3
Roy and David both play football for the same team. A football match is 90 minutes long.
In one match, Roy plays for 70% of the 90 minutes and David plays for of the 90 minutes.
Who plays for the longer time and by how many minutes?

Answer:

(a) [tex]\log_72 \approx 0.3562[/tex]

(b) [tex]\log_7(\frac{147}{16} ) = 2[/tex]

Step-by-step explanation:

For the point a:

For this problem we use the information of [tex]\log_716 \approx 1.4248[/tex]

16 can be re-write as [tex]2^4[/tex]. Then you have:

[tex]\log_72^4[/tex]

Using the power property of the logarithm we have:

[tex]\log_ba^c = c\log_ba[/tex]

[tex]\log_72^4 = 4\log_72[/tex]

And this expression is equal to:

[tex]4\log_72 \approx 1.4248\\\log_72\approx \frac{1.4248}{4} \approx 0.3562\\[/tex]

For the point b:

For this problem we use the information of [tex]\log_716 \approx 1.4248[/tex] and [tex]\log_73 \approx 0.5646[/tex]

The first is use the quotient property in the given log.

[tex]\log_c\frac{a}{b} = \log_ca-\log_cb[/tex]

[tex]\log_7\frac{147}{16} = \log_7147 -\log_716[/tex]

We already know the value of [tex]\log_716[/tex] then we have to calculate the value of [tex]\log_7147[/tex].

So we factorize the number 147 in [tex]3 \cdot 7 \cdot 7[/tex] (for factorize the number start with the smaller prime and check if the remainder is 0, it is then is a primer factor of the number).

Now re-write [tex]\log_7147[/tex] as [tex]\log_73 \cdot 7^2[/tex] and by the product property get:

[tex]\log_bmn = \log_b m +\log_b n\\\log_73 \cdot 49 = \log_7 3 +\log_7 49 = 0.5646 + 2 = 2.5646[/tex]

Know replace each value in the subtraction and get the result:

[tex]\log_7147 -\log_716 = 2.5646 - 0.5646 = 2[/tex]

Answer:

4/5 divide 100 by the denominator in this case 5 get 20 as the unit percent and multiply by the numerator to get 80% which is 8/10 as a fraction.

Answer:

He must get a 96% on the fourth test to raise his average to an 87

Answer:

Step-by-step explanation:

The number of black pieces is 5 more than 3 times the white pieces:

Let the number of rounds is x.

Initial number of white nd black pieces:

Substitute the values of b and w into first equation and find the value of x:

Find the number of pieces:

Correct choice is D

Answer:

A game consists of black and white pieces. The number of black pieces is 5 more than 3 times the white pieces. Seven white and 15 black pieces are removed each round. After several rounds, there are 3 white and 56 black pieces left. How many pieces were there in the beginning?

A. 52

B. 158

C. 210

D. 213

E. 218

Answer: D. 16.33

Step-by-step explanation:

Answer:

See attached

Expressions matching the properties

The associative property:

The commutative property:

Distributive property:

Pretty sure the answer is d

[tex]\\ \sf\longmapsto (5x^3+5x^2+5)-(6x^3-6x^2+8x-5)[/tex]

[tex]\\ \sf\longmapsto 5x^3+5x^2+5-6x^3+6x^2-8x+5[/tex]

[tex]\\ \sf\longmapsto 5x^3-6x^3+5x^2+6x^2-8x+5+5[/tex]

[tex]\\ \sf\longmapsto -x^3+11x^2-8x+10[/tex]

[tex]\\ \sf\longmapsto x^3-11x^2+8x-10[/tex]

[tex]\large \boldsymbol{} \longmapsto (5x^3+5x^2+5) -(6x^3-6x^2+8x-5 ) \\\\\\ \longmapsto5x^3+5x^2+5-6x^3+6x^2-8x+5 \\\\\\ \longmapsto 5x^3-6x^3+5x^2+6x^2-8x+5+5 \\\\\\ \longmapsto \boxed{ - x^3+11x^2-8x+10}[/tex]

Answer:

Area= 18 x 18=324 sq.cm

Step-by-step explanation:

p=36 x2=72 (as it is twice that of the original paper)

since it is a square, length of 1 side = 72/4= 18

so, the area = l x l= 18 x 18= 324 sq.cm

Answer:

Area= 18 x 18=324 sq.cm

Step-by-step explanation:

p=36 x2=72 (as it is twice that of the original paper)

Since it is a square, length of 1 side = 72/4= 18

Therefore, the area = l x l= 18 x 18= 324 sq.cm

Hope this helps :)

Answer: B.

Step-by-step explanation:

brainliest me

Answer:

Step-by-step explanation:

Answer:

Ms. April will not have enough students.

Step-by-step explanation:

This is because 180 days of the year divided by 3 students per day = 60 students per year. The class only has 20 students, therefore, there is not enough students needed to collect milk.

Answer:

Ms. April will not have enough students.

Step-by-step explanation:

This is because 180 days of the year divided by 3 students per day = 60 students per year. The class only has 20 students, therefore, there is not enough students needed to collect milk.

Answer:

$1.33

Step-by-step explanation:

32-20 = 12

12/9 = $1.33

Answer:

Unsure but it might be -8/3

Step-by-step explanation:

Step-by-step explanation:

I'm not sure if I'm using substitution method but I guess it's x = 12.4

Answer:

160000

Step-by-step explanation:

Step-by-step explanation:

Avg = 20 + 14 + 28 + 18 /4

Avg = 80/4 = 20

Answer:

18 and 29

Step-by-step explanation:

8+0=8

8+1=9

9+2=11

11+3=14

14+4=18

18+5=23

23+6=29

As you can see, the number that you add to the previous number in the sequence is increased by 1 as the sequence grows in length. The number added goes from 0 to 1 to 2 to 3 and so on. :-)

[tex]0.18[/tex]

is the decimal point

Answer:

The equation of a straight line is always

[tex]y=mx+b[/tex]

The constant m always refers to the slope, and the constant b always refers to the y-intercept.

Simply substitute the numbers in:

[tex]y=-\frac{1}{2}x+3[/tex]

There's your equation!

Answer:

See below:

Step-by-step explanation:

Hello! My name is Galaxy and I will be helping you today!

We can check your answer in 1 step.

We need to find how much they earn if they worked 37 hours at a rate of 26 dollars per hour.

We can mutliply to figure this out:

[tex]37*26=962[/tex]

Therefore, yes, your answer is correct!

Cheers!

Answer:

$26=1hr

x   =37hr

$26 x 37=$ 962

Step-by-step explanation:

Answer:

160

Step-by-step explanation:

We know that [tex]\left \{ {{t=2.5} \atop {v=64}} \right.[/tex]

Formulate and substitute: [tex]d=2.5[/tex]×[tex]64[/tex]

Calculate the product or quotient: [tex]160[/tex]

Answer: [tex]160[/tex]

In what context? Do you mean calculus If you are talking about graphing on a graph plane it would be the two accelerates on the x axis so (left or right) and then the 1.5 accelerates on the y axis so 1.5 on the y axis would be one and halfway to the 2 mark on the y axis so in the middle of 1 to 2 on the y axis the y axis goes (up and down)

Cost is 65x + 3500 where x is = 326.

65(326) + 3500

21,190 + 3500 = $24,690 is the cost.

Revenue is 365x where x is 326.

365(326) = $118,990

Now we subtract the two:

118,990 - 24,690 = $94,300

This means that the answer is C) $94,300.

I hope this helps! :)

Answer:

(2,5)

(3,8)

(4,13)

(5,12)

(6,18)

(7,20)

Plug those into the scatter plot graph

Step-by-step explanation:

The left side is the x axis and the right side is the y axis

[tex]\begin{cases} \stackrel{apples}{10^3}\\ \stackrel{grapes}{10^2}\\ \stackrel{oranges}{10^1} \end{cases}\qquad \begin{cases} \stackrel{lbs}{32}\\ \stackrel{lbs}{25}\\ \stackrel{lbs}{42} \end{cases}\qquad \begin{array}{rllll} 10^3\cdot 32\\ 10^2\cdot 25\\ +\qquad 10\cdot 42\\\cline{1-1} 34920&lbs \end{array}[/tex]

Answer:

the answer is 26.6666667 and when rounded off is 26.7

Answer:

8

Step-by-step explanation:

35-3×9=35-27

=8

Hope this helps!!!

Answer:

(3, 9)

Step-by-step explanation:

Set 3x and 2x+3 equal to each other forming an equation in x.

3x=2x+3

Solve for x.

x=3

Substitute the given value of x into the equation y=3x.

y=3x3

Solve for y.

y=9

(x, y) = (3, 9)

Hope this helps :)