4) Nicole spent half of her weekly allowance

on candy. To earn more money her

parents let her wash the car for $4. What

is her weekly allowance if she ended with

$8?

The answer to the equation 6- x/3x = 3x/4 + 1/2 is

x= \(\frac{-5+ \sqrt{241} }{9}\) or x= \(\frac{-5 -\sqrt{241} }{9}\)

Quadratic equations are a type of polynomial equation because they consist of two or more algebraic terms

6- x/3x = 3x/4 + 1/2

Find the LCM (Lowest common Multiple) of the right hand side of the equation

6 - x/3x=  \(\frac{3x +2}{4}\)

cross multiply to find the value of x

4(6-x) = 3x(3x + 2)

Open the bracket

24 - 4x = \(9x^{2}\) + 6x

rearrange the equation

\(9x^{2}\)+6x +4x -24 =0

simplify the equation

\(9x^{2}\) + 10x -24 =0

then, solve the equation using quadratic formula

x= \(\frac{-b + or - \sqrt{b^{2} -4ac } }{2a}\)

Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula.

where a= 9, b= 10, c= -24

substitute the value of the variable into the the quadradic equation

x= \(\frac{-10 + or - \sqrt{10^{2 }-4(9)(-24)} }{2.9}\)

x= \(\frac{-10 + or - 2\sqrt{241} }{18}\)

solve for the unknown x by separating the equations: one with a plus and the other with a minus,

x= \(\frac{-10 + 2\sqrt{241} }{18}\)

x= \(\frac{-10 - 2\sqrt{241} }{18}\)

Therefore the value of x in the equation is ;x= \(\frac{-5+ \sqrt{241} }{9}\) or x= \(\frac{-5 -\sqrt{241} }{9}\)

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Answer:

13.7

Step-by-step explanation:

Hope this helps

The level of significance, typically set at 0.05, is used to determine whether the observed difference is statistically significant or simply due to chance

To determine whether the difference between groups is statistically significant, you would typically use a hypothesis test such as a t-test, ANOVA (analysis of variance), or a chi-square test. These tests are used to compare the means or proportions of different groups and calculate the probability of obtaining the observed difference by chance. The level of significance, typically set at 0.05, is used to determine whether the observed difference is statistically significant or simply due to chance. To determine if the difference between groups is statistically significant, you can use a hypothesis test called the t-test. The t-test compares the means of two groups and takes into account the sample size and variance within each group. This test helps you determine if there is a significant difference between the groups or if the observed difference is due to random chance.

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Answer:

\(\dfrac{47}{42} \ \ \ \ \ OR \ \ \ \ 1.1\)

Step-by-step explanation:

The objective of this question is to find the  sum of the greatest and least numbers below:

\(\[8\frac15, \qquad -8\frac25, \qquad -\frac{26}{3}, \qquad -\frac{54}7, \qquad \frac{53}{6}.\]\)

To do this ; we will need to find the decimal component of each of them and equate them on a number line before summing the greatest and least numbers.

\(8 \frac{1}{5} = \dfrac{8*5+1}{5} \\ \\ = \dfrac{41}{5} \\ \\ = 8.2\)

\(-8 \frac{2}{5} =- \dfrac{8*5+2}{5} \\ \\ =- \dfrac{42}{5} \\ \\ = -8.4\)

\(-\dfrac{26}{3}= - 8.7\)

\(-\dfrac{54}{7} = - 7.7\)

\(\dfrac{53}{6}= 8.8\)

Thus; the above decimal component of the fractions given are :

8.2, -8.4, -8.7 , -7.7 and 8.8

We are to find the sum of the greatest and the smallest number ; on a number line; we will realize that the positive side is greater than the negative side , As such the greatest number from the positive side will be 8.8 and the smallest number will be -7.7

The sum of 8.8 + ( -7.7 ) = 8.8 - 7.7

= 1.1

i.e

\(\dfrac{53}{6} + (- \dfrac{54}{7} )\)

\(\dfrac{53}{6} - \dfrac{54}{7}\)

\(\dfrac{53}{6} - \dfrac{54}{7} = \dfrac{53*7 - 6*54}{42} \\ \\ = \dfrac{47}{42} \\ \\ = 1.1\)

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

1.0.4

2. 2.5

3. 17.5

4. 2.4

Answer:

1.0.4

2. 2.5

3. 17.5

4. 2.4

Step-by-step explanation

Answer:

x=58 y=26

Step-by-step explanation:

32+90=122

180-122=58

x=58

64+90=154

180-154=26

y=26

The F ratio in a completely randomized ANOVA is a) MSTR/MSE.

