The difference of two numbers is five. Five times the lesser number minus the greater number is -9. What are the two numbers?

Mileage tests are conducted for a particular model of automobile. If a 98% confidence interval with a margin of error of 1 mile

Llana [10]

Answer: 37

Step-by-step explanation:

Given : Significance level : $\alpha:1-0.98=0.02$

Critical value : $z_{\alpha/2}=z_{0.01}=2.33$

margin of error : E= 1 mile per gallon

Population standard deviation: $\sigma=2.6$ miles per gallon.

We know that when the population standard deviation is known then the formula to find the sample size is given by :

$n=(\dfrac{z_{\alpha/2}\times \sigma}{E})^2$

$n=(\dfrac{(2.33)\times 2.6}{1})^2=36.699364\approx37$ [Round to the next whole number.]

Hence, the required number of automobiles should be used in the test = 37

7 0

2 years ago

Graph 6x-2y=2 ,9x-3y=1

enot [183]

It's a linear function. We need only two points to draw a graph.

We choose any values of x and calculate the value of y.

$6x-2y=2\qquad|-6x\\\\-2y=-6x+2\qquad|:(-2)\\\\y=3x-1$

for x= 0 → y = 3(0) - 1 = 0 - 1 = -1 → (0, -1)

for x = 2 → y = 3(2) - 1 = 6 - 1 = 5 → (2, 5)

$9x-3y=1\qquad|-9x\\\\-3y=-9x+1\qquad|:(-3)\\\\t=3x-\dfrac{1}{3}$

for x = 0 → y = 3(0) - 1/3 = 0 - 1/3 = -1/3 → (0, -1/3)

for x = 2 → y = 3(2) - 1/3 = 6 - 1/3 = 5 2/3 → (2, 5 2/3)

4 0

2 years ago

Point E has coordinates (-11, 7), and point F has coordinates (-5, 1). To the nearest unit, what is the distance between the two

Zigmanuir [339]

Answer:

8 units

Step-by-step explanation:

We can use the distance formula. Recall the distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Let (-11,7) be $x_1$ and $y_1$ , and (-5,1) be $x_2$ and $y_2$

Plug in the numbers:

$d=\sqrt{(-5-(-11))^2+(1-7)^2$

$d=\sqrt{6^2+(-6)^2}$

$d=\sqrt{36+36}=\sqrt{72}=6\sqrt2\approx8$

4 0

2 years ago

Joey wants to build a rectangular garden. He plans to use a side of a river for one side of the garden, he will not place fencin

jonny [76]

We let x and y be the measures of the sides of the rectangular garden. The perimeter subtracted with the other side should be equal to 92.

2x + y = 92

The value of y in terms of x is equal to,

y = 92 – 2x

The area is the product of the two sides,

A = xy

Substituting,

A = x (92 – 2x) = 92x – 2x2

Solving for the derivative and equating to zero,

0 = 92 – 4x ; x = 23

Therefore, the area of the garden is,

A = 23(92 – 2(23)) = 1058 yard2

4 0

2 years ago

Read 2 more answers

A town in east Texas recieved 10 inches of rain in two weeks. If it kept raining at this rate for a 31-day month, how much rain

Gelneren [198K]

The best way to approach this problem is to find out how much fell in week. As you know what two weeks is, you simply have to halve this, giving you that one week is 5 inches of rain. One you have this, you can multiply this by 4 (as this will give you 4 weeks, or 28 days), and this gives you 20 inches in 28 days. You should then find the odd three days. If you divide 5 by 7, this will give you the rain fall in one day. 5/7= 0.8 inches per day. You then have top multiply this by 3 (as you've got three odd days), and this gives you 2.4. You then have to add together 2.4 and 20, giving you 22.4
Therefore, if the rain continued to fall at the same rate for 31 days, it would receive 22.4 inches of rain.
Hope this helps :)

8 0

2 years ago