The possible values of the length of the rectangle is x > 34, the correct option is A.
How to find the area and the perimeter of a rectangle?For a rectangle with length and width L and W units, we get:
Area of the rectangle = [tex]L \times W \: \rm unit^2[/tex]
Perimeter of the rectangle = [tex]2(L + W) \: \rm unit[/tex]
The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
Given that width is 8 inches less than the length x
Sum of length and width more than 60
Now, the length is x
Width is x-8
x-8+x>60
2x>60
x>30
Therefore, the length of rectangle will be x > 34
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Mr Jacobs travels for 2 hours by car and covers a distance of 220 km Jong (in hours and minutes will it take Mr Jaces to cover a distance of 352 km at the same average speed?
At the same average speed, it would take Mr Jacobs 3 hours and 12 minutes to cover a distance of 352 km.
To calculate the time it would take Mr Jacobs to cover a distance of 352 km at the same average speed, use the following formula:
Time = (Distance / Average Speed) * 60
Time = (352 km / 220 km/h) * 60
Time = (1.6) * 60
Time = 96 minutes
Time = 1 hour and 36 minutes
Therefore, it would take Mr Jacobs 3 hours and 12 minutes to cover a distance of 352 km at the same average speed.
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The average daily balance is the mean of the balance in an account at the end of each day in a month. The following table gives the dates and amounts of the transactions in Elliott's account in June.
Day of June Transaction type Transaction amount (in dollars)
1 Starting balance 1223
10 Deposit 615
15 Withdrawal -63
22 Withdrawal -120
There are 30 days in June.
What is the average daily balance of Elliott's account for the month of June?
Answer: 1583.90
In June it’s 1583.90$
the average daily balance of Elliott's account for the month of June is $902.
calculate the average daily balance for Elliott's account in June. To calculate the average daily balance, we need to determine the balance at the end of each day in June. Starting with a balance of $1223 on June 1st, we can calculate the balance at the end of each day by adding or subtracting the amount of each transaction. The table below shows the daily balances: Day of June - Transaction type - Transaction amount -Balance
1 - Starting balance - 1223 - 1223
5 - Deposit - 615 - 1838
8 - Withdrawal - -632 - 1206
9 - Withdrawal - -120- 1086
10 - 30 - No transactions - 0 1086
The sum of the daily balances is: 01086 × 30 = 32580
The average daily balance is the sum of the daily balances divided by the number of days in June:
average daily balance = 32580 / 30 = 902
Therefore, the average daily balance of Elliott's account for the month of June is $902.
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Mr. Lopez must drive 340 miles to
attend an origami convention. His
car averages 28 miles per gallon and so far he has traveled 102 miles. How much gasoline must be left in his tank if he wants to complete the trip without stopping?
made
The quantity of gasoline that must be left in his tank if he wants to complete the trip without stopping is 8.5 gallons of gasoline.
What is the slope-intercept form?Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x represents the quantity of gasoline.y represents the total distance.c represents the y-intercept or initial value.In this context, an equation that models the situation is given by:
y = mx + c
340 = 28x + 102
28x = 340 - 102
28x = 238
x = 238/28
x = 8.5 gallons of gasoline.
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what is the solution to 4+5ex+2=11?
The solution to the equation is (a) x = ln(7/5) - 2
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
4 + 5e^(x + 2) = 11
Evaluate the like terms in the equation
So, we have the following representation
5e^(x + 2) = 7
Divide through the equation by 5
This gives
e^(x + 2) = 7/5
Take the natural logarithm of both sides
x + 2 = ln(7/5)
So, we have
x = ln(7/5) - 2
Hence, the solution is x = ln(7/5) - 2
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which of the points shown below are on the line given by the equation y=x+4? check all that apply.
point a: (-1,3)
point b: (2,6)
point c: (-2,-2)
point d: (2,4)
Step-by-step explanation:
These points are in (X, Y) form. What you want to do is plug in the X coordinates into the equation and see if it equals the Y coordinate.
Equation: Y = X + 4
Point A: (-1, 3)
(-1) + 4 = 3
Point B: (2, 6)
(2) + 4 = 6
Point C: (-2, -2)
(-2) + 4 = 2
Point D: (2, 4)
(2) + 4 = 6
Only point A and point B equal their Y coordinate, making A and B the only correct answers.
Find the average value fave of the function f on the given interval. f(x) = 3x2 + 4x, [−1, 2]
The average value of the function f(x) = 3x2 + 4x on the interval [-1, 2] is about 4.67.
To find the average value fave of the function f(x) = 3x2 + 4x on the interval [-1, 2], solve the definite integral of f(x) over the interval and then divide by the interval length.
The definite integral of f(x) over the interval [-1, 2] can be calculated as follows:
[tex]∫[-1,2] (3x^2 + 4x) dx = [x^3 + 2x^2] between x = -1 and x = 2 = (23 + 2(22)) - ((-1)^3 + 2(-1)^2) \s= 14[/tex]
The interval length is 2 - (-1) = 3.
As a result, the average value fave of f(x) on the interval [-1, 2] is as follows:
fave =[tex](1/3) * ∫[-1,2] (3x^2 + 4x) dx \s= (1/3) * 14 \s[/tex]= 4.67 (rounded to two decimal places) (rounded to two decimal places)
As a result, the average value of the function f(x) = 3x2 + 4x on the interval [-1, 2] is about 4.67
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.
Find a function rule for the line that passes through the origin (0,0) and the point ( -6 - 12,).
The function rule for the line that passes through the origin and (-6,-12) is y = 2x.
In mathematics, a function is a rule that assigns to each element in a set a unique output value.
To find a function rule for the line that passes through the origin (0,0) and the point (-6,-12), we first need to determine the slope of the line. The slope of a line represents the rate of change between the x and y coordinates. We can find the slope using the formula:
slope = (y₂ - y₁)/(x₂ - x₁)
where (x₁, y₁) represents the coordinates of the first point, and (x₂, y₂) represents the coordinates of the second point.
Using the given points, we can substitute in the values:
slope = (-12 - 0)/(-6 - 0)
slope = -12/-6
slope = 2
Now that we have the slope, we can use the point-slope form of a linear equation to find the function rule:
y - y₁ = m(x - x₁)
where m is the slope, and (x₁, y₁) represents the coordinates of a point on the line.
Substituting in the values we have so far, we get:
y - 0 = 2(x - 0)
y = 2x
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Andy and dale solved 35 puzzles together. 1/3 of the puzzles that Andy solved are twice the number of puzzles Dave solved. How many puzzles did each boy solve?
Answer:
Andy: 30Dale: 5Step-by-step explanation:
You want to find the number of puzzles solved by each boy if they solved 35 puzzles together, and 1/3 of the number Andy solved is twice the number Dale solved.
EquationsLet 'a' and 'd' represent the numbers of puzzles solved by Andy and Dale, respectively. Then ...
a + d = 35
1/3a = 2d
SolutionMultiplying the second equation by 3, we get an expression for 'a' that can be used in the first equation:
a = 6d
6d +d = 35
d = 35/7 = 5
a = 6(5) = 30
Andy solved 30 puzzles; Dale solved 5.
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What is 5’7 in cm
Please can I have help
Step-by-step explanation:
Sure, I'd be happy to help!
5 feet 7 inches is equivalent to 170.18 cm.
Five packets of marshmallows cost £4. 80. How much will eight packets cost?
Five packets of marshmallows cost £4. 80. Then, eight packets of marshmallows cost £7.68.
The problem states that five packets of marshmallows cost £4.80. We need to find out how much eight packets of marshmallows will cost.
