The weights of 3 kittens at one week of age were 3.6 ounces, 4.2 ounces, and 3.3 ounces. If each kitten has gained 2.3 ounces, how much does each of the kittens weigh?

Answer:

y=-28 and x=6

Step-by-step explanation:

y=-6x+8...... eqn(1)

7x+2y=-14.......eqn(2)

Two times equation (1)

2y=-12x+16..... eqn(3)

2y=-14-7x........ eqn (2)

eqn(3) - eqn(2)

0=-5x+30

5x=30

x=6

from eqn (1) where x=6

y=-6(6)+8

y= -36+8

y=-28

The value of f(5) is positive

At f(x) = 0, the value of x is 1

For the interval f(x) ≤ 0, the values of x are [-2, 1]

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have

f(5) = 1

This means that f(5) is positive

Also, we have

When f(x) = 0, the value of x is 1

For the interval f(x) ≤ 0, we have the values of x to be

-2 ≤ x ≤ 1

When represented as an interval, we have

[-2, 1]

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An orthonormal set is a set of orthogonal unit vectors.

Normalization is the process of making unit vectors.

A set of vectors in which each vector is orthogonal to every other vector in the set is called an orthogonal set of vectors.

Two vectors are orthogonal when their dot product equals zero.

An orthonormal set is one in which each vector has length 1 and is orthogonal.

The process of creating a vector of length 1 in the same direction of the original vector is called "normalization".

An orthonormal set of vectors that is a basis of a vector space is quite useful. We can use the Gram-Schmidt process to transform a basis of a vector space (which may not be orthogonal) into an orthonormal basis.

To normalize vectors to produce an orthonormal set of vectors, we calculate the length of the vector and divide the vector by its length, to obtain a unit vector.

Since the question asked about "how to normalize vectors to produce an orthonormal set" that implies that the vectors already form an orthogonal set.

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The given question is incomplete,

So , I take another question, The question is:

How to normalize vectors to produce an orthonormal set?

Answer:

LHS.= Sin 2x /( 1 + cos2x )

We have , sin 2x = 2 sinx•cosx

And. cos2x = 2cos^2 x - 1

i.e . 1+ cosx 2x = 2cos^2x

Putting the above results in the LHSwe get,

Sin2x/ ( 1+ cos2x ) =2 sinx•cosx/2cos^2x

=sinx / cosx

= Tanx

.•. sin2x/(1 + cos2x)= tanx

Step-by-step explanation:

Note that if the angles are complementary with each other, the sine and cosine are the same.

From the problem, sin 60 = √3/2, the complement of 60 degrees is 30,

so cos 30 is the same as sin 60.

The best answer is Choice A

Answer:

We use the rule,

\((a^b)^c = a^{bc}\)

a. (10^7)²

\((10^7)^2 = 10^{(7)(2)} = 10^{14}\)

10^14

b. (10^9)³

\((10^9)^3 = 10^{(9)(3)} = 10^{27}\)

10^27

c. (10^6)³

\(10^{(6)(3)}= 10^{18}\)

10^18

d. (10^2)³

\(10^{(2)(3)} = 10^{6}\)

10^6

e. (10³)²

\(10^{(3)(2)}=10^{6}\)

10^6

f. (10^5)^7

\(10^{(5)(7)} = 10^{35}\)

10^35

Step-by-step explanation:

Recall that:

Then:

Therefore:

Finally, we get that:

Answer:

a. The answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.

b. The answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.

a. To represent 20 longs in base seven, we need to find the fewest number of multibase blocks required.

In base seven, we have the following conversions:

1 long = 1 unit

1 flat = 10 units

1 block = 10 flats

To represent 20 longs, we can use 2 flats (each flat representing 10 units) and 0 units since there are no remaining units.

So, the fewest number of multibase blocks required would be 2 flats.

Therefore, the answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.

b. To represent 10 longs in base three, we need to find the fewest number of multibase blocks required.

In base three, we have the following conversions:

1 long = 1 unit

1 flat = 3 units

1 block = 3 flats

To represent 10 longs, we can use 3 flats (each flat representing 3 units) and 1 unit since there is one remaining unit.

So, the fewest number of multibase blocks required would be 3 flats and 1 unit.

Therefore, the answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.

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Answer:

A) \(x=-1\pm\sqrt{\frac{13}{6}}\)

Step-by-step explanation:

\(\displaystyle x=\frac{-12\pm\sqrt{12^2-4(6)(-7)}}{2(6)}\\\\x=\frac{-12\pm\sqrt{144+168}}{12}\\\\x=\frac{-12\pm\sqrt{312}}{12}\\\\x=\frac{-12\pm2\sqrt{78}}{12}\\\\x=-1\pm\frac{\sqrt{78}}{6}\\\\x=-1\pm\sqrt{\frac{78}{36}}\\\\x=-1\pm\sqrt{\frac{13}{6}}\)

Answer: 101

Step-by-step explanation: 1+5x20 then 100+1= 101

The surface area of the base ball to the nearest whole number is 26 in²

A sphere is defined as the set of all points in three-dimensional Euclidean space that are located at a distance.

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The surface area of a sphere is expressed as;

SA = 4πr²

where r is the radius and it's calculated as;

C = 2πr

9 = 2πr

r = 4.5/π =

SA = 4 π × (4.5/π)²

SA = 81/π

SA = 26 in²( nearest whole number)

Therefore the surface area of the sphere is 26 in²

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Answer:

2.592 x 10^5

Step-by-step explanation:

1st step: Calculate for 1 day.

if 1 hour = 3.6 X 10³

24 hrs = (3.6 x 10³) X (2.4 x 10¹)

= 3.6 x 2.4 X 10⁴

= 8.64 x 10⁴

2nd Step: Calculate for 3 days;

if 1 day = 8.64 x 10⁴

3 days = (8.64 x 10⁴) X (0.3 x 10¹)

= 8.64 x 0.3 x 10^5

= 2.592 x 10^5

The powers, (index) and coefficients of the polynomial indicates;

(A) The standard form is; 2·x⁴ + 3·x³ + 9·x² - 12·x + 6

(B) 4

(C) Positive zeroes; 2 or 0, negative zeroes; 0 or 2, complex zeroes; 0 or 2 or 4

(D) ±1/2, ±1, ±3/2, ±2, ±3, ±6

(E) Please find attached the graph of the polynomial created with MS Excel

(F) Four complex roots

A polynomial is a mathematical expression that consists of variables and coefficients joined together by addition, subtraction and multiplication, with the exponents of the variables consisting of positive integer values.

Part A) The polynomial in standard form is; 2·x⁴ + 3·x³ + 9·x² - 12·x + 6

Part B) The degree of the polynomial is 4, as the highest power of the polynomial is 4

Part C) The use of the Rule of Signs, to determine the options for the number of positive zeroes, negative zeroes and complex zeroes, can be presented as follows;

Positive zeroes options; The number of time the signs coefficients of the expression; 2·x⁴ + 3·x³ + 9·x² - 12·x + 6, changes are two as follows;

+6 to -12, and from -12 to +9, therefore, the number of possible positive zeroes are 2 or 0, positive zeroes

The negative zeroes options; The negative zeroes options can be found by changing the sign of all the coefficients as follows; -2·x⁴ - 3·x³ - 9·x² + 12·x - 6, therefore, the number of times the sign of the coefficients change are again from -6 to +12, and from +12 to -9, which is 2 times, therefore;

The possible number of negative zeros are 2 or 0, negative zeroes

Whereby there are possibly 0 negative zeros and 0 positive zeroes, the possible number of complex zeroes are 4

Whereby there are 2 negative zeros and 0 positive zeroes, the possible number of complex zeroes are 2 complex zeroes

Whereby there are possibly 0 negative zeros and 2 positive zeroes, the possible number of complex zeroes are 2 complex zeroes

Part D) The rational roots theorem indicates that for a polynomial the rational roots are in the form p/q, where p is a factor of the constant term, and q is a factor of the leading coefficient.

The constant term is 6, and the leading coefficient is 2. The factors of 6 are ±1, ±2, ±3, and ±6 and the factors of 2 are; ±1, ±2 therefore;

p/q = ±1/1, ±2/1, ±3/1, ±6/1, ±1/2, ±2/2, ±3/2, ±6/2, which can be summarized as; ±1/2, ±1, ±3/2, ±2, ±3, ±6

Part E) Please find attached a screenshot of the graph of the polynomial created with MS Excel

Part F) The attached graph of the polynomial, created with MS Excel, indicates that there are no real zeros of the polynomial, therefore, there are four complex zeroes of the polynomial

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Answer:

4.

Step-by-step explanation:

Degree will he 4, since the largest exponent will still be 4 after the addition.

Answer:

Step-by-step explanation:

\(x^{4} +4y^{2} -5xy + x^{3} -y+2xy=x^{4}+x^{3}+4y^{2-y-3xy\)

Therefore, grade of the sum is 4.

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities.

If Mofor only has time to do two homework assignments out of the five subjects, he will need to choose which subjects to prioritize. The specific subjects he chooses to work on will depend on various factors such as his strengths, weaknesses, upcoming deadlines, and personal preferences. Here are a few strategies he could consider:

1. Prioritize based on importance: Mofor can prioritize the homework assignments that carry more weight in terms of grades or have upcoming deadlines. This way, he ensures that he completes the assignments that have a higher impact on his overall academic performance.

2. Focus on challenging subjects: If Mofor finds certain subjects more difficult or time-consuming, he can prioritize those assignments to allocate more time and effort to them. This approach allows him to concentrate on improving his understanding and performance in subjects that require extra attention.

3. Balance workload: Mofor can choose to distribute his efforts evenly across subjects, selecting two assignments from different subjects. This strategy ensures that he maintains a balanced workload and avoids neglecting any particular subject.

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities. It is essential for him to consider his academic goals, time constraints, and personal strengths to make an informed decision.

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Part a: The data points appear to follow an exponential pattern. This is because the balance is increasing at a rate that is proportional to the current balance.

Part b: The equation of the best fit is y = 50(1.06)^x. This can be found using a variety of methods, including graphing the data points and fitting a curve to them, or using a statistical software package.

Part c: When x = 32, y = 50(1.06)^32 = $2,499.82.

Years since 1990, x 0 5 10 15 20 25 30

Balance, y $50 $62.31 $77.65 $96.76 $120.59 $150.27 $187.27 $2,499.82

The equation of the fitted curve is y = 50(1.06)^x.

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Answer:

The sum of squares is the sum of the square of variation, where variation is defined as the spread between each individual value and the mean. To determine the sum of squares, the distance between each data point and the line of best fit is squared and then summed up. The line of best fit will minimize this value.

Answer:

See below for explanation

Step-by-step explanation:

The area of an isosceles triangle is \(A=\frac{1}{2}bh\), so let's write the base as an equation of y:

\(\displaystyle 9x^2+4y^2=36\\\\4y^2=36-9x^2\\\\y^2=9-\frac{9}{4}x^2\\\\y=\pm\sqrt{9-\frac{9}{4}x^2\)

As you can see, our ellipse consists of two parts, so the hypotenuse of each cross-section will be \(\displaystyle 2\sqrt{9-\frac{9}{4}x^2\), and each height will be \(\displaystyle \sqrt{9-\frac{9}{4}x^2}\).

Hence, the area function for our cross-sections are:

\(\displaystyle A(x)=\frac{1}{2}bh=\frac{1}{2}\cdot2\sqrt{9-\frac{9}{4}x^2}\cdot\sqrt{9-\frac{9}{4}x^2}=9-\frac{9}{4}x^2\)

Since we'll be integrating with respect to x because the cross-sections are perpendicular to the x-axis, then our bounds will be from -2 to 2 to find the volume:

\(\displaystyle V=\int^2_{-2}\biggr(9-\frac{9}{4}x^2\biggr)\,dx\\\\V=9x-\frac{3}{4}x^3\biggr|^2_{-2}\\\\V=\biggr(9(2)-\frac{3}{4}(2)^3\biggr)-\biggr(9(-2)-\frac{3}{4}(-2)^3\biggr)\\\\V=\biggr(18-\frac{3}{4}(8)\biggr)-\biggr(-18-\frac{3}{4}(-8)\biggr)\\\\V=(18-6)-(-18+6)\\\\V=12-(-12)\\\\V=12+12\\\\V=24\)

Therefore, this explanation confirms that the correct volume is 24!

