At the start of an experiment, there are 2,500 bacteria in a colony. The colony grows at a rate of 11% every hour. What will be the number of bacteria in the colony after n hours?

Answer:

-$336.00

Step-by-step explanation:

-$248.00+-$73.00+-$15.00=-$336.00

Answer:

The hotel charge in each city before tax was $5125 of the first city and $3625 of the second city.

Step-by-step explanation:

Given:

A theater group made appearances into cities the hotel charge before tax and the second city was 1500 higher than the first.

The tax of the first city was 6% and the tax of the second city was 10%.

Total hotel tax paid for two cities with $670.

Now, to find the hotel charge in each city before tax.

Let the hotel charge in first city before tax be [tex]x.[/tex]

And the hotel charge in second city before tax be [tex]y.[/tex]

So, as the hotel charge of the second city was 1500 higher than the first.

Thus,

[tex]y=x-1500[/tex]   ........(1)

And as given, the tax of the first city was 6% and the tax of the second city was 10%, total hotel tax paid for two cities with $670.

6% of [tex]x[/tex] + 10% of [tex]y[/tex] = $670.

[tex]\frac{6x}{100} +\frac{10y}{100} =670[/tex]

[tex]0.06x+0.10y=670[/tex]

Substituting the value of [tex]y[/tex] from equation (1) we get:

[tex]0.06x+0.10(x-1500)=670[/tex]

[tex]0.06x+0.10x-150=670[/tex]

[tex]0.16x-150=670[/tex]

Adding both sides by 150 we get:

[tex]0.16x=820[/tex]

Dividing both sides by 0.16 we get:

[tex]x=5125.[/tex]

The hotel charge in first city before tax = $5125.

Now, substituting the value of [tex]x[/tex] in equation (1) we get:

[tex]y=x-1500[/tex]

[tex]y=5125-1500[/tex]

[tex]y=3625.[/tex]

The hotel charge in second city before tax = $3625.

Therefore, the hotel charge in each city before tax was $5125 of the first city and $3625 of the second city.

[tex]-2\frac{1}{2} +1\frac{1}{3}=\frac{-1}{6}[/tex]

Solution:

Given expression is [tex]-2\frac{1}{2} +1\frac{1}{3}[/tex].

Let us first convert mixed fraction into improper fraction.

[tex]-2\frac{1}{2} +1\frac{1}{3}=\frac{(-2\times 2) +1}{2} +\frac{(1\times 3) + 1}{3}[/tex]

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

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

Take LCM for the denominators (LCM of 2, 3 = 6) and make the same.

              [tex]=\frac{-3\times3}{2\times3} +\frac{4\times2}{3\times2}[/tex]

              [tex]=\frac{-9}{6} +\frac{8}{6}[/tex]

              [tex]=\frac{-1}{6}[/tex]

[tex]-2\frac{1}{2} +1\frac{1}{3}=\frac{-1}{6}[/tex]

Hence the fraction form of [tex]-2\frac{1}{2} +1\frac{1}{3}[/tex] is [tex]\frac{-1}{6}[/tex].

Answer:

by definition

The coordinates of point A are:

(cosθ , sinθ)

The midpoint is [tex](\frac{1}{2}, \frac{13}{2})[/tex]

The distance between points S and T is 7.1 units

Solution:

Given points are S(−2, 4) and T(3, 9)

Find the coordinates of the midpoint of ST

The midpoint is given as:

[tex]m(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)[/tex]

Here in this sum,

[tex](x_1, y_1) = (-2, 4)\\\\(x_2, y_2) = (3, 9)[/tex]

Substituting the values, we get

[tex]m(x, y)=\left(\frac{-2+3}{2}, \frac{4+9}{2}\right)\\\\m(x, y)=\left(\frac{1}{2}, \frac{13}{2})[/tex]

Thus the midpoint is [tex](\frac{1}{2}, \frac{13}{2})[/tex]

Find the distance between points

The distance is given by formula:

[tex]d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}[/tex]

Here in this sum,

[tex](x_1, y_1) = (-2, 4)\\\\(x_2, y_2) = (3, 9)[/tex]

Substituting the values, we get

[tex]\begin{aligned}&d=\sqrt{(3-(-2))^{2}+(9-4)^{2}}\\\\&d=\sqrt{5^{2}+5^{2}}\\\\&d=\sqrt{25+25}\\\\&d=\sqrt{50}=7.071 \approx 7.1\end{aligned}[/tex]

Thus the distance between points S and T is 7.1 units

The coordinates of the midpoint [tex]\( M \) are \( (0.5, 6.5) \),[/tex] and the distance between points S and T approximately 7.0 units.

