To find the probability that the average weight of four babies will be more than 7.5 pounds, we calculate the z-score and look it up in the standard normal distribution table. The probability is approximately 0.2843, or 28.43%.
Explanation:To find the probability that the average weight of four babies will be more than 7.5 pounds, we need to calculate the z-score and look it up in the standard normal distribution table.
First, we convert the weight of 7.5 pounds to ounces: 7.5 pounds * 16 ounces = 120 ounces.
Next, we calculate the z-score using the formula: z = (x - &μ) / &σ, where x is the given weight, &μ is the mean weight, and &σ is the standard deviation. In this case, z = (120 - 112) / 14 = 0.571.
Finally, we can look up the probability using the z-score in the standard normal distribution table. The probability of the average weight of four babies being more than 7.5 pounds is approximately 0.2843, or 28.43%.
Learn more about Probability here:https://brainly.com/question/32117953
#SPJ12
Alan is building a garden shaped like a rectangle with a semicircle attached to one short side. If he 21) has 20 feet of fencing to go around it, what dimensions will give him the maximum area in the garden?
Let the short side be W
The half circumference of the semi-circle = .5 * pi *W
2Lengths + width + semicircle = 20 ft
2L + W + (.5*pi*W) = 20
2L + W + 1.57W = 20
Combine like terms
2L + 2.57W = 20
Simplify divide by 2
L + 1.285W = 10
L = (10 - 1.285W); for substitution:
Get the area equation:
Rectangle area + semicircle area
A = L * W + (.5*pi*(.5W) ^2)
A = LW + (1.57*.25W^2)
A = LW + .3925W^2
Replace L with (10-1.285W)
A = W(10-1.285W) + .3925W^2
A = -1.285W^2 + .3925W^2 + 10W
A = -.8925W^2 + 10W
Find W by finding the axis of symmetry of this equation a=-.8925, b=10
W = -10 / 2 * (-.8925)
W = -10 / -1.785
W = 5.60 is the width for max area
then we solve for the length
L = 10 - 1.285(5.60)
L = 10 – 7.20 = 2.8 ft is the length
Then, Check the perimeter
2(2.8) + 5.60 + 1.57(5.60) = 20ft
5.6 + 5.6 + 8.736 = 20ft
Rectangle: 2.8 by 5.60 has semicircle circumference 8.736 has a maximum area: (2.8*5.60)
+ (.5 * pi * 2.8 ^ 2)
=15.68 + 12.31
=28 sq/ft
What is the simplified form of the left side of the following equation?
2x-4+5x=8
Select the correct answer below.
A.2x+1
B.3x-4
C.5x-2
D.7x-4
find all sets of three consecutive even integers whose sum is greater than 102 and less than 116
Assume that the salaries of elementary school teachers in the united states are normally distributed with a mean of $32,000 and a standard deviation of $3000. if 100 teachers are randomly selected, find the probability that their mean salary is less than $32,500.
Answer: 0.9525
Step-by-step explanation:
Given : The salaries of elementary school teachers in the united states are normally distributed with a mean of [tex]\mu=\$32,000[/tex] and a standard deviation of [tex]\sigma=\$3000[/tex].
Sample size : n= 100
Let x be a random variable that denotes the salaries of elementary school teachers in the united states.
Formula : [tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
Then, the probability that their mean salary is less than $32,500 will be :-
[tex]P(x<32500)=P(\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}<\dfrac{32500-32000}{\dfrac{3000}{\sqrt{81}}})\\\\=P(z<\dfrac{500}{\dfrac{3000}{10}})\approx P(z<1.67)=0.9525\ \ [\text{Using z-value}][/tex]
Hence, the probability that their mean salary is less than $32,500 = 0.9525
plz help me so confused
If there is a positive correlation between salary and education, then based on the table shown, which of the following careers requires the most education? a. accountant b. paralegal c. photographer d. surveyor
Answer:
Option a. accountant.
Step-by-step explanation:
We have been given the positive correlation graph between salary and education
Positive correlation means a linear relationship between two that means if education increases salary increases.
We need to tell which among the given options requires most education the one which will have highest salary.
That means the Accountant among the given option requires most education.
Because he has highest salary among given four options.
Consider a point on the trans-australian highway, where two old wombats live. arrivals of cars at this point follow a poisson distribution; the average rate of arrivals is 1 car per 12 seconds.
An airplane allows each passenger 36 kilograms of luggage. Carl has to lower the weight of his suitcase by 25% to stay within the limit. How much did the suitcase originally weight?
solve the equation 0.35(x+4)=0.25(x-6)
Answer:
x=-29
Step-by-step explanation:
First multiply 0.35 by x+4 and 0.25 by x-6 after you do that you will get
0.35x+1.4=0.25x-1.5
now add 1.5 from -1.5 and 1.4 now your equation on will look like this
0.35x+2.9=0.25x
Now subtract 0.35x from both sides of the equation and your equation will look like this
2.9=0.1x
at this point you divide to get your answer, divide 2.9 and 0.1x by -0.1 and you will end up with 2.9 over -0.1 once you divide you will get -29=x
The value of x is -29.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
0.35(x+4)=0.25(x-6)
Now, solving for x
0.35 x + 1.4 = 0.25x - 1.5
0.10x = -2.9
x= -29
Hence, the value of x is -29.
Learn more about Equation here:
https://brainly.com/question/10413253
#SPJ5
A circle with a central that measures 1° has a radius of 10 inches. Find the length of the intercepted .
a picnic start at 12:10 pm .kevin arrives at 1:40 pm the picnic continues until 3 pm.how much time elapsed betwwen the picinic and keven arrivals
Final answer:
To determine the time elapsed between the start of the picnic and Kevin's arrival, subtract the start time (12:10 pm) from Kevin's arrival time (1:40 pm), which results in 1 hour and 30 minutes.
Explanation:
To find out the amount of time that elapsed between the start of the picnic and Kevin's arrival, we subtract the start time of the picnic from the time Kevin arrived. The picnic started at 12:10 pm and Kevin arrived at 1:40 pm.
Step-by-step calculation:
Convert the times into a 24-hour format to avoid any confusion.12:10 pm is 12:10 in 24-hour format.Marcus rented a movie for $4 and some video games for $6 each. He paid $22. How many games did he rent?Choose two answers: one for the equation that models this situation and one for the correct answer.
A.Equation: 6 + 4x = 22
B.Answer: 3 video games
C.Answer: 4 video games
D.Equation: 4 + 6x = 22
Answer:
4 + 6x = 22 and 3 video games
Step-by-step explanation:
ape-x
negation of all owls fly?
If P is the midpoint of XY,XP=8x-2 and PY=12x-30 find the value X
Using the midpoint concept, it is found that x = 7.
----------------------
The midpoint divides a segment into two segments of equal length.P is the midpoint of XY, thus XP = PY.----------------------
[tex]XP = 8x - 2[/tex]
[tex]PY = 12x - 30[/tex]
Since they are equal, we use it to find x.
[tex]XP = PY[/tex]
[tex]8x - 2 = 12x - 30[/tex]
[tex]4x = 28[/tex]
[tex]x = \frac{28}{4} = 7[/tex]
The value of x is 7.
A similar problem is given at https://brainly.com/question/10956693
George exercises 15 minutes a day, every day of the year. How many minutes a year does George exercise? Write and solve an equation to find the answer.
Serena has 6 photo albums with 15 photos in each. Her friend Maya has 8 albums with 13 photos in each. If Serena adds another 12 photos to her albums how many photos will Serena and Maya have in all?
What is the value of the expression 54.36 divided by 0.1
Which function has a vertex at the origin?
f(x) = (x + 4)^2
f(x) = x(x – 4)
f(x) = (x – 4)(x + 4)
f(x) = –x^2
Answer:
fdx = x-4 2
Step-by-step explanation:The test was right
A problem states: "There are 9 more children than parents in a room. There are 25 people in the room in all. How many children are there in the room?"
Let c represent the number of children.
Which expression represents the number of parents?
c−9
9−c
c⋅9
c + 9
Answer: c-9
Step-by-step explanation: i did the quiz
The cartesian coordinates of a point in the xy-plane are (x, y) = (-3.84, -2.87) m. find the polar coordinates of this point.
Help Dana find the sum 346 421 152
For numbers 13a-13d, select yes or no to tell Dana when to regroup
A point P is 100m away from a vertical flag pole, which is 13m high. What is the angle of elevation to the top of the flagpole from P?
5/2(6x-7)+ 4/3(2+9x)
For each sequence, find a formula for the general term, a_n. for example, answer n ^2 if given the sequence: \lbrace 1, 4, 9, 16, 25, 36, . . . \rbrace
Can the leaves of an ordered rooted tree have the universal address 1.1, 1.2.1, 1.2.2, 1.2.3, 2.1, 2.2.1, 2.3.1, 2.3.2, 2.4.2.1, 2.4.2.2, 3.1, 3.2.1, 3.2.2? if so, identify such an ordered rooted tree.
What is 7 divided by 28
7 divided by 28 is 1/4 or 0.25.
To calculate 7 divided by 28.
What is simplification?
Simplification is defined as solving mathematical problems using arithmetic operators.
7 divided by 28 = 7/28
= 1/4
= 0.25
Thus, 7 divided by 28 is 1/4 or 0.25.
Learn more about simplification here:
ttps://brainly.com/question/12501526
#SPJ2
Suppose you are a small business owner. How would a market demand schedule or a market demand curve be useful?
find f(-2) for f(x)=2×3^x
a.-18
b.1/18
c.-36
d.2/9
Marcel is planning a vacation. The travel agent says the average high temperature at the resort is 20 degrees Celsius. What is the equivalent Fahrenheit temperature
The equivalent Fahrenheit temperature for 20 degrees Celsius is 68 degrees Fahrenheit.
Explanation:To convert Celsius to Fahrenheit, you can use the formula: F = (C × 9/5) + 32
Using this formula, we can calculate the equivalent Fahrenheit temperature for 20 degrees Celsius:
F = (20 × 9/5) + 32 = 68 degrees Fahrenheit
Suppose that you invest $5873 in an account that earns interest at an APR of 4.4%, compounded monthly. Determine the accumulated balance after 7 years.