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gregori [183]
3 years ago
15

The product of two positive consecutive odd integers is 2703. What are the positive numbers?

Mathematics
1 answer:
liberstina [14]3 years ago
7 0

Answer:

The positive numbers are 51 and 53

Step-by-step explanation:

Let first odd integer be x and another odd integer is (x+2).

According to the given condition,

The product of two positive consecutive odd integers is 2703 i.e.

x(x+2) = 2703

x^2+2x-2703=0

It is a quadratic equation. It can be solved as follows :

x = 51 and x = -53

Neglecting negative sign,

The first number = 51

Another number =(51+2) = 53

Hence, the positive numbers are 51 and 53.

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What is 1.83 as a mixed fraction
lora16 [44]

Answer:

1\frac{83}{100}

Step-by-step explanation:

First of all, the number before the decimal would be the whole number of the fraction.

So, 1\frac{?}{?}

Then, you would put 0.83 over a fraction.

So because you cannot simplify it anymore, it would be 1\frac{83}{100}

6 0
3 years ago
Please help me with #4 <br> (10 points )
myrzilka [38]

Answer:

40 feet

Step-by-step explanation:

We are given a right isosceles triangle having lengths of two sides 12 feet and 16 feet.

<em>Since, the triangle is an isosceles triangle i.e. two sides of the triangle are equal.</em>

That is, the three sides of the triangle are 12 feet, 12 feet and 16 feet.

We know that, Perimeter of a triangle = Sum of the sides

Thus, Perimeter of the given triangle = 12 + 12 + 16 = 24 + 16 = 40 feet.

Hence, the total length of the fencing needed is 40 feet.

8 0
3 years ago
Which expression is the factorization of x2 + 10x + 212
Montano1993 [528]

Answer:

The answer is option 1.

Step-by-step explanation:

Firstly, you have to elaborate the expression :

{x}^{2}  + 10x + 21

=  {x}^{2}  + 3x + 7x + 21

Next you have to take out the common factors and factorize it :

{x}^{2}  + 3x + 7x + 21

= x(x + 3)  +  7(x + 3)

= (x + 7)(x + 3)

8 0
3 years ago
Read 2 more answers
The number of "destination weddings" has skyrocketed in recent years. For example, many couples are opting to have their wedding
melamori03 [73]

Answer:

We conclude that the mean wedding cost is less than $30,000 as advertised.

Step-by-step explanation:

We are given the following data set:(in thousands)

29100, 28500, 28800, 29400, 29800, 29800, 30100, 30600

Formula:

\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}  

where x_i are data points, \bar{x} is the mean and n is the number of observations.  

Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}

Mean =\displaystyle\frac{236100}{8} = 29512.5

Sum of squares of differences = 3408750

S.D = \sqrt{\frac{3408750}{7}} = 697.82

Population mean, μ = $30,000

Sample mean, \bar{x} = $29512.5

Sample size, n = 8

Alpha, α = 0.05

Sample standard deviation, s = $ 697.82

First, we design the null and the alternate hypothesis

H_{0}: \mu = 30000\text{ dollars}\\H_A: \mu < 30000\text{ dollars} We use one-tailed t test to perform this hypothesis.

Formula:

t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }

Putting all the values, we have

t_{stat} = \displaystyle\frac{29512.5 - 30000}{\frac{697.82}{\sqrt{8}} } = -1.975

Now,

t_{critical} \text{ at 0.05 level of significance, 7 degree of freedom } = -1.894

Since,                  

t_{stat} < t_{critical}

We fail to accept the null hypothesis and reject it.

We conclude that the mean wedding cost is less than $30,000 as advertised.

8 0
3 years ago
Circle has a radius of 25 ft which of the following values is closest to the area of the circle in square feet a 80 B 160 C 310
Marina CMI [18]
To find the area that is the closest, use the formula for finding the area of a circle.

A = pi x r^2
      3.14 x 25^2
A = 1962.5 square feet

This is closest to answer choice D.
4 0
3 years ago
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