The expression for the sum of 1 cubed, 2cubed and 3 cubed is 1² + 2³ + 3³ and the value is 36.

It should be noted that the information is to find the expression for the sum of 1 cubed, 2cubed and 3 cubed.

This will be:

= 1³ + 2³ + 3³

= 1 + 8 + 27

= 36

Therefore, the correct answer is 36.

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The exponential form of the given information 3^2x3^3 is 3⁵.

The exponential form is a convenient way of expressing or writing repeated multiplication expressions concerning their bases and power.

From the information given, the given expression can be written in exponential form by using the law of indices.

= 3^2x3^3  

\(\mathbf{=3^{2+3}}\)

\(\mathbf{=3^{5}}\)

Therefore, we can conclude that the exponential form of the given expression is 3⁵.

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Answer:

By finding the differences between dependent values, you can determine the degree of the model for data given as ordered pairs. If the first difference is the same value, the model will be linear. If the second difference is the same value, the model will be quadratic.

The probability that either event will occur is 0.33

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

Total = A + B + C

So, we have

Total = 8 + 7 + 30

Evaluate

Total = 45

So, we have

P(A) = 8/45

P(B) = 7/45

For either events, we have

P(A or B) = 8/45 + 7/45

P(A or B) = 15/45

Evaluate

P(A or B) = 0.33

Hence, the probability that either event will occur is 0.33

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The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.

To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.

The GCD represents the largest number that can divide all the quantities without leaving a remainder.

The GCD of the quantities of crayons can be found by considering the prime factorization:

72 = 2³ × 3²

48 = 2⁴ × 3

48 = 2⁴ × 3

48 = 2⁴ × 3

The GCD of the crayons is 2³ × 3 , which is 24.

Now, we need to find the GCD of the quantity of drawing paper:

120 = 2³ × 3 × 5

The GCD of the drawing paper is also 2³ × 3 , which is 24.

Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.

Each kit would contain an equal distribution of crayons and drawing paper.

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Answer:

3/4

Step-by-step explanation:

Ok, so I see that the x-intercept is (4,0), while the y-intercept is(-3,0)

Slope is rise/run

Between these two points, the line rose 3 and horizontally went 4 units to the right. Therefore, the slope is 3/4.

Feel free to tell me if I did anything wrong! :)

Also, if you're still confused, I could explain it another way.

Number of ways total inventory of 32 batteries  be distributed among the 8 different types - 15257889504

The number of possible arrangements for a given set is determined mathematically, and this process is known as permutation. The term "permutation" simply refers to the variety of possible arrangements or orders. The positioning of the permutations matters a lot.

Number of ways total inventory of 32 batteries  be distributed among the 8 different types -

39!/30! 7! = 39X38X37X36X35X34X33X32X31 / 7X6X5X4X3X2X1

= 15257889504

Number of ways total inventory of 32 batteries  be distributed among the 8 different types, in inventory must include A76 - 35! / 28! 7!

= 35X34X33X32X31X30X29 / 7X6X5X4X3X2X1 = 6714520

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The amount insurance company will pay is $700000.

We are given that

Age of Mr. lewis= 63

Policy value= $700,000

Now,

If Mr. Lewis dies after paying for the policy for 24 months, he would have paid a total of 24 * $72 = $1728 in premiums. Since he has a five-year level-term life insurance policy with a face value of $700,000, his beneficiaries would receive the full face value of the policy if he dies within the five-year term.

Therefore, by algebra the answer will be $700000.

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Answer:B

Step-by-step explanation:

Step-by-step explanation:

999 × 109 = 999000000000, 999 → 9,990 → 99,900 → 999,000 → 9,990,000 → 99,900,000 → 999,000,000 → 9,990,000,000 → 99,900,000,000 → 999,000,000,000. Nine hundred ninety-nine billion in numbers, generally speaking, is 999000000000. In figures, 999000000000 is written with thousand separators as 999,000,000,000.