what decimal fraction of 200g of 1kg

Answer:

The positive angle less than 360° that is coterminal with -215° has a measure of 145°.

Step-by-step explanation:

From Geometry, we know that angles form a family of coterminal angles as function of number of revolutions done on original angle. We can represent the set of all coterminal angles by means of the following expression:

\(\theta_{c} = \theta_{o} + 360\cdot i\), \(i \in \mathbb{Z}\) (1)

Where:

\(\theta_{o}\) - Original angle, in sexagesimal degrees.

\(\theta_{c}\) - Coterminal angle, in sexagesimal degrees.

\(i\) - Coterminal angle index, no unit.

If we know that \(\theta_{o} = -215^{\circ}\) and \(i = 1\), then the coterminal angle that is less than 360° is:

\(\theta_{c} = -215^{\circ} + 360\cdot (1)\)

\(\theta_{c} = 145^{\circ}\)

The positive angle less than 360° that is coterminal with -215° has a measure of 145°.

Answer:

Even

Step-by-step explanation:

Answer:

The answer is 5/30

Step-by-step explanation:

The answer is 5/30 because when multiplying a fraction by a fraction you have to multiply the numerator by the numerator and the denominator by the denominator so if you multiply 5 by 1 you get 5 and when you multiply 6 by 5 you get 30 so the answer is 5/30

Answer:

B) 6x^2-31x+35

Step-by-step explanation:

(3x-5)(2x-7)

6x^2-10x-21x+35

6x^2-31x+35

Answer:

10

Step-by-step explanation:

a=1 b=5

a=2 c=1  

5*2=10

The value of b will be 10 times bigger than the value of c. for the given ratio a:b=1:5 and a:c=2:1

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.

It is given that

\(\dfrac{a}{b}=\dfrac{1}{5}\)

\(b=5a\)..............1

Also the second relation

\(\dfrac{a}{c}=\dfrac{2}{1}\)

\(a=2c\)..................2

Put the value of an in equation 1

\(b=5\times 2c=10c\)

Hence the value of b will be 10 times bigger than the value of c. for the given ratio a:b=1:5 and a:c=2:1

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The given p, α, and i using the exponentiation by squaring algorithm.

To prove that 2 is a primitive root of 11, to show that every integer a with 1 ≤ a ≤ 10 can be expressed as a ≡ 2²i (mod 11) for a unique i with 0 ≤ i ≤ 9.

verify this by checking the powers of 2 modulo 11:

2² ≡ 1 (mod 11)

2²≡ 2 (mod 11)

2² ≡ 4 (mod 11)

2³ ≡ 8 (mod 11)

2² ≡ 5 (mod 11)

2³ ≡ 10 (mod 11)

2³ ≡ 9 (mod 11)

2³ ≡ 7 (mod 11)

2² ≡ 3 (mod 11)

2³ ≡ 6 (mod 11)

The remainders obtained from the powers of 2 cover all the integers from 1 to 10 modulo 11. Additionally, each remainder is unique, express any integer between 1 and 10 as a power of 2 modulo 11.

To find log₂(9), to determine the exponent i such that 9 (mod 11). From the list of powers of 2 above, that 2³= 9 (mod 11). Therefore, log₂(9) = 6.

A given p, α, and i, where α is a primitive root of p and i is the discrete logarithm or index use the algorithm of exponentiation by squaring.

The algorithm for computing a given p, α, and i is as follows:

Set result = 1.

Initialize a binary representation of i, e.g., i = b[m]b[m-1]...b[1]b[0].

For j from m to 0:

a. Square the current result: result = result × result (mod p).

b. If bj = 1, multiply the current result by α: result = result × α (mod p).

Return the final result.

This algorithm takes advantage of the binary representation of i to compute a efficiently. By squaring the current result and multiplying by α only when necessary, compute a in logarithmic time complexity with respect to i.

