If p (x) = x4 + 2x2 + 1 and q (x) = x4 – 2x2 + 1, find p (x) -q (x).
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Answer:

0.625

Step-by-step explanation:

Since there are 4 options each time the spinner is spun, there are a total of [tex]4\cdot 4=16[/tex] non-distinct sums possible when we spin it twice.

Out of these, the possible sums that meet the condition (less than 6) are 2, 3, 4, and 5 (since the smallest sum possible is 1+1=2).

Count how many ways there are to achieve each of these sums:

[tex]1+1=2\\\\1+2=3\\2+1=3\\\\2+2=4\\1+3=4\\3+1=4\\\\2+3=5\\3+2=5\\4+1=5\\1+4=5[/tex]

Totally there are 10 ways to achieve a sum less than 6. Therefore, the desired probability is [tex]\frac{10}{16}=\frac{5}{8}=\boxed{0.625}[/tex]

Answer: 55, 62, 69, 76

Step-by-step explanation:

(to complete the table, plug d values into the equation to find p values)

p = 7d + 6, d = 7

p = 7(7) + 6 = 49 + 6 = 55

p = 7d + 6, d = 8

p = 7(8) + 6 = 56 + 6 =62

p = 7d + 6, d = 9

p = 7(9) + 6 = 63 + 6 =69

p = 7d + 6, d = 10

p = 7(10) + 6 = 70 + 6 =76

Answer:

32 ounces

Step-by-step explanation:

Answer:

8.80

Step-by-step explanation:

(S. D.)^2=summation(x-mean)^2/(n-1)

S. D.=sqrt(388/5)

S. D.=8.80

Given:

The probability of drawing a red candy at random from a bag of 25 candies is [tex]\dfrac{2}{5}[/tex].

To find:

The probability of randomly drawing a red candy from the bag after removing 5 candies from the bag.

Solution:

Let n be the number of red candies in the bag. Then, the probability of getting a red candy is:

[tex]P(Red)=\dfrac{\text{Number of red candies}}{\text{Total candies}}[/tex]

[tex]\dfrac{2}{5}=\dfrac{n}{25}[/tex]

[tex]\dfrac{2}{5}\times 25=n[/tex]

[tex]10=n[/tex]

After removing the 5 candies from the bag, the number of remaining candies is [tex]25-5=20[/tex] and the number of remaining red candies is [tex]10-5=5[/tex].

Now, the probability of randomly drawing a red candy from the bag is:

[tex]P(Red)=\dfrac{5}{20}[/tex]

[tex]P(Red)=\dfrac{1}{4}[/tex]

Therefore, the required probability is [tex]\dfrac{1}{4}[/tex].

Answer:

see explanation

Step-by-step explanation:

Given

AB + BC = 31

AB - BC = 17

Add the 2 equations

2AB = 48 ( divide both sides by 2 )

AB = 24

Substitute AB = 24 into the first equation

24 + BC = 31 ( subtract 24 from both sides )

BC = 7

Using Pythagoras' identity to find the hypotenuse AC

AC² = AB² + BC² = 24² + 7² = 576 + 49 = 625 ( take square root of both sides )

AC = [tex]\sqrt{625}[/tex] = 25

Then

sinA = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{7}{25}[/tex]

cosA = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{24}{25}[/tex]

sinC = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{24}{25}[/tex]

cosC = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{7}{25}[/tex]

Answer:

81

Step-by-step explanation:

from 4 to 5,the difference is 1 ,and when you multiply by 3, then add 3 to 5 ,it gives you 8 ,to get 17,I multiple 3by 3 and add the answer to 8 ,and the same continues upto when you get the final answer which is 81.

difference is just multiplying the previous difference with 3 and add it with the previous number .

Answer:

b=12

Step-by-step explanation:

b^2+35^2=37^2

b^2+1225=1369

b^2=144

b=12,-12

Lengths can't be negative, so b=12

Answer:

b=12

Step-by-step explanation:

The Pythagorean theorem is

a^2+b^2 = c^2  where a and b are the legs and c is the hypotenuse

35^2 + b^2 = 37^2

1225+b^2 =1369

b^2 =1369-1225

b^2 = 144

Taking the square root of each side

sqrt(b^2) = sqrt(144)

b=12

Answer:

Divide the tens column dividend by the divisor. Multiply the divisor by the quotient in the tens place column. Subtract the product from the divisor

Step-by-step explanation:

Answer:

[tex] \frac{9}{2} [/tex]

Step-by-step explanation:

[tex] \frac{15}{2} \div \frac{5}{3} = \frac{15}{2} \times \frac{3}{5} = \frac{3}{2} \times \frac{3}{1} = \frac{9}{2} [/tex]

Answer:

The first row

Step-by-step explanation:

Letters A,B,C,D

==================================================

Explanation:

Check out the diagram below to see where the lines of symmetry are located.

For the letter A, we have a vertical line through the center that is the mirroring line. Reflecting one half over that line generates the other half.

For letter B, we have a horizontal line through the center. This applies to letters C and D as well.

This is why answer choice 1 is the final answer.

-----------

For letter Z, we have neither a vertical nor a horizontal mirror line. This letter doesn't have any lines of symmetry (though it does have rotational symmetry). So we can rule out answer choice 2.

Letter N is pretty much the same idea as letter Z. There aren't any lines of symmetry but we do have rotational symmetry. So we can rule out answer choice 3.

Lastly, we can rule out answer choice 4 because letter S has the same properties as letters Z and N.

Answer:

Step-by-step explanation:

Given,

Vince used a cup of lemonade will be = 3/5

We know that,

Amount of lemonade used by Luva is 6 times of Vince

Therefore,

Lemonade used by Luca

[tex] = \frac{3}{5} \times 6[/tex]

[tex] = \frac{18}{5} [/tex]

[tex] = 3 \frac{3}{5} (ans)[/tex]

Answer:

Y =-2.5X +3.5

Step-by-step explanation:

x1 y1  x2 y2

-1 6  3 -4

(Y2-Y1) (-4)-(6)=   -10  ΔY -10

(X2-X1) (3)-(-1)=    4  ΔX 4

slope= -2  1/2    

B= 3  1/2    

Y =-2.5X +3.5    

Answer:

Data is:

Mean:

Standard deviation:

Correct choice is d

Data is:

Mean:

Standard deviation:

Correct choice is d

Data is:

Mean is:

Standard deviation:

Correct choice is d

Let the number be x

ATQ

[tex]\\ \sf\longmapsto 3x+2=18[/tex]

[tex]\\ \sf\longmapsto 3x=18-2[/tex]

[tex]\\ \sf\longmapsto 3x=16[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{16}{3}[/tex]

[tex]\\ \sf\longmapsto x=5.3[/tex]

[tex]\\ \sf\longmapsto x\approx 5[/tex]

Answer:

b because it is an expressio n

Step-by-step explanation:

Answer: 13

Step-by-step explanation:

Take 7 to the other side and divide 91 by 7, the answer will be 13.

Answer:

120 different meals.

Step-by-step explanation:

Start with the entrees:  There are 4

There are side dishes : 4

Drinks: 5

The side dishes can be 4!/(2!2!) (order does not matter here). There are 6 ways.

The entrees are 1 of 4: 4

And 5 drinks

P(dinner) = 5 * 4 * 6 = 120

Answer:

120

4 * (4C2) * 5

4 * (6) * 5

Step-by-step explanation:

burrito,

pasta,

soup,

taco.

french fries,

salad,

potato salad

, coleslaw.

soda,

coffee,

water,

milk,

juice.

For dinner, the cafe offers diners a special, customers can order 2 sides with their entree. In how many different ways can dinner be ordered?

Answer:

The average, mode, and median of the results are 5, meaning that half of the time the quarter will land on heads.

Step-by-step explanation:

The required dot plot shows the result of the experiment performed by flipping a quarter 21 times.

In an experiment, a student is to flip a quarter 10 times and record the number of times heads appears. A group of students performs the experiment 21 times, with these results. 6 4 5 6 5 6 4 6 2 4 3 4 5 7 5 8 7 5 3 5 5.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Statistics is the study of mathematics that deals with relations between comprehensive data.

Here,
The dot plot has been made, for the number of outcomes and their frequencies. The dot plot gives the info about the mean mode and median.

Thus, the required a dot plot showing the result of the experiment performed by flipping a quarter 21 times.

Learn more about arithmetic here:

brainly.com/question/14753192

#SPJ2

Answer:

Step-by-step explanation:

Look at the y-values as x-values are same for all tables.

We see that:

Answer:

top to bottom, the answers are b, c, a

Step-by-step explanation:

One way to find the solution to a system of equations is to substitute values in. For the first one,

y=2x+3

y=2x+5,

we can substitute 2x+3 =y into the second equation to get

y=2x+5

2x+3 = 2x+5

subtract 2x from both sides

3 = 5

As 3 is not equal to 5, this is never equal and therefore has no solution

For the second one,

y= 2x+7

y = (-2/3)x + 10

We can plug y=2x+7 into the second equation to get

2x + 7 = y = (-2/3)x + 10

2x + 7 = (-2/3)x + 10

add (2/3)x to both sides to make all x values on one side

2x + (2/3)x + 7  = 10

subtract 7 from both sides to make only x values on one side and only constants on the other

2x + (2/3)x = 3

(6/3)x + (2/3)x = 3

(8/3)x = 3

multiply both sides by 3 to remove a denominator

8x = 9

divide both sides by 8 to isolate x

x=9/8

There is only one value for when the equations are equal, so this has one solution

For the third one

y = x-5

2y = 2x - 10

Plug x-5 = y into the second equation

2 * y= 2*(x-5)

2 * (x-5) = 2x - 10

2x-10 = 2x-10

add 10 to both sides

2x=2x

As 2x is always equal to 2x, no matter what x is, there are infinitely many solutions for this system

Answer:

C.

–5; –135; –10,935

Step-by-step explanation:

Answer:

C. -5; -135, -10,935

Step-by-step explanation:

...............................................................................................................................................

Answer: 100 tickets.

Step-by-step explanation:

Set up two equations: one representing total amount sold and another representing total dollars earned.

[tex]\left \{ {{x+y=215} \atop {8x+12y=2180}} \right.[/tex]

Rearrange x + y = 215 and find the value of x:

[tex]x+y=215\\x=215-y[/tex]

Substitute it into the other equation and solve for y:

[tex]8x+12y=2180\\8(215-y)+12y=2180\\1720-8y+12y=2180\\4y=2180-1720\\4y=460\\y=\frac{460}{4} =115[/tex]

Substitute in the y-value to the other expression to find x:

[tex]x+y=215\\x+115=215\\x=215-115=100[/tex]

Therefore, they sold 100 of the $8 tickets.

Answer:

Size of each monthly payment = $161.69 per month

Step-by-step explanation:

Given:

Value of property = $20,000

Downpayment = 20%

Number of payment = 12 x 10 = 120

Interest rate = 4% = 4% / 12 = 0.33 %

Computation:

Loan balance = 20,000 - 20%

Loan balance = $16,000

A] Size of each monthly payment [In Excel]

Size of each monthly payment = PMT(0.33%,120,16000,0)

Size of each monthly payment = $161.69 per month

Answer:

185/198

Step-by-step explanation:

Since the are 12 Cd and we require them to be selected in 5 ways, the number of selections is ¹²C₅ = 12 × 11 × 10 × 9 × 8/5! = 95040/120 = 792 ways

Since we have Four are rap music, five are country music, and three are heavy metal music, the number of ways to select them in groups of five so as to have at least one of each CD from each category, we have

For the first selection 3 of one category, and 1 each of the other categories.

The second selection is 2 each of two categories and 1 of the last category.

So, doing this for each category, we have

⁴C₃ × ⁵C₁ × ³C₁ + ⁴C₂ × ⁵C₂ × ³C₁ + ³C₃ × ⁴C₁ × ⁵C₁ + ³C₂ × ⁴C₂ × ⁵C₁ + ⁵C₃ × ⁴C₁ × ³C₁ + ⁵C₂ × ³C₂ × ⁴C₁

= (4 × 3 × 2/3! × 5 × 3) + (4 × 3/2! × 5 × 4/2! × 3) + (1 × 4 × 5) + (3 × 2/2! × 4 × 3/2! × 5) + (5 × 4 × 3/2! × 4 × 3) + (5 × 4/2! × 3 × 2/2! × 4)

= 360/6 + 720/4 + 20 + 360/4 + 720/2 + 120/4

= 60 + 180 + 20 + 90 + 360 + 30

= 740 ways

So, the required probability is P = number of ways of selecting at least one CD/ total number of ways = 740/792 = 185/198