Answers
1/2 - 5i/4 is the simplified form of the expression ( 5 + 2i ) / 4i.
What is the simplified form of the expression?Given the expression in the question;
( 5 + 2i ) / 4i
To simplify, multiply the numerator and denominator by the conjugate of 4i
( 5 + 2i ) / 4i
( 5 + 2i ) × i / 4i × i
( 5 + 2i )i / 4ii
Apply distributive property
( 5i + 2ii ) / 4ii
Not that i × i = i² = -1
( 5i + 2i² ) / 4i²
( 5i + 2( -1 ) ) / 4( -1 )
( 5i - 2 ) / -4
( -2 + 5i ) / -4
Split the fraction
-2/-4 + 5i/-4
1/2 - 5i/4
Therefore, the simplified form is 1/2 - 5i/4.
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Related Questions
Consider the equation and the following ordered pairs: (6,y) and (x,1).
y=−2x+5
Answers
The values of y and x are -7 and 2 respectively, completing the ordered pairs: (6,-7) and (2,1).
What are the values of y and x?Given the equation in the question;
y = −2x + 5Ordered pairs: (6,y) and (x,1)To find the y-value that completes the ordered pair ( 6,y ), replace all occurrence of x with 6 in the equation and solve for y.
y = −2x + 5
y = −2( 6 ) + 5
Multiply -2 and 6
y = -12 + 5
y = -7
Hence, the output value is -7, this forms an ordered pair of (6,-7).
To find the x-value that completes the ordered pair ( x,1 ), replace all occurrence of y with 1 in the equation and solve for x.
y = −2x + 5
1 = −2x + 5
Add 2x to both sides
1 + 2x = −2x + 2x + 5
1 + 2x = 5
2x = 5 - 1
2x = 4
x = 4/2
x = 2
Hence, the input value is 2, this forms an ordered pair of (2,1).
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Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
Answers
The statement that is true about the quadratic function is (b) the graph of the function is a parabola.
How to determine the true statements?The quadratic function is given as
f(x) = x2 – 5x + 12
Rewrite as
f(x) = x² – 5x + 12
All quadratic functions are parabola
This means that option (b) is true
Set x = -10 to calculate f(-10)
So, we have
f(-10) = (-10)² – 5(-10) + 12
Evaluate
f(-10) = 162
This means that option (a) is false
Set x = 20 to calculate f(20)
So, we have
f(20) = (20)² – 5(20) + 12
Evaluate
f(20) = 312
This means that option (d) is false
Set x = 0 to calculate f(0)
So, we have
f(0) = (0)² – 5(2) + 12
Evaluate
f(0) = 12
This means that option (e) is false
The leading coefficient in f(x) = x² – 5x + 12 is positive
Graphs with positive leading coefficient opens up
This means that option (c) is false
Hence, the true statement about the quadratic function is (b)
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PLEASE HELP ASAP 30 POINTS PLUS BRAINLEST Simplify (3.2 x 10^−9) − (6.4 x 10^−8). Write the final answer in scientific notation.
−6.08 x 10^−9
−6.08 x 10^−8
−3.2 x 10^−1
−3.2 x 10^1
Answers
Answer:
B. -6.08 x 10^-8
Write these as normal numbers.
b)
9.6 × 10⁹
Answers
Answer:
9600000000
Step-by-step explanation:
9.6 x (10^9)
First, write 10^9 as 1000000000
Multiply by 9.6
= 9600000000.
In triangle GHJ, K(8,6) is the midpoint of GH, L(2,2) is the midpoint of HJ, and
M(10,4) is the midpoint of GJ. Find the coordinates of G, H, and J.
Answers
The coordinates of G(4, 4) , H (0, 2), J(8, 0)
In order to construct the three sets of relationships between the coordinates of each triangle's three sides' ends and the shared midpoint, we must first set up the three sets of relationships.
G(x(G), y(G))
K(2, 3) (2, 3)
M(6, 2) (6, 2)
H(x(H) and y(H))L (4, 1)
J(x(J), y(J))
K(2, 3) at the midway of side GH
According to the x-component:
x(H) = x(G - x(H))/2
x(G)-[x(H)-x(G)] = 2*x(H)
x(H) + x(G) = 4
x(H) = 4 - x(G) (G)
According to the y-component:
y(H) plus [y(G) - y(H)]/2 = 3.
2*y(H) plus [y(G-y(H)] = 6
y(H) + y(G) = 6
y(H) = 6 - y(G) (G)
Midpoint L(4) and side JH(1):
According to the x-component:
(x(H) + [x(J) - x(H)]/2) equals four.
2*x(H) plus [x(J)-x(H)] = 8
x(H) + x(J) = 8
x(H) = 8 - x(J) (J)
According to the y-component:
y(H) = y(J - y(H)]/2 + y(J) = 1
y(J) - y(H) = 2*y(H)
y(H) + y(J) = 2
y(H) = 2
Side GJ with M(6, 2) as the midpoint:
For the x - component, the formula is: x(J) = [x(G) - x(J)]/2 = 6 2*x(J) = [x(G)- x(J)] = 12 x(J) = 12 - x (G)
y(J) + [y(G) - y(J)]/2 = 2 2*y(J) + [y(G)- y(J)] for the y-component. = 4 y(J) = 4 - y + y(G) = 4 y(J) (G)
The x and y coordinates may now be easily separated, and we can use algebra to isolate each one and determine its location.
x(H) = 4 - x(G), 8 - x(J), and 12 - x(J) (G)
Because x(H) = x (H)
4 - x(G) = 8 - x(J) (J)
8 - x(J) - 8 - x(G) - 4 = -x(J) x(J) x(J) = 4 + x (G)
Using 1.c above and this relationship now x(J) = x(J), so:
-2 * x(G) = -8 x(G) =, 4 12 - x(G) = 4 + x(G) 12 - x(G) - x(G) - 12 = 4 + x(G) - x(G) - 12
Given that x(J) = 4 + x(G) above, x(J) = 4 + 4 = 8 and x(H) = 4 - x(G) = 4 - 4 = 0 respectively.
Let's now perform the identical procedure using the y-coordinates.
y(H) = 6 - y(G), y(H) = 2 - y(J), y(J) = 4 - y(G),
and since y(H) = y(H), 6 - y(G) = 2 - y(J), -y(G) = 2 - y(J) - 6 = -y(J) - 4 y(G) = y(J) + 4 Now that y(J) = 4 - y,
we may substitute (G).
y(H) = y(G) - 2 and y(H) + 4 - y(G) = 2
and y(H) + 4 - y(G) = 2 - 4 and y(G)
Since y(H) = 6 - y(G)
according to 1. above, y(H) = y(G) - 2 + 6 - y(G) 2 * y(H) = 4 y(H) = 2 y(H) = 2 - y(J) 2 = 2 - y(J) y(J) = 4 - y(G) 0 = 4 - y(G) y(G)
H(x(H), y(H)), G(x(G), y(G)), and J(x(J), y(J)) are the results.
To determine the coordinates of the angles or triangle's tips, we used the midpoints of each side.
The coordinates are: H (0, 2) G(4, 4) J(8, 0)
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If the sum of two numbers is 10 and the difference of their squares is also 10, find the numbers?
Answers
The two numbers with sum is 10 and difference of their squares is 10 are 5.5 and 4.5.
What is square of numbers?
A square number, sometimes known as a perfect square, is an integer that is the square of another integer, or the result of multiplying another integer by itself. For instance, 9 is a square number since it equals 3^2 and is represented by the symbol 3 x 3.
Suppose x and y are the two numbers with sum is 10 and difference of their squares is 10.
As sum of two numbers is 10.
So, x + y = 10 ..(1)
As difference of their squares is 10.
