The length, l, of a rectangle is 3 inches greater than its width, w. The perimeter of the rectangle is at least 30 inches. Which inequalityshows the range of possible lengths of the rectangle?

Answer:

Vertical

Step-by-step explanation:

Hope it helps you in your learning process

Answer:

I am assuming the 8:15 was a typo and was actually supposed to be a 8:14. Anyways, they are equivalent because they all make 4:7 when simplified.

Step-by-step explanation:

4:7 = itself at this point, as they don't have numbers that can simplify each other on both sides, unless you are looking for a decimal answer.

8:14 = 4:7 <- You can divide the 8 and 14 by two. 8 divided by 2 is four, and 14 divided by 2 is 7.

16:28 = 4:7 <- You can divide the 16 and the 28 by four. 16 divided by 4 is 4, and 28 divided by 4 is 7.

20:35 = 4:7 <- You can divide both sides by 5. 20 divided by 5 is 4, and 35 divided by 5 is 7.

Yes, the system is consistent. This is because the number of pivot columns (3) is equal to the number of unknowns in the system (3).

This means that the system has a unique solution that can be determined by performing Gaussian Elimination or other linear algebra techniques.

If the coefficient matrix for a system has n columns, and there are only n pivots, then the system is consistent because every equation has a pivot column.

In this case, the matrix has three pivot columns, therefore the system is consistent because each equation has a pivot column.

Therefore, the system is consistent.

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Answer:

its B

Step-by-step explanation:

edg

Answer:

Step-by-step explanation:

In step 2, the like terms were not combined properly on the right side of the equation. or B

Step-by-step explanation:Step-by-step explanation:

For Sienna to be able to take the square root of both sides while solving a quadratic equation, she must have an expression with square on at least, the side that contains the variable she is trying to determine. Equation of the form:

(x + a) ² = b

'a' and 'b' could be any number, -1, 0, 1/3, -5/6, anything really.

So, she can take square roots of both sides then, like this

√(x + a)² = √b

x + a = ±√b

x = -a ± √b

Square roots always cancel out squares, and the '±' is because a square is satisfies by both + and -, 3² = 9, and (-3)² = 9.

It is the nature of the problem being solved that determines if we take just one or both of these answers.

the maximum profit, we plug q = 83.33 into the profit function: P(83.33) = -0.03(83.33)^2 + 5(83.33) - 38 = $348.89 thousand.

1. To maximize profit, we need to find the production level where revenue (p(x)*x) minus cost (C(x)) is highest. So we need to find the derivative of the profit function:
P(x) = p(x)*x - C(x) = 1320x - 8700 - 440x - 0.5x^2
P'(x) = 1320 - 440 - x = 880 - x
Setting P'(x) = 0, we get x = 880. So the production level that will maximize profit is 880 units.

2. Let x be the length of one side of the square base, and h be the height of the box. We know that volume V = x^2*h = 186624, so h = 186624/x^2. The surface area of the box is A = x^2 + 4xh = x^2 + 4x(186624/x^2) = x^2 + 746496/x.

3. To find the average cost function, we divide the cost function by the production level:
AC(x) = C(x)/x = (48400+600x+x^2)/x = 48400/x + 600 + x
To minimize AC(x), we need to find the derivative of AC(x):
AC'(x) = -48400/x^2 + 1
Setting AC'(x) = 0, we get x = sqrt(48400) = 220. To confirm that this is the minimum, we can take the second derivative:
AC''(x) = 96800/x^3 > 0, so x = 220 is indeed the production level that minimizes average cost.
To find the minimal average cost, we plug x = 220 into the AC(x) equation:
AC(220) = 48400/220 + 600 + 220 = 802.

4. We need to find the derivative of the revenue function with respect to time:
R(x) = 1000x - 2x^2
dR/dt = dR/dx * dx/dt = (1000 - 4x) * 55
When 210 units have been sold, x = 210, so dR/dt = (1000 - 4*210) * 55 = $22,000 per day.

