The lower bound for a 95% confidence interval for the proportion of defective iphones from this assembly line is 0.0524.
With the probability of a success of π , and a confidence level of 1-α, we have the following confidence interval of proportions:
π± z[tex]\sqrt{\frac{\pi (1-\pi }{n} }[/tex]
z is the z-score having a p-value of 1-α/2.
we have η = 605 and ρ = 0.07
So, α = 0.1 and z is the value of Z that has a pvalue of:
1 - 0.1/2 = 0.95
Z= 1.645
Now the lower limit:
π - z[tex]\sqrt{\frac{\pi (1-\pi }{n} }[/tex]
= 0.07-1.645[tex]\sqrt\frac{(0.07*0.93)}{605}[/tex]
= 0.07 - 0.01706
= 0.0524
The lower bound for a 95% confidence interval for the proportion of defective Galaxy phones from this assembly line is 0.0524
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A family wants to build a pen for their new puppy. They
want the area of the pen to be more than 225 square feet.
If the width of the pen is 25 feet, what is the set of possi-
ble lengths for the pen?
The value of length of pen should always be greater than 5 feet.
Rectangle:
Rectangle is a special kind of parallelogram in which opposite sides are equal and adjacent sides are perpendicular to each other.It contains of length and breadth,The area of rectangle is given by,
Area = length x breadth
Now as per question,
A family wants to build a pen for their new puppy.
They want's the area of the pen to be more than 225 square feet.
width of the pen is = 25 feet
let,
The length of the pen is [tex]x[/tex] feet.
Area of pen = length * width
= [tex]x[/tex] * 25
= 25x
According to the question,
Area of pen > 225 square feet
25x > 225
x >225/25
x > 5 feet
Thus,
The value of length should always be greater than 5 feet.
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What is the next term in the sequence 4, 11, 18, 25, ...?
Answer: 32
Step-by-step explanation: you have to count by 7 everytime
2 step equations
3y+4=22
Answer:
3y+4=22
3y+4-4=22-4
3y=18
(3y)/3=18/3
y=6
Step-by-step explanation:
pls mark brainliest
The comprehensive graph of a polynomial function y=f(x) is shown
how many real zeros does the function f have?
There is only 1 real zero of the function.
What are Zeros of a Function?
The zeros of a function are the values of the function's variables that fulfil the equation and yield the function's value of 0. The zeros of a function can be represented graphically as the x-coordinates (x-intercepts) where the graph intersects the x-axis.
Solution:
As mentioned above,
The zeros of a function can be represented graphically as the x-coordinates (x-intercepts) where the graph intersects the x-axis.
So,
We can see that there is only one point where the graph intersects the x-axis.
Therefore, it can be said that there is only 1 real zero of the function.
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2x + 7 < -11 or -3x - 2 < 13
The value of x is in the range (-∝,-9)∪(-5,∝)
Given inequalities :
2x + 7 < -11 or -3x -2 < 13
⇒ 2x < -11 -7 or -3x < 13+2
⇒ 2x < -18 or -3x < 15
⇒ x < -9 or -x < 5
⇒ x < -9 or x > -5
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A car rental charges an initial fee of $42 and a daily fee of $12. A costumer pays a total of $138. How many days did the customer rent the car?
Answer: 8 days
Step-by-step explanation: 138-42 = 96 then you divide that by daily fee of 12 to get 8 days
7) Find the discriminant to determine the number of roots, then solve the quadratic equation
using the quadratic formula.
2x² + 7x-4 = 0
The Determinant of the equation is 17
What is the determinant of the equation?
The determinant is a scalar variable in mathematics that is a function of the elements of a square matrix. It enables the characterization of some characteristics of the matrix as well as the linear map expressed by the array. The determinant is nonzero, in particular, if and only if the matrix is invertible and the linear map represented by the matrix is an isomorphism. The determinant of a matrices product is the product of their determinants (the preceding property is a corollary of this one). The determinant is a scalar variable in mathematics that is a function of the elements of a square matrix. It enables the characterization of some attributes of the matrix as well as the vertical map presented by that of the array.
Given equation is 2x² + 7x - 4 = 0
Therefore, determinant = (7)² - 4x2x(-4)
= 49 - 32
= 17
Hence, the determinant of the given equation is 17
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please help thank you
9. The perimeter and the ratio of the
length to the width of a rectangle are
given. Find the length and width of the
rectangle.
Perimeter: 132 cm 1:w = 7:4
Answer:
Length: 42, width: 24
Step-by-step explanation:
Perimeter: 132
L: W = 7:4
7u+7u+4u+4u= 22u (Length + length + width + width)
132/22= 6 (1u)
6x4= 24 (Width/ 4u)
6x7=42 (length/7u)
recheck:
42+42+24+24= 132cm
perimeter= 132
A square has an area of 36 squares centimetres what is the perimeter of the square
Answer:
24 centimeters
Step-by-step explanation:
we find a side by finding the square root of the area
Square root of 36 is 6
Now we find the perimeter by multiplying 6 by 4
6x4=24
Hopes this helps please mark brainliest
If a board of directors consists of 18 people, how many ways can a chief executive officer, a director, a treasurer, and a secretary be selected?.
There are 204 possible methods to choose a chief executive officer, a director, a treasurer, and a secretary, if there are 18 members on the board of directors.
What is combination?Combinations are mathematical procedures that count how many different ways a collection of items might be arranged when the order in which they are chosen is immaterial. Regardless of the order in which the things are chosen, a combination is the choice of all or part of a collection of objects. A combination is "an arrangement of items where the order of the components is unimportant," according to the definition. When these two terms are combined, "Selection of things" is meant, where the order of the items is not important.
Here,
If the order doesn't matter then we have a combination, if the order do matter then we have a permutation.
18C4=18!/(18-4)!(4)!
=18!/14!4!
=18*17*16*15/4*3*2*1
=3*17*4
=204 ways
A chief executive officer, a director, a treasurer, and a secretary be can be selected in 204 ways If a board of directors consists of 18 people.
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A sign company is building a sign with the dimensions shown. What is the area, in square feet, of the sign.
A.) 65ft^2
B.) 60ft^2
C.) 130ft^2
The area of the triangle will be 60ft².
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
Now using the Pythagoras theorem we can find out the length of the other wall
b²+p²=h²
So here h=13ft and b=5ft
p²= h²-b²
= 13²-5²
=169-25
p = √144 = 12ft
So the area of the trinagle is = 1/2*b*p
1/2(10*12)= 60ft²
Hence the area of the triangle will be 60ft².
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Pete,Joe, and Blake shared a large pizza. The pizza was cut into eight pieces. Pete ate two pieces, Joe ate two piece, and Blake ate one piece. Which fraction is equivalent to the amount of pizza that was eaten by all the boys.
Answer:
Pete ate 2, Joe ate two, and Blake ate 1
2 + 2 + 1 = 5
They ate 5 out of 8 slices. The boys ate 5/8 of the pizza
A bread company makes two types of wheat bread, light whole wheat and regular
whole wheat. A loaf of light whole wheat bread requires 2 cups of flour and 1
egg. A loaf of regular whole wheat bread requires 3 cups of flour and 2 eggs. The
bakery has 90 cups of flour and 80 eggs on hand. The profit on the light bread is
$1 per loaf and on the regular bread is $1.50 per loaf. In order to maximize
profits, how many of each loaf should the bakery make?
By the equations, he should make 70 whole wheat bread that would earn a profit of $105 that is maximum he can earn with the given amount of flour and egg.
What is system of equation?simultaneous equations, system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution. A group of two or more equations that share the same variables is known as a system of equations. A set of values for a variable that simultaneously satisfy each equation is the solution to a system of equations. When there are multiple unknowns and there is sufficient data to set up equations in those unknowns, systems of equations are used to solve applications. In general, we need sufficient information to construct equations in the n unknowns.
Here,
Let x be light whole wheat and y be the regular whole wheat.
given,
A loaf of light whole wheat bread requires 2 cups of flour and 1 egg.
A loaf of regular whole wheat bread requires 3 cups of flour and 2 eggs.
The bakery has 90 cups of flour and 80 eggs on hand.
So the system of equation will be,
2x+3y=90
x+2y=80
multiply the second equation by 2,
2x+4y=160
2x+3y=90
subtract the equations,
y=70
by this,
x=-60
So by this he should make 70 whole wheat bread that will make him earn a profit of,
=70*1.5
=$105
According to the calculations, he should produce 70 loaves of whole wheat bread for a profit of $105; this is the most he can make with the supplied quantities of flour and egg.
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Complete the frequency distribution table.
Score: 6, 9, 7, 8, 5, 9, 8, 7, 8, 7, 6, 9, 5, 8, 7, 6, 10, 10
According to the given frequency distribution table the values are as follows:
Frequency of 6 is 3
Frequency of 7 is 4
Frequency of 8 is 4
Frequency of 9 is 3
Frequency of 10 is 2
What is statistics?Statistics is the field concerned with collecting, organizing, analyzing, interpreting and presenting data to draw conclusions by analyzing it.
