Answer:
Step-by-step explanation:
Considering the polynomial 2x⁵ + 4x³ - 3x⁸. The polynomial is not yet in standard form. For a polynomial to be in standard form, the power of the variables must decrease as we progress to the right of the expression.
A) The polynomial in standard form is therefore - 3x⁸ + 2x⁵ + 4x³. We can see that the power are reducing as we move through each terms i.e from 8 to 5 then to 3.
B) The degree of a polynomial is the maximum degree among all the terms of the polynomial. The term that has the maximum degree is -3x⁸. Hence, the degree of the polynomial is 8
C) There are only 3 terms in the polynomial given. The terms are separated by mathematical signs. The terms if the polynomial are 2x⁵, 4x³ and - 3x⁸.
D) The leading term of the polynomial is the term that comes first after rewriting the polynomial in standard format. Given the standard from of the polynomial given as -3x⁸ + 2x⁵ + 4x³, the leading term will be - 3x⁸
E) Given the leading term to be - 3x⁸, the leading coefficient of the polynomial will be the coefficient of the leading term. The coefficient of -3x⁸ is -3
Consider F and C below.
F(x, y) = x2 i + y2 j
C is the arc of the parabola y = 2x2 from (−1, 2) to (2, 8)
(a) Find a function f such that F = ∇f. f(x, y) =
(b) Use part (a) to evaluate C ∇f · dr along the given curve C.
(a)
[tex]\dfrac{\partial f}{\partial x}=x^2\implies f(x,y)=\dfrac{x^3}3+g(y)[/tex]
[tex]\dfrac{\partial f}{\partial y}=\dfrac{\mathrm dg}{\mathrm dy}=y^2\implies g(y)=\dfrac{y^3}3+C[/tex]
[tex]\implies f(x,y)=\dfrac{x^3+y^3}3+C[/tex]
(b)
[tex]\displaystyle\int_C\nabla f\cdot\mathrm d\mathbf r=f(2,8)-f(-1,2)=\boxed{171}[/tex]
(a^8)3/2 in simplest form
Answer:
[tex]\large\boxed{\frac{3}{2}a^{8}}[/tex]
Step-by-step explanation:
([tex]a^{8}[/tex]) * [tex]\frac{3}{2}[/tex]
Remove the parenthesis by multiplying
[tex]\frac{3}{2}[/tex][tex]a^{8}[/tex]
This expression cannot be simplified further
[tex]\large\boxed{\frac{3}{2}a^{8}}[/tex]
Hope this helps :)
idk how to put the picture but can someone just tell me the points where the two dots go plz will give good rate nd say thx plz answer fast
Graph -8x-y=8
Answer:
(-1,0) and (0,-8)
Step-by-step explanation:
Hey there!
Well first we’ll graph -8x - y = 8,
Look at the image below
By lookig at the image below we can tell the 2 points are at,
(-1,0) and (0,-8)
Hope this helps :)
Simplify to create an equivalent expression. 7n-(4n-3) a=3n+3 b=3n−3 c=11n+3 d=11n−3 I will rate you brainliest. :)
Answer:
3n +3
Step-by-step explanation:
7n-(4n-3)
Distribute the minus sign
7n -4n +3
3n +3
Complete the recursive formula of the geometric sequence -0.3,0.9,-2.7,8.1
Answer:
[tex]a_{n}[/tex] = - 3[tex]a_{n-1}[/tex] with a₁ = - 0.3
Step-by-step explanation:
The recursive formula for a geometric sequence is of the form
[tex]a_{n}[/tex] = r[tex]a_{n-1}[/tex]
where r is the common ratio
r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{0.9}{-0.3}[/tex] = - 3 , thus
[tex]a_{n}[/tex] = - 3[tex]a_{n-1}[/tex] with a₁ = - 0.3
List the sides of ΔRST in ascending order (shortest to longest). m∠R=2x+11°, m∠S=3x+23°, and m∠T=x+42°
Answer:
ST, RS, RT
Step-by-step explanation:
Angles of a triangle add up to 180°.
