Answer:
Step-by-step explanation:
To predict the number of bacteria after 10 hours using the formula P = Aekt, where P is the final population, A is the initial population, k is the growth rate, and t is the time elapsed, we need to first find the value of k.
dw
We know that after 4 hours, the population grew from 3,000 bacteria to 3,600 bacteria. So we can set up an equation:
3,600 = 3,000e^(4k)
Dividing both sides by 3,000 gives:
1.2 = e^(4k)
Taking the natural logarithm of both sides gives:
ln(1.2) = 4k
Solving for k, we get:
k = ln(1.2)/4
k ≈ 0.051
Now that we have the value of k, we can use the formula to predict the number of bacteria after 10 hours:
P = 3,000e^(0.051*10)
P ≈ 5,426
Therefore, we predict that after 10 hours, there will be approximately 5,426 bacteria present in the culture.
I deposited #300.00 in a bank for
four years. If it earned simple
interest at the rate of 6% per annum,
how much interest did I get for the
four years?
Answer:
Simple interest= PRT/100
parameters
price =300
Rate=6%
Time=4years
300*6*4/100
7200/100
=72
Question 6(Multiple Choice Worth 5 points)
(Reflections MC)
Triangle NMO has vertices at N(−5, 2), M(−2, 1), and O(−3 , 3). Determine the vertices of image N′M′O′ if the preimage is reflected over y = −2.
N′(−3, 2), M′(0, 1), O′(−5, 3)
N′(−5, 0), M′(−2, −1), O′(−3, 1)
N′(−5, 1), M′(−2, 0), O′(−3, 2)
N′(−5, −6), M′(−2, −5), O′(−3, −7)
Please Fast only have 10 minutes.
The image coordinates of NMO after the translation is option d: N′(−5, −6), M′(−2, −5), and O′(−3, −7).
What is the image coordinates?To get the image coordinates of the preimage translated -2 units to the left, we simply subtract -2 from the y-coordinates of each vertex:
N' = (Nx - (-2), Ny) = (−5 , 2- (-2)) = (−5, 4)
M' = (Mx - (-2), My) = (−2 , 1 - (-2)) = (−2, 3)
O' = (Ox - (-2), Oy) = (−3 , 3- (-2)) = (−3, 5)
Therefore, based on the above, the image coordinates of NMO after the translation are N′(−5, 4), M′(-2,3 ), O′(−3, 5)
So the reflected vertices are:
The distance from N to the line y = -2 is 4, and -6 - (-2) = -4, so one need to move down 4 units to have a y-coordinate of -6.
The distance from M to the line y = -2 is 3, and -5 - (-2) = -3, so one need to move down 3 units to have a y-coordinate of -5.
The distance from O to the line y = -2 is 5, and -7 - (-2) = -5, so one need to move down 5 units to have a y-coordinate of -7.
So it will be: N′ (−5, −6), M′(−2, −5), O′(−3, −7)
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Answer:
D) N′(−5, −6), M′(−2, −5), O′(−3, −7)---------------------
Given triangle MNO with vertices:
N = (-5, 2), M = (-2, 1) and O = (-3, 3)It is reflected in line y = - 2.
This reflection doesn't affect the x-coordinates of the vertices and the y-coordinates change.
Since y = - 2 is the line of symmetry, it also represents midpoints of the segments formed by corresponding endpoints of image and preimage.
Using midpoint equation, find the y-coordinates.
Point N'(2 + y)/2 = - 2 ⇒ 2 + y = - 4 ⇒ y = - 6Point M'(1 + y)/2 = - 2 ⇒ 1 + y = - 4 ⇒ y = - 5Point O'(3 + y)/2 = - 2 ⇒ 3 + y = - 4 ⇒ y = - 7So the coordinates of the image are:
N′(−5, −6), M′(−2, −5), O′(−3, −7)This is matching the option D.
See attached for visual representation of the problem.
Please hurry due in an hour
could someone help me on this (have to turn it in by tomorrow)
Among the given options, V [tex]57^\circ[/tex] is the closest estimate for the measure of the other acute angle.
What is the measure of the other acute angle?To find the measure of the other acute angle, we can use the fact that the sum of the angles of a triangle is 180°. Let x be the measure of the other acute angle. Then we have:
[tex]x + 32.9^\circ + 90^\circ = 180^\circ[/tex]
Simplifying the equation, we get:
[tex]x = 180^\circ - 32.9^\circ - 90^\circ[/tex]
[tex]x = 57.1^\circ[/tex]
So the exact measure of the other acute angle is [tex]57.1^\circ.[/tex]
Therefore, Among the given options, V [tex]57.1^\circ.[/tex] is the closest estimate for the measure of the other acute angle.
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A recent study of high school students shows the percentage of females and males who took advanced math courses. A simple random sample of high school students was interviewed. The students were asked whether they had taken an advanced math course. Of the 150 females, 53 answered yes, as did 89 of the 275 males.
Part A: Construct and interpret a 98% confidence interval for the difference in population proportions of females and males who took advanced math courses. Be sure to state the parameter, check conditions, perform calculations, and make conclusion(s). (8 points)
Part B: Does your interval from part A give convincing evidence of a difference between the population proportions? Explain. (2 points)
Construct and interpret a 98% confidence interval for the difference in population proportions of females and males who took advanced math courses.
The parameter of interest is the difference in population proportions of females and males who took advanced math courses. We can denote this parameter by p₁ - p₂, where p₁ is the population proportion of females who took advanced math courses, and p₂ is the population proportion of males who took advanced math courses.
To construct a confidence interval for the difference in population proportions, we need to check the following conditions,
The sample of high school students should be a simple random sample.
The sample of high school students should be independent of each other.
Both groups of females and males who took advanced math courses should have at least 10 successes and 10 failures.
The sample proportions of females and males who took advanced math courses can be calculated as follows,
p₁ = 53/150 = 0.353
p₂ = 89/275 = 0.324
The sample size of females and males can also be calculated as follows,
n₁ = 150
n₂ = 275
The standard error of the difference in sample proportions can be calculated as follows,
SE = √[(p₁(1 - p₁))/n₁ + (p₂(1 - p₂))/n₂]
= √[(0.353(1 - 0.353))/150 + (0.324(1 - 0.324))/275] ≈ 0.048
Using a t-distribution with (n₁ + n₂ - 2) degrees of freedom and a 98% confidence level, we can construct a confidence interval for the difference in population proportions as follows:
(p₁ - p₂) ± t*SE
where t is the t-score corresponding to a 98% confidence level and (n₁ + n₂ - 2) degrees of freedom. Using a t-table, we can find that t ≈ 2.33.
Substituting the values into the formula, we get,
(0.353 - 0.324) ± 2.33*0.048
0.029 ± 0.112
True difference in population proportions of females and males who took advanced math courses lies between 0.029 and 0.147.
Part B: Does your interval from part A give convincing evidence of a difference between the population proportions? Explain.
Yes, our interval from part A gives convincing evidence of a difference between the population proportions because it does not contain zero. The interval (0.029, 0.147) is entirely positive, which means that the proportion of females who took advanced math courses is higher than the proportion of males who took advanced math courses. Additionally, the interval does not contain the value of one, which means that the difference in population proportions is not due to chance. Therefore, we can conclude that there is a significant difference in the population proportions of females and males who took advanced math courses.
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Three friends, Jessa, Tyree, and Ben, are collecting canned food for a culinary skills class. Their canned food collection goal is represented by the expression 24x2 − 6xy − 2. The friends have already collected the following number of cans:
Jessa: 9x2
Tyree: 6x2 − 4
Ben: 4xy + 3
Part A: Write an expression to represent the amount of canned food collected so far by the three friends. Show all your work. (5 points)
Part B: Write an expression that represents the number of cans the friends still need to collect to meet their goal. Show all your work. (5 points)
Therefore , the solution of the given problem of expressions comes out to be the buddies need to gather to reach their objective is
9x² - 10xy - 1.
What does an expression exactly mean?It is preferred to employ shifting numbers, which may also prove to be increasing, diminishing, or blocking, rather than random estimations. Only by exchanging tools, information, or answers to problems could they assist one another. The statement of truth equation may comprise the arguments, elements, or quantitative remarks for strategies like increased disagreement, production, and blending.
Here,
Part A:
=> Jasmine: 9x²
=> 6x² - 4 for Tyree
=> Ben: 4xy + 3
These three phrases added together represent the total amount of canned food collected:
=> 9x² + (6x² - 4) + (4xy + 3)
=> 15x² + 4xy - 1
As a result, the expression for how many cans of food the three buddies have so far amassed is 15x² + 4xy - 1.
Part B's collection objective is 24x² - 6xy - 2.
Collection total: 15x² + 4xy - 1
The distinction between these two phrases shows the quantity of cans the buddies still need to gather:
=> (24x² - 6xy - 2) - (15x² + 4xy - 1)
=> 9x² - 10xy - 1
As a result, the phrase for how many more cans the buddies need to gather to reach their objective is 9x² - 10xy - 1.
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find the length of the segment and round to the nearest tenth if necessary
Answer:
14
Step-by-step explanation:
line from center to chord bisect chord
so x = 14
A car salesperson sells a used car for $8,800 and earns 9% of the sale price as commission. How many dollars does the salesperson earn in commission?
Answer:
Step-by-step explanation:
8,800x0.09=792. The salesperson earns $792 in commission.
Answer:
$792
Step-by-step explanation:
8800×0.09= 792
9÷100=0.09
commission =$792
Triangle ABC is dilated to create triangle A'B'C'. If AB=12 and A'B'=9, what is the scale factor of the dilation?
If the side AB=12 and side A'B'=9, then the scale factor of the dilation is 3/4.
The "Scale-Factor" of a dilation is the ratio of the corresponding side lengths of the two similar figures.
In this case, we can find the scale factor by dividing the length of side A'B' by the length of the corresponding side AB:
So, scale factor = A'B'/AB,
Substituting the values,
We get,
Scale factor = 9/12,
Scale Factor = 3/4,
Therefore, the scale factor of the dilation is 3/4. This means that all corresponding side lengths of the dilated triangle A'B'C' are 3/4 of the length of the corresponding side lengths of the original triangle ABC.
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A regular pentagon has an apothem of
3 cm and a side length of 4.4 cm, find
its area.
The area of the polygon is 33cm²
What is area of polygon?A polygon is any closed curve consisting of a set of line segments (sides) connected such that no two segments cross.
The area of a polygon is expressed as;
A = 1/2 × p × a
where p is the perimeter of the polygon and a is the apothem.A pentagon is a 5 sides polygon.
Therefore;
Perimeter = 5 × 4.4
= 22cm
apothem = 3cm
area = 1/2 × 22 × 3
= 11× 3
= 33 cm²
therefore the area of the Pentagon in is 33cm²
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A study found that 18% of dog owners brush their dogs teeth. Of 639 owners, about how many would he expected to brush their dog’s teeth? Explain
To find the expected number of dog owners who brush their dog's teeth, we can multiply the total number of dog owners (639) by the percentage that brush their dog's teeth (18% or 0.18).
Expected number of dog owners who brush their dog's teeth = 639 x 0.18
= 115.02 (rounded to the nearest whole number)
So, we can expect about 115 dog owners out of 639 to brush their dog's teeth.
Find the circumference of a circle that has a diameter of
2.75 yards. Round your answer to the nearest yard.
Answer:
3 yards
Step-by-step explanation:
ACTIVITY 3: Given the following functions, find the following:
The values of the composite functions are (g o f)(x) = [tex]\frac{9x^2-18x+4}{4}-5[/tex], (j o g)(x) = 3x² - 15x + 1, (g o h)(x) = [tex]\frac{\left(2x-1\right)^2}{1089}-\frac{5\left(2x-1\right)}{33}[/tex] and (g o g)(-2) = 126
Calculating the composite functionsGiven that we have the function definitions
The composite functions are calculated below
(g o f)(x) = g(f(x))
(g o f)(x) = (f(x))² - 5f(x)
So, we have
(g o f)(x) = (3/2x + 1)² - 5(3/2x + 1)
Evaluate
(g o f)(x) = [tex]\frac{9x^2-18x+4}{4}-5[/tex]
Next, we have
(j o g)(x) = j(g(x))
(j o g)(x) = 3g(x) + 1
So, we have
(j o g)(x) = 3(x² - 5x) + 1
(j o g)(x) = 3x² - 15x + 1
Next, we have
(g o h)(x) = g(h(x))
(g o h)(x) = (h(x))² - 5h(x)
So, we have
(g o h)(x) = ((2x - 1)/33)² - 5((2x - 1)/33)
Evaluate
(g o h)(x) = [tex]\frac{\left(2x-1\right)^2}{1089}-\frac{5\left(2x-1\right)}{33}[/tex]
Lastly, we have
(g o g)(-2) = g(g(-2))
(g o g)(-2) = (g(-2))² - 5g(-2)
So, we have
(g o g)(-2) = ((-2)² - 5(-2))² - 5((-2)² - 5(-2))
(g o g)(-2) = 126
Hence, the values are (g o f)(x) = [tex]\frac{9x^2-18x+4}{4}-5[/tex], (j o g)(x) = 3x² - 15x + 1, (g o h)(x) = [tex]\frac{\left(2x-1\right)^2}{1089}-\frac{5\left(2x-1\right)}{33}[/tex] and (g o g)(-2) = 126
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When Sarah opens a map of her neighborhood on her cell phone, she notices that the park near her house is 0.5 cm wide. She zooms in until it is 3 times as large. If the park is 15 m wide, what is the scale of her zoomed-in map?
A 10cm=1 m
B 1cm= 10 m
C 1cm= 30 m
D 3cm= 10m
The scale of Sarah's zoomed-in map is 1cm = 1000 cm or 1cm = 10 m. So the answer is (B) 1cm = 10 m.
To find the scale of Sarah's zoomed-in map, we can use the ratio of the width of the park on the map to its actual width.
Let's first convert the width of the park from meters to centimeters, since the width of the park on the map is given in centimeters.
15 m = 1500 cm
Next, we can set up a proportion:
0.5 cm / x = 1500 cm / (3x)
where x is the scale of the zoomed-in map.
Simplifying the proportion, we get:
0.5(3x) = 1500
1.5x = 1500
x = 1000
Therefore, the answer is (B) 1cm = 10 m.
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A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
10, 11, 35, 39, 40, 42, 42, 45, 49, 49, 51, 51, 52, 53, 53, 54, 56, 59
A graph titled Donations to Charity in Dollars. The x-axis is labeled 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Frequency. There is a shaded bar up to 2 above 10 to 19, up to 2 above 30 to 39, up to 6 above 40 to 49, and up to 8 above 50 to 59. There is no shaded bar above 20 to 29.
Which measure of variability should the charity use to accurately represent the data? Explain your answer.
The range of 13 is the most accurate to use, since the data is skewed.
The IQR of 49 is the most accurate to use to show that they need more money.
The range of 49 is the most accurate to use to show that they have plenty of money.
The IQR of 13 is the most accurate to use, since the data is skewed.
Answer:
The IQR (interquartile range) of 13 is the most accurate measure of variability to use in this case, since the data is skewed and contains some outliers.
The IQR is a measure of variability that is less sensitive to extreme values than the range, and is calculated as the difference between the upper and lower quartiles (the 75th and 25th percentiles). It provides a measure of the spread of the middle 50% of the data, which is useful for understanding the typical range of donations received.
In this case, the IQR is calculated as follows:
- The median of the data is 51 (the value in the middle).
- The lower quartile (Q1) is the median of the lower half of the data, which is 42.
- The upper quartile (Q3) is the median of the upper half of the data, which is 54.
- The IQR is the difference between Q3 and Q1: IQR = Q3 - Q1 = 54 - 42 = 12.
So the IQR of 13 is a useful measure of variability to use for this data set, since it captures the spread of the middle 50% of the data while being less sensitive to the outliers at the higher end of the distribution.
I would love some help please 11-13
(11) The value of expression 3/y + 2y/4 when y = 4 is [tex]2\frac{3}{4}[/tex].
Hence the correct option is (b).
(12) The value of expression 12/y + 3y/4 when y = 8 is [tex]7\frac{1}{2}[/tex].
Hence the correct option is (c).
(13) 2x/3 + 4 = 10 equation does x = 9.
Hence the correct option is (b).
(11) The given expression is,
3/y + 2y/4 = 3/y + y/2
Substituting the value of y = 4 we get,
3/4 + 4/2 = 3/4 + 2 = [tex]2\frac{3}{4}[/tex].
Hence the correct option is (b).
(12) The given expression is,
12/y + 3y/4
Substituting y = 8 in the given equation we get,
12/8 + (3*8)/4 = 3/2 + 6 = 1 + 1/2 + 6 = [tex]7\frac{1}{2}[/tex].
Hence the correct option is (c).
(13) Given the solution is x =9.
For first option: (2/3)*9 - 6 = 6 - 6 = 0
2x/3 - 6 = 12 does not satisfied by x = 9.
For second option: (2/3)*9 + 4 = 6 + 4 = 10
So, x = 9 satisfies 2x/3 + 4 = 10.
For third option: 3*9 - 12 = 27 - 12 = 15
So x = 9 does not satisfy 3x - 12 = 21.
For fourth option: 3*9 + 12 = 27 + 12 = 39
So x = 9 does not satisfy 3x + 12 = 19.
Hence the correct option is (b).
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a couple decides to keep having children until they have a girl, at which point they will stop having children. they also agree to having a maximum of 3 children. the table shows the probability distribution of X=the number of children such a couple would have.
From the discrete distribution given, the standard deviation is of 0.83 children.
How to solveThe distribution is:
P(X=1) =0.5
P(X=2) =0.25
P(X=3) =0.25
The mean is 1.75.
The standard deviation is the square root of the sum of the difference squared between each value and the mean, multiplied by it's respective probability.
Hence:
The standard deviation is 0.83 children.
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Find the area of this triangular prism. Be sure to include the correct unit in your answer
The surface area of the prism is 360in²
What is surface area of prism?A prism is a solid shape that is bound on all its sides by plane faces.
The surface area of a prism is expressed as;
SA = 2B + ph
where h is the height of the prism and B is the base area , p is the perimeter of the base.
Base area = 1/2 × 5 × 12
= 5 × 6 = 30 in²
Perimeter of the base = 5+12+13
= 30 in²
height = 10 in
SA = 2 × 30+30× 10
= 60 + 300
= 360 in²
therefore the surface area of the prism is 360 in²
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The radius of a circle is 7 inches the radius of circle, B is 3inches greater than the radius of circle A. If the radius of circle C is 4 inches greater than the radius of circle B the radius of circle D is 2 inches less than the radius of circle C, see what is the area of each circle
The area of each circle would be given below:
Circle A= 153.86 in²
Circle B = 314in²
Circle C = 615.44in²
Circle D = 452.16 in²
How to calculate the area of circle?To calculate the area of a circle, the formula that should be used is given below such as follows:
Area of circle = πr²
For circle A;
radius = 7 in
area = 3.14×7×7 = 153.86 in²
For circle B;
radius = 3+7 = 10in
area = 3.14×10×10 = 314in²
For circle C;
radius = 10+4 = 14 in
area = 3.14×14×14
= 615.44in²
For circle D;
radius = 14-2 = 12in
radius = 3.14×12×12
= 452.16 in²
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PLEASE SOMEONE !! 15 POINTS!!!
Answer:
The answer is -5
Step-by-step explanation:
Each number moves down 5 as it moves to the right 1. Right is positive, and down is negative. -5 divided by 1 is -5.
Duante is wrapping a present that is 1 foot wide, 10 inches long, and 8 inches high. What is the minimum amount of
wrapping paper he will need?
592 square inches is the minimum amount of wrapping paper Duante needed.
Duante will need a minimum of 592 square inches of wrapping paper.
Lets convert the dimensions to the same units.
Since there are 12 inches in a foot, the dimensions are:
Width = 1 foot = 12 inches
Length = 10 inches
Height = 8 inches
The rectangular box is known as a cube
The surface area of a b=cuboid is given by SA = 2lw + 2lh + 2wh
where l is length, w is width and and h is the height of the cuboid
Substituting the given values, we get:
SA = 2(10)(12) + 2(10)(8) + 2(12)(8)
= 240 + 160 + 192
= 592
Therefore, Duante will need a minimum of 592 square inches of wrapping paper.
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m<1 =
m<3 =
m<5=
m<7=
m<2 =
m<4=
m<6=
Explain how you found m<3.
Explain how you found m<1.
By using the corresponding angles, vertically opposite angles, alternate interior angles, and linear pair theorems, the measure of the angles are:
m ∠1 = 39°
m ∠2 = 141°
m ∠3 = 141°
m ∠4 = 39°
m ∠5 = 39°
m ∠6 = 141°
m ∠7 = 39°
Calculating the measure of anglesFrom the question, we are to calculate the measure of the unknown angles in the given diagram
By the Linear pair theorem,
We can write that
m ∠5 + 141° = 180°
Thus,
m ∠5 = 180° - 141°
m ∠5 = 39°
Likewise
m ∠7 + 141° = 180°
m ∠7 = 180° - 141°
m ∠7 = 39°
By the vertical angles theorem,
We can write that
m ∠6 = 141° (Vertically opposite angles)
By the corresponding angles theorem,
We can write that
m ∠2 = 141° (Corresponding angles)
m ∠2 = m ∠3 (Vertically opposite angles)
Therefore,
m ∠3 = 141°
m ∠4 = m ∠5 (Alternate interior angles)
m ∠4 = 39°
m ∠1 = m ∠4 (Vertically opposite angles)
Therefore,
m ∠1 = 39°
Hence,
The measure of angle 1 is 39°
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A, B and C form the vertices of a triangle.
BC = 6.9cm and
∠
CBA = 137°.
Given that the area of the triangle is 12.6cm2, calculate the perimeter of the triangle rounded to 1 DP
Who can help mee??
well, let's find out how much she made on each week
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8\% of 4700}}{\left( \cfrac{8}{100} \right)4700}\implies 376\qquad \textit{ first week} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{9\% of 5500}}{\left( \cfrac{9}{100} \right)5500}\implies 495\qquad \textit{ second week}\hspace{8em}\underset{ \textit{more on the 2nd week} }{\stackrel{ 495~~ - ~~376 }{\text{\LARGE 119}}}[/tex]
Simplify with steps. (Write each expression without using the absolute value symbol)
|x+3| if x>5
The expression without the absolute value symbol is:
|x + 5| = x + 5, if x > 5
|x - 5| = 0, if x = 5
|x - 5| = 5 - x, if x < 5
Since, An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
|(x + 3) | if x > 5
This can be written as,
= |x + 3|
Now,
|x + 5| = x + 5, if x > 5
|x - 5| = 0, if x = 5
|x - 5| = 5 - x, if x < 5
Thus,
The expression without the absolute value symbol is:
|x + 5| = x + 5, if x > 5
|x - 5| = 0, if x = 5
|x - 5| = 5 - x, if x < 5
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In a large school, it was found that 79% of students are taking a math class, 70% of student are taking an English class, and 67% of students are taking both.
