There are 500 sheets in a pack of paper. 500 sheets of paper weigh 2.5kg.
Work out the weight of 50 sheets of paper.

Answer:

Select the correct answer.

Scientists studying biodiversity of amphibians in a rain forest have discovered that the number of species is decreasing by 2% per year. There are currently 74 species of amphibians in the rain forest. Which logarithmic function models the time, , in years, it will take the number of species to decrease to a value of n?

The answer is D.

Step-by-step explanation:

The logarithm function that models the time, f(n) , in years is [tex]\rm f(n) = log_{0.98} (\dfrac{n}{74})[/tex], the correct option is D.

An exponential function can be represented in the form f(x) = abˣ.

The number of species is decreasing by 0.02

Current number of species = 74

The time f(n) years is given by

f(n) = 74 (0.98)ⁿ

Converting exponent to logarithm form

x = aⁿ

y = logₓ a

f(n) = 74 (0.98)ⁿ

[tex]\rm f(n) = log_{0.98} (\dfrac{n}{74})[/tex]

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A) y intercept is (0,3)

C) Axis of symmetry is x = -1

D) Vertex is (-1, 4)

So basically everything but choice B is true.

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

Explanation:

Choice A is true because plugging in x = 0 leads to y = 3. Effectively, anything with an x goes away when x = 0 leaving that 3 behind. So finding the y intercept in this form is fairly fast.

-------------------

To check choices B through D, let's convert the equation into vertex form.

y = -1x^2 - 2x + 3 is in the form y = ax^2 + bx + c where

a = -1

b = -2

c = 3

The vertex is located at (h,k) such that h = -b/(2a)

Plug the values of 'a' and 'b' into the equation below

h = -b/(2a)

h = -(-2)/(2*(-1))

h = 2/(-2)

h = -1

The x coordinate of the vertex is x = -1

Then use this to find the y coordinate of the vertex

y = -1x^2 - 2x + 3

y = -1(-1)^2 - 2(-1) + 3

y = 4

The y coordinate of the vertex is 4, meaning k = 4

The vertex overall is (h,k) = (-1, 4)

This shows choice D is true, meaning choice B has to be false.

Choice C is true because the axis of symmetry is the x coordinate of the vertex. This is the vertical line that cuts the parabola into two mirrored halves. This vertical line always goes through the vertex.

Answer:

1. 36

2. 90

3. 9

4. 6

Step-by-step explanation:

Answer:

Step-by-step explanation:

y=2x+1

y=x^2

The other one isn't a function because it won't pass the vertical line test. You can not use the same X in a function.

Answer:

Step-by-step explanation:

Associative property of multiplication:

It makes calculations easier by by grouping easy ones. Applying to given expression:

Answer:

(6*3/2)1/5

Step-by-step explanation:

A-P-E-X

3.6.2 CST

Answer:

Create a proportion.

[tex]\frac{5}{6} = \frac{305}{x}\\[/tex]

This proportion is saying,

"If 5 corresponds to 6, then 305 corresponds to what?"

Cross multiply.

5x = 305(6)

5x = 1830

x = 1830 / 5

x = 366

So, the shadow of the statue should be 366 feet.

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

Explanation:

Inscribed angle ADB subtends the minor arc AB. Inscribed angle ACB subtends the same minor arc AB. The rule is that if two inscribed angles subtend the same arc, then they are the same measure.

We can prove this with the inscribed angle theorem which says

central angle = 2*(inscribed angle)

Let's say point E is the center of the circle. By the inscribed angle theorem, we know that,

angle AEB = 2*(angle ADB)

angle AEB = 2*43

angle AEB = 86

Then we go in reverse of this process to find angle ACB

angle AEB = 2*(angle ACB)

86 = 2*(angle ACB)

2*(angle ACB) = 86

angle ACB = 86/2

angle ACB = 43

So this is how we prove the two inscribed angles are congruent.

Theres supposed to be a picture i think.

Answer:

I think it's D

Step-by-step explanation:

Answer:

what's is the answer I need help I'm begging you guys please help me

Answer:

1680 girls

Step-by-step explanation:

if the amount of boy is 5/1200 you divide 5 by 1200 to get 240 so multiply 240 by 7

Answer:

-70b+22

Step-by-step explanation:

Simplify each term

apply the distributive property

2-10(7b)-10 *2

multiply 7 by -10

2-70b+-10*-2

multiply -10 by -2

2-70b+20

add 2 and 20

-70b+22

Answer:

54

Step-by-step explanation:

1/4 of 72 is 18

72-18=54

Answer:

She would give her friend 54 sweets. I hope this is right, sorry if it's not.

Step-by-step explanation:

1/4 = 0.25

72*0.25 = 18

72 - 18 = 54

Answer: it’s not 5 I got that wrong

Step-by-step explanation:

y-intercept of function f is 1.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given function

f(x) = -3x -2 , -∞ < x < -2

     = -x + 1, -2 ≤ x < 3

     = 2x + 5, 3 ≤ x < ∞

For y-intercept, x =0, f(x) = -x + 1                   [∵ -2 < 0 < 3]

f(0) = -0 + 1

= 1

Hence, y-intercept of function f is 1.

