−3x + 2 ≥−1 in a number line

Answer:

36

Step-by-step explanation:

3=3

9=3*3 = 3^2

12=2*2*3 = 2^2*3

lcm = 2^2*3^3

      = 4*9

therefore lcm= 36

Answer:

36

Step-by-step explanation:

\(\bold{3} \times \bold{12} = 36\\\bold{9} \times 4 = 36\)

The length and width of the rectangle is found as 19 inches and 5 inches respectively.

Now, as per the given question;

Let width of a rectangle = w inches

Then, length of a rectangle = 3w + 4

Perimeter of a rectangle = 2(length + width)

Substitute the values in the formula of perimeter.

48 = 2(3w + 4 + w)

48/2 = 4w + 4

24 = 4w + 4

20 = 4w

w = 5

Thus, the width of the rectangle is 5 inches.

Put w = 5 inches in its length.

l = 3w + 4

l = 3×5 + 4

l = 15 + 4

l = 19 inches.

Therefore, the length of rectangle is found as 19 inches.

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The average pace is computed as follows:

Replacing with data:

The difference between Shaunice's average pace per lap and Joshua's average pace per lap is 66.5 - 63 = 3.5 seconds

Therefore, the approximate value of the integral is 0.42 (rounded to the nearest hundredth).

To approximate the integral ∫ from 1 to 2 of √(1 + cos(x)) dx using a Left Riemann sum with 20 subintervals, we need to divide the interval [1, 2] into 20 equal subintervals.

The width of each subinterval, Δx, is given by:

Δx = (b - a) / n = (2 - 1) / 20 = 1/20 = 0.05

Now, we evaluate the function at the left endpoint of each subinterval and sum the areas of the rectangles formed by multiplying the function value by the width.

Approximation using Left Riemann sum:

∫ from 1 to 2 of √(1 + cos(x)) dx ≈ Σ[√(1 + cos(xᵢ)) Δx] for i = 0 to 19

where xᵢ = a + iΔx, and a = 1.

Calculating the approximation:

∫ from 1 to 2 of √(1 + cos(x)) dx ≈ Σ[√(1 + cos(1 + i*0.05)) * 0.05] for i = 0 to 19

Now, we calculate the sum by substituting the values:

∫ from 1 to 2 of √(1 + cos(x)) dx ≈ (√(1 + cos(1))*0.05) + (√(1 + cos(1.05))*0.05) + ... + (√(1 + cos(1.95))*0.05)

Evaluating this expression using a calculator or software, we get the approximation to the nearest hundredth:

∫ from 1 to 2 of √(1 + cos(x)) dx ≈ 0.42

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Answer:

The answer is 3

Step-by-step explanation:

The chain should be attached at (3, 4) to balance the triangular piece of the mobile.

To find the coordinates where the chain should be attached to balance the triangular piece of the mobile, we can determine the centroid of the triangle. The centroid is the point of intersection of the medians, which are line segments connecting each vertex of the triangle to the midpoint of the opposite side.

Using the given coordinates: (0, 4), (3, 8), and (6, 0), we find the midpoints of the sides: (1.5, 6), (4.5, 4), and (3, 2). The centroid is the average of these midpoints: (3, 4).

Therefore, the chain should be attached at the coordinates (3, 4) to achieve balance. This point represents the center of mass of the triangular piece, ensuring equal distribution of weight and stability when hung from a chain.

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The domain of the function f(x) = ln(x^2 - 1) is (-∞, -1) ∪ (-1, 1) ∪ (1, ∞).

To find the domain of the function f(x) = ln(x^2 - 1), we need to consider the values of x for which the function is defined.

In this case, since we have a natural logarithm function, the argument inside the logarithm must be greater than zero (x^2 - 1 > 0) to ensure a real-valued result.

We can solve the inequality x^2 - 1 > 0 by factoring:

(x - 1)(x + 1) > 0

Now, let's determine the sign of the expression (x - 1)(x + 1) for different intervals:

When x < -1, both factors are negative, so the expression is positive.

When -1 < x < 1, the factor (x - 1) is negative, and the factor (x + 1) is positive, so the expression is negative.

When x > 1, both factors are positive, so the expression is positive.

Therefore, the solution to the inequality is x < -1 or x > 1.

However, we also need to consider the restriction that x^2 - 1 should not be equal to zero, as ln(0) is undefined. Therefore, x = -1 and x = 1 are not included in the domain.

