5.1: Math Talk: Distribution
Distribute each expression mentally.
5(x + 3)
x(x − 3)
(x + 4) (x + 2)
(x - 5)(x - 5)
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The total volume of the party hat shaped cone is V = 39.3 inches³

Given data ,

Let the diameter of the party shaped cone be d = 5 inches

So , the radius of the cone r = 2.5 inches

Now , the height of the hat = 6 inches

And , Volume of Cone = ( 1/3 ) πr²h

V = ( 1/3 ) ( 3.14 ) ( 2.5 )² ( 6 )

V = ( 1/3 ) ( 117.75 )

V = 39.3 inches³

Hence , the volume of cone is V = 39.3 inches³

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Answer:

14

Step-by-step explanation:

5[tex]\frac{1}{5}[/tex] + 8[tex]\frac{5}{6}[/tex]

5 1/5 = 26/5

8 5/6 = 53/6

26/5 + 53/6 = 156/30 + 265/30 = 412/30 = 206/15 ≈ 13.75

So, I say the answer is 14

The correct statement regarding p-values and decision of the hypothesis is given by:

c.) With a p-value of 0.04 and a significance level of 3%, you failed to reject the null hypothesis.​

Given that;

To find the correct statement regarding p-values and decision of the hypothesis

Since, Depends on if the p-value is less or more than the significance level:

If it is more, the null hypothesis is not rejected.

If it is less, it is rejected.

Hence the correct statement for this problem is given by:

c.) With a p-value of 0.04 and a significance level of 3%, you failed to reject the null hypothesis.​

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The simplest form of 4/81x^85 is 3x^2(√1)/75.

Option A is correct.

How do we write an expression on its simplest form?

In order to reduce an algebraic expression to its simplest form, we need to reduce or simplify an expression as much as feasible by carrying out any suggested processes in order to write it in its simplest form.

During the process, we should factor, combine like words, eliminate common factors, and simplify any fractions or radicals.

In conclusion, the simplest form of the expression 4/81x^85 is  written as 3x^2(√1)/75.

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Answer:

0.03

Step-by-step explanation:

Round to the Nearest Hundredth

Find the number in the hundredth place

2

and look one place to the right for the rounding digit

5

. Round up if this number is greater than or equal to

5

and round down if it is less than

5

.

The value of dy/dx is -2 at the given points.

We need to find dy/dx at the point (1/2,2) for the equation [tex]ln(xy) + y^2 = 4[/tex].

First, we can take the partial derivative of both sides of the equation with respect to x, treating y as a constant:

[tex]d/dx [ln(xy) + y^2] = d/dx [4][/tex]

Using the chain rule on the first term, we get:

[tex](1/xy) * y * dy/dx + 2y * dy/dx = 0[/tex]

Simplifying the expression:

[tex]dy/dx = -(2y)/(y + x(ln(xy)))[/tex]

Now we can plug in the values x = 1/2 and y = 2:

dy/dx = -(2(2))/(2 + 1/2(ln(1/2*2)))

dy/dx = -(4)/(2 + ln(1))

dy/dx = -4/2

dy/dx = -2

Therefore, the value of dy/dx at the point (1/2,2) is -2.

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Answer:

The number of times the coin landed on heads is 32 - 8 = 24 since there were 32 flips in total and 8 of them resulted in tails.

The ratio of heads outcomes to tails outcomes can be expressed as 24:8. To simplify this ratio, we can divide both the numerator and denominator by their greatest common factor, which is 8.

So, 24/8 = 3 and 8/8 = 1. Therefore, the ratio of heads outcomes to tails outcomes in simplified form is 3:1.

Answer:

The margin of error in a confidence interval depends on the sample size, the standard deviation of the population (which is not given in the problem), and the level of confidence. Since the standard deviation is not given, we cannot calculate the margin of error exactly. However, we can estimate the margin of error using a standard deviation of 1 (which is a common assumption) and a level of confidence of 95%, which corresponds to a z-score of 1.96.

The formula for the margin of error for a 95% confidence interval is:

Margin of error = z * (standard deviation / sqrt(sample size))

Assuming a standard deviation of 1 and a sample size of 1 (since we are talking about the average time of a single child), we get:

Margin of error = 1.96 * (1 / sqrt(1)) ≈ 1.96

Therefore, we can estimate the margin of error in the report to be around 1.96 minutes. This means that the true average time a 10-year-old American child spends playing outdoors per day is likely to be within 1.96 minutes of the reported average, with a 95% level of confidence.

Step-by-step explanation:

Answer:
x = 4.2071

​x = 3.1464

Step-by-step explanation:

(x-7/2)^2+(x-7/2)^2=1

x^2 - 7x + 49/4 + x^2 - 7x + 49/4 = 1

2x^2 - 14x + 49/2 = 0

x = −(−14) ± (√(−14) − (4×2×(47/2)) / 2 x 2

x = 14 ± 2.8284 / 4

x = 14 + 2.8284 / 4

x = 4.2071

x = 14 - 2.8284 / 4

​x = 3.1464

Answer:

48 = 1/2 * b * (b - 4)

b

Step-by-step explanation:

According to the problem, the height of the triangle is 4m less than the base. We can express this mathematically as:

height = b - 4

The area of a triangle is given by the formula:

area = 1/2 * base * height

Substituting the given values, we get:

48 = 1/2 * b * (b - 4)

Simplifying the equation:

96 = b^2 - 4b

Rearranging and setting the equation equal to zero:

b^2 - 4b - 96 = 0

We can solve for b using the quadratic formula:

b = (-(-4) ± sqrt((-4)^2 - 4(1)(-96))) / (2(1))

b = (4 ± sqrt(16 + 384)) / 2

b = (4 ± 20) / 2

We take the positive root since the base of a triangle cannot be negative:

b = (4 + 20) / 2

b = 12

Therefore, the length of the base is 12 meters.

but in the question above is b

The 99% confidence interval for mean temperature of human is :

( 98.04f, 98.40f )

A data set includes 108 body temperatures of healthy adult humans having a mean of 98.2 and a standard deviation of 0.64 .

Now, We have to construct  a 99% confidence interval estimate of the mean body temperature of all healthy humans.

We use these formula for upper limit and lower limit:

u = x + Zα/2 × (s/√n) (For the upper limit)

u = x - Zα/2 × (s/√n) (For the lower limit)

We have the information from question:

x = sample mean = 98.2

s = standard deviation = 0.64

n = sample size = 108.

[tex]Z_\frac{\alpha }{2}[/tex] = critical value for a 2 tailed test performed at a 1% level of significance ( 100% - 99%) = 2.58

Now, Substitute the parameter,

For upper limit:

u = x + Zα/2 × (s/√n)

u = 98.2 + 2.58 ( 0.64/√108)

u = 98.2 + 2.58 ( 0.0616)

u = 98.2 + 0.1589

u = 98.4

For lower limit:

u = x - Zα/2 × (s/√n)

u = 98.2 - 2.58 ( 0.64/√108)

u = 98.2 - 2.58 ( 0.0616)

u = 98.2 - 0.1589

u = 98.04.

The 99% confidence interval for mean temperature of human is :

( 98.04f, 98.40f )

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I think

Step-by-step explanation:

in order to find x and y we use pythagorus theorem ok

Answer:

Step-by-step explanation:

This is a 30-60-90

Short leg is x because that is across 30 which is x

long leg is y which is x√3

and hypotenuse is 2x

S to find x

2x=[tex]\frac{4\sqrt{3} }{3}[/tex]

x = [tex]\frac{2\sqrt{3} }{3}[/tex]

y=[tex]\frac{2\sqrt{3} }{3}[/tex] *[tex]\sqrt{3}[/tex]

y=2*3/3

y=2

you can also use pythagorean if you don't remember the rules for 30-60-90.  I can show you how and edit this if you want more, mention in comments

1kg of prawn costs $18.

Let's use algebra to determine how much 1 kg of prawns would cost.

We know that 3kg of fish cost $12, so the cost per kg of fish is:

$12 ÷ 3kg = $4/kg

We can set up an equation since we also know that the combined cost of 3 kg of fish and 1 kg of prawn is $30:

3($4/kg) + 1($x/kg) = $30

Simplifying the left side of the equation, we get:

$12/kg + $x/kg = $30

Subtracting $12/kg from both sides, we get:

$x/kg = $18

Therefore, 1kg of prawn costs $18.

