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3 years ago

Plz help me :(Show work if u know

Mathematics

1 answer:

frutty [35]3 years ago

6 0

Answer: its 29

Step-by-step explanation:

because it is a right angle you know it is 90 degrees,

so you subtract 32 from 90 that leaves

58 than divide 58 in half

You might be interested in

Determine all prime numbers a, b and c for which the expression a ^ 2 + b ^ 2 + c ^ 2 - 1 is a perfect square .

kogti [31]

Answer:

The family of all prime numbers such that $a^{2} + b^{2} + c^{2} -1$ is a perfect square is represented by the following solution:

$a$ is an arbitrary prime number. (1)

$b = \sqrt{1 + 2\cdot a \cdot c}$ (2)

$c$ is another arbitrary prime number. (3)

Step-by-step explanation:

From Algebra we know that a second order polynomial is a perfect square if and only if $(x+y)^{2} = x^{2} + 2\cdot x\cdot y + y^{2}$ . From statement, we must fulfill the following identity:

$a^{2} + b^{2} + c^{2} - 1 = x^{2} + 2\cdot x\cdot y + y^{2}$

By Associative and Commutative properties, we can reorganize the expression as follows:

$a^{2} + (b^{2}-1) + c^{2} = x^{2} + 2\cdot x \cdot y + y^{2}$ (1)

Then, we have the following system of equations:

$x = a$ (2)

$(b^{2}-1) = 2\cdot x\cdot y$ (3)

$y = c$ (4)

By (2) and (4) in (3), we have the following expression:

$(b^{2} - 1) = 2\cdot a \cdot c$

$b^{2} = 1 + 2\cdot a \cdot c$

$b = \sqrt{1 + 2\cdot a\cdot c}$

From Number Theory, we remember that a number is prime if and only if is divisible both by 1 and by itself. Then, $a, b, c > 1$ . If $a$ , $b$ and $c$ are prime numbers, then $2\cdot a\cdot c$ must be an even composite number, which means that $a$ and $c$ can be either both odd numbers or a even number and a odd number. In the family of prime numbers, the only even number is 2.

In addition, $b$ must be a natural number, which means that:

$1 + 2\cdot a\cdot c \ge 4$

$2\cdot a \cdot c \ge 3$

$a\cdot c \ge \frac{3}{2}$

But the lowest possible product made by two prime numbers is $2^{2} = 4$ . Hence, $a\cdot c \ge 4$ .

The family of all prime numbers such that $a^{2} + b^{2} + c^{2} -1$ is a perfect square is represented by the following solution:

$a$ is an arbitrary prime number. (1)

$b = \sqrt{1 + 2\cdot a \cdot c}$ (2)

$c$ is another arbitrary prime number. (3)

Example: $a = 2$ , $c = 2$

$b = \sqrt{1 + 2\cdot (2)\cdot (2)}$

$b = 3$

4 0

3 years ago

The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 330 grams and a standard deviati

just olya [345]

Answer:

Weights of at least 340.1 are in the highest 20%.

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:

$\mu = 330, \sigma = 12$

a. Highest 20 percent

At least X

100-20 = 80

So X is the 80th percentile, which is X when Z has a pvalue of 0.8. So X when Z = 0.842.

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

$0.842 = \frac{X - 330}{12}$

$X - 330 = 12*0.842$

$X = 340.1$

Weights of at least 340.1 are in the highest 20%.

3 0

3 years ago

PLS PLS PLS HELP 20 POINTS PLS HELP THX

Flura [38]

The first one- the rest don’t add up

8 0

2 years ago

Alemu, Tulu, Kassa and Tegitu worked for 4 hours, 6 hours, 5 hours

GaryK [48]

As a group they were paid $1000 after putting in 4+6+5+5 = 20 worker-hours.
$1000/(20 worker-hours) = $50/(worker-hour)
Alemu received 4*$50 = $200
Tulu received 6*$50 = $300
Kassa and Tegitu each received 5*$50 = $250

6 0

3 years ago

Which expression represents the composition [g-f. h](x) for the functions below?

ss7ja [257]

Answer:

the composition of the expression [g-f.h](x) is g(x)=5x2

7 0

3 years ago

Plz help me :(Show work if u know​

Plz help me :(Show work if u know