So, x^2 - y^2 = 10 ..(1)
From equation (1), x = 10 - y
Plug value of x in equation (2)
(10 - y)^2 - y^2 = 10
100 - 20y + y^2 - y^2 = 10
100 - 20y = 10
20y = 100 + 10
2y = 110
y = 5.5
Plug y = 5.5 in equation (1)
x + 5.5 = 10
x = 10 - 5.5
x = 4.5
Therefore, The two numbers with sum is 10 and difference of their squares is 10 are 5.5 and 4.5.
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Use the literal symbols listed at the end of the problem to translate the given statement into an algebraic formula.
In a given weight, the number of grams equals 454 times the number of pounds. (g. p)
Choose the correct formula below.
A. g=454 +p
C. p=454g
E. g=454-p
G. g= 454
——
p
B. p=454 +g
D. p=454-g
F. g=454p
H. g= p
—
454
Answers
Pounds = p
Number(g) = 454 x p
Which means;
g = 454p
NO LINKS!! Please help me with this probability question Part 1j
Answers
Answer:
[tex]\textsf{b)} \quad \text{P}(A\;\text{and}\;B)=\dfrac{1}{5}[/tex]
Step-by-step explanation:
Given:
[tex]\text{P}(A)=\dfrac{1}{4}[/tex]
[tex]\text{P}(B)=\dfrac{1}{4}[/tex]
[tex]\text{P}(A|B)=\dfrac{4}{5}[/tex]
Conditional Probability Formula
[tex]\text{P}(A \cap B)=\text{P}(B)\;\text{P}(A|B)[/tex]
Substitute the given values into the formula:
[tex]\begin{aligned}\implies \text{P}(A \cap B)&=\dfrac{1}{4} \cdot \dfrac{4}{5}\\\\&=\dfrac{4}{20}\\\\&=\dfrac{1}{5}\end{aligned}[/tex]
What is 1 5/9+2 7/9 in simplest form
Answers
Answer:
13/3
Step-by-step explanation:
3 [tex]\frac{12}{9}[/tex]
[tex]\frac{12}{9}[/tex]= 1 [tex]\frac{1}{3}[/tex]
3+1 1/3
4 [tex]\frac{1}{3}[/tex]
13/3
Answer:
Step-by-step explanation:
step one just add 5/9 +7/9 since they have the same denominator then that will equal 4/3
2nd step add the 1 and 2 together since they are both whole numbers. which equals 3
3rd step 4/3 + 3/1 which equals 13/3 maybe or if the answers wants a mixed number than the answer might be 4 1/3!
I'm not quite sure but try and see if its correct! :)
(7x2) x 3
Drag numbers to the boxes to show how to find the product.
(7x2) x3 = 7x (
(7x2) x3 = 7x
(7×2)×3={______
x3
2 3 6 7 13 21 42 49
Answers
Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3
Answers
The steps that Patel could he use to solve the quadratic equation include:
8(x² + 2x) = –3
8(x² + 2x + 1) = –3 + 8
x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot
How to illustrate tye information?It is preferred to solve quadratic equations without the use of the known quadratic formula solver. This can be completing squares and solving for x.
The equation given is:
8x² + 16x + 3 = 0
8(x² + 2x) = -3
Completing squares in the brackets and balancing the equation:
8(x² + 2x + 1) = -3 + 8
Factoring the perfect square will give 8(x + 1)² = 5.
This is illustrated in the options picked for the step.
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shopping at savers mart, Lisa buys her children four shirts and three pairs of pants for $85.50. she comes back the next day and buys three shirts and five pairs of pants for $115. What is the price of each shirt and each pair of pants.
Answers
=
$
7.50
price for one pair of pants
=
$
18.50
Explanation:
Start by letting variables
x
and
y
represent the pieces of clothing from the problem.
Let
x
be the price of one shirt.
Let
y
be the price of one pair of pants.