To find the coordinates of the midpoint M of the line segment ST, we use the midpoint formula:

[tex]\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]

 Given the coordinates of [tex]\( S \) and \( T \) are \( S(-2, 4) \) and \( T(3, 9) \)[/tex] respectively, we substitute these values into the formula:

[tex]\[ M = \left( \frac{-2 + 3}{2}, \frac{4 + 9}{2} \right) \][/tex]

[tex]\[ M = \left( \frac{1}{2}, \frac{13}{2} \right) \][/tex]

[tex]\[ M = (0.5, 6.5) \][/tex]

Now, to find the distance between points S and T,  we use the distance formula:

[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]

Substituting the coordinates of S and T into the formula:

[tex]\[ d = \sqrt{(3 - (-2))^2 + (9 - 4)^2} \][/tex]

[tex]\[ d \approx 5 \times 1.4 \][/tex]

[tex]\[ d \approx 7 \][/tex]

The coordinates of the midpoint  [tex]\( M \) are \( (0.5, 6.5) \),[/tex] and the distance between points S and T  is approximately 7.0 units.

Answer:

-x^2

Step-by-step explanation:

Answer:

-x^2

Step-by-step explanation:

Answer:

Step-by-step explanation:

The only possible simplification of the slope -5/1 is -5.

Answer:

Therefore the scale used is 1 inch : 6.667 inches

Step-by-step explanation:

i) Scale used is 9 inches = 5 feet

ii) Scale used 9 inches = 5 [tex]\times[/tex] 12 inches = 60 inches

iii) Scale used is 1 inch  [tex]= \dfrac{60}{9}\hspace{0.2cm} = \hspace{0.2cm}\dfrac{20}{3} \hspace{0.2cm} = 6.667\hspace{0.2cm} inches[/tex]

iv) Therefore the scale used is 1 inch : 6.667 inches

Answer:

54

Step-by-step explanation:

4.5x=3(x+27)

4.5x=3x+81

1.5x=81

x=54

The percent of the market will teddy bears occupy in November is 28.47%.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. With the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Form a table as shown

Months         Teddy Bears    Rabbits     Cats    Horses    Others    Totals toys

September      225                275           245      260          199        1204

October           346                 308           186      297          285       1422

November       467                 341            127       334          371         1640

So, the percent of the market will teddy bears occupy in November

= 467 / 1640 x 100

= 0.2847 x 100

= 28.47%

Learn more about Percentage here:

https://brainly.com/question/29306119

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Answer:

∠ U = 117°

Step-by-step explanation:

Since the triangles are congruent then corresponding angles are congruent.

∠ T = ∠ Q = 27°

The sum of the 3 angles in a triangle = 180°, thus

∠ U = 180° - (∠ s + ∠ T) = 180° - (36 + 27)° = 180° - 63° = 117°

Answer:

Your answer is C Straight angle

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

You only distribute the 3 to the x but not to 1 1/2. In order for the two equations to be the same, you have to distribute 3 to both the x and 1 1/2. Then the answer will look like this : 3x + 4 1/2 or 3x + 9/2

The original expression 3(x + 1 1/2) is not equivalent to 3x + 1 1/2; rather,it simplifies to 3x + 4.5 after distribution and simplification.

Step 1: Distribute the Number Outside the Parentheses:

To determine equivalence, distribute the 3 to both terms inside the parentheses: 3(x) + 3(1 1/2).

Step 2: Simplify Inside the Parentheses:

Multiply 3 by x: 3x.

Multiply 3 by 1 1/2: 3 × 1 + 3 × 1/2

= 3 + 1.5

= 4.5.

Step 3: Combine the Terms:

The distributed expression simplifies to 3x + 4.5.

Step 4: Evaluate the Expression in Question:

The expression provided is 3(x + 1 1/2).

The equivalent expression, as derived, is 3x + 4.5.

Step 5: Compare the Expressions:

The expression 3(x + 1 1/2) simplifies to 3x + 4.5, not 3x + 1 1/2.

Therefore, the original expression 3(x + 1 1/2) is not equivalent to 3x + 1 1/2; rather,it simplifies to 3x + 4.5 after distribution and simplification.

