Answer:
i) [tex]P(X=12)=0.0355[/tex]
ii) [tex]P(X<10)=0.7553[/tex]
iii) [tex]P(X\geq 5)=0.9490[/tex]
Step-by-step explanation:
Let's start by defining the random variable ⇒
[tex]X:[/tex] '' Number of students that will get 7 marks out of 10 in first attempt of a certain Quiz while attempting Quiz on BlackBoard LMS ''
[tex]X[/tex] is a discrete random variable.
The probability of a randomly selected student getting 7 marks out of 10 is 0.4
(This is a data from the question).
Now, if we assume independence between the students while they are doing the Quiz and also we assume that this probability remains constant , we can modelate [tex]X[/tex] as a binomial random variable ⇒
[tex]X[/tex] ~ Bi (n,p)
Where ''n'' and ''p'' are the parameters of the variable.
''n'' is the number of students attempting the Quiz and ''p'' is the probability that a student will get 7 marks out of 10 which is 0.4 ⇒
[tex]X[/tex] ~ Bi (20, 0.4) in the question.
The probability function for [tex]X[/tex] is
[tex]p_{X}(x)=P(X=x)=\left(\begin{array}{c}n&x\end{array}\right)p^{x}(1-p)^{n-x}[/tex] (I)
Where [tex]\left(\begin{array}{c}n&x\end{array}\right)[/tex] is the combinatorial number define as
[tex]\left(\begin{array}{c}n&x\end{array}\right)=\frac{n!}{x!(n-x)!}[/tex]
Replacing the parameters in the equation (I) ⇒
[tex]P(X=x)=\left(\begin{array}{c}20&x\end{array}\right)(0.4)^{x}(0.6)^{20-x}[/tex] (II)
For i) we need to find [tex]P(X=12)[/tex]
Then, we only need to replace by [tex]x=12[/tex] in equation (II) ⇒
[tex]P(X=12)=\left(\begin{array}{c}20&12\end{array}\right)(0.4)^{12}(0.6)^{8}=0.0355[/tex]
For ii) we need to calculate [tex]P(X<10)[/tex]
This probability is equal to ⇒ [tex]P(X<10)=P(X\leq 9)[/tex] and to calculate it we need to sum [tex]P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)[/tex]
[tex]+P(X=6)+P(X=7)+P(X=8)+P(X=9)[/tex]
We can do it summing each term or either using any program.
The result is [tex]P(X<10)=P(X\leq 9)=0.7553[/tex]
Finally for iii) we need to find ⇒ [tex]P(X\geq 5)[/tex]
This probability is equal to ⇒ [tex]P(X\geq 5)=1-P(X\leq 4)[/tex] ⇒
[tex]1-P(X\leq 4)=1-[P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)][/tex]
Again we can find each term by using the equation (II) or either using a program. The result is [tex]P(X\geq 5)=0.9490[/tex]
Solve the triangle, find m∠A and m∠C. Round angles to the nearest degree.
m∠A= __∘
m∠C= __∘
Answer:
[tex]m\angle A=63^\circ\\m\angle C=26^\circ[/tex]
Step-by-step explanation:
Trigonometric Ratios
The ratios of the sides of a right triangle are called trigonometric ratios. The longest side of the triangle is called the hypotenuse and the other two sides are called the legs.
Selecting any of the acute angles as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides.
The cosine ratio is defined as:
[tex]\displaystyle \cos\theta=\frac{\text{adjacent leg}}{\text{hypotenuse}}[/tex]
Note the angle A of the figure has 17 as the adjacent leg and 38 as the hypotenuse, so we can directly apply the formula:
[tex]\displaystyle \cos A=\frac{17}{38}[/tex]
[tex]\cos A=0.4474[/tex]
Using a scientific calculator, we get the inverse cosine:
[tex]A=\arccos(0.4474)[/tex]
[tex]A\approx 63^\circ[/tex]
Since A+B+C=180°, we can solve for C:
C = 180° - A - B
C = 180° - 63° - 90°
C = 26°
Thus:
[tex]m\angle A=63^\circ\\m\angle C=26^\circ[/tex]
In the given right triangle ABC, m∠A ≈ 26.44° and m∠C ≈ 63.56°.
To solve the right triangle ABC, we can use trigonometric ratios. In a right triangle, the three main trigonometric ratios are:
1. Sine (sin): [tex]\(\sin(\theta) = \frac{{\text{opposite side}}}{{\text{hypotenuse}}}\)[/tex]
2. Cosine (cos): [tex]\(\cos(\theta) = \frac{{\text{adjacent side}}}{{\text{hypotenuse}}}\)[/tex]
3. Tangent (tan): [tex]\(\tan(\theta) = \frac{{\text{opposite side}}}{{\text{adjacent side}}}\)[/tex]
Given:
AC = 38
AB = 17
To find the angles m∠A and m∠C, we can use the sine and cosine ratios, respectively.
1. For m∠A:
[tex]\(\sin(m\angle A) = \frac{{AB}}{{AC}} = \frac{{17}}{{38}}\)\\\\\(m\angle A= \sin^{-1}\left(\frac{{17}}{{38}}\right)\)[/tex]
2. For m∠C:
[tex]\(\cos(m\angle C) = \frac{{AB}}{{AC}} = \frac{{17}}{{38}}\)\\\\\(m\angle C = \cos^{-1}\left(\frac{{17}}{{38}}\right)\)[/tex]
Let's calculate the angles:
[tex]1. \(m\angle A \approx \sin^{-1}\left(\frac{{17}}{{38}}\right) \approx 26.44^\circ\)\\\\2. \(m\angle C \approx \cos^{-1}\left(\frac{{17}}{{38}}\right) \approx 63.56^\circ\)[/tex]
Therefore, m∠A ≈ 26.44° and m∠C ≈ 63.56° (rounded to the nearest degree).
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A cab company charges $3.10 flat rate in addition to $0.85 per mile. Rex has no more than $15 to spend on a ride. Write an inequality that represents Rex's situation. How many miles can Rex travel without exceeding his limit? Round off your answer to nearest tenth.
Answer:
Step-by-step explanation:
Let the total number of miles Rex can travel be x;
If a cab company charges $0.85 per mile, then x miles will cost $0.85x
If the flat rate rate charge is $3.10, the total price for x miles will be;
0.85x + 3.10
Since Rex has no more than $15 to spend on a ride, the inequality to represent the equation will be;
0.85x + 3.10 ≤ 15 (less than or equal to means that the total value cannot exceed $15)
Next is to solve for x
Given
0.85x + 3.10 ≤ 15
subtract 3.10 from both sides
0.85x + 3.10-3.10 ≤ 15-3.10
0.85x ≤ 15-3.10
0.85x ≤ 11.90
x ≤ 11.90/0.85
x ≤ 14
This means that Rex can travel 14 miles without exceeding his limit
Answer:
[tex]3.10 + 0.85m \leq 15[/tex]
[tex]m \leq 14.0[/tex]
Step-by-step explanation:
Given
[tex]Flat\ Rate = \$3.10[/tex]
[tex]Addition = \$0.85[/tex] (per mile)
[tex]Maximum\ Amount = \$15[/tex]
Required
Determine the inequality that represents the scenario and solve
Let the number of miles be represented by m.
The company's charges can be calculated using:
[tex]Flat\ Rate + Additional\ Charges * m[/tex]
Substitute values
[tex]\$3.10 + \$0.85 * m[/tex]
Rex can't exceed $15 implies that the company's charges can't exceed Rex's budget.
This is expressed as:
[tex]\$3.10 + \$0.85 * m \leq \$15[/tex]
[tex]\$3.10 + \$0.85m \leq \$15[/tex]
[tex]3.10 + 0.85m \leq 15[/tex] ---- The inequality
Solving for m: Collect Like Terms
[tex]0.85m \leq 15 - 3.10[/tex]
[tex]0.85m \leq 11.9[/tex]
Divide through by 0.85
[tex]m \leq 11.9/0.85[/tex]
[tex]m \leq 14.0[/tex] ---- The solution
Henry left for the lake in the morning and it was 78°F.
