Answer:
a. 74.86%
b. 50%
c. 50%
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Normally distributed with a mean of 49 pounds, and a standard deviation of 6 pounds.
This means that [tex]\mu = 49, \sigma = 6[/tex]
a. Find the percentage of dogs of this breed that weigh less than 53 pounds.
The proportion is the p-value of Z when X = 53. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{53 - 49}{6}[/tex]
[tex]Z = 0.67[/tex]
[tex]Z = 0.67[/tex] has a p-value of 0.7486.
0.7486*100% = 74.86%, which is percentage of dogs of this breed that weigh less than 53 pounds.
b. Find the percentage of dogs of this breed that weigh less than 49 pounds.
p-value of Z when X = 49, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{49 - 49}{6}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a p-value of 0.5
0.5 = 50% of dogs of this breed that weigh less than 49 pounds.
c. Find the percentage of dogs of this breed that weigh more than 49 pounds.
1 subtracted by the p-value of Z when X = 49, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{49 - 49}{6}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a p-value of 0.5.
1 - 0.5 = 0.5 = 50% of dogs of this breed that weigh more than 49 pounds.
Expand, and simplify the following expressions a. (2x+y)(x+y) + (2x-y)(x+y)
Step-by-step explanation:
2x²+2xy+yx+y²+2x²+2xy-yx+y²
2x²+2x²+2xy+2xy+yx-yx+y²+y²
2x²+2x²+2xy+2xy
4x²+4xy
Your Answer is in the above image.
Hope this solution may help you
express the standard form53630000
Answer:
5.363×10^8pls mark me as brainliestAnswer:
5.363×10^8
Step-by-step explanation:
Consider the graph below: Point T(-2; 3) is a point on the Cartesian Plane such that B is the angle of inclination of OT. T(-2;3) у х 2.1 Calculate the following without the use of a calculator: a) tanſ b) 13 sin B.cosB (2)
Answer:
(a) - 3/2
(b) - 78/25
Step-by-step explanation:
According to the trigonometry, the tangent of any angle is the ratio of rise to the run of the right angle triangle .
The sine of an angle is the ratio of rise to the hypotenuse of the right angle triangle.
The cosine of an angle is the ratio of run to the hypotenuse of the right angle triangle.
(a)
[tex]tan\beta = \frac{3}{-2} = \frac{-3}{2}[/tex]
(b)
[tex]13 sin\beta cos \beta = 13\times \frac{3}{\sqrt{3^2+2^2}}\times\frac{-2}{\sqrt{3^2+2^2}}\\\\13 sin\beta cos\beta = \frac{- 78}{25}[/tex]
If paper was £1.99 a pack and is now £3.98 a pack, what is the percentage increase in the price of the product?
Answer:
100%
Step-by-step explanation:
The initial price of the paper = 1.99
The final price of the pack of paper = 3.98
We need to find the percentage increase in the price of the product. It can be solved as follows :
[tex]\%=\dfrac{3.98-1.99}{1.99}\times 100\\\\=100\%[/tex]
So, the percentage increase in the price of the product is 100%.
A and B are independent events. Use the following probabilities to answer the question. Round to 4 decimal places.
P(A) = 0.32, P(A and B) = 0.09, find P(B)
P(B) =
Answer:
.2813
Step-by-step explanation:
If two events are independent that means that
A*B= A and B
so
let p(b)= x
.09=.32*x
x= .28125
Round this to
.2813
Step-by-step explanation:
since p(a) and p(b) are independent events
p(a).p(b)= p(a and b)
0.32×p(b)=0.09
p(b)=0.09÷0.32
p(b)=0.28
How do I factor this equation fully?
work out the value of 6.8x10^2 x 1.3x10^-3
Answer:
0.884
Step-by-step explanation:
just use a calculator
9x5
pls help meeeeeeeeee
Answer:
45
hope this helps
Answer:
45
Step-by-step explanation:
9x5=45
Solve the inequality: 13 + 2 v − 8 + 6 > − 7 − v
Answer:
V< 6
Step-by-step explanation:
11+2v > -7-v
3v> -18
v<6
Bryan is sitting on a bench in the mall. He noticed that 18 out of the last 60 men who walked by had a beard . Considering this data how many of the next 90 men who walk by should Bryan expect to have a beard?
Answer:
27
Step-by-step explanation:
every 30 men = 9 men with beards
you have 30 3 times in 90 so you get 27
60÷2=30
18÷2=9
30 men normal = 9 men with beards
90÷30=3
3×9=27
Which expression is equivalent to 4p^-4 10q -3? Assume
Step-by-step explanation:
Derive an expression for the equivalent width in a saturated line. Assume a Voigt profile, with the difference in optical depth between the center of the line and the wings being ~104. The wings of the line can be ignored. Define a frequency x1 = (v1 − v0)/ΔvD, where the optical depth τv = 1. Inside of x1 the line is fully saturated, and outside x1 the line is optically thin. Show that the equivalent width is

Note that the equivalent width is practically insensitive to the number density of absorbing material.
What is the exponential regression equation that fits these data? x у 1 4 2 9 3 27 4 90 5 250 6 580 O A. y = 39.16x2 - 169.38x+ 158.9 O B. y = 1.31(2.804) O C. y = 2.80(1.31") O D. y = 104.74x - 206.6
Answer:
1.31(2.80)^x
Step-by-step explanation:
Given the data :
x : 1 2 3 4 5 6
y : 4 9 27 90 250 580
Using technology, the exponential regression data obtained by fitting the data is :
y = 1.31(2.80)^x
Where, y = predicted value
1.31 = Initial value
2.80 = growth fractor
x = period
Answer:
1.31(2.80)^x
trust me i just did the cst
Step-by-step explanation:
Find the area for me pls
this figure can be divided into three parts one is rectangle other one is semicircle and the third one is one fourth of the circle .so let's find the area of each figure one by one. For the rectangle 12×8 =96
for semicircle that is on the top it has the radius 6 which is a half of 12
so area of the semicircle is
[tex] \frac{1}{2} \pi \: r {}^{2} \\ \frac{1}{2} \times 3.14 \times 6 {}^{2} \\ 3.14 \times 18 \\ 56.52[/tex]
no that's fine. 80 of the 1/4 of the other Circle
[tex] \frac{1}{4} \pi {}^{2} \\ \frac{1}{4} 3.14 \times 8 {}^{2} \\ 3.14 \times 16 \\ 50.24[/tex]
add all these areas
96+56.52+50.24 =202.76
Which angles are supplementary to 24? Select all that apply.
Answer:
<2, <3, <6, <7
Step-by-step explanation:
Supplementary to <4 means that, <4 and that angle equals 180. So we will move angle by angle.
<1 = Is not supplementary because both are virtually opposite angle and virtually opposite angles are equal.
<2 = Is supplementary angle because it is a vertical linear pair with <4.
<3 = Is supplementary angle because it is horizontal linear pair with <4
<5 = Is not supplementary angle because they are alternate interior angles and alternate angles are equal.
<6 = Is supplementary because angles on the same side and same interior/exterior are supplementary. (By interior/exterior, I meant that they have to be either interior or exterior. No both)You can also use the reason that 6 and 2 are corresponding angles, and corresponding angles are equal. So, if 2 is supplementary to 4, then 6 is also supplementary to 4. I think the latter is better than the first.
<7 = Is supplementary because it is vertically opposite to 6 and 6 is supplementary, so 7 is also supplementary.
<8 = Not supplementary. Because 4 and 8 are corresponding angles and corresponding angles are not equal. And also 8 is equal to 5. And 5 is not supplementary to 4. That means 8 is also not.
Ugh... I really hope u understand, and don't think that I am blabbering.
Thank You
Please mark me as the brainliest
If l=10, b=5, h=2, find the values of 2h(l+b)
Answer:
60
Step-by-step explanation:
given:
l = 10
b = 5
h = 2
to find:
2h(l + b)
substitute the given values of l , b and h
=2*2(10 + 5)
=4*15
=60
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{2h(l + b)}[/tex]
[tex]\large\text{If l = 10, b = 5, and h = 2, then substitute it into the equation!}[/tex]
[tex]\large\textsf{= 2(2)((10)+ 5)}[/tex]
[tex]\large\textsf{2(2) = \boxed{\bf 4}}[/tex]
[tex]\large\textsf{= 4(10 + 5)}[/tex]
[tex]\large\textsf{10 + 5 = \boxed{\bf 15}}[/tex]
[tex]\large\textsf{4(15)}[/tex]
[tex]\large\textsf{= \boxed{\bf 60}}[/tex]
[tex]\boxed{\boxed{\huge\text{Answer: \textst \bf 60}}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
The amount of increase from the cost to the selling price is called the?
Answer:
profit
hope it is helpful to you
Step-by-step explanation:
Markup is the percentage amount by which the cost of a product is increased to arrive at the selling price.
there is 300ml of oil in the small bottle there is six times as much in the big bottle how much oil is in the big bottle?
Answer:
1800 ml of oil
Step-by-step explanation:
300*6
Differentiate the function, y = (2x - 5)^2 (5-x^5)^2?
Answer:
[tex]\displaystyle y' = 2(2x - 5)(x^5 - 5)(12x^5 - 25x^4 - 10)[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Terms/CoefficientsFactoringCalculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
y = (2x - 5)²(5 - x⁵)²
Step 2: Differentiate
Derivative Rule [Product Rule]: [tex]\displaystyle y' = \frac{d}{dx}[(2x - 5)^2](5 - x^5)^2 + (2x - 5)^2\frac{d}{dx}[(5 - x^5)^2][/tex]Chain Rule [Basic Power Rule]: [tex]\displaystyle y' = [2(2x - 5)^{2-1} \cdot \frac{d}{dx}[2x]](5 - x^5)^2 + (2x - 5)^2[2(5 - x^5)^{2-1} \cdot \frac{d}{dx}[-x^5]][/tex]Simplify: [tex]\displaystyle y' = [2(2x - 5) \cdot \frac{d}{dx}[2x]](5 - x^5)^2 + (2x - 5)^2[2(5 - x^5) \cdot \frac{d}{dx}[-x^5]][/tex]Basic Power Rule: [tex]\displaystyle y' = [2(2x - 5) \cdot 1(2x^{1 - 1})](5 - x^5)^2 + (2x - 5)^2[2(5 - x^5) \cdot -5x^{5 - 1}][/tex]Simplify: [tex]\displaystyle y' = [2(2x - 5) \cdot 2](5 - x^5)^2 + (2x - 5)^2[2(5 - x^5) \cdot -5x^4][/tex]Multiply: [tex]\displaystyle y' = 4(2x - 5)(5 - x^5)^2 - 10x^4(2x - 5)^2(5 - x^5)[/tex]Factor: [tex]\displaystyle y' = 2(2x - 5)(5 - x^5)[2(5 - x^5) - 5x^4(2x - 5)][/tex][Distributive Property] Distribute 2: [tex]\displaystyle y' = 2(2x - 5)(5 - x^5)[10 - 2x^5 - 5x^4(2x - 5)][/tex][Distributive Property] Distribute 5x⁴: [tex]\displaystyle y' = 2(2x - 5)(5 - x^5)[10 - 2x^5 - 10x^5 + 25x^4][/tex][Addition] Combine like terms (x⁵): [tex]\displaystyle y' = 2(2x - 5)(5 - x^5)(10 - 12x^5 + 25x^4)[/tex]Rewrite: [tex]\displaystyle y' = 2(2x - 5)(x^5 - 5)(12x^5 - 25x^4 - 10)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
Area of a trapezoid
Find the area of this trapezoid. Be sure to include the correct unit in your answer.
6 cm
0
10 cm
8 cm
12 cm
Answer:
h
Step-by-step explanation:
h
Kay leaves a $6 dollar tip for a $60 dollar bill what percentage is the tip
Answer: uhh 10%??
Step-by-step explanation:
I'm not rlly good at percentage-
Is it true or false that for all sets A, B, and C, A U (B - C) = (A U B) - C?
Answer:yes
Step-by-step explanation:66
The given statement A U (B - C) = (A U B) - C is true.
What is a set ?A set is collection of well defined objects.
According to the given question we have to state whether A ∪ ( B - C ) = ( A ∪ B ) - C.
Lets consider we have three sets A, B and C and we also consider they intersect each other.
( B - C ) represents the elements which belongs to B but not in C.
∴ A ∪ ( B - C ) represents the no. of elements which belongs to the set B but not in C union the no. of elements which belongs to A.
AND
( A ∪ B ) - C represents no. of elements which belongs to A or B but not in C.
learn more about sets here :
https://brainly.com/question/8053622
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The relationship between the amounts of blue
and red paint needed to make a certain shade
of purple is shown in the following graph.
10+
9+
8+
7
6
Liters of red paint
5+
4+
3+
2
1
→
3
1
2
Liters of blue paint
Which statements about the graph are true?
Choose all answers that apply:
Answer:
B
Step-by-step explanation:
Had it on Khan Academy.
True statement for the given graph is the point [tex](3,9)[/tex] shows that [tex]9[/tex] liters of red paint are needed for every [tex]3[/tex] liters of blue paint.
What is graph?
" Graph is defined as diametrical representation of the relation between the variables on the coordinate plane along x-axis and y -axis."
According to the question,
As given in the graph,
Graph represents the linear relation between red paint and blue paint.
'x -axis' on the graph represents the blue paint
'y- axis' on the graph represents red paint
A. The point [tex](0,0)[/tex] shows that any amount of red and the blue paint will make same shade of purple.
From the graph coordinates [tex](1,3)[/tex] and [tex](2, 6)[/tex]represents that proportion of blue : red to make required purple shade is [tex]1: 3[/tex].
