Which equation is true?

Answer:

Step-by-step explanation:

The slopes of both those lines are the same so there is no solution. Use slope triangles to find out the slope. They are both 1/4.

A. No solution

y = 1/4x+5

x - 4y = 4

You can simplify the second equation into y = 1/4x - 1

Since these equations both have the same slope, they are parallel. When two lines are parallel, they have no solutions.

Answer:

Meaning: If the company sells -2 shirt, they would make a profit of -66 dollars. This interpretation of loss in the context of the problem.

Meaning: If the company sells 6- shirt, they would make a profit of -2 dollars. This interpretation of loss in the context of the problem.

Meaning: If the company sells 9.5shirt, they would make a profit of 26 dollars. This interpretation of profit in the context of the problem.

R(all real numbers)

Step-by-step explanation:

We are given that the profit in dollars when the company sells x shirt is given by

f(x)=8x-50

Substitute x=-2

\(f(-2)=8(-2)-50=-66\)

Meaning: If the company sells -2 shirt, they would make a profit of -66 dollars. This interpretation of loss in the context of the problem.

f(6)=8(6)-50=-2

Meaning: If the company sells 6- shirt, they would make a profit of -2 dollars. This interpretation of loss in the context of the problem.

f(9.5)=8(9.5)-50=26

Meaning: If the company sells 9.5shirt, they would make a profit of 26 dollars. This interpretation of profit in the context of the problem.

The given function is linear function. Therefore, the domain of the function is R(all real numbers).

Answer:

srry i wish i could help but i cant

Step-by-step explanation:

Answer:

84

Step-by-step explanation:

Surface area is the combined area of the 2 dimensional planes.

6 × 5 + 3 × 4 × 1/2 × 2 + 6 × 3 + 4 × 6

30 + 12 + 18 + 24

= 84

The surface area is 84 square centimeters.

The exponential growth formula for bacteria growth is P(t) = 8600 \((2)^(t/5)\).

What is exponential growth?

     Exponential growth is a pattern of data that exhibits a greater increase over time, resulting in an exponential curve. Exponential is also a mathematical term meaning "with exponents". For example, if you raise a number to the 10th power, the number increases exponentially. Exponential growth is growth that increases at a constant rate.

Here given take Initial number of bacteria = 8600. rate of growth = 2.

It doubles every year. Then doubling time = 5 hours.

Now population growth after t years,

P(t) = Po \((2)^(t/5)\)

=> P(t) = 8600 \((2)^(t/5)\)

Therefore exponential growth formula is P(t) = 8600 \((2)^(t/5)\).

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The 90% confidence interval for the mean length of stay for patients with abdominal surgery is [5.64, 5.86].

The formula for the confidence interval is given by: \($CI=\bar{X}\pm Z_{\alpha/2} \times \frac{S}{\sqrt{n}}$\)

Given data:Sample size, n = 2121,Sample mean, \($\bar{X}$\) = 5.75,Sample standard deviation, S = 1.11 Confidence interval, CI = 90%

Now, we need to find the value of Zα/2 from the Z-table.

The value of α/2 is given by 1-90/100 = 0.1.

Therefore, α/2 = 0.05.From the Z-table, we can find the Z-value corresponding to 0.05, which is 1.645.

Substituting all these values in the formula, we get:\(\[\begin{aligned}CI&=\bar{X}\pm Z_{\alpha/2} \times \frac{S}{\sqrt{n}}\\&=5.75\pm 1.645 \times \frac{1.11}{\sqrt{2121}}\\&=5.75\pm 0.106\\&=[5.64, 5.86]\end{aligned}\]\)

Therefore, the 90% confidence interval for the mean length of stay for patients with abdominal surgery is [5.64, 5.86].

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y = - 8

I hope this helps!

Step-by-step explanation:

by subtracting 2 from both sides we get

Significant figures with representation of x are a) 14.8 m = 14.x m. b) $10.25 = 10.2x. c) 0.05 L = 0.0x L. d) 1.000 g/mL = 1.00x g/mL. e)  6200cm = 6200x cm. f)  403 kg = 40x kg.

