Answer:
n = -15
Step-by-step explanation:
Given
Sum of Integers from 15 to 50 (inclusive) = Sum of integers from n to 50 (inclusive)
n < 15
Required
Find n
We can split the given parameters to 2
i. Sum of Integers from 15 to 50 (inclusive)
ii. Sum of integers from n to 50 (inclusive)
Solving for (i): Sum of Integers from 15 to 50 (inclusive)
We'll make use of sum of n terms of an arithmetic;
This is given as follows
[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]
Where n is the number of terms from 15 to 50
T1 is the first term; T1 = 15
Tn is the last term; Tn = 50
n is calculated using
[tex]n = T_n - T_1 + 1[/tex]
[tex]n = 50 - 15 + 1[/tex]
[tex]n = 36[/tex]
The formula becomes
[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]
[tex]S_n = \frac{36}{2}(15 + 50)[/tex]
[tex]S_n = \frac{36}{2}(65)[/tex]
[tex]S_n = 18(65)[/tex]
[tex]S_n = 1170[/tex]
Solving for (ii): Sum of integers from n to 50 (inclusive)
We'll also make use of the same formula used above
[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]
Where n is the number of terms from n to 50
T1 is the first term; T1 = n
Tn is the last term; Tn = 50
n is calculated using
[tex]n = T_n - T_1 + 1[/tex]
[tex]n = 50 - n + 1[/tex]
[tex]n = 50 + 1 - n[/tex]
[tex]n = 51 - n[/tex]
The formula becomes
[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]
[tex]S_n = \frac{51 - n}{2}(n + 50)[/tex]
Recall that the Sum of Integers from 15 to 50 (inclusive) = Sum of integers from n to 50 (inclusive);
This implies that
Sn (i) = Sn (ii)
As such; we have
[tex]S_n = \frac{51 - n}{2}(n + 50) = 1170[/tex]
[tex]\frac{51 - n}{2}(n + 50) = 1170[/tex]
Multiply both sides by 2
[tex]2 * \frac{51 - n}{2}(n + 50) = 1170 * 2[/tex]
[tex](51 - n)(n + 50) = 1170 * 2[/tex]
[tex](51 - n)(n + 50) = 2340[/tex]
Open Brackets
[tex]51(n + 50) - n(n + 50) = 2340[/tex]
[tex]51*n + 51 * 50 - n * n - n * 50 = 2340[/tex]
[tex]51n + 2550 - n^2 - 50n = 2340[/tex]
Reorder
[tex]-n^2 + 51n - 50n + 2550 = 2340[/tex]
[tex]-n^2 + n + 2550 = 2340[/tex]
Subtract 2340 from both sides
[tex]-n^2 + n + 2550 -2340 = 2340 -2340[/tex]
[tex]-n^2 + n + 210 = 0[/tex]
Multiply both sides by -1
[tex]-1(-n^2 + n + 210) = -1 * 0[/tex]
[tex]n^2 - n - 210 = 0[/tex]
At this point, we have a quadratic equation; as such, it'd be solved as follows:
[tex]n^2 - n - 210 = 0[/tex]
Expand
[tex]n^2 + 15n - 14n - 210 = 0[/tex]
Factorize
[tex]n(n + 15) - 14(n + 15) = 0[/tex]
[tex](n - 14)(n + 15) = 0[/tex]
Split the above expression
[tex](n - 14) = 0 \ or\ (n + 15) = 0[/tex]
[tex]n - 14 = 0 \ or\ n + 15 = 0[/tex]
[tex]n = 14\ or\ n = -15[/tex]
The question states that n < 15;
This means that we'll discard the value of n = 14
Hence, n = -15
what pattern exists in each period of 356,039?
Answer:
1/1
Step-by-step explanation:
because that is it
7. A clerk at a bookstore is restocking a shelf of best-selling novels. He has five copies each of three different novels.
a) How many different ways can he arrange the books on the shelf?
b) How many different ways can these books be arranged on the shelf if the copies of the same novel must be grouped together?
Answer:
He can sort the books by alphabetical order.
I would estimate around 5
Step-by-step explanation:
The number of the different ways that the books can be arranged will be 126126 and 6.
What are permutation and combination?A permutation is an act of arranging items or elements in the correct order. Combinations are a way of selecting items or pieces from a group of objects or sets when the order of the components is immaterial.