2x + 11° + 3x + 23° + x + 42° = 180°
6x + 76° = 180°
x = 17⅓
m∠R = 2x+11° = 45⅔°
m∠S = 3x+23° = 75°
m∠T = x+42° = 59⅓°
The shortest side is opposite the smallest angle, and the longest side is opposite the largest angle.
ST, RS, RT
In this diagram, bac~edf. if the area of bac= 6 in.², what is the area of edf? PLZ HELP PLZ PLZ PLZ
Answer:
2.7 in²
Step-by-step explanation:
Given that ∆BAC ~ is similar to ∆EDF, the ratio of the area of ∆BAC to the area of ∆EDF = the square of the ratio of their corresponding sides.
Thus, let x be the area of ∆EDF
[tex] \frac{6}{x} = (\frac{3}{2})^2 [/tex]
[tex] \frac{6}{x} = \frac{9}{4} [/tex]
Cross multiply
[tex] x*9 = 4*6 [/tex]
[tex] 9x = 24 [/tex]
[tex] \frac{9x}{9} = \frac{24}{9} [/tex]
[tex] x = 2.67 [/tex]
Area of ∆EDF = 2.7 in²
-8 + (-15)
Evaluate this expression
Answer:
-23
Step-by-step explanation:
-8+(-15) means that you are subtracting 15 from -8. So you end up with -8-15=-23.
Which set of numbers is arranged from least to greatest?
Answer:
The correct answer is option B
Given y(x) = f(x)g(x). Find the slope of the tangent line to y(x) at x = 7.
Answer:
Step-by-step explanation:
Interesting problem.
At 6<x<8,
f(x) = x-7
at 5<x<8
g(x) = (15-x)/2
=>
y(x)
= f(x)*g(x)
= (x-7)(15-x)/2
= (x^2+22x-105)/2
differentiate y(x) with respect to x,
y'(x) = -x+11
at x = 7,
y'(7) = -(7) + 11 = 4
Jaclyn is one-fourth of a foot taller than John. John is 31/6 feet tall. How many feet tall is Jaclyn
Answer:
5 5/12
Step-by-step explanation:
31/6 feet + 1/4 foot
= 31/6 + 1/4
= [(31 * 4) / 6 * 4] + [(1 * 6) / 4 * 6]
= [ 124/24 ] + [ 6/24 ]
= (124 + 6) / 24
= 130 / 24
= 5 10/24
= 5 5/12
Hope this helps! Tell me if I'm wrong!
The locksmith is 37.9 kilometers west of the bank and 77.9 kilometers west of the garbage dump. The garbage dump is 128.6 kilometers east of the pet store. The pet store is 35.0 kilometers north of the hardware store. Which is closer to the pet store, the hardware store or the locksmith?
The correct answer is Hardware store
Explanation:
In this case, you need to determine the distance between the pet store and the locksmith to know if the distance is longer than the one from the pet store and the hardware (35 kilometers). Now this distance can be calculated by subtracting the distance from the locksmith to the garbage dump from the total distance between the pet store and the garbage dump. This is because the locksmith is between the pet store and the garbage, which means the distance between the pet store and the locksmith is a portion of the total distance, which is the distance from the pet store and the garbage dump. The process is shown below:
128.6 kilometers (distance from the garbage dump to the pet store) - 77.9 kilometers (distance from the garbage dump to the locksmith) = 50.7 (distance from the locksmith to the pet store
50.7 kilometers is greater than 35 kilometers, which means the hardware store is closer to the pet store
A 95% confidence interval for the mean number of television per American household is (1.15, 4.20). For each of the following statements about the above confidence interval, choose true or false.
a. The probability that u is between 1.15 and 4.20 is .95.
b. We are 95% confident that the true mean number of televisions per American household is between 1.15 and 4.20.
c. 95% of all samples should have x-bars between 1.15 and 4.20 televisions.
d. 95% of all American households have between 1.15 and 4.20 televisions
e. Of 100 intervals calculated the same way (95%), we expect 95 of them to capture the population mean.
f. Of 100 intervals calculated the same way (95%), we expect 100 of them to capture the sample mean.
Answer:
a. False
b. True
c. False
d. False
e.True
f. True
Step-by-step explanation:
The 95% is confidence interval its not a probability estimate. The probability will be different from the confidence interval. Confidence interval is about the population mean and is not calculated based on sample mean. Every confidence interval contains the sample mean. There is 95% confidence that the number of televisions per American household is between 1.15 to 4.20.
AC is included between __________
Answer:
AC is included between <A and <C.
Step-by-step explanation:
i think, not sure tho
A jar contains 8 pennies, 5 nickels and 7 dimes. A child selects 2 coins at random without replacement from the jar. Let X represent the amount in cents of the selected coins. Be very precise with your answers.
a. Find the probability x = 2 cents.
b. Find the probability x = 6 cents.
c. Find the probability x = 10 cents.
d. Find the probability x = 11 cents.
e. Find the probability x = 15 cents.
f. Find the probability x = 20 cents.
g. Find the expected value of x.
Answer:
a. The probability x = 2 cents = 7/22
b. The probability x = 6 cents = 35/66
c. The probability x = 10 cents = 5/33
d. The probability x = 11 cents= 28/33
e. The probability x = 15 cents = 20/33
f. The probability x = 20 cents = 14/33
g. The expected value of x = 5.9
Step-by-step explanation:
This is a binomial probability distribution. The number of trials is known .
a. The probability x = 2 cents.
Probability ( X=2) P( selecting 2 dimes)= 7C2 / 12c2
= 21 / 66 = 7/22
b. The probability x = 6 cents.
Probability ( X=6) P( selecting a nickel and a dime)= 5C1 * 7C1/ 12c2
= 5*7 / 66 = 35/66
c. The probability x = 10 cents.
Probability ( X=10) P( selecting two nickels )= 5C2 / 12c2)
= 10/ 66 = 5/33
d. The probability x = 11 cents.
Probability ( X=11) P( selecting a penny and a dime)= 8C1 * 7C1/ 12c2)
= 8*7 / 66 = 56/66= 28/33
e. The probability x = 15 cents.
Probability ( X=15) P( selecting a penny and a nickel)= 8C1 * 5C1/ 12c2)
= 8*5 / 66 = 40/66= 20/33
f. The probability x = 20 cents.
Probability ( X=20) P( selecting 2 pennies )= 8C2 / 12c2)
= 28 / 66 = 14/33
g. The expected value of x.
E(X) = np
E(X) = 2 * (8C2+ 5C2+ 7C2)/(8+5+7) = 2( 28+10+21)/20
=2(59)/20= 5.9
HELP
PLSFind all the missing elements:
Answer:
a = 6.7 , c = 2.0
Step-by-step explanation:
For side aTo find the missing side a we use the sine rule
[tex] \frac{ |b| }{ \sin(B) } = \frac{ |a| }{ \sin(A) } [/tex]From the question
B = 58°
b = 6
A = 109°
Substituting the values into the above formula we have
[tex] \frac{6}{ \sin(58) } = \frac{ |a| }{ \sin(109) } [/tex][tex] |a| \sin(58) = 6\sin(109) [/tex]Divide both sides by sin 58°
[tex] |a| = \frac{6 \sin(108) }{ \sin(58) } [/tex]a = 6.728791
a = 6.7 to the nearest tenthFor side cTo find side c we use the sine rule
That's
[tex] \frac{ |b| }{ \sin(B) } = \frac{ |c| }{ \sin(C) } [/tex]C = 13°
[tex] \frac{6}{ \sin(58) } = \frac{ |c| }{ \sin(13) } [/tex][tex] |c| \sin(58) = 6 \sin(13) [/tex]Divide both sides by sin 58°
[tex] |c| = \frac{6 \sin(13) }{ \sin(58) } [/tex]c = 1.591544
c = 2.0 to the nearest tenthHope this helps you
Answer:
B=58 a=6.7 c=1.6
Step-by-step explanation:
It was right on Acellus
Sorry I cant give a better explanation but this unit is killing me.
