simplify the following polynomial expression. (5^4-9^3+7x-1)+(-8^4x^2-3x+2)-(-4x^3+5x-1)(2x-7)

The events "male” and "buys lunch” are not independent because P(male | buys lunch) = 0.4 and P(male) = 0.3.

James surveyed people at school and asked whether they bring their lunch to school or buy their lunch at school more often. The results are shown below.

Bring lunch: 46 males, 254 females

Buy lunch: 176 males, 264 females

The events "male" and "buys lunch" are not independent because

The number of male students is:

Male = 46 + 176

Male = 222

The number of female students is:

Female = 254 + 264

Female = 518

The total student is:

Total = 222 + 518

Total = 740

Next, calculate the probability of selecting a male student

P(Male) = 222/740

P(Male) = 0.3

Of all the 440 that buy lunch, 176 are male,

So, we have:

P(male | buy lunch) = 176 / 440

P(male | buy lunch) = 0.4

Because

P(male | buy lunch) and P(male) are not equal.

Then, the events "male” and "buys lunch” are not independent

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Answer:

Side Length and Perimeter of One Face

Step-by-step explanation:

See attached image.

The probability of hitting the shaded area is 0.64

The diameters are given as:

D = 10

d = 6

The shaded area is calculated as:

Shaded = π((D/2)² - (d/2)²)

So, we have:

Shaded = π((10/2)² - (6/2)²)

Evaluate the exponents

Shaded = 16π

The area of the big circle is calculated as:

Area = π(D/2)²

So, we have:

Area = π(10/2)²

Evaluate the exponents

Area = 25π

The probability of hitting the shaded area is:

P = 16π/25π

Evaluate

P = 0.64

Hence, the probability of hitting the shaded area is 0.64

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Answer:

angle A=angleB .…(समदिबाहु त्रिभुज भएर)

34°=(x-5)°

or, 34=34

angleA+angleB+angleC=180°

or, 34+34+4y=180

or, 68+4y=180

or, 4y=180-68

or, 4y=112

or, y=112÷4

or, y=28

The value of x, given the data From the question is 2

Left = Right (since the system is balanced)

3 + 3x = 2x + 5

Collect like terms

3x - 2x = 5 - 3

x = 2

Complete question

See attached photo

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Answer:

576 m

__________________________________________________________ The surface area of the triangular prism is (Perimeter of the base × Length of the prism) + (2 × Base Area) = (S1 + S2+ S3)L + bh

For this question,
you know that the perimeter of the base is 6+10+8 which is 24.
and the length of the prism is 22,
so (22x24) + Base Area which is (6x8)/2-> 24x2
(22x24)+(24x2)= 528 + 48 = 576
so your answer is 576
__________________________________________________________

Hope this helped!

Answer:

x = 64

Step-by-step explanation:

Solve for x: √x + 3-4=7

√x + 3-4=7

= √x + 1 = 7

= √x = 7 + 1

= √x = 8

= (√x)² = 8²

x = 64

Answer:

(2.5, - 10 )

Step-by-step explanation:

given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

here (x₁, y₁ ) = (- 16, - 12 ) and (x₂, y₂ ) = (21, - 8 ) , then

midpoint = ( [tex]\frac{-16+21}{2}[/tex] , [tex]\frac{-12-8}{2}[/tex] ) = ( [tex]\frac{5}{2}[/tex], [tex]\frac{-20}{2}[/tex] ) = (2.5, - 10 )

Answer: c - (2 1/2 - 10)

Step-by-step explanation:

x = 90°

2x = 180°

Step-by-step explanation:

angle VTS= angle TSR (alternate angle)

now in ∆TRS,

2x + x + x = 360° (angle sum property of ∆)

4x = 360°

x = 90°

Answer:

slope = [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (6,3) and (x₂, y₂ ) = (9,4) ← 2 ordered pairs from the table

m = [tex]\frac{4-3}{9-6}[/tex] = [tex]\frac{1}{3}[/tex]

Answer:

Before discount = $61.25

After discount = $49.00

Step-by-step explanation:

Given information:

The price of the gift before the discount is 100%.

If the $12.25 discount was 20% of the purchase price, then:

⇒ original price (before discount) = (12.25 / 20) × 100 = $61.25

To find the price after the discount, simply subtract the discount from the found original price:

⇒ $61.25 - $12.25 = $49.00

Conclusion

Answer:

A. True

Step-by-step explanation:

One of the ways to check this is solving each side of the equation.

(5+4)+10=5+(4+10)

Remember PEMDAS.

Parenthesis first.

(9)+10=5+(14)

Now, you can drop the parenthesis and add the numbers together.

9+10=19

5+14=19

19=19

This is a true statement.

Hope this helps!

If not, I am sorry.

If the result is reflected over x-axis and vertically stretched by a factor of 5, the result will be g(x) = -5(x - 1)²

Transformation is a way of changing the position of an object o the xy plane. Given the parent function expressed as

f(x) = x^2

If the function is shifted to the left by unit, then we will have h(x) = (x - 1)²

If the result is reflected over x-axis and vertically stretched by a factor of 5, the result will be g(x) = -5(x - 1)²

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Answer:

B) 7.8 and 7.9

Step-by-step explanation:

Taking the square root of 61, we can conclude that the decimal form is 7.810, which falls between the range of 7.8 and 7.9

Answer:

√61 lie between 7.8 and 7.9

A person can immigrate to another country for educational purposes.