A clerk at a bookstore is restocking a shelf of best-selling novels. He has five copies each of three different novels.
Then the number of the different ways by which he can arrange the books on the shelf will be
⇒ 15! / (5! x 5! x 5! x 3!)
⇒ 126,126
Then the number of the different ways can these books be arranged on the shelf if the copies of the same novel must be grouped together will be
⇒ 3!
⇒ 6
More about the permutation and the combination link is given below.
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A family has two cars. The first car has a fuel efficiency of 30 miles per gallon of gas and the second has a fuel efficiency of 15 miles per gallon of gas. During one particular week, the two cars went a combined total of 1050 miles, for a total gas consumption of 50 gallons. How many gallons were consumed by each of the two cars that week?
Answer:
Car 1 consumes 30 gallons of gas.
Car 2 consumes 20 gallons of gas.
Step-by-step explanation:
74°
X +85
33°
A) 4
C) -12
B) -5
D) -11
74+x+85+33= 180 (bc the sum of the angles of a triangle is 180º)
192=180-x
192-180=-x
12=-x
-12=x
A computer randomly generates a 5-digit string using numbers between 0 and 9 inclusive. What is the probability that the first two digits in the string are a 4 and a 2 , in that order?
Answer: 0.01.
Step-by-step explanation:
Given: A computer randomly generates a 5-digit string using numbers between 0 and 9 inclusive.
i.e. each place in 5 digit number has 10 choices.
Total ways to make such a number = [tex]10^5=100000[/tex].
If the first two digits in the string are a 4 and a 2, in that order, then the number of ays to make this kind of number = 1 x 1 x 10 x 10 x 10 = 1000 [as 4 and 2 can be put on first and second place in 1 way ]
Now, the probability that the first two digits in the string are a 4 and a 2 , in that order = [tex]\dfrac{1000}{100000}=\dfrac{1}{100}=0.01[/tex]
Hence, the probability that the first two digits in the string are a 4 and a 2 , in that order = 0.01.
p% of m PLEASE HELP IMMEDIATELY
Answer:
pm/ 100 is answer.
Step-by-step explanation:
here, p% of m
=p/100× m
= pm/ 100 ...is answer.
hope its what you are searching for..
Multiply the following using the vertical multiplication method:
3x2 + 5x + 1
x x2 - 2x + 4
Answer:
Step-by-step explanation:
the answer is b
The product of the given polynomials is 3x⁴-x³+3x²+18x+4. Therefore, option B is the correct answer.
What is multiplication?Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.
The given expression are 3x² + 5x + 1 and x² - 2x + 4
Now,
3x² + 5x + 1
× x² - 2x + 4
__________
12x²+20x+4
-6x³-10x²-2x
3x⁴+5x³+x²
_______________
3x⁴-x³+3x²+18x+4
Therefore, option B is the correct answer.
Learn more about the multiplication here:
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Which statement is true? All quadrilaterals have at least 1 pair of parallel sides. Parallelograms have 2 pairs of congruent angles. A rhombus is a rectangle. A trapezoid is a parallelogram.
Answer:
PARALLELOGRAM have 2 pairs of congruent angles
Step-by-step explanation:
QUADRILATERALS have one pair of parallel lines. If it has two sets, it NOW become a PARALLELOGRAM.
The statement first is All quadrilaterals have at least 1 pair of parallel sides. and Parallelograms have 2 pairs of congruent angles that are true.
What is quadrilateral?A figure enclosed by the four sides and the sum of all the angles are equal to 360.
Properties of a quadrilateral are:-
A quadrilateral has four sides (edges)
A quadrilateral has four vertices (corners)
A quadrilateral has interior angles that add to 360 degrees:
Types of quadrilateral are square, rectangle, rhombus, trapezoid, and parallelogram.
So here All quadrilaterals have at least 1 pair of parallel sides. and Parallelograms have 2 pairs of congruent angles that are true.
