Answer:
0
Step-by-step explanation:
Hello, please consider the following.
For any a and b real numbers we can write.
[tex](a-b)(a+b)=a^2-b^2[/tex]
We apply this formula two times here, as below.
[tex](x+1)(x^{2}+1)(x-1)=(x+1)(x-1)(x^{2}+1)\\\\=(x^2-1^2)(x^2+1)=(x^2-1)(x^2+1)\\\\=(x^2)^2-1^2=x^4-1[/tex]
We have the coefficient of 1 for [tex]x^4[/tex] and the constant term is -1, so the sum of the coefficients is 0.
Thank you.
Answer:
1
Step-by-step explanation:
(x + 1)(x² + 1)(x - 1)
= (x³ + x + x² + 1)(x - 1)
= x^4 - x³ + x² - x - x³ - x² + x - 1
= x^4 - 1
Coefficient of x^4 = 1
Express the function F in the form f∘g. (Enter your answers as a comma-separated list. Use non-identity functions for f(x) and g(x).)
F(x) = (x − 1)4
Answer:
[tex]f(x) = x^{4}[/tex], [tex]g(x) = x-1[/tex]
Step-by-step explanation:
Let be [tex]F(x) = f\circ g (x) = (x-1)^{4}[/tex], then expression for [tex]f(x)[/tex] and [tex]g(x)[/tex] are, respectively:
[tex]f(x) = x^{4}[/tex] and [tex]g(x) = x-1[/tex]
Kevin's total payroll deductions are 30% of his earnings. If his deductions add up to $369 for a two week period, how much were his earnings for the period?
Answer:
His earnings for the period= $123
Step-by-step explanation:
Kevin's total payroll deductions are 30% of his earnings. His deductions add up to $369 for a two week period.
If 30% of his earnings = $369
His earnings = x
30/100 * x= 369
X= 369*100/30
X= 123*10
X=$ 1230
His earnings for the period= $123
A random sample of 1003 adult Americans was asked, "Do you think televisions are a necessity or a luxury you could do without?" Of the 1003 adults surveyed, 521 indicated that televisions are a luxury they could do without. Construct and interpret a 95% confidence interval for the population proportion of adult Americans who believe that televisions are a luxury they could do without out.
Answer:
The 95% confidence interval is [tex]0.503 < p < 0.535[/tex]
The interpretation is that there is 95% confidence that the true population proportion lie within the confidence interval
Step-by-step explanation:
From the question we are told that
The sample size is n = 1003
The number that indicated television are a luxury is k = 521
Generally the sample mean is mathematically represented as
[tex]\r p = \frac{k}{n}[/tex]
[tex]\r p = \frac{521}{1003}[/tex]
[tex]\r p = 0.519[/tex]
Given the confidence level is 95% then the level of significance is mathematically evaluated as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table, the value is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
The margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{\r p (1- \r p )}{n} }[/tex]
=> [tex]E = 1.96 * \sqrt{ \frac{ 0.519 (1- 0.519 )}{1003} }[/tex]
=> [tex]E = 0.016[/tex]
The 95% confidence interval is mathematically represented as
[tex]\r p -E < p < \r p +E[/tex]
=> [tex]0.519 - 0.016 < p < 0.519 + 0.016[/tex]
=> [tex]0.503 < p < 0.535[/tex]
Determina el valor absoluto de 13 – 11|
Responder:
2
Explicación paso a paso:
El valor absoluto de una expresión es el también conocido como valor positivo devuelto por la expresión. Una expresión en un signo de módulo se conoce como valor absoluto de la expresión y dicha expresión siempre toma dos valores (tanto el valor positivo como el negativo).
Por ejemplo, el valor absoluto de x se escribe como | x | y esto puede devolver tanto + x como -x debido al signo del módulo.
Pasando a la pregunta, debemos determinar el valor absoluto de | 13-11 |. Esto significa que debemos determinar el valor positivo de la expresión como se muestra;
= | 13-11 |
= | 2 |
Este módulo de 2 puede devolver tanto +2 como -2, pero el valor absoluto solo devolverá el valor positivo, es decir, 2.
Por tanto, el valor absoluto de la expresión es 2
distance between 2,-5 and 3,-7
Answer:
√5
Step-by-step explanation:
[tex](2 ,-5) = (x_1,y_1)\\(3,-7)=(x_2,y_2)\\\\d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\ \\d = \sqrt{(3-2)^2 +(-7-(-5))^2}\\ \\d = \sqrt{(1)^2+(-7+5)^2}\\ \\d = \sqrt{(1)^2 + (-2)^2}\\ \\d = \sqrt{1 +4}\\ \\d = \sqrt{5}[/tex]
2 lines intersect a horizontal line to form 8 angles. Labeled clockwise, starting at the top left, the angles are: A, B, C, D, E, F, G, D. Which of the pairs of angles are vertical angles and thus congruent? ∠A and ∠G ∠A and ∠B ∠C and ∠F ∠D and ∠H
Answer:
∠A and ∠G is the pair of vertical angles.
Step-by-step explanation:
From the figure attached,
Two lines 'm' and 'n' are two parallel lines. These lines intersect a horizontal line 'l'.
Since, "Pair of opposite angles formed at the point of intersection are the vertical angles and equal in measure."
Therefore, Opposite angles ∠A ≅ ∠G, ∠B ≅ ∠H, ∠C ≅ ∠E and ∠D ≅ ∠F are the vertical angles.
From the given options,
∠A and ∠G is the pair representing the pair of vertical angles and thus congruent.
Answer:
a
Step-by-step explanation:
A girl has 98 beads, and all but 14 were lost. how many beads did she loose?
Answer:
84 beads
Step-by-step explanation:
She had 98 beads and lost all but fourteen. So it would be 98 - 14 which would get you 84 beads that the girl has lost
Use the graph showing Debra's account balance to answer the question that follows. ^
About how long will it take for Debra's account balance to equal $60?
A - 6 months
B - 6 years
C - 3 months
D - 3 years
Answer: 2 years
Step-by-step explanation:
In the given graph, we have
Account Balance ($) on y-axis
Time (years) on x-axis.
To know the time taken to get a balance of $60 , we check the point corresponding to 60 at y-axis and then join it to the line of the function and stop.
Then from there we drop a line to x-axis.
We get x=2.
That is it will take 2 years to get $60 balance in Debra's account.
So the correct answer is 2 years.
A researcher wishes to determine whether people with high blood pressure can lower their blood pressure by performing yoga exercises. A treatment group and a control group are selected. The sample statistics are given below. Construct a 90% confidence interval for the difference between the two population means, Would you recommend using yoga exercises? Treatment Group Control Group n1 = 100 n2 = 100 1 = 178 2 = 193 s1 = 35 s2 = 37
Answer:
90% confidence interval for the difference between the two population means
( -23.4166 , -6.5834)
Step-by-step explanation:
Step(i):-
Given first sample size n₁ = 100
Given mean of the first sample x₁⁻ = 178
Standard deviation of the sample S₁ = 35
Given second sample size n₂= 100
Given mean of the second sample x₂⁻ = 193
Standard deviation of the sample S₂ = 37
Step(ii):-
Standard error of two population means
[tex]se(x^{-} _{1} -x^{-} _{2} ) = \sqrt{\frac{s^{2} _{1} }{n_{1} }+\frac{s^{2} _{2} }{n_{2} } }[/tex]
[tex]se(x^{-} _{1} -x^{-} _{2} ) = \sqrt{\frac{(35)^{2} }{100 }+\frac{(37)^{2} }{100 } }[/tex]
[tex]se(x^{-} _{1} -x^{-} _{2} ) = 5.093[/tex]
Degrees of freedom
ν = n₁ +n₂ -2 = 100 +100 -2 = 198
t₀.₁₀ = 1.6526
Step(iii):-
90% confidence interval for the difference between the two population means
[tex](x^{-} _{1} - x^{-} _{2} - t_{\frac{\alpha }{2} } Se (x^{-} _{1} - x^{-} _{2}) , x^{-} _{1} - x^{-} _{2} + t_{\frac{\alpha }{2} } Se (x^{-} _{1} - x^{-} _{2})[/tex]
(178-193 - 1.6526 (5.093) , 178-193 + 1.6526 (5.093)
(-15-8.4166 , -15 + 8.4166)
( -23.4166 , -6.5834)
What is the value of x?
Answer:
58
Step-by-step explanation:
By the property of intersecting secants outside of a circle, we have:
x° = 1/2( 141° - 25°) = 1/2 * 116° = 58°
Therefore, x = 58
Gavin goes to the market and buys one rectangle shaped board. The length of the board is 16 cm and width of board is 10 cm. If he wants to add a 2 cm wooden border around the board, what will be the area of the rectangle board?
Answer:
The answer is 216
Step-by-step explanation:
if there is a 2 cm border, that means that the sides will both become 2 centimeters longer. so (16+2)*(10*2) = 18*12 = 216.
The time, X minutes, taken by Tim to install a satellite dish is assumed to be a normal random variable with mean 127 and standard deviation 20. Determine the probability that Tim will takes less than 150 minutes to install a satellite dish.
Answer: 0.8749
Step-by-step explanation:
Given, The time, X minutes, taken by Tim to install a satellite dish is assumed to be a normal random variable with mean 127 and standard deviation 20.
Let x be the time taken by Tim to install a satellite dish.
Then, the probability that Tim will takes less than 150 minutes to install a satellite dish.
[tex]P(x<150)=P(\dfrac{x-\text{Mean}}{\text{Standard deviation}}<\dfrac{150-127}{20})\\\\=P(z<1.15)\ \ \ [z=\dfrac{x-\text{Mean}}{\text{Standard deviation}}]\\\\=0.8749\ [\text{By z-table}][/tex]
hence, the required probability is 0.8749.
Emily made a pot cream of pumpkin soup for thanksgiving dinner she put 5 cups of cream in the soup she poured the soup into 24 small bowl show much cream measured in oz is used for each small bowl of soup?
Answer:
each bowl can contain 5/3 oz. of soup.
Step-by-step explanation:
1 cup = 8 oz.
8 oz.
5 cups x -------------- = 40 oz.
1 cup
to get the measurement of each bowl,
40 oz. divided into 24 bowls.
therefore, each bowl can contain 5/3 oz. of soup.
Solve for x if 2(1+3x)=14
Answer:
x=2
Step-by-step explanation:
2(1+3x)=14
Divide each side by 2
2/2(1+3x)=14/2
1+3x = 7
Subtract 1 from each side
3x =7-1
3x = 6
Divide by 3
3x/3 = 6/3
x =2
22/25of a number is what percentage of that number?
Answer:
88%.
Step-by-step explanation:
Multiply the fraction by 100:
(22/25) * 100
= 22 * 4
= 88%.
2 divided by ___=42 two divided by what equals 42?
[tex]\sqrt{x+1+5=x}[/tex] Please help [tex]\sqrt{5x-x=0}[/tex] I actually can't do this, also thirty points
Answer:
It is undefined.
Step-by-step explanation:
Let's take a look at the first equation- if we simplify and move the terms, it becomes sqrt of 6 = 0, which results in an undefined value of x. The second equation works with x=0 but not the first so the value of x is undefined.
The population of Jacksonville is 836,507. What is the population rounded to the
nearest hundred thousand?
A. 900,000
O
B. 850,000
C. 840,000
o D. 800,000
Answer:
D. 800,000
Step-by-step explanation:
It is D because you find the hundred thousand place which is the 8, the you go to the number next door which is 3, if the 3 is 5 or greater the 8 will become a 9 or if it is not then it will stay the same. And everything to the left stays the same, everything to the right turns into zeros.
What is the missing statement in step 10 of the proof?
Answer:
c/sin C = b/sin C
Step-by-step explanation:
Look at the statement in the previous step and the reason in this step.
c sin B = b sin C
Divide both sides by sin B sin C:
(c sin B)/(sin B sin C) = (b sin C)/(sin B sin C)
c/sin C = b/sin B
What is the probability that a randomly selected individual on this campus weighs more than 166 pounds? (express in decimal form and round final answer to 4 decimal places)
Answer:
hello attached is the missing part of your question and the answer of the question asked
answer : 0.2951
Step-by-step explanation:
Given data:
number of persons allowed in the elevator = 15
weight limit of elevator = 2500 pounds
average weight of individuals = 152 pounds
standard deviation = 26 pounds
probability that an individual selected weighs more than 166 pounds
std = 26 , number of persons(x) = 15, average weight of individuals(u) = 152 pounds
p( x > 166 ) = p( x-u / std, 166 - u/ std )
= p ( z > [tex]\frac{166-152}{26}[/tex] )
= 1 - p( z < 0.5385 )
p( x > 166 ) = 1 - 0.70488 = 0.2951
Suppose a vine maple grows in height linearly. Four weeks after it is planted it stands 10.67 inches, and after seven weeks it is 15.67 inches tall. Write an equation that models the growth, in inches, of the vine maple as a function of time, in weeks. 1. What is the slope of the function? 2. How tall was the tree when it was first planted? 3. Write the function 4. How tall will the vine maple be after 16 weeks?
Answer:
Height (z)= 4+(5/3)(z)
Where z is the number of weeks
1). Slope = 4
2). Height= 5.67 inches
3).Height (z)= 4+(5/3)(z)
4).Height= 30.67 inches
Step-by-step explanation:
At week four
10.67= x+4y
Week 7
15.67= x+7y
Solving both equation simultaneously
3y= 5
Y= 5/3
15.67= x+7y
15.67= x+7(5/3)
15.67-35/3= x
15.67-11.67= x
4= x
The modeled equation is
Height (z)= 4+5/3(z)
Where z is the number of weeks
Slope of the function as compared to y= mx+c is 4
The first week of it's plantation
Height (z)= 4+5/3(z)
Height (1)= 4+5/3(1)
Height= 5.67 inches
After 16 weeks
Height (z)= 4+(5/3)(z)
Height (16)= 4+(5/3)(16)
Height= 30.67 inches
Which of the following points IS a solution to the system: y > - 3x + 4 / y > 2x / - y < 7 Selected answer is not correct.
Answer:
Solution : Third Option
Step-by-step explanation:
The first step here is to make all the signs uniform. As you can see the third inequality has a less than sign, which we can change to a greater than sign by dividing negative one on either side, making the inequality y > - 7.
[tex]\begin{bmatrix}y>-3x+4\\ y>2x\\ y>-7\end{bmatrix}[/tex]
Now take a look at the third option. Of course the y - coordinate, 3, is greater than - 7, so it meets the third requirement ( y > - 7 ). At the same time 3 > 1( 2 ) > 2, and hence it meets the second requirement as well. 3 > - 3( 1 ) + 4 > - 3 + 4 > 1, meeting the first requirement.
Therefore, the third option is a solution to the system.
1.
The ratio of the numbers of sides of two regular polygons is 1:2 .If each interior angle of the first
polygon is 1200 then the measure of each interior angle of the second polygon
is
(1)1400
(2)1350
(3)1500
(4)1600
first polygon
ext. angle=180°-120°
=60°
[tex]ext \: ang = \frac{360}{n} [/tex]
n=360°/60°
n=6
second polygon
n=2(6)=12
ext. ang= 360°/n = 360°/12° = 30°
int. ang = 180°-30°= 150°
answer is C
If the ratio of the numbers of sides of two regular polygons is 1:2 and each interior angle of first angle is 120° then the measure of each interior angle of the second polygon is 150° which is option 3).
What is regular polygon?A regular polygon is a polygon whose all sides are equal to each other.
How to find interior angle?We have been given ratio of sides of two polygon that is 1:2 and the interior angle of first polygon that is 120 degrees.
Exterior angle will be 180-120=60°
We know that exterior angle =360/n where n is the sides of the polygon.
60=360/n
n=360/60
n=6
Number of sides of other polygon=2*6=12
Exterior angle=360/n
=360/12
=30
Interior angle=180-30=150°
Hence the interior angle of the second polygon is 150 degrees.
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Carol owns a BBQ company that sells brisket for $11.75 per pound (after it is smoked for 10 hours). She buys the brisket for an AP$ of $4.72 per pound and they weigh 10.4 lbs each. Once they are done smoking, they weigh 6.24 lbs each.
What is the yield % of the briskets after Carol is done smoking them?
Answer: 60%
Step-by-step explanation:
Given, AP$ of Brisket = $4.72
Weight of each brisket on purchase : 10.4 lbs
Weight of each brisket after smoking : 6.24 lbs
Yield % of the briskets after Carol is done smoking them=[tex]\dfrac{\text{Weight after smoking}}{\text{Weight on purchase}}[/tex]
[tex]\dfrac{6.24}{10.4}\times100\\\\=60\%[/tex]
Hence, the yield % of the briskets after Carol is done smoking them = 60%
In a factory there are 100 units of a certain product, 5 of which are defective. We pick three units from the 100 units at random. What is the probability that none of them are defective
Answer:
Probability of picking all three non-defective units
= 7372/8085 (or 0.911812 to six decimals)
Step-by-step explanation:
Let
D = event that the picked unit is defective
N = event that the picked unit is not defective
Pick are without replacement.
We need to calculate P(NNN) using the multiplication rule,
P(NNN)
= 97/100 * 96/99 * 95/98
=7372/8085
= 0.97*0.969697*0.9693878
= 0.911812
The probability that none of the picked products are defective is;
P(None picked is defective) = 0.856
We are told that 5 are defective out of 100.This means the number of good products that are not defective are 95.
Probability of the first picked product not being defective is written as; P(First picked not defective) = 95/100Since the good ones have been picked, there will be 99 left of which the good ones are now 94. Thus, probability of second one not being defective = 94/99Since two good ones have been picked, there will be 98 left and 93 good ones left. Thus, probability of third one not being defective = 93/98Finally, Probability of none of the three being defective is;95/100 × 94/99 × 93/98 = 0.856
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Drag the ruler over each side of the triangle to find its length. The length of AB is . The length of BC is . ASAP Drag the protractor over each angle to find its measure. The measure of angle C is . The measure of angle B is .
Answer:
Drag the ruler over each side of the triangle to find its length.
The length of AB is
✔ 5
.
The length of BC is
✔ 4
.
Drag the protractor over each angle to find its measure.
The measure of angle C is
✔ 90°
.
The measure of angle B is
✔ 36.9°
.
Step-by-step explanation:
The length of sides AB and BC of the triangle will be 5 units and 4 units. And the measure of angle C and angle B of the triangle will be 90° and 37°.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Drag the ruler over each side of the triangle to find its length.
The length of side AB of the triangle is 5 units.
The length of side BC of the triangle is 4 units.
Drag the protractor over each angle to find its measure.
The measure of angle C of the triangle is 90°.
The measure of angle B of the triangle is 37°.
The length of sides AB and BC of the triangle will be 5 units and 4 units.
And the measure of angle C and angle B of the triangle will be 90° and 37°.
More about the right-angle triangle link is given below.
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Find the missing side of the triangle. A. √321 yd B. √221 yd C. 3√38 yd D. √21 yd
Answer:
(B) [tex]\sqrt{221}[/tex] yards
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean Theorem to find the length of x.
The Pythagorean Theorem states that [tex]a^2 + b^2 = c^2[/tex], where a and b are our legs and c is the hypotenuse.
We need to find c, and we already know a and b, so let's substitute.
[tex]10^2 + 11^2 = c^2\\\\100+121=c^2\\\\221=c^2\\\\c=\sqrt{221}[/tex]
Hope this helped!
Which option is correct and how would one solve for it?
Answer:
-3/5, -1, -5/3, -3, -7
Step-by-step explanation:
Let x go from 1 to 5
x =1 (1+2)/(1-6) = 3/-5 = -3/5
x =2 (2+2)/(2-6) = 4/-4 = -1
x =3 (3+2)/(3-6) = 5/-3 = -5/3
x =4 (4+2)/(4-6) = 6/-2 = -3
x =5 (5+2)/(5-6) = 7/-1 = -7
You’ve been contracted to wallpaper a wall 10 feet wide and 12 feet high with a square window with 3 foot sides. How many square feet of wallpaper do you need to cover the wall if you were to exclude the opening for the window? _____ square feet
Answer:
111 ft²
Step-by-step explanation:
wall: 10 x 12 = 120
window: 3 x 3 = 9
wall - window = area to wallpaper
120 - 9 = 111
111 ft²
Answer:
111 sq ft
Step-by-step explanation:
wall: 10 x 12 = 120
window: 3 x 3 = 9
wall - window = area to wallpaper
120 - 9 = 111
111 ft²
Question: 2. Musah Stands At The Centre Of A Rectangular Field. He First Takes 50 Steps North, Then 25 Steps West And Finally 50 Steps On A Bearing Of 3150 Sketch Musah's Movement Mark 41 Ii. How Far West Is Musah's Final Point From The Centre? [Mark 41 Iv. How Far North Is Musah's Final Point From The Centre? Mark 41 Describe How You Would Guide A JHS Student
Answer:
60.36 steps West from centre
85.36 steps North from centre
Step-by-step explanation:
Refer to attached
Musah start point and movement is captured in the picture.
1. He moves 50 steps to North, 2. Then 25 steps to West, 3. Then 50 steps on a bearing of 315°. We now North is measured 0°or 360°, so bearing of 315° is same as North-West 45°.
Note. According to Pythagorean theorem, 45° right triangle with hypotenuse of a has legs equal to a/√2.
How far West Is Musah's final point from the centre?
25 + 50/√2 ≈ 60.36 stepsHow far North Is Musah's final point from the centre?
50 + 50/√2 ≈ 85.36 steps