The number of terms in the Arithmetic Progression is 20 if the sum is 990.
How to find the number of terms in an Arithmetic Progression?We should know that Arithmetic Progression is a type of sequence in which the difference between consecutive terms are derived from the addition or subtraction of a common tern known as the common difference (d).
The given parameters are
Sum of the Arithmetic Progression (n)=990
Common difference (d) =5
The common difference is derived as follows:
5*0+2=2
5*1+2=7
5*2+2=12
5*3+2=17
d=7-2=12-7=17-12=5
The formed AP is 2,7,12,17,.....
Using the formula
[tex]S_{n} =[/tex]n/2[{2a+(n-1)d}
Where:
a=first term n=number of termsd=common differenceSn=sum of termApplying the formula
990=[tex]\frac{n}{2}[/tex][2*2(n-1)5]
1980=n[4+5n-5]
1980=4n+5n²-5n
Rearrange the equation
5n²-n-190=0
Solving the equation
[tex]n=\frac{-b \frac{+}{-}\sqrt{b^{2}-4ac } }{2a}[/tex]
Where
a=5
b=-1
c=-1980
Applying the formula
n=[tex]\frac{1+199}{10} or \frac{1-199}{10} \\[/tex]
200/10 or -198/10
n=20 or n=-19.8
Taking the positive value of n=20
There the number of terms in the AP is 20
In conclusion, the number of terms in the Arithmetic Progression is 20 if the sum is 990.
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serena's company decided to reduce the number of levels within the job structure and as a result, she has 20 more people who report to her. her company implemented .
Serena's company implemented the process of Delayering.
Process of Delayering:To improve operational efficiency, delayering is the act of removing levels of hierarchy between the top and bottom levels of staff.
Delayering often involves the removal of intermediate managers, giving top managers better access to the business as a whole and fostering the necessary openness.
The delayering process has benefits and drawbacks of its own. Although the employer can lower pay costs, the company's ability to make decisions may suffer as a result of top managers' diminished visibility.
Delayering is helpful for reducing bureaucracy and increasing flexibility in the organizational structure. Additionally, it enhances internal communication and participation. Other advantages include increased drive and empowerment.
Given that
Serena's company decided to reduce the number of levels within the job structure and as a result, she has 20 more people who report to her. her company implemented.
By the given observation about Delayering, we can conclude that the company implemented the process of Delayering.
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Explain how you can model 3 x 2/4
The value of [y] will be 1.
What is a expression? What is a mathematical equation? What is degree of a equation?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Degree of equation is the highest power of x in the given equationGiven is the following expression -
y = 2 x (2/4)
We can write the value of [y] as -
y = 4/4 = 1
y = 1
Therefore, the value of [y] will be 1.
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A tennis ball is a sphere with a radius of 1.56 inches. A squash ball is also
a sphere with a radius of 0.78 inches. Select all the true statements.
The volume of the tennis ball is exactly 2 times the volume of the squash
ball.
The volume of the tennis ball is approximately 3 times the volume of the
squash ball.
The volume of both the tennis ball and squash ball is proportionate to the
scale factor of the radii.
The scale factor of the volume of the tennis ball to the volume of the
squash ball is approximately 8.
The volume of the tennis ball is 5.067 cubic inches and the volume of the
squash ball is about 0.63 cubic inches.
The two true statements about these are,
The volume of both the tennis ball and squash ball is proportionate to the
the scale factor of the radii.
The scale factor of the volume of the tennis ball to the volume of the
squash ball is approximately 8.
In geometry, a sphere is a three-dimensional solid figure, which is round in shape.
The surface area is 4πr².
The volume is (4/3)πr³.
The diameter is 2×radius of the sphere.
Given, A tennis ball is a sphere with a radius of 1.56 inches. A squash ball is also a sphere with a radius of 0.78 inches.
So, The volume of the tennis ball is (4/3)π(1.56)³ = 16 cubic inches.
The volume of the squash ball is (4/3)π(0.78)³ = 2 cubic inches.
