When proved, the total surface area of the solid is π/4 r(11r - 2l)
What is the total surface area of the solid?
The Solid comprise a cone mounted on top of a hemisphere. The total surface area of the object is given as follows
Total surface area = Total surface area of cone -total surface area of the hemisphere.
This implies that TSA = 1/2πr(1/2r +l) -3πr²
πr/2(r+2l)/2 -3πr²
This implies that the expression will be (πr² +2πrl)/4 - 3πr²
⇒(πr² +2πrl - 12πr²)/4
Conclusively, the expression finally gives π/4 r (11r - 2l)
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Apply the distributive property to create an equivalent expression.
5×(−2w−4
The equivalent expression when we apply distributive property is -10w -20
What is distributive property?You should understand that distributive property states that every term inside a grouping symbol multiplied by every term outside the grouping symbol yields the same result.
To this effect, the formula to do this is x(y+z) = xy+xz
The given expression is
5×(−2w−4)
= 5*-2w- 5*4
= -10w -20
In the expression every term outside the symbol is multiplied by every term inside the symbol to give the result of the expression
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find the quotient 2 divided by 3/7.
Answer:
14/3
Step-by-step explanation:
Flip the second fraction's numerator and denominator to get its reciprocal of 7/3. Then, you simply multiply it by 2, which equals 14/3.
In δcab, point e is the midpoint of segment ac and point d is the midpoint of segment bc. if the measure of segment ab is 8 units, what is the measure of segment segment ed? triangle cab, point e is on segment ac between points a and c and point d is on segment bc between points b and c, creating segment ed 3 units 4 units 5 units 6 units
The line ED has a length of 4 units.
Given,
Points E and D in the ΔCAB
equation represent the midpoints of the segments AC and BC, respectively.
AB is 8 units as well.
The length of segment ED needs to be determined.
We are aware that a triangle's third side and the line segment connecting its midpoint are both said to be parallel to the triangle's third side and to be half its length. The mid point theorem is what is known as this.
E and D are the midpoints of AC and BC in the equation CAB, and E's length is equal to half of AB's length is
=> 8/2
=> 4 units
so the length of the segment ED is 4 units
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The measure of segment ED is 4 units.
4 units
We know that the measure of segment AB is 8 units and that point E is the midpoint of segment AC and point D is the midpoint of segment BC. This means that the measure of segment AC is 8/2, or 4 units. Since point E is the midpoint of segment AC, it is also the midpoint of segment ED, meaning that the measure of segment ED is 4 units.
The measure of segment ED is 4 units.
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1.5 = 0.6 (w + 0.4)
SOLVE FOR W!!!!
Answer:
3.75
Step-by-step explanation:
Just divide 1.5 by 0.4
just ask your teacher for extra help if needed
Suppose x is 5 and y is 7. Choose the value of the following expression: (x != 7) && (x <= y) a. false b. true c. 0 d. null
The value of the expression (x != 7) && (x <= y) is: B. true
The expression is a combination of two logical conditions joined by the logical operator "&&" which means "and". The first condition "x != 7" checks if x is not equal to 7, which is true because x is 5. The second condition "x <= y" checks if x is less than or equal to y, which is also true because x is 5 and y is 7.
Since both conditions are true, the entire expression evaluates to true. The logical operator "&&" only returns true if both the conditions are true, else it will return false.
