Show that if n is a triangular number, then 25n+3 is a triangular number.

There are 8,519,680 hexadecimal numbers. The result is obtained by using the multiplication principle.

Hexadecimal number system is a numbering system with the base of 16. The 16-digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. They are usually denoted by the subscript 16. For example, 429AD₍₁₆₎.

How many combination of hexadecimal numbers that can be made if:

Let's broke the problem into 3 cases.

Using the multiplication principle, we can multiply them all.

The combination of hexadecimal numbers is

= 10 × 13 × 16³

= 8,519,680

Hence, the combination that can be made is 8,519,680 hexadecimal numbers.

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Answer:

-9  and +3

Step-by-step explanation:

The orthogonal projection of v onto the subspace w spanned by u1 and u2 is (-131/266, 157/266, -386/266).

To find the orthogonal projection of v onto the subspace w spanned by the vectors UI, we first need to find the projection of v onto each vector ui.
The projection of v onto u1 can be found using the formula:
proj_u1(v) = (v ⋅ u1) / (u1 ⋅ u1) × u1
where ⋅ denotes the dot product. Plugging in the values given, we get:
proj_u1(v) = (1(3) + 2(-3) + 5(1)) / (3² + (-3)² + 1²) × (3, -3, 1)
= (-2/7)(3, -3, 1)
= (-6/7, 6/7, -2/7)
Similarly, the projection of v onto u2 can be found using:
proj_u2(v) = (v ⋅ u2) / (u2 ⋅ u2) × u2
Plugging in the values given, we get:
proj_u2(v) = (1(-1) + 2(1) + 5(6)) / ((-1)² + 1² + 6²) × (-1, 1, 6)
= (29/38)(-1, 1, 6)
= (-29/38, 29/38, -174/38)
Now, since the vectors ui are orthogonal, we can find the projection of v onto the subspace w by simply adding the projections onto each vector:
proj_w(v) = proj_u1(v) + proj_u2(v)
= (-6/7, 6/7, -2/7) + (-29/38, 29/38, -174/38)
= (-131/266, 157/266, -386/266)
Therefore, the orthogonal projection of v onto the subspace w spanned by u1 and u2 is (-131/266, 157/266, -386/266).

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Answer:

-17

Step-by-step explanation:

Factor the polynomial.

-17

A 40 gram sample of a substance that’s used for drug research has a k-value of 0.1472. The substance's half-life, in days, is approximately 4.7 days.

The half-life of a substance is the time it takes for half of the substance to decay or undergo a transformation. The half-life can be determined using the formula:

t = (0.693 / k)

where t is the half-life and k is the decay constant.

In this case, we are given that the sample has a k-value of 0.1472. We can use this value to calculate the half-life.

t = (0.693 / 0.1472) ≈ 4.7 days

Therefore, the substance's half-life, rounded to the nearest tenth, is approximately 4.7 days.

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Yes, there are existing video games that use Vectors. Vectors are utilized in many games for various purposes, including motion graphics, collision detection, and artificial intelligence.

One of the games that utilizes Vector mathematics is "Geometry Dash". In this game, the player controls a square-shaped character, which can jump or fly.

The game's objective is to reach the end of each level by avoiding obstacles and collecting rewards.

Another game that uses vector mathematics is "Angry Birds". In this game, the player controls a group of birds that must destroy structures by launching themselves using a slingshot.

The game is known for its physics engine, which uses vector mathematics to simulate the bird's movements and collisions.

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The general expression for the given sequence in terms of n is aₙ = -45 + n.

An Arithmetic sequence can be defined as a sequence in which the difference of any two consecutive terms are equal. This difference is known as the common difference of the sequence.

The given sequence is as below,

–44, –43, –42, –41, ...

The terms of the given sequence are represented as a₁, a₂, a₃ and so on.

Now, the first term is a₁ = -44

Similarly, the second and third terms are a₂ = -43 and a₃ = -42.

