the sum of two numbers is 31. twice the smallernumber is 11 more than the larger number.ehat is the value of the large number?

Answer:

508.4

Step-by-step explanation:

This is on delta math

Answer:

508.4

Step-by-step explanation:

delta math

Answer:

Let the length of the rectangle be L. Then we can use the formula for the area of a rectangle:

Area = Length x Width

Substituting the given values, we get:

16 1/3 = L x 4 2/3

To solve for L, we can first convert the mixed numbers to improper fractions:

16 1/3 = 49/3

4 2/3 = 14/3

Substituting these values, we get:

49/3 = L x 14/3

To solve for L, we can multiply both sides by the reciprocal of 14/3:

49/3 ÷ 14/3 = L

Simplifying, we get:

L = 49/3 x 3/14

L = 7/1

L = 7

Therefore, the length of the rectangle is 7 inches.

Step-by-step explanation:

Answer: C=2πr

r Radius

Answer:

14:46= 0.3

Step-by-step explanation:

Ratios can be expressed as a decimal, fraction or a math expression as above. (2 weeks is 14 days.)

Navern's manufacturing cycle efficiency (MCE) for its elevators is: 41.4%

The formula for obtaining the manufacturing cycle efficiency is value-added time divided by the production cycle time * 100. In the data given, the process and inspection times qualify as a value-added time

Process time = 23 days

Inspection time = 13 days

Value added time = 23 + 13 = 36days

The production cycle time = Move time + process time + queue time + inspection time + wait time

= 22 + 12 + 23 + 13 + 17 days

= 87 days

So, the manufacturing efficiency time = 36/87 * 100

= 41.4%

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Answer:

A

Step-by-step explanation:

To simplify the expression 3 11 5 ÷ 3 − 9 5, let's break it down step by step:

First, let's simplify the division 3 11 5 ÷ 3:

3 11 5 ÷ 3 = (3 × 115) ÷ 3 = 345 ÷ 3 = 115.

Next, let's subtract 9 5 from the result we obtained:

115 - 9 5 = 115 - (9 × 5) = 115 - 45 = 70.

Therefore, the simplified expression is 70.

The correct answer is A. 70.

From the solution;

x = 62.62°

y = 8.9 cm

The sine rule (also known as the law of sines) is a mathematical formula that relates the sides and angles of a triangle. Specifically, it relates the ratios of the lengths of the sides of a triangle to the sine of the opposite angles.

By the use of the sine rule;

a/Sin A = c/Sin C

Sin C = cSin A/a

C = Sin-1(cSin A/a)

C = Sin-1(7.8 * sin 66.4/9.2)

C = 50.98°

B = 180 - (50.98° + 66.4)

B = 62.62°

Then;

a/Sin A = b/Sin B

9.2/Sin66.4 = b/Sin 62.62

b = 9.2 * Sin 62.62/Sin66.4

b = 9.2 * 0.89/0.92

b = 8.9 cm

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Answer:

The weight of the displaced water is the weight of the body

Step-by-step explanation:

In situations like this, the volume of the displaced water is not important.

However, it should be noted that when a body is immersed (fully or partially) in a liquid, the weight of the displaced liquid is equal to the weight of the body immersed in the liquid.

Since the weight of the body is not given, I'll conclude that the displaced water has the same weight as the body floating on the water.

The right response is C. A has a pivot location in each row if the equation Ax-b has a solution for each b in \(R^n\).

The pivots must be on A's diagonal since A is square. Hence, A is a row that is identical to In. A is hence invertible.

If there is an answer to the equation Ax-b for each b in \(R^n\), then there is an answer to the equation Ax = b for each b. This indicates that A has complete rank since the column space of A is all of \(R^n\).

A must-have n pivot points (one in each row), and the pivots must be on the diagonal of A since A is a square matrix with complete rank.

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The sum of the first 39 terms is 3771 for the given arithmetic sequence.

What is the sum?

The given sequence is an arithmetic sequence with the first term (a1) equal to 2 and the common difference (d) equal to 5. To find the sum of the first 39 terms, we can use the formula:

Sn = (n/2)×(a1 + an)

where Sn is the sum of the first n terms, a1 is the first term, and an is the nth term.

We can find the value of the 39th term using the formula:

an = a1 + (n×-1)d

an = 2 + (39-1)5

an = 2 + 190

an = 192

Therefore, the sum of the first 39 terms is:

Sn = (39/2)×(2 + 192)

Sn = 19.5(194)

Sn = 3771

Rounding to the nearest integer, the sum of the first 39 terms is 3771.