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Answer:

Step-by-step explanation:

To show that the points A(-1,-3), B(6, 1), and C(2,-5) form the vertices of a right angle triangle, we need to show that one of the angles of the triangle is a right angle, i.e., it measures 90 degrees.

We can use the Pythagorean theorem to check if the triangle is a right triangle. According to the Pythagorean theorem, the square of the length of the hypotenuse (the side opposite the right angle) of a right triangle is equal to the sum of the squares of the lengths of the other two sides.

First, let's calculate the lengths of the sides of the triangle:

AB = sqrt((6 - (-1))^2 + (1 - (-3))^2) = sqrt(49 + 16) = sqrt(65)

BC = sqrt((2 - 6)^2 + (-5 - 1)^2) = sqrt(16 + 36) = sqrt(52)

AC = sqrt((2 - (-1))^2 + (-5 - (-3))^2) = sqrt(9 + 4) = sqrt(13)

Next, let's check if the Pythagorean theorem holds true for this triangle:

If AB is the hypotenuse:

AB^2 = 65

BC^2 + AC^2 = 52 + 13 = 65

Since AB^2 = BC^2 + AC^2, we can conclude that angle BAC is a right angle.

Therefore, the points A(-1,-3), B(6, 1), and C(2,-5) form the vertices of a right angle triangle, with angle BAC measuring 90 degrees.

The height of the triangle in inches is 14 inches if the area is 105 square inches.

Given that,

Area of the triangle = 105 square inches

Base of the triangle = 15 inches

We know that, the formula to find the area of the triangle is given by,

Area of the triangle = [tex]\frac{1}{2}[/tex] × base × height

Let h be the height.

Substituting,

[tex]\frac{1}{2}[/tex] × 15 × h = 105

15h = 210

h = 14 inches.

Hence the height of the triangle is 14 inches.

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Answer:

  ∠2 = 60°

Step-by-step explanation:

You want the measure of angle 2, where angles 1 and 2 form a linear pair and are marked ∠1 = 5x-5, and ∠2 = 2x+10. You are shown that x=25 and angle 1 is 120°.

There are two ways you can find the measure of angle 2.

1. Use the fact that angle 2 is supplementary to angle 1, which is given as 120°.

  ∠2 = 180° -∠1 = 180° -120°

  ∠2 = 60°

2. Use the expression in x to find angle 2, since you know the value of x.

  ∠2 = 2x +10 = 2(25) +10 = 50 +10

  ∠2 = 60°

__

Additional comment

It looks like you have figured out how to find x. You use the fact that the total of the two angle measures of a linear pair of angles is 180°.

  (5x -5) +(2x +10) = 180

  7x = 175 . . . . . . subtract 5

  x = 25 . . . . . . . divide by 7

20 degrees is the value of the variable x.

Angle ABD is 90 degrees, angle ABC is X degrees, and the measure of angle DBC (3x+10)

x + 3x +10=90

4x +10 =90

4x= 90-10

4x =80

x= 80÷4

x=20

Therefore, the value of the variable x is 20 degrees

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The graph C represents the image of the triangle PQR, after a translation of 2 units right and a reflection across the line x = 1

A translation in math moves a shape left or right or up or down.

The graph C represents the image of the triangle PQR

After a translation of 2 units right and a reflection across the line x = 1

Because if you move the triangle two to the right then X=1

X=1 means the line is up and down going thought x=1

and if that line you make you reflect across it would be C

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Answer:

All the choices except Trapezoid are correct.

Answer:

42

Step-by-step explanation:

x = 4

x³

= 4³

= 4 x 4 x 4

= 64

x³ - 12

= 64 - 12

= 42

Answer:

1440 in^3

Step-by-step explanation:

Note: this is a rectangular prism, where V= lwh. In this case, l=12, w=10, h=12. Multiplying them, we find that the volume is 1440 in^3

Answer:

  |x -8| = 6

Step-by-step explanation:

You want an absolute value equation of the form |x -b| = c with solutions x=2 and x=14.

The solutions to the given equation are ...

  |x -b| = c

  -c = x -b   or   x -b = c . . . . . "unfold" the function

  x = b -c   or   x = b + c . . . . . solve for x

Adding the two solution equations together, we get ...

  (2) +(14) = (b -c) +(b +c)

  16 = 2b

  b = 8

Then ...

  c = x -b = 14 -8 = 6

The equation you want has (b, c) = (8, 6), so is ...

  |x -8| = 6

Answer:

rate of change is 3/4 or 3/4x

Step-by-step explanation:

The simplified algebraic expression is given as follows:

[tex]5\frac{(-1 + \sqrt{3})}{3}[/tex]

The algebraic expression in the context of this problem is defined as follows:

[tex]\frac{-5 + 5\sqrt{3}}{3}[/tex]

To simplify, we must obtain the common factor of the numerator, which is of 5, as both terms are divisible by 5, as follows:

Hence the simplified algebraic expression is given as follows:

[tex]5\frac{(-1 + \sqrt{3})}{3}[/tex]

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Answer:

204 inches

Step-by-step explanation:

17ft * 12inches/ft = 204inches

Answer:204

Step-by-step explanation:

17ft = to 204 inches

The unknown angles of the similar triangle are as follows:

m∠W =  55°

m∠X = 90°

m∠Y = 35°

Similar triangles are triangles that have the same shape, but their sizes may vary.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

Therefore, the corresponding angles of the triangles are congruent.

Hence, the triangle is assume to be drawn accurately.

Therefore,

m∠W = m∠D

m∠X = m∠E

m∠Y = m∠C  

Therefore,

m∠W = 180 - 90 - 35 = 55 degrees

m∠X = 90 degrees

m∠Y = 35 degrees

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Answer: 225

Step-by-step explanation:

Create a ratio part/whole for radians = part/whole for degrees

[tex]\frac{\frac{5\pi }{4} }{2\pi } = \frac{x}{360}[/tex]      Keep change flip because you are dividing fractions for left side

[tex]\frac{5\pi }{4} (\frac{1}{2\pi }[/tex]) = [tex]\frac{x}{360}[/tex]

[tex]\frac{5}{8} (\frac{360}{1} ) =x[/tex]

x = 225

Based on this W-2, a statement which is true include the following: D. Lily earned more than $12,950 (which is the standard deduction amount).

In Economics, there are different types of tax which are levied on individuals (employees) or business firms (employers of labor) by the government, and these include the following:

In Economics, W-2 Tax form can be defined as an internal revenue service (IRS) tax form which is used to indicate the amount of money that is earned by an employee at the end of a period, including the correct federal income tax that should be withheld from an employee's paycheck in the United States of America.

Based on the W-2 Tax form, we can logically deduce that Lily earned more than $12,950 because her gross earnings (wages) is $14,450.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The trigonometric identity sin(x + y) = (√95 + 3√17)/27

Trigonometric identities are identities containing trigonometric ratios.

Given that tanx = 1/√8 and siny = √17/6 and angles x and y are both in Quadrant 1, we need to find the value of sin(x + y)

So, using the trigonometric identity sin(x + y) = sinxcosy + cosxsiny

First we need to find sinx, cos x and cosy

Using trigonometric identity 1 + tan²x = sec²x

sec²x = 1 + tan²x

= 1 + (1/√8)²

= 1 + 1/8

= (8 + 1)/8

= 9/8

sec²x = 9/8

secx = √(9/8)

= ±3/2

secx = 1/cosx

1/cosx = ±3/2

cosx = ±2/3

Now sinx = √(1 - cos²x)

= √(1 - (2/3)²)

= √[(1 - 4/9)]

= √[(9 - 4)/9]

= √(5/9)

= ±√5/3

Also, cosy = √(1 - sin²y)

= √(1 - (√17/6)²)

= √(1 - 17/36)

= √[(36 - 17)/36]

= √(19/36)

= ±√19/6

Since sin(x + y) = sinxcosy + cosxsiny, substituting the positive values of the variables into the equation since they are in the first quadrant, we have that

sin(x + y) = sinxcosy + cosxsiny

sin(x + y) = √5/3 × √19/6 + 2/3 × √17/6

= √95/27 + √17/9

= √95/27 + √17/9

= 1/9(√95/3 + √17)

= 1/9(√95 + 3√17)/3

= (√95 + 3√17)/27

So, sin(x + y) = (√95 + 3√17)/27

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