The mistake is made in the second step. The correct steps are given below.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Wilma estimates that she’ll drive about 18,000 miles during the year.
The car she wants to purchase gets an average of 24 miles per gallon, and the average cost per gallon of gas in her neighbourhood is $2.72.
Locate the error in her calculations, and select the correction.
Step - 1
18000 miles/year
18000 miles / 12 months = 1500 miles/month
Step 2
1500 miles/month
1500 miles/month / 24 miles per gallon = 62.5 gallons/month
62.5 gallons/month
Step 3
(62.5 gallons/month) x ($2.72/gallons) = $170 cost/month
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Please show work and thank you
Answer: [tex]\sqrt{109} \text{ m }[/tex]
Step-by-step explanation:
If we let the length of the ladder be [tex]x[/tex], as shown in the diagram, this means that by the Pythagorean theorem, [tex]x=\sqrt{10^{2}+3^{2}}=\boxed{\sqrt{109}}[/tex] m.
Find the middle term of the expansion of (√x+√y)^8. a. 40x2y2 c. 40x4y4 b. 70x2y2 d. 70x4y4
The middle term of the expansion of (√x + √y)⁸ is; B: 70 * x² * y²
How to solve binomial theorems?We want to expand the expression;
(√x + √y)⁸
Now, according to binomial expansion, we know that;
(x + y)ⁿ = ⁿC₀ xⁿ y⁰ + ⁿC₁ xⁿ ⁻ ¹ y¹ + ⁿC₂ xⁿ ⁻ ² y² + ..... + ⁿCₙ x⁰ yⁿ.
Now, for an 8 power binomial, the coefficient of each term from formula are respectively;
1 8 28 56 70 56 28 8 1
The mid term is the fifth term and so, we have;
(⁸C₄ * (√x)⁽⁸ ⁻ ⁴⁾ * (√y)⁴)
⇒ 70 * x² * y²
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If the area of a certain square is 81 square inches or less, which set
describes the domain of the function?
F(s)=s^2
(0,81]
[0, 9]
(0,91
[0,81)
Answer:
(0, 9]
Step-by-step explanation:
√81 = 9
We must take positive numbers into consideration here.
What key features do the functions f(x) = 4-x and g of x equals negative one times the square root of the x minus 4 end root have in common?
A.)Both f(x) and g(x) include domain values of [–4, ∞) and range values of (–∞, ∞), and both functions have an x-intercept in common.
B.)Both f(x) and g(x) include domain values of [4, ∞), and both functions decrease over the interval (4, ∞).
C.) Both f(x) and g(x) include domain values of [4, ∞) and range values of [0, ∞), and both functions have a y-intercept in common.
D.) Both f(x) and g(x) include domain values of [–4, ∞) and range values of (–∞, ∞), and both functions are negative for the entire domain.
The key features are (1) both f(x) and g(x) include domain values of [–4, ∞) and range values of (–∞, ∞), and both functions have an x-intercept in common.
How to determine the key featuresThe functions are given as:
f(x) = 4 - x
[tex]g(x) = -\sqrt{x - 4}[/tex]
Using a graphing calculator:
The domain of g(x) is [4,∞)The range of g(x) is (-∞,0]The domain of f(x) is (-∞,∞) The range of f(x) is (-∞,∞) Both functions have positive values for their domainsBy comparing the above highlights, the true statement between functions g(x) and f(x) is option (1)
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Answer:
B.)Both f(x) and g(x) include domain values of [4, ∞), and both functions decrease over the interval (4, ∞).
Step-by-step explanation:
b is correct
Cynthia beach wants to buy a rug for a room that is 22 ft wide and 31 ft long.she wants to leave a uniform strip of floor around the rug.she can afford to buy 580 square feet of carpeting.what dimensions should the rug have?
The dimensions the rug should have is 20 by 29
How to determine the dimension?The dimension of the rug is given as:
22 ft by 31 ft
The area of the carpet is given as:
Area = 580
Represent the length of the empty space with x.
