Factor the higher degree polynomial


5y^4 + 11y^2 + 2

Answer:

True

Step-by-step explanation:

6m (2m + 10)

= (6m)(2m) + (6m)(10)

= 12m² + 60m

= 4(3m² + 15m)

Because we factored out a "4" in the expression, by observation, we can see that regardless of what value of integer m is chosen, the entire expression is divisible by the "4" which has been factored out of the parentheses. Hence it is True.

What is the divisibility test of 4?

If a number's last two digits are divisible by 4, the number is a multiple of 4 and totally divisible by 4.

6m(2m+10) = 6m cannot be said to be always divisible by 4 but is divisible by 2 as 6m = 2*3m

(2m+10) cannot say if it is divisible by but can say is divisible by 2 as we can take 2 commons from both the integer and rewrite it as 2*(m+5).

Hence multiplying both the numbers we get = 2*3m*2(m+5) and now we group 2's together we get 4*3m*(m+5), as the whole number is multiplied by 4 it is at least divisible by 4 once.

Hence proved that 6m(2m+10) is divisible by 4 and the answer is true.

learn more about Divisibility here

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Answer:

The population standard deviation is not known.

90% Confidence interval by T₁₀-distribution: (38.3, 53.7).

Step-by-step explanation:

The "standard deviation" of $14 comes from a survey. In other words, the true population standard deviation is not known, and the $14 here is an estimate. Thus, find the confidence interval with the Student t-distribution. The sample size is 11. The degree of freedom is thus [tex]11 - 1 = 10[/tex].

Start by finding 1/2 the width of this confidence interval. The confidence level of this interval is 90%. In other words, the area under the bell curve within this interval is 0.90. However, this curve is symmetric. As a result,

Look up the t-score of the upper end on an inverse t-table. Focus on the entry with

[tex]t \approx 1.812[/tex].

This value can also be found with technology.

The formula for 1/2 the width of a confidence interval where standard deviation is unknown (only an estimate) is:

[tex]\displaystyle t \cdot \frac{s_{n-1}}{\sqrt{n}}[/tex],

where

For this confidence interval:

Hence the width of the 90% confidence interval is

[tex]\displaystyle 1.812 \times \frac{14}{\sqrt{10}} \approx 7.65[/tex].

The confidence interval is centered at the unbiased estimate of the population mean. The 90% confidence interval will be approximately:

[tex](38.3, 53.7)[/tex].

Answer:

The last option is correct

Step-by-step explanation:

Hope this helps!

Answer:

[tex]\large\boxed{5y^4+11y^2+2=(y^2+2)(5y^2+1)}[/tex]

Step-by-step explanation:

[tex]5y^4+11y^2+2=5y^4+10y^2+y^2+2=5y^2(y^2+2)+1(y^2+2)\\\\=(y^2+2)(5y^2+1)[/tex]

Answer:

The probability of E and F is 0.367236 ≅ 0.367

Step-by-step explanation:

* Lets study the meaning independent probability  

- Two events are independent if the result of the second event is not

  affected by the result of the first event

- If A and B are independent events, the probability of both events  

 is the product of the probabilities of the both events

- P (A and B) = P(A) · P(B)

* Lets solve the question  

- There are two events E and F

- E and F are independent

- P(E) = 0.404

- P(F) = 0.909

∵ Events E and F are independent

- To find P(E and F) find the product of P(E) and P(F)

∴ P (E and F) = P(E) · P(F)

∵ P(E) = 0.404

∵ P(F) = 0.909

∴ P(E and F) = (0.404) · (0.909) = 0.367236 ≅ 0.367

* The probability of E and F is 0.367236 ≅ 0.367

the probability that both event E and event F occur is 0.36.

When dealing with independent events, the probability of both events E and F occurring, denoted as P(E and F), is determined by multiplying the probability of event E by the probability of event F. In this case, since P(E)=0.4 and P(F)=0.9 and the events are independent, you calculate P(E and F) as follows:

P(E and F) = P(E)  × P(F) = 0.4 × 0.9 = 0.36.

