A bacteria culture contains 2000 bacteria and doubles every half hour, find the size of the bacterial population after 5 hours

Answers

Answer 1
To find the size of the bacterial population after 5 hours, we can first determine the number of half hours in 5 hours, which is 5 / 0.5 = 10 half hours.

Since the bacteria culture doubles every half hour, the size of the bacterial population after 1 half hour is 2000 * 2 = 4000 bacteria.

The size of the bacterial population after 2 half hours is 4000 * 2 = 8000 bacteria.

This pattern continues, so the size of the bacterial population after 10 half hours (or 5 hours) is 8000 * 2^(10-2) = 8000 * 2^8 = 8000 * 256 = 2048000 bacteria.

Thus, the size of the bacterial population after 5 hours is 2048000 bacteria.

Related Questions

Given: KM and JN bisect each other
Prove: JK || MN

Answers

Answer:

JN

Step-by-step explanation:

help please no need to do alot of steps

Answers

[tex]x = \sqrt{\frac{z-3y^{2}+9 }{3} }[/tex]   ,   [tex]x = -\sqrt{\frac{z-3y^{2}+9 }{3} }[/tex]

Step-by-step explanation:

[tex]z= -9+3x^{2} +3y^{2} : x= \sqrt{\frac{z-3y^{2}+9 }{3} } ,x = - \sqrt{\frac{z-3y^{2}+9 }{3} }[/tex]

[tex]z= -9+3x^{2} +3y^{2}[/tex] :   [tex]-9+3x^{2} +3y^{2} =z[/tex]

[tex]-9+3x^{2} = z- 3y^{2}[/tex]

[tex]3x^{2} = z - 3y^{2} +9[/tex]

[tex]\frac{3x^{2} }{3} = \frac{z}{3} - \frac{3y^{2} }{3} + \frac{9}{3}[/tex]

[tex]x^{2} = \frac{z-3y^{2}+9 }{3}[/tex]

for [tex]x^{2} =[/tex][tex]f(a)[/tex] the solutions are [tex]x= \sqrt{f(a)} , -\sqrt{f(a)}[/tex]

[tex]x = \sqrt{\frac{z-3y^{2}+9 }{3} }[/tex]  ,  [tex]x = -\sqrt{\frac{z-3y^{2}+9 }{3} }[/tex]

[tex]x = i \sqrt{\frac{z+2y^{2}-5 }{2} } , x = -i \sqrt{\frac{z+2y^{2}-5 }{2} }[/tex]

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Let f : Z -> Z be defined by f(x) = x^2 + 1, and let C = {1, 2, 3}.

Find f(C), f^-1(C), f^-1 (f(C)) and f(f^-1 (C)).

Answers

We take the inverses of the function and get the results as follows:

[tex]f(1)=1+1=2\\f^{-1}(1)=\sqrt{1-1}=0\\f^{-1}(f(1))=\frac{\sqrt{\sqrt{4(1)+1} -3}}{\sqrt{2} } \\f(f^{-1} (1))=1[/tex],  [tex]f(2)=4+1=5\\f^{-1}(2)=\sqrt{2-1}=1\\f^{-1}(f(2))=\frac{\sqrt{\sqrt{4(2)+1} -3}}{\sqrt{2} } \\f(f^{-1} (2))=2[/tex], [tex]f(3)=9+1=\sqrt{10} \\f^{-1}(3)=\sqrt{3-1}=\sqrt{2} \\f^{-1}(f(3))=\frac{\sqrt{\sqrt{4(3)+1} -3}}{\sqrt{2} } \\f(f^{-1} (3))=3[/tex]

What are the inverses of a function?

A function that can change into another function is referred to as being inverse or anti. In other words, the inverse of any function "f" will take y to x if it takes x to y in the first place. The inverse function is indicated by  F^-1 if the function is denoted by F.

