Step-by-step explanation:
Rate of growth equals 420/100 = 4.2 times per hour
So after t=three hours,
size of culture = 100*(4.2)^t = 100*4.2^3=7408.8 bacteria,
round to nearest unit 7409 bacteria after three hours (after initial size of 100).
Answer:
a) 100•4.2^t
b) P(3)= about 7409 bacteria
c) P’(3)= about 10,632 bacteria per hour
d) t= about 3.2 hours
Step-by-step explanation:
i need this asap guys im giving brainliest
An aquarium is in the shape of a rectangular prism. How much water will it take to fill the aquarium if the dimensions are 2ft by 4ft by 3ft? 12 cubic feet 24 cubic feet 36 cubic feet 8 cubic feet
Answer:
24 cubic feet.
Step-by-step explanation:
What we need to do here, is to find the volume of the aquarium.
The Aquarium is a rectangular prism.
The volume of a rectangular prism is length*width*height (we just multiply the dimensions together)
2*4*3=8*3=24
The volume of the aquarium is 24 cubic feet, and therefore 24 cubic feet of water is required to fill the tank.
Answer:
Hello! :) The answer will be under “Explanation”
Step-by-step explanation:
The answer will be 24 cubic feet.
Work:
LxWxH
(Length,Width,Hight)
So you the question is asking about volume, we need to do the formula (length,width, and hight)
Now we have to multiply
2x4=8
8x3=24
So the answer will be 24 cubic feet.
Hope this helps! :)
Which of the following is a secant on the circle below?
DE is secant on the circle below.
What is Secant?A secant line is a straight line that twice intersects a circle.
We have a diagram of circle.
As, Either a secant or a tangent will arise from the circle's junction.
A secant is a line that intersects a circle twice. The relationship between the circle and the line that intersects it is explained by this idea.
Again from the figure CA and CE intersect circle at B and D.
It can also represented that the AB and DE intersects at a point C.
So, the secant line that intersects the circle twice.
Learn more about Secant here:
https://brainly.com/question/14348796
#SPJ7
please help! the number of candies consumed varies inversely with the number of children present
Answer:
The answer is
210 candiesStep-by-step explanation:
Let n represent the number of children
Let c represent the number of candies
The above variation is written as
[tex]c = \frac{k}{n} [/tex]
when n = 12 c = 140
So we have
[tex]140 = \frac{k}{12} [/tex]
Cross multiply
That's
k = 1680
So the formula for the variation is
[tex]c = \frac{1680}{n} [/tex]
when n = 8
[tex]c = \frac{1680}{8} [/tex]
c = 210
Therefore there are 210 candies consumed when there are 8 children
Hope this helps you
To get from North to East, you walk 12 meters south and 16 meters east, as shown
in the diagram below. If you wanted to walk straight from North to East, what would
the distance be? Solve for x
Answer:
ur pito is to small
Step-by-step explanation:
it to little
g A catering service offers 7 %E2%80%8b Appetizers, 9 main%E2%80%8B courses, and 5 desserts. A banquet committee is to select 2 %E2%80%8b Appetizers, 8 main%E2%80%8B courses, and 4 desserts. How many ways can this be%E2%80%8B done
Answer:
945 ways
Step-by-step explanation:
Total
Number of Appetizers = 7Number of main courses = 9Number of desserts =5Required Selection
Number of Appetizers = 2Number of main courses = 8Number of desserts =42 Appetizers out of 7 can be selected in [tex]^7C_2[/tex] ways
8 main courses out of 9 can be selected in [tex]^9C_8[/tex] ways
4 desserts out of 5 can be selected in [tex]^5C_4[/tex] ways
Therefore, the number of ways this can be done
[tex]=^7C_2 \times ^9C_8 \times ^5C_4[/tex]
=945 ways
Select the correct answer from each drop-down menu. The given equation has been solved in the table.
Answer:
1). SUBTRACTION property of equality
2). MULTIPLICATION property of equality
Step-by-step explanation:
Step 2:
When we subtract the same number from both the sides of an equation it represents the subtraction property of equality.
[tex]\frac{x}{4}+5-(5)=23-(5)[/tex]
Here 5 has been subtracted from both the sides.
Therefore, SUBTRACTION property of equality was applied.
Step 4:
If the same number is multiplied to both the sides of an equation, multiplication property of equality is applied.
[tex]4\times \frac{x}{4}=4\times (18)[/tex]
Here 4 has been multiplied to both the sides.
Therefore, MULTIPLICATION property of equality was applied.
What is the area of this composite shape? Enter your answer in the box. in²
Answer:
53 in.
Step-by-step explanation:
to find the area u do 8 times 6 and 1/2 2(5)
triangle = 1/2bh
rectangle = bh
hope this helps
The scores on an exam are normally distributed, with a mean of 85 and a standard deviation of 8. What percent of the scores are greater than 93?
Answer:
16%
Step-by-step explanation:
Find the z-score.
z = (x − μ) / σ
z = (93 − 85) / 8
z = 1
This means 93 is one standard deviation above the mean.
According to the empirical rule, 68% of a normal distribution is between -1 and +1 standard deviations. So 32% is either less than -1 or greater than +1 standard deviations. Normal curves are symmetrical, so 16% is greater than +1 standard deviations.
A cylinder fits inside a square prism as shown. For every
cross section the ratio of the area of the circle to the
area of the square is on
since the area of the circle is the area of the square,
the volume of the cylinder equals
Cross section
o
o
o
o
the volume of the prism or (20(h) or turh.
the volume of the prism or (47)(h) or 2nuh.
the volume of the prism or (20)(h) or Ph.
the volume of the prism or (47)(h) or iPh.
kl *
Answer:
Volume of cylinder = π/4 (the volume of the prism) or π/4 (4r²)(h) or πr²h (D)
The complete question related to this found on brainly (ID: 4049983 and 4265826) is stated below:
A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or πr^2 or π/4. Since the area of the circle is π/4 the area of the square, the volume of the cylinder equals
A) π/2(the volume of the prism) or π/2 (2r)(h) or πrh.
B) π/2 (the volume of the prism) or π/2 (4r2)(h) or 2πrh.
C) π/4(the volume of the prism) or π/4 (2r)(h) or π/4(r2h).
D) π/4(the volume of the prism) or π/4 (4r2)(h) or πr2h.
See attachment for diagram
Step-by-step explanation:
Area of the cross section in the cylinder
Area of circle = πr²
Area of the cross section in the square prism
Area of square = (side length)²
Here the side length = diameter
Diameter = 2×radius = 2r
Area of square = (2r)² = 4r²
Ratio of area of circle to area of square = πr²/4r² = π/4
Area of circle/area of square = π/4
Area of circle = π/4 × area of square
Area of circle = π/4 × 4r²
Volume of cylinder = area of circle × height
Volume = πr² ×h = πr²h
Volume of square prism = area of square × height = (2r)²h = 4r²h
Ratio of volume of cylinder to volume of square prism = πr²h/4r²h = π/4
Volume of cylinder/volume of square prism = π/4
Volume of cylinder = π/4 × volume of square prism = π/4 × 4r²h
= πr²h
Therefore Volume of cylinder = π/4 (the volume of the prism) or π/4 (4r²)(h) or πr²h (D)
3. Find the measure of x.
a 18°
b. 54°
C 126
d. 45
Answer:
18 degrees
Step-by-step explanation:
The triangle is an iscoceles right triangle.
The angles in a triangle add up to 180.
90+2y (iscoceles) =180
2y=90
y=45
So the angles of the right triangle are 45. However, you have to take away 27 because you are solving for only a part of 45. 45-27=18
Which of the following statements about trapezoids is true?
