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3 years ago

What is 35% of $100?

Mathematics

2 answers:

Ann [662]3 years ago

5 0

7nadin3 [17]3 years ago

3 0

35% refers to the fraction $\frac{35}{100}$ . Therefore, 35% of 100 is just 35.

$35

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If θ is an angle in standard position and its terminal side passes through the point (-4,-5), find the exact value of

NARA [144]

9514 1404 393

Answer:

cot(θ) = 4/5

Step-by-step explanation:

In the polar/rectangular coordinate representation (x, y) ⇔ (r; θ), we know that ...

(x, y) = (r·cos(θ), r·sin(θ))

From the various trig definitions and identities, we also know that ...

cot(θ) = cos(θ)/sin(θ) = (x/r)/(y/r) = x/y

For the given (x, y) = (-4, -5), the cotangent is ...

cot(θ) = -4/-5 = 4/5

7 0

3 years ago

The heights (measured in inches) of men aged 20 to 29 follow approximately the normal distribution with mean 69.3 and standard d

Zolol [24]

Answer:

The middle 92% of all heights fall between 64.4 inches and 74.2 inches.

Step-by-step explanation:

Problems of normally distributed samples are 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.

In this problem, we have that:

$\mu = 69.3, \sigma = 2.8$

Between what two values does that middle 92% of all heights fall?

The middle 92% falls from X when Z has a pvalue of 0.5 - 0.92/2 = 0.04 to X when Z has a pvalue of 0.5 + 0.92/2 = 0.96. So from the 4th percentile to the 96th percentile.

4th percentile

X when $Z = -1.75$

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

$-1.75 = \frac{X - 69.3}{2.8}$

$X - 69.3 = -1.75*2.8$

$X = 64.4$

96th percentile

X when $Z = 1.75$

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

$1.75 = \frac{X - 69.3}{2.8}$

$X - 69.3 = 1.75*2.8$

$X = 74.2$

The middle 92% of all heights fall between 64.4 inches and 74.2 inches.

6 0

3 years ago

The lenths of the 2 legs of right triangle abc show below are given in inches. The midpoint of ab is how many inches from A ?

fenix001 [56]

Answer:

Option B

Step-by-step explanation:

The complete question is attached

As we can see in the image , ABC is a right angle triangle

Thus as per Pythagorean theorem, to find line AB

AB2 = 322 + 242

AB2 = 1024 + 576

AB2 = 1600

Taking square root of both the sides, we get –

AB = √1600

AB = 40

The mid point of AB = AB/2 = 40/2 = 20

6 0

3 years ago

Can you please help me

erica [24]

Answer:

p = 4.0

q = 2.0

angle <P = 64 degrees

Step-by-step explanation:

We can use the definition of cosine to find the value of side p (the adjacent side to the 26 degree angle, via the formula:

$cos(26^o)= \frac{adjacent}{hypotenuse} \\cos(26^o)= \frac{p}{4.5}\\p= 4.5 *cos(26^o)\\p=4.0445$

which rounded to the nearest tenth gives : p = 4.0

Now we use the sine function to help us determine side q:

$sin(26^o)= \frac{opposite}{hypotenuse} \\sin(26^o)= \frac{q}{4.5}\\q= 4.5 *sin(26^o)\\q=1.9726$

which rounded to the nearest tenth gives:

q = 2.0

Finally, we determine the measure of angle P using the fact that the addition of all internal angles of a triangle must add to 180 degrees:

< P + < Q + < R = 180

< P + 26 + 90 = 180

< P = 180 - 26 - 90

< P = 64 degrees

6 0

3 years ago

Clara did not want to tell Carl how old she was. All she said was that every year on her birthday, her Mom puts as many coins in

Anestetic [448]

Clara is 15 years old, and there are 120 coins on the box.

<h3>How old is Clara?</h3>

Each year her mom puts as many coins in her money box as how old she turns that day.

So on her first birthday, 1 coin is put in the box.

On her second birthday, 2 coins are put in the box

And so on.

So we have the simple summation:

$\sum_{n = 1} n$

We know that the outcome of that summation is a number in the interval [110, 130]

If we know that the sum goes from n = 1 to n = N (N is the age of Clara) then we can rewrite the summation as:

$N*(N + 1)/2$

Now we can solve:

$N*(N + 1)/2 = 110\\\\N^2 + N = 220\\\\N^2 + N - 220 = 0$

The two solutions of the quadratic equation are:

$N = \frac{-1 \pm \sqrt{1^2 - 4*1*(-220)} }{2} \\\\N = (-1 \pm 29.7) /2$

If we take only the positive solution:

N = (-1 + 29.7)/2 = 14.35

Now, notice that we got this number by taking the smallest possible number of coins (110) So we can round this to the next whole number, which is 15.

If N = 15, then the number of coins in the box is:

15*(15 + 1)/2 = 120

Which lies on the wanted interval.

If you want to learn more about summations:

brainly.com/question/542712

#SPJ1

5 0

1 year ago