a supply of 50% sugar solution and a supply of 80% sugar solution. How much of each solution should the teacher mix together to get 105 ML of 60% sugar solution for an experiment
70 ML of the 50% solution and 35 ML of the 80% solution
35 ML of the 50% solution and 70 ML of the 80% solution
70 ML of the 50% solution and 70 ML of the 80% solution
35 ML of the 50% solution and 35 ML of the 80% solution
How to list rational numbers from least to greatest on a number line?
Scholastic Aptitude Test (SAT) scores are normally distributed with a mean of 500 points and a standard deviation of 100 points. Suppose you take the SAT and several weeks later you receive a letter telling you that your results on the math portion of the test were in the 95th percentile.
Recalling that SAT scores are always expressed as multiples of 10, how many points did you get on the test? ...?
Answer:
Step-by-step explanation:
Given that Scholastic Aptitude Test (SAT) scores are normally distributed with a mean of 500 points and a standard deviation of 100 points.
If X is the score in SAT, then X is N(500,100)
From std normal table we find 95th percentile as 1.645
i.e. your Z score = 1.645
Convert this to X score by [tex]X =1.645]\sigma + Mean\\= 1.645(100)+500\\=664.5[/tex]
Since expressed as multiples of 10, this equals 660
So points you got = 660
The following table represents Tracie's earnings:
1 hour $25
2 hours $50
3 hours $75
How much does she make per hour?
$25
$50
$75
$150
Determine the zeros of x^2 + 4x - 16 = -2x .
Gina invests $1,677 in an account paying 8.61% simple interest annually. How much interest has Gina gained after six years? a. $668.65 b. $240.65 c. $866.34 d. $2,543.34
Answer:
Option (c) is correct.
The interest gained by Gini in 6 years is $ 866.34
Step-by-step explanation:
Given: Gina invests $1,677 in an account paying 8.61% simple interest annually for 6 years.
We have to calculate the interest gained by Gina in 6 years.
Using formula for simple interest
[tex]S.I.=\frac{P\times I\times T}{100}[/tex]
Where,
S.I = simple interest
P is principal
R is interest rate
T is time
Given : P = $ 1677
R = 8.61%
T = 6 years
Substitute, we get,
[tex]S.I.=\frac{1677\times 8.61\times 6}{100}[/tex]
Simplify, we get,
S.I. = $ 866.3382
Rounding off to nearest hundred we get, Interest is $866.34
Thus, the interest gained by Gini in 6 years is $ 866.34
Gina has gained $866.34 in interest after six years.
To find the interest gained, we can use the formula: Interest = Principal * Rate * Time. In this case, the principal is $1,677, the rate is 8.61%, and the time is 6 years. Plugging these values into the formula, we get: Interest = $1,677 * 0.0861 * 6 = $866.34. Therefore, Gina has gained $866.34 in interest after six years.
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What comes next in the following sequence? 13, 1113, 3113, 132113
1337
1332113
1113122113
3313121221
11311242321
the answer is :
1332113
Shirabi spent $208 on a sewing machine to make purses. She spends a total of $10 on thread, fabric, and accessories for each purse and plans to charge $36 for each purse. The equation represents her break-even point, when x represents the number of purses sold.
208 + 10x = 36x
How many purses must she sell in order to break even?
5
6
7
8
Answer:
the answer is 8
Step-by-step explanation:
The total fare for two adults and three children on an excursion boat is $14. If each childs fare is one half of each adults fare, what is the adult fare ...?
Answer:
$4
Step-by-step explanation:
In order to solve this problem you just have to create an equation, and it´s very simple, each kid ticket will be represented by the letter "x", and as we know a kid´s ticket is worth half what is worth an adult ticket, so the adult ticket = 2 kids tickets=2x
So we know that there are 2 adults and three kids, and the totla was $14, we create our equation:
[tex]2 adults+3kids=14\\2(2x)+3x=14\\4x+3x=14\\7x=14\\x=\frac{14}{7}\\ x=2[/tex]
Now we know that the kids ticket is $2, so the adult ticket would be twice that, $4 is the price of the adult ticket.
A cookie recipe calls for two eggs and yields 4 dozen cookies. how many eggs would be necessary to make 10 dozen cookies?
