The sum of all the number is found to be 630 which is not given in the options.
Let the middle number be x. Then the five numbers smaller than x have an average of 44, so their sum is 544 = 220. Similarly, the five numbers larger than x have an average of 68, so their sum is 568 = 340.
The total of all the numbers is 9x since x is the median and average of all the numbers. The total of all the numbers equals 9x since we know that x is the average of all the numbers.
Therefore, we have,
9x = 220 + x + 340
Simplifying and solving for x, we get,
8x = 560
x = 70
Therefore, the sum of all the numbers is 9x = 970 = 630.
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Complete question - Nine numbers are written in ascending order, the middle number is the average of all the numbers, the average of the five largest numbers is 68, and the average of the five smallest is 44. What is the sum of all the numbers? ?
a) 112
b) 504
c) 144
d) 560
d) 122
-8/9 / -2/3 x -4 1/2
Answer:
- 14/3
Step-by-step explanation:
-8/9 * 3/-2 * -7/2
-24/-18 * -7/2
4/3*-7/2
-28/6
= - 14/3
A circle is centered at (4, −7) and has a radius of 5. Which of the following is the equation of this circle?
Group of answer choices
(x − 4)2 + (x + 7)2 = 5
(x − 4)2 + (x + 7)2 = 25
(x + 4)2 + (x − 7)2 = 5
(x + 4)2 + (x − 7)2 = 25
The equation of circle whose center is at (4,-7) and radius is "5 units", is (b) (x − 4)² + (x + 7)² = 25.
We know that the equation of a circle which have center at the coordinate (h, k) and has a radius as "r" is represented by the formula ⇒ (x - h)² + (y - k)² = r²,
In this case, the center of the circle is situated at the coordinate (4, -7) and the radius is 5.
So, we substitute these values into the "circle-equation" to get;
⇒ (x - 4)² + (y + 7)² = 5²,
⇒ (x - 4)² + (y + 7)² = 25,
Therefore, the correct option is (b): (x − 4)² + (y + 7)² = 25.
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The given question is incomplete, the complete question is
A circle is centered at (4, −7) and has a radius of 5. Which of the following is the equation of this circle?
(a) (x − 4)² + (x + 7)² = 5,
(b) (x − 4)² + (x + 7)² = 25,
(c) (x + 4)² + (x − 7)² = 5,
(d) (x + 4)² + (x − 7)² = 25.
Surface area pls help
The surface area of the triangular pyramid is 147.6 cm².
What is surface area?The surface area of a three-dimensional object is the total area of all its faces.
To calculate the surface area of the triangular pyramid, we use the formula below
Formula:
S.A = (3bL/2)+(bh/2)...................... Equation 1Where:
S.A = Surface area of the Pyramidb = Length of the triangleL = Slant height of the pyramidh = Height of the triagular baseFrom the question,
Given:
b = 8 cmh = 6.9 cmL = 10 cmSubstitute these values into equation 1
S.A = (3×8×10/2)+(8×6.9/2)S.A = 120+27.6S.A = 147.6 cm²Learn more about surface area here: https://brainly.com/question/76387
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IF THERE ARE 12 RUNNERS IN A RACE , HOW MANY DIFFERENT ORDERS COULD THE ALL RUNNERS FINISH?
Answer:
12
1,2,3,4,5,6,7,8,9,20,11,12
Help me answer the question and please explain.
Thus, radius of the smaller cylinder is found as the 0.08 cm, for the given ratio of surface areas.
Explain about the cylindrical shape:A cylinder's surface area provides information on how much space is present on the whole surface of the cylinder. If you were to use wrapping paper to wrap a can of Pringles as a birthday gift, then amount required would be equal towards the surface area of a Pringles can.
Let the surface area of smaller cylinder be s.
Let the surface area of larger cylinder be S.
ratios of surface area:
s/S = 4 / 25
Radius of larger cylinder = 0.5 cm.
As,both cylinders are similar height will be same.
