Are the following expressions equivalent?<br><br> A. 3x - 2x + 0.5x3x−2x+0.5x.<br> a. 1.5x1.5x

A local yoga studio

Andrews [41]

Answer:

Let's call the first studio, yoga studio A.

Let's call the second studio, yoga studio B.

The equations:

Yoga Studio A: y=10x+55

Yoga Studio B: y=12.5x+25

So, for 12 classes:

Yoga Studio A: y=10(12)+55, y=175

Yoga Studio B: y=12.5(12)+25, y=175

These two numbers are equal, so Griffin is right.

For 10 classes:

Yoga Studio A: y=10(10)+55, y=155

Yoga Studio B: y=12.5(10)+25, y=150.

These two numbers are not equal, so Gigi is wrong.

Let me know if this helps!

5 0

3 years ago

The school cafeteria is holding an election for students to vote on which items they would like to see on the lunch menu. The ch

d1i1m1o1n [39]

There are two choices to choose from:

a) Grilled chicken
b) Veggie Pizza

36% students voted for veggie pizza. This means the remaining votes will go to the Grilled chicken. Thus grilled chicken received 64% of the student votes.

Since more students voted for the Grilled chicken, it will be on the lunch menu.

3 0

3 years ago

Find the first term and the common ratio <br>third term =6 and seventh term= 96

mamaluj [8]

Answer:

First term a₁ = 3/2 and common ratio r = 2

Step-by-step explanation:

We need to find the first term and common ratio while we are given third term = 6 and seventh term = 96

Since common ratio is required so, the sequence is geometric sequence

The formula used is: $a_n= a_1r^{n-1}$

We are given: third term = 6 i,e

$a_3=a_1r(3-1)\\6=a_1r^2----eq(1)$

Seventh term = 96

$a_7=a_1r(7-1)\\96=a_1r^6----eq(2)$

Dividing eq(2) and eq(3)

$\frac{96}{6}=\frac{a_1r^6}{a1r2}\\16=\frac{r^6}{r^2}\\16=r^{6-2}\\=> r^4=16\\Taking \ fourth \ root\\ r=2,-2,2i,-2i\\ \ We \ will \ consider \ only \ positive \ value \ of \ r \ i.e \ \textbf{ r= 2}$

So, Common Ratio r = 2

Finding First term using eq(1)

$a_3=a_1r^2\\6=a_1(2)^2\\6=a_1(4)\\a_1= \frac{6}{4}\\a_1= \frac{3}{2}$

So, First term a₁ = 3/2 and common ratio r = 2

6 0

3 years ago

Winning the jackpot in a particular lottery requires that you select the correct five numbers between 1 and 34 and, in a separa

Marina CMI [18]

<h3>The probability of winning the lottery is $\frac{1}{10,295,472}$ </h3>

Step-by-step explanation:

Here, the total numbers in the jackpot = 1 to 34

Now, the number that needed to be drawn = 5

The number of ways , 5 number can be drawn from total 34 numbers :

$^{34} C _5 = \frac{34!}{5!(34-5)!} = 278,256$

Also, in separate draw, the correct number drawn = 1

So, the number of ways that can be done = 30 C 5 x 37

= 278,256 x 37 = 10,295,472

Now, P(win) = $\frac{\textrm{Total favorable attempts}}{\textrm{Total attempts}} = \frac{1}{10,295,472}$

Hence, the probability of winning the lottery is $\frac{1}{10,295,472}$

6 0

3 years ago

M<br> (9x + 2)<br> 1<br> (5х – 1)°<br> 740<br> What is mz2?<br> 39°<br> 570<br> ОООО<br> 67°<br> 740

Elodia [21]

Answer:

Step-by-step explanation:

m║n ⇒ (9x + 2)° = 74° {Corresponding Angles}

(9x)° = 72°

x = 8

Angles: angle corresponding to angle (5x-1)°, angle 74° and angle 2 add to 180° (straight angle)

(5×8 - 1)° + 74° + m∠2 = 180°

39° + 74° + m∠2 = 180°

113° + m∠2 = 180°

m∠2 = 180° - 113°

m∠2 = 67°

7 0

3 years ago

Are the following expressions equivalent? A. 3x - 2x + 0.5x3x−2x+0.5x. a. 1.5x1.5x