The probability of being able to toast at least 7 pieces of bread before the toaster catches on fire and destroys itself is approximately 0.0128
We can approach this problem using the negative binomial distribution, which models the number of successful trials (toasting without the toaster catching on fire) before a specified number of failures (the toaster catching on fire and destroying itself) occur.
Let X be the number of successful toasting trials before the toaster catches on fire and destroys itself. We want to find P(X ≥ 7), the probability that at least 7 pieces of bread can be toasted before the toaster is destroyed.
The negative binomial distribution can be expressed as
P(X = k) = (k+r-1)C(r-1) × p^r × (1-p)^k
where r is the number of failures (the toaster catching on fire and destroying itself), p is the probability of success (toasting without the toaster catching on fire), and (k+r-1)C(r-1) is a combination factor that represents the number of ways to arrange k successes and r-1 failures in a sequence.
In this case, r = 1 (we want to know the probability of the first failure occurring after at least 7 successes), p = 0.75 (the probability of successfully toasting a piece of bread), and we want to find P(X ≥ 7).
P(X ≥ 7) = 1 - P(X < 7)
= 1 - Σ[k=0 to 6] (k+1) × p × (1-p)^k
≈ 0.0128
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The given question is incomplete, the complete question is:
I bought a cheap toaster. Every time I use it there is a chance that it will catch on fire with
probability p = 0.25, burn my toast, and destroy itself. But with probability (1 − p) it makes
perfect toast!
What is the probability I put at least 7 pieces of bread into my cheap toaster before it
destroys itself?
There are 6 cups of oatmeal in a container. Stella eats ¼ cup of oatmeal every day for breakfast. In how many days will Stella finish all the oatmeal in the container?
It will take Stella 24 days to finish all the oatmeal in the container if she eats 1/4 cup every day for breakfast.
The container has 6 cups of oatmeal and Stella eats 1/4 cup every day for breakfast.
To find the number of days it will take Stella to finish all the oatmeal, we can use the formula:
Number of days = Total amount of oatmeal ÷ Amount of oatmeal consumed per dayTotal amount of oatmeal in the container = 6 cups
Amount of oatmeal consumed by Stella per day = 1/4 cup
Number of days = 6 cups ÷ 1/4 cup = 24 daysTherefore, it will take Stella 24 days to finish all the oatmeal in the container if she eats 1/4 cup every day for breakfast.
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A math teacher gives her class the following problem.
Barry is selling magazine subscriptions for a school fundraiser. He has already sold 15 subscriptions. He plans to sell 3 subscriptions per week until he reaches a total of 30 subscriptions sold. How many weeks will it take Barry to achieve his goal.
One student in the class solves the problem arithmetically as shown below.
The linear expression that could be used to find the number of weeks until he reaches 30 subscriptions is given as follows:
A. 15 + 3x = 30.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the rate of change.b is the y-intercept of the function, which is the initial value.The parameters for this problem are given as follows:
m = 3, as each week, 3 subscriptions are sold.b = 15, which is the initial number of subscriptions.Hence the number of subscriptions after x weeks is given as follows:
y = 3x + 15.
The number of weeks to reach 30 subscriptions (y = 30) is given as follows:
3x + 15 = 30.
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a bag contains 2 black marbles, 8 white marbles, and 27 red marbles someone offers to play this game: you randomly select one marble from the bag if it is black, you win $3. if it is white, you win $2. if it is red, you lose $1. what is your expected value if you play this game?
The expected value of the game is -$0.054, which means that if you play this game many times, you can expect to lose around 5 cents per game on average.
We need to calculate the expected value of a game where you randomly select a marble from a bag containing 2 black marbles, 8 white marbles, and 27 red marbles.
If the marble is black, you win $3.
If the marble is white, you win $2.
If the marble is red, you lose $1.
The expected value of a game is the sum of the products of each outcome and its probability.
To find the expected value of this game,
we need to first calculate the probabilities of each outcome.
