The ladder needs to make an angle of approximately 54.7 degrees with the house in order for Brigid to reach 18 feet up the side of the house.
To determine the angle the ladder needs to make with the house, we can use the tangent function.
First, we'll need to determine the opposite side (the height that the ladder needs to reach) and the adjacent side (the distance from the base of the ladder to the house) of the triangle formed by the ladder and the house.
Opposite side = 18 feet
Adjacent side = 25 feet
We can then use the tangent function to find the angle:
tan(angle) = opposite / adjacent
Solving for the angle, we get:
angle = arctan(18/25) = approximately 54.7 degrees
Therefore, the ladder needs to make an angle of approximately 54.7 degrees with the house in order for Brigid to reach 18 feet up the side of the house.
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A carpet, measuring 4m by 2. 5 m, cost $86. Find the cost of a carpet of the same quality, measuring 5m by 3m.
The cost of a carpet of the same quality, measuring 5m by 3m is $129.
We can use the unitary method to solve this problem. The unitary method is a technique used for solving a problem by first finding the value of a single unit, and finding the necessary value by multiplying the single unit value.
In this question, it is given that a carpet measuring 4m × 2.5m costs $86. That means the 10m² area of carpet costs $86 if we divide 10 by both the cost and area of the carpet we will find that, 1 m² area of carpet will cost $8.6. So the cost of a carpet of 5m × 3m will be the area of the carpet multiplied by the cost of the carpet per 1 m² i.e, 15m² of carpet will cost $8.6 × 15 which is equal to $129.
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What are angles 2 and 8 called?
The Angle 2 and angle 8 in the given figure are called as the alternate interior angle and they are equal .
What are Alternate Interior Angles ?
The alternate interior angles are defined as the angles that are formed when a transversal intersects the two coplanar lines.
The alternate interior angles lie on inner side of parallel lines but they are on the opposite sides of the transversal.
So , From the figure we can conclude that the angle 2 , angle 8 and angle 3 and angle 5 are the alternate interior angles .
Therefore , the angle 2 and 8 are alternate interior angles.
The given question is incomplete , the complete question is
What are the angles 2 and 8 called in the given figure ?
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A family of 3 children and 2 adults visited a health club. The club charges sy an hour for each child and $x an hour for each adult. If the family does not want to spend more than $30 an hour at the health club, which of the following graphs best models the situation? Your answer: 16 14 12 10 O 2 2 8 10 12 14 14 12 4 2. + -2 -2 2 4 6 8 10 12 14 10 10 14 101214 a O 2 2 4 8 101214 -2
We have inequality. So, we have to take a test point (0,0) and as the statement is true therefore Graph will shade towards the test point (0,0).
2(0)+3(0) ≤ 30 => 0≤ 30
What is inequality?An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.
A family of 3 children and 2 adults visited a health club. The club charges $y an hour for each child and $x an hour for each adult.
First we make inequality according to question.
In a family number of children 3
Charge for 1 child = $y per hour
Charge for 3 children = 3y
Charge for 1 Adult = $x per hour
Charge for 2 adults = 2x
If the family does not want to spend more than $30 an hour at health club.
2x+3y≤30
Where, x and y should be greater than 0.
x≥0 and y ≥0
Now we make the graph of this inequality.
First we take equality of equation and then find x and y table.
2x+3y=30
x y
0 10
6 6
15 0
Here we have inequality. So, we have to take a test point (0,0)
2(0)+3(0) ≤ 30 => 0≤ 30
This statement is true. So, Graph will shade towards the test point (0,0)
Please see the attachment for graph:
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Find m (angle) 1 . Then classify the triangle by its angles.
M (angle) 1 =
Answer:
60 degrees and an equilateral triangle
Step-by-step explanation:
every triangle adds to 180 degrees
add 60+60=120
180-120=60 to find remaining angle
all angles are the same which makes all sides the same: equilateral
Answer:
1 =60
Step-by-step explanation:
a+b+c=180
60+60+c=180
120+c=180
-120. -120
c=60
Jaimie ran 3 1/2 on Monday. She ran half
as far on Tuesday as she did on Monday. How
far did Jaimie run in all on Monday and
Tuesday?
Answer: So Jamie ran 3 1/2 miles on Monday and half that distance on Tuesday. We need to know how far she ran "in all" which are key words for "addition".
We need to add 3 1/2 + (1/2)(3 1/2)
It's probably easiest to do this by converting to an improper fraction.
So let's convert:
3 1/2 is the same as 7/2. now we can rewrite the problem:
7/2 + (1/2)(7/2)
= 7/2 + 7/4 . Now we need a common denominator:
7/2 = 14/4
Now we have 14/4 + 7/4 = 21/4. Now we should convert to a mixed number.
21/4 = 5 1/4
So Jamie ran 5 1/4 miles in all.
Step-by-step explanation:
Answer:
5.25 or 5 1/4 (Whichever you prefer)
Step-by-step explanation:
To make it simpler, we will convert 3 1/2 to decimal format.
First, take 3 and multiply it by the denominator 2 of 1/2, then add that number to the numerator of 1/2
3 x 2=6 -> 6+1=7
now add the denominator 2 under 7 and we now have 7/2, the equivalent to the mixed number 3 1/2
Afterward, to get the decimal, divide the numerator by the denominator:
7 divided by 2= 3.5
Now halve 3.5 to get the number Jaimie ran on Tuesday -> 1.75
Then add both 3.5 (3 1/2) and 1.75 (1 3/4), to get 5.25 or 5 1/4, which is your answer.
X is an odd number , if the next odd number is 3x
Since X is an odd number, x+2 is the following odd number. If x is an even number, the subsequent odd number is x + 1.
The odd even rule is what ?The vehicles that will travel on the highways on particular days are decided by the Odd-Even rule, a space rationing system. According to the plan, vehicles with odd and even numbers will travel the roads on alternate days.
The unusual method is what?In jQuery, the odd() method is used to pick elements with odd index numbers (such as 1, 3, 5, etc.). The index begins at zero. It picks odd numbers, unlike the even() function, which is comparable. From the set of chosen items, the odd() method returns the odd indexed elements.
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Four people each roll a fair die once. Quantity A: The probability that at least two people will roll the same number Quantity B: 70%
How likely something is to occur is known as its probability.Probability when die rolled 1st time is 6C1 i.e. (1,2,3,4,5,6).
Find the probability ?How likely something is to occur is known as its probability.We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability.
Probability when die rolled 1st time=6C1 i.e. (1,2,3,4,5,6) suppose 1 comes, then 2nd time it should not be .as it is given that no 2 people will roll same number.
so 2nd time probability=5C1 i.e. (2,3,4,5,6). same way 3rd and 4th time probability=4C1 and 3C1 respectively.Probability that no one rolls the same no. = 6*5*4*3and total possibility =6^4
p(same number)= 6*5*4*3/ 6^4
= 5/18
p(no same number will roll)=1-5/18
=13/18
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a pair of sneakers in on sale as shown the sale price is $51. This is 75% of the original price. what was the original price of the shoes
pls help explanation required
Answer:
$68
Step-by-step explanation:
Let x = original price.
The sale price is 75% of the original price, so the sale price is 75% of x.
75% as a decimal is 75/100 = 0.75
75% of is the same as 0.75x
We are told the sale price is $51, so 0.75x must equal $51.
0.75x = 51
Divide both sides by 0.75 to find the value of x.
x = 51/0.75
x = 68
Answer: $68
Answer:
Step-by-step explanation:
$51 is 75% of 100%
75% = 3/4
51 / 3 = 17
17 = 1/4
51 + 17 = 68
$68 is the original price of the shoes
What are the 4 types of polynomials terms )?
Constant or Zero polynomial, Linear polynomial, Quadratic polynomial, Cubic polynomial, and Quartic polynomial are the five kinds of polynomials.
A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.
An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
By noticing which formulas only contain the operations of addition, subtraction, multiplication, and non-negative integer exponents, the polynomials may be located. Expressions with additional operations are considered non-polynomial expressions.
Constant Polynomial Function: P(x) = a = ax.
Zero Polynomial Function: P(x) = 0; where all ai's are zero, i = 0, 1, 2, 3, …, n.
Linear Polynomial Function: P(x) = ax + b.
Quadratic Polynomial Function: P(x) = ax2+bx+c.
Cubic Polynomial Function: ax3+bx2+cx+d.
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Graph the solution to this inequality on the number line.
−8+x<−3
marking brainliest
The inequality is solved as x < 5 and it is plotted on the number line.
What is linear inequality?Linear inequality refers to the relation between a linear algebraic expression to some known value that contains inequality sign.
Unlike a linear equation it can have a range of values inside an interval.
The given inequality is −8 + x < −3.
It can be solved as follows,
⇒ −8 + x < −3
Add 8 both sides as,
⇒ 8 + −8 + x < −3 + 8
⇒ x < 5
It can be plotted on the number line as follows,
Hence, the solution is given as x < 5 and it is represented on the number line with clarity.
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What do you call the angle measures 90 180 and 270?
An angle that measures 90 degrees is called a right angle, an angle that measures 180 degrees is called a straight angle and an angle that measures 270 degrees is called a reflex angle.
A right angle is an angle that measures exactly 90 degrees. It is formed by the intersection of two lines that are perpendicular to each other. A right angle is symbolized by a small square at the vertex of the angle.
A straight angle is an angle that measures exactly 180 degrees. It is formed by the intersection of two lines that are collinear, that is, they lie on the same line. A straight angle is represented by a straight line, usually with an arrow on one end pointing in the direction of the other end.
A reflex angle is an angle that measures greater than 180 degrees but less than 360 degrees. It is formed by the intersection of two lines that are not collinear, that is, they don't lie on the same line and the angle is greater than a straight angle. A reflex angle is represented by an arc with a curved arrow on one end, pointing in the direction of the other end.
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0.7 times square root of 300
The value of the expression 0.7 x √300 is 12.124.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
0.7 x √300
This can be written as,
= 0.7 x √3 x √100
= 0.7 x 1.732 x 10
= 12.124
Thus,
The value is 12.124.
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You are given that $x$ is directly proportional to $y^3$, and $y$ is inversely proportional to $\sqrt{z}$. If the value of $x$ is 3 when $z$ is $12$, what is the value of $x$ when $z$ is equal to $75$
The value of x when z is equal to 75 is [tex]$3\sqrt{75}$[/tex]
To calculate the value of $x$ when $z$ is equal to $75$, first rewrite the given proportionality as equations.
When x is directly proportional to [tex]$y^3$[/tex], the equation is given by:
[tex]$x = ky^3$[/tex]
where k is the constant of proportionality.
Similarly, when y is inversely proportional to [tex]$\sqrt{z}$[/tex], the equation is given by:
[tex]$y = \frac{m}{\sqrt{z}}$[/tex]
where m is the constant of proportionality.
Substituting the second equation into the first equation gives:
[tex]$x = k\left(\frac{m}{\sqrt{z}}\right)^3$[/tex]
Since the value of x is 3 when z is 12, the equation can be written as:
[tex]$3 = k\left(\frac{m}{\sqrt{12}}\right)^3$[/tex]
Rearranging gives:
[tex]$k = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}$[/tex]
Substituting this value of k into the original equation gives:
[tex]$x = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}\left(\frac{m}{\sqrt{z}}\right)^3$[/tex]
Substituting z as 75 gives:
[tex]$x = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}\left(\frac{m}{\sqrt{75}}\right)^3$[/tex]
Simplifying gives:
[tex]$x = \frac{3}{\left(\frac{m}{\sqrt{12}}\right)^3}\left(\frac{\sqrt{12}}{\sqrt{75}}\right)^3m^3$$x = \frac{3m^3}{\left(\frac{m}{\sqrt{75}}\right)^3}$$x = \frac{3m^3\sqrt{75}}{m^3}$$x = 3\sqrt{75}$[/tex]
Therefore, the value of x when z is equal to 75 is [tex]$3\sqrt{75}$[/tex].
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What is the value of x in3 √ x 9?
In the given equation x = 9 is the value that satisfies the equation.
What are Square root?The square root of a number is a value that, when multiplied by itself, equals the original number. For example, the square root of 9 is 3, because [tex]3*3 = 9[/tex]. The symbol for square root is "√" and it can also be represented as "sqrt".
In the given equation [tex]x = 9[/tex] is the value that satisfies the equation.
To find the value of x in the equation [tex]3 \sqrt{x} = 9[/tex], we first need to square both sides of the equation to eliminate the square root.
[tex]3 \sqrt{x} = 9[/tex]
Squaring both sides:
[tex](3 \sqrt{x} )^2 = 9^2[/tex]
[tex]x = 9^2 / 3^2 = 9^2 / 9 = 9[/tex]
Therefore, x = 9 is the value that satisfies the equation.
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If $x$ is a positive multiple of 8 and $x^2>100$, but $x<20$, what is $x$?
Answer:
16
Step-by-step explanation:
16 is a positive multiple of 8, in which 16²=256>100 and 16<20 are true statements.
Answer:
[tex]$x=\boxed{16}$[/tex]
Step-by-step explanation:
Since $x$ is a positive multiple of 8, it must be at least 8. Since $x^2>100$ and $x$ is at least 8, the only solution is $x=16$.
To verify this, note that $x=8$ does not satisfy the inequality $x^2>100$, but $x=16$ does, so $x=16$ is the only solution that works.
Therefore, $x=\boxed{16}$.
F18) if y varies jointly as x and the inverse of z, and y = -5 and z = 6, find y when x = 5 and z = -8
Answer:
gfifhdrtjttt9668ztjt*
Jaidyn’s family drinks a total of 10 gallons of milk every 5 weeks . How many gallons of milk does the family drink per week? How many weeks does it take the family to consume one gallon of milk?
Answer:
2 gallons of milk per week
0.35 weeks(3.5 days) to consume 1 gallon
Step-by-step explanation:
Jaidyn's family drinks 10 gallons of milk every 5 weeks, which is a ratio of
10:5
To find how many gallons of milk they drink per week, you'd have to divide 10/5
10 ÷ 5 = 2
Considering that 1 week is 7 days, it would take them 0.35 weeks to consume 1 gallon of milk, which is the same as 3 and a half days.
Please hurry it's timed i need help
The solution of the given function cosx - √(3 - 3cos³x) = 0 is C. 30° + 360° n, 330° + 360°n
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
We are given the function as;
cosx - √(3 - 3cos³x) = 0
cosx = √(3 - 3cos³x)
Taking square root on both sides.
cos ²x = √(3 - 3cos³x) ²
cos ²x = (3 - 3cos³x)
For solving for x in
cos ²x = (3 - 3cos³x)
cos ²x = 3 (1 - cos³x)
(1 - cos³x) = cos ²x/3
x= π/6 + 2πn
or
x=11π/6 + 2πn
where n is an integer.
30° + 360° n, 330° + 360°n
The correct answer is C.
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Grant reads as part of his homework each week. he must read for at least 4 hours each week as part of his homework. This past weekend, he reads for 1.5 hours. Grant makes a graph of the inequality 5n +1.5 greater than or equal to 4 to determine all the numbers,n,of hourse he could read on each of the 5 weekdays this week. The graph is shown. Which describes the solution set of the inequality.
Answer:
It appears that the solution set of the inequality 5n + 1.5 ≥ 4 is the set of all real numbers greater than or equal to -0.3. This can be determined by looking at the graph and noting that the region to the right of the vertical line x = -0.3 is shaded, which indicates that all values of x in that region are included in the solution set.
To verify this, we can substitute -0.3 into the inequality in place of n to see if the inequality is satisfied:
5(-0.3) + 1.5 ≥ 4
This simplifies to:
-1.5 + 1.5 ≥ 4
Which further simplifies to:
0 ≥ 4
Since this is not true, -0.3 is not a solution of the inequality. However, all values of x that are greater than or equal to -0.3 are solutions, as indicated by the shaded region on the graph.
Step-by-step explanation:
30% of n = 84
please help I'll put as brainlisest
Write 30% as 30100Since, finding the fraction of a number is same as multiplying the fraction with the number, we have
30100 of 84 = 30100 × 84Therefore, the answer is 25.2
If you are using a calculator, simply enter 30÷100×84 which will give you 25.2 as the answer.
How do you find the mean and standard deviation of a simple random sample?
The steps of finding mean and standard deviation of a simple random sample are given below.
What is standard deviation and mean?
The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.
There are various mean types in mathematics, particularly in statistics. Each mean serves to summarize a specific set of data, frequently to help determine the overall significance of a specific data set.
The steps of finding mean and standard deviation of a simple random sample are:
Divide the population standard deviation (σX) by the square root of the sample size (n) to get the standard deviation of the sample mean (σX): = σ/n.
How to determine sample means
Add up the examples' components. You must first count the number of sample items in each data set and then add up all of the sample items. ...
Sum divided by the quantity of samples.
The outcome is the mean.
To determine the variance, use the mean.
To determine the standard deviation, use the variance.
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A large helium balloon is tethered to the ground by two taut lines. One line is 100 ft. Long and makes an 80 degree angle with the ground. The second line makes a 40 degree angle with the ground. How long is the second line?
The second line is 153ft long.
We are making a figure out of the given statment. Where we have the Triangle ABC and other two Triangle ADB and ADC inside Triangle ABC. Here Angle ADC = 80 degress and Angle ACD = 40 egress.
According to given statement and figure,
In triangle ABO, AD= 100 ft
Hence, BD/AD = Cos80
or, BD = (100 * Cos80)
or, BD = 17.36 ft
Now, AB/AD = Sin80
or, AB = (100* Sin 80)
or, AB = 98.48
Now, In case of triangle ABC
AB/AC = Sin40
or, AC = AB/ Sin 40
or, AC = 98.48/ Sin40
or, AC = 153.2 ft (nearly equal to 153 ft)
The second line is 153ft long.
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Find (angle) Then classify the triangle by its angles.
M (angle) 1 =
Answer:
m∠1 = 110°obtuse triangleStep-by-step explanation:
You want to find the measure of the angle designated as ∠1, given the other two have measures of 40° and 30°. You also want the classification of the triangle based on its angles.
Angle sumThe sum of angles in a triangle is 180°.
40° +∠1 +30° = 180°
∠1 = 110° . . . . . . . . . . . . subtract 70°
Triangle classificationThe classification of a triangle as acute, right, or obtuse is based on the measure of its largest angle. If that angle is 90°, the triangle is a right triangle. If it is less, the triangle is acute; if it is more, the triangle is obtuse.
The angle measure 110° is more than 90°, so this triangle is an obtuse triangle.
HELP!!! Find the value of..
Answer:
The answer to your question is C, 15
Step-by-step explanation:
Answer is 15, C
What are the terms of expression 4x² 3xy?
The given expression , 4x2 – 3xy is having two terms which are 4x2 and –3xy.
The term 4x2 is a product of 4 and x, whereas the other term (–3xy) is a product of (–3), x and y.
When we will join these two terms using the addition operation we will get the result as 4x2 – 3xy .
The given equation is an example of an algebraic expression and they are made up of combination of constants and variables. They are joined to each other by various operations such as addition , multiplication , division and subtraction.
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Is (- 2 4 a solution to the system?
yes, (-2,4) is the solution of the system of equation 4x² - 4y = 0.
To check whether the given points are the solution of the given system of equation 4x² - 4y = 0. We have to put the values of x = -2 and y = 4 in the given equation. If we get the result equals zero then (-2, 4) is the solution of 4x² - 4y = 0 and if the result is a non-zero number then (-2, 4) is not the solution of 4x² - 4y = 0.
⇒4x² - 4y = 0
⇒4(-2)² - 4 × 4 = 0
⇒4 × 4 - 4 × 4 = 0
⇒0 = 0
Here we get the result equal to zero, hence (-2,4) is the solution of the system of equation 4x² - 4y = 0.
--This question is incomplete, the complete question is
''Is (-2,4) a solution of the system of equation 4x² - 4y = 0?''--
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HI!!
can someone help with ts
Function Notation: another way of representing the relation between two variables, y is denoted as f(x) and x remains.
x is the input and f(x) is the output
This question is essentially asking what is the output of the function when the input is equal to 5.
[tex]f(5) = (5)^2-2(5)[/tex]
[tex]f(5) = 25-10[/tex]
[tex]f(5) = 15[/tex]
the range of daliyh temperatures during march was 32 degreed and the range of the daily temperatures during july was 8 degrees which month had a greater difference between the hottest abd coldeest temperaturw4
Difference between coldest and hottest temperature was greater in march than July.
What is range?The range is the difference between the highest and lowest values within a set of numbers. To calculate range, subtract the smallest number from the largest number in the set.
Given,
Range of temperature in march = 32°
⇒ difference in temperature in march ΔT = 32°
Range of temperature in July = 8°
⇒ difference in temperature in July Δt = 8°
By the above observation
ΔT > Δt .
difference in temperature in march > difference in temperature in July.
Hence, In month of march, there was greater difference between the hottest and coldest temperature than in month of July.
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Graph the system.
What is the estimated solution of the system?
Enter your answer in the blanks. Round each coordinate to the nearest integer.
The lines intersect closest to the integer coordinates
The solution to the system of linear equations (x, y) lies along 4 and 7 and the graph is attached below.
What is Graph of System of Linear EquationsA graph of a system of linear equations is a set of points in a coordinate plane that represent all the solutions to the system of equations. The graph can be visualized as a collection of lines that intersect at the points that are solutions to the system.
In the given problem, we have two linear equations which are
y = 3x - 6 ...eq(i)
y = 2/5x + 5 ...eq(ii)
Plotting the two equations on a graph using a graphing tool, the point of intersection is the solution to the system of linear equation.
The coordinates to the nearest integer are (x, y) 4 and 7
The value of x is 4 and y is 7
Kindly find attached graph below.
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Find the volume of the following figure.
(I need a answer to this very soon so if anybody can answer id really appreciate it :))
The volume of the prism is 103.32 cubic inches (optionD)
What is the volume of a prism?Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.
The formula for the volume of a prism is V=Bh , where B is the base area and h is the height.
The base area of the prism = 4.1×7.2 = 29.52 inches squared.
The height of the prism is 3.5 inches
Therefore volume = base area × height
volume = 29.52× 3.5 = 103.32 cubic inches.
Therefore the volume of the shape is 103.32 cubic inches.
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