Suppose y varies directly with x and inversely with z. If y = 14 when x = 7 and z = 3, what is x when y = 3 and z = 8? Use the step-by-step process you learned to solve this problem.

Step 1: Set up the correct type of variation equation.
y =
✔ kx/z
Step 2: Determine the constant of variation.
k =

Answer:

13

Step-by-step explanation:

5²+12²=25+144=169

square root of 169 = 13

Answer:

D is the answer

Step-by-step explanation:

Using bags that will make the balloon and the stickers have the same number in each bag, mere looking at the answers, 100/2 gives you 50 while 68/2 gives you 34. it means that it was splitted equally into the two bags.

The value of y of the inequality 4y + 1/5 ≤ 4/5 is: y ≤ 3/20.

Inequalities can be solved the way a normal algebraic equation is being solved. It is solved by isolating the value of the variable.

The inequality given is, 4y + 1/5 ≤ 4/5. Solve as shown below:

Subtract both sides by 1/5:

4y + 1/5 - 1/5 ≤ 4/5 - 1/5 [subtraction property of equality]

4y ≤ 3/5

Divide both sides by 4:

4y/4 ≤ 3/5 / 4

y ≤ 3/5 × 1/4

y ≤ 3/5 × 1/4

y ≤ (3 × 1) / (5 × 4)

y ≤ 3/20

The value of y is: y ≤ 3/20.

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Answer:

309 chemistry textbooks and 103 math textbooks.

Step-by-step explanation:

Let c be the number of chemistry textbooks sold and m be the number of math textbooks sold. We know that c + m = 412, because the total number of textbooks sold is 412. We also know that c = 3m, because the number of chemistry textbooks sold is three times the number of math textbooks sold.

We can substitute 3m for c in the first equation to get 3m + m = 412. This simplifies to 4m = 412. Dividing both sides by 4 gives us m = 103.

Since we know that c = 3m, the number of chemistry textbooks sold is 3 * 103 = 309. Therefore, the store sold 309 chemistry textbooks and 103 math textbooks.

The cups of diced tomatoes the Alfonso should put in the chili is 6 1/2 cups.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

Let the number of cups be x.

Based on the information, this will be illustrated as:

1.5 / x = 3/13

Cross multiply

3x = 13 × 1.5

3x = 19.5

Divide

x = 19.5 / 3

x = 6 1/2

The cups needed is 6 1/2 cups.

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Answer:

a= 108 degrees

b=88 degrees

c= 90 degrees

d= 90 degrees

Step-by-step explanation:

For a degrees since 72 degrees and a degrees make a straight angle:

180-72= a

So, a=108 degrees

Same goes for b degrees:

180-92=b

So, b=88 degrees

For c degrees, you need to know that the sum of the angles in a quadrilateral equal to 360 degrees.

So, 74+a+b+c=360

= 360- (74+108+88)=c

= 90 degrees= c

So since d degrees and c degrees make a straight angle,

180-90=d

90 degrees= d

Mean = 95.125

Variance = 198.90625

Standard deviation = 14.06,

Confidence interval = 95.125 +/- 3.45

To find the 95% confidence interval of the mean score for all bowlers in this league, we need to first calculate the sample mean and sample standard deviation of the given data set.

The sample mean is calculated as follows:

mean = 95.125

The sample standard deviation is calculated as follows:

First, we need to calculate the variance of the data set, which is done by taking the sum of the squared differences between each score and the mean, and dividing by the sample size minus 1:

variance = 198.90625

The sample standard deviation is then the square root of the variance:

standard deviation = sqrt(198.90625)

standard deviation = 14.06

Now that we have the sample mean and sample standard deviation, we can use these values to calculate the 95% confidence interval of the mean score for all bowlers in this league.

We can use the following formula to calculate the confidence interval:

confidence interval = mean +/- (1.96 * (standard deviation / sqrt(sample size)))

Substituting in the values we calculated above, we get:

confidence interval = 95.125 +/- (1.96 * (14.06 / sqrt(40)))

Hence , confidence interval = 95.125 +/- 3.45

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Answer:

(90.78, 98.22)

Step-by-step explanation:

A 95% confidence interval for μ is (x¯−zα/2σn‾√,x¯+zα/2σn‾√). Here, α=0.05, σ=12, and n=40. Use Excel to calculate the 95% confidence interval.1. Open Excel, enter the given data in column A, and find the sample mean, x¯, using the AVERAGE function. Thus, the sample mean is x¯=94.5.2. Click on any empty cell, enter =CONFIDENCE.NORM(0.05,12,40), and press ENTER.3. The answer rounded to two decimal places is zα/2σn‾√≈3.72. The confidence interval for the population mean has a lower limit of 94.5−3.72=90.78 and an upper limit of 94.5+3.72=98.22.Thus, the 95% confidence interval for μ is (90.78, 98.22).

