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torisob [31]
2 years ago
5

Solve for x: 3-(2x-5) is less than -4(x+2)

Mathematics
1 answer:
Svetlanka [38]2 years ago
6 0

x< 0.7 if i'm correct

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A molasses can is made with a cylindrical base having a radius of 6 cm, that is topped by a smaller cylindrical pouring spout wi
wariber [46]

Answer:

The total height of the can is 20cm

7 0
2 years ago
PLS HELP ASAP!! WILL MARK BRAINLYIST
son4ous [18]

Answer:

$39,851.25

Step-by-step explanation:

If the sales increase at a rate of 9% per year, this means it will be 109% of the previous year's value since 100% + 9% = 109%

109% in decimal form = 109/100 = 1.09

Therefore, the exponential function is:

y = 20000 \cdot 1.09^x, where x is the number of years

So when x=8,  

y = 20000 \cdot 1.09^8=39851.252...

After 8 years, annual sales = $39,851.25

7 0
2 years ago
Find the critical numbers of the function. (Enter your answers as a comma-separated list. Use n to denote any arbitrary integer
lyudmila [28]

If

f(\theta)=10\cos\theta+5\sin^2\theta

then the derivative is

f'(\theta)=-10\sin\theta+10\sin\theta\cos\theta

Critical points occur where f'(\theta)=0. This happens for

-10\sin\theta+10\sin\theta\cos\theta=0

-10\sin\theta(1-\cos\theta)=0

\implies-10\sin\theta=0\text{ or }1-\cos\theta=0

In the first case, we find

-10\sin\theta=0\implies\sin\theta=0\implies\theta=n\pi

In the second,

1-\cos\theta=0\implies\cos\theta=1\implies\theta=2n\pi

So all the critical points occur at multiples of \pi, or n\pi. (This includes all the even multiples of \pi.)

3 0
3 years ago
The Town of Hertfordshire clerk knows that 23% of dogs in the town have completed emotional support training. Hertfordshire plan
Nataly_w [17]

Answer:

95.64% probability that under 30% of the dogs are emotional support trained

Step-by-step explanation:

For each dog, there are only two possible outcomes. Either they have completed emotional support training, or they have not. So we use the binomial probability distribution to solve this problem.

However, we are working with samples that are considerably big. So i am going to aproximate this binomial distribution to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed samples can be solved using 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.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

\mu = E(X) = np = 100*0.23 = 23

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.23*0.77} = 4.21

What is the probability that under 30% of the dogs are emotional support trained?

30% of 100 is 0.3*100 = 30

So this is the pvalue of Z when X = 30.

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

Z = \frac{30 - 23}{4.1}

Z = 1.71

Z = 1.71 has a pvalue of 0.9564.

So there is a 95.64% probability that under 30% of the dogs are emotional support trained

5 0
3 years ago
What is the area of the figure?<br><br> 40 ft2<br> 84 ft2<br> 96 ft2<br> can't be determined
mina [271]

Answer:

A=80\ ft^2

Step-by-step explanation:

we know that

The area of the figure is equal to the area of an isosceles triangle (has two equal sides) plus the area of a rectangle

step 1

Find the area of the triangle

The area of the triangle is equal to

A=\frac{1}{2}bh

we have

b=16\ ft

To find out the height of the triangle Apply the Pythagorean Theorem

10^2=(16/2)^2+h^2

solve for h

100=64+h^2

h^2=100-64

h^2=36

h=6\ ft

<em>Find the area of triangle</em>

A=\frac{1}{2}(16)(6)

A=48\ ft^2

step 2

Find the area of rectangle

The area of rectangle is equal to

A=LW

we have

L=16\ ft\\W=2\ ft

substitute

A=(16)(2)=32\ ft^2

step 3

Find the area of the figure

Adds the areas

A=48+32=80\ ft^2

5 0
3 years ago
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