If Amanda stays on her current course, she will go 72,000 km in three years.
Given data,
In the first four months after purchasing a new car, Amanda Chicopee covered 8,000 kilometers. How many miles will Amanda log in three years if she continues on her path?
Here,
She drove 8000 km in 4 months.
⇒ In 1 month = 8000/4 = 2000 km
To find how many miles in 3 years,
⇒ In 36 months = 2000 * 36
= 72000 km
Hence, 72000 km will Amanda log in three years if she continues on her path.
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9^2/9^-4 using a single positive exponent
Answer:
9⁶
Step-by-step explanation:
[tex]\dfrac{9^2}{9^{-4}} = 9^2 9^{4} = 9 ^ {(2 + 4)} = 9^6[/tex]
Reciprocal of a number raised to exponent is the same as the number raised to the negative of the original exponent
So
[tex]\dfrac{1}{9^{-4}} \text{ becomes } 9^4[/tex]
the population of the world was 7.1 billion in 2013, and the observed relative growth rate was 1.1% per year. (a) estimate how long it takes the population to double.
As the population of the world was 7.1 billion in 2013, and the observed relative growth rate was 1.1% per year and according to that it will take 63.36 years to double the population.
A population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic. In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study.
According to the question:
We have been given that the population of the world was 7.1 billion in 2013, and the observed relative growth rate was 1.1% per year.
A) Since we know that population increases exponentially, therefore we will use our given information to form an exponential model for population increase and then we will solve for the time by which our population will be double.
P(t) = [tex](1.011)^{t}[/tex]
⇒ [tex]7.1[/tex] × [tex]2 = 7.1 (1.011^{t}[/tex]
⇒ [tex]\frac{7.1 * 2}{7.1} = 1.011^{t}[/tex]
⇒ [tex]1.011^{t}[/tex] = 2
Now let us solve for t using logarithm.
[tex]ln(2) = ln(1.011)^{t}[/tex]
⇒ ln(2) = t . ln(1.011)
⇒ 0.6931471805599 = t × 0.0109399400383
⇒ t = 0.0109399400383/ 0.6931471805599
⇒ t = 63.3593217
⇒ t ≈ 63.36
Therefore, it will take 63.36 years the population to be double.
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I need HELP! I dont understand and need help!
algebra 2 please HELP
Answer:
[tex]y = 3.48(1.32)^{x}[/tex]
Step-by-step explanation:
8 = ab^3
42 = ab^9
b = 1.32
[tex]\frac{8}{(1.32)^{3} } =\frac{a(1.32)^{3} }{(1.32)^{3} }[/tex]
a = 3.48
Answer:
[tex]y = 3.48(1.32)^{x}[/tex]
Using your answer from the previous question, state the value of ‘w’ if the perimeter of the rectangle is equal to 37 feet and the length is equal to 4 feet.
Answer:
16.5
Step-by-step explanation:
hence the answer is 16.5 feet
What is the slope of the black line?
What is the slope of the blue line?
Answer:
Blue line: -1/2
Black line: 3/4
Step-by-step explanation:
The slope of the blue line is a negative cause its a negative slope and the slope of the black line is positive cause its a positive slope.
Hope it helps!
Could you please give me brainiest for this? Thank you!
how many integers can be represented as a difference of two distinct members of the set $\{1, 2, 3\}$?
We can represent 4 integers as a difference of two distinct members i.e. {1, -1, 2, -2}.
What are Integers ?
The collection of positive and negative integers is known as an integer. Integers, like whole numbers, do not include the fractional portion. Integers can therefore be defined as numbers that can be positive, negative, or zero but not as fractions.
Here, we have 3 distinct positive integers which are {1, 2, 3}.
We can list down the integers as a difference of the two distinct members as follows :
1 - 2 = -1
2 - 1 = 1
2 - 3 = -1
3 - 2 = 1
1 - 3 = -2
3 - 1 = 2
So, we can see clearly it is representing only 4 integers which are {1, -1, 2, -2}.
