Answers
Volume of object = 42 cubic cm
Surface area of object = 96 square cm
Explanations:The given figure is a triangular prism.The formula for calculating its volume is expressed as:
[tex]volume\text{ }of\text{ prism}=BH[/tex]where:
B is the base area
H is the height of prism
[tex]\begin{gathered} volume\text{ of }prism=(\frac{1}{2}\times4\times3)\times7 \\ volume\text{ of }prism=6\times7 \\ volume\text{ of }prism=42cm^3 \end{gathered}[/tex]Determine the surface area of the prism
The surface area if the sum of all the faces of the prism.The faces consists of 3 rectangles and 2 triangles. The surface area is calculated as:
[tex]\begin{gathered} Surface\text{ area}=2(0.5\times3\times4)+(7\times4)+(3\times7)+(5\times7) \\ Surface\text{ area}=12cm^2+28cm^2+21cm^2+35cm^2 \\ Surface\text{ area}=96cm^2 \end{gathered}[/tex]Hence the surface area of the object shown is 96 square cm
Related Questions
REDUCE 48/96 TO THE LOWEST TERMS
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A) Write an expression for the given number trick B) Simplify the expression you came up with
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a)
Since we need an Expression, we also need a variablel for the "number".
Let's use "n".
We will translate each of the lines:
Pick a number : n
Mutiply that number by 12, so it becomes: n x 12
Add 15 to that, so we put parenthesis around that expression and add "15" to it:
(n x 12) + 15
Divide by 3, then we simply divide whole thing by 3, so we have:
[tex]\frac{(n\times12)+15}{3}[/tex]b)
To simplify, let's re-write:
[tex]\begin{gathered} \frac{(n\times12)+15}{3} \\ =\frac{12n+15}{3} \\ =\frac{12n}{3}+\frac{15}{3} \\ =4n+5 \end{gathered}[/tex]This is the simplified form.
1. Jessica finishes her book in 2 1/3
hours. Eric takes 1 1/2
times longer than
Jessica to finish his book.
This model represents the amount of time Jessica takes to finish her
book. It has a width of 1 and a length of 2 1/3
. The model is 2 1/3 out of 3
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Proportionately, the number of hours it takes Eric to finish the book as Jessica is 3¹/₂ hours.
What is proportion?Proportion refers to the ratio of the quantity contained in a number or value concerning another value's ratio.
Proportions, like ratios, are fractional values, represented using decimals, fractions, or percentages.
In ratio terms, Eric's reading time is 3¹/₂ hours to Jessica's 2¹/₃ hours, giving an absolute ratio of 3: 2 with a constant proportionality of 1.5 hours.
For instance, the product of Eric's reading time, compared to Jessica's reading time, shows that Jessica does a faster reading than Eric.
The total number of hours it takes Jessica to finish her book = 2¹/₃ hours
The total hours it takes Eric to finish the book = 2¹/₃ hours x 1¹/₂
= 3¹/₂ hours (2¹/₃ x 1¹/₂).
Thus, whereas Jessica takes 2¹/₃ hours to finish the book, in proportion, Eric consumes 3¹/₂ hours reading the same book.
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Complete Question:Jessica finishes her book in 2¹/₃ hours. Eric takes 1¹/₂ times longer than Jessica to finish his book. How long did Eric take to finish the book?
What is theUpper Quartile (the median of 35, 38, 39, 61)?
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Solution:
Given the following data below
[tex]35,38,39,61[/tex]The upper quartile, Q₂, (median) will be
[tex]\begin{gathered} Q_2=\frac{38+39}{2}=\frac{77}{2}=38.5 \\ Q_2=38.5 \end{gathered}[/tex]Hence, the answer is 38.5
6. The graph shows how much money Priya has in her savings account weeksafter she started saving on a regular basis.
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Given:
Graph is given.
6a.
[tex]\text{Money in the account after 10 weeks= \$320}[/tex]6b.
[tex]\text{Number of weeks take to save \$200= 5 weeks}[/tex]6c.
[tex]\text{Priya have \$80 in her account when she started the savings regularly}[/tex]Hello, I need some assistance with this precalculus question, please?HW Q8
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STEP - BY - STEP EXPLANATION
What to find?
• The system of equation of the argumented matrix.
,• The resultant after the given row operations.
Given:
The system of equation is:
7x - 7y + z = -5
3x - 3y + 8z = -5
-6x + y + 3z = 7
Hence, the correct option is D
The following row operations are to be performed;
[tex]\begin{gathered} R_1=-2r_2+r_1 \\ \\ R_3=2r_2+r_3 \end{gathered}[/tex]The first row operation implies that you will multiply row 2 by -2 and then add to row. The resultant gives a new row 1.
This means that the elements in row 1 becomes:
Row 1 : 1 -1 - 15 | 5
Row 2: 3 -3 8 | -5
As for row 3, we will multiply row 2 by 2 and then add to row 3 to get a new row 3.
That is;
Row 3 : 0 -5 19 | -3
ANSWER
Option D
Part B
[tex]\begin{bmatrix}{1} & {-1} & {-15\text{\mid}} & {5} \\ {3} & {-3} & {8\text{ }}| & {-5} \\ 0{} & -5{} & {19\text{ }|} & {-3} \\ {\placeholder{⬚}} & {\placeholder{⬚}} & {\placeholder{⬚}} & {\placeholder{⬚}}\end{bmatrix}[/tex]1 -1 - 15 | 5
3 -3 8 | -5
0 -5 19 | -3
if a fraction product always l esser than the lesser factor
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We have that whenever you multiply two positive fractions, the product will be smaller than both factors. For example, if we have the following:
[tex]\frac{1}{2}\cdot\frac{3}{4}=\frac{3}{8}[/tex]notice that both factors are fractions and the product is less than both factors.
Owners of a recreation area are adding water to a pond. The graph below shows the amount of water in the pond (in liters) versus the amount of time that water is added (in hours).Use the graph to answer the questions.(a)How much does the amount of water increase for each hour that water is added?liters=(b)What is the slope of the line?
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GIVEN:
We are given a graph showing the increase in the amount of water pumped into a pond for every passing hour.
Required;
To determine the amount of increase in the water level for each hour that water is added.
Also, to determine the slope of the line as shown in the graph.
Step-by-step solution;
(a) Notice that the graph shows an increase in the water level for every passing hour. Notice also the following relationship;
[tex]\begin{gathered} (hours,liter) \\ \\ (0,100) \\ \\ (1,400) \\ \\ (2,700) \\ \\ (3,1000) \end{gathered}[/tex]We can see that the rate of change for every hour is 300 liters increment.
Therefore, for each hour that water is added, there is an increase of 300 liters.
(b) To calculate the slope of the line shown in the graph, we shall take the change in liters and divide by the corresponding change in the hours.
We now have the following;
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \end{gathered}[/tex]The variables are;
[tex]\begin{gathered} (x_1,y_1)=(0,100) \\ \\ (x_2,y_2)=(1,400) \end{gathered}[/tex]We now have the slope as follows;
[tex]\begin{gathered} m=\frac{400-100}{1-0} \\ \\ m=\frac{300}{1}=300 \end{gathered}[/tex]The slope therefore is 300.
ANSWER:
[tex]\begin{gathered} (a)\text{ }Liters=300 \\ \\ (b)\text{ }slope=300 \end{gathered}[/tex]Which expressions simplify to a rational answer.
Question is attached below
Answers
The expression that simplify to rational number are as follows:
1 / 4 + 1 / 2 2.√9 3.7.(1 / 3) 7. √81 How to find rational numbers?A rational number is a number that is in the form of p/q, where p and q are integers, and q is not equal to 0.
In a simpler terms, If a number can be expressed as a fraction where both the numerator and the denominator are integers, the number is a rational number.
Rational numbers can also be expressed in decimal form.
Rational numbers have terminating decimals.
Therefore, let's find the rational simplification in the options.
1 / 4 + 1 / 2 = 3 / 4 2.√9 = 2 × 3 = 93.7.(1 / 3) = 21 × 1 / 3 = 77. √81 = 7 × 9 = 72learn more on rational numbers here:https://brainly.com/question/7129080
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Which mapping diagram is NOT a function?
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Answer:
D is not a function--an x-value cannot correspond to more than one y-value.
I don’t really need explanation just give answer honestly I will rate you a 5star regardless I thankyou so much for the help!
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Explanation
The information given directly by the picture is that:
[tex]\begin{gathered} CG\cong CH \\ \angle G\cong\angle H \end{gathered}[/tex]This means we have a pair of congruent sides and a pair of congruent angles.
We need one more information to prove congruency. There is no way of getting side information, by if we see the vertex C, the angles make a pair of vertical angles. Vertical angles are congruent, so:
[tex]\angle FCG\cong\angle JCH[/tex]This means now that we have 2 pairs of congruent angles and one pair of congruent sides, so we will use either AAS or ASA.
To determine which is the case, we can visualize the order in which the angles and side appear going around the triangle.
We can see that we have an Angle then the side then the other Angle, so the order is Angle-Side -Angle, so the rule we need to use is ASA.
Answer
Angle-Side-Anlge, that is ASA.
helpppppppppppppppppp
Answers
Answer:
Inverse should be:
f^(-1)(x) = -2x + 5
Step-by-step explanation:
Lesson 4-2: Relations VA Name the ordered pair for each point. C С 1.A 2.B DI 3.C 4.D e е )
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Assign the pair of coordinates for each point (use the graph)
A. (1,4)
B. (-2,-4)
C. (-2,2)
D. (4,-2)
pls help fast I have to submit this soon!! :)
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Since the rectangles are similar, that means their sides are proportional.
Since the bigger rectangle has a base of 24cm and the smaller one's base is 20cm, the proportion the sides hold is
[tex]\frac{24}{20}=1.2[/tex]This means the sides of the larger rectangle are 1.2 times larger than those of the smaller one.
The area of the small rectangle is 80cm². Since
[tex]A=b\mathrm{}h[/tex]where b is the lenght of the base and h is the lenght of the height, then
[tex]80=20\cdot h_1[/tex][tex]\frac{80}{20}=h_1=4[/tex]So the height of the small rectangle will be 4cm. But as we previously deduced, the height of the larger rectangle will be 1.2 times larger than that of the smaller one, so it's height will be
[tex]h_2=4\cdot1.2=4.8[/tex]And so, its are is
[tex]A_2=24\cdot4.8=115.2[/tex]We can confirm this because
[tex]\frac{115.2}{80}=1.44=1.2^2[/tex]which is the proportion the areas of the rectangles hold.
What is the area of the blue shape?
Pls help :(
Answers
Answer:
38.5 sq units
Step-by-step explanation:
Hello!
We can split the shape into two rectangles.
The small rectangle at the top has an area of 14 sq units (2 * 7).
The middle rectangle has an area of 49 sq units ( 7*7).
Since the blue part in the middle rectangle is half of the whole rectangle, the area of the blue part there is 24.5 sq units.
Adding that to 14 sq units will give us 38.5 sq units.
Original amount: 25End amount: 18
Answers
The formula to calculate the percentage change is given as
[tex]\text{Percentage Change = }\frac{Original\text{ Amount}-\text{Final Amount}}{Original\text{ Amount}}\times100[/tex]The question gives us:
Original amount: 25
End amount: 18
Substituting, we have
[tex]\begin{gathered} C=\frac{25-18}{25}\times100 \\ =\frac{7}{25}\times100 \\ =28 \end{gathered}[/tex]The percentage change is a 28% decrease.
Select the postulate that is illustrated for the real numbers.
2(x + 3) = 2x + 6
A. The multiplication inverse
B. The addition inverse postulate
C. The commutative postulate for multiplication
D. Multiplication identity
E. The distributive postulate
F. The addition of zero postulate
G. Commutative postulate for addition
Answers
The postulate that is illustrated for the real numbers 2(x + 3) = 2x + 6 is The Distributive postulate , the correct option is (E) The Distributive postulate .
The Distributive Postulate states that for any three numbers a,b and c ,
a(b+c) = a*b + a*c
For Example : 5(6+1) = 5*6 + 5*1
5*7 = 30+5
35=35
In the question ,
it is given that
2(x + 3) = 2x + 6
On applying Distributive postulate in 2(x + 3)
we get
= 2*x + 2*3
= 2x + 6
hence Distributive postulate is applied in 2(x + 3) = 2x + 6 .
Therefore , the postulate that is illustrated for the real numbers 2(x + 3) = 2x + 6 is The Distributive postulate , the correct option is (E) The Distributive postulate .
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Write the decimal for each word. Then round the answer to the nearest tenthc) nine hundred forty-two ten-thousandths
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nine hundred forty-two ten-thousandths:
1. Write the first part as a number: nine hundred forty-two
nine hundred: 900
forty-two: 42
900+42= 942
2. Identify the position of number above in the decimal knowing that ten-thousandths ends in 4 disgits after the decimal point (the last digit of number above needs to be in the ten-thousandths position):
The given number is: 0.0942Rounded the answer to the nearest tenth: 0.1Drag and drop the correct value next to its equivalent expression number maybe use ones are not at all.
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Solution:
Expression:
[tex]\begin{gathered} \frac{2}{3}\times42=2\times14 \\ \frac{2}{3}\times42=28 \end{gathered}[/tex]Expression:
[tex]\begin{gathered} \frac{5}{12}\times26=\frac{5}{6}\times13 \\ \\ \frac{5}{12}\times26=\frac{65}{6} \\ \\ \frac{5}{12}\times26=10\frac{5}{6} \end{gathered}[/tex]ANSWER:
[tex]\frac{5}{12}\times26=10\frac{5}{6}[/tex]Expression:
[tex]\begin{gathered} \frac{11}{15}\times20=\frac{11}{3}\times4 \\ \\ \frac{11}{15}\times20=\frac{44}{3} \\ \\ \frac{11}{15}\times20=14\frac{2}{3} \end{gathered}[/tex]ANSWER:
[tex]\frac{11}{15}\times20=14\frac{2}{3}[/tex]Expresion:
[tex]\begin{gathered} \frac{3}{8}\times54=\frac{3}{4}\times27 \\ \\ \frac{3}{8}\times54=\frac{81}{4} \\ \\ \frac{3}{8}\times54=20\frac{1}{4} \end{gathered}[/tex]ANSWER:
[tex]\frac{3}{8}\times54=20\frac{1}{4}[/tex]Maria is planting a row of flowers in a bed 77 feet long. The instructions say to space the plants 1 foot apart, allowing room for 77 flowers. The flowers come in flats containing 6 plants per flat.
Answers
She will need 12 flats and there will be 5 leftovers
The number of flats she will needFrom the question, we have
Length = 77 feetDistance apart = 1 footNumber of flowers = 77Rate = 6 plants per flatThe number of flats is calculated as
So, we have the following equation
Number of flats = (Length)/Rate
So, we have
Number of flats = (77)/6
Evaluate
Number of flats = 12
The number of plants leftoverThis is calculated as
Leftover = Length - Number of flats * Rate
So, we have
Leftover = 77 - 12 * 6
Evaluate
Leftover = 5
Hence, the left over is 5
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Missing information in the question
How many flats will she need?How many plants will she have left over?Convert the numeral in base ten. (Explanation please)
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Converting the given expression which is [tex]43_{8}[/tex] to base ten gives 35 in base ten.
How to convert a number in base eight to base tenConversion of bases is achieved based on how the conversion to be done are are basically of two methods which are
conversion from other bases to base tenconversion from base ten to other basesThe question is about converting other bases (base eight) to base ten. The steps required are as follows:
For other bases, the number 8 as used is replaced by the number required to be convertedThe exponents starts from zero and increases from left to right as seen belowThe given data is a number in base eight
[tex]43_{eight}[/tex]
[tex]43_{eight}=4*8^{1}+3*8^0[/tex]
[tex]43_{eight}=4*8+3*1[/tex]
[tex]43_{eight}=32+3[/tex]
[tex]43_{eight}=35[/tex]
The number 35 is now in base ten and can be written as [tex]35_{10}[/tex]
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A savings account has $2000 in it, earns no interest, andreceives a deposit of $150 per month.What type of growth characterizes the account's change invalue?
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SOLUTION
The question can be written in equation form as:
2. what is equivalent ratio of 9:63. How will you find equivalent ratiosA. add counting number to both ends of given ratioB. divide a counting number to the numerator off the first termC. multiply a counting number to the denominator onlyD. multiply divide a counting number both terms of the given ratio4. what is equivalent ratio of 3:8 5. what kind of rats you have different numbers but represent the same relationshipA. Fraction B. rate C. terms D. equivalent ratios
Answers
Given:
The ratio is 9:6.
The equivalent ratio is,
[tex]9\colon6=\frac{9}{6}=\frac{3\cdot3}{3\cdot2}=\frac{3}{2}[/tex]Answer: the ratio equivalent to 9:6 is 3:2.
A study done by researchers at a university concluded that 60% of all student athletes in the country have been subjected to 74 repeating the study is based on responses from 1600 athlete what is the margin of error and the 95% confidence interval of the study 
Answers
The marginal error is 0.0240
The 95% confidence interval for the proportion of all student athletes in this country have been subjected to some form of hazing is (0.576, 0.624).
Given,
The percentage of students surveyed = 60%
Number of athletes = 1600
Confidence interval = 95%
We have to find the marginal error and 95% confidence interval of the study;
The following results are obtained from a sample of n people that were surveyed, with a probability of success of π and a level of confidence of 1 - ∝
π ± z [tex]\sqrt{\frac{\pi (1-\pi )}{n} }[/tex]
Where,
z is the z score with a p value of 1 - ∝/2
Here we have,
n = 1600 and π = 0.6
95% confidence level
So ∝ = 0.05 , z is the value of Z that has a pvalue of 1 - 0.05/2 , so Z = 1.96.
Then, the margin of error is;
M = [tex]z\sqrt{\frac{\pi (1-\pi )}{n} }[/tex]
M = [tex]1.96\sqrt{\frac{0.6.0.4}{1600} }[/tex]
M = 0.0240
M = 2.40 percentage points.
Lower limit of the interval;
π - M = 0.6 - 0.0240 = 0.576
Upper limit of the interval;
π + M = 0.6 + 0.0240 = 0.624
The 95% confidence interval for the proportion of all student athletes in this country have been subjected to some form of hazing is (0.576, 0.624).
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mark wrote this description of a quadrilateral he drew it has one pair of parallel lines and two congruent lines but the lines that are congruent are not parallel
Answers
First, draw two parallel lines:
Next, draw to additional lines of the same length that connect both parallel lines:
Notice that this can be done in two different ways. In the case in red, both lines are not parallel. In the case shown in blue, they are. Since the problem asks for the case when they are not parallel, keep in mind the figure with the lines in red. That figure is a trapezoid.
May I please help with this. I have tried to find the correct answers but still couldn’t get them right
Answers
Solution
[tex]1cm\text{ to 7in}[/tex]We can use ratio to solve the problem
Part A
5cm to x in
[tex]\begin{gathered} 1cm\colon7in \\ 5cm\colon x\text{ in} \end{gathered}[/tex]Now
[tex]\begin{gathered} 1\colon7 \\ 5\colon x \\ \therefore\frac{1}{7}=\frac{5}{x} \\ \\ \text{cross multiply} \\ 1\times x=5\times7 \\ x=35 \end{gathered}[/tex]The final answer
[tex]5cm\text{ to 35inches}[/tex]Part B
Similar step as part a
[tex]\begin{gathered} 1\colon7 \\ y\colon63 \\ \frac{1}{7}=\frac{y}{63} \\ \\ \text{cross multiply} \\ 7y=63 \\ \text{divide both sides by 7} \\ \frac{7y}{7}=\frac{63}{7} \\ y=9 \end{gathered}[/tex]The final answer
[tex]9cm\text{ to 63inches}[/tex]Summary
Given the exponential decay function below:Determine the intervals of increase and decrease.
Answers
Given the equation of exponential decay function:
[tex]y=(\frac{1}{3})^x-3[/tex]The given function always decreases overall the domain
so, the answer will be the intervals of decrease is:
[tex](-\infty,\infty)[/tex]1 x(x-2) how I do this
Answers
x(x-2)
Apply the distributive property:
x(x)+x(-2)
x^2-2x
Solve for u.u + 8 = 16
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In this case the answer is very simple. .
We must apply algebraic rules to find the solution.
u + 8 = 16
u = 16 - 8
u = 8
The answer is:
u = 8
Identify the outlier in the data set. Then find the mean, median, and mode of the data set when the outlier is included and when it is not. 117 211 186 17637275122922283129142197102
Answers
SOLUTION:
Case: Outliers in a data set
Given: A set of numbers:
117, 211, 186, 176, 372, 7, 51, 229, 222, 83, 129, 142, 197, 102.
Required:
A) Identify the outliers
B) Mean with outliers
C) Median with outliers
D) Mode with outliers
E) Mean without outliers
F) Median without outliers
G) Mode without outliers
Final Answers
A) The outliers
First we arrange the data:
7, 51, 83, 102, 117, 129, 142, 176, 186, 197, 211, 222, 229, 372
Now we select the outliers
Because of the space in the data, the suspected outliers are:
7
because it is far from the central values
B)
The mean with outliers
[tex]\begin{gathered} mean=\frac{7+51+83+102+117+129+142+176+186+197+211+222+229+372}{14} \\ Mean=\text{ 158.9} \end{gathered}[/tex]C)
Median with outlier
Median = (142+176)/2
Median= 159
D) Mode with outlier
This data has no mode
E) Mean without outlier
51, 83,102, 117, 129, 142, 176, 186, 197, 211, 222, 229, 372
[tex]\begin{gathered} Mean=\text{ }\frac{51+83+102+117+129,+142+176+186+197+211+222+229+372}{10} \\ Mean=\text{ 170.5} \end{gathered}[/tex]F) Median without outlier
Median = 176
G) Mode without outlier
The data has no mode