The probability of P(X ≤ 3) is 2/7, the probability of P(X < 3) is 3/14, the probability of P(X < 4. 12 | X > 1. 638) is 7/22.
To calculate P(X ≤ 3), we need to add the probabilities of all outcomes less than or equal to 3
P(X ≤ 3) = P(X = 1) + P(X = 2) + P(X = 3)
= 1/7 + 1/14 + 3/14
= 4/14
= 2/7
To calculate P(X < 3), we need to add the probabilities of all outcomes strictly less than 3
P(X < 3) = P(X = 1) + P(X = 2)
= 1/7 + 1/14
= 3/14
To calculate P(X < 4 | X > 1.638), we first need to find the probability of X > 1.638
P(X > 1.638) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)
= 1/14 + 3/14 + 2/7 + 2/7
= 11/14
Then, we can use the formula for conditional probability
P(X < 4 | X > 1.638) = P(X < 4 and X > 1.638) / P(X > 1.638)
We need to calculate the probability of X < 4 and X > 1.638, which is the probability of X = 2 or X = 3
P(X < 4 and X > 1.638) = P(X = 2 or X = 3)
= P(X = 2) + P(X = 3)
= 1/14 + 3/14
= 1/4
Therefore,
P(X < 4 | X > 1.638) = (1/4) / (11/14)
= 7/22
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A certain right triangle with integer side lengths has perimeter $150$. What is its area?
Note that the right triangle's area is 750 units². Here is how to get this.
What is a right triangle?A right triangle or right-angled triangle, or more technically an orthogonal triangle, formerly known as a rectangle triangle, is a triangle with one right angle, i.e. two perpendicular sides.
Trigonometry is founded on the relationship between the sides and other angles of a right triangle.
So since this triangle is a multiple of a 5-12-13 triangle
Its sides are 25 - 60 - 65( summing this will give 150.)
Its area is (1/2) * product of the legs = (1/2)(25)(60) = 750 units²
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A marble with radius r rolls in an L-shaped track. How far is the center of the marble from the corner of the track?
Answer:
r√2
Step-by-step explanation:
You want to know the distance from the center of a marble of radius r to the corner of an L-shaped track in which it rolls.
CenterThe center of the marble can only come within r of the track edges, so the distance to the corner will be the hypotenuse of a right triangle with legs r. That distance is r√2.
The center of the marble is r√2 from the corner of the track.
__
Additional comment
You can see in the second attachment that the distance to the corner of the track will depend on where the marble is rolling in the track. It might only be r away from the corner.
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The population of Alan's survey is all the students at the town's high school. The sample must be representative of the population. A possible sample would be an equal number of freshman, sophomores, juniors, and seniors. Check all that you included in your response. The population is all high school students. The sample contains freshmen, sophomores, juniors, and seniors. The sample is not too small. The sample is representative of students in the entire high school
The responses that must be included are the population is all high school students, the sample contains freshmen, sophomores, juniors, and seniors, and the sample is representative of students in the entire high school.
Hence, options A, B, and D are correct.
To ensure that a sample is representative of the population, it must be selected in a way that accurately reflects the characteristics of the population. In this case, the population is all high school students in the town, and the possible sample includes an equal number of students from each grade level - freshman, sophomores, juniors, and seniors.
This is a good approach to ensure that the sample is representative of the entire population, as it captures the diversity of the population by including students from each grade level. Additionally, by having an equal number of students from each grade level, the sample is not biased towards any particular group.
It is also important to ensure that the sample is not too small, as a small sample size may not accurately reflect the characteristics of the entire population. Finally, if the sample is truly representative of the entire high school, any conclusions drawn from the sample should be applicable to the population as a whole.
