The probability that she got exactly 3 questions correct is 0.208 , Option B is the correct answer.
What is Probability ?Probability can be defined as the likeliness of
If you use the formula P(r)=[tex]^nC_r P^rq^{n-r}[/tex]
P is the probability of success = 3/4 = .25
the total number of questions is n = 8
the total number of questions that Johnni got correct is r = 3
the probability of getting an answer wrong is q = 1-0.25 = 0.75
Substituting all of these values
[tex]^8C_3 P^3 (0.75)^{8-3}[/tex]
= .208.
The probability that she got exactly 3 questions correct is 0.208 , Option B is the correct answer.
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Answer:
B. 0.208
Step-by-step explanation:
edge 2023
One of the legs of a right triangle measures 6 cm and its hypotenuse measures 8 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
What is the outlier of 35, 39, 35, 34, 38, 39, 38, 33, 88, 33, 35, 38
Answer:
88
Step-by-step explanation:
All of the numbers are in the thirties (30's) except for 88, so that is the outlier
A rectangle has sides of length 8a cm and 7a cm respectively. The perimeter of the rectangle is 42 cm more than the perimeter of a square with side 4a cm. Find the length of the side of the square.
Answer:
Length of the side of the square is 12 cm.
Step-by-step explanation:
Given information:
[tex]\text{side}_1 = 8a \text{ cm (side of a rectangle)}\\\text{side}_2 = 7a \text{ cm (side of a rectangle)}\\P_\text{rec} = 42 + P_\text{sq} \text{ cm } (P_\text{rec} \text{ is perimeter of the rectangle and } \\P_\text{sq} \text{ is the perimeter of the square)}\\\text{side}_\text{sq} = 4a \text{ cm (side of a square)}[/tex]
Our mission is to find the length of the side of the square. We know that the side of the square is 4a cm, so to be able to answer we have to find the value of a first.
Step 1: Finding the value of a
Key to finding the value of a is the perimeter of the rectangle. Notice that we can calculate the perimeter of the rectangle in two different ways.
One way was given in the question:
[tex]P_\text{rec} = 42 + P_\text{sq}[/tex]
We want equations in terms of a, so we can calculate a. Perimeter of the square can be calculated as:
[tex]\text{perimeter}_\text{square} = 4 \times \text{side}[/tex]
Substituting the values in equation:
[tex]P_\text{sq} = 4 \times 4a\\P_\text{sq} = 16a[/tex]
Therefore the first equation for perimeter of the rectangle becomes:
[tex]P_\text{rec} = 42 + P_\text{sq}\\\fbox{\begin{test}P_\text{rec} = 42 + 16a\end{test}}[/tex]
For the second way we use formula for the perimeter of rectangle which is:
[tex]\text{perimeter}_\text{rectangle} = 2 \times \text{width} + 2 \times \text{length}[/tex]
Substituting the values in equation:
[tex]P_\text{rec} = 2 \times 7a + 2 \times 8a\\P_\text{rec} = 14a + 16a\\\fbox{\begin{test}P_\text{rec} = 30a\end{test}}[/tex]
Now let's equate both perimeters of the rectangle.
[tex]P_\text{rec} = P_\text{rec}\\42+16a = 30a\\42 =14a\\3 = a[/tex]
Step 2: Find the length of the side of the square
It's given that side of the square is 4a cm. All we have to do is substituting a with its value, which we got in the previous step.
[tex]\text{side}_\text{sq} = 4a\\\text{side}_\text{sq} = 4(3)\\\text{side}_\text{sq} = 12 \text{ cm}[/tex]
Which equations represent inverse variation? Check all that apply.
y=2x
pv = 13
z = ²/x
4=v/x
h=9g/5
The equations representing inverse variation are: pv = 13 and z = (2 / x) , option B and C are the answer.
What is an Inverse Variation ?When on increasing one quantity the other quantity decreases , such variation between the two entities is called Inverse Variation
For this case, what you should know is that the equations that represent an inverse variation are those that could not form a straight line, for example.
The equations are given in the question and it has to be checked if they represent inverse variation
y = 2x
y and x are in a direct variation
pv = 13
p = 13 / v
P and v are represent an inverse variation.
z = (2 / x)
z and x are represent an inverse variation.
4 = v/x
v =4x
v and x are in direct variation
h=9g/5
h and g are in direct variation
therefore , the equations representing inverse variation are:
pv = 13 and z = (2 / x)
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Find the volume (to the nearest cubic foot) of a cone with base radius 4 ft. and height 8 ft. a. 43 cu. ft. c. 134 cu. ft. b. 128 cu. ft. d. 402 cu. ft.