Option C is correct,4.5 is greater than 3.8, so this solution does work.

If x represents the number of hours and y represents the number of liters of water, then we can plug the possible solutions into our inequality to see which solution(s) work.

Inequality

In mathematics, an inequality is a relation that makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.  

The first option is having 0.5 liters of water for 4.5 hours of hiking. So will plug 3 in for y and 4.5 in for x:

y > 0.5x + 1.8

3 > 0.5(4.5) + 1.8

3 > 4.05  

But 3 is not greater than 4.05, this solution does not work.

The next option is having 2 liters of water for 2.5 hrs of hiking:

2 > 0.5(2.5) + 1.8  

2 > 3.05

But 2 is not greater than 3.05, so this solution does not work.

Option c is having 4.5 liters of water for 4 hours of hiking:

4.5 > 0.5(4) + 1.8

4.5 > 3.8

So 4.5 is greater than 3.8, this solution does  work.

The last option is having 2.5 liters of water for 3 hours of hiking:

2.5 > 0.5(3) + 1.8

2.5 > 3.3

2.5 is not greater than 3.3, so this solution does not works

Option c is correct,4.5 is greater than 3.8 so this solution does work.

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y > 0.5x + 1.8

3 > 0.5(4.5) + 1.8

3 > 4.05  

But 3 is not greater than 4.05, this solution does not work.

2 > 0.5(2.5) + 1.8  

2 > 3.05

But 2 is not greater than 3.05, so this solution does not work.

4.5 > 0.5(4) + 1.8

4.5 > 3.8

2.5 > 0.5(3) + 1.8

2.5 > 3.3

2.5 is not greater than 3.3, so this solution does not works

Option c is correct,4.5 is greater than 3.8 so this solution does work.

Therefore , the answer to this problem is that  y-coordinate for the solution is option a) y = -8

A number, a variable, or a mix of both are used in an expression coupled with specific operation symbols. An equal sign is used to denote the division of two expressions that make up an equation.

Here,

6x + y = -32 and

y = x - 4

=> 6x +( x - 4) = -32

=>7x -4=-32

=>7x =-28

=> x = -4

Thus,

y = -4 - 4 = -8

Therefore , the  y-coordinate comes out to be y = -8

Thus, the correct option in the following option is option a)y=-8.

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The equation of the graph of the function g(x) is A. g(x) = (x - 2)²

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

f(x) = x²

Also, we have the given graph

From the graph, we can see that the graph f(x) is shifted right y 2 units

This means that

g(x) = f(x - 2)

So, we have

g(x) = (x - 2)²

Hence, the equation is (a) g(x) = (x - 2)²

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In this case, with four treatment groups and n = 12 participants in each group, dfwithin treatments would be equal to 3, because there are 4 - 1 = 3 treatment groups.

In a one-factor ANOVA, dfwithin treatments refers to the degrees of freedom within the treatment groups, which is a measure of the amount of variability that is present within each group.

The degrees of freedom within the treatment groups is used to calculate the mean square within treatments (MSwithin), which is a measure of the variability within each group. MSwithin is calculated by dividing the sum of the squared differences between each participant's score and the group mean by dfwithin. This value is then used to determine the statistical significance of the treatment effects, by comparing it to the mean square between treatments (MSbetween), which is a measure of the variability between the treatment groups.

In a one-factor ANOVA, the total degrees of freedom is equal to the number of participants in all of the groups combined (4 groups * 12 participants per group = 48) minus the number of groups (48 - 4 = 44). The degrees of freedom between treatments is equal to the number of groups minus 1 (4 - 1 = 3), and the degrees of freedom within treatments is equal to the total degrees of freedom minus the degrees of freedom between treatments (44 - 3 = 41).

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Answer:

it might be 4

Step-by-step explanation:

that's all I have

Answer:

6(12), multiplication

Step-by-step explanation:

Since it takes 12 minutes to mow one lawn, multiplying would give you the answer of how long 6 lawns would take, which is 72

The price before tax of the books at Barnes and Noble would be 44$ - 25.1$ = 18.9$ if you use your coupon.

The price before tax of the books at Target would be 35$ - 51.1$ = -16.1$ if you use your Red card discount. However, the final price of the books cannot be negative, so the price before tax of the books at Target would be 35$ if you use your Red card discount.

