Answer:
a.) .95
b.) The expected number of baskets is 10.50.
c.) 1.7748
Step-by-step explanation:
a.) This is a binomial distribution as there are two possibilities: makes a free throw or doesn't. This means that you can use the binomial function on a calculator to figure out the answer. Use the binomial CDF function on a calculator and the number of trials=15, probability of success=.7, lower bound=0, upper bound=7. Once you have evaluated the answer, .0500, it will need to be subtracted from1, as you want everything not included in this section. The answer to part a is thus 1-.0500=.95.
b.) The expected value is calculated by taking the total number of shots and multiplying it by the probability of making the shot: 15×.7=10.5 shots.
c.) The standard deviation of a binomial distribution can be calculated by the formula [tex]\sqrt{(sample size)(probability)(1-probability)}[/tex]. Plugging in the numbers you get [tex]\sqrt{(15)(.7)(.3)}[/tex]=1.7748.
A. The probability of more than 7 throws is 0.95,
B. The player expects to make it he takes 15 shots at 10.50,
C. The standard deviation of the number of successful free throws out of 15 total of 1.775.
What is binomial probability?The probability of exactly x successes on n repeated trials in an experiment with two possible outcomes, also known as a binomial experiment, is referred to as binomial probability.
The binomial probability is ⁿCₓpₓ(1 - p)ⁿ⁻ˣ if the probability of success on an individual trial is p.
In this case, the number of distinct combinations of x objects chosen from a set of n objects is shown by ⁿCₓ. A few course readings utilize the documentation (ⁿₓ) rather than ⁿCₓ.
Keep in mind that if p is the probability of a single trial's success, then (1p) is the probability of a single trial's failure.
Given the probability of free throws at 0.7
total free throws 15
Let x be the random variable
A. the probability that he will make more than 7 throws
p(x > 7)
ⁿCₓpₓ(1 - p)ⁿ⁻ˣ
where n = 15, x = 8
¹⁵C₈(0.7)⁸(0.3)⁷
0.94998 = 0.95
B: player expect to make it he takes 15 shots
E(x) = n x p(x)
E(x) = 15 × 0.7 = 10.50
C: The standard deviation
variance = n x p x q
variance = 15 x 0.7 x 0.3 = 3.15
SD = √(variance) = √(3.15)
SD = 1.77482 ≈ 1.775
Hence the probability that he will make more than 7 throws is 0.95,
the player expects to make it if he takes 15 shots is 10.50,
The standard deviation is 1.775.
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Which table represents a nonlinear function?
A two column table with five rows. The first column, x, has the entries, 0, 1, 2, 3. The second column, y, has the entries, negative 19, negative 11, negative 3, 5.
A two column table with five rows. The first column, x, has the entries, 0, 1, 2, 3. The second column, y, has the entries, negative 1.5, 1.5, 3, 4.5.
A two column table with five rows. The first column, x, has the entries, 0, 1, 2, 3. The second column, y, has the entries 15, 12, 9, 6.
Answer:
A two column table with five rows. The first column, x, has the entries, 0, 1, 2, 3. The second column, y, has the entries, negative 1.5, 1.5, 3, 4.5.
Step-by-step explanation:
When the x-values are evenly spaced, a linear function will have evenly-space y-values.
In the first table, the y-differences are all +8.
In the second table, the y-differences are 0, 1.5, 1.5, so are not all the same.
In the third table, the y-differences are all -3.
The second table represents a non-linear function.
__
In the graph, you can see that the points from the second table (purple) are not on a straight line.
Answer:
B
Step-by-step explanation:
The difference of a rational number and an irrational number is ____ an irrational number. Which word correctly fills in the blank to create a true statement?
A) sometimes
B) always
C) never
Answer:
a
Step-by-step explanation:
The difference between a rational number and an irrational number is always an irrational number. The correct option is B.
