Answer:
7614
Step-by-step explanation:
The exponential growth of the bacteria culture can be modeled by the equation ...
p = a·b^(t/c)
where 'a' is the initial population, 'b' is the growth factor, and 'c' is the period over which that growth factor applies.
__
modelIn the given scenario, we have ...
a = 6000 bacteriab = 6600/6000 = 1.1 . . . . growth factorc = 4 hoursSo, our model is ...
p = 6000·1.1^(t/4)
__
applicationAfter 10 hours, the population is predicted to be ...
p = 6000·1.1^(10/4) ≈ 7614
We predict 7614 bacteria will be present after 10 hours.
__
Additional comment
If we compare the form we used to the one suggested in the proglem statement, we see
p = 6000·1.1^(t/4)p = 6000·e^(kt)For the bases of the exponential term to be the same, we must have ...
1.1^(t/4) = e^(kt)
(1.1^(1/4))^t = (e^k)^t . . . . . factor t from the exponent
1.1^(1/4) = e^k . . . . . . . match the bases
k = ln(1.1)/4 . . . . . take natural logs
k ≈ 0.0238275
and the equation becomes ...
p = 6000·e^(0.0238275t)
__
In terms of 'a', 'b', and 'c' used above, we find ...
k = ln(b)/c
What is the value of a,c ?
Answer:
Step-by-step explanation:
Inscribed angle of diameter is 90°
⇒ ∠ACB = 90°
In ΔACB,
∠A + ∠ B + ∠ACB = 180° {Angle sum property of triangle}
a + 4a + 90 = 180
5a + 90 = 180
5a = 180 - 90
5a = 90
a = 90 ÷ 5
a = 19 -----------(I)
In ΔCOB,
OC = OB {Radius}
⇒ΔCOB is an isosceles triangle.
c = 4a {angles opposite to equal angles are conguent}
c = 4*19 {From (I)}
c= 76
How many solutions are there to equation square root x = -16
In the diagram, rectangle ABCD is split in half by AC . What is the value of tan x?
Splitting the rectangle in half creates two right triangles
The value of tan(x) is 4/3
How to determine the value of tan x?To calculate tan(x), we make use of the following tangent ratio
tan(x) = Opposite/Adjacent
From the figure, we have:
Opposite = AD = 4
Adjacent = CD = 3
So, we have:
tan(x) = 4/3
Hence, the value of tan(x) is 4/3
Read more about tangent ratio at:
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Answer:
4/3
Step-by-step explanation:
Solve for x.
7.5x11=4.85
Enter your answer as a decimal in the box.
x =
7.5x11 = 4.85
82.5x = 4.85
*divide 82.5 on both sides*
x = 4.85 ÷ 82.5
x = 0.058788
Answer:
0.058787879
Step-by-step explanation:
(7.5)(x)(11)=4.85
82.5(x)=4.85
x=4.85÷82.5
x= 0.058787879
Jacori wants to estimate the proportion on seniors who will participate in graduation. He interviews a simple random sample of 40 of the 514 seniors at his school. He find that 34 are planning to participate. Is the normal condition for finding a confidence interval met?
Using the Central Limit Theorem, it is found that the condition is not met, as there are less than 10 failures.
What does the Central Limit Theorem states?It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].
In this problem, 34 of the 40 seniors are planning to participate in graduation, hence:
np = 34.n(1 - p) = 6 < 10.Since there are less than 10 failures, the normal condition for finding a confidence interval is not met.
More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213
Write the equation of the line perpendicular to y=5/6x+7/6 that passes through the point (-8,9) .
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y = \stackrel{\stackrel{m}{\downarrow }}{\cfrac{5}{6}}x+\cfrac{7}{6}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so we can say that
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{5}{6}} ~\hfill \stackrel{reciprocal}{\cfrac{6}{5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{6}{5}}}[/tex]
so we're really looking for the equation of a line with a slope of -6/5 and that passes through (-8 , 9)
[tex](\stackrel{x_1}{-8}~,~\stackrel{y_1}{9})\qquad\qquad \stackrel{slope}{m}\implies -\cfrac{6}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{9}=\stackrel{m}{-\cfrac{6}{5}}(x-\stackrel{x_1}{(-8)})\implies y-9=-\cfrac{6}{5}(x+8) \\\\\\ y-9=-\cfrac{6}{5}x-\cfrac{48}{5}\implies y=-\cfrac{6}{5}x-\cfrac{48}{5}+9\implies y=-\cfrac{6}{5}x-\cfrac{3}{5}[/tex]
Smokers: Out of 780 smokers, 376 have been divorced.
