the sum of two prime numbers is 30 and their difference is a perfect square less than 10. Determine the two prime numbers​

Answer:

8.439

Step-by-step explanation:

Since the marathon is divided on 5 EQUAL sections, and it is 42.195 km long, you only need to divide the length of the marathon by 5.

Answer:

Explanation:

-12.4x + 8x > -0.4x - 5.2 - 2.7

Add similar elements: -12.4x + 8x = -4.4x

-4.4x > -0.4x - 5.2 - 2.7

Subtract -5.2 - 2.7: -7.9

-4.4x > -0.4x - 7.9

Multiply both sides by 10

-4.4x · 10 > -0.4x - 7.9 · 10

Refine

-44x > -4x - 79

Add 4x to both sides

-44x + 4x > -4x - 79 + 4x

Simplify

-40x > -79

Multiply both sides by -1 (Reverse the inequality)

-40x (-1) > -79 (-1)

Simplify

40x < 79

Divide both sides by 40

40x / 40 < 79 / 40

Simplify

x < ⁷⁹⁄₄₀

Turn the fraction into a decimal

The answer is:

Work/explanation:

Bear in mind that the sum of all the angles in a triangle is 180°.

Given two angles, we can easily find the third one.

Let's call it x.

Next, we set up an equation:

\(\sf{54+87+x=180}\)

\(\sf{141+x=180}\)

Subtract 141 on each side.

\(\sf{x=180-141}\)

\(\sf{x=39}\)

Answer:

140 degrees.

Step-by-step explanation:

180-110 is 70. Bottom triangle is isosceles, meaning that the bottom left corner is also 70 degrees. The top angle in the bottom triangle is 180-70-70, 40. Flip it to the other side and the bottom angle of the top triangle is 40. Again, an isosceles triangle, so that the top left angle of the top triangle is also 40. 180-40 is 140.

Answer:

its 2.2 cm

Step-by-step explanation:

Answer: B) 2.2 cm

I took the test 3.02 Quiz: Construct Two-Dimensional Figures.

The graph will provide a V-shaped graph with (-1,0) as the vertex when the values are substituted into the function f(x) = |x+1|

The graph consists of two parts: one above the x-axis and one below the x-axis.

For x values greater than or equal to -1, the absolute value of (x + 1) is equal to (x + 1), resulting in a positive y-value. This is represented by the diagonal line starting at (-1, 0) and extending upward to the right.

For x values less than -1, the absolute value of (x + 1) is equal to -(x + 1), resulting in a negative y-value. This is represented by the diagonal line starting at (-1, 0) and extending downward to the left.

The graph is symmetric with respect to the vertical line x = -1. The point (-1, 0) is the vertex of the "V" shape formed by the graph.

The domain of the function is all real numbers, as there are no restrictions on x. The range consists of y-values greater than or equal to 0 for integer values of y and y-values less than 0 for integer values of y.

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Answer:

21

Step-by-step explanation:

Answer:

33

Step-by-step explanation:

7 x 4 = 28

33 - 5 = 28

Answer:(4005/16) ÷ 2 = 125.15625

Step-by-step explanation:

Answer:

20/3

Step-by-step explanation:

Start with multiplying  the numerator by 5, keep the 6 then simply,

The value of the longest of the four side lengths is 13 meters.

Let us assume the smallest side of quadrilateral be x. The consecutive sides of quadrilateral will be (x + 1), (x + 2) and (x + 3). As per the known fact, the perimeter is the sum of all the sides of quadrilateral.

x + x + 1 + x + 2 + x + 3 = 42

Performing addition on Left Hand Side of the equation

4x + 6 = 42

Shifting 6 to Right Hand Side of the equation

4x = 42 - 6

Performing subtraction on Right Hand Side of the equation

4x = 36

Shifting 4 to denominator on Right Hand Side of the equation

x = 36 ÷ 4

Performing division Right Hand Side of the equation

x = 9 meters

Longest side of quadrilateral = x + 4

Longest side of quadrilateral = 9 + 4

Longest side of quadrilateral = 13 meters

Therefore, the longest side of quadrilateral is 13 meters.

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Let X represent the number of cars sold a salesman at a dealership in one week.

The moment generating function of X is \(M(t) = 0.45e^t + 0.30e^2t +0.25e^3t\) .the variance of X is 4.02.

Calculate the variance of X

The formula for the variance of X is;

Var(X) = E(X²) - [E(X)]²

To compute the variance of X, we would first calculate E(X) and E(X²).

The formula for E(X) is;

E(X) = M'(0)

where M'(t) is the derivative of the moment generating function M(t) with respect to t.

