Q.3. Set up the equations and solve them to find the unknown numbers in the cases given below:
1) If you add 6 to five times a number, it gives 46.
2) Two-third of a number minus 5 gives 11.
3) If you take onethird of a number and add 4 to it, gives 45.
4) When person X subtracts 12 from thrice of a number, it gives 18.
5) When Jenny subtracts twice the number of pens, she has from 40, she gets 16.
6) Virat guesses a number. If he adds 18 to that number and then divides the sum by 6, he gets answer 7.
7) Ami guesses anumber. If she subtracts 8 from two third of a number, she gets 6

I want Answer quickly ​

Answer:

for what lol

Step-by-step explanation:

Probability someone chosen at random will not have brown hair = 1/6

The number of girls = 15

The number of boys = 15

The total number of children = 15 + 15 = 30

Probability that someone chosen at random will have a brown hair, P(Brown hair) = 5/6

P(Brown hair) + P(Not Brown hair) = 1

5/6  +  P(Not brown hair) = 1

P(not brown hair) = 1 - 5/6

P(not brown hair) = 1/6

Therefore, if someone is chosen at random, probability that they will not have brown hair = 1/6

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Answer:

$6.45/hour

110.26%

Step-by-step explanation:

The absolute change is the difference between salaries now ands then.

12.30 - 5.85 = 6.45

The relative change in the percent increase.

percent increase = (new number - old number)/(old number) × 100%

percent increase = (12.3 - 5.85)/(5.85) × 100%

percent increase = 110.26%

The individual-size box of cereal is a rectangular prism with a volume of 44.625 inches³.

The volume of rectangular prism of length l, width w and height h is given by:

V = lwh.

In this problem, the standard dimensions are:

The individual-size box has a 1/10 of the volume of the original box, hence:

V = 0.1 x 3.5 x 8.5 x 15 = 44.625 inches³.

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Answer:

a. 13/26 = 1/2

b. 3/13

c. 2/26 = 1/13

Step-by-step explanation:

A. 26 red cards and 13 of them are hearts so 13/26 which can be simplified to 1/2

B. 13 hearts but only jack, queen king are higher than 10 so 3/13

C. 26 red cards altogether and we have a total of 2 red jacks so 2/26 which can be simplified to 1/13

is this what you wanted?

Answer:

  h > 5

  h < 0

Step-by-step explanation:

We suppose that a "Special Solution" inequality is one that is technically incorrect, but is written using a compact "shorthand" form.

As written, the inequality claims that 17 < 2, which is false. There can be no value of the variable that will make this true. We presume the intended meaning is ...

  17 < 3h +2   or   3h +2 < 2

Subtracting 2 from the inequality gives ...

  15 < 3h < 0

Dividing by 3 gives ...

  5 < h < 0

There is no value of h that is both greater than 5 and less than 0, so we presume this means the OR (union) of the solution sets ...

  h > 5

  h < 0

The large cone can hold more ice cream than the four smaller cones combined.

The large cone is a better deal.

A cone is a three-dimensional structure with a round base and a point at the top, known as the vertex.

A cone is a three-dimensional solid geometric object with a point at the top and a circular base. A cone has a vertex and one face. For a cone, there are no edges.

The radius, height, and slant height of the cone are its three constituent parts.

For the supersized cone,

Volume = π(5)(5)(12)/3 = 314.29 cubic inches

For a small cone,

Volume= π(2.5)(2.5)(6)/3 = 39.29 cubic inches

Combined volume of 4 such cones = 4*39.29 = 157.16 cubic inches

As the volume of the larger cone is more, thus it holds more ice cream. Also it is a better deal, as it costs less than 4 small cones.

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Answer:

Undefined (DNE)

Step-by-step explanation:

Any vertical line has an undefined slope.

Step-by-step explanation:

x is the number

x = 3y + 2

the square

x² = (3y + 2)² = 9y² + 12y + 4

9y² is a multiple of 3 (because of the factor 9)

12y is a multiple of 3 (because of the factor 12)

4 is 1 more than a multiple of 3 (1×3).

so, the sum of all 3 terms is 1 more than a multiple of 3.

Answer:

8

Step-by-step explanation:

The cos of 30 is [tex]\sqrt{x}[/tex] / 2.  Since the adjacent angle is 4 times that.  We would multiply 2 x 4 and get 8

When [tex]n=0[/tex], we have

[tex]5^{3^0} + 1 = 5^1 + 1 = 6[/tex]

[tex]3^{0 + 1} = 3^1 = 3[/tex]

and of course 3 | 6. ("3 divides 6", in case the notation is unfamiliar.)

Suppose this is true for [tex]n=k[/tex], that

[tex]3^{k + 1} \mid 5^{3^k} + 1[/tex]

Now for [tex]n=k+1[/tex], we have

[tex]5^{3^{k+1}} + 1 = 5^{3^k \times 3} + 1 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k}\right)^3 + 1^3 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k} + 1\right) \left(\left(5^{3^k}\right)^2 - 5^{3^k} + 1\right)[/tex]

so we know the left side is at least divisible by [tex]3^{k+1}[/tex] by our assumption.

It remains to show that

[tex]3 \mid \left(5^{3^k}\right)^2 - 5^{3^k} + 1[/tex]

which is easily done with Fermat's little theorem. It says

[tex]a^p \equiv a \pmod p[/tex]

where [tex]p[/tex] is prime and [tex]a[/tex] is any integer. Then for any positive integer [tex]x[/tex],

[tex]5^3 \equiv 5 \pmod 3 \implies (5^3)^x \equiv 5^x \pmod 3[/tex]

Furthermore,

[tex]5^{3^k} \equiv 5^{3\times3^{k-1}} \equiv \left(5^{3^{k-1}}\right)^3 \equiv 5^{3^{k-1}} \pmod 3[/tex]

which goes all the way down to

[tex]5^{3^k} \equiv 5 \pmod 3[/tex]

So, we find that

[tex]\left(5^{3^k}\right)^2 - 5^{3^k} + 1 \equiv 5^2 - 5 + 1 \equiv 21 \equiv 0 \pmod3[/tex]

QED

Answer:

1. 30

Step-by-step explanation:

∠H + ∠T = 180

(2x+60)+(x+30)=180

3x+90=180

3x=90

x=30

samples confidence intervals needed is Option C 136.

According to the Empirical rule, if data exists normally distributed then about 68% of the population lies within one standard deviation from the mean.

We assume that the mean of a normally distributed population exists at 300, and 200 simple random samples exist drawn from the population.

Number of simple random samples, n= 200

By Empirical rule, approximately 68% of 200 samples’ confidence intervals we would expect to have the population mean.

Required number of samples = 68% of 200

= 0.68 x 200 = 136

The required number of samples = 136

Therefore, the correct answer is option C) 136.

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Answer:

==============

We know each interior angle of an equilateral triangle is 60°, since each of three angles are of same value.

The middle triangle with two interior angles 4x and y has the missing angle also y, since it is isosceles, because both adjacent angles are equal at vertex N.

First

Measure of any angle in an equilateral triangle is 60°

So

And

Apply angle sum property

the table complete is:

x      y

1       4

2      8

3      12

4      16

Where x is the ribbon length in yards and y is the number of bows she can make.

We know that Marina needs 1/4 yards of ribbon for each bow.

Then, with one yard of ribbon, she can make 4 bows, then the relation between y, the number of bows she can make, and x, the yards of ribbon that she has, is:

y = 4*x

Now we want to complete the table:

x           y

1

2

3

4

To do so, we just need to evaluate the above function.

when x = 1.

y = 4*1 = 4

When x = 2:

y = 4*2 = 8

when x = 3

y = 4*3 = 12

when x = 4

y = 4*4 = 16

Then the table complete is:

x      y

1       4

2      8

3      12

4      16

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The after-tax rate of return is 1.84%, the real return is 0.721%, the total monetary return is $1530 and the implications become very challenging to grow with such a return as the taxes

Given that money market account investment at 2.55 percent​ (APY), a ​1.11 % inflation​ rate, a 28 percent marginal tax​ bracket, and a constant ​$60000 ​balance.

Cash management is the backbone of any business. Cash management ensures that the company operates according to established standards and optimizes the use of funds to avoid wasting resources. Liquidity management decisions are therefore key to preserving a company's capital and profitability.

Firstly, we will find the after-tax return rate, we get

After-tax return rate= Before tax rate of return \times ( 1 - tax rate)

After-tax rate of return = 0.0255× ( 1 - 0.28)

After-tax rate of return = 0.0255×0.72

After-tax rate of return=1.84%

Now, we will find the real return, we get

Real  return=((1+After-tax Return)/(1+inflation rate))-1

Real return=((1+0.0184)/(1+0.0111))-1

Real return=(1.0184/1.0111)-1

Real return=1.00721-1

Real return=0.721%

Furthermore, we will find the total monetary return, we get

Total monetary rate=Balance×Before tax rate of return

Total monetary rate=60000×2.55%

Total monetary rate=$1530.

The implications of this result for cash management​ decisions is that it becomes very challenging to grow with such a return as the taxes and inflation is draining the returns and leaving only with negative returns.