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Answer:

I think its 3 but im not sure

Step-by-step explanation:

2x-1 you would do the opposite so you would add 1 to both sides. That would cancel the -1. Which leaves you with 3x

Answer:

126

Step-by-step explanation:

x=24

140-24= 126

[tex]d. \: \frac{hi}{eg} = \frac{ij}{jk} [/tex]

dont forget to follow me

Answer:

Slope=2

x−intercept=−  

2

4

​  

=−2

y−intercept=  

1

4

​  

=4.00000

Step-by-step explanation:

Answer:

I am thinking that the answer is B.

Step-by-step explanation:

Answer:

we conclude that an inequality 'c ≥ 5' denotes this situation.

Step-by-step explanation:

Given

When we talk about 'at least', it means we are talking about '≥' in terms of representing the 'at least' in inequality symbol.

For instance,

'm≥n' means 'm' is greater than or equal to 'n'.

It means 'm' is at least equal to 'n'.

Coming back to the question,

As the car dealer ship sells at least 5 minivans. so the

inequality will be: c ≥ 5

Thus, we conclude that an inequality 'c ≥ 5' denotes this situation.

Answer:

y = 2/3x + 4

Step-by-step explanation:

Let the equation of the line be y = mx + c

m = (2-8)/(-3-6) = 2/3

sub (6, 8):

8 = 2/3(6) + c

c = 4

the equation if the line is y = 2/3x + 4

This is a question on coordinate geometry. If you wish to venture further into it/understand this topic better, you may want to follow my Instagram account (learntionary), where I post some of my own notes on certain topics and also some tips that may be useful to you :)

Answer: y=17-5x/-9

Step-by-step explanation: 5x-9y=17

-9y=17-5x

Y=17-5x/-9

You can’t go any further than that because you can’t combine unlike Terms on the right side of the equation.

[tex]\text {Hey! Let's Solve this Equation!}[/tex]

[tex]\text {\underline {The First Step is to Add 17}}[/tex]

[tex]\text {3w-17+17=4+17}[/tex]

[tex]\text {3w=21}[/tex]

[tex]\text {\underline {The Final Step is to Divide 3}}[/tex]

[tex]\text {3w/3=21/3}[/tex]

[tex]\text {Your Answer Would Be:}[/tex]

[tex]\Huge\boxed {w=7}[/tex]

[tex]\text {Best of Luck!}[/tex]

Answer:

[tex]\boxed{\sf{w=7}}[/tex]

Step-by-step explanation:

To find the value of w, isolate it on one side of the equation.

Add by 17 from both sides.

3w-17+17=4+17

Solve.

Add the numbers goes from left to right.

4+17=21

3w=21

Divide by 3 from both sides.

3w/3=21/3

Solve.

Divide the numbers from left to right.

21/3=7

w=7

I hope this helps! Let me know if you have any questions.

Answer:

20 kph

Step-by-step explanation:

Step 1:

10 : 30         Ratio

Step 2:

60 mins in hour        

Step 3:

10 : 30 = x : 60        Equation

Step 4:

30x = 600       Multiply

Step 5:

x = 600 ÷ 30         Divide

Answer:

x = 20

Hope This Helps :)

Answer:

[tex] \huge{ \boxed{ \bold{ \tt{m \angle \: abc \: = 35 \degree}}}}[/tex]

Option C is the best choice.

Step-by-step explanation:

✺ First , Let's know about Corresponding angles :

✎ Now, In our case , x ° and ( 3x - 70 ) ° are corresponding angles. Set up an equation and solve for x.

[tex] \sf{x = 3x - 70\: ( \: being \: corresponding \: angles})[/tex]

[tex] \longrightarrow{ \sf{x - 3x = - 70}}[/tex] { Move 3x to left hand side and change it's sign )

[tex] \longrightarrow{ \sf{ - 2x = - 70}}[/tex] { Combine like terms }

[tex] \longrightarrow{ \sf{ \frac{ - 2x}{ - 2} = \frac{ - 70}{ - 2} }}[/tex] { Divide both sides by -2 }

[tex] \longrightarrow{ \sf{x = 35}}[/tex]

The value of x is 35°

Now, As we are asked to find the value of m [tex] \angle[/tex] ABC , replace the value of x :

[tex] \sf{m \angle \: ABC \: = (3x - 70) \degree}[/tex]

[tex] \dashrightarrow{ \sf{(3 \times 35 - 70) \degree}}[/tex]

[tex] \dashrightarrow{ \sf{(105 - 70) \degree}} [/tex]

[tex] \longrightarrow{ \boxed{ \sf{35 \degree}}}[/tex]

Therefore , m [tex] \angle[/tex] ABC = 35°

And we're done !

Hope I helped!

Best regards! :)

~TheAnimeGirl

Answer:

Domain: {x|x∈R}

Range: ,{y|y∈R}

Step-by-step explanation: