simplify (x^4-4x^3+9x^2-5x) (x^3-3x^2+7) -30x^2+25x^4

Answer:

3.  3x^2 + 15x

4.  x=36

Step-by-step explanation:

The area of a rectangle is

A = l*w

A = (3x)*(x+5)

Distribute

3x^2 + 15x

2/3x - 4 = 20

Add 4 to each side

2/3x -4+4 = 20+4

2/3x = 24

Multiply each side by 3/2

2/3*3/2 =24*3/2

x = 12*3

x=36

It's divergent because 1/√(5 - x) is defined only for x < 5, which means the integral from 5 to infinity doesn't exist.

Answer:

The p-value of the test is 0.2262 > 0.02, which means that the decision is to fail to reject the null hypothesis.

Step-by-step explanation:

An automobile manufacturer has given its jeep a 51.3 miles/gallon (MPG) rating.

At the null hypothesis, we test if the mean is of 51.3, that is:

[tex]H_0: \mu = 51.3[/tex]

An independent testing firm has been contracted to test the actual MPG for this jeep since it is believed that the jeep has an incorrect manufacturer's MPG rating.

This means that at the alternative hypothesis, we test if the mean is different of 51.3, that is:

[tex]H_0: \mu \neq 51.3[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

51.3 is tested at the null hypothesis:

This means that [tex]\mu = 51.3[/tex]

After testing 230 jeeps, they found a mean MPG of 51.1. Assume the population variance is known to be 6.25.

This means that [tex]n = 230, X = 51.1, \sigma = \sqrt{6.25} = 2.5[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{51.1 - 51.3}{\frac{2.5}{\sqrt{230}}}[/tex]

[tex]z = -1.21[/tex]

P-value of the test and decision:

The p-value of the test is the probability of the sample mean differing from 51.1 by at least 0.2, which is P(|z| > 1.21), which is 2 multiplied by the p-value of z = -1.21.

Looking at the z-table, z = -1.21 has a p-value of 0.1131.

2*0.1131 = 0.2262

The p-value of the test is 0.2262 > 0.02, which means that the decision is to fail to reject the null hypothesis.

Answer:

The hottest month for the northern hemisphere is August.

The hottest month for the southern hemisphere is January and February (these top two might be the opposite)

It's globally warmer during the months of June July and August

During april and november, the southern hemisphere and northern hemisphere are the same, or very close.

During July and August the southern and northern hemispheres have the largest difference in temperature

Answer:

x=12,y=3

Step-by-step explanation:

x/6-y/3=1

x can equal 12 because 12/6 is equal to 2.

y can equal 3 because 3/3 equals 1

2-1=1

Answer:

2 sinh viên sẽ làm đc 0,452

Answer:

1/8=12.50%

Step-by-step explanation:

Take the pizza as a whole = 100

Then consider 1/8 of 100

or   1/8 * 100  

= 1/4 * 50

=   1/2 * 25

= 12.50

Therefore it is 12.50%

If they run 3 miles west then 8 miles north, it forms a right triangle. So just use the Pythagorean Theorum.

A^2+B^=C^2

3^2+8^3=C^2

9+64=C^2

Square root 73=C or 8.54=C (Miles)

The runner is 8.54 miles from her starting point if she plans to run straight back.

From the question, a runner jogs 3 miles west and then jogs 8 miles north.

An illustrative diagram for the journey is shown in the attachment below.

In the diagram, S is the starting point. That is, the runner jogs 3 miles west to a place R and then 8 miles north to a place E.

The cardinal points (North, East, West and South) are indicated beside the diagram.

Now, to calculate how far she is from her starting point if she plans to run straight back, we will determine the length of /ES/ in the diagram.

The diagram is a right-angled triangle and /ES/ can be determined using the Pythagorean theorem.

The Pythagorean theorem states that, in a right-angled triangle, the square of the longest side ( that is hypotenuse) equals sum of the squares of the other two sides.

In the diagram, hypotenuse = /ES/

∴ /ES/² = /SR/² + /RE/²

/SR/ = 3 miles

/RE/ =8 miles

/ES/² = 3² + 8²

/ES/² = 9 + 64

/ES/² = 73

/ES/ = [tex]\sqrt{73}[/tex]

/ES/ = 8.54 miles

Hence, the runner is 8.54 miles from her starting point if she plans to run straight back.