When he arrived at the lake the temperature had increased
7° and by lunch it increased another 5°. What is the
temperature when Henry was eating lunch?
Answer:
The temputure is -64
Step-by-step explanation:
IL GIVE BRAINLIST!! PLEASE HELP! THERES 2 ANSWERS JUST SAYING!!
Answer: Option 2
Pls mark me brainilest!
Step-by-step explanation:
QUICK!!!!!
Analyze the conditional statement below and complete the instructions that follow.
If m is the midpoint of AB, then M divides AB into two congruent segments.
Identify the inverse of the converse of the conditional statement.
O If M is not the midpoint of AB, then M does not divide AB into two congruent segments.
If M is the midpoint of AB, then M divides AB into two congruent segments.
If M divides AB into two congruent segments, then M is the midpoint of AB.
Olf M does not divide AB into two congruent segments, then M is not the midpoint of AB.
Answer:
D. If M does not divide AB into two congruent segments, then M is not the midpoint of AB.
Step-by-step explanation:
A conditional statement is one that include 'if'. Thus it is also referred to as an 'if' statement.
Given a conditional statement:
If M is the midpoint of AB, then M divides AB into two congruent segments.
The converse of the given statement is done by interchanging the two parts of it. So that we have:
If M divides AB into two congruent segments, then M is the midpoint of AB.
Then, the inverse can be obtained by getting the negative of both parts of the converse. Therefore, the inverse is:
If M does not divide AB into two congruent segments, then M is not the midpoint of AB.
The correct option is D.
One Saturday, a butcher sells a total of b pounds of beef at $6.00 per pound. She also sells some pork for $7.00. On Sunday she sells b pounds of beef again, but at the sale price of $4.00 per pound. She also sells some pork for $9.00. Given that she made the same revenue of d dollars each day, which of the following systems of equations can be used to find out how many pounds of beef, b, she sold each day?
The equations that can be used to find out how many pounds of beef, b, she sold each day will be:
d = 6b + 7.
d = 4b + 9
How to illustrate the equation?From the information given, the butcher sells a total of b pounds of beef at $6.00 per pound and she also sells some pork for $7.00.
Therefore, the equation will be:
d = (6 × b) + 7.
d = 6b + 7.
d = (4 × b) + 9
d = 4b + 9
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what expression is equal to(5+x-2)×2
Given the following linear function sketch the graph of the function and find the domain and range. ƒ(x) = -5x + 4
Answer:
Domain: (-∞,∞)
Range:(-∞,∞)
Step-by-step explanation:
The sketch of the given function has been attached and the domain and range both will be (-∞,∞ ).
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A function that fluctuates linearly with respect to the changing variable is referred to as being linear.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
Given the function,
ƒ(x) = -5x + 4
Range of the function ;
Since the value of the function is defined for all real x and the value will be unique so
Range = (-∞,∞ ).
The domain of the function ;
Since it is defined for all real x so,
Domain = (-∞,∞ )
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Justin and his children went into a grocery store and he bought $18 worth of bananas and mangos. Each banana costs $0.60 and each mango costs $1.50. He bought 2 more bananas than mangos. Graphically solve a system of equations to determine the number of bananas, x, and the number of mangos, y, that Justin bought.
Write an answer in y=mx+b form, please.
Two equations.
Answer:
x=10 and y= 8.
Step-by-step explanation:
Given that the cost of 1 banana = $0.60
Cost of 1 mango = $1.50.
Total cost= $ 18
Here, x be the number of bananas and y be the numbers of mangos,
As the number of bananas is 2 more than the number of mangos,
So, x=y+2
[tex]\Rightarrow y=x-2 \cdots(i)[/tex]
Cost of x bananas [tex]=\$ 0.60 \times x[/tex]
Cost of y mangos [tex]=\$ 1.50 \times y[/tex]
Total cost = 0.6x+1.5y
[tex]\Rightarrow 18 = 0.6x+1.5y\\\\\Rightarrow 1.5y=18-0.6x\\\\\Rightarrow y= 12 - 0.4 x \cdots(ii).[/tex]
Solving both the equations (i) as well as (ii), graphically as shown in the figure by plotting both the graphs.
