5 cm3 cm3 cm5 cm3 cmPrisma5 cmPrism BWhich of the following statements are true about the solids shown above?Check all that apply.A. Prisms A and B have different values for lateral surface area.O B. Prism B has a total surface area of 110 cm?O C. Prism A has a lateral surface area of 60 cm?D D. Prism B has a larger surface area.
Answers
Note that the lateral surface area is the area of the faces of the solid, excluding the cross-sectional faces i.e. faces which are perpendicular to the longitudinal axis.
The lateral surface area of prism A is calculated as,
[tex]\begin{gathered} LSA_A=2(5\times3)+2(5\times3)_{} \\ LSA_A=30+30 \\ LSA_A=60 \end{gathered}[/tex]Similarly, the lateral surface area of prism A is calculated as,
[tex]\begin{gathered} LSA_B=2(3\times5)+2(5\times5)_{} \\ LSA_B=30+50 \\ LSA_B=80 \end{gathered}[/tex]Clearly, prisms A and B have different values of lateral surface area.
So option A is the correct statement.
The total surface area is the sum of all the faces of the solid.
Since we have already calculated the LSA i.e. sum of area of 4 faces of the prism, we can add the area of the two remaining cross sectional faces to get the total area.
The total cross section area of prism B is calculated as,
[tex]\begin{gathered} A_B=2(5\times3) \\ A_B=30 \end{gathered}[/tex]So the total surface area of prism B becomes,
[tex]\begin{gathered} TSA_B=LSA_B+A_B_{} \\ TSA_B=80+30 \\ TSA_B=110 \end{gathered}[/tex]The total surface area of prism B is 110 sq. cm.
So option B is also correct.
Note that we have already found that the lateral surface area of prism A is 60 sq. cm.
Therefore, option C is also correct.
The total cross section area of prism A is calculated as,
[tex]\begin{gathered} A_A=2(3\times5) \\ A_A=30 \end{gathered}[/tex]So the total surface area of prism A becomes,
[tex]\begin{gathered} TSA_A=LSA_A+A_A \\ TSA_A=60+30 \\ TSA_A=90 \end{gathered}[/tex]The total surface area of prism A is 90 sq. cm.
It is oberved that prism B has a larger surface area.
So, option D is also correct.
Hence, we can conclude that all the given statements are correct.
Related Questions
how do I determine the hypotenuse, opposite, and adjacent angles when I'm only given sides and no angles?
Answers
[tex]\angle J = 90^{\circ}\\\\\cos (\angle K)=\frac{5}{23} \implies \angle K=\arccos(5/23)\\\\\sin (\angle I)=\frac{5}{23} \implies \angle I=\arcsin(5/23)[/tex]
Select the correct answer from each drop-down menu.
Given: Kite ABDC with diagonals AD and BC intersecting at E
Prove: AD L BC
A
C
E
LU
D
B
Determine the missing reasons in the proof.
Answers
The missing reasons are
ΔCDA ≅ ΔBDA by SSS [side side side]
ΔCED ≅ ΔBED by SAS [side angle side]
What is Kite?
A kite is a quadrilateral having reflection symmetry across a diagonal in Euclidean geometry. A kite has two equal angles and two pairs of adjacent equal-length sides as a result of its symmetry.
Given,
ABCD is a kite, with the diagonal AD and BC
We have,
AC = AB
and
CD = BD [Property of Kite]
In ΔACD and ΔABD
AC = AB
and
CD = BD [Property of Kite]
AD = AD [Common]
By rule SSS Criteria [Side Side Side ]
ΔACD ≅ ΔABD
∴ ∠CDA = ∠BDA [CPCT]
Now,
In ΔCDE and ΔBDA
CD = BD
∠CDE = ∠BDE
DE = DE [Common]
By rule SAS Criteria [Side Angle Side]
ΔCDE ≅ ΔBDA
∴ CE = BE [CPCT]
Hence, AD bisects BC into equal parts
The missing reasons are
ΔCDA ≅ ΔBDA by SSS [side side side]
ΔCED ≅ ΔBED by SAS [side angle side]
To learn more about Kite click on the link
https://brainly.com/question/23279609
#SPJ13
which transformation occurred to create the graph shown below from square root parent function?
Answers
Solution:
Given the function:
[tex]f(x)=\sqrt{x+4}[/tex]whose graph is shown below:
Suppose that the parent function is expressed as
[tex]f(x)=\sqrt{x}[/tex]This implies that the parent function is transformed by a horizontal shift to the left by four spaces.