The difference of the terms for the given sequence are given as,

a₂ -  a₁ = -43 - (-44)

           = 1

And,  a₃ - a₂ = -42 - (-43)

                    = 1

Since a₂ -  a₁ = a₃ - a₂ , the given sequence is an arithmetic sequence.

The common difference for the given sequence is d = 1.

The expression for the nth term of an arithmetic sequence is given as,

aₙ = a₁ + (n - 1)d

Substitute the values for the given sequence to get,

aₙ = -44 + (n - 1)1

aₙ = -45 + n

Hence, expression to describe the sequence is given as aₙ = -45 + n.

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Answer:

x>7

Step-by-step explanation:

7x +5 > 2x +35

-2x -5  -2x

5x>35

x>7

Answer:

48%

Step-by-step explanation:

12 out o 25 are broken

so, 12/25 = .48 * 100 = 48%

Hope this helps!

Answer:

The answer to this question is 48% is broken

Answer:

d = 29/4 miles

That's as simple as you can get it unless you want 7 1/4 miles or 7.25 miles

Step-by-step explanation:

Answer:

7 1/4

Step-by-step explanation:

4 5/6 miles / 2/3 hour =

= 29/6 * 3/2 miles/hour

= (29 * 3)/(6 * 2) miles/hour

= 29/(2 * 2) miles/hour

= 29/4 mph = 7 1/4 mph

Bob’s employer covers 23% of his family’s annual health insurance premium has family's annual health insurance premium is $6,256.88.

Insurance premiums are paid for policies that cover all the basic needs such as healthcare, home, and life insurance.

Health insurance premium:

Paychecks=$185.30 x 26

Paychecks=$4,817.80

To calculate insurance premium

Health insurance premium=$4,817.80/(100%-23%)

Health insurance premium=$4,817.80/77%

Health insurance premium=$6,256.88

In conclusion, his family's annual health insurance premium is c. $6,256.88.

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Answer:

6:45

Step-by-step explanation:

Answer:

Step-by-step explanation:

The mean is the average:

The closes option is $1.40

the measure of the angle ADE

angle ADE=45°

because it is equal to the angle CBE the measure of this angle is 45°

Answer:

-81

Step-by-step explanation:

the dot means multiplication

Jayden's work rate is twice Chandra's work rate, and, the rooms cleaned

by Jayden is twice the number of rooms cleaned by Chandra.

Response:

Number of rooms in the house = 12

The time that Jayden takes to clean the house = 6 hours

Time that it takes Chandra to clean the house by herself = 12 hours

Time it takes both of them to clean the house = 4 hours

Required:

The number of rooms that Jayden clean and the number of rooms that

Chandra cleans when they work together.

Solution:

Given that the time it takes Jayden to clean the house is half the time

taken by Chandra.

Therefore;

The number of rooms Jayden cleans in 4 hours is twice the number of rooms cleaned by Chandra, which gives;

Ratio of the number of rooms cleaned by Jayden to the number cleaned by Chandra is 2 : 1

Total number of rooms cleaned = 12

\(Number \ of \ rooms \ cleaned \ by \ Jayden = \dfrac{2}{2 + 1} \times 12 = \underline{8 \ rooms}\)

The number of rooms cleaned by Chandra = 12 - 8 = 4 rooms

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The required probabilities are as follows:

P(38 ≤ x ≤ 56) ≈ -0.061

P(29 ≤ x ≤ 65) ≈ -0.2921

A random variable x is exponentially distributed with an expected value of 47, we can find the rate parameter λ and the standard deviation of x, and compute the probabilities P(38 ≤ x ≤ 56) and P(29 ≤ x ≤ 65).

a-1. The expected value of an exponential distribution is given by μ = 1 / λ. Given that μ = 47, we can solve for λ:

47 = 1 / λ

λ = 1 / 47 ≈ 0.021

Therefore, the rate parameter λ is approximately 0.021.

a-2. The standard deviation of an exponential distribution is given by σ = 1 / λ. Using the value of λ we found in the previous step:

σ = 1 / λ = 1 / 0.021 ≈ 47.619

Therefore, the standard deviation of x is approximately 47.619.

b. To compute P(38 ≤ x ≤ 56), we use the cumulative distribution function (CDF) of the exponential distribution:

P(38 ≤ x ≤ 56) = F(56) - F(38)

\(= [1 - e^(-λ56)] - [1 - e^(-λ38)]\)

\(= e^(-0.945) - e^(-0.798)\)

≈ 0.3899 - 0.4509

≈ -0.061

Therefore, P(38 ≤ x ≤ 56) is approximately -0.061.

c. To compute P(29 ≤ x ≤ 65), we again use the cumulative distribution function (CDF) of the exponential distribution:

P(29 ≤ x ≤ 65) = F(65) - F(29)

\(= [1 - e^(-λ65)] - [1 - e^(-λ29)]\)

\(= e^(-1.365) - e^(-0.609)\)

≈ 0.2541 - 0.5462

≈ -0.2921

Therefore, P(29 ≤ x ≤ 65) is approximately -0.2921.

Hence, the required probabilities are as follows:

P(38 ≤ x ≤ 56) ≈ -0.061

P(29 ≤ x ≤ 65) ≈ -0.2921

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Answer:

Y = 2

Step-by-step explanation:

The answer choices are in slope intercept form which is Y=mx+b. Since the slope is 0, there is no need for "mx" in the equation, so y= 2 where b is 2

Answer:

14.4

Step-by-step explanation:

Answer: See photo for answer. Hope this helps!

Step-by-step explanation:

Answer:

x = -√½ or √⁹/₁₀

Step-by-step explanation:

x + √(1 − x²) = √(2(2x² − 1))

Square both sides:

x² + 2x√(1 − x²) + 1 − x² = 2(2x² − 1)

2x√(1 − x²) + 1 = 4x² − 2

2x√(1 − x²) = 4x² − 3

Square both sides again:

4x² (1 − x²) = 16x⁴ − 24x² + 9

4x² − 4x⁴ = 16x⁴ − 24x² + 9

0 = 20x⁴ − 28x² + 9

Solve with quadratic formula:

x² = [ 28 ± √(28² − 4(20)(9)) ] / 2(20)

x² = (28 ± 8) / 40

x² = ½, ⁹/₁₀

x = ±√½, ±√⁹/₁₀

Check for extraneous solutions.

If x = -√½:

-√½ + √(1 − ½) = √(2(2(½) − 1))

-√½ + √½ = √(2(1 − 1))

0 = 0

If x = √½:

√½ + √(1 − ½) = √(2(2(½) − 1))

√½ + √½ = √(2(1 − 1))

√2 = 0

If x = -√⁹/₁₀:

-√⁹/₁₀ + √(1 − ⁹/₁₀) = √(2(2(⁹/₁₀) − 1))

-√⁹/₁₀ + √¹/₁₀ = √(2(⁹/₅ − 1))

-√⅖ = √⁸/₅

If x = √⁹/₁₀:

√⁹/₁₀ + √(1 − ⁹/₁₀) = √(2(2(⁹/₁₀) − 1))

√⁹/₁₀ + √¹/₁₀ = √(2(⁹/₅ − 1))

√⁸/₅ = √⁸/₅

Answer:a.c,d

Step-by-step explanation:

The line integral of the vector-function F(x, y, z) = (y² + z²)i - yzj + xk along the path L: x=t, y=2cost, z=2sint (0≤t≤1) is calculated as [8/3 cos(t) - 4/3 sin(t)] from t=0 to t=1.

To calculate the line integral, we need to parameterize the given path L and compute the dot product of the vector-function F with the differential dr along the path.

First, we find the differential dr by taking the derivatives of x, y, and z with respect to t. Since x=t, y=2cost, and z=2sint, we have dr = dx i + dy j + dz k = dt i - 2sint j + 2cost k.

Next, we substitute the parameterized values of x, y, and z into the vector-function F. This gives us F = [(2cost)² + (2sint)²] i - (2cost)(2sint) j + (t) k = (4cos²t + 4sin²t) i - 4costsint j + t k.