This??? What is wrong with it?
Answer:
15.8 sq. in. of paper will be required.
Step-by-step explanation:
The problem is that a drinking cup does not have a cover, so only the lateral surface area counts.
I.e. We need only the first term.
A = pi r l = pi * 1.5 * sqrt(3^2+1.5^2)
= 15.81 sq. in.
A professor of women's studies is interested in determining if stress affects the menstrual cycle. Ten women are randomly sampled for an experiment and randomly divided into two groups. One of the groups is subjected to high stress for two months while the other lives in a relatively stress-free environment. The professor measures the menstrual cycle (in days) of each woman during the second month. The following data are obtained.
High stress 20 23 18 19 22
Relatively stress free 26 31 25 26 30
Required:
1. The obtained value of the appropriate statistic is _______
a. tobt = -4.73
b. tobt = -4.71
c. tobt = -3.05
d. tobt = -.047
2. The df for determining tcrit are ____.
a. 4
b. 9
c. 8
d. 3
3. Using a = 0.052 tail, tcrit = ____.
a. +- 2.162
b. +- 2.506
c. +- 2.462
d. +- 2.306
4. Using a = .052 tail, your conclusion is ____.
a. Accept H0; stress does not affect the menstrual cycle
b. Retain H0; we cannot conclude that stress affects the menstrual cycle
c. Retain H0; Stress affects the menstrual cycle
d. Reject H0; stress affects the menstrual cycle
Answer:
1. a. tobt = -4.73
2. b. 9
3. a. +- 2.162
4. d. Reject H0; stress affects the menstrual cycle.
Step-by-step explanation:
The degrees of freedom is number of independent variable factors that affect the range of parameters. The degrees of freedom is the calculation of number values that are free to vary. The degrees of freedom is calculated by N-1. Standard error is the estimated deviation of standard deviation from its sample mean distribution. The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted.
If is an angle bisector of ∠QOR and ∠QOP = 71°, then find the angle measure of ∠QOR. Question 8 options: A) 71° B) 142° C) 35.5° D) 35°
Answer: B. 142°.
Step-by-step explanation:
Given: OP is an angle bisector of ∠QOR and ∠QOP = 71°.
We know that an angle bisector divides an angle into two equal parts.
So, if OP is an angle bisector of ∠QOR and ∠QOP = 71°.
Then, the angle measure of ∠QOR = Twice of ∠QOP
⇒ Angle measure of ∠QOR = 2 (71°)
⇒ Angle measure of ∠QOR = 142°
Hence, correct option is B. 142°.
Which of the following is true about congruent figures?
They're the same shape and the same size.
They're the same size, but not the same shape.
They're not the same shape or size.
They're the same shape, but not the same size.
Answer:
A
Step-by-step explanation:
congruent means they have the same shape and size. hope this helps :)
14. Twice the sum of a number and eight
Answer: 2(x + 8) is the expression.
Use distributive property to simplify,
2x+16
I didn't know which answer you wanted so....
Answer:
2(x + 8)
Step-by-step explanation:
Hello!
Twice the sum means we multiply by 2
2
the sum of a number and eight is x + 8
2 * x + 8
Since we have to twice the sum we put x + 8 in parenthesis to show to do that first
2(x + 8)
Hope this Helps!
IM GIVING BRAINLIEST TO THE FIRST PERSON TO ANSWER!
Show ALL work please! <3
Answer:
B
Step-by-step explanation:
What work is there to show? you basically isolate x. add 2 to both sides. and you get x is greater than or equal to 5. So the answer is B.
x-2[tex]\geq[/tex]3
+2 +2
x[tex]\geq[/tex]5
This solid shape is made from 5 cubes. Which of the diagrams show the plan of the solid? Please help!