What is an arithmetic sequence?

An arithmetic sequence is a sequence of numbers where each term is equal to the previous term plus a constant difference. This constant difference is called the common difference of the sequence.

For example, the sequence 2, 5, 8, 11, 14, 17, ... is an arithmetic sequence because each term after the first is obtained by adding 3 to the previous term.

The nth term of an arithmetic sequence can be found using the formula:

an = a1 + (n-1)d

where an is the nth term of the sequence, a1 is the first term, n is the term number, and d is the common difference.

The sum of the first n terms of an arithmetic sequence can be found using the formula:

Sn = (n/2)×(a1 + an)

where Sn is the sum of the first n terms, a1 is the first term, and an is the nth term.

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Complete question is:The sum of the first 39 terms is 3771 to the nearest integer 2,7,12..

The sum of the first 39 terms of the given sequence to the nearest integer is 3783.

What is binomial?

Binomial refers to a type of probability distribution that describes the number of successes in a fixed number of independent trials.

To find the sum of the first 39 terms, we need to determine the pattern of the given sequence 2, 7, 12, ...

We can observe that each term in the sequence is obtained by adding 5 more than the previous term. Thus, the sequence can be written as:

2, (2+5), (2+25), (2+35), ...

Generalizing this, the nth term of the sequence can be written as:

2 + (n-1)*5

So, the sum of the first 39 terms of the sequence can be found using the formula for the sum of an arithmetic series:

S = n/2 * (a + l)

where S is the sum of the first n terms, a is the first term, l is the last term, and n is the number of terms.

In this case, a = 2, l = 2 + (39-1)*5 = 192, and n = 39. Substituting these values into the formula, we get:

S = 39/2 * (2 + 192)

S = 39/2 * 194

S = 3783

Rounding this to the nearest integer, we get the final answer:

S ≈ 3783

Therefore, the sum of the first 39 terms of the given sequence to the nearest integer is 3783.

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Answer:

no its not

Step-by-step explanation:

radius doesn't make 90 degree with AB. use Pythagoras theorem

The equation of the line of best fit is: y = (-2/3)x + 26/3

To estimate the line of best fit using two points on the line, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope of the line and b is the y-intercept.

Given the two points (7, 4) and (10, 2), we can calculate the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the coordinates of the points:

m = (2 - 4) / (10 - 7)

m = -2 / 3

Now that we have the slope, we can substitute it into the equation and solve for the y-intercept (b). Let's use the coordinates of one of the points, such as (7, 4):

4 = (-2/3)(7) + b

4 = -14/3 + b

To find the value of b, we can rearrange the equation:

b = 4 + 14/3

b = 12/3 + 14/3

b = 26/3

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Answer:

A

Step-by-step explanation:

So we know that the point-slope form of the line that passes through the points (-4,-3) and (12,1) is:

\(y-1=\frac{1}{4}(x-12)\)

And we want to convert this to standard form.

The standard form of a linear equation is:

\(Ax+By=C\)

Where A, B, and C are integers, and, traditionally, A is positive.

So, first, multiply everything by 4 to remove the negative:

\(4(y-1)=4(\frac{1}{4}(x-12))\)

Distribute the left. The right cancels:

\(4y-4=x-12\)

Add 4 to both sides. The left cancels:

\(4y=x-8\)

Subtract x from both sides:

\(-x+4y=-8\)

As I mentioned previously, the coefficient of A tends to be positive. So, divide everything by -1:

\((-x+4y)/-1=(-8)/-1\)

Simplify:

\(x-4y=8\)

So, our answer is A

And we're done!

Answer:

what do u need help with?

Step-by-step explanation:

From Pythagoras theorem,

(Hypotenuse) ²=(Base)²+(Height/Perpendicular)²

b²=(11²-3²) units²

b= √(121-9)[units²].

b= √(112) unit

b=10.58 unit.

hope this helps you.

Answer:

?

Step-by-step explanation

my 4th person to ask a question

Answer

-15

Step-by-step explanation: your welcome

The solution of the system of linear equations, is (1.167, 3.667).

Given that the system of linear equations, y = -2x+6 and y = 4x - 1, we need to find the solution for the same,

y = -2x+6............(i)

y = 4x - 1.......(ii)

Equating the equations since the LHS is same,

-2x+6 = 4x-1

6x = 7

x = 1.167

Put x = 1.16 to find the value of y,

y = 4(1.16)-1

y = 4.66-1

y = 3.667

Therefore, the solution of the system of linear equations, is (1.167, 3.667).

