There is a 9/25 chance that two numbers will be added together such that their total exceeds their product.
How to find out the probabilityThe set of positive numbers are:
{1,2,3,4,5}
We have to independently select two numbers from these sets.
We are trying to determine the likelihood that the sum is larger than the product of the integers.
When one of the chosen numbers is 1, the total will always be greater than the product because:
1*1=1 & 1+1=2
1*2=2 & 1+2=3
1*3=3 & 1+3=4
1*4=4 & 1+4=5
1*5=5 & 1+5=6
and so on.
If we select 2 as both numbers then,
2*2=4 & 2+2=4
Here sum and the product are equal.
If not, the product will be bigger than the sum.
Now, the first stage is to evaluate the total number of two combinations that are feasible:
We have 5 alternatives for the first number and 5 alternatives for the second number.
The product of the number of possibilities in each scenario yields the total number of combinations:
C= 5*5=25
The following combinations have a sum that is greater than the product :
1 and 1
1 and 2
1 and 3
1 and 4
1 and 5
2 and 1
3 and 1
4 and 1
5 and 1
So, we get 9 combinations.
So, Probability,p=9/25
Therefore it is concluded that the probability is 9/25.
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This Stem-and-Leaf Plot represents test scores of students in a math class. If two test scores, 68 and 75, are added to the data, which statement will be true?
A. The median will change; the mode will stay the same.
B. The mode will change; the median will stay the same.
C. The median and the mode will both change.
D. The median and the mode will stay the same.
The median will change; the mode will stay the same.
Will the median and mode change?The median is the number that is at the center of a data set when the data are arranged either in ascending or descending order.
Median = 23
When 68 and 75 are added, the median would change.
Mode refers to a value that appears most frequently in a data set.
The mode = 75
So, when 75 is added, the mode does not change.
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Which table represents a quadratic function?
Answer:
A (see attached)
Step-by-step explanation:
There are a couple of things you can look for to see if a table represents a quadratic function:
do the values increase, then decrease, or vice versado the differences have a constant difference.ObservationIn the first of the given tables, the f(x) values start out decreasing, and end up increasing. This is a good indication the table represents a quadratic function.
In the remaining tables, the f(x) values are always increasing.
table 2: differences are always +2 (linear function)table 3: differences are always +4.5 (linear function)table 4: table values have a common ratio of 2 (exponential function)AnalysisThe f(x) values in table 1 have differences of ...
-3, -1, 1, 3
These values have differences of ...
2, 2, 2
The constant "second differences" mean that the function can be represented by a 2nd-degree polynomial, a quadratic. In fact, the equation for this table is ...
f(x) = x² +2
One can convert temperature from kelvin into fahrenheit using the formula . what is the temperature in kelvin corresponding to f degrees fahrenheit?
One can easily convert the temperature using temperature conversion formula given below
K = [tex]\frac{5(F - 32)}{9} + 273.15[/tex]
where F = degrees in Fahrenheit
K = degrees in Kelvin
What is temperature conversion? The measuring units of the temperature recorded in a particular unit can be converted with the aid of a temperature converter. The degree of heat or cold that a solid, liquid, or gas has is expressed by its temperature. A thermometer is used to determine temperature. Although the SI unit for temperature is Kelvin (K), most people measure temperature in Centigrade or Celsius (°C) and Fahrenheit (°F).Know more about temperature conversion https://brainly.com/question/13421795
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HELP ME, IT'S AN EMERGENCY
Answer:
(A) 36°
Step-by-step explanation:
Find intercepted arc (RT):
360° - 288° = 72
*A circle is 360°*
Find angle RST:
An inscribed angle = 1/2 intercepted arc
angle RST = 1/2(72)
Angle RST = 36°
What is the standard deviation of the data set? 6.5, 11.2, 13, 6.3, 7, 8.8, 7.4
Using it's concept, the standard deviation of the data-set is of 2.39.
What are the mean and the standard deviation of a data-set?The mean of a data-set is given by the sum of all values in the data-set, divided by the number of values.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.The mean of the data-set in this problem is given by:
M = (6.5 + 11.2 + 13 + 6.3 + 7 + 8.8 + 7.4)/7 = 8.6.
Hence the standard deviation is:
[tex]S = \sqrt{\frac{(6.5-8.6)^2+(11.2-8.6)^2+(13-8.6)^2+(6.3-8.6)^2+(7-8.6)^2+(8.8-8.6)^2+(7.4-8.6)^2}{7}} = 2.39[/tex]
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Please answer the question below..
The value of x that makes the unshaded area equal to the shaded area is 7.07 inches.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The area of big sector = (60/360) * π(10)² = (50π /3) cm²
Area of small sector = (60/360) * π(x)² = (x²π /6) cm²
Unshaded area = (x²π /6) cm²
Shaded area = (50π /3) - (x²π /6) = (100π - x²π) /6
Shaded area = unshaded area
(100π - x²π) /6 = (x²π /6) cm²
x = 7.07
The value of x that makes the unshaded area equal to the shaded area is 7.07 inches.
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The length of x in the sector is 7.08 cm.
How to find area of a sector?area of a sector = ∅ / 360 × πr²
where
r = radiusTherefore,
area of a sector = 60 / 360 × π × 10²
area of a sector = 60 / 360 × π × 100
area of a sector = 6000 / 360 π
Hence,
area of the unshaded portion = 6000 / 360 π ÷ 2 = 6000π / 720 = 26.1666666667 = 26.2 cm
Hence,
26.2 = 60 / 360 × 3.14 × x²
x² = 26.2 / 0.52333333333
x = √50.0637261552
x = 7.07557064836
x = 7.08 cm
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Find the x - and y -intercepts of the graph of the linear equation 2 x plus 3 y is equal to 2x+3y=12
Answer:
x-intercept is 6 [(6, 0) is the point]
y-intercept is 4 [(0, 4) is the point]
Step-by-step explanation:
To find the x-intercept, we can set y equal to 0 and solve for x. This works because the x-intercept is the point of the graph where the line crosses the x-axis (meaning y is equal to 0 at this point. So, if we set y=0 and solve, we get this:
[tex]2x+3(0)=12\\2x=12\\x=6[/tex]
So, the x-intercept is 6; if it is written as a point, it is (6, 0) since y is 0
To find the y-intercept, we can set x equal to 0 and solve for y. This works the same way - x is equal to 0 at the point where the line crosses the y-axis. If we set x=0 and solve, we get this:
[tex]2(0)+3y=12\\3y=12\\y=4[/tex]
So, the y-intercept is 4; if it is written as a point, it is (0, 4) since x is 0
given points (8,6) and ( 8, 0) as the endpoints of a radius ,what is the equation of the circle with center ( 8,6)
The general equation of a circle is written like [tex](x-h)^2+(y-k)^2=r^2[/tex], where (h,k) is the centre and r is the radius.
Solving the QuestionFirstly, we're given that the centre is (8,6).
Plug this into the general equation:
[tex](x-h)^2+(y-k)^2=r^2\\(x-8)^2+(y-6)^2=r^2[/tex]
We're given this other point on the circumference of the circle, (8,0), which is 6 units away from the center.
Therefore, the radius is 6 units. Plug this into the general equation too:
[tex](x-8)^2+(y-6)^2=r^2\\(x-8)^2+(y-6)^2=6^2\\(x-8)^2+(y-6)^2=36[/tex]
Answer[tex](x-8)^2+(y-6)^2=36[/tex]
PLEASE HELP!!!!
Question 8(Multiple Choice Worth 5 points)
(05.02 MC)
Based on the figure below, what is the value of x?
A right angle is shown divided in two parts. The measure of the angle of one part is 20 degrees and the measure of the other part is 5x plus 15 degrees.
A) 1
B) 9
C) 11
D) 15
The value of x from the given figure is 11
Complementary anglesThe sum of two complementary angles is 90 degrees.
The angles shown in the diagram are complementary such that;
20 + 5x + 15 = 90
5x + 35 = 90
5x = 90- 35
5x = 55
x = 55/5
x = 11
Hence the value of x from the given figure is 11
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For 19-20, Decide whether the polygons are similar. If so, find the scale factor of Figure A to Figure B.