a) 14.8m has 3 significant figures. Representation with x in place of estimated digit: 14.x m. b) $10.25 has 4 significant figures. Representation with x in place of estimated digit: 10.2x. c) 0.05 L has 1 significant figure. Representation with x in place of estimated digit: 0.0x L. d) 1.000 g/mL has 4 significant figures. Representation with x in place of estimated digit: 1.00x g/mL. e) 6200cm has 2 significant figures. Representation with x in place of estimated digit: 6200x cm. f) 403 kg has 3 significant figures. Representation with x in place of estimated digit: 40x kg. Significant figures are the digits in a measurement that are reliable and accurate. They provide an indication of the precision of a measurement, and allow us to communicate the level of certainty we have in a particular value. When determining the number of significant figures in a measurement, we typically follow a set of rules. Non-zero digits are always significant, zeros between non-zero digits are significant, and trailing zeros to the right of the decimal point are significant. Zeros at the beginning of a number or to the left of a non-zero digit are not significant. The use of significant figures is important in science and engineering to ensure accurate and reliable measurements. When performing calculations with measurements, the result should be reported with the same number of significant figures as the least precise measurement used in the calculation. In addition, when rounding a number, the last digit should be rounded to the nearest value consistent with the number of significant figures being used. Understanding significant figures is an important part of scientific and mathematical communication, and can help to ensure accuracy and consistency in the reporting of data and calculations.

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2 4\(m^{3}\) − 5 4\(m^{2}\) + 8 1 − 1 0 5

Answer:

24m^3−54m^2+81m−105

Step-by-step explanation:

Answer:

j = 2

Step-by-step explanation:

Combine like terms

6j-11j-11j+10=-13

-16j+19=-13

Subtract 19 from both sides of the equation

-16j+19=-13

-16+19-19=-13-19

Simplify

-16j=-32

Divide both sides of the equation by the same term

Simplify again

Which gives you j=2

Answer:

23:119

Step-by-step explanation:

all pens:

77 blue + 23 red + 15 pink + 4 purple

77 + 23 + 15 + 4 = 119

119 total pens

23 red / 119 total

23/119

23 is prime, so this cannot be simplified further

the ratio of red : total pens is 23:119

Answer:

23 to 119 (23:119)

Step-by-step

you first have to add all of the pens together and then take the number of red pens and make that a ratio

The area of the circle is  113.04 square units.

The area of a circle of radius R is given by:

A = π*R²

Where π = 3.14

Here we know that the center is at (2, 2) and the point (8, 2) is on the circle, then the radius is:

R = √( (2 - 2)² + (8 - 2)²)

R = 6

Then the area of the circle is:

A = 3.14*(6)² = 113.04 square units.

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The correct values for a, b, c, d, and e are a = 16, b = 29, c = 24, d = 22, and e = 30 for group of 75 students on asking whether they like Algebra or Geometry.

For the values of a, b, c, d, and e, we can use the information provided in the table. Let's break it down step-by-step:

We are given that a total of 75 math students were surveyed. Therefore, the total number of students should be equal to the sum of the students who like algebra, the students who like geometry, and the students who do not like either subject.

75 = 45 (Likes Algebra) + 53 (Likes Geometry) + 6 (Does Not Like Either)

Simplifying this equation, we have:

75 = 98 + 6

75 = 104

This equation is incorrect, so we can eliminate options c and d.

Now, let's look at the information given for the students who do not like geometry. We know that a + b = 6, where a represents the number of students who like algebra and do not like geometry, and b represents the number of students who do not like algebra and do not like geometry.

Using the correct values for a and b, we have:

16 + b = 6

b = 6 - 16

b = -10

Since we can't have a negative value for the number of students, option a is also incorrect.

The remaining option is option e, where a = 29, b = 16, c = 24, d = 22, and e = 30. Let's verify if these values satisfy all the given conditions.

Likes Algebra: a + c = 29 + 24 = 53 (Matches the given value)

Does Not Like Algebra: b + d = 16 + 22 = 38 (Matches the given value)

Likes Geometry: c + d = 24 + 22 = 46 (Matches the given value)

Does Not Like Geometry: b + e = 16 + 30 = 46 (Matches the given value)

All the values satisfy the given conditions, confirming that option e (a = 29, b = 16, c = 24, d = 22, and e = 30) is the correct answer.

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Answer:

o.8

Step-by-step explanation:

The planned order releases for each item are as follows: A: 20 units in period 1, B: 10 units in period 1, C: 40 units in period 3, D: No planned order release, E: 100 units in period 5, F: 100 units in period 5

To determine the planned order releases for all items, we need to calculate the net requirements for each period based on the given information. We will start with the highest-level item and work our way down the bill of materials.

Item A:

Period 1: Gross requirement of 20 units.