The volume of both the tennis ball and squash ball is proportionate to the
the scale factor of the radii.
The scale factor of the volume of the tennis ball to the volume of the
squash ball is approximately 8.
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33. Let M2x2 be the vector space of all 2x 2 matrices, and define T : M2x2 → Mo by T(A) A + AT, where a. Show that T is a linear transformation. b. Let B be any element of M2 c. Show that the range of T is the set of B in M2x2 with the d. Describe the kemel of T such that BT B. Find an A in M2xz such that T(A) B property that B B
a) T( K₁A₁+K₂A₂)= K₁T(A₁)+K₂T(A₂). So, T is a linear transformation.
b) T(A)=B, if B be any element of M₂
c) Range of T=={A∈ [tex]M_{ 2*2}[/tex]/[tex]A^{T}[/tex]=-A}
What is meant by matrix?A matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions arranged in rows and columns that is used to represent a mathematical object or an attribute of such an item.
A square matrix's determinant is a number connected with the matrix that is crucial for studying a square matrix; for example, a square matrix is invertible if and only if it has a nonzero determinant, and a square matrix's eigenvalues are the roots of a polynomial determinant.
Define T: [tex]M_{ 2*2}[/tex] ⇒ [tex]M_{ 2*2}[/tex] by T(A)=A+[tex]A^{T}[/tex]
a) Let T is a linear transformation
Consider K₁A₁+K₂A₂ ∈ [tex]M_{ 2*2}[/tex]
T( K₁A₁+K₂A₂)= K₁A₁+K₂A₂+( K₁A₁+K₂A₂)[tex]( K₁A₁+K₂A₂)^{T}[/tex]
= K₁T(A₁)+K₂T(A₂)
T( K₁A₁+K₂A₂)= K₁T(A₁)+K₂T(A₂)
Therefore, T is a linear transformation.
b) Let B∈ [tex]M_{ 2*2}[/tex] such that [tex]B^{T}[/tex]=B
Therefore, B is a symmetric matrix.
Let A=(1/2)B∈ [tex]M_{ 2*2}[/tex]
T(A)=A+[tex]A^{T}[/tex]
=(1/2)B+[tex](1/2B)^{T}[/tex]
T(A)=B
A=(1/2)B such that T(A)=B
c) Range of T is the set of B in [tex]M_{ 2*2}[/tex], [tex]B^{T}[/tex]=B
T( [tex]M_{ 2*2}[/tex])={B∈ [tex]M_{ 2*2}[/tex]/ [tex]B^{T}[/tex]=B}
d) Kernel of T={A∈ [tex]M_{ 2*2}[/tex]/T(A)=0)
={A∈ [tex]M_{ 2*2}[/tex]/A+[tex]A^{T}[/tex]=0}
={A∈ [tex]M_{ 2*2}[/tex]/[tex]A^{T}[/tex]=-A}
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Three points Assuming M22 is the vector space containing all 22 matrices, T: M22 M22 is defined as T(A) = A + AT.
T is a linear transformation, therefore demonstrate it.
b) Assume that B is any element from M22 where BT = B. In M22, look for an A such that T(A) = B.
c) Explain the T kernel.
a) Verifying that T preserves sums and multiplication by scalars—which implies that T(0) = 0 in particular—is sufficient to determine if T is linear.
Additions: T(A+B) = A+B+A+B T = A+B+A T +B
T = (A + A T ) + (B + B T ) = T(A) + T (B).
Scalar multiplication
T(c · A) = (c · A)
T = c · A
T = c · T(A) (A).
b) Calculate A = 1 2B. Since AT = 1 2BT = 1 2B, T(A) = A + A.
T = \s1 \s2 \sB + \s1 \s2 \sB = B.
c) If 0 0 0 0 = A + A, then and only if A = a b c d, A is in the kernel of T.
If and only if 2a = b + c = 2d = 0, i.e., a = d = 0 and c = b, then T = a b c d + a c b d = 2a b + c b + c 2d. Therefore, the set ker(T) = 0 b b 0 : b R is the kernel of T.
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In a company, 90% of the workers are woman. If 430 people work for the company who aren’t woman, how many workers are there in all? Use pencil and papare. Show two different ways that you can solve this problem
4300 workers are there in all.
What is algebra?
One of the many branches of mathematics is algebra. Algebra, which is a common thread throughout practically all of mathematics, is broadly defined as the study of mathematical symbols and the rules for using these symbols in formulas.
Here, we have
In a company, 90% of the workers are women.
430 people work for the company who aren’t women.
% of male = 10%
Now,
10% of x = 430
10÷100 × x = 430
x = 4300
Hence, 4300 workers are there in all.
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On a number line, point d is at -6, and point e is at 8. point f lies between points d and e. if is , where does point f lie on the number line? point f is at on the number line.
The point F lies on 4.5 in the number line.
What is the number line?
The number line is a One dimensional representation of point referring by a number only.
We know that if a point divides a line joining the points at x, y in the number line respectively in m:n ratio then that point lies on
= (my+nx)/(m+n) in the number line.
Here in the given problem that,
Point D lies on -6 in the number lin
Point E lies on 8 in the number line
And F lies between D and E points and DE:EF = 3:1
So the point F clearly divides the staright line DE joining the point D at -6 and E at 8 in 3:1 ratio.
So the point F lies on = (1*(-6)+3*8)/(3+1) = (-6+24)/4 = 18/4 = 4.5
Hence, the point F lies on 4.5 in the number line.
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An electronic manufacturer determine that the profit P (in dollar) obtained by producing x unit of a DVD player and y unit of a DVD recorder i approximated by the model P(x, y) = 8x 10y − (0. 001)(x2 xy y2) − 10, 000. Find the production level that a maximum profit. What i the maximum profit?
The production level that a maximum profit is 186000 and the maximum profit will at the points of (200, -4000) , under the concept of absolute maximum value.
The P(x, y) = 8x+ 10y − (0. 001)(x²+ xy+ y²) − 10, 000, the first partial differentiate of the given equation with respect to x and y,
Px= ( 8x+ 10y − (0. 001)(x²+ xy+ y²) − 10, 000) = 8-0.001(2x-y) ....2
Py= 8x+ 10y − (0. 001)(x2+ xy+ y2) − 10, 000) = 10-0.001(x-2y) ... 3
Considering the above equation to be equal to zero :
=>8-0.001(2x-y) =0 =>0.001(2x-y) =8 .....4
=>10-0.001(x-2y) =0 =>0.001(x-2y) = 10 ...5
Solving the equations 4 and 5 we get the lues of x and y we get are :
x= 2000, and y = -4000 , Now the partial differentiate for the equations 2 ad 3 are with respect to x and y :
pxx(x,y)=-0.002
pyy(x,y)= 0.002
pxy(x,y) =-1
The discriminant of the function wil be at (2000,-4000):
D = 0.002*-0.002 -(-1)^2 =-1.0004 ,here D <0, so the critical values (200, -4000) reaches the maximum value .So the production level will be :
P(2000, -4000) = 8x+ 10y − (0. 001)(x2+ xy+ y2) − 10, 000 = 186000
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The F distribution's curve is positively skewed.
T/F
Answer: True
Step-by-step explanation:
-The f-distribution curve is positively skewed towards the right with a range of 0 and ∞
The value of F is always positive or zero. It never has negative values.
О
A
13x + 13
7x+7
60°
с
B
Answer:
x = 9
Step-by-step explanation:
(7x + 7) + 60 = 13x + 13 (exterior angle)
7x + 67 = 13x + 13
6x = 54
x = 9
show that if f is a function from s to t, where s and t are finite sets with |s| > |t|, then there are elements s1 and s2 in s such that f(s1)
T|=|S|⟹ there is bijection F:S→T.
What are bijection function?A bijection is a function between the elements of two sets in mathematics that is also referred to as a one-to-one correspondence, an invertible function, or a bijective function.
In this function, each element of one set is paired with exactly one element of the other set, and each element of the second set is paired with exactly one element of the first set.
No elements are left unpaired. A one-to-one (injective) and onto (surjective) mapping of a set X to a set Y is known as a bijective function, or f: X Y in mathematics.
One-to-one function (an injective function; a bijection from the set X to the set Y has an inverse function from Y to X) should not be confused with one-to-one correspondence. X and Y must be finite if.
According to our question-
The function f:ST |S||T| has an injective and not a surjective nature.
Assume an injective function exists: g:TS|T||S|. |T|=|S|
(this follow from the Cantor-Bernstein theorem).
|T|=|S|⟹ F:S:T has a bijection.
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If Jodie works on the computer for 6 hours every 2 days how many hours will she work on the computer in 14 days?
[tex]\begin{array}{ccll} hours&days\\ \cline{1-2} 6 & 2\\ x& 14 \end{array} \implies \cfrac{6}{x}~~=~~\cfrac{2}{14} \implies \cfrac{6}{x}=\cfrac{1}{7}\implies 42=x[/tex]
Answer: 42 hours
add 6 every 2 days
What is the slope of this graph?
Responses
Answer:
slope = -4
Step-by-step explanation:
A (-2,5)
B (0, -3)
slope = (-3-5)/(0-(-2)
-8/2
-4
evaluate the sum of 4.2 and 466.99
The sum of decimals 4.2 and 466.99 evaluates to 471.19
How to evaluate the sum of decimals?
Decimals are numbers that consist of two parts namely, a whole number part and a fractional part separated by a decimal point e.g 2.35
Given: 4.2 and 466.99
To evaluate the sum of 4.2 and 466.99, you simply need to add the two numbers. Arrange the numbers as shown below and add as you would add other numbers.
4.2
466.99
.................
471.19
................
Therefore, the sum 4.2 and 466.99 is 471.19
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What is the answer?? please and thank you
Answer:
the answer is no
Step-by-step explanation:
The ale tax on a car that old for $13,500 i $910. At thi rate, how much higher i the tax on a car that ell for $16,500
The tax on a car that sells for $16,500 at the rate of 6.7% is $195.5 higher.
What is the percentage?
A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.
We have,
First car price is = $13,500
and tax of the first car is = $910
Second car price is = $16,500
and tax of the second car is = ?
so,
$13,500 ----- 100,
$910 ----- x
x = 910 * 100 / 13500
x = 6.7
therefore, the rate of tax is 6.7%
so, we will calculate the tax for the second car,
$16,500 ----- 100,
y ----- 6.7
y = 6.7 * 16,500 / 100
y = $1105.5
difference of tax price between two cars = $1105.5 - $910 = $195.5
Hence, the tax on a car that sells for $16,500 at the rate of 6.7% is $195.5 higher.
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a very long straight wire carries steady current in the positive direction a closed mathematical curface ahs length along the z direction
According to Fleming's left hand rule, the thumb points along + y direction, so the magnetic force will be directed along + y axis (or in the direction of flow of current.
From relation vector F= qvB [i (–k )] = + qvB(j)
Magnetic force vector F along + y axis.
The Fleming Left-hand Rule According to Fleming's left-hand rule, if we stretch the thumb, middle finger, and index finger of the left hand to make an angle of 90 degrees (perpendicular to each other) and the conductor placed in the magnetic field experiences the magnetic force.
This rule was invented in the late 1800s by John Ambrose Fleming as a simple method of determining the direction of electric current in an electric generator or the direction of motion in an electric motor.
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Which is equivalent to (3^4n)^1/2
The expression which is equivalent to the given expression as in the task content by virtue of the laws of indices is; ( 3 )^2n.
Which expression is equipped to the given expression?It follows from the task content that the expression which is equivalent to the given expression is to be determined.
Since the given expression is;
( 3^4n ) ^(1/2)
However, it follows from the power of power law of indices that the expression above can be written as follows;
( 3 ) ^ (4n × 1/2)
= ( 3 )^2n
Therefore, the required equivalent expression is; ( 3 )^2n.
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Please Help me With this ASAP (20 Points)
Answer:
200*1-0.95-0.95+0.9025
200*1-1.9+0.9025
200*0.0025
0.5
Find only the margin of error to construct a 98% confidence interval for p1 - P2. Assume the samples are random and independent. Do not construct a confidence interval. Sample statistics: nâ = 1000, x1 = 250, and n2 = 1200, x2 = 195
The required margin of error construct a 98% confidence interval for p1 - P2 is 0.0403.
What is margin of error?Margin of errors, in statistics, is the level of blunder in results got from irregular examining overviews. A higher wiggle room in measurements shows less probability of depending on the consequences of a review or survey, for example the certainty on the outcomes will be lower to address a populace.
According to question:given data
n1 =1 000 x1 = 250
pˆ1 = x1n1 = 2501000 = 0.250
n2 = 1200 x2 = 195
pˆ2 = x2n2 = 1951200 = 0.1625
We have given confidence interval ,
98% ci for p1−p2.
Then,
α = 1 - 0.98 = 0.02
[tex]Z_{\alpha /2}[/tex] = [tex]Z_{0.01}[/tex] = 2.326
Again,
E = [tex]Z\sqrt{\frac{p1(1-p1)}{n1}+ \frac{p2(1-p2)}{n2} }[/tex]
E = [tex]2.326\sqrt{\frac{0.250(1-0.250)}{1000}+ \frac{0.1625(1-0.1625)}{1200} }[/tex]
E = 0.0403
Thus, required margin of error is 0.0403.
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pls help right now I need help
giving brainliest
this is reading btw
Answer:
The answer is A
Step-by-step explanation: I'm so smart
need help with finding angle
Answer:75
Step-by-step explanation:
Since the total angle in the rhombus adds to 360, we minus the 2 110 and get 140. The 65 degrees is reflected on the other side, so we subtract 65 from 140, leaving 75.
A. Ue Pythagora’ Theorem to find the altitude of the triangle hown. B. Write the trigonometric ratio for a 60° angle. C. Write the trigonometric ratio for a 30° angle
The Trigonometric ratios are:
P/H = Sinθ
B/H = Cosθ
P/B = Tanθ
H/P = Cosecθ
H/B = Secθ
B/P = Cotθ
Where,
'P' represents the perpendicular
'B' represents the base
'H' = represents the hypotenuse
P/H = Sinθ
B/H = Cosθ
P/B = Tanθ
A. As the values of p, b or h are not given.
Pythagoras Theorem states that:
h² = p² + b² or h = [tex]\sqrt{p^2 + b^2}[/tex]
Altitude of a triangle is usually given by the perpendicular,
So,
h² = p² + b²
h² - b² = p²
p² = h² - b²
p = [tex]\sqrt{h^2 - b^2}[/tex]
B. The trigonometric ratios for θ = 60°
Sin 60 = √3/2
Cos 60 = 1/2
Tan 60 = √3
C. The trigonometric ratios for θ = 30°
Sin 30 = 1/2
Cos 30 = √3/2
Tan 30 = 1/√3
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eighty-seven and seven hundred twenty-eight thousandths in  Decimal form help plssss
Eighty-seven and Seven hundred twenty-eight thousandths in decimal form is 87.728.
How to change in decimal form?
Given the unclear wording, there are various ways to respond to this question, depending on exactly what you mean.The answer is 338.14 if you meant "three hundred and thirty-eight and seven hundred divided by five thousand."The answer is 338.705 if you mean "three hundred and thirty eight and seven hundred five divided by one thousand."The two solutions are 0.0676 and 0.14 if you meant "three hundred thirty eight divided by five thousand AND seven hundred divided by five thousand."Eighty-seven and Seven hundred twenty-eight thousandths in decimal form:
= 87 + 728/1000
= 87 + 0.728
= 87.728
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Determine which integer will make the inequality 5x + 12 > 2x + 6 false.
S:{−3}
S:{3}
S:{−1}
S:{1}
Answer:
-3
Step-by-step explanation:
we just fill in x to see if it is true
5(-3)+12>2(-3)+6
-15+12>-6+6
-3>0
false
5(3)+12>2(3)+6
15+12>6+6
27>12
true
5(-1)+12>2(-1)+6
-5+12>-2+6
7>4
true
5(1)+12>2(1)+6
5+12>2+6
17>8
true
Hopes this helps please mark brainliest
Roman numeral representing least 3 digit number is??
The solution is Option 4.
Roman numeral representing the least 3 digit number which is 100 is C
The Roman numeral for 100 = C
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 least 3 digit number be A
Now , the value of A = 100
where 100 is the lease 3 digit number
And , the Roman numeral for 100 is given by C
Therefore , the value of 100 in Roman Numeral is C
Hence , The Roman numeral representing the least 3 digit number which is 100 is C
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PLEASE HELP ME
What is the y-intercept of this line?
I keep getting confused someone please help me and explain it better to me
Answer:
2
Step-by-step explanation:
The y-intercept is the point at which the graph crosses the y-axis.
(I have marked it in blue on the attached graph).
From inspection of the given graph, the line crosses the y-axis at point (0, 2). So the y-intercept is 2.
50 Points!!! Are RHS and HL triangles the same? Yes or no? Explain.
Answer:
Yes------------------
RHS and HL refer to same thing.
A right angled triangle has one hypotenuse and two sides.
If the hypotenuse and one side of one triangle is congruent to hypotenuse and one side of another triangle, then the two triangles are congruent.
We know sides of a right triangle are also called the hypotenuse and legs. RHS is also called HL because they both refer to hypotenuse and one side or leg.
Which equation represents the partial sum of the geometric series? 125 + 25 + 5 + 1.
The correct option which represents sum expressed in sigma notation is A.
What is sigma notation?
A series is represented in an exceedingly compact type, referred to as summation or sigma notation. The greek capital letter, ∑ , is employed to represent the total.
The series 4+8+12+16+20+24 is expressed as ∑n= 4n . The expression is browse because the total of 4n as n goes from one to six . The variable n is termed the index of summation.
The geometric series.
Main body:
∑ 125 (1/5)ⁿ⁻¹ ; where, n = 1 to 4.
Now, Calculate the partial sum of the geometric series as;
The geometric series = ∑ 125 (1/5)ⁿ⁻¹
Substitute n = 1, 2, 3, 4, we get;
= 125 (1/5)¹⁻¹ + 125 (1/5)²⁻¹ + 125 (1/5)³⁻¹ + 125 (1/5)⁴⁻¹
= 125 (1/5)⁰ + 125 (1/5)¹ + 125 (1/5)² + 125 (1/5)³
= 125 + 25 + 125/25 + 125/125
= 125 + 25 + 5 + 1
Thus, The partial sum of the geometric series is;
⇒ 125 + 25 + 5 + 1
Option A is true.
The correct question is in the figure.
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the hudson valley renegades stadium hold a maximum of 4,505 people. During the height of their popularity, they sold out 219 consecutive games. how many tickets were sold during this time?
Answer:
Step-by-step explanation:
4,505 tickets were sold 219 times.
4,505 x 219
The answer is 986,595
At a football stadium, 5% of the fans in attendance were teenagers. If there were 340 teenagers at the football stadium, what was the total number of people at the stadium?.
The total number of people at the stadium was 6800 people .
A Percent in mathematics is defined as a number or ratio that is expressed as a fraction of 100 , it is denoted by sign "%" .
For Example : 2% is = 2/100 .
In the question ,
it is given that ,
percent of teenagers fans in the stadium is = 5%
number of teenagers present at the football stadium is = 340
which means 5% represents 340 people ,
So , 1% will be 340/5 = 68 people .
the total percent of people present in the stadium is = 100% ,
multiplying both sides by 100 ,
we get ,
So , 100% = 68 × 100 = 6800 people
Therefore , The total attendance at the football stadium was 6800 people .
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