The probability that the shirt that is chosen at random from the drawer is not a white shirt, can be found to be 47 %
How to find the probability ?The probability that the shirt picked is not a white shirt can be found by first finding the number of shirts that are not white shorts in the drawer. This number is :
= Number of black shirts + Gray shirts
= 3 + 4
= 7 shirts
Then, find the total number of shirts in the drawer, including the white shirts :
= Number of black shirts + Gray shirts + White shirts
= 3 + 8 + 4
= 15 shirts
The probability that when a shirt is chosen at random, that it is not a white shirt is :
= Number of shirts that are not white / Total number of shirts
= 7 / 15
= 47 %
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Solve the given systems of equations:
x-y+z=1
-3x+2y+z=1
2x-3y+4z=3
Answer:
x = 3/2
y = 2
z = 3/2
Step-by-step explanation:
There are multiple methods to solve these. Message me for the method you need to see step by step.
At a deli counter, there are sandwiches with meat and vegetarian sandwiches. Kira is at the counter buying sandwiches for a picnic. In how many ways can she choose sandwiches if fewer than must be vegetarian sandwiches
Answer:
The number ways to choose between meat and vegetarian sandwiches can be computed using computation technique.
Step-by-step explanation:
There are two types of sandwiches available at the deli counter. The possibility of combinations can be found by computation technique of statistic. It is assumed that order does not matter and sandwiches will be selected at random. The sandwiches can be arranged in any order and number ways can be found by 2Cn.
About 9% of the population has a particular genetic mutation. 600 people are randomly selected.
Find the standard deviation for the number of people with the genetic mutation in such groups of 600.
Answer:
The mean for all such groups randomly selected is 0.09*800=72.
Step-by-step explanation:
The value of the standard deviation is 7.
What is the standard deviation?Standard deviation is defined as the amount of variation or the deviation of the numbers from each other.
The standard deviation is calculated by using the formula,
[tex]\sigma = \sqrt{Npq}[/tex]
N = 600
p = 9%= 0.09
q = 1 - p= 1 - 0.09= 0.91
Put the values in the formulas.
[tex]\sigma = \sqrt{Npq}[/tex]
[tex]\sigma = \sqrt{600 \times 0.09\times 0.91}[/tex]
[tex]\sigma[/tex] = 7
Therefore, the value of the standard deviation is 7.
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Help!! It’s much appreciated in this time
Answer: D. y = (x - 3)² + 2
Step-by-step explanation:
Inverse is when you swap the x's and y's and solve for y.
y = [tex]\sqrt{x-2}[/tex] + 3
Swap: x = [tex]\sqrt{y-2}[/tex] + 3
Solve: x - 3 = [tex]\sqrt{y-2}[/tex]
(x - 3)² = [tex](\sqrt{y-2})^2[/tex]
(x - 3)² = y - 2
(x - 3)² + 2 = y
Evan wants to build a rectangular enclosure for his animals. One side of the pen will be against the barn, so he needs no fence on that side. The other three sides will be enclosed with wire fencing. If Evan has 1000 feet of fencing, you can find the dimensions that maximize the area of the enclosure. a) Let w be the width of the enclosure (perpendicular to the barn) and let l be the length of the enclosure (parallel to the barn). Write an function for the area A of the enclosure in terms of w . (HINT first write two equations with w and l and A . Solve for l in one equation and substitute for l in the other). A(w) = ___________ b) What width would maximize the area? w = __________ c) What is the maximum area? A = _________ square feet
Answer: A. A=(1000-2w)*w B. 250 feet
C. 125 000 square feet
Step-by-step explanation:
The area of rectangular is A=l*w (1)
From another hand the length of the fence is 2*w+l=1000 (2)
L is not multiplied by 2, because the opposite side of the l is the barn,- we don't need in fence on that side.
Express l from (2):
l=1000-2w
Substitude l in (1) by 1000-2w
A=(1000-2w)*w (3) ( Part A. is done !)
Part B.
To find the width w (Wmax) that corresponds to max of area A we have to dind the roots of equation (1000-2w)w=0 ( we get it from (3))
w1=0 1000-2*w2=0
w2=500
Wmax= (w1+w2)/2=(0+500)/2=250 feet
The width that maximize area A is Wmax=250 feet
Part C. Using (3) and the value of Wmax=250 we can write the following:
A(Wmax)=250*(1000-2*250)=250*500=125 000 square feets
A table of values of a linear function is shown below. Find the output when the input is N. Type your answer in the space provide
Answer:
[tex] -3n - 7 [/tex]
Step-by-step explanation:
Considering the linear function represented in the table above, to find what output an input "n" would give, we need to first find an equation that defines the linear function.
Using the slope-intercept formula, y = mx + b, let's find the equation.
Where,
m = the increase in output ÷ increase in input = [tex] \frac{-13 - (-10)}{2 - 1} [/tex]
[tex] m = \frac{-13 + 10}{1} [/tex]
[tex] m = \frac{-3}{1} [/tex]
[tex] m = -3 [/tex]
Using any if the given pairs, i.e., (1, -10), plug in the values as x and y in the equation formula to solve for b, which is the y-intercept
[tex] y = mx + b [/tex]
[tex] -10 = -3(1) + b [/tex]
[tex] -10 = -3 + b [/tex]
Add 3 to both sides:
[tex] -10 + 3 = -3 + b + 3 [/tex]
[tex] -7 = b [/tex]
[tex] b = -7 [/tex]
The equation of the given linear function can be written as:
[tex] y = -3x - 7 [/tex]
Or
[tex] f(x) = -3x - 7 [/tex]
Therefore, if the input is n, the output would be:
[tex] f(n) = -3n - 7 [/tex]
Simplify the expression . 39*x / 13
Answer:
3x
Step-by-step explanation:
39*x / 13
39/13 * x
3*x
3x
Answer:
3x
Step-by-step explanation:
We are given the expression:
39*x /13
We want to simplify this expression. It can be simplified because both the numerator (top number) and denominator (bottom number) can be evenly divided by 13.
(39*x /13) / (13/13)
(39x/13) / 1
3x / 1
When the denominator is 1, we can simply eliminate the denominator and leave the numerator as our answer.
3x
The expression 39*x/13 can be simplified to 3x
Identify an equation in point-slope form for the line perpendicular to
y= - 1/3x - 6 that passes through (-1,5).
O A. y + 1 = 3(x - 5)
O B. y + 5 = 1/3(x - 1)
O C. y - 5 = 3(x + 1)
O D. y - 5 = - 1/3(x + 1)
Answer:
hope you get it....sorry for any mistake calculations
Help ASAP it’s Math I need this rightnow 31 points
Answer:
AC (b)
Step-by-step explanation:
Since 10 is half of 20, you have to find the variable closest to the middle. Which in this case, is C. So, your awnser is B. (AC)
Answer:
[tex]\boxed{\sf C}[/tex]
Step-by-step explanation:
The whole segment is [tex]\sf \sqrt {20}[/tex], we can see that AD is approximately 75% of the segment AE.
[tex]75\%*\sqrt{20} = 3.354102[/tex]
[tex]\sqrt{10}= 3.162278[/tex]
AC is almost half of AE.
[tex]\frac{\sqrt{20} }{2} = 2.2360679775[/tex]
[tex]\sqrt{10} = 3.16227766017[/tex]
It isn’t close to the option C.
Construct a frequency distribution and a frequency histogram for the given data set using the indicated number of classes. Describe any patterns.
Number of classes: 8
Data set: Reaction times (in milliseconds) of 30 adult females to an auditory stimulus.
430 386 352 301 450 291 429 467 454 385 380
373 386 307 321 336 310 413 306 357 514 443
442 326 508 424 386 429 412 418
Answer:
The histogram for the data is attached below.
