In order to calculate the probability of a student from this sample to be a seventh grader, we need to divide the number of seventh graders by the total number of students. This is done below:
[tex]\begin{gathered} P(\text{seventh grader)}=\frac{4}{10+4+6} \\ P(\text{seventh grader)}=\frac{4}{20} \\ P(\text{seventh grader)}=\frac{1}{5} \end{gathered}[/tex]A. The probability of a random selected student being a seventh grader is 1/5.
In order to calculate the probability of the selected student not being a seventh grader, we need to subtract the probability of them being a seven grader from one, because these two events are mutually exclusive. So we have:
[tex]\begin{gathered} P(\text{not seventh grader)}=1-\frac{1}{5} \\ P(\text{not seventh grader)}=\frac{5}{5}-\frac{1}{5} \\ P(\text{not seventh grader)}=\frac{4}{5} \end{gathered}[/tex]B. The probability of a random selected student not being a seventh grader is 4/5.
Which equation has a constant of proportionality equal to 5?Choose 1 answerY = 5xY = 10/5xY = 5/25xY = 1-2x
The constant of proportionality is seen as k in this formula:
[tex]\text{ y = kx}[/tex]All of the choices are already in this form, however, the only expression that shows a constant of proportionality of 5 is y = 5x.
[tex]\text{ y = (}k)(x)\text{ }\rightarrow\text{ y = (5)(x)}[/tex]Therefore, the answer is A.
Supposed that the future price p(t) of a certain item is given by the following exponential function.inthis function, p(t) is measured in dollars and t is the number of year's from today. p(t)= 2500 (1.026)t
Answer:
Initial price of the item = 2500
The function represents growth
The percent by which the price changes each year is 2.6%
Explanation:
The given function is expressed as
P(t) = 2500(1.026)^t
Recall, the exponential growth function is expressed as
P(t) = Po(1 + r)^t
where
Po is the initial value
P(t) is the future value
r is the growth rate
By comparing both functions,
Po = 2500. Thus,
Initial price of the item = 2500
Also,
1 + r = 1.026
Since 1.026 is greater than 1,
The function represents growth
r = 1.026 - 1
r = 0.026
This means that the growth rate is 0.026. We would convert it to percentage by multiplying by 100. It becomes
0.026 x 100 = 2.6%
The percent by which the price changes each year is 2.6%
what is the constant of proportionality of: y= 6.28x
The constant of proportionality is the number that relates two variables. In this case the variables are "x" and "y", we need to find which number multiplies the value of "x" and results in "y". In this case it is "6.28". The constant of proportionality on a linear equation is always the number multiplying x.
The answer is 6.28.
Pleas help me on this problem you have to do both because it is 2 questions for one problem
Given:
The cost price of the deck of cards is $72.78 dollars.
Mark up percent is 5%.
a) To find the amount of mark up:
So, we can write it as,
[tex]\begin{gathered} 5\text{ \% of 72.78=}\frac{5}{100}\times72.78 \\ =\text{ \$}3.639 \end{gathered}[/tex]Thus, the amount of mark-up is $3.64 (rounded to the nearest hundredth).
b) To find the new price:
The new price = Cost price + Amount of mark up
So, we get,
[tex]\begin{gathered} =72.78+3.64 \\ =76.42 \end{gathered}[/tex]Thus, the new price is $76.42.
Let the sample space be S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10). Suppose the outcomes are equally likely. Compute the probability of the event E = 'an odd number less than 9."P(E)=(Type an integer or a decimal. Do not round.)
We have a sample space S = {1, 2, 3, 4, 5, 6, 7, 8 ,9, 10}.
Each outcome of this sample space is equally likely.
We have to compute the probability of the event E = 'an odd number less than 9'.
Then, event E happens when one of this outcomes happens: 1, 3, 5 or 7. That is 4 outcomes out of 10.
As all the outcomes are equally likely, the probability of event E will be the quotient between the number of success outcomes (4) and the number of total outcomes (10):
[tex]P(E)=\frac{4}{10}=0.4[/tex]Answer: the probability of event E is P(E) = 0.4.
A lawn had an area of 12 square ft. If it was width, how long was it?