Hence, the after-tax rate of return is 1.84%, the real return is 0.721%, the total monetary return is $1530 and the implications become very challenging to grow with such a return as the taxes and inflation is draining the returns and leaving only with negative returns.

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Answer:

It is an open circle and you would shade to the right on a number line.

Step-by-step explanation:

The circle is open because you are not including 3.  Put numbers in for t and you will see that the numbers greater than 3 are all on the right side of the number line.

Answer:

Yes because putting value of x and y as 1 and -1 in equation :

y=3x-4

-1 = 3 * 1 - 4

-1 = -1 (True)

electronic data interchange

Thermal energy can be used in the heating systems either at home or in the industries

However, when solar energy is converted to thermal energy, the radiant energy from the sunlight is converted into heat which can then be used as space and hot water heating, power generation and industrial process heat

Energy simply refers to the capacity of doing work. Some forms of energy are:

So therefore, thermal energy can be used in the heating systems either at home or in the industries.

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95% men are between 165 cm and 186 cm.

What is the empirical rule?

The empirical rule is also referred to as the Three Sigma Rule or the 68-95-99.7 Rule.

z-score = (raw-score minus mean) / standard deviation.

z1 = (165-176)/5 = -2.2

z2 = (186-176)/5 = 2

The empirical rule tells us that about 95% of all values are within standard deviations of the mean,

so, 95% men are between 165 cm and 186 cm.

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95% of men are between 165 cm and 186 cm.

Given:

Find:

Solution:

The empirical rule is also referred to as the three sigma rule or the 68-95-99.7

Rule:

z - score = (raw - score minus mean) / standard deviation.

z1 = (165-176)/5 = -2.2

z2 = (186-176)/5 = 2

The empirical rule tells us that about 95% of all values are within standard deviations of the mean.

So, 95% of men are between 165 cm and 186 cm.

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Option C. The statement that describes the graph of the equation y + 2 ≥ –4(x – 3)2 is a a parabola opening down, with shading above the vertex.

To do this you have to create a graph of the equation as seen in the attachment.

From the attachment we can see that the parabola is shaped downwards while we have the shading to be at the top of the vertex.

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Answer:

[tex]x \approx 1.16[/tex]

Step-by-step explanation:

a.

To find the values of m and n, we have to first expand  [tex](x + m)^2 + n[/tex] :

[tex](x + m)^2 + n[/tex]

⇒ [tex]x^2 + 2mx + m^2 + n[/tex]

[tex]f(x) = x^2 + 4x - 6[/tex]

Now  compare the coefficients of the x-terms:

• [tex]2mx = 4x[/tex]

⇒ [tex]\bf m = 2[/tex]

• [tex]m^2 + n = -6[/tex]

⇒  [tex]2^2 + n = -6[/tex]

⇒ [tex]n = -10[/tex]

b.

[tex]x^2 + 4x - 6 = 0[/tex]

∴ [tex](x + 2)^2 - 10 = 0[/tex]

⇒ [tex](x + 2)^2 = 10[/tex]

⇒ [tex]x + 2 = \sqrt{10}[/tex]

⇒ [tex]x = \sqrt{10} -2[/tex]

⇒ [tex]x \approx 1.16[/tex]

Answer:

x = 12

Step-by-step explanation:

6x - 4 and 112 are same- side interior angles and sum to 180° , that is

6x - 4 + 112 = 180

6x + 108 = 180 ( subtract 108 from both sides )

6x = 72 ( divide both sides by 6 )

x = 12

Answer:

x = 12

Step-by-step explanation:

Consecutive Interior Angles Theorem

When a straight line intersects two parallel straight lines, the consecutive interior angles formed are are supplementary (sum to 180°).

Therefore:

⇒ 6x - 4 + 112 = 180

⇒ 6x + 108 = 180

⇒ 6x + 108 - 108 = 180 - 108

⇒ 6x = 72

⇒ 6x ÷ 6 = 72 ÷ 6

⇒ x = 12

Answer: equation: y=-4x+1

slope: -4

y intercept:1

The value for x that is a double root of this function is x = -1

The function is given as:

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

From the graph of the above function (see attachment), we have the following highlights:

The point that it touches the x-axis is the double root point

Hence, the value for x that is a double root of this function is x = -1

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Using a system of equations, the translated expression is:

P - 32.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variable is the number of dollars Paul owes, which is P. That amount minus 32 is represented by:

P - 32.

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= 4×8 +2×3 -1+9

___________

20

= 8+6-9

_______

20

= 14 - 9

_______

20

= 5

____

20