5. The marginal profit function is the derivative of the profit function:
P(q) = -0.03q^2 + 5q - 38
MP(q) = dP/dq = -0.06q + 5

To find the quantity that maximizes profit, we need to set MP(q) = 0:
-0.06q + 5 = 0
q = 83.33 thousand pairs of sunglasses.

To find the maximum profit, we plug q = 83.33 into the profit function:
P(83.33) = -0.03(83.33)^2 + 5(83.33) - 38 = $348.89 thousand.

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Answer: 75.2

Step-by-step explanation:

Well, if it isn't the most confusing question ever.

First of all, what is P?

I'll assume its the perimeter...

2*(1.2*2)+4*(8.8*2)

Or

2*2.4+4*17.6

75.2

Answer:

B

Step-by-step explanation:

the correct answer is b

4.16×10= 41.6

a) We can say with 95% confidence that the true difference in wages between southern and non-southern workers is between $7.07 and $0.53 less for southern workers.

b)  Using a two-tailed test with α = 0.05, the critical values of t are ±1.968.

a) To find the 95% confidence interval for the difference in wages between southern and non-southern workers, we can use the formula:

CI = (x1 - x2) ± tα/2,df * sqrt(s1^2/n1 + s2^2/n2)

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, n1 and n2 are the sample sizes, and tα/2,df is the t-value with α/2 probability and degrees of freedom df, which is calculated as:

df = (n1 + n2 - 2)

Plugging in the values given in the problem, we get:

CI = (19.0 - 22.8) ± t0.025,532 * sqrt(11.4^2/156 + 12.5^2/378)

where t0.025,532 is the t-value with 0.025 probability and 532 degrees of freedom (calculated using a t-table or a calculator), which is approximately equal to 1.96.

Evaluating the formula, we get:

CI = -3.8 ± 1.96 * 1.672

which simplifies to:

CI = (-7.07, -0.53)

Therefore, we can say with 95% confidence that the true difference in wages between southern and non-southern workers is between $7.07 and $0.53 less for southern workers.

b) To test the null hypothesis that southern and non-southern workers have the same wage without assuming equal variance, we can use the two-sample t-test with unequal variances. The null hypothesis is:

H0: μ1 - μ2 = 0

where μ1 and μ2 are the population means for southern and non-southern workers, respectively.

The test statistic for the two-sample t-test with unequal variances is:

t = (x1 - x2) / sqrt(s1^2/n1 + s2^2/n2)

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Plugging in the values given in the problem, we get:

t = (19.0 - 22.8) / sqrt(11.4^2/156 + 12.5^2/378) = -3.55

The degrees of freedom for the test is calculated as:

df = ((s1^2/n1 + s2^2/n2)^2) / ( (s1^2/n1)^2/(n1-1) + (s2^2/n2)^2/(n2-1) )

which simplifies to:

df = 313.75

We can use a t-table or a calculator to find the p-value associated with the test statistic. Using a two-tailed test with α = 0.05, the critical values of t are ±1.968. Since our test statistic (-3.55) falls outside this range, the p-value is less than 0.001 (very small). Therefore, we can reject the null hypothesis and conclude that there is a significant difference in wages between southern and non-southern workers.

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Answer:

6

Step-by-step explanation:

Let the amount of cars washed be x

120-12

---------- = x

18

108/18 =x

x=6

Answer:

B. 5i + 12b < 100

Step-by-step explanation:

I used process of elimination on to figure this one out.

I first eliminated A because I knew the i should be next to the 5. I know this because i (ink) costs 5 dollars each.

I next eliminated D because this equation is looking to find the sum of the ink and the new brushes, not the ink plus the total cost equaling the brushes.

Finally, I eliminated C because Emily only has $100, so the cost of the ink (i) and the brushes (b) must NOT excede 100 dollars. From this, I can see that C states that the sum exceeds Emily’s $100 budget

This leaves us with B as the final answer

Hope this helps! Have a lovely rest of your day!

Answer: 17/50

Multiply

0.34/1×100=34/100

Simplify

34/100÷2/2=17/50

A fraction which is equivalent to 0.34 is; 17/50

The decimal number, 0.34 can be represented in words as; 34 hundredths.

In essence, mathematically, we have;

17/50 is obtained by factorisation of 2 out of the numerator and denominator.

Hence, a fraction which is equivalent to 0.34 is 17/50.

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Answer:

Starting paragraphs:

My name is _______. I was born on a cloudy night on the ___ of _______, _____ in ___________ . My parents were very happy as they had been blessed with a baby boy/girl, and that girl/boy is me!

1 year passed by and my 1st birthday was celebrated with much joy and it turned out to be a super extravagant event.

I do not remember much of my early childhood but my parents said that I was a very active, curious and a communicative child. I would ask dozen of questions each minute, without waiting for the answers. I suppose that's why my parents offered me books as early as my third birthday.

Ending paragraph:

I am thankful for my parents, teachers and friends for making me the person who I am today.

Explanation:

Compose your autobiography with the help of the following points:

The part in the steering column that allows for changes in the angle between the upper and lower shafts is the universal joint.

The universal joint, also known as a U-joint or Cardan joint, is a mechanical device that enables changes in the angle between two shafts that are not in a straight line. In the context of a steering column, the upper and lower shafts are connected by a universal joint.

As the steering wheel is turned, it exerts rotational force on the upper shaft of the steering column. The universal joint allows for the transmission of this rotational motion while accommodating changes in the angle between the upper and lower shafts. It provides flexibility and compensates for any misalignment between the two shafts, ensuring smooth and continuous rotation of the steering column.

The universal joint typically consists of two yokes connected by a cross-shaped component with needle bearings. These bearings allow for rotation in multiple axes, allowing the steering column to handle variations in the angle between the upper and lower shafts during steering movements.

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Answer:

X= 5

Explanation (Steps):

Step 1: Simplify both sides of the equation.

−3.4(x−2)=9.8−4x

(−3.4)(x)+(−3.4)(−2)=9.8+−4x(Distribute)

−3.4x+6.8=9.8+−4x

−3.4x+6.8=−4x+9.8

Step 2: Add 4x to both sides.

−3.4x+6.8+4x=−4x+9.8+4x

0.6x+6.8=9.8

Step 3: Subtract 6.8 from both sides.

0.6x+6.8−6.8=9.8−6.8

0.6x=3

Step 4: Divide both sides by 0.6.

0.6x0.6=3/0.6

x=5

Answer:

y = 3x - 19.

Step-by-step explanation:

To find the slope and y-intercept of the line passing through the points (7,2) and (9,8), we can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.First, we need to find the slope m:m = (y2 - y1) / (x2 - x1)

m = (8 - 2) / (9 - 7)

m = 6 / 2

m = 3So the slope of the line passing through the points (7,2) and (9,8) is 3.Next, we can use one of the points and the slope to find the y-intercept b:y = mx + b

2 = 3(7) + b

2 = 21 + b

b = -19So the y-intercept of the line is -19.Finally, we can write the equation of the line using the slope and y-intercept:y = mx + b

y = 3x - 19Therefore, the equation of the line passing through the points (7,2) and (9,8) is y = 3x - 19.

a = 4 and b = 5 are the answers to the system of equations.

Let's square both sides of the first equation to eliminate the square root:

√a + b = 7

(√a + b)² = 7²

a + 2√ab + b² = 49

a + b² = 49 - 2√ab ---(1)

Now, let's square both sides of the second equation:

√b + a = 11

(√b + a)² = 11²

b + 2√ab + a² = 121

a² + b + 2√ab = 121 ---(2)

We can use equation (1) to substitute for √ab in equation (2):

a + b² = 49 - 2√ab

√ab = (49 - a - b²)/2

Substituting for √ab in equation (2), we get:

a² + b + 2(49 - a - b²)/2 = 121

Simplifying and rearranging, we get:

a² - a + b² - b - 36 = 0

(a - 1/2)² + (b - 1/2)² = 37.25

This is the equation of a circle centered at (1/2, 1/2) with a radius √37.25. We need to find the points where this circle intersects the line defined by equation (1).

