Answer:
The probability of thickness exceeding 101 is 0.4483.
Step-by-step explanation:
Let X denote the thickness of the part manufactured by plastic injection molding.
Assume that X follows a normal distribution with mean, μ = 100 and standard deviation, σ = 8.
Compute the probability of thickness exceeding 101 as follows:
[tex]P(X>101)=P(\frac{X-\mu}{\sigma}>\frac{101-100}{8})[/tex]
[tex]=P(Z>0.125)\\\\=1-P(Z<0.125)\\\\=1-0.55172\\\\=0.44828\\\\\approx 0.4483[/tex]
Thus, the probability of thickness exceeding 101 is 0.4483.
Which is the better deal 8 ounces of shampoo for $0.99 or 12 ounces for $1.47?
Answer:
12 ounces for $1.47.
Step-by-step explanation:
:) ello
POSSIBLE POINTS: 3.33
Tracy wants to buy some pies for her sisters and she has a budget of $82 to spend on $5
apple pies, $4.5 banana pies, and $5.5 chocolate pies. She wants to buy 16 pies for her
sisters and must buy as many chocolate pies as apple pies and banana pies combined.
How many of each item should she buy? Write a system of equations to help you solve
this problem.
# of applie pies =
# of banana pies =
# of chocolate piles =
1
2 3
Answer:
From the information given, you can write the following system of equations:
x+y+z=16 (1)
5x+4.5y+5.5z=82 (2)
z=x+y (3)
You can replace (3) in (1) and (2):
x+y+x+y=16
2x+2y=16 (4)
5x+4.5y+5.5(x+y)=82
5x+4.5y+5.5x+5.5y=82
10.5x+10y=82 (5)
Now, you have the following equations:
2x+2y=16 (4)
10.5x+10y=82 (5)
You can isolate x in (4):
2x=16-2y
x=8-y (6)
Then, you have to replace (6) in (5):
10.5(8-y)+10y=82
84-10.5y+10y=82
84-82=10.5y-10y
2=0.5y
y=2/0.5
y=4
Now, you can replace the value of y in (6) to find x:
x=8-4
x=4
Finally, you can replace the vaue of x and y in (3) to find z:
z=4+4
z=8
According to this, she should buy 4 apple pies, 4 banana pies and 8 chocolate pies.
Please help me I don’t get this
Sum of the interior angles of any triangle equal 180° .
Thus ;
[tex]x + 2x + x + 8 = 180[/tex]
[tex]4x + 8 = 180[/tex]
Subtract sides -8
[tex]4x + 8 - 8 = 180 - 8[/tex]
[tex]4x = 172[/tex]
Divided sides by 4
[tex] \frac{4}{4}x = \frac{172}{4} \\ [/tex]
[tex]x = 43[/tex]
So the angles are :
x = 43°
2x = 2 ( 43 ) = 86°
x + 8 = 43 + 8 = 51°
Thus the order from least to greatest ,
is : 43° , 51° , and 86°
_________________________________
And we're done.....♥️♥️♥️♥️♥️
2) Chicken soup is 3 cans for $0.55. How much would a
dozen soup cans cost?
Answer:
It would cost $2.20
Step-by-step explanation:
If 3 cans = $.55
then 3*4 = 12
soooo 4*.55 = 2.20
Hope this helps!!!
Walter is helping to make cookies for a basketball tournament. He's made 15 cookies so far. His coach asked him to make at least 20 cookies but no more than 55. Solve the inequality and interpret the solution.
Answer:
[tex]5\leq x\leq 40[/tex]
Here, [tex]x[/tex] denotes the additional cookies that need to be made by Walter besides 15 cookies made by him so far
Step-by-step explanation:
Number of cookies made by Walter so far = 15
He is asked by his coach to make at least 20 cookies but no more than 55.
Let [tex]x[/tex] denotes the additional cookies that need to be made by Walter besides 15 cookies made by him so far.
The inequality is [tex]20\leq x+15\leq 55[/tex]
Now solve this inequality.
[tex]20\leq x+15\leq 55\\20-15\leq x\leq 55-15\\5\leq x\leq 40[/tex]
Answer: a
Step-by-step explanation: because its right
g What is the max number of 4-element-subsets of we can select, such that intersection of any 3 of them is empty?