The F ratio in ANOVA is a measure of the variability between groups compared to the variability within groups. MSTR (mean square treatment) represents the variability between groups, while MSE (mean square error) represents the variability within groups.

The F ratio is the ratio of MSTR to MSE. A high F ratio indicates that the variability between groups is larger than the variability within groups, suggesting that there is a significant difference between at least two of the group means.

In contrast, a low F ratio suggests that there is little difference between group means, and any observed differences may be due to chance. Therefore, the F ratio is an essential statistic in ANOVA for determining the significance of the observed differences between groups.

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The absolute value function that could represent this situation is:

\(|D - 42.67| = 0.002\)

The absolute value function is defined by:

\(|x| = x, x \geq 0\)

\(|x| = -x, x < 0\)

The diameter should be of 42.67 mm with an allowance of 0.002 mm. Thus, the absolute value of the difference between the diameter and of 42.67 should be of 0.002, that is:

\(|D - 42.67| = 0.002\)

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The volume of the solid region is approximately 10.4109 cubic units.

To find the volume of the solid region lying below the surface z = f(x,y) and above the plane region R, we can use the formula:

V = ∬R f(x,y) dA

where dA is the area element in the xy-plane and the double integral is taken over the region R.

To evaluate this integral, we first need to perform a change of variables. Let u = x + y and v = x - y. Then the inverse transformations are x = (u + v)/2 and y = (u - v)/2. The Jacobian of this transformation is:

J = ∂(x,y) / ∂(u,v) = 1/2

Next, we need to express the surface z = f(x,y) in terms of u and v. Using the substitutions x = (u + v)/2 and y = (u - v)/2, we get:

f(x,y) = (x+y)ex-y = [(u+v)/2 + (u-v)/2]e(u-v)/2 = ueu/2

So the volume of the solid is:

V = ∬R f(x,y) dA

= ∬R ueu/2 dA

= ∫₂⁴ ∫₂⁶ (u/2)e^(u/2) du dv (using the limits of integration for R in terms of u and v)

= ∫₂⁶ [e^(u/2)u²/4] from 2 to 4 dv

= ∫₂⁴ [e^(u/2)u²/4] from u-2 to 6 du

= 16(e^3 - e^2)/3

Therefore, the volume of the solid region is approximately 10.4109 cubic units.

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Ways can n identical balls be distributed into r bins such that each bin contains at least two balls are 20 ways.

1 ball in each of 3 boxes: 4 ways

3 balls in one box: 4 ways

2 balls in one box and 1 ball in another box: 3*4=12 ways

There are 20 ways to arrange the balls .

In mathematics, a combination is a way of selecting items from a collection where the order of selection does not matter. Suppose we have a set of three numbers P, Q and R. Then in how many ways we can select two numbers from each set, is defined by combination.

The combination can also be represented as: –nCr, nCr, C(n,r), Crn

Proof:

nPr = nCr.r!

= [n!/r!(n-r)!].r!

= n!/(n-r)!

Hence the theorem states true.

A permutation is an act of arranging objects or numbers in order. Combinations are the way of selecting objects or numbers from a group of objects or collections, in such a way that the order of the objects does not matter.

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it is true that  0.5% of 200 is 10.

True.

To find 0.5% of a number, we need to multiply the number by 0.5/100, which can be simplified to 5/100 or 1/20. This is because "percent" means "per hundred", so 0.5% is equivalent to 0.5 per 100 or 0.5/100.

Multiplying the number by 5/100 is the same as multiplying it by 0.5/100, so it will give us the correct result.

For example, if we want to find 0.5% of 200, we can multiply 200 by 5/100 or 0.5/100:

\(0.5% of 200 = 200 \times 5/100 = 10\)

Therefore, it is true that  0.5% of 200 is 10.

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Answer:

only the expression -5x + 4x + 3 contains like terms.

