Solve the equations. Simplify your answers completely.

A) -1/3p=7

b) 48 = 4/5x

Answer:

659.375

Step-by-step explanation:

big brain

use a calculator

Using Equivalent equation, equation in option (b) i.e 2x+3 = 4 is equivalent to equation, 6x + 9 = 12. So, The Correct option is Option (b) .

Equivalent equation (Algebra) :

Combine any like terms on each side of the equation: x-terms with x-terms and constants with constants. Arrange the terms in the same order, usually x-term before constants. Then equivalent equation are algebaric expression which having same roots or solution .

We have given an expression as

6x + 9 = 12 --(1)

we have to find out an equation out of given options which is equivalent to equation(1) .

firstly , we evaluate the given expresion and find out solution i.e x .

6x + 9 = 12

Substracts 9 from both sides

=> 6x = 12 -9 = 3

both sides dividing by 6

=> x = 3/6 = 1/2

so, 1/2 is solution

Now, we check the options one by one

a) x + 9 = 6

solving it we get, x = 6- 9 = -3

=> not equivalent

b) 2x + 3 = 4

=> 2x = 4 - 3 = 1

=> x = 1/2

same solution as solution of given expresion

c) 3x+9 = 6

=> 3x = 6-9 = -3

=> x =-1

i.e not equivalent

d) 6x + 12 = 9

=> 6x = 9-12 = -3

=> x = -3/6 = -1/2

=> not equivalent

Hence, the required expression is 2x + 3 = 4

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Pilot program means  is a small scale, short term experiment that helps an organization or company to learn how a large scale project might work in practice.

Pilot program:

The best  pilot program provides a platform for the organization to test logistics, prove value before spending a significant amount of time, energy or money on a large scale project.

The pilot program is also called as feasibility study or experimental trial.

Steps for pilot program:

1.

set clear goals

2.

Decide on a length of time

3.

Choose your testing group

4.

Develop a plan for on-boarding

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The last year's salary was Rs 8250 and he is drawing this year Rs 9075.

What is the percentage of a number?

The percentage of a number is the part of the number expressed in the in every hundred. Percentage of a number is expressed with the symbol '%'  known as percentage symbol.

The monthly salary of Mr. Maharjan was Rs 7500 before last year and it was increased by 10% last year.

So, The last year's Salary was 7500 +750 = 8250

Again, it increased by 20% this year.

Then, Drawings of current year = 7500 + 20% of 7500

7500 + 1500 = 9000

8250 + 10% of 8250 = 9075

Drawings of current year = 9075.

Hence, the last year's salary was Rs 8250 and he is drawing this year Rs 9075.

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Using the triangle inequality theorem, the possible values for x is: x < 11.

The triangle inequality theorem states that two sides of a triangle, when added together must be greater than the length of the third side of the triangle.

Applying the triangle inequality theorem, we have the following inequality statement:

15 + 3 > 2x - 4

18 > 2x - 4

Add both sides by 4

18 + 4 > 2x - 4 + 4

22 > 2x

Divide both sides by 2

22/2 > 2x/2

11 > x

or  x < 11.

The possible values for x is x < 11.

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The equation 2y  = 10x - 16 in standard form is  10x - 2y = 16 where A = 10, B = - 2 and C = 16

Linear equation can be represented in various form such as general form, standard form, slope intercept form and point slope form.

Therefore, linear equation in standard form can be represented as follows:

Ax + By = C

where

Therefore, let's write 2y  = 10x - 16 in standard  form.

2y  = 10x - 16

Hence,

10x - 2y = 16

Therefore,

A = 10

B = - 2

C = 16

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For the given average principal $28650 of per student loan at the rate of interest increases from 5.05% to 6.8% , the amount of interest increases for the period of 10 years is equal to $8424 (nearest dollars).

As given in the question,

Principal amount owed by student for student loan 'P' = $28,650

Rate of interest increases from 5.05% to 6.8%

Time period of repayment of student loan 'T' = 10-years

Interest for the first rate of interest 'R' = 5.05%

Interest = P ×( 1+ R/100)^T

             = 28,650 × ( 1 + 5.05/100 ) ^10

             = 28,650 × ( 1 + 0.0505 )^10

             = 28,650 × 1.63667

             = $46,890.6

Interest for the second rate of interest 'R' = 6.8%

Interest = P ×( 1+ R/100)^T

             = 28,650 × ( 1 + 6.8/100 ) ^10

             = 28,650 × ( 1 + 0.068 )^10

             = 28,650 × 1.930689

             = $55,314.2

Increase in interest amount for increase in rate of interest from 5.05% to 6.8%

=  $( 55,314.2 - 46,890.6 )

= $8423.6

=$8424 ( nearest dollar)

Therefore,  for the given average principal $28650 of per student loan at the rate of interest increases from 5.05% to 6.8% , the amount of interest increases for the period of 10 years is equal to $8424 (nearest dollars).