Hence, Option A is not a correct answer.
B. The point [tex](3,9)[/tex] shows that [tex]9[/tex] liters of red paint are needed for every [tex]3[/tex] liters of blue paint.
Coordinate [tex]( 3,9)[/tex] on the graph represents the ratio of blue : red [tex]= 3 : 9[/tex] which is equals to [tex]1:3[/tex] .
Hence, Option(B) is the correct answer.
Learn more about graph here
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John buys 20 bunches of bananas for 5naira. He sells them for 6.50. what is his percentage profit?
What is the equation, in point-slope form, of the line that
is perpendicular to the given line and passes through the
point (-4,-3)?
Answer:
Step-by-step explanation:
We first need to find the slope of the line that is graphed. We can wither use the slope formula or you can use the slope triangle. From the upper point on the line (-1, 1) count down til you're on the same horizontal as the lower point on the line (0, -3). You have to count down 4 (which is -4) and over to the right 1 (which is +1). So -4/+1 = -4 and the slope is -4. That means that the perpendicular slope, the opposite reciprocal of that, is 1/4. Using that slope and the point (-4, -3), the point-slope form of the line is
[tex]y-(-3)=\frac{1}{4}(x-(-4))[/tex] which we can simplify a bit to
[tex]y+3=\frac{1}{4}(x+4)[/tex]. That's the line in point-slope form.
the sum of two consecutive numbers is 2x+3. What are the numbers
Answer: 2 and 3
Step-by-step explanation:
its numbers
Type the correct answer in the box. Use numerals instead of words. Tony bought a new car at a cost of $20,000. The value of the car decreases by approximately 12% each year. Formulate the equation that gives the value, A(+), of the car xyears since Tony bought the car. A(t)-
9514 1404 393
Answer:
A(x) = 20000(0.88)^x
Step-by-step explanation:
The general form of these exponential equations is ...
A(x) = a·b^x
where 'a' is the initial value, and b is the annual growth factor. x is the elapsed time in years.
The growth factor is ...
growth factor = 1 + growth rate
Here, the growth rate per year is -12%, so the growth factor is ...
b = 1 -12% = 88% = 0.88
Of course, the initial value is a=20,000, so the equation is ...
A(x) = 20000(0.88)^x
Here is a table of values for y = f(x).
Х
-2 -1 0 1 2 3
4.
5
6
f(x) 5
6 7 8 9 10 11 12 13
Mark the statements that are true.
Step-by-step explanation:
the true answers are:
A. f(-1)=6
D. the domain for f(x) is the set
{-2,-1,0,1,2,3,4,5,6}
The function f(x) = –x2 – 4x + 5 is shown on the graph. On a coordinate plane, a parabola opens down. It goes through (negative 5, 0), has a vertex at (negative 2, 9), and goes through (1, 0). Which statement about the function is true? The domain of the function is all real numbers less than or equal to −2. The domain of the function is all real numbers less than or equal to 9. The range of the function is all real numbers less than or equal to −2. The range of the function is all real numbers less than or equal to 9.
Answer:
D
Step-by-step explanation:
We have the quadratic function:
[tex]f(x)=-x^2-4x+5[/tex]
First, the domain of all quadratics is always all real numbers unless otherwise specified. You can let x be any number and the function will be defined.
So, we can eliminate choices A and B.
Note that since the leading coefficient is negative, the parabola will be curved downwards. Therefore, it will have a maximum value. This maximum value is determined by its vertex, which is (-2, 9).
Since it is curving downwards, the maximum value of the parabola is y = 9. It will never exceed this value. Therefore, the range or the set of y-value possible is always equal to or less than 9.
So, the range of the function is all real numbers less than or equal to 9.
Our answer is D.
It is not C because the maximum value is dependent on y and not x.
Given f(x) = x2 + 24 - 12, find f(3)
Answer:
f(3) = 12
Step-by-step explanation:
f(3) = (3 x 2) + 24 - 12
= 6 + 24 - 12
f(3) = 12
If this helps you, please give brainliest!
Answer:
Step-by-step explanation:
f(x) = [tex]x^{2}[/tex] + 24 - 12
substitute 3 inplace of x
f(3) = [tex]3^{2}[/tex] + 24 - 12
=9 + 24 - 12
21
If the question is f(x) = x2 + 24 - 12 {x*2 + 24 - 12}
now substitute 3 in place of x
f(3) = 3*2 + 24 - 12
=6 + 24 - 12
18
in which quadrant or axis will the poit lie if...
Step-by-step explanation:
a.fourth quadrent
b.third quadrent.