Answer:
A Maybe
Step-by-step explanation:
Cogntive identification
Unable to answer mathematically or analytically
The Plan of the solid shape is shown by : (A)
What is the Meaning of solid shape?A solid shape can be defined as a shape that possesses three dimensions. that is to say they are three dimensional shapes.
A solid shape has both length, width and height. They are more tangible and look physical than two dimensional shape.
solid shapes can take up space in the universe because they are more tangible and realistic.
In conclusion, the Plan of the solid shape is shown by : (A)
Learn more about solid shape: https://brainly.com/question/16717260
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12. 12 ounces is roughly the same as
O A. 340 grams.
B. 356 grams.
O C. 400 grams.
O D. 120 grams.
Mark for review (Will be highlighted on the movin
Answer:
A. 340 grams
Step-by-step explanation:
My brain
Find the maximum and minimum values of the function f(x,y)=2x2+3y2−4x−5 on the domain x2+y2≤100. The maximum value of f(x,y) is:
First find the critical points of f :
[tex]f(x,y)=2x^2+3y^2-4x-5=2(x-1)^2+3y^2-7[/tex]
[tex]\dfrac{\partial f}{\partial x}=2(x-1)=0\implies x=1[/tex]
[tex]\dfrac{\partial f}{\partial y}=6y=0\implies y=0[/tex]
so the point (1, 0) is the only critical point, at which we have
[tex]f(1,0)=-7[/tex]
Next check for critical points along the boundary, which can be found by converting to polar coordinates:
[tex]f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t[/tex]
Find the critical points of g :
[tex]\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0[/tex]
[tex]\implies\sin t=0\text{ OR }1+5\cos t=0[/tex]
[tex]\implies t=n\pi\text{ OR }t=\cos^{-1}\left(-\dfrac15\right)+2n\pi\text{ OR }t=-\cos^{-1}\left(-\dfrac15\right)+2n\pi[/tex]
where n is any integer. We get 4 critical points in the interval [0, 2π) at
[tex]t=0\implies f(10,0)=155[/tex]
[tex]t=\cos^{-1}\left(-\dfrac15\right)\implies f(-2,4\sqrt6)=299[/tex]
[tex]t=\pi\implies f(-10,0)=235[/tex]
[tex]t=2\pi-\cos^{-1}\left(-\dfrac15\right)\implies f(-2,-4\sqrt6)=299[/tex]
So f has a minimum of -7 and a maximum of 299.
I buy 6 CDs costing £6.99.
How much change do I get from
£50?
Answer:
subtract the 6.99 from 50 and you get your answer
Step-by-step explanation:
Answer:
8.06
Step-by-step explanation:
Take the cost of a cd and multiply by 6
6.99 *6
41.94
Subtract this from 50.00
50.00 - 41.94
8.06
You will get 8.06 back
Carl recorded the number of customers who visited his new store during the week:
Day Customers
Monday 17
Tuesday 13
Wednesday 14
Thursday 16
He expected to have 15 customers each day. To answer whether the number of customers follows a uniform distribution, a chi-square test for goodness of fit should be performed. (alpha = 0.10)
What is the chi-squared test statistic? Answers are rounded to the nearest hundredth.
Answer:
The chi - square test can be [tex]\approx[/tex] 0.667
Step-by-step explanation:
From the given data :
The null hypothesis and the alternative hypothesis can be computed as:
Null hypothesis: The number of customers does follow a uniform distribution
Alternative hypothesis: The number of customers does not follow a uniform distribution
We learnt that: Carl recorded the number of customers who visited his new store during the week:
Day Customers
Monday 17
Tuesday 13
Wednesday 14
Thursday 16
The above given data was the observed value.
However, the question progress by stating that : He expected to have 15 customers each day.
