Answer:
[tex]x = 97[/tex]
Step-by-step explanation:
Given
[tex]t = 20[/tex] --- time (years)
[tex]A =1000[/tex] --- amount
[tex]r = 10\%[/tex] --- rate of interest
Required
The last 10 payments (x)
First, calculate the end of year 1 payment
[tex]y_1(end) = 10\% * 1000 * 150\%[/tex]
[tex]y_1(end) = 150[/tex]
Amount at end of year 1
[tex]A_1=A - y_1(end) - r * A[/tex]
[tex]A_1=1000 - (150 - 10\% * 1000)[/tex]
[tex]A_1 =1000 - (150- 100)[/tex]
[tex]A_1 =950[/tex]
Rewrite as:
[tex]A_1 = 0.95 * 1000^1[/tex]
Next, calculate the end of year 1 payment
[tex]y_2(end) = 10\% * 950 * 150\%[/tex]
[tex]y_2(end) = 142.5[/tex]
Amount at end of year 2
[tex]A_2=A_1 - (y_2(end) - r * A_1)[/tex]
[tex]A_2=950 - (142.5 - 10\%*950)[/tex]
[tex]A_2 = 902.5[/tex]
Rewrite as:
[tex]A_2 = 0.95 * 1000^2[/tex]
We have been able to create a pattern:
[tex]A_1 = 1000 * 0.95^1 = 950[/tex]
[tex]A_2 = 1000 * 0.95^2 = 902.5[/tex]
So, the payment till the end of the 10th year is:
[tex]A_{10} = 1000*0.95^{10}[/tex]
[tex]A_{10} = 598.74[/tex]
To calculate X (the last 10 payments), we make use of the following geometric series:
[tex]Amount = \sum\limits^{9}_{n=0} x * (1 + r)^n[/tex]
[tex]Amount = \sum\limits^{9}_{n=0} x * (1 + 10\%)^n[/tex]
[tex]Amount = \sum\limits^{9}_{n=0} x * (1 + 0.10)^n[/tex]
[tex]Amount = \sum\limits^{9}_{n=0} x * (1.10)^n[/tex]
The amount to be paid is:
[tex]Amount = A_{10}*(1 + r)^{10}[/tex] --- i.e. amount at the end of the 10th year * rate of 10 years
[tex]Amount = 1000 * 0.95^{10} * (1+r)^{10}[/tex]
So, we have:
[tex]Amount = \sum\limits^{9}_{n=0} x * (1.10)^n[/tex]
[tex]\sum\limits^{9}_{n=0} x * (1.10)^n = 1000 * 0.95^{10} * (1+r)^{10}[/tex]
[tex]\sum\limits^{9}_{n=0} x * (1.10)^n = 1000 * 0.95^{10} * (1+10\%)^{10}[/tex]
[tex]\sum\limits^{9}_{n=0} x * (1.10)^n = 1000 * 0.95^{10} * (1+0.10)^{10}[/tex]
[tex]\sum\limits^{9}_{n=0} x * (1.10)^n = 1000 * 0.95^{10} * (1.10)^{10}[/tex]
The geometric sum can be rewritten using the following formula:
[tex]S_n = \sum\limits^{9}_{n=0} x * (1.10)^n[/tex]
[tex]S_n =\frac{a(r^n - 1)}{r -1}[/tex]
In this case:
[tex]a = x[/tex]
[tex]r = 1.10[/tex]
[tex]n =10[/tex]
So, we have:
[tex]\frac{x(r^{10} - 1)}{r -1} = \sum\limits^{9}_{n=0} x * (1.10)^n[/tex]
[tex]\frac{x((1.10)^{10} - 1)}{1.10 -1} = \sum\limits^{9}_{n=0} x * (1.10)^n[/tex]
[tex]\frac{x((1.10)^{10} - 1)}{0.10} = \sum\limits^{9}_{n=0} x * (1.10)^n[/tex]
[tex]x * \frac{1.10^{10} - 1}{0.10} = \sum\limits^{9}_{n=0} x * (1.10)^n[/tex]
So, the equation becomes:
[tex]x * \frac{1.10^{10} - 1}{0.10} = 1000 * 0.95^{10} * (1.10)^{10}[/tex]
Solve for x
[tex]x = \frac{1000 * 0.95^{10} * 1.10^{10} * 0.10}{1.10^{10} - 1}[/tex]
[tex]x = 97.44[/tex]
Approximate
[tex]x = 97[/tex]
Denver is about 5,200 feet above sea level. Which number line best represents this interger?