Given C={1,2,3}, and

[tex]f(x)=x^{2} +1\\ f^{-1}(x)=\sqrt{x-1} \\f^{-1}(f(x))=\frac{\sqrt{\sqrt{4(x)+1} -3}}{\sqrt{2} } \\f(f^{-1} (x))=x[/tex]

Now,

For C=1,

[tex]f(1)=1+1=2\\f^{-1}(1)=\sqrt{1-1}=0\\f^{-1}(f(1))=\frac{\sqrt{\sqrt{4(1)+1} -3}}{\sqrt{2} } \\f(f^{-1} (1))=1[/tex]

For C=2

[tex]f(2)=4+1=5\\f^{-1}(2)=\sqrt{2-1}=1\\f^{-1}(f(2))=\frac{\sqrt{\sqrt{4(2)+1} -3}}{\sqrt{2} } \\f(f^{-1} (2))=2[/tex]

For C=3

[tex]f(3)=9+1=\sqrt{10} \\f^{-1}(3)=\sqrt{3-1}=\sqrt{2} \\f^{-1}(f(3))=\frac{\sqrt{\sqrt{4(3)+1} -3}}{\sqrt{2} } \\f(f^{-1} (3))=3[/tex]

Hence, the solution is provided.

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A cable company offers its customers two plans.
- Plan A costs $135 per month plus $15 for each premium channel.
- Plan B uses the equation C=5 p+180 to determine the cost, where C represents the total cost and p represents the number of premium channels.
If a customer wants 5 premium channels, which statement comparing the cost of Plan A and Plan B is true?
A. Plan A will cost $5 less than Plan B.
B. Plan A will cost $10 less than Plan B.
C. Plan A will cost $5 more than Plan B.
D. Plan A will cost $10 more than Plan B.

Answers

After solving the equation we can say that Plan A will cost $10 more than Plan B. So, D is the Correct answer

What is an Equation?

A statement that affirms the equality of two expressions connected by the equals sign "=" is known as an equation.

For illustration, 2x - 5 = 13.
The two most well-known groups of equations in algebra are the linear

equations and the polynomial equations.
P(x) = 0 can be used to represent polynomial equations with a single variable. P is a polynomial, and axe + b = 0 is the standard form for linear equations.

Here, the parameters a and b. To solve these equations, we can use geometric or computational techniques from linear algebra or mathematical analysis. There are several sorts of equations

as well, including:

linear algebra quadratic formulas cube-based equations linear equations Equations that differ Statistical equations

Plan A:- $135 + $15(no. of premium channel)
Plan A for 5 premium channels will be
=$135 + $15(5)
= $135 + $75
=$210

Plan B:-
equation
C=$(5p+180)  
p = no. of premium channel
Plan B for 5  premium channels will be equation
C = $25 + $180
= $205

Thus,
Plan A will cost $5 more than Plan B
As Plan A cost $210 and Plan B cost $205

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The fraction 5/7 is equivalent to what percent? Round your percent to the nearest tenth.

Answers

Answer:

the fraction 5/7 is equivalent to approximately 71.4%

Step-by-step explanation:

if you divide 5/7, you'll get an answer like 0.71428

to convert decimals to fractions, you have to multiply by 100 to get 71.428

to round to the nearest tenth, round the 2 up to 3

71.43

and then, round 4 down

71.4%

hope this helped!

Question 12 (1 point) In order for this ratio of volumes to be true, what measurements would have to be equal in all 3 solids?
the three solids are cylinder, cone, and sphere

a The radius and the surface area
b The volume and the height
c The surface area and the base
d The radius and the height

Answers

Answer:

Step-by-step explanation:

In order for the ratio of volumes of a cylinder, cone, and sphere to be true, the radius of each solid would have to be equal. This is because the radius is a factor in the volume formulas for all three solids:

Volume of cylinder: πr^2h

Volume of cone: (1/3)πr^2h

Volume of sphere: (4/3)πr^3

If the radius is equal in all three solids, then the volumes will be in the same ratio as the given ratio, regardless of the values of h or the surface area. Therefore, the correct answer is : The radius and the height.

I know, the answer is A.

I need some help, explaining how the answer is A although, I have a bit of a rational mind when it comes to explaining stuff unfortunately.

Answers

On solving the question, by the help of angle sum property of triangle, we got that x= 14

What is Triangle?

Having three edges and three vertices, a triangle has three sides. The most significant characteristic of triangles is the fact that their interior angles add up to 180 degrees.

According to sides, what are the three different types of triangles?