Equation
1
:
4
x
+
3
y
=
85.50
Equation
2
:
3
x
+
5
y
=
115.00
You can solve for each variable by using elimination or substitution. However, in this case, we will use use elimination. First, we will solve for
y
, the price of each pair of pants.
To isolate for
y
, we must eliminate
x
. We can do this by making the two equations have the same
x
values. First, we find the LCM of
4
and
3
, which is
12
. Next, multiply equation
1
by
3
and equation
2
by
4
so that
4
x
and
3
x
becomes
12
x
in both equations.
Equation
1
:
4
x
+
3
y
=
85.50
3
(
4
x
+
3
y
)
=
3
(
85.50
)
12
x
+
9
y
=
256.50
Equation
2
:
3
x
+
5
y
=
115.00
4
(
3
x
+
5
y
)
=
4
(
115.00
)
12
x
+
20
y
=
460.00
Now that we have two equations with
12
x
, we can subtract equation
2
from equation
1
to solve for
y
.
12
x
+
9
y
=
256.50
12
x
+
20
y
=
460.00
−
11
y
=
−
203.50
y
=
18.50
⇒
price for one pair of pants
Now that we know that a pair of pants is
$
18.50
, we can substitute this value into either equation
1
or
2
to find price for one shirt. In this case, we will choose equation
1
.
4
x
+
3
y
=
85.50
4
x
+
3
(
18.50
)
=
85.50
4
x
+
55.5
=
85.50
4
x
=
28
x
=
7.50
⇒
price for one shirt
∴
, the price for one shirt is
$
7.50
and the price for one pair of pants is
$
18.50
.
(−3,y) and (x,2).
y=4x+6
orderd pair
Answers
The values of x and y are -1 and 6 respectively, this forms an ordered pair of (-3,6) and (-1,2).
What are the missing x and y values values of the given ordered pair?Given the equation and ordered pair in the question;
y = 4x + 6Point: (-3,y) Point; (x,2)Find the y-value by substituting the x-value into the equation and solving for y.
y = 4x + 6
Plug in x = -3
y = 4( -3 ) + 6
y = -12 + 6
y = 6
Find the x-value by substituting the y-value into the equation and solving for x.
y = 4x + 6
Plug in y = 2
2 = 4x + 6
2 - 6 = 4x
-4 = 4x
x = -4/4
x = -1
Therefore, the ordered pair are (-3,6) and (-1,2).
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Select the correct answer. Maria donates a fixed amount, a, to a charity each month. If she donates $300 in 12 months, what is the equation for a? A. a + 300 = 12 B. a × 300 = 12 C. a × 12 = 300 D. a + 12 = 300 E. a + 32 = 100
Answers
Answer: C
she donates a for 12 months, the 12 in the a * 12=300. the a is the fixed amount, meaning she will donate a 12 times in a year.
On average, Jaya drinks of a 6-ounce glass of water in 13 hours. How many glasses of water does she drink in one hour?
Answers
On average, Jaya drinks 0.46 ounces glasses of water does she drink in one hour.
Average:
Average refers the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.
Given,
On average, Jaya drinks of a 6-ounce glass of water in 13 hours.
Here we need to find the number of glasses of water does she drink in one hour.
Let x be the number of glasses of water does she drink in one hour.
We know that, Jaya drinks of a 6-ounce glass of water in 13 hours.
So, in order to find the average we have to divide the number of glasses by the time taken.
So, it can be written as,
=> 6/13
=> 0.46
Therefore, for one hour Jaya drinks 0.46 ounces of water.
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Compute ending work in process inventory for a manufacturer using the following information.
Rav materials purchased
Direct materials used
Direct labor used
Factory overhead
Work in process inventory, beginning
Cost of goods manufactured
Ending Work in Process Inventory is Computed as:
Work in process inventory, beginning
Total manufacturing costs
Total cost of work in process
Work in process inventory, ending
$ 133,200
82,600
61,000
103,400
26,800
234,000
Answers
Total cost of work in process Work in process inventory, ending=$1,320,000
What is computation?Any sort of arithmetic or non-arithmetic calculation that adheres to a well defined paradigm is referred to as computation.The scenario dictates that the computation of the provided data be as follows:-
Buying raw materials will cost $1,800,000.
