Question

Find the sum.

1/3(9−6m)+1/4(12m−8)

We need to find value of x from the equation, so let write the equation first;

\({:\implies \quad \sf \dfrac{7x+14}{3}-\dfrac{17-3x}{5}=6x-\dfrac{4x+2}{3}-5}\)

Taking LCM both sides ;

\({:\implies \quad \sf \dfrac{35x+70-(51-9x)}{15}=\dfrac{18x-(4x+2)-15}{3}}\)

Multiplying both sides by 15 and simplifying ;

\({:\implies \quad \sf 35x+70-51+9x=5(18x-4x-2-15)}\)

\({:\implies \quad \sf 44x+19=5(14x-17)}\)

\({:\implies \quad \sf 44x+19=70x-85}\)

\({:\implies \quad \sf 70x-44x=19+85}\)

\({:\implies \quad \sf 26x=104}\)

\({:\implies \quad \sf x=\dfrac{104}{26}=\boxed{\bf 4}}\)

Hence, The required answer is 4

Given: {(7x + 14)/3} - {(17 - 3x)/5} = 6x - {(4x + 2)/3} - 5

Asked: Find the value of x = ?

Explanation: Given equation is {(7x + 14)/3} - {(17 - 3x)/5} = 6x - {(4x + 2)/3} - 5

⇛{(7x + 14)/3} - {(17 - 3x)/5} = {(6x)/1} - {(4x + 2)/3} - (5/1)

⇛{(7x*5 + 14*5 - 17*3 + 3x*3)/15} = {(6x*3 - 4x*1 - 2*1 - 5*3)/3}

⇛{(35x + 70 - 51 + 9x)/15} = {(18x - 4x - 2 - 15)/3}

⇛{(35x + 9x + 70 - 51)/15} = {(18x - 4x - 2 - 15)/3}

⇛{(44x + 19)/15} = {(14x - 17)/3}

⇛[{1/15}(44x + 19)] = [{1/3}(14x - 17)}]

⇛{(44x + 19)/15} = {(14x - 17)/3}

Since (a/b) = (c/d) ⇛a(d) = b(c) ⇛ad = bc

Where, a = 44x + 19, b = 15

c = 14x - 17 and d = 3

On applying cross multiplication then

⇛3(44x + 19) = 15(14x - 17)

Multiply the numbers outside of the bracket with numbers in the bracket.

⇛132x + 57 = 210x - 255

Shift the variable value on LHS and constant value on RHS.

⇛132x - 210x = -255 - 57

Subtract the values on LHS and RHS.

⇛(-78x) = (-312)

Shift the number (-78) from LHS to RHS.

⇛x = {(-312)/(-78)

Simplify the RHS fraction to get the final value of x.

⇛x = 4/1

Therefore, x = 4

Answer: Hence, the value of x for the given problem is 4.

EXPLORE MORE:

Verification:

Check whether the value of x for the given problem is true or false.

If x = 4 then LHS of the equation is

{(7x + 14)/3} - {(17 - 3x)/5}

= [{7(4) + 14}/3] - [{17 - 3(4)}/5]

= {(7*4 + 14)/3} - {(17 - 3*4)/5}

= {(28 + 14))3} - {(17 - 12)/5}

= (42/3) - (5/5)

= (42/3) - 1

= (42/3) - (1/1)

= {(42 - 1*3)/3

= {(42 - 3)/3}

= (39/3)

= 13/1

= 13

And RHS = 6x - {(4x + 2)/3} - 5

= 6(4) - [{4(4) + 2}/3] - 5

= 24 - {(16 + 2)/3} - 5

= 24 - (18/3) - 5

= 24 - (6/1) - 5

= (24/1) - (6/1) - (5/1)

= (24*1 - 6*1 - 5*1)/1

= (24 - 6 - 5)/1

= (24 -11)/1

= 13/1

= 13

On comparing with both the sides, we notice that LHS = RHS is true for x = 4

Hence, verified.

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Solve the equation: 5(3p - 5) + 4p = 5p - 6( p + 4)....

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It should be noted that z^4 will be -32 in rectangular form.