To know more about Quadrilaterals follow
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The length of a rectangle is 2 inches less than three times it’s width.and it’s perimeter is 36 inches .find the width of the rectangle. A. 5 in B .10 in C.4in
Answer:
A
Step-by-step explanation:
Let width =w in
Length = 3w - 2 in
Perimeter of rectangle = 36 inches
2* (length + width ) = 36
2*(3w -2 + w) = 36
2* (4w -2 ) = 36
2*4w - 2*2 = 36
8w - 4 = 36
Add 4 to both sides
8w - 4 + 4 = 36 +4
8w = 40
Divide both sides by 8
8w/8 = 40/8
w = 5
Width = 5 in
The graph shows the speed of Sam's car over time.
Which best describes what is happening in section C?
Speed of Car
His car is stopped.
His car is speeding up.
His car is slowing down.
His car is traveling at a constant speed.
Answer:
Its C
Step-by-step explanation:
The statement which best describes what is happening in section C is His car is slowing down.
What is Speed?Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.
Speed is a scalar quantity as it only has magnitude and no direction.
The graph is attached below.
There are 4 sections on the graph.
In the section A, the car is speeding up since the speed is increasing as the time increases.
In the section B, the speed is constant as the time increases. This means his car is traveling at a constant speed.
In the section C, speed is decreasing with time. So the car is slowing down.
In the section D again the car travels at a constant speed.
Hence in section C, car is slowing down.
Learn more about Speed here :
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If F(x) =5x/3 +5
+5, which of the following is the inverse of F(x)?
O A. F'(x) = 5(x+5)
3
O B. F'(x) = 3(x+5)
5
C. F1(x) = 5(x-5)
O D. F'(x) = 3(-5)
Answer:
[tex]f^{-1}(x)=\frac{3(x-5)}{5}[/tex]
Step-by-step explanation:
[tex]f(x)=y=\frac{5x}{3}+5\\y-5=\frac{5x}{3}\\3(y-5)=5x\\x=\frac{3(y-5)}{5}\\ => f^{-1}(x)=\frac{3(x-5)}{5}[/tex]
The inverse of the linear function, f(x), f(x) =5x/3 +5 is f⁻¹(x) = 3 (x -5) / 5. The correct option is f⁻¹(x) = 3 (x -5) / 5
What is the inverse of a function?The inverse of a function is a function that reverses the effect the original function.
Here, we have,
The original function is; f(x) =5x/3 +5
The inverse of f(x) can therefore be found by making x the subject of the equation as follows;
f(x) = 5x/3 +5
f(x) -5 = 5x/3
(f(x) -5) 3 = 5·x
x = (f(x) -5) 3 / 5
x = 3 (f(x) -5) / 5
Plugging in x = f⁻¹(x) and f(x) = x, in the above equation, we get;
f⁻¹(x) = 3 ((x) -5) / 5
f⁻¹(x) = 3 (x -5) / 5
The correct option that is an inverse of f(x) is f⁻¹(x) = 3 (x -5) / 5.
Learn more on the inverse of a function here: brainly.com/question/29652632
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Please Help 100 points
Which graph shows the solution set for Negative 1.1 x + 6.4 greater-than negative 1.3?
A number line going from negative 10 to 0. An open circle is at negative 7. Everything to the left of the circle is shaded.
A number line going from negative 10 to 0. An open circle is at negative 7. Everything to the right of the circle is shaded.
A number line going from 0 to 10. An open circle is at 7. Everything to the left of the circle is shaded.
A number line going from 0 to 10. An open circle is at 7. Everything to the right of the circle is shaded.
Answer:
see below
Step-by-step explanation:
-1.1 x + 6.4 >- 1.3
Subtract 6.4 from each side
-1.1 x + 6.4 -6.4 >- 1.3-6.4
-1.1x > -7.7
Divide each side by -1.1, remembering to flip the inequality
-1.1x/-1.1< -7.7/-1.1
x < 7
There is an open circle at 7 and a line going to the left
Hey there! :)
Answer:
C.
Step-by-step explanation:
Given:
-1.1x + 6.4 > -1.3
Subtract 6.4 from both sides:
-1.1x > -7.7
Divide both sides by -1.1. Flip the sign because you are dividing by a negative sign.
-1.1x/ (-1.1) < -7.7/(-1.1)
x < 7.
Therefore, C is the correct answer. Since the sign used is < without the equal to, an open circle would be used.
Which of the following functions best describes this graph
Answer: its c i took the test
Step-by-step explanation:
The total cost of a new calculator is
$81.05. This price includes a 10% student
discount. Followed by a 6.5% sales tax.
