Three integers have a mean of 10, a median of 14 and a range of 12.
Find the three integers.

The Measurement of SRV is 120°

The possible widths of the play area is  mathematically given as

This is further explained below.

Generally, the equation for perimeter  is  mathematically given as

P =2(l+w)

180 =2(l+w)

2(l+w) =180

\(l+w = \frac{180}{2}\)

l+w =90

A =l \times w

1800 &=l *w

l *w =1800

l *w =1800

Substitute Eq. 3 in the Eq. 2:

l *w=1800

(90-w) *w=1800

90w-ww=1800

90w-w^2=1800

w^2-90 w+1800=0

Therefore

w^2-90 w+1800 =0

\(\left(w^2-30 w\right)+(-60 w+1800) =0\)

w(w-30)-60(w-30) =0

(w-30)(w-60) =0

Thereofre

w =30

w=60

In conclusion, Because of this, the width of the rectangular play space is either thirty or sixty feet.

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Answer:

Step-by-step explanation:

A triangle has 180 degrees in total. One of the angles are 145 degrees, so we can subtract and get 35 degrees. Then, it says that the remaining angles are in a ratio 2:3. So, we would have:

\(2x:3x = 35 \\2x+3x = 35\\5x=35\\x=7\)

Now that we know what x is, we can multiply that to our ratio:

\(2\cdot7=14 \text{ degrees for the first angle}\\3\cdot7=21 \text{ degrees for the second angle }\)

Answer:

Step-by-step explanation:

y=10

Answer:

1

Step-by-step explanation:

from the rule of exponents

• \(a^{0}\) = 1 , then

\((5x)^{0}\) = 1

The solution of 30 \(\div\) 5 is 6 by the method shown in the question.

Using the same method given in the question, we can solve 30 \(\div\) 5

We can express 30 as the sum of 25 and 5, and dividing both 25 and 5 by 5,

⇒ 30 / 5 = ( 25 / 5 ) + ( 5 / 5 )

= 5 + 1

= 6

Therefore, 30 ÷ 5 equals 6. The division process involves breaking down the number into two numbers, so that the second number gives 1 after dividing by the divisor and then adding it with the division of first number by the divisor.

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Answer:

students= 110

adults= 40

Step-by-step explanation:

Step one:

given data

Tickets for students were $2 and tickets for adults were $3.

let students be x

and adults be y

so

2x+3y= 340--------------1

and

x+y= 150--------------------2

from 2

x= 150-y

from 1

2(150-y)+3y= 340

300-2y+3y= 340

collect like terms

y=340-300

y= 40

put y= 40 in 2

x+40=150

x= 150-40

x= 110

Answer:

R = 5

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

 =  5

Step-by-step explanation:

1. Add 8 to both sides of the equation

2 . Simplify

3 . Subtract  4  from both sides of the equation

4 . Simplify  ( combine like terms )

5 . Divide both sides of the equation by the same term

6 . Simplify

Answer:

y ≤ 45

Step-by-step explanation:

First y must be less than or equal to 45.

y ≤ 45 x + y  ≤  80

And total number of reservations cannot exceed 80:

x + y  ≤  80.

The statements that are true about rectangles are mentioned in options  

A,B,C,E.

Rectangles -A shape with four sides and internal angles is a rectangle. The lengths of the other two sides are offset by two. The rectangle's diagonal sides are of identical length.

The opposite sides of a rectangle are equal and parallel to one another.

The diagonals cut each other in half, but not exactly.

All diagonals are the same length.

The rectangle's diagonals line up.

The total internal angles add up to the same value

Every internal angle has the same value.

A rectangle has congruent angles on all sides.

A rectangle's opposing angles are congruent.

We may thus infer that the statements about rectangles in the options are accurate based on the aforementioned features.

Q. Select all the statements that are true about rectangles.

A Diagonals are congruent.

B Diagonals bisect angles.

C Opposite angles are congruent.

D Diagonals are perpendicular.

E Diagonals bisect each other.​

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We can conclude that the marketing manager's claim is true.

To determine whether the marketing manager's claim is true, we need to conduct a hypothesis test.

Let p be the proportion of all children aged 8-12 who have cell phones. The marketing manager claims that p > 0.5, while the national consumers group survey found that 39/54 or p' = 0.722 have cell phones.

The null hypothesis is that the true proportion of children with cell phones is less than or equal to 0.5:

H0: p ≤ 0.5

The alternative hypothesis is that the true proportion of children with cell phones is greater than 0.5:

Ha: p > 0.5

We will conduct a one-tailed hypothesis test with a level of significance of 0.05.

Under the null hypothesis, the sample proportion follows a binomial distribution with parameters n = 54 and p = 0.5. The standard error of the sample proportion is given by:

SE = √[p(1-p)/n] = √[0.5(1-0.5)/54] = 0.070

The test statistic is calculated as:

z = (p' - p) / SE = (0.722 - 0.5) / 0.070 = 3.14

The critical value for a one-tailed test with a level of significance of 0.05 is 1.645, using the standard normal distribution table.

Since the test statistic (z = 3.14) is greater than the critical value (1.645), we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that more than half of the children aged 8-12 have cell phones.

Therefore, we can conclude that the marketing manager's claim is supported by the data from the survey.

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To solve for t2 in the equation t2/t1=(p2/p1)^(n-1/n), we can cross-multiply to get t2=(p2/p1)^(n-1/n) * t1.


In the given equation, t2/t1 represents the ratio of two temperatures, while (p2/p1)^(n-1/n) is a ratio of pressures raised to a power. The exponent of (n-1/n) in the equation represents the ratio of specific heats, which is a constant value for a given gas. Thus, we can rewrite the equation as t2/t1= (p2/p1)^k, where k = (n-1/n).

To solve for t2, we can multiply both sides of the equation by t1, which gives us t2= (p2/p1)^k * t1.


Therefore, the equation to solve for t2 is t2= (p2/p1)^(n-1/n) * t1.

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Answer:

10%

Step-by-step explanation:

250/25 is 10%

Answer:

10%

Step-by-step explanation:

hope this helps. . . <3

good luck!      UwU

Answer:

\(x^3 - 10 x^2 -53x -42 = ( x + 1)(x + 3) (x - 14)\)

Step-by-step explanation:

 \(x^3 - 10x^2 -53x - 42\)

The factors of 42 : ±1 , ±2 , ±3 , ±6, ±7, ±14, ±21 , ±42

Using trial and error method we will find the first root of the polynomial.

1 : ( 1 )³ - 10 ( 1 )² - 53 ( 1 ) - 42

     1 - 10 - 53 - 42  ≠ 0

   Therefore 1 is not a root

-1 : ( -1 )³ - 10 (- 1 )² - 53 (- 1 ) - 42

      - 1 - 10 + 53 - 42

       53 - 53 = 0

Therefore - 1 is a root of the polynomial.

Therefore ( x + 1) is a factor.

Now by long division or by using synthetic division we can find other factors.

Synthetic Division :

                             -1 | 1      -10       -53      - 42

                                | 0     - 1          11          42

                                |______________________

                                  1      - 11       - 42        0

Therefore ,

\(x^3 - 10 x^2 -53x -42 = ( x + 1)(x^2 - 11x +42)\)  ------ ( 1 )

Next further factorize x² - 11x - 42

   x² - 11x - 42

= x² -  14x + 3x - 42

=x(x - 14) + 3 (x - 14)

=(x + 3 )(x - 14)

Therefore ,

\(x^3 - 10 x^2 -53x -42 = ( x + 1)(x + 3) (x - 14)\)

There are only one way to pick exactly 6 of the 7 winning numbers without regard to order.

There are "1 to 70 numbers, choose 7 " or 70C7 ways to pick 7 correctly.

AND

you must also pick 1 wrong number.  That wrong number has to be

different from any of the 7 correct numbers, and so there are

40-6 or 34 wrong numbers you could have picked.  That's 34 wrong

numbers, choose 1 or 34C1. Since AND means to multiply, the

numerator is 6C5 X 34C1=204

The denominator is the same 3838380 as in part (A)

So the desired probability is 204 / 38380 = 17 / 319865.

However that's just the probability of winning the $10000.

The words "probability of winning" could be taken as the

probability of winning either $1,000,000 OR $10,000. So

P(winning $1,000,000 OR winning $10,000) and since

"OR" means "ADD", we add the probability found in part A,

so the correct answer is 1 / 38380 + 204 / 38380 = 205 / 3838380

=41 / 767676,

the probability of winning a million or ten thousand.

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Answer:

10 1/2 lbs = 168 oz

Answer:

168

Step-by-step explanation:

i think

Answer:

The first one is x.

Second one is z

Third one is y.

Step-by-step explanation:

The answers to your questions are:

From the diagram there are three different planes and three different lines. one line intersects two of the planes ( Line X ) while another line intersects just one of the planes ( Line Z ) while line Y has points on all three planes.

Line y has points  A and B on all three planes

A plane is simply a flat surface that can be cut across with a straight line joining any two points of the plane.

Therefore from the diagram we can conclude that

The line that intersects two of the planes is : Line X

The line that intersects one of the planes is : Line Z

The line that that has points on three of the planes shown is Line Y

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Answer:

14.87 units

Step-by-step explanation:

Pythagorean Theorem states that the sum of the square of the legs equals the square of the hypotenuse.

5² + 14² = y²

25 + 196 = y²

y² = 221

y = \(\sqrt{221}\) which is equal to 14.87

We square the residuals when using the least-squares line method to find the line of best fit because we believe that huge negative residuals (i.e., points well below the line) are just as harmful as large positive residuals (i.e., points that are high above the line).

We treat both positive and negative disparities equally by squaring the residual values.  We cannot discover a single straight line that concurrently minimizes all residuals. The average (squared) residual value is instead minimized.

We might also take the absolute values of the residuals rather than squaring them. Positive disparities are viewed as just as harmful as negative ones under both strategies.

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Answer:

-5 x X < -6x + 12

Step-by-step explanation:

I THINK im not really used to this but yes this is my expression i would present.

the completed multiplication table is:  40  45  50  ,72  54  60 and 56  90  70 .by using common factor  logic we can solve this question.

what is  common factor ?

A common factor is a number that divides evenly into two or more other numbers. For example, the common factors of 12 and 18 are 1, 2, 3, and 6, because all of these numbers divide evenly into both 12 and 18.

In the given question,

From the given table, we can see that:

The first row reads 40, 45, 50 (which are multiples of 5).

The second row has an unknown number (let's call it x), 54, and 60.

The third row reads 56, an unknown number (let's call it y), 70 (which are also multiples of 7).

To find the missing numbers, we can use the fact that multiplication is commutative, meaning that the order of the factors does not matter. Therefore, we can fill in the missing numbers by looking for factors that are common to both the row and column headers.

Starting with the second row, we can see that the common factor between x and 54 is 9, since 9 x 6 = 54 and 9 x x = ?. So, the missing number in the second row is 9 x 10 = 90.

Moving on to the first column, we can see that the common factor between 40 and 56 is 8, since 8 x 5 = 40 and 8 x 7 = 56. So, the missing number in the second row, first column is 8 x 9 = 72.

Finally, we can find the missing number in the first row, second column by finding the common factor between 45 and 60, which is 15, since 15 x 3 = 45 and 15 x 4 = 60. So, the missing number in the first row, second column is 15 x 5 = 75.

Therefore, the completed multiplication table is:

40  45  50

72  54  60

56  90  70

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Answer:1430 ft^3

Step-by-step explanation: you have to divide by 36

It costs 441 dollars to carpet the den.

Two figures are similar if they have the same shape but different sizes. The corresponding angles are equal and the ratios of their corresponding sides and areas are also equal.

Using the above concept, we can equate the ratio of the corresponding sides and areas.

The ratio of the width of the den to the bedroom is:

14/10 = 7/5

The ratio of the area of the den to the bedroom is:

(7/5)² = 49/25

The ratio of the cost of carpet and area of the den to the bedroom is:

49/25 = den/225

den = 49/25 * 225

den = $441

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Answer:

12/13

Step-by-step explanation:

there are 4 7's in a 52 card deck, that means the other 48 cards are not 7's. 48/52 = 12/13

The point [-8,-6] would be graphed 8 units left and 6 units down from the origin (0,0) on a coordinate grid.

A coordinate grid, also called a Cartesian plane, is a two-dimensional plane formed by a horizontal x-axis and a vertical y-axis that intersect at the origin (0,0). It is used to graph and locate points in a two-dimensional space by their x- and y-coordinates.

The coordinate grid is formed by two perpendicular lines, the horizontal x-axis and the vertical y-axis.

The point [-8,-6] represents an ordered pair where -8 is the x-coordinate and -6 is the y-coordinate.

To graph this point on a coordinate grid, start at the origin (0,0), which is where the x-axis and y-axis intersect. Then, move 8 units to the left along the x-axis since the x-coordinate is negative.

After that, move 6 units down along the y-axis since the y-coordinate is negative. The point where you end up after moving left 8 units and down 6 units is the point (-8,-6).

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Answer:

It would be 828 inches cubed

Step-by-step explanation:

Because the boxes on top and bottom are both 6x8x6 and the middle portion is 6x7x6

6x8x6=288

6x7x6=252

288+288+252=828

Answer:

D / 10

Step-by-step explanation:

X - 1 over 3 = 3

10-1 = 9/3 = 3

Answer:

\(value \: of \: k \: = 3 \\ \\ \frac{x - 1}{3} = k \\ put \: value \: of \: k \: which \: is \: 3 \\ \frac{x - 1}{3} = (3) \\ as \: 3 \: is \: dividing \: here \: it \: will \\ be \: multiplied \: on \: anthor \: side \: \\ x - 1 = 3 \times 3 \\ x - 1 = 9 \\ x = 9 + 1 \\ x = 10 \: \: \: answer \\ \\ so \: answer \: is \: option \: d) \: 10\)

Answer:165degrees

Step-by-step explanation

Use formula N-2 × 180 N is the number of sides

24-2=22

22x180=3960 total

for each angle divide total by 24=165 degrees