5.6/2^3+(12.75+7.45)

Answer:

[tex]\log \:_{10}\left(\frac{1}{2}\right)=-\log \:_{10}\left(2\right)=-0.30102[/tex]

Thus, option A is true.

Step-by-step explanation:

Given the expression

[tex]log\left(\frac{1}{2}\right)[/tex]

[tex]=\log _{10}\left(2^{-1}\right)[/tex]

[tex]\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right),\:\quad \:x>0[/tex]

[tex]\log _{10}\left(2^{-1}\right)=-1\cdot \log _{10}\left(2\right)[/tex]

so the expression becomes

[tex]=-1\cdot \log _{10}\left(2\right)[/tex]

[tex]\mathrm{Multiply:}\:1\cdot \log _{10}\left(2\right)=\log _{10}\left(2\right)[/tex]

[tex]=-\log _{10}\left(2\right)[/tex]

substituting the value of log 2 = 0.30103

[tex]\:=-0.30102[/tex]

Thus,

[tex]\log \:_{10}\left(\frac{1}{2}\right)=-\log \:_{10}\left(2\right)=-0.30103[/tex]

Therefore, option A is true.

Answer:

The equation is;

y = -3/4x + 12

Step-by-step explanation:

The general form for the equation of a straight line is;

y = mx + b

where m is the slope and b is the y-intercept

With respect to this question;

4/3 is the slope and 1 is the intercept

If two lines are perpendicular, then the product of their slopes is -1

Mathematically;

4/3 * m2 = -1

m2 = -3/4

So to find the equation of this second line, we use the point slope form

This is;

y-y1 = m(x-x1)

y-4 = -3/4(x + 8)

y- 4 = -3/4x + 8

y = -3/4x + 12

Answer:

w = weight of Adrian's cat

c = weight of Lauren's cat

c = 3 + w/2

given: c=10

10 = 3 + w/2

Solve to get 'w':    20=6+w; w=14 pounds

Step-by-step explanation:

Answer:

slope = -6

Step-by-step explanation:

slope = Δy/Δx

slope = (4+2)/(2-3)

         = 6/-1

slope = -6

Answer:

The Drama Club needs to sell more than 3 pictures to make a profit.

The inequality 10x ≥ 2.55x +25  represents the situation.

Step-by-step explanation:

Given that:

Rent for lighting equipment = $25

Price per print = $2.55

Selling price of one picture = $10

x be the number of pictures.

Selling price * No. of pictures sold ≥ Price of per print * pictures printed + rent

10x ≥ 2.55x +25

10x-2.55x≥25

7.45x≥25

Dividing both sides by 7.45

[tex]\frac{7.45x}{7.45}\geq \frac{25}{7.45}\\x\geq 3.35[/tex]

Hence,

The Drama Club needs to sell more than 3 pictures to make a profit.

The inequality 10x ≥ 2.55x +25  represents the situation.

Answer:

$5.08

Step-by-step explanation:

Step one:

given data

We are told that a credit card company applies a 6% fee on all transactions under $10

since the cost of coffee bellow $10 that is $4.80, the 6% fee is applicable

so

=6% of 4.80

=6/100*4.80

=0.06*4.8

=$0.288

Step two:

the total fee will be

=0.288+4.80

= $5.08

Answer:

She used 1/4 of a pounds for salad

Step-by-step explanation:

Here, we want to calculate the amount of pounds of tomatoes used to make salad

From the question, she has 3/4 pounds and used 1/3 of what she has to make salad

What she used will be;

3/4 * 1/3 = 1/4

Answer:

15m-30

Step-by-step explanation:

To simplify this expression we simply need to multiply the equation out to get rid of the parenthesis.

So, 5 X 3m = 15 m and 5 X 6 = 30

So, our simplified expression is 15m-30

Hope this Helps!!! :)

Let me know in the comments if I should change anything or if the answer was perfect!

The simplest form of the expression is 15 (m - 2).

We have,

5 (3m - 6)

- Distributive property in the expression.

5 x 3m - 5 x 6

15m - 30

- Factoring out 15.

15 (m - 2)

Now,

It can not be further simplified.

Thus,

15 (m - 2) is the simplified form of the expression.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ6

Step-by-step explanation:

20 X _15 = 5X +90

15 X =105

X= 7

< A = 35

<B = 55

Answer:

12x^2-6x+9

Step-by-step explanation:

f(x) = 4x^3 - 3x^2 + 9x -5

f'(x) = nx^n-1

f'(x) = 12x^2 - 6x + 9

Answer:

[tex]y = \frac{3}{5}x + 2[/tex]

Step-by-step explanation:

3x - 5y + 10 = 0

         -5y = -3x - 10

            [tex]y = \frac{-3}{-5}x - \frac{10}{-5}\\\\ y = \frac{3}{5}x + 2[/tex]

Answer:

C

Step-by-step explanation:

the fraction 2/3 is in between 0 and 1 and C is the only plotted point that could represent the fraction.

Answer:

x=2

Step-by-step explanation:

26 divided by 13 is 2

Answer:

D

Step-by-step explanation:

Answer:

It's the B

Step-by-step explanation:

The arithmetic sequence here is made by subtracting 3 every time

Hope this helps, have a good day

Step-by-step explanation:

1.5 : 2.5

= 1.5/2.5

15/25

3/5

the ratio is 3 : 5

The ratio of 1.5-inch screws to 2.5-inch screws is 3/5.

Given,

- 1.5 inch screws

- 2.5-inch screws

We need to find what is the ratio of 1.5-inch screws to 2.5-inch screws.

Ratios are denoted by A:B.

Example: 1/2, 3/4

If two ratios are equal we called the ratios are in proportion.

Example:

1/2 and 5/10

5/10 = 1/2

We have,

1.5 and 2.5

We can write it as:

= 1.5 : 2.5

= 1.5 / 2.5

= 150 / 250

= 15/25

= 5x3 / 5x5

= 3/5

Thus the ratio of 1.5 and 2.5 is 3/5,

Learn more about how to find equivalent ratios here:

https://brainly.com/question/2462048

#SPJ2

Answer: Identity Property of Zero

Answer:

193.8125

Step-by-step explanation:

Answer: See explanation

Step-by-step explanation:

Here is the complete question:

A museum requires a minimum number of chaperones proportional to the number of students on a field trip. The museum requires a minimum of 3 chaperones for a field trip with 24 students. Which of the following could be combinations of values for the students and the minimum number of chaperones the museum requires? Choose 2 answers.

A. Students: 72

Minimum of chaperones: 9

B. Students: 16

Minimum of chaperones: 2

C. Students: 60

Minimum of chaperones: 6

D. Students: 45

Minimum of chaperones: 5

E. Students: 40

Minimum of chaperones: 8

Since the museum requires a minimum of 3 chaperones for a field trip with 24 students. This means that there will be 24/3 = 8 students per chaperone.

We then divide the number of students given in the question by the number of chaperone to know our answers. This. Will be:

Students: 72

Minimum of chaperones: 9

This will be: 72/9 = 8

Therefore, this is correct.

B. Students: 16

Minimum of chaperones: 2

This will be: 16/2 = 8

This is correct

C. Students: 60

Minimum of chaperones: 6

This will be: = 60/6 = 10.

Therefore, this is wrong

D. Students: 45

Minimum of chaperones: 5

This will be 45/5 = 9

Therefore, this is wrong.

E. Students: 40

Minimum of chaperones: 8

This will be: 40/5 = 8.

Therefore, this is wrong.

Therefore, options A and B are correct.

Answer:

If the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle, the two triangles are congruent.

Step-by-step explanation:

If the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle, the two triangles are congruent.

Answer:

the HL property

Step-by-step explanation:

Answer:

[tex]\frac{23}{66}[/tex]

Step-by-step explanation:

Answer:

1=3.5 2=10/3

Step-by-step explanation:

they pass each other at the point (3.5,3).

if you find the exact form for both equations you get 10/3 for both

Answer:

The number of students whose grade was 8 is more than twice the number of students whose grade was 5.

Step-by-step explanation:

N(8) models the number of students whose grades on exam was g.

(The answer is correct, I did it on Khan Academy

Answer:

154.3

Step-by-step explanation:

Use the formula 180(x-2)

Then divide your answer by x

X is the number of sides

Answer:

-75.7224

Step-by-step explanation:

Answer:

For your first question, the solution is x> -12

Step-by-step explanation:

First, expand 2(-3x+1), writing it as -6x+2

Next, subtract both sides by 2;

-6x + 2 - 2 < -5x + 14 - 2

Then, we simplify;

-6x < -5x + 12

Next, add both sides to 5x;

-6x + 5x < -5x + 12 + 5x

Simplify;

-x<12

Then, multiply both sides by -1, using reverse of inequality;

(-x)(-1)>12(-1)

Finally, simplify;

x>-12

Answer:

The answer to your second question is x is greater than or equal to -12.

Step-by-step explanation:

First, multiply both sides by -1, reversing the inequality;

(-2(3x+15))(-1) greater than or equal to 42(-1)

Next, simplify;

2(3x+15) greater than or equal to -42

Then, divide 2 from both sides;

2(3x+15/2 greater than or equal to -42/2

Next, simplify;

3x + 15 greater than or equal to -21

Then, we subtract both sides by 15;

3x+15-15 greater than or equal to -21-15

Simplify;

3x greater than or equal to -36

Next, divide 3 from both sides;

3x/3 greater than or equal to -36/3

Finally, simplify;

x greater than or equal to -12

I hope we helped you answer your question.

Answer: E) Even with a correlation value of 0.94, it is possible that the relationship could still be better represented by a nonlinear model.

Step-by-step explanation:

The correlation Coefficient of 0.94 obtained is peculiar to the linear model upon which the data was represented. Since the correlation Coefficient usually span between - 1 to + 1, it is very possible that, if the dataset is represented on a different model such as an exponential or quadratic model, the correlation percentage obtained may be better than that produced by the linear model.

Answer:

The probability is 0.0442

Step-by-step explanation:

If they all come from the same class, what it means is that we select 4 sophomores or , 4 juniors or 4 seniors

When we have or, it means we are to add each possible probability scenarios

The total number from which we want to select from is;

5 + 11 + 13 = 29

So the probability will be;

5C4/29C4 or 11C4/29C4 or 13C4/29C4

= 5C4/29C4 + 11C4/29C4 + 13C4/29C4

=0.0442

Answer:

222

Step-by-step explanation:

Closely pay attention to the transversal line running from up-left to down-right.

y) you will notice that the angle to the right of z is corresponding with 50 then 50 will be vertically opposite 6y + 2 hence making them equal.

6y - 2 = 50

6y = 50 - 2

6y = 48

y = 6

z) vertically opposite angles are equal hence the 50 will be equal to the empty space in the triangle.

z + 60 + 50 = 180

z + 110 = 180

z = 180 - 110

z = 70

2y + 3z

2(6) + 3(70)

12 + 210

= 222

Answer:

129

Step-by-step explanation:

The sum of all angles in any quadrilateral is 360°

so, you can make the following equation:

71 + 48 + 112 + x = 360

231 + x = 360

Subtract 231 from both sides of the equation

231 + x - 231 = 360 - 231

x = 360 - 231

x = 129

Step-by-step explanation:

The given image is a trapezium. A trapezium is a quadilateral. Hence , it's sum of angles is 360°

To solve for x ;

[tex]71° + 48° + 112 ° + x° = 360° \\ 231 + x = 360 \\ x = 360 - 231 \\ x = 129[/tex]