1) Write these using index notation:
a. 2 X 2 X 2 X 2
b. 5 X 5 X 5 X 7 X 7

Answer:

Step-by-step explanation:car 10 percent

Phone 1 percent

Clothes 5 percent

Charity 3.84 percent

Mac 0.4percent

Apple watch 0.2 percent

Hawaai trip 1.57 percent

Home 73 percent

Answer:

20.4 years

Step-by-step explanation:

The nper formula in excel comes handy in this scenario:

=nper(rate,pmt,-pv,fv)

Rate is the monthly rate of 5.4%/12

Assuming actual investment is $5,000 which is pv

The triple amount would be $5,000*3=$15,000 which is future value fv.

pmt is the regular cash flow the investment which is zero

=nper(5.4%/12,0,-5000,15000)= 244.68  months

Yearly it can be expressed as = 244.68/12  =20.39  years

When rounded to one decimal place it becomes 20.4 years

Answer:

29 ounces

Step-by-step explanation:

1 pound equals to 16 ounces

Answer:

29 ounces

Step-by-step explanation:

1 pound is 16 ounces so 29 ounces is equal to 1.8 pounds.

Answer:

sqrt21/5

Step-by-step explanation:

You can solve this by taking advantage of the trigonometric identity of sin^2(x) + cos^2(x) = 1

So square sinθ to get, 4/25

Subtract that from one to get:

cos^2(θ) = 21/25

Take the square root to get:

cosθ = sqrt21/5

The value of cosθ = (√21)/ 5.

The sine function in trigonometry is the ratio of the hypotenuse's length to the opposite side's length in a right-angled triangle. To determine a right triangle's unknown angle or sides, utilize the sine function.

Given that the angle θ lies in Quadrant I.

That means all the value of in θ the first quadrant are positive from 0° to 90°.

Here sinθ =  2/5.
And we know cosθ = √(1-sin²θ )

So cosθ = √{1- (2/5)²}

⇒  cosθ = √{1- (4/25)}

⇒  cosθ = √{21/25)}

⇒  cosθ = (√21)/ 5

Therefore, cosθ = (√21)/ 5

To learn more about the sine function;

https://brainly.com/question/12015707

#SPJ2

Answer:

An unclosed shape or one with lines not straight.

Step-by-step explanation:

Answer:

I have provided a picture of the typical polygons so if an option doesn't look like this, then it's probably not a polygon. Also, polygons are any 2-d shape made with straight lines, so a circle or a 3D shape is wrong

Answer:

a) 21, 24, 29

b) 5 terms in the sequence are less than 50

Step-by-step explanation:

[tex]t_n = n^2+20\\t_1 = 1^2+20 = 1+20= 21\\t_2 = 2^2+20 = 4+20= 24\\t_3 = 3^2+20 = 9+20= 29\\\\\\t_5 = 5^2+20 = 25+20= 45\\\\\\t_6 = 6^2+20 = 36+20= 56\\[/tex]

Since, 5th term is less than 50 and 6th term exceeds 50, therefore 5 terms in the sequence are less than 50.

Answer:

[tex]12[/tex]

Step-by-step explanation:

[tex]\frac{3}{5} \times 20[/tex]

[tex]\frac{60}{5}[/tex]

[tex]=12[/tex]

Answer:

12 students

Step-by-step explanation:

First make 3/5 into a percent or whole number because it's easier to solve that way. How do you do that? Divide it how it is, so 3/5 = 0.60. So 60% of her class has at least one pet.

Knowing this, we multiply 60% by 20 to know how many students are that 60% that have pets. So 0.6 x 20= 12

12 students have pets in Ms. Johnson's class

Answer:

6 Celsius

Step-by-step explanation:

Initial temperature at 12pm is 0 Celsius.

Rises by 6 (add by 6).

[tex]0+6[/tex]

[tex]6[/tex]

Answer:

This is because when you multiply the fraction what you get is 60/30. This is equal to the number of 2. So the volume is 2.

5/3 * 3/2 * 4/5

= 5*3*4 = 15*4 = 60

= 3*2*5 = 6*5 = 30

Volume = 5/3 x 3/2 x 4/5

5/3 x 3/2 = 15/6

15/6 x 4/5 = 60/30 = 2

Volume = 2 cubic units

Answer: 4 and 5

Step-by-step explanation:

4.89 is higher than 4 and lower than 5

Answer:

-7 and 3

-5 and 1

-3 and -1

They all give the same total i.e. -4

Answer:

-7 and 3

-5 and 1

-3 and -1

Step-by-step explanation:

The total is -4

Answer:

57 degree

Step-by-step explanation:

Using cos formula again~

So AB^2=BC^2+AC^2-2*BC*AC*cosC

AB= 25.15cm

BC^2=AB^2+AC^2-2ABACcosA

Cos A=0.55

A=56.58degree

Answer:

Hello, the answer to this question is A the other person is wrong

Step-by-step explanation:

Answer:

A) –2x + 3

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

The area (A) of the square = s² ( s is the measure of the side )

Here s = x + 2 and A = 7 , thus

(x + 2)² = 7 ← expand left side using FOIL

x² + 4x + 4 = 7 ( subtract 4 from both sides )

x² + 4x = 3 ← as required

Answer:

(x + 2)² = 7  

x² + 4x + 4 = 7  

x² + 4x = 3

Step-by-step explanation:

Answer:

Length of the string let out by Jim is 156.9 m.

Step-by-step explanation:

From the figure attached,

Jim observes the angle of elevation of the kite = 85°

And Patty observes the angle of elevation of the kite = 40°

Angle formed between the lines joining kite to Jim and Patty = 180° - (85 + 40)° = 55°

Distance between Jim and Patty = 200 m

Let the length of the string between Jim and the kite = x meters

By applying Sine rule in the triangle formed between Jim, Patty and the kite,

[tex]\frac{\text{Sin}55}{200}=\frac{\text{Sin}40}{x}[/tex]

x = [tex]\frac{200\times \text{Sin}40}{\text{Sin}55}[/tex]

x = 156.94 m

  ≈ 156.9 m

Therefore, length of the kite string from Jim and the kite is 156.9 m.

Answer:

There were 12 people at the party

Answer:

Step-by-step explanation:

Other answers have already shown that there are  n=12  people at the party, either using combinatorial choose notation

(n2)=n!2!(n−2)!=66  

or by counting handshakes person by person, noting that each successive person has one fewer unique handshake than the prior (as the previously counted people are disregarded), and then using the sum-of-consecutive-integers formula to get

(n−1)+(n−2)+...+2+1=∑n−1k=1k=(n−1)n2=66  

and solving for n .

Here I will provide another method of arriving at n(n−1)2=66.

Instead of keeping track of unique handshakes from the start, note that each person shakes hands with  n−1  other people. As there are n  people at the party, this gives us n(n−1)  handshakes. However, notice that we counted each handshake twice; for example, if Alice and Bob shook hands, we counted that once for Alice, and then again for Bob. To account for the double-counting, we can divide by  2, which gives us the previously mentioned formula of n(n−1)2.

As a side note, if we did not previously know the sum formula, we could use this as a combinatorial proof to show that it works. Also, if we account for repeated counting by dividing by k! , the number of permutations of k  objects, a similar method can be used to derive the chosen formula  (nk)=n!k!(n−k)!.

Answer:

10ftx15ft could be possibility.

Step-by-step explanation:

157 dollars per ticket

Show work

5 tickets times 18 dollars equals 90 dollars

875 minus 90 dollars in insurance equals 785

785 dollars divided by 5 tickets equals $157

Answer:

2%

Step-by-step explanation:

1900(x)^4= 1900+152

1.019 and is closer to 2%

Answer:

4y^2 + 12y + 9

Step-by-step explanation:

Unclear what your (2y + 3) represent.  If it's the length of one side of the square, please say so.

If that's the case, then the area of the square is (2y + 3)^2, or 4y^2 + 12y + 9, which is a trinomial.

Answer:

B. Equilateral triangle

Step-by-step explanation:

The shape that contains exactly three congruent sides is an equilateral triangle.

Answer: its d

Step-by-step explanation:

Answer:

c = 68

Step-by-step explanation:

Use pythagorean theorem, which states that [tex]a^{2} +b^{2} =c^{2}[/tex].

In this diagram, we are given the values of a and b.

a = 32      b = 60

Simply put these into the equation.

(32)^2 + (60)^2 = c^2

1024 + 3600 = c^2

4624 = c^2

Find the square root of both sides to solve for c.

[tex]\sqrt{4624}[/tex] = c

c = 68

7!/2!

Step-by-step explanation:

nCr=(nr)=n!r!(n−r)! 7C2=(72)=7!2!(7−2)!=7!2!⋅5!=50402⋅120=5040240=21.

Answer:

  see below

Step-by-step explanation:

In order by increasing number of angle marks, the vertices of the lower triangle are ...

  I H G

In the same order, the vertices of the upper triangle are ...

  H I E

Using these as the names of the triangles, we can write the congruence statement ...

  ΔIHG ≅ ΔHIE . . . . . matches the 2nd choice

Answer:

10

Step-by-step explanation:

Use the Pythagorean theorem: a^2+b^2=c^2 to find the hypotenuse

a=6

b=8

6^2+8^2=c^2

36+64=c^2

100=c^2

10=c

Hope this helps! :)

Answer:

10 cm.

Step-by-step explanation:

By Pythagoras:

BC^2 = 6^2 + 8^2

BC^2 = 100

BC = 10.

Answer:

B. -2/5

Step-by-step explanation:

Use the "rise over run method"

Do this by finding two points on the graph, then finding the distance between the two points. First find the vertical distance, then the horizontal. The direction represents whether the slope will be negative or positive. When it goes up, it'll be positive, down=negative. Right=positive, left=negative. Two negatives make a positive, but one positive and one negative make a negative.

Answer: B

Step-by-step explanation:

Let's solve the given equation. Then we can see which other equation has the same answer.

-5n+31=-14n-5

36=-9n

n=-4

We need to fina another equation that gives n=4 as the answer.

A. Incorrect

3-6n+3n=-3+4-4n

3-3n=1-4n

n=-2

B. Correct

[tex]\frac{11}{4} n+2=-3+\frac{3}{2}n[/tex]

[tex]\frac{5}{4}n=-5[/tex]

[tex]n=-4[/tex]

C. Incorrect

1=0.75n+3.25

-2.25=0.75n

n=-3

D. Incorrect

-1-22n=-20n-9

8=2n

n=4