To solve the problem, we can use the concept of proportionality. If we assume that the cost of marshmallows is directly proportional to the number of packets, then we can set up a proportion between the cost of five packets and the cost of eight packets.
The proportion can be written as follows:
5 packets / £4.80 = 8 packets / x
where x is the cost of eight packets.
To solve for x, we can cross-multiply the proportion and simplify:
5 packets x = £4.80 x 8 packets
5x = £38.40
x = £38.40 / 5
x = £7.68
Therefore, eight packets of marshmallows will cost £7.68.
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in a particular county of our state, it was revealed that 5% of all automobiles did not pass inspection. of the next ten automobiles entering the inspection station, a. what is the probability that none will pass inspection? b. what is the probability that all will pass inspection? c. what is the probability that exactly two will not pass inspection? d. what is the probability that more than three will not pass inspection? e. what is the probability that fewer than two will not pass inspection?
According to the question, it was revealed that 5% of all automobiles did not pass inspection. Of the next ten automobiles entering the inspection station
a. The probability that none will pass inspection is
P(x = 0) = [tex]^{10}C_{0}(0.05)^{0}(0.95)^{10}[/tex]
P(x = 0) = 0.5987
b. The probability that all will pass inspection is
P(x = 10) = [tex]^{10}C_{0}(0.05)^{10}(0.95)^{0}[/tex]
P(x = 10) = 0.5987
c. The probability that exactly two will not pass inspection is
P(x = 2) = [tex]^{10}C_{2}(0.05)^{2}(0.95)^{8}[/tex]
P(x = 2) = 0.0746
a. The probability that none will pass inspection is 0.001%.
b. The probability that all will pass inspection is 59.87%.
c. The probability that exactly two will not pass inspection is 0.27%.
d. The probability that more than three will not pass inspection is 0.0102.
e. The probability that fewer than two will not pass inspection is 6.48%.
In statistics, probability is the measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 means that the event is impossible, and 1 means that the event is certain.
In a particular county of our state, it was revealed that 5% of all automobiles did not pass inspection. This means that the probability of an automobile not passing inspection is 0.05, and the probability of an automobile passing inspection is 0.95.
To find the probability of none of the ten automobiles passing inspection, we need to multiply the probability of an automobile not passing inspection by itself ten times since the events are independent. Therefore, the probability of none of the ten automobiles passing inspection is 0.05¹⁰, which is approximately 0.00001 or 0.001%.
To find the probability of all ten automobiles passing inspection, we need to multiply the probability of an automobile passing inspection by itself ten times since the events are independent. Therefore, the probability of all ten automobiles passing inspection is 0.95¹⁰, which is approximately 0.5987 or 59.87%.
To find the probability of exactly two of the ten automobiles not passing inspection, we need to use the binomial distribution formula. The formula is P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, p is the probability of success, and (n choose k) is the binomial coefficient. Therefore, the probability of exactly two of the ten automobiles not passing inspection is P(X=2) = (10 choose 2) * 0.05² * 0.95⁸, which is approximately 0.0027 or 0.27%.
The complement rule states that the probability of an event occurring is equal to one minus the probability of the event not occurring. Therefore, the probability of more than three of the ten automobiles not passing inspection is 1 - P(X<=3), where P(X<=3) is the probability of three or fewer automobiles not passing inspection.
To find P(X<=3), we can use the binomial distribution formula with k=0,1,2, and 3. Therefore,
P(X<=3) = P(X=0) + P(X=1) + P(X=2) + P(X=3)
=> (10 choose 0) * 0.05⁰ * 0.95¹⁰ + (10 choose 1) * 0.05¹ * 0.95⁹ + (10 choose 2) * 0.05² * 0.95⁸ + (10 choose 3) * 0.05³ * 0.95⁷, which is approximately 0.9898 or 98.98%.
Therefore, the probability of more than three of the ten automobiles not passing inspection is 1 - 0.9898, which is approximately 0.0102.
To find the probability of fewer than two of the ten automobiles not passing inspection, we need to use the complement rule again. The probability of fewer than two automobiles not passing inspection is the same as the probability of one or zero automobiles not passing inspection.
To find the probability of more than two automobiles not passing inspection, we can use the complement rule again:
=> P(X>2) = 1 - P(X<=2) = 1 - (P(X=0) + P(X=1) + P(X=2)) = 1 - [((10 choose 0) * 0.05⁰ * 0.95¹⁰ + (10 choose 1) * 0.05¹ * 0.95⁹ + (10 choose 2) * 0.05² * 0.95⁸]
which is approximately 0.0648 or 6.48%.
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the expression n^2 - n - 30 can be written in Factored Form as (n + 5) (n + k), where k represents a number
Answer:
k = -6
Step-by-step explanation:
Expand by substituting -6:
(n+5) (n-6) = n^2 + 5n - 6n (-6×5)
Thus, (n+5)(n-6) = n^2 -1n -30
(In a facotrised form for quadratics, the numbers need to add to 'bx', in this case -1, and multiply to form 'c' (-30). So -6×5 = -30 and k= -6)
Los 2/5 de los ingresos de una comunidad de vecinos
se emplean en combustible; 1/8 en electricidad, 1/12
en recogida de basuras, 1/4 en mantenimiento del
edificio y el resto se emplea en limpieza.
¿Qué fracción de los ingresos se emplea en limpieza?
The fraction of income spent on cleaning is 71/50.
What is fraction?A fraction is represented by the ratio in the form -
{x} : {y} = {x}/{y}
In terms of numbers, we can write -
2 : 3 = 2/3
Given is that 2/5 of the income of a community of neighbors they are used in fuel, 1/8 in electricity, 1/12 in garbage collection, 1/4 in maintenance of the building and the rest is used for cleaning.
Assume the fraction to be {x}. Then, we can write -
2/5 + 1/8 + 1/12 + 1/4 + x = 1
0.4 + 0.125 + 0.083 + 0.25 + x = 1
x = 0.142
x = 142/100
x = 71/50
Therefore, the fraction of income spent on cleaning is 71/50.
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{Question in english -
2/5 of the income of a community of neighbors
they are used in fuel; 1/8 in electricity, 1/12
in garbage collection, 1/4 in maintenance of the
building and the rest is used for cleaning.
What fraction of the income is spent on cleaning?}
Rectangle ABCD is graphed in the
coordinate plane. The following are the
vertices of the rectangle: A(5,5), B(7,5),
C(7, -1), and D(5, -1).
Given these coordinates, what is the length
of side BC of this rectangle?
Answer:
Rectangle ABCD is graphed in the
coordinate plane. The following are the
vertices of the rectangle: A(5,5), B(7,5),
C(7, -1), and D(5, -1).
Given these coordinates, what is the length
of side BC of this rectangle?
Step-by-step explanation:
Sam bought six pens for an unknown price plus a backpack. If he spent a total of $28.50, write an equation to find the cost of each pen.
Answer: $4.75 for each pen
Step-by-step explanation:
$28.50/6= 4.75$
Which of the following sequences are geometric?
Check all that apply.
Answer: A and C
Step-by-step explanation:
- Geometric sequences are sequences where there is a constant number being multiplied or divided.
- In A, we are dividing by 2 each time. In C, we are multiplying by 3
each time.
- B is not multiplication or division. Neither is D.
(っ◔◡◔)っ ♥
Hope this helps.
MM4343
How do you score 102 students play at least once by there is 40% of the students at the school how many students are at the school
If 102 students at least plays one sport and this is 40% of the students at the school, then there 255 students at the school
Let's assume that the total number of students in the school is "x".
40 percentage of the students at the school play at least one sport. So, the number of students who play at least one sport is 0.4x.
