(a) 2.79 seconds after its release the bag will strike the ground.
(b) At a velocity of 73.28 ft/second it will hit the ground.
What is velocity?
We are given that a balloon, rising vertically with a velocity of 16 feet per second, releases a sandbag at the instant when the balloon is 80 feet above the ground.
Assume the acceleration of the object is a(t) = −32 feet per second.
(a) For finding the time it will take the bag to strike the ground after its release, we will use the following formula;
[tex]s=u t+\frac{1}{2} a t^2[/tex]
Here, s= distance of the balloon above the ground =-80 feet
[tex]$\mathrm{u}=$[/tex] intital velocity =16 feet per second
[tex]$\mathrm{a}=$[/tex]acceleration of the object =-32 feet per second
[tex]$\mathrm{t}=$[/tex] required time
So, [tex]$s=u t+\frac{1}{2} a t^2$[/tex]
[tex]$$\begin{aligned}& -80=(16 \times t)+\left(\frac{1}{2} \times-32 \times t^2\right) \\& -80=16 t-16 t^2 \\& 16 t^2-16 t-80=0 \\& t^2-t-5=0\end{aligned}$$[/tex]
Now, we will use the quadratic D formula for finding the value of t, i.e;
[tex]t=\frac{-b \pm \sqrt{D}}{2 a}[/tex]
Here, a=1, b=-1, and c=-5
Also, [tex]$\mathrm{D}=b^2-4 a c=(-1)^2-(4 \times 1 \times-5)=21$[/tex]
So, [tex]$t=\frac{-(-1) \pm \sqrt{21}}{2(1)}$[/tex]
[tex]t=\frac{1 \pm \sqrt{21}}{2}[/tex]
We will neglect the negative value of t as time can't be negative, so;
[tex]t=\frac{1+\sqrt{21}}{2}=2.79 \approx 3 \text { seconds. }[/tex]
Hence, after 3 seconds of its release, the bag will strike the ground.
(b) For finding the velocity at which it hit the ground, we will use the formula;
v=u+a t
Here, v= final velocity
So,[tex]$v=16+(-32 \times 2.79)$[/tex]
v=16-89.28=-73.28 feet per second.
Hence, the bag will hit the ground at a velocity of [tex]$-73.28 \mathrm{ft} / \mathrm{second}$[/tex].
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Critical Thinking Consider a family with three children . Assume the prob- ability that one child is a boy is 0.5 and the probability that one child is a girl is also 0.5 and that the events "boy" and "girl" are independent . ( a ) List the equally likely events for the gender of the three children , from oldest to youngest (b) What is the probability that all three children are male ? Notice that the complement of the event " all three children are male " is "at least one of the children is female ." Use this information to compute the probability that at least one child is female .
The equally likely events are
Boy, Boy, BoyBoy, Boy, GirlBoy, Girl, BoyBoy, Girl, GirlGirl, Boy, BoyGirl, Boy, GirlGirl, Girl, BoyGirl, Girl, GirlThe probability that all three children are male
0.875.
the probability that at least one child is female.
0.875.
What are the probabilities?(a) The equally likely events for the gender of the three children, from oldest to youngest, are:
Boy, Boy, BoyBoy, Boy, GirlBoy, Girl, BoyBoy, Girl, GirlGirl, Boy, BoyGirl, Boy, GirlGirl, Girl, BoyGirl, Girl, Girl(b) The probability that all three children are male is (0.5)^3 = 0.125.
The probability that at least one child is female is the complement of the event "all three children are male," which means it is 1 - 0.125 = 0.875.
In conclusion, The probability that at least one child is female is 1 - (0.5)^3 = 0.875.
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1. Consider the system described by the differential equation: d3y(t)/dt3 + 4d2y(t)/dt2 + 6dy(t)/dt + 8y(t) = 20u(t)
(i) Find the transfer function of the system.
(ii) Derive a state space representation for the system
2. A single input, single output system has the matrix equations:
x.(t)= [0 1 -3 -4] x(t) +[0 1]u(t) and y(t) = [3 0]x(t)
Determine the transfer function G(s) = Y(s)/U(s)
20 is the system's transfer function. A differential equation is a mathematical formula that includes one or more terms
What is a differential equation's formula?A differential equation is a mathematical formula that includes one or more terms as well as the derivatives of one variable (the dependant variable) with respect to another variable (i.e., independent variable) dy/dx = f (x) In this case, "x" is an independent variable and "y" is a dependent variable. For instance, dy/dx = 5x.The Laplace transform of the input variable divided by the Laplace transform of the output variable, with initial conditions of zero, is the definition of transfer functions.Explanation:
4 +2 + 6 + 8 = 20.
