Answer:
a) The probability that the thickness is less than 3.0 mm
P(X<3.0) = 0.057
b) The probability that the thickness is less than 7.0 mm
P(X>7) = 0.0401
c) The probability that the thickness is between 3.0 mm and 7.0 mm
P( 3 < x < 7)= 0.9029
Step-by-step explanation:
Step(i):-
Given mean of the Population (μ) = 4.9 mm
Standard deviation of the Population(σ) = 1.2 mm
a)
Let 'X' be the random variable in normal distribution
[tex]Z = \frac{x-mean}{S.D} = \frac{3.0-4.9}{1.2} = -1.583[/tex]
The probability that the thickness is less than 3.0 mm
[tex]P(X<3.0) = P(Z < -1.583) = 1 - P( Z>1.583)[/tex]
= 1 - ( 0.5 + A(1.583)
= 0.5 - A(1.583)
= 0.5 - 0.4430
= 0.057
The probability that the thickness is less than 3.0 mm
P(X<3.0) = 0.057
b)
Let 'X' be the random variable in normal distribution
[tex]Z = \frac{x-mean}{S.D} = \frac{7.0-4.9}{1.2} = 1.75[/tex]
The probability that the thickness is less than 7.0 mm
[tex]P(X>7.0) = P(Z >1.75) = 0.5 - A(1.75)[/tex]
= 0.5 - 0.4599 ( from normal table )
= 0.0401
The probability that the thickness is less than 7.0 mm
P(X>7) = 0.0401
c)
Let 'X' be the random variable in normal distribution
[tex]Z_{1} = \frac{x_{1} -mean}{S.D} = \frac{3.0-4.9}{1.2} = -1.583[/tex]
[tex]Z_{2} = \frac{x_{2} -mean}{S.D} = \frac{7.0-4.9}{1.2} = 1.75[/tex]
The probability that the thickness is between 3.0 mm and 7.0 mm
P( 3 < x < 7) = P( - 1.583 < X < 1.75 )
= A( 1.75 ) + A( -1.583)
= A(1.75)+A(1.583)
= 0.4599 + 0.4430
= 0.9029
The probability that the thickness is between 3.0 mm and 7.0 mm
P( 3 < x < 7)= 0.9029
If 10 men can cut a piece of lawn in 4
days, how long will it take 8 men to
cut the same lawn?
Answer:
About 3
Step-by-step explanation:
Step-by-step explanation:
10 men =4 days
8 men =x days
cross multiply
10×x=8×4=24
(21.) A writer earns $3400 a month. Last month she spent $204 on food.
What percent of her income was spent on food?
Answer: 6%
Step-by-step explanation:
3400's x%=204
(3400)x/100=204
34x=204
34x/34=204/34
I used my calculator to divide
x=6
So 6%
Asphere has a radius of 27 inches. A horizontal plane passes through the center of the sphere.
Part 1 out od 2
Describe the cross section formed by the plane and the sphere.
9514 1404 393
Answer:
circle of radius 27 inches
Step-by-step explanation:
Anywhere a plane cuts a sphere, the cross section is a circle. When the plane includes the center of the sphere, the circle has the same radius the sphere has.
The cross section is a circle of radius 27 inches.
Need help ASAP swill mark Brainly
Answer:
B
Step-by-step explanation:
Hope it helps!
Answer:
-1 and 1/7
Step-by-step explanation:
hope this helps! have a great day!
write 36/48 in simplest form
Answer:
3/4
Step-by-step explanation:
heyyyyyyyyyyyyyyyyyyyyy
Answer:
3/4 (find the GCF, greatest common factor, and divide both sides [12])
Step-by-step explanation:
please mark brainliest, give a thanks, and rate a five stars if this helped! feel free to ask anymore questions if you need any more help! thanks!
(lol optional): add my sc: tealyn337
Solve for the missing monomial F.
-27x3y - (-3x)(F)
Answer:
7
Step-by-step explanation:
Find the 43rd term in the sequence: -6, -3, 0,...
Answer: 129
Step-by-step explanation: 43•3=129
Can y’all help me? I think it’s the last one but I’m not sure
Write the ratio 3/9 4/9 in simplest form
Answer:
3/9 is 1/3 but 4/9 is already simplified :D
if you are happy with my answer, please give brainliest :)
Step-by-step explanation:
write an absolute value inequality for the graph below.
use x for your variable.
Step-by-step explanation:
The magnitude of x is equal or less than 7.
=> We have |x| <= 7.
which expression is equivalent to the following expression: 4.7z + 13y - 1/5 + 7
Answer:
Step-by-step explanation:
I'm not sure if you wanted the answer or not but here's the answer to that.
4.7z + 13y + 34/5
The market is located at point (−3, −2) on the coordinate graph.
The barber shop is 6 units to the right and 5 units up from the market.
Graph two points on the coordinate grid to show the location of the market and the location of the barber shop.
Answer:
(2,4)
Step-by-step explanation:
find the area or this triangle
Answer:
Area of triangle = 15 square units
Step-by-step explanation:
We need to find area of the triangle, given the vertices:
A=(4,0)
B=(1,5)
C=(7,5)
The formula used is: [tex]Area\:of\:triangle=\frac{1}{2}(x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2))[/tex]
We have: [tex]x_1 =4, y_1 =0, x_2 =1, y_2=5, x_3=7 , y_3=5[/tex]
Putting values and finding area
[tex]Area\:of\:triangle=\frac{1}{2}(x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2))\\Area\:of\:triangle=\frac{1}{2}(4(5-5)+1(5-0)+7(0-5))\\Area\:of\:triangle=\frac{1}{2}(4(0)+1(5)+7(-5))\\Area\:of\:triangle=\frac{1}{2}(0+5-35)\\Area\:of\:triangle=\frac{1}{2}(-30)\\Area\:of\:triangle=-15[/tex]
We will be ignoring negative sign, because area of triangle is positive.
So, Area of triangle = 15
Which of the following statements are true?
The value of the 5 in 592,841 is 10 times the value of the 5 in 358,764.
The value of the 6 in 861,257 is 10 times the value of the 6 in 651,042.
The value of the 8 in 358,764 is 10 times the value of the 8 in 592,841.
The value of the 5 in 592,841 is in of the value of the 5 in 358,764.
The value of the 6 in 861,257 is in of the value of the 6 in 651,042.
The value of the 8 in 358,764 is id of the value of the 8 in 592,841.
Answer:
5/6 is eaqual to 2.5/3
Step-by-step explanation:
For addition, drag tiles onto the board.
To form a group, place one tile on top of another.
What is the sum of -2 and -7?
Board sum: 0
Reset
Answer:
-9
Step-by-step explanation:
The sum of -2 and -7 is given as follows;
-2 + (-7)
In mathematical operations, + * - is -.
So we have;
-2 - 7
This gives us: -9
Answer:
10
Step-by-step explanation:
im on enginuity leson multiplying with intager tiles qestion 4
What is always true about the net of a prism? O It contains 0 triangles. o It contains O or 2 triangles. olt contains 3 or more triangles. O It contains 4 or more triangles. HURRY ITS A TEST
Answer:
It contains 0 or 2 triangles.
Step-by-step explanation:
Answer:
its b
Step-by-step explanation:
Decide whether the two equations are equations are equivalent 7v-3/2=5 14v-3=15 sho work
Answer:
Not equivalent.
Step-by-step explanation:
The given equations are :
7v-3/2=5 ....(1)
14v-3=15 ....(2)
Taking equation (1) first,
7v-3/2=5
Adding 3/2 to both the sides.
7v-3/2+3/2=5+3/2
7v = 6.5
v = 0.928
Taking equation (2).
14v-3=15
Adding 3 to both sides.
14v-3+3=15+3
14v=18
v = 1.285
So, the values of v in both equations ar not the same. It means two equations are not equivalent.
Why is it impossible for m
Answer:
? What M? What is impossible?
I'm supposed to solve for PQ. it's pythagorean theorem.
Answer:
29 i think
Step-by-step explanation:
pythagoreon thereom is a^2+b^2=c^2 so c^2 being the hypotneuse you would do 2*2=4 +5*5=25 and 4+25=29
Ivan has 6 times as many blue beads as red beads. he has 49 red and blue beads in all. how many blue beads does Ivan have
Answer:
Ivan has 42 blue beads.
Step-by-step explanation:
We need to find how many blue beads Ivan has.
Blue beads = 6 times as many as red beans
b = 6r
r + b = 49
r + (6r) = 49
7r = 49
Divide both sides by seven to isolate r
r = 7
b = 6(7)
b = 42
What is | -7.9 ?
help
What interval notation represents the data graphed below?
A. [-∞, -2) U [4, ∞]
B. [-∞, -2] U (4, ∞]
C. (-∞, -2] U (4, ∞]
D. (-∞, -2) U [4, ∞)
Answer: Choice D
[tex](-\infty, -2) \cup [4, \infty)[/tex]
=====================================================
Explanation:
The left portion is the interval (-∞, -2)
This is a shorthand way of saying [tex]-\infty < x < -2[/tex]
The curved parenthesis says "do not include this endpoint as part of the solution set". Note the open hole at x = -2 in the diagram.
In contrast, the value x = 4 is included (due to the filled in circle), so we use a square bracket for this endpoint. Therefore, the right-hand portion is represented by [4, ∞) which translates to [tex]4 \le x < \infty[/tex]
Negative and positive infinity will always use a parenthesis, and never a square bracket. This is because we can only approach infinity but never reach it, so we cannot include it as an endpoint.
All of this builds up to the full interval notation to be [tex](-\infty, -2) \cup [4, \infty)[/tex]
The only square bracket is near the 4; everything else is a curved parenthesis. This is why choice D is the final answer.
write the equation of the line for the following table of values.
x. -3 -5 -7 -9 -11
y. -16 -26 -36 -46 -56
Plz helppp 35 points:)
Answer:
We conclude that the equation of the line is:
[tex]y = 5x + 1[/tex]Step-by-step explanation:
The slope-intercept form of the line equation
[tex]y = mx+b[/tex]
where
m is the slopeb is the y-interceptGiven the data table
x -3 -5 -7 -9 -11
y -16 -26 -36 -46 -56
From the table taking two points
(-3, -16)(-5, -26)Determining the slope between (-3, -16) and (-5, -26)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-3,\:-16\right),\:\left(x_2,\:y_2\right)=\left(-5,\:-26\right)[/tex]
[tex]m=\frac{-26-\left(-16\right)}{-5-\left(-3\right)}[/tex]
[tex]m=5[/tex]
Thus, the slope of the line is: m = 5
substituting m = 5 and (-3, -16) in the slope-intercept form of the line equation to determine the y-intercept b
[tex]y = mx+b[/tex]
-16 = 5(-3) + b
-16 = -15 + b
b = -16+15
b = 1
Thus, the y-intercept b = 1
now substituting m = 5 and b = 1 in the slope-intercept form of the line equation
[tex]y = mx+b[/tex]
[tex]y = 5x + 1[/tex]
Therefore, we conclude that the equation of the line is:
[tex]y = 5x + 1[/tex]answer quick will give 20 points
Answer:
I think c but I'm not sure
Answer:
C: (-3,6)
Step-by-step explanation:
add both equations
5x+2x+2y-2y=-15+(-6)
7x=-21
x=-3
input x=3 into any equation in system and solve for y
2(3)-2y=-6
-2y=-12
y=6
solution: (-3, 6)
Rachel wants to use the Distributive Property to rewrite 72 + 45. Which expression could she use?
Answer:
1.17 x 10^2
Step-by-step explanation:
Im pretty sure its right
Mrs. Fuller is trying to organize all of her children's toys into a large toy box. Each toy
has the dimensions of 4 inches x 3 inches x 3 inches. The toy box measures 4 feet x 2
feet x 3 feet. How many toys will be stored in the large toy box?
Answer: 1,152 toys can be stored in the box.
Step-by-step explanation:
For an object with measures L (length) by W (width) by H (height) the volume is calculated as:
V = L*W*H
We know that the measures of each toy are: 4in x 3in x 3in
Then the volume of each toy is:
V = 4in*3in*3in = 36in^3
The toy box is 4ft x 2ft x 3 ft
First we should write the measures in the same units as before, we know that:
1ft = 12 in.
Then:
4ft = 4*12 in = 48 in
2ft = 2*12in = 24in
3ft = 3*12in = 36in
Then the measures of the box are:
48in x 24in x 36in
Then the volume of the box is:
V = 48in*24in*36in = 41,472 in^3
Now, the number of toys that can be stored in the box is the same as the number of times that 36in^3 is in 41,472 in^3
this is equal to the quotient between 41,472 in^3 and 36in^3
N = 41,472 in^3/36in^3 = 1,152
1,152 toys can be stored in the box.
Factor 24x – 18 using the GCF
Answer:
24x – 18
6(4x-3)is required factor.
8 + 3 × (4 ÷ 2) − 7
Step 1: 8 + 3 × 2 − 7
Step 2: 11 × 2 − 7
Step 3: 22 − 7
Step 4: 15
In which step does a mistake first appear?
Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of 5.4 millimeters (mm) and a standard deviation of 0.8 mm. For a randomly found shard, find the following probabilities.
a. the thickness is less than 3.0 mm
b. the thickness is more than 7.0 mm
c. the thickness is between 3.0 mm and 7.0 mm
Answer:
a) the required probability is 0.0013
b) the required probability is 0.0288
c) the required probability is 0.9759
Step-by-step explanation:
Given the data in the question;
let x be the thickness measurements
Given that X follows a Normal distribution with mean μ = 5.4
standard deviation σ = 0.8
then z = x-μ / σ = x-5.4 / 0.8 follows standard Normal
a) probability that the thickness is less than 3.0 mm
P( x<3 ) = P( x-5.4 / 0.8 < 3-5.4 / 0.8 ) = P( Z < -3.00 ) = 0.0013
Therefore, the required probability is 0.0013
b) the thickness is more than 7.0 mm
P( x>7 ) = P( x-5.4 / 0.8 > 7-5.4 / 0.8 ) = P( Z > 2.00)
= 1 - P( Z ≤ 2)
= 1 - 0.9772
= 0.0288
Therefore, the required probability is 0.0288
c) the thickness is between 3.0 mm and 7.0 mm
P(3< x<7 ) = P( x<7) - P(x<3)
= P( x-5.4 / 0.8 > 7-5.4 / 0.8 ) - P( x-5.4 / 0.8 < 3-5.4 / 0.8 )
= P( Z< 2 ) - P( Z < -3)
= 0.9772 - 0.0013
= 0.9759
Therefore, the required probability is 0.9759
Which of the following graphs represents a function?
9514 1404 393
Answer:
(a) see below
Step-by-step explanation:
The graph that has no two points one above the other is the graph of a function. That is the first of your attachments.