The correct option is
how do I know where which choices below go into the correct blanks for number 1-4?
Answers
For 1, we have the following triangle:
Using the cosine function to get the hypotenuse we get:
[tex]\begin{gathered} \cos (45)=\frac{7}{h} \\ \Rightarrow h=\frac{7}{\cos(45)}=\frac{7}{\frac{1}{\sqrt[]{2}}}=7\cdot\sqrt[]{2} \\ h=7\cdot\sqrt[]{2} \end{gathered}[/tex]Now that we have the hypotenuse, we can find the remaining side using the pythagorean theorem:
[tex]\begin{gathered} h^2=7^2+x^2 \\ \Rightarrow x^2=h^2-7^2=(7\cdot\sqrt[]{2})^2-7^2=49\cdot2-49=49 \\ \Rightarrow x^2=49 \\ x=7 \end{gathered}[/tex]Therefore, the value of the remaining side is 7.
The number of milligrams D (h) of a certain drug that is in a patients bloodstream h hours after the drug is injected is given by the following function. D (h)=40e ^0.2h When the number of milligrams reaches 9, the drug has to be injected again. How much time is needed between injections? Round your answer to the nearest tenth, and do not round any intermediate computations.
Answers
we need to find the value of h when D is 9, so we need to replace D by 9 and find h:
Write an explicit formula that represents the sequence defined by the following recursive formula: a1=7 and an=2a_n-1
Answers
Answer:
[tex]a_n=7(2^{n-1})[/tex]Explanation:
Given the sequence with the recursive formula:
[tex]\begin{gathered} a_1=7 \\ a_n=2a_{n-1} \end{gathered}[/tex]First, we determine the first three terms in the sequence.
[tex]\begin{gathered} a_2=2a_{2-1}=2a_1=2\times7=14 \\ a_3=2a_{3-1}=2a_2=2\times14=28 \end{gathered}[/tex]Therefore, the first three terms of the sequence are: 7, 14 and 28.
This is a geometric sequence where:
• The first term, a=7
,• The common ratio, r =14/7 = 2
We use the formula for the nth term of a GP.
[tex]\begin{gathered} a_n=ar^{n-1} \\ a_n=7\times2^{n-1} \end{gathered}[/tex]The explicit formula for the sequence is:
[tex]a_n=7(2^{n-1})[/tex]3) There are 24 applicants for three jobs: computer programmer, software tester, and manager. How many ways can this be done?
Answers
this is a combination, so
[tex]24C3=\frac{24\cdot23\cdot22}{3\cdot2\cdot1}=2024[/tex]answer: 2024 ways
The data for numbers of times per week 20 students at Stackamole High eat vegetables are shown below. A dotplot shows 4 points above 1, 4 points above 3, 5 points above 2, 3 points above 4, 3 points above 5, and 1 point above 9.
Answers
Considering the given dot plot for the distribution, it is found that:
a) The distribution is right skewed.
b) There is an outlier at 9.
c) Since there is an outlier, the best measure of center is the median.
Dot plotA dot plot shows the number of times that each measure appears in the data-set, hence the data-set is given as follows:
1, 1, 1, 1, 2, 2, 2, 2, 2 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 9.
To find the skewness of the data-set, we need to find the mean and the median.
The mean is the sum of all values divided by the number of values of 20, hence:
Mean = (4 x 1 + 5 x 2 + 4 x 3 + 3 x 4 + 3 x 5 + 9)/20 = 3.1.
The median is the mean of the 9th and the 10th elements(even cardinality) of the data-set, hence:
Median = (2 + 3)/2 = 2.5.
The mean is greater than the median, hence the distribution is right skewed.
To identity outliers, we need to look at the quartiles, as follows:
First quartile: 0.25 x 20 = 5th element = 2.Third quartile: 0.75 x 20 = 15th element = 4.The interquartile range is:
IQR = 4 - 2 = 2.
Outliers are more than IQR from the quartiles, hence:
4 + 1.5 x 2 = 4 + 3 = 7 < 9, hence 9 is an outlier in the data-set, and hence the median will be the best measure of center.
Missing information
The questions are as follows:
Part A: Describe the dotplot. (4 points)
Part B: What, if any, are the outliers in these data? Show your work. (3 points)
Part C: What is the best measure of center for these data? Explain your reasoning. (3 points) (10 points)
More can be learned about dot plots at https://brainly.com/question/24726408
#SPJ1
Please help me with this problem so my son can better understand I have attached an image of the problem
Answers
We have to solve for c:
[tex](c+9)^2=64[/tex]When we have quadratic expressions, we have to take into account that each number has two possible square roots: one positive and one negative.
We can see it in this example: the square root of 4 can be 2 or -2. This is beacuse both (-2)² and 2² are equal to 4.
Then, taking that into account, we can solve this expression as:
[tex]\begin{gathered} (c+9)^2=64 \\ c+9=\pm\sqrt[]{64} \\ c+9=\pm8 \end{gathered}[/tex]We then calculate the first solution for the negative value -8:
[tex]\begin{gathered} c+9=-8 \\ c=-8-9 \\ c=-17 \end{gathered}[/tex]And the second solution for the positive value 8:
[tex]\begin{gathered} c+9=8 \\ c=8-9 \\ c=-1 \end{gathered}[/tex]Then, the two solutions are c = -17 and c = -1.
We can check them replacing c with the corresponding values we have found:
[tex]\begin{gathered} (-17+9)^2=64 \\ (-8)^2=64 \\ 64=64 \end{gathered}[/tex][tex]\begin{gathered} (-1+9)^2=64 \\ (8)^2=64 \\ 64=64 \end{gathered}[/tex]Both solutions check the equality, so they are valid solutions.
Answer: -17 and -1.
The function h (t) = -4.9t² + 19t + 1.5 describes the height in meters of a basketball t secondsafter it has been thrown vertically into the air. What is the maximum height of the basketball?Round your answer to the nearest tenth.1.9 metersO 19.9 meters16.9 metersO 1.5 meters
Answers
Since the function describing the height is a quadratic function with negative leading coefficient this means that this is a parabola that opens down. This also means that the maximum height will be given as the y component of the vertex of the parabola, then if we want to find the maximum height, we need to write the function in vertex form so let's do that:
[tex]\begin{gathered} h(t)=-4.9t^2+19t+1.5 \\ =-4.9(t^2+\frac{19}{4.9}t)+1.5 \\ =-4.9(t^2+\frac{19}{4.9}t+(\frac{19}{9.8})^2)+1.5+4.9(\frac{19}{9.8})^2 \\ =-4.9(t+\frac{19}{9.8})^2+19.9 \end{gathered}[/tex]Hence the function can be written as:
[tex]h(t)=-4.9(t+1.9)^2+19.9[/tex]and its vertex is at (1.9,19.9) which means that the maximum height of the ball is 19.9 m
10 Zara writes a sequence of five numbers. The first number is 2. The last number is 18. Her rule is to add the same amount each time. Write the missing numbers. 2,____ ,_____,______, 18
Answers
If the first number is 2. The last number is 18. The sequence of five numbers will be 2,6,10,14,18.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity, approaching either infinity or -infinity.
It is given that, the first number is 2 and the last number is 18,
a = 2
L=18
n=5
a₅=5
a₅=a+(5-1)d
18=2+4d
4d = 18-2
4d = 16
d= 16 / 4
d=4
The terms of the sequence are,
a₁=2
a₂=2+4=6
a₃=6+4=10
a₄=10+4=14
a₅=14+4=18
Thus, if the first number is 2. The last number is 18. The sequence of five numbers will be 2,6,10,14,18.
Learn more about the sequence here:
brainly.com/question/21961097
#SPJ1
Rearrange the formula 5w-3y +7=0 to make w the subject.
Answers
estimate 328 divided by 11=?
Answers
Answer:
30
Step-by-step explanation:
the inside diameter (I.D.) and outside diameter (O.D.) of a pope are shown in the figure. The wall thickness of the pope is the dimension labeled t. Calculate the wall thickness of the pipe if its I.D. is 0.599 in. and its O.D. is 1.315 in.
Answers
Given:
The inside diameter of the pope, I.D.=0.599 in.
The outside diameter of the pope, O.D.=1.315 in.
The inside radius of the pope is,
[tex]IR=\frac{ID}{2}=\frac{0.599}{2}=0.2995\text{ in}[/tex]The outside radius of the pope is,
[tex]OR=\frac{OD}{2}=\frac{1.315}{2}=0.6575\text{ in}[/tex]The wall thickness of the pope can be calculated as,
[tex]t=OR-IR=0.6575-0.2995=0.358\text{ in}[/tex]Therefore, the wall thickness of the pope is t=0.358 in.
I need help with part b, c ii, and d
Answers
Recall that:
[tex]\text{average speed=}\frac{total\text{ distance}}{total\text{ time}}.[/tex](b) Since Marcos traveled for 2 hours and 17 minutes a distance of 155 miles, then Marco's average speed for the 155 miles trip is:
[tex]\frac{155mi}{(2+\frac{17}{60})h}=\frac{155mi}{\frac{137}{60}h}=\frac{9300}{137}miles\text{ per hour}\approx67.89miles\text{ per hour.}[/tex](c ii) Since Devon also traveled the 155 miles in 2hours and 17 minutes but at a constant speed, then the constant speed at which he traveled is equal to his average speed, which is equal to:
[tex]\frac{155mi}{(2+\frac{17}{60})h}=\frac{155mi}{\frac{137}{60}h}=\frac{9300}{137}miles\text{ per hour}\approx67.89miles\text{ per hour.}[/tex](d) Marco needs to drive 2 miles in 5 minutes to be able to complete the 155 miles trip in 2 hours and 17 minutes, then he must drive at a constant speed of:
[tex]\frac{2mi}{5\min }=\frac{2mi}{\frac{5}{60}h}=\frac{120mi}{5h}=24\text{miles per hour.}[/tex]Answer:
(b) 67.89 miles per hour.
(c ii) 67.89 miles per hour.
(d) 24 miles per hour.
Write an equation of the line containing the given point and parallel to the given line.
(9,−6); 4x−3y=2
Answers
Answer:
y=4/3x-18
Step-by-step explanation:
4x-2=3y
y=4/3x-2/3
to parallel slope has to be the same
-6=9*(4/3)+b
b=-18
y=4/3x-18
Simplify 17(z-4x)+2(x+3z)
Answers
Answer:
23z-66x
Step-by-step explanation:
Look at the attachment please :D
The diagonal of a rectangle is 25 inches. The width is 15 inches. What is the area of the rectangle?
Answers
Answer:
300 in²
Step-by-step explanation:
Hello!
Because the diagonal forms right triangles, we can use the Pythagorean Theorem to find the missing length of the rectangle.
a² + b² = c²
a = legb = legc = hypotenuseIn this case, 25 is c, and 15 is a. We can solve for b using the formula.
Solve for ba² + b² = c²15² + b² = 25²225 + b² = 625b² = 400b = 20So the missing length of the rectangle is 20. We can find the area by multiplying 15 and 20
15 * 20 = A300 = AThe area is 300 in².
In the figure below, BAC~QPR. Use this information and the diagram below to name the corresponding parts of the similar triangles
Answers
a.
∠A is the right angle of the triangle ABC, so the corresponding angle is ∠P, which is the right angle of the triangle PQR.
b.
BC is the hypotenuse of the triangle ABC, so the corresponding side is QR, which is the hypotenuse of the triangle PQR.
c.
∠C is the smaller angle of the triangle ABC, so the corresponding angle is ∠R.
d.
∠Q is the bigger angle of the triangle PQR, so the corresponding angle is ∠B.
e.
PQ is the smaller leg of the triangle PQR, so the corresponding side is AB.
what times what equals 38
Answers
Question 19 of 25Which of the following equations is an example of inverse variation betweenthe variables x and y?O A. y -O B. y = 8xO C. y -OD. y=x+8SUBMIT
Answers
Where 8 is the constant
The Final answerOption CFrankenstein was in charge of bringing punch to the Halloween party. He brought 36 liters of his famous eyeball punch. How many gallons was this?
Answers
Answer: 9.5112
Step-by-step explanation:
There are 0.2642 gallons in a liter. So, in 36 liters, there are [tex]36(0.2642)=9.5112 \text{ gal }[/tex]
1/2+1/9Please help me
Answers
If the fraction whose denominator are equal then they will add up
In the given fraction 1/2 +1/9, the denominator of both the fraction 1/2 & 1/9 is not same
so, to make the base same we take the LCM of the 2 & 9
[tex]\begin{gathered} \text{LCM of 2 \& 9 is 18} \\ Si,\text{ the fraction will be :} \\ \frac{1}{2}+\frac{1}{9}=\frac{9+2}{18} \\ \frac{1}{2}+\frac{1}{9}=\frac{11}{18} \end{gathered}[/tex]Answer : 11/18
andrew went to the store to buy some walnuts. the price pee walnut is $4 per pound and he has a coupon for $1 off the final amount. with the coupon, how much would andrew have to pay to buy 4 pounds of walnuts? what is the expression for the cost to buy p pounds of walnuts , assuming at least one pound is purchased.
Answers
The amount Andrew have to pay to buy 4 pounds of walnuts = $19
The expression for the cost to buy p pounds of walnuts= 4p - 1
Explanation:
Amount per pound of walnut = $4
Amount of coupon = $1
The cost of 4 pounds of walnuts:
[tex]\text{Cost = 4 }\times5=\text{ \$20}[/tex]The amount Andrew have to pay to buy 4 pounds of walnuts:
Amount = cost - coupon
Amount = $20 - $1
The amount Andrew have to pay to buy 4 pounds of walnuts = $19
The expression for the cost to buy p pounds of walnuts:
let number of pounds = p
Cost for p pounds of walnut = Amount per walnut * number of walnut
Cost for p pounds of walnut = $4 * p
= $4p
The expression for the cost to buy p pounds of walnuts= cost for p - coupon
= 4p - 1
4. Martin was asked to solve the following system of equations. Hegraphed the two equations below, and decided that the answer was"infinitely many solutions". Do you agree with Martin? Why or why not? Ifyou disagree, what should the answer be?*y=-x-3y=-***+3
Answers
Types of solutions in a system of equations:
Based on this image, we can see that when they are parallel lines (same slope), there is no solution because the lines never touch.
The type of solution Martin was describing is when the lines are the same (letter b in the image) and it looks like one line when graphed.
Answer: We disagree with Martin because the lines never touch, meaning that the system has no solutions.
Jack bought 3 slices of cheese pizza and 4 slices of mushroom pizza fora total cost of $12.50. Grace bought 3 slices of cheese pizza and 2 slices of mushroom pizza for a total cost of $8.50. What is the cost of one slice of mushroom pizza?
Answers
c = price of a slice of Cheese pizza
m= price of a slice of mushroom pizza
Jack bought 3 slices of cheese pizza and 4 slices of mushroom pizza fora total cost of $12.50
3c + 4 m = 12.50
Grace bought 3 slices of cheese pizza and 2 slices of mushroom pizza for a total cost of $8.50.
3c + 2m = 8.50
We have the system of equations:
3c + 4 m = 12.50 (a)
3c + 2m = 8.50 (b)
Subtract (b) to (a) to eliminate c
3c + 4m = 12.50
-
3c + 2m = 8.50
_____________
2m = 4
Solve for m:
m = 4/2
m=2
The cost of one slice of mushroom pizza is $2
Find the distance between the pair of points. (16,0) and (1, -7) The distance is. (Round to the nearest thousandth as needed.)
Answers
Solution
For this case we can use the formula for the distance between two points:
[tex]d=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]and replacing we got:
[tex]d=\sqrt[]{(-7-0)^2+(1-16)^2}=\sqrt[]{274}[/tex]And the correct answer after round would be:
16.553
Please help me on #1 Please show your work so I can follow and understand
Answers
Answer:
Between markers 3 and 4.
Explanation:
We know that each student runs 2 / 11 miles. Given this, how many miles do the first two students run?
The answer is
[tex]\frac{2}{11}\cdot2=\frac{4}{11}\text{miles}[/tex]Now, we know that the course has markers every 0.1 miles. How many markers are ther in 4 /11 miles?
The answer is
[tex]\frac{2}{11}\text{miles}\times\frac{1\text{marker}}{0.1\; miles}[/tex][tex]=3.6\text{ markers}[/tex]This is between markers 3 and 4. Meaning that the second student finishes between markers 3 and 4.
Rounded to three decimal places, the value of the irrational number e is .A.3.142B.3.615C.2.718D.2.947
Answers
REQUIRED:
Round to 3 decimal placed the value of the irrational number e.
Step-by-step solution/explanation;
The letter e in mathematics is also known as the Eular's number and is a mathematical constant used in many calculations especially natural logarithms of numbers.
The value of the Eular's number is approximately;
[tex]e\approx2.71828182846...[/tex]It can continue till infinity, however approximations of this number is always used to avoid unnecessary complications.
Therefore, rounded to 3 decimal places, the value of e is now;
ANSWER:
[tex]e\approx2.718[/tex]Note that we take 3 digits aftre the decimal and then if the fourth digit after the decimal is 5 or greater than 5, we make it 1 and add that 1 to the third digit after the decimal. Otherwise we simply make it zero and cancel it along with all other digits after it.
The digit that follows 8 (third digit) is less than 5, therefore, we write it off along with all other digits after it, and we are left with the decimal point and then ...718.
Option C is the correct answer.
cuántos cifras tiene el cociente de 900÷25
Answers
Given the expression