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4 years ago

Simplify the expression

Mathematics

1 answer:

bearhunter [10]4 years ago

7 0

First we want to simplify the denominator
$\frac{1}{4} - \frac{5}{2}$

to subtract, we convert 5/2 to have a denominator of 4
$\frac{1}{4} - \frac{10}{4}$
$- \frac{9}{4}$

now we can put this back into the original problem
$\frac{4}{ - \frac{9}{4} }$
this equation can also be read as
$4 \div - \frac{9}{4}$

when dividing, we flip the right side and switch to multiplication
$\frac{4}{1} \times - \frac{4}{9} = - \frac{16}{9}$

$answer = - \frac{16}{9}$

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Convert 2.4 kg into cg. Please show your work.

Sphinxa [80]

1 kg = 1000 g
1 cg = (1/100) g

2.4 kg
2.4 * 1000 g
2400 g
2400/100 cg
24 cg

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3 years ago

For which angle theta is cos theta =-1?<br>a) 270<br>b) 360<br>c) 450<br>d) 540

yanalaym [24]

Answer:

540°.

Step-by-step explanation:

On a unit circle, cos θ = -1 at 180°.

However, cos θ has a period of 2π, or 360°. This means that cos θ will equal to -1 again after 2π.

To solve for the angle:

180° + 360° = 540°. This is the next angle at which cos θ = -1.

7 0

3 years ago

Read 2 more answers

A firm’s marketing manager believes that total sales for next year will follow the normal distribution, with a mean of $3.2 mill

klasskru [66]

Answer:

The sales level that has only a 3% chance of being exceeded next year is $3.67 million.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

In millions of dollars,

$\mu = 3.2, \sigma = 0.25$

Determine the sales level that has only a 3% chance of being exceeded next year.

This is the 100 - 3 = 97th percentile, which is X when Z has a pvalue of 0.97. So X when Z = 1.88.

$Z = \frac{X - \mu}{\sigma}$

$1.88 = \frac{X - 3.2}{0.25}$

$X - 3.2 = 0.25*1.88$

$X = 3.67$

The sales level that has only a 3% chance of being exceeded next year is $3.67 million.

7 0

3 years ago

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 21 meters cubed. A sphere with height h a

8090 [49]

Answer:

C. 14 metres cubed

Step-by-step explanation:

The volume of a sphere is denoted by: $V=\frac{4}{3} \pi r^3$ , where r is the radius, while the volume of a cylinder is denoted by: $V=\pi r^2h$ , where r is the radius and h is the height.

Here, we know that the sphere and cylinder have the same radius and height. However, the "height" of the sphere is technically just the diameter, which is twice the radius. So, h = 2r. We know the volume of the cylinder is 21, so:

$V=\pi r^2h=\pi r^2*2r=2\pi r^3$

$21=2\pi r^3$

πr³ = 21/2 = 10.5

Now plug this into the volume of a sphere formula:

$V=\frac{4}{3} \pi r^3$

$V=\frac{4}{3} *10.5=14$

The answer is C, 14 metres cubed.

5 0

3 years ago

Read 2 more answers

A 28 first slide at a waterpark makes an angle of 60° with the ground as it descends into a pool. What is a vertical distance fr

IceJOKER [234]

Answer:

The vertical distance from the top of the slide go the ground is 24.25 feet

Step-by-step explanation:

Here, we want to calculate the vertical distance from the top of the slide to the ground.

To answer this properly, we shall need the aid of a diagram. Please check the attachment for this;

Mathematically, to calculate this vertical distance, we shall be employing the use of a trigonometric ratio since the shape we are considering is a right-angled triangle

The vertical distance faces the angle given and we can refer to it as the opposite. The length of the slide refers to the hypotenuse

So the trigonometric ratio we are to use will consider the opposite and the hypotenuse

This is the sine

Mathematically sine of an angle = length of the opposite/length of the hypotenuse

let’s call the length of the opposite x

sin 60 = x/28

x = 28 sin 60

x = 24.248 which is 24.25 feet

7 0

3 years ago