In Mathematics, statistics is the branch which is concerned with collecting, analyzing, interpreting, and presenting large amounts of numerical or quantitative data.
What does frequency mean in Statistics?It is the number of times a data or figure occurs in a set of given or collected data.
Which frequency distribution does the table have?In order to make the provided data more meaningful and understandable, it can be organized using a frequency distribution table. There are two or three columns in a frequency distribution table. All of the results are represented as individual values or as class intervals in the first column.
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the sum of three numbers is 2020. the first is four times the sum of the other two. the second is seven times the third. what is the product of all three?
28 is the product of all three numbers .
What are the algebraic expressions ?An algebraic expression is the idea of using letters or alphabets to represent numbers without specifying the actual values. In Algebra Basics, we learned how to use letters such as x, y, and z to represent unknown values. These characters are called variables here. An algebraic expression can be a combination of variables and constants. The multiplied value before the variable is the coefficient.
Calculation3rd = x
2 nd = 7x
1 st = 4(x + 7x ) = 32x.
x + 7x + 32x = 20
x = 1/2.
we are looking for product = x*7x*32x = 1/2 * 7 * 1/2 * 32*1/2 = 1/2 * 1/2 * 1/2 * 32 * 7 = 28.
28 is the product of all three numbers
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Can anyone help me This is for math
The value of x is 1.94 units approximately.
Since the triangle is equilateral and each side is [tex]\sqrt{10}[/tex].
we know that, in equilateral triangle base is bisected by the perpendicular drawn from the opposite vertex.
So here for one small triangle by Pythagoras theorem,
[tex]x^2+(\frac{\sqrt{10}}{2})^2=(\sqrt{10})^2\\x^2+\frac{10}{4}=10\\x^2=10-\frac{10}{4}=\frac{30}{4}=\frac{15}{2}\\x=\frac{\sqrt{15}}{2}\approx1.94[/tex]
Hence the value of x is 1.94 units approximately.
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Fatima has a total of $12 to spend to make some fruit smoothies. She will use mango and strawberries. Strawberries cost $4 per pound and mango costs $2 per pound. Let x = the number of pounds of strawberries and y = the number of pounds of mango.
A) Write a linear equation in standard form that could model how many cups of fruit she can buy: __x+__=__
B) What is the greatest number of pounds of strawberries can she buy if she doesn't buy any mango? ____ pounds
C) What is the greatest number of pounds of mangoes can she buy if she doesn't buy any strawberries? ____ pounds
D) If Fatima buys 2.5 pounds of strawberries, how many pounds of mangoes can she buy? ____ pounds
Help fill in the spaces.
Answer:
B 2020 on edge
Step-by-step explanation:
18.9x{2x2.7}-4.6} - to the second power
The equivalent value to the expression 18.9 x [(2 x 2.7) - 4.6] - 2² is given by the following option:
C. 11.12.
How to obtain the equivalent value to the expression?The equivalent value to an expression is given by the solution to the expression.
The expression in this problem is given as follows:
18.9 x [(2 x 2.7) - 4.6] - 2²
The brackets take precedence, hence the first operation to be solved is of:
(2 x 2.7) - 4.6
The parenthesis take precedence relative to the subtraction, hence:
(2 x 2.7) - 4.6 = 5.4 - 4.6 = 0.8.
Then the expression is given by:
18.9 x [(2 x 2.7) - 4.6] - 2² = 18.9 x 0.8 - 2².
The square takes precedence, hence:
18.9 x 0.8 - 4.
Then the multiplication takes precedence, which means that the equivalent result is of:
18.9 x 0.8 - 4 = 15.12 - 4 = 11.12.
Given by option C.
Missing InformationThe problem is given by the image shown at the end of the answer.
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An airplane
30,000 feet above the
ground begins descending at a rate of
2,000 feet per minute. Write an
equation to model the situation. Find
the altitude of the plane after 5
minutes.
An equation to model the situation: h = 30000 - 2000t
the altitude of the plane after 5 minutes is 20000 feet
In this question, an airplane 30,000 feet above the ground.
It begins descending at a rate of 2,000 feet per minute.
We need to write an equation to model the situation. Also, we need to find
the altitude of the plane after 5 minutes.
Let h be the altitude of plane after t hours.
So, we get an equation,
h = 30000 - 2000t
For t = 5 minutes,
h = 30000 - 2000(5)
h = 30000 - 10000
h = 20000 feet
Therefore, an equation to model the situation: h = 30000 - 2000t
the altitude of the plane after 5 minutes is 20000 feet
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each roll of black ribbon has 3 2/3ths yards of ribbon if amanda has 4 1/2th rolls of black robbin how many yards does amanda have
Amanda have roll of black ribbon [tex]= 3_3^2th[/tex]
If Amanda has rolls of black ribbon [tex]= 4_2^1th[/tex]
total rolls of black ribbon amanda have [tex]= 3_3^2th+4_2^1th[/tex][tex]= 8_6^1 th[/tex]
What is Fraction?
A fraction is a piece of the entire. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction. A correct fraction has a numerator that is lower than its denominator.
What is mixed fraction?
A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.
Consider the expression;
[tex]= 3_3^2th+4_2^1th[/tex]
Rewriting our equation with parts separated
[tex]= 3+\frac{2}{3}+4+\frac{1}{2}[/tex]
Solving the whole number parts
3 + 4 = 7
Find the LCD of 2/3 and 1/2 and rewrite to solve with the equivalent fractions.
LCD = 6
[tex]\frac{4}{6}+\frac{3}{6} = \frac{7}{6}[/tex]
Combining the whole and fractional parts
[tex]7+1+\frac{1}{6} = 8_6^1[/tex]
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The figure below was made with a scale of 1 unit = 3 ft.
Draw the figure with a new scale of 1 unit = 6 ft.
You can place your figure anywhere on the grid on the right
The second side will therefore be 12 feet long if one side is 6 feet long. We just need to calculate two sides because each comparable side is equal.
Define scaling.A linear transformation known as uniform scaling in affine geometry enlarges or reduces objects in all directions by the same scale factor. The final product of uniform scaling resembles the initial. Normal practize allows for a scale factor of 1, which allows for the classification of congruent shapes as similar.
Given,
The process for scaling a rectangle is as follows:
Let's say one of the sides is two units long, and you count the number of units on that side.
1 unit = 6 feet.
12 feet = 2 units
We only need to double the rectangle's size to rescale. The second side will therefore be 12 feet long if one side is 6 feet long. You just need to calculate two sides because each comparable side is equal.
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Primo car rental agency charges $25 per day plus $0.30 per mile. Ultimo car rental agency charges $30 per day plus $0.95 per mile. Find the daily mileage for which the Ultimo charge is three times the Primo charge.
The mileage is
Answer:
[tex]28\frac{4}{7}[/tex] miles
Step-by-step explanation:
mileage = m
Primo: cost = 0.3m + 20
Ultimo: cost = 0.95m + 30
Ultimo = twice Primo
0.95m + 30 = 0.6m + 40
subtract 0.60m and 30 from each side and simplify to get
0.35m = 10
divide by 0.35 into both sides to get
m = [tex]28\frac{4}{7}[/tex]
therefore, the daily mileage would be [tex]28\frac{4}{7}[/tex] miles
You can choose a prize of either a $25,000 car or one penny on
the first day, triple that (3 cents) on the second day, and so on for a month. On what
day would you receive more than the value of the car?
If you can choose a prize of either a $25,000 car or one penny on the first day. The number of days you receive more than the value of the car is 15 days.
How to find the number of days?Let x represent the number of days
Convert $25,000 to cents by multiplying it by 100
$25,000 × 100 = 2,500,000 cents
Hence:
3^x-1 > 2,500,000
(x-1) log3/log 3 > log 2500000/log 3
x-1 > 13.409
x = 13.409+1
x =14.409
x = 15 days (Approximately)
Therefore the number of days is 15.
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Find the perimeter of the figure below. Use 3.14 for pi
10 m
16 m
I hope this is the last on I need help with!-
I need an answer immediately and i will give a lot of points
╔══╗
╚╗╔╝
╔╝ (¯`v´¯)
╚══`.¸.*when you answer*
Answer:
72.52
Step-by-step explanation:
circumference of a circle formula = [tex]2\pi r[/tex]
where r is the radius
the radius is half of diameter, and the diameters for all semicircles are given.
so the radius for the smaller semicircles is 10/2 which is 5
so [tex]2\pi 5[/tex] = 2(3.14)(5) = 31.4
31.4 is the circumference of the whole circle, since we have 2 semicircles with the same radius, we don't need to divide this by 2, we will simply use 31.4 for instead of doing this exact calculation again for the other small semicircle.
for the larger cemicircle, the diameter is 16 so the radius will be 16/2 which is 8
[tex]2\pi 8[/tex] = 2(3.14)(8) = 50.24
since 50.24 is the circumference of an entire circle, we will have to divide this by 2 to d=find the circumference of the semicircle.
50.24/2 = 25.12
Now we will simply add up the lengths of the borders,
31.4 + 25.12 + 16 = 72.52
Answer:
57.7 meters total perimeter for the object.
Step-by-step explanation:
See the attached worksheet. Break up the object into three circles and one rectangle. Label them to keep track of the work. The object's perimeter is coprised of:
- One side of rectangle R (16 m)
- 1/2 the circumference of circles b and c, each with a radius of 5 m
- 1/2 the circumference of circle a, with a circumference of 8 m.
The perimeter of a circle is 2πr. The perimeter of circles b and c is 31.4 meters in total, which is reduced to (1/2) or 15.7 m total. Circle a contributes 26 meters to the object's perimeter.
The sum of these measurements is (16m) + (15.7m) + (26m) = 57.7 meters total perimeter for the object.
can anybody help please?
A box is a cuboid with dimensions 26 cm by 15 cm by 20 cm all measured to the nearest centimetre. Disc cases are cuboids which measure 1.6 cm by 14.2 cm by 19.3 cm all measured to the nearest millimetre. 20 cm If the disc cases are stacked as shown, show that it may not be possible for 16 cases to fit in the box. box measurements: 26 cm 15 cm 20cm disc measurements: 1.6 cm 19.3 cm 14.2 cm
The number of discs that can be filled in the box is 17.
length of box , l =26 cm , breadth , b =15 cm , height = 20 cm
So,the volume of the box = l × b × h
= 26 × 15 ×20 cm³
= 7800 cm³
Now length of a disc case, l= 1.6 cm
breadth ,b =14.2 cm
height, h =19.3 cm
So the volume of a disc case = 1.6×14.2×19.3 cm³
= 438.496 cm³
No of disc cases can be stacked inside the box
= 7800 ÷ 438.496
=7800000÷438.496
= 17.8
Hence 17 disc cases can be fitted into the box.
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Which reason should you use to prove the following triangles are congruent?
A. SAS
B. AAS
C. Not enough information (Not Congruent)
D. ASA
E. HL
Answer:
A A S
Step-by-step explanation:
Angle - Angle- side: they have two consecutive equal angles and a non-included side that is equal
Which of the following statements explains how you should round 213.709?
A.
Since the digit in the hundreds place is less than 5, keep the digit in the hundredths place. Then drop the digits on the right.
B.
Since the digit in the hundredths place is less than 5, keep the digit in the tenths place. Then drop the digit in the hundredths and thousandths places.
C.
Since the digit in the thousandths place is greater than or equal to 5, increase the digit in the hundredths place by 1. Then drop the digit in the thousandths place.
D.
Since the digit in the hundredths place is less than 5, leave the digit in the hundredths place and drop all the numbers on the right.
Option C is correct. Since the digit in the thousands place is 5 or greater than 5.
Given that in option C:
Since the digit in the thousandth place is greater than or equal to 5, increase the digit in the hundredth place by 1. Then drop the digit in the thousandth place.
Also, 213.709 is given in the question in which we have to round off these digits.
The digit which is just after the decimal is called tenths and just after that is hundredths and just after that is called thousandths.
Seeing the value in option C is correct as it tells the value of thousandths is greater than or equal to 5 is correct as 9 is in thousandths place and is greater than 5.
Increasing the value in the hundredth which is zero to one and dropping the digit in the thousandth place is correct as it makes the value 213.71.
All the other options don't satisfy the round of the value 213.709.
Hence, 213.71 can be rounded as per the statement written in option C.
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Can u help me with this problem?
Answer:
No because the determinant of A is 0 .
Step-by-step explanation:
A starts the a -85 so n32 -24 = A- because 540i.7 is a so 0 so a is 0
help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The values of the function are 1/9, 1/3, 1, 3 and 9.
What is a function?A function is defined as a relation between a set of inputs having one output each.
Given a function, f(x) = [tex]3^{x}[/tex]
When x = -2
y = [tex]3^{-2}[/tex] = 1/3² = 1/9
When x = -1
y = [tex]3^{-1}[/tex]
y = 1/3
When x = 0
y = [tex]3^{0}[/tex]
y = 1
When x = 1
y = 3
When x = 2
y = 3² = 9
Hence, The values of the function are 1/9, 1/3, 1, 3 and 9.
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