Answer:
33.33%
Step-by-step explanation:
Add them together 8 plus 8 plus 8 which is 24 there are 8 tp so its 8/24 which is equal to 1/3 so the percent is
Please help! Correct answer only, please! Consider the matrix shown below: Find the determinant of the matrix Q. A. -67 B. -65 C. 65 D. 67
Answer: d) 67
Step-by-step explanation:
[tex]determinant\ \left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&j\end{array}\right] = a\cdot det\left[\begin{array}{cc}e&f\\h&j\end{array}\right] -\ b\cdot det\left[\begin{array}{cc}d&f\\g&j\end{array}\right] +\ c\cdot det\left[\begin{array}{cc}d&e\\g&h\end{array}\right][/tex]
[tex]determinant\ \left[\begin{array}{ccc}2&3&4\\-3&2&1\\5&-1&6\end{array}\right] \\\\\\= 2\cdot det\left[\begin{array}{cc}2&1\\-1&6\end{array}\right] -\ 3\cdot det\left[\begin{array}{cc}-3&1\\5&6\end{array}\right] +\ 4\cdot det\left[\begin{array}{cc}-3&2\\5&-1\end{array}\right]\\\\\\=2[2(6)-1(-1)]-3[-3(6)-1(5)]+4[3(-1)-2(5)]\\\\\\=2(13)-3(-23)+4(-7)\\\\\\=26+69-28\\\\\\=\large\boxed{67}[/tex]
the terminal side of an angle in standard position rotated one-sixth of a revolution counterclockwise from the positive x-axis. Describe how to find the measure of the angle in both degree and radian
Measure of the angle which is made by rotating a side as terminal side by one-sixth of a revolution counterclockwise is 60 degree and π/3 radian.
What is the terminal side of an angle?The terminal side of an angle is the rotated side of the initial side around a point to form an angle. This rotation can be clockwise or counter clock wise.
The terminal side of an angle in standard position rotated one-sixth of a revolution counterclockwise from the positive x-axis.
The total degree in a complete rotation of a side is 360 degrees. The side is rotated 1/6. Thus the angle is rotated is,
[tex]\theta=\dfrac{1}{6}\times360\\\theta=60^o[/tex]
Multiply it with π/180 to find the measure of the angle in radian.
[tex]\theta=60\dfrac{\pi}{180}\\\theta=\dfrac{\pi}{3}\\[/tex]
Hence, the measure of the angle which is made by rotating a side as terminal side by one-sixth of a revolution counterclockwise is 60 degree and π/3 radian.
Learn more about the terminal side of an angle here
https://brainly.com/question/7040335
A rectangular fish tank is 50 cm long, 40 cm wide, and 20 cm high. a) How many cubic centimeters of water will the tank hold? b) How many milliliters of water will the tank hold? c) How many liters of water will the tank hold?
Answer:
40 litres
Step-by-step explanation:
V = l x w x h
50 x 40 x 20 = 40000
40000 cm^3
1cm^3 = 1ml
40000 cm^3/ 1cm^3 = 40000ml
40000 x 10^-3 = 40 litres
What is the square root of 100?
Answer:
10
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
Square root is finding what number times what gets your goal.
10 x 10 = 100 so 100 squared is 10.
5 x 5 = 25 so 25 squared is 5.
4 x 4 = 16 so 15 squared is 4.
You get it? :)
Have a nice day!
A recent survey found that 86% of employees plan to devote at least some work time to follow games during the NCAA Men's Basketball Tournament. A random sample of 100 employees was selected. What is the probability that less than 80% of this sample will devote work time to follow games?
Answer:
4.18% probability that less than 80% of this sample will devote work time to follow games
Step-by-step explanation:
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, we have that:
[tex]p = 0.86, n = 100[/tex]
So
[tex]\mu = 0.86, s = \sqrt{\frac{0.86*0.14}{100}} = 0.0347[/tex]
What is the probability that less than 80% of this sample will devote work time to follow games?