Therefore, the probability that both event E and event F occur is 0.36.

Answer:

  1.94%

Step-by-step explanation:

The desired percentage can be found using an appropriate calculator or spreadsheet. A nice on-line calculator is shown in the attachment.

Hence, the probability is:

               0.8846

D be the event that the card drawn is red.

and F denote the event that the card drawn is a face card.

We are asked to find:

P(D'∪F')

We know that D' denote the complement of event D

and F' denote the complement of event F.

Hence, we have:

[tex]P(D'\bigcup F')=(P(D\bigcap F))'\\\\i.e.\\\\P(D'\bigcup F')=1-P(D\bigcap F)[/tex]

D∩F denote the event that the card is a red card and is a face card as well

Since there are 6 cards which are face as well as red cards out of a total of 52 cards.

Hence, we get:

[tex]P(D'\bigcup F')=1-\dfrac{6}{52}\\\\i.e.\\\\P(D'\bigcup F')=\dfrac{52-6}{52}\\\\i.e.\\\\P(D'\bigcup F')=\dfrac{46}{52}\\\\P(D'\bigcup F')=0.8846[/tex]

Answer:

any length less then 5 ft

Answer:

D. 1/2

Step-by-step explanation:

Coin tosses are independent.  Past results don't affect future probabilities.  So the probability of getting heads on the fourth toss is still 1/2.

Answer:

D. 1/2

Step-by-step explanation:

Flipping coin is an INDEPENDENT event, meaning that if you flip a coin before, it is NOT going to affect the outcome of the next coin flipping

Since a coin has 2 sides, so the probability is 1/2

Answer:A

Step-by-step explanation:

Answer:

3.73%

Step-by-step explanation:

The formula is

[tex]A=P(1+\frac{r}{n})^{tn}[/tex]

Here we are given that A= 5809.81 , P=4000 , t=10 years and n = 4 (compounded quaterly)

Now we have to substitute them in the formula

[tex]5809.81=4000(1+\frac{r}{4})^{40}[/tex]

[tex]\frac{5809.81}{4000}=(1+\frac{r}{4})^{40}[/tex]

[tex] (\frac{5809.81}{4000})^{\frac{1}{40}}=1+\frac{r}{4}[/tex]

[tex] (1.45)^{\frac{1}{40}}=1+\frac{r}{4}[/tex]

[tex]1.0093 = 1+\frac{r}{4}[/tex]

Subtracting 1 on both sides

[tex]0.0093=\frac{r}{4}[/tex]

[tex]r=0.0093*4[/tex]

r=0.03732

Rate is 3.73%

The number of possible arrangements is : 120

We know that in order to find the different arrangements which are possible we need to use the method of permutation.

The arrangement of a given word is calculated as the ratio of the factorial of number of letters to the product of factorial of numbers the number of times each letter is repeating.

The word is given to be:

                    ALASKA

There are a total of 6 letters in the given word

Out of which a letter "A" is  repeating  3 times.

Hence, the number of arrangements possible are:

        [tex]=\dfrac{6!}{3!}\\\\\\=\dfrac{6\times 5\times 4\times 3!}{3!}\\\\\\=6\times 5\times 4\\\\\\=120[/tex]

Answer:

f(t)=9,220,000(0.888)^t

Step-by-step explanation:

We use 9,220,000 as our base because this is where the decay begins. To get the correct amount of decay, we need to subtract 11.2% from 1, or 100%. We get 88.8% so we turn this into a decimal by dividing by 100 and getting 0.888. We put this to the power of t to represent the decay because it has to be an exponent to be exponential decay, not linear decay. f(t) is not necessary, you could also use y. Hope this helps :)

Answer: 1527

Step-by-step explanation:

Given: Mean : [tex]\mu = 3234\text{ grams}[/tex]

Standard deviation : [tex]\sigma=871\text{ grams}/tex]

Sample size : [tex]n=1600[/tex]

The formula to calculate the z score is given by :-

[tex]z=\dfrac{X-\mu}{\sigma}[/tex]

For X=1492

[tex]z=\dfrac{1492-3234}{871}=-2[/tex]

The p-value of z =[tex]P(z<-2)=0.0227501[/tex]

For X=4976

[tex]z=\dfrac{4976-3234}{871}=2[/tex]

The p-value of z =[tex]P(z<2)=0.9772498[/tex]

Now, the probability of the newborns weighed between 1492 grams and 4976 grams is given by :-

[tex]P(1492<X<4976)=P(X<4976)-P(X<1492)\\\\=P(z<2)-P(z<-2)\\\\=0.9772498-0.0227501\\\\=0.9544997[/tex]

Now, the number  newborns who weighed between 1492 grams and 4976 grams will be :-

[tex]1600\times0.9544997=1527.19952\approx1527[/tex]

Answer: 30 cards

Step-by-step explanation:

To find the greatest possible number of cards in each pile such that there is the same number of cards in each​ pile we need to find the greatest common factor of 750 and 660.

Using Euclid division method , we have

[tex]750=1(660)+90\\\\660=7(90)+30\\\\90=3(30)+0[/tex]

Hence, the greatest common factor of 750 and 660 = 30

Thus, there will be 30 cards in each pile.

Step-by-step explanation:

The probability he makes both shots is:

P = (0.90)^2

P = 0.81

There's a 81% probability he makes both shots.

Answer:

[tex]\boxed{\text{\$581.25; \$81.25}}[/tex]

Step-by-step explanation:

The formula for the total accrued amount is

A = P(1 + rt)

Data:

P = $500

r = 6.5 % = 0.065

t = 30 mo

Calculations:

(a) Convert months to years

t = 30 mo × (1 yr/12 mo) = 2.5 yr

(b) Calculate the accrued amount

A = 500(1 + 0.065 × 2.5)

  = 500(1 + 0.1625)

  = 500 × 1.1625

  = 581.25

[tex]\text{Dasha will have to pay back }\boxed{\textbf{\$581.25}}[/tex]

(c) Calculate the accumulated interest

[tex]\begin{array}{rcl}A & = & P + I\\581.25 & = & 500 + I\\I & = & 81.25\\\end{array}\\\text{The accumulated interest is }\boxed{\textbf{\$81.25}}[/tex]

Answer:

Here is one idea:

You can use a regression line to predict what will happen at a time not given by your data.  You can use it to make predictions about future times.

Here is another one:

The equation for the regression line or even the graph of can tell us if the data is increasing as we move through future times or if it is decreasing as we move through future times.

Try to come up with one of your own so you can have three. :)

Answer:

  "unchanged"

Step-by-step explanation:

Congruence transformations (translation, rotation, reflection) do not change lengths, angles, area (of 2D figures), or volume (of 3D figures). The area would remain unchanged.

Answer:

If the conclusion is false, then one or more of the premises must also have been false.

Step-by-step explanation:

One important distinguishing feature of valid arguments is that - if the conclusion is false, then one or more of the premises must also have been false.

An argument form is said to be valid, if and only if, when all premises are true, then the conclusion is true.

A valid argument in philosophy is characterized by the fact that if its premises are true, the conclusion must also be true. This follows a process called deductive inference. It is impossible for the premises of a valid argument to be true and the conclusion to be false

One distinguishing feature of valid arguments is that if the premises are true, then the conclusion must also be true. This follows a process called deductive inference. A premise in an argument is a statement or assumption that forms the basis for a conclusion. An argument is set to be valid when its structure or form guarantees the truth of the conclusion if the premises upon which it's built are true.

In a valid argument, therefore, the truth of its premises guarantees the truth of its conclusion-it's impossible for the premises to be true and the conclusion to be false at the same time.

If you can construct a scenario where the premises are true but the conclusion is false, then that argument is invalid. Understanding this concept is fundamental to the evaluation of arguments in logic, for it plays a critical role in ensuring coherent, reasonable and valid reasoning.