Scalene, isosceles, and equilateral triangles are the three types of triangles that can have three sides.

Now, value of x is -

(x+27)° + 70° + (x + 55)° = 180° ( Sum of  al angles in a triangle is 180°)

2x + 152 = 180°

2x = 28

x=14

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Courtney made 3 withdrawals of equal amount from her savings account. The equation below can be used to determine x the amount in dollars of each withdrawal. What was the amount in dollars of each of Courtney’s withdrawals?

Answers

By solving the given equation, we know that Courtney withdrawals $25.75 each time from her bank account.

What are equations?

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

A formula would be 3x - 5 = 16, for instance.

When this equation is solved, we discover that the value of the variable x is 7.

So, we have the equation:

400-3x=322.75

Now, solve the equation for x to get the amount Courtney withdrawals each time:

400-3x=322.75

-3x = 322.75 - 400

-3x = -77.25

x = -77.25/-3

x = $25.75


Therefore, by solving the given equation, we know that Courtney withdrawals $25.75 each time from her bank account.

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Complete question:
Courtney made 3 withdrawals of equal amounts from her savings account. The equation below can be used to determine x, the amount in dollars of each withdrawal.

400-3x=322.75

What was the amount in dollars of each of Courtney's withdrawals?

answer choices

a. $24.09

b. $25.75

c. $74.25

d. $77.25

Please help!
A basketball has the radius of 13 inches
What is the volume?

Answers

Answer:

9203 in.³

Step-by-step explanation:

V = (4/3)πr³

V = (4/3) × 3.14159 × (13 in.)³

V = 9203 in.³

Judy wants to buy a sandwich platter. Every 6 inches of sandwich costs $2.50. What is the total
cost in dollars if Judy buys 18 inches?

Answers

Answer:

[tex]\huge\boxed{\sf \$ 7.50}[/tex]

Step-by-step explanation:

Given that,

6 inches of sandwich = $2.50

Multiply 3 to both sides

6 × 3 inches of sandwich = $2.50 × 3

18 inches of sandwich = $7.50

[tex]\rule[225]{225}{2}[/tex]

if you use a 0.05 level of significance in a​ two-tail hypothesis​ test, what decision will you make if ZSTAT​- -1.71?

Determine the decision rule. Select the correct choice below and fill in the answer​ box(es) within your choice.
​(Round to two decimal places as​ needed.)
A.
Reject H0

enter your response hereZSTAT

enter your response here.
B.
Reject H0 if ZSTAT

enter your response here.
C.
Reject H0 if ZSTAT

enter your response here.
D.
Reject H0 if ZSTAT

enter your response here or ZSTAT

enter your response here.

Answers

A hypothesis is an assumption, an idea that is proposed for the sake of argument so that it can be tested to see if it might be true.

What is the relation between the p-value and the conclusion of the test hypothesis?A hypothesis expresses your predictions about what your research will uncover. It is an untested preliminary answer to your research question. For some research projects, you may be required to write several hypotheses that address different aspects of your research question. It depends on whether the p-value is less or greater than the significance level.

According to the statement, the value of Z-Stat is +2.10. And we must find the P value when H0 is rejected only in the upper tail. The Z-stat is defined as the Z-score, which indicates how much a given value differs from the standard deviation.

The Z-score, also known as the standard score, is the number of standard deviations a given data point is above or below the mean.

And we know that the P-Value is calculated by converting your statistic into a Z-Score.

As a result, the p value is 0.0179.

So, When ZSTAT = +2.10, the resulting P-Value is 0.0179.

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an exploring ship is pulling up a diver at the rate of 25 feet per minute. The diver is currently 100 feet below the sea level. How deep was the diver 15 minutes ago?

Answers

equation: 25x+100
and x=minutes
so 25 minutes multiplied by 15 is 375 and he’s 100 below right now so 375+100=475 therefore he was 475ft. below sea level

To celebrate Ripton's bicentennial fireworks are launched off a dam 36 ft above Lake Marley. The height of a display t seconds after it has been launched is given by h 16 64 36. After how long will the shell from the fireworks reach the water?