The direct relationship of the variables is y = (t^2 - 6t)/(t - 5) * x

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

x = t - 5 and y = t^2 - 6t

The direct relationship between x and y is calculated using

Y = (y/x) * X

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

y = (t^2 - 6t)/(t - 5) * x

Hence, the direct relationship is y = (t^2 - 6t)/(t - 5) * x

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Option of the matrices a, b, and d are non symmetric.

Symmetric matrices are those matrices that have equal dimensions, i.e. the number of rows is same as the number of columns. They are also known as square matrices.

It is provided that A and B are symmetric n × n matrices.

To multiply two matrices of different order, the number of rows of the first matrix must be same as the number of columns of the second matrix.

Suppose X is a 2 × 3 matrix and Y is a 3 × 2.

Then the product AB will be a n × n matrix.

(a) A= C+CT

Thus the sum of matrix A and B will be a n × n matrix.

Thus, the matrix A is non symmetric.

(b) B = C-CT

So, matrix D will also be a n × n matrix.

Thus, the matrix D is non symmetric.

(c) D = CTC = (CT) × C

Then the product CT will be a n × n matrix.

The next step would be to multiply CT and C.

Both are n × n matrices.

Thus, the matrix D is symmetric.

(d) E = CTC - CCT

Then he product CT will be a n × n matrix.

Similarly, the product CT will be a n × n matrix.

Thus, the matrix E is non symmetric.

Similalry,

(e) F = (I +C)(I + CT

Thus, the matrix F is symmetric.

(f) G = (I +C)(I -CT)

Thus, the matrix G is symmetric.

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Answer:

When a block with mass M moving at a velocity of V collides and sticks to a block of mass 2M initially at rest, their velocity after the collision is equal to the original velocity of the first block. This is because, in a collision where the two objects stick together, the final velocity of the combined system is equal to the initial velocity of the first object.

To calculate the final velocity of the combined system, we can use the formula vf = vi + (2mv)/(m1+m2), where vf is the final velocity, vi is the initial velocity, m is the mass of the first object, v is the velocity of the first object, and m1 and m2 are the masses of the two objects. Plugging in the values from the problem, we get:

vf = V + (2 * M * V)/(M + 2M) = V + (2 * M * V)/(3M) = V + (2/3) * V = (5/3) * V

Therefore, the final velocity of the combined system is (5/3) * V, which is equal to the original velocity of the first block.

The velocity of the mass 2M after the collision will be V/2 which is half of the velocity of mass M.

An elastic collision is one during which the system does not experience a huge reduction of kinetic energy as a result of the collision. In elastic collisions, mass and kinetic energy are both preserved. Imagine two trolleys that resemble one another moving in the same direction at the same pace.

A block with mass M moving at a velocity of V collides and sticks to a block of mass 2M initially at rest.

Let 'v' be the velocity after the collision. Then the velocity of the mass 2M after the collision will be calculated as,

MV = 2Mv

v = V / 2

Thus, the velocity of the mass 2M after the collision will be V/2 which is half of the velocity of the mass M.

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The slope of y = 7x - 10 is 7 while the y-intercept is -10 thus it has a high slope but a lower y-intercept so option (D) is correct.

A straight line on the coordinate plane is represented by a linear function.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

A linear function with slope m and y-intercept c is given as y = mx + c.

Compare the given function y = 7x - 10

Slope m  = 10

y-intercept = -10

Hence "Y = 7x - 10 has a slope of 7 and a y-intercept of -10, meaning it has a high slope but a low y-intercept".

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Answer: 13 + 6√5

Step-by-step explanation: None

Answer:

"the circumference divided by the diameter"

Step-by-step explanation:

Circles are all similar, and "the circumference divided by the diameter" produces the same value regardless of their radius. This value is the ratio of the circumference of a circle to its diameter and is called π (Pi).

Answer:

A

Step-by-step explanation:

The problem is a little unclear with its format(random bracket) but given the following it should be A even though a parenthesis is missing but with going from left to right with parenthesis first depending on where the extra parenthesis is placed it is either A or B but it looks like there should be one grouping ((-8)+6) so it should be A

The formulae that specify how much 8% solution and how much 24% solution were utilized are [tex]x+ y=200 and x+3y=450.[/tex]

A mathematical equation is a formula that uses the equals symbol (=) to link two expressions and represent their equivalence. A mathematical statement that demonstrates the equality of two mathematical expressions is an equation in algebra, in its most basic form. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."

Let x and y be the volume of the 8% and 24% solutions, respectively, that were utilized.

The entire solution volume, as stated in the question, will be 200ml. The resulting equation is: [tex]x +y=200[/tex]

Now that it has been stated that 8%, 18%, and 24% saline mixes would be employed as the solution, the following equation will be:

[tex]0.08x+ 0.24y=0.18*200\\8x/100+24/100=18/100*200\\8x+24y=3600\\\\8(x+3y)=3600\\ x+3y=450\\[/tex]

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Number of ways total inventory of 32 batteries  be distributed among the 8 different types - 15257889504

The number of possible arrangements for a given set is determined mathematically, and this process is known as permutation. The term "permutation" simply refers to the variety of possible arrangements or orders. The positioning of the permutations matters a lot.

Number of ways total inventory of 32 batteries  be distributed among the 8 different types -

39!/30! 7! = 39X38X37X36X35X34X33X32X31 / 7X6X5X4X3X2X1

= 15257889504

Number of ways total inventory of 32 batteries  be distributed among the 8 different types, in inventory must include A76 - 35! / 28! 7!

= 35X34X33X32X31X30X29 / 7X6X5X4X3X2X1 = 6714520

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Answer:

x  =  -7 + √(73)

y  =  -7 - √(73)

Step-by-step explanation:

Product p = x × y = -24

Somme s = x + y = -14

Then

x and y are solutions to the equation:

z² - sz + p = 0

Then

x and y are solutions to the equation:

z² + 14z - 24 = 0

Using the quadratic formula:

x  =  ( -14 + √[(14² - 4×(1)×(-24)] ) / ( 2×(1) )  =  -7 + √(73)

and

y  =  ( -14 - √[(14² - 4×(1)×(-24)] ) / ( 2×(1) )  =  -7 - √(73)

The option that  correctly describes the graph of the relationship is; D: A line that goes through (0, 0) and (4.5, 13.5)

The formula for the slope between two coordinates is;

Slope = (y₂ - y₁)/(x₂ - x₁)

Let us take two coordinates from the table which are;

(2.4, 7.2) and (4.5, 13.5)

Thus;

Slope = (13.5 - 7.2)/(4.5 - 2.4)

Slope = 3

Now, looking at the options, the first 3 cannot be correct because they have mixed up x-coordinate values with y-coordinate values.

Let us check the last option which is a line that goes through (0, 0) and (4.5, 13.5). Thus;

Slope = (13.5 - 0)/(4.5 - 0)

Slope = 13.5/4.5

Slope = 3

Thus, we conclude that it is correct.

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Answer:

30 oz

Step-by-step explanation:

x = size of original cup

x - (0.10)x = 27 oz

(0.90)x = 27 oz

x = 27 / 0.90 = 30 oz

Step-by-step explanation:

she made shots = 34%of 54

=50*34/100

=17

he made 17 shots

Step-by-step explanation:

To make the equation AFGHACBD true, the value of y must be 7, and the value of z must be 32-1=31.

Here is how the equation works out:

2z + 14 = 2 * 31 + 14 = 68

2y + 35 = 2 * 7 + 35 = 49

68 + 2 = 70

70 > 49

49 + 7y = 49 + 7 * 7 = 98

98 > 70

70 + 32 - 1 = 70 + 31 = 101

101 > 98

98 + 2y + 35 = 98 + 2 * 7 + 35 = 146

146 > 101

So, the values of y and z that make the equation AFGHACBD true are y=7 and z=31.

So, the insurance company should be concerned that they could potentially lose money.

To test whether the insurance company should be concerned about the true mean claim amount being higher than the original estimate of $1,800, we can perform a one-sample t-test.

The null hypothesis for this test is that the true mean claim amount is equal to the original estimate of $1,800, and the alternative hypothesis is that the true mean claim amount is greater than the original estimate.

The t-statistic for this test is calculated as follows:

t = (sample mean - null mean) / (standard deviation / sqrt(sample size))

Plugging in the values from the problem, we have:

t = ($1,950 - $1,800) / ($500 / sqrt(40)) = 2.5.

We can then use a t-table or a computer to find the critical value of t for a one-tailed t-test with 39 degrees of freedom and a significance level of 0.05. The critical value is 1.68.

Since the calculated t-value of 2.5 is greater than the critical value, we can reject the null hypothesis and conclude that the true mean claim amount is significantly greater than the original estimate of $1,800.

Therefore, the insurance company should be concerned that they could potentially lose money.

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To test whether the insurance company should be concerned about the true mean claim amount being higher than the original estimate of $1,800, we can perform a one-sample t-test.

t = (sample mean - null mean) / (standard deviation / sqrt(sample size))

Plugging in the values from the problem, we have:

t = ($1,950 - $1,800) / ($500 / sqrt(40)) = 2.5.

We can then use a t-table or a computer to find the critical value of t for a one-tailed t-test with 39 degrees of freedom and a significance level of 0.05. The critical value is 1.68.

Therefore, the insurance company should be concerned that they could potentially lose money.