if there are 574 cals in 160 grams,
how many are there in 100 grams

Answer:

lemonade = 11

Step-by-step explanation:

let p = pink lemonade

let t = sweet tea

create a system of equations -- one with quantity, one with associate costs

p + t = 21      

2.5p + 4t = 67.5

substitution method:  let t = 21 - p

2.5p + 4(21 - p) = 67.5

2.5p + 84 - 4p = 67.5

-1.5 p = -16.5

p = 11

t = 21 - 11

t = 10

Answer: 22( w + 2 ) =77 and the amount of the water bottle would be 1.50

Step-by-step explanation: i dont know what to write??

To fill in the missing values in the ANOVA summary table, we need to calculate the values based on the given information.

The missing values are:

To calculate the missing values:

1. S.S. (Sum of Squares) for Between:

Since the total S.S. is given as 27 and the S.S. for Within is 2461, we can subtract the Within S.S. from the Total S.S. to obtain the S.S. for Between:

S.S. Between = Total S.S. - Within S.S. = 27 - 2461 = -2434

2. D.F. (Degrees of Freedom) for Between:

The D.F. for Between is equal to the number of groups minus 1. The number of groups is not provided in the table, so we cannot determine the D.F. for Between.

3. F (F-value):

The F-value can be calculated by dividing the M.S. for Between by the M.S. for Within:

F = M.S. Between / M.S. Within = 1.256 / 107 = 0.0118 (rounded to 4 decimal places)

To locate the p-value for this ANOVA, we can use statistical software such as Excel or R. In Excel, we can use the FDIST(∙) function, while in R, we can use the pf(∙) function.

Using Excel:

p-value = 1 - FDIST(F, D.F. Between, D.F. Within) = 1 - FDIST(0.0118, D.F. Between, 107)

Using R:

p-value = 1 - pf(F, D.F. Between, D.F. Within, lower.tail = TRUE) = 1 - pf(0.0118, D.F. Between, 107, lower.tail = TRUE)

Since the Degrees of Freedom for Between is not provided, we cannot calculate the p-value accurately. The p-value depends on the specific Degrees of Freedom for Between.

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To calculate the cash balance at the end of the period, we need to consider the cash inflows and outflows.

Starting cash balance: $4,520

Cash inflows: $1,654 (receivables collected)

Cash outflows: $1,961 (payments to suppliers) + $500 (cash expenses)

Total cash inflows: $1,654

Total cash outflows: $1,961 + $500 = $2,461

To calculate the cash balance at the end of the period, we subtract the total cash outflows from the starting cash balance and add the total cash inflows:

Cash balance at the end of the period = Starting cash balance + Total cash inflows - Total cash outflows

Cash balance at the end of the period = $4,520 + $1,654 - $2,461

Cash balance at the end of the period = $4,520 - $807

Cash balance at the end of the period = $3,713

Therefore, the cash balance at the end of the period is $3,713.

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The task is to find the average rate of change of the function f(x) = x³ - 8x + 4 over different intervals: (a) from -8 to -6, (b) from 2 to 3, and (c) from 3 to 8.

The average rate of change of a function over an interval is determined by finding the difference in function values at the endpoints of the interval and dividing it by the difference in the x-values of the endpoints.

(a) From -8 to -6:
To find the average rate of change from -8 to -6, we evaluate f(x) at the endpoints and calculate the difference:
F(-8) = (-8)³ - 8(-8) + 4 = -328
F(-6) = (-6)³ - 8(-6) + 4 = -100
The difference in function values is: -100 – (-328) = 228
The difference in x-values is: -6 – (-8) = 2
Therefore, the average rate of change from -8 to -6 is 228/2 = 114.

(b) From 2 to 3:
Evaluate f(x) at the endpoints:
F(2) = (2)³ - 8(2) + 4 = -4
F(3) = (3)³ - 8(3) + 4 = -5
The difference in function values is: -5 – (-4) = -1
The difference in x-values is: 3 – 2 = 1
Therefore, the average rate of change from 2 to 3 is -1/1 = -1.