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Answer:

The percentage of the components bought from supplier C that are faulty = 88%

Complete Question:

A factory buys 10% of its components from supplier A, 30% from supplier B,and the rest from supplier C. it is known that 6% of the components it buys are faulty. of the components bought from supplier A, 9% are faulty and of the components bought from supplier B, 3% are faulty.

find the percentage of the components bought from supplier C that are faulty ?

Step-by-step explanation:

Let x be the total components bought by the factory

Components supplied by A = 10% of x

Components supplied by B = 30% of x

The rest supplied by C:

Percentage supplied by C = 100-(30+10) = 100-40 = 60%

Components supplied by C = 60% of x

% of all faulty components = 6%

Amount of faulty component = 6% of x

faulty components from A= 9%

Amount of faulty component from A= 9% × (6% of x) = 0.0054x

faulty components from B= 3%

Amount of faulty component from A= 3% × (6% of x) = 0.0018x

Amount of faulty component from C = (6% of x) - (0.0054x+0.0018x)

= 0.06x - 0.0072x

= 0.0528x

Let the percentage of the components bought from supplier C that are faulty = y%

y% × 6% of x = 0.0528x

y% × 0.06x = 0.0528x

y% = 0.0528x/0.06x

y% = 0.88 = 88%

The percentage of the components bought from supplier C that are faulty = 88%

Answer:

3 student.

Step-by-step explanation:

From the first statement:

Let the total score be T

Let the total number of student be x

The average of the score = 72

Average = Tota score / number of student

72 = T/x

Cross multiply

T = 72x ..... (1)

Second statement:

One more student took the test and the average becomes 76 with the student having a score of 88.

Therefore,

Overall score = T + 88

Total student = x + 1

Average = 76

Average = overall score / total number of student

76 = (T + 88) /(x + 1)

Cross multiply

76(x + 1) = T + 88

Clear bracket

76x + 76 = T + 88

From equation 1

T = 72x

76x + 76 = 72x + 88

Collect like terms

76x – 72x = 88 – 76

4x = 12

Divide both side by the coefficient of x i.e 4

x = 12/4

x = 3

Therefore, the initial number of the student were 3.

Graph C best represents the distance of the two runners from the lake, D, in meters, over time, t, in minutes.

What is the rate of change?

The rate of change is also called the slope. On a graph, the rate of change is the ratio of the change in the y-values to the change in the x-values between two data points.

As Carlos has a steady pace and his changes in distance from the lake are constant, his distance graph would be a straight line with a constant slope. On the other hand, Stephanie has a slower rate of change when she turns at the lake. Therefore, her distance graph would be a curve.

Since the graph should show the distance of the two runners from the lake over time, the X-axis should represent time (in minutes), and the Y-axis should represent the distance (in meters).

Based on the given information, the graph that best represents the distance of the two runners from the lake over time is:

Graph C:

In Graph C, the line represents Carlos's distance from the lake, and the curve represents Stephanie's distance from the lake.

The line is straight, indicating that Carlos's rate of change is constant, and the curve shows that Stephanie's rate of change is slower as she turns at the lake.

Hence, the graph C best represents the distance of the two runners from the lake, D, in meters, over time, t, in minutes.

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Answer:

$4

Step-by-step explanation:

12÷4=3

20÷4=5

56÷4=14

Answer:

Step-by-step explanation:

OB = 10 cm

OA = OC = Radius = 4 cm

COS <AB = OA/OB = 4/10 = 2/5 =

COS< COB = OC/OB = 4/10 = 2/5

=> <AOC = <AOB + <COB

=> <AOC = Cos-¹(2/5) + Cos-¹(2/5)

=> <AOC = 2 Cos-¹(2/5)

=> <AOC = 2 * 66.42

=> <AOC = 132.84°

if D is in minor arc then length of arc ADC. = ( 132.84°/360°) 2π = 9.274 cm

if D is in major arc then length of arc ADC. = ((360° -132.84°)/360°) 2π = 15.859 cm

The range of a data set is determined by subtracting the smallest value from the largest value. In this case, the smallest value is 2.0 and the largest value is 15. Thus, the range is 15 - 2.0 = 13.

To find the mean of a data set, we sum all the values and divide by the total number of values. Adding up the given values, we have 2.0 + 15 + 5 + 14 + 7 + 13 + 9 + 3 + 10 = 78. Dividing this sum by 9 (since there are 9 values), we get a mean of 78/9 ≈ 8.7.