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A truck cost 60,000 it depreciate in value 4000 per year write a linear model in the form VT equals MT plus b
When the truck cost 60,000 it depreciate in value 4000 per year, the model is 60000 - 4000x
How to calculate the equation?Equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario
In this case, the truck cost 60,000 it depreciate in value 4000 per year.
Let the number of years be x.
The linear model in the representation will be:
60000 - 4000(x)
= 60000 - 4000x
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Which expressions are equivalent to 8(-10x+ 3.5y - 7)? Select two options.
-80x+ 24.5y-56
-80x+28y-56
80x+28y+56
4(-20x+7y-14)
-4(-20x+ 7y-14
Answer:
-80x + 28y -56
4(-20x + 7y -14)
Step-by-step explanation:
The first answer is distributing the 8 through the whole expression. The second answer is when you factor out a 4.
Given that ABCD is a rectangle, where EC=7 x-3 and AE=4 x+8 . Find DE.
The length of side DE of the rectangle ABCD is 11/5 units .
What is rectangle?
In euclidean plane geometry, a rectangle may be a quadrilateral with four right angles. It also can be outlined as: an angular quadrilateral, since angular means all of its angles square measure equal; or a tetragon containing a right angle.
Main body:
given:
AE = 4x+8 -----------(1)
CE = 7x - 3 -----------(2)
as we know diagonal of rectangle bisect each other , which means AE = CE
using the property , we get
4x+ 8 = 7x -3
taking like terms to one side,
7x - 4x = 8+3
3x = 11
x = 11/3
put the value of x in any equation,
AE = 4(11/3) +8
AE = 44/3 +24/3
AE = 68/3
as AE = DE
Hence the value of DE is 68/3 units.
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b. [4 pts] Factor f(x). Show all your work. (Hint: You can use the fact that if f(a)=0, then the f(x) must have (x-a) as a factor.
a. [5 pts] How much would he have to invest initially to have the necessary money in 4 years? Round your answer to the nearest whole dollar
1(a) The value of f(2) in the fuction f(x) = x³+7x²-36 0, 1 (b) The factors of the function f(x) = (x-2)(x+3)(x+6) 2 The initial amount that must be invested is $53263.
What is a function?function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
(a) To calculate the f(2), we substitute 2 into the function below.
f(x) = x³+7x²-36f(2) = (2³)+(7×2²)-36f(2) = 8+28-36f(2) = 36-36f(2) = 0(b) To factor f(x), we need to look for the zeros of f(x). The zeros of f(x) are
2, -3, -6Putting them in polynomial form
Facctorizing f(x) = (x-2)(x+3)(x+6)(2) To calculate the amount he would invest initially to have the neccessary amount in 4 years, we use the formula below.
Formula:
A = P(1+R/n)ⁿˣ........................... Equation 1Where:
A = Amount after four years price of the carP = Initial investmentR = Raten = Number of time the rate is compounded per yearx = Number of yearsMake P the subject of the equation
P = A/(1+R/n)ⁿˣ..................Equation 2From the question,
Given:
A = $60000R = 3% = 0.03n = 2x = 4Substitute these values into equation 2
P = 60000/(1+0.03/2)²ˣ⁴P = 60000/(1.015)⁸P = $53263Hence, 1(a) The value of f(2) = 0, 1 (b) The factors of f(x) = (x-2)(x+3)(x+6) 2 The initial amount that must be invested is $53263.
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Which of the following statements best summarizes the pattern of causality captured by the graph above? Check all that apply.O a change in e causes a shift of the budget constraint. O a change in p causes O a change in s. the relationship between s and p is not a causal relationship. O a change in s causes a change in p.
The statements which best summarizes the pattern of causality captured by the graph attached are: A change in E causes a shift of the budget constraint; and, the relationship between S and P is not a causal relationship.
What is causality in linear regression?Causality means that there is a clear cause-effect relationship between two variables. By using a controlled study is the most effective way of establishing causality among variables. In a controlled study, the sample or population is split in two, with both groups being comparable in almost every way. Then, the two groups receive different treatments, and the outcomes of each group are assessed.
