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2 years ago

A basketball team scores 37 points in one quarter is the number 37 prime or composite show your work

Mathematics

1 answer:

Andrews [41]2 years ago

6 0

Answer: Prime

Step-by-step explanation: To tell if 37 is a prime number or a composite number, begin by finding the factors of 37.

To find the factors of 37, begin by dividing 37 by 1 which gives us 37. This means that 1 and 37 are factors.

Notice however that 37 is not divisible by any other number except 37. When we divide 37 by 37 we get 1. Since 37 and 1 are repeat factors, the only factors of 37 are 1 and 37.

When there are only two factors of a number, we call the number prime.

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A. Plot the data for the functions f(x) and g(x) on a grid and connect the points.

labwork [276]

Answer:

a) see the plots below

b) f(x) is exponential; g(x) is linear (see below for explanation)

c) the function values are never equal

Step-by-step explanation:

a) a graph of the two function values is attached

b) Adjacent values of f(x) have a common ratio of 3, so f(x) is exponential (with a base of 3). Adjacent values of g(x) have a common difference of 2, so g(x) is linear (with a slope of 2).

c) At x ≥ 1, the slope of f(x) is greater than the slope of g(x), and the value of f(x) is greater than the value of g(x), so the curves can never cross for x > 1. Similarly, for x ≤ 0, the slope of f(x) is less than the slope of g(x). Once again, f(0) is greater than g(0), so the curves can never cross.

In the region between x=0 and x=1, f(x) remains greater than g(x). The smallest difference is about 0.73, near x = 0.545, where the slopes of the two functions are equal.

4 0

3 years ago

Show that the following statement is an identity by transforming the left side into the right side. sin θ (sec θ + csc θ) = tan

ExtremeBDS [4]

Answer:

Step-by-step explanation:

Required to prove that:

Sin θ(Sec θ + Cosec θ)= tan θ+1

Steps:

Recall sec θ= 1/cos θ and cosec θ=1/sin θ

Substitution into the Left Hand Side gives:

Sin θ(Sec θ + Cosec θ)

= Sin θ(1/cos θ + 1/sinθ )

Expanding the Brackets

=sinθ/cos θ + sinθ/sinθ

=tanθ+1 which is the Right Hand Side as required.

Note that from trigonometry sinθ/cosθ = tan θ

8 0

3 years ago

What is five x plus negative three equals fifteen

bearhunter [10]

You write the equation like this:
$5x + (-3) = 15$

But if you want to solve it then you do it like this:
$5x + (-3) = 15$
$5x - 3 = 15$
$5x = 18$
$x = 18/5$

7 0

3 years ago

Read 2 more answers

A man invests $2000 in an account that pays 6.5% interest per year, compounded quarterly.

skelet666 [1.2K]

Answer:

The correct answer is a. $2275.28; b. 17.04 years

Step-by-step explanation:

Principal to be invested is $2000

Interest rate (r) per year is 6.5 quarterly.

Interest is calculated compoundly.

a. Time (t) for the investment is given to be 2 years.

Amount after two years is = Principal × $( 1+ \frac{r}{100n}) ^ {nt}$ where the value of n is 4.

⇒ A = 2000 × $( 1+ \frac{6.5}{400}) ^ {8}$

⇒ A = $2275.28.

b. Now the value of A is given to be triple the principal = $ (3 × 2000).

Therefore we need to find the value of t.

⇒ 3 × 2000 = 2000 × $( 1+ \frac{6.5}{400}) ^ {4t}$

⇒ ㏑ 3 = 4t × ㏑ ( 1.01625)

⇒ t = 17.04

Therefore it would take 17.04 years for the principal to triple.

5 0

2 years ago

If a point is chosen inside the square, what is the probability that it will also be inside the circle?

Feliz [49]

Answer:

$79\%$

Step-by-step explanation:

The probability that the point is chosen in the circle is equal to the area of the circle divided by the area of the square.

Formulas used:

Area of a square with side length $s$ is given by $A=s^2$
Area of a circle with radius $r$ is given by $A=r^2\pi$

The segment marked as 1 represents not only the radius of the circle, but also half the side length of the square. Therefore, the side length of the square is 2, and we have:

Area of square: $A=2^2=4$

Area of circle:

$A=1^2\pi=\pi$

Therefore, the probability that the point will be inside the circle is:

$\frac{\pi}{4}=0.78539816339\approx \boxed{79\%}$

3 0

2 years ago