A sum lent out at simple interest becomes rs4480 in 3 years and rs 4800 in 5years.find the rate of interest​

Answer:

Choice C.

Step-by-step explanation:

Your choice is correct

2 stands for a starting point which is 2 feet from the home

As the ant moves, over time, the distance increases according to the function

Answer:

Step-by-step explanation:

a+b-c+d is expression

1/3<r/9 is inequality

and the last one is an equation

an inequality contains one of the 4 symbols

in an expression there is no equal sign

Answer:

Option (c).

Step-by-step explanation:

It is given that, I paid twice as much by not waiting for a sale and not ordering online.

Let the cost of items ordering online be x.

So, now i am paying twice of x = 2x

Now, we have find 2x is what percent of x.

[tex]Percent =\dfrac{2x}{x}\times 100=200\%[/tex]

It means, I paid 200% of what I could have online and on sale.

Therefore, the correct option is (c).

Answer:

Step-by-step explanation:

The graph below was created by a graphing utility.

It shows no horizontal gaps: f(x) is defined for all values of x, so the domain is all real numbers.

It shows a vertical gap between y=-6 and y>-5. So, the range is in two parts:

  {-6} ∪ {y > -5}

Answer:

$ 2,4

Step-by-step explanation:

135% .............$ 3,24

100% .............$ x

x = 3,24×100/135

= 324/135

= $ 2,4

Angle b= 50

Angle c= 130

Complementary angles are two angles that add to equal 90

Supplementary angles are two angles that add to equal 180

To find the measurement of angle b, subtract 40 from 90 (50)

To find the measurement of angle c, subtract 50 from 180 (130)

The measures of complementary and supplementary angles are given by m∠B = 50° and m∠C = 130°

Supplementary angles are two angles that add up to 180 degrees. In other words, if angle A and angle B are supplementary, then:

A + B = 180°

Complementary angles are two angles that add up to 90 degrees. In other words, if angle A and angle B are complementary, then:

A + B = 90°

Given data ,

If m∠A = 40°, then its complement ∠B = 90° - m∠A = 90° - 40° = 50°.

Since ∠C is a supplement of ∠B, we know that m∠C + m∠B = 180°.

Therefore, we can solve for m∠C by rearranging this equation to get:

m∠C = 180° - m∠B

Substituting the value we found for m∠B, we get:

m∠C = 180° - 50° = 130°

Hence , the angles are mZB = 50° and mZC = 130°.

To learn more about complementary and supplementary angles click :

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Answer:

6

Step-by-step explanation:

12*5=60

6*3=18

1*7=7

hope this help

Answer:

prime factors in ascending order of 1729 is 7 , 13 , 19

relation between  consecutive prime factors is 6

Step-by-step explanation:

given data

number = 1729

solution

we get here factors of 1729

1729 = 7 × 13 × 19

so that required prime factors in ascending order of 1729 is 7 , 13 , 19

and

now we get relation between these prime factors is the difference between consecutive prime factors is

13 - 7 =  6

19 - 13 = 6

so relation between  consecutive prime factors is 6

Step-by-step explanation:

Prime factors of the number 1729 are 7,13,19

i.e. 1729 =7×13×19

The factors in ascending order are 7,13,19.

Clearly we can see that each consecutive prime factors​ have difference of 6.

13-7=6

19-13=6

Answer:

Explanation;

Associated line with this equation is:

y=mx+c

when,

X=0

y=-4

so, c=-4

X=1

y=-1

[tex] - 1 = m- 4 \\ - m = - 4 + 1 \\ - m = - 3 \\ m =3 \\ [/tex]

[tex]y = 3x - 4 \\ or \: y + 4 = 3x \\ or \: \frac{y + 4}{3} = x[/tex]

Inequality representated by graph:

[tex]x \geqslant \frac{y + 4}{3} [/tex]

Hope this helps...

Good luck on your assignment...

Answer:

The test statistic value  t =  1.64 < 2.0086 at 0.05 level of significance

Null hypothesis is accepted

The mean portfolio value for all senior citizen shareholders in this region might not be the same as the mean value reported for their counterparts across the nation

Step-by-step explanation:

Step(i):-

Given mean of the population (μ) =  $183,000

Given mean of the sample (x⁻)  = $198,000

Given standard deviation of the sample (S) =  $65,000.

Mean of the sample size 'n' = 51

level of significance  α = 0.05

Step(ii):-

Null hypothesis : H₀ : There is no significance difference between the means

Alternative Hypothesis :H₁: There is  significance difference between the means

Test statistic

             [tex]t = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]

           [tex]t = \frac{198,000- 183,000 }{\frac{ 65,000}{\sqrt{51} } }[/tex]

          t =  1.64

Step(iii)

Degrees of freedom  ν = n-1 = 51-1 =50

t₀.₀₅ =  2.0086

The calculated value  t =  1.64 < 2.0086 at 0.05 level of significance

Null hypothesis is accepted

Final answer:-

There is no significance difference between the means

The mean portfolio value for all senior citizen shareholders in this region might not be the same as the mean value reported for their counterparts across the nation

Answer:

The maximal area will be "1093.5 square feet".

Step-by-step explanation:

Let,

Length = L feet

Breadth = b feet

Given Total fencing = 162 feet

According to the question,

 [tex](2\times L)+(3\times b)=162[/tex]

              [tex]2L+3B=162[/tex]

                         [tex]L=\frac{162-3b}{2}[/tex]

                         [tex]L=81-\frac{3}{2}b[/tex]

As we know,

 [tex]Area=Length\times breadth[/tex]

          [tex]=(81-\frac{3}{2}b)\times b[/tex]

          [tex]=81b-\frac{3}{2}b^2[/tex]

Now, we required to decrease or minimize the are. So for extreme points:

 [tex]\frac{dA}{db}=0[/tex]

or,

 [tex]\frac{dA}{dB}=\frac{d}{db}(81-\frac{3}{2}b^2 )=0[/tex]

       [tex]81-\frac{3}{2}\times 2\times b=0[/tex]

                            [tex]b=\frac{81}{3}[/tex]

                            [tex]b=27 \ feet[/tex]

Now on putting the value of b, we get

 [tex]l=81-\frac{3}{2}\times 27[/tex]

   [tex]=81-40.5[/tex]

   [tex]=40.5 \ feet\\[/tex]

So that the dimensions will be:

⇒  40.5 feet by 27 feet

Therefore when the dimension are above then the area will be:

=  [tex]81\times 27-\frac{3}{2}\times 27\times 27[/tex]

=  [tex]2187-\frac{3}{2}\times 729[/tex]

=  [tex]2187-1093.5[/tex]

=  [tex]1093.5 \ square \ feet[/tex]

Answer:

The given equation has two solutions

[tex]v = (-5.29, \: 5.29)[/tex]

Step-by-step explanation:

The given equation is

[tex]3v^2 - 84 = 0[/tex]

Let’s solve the equation

[tex]3v^2 - 84 = 0 \\\\3v^2 = 84 \\\\v^2 = \frac{84}{3} \\\\v^2 = 28 \\\\[/tex]

Take the square root on both sides

[tex]\sqrt{v^2} = \sqrt{28} \\\\v = \sqrt{28} \\\\v = \pm 5.29 \\\\[/tex]

So the equation has two solutions

[tex]v = (-5.29, \: 5.29)[/tex]

Also refer to the attached graph of the equation where you can verify that the equation has two solutions.

Note:

It is a very common mistake to consider only the positive value and not the negative value.

Consider the square root of 25

[tex]\sqrt{25} = \pm 5 \\\\Since \\\\5 \times 5 = 25 \\\\-5 \times -5 = 25 \\\\[/tex]

That is why we have two solutions for the given equation.

Answer:

x = -8/3

Step-by-step explanation:

Step 1: Write equation

-3/4(-3/8)(x) = -3/4

Step 2: Multiply

9/32(x) = -3/4

Step 3: Divide

x = -3/4/(9/32)

x = -3/4(32/9)

x = -8/3

Answer:

-8/3

Step-by-step explanation:

-(3/4) x (-3/8)= 9/32

9/32 times (-8/3) = -3/4

Answer: -8/3

Answer:

1/5

Step-by-step explanation:

The number 5 or greater than 4 is 5.

1 number out of 5 total parts.

= 1/5

P(5 or greater than 4) = 1/5

Answer:

2.19 km

Step-by-step explanation:

If x is the distance she walks down the road before turning, then the total time is:

t = x/8 + √((3 − x)² + 2²) / 3

t = x/8 + √(9 − 6x + x² + 4) / 3

24t = 3x + 8√(13 − 6x + x²)

24t = 3x + 8(13 − 6x + x²)^½

Take derivative of both sides with respect to x.

24 dt/dx = 3 + 4(13 − 6x + x²)^-½ (-6 + 2x)

When t is a minimum, dt/dx = 0.

0 = 3 + 4(13 − 6x + x²)^-½ (-6 + 2x)

-3 = 4(13 − 6x + x²)^-½ (-6 + 2x)

3 / (6 − 2x) = 4(13 − 6x + x²)^-½

3 / (24 − 8x) = (13 − 6x + x²)^-½

(24 − 8x) / 3 = (13 − 6x + x²)^½

(24 − 8x)² / 9 = 13 − 6x + x²

576 − 384x + 64x² = 117 − 54x + 9x²

459 − 330x + 55x² = 0

Solve with quadratic formula.

x = [ 330 ± √((-330)² − 4(55)(459)) ] / 2(55)

x = (330 ± √7920) / 110

x = 2.19 or 3.81

Since 0 < x < 3, x = 2.19.

Answer:

Option B

Step-by-step explanation:

We are given the following system of equations -

[tex]\begin{bmatrix}-5x+2y-2z=26\\ 3x+5y+z=-22\\ -3x-5y-2z=21\end{bmatrix}[/tex]

Now by Cramer's Rule, we would first write down the matrix of the coefficients , replacing each column with the answer column -

[tex]\begin{bmatrix}-5&2&-2\\ 3&5&1\\ -3&-5&-2\end{bmatrix}[/tex] ,

[tex]\begin{bmatrix}26\\ -22\\ 21\end{bmatrix}[/tex]

Replace each column of the coefficients shown at the top, with the answer column at the bottom respectively -

[tex]\begin{bmatrix}-5&2&26\\ 3&5&-22\\ -3&-5&21\end{bmatrix}[/tex]

Now solve through Cramer's Rule -

x = Dx / D = - 6,

y = Dy / D = - 1,

z = Dz / D = 1

Solution = ( - 6, - 1, 1 ) = Option B

-5 x + 2 y - 2 z = 263 x + 5 y + z = -22 - 3 x - 5 y - 2 z = 21

Answer is x=-6,\:z=1,\:y=-1

You are told up to 40 people are going and that the van holds 12.

40-12 = 28

So up to 28 people will need to buy train tickets.

Let n be the number of people buying train tickets and x is the total number of people going

N <= (x-12)

Answer:

31.4 inches

Step-by-step explanation:

The circumference of a circle has the formula 2πr.

2 × π × 5

= 10 × 3.14

= 31.4

31.4 inches of ribbon is needed to go once around the rim.

Answer:

15.7 inches of ribbon.

Step-by-step explanation:

This question is basically asking for the circumference of the glass vase's rim. We can calculate that by multiplying the diameter by π, which in this case, is 3.14.

The diameter is 5 inches, so all you need to do is 5 * 3.14 = 15.7 inches of ribbon.

Hope this helps!

Answer:

x^2-2x+1

Step-by-step explanation:

We can solve this by using FOIL

First, Outside, Inside, Last

Multiply the x with the x to get x^2

Then x times -1 for the outside numbers to get -x

Then -1 times x for the inside numbers to get -x

And finally -1 and -1 for the last numbers to get 1

Add the two -x to get -2x.

Put it all together

x^2-2x+1

Answer:

[tex]x^2-2x+1[/tex]

Step-by-step explanation:

=> (x-1)(x-1)

USING FOIL

=> [tex]x^2-x-x+1[/tex]

=> [tex]x^2-2x+1[/tex]

n=m+4

given formula,

n=3m-2l

and,

l=m+2

here in this question We have to substitute the values of "l" in the formulae

we get,

n=3m-2(m+2)

n=3m-2m+4

n=m+4

so if we complete the process correctly we get n=m+4

Answer:

x=∛4 x

Step-by-step explanation:

Let the number be x.

According to the question,

x^3=4 x

x=∛4 x

This is the only answer we can conclude from the information given in the question.

The required expression is x³ + 4x.

Given that,

The cube of a number increased by 4 times the same number is to be determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Let the number be x,
cube of number = x³
4 time of number = 4x
The cube of a number increased by 4 times the same number, which implies,
x³ + 4x

Thus, the required expression is x³ + 4x.

Learn more about arithmetic here:

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Answer:

a. 4650

b.

1. 332

2. 2076

3. 8306

Step-by-step explanation:

a. The planning value for population standard deviation is,

s = (maximum - minimum) / 4

s = (61600 - 43000) / 4

s = 4650

that is, it would be 4650, the planning value for population standard deviation

b. we have to:

n = (z * s / E) ^ 2

z for confidence level 95% is 1.96, E = 500; 200; 100

replacing:

1.

n = (1.96 * 4650/500) ^ 2

n = 332.2 = 332

2.

n = (1.96 * 4650/200) ^ 2

n = 2076.6 = 2076

3.

n = (1.96 * 4650/100) ^ 2

n = 8306.4 = 8306

Answer:

H=5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

S=4lw+2wh

Put S as 136, l as 6, w as 4, and solve for h.

136 = 4(6)(4)+2(4)H

136 = 8h + 96

-8h = 96 - 136

-8h = -40

h = -40/-8

h = 5

Answer:

  0 ≤ g(x) < ∞

Step-by-step explanation:

The range is all non-negative numbers.

___

g(x) is an even-degree polynomial with a positive leading coefficient, so it opens upward. There is no added constant, so its minimum value is zero. The function can take on all values zero or greater.

  range: [0, ∞)

Answer:

The correct option is (C).

Step-by-step explanation:

The general form of a confidence interval is:

[tex]CI=SS\pm CV\cdot SE[/tex]

Here,

SS = Sample statistic

CV = critical value

SE = standard error

The width of the confidence interval is:

[tex]\text{Width}=2\cdot CV\cdot SE[/tex]

The width of the confidence interval is dependent upon the critical value and hence dependent upon the confidence level.

As the confidence level increases the critical value increases hence in turn increasing the width of the interval.

And as the confidence level decreases the critical value decreases hence in turn decreasing the width of the interval.

In this case the 95% confidence interval is, (90.21,100.37).

And the 99% confidence interval is, (93.61.98.53).

It is clear by looking at the two intervals that the 95% confidence interval is wider than the 99%. Thus, this clearly indicates that the co-worker made a mistake.

The correct option is (C).

Answer:

Step-by-step explanation:

8P3=8*7*6=336

Answer:

Experiment 1 and 3 are clear binomial experiments.

Experiment 2 needs tweaking to be a binomial experiment.

Check Explanation.

Step-by-step explanation:

A binomial experiment is one in which

1) The probability of success doesn't change with every run or number of trials.

2) It usually consists of a fixed number of runs/trials with only two possible outcomes, a success or a failure.

3) The outcome of each trial/run of a binomial experiment is independent of one another.

Checking each of the experiments one at a time

- You observe the gender of the next 850 babies born at a local hospital. The random variable represents the number of boys.

For this experiment,

1) The probability of success doesn't change with every run or number of trials as it is a 50% chance that each child examined is a boy.

2) It consists of a fixed number of runs (850) with only two possible outcomes, success (if it's a boy) and failure (if it's a girl).

3) The probability of each trial being a boy is independent from all the other trials.

Hence, this experiment is a binomial experiment.

- You draw a marble 350 times from a bag with three colors of marbles. The random variable represents the color of marble that is drawn.

For this experiment,

1) If the marbles aren't being replaced after each draw, the probability of success, that is, picking a particular marble colour changes from trial to trial.

2) Although, it consist of a fixed number of runs/trials, there are more than two possible outcomes with 3 types of colours. Unless the experiment focuses on one colour and treats the other two colours as 'others', this condition too isn't satisfied.

3) Without replacement, the probability of success (picking a particular marble colour) in one trial isn't independent of the other trials.

This is not a binomial experiment as it doesn't satisfy all the required conditions to be one.

- Testing a cough suppressant using 820 people to determine if it is effective. The random variable represents the number of people who find the cough suppressant to be effective.

1) The probability of success doesn't change with every run or number of trials as it is the same chance that each person finds the cough suppressant to be effective.

2) It consists of a fixed number of runs (820) with only two possible outcomes, success (cough suppressant is effective) and failure (cough suppressant isn't effective).

3) The probability of each trial being a person that finds the cough suppressant to be effective, is independent from all the other trials.

Hence, this experiment is a binomial experiment.

Hope this Helps!!!

Answer:

Step-by-step explanation:

vector u=<(11-(-7),(-5-2)>=<18,-7>

as direction is opposite to u

so vector v=-3(18,-7)=(-54,21)

Answer:

46

Step-by-step explanation:

Answer:

The answer is [tex]\frac{25}{4}[/tex]

Step-by-step explanation:

Velocity formula:

[tex]v = \frac{d}{t}[/tex]

In which v is the velocity, d is the distance, and t is the time.

A tourist can bicycle 28 miles in the same time as he can walk 8 miles. He can ride 10 mph faster than he can walk:

This means that:

[tex]v = \frac{8}{t}[/tex]

And

[tex]v + 10 = \frac{28}{t}[/tex]

[tex](v + 10)t = 28[/tex]

From the first equation:

[tex]vt = 8[/tex]

So

[tex]vt + 10 = 28[/tex]

[tex]8 + 10t = 28[/tex]

[tex]10t = 20[/tex]

[tex]t = \frac{20}{10}[/tex]

[tex]t = 2[/tex]

He walks 8 miles in two hours, so:

[tex]v = \frac{8}{2} = 4[/tex]

4 miles per hour.

How much time (in hr) should he allow to walk a 25-mile trail?

This is t when [tex]d = 25[/tex]. So

[tex]v = \frac{d}{t}[/tex]

[tex]4 = \frac{25}{t}[/tex]

[tex]4t = 25[/tex]

[tex]t = \frac{25}{4}[/tex]

The answer is [tex]\frac{25}{4}[/tex]