The balance after 7 years will be $11240.60
Explanation:
We would apply the compound interest formula:
[tex]FV\text{ = P(1 + }\frac{r}{n})^{nt}[/tex]FV = future value = balance,
P = Principal = $7000
r = interest rate = 7%
n = number of times compounded per year = annually = 1 year
t = time = 7 years
[tex]FV\text{ = 7000(1 + }\frac{0.07}{1})^{1\times7}[/tex][tex]\begin{gathered} FV=7000(1+0.07)^7\text{ } \\ =7000(1.07)^7\text{ = 7000(}1.6058) \\ FV=\text{ \$11240.6} \end{gathered}[/tex]The balance after 7 years will be $11240.60
pictures is down below , i have to include C & D
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
f(x) = x² - 2
Step 02:
functions:
function:
f(x) = x² - 2
domain:
(-oo, oo)
all real numbers
range:
[-2 , oo)
y ≥ - 2
inverse function:
[tex]\begin{gathered} y=x^2-2 \\ \\ x\text{ ===> y} \\ \\ x=y^2-2 \\ \\ solve\text{ for y:} \\ \\ y=\pm\sqrt{x+2} \\ \end{gathered}[/tex]domain:
[-2, oo)
x ≥ -2
range:
(oo, 0] U [0 , oo)
all real numbers
That is the full solution.
I need helping finding out the answer (don’t mind my last name so n the picture)
Answer:
[tex]\text{base}=\text{ 9.5 inches}[/tex]Step-by-step explanation:
The area of a triangle is represented by the following equation;
[tex]\text{Area}=\frac{\text{base}\cdot\text{height}}{2}[/tex]Then, if the height is 82.65 square inches and the height is 17.4 inches, solve for the base:
[tex]\begin{gathered} 82.65=\frac{1}{2}\cdot b\cdot17.4 \\ b=\frac{82.65\cdot2}{17.4} \\ b=\frac{19}{2} \\ b=9.5\text{ inches} \end{gathered}[/tex]List 4 numbers that are following an Exponential pattern, explain how you knowthe pattern is Exponential.
A sequence follows an exponential pattern when each successive number increases (or decreases) by the same percent.
Then, we can define the intial value as 3 and we want the common ratio to be 2, meaning that each term doubles its previous value:
[tex]\begin{gathered} a_1=3 \\ a_2=2\cdot a_1=2\cdot3=6 \\ a_3=2\cdot a_2=2\cdot6=12 \\ a_4=2\cdot a_4=2\cdot12=24 \end{gathered}[/tex]We know it follows an exponential pattern because the ratio between consecutive terms has a constant value:
[tex]\frac{a_n}{a_{n-1}}=2[/tex]for any value of n.
Answer:
3, 6, 12, 24 are four terms of an exponential pattern where each term is the double of the previous one.
As the ratio between consecutive terms is constant, we know we have a exponential sequence or pattern.
Find the coordinates of the vertices of the figureafter the given transformation: T<-5,-2>.
The coordinates of the vertices of a quadrilateral are given in the figure.
It is required to find the coordinates of the vertices of the figure
after the given transformation: T<-5,-2>.
Notice from the figure that the coordinates of the vertices of the figure before transformation are:
[tex]X(2,-1),V(1,2),E(4,1),K(5,-3)[/tex]The transformation T<-5,-2> is a translation of 5 units to the left and 2 units down.
To find the coordinates after transformation, add -5 to the x-coordinates and -2 to the y-coordinates.
The coordinates after translation are:
[tex]\begin{gathered} X^{\prime}(2-5,-1-2),V^{\prime}(1-5,2-2),E^{\prime}(4-5,1-2),K^{\prime}(5-5,-3-2) \\ =X^{\prime}(-3,-3),V^{\prime}(-4,0),E^{\prime}(-1,-1),K^{\prime}(0,-5) \end{gathered}[/tex]The answer is option D.A) number of people attended the 9 screening of a movie:196, 197, 200, 201, 206, 207, 208, 209, 211which measure should be used to summarize the data?Mean, Median, or ModeB) In Prof. Matinez's class 9 students had the following scores on the last midterm 127, 129, 131, 134, 135, 137, 138, 143, 190which measure should be used to summarize the data?mean, median, or modeC) on a test , each student is given a grade of A,B,C,D,F which measure tells the grade most often? mean, median, or mode
SOLUTION:
A) For data without repeating values (normally distributed or not skewed). The mean works quite well for summary statistics.
Hence, Mean is the answer.
B) For data without repeating values (normally distributed or not skewed). The mean works quite well for summary statistics.
Hence, Mean is the answer.
C) The answer is mode becuase it says 'Most'
The table below shows the February balance of simple interest savings account each year from 2015 to 2021Year 2015 2016 2017 2018 2019 2020 2021Balance $12,000 14018 16036 18054 20072 22090 241081. Do the balances form an arithmetic or geometric sequence?2. What is the d or the r?3. Write a formula for the balance in the account n years after February 2015.4. Find the sum of the February balances from 2015 to 2032, inclusive.
ANSWER:
1. arithmetic
2. 2018
3.
[tex]b=12000+2018y[/tex]4. $524754
STEP-BY-STEP EXPLANATION:
1.
The balance is an arithmetic sequence, because the increase is constant, that is, the increase from one year to another is always the same.
2.
We calculate the value of d, using the table, subtracting the values, just like this:
[tex]\begin{gathered} d=14018-12000=2018 \\ \\ d=16036-14018=2018 \\ \\ d=18054-16036=2018 \\ \\ d=20072-18054=2018 \\ \\ d=22090-20072=2018 \\ \\ d=24108-22090=2018 \end{gathered}[/tex]The value of d is 2018
3.
Therefore, the formula for the balance in the account n years after February 2015 would be:
[tex]\begin{gathered} b=12000+2018y \\ \\ \text{ where b is the balance in \$ and y is years after February 2015} \end{gathered}[/tex]4.
To determine the sum of the values, we must calculate the balance for the year 2032.
In this case y is equal to 17 (2032 - 2015), we replace:
[tex]\begin{gathered} b=12000+2018\cdot17 \\ \\ b=12000+34306=\text{\$}46306 \end{gathered}[/tex]Now, we determine the sum with the following formula:
[tex]\begin{gathered} s=\frac{a_0+a_n}{2}\cdot(n+1) \\ \\ \text{ we replacing} \\ \\ s=\:\frac{12000+46306}{2}\cdot(17+1) \\ \\ s=29153\cdot18 \\ \\ s=524754 \end{gathered}[/tex]So the sum of the February balances from 2015 to 2032 is $524754
Hello. Need to solve problem four. I’m addition need to estimate the length at three year old Gila and Estimate the age of a 25 cm long GilaThank you
Since the lizard increases by about 8% each year, it can be understood as an exponential function as:
[tex]L(t)=L_0\ast(1+r)^t[/tex]since the initial length and the rate of increase is also given, replace ins the formula
[tex]\begin{gathered} L(t)=16\ast(1+0.08)^t \\ simplify \\ L(t)=16\ast(1.08)^t \end{gathered}[/tex]Then replace in the formula t as 3
[tex]\begin{gathered} L(3)=16\ast(1.08)^3 \\ L(3)=20.155\cong20.16cm \end{gathered}[/tex]Answer:
The equation that models the length of the lizard for the first 8 years is:
[tex]L(t)=16(1.08)^t[/tex]And the approximate length of the lizard after 3 years is about 20.16 cm
At the park there is a pool shaped like a circle. A ring-shaped path goes around the pool. Its inner radius is
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the dimension of the given circles
[tex]\begin{gathered} Radius\text{ of big circle}\Rightarrow8yards \\ Radius\text{ of small circle}\Rightarrow6yards \end{gathered}[/tex]STEP 2: Find the Area of the two circular paths
[tex]\begin{gathered} Area=\pi r^2 \\ Area\text{ of big circle}\Rightarrow3.14\times8^2=200.96yards^2 \\ Area\text{ of small circle}\Rightarrow3.14\times6^2=113.04yards^2 \end{gathered}[/tex]STEP 3: Calculate the area of the ring-shaped path
[tex]\begin{gathered} Area\text{ of ring shaped path}\Rightarrow Area\text{ of big circle - Area of small circle} \\ Area\text{ of ring shaped path}\Rightarrow200.96-113.04=87.92yard^2 \end{gathered}[/tex]STEP 4: Find the number of gallons needed to coat the ring-shaped path
[tex]\begin{gathered} 1\text{ gallon}\Rightarrow8yards^2 \\ x\text{ gallons}\Rightarrow87.92yards^2 \\ By\text{ cross multiplication,} \\ x\times8=87.92\times1 \\ Divide\text{ both sides by 8} \\ x=\frac{87.92}{8}=10.99 \\ x\approx11\text{ gallons} \end{gathered}[/tex]Hence, it will take approximately 11 gallons to coat the ring shaped path
find the value for b that will make the trinomial 4x^2+bx+81 a perfect square trinomial. FACTOR the resulting:
Answer:
Explanation:
Given the below trinomial;
[tex]4x^2+bx+81[/tex]We're asked to determine the value of b to make the above trinomial a perfect square.
To solve the above, note that perfect square trinomials are generally written in the below form;
[tex](ax\pm b)^2=(ax)^2\pm2axb+b^2[/tex]Let's rewrite the given trinomial in the above form, we'll have;
[tex]4x^2+bx+81=(2x)^2+2bx+9^2[/tex]If we compare both expressions, we can observe the below;
[tex]undefined[/tex]9. Millie intends on creating a breath-taking African Pond Diorama. She orders 8 stuffedhippos as well as a bronze zebra which cost $5.75. She pays $4.25 for shipping, makingthe total price $62. How much per stuffed hippo?
Given:
The cost of bronze zebra is $5.75.
The shipping charge is $4.25.
The total price is $62.
Let us assume that the cost of a stuffed hippo is 'x' dollars, then the cost of 8 such hippos will be,
[tex]\begin{gathered} =\text{ Number of hippos}\cdot\text{ Price of one hippo} \\ =8\cdot x \\ =8x \end{gathered}[/tex]The total cost must be equal to the sum of the cost of 8 hippos, 1 zebra, and the shipping charges,
[tex]62=8x+5.75+4.25[/tex]Simplify the equation to obtain the value of 'x' as follows,
[tex]\begin{gathered} 62=8x+10 \\ 8x=62-10 \\ x=\frac{52}{8} \\ x=6.5 \end{gathered}[/tex]Thus, the cost is $6.5 per stuffed hippo.
pweeze help Use the following net to find the surface area of the solid figure it represents.144 yd 248 yd 288 yd 294 yd 2
In order to determine the surface area of the given figure, add all areas of the faces, as follow:
A = (12 + 12 + 8 + 8 + 24 + 24)yd^2
A = 88 yd^2
Hence, the surface are is 88 yd^2 (third option)
A flower garden is shaped like a circle. Its diameter is 28 yd. A ring-shaped path goes around the garden. Its outer edge is a circle with diameter 36 yd. The gardener is going to cover the path with sand. If one bag of sand can cover 6 yd^2?, how many bags of sand does the gardener need? Note that sand comes only by the bag, so the number of bags must be a whole number. (Use the value 3.14 for T.)
Answer:
67 bags of sand
Explanation:
First, we need to calculate the area of the path. So, this area can be calculated as the difference between the area of the circle with a diameter of 36 yd and the area of the circle with 28 yd.
The area of a circle can be calculated as:
[tex]A=\pi\cdot r^2[/tex]Where π is 3.14 and r is the radius of the circle.
The radius of a circle is half the diameter. So, the radius of the circle with a diameter of 36 yd is 18 yd and its area is:
[tex]\begin{gathered} A_1=3.14\times(18)^2 \\ A_1=1017.36yd^2 \end{gathered}[/tex]In the same way, the radius of the circle with a diameter of 28 yd is 14 yd and its area is equal to:
[tex]\begin{gathered} A_2=3.14\times(14)^2 \\ A_2=615.44yd^2 \end{gathered}[/tex]Then, the area of the path is equal to:
[tex]\begin{gathered} A_1-A_2=1017.36-615.44 \\ A_1-A_2=401.92yd^2 \end{gathered}[/tex]Now, the number of bags of sand can be calculated as:
[tex]\text{Bags = }\frac{401.82yd^2}{6yd^2}=66.98\approx67\text{ bags of sand}[/tex]Because each bag of sand covers 6 yd².
Therefore, the gardener needs 67 bags of sand
If you can't read the numbers they say 8. p. 0
The rule of the permutation is
[tex]\text{nPr}=\frac{n!}{(n-r)!}[/tex]From the given picture we need to find 8P6, then
n = 8
r = 6
[tex]\begin{gathered} 8P6=\frac{8!}{(8-6)!} \\ 8P6=\frac{8!}{2!} \\ 8P6=\frac{8\times7\times6\times5\times4\times3\times2\times1}{2\times1} \\ 8P6=20160 \end{gathered}[/tex]8P6 = 20160
If it is 8P0, then
n = 8
r = 0
[tex]\begin{gathered} 8P0=\frac{8!}{(8-0)!} \\ 8P0=\frac{8!}{8!} \\ 8P0=1 \end{gathered}[/tex]8P0 = 1
Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. Carly is a server at an all-you-can eat sushi restaurant. At one table, the customers ordered 4 child buffets and 2 adult buffets, which cost a total of $120. At another table, the customers ordered 3 child buffets and 3 adult buffets, paying a total of $132. How much does the buffet cost for each child and adult? The cost for a child is $ and the cost for an adult is $ Submit
1) Gathering the data
4 child buffets + 2 adult buffets = $120
3 child buffets + 3 adult buffets = $132
Let's call child buffet 'c' and adult buffet by 'a' and then set the system
4c +2a = 120
3c +3a=132
2) Solving the system by elimination method
4c +2a = 120 Multiply by -3 t
3c +3a=132 Multiply by 2
-12c -6a = -360 Adding both equations, we can eliminate one variable
6c -6a = 264
------------------------
-6c =-96
6c = 96 Divide both sides by 6
c=16
2.2 Let's plug that into one of those original equations, usually the simplest one
3c +3a = 132
3(16) +3a = 132
48 + 3a = 132 Subtract 48 from both sides
3a =132-48
3a=84 Divide both sides by 3
a=28
3) So the answers are:
How much does the buffet cost for each child and adult?
Each child: $16 Each adult: $28
Based on this sequence, will Leonard ever give Penny 51 roses?If yes, on which day? If not, explain why not.
Leonard will give Penny 51 roses.
This will happen on the 11th day
Explanation:To detrmine if Leonard will ever give Penny 51 roses, we need to find the equation of the values we have in the table
Equation of line:
y = mx + b
m = slope, b = y-intercept
First let's find the slope of the line:
Using any two points on the table: (1, 1) and (2, 6)
[tex]\begin{gathered} \text{Slope formula:} \\ m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ x_1=1,y_1=1x_2=2,y_2\text{ = }6 \\ m\text{ = }\frac{6-1}{2-1} \\ m\text{ = 5/1 = 5} \end{gathered}[/tex]Slope of the line = 5
We need to find the y-intercept. Using the slope and any of the two points:
[tex]\begin{gathered} y\text{ = mx + b} \\ point\text{ (1, 1): x = 1, y = 1} \\ 1\text{ = 5(1) + b} \\ 1\text{ = 5 + b} \\ 1-5\text{ = b} \\ b\text{ = -4} \end{gathered}[/tex]The equation of the line:
[tex]\begin{gathered} \text{y = 5x + (-4)} \\ y\text{ = 5x - 4} \end{gathered}[/tex]To determine if Penny gets 51 roses, we will substitute 51 for y in our equation:
[tex]\begin{gathered} 51\text{ = 5x - 4} \\ \text{Add 4 to both sides:} \\ 51\text{ + 4 = 5x - 4 + 4} \\ 55\text{ = 5x} \\ \\ \text{divide both sides by 5:} \\ \frac{55}{5}\text{ = }\frac{5x}{5} \\ x\text{ = 11} \end{gathered}[/tex]From our calculaton, x = number of days and y = number of roses
When number of roses was 51, the day was on the 11th
Hence, Leonard will give Penny 51 roses.
This will happen on the 11th day
Complete the ordered pairs so they are solutions of the equation: 6x+y=12( , 0 )( 0 , )( , 6 )
Incomplete ordered pairs which are solutions to the equation 6x+y=12 are given.
Ordered pairs that are solutions to the given equation satisfy the equation.
To find the missing coordinate, substitute the known coordinate into the equation and solve for the missing one.
Recall that the first coordinate is the x-coordinate while the second is the y-coordinate.
The first incomplete ordered pair is ( ,0). So substitute y=0 and solve for x in the resulting equation:
[tex]\begin{gathered} 6x+y=12;y=0 \\ \Rightarrow6x+0=12 \\ \Rightarrow6x=12 \\ \Rightarrow\frac{6x}{6}=\frac{12}{6} \\ \Rightarrow x=2 \end{gathered}[/tex]Hence, the complete ordered pair is (2,0).
The second ordered pair is given as (0, ). So substitute x=0 into the equation and solve for y:
[tex]\begin{gathered} 6x+y=12;x=0 \\ \Rightarrow6(0)+y=12 \\ \Rightarrow0+y=12 \\ \Rightarrow y=12 \end{gathered}[/tex]Hence, the complete ordered pair is (0,12).
The third ordered pair is ( ,6). So substitute y=6 into the equation and solve for x:
[tex]\begin{gathered} 6x+y=12;y=6 \\ \Rightarrow6x+6=12 \\ \Rightarrow6x=12-6 \\ \Rightarrow6x=6 \\ \Rightarrow\frac{6x}{6}=\frac{6}{6} \\ \Rightarrow x=1 \end{gathered}[/tex]Hence, the complete ordered pair is (1,6).
The complete ordered pairs are: (2,0), (0,12), (1,6)
Find the midline for f(x) = −2+ 4 cos z. OA.y = -2 OB. y = 0 Oc.y = 4 OD.y=2
Explanation
For the given question, we have that
[tex]\begin{gathered} f(x)=-2+4cosx \\ \end{gathered}[/tex]We are asked to find the midline of the function
The function is
The midline is
The midline is
[tex]y=-2[/tex]Therefore, option A is correct
Several points are shown on the polar coordinate plane. Show the correct point.
The angle of rotation is:
[tex]\frac{4\pi}{3}[/tex]Since the given angle is positive , the direction of rotation is counterclockwise.
The size of the anglel spacing is:
[tex]\frac{\pi}{6}[/tex]Therefore, the number of spacing between the given angle and the standard position is given by:
[tex](\frac{4\pi}{3}-0)\div\frac{\pi}{6}=8[/tex]Therefore, Rotating a length of 5 units by 4π/3 from the standard position moves the point to V(5, 4π/3).
Since
Are equations (3x+9)=6 and x+3=2 equivalent?
Yo can prove that this set of equations is equivalent by applying some math operations on one of the equation and making it look like the other one.
In this case, we could transform the second equation x+3=2 into the first one (3x+9)=6 by multiplying both sides of this equation by 3, like this:
x+3=2
3*(x+3)=3*2
3x+3*3=3*2
3x+9=6
As you can see, now the second equation look exactly the same as the first one, then we can say that this pair of equations is equivalent
Leroy was asked to repaint the sign for this mother's ce cream shop, so he needs to figure out how much paint he will need. Determine the area of the ice cream cone. A. 54.84 inches squaredB. 90.84 inches squaredC. 50.13 inches squaredD. 100.26 inches squared
Answer
Option C is correct.
Area of the figure = 50.13 inches squared
Explanation
The Pythagoras Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.
The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.
The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,
a² + b² = (hyp)²
So, we need to calculate the radius of the semicircle on top of the figure.
a = radius of the semicircle = ?
b = 12
hyp = √153
a² + b² = (hyp)²
a² + 12² = (√153)²
a² + 144 = 153
a² = 153 - 144
a² = 9
Take the square root of both sides
√a² = √9
a = 3 in.
So,
Area of the figure = (Area of triangle) + (Area of semicircle)
Area of triangle = ½bh
b = Base of the triangle = a + a = 3 + 3 = 6 in.
h = perpendicula height of the triangle = 12 in.
Area of triangle = ½bh = ½ (6) (12) = 36 square inches
Area of semi circle = ½ (Area of circle) = ½ (πr²)
r = Radius = 3 in.
Area of semi circle = ½ (πr²) = ½ (π (3²)) = 4.5π = 14.13 square inches
Area of the figure = (Area of triangle) + (Area of semicircle)
= 36 + 14.13
= 50.13 inches squared
Hope this Helps!!!
Which of the following is the equation for the graph?
The graph shows a parabola opening upda
The location of thecircumcenter of AABC is:A. Point DB. Point EC. Point F
To find:
The circumcenter of the circle.
Solution:
The circumcenter is the point where the perpendicular bisectors of all sides intersect.
Here, in the given figure, all the perpendicular bisectors intersect at point F.
So, option C is correct.
I would love some help! What needs to be done here is determine whether there is enough information to show that the triangles are congruent using SAS Congruence Theorem. If the answer is yes, write a congruence statement, make sure the notation is correct.
You have the next:
- Sides JK and LK are congruent:
[tex]JK\cong LK[/tex]-Angles MKJ and MKL are congruent:
[tex]\angle MKJ\cong\angle MKL[/tex]-Side MK is part of both triangles.
Then, as angle MKJ is between sides JL and MK, angle MKL is between sides LK and MK:
[tex]\Delta JMK\cong\Delta LMK\text{ by SAS}[/tex]Triangles JMK and LMK are congruent by SAS (side, angle, side)Charmaine, Dante, and Rafael sent a total of 77 text messages over their cell phones during the weekend. Charmaine sent 9 fewer messages than Dante. Rafaelsent 2 times as many messages as Charmaine. How many messages did they each send?Number of text messages Charmaine sent:Number of text messages Dante sent:Number of text messages Rafael sent:
Let x be the number of messages Dante sent.
We know that Charmaine sent 9 fewer messages than Dante this means that Dante sent:
[tex]x-9[/tex]messages.
We also know that Rafael sent 2 times as many messages as Charmaine, then Rafael sent:
[tex]2(x-9)[/tex]messages.
Now that we have an expression for the messages each of them sent we add them and equate the sum to 77, the total number of text. Hence we have the equation:
[tex]x+x-9+2(x-9)=77[/tex]Solving for x we have:
[tex]\begin{gathered} x+x-9+2(x-9)=77 \\ 2x-9+2x-18=77 \\ 4x-27=77 \\ 4x=77+27 \\ 4x=104 \\ x=\frac{104}{4} \\ x=26 \end{gathered}[/tex]Now that we have the value of x, we plug it in each of the expressions for the number of messages each one of them sent and we conclude that:
Charmaine sent 17 messages.
Dante sent 26 messages.
Rafael sent 34 messages.
Darrell and Lyle are college basketball players. Darell is 198.1 centimeters tall. Lyle is 190.5 centimeters tall. how much taller is Darell than lyle?
Answer:
7.6cm
Explanation:
Darell's height = 198.1 centimeters
Lyle's height = 190.5 centimeters
The difference in their height:
[tex]\begin{gathered} =198.1-190.5 \\ =7.6\operatorname{cm} \end{gathered}[/tex]Thus, Darell is 7.6cm taller than Lyle.
fine the value of x in (9x-7)(7x-3)
it is given that the expression is
[tex]9x-7=7x-3[/tex][tex]\begin{gathered} 9x-7x=7-3 \\ 2x=4 \\ x=\frac{4}{2}=2 \end{gathered}[/tex]so the answer is 2.
\
To determine the amount of wrapping paper needed for a rectangular box, Ryan finds the surface area of the box. How much wrapping paper is needed if the boxmeasures 10 cm by 3 cm by 8 cm?O 134 cm? of wrapping paper0 220 cm? of wrapping paperO 268 cm? of wrapping paperO 240 cm? of wrapping paper
268 cm²
Explanation:The dimension of the box is 10cm by 3cm by 8cm
The box is rectangular. To find the surface area, we will use formula of surface area of rectangular prism
[tex]\text{Surface area = 2(lh + wh + lw)}[/tex]let the length = l = 10cm,
width = w= 3cm
height = h = 8cm
substitute for the values in the formula:
[tex]\begin{gathered} \text{Surface area of the box = }2((10\times8)\text{ + (3}\times8)\text{ + (10}\times3)) \\ \text{surface area of the box = 2(80 + 24 + 30)} \end{gathered}[/tex][tex]\begin{gathered} \text{surface area of the box = 2(134)} \\ \text{surface area of the box = 268 cm}^2 \end{gathered}[/tex]Hence, the amount of wrapping paper needed for the box is 268 cm²
Express your answers in scientific notation.5.8 * 10^1-7.4*10^0
In scientific notation, the exponent of the number 10 tells us how many spots the digital point must move to the right, if it is positive, or to the left, if it is negative. So
[tex]\begin{gathered} 5.8\times10^1=58 \\ 7.4\times10^0=7.4 \\ 5.8\times10^1-7.4\times10^0=58-7.4=50.6 \end{gathered}[/tex]Then, the answer, ater expressingi t in scientific notation, is
[tex]5.8\times10^1-7.4\times10^0=5.06\times10^1[/tex]a movie theater sold 155 adult tickets and 230 childrens tickets to a movie in total the theater made 1285.50 in ticket sales Mrs.ramierez paid 53.75 for 2 adult tickets and 3 children. tickets. what is the cost of one adult ticket
a. Let the cost of an adult ticket be x and Let the cost of an children's ticket be y
We can deduce that;
[tex]155x+230y=1285.5[/tex]Also Mrs. Ramirez paid 53.75 for 2 adult tickets and 3 children tickets, so;
[tex]2x+3y=53.75[/tex]We can solve this simultaneously for x and y.
So, we have;
[tex]\begin{gathered} 155x+230y=1285.5----i \\ 2x+3y=53.75\text{ ----i}i \end{gathered}[/tex]Let's make x the subject of the relation, we have
[tex]\begin{gathered} 2x=53.75-3y \\ x=\frac{53.75-3y}{2} \\ \end{gathered}[/tex]Let us substitute this relation for x in equation i
[tex]undefined[/tex]Represent the sample space using set notation.A sandwich shop has three types of sandwiches: ham, turkey, and chicken. Each sandwich can be ordered with white bread or multi- grain bread.
Let's say:
Ham sandwich: H
Turkey sandwich: T
Chicken sandwich: C
White bread: W
Multigrain bread: M
The representation using set notations would be:
[ (H,W), (H,M), (T,W), (T,M), (C,W), (C,M) ]