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The integer variable bonus is assigned a value based on the value of the integer variable score

score > 100 implies bonus = 10 * score

score between 50 and 100 implies bonus = score

score < 50 implies bonus = 0

First, we need to analyze the conditions:

score > 100 implies bonus = 10 * score

score between 50 and 100 implies bonus = score

score < 50 implies bonus = 0

Writing the above as programming instructions, we have:

if(score > 100){//This represents the first condition

bonus = 2 * score;

}

else if(score >=50 && score<=100){//This represents the second

bonus = score;

}

else{//This represents the last condition

bonus = 0;

}

Hence, if score > 100 implies bonus = 10 * score

score between 50 and 100 implies bonus = score

score < 50 implies bonus = 0

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The Rate at which she practices piano per day will be 34 minutes.

We know that Proportional relationships are relationships between two variables like x and y when their ratios got equivalent.

For example,  [tex]\frac{a}{b}[/tex] = [tex]\frac{c}{d}[/tex]. This is the proportional relationship between the variables, a, b, c, and d. In this a is equal to c (a = c) and b is equal to d(b = d).

In our question, the proportional relationship between total minutes (m) and the number of days (d) is given by:
m = 34d.

We need to find the rate, which can be defined as the total minutes spent on practice piano per day.

Minutes spent = m
Days = d

Rate = [tex]\frac{m}{d}[/tex]

So, we know, m  = 34d

[tex]\frac{m}{d}[/tex] = [tex]\frac{34}{1}[/tex] = 34

Hence, The rate is 34 minutes per day.

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Using the formula of compound interest, the amount compounded annually for 30 years at a rate of 7% is $76,122.55

The compound interest is the interest-based on the initial principal amount and the interest collected over the period of time.  The compound interest formula is given below:

A = P(1 + r/n)^nt

Substituting the values into the equation above;

A = 10000(1 + 0.07/1)^1 * 30

A = $76,122.55

The amount at the end of 30 years is equal to $76,122.55

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No, because the sample size is insufficient and the sample does not represent a distribution that is roughly normal.

What do the numbers mean?

Statistics is the study and manipulation of data, including methods for data collection, evaluation, analysis, and interpretation. Descriptive statistics and inferential statistics are the two main subfields of statistics.

What three sorts of statistics are there?

They are (i) the mean, (ii) the median, and (iii) the mode. The study of statistics involves gathering, analyzing, interpreting, presenting, and organizing data in a particular way.

The population must have a normal distribution, or the sample size must be sufficient to use the central limit theorem, in order to generate a confidence interval. It is not appropriate to create the confidence interval for mean because neither of the two conditions were met in this instance.

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Answer:

Answer:

x= 8.8

Step-by-step explanation:

-12.6x-4.9x=-154

-17.5x=-154

-17.5x/-17.5 = -154/-17.5

x = 8.8

For n is positive integer and d is a digit such that gives the numerical value and satisfied all given conditions. We get the base value i.e n is 9

and d = 2 . So, required value n+d = 11 .

We can start by setting up an equation to convert 32d base n to base 10. To convert this to base 10, it would be 3n²+2n+d. Because it is equal to 263, we can set this equation to 263. Finally, subtract d from both sides to get

3n²+2n = 263-d.

We can also set up equations to convert 324 base n and 11d1 base 6 to base 10. The equation to covert 324 base n to base 10 is 3n²+2n+4. The equation to convert 11d1base 6 to base 10 is 6³+ 6²+6d+1.

Simplify , 6³+6²+6d+1 so it becomes 6d+253. Setting the above equations equal to each other, we have3n²+2n+4 = 6d+253. Subtracting 4 from both sides gets 3n²+2n = 6d+249.

We can then use equations

3n²+2n = 263-d

3n²+2n = 6d+249 to solve for d.

Set 263-d equal to 6d+249 and solve to find that d=2.

Plug d=2 back into the equation 3n²+2n = 263-d. Subtract 261 from both sides to get your final equation of 3n²+2n-261 = 0.

We solve using the quadratic formula to find that the solutions are 9 and -10. Because the base must be positive, n=9.

Adding 2 to 9 we get, n+ d = 9+2 = 11

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The combined inventory of the two stores  is  [tex]\frac{7g^{2} }{2} -\frac{4g}{5}+\frac{15}{4}[/tex]

A polynomial is an expression that consists of variables and coefficients in which we can perform addition subtraction and multiplication. Let us understand polynomials with one illustration[tex]x^{2}+x-14[/tex] . In the given illustration, their exists three terms: [tex]x^{2}[/tex], x and 14

According to the given information :

Store A :       [tex]\frac{g^{2} }{2} + \frac{7}{2}[/tex]

Store B :       [tex]3g^{2}-\frac{4g}{5} +\frac{1}{4}[/tex]

Now to find the combined inventory of two stores , we need to find the combination of the above polynomials.

Combining polynomials means adding the polynomials.

Combined inventory = [tex]\frac{g^{2} }{2} + \frac{7}{2} + 3g^{2} -\frac{4g}{5} +\frac{1}{4}[/tex]

By combining the like terms,

Combined inventory = [tex]\frac{g^{2} }{2}+3g^{2} -\frac{4g}{5}+\frac{7}{2}+\frac{1}{4}[/tex]

Combined inventory = [tex]\frac{7g^{2} }{2} -\frac{4g}{5}+\frac{15}{4}[/tex]

The combined inventory of the two stores is  [tex]\frac{7g^{2} }{2} -\frac{4g}{5}+\frac{15}{4}[/tex]

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The function will be designed in the python computing language

Python is an interpreted, object-oriented, high-level, dynamically semantic programming language. Its straightforward syntax prioritizes readability and makes it simple to understand, which lowers the cost of program sustenance.

The code will be -

def main():

number = int(input('Enter a positive integer: '))

finalSum = addition(number)

print("The integral of this number is ", finalSum, ".")

def addition(num):

if num == 1:

return 1

else:

return num + addition(num-1)

main()

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Answer:

95

Step-by-step explanation:

To find the average you take the sum of the scores and then divide it by the number of exams. Let x equal the score Lucy must obtain on the next math test.

[tex]\frac{85+64+76+x}{4} =80[/tex]

Add the scores and multiply both sides by 4

225 + x = 320

Subtract 225 from both sides

x = 95

Using formula Work done against gravity,

The work done by person against the gravity is 5880 J .

Work done against gravity:

The work done in lifting an object against gravity becomes the potential energy of the object-earth system. The change in gravitational potential energy Δ P.Eg is Δ P.Eg = mgh, where h is the increase in altitude and g is the acceleration due to gravity.

Mathematically, work done against gravity is given by,

W = Fg×d×cosθ

where, Fg --->force of gravity = weight = m×g

m --> mass

g --> gravity

d---> displacement

θ--> angle between force and displacement

we have given that

g = 9.8 m/s²

d = displacement = height = 2×4 = 8m

θ =angle between force and displacement = 180°

Combined mass = 75 kg

So, W = 75×9.8×8×cos 180°

W = -5880 J

Hence, the required work done is -5880J.

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Complete question:

A spiral staircase in a building is in the shape of a helix of radius 5 meters Between two floors of the building; the stairs make one full revolution and climb by 4 meters A person carries a bag " of groceries up two floors The combined mass of the person and the groceries is 75 kg and the gravitational force is 75g downward, where g 9.8 m/sec? is the acceleration due to gravity: Calculate the work done by the person against gravity in joules. Enter an exact answer.

The entries for July 15 and August 1 transaction and entries for November 3 and November 20 transaction are given below.

What is sales tax?

A tax that is paid to a governing body for the sale of particular goods and services is known as a sales tax. Typically, laws let the merchant to collect money from the customer at the time of purchase to cover the tax. It is typically referred to as a usage tax when a tax on goods or services is paid directly to a governing body by a customer.

The entries for July 15 and August 1 transaction and entries for November 3 and November 20 transaction are as below.

1) Journal entry

Date account and explanation                 debit credit

July 15              Cash                                        10400  

                   Sales revenue                                     1000

                  Sales tax payable                                      400

                  (To record sales)    

                  Cost of goods sold                5000  

                        Inventory                                            5000

                 (To record cost of goods sold)    

Aug 1          Sales tax payable                          400  

                         Cash                                              400

2) Journal entry

Date account and explanation            debit      credit

Nov 3                Cash                                    300  

             Unearned ticket revenue                          300

             (To record revenue)    

Nov 20      Unearned ticket revenue      50  

                   Ticket revenue                                    50

               (To record adjusting entry)    

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A rectangle and another rectangle can occasionally be mapped onto one another using solely stiff transformations and dilations.

By altering the initial shape, shapes can be mapped to other comparable shapes.

The following needs to be accurate for a shape to change.

The respective side lengths of the rectangles must have an equivalent ratio in order for one rectangle to be transferred to another.

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The relationship between m number of songs downloaded  and the total cost of $20 Mariana receives will be represented by inequality :

1.29m ≤ 20.

Given,

The value of gift card which Mariana have $20.

The costs of each downloaded song is $1.29.

Since m represents the number of songs downloaded and she has in total $20, so the inequality represents the given situation is,

1.29m ≤ 2.

Hence the required inequality is 1.29m ≤ 2.

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Because the p-value is less than 0.05, the null hypothesis should be rejected.

Given,

Null Hypothesis;-

The null hypothesis presupposes that any variation in the selected characteristics you observe in a set of data is the result of chance.

Alternative Hypothesis;-

The alternate response to your research question is the alternative hypothesis (Ha). It asserts that the populace is affected. Your research hypothesis and your alternate hypothesis are frequently identical. Alternatively said, it's the assertion that you anticipate or hope will be accurate.

Here,

Because the p-value is less than 0.05, the null hypothesis should be rejected. The allegation that the proportion of ball bearings with dimension values smaller than 2.20 cm in the current manufacturing process is the same as the proportion in the new process is sufficiently refuted by the evidence.

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Binomial distribution will be followed for grade of student.

Binomial Distribution:

                              When an experiment or survey is repeated numerous times, the likelihood that the results will be SUCCESS or FAILURE is known as the binomial distribution. The prefix "bi" implies "two" or "twice," therefore the term "binomial" refers to a distribution type with two probable outcomes. A coin flip, for instance, can only result in one of two outcomes: heads or tails, and completing a test can result in either passing or failing.

          What do we need for a Binomial Distribution?

1. one base experiment which will be repeated many times (n times).

2. only two outcomes in the base experiment: success or no success; property fulfilled or not fulfilled.

3. a success probability p that does not change from one experiment to the next (this means the experiments are independent).

So,

        Binomial distribution will be followed for grade of student.

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The relevant parameter of interest for this numerical variable would be the average filling weight of all cereal packages.

What is the standard deviation in statistics?

The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values are close to the set's mean, whereas a high standard deviation indicates that the values are spread out over a larger range.

If a machine that is programmed to package 1.20 pounds of cereal is being tested for its accuracy. in a sample of 36 cereal boxes, the sample mean filling weight is calculated as 1.22 pounds. the population standard deviation is known to be 0.06 pounds.

The parameter of interest is the average filling weight of all cereal packages.

Hence, the relevant parameter of interest for this numerical variable would be the average filling weight of all cereal packages.

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The positive square root of 5⁴ × 7² using index notation 5²×7

Index notation is a way of writing numbers and letters that have been multiplied by themself multiple times e.g 2×2×2 = 2³

Given: 5(to the power of 4) x 7 (to the power of 2). That is 5⁴ × 7²

In order to find the positive square root of 5⁴ × 7² using index notation, we have to separate the number into two identical parts. Thus:

5⁴×7² = 5²×5²×7×7 = ( 5²×7) × ( 5²×7)

Therefore, the positive square root of 5⁴×7² is 5²×7

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(a) P( Type -I error) = P (rejecting [tex]H_0[/tex] |  when  [tex]H_0[/tex] is true )

(b)  P( Type -II error)= P(not rejecting  [tex]H_0[/tex] |  when  [tex]H_0[/tex] is false )

Given,

In the question:

We are interested in testing whether or not a coin is balanced based on the number of heads Y on 36 tosses of the coin.

To find the:

a) the value of α

b) the value of β if p = .7

Now, According to the question:

Hypothesis Testing:

The hypothesis testing evaluates two mutually exclusive statements about the population parameters to determine which statement is correct among them. There are two types of error :

1. Type -I

2. Type -II

The data is given as:

X ~ Bin(36, p)

[tex]H_0:p = 0.5\\\\H_1:p \neq 0.5[/tex]

(a) P( Type -I error) = P (rejecting [tex]H_0[/tex] |  when  [tex]H_0[/tex] is true )

                               = P(|X- 18| [tex]\geq[/tex] 4 ; p = 0.5)

                               = 1 - {P(14 < X < 22)}

                               = 1 - {P(X < 22) - P(X < 14)}

                                = 1 -  {P(X ≤ 21) - P(X ≤ 13)}

                                = 1 - {0.87851 - 0.066249}

                                = 0.18774

(b)  P( Type -II error)= P(not rejecting  [tex]H_0[/tex] |  when  [tex]H_0[/tex] is false )

                                  = P(|X- 18| [tex]>[/tex] 4 ; p = 0.7)

                                  = P(14< X < 22)

                                  =  P(X < 22) - P(X < 14)

                                  =  P(X ≤ 21) - P(X ≤ 13)

                                  = 0.091662 - 0.018322

                                  = 0.07334

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There is no solution for the given system of equations, 2x-4y = 6 and -4x+8y = -12, by the elimination method.

According to the question,

We have the following system of equations:

2x-4y = 6 ...(1)

-4x+8y = -12 ...(2)

Now, we will multiply equation 1 by 2 and add the obtained result to equation 2:

2(2x-4y) = 2*6

4x-8y = 12

Now, adding this equation to second one (note that the left hand side will be added to only left hand side):

-4x+8y+4x-8y = -12+12

Now, there is no variable left on the left hand side.

Hence, there is no solution for the given system of equations.

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When the graph touches the x-axis then, it makes contact with the x - axis and not passes through the x - axis,

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The graph touches the x-axis.

Now,

Let the function of graph is circle.

Then, If it is touches the x-axis then, the y-co-ordinate of the center will be equal to the radius of the circle.

Thus, When the graph touches the x-axis then, it makes contact with the x - axis and not passes through the x - axis.

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Using the Quadratic function,

a) The age of unmarried women with the highet birth rate is 27.1

b) The highet birth rate of unmarried women is 61.42..

Quadratic Function:

A quadratic function is a polynomial function of degree 2 which can be written in the general form, f(x) = ax²+ bx + c

here a, b , c are real numbers and a not equal to zero.

The quadratic function f(x) will have only the maximum value when the the leading coefficient or the sign of 'a' is negative.

when "a" is negative then maximum value of f(x) is -b/2a .

We have given that,

United State ,the birth rate B of unmarried women (birth per 1000 unmarried women) for women whoe age say a modeled function is

B(a) = −0.30a² + 16.26a −158.90 ---(*)

which is a quadratic function .

comparing (*) with ax²+bx +c = 0

we get, a = - 0.30 , b = 16.26, c = - 158.90

we have to find out the age of unmarried women with highest birth rate .

Highest birth rate means B(a) is maximum.

and using above facts , B(a) is Maximum at -b/2a

a) so, the age of unmarried women with highest birth rate = - b/2a = - 16.26/2×(-0.30) = 27.1

b) birth rate will be highest or max. when a = 27.1

the highet birth rate of unmarried women = B(27.1)

= −0.30(27.1)²+ 16.26(27.1) −158.90

= 61.42

Hence, the age of unmarried women with the highet birth rate is 27.1 and the highet birth rate of unmarried women is 61.42..

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The order of H can be |H| = 84, or |H| = 210 or |H| = 420.

In the mathematical field of group theory, Lagrange's theorem is a theorem that states that for any finite group G, the order (number of elements) of every subgroup of G divides the order of G.

By Lagrange's Theorem, we know |K| divides |H|, so |H| = 42k for some k (bigger than 1 since K is a proper subgroup of H).

Likewise, 42k divides 840, so k divides 840/42 = 20.

Since H is a proper subgroup of G, we know k < 20,

so either k = 2 , k = 5 or k = 10, and

Hence either |H| = 2(42) = 84, or |H| = 5(42) = 210 or |H| = 10(42) = 420.

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Answer:

5

Step-by-step explanation:

FV =PV(1+r)^n

3445.51= 2400(1+0.075)^n

n=4.836

n is about 5