Non-smokers: Out of 2855 non-smokers, 902 have been divorced.
a) Find the 95% confidence interval for the proportion of smokers that have been divorced.
b) Find the 95% confidence interval for the proportion of non-smokers that have been divorced.
c) What do the results above indicate about smoking and divorce?
For statictics of Out of 780 smokers, 376 have been divorced, Non-smokers: Out of 2855 non-smokers, 902 have been divorced, the 95% confidence interval for smokers and non-smokers is mathematically given as
95% confidence interval = (0.5352, 0.4462)95% confidence interval = (0.3424, 0.2894)53% increased risk of divorce for smokers.What is the 95% confidence interval for smokers and non-smokers?Generally, the equation for the Confidence interval is mathematically given as
p ± Z/2[p(1-p)]/n
Where
Z1/2=1-(0.05/2)
Z1/2=0.975
Read z table we have
Z score= 1.96
Hence
0.4907 ± 1.96 (0.4907)(1-0.4907)/485
0.4907±0.0445
Therefore
95% confidence interval = (0.5352, 0.4462)
b)
Z1/2 = 1- (0.05/2)
Z1/2 = 0.975
Z score= 1.96
0.3159 ± 1.96 (0.3159)(1-0.3159)/1184
0.3159±0.0265
Thereofore
95% confidence interval = (0.3424, 0.2894)
c)
In conclusion, The 95% confidence interval helps us read that 53% increased risk of divorce for smokers.
Read more about Confidence interval
https://brainly.com/question/17097944
Reflections on a Coordinate Plane
Answer:
The reflection coordinates of JKL would be:
J (3,7)
K (2,3)
L (-1,5)
The reflection coordinates of MNP would be:
M (8,-6)
N (2,-4)
P (8,-4)
Step-by-step explanation:
La medida de cada ángulo interno de un polígono regular es 162º. Hallar el número de lados.
Número de lados=
Answer:
n = 20
Step-by-step explanation:
[ 180° ( n - 2 ) ] / n = 162°
180 ( n - 2 ) = 162 n
180n - 360 = 162n
18n = 360
n = 20
If z7=4-3i, thenz7 is
Select one:
O-7
O 7
O 5
O -5
By using Euler's notation, we will see that:
z^7 = 78,125*e^(-i*4.48)
How to get z^7?
We know that:
z = 4 - 3i
Remember that for a complex number:
w = a + bi
In Euler's notation, we can write this as:
w = √(a^2 + b^2)*e^(i*Atan(b/a))
Then, for z, we will get:
z = √(4^2 + (-3)^2)*e^(i*Atan(-3/4))
z = 5*e^(-i*0.64)
Now, if we apply an exponent of 7 to this number, we will get:
z^7 = ( 5*e^(-i*0.64))^7
z^7 = 5^7*e^(-i*7*0.64) = 78,125*e^(-i*4.48)
If you want to learn more about complex numbers, you can read:
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SOMEONE PLSSS HELP ME FAST
WILL MARK BRAINLIEST
Answer:
D. 45
Step-by-step explanation:
To find out how many games will be played with 10 people, we need to first find the pattern of the given table. To start out, we can see that for the numbers of players added, it adds one each time it goes up one number. And, we can also see that starting at 1 games played, it adds 2 for the next and gets 3 games. Then it adds 3 to get 6 games. So, we can see that for every added person added, it starts at 1 and adds 2, then adds, 3, 4, 5, 6, etc... Knowing this, we can figure out how many games will be played with 10 people.
2 people gets 1 games
+1 +2
3 people get 3 games
+1 +3
4 people get 6 games
So, now we can simply skip to 6 and seven players becuase we know that the pattern holds true to itself.
6 people get 15 games
+1 +6
7 people get 21 games
+1 +7
8 people get 28 games
+1 +8
9 people get 36 games
+1 +9
10 people get 45 games
Trigonometric equations
5sinx = 3sinx + square root of 2
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♪[/tex]
Let's solve for x ~
[tex]\qquad \sf \dashrightarrow \:5 \sin(x) = 3 \sin(x) + \sqrt{2} [/tex]
[tex]\qquad \sf \dashrightarrow \:5 \sin(x) - 3 \sin(x) = \sqrt{2} [/tex]
[tex]\qquad \sf \dashrightarrow \:2 \sin(x) = \sqrt{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sin(x) = \sqrt{2} \div 2[/tex]
[tex]\qquad \sf \dashrightarrow \: \sin(x) = \frac{1}{ \sqrt{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \:x = 45 \degree \: \: or \: \: \frac{\pi}{4} \: rad[/tex]
・ ．━━━━━━━†━━━━━━━━━．・
answer this question
9. The rational number that is equal to its negative is zero (0)
10. [tex]\sf \dfrac{1}{3} ( 6 \ * \ \dfrac{4}{3} )[/tex] can be written as [tex]\sf ( \dfrac{1}{3} *6)*\dfrac{4}{3}[/tex] using associate property.
associative property is when numbers are changed within the parenthesis with out the change in result.
formula of associative property : a(bc) = (ab)c
5. Gavin makes a homemade cleaner using į cup vinegar
for every 2 quarts of water.
Answer:
For every 2 quarts of water, ¹/₂ cup of vinegar is used.
⇒ To find the amount of vinegar, divide the number of quarts by 4.
⇒ To find the number of quarts, multiply the amount of vinegar by 4.
4 qt water = 4 ÷ 4 = 1 cup vinegar
1¹/₂ cups vinegar = 1¹/₂ x 4 = 6 qt water
8 qt water = 8 ÷ 4 = 2 cup vinegar
Plot the points on the graph (see second attached image).
Draw a line through the points.
Find 3 along the x-axis and trace up to the line. Trace along to the y-axis.
Therefore, Gavin would need to use 12 quarts of water with 3 cups of vinegar.
A rectangular container that has a length of 30 cm, a width of 20 cm, and a height of 24 cm is filled with water to a depth of 15 cm. When an additional 6.5 liters of water are poured into the container, some water overflows
Answer:
Step-by-step explanation:
1.1 L
Given:
A rectangular container that has:
a length of 30 cm,
a width of 20 cm, and
a height of 24 cm
It is filled with water to a depth of 15 cm.
When an additional 6.5 L of water are poured into the container, some water overflows.
Question:
How many liters of water overflow the container?
The Process:
Step-1: calculate the volume of rectangular container
The volume of rectangular container is 14,400 cm³, then converted to 14,4 L.
Step-2: calculate the volume of water filled in the container to a depth of 15 cm
The volume of water filled is 9,000³ cm, then converted to 9 L.
Step-3: calculate the volume of water overflow when an additional 6.5 L of water is poured into a container.
The volume of water overflow equals the initial water volume is added to the additional water volume then subtracted by the container volume.
The volume of water overflow =
Thus, the volume of water overflow of the container is 1.1 L.
amina and cara take a math test amina scores 40 marks,cara scores 60 marks write the ratio of amin to cara's marks
-they are given $20 to share,they share the money in the ratio of their marks how much does amina recieves
Answer
8
Step-by-step explanation:
Ratio: 40 : 60
Total amount - $20
40/100 x 20
= 8 (ANS)
i hope my answer is correct if not i apologize.
Here are the types of sandwiches sold in a cafe last week.
Sandwiches
Tuna
Cheese
Chicken
Egg
56 tuna sandwiches were sold.
This was 40% of the total number of sandwiches sold.
(a) Work out the total number of sandwiches sold.
Answer:
(a) 140 sandwiches
Step-by-step explanation:
The total number sold can be found from the given relation:
56 sandwiches = 40% × total sold
__
Dividing by the coefficient of the variable, we find ...
total sold = (56 sandwiches)/0.40 = 140 sandwiches
The total number of sandwiches sold last week was 140.
Find the average of this set of numbers.16, 20, 30, 30
A) 14
B) 15
C) 25
D) none of the above
Answer:
D) none of the above
Step-by-step explanation:
To find an average, you add up all of the numbers and divide by how many numbers there were. for example, in this equation, the sum of all of the numbers was 96. then I divided 96 by 4(the amount of numbers shown)
1. Match the picture of the triangle to the correct name for its center,
1. d 2. a 3. c 4. b
Step-by-step explanation:[tex]1.d\ \{The\ intersection\ of\ three\ high\ lines\}[/tex]
[tex]2.\ a[/tex]
[tex]3.\ C[/tex]
[tex]4.\ b\ \{The\ intersection\ of\ three\ angular[/tex]
[tex]bisectors\}[/tex]
I hope this helps you
:)
Answer:
dbcaStep-by-step explanation:
Various centers are defined for a triangle, depending on how they're constructed. Here, you're asked to match the construction with the name.
__
OrthocenterThe orthocenter is the intersection of the altitudes of the triangle. Each altitude intersects a vertex and is orthogonal to the opposite side. The orthocenter will not be inside the triangle if the triangle is obtuse. The orthocenter of a right triangle is the right-angle vertex.
Figure D depicts the intersection of altitudes.
__
IncenterThe incenter is the center of an inscribed circle of a triangle. The incenter must be the same distance from each side, so will be at the point of intersection of the angle bisectors. It always lies inside the triangle.
Figure B depicts the intersection of angle bisectors.
__
CentroidThe centroid is the "center of gravity" of the triangle, the point at which the triangle could be balanced. Each median divides the triangle into two equal areas, so the intersection of medians marks a spot with equal area (weight) in every pair of opposite directions.
Figure C depicts the intersection of medians.
__
CircumcenterThe circumcenter is the center of a circle that circumscribes the triangle. It is equidistant from the three vertices, so lies on the intersection of the perpendicular bisectors of the sides. It will lie outside the triangle for obtuse triangles. It is the midpoint of the hypotenuse of a right triangle.
Figure A depicts the intersection of perpendicular bisectors of the sides.
1. Jill bikes 15 miles in the morning and 17 miles in the afternoon. How many miles does she bike in all? Equation: miles 7 | Lesson 1
Add the two together:
15 + 17 = 32
total miles = 32
Determine whether each of these sets is countable or un- countable. For those that are countably infinite, exhibit a one-to-one correspondence between the set of positive integers and that set. a. integers not divisible by 3 b. integers divisible by 5 but not by 7 c. the real numbers with decimal representations con- sisting of all 1s d. the real numbers with decimal representations of all 1s or 9s
Answer:
i do not understand the questions
Step-by-step explanation:
You are building a ramp that must cover a horizontal distance of exactly 28 feet. The angle of the ramp from the ground is 8°. Determine the length of the ramp, in feet.
Kaya brought $30 to the mall. She spent $7.28 on food, and $18.94 on a necklace. How much does she have left?
Answer:
$3.78
Step-by-step explanation:
30 dollars minus 7 dollars and 28 cents is twenty-two and seventy-two cents, then minus another eighteen and ninety-four cents, would end up at three dollars and seventy-eight cents.
Answer:
[tex]\boxed{\$3.78}[/tex]
Step-by-step explanation:
To find out how much money does Kaya have left, we need to subtract the total money spent from the total money brought to the mall.
In this problem, we can tell that Kaya brought $30 to the mall as stated in the question. Furthermore, the problem states that she spent $7.28 on food, and $18.94 on a necklace. This means that the sum of 7.28 and 18.94 is the money spent by Kaya.
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[tex]\$30 - (\$7.28 + \$18.94) = \text{Money remained}[/tex]
➡ [tex]\$30 - (\$26.22) = \text{Money remained}[/tex]
➡ [tex]\$30 - \$26.22 = \text{Money remained}[/tex]
➡ [tex]\bold{\underline{\$3.78} = Money \ remained}}[/tex]
≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡
For f(x) = 3x^3 - 9x^2 - 5x + 2
A. Find f(-1)
B. Find f(2)
Answer:
(3x2 + 3x - 1) • (x + 2)
Step-by-step explanation:
3.4 Polynomial Long Division
Dividing : 3x3+9x2+5x-2
("Dividend")
By : x+2 ("Divisor")
dividend 3x3 + 9x2 + 5x - 2
- divisor * 3x2 3x3 + 6x2
remainder 3x2 + 5x - 2
- divisor * 3x1 3x2 + 6x
remainder - x - 2
- divisor * -x0 - x - 2
remainder 0
Quotient : 3x2+3x-1 Remainder: 0
The area of the rectangle is
432 square units. If the width
is 24 units, what is the length?
Answer:
18 units
Step-by-step explanation:
Area = length * width (A = L * w)
So, in order to find the length when given the width and area, you have to divide the area by the width.
432 / 24 = 18
I hope this helps! Have a lovely day!! :)
Multiply (2 – 7i)(–1 + 4i).
Answer:26 + 15i
Step-by-step explanation: 26+ 15i is the answer because i did the assignemnt
can someone please help with this problem please
Answer:
1360 seats sold
Step-by-step explanation:
total seats = 1600
total seats sold = 85% of 1600
= 85/100 × 1600
= 85 × 16
= 1,360 seats sold
A box of 800 paper clips costs $5.60. What is the unit price of the paper clips?
Answer:
70 cents
Step-by-step explanation:
To figure out how much 1 paper clip costs we must divide :)
5.60/800 = 70 cents
Have an amazing day!!
Please rate and mark brainliest!!
write the fractions in least to greatest
1/5 3/4 1/3 2/4 6/24
Answer: 1/5 6/24 1/3 2/4 3/4
Step-by-step explanation: bigger the denominator smaller the value.
Find the values of x for which the denominator is equal to zero for y=3x+5/x-6.
x = −5
x = 6
x = −6
none
Answer:
x=6 is the answers for the question
Step-by-step explanation:
please mark me as brainlest