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3 years ago

9

I thought of a number, divided it by 1 1/2 , then added 2 1/2 to the result, then multiplied the sum by 1 2/3 . Then I subtracte

d 1 2/3 and got the result 2 5/6 . What was my number?

1 answer:

vekshin13 years ago

7 0

Answer:

12

Step-by-step explanation:

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the mean average distance that jack runs in his last 10 runs is 5.7 miles. work out the distance that he would need to make this

ziro4ka [17]

Answer:

9 miles

Step-by-step explanation:

mean is calculated as

mean = $\frac{sum}{count}$ , then

$\frac{sum}{10}$ = 5.7 ( multiply both sides by 10 )

sum = 57

let x be the distance he needs to cover so mean is 6 , that is

$\frac{sum+x}{11}$ = 6 ( multiply both sides by 11 )

sum + x = 66 , that is

57 + x = 66 ( subtract 57 from both sides )

x = 9

That is he would have to run 9 miles

3 0

2 years ago

Suppose we have a right triangle with legs of length a and b and hypotenuse of length c. Suppose b=3 and c=5. Then a= , For the

ANTONII [103]

Answer:

Length of right-angle triangle 'a' = 4

b)

<u><em></em></u> $sin(A) = \frac{opposite side}{Hypotenuse} = \frac{a}{c} = \frac{4}{5}$ <u><em></em></u>

<u><em></em></u> $cos(A) = \frac{Adjacent side}{Hypotenuse} = \frac{b}{c} = \frac{3}{5}$ <u><em></em></u>

<u><em></em></u> $tan(A) = \frac{opposite side}{Adjacent side} = \frac{a}{b} = \frac{4}{3}$ <u><em></em></u>

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given b = 3 and hypotenuse c = 5

Given ΔABC is a right angle triangle

By using pythagoras theorem

c² = a² + b²

⇒ a² = c² - b²

⇒ a² = 5²-3²

=25 - 9

a² = 16

⇒ a = √16 = 4

The sides of right angle triangle a = 4 ,b = 3 and c = 5

<u><em>Step(ii):-</em></u>

<u><em></em></u> $sin(A) = \frac{opposite side}{Hypotenuse} = \frac{a}{c} = \frac{4}{5}$ <u><em></em></u>

<u><em></em></u> $cos(A) = \frac{Adjacent side}{Hypotenuse} = \frac{b}{c} = \frac{3}{5}$ <u><em></em></u>

<u><em></em></u> $tan(A) = \frac{opposite side}{Adjacent side} = \frac{a}{b} = \frac{4}{3}$ <u><em></em></u>

7 0

2 years ago

Accountants at the Tucson firm, Larry Youdelman, CPAs, believed that several traveling executives were submitting unusually hi

77julia77 [94]

Answer:

a) $Y= 90 +46.50(5) +0.35 (340) =441.50$

b) The accountant should not question the voucher as the request is much higher than expected.

c) We can add the following variables

d) The percentage of variation in the trip cost that can be explained by the model = (0.64)^2 =0.4096 or 40.96%

A. Type of travel (air/car)

B. Gender of the executive (male/female)

The last option is not too important since we are analyzing the traveling executives not the type of business

Step-by-step explanation:

Part a

For this case we have the multiple regression model given by:

$Y= 90 +46.50 x_1 +0.35 x_2$

Where $x_1$ represent the number of days on the road and $x_2$ the distance traveled in miles.

And we want to find the expected amount from a 340-mile trip that took her out of town for 5 days, so we just need to replace x1= 5 and x2=340 and we got:

$Y= 90 +46.50(5) +0.35 (340) =441.50$

Part b

The expected value taking in count that x1 = 5 and y = 340 is:

$Y= 90 +46.50(55) +0.35 (340) =441.50$

And the difference from the obtained value is : 685-441.50=243.5

So then the correct answer would be:

The accountant should not question the voucher as the request is much higher than expected.

Part c

We can add the following variables

A. Type of travel (air/car)

B. Gender of the executive (male/female)

The last option is not too important since we are analyzing the traveling executives not the type of business

Part d

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

The coefficient of determination "is a measure used in statistical analysis that assesses how well a model explains and predicts future outcomes. It is indicative of the level of explained variability in the data set".

The percentage of variation in the trip cost that can be explained by the model = (0.64)^2 =0.4096 or 40.96%

6 0

3 years ago

Work out the gradient of the line joining the points (2, 3) and (5,7)

Debora [2.8K]

Answer:

The gradient of the line joining the points $P(x,y) = (2,3)$ and $Q(x,y) = (5,7)$ is $\frac{4}{3}$ .

Step-by-step explanation:

The gradient of the line joining two distinct point on a plane is represented by the slope of a secant line ( $m_{PQ}$ ), that is:

$m_{PQ} = \frac{y_{Q}-y_{P}}{x_{Q}-x_{P}}$ (1)

If we know that $P(x,y) = (2,3)$ and $Q(x,y) = (5,7)$ , then the gradient of the line is:

$m_{PQ} = \frac{7-3}{5-2}$

$m_{PQ} = \frac{4}{3}$

The gradient of the line joining the points $P(x,y) = (2,3)$ and $Q(x,y) = (5,7)$ is $\frac{4}{3}$ .

4 0

3 years ago

Jaclyn's company required an initial investment of $2,125 for starting costs and sells construction toys for $49.99 each. Richie

Darina [25.2K]

The the number of construction toys that must be bought so that the profit for Jacelyn's company and Richie's company is the same. is t= 204.3269230769231

<h3>what is equation?</h3>

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side). Equations can be solved to find the value of an unknown variable representing an unknown quantity. If there is no 'equal to' symbol in the statement, it means it is not an equation. It will be considered as an expression.

As, per the given situation the equation can be

2125 + 49.99 t = 39.95 t

10.4 t= 2125

t= 2125 / 10.4

t= 21250/104

t= 204.3269230769231

Learn more about equation here:

brainly.com/question/10413253

#SPJ1

6 0

2 years ago