During the summer, many homeowners struggle to keep ant's out of their homes. In a specific
kitchen, the population of a colony of ants is given by
P(t) = 42(1.168)
where P(t) is the populationand t is the number of days after June 1st.
(a)What is the daily growth rate of this ant population?
Write your answer as a percent rounded to two decimal places.
(b)What is the continuous growth rate of this ant population?
Write your answer as a percent rounded to two decimal places.
(c)When will the population reach 500 ants? Use an algebraic solving process to show
that it will take 15.95 days to reach 500 ants.
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You spin each spinner once. You get $39 if you spin a 2 and a vowel. You get $26 if you spin a 2 and a consonant. You get $9 if you spin a 1 and a vowel. Everything else earns $0. What is the expected value of this game? Round your answer to the second decimal if necessary
The expected value of the game is the mean value of the game
The expected value of the game is $9
For the first spinner;
The probability to spin 2 is 1/4The probability to spin 1 is 3/4For the second spinner;
The probability to spin a vowel is 1/4The probability to spin a consonant is 3/4So, the probability of spinning a 2 and a vowel is:
[tex]\mathbf{P(2\ and\ vowel) = \frac 14 \times \frac 14 = \frac{1}{16}}[/tex]
The earning for spinning a 2 and a vowel is $39.
So, the expected earning is:
[tex]\mathbf{Expected = 39 \times \frac{1}{16} = 2.4375}[/tex]
So, the probability of spinning a 2 and a consonant is:
[tex]\mathbf{P(2\ and\ consonant) = \frac 14 \times \frac 34 = \frac{3}{16}}[/tex]
The earning for spinning a 2 and a consonant is $26.
So, the expected earning is:
[tex]\mathbf{Expected = 26 \times \frac{3}{16} = 4.875}[/tex]
So, the probability of spinning a 1 and a vowel is:
[tex]\mathbf{P(1\ and\ vowel) = \frac 34 \times \frac 14 = \frac{3}{16}}[/tex]
The earning for spinning a 1 and a vowel is $9.
So, the expected earning is:
[tex]\mathbf{Expected = 9 \times \frac{3}{16} = 1.6875}[/tex]
So, the expected value of the game is:
[tex]\mathbf{Game =2.4375+ 4.875 + 1.6875}[/tex]
[tex]\mathbf{Game =9}[/tex]
Hence, the expected value of the game is $9
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What's 3 1/200 as a percent?
Answer:
31200=300.5%
Step-by-step explanation:
31200=3+1200
=31+1200
=(31×200200)+1200
=600200+1200=601200
We know that
601200
is the same as
601÷200
Then using
gives us
=3.005
Convert the decimal to a percent:
3.005×100
and rounding to a Max of 2 Decimal Places
=300.5%
hallar una ecuacion de la parabola cuyo foco es (-2,2) y cuya directriz es = -8
The equation of the parabola whose focus is (-2,2) and whose directrix is x= -8 is [tex](y+2)^2=-20(x+5)[/tex]
The standard formula for finding an equation of a parabola is expressed as [tex]y^2=4ax[/tex]
If the curve is shifted to the left and down, the equation becomes [tex](y-k)^2=4a(x-h)[/tex] where:
(h, k) is the vertex of the parabola
If the focus is at (-2, 2) and the directrix is at x = -8, the equivalent vertex of the parabola will be at (-5, -2) and the midpoint between the vertex and directrix is at a = -5
Substitute these values into the formula of the parabola.
[tex](y-k)^2=4a(x-h)\\(y-(-2))^2=4(-5)(x-(-5))\\(y+2)^2=-20(x+5)\\[/tex]
Hence the equation of the parabola whose focus is (-2,2) and whose directrix is x = -8 is [tex](y+2)^2=-20(x+5)[/tex]
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2 paisa per 2 rupees per month
Answer:
2 paisa per rupees per month
So rate= 2%
If the equation of the line is f(x) = 1/3x - 5 , what would be the new equation if there was a reflection over the y- axis, a dilation of -6, and a translation of 4 units up?
pls help I already solved but I'm not sure if I did a step out of order
Answer: Thus, after the transformation, the graph consists of points (x,y) satisfying y=2(x−3)2. This is the equation of the transformed graph.
Step-by-step explanation:
Consider the graph y=x2. Suppose the graph is dilated from the x-axis by a factor of 2, and then translated 3 units to the right. What is the equation of the resulting graph?
Solution
The transformation given is Trans(3,0)∘Dilx-axis,2. Denote by (x′,y′) the image of a point (x,y) under this transformation. A point (x,y) is sent to (x,2y) by the dilation, and then to (x+3,2y) by the translation, so (x′,y′)=(x+3,2y).
The original graph consists of points (x,y) such that y=x2. Then it is transformed so that (x,y)↦(x′,y′)=(x+3,2y). We must find what equation is satisfied by x′ and y′.
Since x′=x+3 and y′=2y, we have x=x′−3 and y=y′/2. Thus y=x2 implies
y′2=(x′−3)2or equivalentlyy′=2(x′−3)2.
Three friends each create 4 bags of starter bread dough. After ten
days, each of those four bags is then divided into four more bags of
dough. How many days pass before 192 of dough are created?
1.20
2.40
3.30
Answer:
20
Step-by-step explanation:
4x3=12
12x4=48 after 10
48x4=192 after another 10
la quinta parte de 20
Answer:
4
Step-by-step explanation:
20/5 = 4
A 6 pound bag of grass seed covers 7,000 square feet. How many pounds would be needed to cover 23,000 square feet?
Write answer as an integer or a reduced fraction.
Answer:
Step-by-step explanation:
You can setup a proportion as follows:
4 lb = 9000 ft2
x lb = 25000 ft2
Solve for x = 25000 ft2 x 4 lb / 9000 ft2 = 11.11 lb ~ 11 lb rounded to a whole number
Kim, Jenny, and Wendy are basketball players. Each plays a different position (guard, forward, and center) and wears a different number (30, 32, and 35). Kim and number 30 are too small to play center. Number 35 in the center. Neither Kim nor Wendy is the forward. Who plays guard, and what uniform number does she wear? Be sure to check both answers. A.30 B.Wendy C.Jenny D.Kim E.35 F.32
Answer:its f
Step-by-step explanation:
the only answer left i hope this helps =)
you are slicing pie for your family. Your grandmother asks for 1/3 of the pie. Your brother asks for 1/4 of the same pie. Your aunt asks for 1/2 of the remainder of the pie. How much pie is left?
Determine the correct equation for the following verbal sentence:
The ticket price, t, for a concert attended by 220 people equals the total revenue, r, divided by the number of people who attended.
a.
t = StartFraction r Over 220 EndFraction
c.
t = 220r
b.
t = 220 - r
d.
t = 220 + r
Answer:
t =
Given:
The total ticket price =t
Total number of people attended the concert = 350
Total revenue = r
To Find:
The expression for finding the t value
Solution:
The ticket price t =
Substituting the total number of people who attended the concert
t =
Step-by-step explanation:
Hope this helps:)
Please view the image above for the question ^^
Answer:
2
Step-by-step explanation:
After reflecting ABC over the y-axis and translating that image down, ABC will map onto DEF.
Answer:
(2)
Step-by-step explanation:
If you reflect ABC across the y axis it would look like DEF but above the x axis; translate it down and you get DEF.
what is the next number 3 7 8 3 12 9
Find the equation of the line
Graph the number on the number line.
Answer:
Step-by-step explanation:
can u take good picture
If Esteban continues at the same rate, how many miles will he have traveled in 6 hours?
A. 36
B. 300
C. 360
D. 420
Answer360
Step-by-step explanation:
PLEASE I NEED HELP ITS URGENT.
Answer:
Step-by-step explanation:
Plane B is flying 55mph
55
mph
faster than Plane A and can fly 4275
4275
miles in the same amount of time it takes Plane A to fly 4000
4000
miles. Find the amount of time it takes for each plane to travel their respective distances.
Answer:
It takes around 5s for each plane to travel their respective distances.
Step-by-step explanation:
These points are linear.
Find the slope.
m = [?]
A $600 fax machine is on sale for 20% off. Find the amount of the discount and the sale price.
The amount of discount is $0.
The sale price is $0
Answer:
The amount of discount is $120
The sale price is $480
Step-by-step explanation:
The amount of discount = Original price × the Percentage off
The amount of discount = $600 × 20 %
The amount of discount = $600 × .20
The amount of discount = $120
The sale price = Original price - Discount
The sale price = $600 - $120
The sale price = $480
does 17/10 and 12/5 form a proportion?