What was the original price of the
calculator, not including the tax or the
discount?
This question bus incomplete because it lacks the appropriate options.
Complete Question
The total cost of a new calculator is
$81.05. This price includes a 10% student discount. Followed by a 6.5% sales tax. What was the original price of the calculator, not including the tax or the discount?
A. $77.69
B. $83.99
C. $78.80
D. $84.56
Answer:
D. $84.56
Step-by-step explanation:
From the question, we are given the following values
Total cost of a new calculator = $81.05
Student discount = 10%
Sales tax = 6.5%
The formula to use is
Total price = Original price ( 1 ± r)
Where r = rate of the discount or sales tax
Step 1
Find the original price of the calculator without the discount
Because we are calculating using discount we are using the minus sign
Total price = $81.05
r = 10% = 0.1
Total price = Original price ( 1 - r)
$81.05 = Original price (1 - 0.1)
$81.05 = Original Price × 0.9
Original price = $81.05÷ 0.9
= $90.055555556
Approximately, the original price without the 10% discount is $90.06
Step 2
Find the Original price without the sales tax
Because we are calculating using sales tax we are using the plus sign
Total price = $90.06
This is because the Original price without the discount = Current total price with sales tax for step 2
r = 6.5% = 0.065
Total price = Original price ( 1 + r)
$90.06 = Original price (1 + 0.065)
$90.06 = Original Price × 1.065
Original price = $90.06÷ 1.065
= $84.563380282
Approximately, the original price without the 10% discount and 6.5% sales tax is $84.56
Solve for x: –|2x+3|=1
Step-by-step explanation:
-|2x+3|=1
-|2x+3|/-1=1/-1
|2x+3|=-1
2x=-1-3
2x=-4
2x/2=-4/2
x= -2
The length of a rectangle is three times its width.
The perimeter of the rectangle is 24cm
Calculate the area
Area of a rectangle is 27 cm²
Given:
Perimeter of a rectangle = 24 cm
Length = 3x
Width = x
p = 2(l + w)
24 = 2(3x + x)
24 = 6x + 2x
24 = 8x
24/8 = x
3 = x
Width = 3 cm ; Length = 3x = 3(3) = 9 cm
Area = length * width
= 9cm * 3 cm
Area = 27 cm²
Answer:
Area of a rectangle is 27 cm²
Step-by-step explanation:
What is 4.3 as a fraction in simplest form
Find the interest on $5,432 at 6% for 2 years.
Answer:
the interest is 5.42
Step-by-step explanation:
Answer:
Interest = 5.42
Step-by-step explanation:
what is 1 1/16 rounded to the nearest half? ( need answer now please)
Answer:
1
Step-by-step explanation:
Halves:
0
0.5
1
1.5
2
1 1/16 = 1.0625
1.0625 is between 1 and 1.5, but it is much closer to 1 than to 1.5, so answer is 1
Image attached: geometry
===================================================
Explanation:
For me, I find it easier to find the exterior angle first. For any convex polygon, the sum of the exterior angles is 360 degrees. When we talk about regular polygons with n sides, each exterior angle is 360/n degrees. In this case, we have a nonagon with 9 sides. So n = 9 is plugged into 360/n to get 360/9 = 40 as the exterior angle measure
exterior angle = 40
We could stop here since we can see the answer must be choice A. But let's keep going. To get the interior angle, we subtract the result we got from 180
interior angle = 180-(exterior angle) = 180-40 = 140
This is because any adjacent pair of interior and exterior angles must form a straight angle of 180 degrees.
--------------------
side note: you could use the formula [tex]i = \frac{180(n-2)}{n}[/tex] to find the measure of the interior angle.
A hot air balloon holds 74,000 m3 of helium. The density of helium is 0.1785 kg/m3. What’s the mass of the helium inside the balloon when it’s full? ANSWERS: 6,529 kg 414,565 kg 740 kg 13,209 kg
What is the solution to (5m)² - (2n-3m)³ if m=-3 and n=5
Answer:
-6634
Step-by-step explanation:
(5m)² - (2n-3m)³ if m=-3 and n=5
= (5 * (-3))^2 - (2 * 5 - 3 * (-3))^3
= (-15)^2 - (10 - (-9))^3
= 225 - (19)^3
= 225 - 6859
= -6634
Suppose that y varies directly as x. When x is 7, y is 2. Solve for y when x is 63. (Enter an exact number.)