Answer: First Number Line
Step-by-step explanation:
Find sin θ, cot θ, and csc θ, where θ is the angle shown in the figure.
Give exact values, not decimal approximations.
Step-by-step explanation:
everything can be found in the picture
As per the given angle values, the value of sin θ = √19 / 10, cot θ = 9 / √19 and csc θ = 10 / √19.
Let's begin by labeling the sides of the right-angled triangle. The hypotenuse is the side opposite the right angle and has a length of 10 units. The adjacent side, which is the side adjacent to the angle θ, has a length of 9 units.
Using these side lengths, we can apply the trigonometric definitions to find the required values:
Sine (sin θ):
The sine of an angle θ in a right-angled triangle is defined as the ratio of the length of the side opposite the angle (opposite side) to the length of the hypotenuse. The formula for sine is: sin θ = opposite / hypotenuse.
In our case, the opposite side is the side we want to find, and the hypotenuse is 10 units. Therefore, sin θ = opposite / 10.
Using the Pythagorean theorem:
opposite² + 9² = 10²
opposite² + 81 = 100
opposite² = 100 - 81
opposite² = 19
opposite = √19 (taking the positive square root as the length cannot be negative)
Now, we can calculate sin θ:
sin θ = √19 / 10
Cotangent (cot θ):
The cotangent of an angle θ in a right-angled triangle is defined as the ratio of the length of the adjacent side to the length of the opposite side. The formula for cotangent is: cot θ = adjacent / opposite.
In our case, the adjacent side is 9 units, and we have already found the length of the opposite side, which is √19. Therefore, cot θ = 9 / √19.
Cosecant (csc θ):
The cosecant of an angle θ in a right-angled triangle is defined as the ratio of the length of the hypotenuse to the length of the opposite side. The formula for cosecant is: csc θ = hypotenuse / opposite.
Again, the hypotenuse is 10 units, and the opposite side is √19. Thus, csc θ = 10 / √19.
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The length of a rectangle should be 9 meters longer than 7 times the width. If the length must be
between 93 and 163 meters long, what are the restrictions for the width, p?
Write the solution set as an algebraic inequality solved for the variable.
Answer:
If we define W as the width:
12m ≤ W ≤ 22m
Step-by-step explanation:
We have a rectangle with length L and width W.
We know that:
"The length of a rectangle should be 9 meters longer than 7 times the width"
Then:
L = 9m + 7*W
We also know that the length must be between 93 and 163 meters long, so:
93m ≤ L ≤ 163m
Now we want to find the restrictions for the width W.
We start with:
93m ≤ L ≤ 163m
Now we know that L = 9m + 7*W, then we can replace that in the above inequality:
93m ≤ 9m + 7*W ≤ 163m
Now we need to isolate W.
First, we can subtract 9m in the 3 sides of the inequality
93m - 9m ≤ 9m + 7*W -9m ≤ 163m -9m
84m ≤ 7*W ≤ 154m
Now we can divide by 7 in the 3 sides, so we get:
84m/7 ≤ 7*W/7 ≤ 154m/7
12m ≤ W ≤ 22m
Then we can conclude that the width is between 12 and 22 meters long.
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW. Use the following for problems 22-25
Problem 22
a)
The face cards are Jack, Queen, King. We have four copies of each.
There are 3*4 = 12 face cards total.
12/52 represents the probability of picking a face card.
4/52 represents the probability of picking an ace, since we have 4 aces out of 52 cards. We don't drop to 51 since we put the first card back.
