Using the normal distribution, it is found that there is a 0.0571 = 5.71% probability that the total weight exceeds the maximum weight.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem, we have that the parameters are given as follows:
[tex]\mu = 60, \sigma = 10, n = 10, s = \frac{10}{\sqrt{10}} = 3.1623[/tex]
The probability that the total weight exceeds the maximum weight is the probability of a sample mean above 650/10 = 65 kg, which is one subtracted by the p-value of Z when X = 65.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{65 - 60}{3.1622}[/tex]
Z = 1.58.
Z = 1.58 has a p-value of 0.9429.
1 - 0.9429 = 0.0571.
0.0571 = 5.71% probability that the total weight exceeds the maximum weight.
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Which of these ordered pairs is a solution to the inequality
y – 2x ≤ –3?
Question 3 options:
(2, 4)
(–2, 3)
(3, 4)
(1, –1)
The answer is: (1, –1)
The box plot below represents some data set. What is the interquartile range (IQR) of
the data?
-
42
45
48
51
54
57
60
Answer:
IQR = 5
Step-by-step explanation:
the IQR is the difference between the upper quartile Q₃ and the lower quartile Q₁
Q₃ is the value at the right side of the box plot , that is
Q₃ = 51
Q₁ is the value at the left side of the box plot , that is
Q₁ = 46
then
IQR = Q₃ - Q₁ = 51 - 46 = 5
 Hamza decides to increase the prices of all items in his shop by 10%
a)
Work out the new price of an item normally priced at £210
b)
Work out the new price of an item normally priced at £48
Answer:
a=£231
b=£32.8
Step-by-step explanation:
get the percentage multiplied by the current price to get the increase then add the increaseto the current price
what is 3.20 divided by 5
Answer:
0.64
Step-by-step explanation:
...........................
Answer:
0.64
Step-by-step explanation:
3.20 divided by 5 is 0.64.
14=v/17.92+7. Solve for v
Answer:
125.44 = v
Step-by-step explanation:
14 = [tex]\frac{v}{17.92}[/tex] + 7
7 = [tex]\frac{v}{17.92}[/tex]
7(17.92) = v
125.44 = v
Hope this helps!
Answer:
[tex]v = 125.44[/tex]
Step-by-step explanation:
I assume you mean to solve [tex]14=\frac{v}{17.92}+7[/tex]Subtract 7 from both sidesThis gives [tex]7=\frac{v}{17.92}[/tex]Multiply both sides by 17.92[tex]v=125.44[/tex]Write the ratio in simplest form: there are 6 red marbles and 22 blue marbles in a jar. What is the ratio of red marbles to blue?
Answer:
3 : 11Step-by-step explanation:
Given : the ratio of red marbles to blue marbles is 6 to 22
But ,we want to write the ratio in simplest form
therefore ,we have to divide both sides of the ratio by their greatest common factor GCF.
→ So Let’s find the GCF(6 , 22)
Since 6 = 2 × 3
22 = 2 × 11
then ,GCF(6 , 22) = 2
Eventually ,the ratio 6 : 22 in its simplest form I suppose 3 : 11
...................................
Since, the fundraiser only have three prices for books($2, $5 and $10), the number of $5 book that was sold is 12.
How to form equation and solve ?The fundraiser only have 3 prices for books which are $2, $5 and $10.
There were 6 more $5 books sold than $10 books sold.
Let
x = number of $10 book sold
Therefore,
number of $5 books sold = x + 6
There are 8 more $2 book sold than $10 book sold. Therefore,
number of $2 books sold = x + 8
A total of $250 was raised.
Therefore, the total amount sold forms the following equation:
10x + 5(x + 6) + 2(x + 8) = 250
10x + 5x + 30 + 2x + 16 = 250
17x = 250 - 30 - 16
17x = 204
x = 204 / 17
x = 12
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Simplify the expression
3 (2d + 5) + 4d
Answer:
The answer is 10d + 15.
Step-by-step explanation:
Simplify the expression. Calculators are helpful for problems such as these...
Pablo wanted to see if a 12-inch straw would fit inside a small retangular box. He noticed that it only fits diagonally. The box has a height of 2 inches and width of 3 inches. What is the length of the box?
Answer:
11.61895003862225
Step-by-step explanation:
Which of the following inequalities matches the graph?

Answer:
y≥-1
Step-by-step explanation:
First you have to find out whether the inequality has x or y. You can first look at the x coordinate -1. This means that x will always be equal to -1. If you look at the graph than you can see that x is only equal to -1 at one place. So now you know that y is in the inequality. To tell whether this graph is greater than or less than you can look at the line and see whether the shaded section is to the positive side or the negative side. You can see that the shaded area goes in the positive direction so you know that it is greater than.
¿Alguien me ayuda con estas ecuaciones? :(
Answer:
see below
Step-by-step explanation:
7x-12=30
7x=30-+12
x=42/7
x=6
5x-18=77
5x=77+18
x=95/5
x=19
8x+12=36
8x=36-12
x=24/8
x=3
x+45=72
x=72-45
x=27
x+27=82
x=82-27
x=55
x-13=66
x=66+13
x=79
What is the surface area of an ice cream cone if the radius is 2 inches
Can someone please help me again! Tysm!!!
Answer:
129
Step-by-step explanation:
so they are basically the same angles but on different planes. Set them equal to each other.
14x+17=19x-23 solve for x
40=5x isolate x by dividing by 5
x=8
check
14(8)+17=19(8)-23
129=129
Find the surface area of the cube shown below.
units 2 1/2
Answer:
Step-by-step explanation:
Answer: 37.5
Explanation: find the surface area of one side, which is 2.5*2.5=6.25 then multiply that product by six, since there’s six sides in a square, and you’ll get 37.5
PLEASE PLEASE HELP ME WITH THIS I NEED ASAP THESE ARE TRUE OR FALSE QUESTIONS
Are the following statements true or false? (20 Points)
a. If the domain of a uniform continuous probability density function is 8.0
then its height is = 0.1684
b.
If the domain of a uniform continuous probability density function is 8.0
then P(14.0< X<26.0) = 0.6092
c.
All normal curves are symmetric and bell-shaped.
d.
By the Empirical Rule 99.7% of the area under a normal curve is within two
standard deviations of the mean.
I
e.
All uniform density functions are symmetric and bell-shaped.
f.
The Standard Normal curve has a mean of zero and a standard deviation of one.
0075
Answer:
1. true 2. false 3. false 4. true 5. false 6. false or true
Step-by-step explanation:
you're welcome
What is the equation of the line that is perpendicular to y = one-fifth x + 4 and that passes through (5,–4)?
On a coordinate plane, a line goes through (0, 4) and (5, 5). A point is at (5, negative 4).
y = negative 5 x minus 29
y = negative 5 x + 21
y = one-fifth x minus 4
y = one-fifth x minus 5
Answer:
2nd option
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{1}{5}[/tex] x + 4 ← is in slope- intercept form
with slope m = [tex]\frac{1}{5}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{5} }[/tex] = - 5 , then
y = - 5x + c ← is the partial equation
to find c substitute (5, - 4 ) into the partial equation
- 4 = - 25 + c ⇒ c = - 4 + 25 = 21
y = - 5x + 21 ← equation of perpendicular line
3x-2y=-3,-9x+6y=9 solve each system using elimination, state the solution and type of system.
We will see that the system of equations has infinite solutions, each of the form:
y = (3/2)*(x + 1)
How to solve the system of equations?Here we have the system:
3x - 2y = -3
-9x + 6y = 9
Notice that if we add 3 times the first equation to the second one, we get zero.
3*(3x - 2y) + -9x + 6y = 3*(-3) + 9
9x - 6y - 9x + 6y = -9 + 9
0 = 0
This actually means that both equations represent the same line, then, the "two" lines intersect in infinite points, meaning that the system of equations has infinite solutions, which are of the form:
3x - 2y = -3
2y = 3 + 3x
y = (3/2)*(x + 1)
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Late night math for you guys to solve
what is 2.5 multiplied to ten to the three power
Answer:
the answer is 2500
Step-by-step explanation:
10 ^3 =1000
next you multiply 1000 x 2.5 = 2500
There are 32 students in mr.Ryan’s class. 3/4 of the students have brown hair. The rest have blond hair. How many students have blond hair
Answer:
8
Step-by-step explanation:
32/4 = 8
8 = 1/4(32)
Answer:
8
Step-by-step explanation:
Since there is 32 students and 3/4 of them have brown hair right. We can change the 3/4 fraction to a similar fraction to help. We can bump it up. As it is similar to 6/8 and 12/16 and 24/32
So 24/32 would have brown hair leaving 8 with blonde
-1.9y=2.47
rational equations!
please helP!
Answer: y = -1.3
Step-by-step explanation:
A gallon of milk costs $2.30. What is the cost per quart?
Answer:
57.5p
Step-by-step explanation:
$2.30 / 4 = 57.5p
Send helppppppppppppppp;((
Answer:
I will do only 1 sum bru.h
In the 1st sum
the 1st no. can be in 9 ways
the 2nd no. can be in 10 ways
the 3rd no. can be in 10 ways
the 4th no. can be in 10 ways
total no. of ways = 9 × 10 × 10 × 10
= 90 × 100
= 9000 ways
2nd one..
the 1st letter can be written in 4 ways
the 2nd letter can be written in 4 ways
the 3rd letter can be written in 4 ways
the 4th letter can be written in 4 ways
Total no. of ways = 4 × 4 × 4 × 4
= 16 × 16
= 196 ways
Determine the length of DC.
Need the answer urgently.
Answer:
DC = 39
Step-by-step explanation:
From inspection of the diagram:
EA is tangent to both circlesDE is the radius of circle DCA is the radius of circle CThe tangent of a circle is always perpendicular to the radius, therefore:
DE ⊥ EA and CA ⊥ EA
As ∠DEB and ∠BAC are both 90°, then DE is parallel to CA.
Therefore, ∠DBE and ∠ABC are vertically opposite angles, and are therefore equal.
As triangles ΔBED and ΔBAC have two pairs of corresponding congruent angles, the triangles are similar.
Therefore:
[tex]\implies \sf \dfrac{DE}{CA}=\dfrac{EB}{BA}[/tex]
[tex]\implies \sf \dfrac{10}{5}=\dfrac{24}{BA}[/tex]
[tex]\implies \sf BA=12[/tex]
Using Pythagoras' Theorem for ΔBED to find DB:
[tex]\implies \sf DE^2+EB^2=DB^2[/tex]
[tex]\implies \sf 10^2+24^2=DB^2[/tex]
[tex]\implies \sf DB^2=676[/tex]
[tex]\implies \sf DB=\sqrt{676}[/tex]
[tex]\implies \sf DB=26[/tex]
Using Pythagoras' Theorem for ΔBAC to find BC:
[tex]\implies \sf CA^2+BA^2=BC^2[/tex]
[tex]\implies \sf 5^2+12^2=BC^2[/tex]
[tex]\implies \sf BC^2=169[/tex]
[tex]\implies \sf BC=\sqrt{169}[/tex]
[tex]\implies \sf BC=13[/tex]
Therefore, the distance between the center of the circles DC is:
[tex]\begin{aligned} \implies \sf DC & = \sf DB + BC\\& = \sf 26 + 13\\& = \sf 39\end{aligned}[/tex]
Use Pythagorean theorem
DB²=DE²+EB²DB²=10²+24²DB²=100+576DB²=676DB=26Now use proportion
DE/DB=AC/BC10/26=5/BC5/13=5/BCBC=13Now
DC=DB+BC=26+13=39
100 points what is the percent of change from 75 to 14 round to the nearest percent
Let's see
75-14/75×10061/75×1006100/7581.33%Gavin invested $100 into a CD account. The account grow at a rate of 5%
each year. What type of equation do this scenario represent?
Answer: y=5x+100
Step-by-step explanation:
the y intercept is the 100$ invested into the account, and the rate of change is 5
How many solutions does this equation have? 6x + 9 = 3x + 9
Answer:
Step-by-step explanation:
If an equation for example is x=5, the equation has one solution. If the equation is for example 4=4, there is an infinite amount of solutions. for your problem we would simplify the equation to get:
6x+9=3x+9
6x=3x
when dividing the x's to cancel eachother out we are left with 6=3. This means we have no solutions possible.
Answer:
in every way it's possible answer is 0!!
Step-by-step explanation:
method 1:
6x-3x=9-9
3x=0
x=0/3
x=0
method 2:
0=3x-6x+9-9
0=-3x
x=0
check
6*0+9=3*0+9
9=9
proved
The zeros of a quartic polynomial function are 2, -2, 4, and -4. Use the zeros to construct a possible sketch of the function on the set of axes
The sketch of the function on the set of axes is given below:
What are Zeros?The zero of any real-, complex-, or generally vector-valued function f, is a member x of the domain of function such that f(x)=0 at x; x is the solution to the equation f(x) = 0.
Finding the function:As we have the zeros 2,-2,4,-4
The function can be:
[tex]f(x)=(x-2)(x+2)(x-4)(x+4)\\f(x)=(x^2-4)(x^2-16)\\f(x)=x^4-20x^2+64[/tex]
The sketch using a graphing calculator:
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If r(x) = 3x – 1 and s(x) = 2x 1, which expression is equivalent to (startfraction r over s endfraction) (6)? startfraction 3 (6) minus 1 over 2 (6) 1 endfraction startfraction (6) over 2 (6) 1 endfraction startfraction 36 minus 1 over 26 1 endfraction startfraction (6) minus 1 over (6) 1 endfraction
The expression which is equivalent to the given ratio of the two provided binary fraction is startfraction 3 (6) minus 1 over 2 (6) 1 endfraction.
What is the equivalent expression?Equivalent expressions are the expression whose result is equal to the original expression, but the way of representation is different.
The given binary functions are.
[tex]r(x) = 3x - 1[/tex]
[tex]s(x) = 2x +1[/tex]
The expression which has to be found out is,
[tex]\left(\dfrac{r}{s}\right)(6)=\left(\dfrac{3(6)-1}{2(6)+1}\right)\\\left(\dfrac{r}{s}\right)(6)=\left(\dfrac{18-1}{12+1}\right)\\\left(\dfrac{r}{s}\right)(6)=\left(\dfrac{17}{13}\right)[/tex]
Thus, the expression which is equivalent to the given ratio of the two provided binary fraction is startfraction 3 (6) minus 1 over 2 (6) 1 endfraction.
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CAN u pls pls pls help its easy for yall not me im slow
Answer:
A
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
2.25/.5