Answer:
Thomas is 28.
Step-by-step explanation:
Let Huilan’s age be “x + 11”
Let Thomas’s age be “x”
x + x + 11 = 67
2x + 11 = 67
2x = 56
x = 28 years
x + 11 = 39 years
Thomas is 28.
Given the statement 11^(n -6) is divisible by 5 for every positive integer n. What must be shown in the induction step?
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
please please help me please I really need help please
A marching band has 64 members. The band director wants to arrange the band members into a square formation. How many band members will be in each row?
A. 8
B. 7
C. 6
D. 5
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
PLEASE LOOK BELOW!!! (Will give Brainliest)
No links and pls explain!!!!
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
5(x+2)-4 = 13-7(x+1)
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
Find the quotient for 12 2/5 ÷ 1/4
ASAP Pls!!!
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
Steve earns extra money babysitting. He charges $37.00 for 4 hours and $64.75 for 7 hours. Let x represent the number of hours Steve babysits and y represent the amount he charges
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
Snail A moved 6 feet in 7 hours. Snail B moved 7 feet in 8 hours. Both snails moved at constant speeds. Which snail went faster?
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
(1/2)5 standard form
Answer:
[tex]\frac{5}{2}[/tex] or 2.5
Hope that this helps!
Evaluate this expression for x=-5 and y=-5
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]
Determine the number of solutions for the system 2x+3y=5 and -9y=6x-15
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.
How many solutions are there for the system of equations shown on the graph?
A coordinate plane is shown with two lines graphed. One line crosses the y axis at 3 and has a slope of negative 1. The other line crosses the y axis at 3 and has a slope of two thirds.
No solution
One solution
Two solutions
Infinitely many solutions
A sphere has a radius of 7.9 cm. Calculate the spheres volume. Use 3.14 and don't round.
Answer:
[tex]\displaystyle V = 2064.19 \ cm^3[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightGeometry
Volume of a Sphere Formula: [tex]\displaystyle V = \frac{4}{3} \pi r^3[/tex]
r is radiusStep-by-step explanation:
Step 1: Define
Identify variables
r = 7.9 cm
Step 2: Find Volume
Substitute in variables [Volume of a Sphere Formula]: [tex]\displaystyle V = \frac{4}{3}(3.14)(7.9 \ cm)^3[/tex]Evaluate exponents: [tex]\displaystyle V = \frac{4}{3}(3.14)(493.039 \ cm^3)[/tex]Multiply: [tex]\displaystyle V = 2064.19 \ cm^3[/tex]There is a bag filled with 3 blue and 4 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting 2 blues?
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.
Select all that apply.
A spinner is divided into 4 equal sections. Which of the following are true?
The experimental probability is for each section.
If the spinner is spun 64 times, you would predict it to land on each section 16 times.
The spinner will land on each section of the spinner an equal number of times.
The theoretical probability is 25% for each section.
Multiple choice!!!
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
x[tex]x^{2}-8x+14=2x-7[/tex]
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]
Shift parabolas
f(2)=z²
g(x) = (x+4)^2 - 1
We can think of g as a translated (shifted) version of fi
Complete the description of the transformation.
Use nonnegative numbers.
To get the function g, shift f up/down
by
units and to the right/left
by
units.
In each diagram, abc is a straight line. Find the unknown angles.
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°
Only answer if you're very good at Math.
Given f(x) = x + 1 and g(x) = x^2, what is ( g o f) (x)?
A: ( g o f) (x) = x^2 + 1
B: ( g o f) ( x) = ( x + 1)^2
C: ( g o f) (x) = x^2 + x + 1
D: ( g o f) ( x) = x^2 ( x + 1)
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
) A desk organizer sells for $35, which includes a markup rate of 60% based on the selling price.
a. Find the markup.
b. Find the cost.
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
which statement is true?
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.
The quotient of 4/1/2
Answer:
the quotient is 2
Step-by-step explanation:
4/1=4
4/2=2
The sum of two numbers is 45 and their difference is 7. Find the numbers. *
the sum of two numbers that is 45 and their difference is 7 it is 39 and 6 more like 39+6
There are 10 boys and 13 girls in Mr. Benson's fourth-grade class and 12
boys and 11 girls in Mr. Johnson fourth-grade class. A picnic committee
of six people is selected at random from the total group of students in both
clasties.
(a) What is the probability that all the committee members are girls?
(b) What is the probability that the committee has three girls and three
boys?
Christian Robbie are construction arytenoids stained glass window whose length is 7.3 inches longer than its width if the area of the window is 596.9 in.² find the width and the length
Answer:
w ≈ 21.053 inches
l ≈ 28.353 inches
Step-by-step explanation:
rewrite 2/7 and 1/4 so they have a common denominator
a + b = 300 pls help i cant find out the answer
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:
Someone help me please
Square root of 121
4. How many days of selling bicycles is involved in the study?
b. 40
c. 35
d. 10
a. 45
It takes Alice 90 minutes to put a futon frame together, and it takes Maya 60 minutes to put the same
type of frame together. If they worked together, how long would it take to put a frame together?
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
(Right angle) Trigonometry
Help me find the X value please! Explain what you did to get the answer aswell
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]