Volume is a three-dimensional scalar quantity. The volume of a cone with a base radius of 4 ft. and height of 8 ft. is 134 ft³.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
The volume of a cone with a base radius of 4 ft. and height of 8 ft. can be written as,
Volume = (π/3)×(Radius)²×Height
= (π/3)×(4)²×8
= 134.0412 ft³ ≈ 134 ft³
Hence, the volume of a cone with a base radius of 4 ft. and height of 8 ft. is 134 ft³.
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In her monthly tests, Mary got 20 more marks in Mathematics than in English. The total of her
marks for both tests were 130. Find her marks in each test
Answer:
75 on mathematics and 55 on English!
Step-by-step explanation:
Answer:
English test score: 55
Mathematics test score: 75
Step-by-step explanation:
Let [tex]e[/tex] be Mary's score on the English test.
We can say that [tex]e + 20[/tex] is her score on the Mathematics test, as the score for the Mathematics test is just the English test score but 20 higher.
Since both scores add up to 130, we can set up an equation to solve for the English test score. Since we said [tex]e + 20[/tex] is Mary's score on the Mathematics test, [tex]e + e + 20[/tex] is the total of her 2 test scores.
[tex]e + e + 20 = 130\\2e + 20 = 130\\2e = 110\\\boxed{e = 55}[/tex]
This means that Mary got a 55 on her English test score.
To solve for the Mathematics test score we can substitute 55 for [tex]e[/tex] in [tex]e + 20[/tex].
[tex]e + 20 = 55 + 20 \rightarrow \boxed{75}[/tex]
This means Mary got a 75 on her Mathematics test.
Those are the answers
- Kan Academy Advance
4.
In the diagram of AABC below, DE || BC,
AD= 3, DB=2, and DE = 6.m
6
E
2
B
What is the length of BC?
1) 12
2) 10
3) 8
4) 4
C
Which of the following graphs shows the solution for the inequality
y-4> 2(x+2)?
Answer:
Answer:
Graph C shows the solution for the inequality
Step-by-step explanation:
y - 4 > 2(x + 2)
y > 2x + 4 + 4
y > 2x + 8
Let y = 2x + 8, Then
X-intercept (0, 8)
Y-intercept (-4, 0)
Since the inequality sign is > we use broken line.
Put, (0, 0)
y > 2x + 8
0 > 0+ 8
0 > 8 Which is false
so, the answer will be above the broken line
Hence , Graph C shows inequality
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Concentrate is diluted with water in the ratio 3 : 2. How much concentrate is there in 125 mL of total solution?
Answer:
75 mL.
Step-by-step explanation:
3/(3+2) = 3/5 of the solution is concentrate.
So the answer is 125 * 3/5
= 3*25
= 75 mL.
The age of a father is 2 less than 7 times the age of his son. In 3 years, the sum of their ages will be 52. If the son’s present age is s years, which equation models this situation? A. B. C. D.
Answer:
First,
the age of the son: s
the age of the father is 2 less than 7 times the age of his son: 7s - 2
In 3 years, the sum of their ages will be 52, In 3 years, the age of the sun will
increase 3, so s+3. Also, the age of his
father also increase 3, (7s-2)+3
(s+3)+ [(7s-2)+3] = 52 is the equation.
The correct answer is :
( 7s - 2 ) +3+ ( s + 3 ) = 52 , or 8s + 4 = 52 .
Explanation :Since s is the son's age , " two less than seven times " the son's age would be represented by 7s - 2 .
To represent this in 3 years , we would add 3 : ( 7s - 2 ) +3 .
In 3 years , the son's age , s , would be represented by s + 3 . We are told that the sum of these ages will be 52 ; this gives us ( 7s - 2 ) +3+ ( s + 3 ) = 52 .
To simplify this , combine like terms .
7s + s = 8s ; -2 + 3 + 3 = 4 .
This gives us 8s + 4 = 52 .
Which of the following is true about a function that is constant?
It is a horizontal line.
It moves in an upward direction.
It moves in a downward direction.
It is a curve.
A function assigns the values. The correct option that describes a constant function is that It is a horizontal line.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The correct option that describes a constant function is that It is a horizontal line.
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Answer: the answer is A the others are linear or higher
It moves in a horizontal line. Its 'y value' does not change.
Step-by-step explanation:
Frank has $500 in a savings account that earns 2% interest per year. The interest is not compounded. How much interest will Frank earn in 5 years?
Answer:
$50 interest
Step-by-step explanation:
Simple interest formula
I = Prt
where:
I = interested earnedP = principal amountr = interest rate (in decimal form)t = time (in years)Given:
P = $500r = 2% = 0.02t = 5 yearsSubstitute the given values into the formula and solve for I:
⇒ I = 500 · 0.02 · 5
⇒ I = 50
Therefore, Frank will earn $50 interest in 5 years.
