Answers
Answer:
[tex]\dfrac{6^2-3^2}{2}=\dfrac{27}{2}[/tex]
Step-by-step explanation:
You can go to the trouble to integrate y = x from 3 to 6, or you can figure the area geometrically.
[tex]\displaystyle\int_3^6{x}\,dx=\left.\dfrac{x^2}{2}\right|_3^6=\dfrac{6^2-3^2}{2}\quad\text{using integration}\\\\A=\dfrac{1}{2}(b_1+b_2)h=\dfrac{1}{2}(6+3)(6-3)=\dfrac{6^2-3^2}{2}\quad\text{using geometry}[/tex]
Related Questions
if 7 is added to a number then it becomes at least 15 what is the number?
Answers
Step-by-step explanation:
yeah,when 15-7=8
the number is 8
Find the fourth term in the expansion of the binomial
(4x + y)^4
a) 16xy^3
b) 256x^4
c) 64y^4
d) 4xy^3
Answers
Answer:
a) 16xy³
Step-by-step explanation:
For a binomial expansion (a + b)ⁿ, the r+1 term is:
nCr aⁿ⁻ʳ bʳ
Here, a = 4x, b = y, and n = 4.
For the fourth term, r = 3.
₄C₃ (4x)⁴⁻³ (y)³
4 (4x) (y)³
16xy³
the required condition for using an anova procedure on data from several populations for mean comparison is that the
Answers
Answer:
The sampled populations have equal variances
Step-by-step explanation:
ANOVA which is fully known as Analysis of variances can be defined as the collection of statistical models as well as their associated estimation procedures which enables easily and effectively analyzis of the differences among various group means in a sample reason been that ANOVA is a total variance in which the observed variance in a specific variable is been separated into components which are attributable to various sources of variation which is why ANOVA help to provides a statistical test to check whether two or more population means are equal.
Therefore the required condition for using an ANOVA procedure on data from several populations for mean comparison is that THE SAMPLED POPULATION HAVE EQUAL VARIANCE.
what is the solution for the inequality l2x-6l<4
Answers
Answer:
x < 5 or x > 1
Step-by-step explanation:
2x - 6 < 4
2x < 4 + 6
2x < 10
x < 10/2
x < 5
2x - 6 > - 4
2x > - 4 + 6
2x > 2
x > 2/2
x > 1
What steps are used to solve the equation? g – 8 = 14 Complete the statements. First, both sides of the equation. The solution of the equation is . Check the solution by substituting for g and simplifying.
Answers
Answer:
g=22
Step-by-step explanation:
add 8 to both sides
g-8=14
g-8+8=14+8
g=14+8
g=22
The solution of expression g - 8 = 14 is,
⇒ g = 22
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The equation is,
⇒ g - 8 = 14
Now, We can simplify as,
⇒ g - 8 = 14
Add 8 both side,
⇒ g - 8 + 8 = 14 + 8
⇒ g = 22
Thus, The solution of expression g - 8 = 14 is,
⇒ g = 22
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An athletics coach states that the distribution of player run times (in seconds) for a 100-meter dash is normally distributed with a mean equal to 13.00 and a standard deviation equal to 0.2 seconds. What percentage of players on the team run the 100-meter dash in 13.36 seconds or faster
Answers
Answer:
96.41% of players on the team run the 100-meter dash in 13.36 seconds or faster
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 13, \sigma = 0.2[/tex]
What percentage of players on the team run the 100-meter dash in 13.36 seconds or faster
We have to find the pvalue of Z when X = 13.36.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{13.36 - 13}{0.2}[/tex]
[tex]Z = 1.8[/tex]
[tex]Z = 1.8[/tex] has a pvalue of 0.9641
96.41% of players on the team run the 100-meter dash in 13.36 seconds or faster
The mean height of women in a country (ages 20-29) is 63.5 inches. A random sample of 50 women in this age group is selected. What is the probability that the mean height for the sample is greater than 64 inches? Assume the standard deviation equals 2.96.
