Answer:
25000 mg.
Step-by-step explanation:
There are 1000 mg per gram. If we multiply 1000*25 we will get 25000 mg of sugar.
In a parenting magazine, Mrs. Smith read an advertisement about all the different ways that bleach can be used to kill bacteria. The advertisement claimed that some forms of bacteria triple in amount after each hour. Consider the situation where one bacterium is found on Mrs. Smith's countertop at home.
Question:
(a) How many bacteria would be found in 24 hours
(b) How many bacteria would be found in 2 days
(c) How long for 1000 bacteria to be found
Answer:
(a) 282429536481 bacteria
(b) [tex]7.97*10^{22[/tex] bacteria
(c) 6 days
Step-by-step explanation:
The question illustrates an exponential function
[tex]y = ab^x[/tex]
Where
[tex]a = Initial\ Value = 1[/tex]
[tex]b=Rate = 3[/tex] --- i.e. triples
[tex]x = number\ of\ hours[/tex]
Solving (a): Bacteria in 24 hours
In this case:
[tex]x = 24[/tex]
Substitute [tex]x = 24[/tex], [tex]b = 3[/tex] and [tex]a = 1[/tex]
So:
[tex]y = ab^x[/tex]
[tex]y = 1 * 3^{24[/tex]
[tex]y = 1 * 282429536481[/tex]
[tex]y = 282429536481[/tex] bacteria
Solving (b): Bacteria in 2 days
[tex]2\ days =48\ hours[/tex]
So:
[tex]x = 48[/tex]
Substitute [tex]x = 48[/tex], [tex]b = 3[/tex] and [tex]a = 1[/tex]
So:
[tex]y = ab^x[/tex]
[tex]y = 1 * 3^{48[/tex]
[tex]y =7.97*10^{22[/tex] bacteria
Solving (c): How long for 1000 bacteria
In this case:
[tex]y = 1000[/tex]
Substitute [tex]y = 1000[/tex], [tex]b = 3[/tex] and [tex]a = 1[/tex]
So:
[tex]y = ab^x[/tex]
[tex]1000 = 1 *3^x[/tex]
[tex]1000 = 3^x[/tex]
Take Log of both sides
[tex]Log1000 = Log3^x[/tex]
This gives:
[tex]Log1000 = xLog3[/tex]
Make x the subject
[tex]x = \frac{Log1000}{Log3}[/tex]
[tex]x \approx 6[/tex]
Hence: It takes 6 days
4. The graph of h(x) = x^2 was transformed to create the graph of k(x) = -4x^2? Which of these describes the transformation from the graph of h to the graph
of k? A.) A reflection over the x-axis and a vertical
stretch
B.) A reflection over the x-axis and a vertical
compression
C.) A reflection over the y-axis and a vertical
compression
D.) A reflection over the y-axis and a vertical stretch
Answer:
A. A reflection over the x-axis and a vertical stretch.
Step-by-step explanation:
Let [tex]h(x) = x^{2}[/tex], to obtain [tex]k(x) = -4\cdot x^{2}[/tex], we need to use the following two operations:
(i) Vertical stretch
[tex]g(x) = k\cdot f(x)[/tex], [tex]k\in \mathbb{R}^{+}[/tex]
(ii) Reflection over the x-axis
[tex]g(x) = -f(x)[/tex]
Let prove both transformations in [tex]h(x)[/tex]:
Step 1 - Vertical stretch ([tex]k = 4[/tex])
[tex]h'(x) = 4\cdot x^{2}[/tex]
Step 2 - Reflection over the x-axis
[tex]k(x) = -4\cdot x^{2}[/tex]
Hence, correct answer is A.
Trigonometry can anyone help me out
Answer:
y = 11
x = 11 root 3
[tex]x = 11\sqrt{3} [/tex]
[tex]y = 11[/tex]
Step-by-step explanation:
Cos 60 =
[tex] \frac{y}{22} \\ 0.5 = \frac{y}{22} \\ 0.5 \times 22 = y \\ 11 = y[/tex]
[tex]for x \\ \sin(60) = \frac{x}{22} \\ \frac{ \sqrt{3} }{2} = \frac{x}{22} \\ \frac{ \sqrt{3} }{2} \times 22 = x \\ 11 \sqrt{3 } = x[/tex]
Answer:
y = 11
x = 11 root \3
Step-by-step explanation:
Help If don't know do not answer(if link will report)
Answer:
x = 14
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsGeometry
Supplementary Angles: Angles that add up to 180°Step-by-step explanation:
Step 1: Define
We can see from the diagram that the 2 angles are supplementary
(6x - 10)° + (7x + 8)° = 180°
Step 2: Solve for x
Combine like terms: 13x - 2 = 180[Addition Property of Equality] Add 2 on both sides: 13x = 182[Division Property of Equality] Divide 13 on both sides: x = 14Find the future amount at the end of two years for a $7000 investment that earns 7% at the end of each year
Answer:
$8,014.30
Step-by-step explanation:
I really need help with these, if you know any it would help so much
1 - 53 is 45% of what number?
2 - if you got scored 20 out of 24 what percentage would that be?
3 - 80 is 55% of what number?
Answer:
1: 23.85
2: 83%
3: 44
Step-by-step explanation:
1 - do 53x0.45 (23.85)
2 - Divide 20 by 24, which you get 0.833333333 and move the decimal 2x to the right. You get 83.3333333, but round. So 83%
3 - do 80x0.55 (44)
In an isosceles triangle, one side is 6 more than 3 times a number and the congruent side is 10 less than
5 times the same number, what is that number?
a.2
b.8
c.16
d. none of above
A and b are positive integers and a-b=2 ... Evaluate the following:
27^1/3 b / 9^1/2 a
There is an image attached of the problem
Answer:
Step-by-step explanation:
a-b=2
[tex]\frac{27^{\frac{1}{3} b} }{9^{\frac{1}{2}a } } \\=\frac{(3^{3}) ^{\frac{1}{3} b} }{(3^{2} )^{\frac{1}{2} a} } \\=\frac{3^b}{3^a} \\=3^{b-a} \\=3^{-(-b+a)} \\=3^{-2}\\=\frac{1}{3^2} \\=\frac{1}{9}[/tex]
Write an equation in point-slope form of the line that passes through (-1, – 4) with slope -2.
Answer:
y+4=-2(x+1)
Step-by-step explanation:
y-y1=m(x-x1)
y-(-4)=-2(x-(-1))
y+4=-2(x+1)
please help, i will give 20 points
4. Overall, there are 45 students.
13 students achieved a mark over 65
[tex]\frac{13}{45} *100[/tex] = 29%
Therefore the answer is b. 29%
5. b is incorrect.
This is because retrievers account for 10% of the dogs, not 15%.
100%-(35% + 45% + 10%) = 10%
* This is the correct answer, I have taken the test and am posting the answers in hopes of helping other people :] *
What is the value of y?
Triangle A B C has right angle C with side A C labeled 5. Angle A is 60 degrees and its opposite side B C is labeled y.
Enter your answer, as an exact value, in the box.
y =
Answer:
OMG THANK YOU-
A magician performing a magic act has asked for 2 volunteers from the audience to help with his routine. If there are
250 people in the audience, which of the following expressions represents the number of possible pairs of volunteers ?
.
Answer:
The answer is 125. If you were to pair 250 people in 2, that would be 250 divided by 2. And 250 divided by 2 is 125.
Step-by-step explanation:
whts the factored answer
Step-by-step explanation:
x^2-25=
[tex] {x}^{2} - 25 = (x - 5)(x + 5) [/tex]
Please can someone help I don’t understand the question if it’s right I’ll give more plsssssesssssssssssddsd
Answer:
x = 33°
Step-by-step explanation:
From the figure attached,
FB and FC are two secants intersecting each other at point F outside the circle.
Measure of angles between the secants measures half of the difference between the intercepted arcs.
x° = [tex]\frac{1}{2}(\text{arc BC}-\text{arc DE})[/tex]
x° = [tex]\frac{1}{2}(108-42)[/tex]
x = 33°
Find the area of the figure below
Answer:
4.5 x 14 = 63
Explanation:
The area of a parallelogram is the product of any base and the altitude to that base: A = bh.
