The complete statement is:
There were 59 bacteria after 5 hours
The initial population of the bacteria is given as:
[tex]a =100[/tex]
The proportion left after each hour is given as:
[tex]b = 90\%[/tex]
An exponential function is represented as:
[tex]f(x) = ab^x[/tex]
Substitute values for (a) and (b)
[tex]f(x) = 100 \times (90\%)^x[/tex]
Express percentage as decimal
[tex]f(x) = 100 \times (0.9)^x[/tex]
After 5 hours, the value of x is 5
i.e. x = 5
So, we have:
[tex]f(x) = 100 \times (0.9)^5[/tex]
Evaluate the exponent
[tex]f(x) = 100 \times 0.59049[/tex]
Multiply
[tex]f(x) = 59.049[/tex]
Approximate
[tex]f(x) = 59[/tex]
Hence, there were 59 bacteria after 5 hours
Read more about exponential population function at:
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Elisa made 0.44 of the free throws she attempted . What is that amount written as a fraction in simplest form
Using the pythagorean theorem find the length of a leg of a right triangle if the other leg is 8feet long and the hypotenuse is 10 feet long
The Pythagorean Theorem is a² + b² = c². Since the hypotenuse is 10 ft, c=10. The other leg is 8 ft, so b=8. Plug 10 into c, and 8 into b.
a² + 8² = 10²
Square 8 and 10.
= a² + 64 = 100
Subtract 64 from both sides.
= a² = 36
Find the square root of 36.
a = 6
What is 840,449 to the nearest hundred thousand place
Answer:840,400
Step-by-step explanation:840,449
840,400
What is the pre-image of vertex A' if the rule that created the image is ry-axis(x, y) → (–x, y)?
Answer:
It is given that image of any point (x,y) is (-x,y).
It is the case of reflection of a point through Y - axis.
So , Image of point (x,y) is (-x,y).
it's pre-image will be Point A whose coordinate is (x,y).
Answer: Preimage of A' is A (x,y).
Step-by-step explanation:
Suppose we have given a point A' (-x,y) and let [tex]r_y[/tex] be the rotation transformation with center of rotation at origin(0,0) such that
[tex]r_y (x,y) =(-x,y) \\[/tex]
Now in rotation transformation of any point about y axis i.e.( [tex]r_y[/tex]) it produces the reflected image by changing the polarity of x abscissa only and not of y. Therefore, by applying rotation transformation about y axis on image A'(-x,y) gives the pre-image of (-x,y) = (x,y) [which is the reflection of A'].
For example :- let P (1,2) be any point then after rotation transformation about y axis it will become P'(-1,2).
An attendant collected 45 coins from a parking meter. the value of the coins was $7.25, and there were 5 more quarters than nickels. which system models this situation?
a.) n+5=q and .05n +.25q=7.25
b.) q+5=n and .05n +.25q=7.25
c.) n+5=q and n+q=7.25
d.) n+5=q and 5n+2q=7.25
Answer:
a.) [tex]n+5=q[/tex] and [tex].05n +.25q=7.25[/tex]
Step-by-step explanation:
1. You have that there were 5 more quarters ([tex]q[/tex]) than nickels ([tex]n[/tex]. Therefore, you can express it as below:
[tex]n+5=q[/tex]
2. Keeping on mind that the value of the coins was $7.25 and that a quarter is 25 cents and a nickel is 5 cents, you can write the following expression:
[tex].05n +.25q=7.25[/tex]
3. Therefore, the answer is the option a.
please help asap 30 pts
Given
43 - 3d= d + 9
Solution
Add 3d to both sides of the equal sign
43 = d + 3d + 9
43 = 4d + 9 Subtract 9 from both sides
43 - 9 = 4d Collect like terms on the left
34 = 4d Divide by 4 on both sides.
34/4 = 4d/4
8 2/4 = d
d = 8 2/4 = 8 1/2 = 8.5
Check
LHS
43 - 3 * 8.5
43 - 25.5
17.5
RHS
d + 9
8.5 + 9
17.5
and the problem checks.
C is the answer
[tex]43-3d=d+9\qquad|\text{subtract 43 from both sides}\\\\-3d=d-34\qquad|\text{subtract d from both sides}\\\\-4d=-34\qquad|\text{divide both sides by (-4)}\\\\d=\dfrac{-34}{-4}\\\\d=\dfrac{34:2}{4:4}\\\\d=\dfrac{17}{2}\\\\\boxed{d=8\dfrac{1}{2}}\to\boxed{c.}[/tex]
An angle that measure greater than 0 degrees but less than 90 degrees is the
20 POINTS >>>> The rent for an apartment is represented by R(a) = 2.00a + 50.00, where a is the area of the apartment in square feet. The rent increases by $50.00 when the apartment is furnished. Identify the new function S(a) for the rent of a furnished apartment and the transformation that has been applied.