O A. Opposite angles are equal
B. One pair of opposite sides is paralel.
C. Opposite sides are equal
O D. Both pairs of opposite sides are parallel
Answer:
B
Step-by-step explanation:
Trapezoids have only one pair of parallel lines.
In the xy-plane, what is the y-intercept of the graph of the equation y=V4-?
O a. 2
O b.4
O c. 16
O d. There is no y-intercept.
Answer:
D
Step-by-step explanation:
There isn't enough information to find a y-intercept.
What is the next item in the sequence −10,−3,4,11
Answer:
18
Step-by-step explanation:
The pattern in this sequence is that you add 7 from the previous number to get the next number (-10 + 7 = -3, -3 + 7 = 4, etc). The next item will be 11 + 7 + 18. Hope this helps!
The next item in the sequence is 18.
What is sequence and series ? A series is the total of all elements, but a sequence is an ordered group of elements in which repetitions of any kind are permitted. One of the typical examples of a series or a sequence is a mathematical progression.A number sequence is a collection of numbers that move from term to term according to a specific pattern or rule.You should be familiar with the following four main categories of sequences: arithmetic sequences, geometric sequences, quadratic sequences, and special sequences.
The sequence is -10 ,-3, 4, 11,........
this sequence is following pattern ,you add 7 from the previous number to get the next number
First term = -10 + 7 = -3,
Second term =-3 + 7 = 4, .
The next item will be 11 + 7 = 18.
Therefore, The next item in the sequence is 18.
Learn more about sequence brainly.com/question/12474324 here
#SPJ2
PLEASE HELP ME!! A hexagon has vertices (3,1) and (4,1). The hexagon is dilated. The new hexagon has vertices (6,1) and (10,1). {In the same spots as the old hexagon}. What is the center of dilation? What is the dilation factor? I can try to add information.
Answer:
( 2,1) is the center of dilation and 4 is the scale factor
Step-by-step explanation:
A' = k( x-a) +a, k( y-b)+b where ( a,b) is the center of dilation and k is the scale factor
3,1 becomes 6,1
6,1 = k( 3-a) +a, k( 1-b)+b
6 = 3k -ka+a
1 = k -kb +b
4,1 becomes 10,1
10,1 = k( 4-a) +a, k( 1-b)+b
10 = 4k -ka+a
1 = k -kb +b
Using these two equations
6 = 3k -ka+a
10 = 4k -ka+a
Subtracting the top from the bottom
10 = 4k -ka+a
-6 = -3k +ka-a
------------------------
4 = k
Now solving for a
6 = 3k -ka+a
6 = 3(4) -4a+a
6 =12 -3a
Subtract 12
6-12 = -3a
-6 = -3a
Divide by -3
-6/-3 = -3a/-3
2 =a
Now finding b
1 = k -kb +b
1 = 4 - 4b+b
1 =4 -3b
Subtract 4
-3 = -3b
Divide by -3
1 = b
Answer:
Dilation factor: 4.
Center of dilation: (2, 1).
Step-by-step explanation:
The distance between the old vertices was 4 - 3 = 1. The distance between the new vertices is 10 - 6 = 4. 4 / 1 = 4. That means that the dilation factor is 4.
Now that we have a dilation factor, we can use the formulas x1 = d(x-a) +a and y1 = d( y-b)+b to solve for the center of dilation.
In this case, d = 4, x1 = 10, x = 4, y1 = 1, and y = 1.
10 = 4(4 – a) + a
10 = 16 – 4a + a
10 = 16 – 3a
-3a + 16 = 10
-3a = -6
a = 2
1 = 4(1 – b) + b
1 = 4 – 4b + b
1 = 4 – 3b
-3b + 4 = 1
-3b = -3
b = 1
And so, your center of dilation will be (2, 1).
Hope this helps!
Please help ASAP thanks in advance
Answer:
Make a point at (3pm, 45), (4.5 pm, 45), (5.5pm, 30), (6.5pm, 15), and (7.5pm, 0). Then connect the dots starting at (0,0) Then you have your graph :)
Step-by-step explanation:
What is y - 8 = 4(x - 4) in slope intercept form?