(c) From 3 to 8:
Evaluate f(x) at the endpoints:
F(3) = (3)³ - 8(3) + 4 = -5
F(8) = (8)³ - 8(8) + 4 = 68
The difference in function values is: 68 – (-5) = 73
The difference in x-values is: 8 – 3 = 5
Therefore, the average rate of change from 3 to 8 is 73/5 = 14.6.

Hence, the average rates of change for the given intervals are:
(a) From -8 to -6: 114
(b) From 2 to 3: -1
(c) From 3 to 8: 14.6.


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Answer:

3. y = 4

4. y = 40

Step-by-step explanation:

3. To find y, input the value of 2 for x in the equation y = 3x - 2.

y = 3(2) - 2

y = 6 - 2

y = 4

y is 4 when x is 2.

4. To find the answer we first have to make an equation in y=mx + b form, where b is the y-intercept and m is the slope. We know that the y-intercept is -5 because the table tells us that when x is zero, y is -5. So, we can use the y-intercept and a point In this example I will use point (6, 13)) to find the slope:

Input the values you know into the equation:

13 = 6m - 5

Add 5 to both sides to isolate the 6m:

18 = 6m

Divide both sides by 6 to isolate the m:

3 = m

Our slope is 3. Now that we know the slope and y-intercept, we can make our equation:

y = 3x - 5

We can use this equation to find y when x is 15:

Input 15 in place of x:

y = 3(15) - 5

Solve:

y = 45 -5

y = 40

When x is 15, y is 40.

Hope this helps :)

The equivalent expression is -1. 8h + 0.7

Algebraic expressions are defined as expression that are composed of variables, terms, coefficients, factors and constants.

They are also made up of arithmetic operations.

From the information given, we have that;

2.1 + (–3.7h) + 1.9h – 1.4

To simply this, we need to expand the bracket, we get;

2.1 - 3. 7h + 1.9h - 1.4

Now, collect the like terms, we get;

-3. 7h + 1. 9h + 2.1 - 1.4

Add or subtract the like terms

-1. 8h + 0.7

Hence, the expression is-1. 8h + 0.7

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In a study conducted by Ellis and colleagues (2012), a new psychotherapy for depression was tested on a sample of 20 inpatients at a psychiatric hospital.

The participants rated their sense of hopelessness before and after treatment using the Beck Hopelessness Scale (BHS). The researchers found that after completing the psychotherapy, the sample had an average decrease in hopelessness score of -5.34. They conducted a two-tailed t-test with a significance level of 0.05 and calculated a t-value of -2.62 and an effect size (Cohen's d) of 0.83.

The researchers used the t-test to examine whether the difference in hopelessness scores before and after treatment was statistically significant. The calculated t-value of -2.62 represents the difference between the sample mean (-5.34) and the population mean (assumed to be 0) divided by the standard error of the mean. The negative t-value indicates that the sample mean is significantly lower than the assumed population mean.

The effect size, measured by Cohen's d, is a standardized measure of the difference between the means. A d-value of 0.83 indicates a moderate effect size, suggesting that the psychotherapy had a noticeable impact on reducing feelings of hopelessness.

Overall, the findings suggest that the new psychotherapy had a significant and meaningful effect on reducing hopelessness in the sample of inpatients with depression, as indicated by the significant t-value and moderate effect size.

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Answer: A. 7

Step-by-step explanation:

3y-2=19

3y-2+2=19+2 (add 2 to both sides)

3y=21

3y/3=21/3 (divide by 3 on each side)

y=7

Answer:

x = 40

Step-by-step explanation:

a²+b²=c²

x²+9²=(x+1)²

x²+81=x²+2x+1

81=x²-x²+2x+1

81=2x+1

81-1=2x

80=2x

x=40

Answer:

y > 3

Step-by-step explanation:

Instead of saying 3 < y, you could say that y > 3.

If this answer helped you, please leave a thanks!

Have a GREAT day!!!

Each month we have to deposit 1389 of amount and we get interest of 30000

percentage, a relative value indicating hundredth parts of any quantity.

Given 500000 to be in our account in retirement of 30 years.

We need to find how much we have to deposit each month.

We know that in a year there are 12 months.

For 30 years the number of months are 12×30=360

So Now divide 500000 by 360 to find each month deposit

500000/360=1388.8

So each month one has to deposit 1389 into account.

Now if account earns 6% of interest. We need to find how much amount we earned.