So, the dimension of the carpet is:
22 - 2x by 31 - 2x
The area is calculated as:
Area = (22 - 2x) * (31 - 2x)
Expand
Area = 682 - 62x - 44x + 4x^2
Evaluate the difference
Area = 682 -106x + 4x^2
Substitute Area = 580
682 -106x + 4x^2 = 580
Subtract 580 from both sides
102 -106x + 4x^2 = 0
Rewrite as:
4x^2 - 106x +102 = 0
Using a graphing calculator, we have:
x = 1 and x = 22.5
Substitute these values in 22 - 2x by 31 - 2x
So, we have:
Length = 22 - 2(1) = 20 or Length = 22 - 2(22.5) = -23
Width = 31 - 2(1) = 29 or Length = 31 - 2(22.5) = -14
The dimensions cannot be negative.
So, we have:
Length = 20 and Width = 29
Hence, the dimensions the rug should have is 20 by 29
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Triangle ABC is defined by the points A(2,9), B(8,4), and ((-3,-2).
Complete the following equation for a line passing through point C and perpendicular AB.
The equation of the line is 5y = 6x + 8 which passes through point C and perpendicular AB.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have a triangle ABC is defined by the points A(2,9), B(8,4), and C(-3,-2).
The slope of the segment AB:
[tex]\rm m =\dfrac{4-9}{8-2}[/tex]
m = -5/6
The slope of the line perpendicular to AB:
Let M is the slope of the line:
mM = -1
(-5/6)M = -1
M = 6/5
The line:
y = Mx + c
y = (6/5)x + c
The line passing through the point C(-3, -2)
-2 = (6/5)(-3) + c
c = 8/5
y = (6/5)x + 8/5
5y = 6x + 8
Thus, the equation of the line is 5y = 6x + 8 which passes through point C and perpendicular AB.
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Which graph shows the solution to the following system of inequalities x+y>4
The solution to this system of inequalities x + y>4 , x + y <3 is Option A
The complete question is
Which graph shows the solution to this system of inequalities? x + y>4 x + y <3
The image are attached with the answer.
What are Inequality ?When an expression is equated with another expression by an Inequality operator (< , > < etc) then the mathematical statement formed is called Inequality.
The inequalities are
x+y>4
x + y <3
After plotting both the inequalities in the graph the following graph that is attached with the answer is obtained.
Therefore the correct answer is Option A
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Which of the following are exterior angles? Check all that apply.
A. <4
B. <1
C. <5
D. <2
E. <3
F. <6
All of the ppl that answered this for it wrong, it is <6!! ( < = angle)
Which graph represents the function f(x) = |x + 3|?
On a coordinate plane, an absolute value graph has a vertex at (0, 3).
On a coordinate plane, an absolute value graph has a vertex at (negative 3, 0).
On a coordinate plane, an absolute value graph has a vertex at (0, negative 3).
On a coordinate plane, an absolute value graph has a vertex at (3, 0).
Answer:
Graph of Modulus
The graph of a modulus or absolute value function is in a form of a 'V' shape whose vertex depends upon the coordinates. The equation for the graph is given as,
where,
(a, b) are the coordinates of the vertex of 'v' in the form of (x, y),
And h shows how wider or lean will be the function, for h=0, it is a straight line, while for a negative value the graph will face downwards and opposite for a positive value.
Given to us
y = |x-3|
On the coordinate plane
The graph will be in the shape of a 'V' whose vertex will lay at the coordinates (3, 0). As the value of a is 1 the graph will face upwards. As shown below on the graph.
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Step-by-step explanation:
Answer:
C
Step-by-step explanation:
edge 23
Determine whether the relation represents a function. State the domain and range of the relation.
