suppose that a six sided die is rolled twice.What is the probability that the sum of the two rolls is 5?

Answer:

The formula for density (ρ) is:

Density (ρ) = Mass (m) / Volume (V)

Step-by-step explanation:

Where:

Answer:

I think is higher

Step-by-step explanation:

1. Find the graph of the parabola attached below

2. Vertex (-4, 2)   Focus (-7/2, 2)  Directrix (x = -9/2)  Endpoints (-7/2, 1) (-7/2, 3)

For the parabola,  x = 1/2(y-2)² - 4 we will use the equation x = 4p(y-k)² + h,

Vertex → (h, k)

In our given equation, (y - 2) → (y - k), so k = 2. The term on the rightmost side of our equation (-4) → h in the form, so we know h = -4. ∴  vertex (-4, 2).

focus → (h, k) = (-4, 2); P = 1/2

Parabola is symmetric around the x axis and so the focus lies a distance P, from the center, along the x axis.

∴  Focus is (-4 + p, 2)

(-4 + 1/2, 2) ⇒ (-7/2, 2)

directrix → x = d

Parabola is symmetric around the x axis and therefore the directrix is a line paralled to the y axis a distance away from the ceter (-4, 2) x coordinate.

∴ x = -4 - p   ⇒ x = -4 - 1/2

x = 9/2

focal chord endpoints →

The focus of the parabola is (-7/2, 2).

The y-coordinate of the focus is 2, so the y-coordinates of the endpoints of the focal chord are 2 + 1 and 2 - 1, → 3 and 1.

Therefore, the endpoints of the focal chord are:

(-7/2, 3) and (-7/2, 1).

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Answer:

You need a protractor

Step-by-step explanation:

to measure the angles

Answer:

(a) D. All the above

(b) \(p = 10\) --- Mean

(c) \(s = 3\) --- Standard Deviation

(d) A. No, 15 is not a significantly high number of golf balls, because the probability of 15 is greater than 0.05

Step-by-step explanation:

Solving (a):

Option (d) answers the question because (a), (b) and (c) are all true

For (a): x must be a random variable

For (b): \(\sum p(x) = 1\)

For (c): \(0 \le p(x) \le 1\)

Solving (b): The mean

Mean (p) is calculated as:

\(p = \sum xp(x)\)

So, we have:

\(p = 3 * 0.14 + 6 * 0.03 + 9 * 0.36 + 12 * 0.37 + 15 * 0.10\)

\(p = 9.78\)

\(p = 10\)

Solving (c): The standard deviation

This is calculated as:

\(s = \sqrt{\sum[ x*p(x) *(1-p(x))]}\)

So, we have:

\(s = \sqrt{3 * 0.14 *(1 - 0.14) + 6 * 0.03 * (1 - 0.03) +..............+ 15 * 0.10 * (1 - 0.10)}\)\(s = \sqrt{6.7566}\)

\(s = 2.599\)

\(s = 3\)

Solving (d): Is P(x = 15) significantly high?

From the question:

\(P(x = 15) = 0.10\)

In probability:

\(0 \le x \le 0.15\) is considered to be low (i.e. not high) because it is almost not sure to occur

Hence, (a) is true

The area of the overlapping region is of: 6.25 units squared.

The area of a rectangle of length l and width w is given by the multiplication of the dimensions, as follows:

A = lw.

The dimensions of the right triangle as follows:

Hence the remaining leg on the overlapping region is:

4 - x, as AD = 4.

By symmetry, the other dimension of the overlapping region is also of:

4 - x.

Being also the hypotenuse of the right triangles.

The value of x can be found applying the Pythagorean Theorem as follows:

x² + 2² = (4 - x)²

x² + 4 = 16 - 8x + x²

8x = 12

x = 1.5.

Then the two dimensions of the shaded region are:

4 - 1.5 = 2.5.

Meaning that the area is of:

A = 2.5 x 2.5 = 6.25 units squared.

The figure is missing and is given by the image at the end of the answer.

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Answer:

D. 7

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Answer: D) 54 inches = 1 1/2 yards

explanation: 1 1/2 yards = 54 inches.

Answer:

75/7

Step-by-step explanation:

69=7v-6 rewrite as 69+6=7v

75 = 7v

75/7 = v

Answer:

2x+6 or 2 ( 3x + 1 )

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

42 is 2 x 3 x 7

81 is 3 x 3 x 3 x 3

3 is the greatest common factor

Answer:

3

Step-by-step explanation:

3 is the greatest common factor of 42 and 81

163. The distance between A(-5, 6) and B(5, -5) is: AB ≈ 14.9 units

164. Applying the Pythagorean theorem, we have: Diagonal ≈ 21.2 ft.

165. Marissa's final answer is wrong. It should be, c = √676 = 26 units.

166. Missing side = 29 ft.

The Pythagorean theorem states that c² = a² + b², given that a and b are shorter legs and c is the hypotenuse or longest leg of the right triangle.