P(bag contains a black marble) = 2/37P(bag contains a white marble)
= 8/37
P(bag contains a red marble)
= 27/37
Probability of winning $3
= P(black marble)
= 2/37
Probability of winning $2
= P(white marble)
= 8/37
Probability of losing $1
= P(red marble) = 27/37
Expected value
= (Probability of winning $3 × $3) + (Probability of winning $2 × $2) + (Probability of losing $1 × $-1)
Expected value = (2/37 × 3) + (8/37 × 2) + (27/37 × -1)
Expected value = -0.054$
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Find the equation of L
[tex]y=\frac{7}{2.4} x-6[/tex] ; if estimated then : [tex]y=\frac{7}{2.5} x-6[/tex]
Explination:
Y-intercept is -6, (0,-6)
The rise over run it [tex]\frac{7}{2.4} x[/tex]. The denominator is 2.4 because it nearly 2.5.
what did one dog say to the other dog
Answer: I like "Hot Dogs"?
Step-by-step explanation:
The expected value of the number of points for one roll is:_____.a. 0 b. 1 c. 3 d. 6
Answer:
2023- answer is A-0
Step-by-step explanation:
Jeriel is going to invest in an account paying an interest rate of 6.5% compounded continuously. How much would Jeriel need to invest, to the nearest cent, for the value of the account to reach $137,000 in 5 years?
Jeriel would need to invest approximately $98,986.25 for the value of the account to reach $137,000 in 5 years, assuming continuous compounding.
How much would Jeriel need to invest for the account to reach the accrued amount?The formula accrued amount compounded continuously is expressed as;
A = P × e^(rt)
Where A is accrued amount, P is principal, r is interest rate and t is time.
In this case, we are given that the final amount to be $137,000, the interest rate is 6.5% and the time is 5 years.
We want to solve for Principal P.
First, convert R as a percent to r as a decimal
r = R/100
r = 6.5/100
r = 0.065 per year
Plug these values into the above formula and solve for P.
A = P × e^(rt)
P = A / e^(rt)
P = 137,000.00 / e^(0.065 × 5)
p = $98,986.25
Therefore, the value of the principal P is $98,986.25.
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I NEED HELP RIGHT NOW AND CANNOT ASK A TEACHER I AM AT HOME PLEASE HELP 15 POINT IS ALL I HAVE
Step-by-step explanation:
[tex]\textsf{For this problem, we are asked to create an equation, and to find the measures of each angle.}[/tex]
[tex]\textsf{Angle 1 and Angle 2 form a Linear Pair.}[/tex]
[tex]\large\underline{\textsf{What is a Linear Pair?}}[/tex]
[tex]\textsf{A Linear Pair is 2 Adjacent angles that form a 180 Degree angle.}[/tex]
[tex]\textsf{This means that Angle 1 and Angle 2 add up to 180}^{\circ}.[/tex]
[tex]\large\underline{\textsf{Creating an Equation:}}[/tex]
[tex]\textsf{We are given 2 expressions for Angles 1 and 2. Add them together to equal 180}^{\circ}.[/tex]
[tex]\large\boxed{\mathtt{5x+x-18=180^{\circ}}}[/tex]
[tex]\large\underline{\textsf{Solving the Equation:}}[/tex]
[tex]\textsf{Solve x by isolating the variable. Let's first add 18 to both sides of the equation.}[/tex]
[tex]\mathtt{5x+x=198^{\circ}}[/tex]
[tex]\textsf{Because 5x and x are like terms, we can combine them.}[/tex]
[tex]\mathtt{6x=198}[/tex]
[tex]\textsf{Now, divide each side of the equation by 6 to find x.}[/tex]
[tex]\mathtt{\frac{6x}{6}=\frac{198}{6} }[/tex]
[tex]\large\boxed{\mathtt{x=33^{\circ}}}[/tex]
[tex]\large\underline{\textsf{Finding the Measures:}}[/tex]
[tex]\textsf{Because we know the value x, we can substitute the known value of x into the expressions given.}[/tex]
[tex]\boxed{\mathtt{\angle 1 =5(33)=165^{\circ}}}[/tex]
[tex]\boxed{\mathtt{\angle 2=33-18=15^{\circ}}}[/tex]
please help quick
6d = 54
answer
6 divided by 54 is equal to 9
therefore
answer = d=9
candace is designing a card game with a standard deck of cards. each player gets points based on collecting groups of cards. which statements are true about certain groups of cards? select all of the true statements.