A person can emigrate to another country for work.

A person can emigrate to another country due to war in their own country.

Migration is when a person moves from one geographical location or another. Immigration and emigration are types of migration.

Immigration is when a person moves to a foreign country. For example, when a US citizen moved to Italy for work. Emigration is when a person lives his home country.

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(a) 10% of x = 9

x = 9 ⋅ (100/10)

x = 90 kg

(b) 12% of x = 12/100 of 90

Weight she lost = 10.8

Her new weight = 90 - 10.8

= 79.2kg

Answer: These ARE congruent to each other.

Step-by-step explanation: Do you see the ''tick marks?'' They both have 1 set of 2, and 1 set of 1. If that makes sense. They also have a "angle" in one of their acute angles.

Answer: [tex]8\sqrt{5}[/tex]

Step-by-step explanation:

By the geometric mean theorem,

[tex]\frac{y}{16}=\frac{4}{y}\\\\y^{2}=64\\\\y=8[/tex]

Thus, by the Pythagorean thoerem,

[tex]8^2 +16^2=x^2\\\\320=x^2\\\\x=\boxed{8\sqrt{5}}[/tex]

Answer:

[tex]3a^2+12a+12[/tex]

Step-by-step explanation:

first, you have to plug in x = a+2 into the function, which would look like:

[tex]f(a+2) =3(a+2)^2[/tex]

then, you can first simplify [tex](a+2)^2[/tex]. to do this, use the rule [tex](a+b)^2 = a^2 +2ab + b^2[/tex], so it would be [tex]a^2+(2*a*2)+2^2 = a^2 + 4a + 4[/tex]

this means your new equation is:

[tex]3(a^2+4a+4)[/tex]

you can then distribute the 3:

[tex]3*a^2+3*4a + 3*4 = 3a^2+12a+12[/tex]

let me know if there's anything you want me to clarify!

Answer:

choice C

Step-by-step explanation:

x could be any number except -1.

Cause for x=-1 the denominator becomes undefined.

The inverse of the function will be [tex]f(x) ^{-1}= 2x - 12\\[/tex]. option C is correct.

Suppose that the given function is

[tex]f:X\rightarrow Y[/tex]

Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist),

then, the inverse of the considered function is

[tex]f^{-1}: Y \rightarrow X[/tex]

The function is given as

[tex]f(x) = \dfrac{1}{2} x - 6\\\\[/tex]

The inverse of the function will be

[tex]f(x) ^{-1}= 2x - 12\\[/tex]

Therefore, option C is correct.

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Answer:

√30/6 = √5

The correct answer would be E

The value of the expression √30/√6 is √5, option E is correct.

A number system is defined as a system of writing to express numbers.

The given property is √a/√b = √(a/b)

Now we have to find the equivalent to the quotient √30/√6

By the given property let us plug in a as 30 and b as 6

√30/√6

= √(30/6)

When we simplify the fraction inside the root we get 5

= √5

Hence, the value of the expression √30/√6 is √5, option E is correct.

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The equation in Slope-Intercept Form is y = -2/5 x + 4.

We have given that,

y−2=−2/5(x−5)

We have to rewrite the equation in Slope-Intercept Form.

slope-intercept form is y = mx + b

for equation y - 2 = -2/5 (x - 5) we need to simplify/rearrange

so y - 2 = -2/5 x + -2/5 (-5)

= -2/5 x + 2

=> y = -2/5 x + 4

This line has a gradient of -2/5 (goes down 2 units and across 5 units) and a y-intercept of 4 so passes through the point (0,4).

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Answer:

A = 27π cm²

Step-by-step explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

the central angle of the shaded sector = 360° - 90° = 270° , then

A = πr² × [tex]\frac{270}{360}[/tex]

  = π × 6² × [tex]\frac{3}{4}[/tex]

  = 36π × [tex]\frac{3}{4}[/tex]

  = 9π × 3

 = 27π cm²

Answer:

D. 11

Step-by-step explanation:

Take the two horizontal line measurements and subtract them.

13-9=4

That is how much it changed between these two numbers. Since x is exactly halfway between, simply divide 4 and 2.

4/2=2

Now, add that to 9 or subtract it from 13.

9+2=11

or

13-2=11.

Hope this helps!

If not, I am sorry.

Answer:

D. 11

Step-by-step explanation:

Since segment AC bisects segments ED and BF, the length of AC is the average of the lengths of EB and DF.

AC = x = (EB + DF)/2 = (9 + 13)/2 = 22/2 = 11

Answer: D. 11

Answer:

88 sq. units

Step-by-step explanation:

1st. BxH

12-4 = 8 is our Base

8x8=64 that is out 1st area

and 2nd area is LxW which is 12x2 = 24

64+24= 88 sq. units

We conclude that after the discount and the coupon, Will paid $36 for the skateboard.

We know that the original price was $60, and two discounts were applied. One of 20% and other of 25%.

Then the amount that he paid is given by:

P = $60*(1 - 20%/100%)*(1 - 25%/100%)

P = $60*(0.8)*(0.75)  = $36

We conclude that after the discount and the coupon, Will paid $36 for the skateboard.

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Answer: (-2, -4)

Step-by-step explanation:

The translation that maps point A onto point B must also map point D onto point C.

Point A maps onto point B after a translation 8 units right and 6 units up, so point C maps onto point D after a translation 8 units left and 6 units down.

Thus, D has coordinates (-2, -4)