Find the probability that a randomly selected student is taking a math class or an English class. Write your answer as a decimal, and round to 2 decimal places if necessary.
Find the probability that a randomly selected student is taking neither a math class nor an English class. Write your answer as a decimal, and round to 2 decimal places if necessary.
a) The probability that a randomly selected student is taking a Math class or an English class is 0.82.
b) The probability that a randomly selected student is taking neither a math class nor an English class is 0.18.
What is the probability?Probability refers to the chance or likelihood that an expected success, event, or outcome occurs from many possible successes, events, or outcomes.
Probability is represented as a fractional value using decimals, fractions, or percentages.
The percentage of students taking a math class =79%
The percentage of students taking an English class = 70%
The percentage of students taking both classes = 67%
Let the event that a student is taking a math class = m
Let the event that a student is taking an English class = e
The probability of m is p(m) = 0.79
The probability of e is p(e) = 0.70
The probability of m and e is p(m and e) = 0.67
The probability that a randomly selected student is taking a math class or an English class = 0.82 (0.79 + 0.70 - 0.67)
The probability that a randomly selected student is taking neither a math class nor an English class = 0.18 (1 - 0.82)
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A single fair dice is rolled. Find the probability of getting a 2?
Answer:
1/6
Step-by-step explanation:
Chances of getting 2 = 1/6
College Level Trigonometry!!!
An equation that models the position of the object at time t is:
s(t) = -2cos(2πt/5).
How to interpret the trigonometric graph?The general form for the equation that will model a wave is:
±a (sin/cos) (2π(x - p)/T)
where:
a is the amplitude
p is the phase shift
T is the period.
The ± will become +ve provided that the graph starts in the positive direction, and the will become -ve provided it starts in the negative direction.
The (sin/cos) will become sine provided the graph starts at 0 before it is being shifted. Then, it becomes cosine provided that the graph starts at the amplitude.
In this case, our graph begins at negative, and the at the amplitude that has no phase shift, the ±ve will become -ve, (sin/cos) will now become cos, and p will become zero. Plugging in the values that were given in the problem, we see that a = 2 and T = 5.
Thus, this equation is: s(t) = -2cos(2πt/5).
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Helppppppp pleaseeeee
Erica spins a spinner with equal sections numbered 1 through 4 and selects a colored tile from a bag. Based on the tree diagram given, what is the probability of spinning a 2 or 3 on the spinner and drawing a blue tile?
Therefore, the probability of spinning a 2 or 3 on the spinner and drawing a blue tile is 1/6.
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible, and 1 indicating that the event is certain to occur. Probability theory is an important branch of mathematics used in many fields, including statistics, economics, engineering, and science, to help make predictions and informed decisions based on data and uncertain events.
Here,
Based on the given tree diagram, the probability of spinning a 2 or 3 on the spinner is 1/2 since there are two possible outcomes (2 or 3) out of four equally likely outcomes (1, 2, 3, or 4).
The probability of drawing a blue tile after spinning a 2 or 3 is 1/3 since there is only one blue tile out of three possible outcomes (blue, green, or red) for each spin result of 2 or 3.
To calculate the probability of both events happening together (spinning a 2 or 3 and drawing a blue tile), we need to multiply the two probabilities:
P(2 or 3 and blue) = P(2 or 3) x P(blue | 2 or 3)
= (1/2) x (1/3)
= 1/6
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