This is the pvalue of Z when X = 0.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.8 - 0.86}{0.0347}[/tex]
[tex]Z = -1.73[/tex]
[tex]Z = -1.73[/tex] has a pvalue of 0.0418
4.18% probability that less than 80% of this sample will devote work time to follow games
A 2-pack of scented candles costs $0.95. What is the unit price, rounded to the nearest cent?i mark the 1st answer brainliest
Step-by-step explanation:
Cost of 2 pack = 0.95
Cost of 1 pack = 0.95 ÷ 2 = 0.475
Unit price = 0.475
For circle O, and m∠ABC = 55°. In the figure, ∠ and ∠ have measures equal to 35°.
Answer:
In the figure ∠ABO and ∠BCO have measures equal to 35°.
Step-by-step explanation:
Measure of arc AD = 180-measure of arc CD= 180-125 =55
m<AOB= 55 ( measure of central angle is equal to intercepted arc)
<OAB= 90 degrees (Tangent makes an angle of 90 degrees with the radius)
In triangle AOB ,
< AB0 = 180-(90+55)= 35 degrees( angle sum property of triangle)
In triange BOC ,< BOC=125 ,
m<, BCO=35 degrees
Answer:
∠ABO and ∠BCO
Step-by-step explanation:
Which is the best estimate of 90/7 divided by 1 3/4
Answer:
90/4= 12.9
1*3/4= 0.75
Step-by-step explanation:
Evaluate x - 2y when x = 5 and y = 5.
Determine whether the ordered pair satisfies the equation.
x - 2y = -5; (5,5)
Yes, the ordered pair satisfies the equation.
No, the ordered pair does not satisfy the equation.
Answer:
For the first question we just plug in the values so we get 5 - 2 * 5 = -5.
Again, for the second one we'll plug in the values and see if it's a true statement. 5 - 2 * 5 = -5 and -5 = -5 so the answer is yes.
If the size of the sample to be used in a particular test of attributes has not been determined by utilizing statistical concepts, but the sample has been chosen in accordance with random selection procedures
A) No inferences can be drawn from the sample.
B) The auditor has committed a nonsampling error.
C) The auditor may or may not achieve the desired risk of assessing control risk too low.
D) The auditor will have to evaluate the results by reference to the principles of discovery sampling.
E) The auditor may or may not achieve the desired
Answer:
C) The auditor may or may not achieve the desired risk of assessing control risk too low.
Step-by-step explanation:
In a concept of risk sampling, if the sample size is chosen randomly in accordance with random selection procedures, the auditor may or may not achieve the desired risk of assessing risk too low. In other words the auditor may or may not achieve desired precision. This is because a samole chosen randomly may not represent the true population.
This depends largely on the sample size. If the sample size selected is too small, the allowance for sampling risk will be larger than what is required because it will lead to a large standard error of the mean
Marta recorded the temperature at 8 p.m. as 56°F and the temperature at 8 a.m. the next morning as 36°F. Marta assumed the temperature changed at a constant rate. She wrote an equation to find the number of degrees the temperature dropped each hour, h, of the night. Which equation did Marta write?
Answer: 5h/3
Step-by-step explanation:
12 hours passed, and 20 degrees dropped.
Every hour, that's 20/12 = 5/3 degrees dropped. Therefore, the equation is 5h/3.
Hope that helped,
-sirswagger21
Answer:
5h 3
Step-by-step explanation:
12 hours passed, and 20 degrees dropped.
Every hour, that's 20/12 = 5/3 degrees dropped. Therefore, the equation is 5h/3.
Hope that helped,
-sirswagger21
What is the value of X ?
Answer:
D
Step-by-step explanation:
2² + 6² = x²
4 + 36 = x²
40 = x²
x = 2√10
A spherical gemstone just fits inside a plastic cube with edges 12cm. a) calculate the volume of gemstone, to the nearest cubic centimeter. b) how much empty space is there.
Answer:
a) (V) = 904.78 of a sphere = 288pi diameter = 12
(V) = 1728cm^3 of a cube = face diagonal = 16.9cm
b) Difference Volume = 1728-904.78 = 823.22cm^3
Step-by-step explanation:
To find volume of an inscribed sphere within a square cube
We use 4 π/3 * r^3 for the equation
As Radius = 6 = 6cm this is the only thing plugged into the equation to create a division first then a multiplication square of radius and then a multiplication. 4pi /3 * 6^3
r^3 = 216
4pi/3 = 4.18
4.18 * 216 = 904.78
This means the answer is 288 pi cm^3.