Answer:
16Step-by-step explanation:
In order to get the max number of 4-element-subsets of we can select, such that intersection of any 3 of them is empty, we need to calculate the power of the set having four elements. Let the set containing the element be A as shown;
Let set A = {a, b, c, d}
Power of the set P(A) = [tex]2^n[/tex] where:
n is the total number of element in the set. Since we have four elements in the set, n = 4
[tex]P(A) = 2^4\\P(A) = 16[/tex]
This means that the set A have 16 subsets. The subsets of the set are:
{}, {a}, {b}, {c}, {d}, {a, b}, {a, c}, {a, d}, {b, c}, {b, d}, {c, d}, {a, b, c}, {a, b, d}, {b, c, d}. {a, c, d}, {a, b, c, d}.
From all the subsets, it can be seen that intersection of set {a} and {b}, {a} and {c}, {c} and {d} are empty.
Hence the max number of 4-element-subsets of we can select, such that intersection of any 3 of them is empty is 16
7. Which statements about the values of 2.044
and 20.44 are true?
Answer:
20.44>2.044
Step-by-step explanation:
What is 2+2-2X2 divided by 2??
Answer:
0
Step-by-step explanation:
cause 2+2 is 4 and 2x2 is four and since u put - it take it away a then divide 0 by 2 u get 0
The terminal side of angle θ intersects the unit circle in the first quadrant at (925,y). What are the exact values of sinθ and cosθ?
Correct question is;
The terminal side of angle θ intersects the unit circle in the first quadrant at (9/25,y). What are the exact values of sinθ and cosθ?
Answer:
sinθ = (√544)/25) and cosθ = 9/25
Step-by-step explanation:
We are given that (9/25,y) lies on the unit circle. Thus, from general representation of equation of a circle, we can write that;
(9/25)² + y² = 1²
y² = 1 - (9/25)²
y² = (625 - 81)/25²
y² = 544/25²
y = ±(√544)/25
We are told the point is in the first quadrant and so we will choose the positive value of y = (√544)/25.
Therefore, the terminal side of the angle θ intersects the unit circle at [9/25, (√544)/25)]
In unit circle geometry, cosθ = x, while sinθ = y.
Thus; sinθ = (√544)/25) and cosθ = 9/25
The exact value of [tex]sin\theta[/tex] and [tex]cos\theta[/tex] is [tex]cos\theta = \frac{9}{25} , sin\theta = \frac{\sqrt{544} }{25}[/tex] and this can be determined by forming the equation of circle.
Given :
The terminal side of angle [tex]\theta[/tex] intersect at unit circle ([tex]\frac{9}{25}, y[/tex]).
From general representation of equation of circle , we can write
[tex]x^{2} + y^{2} = a^{2}\\[/tex]
[tex](\frac{9^{2} }{25^{2} })[/tex] + [tex]y^{2} = 1^{2}[/tex]
[tex]y^{2} = 1 - \frac{81}{625}[/tex]
[tex]y^{2} = \frac{625-81}{625}[/tex]
[tex]y^{2}=\frac{544}{625}[/tex]
Taking square root both sides
[tex]y= \frac{\sqrt{544} }{\sqrt{625} }[/tex]
[tex]y = \frac{\sqrt{544} }{25}[/tex]
We are taking only because point lies in first quadrant.
The terminal side of angel [tex]\theta[/tex] unit circle in first quadrant at [tex](\frac{9}{25} , \frac{\sqrt{544} }{25})[/tex]
In unit circle
[tex]x = cos\theta , y = sin\theta[/tex]
[tex]\rm cos\theta = \frac{9}{25} , sin\theta = \frac{\sqrt{544} }{25}[/tex].
For more information click on the link gives below
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The sum of three consecutive odd integers is 18 less than five times the middle number fimd the three integers
Answer:
7, 9, 11
Step-by-step explanation:
x+x+2+x+4=5(x+2)-18
3x+6=5x+10-18
3x+6=5x+-8
3x=5x+-14
-2x=-14
x=7
Which expression is equivalent to 27 + 15?
1) 3(24 + 12)
2) 319 + 5)
3) 9(3 + 15)
4) 9(18+ 6)
Describe the similarities and differences between a bar graph and a histogram.
Answer:
Bar graphs are used with nominal or ordinal scores; histograms are used with interval or ratio scores.