M'(t) = \((0.45e^t) + (0.30 × 2e^2t) + (0.25 × 3e^3t)\)

M'(0) = 0.45 + 0.60 + 0.75

M'(0) = 1.8E(X) = 1.8

The formula for E(X²) is;

E(X²) = M''(0) + [M'(0)]²

where M''(t) is the second derivative of the moment generating function M(t) with respect to t.

M''(t) = \((0.45e^t) + (0.30 × 4e^2t) + (0.25 × 9e^3t)\)

M''(0) = 0.45 + 1.2 + 2.25

M''(0) = 3.9E(X²) = 3.9 + (1.8)²

E(X²) = 7.14

The variance of X is;

Var(X) = E(X²) - [E(X)]²

Var(X) = 7.14 - (1.8)²

Var(X) = 4.02

Therefore, the variance of X is 4.02.

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Answer:

B

Step-by-step explanation:

That is the answer

Answer:

The answer is B 17:21

Step-by-step explanation:

68:84

68/2=34

84/2=42

34:42 but we can also divide again so 34:42 can't be the simplest form of 68:84

so 34/2=17

42/2=21

17:21

Answer:

the monthly rents of the apartments

Step-by-step explanation:

In the field of statistics, the population of interest may be defined as the group or the population from which the experimenter or the researcher tries to make conclusions or draw their results.

In the context, I am interested to study the cost of the rented house that is more than others in the West Campus area.

So I recorded the monthly rents of the apartments from a sample of 30 one bedroom apartments.

Therefore, the population of interest for my study here is the monthly rents recorded from the sample of one bedroom apartments.

9514 1404 393

Answer:

  (x, y, z) = (2+44t, 2+14t, 7-20t)

Step-by-step explanation:

One way to write parametric equations for line L is ...

  L = P + t·v

where P is the given point and v is the given direction vector. Using that form, we have ...

  (x, y, z) = (2+44t, 2+14t, 7-20t)

__

If you like, you can remove a common factor of 2 from the coefficients of t.

  (x, y, z) = (2+22t, 2+7t, 7-10t)

Answer:

y=2/3x−2

Step-by-step explanation:

Answer:

Point-slope form: \(y-2=\frac{2}{3} (x-6)\)

y-intercept form: \(y=\frac{2}{3} x-2\)

Step-by-step explanation:

To find the equation of a parallel line through a point, we can use the point-slope form as our basis.  To do this, we need the coordinates of a point on the line and the slope of the line.  A point is already given, (6,2).  Now, we must find the slope, m.

Parallel lines always have the exact same slope as the line they are parallel to.  So, all we need to do to find the slope of the equation we want is by finding the slope of the first equation. The equation we are given is in standard form, or \(Ax+By=C\).  We can find the slope m from this equation using \(m=-\frac{A}{B}\).  In \(2x-3y=7, A=2\) and \(B=-3\).  Thus, \(m=-\frac{2}{-3}\), or just \(\frac{2}{3}\).  Now we can begin to plug the numbers into the formula.

Point-slope form is written as \(y-y_{1} =m(x-x_{1} )\).  We can fill in m with the value we found above, as we can fill in \(y_{1}\) and \(x_{1}\) from the given point of (6,2).  Filling in the information, we get the equation \(y-2=\frac{2}{3} (x-6)\), which simplifies to \(y=\frac{2}{3} x-2\).  Either answer usually works, but you should watch out to see if the question asks for a certain form.

Answer:

Y = -½x + 3/2

Y = -3x + 5

Y = 1/4x - 3¼

Step-by-step explanation:

Parallel implies they have the same gradient

Perpendicular implies the gradient is a negative reciprocal of the other.

Answer:

11 buses

Step-by-step explanation:

Answer:

hope this helps you

They will be when they pass each other at 44 4/9 mins.

This is a classic question on Speed, time, & distance.

1. When time traveled in each segment is constant, then average speed is simple mean of speeds.

2. When distance traveled in each segment is constant, then average speed is reciprocal of simple mean of reciprocal of speeds. It is basically called Harmonic mean.

So this question falls in the category of 2.

=> So, average speed = Reciprocal of mean of reciprocals of 40 & 50.

=> Average speed = Reciprocal of mean of 1/40 & 1/50.

=> Average speed = Reciprocal of (1/40 + 1/50)/2

= Reciprocal of (5+4)/400

= 44 4/9 mins

Hence, they will be when they pass each other at 44 4/9 mins.

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Answer:

C. 43.00

Step-by-step explanation:

If we add up the amount she paid for shirts we would get 35, then we subtract 78 by 35 to get our answer.

Answer:

85cm^3

Step-by-step explanation:

Volume = Base Area * Height

17*5=85

Answer: 13x+8

Step-by-step explanation: You add all of the like terms. so 9x+4x. You get 13x. Then you should do 5+3 which is 8. You’re left with 13x+8, and you can’t combine them so that’s your simplified equation.

Step-by-step explanation:

1Remove parentheses.

9x+5-4x-3

2 Collect like terms.

(9x-4x)+(5-3)

3 Simplify.

5x+2

(Sorry if its wrong, but I hope I helped ^-^)

Answer: q=13

Step-by-step explanation:

add the separate the q, add 4 to the 9= 13

13=q

Answer:

Step-by-step explanation:

You want the least common multiple (LCM) of {6a²b, 9b²c, 3c²a} and of {4x²y²z², 6x³yz, 12xy²z}.

The LCM of two or more terms is a product that has includes all of the factors of each of the terms. One way to find the LCM is to list the factors of the terms, identify the different ones and the powers of each, then choose the highest power of each of the different factors.

  6a²b — factors are ...

  9b²c — factors are ...

  3c²a — factors are ...

The distinct factors are ...

The product of highest powers is the LCM:

  LCM = 2¹·3²·a²·b²·c² = 18a²b²c²

The distinct factors are ...

The product of the highest powers is ...

  LCM = 2²·3¹·x³·y²·z² = 12x³y²z²

__

Additional comment

Sometimes the process of finding the LCM can be confused with finding the GCF (greatest common factor). The GCF will be the product of the lowest of the powers of the distinct factors. That power may be zero for any given factor in any given term.

For example, in the first set of terms, the factor 2 has a power of 0 in the last two terms. The factor 'a' has a power of zero in the second term; b has a power of 0 in the third term; c has a power of 0 in the first term. Then the GCF is ...

  2⁰·3¹·a⁰·b⁰·c⁰ = 3 . . . . . GCF of {6a²b, 9b²c, 3c²a}

In the second set of terms, 2 has a power of 1 in the 2nd term; 3 has a power of 0 in the 1st term; x, y, z all have powers of 1 in at least one of the terms. Then the GCF is ...

  2¹·3⁰·x¹·y¹·z¹ = 2xyz . . . . . GCF of {4x²y²z², 6x³yz, 12xy²z}

In short, every term must be a factor of the LCM, and the GCF must be a factor of every term.

One way to find the LCM of two terms is to divide their product by their GCF. The process can be repeated to include more terms in the LCM.

The total value of the loan with quarterly compounded interest is approximately $45,288.38, while the total value of the loan with monthly compounded interest is approximately $45,634.84. The difference in total interest accrued is approximately $346.46.

Part A: To determine the total value of the loan with quarterly compounded interest, we can use the formula for compound interest:

A = P(1 + r/n)^(nt),

where:

A is the total value of the loan,

P is the principal amount (initial loan amount),

r is the interest rate (in decimal form),

n is the number of times interest is compounded per year,

and t is the number of years.

Given:

P = $20,000,

r = 9% or 0.09,

n = 4 (quarterly compounding),

t = 10 years.

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/4)^(4*10).

Calculating this value, we find:

A ≈ $45,288.38.

Therefore, the total value of the loan with quarterly compounded interest is approximately $45,288.38.

Part B: To determine the total value of the loan with monthly compounded interest, we follow the same formula but with a different value for n:

n = 12 (monthly compounding).

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/12)^(12*10).

Calculating this value, we find:

A ≈ $45,634.84.

Therefore, the total value of the loan with monthly compounded interest is approximately $45,634.84.

Part C: The difference between the total interest accrued on each loan can be calculated by subtracting the principal amount from the total value of each loan.

For the loan with quarterly compounding:

Total interest = Total value - Principal

Total interest = $45,288.38 - $20,000

Total interest ≈ $25,288.38.

For the loan with monthly compounding:

Total interest = Total value - Principal

Total interest = $45,634.84 - $20,000

Total interest ≈ $25,634.84.

The difference between the total interest accrued on each loan is approximately $346.46.

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By the binomial theorem,

\(\displaystyle (1+ax)^p = \sum_{i=0}^p \binom pi (ax)^i\)

For i = 1, the corresponding term in the expansion is

\(\dbinom p1 ax = apx = 20x\)

so that ap = 20, while for i = 2 we get

\(\dbinom p2 (ax)^2 = \dfrac{a^2p(p-1)}2x^2 = 160x^2\)

so that a²p(p - 1)/2 = 160.