You can also find the solution using the graphical method,

Plot the equations in the graph, the point of the intersection of both the lines will be the solution of the system of linear equations, [attached]

Hence, the solution of the system of linear equations, is (1.167, 3.667).

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Given equation of the Circle is ,

\(\sf\implies x^2 + y^2 = 25 \)

And we need to tell that whether the point (-4,2) lies inside or outside the circle. On converting the equation into Standard form and determinimg the centre of the circle as ,

\(\sf\implies (x-0)^2 +( y-0)^2 = 5 ^2\)

Here we can say that ,

• Radius = 5 units

• Centre = (0,0)

Finding distance between the two points :-

\(\sf\implies Distance = \sqrt{ (0+4)^2+(2-0)^2} \\\\\sf\implies Distance = \sqrt{ 16 + 4 } \\\\\sf\implies Distance =\sqrt{20}\\\\\sf\implies\red{ Distance = 4.47 }\)

Hence the point lies within the circle .

Answer:

inside the circle

Step-by-step explanation:

The equation of a circle centred at the origin is

x² + y² = r² ( r is the radius )

x² + y² = 25 ← is in this form

with r = \(\sqrt{25\) = 5

Calculate the distance d from the centre to the point (- 4, 2 ) using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (- 4, 2)

d= \(\sqrt{(-4-0)^2+(2-0)^2}\)

   = \(\sqrt{(-4)^2+2^2}\)

   = \(\sqrt{16+4}\)

    = \(\sqrt{20}\)

    ≈ 4.5 ( to 1 dec. place )

Since 4.5 is less than the radius of 5

Then (- 4, 2 ) lies inside the circle

The population of North Carolina will reach 12 million in the year 2028.

Population growth is defined as the increase in the number of people which is calculated using population growth rate.

Given that,

Population in 2010 = 9.5 million

Population is increasing to 1.3% per year.

Annual growth rate = 1.3% = 1.3/100 = 0.013

We have the population growth formula,

P = P₀ e^(r t)

Here, P₀ = 9.5 million = 9,500,000

and P = 12 million = 12,000,000

r = 0.013

We have to find t.

12,000,000 = 9,500,000 e^(0.013t)

120 / 95 = e^(0.013t)

Taking natural logarithm on both sides and also ㏑(e^m) = m ㏑ e, we get,

㏑(12/9.5) = 0.013t × ㏑e

[㏑(12/9.5) ÷ 0.013] = t  [since ln e = 1]

t = 17.97 ≈ 18 years

The year is 2010 + 18 = 2028

Hence in the year 2028, the population will be 12 million.

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Answer:

600,000,000,000,000

Step-by-step explanation:

14 zeros after the 6 because you make 6 a whole number with one of them.

Answer:

mean=10*1/2=5

variance=10*1/2*1/2=2.5

standard deviation=sqrt2.5=1.58

Step-by-step explanation: Hope this helps Have a good day :)

Answer:

\(P(X\geq 1)= 1 - 0.0497 8 =0.95022\)            

Step-by-step explanation:

Step(i):-

Let 'X' be the random variable in Poisson distribution

Mean of the Poisson distribution λ or ∝ = 3 per  (cm³)

Given n = 5 samples

\(P(X=r) = \frac{e^{-\alpha }\alpha ^{r} }{r!}\)

Step(ii):-

The probability that at least one sample will contain one or more bacterial colonies

P(X≥1)    = 1-P(X< 1)

             = 1 - P( X=0)

\(P(X\geq 1)= 1 - \frac{e^{-\alpha }\alpha ^{r} }{r!}\)

\(P(X\geq 1)= 1 - \frac{e^{-3 }3 ^{0} }{0!}\)

\(P(X\geq 1)= 1 - 0.0497 8 =0.95022\)            

Answer:PLEASE HELP ME

Step-by-step explanation:

here can you guys please help me with this question.

I have been asking help from so many people but no one is nice enough to give it so im hoping that anyone over here can help me. this is the problem

Carl is standing at the base of a zip line which is 400 ft away from the base of the building that is connected to the top of a building. Standing 5.5 ft tall, he looks up to the top of the building at an angle of elevation of 25 degrees. A weight is released and travels down the zip line to his feet. How far did the weight travel? Round to nearest 10th of a foot and do not use units in your answer.

Please show work

(A) Triangle ABC, and triangle QPR are similar based on side-side-side (SSS) similarity.

