Answer:
p≥35
Step-by-step explanation:
because you have done 15 so you subtract 15 from 50 giving you 35 and then you would say p is greater than or equal to 35 cause 50 pages is your minimum
Find the volume of the triangular prism described below
The volume of the triangular base prims is 21.6 inches cube.
How to find the volume of a triangular base prism?A triangular base prism is a prism with a triangular base. Therefore, let's find the volume of the triangular prism.
volume of a triangular prism = base area × height
Therefore,
base area = 1 / 2 bh
where
b = baseh = heightTherefore, the triangular base has angles 45, 45 and 90 degrees. Using trigonometric ratios let's find the other legs.
tan 45 = opposite / adjacent
tan 45 = x / 6
x = 6 inches
Therefore,
base area = 1 / 2 × 6 × 6
base area = 36 /2
base area = 18 inches²
Hence,
volume of the triangular base prism = 18 × 1.2
volume of the triangular base prism = 21.6 inches³
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How many liters each of a 50% acid solution and a 60% acid solution must be used to produce 60 liters of a 55% acid solution? (Round to two decimal places if necessary.)
To produce 60 liters of a 55% acid solution, we need 18 liters of a 50% acid solution and 42 liters of a 60% acid solution.
Let x be the number of liters of the 50% acid solution needed, and y be the number of liters of the 60% acid solution needed.
We can set up two equations based on the amount of acid and the total volume:
0.50x + 0.60y = 0.55(60)
x + y = 60
Simplifying the first equation:
0.50x + 0.60y = 33
5x + 6y = 330 (multiplying both sides by 10)
We can solve for one variable in terms of the other in the second equation, and substitute into the first equation:
y = 60 - x
5x + 6(60 - x) = 330
Simplifying:
x = 18
So we need 18 liters of the 50% acid solution, and:
y = 60 - x = 42
So we need 42 liters of the 60% acid solution.
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Mrs.lealas living room has an area of 144 square feet.
Her dining room is ⅓ the area of the living room and ⅖ the area of the kitchen. What is the area, in square feet, of the kitchen?
The Area of Kitchen is 120 square feet.
We have,
Area of living room = 144 square feet
So, the dining room
= 1/3 (area of living room)
= 1/3 (144)
= 48 square feet
and, Area of Dining room = 2/5 x Area of kitchen
48 = 2/5 x Area of kitchen
Area of kitchen = 48 x 5/2
Area of Kitchen = 24 x 5
Area of Kitchen = 120 square feet
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What side-angle relationship is given in the following triangle?
A. ASA
B. AAA
C. SSS
D. SAS
Without more information or a diagram, it's not possible to definitively determine which side-angle relationship (ASA, AAA, SSS, SAS) the triangle fits. These acronyms represent different combinations of sides and angles known in a triangle.
Explanation:Given the question, it's clear that we are discussing a concept in Geometry - the side-angle relationships in a triangle. However, without more information or an accompanying diagram, it isn't possible to definitively determine which of the side-angle relationships (ASA, AAA, SSS, SAS) the triangle fits. These acronyms represent different combinations of side and angle information known about a triangle. For example, ASA means that we know two Angles and the Side between them. SAS relates to knowledge of two Sides and the Angle between them, and so forth. More information or a visual representation would allow a more conclusive answer.
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L={d,e,g} J ={b,c,h} what is the union of L and J
Step-by-step explanation:
well, the combination of all set elements.
FYI : if some elements appear in both sets, we only use these once for the result set (this is not the case here, but it might be in other questions).
the combination of both sets is then
{b, c, d, e, g, h}
A Certain sum of money of simple
interest amount to $$1,300 ire 4 years
and to #11525 in 7 years - Find
the sum and the rate percent
The required rate of simple interest is 1.75%.
Here, we have,
(Principal + Interest) is a straightforward interest equation.
A = P(1 + rt)
Where: A is the sum of the accrued principal and interest.
Principal Amount is P.
I is the interest rate.
r is the annual percentage rate of interest, or R/100.
R is the annual percentage rate of interest; R = r * 100 t is the length of time involved in months or years.
Since I = Prt,
the initial formula A = P(1 + rt) evolved from A = P + I to A = P + Prt,
which may be represented as A = P(1 + rt).
