The course of the Iditarod Trail ultra-marathon is approximately 38.09524 times longer than the course of the Boston Marathon.
Explanation:To find out how many times longer the course of the Iditarod Trail ultra-marathon is compared to the Boston Marathon, we can divide the length of the Iditarod Trail ultra-marathon by the length of the Boston Marathon.
Length of Iditarod Trail ultra-marathon = 1.6x106 meters
Length of Boston Marathon = 4.2x104 meters
Dividing the length of the Iditarod Trail ultra-marathon by the length of the Boston Marathon:
1.6x106 / 4.2x104 = 38.09524
The course of the Iditarod Trail ultra-marathon is approximately 38.09524 times longer than the course of the Boston Marathon.
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The course of the Iditarod Trail ultra-marathon is about 38.095 times longer than the course of the Boston Marathon.
Explanation:To determine how many times longer the course of the Iditarod Trail ultra-marathon is compared to the Boston Marathon, we can divide the length of the Iditarod Trail (1.6×106 meters) by the length of the Boston Marathon (4.2×104 meters). Performing the division, we get:
(1.6×106 meters) / (4.2×104 meters)
= 38.095
The course of the Iditarod Trail ultra-marathon is about 38.095 times longer than the course of the Boston Marathon.
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Greta must volunteer 225 hours for a community service project. She plans to volunteer for 6 hours
each week. The sequence shown represents the number of volunteer hours she has left after three
weeks have passed.
225, 219, 213, 207, ...
a.
A. Describe this sequence.
B. Use a formula to determine how many volunteer hours Greta has left to fulfill her requirement after 33 weeks have passed. Show your work.
C. Which formula should you use to determine how many volunteer hours Greta has left to fulfill her requirement after 40 weeks have passed? Explain your reasoning.
D. Calculate the number of volunteer hours Greta has left to fulfill her requirement after 40 weeks have passed. Explain what your answer means in terms of the problem situation.
Answer:
A. "an arithmetic sequence with a common difference (d) of -6."
B. 33 hours
C. [tex]a_n=a_1+(n-1)d[/tex]
D. See below
Step-by-step explanation:
A.
Since the sequence lessens by 6, this is an arithmetic sequence with a common difference (d) of -6.
B.
The formula for term of arithmetic sequence is:
[tex]a_n=a_1+d(n-1)[/tex]
Wher a_1 is the first term and d is the common difference. Since we want to find after 33 weeks, we plug in 33 into n:
[tex]a_{33}=225 + (-6)(33-1)\\a_{33}=33[/tex]
She will have left 33 hours
C.
We will use the arithmetic sequence term formula written above, that is:
[tex]a_n=a_1+(n-1)d[/tex]
THis gives us the amount of hours left after a certain number of weeks.
D.
We plug in 40 into n and find the hours left:
[tex]a_{40}=225+(40-1)(-6)\\a_{40}=225-234\\a_{40}=-9[/tex]
THis term is NEGATIVE, which means that Greta will not have to work 40 weeks to fulfill the target of 225 hours. She needs to work less.
This sequence represents the number of volunteer hours Greta has left after each week has passed. After 33 weeks, Greta has 27 hours left to fulfill her requirement. After 40 weeks, the formula gives a negative value, which means she has completed her requirement and has 15 extra hours of volunteer work completed.
Explanation:a. This sequence represents the number of volunteer hours Greta has left after each week has passed for her community service project.
b. To determine how many volunteer hours Greta has left after 33 weeks, we can subtract the number of hours she has volunteered in those 33 weeks from the initial requirement of 225 hours. Therefore, Greta has 225 - (6 * 33) = 225 - 198 = 27 hours left.
c. To determine how many volunteer hours Greta has left after 40 weeks, we can use the same formula as in part b. Therefore, Greta has 225 - (6 * 40) = 225 - 240 = -15 hours left.
d. Since we cannot have negative hours, the answer in part c does not make sense in the context of the problem situation. It means that Greta has fulfilled her requirement and has 15 extra hours of volunteer work completed.
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Find the area of a trapezoid with bases of 6 and 14 and height of 8
Answer:
Trapezoid Area = (Sum of Bases / 2) * Height =
(6 + 14 / 2) * Height =
10 * 8 =
80
Step-by-step explanation:
if chocolate chips have 20 calories in 1 tbsp how many calories are in 1 cup
Answer: 320
Step-by-step explanation:
there are 16 tablespoons in one cup so 20*16=320
To calculate the calories in one cup of chocolate chips, you multiply the number of calories per tablespoon (20) by the number of tablespoons in a cup (16), resulting in 320 calories per cup.