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Answer:

Step-by-step explanation:

Just so you see what you are trying to do, the graph shows you what you are given.

Graph

Red: y = e^x

blue: y = e^(2x)

green x = 1

equations

integral e^(2*x) = e^(2x)/2

integral e^x = e^x

Solution

e^(2x)/2 between 1 and 0 equals e^(*2*1)/2 - e^0

e^(2x) / 2 = 7.3891 - 1 = 6.3891

e^(x )  between 1 and 0 equals e^(1) - e^0

2.7183 - 1

1.7183

The area between 1 and 0 is 6.3891 - 1.7183 = 4.6708

Answer: Hence, the value of real output produced Y = 900.

Step-by-step explanation:

Since we have given that

[tex]Y=C+I_g+G+Xn------------(1)[/tex]

and

[tex]C=50+0.9Y-----------------(2)[/tex]

And

[tex]I_g=30\\\\G=0\\\\X_n=10[/tex]

We need to find the value of Y:

From eq(1) and eq(2), we get that

[tex]Y=50+0.9Y+I_g+G+X_n\\\\Y-0.9Y=50+30+0+10\\\\0.1Y=90\\\\Y=\dfrac{90}{0.1}\\\\Y=900[/tex]

Hence, the value of real output produced Y = 900.

Answer:

Assumption: [tex]f(x)[/tex] is defined for all [tex]x\in \mathbb{R}[/tex] (all real values of [tex]x[/tex].)

Step-by-step explanation:

Evaluating [tex]f(x)[/tex] for a root of this function shall give zero.

Equate [tex]f(x)[/tex] and zero [tex]0[/tex] to find the root(s) of [tex]f(x)[/tex].

[tex]f(x) =0[/tex].

[tex](x - 6) \cdot 2 \cdot (x + 2) \cdot 2 = 0[/tex].

Multiply both sides by 1/4:

[tex]\displaystyle (x - 6) \cdot (x + 2) = 0\times\frac{1}{4} = 0[/tex].

[tex]\displaystyle (x - 6) \cdot (x + 2) = 0[/tex].

This polynomial has two factors:

Apply the factor theorem:

Answer:

X=6 , X = -2

Step-by-step explanation:

For any polynomial given in factorised form , the roots are determined as explained below:

Suppose we have a polynomial

(x-m)(x-n)(x+p)(x-q)

The roots of above polynomial will be m,n,-p, and q

Also if we have same factors more than once , there will be duplicate roots.

Example

(x-m)^2(x-n)(x+p)^2

For above polynomial

There will be total 5 roots . Out of which 2(m and -p) of them will be repeated. x=m , x=n , x =-p

Hence in our problem

The roots of f(x)= (x-6)^2(x+2)^2 are

x=6 And x=-2

Answer:

[tex]Pr=\dfrac{1}{1,140}[/tex]

Step-by-step explanation:

The probability definition is

[tex]Pr=\dfrac{\text{Number of favorable outcomes}}{\text{Number of all possible outcomes}}[/tex]

1. The number of favorable outcomes is 1, because there is the only way to choose The Entertainer, Something Doing, and The Ragtime Dance.

2. The number of all possible outcomes is

[tex]C^{20}_3=\dfrac{20!}{3!(20-3)!}=\dfrac{17!\cdot 18\cdot 19\cdot 20}{2\cdot 3\cdot 17!}=\dfrac{18\cdot 19\cdot 20}{6}=3\cdot 19\cdot 20=1,140[/tex]

Hence, the probability is

[tex]Pr=\dfrac{1}{1,140}[/tex]

The probability of Noam choosing 'The Entertainer', 'Something Doing', and 'The Ragtime Dance' from a pile of 20 songs for a piano recital is found by calculating the number of favorable outcomes (1 way to select these three songs) over the total number of ways to choose any 3 songs from 20, which is given by the combination formula C(20, 3).

