Answer:
SSS, SAS, ASA, AAS
Step-by-step explanation:
s = sides
a = angle
it has been estimated that about 30% of frozen chickens are contaminated with enough salmonella bacteria to cause illness if improperly cooked. chickens are delivered to grocery stores in crates of 24. assume the chickens are chosen for inclusion in a crate at random. what is the probability that a randomly selected crate has more than 4 contaminated chickens?
Using the binomial distribution, it is found that there is a 0.1111 = 11.11% probability that a certain crate has more than 4 contaminated chickens.
For each chicken, there are only two possible outcomes, either they are contaminated, or they are not. The chickens are independently selected, hence, the binomial distribution is used.
What is the binomial probability distribution formula?
The formula is:
P(X=x) = Cₙ,ₓ.pˣ.(1-p)ⁿ⁻ˣ
Cₙ,ₓ = n!/x!(n-x)!
The parameters are:
x is the number of successes.
n is the number of trials.
p is the probability of a success on a single trial.
In this problem:
About 30% of frozen chickens are contaminated, hence p=0.3.
Chickens are delivered to grocery stores in crates of 24, hence n=24
The probability that a certain crate has more than 4 contaminated chickens is:
P(X>4)=1-P(X≤4)
In which:
P(X≤4) = (P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)
Then
P(X=x) = Cₙ,ₓ.pˣ.(1-p)ⁿ⁻ˣ
P(X=0) = C₂₄,₀.(0.3)⁰.(0.7)²⁴ = 0.0002
P(X=1) = C₂₄,₁.(0.3)¹.(0.7)²³ = 0.0020
P(X=2) = C₂₄,₂.(0.3)².(0.7)²² = 0.0097
P(X=3) = C₂₄,₃.(0.3)³.(0.7)²¹ = 0.0305
P(X=4) = C₂₄,₄.(0.3)⁴.(0.7)²° = 0.0687
Hence
P(X≤4) = (P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)
= 0.0002+0.0020+0.0097+0.0305+0.0687
= 0.1111
0.1111 = 11.11% probability that a certain crate has more than 4 contaminated chickens.
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the manager at a local movie theater has collected data for a long period of time and has concluded that the revenue from concession sales during the first show each evening is normally distributed with a mean equal to $336.25 and a variance equal to 1,456. based on this information, what are the chances that the revenue on the first show will exceed $800?
The chances that the revenue on the first show will exceed $800 when mean revenue is $336.25 and standard deviation is $38.16 is essentially zero. i.e. 0
A normal distribution is a type of continuous probability distribution in which the majority of data points cluster in the middle of the range, while the remainder taper off symmetrically toward either extreme. The mean of the distribution is also known as the middle of the range.
The normal distribution is primarily used to calculate the likelihood of an observation in a distribution falling above or below a given value.
Given,
Mean, [tex]\mu[/tex] = 336.25
variance, [tex]\sigma^2[/tex]= 1456
then,
standard deviation, [tex]\sigma = \sqrt{1456}[/tex] = 38.16
To determine the chances that the revenue on the first show will exceed 800 is1:
[tex]1-p(z=\frac{x-\mu}{\sigma})\\\\=1-p(z=\frac{800-336.25}{38.16})\\\\=1-p(z=\frac{436.75}{38.16})\\\\=1-p(z=12.15)\\\\=1-1=0[/tex]
Hence, there is no chance that the revenue will exceed $800 on the first show.
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∠Cis a right angle and AB=14 miles, determine the length of BC and AC.
The length of BC is approximately 5.72 miles and the length of AC is approximately 12.67 miles.
Let's represent the length of the side opposite angle A "BC" and the length of the side adjacent to angle A "AC". We can then use the sine function to find BC:
sin(A) = BC / AC
Substituting the given values, we get:
sin(24°) = BC / 14
We can use a calculator or look up the value of sin(24°) to get:
sin(24°) ≈ 0.406
Solving for BC, we get:
BC = 14 * sin(24°) ≈ 5.72
To find AC, we can use the cosine function:
cos(A) = AC / AC
Substituting the given values, we get:
cos(24°) = AC / 14
We can use a calculator or look up the value of cos(24°) to get:
cos(24°) ≈ 0.913
Solving for AC, we get:
AC = 14 x cos(24°) ≈ 12.67
Thus, BC is about 5.72 miles long while AC is about 12.67 miles in length.
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find an equation for a line perpendicular to y=2x-3, passing through the origin.
Jill made a popcorn container that is shaped like a cone. The diameter of the opening is 8 inches and the height is 9 inches. What is the volume of the popcorn container? Leave answer alone, do not round.
Domain:1,2,3,4,5 range:68,71,74,77,80 what is a reasonable domain for this
The reasonable domain for the range: 68,71,74,77,80 is { 1,2,3,4,5 } .
What are domain and range of a function ?
The range of values that we are permitted to enter into our function is known as the domain of a function. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.
The collection of all feasible independent variable values is known as the mathematical domain. The set of all independent variable values that are conceivable yet make sense in the context at hand is known as the reasonable domain.
Given:
range: 68,71,74,77,80
Domain:1,2,3,4,5
Here, the situation is not given.
So, the reasonable domain is { 1,2,3,4,5 }
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Solve for the shaded region
The Area of the Shaded Region is 184.61 sq. mm
What is Area?
The quantity area indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina.
Solution:
Area of the Shaded Region = Area of Rectangle - 2 * Area of Circles
Area of Recatangle = Length * Breadth = 21 * 13 = 273 sq. mm
2 * Area of Circle = 2* πr² = 2 * 22/7 * 7.5/2 * 7.5/2
= 88.39 sq. mm
Area of the Shaded Region = 273 - 88.39 = 184.61 sq. mm
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What is the smallest prime number that is the sum of two other distinct prime numbers?
Answer:
5
Step-by-step explanation:
2 +3 = 5
Is this true or false?
TRUE: The given contrapositive statement are correct,
If m ≤ 3, then, m < 5.
Explain the contrapositive statement?An inference rule called proof by contrapositive, also known as proof by contraposition, is used in proofs to infer a conditional assertion from its contrapositive. To put it another way, the assertion "if B, then not A" is proven rather than the conclusion "if A, then B."When you reverse the hypothesis as well as the conclusion in a statement and reject both of them, you have a contrapositive statement.For the stated conditional statement -
If m ≤ 3, then, m < 5.
Then, contrapositive statement for the given statement will be
(m < 5)' ⇒ (m ≤ 3)'
That is;
(m > 5) ⇒ (m > 3)
That is, if m> 5 then, m > 3, which is true.
Thus, the contrapositive statement for the given conditional statement is true.
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in a hypothetical case-control study of female participants regarding exposure to emf's and breast cancer, the following data were obtained: 11 cases exposed, 108 controls exposed, 5 cases not exposed, 436 controls not exposed. what is the odds ratio for the association between exposure to emf's and breast cancer?
The odds ratio for the association between exposure to emf's and breast cancer would be (11/5) / (108/436) = 2.2.
1. Calculate the odds of exposure for cases: 11/5 = 2.2
2. Calculate the odds of exposure for controls: 108/436 = 0.25
3. Divide the odds of exposure for cases by the odds of exposure for controls: 2.2/0.25 = 8.8
4. Finally, the odds ratio for the association between exposure to EMF's and breast cancer is 2.2.
The odds ratio for the association between exposure to EMF's and breast cancer can be calculated by dividing the odds of exposure for cases by the odds of exposure for controls. To calculate this, first take the number of cases exposed (11) and divide it by the number of cases not exposed (5). This will give the odds of exposure for cases (2.2). Second, take the number of controls exposed (108) and divide it by the number of controls not exposed (436). This will give the odds of exposure for controls (0.25). Finally, divide the odds of exposure for cases (2.2) by the odds of exposure for controls (0.25). This will give the odds ratio for the association between exposure to EMF's and breast cancer (2.2).
Odds ratio = (11/5) / (108/436) = 2.2
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13. If f(x)=x² + 3x-2, find f(-2).
By using the substitution property, the value of f(-2) is -4.
What is the substitution property of equality?
In an expression or equation, one value can be substituted for another and the result will still be the same. This is known as the substitution property of equality. If the values of x and y are the same, then x and y can be substituted for one another.
Given, f(x) = x² + 3x - 2
To find the value of f(-2), apply substitution property
f(-2) = (-2)² + 3(-2) - 2 = 4 - 6 - 2 = -2-2 = -4
Hence, the value of f(-2) is -4.
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Ms. Hall is buying Ms. Ward some gifts for Christmas. She is buying one big gift that
will cost $90 as well as some small gifts that cost $7 each.
1+90 +7
What is its :
Constant:
Coefficient
Equation:
When Ms. Hall is buying Ms. Ward some gifts for Christmas as described in the problem,
the Constant: $90 and $7
the Coefficient: $7
the Equation: $90 + $7x
How to find the constantInformation form the problem shows that
one big gift that will cost $90
some small gifts that cost $7 each
the constant in this case is the price of the gifts
$90 and $7
the coefficient is $7
the equation is
$90 + $7x
where x is the number of the small gifts
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Find the minimum value of the function f ( x ) = x 2 + 8 x + 9.6 f(x)=x 2 +8x+9.6 to the nearest hundredth.
The maximum and minimum values of the given function will be equal to -1.47 and -6.52.
What is the quadratic equation?The 2nd equation in x is known as a quadratic function. ax² + bx + c = 0 is the quadratic equation in standard form, wherein there a and b are the coefficient, x is the constant, and c is the constant.
As per the equation given in the question,
f(x) = x² + 8x + 9.6
D = b² - 4ac
= 8² - 4(1)(9.6)
D = 25.6
Now, find the roots,
-(b ± √D)/2a
-(8 ± 5.05)/2
So, the roots are,
-(8 + 5.05)/2 = -1.47, (x + 1.47)
-(8 - 5.05)/2 = -6.52, (x + 6.52)
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Need help with this equation and graphing table asap!! Look at the image
first 2;
a) 7(2) + 8 = 22 > 16, 7(4) + 8 = 36>32
36 - 22 = 14/2 = 7
32 - 16 = 16/2 = 8
7<8
the table has a greater rate of change
y intercept
equation; 8
table; 0
8> 0
the equation has a greater y intercept
You are planning a trip to an amusement park with a new water slide. It costs $25
for admittance to the park, plus $5 each time you ride the new water slide. Let w
represent the number of times you go down the slide and c represent the total cost
in dollars.
Write the amount that you will spend as a function of the number of times you
ride the new water slide. What is the total cost if you go down the slide 6 times?
Answer
55
Step-by-step explanation:
5w+25= c
5(6)+25=55
Which of the following is the solution to the following system of inequalities?
x+2y<=4
3x-y>=2
See the picture for the graphs. Any help is appreciated!! This is honors algebra 2 on Apex learning.
Answer: B.
Step-by-step explanation:
x+2y≤4
3x-y≥2
How to solve this problem? I need the answer quick as possible!
Consider the following three systems of linear equations. Answer the questions below.
For each, choose the transformation and then fill in the blank with the correct number.
The arrow → means the expression on the left becomes the expression on the right.
Answer:
24 Inches
Step-by-step explanation:
The length of a piece of wood that uses 8 nails as required in the task content is; 24 inches.
What is the length of a piece of wood that uses 8 nails?
It follows from the task content that the length of a piece of wood that uses 8 nails is to be determined from the task content.
Pleaseeee help I’m so confused
Answer:
D
Step-by-step explanation:
if you move the preimage on the image you can see that the two figures are equals
Aniyah invests $2300 in one account and $1400 in an account paying 4 % higher interest. At the end of one year she had earned $130 in interest. At what rates did she invest
The rate of interest in one account whose investment is $2300 will be 3.21%.
What is simple interest?Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.
I = (PRT)/100
Where P is the principal, R is the rate of interest, and T is the time.
Aniyah puts $2300 in one record and $1400 in a record paying 4 % higher interest. Toward the finish of one year, she had procured $130 in interest.
Let 'x' be the interest. Then the equation is given as,
(2300 × x × 1)/100 + (1400 × 4 × 1) / 100 = 130
Simplify the equation, then we have
23x + 56 = 130
23x = 74
x = 3.21%
The pace of revenue in one record whose speculation is $2300 will be 3.21%.
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Identify the pattern.
-4. -5.5, -7, -8.5, -10, -11.5, -13,..
Answer:
The pattern is that each number in the sequence is the previous number minus 1.5. For example, -5.5 is -4 minus 1.5, -7 is -5.5 minus 1.5, and so on.
Answer:
-1.5
Step-by-step explanation:
You take two of the variables in the pattern and subtract them with the second one being the minuend, and the first being the subtrahend.
For example we will use -4 and -5.5
(-5.5) - (-4) = -1.5
There is a negative sign present so it indicates subtraction towards the pattern.
Hence, the pattern change rate is -1.5
Use the tax table below to answer the following question.
A 9-column table with 7 rows is shown. Column 1 is labeled If the wages are at least with entries 720, 740, 760, 780, 800, 820, 840. Column 2 is labeled But less than with entries 740, 760, 780, 800, 820, 840, 860. Column 3 is labeled And the number of withholding allowances is 0, the amount of income tax withheld is, with entries 80, 83, 86, 89, 92, 95, 98. Column 4 is labeled And the number of withholding allowances is 1, the amount of income tax withheld is, with entries 62, 65, 68, 71, 74, 77, 80. Column 5 is labeled And the number of withholding allowances is 2, the amount of income tax withheld is, with entries 44, 47, 50, 53, 56, 59, 62. Column 6 is labeled And the number of withholding allowances is 3, the amount of income tax withheld is, with entries 26, 28, 31, 34, 37, 40, 43. Column 7 is labeled And the number of withholding allowances is 4, the amount of income tax withheld is, with entries 14, 16, 18, 20, 22, 24, 26. Column 8 is labeled And the number of withholding allowances is 5, the amount of income tax withheld is, with entries 1, 3, 5, 7, 9, 11, 13. Column 9 is labeled And the number of withholding allowances is 6, the amount of income tax withheld is, with entries 0, 0, 0, 0, 0, 0, 1.
Consider cases where the number of withholding allowances is less than 6. Which will cause the amount of federal income tax withheld to increase?
a.
Gross pay stays the same and withholding allowances increase.
b.
Gross pay increases by more than $20 and withholding allowances stay the same.
c.
Gross pay increases by more than $20 and withholding allowances increase.
d.
Gross pay decreases by more than $20 and withholding allowances stay the same.
Using percentages, we can determine that the Luce family pays $16.34 in state tax because there are no federal withholding exemptions.
What is the Percentage?A percentage is a relative figure that has the ability to represent 1/100th of any quantity.
Since 1% denotes one percent, 100 percent and 200 percent indicate the full amount and double the quantity, respectively.
By multiplying by 100 and inserting the "percentage sign"%, a ratio and fraction can be transformed into a percentage.
So, Luce is single and makes $763 twice weekly.
She does not request any compensation from federal withholding.
The value of this amount ranges from $760 to $780.
If we look at the table in the issue, the federal tax for this slab is $86.
Federal taxes now make up 19% of all state taxes.
Hence, the $86 in federal tax at a rate of 19% is:
Tax = 86 * 19/100
Tax = 16.34
Therefore, using percentages, we can determine that the Luce family pays $16.34 in state tax because there are no federal withholding exemptions.
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Correct question:
Use the tax table to help answer the following question.
A 9-column table with 7 rows is shown. Column 1 is labeled If the wages are at least with entries 720, 740, 760, 780, 800, 820, 840. Column 2 is labeled But less than with entries 740, 760, 780, 800, 820, 840, 860. Column 3 is labeled And the number of withholding allowances is 0, the amount of income tax withheld is, with entries 80, 83, 86, 89, 92, 95, 98. Column 4 is labeled And the number of withholding allowances is 1, the amount of income tax withheld is, with entries 62, 65, 68, 71, 74, 77, 80. Column 5 is labeled And the number of withholding allowances is 2, the amount of income tax withheld is, with entries 44, 47, 50, 53, 56, 59, 62. Column 6 is labeled And the number of withholding allowances is 3, the amount of income tax withheld is, with entries 26, 28, 31, 34, 37, 40, 43. Column 7 is labeled And the number of withholding allowances is 4, the amount of income tax withheld is, with entries 14, 16, 18, 20, 22, 24, 26. Column 8 is labeled And the number of withholding allowances is 5, the amount of income tax withheld is, with entries 1, 3, 5, 7, 9, 11, 13. Column 9 is labeled And the number of withholding allowances is 6, the amount of income tax withheld is, with entries 0, 0, 0, 0, 0, 0, 1.
Luce is single and makes $763 biweekly. She claims no federal withholding allowances. If the state tax is 19% of the federal tax, how much in state tax does Luce contribute?
a. $12.92
b. $15.13
c. $15.77
d. $16.34
Grace has 2 quartera . Jen have 4 dimesss were ans 1 nickels. Keesha has 3 dimes and 3 nickels. Terry has 1 quarters , 1 dime who has the most money
Answer: grace has the most money
Step-by-step explanation:
Because
Grace has 2 quarters = 50 cents
Jen has 4 dimes and 1 nickel = 45 cents
Keesha has 3 dimes and 3 nickels = 33 cents
Terry has 1 quarter and 1 dime = 26 cents
so as you can see grace has the most money
The height, h, in feet of a piece of cloth tied to a waterwheel in relation to sea level as a function of time, t, in seconds can be modeled by the equation h = 15 cosine (startfraction pi over 20 endfraction t). How long does it take for the waterwheel to complete one turn?.
The waterwheel takes 40 seconds to make one turn.
To find the period of the function, we need to find the time it takes for the function to repeat itself. In this case, we want to find the time it takes for the waterwheel to complete one turn.
The function h = 15 cos (π/20) t models the height of the cloth in relation to sea level as a function of time.
The cosine function has a period of 2π, so the period of the function h = 15 cos (π/20) t will be 2π divided by (π/20) which simplifies to 40 seconds.
Therefore, it takes 40 seconds for the waterwheel to complete one turn.
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you are dealt a hand of three cards, one at a time. find the probability that your cards are all face cards.
The probability that your cards are all face cards are,
The first club you get is the third card dealt P = 0.145Your cards are all black [tex]P_{all are black}[/tex] = 0.116You get no hearts [tex]P_{no heart}[/tex] = 0.413You have at least one red card [tex]P_{at least one red}[/tex] = 0.884We know that Total number of cars is 52 .
26 red and 26 is black.
13 are hearts ,
13 are diamonds,
13 are clubs,
13 are spades.
(a) The first club you get is the third card dealt,
Probability P (first club get is the third card dealt) = P(Non-club x Non club x club)
So,
P = [tex]\frac{39}{52} * \frac{38}{51} * \frac{13}{50}[/tex]
P = 0.145
(b) Your cards are all black,
[tex]P_{all are black}[/tex] = [tex]\frac{26}{52} *\frac{25}{51} *\frac{24}{50}[/tex]
[tex]P_{all are black}[/tex] = 0.116
(c) You get no hearts,
[tex]P_{no heart}[/tex] = [tex]\frac{39}{52} *\frac{38}{51} *\frac{37}{50}[/tex]
[tex]P_{no heart}[/tex] = 0.413
(d) You have at least one red card,
[tex]P_{at least one red}[/tex] = 1 - [tex]P_{no red}[/tex]
[tex]P_{no red}[/tex] = [tex]\frac{26}{52} *\frac{25}{51} *\frac{24}{50}[/tex]
[tex]P_{no red}[/tex] = 0.116
[tex]P_{at least one red}[/tex] = 1 - 0.116
[tex]P_{at least one red}[/tex] = 0.884
Therefore,
The probability that your cards are all face cards are,
The first club you get is the third card dealt P = 0.145Your cards are all black [tex]P_{all are black}[/tex] = 0.116You get no hearts [tex]P_{no heart}[/tex] = 0.413You have at least one red card [tex]P_{at least one red}[/tex] = 0.884To learn more about Probability visit :
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Type the correct answer in each box. Use numerals instead of words. If necessary, round to the nearest hundredth.
The relationship between the values of two different currencies is modeled by a linear function that varies depending on the current value of each currency. The table shows the relationship between an amount in U.S. dollars, x, and the equivalent amount in euros, f(x), where f(x) = x/1.06.
The inverse function is given by f⁻¹(x) = 1.06x. 2 euros is equivalent to 2.12 U.S. dollars. 4 euros is equivalent to 4.24 U.S. dollars
How to find the inverse function?Given that: the two different currencies is modeled by a linear function f(x) = x/1.06
where, x = an amount in U.S. dollars and f(x) = the equivalent amount in euros
To find the inverse function f⁻¹(x). Let y = f(x):
y = x/1.06
x = 1.06y
Since x = f⁻¹(y) = 1.06y
Thus, f⁻¹(x) = 1.06x
Note: f⁻¹(x) will help you convert from euros to dollar
2 euros to dollars will be:
f⁻¹(x) = 1.06x
f⁻¹(2) = 1.06(2) = 2.12
Thus, 2 euros is equivalent to 2.12 U.S. dollars
4 euros to dollars will be:
f⁻¹(x) = 1.06x
f⁻¹(4) = 1.06(4) = 4.24
Thus, 4 euros is equivalent to 4.24U.S. dollars
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aiudaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa plsssssss
Cora plans to buy some calligraphy pens priced at $5 each. Write an equation that shows how the total cost, y, depends on the number of calligraphy pens Cora buys, x. Do not include dollar signs in the equation.
Answer: y = 5x
Step-by-step explanation:
(x-14)÷7=12 I just need help
Answer:
x = 98
Step-by-step explanation:
Solve for x:
(x - 14)/7 = 12
Multiply both sides of (x - 14)/7 = 12 by 7:
(7 (x - 14))/7 = 7×12
(7 (x - 14))/7 = 7/7×(x - 14) = x - 14:
x - 14 = 7×12
7×12 = 84:
x - 14 = 84
Add 14 to both sides:
x + (14 - 14) = 14 + 84
14 - 14 = 0:
x = 84 + 14
84 + 14 = 98:
Answer: x = 98
Billy pulled a number of colored marbles from a large bag. green 1 orange 4 red 1 yellow 9 white 3 Based on experimental probability, how many of the next 20 marbles selected should you expect to be yellow marbles?
The likelihood that the next 20 marbles picked will be yellow marbles is 9/20.
What is probability?Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.
Here,
The probability that of the next 20 marbles selected it is expect to be yellow marbles,
=9/20
The probability that of the next 20 marbles selected it is expect to be yellow marbles will be 9/20.
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Answer:
the answer is 10
Step-by-step explanation:
ixl says its ten
Determine whether the distribution represents a probability distribution. If not, identify any requirements that are not satisfied.
x P(x)
10.49
20.05
30.32
40.07
50.07
Answer: This is a valid probability distribution.
The P(x) values add to 1; each P(x) is between 0 and 1 inclusive.
============================================================
Further Explanation:
A valid probability distribution is when,
The P(x) values add to 1.Each P(x) value is between 0 and 1 inclusive; i.e. [tex]0 \le P(\text{x}) \le 1[/tex]The given data table is:
[tex]\begin{array}{|c|c|} \cline{1-2}\text{x} & \text{P(x)}\\\cline{1-2}1 & 0.49\\\cline{1-2}2 & 0.05\\\cline{1-2}3 & 0.32\\\cline{1-2}4 & 0.07\\\cline{1-2}5 & 0.07\\\cline{1-2}\end{array}[/tex]
It's fairly clear that rule 2 has been satisfied. Something like [tex]0 \le 0.49 \le 1[/tex] is indeed a true statement. It's like saying 49% is between 0% and 100%. The other P(x) values are similar in nature.
---------
Let's see what the P(x) probability values add to:
0.49+0.05+0.32+0.07+0.07 = 1
We see that rule 1 has been met as well.
Since both rules have been satisfied, this means we have a valid probability distribution.
