[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to 3.2\%\to \frac{3.2}{100}\dotfill &0.032\\ t=years\dotfill &1 \end{cases} \\\\\\ I = (500)(0.032)(1) \implies I = 16[/tex]
A ladder leans against a wall inside a spaceship. From the point of view of a person on the ship, the base of the ladder is 2.70 m from the wall, and the top of the ladder is 5.13 m above the floor. The spaceship moves past the Earth with a speed of 0.85c in a direction parallel to the floor of the ship. Find the angle the ladder makes with the floor, as seen by an observer on Earth.
Angle of the ladder with the floor is 74.5°.
We have given that,
base of the ladder from the wall, x₀ = 2.70 m
top of the ladder above the floor y = 5.13 m
speed of the spaceship = 0.85 c
and we have to find the angle ladder makes with the floor, θ.
From the given information we will construct a diagram.
From the diagram,
tanθ = y/x₀
tanθ = y / x₀√(1- V^2 / c^2)
we will substitute all the values,
tanθ = 5.13 / 2.70√(1-((0.85c)^2 / c^2))
= 5.13 / 2.70√(1-(0.85^2))
= 5.13 / 2.70√(1 - 0.7225)
= 5.13 / 2.70√0.2775
= 5.13 / 1.4223
tanθ = 3.606
θ = tan⁻¹(3.606)
θ = 74.5°
Therefore angle the ladder makes with the floor is 74.5°.
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what is the ratio of cups to flour to eggs
Answer:
Step-by-step explanation:
Answer= use 2 eggs per 1 cup of flour to make 1 serving.
a study is conducted to determine if one can predict the yield of a crop based on the amount of fertilizer applied to the soil.
The response variable in this study is
Yield of crop.
"Information available from the question"
In the question:
A study is conducted to determine if one can predict the yield of a crop based on the amount of fertilizer applied to the soil.
Now, According to the question:
Let's know:
What is called fertilizer?
A fertiliser is a natural or artificial substance containing chemical elements (such as Nitrogen (N), Phosphorus (P) and Potassium (K)) that improve growth and productiveness of plants. Some synonyms include the terms "enrichment" or "plant nutrient".
The answer is:
Yield of crop.
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The complete question is this:
A study is conducted to determine if one can predict the yield of a crop based on the amount of fertilizer applied to the soil. The response variable in this study is
5) Simplify the expression and identify any restrictions on x.
Answer:
attached in the file
3x-5y=15
x-4y=12
solve with substitution
system of equations
The solution of the equations 3x - 5y = 15 and x - 4y = 12 will be (0, -3).
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The system of equations is given below.
3x - 5y = 15 ...1
x - 4y = 12 ...2
From equation 2, then we have
x = 4y + 12
Put in equation 1, then we have
3(4y + 12) - 5y = 15
12y + 36 - 5y = 15
7y = -21
y = - 3
Then the value of the variable 'x' is calculated as,
x = 4(-3) + 12
x = - 12 + 12
x = 0
The solution of the equations 3x - 5y = 15 and x - 4y = 12 will be (0, -3).
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Suppose that f is an exponential function with growth factor 2.4 and that f(0) = 3. Find f(3)
For the given exponential function, the value of f(3) would be f(3) = 41.472.
What is an exponential function?
The exponential function is a mathematical function that is represented by f(x)= e^x. Unless otherwise specified, the term refers to a positive-valued function of a real variable, though it can be extended to complex numbers or generalized to other mathematical objects such as matrices or Lie algebras.
The given function would be [tex]f(x)=ab^x[/tex].
The growth factor is b = 2.4
[tex]f(0) = ab^0\\\\a=3\\[/tex]
Now find f(3),
[tex]f(3)=3.(2.4)^x\\\\ f(3) = 3*(2.4)^3\\\\\f(3) = 41.472[/tex]
Hence, the value of f(3) would be f(3) = 41.472.
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The volume of a sphere with radius x is 3x³ units, and the volume of
a cube with side length x is x³ units³.
a. Find the total combined volume of the sphere and cube.
b. How much more volume does the sphere contains
V = 4/3 r3, where V is the volume and r is the radius, is the formula for a sphere's volume. A sphere's radius is equal to half of its diameter.