Although part of your question is missing, you might be referring to this full question: Which of the following statements best summarizes the pattern of causality captured by the graph above? Check all that apply. (Graph is attached.)
A change in E causes a shift of the budget constraint.A change in P causes a change in S.The relationship between S and P is not a causal relationship.A change in S causes a change in P.Learn more about causality at: https://brainly.com/question/14127087
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. Suppose x is inversely proportional to y. if x is tripled, what happens to y?
Answer:
it also decreased by 3 times.
hope this work out.
Suppose that you were trying to use the Putzer method to exponentiate the matrix A which has eigenvalues dı = 4 and A2 = 6, in that order. ao(t) is always the function et. Choose the correct equation for a1(t) da1О (а) 6a1 + e4t a1(0) = 1 O (b) dt da1 : 4a1 + e4t P (g) da1 a1(0) = 1 O (c) dt -4a1 + ett a1(0) = 0 da1 O (d) dt 4a1 + et a1(0) = 0 da1 O (e) : 6a1 + e4t a1(0) = 0 dt da1 O (f) dt — 4а, + e# a,(0) — 1
In that order. ao(t) is always the function is [tex]$$m_1=A-2 I $$[/tex].
What is function ?
A function is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.
The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets.
given: [tex]$\quad d_1=4 \quad$[/tex] and [tex]$A_2=6$[/tex]
[tex]$$m_0=\Sigma=\left[\begin{array}{cc}1 & 0 \\0 & 1\end{array}\right]$$[/tex]
By putzes method
[tex]$$\text { matrix } m_1=A-N_1 p_0=A-d_1 m_0$$[/tex]
here [tex]$r_1=2, m_0=I$[/tex]
[tex]$$m_1=A-2 I $$[/tex]
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What are the values of x and y that simultaneously satisfy the two linear equations graphed below? HELP PLEASE
Answer:
D
Step-by-step explanation:
x=9 and y=4 is given in the graph, this makes the answer between B and D
Since y=-⅔x+10 and y=x-5, 4=-⅔(9)+10 and 4=9-5
So the answer is D
The unknown in an expression is called the__________________.
-Constant
-Exponent
-Variable
-Coefficient
Pls answer fast thank u!
Answer: The variable
Hope this helps :)
Step-by-step explanation:
Find the absolute extrema if they exist, as well as all values of x where they occur, for the function f(x)=(x²-64)^{1/11} on the domain [-8,9]
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
A. The absolute maximum is , which occurs at x= (Round the absolute maximum to two decimal places as needed. Type an exact answer for the value of x where the maximum occurs. Use a comma to separate answers as needed.)
B. There is no absolute maximum.
The absolute maximum is 1.29, which occurs at x= 9
What is absolute extrema?
An absolute extremum of a perform in an exceedingly given interval is that the purpose at that a most or minimum worth of the perform is obtained. Frequently, the interval given is that the function's domain, and therefore the absolute extremum is that the purpose admire the most or minimum worth of the complete perform.
Main body:
Given =
f(x) = [tex](x^{2} -64)^{1/11[/tex]
f' (x) = derivative of function f(x)
f'(x) = 1/11 . 2x[tex](x^{2} -64)^{-10/11[/tex]
= 2x/11[tex](x^{2} -64)^{-10/11[/tex]
putting f'(x) = 0
2x/11[tex](x^{2} -64)^{-10/11[/tex] = 0
[tex](x^{2} -64)^{-10/11[/tex] = 0
[tex]x^{2} -64[/tex] = 0
x² = 64
x = ±8
We are given interval [-8,9].
Hence, calculating f(x) at -8, 8, 9.
f(-8) = 0
f(8) = 0
f(9) = [tex]17^{1/11[/tex]
= 1.29
Hence, absolute maximum value is 1.29 at x=9.
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please help!!!! need help asap!!!!!
Answer:
third option
Step-by-step explanation:
sinX = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{YZ}{XY}[/tex] = [tex]\frac{3}{\sqrt{34} }[/tex]
tanY = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{XZ}{YZ}[/tex] = [tex]\frac{5}{3}[/tex]
somebody please help!!
Step-by-step explanation:
since AD is an altitude (height) of ABC, the angle at D must be 90° (that is the definition of an altitude or height).
so,
90 = x² + 6x + 18
72 = x² + 6x
0 = x² + 6x - 72
the general solution to such a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = (-6 ± sqrt(6² - 4×1×-72))/(2×1) =
= (-6 ± sqrt(36 + 288))/2 = (-6 ± sqrt(324))/2 =
= (-6 ± 18)/2 = -3 ± 9
x1 = -3 + 9 = 6
x2 = -3 - 9 = -12
so, the 2 solutions are
x = 6
x = -12
The bill at dinner was $58.24 before tax and tip.
There is a 6% sales tax. After the tax, an 18% tip is
added.
What is the total including tax and tip? show answer
Total amount payable including sales tax and tip = $68.12
What is sales tax?A sales tax is a tax levied by a government on the sale of certain goods and services. Generally, laws allow the seller to collect tax funds from the consumer at the point of sale. A use tax is a tax on goods or services paid directly to a governing body by a consumer.
Given:
Bill at dinner was before tax and tip = $58.24
Sales tax = 6%
Tip = 18%
As per the question:
first, we will calculate the amount payable after adding tax.
The amount payable after adding sales tax = bill + 6% sales tax of the bill
The amount payable after adding sales tax = 58.24 + [tex]\frac{6}{100} 58.24[/tex]
Amount payable after adding sales tax = A = $57.73
Now we will calculate the total amount payable after adding the tip.
Total amount payable = A + 18% of A
Total amount payable = $57.73 + 18% of $57.73
Total amount payable = 57.73 + 10.40
Total amount payable including sales tax and tip = $68.12
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Total amount payable including sales tax and tip = $68.12
What is sales tax?A sales tax is a tax levied by a government on the sale of certain goods and services. Generally, laws allow the seller to collect tax funds from the consumer at the point of sale. A use tax is a tax on goods or services paid directly to a governing body by a consumer.
Given:
Bill at dinner was before tax and tip = $58.24
Sales tax = 6%
Tip = 18%
As per the question:
first, we will calculate the amount payable after adding tax.
The amount payable after adding sales tax = bill + 6% sales tax of the bill
The amount payable after adding sales tax = 58.24 +
Amount payable after adding sales tax = A = $57.73
Now we will calculate the total amount payable after adding the tip.
Total amount payable = A + 18% of A
Total amount payable = $57.73 + 18% of $57.73
Total amount payable = 57.73 + 10.40
Total amount payable including sales tax and tip = $68.12
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8 . How can we prove these triangles congruent?
F ASA
G AAS
H SAS
J SSS.
A triangle with } 3congruent angles is called a ______
1. We can prove these triangles are congruent through J. SSS.
2. A triangle with 3 congruent angles is called an equilateral triangle.
What is congruence?If all three corresponding sides are equal and all three corresponding angles are equal in measure, two triangles are said to be congruent. These triangles can be moved, rotated, flipped, and turned to look exactly the same. They coincide if they are repositioned.
SSS rule states that two triangles are congruent if all three sides of one triangle are equivalent to the corresponding three sides of the other triangle.
An equilateral triangle has all three sides and angles equal.
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Grasshopper is 5cm and can jump 10 times its length. How many jumps will it take to get to 9m?
Answer:
18 jumps
Step-by-step explanation:
5*10 = 50cm
50/100 = 0.5m (metre conversion)
9/0.5 = 18
What is the approximate volume of this cylinder? 3,140 cm³ 7,850 cm³ 10,000 cm³ 31,400 cm -20 cm 25 cm
Answer: 28055
Step-by-step explanation:
Melody made a brownie for a potluck. She cut the pan of brownies into equal size pieces. At the end of the potluck, there were 6 brownies left over. Explain how you can find the number of pieces in the whole pan of brownies if Melody told you that 2⁄5 of the
pan was left. Use a drawing to show your work.
We are told that 6 is two-fifths of the brownies. So we can figure it out as such:
[tex]\frac{6}{x} = \frac{2}{5}[/tex]
Cross multiply
6 * 5 = x * 2
30 = 2x
Divide both sides of the equal sign by 2 to get x by itself
[tex]\frac{30}{2} =\frac{2x}{2}[/tex]
15 = x
15/5 = 3. Every third piece is 1/5 of the pan.
Determine each total cost, including a 20% tip,
$103.65
Answer:124.38
Step-by-step explanation:
103.65*.20=20.73 103.65+20.73=124.38
Suppose a 3 X 3 real matrix A has only two (real) distinct eigenvalues. Suppose that tr(A) -2 and det(A) 96. Find the eigenvalues of with their algebraic multiplicities. smaller eigenvalue has mulitiplicity and larger eigenvalue has mulitiplicity
The smaller eigenvalue is -4 with multiplicity 2 and larger eigenvalue is 6 has multiplicity 1
If A is a square matrix of order n x n and v is a non-zero column vector of order n x 1 such that Av = λv , then the scalar (real number) λ is called an eigenvalue of the matrix A that corresponds to the eigenvector v.
According to the question,
We have a 3 x 3 matrix that has only two real distinct eigenvalues
Let two distinct eigen values be a and b
Its given that tr(A) = - 2
Det(A) = 96
If we add all the eigen values of a matrix it gives us trace of this and product of eigen values result to the determinant
Therefore , 2a + b = -2 --------(1)
a²b = 96 --------(2)
Using substitution method for solving these equations
=> b = -2 - 2a
Substituting the value of b in equation (2)
=> a²( -2 -2a) = 96
=> -2a² - 2a³ = 96
=> a²(1 + a) + 48 = 0
=> a³ + a² + 48 =0
Solving the cubic equation
a = -4 , 1.5-3i , 1.5+3i (but eigen values are only real)
therefore , a = -4
b = -2 -2(-4)
=> -2+8
=> 6
hence, the eigen values = -4 and 6
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Match the expression and its value to the value of x that gives the expression its value by filling in the box in the correct column.
Evaluate the expression 4 n-5 r for n=-2 and r=3
(A) 23
(C) 7
(B) -7
(D) -23
The surface area for a rectangular prism with a square base is given the expression 2 s²+4 s h, where s is the side length of the square h is the height of the prism. What is the surface area in square feet rectangular prism when s=4 feet and h=6feet?
Part 1:- The answers are 12, 30, 56, 90
30, 35, 40, 45
2, 3, 4, 5
Part 2:-The correct answer is (D) -23
Part 3:-The surface area for the rectangular prism is 128 square feet.
What is a mathematical expression?
In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
part 1:-
Solving expression 1:-
for x=2
[tex]4 {x}^{2} - 2x = 4 \times {2}^{2} - 2 \times 2[/tex]
=4×4 - 4
=16 - 4
=12
for x=3
[tex]4 {x}^{2} - 2x = 4 \times {3}^{2} - 2 \times 3[/tex]
= 4 × 9 - 6
= 36 - 6
= 30
for x=4
[tex]4 {x}^{2} - 2x = 4 \times {4}^{2} - 2 \times 4[/tex]
= 4 × 16 - 8
= 64 - 8
= 56
for x=5
[tex]4 {x}^{2} - 2x = 4 \times {5}^{2} - 2 \times 5[/tex]
= 4×25 - 10
= 100 - 10
= 90
solving expression 2:-
for x = 2
[tex]5x + 20 = 5 \times 2 + 20[/tex]
= 10 + 20
= 30
for x = 3
[tex]5x + 20 = 5 \times 3+ 20[/tex]
= 15 + 20
= 35
for x = 4
[tex]5x + 20 = 5 \times 4 + 20[/tex]
= 20 + 20
= 40
for x = 5
[tex]5x + 20 = 5 \times 5 + 20[/tex]
= 25 + 20
= 45
solving expression 3:-
for x=2
[tex] \frac{8x}{2} - 3x = \frac{8 \times 2}{2} - 3 \times 2[/tex]
= 8 - 6
= 2
for x=3
[tex] \frac{8x}{2} - 3x = \frac{8 \times 3}{2} - 3 \times 3[/tex]
= 12 - 9
= 3
for x=4
[tex] \frac{8x}{2} - 3x = \frac{8 \times 4}{2} - 3 \times 4[/tex]
= 16 - 12
= 4
for x= 5
[tex] \frac{8x}{2} - 3x = \frac{8 \times 5}{2} - 3 \times 5[/tex]
= 30 - 15
= 15
Hence the answers are, 12, 30, 56, 90
30 35, 40, 45
2, 3, 4, 5
part 2:-
Given,
4n - 5r;
for n=-2 and r=3
4n - 5r = 4 × (-2) - 5 × 3
= -8 - 15
= -23
Hence the answer is (D) -23
Part 3:-
Given,
The surface area for a rectangular prism with a square base is given the expression 2 s²+4 s h
s = 4 feet
h = 6 feet
then,
2 s²+4 s h = 2×4²+4×4×6
= 2×16+96
= 32+96
= 128
Hence the answer is 128 square feet.
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You are dealt one card from a 52-card deck. Find the probability that you are not dealt a card with number from 3 to 8.
Answer: There is a 54% chance that you will not choose one of those cards.
Step-by-step explanation: There are 4 of ever card in a deck.
3, 4, 5, 6, 7, and 8 are 6 different types of cards
6 x 4 = 24
24 divided by 52 ( the total cards ) = .46
So there is a 54% chance that you will not choose one of those cards.
Find an equation of a line with slope m = −25 that contains the point (10,−5). Write your answer in slope-intercept form
Answer:
-25
Step-by-step explanation:
Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t increases.
The curve for the vector equation r(t) = <t, -t, 2t>, is |r(t)| = (√6)t.
Find the curve in the attachment
What is a vector?A vector is a physical quantity that has both magnitude and direction
What is a vector equation?A vector equation is a linear combination of vector quantities
What is a curve?A curve is a path which an object follows.
How to sketch the curve of the given vector?Since we are given the vector equation r(t) = <t, -t, 2t>, to sketch the curve of the vector equation, we need to know the magnitude of the vector.
What is the magnitude of a vector?The magnitude of a vector r = <a, b, c> is |r| = √(a² + b² + c²)
So, to sketch the vector equation, since r(t) = <t, -t, 2t>, comapring bothnequations,
a = t, b = -t and c = 2tSo, the magnitude of r(t) = √(a² + b² + c²)
= √(t² + (-t)² + (2t)²)
= √(t² + t² + 4t²)
= √(6t²)
= (√6)t
Since |r(t)| = (√6)t, we sketch the curve for this equation
Find the curve in the attachment
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The table summarizes results from 975 pedestrian deaths that were caused by automobile accidents.
Driver
Intoxicated? Pedestrian Intoxicated?
Yes No
Yes 48 78
No 241 608
If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was not intoxicated or the driver was intoxicated.
Report the answer as a percent rounded to one decimal place accuracy. You need not enter the "%" symbol.
Therefore, the probability of the first case : 94.5% and second case:9.7%
Define probability.the likelihood that an event will take place. The proportion of feasible outcomes to outcomes in an exhaustive set of equally likely outcomes that result in a particular event. a field of mathematics that focuses on the investigation of probability.
Here,
Thus, the probabilities of following cases comes out to be:
1) The odds that either the pedestrian or the driver weren't are
=>(246+603+83)*100/986
=>(932/986)*100 =94.5%
2) The likelihood that both incidents involved inebriated pedestrians is equal to
=>(305/978)*(304/977)*100 = 9.7%
Therefore, the probability of the first case : 94.5% and second case:9.7%
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"constant of proportionality" between to cost and number of classes is 16. what is the unit rate for dollers per class?
The required unit rate for the dollars per class is 16 dollars per class,
Given that,
The "constant of proportionality" between to cost and the number of classes is 16. The unit rate for dollars per class is to be determined.
proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
Here,
Let, y be the dollars is directly proportional to the x classes,
According to the question,
y = kx
k = 16
y = 16x
Now,
y/x = 16 dollars per class
Thus, the required unit rate for the dollars per class is 16 dollars per class,
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I solved my question
Good now whats the question?
Please help me in this grade 7 percentage question
The number 490 is 72% of the number 680.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that 490 is some percentage of the number 680.
The percentage of 490 to the number 680 will be calculated as,
680 x (x / 100) = 490
x = (490 x 100)/680
x = 72%
Therefore, the number 490 is 72% of the number 680.
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convert 34 in base 5 into base 2
Answer:
34 in base 2 = 10011
Step-by-step explanation:
34 written in base 2 or in binary form is 10011 . 34 written in base 10 or decimal form is 19 .
Given, Convert 34 in base 5 to base 2
Firstly convert base 5 to base 10 .
34(base 5) = [tex]3\times 5 ^1 + 4\times 5^0[/tex]
34(base 5) = 19(base 10)
Convert base 10 to base 2 .
To convert 19 to binary, divide it by 2 repeatedly and note the remainders:
19 ÷ 2 = 9, remainder 1
9 ÷ 2 = 4, remainder 1
4 ÷ 2 = 2, remainder 0
2 ÷ 2 = 1, remainder 0
Reading the remainders from bottom to top including the last 1.
10011.
So, 19 in binary is 10011.
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