The variance of a population data set measures the average of the squared deviations from the mean. To calculate it, we need to find the squared differences between each data point and the mean, sum them up, and divide by the total number of data points. The squared differences for each value are as follows: (2.0 - 8.7)², (15 - 8.7)², (5 - 8.7)², (14 - 8.7)², (7 - 8.7)², (13 - 8.7)², (9 - 8.7)², (3 - 8.7)², (10 - 8.7)². Summing up these squared differences, we get a value of approximately 117.8. Dividing this sum by 9, the total number of data points, we find the variance to be approximately 13.1.

The standard deviation is the square root of the variance. Taking the square root of the calculated variance of 13.1, we find the standard deviation to be approximately 3.6.

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False. The metric system is a decimalized system of measurement, but it is not used exclusively in the United States.

In fact, the United States primarily uses the U.S. customary system, while the metric system is widely used in most other countries around the world.

Most nations throughout the world use the metric system, a decimal-based measurement system that is universally recognised. It offers a standardised method for gauging temperature, length, mass, and other physical attributes. The metre (for length), kilogramme (for mass), second (for time), ampere (for electric current), kelvin (for temperature), mole (for amount of material), and candela (for luminous intensity) are the basic units of the metric system. Because the metric system is based on powers of 10, converting between units is simple. Global communication and trade are made easier by its promotion of usability, consistency, and compatibility across scientific, industrial, and everyday uses.

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Answer:

6.3 x 106 ÷ 7 x 10-5 = 0.9 x 1011 or 9 x 1010

Step-by-step explanation:

Answer:

x = 7

Step-by-step explanation:

2x + 34 = 4(x + 5) ← distribute parenthesis by 4

2x + 34 = 4x + 20 ( subtract 4x from both sides )

- 2x + 34 = 20 ( subtract 34 from both sides )

- 2x = - 14 ( divide both sides by - 2 )

x = 7

3/10 (option B)

fraction that chose vanilla ice cream = 2/5

fraction that chose chocolate ice cream = 3/10

let the fraction that chose strawberry ice cream = y

Total fraction = 1

fraction that chose vanilla ice cream + fraction that chose chocolate ice cream + fraction that chose strawberry ice cream = 1

2/5 + 3/10 + y = 1

Fraction of the class chose strawberry ice cream is 3/10 (option B)

Answer:

y=-x-3

Step-by-step explanation:

Formula (point slope): y-y1=m(x-x1)

y-(-3)=-1(x-0)

(distribute the -1)

y+3=-1x+0

(combine like terms)

y=-1x-3

To find the required sample size for a margin of error less than 3%, we can rearrange the formula for the margin of error:

\(n = (Z^2 * p * (1 - p)) / (E^2)\)

Here, Z represents the critical value, p is the estimated proportion (0.51), and E is the desired margin of error (0.03)

To determine the margin of error for the 95% confidence interval, we need to use the formula:

Margin of Error = Critical value * Standard error

The critical value for a 95% confidence level can be obtained from the standard normal distribution table, which corresponds to 1.96. The standard error can be calculated using the following formula:

Standard error = \(\sqrt{(p * (1 - p) / n)}\)

Given that the proportion of North Carolina residents planning to set off fireworks is estimated to be 51% (0.51) based on the survey, we can substitute the values into the formula. However, the sample size (n) is not provided in the question, so we need to determine it in the next part.

To find the required sample size for a margin of error less than 3%, we can rearrange the formula for the margin of error:

\(n = (Z^2 * p * (1 - p)) / (E^2)\)

Here, Z represents the critical value, p is the estimated proportion (0.51), and E is the desired margin of error (0.03). Substituting these values into the formula, we can solve for the required sample size.

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Answer:

21/55

Step-by-step explanation:

dividamos por 5

= 21/55

Answer:

The estimated total to the nearest dollar is $31, so he cannot afford both items.

Step-by-step explanation:

10.58 rounded is 11

19.50 rounded is 20

11+20=31

Answer:

I think it would be last one. Based on the idea that 10.58 would round up to 11.00, and the DVD would add up to 20.oo

that would equal 31.00, and he only has 30.00 to spend.

So I would say D.

Step-by-step explanation:

Aggregate Demand (AD) is a macroeconomic concept that represents the total demand for goods and services in an economy. The X factor in the AD equation represents exports, which are an important part of the economy.

AD is calculated by adding up the individual components of demand, which include consumer spending (C), investment spending (I), government spending (G), and net exports (X-M). The X-M component represents the difference between exports (X) and imports (M).

The X component in the equation represents exports, which are the goods and services produced domestically and sold to foreign countries. Exports are an important part of the economy as they generate income and create jobs. The M component in the equation represents imports, which are the goods and services purchased from foreign countries and consumed domestically. Imports can have a negative impact on the economy as they represent a drain on resources and can lead to a trade deficit. The X factor in the equation is used to represent exports because it is a variable that can change over time. Factors that can affect exports include exchange rates, tariffs, and global demand for certain products. If the exchange rate between two currencies changes, it can make exports more or less expensive for foreign buyers, which can affect the level of exports. Tariffs are taxes on imports, which can make domestic products more competitive in foreign markets.

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1. The values which the given number sentences true are:

a) 11 b) 5 c) 36

2. After substituting the value of  x we get the value for y as :

a) 6 b) 0 c) 7 d) 15

3. The number sentences are :

a) x ₋ y = 25

b) 5 × p = q ÷ 2

c) 2y ₋ 14 = 6

d) 15 × 4 = 4 ₋ (x₊y)

Given in the first bit we need to find the variables:

a) h ₊ 8 = 19

arrange the constants on one side.

h = 19 ₋ 8

h = 11

b) 2p ₋ 6 = 4

arrange the constants on one side.

2p = 4 ₊ 6

2p = 10

p = 10/2

p = 5

c) 1/3 y = 12

cross multiply.

y = 36

Now in the second exercise we are asked to substitute the x value and get the value of y.

a) y = 3x ₊ 2 if x =8

substitute x value in the equation.

y = 3(8) ₊ 2

y = 24 ₊ 2

y = 26

b) y = 4x ₋ 1 if  x = 1/4

y = 4(1/4) ₋ 1

y = 1 ₋ 1

y = 0

c) y = 0.2x ₊ 5 if x = 10

y = 0.2(10) ₊ 5

y = 2 ₊ 5

y = 7

d) y = 10x ₊ 12 if x = 0.3

y = 10(0.3) ₊ 12

y = 3 ₊ 12

y = 15

In the last third bit we need to frame equations for the given word problems.

a) The difference between two numbers is 25.

let the two numbers be x and y.

x ₋ y = 25.

b) The product of 5 and p is equal to quotient of q and 2.

5 × p = q ÷ 2

c) The difference between 14 and 2y is equal to 6.

2y ₋ 14 = 6

d) The product of 15 and 4 is equal to four less than the sum of x and y.

15 × 4 = 4 ₋ (x₊y)

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The probability of exactly one successes in five trials  is 0.20

From the question, we have the following parameters that can be used in our computation:

The probability is calculated as

P(x) = nCx * p^x * (1 - p)^(n -x)

Where

n = 5

p = 5%

x = 1

Substitute the known values in the above equation, so, we have the following representation

P(1) = 5C1 * (5%)^1 * (1 - 5%)^(5 -1)

Evaluate

P(1) = 0.20

HEnce, the probability value is 0.20

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Answer:

The output of (-6,0) is (-9,4)

Step-by-step explanation:

Given

\((x,y) \to (x -3,y+4)\) --- rule

Required

The output of \((-6,0)\)

\((-6,0)\) implies that:

\((x,y) = (-6,0)\)

So, we have:

\((x,y) \to (x -3,y+4)\)

\((-6,0) \to (-6 -3,0+4)\)

\((-6,0) \to (-9,4)\)

The output of (-6,0) is (-9,4)

Answer:

See attached image.

Step-by-step explanation:

The number of bacteria there would be in the petri dish after 7 hours is 7,324.

As the bacteria placed in a petri dish doubles every 15 hours, it represents a geometric growth model.  Geometric growth refers to the situation where successive changes in a population differ by a constant ratio. Hence, the nth term (after the first term) is given by ar^n where a is the initial amount, r is the constant ratio also called common ratio, and n is the number of periods/terms. Based on the given information. the initial number of bacteria a = 5300 and the constant ratio = 2. The number of period n = x/15. As x = 7 hours,

The number of bacteria = 5300*2^(7/15) = 7324.13 ≈ 7324

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The property which guarantees that a twice-differentiable function has a relative minimum at x =c is the statement that f(c) = 0 and f''(c) > 0. Hence, option B is the correct answer.

Explanation:According to the second derivative test, if f''(c) > 0 and f(c) = 0, then the function f has a relative minimum at x = c. We're given that f is a function with two continuous derivatives. If f(c) = 0 and f(c) is less than zero, it is still possible for f to have a relative minimum, but only if the second derivative is negative and changes to positive at x = c.If f(0) = 0 and f(c) is less than zero, then we cannot conclude that f has a relative minimum at x = c since the second derivative is not guaranteed to be greater than zero at x = c. We can rule out f(x) > 0 for x since this is not a property that has anything to do with relative minima.

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