(B) Triangle ABC and triangle DEF are similar based on side-side-side (SSS) similarity.

(C) ) Triangle STU and triangle JPM are similar based on side-angle-side (SAS) similarity.

(D) ) Triangle SMK and triangle QTR are similar based on angle-angle (AA) similarity.

Similar triangles have the same corresponding angle measures and proportional side lengths.

The triangle similarity criteria are:

(A) Triangle ABC, and triangle QPR are similar based on side-side-side similarity.

12/8 = 9/6

1.5 = 1.5

(B) Triangle ABC and triangle DEF are similar base on side-side-side similarity as shown in the side lengths.

(C) ) Triangle STU and triangle JPM are similar base on side-angle-side similarity.

14/10 = 21/15

1.4 =

(D) ) Triangle SMK and triangle QTR are similar base on angle-angle similarity.

SMK = 90⁰, 60⁰, 30⁰

QTR =  90⁰, 30⁰, 60⁰

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Expression for given numerical is: 9+ (2/x)

Given that we have an word equation that is 9 more than the quotient of 2 and  x

A quotient is a quantity produced by the division of two numbers.

Quotient of 2 and x is \(\frac{2}{x}\).

Nine(9) more  than 2/x is = 9+ (2/x)

So we have an expression that is:

              9+ (2/x)                          

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Answer:

30 so this math is hard

Step-by-step explanation:

1$$$118*+,>

The slope of the curve at the given point is approximately -28

What is the derivative of a function?

Geometrically, the derivative of a function can be interpreted as the slope of the graph of the function or, more precisely, as the slope of the tangent line at a point. Its calculation, in fact, derives from the slope formula for a straight line, except that a limiting process must be used for curves.

To find the derivative of y with respect to x using implicit differentiation, we need to take the derivative of both sides of the equation cos(y) = 7x^4 - 7.

On the left side of the equation, we can use the chain rule to find the derivative of cos(y) with respect to x:

d/dx[cos(y)] = -sin(y) * dy/dx

On the right side of the equation, we can use the power rule to find the derivative of 7x^4 - 7 with respect to x:

\(d/dx[7x^4 - 7] = 28x^3\)

Substituting these expressions into the original equation, we get:

\(-sin(y) * dy/dx = 28x^3\)

To solve for dy/dx, we can divide both sides of the equation by -sin(y):

\(dy/dx = -(28x^3)/sin(y)\)

To find the slope of the curve at the given point, we need to substitute the values of x and y into the expression for dy/dx.

The slope at (1, π/2). would be

slope = -(28((1)^3))/sin(π/2) = -28.

Hence, the slope of the curve at the given point is approximately -28.

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Answer:

(x - 5)² -121 = 0

Step-by-step explanation:

if you need to find the roots you can take the square root of each side:

(x-5)² = 121

(x-5)² = 121

square root of (x-5)² is x-5

square root of 121 is ±11

first root:  x-5 = 11

x = 16

second root: x-5 = -11

x = -6

Answer:

\(f(x) = (x - 5)^{2} - 121\).

Step-by-step explanation:

The goal is to rewrite \(f(x)\) in the vertex form \(a\, (x - h)^{2} + k\) by completing the square (where \(a\), \(h\), and \(k\) are constants.)

Expand the vertex form expression:

\(\begin{aligned}& a\, (x - h)^{2} + k\\ &= a\, (x - h)\, (x - h) + k \\ &= a\, \left(x^2 - h\, x - h\, x + h^2\right) + k \\ &= a\, \left(x^2 - 2\, h\, x + h^2\right) + k\\ &= a\, x^2 - 2\, a\, h\, x + \left(a\, h^2 + k\right) \end{aligned}\).

Compare this expression to \(f(x) = x^2 - 10\, x - 96\) and solve for the constants \(a\), \(h\), and \(k\). Make sure that the coefficient of each term matches:

Substitute \(a = 1\) into the second equation, \(-2\, a\, h = -10\), and solve for \(h\).

\(-2 \, h = -10\).

\(h = 5\).

Substitute both \(a = 1\) and \(h = 5\) into the third equation, \(a\, h^{2} + k = -96\), and solve for \(k\).

\(5^2 + k = -96\).

\(k = -121\).

Therefore, \(a\, (x - h)^{2} + k\) becomes \((x - 5)^2 + (-121)\).

Hence, the vertex form of the parabola \(f(x)\) would be:

\(f(x) = (x - 5)^{2} - 121\).