To determine how many calories are in 1 cup of chocolate chips, knowing that there are 20 calories in 1 tablespoon, we first need to understand the conversion between tablespoons and cups. There are 16 tablespoons in a cup.
Therefore, to find out how many calories are in a full cup, you would simply multiply the number of calories in one tablespoon by the number of tablespoons in a cup:
20 calories / tablespoon × 16 tablespoons / cup = 320 calories / cup.
Thus, there are 320 calories in 1 cup of chocolate chips.
A baby robin eats 14 feet of earthworms every day. Find the number of miles a robin would eat in its first year.
Solve for X:
8x - 41°
4x + 35°
Answer:
This is not an linear equation thus cant be solved
Answer Step-by-step explanation:
[tex]The~question~here~is~not~a~linear~equation.~So~this~can~not~be~solved~![/tex]
17) Given f(x) = 2x + 4, if the output is 12, what is the input? (Solve for x)
_ as an ordered pair:(, )
Answer:
the answer is 8 because when you set the equation equal to 12 and solve it you get 12
Step-by-step explanation:
Final answer:
To find the input for f(x) = 2x + 4 when the output is 12, solve the equation 12 = 2x + 4 for x, resulting in the input-value x being 4, with the ordered pair being (4, 12).
Explanation:
The question concerns finding the input for a given function when the output is known. The function provided is f(x) = 2x + 4, and we want to find the input value, or x, that produces an output, or f(x), of 12. To do this, we set up an equation where 12 = 2x + 4 and solve for x.
We first subtract 4 from both sides of the equation to get 8 = 2x. Then, we divide both sides by 2 to isolate x, resulting in x = 4.
The ordered pair representing the input-output relationship for the function when the output is 12 is (4, 12).
What number is a multiple of 12
Good evening ,
______
Answer:
{ ... , -24, -12 ,0 , 12 , 24 , 36 , ... }
___________________
Step-by-step explanation:
Any number that can be written in the form: 12×k is a multiple of 12 , k∈Z
12×0=0 then 0 is a multiple of 12
12×1=12 then 0 is a multiple of 12
12×2=24 then 0 is a multiple of 12
12×3=36 then 0 is a multiple of 12
12×4=48 then 0 is a multiple of 12
.
.
.
etc.
___________
:)
if two circles have the same circumfrence, what do you know about their areas
Answer:
They would have the same area.
Step-by-step explanation:
The area of a circle = pi x the circumfrence. or pi x the radious squared. so if they had the same circumfrence they would have the same area.
Sole this equation:
2x-15=43
Answer: Your answer would have to be x= 29
Answer:
x=29
Step-by-step explanation:
43+ 15 is 58
58 divided by 2 is 29
2*29= 58
58-15=43
Each data pair shown is of the form below:
(years since purchase, value of car)
Based on the correlation coefficient, there is a(n)
linear correlation between the
data
Answer:
Each data pair shown is of the form below:
(years since purchase, value of car)
Based on the correlation coefficient, there is a(n) strong linear correlation between the data.
Use the regression equation to estimate the value of the car 8 years after purchase. Round to the nearest dollar. $ 6019
As more years go by, the prediction (extrapolation) becomes less reliable.
Explanation:
the answer are in bold :)
Based on the correlation coefficient, there is a(n) strong linear correlation between the data.
The correlation coefficient, often denoted as "r," measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, with:
r = 1 indicating a perfect positive linear correlation (as one variable increases, the other increases proportionally).r = -1 indicating a perfect negative linear correlation (as one variable increases, the other decreases proportionally).r = 0 indicating no linear correlation (variables are not related linearly).The regression equation to estimate the value of the car 8 years after purchase, as more years go by, the accuracy of this prediction becomes less reliable.
Thus, there is strong linear correlation.
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Simplify these expressions. a.2r+3+4r. b.8+3d+d. c.mn+ (-3mm)+6 d. 10s + (-10) + (-4s)
Step-by-step explanation:
Combine like terms
a. 2r + 3 + 4r = (2r + 4r) + 3 = 6r + 3
b. 8 + 3d + d = (3d + d) + 8 = 4d + 8
c. mn + (-3mn) + 6 = (mn - 3mn) + 6 = -2mn + 6
d. 10s + (-10) + (-4s) = (10s - 4s) - 10 = 14s - 10
Terms are called "like terms" if they have the same variable part (the same letters in the same powers). Like terms differ at most coefficient.
Answer:
a. 2r + 3 + 4r
Combine the coefficients of the like monomials.
(2 + 4 = 6)
Answer: 6r + 3
b. 8 + 3d + d
Combine the coefficients of the like monomials.
(3 + 1 = 4)
Answer: 8 + 4d
c. mn + (–3mn) + 6
Combine the coefficients of the like monomials.
[1 + (–3) = –2]
Answer: –2mn + 6
d. 10s + (–10) + (–4s)
Combine the coefficients of the like monomials.
[10 + (–4) = 6]
Answer: 6s + (–10)
Step-by-step explanation:
straight from Penn
Can you help me with number 7?
Answer:
512 in³
Step-by-step explanation:
Given the volume (V) of a cube is calculated using
V = s³ ← s is the side length
When s = 8, then
V = 8³ = 8 × 8 × 8 = 64 × 8 = 512 in³
Answer: 512 in.³
Step-by-step explanation: To find the volume of a cube, first start with writing down the formula for the volume of a cube which is as followed.
Volume = Length × Width × Height
In this problem, our prism is a cube. Since the length, width, and height of a cube are all equal, we can find the volume of a cube by simply multiply side times side times side or s³.
Volume = Length x Width x Height
Volume = (8) (8) (8)
Volume = 512 in³.
Therefore, the volume of the cube is 512 in.³.
Evaluate (4+4×4-5)×2
Answer:
30
Step-by-step explanation:
By following PEMDAS
P - parenthesis | E - exponent | M - multiply | D - divide | A - add | S - subtract
You first work out what is in the parenthesis first. The order of operation would first have you multiply 4×4 = 16, next you will add 4 and subtract 5... 4-16+5 = 15. Finally multiply to what's outside the parenthesis (15)×2. And that's how you arrive to 30 as the final answer.
122200000000000000000000000000000000000 in scientific notation
Answer:
1.222x10^38
Step-by-step explanation:
there are 35 0's in the number
John made 12 dollars per delivery plus a base pay of 30 dollars.
If he made 150 dollars, how many deliveries did John make
Answer:
10
Step-by-step explanation:
$150 minus the base pay of $30 is $120. Divide this by the $12 he makes each delivery. 120/12=10
what is the distance between -4 and -1 on a number line
Answer: The distance is 3.
Step-by-step explanation: Start on a number line from 0. Go back 4 and mark it at -4. Then go back to 0 and go back 1 and mark it at -1. If you count the space between -4 and -1 you will get 3 spaces.
61/6 to mixed number
Answer:
10 1/6
Step-by-step explanation:
61/6= 10.1666667
Answer: 10 1/6
Divide using long division, the whole number proportion will be the number of times the denominator of the original fraction divides evenly into the numerator of the original fraction, and the fraction portion of the mixed number will be the remainder of the original fraction division over the denominator of the original fraction.
What is the area of the following circle? d = 10
Answer:100
Step-by-step explanation:
10*10
Answer:
78.54
Step-by-step explanation:
The radius of this is 5 (diameter divided in half is radius). 5 squared is 25, then you multiply that by 3.14. Voila!
A lot is 60 m by 38 m. A house 23 m by
9 m is built on the lot. How much area is left over?
Answer:
2073m
Step-by-step explanation:
House Area:
23*9 = 207m
Lot Area:
60*38 = 2208m
We can make an equation,
Lot Area - House Area = LeftOver Area
2208-207=2073m
–27x^6b^9 as a cube of a monomial
[tex]\bf -27x^6b^9~~ \begin{cases} -27=&-3^3\\ x^6=&x^{2\cdot 3}\\ &(x^2)^3\\ b^9=&b^{3\cdot 3}\\ &(b^3)^3 \end{cases}\implies (-3)^3(x^2)^3(b^3)^3\implies (-3x^2b^3)^3[/tex]
y
=
–x + 4
x + 2y
=
–8
How many solutions does this linear system have?