$20k is the opening stock of raw materials.
Raw material closing stock: $3,140,000.
Purchase of raw materials plus opening stock of raw materials minus closing stock of raw materials equals direct material used.
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Solve for X in the equation;
2x+5=7
Answers
Answer:
x=1
Step-by-step explanation:
Answer: x=1
Step-by-step explanation:
2x + 5 = 7
2x + 5 - 5 = 7 - 5
2x = 2
2x/2 = 2/2
x=1
1. Assuming the cost of mortgage is $720,000, and the owner of the house makes a down payment of $60,000, with 7.5% interest rate and 25 years repayment plan. a. Calculate the total amount of loan, monthly rate, number of payment periods, monthly payment, total interest paid, and amount borrowed. b. With the aid of what PMT function in a one variable condition, calculate monthly payment, total amount payable, total interest payable for: 11 yrs, 14 yrs, 18 yrs ,20 yrs, 28 yrs, 31 yrs mortgage.
Answers
The total amount he will pay after 25 years is $18,97,500.
His monthly payment will be $6,325.
Given, the cost of mortgage is $720,000, and the owner of the house makes a down payment of $60,000, with 7.5% interest rate and 25 years repayment plan.
Now, the total amount of the loan be,
720000 - 60000 = 660,000
monthly rate = 7.5/12 = 0.625%
Number of payment periods = 25
Total amount he has to pay after 25 years,
660000 + (660000×7.5×25)/100
= $18,97,500
His monthly payment will be
1897500/25×12
= $6,325
Hence, the total amount he will pay after 25 years is $18,97,500
also, his monthly payment will be $6,325.
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Solve for (A) current ratio, (B) acid test (quick), (C) average day's collection (D) asset turnover, and (E) profit margin on sales. Round to nearest hundredth or hundredth percent as needed. Current Assets $ 21,000 Accounts Receivable 4,200 Current Liabilities 16,000 Inventory 3,500 Net Sales 41,000 Total Assets 32,000 Net Income 6,000
Answers
a. The current ratio is 1.3125
b. The acid test is 1.09375.
c. The average day collection is 37 days.
d. The asset turnover is 1.28.
e. The profit margin on sales is 14.63%.
How to calculate the current ratio?a. The current ratio will be:
= Current asset / Current liability
= 21000 / 16000
= 1.3125
b. Acid test quick ratio will be:
= (Current asset - Inventory) / Current liability
= (21000 - 3500) / 16000
= 1.09375
c. Average day collection will be:
= Account receivable / (Net sales / 360)
= 4200 / (41000 / 36)
= 4200 / 114
= 37 days.
d. Asset turnover will be:
= Net sales / Total asset
= 41000 / 28000
= 1.28
e. Profit margin will be:
= Net income / Net sales
= 6000 / 41000
= 14.63%
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help please??? brainlest
Answers
Hope it helps
A frozen yogurt stand charges per ounce of frozen yogurt purchased. There is an extra charge for a waffle bowl. The total cost (c), in dollars, for f ounces of frozen yogurt in a waffle bowl, is described by the function c = 0.45f + 1.
Which statement is true?
A.
The cost of 0.45 ounce of frozen yogurt in a waffle bowl is $1.
B.
Each ounce of frozen yogurt costs $1 and a waffle bowl is $0.45 extra.
C.
Each ounce of frozen yogurt costs $0.45 and a waffle bowl is $1 extra.
D.
The cost of 0.45 ounce of frozen yogurt in a waffle bowl is $1.45.
Answers
Answer:
$0.45 and a waffle bowl is $1 extra.