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The solution of the recurrence relation is \(a_n=3.2^n\)

For given question,

We have been given a recurrence relation \(a_n = 2a_{n-1}\) for n ≥ 1

and an initial condition \(a_0=3\)

Let \(a_n\) = m², \(a_{n-1}\) = m and \(a_{n-2}\) = 1

So from given recurrence relation we get an characteristic equation,

⇒ m² = 2m

⇒ m² - 2m = 0                     .........( Subtract 2m from each side)

⇒ m(m - 2) = 0                     .........(Factorize)

⇒ m = 0    or  m - 2 = 0

⇒ m = 0   or   m = 2

We know that the solution of the recurrence relation is then of the form

\(a_n=\alpha_1 {m_1}^n + \alpha_2 {m_2}^n\)  where \(m_1,m_2\) are the roots of the characteristic equation.

Let, \(m_1\) = 0   and \(m_2\) = 2

From above roots,

\(\Rightarrow a_n=\alpha_1 {0}^n + \alpha_2 {2}^n\\\\\Rightarrow a_n=0+\alpha_2 {2}^n\\\\\Rightarrow a_n=\alpha_2 {2}^n\)

For n = 0,

\(\Rightarrow a_0=\alpha_2 {2}^0\\\\\Rightarrow a_0=\alpha_2 \times 1\\\\\Rightarrow a_0=\alpha_2\)

But  \(a_0=3\)

This means \(\alpha_2=3\)

so, the solution of the recurrence relation would be \(a_n=3.2^n\)

Therefore, the solution of the recurrence relation is \(a_n=3.2^n\)

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The real root of the equation is x = 40 - 39√2, which gives a value of S = 2231 approximately.

Given,The strength, S, of a wooden beam depends on the width and depth of the rectangular cross-section of the beam, but not on the length of the beam.

For a particular type of wood, the value of S of a beam is proportional to the product of the width and the square of the depth of its cross-section.

The strength of an oak beam is 69, when the beam is 7 inches wide and 3 inches deep.Thus, we can conclude that k, a constant of proportionality exists, such that: S=k(W x D²), where W is the width, D is the depth of the rectangular cross-section and S is the strength of the beam.

Let's use this to calculate k: When the beam is 7 inches wide and 3 inches deep, S=69. Thus, we get:k = S/W x D²=69/(7 x 3²)=1.

Thus, the equation for S becomes:S = W x D²The radius of the oak tree is 28/2 = 14 inches and the beam must be 14 inches wide.

This implies that the rectangular cross-section of the beam must be square (or the largest rectangular cross-section is a square). Let the side of the square cross-section be x.

Thus, we can write:S = x²Diameter, d = 28 inches => radius, r = 14 inchesWe need to determine the depth of the beam. The depth of the beam is half the height of the cylindrical log from which the beam is cut. The cylindrical log has a diameter of 28 inches. The beam has a width of 14 inches.

The largest rectangular cross-section is a square with sides of length x. This cross-section can be obtained by cutting the log at a height of x/2 from its center.Since the diameter is 28 inches, the radius is 14 inches. The height at which the beam is cut is h = 14 - x/2.

Thus, the depth of the rectangular beam cut from the cylindrical log is given by: D = 2(h) = 2(14 - x/2) = 28 - x.Using the relationship S = W x D² with S = 69, W = 14 and k = 1, we can write:x² (28 - x)² = 69Simplifying the above equation,x⁴ - 56x³ + 784x² - 69 = 0.

Using polynomial long division, we get:(x² + 16x - 69)(x² - 40x + 1) = 0The real root of the equation is x = 40 - 39√2, which gives a value of S = 2231 approximately.Therefore, the  answer is (b) S = 2231.

The strength, S, of a wooden beam depends on the width and depth of the rectangular cross-section of the beam, but not on the length of the beam. Let the side of the square cross-section be x. Thus, we can write:S = x²Diameter, d = 28 inches => radius, r = 14 inches. Using the relationship S = W x D² with S = 69, W = 14 and k = 1, we can write:x² (28 - x)² = 69.The real root of the equation is x = 40 - 39√2, which gives a value of S = 2231 approximately.

