Explanation
Given
[tex]a^x=y[/tex]Therefore;
Answer:
[tex]x=\log_ay[/tex]/ Week 1 / Week 1 Monday - Daily Quiz
A rectangle is 5 feet long and 12 feet wide.
What is it's area?
60 feet² is the area of rectangle.
What is rectangle?
A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. As a result, it is sometimes referred to as an equiangular quadrilateral. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.The four sides of a laptop are equal in length and have opposite sides that are parallel to one another.length = 5 feet
wide = 12 feet
area of rectangle = length × width
= 5 × 12
= 60 feet²
Learn more about rectangle
brainly.com/question/15019502
#SPJ10
7.) Use the information to prove:
Given: The Diagram
Prove: EC AD
With the given information, we have proved that EC ≅ AD as corresponding sided of congruent triangles are congruent too.
What is congruent triangles?Both triangles are said to be congruent if the three angles and three sides of one triangle equal the corresponding angles and sides of the other triangle. We can see in the examples PQR and XYZ that PQ = XY, PR = XZ, and QR = YZ, and that P = X, Q = Y, and R = Z. Then, we can state that XYZ and PQR are related.
We have given that that ∠ADB = ∠ECB
And ∠ABC = ∠EBC as they are vertically opposite angles
And given that AB = EB
Thus, Triangle ABC ≅ Triangle EBC
And as ABC ≅ EBC
EC ≅ AD as corresponding sided of congruent triangles are congruent too.
Learn more about congruent triangles
https://brainly.com/question/11329400
#SPJ13
A motorcyclist starts his trip at noon and drives 10 miles in the first hour, and then in
each hour after that, he drives 6 more miles than in the previous hour.
After how many hours of driving will the motorcyclist drive a total of 248 miles?
After 248 miles, the motorcycle rider would have put in 40.6 hours of driving.
By using the arithmetic progression formula, we may find the answer to this problem.
The definition of arithmetic progressionA series of numbers in order known as an arithmetic progression has a constant value as the difference between any two consecutive numbers.
According to what we've been told, the first hour is separated by an arithmetic difference of six miles, or 10 miles. He covered a distance of 248 miles, according to the information we have. It follows that
An = a + (n-1)d, where
An = 248
a = 10
n = ?
d = 6
applying the formula, we have
248 = 10 + (n - 1)6
248 = 10 + 6n - 6
248 = 6n + 4
6n = 248 - 4
6n = 244
n = 244/6
n = 40.6 hours
To know more about arithmetic progression, visit:
https://brainly.com/question/25311950
#SPJ13
The amount of time a certain brand of light bulb lasts is normally distributed with a
mean of 1300 hours and a standard deviation of 65 hours. What is the probability
that a randomly chosen light bulb will last between 1390 hours and 1460 hours, to the
nearest thousandth?
The probability that a randomly chosen light bulb will last between 1390 hours and 1460 hours is 3.1% to the nearest thousandth.
What is Normal Probability Distribution?In a normal distribution with mean and standard deviation, the z-score of a measure X is given by:
[tex]z = x - \mu/ \sigma[/tex]
The Z-score measures how many standard deviations the measure is from the mean.
In a set with mean and standard deviation , the z-score of a measure X is;
Mean of 1300 hours and a standard deviation of 65 hours.
This is the p-value of Z when X = 1460. So
[tex]z = x - \mu/ \sigma[/tex]
z = 1460 - 1300 /65
z = 1.87
Then has a p-value of 0.031.
0.031 = 3.1% is the probability that a randomly chosen light bulb will last between 1390 hours and 1460 hours, to the nearest thousandth.
Learn more about probability here:
brainly.com/question/1210781
#SPJ1
In a rectangle the base measures (x + 7), height (x + 2), area = 36 cm
Calculate perimeter, height and base.
The values are given as;
Perimeter = 26cm
Height = 4cm
Base = 9cm
How to determine the valueThe formula for determining the area of a rectangle is expressed as;
Area = lw
Where;
l is the length of the rectanglew is the width of the rectangleNow, substitute the values into the formula, we have;
36 = (x +7)(x + 2)
Now, expand the bracket
36 = x^2 + 2x + 7x + 14
collect like terms
36 = x^2 + 9x + 14
Make into quadratic equation
x^2 + 9x + 14 -36 = 0
x^2 + 9x - 22 = 0
Factorize the equation
x^2 + 11x - 2x - 22 = 0
Factorize further
x(x + 11) - 2( x + 11) = 0
Then, x - 2 = 0, x = 2
or x + 11 = 0
x = -11
Height = x + 2 = 4cm
Base = x + 7 = 9cm
The formula for perimeter is expressed as;
Perimeter = 2( l +w )
Perimeter = 2( 4 + 9)
Perimeter = 2(13)
Perimeter = 26 cm
Hence, the values are 26cm, 4cm and 9cm respectively.
Learn more about rectangles here:
https://brainly.com/question/25292087
#SPJ1
Look at the following equation:
12,400 × [] = 1,240
What number should go in the box to make the equation true? (1 point)
1/10
1/100
10
100
The diameter D of a sphere is 13.6 mm calculate thr sphere volume Vuse the value 3.14 for pie, and around to the nearest 10th
Step 1
State the volume of a sphere
[tex]\begin{gathered} v=\frac{4}{3}\pi r^3 \\ \pi=3.14 \\ \frac{Diameter}{2}=\text{radius}=\frac{13.6}{2}=6.8\operatorname{mm} \end{gathered}[/tex]Step 2
Find the volume of the sphere by substitution of values.
[tex]\begin{gathered} v=\frac{4}{3}\times3.14\times(6.8)^3 \\ v=\frac{4}{3}\times3.14\times314.432 \\ v=1316.421973\operatorname{mm} \\ v\approx1316.4\operatorname{mm}^3\text{ to the nearest tenth} \end{gathered}[/tex]Hence, the volume of the sphere= 1316.4mm³ to the nearest tenth
1. Provide a summary of the story “The Stone” Summarize the events in the exposition, rising action, climax, falling action, and resolution. Your written response should include 5 complete sentences.
Answer:
pls hurry
According to the plot synopsis for the novel "The Stone," a young homosexual guy experiences Taipei's nightlife, complete with all of its thrills and heartbreaks, perils, and hopes.
The Story of the Stone, sometimes referred to as "The Dream of the Red Chamber," was one of the finest books in Chinese literature when it was published about 1760. Gao E painstakingly edited and finished Cao Xueqin's majestic saga's fifth chapter, "The Dreamer Awakens," decades later.
The Story of the Stone has several references to or hints at the issue of the difference between what is true and what is untrue. The first volume in a five-volume series on the illustrious Chinese Jia family is titled "The Story of the Stone."
The major storyline chronicles the development of the love triangle between the three main characters—cousins Bao-yu, Dai-yu, and Bao-chai—as they grow up.
To know more about The Stone here
https://brainly.com/question/19580622
#SPJ1
use the image to find angles Q & U. explain your reasoning.
Solution
Given
[tex]\begin{gathered} m<3=45^0 \\ m<1=50^0 \\ m<6=135^0 \end{gathered}[/tex][tex]\begin{gathered} m<6\text{ = m<1 + m<2 + m<3 \lparen corresponding angles are equal\rparen} \\ 135=50+m<2+45 \\ 135=95+m<2 \\ m<2=135-95 \\ m<2=40^0 \end{gathered}[/tex][tex]\begin{gathered} mA candy stand sells lollipops, gumballs, and chocolates. The gumballs cost 5 cents more than the chocolates. The lollipops cost twice as much as the chocolates. A particular handful containing 3 gumballs, 2 lollipops, and 7 chocolates costs $2.11. What is the cost of each item?
The cost of lollipops, gumballs, chocolate is $ 0.268, $0.184, $0.134
What is an equation?
An equation is a formula that describes the equality between two expressions, by connecting them with the equals sign '='.
Let the cost of lollipops be x
The cost of gumballs be y
and cost of chocolates be z
We are given that the gumballs cost 5 cents more than the chocolates
mathematically this can be written as
[tex]y=z+0.05[/tex]
Similarly,
The lollipops cost twice as much as the chocolates
mathematically this can be written as,
[tex]x=2z[/tex]
Now finally we purchase 3 gumballs, 2 lollipops and 7 chocolates
The equation can be given as,
[tex]3x+2y+7z=2.11[/tex]
Substituting the values of x and y in this equation we get,
[tex]6z+2(z+0.05)+7z=2.11\\6z+2z+0.1+7z=2.11\\15z=2.01\\z=0.134[/tex]
The cost of chocolates is $0.134
The cost of gumballs is $0.184
And the cost of lollipops is $0.268
Hence, The cost of lollipops, gumballs, chocolate is $ 0.268, $0.184, $0.134
To learn more about equation please refer
https://brainly.com/question/22688504
#SPJ9
6.5 in. 5 in 7.5 in. What is the total surface area of this prism in square inches?
6.5 in. 5 in 7.5 in. What is the total surface area of this prism in square inches?
we have that
the total surface area of a prism is equal to
SA=2B+Ph
where
B is the area of the base
P is the perimeter of the base
h is the height of the prism
Let
L=6.5 in
W=5 in
H=7.5 in
so
B=L*W=(6.5*5)=32.5 in2
P=2(L+W)=2(6.5+5)=23 in
H=7.5 in
therefore
SA=2(32.5)+23(7.5)
SA=237.5 in2
surface area is 237.5 square inchessee the attached figure to better understand the problem
the surface area is the area of its six rectangular faces
so
SA=2(6.5)8(5)+2((5)(7.5)+2(6.5)*(7.5)=237.5 in2
A car left the warehouse at 3:00 P.M. The car traveled 62 miles by 4:00 P.M. The car continued traveling at the same average speed. How many miles, altogether, did the car travel by 9:45 P.M.? Round the final answer to the nearest whole number.
From 3 PM to 4 PM = 1 hour
Speed rate = distance / time
Distance = 62 miles
Replacing:
Speed = 62 / 1 = 62 miles per hour
By 9:45 PM
9:45 - 3 PM = 6 hours .45 minutes = 6.75 hours
Distance = Speed x time = 62 x 6.75 = 418.5 miles
Use the figure to the right to name each of the following.1. A line2. A plane
ANSWER and EXPLANATION
We want to name a line and a plane.
LINE
In naming a line, we use two lettters. The two letters are the letters at the beginning and the end of the line.
Now, from the diagram, we have the following lines:
- nY
- Xm
- Zl
PLANE
A plane is made up of two lines intersecting one another.
In naming a plane, three letters are used, with the letter at the intersection in the middle.
The planes in the diagram are:
- mYn plane
- lRm plane
Choose the expression that is equivalent to the one shown
1. Rewrite the expression to get the numerator and denominator with the same base:
[tex]\frac{(2^3)^{12}}{(2^2)^3}=\frac{2^{36}}{2^6}[/tex]2. Divide by leavinfg the same base and subtracting the exponents:
[tex]\frac{2^{36}}{2^6}=2^{36-6}=2^{30}[/tex]Write the result with base 4:
[tex]2^{30}=(2^2)^{30/2}=4^{15}[/tex]As you can see above any of the given expression is equivalent to the given expression.Answer: none of these-10+*+5> 7-5
3
3. Here is an inequality:
What value of x will make the two sides equal?
35 225
4
Fraction, A number that is stated mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
What is denominator?A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters. The denominator is simply the bottom number.
-10+*+5>7-5 justification
-10+*+5> 7-5
Step 1:
Multiply
-10 * 5 = -50.
Step 2:
Subtract:
7 - 5 = 2
the result of step No. 1 > the result of step No. 2
= -50 > 2 = No
The result:
-10 * 5> 7 - 5 = No
To Learn more About Fraction, Refer:
https://brainly.com/question/78672
#SPJ13
A cellphone company offers two talk and text plans. The company charges a monthly service fee of $20 for either plan the customer chooses: Customers that choose Talk and Text Plan A are charged five cents a minute and twenty dollars for 250 texts. Customers that choose Talk and Text Plan B are charged ten cents a minute (first 100 minutes free) and fifteen dollars for 200 texts. The equation c = .10(m – 100) + 15 + 20 can be used to represent how much a customer would spend monthly for the minutes used. ** Express Plan A as an equation where c equals the cost and m equals the minutes used. a. Graph each Talk and Text plan to determine when both plans cost the same.
For question a), we have to write the equation of the cost (c) as a function of the minutes (m), so:
[tex]c_A=0.05\cdot m+20+20[/tex]In the equation above the term 0.05*m represent the 5 cents for minute then we have to sum the $20 for 250 texts and $20 of service fee.
Before we draw the lines, we can solve the question c). If a customer wants to spend $75 monthly we can recommen him the plan wich more minutes for that cost, so we need to calculate the minutes for each plan:
[tex]\begin{gathered} \text{For Plan A:} \\ c_A=75=0.05\cdot m+20+20 \\ 0.05\cdot m=75-20-20=35 \\ m=\frac{35}{0.05}=700 \\ \text{For Plan B:} \\ c_B=75=0.1\cdot(m-100)+15+20 \\ 0.1\cdot(m-100)=75-15-20=40 \\ m-100=\frac{40}{0.1}=400 \\ m=400+100=500 \end{gathered}[/tex]The customer should choose the Plan A, because it has more minutes and more texts for $75.
For point b), we can evaluate each equation in two differents m-values and found the pairs (m, c) to graph the lines, so:
[tex]\begin{gathered} \text{For Plan A, we can choose m=100 and m=500}\colon \\ m=100\Rightarrow c_{}=0.05\cdot100+20+20=45 \\ m=500\Rightarrow c=0.05\cdot500+20+20=65 \\ P_{1A}=(100,45),P_{2A}=(500,65) \end{gathered}[/tex][tex]\begin{gathered} \text{For Plan B, we can choose m=100 and m=500:} \\ m=100\Rightarrow c=0.1\cdot(100-100)+15+20=35 \\ m=500\Rightarrow c=0.1\cdot(500-100)+15+20=75 \\ P_{1B}=(100,35),P_{2B}=(500,75) \end{gathered}[/tex]And the graphs are:
In the Graphs we can see the lines intercept in m=300 and evluating the equations in that value the cost is $55.
Tammy invested $2000 in a fund for 4 years and was paid simple interest. The total interest that she received on the investment was $400. As a percentage, what was the annual interest rate of her investment?
Answer:
Use this steps to find your answer
Decay (calculus problem)
Answer:
Step-by-step explanation:
If the half-life is k days, then you have
(1/2)^(300/k) = 0.696
k = 573.788
makes sense, since 69.6% is greater than 50%
Now solve for t in
(1/2)^(t/573.788) = 1/3
t = 909.432 days
makes sense -- about 1.5 half-lives
K
Find the average rate of change of the function f(x) = 6x from x₁ = 0 to x₂ = 3.
The average rate of change is
(Simplify your answer.)
Calculus
SCIENCE
Anatomy & Physiology
Astronomy
Astrophysics
Biology
Chemistry
Earth Science
Environmental Science
Organic Chemistry
Physics
MATH
Algebra
Calculus
Geometry
Prealgebra
Precalculus
Statistics
Trigonometry
HUMANITIES
English Grammar
U.S. History
World History
... AND BEYOND
Socratic Meta
Featured Answers
Topics
Search icon
Search...
How do you find the average rate of change of
f
(
x
)
=
2
x
2
+
1
on [x,x+h]?
Calculus Derivatives Average Rate of Change Over an Interval
1 Answer
Steve M
Feb 28, 2017
4
x
+
2
h
Explanation:
The average rate of change of a continuous function,
f
(
x
)
, on a closed interval
[
a
,
b
]
is given by
f
(
b
)
−
f
(
a
)
b
−
a
So the average rate of change of the function
f
(
x
)
=
2
x
2
+
1
on
[
x
,
x
+
h
]
is:
A
r
o
c
=
f
(
x
+
h
)
−
f
(
x
)
(
x
+
h
)
−
(
x
)
=
f
(
x
+
h
)
−
f
(
x
)
h
...
.
.
[
1
]
=
2
(
x
+
h
)
2
+
1
−
(
2
x
2
+
1
)
h
=
2
(
x
2
+
2
x
h
+
h
2
)
+
1
−
2
x
2
−
1
h
=
2
x
2
+
4
x
h
+
2
h
2
−
2
x
2
h
=
4
x
h
+
2
h
2
h
=
4
x
+
2
h
Which is the required answer.
Additional Notes:
Note that this question is steered towards deriving the derivative
f
'
(
x
)
from first principles, as the definition of the derivative is:
f
'
(
x
)
=
lim
h
→
0
f
(
x
+
h
)
−
f
(
x
)
h
This is the function we had in [1], so as we take the limit as
h
→
0
we get the derivative
f
'
(
x
)
for any
x
, This:
f
'
(
x
)
=
h
→
0
4
x
+
2
h
=
4
x
this is a example
7/8 ^2
Choose the correct expanded form for the following expression .
Evaluate 7/8^2
The correct expanded form for the following expression is 7/8 × 7/8.
What is expanded form?The division of numbers into their component ones, tens, hundreds, thousands, ten thousand, and so forth creates the expanded form of the number. The expanded version of the number is the sum of each digit times its place value, which is used to represent the number. A number is broken down to show the value of each of its digits in order to be written in expanded form. 144 would then be converted to 100 + 40 + 4 = 144. It can be used to compute sums as well. When a number is expanded to show the value of each digit, it is written in expanded form. The numerical value of each digit in the number we are writing is represented using extended form.
To know more about expanded form visit:
https://brainly.com/question/26337896
#SPJ13
(a)does the figure have reflectional symmetry? if so, give the n-fold number of the symmetry. (b)does the figure have rotational symmetry? if so, give the order and angle measure of the rotation.
(b) A figure is said to have an n-fold rotational symmetry if rotating through an angle of 360° / n does not change the figure.
In the case of the given figure, rotation through 180° does not change the figure.
Therefore,
[tex]\frac{360^o}{n}=\frac{180^o}{1}[/tex]Cross-multiplying, we have
[tex]\begin{gathered} 180^on=360^o \\ \text{ Dividing both sides by 180, we have} \\ n=\frac{360^o}{180^o}=2 \end{gathered}[/tex]Hence, the order of rotation is 2 and the angle is 180°
which measurement is closest to the volume of the container in cubic inches
The volume of a cylinder is given as;
[tex]\begin{gathered} Vol=\pi\times r^2\times h \\ r=3 \\ h=10.5 \\ \text{Vol}=3.14\times3^2\times10.5 \\ Vol=3.14\times9\times10.5 \\ \text{Vol}=296.73in^3 \end{gathered}[/tex]Therefore, from the options provided, the closest to the volume of the container is 296.88 cubic inches.
Option B is the correct answer
Find the value of X and each arc measurex =mAD=mBC = mDC =mDBC=
The value of x can be calculated as,
[tex]\begin{gathered} \text{ summation of angles = 360}^{\circ} \\ 12x+90+(2x+5)+(17x-14)=\text{ 360}^{\circ} \\ 31x+95-14=360 \\ 31x=360-81 \\ 31x=279^{\circ} \\ x=\frac{279^{\circ}}{31} \\ x=9 \end{gathered}[/tex][tex]\begin{gathered} \text{mAD }=\text{ 12x} \\ =12\times9 \\ =108^{\circ} \end{gathered}[/tex][tex]\begin{gathered} \text{mBC}=(2x+5)^{\circ} \\ =(2\times9)+5 \\ =18+5 \\ =23^{\circ} \end{gathered}[/tex][tex]\begin{gathered} \text{mDC }=(17x-14)^{\circ} \\ =(17\times9)-14 \\ =153-14 \\ =139^{\circ} \end{gathered}[/tex][tex]\begin{gathered} \text{mDBC }=\text{ }(2x+5)^{\circ}+(17x-14^{})^{\circ} \\ =23^{\circ}+139^{\circ} \\ =162^{\circ} \end{gathered}[/tex]The table shows the changes in a city's average weekly temperature.
Week Average Temperature (ºF)
1 24.4
2 24.8
5 26.1
8 27.2
15 30.1
24 33.6
The data shows
trend.
Based on the table, we can assume that the city's average weekly temperature in the 26th week will
The city's average weekly temperature in the 26th week will be between 30.1 and 33.6 degrees be more than 33.6 degrees.
What is mean by linear expression?
A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Given that;
The regression line shows slope of 0.4 and has y - intercept as 24.029.
Now,
Since, The slope is positive, we find that when week increase temperature as;
The regression equation will be;
y = 24.029 + 0.4x
For week = 26
y = 24.029 + 0.4x
y = 24.029 + 0.4 × 26
y = 24.029 + 10.4
y = 34.429
Which is greater than 33.6.
Thus, The city's average weekly temperature in the 26th week will be between 30.1 and 33.6 degrees be more than 33.6 degrees.
Learn more about the linear expression visit:
https://brainly.com/question/19961655
#SPJ1
The complete question is this;
The table shows the changes in a city's average weekly temperature. Week Average Temperature (ºF) 1 24.4 2 24.8 5 26.1 8 27.2 15 30.1 24 33.6. The data shows a positive linear a negative linear an exponential an unrecognizable trend. Based on the table, we can assume that the city's average weekly temperature in the 26th week will be between 30.1 and 33.6 degrees be more than 33.6 degrees be less than 33.6 degrees not change .
John recently joined a bowling team and each night plays three games. During his first two games he scored 112 and 134. What must John score on his last game to ensure his average for that night will be exactly 132?explain pls.
Let the score in his last game be
[tex]=x[/tex]The average of the three games is given as
[tex]=132[/tex]Step 1: The formula for average is
[tex]\text{average}=\text{ }\frac{\text{sum of the thre}e\text{ scores}}{3}[/tex]Step 2:Substituting the values of the three scores in the formula above, we will have
[tex]\begin{gathered} \text{average}=\text{ }\frac{\text{sum of the thre}e\text{ scores}}{3} \\ \text{average}=\frac{112+134+x}{3}=132 \end{gathered}[/tex]Step 3 : Cross multiply the equation below
[tex]\begin{gathered} \frac{112+134+x}{3}=\frac{132}{1} \\ \frac{246+x}{3}=\frac{132}{1} \\ 246+x=3\times132 \\ 246+x=396 \end{gathered}[/tex]Step 4: Subtract 246 from both sides
[tex]\begin{gathered} 246+x=396 \\ 246-246+x=396-246 \\ x=150 \end{gathered}[/tex]Hence,
John must score a point of 150 to ensure that his average is 132
Therefore,
Final answer = 150
The figure below is a net for a triangular prism. What is the surface area of the triangular prism, in square feet?
The figure consists of,
A rectangle with dimension 15 ft by 7 ft.
Two triangles with base b = 7 ft and height h = 5 ft.
A rectangle with dimension 15 ft by 5 ft.
A rectangle with dimension 15 ft by 8.6 ft.
Determine the surface area of triangular prism.
[tex]\begin{gathered} A=15\cdot7+2\cdot\frac{1}{2}\cdot7\cdot5+15\cdot5+8.6\cdot15 \\ =105+35+75+129 \\ =344 \end{gathered}[/tex]So, surface area of triangular prism is 344 square feet.
1.5.PS-9Question HelpError Analysis Simplify the expression - 1.8+(-1.2). On the test, when Tom simplified theexpression he got 0.6. What mistake did Tom likely make when he simplified the expression?- 1.8+(-1.2) = 1 (Type an integer or a decimal.)
Answer:
-3.0
Explanation:
First, we open the bracket and take note that:
[tex]+\times-=-[/tex][tex]\begin{gathered} -1.8+\left(-1.2\right)=-1.8-1.2 \\ =-3.0 \end{gathered}[/tex]Next, we determine Tom's mistake.
[tex]\begin{gathered} 1.8+(-1.2)=1.8-1.2 \\ =0.6 \end{gathered}[/tex]Therefore, the mistake Tom made was that he ignored/forgot the negative sign before 1.8.
whats the middle of 130 - 170
Answer:
middle number is 150
Step-by-step explanation:
the middle of 130 - 170:
170 - 130 = 40
40/2 = 20
so the middle is:
130 + 20 = 150
or can be found:
170 - 20 = 150
middle number is 150
Answer:
150
Step-by-step explanation:
Add the two extreme numbers and take the average
130 + 170 = 300
300/2 = 150
150 is 20 distant from 130 and also 20 distant from 170
Which expression is equivalent to9 30429O-49 20-13O4 301-(-3)O22COIN | ST
We must find the expression equivalent to:
[tex]\frac{-2\frac{1}{4}}{-\frac{2}{3}}.[/tex](1) The numerator is a mixed fraction, we can write it as a simple fraction:
[tex]\frac{-2\frac{1}{4}}{-\frac{2}{3}}=\frac{-2-\frac{1}{4}}{-\frac{2}{3}}=\frac{-\frac{8}{4}-\frac{1}{4}}{-\frac{2}{3}}=\frac{(-\frac{9}{4})}{(-\frac{2}{3})}.[/tex](2) Finally, we can rewrite the quotient between numerator and denominator using the symbol ÷, we get:
[tex]\frac{-2\frac{1}{4}}{-\frac{2}{3}}=\frac{(-\frac{9}{4})}{(-\frac{2}{3})}=(-\frac{9}{4})\div(-\frac{2}{3}).[/tex]Answer[tex](-\frac{9}{4})\div(-\frac{2}{3})[/tex]The volumes, in ml, of olive oil can be modeled by a normal distribution, with mean 508 mL and standard deviation 12 ml.. a. Find the probability that a randomly selected bottle has a volume less than 500 mL. Round your answer to 3 significant figures. b. The probability that a randomly selected bottle has a volume greater than v mL is 0.366. Find the value of v.
A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.
Explain the normal distribution with an example?
One straightforward example of anything that has a normal distribution pattern is height: The majority of people are normal height, although there are nearly equal numbers of people who are taller or shorter than average and a very small (but roughly comparable) number who are either extraordinarily tall or extremely short.
The four properties of a normal distribution are visible here. The mean, median, and mode are all equal in normal distributions, which are symmetric, unimodal, and asymptotically distributed.
Add the mean to the x value in step 1. Subtract the difference from the standard deviation in step two. A value of 1380 has a z-score of 1.53. Thus, 1380 is 1.53 standard deviations away from the distribution's mean.
To learn more about Normal distribution refer to:
https://brainly.com/question/27275125
#SPJ9