Step-by-step explanation:
A cone has a volume of 2411.52 cubic millimeters and a radius of 12 millimeters. What is its height? Use ≈ 3.14 and round your answer to the nearest hundredth.
Answers
The height of the cone given the volume of 2411.52 cubic millimeters and a radius of 12 millimeters is 16 millimeters.
How to find height of a cone?Volume of a cone = 2411.52 cubic millimetersRadius of the cone = 12 millimetersVolume of a cone = 1/3πr²h
2411.52 = 1/3 × 3.14 × 12 x 12 × h
2411.52 = 1/3 × 3.14 × 144h
2411.52 = 452.16h / 3
cross product7,234.56 = 452.16h
divide both sides by 452.16h = 7,234.56 / 452.16
h = 16 millimeters
In conclusion, the height of the cone is given by 16 milliliters.
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Use the compound interest formula to compute the total amount accumulated and the interest earned.
$3500 for 2 years at %3 compounded quarterly.
The total amount accumlated after 2 years is ____.
(Round to the nearest cent as needed.)
Answers
The total amount accumulated after 2 years is $3704. 0
How to determine the compound interestThe formula for calculating compound interest is expressed as;
A = P ( 1 + r/ n) ^nt
Where;
A is the final amountP is the principal amountr is the ratet is the timen is the number of times interest applied per periodNow, let's substitute the values into the formula, we have;
A = $3500 ( 1 + 0. 03 / 0. 25) ^(0.25× 2)
Find the exponent
A = $3500 ( 1 + 0. 03 / 0. 25) ^0.5
A = $3500( 1+ 0. 12)^0. 5
Expand the bracket
A = $3500 (1. 12)^0. 5
A = $3500(1. 05)
multiply the values
A = $3704. 0
Hence, the value is $3704. 0
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Ray's favorite activity is taking a leisurely bike ride through the park after work. Suppose his bike has a flat tire, so he decides to go for a jog instead. Jogging burns 745 calories an hour. How long does he need to jog in order to burn off that same extra doughnut and large frozen latte that he ate that afternoon? The doughnut had approximately 320 calories, and the latte had 820 calories.
Answers
Ray have to jog 1.53 hours to burn the calories he had taken by eating doughnut and latte.
Given,
The amount of calorie burns while jogging = 745 calories
The amount of calorie in Doughnut = 320 calories
The amount of calorie in latte = 820 calories
Here,
Total calorie intake by Ray = 320 + 820 = 1140
The calorie burnt while jogging = 745
Number of hours Ray needs to jog for burning 1140 calories;
1140/745 = 1.53 hours.
That is,
Ray have to jog 1.53 hours to burn the calories he had taken by eating doughnut and latte.
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LoWatts Ltd makes light bulbs that are identical in size
They have regular orders from company A for 120 light bulbs and from Company B for 168 light bulbs.
LoWatts Ltd uses one size of box to supply both company A and company B. Each box used contains the same number of light bulbs and is full.
The number of boxes used is as few as possible
How many light bulbs does each box hold?
Answers
Using the greatest common factor, the number of light bulbs in each box is 24.
What is the greatest common factor?The greatest common factor (GCF) is the number that can divide two or more numbers without a remainder.
The GCF is a divisor that divides dividends evenly, leaving only quotients without remainders.
For instance, the greatest common factor of 120, 168, and even 288 is 24.
Using this GCF implies that 24 can divide 120, 168, and 288 without leaving any remainders.
Company A Company B Total
Total orders for light bulbs 120 168 288
Greatest common factor of 24 24 24
Number of boxes delivered 5 7 12
Thus, with the greatest common factor as 24 light bulbs in each box, Company A will be supplied 5 boxes, while Company B will be supplied with 7 boxes.
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If the shared side between angles 1 and 2 has a measure of 2x+7 and the shared side between angles 3 and 4 has a measure of 7x+3, what is the value of X?
Round your answer to the nearest hundredth.