Multiplying the fractions gives (12/52)*(4/52) = 48/2704 = 3/169
Answer: 3/169----------------------
b)
We do the same steps as before, but the 4/52 will be changed to 4/51. This is because the first card is not put back.
(12/52)*(4/51) = 48/2652 = 4/221
Answer: 4/221========================================================
Problem 23
a)
4/52 represents the probability of picking a '2', and it also represents the probability of picking a '10' if we put the first card back
(4/52)*(4/52) = 16/2704 = 1/169
Answer: 1/169----------------------
b)
We'll change the second instance of 4/52 into 4/51 because that first card isn't put back
(4/52)*(4/51) = 16/2652 = 4/663
Answer: 4/663========================================================
Problem 24
a)
4/52 = probability of picking an ace
12/52 = probability of picking a face card
4/52 = probability of picking '7'
Each denominator is 52 because we are putting the cards back
(4/52)*(12/52)*(4/52) = 192/140608 = 3/2197
Answer: 3/2197----------------------
b)
We do the same thing as before, but we decrease the denominator by 1 each time we pull out another card
(4/52)*(12/51)*(4/50) = 192/132600 = 8/5525
Answer: 8/5525========================================================
Problem 25
a)
The probability of picking a king is 4/52. This is the same whether we're on the first king, second or third. This is because we're putting the card back.
(4/52)*(4/52)*(4/52) = 64/140608 = 1/2197
Answer: 1/2197----------------------
b)
Now that the cards aren't put back, we'll have the denominators drop by 1 each time (52,51,50)
So the probability is
(4/52)*(4/51)*(4/50) = 64/132600 = 8/16575
Answer: 8/16575if a loaf of bread coast £1.52 how much change will you get from £10 if you buy 4loaves
Answer:
Balance will be £3.92
Step-by-step explanation:
Cost of 1 loaf = £1.52
Therefore, cost of 4 loaves = 4 x 1 . 52 = £6.08
So if you pay with £10 your balance will be = 10.00 - 6.08 = £3.92
The solution is £ 3.92
The amount of money after the purchase of 4 loaves of bread is given by the equation A = £ 3.92
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 equation be represented as A
Now , the value of A is
The total amount of money = £ 10
The cost of one loaf of bread = £ 1.52
Now , the number of loaves of bread = 4 loaves
So , the cost of 4 loaves of bread = 4 x cost of one loaf of bread
Substituting the values in the equation , we get
The cost of 4 loaves of bread = 4 x 1.52
The cost of 4 loaves of bread = £ 6.08
The amount of money after the purchase A = total amount of money - cost of 4 loaves of bread
Substituting the values in the equation , we get
The amount of money after the purchase A = £ 10 - £ 6.08
The amount of money after the purchase A = £ 3.92
Therefore , the value of A is £ 3.92
Hence , the amount is £ 3.92
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Contains the point (-5, 1) and is perpendicular to the line 2x − y = 4
Answer:
Step-by-step explanation:
2x − y = 4
2x − 4 = y
y = 2x - 4
negative inverse of slope is perpendicular
y = -1/2 x - 4
~~~~~~~~~~~~~~~~~~~~~~~
point slope form of a line
(-5, 1) & m = -1/2
1 = -1/2 (-5) + b
1 = 5/2 + b
b = -3/2
Final answer: y = -1/2 x - 3/2
or if you prefer: 2y + x = -3
Factor each trinomial completely.
A. 2x^2 + 17x + 21
B. 3x^2 - 17x + 10
Answer:
A) (2x+3)(x+7) B) (3x-2)(x-5)
Step-by-step explanation:
A) 2x^2+17x+21=(2x+3)(x+7)
B) 3x^2-17x+10=(3x-2)(x-5)
show that the slope of the line joining the points A(1,1) and B(1,1+h)^2 is 2+h.
Answer:
??????????????
