Magician Anthony has in his magic hat 14 grey, 8 white and 6 black mice. What is
the least number of mice he has to take out of his hat blindfolded to be absolutely
certain that he has got at least one mouse of each colour?

Answer:

a) -6

b) -9

c) 27

Step-by-step explanation:

Since a=-3, plug in -3 for a and solve.

Answer:

see explanation

Step-by-step explanation:

Using the identity

cos²Θ = 1 - sin²Θ

Consider the left side

sin²Θ - cos²Θ

= sin²Θ - (1 - sin²Θ ) ← distribute parenthesis by - 1

= sin²Θ - 1 + sin²Θ

= 2sin²Θ - 1

= right side , thus verified

Answer:

third answer

Step-by-step explanation:

solve for and isolate x by moving over all other numbers to the left and then take the fifth power to make x^1/5 = to x

Answer:

[tex]18=2^x[/tex]

Step-by-step explanation:

[tex]log_2(18)=x\\\\2^{log_2(18)}=2^x\\\\18=2^x[/tex]

Answer:

3

Step-by-step explanation:

7x² is the first term,

14x is the second term and

2 is the third term.

Problem 1

If you need to convert to a mixed number, then follow these steps.

27.2 = 27 + 0.2

27.2 = 27 + 1/5

27.2 = 27 & 1/5

27.2 pizzas is the same as 27 & 1/5 pizzas. In other words, you have 27 whole pizzas plus 1/5 of an extra one.

===========================================

Problem 2

The decimal 1.75 converts to the mixed number 1 & 3/4 because of the steps below.

1.75 = 1 + 0.75

1.75 = 1 + 3/4

1.75 = 1 & 3/4

In my opinion, it is optional to convert to a mixed number for either problem 1 or problem 2. So you can stick with 1.75 as the answer if you want.

===========================================

Problem 3

16 & 3/4 = 16 + 3/4 = 16 + 0.75 = 16.75

To get the unit rate, which is the cost per unit, we divide the total cost over the amount.

cost/amount = (2.89)/(16.75) = 0.1725373

which is approximate.

Round to the nearest penny to get a unit cost of $0.17 per fluid ounce, i.e. a unit cost of 17 cents per fluid ounce.

===========================================

Problem 4

We follow the same idea as problem 3.

4 & 3/5 = 4 + 3/5 = 4 + 0.6 = 4.6

unit cost = (total cost)/(amount)

unit cost = (7.56)/(4.6)

unit cost = 1.643478 dollars approximately

unit cost = 1.64 dollars approximately

===========================================

Problem 5

6 & 1/2 = 6 + 1/2 = 6 + 0.5 = 6.5

Like before, we'll divide the total cost over the total amount.

unit cost = (total cost)/(amount)

unit cost = (8.22)/(6.5)

unit cost = 1.264615 dollars approximately

unit cost = 1.26 dollars approximately

===========================================

Here's another way to look at the unit cost or unit rate.

Notice in problem 5 it says "cost per yard". This is the same as "cost per 1 yard" or "cost for each yard".

We can express the given info as the ratio

6.5 yards:$8.22

Now we want the "6.5 yards" to become "1 yard" to achieve the unit rate.

So we'll divide both parts by 6.5

6.5 yards:$8.22

6.5/6.5 yards:$8.22/6.5

1 yard: $1.26 approximately

For each yard, we'll spend $1.26

Problems 3 and 4 follow similar ideas. So this is why we divided the total cost over the total amount.

Answer:

Option B

Step-by-step explanation:

Given the following question:

53 oz = c?
[tex]1c=8oz[/tex]
[tex]53\div8=6.625[/tex]
[tex]6.625=\frac{6625}{1000}\div125=\frac{53}{8}[/tex]
[tex]\frac{53}{8} =53\div8=6\frac{5}{8}[/tex]
[tex]=6\frac{5}{8}[/tex]

Your answer is option B or "6 5/8 cups."

Hope this helps

Answer:

x=4.285714286

Step-by-step explanation:

Let the number be x

Now we have,

→ [tex]32-7x=2\\\\[/tex]

→ [tex]32-2=7x\\\\[/tex]

→ [tex]30=7x\\[/tex]

→ [tex]x=\frac{30}{7} \\[/tex]

→ x=4.285714286

Answer:

-10

Step-by-step explanation:

if negative meets a negative its gone come out as a positive

the answer is just 50° for both

Solution:

Given:

Let's substitute the values of Length, Breadth, and Height to obtain the volume of the tank.

Now, let's convert meters into liters.

Hoped this helped!

answer:

y = 3x + 5

steps-explanation:

given sample equation:

comparing to the formula of slope intercept form: y = mx + b

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

we can determine here that the slope is 3 and -1 is the y-intercept.

but here we need only the slope.

in parallel, the slope is same: 3

formula:                  

using the formula:                     [ here known that y1 is -1 and x1 is -2 ]

Linear functions are functions that change at a constant rate

The linear function that models the data is [tex]P(x) = 0.025x -49.695[/tex]

From the question, we have the following ordered pairs

(x,P(x)) = (2005,43%) and (2011,58%)

Start by calculating the slope (m)

[tex]m = \frac{P(x2) - P(x1)}{x_2 -x_1}[/tex]

So, we have:

[tex]m = \frac{58\% - 43\%}{2011 - 2005}[/tex]

Evaluate the differences

[tex]m = \frac{15\%}{6}[/tex]

Evaluate the quotient

[tex]m = 2.5\%[/tex]

The linear function is then calculated as:

[tex]P(x) = m(x - x_1)+ P(x_1)[/tex]

So, we have:

[tex]P(x) = 2.5\%(x - 2005) + 43\%[/tex]

Rewrite as:

[tex]P(x) = 0.025(x - 2005) + 0.43[/tex]

This gives

[tex]P(x) = 0.025x -50.125 + 0.43[/tex]

[tex]P(x) = 0.025x -49.695[/tex]

Hence, the linear function that models the data is [tex]P(x) = 0.025x -49.695[/tex]

Read more about linear functions at:

https://brainly.com/question/15602982

Answer:28.16

Step-by-step explanation:

A markup of 220% would bring 11 to 35.20, and a mark down of 20% would bring 35.20 to 28.16.

Your'e Welcome  (ФДФ) .

The solution to the trigonometric equation in the interval is given by:

[tex]x = \frac{\pi}{4}[/tex]

In this problem, the equation is given by:

[tex]\frac{1}{\sin{\theta}} = 2\cos{\theta}[/tex]

Applying cross multiplication, we have that:

[tex]2\sin{\theta}\cos{\theta} = 1[/tex]

Applying a trigonometric identity, we have that:

[tex]\sin{2x} = 1[/tex]

We have that on the interval [0, 2π), [tex]\sin{\left(\frac{\pi}{2}\right)} = 1[/tex]

Hence:

[tex]\sin{2x} = 1[/tex]

[tex]\sin{2x} = \sin{\left(\frac{\pi}{2}\right)}[/tex]

[tex]2x = \frac{\pi}{2}[/tex]

[tex]x = \frac{\pi}{4}[/tex]

For [tex]\frac{3\pi}{4}[/tex], we have that:

[tex]\sin{2x} = \sin{\left(\frac{3\pi}{2}\right)} = -1[/tex]

Hence only the first solution is correct.

More can be learned about trigonometric equations at https://brainly.com/question/24680641

Answer:

9, 30, 27

Step-by-step explanation:

To find the perimeter, you must add up each side. In this scenario, we know that the perimeter is 66 feet. We also know the sides, which are n, 3n+3 and 4n-9.

So, we must add the sides to get 66 feet.

n+3n+3+4n-9=66

Combine like terms, and solve:

(n+3n+4n)+(3+-9)=66

8n+-6=66

8n-6=66

n=9

So if n=9, we can easily find the value of the other sides.

3(9)+3=30 feet.

4(9)-9=27 feet

So, the sides are 9, 30, and 27 feet (in order).

Answer:

1[tex]\frac{4}{15}[/tex] of straw

Step-by-step explanation:

The total amount of straw and hay together is, [tex]4 \frac{2}{3}[/tex].

and the total amount of hay alone is, [tex]3\frac{2}{5}[/tex]

All you need to do is subtract the hay from the total, which gives you, the answer above.

Answer:

3884.4 is what percent of 46.8 is 8300

Answer:

yards: 14080

miles: 8

that's basically it

Answer:

14080 yards

Step-by-step explanation:

A yard is 1/1760 mile, meaning 1 mile = 1760 yards.

5 miles + 3 miles = 8 miles

8 miles to yards = ?

8 x 1760 = 14080.

The Sims family drove 14.08k yds or 14080 yards.

Answer:

230

Step-by-step explanation:

multiply 12 by 15 and add it onto the 50 to get your answer!

Have a good day!

Answer:

Step-by-step explanation:

im pretty sure its the 1st one

Answer:

[tex]y = -\frac54x -7[/tex]

Step-by-step explanation:

Slope:

Y-intercept:

y = -5/4x -7

-Chetan K

Answer:

I think its obtuse but I'm not sure

Answer:

it's obtuse because one of the angle is obtuse and other two are acute so it's obtuse angles triangle

Answer:

[tex] \frac{ - 2 - 1}{4 - 0} \\ \\ \frac{ - 3}{4} \\ \\ \frac{3}{ - 4} [/tex]

Answer:

10

Step-by-step explantion

Simplifying

2x + 3 + 25 = 3x + -17

Reorder the terms:

3 + 25 + 2x = 3x + -17

Combine like terms: 3 + 25 = 28

28 + 2x = 3x + -17

Reorder the terms:

28 + 2x = -17 + 3x

Solving

28 + 2x = -17 + 3x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3x' to each side of the equation.

28 + 2x + -3x = -17 + 3x + -3x

Combine like terms: 2x + -3x = -1x

28 + -1x = -17 + 3x + -3x

Combine like terms: 3x + -3x = 0

28 + -1x = -17 + 0

28 + -1x = -17

Add '-28' to each side of the equation.

28 + -28 + -1x = -17 + -28

Combine like terms: 28 + -28 = 0

0 + -1x = -17 + -28

-1x = -17 + -28

Combine like terms: -17 + -28 = -45

-1x = -45

Divide each side by '-1'.

x = 45

Simplifying

x = 45

Answer:

Step-by-step explanation:

Exterior angle is same as sum of two remote interior angles:

Answer:

2 rhombus

3 parallelogram