1. An open box is to be made from a sheet of card 40cm by 30cm. A square of side x cm is to be
cut from each corner, as shown in the diagram, and then the sides will be folded up so that the
depth of the box will be x cm.
(a) Find in terms of x the length and width of the base of the box (ie AB and AD).
(b) The volume of the box is y. Write down an equation expressing y in terms of x.
Step-by-step explanation:
AB = DC = 40 - 2x
AD = BC = 30 - 2x
there is not more explanation possible, I think.
we cut off from each side 2 pieces of x cm. so, AB, DC, AD, BC are the the remaining lengths.
the volume of the box is ground area times height (x is the length of the remaining flaps after the cut, so, when folding up these flaps/sides, they will be x cm high).
Volume = y = AB×AD×x
=> y = (40-2x)×(30-2x)×x = (1200 - 60x - 80x + 4x²)×x =
= (1200 - 140x + 4x²)×x = 4x³ - 140x² + 1200x
A survey of 100 high school students provided this frequency table on how students get to school: What is the probability that a randomly selected student is a senior or a student who drives to school? [ ? P(Senior U Drive to school) Remember to reduce your answer.
Answer:
I am kind of brain dead I haven't did this type of math for a long time but I am pretty sure the answer is 1/7.
Step-by-step explanation:
Answer:
1/2
Step-by-step explanation:
Riders must be at least 42 inches tall to ride the coaster. Write an addition inequality to determine how much taller William must be to ride the coaster. Let x be the variable representing how much taller
An addition inequality to determine how much taller William must be to ride the coaster is, Height of William + x ≥ 42.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, Riders must be at least 42 inches tall to ride the coaster, and 'x' be the variable representing how much taller William should be.
Therefore, Height of William + x ≥ 42 is an inequality that may be used to calculate how much taller William has to be in order to ride the coaster.
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On a coordinate plane, a line is drawn from point C to point D. Point C is at (negative 1, 4) and point D is at (2, 0).
Point C has the coordinates (–1, 4) and point D has the coordinates (2, 0). What is the distance between points C and D?
d = StartRoot (x 2 minus x 1) squared + (v 2 minus v 1) squared EndRoot
units
The length of the line is 5 units.
What is distance?The distance between two points is the length of the line joining the two points.
Formula: distance= √(x_2-x_1)²+(y_2-y_1)²
Given that, endpoints are (-1,4) and (2,0) of the line segment.
The length= √(2+1)²+(0-4)²
=5units
Hence, The length of the line is 5 units.
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the current ratio of Sara's sales to Ravi's sales is 100:2 would you earn a greater total commission with Sara or Ravi?
as a professional artist assume you will make pieces of art that sell at the same sales ratio as the artist with whom you apprenticed. would you earn more as a professional after apprenticed for Sara or Ravi?
One would earn more if one apprenticed for Sara as a professional artist as evident judging from the current sales ratio and commission rates.
Which of Sara and Ravi guarantees more earnings after apprenticeship?As evident in the task content; the current ratio of Sara's sales to Ravi's sale is 100 : 2.
Since Sara's pieces of art sell for $25, the total earnings is; 25 × 100 = $2500.
Hence, since the commission rate is 60%, it follows that the commission earned on sales of Sara's pieces is; 60% of 2500 = 0.6 × 2500 = $1500.
Also, since Ravi's pieces each cost $2000, it follows that for 2 pieces, the total earnings is; 2 × $2000 = $4,000.
Hence, since the commission rate for Ravi's pieces is 25%, the commission earned is therefore; 25% of 4000 = 0.25 × 4000 = $1000.
Ultimately, one would earn more if one apprenticed for Sara.
Complete question; Sara's pieces of art sell for $25 each your commission is 60%.
Ravi's pieces of art sell for $2000 each and your commission is 25%.
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The surface area of a cube is 24cm^2 . Find the
length of the sides.
Help please
The length of the sides of cube will be;
⇒ 2 cm
What is mean by Cube?A cube is the solid shape or three-dimensional shape. A convex polyhedron which is bounded by six squared faces with eight vertices and twelve edges is called cuboid.
Given that;
The surface area of a cube = 24 cm².
We know that;
The surface area of a cube with side 'a' is,
⇒ S.A = 6a²
Here, The surface area of a cube = 24 cm²
Hence, We get;
⇒ 24 = 6a²
⇒ 24/6 = a²
⇒ a² = 4
⇒ a = √4
⇒ a = 2 cm
Thus, The side of cube = 2 cm
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anyone help me with 4? it would mean a lot!
HELP ME ASAP!!!!
A vertical mast is on top of building and is positioned 6' from edge of building. The mast casts a 90' shadow from front of building. Another building 24' tall casts a shadow 64'. What is the height of the mast?
a. 7ft 6in
b. 9ft 9in
c. 12ft
d. 33ft
Answer:
33.75
Step-by-step explanation:
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Is 10 12 15 a right triangle?
No, 10, 12, and 15 are not the lengths of the sides of a right triangle.
A right triangle is a triangle with one 90 degree angle. The other two angles must be acute angles (less than 90 degrees).
The Pythagorean Theorem is a formula used to determine if three given side lengths can form a right triangle. The Pythagorean Theorem states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the longest side, also known as the hypotenuse.
In this case, the side lengths of the triangle are 10, 12, and 15. Therefore, the Pythagorean Theorem can be written as:
10^2 + 12^2 = 15^2
100 + 144 = 225
244 ≠ 225
Therefore, 10, 12, and 15 are not the side lengths of a right triangle.
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How many 1/3 cubes does it take to fill a box with a width of 2 2/3 inches length 3 1/3 inches and height 2 1/3
It takes 560 of 1/3 inch cubes to fill a box with width 2 2/3 inches, length 3 1/3 inches, and height 2 1/3 inches.
In Math's or in Geometry, a Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.
It is also said to be a regular hexahedron.
We will convert the dimensions of the given box into simple fractions for easy calculations.
The dimensions of the given box:
Length = 3 + 1/3 inches = 10/3 inches
Breadth = 2 + 2/3 inches = 8/3 inches
Height = 2 + 1/3 inches = 7/3 inches
The side of each cube = 1/3 inches
Therefore,
The no. of cubes required to fill the box is,
= (volume of the box) / (volume of each 1/3 inch cube)
= ( 10/3 * 8/3 * 7/3 ) / (1/3)^2
= 10 * 8 * 7
= 560
Thus, it takes 560 of 1/3 inch cubes to fill a box with width 2 2/3 inches, length 3 1/3 inches, and height 2 1/3 inches.
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area of a circle of radius is 6.5?
Answer:
see below
Step-by-step explanation:
The area of a circle is given by
A = pi r^2 where r is the radius
A = pi (6.5)^2
A =42.25 pi
If we approximate pi by 3.14
A = 42.25 * 3.14 =132.665
If we use the pi button
A = 132.7322896
Answer:
132.73
Step-by-step explanation:
Cos (A) + Tan (A) Sin (A), Sec (A)=
Answer: you need more info
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
Find the area of each
Answer:
176/77 is the answer I think so
Answer:
look at the picture I sent
Find the value of angle z. Need ASAP. STEP BY STEP
Answer:
71 degrees
Step-by-step explanation:
y=19 degrees
z and y=90degrees
90 _19 to get y
Given the lengths of two sides of a triangle, determine the range, a, of possible side lengths of the third side.
5 km and 11 km
12 mi and 12 mi
25 yd and 10 yd
By using the triangular inequality, we will get the possible lengths:
a) 6km < x < 16km
b) 0mi < x < 24mi
c) 15yd < x < 30yd
How to estimate the lengths of the possible third side?If A, C, and D are the lengths of the sides of a triangle, then the triangular inequality says that:
A + C > D
A + D > C
C + D > a
Now, if the two sides are 5km and 11 km, and the other side is x, then we can write:
x + 5km > 11km
x + 11km > 5km
11 km + 5 km > x
From these inequalities we can get:
16km > x
x > 11km - 5km
x > 6km
Then the possible lengths of the third side are:
6km < x < 16km
b) Now the sides are 12 mi and 12mi, then the inequalities are:
x + 12mi > 12mi
12mi + 12mi > x
The first one gives:
x > 0mi
The second:
24mi > x
The possible lenghts are 0mi < x < 24mi
c) 25 yd and 10 yd
Here we will get:
25yd + 10yd > x ----- > 30yd > x
x + 10 yd > 25yd -------> x > 15yd
The possible lengths are:
15yd < x < 30yd
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As a nurse, part of your daily duties is to mix medications in the proper proportions for your patients. For one of your regular patients, you always mix Medication A with Medication B in the same proportion. Last week, your patient's doctor indicated that you should mix 20 milligrams of Medication A with 16 milligrams of Medication B. However this week, the doctor said to only use 8 milligrams of Medication B. How many milligrams of Medication A should be mixed this week?
Answer:
10 milligrams of Medication A
Step-by-step explanation:
We'll write proportions/ratios for this:
20:16 is the usual proportion, and x:8 is this week's dose. The ratio from A to B has to be equal, so
20/16 = x/8
Cross-multiply:
(20)(8) = (16)(x)
160 = 16x
divide both sides by 16
x = 10
Please let me know if you have questions about this answer.
What is the solution?
How do you find the base and height of an isosceles triangle?
The base and height of an isosceles triangle can be found by using the Pythagorean theorem.The hypotenuse is also the base of the triangle.
First, you need to determine the length of the two sides that are equal, which are referred to as the "legs" of the triangle. Then, use the Pythagorean theorem to find the length of the hypotenuse, which is the longest side of the triangle.
Once you have determined the length of the hypotenuse, the height of the triangle can be found using the formula, h = √(b^2 - (l/2)^2). In this formula, b is the length of the hypotenuse, and l is the length of the legs.
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best buy has a sale on video games and dvds for labor day weekend Katie bought 2 games and 3DVD's and spent $134 dollars Emily bought 1 less game but 2 more DVD's and spent $179 how much does each DVD and game cost
Each video game = $19 and each DVD = $ 32
What is equation?An equation is a mathematical statement that represent that two expressions are equal. An equation can be formed by one or more variables along with numerical terms.
How to solve the equation as stated in the question?let, x denotes the cost of each video games.
y denotes the cost of each DVD
Katie bought 2 games and 3 DVD and total spent $134.
the equation can be written as 2x + 3y = $134 .......equation 1
Emily bought 1 less video game than Katie that means she bought 1 game.
and 2 more DVD than Katie that means 5 DVD bought by Emily.
total spent of Emily = $179
The equation will be x + 5y = $179...... equation 2
in order to solve the two equations by addition method
we multiply by 2 to the second equation.
2x + 10y = 358
the first equation 2x +3y = 134
2x + 10y = 358
- - -
by subtracting we get,
- 7y = -224
y = 32
from the 2nd equation we get x = -5×32 + 179
x = 19
each video game cost $ 19 and each DVD cost $ 32
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6 kids shared 4 1/2 candy bars, how much did each kids get
Answer: They each got 3/4 candy bars. (0.75 candy bars)
y= x^2+6x+4
axis of symmetry:
vertex:
Answer:
vertex (-3,-5) axis of symmetry x = -3
Step-by-step explanation:
Two tangents each intersect a circle at opposite endpoints of the same diameter. Is it possible for the two tangents to intersect each other outside the circle
No, the tangents cannot intersect outside the circle.
When tangents intersect outside a circle, the measure of the angle they form is one half the difference of the intercepted arcs. Since the tangents are at the endpoints of the same diameter, both intercepted arcs would have to measure 180 degrees.
tangent
a tangent is the line drawn from an external point and passes through a point on the curve.
One real-life example of a tangent is when you ride a bicycle, every point on the circumference of the wheel makes a tangent with the road.
curve
A curve is a shape or a line which is smoothly drawn in a plane having a bent or turns in it.
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Solve the equation −14 - 1 4 (x – 26) = –200 for x.
Hello there!
Answer:
x = 39 2/7
Step-by-step explanation:
-14 - 14(x - 26) = -200
- 14 + 14 - 14(x - 26) = -200 + 14
-14(x - 26) = -186
-14(x - 26)/(-14) = -186/(-14)
x - 26 = 93/7
x - 26 + 26 = 93/7 + 26
x = 275/7
x = 39 2/7
These two figures are the image and pre-image of a
dilation.
Find the lengths of the missing sides.
X= 2.5
y = 5
You’re welcome :(
Answer:
The answer is 2.5 and 5
Step-by-step explanation:
List 3 whole numbers immediately after 10
The answer is 11, 12, 13
Translate this sentence into an equation.
45 is the sum of 19 and Victor's score
Answer:
Victors score= v
19 + v =45
Two bags contain marbles. Bag A contains 110 marbles, and Bag B contains 160 marbles. What percent fewer marbles does Bag A has than Bag B?
Bag A as required by the task content has 31.25 percent fewer marbles than Bag B.
How much as a percent is the number of fewer marbles in Bag A as that in bag B?It follows from the task content that the percent fewer marbles which Bag A has relative to Bag B is to be determined.
As given in the task content; Bag A contains 110 marbles, while Bag B contains 160 marbles.
On this note, the difference between the number of marbles is; 160 - 110 = 50 marbles.
Hence, the percent of fewer marbles in Bag A relative to Bag B is;
= ( 50 / 160 ) × 100%
= 31.25%.
Therefore, Bag A has 31.25% fewer marbles than Bag B.
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what is the mode of this data set? 4, 69, 84, 69, 90, 75, 94, 90, 90, 1, 5
Answer:
90
Step-by-step explanation:
90 because it occurs most in the data set.
Answer:
90
Step-by-step explanation:
The mode of a data set is the number that occurs most frequently in the set. To easily find the mode, put the numbers in order from least to greatest and count how many times each number occurs. The number that occurs the most is the mode!
Marcos needs to buy a piece of fabric with a length of 1.3 meters. The fabric costs $0.45 per inch.
2.54cm $0.45
Marcos determines the calculation as 1.3m (100 cm -) ( :)
= 148.59
lin
lin.
What is the error in Marcos' reasoning, and how much will the fabric cost?
CA Marcos made an incorrect conversion from centimeters to inches. The correct price is $23.03.
B
Marcos made an incorrect conversion from centimeters to inches. The correct price is $14.86.
С
Marcos made an incorrect conversion from meters to centimeters. The correct price is $23.03.
D
Marcos made an incorrect conversion from meters to centimeters. The correct price is $14.86.
Marcos made an incorrect conversion from centimeters to inches. The correct price is $23.03. Option C is correct.
What is the error?An error is a mistaken or erroneous action. In some contexts, an error is interchangeable with a mistake.
The discrepancy between the calculated value and the correct value is referred to as an “error” in statistics.
The length of fabric= 1.3 meters.
Cost of fabric=$0.45 per inch
1 meter =39.3701 inch
1.3 meter =1.3 × 39.3701 inch
1.3 meter = 51.18 inch
Cost of fabric per unit length(inch);=$0.45
The cost of the fabric is;
Cost of fabric=$0.45 ×51.18 inch
Cost of fabric=$23.03
Marcos made an incorrect conversion from centimeters to inches. The correct price is $23.03. The fabric cost will be, $23.03
Hence,option C is correct.
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what is the magnitude of the net electric field at point p due to the particles?
The magnitude of the net electric field at point P due to the particle is 0 . explanation is given as
let us assume that , The charges of the four particles and the distance are given then on understanding the concept of electric field at electrostatics concept. on using the concept of the electric field at any given point, then production of individual electric field by a charge. and we known the concept of superposition law, on applying the law we get the value of the electric field in its direction and this shows the determination of the net electric field at that point.
The magnitude of the electric field,
E = q * R
where R = The distance of field at point from the charge, and q = charge of the individual particle
According to the superposition principle, the electric field at a single point due to more than one charges present ,hence on calculation of net electric field we get the origin of the coordinate system which is placed at point P and the y-axis is situated and oriented in the direction of the charge, (passing through the charge, ). The x-axis which is perpendicular to the y axis, and thus passes through the identical charges, then the individual magnitudes of an electric field is due to the charges are demonstrated by using the absolute signs of the charges. Now let us assume that the point charge which being positive i.e ( q > 0), we can see that the contributions coming from each charge gets cancel to each other. Therefore the net electric field in the direction of the y-axis is given using equation as E= 0
hence the net electric field is zero .
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