Answer: A. -14

Step-by-step explanation:

Answer: A. -14

Step-by-step explanation: Use PEMDAS

(5+4-2) x (-2)

= (9-2) x (-2)

= 7 x (-2)

= -14

Answer:

6. ○ [tex]\displaystyle 33,1°; 123,1°[/tex]

5. [tex]\displaystyle See\:above\:image[/tex]

4. [tex]\displaystyle See\:above\:image[/tex]

Explanation:

6. Supplementary Angles sum up to 180°, whereas complementary angles sum up 90°. So, use subtraction for both types of angles:

[tex]\displaystyle 123,1° = -56,9° + 180° \\ 33,1° = -56,9° + 90°[/tex]

* Make sure that they are in the exact same order that exercise gives you.

5. Acute Angles measure greater than 0° and less than 90°.

4. Every segment must have C in it, and you must be EXTREMELY CAREFUL of their markings [ray, segment, and line].

I am joyous to assist you anytime.

Answer:

1/3

Step-by-step explanation:

David cooks 6 cups of rice and his family eats 4 cups. To find the fraction, we must first do 6-4 to get 2. We place 2 in the numerator and 6 in the denominator. We have 2/6. We can simplify 2/6 by dividing both the numerator and the denominator by 2 to get 1/3.

Answer:

5) The correct answer is D.

6) The correct answer is A.

7) m = (10 - 6)/(1 - 0) = 4/1 = 4

The correct answer is C.

8) The correct answer is B.

Answer:

The Proof is below.

Therefore the Perimeter of Christmas paper is 32 feet  ..Proved

Step-by-step explanation:

Let the Christmas Paper have Dimensions as

Length = 8 feet

Width = 8 feet

To Show:

Perimeter of Christmas Paper = 32

Solution:

Christmas Paper is in Rectangle  Shape,

Therefore Perimeter of a Rectangle is given as

[tex]Perimeter\ of\ Rectangle=2(Length+Width)[/tex]

Substituting the values we get

[tex]Perimeter=2(8+8)=2\times 16=32\ feet[/tex]

Therefore the Perimeter of Christmas paper is 32 feet  ..Proved

The perimeter of a square is calculated by adding the lengths of all four sides. An 8 ft by 8 ft square has a perimeter of 32 ft, because 8 ft multiplied by 4 (the number of sides in a square) equals 32 ft.

This question involves understanding the concept of perimeter in the context of a square. If you have a piece of Christmas paper that is 8 feet long and 8 feet wide, you actually have a square because all sides are of equal length. To calculate the perimeter of a square, you simply add up the lengths of all four sides.

Since each side is 8 feet, the perimeter P is given by:

P = side + side + side + side
P = 8 ft + 8 ft + 8 ft + 8 ft
P = 32 ft

So, the perimeter of the Christmas paper, if shaped like a square, is 32 feet, which is simply four times the length of one side.

Answer:

14/25

Step-by-step explanation:

p(red or blue)=6/(6+8+11) +8/(6+8+11)=6/25+8/25=14/25

Answer:

56% yall

Step-by-step explanation:

m x H = [tex]\left[\begin{array}{ccc}-25&37.5&-12.5\\\9\end{array}\right][/tex]

Step-by-step explanation:

Step 1; Multiply 5 with this matrix  [tex]\left[\begin{array}{ccc}-1&2\\4&8\\\end{array}\right][/tex] and we get a matrix [tex]\left[\begin{array}{ccc}-5&10\\20&40\\\end{array}\right][/tex]

Multiply the fraction  [tex]\frac{2}{5}[/tex] with the matrix  [tex]\left[\begin{array}{ccc}-1&2\\4&8\\\end{array}\right][/tex] and we get [tex]\left[\begin{array}{ccc}-\frac{2m}{5} &\frac{4m}{5} \\\frac{8m}{5} &\frac{16m}{5} \\\end{array}\right][/tex]

Step2; Now equate corresponding values of the matrices with each other.

-5 = [tex]\frac{-2m}{5}[/tex] and so on. By equating we get the value of m as [tex]\frac{25}{2}[/tex]

Step 3; Add the matrices to get the value of matrix m.

Adding the three matrices on the RHS we get  [tex]\left[\begin{array}{ccc}2&9&-9\\\end{array}\right][/tex].

Step 4; Adding the matrices on the LHS we get the resulting matrix as H +

[tex]\left[\begin{array}{ccc}4&6&-8\\\9\end{array}\right][/tex]. Equating the matrices from step 3 and 4 we get the value of H as [tex]\left[\begin{array}{ccc}-2&3&-1\\\9\end{array}\right][/tex]

Step 5; Now to find the value of m x H we need to multiply the value of [tex]\frac{25}{2}[/tex] with the matrix [tex]\left[\begin{array}{ccc}-2&3&-1\\\9\end{array}\right][/tex]

Step 6; Multiplying we get the matrix m x H = [ -25  [tex]\frac{75}{2}[/tex]  [tex]\frac{-25}{2}[/tex] ]

Answer:

your answer is 70

Step-by-step explanation:

Answer:

x = 36.87 degrees.

Step-by-step explanation:

4 cos x + 3 sin x = 5    

Use the Auxiliary angle method:

R sin (α  + x) = R sin α cos x + R cos α  sin x

Comparing coefficients:

R sin α  = 4 and R cos α  = 3

R sin α / R cos α  = 4/3

So tan α  = 4/3

α  = 53,13 degrees.

Now R^2(sin^2 α + cos^2 α ) = 3^2 + 4^2 = 25

R^2 = 25

R = 5.

R sin (x + 53.13) = 5

5 sin ( x + 53.13) = 5

sin (x + 53.13) = 1

x  + 53.13 = 90

x = 36.87 degrees.

Answer:

Investor invested $7,800 at 8% and $6,200 at 6.5%

Step-by-step explanation:

Use formula

[tex]I=P\cdot r\cdot t,[/tex]

where

I = interest

P = principal

r = rate (as decimal)

t = time

First investment:

[tex]P_1=x\\ \\r_1=0.08\\ \\t_1=1[/tex]

then

[tex]I_1=x\cdot 0.08\cdot 1\\ \\I_1=0.08x[/tex]

Second investment:

[tex]P_2=14,000-x\\ \\r_2=0.065\\ \\t_2=1[/tex]

then

[tex]I_2=(14,000-x)\cdot 0.065\cdot 1\\ \\I_2=0.065(14,000-x)[/tex]

The amount of interest earned for 1 year was $1,027, then

[tex]I_1+I_2=1,027\\ \\0.08x+0.065(14,000-x)=1,027\\ \\0.08x+910-0.065x=1,027\\ \\0.08x-0.065x=1,027-910\\ \\0.015x=117\\ \\x=7,800\\ \\14,000-x=6,200[/tex]

Investor invested $7,800 at 8% and $6,200 at 6.5%

Answer:

6(26-4)= 132

Step-by-step explanation:

There isn't any variable in the equation

Answer:
it is proportional

Step-by-step explanation:

Proportional functions will be in the form y = kx and non-proportional functions will be in the form y = mx + b

Final answer:

The greatest common factor of 75 and 20 is 5, and by applying the distributive property, the expression 75+20 can be factored as 5(19).

Explanation:

The greatest common factor (GCD) of 75 and 20 is 5. Applying the distributive property to factor out 5, we get:

75 + 20 = 5 × (15 + 4)

Here's the breakdown:

Find the GCD: The largest factor that divides both 75 and 20 is 5.

Divide each term by the GCD: Divide 75 by 5 to get 15 and divide 20 by 5 to get 4.

Rewrite with the GCD factored out: Combine the results from step 2 and multiply by the GCD: 5 × (15 + 4).

Therefore, the factored expression using the distributive property is 5 × (15 + 4).

Thus, the factored form of the expression 75+20 is 5(19).

Answer:

[tex]PN=64\ units[/tex]

Step-by-step explanation:

The complete question is

Given the quadrilateral is a rectangle, if LO = 15x+19 and QN = 10x+2 find PN

see the attached figure to better understand the problem

we know that

The diagonals of a rectangle are congruent and bisect each other

so

[tex]QN=\frac{1}{2}LO[/tex]

substitute the given values

[tex]10x+2=\frac{1}{2}(15x+19)[/tex]

solve for x

[tex]20x+4=15x+19\\20x-15x=19-4\\5x=15\\x=3[/tex]

Find the length of PN

Remember that

[tex]PN=LO[/tex] ----> diagonals of rectangle are congruent

[tex]LO=15x+19[/tex]

substitute the value of x

[tex]LO=15(3)+19=64\ units[/tex]

therefore

[tex]PN=64\ units[/tex]