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what is 4 times (5+3) divided by 8-2
Answer: 5.3
Step-by-step explanation: First, you have to use PEMDAS and then you will get 32 divided by 6, which is 5.3 repeating
5а – 2 = 8
6
a = [?]
Answer:
5a=8+2
5a=10/:5
a=2
it is okay?
Colin buys a car for £45500.
It depreciates at a rate of 6% per year.
How much will it be worth in 3 years?
Give your answer to the nearest penny
where appropriate.
Use the appropriate normal distribution to approximate the resulting binomial distributions. A fair coin is tossed 130 times. What is the probability of obtaining between 56 and 73 tails, inclusive?.
The probability of obtaining between 56 and 73 tails, inclusive will be approximately 0.8561.
To approximate the resulting binomial distribution, we will use the normal distribution as an approximation when certain conditions are met.
The number of trials, n, is large n = 130.
The probability of success, p, is not too close to 0 or 1
Then the coin is fair, so p = 0.5.
We have to calculate the probability of obtaining between 56 and 73 tails, inclusive.
Mean (μ) = n x p = 130 x 0.5 = 65
Standard Deviation (σ) = √(np (1 - p))
(σ) = √(130 x 0.5 x 0.5) ≈ 5.7
Using a standard normal distribution, we can determine the z-scores corresponding to 56 and 73 tails:
z1 = (56 - μ) / σ ≈ (56 - 65) / 5.7
≈ -1.58
z2 = (73 - μ) / σ ≈ (73 - 65) / 5.7
≈ 1.40
P(56 ≤ x ≤ 73) ≈ P(-1.58 ≤ z ≤ 1.40)
Now we can determine these probabilities and subtract them.
P(-1.58 ≤ z ≤ 1.40) ≈ 0.9155 - 0.0594
P(-1.58 ≤ z ≤ 1.40) ≈ 0.8561
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ms. wilson's science test scores are normally distributed with a mean score of 84 (μ) and a standard deviation of 3 (σ). using the empirical rule, about 99.7% of the scores lie between which two values?
Using the empirical rule, about 99.7% of the scores lie between 75 to 93
In this question, we have been given ms. wilson's science test scores are normally distributed with a mean score of 84 (μ) and a standard deviation of 3 (σ).
We know that the empirical rule predicts that 99.7% within the first three standard deviations (µ ± 3σ).
An empirical rule is also known as 68-95-99.7 rule.
We find the interval (µ ± 3σ)
The upper value would be,
µ + 3σ
= 84 + 3(3)
= 84 + 9
= 93
and the lower value would be,
µ - 3σ
= 84 - 3(3)
= 84 - 9
= 75
Therefore, about 99.7% of the scores lie between (75, 93)
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the equation x^3-6x=72 has a solution between 4 and 5
The solution of the given equation is between 4 and 5.
What is solution of an equation?
The points where the lines representing the intersection of two linear equations intersect are referred to as the solution of a linear equation. In other words, the set of all possible values for the variables that satisfy the specified linear equation constitutes the solution set of the system of linear equations.
Consider the given equation,
x^3 - 6x = 72
Subtract 72 from both sides,
x^3 - 6x - 72 = 72 - 72
x^3 - 6x - 72 = 0
After solving this equation we get
x ≈ 4.63902
This value is exactly between the 4 and 5.
Hence, the solution of the given equation is between 4 and 5.
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# 3 Mia has $50 on a gift card to her favorite
coffee shop. Each time she visits the coffee
shop she spends $3.75 on her favorite drink.
Write an equation to represent the relationship
between n, the number of times she visits the
coffee shop, and b, the total balance on her
gift card.
+
The equation to represent the relationship between n, the number of times she visits the coffee shop, and b, the total balance on her gift card is b = - 3.75n + 50
How to represent a situation with equation?Mia has $50 on a gift card to her favourite coffee shop. Each time she visits the coffee shop she spends $3.75 on her favourite drink.