Both the graphs intersect at the point (10,8) as shown in the graph.
So, the solution of both the equations is, (x,y)=(10,8). i.e
The number of bananas = x= 10 and
the number of mangos = y = 8.
44.8 is what percent of 160?
Answer:
28% .................
Answer:
28%
Step-by-step explanation:
100%/x%=160/44.8
(100/x)*x=(160/44.8)*x - we multiply both sides of the equation by x
100=3.5714285714286*x - we divide both sides of the equation by (3.5714285714286) to get x
100/3.5714285714286=x
28=x
x=28
now we have:
44.8 is 28% of 160
Choose the correct answer choice.
Answer:
The T shirt choice
Step-by-step explanation:
Both values increase at the same rate therefore is proportional.
I need help please
Solving the system using equations ( 15 points)
3x+2y=17
2x+5y=8
Answer:
{x,y}={ 11 /69 ,− 11 /10 }
Step-by-step explanation:
3*10^4+2.5*10^0
ghfuigffhh
Answer:
30002.5
Step-by-step explanation:
I don’t understand.
Answer:
y = -2/3x
Step-by-step explanation:
A perpendicular line is the negative reverse of the slope of the other line. I'm not sure about the options you have there but hopefully this helps you get your answer.
The figures below are similar. Find the length of the missing side.
90
10
7
Х
36
4
14
126
X=
Answer:
63
Step-by-step explanation:
multiply the side by 9
A retail grocer bought a case of 12 packages of coffee for $52.32.
How much did the retailer pay for each package of coffee?
The retailer sold each package for $12.59.
What is the difference between the retailer’s cost and the selling price for each package of coffee?
Answer:
4.36
8.23
Step-by-step explanation:
Answer:
4.36
Step-by-step explanation:
A bag contains 95 blue marbles, 7 red marbles, and 5 green marbles. One marble is randomly
chosen. Select all true statements about the marble chosen.
A It is certain that the marble was blue.
B. It is unlikely that the marble chosen was green.
C. It is unlikely that the marble chosen was orange.
D. It is likely that the marble chosen was blue.
E It is not possible that the marble chosen was green.
E It is neither likely nor unlikely that the marble chosen was red.
Answer:
B,D, and the last E
Step-by-step explanation:
A newspaper is rolled into a cylindrical shape of approximate diameter 4cm It is wrapped for posting with a strip of paper which goes about 2 1/2 times round the newspaper Use the value 3 for π to find the approximate length of the wrapping paper. And 2. Calculate the total surface area of a solid cone of slant hight 10cm and base diameter 10 cm.Use the value 3.14 for π
Answer:
30 cm
[tex]863.5\ \text{cm}^2[/tex]
Step-by-step explanation:
d = Diameter of cylinder = 4 cm
n = Number of times the strip of paper is turned = [tex]2\dfrac{1}{2}=2.5[/tex]
Diameter of the cylinder will be approximately equal to the diameter of the paper wound. Length of one turn will be circumference of the paper
Circumference of the paper
[tex]c=\pi d\\\Rightarrow c=3\times 4\\\Rightarrow c=12\ \text{cm}[/tex]
Total length of the paper will be the number of turns multiplied by the length of one turn
[tex]l=nc\\\Rightarrow l=2.5\times 12\\\Rightarrow l=30\ \text{cm}[/tex]
Length of the strip of paper is 30 cm.
2.
l = Slant height = 10 cm
d = Base diameter = 10 cm
r = Radius of base = [tex]r=\dfrac{d}{2}=\dfrac{10}{2}=5\ \text{cm}[/tex]
Total surface area of cone is given by
[tex]S=\pi r^2+\pi rl\\\Rightarrow S=\pi r(r+rl)\\\Rightarrow S=3.14\times 5(5+5\times10)\\\Rightarrow S=863.5\ \text{cm}^2[/tex]
The total surface area of cone is [tex]863.5\ \text{cm}^2[/tex].
An isosceles triangle has base angles that each measure 42 degrees.Which equation can be used to find z, the measure of the third angle of this isosceles triangle in degrees
Answer:
z+42+42=180
Step-by-step explanation:
Since it is an isosceles triangle, the two base angles are the same and remember all the angles add to 180. So use this equation:
z+42+42=180
If you need to find z, it is 96.
Check: 96+42+42=180
What is the image point of (-3,3) after the transformation R180° 0 T-3, -4?
Answer:
Image point → (6, 1)
Step-by-step explanation:
Given point → (-3, 3)
Transformation to be done → [tex]R_{180}0T_{-3,-4}[/tex]
Transformations to be done,
Step - (1). Translation of the given by 3 units left and 4 units down.
Step - (2). Followed by the rotation counterclockwise 180° about the origin.
Rule for step (1),
(x, y) → (x - 3, y - 4)
By this rule,
(-3, 3) → [(-3 - 3), (3 - 4)]
→ (-6, -1)
Rule for step -2,
(x, y) → (-x, -y)
(-6, -1) → (6, 1)
Therefore, following these two steps coordinates of the image point → (6, 1)
Hellllllllllllppppppppppp
Answer:
The answer is 5 1/2! So what you are looking for is 1/2.
Step-by-step explanation:
Answer:
11/2
Step-by-step explanation:
YALL BETTER ANSWER THIS PLSSSSSSSSSSS
Answer:
= 3/16(0.1875)Step-by-step explanation:
explanation in the image.Answer:
Step-by-step explanation:
Take out lignes
-1/4x-3/7
= -7/12
What is the Value of the angle AEX
Answer:
52
Step-by-step explanation:
I take it that x is somewhere near the end of the diagonal line, so you want to know the value of 3x + 1???
We know that (3x + 1) + (2x + 4) = 90 degrees. That's because AEF = 90 degrees.
So begin by removing the brackets.
3x + 1 + 2x + 4 = 90 Combine the like terms.
5x + 5 =90 Subtract 5 from both sides.
5x + 5 - 5 = 90 - 5 Combine
5x = 85 Divide by 5
x = 17
3x + 1 = 3*17 + 1 = 51 + 1 = 52
Same factory has supplies expenses of $1135.78 a day, in addition to the wages above and makes $60,128.72 in one week, what is the factory's total profit or loss in one week?
Given :
Factory has supplies expenses of $1135.78 a day.
Company earns $60,128.72 in one week.
To Find :
The factory's total profit or loss in one week.
Solution :
Expenses of factory of a week :
E =$( 1135.78 × 7 ) = $7950.46 .
Now, profit is given by :
P = $60,128.72 - $7950.46
P = $52178.26
Therefore, total profit of factory in one week is $52178.26 .
Hence, this is the required solution.
Can somebody plz answer all of them correct! (Only if u done this before)
thanks! WILL MARK BRAINLIEST
(Don’t judge me..I didn’t study so I need to do corrections)
Answer:
23) 53/100
24)2/5
25)3/5
26)11/50
27)17/50
28)19/1000
29)4/5
30)1/250
31)9/25
32)1 3/10
33)11 1/2
34) 7 3/40
Step-by-step explanation: Hope this helps!
Can someone help me cuz i need help
Answer:
f
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Step-by-step explanation:
if g(x)=x²-2 and p(x)=2x+3, find (g·p)(x)
Brad had 10 crickets in his pet lizard’s cage. After one day, Brad’s lizard has eaten 20% of the crickets he had put in the cage. By the end of the next day, the lizard had eaten 25% of the remaining crickets. how many crickets were left in the cage at the end of the second day?
Find tan-1 1.4281 to the nearest degree.
a. 10°
b. 55°
C. 5°
d. 35°
Answer:
[tex]\:x=55^{\circ \:\:}[/tex]
Therefore, option 'b' is correct.
Step-by-step explanation:
Let x be the angle
tan x = 1.4281determining the [tex]\tan ^{-1}\left(1.4281\:\right)[/tex]
[tex]\:\tan \:x\:=1.4281\:[/tex]
[tex]x=\tan ^{-1}\left(1.4281\:\right)[/tex]
[tex]\:x=55^{\circ \:\:}[/tex]
Therefore, option 'b' is correct.