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Answer:

15 people

Step-by-step explanation:

We are told that there are 90 males and 75 females.

This question is a greatest common factor question.

We find the factors of 75 and 90

The factors of 75 are: 1, 3, 5, 15, 25, 75

The factors of 90 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

Then the greatest common factor is 15.

The greatest number of people that can be in each group is 15

Speed is regarded as the rate at which a particular distance is traveled over time. 138.92 miles  has charlotte traveled in feet during this time

From the information given:

The speed at which charlotte is driving = 64.3 ml/h

The time which she took of her eyes from the road = 3.36 s

During the entire journey, the time at which she took her eyes off the road, she is probably not driving.

∴We will have to convert the 64.3 mi/h to m/s

Since 1 mi/hr = 0.44704 m/s

64.3 mi/h will be:

= (64.3 mi/hr × 0.44704 m/s) ÷ 1 mi/hr

= 30.39872 m/s

Now, using the relation:

Speed = distance/ time

30.39872 m/s = (distance)  / 3.36 s

By Cross multiplying

Distance = 30.39872 m/s  × 3.36 s

Distance = 138.92 m

in conclusion, Charlotte traveled by feet for 138.92 m during this time

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Answer:

A) 95

B) 1140

Step-by-step explanation:

If you need explanation I will give one

Answer: 13%

Step-by-step explanation:

Step 1:

5000

10% of 5000=500

5% of 5000=250

25%=500+500+250= 1250 rupees

so...

5000-1250= 3750 INR, which is the original price, BEFORE THE 25% WAS ADDED

but..

They only want a 10% discount of the price which is 25% above the cost (5000). So essentially we want to find  15%, because 25%-10%=15%

so if...

10%=500

5%=250

15%=750 INR

this means the price with the 10% discount off 25%= 4250 INR (5000-750)

now we need to find the percentage change. For this we need to subtract the price with the 15% discount with the price BEFORE THE 25% was added

e.g 4250-3750= 500INR

Then.. divide this price with the original price before the 25% was added

e.g 500/3750= 2/15=0.13

So...

Convert 0.13 into a percentage=13%

The PERCENTAGE PROFIT of the owner is 13%

P.S Please could someone double check this answer as I am only 15 years old and may have gotten some working out wrong! Thank you

Answer:

C

Step-by-step explanation:

The reciprocal is always the number flipped over.

E.g. reciprocal of 9 is 1/9 and the reciprocal of 1/9 is 9

Answer:

C. 1/5

Step-by-step explanation:

Answer:

A  8º

B  76º

C  74º

D  128º

Step-by-step explanation:

The sum of the angles is 360

(3x + 10) + (3x + 4) + (x + 50) + (5x + 8) = 360

Combine like terms

12x + 72 = 360

Subtract 72 from both sides

12x = 288

Divide both sides by 12

x = 24

--------------

A (3x+10) = 3*24 + 10 = 82

B (3x+4) = 3*24 + 4 = 76

C (x+50) =  24 + 50 = 74

D (5x+8) = 5*24 + 8 = 128

Answer:

f(-2) = 8

Step-by-step explanation:

Graph y = f(x)

Find value of f(-2)

when f(x) = f(-2)

Here we are looking for the value of y when x = -2

From the graph when x = -2 then y = 8

Therefore, f(-2) = 8

To determine whether there is a decrease in voter support for the candidate after the scandal, we can test the hypothesis using the proportions of the two polls. The first poll showed 54% support among 630 randomly selected voters, while the second poll showed 51% support among 1010 voters. By conducting a hypothesis test, we can determine if the difference in proportions is statistically significant.

To test the hypothesis, we can use the two-sample z-test for proportions. The null hypothesis (H0) assumes no difference in voter support, while the alternative hypothesis (H1) assumes a decrease in support. We can calculate the test statistic using the formula:

z = (p1 - p2) / √[(p(1 - p) / n1) + (p(1 - p) / n2)]

where p1 and p2 are the proportions from the two samples, and n1 and n2 are the respective sample sizes. p is the pooled proportion, calculated as (x1 + x2) / (n1 + n2), where x1 and x2 are the respective number of successes (votes for the candidate) in each sample.

By calculating the z-value, we can compare it to the critical value for the desired significance level (e.g., α = 0.05). If the z-value exceeds the critical value, we reject the null hypothesis in favor of the alternative hypothesis, indicating a statistically significant decrease in voter support.

After performing the calculations, if the z-value exceeds the critical value, we can conclude that there is evidence to support the claim of a decrease in voter support for the candidate after the scandal. Conversely, if the z-value does not exceed the critical value, we fail to reject the null hypothesis, suggesting that there is insufficient evidence to conclude a significant decrease in support.

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Yes, the columns of exra5 do form a basis for r4. A basis is a set of linearly independent vectors that span a vector space, and in this case the vector space is R4. The four columns of exra5 are linearly independent, and they span the entire R4 space, so they form a basis for R4.

Yes, the columns of exra5 do form a basis for r4. A basis is a set of linearly independent vectors that span a vector space, and in this case the vector space is R4. The columns of exra5 must be linearly independent, which means that no linear combination of them can equal the zero vector. Furthermore, the columns of exra5 must span the entire R4 space, meaning that any vector in R4 can be expressed as a linear combination of the columns of exra5. This is equivalent to saying that the columns of exra5 can be used to generate the entire vector space R4. If these two conditions are met, then the columns of exra5 form a basis for R4. In this case, both conditions are met, so the columns of exra5 do form a basis for R4. Moreover, since there are four columns, the basis for R4 is called a basis of size four. The special property of a basis of size four is that it is the smallest possible basis for R4, meaning that no other set of vectors can form a basis for R4 with fewer than four vectors.

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Answer:

The median is 33.5

Step-by-step explanation:

In order to solve for a median it would either be the middle or it would be the average of the middle if there are even amount of numbers. First you would put them in order. 12 17 28 31 36 54 55 and 71. This would mean the the middle number would be 31 and 36. Since you can't have two medians you would find the average of the two so add 31 and 36 which would be equal to 67 then divide by 2 which would equal to 33.5.

The median of numbers 17, 12, 54, 36, 71, 28, 31, 55 is 33.5.

The median of a set of numbers is the middle value when the numbers are arranged in ascending or descending order.

To find the median of the given numbers, we first need to arrange them in ascending order:

12 17 28 31 36 54 55 71

Since there are an even number of numbers (8), the median will be the average of the two middle values, which are 31 and 36.

To find the average, we add the two numbers and divide by 2:

(31 + 36) / 2 = 67 / 2 = 33.5

Therefore, the median of the given numbers is 33.5.

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The outliers in the given data set are 106 and 126. To determine the outliers in a data set, we typically use the concept of the interquartile range (IQR) and the 1.5 IQR rule.

The IQR is the range between the first quartile (Q1) and the third quartile (Q3) of the data set.

First, we need to find the quartiles of the data set. Arranging the data in ascending order, we have:

27, 31, 35, 43, 49, 53, 61, 65, 66, 74, 106, 126

The first quartile, Q1, is the median of the lower half of the data set, which is 43.

The third quartile, Q3, is the median of the upper half of the data set, which is 66.

Next, we calculate the IQR by subtracting Q1 from Q3: IQR = Q3 - Q1 = 66 - 43 = 23.

According to the 1.5 IQR rule, any value that is more than 1.5 times the IQR away from either Q1 or Q3 is considered an outlier. In this case, any value below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR is an outlier.

