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alexandr402 [8]

2 years ago

15

A campus coffee shop charges $1.30 for a cup of coffee, and the tenth cup is free. If you take advantage of this offer, how much

do you actually pay per cup of coffee, on average?

2 answers:

Nata [24]2 years ago

4 0

The answer would be
$1.30 x 9 = $11.70
$11.70 / 10 = $1.17
Answer: $1.71

Reika [66]2 years ago

4 0

The answer is $1.17 !

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What is the sum of the first seven terms of the geometric series 2 - 10 +50 -...?

Umnica [9.8K]

Answer:

26042.

Step-by-step explanation:

What's the first term of this geometric series?

2.

What's the common ratio of this geometric series?

Divide one of the terms with the previous term. For example, divide the second term -10 with the first term 2.

$\displaystyle r = \frac{-10}{2} = -5$ .

What's the sum of this series to the seventh term?

The sum of the first n terms of a geometric series is:

$\displaystyle a_1 \cdot \frac{1-r^{n}}{1-r}$ ,

where

$a_1$ is the first term of the series,
$r$ is the common ratio of the series, and
$n$ is the number of terms in this series.

$\displaystyle 2 \times\frac{1- (-5)^{7}}{1- (-5)}=26,042$ .

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3 years ago

What is $45.27 plus 16%?

Ghella [55]

Answer:

$52.51

Step-by-step explanation:

16% of 45.27 is 7.24

45.27 + 7.24 is $52.51

Hope this helps!

Stay safe!!

8 0

3 years ago

Read 2 more answers

For 0 ≤ ϴ < 2π, how many solutions are there to tan(StartFraction theta Over 2 EndFraction) = sin(ϴ)? Note: Do not include va

Black_prince [1.1K]

Answer:

3 solutions:

$\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}$

Step-by-step explanation:

So, first of all, we need to figure the angles that cannot be included in our answers out. The only function in the equation that isn't defined for some angles is $tan(\frac{\theta}{2})$ so let's focus on that part of the equation first.

We know that:

$tan(\frac{\theta}{2})=\frac{sin(\frac{\theta}{2})}{cos(\frac{\theta}{2})}$

therefore:

$cos(\frac{\theta}{2})\neq0$

so we need to find the angles that will make the cos function equal to zero. So we get:

$cos(\frac{\theta}{2})=0$

$\frac{\theta}{2}=cos^{-1}(0)$

$\frac{\theta}{2}=\frac{\pi}{2}+\pi n$

or

$\theta=\pi+2\pi n$

we can now start plugging values in for n:

$\theta=\pi+2\pi (0)=\pi$

if we plugged any value greater than 0, we would end up with an angle that is greater than $2\pi$ so, that's the only angle we cannot include in our answer set, so:

$\theta\neq \pi$

having said this, we can now start solving the equation:

$tan(\frac{\theta}{2})=sin(\theta)$

we can start solving this equation by using the half angle formula, such a formula tells us the following:

$tan(\frac{\theta}{2})=\frac{1-cos(\theta)}{sin(\theta)}$

so we can substitute it into our equation:

$\frac{1-cos(\theta)}{sin(\theta)}=sin(\theta)$

we can now multiply both sides of the equation by $sin(\theta)$

so we get:

$1-cos(\theta)=sin^{2}(\theta)$

we can use the pythagorean identity to rewrite $sin^{2}(\theta)$ in terms of cos:

$sin^{2}(\theta)=1-cos^{2}(\theta)$

so we get:

$1-cos(\theta)=1-cos^{2}(\theta)$

we can subtract a 1 from both sides of the equation so we end up with:

$-cos(\theta)=-cos^{2}(\theta)$

and we can now add $cos^{2}(\theta)$

to both sides of the equation so we get:

$cos^{2}(\theta)-cos(\theta)=0$

and we can solve this equation by factoring. We can factor $cos(\theta)$ to get:

$cos(\theta)(cos(\theta)-1)=0$

and we can use the zero product property to solve this, so we get two equations:

Equation 1:

$cos(\theta)=0$

$\theta=cos^{-1}(0)$

$\theta={\frac{\pi}{2}, \frac{3\pi}{2}}$

Equation 2:

$cos(\theta)-1=0$

we add a 1 to both sides of the equation so we get:

$cos(\theta)=1$

$\theta=cos^{-1}(1)$

$\theta=0$

so we end up with three answers to this equation:

$\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}$

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2 years ago

Help me please I am begging y’all

cupoosta [38]

2 is the answer i think

7 0

2 years ago

What is the value of x?

EastWind [94]

6+16=5x

5x=22

x=22/5

x=4.4

8 0

3 years ago

Read 2 more answers