{(-2,-9).(-4,-4). (1,5), (5, -7)}
Answer:
It is a functionDomain: {-4, -2, 1, 5}Range: {-9, -7, -4, 5}Step-by-step explanation:
A function is defined so that for each input (known as the domain), there is no more than one output (known as the range).
Write a doubles fact that can help you find the
sum. Write the sum.
3+4
Step-by-step explanation:
4 + 4 = 8 is one of the two closest double to 3 + 4
W.K.T(we know that )..
4 is 1 more than 3 this means ;
4 + 4 will be 1 more than 3 + 4
4 + 4 = 8 ,so finding 1 Less ;
3 + 4 = 7
here is the answer hope It helped U
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A dartboard consists of a circle inscribed in a square. The area of the circle is square inches. The area of the square is 64 square inches.
A dartboard consists of a circle inscribed in a square.
Izzy randomly throws a dart at the square, and it lands inside the square. To the nearest percent, what is the probability that the dart lands inside the square but not on the circular dartboard? Use 3.14 for π.
22%
25%
75%
79%
The probability that the dart lands inside the square but not on the circular dartboard is 22% option first is correct.
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
A dartboard consists of a circle inscribed in a square.
The area of the square is 64 square inches.
We know the area of the square:
A = a²
a is the side of the square.
64 = a²
a = 8 inches
As the circle inscribed in a square.
The diameter will be 8 inches
The radius of the circle r = 8/2 = 4 inches
Area of the circle = πr² = π(4)² = 16×3.14 = 50.24 inches
P(dart will land on circular dartboard) = 50.24/64 = 0.785
P(dart will not land on circular dartboard) = 1 - 0.785 = 0.215
or
P(dart will not land on circular dartboard) = 21.5% ≈ 22%
Thus, the probability that the dart lands inside the square but not on the circular dartboard is 22% option first is correct.
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Answer:
22%
Step-by-step explanation
Edge.2023!
Based on probability and if it is appropriate for a decision to be left up to chance, choose every situation that is both statistically fair and morally fair.
Situation #1 A high school student is deciding whether to first clean his room or do his homework. He decides by picking a tile at random from a bag of lettered tiles. If he picks a consonant he will clean his room, and if he picks a vowel he will do his homework.
Situation #2 There are four candidates eligible for a vacancy at a company. Ignoring qualifications and experience, the recruitment manager decides which candidate to hire by writing their names on pieces of paper, shuffling the papers, and drawing one at random.
Situation #3 Five cousins are deciding which board game to play. They each write their preferred game on a different section of a spinner that has five equally-sized sections. They spin the spinner and will play the game written on the section where the spinner lands.
Situation #4 To determine who can choose the spot for a picnic, Kate picks a tile at random from a collection of five tiles, numbered 2 through 6. Kate chooses the spot if she picks a prime number, and Charles chooses if Kate picks a composite number.
Situation #5 Five roommates all want to attend an event, but they only have four invites. To decide who will attend, they shuffle a set of five cards consisting of four aces and a king. Each roommate is randomly dealt a card. The ones dealt an ace will attend the event.
Reset Next
The situations that are both statistically fair and morally fair are Situation 2, Situation 3 and Situation 5
How to categorize the situations?For a situation to be fair, the probability of every outcome must be equal.
We can now analyze each option using the above highlight
Situation 1
Alphabets = 26Probability of vowel = 5/26Probability of consonant = 21/26The probabilities of vowels and consonant are not equal.
Hence, this situation is not fair
Situation 2
People = 4
P(Each) = 1/4
The probability of each participant is equal in the above scenario i.e. 1/4
Hence, this situation is fair
Situation 3
People = 5P(Each) = 1/5The probability of each cousin is equal in the above scenario i.e. 1/5
Hence, this situation is fair
Situation 4
Numbers = 5 i.e. 2 to 6P(Prime) = 3/5P(Composite) = 4/6The probabilities of prime and composite numbers are not equal.
Hence, this situation is not fair
Situation 5
Roommates = 5Cards = 5Aces = 4P(Each) = 1/5All probabilities are equal in the above scenario i.e. 1/5
Hence, this situation is fair
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HELP ASAP WILL GIVE BRAINLIST
Answer:
Step-by-step explanation:
Remark
This is a proportion question. A proportion is 2 equal ratios that requires you to solve the 4th part when you know the other 3.
Givens
1 foot scale model length
5 feet of actual length
x = length of model
65 feet of actual length
Formula
1 foot / 5 feet = x / 65 feet
Solution
1/5 = x / 65 Cross multiply
5x = 65 Divide by 5
5x/5 = 65/5
x = 13
Answer
The model is 13 feet long
what are the missing values
Answer:
The answer is on the image, which is color coordinated with the how i got it
Which is equivalent to 64 1/4
Answer:
4*64=256
256+1=256
there fore 64 1/4 is equivalent to 257/4
If the present value of an item is P
and we experience an inflation rate
of r for t years, what will the future
value of the item be?
P = $100
r = 4%
t = 15
inflation means, the same item costs more however is the same item, so if a tomato in January 1st costs $1 and by December 31st it costs $2, the price went up by twice, however is same tomato, it didn't become twice as large, anyhow, inflation eats away value and thus is a Decay case.
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &100\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=\textit{elapsed time}\dotfill &15\\ \end{cases} \\\\\\ A=100(1 - 0.04)^{15}\implies A=100(0.96)^{15}\implies A\approx 54.21[/tex]
now, we can look at this value reduction as value that was eaten away from the original.
we can also see the inflationary effect as the new value of the tomato in money terms, that means the tomato went up in price, exponentially by 4% per year, so we can see that as a Growth case in terms of money spent on it.
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &100\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=\textit{elapsed time}\dotfill &15\\ \end{cases} \\\\\\ A = 100(1 + 0.04)^{15} \implies A \approx 180.09[/tex]
now, this is how much the tomato will be priced in money terms in 15 years.
Crispy Clover, a popular vegetarian restaurant, introduced a new menu that has 20% more dishes than the previous menu. The previous menu had D dishes. Which of the following expressions could represent how many dishes Crispy Clover's new menu has?
Answer:
D*1.2 (OR) 1.2D
Step-by-step explanation:
Because the new menu has one hundred percent of the original menu (D), plus twenty percent, the new menu is 120%, or 1.2
You can then multiply the number of items on the original menu (D), by the new menu's value, which is 1.2 (or 120%).
This brings you to the answer of 1.2D
Abby takes a 75-centimeter by 40-centimeter rectangle of fabric and cuts from one corner of
the piece of fabric to the diagonally opposite corner. Now Abby has two equally sized triangles of fabric. What is the perimeter of each triangle centimeters
answer: 195cm
the photo should explain
A rectangle has an area of 65 cm² and a length of
13 cm. Find the perimeter of this rectangle.
Answer:
36 cm
Step-by-step explanation:
See attached image
Joe went shopping and purchased a pair of pants for $56 and a pair of shoes for $45. The tax in Joe's city is 4%. How much will Joe pay when he checks out ?
Answer:
$105.04
Step-by-step explanation:
First add $56 plus 45$ and you will get $101, then times $101 and 1.04 together.
Your answer should be $105.04.
Find the surface area of the regular pyramid.
The surface area of the regular pyramid as given in the task content is; 16m².
What is the surface are of the regular pyramid?The task content requires that the surface area of the pyramid be determined. This surface area can therefore be evaluated as follows;
Surface area = (2×2) + 4((1/2)×2×3) = 4 + 12 = 16m².
The surface area of the regular pyramid is therefore; 16m².
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Karen runs for 45 minutes every day. Which unit best describes the distance Karen runs for each day?
A. 50 kilometers
B. 5 kilometers
C. 50 meters
D. 50 centimeters
! URGENT !
Answer:
your mom fat as he'll that way you are adopted
find the perimeter of a triangular field whose length of edges are 14 m, 12m 10 m Also find the length of required to fence 4 times around it?
Answer: 36 m, 144 m
Step-by-Step Explanation:
a = 14 m
b = 12 m
c = 10 m
Perimeter = a + b + c
Therefore,
= a + b + c
= 14 + 12 + 10
= 26 + 10
=> 36
Perimeter = 36 m
Length of Fence required for Fencing 4 times = Perimeter * 4
Therefore,
= Perimeter * 4
= 36 * 4
= 144
Length of Fence required for Fencing 4 times = 144 m
Which description best describes parallel lines?
OA. Lines that intersect at a right angle
B. Lines that lie in the same plane but will never intersect
C. Lines that are not in the same plane and will never intersect
OD. Lines that intersect
SUBIT ?
Peter and Henry went to the movies Peter bought the two Movie tickets for 7 dollars each. How much did he spend for the movie tickets Henry bought two buckets of popcorn for 5 dollars each. How much did Henry spend on popcorn. What was the total expenditure
Answer:
tickets: $14
popcorn: $10
total: $24
Step-by-step explanation:
2 movie tickets at $7 each is 2*7 which is $14
2 buckets of popcorn at $5 each is 2*5 which is $10
adding these together we get a total spending of $24
A long novel is opened to a random page; the probability that the page is numbered something between 21 and 31.
Using the uniform distribution, considering that the novel has 435 pages, the probability that the page is numbered something between 21 and 31 is:
[tex]p = \frac{10}{435}[/tex]
What is the uniform probability distribution?It is a distribution with two bounds, a and b, in which each outcome is equally as likely.
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
Researching the problem on the internet, it is found that the novel has 435 pages, hence a = 0, b = 435, and the probability that the page is numbered something between 21 and 31 is given by:
[tex]P(21 \leq X \leq 31) = \frac{31 - 21}{435 - 0} = \frac{10}{435}[/tex]
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Which sentence correctly compares the two numbers 5.395 and 5385 ?
5.395= 5385
5.385 > 5.395
5395< 5.385
5385 < 5.395
The sentence that correctly compares the two numbers is 5385 > 5.395
What is the correct sentence?Here are inequality signs and what they mean:
Note that
5385 is greater than 5.385. Thus, the correct statement is 5385 > 5.395.
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Credit cards and charge cards differ in two important ways. One is the method of payment. What is the other difference? A. You earn interest when you use a credit card but not a charge card. B. You have to pay interest on credit cards but not on charge cards. C. You have to pay interest on charge cards but not on credit cards. D. You earn interest when you use a charge card but not a credit card. Reset Next
The difference is "You have to pay interest on credit cards but not on charge cards" , Option B
What are Credit Cards ?The cards is a financial tool generally issued by banks which let you to borrow money for expenses and make payments afterward in installments.
Credit cards and charge cards differ in two important ways. One is the method of payment
The other difference is
You have to pay interest on credit cards but not on charge cards, as in credit card the person gets lot of time for the payment and the payment can be made in installments and so for this facility extra charge in terms of interest.
Therefore Option b is the correct answer.
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y-intercept: 4
-: x-intercepts: -2, 5, 7
-: Relative maximum at (0,4)
-: Relative maximum at (6, -3)
-: As → −∞, → −∞
-: As → ∞, →
The attached figure represents the sketch of the graph
The missing part of the questionThe complete question requires that we sketch the graph that follows the given parameters
How to sketch the graph?The given parameters are:
y-intercept: 4x-intercepts: -2, 5, 7Relative maximum at (0,4)Relative maximum at (6, -3)As x → −∞, y → −∞As x → ∞, y → ∞To start with, we plot the points on an empty coordinate plane.
Next, we connect the points using a rough curve
Lastly, the points are labelled
See attachment for the sketch of the graph
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