Answer:
y=4x-8
Step-by-step explanation:
First you must use the distributive property and get y-8=4x-16.
Then you have to add 8 on both sides so just y is left on the left side.
This will get you y=4x-8 in slope-intercept form.
A rookie quarterback is negotiating his first NFL contract.His opportunity cost is 10%. He has been offered three possible 4-year contracts. Payments are guaranteed, and they would be made at the end of each year. Terms of each contract are as follows:________.
1 2 3 4
Contract 1 $3,000,000 $3,000,000 $3,000,000 $3,000,000
Contract 2 $2,000,000 $3,000,000 $4,000,000 $5,000,000
Contract 3 $7,000,000 $1,000,000 $1,000,000 $1,000,000
As his advisor, which contract would you recommend that he accept?
Answer:
He should accept contract 2 because it has a higher present value.
Step-by-step explanation:
we need to find the present value of each contract:
Contract 1 = $3,000,000/1.1 + $3,000,000/1.1² + $3,000,000/1.1³ + $3,000,000/1.1⁴ = $2,727,273 + $2,479,339 + $2,253,944 + $2,049,040 = $9,509,596
Contract 2 $2,000,000/1.1 + $3,000,000/1.1² $4,000,000/1.1³ + $5,000,000 /1.1⁴ = $1,818,182 + $2,479,339 + $3,005,259 + $3,415,067 = $10,717,847
Contract 3 $7,000,000/1.1 + $1,000,000/1.1² + $1,000,000/1.1³ + $1,000,000/1.1⁴ = $6,363,636 + $826,446 + $751,315 + $683,013 = $8,624,410
It is believed that 11% of all Americans are left-handed. A college needs to know how many left-handed desks to place in the big lecture halls being constructed on its campus. In a random sample of 120 students from that college, whether or not a student was left-handed was recorded for each student. The college wants to know if the data provide enough evidence to show that students at this college have a higher percentage of left-handers than the general American population?
Required:
a. State the random variable, population parameter, and hypotheses.
b. State the Type I and Type II errors in the context of this problem.
Answer:
(a) H₀: p = 0.11 vs. Hₐ: p > 0.11.
(b) A type I error occurs when we discard a true null hypothesis (H₀) and a type II error is made when we fail to discard a false null hypothesis (H₀).
Step-by-step explanation:
A college needs to know how many left-handed desks to place in the big lecture halls being constructed on its campus.
From past data, it is believed that 11% of all Americans are left-handed.
The college wants to know if the data provide enough evidence to show that students at this college have a higher percentage of left-handed people than the general American population.
(a)
The hypothesis can be defined as follows:
H₀: The percentage of left-handed people in the college is 11%, i.e. p = 0.11.
Hₐ: The percentage of left-handed people in the college is more than 11%, i.e. p > 0.11.
(b)
A type I error occurs when we discard a true null hypothesis (H₀) and a type II error is made when we fail to discard a false null hypothesis (H₀).
In this case, a type I error would be committed if it is concluded that the percentage of left-handed people in the college is more than 11% when in fact it is 11%.
And, a type II error would be committed if it is concluded that the percentage of left-handed people in the college is 11% when in fact it is more than 11%.
Find the value of x geometry
Answer:
x = 22
Step-by-step explanation:
Since the the 2 bisectors are equal, that means the chords are also equal. Since bisector splits into 2 equal parts, 11 + 11 equals 22
A simple random sample of size nequals17 is drawn from a population that is normally distributed. The sample mean is found to be x overbar equals 56 and the sample standard deviation is found to be sequals10. Construct a 95% confidence interval about the population mean. The lower bound is nothing. The upper bound is nothing. (Round to two decimal places as needed.)
Answer:
95% confidence intervals about the population mean is
(51.7656 , 60.2344)
Step-by-step explanation:
Step(i):-
Given random sample of size 'n' =17
Given mean of the sample 'x⁻' = 56
Given standard deviation of sample 's' = 10
95% confidence intervals about the population mean is determined by
[tex](x^{-} - t_{0.05} \frac{s}{\sqrt{n} } ,x^{-} + t_{0.05} \frac{s}{\sqrt{n} } )[/tex]
Degrees of freedom
ν = n-1 = 17-1 =16
t₀.₀₅ = 1.7459 (from t-table)
Step(ii):-
95% confidence intervals about the population mean is determined by
[tex](x^{-} - t_{0.05} \frac{s}{\sqrt{n} } ,x^{-} + t_{0.05} \frac{s}{\sqrt{n} } )[/tex]
[tex](56 - 1.7459 \frac{10}{\sqrt{17} } ,56 + 1.7459 \frac{10}{\sqrt{17} } )[/tex]
( 56 - 4.2344 , 56 + 4.2344)
(51.7656 , 60.2344)
Conclusion:-
95% confidence intervals about the population mean is
(51.7656 , 60.2344)
what is the answer to this ??
Answer:
[tex] A.\angle 1\: \\\\D. \angle 3[/tex]
Step-by-step explanation:
[tex] \angle 1\: \&\: \angle 3[/tex] are remote interior angles of [tex] \angle 6[/tex]
A couple has three children. Assuming each child has an equal chance of being a boy or a girl, what is the probability that they have at least one girl
Answer: 7/8
Step-by-step explanation:
Let the boy is letter B and the girl is letter G.
So the possible outcomes are as follows below
BBB, BBG, BGB, GBB, BGG, GBG, GGB, GGG
SO the number of possible outcomes is 8
The number of outcomes where is at least 1 girl ( triples where is 1 girl, 2 girls or all 3 children are the girls) is 7
So the probability, that family with 3 kids has at least 1 girl is
P(number of girls >=1)= 7/8
plz answer question in screen shot
Answer: 342.32
Step-by-step explanation: sin(25) = h/a
Sin(25)= h/27
27*sin(25) = h
b*h = area
A company buys a machine for $575,000 that depreciates at a rate of 30% per year. Find a formula for the value of the machine after n years. V(n)
Answer:
[tex]V(n) = 575000(0.7)^{n}[/tex]
Step-by-step explanation:
The value of the machine after n years is given by an exponential function in the following format:
[tex]V(n) = V(0)(1-r)^{n}[/tex]
In which V(0) is the initial value and r is the yearly rate of depreciation, as a decimal.
A company buys a machine for $575,000 that depreciates at a rate of 30% per year.
This means, respectively, that: [tex]V(0) = 575000, r = 0.3[/tex]. So
[tex]V(n) = V(0)(1-r)^{n}[/tex]
[tex]V(n) = 575000(1-0.3)^{n}[/tex]
[tex]V(n) = 575000(0.7)^{n}[/tex]
Now that we have our linear regression model, let’s try to make a prediction for the sales given a new set of advertising budgets as follows: new.dat <- data.frame(TV=200, Radio=10, Newspaper=20) You are required to report the predicted sales as well as the lower and upper bound for the 95% prediction interval. What will you report?
Answer:
The predicted sales for the new set of advertising budgets is 14.
Step-by-step explanation:
The linear regression model is:
[tex]\text{Sales}=2.9389+0.0458\cdot(\text{TV})+0.1885\cdot(\text{Radio})-0.0010\cdot(\text{Newspaper})[/tex]
Compute the value of sales for:
TV = 200,
Radio = 10,
Newspaper = 20
[tex]\text{Sales}=2.9389+0.0458\cdot(\text{TV})+0.1885\cdot(\text{Radio})-0.0010\cdot(\text{Newspaper})[/tex]
[tex]=2.9389+0.0458\cdot(200)+0.1885\cdot(10)-0.0010\cdot(20)\\=2.9389+9.16+1.885-0.0002\\=13.9837\\\approx 14[/tex]
Thus, the predicted sales for the new set of advertising budgets is 14.
