Jenny works at Sammy's Restaurant and is paid according to the rates in the following
table.
Jenny's weekly wage agreement
Basic wage $600.00
PLUS
$0.90 for each customer served.
In a week when Jenny serves n customers, her weekly wage, W, in dollars, is given by
the formula
W = 600+ 0.90n.
(i) Determine Jenny's weekly wage if she served 230 customers.
(ii) In a good week, Jenny's wage is $1 000.00 or more. What is the LEAST number
of customers that Jenny must serve in order to have a good week?
(iii) At the same restaurant, Shawna is paid a weekly wage of $270.00 plus $1.50 for
each customer she serves.
If W, is Shawna's weekly wage, in dollars, write a formula for calculating Shawna's
weekly wage when she serves m customers.
(iv) In a certain week, Jenny and Shawna received the same wage for serving the same
number of customers.
How many customers did they EACH serve?
3 / 3
(i) If Jenny serves 230 customers, her weekly wage is
W = 600 + 0.90n = 600 + 0.90(230) = $807.00
Therefore, Jenny's weekly wage if she serves 230 customers is $807.00.
(ii) We want to find the least number of customers, n, that Jenny must serve in order to earn $1,000 or more. That is,
600 + 0.90n ≥ 1,000
0.90n ≥ 400
n ≥ 444.44
Since n must be a whole number, Jenny must serve at least 445 customers in order to earn $1,000 or more in a week.
(iii) Shawna's weekly wage, W, in dollars, when she serves m customers is given by the formula:
W = 270 + 1.50m
Therefore, Shawna's weekly wage when she serves m customers is $270.00 plus $1.50 for each customer she serves.
(iv) Let's assume that Jenny and Shawna received the same wage, W, for serving the same number of customers, x. Then we have:
Jenny's wage = 600 + 0.90x
Shawna's wage = 270 + 1.50x
Setting these two expressions equal to each other, we get:
600 + 0.90x = 270 + 1.50x
330 = 0.60x
x = 550
Therefore, Jenny and Shawna each served 550 customers.
write the equation in standard form for the circle with center (5,0) passing through (5, 9/2)
The equation in standard form for the circle with center (5,0) passing through (5, 9/2) is 4x² + 4y² - 40x + 19 = 0
Calculating the equation of the circleGiven that
Center = (5, 0)
Point on the circle = (5. 9/2)
The equation of a circle can be expressed as
(x - a)² + (y - b)² = r²
Where
Center = (a, b)
Radius = r
So, we have
(x - 5)² + (y - 0)² = r²
Calculating the radius, we have
(5 - 5)² + (9/2 - 0)² = r²
Evaluate
r = 9/2
So, we have
(x - 5)² + (y - 0)² = (9/2)²
Expand
x² - 10x + 25 + y² = 81/4
Multiply through by 4
4x² - 40x + 100 + 4y² = 81
So, we have
4x² + 4y² - 40x + 19 = 0
Hence, the equation is 4x² + 4y² - 40x + 19 = 0
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4) Ella drives 60 miles per hour. How far will she drive in 2% hours?
Answer: 1.2 miles
Step-by-step explanation:
1 hour = 60 min
60 x 0.02 = 1.2 1 minute and 20 seconds has elapsed
60 miles/ every 60 minutes or 1 mile a minute
1 x 1.2 = 1.2
she has traveled 1.2 miles
Answer: The answer is 120 mph (miles per hour)
Step-by-step explanation:
The one thing you need to do is to figure out how many mph did Ella drive for 2 hours.
So, you need to do 60 x 2, and you will get the answer 120.
And there's your answer!
Arun’s mother’s age is 6 years more than 4 times Arun’s age. If Arun’s age is m years, find
mother’s age
As per the unitary method, Arun's mother would be 36 years old if Arun is 3 years old.
Let Arun's age be m years.
Let Arun's mother's age be n years.
From the problem statement, we know that n = 4m + 6. This means that Arun's mother's age is directly proportional to Arun's age, with a constant ratio of 4 and a constant difference of 6.
To solve for n, we can use the unitary method. We can set up a proportionality between the two ages as follows:
n / m = (4m + 6) / m
To solve for n, we can cross-multiply to get:
n = m x (4m + 6)
Expanding the right-hand side of the equation, we get:
n = 4m² + 6m
Therefore, Arun's mother's age is 4m² + 6m years. We can simplify this expression by factoring out 2m:
n = 2m(2m + 3)
This gives us a simpler form of the equation for Arun's mother's age. To find her age, we simply substitute Arun's age (m) into this expression and simplify.
If Arun is 3 years old (m = 15), then his mother's age would be:
n = 2m(2m + 3) = 2(3)(2(3) + 3) = 2(3)(6) = 36
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Can someone help me with this please?
To solve the question asked, you can say: So, the other angle of the figure is 49 degree.
what are angles?In Euclidean geometry, an angle is a shape consisting of two rays, known as sides of the angle, that meet at a central point called the vertex of the angle. Two rays can be combined to form an angle in the plane in which they are placed. Angles also occur when two planes collide. These are called dihedral angles. An angle in planar geometry is a possible configuration of two rays or lines that share a common endpoint. The English word "angle" comes from the Latin word "angulus" which means "horn". A vertex is a point where two rays meet, also called a corner edge.
here the given angles are as -
107 + (180-156) + x = 180
as total angle sum of a triangle is 180
so,
x = 180 - 131
x = 49
So, the other angle of the figure is 49 degree.
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Isaiah is grounded and has to stay in his room all day. He made up a game where he throws balled-up paper called a "trashball" into his trash can. The diameter of the top of the trash can 1 the diameter of the top of is 12 in. Isaiah wants the "trashball" to have a diameter that is the trash can. > What should the diameter of Isaiah's "trashball" be? d Level G ? in. 12 in.
Answer:
Isiah Thomas
Step-by-step explanation:
I amazing fact
Answer:
the correct answer is 4
Step-by-step explanation:
yea sorry i don’t know step-by-step
Ten percent of customers who walk into a golf store purchase a golf club and 30% of customers purchase golf balls. Six percent of customers purchase both clubs and balls. The percentage of customers who do not purchase clubs or balls is______. A) 0.24 B) 0.34 C) 0.41 D) 0.66
The percentage of customers who do not purchase clubs or balls is 0.66 or 66%.
Ten percent of customers who walk into a golf store purchase a golf club and 30% of customers purchase golf balls. Six percent of customers purchase both clubs and balls. The percentage of customers who do not purchase clubs or balls is 0.66.
Given that, The percentage of customers who purchase golf clubs = 10%The percentage of customers who purchase golf balls = 30%The percentage of customers who purchase both clubs and balls = 6%To find out the percentage of customers who do not purchase clubs or balls, we have to subtract the percentage of customers who purchase either clubs or balls or both from 100%.
Percentage of customers who purchase either clubs or balls or both = 10% + 30% - 6% = 34% Percentage of customers who do not purchase clubs or balls = 100% - 34% = 66%.
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A dolphin was swimming 6 feet below sea level. The number line shows the
location of the dolphin. It then swam down 3 feet. Describe how to use the
number line to find the new location of the dolphin.
-10-9-8-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
OA. On the number line, move 3 units to the left. End at -9. The dolphin
was 9 feet below sea levelsm
OB. On the number line, move 3 units to the right. End at 9. The dolphin
was 9 feet above sea level.
OC. On the number line, move 3 units to the left. End at 3. The dolphin
was 3 feet above sea level.
OD. On the number line, move 3 units to the right. End at -3. The
dolphin was 3 feet below sea level.
On the number line, move 3 units to the left. End at -9. The dolphin was 9 feet below sea level.
What is location?
Location refers to the specific position or coordinates of an object or point in space or time. It can refer to the physical location of an object or place on Earth, such as a building or city, or the position of an astronomical object in the universe.
In a mathematical context, location is often expressed as a set of coordinates or points in a coordinate system.
Location is an important concept in various fields, including geography, cartography, astronomy, and mathematics, and is often used to describe and locate objects, places, or events in a precise and accurate manner.
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Your monthly take-home pay is $900. Your monthly credit card payments are about $135. What percent of your take-home pay is used for your credit card payments?
i came up with $765
Answer:15 percent
Step-by-step explanation:
Will give brainlest to first correct answer!!!
Evelyn has a bag that contains 3 red marbles and 2 blue marbles.
Evelyn randomly pulls a marble from the bag and then puts it back in the bag. She repeats this 20 times. How many times should she expect to draw a red marble from the bag?
Answer:
She will draw 120 times for a red marble
Step-by-step explanation:
A bus arrives every 10 minutes at a bus stop. It is assumed that the waiting time for a particular individual is a random variable with a continuous uniform distribution.
a) What is the probability that the individual waits more than 7 minutes?
b) What is the probability that the individual waits between 2 and 7 minutes?A continuous random variable X distributed uniformly over the interval (a,b) has the following probability density function (PDF):fX(x)=1/0.The cumulative distribution function (CDF) of X is given by:FX(x)=P(X≤x)=00.
In the following question, among the various parts to solve- a) the probability that the individual waits more than 7 minutes is 0.3. b)the probability that the individual waits between 2 and 7 minutes is 0.5.
a) The probability that an individual will wait more than 7 minutes can be found as follows:
Given that the waiting time of an individual is a continuous uniform distribution and that a bus arrives at the bus stop every 10 minutes.Since the waiting time is a continuous uniform distribution, the probability density function (PDF) can be given as:fX(x) = 1/(b-a)where a = 0 and b = 10.
Hence the PDF of the waiting time can be given as:fX(x) = 1/10The probability that an individual waits more than 7 minutes can be obtained using the complementary probability. This is given by:P(X > 7) = 1 - P(X ≤ 7)The probability that X ≤ 7 can be obtained using the cumulative distribution function (CDF), which is given as:FX(x) = P(X ≤ x) = ∫fX(t) dtwhere x ∈ [a,b].In this case, the CDF of the waiting time is given as:FX(x) = ∫0x fX(t) dt= ∫07 1/10 dt + ∫710 1/10 dt= [t/10]7 + [t/10]10= 7/10Using this, the probability that an individual waits more than 7 minutes is:P(X > 7) = 1 - P(X ≤ 7)= 1 - 7/10= 3/10= 0.3So, the probability that the individual waits more than 7 minutes is 0.3.
b) The probability that the individual waits between 2 and 7 minutes can be calculated as follows:P(2 < X < 7) = P(X < 7) - P(X < 2)Since the waiting time is a continuous uniform distribution, the PDF can be given as:fX(x) = 1/10Using the CDF of X, we can obtain:P(X < 7) = FX(7) = (7 - 0)/10 = 0.7P(X < 2) = FX(2) = (2 - 0)/10 = 0.2Therefore, P(2 < X < 7) = 0.7 - 0.2 = 0.5So, the probability that the individual waits between 2 and 7 minutes is 0.5.
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What is the quotient of 6. 208 × 10^9 and 9. 7 × 10^4 expressed in scientific notation?
The quotient of 6. 208 × 10⁹ and 9. 7 × 10⁴ expressed in scientific notation is 6.4 × 10¹².
Quotient:
The quotient is the answer we get when we divide one number by another. For example, if we divide the number 6 by 3, we get 2, the quotient. The quotient can be integer or decimal. For an exact division like 10 ÷ 5 = 2, we have a whole number as the quotient, and for a division like 12 ÷ 5 = 2.4, the quotient is a decimal number. The quotient can be greater than the divisor, but always less than the dividend.
Based on the given conditions, Formulate:
6.208× 10⁹ /9.7×10⁴
Simply using exponent rule with same base:
[tex]a^n. a^m = a^(n+m)[/tex]
= 6.208 × 1/9.7
Now,
the sum or difference = [tex]6.208*\frac{1}{9.7}[/tex] × 10¹³
Now solving, we get:
6.208/9.7 × 10¹³
Converting fraction into decimal, we get:
0.64× 10¹³
⇒ 6.4 × 10¹²
Therefore,
The quotient of 6. 208 × 10⁹ and 9. 7 × 10⁴ expressed in scientific notation is 6.4 × 10¹².
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Determine the overall resistance of a 100-meter length of 14 AWA (0.163 cm diameter) wire made of the following materials. a. copper (resistivity = 1.67x10-8 O•m) b. silver (resistivity = 1.59x10-8 O•m) c. aluminum (resistivity = 2.65x10-8 O•m) d. iron (resistivity = 9.71x10-8 O•m)
On the material was used, the 100-meter flex of 14 AWA wire's entirety would range. If the silver and copper cable are in 0.0013 and 0.0014, aluminum spans 0.002 and 0.004, and iron is between 0.007 and 0.008
What is a case of resistance?A force that works to slow something down or halt its progress: The air/wind drag slowed the vehicle down. the extent to which a material obstructs an electric charge from passing through it: There is little reluctance in copper.
The resistance (R) of a wire is given by the formula:
R = (ρ x L) / A
where:
ρ is the resistivity of the material
L is the length of the wire
A is the wire's cross-sectional size.
The cross-sectional area (A) of a wire with diameter d is given by the formula:
A = π x (d/2)²
where pi is a number in mathematics. (approximately equal to 3.14).
For a 100-meter length of 14 AWA wire with diameter 0.163 cm, we first need to convert the diameter to meters:
d = 0.163 cm = 0.00163 m
The cross-sectional area of the wire is then:
A = π x (0.00163/2)² = 2.087 x 10⁻⁶ m²
Using this value of A and the given resistivities, we can calculate the resistance for each material:
For copper:
R_copper = (1.67 x 10⁻⁸ O•m x 100 m) / (2.087 x 10⁻⁶ m²) = 0.00134 Ω
For silver:
R_silver = (1.59 x 10⁻⁸ O•m x 100 m) / (2.087 x 10⁻⁶ m²) = 0.00128 Ω
For aluminum:
R_aluminum = (2.65 x 10⁻⁸ O•m x 100 m) / (2.087 x 10⁶ m²) = 0.00199 Ω
For iron:
R_iron = (9.71 x 10⁻⁸ O•m x 100 m) / (2.087 x 10⁻⁶ m²) = 0.00735 Ω
Therefore, the overall resistance of the 100-meter length of 14 AWA wire made of these materials would depend on which material was used. If copper or silver were used, the resistance would be relatively low, around 0.0013-0.0014 Ω. If aluminum were used, the resistance would be higher, around 0.002 Ω. If iron were used, the resistance would be much higher, around 0.007 Ω.
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Find the following percentiles for the standard normal distribution. Interpolate where appropriate. (Round your answers to two decimal places.)a. 81stb. 19thc. 76thd. 24the. 10 th
The percentiles for the standard normal distribution
a. 0.93
b. -0.88
c. 0.67
d. -0.65
e. -1.28
To determine the percentiles for the standard normal distribution, use the standard normal distribution table. Percentiles for standard normal distribution are given by the standard normal distribution table.
The standard normal distribution is a special type of normal distribution with a mean of 0 and a variance of 1.
Step 1: Write down the given percentiles as a decimal and round to two decimal places.
For example, for the 81st percentile, 0.81 will be used.
Step 2: Use the standard normal distribution table to find the corresponding z-score.
Step 3: Round off the obtained answer to two decimal places.
a) 81st percentile:
The area to the left of the z-score is 0.81.
The corresponding z-score is 0.93.
Hence, the 81st percentile for the standard normal distribution is 0.93.
b) 19th percentile:
The area to the left of the z-score is 0.19.
The corresponding z-score is -0.88.
Hence, the 19th percentile for the standard normal distribution is -0.88.
c) 76th percentile:
The area to the left of the z-score is 0.76.
The corresponding z-score is 0.67.
Hence, the 76th percentile for the standard normal distribution is 0.67.
d) 24th percentile:
The area to the left of the z-score is 0.24.
The corresponding z-score is -0.65.
Hence, the 24th percentile for the standard normal distribution is -0.65.
e) 10th percentile:
The area to the left of the z-score is 0.10.
The corresponding z-score is -1.28.
Hence, the 10th percentile for the standard normal distribution is -1.28.
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Can some one solve this and show their work please
Answer:
m = 2n = 7Step-by-step explanation:
we solve with two equations between the corresponding sides
9m = 7m + 4
9m - 7m = 4
2m = 4
m = 2
----------------------------------
check
9 x 2 = 7 x 2 + 4
18 = 18
this answer is good
n + 6 = 2n - 1
n + 7 = 2n
7 = n
-----------------------------------
7 + 6 = 2 x 7 - 1
13 = 13
this answer is good
When a homeowner has a 25-year variable-rate mortgage loan, the monthly payment R is a function of the amount of the loan A and the current interest rate i (as a percent); that is, R = f(A). Interpret each of the following. (a) R140,000, 7) - 776.89 For a loan of $140,000 at 7% interest, the monthly payment is $776.89. For a loan of $140,000 at 7.7689% interest, 700 monthly payments would be required to pay off the loan. For a loan of $140,000 at 7% interest, 776.89 monthly payments would be required to pay off the loan. For a loan of $140,000 at 7.7689% interest, the monthly payment is $700.
The monthly payment required to pay off a loan of $140,000 at 7% interest would be $776.89 is the correct statement(A).
The statement given is describing a function that relates the monthly payment R of a 25-year variable-rate mortgage loan to the loan amount A and the current interest rate i.
The given values are R = $776.89 and A = $140,000, with an interest rate of 7%. This means that the monthly payment required to pay off a loan of $140,000 at 7% interest would be $776.89.
However, the other statements are incorrect interpretations. For instance, the statement "For a loan of $140,000 at 7.7689% interest, 700 monthly payments would be required to pay off the loan" is incorrect.
This is because the number of payments required to pay off a loan depends not only on the loan amount and interest rate, but also on the term of the loan.
Similarly, the statement "For a loan of $140,000 at 7% interest, 776.89 monthly payments would be required to pay off the loan" is also incorrect, as the number of payments required would be determined by the term of the loan.
Finally, the statement "For a loan of $140,000 at 7.7689% interest, the monthly payment is $700" is also incorrect. This is because, for the given loan amount and interest rate, the monthly payment required would be $776.89, as calculated above.
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Three softball players discussed their batting averages after a game.
Probability
Player 1 four sevenths
Player 2 five eighths
Player 3 three sixths
By comparing the probabilities and interpreting the likelihood, which statement is true?
The statement that is true is: Player 2 has the highest likelihood of getting a hit in their at-bats.
How to determine the true statement from the optionsBy comparing the probabilities, we can interpret the likelihood of each player getting a hit in their at-bats. The highest probability indicates the highest likelihood of getting a hit.
Comparing the probabilities of the three players, we can see that:
Player 2 has the highest probability (5/8), which means they are the most likely to get a hit in their at-bats.
Player 1 has a lower probability (4/7) than Player 2, but a higher probability than Player 3. This means they are less likely to get a hit than Player 2, but more likely to get a hit than Player 3.
Player 3 has the lowest probability (3/6 = 1/2) of getting a hit, which means they are the least likely to get a hit in their at-bats.
Therefore, the statement that is true is: Player 2 has the of getting a hit in their at-bats.
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Seven bags of cement weighs 3kg 52g what Is the weight of the each?
Answer:
436g
Step-by-step explanation:
1kg=1000g
3kg=3000g
3000+52=3052
3052÷7=436
A triangle has a side that is 5 inches long that is adjacent to an angle of 61. In addition, the side oppositethe 61 angle is 4,8 inches long. There are two triangles with these measurements. For each one,determine the other two angles of the triangle and the length of the third side..acute:(a) The triangle in which the angle opposite the 5-inch side-The angle between the two given sides measuresnearest tenth of a degree.)The third angle measuresThe remaining side is approximatelyan inch.)(b) The triangle in which the angle opposite the 5-inch side is obtuse:The angle between the two given sides measuresnearest tenth of andegree.)WThe third angle measuresThe remaining side is approximatelyan inch.)degrees. (Round to thedegrees. (Round to the nearest tenth of a degree.)Ainches long. (Round to the nearest tenth ofdegrees. (Round to thedegrees. (Round to the nearest tenth of a degree.)inches long. (Round to the nearest tenth of an inch
The two remaining angles are 58°, and the length of the third side of the triangle is 6.5 inch.
In order to determine the other two angles of each triangle as well as the length of the third side, we need to use the Cosine Rule. According to the Cosine Rule, for any triangle with sides of length a, b, and c, and angles of A, B, and C, the following equation holds:
[tex]c^2 = a^2 + b^2 - 2ab cos(C)[/tex]
For the first triangle, we are given that the side of length 5 is adjacent to an angle of 61°. Therefore, a = 5, C = 61°. Using the information provided, we can also determine that b = 4.8. Substituting these values into the Cosine Rule equation, we get:
[tex]c^2 = (5)^2 + (4.8)^2 - 2(5)(4.8) cos(61°)[/tex]
We can solve this equation to get c = 6.5. Therefore, the length of the third side in the first triangle is 6.5. Additionally, we can use the Triangle Angle Sum theorem to determine the other two angles. According to this theorem, the sum of the three angles of a triangle is 180°. Therefore, for the first triangle, the two remaining angles are 180 - 61 - (180 - 61) = 58°.
For the second triangle, we use the same process, but with the given side lengths reversed. That is, we set a = 4.8, b = 5, and C = 61°. Again, substituting these values into the Cosine Rule equation, we get:
[tex]c^2 = (4.8)^2 + (5)^2 - 2(4.8)(5) cos(61°)[/tex]
We can solve this equation to get c = 6.5. Therefore, the length of the third side in the second triangle is also 6.5. We can use the Triangle Angle Sum theorem again to determine the other two angles. Again, for the second triangle, the two remaining angles are 180 - 61 - (180 - 61) = 58°.
In conclusion, for each triangle, the two remaining angles are 58°, and the length of the third side is 6.5 inch.
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Which state is located at point C?
a map of the United States. New York, Indiana, and Kansas are labeled. There is an A marking the state south of New York along the Atlantic coast. There is a B marking the state east of Indiana. There is a C marking the state north of Indiana. There is a D marking the state northeast of Kansas. There is an E marking the state south of Kansas.
New Jersey
Ohio
Michigan
Iowa
According to the information provided, the state is at point C, Michigan.
Based on the information provided, the state located at point C is Michigan.
What is logical thinking?Logical reasoning consists of aptitude questions that require logical analysis to arrive at a suitable solution. Most of the questions are conceptual, the rest are unconventional.
Logical thinking follows he is divided into two types.
Oral reasoning:
It is the ability to logically understand concepts expressed in words and solve problems. Oral reasoning tests your ability to extract information and meaning from sentences. Non-verbal thinking:
It is the ability to logically understand concepts represented by numbers, letters, and combinations of numbers and words and solve problems. Nonverbal reasoning tests your ability to reason and guide the logic and implications of information in a problem.
Much of the logic curriculum can be classified into his two types above.
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Susan jogged for 1 1/2hours on Monday and 90 minutes on Tuesday. On which day did she jog longer?
question if all other factors are held constant, which of the following results in an increase in the probability of a type ii error? responses the true parameter is farther from the value of the null hypothesis. the true parameter is farther from the value of the null hypothesis. the sample size is increased. the sample size is increased. the significance level is decreased. the significance level is decreased. the standard error is decreased. the standard error is decreased. the probability of a type ii error cannot be increased, only decreased.
If all other factors are held constant, decreasing the significance level results in an increase in the probability of a type II error. This is true. we can say that the probability of making a type II error increases when the significance level is lowered.
What is a type II error? In hypothesis testing, a type II error occurs when a false null hypothesis is not rejected. When there is a real effect and the null hypothesis is false, this happens. It's a mistake that occurs when a researcher fails to reject a false null hypothesis.
A false negative is another term for a type II error. The power of the test, the size of the sample, the confidence level, and the effect size are all factors that influence the probability of making a type II error. Only if we decrease the significance level can the probability of a type II error be increased.
What is the significance level? The significance level is also known as alpha. It is the probability of rejecting a null hypothesis when it is true. It is represented by α. It is usually set at 0.05 or 0.01 in most studies. When the significance level is lowered, the probability of making a type I error decreases, but the probability of making a type II error increases. Therefore, we can say that the probability of making a type II error increases when the significance level is lowered.
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cosθ(1+tanθ)=cosθ+sinθ
Answer:
Starting with the left side of the equation:
cosθ(1+tanθ) = cosθ(1+sinθ/cosθ) (since tanθ = sinθ/cosθ)
= cosθ + sinθ
Therefore, the left side of the equation is equal to the right side of the equation, which means that cosθ(1+tanθ) = cosθ+sinθ is true.
Which of the following are equations of straight lines? Select all that apply. Please keep in mind that for questions like this where there are one or more correct answers, Canvas will deduct points for incorrect selections. yhat = 23 + 4w yhat = 2c +34 yhat = 2h yhat= d2 + 3 yhat = 23r+ 4 yhat=2s + 3t yhat= 3
The equations of straight lines are \hat{y} = 2h, \hat{y} = 23r + 4 and \hat{y}= 2s + 3t. Option(A),(B) and (F) are correct.
A line in the coordinate plane can be described with the help of a linear equation, that is, an equation that has a first-degree expression, like y = 2x – 3.
There are many ways to put the equation of a line in the form y = mx + b,
where m is the slope and
b is the y-intercept,
but they all require the use of algebraic properties of equations, such as addition, subtraction, multiplication, division, and substitution.
The equations of straight lines among the following are: \hat{y} = 2h, \hat{y} = 23r + 4 and \hat{y}= 2s + 3t
Hence, the correct options are:Option A: \hat{y} = 2h , Option B: \hat{y} = 23r + 4 and Option F: \hat{y}= 2s + 3t.
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Hi help me with this question
Solve for X
30=5(X+5)
X=?
The solution for X in equation 30=5(X+5)X is X= 1.
To solve the equation, we can start by distributing the 5 on the right-hand side of the equation, which gives us:
30 = 5X + 25X
Combining like terms, we get:
30 = 30X
Dividing both sides by 30, we get:
X = 1
However, we need to check whether this value satisfies the original equation. Plugging X=1 into the equation gives us:
30 = 5(1+5)(1)
30 = 5(6)
30 = 30
Therefore, the only valid solution is X=1.
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16 ft
Find the area.
20 ft
12 ft
10 ft
15 ft A = [?] ft²
Round to the nearest
hundredth.
then the area would be: [tex]Area=\frac{(a+b)}{2*h}[/tex] = (16 ft + 10 ft)/2 x 15 ft = 150 ft²
What is area?Area is a mathematical term that refers to the measurement of the size or extent of a two-dimensional region or surface. It is typically expressed in square units, such as square meters (m²), square centimeters (cm²), square feet (ft²), or square inches (in²). The area of a shape is determined by multiplying the length and width of the shape in the case of a rectangle or square, or by using more complex formulas for irregular shapes such as circles, triangles, or polygons. The concept of area is important in various fields such as mathematics, geometry, physics, engineering, and architecture, among others.
by the question.
. If we assume that these are the dimensions of a rectangle, then the area would be:
Area = length x width = 20 ft x 12 ft = 240 ft²
However, if we assume that the area is a trapezoid with a height of 15 ft, and the parallel sides of length 16 ft and 10 ft.
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a pastry chef accidentally inoculated a cream pie with six s. aureus cells. if s. aureus has a generation time of 60 minutes, how many cells would be in the cream pie after 7 hours?
After the time of seven hours, the cream pie would have approximately 768 S. aureus cells after 7 hours with a generation time of 60 minutes.
How many cells would be in the cream pie after 7 hours?Six S. aureus cells have been accidentally inoculated into a cream pie. S. aureus has a generation time of 60 minutes. S. aureus is a pathogenic bacterium found in the environment, as well as on the skin, and in the upper respiratory tract.
The generation time of this bacterium is 60 minutes, meaning that a single bacterium can produce two new cells in 60 minutes.
If there are 6 S. aureus cells in a cream pie, the number of bacteria will continue to increase as time passes.
The number of generations (n) in seven hours is calculated as:
n = t/g
n = 7 hours × 60 minutes/hour/60 minutes/generation = 7 generations
The number of cells in the cream pie after 7 hours is calculated as :
N = N₀ × 2ⁿ
N = 6 cells × 2⁷
N = 768 cells
Therefore, after seven hours, the cream pie would have approximately 768 S. aureus cells.
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What’s the area?
7 yd
4 yd
7 yd
3 yd
The area is 49 square yards.
HELPPPPPPP PLEASEEEEEEEEEEEEEEE
y=mx+b
The required equation of straight line is y = 0.03x + 20.
What is an equation?
A mathematical equation states that two quantities or values are identical. Equations are used when more than one factor has to be examined in order to fully understand or explain a situation.
The general form of an equation is y = mx + b, where m is the slope of equation and b is a constant.
From the given graph we get 2 points.
i.e., (0, 20) and (2000, 80)
Slope of the line is
[tex]m=\frac{80-20}{2000-0}\\\ \ = \frac{60}{2000}\\ = \frac{6}{200} \\= \frac{3}{100}[/tex]
Then the equation will be
[tex]y-20=\frac{3}{100}(x-0)\\\Rightarrow y-20=0.03x\\\Rightarrow y-0.03x-20=0\\\Rightarrow y = 0.03x+20[/tex]
Therefore, the required equation is y = 0.03x + 20, calculating with the help of given graph.
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=
Suppose that a new employee starts working at $7.32 per hour and receives a 4% raise each year. After time t, in years, his hourly wage is given by the equation y = $7.32(1.04). Find
the amount of time after which he will be earning $10.00 per hour.
After what amount of time will the employee be earning $10.00 per hour?
years (Round to the nearest tenth of a year as needed.)
HELP PLEASE
Using the equation [tex]y = $7.32(1.04)^t[/tex], the amount of time after which the employee will be earning $10.00 is about 9.64 years, or approximately 9 years and 8 months.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
We can start by setting up the equation for the employee's hourly wage y after t years -
[tex]y = $7.32(1.04)^t[/tex]
We want to find the amount of time t after which the employee will be earning $10.00 per hour, so we can set y equal to 10 and solve for t -
[tex]10 = $7.32(1.04)^t[/tex]
Dividing both sides by $7.32, we get -
[tex]1.367 = 1.04^t[/tex]
Taking the natural logarithm of both sides, we get -
[tex]ln(1.367) = ln(1.04^t)[/tex]
Using the property of logarithms that [tex]ln(a^b) = b ln(a)[/tex], we can simplify the right-hand side -
ln(1.367) = t ln(1.04)
Dividing both sides by ln(1.04), we get -
t = ln(1.367)/ln(1.04) ≈ 9.64
Therefore, the employee will be earning $10.00 per hour after about 9.64 years.
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If the pyramids below are similar, what is the
ratio of their surface area?
21 in
14 in
A. 3:2
B. 6:4
C. 9:4
D. 27:8
The required ratio of the surface area of the given pyramids is (A) 3:2.
What are ratios?A ratio can be used to show a relationship or to compare two numbers of the same type.
To compare things of the same type, ratios are utilized.
We might use a ratio, for example, to compare the proportion of boys to girls in your class.
If b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio.
A proportion is an equation that equalizes two ratios.
For illustration, the ratio may be expressed as follows: 1: 3 in the case of 1 boy and 3 girls (for every one boy there are 3 girls)
So, the given surface area is:
- 21 in
- 14 in
Now, calculate the ratio as:
= 21/14
= 3/2
= 3:2
Therefore, the required ratio of the surface area of the given pyramids is (A) 3:2.
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