6% is converted to decimal by dividing 6 by 100

0.06

Now multiply with 500000

0.06×500000

30000

Hence, each month we have to deposit 1389 of amount and we get interest of 30000.

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The price of each book is $6 and the price of each backpack is $14.

Given that,

Cost of 2 books and a backpack = $26

Each book cost $8 less than the backpack.

Let the cost of each book be b and the cost of the backpack be p

2b + p =26  (i)

Each book cost $8 less than a backpack

b=p-8  (ii)

Substitute for b in equation (i)

2(p-8) +p = 26

2p - 16 +p =26

3p = 42

p =14 (Cost of backpack)

b = cost of book = 14-8 =6

Thus, the price of each book is $6 and the price of each backpack is $14.

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Peter's contribution to the whole job is the fraction of the job he completed during the second hour, which is 5/12.

So, Peter completed 5/12 of the whole job.

Let's calculate the rate at which each person completes the job.

Tom can complete 1/6 of the job per hour, Peter can complete 1/3 of the job per hour, and John can complete 1/2 of the job per hour.

During the first hour, Tom completes 1/6 of the job.

So, there is 1 - 1/6 = 5/6 of the job left to be done.

When Peter joins Tom, they work together for one hour.

Their combined rate is (1/6 + 1/3) = 1/2 of the job per hour.

So, in that hour, they complete 1/2 of the remaining job, which is (1/2) * (5/6) = 5/12 of the whole job.

Finally, when John joins them, the three of them work together at a combined rate of (1/6 + 1/3 + 1/2) = 11/12 of the job per hour.

Since they work together until the job is completed, the remaining (5/6) of the job is completed in (5/6) / (11/12) = 10/11 of an hour.

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The solution range of the inequality {5x+7<3  and  3x-4>11} to is in range : x < -4/5 or x > 5.

Given are the following inequalities -

5x+7<3  and  3x-4>11

We have -

5x + 7 < 3

5x < - 4

x < -4/5

and

3x - 4 > 11

3x > 15

x > 5

So, we can write the solution of the inequality as -

x < -4/5 or x > 5

Therefore, the solution to the inequality is in range : x < -4/5 or x > 5.

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Answer:

see explanation

Step-by-step explanation:

If there is a solution between x = 1.1 and x = 1.2 then there will be a change in sign when the equation is evaluated at the points, indicating the graph has crossed the x- axis, where the solution lies.

Given

x³ + 4x = 6 ( subtract 6 from both sides )

x³ + 4x - 6 = 0 ← in standard form

Evaluating for x = 1.1

(1.1)³ + 4(1.1) - 6

= 1.331 + 4.4 - 6 = - 0.269 ← < 0

Evaluating for x = 1.2

(1.2)³ + 4(1.2) - 6

= 1.728 + 4.8 - 6 = 0.528 ← > 0

Since there is a change in sign the graph has crossed the x-axis from below /   indicating a solution between x = 1.1 and x = 1.2

Test statistic is less than the critical value, we reject the null hypothesis in favor of the alternative hypothesis.

To test the claim that less than 10 percent of the test results are wrong, we can set up a hypothesis test.

Let's define the null hypothesis (\(H_{0}\)) and the alternative hypothesis (\(H_{1}\)) as follows:

\(H_{0}\): The proportion of wrong test results is equal to or greater than 10%.

\(H_{1}\): The proportion of wrong test results is less than 10%.

We will use a significance level (α) of 0.05.

To conduct the hypothesis test, we need to calculate the test statistic and compare it to the critical value from the appropriate distribution.

Let's calculate the test statistic using the given information:

n = 308 (total number of subjects)

x = 29 (number of wrong test results)

\(p_{0}\) = 0.10 (proportion under the null hypothesis)

The test statistic for testing proportions is given by:

z = (x - n\(p_{0}\)) / √(n\(p_{0}\)(1 - \(p_{0}\)))

Using the values:

z = (29 - 308 * 0.10) / √(308 * 0.10 * 0.90)

Simplifying this expression:

z = -4.716

To determine the critical value, we need to find the z-score corresponding to a 0.05 significance level in the left tail of the standard normal distribution. A z-score table or a statistical calculator can be used to find this critical value.

Assuming a standard normal distribution, the critical z-value for a 0.05 significance level is approximately -1.645.

Since the calculated test statistic (-4.716) is less than the critical value (-1.645), we reject the null hypothesis (\(H_{0}\)) in favor of the alternative hypothesis (\(H_{1}\)). The evidence suggests that less than 10% of the test results are wrong.

Therefore, based on the provided data, we have sufficient evidence to support the claim that less than 10 percent of the test results are wrong for marijuana usage.

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There are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

The multiplication principle states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.

To find the number of ways to choose 3 men from the 12 men, we can use the formula for combination, which is: ⁿCᵣ = n! / (r! (n-r)!).

where n is the total number of men and r is the number of men chosen

so, the number of ways to choose 3 men from the 12 men = ¹²C₃ = 1.

Similarly, we evaluate the number of ways to choose 2 women from the 8 women

as = ⁸C₂ = 14

Now, using the multiplication principle, we can find the total number of ways 3 men and 2 women be chosen if they are equally considered.

220 x 14 = 3080

Therefore, there are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

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Looking at the right triangle that has been shown here, the statements that are not true are; ABC .

A right triangle is a particular kind of triangle with a right angle, which is an angle that measures 90 degrees. The other two angles in a right triangle are acute, which means that they have a degree value below 90. The hypotenuse is the side that forms the right angle; the legs are the other two sides.

The length of the hypotenuse squared in a right triangle is equal to one leg's squared length plus the other leg's squared length. The Pythagorean theorem, which refers to this relationship, is a cornerstone of geometry.

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The margin of error for the survey, rounded to the nearest tenth, is approximately 4.0% when expressed as a percentage.

To determine the margin of error for a survey at the 95% confidence level, we need to calculate the standard error. The margin of error represents the range within which the true population proportion is likely to fall.

The formula for calculating the standard error is:

Standard Error = sqrt((p * (1 - p)) / n)

where p is the sample proportion and n is the sample size.

In this case, the sample proportion is 64% (or 0.64) since 64% of the 1350 surveyed residents support the plan.

Plugging in the values:

Standard Error = \(\sqrt{(0.64 * (1 - 0.64)) / 1350)}\)

\(= \sqrt{(0.2304 / 1350)} \\= \sqrt{(0.0001707)}\)

≈ 0.0131

Now, to find the margin of error, we multiply the standard error by the appropriate critical value for a 95% confidence level. The critical value corresponds to the z-score, which is approximately 1.96 for a 95% confidence level.

Margin of Error = z * Standard Error

= 1.96 * 0.0131

≈ 0.0257

Finally, to express the margin of error as a percentage, we divide it by the sample proportion and multiply by 100:

Margin of Error as Percentage = (Margin of Error / Sample Proportion) * 100

= (0.0257 / 0.64) * 100

≈ 4.0%

Therefore, the margin of error for this survey, expressed as a percentage to the nearest tenth, is approximately 4.0%.

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20.2% of trainees at the local mill earn less than 880.0 dollars a month.

The incomes of trainees at the local mill are normally distributed with a mean of 1210.0 dollars and a standard deviation of 140.0 dollars. This means that the distribution of incomes follows a normal curve, with most trainees earning close to the mean income of 1210.0 dollars, and fewer trainees earning significantly more or less than the mean.

To find the percentage of trainees earning less than 880.0 dollars a month, we can use the standard normal distribution table (also known as the z-table) to find the proportion of the distribution that is less than 880.0 dollars.

First, we need to convert the income of 880.0 dollars to standard units by subtracting the mean income and dividing by the standard deviation. This gives us (880.0 - 1210.0) / 140.0 = -1.29.

Next, we can look up the proportion of the standard normal distribution that is less than -1.29 on the z-table. This value is approximately 0.202, which means that approximately 20.2% of trainees at the local mill earn less than 880.0 dollars a month.

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Answer:

1 metro hace 100 cm

Step-by-step explanation:

100* 10^-2m

ZW is 37 units long. By subtracting the length of WY, which is found to be -1, from ZW, we found that ZY is 38 units long. However, the lengths of TX and WY are negative, suggesting a potential error in the given information.

