Answer:
To avoid cutting out a fraction of an inch, we need to choose a value of x that is a factor of both 36 inches and 48 inches, since those are the lengths of the sides of the rectangular sheet of cardboard we are using.
The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, and 36.
The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
The largest factor that both 36 and 48 have in common is 12. However, we can't choose x to be 12 inches because that would mean the length and width of the rectangular box would also be 12 inches, which is too small for our purposes.
Therefore, we should choose x to be the next largest factor that both 36 and 48 have in common, which is 6 inches. This means we will cut six 6-inch by 8-inch rectangles from the cardboard sheet.
The dimensions of the rectangular box will be:
Length = 2x + 2h = 2(6 in) + 2(8 in) = 12 in + 16 in = 28 in
Width = 2x + 2w = 2(6 in) + 2(12 in) = 12 in + 24 in = 36 in
Height = h = 8 in
Therefore, the dimensions of the rectangular box are 28 inches by 36 inches by 8 inches
Lavaughn wraps a gift box in the shape of a right rectangular prism. The figure below shows a net for the gift box. 9 m 9 m 8 m 8 m 15 m 8 m 8 m How much wrapping paper did he use, in square meters?
The length of paper he used for wrapping paper is, 702 meters²
What is surface area ?Surface area is the sum of the areas of all the faces (or surfaces) of a three-dimensional object. It is a measure of how much area the surfaces of an object take up in two dimensions. The surface area of a solid can be found by adding up the areas of its faces.
To calculate the amount of wrapping paper needed, we need to find the total surface area of the gift box. The surface area of a right rectangular prism is given by the formula:
surface area = 2(lw + wh + lh)
where l, w, and h are the length, width, and height of the prism, respectively.
In this case, the dimensions of the gift box are 9 meters, 9 meters, and 15 meters, so:
surface area = 2(9 x 9 + 9 x 15 + 15 x 9)
= 2(81 + 135 + 135)
= 2(351)
= 702 square meters
Therefore, Lavaughn used 702 square meters of wrapping paper for the gift box.
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A ping-pong ball rolls forward 6 meters, and bounces backward 3 meters. It traveled a total distance of:.
The distance traveled by the ping-pong ball as it rolls forward 6 meters and bounces backward 3 meters is 3 meters.
Distance is a concept that is important to understand in physics and mathematics. It refers to the amount of space between two points. In this scenario, we will be discussing the distance traveled by a ping-pong ball as it rolls forward and bounces backward.
When the ping-pong ball rolls forward, it covers a distance of 6 meters. This can be represented mathematically as d1 = 6 meters.
When the ball bounces backward, it covers a distance of 3 meters. This can be represented as d2 = -3 meters which means the negative sign indicates that it is moving in the opposite direction.
The total distance traveled by the ball can be found by adding the distance traveled in each direction. This can be represented as
=> d = d1 + d2 = 6 + (-3) = 3 meters.
In other words, the total distance traveled by the ball is 3 meters, which is the net distance covered after taking into account both the forward and backward movements.
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True or false a square is a parallelogram
True (but a parallelogram is not always a square). This is because a parallelogram is a quadrilateral with 2 pairs of parallel sides, and a square fits the requirements.
On a certain hot summer's day, 353 people used the public swimming pool. The daily prices are 1.50 for children and 2.50 for adults. The receipts for admission totaled 709. How many children and how many adults swam at the public pool that day?
Answer:
21
Step-by-step explanation:
21
round the number 125.3546 to 1 decimal place
Answer: 125.4
llllljkjkjkjkkjkjkjkjkjkkjkjjkjkjkjkjkjkjjkjkjkjkjkkjkjkjjkjkjjkjkjkjkjkjkjkjkjkjkjkjkjkjjkjkjkjkjkjkjkjkjkjkkjjkkjkjkjkjkkjkjkjkjkjkjjkjkkjkjkjkjkjkjkjkjkjkjkjkkjkjkjkjkjkjkjkjkj
Which expression is equivalent to 10+5 to the fourth power?
The expression [tex](3 \times 5)^4[/tex] is equivalent to 10+5 to the fourth power.
What are equivalent expressions?Those expressions that might look different but their simplified forms are the same expressions are called equivalent expressions.
To find equivalent expressions of some expressions, we can either make it look more complex or simple. Usually, we simplify it.
We need to find the expression into an equivalent form 10+5 to the fourth power
Therefore,
This expression 10+5 to the fourth power could also be given as;
10 + 5 = 15
That is [tex]15^4[/tex]
We can also write as;
[tex](3 \times 5)^4[/tex]
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What is the length of segment AC
(Please explain how you got your answer)
The length of the segment AC is 40 units
How to determine the length of the segment ACFrom the question, we have the following parameters that can be used in our computation:
The quadrilateral ABCD is a rhombus
The diagonals of rhombus bisect each other
Using the above as a guide, we have the following:
AC = 2 * EC
Substitute the known values in the above equation, so, we have the following representation
AC = 2 * 20
Evaluate
AC = 40
Hence, the length is 40 uints
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How to find a vector equation and parametric equations for the line segment that joins p to q?
The vector and parametric equations are r(t) = [t/2, (4t/3 - 1), (1 - 3t/4)] and x = t/2, y = -1 + 4t/3, z = 1 - 3t/4.
We have P(0, -1, 1), Q(1/2, 1/3, 1/4)
We have to find a vector equation and parametric equations for the line segment that joins P to Q.
Vector equation of a line segment joining the points with position vectors r0 and r1 is given by
r =(1 - t)r0 + tr1
Where, t ∈ [0, 1]
Here, r0 = (0, -1, 1) and r1 = (1/2, 1/3, 1/4)
So, r(t) = (1 - t)(0, -1, 1) + t(1/2, 1/3, 1/4)
r(t) = [((1 - t)(0) -1(1 - t) + 1(1 - t)] + [t/2, t/3, t/4]
r(t) = [0, (t - 1), (1 - t)] + [t/2, t/3, t/4]
On simplification,
r(t) = [(t/2 + 0), (t + t/3 - 1), (1 - t + t/4)]
r(t) = [t/2, (4t/3 - 1), (1 - 3t/4)]
Where, t ∈ [0,1]
The parametric equations for the line segment are
x = t/2, y = -1 + 4t/3, z = 1 - 3t/4
Where, t ∈ [0, 1]
Therefore, the vector and parametric equations are r(t) = [t/2, (4t/3 - 1), (1 - 3t/4)] and x = t/2, y = -1 + 4t/3, z = 1 - 3t/4.
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The given question is incomplete, complete question is:
Find a vector equation and parametric equations for the line segment that joins P to Q. P(0, - 1, 1), Q(1/2, 1/3, 1/4).
Exponents power of power multiplication properties
(4a³b^4)³
The expression (4a³b^4)³ when evaluated is 64a^9b^12
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
(4a³b^4)³
When expanded, we have
(4a³b^4)³ = 4³ * (a³)³ * (b^4)³
Evaluate the exponents
So, we have the following representation
(4a³b^4)³ = 64a^9b^12
Hence, the solution si 64a^9b^12
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What is the area of the shape for the quilt block? ninety-four and one half in2 one hundred sixty-six and one half in2 189 in2 333 in2
The area of the shape for the quilt block is 166.5 in²
What is an area?The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape
Given that, a quilt has blocks of design on it, we need to find the area of the block,
To find the area of the block = sum of the areas of the right triangle and the rectangle,
Area of the block = 16 × 9 + 6 × 7.5 × 1/2 = 166.5 in²
Hence, the area of the shape for the quilt block is 166.5 in²
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The figure is unavailable is the question is solved for the figure attached
A swimming pool is 50 m in length, 30 m in breadth, and 2.5 m in depth. find the cost of cementing its floor and walls at the rate of rupees 27 per square metre?
Answer:
51,300 rupees
Step-by-step explanation:
Surface area of the 2 short walls = 2 x 30 x 2.5 = 150
Surface area of the 2 long walls = 2 x 50 x 2.5 = 250
Surface area of the floor = 50 x 30 = 1500
Total surface area = 150 + 250 + 1500 = 1900 m²
27 rupees/m² x 1900 m² = 51300 rupees
A gopher is in a hole that is 12% in. below the surface of the ground. It then
digs 2½ in. deeper. What is the gopher's new elevation relative to the surface
of the ground?
-14%
-10%
10%
14%
The gopher’s new elevation relative to the surface of the ground will be
13¹/₄ inches.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.
Given that a gopher is in a hole that is 6¹/₄ in. below the surface of the ground. and, Then digs 7¹/₂ in. deeper.
The gopher’s new elevation relative to the surface of the ground will be calculated as;
⇒ 6¹/₄ + 7¹/₂
⇒ 25/4 + 15/2
Make denominators the same as;
⇒ 25/4 + 30/4
⇒ (25 + 30) / 4
⇒ 55 / 4
⇒ 13¹/₄ inches.
Thus, the gopher’s new elevation relative to the surface of the ground will be 13¹/₄ inches.
The complete question is given below,
A gopher is in a hole that is 6 1/4 in. below the surface of the ground. It then digs 7 1/2 in. deeper. What is the gopher’s new elevation relative to the surface of the ground? Show your work.
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Can somebody explain how to solve -4(2a+7)+3a+18? What type of polynomial is it?
Simplified form of the polynomial -4(2a+7)+3a+18 is -5a - 10. It is a binomial.
What is polynomial?A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.
Given expression,
-4(2a+7)+3a+18
using distributive property
-4(2a) -4(7) + 3a + 18
-8a - 28 + 3a + 18
Solving like terms
-5a - 10
The solved polynomial is a binomial, since it has two terms.
Hence, simplified form of the given polynomial is -5a - 10, it is a binomial
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How do you write 0.11111 as a fraction?
Answer:
Step-by-step explanation:1/9
stuart sold 8 couches and 11 armchairs at his furniture store yesterday he made a 10$ loss on each couch and a 12$ profit on each armchair what was his overall profit or loss
The overall profit of what Stuart sold is 52 dollars.
How to find loss and profit ?Stuart sold 8 couches and 11 armchairs at his furniture store yesterday and he made a 10 dollars loss on each couch and a 12 dollars profit on each armchair.
Therefore, the overall profit or loss can be calculated as follows:
Total loss on the couch = 8 × 10 = 80 dollars
Total profit on the armchairs = 11 × 12 = 132 dollars
Therefore,
Overall profits = 132 - 80
Overall profits = 52 dollars
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Write each as a percent. MAKE SURE YOU PUT THE % SIGN.
27) 1/2
28) 1/8
29) 1/100
30) 1/10
31) 3/8
32) 87/100
Answer:
50%
12.5%
1%
10%
37.5%
87%
Answer:
27)50%
28)12.5%
29)1%
30)10%
31)38.4%
32)87%
A shadow 30 meters long is cast by a fir tree that is 16 meters tall. If a nearby maple tree is 8 meters tall, then how long will the maple tree's shadow be?
The length of the shadow of the maple tree will be 15 meters.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
A shadow 30 meters long is cast by a fir tree that is 16 meters tall. If a nearby maple tree is 8 meters tall.
Let 'S' be the shadow of the maple tree. Then the equation is given as,
16 / 30 = 8 / S
0.533 = 8 / S
S = 8 / 0.533
S = 15 meters
The length of the shadow of the maple tree will be 15 meters.
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the sum of all frequencies in a frequency distribution should sum to
The relative frequency is the proportion of the total numbers in a data set corresponds to a specific class interval and hence summing over all the relative frequencies must add up to 1, or 100%.
Frequency Distribution Table:The frequency distribution table is made by building the class intervals of the raw data set, specifically when too many values are occurring many times; we group similar values in the same category, according to a pre-determined range of values. It is a two-column table in which the first column consists of class intervals and the second consists of the frequency corresponding to each interval.
The frequency distribution is made when the raw data is large and when the same number is repeated many times, that is where the concept of frequency comes into play.
Since, the frequency is the count of specific numbers in a data set, the sum of all frequencies corresponding to every class interval has to be the total number of values in the data set.
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The given question is incomplete, complete question is:
What is the sum of all frequencies in a frequency distribution? and why is the sum of all relative frequencies equal to 1?
A zookeeper is preparing to care for snakes in an exhibit. For every
feeding, she needs three mice and an additional two mice for each
snake. How many mice are needed if the number of the snakes is:
A- 10
B-6
C- x
The number of mice needed is given as follows:
a) 10 snakes: 23 mice.
b) 6 snakes: 15 mice.
c) x snakes: (3 + 2x) mice.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change.b is the intercept, representing the value of y when x = 0.For every feeding, she needs three mice and an additional two mice for each snake, hence the slope and the intercept of the function are given as follows:
m = 2, b = 3.
The function is then defined as follows:
y = 2x + 3.
For 10 snakes, the number of mice is given as follows:
y = 2(10) + 3
y = 23 mice.
For 6 snakes, the number of mice is given as follows:
y = 2(6) + 3
y = 15 mice.
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ABC PON 30 36 12 8 20 24 determine if the following triangles are similar?
Applying the properties of similar triangles, the other side lengths of ΔDEF are: B. 9 and 12
What is Properties of Similar Triangles?The ratio of the corresponding sides two triangles that are similar to each other are the same/equal.
here, we have,
Given that ΔABC and ΔDEF are similar triangles, therefore:
Let, a = 6, b = 8, and c = 12 be the sides of ΔABC.
Let, x, y, and z be the sides of ΔDEF.
Let z = 18
Thus:
a/x = b/y = c/z
Substitute
6/x = 8/y = 12/18
Find x using 6/x = 12/18:
6/x = 12/18
Cross multiply
x = 18*6/ 12
x = 9
Find x using 8/y = 12/18:
8/y = 12/18
Cross multiply
x = 18*8/12
x = 12
Therefore, applying the properties of similar triangles, the other side lengths of ΔDEF are: B. 9 and 12
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how to convert m/s to rad/s?
By using the formula that connects the linear velocity to the angular velocity, we may convert metres per second (m/s) to radians per second (rad/s).
Using the formula that connects the linear velocity to the angular velocity, we may convert metres per second (m/s) to radians per second (rad/s).
The equation reads: Radius divided by linear velocity gives you the angular velocity (). (r) where R is in metres, V is in m/s, and is in rad/s.
Direct conversion from m/s to rad/s is not possible if the radius is omitted. The aforementioned formula can be used to determine the missing value and then convert m/s to rad/s if you know the radius or the angular velocity. You can use the formula to determine the angular velocity in rad/s, for instance, if you know the linear velocity v in m/s and the radius r in metres.
ω = v / r
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14. 15x5y
= -20
-3x + y = 4
Answer:
The answer is: y=4+3x
Step-by-step explanation:
I know this because I believe we are solving for the system of equations or solving by the system of subtraction.
I will say I am not completely sure this is right but I hope I helped out a little :)
Mrs. Chen wrote two checks and made a deposit of $1,987.09 since her october statement. The october statement shows a balance of $3,611.08, and her checkbook shows she currently has $2,778.09. What is the total amount of the checks that Mrs. Chen wrote?
Warren earns $21.75 per hour and worked 36.5 hours last week and 32 hours the
week before. What is Warren's gross pay for the two weeks? Show your work.
Answer:
$1,489.88 (nearest cent)
Step-by-step explanation:
To calculate gross pay, multiply the number of hours worked by the pay per hour.
Warren worked 36.5 hours one week and 32 hours the week before.
Therefore, the total number of hours Warren worked was:
36.5 + 32 = 68.5 hoursMultiply the total number of hours worked by Warren's rate of pay of $21.75 per hour:
68.5 × 21.75 = 1489.875Therefore, Warren's gross pay for the two weeks was $1,489.88 (nearest cent).
Answer:
$1489.875
Step-by-step explanation:
Warren's gross pay for 36.5 hours last week can be calculated as follows:
Gross pay for 36.5 hours = $21.75/hour * 36.5 hours = $793.875
Similarly, Warren's gross pay for 32 hours the week before can be calculated as follows:
Gross pay for 32 hours = $21.75/hour * 32 hours = $696
Adding the gross pay for the two weeks, we get:
Gross pay for 2 weeks = $793.875 + $696 = $1489.875
Solve for x. -6 + 14 < -28 AND 3x + 28 <25
A) x < - 1 or x >7
B) -1 < x < 7
C) x < 7
D) There are no solutions.
E) All values of x are solutions
The option representing the solution of the inequality is given as follows:
D) There are no solutions.
How to solve the inequality?The inequality for this problem is defined as follows:
-6x + 14 < -28 and 3x + 28 < 25.
The and operation means that we must solve each inequality, and then obtain the intersection of the two solutions.
The solution to the first inequality is given as follows:
-6x + 14 < -28
6x - 14 > 28
6x > 42
x > 7.
The solution to the second inequality is given as follows:
3x + 28 < 25.
3x < -3
x < -1.
There is no intersection between x > 7 and x < -1, hence the system has no solutions.
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what is 65kgs in lbs ?
Since, 01 kilogram is approximately equal to 2.2046226218 lbs.
Therefore, 65 Kilogram is 143.3 lbs.
Pound:
Pound is the name of a series of units of mass ranging from 300 to 600 grams. It refers to an avoirdupois pound (454 grams), most commonly divided by 16 avoirdupois ounces.
Kilogram:
The kilogram or kilogram (symbol: kg) is the basic unit of mass in the SI system. It is defined equal to the mass of the International Prototype in kilograms. It is the only SI base unit that uses prefixes and is still defined in terms of artifacts rather than basic physical properties. A kilogram is equivalent to £2.205 in the English system used in the United States.
According to the Question:
To find how many pounds are in kilograms, you can convert kg to pounds using this formula:
X(lb) = Y(kg) / 0.45359237
Now,
Converting 65 kg to lbs:
To convert 65 kg to pounds:
⇒ X(lbs) = 65(kg) / 0.45359237
⇒ 143.3005 lbs
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In a perfectly symmetrical distribution:
a. the range equals the interquartile range.
b. the interquartile range equals the mean.
c. the median equals the mean.
d. the variance equals the standard deviation.
In a perfectly symmetrical distribution, the median equals the mean. This means that half of the values in the distribution fall below the mean and half fall above it. So , the correct option is C.
In a perfectly symmetrical distribution, the median equals the mean. This means that half of the values in the distribution fall below the mean and half fall above it. The mean and median are both measures of the central tendency of a distribution and in a symmetrical distribution, they are the same value.
Option (a) is false because the range is the difference between the largest and smallest values in a distribution, whereas the interquartile range is the difference between the first quartile (25th percentile) and the third quartile (75th percentile), which are measures of variability.
Option (b) is false because the interquartile range is always smaller than the mean in any distribution, symmetrical or not.
Option (d) is false because in a symmetrical distribution, the variance and standard deviation may be equal, but this is not always the case.
So , the correct option is c.
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction barts).
In the given diagram, ARST is a right triangle with MPL ST. Segment RT is divided into 5 equal parts.
R(4.3,7.4)
T(-8.5,-2.2)
M
S(4.3,-2.2)
The coordinates of point O are (
), and the coordinates of point M are (
The coordinates of P are (-0.82, 3.56).
The coordinates of M are (-2.1, -2.2).
What is a midpoint of a line segment?The midpoint of a line segment is written as,
x = (a + c)/2
y = (b + d) / 2
Where (x, y) are the coordinates of the midpoint and (a, b) and (c, d) are the two endpoints.
We have,
R = (4.3, 7.4)
T= (-8.5, -2.2)
S = (4.3, -2.2)
Segment RT is divided into 5 equal parts.
So,
TP : PR = 3 : 2 = m : n
The coordinates of P.
T= (-8.5, -2.2) = (a, b)
R = (4.3, 7.4) = (c, d)
x = [tex]\frac{mc + na}{m + n}[/tex]
x = [tex]\frac{3\times4.3 + 2\times-8.50}{5}[/tex]
x = [tex]\frac{12.9 - 17}{5}[/tex]
x = [tex]\frac{-4.1}{5}[/tex]
x = -0.82
And,
y = [tex]\frac{md + nb}{m + n}[/tex]
y = [tex]\frac{3\times7.4 + 2\times-2.2}{5}[/tex]
y = [tex]\frac{22.2 - 4.4}{5}[/tex]
y = 3.56
The coordinates of P are (-0.82, 3.56).
Now,
T= (-8.5, -2.2)
S = (4.3, -2.2)
M is the midpoint of TS.
So,
M = (x, y)
x = [tex]\frac{(4.3 - 8.5)}{2}[/tex] = [tex]\frac{x-4.2}{2}[/tex] = -2.1
y = [tex]\frac{-2.2 - 2.2}{2}[/tex] = [tex]\frac{-4.4}{2}[/tex] = -2.2
M = (x, y) = (-2.1, -2.2)
Thus,
The coordinates of P = (-0.82, 3.56).
The coordinates of M = (-2.1, -2.2).
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Answer:
The answer is (-3.38,1.64),(-0.82,-2.2)
Step-by-step explanation:
I just got it right on the test
What is the value of the geometric mean of the numbers 3, 4, and 18?
A. 8 1/3
C. 8 2/3
B. 8
D. 6
E. 5.5
What are the measures of angles Q and R?
187/17 is 11, so x = 11. Substituting 11 in for x gives you 93 for the measure of angle Q and 87 for the measure of angle R.