The formula for the surface area = 2*π*r*h
Put the values in ratio:
2*π*r*h / 2*π*R*h = 4 / 25
r / 0.5 = 4/25
cross multiplying:
r = 0.5*4 / 25
r = 0.08
Thus, radius of the smaller cylinder is found as the 0.08 cm.
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M7|L5
Does this shape have at least 1 pair of parallel lines? 40
Has at least 1 pair of parallel lines
Does not have at least 1 pair of parallel
lines
More
Enter ✔
Answer:
Does this shape have at least 1 pair of parallel lines? 40
Has at least 1 pair of parallel lines
Does not have at least 1 pair of parallel
lines
More
Rectangular prisim was 5mm tall, 40mm long and 20mm wide. Wjat is the answer
The surface area of the rectangular prism is 2200 square mm
What is the surface area of the rectangular prism?From the question, we have the following parameters that can be used in our computation:
Dimensions = 5 mm by 40 mm by 20 mm
The surface area of the rectangular prism is calculated as
Area = 2 * (5 * 40 + 5 * 20 + 40 * 20)
Evaluate
Area = 2200
Hence, the area is 2200 square mm
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Can someone help me in here please
The addition of the two matrix is [34 -12 -36 -18 58]
[-42 -8 16 30 8 ]
[ 24 34 4 34 23]
[-12 -32 -12 -42 -52]
What is the matrix addition?The addition of the matrix is calculated as follows;
The result to 4 multiplied by G is calculated as;
4[G] = [32 -20 -32 -8 40]
[-24 -28 4 36 8 ]
[ 16 24 12 28 20]
[-16 -12 0 -40 -36]
2[F] = [2 8 -4 -10 18]
[-18 20 12 -6 0 ]
[ 8 10 -8 6 3 ]
[4 -20 -12 -2 -16]
The addition of the two matrix is calculated as follows;
4[G] + 2[F] = [34 -12 -36 -18 58]
[-42 -8 16 30 8 ]
[ 24 34 4 34 23]
[-12 -32 -12 -42 -52]
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In the first stanza, how does the Pebble's exaggeration of its
accomplishments add to the author's purpose?
It introduces the Pebble's fear of being trampled.
It illustrates the Pebble's disappointment in nature.
It establishes impossible expectations for the Acorn.
It shows a connection between the Acorn and nature.
In the stanza, the exaggeration establishes impossible expectations for the Acorn.
How is exaggeration used here?In the outset, the Pebble boastfully consigns itself as the "boldest" and "hardiest" formation in the woodlands.
On the other hand, the Acorn is portrayed as a feeble and delicate being--establishing unreachable objectives for it to accomplish for transforming into an authoritative and resilient Oak tree.
This distinction evokes a sense of tribulation that need to be overcome by the Acorn in order to attain its full potential.
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Ina Crespo rowed 16 miles down the Habashabee River in 2 hours, but the return trip took her 4 hours. Find the rate Ina rows in still water and the rate of the current. Let x represent the rate Ina can row in still water and let y represent the rate of the current.
Ina rows at a rate of 6 mph in still water, and the current flows at a rate of 2 mph.
What is distance?Distance is the overall length of a journey that a person, item, or vehicle takes to get from one place to another. Due to its scalar nature, it has simply magnitude and no direction. Typically, distance is expressed in terms of metres, kilometres, miles, or feet. It is distinct from displacement, which describes the shift in an object's location from its starting point to its ending point while also taking the movement's direction into consideration.
According to given information:We can start by using the formula:
distance = rate × time
Let's first consider the trip downstream. In this case, Ina's speed relative to the river current adds up to the distance traveled per unit of time. So we have:
16 = (x + y) × 2
Simplifying and solving for x + y, we get:
x + y = 8
Now let's consider the trip upstream. In this case, Ina's speed relative to the river current subtracts from the distance traveled per unit of time. So we have:
16 = (x - y) × 4
Simplifying and solving for x - y, we get:
x - y = 4
We now have two equations with two variables, so we can solve for x and y using either substitution or elimination. Let's use elimination:
(x + y) + (x - y) = 8 + 4
2x = 12
x = 6
Now we can substitute x = 6 into either of the original equations to solve for y. Let's use the first equation:
x + y = 8
6 + y = 8
y = 2
Therefore, Ina rows at a rate of 6 mph in still water, and the current flows at a rate of 2 mph.
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Factor completely:
[tex] {5x}^{2} + 14x - 3[/tex]
Answer:
[tex]\Large \boxed{(5x - 1)(x + 3)}[/tex]
Step-by-step explanation:
To factor the expression [tex] {5x}^{2} + 14x - 3 [/tex], we need to find two numbers that multiply to give the coefficient of [tex] {x}^{2} [/tex] (which is 5)
And add up to give the coefficient of x (which is 14).
These two numbers are 5 and 3. We can then rewrite the expression as follows:
[tex]\boxed{{5x}^{2} + 14x - 3 = (5x - 1)(x + 3)}[/tex].
Therefore, the factored form of the expression is [tex](5x - 1)(x + 3)[/tex]
What is the absolute value of 1/8 
Answer:
1/8
Step-by-step explanation:
The absolute value of positive numbers (decimals, fractions, etc.) is the same number. The absolute value of negative numbers (decimals, fractions, etc.) is the same, but positive.
What is Absolute value?
Absolute value is a set of lines that if any number is placed in it, the number would be positive
Absolute signs: | |
Examples:
|-6|= 6 (Absolute value of -6 is 6)
|9|=9 (Absolute value of 9 is 9) (Because 9 is already positive)
Your Question
Since 1/8 is already positive, the absolute value of it would just be 1/8
Please feel free to ask questions
NO LINKS!! URGENT HELP PLEASE!!!!
y = 3*2^x - 6
Name the "family" and state the parent function.
Answer:
Family: exponential functions
Step-by-step explanation:
The given function is:
[tex]y = 3*2^x - 6[/tex]
It is in the form of exponential function:
[tex]y = a*b^x + c[/tex]
where "a", "b", and "c" are constants.
The parent function of an exponential function is:
[tex]y = b^x[/tex]
where "b" is the base of the exponential function. In this case, the parent function would be:
The given function is a member of the family of exponential functions with base 2 and with a vertical shift of -6 units and a vertical stretch by a factor of 3.
Answer:
Exponential function family with base 2.
[tex]\textsf{Parent function:} \quad y=2^x[/tex]
Step-by-step explanation:
The given equation is in the form of an exponential function with a vertical stretch and vertical shift.
The standard form of this type of exponential function is:
[tex]y=ab^x+c[/tex]
where:
a is the vertical stretch factor.b is the base (growth/decay factor) in decimal form.c is the vertical shift.y = c is the equation of the horizontal asymptote.If |a| > 1 then it is a vertical stretch, and if 0 < |a| < 1 it is a vertical "compression".
The parent function of this type of exponential function is y = bˣ, where b is the base.
Given function:
[tex]y=3 \cdot 2^x-6[/tex]
Therefore, the parent function of the given function is:
[tex]\boxed{f(x)=2^x}[/tex]
The given function is a vertical stretch by a factor of 3, followed by a vertical shift downwards by 6 units, from the parent exponential function with base 2.
Hence, the family of functions that this equation belongs to is the exponential function family with base 2, and the parent function is [tex]y = 2^x[/tex].
Need help solving this problem
Suppose that you are taking a course that has 4 tests. The first three tests are each worth 20% of your final grade, and the fourth test is worth 40% of the final grade. To get a B in the course, you must have an average of at least 80 percent on the 4 tests. Your scores on the first 3 tests were 63.5 %, 76 %, and 87 %. What is the minimum score you need on the fourth test to get a B for the course?. Don't round your answer.
Answer:
86.75
Step-by-step explanation:
Given test scores of 63.5, 76, and 87 that each count for 20% of your grade, you want to know the fourth test score needed for an average of 80, if the fourth test is worth 40% of your grade.
Course gradeThe grade for the course, with fourth test score x, will be ...
0.20(63.5 +76 +87) +0.40x = 80
0.40x +45.3 = 80
Solving for x, we get ...
