a number is between 58 and 60 it has prime factors between 2,3,and 5. what is the number?
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Answer:

See Explanation for answers

Step-by-step explanation:

Given

\(Grade\ X: 568, 570, 575, 578, 584\)

\(Grade\ Y: 573, 574, 575, 577, 578\)

Solving (a): Mean, median, and standard deviation of both grades

Mean is calculated as:

\(Mean = \frac{\sum x}{n}\)

For grade X:

\(Mean = \frac{568 + 570+ 575+578+584}{5}\)

\(Mean = \frac{2875}{5}\)

\(Mean = 575\)

For Grade Y

\(Mean = \frac{573+ 574+ 575+ 577+ 578}{5}\)

\(Mean = \frac{2877}{5}\)

\(Mean = 575.4\)

\(Median = \frac{N+1}{2}th\)

\(Median = \frac{5+1}{2}th\)

\(Median = \frac{6}{2}th\)

\(Median = 3rd\ item\)

For grade X and Y.

\(Median = 575\)

Standard deviation (s) is calculated as:

\(s = \sqrt{\frac{\sum(x_i - \bar x)^2}{n}}\)

For Grade x

\(s = \sqrt{\frac{(568 - 575)^2+(570 - 575)^2+(575 - 575)^2+(578- 575)^2+(584- 575)^2}{5}}\)

\(s = \sqrt{\frac{164}{5}}\)

\(s = \sqrt{32.8}\)

\(s = 5.73\)

For Grade Y

\(s = \sqrt{\frac{(573 - 575.4)^2+(574 - 575.4)^2+(575 - 575.4)^2+(577 - 575.4)^2+(578 - 575.4)^2}{5}}\)

\(s = \sqrt{3.44}\)

\(s = 1.85\)

Solving (b): If the last value is  b, the following will occur.

The mean will increase.

The median will remain unaltered

The standard deviation will increase.

See proof below

For Grade Y: Mean is:

\(Mean = \frac{573+ 574+ 575+ 577+ 588}{5}\)

\(Mean = \frac{2887}{5}\)

\(Mean = 577.4\)

Median still remains the 3rd item.

\(Median = 575\)

The standard deviation is:

\(s = \sqrt{\frac{(573 - 575.4)^2+(574 - 575.4)^2+(575 - 575.4)^2+(577 - 575.4)^2+(588 - 575.4)^2}{5}}\)

\(s = \sqrt{\frac{169.2}{5}}\)

\(s = \sqrt{33.84}\)

\(s = 5.82\)

Solving (c): Which grade provides better quality.

Grade X provides better quality.

This is so because the mean value, the standard deviation of grade X is greater than grade Y

Mean medium and standard deviation are the statistics tools used to measure the center tendency of the given data set.

Grade X: 568, 570, 575, 578, 584

Grade Y: 573, 574, 575, 577, 578

Mean is the average of the given data or the ratio of the sum of the given data set to the number of data in the set.

Mean for grade X,

\(\overline x=\dfrac{568+570+575+578+584}{5} \\ \overline x=575\)

Mean for grade Y,

\(\overline x=\dfrac{573+574+575+577+578}{5} \\ \overline x=575.4\)

Median is the middle number when the data set is arranged in the assenting or descending order.

The middle number for both the data set is 575 milimeter. Thus the median is 575 for both the data set.

Standard deviation refers that how much the group member of a data set is differ from the mean value. Standard deviation can be given as,

\(\sigma=\sqrt{\dfrac{\sum(x_i-\mu)^2}{N} } \)

Standard deviation for X

\(\sigma=\sqrt{\dfrac{(568-575)^2+(570-575)^2+(575-575)^2+(578-575)^2+(584-575)^2}{5} } \\ \sigma=5.73\)

Standard deviation for Y

\(\sigma=\sqrt{\dfrac{(573-575.4)^2+(574-575.4)^2+(575-575.4)^2+(577-575.4)^2+(578-575.4)^2}{5} } \\\sigma=1.85\)

b) Effect on the answers in (a) and (b) if the last value for grade Y was 588 instead of 578.

Mean for grade Y,

\(\overline x=\dfrac{573+574+575+577+588}{5} \\ \overline x=577.4\)

Thus the mean increased with value 2 mm.

Medium remain the same as the middle value is still 575.

Standard deviation for Y

\(\sigma=\sqrt{\dfrac{(573-575.4)^2+(574-575.4)^2+(575-575.4)^2+(577-575.4)^2+(588-575.4)^2}{5} } \\\sigma=5.82\)

c) Tire which provide better quality-

The value of mean and standard deviation of the Tyre X is greater thus the Tyre X provide the better quality.

Hence

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The distance between Ray-Ann and Steve, using the law of cosines, is given as follows:

11.5 feet.

The law of cosines states that we can find the length of the missing side c of a triangle as follows:

c² = a² + b² - 2abcos(C)

The parameters of the equation are given as follows:

In the context of this problem, the values of these parameters are given as follows:

Hence the distance between Ray-Ann and Steve is obtained as follows:

c² = 6²+ 7² - 2 x 6 x 7 x cos(124)º

c² = 132

c = square root of 132

c = 11.5 feet.

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The number of tourists who visited the city at the end of February that year is 4x.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

The number of tourists visiting the city doubles every month, which means the number of tourists at the end of January is 2 times the number of tourists at the beginning of January, or 2x.

Similarly, the number of tourists at the end of February is 2 times the number of tourists at the end of January, or 2(2x) = 4x.

Therefore,

The number of tourists who visited the city at the end of February that year is 4x.

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Answer:

34

Step-by-step explanation:

f = 202

Step-by-step explanation:

\(7 \times 5f = 7070\)

\(5f = \frac{7070}{7} \)

\(5f = 1010\)

\(f = \frac{1010}{5} \)

\(f = 202\)

Verification to check the given answer is correct, then put the value of f in the given question.

\(7 \times 5(202) = 7070\)

\(35(202) = 7070\)

\(7070 = 7070\)

L.H.S. = R.H.S

\({ \green { \boxed{ \red{ \sf{f = 202}}}}}\)

Step-by-step explanation:

The given Eqⁿ is, \({ \purple{ \sf{7 \times 5f = 7070}}}\)

We need to find the value of f. So, let us cancel the numbers one by one.

First, let us cancel 7 by dividing both the sides by 7 in the given Eqⁿ.

\({ \purple{ \sf \frac{ \cancel7 \times 5f}{ \cancel7}}} = { \purple{ \sf{ \frac{ \cancel{7070} ^{ \green{ \tt{1010}}} }{ \cancel 7_{ \green{ \tt{1}}}}}}}\)

\({ \purple{ \sf{5f = 1010}}}\)

Now, let us cancel 5 by dividing both the sides by 5. then,

\({ \purple{ \sf{ \frac{ \cancel5}{ \cancel5}f}}} = { \purple{ \sf{ \frac{ \cancel{1010^{ \red{ \tt{ \: \:202}}}}}{ \cancel 5_{ \red{ \tt{1}}}}}}}\)

\({ \boxed{ \blue{ \sf{f = 202}}}}\)

Answer:

Multiply the top equation by -3 and the bottom equation by 2

Step-by-step explanation:

Given system of equations:

\(\begin{cases}4x-2y=7\\3x-3y=15 \end{cases}\)

To solve the given system of equations by addition, make one of the variables in both equations sum to zero.  To do this, the chosen variable must have the same coefficient, but it should be negative in one equation and positive in the other, so that when the two equations are added together, the variable is eliminated.

To eliminate the variable y:

Multiply the top equation by -3 to make the coefficient of the y variable 6:

\(\implies -3(4x-2y=7) \implies -12x+6y=-21\)

Multiply the bottom equation by 2 to make the coefficient of the y variable -6:

\(\implies 2(3x-3y=15) \implies 6x-6y=30\)

Add the two equations together to eliminate y:

\(\begin{array}{l r r}& -12x+6y= &-21\\+ & 6x-6y= & 30\\\cline{1-3}& -6x\phantom{))))))} = & 9\end{array}\)

Solve for x:

\(\implies -6x=9\)

\(\implies x=-\dfrac{9}{6}=-\dfrac{3}{2}\)

Substitute the found value of x into one of the equations and solve for y:

\(\implies 3\left(-\dfrac{3}{2}\right)-3y=15\)

\(\implies -\dfrac{9}{2}-3y=15\)

\(\implies -3y=\dfrac{39}{2}\)

\(\implies y=-\dfrac{39}{2 \cdot 3}\)

\(\implies y=-\dfrac{13}{2}\)

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Answer:

Exact Form:

17/2

Decimal Form:

8.5

Mixed Number Form:

8 1/2

Answer:

4x² + 22x - 12

Step-by-step explanation:

A = bh/2

A = (4x - 2)(2x + 12)/2

A = (8x² + 48x - 4x - 24)/2

A = (8x² + 44x - 24)/2

A = 4x² + 22x - 12

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

Answer:

the difference is -46 degrees

Step-by-step explanation:

Answer:

the answer in fraction form is 16/7

Step-by-step explanation:

but if you want it in decimal form its 2.2857142857

you can also round it off to 2.3

Literally have the same question on my test and i dont know if i got it right or wrong. I know it has nothing to do with this :/ im sorry.

Answer:

The p-value of the test is 0.0066 < 0.05, which means that there is sufficient evidence at the 0.05 significance level to conclude that the mean salary differs from $39,385

Step-by-step explanation:

The average salary for public school teachers for a specific year was reported to be $39,385. Test if the mean salary differs from $39,385

At the null hypothesis, we test if the mean is of $39,385, that is:

\(H_0: \mu = 39385\)

At the alternative hypothesis, we test if the mean differs from this, that is:

\(H_1: \mu \neq 39385\)

The test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.

39385 is tested at the null hypothesis:

This means that \(\mu = 39385\)

A random sample of 50 public school teachers in a particular state had a mean of $41,680, and the population standard deviation is $5975.

This means that \(n = 50, X = 41680, \sigma = 5975\)

Value of the test statistic:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{41680 - 39385}{\frac{5975}{\sqrt{50}}}\)

\(z = 2.72\)

P-value of the test and decision:

The p-value of the test is the probability that the sample mean differs from 39385 by at least 2295, which is P(|Z| > 2.72), which is 2 multiplied by the p-value of Z = -2.72.

Looking at the z-table, Z = -2.72 has a p-value of 0.0033

2*0.0033 = 0.0066

The p-value of the test is 0.0066 < 0.05, which means that there is sufficient evidence at the 0.05 significance level to conclude that the mean salary differs from $39,385

The length (in inches) of the second tablecloth is 43.75 inches

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

Width = 48 inches. and Length = 72 inches ⇒ Small tablecloth

Width = 30 inches. and Length = ?? inches ⇒ Large tablecloth

Represent the unknown length with x

So, we have

Width = 48 inches. and Length = 72 inches ⇒ Small tablecloth

Width = 30 inches. and Length = x inches ⇒ Large tablecloth

This shows a direct variation

So, we cross multiply the equation

x * 48 = 70 * 30

So, we have

x = 70 * 30/48

Evaluate

x = 43.75

Hence, the length is 43.75 inches

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Answer:

-3

Step-by-step explanation:

since the lines are parallel, they have the same slope because they never intersect

The form that most quickly reveals the y intercept is

The y intercept is (0, 21/2)

The y-intercept is the point where a function or a curve intersects the y-axis. In other words, it is the value of the dependent variable (y) when the independent variable (x) is equal to zero.

In the form,  f(x) = 1/2 x² - 5x + 21/2 it is easier to see that eliminating x by plugging in 0 leaves 21/2 which is the y intercept

hence we can easily say that the y intercept is (0, 21/2)

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The cost of making 35 items is 1100 and the domain is (-∞,∞)

The cost of making 35 items :

plug the value into the cost equation

C(35) = 10(35) + 800

C(35) = 350 + 800

C(35) = 1100

Hence, cost of making 35 items is 1100

Since the value of X can be any real number, we can plug in any real number for x and get a real number output.

Hence, the domain = (-∞,∞)

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The solution of the integral of 8 cos(x)+ √3 = 5√3 is  8π√3.

The given function is 8 cos(x)+ √3 = 5√3

The function can be simplified as follows;

8 cos(x) + √3 = 5√3

collect similar terms together;

8 cos(x) + √3 - 5√3 = 0

8 cos(x)  - 4√3 = 0

integral of  8 cos(x)  - 4√3  = 8 sin(x) - 4√3x

the value of the integral over (0, 2π)

= 8 sin(0) - 4√3(0) -  (8 sin(2π) - 4√3(2π))

= 0 + 8π√3

= 8π√3

Thus, the solution of the integral of 8 cos(x)+ √3 = 5√3 is  8π√3.

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Answer:

\(\text{\textit{x}} \ \ = \ \ \displaystyle\frac{\pi}{6} \ \ \ \text{or} \ \ \ \displaystyle\frac{11\pi}{6}\)

Step-by-step explanation:

Given the trigonometric equation

                               \(8 \ \cos{\left(\textit{x}\right)} \ + \ \sqrt{3} \ = \ 5\sqrt{3}\),

hence solving for \(\textit{x}\) yields

                                  \(8 \ \cos{\left(\textit{x}\right)}\ = \ 5\sqrt{3} \ - \ \sqrt{3} \\ \\ \\ \-\hspace{8px} \cos{\left(x\right)} \ = \ \displaystyle\frac{4\sqrt{3}}{8} \\ \\ \\ \-\hspace{8px} \cos{\left(x\right)} \ = \ \displaystyle\frac{\sqrt{3}}{2} \\ \\ \\ \-\hspace{29px} \textit{x} \ \ \ = \ {\cos}^{-1}\left(\displaystyle\frac{\sqrt{3}}{2}}}\right) \\ \\ \\ \-\hspace{29px} \textit{x} \ \ \ = \ \displaystyle\frac{\pi}{6}\).

Since cosine is positive in both quadrant I and quadrant IV, thus

                                     \(\textit{x} \ \ = \ \ 2\pi \ - \ \displaystyle\frac{\pi}{6} \ \ = \ \ \displaystyle\frac{11\pi}{6}\).

Therefore the solutions are

                                               \(\textit{x} \ \ = \ \ \displaystyle{\frac{\pi}{6}} \ \ \text{or} \ \ \displaystyle{\frac{11\pi}{6}}\).

Thoughts:  The best that I was able to do was simplify it in this form.

Answer:    V    

Answer:

A=30t+200

B=50t+100

The number of hours,t, that would make the cost of each company the same is 5.

30(5)+200= A

 150+200=350

50(5)+100= B

 250+100=350

Therefore, the answer is A. {5, 5√3, 10}.

The set of values {5, 5√3, 10} could be the side lengths of a 30-60-90 triangle.

In a 30-60-90 triangle, the sides are in a specific ratio. The ratio is 1 : √3 : 2, where the shortest side (opposite the 30-degree angle) has length x, the side opposite the 60-degree angle has length x√3, and the hypotenuse (opposite the 90-degree angle) has length 2x.

Let's check if the given set of values satisfies this ratio:

   If x= 5, then the side opposite the 60-degree angle should be 5√3, and the hypotenuse should be 10. These values match the ratio, so the set {5, 5√3, 10} could be the side lengths of a 30-60-90 triangle.

