Answer:
13 and three-fourths inches
Step-by-step explanation:
The map distance can be found using a proportion with the map scale.
__
map distance / (1100 mi) = (1 in) / (80 mi)
map distance = (1100×1)/80 in = 13 3/4 in . . . multiply by 1100 mi; cancel mi
The trip will be about 13 3/4 inches on the map.
A box is in the shape of an equilateral triangular prism. if the box is to be covered with paper on its lateral sides, how many square inches of paper are needed?
The total surface area of the triangular prism that has a height of h and the side length of a is given below.
[tex]\rm a(\dfrac{\sqrt3}{2} \ a + 3h)[/tex]
What is a triangular prism?A triangular prism is a closed solid that has two parallel triangular bases connected by a rectangle surface.
A box is in the shape of an equilateral triangular prism.
If the box is to be covered with paper on its lateral sides.
Let a be the side length of the equilateral triangle and h be the height of the prism.
Then the surface area of the triangular prism will be
Surface area = 2 × area of triangle + 3 × area of the rectangle
The area of the triangle will be
[tex]\rm Area\ of\ triangle = \dfrac{\sqrt{3}a^2}{4}[/tex]
The area of the rectangle will be
[tex]\rm Area \ of \ rectangle = a \ h[/tex]
Then the total surface area will be
[tex]\rm Surface\ area = 2 \times \dfrac{\sqrt3 a^2 }{4} + 3 ah\\\\\\Surface\ area = a(\dfrac{\sqrt3}{2} \ a + 3h)[/tex]
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Answer:
72 square inches
Step-by-step explanation:
A teacher used the change of base formula to determine whether the equation below is correct. (log Subscript 2 Baseline 10) (log Subscript 4 Baseline 8) (log Subscript 10 Baseline 4) = 3 Which statement explains whether the equation is correct? The equation is correct since (log Subscript 2 Baseline 10) (log Subscript 4 Baseline 8) (log Subscript 10 Baseline 4) = log (2 times 10) times log (4 times 8) times log (10 times 4). = log (20) times log (32) times log (40). =3 The equation is correct since (log Subscript 2 Baseline 10) (log Subscript 4 Baseline 8) (log Subscript 10 Baseline 4) = StartFraction log 10 Over log 2 EndFraction times StartFraction log 8 Over log 4 EndFraction times StartFraction log 4 Over log 10 EndFraction. = StartFraction log 8 Over log 2 EndFraction. = 3 The equation is correct since (log Subscript 2 Baseline 10) (log Subscript 4 Baseline 8) (log Subscript 10 Baseline 4) = StartFraction log 10 Over log 2 EndFraction times StartFraction log 8 Over log 4 EndFraction times StartFraction log 4 Over log 10 EndFraction. = StartFraction log 8 Over log 2 EndFraction. = 4. The equation is not correct since (log Subscript 2 Baseline 10) (log Subscript 4 Baseline 8) (log Subscript 10 Baseline 4) = log StartFraction 10 Over 2 EndFraction times log eight-fourths times log four-tenths. = log 5 times log 2 times log 0. 4. = negative 0. 8.
The solution to the problem is correct and the correct option from the given options is B.
What is Logarithm?A log function is a way to find how much a number must be raised in order to get the desired number.
[tex]a^c =b[/tex]
can be written as
[tex]\rm{log_ab=c[/tex]
where a is the base to which the power is to be raised,
b is the desired number that we want when power is to be raised,
c is the power that must be raised to a to get b.
For example, let's assume we need to raise the power for 10 to make it 1000 in this case log will help us to know that the power must be raised by 3.
The given logarithmic problem can be solved in the following manner, therefore,
[tex]\rm log_210\ log_48\ log_{10}4\\\\[/tex]
Using the logarithmic properties, we can write,
[tex]=\rm \dfrac{log10}{log2}\cdot \dfrac{log8}{log4}\cdot \dfrac{log4}{log10}\\\\[/tex]
Now cancelling out the values we will get,
[tex]=\rm \dfrac{log2^3}{log2}\\\\=\rm \dfrac{3log2}{log2}\\\\= 3[/tex]
Thus, the solution to the problem is correct and the correct option from the given options is B.
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Answer:
B
Step-by-step explanation:
on edge
Does anyone know the answer?
Answer:
I think the answer must be c because the length is 6\5 feet so there no chances to be the answer is more than so the base is divited and the ft should be multiplied
EASY GIVING BRAINLIEST JUST GRAPH TO FIND ANSWER While warming up for a game, two basketball players shoot balls in parabolic paths. The path of the first player's ball can be represented by the function g(x) = –2x2 + 13x + 7, where x represents the distance from the coach. The path of the second player's ball can be represented by the function h(x) = –x2 + 4x + 21.
Part A: Find the distances in which the two basketball paths will cross. Show all necessary calculations.
Answer:
2 ft, 7 ft
Step-by-step explanation:
We are interested in the values of x such that g(x) = h(x). These will be solutions of the difference g(x) -h(x) = 0. Hence the x-intercepts of a graph of g(x) -h(x) will be solutions to the problem.
__
The graph shows the difference between the paths will be zero at distances of 2 feet and 7 feet.
a company’s profit of 18000 is shared by 2 directors and 24 employees 1-3 of the profit is shared equally by 2 directors of the company
Using proportions, it is found that:
Each director gets 6000.Each employee gets 500.What is a proportion?A proportion is a fraction of a total amount.
In this problem, the directors share one-third of the profit, hence:
18000/3 = 6000
6000/2 = 3000.
That is, each director gets 6000.
The remaining 18000 - 6000 = 12000 will be shared equally by the 24 employees, hence:
12000/24 = 500
Each employee gets 500.
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What are the zeros of this function?
A. x=0 and x=6
B. x=0 and x= -9
C. x=0 and x= -6
D. x=3 and x= -9
Answer:
A
Step-by-step explanation:
The zeros are the roots or x-intercepts
They are located at coordinate points (0, 0) and (6, 0)
This means the answer is A
Hope it makes sense!
Answer:
A. x = 0 and x = 6
Step-by-step explanation:
So, the zeroes of a quadratic are the parts of it that touch the x-axis. When you find those parts, take their x value and you will get the zero.
So, in this parabola, it touches the x-axis at (0, 0) and (6, 0).
The x-values of these are 0 and 6, respectively.
i need helppppppppppppppppppppppppppppppppppppppp
how many solutions does 8B + 7v - 5 equals -11 + 15b
Answer: No solutions
- by graphing-
First I will simplify:
8B + 7v - 5 equals -11 + 15b
8b + 7v - 5 = -11 + 15b
7v = -6 + 15b
7v = -6 + 7b
Let's graph this and see what happens!
-> I will graph y = 7x and y = 7x - 6
-> See attached.
-> Since there are no points of intersection (they have the same slope), there is no solutions.
Answer the questions about the following polynomial. 1- x³/8
the expression represents a quadratic polynomial with 2 terms.The constant term is 1, the leading tern is x and the leading coefficient is 1
In a class of 25 pupils, if 15 are females. Calculate the ratio of males : total
Answer:
2:5
Step-by-step explanation:
15 are female. 10 must be male.
Out of 25 pupils, 10 are male, so it's 10:25, or 2:5
a sphere and a cylinder have the same volume. each figure has a radius of 13. what is the height of the cylinder?
Answer:
V = 4/3 π R^3 volume of a sphere
V = π R^2 H volume of cylinder area of base X height
4/3 π R^3 = π R^2 H equal volumes
H = 4/3 R relationship of height to radius for cylinder
H = 4/3 * 13 = 52 / 3 cm = 17 1/3 cm
A frequency generator sends a 550 Hz sound wave through both water and ice. A 3 column by 4 row table. Column 1 is titled Medium and includes the following entries: Ice, Water, Steam. Column 2 is titled Temperature (degrees Celsius) and includes the following entries: 0, 25, 100. Column 3 is titled Speed of Sound (meters per second) and includes the following entries: 3200 meters per second, 1500 meters per second, 346 meters per second. What is the difference in wavelength between the wave produced in ice and the wave produced in water? 2. 1 m 3. 1 m 5. 2 m 8. 5 m.
The difference in wavelength between the wave produced in ice and the wave produced in water is 3.1 m. Then the correct option is B.
What is wavelength?The distance between two successive troughs or crests is known as the wavelength. The peak of the wave is the highest point, while the trough is the lowest.
The wavelength is also defined as the distance between two locations in a wave that have the same oscillation phase.
A frequency generator sends a 550 Hz sound wave through both water and ice.
The wavelength is given as
[tex]\lambda = \dfrac{v}{f}[/tex]
f = frequency
v = velocity
Then the wavelength in the water will be
[tex]\rm \lambda _w = \dfrac{1500}{550}\\\\\lambda _w = 2.73[/tex]
The wavelength in the ice will be
[tex]\rm \lambda _I = \dfrac{3200}{550}\\\\\lambda _I = 5.82[/tex]
Then the difference in wavelength between the wave produced in ice and the wave produced in water will be
[tex]\rightarrow \lambda _I - \lambda_w \\\\\rightarrow 5.82 - 2.73 \\\\\rightarrow 3.09 \approx 3.1[/tex]
Thus, the difference in wavelength between the wave produced in ice and the wave produced in water is 3.1 m.
More about the wavelength link is given below.
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Answer:
3.1
Step-by-step explanation:
B
Solve the following equations and check your solution using substitution.
6 - 5x = 16
4 - 9x = -7
(BTW pls show your working out)
Answer: 1. [tex]x=-2[/tex]; 2. [tex]x=\frac{11}{9}[/tex]
Step-by-step explanation :
1.
[tex]6-5x=16\\6-5x-6=16-6\\-5x=10\\\frac{-5x}{-5}=\frac{10}{-5}\\x=-2[/tex]
2.
[tex]4-9x=-7\\4-9x-4=-7-4\\-9x=-11\\\frac{-9x}{-9}=\frac{-11}{-9}\\x=\frac{11}{9}[/tex]
Answer:
Q1) x =2 Q2) x = 11/9
Step-by-step explanation:
Q1) 6 - 5x = 16 check : -5(2) = -10
-6 -6 6 -- 10 = 6+ 10 = 16
-5x = 10 Q2) 4 - 9x = -7
-x = -2 -4 -4
x = 2 -9x = - 11
-------------- -x = -11 /9 -----> x = 11/9
6. The circle in the center of basketball court is being painted. The circle has a radius of 9 feet. What is the circumference of the circle? Leave your solution in terms of pi.
Answer:
18pi
Step-by-step explanation:
Circumference = 2 Pi R
c = 2 x 9 x Pi
c = 18Pi
The terminal side of an angle measuring StartFraction pi Over 6 EndFraction radians intersects the unit circle at what point?.
Thee intersection point of the terminal side which measure the angle pi/6 radians is (0.886, 0.5).
What is the meaning of a circle?A circle is a special type of ellipse in which the eccentricity is zero and the two foci are coincident.
The distance from the center to the circumference is called the radius of the circle.
Given that the terminal side of an angle measuring π/6 radians.
The coordinate point on the circle has to be find out It is known that, the formula for the coordinate is given by
x = r cos∅ and y = r sin∅
Let the r be unity.
Then, x will be
[tex]x=\frac{\pi }{6} \\x=cos(\frac{\pi }{6}) \\\x=0.866[/tex]
The variable y will be
[tex]y=sin\frac{\pi }{6}[/tex]
y=0.5
Thus, the intersection point is (0.886, 0.5).
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At a concession stand 6 hot dogs cost $6.72. At this rate, how much would 8 hot dogs cost, in dollars and cents?
Answer:
$8.96
Step-by-step explanation:
Since 6 hot dogs are $6.72, 1 hot dog would be that divided by 6, which is $1.12. Now we want the cost of 8 of those hot dogs, so we have to multiply by 8. Hence the answer is $1.12 * 8 = $8.96.
Marcy charges $3 to walk a small dog and $5 to walk a big dog. If Marcy walks 15 small dogs and 6 big dogs, how much money will she make?
Answer:
hee-hee!
Step-by-step explanation:
Marcy charges $3 to walk a small dog and $5 for a big dog.
She walks 15 small dogs and 6 big dogs.
We can use an expression that would show the problem:
3s + 5b
(s = small dogs & b = big dogs)
s = 15 | b = 6
3(15) + 5(6)
45 + 30 = 75
Marcy earns $75 of profit.
Find the surface area of the solid figure
Answer:
150
Step-by-step explanation:
area of your base (bh/2) 3x8/2 = 12
2 bases = 24
3 faces ---- Face1 - 7x5= 35 ------Face2 - 7x5 = 35 ------Face3 - 8x7 = 56
24 + 35 + 35 + 56 = 150
i need help with this
Answer:
A tangent to a circle is a straight line which touches the circle at only one point. Therefore, if [tex]x=2y+5[/tex] is a tangent of [tex]x^2+y^2=5[/tex] then there will be one point of intersection.
To find the point of intersection, substitute [tex]x=2y+5[/tex] into [tex]x^2+y^2=5[/tex] and solve for y:
[tex]\implies (2y+5)^2+y^2=5[/tex]
[tex]\implies 4y^2+20y+25+y^2=5[/tex]
[tex]\implies 5y^2+20y+20=0[/tex]
[tex]\implies y^2+4y+4=0[/tex]
[tex]\implies (y+2)^2=0[/tex]
[tex]\implies y+2=0[/tex]
[tex]\implies y=-2[/tex]
Substitute found value of y into [tex]x=2y+5[/tex] and solve for x:
[tex]\implies x=2(-2)+5=1[/tex]
Therefore, there is one point of intersection at (1, -2), thus proving that the straight line equation is a tangent to the circle.
Help with any questions
1.) right triangle, as it has a right angle
2.) scalene triangle no equal sides
hope this helps
help please
on the image.
Answer:
the women won 1 fewer matches than the men
Step-by-step explanation:
In a pie chart, the fraction of the total that is represented by any sector is the ratio of the angle subtended by that sector to 360°.
__
For the men's team, the winning games represent 150°/360° = 5/12 of all games played. The men played 24 games, so they won ...
5/12 × 24 = 10 . . . . games won
__
For the women's team, the winning games represent 180°/360° = 1/2 of all games played. The women played 18 games, so they won ...
1/2 × 18 = 9 . . . . games won
The number of matches won by the men is larger than the number of matches won by the women. (Yes, the women won a larger fraction of their matches played, but not a larger number.)
On Thursday the cows at the Putnam Dairy produced 70 bottles of milk. Friday, the cows produced 5/8 as much milk as on Thursday. How many bottles of milk did the cows produce on Friday?
Find the next three terms of the sequence 2000 ,200, 20 … and write the term to term rule.
Answer:
2 is the next number in the sequence
Step-by-step explanation:
in this pattern, you go down by one decimal spot ( zero)
this is a geometric sequence since there is a common ratio between each term.
Approximately how many grams of radium will remain after 4 grams have decayed for 2400 years
Answer:
1.4
Step-by-step explanation:
Evaluate each expression using the order of operations
A:-4(-4+3)+2²
B:-3-3-3(-3)
C:-17+2(-2)(-2)
D:-(+2(-3)(5)(3+2)(-6)
Answer:
[A} 8
[B] 3
[C] -9
[D] - 900
Step-by-step explanation:
A:-4(-4+3)+2²
[tex]\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}[/tex]
[tex]-4\left(-1\right)+2^2[/tex]
[tex]-4\left(-1\right)+4[/tex]
[tex]4+4[/tex]
8
-------------------------------------------------------------------------------------------------------------
B:-3-3-3(-3)
[tex]Follow\:the\:PEMDAS\:order\:of\:operations[/tex]
[tex]-3-3-\left(-9\right)[/tex]
3
-------------------------------------------------------------------------------------------------------------
C:-17+2(-2)(-2)
[tex]\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}[/tex]
[tex]-17-\left(-8\right)[/tex]
-9
-------------------------------------------------------------------------------------------------------------
D:-(+2(-3)(5)(3+2)(-6)
[tex]Follow\:the\:PEMDAS\:order\:of\:operations[/tex]
-900
-------------------------------------------------------------------------------------------------------------
[RevyBreeze]
A car used 1/81 of a gallon of gas to drive 1/4 of a mile. At this rate, how many miles can the car travel using 1 gallon of gas? ??????????
Step-by-step explanation:
1/81 gallon for 1/4 mile.
what do I need to multiply 1/81 with to get 1 gallon ?
it is simple, right ? i need to multiply it by 81 to get 1 gallon.
in order to keep the relationship (ratio) unchanged, I need to multiply the other part (1/4 mile) with the same factor :
1/4 × 81 = 81/4 = 80/4 + 1/4 = 20 1/4 miles
so, at this rate, that car can travel 20 1/4 miles using 1 gallon of gas.
PLS HELP
A cone has a volume of 803.84 cubic millimeters and a radius of 8 millimeters. What is its height?
Use ≈ 3.14 and round your answer to the nearest hundredth.
h ≈
millimeters
Answer:
3.19 millimeter round of nearest hundred
1) Find the slope of the line
2) find the slope between the two points
help please, thank you
Answer:
1 = 3/2
2 = -1/14
Step-by-step explanation:
The equation for the slope of a line is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex] (difference in Y divided by the difference in X) or simply just Rise/Run.
For the first one, we have to pinpoint two points on the graph. There's one point placed on the x-axis 2 units away from the origin (2,0) and one four units to the right and 3 units up from the origin (4,3). Since it's on a graph, the easiest way to calculate it is by counting the units up and then right from (2,0) to (4,3). You can count that (4,3) is 3 units up and 2 units right from (2,0). Since slope is Rise/Run, the slope is 3/2.
For the second one, you can use the equation [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. The Y of the second point is 2, and the Y of the first point is 1. The X of the second point is -17, and the X of the first point is -3.
You can plug all 4 numbers in to get (2-1)/(-17- -3)
2-1 = 1 and -17 - -3 = -14. So your slope is 1/-14 or -1/14.
Amira decides to estimate the volume of an apple by modeling it as a sphere. She measures its circumference as 43.4 cm. Find the apples's volume in cubic centimeters. Round your answer to the nearest tenth if necessary.
The formula for the circumference of a circle (or a sphere) is [tex]2\pi r\\[/tex].
The formula the volume of a sphere is [tex]\frac{4}{3}\pi r^3[/tex].
Assuming 43.4 includes the pi, we can do the equation [tex]43.4=2\pi r[/tex]
Solving the equation, we get [tex]\frac{43.4}{2\pi } =r[/tex]
Substituting r into the formua for the volume of a sphere, we get [tex]\frac{4}{3} *\pi *(\frac{43.4}{2\pi } )^3[/tex]
Solving the cube (probably with a calculator), we get [tex]\frac{4}{3} *\pi *\frac{81746.504}{8\pi ^3}[/tex]
It is a bit messy, but we can simplify further by cancelling out the pi's, which leaves us with [tex]\frac{4}{3} *\frac{81746.504}{8\pi ^2}[/tex].
With the butterfly method (or whatever you may call it), we can cancel out the 4 in the numerator and the 8 in the denominator, and multiply the 3 in the denominators.
Which gets us this: [tex]\frac{81746.504}{6\pi ^2}[/tex]
Using a calculator, we get our final answer of (about) 1380.44cm^3
This was very messy, I apologize if I did make any mistakes.
The demand function Q and cost function C(Q) of a commodity are given by the equations \[ Q = 20 - 0{,}01P\]
C(Q)=60+6Q,
where P and Q are the price and quantity, respectively. The total revenue function (TR) in terms of P is
The total revenue of the function is the product of the quantity and the price
The total revenue in terms of P is TR = 20P - 0.01P^2
How to determine the total revenue?The demand and the cost functions are given as:
Quantity function, Q = 20 - 0.01P
Cost function, C(Q)=60+6Q
The total revenue is calculated as:
TR = Q * P
Substitute Q = 20 - 0.01P in the above equation
TR = P * [20 - 0.01P]
Evaluate the product
TR = 20P - 0.01P^2
Hence, the total revenue in terms of P is TR = 20P - 0.01P^2
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