Given
The lawn of area 12 sq feet. width is 4 feet
Answer
area = l x w
12 = l x 4
l = 12/4 = 3 feet
3+5=5+ 3•5=5•2+(-2)=0TRUE OR FALSE ? ( for all three of them )
Take into account that commutative property is present for addition and multiplication operations, then, you have:
3+5=5+3 TRUE
3·5 = 5·3 TRUE
The inverse addition of a number consists in adding the same numbers but with opposite signs, then, you have:
2 + (-2) = 0 TRUE
Find the circumference of each circle. Use ( pie symbol) as 22/7 Number 10. 1 1/3
ANSWER :
The circumference is 88/21 inches or 4.19 inches
EXPLANATION :
From the problem, we have a circle with a diameter of 1 1/3 in.
Note that the circumference of a circle is :
[tex]C=2\pi r\quad or\quad C=\pi D[/tex]Since we have a diameter, we will use the second formula :
The circumference will be :
[tex]\begin{gathered} C=(\frac{22}{7})(1\frac{1}{3}) \\ C=(\frac{22}{7})(\frac{4}{3}) \\ C=\frac{88}{21}\quad or\quad4.19 \end{gathered}[/tex]Complete each statement about multiplying positive and negative integers using word positive or negative. Then provide an example for each statementA. Positive + PositiveB. positive + negativeC. negative + negative
A) Positive
B) Negative
C) Positive
Explanation:[tex]\begin{gathered} A)\text{ Positive }\times\text{ positive:} \\ +\text{ }\times\text{ + = +} \\ mu\text{ltiplication of same signs gives positive sign} \\ \text{Positive }\times\text{ positive = positive} \\ \text{Example: +5 }\times\text{ +6 = +30} \end{gathered}[/tex][tex]\begin{gathered} B)\text{ Positive }\times\text{ negative:} \\ +\text{ }\times\text{ - = -} \\ m\text{ ultiplication of opposite signs give negative sign} \\ \text{Positive }\times\text{ negative = negative} \\ \text{Example: +3 }\times\text{ -2 = -6} \end{gathered}[/tex][tex]\begin{gathered} C)\text{ Negative }\times\text{ Negative} \\ -\text{ }\times\text{ - = +} \\ mu\text{ltiplication of same signs gives positive sign} \\ \text{Negative }\times\text{ Negative = positive} \\ \text{Example: -7 }\times\text{ -8 = +56} \end{gathered}[/tex]Question 41 ptsThe point C(-2,3) has been transformed to C(2, 3). The transformation is described asO Ry-axisO D₂O r(90,0)O Rx-axis< PreviousNext >
Looking at the coordinates (-2, 3) and (2, 3), we can see that the signal of the x-coordinate changed.
This means that the point was reflected over the y-axis:
The effect of a reflection over the y-axis is changing the signal of the x-coordinate.
Therefore the correct option is the first one.
I don't know what to do at the last part
3x³
1) Evaluating that radical expression, we have:
Notice that we can rewrite that, under one and only radical, and then divide 81 by 3 and subtract the exponents (1 from 10)
And then, rewrite that radical as a power
[tex]\frac{\sqrt[3]{81x^{10}}}{\sqrt[3]{3x}}=\sqrt[3]{\frac{81x^{10}}{3\cdot x^{}}}=\sqrt[3]{27x^9^{}}=(27x^9)^{\frac{1}{3}}=3x^3[/tex]2) As the cubic root of 27 is 3 and 9 times 1/3 is 3 we can write the solution as 3x³
3) Hence, that's the answer
Express your answer as a polynomial in standard form.f(x) = x + 10g(x) = 2?= 2? + 2x – 7Find: (fog)(x)
Given function f and g, we can write:
[tex](f\circ g)(x)=f(g(x))[/tex]This means that we can just substitute g(x) into f to obtain the result. So let's do that:
[tex]\begin{gathered} (f\circ g)(x)=f(g(x))=g(x)+10=(x^2+2x-7)+10 \\ (f\circ g)(x)=x^2+2x-7+10 \\ (f\circ g)(x)=x^2+2x+3 \end{gathered}[/tex]This already is in the standard form, so that is the answer.
What is the equation for the graph shown?y=-1/2x+2
y=-1/2x-1
y=1/2x+2
y=-1/2x+3
Answer:
Your answer is [tex]y=-\frac{1}{2} + 2[/tex]
Step-by-step explanation:
The slope, in this case, using the formula [tex]\frac{rise}{run}[/tex], is [tex]-\frac{2}{4}[/tex] or [tex]-\frac{1}{2}[/tex]
The y-intercept is 0,2.
Thus, using the formula [tex]y=mx+b[/tex], we get [tex]y=-\frac{1}{2} + 2[/tex]
the diameter. of a circle is 14 ft. Find its are in terms of pi
The formula to find the area of a circle is
[tex]\begin{gathered} A=\pi r^2 \\ \text{ Where A is the area and} \\ r\text{ is the radius of the circle} \end{gathered}[/tex]So, in this case, you have
[tex]\begin{gathered} r=7ft \\ \text{ Because} \\ \text{ radius }=\frac{\text{ diameter}}{2} \\ \text{ radius }=\frac{14ft}{2} \\ \text{ radius }=7ft \end{gathered}[/tex]Then,
[tex]\begin{gathered} A=\pi r^2 \\ A=\pi(7ft)^2 \\ A=\pi\cdot49ft^2 \\ A=49\pi ft^2 \end{gathered}[/tex]Therefore, the area of this circle in terms of pi is 49 square feet.
Erwin spends at least $11.50 on lunch every day. Write an inequality to represent how much Erwin spends. A. L < $11.50 B. L >$11.50 C. L≤ $11.50 D. L ≥ $11.50
Answer:
D. L ≥ $11.50
Explanation:
If Erwin spends at least $11.50 on lunch, this means that:
• Erwin can spend ,exactly(=), $11.50; or
,• Erwin can spend ,more than(>), $11.50
Combining the two signs gives: ≥
An inequality to represent how much Erwin spends will then be:
[tex]L\ge\$11.50[/tex]The correct choice is D.
Given f (x)=9.2x +11, what is f (12)? If it does not exist, enter DNE
Given:-
[tex]f(x)=9.2(x)+11[/tex]To find:-
[tex]f(12)[/tex]So to find the required value. we substitute 12 for x. so we get,
[tex]\begin{gathered} f(x)=9.2(x)+11 \\ f(12)=9.2(12)+11 \\ f(12)=110.4+11 \\ f(12)=121.4 \end{gathered}[/tex]So the required solution is 121.4
Directions: complete the questions below and show all work. 1. Solve (2x + 1- 2 = 3x + 2 (5 pts) Bonus: Evaluate f(-2) if f(x) = -x3 -- 2x?] – 2.
Part 1
we have the equation
[tex]\mleft|2x+1\mright|-2=3x+2[/tex]Solve for x
[tex]\begin{gathered} |2x+1|=3x+2+2 \\ |2x+1|=3x+4 \end{gathered}[/tex]REmember that the absolute value function has two solutions
First solution (case positive)
[tex]\begin{gathered} +(2x+1)=3x+4 \\ 3x-2x=1-4 \\ x=-3 \end{gathered}[/tex]Second solution (negative case)
[tex]\begin{gathered} -(2x+1)=3x+4 \\ -2x-1=3x+4 \\ 3x+2x=-1-4 \\ 5x=-5 \\ x=-1 \end{gathered}[/tex]therefore
the solutions are x=-3 and x=-1
Part 2
we have the function
[tex]f(x)=-\mleft|x^3-2x^2\mright|-2[/tex]Remember that
f(-2) is the value of f(x) when the value of x=-2
substitute the value of x in the expression above
[tex]\begin{gathered} f(-2)=-|-2^3-2(-2)^2|-2 \\ f(-2)=-|-8-8|-2 \\ f(-2)=-|-16|-2 \\ f(-2)=-(16)-2 \\ f(-2)=-18 \end{gathered}[/tex]According to the US blood bank about 35.7% of the US has A positive blood. 1. If 3 people are chosen at random then what is the probability that no one has A positive blood?2. If 3 people are chosen at random then what is the probability that all 3 have A positive blood?Show all your work and make sure to round your answer to 3 decimal places.
The percentage of the people that have A positive blood is 35.7%,
[tex]35.7\text{ \%=}\frac{35.7}{100}=0.357[/tex]The probability of the people that do not have A positive blood,
[tex]1-0.357=0.643[/tex]The probability of people with A positive blood is 0.357
The probability of people without A positive blood is 0.643
1) The probability that 3 people that do not have A positive blood
[tex]\begin{gathered} =0.643\times0.643\times0.643 \\ =0.2658\approx0.266(nearest\text{ 3decimal places)} \end{gathered}[/tex]2) The probability that 3 people have A positive blood
[tex]\begin{gathered} =0.357\times0.357\times0.357 \\ =0.0455\approx0.046(nearest\text{ 3decimal places)} \end{gathered}[/tex]A hardware supplier manufactures three kinds of clamps types A B and C Production restrictions force it to make 20 more type clamps than the total of the other types and twice as many type clamps as type A clamps. The shop mustproduce 380 clamps per day. How many of each type are made per day?How many type A clamps are produced?How many type B clamps are produced?How many type C clamps are produced?
How many of each type are made per day? A =60 B= 120 and C=200
How many type A clamps are produced? 60
How many type B clamps are produced? 120
How many type C clamps are produced? 200
1) Gathering the data from the question
A=2x
B=2A A= B/2
C=A +B+ 20
A+B+C=380
A +B +A +B+20= 380
2A+2B +20 =380
2(A+B) +20-20=380-20
2(A+B) =360
A+B=180
Since B =2A We can plug in:
A +2A=180
3A=180
A=60
B= 120
C= 180+20
C=200
3)
How many of each type are made per day? A =60 B= 120 and C=200
How many type A clamps are produced? 60
How many type B clamps are produced? 120
How many type C clamps are produced? 200
Which random variable for each distribution below would be discrete?A the maximum height reached by a modelrocket on each launchB the weight of packages shipped each weekby the postal serviceCDthe number of emails sent to your computerthe amount of snow that falls in a town peryearper week
The answer is D cause you can not send half of an email
45 Trent used the expression below to Hind the volume in cubic centimeters of a squarepyramide BasesWhichsuere pyramid has a volume equal to the value of the expression Trent wrote?14 cm14 cm..Н12 cm12 cm12 cm12 cmJ.-14 cm14 cm
The volume of a square pyramid is :
[tex]V=\frac{1}{3}b^2h[/tex]Where :
b = side of the square base
h = perpendicular height from the vertex to the square base
From the given :
Trent wrote :
[tex]\frac{1}{3}(12^2)(14)[/tex]So b = 12 and h = 14
The side of the square base is 12 cm and the perpendicular height from the vertex to the square base is 14 cm.
Only choice H shows the square side of 12 cm and a perpendicular height of 14 cm
The correct answer is :
Choice H
a model of a house is shown. What is the perimeter of the model?
STEP-BY-STEP EXPLANATION:
As you can see from the question given, the fgure is a combination of an Isosceles triangle and a rectangle.
i need help i have no idea how to do this
SOLUTION
Prove 1
[tex]\begin{gathered} AB=3y-1 \\ BC=7y \\ AC=29 \\ AB+BC=AC \\ 3y-1+7y=29 \\ 3y+7y=29+1\text{ (after collecting like terms)} \\ 10y=30 \\ y=\frac{30}{10} \\ \\ y=3 \\ AB=3y-1 \\ \text{then} \\ AB=3(3)-1 \\ AB=9-1 \\ \text{Therefore } \\ AB=8 \end{gathered}[/tex]Prove 2
[tex]\begin{gathered} AB=AC-BC_{} \\ AB=29-7y \\ We\text{ have found y as 3} \\ AB=29-7(3) \\ AB=29-21 \\ AB=8 \end{gathered}[/tex]a box has a length of 6X inches the width equal 1/3 the lamps in the height equals half the length of the volume equals 972 cubic inches what does x equal?
The length of the box is 6x inches
The width of the box is 1/3 of the length, that is:
1/3 * 6x = 2x inches
The height of the box is 1/2 of the length, that is:
1/2 * 6x = 3x inches
The volume of the box is 972 cubic inches.
The volume of a box (rectangular box) is given as:
V = L * W * H
where L = length, W = width, H = height
This means that:
V = 6x * 2x * 3x
[tex]\begin{gathered} 972=36x^3 \\ \Rightarrow x^3\text{ = }\frac{972}{36} \\ x^3\text{ = 27} \\ \Rightarrow\text{ x = }\sqrt[3]{27} \\ x\text{ = 3} \end{gathered}[/tex]What is the value of min the figure below?11mсO A. 336O B. 77O C. V178D. V624O E. 42F. 126
EXPLANATIONS:
We are given a right triangle labelled ABC. The sides indicated are;
[tex]\begin{gathered} Shorter\text{ }leg=m \\ Hypotenuse=(11+7)=18 \end{gathered}[/tex]Also extracted from this triangle we have a smaller right triangle labelled BDC. The sides are labeled;
[tex]\begin{gathered} Shorter\text{ }leg=7 \\ Hypotenuse=m \end{gathered}[/tex]We will begin by recalling the Pythagoras theorem which states;
[tex]\begin{gathered} Pythagoras\text{ }Theorem: \\ c^2=a^2+b^2 \end{gathered}[/tex]Where c is the hypotenuse and a and b are the other two legs.
We can find the ratio between both triangles, because they are both similar by virtue of sharing one common side, that is side BD.
Hence, we will have;
[tex]\begin{gathered} For\text{ }\Delta ABC \\ BC=Shorter\text{ }leg \\ AC=Hypotenuse \\ For\text{ }\Delta BDC \\ DC=Shorter\text{ }leg \\ BC=Hypotenuse \end{gathered}[/tex]We can now set up the following equation;
[tex]\frac{BC^2}{AC^2}=\frac{DC^2}{BC^2}[/tex]We now have;
[tex]\frac{m^2}{18^2}=\frac{7^2}{m^2}[/tex]We can cross multiply and we'll have;
[tex]m^2\times m^2=18^2\times7^2[/tex][tex]m^4=324\times49[/tex][tex]m^4=15876[/tex]Next we take the square root of both sides;
[tex]\sqrt{m^4}=\sqrt{15876}[/tex][tex]m^2=126[/tex]We take the square root of both sides yet again;
[tex]\sqrt{m^2}=\sqrt{126}[/tex][tex]m=\sqrt{126}[/tex]ANSWER:
Option F is the correct answer.
Find the zeros of each function by factoring. F(x)=x^2–10x–11
Answer:
x = -1 and x = 11
Explanation:
your job in a moving company is to fill quart sized bottles of oil from a full 30 gallon oil drum. then you are to pack 8 quart bottle in a case to ship to a store. how many full cases of oil can you get from a full 30 gallon drum of oil?3cases7 cases15 cases16 cases
15 cases
1) Consider that 1 gallon corresponds to 4 quarts. So we can write out:
30 gallon = 120 quarts
8-quart bottle per case
2) So we have in each case 8-quart bottles. Since we have 120 quarts then, let's divide it by the capacity of the case:
[tex]\frac{120}{8}=15[/tex]3) Hence, we'll have 15 full cases with those 30 gallons (120 quarts) bottles of oil.
Dividing Mixed Numbers102) 270-35 =3) 445-9109) 45+210) 29-315) 476-23-
First, I will transform all into a fraction
[tex]\frac{18}{5}\div\frac{5}{2}=\frac{18\cdot\text{ 2}}{5\cdot5}=\frac{36}{25}[/tex]the answer is 36/25
Find the linear function such that f(-1)=7 and f(4)=-5
In a recent year, 16.8% of all doctors were female. If there were 57,600 female registered doctors that year, what was the total number of registered doctors?Round your answer to the nearest whole number.
From the problem statement, we can say,
16.8% of total doctors is 57,600.
16.8% in decimal is
16.8/100 = 0.168
Let total number of doctos be "d", thus we can write the statement "16.8% of total doctors is 57,600" as >>>
[tex]0.168\cdot d=57600[/tex]Now, we can solve for "d", shown below:
[tex]\begin{gathered} 0.168d=57600 \\ d=\frac{57600}{0.168} \\ d=342857.14 \end{gathered}[/tex]Rounding to the nearest whole number,
Total Doctors = 342,857