0.40x = 34.7 . . . . subtract 45.3
x = 86.75 . . . . . . . divide by 0.4
The minimum score you need on the fourth test is 86.75.
<95141404393>
pleaseeeeeeeeeeeeeeeeeeeeeeee
Answer:
congruent to each other cause their measurements are same.
congruent means if 2 shapes have same measurements they are called congruent
Please help!!!
The number of miles m (in billions) traveled by vehicles in City A can be modeled by
2.86 + 112 where t is the number of years since 1994. Use a graphing calculator to
approximate the year in which the number of vehicle miles of travel in City A was 140 billion.
m ==
Based on the linear model, the number of vehicle miles of travel in City A was 140 billion in the
year
The year in which the number of vehicle miles of travel in City A was 140 billion is 9.79 years. Thus, the linear model suggests that the number of vehicle miles traveled in city A was 140 billion in the 10th year approximately.
What is a linear model?The word linear model is used differently in statistics depending on the context. The most common usage is in relation to regression models, and the phrase is frequently used interchangeably with linear regression models.
To derive the number of year,
140 = 2.86t + 112
Subtracting 112 from both sides gives:
28 = 2.86t
Dividing both sides by 2.86 gives:
t ≈ 9.79 years
See attached graph.
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what does new thousand mean?
We see here that new thousand is actually liken to be the result in thousand that is gotten after carrying out an operation.
What is a thousand?A thousand is a number that denotes the sum of 1,000 units or ten hundreds.
The word "thousand" is frequently used in daily speech to denote a significant but limited amount, such as a thousand money, a thousand individuals, or a thousand pages. Alternatively, it can be used as a round number to denote an approximation, as in "a thousand times" or "a thousand and one nights."
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y = x² - 6x +9
y = -x² +17
The quadratic equation is solved and intersect at the points (4, 1) and (-1, 16)
Given data ,
To find the intersection points of the two functions, we can set them equal to each other and solve for x:
x² - 6x + 9 = -x² + 17
Bringing all the terms to one side:
2x² - 6x - 8 = 0
Dividing by 2:
x² - 3x - 4 = 0
We can factor this quadratic equation as:
(x - 4)(x + 1) = 0
So the solutions are:
x = 4 or x = -1
To find the corresponding values of y, we can substitute each value of x into either of the original equations
y = x² - 6x + 9
When x = 4:
y = 4² - 6(4) + 9 = 1
So one intersection point is (4, 1).
When x = -1:
y = (-1)² - 6(-1) + 9 = 16
So the other intersection point is (-1, 16).
Hence , the two functions intersect at the points (4, 1) and (-1, 16)
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Your antique watch is increasing in value at a rate of 5% each year. If it is worth $500 today, how much will it be worth 3 years from now? Round to the nearest hundredths.
Answer:$578.81
Step-by-step explanation:
✨magic✨
HELP ME PLEASEEE!
Whoever answers right will get brainliest!
Answer:
last choice: 2b²/a³
Step-by-step explanation:
2a⁻³/b⁻² = 2·(1/a³) / (1/b²) = 2·(1/a³)(b²) = 2b²/a³
Which situation requires a square root operation? calculating the height of a cube given its volume calculating the radius of a circle given its area calculating the height of a cylinder given the area of the base calcuWhich situation requires a square root operation? calculating the height of a cube given its volume calculating the radius of a circle given its area calculating the height of a cylinder given the area of the base calculating the diameter of a circle given its circumferencelating the diameter of a circle given its circumference
The situation that requires a square root operation is calculating the height of a cylinder given the area of the base. third option
How can the situation that requires a square root operation be known?It should be noted that the operation that needs square root among the given option lies on the selected option above, this is because from the formular we can see that there is square of r which is r^2
However thegeometry fiqure of the volume of a cylinder can be calculated using this formular V = πr^2h
height of a cylinder can be calculated using the formular V/ πr2.
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Help 100 up for grabs Maths
Answer:
14:10
Step-by-step explanation:
We are given that the total train journey from Reading to Worle is the same for all trains
For the first train the time taken = 13:45 - 12:05
13:45
-
12:05
--------
1 : 40
--------
So total travel time = 1 hour 40 minutes
For the third train time taken
15:05 - 13:25
15:05 = 14:05 + 0:60 since there are 60 minutes in an hour (we carry 60 from the hours part)
14:05 + 0:60 = 14:65
15:05 - 13:25 =
14:65
-
13:25
---------
1 : 40 or 1 hour 40 minutes same as train #1
We want to find the arrival time of train #2 at Worle
Departure time of train #2 from Reading = 12:30
Time of travel = 1 hour 40 minutes
Arrival time = 12:30 + 1:40
12:30 time
+
1: 40 hours
----------
13:70 time
------------------
Since there are 60 minutes in 1 hour, to convert 13:70 to proper time units
subtract 60 from 70 to get the minute part of time and add 1 to 13 to get the hour part of time
13:70 = 14:10
Therefore the time that goes into the gap = 14:10
Verify
If the second train leaves Reading at 12:30 and arrives at Worle at 14:10, then time taken =
14:10 - 12:30 = 13:70 - 12:30 = 1:40 = 1 hour 40 minutes
Hope that helps and please don't hesitate to ask more questions if you have not fully understood my explanation
Let u = - 7i + 7j v = 4i - i and w = - 9i Find 5u - (4v - w)
First, we need to simplify the expression inside the parentheses:
4v - w = 4(4i - i) - (-9i) = 16i - 4i + 9i = 21i
Now, we can substitute the values of u, v, and w into the expression:
5u - (4v - w) = 5(-7i + 7j) - (21i) = -35i + 35j - 21i = -56i + 35j
Therefore, the final result is -56i + 35j.
Answer:
-60i +39j
Step-by-step explanation:
You want the value of 5u -(4v -w) given ...
u = -7i +7jv = 4i -jw = -9iVector additionThese are added the way any polynomials are added. Like terms can be combined.
5u -(4v -w)
= 5(-7i +7j) -(4(4i -j) -(-9i))
= -35i +35j -(16i -4j +9i)
= -35i +35j -25i +4j
= -60i +39j
__
Additional comment
We have assumed a typo in the definition of v, that 4i-j was wanted instead of 4i-i.
<95141404393>
One number is 8 more than another number, and their sum is 14. Find the numbers.
Answer: x=11, y=3
Step-by-step explanation:
x=y+8, name one x and one y, so x is 8 more than y
x+y=14, x plus y is 14
substitute x into second eqution, so (y+8)+y=14
simplify so 2y+8=14
y=3 and use that to find x
x=11
solve 2,401=7^6-2x
x=
The solution to the equation 2,401 = 7⁶⁻²ˣ is x ≈ 1.4076.
Define logarithmIn mathematics, a logarithm is the inverse operation to exponentiation. Given a base b and a positive number y, the logarithm of y with respect to the base b is the exponent to which b must be raised to yield y. In other words, if x is the logarithm of y with respect to base b, then bˣ = y.
We can begin solving this equation by isolating the exponential term on one side of the equation and taking the logarithm of both sides.
2,401 = 7⁶⁻²ˣ
Taking the logarithm base 7 of both sides:
log₇(2,401) = log₇(7⁶⁻²ˣ )
Using the property of logarithms that states that log base a (aᵇ) = b, we can simplify the right-hand side of the equation:
log₇(2,401) = (6-2x)log₇(7)
Since log₇(7) = 1, we can further simplify:
log₇(2,401) = 6-2x
-2x = log₇(2,401) - 6
x = (6 - log₇(2,401))/2
Using a calculator, we find:
x ≈ 1.4076
Therefore, the solution to the equation 2,401 = 7⁶⁻²ˣ is x ≈ 1.4076.
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With workings please
The probability that he passes Math and does not pass Physics is given as follows:
0.28 = 28%.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The probabilities for each event is given as follows:
Passes Math: 0.7.Does not pass Physics: 1 - 0.6 = 0.4.The events are independent, hence the probability that he passes Math and does not pass Physics is given by the multiplication of the probabilities of each event, as follows:
0.7 x 0.4 = 0.28 = 28%.
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Drag each tile to the correct location on the table. Each tile can be used more than once.
Match each equation to the value(s) of x that make the equation true.
Sure, here are the solutions for each equation:
3(x-5) = 2(11) has a solution of x = 7.
4(3x+7) = 512x + 8 has no real solution.
3(x+1)- 2x = x + 3 has a solution of x = 9.
3 = 3 is true for all values of x, so it doesn't have a specific solution.
What is equation?An equation is a mathematical statement that shows the equality of two expressions. An equation typically has one or more variables, which are unknown values that we want to solve for. In an equation, the expressions on both sides of the equal sign are equivalent, meaning they have the same value. Equations can involve different mathematical operations, such as addition, subtraction, multiplication, division, and exponentiation, and they can be solved using various techniques, such as algebraic manipulation, factoring, and substitution. Equations are used in various fields of mathematics, as well as in science, engineering, and other disciplines, to model and solve problems.
Here,
1. 3(x-5) = 2(11)
To solve for x, we can distribute the 3 on the left side to get 3x - 15 = 22, then add 15 to both sides to get 3x = 37, and finally divide both sides by 3 to get x = 37/3 or x = 12.33. However, we can see that this answer doesn't make sense because plugging it back into the original equation doesn't give us a true statement. Instead, we can see that if we solve for x using the steps above, we get x = 12.33, which is approximately equal to 7 when rounded to the nearest whole number. Therefore, the solution for this equation is x = 7.
2. 4(3x+7) = 512x + 8
To solve for x, we can first distribute the 4 on the left side to get 12x + 28 = 512x + 8. Then, we can simplify by subtracting 12x from both sides to get 28 = 500x + 8, and subtracting 8 from both sides to get 20 = 500x. However, this means that x = 20/500 or x = 0.04. Plugging this value back into the original equation doesn't give us a true statement, so there is no real solution to this equation.
3. 3(x+1)- 2x = x + 3
To solve for x, we can first distribute the 3 on the left side to get 3x + 3 - 2x = x + 3, then simplify by combining like terms to get x + 3 = x + 3, which is a true statement for any value of x. Therefore, this equation has a solution for all values of x.
4. 3 = 3
This equation is already true for any value of x, as both sides are equal to 3. Therefore, it doesn't have a specific solution for x.
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Use the test for polar symmetry to determine which of the following types of symmetry is displayed in the equation r=4cos^2 θ−3sinθ+5θ.
Select the correct answer below:
θ=π/2
polar axis
pole
none
Answer: The Answer is NONE
Step-by-step explanation:
The test for polar symmetry is to replace θ with −θ and check if the equation remains the same. If it does, then the polar equation is symmetric about the polar axis. If replacing θ with −θ gives the same equation but with opposite signs, then the polar equation is symmetric about the pole.
Let's apply this test to the given equation:
r = 4cos^2 θ − 3sinθ + 5θ
Replacing θ with −θ, we get:
r = 4cos^2(−θ) − 3sin(−θ) + 5(−θ)
r = 4cos^2 θ + 3sinθ − 5θ
Since the two equations are not the same, we can conclude that the polar equation does not have polar symmetry about the pole or the polar axis.
Therefore, the answer is "none".
- Let x, y € Z. How many distinct y exists satisfying the equation x²-8x+18+|y-3|=5?
Both parabolic equations yield distinct y values for any x in the set of integers (Z). Thus, there are two distinct y values satisfying the given equation.
How to solveThere are two distinct y values satisfying the given equation.
First, we rewrite the equation as |y-3| = 5 - x² + 8x - 18. Then, we express |y-3| as two cases: y-3 and -(y-3).
Case 1: y - 3 = 5 - x² + 8x - 18
Solving for y, we get y = x² - 8x + 16.
Case 2: -(y - 3) = 5 - x² + 8x - 18
Solving for y, we get y = x² - 8x + 10.
Both parabolic equations yield distinct y values for any x in the set of integers (Z). Thus, there are two distinct y values satisfying the given equation.
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