Substituting b = 49 - a - 2√(a(49 - a))/2 into equation (1), we get:

a + (49 - a - 2√(a(49 - a)))² = 49 - 2√a(49 - a)

Simplifying and rearranging, we get:

4a³ - 294a² + 2421a - 5929 = 0

Using a numerical solver or the rational root theorem, we can find that one solution of this cubic equation is a = 4.

Substituting this value back into equation (1), we can solve for b:

4 + b² = 49 - 2√(4b)

b² + 2√(4b) - 45 = 0

Using the quadratic formula, we get:

b = 5

Therefore, the solutions of the system of equations are a = 4 and b = 5.

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Complete question:

√a+b=7 and √b +a = 11 If a and b are real numbers that satisfy the equation above, what is the value of a and b respectively?

Answer:

I'm pretty sure the answer is 0.45. I got this by dividing 1.35 by 3 which gave me 0.45. And to check it, I multiplied 0.45 by 3, snice the formula for area is multiplying.

Answer:

-4

Step-by-step explanation:

-4x is a term

Coefficient of variable x = -4

Answer:

60,367

Step-by-step explanation:

i = p x r x t

I = 53000 x 6.7/100 x 17

I = 53000 x 0.067 x 17

I=60,367

Answer:

A≈165553.09

Step-by-step explanation:

Answer:

The first will be the distributive property.

The second will be adding 6x on both sides.
The third will be subtracting 2 on both sides.

The fourth is dividing both sides by 11.

The last is the solution.

Step-by-step explanation:

Whenever you see parentheses with an operator between numbers, you use the distributive property(Meaning to multiply -3x(2) and 2(4).
Which gets you to the second step. Adding 6x on both sides. This action will undo the -6x and adding 5x + 6x will get you 11x.
Then, you subtract +2(canceling it entirely, because remember: we need to isolate x on one side of the equation).
Lastly, you will divide both sides by 11 to get to your solution.

x = 6/11

Chebyshev's theorem says that for any set of observations, the proportion of values that lie within k standard deviations of the mean is  1 - 1/k².

In statistics, Standard deviation is a measure of the variation of a set of values.

σ = standard deviation of population

N = number of observation of population

X = mean

μ = population mean

We know that Chebyshev's theorem states that for a large class of distributions, no more than 1/k² of the distribution will be k standard deviations away from the mean.

This means that 1 - 1/k² of the distribution will be within k standard deviations from the mean.

Lets k = 1.8, the amount of the distribution that is within 1.8 standard deviations from the mean is;

1 - 1/1.8² = 0.6914

= 69.14%

Hence, Chebyshev's theorem says that for any set of observations, the proportion of values that lie within k standard deviations of the mean is  1 - 1/k².

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The given inequality is

To solve this inequality we will move the term x from the left side to the right side and the numerical term from the right side to the left side

Subtract 27x from both sides

Now, add 29 to both sides

Divide both sides by 31 to find x

To determine the three angles in a triangle, we can use the Law of Cosines or the Law of Sines. However, since we are not given any side lengths, we will use the dot product formula to find the angles between the sides.

Then, we can compute the magnitudes of these vectors using the Pythagorean theorem:

|AB| = sqrt((Bx - Ax)^2 + (By - Ay)^2)
|AC| = sqrt((Cx - Ax)^2 + (Cy - Ay)^2)
|BC| = sqrt((Cx - Bx)^2 + (Cy - By)^2)

where (Ax, Ay), (Bx, By), and (Cx, Cy) are the coordinates of points A, B, and C, respectively.

Finally, we can use the dot product formula above to compute the cosines of angles A, B, and C, and then take the inverse cosine to find the angles in radians:

A = acos((AB · AC) / (|AB| · |AC|))
B = acos((AB · BC) / (|AB| · |BC|))
C = acos((AC · BC) / (|AC| · |BC|))

where acos denotes the inverse cosine function.

