Jason bought some bags of green apples and some bags of red apples. He spent £4.20.

Ratling [72]

Hello there! Slope is rise/run. The formula for finding slope is y2 - y1/ x2 - x1, meaning that you subtract the first x and y-coordinates from the second x and y-coordinates. We'll use the points (0, 3) and (3, 2) for this case. Plug in the values into the formula to get this:

2 - 3 / 3 - 0

Subtract the values in order to get -1/3. There. The slope of the line is -1/3.

6 0

2 years ago

The height H of an ball that is thrown straight upward from an initial position 3 feet off the ground with initial velocity of 9

mariarad [96]

Answer:

The ball will be 84 feet above the ground 1.125 seconds and 4.5 seconds after launch.

Step-by-step explanation:

Statement is incorrect. Correct form is presented below:

<em>The height </em> $h(t)$ <em> of an ball that is thrown straight upward from an initial position 3 feet off the ground with initial velocity of 90 feet per second is given by equation </em> $h(t) = 3 +90\cdot t -16\cdot t^{2}$ <em>, where </em> $t$ <em> is time in seconds. After how many seconds will the ball be 84 feet above the ground. </em>

We equalize the kinematic formula to 84 feet and solve the resulting second-order polynomial by Quadratic Formula to determine the instants associated with such height:

$3+90\cdot t -16\cdot t^{2} = 84$

$16\cdot t^{2}-90\cdot t +81 = 0$ (1)

By Quadratic Formula:

$t_{1,2} = \frac{90\pm \sqrt{(-90)^{2}-4\cdot (16)\cdot (81)}}{2\cdot (16)}$

$t_{1} = 4.5\,s$ , $t_{2} = 1.125\,s$

The ball will be 84 feet above the ground 1.125 seconds and 4.5 seconds after launch.

3 0

2 years ago

A jet is coming in for a landing. It's currently 25,000 feet in

Mariana [72]

The angle of depression is 29.0521°. So it is a safe landing.

Step-by-step explanation:

Step 1:

The plane is flying at a height of 25,000 feet and 45,000 feet away from the landing strip. Assume it lands with an angle of depression of x°.

So a right-angled triangle can be formed using these measurements. The triangle's opposite side measures 25,000 feet while the adjacent side measures 45,000 feet. The angle of the triangle is x°.

To determine the value of x, we calculate the tan of the given triangle.

$tanx = \frac{opposite side}{adjacent side}.$

Step 2:

The length of the opposite side = 25,000 feet.

The length of the adjacent side = 45,000 feet.

$tan x = \frac{25,000}{45,000} = 0.5555.$

So x = 29.0521°. Since x < 30°, it is a safe landing.

8 0

2 years ago

A triangle has one angle that measures 56° and one angle that measures 63º.

crimeas [40]

<h2>sum of a triangle= 180°</h2>

63+56=119
180-119=61
ans=61°

7 0

1 year ago

The American Bankers Association reported that, in a sample of 120 consumer purchases in France, 48 were made with cash, compare

tatuchka [14]

Answer:

Step-by-step explanation:

Hello!

You have the information for two variables

X₁: Number of consumer purchases in France that were made with cash, in a sample of 120.

n₁= 120 consumer purchases

x₁= 48 cash purchases

p'₁= 48/120= 0.4

X₂: Number of consumer purchases in the US that were made with cash, in a sample of 55.

n₂= 55 consumer purchases

x₂= 24 cash purchases

p'₂= 24/55= 0.4364

You need to construct a 90% CI for the difference of proportions p₁-p₂

Using the central limit theorem you can approximate the distribution of both sample proportions p'₁ and p'₂ to normal, so the statistic to use to estimate the difference of proportions is an approximate standard normal:

[(p'₁-p'₂) ± $Z_{1-\alpha /2}$ * $\sqrt{\frac{p'_1(1-p'_1)}{n_1} +\frac{p'_2(1-p'_2)}{n_2} }$ ]

$Z_{0.95}= 1.648$

[(0.4-0.4364)±1.648 * $\sqrt{\frac{0.4(1-0.4)}{120} +\frac{0.4364(1-0.4364)}{55} }$ ]

[-0.1689;0.0961]

The interval has a negative bond, it is ok, keep in mind that even tough proportions take values between 0 and 1, in this case, the confidence interval estimates the difference between the two proportions. It is valid for one of the bonds or the two bonds of the CI for the difference between population proportions to be negative.

I hope this helps!

8 0

2 years ago