Form a polynomial, f(x), with real coefficients having the given degree and zeros.
Degree: 4; zeros: 4i and 5i Form a polynomial, f(x), with real coefficients having the given degree and zeros.
Degree: 4; zeros: 4i and 5i
Final answer:
To form a polynomial with real coefficients, given non-real zeros 4i and 5i, include their conjugates -4i and -5i. Multiply the corresponding factors to get f(x) = (x^2 + 16)(x^2 + 25), which simplifies to f(x) = x^4 + 41x^2 + 400.
Explanation:
To form a polynomial, f(x), with real coefficients having a specified degree and given zeros, you must use the fact that non-real roots of polynomials with real coefficients come in conjugate pairs. Since 4i and 5i are given as zeros of the polynomial, their conjugates, -4i and -5i, must also be zeros of the polynomial.
The factors of the polynomial that correspond to these zeros are (x - 4i), (x + 4i), (x - 5i), and (x + 5i). To find the polynomial, these factors are multiplied together.
Multiplying the factors that come in conjugate pairs first:
Next, multiply these two results to obtain the polynomial:
(x^2 + 16)(x^2 + 25) = x^4 + 25x^2 + 16x^2 + 400 = x^4 + 41x^2 + 400
Therefore, the polynomial with degree 4 and zeros 4i and 5i is f(x) = x^4 + 41x^2 + 400.
To form the polynomial f(x) with real coefficients and given the zeros 4i and 5i, we use the conjugate pairs and multiply the resulting factors to get x⁴ + 41x² + 400.
To form a polynomial f(x) with real coefficients given the degree and zeros, we start by noting that complex roots always come in conjugate pairs when dealing with polynomials that have real coefficients. Hence, for the zeros 4i and 5i, the polynomial must also include the conjugate roots -4i and -5i.
Using these roots, we can form the factors:Thus, the polynomial f(x) is x⁴ + 41x² + 400.
If cos 65 degree +cos 55 degree = cos θ, find θ in radians
The given equation, cos 65° + cos 55° = cos θ doesn't follow normal trigonometric relationships. Therefore, a value for θ can't easily be computed without further transformations using a cosine formula. Converting θ from degrees to radians also wouldn't directly work due to the equation's specifics.
Explanation:This question pertains to the field of trigonometry. We have the equation cos 65° + cos 55° = cos θ and we need to find the value of θ in radians. Unfortunately, we cannot resolve this equation directly as the addition of cosines does not equal another cosine. However, one can use cosine formula to transform this equation and solve analytically with a lot of work.
To convert degrees to radians, you would use the formula: θ(radians) = θ(degrees) * π / 180. However, as noted, this task won't work directly for this problem due to the nature of the equation.
This is a particular challenge problem that might not have an easy solution that would fall into the regular high school curriculum.
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543,982 rounded to the nearest thousand
Is the following an example of inductive reasoning or deductive reasoning? Your soccer coach tells you it is wise to drink a lot of fluids during practice so you don’t get dehydrated. Before practice, you buy a two bottles of water and a bottle of sports drink to bring to practice.
A.Inductive reasoning
B.Deductive reasoning
The student buying water and a sports drink to avoid dehydration during soccer practice based on their coach's advice is an example of deductive reasoning, as it applies a general principle to a specific situation.
The scenario described involves a student purchasing fluids to prevent dehydration during soccer practice based on the advice from a coach. This example of reasoning is deductive reasoning. The coach has provided a general principle that drinking a lot of fluids prevents dehydration. The student applies this general principle to a specific situation (soccer practice) and takes action (buying water and a sports drink) to avoid dehydration. This reasoning starts from a general rule and applies it to a particular case, characteristic of deductive reasoning.
Factor 25x2 – 16.
A. (5x – 4)2
B. (5x + 1)(5x – 1)
C. (5x + 4)2
D. (5x + 4)(5x – 4)
Answer:
D. (5x + 4)(5x – 4)
Step-by-step explanation:
This is the difference of two squares
[tex]a^{2} - b^{2} = (a-b)(a+b)\\[/tex]
Following from above,
25[tex]25x^{2} -16[/tex]
Taking the elements of the expression
[tex]25x^{2} = 5^{2}x^{2}[/tex]
Using the law of indices,
[tex]a^{2} b^{2} = (ab)^{2}[/tex]
[tex]25x^{2} = (5x)^{2}[/tex]
[tex]16 = 4^{2}[/tex]
Therefore,
[tex]25x^{2} -16[/tex] = [tex](5x)^{2} - 4^{2}[/tex]
=[tex](5x-4)(5x+4)[/tex]
Hence the correct answer is Option D.
What is the maximum number of intersection points a hyperbola and a circle could have?
A. 4
B. 3
C. 1
D. 2 ...?
Answer: A. 4
Step-by-step explanation:
The characteristic equation of a circle is
[tex]x^2+y^2=r^2[/tex]
The characteristic equation of a hyperbola is
[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]
The intersection points will be obtained as the solution of the both characteristic equations.
[tex]x^2+y^2=r^2[/tex].......(1)
[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex].............(2)
⇒[tex]y^2=r^2-x^2[/tex].....(from 1)
put this in (2)
[tex]\frac{x^2}{a^2}-\frac{r^2-x^2}{b^2}=1[/tex]
⇒[tex]y^2=r^2-x^2\\\frac{x^2}{a^2}+\frac{-x^2}{b^2}=1+\frac{r^2}{b^2}[/tex]
⇒[tex]y^2=r^2-x^2\\x^2(\frac{1}{a^2}+\frac{1}{b^2})=1+\frac{r^2}{b^2}[/tex]
⇒[tex]y^2=r^2-x^2\\x^2(\frac{a^2+b^2}{a^2b^2})=\frac{b^2+r^2}{b^2}[/tex]
[tex]\Rightarrow\ x^2=\frac{a^2(b^2+r^2)}{a^2+b^2}\\y^2=\frac{b^2(r^2-a^2)}{a^2+b^2}[/tex]
So there are 2 different values of x and two different values of y, thus the maximum number of intersection points is 4.
Solve the following system equations:
2x + 4y – 3z = –7
3x + y + 4z = –12
x + 3y + 4z = 4
POSIBBLE ANSWERS:
(–6, 2, 1)
(6, 2, 1)
(6, –2, –1)
(–6, –2, –1)
...?
Answer:
The solution is (–6, 2, 1). (Option A)
Step-by-step explanation:
Given three equations
2x + 4y - 3z = -7 → (1)
3x + y + 4z = -12 → (2)
x + 3y + 4z = 4 → (3)
we have to find the solution of above equations.
By elimination method
Multiply equation (2) by 4 and then subtracting from (1), we get
(2x + 4y - 3z+7)-4(3x + y + 4z + 12)=0
⇒ -10x-19z=41 → (4)
Multiply equation (2) by 3 and then subtracting from (3), we get
(x + 3y + 4z - 4)-3(3x + y + 4z + 12)=0
⇒ -8x-8z=40 ⇒ x+z=-5 → (5)
Solving (4) and (5), we get
-10x-19z-41+10(x+z+5)=0
⇒ -9z=-9 ⇒ z=1
⇒ x+1=-5 ⇒ x=-6
and (3) implies -6 + 3y + 4 = 4 ⇒ y=2
Hence, the solution of above 3 equations will be (x,y,z)=(-6,2,1)
Hence, option (1) is correct.
Please help me with this question !
If triangle RST is congruent to triangle WXY and the area of triangle WXY is 20 square inches, then the area of triangle RST is 20 in.²
True
False
Answer:
statement is true
Step-by-step explanation:
Given : If triangle RST is congruent to triangle WXY and area of triangle WXY is 20 square inches, then the area of triangle RST is 20 in.
To find : Statement is true or false .
Explanation :
Yes,if two triangles are congruent then you can place one above the other perfectly and both cover the same region.
So,we can say that both have the same area.
But the conversion is not true .
Therefore, statement is true .
A young equestrian loved to ride her horse all day long, dreaming of the day she would ride in the Kentucky Derby. One day in early April, she left home at 10:00 am and rode her stallion at a nice, steady 10 miles per hour away from her house. At noon a call came in from the Derby saying she was in! Her father immediately jumped on his scooter to try and track her down and tell her the good news. Riding at a breezy 15 miles per hour, at what time will her father catch up to her?
The equestrian's father will catch up to her at 2:00 pm by using the concept of relative speed and calculating the time it will take for him to close the gap between them.