Answers
Answer:
x = 0.8Step-by-step explanation:
Both mentioned sides have equal length as opposite sides of a parallelogram.
Set equation and solve for x:
2x + 7 = 7x + 37x - 2x = 7 - 35x = 4x = 4/5x = 0.8The amount of Jerry's pay every week before taxes, J, is given below as a function of the number of overtime hours that he works (the number of hours over 40), h.
J = $493.60 + $18.51h
Assuming that Jerry is only paid for each whole hour that he works, how many total hours would Jerry have to work during a week to make at least $700.00?
A. 51
B. 52
C. 62
D. 11
Answers
The total number of hours that Jerry would work during a week to make at least $700.00 is 11 hours
How to determine number of hours that Jerry would workinformation given in the query
The amount of Jerry's pay every week before taxes, J,
a function of the number of overtime hours that he works (the number of hours over 40), h
J = $493.60 + $18.51h
The given equation is an equation of linear function
considering the equation J = $493.60 + $18.51h, the number of hours that Jerry would work is gotten by substituting the value of $700.00 and solving for number of hours
J = $493.60 + $18.51h
700 = 493.60 + 18.5h
18.5h = 700 - 493.60
18.5h = 206.4
h = 11.16
h = 11 hours
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help please??? for brianlest???
Answers
Step-by-step explanation:
Domain is the x value and Range is the y value. (A way to remember is by saying dr since domain is x and range is y)
Y value is also called f(x) as shown on your screen
The points are
(1,-8)
(2,5)
(3,-2)
(4,1)
The domain would be 4,3,2,1 and the range would be -8,-2,1,5
The common difference is that the domain follows a constant change of rate, but not the range.
A constant change of rate means that it's changing at a constant rate.
It can also be called slope.
E.G: 1,2,3,4 (constant change of rate is adding 1) or 9,6,3,0 (subtracting 3)
The domain is subtracting 1, yet the range isn't following a constant change of rate.
A way to find slope is in the image.
Your office window is a 45 feet high. Looking out your window, you find that the top of a statue lines up exactly with the bottom of a building that is b = 600 horizontal feet
from your office. You know that the statue is c= 125 feet from the building. How tall is the statue? (See the figure below. Round your answer to two decimal places.)
Answers
The height of the statue that exactly with the bottom of a building is approximately 9.3926 feet tall.
height of the office window , a = 45 feet
the bottom of a building that is horizontal from the office, b = 600 feet
let x represent the angle
tan(x) = a/b
tan(x) = 45/600
x = tan⁻¹(0.75)
x = 4.28 degree
the height of the statue, h = ?
the statue is from the building, c = 125 feet
tan(45/600) = h/125
h = tan(0.075) x 125
h = 9.3926 feet
The height of the statue that exactly with the bottom of a building is approximately 9.3926 feet tall.
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the data given to the right includes data from 37 candies, and 5 of them are red. the company that makes the candy claims 30% of its candies are red. use the sample data to construct a 95% confidence interval estimate of the percentage of red candies. what do you conclude about the claim of 30%?
Answers
The Sample proportion for the data to construct a 95% confidence interval is 0.1351.
The percentage of red candies is (24.5%, 2.52%)
What do you mean by sample proportion?
The sample proportion (p) indicates the percentage of people in a sample who exhibit a particular quality or attribute. Divide the number of individuals (or items) who have the desired attribute by the overall sample size to obtain the sample proportion.
What is percentage?
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
Sample proportion [tex]=\frac{5}{37}=0.1351[/tex]
For 95% confidence interval, z = 1.96
Hence,
95% confidence interval will be:
[tex]0.1351 \pm 1.96\times \sqrt{0.1351\times(1-0.1351)/37}[/tex]
[tex]0.1351\pm0.1099[/tex]
(0.245, 0.0252)
(24.5%, 2.52%)
Since the confidence interval only contains values less than 30%.
The result is not consistent with 34% rate reported by the candy maker.
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