Step-by-step explanation:

Like terms in algebra refer to terms that have the same variables raised to the same powers.

1. 3x - 3y: This set consists of two terms, 3x and -3y. These terms are not like terms because they have different variables (x and y). Like terms must have the same variable(s) raised to the same power(s).

2. 64/8: This is a single number, 64 divided by 8. Since it is not an algebraic expression with multiple terms, there are no like terms in this set.

3. -5x + 4x + 3: This set contains three terms, -5x, 4x, and 3. The terms -5x and 4x are like terms because they have the same variable (x) raised to the same power (1). Like terms can be combined by adding or subtracting their coefficients while keeping the variable and its exponent unchanged.

4. 5b(4b): This is an algebraic expression that simplifies to 20b^2. Since it contains only one term, there are no like terms in this set.

In summary, among the given sets of numbers, only the expression -5x + 4x + 3 contains like terms, namely -5x and 4x. These terms can be combined by adding their coefficients to give -x + 3.

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The relationship between two variables that begins as a direct correlation and then becomes an indirect correlation, or vice versa, is known as a nonlinear correlation.

A nonlinear correlation is when the relationship between two variables is not linear - that is, the correlation between them does not increase or decrease proportionately as one variable increases or decreases. Nonlinear correlations are important in research as they can suggest that a phenomenon is more complex than a linear correlation would indicate.

For example, if two variables have a direct linear correlation, then a small increase in one variable would result in a predictable increase in the other. However, with a nonlinear correlation, a small increase in one variable may result in a much larger or much smaller increase in the other. This suggests that other factors, not captured in the linear correlation, are influencing the relationship between the two variables.

Nonlinear correlations can be positive (the two variables increase or decrease together), negative (one variable increases as the other decreases, or vice versa), or both. Depending on the circumstances, the type of nonlinear correlation can have important implications for the research question being studied.

It is important to note that nonlinear correlations may be caused by a variety of factors, including chance, measurement errors, or the presence of an extraneous variable that has not been accounted for. As such, they should always be further investigated and not taken as an absolute conclusion.

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The expression to represent the total price of the hats before sales tax is 4.7x.

Given that, Brandon purchased 5 hats.

Calculating the sales tax applied to a purchase is a matter of simply multiplying the tax rate by the purchase price using the equation sales tax = purchase price × sales tax rate. Adding the sales tax to the original purchase price gives the total price paid with tax.

Let the cost of each hat be x.

Here, sales tax is 6%

So, the total price of the hats before sales tax is

5x- 6% of 5x

= 5x-0.06 ×5x

= 5x-0.3x

= 4.7x

Therefore, the expression to represent the total price of the hats before sales tax is 4.7x.

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"Your question is incomplete, probably the complete question/missing part is:"

Brandon purchased 5 hats. Each hat cost the same amount. The total price of the hats was dollars before the store added a 6% sales tax. Write a expression to represent the total cost of hats before sales tax.

Answer:

A.(5,-2)

Step-by-step explanation:

Try yourself man.

The area of the football pitch is 6656 square meters. We can calculate it in the following manner.

To find the area of the football pitch, we need to multiply the length by the width:

Area = Length x Width

In this case, the length is 128 m and the width is 52 m. So we can substitute these values into the formula:

Area = 128 m x 52 m

Area=  6656 square meters.

So, the area of the football pitch is 6656 square meters.

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Answer:

The table is a relation and a function

The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given data ,

Let the function be represented as A

Now , the value of A is

f ( x ) = { 5 , 6 , 7 , 8 , 9 }

Now , the input values of the function are

x = { 1 , 2 , 3 , 4 , 5 }

where a relation is a set of ordered pairs (x, y) where there is a relationship between the first element (x) and the second element (y)

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Hence , the table is a function and relation

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Answer:

Step-by-step explanation:

Unfortunately, I cannot answer this question without additional information about the distances traveled and the time taken by Reiko to travel from point A to point B and back to point A.

The speed at which Reiko traveled is calculated as distance divided by time. Therefore, we need to know both the distance and time for each leg of the journey to determine the speed.

Without this information, it is not possible to determine whether Reiko traveled from A to B at a speed greater than 40 miles per hour.

The ratio if the dimensions are expressed in inches instead of feet is 1/16.