The equation to represent the relationship between n, the number of times she visits the coffee shop, and b, the total balance on her gift card can be represented as follows:
Therefore,
n = number of times she visit the coffee shopb = total balance on her gift cardHence, the equation is as follows;
b = - 3.75n + 50
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if you have 200 meters of fencing and want to enclose a rectangular area up against a long, straight wall, what is the largest area you can enclose?
1600 square meters is the greatest area that may be enclosed.
Rectangle.
The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.
If fencing is required for 200 meters, then the enclosed area's perimeter is 200 meters.
Perimeter of rectangle = 2(L + B)
2(L+B) = 200
Divide both sides by 2
L+B = 100
L = 100 - B
Here,
Area(A) = L X B
Substitute L = 100 - B into the equation above
A = (100 - B) x B
A = 100B - B²
At maximum area dA/dB = 0
dA/dB = 100 - 2B
100 - 2B = 0
2B = 100
B = 100/2
B = 50m
So L = 100 - 50
L = 50m
Maximum area to be enclosed = 50 x 50
Maximum area to be enclosed = 2500 square meters
In conclusion, the 2500 square meters of space that the fence will enclose
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HELP ME PLEASE!!! it’s for algebra and i really need to get this awnser right!! please literally anyone help me
Answer:
Below
Step-by-step explanation:
Start with point (3,5) slope (5/3) form:
(y-5) = 5/3 (x-3) expand
y-5 = 5/3 x -5 re-arrange by adding 5 to both sides
y = 5/3 x done!
I am in 6th grade, can somebody answer in 6th grade skill? Here is an incomplete equation of 534 divided by 6. I only have 4 minutes left and I am stressed out!!!!
The answer would be 89 after 534 divided by 6 and applying the concept of arithmetic operation.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.
It is given that:
534 divided by 6
[tex]\begin{matrix}\:\:\:\:\:\:\emptyspace8\emptyspace9\:\:\:\:\:\:\:\:\:\:\:\:\\ 6\overline{|\smallspace534}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\underline{\emptyspace4\emptyspace8}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\emptyspace5\emptyspace4\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\underline{\emptyspace5\emptyspace4}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\emptyspace0\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}[/tex]
The A = 48
B = 54
C = 54
After applying the concept of arithmetic operation.
Thus, the answer would be 89 after 534 divided by 6 and applying the concept of arithmetic operation.
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Need some help, explain.
Answer:
hope this will help you
Question-2
What is the distance between the zeros of the function defined by
6 (2x²+2-8)-2x (2x - 1)?
Answer:
(2x−1=2x−1) (mark me brainliest) <3!
for each pair of points below think about the line that joins them. for which pairs is the line parallel to the x-axis?
Pair of points representing parallel line to the x-axis from the given pairs is equal to option a. (3.2, 7) and (5, 7).
As given in the question,
Line parallel to the x-axis has slope = 0
Calculate the slope of each pair of points :
a. (3.2, 7) and (5, 7)
Slope = (y₂ - y₁)/ (x₂ - x₁)
= ( 7- 7) / ( 5 - 3.2)
= 0
Pair of points represents parallel line to x-axis.
b. (8, 8.4) and (8, 8.8)
Slope = (y₂ - y₁)/ (x₂ - x₁)
= ( 8.8- 8.4) / ( 8 - 8)
= not defined
Pair of points is not parallel to x-axis.
c. (6 1/2, 12) and (6.2, 11)
Slope = (y₂ - y₁)/ (x₂ - x₁)
= ( 11- 12 / ( 6.2 - 6.5)
= 1/ 0.3
= 10/3
Pair of points is not parallel to x-axis.
Therefore, pair of points represents parallel line to x-axis is equal to
option a. (3.2, 7) and (5, 7).
The complete question is:
For each pair of points below, think about the line that joins them. For which pairs is the line parallel to the x-axis? Circle your answer(s). Without plotting them, explain how you know.
a. (3.2, 7) and (5, 7)
b. (8, 8.4) and (8, 8.8)
c. (6 1/2, 12) and (6.2, 11)
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Students in a fifth-grade class were given an exam. During the next 2 years, the same students were retested several times. The average score was given by the model f(t)=89−17log10(t+1),0≤t≤24 where t is the time in months.
(a) What is the average score on the original exam? (b) What was the average score after one year? (c) After how many months would it take for it to predict that the average dropped to 82? (Assume that the the model could continue past two years, if necessary)
Answer:
Step-by-step explanation:
name all the corresponding sides and angles below if the polygons are congruent
not sure if i need to add more or if there’s some i missed
Answer:
Step-by-step explanation:
write all your sides and angles down
Corresponding sides:
AC≅JL
CB≅LK
AB≅JK
Corresponding angles:
∠A≅∠J
∠C≅∠L
∠B≅∠K
Where does the graph of y = -3x - 18 intersect with the x axis?
Is -2/3 greater then 1 2/4
Answer: No
Step-by-step explanation:
Because 1 2/4 = 6/4 = 3/2 or 1.5
When the other one is a negative fraction which is very obviously that 1 2/4 is greater than -2/3
Answer: 1 2/4 is greater than -2/3
Step-by-step explanation: A positive number is always greater than a negative number, even when dealing with fractions
A synthetic fiber used in manufacturing carpet has tensile that is normally distributed with mean 75.5 psi and standard deviation 3.5 psi. (a) Find the probability that a random sample of n = 6 fiber specimens will have a sample mean tensile strength that exceeds 75.75 psi. 75.75 - р X- р M P[X > 75.75] = P o In o Tn 75.75 – 75.5 P[X > 75.75] = P2> 3.5 va = P[Z > 0.175] = 1-0(0.175) = 0.4325 BC (b) How is the standard deviation of the sample mean changed when the sample size is increased from n = 6 to n = 49?
The probability that a n = 6 fiber specimen random sample will have a sample tensile strength greater than 75.75 psi is 43.25%.
Given that,
The tensile strength of a synthetic fiber used to make carpet is regularly distributed, with a mean of 75.5 psi and a standard deviation of 3.5 psi. We have to determine probability that a n = 6 fiber specimen random sample will have a sample tensile strength greater than 75.75 psi.
We know that,
The Z score is used to determine how far the raw score deviates from the mean, either above or below.
z = (score - mean) / (standard deviation ÷ √sample)
Mean 75.5 psi and standard deviation 3.5 psi. n = 6.
For > 75.75:
z = (75.75 - 75.5) / (3.5 ÷√6) = 0.17
P(z>0.17) = 1-P(z<0.17)
= 1-0.5675
= 43.25%
Therefore, The probability that a n = 6 fiber specimen random sample will have a sample tensile strength greater than 75.75 psi is 43.25%.
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a 8ft thick slice is cut off the top of a cube, resulting in a rectangular box that has volume 44ft . find the side length of the original cube. round your answer to two decimal places.
The side length of the original cube for the given measurements and condition is equal to 8.6ft.
As given in the question,
Let 'x' be the side of the original cube.
Volume of original cube = x³
As given 8ft thick slice is cut from the top of the cube.
Volume of the thick slice = 8x²
Volume of the resulting rectangular box = 44
⇒ x³ - 8x² = 44
⇒ x³ - 8x² -44 =0
Plot the graph of the function.
Graph is attached.
From the graph approximate value of side length 'x' = 8.6 ft.
Therefore, the side length of the original cube is equal to 8.6ft.
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The average time it takes Greg to mown a lawn can be defined by the expression 28x + 5
The number 28 represented by the equation A = 28x + 5 is the average time it takes to mow one lawn
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be = A
Now , the equation A is given as
A = 28x + 5
where x is the number of lawns to mow
Now , A is the average time required to mow a lawn
So , the number 28 is the average time required to mow a single lawn
Therefore , the number 28 average time it takes to mow one lawn
Hence , The number 28 represented by the equation A = 28x + 5 is the average time it takes to mow one lawn
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Which of the equations is NOT equivalent to 6x = 20? Select all that apply. 6x ÷ 6 = 20 ÷ 6 6x ÷ 6 = 20 ÷ 20 6x + 5 = 20 + 5 6x − 1 = 20 − 1 6x × 6 = 20 × 20
These three expressions
6x ÷ 6 = 20 ÷ 6
6x + 5 = 20 + 5
6x − 1 = 20 − 1
will be equal to the given expression.
What is Expression ?Operators, constants, and variables all come together to form an expression. A value can be produced by an expression using one or more operands and zero or more operators.
We have to check which equation will be equal to 6x = 20
6x ÷ 6 = 20 ÷ 6
After Multiplying both sides by 6.
We get, 6x = 20
6x ÷ 6 = 20 ÷ 20
After simplifying we get,
x = 1
Multiplying both sides by 6
6x = 6, Hence it doesn't satisfy.
6x + 5 = 20 + 5
Subtract 5 both sides of the equation
We get, 6x = 20
6x − 1 = 20 − 1
Adding 1 both sides of the equation,
We get, 6x = 20
6x × 6 = 20 × 20
After simplifying, we get
36x = 400
Hence, only
6x ÷ 6 = 20 ÷ 6
6x + 5 = 20 + 5
6x − 1 = 20 − 1
will be equal to the given expression.
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A restaurant is offering a dinner special that includes one starter and one entree. The choices are listed below. How many possible dinner special combinations are there?
Starter: breadsticks, soup, salad
Entree: beef, fish, chicken, shrimp, pork
The total number of possible dinner combinations are 15
What are Combinations?
The number of ways of selecting r objects from n unlike objects is calculated by combination. The formula for combination is
ⁿCₓ = n! / ( ( n - x )! x! )
where
n = total number of objects
x = number of choosing objects from the set
Given data ,
Let the total number of dinner combinations be = T
Now ,
The values of Starters is represented in set = A
The values of Entree is represented in set = B
The values of Set A = { bread sticks , soup , salad }
The values of Set B = { beef , fish , chicken , shrimp , pork }
Now , the total combinations of possible selection of Starters = ³C₁
The total combinations of possible selection of Entree = ⁵C₁
So , the total number of dinner combinations T = total combinations of possible selection of Starters x total combinations of selection of Entree
And , the equation is
The total number of dinner combinations T = ³C₁ x ⁵C₁
The total number of dinner combinations T = 3 x 5
The total number of dinner combinations T = 15
Therefore , the value of T is 15
Hence , The total number of possible dinner combinations are 15
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find the eigenvalues and associated unit eigenvectors of the symmetric matrix the smaller eigenvalue has associated unit eigenvector . the larger eigenvalue has associated unit eigenvector .
The eigenvalues and associated unit eigenvectors of the symmetric matrix the smaller eigenvalue has associated unit eigenvector is Ax = λx.
Symmetric matrix:
In algebra, symmetric matrix a square matrix that remains unaltered when its transpose is calculated.
Given,
Here we need to find the the eigenvalues and associated unit eigenvectors of the symmetric matrix the smaller eigenvalue has associated unit eigenvector and the larger eigenvalue has associated unit eigenvector.
Here the eigenvector is a vector that is associated with a set of linear equations.
And in the eigenvector of a matrix is also known as a latent vector, proper vector, or characteristic vector.
Therefore, those are defined in the reference of a square matrix.
So, the smaller eigenvalue has associated unit eigenvector is Ax is λx.
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please answer this question
The correct equation is Option A which states that x+16 = 70. The reason for this is opposite angles (or vertical angles) in parallel lines are congruent.
What are opposite angles?When two lines intersect they form a pair of opposite or vertical angles. In this case, the vertical angles are:
70° ≅ t
p ≅ s
q ≅ (x +16)°
r ≅ u
Given that lines AB and CD are parallel, and that both cut through lines EF, that means q ≅ 70°
Hence,
∡ ApE = 70° = ∡DrF
If we need to find x
Since DrF (x+16) °= 70°
x = 54°
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