Can someone help me plz

The prime factors or the prime numbers whose product is 51 are 3 and 17.

What is the operation of prime numbers?

The operation of prime numbers refers to the various mathematical operations that can be performed using prime numbers. Prime numbers are positive integers that have exactly two divisors, 1 and the number itself. Some of the important operations involving prime numbers include:

Now,

If you meant to ask for the prime factors of 51, then they are 3 and 17.

because 51 is divisible by 3 because 5+1=6

and after dividing 51/3=17 which is also a prime number.

Hence,

            the prime factors of 51 are 3 and 17.

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Explanation

Step 1

bisectro is s the line or line segment that divides the angle into two equal parts,so

Step 2

angle XYZ

I hope this helps you

Answer:

5x^2 + 17xy - 12y^2

5x^2 + 5xy + 12xy - 12y^2

5x (x - y ) + 12 y ( x - y )

(5x + 12y ) (x-y).

Step-by-step explanation:

Answer:

x = 3 + sqrt(e^3 + 9)

Step-by-step explanation:

Solve for x over the real numbers:

log(x) + log(x - 6) = 3

Hint: | Combine logarithms.

log(x - 6) + log(x) = log(x (x - 6)):

log(x (x - 6)) = 3

Hint: | Eliminate the logarithm from the left hand side.

Cancel logarithms by taking exp of both sides:

x (x - 6) = e^3

Hint: | Write the quadratic polynomial on the left hand side in standard form.

Expand out terms of the left hand side:

x^2 - 6 x = e^3

Hint: | Take one half of the coefficient of x and square it, then add it to both sides.

Add 9 to both sides:

x^2 - 6 x + 9 = e^3 + 9

Hint: | Factor the left hand side.

Write the left hand side as a square:

(x - 3)^2 = e^3 + 9

Hint: | Eliminate the exponent on the left hand side.

Take the square root of both sides:

x - 3 = sqrt(e^3 + 9) or x - 3 = -sqrt(e^3 + 9)

Hint: | Look at the first equation: Solve for x.

Add 3 to both sides:

x = 3 + sqrt(e^3 + 9) or x - 3 = -sqrt(e^3 + 9)

Hint: | Look at the second equation: Solve for x.

Add 3 to both sides:

x = 3 + sqrt(e^3 + 9) or x = 3 - sqrt(e^3 + 9)

Hint: | Now test that these solutions are correct by substituting into the original equation.

Check the solution x = 3 - sqrt(e^3 + 9).

log(x) + log(x - 6) ⇒ log((3 - sqrt(e^3 + 9)) - 6) + log(3 - sqrt(e^3 + 9)) = 2 i π + 3 ≈ 3 + 6.28319 i:

So this solution is incorrect

Hint: | Check the solution x = 3 + sqrt(e^3 + 9).

log(x) + log(x - 6) ⇒ log(3 + sqrt(e^3 + 9)) + log((3 + sqrt(e^3 + 9)) - 6) = 3:

So this solution is correct

Hint: | Gather any correct solutions.

The solution is:

Answer: x = 3 + sqrt(e^3 + 9)

9514 1404 393

Answer:

  x = 3 + √1009 ≈ 34.765

Step-by-step explanation:

Take the antilog and solve the resulting quadratic.

  x(x -6) = 10^3

  x^2 -6x +9 = 1009 . . . . . . add (-6/2)^2 to complete the square

  (x -3)^2 = 1009 . . . . . . . . . write as a square

  x = 3 + √1009 ≈ 34.765 . . . . . square root and add 3

__

Only the positive root makes any sense, since the log of a negative number is not defined (in real numbers).

__

For the graph, we subtracted 3 so we are looking for the x-intercept where f(x)=0.

Answer: 3/10 times 5 equals 15/50

Step-by-step explanation: First you do 3 times 5 which equals 15 and then 10 times 5 to get 50, which together make 15/50 and to make sure it's right check it by finding the greatest common factor they both have.

Answer:

5/5

Step-by-step explanation:

3 will enter 15, 5 times

n 10 will enter 50, 5 times

The first physical coordinate y1 can be expressed as y1 = [1 0 0]Y, & The mass-normalised mode shapes can be  normalising the mode shape vectors f1, f2, and f3.

Part (a)

In Equation Q2, the spectral matrix, undamped natural frequencies, damping ratios, and fundamental frequency need to be calculated.

The mass matrix is given by [85.16400 083.3770 0046.999; 0.079400 00.7030 001.07 × 10; 0.013600 03.1390 005.124 × 10].

The stiffness matrix is given by [0.16400 00.3770 000.999; 0.079400 00.7030 001.07 × 10; 0.013600 03.1390 005.124 × 10].

The damping matrix is given by [0 0 0; 0 0 0; 0 0 0].The undamped natural frequencies, damping ratios, and fundamental frequency for the system in Equation Q2 can be calculated from the spectral matrix.

The characteristic equation can be written as det(K-mω^2M)=0.where K is the stiffness matrix, M is the mass matrix, ω is the angular frequency, and m is the mass-normalised mode shape.

The roots of this equation are the undamped natural frequencies, and the damping ratios can be calculated from the undamped natural frequencies and mode shapes.

The mass-normalised mode shapes can be calculated by normalising the mode shape vectors f1, f2, and f3.

Part (b)

The mass-normalised mode shapes can be calculated using the mode shape vectors f1, f2, and f3.Part (c)The response of the system for the first physical coordinate y1 can be calculated using the mode superposition method. The initial modal displacements and velocities are given in terms of the modal coordinates.

The response is then calculated using the equation y(t)= Σ ai φi(t), where ai are the modal amplitudes, and φi(t) are the modal shapes given by the mode shape vectors f1, f2, and f3.

The first physical coordinate y1 can be expressed as y1 = [1 0 0]Y, where Y is the vector of physical coordinates. The modal amplitudes can be calculated from the initial modal displacements and velocities.

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its lonmg.answer

Step-by-step explanation:

To keep the cost per banana the same, the total cost must remain constant as the number of bananas changes. Therefore, for 4 bananas, the cost is $2, for 6 bananas, the cost is $3, for 7 bananas, the cost is $3.50, and for 10 bananas, the cost is $5.

To keep the cost per banana constant, we need to maintain the ratio of the total cost to the total number of bananas. In other words, the unit price (cost per banana) must remain the same regardless of the number of bananas purchased.

To fill out the table, we can use the formula:

Total cost = unit price × number of bananas

For example, for 4 bananas at a cost of $0.50 per banana, the total cost is:

Total cost = $0.50 × 4 = $2.00

To maintain the same cost per banana for 6 bananas, we need to adjust the unit price so that the total cost is the same as for 4 bananas:

Total cost = $2.00 = unit price × 6

Solving for the unit price, we get:

unit price = $2.00 ÷ 6 = $0.3333 ≈ $0.33 (rounded to two decimal places)

Similarly, for 7 bananas, the unit price must be adjusted so that the total cost is $2.00:

Total cost = $2.00 = unit price × 7

unit price = $2.00 ÷ 7 ≈ $0.29

For 10 bananas, the unit price must also be adjusted to maintain the same cost per banana:

Total cost = $2.00 = unit price × 10

unit price = $2.00 ÷ 10 = $0.20

Finally, for 16.5 bananas, we can use the same formula:

Total cost = $2.00 = unit price × 16.5

unit price = $2.00 ÷ 16.5 ≈ $0.12

Thus, we can fill out the table as follows:

number of bananas cost in dollars

unit price

(dollars per banana)

4 $

$0.50

6 $

$0.33

7 $

$0.29

10 $

$0.20

16.5 $

$0.12

So, we can see that by adjusting the unit price, we can maintain a constant cost per banana for different quantities of bananas.

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Answer:

5. The sum of angles in a triangle is 180° so we can write:

9x - 16 + 3x + 11 + 7x - 5 = 180

19x - 10 = 180

19x = 190

x = 10°

6. Because the measure of an exterior angle is equal to the sum of its two remote interior angles we can write:

17x - 23 = 3x + 17 + 8x - 4

17x - 23  = 11x + 13

6x = 36

x = 6°

Answer:

5. The sum of angles in a triangle is 180° so we can write:

9x - 16 + 3x + 11 + 7x - 5 = 180

19x - 10 = 180

19x = 190

x = 10°

6. Because the measure of an exterior angle is equal to the sum of its two remote interior angles we can write:

17x - 23 = 3x + 17 + 8x - 4

17x - 23  = 11x + 13

6x = 36

x = 6°

Step-by-step explanation:

hope this helps

Answer:

2/3 of 2 is 1.33

Step-by-step explanation:

this because 2/3 times 2 is 1.33

Answer:

4/3

Step-by-step explanation:

2/3 of 2 is basically multiplying 2/3*2/1.

Therefore it's (2*2)/(3*1) which is 4/3.

Answer:

bilang Ng bahagi tatlong bahagi

The Einstein tensor Gμν is given by Gμν = 1/κ (Tμν - (1/2)gμνT), where κ is the gravitational constant, Tμν is the energy-momentum tensor, and gμν is the metric tensor

We have,

To derive the expression for the Einstein tensor

Gμν = 1/κ (Tμν - (1/2)gμνT),

We can follow these steps:

Step 1:

Start with the Einstein field equations, which relate the curvature of spacetime (given by the Einstein tensor Gμν) to the distribution of matter and energy (represented by the energy-momentum tensor Tμν) in general relativity.

Step 2:

Write down the Einstein field equations in covariant form:

Gμν = κTμν

where κ is the gravitational constant.

Step 3:

Express the Einstein tensor Gμν in terms of the metric tensor gμν and its derivatives.

The Einstein tensor is a contraction of the Riemann curvature tensor, which can be expressed in terms of the metric tensor and its derivatives.

Gμν = Rμν - (1/2)gμνR

where Rμν is the Ricci curvature tensor and R is the Ricci scalar.

Step 4:

Replace the Ricci curvature tensor Rμν and the Ricci scalar R in terms of the metric tensor gμν and its derivatives using the contracted Bianchi identities and the Einstein field equations.

Gμν = Rμν - (1/2)gμνR = Rμν - (1/2)gμν(gλσRλσ)

Step 5:

Rearrange the equation to isolate the Einstein tensor Gμν on one side:

Gμν + (1/2)gμν(gλσRλσ) = Rμν

Step 6:

Multiply both sides of the equation by (2/κ) to obtain:

(2/κ)Gμν + (1/κ)gμν(gλσRλσ) = (2/κ)Rμν

Step 7:

The term (2/κ)Rμν on the right-hand side can be recognized as (2/κ)Tμν, where Tμν is the energy-momentum tensor divided by the speed of light squared.

Step 8:

Finally, rewrite the equation in the desired form:

Gμν = (1/κ)(Tμν - (1/2)gμνT)

This is the derived expression for the Einstein tensor Gμν in terms of the energy-momentum tensor Tμν and the metric tensor gμν.

Thus,

The Einstein tensor Gμν is given by Gμν = 1/κ (Tμν - (1/2)gμνT), where κ is the gravitational constant, Tμν is the energy-momentum tensor, and gμν is the metric tensor

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The complete question:

"Show that the Einstein tensor Gμν is given by Gμν = 1/κ (Tμν - (1/2)gμνT), where κ is the gravitational constant, Tμν is the energy-momentum tensor, gμν is the metric tensor, and Gμν is the Einstein tensor. Provide a step-by-step explanation of the derivation."

Answer:

The correct answer should be 11\(\frac{1\\}{4}\)

Step-by-step explanation:

Let me know if this is wrong and I will correct it if it is.

Answer:

42.18

Step-by-step explanation:

Hope this helps and I hope you have a wonderful rest of your day!!! :)

BRAINIEST is appreciated it would really help me

Answer:

Each lap is 1.25 miles, so multiply the number of laps with 1.25 to get your answer.

Step-by-step explanation:

1 lap = 1.25 miles

2 laps = 2.5 miles

3 laps = 3.75 miles

4 laps = 5 miles

5 laps = 6.25 miles

6 laps = 7.5 miles

7 laps = 8.75 miles

8 laps = 10 miles

9 laps = 11.25 miles

10 laps = 12.5 miles

Answer:

.............,...........,.......................... ans is b

The trapezoidal rule is a numerical integration method that uses trapezoids to estimate the area under a curve. The trapezoidal rule can be used for both definite and indefinite integrals. The trapezoidal rule approximation, Tn, to the integral sin r dz is given by:

Tn = (b-a)/2n[f(a) + 2f(a+h) + 2f(a+2h) + ... + 2f(b-h) + f(b)]where h = (b-a)/n. To determine how large n should be so that Tn is accurate to within 0.00001, we can use the error bound given in Section 5.9 of the course text. According to the error bound, the error, E, in the trapezoidal rule approximation is given by:E ≤ ((b-a)³/12n²)max|f''(x)|where f''(x) is the second derivative of f(x). For the integral sin r dz, the second derivative is f''(r) = -sin r. Since the absolute value of sin r is less than or equal to 1, we have:max|f''(r)| = 1.