Answer:
volume of gemstone = 905 cm^3
volume of empty space = 823 cm^3
Step-by-step explanation:
volume of cube = s^3, where s = length of edge
volume of sphere = (4/3)(pi)r^3, where r = radius of sphere
The cube has a 12-cm edge. The sphere fits tightly inside the cube, so the diameter, d, of the sphere is 12 cm. The radius is half the diameter, so radius = r = diameter/2 = 12 cm/2 = 6 cm.
a)
volume of sphere = (4/3)(pi)r^3
volume of sphere = (4/3)(3.14159)(6 cm)^3
volume of sphere = 905 cm^3
b)
The empty space is the difference between the volume of the cube and the volume of the sphere.
volume of cube = s^3
volume of cube = (12 cm)^3
volume of cube = 1728 cm^3
empty space = volume of cube - volume of sphere
empty space = 1728 cm^3 - 905 cm^3
empty space = 823 cm^3
There are 1760 yards in one mile about how many miles will a runner have to run
Answer:
3
I used to be an olimpic runner and I ran the 400 all the time and I did cross country
A recipe submitted to a magazine by one of its subscribers’ states that the mean baking time for a cheesecake is 55 minutes. A test kitchen preparing the recipe before it is published in the magazine makes the cheesecake 10 times at different times of the day in different ovens. The following baking times (in minutes) are observed.
54 55 58 59 59 60 61 61 62 65
Assume that the baking times belong to a normal population. Test the null hypothesis that the mean baking time is 55 minutes against the alternative hypothesis μ > 55. Use α = .05.
Answer:
[tex]t=\frac{59.4-55}{\frac{3.239}{\sqrt{10}}}=4.296[/tex]
The degrees of freedom are given by:
[tex]df=n-1=10-1=9[/tex]
The p value for this case is given by:
[tex]p_v =P(t_{(9)}>4.296)=0.001[/tex]
And for this case the p value is lower than the significance level so we have enough evidence to reject the null hypothesis and then we can conclude that true mean is higher than 55.
Step-by-step explanation:
Information given
We have the following data: 54 55 58 59 59 60 61 61 62 65
The sample mean and deviation can be calculated with the following formulas:
[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex]s=\sqrt{\frac{\sum_{i=1}^n (X-i -\bar x)^2}{n-1}}[/tex]
[tex]\bar X=59.4[/tex] represent the sample mean
[tex]s=3.239[/tex] represent the sample standard deviation
[tex]n=10[/tex] sample size
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to test if the true mean is higher than 55, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 55[/tex]
Alternative hypothesis:[tex]\mu > 55[/tex]
Replacing the info given we got:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
And replacing the info given we got:
[tex]t=\frac{59.4-55}{\frac{3.239}{\sqrt{10}}}=4.296[/tex]
The degrees of freedom are given by:
[tex]df=n-1=10-1=9[/tex]
The p value for this case is given by:
[tex]p_v =P(t_{(9)}>4.296)=0.001[/tex]
And for this case the p value is lower than the significance level so we have enough evidence to reject the null hypothesis and then we can conclude that true mean is higher than 55
Which data collection method would provide an unbiased sample?
Answer:
The best data collection method or sampling method to provide an unbiased sample is the random sampling method.
Step-by-step explanation:
There are 5 popular known sampling methods or data collection methods.
1) Random Sampling
In random sampling, each member of the population would have an equal chance of being surveyed. One of the best ways to use random sampling is to give all the members of the population numbers and then use computer to generate random numbers and pick the members of the population with those random numbers.
2) Systematic sampling is easier than random sampling. In systematic sampling, a particular number, n, is counted repeatedly and each of the nth member is picked to be sampled.
3) Convenience Sampling
This is the worst sampling technique. It is also the easiest. In Convenience sampling, the surveyor just picks the first set of members of the population that they find and surveys.