Step-by-step explanation:
Arrange the data in ascending order as follows:
S = {291 , 301 , 306 , 307 , 310 , 321 , 326 , 336 , 352 , 357 , 373 , 380 , 385 , 386 , 386 , 386 , 412 , 413 , 418 , 424 , 429 , 429 , 430 , 442 , 443 , 450 , 454 , 467 , 508 , 514}
Compute the range:
[tex]Range=Max.-Min.\\=514-291\\=223[/tex]
Compute the class width:
[tex]Class\ Width =\frac{Range}{No.\ of\ classes}=\frac{223}{8}=27.875\approx 28[/tex]
The classes are as follows:
290 - 318
319 - 347
348 - 376
377 - 405
406 - 434
435 - 463
464 - 492
493 - 521
Compute the frequency distribution as follows:
Class Interval Frequency
290 - 318 5
319 - 347 3
348 - 376 3
377 - 405 5
406 - 434 7
435 - 463 4
464 - 492 1
493 - 521 2
The histogram for the data is attached below.
What are the vertical asymptote(s) of y= (x-6)/(x+8) (x-7)
Answer:
x = -8 and x= 7
Step-by-step explanation:
recall that for a rational expression, the vertical asymptotes occur at x-values that causes the expression to become undefined. These occur when the denominator becomes zero.
Hence the asymptototes will occur in x-locations where the denominator , i.e
(x+8)(x-7) = 0
solving this, we get
(x+8) = 0 ----> x = -8
or
(x-7) = 0 ------> x = 7
hence the asymptotes occur x = -8 and x= 7
Answer:
x = -8 and x = 7.
Step-by-step explanation:
The vertical asymptotes are lines that the function will never touch.
Since no number can be divided by 0, the function will not touch points where the denominator of the function is equal to 0.
[tex]\frac{x - 6}{(x + 8)(x - 7)}[/tex], so the vertical asymptotes will be where (x + 8) = 0 and (x - 7) = 0.
x + 8 = 0
x = -8
x - 7 = 0
x = 7
The vertical asymptotes are at x = -8 and x = 7.
Hope this helps!
6th grade math help me, please :))
Answer:
[tex]\sf a) \ 2.5\\b) \ 7.5[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{250}{100}[/tex]
[tex]\sf Express \ as \ a \ decimal.[/tex]
[tex]=2.5[/tex]
[tex]\sf Multiply \ 3\% \ with \ 250.[/tex]
[tex]\displaystyle 250 \times \frac{3}{100}[/tex]
[tex]\displaystyle \frac{750}{100}=7.5[/tex]
when a stone falls freely, the time taken to hit the ground varies as the square root of the distance fallen. If it takes four seconds th fall 78.4m, find how long would it takefor a stone to fall 500m
Answer:
The stone would take approximately 10.107 seconds to fall 500 meters.
Step-by-step explanation:
According to the statement of the problem, the following relationship of direct proportionality is built:
[tex]t \propto y^{1/2}[/tex]
[tex]t = k\cdot t^{1/2}[/tex]
Where:
[tex]t[/tex] - Time spent by the stone, measured in seconds.
[tex]y[/tex] - Height change experimented by the stone, measured in meters.
[tex]k[/tex] - Proportionality constant, measured in [tex]\frac{s}{m^{1/2}}[/tex].
First, the proportionality constant is determined by clearing the respective variable and replacing all known variables:
[tex]k = \frac{t}{y^{1/2}}[/tex]
If [tex]t = 4\,s[/tex] and [tex]y=78.4\,m[/tex], then:
[tex]k = \frac{4\,s}{(78.4\,m)^{1/2}}[/tex]
[tex]k \approx 0.452\,\frac{s}{m^{1/2}}[/tex]
Then, the expression is [tex]t = 0.452\cdot y^{1/2}[/tex]. Finally, if [tex]y = 500\,m[/tex], then the time is:
[tex]t = 0.452\cdot (500\,m)^{1/2}[/tex]
[tex]t \approx 10.107\,s[/tex]
The stone would take approximately 10.107 seconds to fall 500 meters.
A candy store called "Sugar" built a giant hollow sugar cube out of wood to hang above the entrance to their store. It took 13.5\text{ m}^213.5 m 2 13, point, 5, start text, space, m, end text, squared of material to build the cube. What is the volume inside the giant sugar cube?
Answer:
3.375
Step-by-step explanation:
Answer:
3.375
Step-by-step explanation:
Had it on Khan
Construct the confidence interval for the population mean mu. c = 0.90, x = 16.9, s = 9.0, and n = 45. A 90% confidence interval for mu is:______.
Answer:
The 90% confidence interval for population mean is [tex]14.7 < \mu < 19.1[/tex]
Step-by-step explanation:
From the question we are told that
The sample mean is [tex]\= x = 16.9[/tex]
The confidence level is [tex]C = 0.90[/tex]
The sample size is [tex]n = 45[/tex]
The standard deviation
Now given that the confidence level is 0.90 the level of significance is mathematically evaluated as
[tex]\alpha = 1-0.90[/tex]
[tex]\alpha = 0.10[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the standardized normal distribution table. The values is [tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
The reason we are obtaining critical values for [tex]\frac{\alpha }{2}[/tex] instead of that of [tex]\alpha[/tex] is because [tex]\alpha[/tex] represents the area under the normal curve where the confidence level 1 - [tex]\alpha[/tex] (90%) did not cover which include both the left and right tail while [tex]\frac{\alpha }{2}[/tex] is just considering the area of one tail which is what we required calculate the margin of error
Generally the margin of error is mathematically evaluated as
[tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]MOE = 1.645* \frac{ 9 }{\sqrt{45} }[/tex]
[tex]MOE = 2.207[/tex]
The 90% confidence level interval is mathematically represented as
[tex]\= x - MOE < \mu < \= x + MOE[/tex]
substituting values
[tex]16.9 - 2.207 < \mu < 16.9 + 2.207[/tex]
[tex]16.9 - 2.207 < \mu < 16.9 + 2.207[/tex]
[tex]14.7 < \mu < 19.1[/tex]
Find the value of annuity if the periodic deposit is $400 at 4% compounded monthly for 18 years
Answer:
~820.8$
Step-by-step explanation:
The total money (M) after 18 years could be calculated by:
M = principal x (1 + rate)^time
with
principal = 400$
rate = 4% compounded monthly = 0.04/12
time = 18 years = 18 x 12 = 216 months (because of compounded monthly rate)
=> M = 400 x (1 + 0.04/12)^216 = ~820.8$
Determine the t critical value(s) that will capture the desired t-curve area in each of the following cases.
a. Central area = 0.95, df = 10
b. Central area = 0.95, df = 20
c. Central area = 0.99, df = 20
d. Central area = 0.99, df = 60
e. Upper-tail area = 0.01, df = 30
f. Lower-tail area = 0.025, df = 5
Answer:
a) Central area = 0.95, df = 10 t = (-2.228, 2.228)
(b) Central area = 0.95, df = 20 t= (-2.086, 2.086)
(c) Central area = 0.99, df = 20 t= ( -2.845, 2.845)
(d) Central area = 0.99, df = 60 t= (-2.660, 2.660)
(e) Upper-tail area = 0.01, df = 30 t= 2.457
(f) Lower-tail area = 0.025, df = 5 t= -2.571
Step-by-step explanation:
In this question, we are to determine the t critical value that will capture the t-curve area in the cases below;
We can use the t-table for this by using the appropriate confidence interval with the corresponding degree of freedom.
The following are the answers obtained from the table;
a) Central area = 0.95, df = 10 t = (-2.228, 2.228)
(b) Central area = 0.95, df = 20 t= (-2.086, 2.086)
(c) Central area = 0.99, df = 20 t= ( -2.845, 2.845)
(d) Central area = 0.99, df = 60 t= (-2.660, 2.660)
(e) Upper-tail area = 0.01, df = 30 t= 2.457
(f) Lower-tail area = 0.025, df = 5 t= -2.571
Perform the indicated operation. kyz * 1/kyz answer choices is 0 1 and k^2 y^2 z^2
Answer:
1
Step-by-step explanation:
[tex]\frac{kyz}{1}*\frac{1}{kyz} =\frac{kyz}{kyz}=1[/tex]
Find the value of a A.130 B.86 C.58 D.65
Answer:
Option (B)
Step-by-step explanation:
If two chords intersect inside a circle, measure of angle formed is one half the sum of the arcs intercepted by the vertical angles.
Therefore, 86° = [tex]\frac{1}{2}(a+c)[/tex]
a + c = 172°
Since the chords intercepting arcs a and c are of the same length, measures of the intercepted arcs by these chords will be same.
Therefore, a = c
⇒ a = c = 86°
Therefore, a = 86°
Option (B) will be the answer.
amanda teaches the art of quilling to 4 students. These students each teach art of quilling to 4 other students. If this process continues for 5 generation after amanda, BLANK people other than amanda will know the art of qiulling
Answer:
1024
Step-by-step explanation:
4 * 4 * 4 * 4 * 4
If jimmy has 15 apples and give 7 to gohn how many does jimmy have?
Answer:
Hey there!
Jimmy has 15-7, or 8 apples left.
Hope this helps :)
please help me ☣️☢️☢️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️⬅️▫️
Answer:
acute isosceles triangle
vertex angle, y = 44.0 degrees. (smallest angle)
Step-by-step explanation:
If the sides are in the ratio 4:4:3,
two of the sides have equal lengths, so it is an isosceles triangle.
Also, the sum of square of the two shorter sides is greater than the square of the longest side, so it is an acute triangle.
To find the smallest angle, we draw the perpendicular bisector of the base (side length 3) and form two right triangles.
The base angle x is given by the ratio
cos(x) = 1.5/4 = 3/8
Consequently the base angle is arccos(3/8) = 68.0 degrees.
The vertex angle equals twice the complement of 68.0
vertex angle, y = 2 (90-68.0) = 44.0 degrees. (smallest angle)
Please HELP best answer will receive a BRAINLIEST. Given the probability density function f ( x ) = 1/3 over the interval [ 4 , 7 ] , find the expected value, the mean, the variance and the standard deviation.
Answer:
[tex] E(X) =\int_{4}^7 \frac{1}{3} x[/tex]
[tex] E(X) = \frac{1}{6} (7^2 -4^2) = 5.5[/tex]
Now we can find the second moment with this formula:
[tex] E(X^2) =\int_{4}^7 \frac{1}{3} x^2[/tex]
[tex] E(X^2) = \frac{1}{9} (7^3 -4^3) = 31[/tex]
And the variance for this case would be:
[tex] Var(X)= E(X^2) -[E(X)]^2 = 31 -(5.5)^2 = 0.75[/tex]
And the standard deviation is:
[tex] Sd(X)= \sqrt{0.75}= 0.866[/tex]
Step-by-step explanation:
For this case we have the following probability density function
[tex] f(x)= \frac{1}{3}, 4 \leq x \leq 7[/tex]
And for this case we can find the expected value with this formula:
[tex] E(X) =\int_{4}^7 \frac{1}{3} x[/tex]
[tex] E(X) = \frac{1}{6} (7^2 -4^2) = 5.5[/tex]
Now we can find the second moment with this formula:
[tex] E(X^2) =\int_{4}^7 \frac{1}{3} x^2[/tex]
[tex] E(X^2) = \frac{1}{9} (7^3 -4^3) = 31[/tex]
And the variance for this case would be:
[tex] Var(X)= E(X^2) -[E(X)]^2 = 31 -(5.5)^2 = 0.75[/tex]
And the standard deviation is:
[tex] Sd(X)= \sqrt{0.75}= 0.866[/tex]
50 points + brainliest!
Answer:
( x+2) ^2 = 11
x =1.32,-5.32
Step-by-step explanation:
x^2 + 4x -7 = 0
Add the constant to each side
x^2 + 4x -7+7 = 0+7
x^2 + 4x = 7
Take the coefficient of the x term
4
Divide by 2
4/2 =2
Square it
2^2 = 4
Add this to each side
x^2 + 4x +4 = 7+4
Take the 4/2 as the term inside the parentheses
( x+2) ^2 = 11
Take the square root of each side
sqrt( ( x+2) ^2) =±sqrt( 11)
x+2 = ±sqrt( 11)
Subtract 2 from each side
x = -2 ±sqrt( 11)
To the nearest hundredth
x =1.32
x=-5.32
Answer:
[tex](x+2)^2=11[/tex]
[tex]x=-2 \pm \sqrt{11}[/tex]
Step-by-step explanation:
[tex]x^2+4x-7=0[/tex]
[tex]x^2+4x=7[/tex]
[tex]x^2+4x+4=7+4[/tex]
[tex](x+2)^2=11[/tex]
[tex]x+2=\pm\sqrt{11}[/tex]
[tex]x=-2 \pm \sqrt{11}[/tex]
NEED HELP ASAP!!
What is the equation of the line that is parallel to the
given line and has an x-intercept of -3?
O y = x + 3
O y = ?X + 2
Oy=-3x + 3
y=-3x+2
Answer:
B
Step-by-step explanation:
The equation of the line that is parallel to the given line and has an x-intercept of -3 is y= 2/3x + 2.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
We have a graph.
So, slope of line in graph is
= (-1-1)/ (0.-3)
= -2/ (-3)
= 2/3
and, we know that two parallel line have same slope.
so, the slope of parallel line is 2/3 and the x intercept is -3.
So, the Equation line is y= 2/3 x + b
0 = 2/3 (-3) +b
b= 2
Thus, the required equation is y= 2/3x + 2.
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Tosh. Inc.'s bonds currently sell for $980 and have a par value of $1,000. They pay a $95 annual coupon and have a 12-year maturity, but they can be called in 3 years at $1,150. What is their yield to call (YTC)?
Answer:
14.24%
Step-by-step explanation:
We have found that the yield to call (YTC) formula is:
YTC = [C + (F-P) / N] / [(F + P) / 2]
Where:
C = Periodic coupon amount = 95
P = Current Price = 980
F = Redemption amount = 1150
N = time left to redemption = 3
We replace:
YTC = [95 + (1150-980) / 3] / [(1150 + 980) / 2]
YTC = 0.1424
In other words, the yield to call (YTC) is equal to 14.24%
Data was collected for a sample of organic snacks. The amount of sugar (in mg) in each snack is summarized in the histogram below. 2 4 6 8 10 amount of sugar (mg) 180 182 184 186 188 190 192 194 Frequency What is the sample size for this data set?
Answer:
The sample size is 30.
Step-by-step explanation:
The sample size of a histogram can be calculated by summing up all the frequencies of all the occurrences in the data set
From the question the frequency is given as
Frequency = 2 4 6 8 10
The sample size n =
2 + 4 + 6 + 8 + 10
= 30
Therefore the sample size n of the data set = 30
A crew clears brush at a rate 2/3 acre in 2 days. How long will it take the same crew to clear the entire plot of 4 acres?
Answer:
It takes the crew 12 days to clear the bush.
Step-by-step explanation:
Given clears 2/3 acres / 2 days, or 1/3 acre per day
Time to clear 4 acres
= 4 / (1/3)
= 4 * (3/1)
= 12 days
Please help, much needed. A lot of points
Answer:
A. -9
Step-by-step explanation:
If one of the variables were negative than, it would not be able to equal 2/7.
Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 11 ft high
Answer:
0.0526ft/minStep-by-step explanation:
Since the gravel being dumped is in the shape of a cone, we will use the formula for calculating the volume of a cone.
Volume of a cone V = πr²h/3
If the diameter and the height are equal, then r = h
V = πh²h/3
V = πh³/3
If the gravel is being dumped from a conveyor belt at a rate of 20 ft³/min, then dV/dt = 20ft³/min
Using chain rule to get the expression for dV/dt;
dV/dt = dV/dh * dh/dt
From the formula above, dV/dh = 3πh²/3
dV/dh = πh²
dV/dt = πh²dh/dt
20 = πh²dh/dt
To calculate how fast the height of the pile is increasing when the pile is 11 ft high, we will substitute h = 11 into the resulting expression and solve for dh/dt.
20 = π(11)²dh/dt
20 = 121πdh/dt
dh/dt = 20/121π
dh/dt = 20/380.133
dh/dt = 0.0526ft/min
This means that the height of the pile is increasing at 0.0526ft/min