Step-by-step explanation:
sorry di ko po alam godbless po
(d) An insurance company will only sell its Select policy to people for whom the probability of a stroke in the next 10 years is less than 0.01. If a smoker with a systolic blood pressure of 200 applies for a Select policy, under what condition will the company sell him the policy if it adheres to this standard
Answer: Hello your question has some missing data that I was able to find and attach below
A recent 10-year study conducted by a research team at the Great Falls Medical School was conducted to assess how age, systolic blood pressure, and smoking relate to the risk of strokes. Assume that the following data are from a portion of this study. Risk is interpreted as the probability (times 100) that the patient will have a stroke over the next 10-year period. For the smoking variable, define a dummy variable with 1 indicating a smoker and 0 indicating a nonsmoker.
answer :
The condition : Client age ≤ 31.26 years
Step-by-step explanation:
First step : perform a regression analysis via excel ( result attached below )
P-value = 2.06E-07
Next determine the condition on which the company will sell its policy
Y = - 91.7595 + 1.0767x1 + 0.2518x2 + 8.7399x3
1 < -91.7595 + 1.0767x1 + 0.2518*200 + 8.7399*1
make X1 subject of equation above
X1 < 31.26
The transformations to the parent function of a quadratic equation are given below. Write an equation of the new function in vertex form.
translated 3 units down ___
reflected over the x-axis, then translated 5 units left ___
Answer:
What does it mean?
explain properly i will answer your question.
Answer:
11.f(x)=^2-3Step-by-step explanation:12.And slide everything five units down. So a over here that's negative three negative one. So if we slide at five you just down we go one two three four five and get here.I need help with this question. I have a few correct and need help with the ones that are not.
Step-by-step explanation:
For the first one, you have the -2 step right, but now we're at
f(x) -2 = x³
We have to take the cube root of each side to solve for x, which looks like
∛(f(x)-2) = x or (f(x)-2)^(1/3) = x. This makes our inverse function ∛(x-2) Putting a 3 to the side multiplies the value by 3, and doesn't cube root it.
For your next incorrect answer, you simply need to plug the inverse function that I just gave in.
For the one after that, the question is asking to plug in f(x). We know that our inverse is ∛(x-2) , and the question is asking to plug f(x) in for x here. Thus, in the box, simply put down x³+2
For the last incorrect answer, we need to find the cube root of something, and by plugging in f(x) into the previous one, we are left with ∛(x³+2-2). Therefore, in the box, simply put down x³ as that is what's left
2 times the difference between 49.5 and 37.5
Answer:
24
Step-by-step explanation:
diff is 12
12x2 is 24
HELP PLEASE IM STUCK!
1. Which of these describes the relation for this set of coordinate pairs?
{(-1, 5), (12, 18), (0, 6), (-3, 3), (4, ?), (?, 11)}
a. x - y = 6 b. f(x) = x +6 c. f(x) = 6 d. y = 6x e. None of these
Answer:
b) f(x) = x + 6
Step-by-step explanation:
The coordinate (0, 6) makes the y-intercept = 6. Only one of these functions has that intercept: f(x) = x + 6. If you plug in each coordinate the outputted y-value matches up, making this the right answer.
On a coordinate plane, a parabola opens up. It goes through (negative 3.25, 5), has a vertex of (1.75, negative 2.75), and goes through (6.25, 5). Solid circles appear on the parabola at (negative 3, 4), (0, negative 2), (1.75, negative 2.75), (3, negative 2), (6, 4).
Which is f(6) for the quadratic function graphed?
–2
–0.5
1.5
4
Answer:
-2
Step-by-step explanation:
/jwkkskjdkdiifididirit
Answer:
4
Step-by-step explanation:
Which statement is true? Q A) |13| = – 13 B) – |–13| = 13 C) |–13| = 13 D) – |13| = 13
Answer:
C
Step-by-step explanation:
The absolute value of |13| and |-13| is always 13. It never goes negative unless there is a minus sign outside the absolute value | | symbol. A is wrong
B: Not correct. Read the explanation for A. The answer to B is - 13
C: Correct. See the remark the was made about A
D: Incorrect as well. The minus is outside the absolute value symbol. The answer is - 13
Answer:
C .////.