The true statements are:
a) P(3) = 4/52 or 1/13
b) P(black number cards) = 18/26 or 9/13
c) P(red ace) = 2/52 or 1/26
d) P(face card) = 12/52 or 3/13
Define the term Probability?Probability deals with the study of random events and their likelihood of occurrence. It is computed by dividing the proportion of positive results by the total number of possibilities that could occur.
As we know that the standard deck card has 52 cards, in which 26 red cards (13 are diamonds, 13 are hearts) 26 black cards (13 are clubs, 13 are spades). Where 12 cards are face cards, 36 cards are number cards.
a) P(3) = 4/52 or 1/13: This is true. There are four 3s in a standard deck of 52 cards, so the probability is 4/52 or 1/13.
b) P(black number cards) = 18/26 or 9/13: This is a true. There are 26 black cards, out of those there are 9+9=18 black number cards (2 through 10), so the probability of drawing a black number card is 18/26 or 9/13.
c) P(red ace) = 2/52 or 1/26: This is true. There are two red aces in a standard deck of 52 cards, so the probability of drawing a red ace is 2/52 or 1/26.
d) P(face card) = 12/52 or 3/13: This is a true. There are twelve face cards in a standard deck of 52 cards, so the probability of drawing a face card is 12/52 or 3/13.
e) P(even number card) < P(odd number card): This is a false. There are 5×4=20 even number cards (2, 4, 6, 8, and 10 of each suit) and 4×4=16 odd number cards (3, 5, 7, 9 of each suit) in a standard deck of 52 cards. Therefore, the probability of drawing an even number card, (20/52 or 5/13) is greater than the probability of drawing an odd number card, (16/52 or 4/13).
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Complete question-
7. The expression below is evaluated as shown. In which step does the first
mistake appear?
The mistake in the solution of the expression is in step 3, where the product should be solved first.
In which step is the first mistake?Here we have the expression:
0.5*(3*5 + 1) - 2
And we also have the solution in steps, and we want to find in which step we have a mistake.
The first step gives:
0.5*(15 + 1) - 2
Where the first product is solved.
The second step is
0.5*16 - 2
Where we solved the parentheses.
The third step gives:
0.5*14
Here they subtracted the 2 from the 16, but this is incorrect, the first thing that needs to be solved here is the product between 0.5 and 16, we should get:
0.5*16 - 2
8 - 2
6
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a coffee distributor needs to mix a(n) kenya coffee blend that normally sells for $8.20 per pound with a breakfast coffee blend that normally sells for $14.00 per pound to create 10 pounds of a coffee that can sell for $9.36 per pound. how many pounds of each kind of coffee should they mix?
The coffee distributor should mix 8 pounds of Kenya coffee blend and 2 pounds of breakfast coffee blend to make 10 pounds of a coffee blend that can sell for $9.36 per pound.
We can use the idea of weighted averages to overcome this issue. Assume that 10 pounds of the desired blend require x pounds of Kenya coffee blend and y pounds of morning coffee blend.
The price of the Kenya coffee mix per pound is $8.20, while the price of the morning coffee blend per pound is $14.00. The required combination costs $9.36 per pound. On the basis of the weighted average, we can construct the following equation:
8.20x + 14.00y = 9.36(10) (10)
When we simplify this equation, we obtain:
8.20x + 14.00y = 93.60
Given that we are producing 10 pounds of the ideal blend, we also know that x + y = 10. To get the values of x and y, we can use substitution or elimination to solve this system of equations.
Use substitute now. We can find x from the second equation by solving in terms of y:
x = 10 - y
Substitute this into first equation, we get:
8.20(10 - y) + 14.00y = 93.60
82 - 8.20y + 14.00y = 93.60
5.80y = 11.60
y = 2
We obtain x = 8 by substituting y = 2 into x = 10 - y. Hence, to manufacture 10 pounds of a coffee mix that can be sold for $9.36 per pound, we'll need 8 pounds of Kenya coffee blend and 2 pounds of breakfast coffee blend.
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a laptop has a listed price of 882.99 before tax. if the sales tax rate is 6.25% , find the total cost of the laptop with sales tax included. round your answer to the nearest cent, as necessary.
The total cost of the laptop with the sales tax included is 938.18.
The total cost of the laptop with the sales tax included is the sum of the original price and the tax amount. The formula to calculate the total cost is given below:
Total Cost = Original Price + (Original Price * Sales Tax Rate)
In this case, the Original Price is 882.99 and the Sales Tax Rate is 6.25%. Therefore, the Total Cost of the laptop with the sales tax included is calculated as follows:
Total Cost = 882.99 + (882.99 * 0.0625)
Total Cost = 882.99 + 55.19
Total Cost = 938.18
Rounding to the nearest cent, the total cost of the laptop with the sales tax included is 938.18.
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find the value of x and y
Answer:
1/3 y
Step-by-step explanation:
0,6x
i thought of a number. four times the number increased by 30 equals 70 decreased by the number. what was my number?
Answer:
number is 8
Step-by-step explanation:
let n be the number then 4 times the number is 4n and increased by 30 means adding 30 to it , that is 4n + 30
70 decreased by the number means subtracting n fro 70 , 70 - n
then
4n + 30 = 70 - n ( add n to both sides )
5n + 30 = 70 ( subtract 30 from both sides )
5n = 40 ( divide both sides by 5 )
n = 8
(1 point) in a baseball league of 10 teams, how many games are needed to complete the schedule if each team plays 9 games with each other?
Answer:
90
Step-by-step explanation:
In a baseball league of 10 teams, 405 games are needed to complete the schedule if each team plays 9 games with each other.
Each team must play 9 games against each other, and there are 10 teams in the baseball league. We'll need to figure out how many games that means each team will play.Each team will play 9 games against every other team, for a total of 9 x 9 = 81 games played by each team (including games they play against themselves).Since there are 10 teams in the league, the total number of games played will be:
81 x 10 = 810.
However, each game is played between two teams, so we must divide by 2 to get the total number of games:
810 / 2 = 405.So, there will be 405 games played in the league.
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help pls its too much
Answer:
24.13
Step-by-step explanation:
Eric owns and operates the Hot Ham food truck. The expression 3. 25b+2h3. 25b+2h3, point, 25, b, plus, 2, h gives the cost of bbb burgers and hhh hot dogs. What is the cost of 444 burgers and 666 hot dogs?
\$
As per the expression, the cost of 444 burgers and 666 hot dogs from Eric's Hot Ham food truck would be $2773.
In this case, Eric's expression is 3.25b + 2h, where b represents the number of burgers and h represents the number of hot dogs. The expression tells us how much it costs to buy a certain number of burgers and hot dogs from Eric's truck.
To find the cost of 444 burgers and 666 hot dogs, we can substitute b = 444 and h = 666 into the expression. So the cost would be:
3.25(444) + 2(666)
Now we just need to simplify this expression by using the order of operations.
First, we multiply 3.25 by 444 to get 1441. Then, we multiply 2 by 666 to get 1332.
Next, we add these two values together:
1441 + 1332 = 2773
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Given that x = (5,-5) and y = (8,-3), find x•y
If x = (5,-5) and y = (8,-3), x•y is: 55.
How to find the vectors?The dot product (also called scalar product or inner product) of two vectors x = (x1, x2) and y = (y1, y2) is given by:
x•y = x1y1 + x2y2
Using the coordinates of the given vectors:
x = (5, -5)
y = (8, -3)
x•y = (5)(8) + (-5)(-3) = 40 + 15 = 55
Therefore, x•y = 55.
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A researcher found a study relating the distance a driver can see, y, to the age of the driver, When researchers looked at the association of x and y, they found that the coefficient of determination was =0.542. Select two conclusions that the researcher can make from this data. a.) The correlation coefficient, t, is-0 458. b.) About 54% of the variation in distance that the driver can see is explained by a linear relationship with the driver's age. O c.) About 74% of the variation in the driver's age is explained by a linear relationship with the distance that the driver can see O d.) The correlation coefficient, t.is -0736. e.) About 46% of the variation in distance that the driver can see is explained by a linear relationship with the driver's age. 1.) The correlation coeficient 0 271 A data set was grapned using a scatterpion 30 25 20 15 10 5 0 0 5 10 15 20 25 30 The correlation coefficient, r, is 0.813 Which of the following statements explains how the correlation is http/phoenix.sophia.org/tutorials/cautions-about-correlation-2/download ndf The correlation coefficient, r, is 0.813. Which of the following statements explains how the correlation is affected? O a.) It is affected by inappropriate grouping. O b.) It is not affected. c.) It is affected by an influential point. d.) It is affected by non-linearity. SUBMIT MY ANSWER Which of the following statements is TRUE? O a.) Low correlation implies causation b.) A high correlation means that the response variable is caused by the explanatory variable. O c.) High correlation does not always establish causation O d.) To imply causation, the correlation must be 1. SUBMIT MY ANSWER Javascriptvo do)
1)From the data:
Two conclusions that the researcher can make are:
b.) About 54% of the variation in the distance that the driver can see is explained by a linear relationship with the driver's age.
d.) The correlation coefficient, t, is -0.736. (This can be found by taking the square root of the coefficient of determination and considering the negative correlation)
2)"It is not affected" is the correct statement,that is option b
3)The "High correlation does not always establish causation" is the TRUE statement, that is option c .
What is Correlation?
Correlation is a statistical measure that indicates the extent to which two or more variables fluctuate together.
A positive correlation indicates that as one variable increases, the other variable also increases.
A negative correlation indicates that as one variable increases, the other variable decreases. In other words, it shows the relationship between two variables and helps to understand if they are related or independent.
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What is the solution of log2x-7(81) = 4
2x-7 is subscript
Answer:
x=5
Step-by-step explanation:
[tex] log_{2x - 7}(81) = 4[/tex]
Raise both sides with a base of 2x-7
[tex]81 = (2x - 7) {}^{4} [/tex]
We get two solutions
[tex]3 = (2x - 7)[/tex]
[tex]10 = 2x[/tex]
[tex]x = 5[/tex]
The other solutions is
[tex] - 3 = 2x - 7[/tex]
[tex]4 = 2x[/tex]
[tex]x = 2[/tex]
The solution x=2 wont work since it will make our base negative.
So the answer is 5
by how much must the sample size n be increased if the width of the ci (7.5) is to be halved? if the sample size is increased by a factor of 25, what effect will this have on the width of the interval? justify your assertions.
The width of the interval will be reduced to 1.5 if the sample size is increased by a factor of 25.
To find how much the sample size n must be increased if the width of the confidence interval is to be halved, use the following formula:
W = (zα/2 x σ/√n)W/2 = (zα/2 x σ/√n')
Where W is the initial width of the confidence interval,
zα/2 is the critical value of the standard normal distribution that corresponds to the level of significance α and the appropriate two-tailed area,
σ is the population standard deviation,
n is the initial sample size, and
n' is the new sample size needed to halve the width of the interval.
Rearranging the second equation to solve for n', we get:
n' = n(4)
So the sample size needs to be increased by a factor of 4, or 300% if the width of the confidence interval is to be halved.
If the sample size is increased by a factor of 25, the effect it will have on the width of the interval can be found using the following formula:
W' = (zα/2*σ/√25n) = (zα/2*σ/5√n)
The width of the interval will be divided by 5, or reduced to one-fifth of its initial value.
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The path of a firework is described by the function:
h(t) = -4.9(t-5)² + 124 where h(t) is the height of the firework, in meters, and t is the time in
seconds, since the launch.
What is the vertex of the function, and what does it mean in context?
A. (5, 4.9); At 5 seconds, the firework is 4.9 meters above the ground.
B. (124, 5); At 124 seconds, the firework is 5 meters above the ground.
C. (4.9, 124); At 4.9 seconds, the firework is 124 meters above the ground.
D. (5, 124); At 5 seconds, the firework is 124 meters above the ground.
Answer:
D
Step-by-step explanation:
Because this binary function opens down, and it has an extreme point, at t=5, and you plug it in and you get 124 as the maximum.
Find explicit formulas for sequences of the form a1, a2, a3, ... with the initial terms given
0, -1/2, 2/3, -3/4, 4/5, -5/6, 6/7
This formula generates the sequence 0, -1/2, 2/3, -3/4, 4/5, -5/6, 6/7, ...
Notice that the sequence alternates between positive and negative terms and that the denominators of each term increase by 1 while the numerators increase by 1 or -1. To find the explicit formula, we can write it in terms of its general form:
a1 = 0
a2 = -1/2
a3 = 2/3
a4 = -3/4
a5 = 4/5
a6 = -5/6
a7 = 6/7
We can see that the numerator of each term is equal to its index number, n, if n is even and equal to -n if n is odd. The denominator of each term is equal to n+1 for all terms.
Using this observation, we can write the explicit formula for the sequence as:
an = (-1)^(n+1) * n / (n+1)
where (-1)^(n+1) is equal to -1 if n is odd and 1 if n is even. This formula generates the sequence 0, -1/2, 2/3, -3/4, 4/5, -5/6, 6/7, ...
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you randomly select 15 cards from a deck of 52 cards. what is the probability that it contains exactly one queen given that it contains exactly two aces?
The probability that the 15 cards contain exactly one queen given that they contain exactly two aces is approximately 0.060 or 6.0%.
We can use conditional probability. Let A be the event that the 15 cards contain exactly two aces, and B be the event that they contain exactly one queen. Then we want to find the conditional probability P(B|A).
First, let's find the probability of A. There are C(4,2) ways to choose the two aces out of four, and C(48,13) ways to choose the other 13 cards out of the remaining 48 cards. So the total number of ways to choose 15 cards with exactly two aces is:
C(4,2) × C(48,13) ≈ 4.57 × 10^12
Next, let's find the probability of both A and B. There are C(4,2) ways to choose the two aces out of four, C(4,1) ways to choose one queen out of four, and C(47,12) ways to choose the other 12 cards out of the remaining 47 cards. So the total number of ways to choose 15 cards with exactly one queen and exactly two aces is:
C(4,2) × C(4,1) × C(47,12) ≈ 2.76 × 10^11
Finally, we can use the formula for conditional probability:
P(B|A) = P(A and B) / P(A)
P(B|A) = (C(4,2) × C(4,1) × C(47,12)) / (C(4,2) × C(48,13))
P(B|A) ≈ 0.060
Therefore, the probability is approximately 0.060 or 6.0%.
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suppose that iq scores have a bell-shaped distribution with a mean of 96 and a standard deviation of 17 . using the empirical rule, what percentage of iq scores are less than 79 ? please do not round your answer.
Suppose that IQ scores have a bell-shaped distribution with a mean of 96 and a standard deviation of 17. Using the empirical rule, 15.87 percentage of IQ scores are less than 79.
The empirical rule says that for a normal distribution, almost all of the data will fall within three standard deviations of the mean.
Specifically:
Approximately 68% of the data falls within one standard deviation of the mean.
Approximately 95% of the data falls within two standard deviations of the mean.
Almost all (99.7%) of the data falls within three standard deviations of the mean.
Given that the mean of IQ scores is 96 and the standard deviation is 17.
Hence the Z score can be calculated as
z=(x−μ)/σ=(79−96)/17=−1
From the standard normal distribution table, the percentage of the data that is less than z = -1 is 15.87%.
Hence the percentage of IQ scores that are less than 79 is approximately 15.87%.
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PLEASE HELP WITH EXPLANATION PLEASE PLEASE PLEASE NO SCAMMING FOR THE COINS OR I WILL REPORT YOU
The correct solutions for the given equation is given by table in option 3.
Explain about the solution of linear equation?A straight line is produced when a linear equation, which is a two-variable equation, is graphed. The intersection of corresponding values which satisfy the equation results in the line.
The variables x and y are most frequently used in linear equations, hence the associated values can be shown as (x,y) on the coordinate plane, pairs. A collection of two maybe more linear equations is known as a system of linear equations.
The given equation is-
y = x - 6
Put the value of 'x' from the options and check for 'y', if its correct.
The option are the solution of the equation.
option 1:
y = x - 6
x = --5
y = -5 - 6 = -11 (incorrect)
option 2:
y = x - 6
Put x = -8
y = -8 - 6 = -14 (incorrect)
option 3:
y = x - 6
Put x = -7
y = -7 - 6 = -13 (correct)
Thus, the correct solutions for the given linear equation is given by table in option 3.
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DUCK is a rectangle. Solve:
X=
UDK=
For the rectangle, the value x will be 14 and angle UDK will be 35°.
What exactly is a rectangle?
A rectangle is a four-sided polygon with four right angles (90-degree angles). It has opposite sides that are equal in length and parallel to each other. The rectangle is a special case of a parallelogram, where the opposite sides are also parallel. The two sides that are equal in length are called the "width" or "short side", while the other two sides are called the "length" or "long side". The area of a rectangle is found by multiplying its length by its width, while its perimeter is found by adding the lengths of all four sides.
Now,
As we know all angles of a triangle are 90°.
then 5x-15+2x+7=90
7x=98
x=14
and in triangle UDK
sum of all angles = 180°
∠UDK+90+5x-15=180
∠UDK=180-145
∠UDK=35°
Hence,
the value x will be 14 and angle UDK will be 35°.
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Part D When the membrane potential of a neuron begins returning to normal, resting levels, the cell membrane experiences summation repolarization depolarization Ohyperpolarization rest Submit Request Answer Part E Saltatory conduction allows for faster and more efficient conduction because action potentials are confined to which part of a neuron? Cell body Dendrites Axon terminal Axon hillock Nodes of Ranvier Submit Request Answer
The action potential "jumps" from node to node, allowing it to travel faster and with less energy loss than if it had to propagate along the entire length of the axon.
Part D: When the membrane potential of a neuron begins returning to normal, resting levels, the cell membrane experiences hyperpolarization.
During hyperpolarization, the membrane potential becomes more negative than the resting potential, making it more difficult to trigger an action potential.
Part E: Saltatory conduction allows for faster and more efficient conduction because action potentials are confined to the Nodes of Ranvier.
The Nodes of Ranvier are small gaps in the myelin sheath that covers the axon of some neurons. Because the myelin sheath insulates the axon, action potentials can only occur at the nodes, where the membrane is exposed. This means that the action potential "jumps" from node to node, allowing it to travel faster and with less energy loss than if it had to propagate along the entire length of the axon.
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A one-to-one function is given. Write an expression for the inverse function. f(x)=√x+7 Select one: O af¹¹(x)=x²-7 Ob. f¹(x)=(x-7)³ O c.f¹(x) = (x + 7)³ O d. f¹(x)=x³ +7
The correct option B. The expression for the inverse is f¹(x) = (x - 7)².
A one-to-one function is given. We have to write an expression for the inverse function.
Given function: f(x)=√x+7
The inverse of a function is found by switching the x and y coordinates and solving for y.
So, the expression for the inverse function will be:
f¹(x) = y = √x + 7 ... (1)
Replace x with y and simplify to isolate y from the radical.
y = √x + 7
=> y - 7 = √x
=> (y - 7)² = x
Hence, the inverse of the given function is given byf¹(x) = (x - 7)².
So, the correct option is B) f¹(x)=(x-7)².
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