whole part = 3
fractional part = 7/8
===========================================================
Explanation:
1/2 = 4/8
So the mixed number 2 & 1/2 is the same as 2 & 4/8
Adding on 1 & 3/8 will mean the fractional portions add to 4/8+3/8 = 7/8 and the whole number portions add to 2+1 = 3
Overall, the total amount eaten is 3 & 7/8 pounds
Answer:
27 1/8 pounds
Step-by-step explanation:
2.5 multiplied by 7 would be 17.5 and 1 and 3/8's by 7 would be 7 multiplied by 3 = 21/8 which would be 9 and 5/8's added up with the first 7 pounds
A 45 foot ladder is set against the side of a house so that it reaches up 27 feet. If Nicole grabs the ladder at its base and pulls it 4 feet farther from the house, how far up the side of the house will the ladder reach now? (The answer is not 23 ft.) Round to the nearest tenth of a foot.
The ladder will reach a height of 20.6 feet
The given parameters are:
Length = 45-footHeight = 27 feetStart by calculating how far (d) the ladder is, from the bottom of the house using the following Pythagoras theorem
[tex]45^2 = 27^2 +d^2[/tex]
Collect like terms
[tex]d^2= 45^2 -27^2[/tex]
[tex]d^2= 1296[/tex]
Take square roots of both sides
[tex]d= 36[/tex]
When the ladder is moved 4 feet farther, the new distance becomes
[tex]d= 36+4[/tex]
[tex]d= 40[/tex]
The new height (h) of the ladder is then calculated using the following Pythagoras theorem
[tex]45^2=40^2 + h^2[/tex]
Collect like terms
[tex]h^2 = 45^2-40^2[/tex]
[tex]h^2 = 425[/tex]
Take the square roots of both sides
[tex]h = 20.6[/tex]
Hence, the ladder will reach a height of 20.6 feet
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the difference of two numbers is 13/24. if 11/12 of the reciprocal of one number is equal to 5/9 of the reciprocal of the other, what are the 2 numbers?
Answer:
The two numbers are 11/8 and 5/6
Step-by-step explanation:
Let the unknown numbers be x and y
Given that the difference of two numbers is 13/24
x - y = 13/24
and that 11/12 of the reciprocal of one number is equal to 5/9 of the reciprocal of the other
11/12 * 1/x = 5/9 * 1/y
11/12x = 5/9y
cross multiply
12x * 5 = 11* 9y
60x = 99y
x = 99y/60
= 33y/20
substitute into x - y = 13/24
33y/20 - y = 13/24
13y/20 = 13/24
24y = 20
y = 20/24
= 5/6
x = 33y/20
= 33 *5/20*6
= 11/8
1. Find the numbers a, b, c such that
2x4 + 2x3 +5x2 + 3x + 3 = (x2 + x +1)(ax2+bx+c)
for all values of x.
Answer:
a = 2
b = 0
c = 3
Step-by-step explanation:
if I understand correctly the problem should look like
2x⁴ + 2x³ + 5x² + 3x + 3 = (x² + x + 1)(ax² + bx + c)
let's calculate the right side
ax⁴ + ax³ + ax² + bx³ + bx² + bx + cx² + cx + c
as there is only one term of x⁴, we know a = 2
as there is only one term without any x, we know c = 3
now we get
2x⁴ + 2x³ + 2x² + bx³ + bx² + bx + 3x² + 3x + 3
remember, that is equal to
2x⁴ + 2x³ + 5x² + 3x + 3
after subtracting 2x⁴ and 3 from both sides we get
2x³ + 5x² + 3x = 2x³ + 2x² + bx³ + bx² + bx + 3x² + 3x
we subtract 2x³ and 3x from both sides and get
5x² = 2x² + bx³ + bx² + bx + 3x² = 5x² + bx³ + bx² + bx
we subtract 5x² from both sides and get
0 = bx³ + bx² + bx
=> b must be 0 to make this true for all values of x
Please help me with this!!!!! I don't get it
Answer:
y = -1/7
Step-by-step explanation:
Mathematically, the distance between two points on a coordinate plane can be calculated using the formula;
d = √(x2-x1)^2 + (y2-y1)^2
for the first two points;
(5,y) and (1,4) ; we have
d = √(5-1)^2 + (y-4)^2
d = √(y-4)^2 + 16
For the other two;
(5,y) and (10,-3)
We have ;
d = √(5-10)^2 + (y + 3)^2
d = √(y+ 3)^2 + 25
from the question, these two distances are equal
all we have to do here is to equate the two distances
So we have it that;
(y-4)^2 + 16 = (y + 3)^2 + 25
y^2 -8y + 16 + 16 = y^2 + 6y + 9 + 25
-8y + 32 = 6y + 34
-8y -6y = 34-32
-14y = 2
y = -2/14
y = -1/7
A table tennis ball has a radius of 2 cm. There are 3 table tennis balls stacked on top of one another in a cylinder that has the same diameter as the table tennis balls. The table tennis balls reach the top and bottom of the cylinder. How much volume is left inside the cylinder when the container is full?
Answer:
Volume left = 16π cm³ or 50.265 cm³
Step-by-step explanation:
Let's first find the surface area of the tennis ball.
S.A = (4/3)πr³
Radius of a ball = 2 cm
Thus;
S.A = (4/3)π(2)³
S.A = 32π/3
Since there are 3 radius balls that will make the cylinder full, then;
Surface area of 3 balls = 3 × 32π/3 = 32π
Now, formula for volume of cylinder is;
V = πr²h
r = 2 cm
h = 4 × 3 = 12 (since diameter of tennis ball is 4 cm)
Thus;
V = π × 2² × 12
V = 48π
Thus;
Volume left = Volume of cylinder - surface area of 3 balls = 48π - 32π = 16π cm³ or 50.265 cm³
Calculate the measure of angle P:
Answer:
122.3 degrees
Step-by-step explanation:
To get the measure, we use the appropriate method
The method we are going to use here is the cosine rule
We have the general form as;
a^2 = b^2 + c^2 -2bc Cos A
where a = 25
b = 9 and c = 19
Substituting these values;
25^2 = 9^2 + 19^2 - 2(9)(19) Cos A
183 = -342 cos A
cos A = -183/342
cos A = -0.54
A = arc cos -0.54
A = 57.65 ( since cosine is negative in the second quadrant, then the value will be 180 - 57.65
= 122.35
find the area of the irregular figure. 2in. 5in. 2in. 4in. 4in. 3in. 3in.
The shape can be split into 3 separate shapes:
On the left side a square 3 x 3 = 9 square inches.
The middle rectangle that is 2 x 5 = 10 square inches
The bottom rectangle which is 4 x 4 = 16 square inches
Total area = 9 + 10 + 16 = 35 square inches
I need to find the sum of the interior angel
Muffins are sold in packages of 18 and cost $27 per package. Each of 6 friends gets an equal share of muffins from p packages of muffins. Write an expression to represent how much each friend must pay.
Answer:
27/18= 1.5
18/6 = 3
3•1.5= 4.5
Step-by-step explanation:
$27 divided by 18 muffins equals $1.50, 18 muffins divided by 6 people equals 3, 3 muffins times $1.50 equals $4.50. So $4.50 is how much each person would have to pay.
Can someone help please
Answer:
geometric
common ratio 2/3
Step-by-step explanation:
We know that the sequence is not arithmetic
3-2 =1
2-4/3 = 6/3 -4/3 = 2/3
The common difference is not the same
Now check geometric
The common ratio:
Take the second term over the first term
2/3
Now take the third term over the second term
4/3 ÷ 2
4/3 * 1/2 = 2/3
The common ratio is the same so the sequence is geometric with a common ratio of 2/3
Jasmine drew triangles on a globe and on a flat map of the world, as shown below.Which is a true statement comparing Jasmine’s two drawings?
A. The angle sum of the triangle on the globe is equal to the angle sum of the triangle on the map.
B. The angle sum of the triangle on the globe is greater than the angle sum of the triangle on the map.
C. The New York to Buenos Aires line and the Paris to Buenos Aires line intersect at only one point on the map and only one point on the globe.
D. There is only one line connecting New York to Paris on the map but more than one line connecting New York to Paris on the globe
Answer:
B
Step-by-step explanation:
OEMJIGOVNarioendsdmarfwsipf JUST BELIEVE, also looking is good
The true statements on comparing Jasmine’s two drawings are B and C.
What is Angle Sum Property of a Triangle ?The sum of a finite traingle's interior angle is equal to 180° and this is called the Angle Sum Property of a Triangle.
It is given in the question
Jasmine drew triangles on a globe and on a flat map of the world
On comparing both the triangle the conclusions are
The triangle drawn on the globe is a spherical triangle and the angle sum of the interior angle will be greater that the two right angles or 180°.
Among the option given this is also true that
The New York to Buenos Aires line and the Paris to Buenos Aires line intersect at only one point on the map and only one point on the globe
Therefore option B and C are both true statement comparing Jasmine’s two drawings .
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9.2\times 10^{-3}-1.3\times 10^{-3}
9.2×10
−3
−1.3×10
−3
Answer:
73
Step-by-step explanation:
9.2 x 10 - 3 - 1.3 x 10 - 3
92 -3 - 13- 3
73 is the answer if that the question
Answer:
[tex](9.2 \times {10}^{ - 3}) - (1.3 \times {10}^{ - 3} ) \\ \\ = { \tt{(9.2 - 1.3) \times {10}^{ - 3} }} \\ \\ = { \tt{7.9 \times {10}^{ - 3} }}[/tex]
What is The answer , what goes in the QR
may be QR also equal to 34
The graph shown below represents the rate at which water drains from a tank once the drain is opened which statement correctly describes the graph
A. The water is draining at constant rate of 1/2 gallon per minute, and the tank contained exactly 14 gallons when the drain opened
B. The water is draining at a constant rate of 2 gallons per minute,and the tank contained exactly 14 gallons when the drain was opened
C. The water is draining at a constant rate of 5 gallons per minute, and the tank contained exactly 14 gallons when the drain was opened
D.the water is draining at a constant rate of 14 gallons per minute, and the tank contained exactly 1/2 gallon when the drain was opened
Answer:
A
Step-by-step explanation:
The slope is -1/2 and the y-intercept is 14
help please hurryyyy!!! help pls hurry
Answer:
3 is 18
4 is 14
5 is 10
6 is 6
I hope this helps
Students at a local high school travel to school by car, bus, and bicycle. 1/5 of the 825 students Tavel by car, 48% of the students travel by bus, 0.08 of the students travel by bicycle. The remaining students travel to school by walking. How many students walk to the local high school?
Answer:
198 students walk to the local high school
Step-by-step explanation:
Total number students = 825
1/5 of the students travel by car
48% of the students travel by bus
0.08 of the students travel by bicycle
To find the number of students who wal to school we have to find the exact number of students who travel to school by car, bus and bicycle and subtract the result from the total number of students
Students who travel by car = 1/5×825
= 165 students
Students who travel by bus = 48% × 825
= 48/100 × 825
= 12/25 × 825
= 396 students
Students who travel by bicycle = 0.08 × 825
= 66
So now we add the results fo the equations above and subtract it from the total number of students to get the number of students that walk to school
Students that walk to school = 825 - (165 + 396 + 66)
= 825 - 627
= 198 students
Therefore 198 students walk to the local high-school
evaluate the expression 4(n+5)-8 when n =1/4 and m=0.5
Answer:
17
Step-by-step explanation:
Given
4(n + 5) - 8m ← substitute n = 0.25, m = 0.5 into the expression
= 4(0.25 + 5) - 8(0.5)
= 4(5.25) - 4
= 21 - 4
= 17
–6(2 + a) = –48 please answer
Answer:
a = 6
Step-by-step explanation:
–6(2 + a) = –48
Divide each side by -6
–6(2 + a) / -6 = –48/-6
2+a = 8
Subtract 2 from each side
2+a-2 = 8-2
a = 6
The two lines below intersect as shown what the value of x (2x+29) (9x-13)
Given:
Two lines intersect each other.
Consider the below figure attached with this question.
To find:
The value of x.
Solution:
If two lines intersect each other then the vertically opposite angles are congruent and their measures are equal.
In the given figure, the measures of two vertically opposite angles are (2x+29)° and (9x-13)°.
[tex]2x+29=9x-13[/tex]
[tex]2x-9x=-29-13[/tex]
[tex]-7x=-42[/tex]
Divide both sides by -7.
[tex]x=\dfrac{-42}{-7}[/tex]
[tex]x=6[/tex]
Therefore, the value of x is 6.
Help someone plsss!!!!!!!!!!
Answer:
150 degrees.
Step-by-step explanation:
We know, 1 Hour angles = 15 Degrees
So, 10 hour walking = 10*15 = 150 degrees
Hope this will help. Please mark me brainliest.
What is the solution to the system of equations
Answer:
Y = -8.17
X= -4.936
For the first one
Step-by-step explanation:
4x=26+6y
X = 6.5+1.5y
5(6.5+1.5y)-4y = 8
32.5+7.5y-4y = 8
24.5=-3y
Y = -8.17
X= -4.936
Which side lengths form a right triangle?
Answer:
answer is option B
9² +40² =41²
81+1600=1681
Answer:
B) 9 , 40, 41
............
Please help me with these questions
Answer:
A. <EKH and <EKF
B. <EKH and <FKG
C. <HKJ and <GKJ
Step-by-step explanation:
A. A linear pair are two adjacent angles that forms a straight line that equals 180°.
<EKH and <EKF is a linear pair
B. A pair of vertical angles are opposite angles formed when two straight lines intersect. They share a common vertex.
<EKH and <FKG
C. Adjacent angles share a common vertex and a common side. The pair of adjacent angles that are not a linear pair will not form a straight line.
