Ratio:
cost / number of eggs
1.56 / 12
For 18 eggs:
Cost / number of eggs = x/18
Equal both expressions:
1.56/12 = x/18
Solve for x:
0.13 = x/18
0.13 (18) = x
x=2.34
18 eggs will cosr $2.34
Need help with #81, specifically don’t understand how to determine the domain
ANSWERS
a) Domain: x ∈ (-∞, -1) ∪ (-1, ∞)
b) Domain: x ∈ (-∞, 0) ∪ (0, ∞)
EXPLANATION
These compositions are:
a)
[tex]f\circ g=f(g(x))=\frac{2}{g(x)}=\frac{2}{x+1}[/tex]And
b)
[tex]g\circ f=g(f(x))=f(x)+1=\frac{2}{x}+1[/tex]To find the domain in each function we have to find the values that x cannot take. If there aren't any, then the domain is all real values.
For composition a) note that x is in the denominator as (x+1). As we know, for real numbers the denominator can't be 0, so that's our restriction:
[tex]x+1\ne0[/tex]Solving for x:
[tex]x\ne-1[/tex]The domain for f º g is all real values except x = -1
For composition b) we have x in the denominator too, but it is alone. Therefore, as said before, x cannot be 0.
Determine the expected value for the equal segment spinner below:
sam was charged $1,050 in interest on a loan with a 2.5% interest rate. What was the original amount of the loan it he took 5 years to pay it back?
Answer:
$8,400
Explanation:
The interest can be calculated using the following equation:
[tex]I=\text{P}\cdot r\cdot t[/tex]Where P is the original amount of the loan, r is the interest rate, and t is the time that the person tool to pay it back.
So, we can replace I by $1,050, r by 2.5% or 0.025, and t by 5 years. Then:
[tex]1050=P\cdot0.025\cdot5^{}[/tex]Finally, we can solve for P as:
[tex]\begin{gathered} 1050=P\cdot0.125 \\ \frac{1050}{0.125}=\frac{P\cdot0.125}{0.125} \\ 8400=P \end{gathered}[/tex]Therefore, the original amount of the loan was $8,400
At the movie theatre, child admission is $5.80 and adult admission is $9.70. On Tuesday, 137 tickets were sold for a total sales of S1094.90. How many adulttickets were sold that day?Number of adult tickets:?
Solution:
Let us denote by x the number of child tickets sold and by y the number of adult tickets sold. According to the problem, we have that 137 tickets were sold, then we get the following equation:
Equation 1:
[tex]x+y\text{ = 137}[/tex]On the other hand, according to the problem, child admission is $5.80 and adult admission is $9.70 and the total sales were S1094.90.
Thus, we get the following equation:
Equation 2:
[tex]5.80x\text{ + 9.70y = }1094.90[/tex]Thus, we get the following system of linear equations:
Equation 1:
[tex]x+y\text{ = 137}[/tex]Equation 2:
[tex]5.80x\text{ + 9.70y = }1094.90[/tex]Now, solving for x, the equation 1, we get:
Equation 3:
[tex]x=\text{ 137-y}[/tex]replacing this into equation 2, we obtain:
[tex]5.80(137-y)\text{ + 9.70y = }1094.90[/tex]now, applying the distributive property, we get:
[tex]794.6-5.80y\text{ + 9.70y = }1094.90[/tex]this is equivalent to:
[tex]-5.80y\text{ + 9.70y = }1094.90-794.6[/tex]this is equivalent to:
[tex]3.90y=300.3[/tex]solving for y, we get:
[tex]y=\frac{300.3}{3.90}=77[/tex]Now, replacing this data into equation 3, we obtain:
[tex]x=\text{ 137-y}=137-77=60[/tex]So that, we can conclude that the correct answer is:
the number of child tickets sold = x = 60
the number of adult tickets sold = y = 77
Consider the following function.f(x) = 6x^2 − 4xFind the limit.
Given:-
[tex]f(x)=6x^2-4x[/tex]To find:-
[tex]\lim _{\Delta x\to0}\frac{f(x+\Delta x)-f(x)}{\Delta x}_{}[/tex]So now we substitute the known values we get,
[tex]\frac{f(x+\Delta x)-f(x)}{\Delta x}_{}=\frac{6(x+\Delta x)^2-6x^2+4x}{\Delta x}[/tex]So by furthur simplification. we get,
[tex]\frac{6(x+\Delta x)^2-6x^2+4x}{\Delta x}=\frac{6x^2+12x\Delta x+(\Delta x)^2-6x^2+4x}{\Delta x}[/tex]So we get is,
[tex]\frac{6x^2+12x\Delta x+(\Delta x)^2-6x^2+4x}{\Delta x}=\frac{12x\Delta x+(\Delta x)^2^{}+4x}{\Delta x}[/tex]So by furthur simplification we get,
[tex]undefined[/tex]sina ½ sin ( a + b) + sin(a = b)] OA. cos a OB.. sina OC. sinb D. cos b
Answer:
A. cos a
Explanation:
The relevant trigonometric formula we have is
[tex]\sin a\cos a=\frac{1}{2}[\sin(a+b)+\sin(a-b)][/tex]Now comparing the above formula with the one given in the question tells us that the missing term in the equation is cos a.
Therefore, choice A is the right answer!
Consider functions fg, and h below. 12 + 25 + 3 8 6 2 6 2 6 FB 2 6 8 Х 0 1 2. 3 h(x) -7 -4 -1 2 5
We have the functions,
[tex]\begin{gathered} f(x)=x^2+2x+3 \\ \text{the rate of change of f(x) over (0,2 ) is } \\ rate-of-change=\frac{f(2)-f(0)}{2-0} \\ f(2)=2^2+2(2)+3=11 \\ f(0)=0^2+0+3=3 \\ so,\text{ average rate of change=}\frac{11-3}{2}=4 \end{gathered}[/tex]We move over to g(x), g(x) is an exponential function;
[tex]\begin{gathered} \text{From the graph,} \\ g(2)=7\text{ and g(0)=4} \\ so\text{ the average rate of change of g(x) over the interval (0,2) is} \\ \frac{g(2)-g(0)}{2-0} \\ =\frac{7-4}{2} \\ =\frac{3}{2}=1.5 \end{gathered}[/tex]We move over to h(x),
[tex]\begin{gathered} \text{From the table, h(0)=-4, h(2)=2} \\ \text{the rate of change of h(x) over the interval (0,2) is;} \\ \frac{2-(-4)}{2-0}=\frac{6}{2}=3 \end{gathered}[/tex]If we rank the rates of change of the function , we see that,
[tex]4>3>1.5[/tex]So, the rates of change from least to greatest is;
g,h,f.
Option B
Find the standard form of the ellipse with the information below:Foci: (7, 10), (7,2)co vertices: (10,6), (4,6)
The general form of the equation of an ellipse is given as:
A roast beef sandwich costs $6.75. A customer buys multiple roast beef sandwiches. write an equation that represents the situation. Use x to represent the number of roast beef sandwiches. then determine how many sandwiches tje customer buys. Amount Used for payment =$50Change Received = $16.25The Customer buys. sandwiches ?
Let x be the number of sandwiches.
Since each sandwich has a cost of $6.75, then for x sandwiches the cost would be:
[tex]\text{6}.75x[/tex]The change received is the difference between the amount used for payment and the cost of the sandwiches.
The difference between the amount used for payment and the cost of the sandwiches can be represented algebraically as:
[tex]50-6.75x[/tex]This number must be equal to the change received. Then:
[tex]50-6.75x=16.25[/tex]Solve for x. To do so, substract 50 from both sides:
[tex]\begin{gathered} \Rightarrow-6.75x=16.25-50 \\ \Rightarrow-6.75x=-33.75 \end{gathered}[/tex]Next, divide both sides by -6.75:
[tex]\begin{gathered} x=\frac{-33.75}{-6.75} \\ \Rightarrow x=5 \end{gathered}[/tex]Therefore, the customer buys 5 sandwiches.
Joe has brownies the length of each brownies is 7 cm and the width is 5 cm is its total area of the pan is 560 cm how many brownies did Joe have
Start by calculating the area of a single brownie using
[tex]A=L\cdot W[/tex][tex]\begin{gathered} A=7\operatorname{cm}\cdot5\operatorname{cm} \\ A=35\operatorname{cm} \end{gathered}[/tex]To find the amount of brownies Joe can make in his pan, divide the area of the pan into the single brownie area
[tex]\frac{560}{35}=16[/tex]Joe had 16 brownies.
3) P(A) = 0.65 P(B) = 0.35 P(A and B) = A.0.2275B.0.2c.0.06d.0.315
For the given probabilities:
[tex]\begin{gathered} p(AandB)=^{}0.65\cdot0.35 \\ p(AandB)=0.2275 \end{gathered}[/tex]Can you please help me out with a question
37.5%
1) Examining the Spinner we can see that the total possibilities are:
90+45+90+135 = 360
2) Since the question is P(green or red) we can write out:
[tex]\begin{gathered} P(g\text{ or r) = }\frac{90}{360}+\frac{45}{360}=\frac{135}{360}=0.375 \\ P(g\text{ or r) = P(g) +P(r) } \end{gathered}[/tex]Note that the event of picking red or picking green can't exist simultaneously so they are mutually exclusive.
The result in percentage will be obtained by multiplying it by 100
3) Hence, the answer is 37.5%
Find the surface area of the square pyramid. 16 in 5 in
Answer:
Explanation:
The below formula can be used to find the surface area of a square pyramid;
[tex]SA=A+\frac{1}{2}ps[/tex]where A = area of the base
p = perimeter of the base
s = slant height = 6 in
Since the base of the pyramid is a square, let's go ahead and find the area of the square;
[tex]A=5^2=25in^2[/tex]Let's go and find the perimeter of the square;
[tex]P=4\times5=20in[/tex]Let's substitute the values into our above formula and solve for SA;
[tex]undefined[/tex]8. What is the radian measure of an angle of 54°
To get the radian measure of an angle we have to do this conversion:
[tex]54°\times\frac{\pi\text{ rad}}{180°}=0.9425[/tex]The radian measure of an angle of 54° is 0.9425 radians.
Parallel lines never meet and will never cross each other.
True
Parallel lens are never meet and cross each other
The bacteria in a dish triples every hour. At the start of the experiment therewere 400 bacteria in the dish. When the students checked again there were32,400 bacteria. How much time had passed?.
Solution:
Given:
[tex]\begin{gathered} At\text{ time (t) = 0, 400 bacteria were present.} \\ \\ \text{The bacteria triples every hour.} \end{gathered}[/tex]Hence, this is an exponential function.
[tex]\begin{gathered} y=ab^x \\ \text{where;} \\ y\text{ is the number of bacteria present} \\ x\text{ is the time} \\ \\ \text{Hence, at the start of the experiment} \\ 400=ab^0 \\ a=400 \\ \\ At\text{ the next hour, the number has tripled} \\ 1200=ab^1 \\ 1200=400(b^1) \\ b=\frac{1200}{400} \\ b=3 \end{gathered}[/tex]Hence, the function can be represented by;
[tex]y=400(3^x)[/tex]The time that had passed when the bacteria was 32,400 will be;
[tex]\begin{gathered} y=400(3^x) \\ 32400=400(3^x) \\ \text{Dividing both sides by 400,} \\ \frac{32400}{400}=3^x \\ 81=3^x \\ 3^4=3^x \\ \\ \text{Equating the exponents since the base are the same,} \\ x=4 \end{gathered}[/tex]Therefore, 4 hours have passed when the bacteria became 32,400
write the equation of the slope intercept form with the given point and slope or two points. (-7,13) slope = -2
Slope-intercept form of a line:
y = mx+ b
where m is the slope and b is the y-intercept.
Replacing into the equation with m = -2 and point (-7, 13) we get:
13 = -2(-7)+ b
13 = 14+ b
13 - 14 = b
-1 = b
Then, the equation is:
y = -2x - 1
Which equation describes a line of symmetry for square ABCD? x = 0 y = x x = -2 y = -2
The equation of the line is DB from y = mx + b
From the graph y = 0 when x =0
this means y = x
The graph cuts through the origin, Meaning the y -intercept = 0
answer is: y = x
A rectangular field has a length that is triple its width and a diagonal of 98 meter find the areaI need help, help me please
Data:
l = 3w
d = 98
To find the area, lets start drawing the field:
The area of rectangle is
[tex]A=b\cdot h[/tex]In this case
b = w
h= l = 3w
To determine the value of w, we can use the right triangle and the value of the diagonal that is the hypotenuse of the triangle. Then using Pythagoras theorem:
[tex]w^2=d^2-(3w)^2[/tex]We can clear the w from this equation:
[tex]w^2=d^2-9w^2[/tex][tex]w^2+9w^2=98^2[/tex][tex]10w^2=98^2[/tex][tex]w^2=\frac{98^2}{10}[/tex][tex]w=\sqrt[]{\frac{98^2}{10}}=\sqrt[]{960.4}=30.99\approx40[/tex]Now we know the value of w = 40
Then the area of the field is:[tex]A=w\cdot3w[/tex][tex]A=40m\cdot3(40m)=4800m^2[/tex]Solve the system using the method of elimination by addition
Given:
There are given the two systems of the equation:
[tex]\begin{gathered} \frac{3}{5}x+\frac{2}{3}y=1...(1) \\ 18x+20y=30...(2) \end{gathered}[/tex]Explanation:
According to the question:
We need to solve the equation by using the elimination method.
So,
To solve the above equation, we need to perform the elimination method.
So,
[tex]\begin{gathered} 18(\frac{3}{5}x+\frac{2}{3}y=1)=(\frac{54}{5}x+12y=18)...(3) \\ \frac{3}{5}(18x+20y=30)=(\frac{54}{5}x+12y=18)...(4) \end{gathered}[/tex]Then,
We need to subtract equation (3) from equation(4):
Then,
[tex]\begin{gathered} (\frac{54}{5}x+12y=18)-(\frac{54}{5}x+12y=18) \\ 0 \end{gathered}[/tex]Final answer:
Hence, the solution is 0.
Use the piecewise-defined function to find the fallowing values for f(x)F(x) =.{. 5-4x if x<1 4x if 16F(-3) =
To look for f(-3) we are going to use the first portion of the formula
f(x) = 5 - 4x, because here we will find all the x - values from -∞ to 1
So
f(-3) = 5 - 4 (-3) = 5 + 12 = 17
In the diagram below, AD bisects ZC AB, mZADB = 95º and mZCAD = 34°. Find mZB.
please send me the picture of your question
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I will start to answer the question
Please let me know if you have any question anytime or if you don’t see the answering tab
we know that
The sum of the interior angles in any triangle must be equal to 180 degrees
so
In the triangle ADB we have that
mwe have that
m because AD bisects angle CAB
so
msubstitute
34+95+m
mmPlease, Do you understand all the steps so far?Does the explanation satisfy your question and do you understand the answer?
If you don’t need further explanation on this question, we can end the session. A pleasure to attend you, Remember that after our session, the answer is saved in your profile. Thanks and have a great day! Good Bye.
Writing an equation of a circle given at Center and radius or diameter
The equation of a circle with Center (a, b) and Radius 'r' is given by,
[tex](x-a)^2+(y-b)^2=r^2[/tex]Given,
Center (-7, -4)
Diameter = 8
We know the radius is half of diameter.
So,
Radius = 8/2 = 4
Now we can write the equation of the cirle,
[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ (x-(-7))^2+(y-(-4))^2=4^2 \\ (x+7)^2+(y+4)^2=16 \end{gathered}[/tex]Answer[tex](x+7)^2+(y+4)^2=16[/tex]Solve for x in the equation −2x + 3b > 5
SOLUTION
We want to solve for x in
[tex]-2x+3b>5[/tex]This becomes
[tex]\begin{gathered} -2x+3b>5 \\ -2x>5-3b \\ \text{divide both sides by -2, and the inequality reverses, we have } \\ \frac{-2x}{-2}<\frac{5-3b}{-2} \\ x<\frac{5-3b}{-2} \end{gathered}[/tex]Hence the answer is
[tex]x<\frac{5-3b}{-2}[/tex]8. Pentagon MNOPQ with M(-4,1),N(-2,3). O(0, 3), P(4, 3), and Q(2,-7): rotate 90° counterclockwise, then dilate by a factor of 2/3 120 What are the two arrow rules to show this composition? 12 b. Is the dilation an enlargement or reduction? How do you know? 710 с. What are the vertices of the image after the transformation?
Given data:
The given coordinates of the pentagon are M(-4,1),N(-2,3). O(0, 3), P(4, 3), and Q(2,-7).
The coordinatte after 90 degrees counterclockwise rotation is,
[tex]\begin{gathered} M(-4,1)\rightarrow M^{\prime}(-1,\text{ -4)} \\ N(-2,\text{ 3)}\rightarrow N^{\prime}(-3,\text{ -2)} \\ O(0,\text{ 3)}\rightarrow O^{\prime}(-3,\text{ 0)} \\ P(4,\text{ 3)}\rightarrow P^{\prime}(-3,\text{ 4)} \\ Q(2,\text{ -7)}\rightarrow Q^{\prime}(7,\text{ 2)} \end{gathered}[/tex]The final coordinates after 2/3 dilation factor is,
[tex]\begin{gathered} M^{\doubleprime}\rightarrow\frac{2}{3}(-1,\text{ -4)} \\ \rightarrow(-\frac{2}{3},\text{ - }\frac{8}{3}) \\ N^{\prime\prime}\rightarrow\frac{2}{3}(-3,\text{ -2)} \\ \rightarrow(-2,\text{ -}\frac{4}{3}) \\ O^{\doubleprime}\rightarrow\frac{2}{3}(-3,\text{ 0)} \\ \rightarrow(-2,\text{ 0)} \\ P^{\doubleprime}\rightarrow\frac{2}{3}(-3,\text{ 4)} \\ \rightarrow(-2,\frac{8}{3})^{} \\ Q^{\doubleprime}\rightarrow\frac{2}{3}(7,\text{ 2)} \\ \rightarrow(\frac{14}{3},\text{ }\frac{4}{3}) \end{gathered}[/tex]Thus, the final coordinates after transformation are M''(-2/3, -8/3), N''(-2, -4/3). O''(-2, 0), P''(-2, 8/3), and Q''(14/3, 4/3).
17. To measure the amount of space in rectangular prism, we need three dimensional figures as unit of measure. Which is the formula for finding the volume?A. V= 1/3 x B x HB. V= S x S x SC. V= L x W x H18. A rectangular prism has length of 4 cm, width of 3 cm and height of 5 cm. Find the volume.A. 50 cu cmB. 55 cu. cmC. 60 cu. cmD. 45 cu. cm19. A wooden box has 20 cm on each edge. Find its volume.A. 875 cu. cmB. 8 000 cu. cmC. 8 875 cu. cm20. Juana’s sewing box is 3 dm long, 2dm wide, and 4 dm high. What is its volume?A. 12 cu. dmB. 24 cu. dmC. 33 cu. dmD. 34 cu. dm21. Five metal cubes with sides of 5 cm were melted and casted into a bigger cube. Find the volume of the new cube.A. 125 cu.cmB. 405 cu. cmC. 325 cu. cmD. 625 cu. cm
(17) The First part of the question asked us to find the formula used in determining measure of the amount of space in a rectangular prism which is invariably the volume.
The three dimensions needed to determine the Volume of a rectangular prism are:
Length
width
Height.
To get the volume, we mutiply the three together.
So:
Volume = Length * Width * Height.
V = L * W * H
Therefore, the correct option is C, which is V = L x W x H.
(18) Givne the following dimensios of a rectangular prism as:
Length = 4 cm
Width = 3 cm
Height = 5 cm
We are to find the volume
Recall, the formula for finding volume of the rectangular prism is:
V = L x W x H
V = 4 x 3 x 5
V = 60 cm³
Therefore, the volume of the rectangular prism = 60 cm³
So, the correct option is C, which is 60 cm³.
Two trains leave towns 508 kilometers apart at the same time and travel toward each other. one train travels 16 km/h slower than the other. if they meet in hours, what is the rate of each train?
Given:
Distance, d = 508 km
Time, t = 2 hours
Let x be the speed of one train.
Let x-16 be the speed of another train.
To find: Speed of the two trains
Explanation:
We know that,
[tex]\text{Speed }\times Time=Dis\tan ce[/tex]Let us frame the equation as follows,
[tex]\begin{gathered} (\text{Speed of the train 1 + Speed of the train }2)\times Time=Dis\tan ce \\ (x+x-16)\times2=508 \\ 2x-16=\frac{508}{2} \\ 2x-16=254 \\ 2x=270 \\ x=135\text{kmph} \end{gathered}[/tex]Final answer:
The speed of the faster train is 135 km/h.
The speed of slower train is 119 km/h
Using the net below, find the surface area of the pyramid. Blin 2 in Surface Area . - [?] in.2 Enter
The Solution:
The correct answer is 16 square in.
Given the net in the picture on the Question section, we are asked to find the surface area of the pyramid that can form using the given net.
The pyramid (or the net) has a total of 5 surfaces, these are:
4 similar triangles, each with a base of 2 inches and a height of 3 inches; and a square of side 2 inches.
So,
The required surface area is the total area of all 5 surfaces.
By formula, the area of a triangle is
[tex]A=\frac{1}{2}bh[/tex]While the area of a square is
[tex]A=l\times l[/tex]So, the required area of the pyramid is
[tex]\text{Area}=4(\frac{1}{2}bh)+(l\times l)[/tex]In this case,
[tex]\begin{gathered} =\text{base}=2\text{ in.} \\ h=\text{height}=3\text{ in.} \\ l=\text{side}=2\text{ in.} \end{gathered}[/tex]Substituting these values in the above formula, we get
[tex]\text{Area}=4(\frac{1}{2}\times2\times3)+(2\times2)=(4\times3)+4=12+4=16in.^2[/tex]Therefore, the correct answer is 16 square in.
question provided in picture and making the two points and equation in bold would be appreciated
Given:
Number of shirts Jose has to fold = 12
Where N is the number of shirts he would have left after folding F of them.
Let's write an equation rlating N to F.
We have the equation:
N = 12 - F
Let's graph the equation.
Let's create points from the equation.
• At F = 1:
Substitute 1 for F and solve for N
N = 12 - 1
N = 11
We have the point:
(F, N) ==> (1, 11)
• At F = 2:
N = 12- 2
N = 10
We have the point:
(F, N) ==> (2, 10)
• At F = 0:
N = 12 - 0
N = 12
We have the point:
(F, N) ==> (0, 12)
• At F = 5:
N = 12 - 5
N = 7
We have the point:
(F, N) ==> (5, 7)
Therefore, we have the points:
(F, N) ==> (1, 11), (2, 10), (0, 12), (5, 7)
Let's plot the points and connect them using a straight edge.
Here, F is represented on the x-axis while N is represented on the y-axis.
We have the graph below:
ANSWER:
N = 12 - F
You deposit $4000 in an account earning 8% interest compounded monthly. How much will you have in the account in 15 years?
Given:
a.) You deposit $4000 in an account earning 8% interest compounded monthly.
Question: How much will you have in the account in 15 years?
We will be using the following formula:
[tex]\text{ A = P(}1\text{ + }\frac{r}{n})^{nt}[/tex]Where,
A=final amount
P=initial principal balance = $ 4,000
r=interest rate = 8% = 8/100 = 0.08
n=number of times interest applied per time period = monthly = 12
t=number of time periods elapsed = 15 years
We get,
[tex]\text{ A = P(}1\text{ + }\frac{r}{n})^{nt}[/tex][tex]\text{ A = (4,000)(}1\text{ + }\frac{0.08}{12})^{(12)(15)}[/tex][tex]\text{ = (4,000)(1 + }0.00667)^{180}=(4,000)(1.00667)^{180}[/tex][tex]\text{ = (4,000)(3.30889307445)}[/tex][tex]\text{ A = 13,235.57229780234 }\approx\text{ \$13,235.57}[/tex]Therefore, in 15 years, you will have $13,235.57 in your account.