Given: Principal is $1,300
Rate is 7% and the amount earned that is A-P is $159.25.
A = P(1 + rt)
Therefore substituting the values in the above mentioned equation, we get:
159.25= 1300(1+r×7)
On solving we get,
r= 1.75%
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complete question:
At the Blue Bank, Barry would earn $159.25 in simple interest in 7 years after depositing $1,300.
What rate of simple interest is offered at the
Blue Bank?
Pythagorean triples are given by these formulas:
(2²-37, 2zy, z²+37²)
The hypotenuse of a right triangle is 29. The lengths of the legs are whole numbers. List your answers in increasing
order.
The lengths of the two legs are
and
The lengths of the two legs of the right triangle are 58 and 839, in increasing order.
We have,
The formula given is incorrect.
The correct formula for Pythagorean triples with a given integer z is:
(z² - 1², 2z, z² + 1²)
Using this formula, we can find the two legs of the right triangle with hypotenuse 29 as follows:
z² + 1² = 29²
z² + 1 = 29²
z² = 29² - 1
z² = 840
z = √840
z = 28.98
Since z must be an integer, we can try integer values close to 28.98 to find one that works.
Trying z = 29,
a = z² - 1² = 840 - 1 = 839
b = 2z = 58
c = z² + 1² = 840 + 1 = 841
Therefore,
The lengths of the two legs of the right triangle are 58 and 839, in increasing order.
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Factorise fully 5a + 15ab
Answer:
Therefore, the fully factorised form is 5a(1 + 3b).
Step-by-step explanation:
5a + 15ab as 5a(1 + 3b) by taking out the common factor of 5a from both terms.
i need help with this lol
The trio of sides that will make a right triangle are the ones in the first option:
5, 12, and 13.
Which set would make a right triangle?Remember that for any right triangle, the sum of the squares of the two shorter sides must be equal to the square of the longest side.
So for example, for the first option we would have:
5^2 + 12^2 = 13^2
25 + 144 = 169
169 = 169
The equation is true, thus, these sides make a right triangle.
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Which term of the sequence 1/4;-1;-21/4;...is equal to -131/2
11, - 6, -1, 4, 9, 14, 19, ... are mapped onto 4. ... A;-l = (-ltQn (mod N),. (A5.34) ... 131 2, 14, 34, 38, 42, 78, 90, 178, 778, 974(1000).
Step-by-step explanation:
the nearest .1/2 incp, we say the 'unit 131/2 incl. 1.4 a measUrement is-stated tp- be 546 inch, this UM= the
Find the values of the 6 trigonometric functions of angle A.
The values of the trigonometric functions are
1. sin A = 12/13
2. cos A = 5/13
3. Tan A = 12/5
4. cot A = 5/12
5. cosec A = 13/12
6. sec A = 13/5
What are trigonometric functions?The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. Examples of these functions are; sin, cos , tan cot, cosec , sec e.t.c
Sin(tetha) = opp/hyp
cos(tetha) = adj/hyp
tan(tetha) = opp/adj
here the opposite side to angle A is 12 and the adjascent is 5 while the hypotenuse is 13.
Therefore,
1. sin A = 12/13
2. cos A = 5/13
3. Tan A = 12/5
4. cot A =1/tan A = 5/12
5. cosec A = 1/sin = 13/12
6. sec A = 1/cos = 13/5
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An entrepreneur invests in a new play. The cost includes an overhead of $33,750 plus production costs of $1700 per performance. A sold-out performance brings in $2325 . Assume every performance is sold out, and let x represent the number of sold-out performances.
The entrepreneur's revenue is $2325x, entrepreneur's cost is $33,750 + $1700x and entrepreneur's profit from x sold-out performances is $625x - $33,750
The entrepreneur's revenue from x sold-out performances is given by the formula:
Revenue = (Price per Performance) x (Number of Performances)
Revenue = $2325 x x
Revenue = $2325x
The entrepreneur's cost from x sold-out performances is given by the formula:
Cost = Overhead + (Production Cost per Performance) x (Number of Performances)
Cost = $33,750 + $1700x
The entrepreneur's profit from x sold-out performances is the revenue minus the cost:
Profit = Revenue - Cost
Profit = $2325x - ($33,750 + $1700x)
Profit = $625x - $33,750
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Which equation is the inverse of 5y+4= (x+3)²+12?
O y = x²+x+1100
y=3± √√5x+ 7/2
O-5-4--(x+3)²--1/
O
O y=-3± √5x+
7
The equation that is the inverse of 5y+4= (x+3)²+12 is y = -3 ± √(5x - 8)
Which equation is the inverse of 5y+4= (x+3)²+12?From the question, we have the following parameters that can be used in our computation:
5y+4= (x+3)²+12
Swap x and y in the equation
So, we have
5x + 4= (y + 3)² + 12
When we make the vairiable y the subject, we have
y = -3 ± √(5x - 8)
Hence, the equation that is the inverse of 5y+4= (x+3)²+12 is y = -3 ± √(5x - 8)
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=3sinθ/2cos2θ
Which of the following gives the Cartesian form of the equation above?
Select the correct answer below:
y=2/3x2
2y4(x2+y2)=3x2
2x4(x2+y2)=3y2
y=√3/2x
Answer: correct answer is A 2/3x^2
Step-by-step explanation:Multiply each side of the equation by 2cos2θ to get 2rcos2θ=3sinθ.
Multiply each side of the equation by r to get 2r2cos2θ=3rsinθ. Using the relationships x=rcosθ and y=rsinθ, the equation becomes 2x2=3y.
Divide each side of the equation by 3 and reverse the order of the equation to find that y=2/3x^2
Every winter, the math club sells cookie dough to raise money. Last year, they sold 1,080 pounds of cookie dough to 360 people. This year, they predict that they will sell cookie dough to between 460 and 500 people. About how many pounds of cookie dough will they need?
A.
2,880
B.
1,440
C.
720
D.
2,160
The number of pounds of cookie dough needed is 1,440. Therefore, option B is the correct answer.
Given that,
Last year, they sold 1,080 pounds of cookie dough to 360 people.
This means that they sold an average of 3 pounds of cookie dough per person.
Number of pounds of cookie dough = 3 pounds/person × Number of people
Here, 3×460=1,380
3×500=1500
To get a more accurate estimate, we can take the average of these two numbers, which is 1,440 pounds of cookie dough.
Therefore, option B is the correct answer.
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Find the area of the green region in the circle to the nearest tenth
The area of the green region of the circle is 96.4 ft².
What is area?Area is the region bounded by a plane shape.
To calculate the area of the green region of the circle, we use the formula below
Formula:
A = πr²∅/360Where:
A = Area of the green regionr = Radius of the circle∅ = Angle of the sector at the center of the circleFrom the diagram,
Given:
r = 17/2 = 8.5 feet∅ = (180-27°) = 153°π = 3.14Substitute these values into equation 1
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The area of the green region in the circle given is expressed as approximately: a. 96.5 square feet.
How to Find the Area of a Sector in a Circle?The sector of a circle is calculated as:
A = ∅/360 * πr², where r is the radius and ∅ is the reference or central angle of the sector.
Given the following:
Central or reference angle (∅) = 180 - 27 = 153 degrees
Radius (r) = 17/2 = 8.5 feet
Plug in the values:
Area of the green region = 153/360 * π * 8.5²
Area of the green region ≈ 96.5 square feet.
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If you can buy one bunch of seedless green grapes for $2, then how many can you buy with $18?
If you can buy 1 bunch of seedless green grapes for $2, then $18 we can buy 9 bunches.
The concept used here is a simple division to find out how many bunches of seedless green grapes can be purchased with a given amount of money.
In this case, we know the cost of one bunch of seedless green-grapes ($2) and we are given a total amount of money ($18) that we can spend on grapes. We can use division to find out how many bunches we can buy with that amount.
⇒ Number of bunches = ($18)/($2) per bunch,
⇒ Number of bunches = 9 bunches;
Therefore, with $18, you can buy 9 bunches of seedless green grapes.
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Identify the pairs of supplementary angles.
Choose all that apply.
A. RQS and SQR
B. SQT and SQR
C. TQP and RQP
D. SQR and RQP
E. PQR and RQP
F. SQT and TQP
G. TQP and PQT
H. SQR and TQP
The pairs of supplementary angles are;
B. <SQT and <SQR
C. <TQP and <RQP
D. <SQR and <RQP
F. <SQT and <TQP
What are supplementary angles?Two or more angles are referred to as supplementary angles if they add up to 180^o. Therefore the sum of angles is equal to the sum of angles on a straight line.
Thus, the pair of supplementary angles in the given diagram are;
B. <SQT and <SQR
C. <TQP and <RQP
D. <SQR and <RQP
F. <SQT and <TQP
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Find the area of a parallelogram.
Answer:
60
Step-by-step explanation:
The area of a parallelogram is base x hight.
A = bh
10(b) x 6(h) = 60
[tex]x-\sqrt{x} +4-2\sqrt{x+3} =0\\[/tex]
The solution of the equation x - √x + 4 - 2√(x+3) =0 is given by x ≈ 0.449 or x = 2.
The expression is equal to,
x - √x + 4 - 2√(x+3) =0
By rearranging the terms and simplifying the expression as follows,
x - √x + 4 - 2√(x+3) = 0
⇒x + 4 = √x + 2√(x+3)
Square both sides to eliminate the square root,
⇒ (x + 4)² = (√x + 2√(x+3))²
⇒ x² + 8x + 16 = x + 4(x+3) + 4√x√x+3
⇒x² + 8x + 16 -x -4x -12 = 4√x√x+3
⇒ x² + 3x + 4 = 4√x√x+3
⇒x² + 3x + 4 = 4√x√(x+3)
⇒ x² + 3x + 4 = 4√(x²+3x)
Squaring both sides again gives,
⇒ (x² + 3x + 4)² = 16(x²+3x)
Expanding the left side gives,
x⁴ + 6x³ + 17x² + 24x + 16 = 16x² + 48x
Simplifying and rearranging the terms,
x⁴ + 6x³ + x² - 24x + 16 = 0
Factor this equation as follows,
(x² + 4x - 2)(x² + 2x - 8) = 0
The solutions are,
x²+ 4x - 2 = 0 or x² + 2x - 8 = 0
Solve each quadratic equation using the quadratic formula,
For x² + 4x - 2 = 0
x = (-4 ± √(4² - 4(1)(-2))) / (2(1))
⇒ x = (-4 ± √24) / 2
Simplifying the expression under the square root gives,
⇒ x = (-4 ± 2√6) / 2
⇒ x = -2 ± √6
For x² + 2x - 8 = 0
x = (-2 ± √(2² - 4(1)(-8))) / (2(1))
⇒x = (-2 ± √36) / 2
Simplifying the expression under the square root gives,
⇒ x = (-2 ± 6) / 2
⇒ x = -4 or x = 2
Discard the negative solution -2-√6 and -4
As it would lead to a negative value under the square root.
The final solutions are,
x ≈ 0.449 or x = 2
Therefore, the solution of the given equation is equal to x ≈ 0.449 or x = 2.
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The above question is incomplete , the complete question is:
Solve for x.
x - √x + 4 - 2√(x+3) =0
Select all the correct answers. What are the solutions to this equation? 2 x 2 = - 10 x + 12 x = - 6 x = - 2 x = 1 x = - 3 x = 6
Answer:
The correct solutions to the equation 2x^2 = -10x + 12 are x = -2 and x = 3.
Step-by-step explanation:
What are the polar coordinates of the point P shown below?
Select the correct answer below:
(5,5π4)
(4,−5π4)
(5,7π4)
(4,5π4)
(4,7π4)
(5,−5π4)
Answer:(4,5π/4)
Step-by-step explanation:
Note that the point is on the circle whose radius is labeled 4, so r=4. The angle of the point is 5π4, so θ=5π4. Thus, the polar coordinates are (4,5π4).
A biker traveled 2/5 of the road on the first day, then traveled 5 kilometers less on the next day, which is equal to 3/8 of the road. How much more does he need to travel? (distance)
The biker needs to travel 45 km more to complete his journey.
Given that, a biker traveled 2/5 of the road on the first day, then traveled 5 kilometers less on the next day, which is equal to 3/8 of the road, we need to find how much he need to cover more,
Let the total distance of the road be x,
So,
2x/5 - 5 = 3x/8
2x/5 - 3x/8 = 5
Solving for x,
Multiply by 40 to both sides,
16x-15x = 200
x = 200
Therefore, the total distance of the road is 200 km.
Since, he travelled =
200 (2/5) = 80 km + 200 (3/8) = 75 km = 155 km
Therefore, he needs to travel 200-155 = 45 km more.
Hence, the biker needs to travel 45 km more to complete his journey.
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help please i need the answer to thus question
The measure of angle 1 is 107° suing the concepts of corresponding angles and linear pair of angles..
Given a line t which is a transversal line that cuts the two parallel lines m and n.
Here the angle which is linear pair to angle 1 and the angle 73° are corresponding angles.
By the corresponding angle theorem, the corresponding angles formed by two parallel lines cut by a transversal are equal.
So,
Measure of angle which is linear pair to 1 = 73°
Now linear pair of angles are supplementary.
∠1 + 73° = 180°
∠1 = 180° - 73°
∠1 = 107°
Hence the measure of angle 1 is 107°.
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Use the image to determine the direction and angle of rotation. Graph of triangle ABC in quadrant 1 with point A at 1 comma 3. A second polygon A prime B prime C prime in quadrant 4 with point A prime at 3 comma negative 1. 90° clockwise rotation 180° clockwise rotation 180° counterclockwise rotation 90° counterclockwise rotation
i need help with math
The relationship between the distance that birds fly in relation to the time they do so, is positive.
There are about 3 outliers but for the most part, the relationship is positive.
How to describe the relationship ?The graph which shows the distance that birds fly in relation to the time they do, shows that there is a positive relationship because as the time increases, the distance that the birds have flown also increases.
There are some outliers such as the bird that flew 1 mile in 7 hours but in general, as the time increases, the distance increases as well. There are two clusters of distance as well.
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Given the definitions of f(x) and g(x) below,
find the value of (gof)(-7).
f(x)
13
g(x) = 2x² - 6x – 10
=
- 2x
The composition of functions is solved and gof ( -7 ) = 1,286
Given data ,
Let the first function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = 13 - 2x
Let the second function be represented as g ( x )
Now , the value of g ( x ) is
g ( x ) = 2x² - 6x - 10
Now , g o f ( x ) = 2 ( 13 - 2x )² - 6 ( 13 - 2x ) - 10
On simplifying , we get
g o f ( x ) = 2 ( 169 + 4x² - 52x ) - 78 + 12x - 10
g o f ( x ) = 250 + 8x² - 92x
Now , the composition of function is
g o f ( -7 ) = 8 ( -7 )² - 92 ( -7 ) + 250
g o f ( -7 ) = 392 + 894
g o f ( -7 ) = 1,286
Hence , the function is g o f ( -7 ) = 1,286
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10. The box plot shows donations in dollars to charity.
Describe the shape of the distribution.
Donations to Charity ($)
20 40 60 80 100 120 140 160 180 200 220
The given shape of the distribution is not symmetric.
Given that, a box plot shows donations in dollars to charity.
We need to describe the shape of the distribution.
Donations to Charity ($) =
20 40 60 80 100 120 140 160 180 200 220
so, as we can see,
The shape of the distribution is not symmetric since the lengths of each box and whisker are not the same. There is an outlier at 220.
Hence, the given shape of the distribution is not symmetric.
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which of the following equations demonstrates the Associative Property of Multiplication?
18(27 • 3) = 18(3 • 27)
8(9 + 2) = 64 + 16
12(17 • 23) = (12 • 17) • 23
18(27 • 3) = 18(81)
Answer:
12 • (17 • 23) = (12 • 17) • 23
Triangle 1 undergoes four different transformations.
The results of these transformations are shown.
1
4
2
5
3
Which statement best describes one of these
transformations?
Triangle 1 is rotated to result in triangle 2.
O Triangle 1 is dilated to result in triangle 3.
O Triangle 1 is reflected to result in triangle 4.
Triangle 1 is stretched to result in triangle 5.
time tables on the map mannnnn