Answer:
Step-by-step explanation:
letters can be chosen in 26×25=650 ways
digits can be chosen in 10×9×8=720 ways
total number of ways=650×720=468000 ways.
Let $r$ and $s$ be the roots of $3x^2 + 4x + 12 = 0.$ Find $r^2 + s^2.$ Pls help.
Answer:
-56/9
Step-by-step explanation:
By Vieta's formulas,
$r + s = -\frac{4}{3}$ and $rs = \frac{12}{3} = 4.$ Squaring the equation $r + s = -\frac{4}{3},$ we get
$r^2 + 2rs + s^2 = \frac{16}{9}.$ Therefore,
$r^2 + s^2 = \frac{16}{9} - 2rs = \frac{16}{9} - 2 \cdot 4 = -\frac{56}{9}}$
3. How many different arrangements can be made with the letters in the word
POWER?
O A 100
B 25
OC 20
OD 120
Answer:
D. 120
Step-by-step explanation:
Array formula: A (n, p) = n! / (n -p)!
At where:
n = Total number of elements in the set.
p = Quantity of elements per arrangement
A (5.5) = 5! / (5-5)! = (5x4x3x2x1) / 0!
By definition: 0! = 1
Then: 120/1 = 120
The Museum of Science in Boston has an exhibit in which metal balls drop down a chute, bounce around, and wind up in one of 21 bins. After 1000 balls have dropped, the heights within the bins clearly follow a bell-shaped curve. The standard deviation is 3 bins. About how many balls are in bins 1 through 17? 500 680 950 975
Answer:
Step-by-step explanation:
The total number of bin is 21
the mean of 21 bins is
[tex]=\frac{21}{2} \\\\=10.5\\\\\approx11[/tex]
The standard deviation is 3 bins.
We calculate , by using z formula
[tex]P(x<7)=P(z<\frac{x-\mu}{\sigma} \\\\=P(z<\frac{7-11}{3} )\\\\=P(z<-1.33)\\\\=0.0918 (z \ \ table)\\\\\therefore P(x<7)=0.0918[/tex]
Since after 1000 balls is drop, we will mutiply with 1000
0.0918 x 1000
= 91.8
≅ 92
Therefore, we have 92 balls
In a recent survey of 500 social media users, 300 stated that they were concerned about privacy. Assuming the distribution is approximately normal, determine the point estimate and standard error for the proportion of social media users who are concerned about privacy.
Answer:
Standard error for the proportion of social media users who are concerned about privacy
S.E = 0.0219
Step-by-step explanation:
Explanation:-
Given data recent survey of 500 social media users, 300 stated that they were concerned about privacy
Size of random sample 'n' = 500
x = 300
sample proportion [tex]p = \frac{x}{n} = \frac{300}{500} = 0.6[/tex]
Standard error for the proportion of social media users who are concerned about privacy is determined by
[tex]S.E = \sqrt{\frac{p(1-p)}{n} }[/tex]
[tex]S.E = \sqrt{\frac{0.6(1-0.6)}{500} }= 0.0219[/tex]
Which of the following verified the triangle COW is similar to triangle PIG? Ignore the answer I filled in I didn’t meant to pick that one.
Answer:
D. SSS theorem
Step-by-step explanation:
The triangles have similarity by 3 sides:
4/12=5/15=7/21So the answer is SSS
Q2 (i). A line “t” is parallel to 3y = 6x + 9. Find the slope of this line “t”. (ii) Another line “r” is perpendicular to the line 3y = 6x + 9. Find the gradient of the line “r”. plz can anyone tell me by doing the practice on the copy I will be thankful
Answer: 6 and -1/6
Step-by-step explanation:
solving for y. You get y = -2x +5, so the slope is –2. Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation y = 1/2x + b and solving for b, we get b = 6.
Answer:
1) 2
2) -1/2
Step-by-step explanation:
1) 3y= 6x+9
y= 2x+3
Slope is 2
Parallel line "t" has the same slope, it will have equation:
y= 2x+b
2) y =2x+3
Perpendicular line"r" has a slope opposite-reciprocal to this, so the slope will be -1/2, the equation for line"r" is:
y= -1/2x +b
The gradient of the line is same as slope and it is -1/2 for line"r"
A grocery store bought ice cream for $2.80 per half gallon and stored it in two freezers. During the night, one freezer malfunctioned and ruined 12 half gallons. If the remaining ice cream is sold for $3.96 per half gallon, how many half gallons did the store buy if they made a profit of $66.16?
Steps:
Add 47.52 to both sides
Divide both sides by 1.16
x= 98
Description:
The first step is to add 47.52 to both sides then simplify it then divide the both sides by 1.16. And your answer will equal as x=98.
Answer: x= 98
Please mark brainliest
Hope this helps.
The concern of a study by Beynnon et al. (A-4) were nine subjects with chronic anterior cruciate ligamenttears. One of the variables of interest was the laxity of the anteroposterior, where higher values indicate more knee instability. The researchers found that among subjects with ACL-deficient knees, the mean laxity value was 17.4mm with a standard deviation of 4.3mm.
(a) What is the estimated standard error of the mean?
(b) Construct the 99 percent confidence interval for the mean of the population from which the nine subjects may be presumed to be a random sample.
(c) What is the precision of the estimate?
(d) What assumptions are necessary for the validity of the conidence interval you constructed?
Answer:
a) Standard error of the mean = 1.433 mm
b) 99% confidence interval = (12.6, 22.2)
c) The precision of the estimate = 4 816
d) The assumptions that are necessary for the validity of the conidence interval constructed include
- The sample must be a random sample extracted from the population, with each variable in the sample independent from one another.
- The sample must be a normal distribution sample or approximate a normal distribution and the best way to establish this is when the population distribution where the sample was extracted from is normal or approximately normal.
Step-by-step explanation:
a) Standard error of the mean is given as
σₓ = (σ/√n)
σ = Sample standard deviation = 4.3 mm
n = sample size = 9
σₓ = (4.3/√9) = 1.433 mm
b) Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample mean) ± (Margin of error)
Sample Mean = 17.4 mm
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the mean)
Critical value will be obtained using the t-distribution. This is because there is no information provided for the population mean and standard deviation.
To find the critical value from the t-tables, we first find the degree of freedom and the significance level.
Degree of freedom = df = n - 1 = 9 - 1 = 8.
Significance level for 99% confidence interval
(100% - 99%)/2 = 0.5% = 0.005
t (0.005, 8) = 3.36 (from the t-tables)
Standard error of the mean = 1.433 mm
99% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]
CI = 17.4 ± (3.36 × 1.433)
CI = 17.4 ± 4.816
99% CI = (12.584, 22.216)
One crate orė
99% Confidence interval = (12.584, 22.216)
c) The precision of the estimate is gven as the length of the, margin of error of the confidence interval. The precision of the estimate = 4.816
d) They include
- The sample must be a random sample extracted from the population, with each variable in the sample independent from one another.
- The sample must be a normal distribution sample or approximate a normal distribution and the best way to establish this is when the population distribution where the sample was extracted from is normal or approximately normal.
Hope this Helps!!!
X is a normally distributed random variable with the standard deviation of 4.00.Find the mean of X when 64.8%
Answer:
μ = 9.504
Step-by-step explanation:
I get complete question that is x is a normally distributed random variable with a standard deviation of 4.00. find the mean of x when 64.8% of the area lies to the left of 11.02
given data
standard deviation = 4
solution
we know that that
X ∞ Normal ( μ , 4²) ...............1
so Probability P will be express as
P ( X < 11.02 ) = 64.8%
so here
P ( Z < [tex]\frac{11.02- \mu }{4}[/tex] ) = 0.648
Z for 0.648 = [tex]\frac{11.02- \mu }{4}[/tex]
0.379 = [tex]\frac{11.02- \mu }{4}[/tex]
solve it we get
μ = 9.504
What is the product of the polynomials below?
(3x2 - 2x - 3)(5x2 + 4x + 5)
Answer:
15x^4+2x^3-8x^2+2x-15
Step-by-step explanation:
What is the square root of 28
Answer:5. 291503
Step-by-step explanation:
√28
2√7
5. 291503
2÷3 ? 4÷5 A. > B. < C. =
Answer: B
Step-by-step explanation:
To know the inequality, we can divide the numbers on each side to see what belongs in the middle.
0.67 ? 0.80
We can see that 0.67 is smaller than 0.8. Therefore, the inequality should be <.
0.67<0.8
Researchers measured the data speeds for a particular smartphone carrier at 50 airports. The highest speed measured was 75.7 Mbps. The complete list of 50 data speeds has a mean of x overbarequals17.02 Mbps and a standard deviation of sequals38.03 Mbps. a. What is the difference between carrier's highest data speed and the mean of all 50 data speeds? b. How many standard deviations is that [the difference found in part (a)]? c. Convert the carrier's highest data speed to a z score.
Answer:
(a) The difference between carrier's highest data speed and the mean of all 50 data speeds is 58.68 Mbps.
(b) The number of standard deviations the highest data speed is from the mean is 3.45.
(c) The z-score for the carrier's highest data speed is 3.45.
Step-by-step explanation:
The random variable X is defined as the data speeds for a particular smartphone carrier.
The highest speed measured was [tex]X_{max.}=75.7\ \text{Mbps}[/tex].
The mean of X is, [tex]\bar X=17.02\ \text{Mbps}[/tex] and the standard deviation is, [tex]s=38.03\ \text{Mbps}[/tex].
(a)
Compute the difference between carrier's highest data speed and the mean of all 50 data speeds as follow:
[tex]d=X_{max.}-\bar X[/tex]
[tex]=75.7-17.02\\\\=58.68[/tex]
Thus, the difference between carrier's highest data speed and the mean of all 50 data speeds is 58.68 Mbps.
(b)
Compute the number of standard deviations the highest data speed is from the mean as follows:
[tex]\text{Number of standard deviations}=\frac{d}{s}[/tex]
[tex]=\frac{58.68}{17.02}\\\\=3.44771\\\\\approx 3.45[/tex]
Thus, the number of standard deviations the highest data speed is from the mean is 3.45.
(c)
In statistics, a standardized score is the number of standard deviations an observation or data point is from the mean.
Thus, z-scores are a type of standardized scores.
So, the z-score for the carrier's highest data speed is 3.45.
How many different ways can the letters of "kissing" be arranged?
Answer:1260
Step-by-step explanation:
Kissing has 7 letters, and there are 2 paris of the same letter.
[tex]\frac{7!}{2!2!}[/tex] = [tex]\frac{7*6*5*4*3*2*1}{4}[/tex]= 1260
Can someone please help me would appreciate it so much
Simplify.
3√45
Answer:
3√45
= 9√5
= 20.12461
Answer:
[tex]9\sqrt{5}[/tex]
Step-by-step explanation:
To simplify this radical, you want to first find the prime factorization of the radicand, which happens to be 45.
The lowest square root factor of 45 is 3.
Now, the radical looks like this:
[tex]\sqrt{3^2\cdot \:5}\\=\sqrt{5}\sqrt{3^2}[/tex]
Of course, The square root of a squared number is still the same number so...
[tex]=3\sqrt{5}[/tex]
Now, we aren't done here, as the 3 which was multiplied by the square root of 45 is still existent so...
[tex]=3 \cdot 3\sqrt{5} \\=9\sqrt{5}[/tex]
#SpreadTheLove<3
Can someone organize these from least to greatest
-4.8 * 3.2 [least],
4.32/3,
-2 3/5 - (-1 2/5),
2 1/4 + (-1 2/5) [greatest]
Step-by-step explanation:
-4.8 * 3.2 = -15.36
4.32 / -3 = -1.44
-2 3/5 - (-1 2/5) = -2 3/5 + 1 2/5 = -2.6 + 1.4 = -1.2
2 1/4 + (-1 2/5) = 2 5/20 - 1 8/20 = 17/20 = 0.85
f(x)=x^2 what is g(x)
Answer:
i got doxxed by skia jackson
Step-by-step explanation:
The indicated function y1(x) is a solution of the given differential equation. Use reduction of order or formula (5), as instructed, to ?nd a second solution y2(x).
y``+2y`+y=0
Answer:
Step-by-step explanation:
We will use the reduction of order to solve this equation. At first, we need a solution of the homogeneus solution.
Consider the equation [tex]y''+2y'+y=0[/tex] We will assume that the solution is of the form [tex]y=Ae^{rx}[/tex]. If we plug this in the equation, we get
[tex]Ae^{rx}(r^2+2r+1)=0[/tex]
Since the exponential function is a positive function, and A should be different to zero to have non trivial solutions, we get
[tex]r^2+2r+1=0[/tex]
By using the quadratic formula, we get the solutions
[tex]r= \frac{-2\pm \sqrt[]{4-4}}{2}=-1[/tex]
So one solution of the homogeneus equation is of the form [tex]y=Ae^{-x}[/tex]. To use the reduction of order assume that
[tex] y = v(x)y_h[/tex]
where [tex]y_h = Ae^{-x}[/tex]. We calculate the derivatives and plug it in the equation
[tex] y' = v'y_h+y_h'v[/tex]
[tex]y'' = v''y_h+v'y_h'+y_h'v'+y_h''v = v''y_h+2v'y_h+y_h''v[/tex]
[tex](v''y_h+2v'y_h'+y_h''v)+2(v'y_h+y_h'v)+vy_h = 0[/tex]
If we rearrange the equation we get
[tex]v''y_h+(2y_h'+2y_h)v'+v(y_h''+2y_h'+y_h)=0[/tex]
Since [tex]y_h[/tex] is a solution of the homogeneus equation we get
[tex]v''y_h+(2y_h'+2y_h)v'=0[/tex]
If we take w = v', then w' = v''. So, in this case the equation becomes
[tex]w'y_h+(2y_h'+2y_h)w=0[/tex]
Note that [tex]y_h' = -1y_h[/tex] so
[tex]w'y_h=0[/tex]. Since [tex]y_h[/tex] cannot be zero, this implies
w' =0. Then, w = K (a constant). Then v' = K. So v=Kx+D where D is a constant.
So, we get that the general solution is
[tex] y = vAe^{-x} = (Kx+D)Ae^{-x} = Cxe^{-x} + Fe^{-x}[/tex] where C, F are constants.
The graphs below have the same shape. What is the equation of the blue
graph?
What is the ratio 16 : 12 in its simplest form?
Answer:
4 : 3
Step-by-step explanation:
16 : 12 can be simplified by 4 to get 4 : 3
Answer:
[tex]4:3[/tex]
Step-by-step explanation:
[tex]16 : 12[/tex]
The common highest factor of the ratio is 4.
Simplify the ratio.
[tex]16 \div 4:12 \div 4[/tex]
[tex]4:3[/tex]
Evelyn pets the box with 1 inch cubes with represents does not show how evelyn can’t find the volume of the box
Question Correction
Evelyn packed this box with 1 inch cubes. Which expression does not show how Evelyn can find the volume of the box?
(A)6+6+6+6+6+6 (B) 2 X 3 X 6 (C) 2 + 3 + 6 (D) 6 X 6Answer:
(C) 2 + 3 + 6
Step-By-Step Explanation
In the diagram,
Height = 6 Units Length =2 Units Width =3 UnitsVolume = Height X Length X Width
= 6 X 2 X 3
=36 cubic units
Consider the options:
(A)6+6+6+6+6+6 =36 cubic units
(B) 2 X 3 X 6 =36 cubic units
(C) 2 + 3 + 6 = 11 cubic units
(D) 6 X 6 =36 cubic units
Out of the option, that which is not equivalent to 36 cubic units is:
(C) 2+3+6
Therefore, it does not show how Evelyn can find the volume of the box.
Answer:
2+3+6
Step-by-step explanation:
i just did it
Write the rectangular equation (x+5) 2 + y 2 = 25 in polar form.
Answer:
r = -10*cos(t)
Step-by-step explanation:
To write the rectangular equation in polar form we need to replace x and y by:
[tex]x=r*cos(t)\\y=r*sin(t)[/tex]
Replacing on the original equation, we get:
[tex](x+5)^2+y^2=25\\x^2+10x+25+y^2=25\\(r*cos(t))^2+10*(r*cos(t))+25+(r*sin(t))^2=25[/tex]
Using the identity [tex]sin^2(t)+cos^2(t)=1[/tex] and solving for r, we get that the polar form of the equation is:
[tex](r*cos(t))^2+10*(r*cos(t))+25+(r*sin(t))^2=25\\r^2cos^2(t)+10rcos(t)+r^2sin^2(t)=0\\r^2cos^2(t)+r^2sin^2(t)=-10rcos(t)\\r^2(cos^2(t)+sin^2(t))=-10rcos(t)\\r^2=-10rcos(t)\\\\r=-10cos(t)[/tex]
A box is 24 inches long, 10 inches wide, and 10 inches deep. About how many cubic feet is the box?
Answer:
1.3888888 ft^3
Step-by-step explanation:
We need to find the volume
V = l*w*h
V = 24*10*10
V =2400 in^3
We want cubic ft
Divide by 12 for each foot
12*12*12 = 1728 ft^3
2400/1728 =1.3888888 ft^3
Answer:
[tex] = 1.388889 {ft}^{3} [/tex]
Step-by-step explanation:
[tex]v = whl \\ = 10 \times 24 \times 10 \\ = 2400 {in}^{3} [/tex]
we know that,
[tex]1 \: \: in = 0.833333ft \\ x = 2400 \\ use \: \: cross \: \: \: multipication \\ 2400 = 0.833333x \\ \frac{2400}{0.833333} = \frac{0.833333x}{0.833333} \\ x = 1.388889 {ft}^{3} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
In a pizza takeout restaurant, the following probability distribution was obtained for the number of toppings ordered on a large pizza. Find the mean and standard deviation for the random variable.
Answer:
The random variable (number of toppings ordered on a large pizza) has a mean of 1.14 and a standard deviation of 1.04.
Step-by-step explanation:
The question is incomplete:
The probability distribution is:
x P(x)
0 0.30
1 0.40
2 0.20
3 0.06
4 0.04
The mean can be calculated as:
[tex]M=\sum p_iX_i=0.3\cdot 0+0.4\cdot 1+0.2\cdot 2+0.06\cdot 3+0.04\cdot 4\\\\M=0+0.4+0.4+0.18+0.16\\\\M=1.14[/tex]
(pi is the probability of each class, Xi is the number of topping in each class)
The standard deviation is calculated as:
[tex]s=\sqrt{\sum p_i(X_i-M)^2}\\\\s=\sqrt{0.3(0-1.14)^2+0.4(1-1.14)^2+0.2(2-1.14)^2+0.06(3-1.14)^2+0.04(4-1.14)^2}\\\\s=\sqrt{0.3(-1.14)^2+0.4(-0.14)^2+0.2(0.86)^2+0.06(1.86)^2+0.04(2.86)^2}\\\\ s=\sqrt{0.3(1.2996)+0.4(0.0196)+0.2(0.7396)+0.06(3.4596)+0.04(8.1796)}\\\\s=\sqrt{0.3899+0.0078+0.1479+0.2076+0.3272}\\\\ s=\sqrt{ 1.0804 }\\\\s\approx 1.04[/tex]
Answer:
mean: 1.14; standard deviation: 1.04
Step-by-step explanation:
A) estimate the value of 9.9^2 x 1.79 B)estimate the value of V^(square root) 97.5/1.96 Thanks.
Answer:
Below in bold.
Step-by-step explanation:
A). 9.9^2 is close to 10^2 = 100
Round 1.79 to 1.8
So an estimate is 1.8 * 100
= 180.
B). √97.5 / 1.96
( I am assuming that the square root is of 97.5 only).
is approximately equal to √100 / 2
= 10/2
= 5.
Working together Wayne and his son Garth can mow the lawn in 30 min, but if Wayne mow the lawn alone then it takes 1h 15min. Find how long does it take for Garth to mow their lawn if he does it alone.
Answer:
105
Step-by-step explanation:
1h and 15 minutes is 75 minutes so
30+75=
70+30=100
100+5=105
Answer:
105
Step-by-step explanation:
I copied the other dude
P(x)=3x² + 4x³-8+x⁴-7x Degree; Type; Leading coefficent;
Answer:
Degree: 4; Type: quartic; Leading coefficient: 1
Step-by-step explanation:
The line of reflection is the ____. y-axis, center of rotation, x-axis
Answer:The line of reflection is the y axis
Step-by-step explanation:
You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion. You would like to be 90% confident that you esimate is within 2.5% of the true population proportion. How large of a sample size is required
Answer:
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.025}{1.64})^2}=1075.84[/tex]
And rounded up we have that n=1076
Step-by-step explanation:
Information given
[tex]ME= 0.025[/tex] represent the desired margin of error
Solution
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by and . And the critical value would be given by:
[tex]t_{\alpha/2}=-1.64, t_{1-\alpha/2}=1.64[/tex]
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
We can assume that the best estimate for the true proportion is [tex]\hat p=0.5[/tex]. And on this case we have that [tex]ME =\pm 0.025[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.025}{1.64})^2}=1075.84[/tex]
And rounded up we have that n=1076
The heights of adult men in America are normally distributed, with a mean of 69.8 inches and a standard deviation of 2.69 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.1 inches and a standard deviation of 2.55 inches.
Required:
a. If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)?
b. What percentage of men are SHORTER than 6 feet 3 inches?
c. If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)?
d. What percentage of women are TALLER than 5 feet 11 inches?
Answer:
a) 1.93
b) 97.32% of men are SHORTER than 6 feet 3 inches
c) 2.71
d) 0.34% of women are TALLER than 5 feet 11 inches
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.
a. If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)?
For man, [tex]\mu = 69.8, \sigma = 2.69[/tex]
A feet has 12 inches, so this is Z when X = 6*12 + 3 = 75. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{75 - 69.8}{2.69}[/tex]
[tex]Z = 1.93[/tex]
b. What percentage of men are SHORTER than 6 feet 3 inches?
Z = 1.93 has a pvalue of 0.9732
97.32% of men are SHORTER than 6 feet 3 inches
c. If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)?
For woman, [tex]\mu = 64.1, \sigma = 2.55[/tex]
Here we have X = 5*12 + 11 = 71.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{71 - 64.1}{2.55}[/tex]
[tex]Z = 2.71[/tex]
d. What percentage of women are TALLER than 5 feet 11 inches?
Z = 2.71 has a pvalue of 0.9966
1 - 0.9966 = 0.0034
0.34% of women are TALLER than 5 feet 11 inches