We also know that the number of students who play at least one sport is 102. Therefore, we can write:
0.4x = 102
Move 0.4 to the right hand side of the equation
x = 102 / 0.4
Divide the numbers
x = 255
Therefore, there are 255 students at the school.
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29 Transformations of linear functions C8G
Find g(x), where g(x) is the translation 1 unit right of f(x) = 7x + 4.
Write your answer in the form mx + b, where m and b are integers.
g(x) =
Submit
Step-by-step explanation:
please review the attachment
the workers in a company are in the ratio femalee:male 1:45
the company has 150 female workers
how many many worker are there altogether
PLSSS NOW 100 points.
Answer: 825 workers altogether
Step-by-step explanation:
well, if the ratio is 4.5 men to every woman, we just have to multiply 150 by 4.5, which means there will be 675 male workers and 150 female workers.
a piece-wise function will always have at least one x-intercept or at least one y-intercept? true or flase
True. A piece-wise function is composed of different functions that are joined together at certain points and each of these functions will either have an x-intercept or a y-intercept.
Yes, a piece-wise function will always have at least one x-intercept or at least one y-intercept. A piece-wise function is composed of different functions that are joined together at certain points. Each of these individual functions can either be linear, quadratic, or any other type of function, and each of these functions will either have an x-intercept or a y-intercept. For example, if a piece-wise function contains two linear equations, each of them will have one x-intercept and one y-intercept. The same is true for quadratic equations, and for any other type of equation. Therefore, since a piece-wise function is composed of these individual functions, it will always have at least one x-intercept or at least one y-intercept.
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..........................................
Answer:
8^4
Step-by-step explanation:
8^8 divided by 8^4
Because they have the same base and it is divided, so we just need to take ^8 - ^4 and get the answer
8^4
PLS HELP ASAP geometry
Find x pls
Answer:
Step-by-step explanation:
i have no idea sorry
Answer:
Ac = 0.833334.
Step-by-step explanation:
SINCE THE QUESTION IS PYTHAGORAS THEOREM.
THE FORMULA IS
[tex] tan = \frac{ |bc| }{ac} [/tex]
From the question tan = 18°
bc = 15
ac= ?
making ac = x
therefore
[tex] tan = \frac{ |bc| }{ |ac| } \\ tan 18 = \frac{15}{x} \\ tan18(x) = x \times \frac{15}{x} \\ tan18x = 15 \\ = \frac{tan18x}{18} = \frac{15}{18} \\ x = 0.8333334[/tex]
therefore x = 0.8333334.
Mr. Schwartz builds toy cars. He begins the week with a supply of 85 wheels, and uses 4 wheels for each car he builds. Mr. Schwartz plans to order more wheels once he has fewer than 40 wheels left.
The inequality that can be used to find the number of cars, x, Mr. Schwartz builds before he places an order for more wheels is
Answer:
solution: Mr. Schwartz will need to order more wheels after building 12 cars.
explanation:
Mr. Schwartz begins with total number of wheels = 85
he has to order more wheels once he left with less than 40 wheels
so min. no. of wheels he can use before ordering more wheels = 85-40 = 45
Mr. Schwartz uses 4 wheels to build 1 car
Mr. Schwartz uses 45 wheels to build 45÷4 = 11.25 cars
then, if he builds 12 cars then he needs 12×4 = 48 wheels
total supply of wheels he begins with = 85
wheels he used to build 12 cars = 48
so total number of wheels remaining are = 85-48 = 37
since 37 is less than 40 so after building 12 cars Mr. Schwartz need to order more wheels.
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for damian's lemonade recipe, 6 lemons are required to make 5 cups of lemonade. at what rate are lemons being used in cups of lemonade per lemon?
The rate at which lemons are being used in cups of lemonade per lemon is 0.83 cups of lemonade per lemon
To find the rate at which lemons are being used in cups of lemonade per lemon, we need to divide the number of cups of lemonade produced by the number of lemons used.