163. The distance between A(-5, 6) and B(5, -5):

AB = √[(5−(−5))² + (−5−6)²]

AB = √221

AB ≈ 14.9 units

164. Apply the Pythagorean theorem to find the diagonal:

Diagonal = √(15² + 15²) ≈ 21.2 ft.

165. The answer Marissa got is wrong. The final answer which is the square root of 676 is:

c = √676 = 26 units.

166. Missing side = √(20² + 21²) = 29 ft.

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Answer:

See below

Step-by-step explanation:

If you are squaring a number, and then taking the square root of it, you are essentially undoing the original operation:

\(\displaystyle \sqrt{\biggr(\frac{4}{7}\biggr)^2}=\biggr[\biggr(\frac{4}{7}\biggr)^2\biggr]^{\frac{1}{2}}=\biggr(\frac{4}{7}\biggr)^{2*\frac{1}{2}}=\frac{4}{7}\)

Hence, we are back starting with the original number

The listing of the given values from the least to the greatest = -$25.18, -$24.72, -$24.12, $25.12, $47.72 and $48.12.

A number line is defined as the expression that represents the location of real numbers as being a positive number or a negative number.

The negative values which are the least in the number line are usually higher in value than the greater numbers, while the greater values are higher for positive numbers.

Therefore,the arrangement of the given values from least to the greatest = -$25.18, -$24.72, -$24.12, $25.12, $47.72 and $48.12.

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Answer:

coordinates of the centroid = \((\frac{2}{3} , \frac{2}{3} )\)

Step-by-step explanation:

The curves to be plotted are : y =2x, y = 0, x =1

The coordinates of the centroid ( visually estimated ) can be found by first calculating the area of the region

A = \(\int\limits^1_0 {2x} \, dx\)  =   2\((\frac{x^2}{2} )\) hence A = 1

attached below is the remaining part of the solution

Answer:

28p + 14q + 21r

Step-by-step explanation:

7(4p + 2q + 3r) ← multiply each term in the parenthesis by the 7 outside

= 28p + 14q + 21r

The Approximation of 14 plus cube root of 81 to the nearest tenth is 18.0

The concept that will be used to solve this is finding cube root of 81 which same thing as \(81^{\frac{1}{3} }\).

Firstly we will need to find the  cube root of 81, which can be expressed as this: \(\sqrt[3]{81}\)  and this can be calculated as 4.33.

This implies that the cube root of 81 will now be 4.33.

Then we can proceed to the simplification that was asked from the question which is 14 plus cube root of 81 and this can be expressed as ( 14) + (4.33) = 18.33

Then we were told to express in the the nearest tenth which is 18.0

Therefore, the third option is correct.

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Answer:

She can buy 7 journals

$30.00-$9.00=$21.00

$3.00x7 journals=$21.00

Answer:

r = -4

Step-by-step explanation:

2r + 7 = - 1

2r = - 1 - 7

2r = - 8

Answer: r=-4

Step-by-step explanation: -3(2r + 7)=3                                                             (−3)(2r)+(−3)(7)=3                                                                                                   −6r+−21=3                                                                                                             −6r−21+21=3+21                                                                                                   -6r/-6=24/-6                                                                                                         r=-4              

(a). The Tanakas paid a total of $523,906.40 for the townhome.

(b). The Tanakas paid $206,906.40 in interest on their mortgage over the 15-year period.

Simple interest is the type of interest that is calculated on the principal amount only.

It is a fixed percentage of the principal amount that is charged or earned over a certain period of time, without any compounding of interest.

(a) The total amount they ended up paying for the townhome is the sum of the down payment and the total amount of the mortgage payments.

Down payment = $41,000

Total amount of mortgage payments = monthly payment x number of payments = $2675.04 x 12 months/year x 15 years = $482,906.40

Total amount paid = down payment + total amount of mortgage payments = $41,000 + $482,906.40 = $523,906.40

(b) The amount of interest paid on the mortgage can be calculated by subtracting the principal (the amount borrowed) from the total amount paid.

Principal = Total cost of townhome - Down payment = $358,000 - $41,000 = $317,000

Total interest paid = Total amount paid - Principal = $523,906.40 - $317,000 = $206,906.40

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Therefore, since 4 times $20 is equal to $80, we can say that the total cost of the water for the 8 miners is equivalent to the cost of 4 sets of 20 dollars each.

In mathematics, an equation is a statement that asserts the equality of two expressions. It consists of two expressions separated by an equals sign (=). The expression on the left side of the equals sign is called the left-hand side (LHS), and the expression on the right side of the equals sign is called the right-hand side (RHS). Solving an equation means finding the value of the variable that makes the equation true.

Here,

If one miner paid $10 for a glass of water, and 8 miners each bought one glass of water, then the total cost of the water for the 8 miners is:

8 x $10 = $80

To use a 4s fact to find this answer, we can note that:

4 x $20 = $80

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Answer:

$180

Step-by-step explanation:

If the perimeter is 30 yards and each yard costs $6 you times 30 and 6 and you get $180

Answer:

i bite my tongue its a baddd habit

28 + 10√3

Step-by-step explanation:

first, multiply the two together. √3 * √3 = 3. √3 * 5 = 5√3. 5 * √3 = 5√3. 5 * 5 = 25.

We have 3 + 5√3 + 5√3 + 25. Combine like terms and you should get 28 + 10√3.

The number of cell phones sold in 2015 is (0.29)(1.28x)

The correct answer is A) (0.29)(1.28x).

What is a linear equation?

A linear equation is an equation in which the highest power of the variable is 1. Linear equations can be written in the form ax + b = 0, where a and b are constants and x is the variable. Linear equations are called "linear" because they represent a straight line when plotted on a graph.

We are told that the number of cell phones Hongbo sold in 2014 was 128% greater than in 2013, which means that he sold 128/100 = 1.28 times as many cell phones in 2014 as he did in 2013. This can be represented by the equation x * 1.28 = number of cell phones sold in 2014.

We are also told that the number of cell phones Hongbo sold in 2015 was 29% greater than in 2014, which means that he sold 29/100 = 0.29 times as many cell phones in 2015 as he did in 2014. This can be represented by the equation (number of cell phones sold in 2014) * 0.29 = number of cell phones sold in 2015.

Substituting the first equation into the second equation, we get:

(x * 1.28) * 0.29 = number of cell phones sold in 2015

This simplifies to:

(0.29)(1.28x) = number of cell phones sold in 2015

Hence, the number of cell phones sold in 2015 is (0.29)(1.28x)

the correct answer is A) (0.29)(1.28x).

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The negations of the given statements with the application of De Morgan's law and/or conditional law.

a) ∃x (¬P(x) ∨ ¬R(x))

De Morgan's law:

∃y ∀z(¬P(y) ∧ ¬Q(z))

b) ∃y ∀z(¬P(y) ∧ ¬Q(z))

The double negation:

∃y ¬∃z(P(y) ∨ Q(z))

c) ¬∃x (P(x) ∨ (∀z (¬R(z)) → (∀z ¬Q(z))))

The conditional law:

¬∃x (P(x) ∨ (∀z (¬R(z)) → (∀z ¬Q(z))))

Let's form the negation of the given statements and apply De Morgan's law and/or conditional law, when applicable:

a) ∀x (P(x) ∧ R(x))

The negation of this statement is:

∃x ¬(P(x) ∧ R(x))

Now let's apply De Morgan's law:

∃x (¬P(x) ∨ ¬R(x))

b) ∀y∃z(¬P(y) → Q(z))

The negation of this statement is:

∃y ¬∃z(¬P(y) → Q(z))

Using the conditional law, we can rewrite the negation as:

∃y ¬∃z(¬¬P(y) ∨ Q(z))

c) ∃x (P(x) ∨ (∀z (¬R(z) → ¬Q(z))))

The negation of this statement is:

¬∃x (P(x) ∨ (∀z (¬R(z) → ¬Q(z))))

Using the conditional law, we can rewrite the negation as:

¬∃x (P(x) ∨ (∀z (R(z) ∨ ¬Q(z))))

Applying De Morgan's law:

¬∃x (P(x) ∨ (∀z ¬(¬R(z) ∧ Q(z))))

Simplifying the double negation:

¬∃x (P(x) ∨ (∀z ¬(R(z) ∧ Q(z))))

Using De Morgan's law again:

¬∃x (P(x) ∨ (∀z (¬R(z) ∨ ¬Q(z))))

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The second pair of points representing the solution set of the system of equations is (-6, 29).

To find the second pair of points representing the solution set of the system of equations, we need to substitute the x-coordinate of the second point into one of the equations and solve for y.

Given the system of equations:

y = x^2 - 2x - 19

y + 4x = 5

Substituting the x-coordinate of the second point (-6) into equation 2:

y + 4(-6) = 5

y - 24 = 5

y = 5 + 24

y = 29

Therefore, the second pair of points representing the solution set of the system of equations is (-6, 29).

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Question

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

y = x2 − 2x − 19

y + 4x = 5

The pair of points representing the solution set of this system of equations is (-6, 29) and

_________.