What is a rational and irrational number?A Rational Number is a number of the form p/q, p & q are integers, and q ≠ 0. An irrational number is all real numbers except rational numbers i.e. it is a non-repeating and non-terminating decimal number or it can not be expressed in a ratio of two integers.
Further, natural numbers can be rational numbers. Also, all repeating and terminating decimals are rational.
The difference between a rational number and an irrational number is always an irrational number. For example:
2 - √3 is always an irrational number where 2 is rational and √3 is an irrational number.
Hence addition and subtraction of rational and irrational numbers is always an irrational number.
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A recursion formula and the initial term of a sequence are given. Write out the first five terms of the sequence. a Subscript font size decreased by 1 1equals6, a Subscript n plus font size decreased by 1 1equalsminusa Subscript n
Answer:
6, -6, 6, -6 and 6.
Step-by-step explanation:
Given the recursion formula for a sequence
[tex]a_{n+1}=-a_n\\$where a_1=6\\[/tex]
The first five terms of the sequence are:
[tex]\text{First Term, }a_1=6\\$Second Term, a_2=a_{1+1}=-a_1=-6\\$Third term, a_3=a_{2+1}=-a_2=6\\$Fourth term, a_4=a_{3+1}=-a_3=-6\\$Fifth term, a_5=a_{4+1}=-a_4=6[/tex]
Therefore, the first five terms of the sequence:
[tex]a_1,a_2,a_3,a_4,a_5=6, -6, 6, -6$ and 6.[/tex]
An attendant at a car wash is paid according to the number of cars that pass through. Suppose that following payments are made with the following probabilities: Payment Probability $7 0.18 $9 0.08 $11 0.09 $13 0.16 $15 0.08 $17 0.41 Find the standard deviation of the attendant's earnings.
Answer:
[tex] E(X) = 7*0.18 +9*0.08 +11*0.09 +15*0.08 +17*0.41 =13.22[/tex]
And we can find the second moment with this formula:
[tex] E(X^2) = \sum_{i=1}^n X^2_i P(X_i)[/tex]
And replacing we got:
[tex] E(X^2) = 7^2*0.18 +9^2*0.08 +11^2*0.09 +15^2*0.08 +17^2*0.41 =189.72[/tex]
And we can find the variance like this:
[tex] Var(X) = E(X^2) -[E(X)]^2= 189.72- (13.22)^2 =14.9516[/tex]
And the deviation would be:
[tex] Sd(X)= \sqrt{14.9516}= 3.867[/tex]
Step-by-step explanation:
For this case we have the following dataset given:
Payment $7 $9 $11 $13 $15 $17
Probability 0.18 0.08 0.09 0.16 0.08 0.41
For this case we can calculate the mean with this formula:
[tex] E(X) = \sum_{i=1}^n X_i P(X_i)[/tex]
And replacing we got:
[tex] E(X) = 7*0.18 +9*0.08 +11*0.09 +15*0.08 +17*0.41 =13.22[/tex]
And we can find the second moment with this formula:
[tex] E(X^2) = \sum_{i=1}^n X^2_i P(X_i)[/tex]
And replacing we got:
[tex] E(X^2) = 7^2*0.18 +9^2*0.08 +11^2*0.09 +15^2*0.08 +17^2*0.41 =189.72[/tex]
And we can find the variance like this:
[tex] Var(X) = E(X^2) -[E(X)]^2= 189.72- (13.22)^2 =14.9516[/tex]
And the deviation would be:
[tex] Sd(X)= \sqrt{14.9516}= 3.867[/tex]
10,25,35,45... What's the pattern?
Answer:
15
Step-by-step explanation:
The pattern is going by 15 because 10+15=25 and then continue going.
Answer:
15 is the answer
Step-by-step explanation:
Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 50.7 degrees. Low Temperature (circleF) 40 minus 44 45minus49 50 minus 54 55 minus 59 60 minus 64 Frequency 2 7 9 5 1 The mean of the frequency distribution is nothing degrees. (Round to the nearest tenth as needed.)