Explanation:The student's father will catch up to the equestrian at 2:00 pm. To solve this problem, we can use the concept of relative speed. The equestrian starts riding away from the house at 10 miles per hour (mph) at 10:00 am. By noon, when the father starts chasing her on his scooter at 15 mph, the equestrian is already 20 miles away (2 hours × 10 mph).
Since the father's speed is 15 mph and the equestrian's speed is 10 mph, the father is closing the gap at a speed of 15 mph - 10 mph = 5 mph. To cover the 20 miles gap, the father will need 20 miles / 5 mph = 4 hours. Therefore, if the father starts at noon, he will catch up to her at 4 hours later, which is 2:00 pm.
What is the description of one-hundredth of 36?
Answer:
0.36
Step-by-step explanation:
One - hundredth =[tex]\frac{1}{100}[/tex]
one hundredth means we have to divide 1 by hundred.
When we divide one by hundred we get 0.01
To find one-hundredth of 36, than we have to multiply 36 by 0.01
After multiplying we get
36×0.01=0.36
OR
36×[tex]\frac{1}{100}[/tex]=0.36
Hence, the correct answer is 0.36
One-hundredth of 36 is 0.36.
To find one-hundredth of 36, we simply need to divide 36 by 100. Dividing by 100 means shifting the decimal point two places to the left. Therefore, one-hundredth of 36 is 0.36.
For example, if we have the number 36, we can represent this as 36/1 to show that we have 36 whole parts. When we want one-hundredth of these 36 parts, we are seeking 1 part out of every 100 parts. So, we would write this as (36/1)/ (100/1) which simplifies to 36/100. After simplification, we get 0.36 as the final answer.
This concept is similar to understanding that 1 cm is 1/100th of a meter. By using division or understanding fractions and decimal places, we can easily find one-hundredth of any given number.
Sally went into the local dollar store because they have so many deals .the following deal that she was debating is 4 bars of soap that cost $5 .what would 8 bars cost her
AB is tangent to the circle at B m< A = 14 and mBC = 112 (The figure is not drawn to scale.
a.Find x
b.Find y.
a. The value of x ≈ 60°
b. The value of y ≈ 93°
The relevant relations are ...
external angle A is half the difference of intercepted arcs BC and BD
inscribed angle y° is half the measure of intercepted arc CD
the sum of arcs of a circle is 360°
Using these relations, we have ...
(a) A = (BC -x°)/2
x° = BC -2A = 112° -2(27°)
x° = 58°
(b) y° = CD/2 = (360° -BC -BD)/2 = (360° -112° -60°)/2
y° = 91°
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What is 0.0012 as a fraction
Bryce lives 26 miles from his grandmother's house .how many kilometers does bryce live from his grandmother's house? round your answer to the nearest tenth of a mile. 1km 0.62 mi
Ralph is 3 times as old as Sara. In 6 years, Ralph will be only twice as old as Sara will be then. Find Ralph's age now. Ralph's age is _____. A)6 B)12 C)18 D)24
Answer:
C)18
Step-by-step explanation:
Let Sara present age = x years.
According to question Ralph present age =3x
Sara age after 6 years =x+6.
Ralph age after 6 years =3x+6.
After 6 years Ralph will be only twice as old as Sara will be then.
3x+6=2(x+6)
Solving for x:
3x+6=2x+12
3x-2x=12-6
x=6.
Ralph present age = 3x=3(6)= 18 years.
Option C.
Number 7. I need to write a ladder diagram
The price of a coat is $114 before sales tax . The sales tax is 7%. Find the total cost of the coat
Final answer:
To calculate the total cost of the coat with a 7% sales tax, multiply the cost of the coat by 0.07 to get the sales tax amount of $7.98, then add it to the original cost for a total of $121.98.
Explanation:
To find the total cost of a coat that costs $114 with a 7% sales tax, you first need to calculate the amount of sales tax by converting the percentage to a decimal. Then multiply the decimail by the price of the coat to get the sales tax amount.
Here is the calculation for sales tax:
$114 × 0.07 = $7.98
Next, add the sales tax to the original price to find the total cost:
$114 + $7.98 = $121.98
So, the total cost of the coat, including sales tax, is $121.98.