Answer:
The time it will take to paint 60 banners is 12 hours.
Step-by-step explanation:
The question is:
Several students from one school painted 15 banners in 3 hours. How many hours will it take for students to paint 60 banners
Solution:
The Unitary method is a mathematical procedure to determine the value of 1 unit from n unit values.
It is provided that the time it takes to paint 15 banners is, t = 3 hours.
Then the time it should have taken to paint 1 banner is, [tex]\frac{3}{15}=\frac{1}{5}\ hours[/tex].
Compute the time it will take to paint 60 banners as follows:
Time = [tex]60\times \frac{1}{5}=12[/tex]
Thus, the time it will take to paint 60 banners is 12 hours.
In your homework, you were introduced to a game, called Under-or-Over-Seven. It has many rules. Here is the particular rule that we are going to use for this question: a pair of fair dice is rolled once, and the resulting sum determines whether the player wins or loses his/her bet; the player wins $9 if the result of the roll is exactly equal to 7 and loses $3 otherwise. Compute the expected value of this game (i.e., the expected gain or loss).
Answer:
EX=-$1
Step-by-step explanation:
Expected Value of Probability Distribution
Assume a discrete probability distribution is
[tex]P=\{p1,p2,p3,...pn\}[/tex]
For
[tex]X=\{x1,x2,x3,...xn\}[/tex]
The expected value is
[tex]EX=\sum x_i.p_i[/tex]
We have two possible outcomes from our random experience: The sum of the die is 7 or different from 7. If it sums 7, the player wins $9, otherwise, they lose $3. Thus
[tex]x=\{9,-3\}[/tex]
We must find the probability of having a 7. Each dice can be a 1, 2, 3 ,4 , 5, or 6. The combinations to sum 7 are 1+6, 2+5, 3+4, 4+4, 5+2, and 6+1. That is 6 possibilities out of 36 in total. The probability of having a 7 is
[tex]\displaystyle p_1=\frac{6}{36}=\frac{1}{6}[/tex]
The probability of not getting 7 is the negation of the previous event
[tex]\displaystyle p_2=1-\frac{1}{6}=\frac{5}{6}[/tex]
The probability set is:
[tex]\displaystyle P=\left\{\frac{1}{6},\frac{5}{6}\right\}[/tex]
The expected value is:
[tex]\displaystyle EX=9\cdot \frac{1}{6}-3\cdot \frac{5}{6}[/tex]
[tex]\displaystyle EX=\frac{3}{2}-\frac{5}{2}=-1[/tex]
Therefore, the player can expect to lose $1
The expected value of the game "Under-or-Over-Seven" is a loss of $1, computed by considering the probabilities of winning $9 or losing $3 based on dice sums.
To compute the expected value of the game, we need to consider all possible outcomes and their associated probabilities.
1. The sum of two fair dice can range from 2 to 12.
2. The probability of each sum can be calculated by considering all possible combinations of the dice.
Here's the breakdown of the sums and their probabilities:
- Sum of 2: Probability = 1/36
- Sum of 3: Probability = 2/36
- Sum of 4: Probability = 3/36
- Sum of 5: Probability = 4/36
- Sum of 6: Probability = 5/36
- Sum of 7: Probability = 6/36
- Sum of 8: Probability = 5/36
- Sum of 9: Probability = 4/36
- Sum of 10: Probability = 3/36
- Sum of 11: Probability = 2/36
- Sum of 12: Probability = 1/36
Now, let's calculate the expected value:
[tex]\[ E(X) = (P(X=7) \times \$9) + (P(X\neq7) \times (-\$3)) \][/tex]
[tex]\[ E(X) = (\frac{6}{36} \times \$9) + (\frac{30}{36} \times (-\$3)) \][/tex]
[tex]\[ E(X) = (\frac{6}{36} \times \$9) - (\frac{30}{36} \times \$3) \][/tex]
[tex]\[ E(X) = \frac{54}{36} - \frac{90}{36} \][/tex]
[tex]\[ E(X) = \frac{-36}{36} \][/tex]
E(X) = -$1
So, the expected value of the game is a loss of $1.