How do you find the volume of a sphere?Every point on the volume's surface will be equally far from its centre if the surface area is doubled by the diameter. The formula shown below is used mathematically to determine a sphere's volume: The formula for a sphere's volume is 4/3 r3, where r is the sphere's radius.In On Sphere and Cylinder, where Archimedes firmly demonstrated that VS:VC=2:3, where VS is the volume of a sphere and VC is the volume of the circumscribed cylinder, was undoubtedly the first significant step (he also gave proportion for the surface area).The Radius of a circle or sphere is equal to the Diameter divided by 2.Given data :
radius = 3x²
volume of sphere = V = 4/3 π r³
v = 4 x π x (3x²)[tex]{3}[/tex] / 3
= 4π.[tex]x^{5}[/tex]
volume of cube = side3
= (x²)[tex]^{3}[/tex]
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From a pack of 52 card, two are drawn, one after another at random. Find the probability that the firt one i a 7 and the econd i a 6. (There are 4 7' and 4 6' in a pack)
The probabilty that the first card is 7 and the second card is 6 numbered would be 0.0059.
What is probability?
Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.
It is given that there is a deck of 52 cards.
So sample space (n) = 52.
Now in the first draw, 7 numbered card should be drawn
and there are four 7 numbered cards in a deck of 52 cards
so probability of drawing a 7 numbered card will be = 4/52 = 2/26
Now in the second draw, 6 numbered cards should be drawn
and there are four 6 numbered cards in a deck of 52 cards but already one card is drawn so there will be 51 cards remaining in the deck.
so probability of drawing a 6 numbered card will be = 4/51
Hence the probability that the first card is 7 and the second card is 6 numbered will be = 2/26 * 4/51
= 0.076 * 0.078
= 0.0059
Hence, the probabilty that the first card is 7 and the second card is 6 numbered would be 0.0059.
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Make x the subject of m=n+x/p
Answer:
x=mp-n
Step-by-step explanation:
Switch sides:
(n+x)/p=m
Then multiply both sides by p:
n+x=mp
Move n to the other side:
x=mp-n
The graph of g(x) was obtained by translating the graph of f(x). Based on the graph, which equation can be used to describe g(x) in terms of f(x) ?
A g(x)=-f(x+2)+1
C g(x)=f(x+2)+1
B g(x)=-f(x-2)+1
D g(x)=f(x-2)+1
The equation that can be used to describe g(x) in terms of f(x), considering the transformations, is given as follows:
A. g(x)=-f(x+2)+1.
What are the transformations?From the image given at the end of the answer, the function f(x) is given as follows:
f(x) = x².
The transformations to obtain function g(x) are given as follows:
Reflection over the x-axis, hence g(x) = -f(x).Shift right by 2 units, hence the transformation is: x -> x - 2.Shift up by 1 unit, hence g(x) - > -f(x - 2) + 1.Meaning that option A gives the correct option to describe the function g(x) as a function of the function f(x).
Missing InformationThe functions are given by the image presented at the end of the answer.
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Student are going on a field trip to a play. The play i elling kid ticket and adult ticket. They old a total of 60 ticket. One kid ticket ell for $3 while the adult ticket i $5. They made a profit of $220 that day. How many kid ticket were old?
Number of kids ticket is 40
What do you mean by system of linear equation?
A set of two linear equations with two variables is a system of linear equations. There are infinitely many possible solutions to a linear equation with two variables. There can be a single solution to a system of two linear equations with two variables that satisfies both solutions. It is necessary to combine two equations with two variables into one equation with one variable while solving a system of equations.
Total number of tickets = 60
Cost of 1 kid ticket = $3
Cost of 1 adult ticket = $5
Total profit = $220
Let number of kid tickets = x
number of adult tickets = y
According to question:
x + y = 60 ......(1)
3x + 5y = 220 ........(2)
Substitute the value of x from eq(1) to eq(2)
3(60 - y) + 5y = 220
180 - 3y + 5y = 220
180 + 2y = 220
2y = 220 - 180
2y = 40
y = 40/2
y = 20
Substitute this value of y in eq(1)
x + 20 = 60
x = 60 - 20
x = 40
Therefore, number of kids ticket is 40
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A family used a professional decorator to help furnish their new home. The decorator selected $1,580 worth of furnishings. The family paid for the furnishings, plus 4.5% tax on the purchases. The decorator’s fee was 12% of the purchases, not including the tax.
Question 1
Part A
Write an equation in the form of y=kx, using x to represent the decorator’s fee. Then use the equation to calculate the amount of that fee.
Answer:
Step-by-step explanation:
Worth of furnishings = $1580
Tax rate = 4.5%
Tax = 4.5% × $1580 = 0.045 × $1580 = $71.10
Amount paid = $1580 + $71.10 = $1651.10
Since the decorator's fee was 12% of the purchases. This will then be calculated as:
y = kx
where,
y = decorators fee
k = percentage of decorators fee on purchases
x = amount paid
y = 12% × $1651.10
= 0.12 × $1651.10
= $198.132
Rewrite the equation shown in slope-intercept form. Identify the slope of the equation, the xintercept and the y-intercept. Then graph the equation. Make sure to show all your work in the
spaces provided.
Answer:
x^2 + 10
Step-by-step explanation:
What is the domain of the function
f(x) = 2x + 3
when the range is {3, 5, 9}?
Answer:
Domain: {9, 13, 21}
Step-by-step explanation:
BRAINLIEST PLEASE!!!Answer:
(0,1,3)Step-by-step explanation:
f(x)=2x+3let y= f(x)y=2x+3interchanging x and y in the expression x=2y+3making y the subject in the equation y=(x-3)/2f(x)-¹=(x-3)/2when x= 3 =(3-3)/2 =0when x=5 =(5-3)/2 = 1when x= 9 =(9-3)/2 = 3A graphing calculator is recommended, A 60-gallon barrel is filled completely with pure water. Salt water with a concentration of 0.3 lb/gal is then pumped into the barrel, and the resulting mixture overflows at the same rate. The amount of salt in the barrel at time t is given by Olt) = 18(1 - e-0.08) where t is measured in minutes and o(t) is measured in pounds. (a) How much salt is in the barrel after 5 min? (Round your answer to two decimal places.) | Iь (b) How much salt is in the barrel after 10 min? (Round your answer to two decimal places.) | ГБ lb (c) Draw a graph of the function Oſt). Qt) Qit) 20 20 15 15 10 10 5 20 t 100 40 80 60 ht 100 O 20 40 60 80 Oxt) Oxt) 20 20 15 15 10 10 5 t Lt O 20 40 60 80 100 O 20 40 60 80 100 (d) Use the graph in part (c) to determine the value that the amount of salt in the barrel approaches as t becomes large. | | lb
t approaches infinity then salt is:
[tex]Q(\infty) = 18lb[/tex]
What is volume?
Volume is a mathematical term used to describe how much three-dimensional space an object or closed surface occupies. Volume is measured in cubic units like m3, cm3, in3, etc. Volume is sometimes referred to as capacity.
The amount of salt in the barrel at time t is given by
where Q(t) is in pounds and time t is in minutes.
(a) Salt after 5 minutes i.e. t=5
[tex]Q(5) = 18(1 - e^{-0.08(5)} ) = 18(1 - e^{-0.4})\\\\Q(5) = 18(1 - 0.6703) = 5.93 \\\\Q(5) = 5.93lb[/tex]
(b) Salt after 10 minutes i.e. t=10
[tex]Q(10) = 18(1 - e^{-0.08(10)} ) = 18(1 - e^{-0.8} )\\\\Q(10) = 18(1 - 0.4493 ) = 9.91\\\\Q(10) = 9.91lb[/tex]
(d) When t becomes large, let say when t approaches infinity then salt is
[tex]Q(\infty) = 18(1 - e^{-0.08(\infty)} ) = 18(1- e^{-\infty})\\\\Q(\infty) = 18(1 - 0) = 18\\\\Q(\infty) = 18lb[/tex]
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Tapiwa raked 5%, percent more leaves than Adam raked. Tapiwa raked 357 liters of leaves. How many liters of leaves did Adam rake?
HELP ASAP!
The number of liters of leaves that Adam rakes will be 340.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Tapiwa raked 5%, percent more leaves than Adam raked. Tapiwa raked 357 liters of leaves.
Let the number of leaves that Adam raked be 'x' and the number of leaves that Tapiwa raked be 'y'. Then the equations are given as,
y = 1.05x ...1
y = 357 ...2
From equations 1 and 2, then we have
1.05x = 357
x = 357 / 1.05
x = 340
The number of liters of leaves that Adam rakes will be 340.
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A landscaper digs a rectangular region for a garden. The length is a one-digit whole number of meters. What is the least possible area? What is the greatest possible area?
The least possible area is 0 meter² and the greatest possible area is 49.5metre².
What is a rectangle?With four sides, four corners, and four right angles (90°), a rectangle is a closed 2-D object.
A rectangle has equal and parallel opposing sides. Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The rectangle's length is its longer side, while its width is its shorter side.
A little information
1) Parallelograms are all squares, yet squares are all not parallelograms
2) A rectangle is divided into four triangles by its diagonals.