Since A uses lot-for-lot (L4L) as the lot-sizing technique, we release an order for 20 units of A.

Item B:

Item B is a component of A, and each A requires 2 units of B.

We need to calculate the net requirements for B based on the planned order release for A.

Period 1: Gross requirement of 20 units * 2 (requirement multiplier for B) = 40 units.

B has a scheduled receipt of 30 units in period 1.

Net requirement for B in period 1: 40 units - 30 units = 10 units.

Since B also uses L4L as the lot-sizing technique, we release an order for 10 units of B.

Item C:

Item C is a component of A, and each A requires 3 units of C.

We need to calculate the net requirements for C based on the planned order release for A.

Period 1: Gross requirement of 20 units * 3 (requirement multiplier for C) = 60 units.

C has a lead time of two periods, so we need to account for that.

Net requirement for C in period 3: 60 units - 20 units (scheduled receipt for A in period 1) = 40 units.

Since C uses L4L as the lot-sizing technique, we release an order for 40 units of C.

Item D:

Item D is a component of C, and each C requires 1 unit of D.

We need to calculate the net requirements for D based on the planned order release for C.

Period 3: Gross requirement of 40 units * 1 (requirement multiplier for D) = 40 units.

D has a lead time of one period, so we need to account for that.

Net requirement for D in period 4: 40 units - 60 units (scheduled receipt for C in period 3) = -20 units (no requirement).

Since the net requirement is negative, we do not release any planned order for D.

Item E:

Item E is a component of C, and each C requires 1 unit of E.

We need to calculate the net requirements for E based on the planned order release for C.

Period 3: Gross requirement of 40 units * 1 (requirement multiplier for E) = 40 units.

E has a lead time of two periods, so we need to account for that.

Net requirement for E in period 5: 40 units - 0 units (no scheduled receipt for E) = 40 units.

Since E requires a multiple of 100 to be purchased, we release an order for 100 units of E.

Item F:

Item F is a component of B and C, and each B requires 1 unit of F, while each C requires 2 units of F.

We need to calculate the net requirements for F based on the planned order releases for B and C.

Period 1: Gross requirement for B = 10 units * 1 (requirement multiplier for F) = 10 units.

Period 3: Gross requirement for C = 40 units * 2 (requirement multiplier for F) = 80 units.

F has a lead time of two periods, so we need to account for that.

Net requirement for F in period 5: 10 units + 80 units - 0 units (no scheduled receipt for F) = 90 units.

Since F requires a multiple of 100 to be purchased, we release an order for 100 units of F.

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Answer:60 degrees

Step-by-step explanation:BAC =90 Degrees

BAD= 30 degrees

Since BAD and DAC are complementary angles, they add up to 90 degrees

So, 90 degrees-30 degrees= DAC which is =60 degrees

HOPE IT WAS CLEAR

Angle DAC is determined to be 60 degrees as it is complementary to angle BAD, which measures 30 degrees.

According to the given information, angle BAD measures 30 degrees. It is stated that angle BAD and angle DAC are complementary angles, meaning they add up to 90 degrees.

To find the measure of angle DAC, we subtract 30 degrees from 90 degrees:
90 degrees - 30 degrees = 60 degrees.

Therefore, the angle DAC measures 60 degrees.

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Answer:

About 5 days (exact answer is 4.975)

Step-by-step explanation:

Take 1990 and divide by 400, it should give you the amount of days.

Answer:

t=1/2u

Step-by-step explanation:

Since t=tens digit and u=units digit, as given in the equation that means that t+u=9. Since the tens digit is one-half the units digit that means: \(t=\frac{1}{2}u\) since it's one half the units digit.

Answer:

6^14/6^15 = 6^-1

Step 1: Solve for one of the equations for either variable.

Step 2: Substitute the expression from Step 1 into the other equation.

Step 3: Solve the resulting equation.

Step 4: Substitute the solution in Step 3 into one of the original equations to find the other variable.

Step 5: Write the solution as an ordered pair.

Step 6: Check that the ordered pair is a solution to both original equations.

Answer:          36x^3 +27x^2 = 9x^2\left(4x+3\right)

Step-by-step explanation: apply exponent rule rewrite factor out common term plz enjoy

Answer:

\(x = 0\; ,-\frac{3}{4}\)

Step-by-step explanation:

\(36x^3 + 27x^2 = 0\)

\(=> 9x^2(4x + 3) = 0\)

Here, x will have 2 values :-

1) \(9x^2(4x + 3) = 0\)

\(=> \frac{9x^2(4x + 3)}{(4x+3)} = \frac{0}{4x+3}\)

\(=> 9x^2 = 0\)

\(=> \frac{9x^2}{9x} = \frac{0}{9x}\)

\(=> x = 0\)

2) \(9x^2(4x + 3) = 0\)

\(=> \frac{9x^2(4x + 3)}{9x^2} = \frac{0}{9x^2}\)

\(=> 4x+3 = 0\)

\(=> 4x+3 -3 = 0 - 3\)

\(=> 4x=-3\)

\(=> \frac{4x}{4} = \frac{-3}{4}\)

\(=> x = -\frac{3}{4}\)

The value of the given expression 3 x 2,746 is 8,238.

We are given the expression:-

3 x 2,746

We have to find the value of the given expression using place value.

According to the data given in the question, we can write,

In 2746,

The place value of 6 is 6

The place value of 4 is 4*10 = 40

The place value of 7 is 7*100 = 700

The place value of 2 is 2*1000 = 2000

Hence, we can write,

3*2746 = 3*2000 + 3*700 + 3*40 + 3*6 = 6000 + 2100 + 120 + 18 = 8,238.

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Answer:

51m

Step-by-step explanation:

tan 21 = y/35;    y=13.43

tan 47 = x/35;    x=37.53

13.43+37.53 = 50.97 = 51m

An given the function f(x) = x²1.5 – 6 3 iterations bisection method x =2.75,Newton Raphson method x = 2.938,Comparison and Justification x = 2.938.

a. Bisection method: To solve for x using the bisection method, to find a bracket [a, b] such that f(a) and f(b) have opposite signs. The starting bracket between 1 and 5. three iterations of the bisection method.

Iteration 1:

a = 1, b = 5

c = (a + b) / 2 = (1 + 5) / 2 = 3

f(a) = f(1) = 1²1.5 - 6 = -4.24

f(c) = f(3) = 3²1.5 - 6 = 0.19

Since f(a) and f(c) have opposite signs, the bracket to [a, c].

Iteration 2:

a = 1, b = 3

c = (a + b) / 2 = (1 + 3) / 2 = 2

f(a) = f(1) =-4.24

f(c) = f(2) = -2.83

Since f(a) and f(c) have the same sign, the bracket to [c, b].

Iteration 3:

a = 2, b = 3

c = (a + b) / 2 = (2 + 3) / 2 = 2.5

f(a) = f(2) = -2.83

f(c) = f(2.5) = -1.41

Since f(a) and f(c) have the same sign, the bracket to [c, b].

After three iterations, the bracket is [2.5, 3]. The root lies within this bracket, and the final estimate to be the midpoint of the bracket, which is x =2.75.

b. Newton-Raphson method:

To solve for x using the Newton-Raphson method, with an initial estimate. The starting estimate is given as 3.Three iterations of the Newton-Raphson method:

Iteration 1:

x1 = 3

f(x1) = f(3) = 3²1.5 - 6 = 0.19

f'(x) = 1.5x²0.5 = 2.12 (derivative of f(x))

Using the formula: x2 = x1 - (f(x1) / f'(x1))

x2 = 3 - (0.19 / 2.12) = 2.91

Iteration 2:

x1 = 2.91

f(x1) = -0.05

f'(x) =2.01

Using the formula: x2 = x1 - (f(x1) / f'(x1))

x2 =2.91 - (-0.05 / 2.01) =2.938

Iteration 3:

x1 = 2.938

f(x1) = -0.001

f'(x) = 1.97

Using the formula: x2 = x1 - (f(x1) / f'(x1))

x2 = 2.938 - (-0.001 / 1.97) = 2.938

After three iterations, the estimated root using the Newton-Raphson method is x = 2.938.

c. Comparison and Justification:

Comparing the estimates obtained from the bisection method (x ≈ 2.75) and the Newton-Raphson method (x ≈ 2.938), the Newton-Raphson method provides a more accurate estimate. The Newton-Raphson method converges faster towards the root, reaching a more accurate solution in fewer iterations compared to the bisection method. This is because the Newton-Raphson method utilizes the derivative of the function, which provides information about the slope and direction of the curve, leading to quicker convergence.

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1 minute and 20 seconds as a decimal = 1.333

60 minutes are in an hour

60/1.333 = 45

He is driving 45 miles per hour.

Answer:c

Step-by-step explanation: