The probability that -2 < x < 2 is given as follows:
P(-2 < x < 2) = 0.16.
How to obtain the probabilities?From the table given in this problem, the probability distribution is defined as follows:
P(X = -5) = 0.17.P(X = -3) = 0.13.P(X = -2) = 0.33.P(X = 0) = 0.16.P(X = 2) = 0.11.P(X = 3) = 0.10.The desired interval in this problem is given as follows:
-2< x <2.
It is an open interval, meaning that the only outcome that satisfies this interval is X = 0, and thus the probability is given as follows:
P(-2 < x < 2) = 0.16.
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what is the math equation what does it equal ∣7−11∣=
The solution for the absolute value equation is:
|7 - 11| = 4
How to solve the given equation?Here we want to solve an absolute value equation:
|7 - 11| = ?
First, remember how the absolute value works, it is:
|x| = x if x ≥ 0
|x| = -x if x < 0.
Now let's return to our equation:
|7 - 11|
If we simplify the left side, we will get:
|-4|
Notice that it is a negative number, so we just need to change the sign:
|-4| = 4
Then the equation is:
|7 - 11| = 4
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Answer:
[tex] \sf \: ∣7-11∣ = 4[/tex]
Step-by-step explanation:
Given problem,
→ ∣7 - 11∣
Let's solve the problem,
→ ∣7 - 11∣
→ ∣-4∣ = 4
=> Absolute value
=> It is always positive
Hence, the answer is 4.
i need help pleaseeee!!!
Answer:
-4 < 2 - a < -8
Step-by-step explanation:
(-5x2 + 10x − 12) − (-4x2 + 8x − 15)
Answer: 1 + 2x
Step-by-step explanation:
To solve this problem, it's helpful to understand "order of operations." The order is: parentheses, exponents, multiplication, division, addition, and lastly, subtraction.
A helpful mnemonic is PEMDAS. I was taught "Parachute Expert My Dear Aunt Sally" to help remember the order.
We must work with the numbers inside the parantheses, since "parantheses" is the first operation. We'll start with the first paranthesis: (-5x2 + 10x - 12).
Since there are no exponents in this equation, we can go to the third operation: multiplication. (I like to use the "·" symbol to show that two numbers are multiplied because it's easy for me to confuse the letter X with "x" when it is used as a multiplication symbol).
-5 · 2 = -10
Two negative numbers are added, so -10 and -12 = -22
This leaves (-22 + 10x)
The -22 and 10x are not added together because numbers without a letter cannot be added to numbers with letters.
Now we'll work with the second paranthesis: (-4 · 2 + 8x - 15)
-4 · 2 = -8
-8 and -15 is added to make -23
The paranthesis now looks like:
(-23 + 8x)
Notice that there is a negative sign outside of the second paranthesis in the equation.
(-22 + 10x) − (-23 + 8x)
When a number or symbol is outside of a paranthesis, that number or symbol is multiplied across everything within the parantheses.
Now, it is:
(23 - 8x)
All of the numbers can be taken out of the parantheses now:
-22 + 10x + 23 - 8x
-22 + 23 = 1
10x - 8x = 2x
The final answer:
1 + 2x
Hope this helps!
Casandras fish bowl holds 9/10 gallon of water. It is now 2/3 full. How much water is in the bowl?
The amount of water in Casandra's bowl, given the gallons of water it can hold and the fraction full it is, is 0.6 gallons
How to find the quantity of water ?Casandra' s fish bowl is able to hold a total of 9 / 10 gallons of water which is also 0.9 gallons of water. This means that you can find out how much water is in the bowl if told the fraction of the bowl that is currently full up to.
This time, the bowl is said to be 2 / 3 full which means that out of the capacity of 9 / 10 gallons or 0 . 9 gallons, the bowl is two - thirds full.
The amount of water in the bowl is therefore:
= Capacity of fish bowl x Proportion of water in the bowl
= 9 / 10 x 2 / 3
= 0. 9 x 2 / 3
= 0 . 6 gallons
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Determine if each pair of triangles is similar. If they are similar, state why. (AA, SAS, SSS, or not similar)
As the trianlges are SAS congurant the side NK = 1.8.
What is congruent by ASA?
The Angle-Side-Angle congruence rule is referred to as ASA. Two triangles are said to be congruent according to this rule if any two angles and the side included between them of one triangle are equal to the corresponding angles and the included side of the other triangle. See if the two triangles given, ABC and XYZ, are congruent according to the ASA rule by looking at the image provided below. According to the ASA congruence rule, two triangles are said to be congruent if two of their respective sides and angles are equal to those of two other triangles and their respective sides and angles, respectively.
∠LJK=∠LMN
LM =4
MJ=2
LN=3.6
So, As the trianlges are SAS congurant the side NK = 1.8.
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At a local hospital, 75% of nurses have diploma qualifications and the rest are working towards diplomas. There are 160 nurses in this hospital. How many nurses do not have a nursing diploma yet?
A total of 40 nurses do not have a nursing diploma yet
How many nurses do not have a nursing diploma yet?From the question, we have the following parameters that can be used in our computation:
Nurses = 160 nurses
Diploma qualitifications = 75%
The above parameters mean that
No diploma qualification = (1 - Diploma qualitifications) * Nurses
Substitute the known values in the above equation, so, we have the following representation
No diploma qualification = (1 - 75%) * 160
Evaluate
No diploma qualification = 40
Hence, the nurses are 40
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Please help me solve this 9th grade math equation
Number of pounds of banana sold is, 14
And, Number of pounds of grapes sold is, 36
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Each pound of banana sell for $2.
And, Each pound of grapes sell for $1.
Now, Let number of pounds of sell banana = x
And, Number of pounds of sell grapes = y
Since, There are 50 pounds of fruits are sell.
So, We can formulate;
⇒ x + y = 50 .. (i)
And, Each pound of banana sell for $2.
And, Each pound of grapes sell for $1.
Hence, We get;
⇒ $2x + $1y = $64
⇒ 2x + y = 64 .. (ii)
Substitute value of y from (i) in (ii), we get;
⇒ 2x + y = 64
⇒ 2x + (50 - x) = 64
⇒ 2x + 50 - x = 64
⇒ x = 64 - 50
⇒ x = 14
And, From (i);
⇒ x + y = 50
⇒ 14 + y = 50
⇒ y = 50 - 14
⇒ y = 36
So, Number of pounds of sell banana = 14 pounds
And, Number of pounds of sell grapes = 36 pounds
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
The equations which represent circles whose diameters are 12 units and a center line lies on the y-axis are:
x² + (y – 3)² = 36 x² + (y – 5)² Equation of a circle.It is noteworthy to know that a center line on the y-axis can be interpreted as a coordinating pair in which case the pair looks like;
( 0, y )
Recall the equation of a circle which takes the form;
(x - h)² + (y - k)² = r²
Hence, since the center that lies on the y-axis, it automatically means that h = 0.
Also, if the diameter of the circle is 12 units
r = 12 / 2 = 6.
On this note, the required equation is;
x² + (y - k) = 6²
where k could be any real number.
Ultimately, the equations which are correct are;
x² + (y – 3)² = 36
x² + (y – 5)²
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5x - 2y = 10
7x - 3y = 13
Use elimination to solve for x and y
Answer:
Step-by-step explanation:
let 5x - 2y = 10 ........... (1)
and 7x - 3y = 13 ............(2)
now multiply equation (1) by 3 and equation (2) by 2, we get,
15x - 6y = 30 ............(3)
14x - 6y = 26 ............(4)
after substracting equation (3) and (4) we get,
x = 4
after putting the value of x in eq (3) we get,
15 * 4 - 6y = 30
=> 60 - 6y =30
=> y = -30/ -6
=> y = 5
so, the vale of x and y is 4 and 5 respectively.
PLSSSS HELP TYYYYYT !!!!!
Answer:
Total people =107
Women =57
Men =50
Men who don't like tea =20
Men who like tea= 30
Women who like tea = (total people who like tea)-(men who like tea)
Women who like tea= 30
Women who don't like tea =27
a=50
b=30
c=20
d=57
e=30
f=27
An isosceles triangular prism can be unfolded into the net shown
below. Find the lateral surface area of the triangular prism.
8.3 in
9 in
7 in
I
17 in
The lateral surface area of the triangular prism is 364.1 square inches.
What is surface area?The Surace area of any 2D or 3D figure is the outer area of the given figure.
Surface areas are of two types they are lateral surface area when we exclude the areas of top and bottom and total surface area is when we include all the sides.
From the given diagram and the concept of lateral surface area where the base and top are excluded here, it has only the base area as the top results to a point.
Therefore, The lateral surface area of this isosceles triangular prism is,
Two rectangles have a length of 17 inches and a width of 9 inches in addition to two triangles having a base of 7 inches and a height of 8.3 inches which is,
= 2(17×9) + 2[(1/2)×7×8.3) square inches.
= 306 + 58.1 square inches.
= 364.1 square inches.
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<1 and <5 are ___ angles.
right
vertical
alternate interior
corresponding
angles.
Answer:
corresponding
Step-by-step explanation:
<1 and <5 are corresponding angles because they are on the same side of the transversal and on the same side of l and m
Please show work on a paper and upload it need it ASAPPP
The value of the summation expression given in the task content is; 16.
What is the value of the summation expression given?It follows from the task content that the value of the summation expression given is to be determined.
