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A scientist counts 35 bacteria present in a culture and finds that the number of bacteria triples each hour. The function y = 35 • 3x models the number of bacteria after x hours. Estimate when there will be about 550 bacteria in the culture.
I think it's about 2.5 hours.
Other answer options:
about 5.5 hours
about 4.5 hours
about 3.5 hours
Answer:
The answer to your question is about 5.5 hours.
Step-by-step explanation:
The equation is y = 35(3x)
Data
# of bacteria = 550 = y
time = ? h
Then 550 = 35(3x) substitution
550 = 105x simplifying
x = 5.23 h.
From 2000-2010 a city had a 2.5% annual decrease in population. If the city had 2,950,000 people in 2000, determine the city's population in 2008.
The population of the city in the year 2008 is 2409122.
Important information:
Initial population in 2000 is 2,950,000.Decreasing rate is 2.5%.Exponential formula:According to the exponential decay formula:
[tex]f(t)=a(1-r)^t[/tex]
Where a is the initial value, r is the decay rate and t is the time period.
The difference between 2008 and 2000 is 8.
Substitute [tex]a=2950000, r=0.025, t=8[/tex] in the above formula.
[tex]f(8)=2950000(1-0.025)^8[/tex]
[tex]f(8)=2950000(0.975)^8[/tex]
[tex]f(8)=2409122.8208[/tex]
Round the value to the previous integer.
[tex]f(8)\approx 2409122[/tex]
Therefore, the population of the city in 2008 is 2409122.
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Estimate the tip on a $19.65 check using a tip rate of 15%
some of the fastest growing occupations in the United States are in which field
a. retail
b. agriculture
c. health care
d. manufacturing
f=uv/u+v
Make v the subject of the equation showing your working f=uv/u+v
Make v the subject of the equation showing your working
(3.2b+0.8)+1.9b simplify the expression.explain each step
To simplify the expression (3.2b+0.8)+1.9b, combine like terms by adding the coefficients. The simplified expression is 5.1b + 0.8.
Explanation:
To simplify the expression (3.2b+0.8)+1.9b, we can combine like terms by adding the coefficients. The variable b remains unchanged. So, we have:
(3.2b + 1.9b) + 0.8
Combine the coefficients: 3.2 + 1.9 = 5.1
The simplified expression is therefore 5.1b + 0.8.
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Which best explains why all equilateral triangles are similar?
A. All equilateral triangles can be mapped onto each other using dilations.
B. All equilateral triangles can be mapped onto each other using rigid transformations.
C. All equilateral triangles can be mapped onto each other using combinations of dilations and rigid transformations.
D. All equilateral triangles are congruent and therefore similar, with side lengths in a 1:1 ratio.
Answer: A. All equilateral triangles can be mapped onto each other using dilations.
Step-by-step explanation:
We know that all equilateral triangles are similar to each but not congruent because they all have same measure of corresponding angles 60° but do not have same side-lengths.
So, equilateral triangles can be mapped onto each other using dilation because they maps similar shapes (sometimes congruent) where as rigid transformations always map congruent shapes so we cannot map all equilateral triangles by using rigid transformations.
Write the expression in standard form.
five divided by quantity three minus fifteen i.
Answer:
[tex]\frac{4}{229}+\frac{30i}{229}[/tex]
Step-by-step explanation:
Bob has a tree house at a height of 20 ft. When he's feeling adventurous he uses a rope to climb the tree house instead of the ladder. If the weight of the rope is 32 lb, then how much work must Bob do to pull the rope up once he has entered the house? ...?
The measures of the angles in a triangle have a ratio of 2:9:1. How do you find the measures of these angles
Final answer:
To find the measures of the angles with a ratio of 2:9:1, represent the angles as 2x, 9x, and x, set up the equation 2x + 9x + x = 180, solve for x, and then use x to calculate each angle. The measures of the angles are 30 degrees, 135 degrees, and 15 degrees.
Explanation:
To find the measures of the angles in a triangle with a given ratio, we apply the fact that the sum of the angles in a triangle is always 180 degrees. If we have the ratio of 2:9:1, we can represent the angles as 2x, 9x, and x, respectively. Since the angles must add up to 180 degrees, we can write the equation 2x + 9x + x = 180, which simplifies to 12x = 180.
Divide both sides of the equation by 12 to find the value of x: x = 180 / 12 = 15 degrees. Now, we can find each angle by multiplying x by the respective ratio number:
The first angle is 2x, which equals 2(15) = 30 degrees.
The second angle is 9x, which equals 9(15) = 135 degrees.
The third angle is 1x, which equals 1(15) = 15 degrees.
Therefore, the measures of the angles in the triangle are 30 degrees, 135 degrees, and 15 degrees.
tom has 6 quarters and 12 dimes in his pocket how many coins does he need to take out his pocket to make sure he has 4 quarters
What is (are) the apparent x-intercept(s) of the function graphed above?
–4, –2, and 6
115 and –9
–3 and 3
50
For this case what we must do is observe the cut points of the function with the x axis.
The cut points with the horizontal axis are:
(-4, 0)
(-2, 0)
(6, 0)
Therefore, the intersections with the axis are:
x = -4
x = -2
x = 6
Answer:
The apparent x-intercept (s) of the function graphed are:
-4, -2, and 6
a surveyor standing 64 meters from the base of a building measures the angle to the top of building and finds it to be 39 degrees . the surveyor then measures the angle to the top of the radio tower on the building and finds that it is 48 degrees. how tall is the radio tower?
To calculate the height of the radio tower, trigonometry is used to first determine the building height and then the total height including the tower. Subtracting the building height from the total height gives the height of just the radio tower.
Explanation:To determine the height of the radio tower, we must first use trigonometry to find the height of the building. We use the tangent of the angle and the distance from the surveyor to the building:
Tan(39°) = Height of Building / 64 metersHeight of Building = 64 meters * Tan(39°)After calculating the height of the building, we use the same approach to find the total height to the top of the radio tower:
Tan(48°) = Total Height / 64 metersTotal Height = 64 meters * Tan(48°)Finally, to find the height of the radio tower alone, we subtract the height of the building from the total height.
Height of Radio Tower = Total Height - Height of Building
By following these steps, we can calculate the height of the radio tower.
Simplify the expression: √18x^4y^3
Answer:
[tex]3x^2y\sqrt{2\cdot y}[/tex]
Step-by-step explanation:
We have been given an radical expression. We are asked to simplify our given expression.
[tex]\sqrt{18x^4y^3}[/tex]
We can rewrite terms of our given function as:
[tex]\sqrt{18\cdot x^4\cdot y^3}[/tex]
[tex]\sqrt{2\cdot 9\cdot x^4}\cdot y^2\cdot y}[/tex]
[tex]\sqrt{2\cdot 3^2\cdot (x^2)^2\cdot y^2\cdot y}[/tex]
Using radical rule [tex]\sqrt[n]{a^n}=a[/tex], we will get:
[tex]3x^2y\sqrt{2\cdot y}[/tex]
Therefore, the simplified form of our given expression would be [tex]3x^2y\sqrt{2\cdot y}[/tex].
A laptop computer sells for $850. the sales tax is 7%. what is the total cost of the laptop?
Answer:
$909.50
Step-by-step explanation:
$850 x 7% = $59.50 (tax amount)
850 x (1+ 0.07) = $909.50
A writer charges $5 per word plus a start up fee of $50 per article.
A curve passes through the point (0, 5) and has the property that the slope of the curve at every point P is twice the y-coordinate of P. What is the equation of the curve? (Use x as the independent variable.) ...?
Given the diagram at the right, which of the following must be true?
A. xfs = xtg
B. sxf = gxt
C. fxs = xgt
D. fxs = gxt
Answer:
SXF ~= GXT
Step-by-step explanation:
SX corresponds to GX,
XF corresponds to XT,
so SF corresponds to GT.
There are 96 students in a speech contest. Yesterday, 1/4 of them gave their speeches. Today, 1/8 of the remaining students gave their speeches. How many students still haven't given their speeches?
lyn has as much money as jo. together they have $63.how much money does each have
take 63 and divide it by 2.
63÷2= 31.5
so they each had $31.5
in the diagram below Bd is parallel to XY . what is the value of x
Answer: The correct option is (B) 60.
Step-by-step explanation: Given that the line BD is parallel ti the line XY.
We are to find the value of x.
We know that
if two parallel lines are cut by a transversal, then the measures of the alternate interior angles are equal.
In the given figure, BD is parallel to XY and they are cut by a transversal.
So, the angles with measures x° and 60° are alternate interior angles.
Therefore, we must have
[tex]x^\circ=60^\circ\\\\\Rightarrow x=60.[/tex]
Thus, the value of x is 60.
Option (B) is CORRECT.
music in 2001, full length cassettes represented 3.4% of total music sales. between 2001 and 2006, the present decreased by about 0.5% per year
x= 1, 2, 3, 4, 5. y=11\4, 25\4, 39\4, 53\4, 67\4. what equation relates y to x in the values x and y?
Explain why the square root of a number is defined to be equal to that number to the 1/2 power.
Answer:
Sample Response: Squaring and square root are inverses, so one should "undo" the other. That is, squaring the square root of a number results in the number. Using the power of a power rule, you multiply the exponents. Since a number to the first power is itself, the product of the exponents must equal 1. This means that the power of the square root must be the reciprocal of 2, or one half.
Pablo deposited 57 into a savings account for which interest is compounded quarterly according to the rule 72 what interest rate will cause his money to double is approximately 44 years
To find the interest rate that will cause Pablo's money to double in approximately 44 years, we can use the rule of 72. The interest rate is approximately 1.64%.
Explanation:To find the interest rate that will cause Pablo's money to double in approximately 44 years, we can use the rule of 72. The rule of 72 states that dividing 72 by the interest rate will give you the approximate number of years it takes for money to double. In this case, we need to find the interest rate that makes the money double in 44 years. So, we divide 72 by 44 to get the interest rate.
Interest rate = 72 / 44 ≈ 1.6363636363636363
Therefore, the interest rate that will cause Pablo's money to double in approximately 44 years is approximately 1.64%.
The ratio of boys to girls in Mrs. Ronilo's math class is 3 to 1. What PERCENT of the class is girls?
Answer:25 %
Step-by-step explanation: there are 4 parts and 1 of those is girls 1 divided by 4 is 0.25, which is 25%
The percent of the class that is girls is 75%
Ratios and proportionGiven the ratio of boys to girls in Mrs. Ronilo's math class is 3 to 1, the total ratio will be:
Total ratio = 3 + 1Total ratio = 4The percent of the class that is girls = 3/4 * 100
The percent of the class that is girls = 75%
Hence the percent of the class that is girls is 75%
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Use the distributive property to create an equivalent expression to 7x 56
If 600 cm2 of material is available to make a box with a square base and a closed top, find the maximum volume of the box in cubic centimeters. Answer to the nearest cubic centimeter without commas. For example, if the answer is 2,000 write 2000.
What is the vertex and the equation of the axis of symmetry of the graph of y=x2-6x-7?
Answer:
The vertex is (3,-16) and axis of symmetry is 3
Step-by-step explanation:
The vertex of a quadratic equation [tex]f(x)=ax^{2}+bx+c[/tex] is calculated as [tex](\frac{-b}{2a},f(\frac{-b}{2a}))[/tex]
and the axis of symmetry is [tex]\frac{-b}{2a}[/tex]
Compare equation [tex]y=x^{2}-6x-7[/tex] with [tex]f(x)=ax^{2}+bx+c[/tex]
Where a= 1 and b = -6
so, [tex]x=\frac{-b}{2a}=\frac{-(-6)}{2}[/tex]
[tex]x=3[/tex]
Now, put the value of x=3 in [tex]y=x^{2}-6x-7[/tex]
[tex]y=(3)^{2}-6(3)-7[/tex]
[tex]y=9-18-7[/tex]
[tex]y=-16[/tex]
Therefore, the vertex is (3,-16) and axis of symmetry is 3
Which of the following represents this function written in intercept form?
y=x^2-8x+12
a. y=-(x+2)(x+6)
b. y=(x-2)(x-6)
c. y=(-x+3)(x-4)
d. y=-(x+2)(x-6) Which of the following represents this function written in intercept form?
y=x^2-8x+12
a. y=-(x+2)(x+6)
b. y=(x-2)(x-6)
c. y=(-x+3)(x-4)
d. y=-(x+2)(x-6)
Answer:
B. y = (x-2)(x-6)
Step-by-step explanation:
The quadratic function y = x²- 8x + 12 can be factored into intercept form as y = (x - 2)(x - 6), which corresponds to option (b).
The function given is y = x² - 8x + 12. To write this function in intercept form, we need to factor it as the product of two binomials, each representing its intersections with the x-axis where y=0.
To do this, we look for two numbers that multiply to give the constant term (12) and add up to give the coefficient of the middle term (-8). These two numbers are -2 and -6.
Thus, the factored intercept form is y = (x - 2)(x - 6). This corresponds to answer choice (b).