Answer:
51.2°FStep-by-step explanation:
Find the exact frequency table in the diagram attached. x is the midpoint of the interval f is the frequency. Using the formula below to find the mean;
[tex]\overline x = \frac{\sum fx}{\sum f} \\[/tex]
[tex]\sum fx = (42*2)+(47*7)+(52*9)+(57*5)+(62*1)\\\sum fx = 84+329+468+285+62\\\sum fx = 1,228\\\sum f = 24\\\\\overline x = \frac{1,228}{24} \\\overline x = 51.17^{0} F[/tex]
The mean of the frequency distribution compare to the actual mean of 50.7°F is 51.2°F(to nearest tenth)
A certain bridge arch is in the shape of half an ellipse 106 feet wide and 33.9 feet high. At what horizontal distance from the center of the arch is the height equal to 12.3 feet
Answer:
The horizontal distance from the center is 49.3883 feet
Step-by-step explanation:
The equation of an ellipse is equal to:
[tex]\frac{x^2}{a^{2} } +\frac{y^2}{b^{2} } =1[/tex]
Where a is the half of the wide, b is the high of the ellipse, x is the horizontal distance from the center and y is the height of the ellipse at that distance.
Then, replacing a by 106/2 and b by 33.9, we get:
[tex]\frac{x^2}{53^{2} } +\frac{y^2}{33.9^{2} } =1\\\frac{x^2}{2809} +\frac{y^2}{1149.21} =1[/tex]
Therefore, the horizontal distances from the center of the arch where the height is equal to 12.3 feet is calculated replacing y by 12.3 and solving for x as:
[tex]\frac{x^2}{2809} +\frac{y^2}{1149.21} =1\\\frac{x^2}{2809} +\frac{12.3^2}{1149.21} =1\\\\\frac{x^2}{2809}=1-\frac{12.3^2}{1149.21}\\\\x^{2} =2809(0.8684)\\x=\sqrt{2809(0.8684)}\\x=49.3883[/tex]
So, the horizontal distance from the center is 49.3883 feet
Rainwater was collected in water collectors at thirty different sites near an industrial basin and the amount of acidity (pH level) was measured. The mean and standard deviation of the values are 4.9 and 1.5 respectively. When the pH meter was recalibrated back at the laboratory, it was found to be in error. The error can be corrected by adding 0.2 pH units to all of the values and then multiply the result by 1.3. Find the mean and standard deviation of the corrected pH measurements.
Answer:
The mean and standard deviation of the corrected pH measurements are 6.63 and 3.8025 respectively.
Step-by-step explanation:
We can correct the values of the mean and standard deviation using the properties of the mean and the variance.
To the original value X we have to add 0.2 and multiply then by 1.3 to calculate the new and corrected value Y:
[tex]Y=1.3(X+0.2)[/tex]
The mean and standard deviation of the original value X are 4.9 and 1.5 respectively.
Then, we can apply the properties of the mean as:
[tex]E(Y)=E(1.3(X+0.2))=1.3E(X+0.2)=1.3E(X)+1.3*0.2\\\\E(Y)=1.3E(X)+0.26\\\\E(Y)=1.3*4.9+0.26=6.37+0.26=6.63[/tex]
For the standard deviation, we apply the properties of variance:
[tex]V(Y)=V(1.3(X+0.2))\\\\V(Y)=1.3^2\cdot V(X+0.2)\\\\V(Y)=1.69\cdot V(X)\\\\V(Y)=1.69\cdot 1.5^2=1.69\cdot 2.25=3.8025[/tex]
The properties that have been applied are:
[tex]1.\,E(aX)=aE(X)\\\\ 2.\,E(X+b)=E(X)+b\\\\3.\,V(aX)=a^2V(X)\\\\4.\,V(X+b)=V(X)+0[/tex]
Does anyone know this? I think its B? Am i correct?
Yes, B. Rising action is correct
15 divided by 6 2/3=
Answer:
The answer is D.
Step-by-step explanation:
First, you have to convert the mixed number into improper fraction :
[tex]6 \frac{2}{3} [/tex]
[tex] = \frac{3 \times 6 + 2}{3} [/tex]
[tex] = \frac{20}{3} [/tex]
Next, you can divide it by cutting out the common factor :
[tex]15 \div \frac{20}{3} [/tex]
[tex] = 15 \times \frac{3}{20} [/tex]
[tex] = 3 \times \frac{3}{4} [/tex]
[tex] = \frac{9}{4} [/tex]
[tex] = 2 \frac{1}{4} [/tex]
The value of the expression after divide is,
⇒ 2 1/4
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The expression is,
⇒ 15 divided by 6 2/3
Now,
We can divide as;
⇒ 15 divided by 6 2/3
⇒ 15 ÷ 6 2/3
⇒ 15 ÷ 20/3
⇒ 15 × 3/20
⇒ 45/20
⇒ 9/4
⇒ 2 1/4
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The equation r(t) = sin(4t)i + cos(4t)j, 0t≥0 describes the motion of a particle moving along the unit circle. Answer the following questions about the behavior of the particle.
a. Does the particle have constant speed? If so, what is its constant speed?
b. Is the particle's acceleration vector always orthogonal to its velocity vector?
c. Does the particle move clockwise or counterclockwise around the circle?
d. Does the particle begin at the point (1,0)?
Answer:
a) Particle has a constant speed of 4, b) Velocity and acceleration vector are orthogonal to each other, c) Clockwise, d) False, the particle begin at the point (0,1).
Step-by-step explanation:
a) Let is find first the velocity vector by differentiation:
[tex]\vec v = \frac{dr_{x}}{dt} i + \frac {dr_{y}}{dt} j[/tex]
[tex]\vec v = 4\cdot \cos 4t\, i - 4 \cdot \sin 4t \,j[/tex]
[tex]\vec v = 4 \cdot (\cos 4t \, i - \sin 4t\,j)[/tex]
Where the resultant vector is the product of a unit vector and magnitude of the velocity vector (speed). Velocity vector has a constant speed only if magnitude of unit vector is constant in time. That is:
[tex]\|\vec u \| = 1[/tex]
Then,
[tex]\| \vec u \| = \sqrt{\cos^{2} 4t + \sin^{2}4t }[/tex]
[tex]\| \vec u \| = \sqrt{1}[/tex]
[tex]\|\vec u \| = 1[/tex]
Hence, the particle has a constant speed of 4.
b) The acceleration vector is obtained by deriving the velocity vector.
[tex]\vec a = \frac{dv_{x}}{dt} i + \frac {dv_{y}}{dt} j[/tex]
[tex]\vec a = 16\cdot (-\sin 4t \,i -\cos 4t \,j)[/tex]
Velocity and acceleration are orthogonal to each other only if [tex]\vec v \bullet \vec a = 0[/tex]. Then,
[tex]\vec v \bullet \vec a = 64 \cdot (\cos 4t)\cdot (-\sin 4t) + 64 \cdot (-\sin 4t) \cdot (-\cos 4t)[/tex]
[tex]\vec v \bullet \vec a = -64\cdot \sin 4t\cdot \cos 4t + 64 \cdot \sin 4t \cdot \cos 4t[/tex]
[tex]\vec v \bullet \vec a = 0[/tex]
Which demonstrates the orthogonality between velocity and acceleration vectors.
c) The particle is rotating clockwise as right-hand rule is applied to model vectors in 2 and 3 dimensions, which are associated with positive angles for position vector. That is: [tex]t \geq 0[/tex]
And cosine decrease and sine increase inasmuch as t becomes bigger.
d) Let evaluate the vector in [tex]t = 0[/tex].
[tex]r(0) = \sin (4\cdot 0) \,i + \cos (4\cdot 0)\,j[/tex]
[tex]r(0) = 0\,i + 1 \,j[/tex]
False, the particle begin at the point (0,1).