one solution: (8, 0)
one solution: (0, 8)
no solution
infinite number of solutions
Answer:
one solution
Step-by-step explanation:
Given two equation
y = -x+4 ... (1)
x+2y = -8 ...(2)
Substituting equation (1) into (2), we will have;
x+2(-x+4) = -8
Opening the bracket up
x-2x+8 = -8
-x = -8-8
-x = -16
x = 16
Substituting x = 16 back into equation 1:
y = -16+4
y = -12
This shows that the linear equation has one solution (16,-12)
Andrea is buying some new shirts and sweaters. She is able to buy 3 shirts and 2 sweaters for $114, or she is able to buy 2 shirts and 4 sweaters for $164. How much does a shirt cost? How much does a sweater cost ?
Answer:
The cost of a shirt is $16 and the cost of a sweater is $33
Step-by-step explanation:
Let
x -----> the cost of a shirt
y -----> the cost of a sweater
we know that
[tex]3x+2y=114[/tex] -----> equation A
[tex]2x+4y=164[/tex]----> equation B
Solve the system by graphing
Remember that the solution of the system is the intersection point both graphs
The solution is the point (16,33)
see the attached figure
therefore
The cost of a shirt is $16 and the cost of a sweater is $33
Answer:
The cost of each shirt is 16$ and the cost of each sweater is 33$
Solution:
Let us consider “x” as the cost of each shirt and “y” as the cost of each sweater.
From question, Andrea has bought 3 shirts and 2 sweaters for 114$. Hence we form equation as,
3x + 2y = 114 ------ eqn 1
Similarly, Andrea has bought 2 shirts and 4 sweaters for $164. Hence we form equation as,
2x + 4y = 164 ----- eqn 2
By solving equation 1 and equation 2, we get the value of “x” and “y”.
On multiplying equation 1 by 2,we get
6x + 4y = 228 -------- eqn 3
Now solving eqn 2 and eqn 3
6x + 4y = 228
-2x - 4y = -164
4x + 0y = 64
4x = 64
[tex]x = \frac{64}{4}[/tex]
x = 16
Substituting the value of x in eqn 1, we get
3(16) + 2y = 114
48 + 2y = 114
2y = 114 - 48
2y = 66
[tex]y = \frac{66}{2}[/tex]
y = 33
Thus the values of x and y are 16 and 33. So the cost of each shirt is 16$ and the cost of each sweater is 33$
Please help *picture attached*
Answer:
[tex]\large\boxed{2.15\cdot10^{-3}}[/tex]
Step-by-step explanation:
[ttex]\text{The scientific notation:}\ a\cdot10^k\\\\\text{where}\ 1\leq a<10,\ k\in\mathbb{Z}[/tex]
[tex]\bold{METHOD\ 1:}\\\\10^{-3}=\dfrac{1}{10^3}=\dfrac{1}{1000}=0.001\qquad\text{used}\ a^{-n}=\dfrac{1}{a^n}\\\\2.8\cdot10^{-3}=2.8\cdot0.001=0.0028\\\\2.8\cdot10^{-3}-0.00065=0.0028-0.00065=0.00215\\\\0\underbrace{.002}_{3\to}15=2.15\cdot10^{-3}[/tex]
[tex]\bold{METHOD\ 2:}\\\\2.8\cdot10^{-3}-0.00065=2.8\cdot10^{-3}-0.65\cdot10^{-3}\\\\=(2.8-0.65)\cdot10^{-3}=2.15\cdot10^{-3}[/tex]
what is the slope ( 6, 5 ) and ( -6,9 )
[tex]\bf (\stackrel{x_1}{6}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{9}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{9}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{-6}-\underset{x_1}{6}}}\implies \cfrac{4}{-12}\implies -\cfrac{1}{3}[/tex]
Answer:
[tex]\large\boxed{slope=-\dfrac{1}{3}}[/tex]
Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
(x₁, y₁), (x₂, y₂) - points on a line
We have the points
(6, 5) → x₁ = 6, y₁ = 5
(-6, 9) → x₂ = -6, y₂ = 9
Substitute:
[tex]m=\dfrac{9-5}{-6-6}=\dfrac{4}{-12}=-\dfrac{4:4}{12:4}=-\dfrac{1}{3}[/tex]
How many solutions are there to the equation below?
12x + 6 = 5x
A. 0
B. Infinitely many
C. 1
Answer:
C
Step-by-step explanation:
This is a linear equation in one variable and has 1 solution
12x + 6 = 5x ( subtract 5x from both sides )
7x + 6 = 0 ( subtract 6 from both sides )
7x = - 6 ( divide both sides by 7 )
x = - [tex]\frac{6}{7}[/tex] ← 1 solution
The equation has a single solution for x, which is -6/7. The correct answer is: C. 1
To determine the number of solutions to the equation 12x + 6 = 5x, let’s solve the equation step by step.
First, we need to get all terms with the variable x on one side of the equation and constants on the other side. To do this, we can subtract 5x from both sides of the equation:
12x + 6 - 5x = 5x - 5x
This simplifies to:
7x + 6 = 0
Now we need to isolate the term with the x variable, so we subtract 6 from both sides of the equation:
7x + 6 - 6 = 0 - 6
This further simplifies to:
7x = -6
Finally, to solve for x, we divide both sides by 7:
7x / 7 = -6 / 7
x = -6/7
Therefore, the equation has a single solution for x, which is -6/7.
The correct answer is:
C. 1
What is the equation that is parallel to the equation
-9x + 3y = 8 and crosses through the point (14, 2)?
what is 7x(-3)x(-2)2=?
Answer:
-24x+2
Step-by-step explanation:
7x(-3) = -21x
x(-2) = -2x
x
2
-24x+2
How hard is the permit test?
The difficulty of the permit test can vary, but with proper preparation and study of the driver's handbook, most individuals can pass the test.
The difficulty of the permit test can vary depending on the individual's level of preparation and understanding of the rules of the road, traffic laws, and safe driving practices. The test typically consists of multiple-choice questions based on information found in the state's driver's handbook.
To pass the permit test, one should:
1. Study the driver's handbook thoroughly, as it contains all the necessary information.
2. Take practice tests to become familiar with the format and types of questions that may be asked.
3. Understand traffic signs, signals, and markings, as well as the rules for sharing the road with other drivers, pedestrians, and cyclists.
4. Learn about the consequences of driving under the influence of alcohol or drugs.
5. Be aware of the laws regarding distracted driving, such as texting while driving.
By dedicating time to study and understand these concepts, most individuals find that they can pass the permit test. It is designed to ensure that new drivers have the knowledge required to drive safely and responsibly.
The difficulty of the permit test can vary, but with proper preparation and study of the driver's handbook, most individuals can pass the test.
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Find the value of x.
Answer:
x = 121
Step-by-step explanation:
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
Here n = 7, thus
sum = 180° × 5 = 900°
Sum the given angles and equate to 900
x + 125 + 119 + 117 + 145 + 133 + 140 = 900, that is
x + 779 = 900 ( subtract 779 from both sides )
x = 121
What else would need to be congruent to show that ABC =XYZ by SAS?
Given:
AB=XY
A=X
In this Congruence of Triangles question, To show that ABC = XYZ by SAS congruence, we also need to show that AC = XZ and ∠A = ∠X.
To show that ABC = XYZ
AB = XY (Given)
A = X (Given)
To prove ABC = XYZ by the Side-Angle-Side (SAS) congruence postulate, we need to show that one pair of corresponding sides and the included angle are congruent. In this case:
AC = XZ (By the reflexive property of congruence)
∠A = ∠X (Given)
Therefore, to fully demonstrate the congruence between the two triangles ABC and XYZ, we also need to show that AC = XZ and ∠A = ∠X.
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We can tell this side on triangle ABC is BC, and the side on triangle XYZ is YZ, so the answer must be B.
SAS stands for side-angle-side, which indicates that for two triangles to be congruent, all two sides and the angle they produce must be congruent and equal.
You have an angle, <B and <Y, and a side, AB and XY, in this instance. The last side, which produces angle B along with side AB on triangle ABC and angle Y along with side XY on triangle XYZ, is all that is needed to finish this.
In this case, you have a side—AB and XY—and an angle, <B and <Y. To complete this, you simply need the final side, which forms angle B along with side AB on triangle ABC, and forms angle Y along with side XY on triangle XYZ.
By looking at the diagram, you can tell this side on triangle ABC is BC, and the side on triangle XYZ is YZ, so the answer must be B. The answer must be the sides of triangles ABC and XYZ are, respectively, BC and YZ.