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

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]

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.

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:

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:

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:

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:

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

Hope that this helps!

Answer:

the quotient is 2

Step-by-step explanation:

4/1=4

4/2=2

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:

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:

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 - 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. 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:

[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: 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:

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:

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:

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.

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

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:$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:

w ≈ 21.053 inches

l ≈ 28.353 inches

Step-by-step explanation:

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]

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