Ratio is defined as the relationship between two quantities. It can be expressed as a to b, a : b, or a / b.

Meanwhile, proportion is defined as the equality between two ratios.

a / b = c / d

If the ratio of the numerical value of the perimeter to the numerical value of the area, expressed in feet, is 3/4, then converting each component to inches will give its ratio, expressed in inches.

perimeter / area

= 3 feet / 4 feet²

= 3 feet(12 inches / 1 foot) / 4 feet²(12 inches / 1 foot)(12 inches / 1 foot)

= 36 inches / 576 inches²

Simplifying the ratio by dividing both by 36.

36 / 576 = 1 / 16

Hence, the ratio will become 1/16.

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Answer:

The Answer Is A. I believe

The bends on a track for car racing are semicircular, and the track is banked at an angle of 28.0° to the horizontal. Suppose the radius of the curvature of the bends is 120 m.

a) The formula to calculate the minimum velocity is given as follows:Vmin = √(rgtanθ)Where;Vmin is the minimum velocity needed to stay on the track;g is the acceleration due to gravity;r is the radius of the turn;θ is the angle of banking.r = 120 m, θ = 28.0°, and g = 9.8 m/s²Substitute the values into the formula, we get;Vmin = √(rgtanθ)=√(9.8 m/s² * 120 m * tan(28.0°))=40.6 m/sTherefore the minimum velocity the car should maintain is 40.6 m/sb) If the car speed is twice that in (a).

(i) The free-body diagram of the car is as shown below;

(ii) The value of the frictional force f is as follows;There are two forces acting on the car, namely; the normal force and the gravitational force. When the car moves at a constant speed around the bend, the centrifugal force Fc is also acting towards the center of the circular path. The centrifugal force Fc is given by the formula;Fc = mv²/rWhere;F c is the centrifugal force;m is the mass of the carv is the velocity of the car in m/sr is the radius of the curve.

Therefore;f = F s, max= μsNWhere;Fs, max is the maximum static frictional force that can be applied;N is the normal force acting on the car;μs is the coefficient of static friction.Because the car is not sliding, the maximum frictional force that can act is equal to the centripetal force, Fc.Thus;Fs, max = F c= 21,333.3 NThe frictional force f can now be determined as;f = Fs, max= μsN= 21,333.3 N= μsmgCosθwhere m is the mass of the car, and g is the acceleration due to gravity.

Substitute the values into the formula;μ s = f/mgCosθ= 21,333.3 N / 800 kg * 9.8 m/s² * Cos(28.0°) = 0.58Therefore the coefficient of static friction is 0.58.

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Answer:

dimension=2a×2a

area=4a^2

Step-by-step explanation:

since the radius of the circle is a

Then l= 2a

area of a square =l^2

area=2a×2a

The length of the microorganism that measure 5μm is equivalent to 0.005 mm

It is the transformation of a value expressed in one unit of measurement into an equivalent value expressed in another unit of measurement of the same nature.

To solve this problem the we have to convert the units with the given information.

1mm is equal to 1000 μm

5μm * (1 mm/1000μm) = (5*1) / 1000 = 5/1000 = 0.005 mm = 5x10^-3 mm

The length of the microorganism that measure 5μm is equivalent to 0.005 mm

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Answer:

1. k = -9

2. m = 15

3. x = -2

4. a = -90

Step-by-step explanation:

When doing these problems set them up as if the equal sign is a dividing line between two sides.

1. -126=14k

Divide both sides by 14 to get rid of the coefficient.

This gives you your answer -9=k

2. -7+m=8

Add 7 to both sides to isolate the variable.

This gives you your answer m=15

3. -17=x-15

Add 15 to both sides to isolate the variable.

This gives you your answer x=-2

4. -5=a/18

Multiply both sides by 18 to get rid of the denominator.

This gives you your answer of a=-90

Hope this helped!

The number of babies in this problem is classified as an:

For each student, we have an input variable and an output variable, given as follows:

For this problem, we have that the number of babies is predicted according to the size of the stork population, hence the variables are given as follows:

This means that the number of babies can be classified as either the target variable or the outcome, as it is the output of the study, and then either the first and the last options are correct.

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Answer:

5/9

Step-by-step explanation:

You can verify me by using the y2-y1/x2-x1 formula