Answer:
Step-by-step explanation:
k = 0.2
On Mrs. Sean's desk,there are pink and yellowmarkers. The ratio of pinkmarkers to total markersis 1:3. If there are 16yellow markers, then howmany markers are pink?
We know that the ratio of pink markers to total markers is 1:3.
This means that for every 3 markers, one of them is pink. The other 2 will be yellow markers.
We can write that the ratio of pink markers to yellow markers is 1:2, based on the last sentence. This means that if we have N yellow markers, we will have N/2 pink markers.
Then, if we have 16 yellow markers, then we will have 16/2=8 pink markers.
The following data are the ACT score of all student in the history class
The frequency means how many times specific data shows up in a set of values.
Score Frequency
1-6 2
7-12 4
13-18 5
...
And so on.
CAN SOMEONE HELP WITH THIS QUESTION?✨
Answer:
t = 0: 372t = 4 hours: 24,382,480Step-by-step explanation:
You want the initial population and the population after 4 hours if its doubling time is 15 minutes, and the population is 60,000 after 110 minutes.
EquationWe like to use the numbers in the problem when writing the exponential equation. Here, we are given a doubling time and a population that is ...
(minutes, population) = (110, 60000)
We can put these numbers in the form ...
p(t) = (value at t1) · (growth factor)^((t -t1)/(growth period))
where the growth factor (2) is applicable over the growth period (15 minutes).
This makes our equation ...
p(t) = 60000(2^((t-110)/15))
ValuesWe want to find p(0) and p(240). (240 is the number of minutes in 4 hours). The attachment shows the calculations.
The population at t=0 was about 372.
The population after 4 hours will be 24,382,480.
__
Additional comment
A lot of times, you'll see this rewritten as an exponential equation with 'e' as the base. Here, that would be ...
p(t) = 372·e^(0.0452098t)
where 372 = p(0) = 60000·2^(-110/15), and 0.0452098 ≈ ln(2)/15
These rounded numbers don't give the problem statement values exactly:
p(110) = 53743, not 60000, for example. You would get a population of 60000 after 112.4 minutes (approximately).
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The monthly mortgage loan payment on the Flynn's home is $609. Additionally, they pay $1,080 in annual real estate taxes and $799 per year in homeowner's insurance.
What is the total amount of their monthly payment?
Vector vector v equals vector RS has points R(−2, 12) and S(−7, 6). What are the magnitude and direction of vector RS question mark Round the answers to the thousandths place.
Take into account that vector v can be written as follow:
[tex]\vec{v}=(x-x_o)\hat{i}+(y-y_o)\hat{j}[/tex]where (x,y) and (xo,yo) are two points on the vector.
In this case, we can use (xo,yo) = R(-2,12) and (x,y) = S(-7,6). By replacing these values into the expression for vector v, we obtain:
[tex]\begin{gathered} \vec{v}=(-7-(-2))\hat{i}+(6-12)\hat{j} \\ \vec{v}=-5\hat{i}-6\hat{j} \end{gathered}[/tex]Now, consider that the magnitude of v is the square root of the sum of the squares of the components. Then, we have for the magnitud of v:
[tex]v=\sqrt[]{(-5)^2+(-6)^2}=\sqrt[]{25+36}=\sqrt[]{61}\approx7.810[/tex]Hence, the magnitude of v is approximately 7.810.
Now, consider that the tangent of the angle of the direction of the vector is equal to the quotient between the y component over the x component of the vector:
[tex]\begin{gathered} \tan \theta=\frac{-6}{-5} \\ \theta=\tan ^{-1}(\frac{-6}{-5})\approx230.194 \end{gathered}[/tex]Hence, the direction of vector v is approximately 230.194 degrees.
-3x^2-24x+7=0 is written in the form (x-p)^2=q
[tex] ({x}^{2} + 8x + 16) \\ bring \: out \: the \: x \: and \: ivide \: the \: 8 \: by \: 2[/tex]
HELP ASAP
Solve 21 ≤ −4z − 21.
z ≤ −10.5
z ≥ −10.5
z ≤ 0
z ≥ 0
[tex]21 + 21 \leqslant - 4z \\ - 4z \geqslant 42 \\ \frac{ - 4z}{ - 4} \geqslant \frac{42}{ - 4} \\ z \leqslant - 10.5[/tex]
ATTACHED IS THE SOLUTION
BE AWARE THE SIGNS <> ONLY CHANGE SIGN WHEN YOU MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER.
A relationship between two expressions or values that are not equal to each other is called 'inequality. Z≤ -10.5 is the solution for inequality 21 ≤ −4z − 21.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
The given inequality is twenty one lesser or equal to minus four z minus twenty one.
21 ≤ −4z − 21.
We need to solve for z
Let us add twenty one on both sides
21+21≤ −4z − 21+21
42≤ −4z
Divide both sides by 4
10.5≤ -Z
-10.5≥Z
Z≤ -10.5
Hence Z≤ -10.5 is the solution for inequality 21 ≤ −4z − 21.
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What is an equivalent expression to 20x - 45y
Equivalent linear expressions are expressions that have the same value. That is, if you have two linear expressions that are equivalent to one another, and you plug the same value in for the variable in each of them, you will get the same result in each of them.
In the case of this question, the equaivalent expression can be gotten by factorizing the expression
[tex]undefined[/tex]3 out of 20 cars passing through an intersection did not fully stop, what is the probability that a car arriving at this intersection will not fully stop
Step 1: State the given in the question
Given that 3 out 20 cars passing through an intersection did not fully stop
Step 2: State what to be determined
We are to determine the probability that a car arriving at this intersection that will not fully stop
Step 3: State the formula for finding probability
The formula for finding the probability of an en event, E, from a sample S, is the ratio of the number of elements of event E to the total number of elements in the sample S.
This can be represented mathematically as
[tex]\begin{gathered} P(E)=\frac{n(E)}{n(S)} \\ \text{Where} \\ P(E)=\text{Probability of an event E occuring} \\ n(E)=\text{Number of element in event E} \\ n(S)=\text{Total number of elements in the sample} \end{gathered}[/tex]Step 4: Use the formula to solve the probability
If the event E is cars passing through an intersection did not fully stop. Then, the number of elements in the event E is given as 3. That is:
[tex]n(E)=3[/tex]The sample is the total number of cars, which is given as 20. This means that
[tex]n(S)=20[/tex]Therefore, the probability of the event occuring would be P(E). This is as calculated below:
[tex]\begin{gathered} P(E)=\frac{n(E)}{n(S)} \\ n(E)=3 \\ n(S)=20 \\ P(E)=\frac{3}{20} \\ P(E)=0.15 \end{gathered}[/tex]Hence, the probability that a car arriving at this intersection will not fully stop is 3/20 or 0.15
diagram 10 shows a straight line PQ with point P(-4,9) and Q(12,1).
We have a line defined by two points, P(-4,9) and Q(12,1).
Knowing two points of the line, we can calculate the slope with the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this case, the slope will be:
[tex]\begin{gathered} m=\frac{y_Q-y_P}{x_Q-x_P} \\ m=\frac{1-9}{12-(-4)}=\frac{-8}{12+4}=-\frac{8}{16}=-\frac{1}{2} \end{gathered}[/tex]With the slope and one point we can express the equation in slope-point form:
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-y_Q=m(x-x_Q) \\ y-1=-\frac{1}{2}(x-12) \\ y=-\frac{1}{2}x+\frac{12\cdot1}{2}+1 \\ y=-\frac{1}{2}x+6+1 \\ y=-\frac{1}{2}x+7 \end{gathered}[/tex]The x-intercept is the value of x that makes the function f(x) become 0.
In this case, we have to find x so that y = 0.
We can replace y in the equation and calculate x as:
[tex]\begin{gathered} y=0 \\ -\frac{1}{2}x+7=0 \\ -\frac{1}{2}x=-7 \\ x=-7\cdot(-2) \\ x=14 \end{gathered}[/tex]Then, for the x-intercept is x = 14.
Answer:
a) The equation of the line is y = (-1/2)*x+7
b) The x-intercept is x = 14.
Given that F( x) = x + 2, evaluate F(2)
Answer:
f(2) = 4
Step-by-step explanation:
Hello!
We can find f(2) by substituting 2 for x in the equation.
Evaluate f(2)f(x) = x + 2f(2) = 2 + 2f(2) = 4The value of f(2) is 4.
Use the given values to write an equation that relates x and y.
We are given that "x" and "y" vary inversely. This means that the variables follow the next relationship:
[tex]y=\frac{k}{x}[/tex]Where "k" is a constant to be determined. To determine "k" we will use the given values:
[tex]\begin{gathered} x=3 \\ y=6 \end{gathered}[/tex]Now, we plug in the values:
[tex]6=\frac{k}{3}[/tex]Now, we solve for "k" by multiplying both sides by 3:
[tex]\begin{gathered} 6\times3=\frac{k}{3}\times3 \\ \\ 18=k \end{gathered}[/tex]Therefore, the value of "k" is 18. Now, we substitute in the relationship:
[tex]y=\frac{18}{x}[/tex]And thus we get the equation.
In the group of ordered pairs shown, the x-values are inputs and the y-values are outputs. Select all the statements that are true.
(2, 4), (6, 3), (5, 4), (7, 3), (8, 2)
A. There is only one input for every output.
B. There is only one output for every input.
C. There is more than one output for some inputs.
D. There is more than one input for some outputs.
E. The group of ordered pairs represents a function.
Since in this group of ordered pairs shown above, the x-values are inputs and the y-values are outputs, all the statements that are true include the following:
A. There is only one input for every output.
B. There is only one output for every input.
What is an ordered pair?An ordered pair can be defined as a pair of two (2) elements or points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate or x-axis (abscissa) and the y-coordinate or y-axis (ordinate) on the coordinate plane of any graph.
Generally speaking, the values on the x-coordinate or x-axis (abscissa) of any graph represents all of the input values while the values on the y-coordinate or y-axis (ordinate) of any graph represents all of the output values.
In this context, we can reasonably and logically deduce that there is a unique input for every output and a unique output for every input.
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is set of even number closed under operation of addition ?
Answer:
Yes
Explanation:
A set S is said to be closed under addition if:
For a, b in S, a+b is in S.
If we add two even numbers, the result will always be an even number.
Therefore, the set of even number is closed under the operation of addition
Jaylen's beta fish holds 4 1/2 gallons of water. It takes him 1 7/8 minutes to fill. What is the flow rate of the water in gallons per minute? show your work.
Let's begin by listing out the information given to us:
Jaylen's beta volume = 4 1/2 gallons = 4.5 gal
Time taken = 1 7/8 minutes = 1.785 min
[tex]Flowrate=\frac{volume}{time\text{ taken}}=\frac{4.5}{1.875}=2.4\text{ gal/min}[/tex]Flow rate = volume / Time taken = 4.5 / 1.875 = 2.4 gal/min
True or false?
Raising prices is the quickest way to resolve excess demand.
Answer:
this is true
Step-by-step explanation:
The formula for the volume of a cylinder is V=²2h. The cylinder to the right has an exact volume of 480 cubic meters. Find its height.
The height of the cylinder is
Help me solve this View an example Get more help.
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(Simplify your answer.)
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The height of cylinder when volume of 480 cubic meters is 480/r^2.
What is volume?Volume serves as a measure for an object's storage capacity. For instance, a cup's volume is said to be 100 ml if it can hold 100 ml of water when filled to the brim. The amount of space a three-dimensional object occupies is another way to define volume.
A solid's volume can be calculated by counting how many unit cubes it contains, such as in the case of a cube or cuboid. The best way to understand volume is to think of it as the area surrounded or occupied by any solid object or object with three dimensions. This can be seen by performing the following easy exercise at home:
volume of cylinder V is = πr²h
where, r = radius of cylinder
h = height of cylinder
V = 480π cubic meters
Now, calculate its height in terms of cylinder radius using the volume of cylinder formula:
V = πr²h
480π = πr²h
h = 480π/ πr²2
h = 480/r²
Therefore, The height of cylinder when volume of 480π is 480/r².
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what is the derivative of sqrt(9x^2-1)
Answer:
900
Step-by-step explanation:
because I know answer
Mrs. long bought 4 types of fruits at the market. she bought 2 cantaloupes that weighed 2.3 pounds each 6 peaches that weighed a total of 1.7 pounds 4 apples that weighed a total of 1.25 pounds and 3 pounds and 3 pounds of grapes. what was the total weigh of the four fruits she bought?
Mrs. long bought 4 types of fruits at the market:
- 2 cantaloupes that weighed 2.3 pounds each:
that is, a total of 2.3x2 = 4.6
- 6 peaches that weighed a total of 1.7 pounds.
- 4 apples that weighed a total of 1.25 pounds.
- and 3 pounds of grapes.
The total weight of the four fruits is:
4.6 + 1.7 + 1.25 + 3 = 10.55 pounds.
one step equations b+0.25=1.15
You will need to make b the subject of the formula:
This you do by subtracting 0.25 from both sides of the equation:
b + 0.25 = 1.15 becomes:
[tex]\begin{gathered} b+0.25-0.25=1.15-0.25\text{ which turns to become:} \\ b=1.15-0.25 \\ b=0.9 \end{gathered}[/tex]If AB = 10 ft, AC = 14 ft, and BC = 20 ft, what is RS?
O 10 ft
14 ft
20 ft
24 ft
of one hundred and forty two students attending college , 23 are criminal justice majors. if 9 are selected at random, determine the probability each 9 criminal justice major. set up the problem as if it were to be solved but don't solve.
The probablity that first one selected is a criminal justice major is,
[tex]P_1=\frac{23}{142}[/tex]Now, the probablity that second one is a criminal justice major is when selected without replacement,
[tex]P_2=\frac{22}{141}[/tex]Simirally,
[tex]\begin{gathered} P_3=\frac{21}{140} \\ P_4=\frac{20}{139} \\ \ldots.\text{.} \end{gathered}[/tex]Thus, using the multiplication theorem,
[tex]\begin{gathered} P=P_1\times P_2\times\ldots\ldots.P_9 \\ =\frac{23}{142}\times\frac{22}{141}\times\frac{21}{140}\times\ldots\ldots\ldots\ldots\ldots\frac{15}{134} \end{gathered}[/tex]Thus, the above equation gives the requried probablity.
What is the slope of the equation: 2x + 3y = 12?
Given the equation : 2x + 3y = 12?
We will find the slope of the equation by re-arranging the equation into the standard form of slope intercept formula:
[tex]\begin{gathered} y\text{ = mx + b } \\ where\text{ m represent a slope } \\ \text{ and b represents y -intercept } \end{gathered}[/tex]Re-arranging the equation will be :
[tex]\begin{gathered} 2x+3y=\text{ 12 } \\ 3y\text{ = -2x + 12 } \\ \frac{3y}{3\text{ }}=\text{ }\frac{-2x\text{ +12}}{3} \\ \therefore\text{ y = }\frac{-2}{3}x\text{ +4 } \end{gathered}[/tex]Therefore the equation will be : y = -2/3x +4 Meaning the slope = -2/3can you draw a quadrilateral with 2 pairs of congruent parallel sides and 4 right angles
ANSWER and EXPLANATION
We want to draw a quadilateral that has 2 pairs of congruent parallel sides and 4 right angles.
There are 2 quadilaterals that fit this description:
A square and a rectangle
The number of legislators has increased approximately linearly from 1138 positions in 2003 to 1222 positions in 2009 . Let n be the number of legislators at t years since 2000. Find an equation of a linear model to describe the data.
The equation of a linear model to describe the data is 14x - y = 26904
To find a linear equation of the provided data,
Let us put the number of legislature on the y axis and the year corresponding at the x axis,
According to provided information,
In year 2003, the number of legislature is 1138.
In year 2009, the number of legislature is 1222.
So here we have two points,
A(2003,1138) and B(2009,1222).
As we have two points now,
We can use the two point form of the line to find the equation of line,
It says if we have two point (a,b) and (c,d), then the equation of line is,
(y-b)/(x-a) = (d-b)/(c-a)
So, our equation of line is with points A and B is,
(y - 1138)/(x-2003) = (1222-1138)/(2009-2003)
(y-1138)/(x-2003) = 14
y - 1138 = 14x - 28042
14x - y = 26904
When,
x = 2000, y = n,
14(2000) - n = 26904
n = 1096.
The Linear Equation is 14x - y = 26904
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The cost of mailing a package is proportional to the weight of the package. The proportional relationship can be represented with the equation c = 0.4w, where c represents the total cost and w represents weight in ounces. A graph for the equation is shown.
graph with x axis labeled weight in ounces and y axis labeled cost in dollars, with a line from 0 comma 0 going through 2 comma 0.8
Which of the following statements is true about the graph shown?
The graph is incorrect and the line should go through the point (0.4, 1).
The equation c = 0.4w is correctly represented by the graph.
The x-axis and y-axis are labeled incorrectly.
The graph does not show a proportional relationship.
The statement which is true about the graph shown is that: B. The equation c = 0.4w is correctly represented by the graph.
How to determine the equation of a proportional relationship?Mathematically, a proportional relationship can be modeled by the following linear equation:
y = kx
Where:
y and x are the variables.k represents the constant of proportionality.Next, we would determine the constant of proportionality (k) for this graph:
k = y/x
k = 0.8/2
k = 0.4.
In this context, the proportional relationship which models the cost of mailing a package to the weight of the package is given by this linear equation:
c = 0.4w
where:
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Answer:
Step-by-step explanation:
The statement which is true about the graph shown is that: B. The equation c = 0.4w is correctly represented by the graph.
How to determine the equation of a proportional relationship?
Mathematically, a proportional relationship can be modeled by the following linear equation:
y = kx
Where:
y and x are the variables.
k represents the constant of proportionality.
Next, we would determine the constant of proportionality (k) for this graph:
k = y/x
k = 0.8/2
k = 0.4.
In this context, the proportional relationship which models the cost of mailing a package to the weight of the package is given by this linear equation:
c = 0.4w
where:
c is the total cost.
w is weight in ounces.
At Everton Middle School, there are 7 students who ride the bus to school for every 4 students who do not ride the bus.
The number of people who ride the bus is 70 students.
How to calculate the value?From the information, at the school, there are 7 students who ride the bus to school for every 4 students who do not ride the bus.
Therefore, the number of people who ride the bus if there are 40 people who do not take the bus will be represented by x.
This will be illustrated as:
4/7 = 40/x
Cross multiply
4x = 40 × 7
4x = 280
Divide
x = 280/4
x = 70
Therefore there are 70 students.
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At Everton Middle School, there are 7 students who ride the bus to school for every 4 students who do not ride the bus. How many people ride the bus of there are 40 people who do not take the bus?
Given a pair of points on each line. use the slope formula to determine whether AB and CD are para el perpendicular, or neither. GH: G(14, 13) and H(-11,0) RS: R(-3, 7) and S(-4,-5)
1) Picking points G( 14,13) , H (-11, 0) and R(-3,7) , S(-4,-5) let's find their slopes using the slope formula
And R(-3,7) , S(-4,-5)
Since the condition to be parallel is share the same slope, and to be perpendicular one line must have the reciprocal and opposite slope in comparison to the first one. We can state that neither that line is parallel nor perpendicular.
3) So the answer is GH is not parallel nor perpendicular.
A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 42 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If one shipment of 3000 aspirin tablets actually has a 6% rate of defects, what is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?
The probability that the entire cargo will be approved is 0.078 = 7.8% using the Binomial probability distribution, while 92.2% will be refused. As a result, many will be rejected.
By Binomial probability distribution,
P(X = x) = [tex]C_{n,x}[/tex] × [tex]p^{x}[/tex] × [tex](1-p)^{n-x}[/tex]
[tex]C_{n,x}[/tex] , various combinations of x items from a collection of n elements given by,
[tex]C_{n,x}[/tex] = n! ÷ x! (n - x)!
n=42, as 42 tablets are tested.
p=0.06 as 6% is defective.
If at most there is 1 defective piece then it will be accepted.
Therefore,
P(X ≤ 1) = P(X = 0) + P(X = 1)
P(X = x) = [tex]C_{n,x}[/tex] × [tex]p^{x}[/tex] × [tex](1-p)^{n-x}[/tex]
P(X = 0) = [tex]C_{42,0}[/tex] × [tex](0.06)^{0}[/tex] × [tex](0.94)^{42}[/tex] = 0.074
P(X = 1) = [tex]C_{42,1}[/tex] × [tex](0.06)^{1}[/tex] × [tex](0.94)^{41}[/tex] = 0.0047
Thus,
P(X ≤ 1) = P(X = 0) + P(X = 1)
P(X ≤ 1) = 0.074 + 0.0047
P(X ≤ 1) = 0.0787
The probability that the entire shipment will be approved is 0.078 = 7.8%, while 92.2% will be refused.
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Sport
Soccer
Jogging
Walking
Skiing
Football
Total
72
Hrs
5
20
10
5
10
50
Calculate the portion for soccer in degrees.
[?]°
5 hrs.
Total Sport Hours
Based on the time spent for the soccer game, the calculated degree of the soccer portion is found to be 72°.
How to find the soccer portion of the pie chart?
In mathematics, the complete pie chart is 360° and to calculate the soccer portion using standard formula which states that the division of the total hours spent on soccer and total sports hours multiply with 360°.
According to the question, the given data states that the pie chart is 360° which represents the total sports hours as 50 hours.
Therefore, the soccer portion is:
= Total hours spent on walking / Total sports hours x 360°
= 10 / 50 x 360°
= 72°
Based on the time spent for the soccer game, the calculated degree of the soccer portion is found to be 72°.
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