Step-by-step explanation:
When you have /13/ its always positive even if there's a negative in there. If there was the negative symbol on the outside its a negative number :)
10x-3(x-6)=x+30 please help me
Step-by-step explanation:
10x-3(x-6)=x+30
10x-3x+18=x+30
7x+18=x+30
6x=12
x=2
Answer:
x=2
Step-by-step explanation:
10x-3(x-6)=x+30
Distribute
10x -3x+18 = x+30
Combine like terms
7x +18 = x+30
Subtract x from each side
7x-x +18 = x+30-x
6x +18 = 30
Subtract 18
6x+18-18 = 30-18
6x = 12
Divide by 6
6x/6 = 12/6
x=2
The filling variance for boxes of cereal is designed to be .02 or less. A sample of 41 boxes of cereal shows a sample standard deviation of 0.16 ounces.
a. Use α= 0.05 to determine whether the variance in the cereal box fillings is exceeding the design specification.
b. State the null and alternative hypotheses.
c. Calculate the value of the test statistic (to 2 decimals).
d. The p-value is:_______
e. What is your conclusion?
Answer:
-
Null hypothesis H₀ : σ² ≤ 0.02
Alternative hypothesis Hₐ : σ² > 0.02
- Chi Square = 51.2
- p-value = 0.1104
- since the calculated p-value ( 0.1104 ) is greater than the level of significance ( 0.05 ).
We fail to reject null hypothesis.
- So at, 5% level of significance, there is no evidence to support that the variance in the cereal box fillings is designed to be 0.02 or less.
Step-by-step explanation:
Given the data in the question;
filling variance for boxes of cereal is designed to be .02 or less
sample size n = 41 boxes
standard deviation S = 0.16 ounces
level of significance = 0.05
Hypothesis;
Null hypothesis H₀ : σ² ≤ 0.02
Alternative hypothesis Hₐ : σ² > 0.02
{ Upper tail test }
Test statistics;
Chi Square = [ ( n-1 ) × S² ] / σ²
Chi Square = [ ( 41-1 ) × (0.16)² ] / 0.02
Chi Square = [ 40 × 0.0256 ] / 0.02
Chi Square = 1.024/ 0.02
Chi Square = 51.2
Degree of freedom df = n - 1 = 41 - 1 = 40
Chi square value at 0.05 and df of 40 = 55.7585
p-value = 0.1104
since the calculated p-value ( 0.1104 ) is greater than the level of significance ( 0.05 ).
We fail to reject null hypothesis.
So at, 5% level of significance, there is no evidence to support that the variance in the cereal box fillings is designed to be 0.02 or less.
HELP ME PLEASE IF YOU DO YOU WILL GET BRAINLESS AND PLEASE EXPLAIN THE BEST YOU CAN
Answer:
<3=75°
Step-by-step explanation:
Angle 3 and angle 2x+95 are supplementary( supplementary angles add up to 180°)
So <3+2x+95=180
<3+2x=180-95
<3+2x=85( let's call this equation 1)
Next, angle 5 and angle 8x+71 are opposite angles (opposite angles are equal) therefore <5=8x+71
Now, <3 and <5 are co-interior angles(co-interior angles are supplementary)
So <3+8x+71=180
<3+8x=180-71=109
Thus, <3+8x=109(let's call this equation 2)
Now solving equation 1 and 2 simultaneously:
Make <3 the subject of equation 1
<3=85-2x
Put <3=85-2x into equation 2
85-2x+8x=109
6x=24
x=24/6=4
Now, remember that angle 2x+95 becomes
2(4)+95
8+95=103°
Therefore<3=180-105=75°
Given a total-revenue function R(x) = 700/x? - 0.2x and a total-cost function 1 3 C(x) = 1400(x² + 2) +600, both in thousands of dollars, find the rate at which total profit is changing when x items have been produced and sold. P'(x) =
Answer:
Step-by-step explanation:
abcdefghijklmnopqrstuvwxyz
What is the value ofWhat is the value of the missing angle?
