Answer:
[tex] P(27.8 < X <30.5)=P(X>27.8)-P(X>30.5)=0.025-0.0015=0.0235[/tex]
Step-by-step explanation:
The empirical rule, also known as three-sigma rule or 68-95-99.7 rule, "is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ)".
Let X the random variable who represent the lifespans of tigers in a particular zoo.
From the problem we have the mean and the standard deviation for the random variable X. [tex]\mu=120 , \sigma=110[/tex]
On this case in order to check if the random variable X follows a normal distribution we can use the empirical rule that states the following:
• The probability of obtain values within one deviation from the mean is 0.68
• The probability of obtain values within two deviation's from the mean is 0.95
• The probability of obtain values within three deviation's from the mean is 0.997
We want to find this probability:
[tex] P(27.8 < X <30.5)[/tex]
And in order to calculate how many deviation we are above/below the mean we can use the z score given by:
[tex]z =\frac{x-\mu}{\sigma}[/tex]
And if we use this formula for the two values given we have:
[tex] z_1 = \frac{27.8-22.4}{2.7}=2[/tex]
[tex] z_1 = \frac{30.5-22.4}{2.7}=3[/tex]
So we have values between 2 and 3 deviations above the mean.
We can use the following probabilities
[tex]P(X<\mu -\sigma)=P(X <19.7)=0.16[/tex]
[tex]P(X>\mu +\sigma)=P(X >25.1)=0.16[/tex]
[tex]P(X<\mu -2*\sigma)=P(X<17)=0.025[/tex]
[tex]P(X>\mu +2*\sigma)=P(X>27.8)=0.025[/tex]
[tex]P(X<\mu -3*\sigma)=P(X<14.3)=0.0015[/tex]
[tex]P(X>\mu +3*\sigma)=P(X>30.5)=0.0015[/tex]
And we can find this probability on this way:
[tex] P(27.8 < X <30.5)=P(X>27.8)-P(X>30.5)=0.025-0.0015=0.0235[/tex]
To estimate the probability of a tiger's lifespan falling between 27.8 and 30.5 years, we can use the empirical rule, which states that approximately 95% of the data falls within two standard deviations of the mean.
Explanation:To estimate the probability of a tiger living between 27.8 and 30.5 years, we can use the empirical rule. According to the empirical rule, approximately 68% of the data falls within one standard deviation of the mean, and approximately 95% falls within two standard deviations. Since the mean is 22.4 years and the standard deviation is 2.7 years, we need to find the probability that a tiger's lifespan falls between 27.8 - 22.4 = 5.4 years and 30.5 - 22.4 = 8.1 years.
Since 5.4 years and 8.1 years are less than two and three standard deviations away from the mean, respectively, the probability can be estimated to be approximately 95% using the empirical rule.
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-5x + sy=-10
- 3x +2y=3
Solve for systems of equations substitution
Hey guys i need help please its slope and im struggling
Answer:
Slope, m = [tex]$ \frac{\textbf{-2}}{\textbf{3}} $[/tex].
Step-by-step explanation:
The slope of the line can be determined by simplifying the given equation to its standard form.
In the standard form, y = mx + c, m represents the slope of the line.
We are given: [tex]$ y - 2 = - \frac{2}{3}(x + 1) $[/tex]
[tex]$ \implies y = -\frac{2}{3}x - \frac{2}{3} + 2 $[/tex]
[tex]$ \implies y = - \frac{2}{3}x + \frac{(-2 + 6)}{3} $[/tex]
[tex]$ \implies y = -\frac{2}{3}x + \frac{4}{3} $[/tex]
Comparing it with the standard equation, we can see that the slope, m = [tex]$ \frac{\textbf{-2}}{\textbf{3}} $[/tex].
Hence, the answer.
what is the volume of the pyramid if the height is 215 and the base is 339
Final answer:
The volume of a pyramid with a height of 215 units and a square base of 339 units on each side is calculated using the formula V = (1/3)Bh, resulting in a volume of 1,304,688.67 cubic units.
