Answer:
n how many ways can a president, vice president, and a secretary be chosen? It is 12X11X10. Permutation of n things taken r at a time: nPr=n!/(n-r)! 12P3=12*11*10*9!/9!= 12*11*10=1320 ways.
Step-by-step explanation:
Can someone plz help me solved this problem I need help ASAP plz help me! Will mark you as brainiest!
Answer:
8
Step-by-step explanation:
y²+by+16= (y+4)²
y²+by+16= y²+2*4*y+4²
y²+by+16= y²+8y+16
by=8y
b=8
x^2 + 5x - 24 = 0 How do I solve by factoring
Answer:
x = -8 or x = 3
Step-by-step explanation:
To factor ax² + bx + c, use AC method.
a times c is 1 × -24 = -24.
Factors of ac (-24) that add up to b (5) are 8 and -3.
Divide by a and reduce: 8/1 and -3/1.
Therefore, the factors are x + 8 and x − 3.
x² + 5x − 24 = 0
(x + 8) (x − 3) = 0
x = -8 or 3
the sum of the three numbers in 2003,two of the numbers are 814 and 519 what is the third number
Answer:
670
Step-by-step explanation:
2003-814=1189
1189-519=670
Answer: The third number is 670.
Step-by-step explanation:
The sum means three numbers being added up is equal to 2003 so give two of those numbers you have to add them up and subtract it from 2003 to find the third number.
814 + 519 + x = 2003 where x is the third number
1333 + x = 2003
-1333 -1333
x = 670 So the third number is 670
Check:
814 + 670 + 519 = 2003
2003 = 2003 so yes again 670 is the third number.
HELP WITH THIS PLEASE
Answer:
a = 35º
b = 140º
c = 40º
d = 140º
e = 58º
Step-by-step explanation:
Angle A is supplementary to the angle that is 145º, and supplementary angles always add up to 180º. Therefore, 180 - 145 = 35, the measure of angle a. Angle B is supplementary to the 40º angle, so its measure is 140. Angle C is opposite the 40º angle, and opposite angles are congruent, so its measure would also be 40º. Angle D is also 140º because it is opposite of angle B. Angle E is supplementary to the angle that measures 122º, so 180 - 122 = 58. Hope this helped!
The Gleason family has a monthly budget of $4,500. Mr. Gleason has a full-time job and takes home $900 each week. Mrs. Gleason works part time and brings home $9 each week. For every hour she works. How many hours per month must Mrs. Gleason work to make sure that she and Mr. Gleason have met their monthly budget?
Answer:
The value of x from the equation is 100. Thus, Mrs. Gleason should work for 100 hours per month.
Step-by-step explanation:
To answer this item, we let x be the number of hours per month that Mrs. Gleason should work. The total budget is equal to sum of the amount acquired by Mr. Gleason and Mrs. Gleason. The equation that would express this is,
4,500 = 900(4) + 9x
The value of x from the equation is 100. Thus, Mrs. Gleason should work for 100 hours per month.
I am sorry if you get this wrong.
how do you add 9 in 1 6 + 2 1/12
Step-by-step explanation:
9 + 1/6 + 2 1/12
9 + 2.25
11.25
The Employment and Training Administration reported that the U.S. mean unemployment
insurance benefit was $238 per week (The World Almanac, 2003). Aresearcher in the state
of Virginia anticipated that sample data would show evidence that the mean weekly unemployment
insurance benefit in Virginia was below the national average.
a. Develop appropriate hypotheses such that rejection of H0 will support the researcher’s
contention.
b. For a sample of 100 individuals, the sample mean weekly unemployment insurance
benefit was $231 with a sample standard deviation of $80. What is the p-value?
c. At αα = .05, what is your conclusion?
d. Repeat the preceding hypothesis test using the critical value approach.
Answer:
Step-by-step explanation:
a) We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
H0: µ = 238
For the alternative hypothesis,
H1: µ < 238
This is a left tailed test
b) Since the population standard deviation is not given, the distribution is a student's t.
Since n = 100
Degrees of freedom, df = n - 1 = 100 - 1 = 99
t = (x - µ)/(s/√n)
Where
x = sample mean = 231
µ = population mean = 238
s = samples standard deviation = 80
t = (231 - 238)/(80/√100) = - 0.88
We would determine the p value using the t test calculator. It becomes
p = 0.19
c) Since alpha, 0.05 < than the p value, 0.19, then we would fail to reject the null hypothesis. Therefore, At a 5% level of significance, the sample data showed insignificant evidence that the mean weekly unemployment insurance benefit in Virginia was below the national average.
d) Since α = 0.05, the critical value is determined from the t distribution table. Recall that this is a left tailed test. Therefore, we would find the critical value corresponding to 1 - α and reject the null hypothesis if the test statistic is less than the negative of the table value.
1 - α = 1 - 0.05 = 0.95
The negative critical value is - 1.66
Since - 0.88 is greater than - 1.66, then we would fail to reject the null hypothesis.
What is the image of (-4,12) after a dilation by a scale factor of 1/4 centered at the origin
Answer:
(-1,4)
Step-by-step explanation:
Divide each imput by 4
The required image of the given point (-4, 12) dilation by a scale factor of 1/4 and centered at the origin is (1, -3).
Given that,
To determine the image of (-4,12) after dilation by a scale factor of 1/4 centered at the origin.
The graph is a demonstration of curves that gives the relationship between the x and y-axis.
What is coordinate?Coordinate, is represented as the values on the x-axis and y-axis of the graph
Here,
For the point, we have a dilation factor of 1/4,
So dilated coordinate,
= (1/4 * - 4 , 1/4 * 12)
= (-1 , 3)
To form the image across the origin
= - (-1, 3)
= (1, -3)
Thus, the required image of the given point (-4, 12) with a scale factor of 1/4 and centered at the origin is (1, -3).
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A recent national survey found that parents read an average (mean) of 10 books per month to their children under five years old. The population standard deviation is 5. The distribution of books read per month follows the normal distribution. A random sample of 25 households revealed that the mean number of books read last month was 12. At the .01 significance level, can we conclude that parents read more than the average number of books to their children
Answer:
Step-by-step explanation:
Null hypothesis: u = 10
Alternative hypothesis: u =/ 10
Using the formula: t = (x - u) / (s /√n)
Where x = 12, u = 10, s = 5 and n = 25
t= (12-10) / (5/√25)
t = (2)/(5/5)
t = 2/1= 2
t = 2.0
At a 0.01 level of significance with a degree of freedom of 24, the p-value is 0.0569, which is greater than 0.01 we will fail to reject the null and conclude that parents do not read more than the average number of books to their children
Given f(xl=x-7 and g(x)=x^2 find g(f(4))
Answer:
So we first need to solve for f(4) because thats what's inside g(_)
It should be 4-7 because I think its f(x)=x-7 you weren't very clear on it.
so that means that we need to solve for g(-3)
-3^2 = 9 because -3*-3 = 9
9 is answer
A fluctuating electric current II may be considered a uniformly distributed random variable over the interval (9, 11)(9,11). If this current flows through a 2-ohm resistor, find the probability density function of the power P = 2I^2P=2I 2 .
Answer:
Step-by-step explanation:
A fluctuating electric current II may be considered a uniformly distributed random variable over the interval (9, 11)
[tex]p_1=\{^{\frac{1}{2}:9\leq i\leq 11}_{0:otherwise[/tex]
Now define
[tex]p = 2I^2[/tex]
[tex]\Rightarrow I^2=(\frac{p}{2} )\\\\\Rightarrow I=(\frac{p}{2} )^{\frac{1}{2} }\\\\\Rightarrow h^{-1}(p)=(\frac{p}{2} )^{\frac{1}{2}}[/tex]
[tex]\frac{dh^{-1}}{dp} =\frac{d[h^{-1}(p)]}{dp} \\\\=\frac{d(p/2)^{\frac{1}{2} }}{dp}[/tex]
[tex]=\frac{1}{2} \times \frac{1}{2} (\frac{p}{2} )^{{\frac{1}{2}-1} }\\\\=\frac{1}{4}(\frac{p}{2} )^{{\frac{1}{2}-1} }\\\\=\frac{1}{2}(\frac{2}{p} )^{{\frac{1}{2}} }[/tex]
using the transformation method, we get
[tex]f_p(p)=f_1(h^{-1}(p))|\frac{d[h^{-1}(p)]}{dp} |\\\\=\frac{1}{2} \times \frac{1}{4} (\frac{2}{p} )^{\frac{1}{2} }\\\\=\frac{1}{8} (\frac{2}{p} )^{\frac{1}{2} }[/tex]
[tex]f_p(p)=\{^{\frac{1}{8} (\frac{2}{p} )^{\frac{1}{2} },162\leqp\leq 242} }_{0,otherwise}[/tex]
What is the slope intercept form.
Answer:
y = 1/4x + 2
Step-by-step explanation:
Since they gave you point slope form already, all you need to do is convert that into slope-intercept form. Just distribute the parenthesis and move the 4 over. Once you do so, you should get C/3rd option as your answer.
In this diagram, BAC – EDF. If the
area of BAC = 24 in2, what is the
area of EDF?
Help please
If the area of ΔBAC = 24 in², the area of ΔEDF is 6 in².
What are similar triangles?If two triangles' angles are congruent and their corresponding sides are proportionate, they are considered similar. To put it another way, similar triangles are the same in shape but not necessarily in size. If ΔPQR and ΔMNO are two similar triangles, then we can write it as ΔPQR ∼ ΔMNO.
Statement:The square of the ratio of any pair of their respective sides is equal to the ratio of the areas of two similar triangles.
How to solve this problem?Since ΔBAC ∼ ΔEDF, we can use the above statement to find the area of ΔEDF. Let the area of ΔEDF be x in². Given that length of EF and BC is 2 in and 4 in respectively.
So, we have to solve this equation,
24/x = 4²/2²
Now, 24/x = 16/4
i.e. 24/x = 4
i.e. 4x = 24
i.e. x = 24/4 = 6
Therefore the area of ΔEDF is 6 in².
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An individual closes out help desk tickets at a rate of 4 tickets per hour for h hours. Write an equation that expresses the situation, let x be the independent variable and y be the dependent variable
Answer:
y=4x
Step-by-step explanation:
an independent variable is the variable that is changed or controlled in an experiment or observation to test the effects on the dependent variable
a dependent variable is variable being tested and measured in a scientific experiment
in this case, the number of help desk tickets closed out is dependent on the number of hours the individual works so y is the number of tickets closed (dependent variable). The number of tickets closed of will be 4 multiplied by the number of hours worked i.e. y=4x
A researcher wants to test the claim that convicted burglars spend an average of 18.7 months in jail. She takes a random sample of 11 such cases from court files and finds x=20.6 months and s=8 months. Test the claim that u=18.7 months at the 0.05 significance level.
Answer:
[tex]t=\frac{20.6-18.7}{\frac{8}{\sqrt{11}}}=0.788[/tex]
The degrees of freedom are given by;
[tex] df =n-1= 11-1=10[/tex]
And the p value would be:
[tex]p_v =2*P(t_{10}>0.788)=0.449[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different than 18.7
Step-by-step explanation:
Information given
[tex]\bar X=20.6[/tex] represent the sample mean
[tex]s=8[/tex] represent the sample standard deviation
[tex]n=11[/tex] sample size
[tex]\mu_o =18.7[/tex] represent the value to test
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypotesis to test
We want to verify if the true mean is equal to 18.7, the system of hypothesis would be:
Null hypothesis:[tex]\mu =18.7[/tex]
Alternative hypothesis:[tex]\mu \neq 18.7[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info we got:
[tex]t=\frac{20.6-18.7}{\frac{8}{\sqrt{11}}}=0.788[/tex]
The degrees of freedom are given by;
[tex] df =n-1= 11-1=10[/tex]
And the p value would be:
[tex]p_v =2*P(t_{10}>0.788)=0.449[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different than 18.7
Find the range of the set of numbers shown by the box-and-whisker plot.
6
6
7
8
9
10
11
12
13
14
16
16
17
18
19
20
21
22
Answer:
16
Step-by-step explanation:
The range is the difference between the highest and lowest number of a data set. 22-6=16
a ford truck enters a highway and travles uniform speed of 50 mph. half an hour later a jaguar enters the highway at the same junction and heads in the same direction at 55 mph. how long after the ford enters the highway does the jaguard catch up
Answer:
5.5 hours
Step-by-step explanation:
We have that the distance is given by:
d = v * t = 50 mph * 1/2 h = 25 miles
The relative speed is given by:
vr = 55 mph - 50 mph = 5 mph
Now the time required to reach
would come being:
t = t '+ d / vr
we know that t '= 1/2 h, replacing:
t = 1/2 h + 25 mi / 5 mph
t = 1/2 h + 5 h
t = 5.5 h
Therefore, the required time is 5.5 hours.
The mean of 6 numbers is 32.If one of the numbers is excluded, the mean reduces by 2.Find the excluded number.
Answer:
42
Step-by-step explanation:
Mean = Sum of numbers/ Total numbers
Sum of 6 numbers = 32 x 6
= 192
If one number is excluded the mean reduce by 2 . so it becomes 30
Sum of 5 Numbers = 5 x 30
=150
Therefore the excluded number is
= 192 - 150
= 42.
Name the x-axis of symmetry for the parabola sketched below
Answer:
x=-3
Step-by-step explanation:
The vertex is at x = -3
The axis of symmetry is along the vertex
x=-3
Answer:
x=-3
Step-by-step explanation:
To find the axis of symmetry, you just need to find the x-coordinate of the vertex using this formula: -b/2a=x
*Only when provided a three variable quadratic equation.
For looking at a graph, you find the center of the parabola in which when you reflect it over itself, it will be symmetrical.
According to the graph, x=-3 is the line which you can draw to fold over to the other side and it can fit perfectly.
22,056 people went to the baseball game on Sunday. Half as many people came on money. How many people were at the baseball game on Sunday and Monday altogether?
Answer:33084
Step-by-step explanation:
22056 divided by 2 = Monday
Monday= 11028
11028+22056=33084
Answer:
33084 People were at the baseball game on Sunday and ~Money~ Monday all together.
Step-by-step explanation:
Sunday - 22056
Monday - "Half as many" 22056 Divided by 2
= 11028
Altogether - Sunday + Monday = 33084
As a shortcut on your calculator, you could do:
22056 + (22056 divided by 2)
= 33084
Researchers want to know about the true proportion of adults with at least a high school education. 1000 adults are surveyed, and 710 of them have at least a high school education. Create a 95% confidence interval for the true population proportion of adults with at least a high school education. Interpret this interval in context of the problem.
Answer:
The 95% confidence interval for the true population proportion of adults with at least a high school education is (0.6819, 0.7381). This means that we are 95% sure that the true proportion of adults in the entire population surveyed with at least a high school education is (0.6819, 0.7381).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 1000, \pi = \frac{710}{1000} = 0.71[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.71 - 1.96\sqrt{\frac{0.71*0.29}{1000}} = 0.6819[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.71 + 1.96\sqrt{\frac{0.71*0.29}{1000}} = 0.7381[/tex]
The 95% confidence interval for the true population proportion of adults with at least a high school education is (0.6819, 0.7381). This means that we are 95% sure that the true proportion of adults in the entire population surveyed with at least a high school education is (0.6819, 0.7381).
if you start with (2,6) and move 2 units right and 3 units down what will you end up with?
For (2,6) the 2 is the x value which is the left/right position and 6 is the y value which is the up/down position.
Moving 2 units to the right, you would add 2 to the x value. Moving 3 units down you would subtract 3 from the y value.
The answer would be (4,3)
At the beginning of an experiment, a scientist has 300 grams of radioactive goo. After 150 minutes, her sample has decayed to 37.5 grams.
What is the half-life of the goo in minutes?
________
Find a formula for
G(t),
the amount of goo remaining at time T.
G= _________
How many grams of goo will remain after 32 minutes?
Answer:
Half-life of the goo is 49.5 minutes
[tex]G(t)= 300e^{-0.014t}[/tex]
191.7 grams of goo will remain after 32 minutes
Step-by-step explanation:
Let [tex]M_0\,,\,M_f[/tex] denotes initial and final mass.
[tex]M_0=300\,\,grams\,,\,M_f=37.5\,\,grams[/tex]
According to exponential decay,
[tex]\ln \left ( \frac{M_f}{M_0} \right )=-kt[/tex]
Here, t denotes time and k denotes decay constant.
[tex]\ln \left ( \frac{M_f}{M_0} \right )=-kt\\\ln \left ( \frac{37.5}{300} \right )=-k(150)\\-2.079=-k(150)\\k=\frac{2.079}{150}=0.014[/tex]
So, half-life of the goo in minutes is calculated as follows:
[tex]\ln \left ( \frac{50}{100} \right )=-kt\\\ln \left ( \frac{50}{100} \right )=-(0.014)t\\t=\frac{-0.693}{-0.014}=49.5\,\,minutes[/tex]
Half-life of the goo is 49.5 minutes
[tex]\ln \left ( \frac{M_f}{M_0} \right )=-kt\Rightarrow M_f=M_0e^{-kt}[/tex]
So,
[tex]G(t)= M_f=M_0e^{-kt}[/tex]
Put [tex]M_0=300\,\,grams\,,\,k=0.014[/tex]
[tex]G(t)= 300e^{-0.014t}[/tex]
Put t = 32 minutes
[tex]G(32)= 300e^{-0.014(32)}=300e^{-0.448}=191.7\,\,grams[/tex]
Please answer this correctly
Answer:
629
Step-by-step explanation:
l x w
25x14
4x7
12x18
5x7
629
There are nine saxophone players in the band. The number of saxophone players is one less than twice the number of tuba players. Find the number of tuba players.
Answer:
[tex]5[/tex]
Step-by-step explanation:
Let [tex]x[/tex] be the number of tuba players.
We are given that the number of saxophone players is one less than twice the number of tuba players.
There are 9 saxophone players.
[tex]9 = 2 x-1[/tex]
[tex]9+1=2x[/tex]
[tex]10=2x[/tex]
[tex]10 \div 2=x[/tex]
[tex]5=x[/tex]
From a sample with nequals24, the mean number of televisions per household is 4 with a standard deviation of 1 television. Using Chebychev's Theorem, determine at least how many of the households have between 2 and 6 televisions. At least nothing of the households have between 2 and 6 televisions.
Answer:
At least 18 of the households have between 2 and 6 televisions.
Step-by-step explanation:
Chebyshev Theorem
The Chebyshev Theorem can also be applied to non-normal distribution. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.
At least 89% of the measures are within 3 standard deviations of the mean.
An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].
In this question:
Mean = 4
Standard deviation = 1
Percentage of households that have between 2 and 6 televisions.
2 = 4 - 2*1
So 2 is two standard deviations below the mean
6 = 4 + 2*1
So 6 is two standard deviations above the mean
By Chebyshev's Theorem, at least 75% of the measures are within 2 standard deviations of the mean.
Out of 24
0.75*24 = 18
At least 18 of the households have between 2 and 6 televisions.
Find all zeros of f(x)=x^3−17x^2+49x−833
Answer:
x = 17 or x = ±7i
Step-by-step explanation:
x³ − 17x² + 49x − 833 = 0
x² (x − 17) + 49 (x − 17) = 0
(x² + 49) (x − 17) = 0
x = 17 or ±7i
WILL GIVE BRAINLIEST! HURRY
Answer:
4
Step-by-step explanation:
2(6x+4)-6+2x=3(4x+3)+1
=14x+2=12x+10
=14x+2-2=12x+10-2
=14x=12x+8
=14x-12x=12x+8-12x
=2x=8
=2x/2=8/2
x=4
$17,500,000 is what percent of $70,000,000?
Answer: 1/4 of 70,000,000
Step-by-step explanation: 17,500,000 / 70,000,000 = 0.25
Answer:
[tex]25\%[/tex]
Step-by-step explanation:
[tex]\frac{17,500,000}{70,000,000}[/tex]
[tex]\frac{1}{4}=0.25=25/100=25\%[/tex]
Find the values of x in the figure below. Express your answer in simplest radical form.
Answer:
Step-by-step explanation:I don't say u must have to mark my ans as brainliest but if it has really helped u plz don't forget to thank me...