Learn more here: https://brainly.com/question/20327506

let the number be x

ATQ

[tex]\\ \sf\longmapsto 5x+2x+2=16[/tex]

[tex]\\ \sf\longmapsto (5+2)x+2=16[/tex]

[tex]\\ \sf\longmapsto 7x+2=16[/tex]

[tex]\\ \sf\longmapsto 7x=16-2[/tex]

[tex]\\ \sf\longmapsto 7x=14[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{14}{7}[/tex]

[tex]\\ \sf\longmapsto x=2[/tex]

Answer:

The number is

2

Explanation:

Let

n

represent the number.

Translating the given statement into algebraic notation, we have

XXX

5

n

+

2

n

+

2

=

16

Therefore

XXX

7

n

+

2

=

16

XXX

7

n

=

14

XXX

n

=

2

answered by: Alan P.

Answer:

x>3

Step-by-step explanation:

8x - 2x > 12+ 6

-> 6x > 18

-> x > 3

[tex] \: \: \: \huge \rm{answer: \blue{ \boxed{ \rm{ \pink{x > 3}}}}}[/tex]

➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖

[tex] \huge \blue{ \boxed{ \pink{\boxed{ \rm{ \blue{armed }\: account}}}}}[/tex]

➙[tex] \huge \rm8x-6>12+2x \\ \rm \huge8x-2x>12+6 \\ \huge\rm6x>18 \\ \huge \boxed{\rm{x>3}}[/tex]

➖➖➖➖➖➖➖➖➖➖➖➖➖➖

I hope you understood!✏

➖➖➖➖➖➖➖➖➖➖➖➖➖➖

Step-by-step explanation:

[tex] \huge \boxed{ \boxed{\rm{Hope \: this \: helps}}}[/tex]

Answer:

Correct answer is 4 because the last 2 terms can be combined:

Step-by-step explanation:

4x3 + 9y2 – 3x + 2 – 1 = 4x3 – 3x + 9y2 + 1.

Answer:

21

Step-by-step explanation:

Answer:

24.8 units

Step-by-step explanation:

Given

[tex]n = 10[/tex] --- sides

The attached decagon

Required

The perimeter

The decagon is made up of 10 isosceles triangles.

The angle at the vertex of each is:

[tex]Angle = \frac{360}{10}[/tex]

[tex]Angle = 36[/tex]

Next, we create a right-angled triangle from the shape (see attachment)

[tex]\theta[/tex] is calculated as:

[tex]\theta = \frac{Angle}{2}[/tex]

[tex]\theta = \frac{36}{2}[/tex]

[tex]\theta = 18[/tex]

Next, calculate x using:

[tex]\sin(\theta) = \frac{Opposite}{Hypotenuse}[/tex]

So, we have:

[tex]\sin(18) = \frac{x}{4}[/tex]

Make x the subject

[tex]x = 4 * \sin(18)[/tex]

[tex]x = 1.24[/tex]

So, the length (L) of one side of the decagon is:

[tex]L = 2x[/tex]

[tex]L = 2 * 1.24[/tex]

[tex]L = 2.48[/tex]

The perimeter (P) of the shape is:

[tex]P = 10 *L[/tex]

[tex]P = 10 * 2.48[/tex]

[tex]P = 24.8[/tex]

The perimeter of the given polygon rounded to the nearest tenth is; 24.7

The given polygon as we can see has 10 sides.

Now, when we draw a line from the center to the next vertex to the left of the one currently having a line, we will see that the angle can be calculated as; 360/10 = 36° because sum of exterior angles of a polygon sums up to 360°.

Thus, the other two angles will be; (180 - 36)/2 = 72° each

Using sine rule, we can find the length of a side of the polygon as;

x/sin 36 = 4/sin 72

x = (4 * sin 36)/sin 72

x = 2.472

Thus, perimeter = 2.472 * 10 = 24.72 ≈ 24.7

Read more about perimeter at; https://brainly.com/question/397857

Answer:

3,8 =

Step-by-step explanation:

3 X 3 + 8 = 9 + 8 = 17

Square the first number and add the second number to it.

X <0 means x would be negative.

For x/y, a negative divided by a positive would give a negative answer.

A negative multiplied by a positive would result in a negative.

The answer would be B. Negative

9514 1404 393

Answer:

  B

Step-by-step explanation:

To find the inverse of y = f(x), solve the equation x = f(y) for y. For these functions, that's about the easiest way to do it.

  A. x = ∛(3y)   ⇒   x³ = 3y   ⇒   x³/3 = y . . . . . does not match g(x)

  B. x = 11y -4   ⇒   x +4 = 11y   ⇒   (x +4)/11 = y . . . . matches g(x)

  C. x = 3/y -10   ⇒   x +10 = 3/y   ⇒   3/(x+10) = y . . . . does not match g(x)

  D. x = y/12 +15   ⇒   x -15 = y/12   ⇒   12(x -15) = y . . . . does not match g(x)

_____

Additional comment

This is repeated application of the "solve for ..." process. In general, that process "undoes" what is "done" to the variable. The order of operations can tell you the order of the things that are done. The undoing is in the reverse order.

