Using the empirical rule, 95% of vehicles travel between 60 miles per hour and 80 miles per hour.
What is the empirical rule?Generally, Given that
Mean = 66 and Standard deviation 4To find the percent of vehicles whose speeds are between 60 miles per hour and 80 miles per hour
60 = 70-(2*5) ,
this shows that the 58 value is 2 standard deviations below the mean
and
80 = 70 +( 2*5)
This shows that the 74 value is 2 standard deviations above the mean
Using the empirical rule, we know that 95% of data fall within 2 standard deviations from the mean.
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Allison can sew three scarves in 75 minutes. How many scarves can she sew in four hours?
The number of scarves in 4 hours is 9.6
How to determine the number of scarves in 4 hoursFrom the question, we have the following parameters that can be used in our computation:
Rate = 3 scarves in 75 minutes
Time = 4 hours
The number of scarves is then calculated as
Scarves = Rate * Time
substitute the known values in the above equation, so, we have the following representation
Scarves = (3/75 minutes) * 4 hours
Evaluate the product
Scarves = 9.6
Hence, the number of scarves is 9.6
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What is 25% of R594180
Answer:
148545
Step-by-step explanation:
it's easy enough
What are the explicit equation and domain for an arithmetic sequence with a first term of 9 and a second term of 1?
Group of answer choices
an = 9 − 1(n − 1); all integers where n ≥ 1
an = 9 − 1(n − 1); all integers where n ≥ 0
an = 9 − 8(n − 1); all integers where n ≥ 0
an = 9 − 8(n − 1); all integers where n ≥ 1
The explicit equation and domain for an arithmetic sequence is a_{n}=9+(n-1)-8, the correct option is C
What is arithmetic sequence?An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.
If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:
a, a + d, a + 2d, ... , a + (n+1)d, ...
Its nth term is
T_n = a + (n-1)d
(for all positive integer values of n)
And thus, the common difference is
T_{n+1} - T_n
for all positive integer values of n
Given;
A first term of 9 and a second term of 1
a=9
D=1-9=-8
We know that the explicit equation of an AP is
a_{n}=a_{1}+(n-1)d
So, substituting the values
a_{n}=9+(n-1)-8
Therefore, the arithmetic sequence will be a_{n}=9+(n-1)-8.
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A utility line runs underground through Shayne's rectangular backyard. Shayne is not allowed to dig within 3 feet of the
utility line. The diagram below shows the dimensions of Shayne's backyard in feet. The dashed line represents the utility
line.
What is the area in square feet of the part of the backyard in which Shayne is allowed to dig?
A) 102ft2
B) 59ft2
C) 374ft2
D) 272ft2
The area in square feet of the part of the backyard in which Shayne is allowed to dig is option D: 272 ft².
What is area?
An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.
The length of the rectangle ADEH is 17 ft.
The breadth of the rectangle ADEH is 22 ft.
The length of the rectangle ABGH is 17 ft.
The breadth of the rectangle ABGH is -
GH = (EH - GE)
GH = [EH - (GF + EF)]
GH = [22 - (6 + 14)]
GH = [22 - 20]
GH = 2 ft
The formula for the area of a rectangle is -
Area = Length × Breadth
The area of part where Shayne is allowed to dig is -
Area = [Area of ABGH + Area of CDEF]
Area = [(17 × 2) + (17 × 14)]
Area = [34 + 238]
Area = 272 ft²
Therefore, the value for area is obtained as 272 ft².
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3 x 10 + 6 x1 + 1 + 8 x 1/1,000 in standred form
The expression in the standard form is 37.008
How to evaluate the expression in standard formFrom the question, we have the following parameters that can be used in our computation:
3 x 10 + 6 x1 + 1 + 8 x 1/1,000
Evaluate the products
This gives
30 + 6 + 1 + 8/1,000
Evaluate the quotients
30 + 6 + 1 + 0.008
Evaluate the sum
37.008
Hence, the number in standard form is 37.008
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Which graph is defined by f(x) = x²-x-2|?
O A.
О в.
OC.
O D.
graph A
graph B
graph C
graph D
Find the volume, V, of the solid obtained by rotating the bounded region in the first quadrant enclosed by the graphs of
y=x^2, x=y^4
To solve for the volume of the rotated region we will use the integration and its formula is V=π∫ba(r21−r22)h where r1 and r2 are the radii of the washer and h is the height. Note that the limits a and b is determined by finding the volume of the solid .
Using the washer method, the volume of the solid is
V=π∫ba[(x14)2−(x4)2]dx
Find the limits, equate the two equations in terms of x
4√x=x4
Raising both sides to fourth power,
x=x8x8−x=0
Factor out x
x(x7−1)=0
x=0,1
Thus, the limits is from x =
V=π∫10[(x^1/4)^2−(x4)^2]dx
Integrate this equation with in limits 0 to 1
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Alexandra invested 40% of his money in mutual funds, 40% in real estate, and 20% in stocks. If the value of the money that he invested in mutual funds, real estate, and stocks grew by 2%, 7%, and 11% respectively, what was the average growth on his total investment?
Answer is: 5.80%
I don't know the steps to get this answer
Answer:
5.80
Step-by-step explanation:
just to make the answer
Find the slope between the points:
(1,7) and (-5, -11)
Slope between the points (1,7) and (-5, -11) is m = 18/6 as a decimal m = 3
What is slope?The slope of a hill describes its steepness. The steepness of a line follows a similar pattern. The rise between two points, which is the vertical change, is divided by the run, which is the horizontal change between those same two points, to determine the slope.
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
step1:
calculate the slope m using the slope formula
slope m=y2-y1/x2-x1
with (x₁, y₁ )=(1,-5) and (x₂, y₂ ) =(-5,-11)
step2:
m=-11-7/-5-1=-18/-6=18/6
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HELP!!!!!
Make a table for each equation
y=x-2
Chart:
x -2 -1 0 1 2
y ? ? ? ? ?
I basically just need he y row
Let f(x)= x^2 + 7 and g(x)= x^2+2. Find the following functions, and simplify each as much as possible: your final answer should be a polynomial with only one term in each power of x. (a) f(x) + g(x) = (b) f(x) - g(x) = (c) f(x).g(x)= (c) f(x)/g(x)= (For part (d), you need not simplify as you did in (a)-(c).)
For function f(x)= x² + 7 and g(x)= x² + 2,
a) f(x) + g(x) = 2x² + 9
b) f(x) - g(x) = 5
c) f(x) . g(x) = x⁴ + 9x² + 14
d) [tex]\frac{f(x)}{g(x)} =\frac{x^2 + 7 }{ x^2+2}[/tex]
Consider given functions f(x)= x² + 7 and g(x)= x² + 2
a) To find addition of functions: f(x) + g(x)
f(x) + g(x)
= (x² + 7) + (x² + 2)
= x² + x² + 7 + 2 .............(associative property of addition)
= 2x² + 9 ................(combine like terms)
b) to find subtraction of functions : f(x) - g(x)
f(x) - g(x)
= ( x² + 7 ) - (x² + 2)
= 7 - 2
= 5
c) To find multiplication of functions: f(x).g(x)
f(x) . g(x)
= ( x² + 7 ).(x² + 2)
= x² (x² + 2) + 7(x² + 2)
= x⁴ + 2x² + 7x² + 14
= x⁴ + 9x² + 14 ................(combine like terms)
d) To find division of functions: f(x)/g(x)
[tex]\frac{f(x)}{g(x)}\\\\ =\frac{x^2 + 7 }{ x^2+2}[/tex]
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Let F(s)=5s2+4s+4 F ( s ) = 5 s 2 + 4 s + 4 . Find a value of d d greater than 0 0 such that the average rate of change of F(s) F ( s ) from 0 0 to d d equals the instantaneous rate of change of F(s) F ( s ) at s=1. s = 1.
The required value of d for the given function is given as d = 2.
The method of determining the derivative of an implicit function by differentiating each term separately, expressing the derivative of the dependent variable as a symbol, and solving the resulting expression for the symbol
Here,
F(s) = 5s²+ 4s +4
F'(s) = 10s + 4
F'(1) = f(d) - f(0)/ d
10(1) + 4 = 5d² + 4d / d
14 = 5d +4
d = 2
Thus, the required value of d is given as d = 2.
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Sasha ran at a constant speed of 3.8 meters per 1/2 hour.Then walked 1.3 meters per second for 1/2 hour. How far did she run and walk in 60 minutes.
Answer: 2343.8 meters
Step-by-step explanation: If 3.8 meters is walked in 1/2 hours then another 4680 meters per hour is ran for a half hour is 2340 meters add those 2 together
Mr. Hanson assigned his students a trigonometry project. Each student was to use a clinometer to determine the angle of elevation to the sun followed by trigonometry to determine the length of their shadows. James and Andy were partners in this assignment. James stood tall and Andy found that the distance from the ground to the clinometer that James was holding was 5.5 feet. James determined the angle of elevation to the sun to be 35 derajat. Draw a picture and write an equation to model this scenario. Then solve for the variable without using your calculator (hint: you should still have a trig function in your answer).
The picture shows James holding the clinometer 5.5 feet off the ground while pointing it up to the sun at an angle of 35 degrees. The equation to model this scenario is y = 5.5sin(35). To solve for y without using a calculator, we can use the inverse trigonometric function arcsin, so y = 5.5 arcsin(35). The answer is y = 4.51 feet.
y = 5.5sin(35)
y = 4.816
arcsin(4.816) = 35
4.816 = 5.5sin(35)
y = 5.5 arcsin(35)
y = 4.51 feet
The picture shows James holding the clinometer 5.5 feet off the ground while pointing it up to the sun at an angle of 35 degrees. The equation to model this scenario is y = 5.5sin(35), which is the length of the shadow. To solve for y without using a calculator, we can use the inverse trigonometric function arcsin, so y = 5.5 arcsin(35). We can then use the Pythagorean Theorem to solve for y: 4.816 = 5.5sin(35), so y = 5.5 arcsin(35). The answer is y = 4.51 feet, so the length of the shadow is 4.51 feet. This demonstrates how trigonometry can be used to calculate the length of shadows, with the help of a clinometer.
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What is 11 divided by 2.5 and can you show the work
If you divide 11 by 2.5 you will end up with 4.4. Answer = 4.4
A heterozygous round pea is crossed with a purebred round pea. Predict the genotypic and phenotypic outcomes.
Consequently, the plant will exhibit a tall phenotype as a result of the T allele's presence. In a heterozygous tall pea plant, the tall trait will therefore be visible.
How do two heterozygous peas fare when they are bred?Punnet square analysis indicates that the progeny of two heterozygous pea plants (Yy) will be 75% (3/4) dominant and 25% (1/4) recessive. In the event that 1000 individuals are created, 750 will therefore be dominating.
Tt will be the genotype of a tall heterozygous plant. It will actually prevail over the recessive t allele because T is primarily the dominant allele. Consequently, the plant will exhibit a tall phenotype as a result of the T allele's presence. In a heterozygous tall pea plant, the tall trait will therefore be visible.
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Moving vertically up from the origin is movement in the direction of positive z
The first hook will be hung at a point 4 feet east of the origin and 7.5 feet above the origin. The second hook will be hung at a point 5 feet east of the origin, 12
feet north of the origin, and 8 feet above the origin.
Provide the coordinates of the following points:
1. the first hook
2. the second hook
3.
the point on the string joining the hooks that is exactly halfway between the hooks
The coordinates of the hooks in three-dimensional space are found and the mid-point of the string is recognised as (4.5, 6, 7.75).
What is meant by three-dimensional space?
A three-dimensional space in geometry is a mathematical structure where a point's location depends on three different values.
For this question, we are considering the east of origin as the positive x-axis, the above origin as the positive z-axis and the north of the origin as the positive y-axis.
a) For the first hook there is no y-axis, it is hung in the xz plane.
So the coordinates are (4,0,7.5)
b) The second hook coordinates are given as (5, 12,8)
c) The point on the string which joins the hook, which is halfway between the hooks can be found using the mid-point formula.
x= (x1 + x2)/2 = (4+5)/2 = 4.5
y = (y1 + y2) /2 = (0+12) / 2 = 6
z = (z1+z2) / 2 = (7.5 + 8) /2 = 7.75
Therefore the mid-point of the string is (4.5, 6, 7.75).
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how many four digit decimal number that has an estimated value of 10 when rounded off to the nearest tenths place
Answer:
There are 10,000 four-digit decimal numbers that have an estimated value of 10 when rounded off to the nearest tenths place. This is because each decimal number from 0.0001 to 0.9999 will have an estimated value of 10 when rounded off to the nearest tenths place.
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The president wants the carpet in the east room of the whits house replaced the east room is 79 feet long by 36 feet wide how much carpet should the decorator order
Answer: the decorator should order 2,844 square feet of carpet to replace the carpet in the east room of the White House.
Step-by-step explanation:
Area = Length x Width
Area = 79 feet x 36 feet
Area = 2,844 square feet
Find the product of the complex number and its conjugate. 1/3 + 2i
Answer:
Step-by-step explanation:
1/3 + 2i is a complex number, with the real part equal to 1/3 and the imaginary part equal to 2i. It can be represented in a Cartesian coordinate system as a point (1/3, 2)
Figure out the polynomial being multiplied on top and then fill in the missing boxes
In order to factor your quadratic polynomials, the box method, as its name suggests, uses a box. You can divide your quadratic into its factors by using the box, which is essentially a square divided into four equal parts.
What is box method ?Be aware that not all quadratics can be factored. Some just lack relevant components. But if a quadratic polynomial does have components, you can utilize the box approach to simplify the operation.Drawing a square divided into four equal sections or a two-by-two grid is the first step. You then enter your first squared term into the upper left box and your final term into the lower right box. the product of your final term and first term.These new term's contributing components are found. You're seeking for a specific combination of elements that, when added together, give you your middle word. Write these elements in the two remaining empty boxes once you've identified this group of components. Your answer will remain the same no matter which empty box each term is entered into. Find the largest common factor for each row and column to determine the quadratic factors. The factors of your polynomial will then be determined by finding the biggest common factors from your columns and rows, respectively.Employing the Box Method
For our first quadratic, 6x2 - x - 12, let's utilize the box approach to solve it.
The first step is to create a two by two grid, as shown here:
using a box
Following that, we place the first term in the upper left box and the last term in the lower right box.
The Complete Question.
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Within the database environment, a data model represents data structures with the purpose of supporting a specific problem domain.a. Trueb. False
True. A data model is an abstract representation of the data structures used in a database.
It is typically used to represent the structure of the data and the relationships between different elements of the data. Data models are used to define the structure of the data in a database, as well as the relationships between different elements of the data. A data model is a combination of entities, attributes, relationships, and constraints. It is used to describe the data that is stored in a database and how the data can be accessed and manipulated. The data model also defines the relationships between the different elements of the data, such as which element of the data is related to which other element. The data model also defines the constraints that must be met in order to ensure the integrity of the data. A data model is also used to define the data types that are used in the database and the operations that can be performed on the data. For example, a data model may define data types such as integers, strings, and dates, as well as operations such as arithmetic, comparison, and sorting. A data model also defines rules for the structure and organization of the data, such as which fields must be present in a record, the order in which records must be stored, and the types of relationships that can exist between records.
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A group of meteorologists recorded the
temperature in some cities at noon on one
day.
They recorded the temperature in Leeds using
a thermometer that measures to the nearest
0.1 °C and found that the temperature was
16.8°C.
The temperature in Copenhagen was 12 °C
colder than in Leeds, to the nearest degree.
The temperature in Valletta was 23 °C warmer
than the temperature in Copenhagen, to the
nearest degree.
Work out the lower and upper bounds of the
temperature at noon in Valletta.
Give your answer in °C.
The lower and upper bounds of the temperature at noon in Valletta are 10.9° C and 27.8° C.
What is Temperature?A physical number known as temperature expresses the concepts of hotness and coolness in numerical form. With a thermometer, the temperature is measured.Thermometers are calibrated using a number of temperature scales that have defined distinct reference points and thermometric substances. The most widely used scales are the Kelvin scale (K), which is mostly used for scientific reasons, the Fahrenheit scale (°F), and the Celsius scale (°C), formerly known as centigrade, with the unit symbol °C. In the International System of Units, one of the seven base units is the kelvin.The upper bound of Valletta = Upper bound of Leeds - Copenhagen +23
upper bound of Valletta = 16.8 -12+23
upper bound of Valletta = 27.8 °C
Lower bound of Valletta = 0.1 -12+23
Lower bound of Valletta = 10.9 °C
Hence, The lower and upper bounds of the temperature at noon in Valletta are 10.9° C and 27.8° C.
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pair of equation are parallel, perpendicular, or neither y=-7/8x-1, 32x-28y=-36
The slope of the given lines are representing that these lines are perpendicular.
What is the Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given, the pair of the equation are parallel, perpendicular, or neither y=-7/8x-1, 32x-28y=-36
Slope intercept form of both equations of a line
1) y = -7/8x - 1
it is already in a slope intercept form
2) 32x - 28y = -36
-28y = -32x -36
y = 8/7x + 9/7
Since their slope is inverse and had a negative constant.
The slope of a perpendicular line from the slope of a given line is obtained by taking the negative reciprocal of the slope of the given line. If the slope of the given line is m1 and the slope of a perpendicular line is m2 then we have m2 = -1/m1.
Therefore, The slope of the given lines are representing that these lines are perpendicular.
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Merle tiene una oferta de un emisor de tarjeta de crédito para una APR del 0
% durante los primeros 60 días y una APR del 23,19 % después, con
capitalización diaria. ¿Qué tasa de interés efectiva se ofrece Merle?
UNA 26.00%
La tarjeta de crédito tiene una tasa efectiva de interés anual de 21,375 %.
¿Cómo determinar la tasa de interés efectiva anual?
En este problema tenemos que Merle obtiene una tarjeta de crédito bajo la siguientes condiciones: 0 % E.A. para los primeros 60 días, 23,19 % E.A. para los 365 restantes.
Debemos determinar la tasa de interés efectiva anual equivalente, esto es posiblemente mediante una aplicación consecutiva del concepto de interés, descrito abajo:
I = (1 + r / 36500)ⁿ
Donde:
r - Tasa de interés anual.n - Número de días.I - Ganancia por interés.La situación es descrita por la siguiente expresión matemática:
1 + R / 100 = (1 + 0 / 36500)⁶⁰ + (1 + 23,19 / 36500)³⁰⁵
Donde R es la tasa efectiva de interés anual.
Finalmente, despejamos la variable correspondiente:
R = 21,375
La tasa efectiva de interés anual a sufragar por Merle por el uso de tarjeta de crédito es 21,375 %.
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Time to walk 3 1/3 miles on Saturday and 2 4/5 mile on Sunday how much farther does Tonya walk on Saturday then on Sunday
The distance that Tonya walk on Saturday more than on Sunday would be = 8/15 miles
What is distance?Distance is defined as the quantity that describes the space that exists between two locations in a field.
The number of miles Tonya covered on Saturday = 3 ⅓ miles
The number of miles that Tonya covered on Sunday = 2 ⅘
Therefore the distance that Tonya walk on Saturday more than on Sunday would be the difference between the distance covered in Saturday and Sunday.
That is; 3⅓ - 2⅘ ( change to single fraction form)
= 10/3 - 14/5
= 50-42/15
= 8/15
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Find the slope of the line graphed below.
The slope of the given graph is 3/8 .
What is Graph ?
Graph can be defined as the visual representation in which we can represent the data.
Given in the graph,
We are given two points: (4, 5) and ( -4, 2 ). Slope is calculated as the change in y over the change in x, or rise over run.
The change in y is the difference of the two y coordinates (it doesn't matter the order): 5- (2) = 3
The change in x is the difference of the two x coordinates (this order depends on the order that you subtracted the y coordinates; they must be the same order): 4 - (-4) = 4+4 = 8.
So, the slope is 3/8
Therefore, The slope of the given graph is 3/8 .
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Find the unit vector perpendicular to the plane of given vectors.P =i−2j+ k^Q =2i+j−k^
The unit vector perpendicular to the plane of given vectors P =i−2j+ k and Q =2i + j − k is ( i + 3j + 5k )/√35
The vector that perpendicular to the plane is equal to the cross product of:
P ⨉ Q
Remember the properties of cross product of two vectors:
i ⨉ i = j ⨉ j = k⨉ k = 0
i ⨉ j = k
j ⨉ i = - k
j ⨉ k = i
k⨉ i = j
i⨉ k = -j
Hence,
P ⨉ Q = (i−2j+ k) ⨉ (2i+j−k)
= k + j +4k + 2i +2j - i
= i + 3j + 5k
The magnitude of P ⨉ Q is:
|| P ⨉ Q || = √(1² + 3² + 5²)
= √35
Therefore, the unit vector = ( i + 3j + 5k )/√35
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A sum of £36000 is divided between ALex ,Bill and claire by the ratio of 2 ×3/4 : 1×1/2 : 2×1/4 what is the amount each individual gets
so hmm £36000 will be split, hmmm let's call the ratios "a,b and c", so the amount will be split in ratios of a : b : c, which means we'll be dividing the 36000 bucks by (a + b + c) and distribute accordingly, let's do that, hmm let's convert also all those mixed fractions to improper fractions.
[tex]\stackrel{mixed}{2\frac{3}{4}}\implies \cfrac{2\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{11}{4}} ~\hfill \stackrel{mixed}{1\frac{1}{2}} \implies \cfrac{1\cdot 2+1}{2} \implies \stackrel{improper}{\cfrac{3}{2}} \\\\\\ \stackrel{mixed}{2\frac{1}{4}}\implies \cfrac{2\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{9}{4}} ~\hfill \boxed{\cfrac{11}{4}+\cfrac{3}{2}+\cfrac{9}{4}\implies \cfrac{13}{2}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{36000}{~~ \frac{13 }{2 } ~~}\implies 36000\cdot \cfrac{2}{13}\implies \cfrac{72000}{13} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{Alex}{\cfrac{11}{4}\cdot \cfrac{72000}{13}}~~ : ~~\stackrel{Bill}{\cfrac{3}{2}\cdot \cfrac{72000}{13}}~~ : ~~\stackrel{Claire}{\cfrac{9}{4}\cdot \cfrac{72000}{13}}\implies \stackrel{Alex}{\cfrac{198000}{13}}~~ : ~~\stackrel{Bill}{\cfrac{108000}{13}}~ : ~\stackrel{Claire}{\cfrac{162000}{13}} \\\\\\ ~\hfill \stackrel{Alex}{15230\frac{10}{13}}~~ : ~~\stackrel{Bill}{8307\frac{9}{13}}~ : ~\stackrel{Claire}{12461\frac{7}{13}}~\hfill[/tex]
Find the following for the given functions.
f(x): =
X/X + 9 ,
g(x) = x³
The values of (f + g) (x), (f - g) (x), (fg) (x) and (f /g) (x) for the functions are x/(x + 9) + x³, x/(x + 9) - x³, x³/(x³ + 9) and 1/ [x² (x + 9)] respectively
How to determine the values for the functions?
A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input
Since f(x) = x/(x + 9), g(x) = x³
(a) (f + g) (x) will be the addition of f(x) and g(x). That is:
(f + g) (x) = x/(x + 9) + x³ or x³ + x/(x + 9)
(b) (f - g) (x) will be the subtraction of f(x) and g(x). That is:
(f - g) (x) = x/(x + 9) - x³
(c) (fg)(x) substitute x = x³ into f(x). That is:
f(x)= x/(x + 9), g(x) = x³
(fg)(x) = x³/(x³ + 9)
(d) (f/g)(x) will be the division of f(x) by g(x). That is:
(f/g)(x) = [x/(x + 9)] / x³ = x/ [x³ (x + 9)] = 1/ [x² (x + 9)]
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