Since the given expression is; 2x - 3,
On this note;
When x = 2; 2(2) - 3 = 1When x = 3; 2(3) - 3 = 3When x = 4; 2(4) - 3 = 5When x = 5; 2(5) - 3 = 7On this note, the sum of all of the results above is the correct Evaluation of the given expression; 1 + 3 + 5 + 7 = 16.
On this note, the result of the evaluation is; 16.
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In the diagram below, D is a point on segment CE such that segments AD and BE are parellel and point A is not on segment BC. Line segments AD and BC intersect at point P.
If angle CAD = 67 degrees, then what is angle CBE?
Answer:
Step-by-step explanation:
Since segment AD and BE are parallel, we can use the Alternate Interior Angles Theorem to solve this. According to this theorem, if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are equal. Since angle CAD = 67 degrees, angle DBE is also equal to 67 degrees.
Now, if we look at the diagram, angle DBE is supplementary to angle CBE, meaning that the two angles add up to 180 degrees. Therefore, angle CBE = 180 degrees - 67 degrees = 113 degrees.
Eva has a points card for a movie theater. She receives 85 rewards points just for signing up. She earns 2.5 points for each visit to the movie theater. She needs at least 310 points for a free movie ticket.
Answer: 90
Step-by-step explanation:
If you're looking for the number of times she has to visit the movie theater in order to have 310 points for the free movie ticket then;
310-85 = 225
225/2.5 = 90
Eva needs 90 visits before she can get a free movie ticket.
log10 2=P,then the value of log10 5 is
The value of log10 5 as required to be determined using the given information is; 0.3979 + P..
What is the value of log10 5 as required?It follows from the task content that; the value of log10 5 is to be determined based on the given information.
Since the given expression is; log10 2 = P;
The expression which can be inferred from the equation above is;
10^P = 2..............(i)
However, let; log10 5 = x
Therefore; 10^x = 5..........(ii)
By dividing the equation (ii) by (i); we have that;
10^(x - P) = 2.5
Therefore, from the converse of logarithmic law;
x - P = log10 2.5
x = P + log10 2.5
where, log10 2.5 = 0.3979
x = 0.3979 + P
Ultimately, the value of log10 5 as required is; 0.3979 + P.
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It took 15 days to build 3/5 of a new road.
At this rate, how long will it take to build the whole road?
Explain your answer.
In an absolute value graph, the slope of one side of the graph is the ______________ of the other side.
Then give an example...If the slope of one side of an absolute value function is _________, then the other side of the equation has a slope of ________.
Answer:
In an absolute value graph, the slope of one side of the graph is the opposite of the other side.
For example, if the slope of one side of an absolute value function is positive, then the other side of the equation has a slope of negative.
Assume you are given the set B where B = {2,4,6,8,10}. Consider this statement.
Answer:false
Step-by-step explanation:
$2750 is invested at an interest rate of 3.5% APR compounded quarterly. Determine the amount after 7 years. Round your answer to the nearest hundredth.
Work Shown:
A = P*(1+r/n)^(n*t)
A = 2750*(1+0.035/4)^(4*7)
A = 2750*(1+0.00875)^(28)
A = 2750*(1.00875)^(28)
A = 2750*1.27626052446017
A = 3509.71644226547
A = 3509.72
What is the fifth term of the arithmetic sequence? 6, 9, 12, 15,...
The fifth term of the arithmetic sequence can be found to be 18.
How to find the next term ?There are two definitions for an arithmetic sequence. It is a "series where the differences between every two succeeding terms are the same" or "each term in an arithmetic sequence is formed by adding a fixed number (positive, negative, or zero) to its preceding term."
In this arithmetic sequence therefore, you can find the common difference to be:
= 9 - 6
= 3
So the fifth term would be:
= 4th term + common difference
= 15 + 3
= 18
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The fifth term of the arithmetic sequence: 6, 9, 12, 15 is 18.
What is the fifth term of the arithmetic sequence?The formula for the nth term of an arithmetic sequence is expressed as;
aₙ = a₁ + d( n - 1 )
Given the data in the question;
6, 9, 12, 15.
First term a₁ = 6Common difference d = 9 - 6 = 3Required term n = 5thPlug the values into the above formula and simplify.
aₙ = a₁ + d( n - 1 )
a₅ = 6 + 3( 5 - 1 )
a₅ = 6 + 3( 4 )
a₅ = 6 + 12
a₅ = 18
Therefore, the fifth term of the sequence is 18.
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A sample of 400 teenagers showed 262 were "hyper-texters", meaning they spent more than 3 hours a day on their smart
phones. If there are 2,000 students at North High School how many would you expect to be "hyper-texters"?
262 "hyper-texters," or teens who spend more than three hours per day on their smartphones, were found in a sample of 400 youngsters. if North High School enrolls 2,000 pupils.