The question you're asking about relates to the probability of Noam choosing three specific songs from a pile of 20. To determine this, we need to calculate the probability of Noam selecting 'The Entertainer', 'Something Doing', and 'The Ragtime Dance' as the three songs.

Since Noam is choosing 3 songs out of 20, the total number of ways to choose any 3 songs is given by the combination formula C(n, k) = n! / (k! (n-k)!) where n is the total number of items, and k is the number of items to choose. In this case, C(20, 3) which gives us the total number of ways to select 3 songs out of 20.

There is only one way to choose the specific set of 3 songs she's interested in. Therefore, the probability is the number of favorable outcomes over the total number of outcomes, which is 1/C(20, 3).

Answer:

The value of [tex]f^{-1}(2)=8[/tex]

Step-by-step explanation:

* Lets revise how to find the inverse function

- At first write the function as y = f(x)

- Then switch x and y

- Then solve for y

- The domain of f(x) will be the range of f^-1(x)

- The range of f(x) will be the domain of f^-1(x)

* Now lets solve the problem

- The inverse of the logarithmic function is an exponential function

∵ [tex]f(x)=log_{4}(x + 8)[/tex]

- Write the function as y = f(x)

∴ [tex]y=log_{4}(x+8)[/tex]

- Switch x and y

∴ [tex]x=log_{4}(y+8)[/tex]

- Lets solve it to find y

# Remember: [tex]log_{a}b=n=====a^{n}=b[/tex]

- Use this rule to find y

∴ [tex]4^{x}=(y + 8)[/tex]

- Subtract 8 from both sides

∴ [tex]4^{x}-8=y[/tex]

∴ [tex]f^{-1}(x)=4^{x}-8[/tex]

- Lets substitute x by 2

∴ [tex]f^{-1}(2)=4^{2}-8[/tex]

- The value of 4² = 16

∴ [tex]f^{-1}(x)=16-8=8[/tex]

* The value of [tex]f^{-1}(2)=8[/tex]

To find the inverse of the function f(x) = log base 4 of (x+8) when evaluated at 2, we solve the equation log base 4 of (x+8) = 2 to find x. This gives us x = 8, so f^-1(2) = 8.

To find the value of f-1(2) for the function f(x) = log4(x+8), we first need to understand that f-1(x) denotes the inverse function of f(x). This means that if f(a) = b, then f-1(b) = a. To solve for f-1(2), we set f(x) equal to 2 and solve for x:

log4(x+8) = 2

42 = x+8 (using the property that if logb(a) = c then bc = a)

16 = x+8

x = 16 - 8

x = 8

Therefore, f-1(2) = 8.

Answer with explanation:

Let me answer this question by taking two decimals less than 1.

A= 0.50

B= 0.25

→A × B

= 0.50 × 0.25

=0.125

It is less than both A and B.

→→A=0.99

B= 0.1

→C=A × B

= 0.99 × 0.1

=0.099

It is less than both A and B.

So, We can say with surety, that if take two decimals ,both less than 1, the product of these two decimals will be  less than each of the original decimals.

General Rule

→A =0. p ,

→ B=0. 0 q,

Product of , A × B, gives a number in which  there will be three digits after decimal which will be always less than both A and B as in A, there is one digit after decimal, and in B there are two digits after decimal.

The correct margin of error (m) for the 95% confidence level for this estimate is approximately 6.36%.

To calculate the margin of error for a 95% confidence level, we use the formula:

[tex]\[ m = z \times \sqrt{\frac{p(1-p)}{n}} \][/tex]

where:

- [tex]\( z \)[/tex] is the z-score corresponding to the desired confidence level (for 95%, [tex]\( z \)[/tex] is approximately 1.96),

- [tex]\( p \)[/tex] is the sample proportion (in this case, 0.88 or 88%),

- [tex]\( n \)[/tex] is the sample size (1000 U.S. residents),

- [tex]\( 1-p \)[/tex] is the proportion of U.S. residents who do not have a credit card.