Answer:
No
Step-by-step explanation:
17/10 is not proportional to 12/5. Proportional relationships are relationships between two variables where their ratios are equivalent. 17/10 as a ratio is 17:10 and 12/5 as a ratio would be 12:5. A proportional relationship for 12/5 would be 24/10.
Hope this helps :)
No, 17/10 and 12/5 do not form a proportion.
What is a proportion?A proportion is an equation that sets two ratios at the same value.
We have two fractions,
17/10 and 12/5.
That means,
17/10 = 1.7
And 12/5 = 2.4
And 1.7 is not equals to 2.4.
So, the fraction does not show the proportional relationship.
Therefore, the fraction does not show the proportional relationship.
To learn more about the proportion:
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¿De qué número es 60 el 80%?
Answer:
48
Step-by-step explanation:
y= -6x + 1/2
PLEASE I NEED THE ANSWER AND EXPLANATION
Answer:
m = -6 (slope)
b = (1/2)
The Y posistion is (0, 0.5) and the slope of the graph is -6/1 (down 6, right 1).
Some examples of where the line is could be:
(1, -5.5)
(-1, 6.5)
Does anybody know the slope for these graphs?
A line has a slope of -4. The line passes through the point (-2,1). What is the point- slope form of the line?
y - 1 = -4 (x + 2)
y - 4 = -2 (x - 1)
y - 1 = 4 (x - 2)
y - 2 = -4 (x - 1)
Answer:
the answer is A
I followed the point slope formula and added in the x and y values
If f (g(x)) = Square root x+8, identify the inside function g(x) and the outside function f(x) of the composite function.
Answer:
Given composite function:
f(g(x)) = √(x + 8)Possible functions that compose it:
g(x) = x + 8and
f(x) = √xA man is walking at 7km/hr. How long will he take to cover a distance of 42km?
[tex] \: \: \: \: \: \: [/tex]
1.75hrsStep-by-step explanation:
it would take 1.75 hrs to cover a distance of 7 kilometres by walking 4 kilometres per hourspeed= Distance/Time
= 4/1 = 4Time Distance/Speed
= 7/4 =1.75hrs.hope it helps[tex] \: \: \: \: \: \: [/tex]
Below is an excerpt from the home loan contract Kyle signed with his bank.
“The sum of the principal of the loan and all applicable interest will be divided into 360 monthly payments according to the amortization schedule.
The Buyer shall make each monthly payment by the first day of the month it is due. A payment not received by the first day of the month it is due will be considered delinquent. A payment not received by the fifteenth day of the month it is due will be subject to a late charge of $75.00. If a payment is not received by the last day of the month it is due, the Buyer and transaction shall be reported to the appropriate credit agencies.
In the event of delinquency, the Buyer may divide any payment not received into not more than three equal installments to be included on the next consecutive monthly payments. Notification of the Buyer’s intent to do so must be made by written letter or phone call to the phone number and address listed below within one business week of delinquency.”
Due to some changes at his job and the resulting loss of income, Kyle will not be able to make his monthly payment by the first of the month. He does expect to be able to make it by the 9th of the month. According to the contract, what does Kyle need to do?
a.
Other than pay the monthly payment, Kyle does not need to do anything.
b.
Notify the bank to let them know that his payment is going to be eight days late
c.
Divide this payment into three payments to be included in future monthly payments.
d.
Include an extra $75.00 with his payment to cover the late fee that will be assessed.
9514 1404 393
Answer:
a. Other than pay the monthly payment, Kyle does not need to do anything.
Step-by-step explanation:
If Kyle plans to make a payment by the 15th of the month, he need do nothing, except make the payment.
If he plans to divide the payment into 3 parts, he needs to contact the bank within a week of the first of the month. If he plans to make a payment after the 15th, he needs to add $75 to it for the late charge.
Answer:
i would think it would be [A Other than pay the monthly payment, Kyle does not need to do anything.]
Step-by-step explanation:
A furniture store receive
order for 456 chairs. They
can fit 9 chairs in a large
shipping box. How many
shipping boxes will they
need to ship all of the
chairs?