The diagram shows a sector of a circle radius 10 cm, 135°. Find the perimeter of the sector
Answer:
22.4 cm
Step-by-step explanation:
Given
r = 10 cm
θ = 135°
Perimeter of sector is:
P = 2r + 2πr(θ/360)
P = 2*10 + 2(3.14)(135/360) = 22.4 cm (rounded)
what's the slope of a line that passes through (-8,-16) and (18,5)?
Answer:
C. 21/26
Step-by-step explanation:
Slope Formula: [tex]m = \frac{y2-y1}{x2-x1}[/tex]
Plug in our coordinates:
m = (5 + 16)/(18 + 8)
m = 21/26
Answer:
C. 21/26
Step-by-step explanation:
Slope is determined by the change (or difference) in the y-coordinates divided by the change (or difference) in the x-coordinates.
Here, our y-coordinates are -16 and 5, so:
5 - (-16) = 5 + 16 = 21
Our x-coordinates are -8 and 18, so:
18 - (-8) = 18 + 8 = 26
Now, we divide: 21/26.
The answer is thus C.
~ an aesthetics lover
Consider the quadratic function f(x) =
3x2–5x + 12. Which statements are true about the function and its
graph? Select three options.
Answer:
A, B, D
Step-by-step explanation:
20 POINTS AND BRAINLIEST! There are 2 Senators from each of 50 states. We wish to make a 3-Senator committee in which no two members are from the same state. A) How many ways can we choose three states to be represented?
Answer:
A) 19,600
Step-by-step explanation:
A) How many ways can we choose three states to be represented?
To solve for the above question, we would be using the Combination formula
The combination formula is given as:
C(n , r) = nCr = n!/r! (n - r)!
Where n = 50
We are told that we are to make a 3-Senator committee in which no two members are from the same state. So,
r = 3 ( senator committee)
nCr = n!/r! (n - r)!
50C3 = 50! / 3! (50 - 3)!
50C3 = 50! / 3! × 47!
50C3 = 19,600
Therefore, the number of ways can we choose three states to be represented is 19,600 ways.
Find the points of intersection of the following function graphs: y=14−2.5x and y=1.5x−18 PLEASE HELP ONLY HAVE 20 MINUTES
Answer:x=8 Y=-6
Step-by-step explanation:
14-2.5x=1.5x-18
+18. +18
32-2.5x=1.5x
+2.5x =2.5x
32= 4x
Divide 4 to both sides you get
8=x
Y=14-2.5(8)
Y=14-20
Y=-6
Put the following numbers in order from greatest to least 7 030 400, 70 000 200, 78 330, 790 300, 709 400, 70 800
Answer:
70 000 200, 7 030 400, 790 300, 709 400, 78 300, 70 800
Step-by-step explanation:
Greatest is always the number with the most digits.
Answer:
70 000 200, 7 030 400, 790 300, 709 400, 78 330, 70 800
Step-by-step explanation:
To answer this I simply needed to know the orders of numbers from ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions, tens of millions, and hundreds of millions. You must also know which digits hold the most value.
[tex]1\\10\\100\\1,000\\10,000\\100,000\\1,000,000\\10,000,000\\100,000,000[/tex]
Find the area of the right triangle. If necessary, round to the nearest tenth.
A right triangle with side 15 yards and hypotenuse 25 yards.
a.
20 yd
b.
150 yd
c.
60 yd
d.
300 yd
Answer:
B - 150 yd
Step-by-step explanation:
Obviously the first step is to find the missing measurement. To do this, you use the Pythagorean theorem; a² + b² = c².
In this case, let's label the the missing side A, the height B, and the hypotenuse C.
X² + 15² = 25²
Then you must figure out what 15² and 25².
15² = 225
25² = 625
The next step is to subtract 15² (225) from 25² (625), which will give you the result of X².
625 - 225 = 400.
Now you know X² = 400, you can find the square root of 400 to give you the length of the triangle.
√400 = 20.
The missing length of the triangle is 20 yards.
Now it's just a matter of finding the area by using the formula;
A = [tex]\frac{bh}{2}[/tex]
Or,
(20 × 15) ÷ 2 = 150.
And there's your answer. Don't forget to add the units.
Hope this helped.