First, we convert the percentage to a proportion:

[tex]\[ p = \frac{88}{100} = 0.88 \][/tex]

Next, we calculate [tex]\( 1-p \):[/tex]

[tex]\[ 1-p = 1 - 0.88 = 0.12 \][/tex]

Now, we can plug these values into the margin of error formula:

[tex]\[ m = 1.96 \times \sqrt{\frac{0.88 \times 0.12}{1000}} \] \[ m = 1.96 \times \sqrt{\frac{0.1056}{1000}} \] \[ m = 1.96 \times \sqrt{0.0001056} \] \[ m = 1.96 \times 0.0325 \] \[ m \approx 1.96 \times 0.0325 \] \[ m \approx 0.0636 \][/tex]

Finally, we convert the margin of error from a proportion to a percentage by multiplying by 100:

[tex]\[ m \approx 0.0636 \times 100 \][/tex]

[tex]\[ m \approx 6.36\% \][/tex]

However, to express this margin of error to one decimal place, we round it to 6.4%. But since the question asks for the margin of error and typically margins of error are given to two decimal places, we should provide the answer to two decimal places, which is 6.36%.

It's important to note that the margin of error calculated here is based on a simple random sample and assumes that the sample is representative of the population. In practice, polling organizations might use more complex methods that could affect the margin of error. Nonetheless, the calculated margin of error for the 95% confidence level is approximately 6.36%. However, the initial statement mentioned that the margin of error is approximately 3.1%. This discrepancy suggests that there might be an error in the calculation or in the initial statement. Let's re-evaluate the calculation:

[tex]\[ m = 1.96 \times \sqrt{\frac{0.88 \times 0.12}{1000}} \] \[ m = 1.96 \times \sqrt{0.0001056} \] \[ m = 1.96 \times 0.0325 \] \[ m \approx 0.0636 \] \[ m \approx 6.36\% \][/tex]

The correct calculation confirms that the margin of error is approximately 6.36%. Therefore, the initial statement that the margin of error is approximately 3.1% is incorrect. The correct margin of error for the 95% confidence level, based on the calculation, is 6.36%.

Answer:

The mean of the data is 26.

Step-by-step explanation:

Consider the provided data:

30, 29, 28, 30, 24, 12, 26, 33, 25, 23

Mean can be calculated as:

The average of all the data in a set.

[tex]x=\frac{\Sigma x_{i}}{n}[/tex]

Therefore,

[tex]x=\frac{30+29+28+30+24+12+26+33+25+23}{10}[/tex]

[tex]x=\frac{260}{10}[/tex]

[tex]x=26[/tex]

Thus, the mean of the data is 26.

Answer:

[tex](x-4)^2+(y-3)^2+(x-5)^2=6[/tex]

Step-by-step explanation:

The the center of the sphere is given as (a,b,c) and the radius is r, then the equation of the sphere would be:

[tex](x-a)^2+(y-b)^2+(x-c)^2=r^2[/tex]

From the info, we can say:

a = 4

b = 3

c = 5

r = [tex]\sqrt{6}[/tex]

Plugging into formula we get the equation:

[tex](x-a)^2+(y-b)^2+(x-c)^2=r^2\\(x-4)^2+(y-3)^2+(x-5)^2=(\sqrt{6} )^{2} \\(x-4)^2+(y-3)^2+(x-5)^2=6[/tex]

Remember to use

Answer:

Pr(z<0.05) = 0.5199

Step-by-step explanation:

We are required to determine the region under a standard normal curve less than z = 0.05. The value 0.05 is a z-score. The area of this region is equivalent to the following probability;

Pr(z<0.05)

In a standard normal curve, this is the region to the left of 0.05. Using the standard normal tables, this cumulative probability is equal to;

Pr(z<0.05) = 0.5199

If a set [tex]A[/tex] contains [tex]n[/tex] elements, then the number of subsets of this set is [tex]|\mathcal{P}(A)|=2^n[/tex].

[tex]A=\{4,5,6\}\\|A|=3[/tex]

[tex]|\mathcal{P}(A)|=2^3=8[/tex]