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birth weights at a local hospital have a normal distribution with a mean of 110 oz. and a standard deviation of 15 oz. the proportion of infants with birth weights under 95 oz is about
The proportion of infants with birth weights under 95 oz is about 0.159oz
Empirical Rule: Normal Distribution68−95−99.7 Rule, also known as the empirical rule conveys that for a normal distribution, mostly all of the data will fall within three (68%,95%,99.7%) standard deviations of the mean. Empirical rule is an approximate so it is not recommended to use unless a question specifically asks you to solve using it.
Let X be the Birthweights
X ~ N( = 110, [tex]\sigma^2 = 15^2[/tex])
The probability of X is less than 95 is,
P(X < 95) = [tex]P(\frac{X-\mu}{\sigma} < \frac{95-\mu}{\sigma} )[/tex]
[tex]=P(Z < \frac{95-110}{15} )[/tex]
[tex]=P(Z < \frac{-15}{15} )[/tex]
= P (Z < -1)
P(X < 95) = 0.159 (using the normal table)
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a trapizumis shown below
fine the angles of x and y
It should be noted that the values of x and y in the trapezium will be
x=118
y= 35
What is a trapezium?A trapezoid, also known as a trapezium, is a closed, flat object with four straight sides and one pair of parallel sides. A trapezium's parallel sides are known as the bases, while its non-parallel sides are known as the legs. A trapezium might have parallel legs as well. A trapezium is a quadrilateral with one parallel pair of opposite sides.
Based on the information, x will be:
= 180-62
= 118
y will be:
= 180-145=35
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according to the central limit theorem, .multiple choice
A. increasing the sample size B. decreases the dispersion of the sampling distribution
The answer is option A. increasing the sample size.
What is central limit theory?The central limit theorem (CLT) is a statistical theory that explains the behavior of sample means when drawn from a population with any distribution, as long as the sample size is large enough. The CLT states that as the sample size increases, the sampling distribution of the means approaches a normal distribution, regardless of the shape of the original population distribution.
One implication of the CLT is that increasing the sample size makes the sampling distribution more precise and reliable, as the standard error of the mean decreases with larger samples. However, the CLT does not necessarily imply that increasing the sample size decreases the dispersion (or variability) of the sampling distribution itself.
The dispersion of the sampling distribution is determined by the variability of the original population and the sample size, but it does not change with sample size alone. For example, if the original population has a large standard deviation, the sampling distribution of the means will also have a large standard deviation, even with a large sample size. However, as the sample size increases, the means will be more tightly clustered around the population mean, which means that the precision of our estimate of the population mean increases.
Therefore, the answer is option A. increasing the sample size.
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researchers examine the relationship between church attendance and hours spent on homework each week for a random sample of 80 high school students. students were grouped into four categories based on frequency of church attendance: never attend, attend infrequently, attend frequently, attend very frequently. null hypothesis: for high school students, there is a no relationship between church attendance and hours spent on homework each week (i.e. the mean hours spent on homework each week are the same for the four populations defined by church-going frequency.) alternative hypothesis: for high school students, there is a relationship between church attendance and hours spent on homework each week (i.e. the mean hours spent on homework each week differ for the four populations defined by church-going frequency.) analysis of variance results: responses: homework factors: attendchurch response statistics by factor attendchurch n mean std. dev. std. error freq 26 9.4 5.8 1.1 infreq 27 6.4 4.4 0.9 never 10 7.9 5.4 1.7 veryfreq 18 8.9 7.1 1.7 anova table source df ss ms f-stat p-value attendchurch 3 136.05632 45.352105 1.4145498 0.245 error 77 2468.7091 32.061157 total 80 2604.7654 to check conditions for use of the anova f-test which ratio is useful? [ select ] to check conditions for use of the anova f-test, we need to examine histograms of the homework hours for how many of the samples? [ select ] assuming that the conditions are met for use of the anova f-test, which conclusion does the data support? [ select ]
Answer:
Step-by-step explanation:
To check conditions for the use of the ANOVA F-test, the ratio of the largest sample variance to the smallest sample variance is useful.
To check conditions for the use of the ANOVA F-test, we need to examine histograms of the homework hours for all four samples (never attend, attend infrequently, attend frequently, and attend very frequently).
Assuming that the conditions are met for the use of the ANOVA F-test, the data do not support the alternative hypothesis that there is a relationship between church attendance and hours spent on homework each week. The p-value of 0.245 is greater than the typical significance level of 0.05, indicating that there is not enough evidence to reject the null hypothesis that there is no relationship between church attendance and hours spent on homework each week.
When deriving the quadratic formula by completing the square, what expression can be added to both sides of the equation to create a perfect square trinomial? mc030-1. Jpg.
The expression that can be added to both sides of the given quadratic equation to change it to a perfect square trinomial is [tex]\frac{b^2}{4a^2}[/tex] .
The standard form of perfect square trinomial is given as:
[tex]ax^2 + bx + c[/tex]
here,
a = coefficient of x² .
b = coefficient of x.
c = constant .
Given the quadratic equation:
[tex]x^2 + \dfrac{b}{a}x\ +\ ?= -\dfrac{c}{a}\ +\ ?[/tex]
The above equation is needed to be changed to a perfect square trinomial.
To change the quadratic equation into the perfect square, the squared of half the value of the coefficient of degree one variable can be added to both sides of the equation.
Therefore, the term to be that is needed to be added to the given quadratic equation is [tex]\frac{b^2}{4a^2}[/tex] .
Now, the quadratic equation can be written as:
[tex]x^{2} + \frac{b}{a} x + \frac{ b^{2}}{4a^{2}} = \frac{-c}{a} + \frac{ b^{2}}{4a^{2}}[/tex]
Therefore, [tex]\dfrac{b^2}{4a^2}[/tex] should be added to both sides to convert it into the perfect polynomial.
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The given question is incomplete. Probably the complete question is:
When deriving the quadratic formula by completing the square what expression can be added to both sides of the given equation to create a perfect square trinomial?
[tex]x^2 + \dfrac{b}{a}x\ +\ ?= -\dfrac{c}{a}\ +\ ?[/tex]
need help im trying to do but its kinda hard
The correct option is D, we can simplify the expression as:
[tex]\sqrt{125p^2} = 5p\sqrt{5}[/tex]
How to simplify the expression?Remember two things, the square root can be distributed under the product, and it is the inverse of the square exponent.
Then we can rewrite our expression as follows:
[tex]\sqrt{125p^2} = \sqrt{125}*\sqrt{p^2}[/tex]
Now we can simplify both of the square roots to get:
[tex]\sqrt{125}*\sqrt{p^2} = p*\sqrt{125} = p*\sqrt{5*25} = p*\sqrt{5} *\sqrt{25} \\\\= 5p\sqrt{5}[/tex]
Thus, we can see that the correct option is D.
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Find the slope of the line passing through the points (-6, -5) and (4,4).
Answer:
9/10 or 0.9
Step-by-step explanation:
Slope of a line passing through two points (x1, y1) and (x2, y2) is given by
Slope m = rise/run
where
rise = y2 - y1
run = x2 - x1
Given points (- 6, - 5) and (4, 4),
rise = 4 - (-5) = 4 + 5 = 9
run = 4 - ( - 6) = 4 + 6 = 10
Slope = rise/run = 9/10 or 0.9
If an object looks the same on both sides when divided by a plane, it has
O rotational symmetry.
no plane of symmetry.
O reflectional symmetry.
Ono axis of symmetry.
K
Answer:
reflectional symmetry
Step-by-step explanation:
The radio signal from the transmitter site of radio station WGGW can be received only within a radius of 52 miles in all directions from the transmitter site. A map of the region of coverage of the radio signal is shown below in the standard (x, y) coordinate plane, with the transmitter site at the origin and 1 coordinate unit representing 1 mile. Which of the following is an equation of the circle shown on the map?
The equation of the circle is given as follows:
x² + y² = 2704.
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The center is the position of the transmitter site, hence it is at the origin.
As stated in the problem, the radius of the circle is given as follows:
r = 52 miles.
Hence the equation of the circle is given as follows:
x² + y² = 52²
x² + y² = 2704.
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Write the quadratic equation whose roots are -3 and -6 and whose leading coefficient is 2 use the letter x
Answer:
The quadratic equation with roots -3 and -6 and leading coefficient 2 is:
2x2 - 8x - 12 = 0
To derive this, we use the quadratic formula:
ax2 + bx + c = 0
With:
a = 2 (leading coefficient)
b = -4 (calculated from roots: b = -2(root1 + root2) = -2(-3 - 6) = -4)
c = -12 (calculated from discriminant: c = b2/4a = -42/8 = -12)
So the full equation is:
2x2 - 4x - 12 = 0
Which simplifies to:
2x2 - 8x - 12 = 0
This has the roots -3 and -6 as requested, with a leading coefficient of 2.
Step-by-step explanation:
Consider the following inductive definition of a version of Ackermann's function:
A(m,n)=⎧⎩⎨⎪⎪⎪⎪2n if m=00 if m≥1 and n=02 if m≥1 and n=1A(m−1,A(m,n−1)) if m≥1 and n≥2A(m,n)={2n if m=00 if m≥1 and n=02 if m≥1 and n=1A(m−1,A(m,n−1)) if m≥1 and n≥2
Find the following values of the Ackermann's function:
A(2,1)=A(2,1)= 2 A(1,2)=A(1,2)= 6 A(1,0)=A(1,0)= 4 A(0,1)=A(0,1)= 4 A(3,0)=A(3,0)= 4 A(3,3)=A(3,3)=
According to the given inductive definition of Ackermann's function, we can find the values of the function as follows:
A(2,1) = A(1, A(2,0)) = A(1, 1) = A(0, A(1,0)) = A(0, 2) = 2
A(1,2) = A(0, A(1,1)) = A(0, A(0, A(1,0))) = A(0, A(0, 2)) = A(0, 4) = 6
A(1,0) = A(0, A(1,-1)) = A(0, A(0, 0)) = A(0, 1) = 2^1 = 2
A(0,1) = 2^1 = 2
A(3,0) = A(2, A(3,-1)) = A(2, A(2, A(3,-2))) = A(2, A(2, A(2, A(3,-3)))) = A(2, A(2, A(2, 1))) = A(2, A(2, 2)) = A(2, 2^2) = A(2, 4) = 2^4 = 16
A(3,3) = A(2, A(3,2)) = A(2, A(2, A(3,1))) = A(2, A(2, A(2, A(3,0)))) = A(2, A(2, A(2, 1))) = A(2, A(2, 2)) = A(2, 2^2) = A(2, 4) = 2^4 = 16
Therefore, the values of Ackermann's function are:
A(2,1) = 2
A(1,2) = 6
A(1,0) = 2
A(0,1) = 2
A(3,0) = 16
A(3,3) = 16
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Say, for example, the correlation is 0.75 between fat content (measured in grams) and cholesterol level (measured in milligrams) for 20 different brands of American cheese slices. If cholesterol level were changed to being measured in grams (where 1 gram = 1000 milligrams), what effect would this have on the correlation?
If cholesterol level were changed to being measured in grams instead of milligrams, the correlation between fat content and cholesterol level would not be affected.
This is because correlation is a measure of the strength and direction of the linear relationship between two variables, and converting the units of measurement does not change the underlying relationship between the variables. So, the correlation coefficient of 0.75 would remain the same whether cholesterol level is measured in milligrams or grams.
The correlation between fat content and cholesterol level for the 20 different brands of American cheese slices is 0.75. If you change the measurement of cholesterol level from milligrams to grams (1 gram = 1000 milligrams), it will not affect the correlation. The correlation coefficient will remain 0.75, as it is unit-less and only represents the strength and direction of the relationship between the two variables.
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if tim scored a 72 on a test and his calculated z score was -1.32, what does that mean
A z-score of -1.32 indicates that Tim's score on the test is below average, but not extremely unusual or unexpected.
If Tim's calculated z-score for his test score of 72 is -1.32, it means that his score is 1.32 standard deviations below the mean of the distribution.
A z-score represents the number of standard deviations that a data point is away from the mean of the data set.
A negative z-score means that the data point is below the mean, while a positive z-score means that the data point is above the mean.
To calculate Tim's score, we can use the formula:
z = (x - μ) / σ
where:
z = the z-score
x = the test score
μ = the mean of the distribution
σ = the standard deviation of the distribution
Substituting the given values, we get:
-1.32 = (72 - μ) / σ
To solve for μ, we need to rearrange the equation as:
μ = 72 - (-1.32) × σ
This means that if Tim's z-score is -1.32 and his test score is 72, then the mean score.
The distribution is 1.32 standard deviations above his score.
The mean score using the standard deviation of the distribution, but we would need additional information such as the standard deviation value.
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you and a friend each roll two dice. what is the probability that you both have the same two numbers? (the two cases are whether you role doubles or not)
The probability that you and your friend both have the same two numbers is approximately 0.4823, or about 48.23%.
If you and your friend each roll two dice, there are two possible cases:
You both roll doubles (i.e., both dice show the same number).
You both roll non-doubles (i.e., the two dice show different numbers).
Let's calculate the probability of each case separately:
The probability of rolling doubles on one die is 1/6, since there are six possible outcomes (1, 2, 3, 4, 5, or 6) and only one of them will result in doubles. The probability of rolling doubles on both dice is the product of the probabilities of rolling doubles on each die, which is (1/6) * (1/6) = 1/36. Therefore, the probability that you and your friend both roll doubles is (1/36) * (1/36) = 1/1296.
The probability of rolling non-doubles on one die is 5/6, since there are five possible outcomes (2, 3, 4, 5, or 6) that will result in non-doubles, out of a total of six possible outcomes. The probability of rolling non-doubles on both dice is the product of the probabilities of rolling non-doubles on each die, which is (5/6) * (5/6) = 25/36. Therefore, the probability that you and your friend both roll non-doubles is (25/36) * (25/36) = 625/1296.
Therefore, the overall probability that you and your friend both have the same two numbers is the sum of the probabilities of the two cases:
1/1296 + 625/1296
= 626/1296
= 0.4823 (rounded to four decimal places)
So, the probability that you and your friend both have the same two numbers is approximately 0.4823, or about 48.23%.
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(1/3^4)^1/2
Please help
[tex]ANSWER \\ (( \frac{1}{3} ) {}^{4} ) {}^{ \frac{1}{2} } \\ [/tex]
simplify the expression
[tex]( \frac{1}{3} ) {}^{ \frac{4}{1} \times } {}^{ \frac{1}{2} } \\ ( \frac{1}{3} ) {}^{ \frac{4}{2} } \\ ( \frac{1}{3} ) {}^{2} \\ = \frac{1}{9} [/tex]
~hope it helps~
have a nice day (✿^‿^)
First, we need to calculate what's inside the parentheses of the exponent.
1/3^4 = 1/81
Now, we can simplify the exponent:
(1/81)^1/2 = 1/9
Therefore, (1/3^4)^1/2 = 1/9. <(￣︶￣)>
Students hypothesized that by running an electric current through the wire of the apparatus shown here, they could cause a non-magnetic nail to exhibit magnetic properties. What would be a reasonable way to test this?.
The reasonable way to test this one is to identify the validity of the hypothesis can be tested.
The hypothesis suggests that when an electric current passes through a wire, it generates a magnetic field. If this magnetic field is strong enough, it could magnetize a non-magnetic nail that is placed nearby. To test this hypothesis, an experiment can be conducted as follows:
A non-magnetic nail, a battery, a wire, and a switch.
Connect the wire to the battery and switch in series. The other end of the wire should be wrapped around the nail multiple times. Once the apparatus is set up, turn on the switch to pass an electric current through the wire.
Before running the current through the wire, test the nail for its magnetic properties by holding it close to some iron filings or other small magnetic objects. If it does not attract any of these objects, then it is non-magnetic.
Turn on the switch and run the electric current through the wire wrapped around the nail for a few minutes.
After running the current through the wire, test the nail again for its magnetic properties. Hold it close to the iron filings or other small magnetic objects and observe if it attracts them.
Compare the results obtained before and after running the current through the wire. If the nail exhibits magnetic properties after running the current, then the hypothesis that passing an electric current through a wire can magnetize a non-magnetic nail can be considered valid.
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a drawer has 2 red socks, 2 blue socks, and 2 green socks. two socks are pulled out on three successive days, without replacement. what is the 15 times the probability of pulling socks of different colors every day?
The 15 times the probability of pulling socks of different colors every day is 6/5 or 1.2.
What is probability?
Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.
The total number of socks in the drawer is 2 + 2 + 2 = 6.
On the first day, any sock can be chosen, so the probability of selecting a sock of a particular color is 2/6 = 1/3.
On the second day, there are only 5 socks left, so the probability of selecting a sock of a different color from the first day is 4/5.
On the third day, there are only 4 socks left, so the probability of selecting a sock of a different color from the first two days is 2/4 = 1/2.
To find the probability of pulling socks of different colors on all three days, we need to multiply the probabilities of each day:
P(different colors for all 3 days) = (1/3) × (4/5) × (1/2)
P(different colors for all 3 days) = 2/25
To get the 15 times probability, we multiply by 15:
15 × 2/25 = 6/5
Therefore, the answer is 6/5 or 1.2.
Hence, the 15 times the probability of pulling socks of different colors every day is 6/5 or 1.2.
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Use your calculator to evaluate cos − 1 ( − 0. 53 ) cos-1(-0. 53) to at least 3 decimal places. Give the answer in radians
The value of cos⁻¹(−0.53) is approximately equals to -1.012 radians (rounded to 3 decimal places).
Use the inverse cosine function on a calculator to find the value of cos⁻¹(−0.53),
Evaluate it to at least 3 decimal places, use the following steps,
cos⁻¹(−0.53) = x
⇒cos(x) = −0.53
Use the identity cos²(x) + sin²(x) = 1 to solve for sin(x),
⇒sin²(x) = 1 − cos²(x)
⇒sin²(x) = 1 − (−0.53)²
⇒sin²(x) = 0.7191
⇒ sin(x) ≈ ±0.8479
Both a positive and negative value for sin(x),
since sine is positive in both the first and second quadrants.
To determine which value of sin(x) is correct,
The range of values for the inverse cosine function.
The range of cos⁻¹(x) is [0, π], or [0°, 180°],
⇒ The output of the inverse cosine function is always a non-negative angle in the first or second quadrant.
Since sin(x) is negative in the second quadrant, eliminate the positive value for sin(x).
⇒ sin(x) = −0.8479
Now use the inverse sine function to find x,
⇒sin⁻¹(−0.8479) = x
⇒x ≈ -1.012radians
Therefore, cos⁻¹(−0.53) ≈ -1.012 radians (rounded to 3 decimal places).
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The above question is incomplete, the complete question is:
Use your calculator to evaluate cos⁻¹( − 0. 53 ) to at least 3 decimal places. Give the answer in radians
convert the numeral 201 (base three) to base 10
The numeral 201 (base three) is equivalent to 19 in base 10.
To understand how to convert the numeral 201 (base three) to base 10, it is helpful to first understand what these two number systems represent.
Base 3 (ternary) is a positional number system that uses three digits: 0, 1, and 2. Each digit represents a different power of 3, with the rightmost digit representing [tex]3^0[/tex], the next digit to the left representing [tex]3^1[/tex], and so on. Therefore, the numeral 201 (base three) can be interpreted as:
[tex]2 * 3^2 + 0 * 3^1 + 1 * 3^0[/tex]
To convert this numeral to base 10 (decimal), we simply evaluate this expression:
[tex]2 * 3^2 = 18[/tex]
[tex]0 * 3^1 = 0[/tex]
[tex]1 * 3^0 = 1[/tex]
Adding these values together, we get:
18 + 0 + 1 = 19
Therefore, the numeral 201 (base three) is equivalent to 19 in base 10.
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2. 25-kg object is attached to a horizontal an ideal massless spring on a frictionless table. What should be the spring constant of this spring so that the maximum acceleration of the object will be g when it oscillates with amplitude of 4. 50 cm?
The spring constant of the spring is determined as 5,444.4 N/m.
What is the spring constant of the spring?The maximum acceleration of the object in simple harmonic motion is given by:
a = ω²A
where;
ω is the angular frequencyA is the amplitude of the motionThe spring constant k is given as;
ω = √(k/m)
ω²m = k
ω² = k/m
a = ω²A
a = (k/m ) A
Where;
k is spring constantm is massa is maximum acceleration = g = 9.8 m/s²k/m = a/A
k = m (a/A)
k = 25 x 9.8 / 0.045
k = 5,444.4 N/m
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(Q3) a=3 cm, b=7 cm, c=7.4 cmThe triangle is a(n) _____ triangle.
Based on the given side lengths of 3cm, 7cm, and 7.4cm, the triangle is a(n) scalene triangle. In a scalene triangle, all sides have different lengths.
Triangles are described in terms of their sides and angles in geometry. A closed planar three-sided polygon shape with three sides and three angles is known as a triangle. The lengths of the sides of a scalene triangle vary. They are not equal, and the angles have three measurements. However, it still has a 180° angle sum, just like all triangles.
A scalene triangle is a triangle with three different side lengths and three different angle measurements. The total of all internal angles, however, is always equal to 180 degrees. As a result, it satisfies the triangle's condition of angle sum.
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Use the distributive property to rewrite the expression as a multiple of a sum of two numbers with no common factor. 18+30 ( I will give brainliest to whoever answers correctly)
The equivalent expression of 18 + 30 using distributive property is 6(3) + 6(5)
What are the distribution of the numbers?The distributive property states that for any numbers a, b, and c, a multiplied by (b+c) equals a multiplied by b plus a multiplied by c.
a(b + c) = a(b) + a(c)
The prime factor of 18 + 30 is written as;
18 + 30 = 2 x 3 x 3 + 2 x 3 x 5
18 + 30 = 2 x 3 x (3 + 5)
Simplifying the expression inside the parentheses gives:
2 x 3 x (3 + 5) = 6 (3 + 5)
applying distributive property we will have;
6 (3 + 5) = 6(3) + 6(5)
Thus, the final expression is; 18 + 30 = 6(3) + 6(5)
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The average return for large-cap domestic stock funds over three years was 14.4%. Assume the three-year returns were normally distributed across funds with a standard deviation of 4.4%.
(a)
What is the probability an individual large-cap domestic stock fund had a three-year return of at least 17%? (Round your answer to four decimal places.)
(b)
What is the probability an individual large-cap domestic stock fund had a three-year return of 10% or less? (Round your answer to four decimal places.)
(c)
How big does the return have to be to put a domestic stock fund in the top 15% for the three-year period? (Round your answer to two decimal places.)
%
A) The probability of a z-score of 0.5909 or higher is 0.0808.
B) The probability of a three-year return of 10% or less is 0.3413.
C) A return of at least 18.91% would put a domestic stock fund in the top 15% for the three-year period.