In this case, 5 cups of lemonade are produced from 6 lemons, so the rate at which lemons are being used in cups of lemonade per lemon is:
5 cups of lemonade ÷ 6 lemons = 0.83 cups of lemonade per lemon (rounded to two decimal places)
the rate at which lemons are being used in cups of lemonade per lemon is 0.83 cups of lemonade per lemon
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PLEASE HELP FAST SHOW WORK AND WILL GIVE BRAINLIEST
The linear function modeled by the table is given as follows:
y = 2x - 5.
The slope and the intercept are given, respectively, by:
m = 2, b = -5.
How to obtain the linear function?
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.From the table, when x increases by 5, y increases by 10, hence the slope m is given as follows:
m = 10/5
m = 2.
Hence:
y = 2x + b.
When x = 3, y = 1, hence the intercept b is given as follows:
1 = 6 + b
b = -5.
Hence the function is:
y = 2x - 5.
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In △ABC, m∠A = x, m∠B = 2x + 2, and m∠C = 3x +4. What is the value of x?
1) 29
2) 31
3) 59
4) 61
Answer: 1) 29 (look at the image for the solution)
Step-by-step explanation:
Alonzo is going to watch a movie in his collection. He has 3 action movies, 11 comedies, and 9 dramas.
He will randomly select one movie. What is the probability that the movie he selects is not a comedy?
Write your answer as a fraction.
The probability that he does not select a comedy is 12/23
What is the probability that the movie he selects is not a comedy?If we assume that all the movies have the same probability of being randomly selected, then the probability of selecting a movie that is not a comedy is equal to the quotient between the number of movies that aren't comedies and the total number of movies.
There are:
3 action ones.
11 comiedies.
9 dramas
For a total of 23 movies, and 12 of them are not comedies, then:
P = 12/23
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2x-y=9,4x+y=21
answer this equation for a bloody cookie mate
Answer:
x=5, y=1
Step-by-step explanation:
2x-y=9
2(5)=10
10-1=9
4x+y=21
4(5)=20
20+1=21
Hope this helps! Please give brainliest!
3. Find the coordinates of the center and the measure of the radius for a circle whose equation is
x²+(y-5)² = 9
Answer:
Radius is 3 units
Center is (0,5)
Step-by-step explanation:
Compared to the standard form of the equation of a circle, [tex](x-h)^2+(y-k)^2=r^2[/tex], we have a center of [tex](h,k)\rightarrow(0,5)[/tex], and a radius of [tex]r=3[/tex].
Add.The numerator should be expanded and simplified. The denominator should be either expanded or factored.\dfrac{8x}{x^2-49}+\dfrac{5}{x^2-4x-21}= x 2−498x + x 2−4x−215 =start fraction, 8, x, divided by, x, squared, minus, 49, end fraction, plus, start fraction, 5, divided by, x, squared, minus, 4, x, minus, 21, end fraction, equals
The simplified expression after factoring numerator and denominator is (x + 7) / x.
We can start by factoring the numerator and denominator of the first fraction:
x^2 - 49 = (x + 7)(x - 7)
The denominator can also be factored using the quadratic formula or by factoring as a product of two binomials:
x^2 - 4x - 21 = (x - 7)(x + 3)
So, the first fraction can be simplified as:
(x + 7)(x - 7)/[(x - 7)(x + 3)]
We can cancel out the (x - 7) factor in the numerator and denominator, leaving:
(x + 7)/(x + 3)
Next, we can simplify the second fraction by canceling out the common factor of (x + 3) in both the numerator and denominator:
(x + 3)/x
Putting it all together, we get:
[(x + 7)/(x + 3)] * [(x + 3)/x] = x + 7 / x
Therefore, the simplified expression is (x + 7) / x.
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____The given question is incorrect, the correct question is given below:
The numerator should be expanded and simplified. The denominator should be either expanded or factored.
Simplify (x^2-49)/(x^2-4x-21)*(x+3)/x
