Answer:
a)8.4kg to 10.6kg
b)7.3 kg to 11.7kg
c)16%
d) 95%
e) 0.15%
Step-by-step explanation:
The empirical rule formula states that:
68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ .
95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .
99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ
From the question,
Mean(μ) = 9.5 kg,
Standard Deviation (σ) = 1.1 kg.
a) 68% of the data is between which 2 values?
68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ .
μ - σ
= 9.5kg - 1.1kg
= 8.4kg
μ + σ
= 9.5kg + 1.1kg
= 10.6kg
Therefore, 68% of the data is between 8.4kg to 10.6kg
(b) 95% of the data is between which 2 values?
95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .
μ - 2σ
9.5kg - 2(1.1)kg
9.5kg - 2.2 kg
= 7.3kg
μ + 2σ
9.5kg + 2(1.1)kg
9.5kg + 2.2 kg
= 11.7kg
Therefore, 95% of the data is between 7.3 kg to 11.7kg
(c) What percentage of the data is less than 8.4 kg?
We need to find how many standard deviations from the mean 8.4kg is, in order to know the percentage it falls under
μ - xσ = 8.4kg
= 9.5kg - 1.1x = 8.4kg
9.5 - 8.4 = 1.1x
1.1 = 1.1x
x = 1.1/1.1
x = 1
Hence, the percentage it falls under according to Empirical rule = 68%
The percentage of the data that is less than 8.4 kg is calculated as:
100 - 68/2 = 32/2 = 16%
(d) What percentage of the data is between 7.3 kg and 11.7 kg?
We have to find the Standard deviation that they fall under
For 7.3 kg
μ - xσ = 7.3kg
= 9.5kg - 1.1x = 7.3kg
9.5 - 7.3 = 1.1x
2.2 = 1.1x
x = 2.2/1.1
x = 2
μ + xσ = 11.7kg
= 9.5kg + 1.1x = 11.7kg
11.7 - 9.5 = 1.1x
2.2 = 1.1x
x = 2.2/1.1
x = 2
Therefore, based on the calculation above and the empirical formula rule, the percentage of the data is between 7.3 kg and 11.7 kg is 95%
(e) What percentage of the data is more than 12.8 kg?
μ + xσ = 12.8kg
9.5kg + 1.1x = 12.8kg
= 12.8- 9.5 = 1.1x
3.3 = 1.1x
3.3 = 1.1x
x = 3.3/1.1
x = 3
Hence, the percentage it falls under according to Empirical rule = 99.7%
The percentage of the data that is more than 12.8kg is calculated as:
100 - 99.7/2 = 0.3/2 = 0.15%
increase 400litres by 20%
Answer:
480 Litres
Step-by-step explanation:
Percentage increase = 20% × 400
New value =
400 + Percentage increase =
400 + (20% × 400) =
400 + 20% × 400 =
(1 + 20%) × 400 =
(100% + 20%) × 400 =
120% × 400 =
120 ÷ 100 × 400 =
120 × 400 ÷ 100 =
48,000 ÷ 100 =
480
Factor( special patterns): 36x^2-84x+49
Answer:
(6x - 7) (6x - 7)
Step-by-step explanation:
A perfect square trinomial will be in the form of [tex]a^2[/tex] ± [tex]2ab + b^2.[/tex] A trick to factoring a perfect square trinomial would to write it as [tex](a^2[/tex]±[tex]b^2)[/tex]. (When doing this, the sign in the middle is determined by the middle sign in the original trinomial).
[tex]36x^2 -84x + 49[/tex] is known as a perfect square trinomial, too. Its first and last terms are both perfect squares (6x squared makes [tex]36x^2[/tex], 7 squared makes 49) and the middle term is 2 times the square roots of both of the other terms ( [tex](2) (7) (6x)[/tex] is [tex]84x[/tex]).
So, we can use the trick described earlier, and the answer would be [tex](6x-7)^2[/tex], also known as (6x-7) (6x-7).
(11x + 2) + (9x − 4)
MARKING BRAINLIST IF YOU CORRECTLY ANSWER
Answer:
20x-2
Step-by-step explanation:
Eliminate redundant parentheses:
(11+2)+(9−4)
11+2+9−4
Subtract the numbers:
11+2+9−4
11−2+9
Combine like Terms:
11−2+9
20−2
Solution:
20x-2
PLEASE answerrrrr this
Answer:
wsp
Step-by-step explanation:
Shane rode his bike for two hours and traveled 12 miles at this rate how long would it take him to ride 22 miles
Answer:
3.66666666667
Step-by-step explanation:
First, we need to find the unit rate to figure out how many miles Shane rides in 1 hour. To do this it is simple, I divided 12 and 2 to get 6 miles per hour. Then we would do 22/6 but we get a decimal so it would be about 3.66666666667.
6. Marissa got an 85% on her math quiz She had 34 que How many questions were on the quiz?
Write the expression in standard form 5(2a)+7(-4b)+2.c.5
Answer: I will be there at about five or seven or later today and then I’m going to be there
Step-by-step explanation:
Question for the answer questions about the question question for you and I have to do a little more
Please helppppppppppppp
Answer:
6.08
Step-by-step explanation:
About 10% of Americans will go to a restaurant or an event for New years. About how many people would that be ?
Answer: 33.1 million
Step-by-step explanation:
The US Census Bureau estimates that as of 2021, the US population is around 331 million people.
If 10% of that number go to a restaurant or an event for New years, that number would be:
= 10% * 331,000,000
= 33.1 million
The value of a bank account is −$28. Money is then deposited into the account. Which could represent the value of the account now? A.-$33 B.-$6 C.-$45 D.$17 E.$0
Answer:
Step-by-step explanation:
depends how much money is deposited, however, the choices can be just D or E
Answer:
B,D,E
Step-by-step explanation:
Does it say how much was deposited? Ok so deposit means your bank gets bigger so it cannot be less than -28.
My guess is that it will be either B,D,E
The reason I say my guess is because I think the question should have given you an amount of how much was deposited.
I'm so confused please help
Answer:
?
Step-by-step explanation:
Answer:
What do you need help with
Step-by-step explanation:
2. angle ABE = angle MNP
Write another valid congruency statement:
Given:
[tex]\Delta ABE\cong \Delta MNP[/tex]
To find:
The congruent angles and sides, then find the another valid congruency statement.
Solution:
We have,
[tex]\Delta ABE\cong \Delta MNP[/tex]
We know that, corresponding parts of congruent triangles are congruent (CPCTC).
Using CPCTC, we get
Angles:
[tex]\angle A\cong \angle M[/tex]
[tex]\angle B\cong \angle N[/tex]
[tex]\angle E\cong \angle P[/tex]
Sides:
[tex]AB\cong MN[/tex]
[tex]BE\cong NP[/tex]
[tex]AE\cong MP[/tex]
The another congruent statement is [tex]\Delta BEA\cong \Delta NPM[/tex].
Therefore, the required table is
Angles Sides
[tex]\angle A\cong \angle M[/tex] [tex]AB\cong MN[/tex]
[tex]\angle B\cong \angle N[/tex] [tex]BE\cong NP[/tex]
[tex]\angle E\cong \angle P[/tex] [tex]AE\cong MP[/tex]
The another congruent statement is [tex]\Delta BEA\cong \Delta NPM[/tex].
John jogged 4.5 miles on Thursday, 7 2/5 miles on Friday, and 10.4 miles on Saturday. How many miles does John have to run in order to run 25 miles for the week
im giving 20 points
Answer:
2.7 miles
Step-by-step explanation:
25 - 10.4 - 4.5 - 7 2/5 will give you 2.7
Answer:
8 miles
Step-by-step explanation:
If we divide 70 by 50, we get the unit rate for the ratio 70 minutes for every 50 miles.
70÷50=1.4
So the runner is running 1.4 minutes per mile. We can multiply this unit rate by the number of miles:
1.4 minutes mile × 5 miles = 7 minutes
Thus it will take her 7 minutes to run 5 miles at this pace.
If it takes her 7 minutes to run 5 miles, it will take her 7÷5 = 1.4 minutes to run 6÷3=2 miles at the same pace.
If it takes her 1.4 minutes to run 5 miles, it will take her 1.4×5=7 minutes to run 4×2=8 miles at the same pace. Since 60 minutes is 1 hour, she is running at a speed of 8 miles per hour.
We found her pace in minutes per miles in part (a).
Molly was going to sell all of her stamp collection to buy a video game after selling half of them she changed her mind she then bought fifteen more how many did she start with if she now has 35
What is the answer to 3x+8=20
Answer:
X=4
Step-by-step explanation:
3x+8=20
3x=20-8=12
X=12/3=4.
X=4
I hope it helps.
Answer:
x=4
Step-by-step explanation:
3x+8=20
3x=20-8
3x=12
x=12÷3
x=4
find two integers whose sum is -1 and product is -42
Answer:
6 and -7
Step-by-step explanation:
6 - 7 = -1
6 * -7 = -42
Hope this helped!
Answer:
-7 and 6
Step-by-step explanation:
-7+6= -1 which is true
-7*6= -42 2hich is also true
help please, i don’t understand
Answer:
if you where to flip CBE on top of ABD they will fit perfect
Step-by-step explanation:
its not rlly that hard if you can see point AD = CE so is AB=CB both triangles end at B they both have a right angle at the end of ABD and CBE and both have an acute angle at the end at point B from AD and CE
Answer:
By AA postulate
Step-by-step explanation:
[tex] In\: \triangle ABD \: \&\: \triangle CBE[/tex]
[tex] \angle BAD\cong\angle BCE... (given) [/tex]
[tex] \angle ABD\cong\angle CBE... (given) [/tex]
[tex] \therefore \triangle ABD\sim\triangle CBE[/tex] (By AA postulate)
Which graph shows a dilation?
Answer:
the last one shows a dialation
Plz help me with this question
Answer:
The equation that models the population growth is y = 90,000(1.02)^x
Step-by-step explanation:
The formula of the exponential growth is y = a [tex](b)^{x}[/tex], where
a is the initial valueb is the factor of growth ⇒ b > 1Let us solve the question
∵ At x = 0, the population y = 90,000
→ That means the initial value is 90,000
∴ a = 90,000
→ Substitute it in the form of the equation above
∴ y = 90,000 [tex](b)^{x}[/tex]
→ To find b use any values from the table to substitute x and y
∵ At x = 1, y = 91,800
∵ 91,800 = 90,000 [tex](b)^{1}[/tex]
∴ 91,800 = 90,000 b
→ Divide both sides by 90,000
∵ [tex]\frac{91,800}{90,000}[/tex] = [tex]\frac{90,000b}{90,000}[/tex]
∴ 1.02 = b
→ Substitute it in the equation above
∵ y = 90,000 [tex](1.02)^{x}[/tex]
∴ The equation that models the population growth is y = 90,000(1.02)^x
3(2b+ 4) +6
Please answer
Answer:
6b+18
Step-by-step explanation:
3(2b + 4) + 6
6b + 12 + 6= 6b+18
Answer:
6b + 18
Step-by-step explanation:
3(2b + 4) + 6
6b + 12 + 6
6b + 18
Write the slope-intercept form of the equation of each line given the slope and y-intercept.
Slope=-1/4, y-intercept =2
Answer:
y = -1/4x+2
Step-by-step explanation:
The SIF (slope intercept form) is pretty easy once you get it down. the slope is the interger before x, and the y-intercept is b. so, if you input each number into it's spot, it would become y = -1/4x + 2.
The double number line shows that 5 kilograms of avocados cost $9 dollar .
Based on the ratio shown in the double number line, what is the cost for 1 kilogram of avocados?
Answer:
hii hope it helps
Step-by-step explanation:
sorry for these pics
Marc plots the point (1, 20) in a coordinate grid to show the number of minutes it takes him to walk 1 mile. Which ordered pair might Marc use to show how many minutes it takes him to walk 3 miles?
Answer:
(3,60)
Step-by-step explanation:
Marc is walking at a rate of 20 minutes per 1 mile; therefore, at that rate he can walk 3 miles in 60 minutes.
]. A local store, Faith Ltd has two options to choose either Big Van or Small Van or both types of van to supply bags of rice to local restaurants. (a) Big Van has capacity of 15 tonnes at £250 (b) Small Van has capacity of 9 tonnes at £151. If the Faith Ltd wants to supply 50 tonnes of rice what is cheapest cost £ to pay?
the sum of length and breadth of a room is 20m,find it's perimeter
Answer:
80 m.
Steps: perimeter =4 x side
=4x20=80m
Answer:
40 m
Step-by-step explanation:
Formula of perimeter of a rectangle = 2(l + b)
where l = Length & b = Breadth
According to the question ,
Sum of length & breadth = l + b = 20m
Perimeter = 2(l + b) = 2 × 20 = 40m
if a car travels at an average of 25 kilometres per hour how long would a journey of 175 km take
Answer:
it'll 7 hours to a journey of 175km
Step-by-step explanation:
25km/per hour
25 x 7 = 175km
A family consumes 4 ⅗ pounds of rice every 2 days. Assuming the family eats the same amount of rice each day, how many pounds of rice will the family consume each year? (1 year = 365 days)
PLS HELP ME
Answer:
839.5
Step-by-step explanation:
365/2=182.5
4.60*182.5=839.5 pounds of rice in a year
Answer:
839.5
Step-by-step explanation:
well you could do this two ways, I simply divided 4.6 into 2 and multiplied it by 365
plases help
Determine the number of solutions of each system of equations.
Answer:
Step-by-step explanation:
this is the same equation, the system has infinitely many solutions
Which is an equivalent expression for 48 + 18x? *
6 (8 + x)
6 (8 + 3x)
2 (24 + 8x)
3 (15 + 6x)
Answer:
6(8+3x)
Step-by-step explanation:
48+18x = 6(8+3x)
What is the quotient of 145.66 and 0.8
Answer: 182.075
Step-by-step explanation: 145.66 divided by 0.8 =182.0.75
Answer:
182.075
Step-by-step explanation:
Divide 145.66 and 0.8 to get=182.075.