1. The percent of cats between 24.16 and 35.84 is 95%
2. The percent of cats who are longer than 35.84 is 2.28 %
3. The percent of cats shorter than 24.16 inches is 2.28%
What is the empirical rule formula in statistics?The empirical rule - formula
95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .
Mean, u = 30 inches
Standard Deviation, s = 2.92 inches
Formula for z-score = (x-u)/s
1. We have to find the percent of cats between 24.16 and 35.84 inches.
24.16, z-score = -2
35.84, z-score = 2
According to the empirical rule,
95% of the data values are within 2 standard deviations of the mean.
So, 95% of the cats are between 24.16 and 35.84 inches.
2. Here, x = 35.84
z=(35.84-30)/2.92
z= 2
According to the Empirical Rule,
95% of the values lie within 2 standard deviations of the mean.
So, the percent of cats who are longer than 35.84
100 - 97.72 = 2.28%
3. Now, x = 36.22
Using the formula mentioned above, we get:
z= 24.16-30/2.92
z=-2
According to empirical rule,
68% of the values lie within 1 standard deviation of the mean.
i.e., remaining 32% are outside the 1 standard deviation and half of the values i.e. 16% are below 1 standard deviation.
The percent of cats shorter than 24.16 inches is 2.28%
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Given
μ = 30 inσ = 2.92 inFind z-scores for x = 24.16 and x = 35.84
Use formula
z = (x - μ)/σ 1) z = (24.16 - 30)/2.92 = - 22) z = (35.84 - 30)/2.92 = 2Find the corresponding percentage from z-score table
z = - 2 ⇒ 2.28%z = 2 ⇒ 97.72%Now find the answers#1The percent of cats between 24.16 and 35.84
97.72 - 2.28 = 95.44%#2The percent of cats who are longer than 35.84
100 - 97.72 = 2.28%#3The percent of cats shorter than 24.16 inches
2.28%PLEASE HELP 20 POINTS!!
[tex]\text{First term,} ~a = 72\\\\\text{Common ratio,}~ r = \dfrac{-36}{72} =-\dfrac 12 \\\\\text{Sum of an infinite geometric series,}\\\\S_{\infty} = \dfrac a{1 - r}\\\\\\~~~~~= \dfrac{72}{1+ \dfrac 12}\\\\\\~~~~~=\dfrac{72 }{\tfrac 32}\\\\\\~~~~~=\dfrac{72 \times 2}3\\\\\\~~~~~=48[/tex]
Series: 72 - 36 + 18 - 9 +...
[tex]\sf S \infty \ =a_1 \ x \ \dfrac{1}{1-r}[/tex]
Identify the following
a1 = 72 - 36r = (18-9) ÷ (72-36) = 1/4Solve:
[tex]\rightarrow \sf S \infty \ =(72-36) \ x \ \dfrac{1}{1-\frac{1}{4} }[/tex]
[tex]\rightarrow \sf S \infty \ =48[/tex]
This series has a sum of 48.
Aiden has $6,000 in an account. The interest rate is 5% compounded annually. To the nearest cent, how much will he have in 5 years?
Answer:
$7,657.69
Step-by-step explanation:
To find this, use the interest formula:
[tex]A = P(1+r)^{t}[/tex]
A = final amount
P = principal amount ($6,000)
r = interest rate (5% or 0.05)
t = time (5 years)
Given this formula, we can plug in the information and find how much Aiden has after 5 years:
[tex]A = 6000(1+0.05)^{5}[/tex]
[tex]A = 6000(1.05)^{5}[/tex]
[tex]A = 7657.69[/tex]
Therefore, after 5 years Aiden will have $7,657.69.
I hope this helps! Good luck!
Find the domain of the graphed function.
j
O A. 1sxs 5
O B. x2 2
O C. 2 sxs 5
D. xis all real numbers.
Answer:
A. -1 ≤ x ≤ 3
Step-by-step explanation:
According to the graph, our x-values span from -1 to 3. Since both are closed dot, they are inclusive in the domain:
[-1, 3] or -1 ≤ x ≤ 3
Warren's window store made a mosaic for the community center. The mosaic had an 8 x 8 array of different color square tiles. If each tile is 2 2/3 ft long, what is the area of the whole
mosaic?
What is the surface area?
2 mm
9 mm
3 mm
Answer:
Surface area of rectangular prism
=P×h
=2(l+w)×h
=2(3+9)×2
=48mm²
[tex] \boxed{ \frak{Answer}}[/tex]
Given,
Length (l) = 9 mm
Breadth (b) = 3 mm
Height (h) = 2 mm
To find: The surface of it.
We, know that
Surface area of a cuboid = 2(lb + bh + lh)
By using the formula,
= 2(lb + bh + lh)
= 2(9*3 + 3*2 + 9*2)
= 2( 27 + 6 + 18)
= 2(51)
= 102 mm²
Therefore the required surface area is 102 mm²[tex] \boxed{ \frak{Keep \: Learning }}[/tex]
What is 75% of 99. Round your answer to the nearest hundredths.
Answer: 74.25
Step-by-step explanation:
75% ÷ 100 = 0.75
0.75 * 99
= 74.25
units and Lino Plots
More
Bags of Oranges
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Jordan fills several bags with oranges. This line plot
shows the weight of each bag.
How many more pounds does one of the heaviest
bags weigh than one of the lightest bags?
Enter your answer as a mixed number by filling in the
boxes.
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х
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х
х
х
х
х
xx
xx
X X
X X
X X X
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X
8
8
4 44 45 46 45 5 5 5 5 5
55 55
Weight (lb)
Ib
1
2
3
4
4
5
6
1
Answer:
1 1/8 or 9/8
Step-by-step explanation:
5 1/2 - 4 3/8 = 1/ 1/8
Solve x^2 - 3x + 5 = 0.
Answer: A
Step-by-step explanation:
x^2 - 3x + 5 = 0 - quadratic equation
Standard quadratic equation form: a^2 + bx + c = 0
Here a = 1, b = -3, c = 5Discriminant formula: D = b^2 - 4acD = (-3)^2 - 4*1*5 = 9 - 20 = -11 (-11 < 0 => no real roots)
x1 = (-b - sqrt(D)) / (2*a)x2 = (-b + sqrt(D)) / (2*a)x1 = (3 - sqrt(-11)) / 2
x2 = (3 + sqrt(-11)) / 2
I need help asap I'm not good at math and this makes no sense
Answer:
Total Volume grain elevator holds - 20357.52
Volume needed for 100-acre field - This is all you need to find. If the volume is more than what the grain elevator can hold than there will need to be a rented one as well. If the volume of the grain is lower than what the grain elevator holds, than that's all you need.
Step-by-step explanation:
You have to find how much volume you would need to hold harvest from a 100-acre field.
Then you have to find how much volume is in the grain elevator.
In order to find the volume of the grain elevator you have to divide it up by the cylinder and the cone.
Cone volume - V=πr^2(h/3)
V=2035.75
Cylinder volume - V=πr^2h
V=18321.77
The prime factorisation of √169 is?
Answer:
Square root of 169 by Prime factorization is 13×13
Answer:
13*13
Hope this helped!
Select the correct answer.
A pizza restaurant starts the day with a certain amount of pizza dough. The length of time the dough will last varies inversely with the number of
medium pizzas made.
If they need to make 32 medium pizzas, the dough will last 5 hours. How long will the dough last if they need to make 40 pizzas?
OA 2.75 hours
OB. 4 hours
OC.
8 hours
OD. 6.25 hours
The length of time needed for the dough to last if 40 pizzas is required is 4 hours.
Inverse variationlet
length of time = lnumber of pizza = pl = k / p
where,
k = constant of proportionality
If l = 5 and p = 32
l = k / p
5 = k / 32
5 × 32 = k
160 = k
Find l when p = 40
l = k / p
l = 160/40
l = 4 hours
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Find two pairs of integers whose product is -20.
Answer:
-10 x 2 and -5 x 4
Step-by-step explanation:
An integer is a number that must be whole and can either be negative or positive. The product is the total value from multiplying values.
Applicable equations:
-10 x 2 = -20
10 x (-2) = -20
-5 x 4 = -20
5 x (-4) = -20
-1 x 20 = -20
1 x (-20) = -20
Please assist with a question I am stuck on.
The two linear equations in this problem are:
a) d(t) = (3.1 mi/h)*tb) t(d) = d/(3.1 mi/h).How to find the linear equations?
a) First, we know the relation:
distance = speed*time.
In this case, we know that the speed is 3.1 miles per hour, so if the runner runs for t hours, we can write:
d(t) = (3.1 mi/h)*t
This is the linear equation that gives the distance as a function of time.
b) Now we want to get the time as a function of the distance, so we just need to isolate t,
t(d) = d/(3.1 mi/h).
This linear equation gives the time as a function of the distance d.
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The volume of a right cone is 3000π units^3. If its radius measures 15 units, find its height.
Answer:
40 unitsStep-by-step explanation:
In the question, it is given that a right cone has a radius of 15 units and volume of 3000π units³ and we have to find the height of the cone.
[tex] \: [/tex]
To Find the height of the cone, we must know this formula :
[tex]\\{\longrightarrow{ \qquad{\underline{\boxed {\pmb{\frak { \dfrac{1}{3} \: \pi {r}^{2}h ={ Volume_{(cone) }}}}}}}}} \\ \\[/tex]
Where,
r refers to the radius of the cone. h refers to the height of the cone.Now, we will substitute the values in the formula :
[tex] \\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{1}{3} \times \pi \times {(15)}^{2} \times h = 3000 \pi}}}}}}} \\ \\[/tex]
Cancelling π from both sides we get :
[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{1}{3} \times \cancel\pi \times {(15)}^{2} \times h = 3000 \cancel\pi}}}}}}} \\ \\[/tex]
[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{1}{3} \times 225 \times h = 3000}}}}}}} \\ \\[/tex]
[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{225}{3} \times h = 3000}}}}}}} \\ \\[/tex]
[tex] \\ {\longrightarrow{ \qquad{{ {\pmb{\sf 75 \times h = 3000}}}}}} \\ \\[/tex]
[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf h = \frac{3000}{75} }}}}}} \\ \\[/tex]
[tex]\\{\longrightarrow{ \qquad{\underline{\boxed {\pmb{\frak { h =40 }}}}}}} \\ \\[/tex]
Therefore,
The height of the cone is 40 units .Which number line represents the solution set for the inequality 3x < –9?
Answer:
oh
Step-by-step explanation:
Mike put 210 baseballs into 7 trash bins. He put the same number of baseballs in each bin. He took 2 trash bins of baseballs to the
baseball field. How many baseballs did Mike take?
A. 30
B. 896
C. 90
D. 60
Answer:
D. 60
Step-by-step explanation:
210 baseballs divided evenly between 7 trash bins = 30 balls per bin
2 trash bins multiplied by 30 balls per bin = 60 balls in two bins
Hope this helps!
Solve the equation. Need HELP!!!
Answer:
[tex]m = 0.664[/tex]
Step-by-step explanation:
We were given the equation: [tex]2.1 + 10m = 8.74[/tex]and we were asked to solve for m. Therefore we have to ensure m the subject of the formula.
[tex]2.1 (-2.1) + 10m = 8.74 (-2.1) \\ \\ 10m = 8.74 - 2.1 \\ \\ 10m = 6.64 \\ \\ \frac{10}{10} m = \frac{6.64}{10} \\ \\m = 0.664[/tex]
Answer: Heyaa! :D
Your Answer Is... m= 0.664
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Hopefully this helps you!
-Matthew (HAVE AN AMAZING DAY)
Please help me do this assignment
I hope this will help you a lot..
Answer:
(30x⁴+36x²y⁴)+(36x⁴y²+30xy⁴).
Step-by-step explanation:
x⁶+3x⁴y⁴+xy⁶
1) df/dx=6x⁵+12x³y⁴+y⁶; d²f/dx²=30x⁴+36x²y⁴;
d²f/(dxdy)=48x³y³+6y⁵ (note, d²f/(dxdy)=d²f/(dydx) !!);
df/dy=12x⁴y³+6xy⁵; d²f/dy²=36x⁴y²+30xy⁴;
2) finally
(30x⁴+36x²y⁴)+(36x⁴y²+30xy⁴).
Select all the correct answers. Which expressions are equivalent to the given expression? √40
Answer:
2√10
Step-by-step explanation:
√40=√4 x 10
2√10
It takes3/4 cup of sugar to make a loaf of bread how much sugar would you need to make 16 loaves of bread
Too make this easier for me or others 3/4 can be represented as 0.75. 3/4 or 0.75 x 16 = 12
More depth explanation:
Multiple: 3/
4
* 16 = 3 · 16/
4 · 1
= 48/
4
= 12 · 4/
1 · 4
= 12
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(48, 4) = 4. In the following intermediate step, cancel by a common factor of 4 gives 12/
1
.
In other words - three quarters multiplied by sixteen = twelve.
What is the domain of the profit function P = 7m + 12n?
O A. Defined for all m> 0 and n_>0
B. Defined for all m _>0 and n > 0
C. Defined for all m> 0 and n > 0
D. Defined for all m _> 0 and n _> 0
Answer:
D
Step-by-step explanation:
without knowing anything about the background of the function and what it is used for, I give it the max. possible domain (the set or interval of all possible input values).
and so,
Defined for all m >= 0 and n >= 0.
there is no information provided that would eliminate m = 0 or n = 0.
The inverse of the function f(x) = 1/2x+10?
Answer:
f'(x) = 2x - 20
Step-by-step explanation:
f(x) = 1/2 x + 10
Switch x and y.
y = 1/2 x + 10
Solve for y by itself.
x = 1/2 y + 10
x - 10 = 1/2 y
y = 2 * (x - 10)
f'(x) = 2x - 20
You invest $2,800 in an account that
pays an interest rate of 5.5%,
compounded continuously. Calculate the balance of your account after 12 years
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$2800\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ t=years\dotfill &12 \end{cases} \\\\\\ A=2800e^{0.055\cdot 12}\implies A=2800e^{0.66}\implies A\approx 5417.42[/tex]
Find the value of cos I rounded to the nearest hundredth, if necessary.
18
K
J
30
24
I
Answer:
the value of cos is 26
k =14
j=30
Step-by-step explanation:
mark me as brainlist
A line passes through the points (-4,8) and (3,-7). Answer all parts of the question. Part A: what is the slope of the line that passes through these points (-4,8) and (3,-7).
Answer: [tex]y=\frac{-15}{7}x-\frac{4}{7}[/tex]
Slope: -15/7
y-int:-4/7
Step-by-step explanation:
slope: rise/run
[tex]\frac{x^2-x^1}{y^2-y^1}[/tex]
[tex]\frac{-7-8}{-4-3}=\frac{-15}{-7} =\frac{-15}{7}[/tex]
thats the answer :)
~rere
Find the distance between the following sets of points: a. (2, −4) and (2, 3) b. (−3, −2) and (−3, 0) c. (1, 4) and (−5, 4) d. (−2, 0) and (−3, 0) e. (4, −6) and (4, −2) f. (5, 1) and (1, 1)
Answer:
Step-by-step explanation:
Distance between set of points parallel to x-axis and y-axis.a) (2,-4) and (2 , 3)
In these two points the x-coordinate are same. So, the distance between the points are given by the absolute value of difference between the y-coordinate.
Distance = I -4-3 I = I -7I = 7 units
b) (-3,-2) and (-3,0)
In these two points the y-coordinate are same. So, the distance between the points are given by the absolute value of difference between the x-coordinate.
Distance = I-2 -0 I = I -2 I = 2 units
c) (1,4) and (-5,4)
In these two points the y-coordinate are same. So, the distance between the points are given by the absolute value of difference between the x-coordinate.
Distance = I 1 - (-5) I = I 1 + 5 I = I 6 I = 6
d) (-2,0) and (-3,0)
In these two points the y-coordinate are same. So, the distance between the points are given by the absolute value of difference between the x-coordinate.
Distance = I -2 - (-3) I = I -2 + 3 I = I 1 I = 1 unit
e) (4,-6) and (4,-2)
In these two points the x-coordinate are same. So, the distance between the points are given by the absolute value of difference between the y-coordinate.
Distance = I -6 - (-2) I = I -6 + 2 I = I-4 I = 4 units
f) (5,1) and (1 , 1)
In these two points the y-coordinate are same. So, the distance between the points are given by the absolute value of difference between the x-coordinate.
Distance= I5 - 1 I = I 4 I = 4 units
Create an equation to convert X feet into y miles
Answer:
y = x/5280
Step-by-step explanation:
y miles = x feet / 5280
help me please :/
Dana is training to run a marathon. On Monday, she ran 10.2 miles. On Tuesday, she ran 11.4 miles. On Wednesday and Thursday, she ran 11.8 miles each day. On Friday, she ran 12.3 miles. Round each amount to the nearest whole mile to find a reasonable estimate of the total number of miles Dana ran over this five-day period.
Answer:
57 miles.
Step-by-step explanation:
to find
⇒ total number of miles dana ran
given
⇒ monday = 10.2 miles
⇒ tuesday = 11.4 miles
⇒ wednesday and thursday = 11.8 miles
⇒ friday = 12.3 miles
∴ total number of miles = 10.2 + 11.4 + 23.6 + 12.3
⇒ 57.5
⇒ 57 miles
Which of the following pairs of numbers contain like fractions
A. 3/2 and 4 44
B. 3/2 and 2/3
C.6/7, and 1 1/5,
D.5/6 and 10/12
Answer:
D. 5/6 and 10/12
Step-by-step explanation:
edmentum, end of semester test, geometry A, answer key ,please anyone?
The equation which can be used to find the minimum or maximum amount, c, of chocolate chips that he can weigh out will be:
|C-78|=2.5
What will be the end of semester test?From the question, we have to determine the equation which can be used to find the minimum or maximum amount, c, of chocolate chips that he can weigh out.
From the question statement, we can easily the information thatSam tends to use an industrial kitchen to bake several batches of his famous chocolate chip bars.Also, it is mentioned that he needs to weigh out 78 ounces of chocolate chips, plus or minus 2.5 ounces.Mathematically, it means:
|C-78|=2.5
Hene, the reqired equation will be :|C-78|=2.5
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