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5 days ago

What value of x is in the solution set of 2(3x – 1) ≥ 4x – 6?

2 answers:

6 0

2(3x - 1) ≥ 4x - 6 | Initial equation
6x - 2 ≥ 4x - 6 | Distributing 2 across the parentheses
2x - 2 ≥ -6 | Removing 4x from both sides
2x ≥ -4 | Adding -2 to both sides of the equation
x ≥ -2 | Dividing each side by 2

Thus, x must be at least -2 for inclusion in the solution set.

AnnZ [11.9K]5 days ago

3 0

Answer:

Solution Value: -2

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A national dental association conducted a survey to find the average (mean) amount of time dentists spend on dental fillings per

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The likelihood of observing a sample mean that is less than 18 hours is 0.0082. \nTo evaluate this probability, we calculate the z-score for a sample mean of 18. Accordingly, the probability of getting a sample mean below 18 hours becomes P(z<z(18)). \nThe z-score is calculated as follows: \nz(18) = [(X - M) / s] where: \n- X is the sample mean (18 hours) \n- M is the average hours dentists devote weekly to fillings (20 hours) \n- s is the standard deviation (10 hours) \n- N is the sample size (144) \nSubstituting the numbers leads to: \nz(18) = [(18 - 20) / (10/sqrt(144))]. Using the z-table, we find that P(z<z(18)) is 0.0082.

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25 days ago

Step 1: –10 + 8x < 6x – 4 Step 2: –10 < –2x – 4 Step 3: –6 < –2x Step 4: ________ What is the final step in solving the

Svet_ta [12331]

Given:

The inequality is

$-10+8x$

To find:

The step that is missing in the resolution of the given inequality.

Solution:

Step 1: The equation provided.

$-10+8x$

Step 2: Subtract 8x from both sides.

$-10+8x-8x$

$-10$

Step 3: Add 4 to both sides.

$-10+4$

$-6$

Step 4: Divide every side by -2, reversing the sign of the inequality because we are dividing by a negative number.

$\dfrac{-6}{-2}>\dfrac{-2x}{-2}$

$3>x$

Consequently, the missing step is $3>x$ .

8 0

1 month ago

Read 2 more answers

The dye dilution method is used to measure cardiac output with 3 mg of dye. The dye concentrations, in mg/L, are modeled by c(t)

lawyer [12140]

Answer:

Cardiac output: $F=0.055 L\s$

Step-by-step explanation:

Details: The cardiac output is assessed using the dye dilution technique with 3 mg of dye.

Goal: To determine the cardiac output value.

Solution:

Cardiac output formula: $F=\frac{A}{\int\limits^T_0 {c(t)} \, dt}$ ---1

A = 3 mg

$\int\limits^T_0 {c(t)} \, dt =\int\limits^{10}_0 {20te^{-0.06t}} \, dt$

Utilize integration by parts

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[20t\int{e^{-0.6t} \,dt}-\int[\frac{d[20t]}{dt}\int {e^{-0.6t} \, dt]dt]^{10}_0$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-20te^{-0.6t}}{0.6}+\frac{20}{0.6}\int {e^{-0.6t} \,dt]^{10}_0$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-20te^{-0.6t}}{0.6}+\frac{20e^{-0.6t}}{(0.6)^2}]^{10}_{0}$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-200e^{-6}}{0.6}+\frac{20e^{-6}}{(0.6)^2}]+\frac{20}{(0.60^2}$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=\frac{20(1-e^{-6}}{(0.6)^2}-\frac{200e^{-6}}{0.6}$

$[\int{20te^{-0.6t}} \, dt]^{10}_0\sim {54.49}$

Insert the value into 1

Cardiac output: $F=\frac{3}{54.49}$

Cardiac output: $F=0.055 L\s$

Consequently, Cardiac output: $F=0.055 L\s$

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1 month ago

From past experience, a company has found that in carton of transistors: 92% contain no defective transistors 3% contain one def

zzz [11880]

To determine the variance, we need to first calculate the second moment as follows: The variance can be determined using this equation: The standard deviation is simply the square root of the variance, which gives us the result.

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26 days ago

Suppose that the last four months of sales were 8, 10, 15, and 9 units, respectively. Suppose further that the last four forecas

Leona [12162]

Response:

MAD value comes out to be 3.

Detailed Breakdown:

The given sales forecasts for the last four months are 5, 6, 11, and 12 units.

To calculate the Mean Absolute Deviation (MAD) for these forecasts:

The average of the forecasts across four months is $\frac{5 + 6 + 11 + 12}{4} = 8.5$ .

Thus, the total of absolute differences between the forecast values and the average is = |5 - 8.5| + |6 - 8.5| + |11 - 8.5| + |12 - 8.5| = 3.5 + 2.5 + 2.5 + 3.5 = 12.

Hence, the MAD value will be = $\frac{12}{4} = 3$ (Final Answer)

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1 month ago