The expression ?/g+1 + (2g+1/g - g+1/2g) simplifies to 3g^2+10g+1/2g^2+2g. The unknown value is...
A.) 1
B.) 2
C.) 3
D.) 4
Answer: 3
Step-by-step explanation:
E2020 answer
Answer:
3
Step-by-step explanation:
answer on edge
Natalie consumes only apples and tomatoes. Her utility function is U(x, y) = x 2y 8 , where x is the number of apples consumed and y is the number of tomatoes con-sumed. Natalie’s income is $320, and the prices of apples and tomatoes are $4 and $3, respectively. How many apples will she consume?
Answer:
16 apples.
Step-by-step explanation:
[tex]U(x, y) = x^2y^8[/tex]
[tex]MU_x =\frac{\partial U}{\partial x} = 2xy^8\\MU_y = \frac{\partial U}{\partial x} = 8x^2y^7\\[/tex]
Price of apples, Px=$4
Price of tomatoes, Py=$3
Ratio of their Marginal Utilities
[tex]\frac{MU_x}{MU_y} = \frac{Px}{Py}[/tex]
[tex]\frac{y}{4x} = \frac{4}{3}[/tex]
[tex]y=\frac{16x}{3}[/tex]
Since Natalie’s income is $320
320 = xPx+yPy
[tex]320=4x + 3*\frac{16x}{3} \\320= 4x+16x = 20x\\x=\frac{320}{20} = 16\\Also\\y=\frac{16x}{3}=\frac{16X16}{3}=\$85.33[/tex]
Since x=16, Natalie will consume 16 apples.
Given Natalie's budget and the prices of apples and tomatoes, plus the fact that her utility function indicates she consumes two as many tomatoes as apples, we determined that Natalie will consume up to 32 apples under these conditions.
Explanation:To determine how many apples Natalie will consume, we first need to solve the utility maximization problem where she chooses 'x' and 'y' to maximize her utility subject to her budget constraint. This problem is typically solved using calculus, but here is a simplified way of solving it:
Firstly, let's consider Natalie's budget constraint. With $320, the prices of apples and tomatoes being $4 and $3 respectively, her budget constraint is $4x + $3y ≤ $320.
Due to the nature of Natalie's utility function U(x, y) = x 2y 8, it's clear that for every apple she buys, she consumes twice as many tomatoes (since y=2x). Replacing 'y' in the budget constraint yields to $4x + $3(2x) ≤ $320, or $10x ≤ $320.
Finally, solving x gives usx ≤ 32, that is, Natalie will consume up to 32 apples.
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Rover’s dog bowl is pictured below. Approximately how much water does it hold? Use 3.14 for π and round your answer to the nearest cubic inch.
Answer:
57 in³
Step-by-step explanation:
Area of cylinder= [tex]\pi {r}^{2} h[/tex]
Let's find the radius.
Radius= Diameter ÷2
Radius= 6 ÷2
Radius= 3 in.
Area of Rover's dog bowl
= 3.14(3)²(2)
= 56.52
= 57 in³ (nearest cubic inch)
Answer:
57 in3
Step-by-step explanation:
What is the volume of the prism?
Answer: the volume is: 280.8
Step-by-step explanation:
volume= length x width x height
Answer:
140.4 cm^3
Step-by-step explanation:
The formula for calculating volume of a triangular prism : 1/2 × h × l × b
1/2 × 4 × 9 × 7.2 = 140.4 cm^3
The function rule of a certain function is y = -3 x + 1. If the input is 7, what is the output?