Explanation:
To find the volume of a pyramid, we can use the formula V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid. If the base is a square with each side being 339 units, then the area of the base (B) can be calculated as 339×339 square units. Given the height (h) of the pyramid is 215 units, the volume can then be calculated.
First, calculate the area of the base:
B = 339×339 = 114921 square units.
Then, use the volume formula by plugging in B and h:
V = (1/3)×114921×215 = 1,304,688.67 cubic units.
Therefore, the volume of the pyramid is 1,304,688.67 cubic units.
What is the equation of the function that is graphed as line b?
y = 1/2 x - 1
y = 2x + 1
y = 1/2 x + 1
y = -4x
Following the slope of the line at x= 0 the line is at y =1 , at x=, it is at Y = 1.5, so the slope is 1/2
The y intercept is where the line crosses the y a is at x =0 which is 1
The equation would be y = 1/2x+ 1
Answer:
y = 1/2x+ 1
Step-by-step explanation:
Between which two integers is the value of the square root of 20
Answer:
4 and 5
Step-by-step explanation:
20 is greater than 4² = 16, and less than 5² = 25. So, the square root of 20 is between 4 and 5.
___
Your calculator will tell you that √20 ≈ 4.472, so is between 4 and 5.
are the two expressions equivalent when x=2 7^2+4x 4x+(7×7)
Answer:
[tex]Give\ Two\ expressions\ are\ equivalent.[/tex]
Step-by-step explanation:
[tex]First\ expression=7^2+4x\\\\At\ x=2,\ value\ of\ first\ expression=7^2+4\times 2=49+8=57\\\\Second\ expression=4x+(7\times 7)\\\\Second\ expression=4x+7^2\ \ \ \ \ \ \ \ \ \ \ as\ m\times m=m^2\\\\Second\ expression=7^2+4x\ \ \ \ \ \ \ \ using\ commutative\ property\ of\ addition\\\\At\ x=2,\ value\ of\ second\ expression=7^2+4\times 2=49+8=57\\\\Hence\ these\ two\ expressions\ are\ equivalent.[/tex]
Given the sequence 2, 4, 8, , 16,........, where x = 0, 1, 2, 3, .......what is the function rule? f(x) = 2x + 2 f(x) = 2(2)x f(x) = (2x) f(x) = 2
f(x) = 2([tex]2^{x}[/tex])
Step-by-step explanation:
Step 1 :
Given
When x =0, f(x) = 2
x =1, f(x) = 4
x =2, f(x) = 8
x =3, f(x) = 16
Step 2 :
Substituting for x in the function f(x) = 2([tex]2^{x}[/tex]) we get,
When x =0, f(x) = 2
x =1, f(x) = 4
x =2, f(x) = 8
x =3, f(x) = 16
This matches the given sequence and this shows that the function represents the given sequence .
Final answer:
The function rule for the given sequence 2, 4, 8, 16, ... is [tex]f(x) = 2^x[/tex], representing the sequence's exponential growth pattern where each term is double the previous term.
Explanation:
The given sequence is 2, 4, 8, 16, ..., which is a geometric sequence where each term is multiplied by 2 to get the next term. This pattern corresponds to an exponential function where the base is 2 and the exponent is the position of the term, which can also be thought of as the function's input, x. Therefore, the function that represents this sequence is f(x) = 2x.
The other function choices given, such as f(x) = 2x + 2 or f(x) = 2, do not correctly represent the pattern observed in the sequence. The correct function rule for the given sequence is f(x) = 2x which fits the pattern where when x is substituted for each term's position (starting from 0), the function provides the corresponding term of the sequence.
What's greater 3/10,1/2,2/5?
[tex]\text{Hey there!}[/tex]
[tex]\bf{What\ is\ greater: \dfrac{3}{10}, \dfrac{1}{2},\&\dfrac{2}{5}?}[/tex]
[tex]\bf{Well, let's\ turn\ our\ fractions\ into\ decimals\downarrow}[/tex]
[tex]\bullet\ \bf{\dfrac{3}{10}=0.30(also\ known\ as\ 0.3)}\\\\\bullet \ \bf{\dfrac{1}{2}=0.50(also\ known\ as\ 0.5)}\\\\\bullet \ \bf{\dfrac{2}{5}=0.40(also\ known\ as\ 0.4)}[/tex]
[tex]\bf{The\ fractions\ in\ percentages\downarrow}[/tex]
[tex]\bullet \ \mathsf{\dfrac{3}{10}=30\%}\\\\\bullet \ \mathsf{\dfrac{1}{2}=50\%}\\\\\bullet \ \mathsf{\dfrac{2}{5}=40\%}[/tex]
[tex]\text{Now that we have that out the way. Let's solve for your answer!}[/tex]
[tex]\bf{\dfrac{1}{2}}\rightarrow\dfrac{2}{5}\rightarrow\dfrac{3}{10}}}} \leftarrow( that's\ for\ GREATEST\ to\ LEAST)[/tex]
[tex]\boxed{{\bf{Answer: \dfrac{1}{2}\ would\ be\ your\ GREATEST\ or \ BIGGEST\ one}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
the length of one of the diagonals of a quadrilateral is 10 cm and the particular drawn from the opposite vertices to this diagonal are the are of length 2.8 cm and 4.2 cm find the area of the quadrilateral
Answer:
Therefore the area of the quadrilateral =35 cm²
Step-by-step explanation:
Given, the length of one of diagonal of quadrilateral is 10 cm and perpendicular drawn from the opposite vertices to this diagonal are the length of 2.8 cm and 4.2 cm.
A diagonal divided a quadrilateral into two triangle.
Therefore the area of the quadrilateral
= sum of the area of the triangles
[tex]=(\frac{1}{2}\times 10\times 2.8+ \frac{1}{2}\times 10\times 4.2)[/tex]cm² [ area of a triangle[tex]= \frac{1}{2}\times base\times height[/tex]]
=35 cm²
Find the area for the following figure.
A. 51.06m^2
B. 74.98 m^2
C. 27.14m^2
D. 102.1^2
area = sum of parallel sides . height/2
= (5.9 + 16.3) 4.6/2
= 22.2 . 2.3
= 51.06 m²
so the answer is A
Find the Quotient.
1,382 divided 4
Answer:
The quotient is 345.5
Step-by-step explanation:
Check image
Final answer:
To find the quotient of 1,382 divided by 4, divide each place value separately. The quotient is 343 with a remainder of 2.
Explanation:
To find the quotient of 1,382 divided by 4, we divide the thousands, hundreds, tens, and ones place separately. Starting from the leftmost digit, we divide 1,382 by 4.
4 divided by 1 is 0 with a remainder of 4. Bring down the next digit 3. So, we have 43. Next, divide 43 by 4. 4 divided by 43 is 10 with a remainder of 3. Bring down the next digit 8. So, we have 38. Finally, divide 38 by 4. 4 divided by 38 is 9 with a remainder of 2.
Therefore, the quotient of 1,382 divided by 4 is 343 remainder 2.
Angle x and angle y are complementary. angle x is supplementary to a 128 angle.What are the measures of angle x and angle y?
Answer:
y = 38°
Step-by-step explanation:
If Angle x and angle y are complementary, then x + y = 90°
Also, if angle x is supplementary to a 128 angle, then x + 128° = 180°.
Solving the latter equation for x, we get x = 52°.
Therefore, by the first equation, x + y = 90° becomes 52° + y = 90°, yielding
y = 38°
Answer:
[tex]\boxed{\mathtt{x=52^{\circ}}}[/tex]
[tex]\boxed{\mathtt{y=38^{\circ}}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to solve for the measures of angles x and y.}[/tex]
[tex]\textsf{First, x is supplementary to an angle that equals 128}^{\circ}.[/tex]
[tex]\Large\underline{\textsf{What are Supplementary Angles?}}[/tex]
[tex]\textsf{Supplementary angles are 2 or more angles that add up to \underline{180}}^{\circ}.[/tex]
[tex]\large\underline{\textsf{This means that;}}[/tex]
[tex]\mathtt{x+128^{\circ}=180^{\circ}.}[/tex]
[tex]\large\underline{\textsf{Subtract 128 from both sides for x:}}[/tex]
[tex]\boxed{\mathtt{x=52^{\circ}}}[/tex]
[tex]\Large\underline{\textsf{What are Complementary Angles?}}[/tex]
[tex]\textsf{Complementary angles are 2 or more angles that add up to \underline{90}}^{\circ}.[/tex]
[tex]\large\underline{\textsf{This means that;}}[/tex]
[tex]\mathtt{x+y=90^{\circ}.}[/tex]
[tex]\textsf{Because we know x, we can solve for y.}[/tex]
[tex]\large\underline{\textsf{Substitute:}}[/tex]
[tex]\mathtt{52^{\circ}+y=90^{\circ}.}[/tex]
[tex]\large\underline{\textsf{Subtract 52 from both sides for y:}}[/tex]
[tex]\boxed{\mathtt{y=38^{\circ}}}[/tex]
Write the polynomial in factored form.
p(x) = (x + 5)(x - 1 )(x +
Answer: 4)
Step-by-step explanation:
Answer:
1st one is 3, 2nd is 4
Step-by-step explanation:
A flying disc has a circumference of 75.36 centimeters. What is the area of the flying disc? (Use 3.14 for .)
The area of flying disk is 452.16 square centimeters
Step-by-step explanation:
The disc is in circular shape so we will use the formulas for circle in this question.
Given
Circumference = C = 75.36 centimeters
We have to find the area of the disc for which we have to find the radius first.
Let r be the radius
Then
Circumference is given by:
[tex]C=2\pi r[/tex]
putting the values
[tex]75.36 = 2*3.14*r\\75.36 = 6.28r[/tex]
Dividing both sides by 6.28
[tex]\frac{6.28r}{6.28} = \frac{75.36}{6.28}\\r = 12\ cm[/tex]
The area of circle is given by:
[tex]A = \pi r^2[/tex]
Putting the values
[tex]A = 3.14 * (12)^2\\A = 3.14*144\\A =452.16\ cm^2[/tex]
Hence,
The area of flying disk is 452.16 square centimeters
Keywords: Circle, area
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Roderick's credit card company calculates a finance charge based upon a periodic rate of 1.2% on all unpaid balances. If Roderick has an unpaid balance of $200, determine the finance charge that he will be assessed. $301.80 $298.20 $2.40 $54.00
Answer:
$2.40
Step-by-step explanation:
You have ...
finance charge = 1.2% × unpaid balance
= 0.012 × $200 . . . . . fill in the value of unpaid balance
finance charge = $2.40
PLEASE ANSWER
What is the slope of the graph?
Answer:
[tex]\frac{5}{3}[/tex]
Step-by-step explanation:
Slope = [tex]\frac{4-(-1)}{3-0} =\frac{5}{3}[/tex]
Mr. Black bought 2 magazines for $9.95 each and 1 book for $14.95. If the sales tax is 6%, what is the total cost of Mr. Black's purchases?
Answer:
$36.94
Step-by-step explanation:
Okay, so. This is what we do. There is two magazines and they cost 9.95 each multiply 9.95 times 2
9.95 x 2 = 19.90
Okay, then he buys a book for 14.95 we add 19.9. and 14.95
19.90 + 14.95 = 34.85
Then we have a sales tax of 6% we would multiply 34.85 time 6%
34.85 x 6% = 2.09
Then we would add. 34.85 + 2.09
34.85 + 2.09 = 36.94
Therefore your answer is $36.94
Hope this helps!!!
The answer is $36.94. You add up the total purchases, multiply them by .06, then add that number to you total purchases.
The dimensions of a triangle are multiplied by 1/4.The area
of the smaller triangle can be found by multiplying the area
of the original triangle by what number?
Please help
Thank you!
Answer:
1/16
Step-by-step explanation:
Area is the product of linear dimensions.
Suppose the area of the triangle is the product of two dimensions p and q*:
A = pq
Then the smaller triangle will have an area that is ...
A = (1/4p)(1/4q) = (1/4)²pq = (1/16)pq . . . . . . 1/16 of the original area
__
If each of the linear dimensions of the triangle is multiplied by 1/4, the area will be multiplied by (1/4)² = 1/16.