A) S(a) = 52.00a + 50.00; shift 50 units up
B) S(a) = 2.00a + 100.00; shift 50 units down
C) S(a) = 52.00a + 50.00; shift 50 units down
D) S(a) = 2.00a + 100.00; shift 50 units up
A police officer had a taxable income of $47,050 last year. If she paid 10% of her income between $0 and $8350, 15% of her income between $8350 and $33,950, and 25% of her income between $33,950 and $47,050 in federal income tax, how much did the police officer pay in federal income tax last year? a. 3840 b. 3275 c.835 d. 7950
Answer:
The correct option will be: d. 7950
Step-by-step explanation:
The police officer paid 10% of her income between $0 and $8350, 15% of her income between $8350 and $33,950 and 25% of her income between $33,950 and $47,050 in federal income tax.
So, the amount of tax at 10% rate [tex]=(\$8350-\$0)*0.10=\$8350*0.10 = \$835[/tex],
the amount of tax at 15% rate [tex]=(\$33950-\$8350)*0.15 = \$25600*0.15=\$3840[/tex]
and the amount of tax at 25% rate [tex]= (\$47050-\$33950)*0.25= \$13100*0.25= \$3275[/tex]
Thus, the total amount of federal income tax will be: [tex](\$835+\$3840+\$3275)= \$7950[/tex]
Answer:
The correct answer is $7950
Step-by-step explanation:
Amelia swam four times as many laps as wesly . Wesley swam 7 laps. How many laps did amelia swim??????
Final answer:
Amelia swam 28 laps, which is four times the 7 laps that Wesley swam.
Explanation:
In solving the question about the number of laps Amelia swam, a straightforward multiplication approach is employed. Given that Amelia swam four times as many laps as Wesley, and Wesley's lap count is specified as 7, the calculation involves multiplying Wesley's laps by 4. In mathematical terms, Amelia's number of laps is determined as Wesley's laps multiplied by 4, resulting in 7 × 4 = 28 laps.
This multiplication process provides a clear and concise method to ascertain Amelia's lap count based on the given relationship, demonstrating a fundamental application of arithmetic principles in solving real-world problems involving numerical relationships and operations.
PLEASE HELP QUICKLY! I suck at vocab...match the word with the definition:
1. Devices, such as parentheses, brackets, and fraction bars, used to set apart an expression that should be simplified before other operations are performed
2. An expression that consists of numbers, operations, and sometimes grouping symbol.
3. The order in which operations must be computed when more than one operation is involve.
4. A number representing how many times the base number should be multiplied by itself.
5. A Symbol that represents a value that can change.
6. A single number or variable, or numbers and variables multiplied together.
7. The numerical factor in a term. A number being multiplied by a variable.
8. A number on its own, it has a fixed value.
9. A combination of variables, numbers, and operations.
10. You replace, or substitute, all the variables with numbers and then simplify.
11. A statement that the values of two math expressions are equal (indicated by the sign =).
12. The relation between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
13. The symbol of a math operation.plus, minus, times, divided by, equals
14. An equation or inequality containing one or more variable.
VOCAB
-------------
variable
equation
evaluate
order of operations
operator
open sentence
coefficient
inequality
exponent (power)
Variable expression
grouping symbol
numerical expression
term
constant
1 : Grouping Symbol, 2 : Operator, 3 : Order of Operations, 4 : Exponent, 5 : Variable, 6 : Term, 7 : Coefficient, 8 : Constant, 9 : Numerical Expression, 10 : Variable Expression, 11 : Equation, 12 : Inequality, 13 : Evaluate, 14 : Open Sentence
What is Number System?
A number system is defined as the representation of numbers by using digits or other symbols in a consistent manner
By given data
1 : Devices, such as parentheses, brackets, and fraction bars, used to set apart an expression that should be simplified before other operations are performed: Grouping Symbol
2 : An expression that consists of numbers, operations, and sometimes grouping symbol: Operator
3 : The order in which operations must be computed when more than one operation is involve: Order of Operations
4 : A number representing how many times the base number should be multiplied by itself :Exponent
5 : A Symbol that represents a value that can change: Variable
6 : A single number or variable, or numbers and variables multiplied together: Term
7 : The numerical factor in a term. A number being multiplied by a variable: Coefficient
8 : A number on its own, it has a fixed value: Constant
9 : A combination of variables, numbers, and operations: Numerical Expression
10 : You replace, or substitute, all the variables with numbers and then simplify: Variable Expression
11 : A statement that the values of two math expressions are equal (indicated by the sign : Equation
12 : The relation between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”: Inequality
13 : The symbol of a math operation. plus, minus, times, divided by, equals: Evaluate
14 : An equation or inequality containing one or more variable: Open Sentence
Hence,
1 : Grouping Symbol, 2 : Operator, 3 : Order of Operations, 4 : Exponent, 5 : Variable, 6 : Term, 7 : Coefficient, 8 : Constant, 9 : Numerical Expression, 10 : Variable Expression, 11 : Equation, 12 : Inequality, 13 : Evaluate, 14 : Open Sentence
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What is the slope of a line that is perpendicular to the line whose equation is 2x + y = 4
The slope of the line of the equation given is -2 (by solving for y, you get y = -2x+4).
So, in order to be perpendicular, you must take the negative reciprocal.
The slope would be -1/2.
slope = [tex]\frac{1}{2}[/tex]
the equation of a line in \ slope-intercept form ' is
y = mx + c ( m is the slope and c the y-intercept )
2x + y = 4 ( subtract 2x from both sides )
y = - 2x + 4 ← in slope-intercept form
with m = - 2
given a line with slope m then the slope ([tex]m_{2}[/tex]) of a line perpendicular to it is
[tex]m_{2}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-2}[/tex] = [tex]\frac{1}{2}[/tex]
A vegetable-oil recovery plant has already recycled 1,400 litters out of 2,500 liters of used oil. If the plants can recycle 24 liters of used oil per hour, about how many hours will it take to recycle what is left?
A vegetable-oil recovery plant has already recycled 1,400 litters out of 2,500 liters of used oil.
Initially plant has 2,500 liters of used oil.
plant has already recycled 1,400 liters
so liters of oil left = 2500 - 1400 = 1,100
So 1,100 liters of oil left
plants can recycle 24 liters of used oil per hour
So for 1,100 liters we divide by 24 to find the number of hours
[tex]\frac{1100}{24}= 45.83[/tex]
Its approximately 46 hours
Approximately 46 hours it will take to recycle 1,100 liters.
I need a lot of help please help me. What is 128.34 as a mixed number in simplest form
A store buys 77 1/2 ponds of mulch in large shipments . they divied mulch into bags that can each hold 2 1/4 pounds . the store sells 1 bag of mulch for $2.25. For each part of the question show your work.
How many full bags of mulch will the store make?
Considering all the full bags, what is the total sales price of all the bags of mulch?
Alissa sells real estate. She makes a 3% commission rate on each sale. Alissa pays 25% of her commission to her home office to pay for expenses. How can Alissa calculate the amount of money she will keep after selling a $250,000 home? Multiply $250,000 by 0.25. Multiply $250,000 by 0.03. Multiply $250,000 by 0.03, and then multiply again by 0.75. Multiply $250,000 by 0.28.
Answer: Third option is correct.
Step-by-step explanation:
Since we have given that
Selling price of home = $250,000
Rate of commission on each sale she get = 3%
Rate of commission pays for expenses = 25%
So, Firstly amount she get on home sale would be
[tex]\dfrac{3}{100}\times 250,000\\\\=0.03\times 250,000\\\\=\$7,500[/tex]
Amount after paying for expenses would be
[tex]7500\times \dfrac{100-25}{100}\\\\=7500\times \dfrac{75}{100}\\\\=7500\times 0.75\\\\=5,625[/tex]
Hence, Multiply $250,000 by 0.03, and then multiply again by 0.75 is correct.
Therefore, Third option is correct.
Answer:
C
Step-by-step explanation:
In a parallel circuit, ET = 208 V, R = 39 kΩ, and XL = 24 kΩ. What is the power factor?
Answer:
Power factor is 0.8517 or 85.17%
Step-by-step explanation:
We are given that in a parallel circuit, [tex]E_{T}=208V[/tex], R=39kΩ and [tex]X_{L}[/tex]=24kΩ.
That means the circuit has a resistor element, inductor element in parallel with 208V applied across the terminal.
Let us find the current through resistor,
[tex]I_{R} =\frac{E_{T}} {R}= \frac{208}{39} =\frac{16}{3}=5.33[/tex] milli amps
And current through inductor,[tex]I_{L} =\frac{E_{T}} {X_{L}} =\frac{208}{24}=\frac{26}{3}=8.667[/tex] milli amps.
Hence total current, [tex]I_{T}= \sqrt{(I_{R})^2+(I_{T})^{2}} =\sqrt{5.33^{2}+8.667^{2}}=10.176[/tex]
Now power factor=[tex]\frac{I_{R}}{I_{T}}=\frac{5.33}{10.176}=0.8517[/tex]
Hence power factor is 85.17% or 0.8517
Is (1,2) a solution of the system y>2x and x+y< 3
Answer: No it is not a solution
Why not? Because it doesn't make the first inequality true. Replace x with 1 and y with 2
y > 2x
y > 2*1 ... replaced x with 1
2 > 2*1 .... replaced y with 2
2 > 2 .... which is a false inequality statement since 2 is not larger than itself
Answer: NO!
Step-by-step explanation:
x = 1, y = 2
y > 2x
2 > 2(1)
2 > 2
False
Sine it already failed, no need to check the other equation.
evaluate f=9/5c + 32 for c=35 degree
PLEASE PLEASE HELP ME OUT! But i ask that you explain how you got your answer and not just give the answer.
ok so first we would do the function d(x) = 3(8)+2
which when solved turns out to be 26
we would then do the function h(x) = 2(26) +7
which when solved turns out to be 59
so he would need 59 dollars for the donuts
I will mark u brainlist
The pic is kinda upside down lol
A: 50x+0.60(200)=1620
B: It's kinda up to you to write what you've learned about the equality property but I'll give you the steps.
50x+0.60(200)=1620
50x+120= 1620
50x=1620-120
50x=1500
x=1500/50
x=30
C= Donna spent 30 days on her trip.
Check:
50(30)+0.60(200)=1620
50(30)+0.60(200)=1620
1500+120=1620
1620=1620
Type the missing value
K^2+5k+6=(k+2)(k+ )
Toronto have lost 25% of their games and tied 10%. If they played 40 games, how many games did they win
If 42% of carmel residents want to have a fireworks celebration, how many total residents live in carmel of only 16,202 people want to have a fireworks display
38,576 people live in Carmel.
70 point for the right answer
Answer:
The answer is A 1/5x^2
Step-by-step explanation:
If a negative exponent is in the numerator, move the expression to the denominator and make the exponent positive
Answer:
The answer is A 1/5x^2
Step-by-step explanation:
If you can buy one can of pineapple chunks for $2 then how manycan you buy with $10?
The answer to your question is,
You can buy 5 cans of pineapple chunks with $10. Since each can is $2, you need to add $2 for each can until you get $10. :3
-Mabel <3
please help will give brainliest
Since the sum of the probabilities of all possible outcomes must be 100%, we can deduce the following:
Cooking in under 20 minutes: 10%Cooking between 20 and 30 minutes: 85%Cooking in more than 30 minutes: 5%In fact, the probabilities of cooking in less than 20 or more than 30 sum up to 15%, which means that the remaining outcome (i.e. cooking time between 20 and 30) must complete this probability to 15, and in fact 15+85=100.
That being said, all three answers are simply a combination of these three scenarios: let C be the cooking time, for aesthetic reasons:
[tex]P(C\geq 20) = P(20 \leq C \leq 30)+P(C\geq30) = 85\%+5\%=90\%[/tex]
[tex]P(20 \leq C \leq 30) = 85\%[/tex]
[tex]P(C\leq 30) = P(C\leq20)+P(20 \leq C \leq 30) = 10\%+85\%=95\%[/tex]
The gateway arch in st louis was builtin 1965. It is the tallest monument in the
Answer:
St. Louis, Missouri, United States.
Step-by-step explanation:
it is the world's tallest arch, the tallest man-made monument in the Western Hemisphere
Solve for x: negative 7 over 6, multiplied by x minus 6 equals negative 48
36
49
−36
−49
-7/6*x-6=-48
X will equal -36.
If y varies inversely as x, find the constant of variation if y = 5 when x = -1.
a) -5
b) 5
c) -2
d) 2
(a) - 5
since y varies inversely as x then k = yx ( k is the constant of variation )
using y = 5 when x = - 1, then k = 5 × - 1 = - 5