Answer:
The probability that the truck she selects will have at least one of the two features that Ella Stella wants is 50%.
Step-by-step explanation:
Since a certain store sells small, medium, and large toy trucks in each of the colors red, blue, green, and yellow, and the store has an equal number of trucks of each possible color / size combination, if Stella wants a medium red truck and her mother will randomly select one of the trucks in the store, to determine what is the probability that the truck she selects will have at least one of the two features that Stella wants, the following calculation must be performed:
3 sizes
4 colors
4 x 3 = 12
4 midsize cars
3 red cars
1 medium red car
4 + 3 - 1 = 6
6/12 = 0.5
Therefore, the probability that the truck she selects will have at least one of the two features that Ella Stella wants is 50%.
Let X be a random variable with density function f(x) = 2e^−2x
Calculate P( X≤ 0.5| X≤ 1)
By definition of conditional probability,
P(X ≤ 0.5 | X ≤ 1) = P((X ≤ 0.5) and (X ≤ 1)) / P(X ≤ 1)
but if X ≤ 0.5, then it's automatic that X ≤ 1, so
P(X ≤ 0.5 | X ≤ 1) = P(X ≤ 0.5) / P(X ≤ 1)
Given the PDF of X,
[tex]f_X(x) = \begin{cases}2e^{-2x}&\text{if }x\ge0\\0&\text{otherwise}\end{cases}[/tex]
the CDF would be
[tex]P(X\le x) = F_X(x) = \displaystyle\int_{-\infty}^x f_X(t)\,\mathrm dt[/tex]
[tex]F_X(x) = \begin{cases}0&\text{if }x<0\\1-e^{-2x}&\text{if }x\ge0\end{cases}[/tex]
So we have
P(X ≤ 0.5 | X ≤ 1) = (1 - exp(-2 × 0.5)) / (1 - exp(-2 × 1))
… = (1 - exp(-1)) / (1 - exp(-2))
… = (1 - 1/e) / (1 - 1/e ²)
… = (e ² - e) / (e ² - 1)
… = e / (e + 1) ≈ 0.7312
Jordan Bikes 4/3 miles in 1/10 hours. whats is his speed in miles per hour?
Help me please :) giving brainliest
Answer:
2.5
Step-by-step explanation:
You can change the equation from multiplication to division to get rate or time. We need the rate, so the equation should look like this now:
[tex]Distance/Time=Rate[/tex]
Now, we need to plug in the numbers we have...
[tex](5)/(2)=Rate[/tex]
...and solve for Rate:
[tex]Rate=2.5[/tex]
Evaluate f(x) = X - 8 for x = -8
Answer:-16
Step-by-step explanation:
This function is _____over the interval
[tex]x < - 1[/tex]
This function is_____ over the interval l
[tex] - 1 < x < 1[/tex]
Select all of the possible degrees of this polynomial function
2
3
4
5
Answer:
the answer to this question is 1
Step-by-step explanation:
the reason to that is because when the line goes over 2 and -2.
Answer:
first part is decreasing and increasing
second part is 3 and 5
Step-by-step explanation:
edg 2021
how do you Determine the x- and y-intercepts. x + (1/2) y = 2
Explain how you could find the shortest distance from A(6, 5) to the line y = 5x – 10. (Use a diagram, be specific, and list all your steps.
Step-by-step explanation:
I cannot draw a diagram here.
but I can explain what to do in general.
the shortest distance from a point to a line is always via a connecting line that is perpendicular to the given line and his through the given point.
and then the distance from the given point to the intersection point is calculated.
every line is defined in the form like
y = ax + b
where a is the slope of the line, and b is the intersection point on the y-axis (the offset from point 0).
the slope of a line is the ratio y/x defining how many units y changes when x changes a certain amount of units.
in our example,
y = 5x - 10
5 (or rather 5/1) is the slope of the line.
it means that y grows by 5 units every time x grows by 1 unit.
a perpendicular line (cuts the original line with a 90 degree angle) has a related slope : it reverts x and y and flips the sign :
5/1 turns into -1/5
that means at the perpendicular line whenever x grows by 5 units, y goes down by 1 unit.
so, the first approach for the perpendicular line is
y = -1/5 x + b
to get b we use the given point (6, 5) that has to be in the perpendicular line.
5 = -1/5 × 6 + b
25/5 = -6/5 + b
31/5 = b
=> y = -1/5 x + 31/5
the intersecting point is now where both lines are equal
5x - 10 = -1/5 x + 31/5
25x - 50 = -x + 31
26x = 81
x = 81/26
y = 5×(81/26) - 10 = 405/26 - 260/26 = 145/26
the distance of the given point (6, 5) to the line intersection point (81/26, 145/26) is the calculated as
distance² = (6 - 81/26)² + (5 - 145/26)²
distance = sqrt((6-81/26)² + (5-145/26)²)
since the result was not requested here, I save us the calculation.
Given the formula x=4ab(b+9), find x if a = 5 and b =7
Answer:
2240
Step-by-step explanation:
4(5)(7)(7+9)
=2240
Answer:
x = 2240
Step-by-step explanation:
x= 4ab(b+9)
x= 4(5)(7)(7+9)
x= 4(35)(16)
x= 4(560)
x= 2240
Part A
What is the relationship between squaring and taking the square root? Because of this relationship, what happens when you square a square
root?
Draw the graph of y +5=0 for two and 3 variables
Answer:
Step-by-step explanation:
y+5=0
y=-5
it is a line down 5 units parallel to x-axis.
you can take infinie points say (1,-5),(5,-5) ,(7,-5) etc.
Answer:
y = - 5
Step-by-step explanation:
In two dimensions, this is a line parallel to the x - axis. You can also think of it as a locus, the infinite set of points fulfilling (,− 5) — any real value of x, but y has to be -5.
Extending it to three dimensions, it is a plane parallel to the x-axis and also to the z-axis, or the locus (,− 5, ).
Pls if anyone knows the answer that will be greatly appreciated :)
Answer:
I think the area is 60 but i couldn't figure out the perimeter, sorry.
Step-by-step explanation:
Answer:
perimeter = 36 m
area = 60 m²
Step-by-step explanation:
there is some missing information. for example about the types of the shapes. e.g. if the triangle on the top is an isosceles triangle (2 equal sides). or if the rectangle at the bottom is actually a square with 6 m on all sides. in order to make the sloped side of the top triangle a round, whole number, i assume that the bottom part is a square.
so, the area of this combined shape is the area of the bottom square plus the area of the top triangle.
area square As = 6×6 = 36 m²
so, one side of the triangle is also 6 m, the other is 14-6 = 8 m.
the area of such a right-angled triangle is half of the full rectangle of 6×8.
area triangle At = 6×8/2 = 48/2 = 24 m²
total area = As + At = 36 + 24 = 60 m²
the perimeter of the total shape is the sum of all sides.
so, 14, 6, 6 and ... the baseline/ Hypotenuse of the top triangle.
for that r need the mentioned Pythagoras :
c² = a² + b²
where a and b are the sides, and c is the Hypotenuse (the side opposite of the 90 degree angle).
so, in our case of an isosceles triangle with a 90 degree angle :
c² = 8² + 6² = 64 + 36 = 100
c = 10 m
so, the perimeter is
14+6+6+10 = 36 m
What is the mode for the set of data?
Ages
Stem Leaves
6 0, 5, 8
7 0, 2, 3, 5, 7, 8, 9
8 0, 2, 3, 4, 5, 6, 8, 9
9 6, 6, 7, 8
6|0 = 60 years old
81
96
38
6
Answer:
96
Step-by-step explanation:
Mode is the number that appears most often
96 appears twice and is the only numbers that appears more than once
96 is the mode
Which expression is equivalent to the following complex fraction?
Answer:
Option B
Step-by-step explanation:
Answered by Gauthmath
lmk if you don't understand my handwriting
Annie bought a 2 3/4 pound roast for the family dinner. A total of 9 people will be at dinner. How many pound of roast will each person get if the roast is divided up equally?
Answer:
11 /36 of a pound
Step-by-step explanation:
Take the pounds and divide by the number of people
2 3/4 ÷ 9
Change the mixed number to an improper fraction
(4*2+3)/4 ÷9
11/4 ÷9
Copy dot flip
11/4 * 1/9
11/36
Solve the right triangle, ΔABC, for the missing side and angles to the nearest tenth given sides a = 14.9 and b = 17.5.
A. A = 31.6 , B = 58.4 , c = 9.2
B. A = 49.6 , B = 40.4 , c = 23
C. A = 40.4 , B = 49.6 , c = 23
D. A = 40.4 , B = 49.6 , c = 9.2
Answer:
C. A = 40.4 , B = 49.6 , c = 23
Step-by-step explanation:
First, we need to get the c using the pythagoras theorem;
c² = a²+b²
c² = 14.9²+17.5²
c² = 222.01 + 306.25
c² = 528.26
c = 22.98
c ≈ 23
Using the sin rule;
a/Sin<A = c/sin<C
14.9/sin<A = 23/sin90
14.9/sin<A = 23
sin<A = 14.9/23
sin <A = 0.6478
<A = arcsin(0.6478)
<A = 40.4degrees
Also, <A + <B + <C = 180
40.4 + <B + 90 = 180
<B = 180 - 130.4
<B = 49.6degrees
Can someone help me on this Please
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Answer:
11.6 cm
Step-by-step explanation:
As the page title tells you, the Pythagorean theorem must be applied more than once. As you know, it tells you the square of the hypotenuse is the sum of the squares of the two sides.
AD² = ED² +EA²
EA² = AD²-ED² = 7² -6² = 13
EA = √13 ≈ 3.606
__
CD² = ED² +EC²
EC² = CD² -ED² = 10² -6² = 64
EC = √64 = 8
__
The length of the horizontal diagonal is ...
AC = EA +EC = 3.6 +8 = 11.6 . . . cm
if one half of a number is 5 more than 6, what is the value when the number is tripled
Answer:
66
Step-by-step explanation:
let's use x to represent the unknown number
1/2x is 5 more than 6:
↓
1/2x=5+6
solve to find x
1/2x=11
x=22
next, it asks us what is the value of the number when the number is tripled
since we already found what x is equal to, we can multiply that by 3 to figure out its value when it's tripled
3(22)=66
Using mathematical equation to model the scenario, the value of the number when tripled is 66
Let the number = n
0.5n = 5 + 6
0.5n = 11
Divide both sides by 0.5
n = 22
When n is tripled :
n = 22 × 3
n = 66
Hence, the value of the number when tripled is 66
Learn more : https://brainly.com/question/25480062
How many pounds of grain is it necessary to grind to get exactly 100 lb of flour, is the payment for the work is 10% of the ground flour? (Assume there are no loses after grinding.)
Answer:
111.1111... lbs
x -.1x = 100
.9x = 100
x = 100/.9 = 111.1111
Step-by-step explanation:
the set of ordered pairs {(6,4),(2,-5),(-2,4)<(6,-4)} is a function?
Answer:
Not a function
Step-by-step explanation:
There are two points in the set that have the same x-value or "input": (6,4) and (6,-4). This fails the vertical line test which means that one input will give two potential outputs. This cannot make a function.
Need help! Thank you :)
Answer:
The value of [tex]x[/tex] is 10.
Step-by-step explanation:
Both angles ABC and CBD are complementary, that is, the sum of the measures of both angles equals 90°, that is:
[tex]\angle ABC + \angle CBD = 90^{\circ}[/tex] (1)
If we know that [tex]\angle ABC = 5\cdot x[/tex] and [tex]\angle CBD = 4\cdot x[/tex], then the value of [tex]x[/tex] is:
[tex]5\cdot x + 4\cdot x = 90^{\circ}[/tex]
[tex]9\cdot x = 90^{\circ}[/tex]
[tex]x = 10[/tex]
The value of [tex]x[/tex] is 10.
Write expression with two terms that is equivalent to the expression shown. 4(2x + 11 - x)
A pooled variance is an estimated weighted variance made up of several different populations when the mean of each population may be different, but one may assume that the variance of each population is the same.
a. True
b. False
Answer:
True
Step-by-step explanation:
Considering the above definition of Pooled Variance, the correct answer is TRUE.
This is because Pooled variance is used to determine the reasonable estimates of variance, where several repeated tests are expected at each value.
This helps to provide greater precision estimates of variance.
What is the quadratic regression equation that fits these data?
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Answer:
D. y = -0.32x² -1.26x +15.81
Step-by-step explanation:
This is one of those multiple-choice questions where you only need a vague idea of what the answer is supposed to look like.
In this case the answer must be a quadratic equation with a negative leading coefficient. (The parabola opens downward.)
The only answer choice that is a 2nd degree polynomial with a negative leading coefficient is choice D.
__
A: linear equation
B: exponential equation
C: quadratic that opens upward (positive leading coefficient)
D: quadratic that opens downward -- the answer you're looking for
A group of 49 randomly selected students has a mean age of 22.4 years with a standarddeviation of 3.8. Construct a 98% confidence interval for the population mean knowing thatthe population standard deviation is 4.2 years.
Answer:
The 98% confidence interval for the population mean is between 21 and 23.8 years.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.327\frac{4.2}{\sqrt{49}} = 1.4[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 22.4 - 1.4 = 21 years.
The upper end of the interval is the sample mean added to M. So it is 22.4 + 1.4 = 23.8 years.
The 98% confidence interval for the population mean is between 21 and 23.8 years.
What is the difference between the temperature - 7 Celsius and - 12 Celsius on a scatter diagram
Answer:
Sự khác biệt giữa nhiệt độ - 7 độ C và - 12 độ C trên biểu đồ phân tán là gì
Step-by-step explanation:
[tex] {ap}^{5} ( {a}^{2} + ap) - 12 {a}^{2} {p}^{6} [/tex]
Remove brackets and simplify
A passenger car will go 455 miles on 17.5 gallons of gasoline in city driving. What is the rate in miles per gallon?
Answer:
26 miles per gallon
Step-by-step explanation:
Take the miles and divide by the gallons
455 miles / 17.5 gallons
26 miles per gallon
The sequence below is arithmetic:
{3, -6, -15, -24}
TRUE OR FALSE
Answer: TRUE
Step-by-step explanation:
An arithmetic sequence is a sequence in which the difference between each term (number) is a constant.
Given the sequence is {3, -6, -15, -24}
3 - (-6) = 9
-6 - (-15) = 9
-15 - (-24) = 9
As we can see from above, the difference between the given terms is all 9. Therefore, it is indeed an arithmetic sequence.
Hope this helps!! :)
Please let me know if you have any questions
Answer:
true
Step-by-step explanation:
I really need help
Dz,2 of X is
(0-4)
(2,-2)
(6,2)
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Answer:
(6,2)
Step-by-step explanation:
As is often the case with multiple-choice problems, you don't actually need to know the detailed working. You just need to know what the answer looks like.
When point X is dilated by a factor of 2 with point Z as the center of dilation, it will move to a location twice as far from Z. You can tell by looking at the graph that X' will be in the first quadrant, above and to the right of the location of X. The only sensible answer choice is ...
X' = (6, 2)
_____
Additional comment
X is a distance of X-Z = (4, 0) -(2, -2) = (2, 2) from Z Doubling that will put the image point a distance of 2(2, 2) = (4, 4) from Z. When this is added to Z, we find ...
X' = Z + (4, 4) = (2+4, -2+4) = (6, 2)
The length of a rectangle is 2 centimeters less than three times its width. Its area is 21 square centimeters. Find the dimensions of the rectangle. Use the formula, area=length*width.
Area = length x width
Area = 21 square cm
Width = x
Length = 3x + 2
21 = 3x+ 2 * x
21 = 3x ^2 + 2x
Subtract 21 from both sides:
3x^2 + 2x -21 = 0
Use the quadratic formula to solve for x:
-2 +/- sqrt(2^2-4*3(-21))/(2*3)
X = 7/3 and -3
A dimension can’t be a negative value so x needs to be 7/3
Width = x = 7/3 = 2 1/3 cm
Length = 3(7/3) + 2 = 9 cm
Check: 9 x 2 1/3 = 21
Dimensions: width 2 1/3 cm length 9 cm
Answer:
The dimensions of the rectangle are 7 by 3 centimeters.
Step-by-step explanation:
We are given that the length of a rectangle is two centimeters less than three times its width. In other words:
[tex]\displaystyle \ell = 3w-2[/tex]
Given that the area of the rectangle is 21 square centimeters, we want to determine the dimensions of the rectangle.
Recall that the area of a rectangle is given by:
[tex]A= w\ell[/tex]
Substitute:
[tex](21)=w(3w-2)[/tex]
Solve foro the width. Distribute:
[tex]3w^2-2w=21[/tex]
Isolate the equation:
[tex]3w^2-2w-21=0[/tex]
Factor. Find two numbers that multiply to 3(-21) = -63 and add to -2.
-9 and 7 suffice. Hence:
[tex]3w^2-9w+7w-21=0 \\ \\ 3w(w-3)+7(w-3) = 0 \\ \\ (3w+7)(w-3)=0[/tex]
Zero Product Property:
[tex]3w+7=0\text{ or } w-3=0[/tex]
Solve for each case. Hence:
[tex]\displaystyle w = -\frac{7}{3}\text{ or } w=3[/tex]
Since width cannot be negative, we can ignore the first solution.
Therefore, our width is three centimeters.
And since the length is two less than three times the width, the length is:
[tex]\ell = 3(3) - 2 = 7[/tex]
The dimensions of the rectangle are 7 by 3 centimeters.
