Find the product with the exponent in simplest
form. Then, identify the values of x and y.
6^1/3x6^1/4=6^x/y
X= ,y=

Oliver travelled the distance of 21.5 ft

What is perimeter?

The complete length of a shape's edge serves as its perimeter in geometric terms. Adding the lengths of all the sides and edges that surround a form yields its perimeter. It is calculated using linear length units such centimeters, meters, inches, and feet.

As shown in the figure, we need to find the perimeter of the triangle ABC.

Perimeter = g + h +f ............(1)

g=f = 6.3 ft

Finding h using pythogoras theorem formula:

h² = g² + f²  

    = 6.3² +  6.3²

   =  79.38

h =√79.38  = 8.909 ≈ 8.9 ft  

So, (1) => Perimeter = 6.3 + 6.3 + 8.9 = 21.5 ft

Thus, Oliver travelled the distance of 21.5 ft

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There is no sufficient evidence to support the claim that there is a difference in the longevity of the two brands of batteries , as the null hypothesis failed to be rejected.

So the mean and standard deviation for the sample of battery 1 is :

M(1)=  106+ 111+ 109+ 105/4 =107.75

standard deviation (1)=r√(x(i)-M/(n-1)=root(22.75/3)=2.754

Similarly, for the second  battery, the mean and   standard deviation  is

M(2)= 125 +103+ 121+ 118/4=116.75

S(2)=√(276.75/3)=√(92.25)=9.605

Here the hypothesis test for the difference between populations means, here the claim is that the longevity of the two brands of batteries differs.So the alternative and null hypotheses are:

H(0)= μ1-μ2=0

H(1)=μ1-μ2 ≠0

Here the  significance level is 0.05(α), The difference between sample means is M(d)=107.75- 116.75=-9 .Now the  estimated standard error of the difference between the means is :

s(Md)=√(2.754²+9.605²/4)=4.996, Now the test static will be, t=-9-0/4.996=-1.8014 and the degree of freedom is 4+4-2=6 .Here  the test is two-tailed  with  degrees of freedom of  the test static is -1.8014, so the P-value for the  test is : 2.P(t< -1.8014)=0.122

Here the P-value (0.122) is greater than the significance level so the effect is insignificant, and the null hypothesis failed to be rejected.

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the operations manager of a manufacturer of television remote controls wants to determine which batteries last the longest in his product. he took a random sample of his remote controls and tested two brands of batteries. the number of minutes of continuous use before the batteries failed for each brand is given in battery.xlsx. if the significance level is 10%, is there statistical evidence of a difference in longevity between the two batteries?

The sample data for each battery is:

Battery 1: 106 111 109 105

Battery 2: 125 103 121 118

Answer: A. No, she would spend $26.

Step-by-step explanation:

Let y be the total cost and x be the number of minutes

So the equation is

y = 1.6x + 2

Now put 15 in for x

y= 1.6(15) + 2

y= $26

So the answer is A. No, she would spend $26.

The right response is that the two linear equation never intersect , because the graph of these two linear equation will be two parallel lines.

How many types of solution are there for two linear equations ?

There are 2 types of solution :
Consistent :

A consistent system is said to be an independent system if it has a single solution.

A consistent system is said to be a dependent system if the equations have the same slope and the same y-intercepts. In other words, the lines coincide, so the equations represent the same line. Each point on the line represents a pair of coordinates that fits the system. So there are an infinite number of solutions.

Non-consistent :

Another type of system of linear equations is the inconsistent system, in which the equations represent two parallel lines. The lines have the same slope and different y-intercepts. There are no common points for both lines; therefore, there is no solution to the system and if we draw the graph of these equations then the graphs of both equation becomes parallel to each other.

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The two linear equations never intersect.

When a system of two linear equations in two variables has no solution, it means that there is no set of values for the variables that satisfies both equations simultaneously. Geometrically, this corresponds to the two lines represented by the equations being parallel. Since parallel lines never intersect, the statement "The two linear equations never intersect" accurately describes the situation.

If the two linear equations were graphed on a coordinate plane, they would appear as two distinct lines that run parallel to each other without ever crossing or intersecting. This indicates that there is no common point of intersection between the lines, and therefore no solution exists for the system of equations.

It is important to note that this scenario is different from the case where the two linear equations represent the same line. In that case, the equations would be equivalent, and every point on the line would satisfy both equations. However, when there is no solution, it means that the lines do not share any common points and never intersect.

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The ending balance is $1032.5.

What is simple interest?

Simple interest is an interest rate that is solely calculated on the principal amount or the portion of the principal that is still owed. It does not take compounding into account. Simple interest may be used on a schedule other than annually, such as every month, week, or even every day.

Here, we have

Given: P = $2,500, r = 5.9%, t = 7 years

Convert 5.9% to a decimal

5.9% = 5.9 ÷ 100

 = 0.059

Substitute the values into the simple interest formula,

I = Prt   and we get

I = Prt

= 2500 × 0.059 × 7

= $1032.5

Hence, the ending balance is $1032.5.

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Answer:

[tex]m = -1[/tex]

Step-by-step explanation:

Use the slope formula:

slope [tex](m) = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Let:

[tex](x_1 , y_1) = (1 , 1)\\(x_2 , y_2) = (-5 , 7)[/tex]

Plug in the corresponding numbers to the corresponding variables:

[tex]m = \frac{7 - 1}{-5 - 1}[/tex]

Simplify. Combine:

[tex]m = \frac{(7 - 1)}{(-5 - 1)} \\[/tex]

[tex]m = \frac{6}{-6} = -\frac{6}{6} = -1[/tex]

[tex]m = -1[/tex] is your answer.

~

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Answer:

Slope (m) = -1

Step-by-step explanation:

Formula we use,

→ m = (y2 - y1)/(x2 - x1)

Now required slope will be,

→ (y2 - y1)/(x2 - x1)

→ (7 - 1)/(-5 - 1)

→ 6/(-6)

→ -1 => {Slope}

Therefore, the slope is -1.

We can factor this polynomial with 4 terms without grouping.

Factor is a thing that influence decision or the situation.

How to factor polynomials with 4 term without groupingLet P(x) be a polynomial with four terms.

To factor P(x) without grouping, substitute

x = -1, 1, -2, 2, -3, 3.......

P(-1) = 0 ----> (x + 1) is a factor of P(x)

P(1) = 0 ----> (x - 1) is a factor of P(x)

P(-2) = 0 ----> (x + 2) is a factor of P(x)

P(2) = 0 ----> (x - 2) is a factor of P(x)

If P(-1) ≠ 0, then (x + 1) is not a factor of P(x).

Then, try x = 1, x = -2, x = 2 and so on.

Once one of the linear factors of P(x) is found, the other factors can bound easily (the rest of the process has been explained in the following examples).

Factor the following polynomials without grouping :

d as (x2 + ax + b).

Then,

(x + 1)((x2 + ax + b) = x3 - 2x2 - x + 2

Comparing the coefficients of x and constants,

b + a = -1 ----(1)

b = 2

Substitute b = 2 in (1).

2 + a = -1

a = -3

x2 + ax + b = x2 - 3x + 2

Factors of (x2 - 3x + 2) are (x - 1) and (x - 2).

Therefore,

x3 - 2x2 - x + 2 = (x + 1)(x - 1)(x - 2)

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The value of the variable I (i.e interest) is $9

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

Principal, P =$400

Rate, R = 9%

Time, T = 0.25 years

The equation to calculate the interest is given as

I = PRT

Where

P, R and T are defined above

And I represents the interest

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

I = 400 * 9% * 0.25

Evaluate the products

I = 9

Hence, the interest is $9

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The ratio between the number of edges and the number of vertice of a cube is 2:3. All Prisms have a ratio of edges and vertices will be the same as that of the cube.

Edge – The outlines where two cube sides touch one another.

Vertices – The indicates the point where a cube's three sides meet.

Number of edges of a cube = 12

Number of vertices in a cube = 8

The ratio of edges in vertices = 12 : 8

                                             = 3 : 2

Hence, the ratio between the number the edges and the number of vertices of a cube is 3 : 2

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Answer: Cost Price = 21,50,000

Step-by-step explanation:

Using PEDMAS to evaluate the expressions given, the values are -14 and 10.5 respectively

Evaluating an expression is the process of simplifying an expression by performing the necessary mathematical operations to determine its value. It involves substituting a given value for each variable and then carrying out the indicated operations.

In the question given, we have two expression which we can evaluate.

A) -2 + 12 - 2³ ÷ 2⁰ * 3

Applying the rules of PEDMAS;

We will have -2 + 12 - 8 ÷ 1 * 3 = -14

The value of the expression is -14

B) 1/2 + √25 - 8 ÷ 2 + 3²

Applying the rules of PEDMAS again;

1/2 + 5 - 8 ÷ 2 + 9 = 10.5

The value of the expression is 10.5

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Answer: A Geometric sequence is a type of sequence in which each subsequent term after the first term is determined by multiplying the previous term by a constant (not 1), which is referred to as the common ratio.

Step-by-step explanation: Hope this was helpful

Step-by-step explanation:

The sequence

a, ar, ar^2, .....ar^n-1,...

where a is the first term and any two consecutive numbers differ by a factor r, is called a Geometric progression (G.P.).

Geometric progression also known as Geometric sequence.

Concept: Proportion, to find the km/h return journer

3 hours to 84 km/hr = 3.5 hours to x km/hr

(since its inverse proportion, multiply the 1st to 2nd and 3rd to 4th)

Inverse proportion: as the other quantities increase, the other one decreases

3 : 84 = 3.5 : x

3(84) = 3.5x

252 = 3.5x                (divide 3.5 both sides)

x = 72

Step-by-step explanation:

The distance from point A(−9,−3) to the line y = x−6 is 8.5 units

What is slope ?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

step 1

Find the slope of the perpendicular line to the given line

y=x-6 ---> given line

The slope is m=1

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

m1*m2 = -1

we have

m1=1

substitute

(1)*m2 = -1

so

m2 = -1

step 2

Find the equation of the perpendicular line to the given line

The equation in point slope form is

y-y1=m(x-x1)

we have

m=-1

(x1,y1)=(−9,−3)

substitute

y+3=-1(x+9)--> equation in point slope form

y+3= -x-9

y= -x-12---> equation in slope intercept form

step 3

Find the intersection point between the given line and the perpendicular line to the given line

we have the system of equations

y = x−6.

y= -x-12

Solve the system by graphing

The intersection point is (-3,-9)

see the attached figure

step 4

we know that

The distance between the point A and the point (-3,-9) is the same that the distance between point A and the line y=x-6

the formula to calculate the distance between two points is equal to

d=√[(y2-y1)² + (x2-x1)²]

substitute the values

d=√[(-9+3)² + (-3+9)²]

d= √72 units

simplify

d= 6√2 = 8.5 units

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Answer:

The total price that Shai must pay is $62.66. This includes the $25 for the haircut, the $30 for the shave, the $3.56 in state sales tax, and the $4.10 in tip.

Answer:

c. 74.42

Step-by-step explanation:

!! calculate the cost of both services, add the percentage of the sales tax then the tip!

The value of the test statistic is  0.711, for the    test at the 5% level of significance that the population variances differ in a random sample  of 20 patients.

Since the information given to us is from a random sample of 20 patients who visited a clinic at medical center 1, a researcher found that the variance of the waiting time (in minutes) was 128.0. in a random sample of 15 patients in the clinic of medical center 2, the researcher found the variance to be 178.8, and tested at the 5% level of significance that the population variances differ. The test statistic for this problem is calculated using the F-test. The formula for the F-test is:

F-test = (variance of sample 1) / (variance of sample 2).  Therefore, the test statistic for this problem is F-test = 128.0 / 178.8 = 0.711.  

To determine the p-value, we need to look up the F-distribution with (df1 = 20-1 = 19, df2 = 15-1 = 14) at a significance level of 5

%. The p-value is 0.347.  Therefore, at a 5% level of significance, the test statistic is 0.711 and the p-value is 0.347. We cannot reject the null hypothesis that the population variances are equal.

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After solving the equation, the value obtained for x will be equal to 5.

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations.

A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

As per the given expression in the question,

5x + 5 = 30

5x = 30 - 5

5x = 25

x = 25/5

x = 5

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Answer:

12

Step-by-step explanation:

Using the side splitter theorem, [tex]\frac{x}{32}=\frac{9}{24} \implies x=12[/tex].

The value of x is 12, option (B) is correct.

A line parallel to one side of a triangle splits the other two sides of the triangle proportionally if the line also crosses the other two sides.

Given that,

Two lines are parallel to each other,

And length of sides are,

32 , x , 24 and 9.

By angle proportionality theorem,

32 / x = 24 / 9

x = (32 × 9) / 24

x = (4 × 9) / 3

x = 4 × 3

x = 12

The required length of x is 12.

Hence, option (B) is correct.

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After subtracting 2/5 from 5/7, the resultant fraction is 11/35.

A fraction, which also symbolizes a piece of a whole, is a mathematical symbol for any number of equal parts.

When expressed in common English, a fraction, such as one-half, eight-fifths, or three-quarters, specifies the number of components of a specific size. In a simple fraction, both are integers.

In a complex fraction, a fraction can be found in either the numerator or the denominator.

A suitable fraction has a numerator that is less than its denominator.

So, we have:

5/7 and 2/5

Now, perform subtraction as follows:

5/7 - 2/5

5*5 - 7*2/35

25 - 14/35

11/35

Therefore, after subtracting 2/5 from 5/7, the resultant fraction is 11/35.

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Correct question:

Subtract. 5/7−2/5 enter your answer as a fraction in simplest form by filling in the boxes.

The equation for curvature is given by κ = |r' × r''|/|r'|3 where r' = dr/dt and r'' = d2r/dt2. the curvature of r(t) at the point (7,1,1), r(t)=<7t,t2,t3> is √14/√490.

The equation for curvature is given by κ = |r' × r''|/|r'|3 where r' = dr/dt and r'' = d2r/dt2.

We are given the point (7,1,1) which is the same as t=1.

Therefore, we can substitute t=1 into the function r(t) to obtain r(1) =<7,1,1>.

From this, we can calculate the derivatives r' and r'' of the function r(t) at the point (7,1,1).

r' = <7,2,3>

r'' = <0,2,6>

Then, we can calculate the curvature κ using the equation κ = |r' × r''|/|r'|3.

κ = |<7,2,3> × <0,2,6>|/|<7,2,3>|3

= |<0,-14,18>|/|<7,2,3>|3

= √14/√490

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Answer:

A) 14

Step-by-step explanation:

Nuts:

[tex]\frac{6}{\frac{1}{3} }[/tex] = [tex]\frac{6}{1}[/tex] ÷ [tex]\frac{1}{3}[/tex]  Get a common denominator of 3 and divide

[tex]\frac{18}{3}[/tex] ÷ [tex]\frac{1}{3}[/tex] = [tex]\frac{\frac{18}{1} }{\frac{3}{3} }[/tex] = [tex]\frac{18}{1}[/tex] = 18

We can make 18 bags with the amount of nuts given.

Raisins:

[tex]\frac{8}{\frac{1}{4} }[/tex] = 8 ÷[tex]\frac{1}{4}[/tex]  Gert a common denominator of 4 and divide

[tex]\frac{32}{4}[/tex] ÷ [tex]\frac{1}{4}[/tex] = [tex]\frac{\frac{32}{1} }{\frac{4}{4} }[/tex] = [tex]\frac{32}{1}[/tex] = 32

We can make 32 bags with the amount of raisins given.

32 - 18 = 14

14 more bags need nuts agged.

Answer:

Endothermic reactions absorb energy

Step-by-step explanation:

Answer: First, order them in the order of smallest to largest, which is 40, 60, 70, 80, 80. Then, since there are 5 numbers, the 3rd number, which is 70, would be the median.

Then, add all numbers:

40+60+70+80+80=330

and divide that by 5:

330/5=66

So, the median is 70 and the mean is 66.

Step-by-step explanation:

This study was conducted to test the effects of dietary supplementation of feed grade L - Met on growth performance.

Given :

based on this scatterplot , we observe that there are 6 groups of turkeys, each group receiving a different amount of methionine supplement (ranging from 0% to 44%).

Initial BW of birds did not differ among treatments. Weight gain of birds during 28 d feeding period increased ( P < 0.05 ) from 690 to 746 g ( an average of 0.33 % DL-Met and L-Met ) as dietary Met supplementation regardless of Met source increased from 0 to 0.33%. However, the source of Met did not affect the weight gain of birds.

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g(x) = x^2 - 3

f(x) = x^3+7x^2-x

Start with the g(x) function. Replace every x with f(x)

g(x) = x^2 - 3

g(f(x)) = ( f(x) )^2 - 3

Then replace the f(x) on the right side with x^3+7x^2-x

g(f(x)) = (x^3+7x^2-x)^2 - 3

The highest term inside the parenthesis is x^3. Squaring this leads to (x^3)^2 = x^(3*2) = x^6

So the highest exponent found in g(f(x)) is 6, meaning the degree of is 6

The pizza is 6.5 feet tall in height

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

Volume = 195 cubic feet

Length = 6 feet

Width = 5 feet

The height of the pizza can be calculate using

Height = Volume/(Length * Width)

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

Height = 195/(6 * 5)

Evaluate

Height = 6.5

Hence, the height is 6.5 feet

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Answer: x= -1

Step-by-step explanation:

5(x+2)= 3(x+3)-1

5x + 10 = 3x + 9 -1

5x + 10 = 3x + 8

2x = -2

x= -1

Answer:

4 gallons = 64 cups

1 gallons = 16 cups

3 gallons = 48 cups

Answer:

25° × π/180 is = 0.4363rad

Step-by-step explanation: