The p-value for the given hypothesis test is 0.0037 (accurate to 4 decimal places)
To find the p-value, we need to use the standard normal distribution table or a calculator. Since the alternative hypothesis is left-tailed, we are interested in finding the area under the curve to the left of the observed test statistic z.
Using a standard normal distribution calculator, we find that the area to the left of z = -2.683 is 0.0037 (rounded to 4 decimal places). This represents the p-value for the hypothesis test.
Therefore, we can conclude that there is strong evidence to reject the null hypothesis at a significance level of 0.05, since the p-value of 0.0037 is less than the chosen significance level. The evidence suggests that the accuracy rate for fingerprint identification is significantly less than 0.16.
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simplify the following
\( \frac{5 {ab } ^{2} + 10 {a}^{4} {b}^{3} - 15 {ab}^{3} }{5ab} \)
An oven is priced at $745.75. There is an 8% sales tax rate.
What is the sales tax for the oven in dollars and cents?
a) $93.22
b) $59.66
c) $652.53
d) $686.09
Answer:
B. 59.66
Step-by-step explanation:
In order to solve this youd have to multiply 745.75 by 8% in order to find it
First you'd need to turn 8% into a decimal
8%/100 = 0.08
0.08 x 745.75 =59.66
So the sales tax rate for this price is 59.66
A special deck of cards has 12 cards. four are green, three are blue, and five are red. When a card is picked, the color of it is recorded. An experiment consists of first picking a card and then tossing a coin. A. How many elements are there in the sample space? 12 B. Let A be the event that a green card is picked first, followed by landing a tail on the coin toss. P(A) = Present your answer as a decimal number rounded to two decimal places of accuracy. C. Let C be the event that a green or red is picked, followed by landing a tail on the coin toss. Are the events A and C mutually exclusive?(Yes or No) D. Let B be the event that a blue or red is picked, followed by landing a tail on the coin toss. Are the events A and B mutually exclusive? (Yes or No)
Answer:
A. Sample space = 6
B. 0.17
C. No
D. Yes
Step-by-step explanation:
A. The sample space of an experiment is the set of all possible outcomes of that experiment.
since there are three colours and 2 outcomes for a coin toss,
sample space = 3 * 2 = 6
B. Probability of picking a green first = 4/12 = 1/3
probability of a tail = 1/2
Probability of a green and a tail, P(A) = 1/3 * 1/2 = 0.17
C. No.
Considering the two events;
A; green card is picked first
C ; a green or red card is picked
There is an intersection point for the two events. Therefore, they are not mutually exclusive.
D. Yes.
Considering the two events;
A; green card is picked first
B ; a blue or red card is picked
There is no intersection point for the two events. Therefore, they are mutually exclusive.
1. At the school store, Juanita bought 2 books and a backpack for a total of $26 before tax. Each book cost $8 less
than the backpack. Use b for book and p for backpack.
a
Write a system of equations that can be used to find the price of each book and the price of the
backpack
The price of each book is $6 and the price of each backpack is $14.
Given that,
Cost of 2 books and a backpack = $26
Each book cost $8 less than the backpack.
Let the cost of each book be b and the cost of the backpack be p
2b + p =26 (i)
Each book cost $8 less than a backpack
b=p-8 (ii)
Substitute for b in equation (i)
2(p-8) +p = 26
2p - 16 +p =26
3p = 42
p =14 (Cost of backpack)
b = cost of book = 14-8 =6
Thus, the price of each book is $6 and the price of each backpack is $14.
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Rewrite the following equation in standard form.
y = 3x + 9
3x-y=-9
Step-by-step explanation:
Answer: 3x - y = - 9
Step-by-step explanation:
Re-write the equation in the following form:
3x + 9 = y
Take the y to LHS:
3x + 9 - y = 0
Now, take the 9 to the RHS:
3x - y = -9. This is your answer.
0.1(-90 + 50a) in distributive property
Given:
\(0.1(-90 + 50a)\)
Apply the distributive law: \(a(b+c)=ab+ac\)
\(0.1(-90 + 50a)=0.1(-90)+0.1\times50a\)
\(=0.1(-90)+0.1\times50a\)
Simplify \(0.1(-90)+0.1\times50a\):
\(\boxed{\bold{=-9+5a}}\)
PLEASE HELP with question 2! BRAINLIEST to correct answer!! NO LINKS AS ANSWERS, or you will be REPORTED!!!
get x = 128 is not a step
Suppose y varies directly with x, and y= 10 when x=-2. What direct variation equation relates x and y? What is the value of y when x=-15. I don't understand how to solve this, can someone explain to me how to get the answer and what it's asking. P. S. It's a practice question so i know the answer just not how to get it
Answer:
y = 75
Step-by-step explanation:
\(y=kx\\10=k(-2)\\10=-2k\\k=-5\\\\y=-5x\\y=-5(-15)\\y=75\)
When y varies directly with x, this means that you need to set up the equation y=kx and solve for k given (x,y)=(-2,10) and then use your new equation to plug in x=-15 to get y=75
Can someone help me with this?
Write the ratios for sin X and cos X.
Answer:
\( \sin(X) = \frac{ \sqrt{119} }{12} \: , \: \cos(X) = \frac{5}{12} \)
Answer:
Its the last choice.
Step-by-step explanation:
sin X = opposite side / hypotenuse
= √119/12.
cos X = adjacent side / hypotenuse
= 5/12.
Someone plz help me
Answer:
I believe it's D (10).
It is the greatest number that you can factor out of 80 and 70.
Josefina ate 3/8 of the pizza and Leando ate 4/16. How much did they eat between the two of them?
To calculate how much they ate between the two of them, the amounts each ate must be added:
\(\begin{gathered} \sf \frac{3}{8} + \frac{4}{16} = \\ \\ \sf\frac{16 \div 8 \times 3 + 16 \div 16 \times 4}{16} = \\ \\ \sf\frac{6 + 4}{16} = \\ \\ \sf \frac{10}{16} = \red {\boxed{ \sf \frac{ \green5}{ \green8} }}\end{gathered}\)
Therefore, between the two of them they ate five eighths of pizza.
To add heterogeneous fractions, fractions with different denominators, follow these steps:
Find the common denominator, which is the least common multiple of the denominators.Divide the common denominator by the other denominator and multiply by the numerator.Write the results obtained above as numerators with the sign of the sum between them.Add the numerators.Simplify the result if possible.Merry Christmas and Happy New Year
The Alpha.To calculate how much they ate between the two of them, the amounts each ate must be added:
\(\begin{gathered}\begin{gathered} \bold{ \frac{3}{8} + \frac{4}{16}} \\ \\ \bold{\frac{16 \div 8 \times 3 + 16 \div 16 \times 4}{16}} \\ \\ \bold{\frac{6 + 4}{16}} \\ \\ \bold{ \frac{10}{16} }= {\boxed{ \sf \frac{ \bold5}{ \bold8} }}\end{gathered}\end{gathered} \)
\(\therefore\) Between the two of them they ate five eighths of pizza.
To add heterogeneous fractions, fractions with different denominators, follow these steps:
Find the common denominator, which is the least common multiple of the denominators.
Divide the common denominator by the other denominator and multiply by the numerator.
Write the results obtained above as numerators with the Sign of the sum between them.
Add the numerators.Simplify the result if possible.Similar polygons have corresponding angles that are congruent, and corresponding sides that are proportional. it is called____
Similar polygons have corresponding angles that are congruent, and corresponding sides that are proportional. it is called Similarity criterion.
Similarity is a fundamental concept in geometry that describes the relationship between two figures that have the same shape but may differ in size.
Two polygons are considered similar if their corresponding angles are congruent, and their corresponding sides are proportional. This means that when two polygons are similar, the corresponding angles have the same degree measures, and the corresponding sides are in the same ratio or proportion.
Similarity criteria can be used to solve a variety of problems in geometry, such as finding missing side lengths or angles of similar triangles. Similarity is a powerful tool for understanding and analyzing geometric shapes and their properties.
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Amanda takes out a loan of $1,200 from a bank that charges 5.4% interest a year. If she borrows the money for 1.5 years, how much money does she repay
The total money she repays to the bank is $1297.2.
Given,
Amanda takes out a loan of $1,200 from a bank.
The bank charges 5.4% interest a year.
She borrows the money for 1.5 years.
We need to find the total amount she repays to the bank after 1.5 years.
we have,
Loan amount = $1200
Bank interest rate per year = 5.4%
So,
The interest amount per year:
= 1200 X (5.4/100)
= $64.8
If,
1 year = $64.8
1/2 year = 1/2 x 64.8
1/2 year = $32.4
In 1.5 years the interest amount will be:
1.5 years = 1 year + half-year
= $64.8 + $32.4
= $97.2
The total money she needs to pay to the bank after 1.5 years is:
= loan amount + 1.5 interest amount
= $1200 + $97.2
= $1297.2
Thus if she borrows the $1200 for 1.5 years with a yearly interest of 5.4%, she needs to repay $1297.2.
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a password is to be 4 to 6 characters long. the first character must be a digit but not 0. the rest of the characters can be any letter or digit. how many such passwords are possible?
On solving the provided question we can say that on permutation choose which two of the six positions contain the two digits = 685464000
what is permutation?The permutation of a set in mathematics is essentially the rearranging of its elements if the set is already ordered, or the arrangement of its members in a linear or sequential order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context. The mathematical calculation of the number of possible arrangements for a given set is known as permutation. Permutation, in its simplest form, refers to the variety of possible arrangements or orders. The placement of the elements matters with permutations. The placement of items in a specific order is known as a permutation. Here, the set's components are sorted in either chronological order or linear order.
Assuming we regard upper and lower case letters as different, there are 52^4 ways = 7311616 ways
sequences of four letters and 100 sequences of two digits
there are 15 ways choose which two of the six positions contain the two digits = 685464000
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Solve for x: −6 < x − 1 < 9
a. 5 < x < 10
b. −5 < x < 10
c. −5 > x > 10
d. 5 > x > −10
Answer:
-5 < x < 10
Step-by-step explanation:
−6 < x − 1 < 9 just get rid of -1 by adding 1 to all three terms
-6 + 1 < x -1 + 1 < 9 + 1
-5 < x < 10
Answer:
| − 2 | − 7 2 x− 9 ⋅ 5 x − 4 − 6 ( y − 3 )
Step-by-step explanation:
Use complex integration techniques to evaluate the integral x² dx (x² + 1)²(x²+2x+2)
Given integral is ∫x² dx (x² + 1)²(x²+2x+2)Let us first take a look at the denominator of the given integrand (x² + 1)²(x²+2x+2)Now, let us try to break it down into its factors for a simpler integration to be done.Therefore,x² + 1 = (x² + 2x + 1) - 2x = (x + 1)² - 2x∴ (x² + 1)²(x²+2x+2) = [(x + 1)² - 2x]² (x² + 2x + 2)= (x + 1)⁴ - 4x(x + 1)² + 4x²(x² + 2x + 2)Therefore, the given integral becomes ∫x² dx [(x + 1)⁴ - 4x(x + 1)² + 4x²(x² + 2x + 2)]Now, let us expand and simplify this expression.∫x² dx [(x + 1)⁴ - 4x³ - 2x² + 4x]Let us integrate this expression using the standard integration technique, integrating the term one by one.∫x² dx [(x + 1)⁴ - 4x³ - 2x² + 4x]= ∫x² dx (x + 1)⁴ - ∫x² dx 4x³ - ∫x² dx 2x² + ∫x² dx 4x= 1/3(x + 1)³ - x⁴ + 2/3 x³ + 2/3x² + C (where C is the constant of integration)
Therefore, the complex integration of the given integral is (1/3(x + 1)³ - x⁴ + 2/3 x³ + 2/3x² + C)Answer:Thus, we have evaluated the integral by using complex integration techniques. Therefore, the solution to the given problem is(1/3(x + 1)³ - x⁴ + 2/3 x³ + 2/3x² + C) where C is the constant of integration.The explanation above clearly demonstrates the use of complex integration techniques to evaluate the given integral.
We began by breaking down the denominator of the integrand and simplifying the expression. After that, we integrated the resulting expression term by term to obtain the solution.
The conclusion of the solution was provided as (1/3(x + 1)³ - x⁴ + 2/3 x³ + 2/3x² + C) where C is the constant of integration.
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Evan, Claire, Jaya and Tim are running a 3km relay race.
Evan ran 9/10 of a km
Claire ran 7/9 of a km
Jaya ran 2/3 of a km
What fraction of a km does Tim need to run to finish the race?
Try to answer ASAP please, thank you.
Answer:
Tim needs to finish 59/90
Step-by-step explanation:
Add together what Evan Claire and Jaya ran
9/10 + 7/9+ 2/3
The common denominator is 90
9/10 (9/9) +7/9 *10/10 + 2/3 *30/30
81/90 + 70/90 + 60/90
211/90
We need 3 km = 3 *90/90 = 270 /90
270/90 - 211/90 = 59/90
find the number of terms and the degree of this polynomial.
\( - 9 {r}^{9} \)
Step-by-step explanation:
there is 1 term
9th degree or degree =9
The value of m varies inversely as the square of n. when , . what is the positive value of n when ?
The necessary positive value of n is 2.
What is Positive Value?
Positive numbers are any numbers that are greater than zero.
Given,
m varies inversely as the square of n.
When n = 3, then m = 6.
Inverse proportion: It is assumed that m is inversely proportional to n squared. So,
m ∝ 1/\(n^{2}\)
m = k/\(n^{2}\) ................. (1)
Where, k is the constant of proportionality.
Substitute m = 6 and n = 3 in the above equation.
6 = k / 3²
6 = k /9
6 * 9 = k
54 = k
Substitute this value in (i).
m = 54 / n²
Substitute m = 13.5 in the equation.
13.5 = 54 / n²
n² = 54 / 13.5
n = ± √4
n = ± 2
As a result, the required positive value of n is 2.
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The ratio of blue pens to black pens in a box is 3:5 what fraction of the pens are black
Answer:
5/8
Step-by-step explanation:
3+5=8
there are 8 parts altogether
5/8
i hope i helped<3
Find the total surface area of this cylinder. Give your answer to one decimal place PLEASE HELP THANK YOUUUU
Answer:
Step-by-step explanation:
surface area of cylinder=2 πr²+2πrh
=2πr(r+h)
=2π×12(12+18)
=24π×30
=720π
≈2261.9 cm²
Danielle surveyed her classmates about the number of movies they saw over summer break. Here are the results
0,0,1,1,2,2,4,5,6,6,8,10,12,12,14
The results of a poll Danielle conducted among her classmates regarding the amount of movies they saw during the summer are listed below in Numerical order: 0, 0, 1, 1, 2, 2, 4, 5, 6, 6, 8, 10, 12, 12, 14.
What is ascending numerical order?
Numbers are organized from smallest to largest when they are placed in ascending order. Before we can put the numbers in any order, we must first compare the numbers.
Compare before ordering. In descending sequence, the following numbers: Count the number of digits in each number.
Numerical order: 0, 0, 1, 1, 2, 2, 4, 5, 6, 6, 8, 10, 12, 12, 14.
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Hi please help , you don't need to show work.
The value of function (f+g)(x) is x²-3x+7, (f-g)(x) is 3x²-3x+7, (fg)(x) is -2x⁴+3x³-7x² and (f/g)(x) is -2x²+3x-7/x²
What is a function?A relation is a function if it has only One y-value for each x-value.
The given two functions are
f(x)=3x-2 and g(x)=4+x
at x=-1
f(-1)=-5, g(-1)=3
at x=2,
f(2)=4, g(2)=6
at x=5,
f(5)=13, g(5)=9
Now the functions are f(x)=2x²-3x+7 and g(x)=-x².
We need to find (f+g)(x)
f(x)+g(x)
2x²-3x+7-x².
x²-3x+7
(f-g)(x)
f(x)-g(x)
2x²-3x+7+x²
3x²-3x+7
(fg)(x)
(2x²-3x+7)(-x²)
-2x⁴+3x³-7x²
f/g(x)=-2x²+3x-7/x²
Hence, the functions (f+g)(x)=x²-3x+7, (f-g)(x)=3x²-3x+7, (fg)(x)=-2x⁴+3x³-7x² and (f/g)(x)=-2x²+3x-7/x²
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16
Adrian, Bhamini and Chas share a sum of money.
1
Adrian gets
6
Bhamini gets
of the money.
1
3
Chas gets the rest of the money.
Adrian gets £42
(a) Work out how much money Bhamini gets.
of the money.
Answer: 84
Step-by-step explanation:
Bhamini =
42 x 6 = 25.2
25.2 x 1/3 = 84
Chas =
252.84 - 42 = 126
Bhamini gets £84!
Hope this answered your question, don't ell Mr Gohil I helped you lol.
Answer provided by Zack.
Chastity ran a hypothesis test with an alpha level of .01 and her test statistic fell outside of the critical region. what should she do?
The critical region is determined based on the alpha level, which is the probability of making a Type I error (rejecting the null hypothesis when it is true). An alpha level of .01 means that there is a 1% chance of making a Type I error.
If Chastity ran a hypothesis test with an alpha level of .01 and her test statistic fell outside of the critical region, it means that the test statistic does not provide enough evidence to reject the null hypothesis.
In this case, Chastity should fail to reject the null hypothesis and accept it as the plausible explanation. This implies that there is not enough evidence to support the alternative hypothesis.
When a test statistic falls outside of the critical region, it indicates that the observed data is not extreme enough to reject the null hypothesis. The critical region is determined based on the alpha level, which is the probability of making a Type I error (rejecting the null hypothesis when it is true). An alpha level of .01 means that there is a 1% chance of making a Type I error.
In summary, when Chastity's test statistic falls outside of the critical region, she should fail to reject the null hypothesis and accept it as the plausible explanation. This means that there is not enough evidence to support the alternative hypothesis at the given alpha level of .01.
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Circle E has a radius of 4.6 meters. FG is a chord and HE is a perpendicular bisector of FG. If FG = 6.2 meters, calculate the distance of EH.
Answer:
4.1 meters is the correct answer
Below is a recipe for chocolate chip cookies. The recipe makes 27 cookies. How many teaspoons of vanilla extract do you need to make 24 cookies? Round to the nearest hundredth if needed.
Answer: 1.78 teaspoons
Step-by-step explanation:
The recipe says: 27 cookies/2 teaspoons Vanilla extract. Let's abbreviation this conversion factor as (27/2)C/V, where C is cookie and V is 1 teaspoon vanilla extract. We have both 13.5C/V and 1V/13.5C as conversion factors. 13.5 cookies is equivalent to 1 teaspoon vanilla, or 1 teaspoon vanilla is equivalent to 13.5 cookies. We can multiply ofr divide either of these factors, since they are both equivalent to 1, and you can mukltiply or divide anything by 1 without changing it's accuracy. The atual numbers will change, but the units will also change, making it a valid result.
We want 24 cookies. Use one of the conversion factors to find the teaspoons vanilla extract required:
1) We can divide by (27C/2V)
24C/((27C/2V) = 1.78 teaspoons
or
2) we can multiply by (1V/13.5C)
24C*(1V/13.5C) = 1.78 teaspoons
35. State the domain and range for each function. (MAFS.912.F-IF.2.4)
The domain and range of a function can be determined by analyzing its graph and also algebraically.
MAFS.912.F-IF.2.4 standard of Florida Mathematics State Standards is based on identifying the domain and range of a function. The domain is a set of input values that the function is defined for, while the range is a set of output values that the function produces. Here are the answers to the given question:35. State the domain and range for each function
.(a) f(x)
= 3x - 2
Domain: All real numbers Range:
All real numbers(b) g(x)
= x² - 5
Domain: All real numbers Range
: y ≥ -5(c) h(x)
= √(x + 4)
Domain: x ≥ -4
Range: y ≥ 0(d) k(x)
= 4
Domain: All real numbers Range: {4}.The domain and range of a function can be determined by analyzing its graph and also algebraically.
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If the bearing of Saaman from Ankaase is 171. What is the bearing of Ankaase from Saaman.
Step-by-step explanation:
A. Theta + 180 (when angle is less than 180)
Theta - 180(when angle is greater than 180)
Thus, 171 + 180 = 351°
B. I. Angle CBF + Angle BFG = 180 (Co interior angles)
CBF + 118 = 180
CBF + 118 –118 = 180 –118
CBF = 62°
Ii. 83 + X + CBF = 180 (Angles on a straight line)
83+X+62 =180
145+x=180
145–145+x=180–145
X = 35°