Answers
Answer:
11.70% probability that the mean height for the sample is greater than 64 inches
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
[tex]\mu = 63.5, \sigma = 2.96, n = 50, s = \frac{2.96}{\sqrt{50}} = 0.4186[/tex]
What is the probability that the mean height for the sample is greater than 64 inches?
This is 1 subtracted by the pvalue of Z when X = 64.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{64 - 63.5}{0.4186}[/tex]
[tex]Z = 1.19[/tex]
[tex]Z = 1.19[/tex] has a pvalue of 0.8830
1 - 0.8830 = 0.1170
11.70% probability that the mean height for the sample is greater than 64 inches
PLEASE HELP!!!! Find the common difference
Answers
Answer:
The common difference is 1/2
Step-by-step explanation:
Data obtained from the question include:
3rd term (a3) = 0
Common difference (d) =.?
From the question given, we were told that the 7th term (a7) and the 4th term (a4) are related by the following equation:
a7 – 2a4 = 1
Recall:
a7 = a + 6d
a4 = a + 3d
a3 = a + 2d
Note: 'a' is the first term, 'd' is the common difference. a3, a4 and a7 are the 3rd, 4th and 7th term respectively.
But, a3 = 0
a3 = a + 2d
0 = a + 2d
Rearrange
a = – 2d
Now:
a7 – 2a4 = 1
Substituting the value of a7 and a4, we have
a + 6d – 2(a + 3d) = 1
Sustitute the value of 'a' i.e –2d into the above equation, we have:
–2d + 6d – 2(–2d + 3d) = 1
4d –2(d) = 1
4d –2d = 1
2d = 1
Divide both side by 2
d = 1/2
Therefore, the common difference is 1/2
***Check:
d = 1/2
a = –2d = –2 x 1/2 = –1
a3 = 0
a3 = a + 2d
0 = –1 + 2(1/2)
0 = –1 + 1
0 = 0
a7 = a + 6d = –1 + 6(1/2) = –1 + 3 = 2
a4 = a + 3d = –1 + 3(1/2) = –1 + 3/2
= (–2 + 3)/2 = 1/2
a7 – 2a4 = 1
2 – 2(1/2 = 1
2 – 1 = 1
1 = 1
A courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the true proportion is 0.050.05. If 212212 are sampled, what is the probability that the sample proportion will differ from the population proportion by less than 0.030.03
Answers
Answer:
95.44% probability that the sample proportion will differ from the population proportion by less than 0.03.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
[tex]p = 0.05, n = 212, \mu = 0.05, s = \sqrt{\frac{0.05*0.95}{212}} = 0.015[/tex]
What is the probability that the sample proportion will differ from the population proportion by less than 0.03?
This is the pvalue of Z when X = 0.03 + 0.05 = 0.08 subtracted by the pvalue of Z when X = 0.05 - 0.03 = 0.02. So
X = 0.08
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.08 - 0.05}{0.015}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772
X = 0.02
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.02 - 0.05}{0.015}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a pvalue of 0.0228
0.9772 - 0.0228 = 0.9544
95.44% probability that the sample proportion will differ from the population proportion by less than 0.03.
Josh and Lucy share some money in the ratio 3:7. What fraction of the money does Josh receive?
Answers
Answer:
3/10ths of the money
Step-by-step explanation:
Add together the two numbers to get the total.
Josh gets 30 percent and Lucy gets 70 percent.
3/10
Answer:
3/10
Step-by-step explanation:
3+7=10
Josh=3
Lucy=7
The length of the rectangle is described by the function y = 3x + 6, where x is the width of the rectangle. Find the domain in this situation.
Answers
Answer:2/3
Step-by-step explanation:
Given that the length of the rectangle is described by the function y = 3x + 6, where x is the width of the rectangle. The domain of the function is (0, ∞).
What is domain of a function?The domain of a function is the set of all possible inputs for the function. In other words, domain is the set of all possible values of x. In this question, x is the width of the rectangle. Width of a rectangle existing in two dimensional space, cannot be negative or zero. Thus it is the set of all positive real numbers, or we say, (0, ∞).
Learn more about domain of a function here
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What is the measure of PSQ?
Answers
Answer:
Do you have an image because I'm a bit confused with you just asking the measure of PSQ.
Step-by-step explanation:
Of 41 bank customers depositing a check, 22 received some cash back. Construct a 90 percent confidence interval for the proportion of all depositors who ask for cash back. (Round your answers to 4 decimal places.)
Answers
Answer:
CI: {0.4085; 0.6647}
Step-by-step explanation:
The confidence interval for a proportion (p) is given by:
[tex]p \pm z*\sqrt{\frac{(1-p)*p}{n} }[/tex]
Where n is the sample size, and z is the z-score for the desired confidence interval. The score for a 90% confidence interval is 1.645. The proportion of depositors who ask for cash back is:
[tex]p=\frac{22}{41}=0.536585[/tex]
Thus the confidence interval is:
[tex]0.536585 \pm 1.645*\sqrt{\frac{(1-0.536585)*0.536585}{41}}\\0.536585 \pm 0.128109\\L=0.4085\\U=0.6647[/tex]
The confidence interval for the proportion of all depositors who ask for cash back is CI: {0.4085; 0.6647}
The weight of a chocolate bar is 4.4 ounces, but can vary. Let W be a random variable that represents the weight of a chocolate bar. The probability density function of Wis given below. If the shaded portion of the graph of the continuous probability density function below is 0.42739, what is the probability that a chocolate bar is at least 4 ounces, but no more than 7 ounces?
Answers
Answer:
Ans) 42.7%
Step-by-step explanation:
For a continuous probability distribution, a curve known as probability density function contains information about these probabilities.
in the given range -
The probability that a continuous random variable = equal to the area under the probability density function curve
The probability that the value of a random variable is equal to 'something' is 1.
As per the diagram,
Weight of chocolate bar between 4 ounces and 7 ounces is highlighted in the blue part. That area is said to be 0.42739 and the total area under the curve is 1.
Hence required probability
=0.42739/1=0.42739
Ans) 42.7%
Round to nearest tenth of a percent
Please answer this correctly
Answers
Step-by-step explanation:
pnotgrt8rthan4 = 3 ÷ 7 × 100
= 42.8571428571 / 43%
Please answer this correctly
Answers
Answer:
2/3
Step-by-step explanation:
There are 2 numbers out of 3 that fit the rule, 1 and 3. There is a 2/3 chance picking one of them.
Answer:
2/3Step-by-step explanation:
This is the answer because one number that is select is one. A number greater than 2 is 3. SO it is 2/3.
A child is 2 -1/2 feet tall. The child’s mother is twice as tall as the child. How tall is the child’s mother
Answers
Answer:
5 feet
Step-by-step explanation:
"Twice as tall" means "2 times as tall".
2 × (2 1/2 ft) = (2 × 2 ft) +(2 × (1/2 ft)) = 4 ft + 1 ft = 5 ft
The child's mother is 5 feet tall.
Answer:
The mother is 5ft tall
Step-by-step explanation:
2 1/2 + 2 1/2 = 5ft
2ft+2ft = 4ft
1/2+1/2= 1ft
4ft+1ft = 5ft
About ____% of the area is between z= -2 and z= 2 (or within 2 standard deviations of the mean)
Answers
Answer:
The percentage of area is between Z =-2 and Z=2
P( -2 ≤Z ≤2) = 0.9544 or 95%
Step-by-step explanation:
Explanation:-
Given data Z = -2 and Z =2
The probability that
P( -2 ≤Z ≤2) = P( Z≤2) - P(Z≤-2)
= 0.5 + A(2) - ( 0.5 - A(-2))
= A (2) + A(-2)
= 2 × A(2) (∵ A(-2) = A(2)
= 2×0.4772
= 0.9544
The percentage of area is between Z =-2 and Z=2
P( -2 ≤Z ≤2) = 0.9544 or 95%
WWW
3.
The expression "5 FACTORIAL" equals
3-A
125
3-B
120
3-C
25
3-D
10
* Select Answer Below
Answers
Answer:
5! = 120
Step-by-step explanation:
5! is basically 5(4)(3)(2)(1).
Please answer this correctly
Answers
Answer:
1/7
Step-by-step explanation:
There are 7 cards, 1 of which is less than 2. Therefore, P (less then 2) = 1/7
Answer:
1/7
Step-by-step explanation:
The number from the list that is less than 2 is 1.
1 number out of a total of 7 numbers.
= 1/7
Given the equation 4x - 3y = 12
1. Write the equation in slope-intercept form.
2. Identify the slope and y-intercept.
3. Graph the line.
4. Identify if it is a positive or negative slope.
Answers
Answer:
see below
Step-by-step explanation:
Slope intercept form is y = mx+b where m is the slope and b is the y intercept
4x - 3y = 12
Solve for y
Subtract 4x from each side
4x-4x - 3y =-4x+ 12
-3y = -4x+12
Divide by -3
-3y/-3 = -4x/-3 + 12/-3
y = 4/3x -4
The slope is 4/3 and the y intercept is -4
The slope is Positive
find the third angle in a triangle when the other two angles are (2a-32)° and (3a+22)°
Answers
Answer:
(190-5a)°
Step-by-step explanation:
Sum of internal angles of a triangle equals to 180°
If the third angle is x, then we have:
(2a-32)°+(3a+22)° +x = 180°(5a- 10)° +x= 180°x= (180+10-5a)°x= (190-5a)°The third angle is: (190-5a)°
What is the equation of the line which passes through (-0.5,-5) and (2,5)
Answers
Answer:
by using distance formula
d=[tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
by putting the values of coordinates
[tex]d=\sqrt{(2-(-0.5))^2+(5-(-5))^2}[/tex]
[tex]d=\sqrt{(2+0.5)^2+(5+5)^2}[/tex]
[tex]d=\sqrt{(2.5)^2+(10)^2}[/tex]
[tex]d=\sqrt{6.25+100}[/tex]
[tex]d=\sqrt{106.25}[/tex]
[tex]d=10.3[/tex]
Step-by-step explanation:
i hope this will help you :)
Will give brainliest answer
Answers
Answer:
[tex]153.86 \: {units}^{2} [/tex]
Step-by-step explanation:
[tex]area = \pi {r}^{2} \\ = 3.14 \times 7 \times 7 \\ = 3.14 \times 49 \\ = 153.86 \: {units}^{2} [/tex]
Answer:
153.86 [tex]units^{2}[/tex]
Step-by-step explanation:
Areaof a circle = πr^2
[tex]\pi = 3.14[/tex](in this case)
[tex]r^{2} =7[/tex]
A = πr^2
= 49(3.14)
= 153.86
Question 15 A party rental company has chairs and tables for rent. The total cost to rent 8 chairs and 3 tables is $38 . The total cost to rent 2 chairs and 5 tables is $35 . What is the cost to rent each chair and each table?
Answers
Answer:
Each table is $6 and each chair is $2.50
Step-by-step explanation:
find the solution set x^2+2x-15=0
Answers
Answer:
x = 3 or x = -5
Step-by-step explanation:
x² + 2x - 15 = 0
Factor left side of equation.
(x - 3)(x + 5) = 0
Set factors equal to 0
x - 3 = 0
x = 3
x + 5 = 0
x = -5
Rebecca collected data from a random sample of 500 homeowners in her state asking whether or not they use electric heat. Based on the results, she reports that 51% of the homeowners in the nation use electric heat. Why is this statistic misleading?
Answers
Answer:
She makes conclusion about a population that is not well represented by the sample.
Step-by-step explanation:
The conclusion she is making is about a population that is not well represented by her sample: the population is the homeowners in the nation, but the sample is made of homeowners or only her state.
The population about which she can make conclusions with this sample is the homeowners of her state, given that the sampling is done right.
Answer: The sample is biased
HELP! will give brainlest or whatever its called... Triangle ABC has vertices A(–2, 3), B(0, 3), and C(–1, –1). Find the coordinates of the image after a reflection over the x-axis. A’ B’ C’
Answers
Answers:
A ' = (-2, -3)
B ' = (0, -3)
C ' = (-1, 1)
=======================================================
Explanation:
To apply an x axis reflection, we simply change the sign of the y coordinate from positive to negative, or vice versa. The x coordinate stays as is.
Algebraically, the reflection rule used can be written as [tex](x,y) \to (x,-y)[/tex]
Applying this rule to the three given points will mean....
Point A = (-2, 3) becomes A ' = (-2, -3)Point B = (0, 3) becomes B ' = (0, -3)Point C = (-1, -1) becomes C ' = (-1, 1)The diagram is provided below.
Side note: Any points on the x axis will stay where they are. That isn't the case here, but its for any future problem where it may come up. This only applies to x axis reflections.
Answer:
(-2,-3)...(0,-3)...(-1,1)
Step-by-step explanation:
After scoring a touchdown, a football team may elect to attempt a two-point conversion, by running or passing the ball into the end zone. If successful, the team scores two points. For a certain football team, the probability that this play is successful is 0.40.
a.â Let X =1 if successful, X= 0 if not. Find the mean and variance of X.
b.â If the conversion is successful, the team scores 2 points; if not the team scores 0 points. Let Y be the number of points scored. Does Y have a Bernoulli distribution? If so, find the success probability. If not, explain why not.
c.â Find the mean and variance of Y.
Answers
Answer:
a) Mean of X = 0.40
Variance of X = 0.24
b) Y is a Bernoulli's distribution. Check Explanation for reasons.
c) Mean of Y = 0.80 points
Variance of Y = 0.96
Step-by-step explanation:
a) The probability that play is successful is 0.40. Hence, the probability that play isn't successful is then 1 - 0.40 = 0.60.
Random variable X represents when play is successful or not, X = 1 when play is successful and X = 0 when play isn't successful.
The probability mass function of X is then
X | Probability of X
0 | 0.60
1 | 0.40
The mean is given in terms of the expected value, which is expressed as
E(X) = Σ xᵢpᵢ
xᵢ = each variable
pᵢ = probability of each variable
Mean = E(X) = (0 × 0.60) + (1 × 0.40) = 0.40
Variance = Var(X) = Σx²p − μ²
μ = mean = E(X) = 0.40
Σx²p = (0² × 0.60) + (1² × 0.40) = 0.40
Variance = Var(X) = 0.40 - 0.40² = 0.24
b) If the conversion is successful, the team scores 2 points; if not the team scores 0 points. If Y ia the number of points that team scores.Y can take on values of 2 and 0 only.
A Bernoulli distribution is a discrete distribution with only two possible outcomes in which success occurs with probability of p and failure occurs with probability of (1 - p).
Since the probability of a successful conversion and subsequent 2 points is 0.40 and the probability of failure and subsequent 0 point is 0.60, it is evident that Y is a Bernoulli's distribution.
The probability mass function for Y is then
Y | Probability of Y
0 | 0.60
2 | 0.40
c) Mean and Variance of Y
Mean = E(Y)
E(Y) = Σ yᵢpᵢ
yᵢ = each variable
pᵢ = probability of each variable
E(Y) = (0 × 0.60) + (2 × 0.40) = 0.80 points
Variance = Var(Y) = Σy²p − μ²
μ = mean = E(Y) = 0.80
Σy²p = (0² × 0.60) + (2² × 0.40) = 1.60
Variance = Var(Y) = 1.60 - 0.80² = 0.96
Hope this Helps!!!
For the functions f(x)=3x−1 and g(x)=4x−3, find (f∘g)(x) and (g∘f)(x)
Answers
(g°f)(x)= 12x-7
Hope this helps