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3 years ago

10

Wendy paints a rectangular wall that is 10.5 feet tall and 9.2 feet wide. What is the area of the wall can she paint with only t

wo cans of paint

1 answer:

RideAnS [48]3 years ago

4 0

Answer: 96.6

Step-by-step explanation:

You multiply 10.5*9.2 to get the answer of 96.6.

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The spinner below is divided into five equal-sized sectors. What is the probability that the spinner will stop on a number great

madreJ [45]

Answer:

40%

Step-by-step explanation: If you have five equal-sized sectors, then the probability that the spinner will stop on 4 and 5 is 40%.

8 0

2 years ago

Consider the circle of radius 5 centered at (0, 0). Find an equation of the line tangent to the circle at the point (3, 4) in sl

Wittaler [7]

Answer:

$\displaystyle y= -\frac{3}{4} x + \frac{25}{4}$ .

Step-by-step explanation:

The equation of a circle of radius $5$ centered at $(0,0)$ is:

$x^{2} + y^{2} = 5^{2}$ .

$x^{2} + y^{2} = 25$ .

Differentiate implicitly with respect to $x$ to find the slope of tangents to this circle.

$\displaystyle \frac{d}{dx}[x^{2} + y^{2}] = \frac{d}{dx}[25]$

$\displaystyle \frac{d}{dx}(x^{2}) + \frac{d}{dx}(y^{2}) = 0$ .

Apply the power rule and the chain rule. Treat $y$ as a function of $x$ , $f(x)$ .

$\displaystyle \frac{d}{dx}(x^{2}) + \frac{d}{dx}(f(x))^{2} = 0$ .

$\displaystyle \frac{d}{dx}(2x) + \frac{d}{dx}(2f(x)\cdot f^{\prime}(x)) = 0$ .

That is:

$\displaystyle \frac{d}{dx}(2x) + \frac{d}{dx}\left(2y \cdot \frac{dy}{dx}\right) = 0$ .

Solve this equation for $\displaystyle \frac{dy}{dx}$ :

$\displaystyle \frac{dy}{dx} = -\frac{x}{y}$ .

The slope of the tangent to this circle at point $(3, 4)$ will thus equal

$\displaystyle \frac{dy}{dx} = -\frac{3}{4}$ .

Apply the slope-point of a line in a cartesian plane:

$y - y_0 = m(x - x_0)$ , where

$m$ is the gradient of this line, and
$(x_0, y_0)$ are the coordinates of a point on that line.

For the tangent line in this question:

$\displaystyle m = -\frac{3}{4}$ ,
$(x_0, y_0) = (3, 4)$ .

The equation of this tangent line will thus be:

$\displaystyle y - 4 = -\frac{3}{4} (x - 3)$ .

That simplifies to

$\displaystyle y= -\frac{3}{4} x + \frac{25}{4}$ .

3 0

3 years ago

Please answer this question now

inn [45]

Answer:

t = 17.3

Step-by-step explanation:

The following data were obtained from the question:

Angle T = 87°

Opposite T = t =?

Opposite V = v = 14

Opposite U = u = 11

The value of t can be obtained by using cosine rule formula as shown below:

t² = v² + u² – 2vu CosT

t² = 14² + 11² – 2 × 14 × 11 × Cos87°

t² = 196 + 121 – 308 × Cos87°

t² = 317 – 16.119

t² = 300.881

Take the square root of both side

t = √300.881

t = 17.3

Therefore, the value of t is 17.3

6 0

3 years ago

Listed below are head injury measurements from small cars that were tested in crashes. The measurements are in "hic," which is

Sholpan [36]

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

Listed below are head injury measurements from small cars that were tested in crashes. The measurements are in "hic," which is a measurement of a standard "head injury criterion," (lower "hic" values correspond to safer cars). The listed values correspond to cars A, B, C, D, E, F, and G, respectively.

514 541 302 400 507 406 369

Find the

a. mean,

b. median,

c. midrange,

d. mode for the data.

Also complete parts e. and f.

e. Which car appears to be the safest?

f. Based on these limited results, do small cars appear to have about the same risk of head injury in a crash?

Answer:

a) Mean = 434.14

b) Median = 406

c) Midrange = 421.5

d) Mode = 0

e) Car C appears to be the safest

f) The small cars does not appear to have about the same risk of head injury in a crash.

Step-by-step explanation:

We are given the head injury measurements from small cars that were tested in crashes.

The measurements are in "hic," which is a measurement of a standard "head injury criterion.

The listed values are;

A = 514

B = 541

C = 302

D = 400

E = 507

F = 406

G = 369

a) Mean

The mean of the measurements is given by

Mean = Sum of measurements/ Number of measurements

Mean = (514 + 541 + 302 + 400 + 507 + 406 + 369)/7

Mean = 3039/7

Mean = 434.14

b) Median

Arrange the measurements in ascending order (low to high)

302, 369, 400, 406, 507, 514, 541

The median is given by

Median = (n + 1)/2

Median = (7 + 1)/2

Median = 8/2

Median = 4th

Therefore, the 4th measurement is the median that is 406

Median = 406

c) Mid-range

The midrange is given by

Midrange = (Max + Min)/2

The maximum measurement in the data set is 541

The minimum measurement in the data set is 302

Midrange = (541 + 302)/2

Midrange = 843/2

Midrange = 421.5

d) Mode for the data

The mode of the data set is the most repeated measurement.

302, 369, 400, 406, 507, 514, 541

In the given data set we don't have any repeated measurement therefore, there is no mode or we can say the mode of this data set is 0.

Mode = 0

e) Which car appears to be the safest?

Since we are given that the measurements are in "hic," which is a measurement of a standard "head injury criterion," (lower "hic" values correspond to safer cars)

The lowest hic value corresponds to car C that is 302

Therefore, car C appears to be the safest among other cars.

f) Based on these limited results, do small cars appear to have about the same risk of head injury in a crash?

302, 369, 400, 406, 507, 514, 541

As you can notice, the hic values differ a lot from each other therefore, we can conclude that the small cars does not appear to have about the same risk of head injury in a crash.

8 0

3 years ago

if a number line plot starts from 2 (including the point) and extends towards positive infinity, the corresponding inequality is

murzikaleks [220]

Answer:

$2 \leqslant y \leqslant \infty$

Step-by-step explanation:

y is equal to 2 and goes up to infinity

6 0

2 years ago