Based on the information, z = r(cos θ + i sin θ), and provided positive integer n, then it is implied that:

z^n = r^n (cos nθ + i sin nθ)

In this instance, we need to solve for z^4 in rectangular form when z = -2 - 2i. Firstly, we must calculate |z| and arg(z):

|z| = √((-2)^2 + (-2)^2) = 2√2

arg(z) = arctan(-2/-2) = π/4

Leveraging De Moivre's theorem, we can effectively deduce the value of z^4 as:

z^4 = (2√2)^4 (cos (4π/4) + i sin (4π/4))

= 32 (cos π + i sin π)

= -32

Concludedly, z^4  resolved in rectangular form is -32.

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Answer:

y= -1/4x + 4

Step-by-step explanation:

4x-y = 12

4x - 12 = y

Slope = 4

Slope of the perpendicular line: -1/4

Point (8,2)

y-intercept: 2 - (-1/4)(8) = 2 + 2 = 4

3 is the ways that she could do this

Let's first find the sum of each list:

List S: 3 + 5 + 8 + 11 + 13 + 14 = 54

List T: 2 + 5 + 6 + 10 + 12 + 13 = 48

The difference between the sums of the lists is 54 - 48 = 6.

two numbers must be half of 6, which is 3. In other words, we're looking for pairs of numbers where the number from List S is 3 greater than the number from List T.

Now we'll compare the numbers in the two lists to see which pairs meet this condition:

(3, 0): No match.

(5, 2): Match.

(8, 5): Match.

(11, 8): No match.

(13, 10): Match.

(14, 11): No match.

We found 3 pairs that meet the condition: (5, 2), (8, 5), and (13, 10). Therefore, there are 3 ways Jenny can swap the numbers to make the sums equal.

The correct answer is C, 3.

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The probability of having, at most, 9 girls, is 0.9515

The probability that a random baby is a girl is:

p = 0.5

And the probability that a random baby is a boy is:

q = 0.5

Then the probability that, at most, 9 out of 11 babys are girls, is given by:

1 - p(10) - p(11)

Where P(10) is the probability that 10 of the babies are girls and p(11) is the probability that the 11 babies are girls.

p(10) = C(11, 10)*(0.5)^10*(0.5)^1 = C(11, 9)*(0.5)^11

Where C(11, 10) is the combinations of 10 elements that we can make with a set of 11 elements, such that:

C(11, 10)=  11!/(11 - 10)!*10! = 11

Replacing that, we get:

P = 11*(0.5)^11 = 0.0054

p(11) = C(11, 11)*0.5^11 = 1*0.5^11 = 0.0005

Then the probability is:

P = 1 - 0.0054 - 0.0005 = 0.9515

The probability of having, at most, 9 girls, is 0.9515

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Answer:

657

Step-by-step explanation:

......................

There are different ways to approach this question, but one possible method is to conduct a one-sample t-test using the formula t = (M - μ) / (s / sqrt(n)), where M is the sample mean, μ is the population mean (null hypothesis), s is the sample standard deviation, and n is the sample size. With the given information, the t-value is (1.6 - 0) / (0.8 / sqrt(16)) = 8.

The degrees of freedom is n - 1 = 15. Using a t-table or a calculator, the p-value for a one-tailed test with 15 degrees of freedom and a t-value of 8 is much smaller than .05 (e.g., < .0005). Therefore, we can reject the null hypothesis and conclude that women find a sense of humor to be important in a long-term relationship at a .05 level of significance. The correct answer is b.

Test 2 is associated with smaller critical values. The critical values for a t-test depend on the level of significance, the degrees of freedom, and whether the test is one-tailed or two-tailed. In general, a smaller level of significance or a larger sample size leads to smaller critical values (i.e., it becomes easier to reject the null hypothesis). Since Test 2 has a larger sample size than Test 1, it is more likely to detect a significant effect (i.e., have a smaller Type II error rate), and therefore requires smaller critical values to achieve a .05 level of significance. The correct answer is b.

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The difference between groups and the sample size makes the results of a study statistically significant.

Statistical significance is a measure of the likelihood that the results of a study are not due to chance. In order for a result to be statistically significant, it must meet two criteria:

The difference between groups must be large enough to be unlikely to occur by chance. This is typically assessed using a statistical test such as a t-test or an ANOVA.

The result of the test is expressed as a p-value, which represents the probability of obtaining the observed results if there were no true difference between groups. A p-value of less than 0.05 (or 5%) is generally considered to be statistically significant.