Calculating the outlier boundaries:

Lower bound = Q1 - 1.5 * IQR = 43 - 1.5 * 23 = 8.5

Upper bound = Q3 + 1.5 * IQR = 66 + 1.5 * 23 = 106.5

From the given data set, the values 106 and 126 are greater than the upper bound, indicating that they are outliers. Therefore, the outliers in the data set are 106 and 126. The correct answer is option d: 106 and 126.

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The area of the segment is 210.25π - 420.5

A segment is an interior region of a circle. It is the space between a chord and an arc.

The area of segment is expressed as;

area of segment = area of sector - area of triangle

The shaded part is a segment.

A sector is a region between two radii and an arc.

Area of triangle = 1/2 × 29 × 29

= 841/2

= 420.5

The area of the sector is given as 210.25

Therefore the area of the segment = 210.25π - 420.5

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Answer: 430,203,663,510?

Step-by-step explanation:

four hundred thirty billion, two hundred three million, six hundred sixty-three thousand five hundred ten, into number form is :

= 430,203,663,510.

Hope this helps?

Answer:

430 ,202 ,663 ,510 this is the answer

Answer:

adjacent interior angle

Step-by-step explanation:

Answer:

\(\frac{2}{9}\)

Step-by-step explanation:

there is a four out of nine change to get a green marble

there is a 1/2 change to get heads

\(\frac{4}{9}\)×\(\frac{1}{2} =\frac{2}{9}\)

Answer:

See below

Step-by-step explanation:

You can always plug in x's and solve for y.

Answer:

Step-by-step explanation:

9 times

6,7,8,9 (4 times starting at 5)

Answer: 1.25

Step-by-step explanation:

you divide/combine 5 and 4 to get Ur anwser 1.25.  Yet it's the same thing as asking ,"How much is 5 divided by 4?" just think of it to yourself as how many times you can fit 4 into 5. One tip you can use is 4(x) = 5 and x will equal 1.25.

Answer:

The answer is below

Step-by-step explanation:

The distance traveled the first day = Distance from San Jose to Santa Barbara = 320 mile.

The distance traveled the second day = Distance from Santa Barbara to Los Angeles.

But From San Jose to Los Angeles = 425 mile. Therefore:

Distance From San Jose to Los Angeles =  Distance from San Jose to Santa Barbara +  Distance from Santa Barbara to Los Angeles

425 = 320 +  Distance from Santa Barbara to Los Angeles.

Distance from Santa Barbara to Los Angeles = 425 - 320 = 105 mile

The distance traveled the second day = Distance from Santa Barbara to Los Angeles = 105 miles

The distance traveled the first day  + The distance traveled the second day = Distance from San Jose to Santa Barbara + Distance from Santa Barbara to Los Angeles = 320 + 105 = 425 miles

The distance traveled the first day  + The distance traveled the second day = 425 miles

Answer:

113 feet

Step-by-step explanation:

I will assume you meant h = -4.9t^2 + 135; "t2" is incorrect.

To answer this question, to find the height of the ball after 2.1 seconds, substitute 2.1 for t in the above equation:

h(2.1) = -4.9(2.1)^2 + 135.  This becomes -21.6 + 135, or 113.4.

The closest result to the height of the ball after 2.1 seconds is 113 feet.

Answer:

Step 4

Explanation:

The initial system of equation is:

5x + 4y = 1

4x + 2y = 8

So, if we take the second equation and isolate y, we get:

y = 4 - 2x

Then, replacing it on the first one, we get:

5x + 4(4 - 2x) = 1

Solving for x, we get:

5x + 4*4 - 4*2x = 1

5x + 16 - 8x = 1

-3x +16 = 1

-3x + 16 - 16 = 1 - 16

-3x = -15

Finally, dividing by -3, we get:

Therefore, the mistake was made in step 4, because he didn't take into account the negative sign. So, the correct answer is x = 5 instead of x = - 5