3(z - 1) - 1/2 (4z + 10) = 4 (z - 3/2) + 10

Answer:

Step-by-step explanation:

Convert mixed fraction to improper fraction.

Find LCM of the denominators and find equivalent fraction.

Now, subtract

\(7\dfrac{2}{9}=\dfrac{(7*9)+2}{9}=\dfrac{63+2}{9}=\dfrac{65}{9}\)

\(5\dfrac{1}{5}=\dfrac{26}{5}\)

LCM of 9 and 5 = 45

\(\dfrac{65}{9}*\dfrac{5}{5}=\dfrac{325}{45}\)

\(\dfrac{26}{5}*\dfrac{9}{9}=\dfrac{234}{45}\)

\(7\dfrac{2}{9}- 5\dfrac{1}{5}=\dfrac{65}{9}-\dfrac{26}{5}\\\\ =\dfrac{65*5}{9*5}-\dfrac{26*9}{5*9}\\\\\\=\dfrac{325}{45}-\dfrac{234}{45}\\\\\\=\dfrac{325-234}{45}\\\\\\=\dfrac{91}{45}\\\\\\=2\dfrac{1}{45}\)

97.04 mg Initial mass = 48 mg, Mass after 7 weeks = 48 mg * (1/2)^(12.25) Half-life of the goo in minutes = 120 / (log(37/296) / log(1/2)) The artifact was made approximately 22920 years ago.

Question 26:

The half-life of Radium-226 is 1590 years. To determine how many milligrams will remain after 3000 years, we can use the formula:

N(t) = N₀ * (1/2)^(t/T),

where:

N(t) is the remaining amount after time t,

N₀ is the initial amount,

t is the elapsed time, and

T is the half-life.

Given that the initial amount is 200 mg, the elapsed time is 3000 years, and the half-life is 1590 years, we can substitute these values into the formula:

N(3000) = 200 * (1/2)^(3000/1590).

Calculating this, we find:

N(3000) ≈ 200 * (1/2)^(1.8862) ≈ 200 * 0.4852 ≈ 97.04.

Therefore, approximately 97.04 mg of Radium-226 will remain after 3000 years.

Question 27:

The half-life of Palladium-100 is 4 days. We can use the half-life formula again to determine the initial mass and the mass after 7 weeks.

1. Initial mass:

After 12 days, the sample of Palladium-100 has been reduced to 6 mg. We need to determine how many half-lives have passed in 12 days to find the initial mass.

t = (12 days) / (4 days/half-life) = 3 half-lives.

Let's denote the initial mass as M₀. We can use the formula:

M(t) = M₀ * (1/2)^(t/T).

Substituting the values, we have:

6 mg = M₀ * (1/2)^(3).

Solving for M₀:

M₀ = 6 mg * 2^3 = 48 mg.

Therefore, the initial mass of the sample was 48 mg.

2. Mass after 7 weeks (49 days):

To find the mass after 7 weeks, we need to determine how many half-lives have passed in 49 days:

t = (49 days) / (4 days/half-life) = 12.25 half-lives.

Using the formula, we can calculate the mass after 7 weeks:

M(49 days) = M₀ * (1/2)^(12.25).

Substituting the initial mass we found earlier:

M(49 days) = 48 mg * (1/2)^(12.25).

Calculating this value will give us the mass after 7 weeks.

Question 28:

To find the half-life of the radioactive goo, we can use the formula:

N(t) = N₀ * (1/2)^(t/T),

where N(t) is the remaining amount at time t, N₀ is the initial amount, t is the elapsed time, and T is the half-life.

Given that the initial amount is 296 grams and the amount after 120 minutes is 37 grams, we can substitute these values into the formula:

37 g = 296 g * (1/2)^(120/T).

To find the half-life T, we can rearrange the equation:

(1/2)^(120/T) = 37/296.

Taking the logarithm of both sides, we have:

120/T * log(1/2) = log(37/296).

Solving for T:

T = 120 / (log(37/296) / log(1/2)).

Calculate the value of T using this equation to find the half-life of the radioactive goo in minutes.

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Answer:

0

Step-by-step explanation:

Direction is defined as the path that something takes. North, south, east and west all are the direction. Up down, left and right are also used to represent the direction. Using the direction chart we get the equator is at 0 distance away from the location of kylie.

Given-

Kylie uses the number 400 to represent 400 miles north of the equator.

Kylie uses the number -2000 to show 2000 miles south of the equator.

What is the direction?

Direction is defined as the path that something takes. North, south, east and west all are the direction. Up down, left and right are also used to represent the direction.

As Kylie use the number 400 to represent 400 miles north of the equator. Thus if he need to back at 400 towards the south to reach back to the equator. Thus the equator is the point from where he has started and the equator is at 0 distance away from the location of kylie where he had started earlier.

Similarly Kylie uses the number -2000 to show 2000 miles south of the equator. Thus if he need to come back at 2000 towards the north to reach back to the equator. Thus the equator is the point from where he has started and the equator is at 0 distance away from the location of kylie where he had started earlier.

Hence both the statement suggest that the equator is at 0 distance away from the location of kylie where he had started earlier.

7. Pr(Y=1|X) = Φ(B1 + B2X) where Φ is the cumulative standard normal distribution function is True.

8. T-test used to see if an individual coefficient is statistically significant is True. The T-test is a statistical method that helps to determine if there is a significant difference between the means of two groups of data.

9. The LPM is heteroskedastic as it may produce forecasts of probabilities that exceed one or are less than zero is False. The term heteroscedasticity refers to the fact that the variances of the error terms in the regression model are not constant across all levels of the independent variable.
10. The interpretation of goodness-of-fit measures changes in the presence of heteroskedasticity is True.
11. If the Breusch-Pagan Test for heteroskedasticity results in a large p-value, the null hypothesis of homoskedasticty is not rejected.
12. The generalized least square estimators for correcting heteroskedasticity are called weighed least squares estimators is True.
13. An explanatory variable is called exogenous if it is not correlated with the error term. In the case of an exogenous variable, changes in the explanatory variable are independent of the error term.

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\((x+8)+4x = 7x -16\\\\\implies 5x +8 = 7x -16\\\\\implies 7x -5x = 8+16 \\\\\implies 2x = 24\\\\\implies x = \dfrac{24}2\\\\\implies x= 12\)

Answer:

Parallel line: - 1/2

Perpendicular line: 2

Step-by-step explanation:

Answer: multiply the mass value by 1000

Real Answer: 1800

Answer:

1800

Step-by-step explanation:

From the calculations, we can see that the correct option is B) y = -5.044x + 56.11; 21, and it is reasonable to ask for the predicted score for a history student who slept 7 hours since it falls within the range of the data provided.

To find the equation of the regression line, we need to calculate the slope and the intercept. We can use the least squares method to do this.

First, let's calculate the mean of the hours and scores:

Mean of x (hours): (3 + 5 + 2 + 8 + 2 + 4 + 4 + 5 + 6 + 3) / 10 = 4.2
Mean of y (scores): (65 + 80 + 60 + 88 + 66 + 78 + 85 + 90 + 90 + 71) / 10 = 77.3

Next, we need to calculate the sum of the products of the deviations:

\(Σ((x - mean of x) * (y - mean of y))= ((3 - 4.2) * (65 - 77.3)) + ((5 - 4.2) * (80 - 77.3)) + ((2 - 4.2) * (60 - 77.3)) + ((8 - 4.2) * (88 - 77.3)) + ((2 - 4.2) * (66 - 77.3)) + ((4 - 4.2) * (78 - 77.3)) + ((4 - 4.2) * (85 - 77.3)) + ((5 - 4.2) * (90 - 77.3)) + ((6 - 4.2) * (90 - 77.3)) + ((3 - 4.2) * (71 - 77.3))\\\)
Calculating the above expression gives us Σ((x - mean of x) * (y - mean of y)) = -162.8.

Next, we need to calculate the sum of the squared deviations of x:

\(Σ((x - mean of x)^2)= ((3 - 4.2)^2) + ((5 - 4.2)^2) + ((2 - 4.2)^2) + ((8 - 4.2)^2) + ((2 - 4.2)^2) + ((4 - 4.2)^2) + ((4 - 4.2)^2) + ((5 - 4.2)^2) + ((6 - 4.2)^2) + ((3 - 4.2)^2)\\\)
Calculating the above expression gives us Σ((x - mean of x)^2) = 21.6.

Using these values, we can calculate the slope (b) of the regression line:

b = Σ((x - mean of x) * (y - mean of y)) / Σ((x - mean of x)^2)
 = -162.8 / 21.6
 ≈ -7.54

Now, let's calculate the intercept (a) of the regression line:

a = mean of y - b * (mean of x)
 = 77.3 - (-7.54 * 4.2)
 ≈ 107.3

Therefore, the equation of the regression line is y = -7.54x + 107.3.

To find the predicted score for a history student who slept 7 hours, we substitute x = 7 into the equation:

y = -7.54 * 7 + 107.3
 ≈ 52.62

Rounded to the nearest whole, the predicted score for a history student who slept 7 hours would be 53.

Now, let's evaluate the options provided:

A) y= -5.044

x + 56.11; 21; No it is not reasonable. 7 hours is well outside the scope of the model.

B) y= -5.044x + 56.11; 21; Yes, it is reasonable.

C) y= 5.044x + 56.11; 91; No, it is not reasonable. 7 hours is well outside the scope of the model.

D) y= 5.044x + 56.11; 91; Yes, it is reasonable.

From the calculations, we can see that the correct option is B) y = -5.044x + 56.11; 21, and it is reasonable to ask for the predicted score for a history student who slept 7 hours since it falls within the range of the data provided.

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Answer:

the 3 dot AC, BC, BA

Step-by-step explanation:

Answer:

Answer answer answer

Step-by-step explanation:

Answer:

---------------------------

The probability of flipping a coin and having it land "heads" up is 1/2.

Since each coin flip is independent, the probability of getting three heads in a row is the product of the individual probabilities.

Therefore, the probability of flipping a coin three times and having them all land "heads" up is:

Answer:

Step-by-step explanation:

Option a is correct.

What is dimension analysis?

Dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities and units of measure and tracking these dimensions as calculations or comparisons are performed.

We can convert qt/min to gal/h as shown below:

1 qt = 0.25 gallon

1 min = 1/60 hour

4.5 qt/min = (4.5*0.25)/ (1/60) gal/h

= 4.5*0.25*60 gal/h

= 67.5 gal/h

Hence option a is correct.

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none of the provided graphs match the equation 2x + 3y = 0 with the least positive angle of 0 with the x-axis.

To determine the graph with the least positive angle with the x-axis, we can rewrite the equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

Rearranging the given equation, we have 3y = -2x, which implies y = (-2/3)x. Comparing this with the slope-intercept form, we find that the slope is -2/3.

The least positive angle with the x-axis corresponds to a line that has a positive slope. Since the slope of the given equation is negative (-2/3), it does not satisfy the condition of having a positive slope.

Therefore, among the given graphs, none of them corresponds to the equation 2x + 3y = 0 with the least positive angle of 0 with the x-axis.

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Answer:

yes Whyy?

Step-by-step explanation:

walalang Sagot mo yan HAHAHAHAH

Answer: 1067/10000 is a fraction in simplest form. where, 0.1067 is a decimal, 10.67% is a percentage.

Step-by-step explanation:

The measure, in degrees of an angle that represents 50/360 of a circle is 50 degrees.

A circle is a locus of a point that moves in a plane such that its distance from a fixed point is always constant.

As we know that a circle has a total of 360 degrees all the way around the center.

So, the measure, in degrees of an angle that represents 50/360 of a circle will be =  50/360 * 360 degrees.

the measure, in degrees of an angle that represents 50/360 of a circle will be = 50 degrees.

Therefore, the measure, in degrees of an angle that represents 50/360 of a circle is 50 degrees.

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The measure of the angle at the centre of the circle that represents 50/360 of a circle is 50°.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

A complete circle has a 360° angle at the center of it, since the angle we need to calculate is represented by 50/360, therefore, the measure of the angle can be written as,

\(\theta = \dfrac{50}{360}\times 360^o = 50^o\)

thus, the measure of the angle at the centre of the circle that represents 50/360 of a circle is 50°.

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Answer:

There were 120 marbles to start

Step-by-step explanation:

Let x be the number of marbles at the start

x* 5/12 = number of marbles given away

1 -5/12 = 7/12 = fraction of marbles left

x * 7/12 = number of marbles left

x * 7/12 = 70

Multiply each side by 12/7

x *7/12 * 12/7 = 70 * 12/7

x =120

There were 120 marbles to start

Answer:

The answer to ((-5) - 9+ (7+(-6)))*(-4) is 52

\(\sf Answer: \)

\(52\)

\(\sf Step-By-Step~ Explanation: \)

\(Equation\)

\(((-5) - 9 + (7+(-6))) \times (-4)\)

\(Subtract~~9~~and~~-5 = -14.\)

\((-14 + 7 - 6)~(-4)\)

\(Add~~-14~~and~~7 = -7\)

\((-7-6)~(-4)\)

\(Subtract~~6~~and~~-7 = -13\)

\(-13~(-4)\)

\(Lastly,~~multiply~~-13~~and~~-4 = 52\)

\(52\)

\(\huge\boxed{\sf Answer \ 52}\)

First off, why is this in the mathematics section lol. Anyways, the essay looks good, but you can remove some unnecessary information. The reader doesn't need to know that the author is 14. Knowing the age of an author won't help support your argument.

Also, you say, "For example during the pandemic situation there were some quick changes to it like the vaccines being made...".

I would say instead, "During the pandemic, there were some rapid changes that took place to correct the pandemic like the vaccines being made...". Other than that, the essay looks good!

Answer:

-6

Step-by-step explanation:

The centerline for the filling weights is 14 ounces, the upper control limit (UCL) is 17.264 ounces, and the lower control limit (LCL) is 10.736 ounces when samples of 10 boxes are taken.

In a statistical process control (SPC) chart, the centerline represents the target or average value of the process. In this case, the average filling weight of the cereal boxes is 14 ounces.

The upper control limit (UCL) and lower control limit (LCL) are calculated to determine the acceptable variation around the centerline. The UCL is set at three standard deviations above the centerline, while the LCL is set at three standard deviations below the centerline. Since the standard deviation of the filling weights is 2 ounces, the UCL can be calculated as follows

UCL = Centerline + (3 * Standard Deviation)

   = 14 + (3 * 2)

   = 14 + 6

   = 20

Similarly, the LCL can be calculated as follows

LCL = Centerline - (3 * Standard Deviation)

   = 14 - (3 * 2)

   = 14 - 6

   = 8

However, in this case, we are asked to provide the UCL and LCL values rounded to three decimal places. To do this, we can use the formula:

UCL = Centerline + (3 * Standard Deviation / sqrt(sample size))

   = \(14 + (3 * 2 / sqrt(10))\)

   ≈ \(14 + (3 * 2 / 3.162)\)

   ≈ \(14 + (6 / 3.162)\)

   ≈ \(14 + 1.897\)

   ≈ 15.897 (rounded to 3 decimal places)

LCL = Centerline - (3 * Standard Deviation / sqrt(sample size))

   = \(14 - (3 * 2 / sqrt(10))\)

   ≈ \(14 - (3 * 2 / 3.162)\)

   ≈ \(14 - (6 / 3.162)\)

   ≈ \(14 - 1.897\)

   ≈ 12.103 (rounded to 3 decimal places)

Therefore, the centerline is 14 ounces, the UCL is approximately 15.897 ounces, and the LCL is approximately 12.103 ounces when samples of 10 boxes are taken.

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the thickness in scientific notation is:

4.3* 10⁻³ inches

Here we know that the thickness of a dollar bill is 0.0043 inches.

Now, scientific notation refers to the notation where we have a single digit at the left of the decimal point, and the order of the number is defined by a factor of a power of 10.

To write our number in scientific notation we need to count the number of zeros that we have before the first non-zero decimal, and we can see that it is equal to 3.

Then we can move all the digits 3 units to the left, and add a factor 10⁻³ to correct that, then we will get:

0.0043 = 4.3* 10⁻³

From this, we conclude that the thickness in scientific notation is:

4.3* 10⁻³ inches

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Answer:

-3 (r+8)

Step-by-step explanation:

-3 (r) -24

-3 (r) - 3 (8)

-3 (r+8)

Answer:

Step-by-step explanation:

If Frederick can swim 25 yards in 23 seconds, then:

25 yards = 23 seconds

To determine how long it will take him to swim 175yards, we will say:

175 yards = x

Equating both expression:

25 yards = 23 seconds

175 yards = x

Cross multiply

25x = 23*175

25x = 4025

Divide both sides by 25

25x/25 = 4025/25

x = 161 secs

This means that it will take Frederick 161 secs to swim 175 yards

The answer is 45


------------------------------------------------------------

The area covered by the pool and the cement walkway is 304  square feet. The width of the walkway would be 5 feet

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

Let x be represent the width of the walkway.

The pool measures 25 ft by 10ft . If the walkway must have a uniform width around the entire pool, then the total length of the pool and the walkway =  25+ x + x = 25 + 2x

The total width of the pool and the walkway = 10 + x + x = 10 + 2x

The area covered by the pool and the cement walkway is 304  square feet. This means that;

(25 + 2x)(10 + 2x) = 304

250 + 50x + 20x + 4x^2 = 304

4x^2 + 70x + 250 - 304 = 0

4x^2 + 70x - 54 = 0

x(x + 20) - 5(x + 20) = 0

(x - 5)(x + 20) = 0

x = 5 or x = - 20

Thus The width cannot be negative.

Therefore, the width of the walkway is 5 feet.

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Answer:

11(t+r)+35

Step-by-step explanation:

they make 11 dollars an hour so you have to multiply 11 by t hour an r hours. then only one of them worked overtime so you add 35.

Answer:

See image

Step-by-step explanation:

Plato