In the given figure, we are provided with the lengths of various line segments. Using this information, we can determine the length of ZW. Given that XY = 15 and ZX = 52, we can subtract the length of XY from ZX to find the length of ZW. Therefore, ZW = ZX - XY = 52 - 15 = 37.

Now let's provide a detailed explanation of each length:

ZY = 37

To find the length of ZY, we need to subtract the length of WY from ZW. From the previous calculation, we know that ZW = 37. However, the length of WY is not given directly. To find it, we can use the fact that WX = 22 and WT = 23. Since WY is a part of WX and WT, we can subtract WT from WX to get WY. Therefore, WY = WX - WT = 22 - 23 = -1.

Now, we can substitute the value of WY into the equation for ZY: ZY = ZW - WY = 37 - (-1) = 38. Thus, ZY is equal to 38.

TX = 15

To find the length of TX, we need to subtract the length of WT from XY. We know that XY = 15 and WT = 23. Therefore, TX = XY - WT = 15 - 23 = -8. However, it is important to note that lengths cannot be negative, so TX cannot be -8. This indicates that there might be an error in the given information or measurements.

WY = -1

As calculated earlier, the length of WY is -1. However, it is important to note that lengths cannot be negative in a geometrical context. Therefore, we can conclude that there might be an error in the given information or measurements. It is advisable to double-check the given lengths or clarify any inconsistencies before proceeding with further calculations.

In summary, using the given information, we determined that ZW is 37 units long. By subtracting the length of WY, which is found to be -1, from ZW, we found that ZY is 38 units long. However, the lengths of TX and WY are negative, suggesting a potential error in the given information. It is recommended to verify the measurements to ensure accurate results.

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The tension in each cable is 6 pounds

When a traffic light is suspended by two cables, the tension in each cable can be calculated based on the weight of the traffic light and the forces acting on it.

In this case, the traffic light weighs 12 pounds. Since it is in equilibrium (not accelerating), the sum of the vertical forces acting on it must be zero.

Let's assume that the tension in the first cable is T1 and the tension in the second cable is T2. Since the traffic light is not moving vertically, the sum of the vertical forces is:

T1 + T2 - 12 = 0

We know that the weight of the traffic light is 12 pounds, so we can rewrite the equation as:

T1 + T2 = 12

Since the traffic light is symmetrically suspended, we can assume that the tension in each cable is the same. Therefore, we can substitute T1 with T2 in the equation:

2T = 12

Dividing both sides by 2, we get:

T = 6

Hence, the tension in each cable is 6 pounds. This means that each cable is exerting a force of 6 pounds to support the weight of the traffic light and keep it in equilibrium.

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Answer:

X= -1

Step-by-step explanation:

2x+5=1(x+4)

2x+5=1x+4

2x-1x=-5+4

x=-1

Answer:

A. 3x+80+2x=180

Step-by-step explanation:

a straight line is 180 degrees

The value of a = -2 and b = 3.

What is a system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

Here, we have

Given: 3a - 5b = -26, a + 2b = 6

We have to solve this equation.

3a - 5b = -26...(1)

a + 2b = 6...(2)

Now we multiply equation (1) by 2 and equation (2) by 5 and we get

6a - 10b = -52....(3)

5a + 10b = 30....(4)

After solving equations (3) and (4), we get

11a = -22

a = -2

Now we put the value of 'a' in equation(3) and we get

6(-2) - 10b = -52

-10b = -52 + 12

-10b =  -30

b = 3

Hence, the value of a = -2 and b = 3.

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The optimal input combination is L* = 4,000 and K* = 500.

To find the optimal input combination for producing 1,000 units of output, we can follow these steps:

1. Set the production function equal to the desired output: min{1/4L, 2K} = 1,000
2. Determine the condition under which each constraint is binding. For 1/4L to be binding, we need 1/4L >= 2K, and for 2K to be binding, we need 2K >= 1/4L.
3. Solve the binding constraints for L and K:

1/4L >= 2K => L >= 8K
2K >= 1/4L => K >= 1/8L

4. Substitute the desired output (1,000 units) into the binding constraints:

1/4L = 1,000 => L = 4,000
2K = 1,000 => K = 500

So, the optimal input combination is L* = 4,000 and K* = 500. The correct answer is option A.

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