Huilan is 11 years older than Thomas. The sum of their ages is 67 . What is Thomas's age?

Answer:

[tex]\frac{5}{2}[/tex] or 2.5

Hope that this helps!

Answer:

Proved

Step-by-step explanation:

The given data is:

[tex]11^n - 6[/tex] not [tex]11^{n - 6[/tex]

Required

Prove by induction that it is divisible by 5

Assume [tex]n = k[/tex]

So, we have:

[tex]11^k - 6 = 5p[/tex] where p is a positive digit

Rewrite as:

[tex]11^k = 5p + 6[/tex]

To solve further, we have to prove that [tex]11^k - 6[/tex] is true for [tex]n=k+1[/tex]

So, we have:

[tex]11^{k+1} - 6[/tex]

[tex]11^{k+1} - 6 = 11^k * 11 - 6[/tex]

Add 0

[tex]11^{k+1} - 6 = 11^k * 11 - 6 + 0[/tex]

Replace 0 with [tex]-5 +5[/tex]

[tex]11^{k+1} - 6 = 11^k * 11 - 6 - 5 + 5[/tex]

[tex]11^{k+1} - 6 = 11^k * 11 - 11- 5[/tex]

Factorize

[tex]11^{k+1} - 6 = 11 (11^k - 1)- 5[/tex]

Substitute [tex]11^k = 5p + 6[/tex]

[tex]11^{k+1} - 6 = 11 (5p + 6- 1)- 5[/tex]

[tex]11^{k+1} - 6 = 11 (5p + 5)- 5[/tex]

Factorize

[tex]11^{k+1} - 6 = 11 *5(p + 1)- 5[/tex]

Factorize

[tex]11^{k+1} - 6 = 5[11(p + 1)- 1][/tex]

The 5 outside the bracket implies that it is divisible by 5

Answer:

[tex]x = 3\ or\ x = 7[/tex]

Step-by-step explanation:

Given

[tex]x^{2}-8x+14=2x-7[/tex]

Required

Solve

Equate to 0

[tex]x^{2}-8x-2x+14+7=0[/tex]

[tex]x^{2}-10x+21=0[/tex]

Expand

[tex]x^{2}-7x-3x+21=0[/tex]

Factorize

[tex]x(x-7)-3(x-7)=0[/tex]

Factor out x - 7

[tex](x-3)(x-7)=0[/tex]

Split

[tex]x - 3 = 0\ \ x - 7 = 0[/tex]

Solve

[tex]x = 3\ or\ x = 7[/tex]

9514 1404 393

Answer:

  infinite number of solutions

Step-by-step explanation:

The two equations describe the same line.

Adding 9y+15 to the second equation makes it be ...

  15 = 6x +9y

Dividing that by 3 gives you ...

  5 = 2x +3y . . . . . . identical to the first equation

The lines intersect at every point, so there are an infinite number of solutions.

Answer:

[tex]49\frac{3}{5}[/tex]

Step-by-step explanation:

Answer:

49 3/5

Step-by-step explanation:

First, convert 12 2/5 into an improper fraction. You should get 62/5. We know that dividing fractions is the same thing as multiplying by the other fraction's reciprical (flip). So, 62/5 divided by 1/4 is the same thing as 62/5*4/1 (4). Lastly multiply straight across to get 248/5. Simplify to get 49 3/5.

Hope this helps

Answer:

[tex]\displaystyle V = 2064.19 \ cm^3[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Geometry

Volume of a Sphere Formula: [tex]\displaystyle V = \frac{4}{3} \pi r^3[/tex]

Step-by-step explanation:

Step 1: Define

Identify variables

r = 7.9 cm

Step 2: Find Volume

Answer:

the quotient is 2

Step-by-step explanation:

4/1=4

4/2=2

Answer:

20 = x

Step-by-step explanation:

All interiror angles in this triangle will equal 180

Set your formula up as 180 = x+5+7x-5+x then solve for x

180 = x+5+7x-5+x

180 = x + 7x + x +5 - 5

180 - 5 + 5 = 9x

180 = 9x

180 / 9 = x

20 = x

You can check your result by pluging in 20 for all x

180 = 20+5+7*20-5+20

180 = 180

Answer:

A. 8

Step-by-step explanation:

sqrt{64} is 8 (8*8)

Answer:

8

Step-by-step explanation:

There are 8 members in each row

Answer:

The value of ∠b = 180°

Step-by-step explanation:

Given that;

ABC is a straight line

Another angle is 137°

Find:

The value of ∠a

The value of ∠b

Computation:

We know that, ABC is a straight line

So,

137 + The value of ∠a = 180

The value of ∠a = 180 - 137

The value of ∠a = 43°

The value of ∠b = 360 - 137 - The value of ∠a

The value of ∠b = 360 - 137 - 43

The value of ∠b = 180°

Answer:

since .875 > .857 Snail B is moving faster

Step-by-step explanation:

divide 6 by 7 to get the number of feet in one hour for Snail A

7 into 6 is .857

divide 7 by 8 to get the number of feet in one hour for Snail B

8 into 7 is .875

I believe the answer to this is:

Snail B went faster than Snail A.