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Quadrilateral pqrs is located at p (−4, 1), q (−2, 3), r (1, 1), and s (−2, −2). russell and jamie have both classified pqrs differently. examine their proofs. who is correct? russell jamie pqrs is a parallelogram because both pairs of opposite sides are parallel segment pq p (−4, 1) and q (−2, 3) m equals 3 minus 1 over negative 2 plus 4 equals 2 over 2 equals 1 segment sr s (−2, −2) and r (1, 1) m equals 1 plus 2 over 1 plus 2 equals 3 over 3 equals 1 segment ps p (−4, 1) and s (−2, −2) m equals negative 2 minus 1 over negative 2 plus 4 equals negative 3 over 2 segment qr q (−2, 3) and r (1, 1) m equals 1 minus 3 over 1 plus 2 equals negative 2 over 3 segments pq and sr are parallel, and segments ps and qr are parallel. pqrs is a parallelogram because both pairs of opposite sides are congruent segment pq p (−4, 1) and q (−2, 3) d equals the square root of the quantity negative 2 plus 4 all squared plus 3 minus 1 all squared equals the square root of the quantity 4 plus 4 equals the square root of 8 equals 2 times the square root of 2 segment sr s (−2, −2) and r (1, 1) d equals the square root of the quantity 1 plus 2 all squared plus 1 plus 2 all squared equals the square root of the quantity 9 plus 9 equals the square root of 18 equals 3 times the square root of 2 segment ps p (−4, 1) and s (−2, −2) d equals the square root of the quantity negative 2 plus 4 all squared plus negative 2 minus 1 all squared equals the square root of the quantity 4 plus 9 equals the square root of 13 segment qr q (−2, 3) and r (1, 1) d equals the square root of the quantity 1 plus 2 all squared plus 1 minus 3 all squared equals the square root of the quantity 9 plus 4 equals the square root of 13 segments pq and sr are congruent, and segments ps and qr are congruent. russell jamie both neither
According to the question quadrilateral pqrs, the russell jamie both neither is neither.
The Quadrilateral pqrs is located at p (−4, 1), q (−2, 3), r (1, 1), and s (−2, −2).
A quadrilateral is defined as a two-dimensional shape with four sides, four vertices, and four angles. There are two main types: concave and convex.Russell:
PQRS is a parallelogram because both pairs of opposite sides are parallel
Segment pq is p (−4, 1), q (−2, 3).
Slope=[tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]
[tex]& m=\frac{3-1}{-2+4}=\frac{2}{2}=1[/tex]
Segment SR is s (−2, −2) and r (1, 1)
[tex]& m=\frac{1+2}{1+2}=\frac{3}{3}=1[/tex]
Segment ps is p (−4, 1), s (−2, −2)
[tex]& m=\frac{-2-1}{-2+4}=\frac{-3}{2}[/tex]
Segment qr is q(-2,3) and r(1,1)
[tex]m=\frac{1-3}{1+2}=\frac{-2}{3}[/tex]
Segments pq and sr are parallel, and segments ps and qr are parallel.
Jamie:
pqrs is a parallelogram because both pairs of opposite sides are congruent
Distance between two points is the length of the line segment that connects the two points in a plane
Segment pq is p (−4, 1), q (−2, 3).
[tex]& d=\sqrt{(-2+4)^2+(3-1)^2}=\sqrt{4+4}=\sqrt{8}=2 \sqrt{2}[/tex]
Segment SR is s (−2, −2) and r (1, 1)
[tex]& d=\sqrt{(1+2)^2+(1+2)^2}=\sqrt{9+9}=\sqrt{18}=3 \sqrt{2}[/tex]
Segment ps is p (−4, 1), s (−2, −2)
[tex]& d=\sqrt{(-2+4)^2+(-2-1)^2}=\sqrt{4+9}=\sqrt{13}[/tex]
Segment qr is q(-2,3) and r(1,1)
[tex]d=\sqrt{(1+2)^2+(1-3)^2}=\sqrt{9+4}=\sqrt{13}[/tex]
Segments pq and sr are congruent, and segments ps and qr are congruent.
Therefore, the correct option is neither.
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Both Russell and Jamie are correct. PQRS is a parallelogram with slope because both pairs of opposite sides are parallel, and it is also a parallelogram because both pairs of opposite sides are congruent.
Russell is correct because he used the slope of the lines to prove that both pairs of opposite sides are parallel. He calculated the slope of the lines using the equation m = (y2 - y1)/(x2 - x1) and found that the slopes of the two pairs of opposite sides (PQ and SR, and PS and QR) are equal, which means that the lines are parallel.
Jamie is also correct because he used the distance formula to prove that both pairs of opposite sides are congruent. He calculated the distance between the points using the equation d = √((x2 - x1)^2 + (y2 - y1)^2) and found that the distances of the two pairs of opposite sides (PQ and SR, and PS and QR) are equal, which means that the lines are congruent.
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Find three consecutive even integers such that the sum of twice the first and three times the third is fourteen more than four times the second.
Step-by-step explanation:
if the three numbers are x,x+1,x+2
2x+3(x+2)=(x+1)4+14
5x+6=4x+18
×=12
Select the correct answer from each drop-down menu. given: prove: a transversal line intersects two parallel lines a and b with values of corresponding angles congruent pairs of corresponding angles are (1, 5), (4, 8), (3, 7), and (2, 6). complete the proof. statements reasons 1. given 2. corresponding angles theorem 3. vertical angles theorem 4. transitive property of congruence
A transversal line intersects two parallel lines a and b with values of corresponding angles congruent pairs of corresponding angles are (1, 5), (4, 8), (3, 7), and (2, 6).
∠1 ≅ ∠5 (corresponding angle theorem)
∠7 ≅ ∠5 (vertical angle theorem)
∠1 ≅ ∠7 (Transitive property of congruence)
Complete question is at the end of solution.
As per the given data, a transversal line intersects two parallel lines a and b.
The values of corresponding angles congruent pairs of corresponding angles are (1, 5), (4, 8), (3, 7), and (2, 6)
How to find angles?Line a is parallel to line b.
Therefore,
a ║ b
Let's prove ∠1 ≅ ∠7
Hence,
∠1 ≅ ∠5 (corresponding angle theorem)
Corresponding angles are the angles that are formed in matching corners or corresponding corners with the transversal when two parallel lines are cut by the traversal.
∠7 ≅ ∠5 (vertical angle theorem)
Vertical angles theorem or vertically opposite angles theorem:
According to the theorem, two opposing vertical angles that are created when two lines cross one other are always equal.
Vertical angles are the angles formed when two lines intersect each other.
∠1 ≅ ∠7 (Transitive property of congruence)
Transitive property of congruence: If two lines, angles, or triangles are congruent with one another, then the first line, angle, or triangle is congruent with the second, third, or fourth line, angle, or triangle.
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The given statement states that a transversal line intersects two parallel lines, a and b, with corresponding angle congruent pairs of (1, 5), (4, 8), (3, 7), and (2, 6). The proof uses the corresponding angles theorem, vertical angles theorem, and transitive property of congruence to show that the angles are congruent.
Given 2. Corresponding angles theorem 3. Vertical angles theorem 4. Transitive property of congruence Reasons: 1. The transversal line intersects two parallel lines a and b with values of corresponding angles congruent pairs of (1, 5), (4, 8), (3, 7), and (2, 6). 2. If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. 3. If two angles are vertical angles, then they are congruent. 4. If two angles are congruent to the same angle, then they are congruent to each other.
The given statement states that a transversal line intersects two parallel lines, a and b, with corresponding angle congruent pairs of (1, 5), (4, 8), (3, 7), and (2, 6). The proof uses the corresponding angles theorem, vertical angles theorem, and transitive property of congruence to show that the angles are congruent.
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When Logan had one cat, he needed to serve 1/8 of a can of cat food each day. Now that Logan has adopted a second cat, he needs to serve a total of 3/8 of a can each day. How much extra food is needed to feed the second cat?
Answer:1/4
Step-by-step explanation:3/8-1/8=1/4
A rectangular deck is built around a square pool. The pool has side length s. The length of the deck is 5 units longer than twice the side length of the pool. The width of the deck is 3 units longer than the side length of the pool. What is the area of the deck in terms of s? write the expression in standard form.
The area of the deck in terms of s is 2s^2 + 7s + 15. The expression can be written in standard form as A = 2s^2 + 7s + 15.
The area of the deck can be expressed in terms of s using the standard form of a rectangular area equation, A = lw, where l is the length and w is the width. The side length of the pool is s and the length of the deck is twice the side length of the pool plus 5, or 2s+5. The width of the deck is 3 units longer than the side length of the pool, or s+3. Substituting these values into the area equation gives us:
A = (2s+5)(s+3)
A = 2s^2 + 7s + 15
Therefore, the area of the deck in terms of s is 2s^2 + 7s + 15.
The expression can be written in standard form as A = 2s^2 + 7s + 15.
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The area of the rectangular deck built around the square pool of side, s in terms of s is 2s² + 11s + 15.
Therefore the answer is 2s² + 11s + 15.
The pool has side length s. The length of the deck is 5 units longer than twice the side length of the pool, that is
l = 2s + 5
The width of the deck is 3 units longer than the side length of the pool, that is
b = s + 3
Deck is in rectangular shape, thus the area of the deck in terms of s can be calculates by
A = lb = (2s + 5)×(s + 3)
= 2s² + 6s + 5s + + 15
= 2s² + 11s + 15
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Please help!! And please explain how you got it I really don’t understand
Answer:
Step-by-step explanation:
do it better than what you did before.
Does someone know how to do this we have a sub
Answer:
1/5, 20 diveded by 5 is 4, 20%
A fair die is rolled 5 times. What is the expected sum of the 5 rolls?
Answer:
5-30
Step-by-step explanation:
expectation of single
HELP ME. What is 12*2/2*100?
Answer:
1200
Step-by-step explanation:
12 multiplied by 2 is 24.
24 divided by 2 is 12.
12 times 100 is 12 plus 2 zeros, or 1200.
Solve the system by graphing. please Help
Answer:
Solution is (-1,7)
Step-by-step explanation:
Graph is shown
y=2x+9 is in red
y=6-x is in blue
Hope this helps :)
How do you solve m =( y2 y1 )/( x2 x1?
For a project in her Geometry class, Shandra uses a mirror on the ground to
measure the height of her school's flagpole. She walks a distance of 13.35
meters from the flagpole, then places a mirror on flat on the ground, marked
with an X at the center. She then steps 1.55 meters to the other side of the
mirror, until she can see the top of the flagpole clearly marked in the X. Her
partner measures the distance from her eyes to the ground to be 1.25 meters.
How tall is the flagpole? Round your answer to the nearest hundredth of a
meter.
An image is always formed at the back of a mirror. Thus, the flagpole is 8.75 m tall.
Let the angle of depression from Madelyn's point of view be represented by θ. Then applying the required trigonometric function, we have;
Tan θ = opposite / adjacent
= 1.65 / 1.7
Tan θ = 0.9706
θ = Tan⁻¹(0.9706)
= 44.2°
θ = 44.2°
Let the height of the flag be represented by h. And for a given mirror, the angle of incidence is equal to that of reflection. Then;
Tan θ = opposite / adjacent
= h / 8.75
0.9706 = h / 8.75
h = 0.9706 x 8.75
= 8.49275
h = 8.5 m
Since the image is formed at the back of the mirror, then the flagpole is 8.5 m tall.
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Based on this data, what is a reasonable estimate of the probability that the Canadian Rounders have 000 players injured for their next match?
The probability that the Canadian Rounders have 0 players injured for their next match is 1/4 or 25%.
What is the probability?This implies the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happeing of the event.
The total number of matches = 4+5+2+3+2
The total number of matches = 16
Total, that has zero injured players = 4
The probability will be:
= 4 / 16
= 0.25
The probability is 0.25.
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Complete question
The following frequency table summarizes this year's injuries on the Canadian Rounders cricket team.
Number of injured players Number of matches
0 | 4
1 | 5
2 | 2
3 | 3
4 | 2
Based on this data, what is a reasonable estimate of the probability that the Canadian Rounders have 0 players injured for their next match?
How do you find 1/3 of a line segment?
To find 1/3 of a line segment, divide the line segment into three equal parts. Measure the length of one of these parts and this will be 1/3 of the line segment.
This can be done by using a ruler or a measuring tape. Alternatively, if the length of the line segment is known, divide it by 3 to find 1/3 of the line segment. For example, if the line segment has a length of 12 inches, then the length of 1/3 of the line segment is 4 inches. If the line segment is curved, you can divide it into three equal arc lengths using a compass.
You can then measure the length of one of these arcs to find 1/3 of the line segment. To make sure that the three parts are equal, you can use the Pythagorean theorem or the triangle inequality theorem. This will help you to accurately divide the line segment into three equal parts.
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PLEASE THIS IS AN EMERGENCY I NEED HELP QUICK!!!!!
1.Compare the expressions 7 + 3^2-2x5÷4-1x2 and (¾+ ⅛) ÷ ⅛ - 2^2using < , =, > or . Show your work.
Answer:
The comparison of the expressions is 7 + 3² -2 * 5 ÷ 4 - 1 * 2 > (¾+ ⅛) ÷ ⅛ - 2²
How to compare the expressionsFrom the question, we have the following parameters that can be used in our computation:
7 + 3^2-2x5÷4-1x2 and (¾+ ⅛) ÷ ⅛ - 2^2
Express the exponents properly
This gives
7 + 3² -2 * 5 ÷ 4 - 1 * 2 and (¾+ ⅛) ÷ ⅛ - 2²
Evaluate the exponents
So, we have the following representation
7 + 9 - 2 * 5 ÷ 4 - 1 * 2 and (¾+ ⅛) ÷ ⅛ - 4
Evaluate the expressions in brackets
So, we have the following representation
7 + 9 - 2 * 5 ÷ 4 - 1 * 2 and 7/8 ÷ ⅛ - 4
Solve the products and quotients
7 + 9 - 2.5 - 2 and 7 - 4
So, we have
11.5 and 3
11.5 is greater than 3
So, we have
11.5 > 3
Rewrite as
7 + 3² -2 * 5 ÷ 4 - 1 * 2 > (¾+ ⅛) ÷ ⅛ - 2²
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Which value of x is the solution to the equation?
3x = 6
Responses
x = 2
x, = 2
x = 3
x, = 3
x = 4
x, = 4
x = 18
x, = 18
Answer:
x = 2
Step-by-step explanation:
6/3 = 2
If xy + 8e^y = 8e, find the value of y" at the point where x = 0. y" =
At the point where x = 0, the equation simplifies to 8e^y = 8e, which can be rearranged to e^y = 1. This means that y = 0.
1. Substitute x = 0 into the equation: xy + 8e^y = 8e
2. Simplify the equation: 8e^y = 8e
3. Rearrange the equation to isolate the exponent: e^y = 1
4. Take the natural logarithm of both sides: y = ln(1)
5. Evaluate the natural logarithm: y = 0
At the point where x = 0, the given equation simplifies to 8e^y = 8e. Rearranging this equation to isolate the exponent on the left hand side, we get e^y = 1. Taking the natural logarithm on both sides, we get y = ln(1). Finally, evaluating the natural logarithm of 1, we get y = 0. Therefore, the value of y" at the point where x = 0 is 0.
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A rectangle has a length of x centimeters and a width of 20 centimeters.
Which expression represents the perimeter of the rectangle?
Answer:
2x + 40
Step-by-step explanation:
Given ,
L = x
B = 20cm
To Find: Expression that represents the Perimeter
Perimeter of rectangle = 2(l+b)
= 2(x+20)
= 2x + 40
Solve the following system of equations. Express your answer as an ordered pair in the format (a,b), with no spaces between the numbers or symbols.
The solution to the system of equations is (3,1).
2x - 3y = 6
3x + 2y = 7
(3,1)
Multiply the first equation by 3:
6x - 9y = 18
Add the two equations:
9x - 7y = 25
Divide both sides by 9:
x - y = 25/9
Substitute 25/9 for x in the second equation:
3(25/9) + 2y = 7
Simplify:
25 + 18y = 63
Subtract 25 from both sides:
18y = 38
Divide both sides by 18:
y = 38/18
Substitute 38/18 for y in the equation x - y = 25/9:
x - (38/18) = 25/9
Simplify:
x = (25/9) + (38/18)
Simplify:
x = 63/9
Therefore, the solution is (63/9, 38/18) or (3,1).
The solution to the system of equations is (3,1).
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The tensile strength for a certain steel wire is 3000 mn/m2. What is the maximum load that can be applied to a wire with a diameter of 3. 0 mm made of this kind of steel?.
The maximum load that can be applied to the wire made of that kind of steel is 21195 N. The result is obtained by using the tensile strength equation.
What is tensile strength?Tensile strength is the maximum load or stress that a material can withstand without fracture when being stretched or pulled per its cross-sectional area.
The statement can be expressed as
σ = F/A
Where
σ = tensile strengthF = force acting on the materialA = cross-sectional areaThe tensile strength of a certain steel wire is 3000 MN/m². The diameter of the wire is 3.0 mm. Find the maximum load that can be applied to the wire!
Let's count the cross-sectional area!
A = πr²
A = 3,14 (½d)²
A = 3,14 [½(3.0 × 10⁻³)]²
A = 3,14 (1.5 × 10⁻³ m)²
A = 3,14 (2.25 × 10⁻⁶) m²
A = 7.065 × 10⁻⁶ m²
The maximum load is the maximum value of the force acting on it.
σ = F/A
3000 MN/m² = F / 7.065 × 10⁻⁶ m²
3000 × 10⁶ N/m² = F / 7.065 × 10⁻⁶ m²
F = 3 × 10⁹ × 7.065 × 10⁻⁶ N
F = 21.195 × 10³ N
F = 21195 N
Hence, the steel wire can have the maximum load of is 21195 N.
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A child's weight (lbs) can be expressed as the function f(x)= 0.5x + 7.8. where x is time in months. How much did the
child weigh when it was born?
On solving the provided question, we can say that - the of the function f(x) = 0.5x + 7.8 = 9.8
what is function?The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.
here, we are provided with the function -
f(x)= 0.5x + 7.8
and given from question, x = 4
f(x) = 2 + 7.8 = 9.8
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What is the slope of the graphed line? Responses −52 negative 5 over 2 25 2 over 5 52 5 over 2 72 7 over 2 A line graphed on a Coordinate plane with x axis ranging from 0 to 10 and y axis ranging from 0 to 10. The line passes through the points begin ordered pair 0 comma 2 end ordered pair comma begin ordered pair 2 comma 7 end ordered pair.
-090
Step-by-step explanation:
The graphs of the equations Ax+By=7 and Ax-By=3 intersect at (1,-2).
Determine the value of A and B
please show work :)
Step-by-step explanation:
we create 2 equations with 2 variables by using the given point coordinates in both :
A×1 + B×-2 = 7
A - 2B = 7
A×1 - B×-2 = 3
A + 2B = 3
to solve we can simply add both equations to temporarily eliminate B and solve for A :
A - 2B = 7
A + 2B = 3
-------------------
2A 0 = 10
A = 10/2 = 5
now, we use one of the original equations to solve for B :
5 + 2B = 3
2B = -2
B = -2/2 = -1
Jamir made 48 cookies for a picnic. He wants to give each of his 3 friends an equal number of cookies. How many cookies will each of Jamir's friends get
Answer:
16
Step-by-step explanation:
48 divided by 3 is 16, so each of his friends will get 16 cookies.
A factory uses 3/8 of a barrel of pecans in each batch of cookies. Yesterday, the factory used 3/4 of a barrel of pecans. How many batches of cookies did the factory make yesterday
Answer:
3/4
Step-by-step explanation:
1 batch of cookies is equal to 0.375. 3/4 a barrel of cookies is equal to 0.75. 0.75/0.375 is equal to 2. So 3/4 a barrel is 2 batches of cookies.