The sample size must be large enough to reduce the possibility of sampling error. A larger sample size generally increases the power of a study, making it more likely to detect a true effect.

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Answer: 730.5 meters of fencing.

Step-by-step explanation:

We are asked to find the perimeter (fence) of a rectangle (the field) with a length of 290 meters and a width of 75.25 meters.

To find the perimeter, we must add the lengths of each individual side of the rectangle. In other words,
290 + 75.25 + 290 + 79.25 =
730.5.

Solution

The recursive formular for geometric sequence:

Recursive formula for a geometric sequence is

where r is the common ratio

This is called recursive formula for geometric sequence.

Hence the recursive formula =

Answer:

nwhbjwhr

Step-by-step explanation:

ewrwrwrwewe

Answer:

24

Step-by-step explanation:

when you open up the parenthesis, you get -8x-3 which is 24.

negative x negative = positive

a. The proportion of genetic abnormalities in recent years is greater than the proportion believed in the 1990s (p > 0.30). b. The number of successes (136) and the number of failures 265 should be at least 10. In this case, both criteria are satisfied. c. The z is 2.048. d. If the p-value is larger than the significance level, it would suggest that there is not enough evidence to reject the null hypothesis and conclude that the proportion has not significantly changed.

a. The hypotheses to test if the proportion of genetic abnormalities has increased in recent years can be stated as follows:

Null hypothesis (H₀): The proportion of genetic abnormalities in recent years is equal to or less than the proportion believed in the 1990s (p ≤ 0.30).

Alternative hypothesis (Ha): The proportion of genetic abnormalities in recent years is greater than the proportion believed in the 1990s (p > 0.30).

b. To conduct the hypothesis test, we need to verify if the conditions for performing the test are met. The conditions are as follows:

Random Sample: The study states that the 401 children were randomly selected, so this condition is met.

Independence: The sample should consist of independent observations. If the children were selected randomly and their genetic abnormalities are unrelated to each other, then the independence condition is likely satisfied.

Large Sample Size: For hypothesis tests involving proportions, it is recommended to have a large enough sample size to ensure the sampling distribution is approximately normal. There is no specific threshold, but as a guideline, both the number of successes (136) and the number of failures (401 - 136 = 265) should be at least 10. In this case, both criteria are satisfied.

c. To find the p-value, we need to perform a hypothesis test based on the given data. Since the sample size is large, we can use the normal approximation for the binomial distribution. We calculate the test statistic, which is the z-score for proportions, and then find the p-value.

The formula for the z-score for proportions is:

z = (\(\hat p\) - p₀) / √((p₀ * (1 - p₀)) / n)

where \(\hat p\) is the sample proportion, p₀ is the proportion under the null hypothesis, and n is the sample size.

In this case, \(\hat p\) (sample proportion) = 136 / 401 = 0.339, p₀ (proportion under the null hypothesis) = 0.30, and n (sample size) = 401.

Calculating the z-score:

z = (0.339 - 0.30) / √((0.30 * (1 - 0.30)) / 401)

z = 2.048

To find the p-value associated with this z-score, we look up the area to the right of the z-score in the standard normal distribution table or use statistical software.

d. The p-value represents the probability of observing a test statistic as extreme as the one calculated (or more extreme) assuming the null hypothesis is true. In this case, since we are testing if the proportion of genetic abnormalities has increased, the p-value is the probability of observing a sample proportion as large as or larger than 0.339, given that the true proportion is equal to or less than 0.30.

Without the actual p-value, it is not possible to provide a specific interpretation. However, if the p-value is smaller than the significance level (commonly chosen as 0.05), it would indicate that there is strong evidence to reject the null hypothesis and conclude that the proportion of genetic abnormalities has increased in recent years.

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Answer:

x=7

2x+45=59

3x+55=76

Step-by-step explanation:

Answer:

7°, 59°, 76°

Step-by-step explanation:

The equation for the sum of the angles:

Solving for x:

The angles:

The largest area of the rectangle is 2 square units.