Add. Write your answer in simplest form. 7/10 + 1/4
Answer:
[tex] \frac{19}{20} [/tex]
Step-by-step explanation:
[tex] \frac{7}{10} + \frac{1}{4} \\ \frac{14 + 5}{20} \\ = \frac{19}{20} [/tex]
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Write an equation that would represent the following word problem: Billy buys one candy bar for $2 and 3 lollipops. If he spends $3.98 in total, how much is each lollipop? [USE x AS YOUR VARIABLE - DO NOT USE SPACES IN YOUR ANSWER]
The risk of a child developing cancer is approx 3 in 1500. If there are approx 11,721,722 children, how many have cancer?
Answer:
Approximately 23,433 children will have cancer.
Step-by-step explanation:
3/1500 can be simplified to 1/500, which can also be written as 0.002. To find the number of children who have cancer, we do 11,721,722 * 0.002, which gives us 23,433.444 which we can round to 23,433.
What value of x is in the solution set of 3(x – 4) ≥ 5x + 2? –10 –5 5 10
Answer:I think it -5 wait lemme check answer again
The solution to the inequality will be greater than or equal to –5. Then the correct option is B.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The inequality is given below.
3(x – 4) ≥ 5x – 2
Simplify the equation, then the solution to inequality will be
3(x – 4) ≥ 5x –2
3x – 12 ≥ 5x –2
5x – 3x ≤ – 12 + 2
2x ≤ – 10
x ≤ –5
The solution to the inequality will be greater than or equal to –5.
Then the correct option is B.
The correct equation is 3(x – 4) ≥ 5x – 2.
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One number is 1/2 another number. The sum of the two numbers is 33. Find the two numbers.
Answer:
11
Step-by-step explanation:
I looked it up for you so no problem
Answer: 11 and 22
Step-by-step explanation:
We can start by making an equation. Since we know we have two numbers added to make 33. One number can be represented by x and the other is half of this x number so we can write this equation.
33 = 1/2x + x
Now we can combine like terms.
33 = 3/2x
Then either multiply by the reciprocal or divide by 1.5 on both sides.
x = 22
And the other number is half this number so divide by 2.
y = 11
On a game show, 14 contestants qualified for the bonus round and 6 contestants did not.
What is the experimental probability that the next contestant will qualify for the bonus round?
Write your answer as a fraction or whole number.
Answer:
The experimental probability that the next contestant will qualify for the bonus round is [tex]\frac{7}{10}[/tex]
Step-by-step explanation:
The experimental probability of an outcome is the number of trials in which the desired outcome happened divided by the total number of trials.
What is the experimental probability that the next contestant will qualify for the bonus round?
14 contestants qualified out of 14+6 = 20 contestants. So
[tex]p = \frac{14}{20} = \frac{7}{10}[/tex]
The experimental probability that the next contestant will qualify for the bonus round is [tex]\frac{7}{10}[/tex]
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absurd answers WILL be recorded!
Please try!!!
Answer:
462cm^3
Step-by-step explanation:
Volume of a pyramid = 1/3 × base area × height
Now the base is a rectangle with sides 7cm and 18cm; area of base is;
7 × 18 = 126cm^2
Therefore volume =
1/3 × 126 × 11 = 42 × 11= 462cm^3
The arithmetic sequence a1 is defined by the formula:
a1 = 4
a1=ai-1 +11
Find the sum of the first 650 terms in the sequence.
Answer:
2,322,775
Step-by-step explanation:
Given a1 = 4 and ai =ai-1 +11
when i = 2
a2 = a2-1+11
a2 = a1+11
a2 = 4+11
a2 = 15
when i = 3
a3 = a2+11
a3 = 15+11
a3 = 26
The sequence formed by a1, a2, a3... is am arithmetic sequence as shown;
4, 15, 26...
Sum of nth term of an arithmetic sequence = n/2{2a+(n-1)d}
a is the first term = 4
d is the common difference = 15-4 = 26-15 = 11
n is the number of terms.
Since we are to find the sum of the first 650 terms in the sequence, n = 650
S650 = 650/2{2(4)+(650-1)11}
S650 = 325{8+(649)11}
S650 = 325(8+7,139)
S650 = 325×7147
S650 = 2,322,775
The area of the trapezoid is 24 in.2.
True or false
Answer:
The answer is true
Step-by-step explanation:
To find the area of a trapezoid, multiply the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then divide by 2
A research company desires to know the mean consumption of meat per week among people over age 29. A sample of 2092 people over age 29 was drawn and the mean meet consumption was 2.9 pounds. Assume that the standard deviation is known to be 1.4 pounds. Construct a 95% confidence interval for the mean consumption of meat among people over age 29. Round your answer to one decimal place.
Answer:
The 95% confidence interval for the mean consumption of meat among people over age 29 is between 2.8 pounds and 3 pounds.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96*\frac{1.4}{\sqrt{2092}} = 0.1[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 2.9 - 0.1 = 2.8 pounds
The upper end of the interval is the sample mean added to M. So it is 2.9 + 0.1 = 3 pounds.
The 95% confidence interval for the mean consumption of meat among people over age 29 is between 2.8 pounds and 3 pounds.
Answer:
[tex]2.9-1.96\frac{1.4}{\sqrt{2092}}=2.84[/tex]
[tex]2.9+1.96\frac{1.4}{\sqrt{2092}}=2.96[/tex]
The confidence interval is given by [tex]2.84 \leq \mu \leq 2.96[/tex]
Step-by-step explanation:
Information given
[tex]\bar X=2.9[/tex] represent the sample mean
[tex]\mu[/tex] population mean
[tex]\sigma =1.4[/tex] represent the population standard deviation
n=2092 represent the sample size
Confidence interval
The confidence interval is given by:
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
Since the Confidence interval is 0.95 or 95%, the significance is [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical value would be [tex]z_{\alpha/2}=1.96[/tex]
Replacing the info we got:
[tex]2.9-1.96\frac{1.4}{\sqrt{2092}}=2.84[/tex]
[tex]2.9+1.96\frac{1.4}{\sqrt{2092}}=2.96[/tex]
The confidence interval is given by [tex]2.84 \leq \mu \leq 2.96[/tex]
What’s the correct answer for this?
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Tangents that meet at a point are equal in length so DB = CB
Let's form an equation:
10x + 16 = 5x + 20
- 16 from both sides
10x = 5x + 4
- 5x from both sides
5x = 4
/5 on both sides
x = 4/5
Sub this value into the expression for CB
5(4/5) + 20 = 24
Thus, the answer is option D. 24
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Answer:
4TH OPTION
Step-by-step explanation:
IN A CIRCLE , TANGENT DRAWN FROM AN EXTERNAL POINT TO THE CIRCLE ARE EQUAL.
ie BD = BC
ie 10x +16 = 5x+20
10x - 5x = 20 -16
5x = 4
x = 4/5
therfore BC = 5x+20 = 5*4/5 +20
BC= 4+20
BC = 24
HOPE IT HELPS...
value of 2 to the 3 power
Answer:
two to the thrid power is 8.
Step-by-step explanation:
2^3= 8
Answer:
I'm not sure what exactly the question is but it should be 8
Step-by-step explanation:
2^3
2×2×2=8
One inlet pipe can fill an empty pool in 6 hours, and a drain can empty the pool in 12 hours. How long will it take the pipe to fill the pool if the drain is left open?
Answer: 12 hours
Step-by-step explanation:
Let x = time it takes to fill the pool if the inlet pipe and drain pipe are both open
1/6 = portion of pool filled per hour by the inlet pipe
1/12 = portion of pool emptied per hour by the drain
1/x = portion of pool filled per hour if the inlet pipe and drain are both open
Then, 1/6 - 1/12 = 1/x
Multiply by the LCD, 12x, to obtain
2x - x = 12
x = 12 hours
You look at a caterpillar under a magnifying glass. The image of the caterpillar is three times the caterpillar's actual size and has a width of 4 in. Find the actual dimension of the caterpillar. Select one: a. 12 in. b. 3 in. c. 4/3 in. d. 3/4 in.