You need to be completely comfortable with the properties of equality (addition, subtraction, multiplication, division), and you need to understand the inverse functions of the functions we usually use: (powers, roots), (exponentials, logarithms), (trig functions, inverse trig functions). Of course, the inverse of addition is subtraction; the inverse of multiplication is division.

__

Above, we used a "shortcut" a couple of times:

  a = b/c   ⇒   c = b/a . . . . . equivalent to multiplying both sides by c/a.

Answer:

sadia is 32

Step-by-step explanation:

sadia : father : total

3          6          9

Divide 96 by 9

96/9 = 32/3

Multiply each by 32/3

sadia :     father : total

3*32/3    6*32/3  9*32/3

32                 64          96

Answer:

x = 12.15 oz

Step-by-step explanation:

z = 1.8808

 1.8808 = (x - 12)/.08

Answer:

p = [tex]\frac{11}{12}[/tex]

Step-by-step explanation:

Probability that you make the hockey team only: 2/3 * (1-3/4) = 1/6

Probability that you make the swimming team only: 3/4 * (1-2/3) = 1/4

Probability that you make the both team: 1/2

the probability that you at least make one of the teams: 1/6 + 1/4 + 1/2 = 11/12

Step-by-step explanation:

Answer is in attached image...

hope it helps

Answer:

its a

Step-by-step explanation:

just did it

Answer:

The standard deviation associated with the time until I see my 25th customer is of 2.5 hours.

Step-by-step explanation:

In this problem, we have the mean time between x successes, which characterizes the exponential distribution.

As in this question context, the important thing to note is that for the exponential distribution, the mean and the standard deviation are the same.

Mean time before I get my 25th customer is 2.5 hours, what is the standard deviation associated with the time until I see my 25th customer?

They are the same in the exponential distribution, so 2.5 hours.

Answer:

f⁻¹(x) = -4 + √x

Step-by-step explanation:

Switch the positions of x and y then solve for x.

[tex]f(x)=(x+4)^2\\x=(y+4)^2\\\sqrt{x} =y+4\\\sqrt{x} -4=y[/tex]

Answer:

a

Step-by-step explanation:

becuse i got it right

Answer:

Step-by-step explanation:

The first 2 walls  are

2 * 16 *  8 = 256

The second 2 walls are

2 * 15 * 8 =  240

Total number of square feet = 496

If you thin it a bit, likely 1 gallon will do you, but this is math. We  don't do anything practical.

you have 96 square feet left over. You should buy 2 gallon cans

1 can cost 17 dollars.

2 cans cost 34 dollars.

You could try buying a quart which just might do. That will be less.

9514 1404 393

Answer:

Step-by-step explanation:

Reflection over the x-axis changes the sign of the y-coordinate. Reflection over the y-axis changes the sign of the x-coordinate. We can summarize the transformations as ...

  preimage point ⇒ reflection over x ⇒ reflection over y

A(−8,−2) ⇒ A'(-8, 2) ⇒ A"(8, 2)

B(−4,−3) ⇒ B'(-4, 3) ⇒ B"(4, 3)

C(−2,−8) ⇒ C'(-2, 8) ⇒ C"(2, 8)

D(−10,−6) ⇒ D'(-10, 6) ⇒ D"(10, 6)

Answer:

Because it's a negative.

Step-by-step explanation:

The value of a positive number is still a positive number.

Answer:

Less than 3.6 years.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 5.8 years, and  standard deviation of 1.7 years.

This means that [tex]\mu = 5.8, \sigma = 1.7[/tex]

The 10% of items with the shortest lifespan will last less than how many years?

Less than the 10th percentile, which is X when Z has a p-value of 0.1, so X when Z = -1.28.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.28 = \frac{X - 5.8}{1.7}[/tex]

[tex]X - 5.8 = -1.28*1.7[/tex]

[tex]X = 3.6[/tex]

Less than 3.6 years.

Answer:

The answer is a.

Answer:

Each chocolate truffle is $2.125

Step-by-step explanation:

Honestly, I'm not 100% sure if this is correct, and I am truly sorry if this is wrong, but its worth a try :)

Answer:

-13 degrees celcius.

Step-by-step explanation:

6 degrees are lowered every hour. 6*8 = 48 degrees, 48 degrees are lowered.

35-48 is -13. The room temperature will be -13 eight hours after the process begins.