Here are the choices,
1. -22
2. -21
3. -20
4. -24
For the following problems, identify the type of investigation used (i.e., non-experimental, experimental, or quasi- experimental) and all independent, dependent, and, if any, extraneous variables
A researcher examines the effects of controlled breaks on reaction times of Air Traffic Controllers. The controllers are randomly assigned to two groups. Group 1 has 20 controllers who spend 45 minutes on a break in a quiet room, with no talking, TV, or other electronics. Group 2 has 20 controllers who spend their 45 minutes on a break in a common area break room where people are allowed to talk, watch TV, or use electronic devices. Following the breaks, each group of controllers returned to their shift where their reaction times were assessed.
What type of investigation is this?
What are the variables?
Answer:
Type of investigation = Experimental
Dependent variable = The reaction time of the controllers
Independent variable = Controlled breaks
Step-by-step explanation:
A researcher is examining the effects of controlled breaks on reaction times of Air Traffic Controllers.
The controllers are randomly assigned to two groups.
Group 1 and Group 2
Group 1 has 20 controllers who spend 45 minutes on a break in a quiet room, with no talking, TV, or other electronics.
Group 2 has 20 controllers who spend their 45 minutes on a break in a common area break room where people are allowed to talk, watch TV, or use electronic devices.
After the breaks, the reaction times of controllers in the two groups were measured.
Type of investigation?
This is clearly an experimental type of investigation where the researcher performs an experiment and after that measures the results.
Type of variables involved?
In this experimental investigation, we have both dependent as well as independent variable.
The controlled break is the independent variable since it can be manipulated by the researcher.
The reaction time of the controllers is the dependent variable since it is being measured and is expected to get affected when the independent variable is manipulated that is controlled breaks.
Final answer:
This is an experimental investigation where the effects of controlled breaks on reaction times of Air Traffic Controllers are examined. The independent variable is the type of break, and the dependent variable is the reaction times of the controllers.
Explanation:
The type of investigation used in this study is an experimental investigation. The independent variable in this study is the type of break given to the Air Traffic Controllers, with two levels: controlled breaks in a quiet room and breaks in a common area with allowed talking, TV, and electronic devices. The dependent variable is the reaction times of the controllers after their breaks. There are no extraneous variables mentioned in the given information.
PLEASE HELP. I’ll mark you as brainliest if correct
Which of the following could be a value that represents x as a solution?
X>9
A. 0
B. 8
C. 9
D. 18
Which of the following represents K as a solution?
K > 55. There’s a greater or equal sign
A. Any number greater than 55
B. Any number less than or equal to 55
C. Any number less than 55
D. Any number greater than or equal to 55
Answer:
Both of them are D
Step-by-step explanation:
1ST QUESTION
D. 18
2ND QUESTION
D. Any number greater than or equal to 55
brainliest?
There are 946 milliliters in a quart. There are 2 pints in a quart. How many milliliters are in 5 pints?
Answer:
473 milliliters in 1 pint
Step-by-step explanation:
divide 946 by 2
Answer:
There are 473 milliliters in 1 pint so 5 pints would be 2,365
Step-by-step explanation:
Angle KJL measures (7x - 8)o. Angle KML measures (3x + 8)o.
Circle N is shown. Angles K J L and K M L intersept arc K L. Angles J K M and J L M intercept arc J M.
What is the measure of arc KL?
20°
40°
48°
96°
The correct answer is 96 degrees for the circle.
Equation
Since angles KJL and KML are opposite angles of a cyclic quadrilateral, their sum is 180 degrees.
(7x - 8) + (3x + 8) = 180° is the equation.
10x = 172
x = 17.2
Therefore, angle KJL measures 7(17.2) - 8 = 115.4 degrees, and angle KML measures 3(17.2) + 8 = 52.6 degrees.
The measure of arc KL is equal to the sum of the measures of angles KJL and KML:
115.4 + 52.6 = 168
So the measure of arc KL is 168 degrees.
Therefore, the correct answer is 96 degrees, which matches one of the answer choices.
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Inquiries arrive at a record message device according to a Poisson process of rate 15 inquiries per minute. The probability that it takes more than 12 seconds for the first inquiry to arrive is approximately _________.