_____
* No doubt, you have learned the area formula for a triangle is ...
A = (1/2)bh
In the above, we might have p=1/2b and q=h. Or, there could be some other relationship between triangle dimensions and p and q.
Write a function that represents the situation. Your $840 annual bonus increases by 5% each year
Answer:
[tex]f(x) = (840)\times (1.05)^{x}[/tex] where f(x) is the bonus every year and x is in number of years
Step-by-step explanation:
The function that represents the situation where $840 annual bonus increases by 5% each year is given by
[tex]f(x) = (840)\times (1.05)^{x}[/tex] where f(x) is the bonus every year and x is in number of years
Final answer:
The function representing an $840 annual bonus that increases by 5% each year is f(x) = 840(1 + 0.05)ˣ
Explanation:
To write a function that represents the situation where an $840 annual bonus increases by 5% each year, we can use an exponential growth model.
The general form of an exponential growth function is f(x) = a(1 + r)ˣ, where a is the initial amount, r is the growth rate, and x is the number of time periods.
In this case, the initial bonus a is $840, the growth rate r is 5% or 0.05, and x represents the number of years. Thus, the function can be written as:
f(x) = 840(1 + 0.05)ˣ
What is the value of the expression when n = 3?
StartFraction 6 (n squared plus 2) Over n EndFraction
The value of expression when n = 3 is 22
Solution:
Given expression is:
[tex]\frac{6(n^2 + 2)}{n}[/tex]
We have to find the value of expression when n = 3
Substitute n = 3 in given expression
[tex]\rightarrow \frac{6(3^2 + 2)}{3}\\\\Simplify\ the\ above\ expression\\\\\rightarrow \frac{6(9+2)}{3}\\\\Solve\ the\ terms\ inside\ the\ bracket\\\\\rightarrow \frac{6(11)}{3}\\\\Divide\ 6\ by\ 3 \\\\\rightarrow 2 \times 11 = 22[/tex]
Thus the value of expression when n = 3 is 22
Answer:
22
Step-by-step explanation:
1.1. Which statement explains why the two systems of equations below have the
same solution?
16x + 8y = -10
12x - 5y = 12
s 8x + 3y = 2
1 12x +16y = - 20
help!!
Answer:
This is Equivalence system of equations. The first equation in B is the sum of the equations in A, while the other is obtained by multiplying the first equation in A by 2
Mr. and Mrs. Lorenzo want to buy a home valued at $213,500. If they have 18% of this amount saved for a down payment, how
much have they saved?
a $384.30
b. $3,843.00
C. $38,043.00
d. $38,430.00
Answer:D
Step-by-step explanation:
Multiply the cost of the house by 0.18.
Emily rides her horse with a constant
speed of 12 km/h. How far can she travel
in 75 minutes?
Answer:
Step by-step explanation:
Speed v = 12km/h = 12/60km/min
Time t = 75min =
Distance d = ?
V = d/t
12/60 = d/75
Cross multiply
60d = 75 × 12
60d = 900
d = 900/60
d = 15km
Evaluate the following expression.
-7+(63/9)
63 divided by 9 is 7, so -7+7 is 0
Hope this helped
Answer:
0
Step-by-step explanation:
using PEMDAS
63/9 = 7
-7 + 7 = 0
rationalize √3+√2/√3-√2
Answer:
5 + 2[tex]\sqrt{6}[/tex]
Step-by-step explanation:
Multiply top and bottom by sqrt(3) + sqrt(2)
Top = (sqrt (3) + sqrt(2)) * (sqrt(3) + sqrt(2))
Top = 3 + sqrt(6) + sqrt(6) + 2
Top = 5 + 2sqrt(6)
Bottom = (sqrt (3) - sqrt(2)) * (sqrt(3) + sqrt(2))
Bottom = (3 - sqrt(6) + sqrt(6) - 2)
Bottom = 1
So, the answer is 5 + 2[tex]\sqrt{6\\}[/tex]
Answer: 5+2√6
Step-by-step explanation: attachment
How do you write 3x+4y=12 in slope-intercept form?