Answer: Not similar
Step-by-step explanation:
The polygons are not similar because the ratio of the corresponding sides is not equal (30/18 is not equal to 18/8)
Find the volume of the composite figure. Round to the nearest tenth if necessary.
The volume of the composite figure is of 425 m³.
What is the volume of a prism?The volume of a prism is given by the base area multiplied by the height.
In this problem:
For the top figure, the base is a square with 5m, with height of 13m.For the bottom figure, the base is a square with 5m, with height of 4m.Hence the volume in m³ is:
V = 5² x 13 + 5² x 4 = 25 x 17 = 425 m³.
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The angle measurements in the diagram are represented by the following expressions.
Answer:
Angle A= 30
Step-by-step explanation:
Angle A and B are same side interior
So A + B = 180
x = 8
6(8)-18=30
Answer:23
Step-by-step explanation:
jaja
Select the correct answer.
Consider these functions:
f(x) = 4x³ - 10
g(x) = 3x - 4/2
What is the value of g(f2))?
Answer:
3x - 4/2
Step-by-step explanation:
2 result(s) for "f(x) = 4x³ - 10 g(x)
2(-2-4) = use the distributive property to expand the expression below.
Answer:
-12
Step-by-step explanation:
First, solve in parentheses.
2(-2-4)
=
2(-6)
Next, multiply 2 by -6.
Which equals -12.
So therefore using the distributive property shown above, the answer would be -12.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{What is the distributive formula?}[/tex]
[tex]\mathsf{a(b + c)}[/tex]
[tex]\mathsf{= a(b) + a(c)}[/tex]
[tex]\mathsf{= ab + ac}[/tex]
[tex]\huge\textbf{What is the equation?}[/tex]
[tex]\mathsf{2(-2 - 4)}[/tex]
[tex]\huge\textbf{What are we simplifying?}[/tex]
[tex]\mathsf{2(-2 - 4)}[/tex]
[tex]\mathsf{= 2(-2) + 2(-4)}[/tex]
[tex]\mathsf{= -4 - 8}[/tex]
[tex]\mathsf{= -12}[/tex]
[tex]\huge\textbf{How are you going to translate to}\\\\\huge\textbf{easier terms?}[/tex]
[tex]\mathsf{2(-2 - 4)}[/tex]
[tex]\mathsf{= 2(-6)}[/tex]
[tex]\mathsf{= -12}[/tex]
[tex]\huge\textbf{What is the ANSWER to the question?}[/tex]
[tex]\huge\boxed{\mathsf{-12}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
-x^2 +x+6=0 (Please solve by completing the square, and show steps)
The solution to the equation using the completing the square are 2 and -3
Quadratic equationThese are equation that has a leading degree of 2. Given the equation below
-x^2 +x+6=0
This can also be written as
x^2-x-6 = 0
Complete the square
x^2-x = 6
x^2-x+ (1/2)^2 = 6 + (1/2)^2
(x-1/2)^2 = 6 + 1/4
(x+1/2)^2 = 25/4
x+1/2 = ±√25/4
x = 5/2 -1/2 or -5/2-1/2
x = 4/2 or -6/2
x = 2 and -3
Hence the solution to the equation using the completing the square are 2 and -3
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How to use the distributive property to multiply two variables together
Distributive property states that A × (B + C) = AB + AC. are always equal.
According to the statement
we have to explain the distributive property over multiplication.
Distributive property is the multiplication property.
According to this property, it generalizes the Distributive Law and it tells us that the an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC.
It means that From distributive property
A × (B + C) = AB + AC.
These are always equal with each other.
Now we will explain with an example,
Let A = 2, B = 3 and C = 4
Then
2 × (3 + 4) = 2(3) + 2(4).
2 × (7) = 2(3) + 2(4).
14 = 6 + 8.
14 = 14.
It proves that the A × (B + C) = AB + AC.
So, Distributive property states that A × (B + C) = AB + AC. are always equal.
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The bars in a _____________ do not touch since data is ______________.
A. bar graph ; continuous
B. bar graph ; discrete
C. histogram ; continuous
D. histogram ; discrete
Answer:
b
Step-by-step explanation:
Bat Graphs represent discrete data. They are spaced and don't touch to represent a discrete value.
Histograms represent continuous data. They are close and connected to represent variation in continuous data.
assuming the pattern continues, what is s12 for the series -5-14-23-32-...?
Answer:
S₁₂ = - 654
Step-by-step explanation:
there is a common difference between consecutive terms , that is
- 14 - (- 5) = - 23 - (- 14) = - 32 - (- 23) = - 9
this indicates the series is arithmetic with sum to n terms
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
here a₁ = - 5 and d = - 9 , then
S₁₂ = [tex]\frac{12}{2}[/tex] [ (2 × - 5) + (11 × - 9) ]
= 6(- 10 - 99 )
= 6 × - 109
= - 654
PLEASE HELP!!!!
This year, the Nature Club made 3 exhibits per month for its annual fair. This year's fair has twice as many exhibits as last year's. How many exhibits were there in last year's fair?
Answer: 18
Step-by-step explanation:
There are 12 months in a year. The club made 3 exhibits each month. 3 times 12 is 36. They made twice as many as last year, so divide 36 by 2 and you get 18.
I hope this helps!
Find the volume of the composite solid.
The volume of the composite solid shown in the diagram is: 80 ft.³.
What is the Volume of Composite Solid?Volume of the composite solid = volume of triangular prism + volume of triangular pyramid.
Volume = 0.5 × base of triangle × height of triangle × length of prism + 1/3 × Base area × Height = 0.5 × 8 × 5 × 3 + 1/3 × 0.5 × 8 × 5 × 3
Volume = 60 + 20
Volume of the composite solid = 80 ft.³.
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Find the circumference and the area of a circle with diameter equal to 8.6 inches. Use 3.14 for pie.
The circumference and area of the circle are 27. 0 inches and 58. 0 inches square respectively.
How to calculate the circumferenceThe formula for circumference of a circle is given as;
Circumference = 2 π r
We have diameter = 8. 6 inches
Radius = diameter/ 2
Radius = 8.6/2 = 4. 3 inches
Circumference = 2 × 3. 14 × 4. 3 = 27. 0 Inches
The formula for area of a circle = π r ^2
Area = 3. 14 × 4. 3 × 4. 3
Area = 58. 0 Inches square
Thus, the circumference and area of the circle are 27. 0 inches and 58. 0 inches square respectively.
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please help asap i am so confused
The table so fined below based on the information given about the function.
How to illustrate the information?The table based on the function given will be:
Plan A. Plan B
Monday. 10. 30
Tuesday. 20. 40
Wednesday. 40. 50
Thursday. 80. 60
Friday. 160. 70
A is illustrated as it's double minutes for each day. B is illustrated by adding 10min each day.
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Compare the graphs of the functions listed below.
Function 1: y = 0.25x2
Function 2: y = 4x2
Function 3: y = -½x2
Function 4: y = -16x2
The graph of
✔ function 1
is the widest.
The graph of
is the narrowest.
Answer:
Function 1 is the widestFunction 4 is the narrowestStep-by-step explanation:
The graph is widest when the coefficient of [tex]x^2[/tex] has the smallest absolute value.
The graph is narrowest when the coefficient of [tex]x^2[/tex] has the largest absolute value.
By comparing the graphs of the functions, function 1: y = 0.25x2 is the widest and function 4: y = -16x2 is the narrowest.
The graph is widest when the coefficient of [tex]x^{2}[/tex] has the smallest absolute value.
The graph is narrowest when the coefficient of [tex]x^{2}[/tex] has the largest absolute value.
The answer lies in the coefficient for the [tex]x^{2}[/tex] term. When the absolute value of the coefficient gets bigger, the graph gets narrower (positive and negative simply show the direction the parabola is pointing, with positive opening up and negative opening down).
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PLEASE HELP 50 POINTS
Step-by-step explanation:
The initial velocity of a particle moving along x−axis is u (at t=0 and x=0) and its acceleration a is given by a=kx.A group of friends wants to go to the amusement
park. They have no more than $420 to spend on
parking and admission. Parking is $8.75, and
tickets cost $25.75 per person, including tax.
Which inequality can be used to determine x, the
maximum number of people who can go to the
amusement park?
Answer:
The maximum amount of people that can go to the amusement park is 15.
Step-by-step explanation:
First you create an equation to represent the question
8.75+25.75x≤420
You put the less than or equal to sign because 420 is the maximum amount of money.
Now you just solve the equation.
25.75x≤420-8.75
25.75x≤411.25
x≤411.25/25.75
x≤15.9708738
Then you have to round down because you cant have .9 of a person.
So x≤15
Then, Check your solution
8.75+(25.75 x 15)≤420
8.75+386.25≤420
395≤420
That is true. But to make sure that is the maximum add another 25.75
395+25.75≤420
420.75≤420
This is equation is false so, our answer is correct.
The maximum amount of people that can go to the amusement park is 15.
Sarah bought two t-shirts and one sweatshirt. The t-shirts cost $\$15.22$ each. If Sarah spent a total of $\$67.94,$ how many dollars did the sweatshirt cost
Answer: $37.50
Step-by-step explanation:
A company designs microphones for use in conference rooms. a new microphone needs to focus on the person speaking and not the voices of other people in the room. which polar equation would best match the desired audible range of the microphone?
r = 3 + 3cos(θ) polar equation would best match the desired audible range of the microphone.
How do you know if an equation is polar?Determine the kind of polar equation. The polar equation has the shape of a limaçon, and is written as r = a - b cos. We just need to assess the equation throughout the range [0, 1] and then reflect the graph about the polar axis because the equation passes the condition for symmetry to the polar axis.What is a polar in math?The polar coordinate system in mathematics is a two-dimensional coordinate system in which the distance from a reference point and the angle from a reference direction are used to identify each point's location on a plane.What is the meaning of polar form?In addition to the rectangular form, a complex number can also be represented in polar form. Typically, we write complex numbers as z = x + iy, where I is an imaginary integer. However, in polar form, complex numbers are modeled as a union of argument and modulus.Learn more about polar form here:
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Answer:
D
Step-by-step explanation:
Enter the degree of the polynomial below.
5,5 + 8,2 + 2x - 319 - 8x1 -4,5
Based on the given polynomial, the degree of the polynomial can be calculated to be 1.
what is the degree of the polynomial?the degree of the polynomial is defined as the highest exponential degree or power in a polynomial.
from the above, we see that the highest power is 1 from 8x¹.
the degree of the polynomial is therefore 1.
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Please explain the answer before, and also help with number line!
The solution to the given inequality is x < -6
For the number line, an open circle will be drawn on the value of -6 and the arrow pointing to the left side.
Number line and inequalityGiven the inequality expression as shown
6x + 6 < -30
Subtract 6 from both sides
6x < -30 - 6
6x < -36
Divide through by 6
x < -36/6
x < -6
For the number line, an open circle will be drawn on the value of -6 and the arrow pointing to the left side.
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What is the percent rate??
Kryton -85 is a radioisotope of krypton that has a half-life of about 10.75years. This isotope is produced by the nuclear fission of uranium and plutonium in nuclear weapons and in nuclear reactors, as well as cosmic rays. An important goal of the Limited Nuclear Test Ban Treaty of 1963 was to eliminate the release of such radioisotopes into the atmosphere. At present, the activity of Krypton -85 in the atmosphere is about 135 mCi.
Using an exponential function, it is found that the decay rate is of 6.24% a year.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.The half-life is of 10.75 years, hence A(10.75) = 0.5A(0) and this is used to find the decay rate r.
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]0.5A(0) = A(0)(1 - r)^{10.75}[/tex]
[tex](1 - r)^{10.75} = 0.5[/tex]
[tex]\sqrt[10.75]{(1 - r)^{10.75}} = \sqrt[10.75]{0.5}[/tex]
[tex]1 - r = (0.5)^{\frac{1}{10.75}}[/tex]
1 - r = 0.9376.
r = 1 - 0.9376.
r = 0.0624.
The decay rate is of 6.24% a year.
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