We have a right angled isosceles triangle with hypotenuse 4 units.

so its base will be equal to the perpendicular  , let it be B

So we know ,

B² + P² = H²

2B² = H²

B²  = 16/2

B = 2√2

So base is equal to perpendicular = 2√2 units

Now let consider a rectangle inside the triangle with length 2x and the width y , and the area will become

A = 2xy  ....(1)

we see from the figure the length of the perpendicular AD drawn on the hypotenuse is

BD² + AD² = AB²

AD² = AB² - BD²

      = 8 - 4

AD² = 4

AD = 2 units

Now we see triangle ABD and AEG are similar to each other , So

AD/BD = AG/GE

2/2 = 2-y/x

therefore

x = 2-y

put this value in eqn (1)

A = 2(2-y)y

A = 4y - 2y²

Now to maximize the area we take the derivative of the equation and then put it equal to zero

∴ 4 - 4y = 0

y = 1

∴ x = 2-y = 2-1 = 1 units

So area will be maximum when length and width are 1 units each.

therefore , largest area (A) of the rectangle is  = 2xy = 2 square units.

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To determine the exact concentration of the solution made, one can divide the mass of the solute with the volume of the solution.

A solution is the substance formed by the mixture of solute in solvent. The solute may or may not be dissolved in the solution. One can determine the exact concentration of the solution if the mass of solute added in the specific volume of solution is known. If the solution is made by someone else, then its concentration can be determined by process of titration.

The concentration of a solution is expressed in the form of moles or grams per unit liter. If the solution is unknown and only its dissolved chemical is known, then titration will help in determining the closest value of concentration if performed without human error. In titration, the use of glassware that that is more precise than the flasks, beakers, and graduated cylinders are used.

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Refer to complete question below:

How do we determine concentration a solution? If it is a solution that we have made up, we can readily do the calculations required. But what if it is a solution that someone else has made? What technique can be used to gather information about a solution that we are given with no other information than the name of the chemical dissolved.

Answer:

that would be nice for you to have to say about me nila rc

Answer:

Is it 12?Yes,I think it's 12.

The hypotheses for the test are H₀: σ₁² = σ₂² and H₁: σ₁² ≠ σ₂². This is a two-tailed test to assess if there is a difference in the standard deviations of sound levels between the areas designated as "casualty doors" and operating theaters. The claim being investigated is whether or not there is a difference in the standard deviations.

The hypotheses for the test are:

H₀: σ₁² = σ₂² (There is no difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

H₁: σ₁² ≠ σ₂² (There is a difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

This hypothesis test is a two-tailed test because the alternative hypothesis is not specifying a direction of difference.

To substantiate the claim that there is a difference in the standard deviations, we will conduct a two-sample F-test at a significance level of 0.10, comparing the variances of the two groups.

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The statement that is not true of the test data approach in a test of a computerized accounting system is B) Test data should consist of data related to all controls prevalent in the organization.

This statement is incorrect because the test data approach aims to test specific controls that the auditor wishes to rely on rather than all controls prevalent in the organization. The test data approach involves the creation of a set of test transactions that are processed by the client's computer program under the auditor's control.

The results of the test data are used to determine whether the application and general controls are functioning properly. By using this approach, the auditor can gain assurance that the system is functioning as intended and identify any control weaknesses that need to be addressed.

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The equation of tangent plane is -x + 2x - 1 = 0

Given,

r = < u² , 8usinv , ucosv >

Here,

r = < u² , 8usinv , ucosv >

Differentiate partially with respect to u and v,

\(r_{u}\) = < 2u , 8sinv , cosv >

\(r_{v}\) = < 0, 8ucosv , -4sinv >

Substitute u = 1 and v = 0

\(r_{u}\) = < 2, 0 , 0 >

\(r_{v}\) = < 0 , 8 , 0 >

Now,

N = \(r_{u}\) × \(r_{v}\)

N = \(\left[\begin{array}{ccc}i&j&k\\2&0&1\\0&8&0\end{array}\right]\)

N = -8i -j(0) +16k

N = < -8 , 0 , 16 >

Tangent plane

-8x + 16z + d = 0

Coordinates of tangent plane : <1, 0 ,1>

Substitute the values in the equation,

-8(1) + 16 (1) + d = 0

d = -8

Substitute in the tangent plane equation,

-8x + 16z - 8 = 0

-x + 2x - 1 = 0

Thus equation of tangent plane: -x + 2x - 1 = 0

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Answer:

see explanation

Step-by-step explanation:

1 loaf requires 565 g of flour , then

p loaves requires 565p g of flour

100 g is required for sprinkling , then

total amount of flour = 565p + 100

Equate expression to 3700 and solve for p

565p + 100 = 3700 ( subtract 100 from both sides )

565p = 3600 ( divide both sides by 565 )

p = 6.37168.....

Thus a maximum of 6 loaves can be made

The ratio of the volume of sphere B to the volume of sphere A is 125. Option C is correct.

The volume of a sphere is given by the formula V = (4/3)πr³, where V is the volume of the sphere, r is the radius of the sphere, and π (pi) is a mathematical constant.

Let the radius of sphere A be r, then the radius of sphere B is 5r.

The volume of sphere A is V_A = (4/3)πr³.

The volume of sphere B is V_B = (4/3)π(5r)^3 = (4/3)π125r³.

The ratio of the volume of sphere B to the volume of sphere A is V_B/V_A

= [(4/3)π125r³]/[(4/3)πr³]

= 125.

Hence, C. 125 is the correct option.

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Answer:

26

Step-by-step explanation:

Examples:

1 x 13 = 13

3 x 13 = 39

Second blank:

2 x 13 = 26

The correct model for the question is:

A comparison of the equality of proportions of 8 sports activities for 3 high school grade levels.

In this scenario, we have three high school grade levels and we want to compare the equality of proportions of 8 different sports activities among these grade levels. We can use a chi-square test to assess whether there is a significant difference in the distribution of sports activities across the grade levels.

The chi-square test is appropriate when we have categorical data and want to test for independence or homogeneity. In this case, we are interested in testing for independence, as we want to determine if the choice of sports activity is independent of the high school grade level.

To perform the chi-square test, we would set up a contingency table that shows the observed frequencies of each sports activity for each grade level. We would then calculate the expected frequencies under the assumption of independence and degrees of freedom equal to (number of rows - 1) multiplied by (number of columns - 1). In this case, the degrees of freedom would be (3 - 1) multiplied by (8 - 1), which equals 14.

Once we have the observed and expected frequencies, we can calculate the chi-square statistic by summing up the squared differences between the observed and expected frequencies, divided by the expected frequencies. This gives us the test statistic, which follows a chi-square distribution with degrees of freedom equal to 14.

Based on the given information, a chi-square distribution with 14 degrees of freedom is a correct model for comparing the equality of proportions of 8 sports activities for 3 high school grade levels. The chi-square test will help determine whether there is a significant association between the choice of sports activity and the high school grade level.

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Answer: Simplification of Fractions.

Step-by-step explanation:

Answer: To find when both farmers charge the same amount for delivered produce, we need to set their equations equal to each other:

Amos: y = 22x

Calvin: y = 16x + 48

22x = 16x + 48

6x = 48

x = 8

So Amos and Calvin will charge the same amount when 8 boxes of potatoes are being delivered. To find the amount they will charge, we can substitute x = 8 into either equation:

Amos: y = 22(8) = 176

Calvin: y = 16(8) + 48 = 176

So they will both charge $176 for delivering 8 boxes of potatoes.

Answer:

240 units^2

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

178^2 units

Answer:

The answer is A. 1/5 of an hour per truck.

Step-by-step explanation:

25/5=5 so that means 5 trucks per hour, or 1/5 of an hour per truck.

Hope this helps!! :)

The actual cost to see the game is $150, as that is the amount you paid for the ticket. The cost in this scenario can be considered an opportunity cost. By choosing to attend the game instead of selling the ticket for $400, you forgo the opportunity to earn that additional $400.

In this scenario, the cost of attending the game refers to the actual amount of money you spent on the ticket, which is $150. This is the out-of-pocket expense that directly affects your financial resources.

On the other hand, the opportunity cost is the potential benefit or value that you give up by choosing one option over another. In this case, if you had sold the ticket for $400, you would have received a higher amount of money, which represents the opportunity cost of attending the game. By deciding to go to the game, you forego the opportunity to earn that additional $400.

Opportunity cost is a concept in economics that emphasizes the value of the next best alternative forgone when making a decision. It helps assess the trade-offs involved in different choices and helps in evaluating the true cost of a decision beyond the immediate financial expenses.

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