Answer:
0.0498 = 4.98%
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given time interval.
Inquiries arrive at a record message device according to a Poisson process of rate 15 inquiries per minute.
Each minute has 60 seconds.
So a rate of 1 inquire each 4 seconds.
The probability that it takes more than 12 seconds for the first inquiry to arrive is approximately
Mean of 1 inquire each 4 seconds, so for 12 seconds [tex]\mu = \frac{12}{4} = 3[/tex]
This probability is P(X = 0).
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498[/tex]
The probability that it takes more than 12 seconds for the first inquiry to arrive in a Poisson process at a rate of 15 inquiries per minute is calculated using the exponential distribution formula: e^{-15*0.2}.
The student is asking for the probability that it takes more than 12 seconds for the first inquiry to arrive at a record message device, with inquiries arriving according to a Poisson process with a rate of 15 inquiries per minute. Since the time between arrivals in a Poisson process follows an exponential distribution, we can calculate this probability using the exponential distribution's formula.
The mean interval between inquiries is the inverse of the rate, which for 15 inquiries per minute is 1/15 minute per inquiry, or 4 seconds per inquiry. To convert minutes to seconds, multiply by 60. Therefore, the average interval is 4 seconds.
The exponential distribution gives us the probability that the time until the first event (inquiry) exceeds a certain amount, t, which is P(T > t) = e-λ*t, where λ is the rate and T is the time. In this case, t is 12 seconds or 0.2 minutes. Therefore, the probability (P) that the time is more than 12 seconds is: P(T > 0.2) = e-15*0.2.
A rectangle has a length of 11 meters less than 10 times its width. If the area of the rectangle is 9888 square meters, find the length of the rectangle.
Step-by-step explanation:
The Length ,
L
=
284
f
t
.
Explanation:
Given:
Rectangle
Area,
A
=
8804
f
t
2
let W bet he width of the rectangle
L be the length of the rectangle
L
=
10
W
−
26
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q
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a
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n
1
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factor
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5
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answer
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this is discarded since this will yield a negative
To find the length of the rectangle, set up an equation using the given information. Solve the quadratic equation to find the width and substitute it back to find the length.
Explanation:To find the length of the rectangle, we can set up an equation using the given information. Let's assume the width of the rectangle is 'w' meters. According to the problem, the length of the rectangle is 10 times its width minus 11 meters, so it can be represented as 10w - 11 meters. The area of the rectangle is given as 9888 square meters. We know that the formula for the area of a rectangle is length times width, so we can write the equation as:
w (10w - 11) = 9888
Expanding the equation and rearranging terms, we get:
10w^2 - 11w - 9888 = 0
Now, we can solve this quadratic equation for 'w' and find the width of the rectangle. Once we have the width, we can substitute it back into the expression for the length (10w - 11) to find the length of the rectangle.
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A particular variety of watermelon weighs on average 21.3 pounds with a standard deviation of 1.07 pounds. Consider the sample mean weight of 90 watermelons of this variety. Assume the individual watermelon weights are independent. a. What is the expected value of the sample mean weight
Final answer:
The expected value of the sample mean weight of watermelons, given a population mean of 21.3 pounds, is also 21.3 pounds.
Explanation:
Expected Value of the Sample Mean Weight of Watermelons
If we have a population in which the average watermelon weighs 21.3 pounds with a standard deviation of 1.07 pounds, and we consider the sample mean weight of 90 watermelons, we can calculate the expected value of this sample mean. In statistics, the expected value of the sample mean is the same as the population mean when the samples are drawn from the population independently. Thus, the expected value of the sample mean weight for the watermelons is 21.3 pounds.
Suppose the investigator believes that virtually all values of breakdown voltage are between 40 and 70. What sample size would be appropriate for the 95% CI to have a width of 2 kV? (so that m is estimated to within 1 kV with 95% confidence)
Approximately 215 samples are needed for a 95% confidence interval estimating the mean breakdown voltage with a 2 kV width and a 1 kV margin of error, assuming the range is 40 to 70 kV.