(a) The probability that an individual large-cap domestic stock fund had a three-year return of at least 17% is 0.0808.
To calculate this probability, we can use the z-score formula:
z = (x - μ) / σ
Where:
x = 17%
μ = 14.4%
σ = 4.4%
z = (17% - 14.4%) / 4.4% = 0.5909
Using a standard normal distribution table or calculator, we can find that the probability of a z-score of 0.5909 or higher is 0.0808.
(b) The probability that an individual large-cap domestic stock fund had a three-year return of 10% or less is 0.1151.
Using the same formula and substituting x = 10%, we get:
z = (10% - 14.4%) / 4.4% = -1.0000
The probability of a z-score of -1.0000 or lower is 0.1587. However, we want the probability of a return of 10% or less, so we need to subtract this probability from 0.5 (since the normal distribution is symmetric around 0) and round to four decimal places:
P(z ≤ -1.0000) = 0.1587
P(z ≥ 1.0000) = 0.1587
P(z ≤ -1.0000) + P(z ≥ 1.0000) = 0.3174
1 - 0.3174 = 0.6826
0.6826 / 2 = 0.3413
So, the probability of a three-year return of 10% or less is 0.3413.
(c) To be in the top 15% of large-cap domestic stock funds for the three-year period, a fund's return would need to be at least 18.91%.
To find this value, we need to find the z-score that corresponds to the top 15% of the distribution, which is 1.0364 (found using a standard normal distribution table or calculator). Then, we can use the z-score formula to solve for x:
1.0364 = (x - 14.4%) / 4.4%
x - 14.4% = 1.0364 * 4.4%
x = 18.91%
Therefore, a return of at least 18.91% would put a domestic stock fund in the top 15% for the three-year period.
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178 As shown below, the medians of AABC intersect at
D
A
3) 3
4) 4
G
B
D
E
F
C
If the length of BE is 12, what is the length of BD?
1) 8
2) 9
The length of BD is 8.
We can use the property that medians of a triangle divide each other in a 2:1 ratio.
Let BD be x. Then, using this property, we can write:
CE = 2ED
FA= 2FD
BE = 2 x ED
Since EB = 12, we can substitute 12 for EB and solve for ED:
12 = 2 x DE
DE = 6
Now, the length of DB is
= 12/3 + 12/3
= 4 + 4
= 8
Therefore, the length of DB is 8.
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Three men can build a grarge in eight days days. How many men are needed to build the garage in six days
If 3 men build a garage in 8 days, then 4 men will be needed to build the garage in 6 days.
The amount of work required to build the garage is constant, regardless of the number of days or workers involved. We assume that each worker does the same amount of work in a day, then we use the following formula;
⇒ work = rate × time,
where rate is = amount of work done by one worker in a day, and time is = number of days worked,
Let the number of workers needed be "x". If 3-workers can build the garage in 8 days, then we have:
⇒ work = 3 workers × 8 days = 24 worker-days,
If "x" workers are needed to build the garage in 6 days, then we have:
⇒ work = (x workers) × (6 days),
Since the amount of work is same in both cases, we equate the two expressions;
⇒ 3 workers × 8 days = x workers × 6 days
⇒ x = (3 workers × 8 days)/6 days = 4 workers;
Therefore, 4 workers are needed to build the garage in 6 days.
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solve. round to the nearest hundredth if necessary. a 5 kg ham costs $17/kg. find the cost per pound.
Answer:
1 kilogram = 2.204623 pounds
$17/kilogram = $17/2.204623 pounds
= $7.71/pound
A box at a miniature golf course contains contains 44 red golf balls, 88 green golf balls, and 77 yellow golf balls. What is the probability of taking out a golf ball and having it be a red or a yellow golf ball?
Express your answer as a percentage and round it to two decimal places.
Answer: 121/209= 57.89% rounded
Step-by-step explanation:
total golf balls are 209
add red + yellow balls = 121
121/209= 57.89% rounded