Answer:
y=-3/4x+3
Step-by-step explanation:
3x+4y=12
4y=12-3x
4y=-3x+12
y=-3/4x+12/4
y=-3/4x+3
The equation of a straight line graph is y = 12 - 0.5x find the coordinates of the intercept on the y axis
Yo sup??
Equation of the given line is
y=12 - 0.5x
on the y axis the x coordinate will be , therefore at x=0 we get
y=12 - 0.5*0
y=12
Therefore the coordinates of the y intercept are (0,12).
Hope this helps.
Final answer:
The y-intercept for the equation y = 12 - 0.5x is found by setting x to 0, resulting in y = 12, giving us the coordinates of the y-intercept as (0, 12).
Explanation:
The equation of a straight line is given by y = mx + b, where m represents the slope of the line, and b is the y-intercept. In your case, the equation is y = 12 - 0.5x. To find the coordinates of the intercept on the y-axis, we set x to 0 and solve for y. This gives us the y-intercept directly from the equation without needing to graph it.
For the equation y = 12 - 0.5x, when x = 0:
y = 12 - 0.5(0)
y = 12 - 0
y = 12
Therefore, the coordinates of the intercept on the y-axis are (0, 12).
Which products result in a difference of squares or a perfect square trinomial? Check all that apply.
(5x + 3)(5x - 3)
(7x + 4)(7x + 4)
(2x + 1)(x + 2)
(4x – 6)(x + 8)
(x – 9)(x – 9)
(-3x - 6)(-3x + 6)
Answer:
A (5x + 3)(5x – 3)
B (7x + 4)(7x + 4)
E (x – 9)(x – 9)
F (–3x – 6)(–3x + 6)
in other words, A,B,E, and F on edge-nuity. just completed with 100%
Step-by-step explanation:
Please help me with this question im stuck on it for an hour im so confused i dont know how to do a but i can do b :)
96 m
2 m/sec²
Step-by-step explanation:
Step 1:
In a velocity and time graph , the area which is under the plotted line represents the distance traveled
In the given graph , the plotted line from t=0 to t=4 ( for the first 4 secs) is a triangle with base = 4 and height = 8
Area of this triangle is (1/2) * b * h = (1/2)* 4*8 = 16 m
Step 2 :
The plotted line from t = 4 to t = 14 is a rectangle with length equal to 10 and breadth equal to 8
Hence its area = length * breadth = 10 * 8 = 80 m
Step 3 :
Total distance traveled is 80 + 16 = 96 m
Step 4 :
In the velocity time graph , slope denotes the acceleration at any given time. Since we want the acceleration for the first 4 secs, we need to find slope of line in from t = 0 to t= 4
when t = 0, v =0 and t= 4, v = 8
Slope = 8-0/4-0 =2 m/sec²
12 5/6x - 14x + 1/6x ?
The result of the given expression 12 5/6x - 14x + 1/6x is -x
Given the expression
12 5/6x - 14x + 1/6x
Convert the mixed fractions into improper fractions as shown:
[tex]\frac{77}{6}x - 14x + \frac{1}{6}x[/tex]
Collect the like terms;
[tex]= \frac{77}{6} x+\frac{1}{6}x - 14x\\= \frac{77x+x}{6} - 14x\\= \frac{78x}{6} - 14x\\= 13x - 14x\\= -x[/tex]
Hence the result of the given expression is -x
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The simplified form of the expression is -x .
Given, expression [tex]12\frac{5}{6}x -14x + \frac{1}{6} x[/tex] .
Expression: [tex]12\frac{5}{6}x -14x + \frac{1}{6} x[/tex]
Firstly solve the mixed fraction.
[tex]12\frac{5}{6} x\\= \frac{77}{6}x[/tex]
Rewriting the expression :
= [tex]\frac{77}{6}x - 14x + \frac{1}{6}x[/tex]
Solve the terms with common denominator.
= [tex]\frac{77+1}{6} x[/tex]
= [tex]13x[/tex]
Solve the like terms,
[tex]= 13x - 14x\\\\=- x[/tex]
Hence the simplified form of expression is -x .
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