Answer: c
Step-by-step explanation: 4/1 x 1/3 = 4/3
Leap years are years in which February has 29 days instead of 28. The device of leap year was invented to keep the calendar in sync with the "True time of year" because a year has approximately 3651/4 days, but actually slightly less, most, but not all, years divisible by 4 have been made leap years. The rule that is used to keep the calendar in sync is:
Answer:
As you know, a year has around 365 + 1/4 days.
This means that in two years, we have:
365 + 356 + 1/4 + 1/4 = 730 + 1/2
and so on.
adding this up, when we have 4 years we have a full day extra, this is:
1460 + 1
When we divide 1461 by 4, we have 365 with a surpass of 1.
The rule used to keep the calendar in sync with this extra day is adding an extra day to each fourth year.
So each fourth year, we have an extra day in Februray (the Februray 29th), this is called a bisiest year.
The "math rule" used to know if a year is leap or not is:
if a year is not divisible by 4, then it is a common year
else if the year is not divisible by 100 then it is a leap year,
else if the year is not divisible by 400, then it is a common year
if not, the year is a leap year.
Where "year" represents the number of the year.
Please help i do not understand this one!
Answer:
B. [[0,4]
[-6,1]
[3,-4]]
Step-by-step explanation:
If you multiply the matrices, you get the answer.
A sample of 60 items from population 1 has a sample variance of 8 while a sample of 40 items from population 2 has a sample variance of 10. If we want to test whether the variances of the two populations are equal, the test statistic will have a value of
Answer:
H0: [tex] \sigma^2_1 = \sigma^2_2[/tex]
H1: [tex] \sigma^2_1 \neq \sigma^2_2[/tex]
The statistic would be given by:
[tex]F=\frac{s^2_2}{s^2_1}=\frac{10}{8}=1.25[/tex]
Step-by-step explanation:
Information given
[tex]n_1 = 60 [/tex] represent the sample size 1
[tex]n_2 =40[/tex] represent the sample size 2
[tex]s^2_1 = 8[/tex] represent the sample variance 1
[tex]s^2_2 = 10[/tex] represent the sample variance 2
The statistic to check the hypothesis is given by:
[tex]F=\frac{s^2_2}{s^2_1}[/tex]
Hypothesis to test
We want to test if the two variances are equal, so the system of hypothesis are:
H0: [tex] \sigma^2_1 = \sigma^2_2[/tex]
H1: [tex] \sigma^2_1 \neq \sigma^2_2[/tex]
The statistic would be given by:
[tex]F=\frac{s^2_2}{s^2_1}=\frac{10}{8}=1.25[/tex]
Rajeev walked 7/8 mile in 1/4 hour. what was his speed in miles per hour?
Answer:
V(speed)=3.5 mile per hour
Step-by-step explanation:
[tex]V=mile per hour[/tex]
[tex]V=\frac{7}{8}/ \frac{1}{4}[/tex]
[tex]V=\frac{7}{8}*\frac{4}{1}[/tex]
[tex]V=\frac{7}{8}*4[/tex]
[tex]V=3.5[/tex]
How many 1/2 are there in 6/4
Answer:
3
Step-by-step explanation:
6/4 (divide numerator and denominator each by 2)
= 3/2
= 3 x (1/2)
hence there are 3 halves in 6/4
Answer:
3
Step-by-step explanation:
To find out, we need to divide.
[tex]\frac{6}{4}[/tex] ÷ [tex]\frac{1}{2}[/tex]
When dividing fractions, you multiply the 1st term by the second term's reciprocal.
so
[tex]\frac{6}{4}[/tex] x 2
If you simplify you get [tex]\frac{6}{2}[/tex] or 3.