Find the slope and this line.
Dilate Point B by a scale factor of 1/2
a (1.5,-4)
b (-1.5,1)
c (-1,-1.5)
d (-2,-2)
PLEASE HELP
Answer:
B
Step-by-step explanation:
Divide each coordinate by 2
3/2=1.5
2/2=1
I'm very confused on what the answer to this one is
Answer:
(-3,1.5) (0,3) (3'3)
Step-by-step explanation:
multiply all the coordinates by 1/2
The Sanchez family had dinner at their favorite restaurant. A 9% sales tax was added to their bill. Amy paid the bill with a $10 gift certificate plus $30.60. How much did the family's dinner cost before tax? Round your answer to the nearest penny.
Answer:
The bill was $36.95 without tax.
The price before tax was the amount of $37.25 which is before a 9% sales tax was added to their bill.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
Their bill was charged a 9% sales tax.
Amy paid the bill with a $10 gift certificate plus $30.60
Use the equation P + rP =T,
where P is the price before tax, r is the sales tax rate, and T is the total price, including tax.
The price before tax (P) is unknown.
The total price(T) = 30.60 + 10 = 40.60
The sales tax rate (r) = 9% = 9/100 = 0.09
⇒ P + rP = T
Substitute the values in the above equation, and we get
⇒ P + (0.09)P = 40.60
⇒ P(1 + 0.09) = 40.60
⇒ P(1.09) = 40.60
⇒ P = 30.60/(1.09)
Apply the Division operation, and we get
⇒ P = 37.247706
Rounded to the nearest hundredth
⇒ P = 37.25
Therefore, the price before tax was the amount of $37.25.
Learn more about Arithmetic operations here:
brainly.com/question/25834626
#SPJ2
Keith bought 5 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 40 cards left. How many cards did Keith
start with?
Answer:
85 cards
Step-by-step explanation:
19. “40 of what number is 34” i need work
Answer:
85%
40% × ? = 34
? =
34 ÷ 40% =
34 ÷ (40 ÷ 100) =
(100 × 34) ÷ 40 =
3,400 ÷ 40 =
85
Noelle and Micah went to the bank to open new checking accounts. The equation C=0.2n+1.20 represents the monthly cost, C, in dollars, where n is the number of checks written by Noelle. In Micah's account, the monthly cost is proportional to the number of checks written. The monthly cost for Micah's account is $1.20 for writing 3 checks. How many checks must Noelle and Micah write, if any, so that the cost of the accounts is the same for one month? What is the cost, if any?
Answer:
C = $2.40
n = 6
Step-by-step explanation:
For Noelle,
Equation that represents the monthly cost 'C',
C = 0.2n + 1.20
Here, n = number of checks written in a month
For Micah,
Monthly cost for writing checks 'C' = $1.20
Number of checks 'n' = 3
Since, Cost of writing checks ∝ Number of checks written
C' ∝ n
C' = kn
k = [tex]\frac{C'}{n}[/tex]
Here, k = proportionality constant
For C' = 1.2 and n = 3
k = [tex]\frac{1.2}{3}[/tex]
k = 0.4
Equation will be,
C' = 0.4n
For any month C = C'
Therefore, 0.2n + 1.20 = 0.4n
0.4n - 0.2n = 1.20
0.2n = 1.20
n = 6
Number of checks written by Noelle and Micah = 6
For n = 6,
C = 0.2(6) + 1.20
C = $2.40
Cost of writing checks = $2.40
x
−
3
4
=
8
Which value of
x
satisfies this equation?
Triangle ABC has side lengths 8 inches, 17 inches, and 15 inches. Sofia uses the following steps to conclude that triangle ABC is not a right triangle.
a2+b2=c282+172=15264+289=225353 ≠ 225
What mistake did Sofia make?
Sofia made a calculation error.
Sofia used the length of one of the legs as c when she should have used the length of the longest side as c.
Sofia does not know if triangle ABC is a right triangle, so she cannot use the Pythagorean Theorem or its converse.
Sofia’s conclusion is incorrect. When the sides of a triangle do not satisfy a2+b2=c2, you cannot conclude that the triangle is a right triangle.
Answer: Sofia used the length of one of the legs as c when she should have used the length of the longest side as c.
Step-by-step explanation: The leg is the smallest number and the hypothenuse is the biggest nunber.
Answer:
Sofia used the length of one of the legs as c when she should have used the length of the longest side as c.
Step-by-step explanation:
Tyler invested $350 in an account paying an interest rate of 4.5% compounded
continuously. Assuming no deposits or withdrawals are made, how long would it
take, to the nearest tenth of a year, for the value of the account to reach $700?
Answer:
15.4 I did this on delta math
It would take approximately 15.4 years, to the nearest tenth of a year, for the value of the account to reach $700 with continuous compounding.
How to calculate compounding time?The formula for calculating the future value (FV) of an investment with continuous compounding is:
[tex]FV = Pe^{rt}[/tex]
Where P is the initial principal, r is the annual interest rate (expressed as a decimal), t is the time period (in years), and e is the mathematical constant e (approximately 2.71828).
In this case, we have P = $350, r = 4.5% = 0.045, and we want to find the time t when the FV is $700. Substituting these values into the formula, we get:
[tex]700 = 350e^{0.045t}[/tex]
Dividing both sides by $350, we get:
[tex]2 = e^{0.045t}[/tex]
Taking the natural logarithm of both sides, we get:
[tex]ln(2) = ln\times e^{0.045t}[/tex]
Using the properties of logarithms, we can simplify this to:
ln(2) = 0.045t ln(e)
Since ln(e) = 1, we can simplify further to:
ln(2) = 0.045t
Finally, solving for t, we get:
t = ln(2) / 0.045 ≈ 15.4
Therefore, it would take approximately 15.4 years, to the nearest tenth of a year, for the value of the account to reach $700 with continuous compounding.
To know more about continuous compounding follow
https://brainly.com/question/14303868
#SPJ2
Show that (16 1/4)3 and (16 3)1/4 are equivalent
Answer:
They are both 12
Change 16 1/4 into 4.
4 • 3
12
16 • 3 is 48
1/4 of 48 is 12
Hope this helps
You are a packer for Acme Bottling Company.
You fill cartons with bottles,
seal the cartons, and stack them on pallets.
Monday through Friday you are paid $0.78 for each carton you fill.
On Saturday you are paid an additional$0.38 for each carton you fill.
What is your total pay for a week in which you
filled the following number of cartons?
Mon-210
Tues-175
Wed-224
Thurs-160
Fri-216
Sat-90
Answer:
$872.70
Step-by-step explanation:
Add all numbers from Mon-Fri.
So 985.
Multiply it by 0.78
So $768.30
Add 0.78 and 0.38
So 1.16
Then multiply 90 by 1.16
So $104.40
Then add the two numbers.
768.30+104.40
So $872.70
Hope this helps
A person in an apartment
building sights the top and bottom of an office
building 500 ft. away. The angle of elevation
for the top of the office building is 23° and the
angle of depression for the base of the building
is 50º. How tall is the office building?
Answer:
Step-by-step explanation:
tan23=h1/500
h1=500tan23
tan50=h2/500
h2=500tan50
The height of the building is h1+h2 so
H=500(tan23+tan50)ft (exact)
H=808.1 ft (rounded to nearest tenth of a foot)
Even more trig ratios see attachment
Step-by-step explanation:
1. Use the Pythagorean theorem to solve for side KM:
16^2+KM^2=34^2256+KM^2=1156KM^2=900KM=302. Cosine is adjacent over hypotenuse, so cosine of M would be KM/34, or 30/34
3. Tangent is opposite over adjacent, so tangent of L will be KM/16, or 30/16
4. Sine is opposite over hypotenuse, so sine of M will be 16/34
5. KM=30, solved for in step 1.
hope this helps!!
You are putting money into a bank account. You start with $100 and add $12 every month. The total amount of money in your account can be represented by the following equation. (where T is total amount and M is the number of months):
T = 100 + 12 M
If you have $208, how many months have passed?
Show the equation and how you got the answer.
Answer:
9 months
Step-by-step explanation:
Answer:
it will be 9 months like the first person said