3) While not all rectangles are squares, all squares are rectangles.
How to solve?
Area of rectangle is given by = length × breadth.
For minimum area, we have one digit whole number.
In whole number smallest digit is 0
so, least possible area =0×breadth=0 metres²,
Now talking about maximum possible area, the greatest one digit whole number is 9.
width of rectangular region is 5.5 meters.
The greatest possible area is =9×5.5=49.5meters².
Hence, the answers are 0 and 49.5 meters².
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(Complete question) is:
A landscaper digs a rectangular region for a garden. The length is a one digit whole number of meters and width is 5.5 meters. What is the least possible area? What is the greatest possible area?
find the derivatives of cos
Step by step solution is above
*16 (b)
(√3-1) cm
A
75°
B
You are given that sin 75º =
5√2 cm
√3+1
2√2
Show that the area of triangle ABC is 2½ cm²
Nof
acc
C
Answer:
Step-by-step explanation:
78 sin
(+0
Michael swam 2,000 yards on each of eighteen days.
The scatterplot above shows his swim time for and
corresponding heart rate after each swim. The line of
best fit for the data is also shown. For the swim that
took 34 minutes, Michael's actual heart rate was
about how many beats per minutes less than the rate
predicted by the line of best fit?
A) 1
B) 2
C) 3
D) 4
Michael's actual heart rate was about 2 beats per minutes less than the rate predicted by the line of best fit. The correct option is B
What is a scatterplot?A scatterplot is a data visualization that depicts the relationship between two numerical variables. Each dataset member is plotted as a point whose x-y coordinates correspond to its values for the two variables.
On each of the eighteen days, Michael swam 2,000 yards. The scatterplot above depicts his swim time and heart rate after each swim. The data's best fit line is also shown.
From the graph the actual heart rate=150
but calculated heart rate from best fit line=148
Difference between actual and calculated=150−148=2
Option B is correct.
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The total variance is $35,000. The total materials variance is $14,000. The total labor variance is twice the total overhead variance. What is the total overhead variance?.
The total overhead variance is $7,000
What is variance?
Data points' variance from the mean is a measure of how they vary. A variance, according to Layman, is a measurement of how widely apart a collection of data (numbers) are from their mean (average) value.
Finding the predicted difference of departure from the actual number is what is meant by variance. As a result, variance is influenced by the data set's standard deviation.
Data is more dispersed from its mean the higher the variance value, and less dispersed from mean if the variance value is low or minimal. As a result, it is referred to as a measure of data dispersion from mean.
Total labor and overhead variance = 35000-14000 = 21000
Total overhead variance = 21000/(2+1)*1 = 7000
Thus, total overhead variance is $7,000
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Given the following Venn diagram:
Find M N.
From the given Venn diagram, the value of M∩N={4,7}.
What is a Venn diagram?A Venn diagram is a prominent diagram type that depicts the logical relationship between sets. It was popularized in the 1880s by John Venn (1834-1923). The diagrams are used to teach elementary set theory and to show simple set relationships in probability, logic, statistics, linguistics, and computer science. To depict sets, a Venn diagram uses basic closed curves drawn on a plane. These curves are almost often circles or ellipses.
Before Venn, similar concepts had been presented. Similar ideas were proposed by Christian Weise in 1712 and Leonhard Euler (Letters to a German Princess) in 1768. Venn popularized the concept in Symbolic Logic, Chapter V "Diagrammatic Representation," 1881.
The intersection of two sets is the set of all the elements that are shared by both.
M={4,7,9,3}
N={4,7,6}
Because M and N share the numbers 4 and 7, M∩N={4,7}.
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Without dividing explain whether the quotient of 9/10 ÷ 3 is greater than or less than the quotient of 9/10 ÷ 2.
Answer:
less than
Step-by-step explanation:
when you divide by a bigger number the smaller the quotient will be
Hopes this helps please mark brainliest
If Tamara travels 10 mi to a store after she leaves the park, what point on the graph represents the store
Answer:
The correct option is C
Step-by-step explanation:
jasmine is 5 years younger than twice her sister age of jasmine sister 22 year old then how old is jasmine
Answer:
100000000000000000000000000
Step-by-step explanation:
Answer:
Step-by-step explanation:
i think the answer is 12
How do I prove that the square of an odd number is always one more than a multiple of 8?
The proper way that you can prove that the square of an odd number is always one more than a multiple of eight is by using an example.
What is an example?An example is a term that refers to a tool that is intended to explain, illustrate, or prove a general statement. When we want to explain a procedure we can give an example (that we have previously chosen) to seek to clarify the understanding of a phenomenon or process.
How to make an example for this case?To prove that the square of an odd number is always a multiple of eight, the first step is to find the square of any odd number. Subsequently, we must subtract 1 from the result. Finally we must divide the previous result by 8 and it must give us an exact number (not a decimal).
3 * 3 = 9
9 - 1 = 8
8 / 8 = 1
123 * 123 = 15,129
15,129 - 1 = 15,128
15,128 / 8 = 1,891
9 * 9 = 81
81 - 1 = 80
80 / 8 = 10
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Examine the table, which represents the number of guests visiting a museum during a period of time.
If the relationship between hours and guests is proportional, what is the value of h?
Enter your answer as a number, like this: 42
Answer:
7
Step-by-step explanation:
649-531=118
We know that there are 118 more guests per hour.
Divide 826 by 118 to get 7.
Answer: 7
Step-by-step explanation:
The first line of the table is 2 and 236 if you divide 236 by 2 you get 118
Then after that you times it by any number after 5.5 until you get 826.
does someone mind helping me with this? Thank you!
Answer:
the answer is 8
Step-by-step explanation:
it's a directly proportional relationship
evaluate the given integral by changing to polar coordinates. sin(x2 y2) da r , where r is the region in the first quadrant between the circles with center the origin and radii 1 and 3
Using polar coordinates, the result for integral is - 0.448[tex]\pi[/tex]
What is polar co-ordinates?
In arithmetic, the polar coordinate system may be a two-dimensional organization within which every purpose on a plane is set by a distance from a indicator and an angle from a reference direction.
Main body:
The most used relation for polar coordinates is:
[tex]x^{2} +y ^{2} =r^{2}[/tex]
An integral in Cartesian coordinates is converted to polar using:
[tex]\int\int{f(x,y)} \, dA = \int\int{ f(r, \beta )d\beta[/tex]
In this problem:
f(x,y) = sin [tex]x^{2} +y^{2}[/tex]
thus
f(r,[tex]\beta[/tex]) = sin[tex]r^{2}[/tex]
Region between the circles with center at the origin and radii 1 and 3, thus the inner limits of integration are r =1 and r =3.
First quadrant, thus, the outer limits of integration are: [tex]\beta[/tex] = 0,[tex]\beta[/tex] = [tex]\pi /2[/tex].
The polar integral is:
I = [tex]\int\limits^3_1 {sinr^{2} r} \, dr[/tex]
Using substitution:
u =[tex]r^{2}[/tex] ⇒ du = 2rdr⇒ dr = du /2
I = 1/2[tex]\int\ {sin u} \, du[/tex]
= -[tex]cos r^{2[/tex] /2 where limits are 3, 1
Applying the fundamental theorem of calculus:
I = [tex]-cos 5^{2} /2[/tex][tex]-cos1^{2}/2[/tex]
I = - 0.996
Then, the outer integral is:
O =[tex]\int\limits^\pi _0 {-0.996} \, d\beta[/tex]
O= - 0.448[tex]\pi[/tex]
Hence the result for integral is - 0.448[tex]\pi[/tex]
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researchers examined the hyper-eating behavior known to occur with cannabis use and the effect of the opioid-blocker naloxone (nalo) on this behavior. they randomly assigned lab mice to 4 conditions (shown below) and measured the mice feeding response (in mg). is there evidence that the treatments affect the mean feeding response in mice? nalo cannabis nalo control cannabis 10 10 20 130 40 50 30 150 40 60 40 150 120 80 80 190 120 120 170 250 140 160 (you can copy/paste the data into crunchit from menu edit / paste spreadsheet.) state the appropriate null and alternative hypotheses run the appropriate test. the test p-value you obtain is a value between
Alpha one is equal to two is the null hypothesis and the alternate hypothesis says at least one pair is different.
Classification modes X is alpha + ц T and X is ц T + alpha
Therefore , P value is 01.0197
Therefore, This value is smaller than 0.0 , this is the decision rule.
The null hypothesis will be rejected at that point since there is enough data to say that the therapy had a meaningful impact.
The null hypothesis means that there will be no observed effect in our experiment. In a mathematical formulation of the null hypothesis, there will typically be an equal sign. This hypothesis is denoted by H0.
The alternate hypothesis means that there will be an observed effect for our experiment. In a mathematical formulation of the alternative hypothesis, there will typically be an inequality, or not equal to symbol. This hypothesis is denoted by either Ha or by H1.
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