A gift shop owner bought fifty vases for $210. she sells seven vases for what she paid for ten originally. what profit does she make on the fifty vases, which were all sold?
The profit earned by the gift shop owner on fifty vases will be $ 91.07.
What is profit?The amount of money earned by any seller on the cost price is called the profit. It is given that A gift shop owner bought fifty vases for $210. she sells seven vases for what she paid for ten originally.
The profit will be calculated as we will create the expressions for all the selling and purchasing given in the question.
The total cost price of vases:-
50 vases = $210
1 Vase = 210 / 50 = 4.25
So 10 vases will be purchased at the price of:-
10 Vase = 4.25 x 10 = 42.5
Now from the question of the amount he paid for 10 vases, he gained it by selling 7 vases.
7 Vase = 42.5
1 Vase = 42.5 / 7 = 6.07
So he sold one vase for $6.07 and purchased it at $4.25.
The profit will be = 6.07 - 4.25 = 1.821
So profit for selling 50 vases will be:-
Profit = 50 x 1.821 = $91.07
Therefore profit earned by the gift shop owner on fifty vases will be $ 91.07.
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A line segment has more then one midpoint true or false
Answer:
false
Step-by-step explanation:
any line segment or distance has only one midpoint.
there is only one middle to everything.
how would that look like, if something had 2 middles ?
then they would not be a middle, and the middle between these 2 middles would then be the real middle ...
Answer:false
Step-by-step explanation: If a line segments has endpoints A and B, then the midpoint of that line segment is a point, M Such that M. Becuase A line segment can only IM SAYING ONLY 1 MIDPOINT!
(100 POINTS) Use the Internet or another resource to find the definition of the Fundamental Counting Principle. What does this principle state? How can the principle be used to help you identify a sample space for a compound event? What are the limitations of using the Fundamental Counting Principle when determining the probability of an outcome? Support your answers with an example.
Answer:
The fundamental counting principle is a rule used to count the total number of possible outcomes in a situation
You translate a line 10 units up. Is the image of the line still a line? O Yes O No
Answer:
It depends on what way the line is facing, if it starts out vertical(meaning up or down), the answer is yes.
Which of the triangles shown are scalene triangles? (2 points)
A group of triangles. Triangle A has three acute angles and two equal sides. Triangle B has two acute angles, one ninety degree angle, and two equal sides. Triangle C has three acute angles and two equal sides. Triangle D has two acute angles and one obtuse angle. All the sides on this triangle are different lengths.
Triangle A and Triangle B
Triangle C
Triangle B and Triangle D
Triangle D
Answer:
Triangle D.
Step-by-step explanation:
A scalene triangle has different sides.
Ginger has 52 stamps and 68 regular
stickers. What is the ratio of stamps to
regular stickers? What is the simplified
ratio?
Answer:
13 stamps : 17 stickers
Step-by-step explanation:
52 stamps : 68 stickers can be simplified down to 13 stamps : 17 stickers because their greatest common factor is 4
Use the function below to find F(3)
F(x) = (1/6)^x
Answer: 1/216
Step-by-step explanation: please mark me brainly
Answer:
f(3)=0.005
Step-by-step explanation:
Plug in 3 for x
f(3)=(1/6)^3
f(3)=0.005
Hope this helps!
If not, I am sorry.
I’m having trouble converting mixed fractions to proper fractions can someone explain?
Answer:
See below
Step-by-step explanation:
To get the fraction from mixed number you just need to take the number standing alone, multiply with the denominator and add with the numerator and keep it on top with the denominator in place to turn it into a fraction.
For example, [2]3/4 = 2*4 + 3 = 11 => the fraction is 11/4.
△ABC ~ △AMN and AM = 6, MB = 4, AN = 8, then what is the value of AC?
Answer:
AC = 13.3
Make proportional relationship:
[tex]\sf \dfrac{AB}{AC} = \dfrac{AM}{AN}[/tex]
Insert values
[tex]\rightarrow \sf \dfrac{10}{AC} = \dfrac{6}{8}[/tex]
Cross multiply
[tex]\rightarrow \sf AC = \dfrac{10(8)}{6}[/tex]
Simplify
[tex]\rightarrow \sf AC =13.3[/tex]
How many fourths are in 3
4
?
So, there are 3 fourths in 3 fourths
Factor 125x9 +64.
O (5x³-4)(25x5+20x³
+ 16)
+ 16)
O (5x³-4)(25x3+20x³
O (5x³+4)(25x5 - 20x³ +16)
O (5x³+4)(25x³ - 20x³ + 16) hurry plsss
[tex]~~~~125x^9+64\\\\=(5x^3)^3+4^3\\\\=(5x^3 +4)[(5x^3)^2 - (5x^3)(4) + 4^2]\\\\=(5x^3 +4)(25x^6-20x^3+16)[/tex]
Graph the function f(x) = 2^x - 7 on the set of axes, if g(x) = 1.5x - 3 determine if f(x) > g(x) when x - 4
The inequality expression f(4) > g(4) is true when x = 4
How to determine if f(x) > g(x)?The functions are given as:
[tex]f(x) = 2^x - 7[/tex]
g(x) = 1.5x - 3
See attachment for the graph of both functions.
From the graph, we have:
f(4) = 9
g(4) = 3
This means that:
f(4) > g(4) when x = 4
Hence, the inequality f(4) > g(4) is true when x = 4
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Write the exponent for the expression.
The exponent for the expression is
The exponent for the expression, 5 × 5 × 5 × 5 × 5, would be expressed as: [tex]5^5[/tex].
What is an Exponent?An exponent can be defined as the power to which the base is to b e raised.
For example, a × a × a can be expressed in exponent form as a³.
In the same vein, given the expression, 5 × 5 × 5 × 5 × 5, we would expressed this in exponent form as: [tex]5^5[/tex].
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Only answer if you knoww
The number of 15-year old students that took part in the survey is 300 students and 20 "15-year old" students spent between 35 and 45 minutes on social media.
What is a frequency polygon?A frequency polygon can be defined as a type of line graph that is used to plot a class frequency against the class midpoint.
For the 15-year old students, the total number of students would be calculated by adding all the data points at each frequency:
Total students = 30 + 30 + 50 + 60 + 40 + 50 + 40
Total students = 300 students.
Part B.In order to determine the number of 15-year old students than 11-year old that spent between 35 and 45 minutes on social media, we would calculate the average and then read it from the frequency polygon.
Average = (35 + 45)/2
Average = 80/2
Average = 40.
For the 11-year old, we have:
Frequency (40) = 40
For the 15-year old, we have:
Frequency (40) = 60
Now, we can calculate the difference as follows:
Difference = 60 - 20
Difference = 20 students.
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For what values of t can 10x2+tx+8 be written as the product of two binomials?
Answer:
7
Step-by-step explanation:
A conditional relative frequency table is generated by column from a set of data. the conditional relative frequencies of the two categorical variables are then compared. if the relative frequencies being compared are 0. 21 and 0. 79, which conclusion is most likely supported by the data? an association cannot be determined between the categorical variables because the relative frequencies are not similar in value. there is likely an association between the categorical variables because the relative frequencies are not similar in value. an association cannot be determined between the categorical variables because the sum of the relative frequencies is 1. 0. there is likely an association between the categorical variables because the sum of the relative frequencies is 1. 0.
The conclusion is there is likely an association between the categorical variables because the sum of the relative frequencies is 1. 0.
What is the true statement?
Categorical variables are variables that can only take on a fixed number of values. An example of categorical variables is gender. One can either be a male or a female.
The sum of the categorical variables is 1. This indicates that the two variables are negatively correlated. It means that someone would be either pick one of the variables.
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Answer:
c
Step-by-step explanation:
How would you write the equation with a slope of 2/3 and a y-intercept of -3
y = (3/2)x + 3
y = (2/3)x - 3
y = 2/3 + 3
y = 3/2 - 3
Answer:
y = (2/3)x - 3
Step-by-step explanation:
The general structure of an equation in slope-intercept form is:
y = mx + b
In this equation, "m" represents the slope and "b" represents the y-intercept. You were given the slope and y-intercept, so finding the final equation is just a matter of substituting the variables.
slope = m = (2/3)
y-intercept = b = -3
y = mx + b
y = (2/3)x + (-3)
y = (2/3)x - 3
10.3--Angles in a Triangle
Please help
The measure of x, p, q and r are 65, 20 , 40 and 40 degrees respectively.
Sum of interior angle of a triangleThe sum of interior angle of a triangle is 180 degrees. Applying the theorem to each question.
3) 40 + x + 75 = 180
115 + x = 180
x = 180 - 115
x = 65 degrees
4) p + 40 + 120 = 180
p + 160 = 180
p = 20degrees
5). The triangle is isosceles showing that the base angles are equal.
100 + q + r = 180
100 + 2q = 180
2q = 80
q =r = 40 degrees
Hence the measure of x, p, q and r are 65, 20 , 40 and 40 degrees respectively.
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