Not sure how I would find the quadrant
www.g A survey of athletes at a high school is conducted, and the following facts are discovered: 19% of the athletes are football players, 79% are basketball players, and 14% of the athletes play both football and basketball. An athlete is chosen at random from the high school: what is the probability that they are either a football player or a basketball player
Answer:
84%
Step-by-step explanation:
The probability that the selected player is a football player, P(F)=19%
The probability that the selected player is a basketball player, P(B)=79%
The probability that the selected player play both football and basketball,
[tex]P(B \cap F)=14\%[/tex]
We want to determine the probability that a randomly chosen athlete is either a football player or a basketball player, [tex]P(B \cup F)[/tex]
In probability theory
[tex]P(B \cup F)=P(B)+P(F)-P(B \cap F)\\=79\%+19\%-14\%\\=84\%[/tex]
The probability that a randomly chosen athlete is either a football player or a basketball player is 84%.
What is the Square root of 42?
Answer:
the square root is 6.48
Answer:
≈6.48
Step-by-step explanation:
[tex]\sqrt{42}=\\6.4807407...[/tex]
If you multiply it by itself, it will equal 42. (Or you can just use a calculator)
I need help plz someone help me solved this problem I need help ASAP! I will mark you as brainiest!
Answer: (a) [tex]\bold{A=900\bigg(1+\dfrac{0.07}{4}\bigg)^{4t}}[/tex]
(b) A = $1680.67
(c) t = 9.99 years
(d) A = $1689.85
Step-by-step explanation:
[tex]A=P\bigg(1+\dfrac{r}{n}\bigg)^{nt}[/tex] where
A is the amount accrued (balance)P is the principal (original/initial amount)r is the interest rate (convert to a decimal)n is the number of times compounded per yeart is the number of yearsa) Given: P = 900, r = 7% = 0.07, n = quarterly = 4
[tex]\bold{A=900\bigg(1+\dfrac{0.07}{4}\bigg)^{4t}}[/tex]
b) Given: P = 900, r = 7% = 0.07, n = quarterly = 4, t = 9
[tex]A=900\bigg(1+\dfrac{0.07}{4}\bigg)^{4(9)}\\\\\\A = 900\bigg(1+\dfrac{0.07}{4}\bigg)^{36}[/tex]
A = 1680.67
c) Given: A = 1800, P = 900, r = 7% = 0.07, n = quarterly = 4
[tex]1800=900\bigg(1+\dfrac{0.07}{4}\bigg)^{4t}\\\\\\2=\bigg(1+\dfrac{0.07}{4}\bigg)^{4t}\\\\\\ln\ 2=ln\bigg(1+\dfrac{0.07}{4}\bigg)^{4t}\\\\\\ln\ 2 = 4t\ ln\bigg(1+\dfrac{0.07}{4}\bigg)\\\\\\\dfrac{ln\ 2}{4\ ln\bigg(1+\dfrac{0.07}{4}\bigg)}=t\\\\\\\bold{t=9.99}[/tex]
d) [tex]A=Pe^{rt}[/tex]
Given: P = 900, r = 7% = 0.07, t = 9
[tex]A=900e^{0.07(9)}\\\\\\A=900e^{.63}\\\\\\\bold{A=1689.85}[/tex]
The price of a vase was increased by 10% to £22.What was the price before the increase
Answer: £20.
Step-by-step explanation:
Let the old price = £x
Percent increase. = 10%
Increment. = 10% of £x
= 10x/100
Now new price = £22
To determine the old price we have
x + 10x/100. = 22
We now multiply everything by 100 to make it a linear expression
100x + 10x = 2200
110x = 2200, therefore
x. = 2200/110
= £20
Therefore, the price before the increase. = £20.