Step-by-step explanation:
4950/6 + 112 x 1.75 = ? x 2
Answer:
1021
Step-by-step explanation:
Answer:
1021 is the answer to this question
12. An object is fired from the top of a 200 ft. tower with an initial velocity of 80 ft/sec. and is
modeled by the equation h(t) = -16t^2+80t + 200.
a) How long after firing does it reach its maximum height?
b) What is the maximum height?
Answer:
a) The object reaches its maximum height at t=2.5 seconds
b) The maximum height is 300 m
Step-by-step explanation:
Maximum Value of a Function
First derivative criteria:
If f(t) is a real continuous function of t and the first derivative of f called f'(t) exists, then solving the equation:
f'(t)=0
Gives the critical points of f, some of which could be maximum or minimum.
Second derivative criteria:
If t=t1 is a critical point of f(t) and the second derivative of f:
f''(t1) is positive, then t1 is a minimum of f
f''(t1) is negative, then t1 is a maximum of f.
f''(t1)=0, no conclusion can be drawn.
The height of the object is modeled by the function:
[tex]h(t) = -16t^2+80t + 200[/tex]
a)
To find the maximum height, we use the above criteria.
Find the first derivative:
h'(t) = -32t+80
Equate h'(t)=0
-32t+80=0
Solve:
[tex]-32t=-80[/tex]
[tex]t=80/32=2.5[/tex]
t=2.5 seconds
Find the second derivative:
h''(t)=-32
Since the second derivative is negative, the critical point is a maximum.
The object reaches its maximum height at t=2.5 seconds
b) Evaluate h(2.5)
[tex]h(2.5) = -16\cdot 2.5^2+80\cdot 2.5 + 200[/tex]
[tex]h(2.5) = -100+200 + 200[/tex]
h(2.5)=300 m
The maximum height is 300 m
Is 18.18 rational or irrational
Answer:
Rational
Step-by-step explanation:
You are able to put 18.18 in a fraction.
Hope this helped, Have an AMAZING day/night!
The length of a rectangle is three times its width.
If the perimeter of the rectangle is 56 yd, find its area.
Answer:
147 yards
Step-by-step explanation:
Use a system of equations
Let x be length of rectangle and y be width of rectangle
x = 3y
2x + 2y = 56
Substitute x = 3y into second equation, we have 2(3y) + 2y = 56. Combine like terms and we have 8y = 56. y = 7.
Substituting y = 7 into the first equation, we have x = 3(7), and x = 21.
Area is length times width, so area is 21 * 7 = 147
Answer:
area= 147 yd
Step-by-step explanation:
l= 21 yd
w= 7 yd
Formula: a=lxw (area=length x width)
a=21 x 7
21 x 7=147 yd
you must have a common denominator when ? fractions
Step-by-step explanation:
ADD::If the denominators are not the same, you must find the common denominator by finding the least common multiple of the 2.
SUBTRACT::If the denominators are not the same, you must find the common denominator by finding the least common multiple of the 2.
Alex has to fill his 10 gallon fish tank with water. He only has a 1 pint bucket. How many times will he have to fill his bucket to fill the tank?????W
Answer:
80
Step-by-step explanation:
8 pints in a gallon so then you multiply 8 x 10 and get 80
Answer:
80
Step-by-step explanation:
1 gallon = 8 pints8 × 10 = 80I hope this helps!
I will give brainliest! 2(6x+3)
Answer: 12x+6
Step-by-step explanation:
distributive property
Answer:
=12x + 6
Step-by-step explanation:
−2(−1 1/4) Multiply. Write your answer as a fraction in simplest form.
Answer:
I want to say 2.5
Step-by-step explanation:
Solve the system by elimination:
-2x + 2y + 3z = 0
-2x - y + z = -3
2x+ 3y + 3z = 5
Please help me solve What is m
Answer:
a=60
b=85
c=35
Step-by-step explanation:
a is shown to be 60 in the text along with c being 85 with its angle so just add 60 and 85 to get 145 and fill in the remaining to get 180 which gives you c as 35
PLEASE HELP
Select the correct answer from each drop-down menu. Options are (equal to, not equal to)
Answer:
Not equal to.
