The water pressure on a submerged object is given by P = 64d, then the
a. The answer to the subject of the formula, "d," is d = P/64.
b. A submerged object will be 10. 5 feet deep at a pressure of 672 pounds per square foot.
What is a function?
A function can be defined as an expression, law or rule that shows the relationship between two variables.
These variables are namely;
Independent variableDependent variablegiven the role as;
P = 64d
Where;
P stands for pounds per square foot of pressure.
d represents the object's depth in feet.
Let's now make the variable "d" the focus of the formula.
The coefficient of the variable "d," which is 64, is used to divide both sides of the equation. So that the variable can stand on its own, this is done.
We possess
P/64 = 64d/64
d = P/ 64
P equals 672 pounds per square foot if there is pressure.
When the variable's value is substituted into the formula, we get;
d = P/64
Then,
d = 672/64
Discover the quotient.
d = 10. 5 ft.
The value is 10.5 feet.
Therefore,
a. The answer to the subject of the formula, "d," is d = P/64.
b. A submerged object will be 10. 5 feet deep at a pressure of 672 pounds per square foot.
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An individual wants to bring multiple copies of two comic books to a convention this week. There are 15 copies of the comic book the individual wants to sell (S), and 8 copies of a comic book the individual wants appraised (A), with a combined weight of 49.9 oz. The individual can only fit 40 oz. of comics in a bag. If the individual brings 10 copies of the comic book he wants to sell (S), 4 copies to be appraised (A), the combined weight would be 30.2 oz. Calculate how much each comic (S) weighs.2.3 oz.2.25 oz.2.1 oz.
Let x represent the weight of the comic book to be sold
Let y represent the weight of the appraised book to be appraised
There are 15 copies of the comic book the individual wants to sell (S), and 8 copies of a comic book the individual wants appraised (A), with a combined weight of 49.9 oz. It means that
15x + 8y = 49.9 equation 1
If the individual brings 10 copies of the comic book he wants to sell (S), 4 copies to be appraised (A), the combined weight would be 30.2 oz, it means that
10x + 4y = 30.2 equation 2
Multiplying equation 2 by 2, it becomes
20x + 8y = 60.4 equation 3
Subtracting equation 3 from equation 1, it becomes
20x - 15x + 8y - 8y = 60.4 - 49.9
5x = 10.5
x = 10.5/5
x = 2.1
Substituting x = 2.1 into equation 2, it becomes
10(2.1) + 4y = 30.2
21 + 4y = 30.2
4y = 30.2 - 21 = 9.2
y = 9.2/4
y = 2.3
Weight of the comic(S) to be sold = 2.1 oz
The store manager put 7 belts in sale. The belts were originally $16. The manager marked down the price of the belts by 40% how much money did the store receive for selling all 7 belts
Original price: $16
Discount: 40%
First, multiply the original price by the percentage discount in decimal form (divided by 100)
16 x 40/100 = 16 x 0.4 = $6.4 ( discount amount)
Subtract the discount amount to the original price
16-6.4 = $9.6 new price
multiply by 7 :
9.6 x 7 = $67.2
Calculate the cone: 1) volume; 2) the area of the lateral surface; 3) the total surface area;for AB = 14, SO = 24.
Given:
AB = 14
SO = 24
To find:
a) the volume
b) the area of the lateral surface
c) the total surface area
a) To find the volume of the cone, we will use the formula:
[tex]Volume\text{ of a cone = }\frac{1}{3}πr²h[/tex]r = radius
diameter = AB = 14
diameter = 2(radius)
radius = diameter/2 = 14/2
radius = 7
height = SO = 24
let π= 3.14
[tex]\begin{gathered} Volume\text{ of the cone = }\frac{1}{3}\times3.14\times7^2\times24 \\ Volume\text{ of the cone = 1230.88 unit}^3 \end{gathered}[/tex]b) To get the lateral surface, we will apply the formula:
[tex]\begin{gathered} lateral\text{ surface of the cone = \pi rl} \\ where\text{ l = }\sqrt{h^2+r^2} \end{gathered}[/tex][tex]\begin{gathered} Lateral\text{ surface of the cone = 3.14 }\times7\times\sqrt{7^2+24^2} \\ \\ Lateral\text{ surface area of the cone = 549.5 units}^2 \end{gathered}[/tex]c) The total surface area formula:
[tex]\begin{gathered} Total\text{ surface area of cone = Area of base + lateral surface area} \\ \\ Total\text{ surface area = \pi r}^2\text{ + \pi rl} \\ \\ Total\text{ surface area = \lparen3.14 }\times\text{ 7}^2)\text{ + 549.5} \end{gathered}[/tex][tex]Total\text{ surface area of cone = 703.36 unit}^2[/tex]solve the equation. (x + 4)^2 = 15 - 2x^2.
Quadratic Formula
The equation has two solutions [tex]x_{1}[/tex] = [-4 + 2√13]/3] and
[tex]x_{2}[/tex] = [-4 - 2√13]/3]
Given the question:
(x + 4)^2 = 15 - 2x^2.
To solve the above Equation by using Quadratic Formula:
Solving Steps of Equation:
[tex](x+4)^2 = 15 -2x^2[/tex]
Expand the expression
[tex]x^{2} +8x+16=15-2x^2[/tex]
Move the expression to the left
[tex]x^{2} +8x+16-15+2x^2[/tex] = 0
Collect like terms
[tex]3x^{2} +8x+1=0[/tex]
Use the Quadratic formula:
x = [-b ± √(b2 – 4ac)]/2a
x = [-8 ± √(8^2 – 4x3x1)]/2x 3
Multiply and evaluate :
x = [-8± √(64 – 12)]/6]
Calculate:
x = [-8± 2√13]/6]
Separate the solutions
[tex]x_{1}[/tex] = [-4 + 2√13]/3]
[tex]x_{2}[/tex] = [-4 - 2√13]/3]
Hence, The equation has two solutions [tex]x_{1}[/tex] = [-4 + 2√13]/3] and
[tex]x_{2}[/tex] = [-4 - 2√13]/3]
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Round all answers to 4 decimal places.
a. A bag contains 4 white marbles, 10 blue marbles, and 3 red marbles. If a marble is drawn from
the bag, replaced, and another marble is drawn, what is the probability of drawing first a white
marble and then a red marble?
b. A bag contains 10 green marbles, 3 red marbles, and 4 blue marbles. If two different marbles
are drawn from the bag, what is the probability of drawing first a green marble and then a blue
marble?
The probabilities are (a) 0.4228, and (b) 0.8382
Define probability?
Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty. The greater the likelihood of an occurrence, the more probable it will occur. Tossing a fair (unbiased) coin is a basic example. Because the coin is fair, the two possibilities ("heads" and "tails") are equally likely; the chance of "heads" equals the probability of "tails," and because no other outcomes are possible, the probability of either "heads" or "tails" is 1/2.
(a) probability of drawing first a white marble and then a red marble
= 4/(4+10+3) x 3(3+10+3) = 4/17 + 3/16 = 0.4228
(b) probability of drawing first a green marble and then a blue marble
= 10/(10+3+4) x 4(9+3+4) = 10/17 + 4/16 = 0.8382
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Choose the best answer
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:-\dfrac{1}{\sqrt{3-2x}} [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
We newd to find the derivative of given function :
[tex]\qquad \tt \rightarrow \: y = \sqrt{3 - 2x} [/tex]
[tex]\qquad \tt \rightarrow \: y = (3 - 2x) {}^{ \frac{1}{2} } [/tex]
[tex]\qquad \displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{d}{dx} (3 - 2x) {}^{ \frac{1}{2} } [/tex]
[tex]\qquad \displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{1}{2} \sdot(3 - 2x) {}^{ - \frac{1}{2} } \sdot( - 2)[/tex]
[tex]\qquad \displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{1}{ \cancel2} \sdot\frac{1}{(3 - 2x) {}^{ \frac{1}{2} } }\sdot( - \cancel2)[/tex]
[tex]\qquad \displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{ - 1}{ \sqrt{ (3 - 2x) {}^{ }} }[/tex]
Correct option : B
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Kingston Federal Bank supervises all banks in Jamaica. One Jamaican dollar is equal to 0.0071 US dollars. If Usain Bolt made a $ 3,000 deposit with Kingston Federal Bank with a 5% growth rate, how much money would Usain Bolt have after two years? (dont use advanced math please)
Principal = $3000
Rate = 5%
time = 2
Amount after 2 years =
[tex]\begin{gathered} =p(1+r)^t \\ =\text{ 3000( 1 + }\frac{5}{100})^2 \end{gathered}[/tex][tex]\begin{gathered} =3000(1+0.05)^2 \\ =\text{ 3000( 1.05)2} \\ =\text{ 3000 }\times\text{ 1.05 }\times\text{ 1.05} \end{gathered}[/tex]= $3307.5
Option D is the correct answer
One boat sails 30 miles west and 22 miles north. Another boat sails 55 miles west and 40 miles north. Which boat traveled in the direction closest to due north?
The boat that sailed in the direction closest to due north is the both that has lesser angle to the vertical ,which is the boat that that sailed 30 miles west and 22 miles north.
How to find the boat that traveled in the direction closest to due northGiven data
One boat sails 30 miles west and 22 miles north
Another boat sails 55 miles west and 40 miles north
Say boat A sail 30 miles west and 22 miles north while boat B sails 55 miles west and 40 miles north
Boat A
let the angle boat A made with the vertical be a. This is given as
tan a = 30 / 22
a = arc tan ( 30 / 22 )
a = 53.746 degrees
Boat B
let the angle boat B made with the vertical be b. This is given as
tan b = 55 / 40
b = arc tan ( 55 / 40 )
b = 53.973 degrees
Comparing angle a and angle b shows that angle a is lesser hence boat A is the boat that sailed in the direction closest to the north
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my aunt's food budget is R 3500 . She save 1/5 of her budget. How much money did she save?
The money she saved is 700.
What are fractions?Simply put, a fraction shows us how many pieces of a whole we have. The slash that is printed between the two numbers indicates that the numbers are a fraction. We have two numbers: the numerator at the top and the denominator at the bottom. The number is represented mathematically as a quotient, where the numerator and denominator are split.Given:
Aunt's food budget = 3500
Fraction of the budget she saved = 1/5
So, the total money she saved = 1/5 of the food budget
= 1/5 × 3500
= 700
Therefore, the money she saved is 700.
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Suppose that the relation S is defined as follows.
s={(3, 0), (1, 2), (4, -1), (3, 9)}
Give the domain and range of S.
Write your answers using set notation.
The most appropriate choice for relation, domain and range will be given by-
Domain of S = {3, 1, 4}
Range of S = {0 , 2, -1, 9}
What is relation, domain and range?
A relation over set A and B is the subset of the cartesian product A x B.
Domain of a relation is the set of values for which the relation is defined.
Range is the set of solution obtained on putting the values of domain.
The relation S is defined as follows
S = {(3, 0), (1, 2), (4, -1), (3, 9)}
Now the set of values for which the relation is defined is the domain of the relation
For each ordered pair, the first number gives the values to be put in S. So the first number of every ordered pair is the domain.
So domain of S = {3, 1, 4}
Now, the second number gives the solution after putting the numbers in S.
So the second number of every ordered pair represents the range.
So, range of S = {0 , 2, -1, 9}
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Pls answer also
Indicate which property is illustrated in Step 2.
Distributive property is illustrated in Step 2.
What is a distributive property ?The distributive law, which states that in elementary algebra, equality is always true, is generalized by the distributive principle of binary operations.A, B, and C are the operands in the formula for the distributive property, which is written as a (b + c) = (a b) + (a c). Here, each phrase included in a bracket multiplies the number outside of it, and the results are added.According to the associative property, any three terms in an expression can be combined together to solve it. The arrangement of the numbers will never alter the outcome of their computation. For addition and multiplication, the associative property holds true.To learn more about : Distributive law
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Julie is solving the equation 3x² + 5x + 15 = 0 and notices that the discriminant b^2 - 4ac has a value of -155. This
tells her that the equation has
A one real roots.
B one imaginary root.
C two real roots.
D two imaginary roots
Answer: i think b
Step-by-step explanation:
Conscider this absolute value function.f(x) = (x – 5)How can function fbe written as a piecewise function?
f(x) = lx – 5l
x-5, if x-5 ≥ 0, x ≥5
-(x-5) = -x + 5 if x-5<0, x < 5
You ask a deli clerk for x pounds of ham and x pounds of cheese. You end up getting 4 extra ounces of ham and
3 fewer ounces of cheese. The ham costs $6.24 per pound, and the cheese costs $4.80 per pound. You spend twice
as much on ham as you do on cheese. How much do you spend in total?
If the ham costs $6.24 per pound, and the cheese costs $4.80 per pound. You spend twice as much on ham as you do on cheese. The amount spent in total is: $187.20.
Total costLet number of ham bought = x + 4
Let number of cheese bought = x - 3
Price of ham = $6.24
Price of cheese = $4.80
Hence,
Amount spent on ham = (x+4)×6.24
Amount spent on ham =6.24x + 24.96
Amount spent on cheese = (x−3)×4.80
Amount spent on cheese =4.80x−14.40
So,
6.24 x + 24.96 = 2 (4.80 x - 14.40)
6.24x + 24.96 = 9.60 x - 28.80
Combine like terms
24.96 + 28.80 = 9.60 x - 6.24 x
3.36 x = 53.76
Divide both side by 3.36x
x = 53.76/3.36
= 16x
Now let find the total money spent where x is 16
Total amount = 6.24(16) + 24.96+ 4.80(16) - 14.40
Total amount = $187.20
Therefore the amount of $187.20 was spent in total.
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Correct each of the following errors by circling the error, describing what is wrong, entering what should be there instead, and entering the correct answer.-the equation is in the photo
As given by the question
There are given that expression:
[tex]4a^2\times3a^5[/tex]Now,
First, multiply the numbers:
[tex]4a^2\times3a^5=(4\times3)a^{2+5}[/tex]In the given solution of the question, there are perform addition, so this is the first error.
Now,
[tex](4\times3)a^{2+5}=12a^7[/tex]Hence, the correct answer is :
[tex]12a^7[/tex]help plssssss I really need help genuinly
I’m begging help me out with this, please
For given function f(x)=8/(x+2) , g(x)=4x² +2 then evaluation of the composition of function (fog)(-1) =1.
As given in the question,
Given function:
f(x) = 8 / (x+2)
g(x) = 4x² +2
Evaluation of the composition of function f(x) and g(x) we get,
(fog)(x)
= f(g(x))
Substitute g(x) = 4x² + 2
= f(4x² +2)
= 8/(4x² +2+2)
= 8/(4x²+4)
= 2/(x²+1)
Substitute x =-1 in the above function
(fog)(-1) = 2/ ((-1)² +1)
= 2/ 2
=1
Therefore, for given function f(x) = 8/ (x+2) , g(x) = 4x² +2 then evaluation of the composition of function (fog)(-1) =1.
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If an object is shot upward with an initial velocity, vo, in feet per second (ft/s), the velocity, v, in ft/s is given by the
formula
v = vo -32t, where t is time in seconds. Find the initial velocity of an object if the velocity after 4 seconds is 41 ft/s.
-
Which set of ordered pairs does not represent a function?O {(2,9), (2,-5),(-6,3), (4, -7)}O {(-7,5), (3,9), (0, 1), (6,5)}O {(0,7), (-5,3), (-9, -1), (1,7)}o {(-1,-8), (2,8), (0,6), (-6, -1)}Submit Answer
{(2,9), (2,-5),(-6,3), (4, -7)} this pair doesn't represent a function
A mathematical function is a relationship that is established between two sets, through which each element of the first set is assigned a single element of the second set or none at all. The initial set or starting set is also called the domain; the final set or arrival set is called the rank.
Since in this set two elements of the range are associated with the same element of the domain [(2,9) and (2,-5)], we can conclude that it is not a function
Whats the solution to this formula?Tan^-1 ( 7 / 420) =
Okay, here we have this:
Considering the provided expression, we are going to solve it, so we obtain the following:
[tex]\begin{gathered} tan^{-1}(\frac{7}{420}) \\ =arctan(\frac{7}{420}) \\ =arctan(\frac{1}{60}) \\ =0.95° \end{gathered}[/tex]Finally we obtain that the expression is equal to 0.95°.
Based on the information below, what are the values of x and y of the solution to the system of equations used to
create the information?
38
141-14 |Ax|- 2141-
26
x = -5, y = 2
x = -0.2, y = 0.5
x=0.5, y = -0.2
x = 2, y = -5
38
8 26
The values of x and y of the solution to the system of equations are 2 and -5, respectively.
We are given three matrices. The matrices are A, Ax, and Ay.
The determinant of the matrix A is [(4*-2)-(-6*8)] = 40.
The determinant of the matrix Ax is [(38*-2)-(-6*26)] = 80.
The determinant of the matrix Ay is [(4*26)-(38*8)] = -200.
We need to find the values of x and y of the solution to the system of equations.
The value of x is |Ax|/|A| = 80/40 = 2.
Hence, the value of "x" is 2.
The value of y is |Ay|/|A| = -200/40 = -5.
Hence, the value of "y" is -5.
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A submarine was situated 800800 feet below sea level.
If it ascends 275275 feet, what is its new position relative to the sea level?
If a submarine was situated 800 feet below sea level. If it ascends 275 feet, its new position relative to the sea level is: -525 feet.
New position relative to the sea levelGiven :
Initial position of the submarine = 800ft below sea level
Ascending =275ft.
Hence, the New position relative to the sea level is calculated as:
New position relative to the sea level = (-800+ 275)
New position relative to the sea level = - 525 feet
Therefore the new position is: -525 feet.
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Write the sentence as an inequality.
A number r is no less than -1.5 and fewer than 9.5
Inequality:
Answer:
-1.5 ≤ r < 9.5
Step-by-step explanation:
All you have to do is just insert the numbers
we use ≤ as it says in the question "no less"
I need help with this practice problem I will send an additional pic that goes along with this, it’s a graph, use the graph to answer
It is given that,
[tex]\begin{gathered} a^-=\langle-3,-5\rangle \\ b^-=\langle1,4\rangle \end{gathered}[/tex]By using parallelogram method,
[tex]a^-+b^-=\langle-2,-1\rangle[/tex]The graph is as shown below:
Scatter Graphs
The best description of a scatter graph does the following:
“tells the story” of the graph from left to right giving specific values and dates for the first data point, the last data point, any relevant high points and low points
explains the overall trend seen on the graph
includes at least one relevant calculation (absolute change, percent change, ratio, etc) to better describe the data, the trends, or changes in the data
ends with some meaningful conclusion or “take away”
uses terminology correctly
1. Write a thorough description of this scatter graph using the guidelines above. [3 pts]
A specific type of graphic or mathematical diagram known as a "scatter plot" employs Cartesian coordinates to display values for typically two variables for a group of data.
A scatter graph, scatter chart, scattergram, or scatter diagram are other names for it.
If the points are color-, shape-, or size-coded, a second variable can be displayed. Each point's location on the horizontal axis is determined by the value of one variable, while its location on the vertical axis is determined by the value of the other. The data is shown as a series of dots.A scatter plot can be used when both continuous variables are independent of one another or when one continuous variable is in the researcher's control and the other one depends on it.The scatter graph can be represented by the line of best fit which is calculated by taking the average of all the x -coordinates and the y-coordinates.
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Tell if each pair of triangles are either 1. Similar By SSS similarity 2.Similar by AA similarity3.Similar by SAS similarity 4.not similar Pls label the triangle also so it’s easy to tell which one you are talk about thank you
We have the following:
1. Similar By SSS similarity
4/2= 2
7.3.5 = 2
6/3 = 2
2. Similar by AA similarity, same angles, 90°, 70° and 50°
3. Similar by SAS similarity
, same angles and related sides.::
4/2 = 2
6/3 = 2
4. Similar by SAS similarity, same angles and related sides:
12/6 = 2
8/4 = 2
The number f of miles a helicopter is from its destination x minutes after takeoff is given by f(x)=60−1.5x. The number f of miles a commercial jet is from its destination x minutes after takeoff is shown in the graph below.
The distance of each flight is 60 miles and the time taken is 40 minutes.
Distance is the total path covered by an object or species in a particular time period.
At x = 0 minutes after takeoff,
f(x)=60−1.5x (given)
= 60-1.5*0 (at 0 minutes)
= 60 miles (distance between the helicopter and destination)
So, the distance of the flight is 60 miles.
When the helicopter reaches the destination, distance left is 0 miles
Thus, f(x) = 0 in x minutes.
Putting the above data in the equation, we get
0 = 60 - 1.5x
1.5x = 60 (bringing unlike terms on different sides)
x = 60/1.5
x = 40 minutes
Therefore, the distance of each flight is 60 miles and the time taken is 40 minutes.
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What are the coordinates of the vertices of the image triangle after a 90 clockwise rotation about the origin? :
A'(1, 3) B'(-3, 4) C'(-2,-3)
A'(3, 1) B'(4,-3) C'(-3,-2)
A'(3,-1) B'(4, 3) C'(-3, 2)
A'(1,-3) B'(-3,-4) C'(-2, 3)
A'(-3, 1) B'(-4,-3) C'(3,-2)
Before carrying out rotation transformation, the coordinates of the vertices of the pre-image are;
A (3, -6)
B(1, 2)
C (7, -1).
What is the effect of clockwise rotation transformation?We are given the coordinates of the transformed image as:
A'(6, 3),
B'(–2, 1),
C'(1, 7).
We need to find the coordinates of the pre-image A, B and C.
The rule for rotation of 90° about the origin is (x,y) ---> (-y,x).
But we need to find the coordinates of the vertices of the pre-image.
So, we need to apply rule (-y,x) ---->(x,y).
Applying the 90 degrees clockwise rotation rule,
A'(6, 3) -----> A (3, -6)
B'(–2, 1) -----> B(1, 2)
C'(1,7) -----> C (7, -1).
Therefore, coordinates of the vertices of the pre-image are
A (3, -6)
B(1, 2)
C (7, -1).
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Complete question is;
After a rotation of 90° about the origin, the coordinates of the vertices of the image of a triangle are A'(6, 3), B'(–2, 1), and C'(1, 7). What are the coordinates of the vertices of the pre-image?
Answer the following:
a) 3 x √25 =
b) √(2 x 50)
=???
After evaluating, we get
3 *√25 = 15√(2 * 50) = 10In the given question, we are given two expressions that include numerical in Roots. We have to calculate their values for each.
These are examples of Products. Product is when two numbers or terms are multiplied together.
The first expression is represented by:
=> 3 *√25, Calculating this expression we get
=> 3 * 5
=> 15
The second expression is represented by:
=> √(2 * 50), calculating this expression we get
=> √(100)
=> 10
Hence, after calculating both A. and B. expressions we get values 15, and 10 respectively
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The ratio of the number of miles run to the number of miles biked is equivalent for each row in the table
When the ratio of the number of miles run to the number of miles biked is equivalent for each row in the table, the value for A is C. 2 3/4.
How to illustrate the information?It should be noted that based on the information, the table has been given and the appropriate figures have been put into it.
The constant rate will be:
7 / 3 1/2 = 2
Now we can then write the relationship and this is illustrated as:
B = 2R
where B is the distance biked
R = the distance that's run.
We want to find the missing value of A. This is illustrated as:
5 1/2 = 2 × A
2A = 5 1/2
A = 2 3/4
Therefore, based on the information given, the correct option is C.
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The ratio of the number of miles run to the number of miles biked is equivalent for each row in the table.
Complete the table for A
A 2 1/4
B 2 2/4
C 2 3/4
D 3 3/4