How many hyper-texters in smart phone ?In order to transmit a digitalized version of your speech during a cell phone call, the phone must send out an electrical signal (mathematics comes into play here through the use of error correction and data compression). Radiation from cell phones is produced in the electromagnetic spectrum's radiofrequency band. The radiofrequency that second-, third-, and fourth-generation cell phones (2G, 3G, and 4G) generate ranges from 0.7 to 2.7 GHz. The frequency range up to 80 GHz is expected to be used by fifth-generation (5G) cell phones.Checking your phone in the middle of a crucial work can make it more difficult for you to finish it. Using your phone in between crucial tasks reduces your ability to concentrate, according to a recent study that was published in the Journal of Behavioral Addictions.To learn more about hyper-texters refer to :
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7. What is 112" in decimal feet?
a. 12.25´
b. 9.33 ´
c. 8.50 ´
d. 6.33 ´
Answer:
B 9.33
Step-by-step explanation:
Choose the table or tables that represent a linear function.
Answer:
A and B
Step-by-step explanation:
You draw the points on the Cartesian plane and draw a straight line that passes through two of the drawn points, if ALL the drawn points are ON the drawn line, then it is a linear function,
If only ONE point lies outside the line, then it is NOT a linear function
Put the answer please!
The inequality that represents the interval shown on the number line is:
5 ≤ x ≤ 9
How to express the interval shown?We want to use inequality notation to define the interval shown on the number line.
We can see that the first point is marked with a closed circle, at x = 5.
And then we have another closed circle at x = 9
The closed circles means that these points are solutions to the inequality, so we need to use the symbols:
≤ and ≥
Then we can write the inequality:
5 ≤ x ≤ 9
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Please look at the picture and answer the question thank you
The formula for t in terms of P, I and r is t=I/Pr.
What is the simple interest?Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.
Simple interest is calculated with the following formula: S.I. = (P × R × T)/100, where P = Principal, R = Rate of Interest in % per annum, and T = Time.
Given that, the formula form simple interest is I=Prt, where I is the interest, P is the principal, r is the interest rate and t is the number of years.
Now, I=Prt
t=I/Pr
Therefore, the formula for t is t=I/Pr.
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Kalen and his friends are running a relay race that is 3/4 mile long.Each person will run 3/20 mile.How many runners are on Kalen’s team in total??
Answer:
5 people
Step-by-step explanation:
Relay race ---> 3/4 mile
Each runner runs 3/20 miles
3/4÷3/20
3/4×20/3=5
OR
3/4 --> 15/20
3/20 goes into 15/20 5 times
Answer:
5 runners
Step-by-step explanation:
Just multiply 3/20 by 3/4
Select the correct answer.
Stephanie is exploring the key features of the functions ƒ (z) = and g(z) = 4=+5
She says that the graphs of the two functions will have the same vertical asymptote but different horizontal asymptotes because she ca
define function g as a transformation of function f and g(x) = f(x) + 4. Which statement is true?
O A. Stephanie correctly rewrote g(x) as a transformation of f(x), and she described the asymptotes of the two functions
correctly.
OB. Stephanie correctly rewrote g(x) as a transformation of f(x), but she described the asymptotes of the two functions
incorrectly.
OC. Stephanie rewrote g(x) as a transformation of f(x) incorrectly, but she described the asymptotes of the two functions
correctly.
O D. Stephanie rewrote g(x) as a transformation of f(x) incorrectly, and she described the asymptotes of the two functions
incorrectly.
Answer:
A. Stephanie correctly rewrote g(x) as a transformation of f(x), and she described the asymptotes of the two functions correctly.
Step-by-step explanation:
The statement is true because, g(x) = f(x) + 4 is indeed a transformation of f(x) by shifting the graph 4 units up, and because the horizontal asymptote is determined by the highest degree term in the function, which in this case is the same for both functions, so the two functions will have the same vertical asymptote, but the horizontal asymptote is determined by the leading coefficient which is different for both functions, so the two functions will have different horizontal asymptotes.
Which overlapping triangles are congruent by ASA?
The overlapping triangles which are congruent by ASA are ΔEBC and ΔADC which is therefore denoted as option C.
What is a Congruent triangle?This is a scenario in which all three corresponding sides are equal and all the three corresponding angles are equal in measure.
Taking ΔEBC and ΔADC, we have the following below:
∠B=∠D (90°)
CB= CD (Given)
∠BCE=∠ACD( Common)
Therefore, by ASA we can deduce that,
Δ EBC ≅ΔADC.
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Solve the following equation: x = 6.0% X 99.5% X 1.3 X 1.6
Answer:
0.124176
Step-by-step explanation:
.06 x .995 x 1.3 x 1.6= 0.124176
You change a percent into a decimal by dividing it by 100%