Substituting this value into the error bound equation gives:E ≤ ((b-a)³/12n²)So we want to choose n so that E ≤ 0.00001. Substituting E and the given values into the inequality gives:((b-a)³/12n²) ≤ 0.00001Simplifying this expression gives:n² ≥ ((b-a)³/(0.00001)(12))n² ≥ (b-a)³/0.00012n ≥ √(b-a)³/0.00012Now we just need to substitute the values of a and b into this expression. Since we don't know the upper limit of integration, we can use the fact that sin r is bounded by -1 and 1 to get an upper bound for the integral.

For example, we could use the interval [0, pi/2], which contains one full period of sin r. Then we have:a = 0b = pi/2Plugging in these values gives:n ≥ √(pi/2)³/0.00012n ≥ 5073.31Since n must be an integer, we round up to the nearest integer to get:n = 5074Therefore, we should choose n to be 5074 so that the trapezoidal rule approximation, Tn, to the integral sin r dz is accurate to within 0.00001.

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In this case, we can assume that each nucleotide has an equal chance of occurring at any position in the sequence. Therefore, the probability of two nucleotides from the two sequences matching at a specific position by chance is 1/4 (since there are four possible nucleotides: A, T, C, and G).

Since the length of each sequence is 100 nucleotides, the expected number of matching positions by chance can be calculated by multiplying the length of the sequences by the probability of a match at each position.

Expected number of matching positions = Length of sequences * Probability of match at each position

Expected number of matching positions = 100 * (1/4)

Expected number of matching positions = 25

Therefore, by chance, the two random sequences are expected to match at approximately 25 positions.

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Answer:

2

Step-by-step explanation:

Let's solve the given system of equations.

Given system

x +3y= 10 ----(1)

-2x -2y= 4 ----(2)

From (2):

-2(x +y)= 4

Dividing both sides by -2:

x +y= -2 ----(2)

Thus, options 3 and 4 are incorrect as x +y≠ -2.

(1) -(2):

(x +3y) -(x +y)= 10 -(-2)

Expand:

x +3y -x -y= 10 +2

2y= 12

Divide both sides by 2:

y= 12 ÷2

y= 6

Substitute y= 6 into (2):

x +6= -2

x= -6 -2

x= -8

Options (1) and (2) differs only by the value of the expression of -x +y. Thus, let's find its value in the given system of equations.

-x +y

= -(-8) +6

= 8 +6

= 14

Thus, option 2 is the correct option.

Answer:

8

Step-by-step explanation:

1/2 of 48 marbles is 24

1/3 of 24 is 8

hope this helps

Answer:

500 + (100 x 5) = 1000

Step-by-step explanation:

The compound will reach 90°C approximately 112.5 minutes after 9:00 a.m., considering the constant rate of temperature increase per minute.

To determine the time when the compound will reach 90°C, we need to find the rate of temperature increase per minute and calculate the number of minutes required to reach 90°C.

From the given information, we know that the compound's temperature increases by the same number of degrees every minute. The temperature change from 10°C to 22°C took 15 minutes (from 9:00 a.m. to 9:15 a.m.).

To find the rate of temperature increase per minute, we divide the temperature change by the number of minutes:

Rate of temperature increase = (Final temperature - Initial temperature) / Time

Rate of temperature increase = (22°C - 10°C) / 15 minutes = 12°C / 15 minutes

Next, we need to determine how many minutes are required for the compound to reach 90°C. We can set up a proportion to solve for the unknown time:

12°C / 15 minutes = 90°C / x minutes

Solving the proportion, we find:

12°C * x minutes = 15 minutes * 90°C

x = (15 minutes * 90°C) / 12°C

x = 112.5 minutes

Therefore, the compound will reach 90°C approximately 112.5 minutes after 9:00 a.m.

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Answer:

76⁰ is the answer to the top one

Answer:

wass the problem use the calc

Step-by-step explanation:

the 2nd function is ur bestie

Answer:

9/30

Step-by-step explanation:

The metric unit that you would probably use to measure the length of a computer keyboard is centimeters (cm). A keyboard is measured in length from one end to the other, and it is easier to measure it in centimeters.Centimeters (cm) is a metric unit of length, and it is a smaller unit of measurement compared to meters (m).

A standard computer keyboard ranges from about 43 to 53 cm in length, so centimeters are a more appropriate unit for measuring its length than meters or kilometers. You could also use millimeters (mm) to measure the length of the keyboard, but this would be a less practical unit as it would give a very large number.A meter stick or a tape measure can be used to measure the length of the keyboard in centimeters.

To ensure accurate measurement, you should measure from one end of the keyboard to the other while making sure to keep the measuring instrument straight. You should also measure the keyboard along its longest dimension, which is usually from left to right.

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The least accurate measurement among the options provided is 18050 m.Therefore, among the given options, 18050 m is the least accurate measurement due to its higher number of significant figures.

To determine the least accurate measurement, we need to consider the number of significant figures in each measurement. The measurement with the fewest significant figures indicates lower accuracy.

Among the options given:

a. 208 m has three significant figures.

b. 18050 m has five significant figures.

c. 0.08 m has two significant figures.

d. 0.750 m has three significant figures.

e. 12.0 m has three significant figures.

The measurement with the least accurate value is 18050 m because it has the highest number of significant figures among the options. A higher number of significant figures suggests a greater level of precision and accuracy in the measurement.

Significant figures represent the digits in a number that contribute to its precision. They include all the non-zero digits and any zeros that appear between non-zero digits or after a decimal point. In this case, the measurement 18050 m has five significant figures, indicating a high level of precision and accuracy.

On the other hand, measurements with fewer significant figures imply less precision and accuracy. For example, the measurement 0.08 m has only two significant figures, suggesting less certainty in the measurement compared to 18050 m.

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Answer:

7 times.

Step-by-step explanation:

Divide 140/20.

You can use a calculator if you want.

140/20 = 7.

To check multiply 20 by 7.

20x7 = 140.

Hope this Helps!

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Answer:

\( \huge{ \boxed{ \bold{ \text{7x + 9}}}}\)

Step-by-step explanation:

\( \text{5x + 4 + 2x + 5}\)

\( \text{Combine \: like \: terms} : \)

\( \text{Like \: terms \: are \: those \: which \: have \: the \: same \: base.}\)

\( ➝ \: \text{5x + 2x + 4 + 5}\)

➝ \( \text{ 7x + 4 + 5}\)

\( \text{Add \: the \: numbers : 4 \: and \: 5}\)

\( ➝ \: \text{7x + 9}\)

\( \text{Hope \: I \: helped}\)!

\( \text{Best \: regards}\)!

~\( \mathfrak{TheAnimeGirl}\)

Answer:

7x + 9

Step-by-step explanation:

Combine like terms, means put the ones that have something in common together; in this case they are the terms with an 'x' value, and a regular numeric value.

5x+2x = 7x

5+4 = 9

therefore:

7x+9  

(a)The appropriate hypothesis test at the 0.01 significance level t-value (2.82) does not exceed the critical t-value (±3.250)

(b) A Type-1 error would occur if we rejected the null hypothesis .

(a) To conduct the appropriate hypothesis test, we can set up the following hypotheses

Null hypothesis (H₀): The mean DBP of diabetic women is equal to the mean DBP of the general public (μ = 76 mmHg).

Alternative hypothesis (H₁): The mean DBP of diabetic women is not equal to the mean DBP of the general public (μ ≠ 76 mmHg).

We can use a t-test since the population mean and standard deviation are unknown, and the sample size is relatively small (n = 10). We will compare the sample mean (85 mmHg) with the hypothesized population mean (76 mmHg) using the t-distribution.

The test statistic is calculated as follows

t = (sample mean - hypothesized mean) / (sample standard deviation / √(sample size))

t = (85 - 76) / (10 / √(10))

t ≈ 2.82

We can find the critical t-value for a two-tailed test with a significance level of 0.01 and degrees of freedom (df) equal to n - 1 (10 - 1 = 9). The critical t-value is approximately ± 3.250.

Since the calculated t-value (2.82) does not exceed the critical t-value (±3.250), we fail to reject the null hypothesis. There is not enough evidence to conclude that the mean DBP of diabetic women is different from the mean DBP of the general public at the 0.01 significance level.

b. In this example, a Type-1 error would occur if we rejected the null hypothesis (stated that the mean DBP of diabetic women is different from the mean DBP of the general public) when it is actually true. In other words, we would conclude a significant difference when there is no real difference in the population means.

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