To determine the required sample size for estimating the mean breakdown voltage with a 95% confidence interval (CI) width of 2 kV and an estimated margin of error (m) of 1 kV, you can use the formula:
[tex]\[ n = \left(\frac{{Z^2 \cdot \sigma^2}}{{m^2}}\right) \][/tex]
Where:
- n is the required sample size,
- Z is the Z-score corresponding to the desired confidence level (for 95%, it's approximately 1.96),
- [tex]\( \sigma \)[/tex] is the estimated standard deviation of the population.
Since you mentioned the investigator believes breakdown voltage is between 40 and 70, assuming a uniform distribution, you might consider using [tex]\( \sigma = \frac{{\text{{range}}}}{4} \)[/tex] as an approximation. Therefore,
[tex]\[ \sigma = \frac{{70 - 40}}{4} = 7.5 \][/tex]
Now plug these values into the formula:
[tex]\[ n = \left(\frac{{1.96^2 \cdot 7.5^2}}{{1^2}}\right) \][/tex]
Let's calculate the required sample size n:
[tex]\[ n = \frac{{(1.96)^2 \cdot (7.5)^2}}{{1^2}} \]\[ n = \frac{{3.841 \cdot 56.25}}{{1}} \]\[ n \approx \frac{{214.6}}{{1}} \]\[ n \approx 214.6 \][/tex]
So, the required sample size for the 95% confidence interval to have a width of 2 kV (with a margin of error of 1 kV) is approximately 215.
Therefore, the investigator would need a sample size of about 215 to estimate the mean breakdown voltage with the desired level of confidence and precision.
What is the probability that a five-card poker hand contains a flush (including straight and royal flushes), that is, five cards of the same suit? (Enter the value of probability in decimals. Round the answer to five decimal places.)
Answer:
0.00198
Step-by-step explanation:
The number of total ways that 5 cards can be selected from a deck of 52 cards is given as
⁵²C₅ = 2,598,960 ways.
Number of ways a flush, including straight and royal flushes, that is, five cards of the same suit can happen is given by
⁴C₁ × ¹³C₅ = 4 × 1287 = 5148
Note that of the 52 cards, each suit has 13 cards, So, ⁴C₁ represents selecting a suit out of 4 different suits and ¹³C₅ represents selecting 5 cards out of 13 cards thay a suit contains.
So, the probability of a flush
= 5148 ÷ 2,598,960 = 0.0019807923 = 0.00198 to 5 d.p
Hope this Helps!!!
The probability of five cards of the same suit is 0.00198
Probability of any event happen is calculated by, divide favourable number of outcomes by total number of outcomes.
The number of total ways that 5 cards can be selected from a deck of 52 cards is given as
Total outcomes = ⁵²C₅ = 2598960
Number of ways a flush, including straight and royal flushes, that is, five cards of the same suit can happen is given by
Number of favourable outcomes = ⁴C₁ × ¹³C₅ = 4 × 1287 = 5148
⁴C₁ represents selecting a suit out of 4 different suits .
¹³C₅ represents selecting 5 cards out of 13 cards that a suit contains.
Therefore, the probability that a five-card poker hand contains a flush,
=[tex]\frac{5148}{2598960}=0.00198[/tex]
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Roll the number cube 20 times to represent 20 purchases. What is the experimental probability of receiving a 50% coupon? Write the probability as a decimal.
Answer:
0.10
Step-by-step explanation:
The experimental likelihood of getting a 50% coupon is thus 2/20, or 0.1 to the decimal place.
What is the probability?The likelihood of rolling any one of the number cube's 6 equally likely results is 1/6. We must roll the number cube 20 times and tally how many times we receive a 50% discount in order to determine the experimental chance of doing so.
Assume that rolling a 1, 2, or 3 means you won't receive a coupon, a 4 means you'll receive a 25% coupon, a 5 means you'll receive a 50% coupon, and a 6 means you'll receive a 75% coupon.
The following outcomes are possible after 20 rolls of the number cube:
10 rolls were not given a coupon (50%)Getting a discount of 25%: 4 rolls (20%)2 rolls (10%) when using a 50% discount.4 rolls (20%) when using a 75% discount.More about the probability link is given below.
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Simplify.
Remove all perfect squares from inside the square root.
V72 =
Final answer:
To simplify √72 by removing all perfect squares, you factor 72 into 2³ × 3², then take out the square root of 4 and 9 to get 6√(2) as the simplified result.
Explanation:
To simplify the square root of 72 and remove all perfect squares from inside the square root, you first need to factor 72 into its prime factors. The prime factorization of 72 is 2³ × 3². This can be rewritten as (2² × 3²) × 2, which simplifies to (4 × 9) × 2.
Since the square root of 4 and 9 are perfect squares, you can take them out of the square root, resulting in √(4) × √(9) × √(2) = 2 × 3 × √(2) = 6√(2).
Therefore, the simplified form of √72 is 6√(2), which removes all perfect squares from inside the square root.
I have a choice between dominoes pizza or pizza hut what should I devour
Answer: Obviously chose Pizza Hut, as no other pizza place can out pizza the hut.
Answer:
I devour the souls of the innocent
Step-by-step explanation:
XD what question is this???
Write the ratio of hands to cellphones in simplest form. it was 8 hands and 4 phones
Answer:
The ratio is 2:1
Step-by-step explanation:
This is since there are 2 times the amount of hands as there are phones
−3x + y = 4,
−9x + 5y = −1
find x and y
Answer:
9x - 3y = -12
-9x +5y = -1
2y = -13
y = -13/2
-3x - 13/2 = 8/2
-3x = 21/2
-6x = 21
x = -21/6 = -7/2
(-7/2, -13/2)
as part of a fundraiser, a local organization collected 418 returnable bottles and cans, some worth 5 cents each and the rest worth 10 cents each. if the total value of the cans and bottles was $25.00, how many 5 cent bottles or cans and how many 10 cent bottles or cans were collected
Using a system of equations, it was determined there were 336 bottles worth 5 cents each and 82 bottles worth 10 cents each, summing up to a total of $25.
The local organization collected 418 returnable bottles and cans, some worth 5 cents each and the rest worth 10 cents each. The total value was $25.00. We need to find out how many bottles were worth 5 cents and how many were worth 10 cents.
We can set up two equations to solve this problem using algebra. Let's assume that the number of 5-cent bottles is x and the number of 10-cent bottles is y.
The first equation will represent the total number of bottles: x + y = 418.
The second equation will represent the total value of these bottles: 0.05x + 0.10y = 25.
To solve this system of equations, we can multiply the second equation by 100 to eliminate the decimals and then apply the method of substitution or elimination to find the values of x and y.
Rewrite the second equation without decimals: 5x + 10y = 2500.
Multiply the first equation by 5: 5x + 5y = 2090.
Subtract the modified first equation from the second equation: 5y = 410.
Divide both sides by 5 to find y: y = 82.
Substitute y = 82 into the first equation and solve for x: x = 418 - 82 = 336.
Therefore, there were 336 bottles or cans worth 5 cents each and 82 bottles or cans worth 10 cents each.
A bag has 2 blue marbles, 3 red marbles, and 5 white marbles. Which events have a probability greater than 5 ? Select three
options
choosing 1 blue marble
choosing 1 red marble
ll choosing 1 red marble, not replacing it, and then choosing a blue marble
choosing 1 white marble, replacing it, and choosing another white marble
choosing 1 white marble
Save and Exit
Submit
Mark this and retum
Answer:
choosing 1 red marble ; choosing 1 white marble, replacing it, and choosing another white marble ; and choosing 1 white marble
Step-by-step explanation:
There are 2+3+5 = 10 marbles. The probability of choosing 1 blue marble is 2/10 = 1/5; this is not greater than 1/5.
The probability of choosing 1 red marble is 3/10; this is greater than 2/10, which is the same as 1/5.
The probability of choosing 1 red marble is 3/10; not replacing it and choosing a blue marble would then be a probability of 2/9. Together this is a probability of 3/10(2/9) = 6/90 = 3/45; this is smaller than 9/45, which is the same as 1/5.
The probability of choosing 1 white marble is 5/10 = 1/2; replacing it and choosing another white marble would be 1/2. Together this is a probability of 1/2(1/2) = 1/4; this is greater than 4/20, which is the same as 1/5.
The probability of choosing 1 white marble is 5/10 = 1/2. This is greater than 2/10, which is the same as 1/5.
Answer:
b,d,e are the awnsers
Step-by-step explanation:
y=2x−1
5x−4y=1
Is (1,1)(1,1)left parenthesis, 1, comma, 1, right parenthesis a solution of the system?
Answer:
(1,1) is a solution of the system.
Step-by-step explanation:
Let's solve the system.
y = 2x - 1
5x - 4y = 1
In the first equation, y is already separated as a function of x. So we replace in the second equation;
5x - 4(2x - 1) = 1
5x - 8x + 4 = 1
4 - 1 = 8x - 5x
x = 1
y = 2x - 1 = 2(1) - 1 = 1
(1,1) is a solution of the system.
in the past year Rita watch 14 movies that he thought were very good he wants 20 movies over the whole year of the movie she watched what percentage did she think we're very good
Answer:
70%
Step-by-step explanation:
Sally invests $10,500 in an account that earns 6% annual simple interest. Assuming she makes no additional deposits or withdrawals, how much interest will Sally earn after 4 years? Will mark brainliest PLSSSSS HELLLLLP
Answer:
$2,520
Step-by-step explanation:
The simple Interest earned on an deposit, P at a rate of r% for a period of t years is calculated using the formula:
[tex]\text{ Simple Interest}=\dfrac{Principal*Time*Rate}{100}[/tex]
P=$10,500
R=6%
T=4 years
Therefore:
[tex]\text{ Simple Interest}=\dfrac{10500*4*6}{100}\\=\$2,520[/tex]
Sally will earn $2520 interest after 4 years.
A plane travels at 3400 miles in 8 hours. How far would it travel in 6 hours?
The plane would travel approximately 4533.33 miles in 6 hours.
Explanation:To find the distance the plane would travel in 6 hours, we can use the formula:
Distance = Speed × Time
Given that the plane travels at 3400 miles in 8 hours, we can substitute the values into the formula:
Distance = 3400 × 8/6
Simplifying the expression:
Distance = 4533.33 miles
Therefore, the plane would travel approximately 4533.33 miles in 6 hours.
Suppose that diameters of a new species of apple have a bell-shaped distribution with a mean of 7.42cm and a standard deviation of 0.36cm. Using the empirical rule, what percentage of the apples have diameters that are between 7.06cm and 7.78cm
Answer:
68% of the diameters are between 7.06 cm and 7.78 cm
Step-by-step explanation:
Mean diameter = μ = 7.42
Standard Deviation = σ = 0.36
We have to find what percentage of diameters will be between 7.06 cm and 7.78 cm. According to the empirical rule, for a bell-shaped data:
68% of the values are within 1 standard deviation of the mean. i.e. between μ - 1σ and μ + 1σ95% of the values are within 2 standard deviations of the mean. i.e. between μ - 2σ and μ + 2σ99.7% of the values are within 3 standard deviation of the mean. i.e. between μ - 3σ and μ + 3σSo, we first need to find how many standard deviations away are the given two data points. This can be done by converting them to z-score. A z score tells us that how far is a data value from the mean. The formula to calculate the z-score is:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
x = 7.06 converted to z score will be:
[tex]z=\frac{7.06-7.42}{0.36}=-1[/tex]
x = 7.78 converted to z score will be:
[tex]z=\frac{7.78-7.42}{0.36}=1[/tex]
This means the two given values are 1 standard deviation away from the mean and we have to find what percentage of values are within 1 standard deviation of the mean.
From the first listed point of empirical formula, we can say that 68% of the data values lie within 1 standard deviation of the mean. Therefore, 68% of the diameters are between 7.06 cm and 7.78 cm
Approximately 68% of the apples have diameters between 7.06cm and 7.78cm.
Explanation:To determine the percentage of apples with diameters between 7.06cm and 7.78cm, we can use the empirical rule which is based on the standard deviation. According to the empirical rule, approximately 68% of the apples will fall within one standard deviation of the mean, which in this case is between 7.42 - 0.36 and 7.42 + 0.36. In other words, between 7.06cm and 7.78cm. Therefore, approximately 68% of the apples have diameters between 7.06cm and 7.78cm.
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Evaluate the following expression for x = 15.
1/5 x -12
Will give Brainliest if correct!
Answer:
-9
Step-by-step explanation:
Plug in 15 for x in the equation
you should get (1/5*15) -12
multiply 1/5 and 15 to get 3
then 3-12=-9
therefore the answer is -9
13
cuadro para
divisible
Juan, Maria y Carlos fueron a un museo.
La entrada general costaba $$ por
persona, pero, por ser estudiantes, les
aplicaba un descuento de $1 por boleto.
Después del recorrido, los tres compraron
lo siguiente para comer:
. 3 combos de pollo y papas fritas a
$4 cada uno
• 3 botellas de agua a $1 cada una
• 3 mantecados de vainilla a $1 cada uno
¿Cuánto dinero pagó cada estudiante si
dividieron el total de los gastos en partes
iguales?
The question is incomplete. The complete question is as follows.
Juan, Carlos and Maria went to the museum. The entrance ticket cost $5 per person, but, as they are students, there is a discount of $1 per ticket. After, they bought: 3 combos of chicken and fries costing $4 each; 3 bottles of water costing $1 each; 3 vanilla cookies costing $1 each; How much money each student paid if they divided the costs in equal amount?
Answer: $10
Step-by-step explanation: As each students split the bill in equal parts, to find how much they spent, we can calculate how much one of the three spent.
For ticket: 5 - 1 (because of the students discount) = $4
Each combo of chicken and fries cost $4, so: combo = $4
Each bottle of water costs $1, so: water = $1
and each vanilla cookie costs $1: cookie = $1
Total spent is:
T = 4+4+1+1
T = 10
Each student spent a total of $10 for this outing.
Finish solving the system of equations, y = x – 15 and y = –2x + 3, using the substitution method. 1. Use substitution to create a one-variable linear equation: x – 15 = –2x + 3 2. Solve to determine the unknown variable in the equation: 3x = 18 x = 6 3. Substitute the value of the variable into either original equation to solve for the other variable. 4. Write the solution to the system of equations as an ordered pair. The solution to the system is .
Answer:
THE ANSWER IS (6,-9)
Step-by-step explanation:
The solution to the equation is ( 6 , -9 )
The value of x = 6
The value of y = -9
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the first equation be represented as A
Now , the value of A is
y = x - 15 be equation (1)
Let the second equation be represented as B
Now , the value of B is
y = -2x + 3 be equation (2)
Substituting the value of equation (1) in equation (2) , we get
x - 15 = -2x + 3
On simplifying the equation , we get
Adding 2x on both sides of the equation , we get
x + 2x - 15 = 3
Adding 15 on both sides of the equation , we get
3x = 18
Divide by 3 on both sides of the equation , we get
x = 6
Therefore , the value of x is 6
Substitute the value of x in equation (1) , we get
y = x - 15
y = 6 - 15
y = -9
Therefore , the value of y is -9
Hence , the values of x and y of the equation is ( 6 , -9 )
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