Answers
Answer:
Width: 20 in
Length: 25 in
Explanation:
We can represent the situation with the following figure
Where x is the width of the rectangular piece of metal, (x + 5) is the length of the rectangular because it is 5 in longer than its wide, and the corners have squares of side 1 in.
Therefore, the volume of the box will be equal to
Volume = Length · Width · Height
Volume = (x + 5 - 1 - 1) · (x - 1 - 1) · (1)
Volume = (x + 3)(x - 2)(1)
Volume = (x + 3)(x - 2)
Because the length of the box will be the length of the rectangle less the length of the squares and the width of the box will be the length of the rectangle less the width of the squares.
The volume is 414 in³, so we need to solve the following equation:
414 = (x + 3)(x - 2)
414 = x² + 3x - 2x + 3(-2)
414 = x² + x - 6
414 - 414 = x² + x - 6 - 414
0 = x² + x - 420
Factorizing x² + x - 420, we get:
(x + 21)(x - 20) = 0
Then
x + 21 = 0
x + 21 - 21 = 0 - 21
x = -21
or
x - 20 = 0
x - 20 + 20 = 0 + 20
x = 20
Since x = -21 doesn't have sense, the width is x = 20 and the length is:
x + 5 = 20 + 5 = 25 in.
So, the original width is 20 in and the original length is 25 in
Related Questions
2.Which data set is more likely to produce a histogram with a symmetric distribution? Explain yourreasoning.Data on the number of seconds on a track of music in a pop album.Data on the number of seconds spent talking on the phone yesterday by everyone in theschool.
Answers
A histogram with a symmetric distribution looks like this:
Leaving aside the quality of the drawing, the left and the right side of the histogram are identical if we split it by the red line. Is like having a reflexion axis.
Now, we have to discuss what of the 2 data sets may have such an histogram. This means that we must think which of them may have the same number of ocurrences for very short and very long durations, for regular to short and regular to long durations, and so on and so furth.
Pop album tracks:
In the same album we may have arround 12 tracks (small number), all of them with a duration of arround 3 minutes. We could imagine a histogram like the following:
All the songs last between 170 and 190 seconds, and one or two last a little bit more.
Phone talks:
In this case, we can think that there are some calls to say something like "mom, I'm on my way home" and other like "let me tell you the hole movie I saw yesterday night", so very short and very long calls, but they are no so common. There are a lot of "regular" calls that might last for 60 seconds.
Also, in this case, we are taking into account all the calls from people in the school in one day (yesterday), so, may be 1.000 calls? The actual number really doesn't matter, but the fact that the number is very big. Because of the big number, we can expect a symmetric distribution.
what is the answer to 3v²/v
Answers
Answer:
3v
Step-by-step explanation:
When we are dividing two terms with the same base and different exponents, we keep the base and subtract the exponents. So
[tex]\frac{3v^2}{v}=3v^{2-1}=3v[/tex][tex]undefined[/tex]Use the table below to determine whether the argument is valid. TableI start to fall asleep if I read a math book. I drink soda whenever I start to fall asleep. If I drink a soda, then I must eat a candy bar. Therefore, if I read a math book, then I eat a candy bar.The argument is _____________
Answers
Okay, here we have this:
Considering the provided information, we obtain the following:
I read a math book. (p)
I start to fall asleep (q)
I drink soda (r)
I must eat a candy bar. (s)
Therefore:
I start to fall asleep if I read a math book. This can be rewritten as: "if I read a math book then I start to fall asleep". And this is p⇒q.
I drink soda whenever I start to fall asleep. This can be rewritten as:"if I start to fall asleep then I drink soda" . And this is q⇒r.
If I drink a soda, then I must eat a candy bar. And this is r⇒s
Now, we need to check: "If I read a math book, then I eat a candy bar.". That is p⇒s.
So, according with the table this argument satisfy the Transitive Reasoning, so this means that the argument is valid.
at a grocery store, the ratio of a price of dozen eggs is the price of a loaf of bread is 5:3 together dozen eggs in a loaf of bread cost $4 what is the price of the loaf of bread in dollars and cents
Answers
Answer:
The price of a loaf of bread in dollars and cents is;
[tex]\begin{gathered} \text{ \$1.50} \\ or \\ 1\text{ dollar and 50 cents} \end{gathered}[/tex]Explanation:
Given that;
The ratio of a price of dozen eggs is the price of a loaf of bread is 5:3
And together dozen eggs and a loaf of bread cost $4.
The price of a loaf of bread in dollars and cents is;
[tex]\begin{gathered} b=\frac{3}{3+5}\times\text{ \$4} \\ b=\frac{3}{8}\times\text{ \$4} \\ b=\frac{\text{ \$12}}{\text{8}} \\ b=\text{ \$1.50} \\ \end{gathered}[/tex]The price is the ratio of a loaf of bread divided by the total ratio multiplied by the total cost of the two items.
Therefore, the price of a loaf of bread in dollars and cents is;
[tex]\begin{gathered} \text{ \$1.50} \\ or \\ 1\text{ dollar and 50 cents} \end{gathered}[/tex]Write an equation and solve for mm degree 37 degree
Answers
37 degrees plus m mus equal 90 degrees; therefore, the equation that m must satisfy is
[tex]m+37=90[/tex]subtracting 37 from both sides of the equation gives us
[tex]m=90-37[/tex][tex]\textcolor{#FF7968}{\therefore m=53^o}[/tex]Ross is saving up to buy a new car. he has been saving for 12 months and so far he has $3,200.in another 12 months, he expects to have $8,000.how much is ross saving each month during his 2nd year saving?
Answers
Answer:
$400
Step-by-step explanation:
For the first 12 months, he saved
3200/12
= $266.7 each month
In another 12 months,
= $3,200 + x = $8000
(Use x as the unknown total money)
= 8000 - 3200
= 4,800
So, in another 12 months, his total savings will be $4,800
For each month,
= 4,800/12
= $400
Shawn’s weekly salary is $978.25. His employer is changing the pay period to semimonthly. What is Shawn’s annual salary? What will his semimonthly salary be?
Answers
Answer:
Annual Salary: $50,869
Semimonthly Salary: $1,956.50
Step-by-step explanation:
Semimonthly: Occurs twice a month
52 weeks in a year times weekly salary
978.25 x 52= 50,869
978.25 x 2= 1,956.50
Graph h(x) = 32(0.45)x. What is the constant percent rate of change of f(x) with respect to x? Does the graph show growth or decay?
45% growth
45% decay
55% growth
55% decay
Answers
Answer:
55% decay, the other guy is wrong
Step-by-step explanation:
Trust me
True or False?
Point (5,y) is a solution of the inequality y+9x>0 for any value of y.
Answers
Answer:
False
Step-by-step explanation:
40 students participated in track. This was 5% of the students at the school. How many students attend the school?
Answers
Answer: 800 students
If there are 40 students who participated and that's 5% of the entire school. 100% of the entire school would be 800.
jack weighs 13 more pounds than his brother andy if a expression to represent jackd weight.
Answers
When we are told that the weight of Jack is 13 pounds more than the weight of his brother this means that the weight of Jack (y) is the weight of his brother (x) plus 13 pounds, then we can express Jack weight with the equation:
y=x+13
Determine the constant of variation for the direct variation given. 2 1
Answers
The constant of variation for the given direct variation is 2.
What is the constant of variation?The quantity that connects two variables that are directly or inversely proportional to one another is known as the constant of variation.So, the origin (0, 0) and the supplied line are intersected by it (3, 6)
The slope of the line is the variation constant for the direct variation.The two on line coordinates (0, 0) and (1, 1) can be used to determine the slope (3, 6).Slope formula: m = y2 - y1/x2 - x1
Where,
x₁ = 0y₁ = 0x₂ = 3y₂ = 6Substitute values as follows:
m = y2 - y1/x2 - x1m = 6-0/3-0m = 6/3m = 2Therefore, the constant of variation for the given direct variation is 2.
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Correct question:
Determine the constant of variation for the direct variation given.
A. 1/2
B. 1
C. 2
Brainliest and 30 points
Determine which integers in the set S:{−2, 2, 12, 24} make the inequality 4(j − 2) > 4(6 − 3j) true.
Answers
{12 , 24} are the integers from the set S which makes the inequality 4(j − 2) > 4(6 − 3j} true.
Inequality are those mathematical expression where both the sides are not equal . Instead of equality sign , we use less than or greater than sign.
Given inequality is
4(j − 2) > 4(6 − 3j}
open the brackets ,
4j − 8 > 24 − 12j
bring right terms on left side,
4j − 8 - 24 + 12j > 0
adding j terms,
16j - 32 > 0
16j >32
j > 32/16
j > 2
Integers making inequality true should be greater than 2
From set S: {-2 , 2, 12, 24}
{12 , 24 } are integers that makes inequality 4(j − 2) > 4(6 − 3j) True .
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Given the slope and y-intercept of the line, write the equation in slope-intercept form. Slope = -2/5 and y-intercept = 3
Answers
Answer:
Below
Step-by-step explanation:
Slope-y-axis -intercept form is y = mx + b
y = - 2/5 x + 3 Done.
Drag each number from the box to complete the equations that follow. Each number may be used once,more than once, or not at all.12894(36:)--(36:= 5X3)-= 12
Answers
Notice that:
[tex]\begin{gathered} 5=9-4, \\ 36\div4=9, \\ 36\div9=4. \end{gathered}[/tex]Therefore:
[tex]5=9-4=36\div4-36\div9.[/tex]Also, notice that:
[tex]3\times8=24=12+12.[/tex]Therefore:
[tex]12=12+12-12=3\times8-12.[/tex]Answer:
[tex]\begin{gathered} (36\div4)-(36\div9)=5, \\ (8\times3)-12=12. \end{gathered}[/tex]Aliyah left the airport and traveled home at an average speed of 40 km/h.
Shanice left at the same time and traveled in the opposite direction with an
average speed of 60 km/h. How long does Shanice need to travel before they are
300 km apart?
Answers
Answer:
3 hoursStep-by-step explanation:
When moving in opposite directions from the same point the speeds add up.
Total speed:
60 + 40 = 100 km/h
Distance is 300 km, find the time.
time = distance / speedt = 300/100t = 3 hoursAnswer:
Time = 3 hours
Step-by-step explanation:
The total speed is,
→ 40 km/h + 60 km/h
→ 100 km/h
Formula we use,
→ v = d/t
Then the time taken will be,
→ v = d/t
→ 100 = 300/t
→ 100 × t = 300
→ t = 300/100
→ [ t = 3 ]
Hence, answer is 3 hours.
Determine whether the function represents exponential growth or exponential decay. Identify the percent rate of change. y=3(7/5)^t
Answers
The function y=3[tex](7/5)^t[/tex] In the function f (x) = bx when b > 1, the function represents exponential growth represents exponential growth.
What is the difference between exponential growth and exponential decay?An exponential function has the generic formula y = abx, where a = 0 and b = a positive real number. When describing an exponential function, the base b is a constant. When the domain is a set of real numbers, the independent variable is the exponent x.Exponential growth and decay: When b > 1, the function f (x) = bx represents exponential growth. If 0 b 1, the function f (x) = bx illustrates exponential decay.To calculate the growth rate, subtract the current value from the previous value. The percentage growth rate is calculated by multiplying the difference by the previous number and dividing by 100.Therefore,
The function y=3[tex](7/5)^t[/tex] In the function f (x) = bx when b > 1, the function represents exponential growth represents exponential growth.
Exponential growth and decay are the two different kinds of exponential functions.
When b > 1, the function
f (x) = bx represents exponential development.
If 0 b 1, then the function
f (x) = bx depicts exponential decay.
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A recent study of business travelers claims they spend an average of $41.00 per day on meals. As a test of this claim, a random sampling of 16 business travelers found they had spent an average of $45.00 per day with a standard deviation of $3.65. What are the critical values for a two-tailed t test of this claim with α = 0.05?Question 19 options:± 2.120± 2.131± 1.753± 1.746
Answers
The critical values for a two-tailed t test of this claim is ± 2.131.
From the question, we have
The null and alternative hypothesis are listed below. u = 41
Additional Hypothesis: 41
Region of Rejection
This test has two tails, with = 0.05 and df = 15.
T has a critical range between -2.131 and 2.131.
Therefore, if t =-2.131 or t =2.131, reject H0.
Hypothesis:
In statistics, hypothesis testing is used to identify the variance in the group of data that results from genuine variation. Based on the presumptions, the sample data are taken from the population parameter. The hypothesis can be divided into many categories. A hypothesis is described in statistics as a formal statement that explains the relationship between two or more variables belonging to the specified population. It aids the researcher in converting the stated issue into an understandable justification for the study's findings.
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Ravi makes lemonade by mixing lemon juice and water.
For every 1 cup of lemon juice, he uses 4 cups of water.
Answers
We need to use 2 cups of lemon juice and 8 cups of water to get a total of 10 cups of lemonade.
We know that the lemonade recipe is:
1 cup of lemon juice and 4 cups of water.
This gives us a total of:
1 cup + 4 cups = 5 cups of lemonade.
Then if we want 10 cups of lemonade, we just need to use the double of each one of the ingredients.
this is:
2*(1 cup) = 2 cups of lemon juice
2*(4 cups) = 8 cups of water.
We need to use 2 cups of lemon juice and 8 cups of water to get a total of 10 cups of lemonade.
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7. What is the domain of the relation? y у O D = (-4,00) OD = (-0,4) O D = (0,00 OD = (-4,5)
Answers
The domain of a function is the value x that varies.
here x is varying from -4 and it is going to infinity
so the answer is
the domain for the given graph is
[tex]D=(-4,\infty)[/tex]So the answer is option (A).
Assessment Practice
Find 3,384 ÷ 47. How can you check the
reasonableness of your answer? 5.NS0.2.2
exact answer.
Think about all the ways
you can estimate.
Answers
The division of 3384 by 47 will give 72 and some ways for checking the reasonableness of solutions include rounding numbers, making numbers compatible, and using characteristics of operations.
What is division?A technique of division is a means of dividing something. The division techniques are classified into three groups based on their complexity degree. These are the chunking method, also known as division by repeated subtraction, the short division method, sometimes known as the bus stop method, and the long division method.
Here,
3384/47=72
Some strategies for determining the reasonableness of answers include rounding numbers, making numbers compatible, and using properties of operations.
Rounding numbers, making numbers compatible, and utilising features of operations are some methods for determining the reasonableness of answers. The division of 3384 by 47 will give 72.
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Answer:
Eating Is importnat
Step-by-step explanation:
Hello me is cool man i am good at math 2-1=110 so ye hello bye
−2×(−6)=?[tex]−2×(−6)=?[/tex]
Answers
When -2 is multiplied by (-6) the result is 12
What is multiplication?One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication.
Multiply in mathematics refers to the continual addition of sets of identical size.
When negative signs multiply each other the result is a positive sign also when positive signs multiply each other the result is a positive sign
However, when the signs are not same the result is always negative
In the given problem, the signs are same like negative 2 and negative 6
hence the result is a positive sign
and the quantity 2 multiply the quantity 6 gives 12
therefore -2 * -6 = 12
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Determine the value of altitude BD to the nearest tenth.
Answers
1) Given the altitude BD, let's find its measure using some trigonometric relations on the Right Triangle:
1.2) Pythagorean Theorem to find the other leg
b²=a²+c² The hypotenuse, in this case, is labeled as "b"
32²=16²+a²
1024=256+a²
1024-256=a²
768=a²
√768=√c²
a=16√3
2) Now, let's use one trigonometric relation on the Right Triangle, based on the similarity of the triangles:
ah=bc Adjusting it:
bh=ac
32h=16√3*16
32h=256√3
h=256√3/32
h=8√3 ≈ 13.85 ≈13.9
3) So the altitude BC of that triangle is approximately 13.9
Billie opened a savings account, which pays 3% intrest per year. If she had a balance of $14,935 after one year, how much was her original deposit?
Answers
Answer: 27.50
Step-by-step explanation:
A swimming pool is being filled with a hose. The hose fills the pool at a constant rate. The pool's water level rose 9 inches in 12 hours. What was the rate per hour of the water level change?
Answers
The rate per hour of the water level change will be 0.75 inches/hour.
What is the rate of change?It is defined as the change in values of a dependent variable with respect to the independent variables. It is also used to find the unit rate for many conditions.
It is given that, A swimming pool is being filled with a hose. The hose fills the pool at a constant rate. The pool's water level rose 9 inches in 12 hours.
The unit rate is obtained as,
=9 inches / 12 hours
=0.75 inches/hour.
Thus, the rate per hour of the water level change will be 0.75 inches/hour.
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what is the slope of a line that is perpendicular to 3x+4y=6?
Answers
Answer:
4/3
Step-by-step explanation:
3x + 4y = 6
4y = -3x + 6
y = -3/4 x + 3/2
For the given line: slope = -3/4
The slopes of perpendicular lines are negative reciprocals.
Perpendicular: slope = 4/3
$14,929 is invested, part at 9% and the rest at 6%. If the interest earned from the amount invested at 9% exceeds the interest earned from the amount invested at 6% by $1139.91, how much is invested at each rate? Round to two decimal places if necessary
Answers
Let x be the amount invested at 9% and y the amount invested at 6%.
Then we have:
I) x + y = $14,929
II) 0.09x - 0.06y = $1,139.91
First, we multiply equation II by 100:
9x - 6y = $113,991
Now, we add to it 6 times equation I:
15x = $203,565
x = $13,571
Now, we replace x in equation I to find y:
$13,571 + y = 14,929
y = $1,358
The perimeter of a
rectangular park is 640 yards.
The length of the rectangle is 40
yards less than twice the width.
What are the dimensions of the
park?
Answers
The dimensions of the rectangular park are 200 yards by 120 yards.
We have a park. The shape of the park is a rectangle. The perimeter of the rectangular park is 640 yards. We know that the length of the rectangle is 40 yards, less than twice its width. We need to find the dimensions of the rectangular park.
Let the perimeter, length, and width of the rectangle be represented by the variables "P", "l", and "b", respectively. The perimeter of the rectangle is twice the sum of its length and width.
l = 2b - 40
P = 2*(l + b)
640 = 2(2b - 40 + b)
320 = 3b - 40
3b = 360
b = 120
Hence, the width of the rectangular park is 120 yards. We will substitute this value in the above equation to find the length.
l = 2b - 40
l = 2(120) - 40
l = 240 - 40
l = 200
Hence, the length of the rectangular park is 200 yards.
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Emma went to the movie theater for her birthday. A mix of adults and children attended, making a total of 19 people. Each adult ticket was $9 and each child’s ticket was $5.50. If the total cost for the party was $150, then how many adults and how many children attended
Answers
Solving the equations for the total number of adults and children and respective ticket costs, we find out that the number of adults and children that attended the movie theater are 13 adults and 6 children.
It is given to us that -
A total of 19 people attended the movie theater which was a mix of adults and children
Each adult ticket was $9
Each child’s ticket was $5.50.
Total cost for the party was $150
We have to find out the number of adults and children that attended the movie theater.
Let us assume that the number of adults and children that attended the movie theater be [tex]x[/tex] and [tex]y[/tex] respectively.
Since, a total of 19 people attended the movie theater including both adults and children, we can say that -
[tex]x+y=19[/tex] ------ (1)
It is also given that each adult ticket was $9 and each child’s ticket was $5.50. So,
For [tex]x[/tex] adults, the ticket price = [tex]9x[/tex], and
For [tex]y[/tex] children, the ticket price = [tex]5.5y[/tex]
It is given that the total cost for the party was $150
[tex]= > 9x+5.5y=150[/tex] ------- (2)
From equation (1), we have
[tex]x+y=19\\= > y =19-x[/tex] ------ (3)
Substituting this value of [tex]y[/tex] in equation (2),
[tex]= > 9x+5.5y=150\\= > 9x+5.5(19-x)=150\\= > 9x +104.5-5.5x=150\\= > 3.5x=45.5\\= > x=13[/tex]------ (4)
Substituting this value of [tex]x[/tex] from equation (4) in equation (3), we get
[tex]y=19-x\\= > y=19-13\\= > y=6[/tex]
Thus, solving the equations, we find out that the number of adults and children that attended the movie theater are 13 adults and 6 children.
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please help i have 10 mins to be doing this
Answers
Height of nth stair from the ground be 18n.
What do you mean by airthmetic sequence?
A sequence of the form a, a + d, a + 2d, a + 3d, a + 4d, etc. is an arithmetic sequence.
The common difference of the sequence is d, and the number a is the first term. [tex]a_{n}[/tex] = a + (n - 1)d is the formula for an arithmetic sequence's nth term.
The common difference, or d, is the difference between any two consecutive terms in an arithmetic sequence, and it may be calculated by deducting any pair of terms beginning with a and ending with [tex]a_{n+1}[/tex] Accordingly, d = [tex]a_{n+1}[/tex] - [tex]a_{n}[/tex]
It is given that height of each stair is 18 cm
Height of first stair = 18 cm
Height of second stair = 18 + 18 = 36 cm
Height of third stair = 36 + 18 = 54 cm
and so on.
This data will make a sequence such as 18 , 36 , 54 , 72 ..........
Here first term , a = 18
Common difference , d = 36 - 18 = 18
For the height of nth stair , use the formula of [tex]a_{n}[/tex]
[tex]a_{n}[/tex] = a + (n-1) d
where a is the first term , d id the common difference and n is the number of terms
Here, [tex]a_{n}[/tex] = 18 + (n-1)18 = 18 + 18n - 18 = 18n
Hence, height of nth stair from the ground be 18n .
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