The volume of the suitcase is 35/8 cubic feet or approximately 4.375 cubic feet.
What is rectangular prism?A rectangular prism is a three-dimensional solid object that has six faces, where each face is a rectangle. It is also called a rectangular parallelepiped. A rectangular prism is a type of prism because it has a constant cross section along its length.
According to question:A rectangular prism's volume V is determined by:
V = l × w × h
where l denotes the prism's length, w its width, and h its height. Here are the facts:
l = 2 3 ft
w = 1 1/2 ft
h = 1 1/4 ft
When we enter these values into the formula, we obtain:
V = (2 3 ft) × (1 1/2 ft) × (1 1/4 ft)
= (7/3 ft) × (3/2 ft) × (5/4 ft)
= 35/8 ft³
Therefore, the volume of the suitcase is 35/8 cubic feet or approximately 4.375 cubic feet.
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At a local Frozen yogurt store their special includes any 4 toppings from their list of 16 toppings. How many different orders are possible?
A. 43,680
B. 65,536
C. 64
D. 1,820
Do I use the equation nCn or nPn to find the answer?
There are 1820 different orders possible for selecting any 4 toppings out of a list of 16 toppings.
How many different orders are possible?To calculate the number of different orders possible for selecting any 4 toppings out of a list of 16 toppings,
we can use the combination formula:
nCr = n! / r!(n-r)!
where n is the total number of items, r is the number of items to be selected, and ! represents the factorial operation.
Substituting the given values, we get:
16C4 = 16! / 4!(16-4)!
16C4 = (16 × 15 × 14 × 13) / (4 × 3 × 2 × 1)
16C4 = 1820
Therefore, there are 1820 different orders possible.
Option D. 1,820 is the correct option.
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The table below gives the probability density of trees in a particular park. If a tree is selected at random, what is the probability that it is an elm or oak?
The probability of selecting an elm or oak tree is 0.38.
The probability of selecting an elm or oak tree is the sum of the probabilities of selecting an elm and selecting an oak:
P(elm or oak) = P(elm) + P(oak)
P(elm) = 0.04
P(Oak) =0.34
Plug in these values
= 0.04 + 0.34
= 0.38
Therefore, the probability of selecting an elm or oak tree is 0.38.
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(cscx+sexc)/(sinx + cosx) = cotx + tanx
It is true. The trigonometric identity [tex]\frac{cscx+secx}{sinx + cosx}[/tex] = cotx + tanx
How do we verify or prove that the trigonometric identity (cscx+secx)/(sinx + cosx) = cotx + tanx?To verify that (cscx+secx)/(sinx + cosx) = cotx + tanx
csc = [tex]\frac{1}{sin}[/tex] and Sec = [tex]\frac{1}{cos}[/tex]
If we insert the values, it would be
[tex]\frac{ 1/sinx + 1/cosx}{sinx + cosx}[/tex]
= [tex]\frac{cosx + sinx}{sinx * cosx}[/tex] ÷ ([tex]\frac{1}{sinx + cosx}[/tex])
= [tex]\frac{1}{sinx * cosx}[/tex]
[tex]\frac{Sin^2 x + Cos^2x}{Sin x Cos x}[/tex] = [tex]\frac{Sin^2x}{SinxCosx}[/tex] + [tex]\frac{Cos^2x}{SinxCosx}[/tex]
= cotx + Tanx
Mind you
cotx = [tex]\frac{1}{tanx}[/tex] = [tex]\frac{cosx}{sinx}[/tex]
tanx = [tex]\frac{sinx}{cosx}[/tex]
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What is the answer to
7 + 60 / (3x5)
Pattern A starts at 1 and uses the rule add 5." Pattern B starts at 28 and uses the rule "subtract 4."
What are the next four terms in each pattern?
Enter your answers in the boxes.
For the pattern A, the terms are 6, 11, 16 and 21
For the pattern B, the terms are 24, 20, 16, 12
How to determine the termsTo determine the consecutive terms of the sequence, we need to take note of the rule of each.
From the information given, we have that;
For the Pattern A
Each term is the previous term plus 5
This is represented as;
Pattern A = a + 5,
The first term = 1
Second term = 1 + 5 = 6
Third term = 6 + 5 = 11
Fourth term = 11 + 5 = 16
Fifth term = 16 + 5 = 21
For Pattern B = a - 4
Second term = 28 - 4 = 24
Third term = 24 - 4 = 20
Fourth term = 20 -4 = 16
Fifth term = 16 - 4 = 12
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HELP QUICKLY PLEASE!!!
What are the x-intercepts of the quadratic function shown?
Answer:
D. 1,0 & -3,0
Step-by-step explanation:
because the two lines pass through points 1,0 and -3,0 at the x-axis
Answer:
your answer is D. 1,0 & -3,0
Step-by-step explanation:
In July 1964, an elderly woman was mugged in Costa Mesa, California. In the vicinity of the crime a tall, bearded man sat waiting in a yellow car. Shortly after the crime was committed, a young, tall woman, wearing her blond hair in a ponytail, was seen running from the scene of the crime and getting into the car, which sped off. The police broadcast a description of the suspected muggers. Soon afterward, a couple fitting the description was arrested and convicted of the crime. Although the evidence in the case was largely circumstantial, the two people arrested were nonetheless convicted of the crime. The prosecutor based his entire case on basic probability theory, showing the unlikeness of another couple being in that area while having all the same characteristics that the elderly woman described. The following probabilities were used. Characteristic Assumed probability Drives yellow car 1 out of 12 Man over 6 feet tall 1 out of 10 Man wearing tennis shoes 1 out of 4 Man with beard 1 out of 11 Woman with blond hair 1 out of 3 Woman with hair in a ponytail 1 out of 13 Woman over 6 feet tall 1 out of 100 Compute the probability of another couple being in that area with the same characteristics. Would you use the addition or multiplication rule? Why? Are the characteristics independent or dependent? How are the computations affected by the assumption of independence or dependence? Should any court case be based solely on probabilities? Would you convict the couple who was arrested even if there were no eyewitnesses? Comment on why in today’s justice system no person can be convicted solely on the results of probabilities. In actuality, aren’t most court cases based on uncalculated probabilities?
No, any court case should not be based solely on probabilities as probability does not imply certainty.
How to solveCompute the probability of another couple being in that area with the same characteristics
CHARACTERISTIC ASSUMED PROBABILITY
Drives a yellow car 1 out of 12
Man over 6 feet tall 1 /10
Man wearing tennis shoes 1/4
Man with beard 1/11
Woman with blond hair 1/3
Woman with hair in a ponytail 1 /13
Women over 6 feet tall 1/100
We will use the multiplication rule as all the characteristics should be present in the couple.
The probability of another couple being in that area with the same characteristics is given as
P(Drives a yellow car) x P(Man with beard) x P(Woman with blond hair) x P(Woman with hair in a ponytail) x P(Woman over 6 feet tall) = 1/12 x 1/11 x 1/3 x 1/13 x 1/100 = 1/514800
The characteristics dependent on the sum of the probabilities is not equal to 1.
The assumption of independence would lead to use of the addition rule instead of the multiplication rule, and hence the probability would change (the probability would increase).
No, any court case should not be based solely on probabilities as probability does not imply certainty.
No, the couple who was arrested should not be convicted if there were no eyewitnesses as probability does not imply certainty.
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Use the form |x – b | ≤ c or |x – b | ≥ c to write an absolute value inequality that has the solution set x ≤ –9 or x ≥ –5
what is the answer?
The inequality |x + 7| ≥ 2 has the solution set x ≤ –9 or x ≥ –5, as required.
Writing an absolute value inequalityWe can write an absolute value inequality with the given solution set as follows:
|x + 7| ≥ 2
Here's how we arrived at this inequality:
First, we find the midpoint of the given solution set:
midpoint = (-9 + (-5)) / 2 = -7
Next, we find the distance from the midpoint to each endpoint of the solution set:
distance to -9 = |-7 - (-9)| = 2
distance to -5 = |-7 - (-5)| = 2
The maximum distance is 2, so we use c = 2 in the inequality.
Since the midpoint is to the left of both endpoints, we use the form |x - b| ≥ c.
Plugging in b = -7 and c = 2, we get:
|x + 7| ≥ 2
This inequality has the solution set x ≤ –9 or x ≥ –5, as required.
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i need help with all 4 thanks
Answer: 5,8,6,1
Step-by-step explanation:
math
Write an equation in slope intercept form for the line perpendicular to y= -2x +9 and containing the point (4,-3)
Step-by-step explanation:
lets call the line (d)
amd the given eq of the line is (d')
so (d) is perpendicular to (d')
slope(d)×slope(d')=-1
-2(1/2)=-1
so (d): y=1/2x + b
point A (4, -3) belongs to (d) so,
Ya=1/2Xa+b
-3=1/2(4)+b
b=-5
(d):y=1/2x-5
Luis's cedar chest measures 4 ft long 2 ft wide and 2 1/4 ft high. What is the volume of the chest? PLEASE USE THE FORMULA IN THE STEP BY STEP EXPLANATION! I REALLY NEED HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Solve 3/8 + n = 7/8
giving away 10 points for this
Type the correct answer in each box. Use numerals instead of words.
Consider this system of linear equations.
4x - 3y = -8
3x + 2y = -6
The solution to this system is ( , )
Last week 12 boxes of recycled paper were used this week double that number are used how many boxes in this?
24 boxes were used this week
12 boxes of recycled paper were used last week
For this week double of this amount was used
When calculating double the amount that was used, this means we have to multiply the initial amount by 2
In this case, we have to multiply 12 by 2
= 12 × 2
= 24
Hence 24 boxes of recycled paper was used this week
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The First National Bank pays 8 1/2%?interest per year compounded annually . City Bank pays 8.25 % terest per year compounded daily . In 5 years , what is the difference in the amounts of interest aid on $ 500 by the two banks ? Which bank gave more interest ?
City Bank paid more interest than First National Bank over the 5-year period.
What is compound interest?
Compound interest is the interest earned on both the principal amount and the accumulated interest from previous periods.
We can use the formula for compound interest to calculate the amounts of interest earned by the two banks over 5 years:
Amount of interest with First National Bank = [tex]$P\left(1 + \frac{r}{n}\right)^{n\cdot t} - P$[/tex]
where P is the principal amount, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the number of years.
Amount of interest with First National Bank
=[tex]$500\left(1 + \frac{0.085}{1}\right)^{1\times 5} - 500$[/tex]
= $235.15 (rounded to two decimal places)
Amount of interest with City Bank =[tex]$P\left(1 + \frac{r}{n}\right)^{n\cdot t} - P$[/tex]
where P is the principal amount, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year (365 in this case, since interest is compounded daily), and t is the number of years.
Amount of interest with City Bank
=[tex]$500\left(1 + \frac{0.0825}{365}\right)^{365\times 5} - 500$[/tex]
= $240.45 (rounded to two decimal places)
The difference in the amounts of interest paid by the two banks is:
$240.45 - $235.15 = $5.30
Therefore, City Bank paid more interest than First National Bank over the 5-year period.
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Given a continuous-time system with the input-output relation:
[tex]y(t) = T\left\{x(t) \right\} = x^2(t)[/tex]
Determine whether this system is:
- Linear
- Time-invariant
The given input-output relation is a nonlinear function of the input signal x(t), since it involves squaring the signal at every point in time. A linear system must satisfy the property of superposition, which states that the output to a linear combination of inputs must be the same as the linear combination of the outputs to each individual input.
To determine whether the system is time-invariant, we need to check if a time shift in the input signal produces the same time shift in the output signal. That is, if: [tex]y(t) = T{x(t)}[/tex] for all values of t. Then we want to check [tex]y(t - τ) = T{x(t - τ)}[/tex] for all values of [tex]τ[/tex] and [tex]t[/tex].
We shall the consider the case where [tex]τ > 0[/tex], then we have:
[tex]y(t - τ) = (x(t - τ))^2[/tex]
[tex]T{x(t - τ)} = (x(t - τ))^2[/tex]
Since [tex]y(t - τ) = T{x(t - τ)}[/tex], we can conclude that the given system is time-invariant.
Therefore, the given system is nonlinear but time-invariant.
The volume of a rectangular prism is 5058
50
5
8
cubic inches.
The dimensions are given below.
What is the missing value in the table?
The missing value in the table include the following: B. 4 1/2 in.
How to calculate the volume of a rectangular prism?In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:
Volume of a rectangular prism = L × W × H
Where:
L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have;
50 5/8 = 5 × W × 2 1/4
Width, W = 4 1/2 inches.
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Complete Question:
The volume of a rectangular prism is 50 5/8 cubic inches.
The dimensions are given below.
What is the missing value in the table?
Length Width Height
5 in. 214 in.
A. 79in.
B. 412in.
C. 134in.
D. 1018in.
12. Mr. Wright is five times as old as
his daughter, Lilly. Lilly is twice
as old as her brother, Micah. If
Micah is 3 years old, how old is
Mr. Wright?
Based on the given data, the age of Mr. Wright currently is 30 years
If Micah is 3 years old, then Lilly is twice as old, which means that
Lilly is 2 * 3 = 6 years old.
Now we know that Mr. Wright is five times as old as his daughter, Lilly, so Mr. Wright's age is:
5 * 6 = 30 years old.
Therefore, Mr. Wright is 30 years old.
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can someone help with 6,7,8,9 (tell me if number 9 is right) and 10? i need someone’s help please
The solutions to the dividing fractions prompts are as follows:
6. 4/3
7. 2/13
8. 33/2
9. 24/35
10. 63/20
How to solve the divisionsTo solve the divisions, note that the second divisor is inversed and multiplied. For the following problems, the divisions can be gotten as follows:
6. 8/9 ÷ 2/3
= 8/9 × 3/2
=24/18
=4/3
7. 12/13 ÷ 6
= 12/13 × 1/6
= 12/78
=6/39
= 2/13
8. 11/5 ÷ 2/15
= 11/5 × 15/2
165/10
= 33/2
9. 6/7 ÷ 5/4
6/7 × 4/5
= 24/35
10. 7/2 ÷ 10/9
7/2 × 9/10
63/20
So, the above are ways to determine the step-by-step answers.
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anyone know this answer cus I don’t
Answer: 13 units
Step-by-step explanation:
If you look at the corresponding side on the other triangle, it is also 13, and in the question it say the side on the other triangle has the same length as the one you are finding.
PLS HURRY FOR 80 POINTS Triangle XYZ is drawn with vertices X(4, −5), Y(6, −1), Z(10, −8). Determine the line of reflection if X′(4, 5).
y-axis
x-axis
y = 1
x = −4
Answer: a
Step-by-step explanation:
Two angles lie along a straight line. If m∠A is five times the sum of m∠B plus 7.2°, what is m∠B?
As a result, angle B has a 24 degree measure as the total of the two angles, which are along a straight line, is 180 degrees.
what is angle ?Thus according their size or measurement, angles can be categorised. An oblique angle is larger than 90 degrees but far less than 180 degrees, a straight angle is exactly 90 degree, a right angle is turned 90 degrees, and an acute angle is less than 90 degrees. Reflex angles are angles that are higher than 180o but a little less than 360 degrees, and complete angles are angles that measure exactly 360 degrees. Geometry, trigonometry, physics, engineering, and many other branches of mathematics and science all make use of angles.
given
The total of the two angles, which are along a straight line, is 180 degrees. Let's refer to the angle B's measurement as x.
The information provided in the problem can then be used to create an equation as follows:
m∠A = 5(m∠B + 7.2°)
Due to the fact that the two angles are perpendicular to one another, we may replace mA with 180 - mB:
180 - m∠B = 5(m∠B + 7.2°)
The right side is being widened:
180 - m∠B = 5m∠B + 36
Simplifying and putting all the mB words to one side:
6m∠B = 144
m∠B = 24
As a result, angle B has a 24 degree measure as the total of the two angles, which are along a straight line, is 180 degrees.
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Question 9: Use the function f(t) = -16t^2 + 60t + 16 to answer Part A, B, & C. Part B: identify the line of symmetry vertex of the parabola ( give exact decimal answers )
The line of symmetry of the parabola is t = 1.875 and the vertex of the parabola is (1.875, 77).
What is a function?A function is a mathematical concept that relates an input value (or values) to an output value (or values) according to a specific rule or set of rules. It can be thought of as a machine that takes in one or more inputs and produces a corresponding output. Functions are often represented using function notation, such as f(x) or g(t), where the variable in the parentheses (x or t) represents the input and the value of the function (f(x) or g(t)) represents the output.
According to the given information:To identify the line of symmetry and vertex of the parabola given by the function [tex]f(t) = -16t^2 + 60t + 16[/tex], we need to use the formula:
t = -b/2a
where "a" is the coefficient of the [tex]t^2[/tex] term (-16 in this case) and "b" is the coefficient of the t term (60 in this case).
Part A: Identify the line of symmetry of the parabola.
Using the formula above, we get:
t = -60 / 2(-16) = 1.875
So the line of symmetry of the parabola is t = 1.875.
Part B: Identify the vertex of the parabola.
To find the vertex, we need to substitute the value we found for t into the original function:
[tex]f(1.875) = -16(1.875)^2 + 60(1.875) + 16 = 77[/tex]
So the vertex of the parabola is (1.875, 77).
Therefore, the line of symmetry of the parabola is t = 1.875 and the vertex of the parabola is (1.875, 77).
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If full employment is $2000, how large is the recessionary or inflationary gap?
Answer:
inflationary expenditure gap of $500
Step-by-step explanation:
At AE2 there is an inflationary expenditure gap of $500 (assuming full-employment output is $2000). The fiscal authority could increase taxes or decrease expenditures, which will shift the aggregate expenditures schedule down to AE0.
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Mary can mow Mrs. Greenway’s lawn in 45 minutes. Mary’s little brother takes twice as long to do the same lawn. How long will it take them if they each have a mower and they work together?
Answer:
30 minutes
Step-by-step explanation:
1/45 m + 1/90 m = 1
2/9 m + 1/90 m = 1
3/90 m = 1 Multiply both sides by 90/3
90/3 x 3/90 m = 1 x 90/3
m = 90/3
m = 30
Helping in the name of Jesus.
Help me plssssss I’ll give brainly
The logarithmic form of the equation (1/7)³ = 1/343 is given as follows:
[tex]\log_3{\left(\frac{1}{343}\right)} = \frac{1}{7}[/tex]
How to represent a logarithm?A logarithm is a mathematical function that represents the power to which a given base must be raised in order to obtain a given number. Logarithms are often used to simplify calculations involving very large or very small numbers.
In this problem, we raise 1/7 to the third power to obtain the number 1/343, hence the logarithm of base 3 of the number 1/343 is of 1/7, and then the expression is given as follows:
[tex]\log_3{\left(\frac{1}{343}\right)} = \frac{1}{7}[/tex]
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If XZ ⊥ WY, XE = 4, and WY = 7, what is the perimeter of WXYZ, rounded to the nearest tenth?
The perimeter of the rhombus is approximately 7.6 units.
XZ is perpendicular to WY and XE is 4,
Since WXYZ is a rhombus because only the diagonal of the rhombus and square bisect each other at 90°
By the Pythagorean theorem, we have:
XE² = XY² + EY²
4² = XY² + (7/2)²
XY = 1.9
So the perimeter of WXYZ is 4(XY), rounded to the nearest tenth:
4(1.9) ≈ 7.6 units.
Therefore, the perimeter of the rhombus is approximately 7.6 units.
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As our scientific and technical knowledge has increased, so has our need for ever-smaller and ever-larger units of measure. The prefixes used to denote some of these units of measure are listed in the table below.
These new units of measure are quickly working their way into our everyday lives. For example, it is quite easy to purchase a 1-terabyte hard drive. One terabyte (TB) is equal to 1012 bytes. As another example, many computers can do multiple operations in 1 nanosecond (ns). One nanosecond is equal to 10−9 s.
In the 1980s, it became possible to measure optical events in nanoseconds and picoseconds. Express 1 ps as a decimal.
The expression of 1 picoseconds as a decimal would be = 0.000000000001 picoseconds.
What is a scientific notation representation of figures?The scientific notation of representation of figures is a systematic way of representation of too large or too small figures encountered in everyday arithmetics.
From the table above, the larger figures are represented with 10 ^ X without a negative sign.
But the smallest figures are represented with 10 ^ -X with a negative sign.
The scientific notation for 1 picoseconds = 10^-12
When converted to decimal
= 0.000000000001 picoseconds.
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6.1: Fill in the Box
For each expression, what value would need to be in the box in order for the expression to
be a perfect square trinomial?
10. x² + 10x + __
11. x²-16x + __
12. x² + 40x+ __
13. x2+5x+ __
Fill the blanks fr
(10) The value that will make the equation a perfect square is 25.
(11) The value that will make the equation a perfect square is 64.
(12) The value that will make the equation a perfect square is 400.
(13) The value that will make the equation a perfect square is 6.25.
What is the required value for a perfect square?To make a perfect square trinomial of the form x² + bx + c, we need to add (b/2)² to both sides.
the perfect square is calculated as;
x² + 10x + __
b = 10,
(b/2)² = 25
the perfect square is calculated as;
x² - 16x + __
b = -16
(b/2)² = 64
the perfect square is calculated as;
x² + 40x + __
b = 40
(b/2)² = 400
the perfect square is calculated as;
x² + 5x + __
b = 5
(b/2)² = 6.25
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solve for f
f/40 = 10/f
Answer:
Step-by-step explanation:
To solve for f, we can cross-multiply the equation:
f/40 = 10/f
Multiplying both sides by 40f gives:
f^2 = 400
Taking the square root of both sides yields:
f = ±20
Therefore, the solutions for f are f = 20 and f = -20. However, since f represents a physical quantity (presumably a frequency), we take only the positive value:
f = 20