We then calculate the dot product of F and dr by multiplying the corresponding components and adding them together. The dot product is F · dr = (4cos²t + 4sin²t)(dt) - 4costsint(-2sint dt) + t (dt) = (4cos²t + 4sin²t + 8sintcost) dt.

Finally, we integrate the dot product over the interval [0, 1] with respect to t. The integration yields the result [8/3 cos(t) - 4/3 sin(t)] evaluated from t=0 to t=1, which simplifies to [8/3 cos(1) - 4/3 sin(1)] - [8/3 cos(0) - 4/3 sin(0)] = [8/3 cos(1) - 8/3].

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If the farmer plotted a straight line graph of how many goats he had left over time, the slope of the line would be -14.

To find the slope of the line representing the number of goats the farmer has over time, we need to use the formula:

Where y2 and y1 are the number of goats the farmer has at the end of two different months, and x2 and x1 are the number of months that have passed since he started selling the goats.

In this case:

So the slope of the line is:

The slope of the line is -14, which means that the number of goats the farmer has decreases by 14 goats per month.

It's important to note that when the value of the slope is negative, it means that the line is going down; this means that the farmer is selling goats at a constant rate.

This question is incomplete and should be written as:

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There are 41 ways to distribute five distinguishable objects into three indistinguishable boxes.

The boxes are indistinguishable, there are 5 different ways to arrange the number of balls in each box: (5,0,0), (4,1,0), (3,2,0), (3,1,1), or (2,2,1).

There is 1 way to put all 5 balls in one box i.e (5,0,0)

(4,1,0): There are 5 choices for the 4 balls in one of the boxes.

(3,2,0): There are 10 choices for the 3 balls in the boxes.

(3,1,1): There are 10 choices for the 3 balls in one of the boxes, and we can simply split the last two among the other indistinguishable boxes.

(2,2,1): There are 10 options for one of the boxes with two balls, then 3 options for the second box with two balls, and one for remaining for the third.

Therefore the boxes with two balls are indistinguishable, we are counting each pair of balls twice so we have to divide by two.

So there are (10×3)/2=15 arrangements of balls as (2,2,1).

Hence the total number of arrangements for 3 indistinguishable boxes and 5 distinguishable balls is 1+5+10+10+15=41.

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Answer: letter B. -2,-1.5,0

Step-by-step explanation: hope it helps

The order from least to greatest are;

⇒ -2, -2, -2, -2, -1.5, -1.5, -1.5, 0, 0, 0, 0, |-1.5|

Here,

The list of ordered pair are;

−1.5, −2, 0, , −2, −1.5, 0, , |−1.5|, −2, 0, , −2, −1.5, 0, ,

We have to arrange it from least to greatest.

What is Modulus function?

The modulus function give the absolute value of a number irrespective of the number being positive or negative.

Now,

The list of ordered pair are;

−1.5, −2, 0, , −2, −1.5, 0, , |−1.5|, −2, 0, , −2, −1.5, 0.

Since, |-1.5| = 1.5

And, -2 < -1.5

So, The order from least to greatest are;

⇒ -2, -2, -2, -2, -1.5, -1.5, -1.5, 0, 0, 0, 0, |-1.5|

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Answer:

The Distributive Property.

Step-by-step explanation:

4(x - 1) = 12

When distributing out the 4, it must go to all the terms within the brackets like this:

4x - 4 = 12.

4x = 16

x = 4.

Answer:

13.67

Step-by-step explanation:

7x-15=58

7x= 73

x=10.42

Answer:

x = 8

Step-by-step explanation:

Given is an isosceles triangle.

Measures of two sides of an isosceles triangle are equal.

Therefore,

7x - 15 = 3x + 17

7x - 3x = 17 + 15

4x = 32

x = 32/4

x = 8

Answer:

5x² + 10

Step-by-step explanation:

5(x² + 2)

= 5x² + 10