Solve for a and p. Observe that

(a²p(p - 1)/2) / (ap) = 160/20

a(p - 1)/2 = 8

ap/2 - a/2 = 8

10 - a/2 = 8

a/2 = 2

a = 4

and it follows that

ap = 20

4p = 20

p = 5

Answer:

Equation of Sphere =  \(x^{2}\) + \(y^{2}\) + \(z^{2}\) - 18x - 4/3y +10z + 142/3 = 0

Step-by-step explanation:

Data Given:

P = (x,y,z)

Distance from P to A (-3,6,3) = Twice the distance from P to B(6,2,-3)

Solution:

Find the equation of the sphere:

It is given that:

PA = 2PB

Squaring both sides:

\((PA)^{2} = (2PB)^{2}\)

\((PA)^{2} = 4 (PB)^{2}\)

\((x - (-3))^{2}\) + \((y - 6)^{2}\) + \((z-3)^{2}\) = 4 x \((x-6)^{2}\) + \((y-2)^{2}\) + \((z-(-3))^{2}\)

Solving the above equation:

\((x + 3))^{2}\) + \((y - 6)^{2}\) + \((z-3)^{2}\) = 4 x {\((x-6)^{2}\) + \((y-2)^{2}\) + \((z + 3))^{2}\)}

\(x^{2}\) + 9 + 6x + \(y^{2}\) + 36 - 12y + \(z^{2}\) + 9 - 6z = 4 { \(x^{2}\) + 36 - 12x + \(y^{2}\) + 4 - 4y + \(z^{2}\) + 9 + 6z}

\(x^{2}\) + 9 + 6x + \(y^{2}\) + 36 - 12y + \(z^{2}\) + 9 - 6z = 4\(x^{2}\) + 144 - 48x +4\(y^{2}\) + 16 - 16y + 4\(z^{2}\) + 36 + 24z

Putting the right hand side = 0 and solving the equation:

\(x^{2}\) - 4\(x^{2}\) + \(y^{2}\) - 4\(y^{2}\) + \(z^{2}\) - 4\(z^{2}\) + 6x + 48x - 12y +16y -6z - 24z + 9 + 36 + 9 -144 - 16 - 36 = 0

-3\(x^{2}\) - 3\(y^{2}\)  -3\(z^{2}\)  + 54x + 4y -30z -142  = 0

Taking (-) common

- ( 3\(x^{2}\) + 3\(y^{2}\) + 3\(z^{2}\)  - 54x - 4y +30z + 142) = 0

3\(x^{2}\) + 3\(y^{2}\) + 3\(z^{2}\)  - 54x - 4y +30z + 142 = 0

dividing the whole equation by 3

\(x^{2}\) + \(y^{2}\) + \(z^{2}\) - 54/3x - 4/3y +30/3z + 142/3 = 0

\(x^{2}\) + \(y^{2}\) + \(z^{2}\) - 54/3x - 4/3y +30/3z + 142/3 = 0

\(x^{2}\) + \(y^{2}\) + \(z^{2}\) - 18x - 4/3y +10z + 142/3 = 0

The equation of the sphere for all surface point P such that \(AP = 2\cdot BP\) is \(x^{2}+y^{2}+z^{2}-18\cdot x -\frac{4}{3}\cdot y + 10\cdot z +\frac{142}{3} = 0\).

Mathematically speaking, we have the following geometric locus:

\(AP = 2\cdot BP\) (1)

Then, we expand the expression presented above by Pythagorean theorem, used to determine the length of a line segment in the field of analytical geometry:

\(\sqrt{(x +3)^{2} + (y-6)^{2} + (z-3)^{2}} = 2\cdot \sqrt{(x-6)^{2}+(y-2)^{2}+(z+3)^{2}}\)

\((x+3)^{2}+(y-6)^{2}+(z-3)^{2} = 4\cdot (x-6)^{2}+4\cdot (y-2)^{2}+4\cdot (z+3)^{2}\)

Now we expand and simplify the resulting expression:

\(x^{2}+6\cdot x + 9 + y^{2}-12\cdot y + 36 + z^{2}-6\cdot z + 9 = 4\cdot (x^{2}-12\cdot x +36) + 4\cdot (y^{2}-4\cdot y +4) + 4\cdot (z^{2}+6\cdot z + 9)\)

\(x^{2} + y^{2} + z^{2} + 6\cdot x -12\cdot y - 6\cdot z +54 = 4\cdot x^{2} +4\cdot y^{2} + 4\cdot z^{2} -48\cdot x -16\cdot y +24\cdot z +196\)

\(3\cdot x^{2} + 3\cdot y^{2} + 3\cdot z^{2} -54\cdot x -4\cdot y + 30\cdot z + 142 = 0\)

\(x^{2}+y^{2}+z^{2}-18\cdot x -\frac{4}{3}\cdot y + 10\cdot z +\frac{142}{3} = 0\) (2)

This expression corresponds to the general form of the equation of the sphere for all surface point P such that \(AP = 2\cdot BP\). \(\blacksquare\)

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Answer:

  reflect over the x-axis and shift down 3

Step-by-step explanation:

The leading coefficient of -1 means the graph is reflected over the x-axis. The addition of -3 to the function means each graphed point is shifted down 3 units from the original.

The graph of y = -x^2 -3 is the result of the transformation ...

  reflect over the x-axis and shift down 3