Answers

The shell from the fireworks will reach the water after 0.75 seconds or -0.625 seconds. Since the time cannot be negative, the shell will reach the water after 0.75 seconds.

How to find time ?

To find the time it takes for the shell from the fireworks to reach the water, we need to solve the equation h = 0 for t.

The given equation for h is h = -16t^2 + 64t + 36, so we can substitute this into the equation h = 0 to get:

0 = -16t^2 + 64t + 36

To solve this equation, we can use the quadratic formula, which is:

t = (-b +/- sqrt(b^2 - 4ac)) / (2a)

In this case, a = -16, b = 64, and c = 36, so the formula becomes:

t = (-64 +/- sqrt(64^2 - 4(-16)(36))) / (-32)

Simplifying this gives us:

t = (-64 +/- sqrt(4096 - 2304)) / (-32)

which simplifies to:

t = (-64 +/- sqrt(1792)) / (-32)

Finally, simplifying gives us:

t = (-64 +/- 44) / (-32)

t = (-20 or 24) / (-32)

t = -0.625 or 0.75

Thus, the shell from the fireworks will reach the water after 0.75 seconds or -0.625 seconds. Since the time cannot be negative, the shell will reach the water after 0.75 seconds.

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Solve the following inequality and graph the solution:
(x-4)(x-5)<0
Choose test values and indicate whether the inequality is true or false in each region.
Enter the test values from smallest to largest.

Answers

The smallest to largest test values of the inequality (x-4)(x-5)<0 are  

(-infinity,4) , (4,5) & (5,+infinity)

What is a inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using the inequality symbols.

A difference between two values indicates whether one is smaller, larger, or simply not equal to the other.

"A connection is termed an inequality if two real numbers or algebraic expressions are connected by the symbols ">," "," "," or "."

(x-4)(x-5)<0

x-4<0             or             x-5<0

x<4                or              x<5

1)

for False the test values of the inequality (x-4)(x-5)<0  from smallest to largest Lies in between (-infinity,4)

2)

for True the  test values  of the inequality (x-4)(x-5)<0 from smallest to largest Lies in between (4,5)

3)

for True the  test values of the inequality (x-4)(x-5)<0  from smallest to largest Lies in between (5,+infinity)

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Match each system on the left with all words that describe the system on the right. Choices on the right can be used
more than once.
2x = y + 3
y = - 2x + 1

2x = y + 3
2y - 4x = -6

2x = y + 3
2y - 4x = 6

inconsistent
consistent
independent
dependent

Answers

Matching the equation to choices

equation                                                classifications

2x = y + 3 and y = - 2x + 1                       consistent and independent

2x = y + 3 and 2y - 4x = -6                     consistent and dependent

2x = y + 3 and 2y - 4x = 6                       inconsistent

What are inconsistent equations?

A system is considered to be inconsistent if there is no solution. There is no solution because the line graphs are parallel and do not overlap.

2x - y = 3... equation * 2

4x - 2y = 6

-4x + 2y  = 6

subtracting gives

8x - 4y = 0

no solution  

What are consistent and independent equations?

A system is deemed consistent if it has at least one solution.

A consistent system is independent if it only has one solution.

y = 2x - 3

y = -2x + 1

subtracting gives

0 = 4x - 4

x = 1

substituting x to get y

y = -1

What are consistent and dependent equations?

A consistent system is dependent if there are an endless number of possible solutions. The two equations represent the same line when you graph them.

-y + 2x =  3 .... equation * 2

-2y + 4x =  6

2y - 4x = -6  

subtracting gives

-4y + 8x = 12 - none cancels out meaning infinite number of possible solutions

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Given m∠1≅m∠2
Proof m∠3≅m∠4
Complete the flow chart to proof m∠3≅m∠4

Answers

The flow chart to prove m∠3≅m∠4 is given below.

What is the vertical angle theorem?

The Vertical Angle Theorem states that when two straight lines cross, they create two linear pairs. Due to the fact that their angles add up to 180 degrees, the adjacent angles created when two lines intersect are known as supplementary angles.

Given, m∠1≅m∠2

Then, m∠1≅m∠3 ( vertical angles theorem)

m∠2≅m∠3 (Given)

Then, m∠2≅m∠4 (vertical angle theorem)

Hence, m∠3≅m∠4 (transitive property of congruence) proved

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Dontrell bought 51/2 pounds of potatoes for $3.52. What equation can be used to represent the total amount he paid, y, for x pounds of potatoes?
Enter the correct equation in the box.

Answers

The equation that represents the the total amount he paid, y, for x pounds of potatoes is y = 0.64x.

How to use equation to represent the total amount paid?

Dontrelle bought [tex]5\frac{1}{2}[/tex] pounds of potatoes for $3.52.

The equation that can be used to represent the the total amount he paid, y, for x pounds of potatoes is as follows:

rate = amount paid / weight in pounds

amount paid = $3.52

weight of potatoes = 11 / 2 pounds

rate = 3.52 ÷11 / 2

rate = 3.52 × 2  / 11

rate = 7.04 / 11

rate = 0.64 dollars per pound.

Therefore, the equation is y = 0.64x

where

x = pounds of potatoesy = amount paid

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(-4)³·7⁰
_____ this a fraction!
(-1³)

Answers

This is my answer I hope it help:))

25% of 24 is what number

Answers

Answer: 6

Step-by-step explanation: you can ask siri

25% of 24 is 6

Multiply 24 x 0.25

7.1.1 use the results of section 3.7 to show that each member of isom (r2) is either a translation or a rotation. 7.1.2 why does an isometry map any circle to a circle? we took care to write the inverse of the isometry r1r2r3 as r3r2r1 because only this ordering of terms will always give the correct result. 7.1.3 give an example of two reflections r1 and r2 such that r1r2

Answers

Every isometry can be expressed as composition of reflection and translation only. Also the composition of isometries is isometry. each member of ISOM+R² is either a translation or rotation.

Given that,

Show that each component of isom (r²) is either a translation or a rotation using the findings from section 3.7.

An isometry of R² is a mapping T:R²⇒R² which preserves distance.

The formula for the distance between x and y is

d(x,y)=|y-x|=√(y₂-x₂)²+(y₁-x₁)²

The preservice means,

d(x,y)=d(T(x),T(y))

A translation is an isometry.

Since,

d(Tv(x),Tv(y))=|(xv)-(y-v)|=d(x,y)

The rotation matrix, for rotating by an angle Θ, is defined as,

cosΘ     -sinΘ

sinΘ       cosΘ

Therefore, every isometry can be expressed as composition of reflection and translation only. Also the composition of isometries is isometry. each member of ISOM+R² is either a translation or rotation.

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Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices. Josiah’s Music Sample 1 Sample 2 R & B 5 R & B 4 Pop 4 Pop 3 Classical 3 Classical 5 Jazz 2 Jazz 4 Rock 6 Rock 4 Josiah’s work: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.

Answers

Based on the information in the fragment, it can be inferred that Josiah's mistake is that he did not multiply the numerator and denominator by the correct number to equal 1,500 (option B). So, the correct statements are A, C, and D.

How to find the ratio?

To find the proportion in this problem we have to do the following procedure:

The first step is multiply both sides by 1500.The second step is to evaluate the expression on the right-hand side.The third step is multiply 10 by 1500 on the left-hand side.The fourth step is divide 15000 by 20 on the left-hand side.

Once we have carried out the previous steps we must continue the procedure rewriting the equation with the data obtained previously. With this information we can conclude that Josian had the necessary information to discover how many songs of each genre were played during an hour on his MP3, however he performed the wrong procedure so his result was wrong.

According to the above, we can infer that the products are not well carried out. So, Josiah's mistake is no multiplying the numerator and denominator by the correct number to equal 1,500 (option B).

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Anybody good at statistics that’s can help outside of here?

Answers

I'm here trying to help my 12 yr old

Organize the angles from largest to smallest.

Answers

Second one. If I’m not mistaken, the angle is the opposite so if q is the smallest, then L would be the replacement.

{ (-3, 4), (7,5), (13, — 7), (15, 4) }

Answers

Answer:

Step-by-step explanation:

0

GIVING BRAINLIEST!!!
What fraction is shown on the number line?

A. 2 over 3
B. 1 over 3
C. 2 over 4
D. 3 over 4

Answers

Answer:

a

Step-by-step explanation:

Answer:a

Step-by-step explanation:

Cameron invests money in a bank account
which gathers compound interest each year.
After 4 years there is $736.80 in the account.
After 7 years there is $788.82 in the account.
Work out the annual interest rate of the bank
account.
Give your answer as a percentage to 1 d.p.

Answers

The annual interest rate of the bank account is 2.3%

Let's check the equation for each year.

Compound Interest earned amount

A = P( 1 + r/n)ⁿˣ

A = accumulated amount

P =  original amount deposited

r =  interest rate

n = times it compounds per year

x = years

when Amount = $736.80, x = 4 years and r% → r/100

736.80 = P(1 +[(r/100)/1] ¹×⁴

736.80 = P(1 + r/100)⁴

when Amount =$788.82 , x = 7 years and r% → r/100

788.82 = P(1 +[(r/100)/1] ¹×⁷

788.82 = P(1 + r/100)⁷

using the 1st equation:

736.80 = P(1 + r/100)⁴

P = 736.80 /[(1 + r/100)⁴]

Substitute on the Using 2nd equation

788.82 = P(1 + r/100)⁷

788.82 =  736.80 /[(1 + r/100)⁴] * (1 + r/100)⁷

788.82 =  736.80 * [(1 + r/100)⁷/(1 + r/100)⁴]

788.82 = 736.80 * (1 + r/100)³

788.82/736.80 = (1 + r/100)³

∛788.82/736.80 = ∛ (1 + r/100)³

∛788.82/736.80 = (100 + r)/100

100 ∛788.82/736.80 = 100 + r

100 ∛788.82/736.80 - 100 = r

r ≈ 2.3%

Hence, the annual interest rate of the bank account is 2.3%

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Sarah and her friends are going blueberry picking. Sarah picks $b$ blueberries. Michael picks $3$ more than half as many as Sarah, and David picks $5$ more than Michael. In addition, Kaycee picks $10$ less than $3$ times as many as David, and Hannah picks twice as many as Kaycee. Find an expression in terms of $b$ for the number of blueberries that Hannah picked.

Answers

Answer:  

~ Sarah = b

!!!Michael = 1/2*b + 3

~~David = b/2 + 8

!!!Hannah = 3b + 28

~~~~~Sarah = 3b/2 + 14

To allow last minute christmas shopping silverburn shopping centre is opening from 8am till midnight on Monday to Saturdays and 8am till 10pm on sundays. How many hours is it open in one week

Answers

The store would be open a total of 117 hours in one week

There were 500 sweets in a box and Mrs. Miller has given out 35% as prizes. How many are left in
the box?

Answers

Answer: 325

Step-by-step explanation:

Lets rewrite this.

35% of sweets are given out of 500.

35% of 500.

35% = 0.35

0.35 x 500 = 175

This means 175 prizes were given. Now we have to subtract.

500 - 175 = 325

Use elimination to solve the system of equations.
4y+3z=-6
y12=15
How can you eliminate the z-terms in this system?
4y+3z=-6
y-z=-5 +
Multiply by ? on both sides.
2
3
4
5

Answers

The solution to the system of equations is (y,z) = (-23/11, 33/11).

What is the system of equations?

A system of equations is a set of one or more equations involving a number of variables. The solutions to systems of equations are the variable mappings such that all component equations are satisfied in other words, the locations at which all of these equations intersect.

To eliminate the z-terms in this system, you can multiply the first equation by 3 and the second equation by -1 and then add the resulting equations together. This will give you an equation in terms of only y, which you can then solve for y.

The resulting equation will be:

(4y + 3z) * 3 + (y - z) * -1 = (-6) * 3 + (-5) * -1

12y - 3z - y + z = -18 - 5

Combining like terms, we get:

11y = -23

Dividing both sides by 11, we get:

y = -23/11

Now that we have solved for y, we can substitute this value back into one of the original equations to solve for z. For example, substituting -23/11 for y in the first equation gives us:

4(-23/11) + 3z = -6

Solving for z, we get:

z = 33/11

Hence, the solution to the system of equations is (y, z) = (-23/11, 33/11).

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