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Answer:

4x+3(3x-4)=1

4x+9x-12=1

13x=13

x=1

The sum of the interior angles of a regular polygon with 9 sides will be 1260°. The correct option is A.

An angle is defined in mathematics as the figure formed by joining two rays at their common endpoint. An interior angle is an angle that exists within a shape. Polygons are closed shapes with sides and vertices. All of the interior angles of a regular polygon are equal.

Given that the number of the sides of the polygon is 9. The sum of the interior angles of the polygons will be calculated as,

Sum = ( n - 2 ) 180°

Sum = ( 9 - 2 ) 180

Sum = 7 x 180

Sum = 1260°

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Answer:

A. thats the answer

Step-by-step explanation:

carry on learning

Answer:

The number of potential members predicted in next year's estimate becomes 193. The further explanation is given below.

Step-by-step explanation:

The slope of the model,

m = 15.345

c = 24

After comparing with the equation,

⇒  \(y=mx+c\)

we get,

⇒     \(=15.345x + 24\)

The slope seems to be a positive value which also means that another always improves this as component decreases. Which ensures that perhaps the number of contributors rising as time went by.

So that the above is the right answer.

The fence in dead center is about 399 feet from the third base.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

For the triangle in this problem, we have that:

Hence the distance is obtained as follows:

d² + 90² = 409²

\(d = \sqrt{409^2 - 90^2}\)

d = 399 ft.

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Answer:

third option

Step-by-step explanation:

under a counterclockwise rotation of 90° about the origin

a point (x, y ) → (y, - x )

Then

A (- 1, - 2 ) → (- 2, - (- 1) ) → (- 2, 1 )

B (2, - 2 ) → (- 2, - 2 )

C (1, - 4 ) → (- 4, - 1 )

The new coordinates are (d) A = (2, -1) B = (2, 2) and C = (4, 1)

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

The figure,

Where, we have

A = (-1, -2)

B = (2, -2)

C = (1, -4)

The rule of 90 degrees counterclockwise is

(x, y) = (-y, x)

Using the above as a guide, we have the following:

A = (2, -1)

B = (2, 2)

C = (4, 1)

Hence, the new coordinates are (d) A = (2, -1) B = (2, 2) and C = (4, 1)

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To solve this problem, we need to find the lengths of the two pieces when the wire is cut into two parts. Let's denote the length of each leg of the triangle as\(\(x\).\)

The perimeter of the triangle is the sum of the lengths of its three sides. Since the two legs are equal in length, the perimeter can be expressed as \(\(2x + x = 3x\).\)

The length of the wire is given as 71 cm, so we have the equation \(\(3x = 71\).\)

Solving for\(\(x\),\) we divide both sides of the equation by 3:

\(\(x = \frac{71}{3}\).\)

Now that we know the length of each leg of the triangle, we can proceed to the next part of the problem.

The circumference of a circle is given by the formula \(\(C = 2\pi r\)\), where\(\(C\)\)is the circumference and r is the radius. In this case, the wire of length xis bent into the shape of a circle, so we can set the circumference equal to x and solve for the radius r:

\(\(x = 2\pi r\).\)

Substituting the value of x we found earlier, we have:

\(\(\frac{71}{3} = 2\pi r\).\)

Solving for r, we divide both sides of the equation by \(\(2\pi\):\)

\(\(r = \frac{71}{6\pi}\).\)

Therefore, the two pieces of wire will have lengths\(\(\frac{71}{3}\)\)cm and the radius of the circle will be\(\(\frac{71}{6\pi}\)\) cm.

In summary, when the 71 cm wire is cut into two pieces, one piece will have a length o\(\(\frac{71}{3}\)\)cm, which can be bent into the shape of an equilateral triangle with legs of equal length, and the other piece can be bent into the shape of a circle with a radius of \(\(\frac{71}{6\pi}\)\) cm.

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