Therefore, we can determine all three angles in the triangle (in radians) using the above formulae.
It seems that the three points of the triangle were not provided in your question. To help you determine the angles of the triangle, please provide the coordinates of the three points (A, B, and C).

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Answer:

d

Step-by-step explanation:

18/36 is equivalent to 1/3

The report based on the given question requirements is:

Mathematician: Évariste Galois

(1) Life History:

Évariste Galois was born in Bourg-la-Reine, France on October 25, 1811. Unfortunately, he passed away at the tender age of 20 on May 31, 1832. Amidst the political unrest in France, he engaged in political activism. Despite his premature death, Galois made a lasting impact on the field of mathematics. His non-conformist attitude and intelligence frequently led to conflicts with those in positions of power, earning him a reputation as a rebel. A fascinating piece of information is that Galois dedicated his night prior to his ultimate combat to jotting down his mathematical concepts, eventually emerging as notable enhancements to Algebra.

(2) Mathematical Discoveries:

Galois made remarkable contributions to the field of Algebra. He developed the theory of Galois groups, which revolutionized the study of polynomial equations and their solvability. Galois showed that the solvability of an algebraic equation by radicals is determined by the properties of its Galois group. This insight led to Galois theory, a cornerstone of modern Algebra. Additionally, he developed the concept of field theory, introducing the notion of field extensions, which provided a powerful framework for studying algebraic structures.

(3) Bibliography:

Artin, E. (1998). Galois Theory: Lectures Delivered at the University of Notre Dame. Springer.

Stillwell, J. (2005). Mathematics and Its History (2nd ed.). Springer.

Edwards, H. M. (1983). Galois Theory. Springer-Verlag.

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Sum of two algebraic expressions is addition of two expressions. The sum of the given expressions is given as: Option B: \(2.8x + 8.7\)

Those terms which have same variables raised with same powers.

For example, \(5x^3\) and \(3x^3\) are like terms since variable is same, and it is raised to same power 3.

For example \(5x^2\) and \(x^3\) are not like terms as the variables are same but powers aren't same.

Constants who are in multiplication with variables are called coefficients of those variables.

For example, in \(10x^2\) we have 10 as coefficient of \(x^2\)

Suppose we have \(5x^2 + 6y\)

Since those terms are not like terms, their coefficient won't be add and the expression we've got right now, is its simplest form and cannot be reduced more.

If we have, suppose,

\(4x + 5x^2 + 2x\) , then we see that 4x and 2x are like terms, their coefficient can be added and thus, the simplified form would be

\((4+2)x + 5x^2 = 6x + 5x^2\)

For the given condition, the needed sum is evaluated as:

\((-2.1x + 3.7) + (5 + 4.9x) = (-2.1 + 4.9)x + 5 + 3.7 = 2.8x + 8.7\)

Thus,

The sum of the given expressions is given as: Option B: \(2.8x + 8.7\)

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Answer:

42 I think LOL

Total number of Chemistry textbooks sold is 81 and total number of Biology textbooks sold is 243

Let there are x biology textbooks sold.

No of chemistry textbooks sold = 3 the number of biology textbooks sold

ATQ,

A textbook store sold a combined total of 324 biology and chemistry textbooks in a week.

x + 3x = 324

4x = 324

x = 81

It means there are 81 biology textbooks sold and 3x = 3(81) = 243 chemistry textbooks sold.

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Answer:

105 m

Step-by-step explanation:

Given that Jules has a mirror that has a shape of a triangle, the length of the border Jules would add = the perimeter of the triangular mirror.

The perimeter of the triangular mirror is simply the sum of all the 3 sides of the triangle.

Since, each side is of equal length (35 cm), therefore, perimeter of the mirror = 35 + 35 + 35 = 105 m

Perimeter of mirror = length of border to add = 105 m

The border is 105 m long.