4) Stratified Sampling
Stratified sampling divides the population into groups called strata. A sample is taken from each of these strata using either random, systematic, or convenience sampling.
5) Cluster sampling
Cluster Sampling divides the population into groups which are called clusters or blocks. The clusters are selected randomly, and some members or every element/member in the selected clusters is surveyed.
Hope this Helps!!!
A tree that is 10 feet tall is growing at a rate of 2 foot each year. A tree that is 14 feet tall is growing at a rate of 2/3 foot each year. What is the number of years it will take for both trees to be the same height, and what will their height be?
Answer:
after three years
Step-by-step explanation:
The body temperatures of a group of healthy adults have a bell-shaped distribution with a mean of 98.19degreesF and a standard deviation of 0.61degreesF. Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of healthy adults with body temperatures within 3 standard deviations of the mean, or between 96.36degreesF and 100.02degreesF? b. What is the approximate percentage of healthy adults with body temperatures between 96.97degreesF and 99.41degreesF?
Answer:
a) From the empirical rule we know that within 3 deviations from the mean we have 99.7% of the data so then that would be the answer for this case.
b) [tex] z=\frac{96.97-98.19}{0.61}=-2[/tex]
[tex] z=\frac{99.41-98.19}{0.61}=2[/tex]
And within 2 deviations from the mean we have 95% of the values.
Step-by-step explanation:
For this case we know that the distribution of the temperatures have the following parameters:
[tex] \mu = 98.19, \sigma =0.61[/tex]
Part a
From the empirical rule we know that within 3 deviations from the mean we have 99.7% of the data so then that would be the answer for this case.
Part b
We can calculate the number of deviations from the mean with the z score with this formula:
[tex]z=\frac{X -\mu}{\sigma}[/tex]
And using this formula we got:
[tex] z=\frac{96.97-98.19}{0.61}=-2[/tex]
[tex] z=\frac{99.41-98.19}{0.61}=2[/tex]
And within 2 deviations from the mean we have 95% of the values.
What is the range of the function in the table
X Y
1 2
2 4
3 3
4 2
A) (1,2,3,4)
B) (1,2) (2,4) (3,3) (4,2)
C) (1,2)
D) (2,3,4)
Answer:
D. (2, 3, 4)
Step-by-step explanation:
The range is the y values. The y values, in numerical order, range from 2 to 4. The 2s do not need to be repeated.
Use the drop-down menus to complete each equation so the statement about its solution is true.
No Solutions
No Solutions
2x+5+2x+3x= _ x +_
One Solution
2x+5+2x+3x=_ x + _
Infinitely Many Solutions
2x+5+2x+3x= _x +_
Answer:
7x+16x+17x+5Step-by-step explanation:
No Solutions
There will be no solutions when the left side is inconsistent with the right side:
2x +5 +2x +3x = 7x +1
7x +5 = 7x +1 . . . . . . no value of x will make this true
__
One Solution
There will be one solution when the left side and right side are not inconsistent and not the same.
2x +5 +2x +3x = 6x +1
7x +5 = 6x +1
x = -4 . . . . . . . . add -6x-5 to both sides
__
Infinitely Many Solutions
There will be an infinite number of solutions when the equation is true for any value of x. This will be the case when the left side and right side are identical.
2x +5 +2x +3x = 7x +5
7x +5 = 7x +5 . . . . . true for all values of x
_____
Comment on these solutions
You have not provided the contents of any of the drop-down menus, so we cannot say for certain what the answers should be--except in the case of "infinitely many solutions." For "no solutions", the coefficient of x must be 7 and the constant must not be 5. For "one solution" the coefficient of x cannot be 7, and the constant can be anything.
Answer:
No Solutions: 7x+1
One Solution: 6x+1
Infinitely Many Solutions: 7x+5
Consider two unique parallel lines. What aspects of
these two lines are the same? What aspects of these two
lines would have to be different? Explain your reasoning.
Answer:
The slope of two parallel lines will always be the same. If the slope was slightly different, then the lines would intersect at some point, which breaks the definition of parallel lines.
The y-intercepts of two parallel lines have to be different, or else the two lines would be the same line. If the y-intercept and the slope are the same, then the lines will essentially equal each other.
Answer:
Sample Response: Two parallel lines will have the same slope. The slopes of parallel lines have to be equal. The y-intercepts of those two lines have to be different, otherwise they would be the same line. The x-intercepts of the parallel lines would also be different.
Step-by-step explanation:
edge 2020
If z=32 and z/2+37=x what is x
Answer:
53
Step-by-step explanation:
Plugging in 32 for z, you get:
(32)/2+37=x
16+37=x
x=53
Hope this helps!
The solution of the linear equation z/2 + 37 = x at x at z = 32 will be 53.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given below.
z/2 + 37 = x
Then the solution of the linear equation z/2 + 37 = x at z = 32. Then the equation will be
x = 32/2 + 37
x = 16 + 37
x = 53
Thus, the solution of the linear equation z/2 + 37 = x at z = 32 will be 53.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ2
3. The difference between two numbers is 5
Answer:
The difference of two numbers is 5 and the difference of their reciprocals is 1/10. find the no.s
Step-by-step explanation:
⇒ x(x-5) = 50
⇒ x2 - 5x - 50 = 0
⇒ x2 - 10x + 5x - 50 = 0
⇒ x (x - 10) + 5 (x - 10) = 0
⇒ (x+5) (x-10) = 0
⇒ (x+5) (x-10) = 0
⇒ x = -5 or 10
⇒ x = 10 (x = -5 , rejected)
A square of area 36cm2 is cut to make two rectangles, A and B The ratio of Area A to Area B is 2 : 1 Work out the dimensions of rectangle A and B
(Need help with this question)
Answer:
Given..hope it helps
Step-by-step explanation:
Area of square= 36cm2 = total area
Side of square= √36= 6cm
Ratio a:b = 2:1
so let's take total area as 3x
while a is 2x and b is 1x
3x= 36 (given)
x= 36/3 = 12
so area of each rectangle--
area A= 2x= 24cm2
area B= x= 12cm2
While finding the dimensions, they both have a common length since they are from the same square which will be 6cm (side)
So,
Dimensions of rectangle A= 6cm * 4cm
Dimensions of rectangle B= 6cm * 2cm
What’s the correct answer for this?
Answer:
1) Antonio's statement
2) <A = 123
Step-by-step explanation:
1) Antonio's statement is incorrect. This is because the opposite angles of a quadrilateral add up to 180°. Erin was incorrect because the opposite angles of this quadrilateral are unequal.
2) 2x+7+5x-2 = 180° (opposite angles of quadrilateral)
Now
7x+5 = 180
7x = 175
x = 25
<A = 5x-2
= 5(25)-2
= 125-2
= 123
A goat is tied to a peg in the ground. The rope is 3m long. What area of grass can the goat eat? (use the value 3.14 for pie)
Answer:
28.26 (Please mark as brainiest if you find it helpful )
Step-by-step explanation:Area the goat will eat is equal to the are of circle having radius 3m.
Area of circle = pi * r ^ 2
⇒ 3.14 * (3) ^ 2 → 3.14 * 9
⇒ 28.26
A student used multiple regression analysis to study how family spending (y) is influenced by income
(x1), family size (x2), and additionsto savings(x3). The variables y, x1, and x3 are measured in thousands
of dollars. The following results were obtained.
ANOVA
df SS
Regression 3 45.9634
Residual 11 2.6218
Total
Coefficients Standard Error
Intercept 0.0136
x1
0.7992 0.074
x2
0.2280 0.190
x3
-0.5796 0.920
a. Write out the estimated regression equation for the relationship between the variables. (1
mark)
b. Compute coefficient of determination. What can you say about the strength of this
relationship? (3 marks)
c. Carry out a test to determine whether y is significantly related to the independent variables.
Use a 5% level of significance. (3 marks)
d. Carry out a test to see if x3 and y are significantly related. Use a 5% level of significance.
Answer:
Step-by-step explanation:
Hello!
Given the variables
Y: family spending
X₁: income of a family
X₂: family size
X₃: additions to savings of a family
And the regression output (see attachment)
The population model is Y= α + β₁X₁ + β₂X₂ + β₃X₃
a)
To write the estimated regression equation of the relationship between the variables you have to use the information given in the regression output. Under the column "coefficients", the value that corresponds to "intercept" is the estimation of the y-intercept (a), the value under X₁ corresponds to the estimation for the slop for the variable "income of the family" (b₁), under X₂ is the estimation of the slope for the variable "family size" (b₂) and under X₃ is the estimation for the slope corresponding to the variable "additions to savings" (b₃)
The estimated regression equation is:
^Y= a + b₁X₁ + b₂X₂ + b₃X₃
^Y= 0.0136 + 0.7992X₁ + 0.2280X₂ -0.5796X₃
b)
Using the SS information you can calculate the coefficient of determination as:
SStotal= SSReg+SSError= 45.9634+2.6218= 48.5852
[tex]R^2= \frac{SS_{Reg}}{SS_{Total}} = \frac{45.9634}{(48.5852)} = 0.946[/tex]
R²= 94.6%
This means that 94.6% of the variability of the average family spending is explained jointly by the family income, the family size and the addition to saving under the estimated model ^Y= 0.0136 + 0.7992X₁ + 0.2280X₂ -0.5796X₃
c)
The hypotheses are:
H₀: β₁= β₂= β₃= 0
H₁: At least one βi≠0 ∀ i=1, 2, 3
α: 0.05
The statistic for the multiple regression is
[tex]F=\frac{MS_{Reg}}{MS_{Error}} ~~F_{Df_{Reg};Df_{Error}}[/tex]
[tex]MS_{Reg}= \frac{SS_{reg}}{Df_{Reg}}= \frac{45.9634}{3} = 15.32[/tex]
[tex]MS_{Error}= \frac{SS_{Error}}{Df_{Error}} = \frac{2.6218}{11} = 0.238[/tex]
[tex]F_{H_0}= \frac{MS_{Reg}}{MS_{Error}}= \frac{15.32}{0.238}= 64.37[/tex]
p-value < .00001
At a 5% significance level, there is enough evidence to reject the null hypothesis. This means that the family income, family size and the addition to savings modify jointly the average spending of families.
d.
Individual tests:
There are two possible statistics to test the significance of each independent variable: [tex]t= \frac{b_i-\beta_i }{S_{b_i}} ~~t_{n-3}[/tex] ∀ i= 1, 2, 3, or [tex]F=\frac{MS_{X_i}}{MS_{Error}} ~F_{Df_{X_i}; Df_{Error\\}}[/tex]
Since the output doesn't give us the information of the individual ANOVA, you have to use the t-test (Df: n-3= 12-3= 9) for these hypotheses. Using the p-value approach. the decision rule for the three hypothesis will be:
If p-value ≤ α ⇒ Reject null hypothesis.
If p-value > α ⇒ Do not reject the null hypothesis.
1)
H₀: β₁ = 0
H₁: β₁ ≠ 0
α: 0.05
[tex]t_{H_0}= \frac{b_1-\beta_1 }{Sb_1}= \frac{0.7992-0}{0.074}= 10.8[/tex]
p-value < .00001 ⇒ Decision is to reject the null hypothesis.
2)
H₀: β₂ = 0
H₁: β₂ ≠ 0
α: 0.05
[tex]t_{H_0}= \frac{b_2-\beta_2 }{Sb_2}= \frac{0.2280-0}{0.190}= 1.2[/tex]
p-value: 0.260773 ⇒ The decision is to not reject the null hypothesis.
3)
H₀: β₃ = 0
H₁: β₃ ≠ 0
α: 0.05
[tex]t_{H_0}= \frac{b_3-\beta_3 }{Sb_3}= \frac{-0.5796-0}{0.920}= -0.63[/tex]
p-value: 0.544355 ⇒ The decision is to not reject the null hypothesis.
So, at a 5% significance level, it seems that the three independent variables influence jointly the variation on the average spending of the families, but looking at them separately, only the income of the families seems to affect their spending habits significantly while the family size or their addition to savings don't seem to have major effect over their spending habits.
I hope this helps!
The longer leg of a 30-60-90° triangle is 18. What is the length of the other leg?
A) 1213
B) 93
C) 9
D) 63
Answer:
D
Step-by-step explanation:
In a 30-60-90 triangle, the longer leg is [tex]\sqrt{3}[/tex] times larger than the smaller leg. The length of the shorter leg is therefore:
[tex]\dfrac{18}{\sqrt{3}}= \\\\\\\dfrac{18\sqrt{3}}{3}= \\\\\\6\sqrt{3}[/tex]
Hope this helps!
The functions r and s are defined as follows. r(x)=2x-1 s(x)=-2x^2-2 Find the value of s(r(-4)).
Answer:
s(r(-4)) = -164
Step-by-step explanation:
r(x) = 2x - 1
s(x) = -2x^2 - 2
r(-4) = 2(-4) - 1 = -8 - 1 = -9
s(r(-4)) = s(-9) = -2(-9)^2 - 2 = -2*81 - 2 = -162 - 2 = -164
Hope this helps!
Directions and Analysis
Task 1: Completing the Square
Look at the quadratic equation below.
2x^2-12x-16=0
This is not an equation that could be easily solved by factoring. Instead, you are going to use the method of completing the square to solve this equation. Follow each step in this task to complete the square and solve the equation.
a. To complete the square, the coefficient of the x2 term must be 1. Divide both sides of the equation by a value and rewrite the equation to meet this criteria.
Type your response here:
b. Rewrite the resulting equation so the constant term is on the right side of the equation and the variable terms are on the left.
Type your response here:
c. Identify the coefficient of the x term in the previous equation. Then divide it by half and square the result. What is the result?
Type your response here:
d. Add the value you identified in part c to both sides of the equation from part b and simplify the right side. Remember that when solving equations, whatever is done to one side of the equation must also be done to the other side the equation: that is why you must add the value to both sides.
Type your response here:
e. Notice that the left side of the equation now represents a perfect square quadratic expression. Use this fact to rewrite the left side of the previous equation as the square of a linear term and create a new equation.
Type your response here:
f. You have now completed the square. Starting with the result from part e, solve the equation for x. Show your work.
Type your response here:
g. Now that you know how to complete the square to solve a quadratic equation, solve the equation 3x^2 – 3x − 6 = 0. Show your work.
Type your response here:
Answer:
a. [tex]x^2-6x-8=0[/tex]
b. [tex]x^2-6x=8[/tex]
c.
[tex]\frac{1}{2}[/tex] (Coefficient of x) = [tex]\frac{-6}{2}=-3[/tex]
Also, [tex](-3)^2=9[/tex]
d. [tex]x^2-6x+9=17[/tex]
e. [tex](x-3)^2=17[/tex]
f, g. [tex]x=3\pm \sqrt{17}[/tex]
Step-by-step explanation:
Given: [tex]2x^2-12x-16=0[/tex]
To solve: the given equation
Solution:
a.
[tex]2x^2-12x-16=0[/tex]
Coefficient of [tex]x^2=2[/tex]
Divide both sides by 2
[tex]x^2-6x-8=0[/tex]
b.
[tex]x^2-6x=8[/tex]
c.
Coefficient of x = -6
[tex]\frac{1}{2}[/tex] (Coefficient of x) = [tex]\frac{-6}{2}=-3[/tex]
Also, [tex](-3)^2=9[/tex]
d.
Add 9 to both sides of the equation: [tex]x^2-6x=8[/tex]
[tex]x^2-6x+9=8+9\\x^2-6x+9=17[/tex]
e.
[tex]x^2-6x+9=17\\x^2-2(3)x+3^2=17\\(x-3)^2=17\,\,\left \{ \because (a-b)^2=a^2+b^2-2ab \right \}[/tex]
f.
[tex](x-3)^2=17\\x-3=\pm \sqrt{17}\\x=3\pm \sqrt{17}[/tex]
g.
[tex]x=3\pm \sqrt{17}[/tex]