Step-by-step explanation:
Real Numbers Quiz Active 1 2 3 4 Which answer describes the type of numbers that are dense? whole numbers and integers O whole numbers but not integers rational numbers and irrational numbers rational numbers but not irrational numbers
Answer:
C. rational numbers and irrational numbers
Step-by-step explanation:
Rational numbers are those numbers that can be used to express the ratio of two whole numbers. An example is the figure 2. It can be expressed as a fraction of another number like when we write 2/8. Both figures are rational. Irrational numbers cannot be used to express the ratio of two whole numbers or integers. An example is a digit like 0.666666... Rational and irrational numbers are real numbers because real numbers encompass all the types of numbers we can think of, positive, negative, decimals, whole, etc.
The density of numbers is seen in the fact that there is no vacuum created between real numbers when plotted on the number line.
Ronald has a 10% solution of the fertilizer Super Grow. How much pure Super Grow should he add to the mixture to get 36 oz of a 12.5% concentration?
Answer:
1 oz
Step-by-step explanation:
Given that:
% solution of super grow fertilizer = 10%
To obtain mixture of 36oz of a 12.5% concentration
Let oz of pure supergrowth to be added = s
(Initial % * (36 - s) + s) / 36 = target concentration
(10% * (36 - s) + s) / 36 = 12.5%
(0.1(36 - s) + s) / 36 = 0.125
Cross multiply:
0.1(36 - s) + s =. 0.125 * 36
3.6 - 0.1s + s = 4.5
3.6 + 0.9s = 4.5
0.9s = 4.5 - 3.6
0.9s = 0.9
s =. 0.9/0.9
s = 1
Hence, 1 oz of pure supergrowth should be added to the 10% solution to get 36 oz of a 12.5% concentration.
A short quiz has two true-false questions and one multiple-choice question with four possible answers. A student guesses at each question. Assuming the choices are all equally likely and the questions are independent of each other, the following is the probability distribution of the number of answers guessed correctly. What is the Probability of two or more questions right? X 0 1 2 3 P(X) .1875 .4375 .3125 .0625
Answer:
[tex]P(X\geq 2) = 0.375[/tex]
Step-by-step explanation:
Given
X ------0 --------1 -------- 2--------- 3
P(X) --.1875 -.4375 ---.3125 --- .0625
Required
Determine [tex]P(X\geq 2)[/tex]
This is calculated as:
[tex]P(X\geq 2) = P(X = 2) + P(X = 3)[/tex]
[tex]P(X\geq 2) = 0.3125 + 0.0625[/tex]
[tex]P(X\geq 2) = 0.375[/tex]
what is another name for <2
Answer:
two, like: both, pair, couple, same, twain, bifurcate, bigeminal, binal, twin, dual and double.
Step-by-step explanation:
On a lunch counter, there are 3 oranges, 5 apples, and 2 bananas. If 3 pieces of fruit are selected, find the probability that 1 orange, 1 apple, and 1 banana are selected (does not have to be in that order).
Answer:
[tex]Probability = \frac{1}{24}[/tex]
Step-by-step explanation:
Given
[tex]Oranges = 3[/tex]
[tex]Apples = 5[/tex]
[tex]Banana = 2[/tex]
[tex]Total = 10[/tex]
Required
Determine the probability of 1 orange, 1 apple and 1 banana
Since, order is not important:
[tex]Probability = P(Orange) * P(Apple) * P(Banana)[/tex]
[tex]Probability = \frac{3}{10} * \frac{5}{9} * \frac{2}{8}[/tex]
The difference in the numerator is as a result of picking the fruit without replacement
[tex]Probability = \frac{30}{720}[/tex]
[tex]Probability = \frac{1}{24}[/tex]
Probability is simply how likely something is to happen.
The probability of 1 orange, 1 apple, and 1 banana are [tex]\frac{1}{24}[/tex]
On lunch counter,
Number of oranges = 3
Number of apples = 5
Number of bananas = 2
If 3 piece of fruit is selected then, probability of 1 orange, 1 apple and 1 banana
[tex]=\frac{3}{10}*\frac{5}{9} *\frac{2}{8} \\\\=\frac{30}{720}\\\\=\frac{1}{24}[/tex]
Therefore, the probability of selecting 1 orange, 1 apple, and 1 banana are [tex]\frac{1}{24}[/tex]
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the answer to the universe, life, and everything
Answer:
my life hurts now
Step-by-step explanation:
Answer:
42
Step-by-step explanation:
GET A BOOK U MORON
4x+7 (3x-3)<-9
Please show steps
Answer: 3x-3 needs to be done first, and then 4x+7, and then multiply and whatever you get will be your answer
Step-by-step explanation: