the two way table represents data from a survey asking schoolchildren whether
Answers
42/96= 44%
Related Questions
Find the length of the diagonal of this rectangle.
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AC = 10 / cos 32
= 11.79 m ( to nearest hundredth)
Answer:
The length of the diagonal of the given Rectangle is, 11.80 m (Approx.)
Step-by-step explanation:
In Rectangle:
* It is a four sided shape where every angle is a right angle.
* The alternative sides are equal.
*Two axes of symmetry bisect each other.
* Diagonals are equal in length.
The figure of rectangle has given the length [tex]l[/tex] = 10m
In right angle triangle ADC.
DC = 10 m ( as alternative sides are equal )
Note that we are given here the adjacent and we have to find the length of hypotenuse, then we use trigonometric ratio that contains both sides adjacent and hypotenuse.
Use: [tex]Cosine = \frac{Adjacent}{hypotenuse}[/tex]
then,
[tex]\cos 32^{\circ} = \frac{10}{AC}[/tex] or
[tex]Ac = \frac{10}{\cos 32^{\circ}} =\frac{10}{0.8480481}[/tex]
On simplify we get;
AC = 11.791784 m
therefore, the length of the diagonal of this rectangle (AC) is, 11.80 m (Approx)
“all integers are rational numbers” true or false? why?
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Every rational number can be written as a fraction a/b , where a and b are integers. ... If a number is a whole number, for instance, it must also be an integer and a rational.
Every rational number can be written as a fraction a/b , where a and b are integers. ... If a number is a whole number, for instance, it must also be an integer and a rational
Kim's softball team is playing in the championship game. They are losing by a score of 171717 to 666. There are 444 innings to go. Kim wants to know how many runs her team needs per inning to win the game if the other team does not score. (Each run is worth 111 point.) Let rrr represent the number of runs per inning. Assume that the team scores the same number of runs per inning, and write an inequality to determine the number of runs per inning needed to win the game.
Answers
171717-666 = 171051 runs are needed.
171051 / 444 = 385.25 points per inning are needed
385.25 / 111 = 3.47 runs are needed per inning, round up to 4
How to solve for a side of a right triangle when you only know one side?
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Hope I helped :)
Angle a has the property that twenty eight times times its complement is equal to thirteen times its supplement. find the measure of angle
a.
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28(90 - a) = 13(180 - a)
2520 - 28a = 2340 - 13a
-28a + 13a = 2340 - 2520
- 15a = - 180
a = -180/-15
a = 12 <=== so < a = 12
I need help with #17
Answers
so for 480 miles we need 480 / 20 = 24 gallons
1. Create a circle. Show and explain the difference between the following:
a. secant line and tangent line
b. inscribed angle and central angle
2. Describe the steps necessary to construct an inscribed circle in a triangle and contrast this with the steps you take to construct a circumscribed circle.
3. Demonstrate on the whiteboard how to find the center and radius of a circle using an equation. Be sure to provide a unique example of your own that shows how to find both of these.
4. A classmate is having difficulty finding the measures of
5. The world’s largest round pizza, which also happened to be gluten-free, was set in December 2012 by five Italian chefs. The diameter of this pizza was 131 feet. If this pizza was cut into 50 slices, what would be the area of each slice and the length of the crust for the slice? Explain what concepts of a circle these calculations related to.
Answers
a.
A secant line is a line which intersects the circle at 2 different points.
A tangent line is a line which has only one point in common with the circle.
Check picture 1: The orange line s is a secant line, the blue line t is a tangent line.
b.
An inscribed angle is an angle formed by using 3 points of a circle.
The main property of an inscribed angle is that its measure is half of the measure of the arc it intercepts.
Check picture 2: If [tex]m(\angle KML)=\beta[/tex], then the measure of arc KL is [tex]2 \beta [/tex].
A central angle is an angle whose vertex is the center of the circle, and the 2 endpoints of the rays are points of the circle.
The main property is: the measure of the central angle is equal to the measure of the arc it intercepts.
Check picture 2
2.
To construct the inscribed circle of a triangle, we first draw the 3 interior angle bisectors of the triangle.
They meet at a common point called the incenter, which is the center of the inscribed circle.
We open the compass, from the incenter, so that it touches one of the sides at only one point. We then draw the circle. (picture 3)
To draw the circumscribed circle, we first find the midpoints of each side. We then draw perpendicular segments through these (the midpoints.) They meet at one common point, which is the circumcenter: the center of the circumscribed circle.
We open the compass from the circumcenter to one of the vertices of the triangle. We draw the circle, and see that it circumscribes the triangle.
(picture 4)
3.
Given an equation of a circle: [tex]x^2-2x+y^2+6y+6=0[/tex].
To determine the center and the radius of the equation we must write the above equation in the form :
[tex](x-a)^2+(y-b)^2=r^2[/tex].
Then, (a, b) is the center, and r is the radius of this circle. We do this process by completing the square.
Note that [tex]x^2-2x[/tex] becomes a perfect square by adding 1, and
[tex]y^2+6y[/tex] becomes a perfect square by adding 9.
Thus we have:
[tex]x^2-2x+y^2+6y+6=0\\\\(x^2-2x+1)+(y^2+6y+9)-4=0\\\\(x-1)^2+(y+3)^2=2^2[/tex]
Thus, the center is (1, -3), and the radius is 2.
4. Not complete
5.
The radius of the pizza is [tex]\displaystyle{ \frac{131}{2}ft=65.5ft [/tex].
The surface of a circle with radius r is given by the formula [tex]\displaystyle{ A=\pi r^2[/tex],
and the circumference is given by the formula C=2πr.
Thus, the area of the whole pizza is given by [tex]\displaystyle{ A=\pi r^2= \pi\cdot65.5^2=4290.25 \pi [/tex] (square ft).
Each of the 50 slices, has an area of [tex]\displaystyle{ \frac{4290.25 \pi}{50} =85.805 \pi [/tex] (square ft)
Notice that the perimeter (the crust) of a slice is made of 2 radii, and the arc-like part.
The arc is 1/50 of the circumference, so it is [tex] \displaystyle{\frac{2 \pi r}{50} = \frac{2\cdot65.5\cdot \pi }{50}= 2.62 \pi [/tex].
So the perimeter of one slice is 65.5+65.5+2.62π=131+2.62π
Final answer:
The differences between secant and tangent lines, and between inscribed and central angles, involve the number of intersection points with the circle and the position of the vertex, respectively. Constructing an inscribed circle involves finding the incenter, while a circumscribed circle requires finding the circumcenter. To find the center and radius of a circle using its equation, we use the standard form (x - h)² + (y - k)² = r².
Explanation:
Differences Between Secant Lines, Tangent Lines, Inscribed Angles, and Central Angles
A secant line is a line that intersects a circle at two points, while a tangent line touches the circle at exactly one point. An inscribed angle is an angle formed by two chords in a circle that meet at one point in the circle, whereas a central angle is an angle whose apex (vertex) is the center of the circle.
Constructing Inscribed and Circumscribed Circles in a Triangle
To construct an inscribed circle (incircle) of a triangle, draw the angle bisectors of the triangle's angles to find the incenter, and then use this point to draw the circle that touches all three sides of the triangle. For a circumscribed circle (circumcircle), draw the perpendicular bisectors of the triangle's sides and the point where they intersect will be the circumcenter; use this as the center to draw the circle that passes through all three vertices of the triangle.
Finding the Center and Radius of a Circle Using an Equation
Given a circle's equation in the standard form (x - h)² + (y - k)² = r², the center is at point (h, k), and the radius is the square root of r². For example, if we have the equation (x - 3)² + (y + 2)² = 16, the center is (3, -2) and the radius is 4 units.
Area and Length of the Crust of a Circular Pizza Slice
For the world's largest round pizza with a diameter of 131 feet, the radius would be 65.5 feet. The area of each slice is a fraction of the whole pizza's area, which can be found using the formula A = πR², and the length of the crust for the slice corresponds to the arc length of that slice.
Area of whole pizza = 3.14 * 65.5² ≈ 13478.2 ft²
Area of each slice = total area /50 = 13478.2/50 ≈ 269.5 ft²
Length of crust = 2πR * (slice area/total area)
= 2 * 3.14 * (1/50)
≈ 0.125 ft
if i have 64,32,16,8 what two numbers comes next
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(Because the pattern is that it is dividing the previous number by 2)
Sample text because sample text is sample text, which is sample text according to sample text.
i hope this helps and have a wonderful day!!
The functions graphed show the snowfall, in inches, in two cities after x hours.
Select each correct answer.
Middletown had a faster rate of snowfall.
Smithville had a faster rate of snowfall.
Snow fell in Smithville at a rate of 4 inches per hour.
Middletown already had snow on the ground at the beginning of the storm.
Answers
we know that
the formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
in this problem
the rate of snowfall is equal to the slope of the linear equation
so
Let
x-------> the time in hours
y---------> the snowfall in inches
Step 1
Find the slope of the line of the Smithville city
Let
[tex]A(0,0)\\B(5,20)[/tex]
substitute the values in the formula above
[tex]m=\frac{20-0}{5-0}[/tex]
[tex]m=4\frac{inches}{hour}[/tex]
Step 2
Find the slope of the line of the Middletown city
Let
[tex]A(0,0)\\B(5,15)[/tex]
substitute the values in the formula above
[tex]m=\frac{15-0}{5-0}[/tex]
[tex]m=3\frac{inches}{hour}[/tex]
Step 3
Verify the statements
case A) Middletown had a faster rate of snowfall
The statement is False
Because Smithville had a faster rate of snowfall with [tex]4\frac{inches}{hour}[/tex]
case B) Smithville had a faster rate of snowfall
The statement is True
case C) Snow fell in Smithville at a rate of 4 inches per hour
The statement is True
case D) Middletown already had snow on the ground at the beginning of the storm
The statement is False
Because at the beginning of the storm the value of the snow is equal to zero
therefore
the answer is
Smithville had a faster rate of snowfall
Snow fell in Smithville at a rate of 4 inches per hour
A company plans to enclose three parallel rectangular areas for sorting returned goods. the three areas are within one large rectangular area and 10641064 yd of fencing is available. what is the largest total area that can be enclosed?
Answers
First get the perimeter
Perimeter: 2l + 2w = 1064 yd
The region inside the fence is the area
Area: A = lw
We need to solve the perimeter formula for either length or width.
2l + 2w = 1064 yd
2w = 1064 yd – 2l
W = 1064– 2l / 2
W = 532 – l
Now substitute than to the area formula
A = lw
A = l (532 – l)
A = 532 – l^2
Since the equation A represents a quadratic expression, rewritte the expression with the exponents in descending order
A(l) = -l^2 + 532l
Then look for the value of the x coordinate
l = -b/2a
l = -532/2(-1)
l = -532/-2
l = 266 yards
Plugging in the value into our calculation for area:
A(l) = -l^2 + 532
A(266) = -(266)^2 + 532 (266)
A(266) = 70756+ 141512
= 70756 square yards.
Thus the largest area that could encompass would be a square where each side has a length of 266 yards and a width of:
W = 532 – l
= 532 – 266
= 266
It should be noted that the largest total area that can be enclosed will be 70756 yards².
How to calculate the area.Firstly, we have to calculate the perimeter. This will be:
2l + 2w = 1064 yd
Area: A = length × width
2l + 2w = 1064 yd
2w = 1064 yd – 2l
W = 1064– 2l / 2
W = 532 – l
Since Area = lw
A = l(532 – l)
A = 532 – l²
A(l) = -l² + 532l
l = -b/2a
l = -532/2(-1)
l = -532/-2
l = 266 yards
The length is 266 yards.
Area = -l² + 532
A( = -(266)² + 532 (266)
Area = 70756+ 141512
Area = 70756 yards²
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Can you find a shortcut in doing two translations in geometry
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how would you graph the solution set of the system of inequalities {3y≤2x+6} { 2x+y>0}
Answers
3y ≤ 2x + 6
=> y ≤ 2x/3 + 2
2) Draw the line y = 2x/3 + 2
3) Shade the region below the line y = 2x/3 + 2
4) Solve the inequality 2x + y > 0
=> y > - 2x
5) draw the line y = -2x
6) Shade the region above the line y = -2x
7) The solution is the region between the two lines shaded including the portion of the line y = 2x/3 + 2
Two cars leave town going in opposite directions. one car is traveling 55 miles per hour (mph), and the other car is traveling 40 mph. how long will it take before the cars are 285 miles apart?
Answers
d = st
Car 1 travels distance 1, d1, at s1 = 55 mph, for t1 time.
Car 2 travels distance 2, d2, at s2 = 40 mph, for t2 time.
The two distances add to 285 miles, so
d1 + d2 = 285
The two times are equal, so t1 = t2 = t
d1 = 55t1
d2 = 40t2
d1 = 55t
d2 = 40t
d1 + d2 = 55t + 40t
d = 95t
285 = 95t
95t = 285
t = 3
Answer: It will take 3 hours.
Note:
This problem shows you that if two cars are traveling along the same line in opposite directions, the speed at which they are distancing themselves is the sum of the two speeds. We can solve the problem in a simpler way:
55 mph + 40 mph = 95 mph
d = st
285 = 95t
t = 3
Answer: 3 hours.
I really need help with these problems please come it will mean a lot if u help.
Answers
2. 59 degrees
3. would be 4
I'm not for sure about the other ones...
Simplify (s)(-3st)(-1/3).
A.) -3 1/3 t
B.) s^2t
C.) 3s^2t
(If this format is too weird I have added a screenshot)
Thanks in advance!
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Can someone help me with this? 18(−8c+16)−13(6+3c) =
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Take care,
Diana
Which expression is equivalent to -3.5(4x – 3)?
A. -3.9x – 3.2
B. -3.9x + 3.2
C. -14x + 10.5
D. -14x – 10.5
Answers
-3.5 * 4x = -14x
-3.5 * -3 = 10.5
C) -14x + 10.5
Hope this helps!
Answer:
The answer is c
Step-by-step explanation:
what did the candle say to the match
Answers
Your Turn: Find the equation of a line that is parallel to y=2x+7, and passes through the point (-4, 7). SHOW YOUR WORK
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y=2x+b
Now, we can use the point we are given to find the y-intercept.
7=2(-4)+b
7=-8+b
b=7+8
b=15
Finally, we can substitute all the information we have discovered to complete the slope-intercept equation.
y=2x+15
Justin is constructing a line through point Q that is perpendicular to line n. He has already constructed the arcs shown. He places his compass on point B to construct an arc. What must be true about the width of the compass opening when Justin draws the arc?
A .It must be wider than when he constructed the arc centered at point A.
B It must be the same as when he constructed the arc centered at point A.
C. It must be equal to BQ .
D.It must be equal to AB .
Answers
Answer:
just to confuse yall less it is indeed b!
Step-by-step explanation:
took the test on k12
What is the angle of elevation from jim to the top of the waterfall
Answers
Answer: <7
Step-by-step explanation:
When two straight lines or rays intersect at a shared endpoint, an angle is generated. The angle of elevation from Jim to the top of the waterfall is ∠5. The correct option is B.
What is an angle?When two straight lines or rays intersect at a shared endpoint, an angle is generated. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."
The angle of elevation is an imaginary angle that is assumed between the horizontal line and the line through which an object at a height is been seen.
In the given image the angle of elevation from Jim to the top of the waterfall is the angle formed by the line parallel to the horizontal plane and the line that connects Jim's eyesight to the top of the waterfall.
Hence, the angle of elevation from Jim to the top of the waterfall is ∠5.
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What is the area of a triangle with vertices at (−4, 1) , (−7, 5) , and (0, 1) ?
Enter your answer in the box.
Answers
we know that
A method for calculating the area of a triangle when you know the lengths of all three sides is the Heron's Formula.
The Heron's Formula states that
[tex]A=\sqrt{p(p-a)(p-b)(p-c)}[/tex]
where
a,b.c are the length sides of the triangle
p is half the perimeter of the triangle
Let
[tex]A(-4,1)\\B(-7,5)\\C(0,1)[/tex]
Step 1
Find the distance AB
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
[tex]A(-4,1)\\B(-7,5)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(5-1)^{2}+(-7+4)^{2}}[/tex]
[tex]d=\sqrt{(4)^{2}+(-3)^{2}}[/tex]
[tex]d=\sqrt{25}[/tex]
[tex]dAB=5\ units[/tex]
Step 2
Find the distance BC
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
[tex]B(-7,5)\\C(0,1)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(1-5)^{2}+(0+7)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(7)^{2}}[/tex]
[tex]d=\sqrt{65}[/tex]
[tex]dBC=8.06\ units[/tex]
Step 3
Find the distance AC
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
[tex]A(-4,1)\\C(0,1)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(1-1)^{2}+(0+4)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(4)^{2}}[/tex]
[tex]d=\sqrt{16}[/tex]
[tex]dAC=4\ units[/tex]
Step 4
Find half the perimeter
[tex]p=\frac{1}{2}(AB+BC+AC)[/tex]
substitute the values
[tex]p=\frac{1}{2}(5+8.06+4)[/tex]
[tex]p=8.53\ units[/tex]
Step 5
Find the area
Applying the Heron's Formula
[tex]A=\sqrt{8.53(8.53-5)(8.53-8.06)(8.53-4)}[/tex]
[tex]A=\sqrt{8.53(3.53)(0.47)(4.53)}[/tex]
[tex]A=\sqrt{64.11}[/tex]
[tex]A=8\ units^{2}[/tex]
therefore
the answer is
the area of the triangle is [tex]8\ units^{2}[/tex]
The area of a shape is the amount of space it occupies.
The area of the triangle is 8 unit square.
The vertices are given as:
[tex]\mathbf{A = (-4,1)}[/tex]
[tex]\mathbf{B = (-7,5)}[/tex]
[tex]\mathbf{C = (0,1)}[/tex]
The area of the triangle is:
[tex]\mathbf{A= \frac{1}{2} \times |A_x(B_y - C_y) + B_x(C_y - A_y) + C_x(A_y - B_y)|}[/tex]
So, we have:
[tex]\mathbf{A= \frac{1}{2} \times |-4(5 - 1) -7(1 - 1) + 0(1 - 5)|}[/tex]
[tex]\mathbf{A= \frac{1}{2} \times |-4(4) -7(0) + 0|}[/tex]
[tex]\mathbf{A= \frac{1}{2} \times |-4(4) -0 + 0|}[/tex]
[tex]\mathbf{A= \frac{1}{2} \times |-16|}[/tex]
Remove absolute brackets
[tex]\mathbf{A= \frac{1}{2} \times 16}[/tex]
[tex]\mathbf{A= 8}[/tex]
Hence, the area of the triangle is 8 unit square.
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nick bought a pet lizard and enjoys the responsibility of taking care of it . every week , the lizard will eat 60 grasshoppers. nick pays $1 for 20 grasshoppers . how many dollars will a year’s worth of food cost for the lizard
Answers
60*52 = 3120 per year
3120/20 = 156
it will cost $156 a year
What? I don’t know what I’m doing???
Answers
Help please !!!!!!!!!!!!!!
Answers
What is the ratio 35 to 15 expressed as a fraction in simplest form?
Answers
Dividing by a factor of 5 should help.
That is the same as 35/15
Let's use 5 to divide to its simplest form. That will be;
35 divided by 5 is 7. And 15 divided by 5 is 3. So you have;
7/3
Hope that helped. Have a nice day
Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $27 monthly fee and charges an additional $0.12 for each minute of calls. The second plan has no monthly fee but charges $0.16 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?
Answers
Second plan : y = 0.16x
27 + 0.12x= 0.16x
27 = 0.04x
x = 67.5 minutes
The sum of two numbers is 67 . the larger number is 5 more than the smaller number. what are the numbers?
Answers
x + y = 67
(y + 5) + y= 67
2y = 62
y = 31
You can use this to find x by plugging in y to either original equation:
x = y + 5
x = 31 + 5
x = 36
The legs of a right triangle measure 30cm and 40cm.what is the length of the hypotenuse
Answers
A^2 + b^2=c^2
Plug in the numbers
30^2 + 40^2 = c^2
900 + 1600 =c^2
2500 = c^2
The square-root of 2500 = c
50=c
The hypotenuse of the triangle is 50
Hope this helps!
30²+40²=c²
900+1600=c²
2500=c²
√2500=√c²
c=50
The hypotenuse is 50cm long.
Hope this helps!
write a word phrase for each algebraic expression
1. 25 - 6
2. 2/3y + 4
factor each expression
3. 45c + 10d
4. 27 - 9x + 15y
Simplify the expression.
5. 3(t - 4) - 8 (2 - 3t )
6. 12x + 24
Answers
Answer:
Step-by-step explanation:
1)Twenty five minus sixty percent times a number.