A
20
B
90
C
120
D
100 the missing angle? A 20 B 90 C 120 D 100
Answer:
The missing angle is 120
Step-by-step explanation:
Given
See attachment
Required
The missing angle (?)
Let the missing angle be x
So:
[tex]x + 60 = 180[/tex] --- angle on a straight line
Collect like terms
[tex]x = 180-60[/tex]
[tex]x = 120[/tex]
1. Cheryl Douglas works 43 hours in a week for an exempt salary of $1,827 per week. What are Cheryl's gross weekly earnings?
Answer:
$1827
Step-by-step explanation:
Since Cheryl is said to be paid an exempt salary. Then it can be said that Cheyk does not qualify for minimum wage or overtime pay, Hence, exempt payment is in terms or salary rather than wage. Similarly. Gross earning refers the amount a worker receives as income over a certain period of time. The gross income has not been subjected to tax charges or any form of deduction. Hence, it could be said to be the outright earning paid to an employee before any deduction is made.
Hence, Cheryl's gross weekly earning is $1827 per week.
Help with number 16 please
Answer:
the answer is c. 300
Step-by-step explanation:
18+32×12÷2
base 1 + base 2 × height ÷ 2
what is the median of 66 69 68 69 70 70.
Question 4-6. Earth is 93 million miles from the Sun. Pluto is 4.67 billion miles from the Earth.Calculate the ratio of the distance from Pluto to Earth to the distance from Earth to the Sun. Use scientific notation to calculate the ratio and express your answer in standard notation. (round to the hundredths place)
Answer:
PE/SE = 5.02×10¹
Step-by-step explanation:
Sun-Earth (SE) = 93×10⁶ miles
Pluto-Earth (PE) = 4.67×10⁹ miles
so, PE/SE = (4.67×10⁹) / (93×10⁶) = (4.67×10³)/93 =
= 50.215053763440860215... =
= 5.02×10¹ / 1 or simply 5.02×10¹
in other words, Pluto is a little bit more than 50 times farther away from Earth, than Earth is from the Sun.
Aldo has been given a list of 3 bands and asked to place a vote. His vote must have the names of his favorite and second favorite bands from the list. How many different votes are possible?
Answer:
6
Step-by-step explanation:
1) A B C
2) B A C
3) C A B
4) A C B
5) B C A
6) C B A
(I probably understood it incorrectly)
After reading the directions to paint, on the paint drum, the information
indicated two coats of paint is required when using the 5 litre paint
and one coat with the 20 litre drum. With both paints 1 litre of paint
covers 9 m2
1.3.1 There are 28 rooms to be painted. Show with calculations which
will be the cheaper paint to buy.
(1
Step-by-step explanation:
jnx-avkj-uup p.l.z join
The following data relate to direct materials costs for February: Materials cost per yard: standard, $1.90; actual, $2.05 Standard yards per unit: standard, 4.65 yards; actual, 5.08 yards Units of production: 9,500 Calculate the direct materials quantity variance. a.$7,761.50 unfavorable b.$8,374.25 favorable c.$8,374.25 unfavorable d.$7,761.50 favorable
Answer:
The correct answer is "7,239".
Step-by-step explanation:
Given values:
Standard price,
SP = $1.90
Actual quantity purchased,
AQP = [tex]5.08\times 9500[/tex]
= [tex]48,260 \ Yards[/tex]
Actual price,
AP = $2.05
Now,
The material price variance will be:
= [tex](AQP\times AP)-(AQP\times SP)[/tex]
By substituting the values, we get
= [tex](48260\times 2.05)-(48260\times 1.90)[/tex]
= [tex]98933-91694[/tex]
= [tex]7,239[/tex]
The average daily volume of a computer stock in 2011 was μ=35.1 million shares, according to a reliable source. A stock analyst believes that the stock volume in 2018 is different from the 2011 level. Based on a random sample of 40 trading days in 2018, he finds the sample mean to be 31.8 million shares, with a standard deviation of s=14.6 million shares. Test the hypotheses by constructing a 95% confidence interval.
(a) State the hypotheses for the test.
(b) Determine if the researcher will reject the null hypothesis.
Answer:
The 95% confidence interval is ( 27.126 , 34.674)
Step-by-step explanation:
Given
The t critical value at 0.05 level = 2.023 for the df = 39
Confidence interval = 95%
Mean
[tex]\bar{x} - t * \frac{s}{\sqrt{n} } < \mu < \bar{x} + t * \frac{s}{\sqrt{n} }[/tex]
Substituting the given values we get -
[tex]\30.9 - 2.023 * \frac{11.8}{\sqrt{40} } < \mu < \30.9 + 2.023 * \frac{11.8}{\sqrt{40} }\\27.126 < \mu < 34.674[/tex]
Hence, the 95% confidence interval is
( 27.126 , 34.674)
If -9x(x + A) + 2 = (Bx + 2)(3x - 1) + 4, find the constants A and B.I am stuck at the step of solving B,can you help me?write down you steps and answer please
Answer:
A = -1
B = -3
Step-by-step explanation:
you need to do all the multiplication on both sides and then simply compare the factors of the various powers of x.
so,
-9x² - 9×A×x + 2 = 3×B×x² + 6x -Bx - 2 + 4
-9x² - 9×A×x + 2 = 3×B×x² + (6-B)x + 2
the x-less constants 2 = 2 are correct. now we need to compare the factors for the other parts of x.
we have left and right only one expression of x²
-9x² on the left
3×B×x² on the right
therefore,
-9 = 3×B
=> B = -3
otherwise the equation would not be correct for all values of x.
the only other parts remaining are
-9×A×x = (6-B)x = (6 - -3)x = (6+3)x = 9x
=>
-9×A = 9
-A = 1
A = -1
remember, all parts of the left and of the right side must be equal for the equation to be true in all cases.
A study attempts to examine whether watching a lot of television or playing a lot of video games will have a detrimental effect on a child's academic success at school and/or their success at sports. he experiment is conducted on the basis that the age of the child will be important in determining this effect but the gender of the child will not. Select all the elements that are FACTORS of this experiment:
a. age of the child
b. gender of the child
c. time spend reading books over a year
d. time spent playing video games over a year
e. success at sports
f. academic success at school
g. time spent watching television over a year
Answer : A,D,G
Step-by-step explanation:
A factor of experiment is the controlled independent variable.
The factor of experiments are,
d) Time spent playing video games over a yeare) Success at sportsf) Academic success at schoolg) Time spent watching television over a yearHence option d,e,f and g is the factor of experiment.
What is the factor of experiment means?A factor of experiment is the controlled independent variable.
Given information
The experiment is conducted on the basis of age.
The experiment is not conducted on the basis of gender.
In the experiment the relation between watching TV a lot or playing video game and child's academic success at school and/or their success at sports tried to obtained.
Factors of this experiment-
a) Age of the child- As in the statement it is cleared, that the age of the child is a base of the experiment but the age can not be a controlled independent variable. Thus the age of the child is the not a factor of this experiment.b) Gender of the child-As for the study for the given problem, the gender is not important. Thus the gender of the child in not a factor of this experiment.c) Time spend reading books over a year-The study is to determine the relation between watching TV a lot or playing video game and child's academic success and not about reading books. Thus the time spend reading books over a year is not a factor of this experiment.d) Time spent playing video games over a year- The study is to determine the relation between playing video game and child's academic success or success in sports. Thus, time spent playing video games over a year is a factor of this experiment.e) Success at sports-As the success at the sports is the part of the study. Thus, success at sports is a factor of this experiment.f) Academic success at school- As the academic success at the school is the part of the study. Thus, academic success at school is a factor of this experiment.g)Time spent watching television over a year-The study is to determine the relation between a lot of television watching and child's academic success or success in sports. Thus, time spent watching television over a years a factor of this experiment.Thus the factor of experiments are,
d) Time spent playing video games over a yeare) Success at sportsf) Academic success at schoolg) Time spent watching television over a yearHence option d,e,f and g is the factor of experiment.
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