The estimate of the population proportion of defectives is 0.05.
Given that,
There are 10 different samples of 50 observations, that is, total of 500 observations.
To find : The estimate of the population proportion of defectives
And total number of defectives from 500 observations is (5+1+1+2+3+3+1+4+2+3) = 25
Thus, the point estimate for the population proportion defectives will be,
=25/500=0.05
or just obtain the individual proportion of each sample and then take their average to obtain the same result.
Thus, the point estimate for the population proportion defectives will be 0.05
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A tree that is 10 feet tall casts a shadow that is 8 feet long. What is the distance from the top of the tree to the tip of the shadow? Round to the nearest tenth.
9.4 feet
12.8 feet
3.2 feet
2.8 feet
The distance from the top of the tree to the tip of the shadow is 12.8 ft
Pythagorean theorem:
According to the Pythagorean theorem, In a right-angled triangle, the sum of the squares of the side will equal the square of the hypotenuse.
Here hypotenuse is the longest side.
=> Hoptenuse² = side² + side²
Here we have
The length of the tree = 10 feet
Length of shadow = 8 feet
Here we need to find the distance from the top of the tree to the tip of the shadow
If we join the top of the tree to the tip of the shadow we will observe a right-angled triangle as shown below
From the figure,
AC² = AB² + BC² [ ∵ ABC is right angle triangle ]
=> AC² = 10² + 8²
=> AC² = 100 + 64
=> AC² = 164
=> AC = 2√41
=> AC = 12.8 ft
Therefore,
The distance from the top of the tree to the tip of the shadow is 12.8 ft
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Answer:
b) 12.8 feet
Step-by-step explanation:
Now we have to,
→ find the required distance.
Forming the equation,
→ x² = 10² + 8²
Then the distance will be,
→ x² = 10² + 8²
→ x² = 100 + 64
→ x² = 164
→ x = √164
→ [ x = 12.8 feet ]
Hence, distance is 12.8 ft.
In peter class three times as many students who wear glasses are those who do not.there are 28 students in the class. How many students do not wear glasses
Step-by-step explanation:
In Peter class three times as many students who wear glasses are those who do not.there are 28 students in the class. How many students do not wear glasses?
with glasses: x
without glasses: 3x
x + 3x = 28
4x = 28
x = 7 with glasses
7 * 3 = 21 without glasses
the little twelve basketball conference has two divisions, with six teams in each division. each team plays each of the other teams in its division twice and every team in the other division once. how many conference games are scheduled?
There are 96 basketball conference games are scheduled.
What is termed as the division?Multiplication is the reciprocal of division. If 3 groups of 4 add up to 12, then 12 classified into three groups of equal size results in 4 in each group. Developing equal groups or defining how many people are within each group after a fair distribution is the basic function of division.For the given question;
Every squad competes in ten games within its own division and six games against opponents from the opposing division. The 12 teams thus play a total of 16 conference games.There are N games on the schedule because there are two teams in each game.
N = 12×16/2
N = 96
Thus, there are 96 basketball conference games are scheduled.
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The first container has 3 gallons 3 quarts 1 pint of diesel fuel, the second container has 5 gallons 2 quarts of diesel fuel, and the third container has 6 gallons 1 quart 1 pint of diesel fuel. what is the total quantity of diesel fuel?
The total quantity of diesel fuel is 15.75 gallons.
The total quantity of diesel fuel can be calculated by summing up all the values. But, firstly converting quarts and pint into gallons.
1 quart = 0.25 gallon
For first container, 3 quarts = 0.25 × 3
3 quarts = 0.75 gallon
For second container, 2 quarts = 0.25 × 2
2 quarts = 0.5 gallon
For third container, it has 0.25 gallon
1 pint = 0.125 gallon
For first and third container, it has 0.125 gallon
So, amount of diesel fuel in first container = 3 + 0.75 + 0.125
Amount of diesel fuel in first container = 3.875 gallons
Amount of diesel in second container = 5 + 0.5
Amount of diesel in second container = 5.5 gallons
Amount of diesel in third container = 6 + 0.25 + 0.125
Amount of diesel in third container = 6.375 gallons
So, the total quantity of diesel fuel = 3.875 + 5.5 + 6.375
The total quantity of diesel fuel = 15.75 gallons
Hence, the total quantity is 15.75 gallons.
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a hospital director is told that 54% of the treated patients are insured. the director wants to test the claim that the percentage of insured patients is below the expected percentage. a sample of 200 patients found that 100 were insured. find the value of the test statistic. round your answer to two decimal places.
The value of test statistic is -1.14
Define Standard error.
The standard error (SE)of a statistic (usually an estimate of a parameter) is the standard deviation of its sampling distribution or an estimate of that standard deviation. If the statistic is the sample mean, it is called the standard error of the mean (SEM).
Null Hypothesis
P = 0.54
Alternate Hypothesis
P < 0.54
For 0.05 level , the value of Z = 1.645
Decision rule ,
reject null Hypothesis if test statistic Z < -1.645
sample size (n) = 200
sample success (x) = 100
Standard error SE = √(p * (1 - p) / n
= √0.54 * (1 - 0.54) / 200
Standard error SE= 0.0352
Sample proportion (р) = x/n
= 100 / 200 ⇒ 0.5
test statistic Z = (р - P) / SE
= (0.5 - 0.54) / 0.0352
test statistic Z = -1.136 or -1.14
Therefore, the value of test statistic is -1.14
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HELP!!
If a₁ = 3 and an
-
= (an-1)2 + 1 then find the value of a4.
The required value of a₄ is 10,202 to the given recursive formula.
What is an arithmetic sequence?An arithmetic sequence is defined as an arrangement of numbers that is in a particular order.
The given recursive formula in the question as:
aₙ = (aₙ ₋₁ )² + 1 ....(i)
And, a₁ = 3
Substitute the value of a₁ = 3 in equation (i), and solve for n = 2
a₂ = (a₁)² + 1
a₂ = (3)² + 1
a₂ = 9 + 1 = 10
Substitute the value of a₂ = 10 in equation (i), and solve for n = 3
a₃ = (10)² + 1
a₃ = 100 + 1 = 101
Substitute the value of a₃ = 101 in equation (i), and solve for n = 4
a₄ = (101)² + 1
a₄ = 10,201 + 1
a₄ = 10,202
Therefore, the required value of a₄ is 10,202.
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a box of buttons contains the same number of each type of button
it contains 220g of buttons
how many of each button are in the box
Button A=8 grams
Button B = 12 Grams
The number of buttons A will be 11. And the number of buttons B will be 11.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
A container of buttons contains a similar number of each kind of button it contains 220g of buttons. The weight of the button is given as,
Button A=8 gramsButton B = 12 GramsLet x be the number of each button. Then the equation is given as,
8x + 12x = 220
20x = 220
x = 11
The number of buttons A will be 11. And the number of buttons B will be 11.
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a pair of shoes is on sale, the original price is $150.99 and they are 30% whats a new price after the discount?
Answer:
Price after discount is $105.69Step-by-step explanation:
It is assumed 30% is the discount.
Original price is $150.99, discount is 30%, sale price is:
150.99 - 30% = 150.99 × (1 - 0.3) = 150.99 × 0.7 = 105.69 (rounded)does this equal to 10 or 5 I’m confused I’ll brainlist .
Answer:
x = 5
Step-by-step explanation:
3x + 5 = 2x + 10
subtract 5 from both sides:
3x + 5 - 5 = 2x + 10 - 5
3x = 2x + 5
subtract 2x from both sides:
3x - 2x = 2x + 5 - 2x
x = 5
0.1 times n equals 89.5
Answer: n=895
Step-by-step explanation:
Answer:
n = 895
Step-by-step explanation:
Here we want to find n , 1st form the Equation then solve it for n
0.1 times n = 0.1n
0.1 times n equal 89.5
Then 0.1n = 89.5
Solve for n , b dividing both sides by 0.1
n = 89.5 / 0.1 = 895
the product of 180 and the positive integer n is a perfect cubic number. what is the least possible value of n?
The least possible value of n, where the product of 180 and the positive integer n is a perfect cubic number is 150.
so, by the question,
n×180 is a perfect cube
on the prime factorization of 180, we get
180 = 2²×3²×5
so the number should be
n = 2 × 3 × 5² =150
when we multiply both of them we get
180×n = (2²×3²×5)×(2 × 3 × 5²)
= (2³×3³×5³)
=(2×3×5)³
=(30)³
=27000
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Walt Disney Co paid a $1.42 annual dividend on a day it closed at a price of $96 per share.
What was the annual dividend for 500 shares?
The annual dividend for 500 shares was $710.
How is the annual dividend computed?The annual dividend is a function of the dividend per share and the number of shares held by a stockholder.
Dividends are always declared per share with a stated dollar amount or percentage.
Dividends represent the portion of the profits earned by an entity that it decides to distribute to the shareholders.
Dividends are a kind of financial reward to stockholders for their investment in the entity.
The dividend per share = $1.42
Market price per share = $96
The number of shares held = 500
The dividend received for the year = $710 ($1.42 x 500)
Thus, the holder of 500 shares in Walt Disney Co. will get $710 in a year the company declared and paid a $1.42 annual dividend.
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Find the value of x.
What is Angle?
An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
From the figure, we can tell that a transversal is passing through the two parallel lines which makes corresponding angles.
In the given figure 14x+7 and 10x+5 are the two angles formed by the transversal.
14x+7=10x+5
Now take all the variable terms to one side
14x-10x=5-7
4x=-2
Divide both sides by 4
x=-2/4
Divide numerator and denominator by 4
x=-1/2
Hence the value of x is -1/2
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Please help me solve as soon as possible
Using the given expression, the number of tiles Mr. Grants will need to buy is 48
Solving an expression to determine the number of tilesFrom the question, we are to use the given expression to determine the number of tiles Mr. Grant would have to buy
From the given information,
The given expression is,
27 ÷ s²
and
Mr. Grants decides to buy square tiles that have side lengths of 3/4 foot
That is,
s = 3/4
Now,
Using the given expression
27 ÷ s²
We get
27 ÷ (3/4)²
27 ÷ 9/16
= 27 × 16 / 9
= 3 × 16
= 48
Hence, he will need to buy 48 of the tiles
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How do you solve this equation to find x?
Answer: x=10
Step-by-step explanation:
Images below
Help this helps
There are 103 fifth graders at brookside elementary .for a read thon 5 students read for 100 minutes 25 students read for 50 minutes and rest of the fifth graders read for 30 minutes . how many minutes did the fifth graders read.
The fifth graders are read for total 180 minutes.
What do you mean by minutes?
A 60-second interval of time. In an hour, there are 60 minutes. For illustration, the time 10:35 is 35 minutes after 10 o'clock. A minute is equivalent to 1/60th of a degree in terms of angles.
According to the given question,
First 5 students read for 100 minutes.
Then, next 25 studenda read for 50 minutes.
And the rest of the fifth graders read for 30 minutes.
Now, we will adding all the minutes to obtain the answer or total minutes of fifth grader read,
Total minutes of fifth graders read= 100+50+30
=180 minutes.
Therefore, the fifth graders take 180 minutes to read.
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A share of Southside stock sold for $37. The annual dividend is $1.85. Three years later the stock has increased 17% in value and the dividend has increased 5%.
What is the yield 3 years later? Round to the nearest tenth of a percent.
The price of the share 3 years later, given the increase in value, can be found to be $43.29
How to find the price per share?The value of the Southside stock sold was $ 37 at the current age. Three years later, this value had increased by 17 %.
This means that the price of the share 3 years later would be:
= Share price currently x ( 1 + increase in value)
= 37 x ( 1 + 17 % )
= 37 x 1. 17
= $ 43. 29
The price is $43.29
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work out
5/6 × 48
120 x 2/3
Answer:
1. 130/6
2. 240/3
Step-by-step explanation:
make the whole numbers into a fraction by putting 1 as the denominator.
48/1.
then multiply together.
48 x 5 = 130
6 x 1 = 6
130/6
do the same with the other
120 x 2 = 240
1 x 3 = 3
240/3
Answer:
40
80
Step-by-step explanation:
5/6 × 48
5 × 48 = 240
240/6
= 40
120 × 2/3
120 × 2 = 240
240/3
= 80
Complete the table and answer the questions that follow. (If a root occurs twice, count it twice; if
thrice, count it three times, and so on. The first one is done
Polynomial Equation
1. (x+1)² (x-5) = 0
2. X-9 0
3. (x+8) (x-8)= 0
4. x² + 3x +2=0
(x+1)(x+2) = 0
5. (x² - 4x + 4)(x-3)²
(x-2)(x-2)(x-3)(x-3) = 0
6. 2
7. (x-3)(x + 1)(x - 1) = 0
8. (x²-4)(x-3)³ = 0
(x+2)(x-2)(x-3)(x-3)(x-3)=0
9. x(x-4)(x + 5)(x - 1) = 0
10. (x + 1)5 (x - 1)² =0
Degree
3
Real Roots of the
Equation
-1 (2times); and 5
Number of Real Roots
3
An equation of the form P=0 is referred to as a polynomial equation. P is a polynomial with coefficients in some field, typically the field of the rational numbers. A polynomial equation, on the other hand, can include a number of variables. The phrase polynomial equation is typically preferred over algebraic equation when discussing situations with multiple variables.
What is Polynomial Equation ?One or more variables, coefficients, and non-negative integer exponents of variables make up a polynomial, which is an expression. A mathematical statement that has a "equal to" symbol between two algebraic expressions with equal values is called an equation.
Sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials.
4x² + 6x + 21=0 where 4x²+6x+21 is considered as a polynomial expression which is written on the left side and has been fixed to make the polynomial expression equal to zero to form a complete polynomial equation.
1 Already answered
2 Degree:1 Real Roots of an equation:8 Number of Real Roots:1
3 Degree:2 Real Roots of an equation:2,-2 Number of Real Roots:2
4 Degree:5 Real Roots of an equation:-1,1-3,-3,-3 Number of Real Roots:5
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[tex]x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} x^{2} \\[/tex]
Answer: [tex]x^{26}[/tex]
Step-by-step explanation:
The [tex]x^2[/tex] appears 13 times. Using the exponent rule [tex]x^a x^b=x^{a+b}[/tex], we get that:
[tex]x^2x^2x^2x^2x^2x^2x^2x^2x^2x^2x^2x^2x^2=x^{2(13)}=x^{26}[/tex]
Find the x- and y-intercepts of the graph of 8x - 10y = 32. State each
answer as an integer or an improper fraction in simplest form.
Feng invests money in an account paying simple interest. He invests $70 and no money is added or removed from the investment. After one year, he has $70.70. What is the simple percent interest per year?
The simple interest is given as PRT/100, thus the simple percent interest per year is 1%.
What is simple interest?Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time.
Unlike compound interest, which adds the interest from the principal of prior years to determine the interest of the following year.
As per the given,
Investment = $70
Investment after one year is $70.70
Interset = 70.70 - 70 = $0.70
The interest is given as = PRT/100
0.70 = PR(1)/100
R = (0.70×100)/70
R = 1%
Hence, "The simple interest is given as PRT/100, thus the simple percent interest per year is 1%".
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Evaluate f(x) = 2|x – 5| for f(–5) and f(0).
Question 20 options:
f(–5) = 10, f(0) = 0
f(–5) = 12, f(0) = 5
f(–5) = –20, f(0) = –2
f(–5) = 20, f(0) = 10
Answer:
D
Step-by-step explanation:
f(-5) = 2|-5-5|
f(-5) = 2|-10|
f(-5) = 2 * 10
f(-5) = 20
f(0) = 2|0-5|
f(0) = 2|-5|
f(0) = 2 * 5
f(0) = 10
if f represents the number of lots of fliptop pens to produce and t represents the number of lots of tiptop pens to produce, the linear programming model for this problem is:
The linear programming model for this problem is Max 1000F + 1000T
Given that,
If the quantity of flip top pens to be produced is f and the quantity of tiptop pens to be produced is t, then
Number of lots of Flip top pens to produce = F
Number of lots of Tip top pens to produce = T
Therefore, The linear programming formulation is given by:
Max 1000F + 1000T
s.t.
Plastic: 3F + 4T <= 39
Ink Assembly: 5F + 4T <= 45
Molding time: 5F + 2T <= 37
F, P >= 0
Hence, the linear programming model for this problem is Max 1000F + 1000P
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In a city school, 60% of students have blue eyes, 55% have dark hair and 20% have neither blue eyes nor dark hair. determine the probability that a randomly selected student will have blue eyes and dark hair
The probability of of a random student having blue eyes and dark hair
is 35% .
let consider the total students in the school be (U) = 100%
out of them ,
students having blue eyes (A) = 60%
students having dark hair (B) = 55%
students with neither blue eyes nor dark hair (A∪B)' = 20%
let the students with blue eyes and dark hair be (A∩B) = x %
Then according to the set theorem
U = n(A∪B) + n(A∪B)'
U = n(A) + n(B) - n(A∩B) + n(A∪B)'
100 = 60 + 55 - x +20
∴ x = 60 + 55 +20 - 100
x = 35 %
So the probability of random student having blue eyes and dark hair is 35% .
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suppose that 10 green balls and 14 purple balls are placed in an urn. two balls are then drawn in succession. what is the probability that the second ball drawn is a purple ball if the first ball is replaced before the second is drawn? a) 0.1224 b) 0.6250 c) 0.8333 d) 0.4167 e) 0.5833 f) none of the above.
The probability that the second ball drawn is a purple ball is (e) 0.5833
How to determine the probability?From the question, we have the following parameters that can be used in our computation:
Green balls = 10
Purple balls = 14
This means that the total number of balls is
Total = 10 + 14
Evaluate the equation
So, we have
Total = 24
From the question, we understand that the ball is replaced
So, the probability that the second ball is purple ie
P(second purple) = purple/total
This gives
P(second purple) = 14/24
Evaluate
P(second purple) = 0.5833
Hence, the probability is (e) 0.5833
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HELPPP MEEeeeeeeeeee
HELP the price of gasoline purchased varies directly with the number of gallons purchased if 10 gallons of gasoline are purchased for$23 what will be the price of 50 gallons be?
Answer:
Step-by-step explanation:
It will be 115$
Answer: the answer is $21.7391304348 or round to $21.74 is the cost for 50 gallons
Step-by-step explanation: I did the calculations and it costs $2.30 a gallon
Point O is the center of this circle. What is mzBCA?
A. 56
B. 62
C. 72
D.76
Answer:
B
Step-by-step explanation:
∠ ADB and ∠ AOB sum to 180° , that is
56° + ∠ AOB = 180° ( subtract 56° from both sides )
∠ AOB = 124°
An angle on the circle is half the central angle subtended on the same arc , so
∠ BCA = [tex]\frac{1}{2}[/tex] ∠ AOB = [tex]\frac{1}{2}[/tex] × 124° = 62°
Please answer part d
Answer:
∆JGF ≅ ∆GJH by the SAA Postulate
Step-by-step explanation:
Given a figure showing two triangles with a common side, and two marked angles not at either end of that side, you want to know the applicable congruence postulate.
SAAThe letters S and A in the congruence postulate references refer to "Side" and "Angle". The sequence of the letters corresponds to the sequence of corresponding parts in the triangles.
In the given figure, two angles in each triangle are marked with a single arc and a double arc. The triangles share a side that has the double-arc angle at one end. Hence, the sequence of corresponding parts can be seen to be (common) Side - (double-arc) Angle - (single-arc) Angle. The SAA congruence postulate applies.
∆JGF ≅ ∆GJH by the SAA Postulate