<HKJ and <GKJ are adjacent angles that share the same vertex (<K) and the same side (KJ). However they do not form a straight line. Therefore, <HKJ and <GKJ are a pair of adjacent angles that are not a linear pair.
Add.
3 7/11 + 9 6/11
Write your answer as a mixed number in simplest form.
Help
Answer:
13 2/11
Step-by-step explanation:
40/11+105/11
145/11
13 2/11
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{= \ 3\dfrac{7}{11}+ 9\dfrac{6}{11}}[/tex]
[tex]\mathsf{ 3\dfrac{7}{11} =\boxed{ \bf \dfrac{40}{11}}}[/tex]
[tex]\mathsf{9\dfrac{6}{11}= \boxed{\bf \dfrac{105}{11}}}[/tex]
[tex]\mathsf{= \ \dfrac{(40\times11)+(105\times11)}{(11\times11)}}[/tex]
[tex]\mathsf{40\times11=\boxed{\bf 440}}[/tex]
[tex]\mathsf{105\times11=\boxed{\bf 1,155}}[/tex]
[tex]\mathsf{=\ \dfrac{440+ 1,155}{11\times11} }[/tex]
[tex]\mathsf{11\times11=\boxed{\bf 121}}[/tex]
[tex]\mathsf{\dfrac{440+1,155}{121}}[/tex]
[tex]\mathsf{440 + 1,155=\boxed{\bf 1,595}}\leftarrow\mathsf{Your\ numerator\ (TOP\ number)}[/tex]
[tex]\mathsf{= \dfrac{1,595}{121}}[/tex]
[tex]\mathsf{= 13\dfrac{2}{11}}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: } \mathsf{\boxed{\bf \dfrac{1,595}{121}\ or\ 13 \dfrac{2}{11}}\\\large\textsf{either one of those should work they equal the same}}}}\huge\checkmark}[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
[tex]\frak{Amphitrite1040:)}[/tex]
On a set of blueprints, the length of a building is 16 inches. The actual building is 85 1/3 feet long. Which of the following is the correct scale?
1:64
1:5
1:32
1:12
Answer:
1 : 64
Step-by-step explanation:
We require the dimensions to be the same units
1 foot = 12 inches , then
85 [tex]\frac{1}{3}[/tex] feet = [tex]\frac{256}{3}[/tex] × 12 = 256 × 4 = 1024 inches
Scale is then
16 in : 1024 in ( divide both parts by 16 )
= 1 : 64
12. The local regional transit authority of a large city was interested in determining the mean
commuting time for workers who drive to work. They selected a random sample of 125
workers who drive to work and asked them how long they spent commuting to work in
minutes). A 95% confidence interval was constructed and reported as (27.74, 30.06).
(a) Show that the conditions for calculating a confidence interval for a mean are satisfied.
(b) Interpret the interval in the context of this problem.
1. We conclude that the conditions for calculating a confidence interval for a mean are satisfied.
2. Since interval was constructed and is reported, we assume that distribution of the sample mean is normal.
Do the conditions for a mean confidence interval calculation hold?Let x be the sample mean
Let s be the sample standard deviation
Let n be the sample size
Let α be the significance level
Let Z be the standard normal distribution value.
To determine if conditions for calculating confidence interval for a mean are met, we have to check the followings:
1. Random sampling:
The sample of 125 workers was selected randomly.
2. Independence:
We assume that each worker's commuting time is independent of each other.
3. Sample size:
n = 125 > 30. This satisfies the condition for the central limit theorem to apply.
4. Normality:
The 95% confidence interval was constructed using the formula x ± Zα/2(s/√n).
Since interval was constructed and is reported, we can assume that the distribution of the sample mean is approximately normal. Therefore, we can conclude that the conditions for calculating a confidence interval for a mean are satisfied.
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Solve for x. Assume that lines which appear tangent are tangent. x=
Answer:
this is a long shot( like rly long) but try either -6 or -3
Step-by-step explanation:
Don't co.e for me if I'm wrong im just a poor girl in year 8
22 dividido en 3 es?
Answer:
Step-by-step explanation:
7.3
Answer:
7.3
Step-by-step explanation:
22/3 = 22/3
(Decimal: 7.333333)
help me with this mathematics
Answer: B
Step-by-step explanation: 65/100 = 65%
How many feet is it from goal line to goal line on a regulation football field
that is 100 yards long? It is measured in the
A. tens
B. thousands
C. millions
D. hundreds
Answer:
D. hundreds
Step-by-step explanation:
if a football field is 100 yards long then it is 300 feet long and that is in the hundreds