Now; we can have an expected value for each customer as:
Observed Value Expected Value
Day Customers
Monday 17 15
Tuesday 13 15
Wednesday 14 15
Thursday 16 15
The Chi square corresponding to each data can be determined by using the formula:
[tex]Chi -square = \dfrac{(observed \ value - expected \ value )^2}{expected \ value}[/tex]
For Monday:
[tex]Chi -square = \dfrac{(17 - 15 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(2)^2}{15}[/tex]
[tex]Chi - square = \dfrac{4}{15}[/tex]
chi - square = 0.2666666667
For Tuesday :
[tex]Chi -square = \dfrac{(13- 15 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(-2)^2}{15}[/tex]
[tex]Chi - square = \dfrac{4}{15}[/tex]
chi - square = 0.2666666667
For Wednesday :
[tex]Chi -square = \dfrac{(14- 15 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(-1 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(1 )}{15}[/tex]
chi - square = 0.06666666667
For Thursday:
[tex]Chi -square = \dfrac{(16- 15 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(1 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(1 )}{15}[/tex]
chi - square = 0.06666666667
Observed Value Expected Value chi - square
Day Customers
Monday 17 15 0.2666666667
Tuesday 13 15 0.2666666667
Wednesday 14 15 0.06666666667
Thursday 16 15 0.06666666667
Total : 0.6666666668
The chi - square test can be [tex]\approx[/tex] 0.667
At level of significance ∝ = 0.10
degree of freedom = n - 1
degree of freedom = 4 - 1
degree of freedom = 3
At ∝ = 0.10 and df = 3
The p - value for the chi - square test statistics is 0.880937
Decision rule: If the p - value is greater than the level of significance , we fail to reject the null hypothesis
Conclusion: Since the p - value is greater than the level of significance , we fail to reject the null hypothesis and conclude that there is insufficient evidence to show that the number of customers does not follows a uniform distribution.
Answer:.67
Step-by-step explanation:
Evaluating function expressions
-1•f(-8)-4•g(4)=
Answer: -7
Step-by-step explanation:
To find f(-8) look at the f function. Find the y value when x = -8
To find g(4) look at the g function. Find the y value when x = 3
Plug these values into the equation
-1 f(-8) - 4 f(4)
-1 (-5) - 4 (3)
5 - 12 = -7
For the given data value, find the standard score and the percentile. A data value 0.6 standard deviations above the mean.
Answer:
The standard score [tex]z = 0.6[/tex]
The the percentile [tex]P(z < 0.6 ) = 72.57\%[/tex]
Step-by-step explanation:
From the question we are told that
A data value is 0.6 standard deviations above the mean.
The above statement can be mathematically represented as
[tex]x = 0.6 \sigma + \mu[/tex]
Where [tex]\sigma[/tex] is the standard deviation and [tex]\mu[/tex] is the mean
Generally the standard score is mathematically represented as
[tex]z = \frac{x - \mu}{\sigma}[/tex]
=> [tex]z = \frac{(0.6 \sigma + \mu) - \mu}{\sigma}[/tex]
=> [tex]z = 0.6[/tex]
Now the percentile is obtained from the z-table , the value is
[tex]P(z < 0.6 ) = 0.7257[/tex]
=> [tex]P(z < 0.6 ) = 72.57\%[/tex]
How much will $1000 deposited in an account earning 7% interest compounded annually be worth in 20 years? (which formula do I use? I am confused...txs)
Answer:
$3870
Step-by-step explanation:
Hello, the initial deposit is $1000.
After one year, we will get 1000 + 7%*1000= 1000 * ( 1+7%) = 1000 * (1+0.07)
= 1000 * 1.07
And we want to compound it so the second year we will get
[tex]1000 * 1.07 * 1.07 = 1000 * 1.07^2[/tex]
And after n years, we will get
[tex]1000 * 1.07^n[/tex]
In that example, we want to know how much we will get after 20 years, so this is:
[tex]1000 * 1.07^{20}=3869.684462...[/tex]
Thank you.
When interest is compounded, it means that both the interest and the amount deposited will earn interest.
We are to determine the future value of $1000 with annual compounding.
The formula for calculating future value:
FV = P (1 + r)^n
FV = Future value
P = amount deposited = $1000
R = interest rate = 7%
N = number of years = 20
$1000 x ( 1.07)^20 = $3,869.68
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