Hope this helps! :D

Answer:

a= 250

b= 50

250 + 50 = 300

Step-by-step explanation:

There's many solutions but this was the first one I could come up with.

Answer:

my opinion is seince a+b=300 then the sqaure of 300= 17.3?

Step-by-step explanation:

Answer:$6.25

Step-by-step explanation:we have that

x------------------> represent the number of hours Steven babysits

y----------------- > represent the amount he charges

for x=6 hours

y=$37.50 ----------------> y/x=37.5/6=6.25

for x=8 hours

y=$50---------------------> y/x=50/8=6.25

therefore

y=6.25x

Answer:

0

Step-by-step explanation:

5x+10-4=13-7x-7

5x+6=6-7x

5x+0= -7x

0=-12x

Divide and u get x=0

Answer: a. $21

b. $14

Step-by-step explanation:

Selling price of desk organizer = $35

Markup rate = 60%

a. The markup will be:

= Markup rate × Selling price

= 60% × $35

= 0.6 × $35

= $21

Therefore, the markup is $21

b. The cost will then be:

Cost price = Selling price - Markup

= $35 - $21

= $14

Answer:

(B)  If the spinner is spun 64 times, you would predict it to land on each section 16 times.

&

(D) The theoretical probability is 25% for each section.

I got this question right

Answer:

[tex]x - 2y=5[/tex]

Step-by-step explanation:

Given

[tex]x = -5; y=-5[/tex]

[tex]x - 2y[/tex] --- missing from question

Required

Evaluate

We have:

[tex]x - 2y[/tex]

Substitute for x and y

[tex]x - 2y=-5 - 2*-5[/tex]

[tex]x - 2y=-5 +10[/tex]

[tex]x - 2y=5[/tex]

Answer:

A. The slope of Function A is greater than the slope of Function B.

Step-by-step explanation:

The slope of a function can be defined as rise/run. In Function A, the rise/run is 4. The slope in Function B is much easier to see: it is 2. Because 4 is greater than 2, Function A has a greater slope than Function B.

Answer:

Solution given:

f(x) = x +1 and g(x) = x²,

now

(gºf)(x) =g(fx)=g(x+1)=(x+1)²

B) (gºf)(x) = (x + 1)^2

Answer:

[tex]x\approx 7.88[/tex]

Step-by-step explanation:

Since we are given the angle and the hypotenuse and we want to find the side opposite to the angle, we can use the sine ratio. Recall that:

[tex]\displaystyle \sin\theta^\circ =\frac{\text{opposite}}{\text{hypotenuse}}[/tex]

Substitute:

[tex]\displaystyle \sin21=\frac{x}{22}[/tex]

Solve for x:

[tex]x=22\sin 21[/tex]

Use a calculator (make sure you're in Degrees mode!):

[tex]x\approx 7.88[/tex]

the sum of two numbers that is 45 and their difference is 7 it is 39 and 6 more like 39+6

Answer:

36 minutes

Step-by-step explanation:

The equation to determine the time together is

1/a + 1/b = 1/c  where a and b are the times alone and c is the time together

1/90  + 1/ 60 = 1/c

Multiply each side by 180c to clear the fractions

180c( 1/90  + 1/ 60 = 1/c)

2c + 3c = 180

5c = 180

Divide each side by 5

5c/5 = 180/5

c =36

Answer:

w ≈ 21.053 inches

l ≈ 28.353 inches

Step-by-step explanation:

3 of 7 and the chances of getting red is 4 of 7

Step-by-step explanation:

====================================================

Explanation:

The fraction 3/7 represents the probability of picking a blue marble since there are 3 blues out of 3+4 = 7 total.

Because the first marble is put back, this means the probability of picking blue does not change. So 3/7 is the probability of picking another blue marble.

Overall, we have (3/7)*(3/7) = 9/49 as the probability of picking two blues in a row.