Answers
Step-by-step explanation:
(a) Your computer may be programmed to allocate borderline cases to the
next group down, or the next group up; and it may or may not manage
to follow this rule consistently, depending on its handling of the numbers
involved. Following a rule which says 'move borderline cases to the next
group up', these are the five classifications.
(i) 1.0-1.2 1.2-1.4 1.4-1.6 1.6-1.8 1.8-2.0 2.0-2.2 2.2-2.4
6 6 4 8 4 3 4
2.4-2.6 2.6-2.8 2.8-3.0 3.0-3.2 3.2-3.4 3.4-3.6 3.6-3.8
6 3 2 2 0 1 1
(ii) 1.0-1.3 1.3-1.6 1.6-1.9 1.9-2.2 2.2-2.5
10 6 10 5 6
2.5-2.8 2.8-3.1 3.1-3.4 3.4-3.7
7 3 1 2
(iii) 0.8-1.1 1.1-1.4 1.4-1.7 1.7-2.0 2.0-2.3
2 10 6 10 7
2.3-2.6 2.6-2.9 2.9-3.2 3.2-3.5 3.5-3.8
6 4 3 1 1
(iv) 0.85-1.15 1.15-1.45 1.45-1.75 1.75-2.05 2.05-2.35
4 9 8 9 5
2.35-2.65 2.65-2.95 2.95-3.25 3.25-3.55 3.55-3.85
7 3 3 1 1
(V) 0.9-1.2 1.2-1.5 1.5-1.8 1.8-2.1 2.1-2.4
6 7 11 7 4
2.4-2.7 2.7-3.0 3.0-3.3 3.3-3.6 3.6-3.9
7 4 2 1 1
(b) Computer graphics: the diagrams are shown in Figures 1.9 to 1.11
Related Questions
Lines m and n are parallel. Which of the other 5 named angles have a measure of 110°?
Which of these are true?
Answers
Answer:
<2, <5
Step-by-step explanation:
<2 is a vertical angle so it is equal to 110
<5 is a corresponding angle and since the lines are parallel it is also equal to 110
The distance from Parrot Point Airport to the Ivy Cliffs is 178 miles at and angle of 7.1 degrees northeast. There is a wind blowing southeast at 30 miles per hour. You want to make this trip in 2 hours by flying straight there. At what speed* and heading should you fly? * Round the speed to the nearest tenth of a mile per hour and angle to the nearest tenth of a degree. Where north is 0 degrees and positive is clockwise.
Answers
Answer:
The speed is 74.0 miles per hour and the angle is 65.1° north-east
Step-by-step explanation:
We resolve the distance moved by the wind and plane into horizontal and vertical components. The direction moved horizontally by the plane is 178sin7.1 = 22 miles.
Since the wind is moving south east, it is at 45 south of east or a bearing of 135.
Since the wind speed is 30 mph and it takes 2 hours to complete the trip, the horizontal distance moved by the wind is vtcos135 = 30 × 2cos45 = 42.43 miles
Also, the vertical displacement moved by the wind is vtsin135 = -30 × 2 sin45 = -42.43 miles
The displacement moved vertically by the plane is 178cos7.1 = 176.64 miles
The total horizontal displacement of the plane is 22 miles + 42.43 miles = 62.43 miles
The total vertical displacement of the plane is 176.64 miles - 42.43 miles = 134.21 miles
The resultant displacement is thus d = √(62.43² + 134.21²) = 148.02 miles
The direction of this displacement is thus
Ф = tan⁻¹(total vertical displacement/total horizontal displacement)
= tan⁻¹(134.21/62.43)
= tan⁻¹(2.1498)
= 65.05°
= 65.1° to the nearest tenth degree.
The speed is thus v = distance/ time = 148.02 miles/ 2 hours = 74.01 mph ≅ 74 mph. Since the direction of the displacement is the direction of the velocity, the velocity is thus 74 miles per hour at 65.1° north-east.
So the speed is 74.0 miles per hour and the angle is 65.1° north-east
Given the sequence 38, 32, 26, 20, 14, ..., find the explicit formula.
Answers
Answer:
The explicit formula for the sequence is
44 - 6nStep-by-step explanation:
The above sequence is an arithmetic sequence
For an nth term in an arithmetic sequence
A(n) = a + ( n - 1)d
where a is the first term
n is the number of terms
d is the common difference
From the question
a = 38
d = 32 - 38 = - 6 or 20 - 26 = - 6 or
14 - 20 = - 6
So the formula for the sequence is
A(n) = 38 + ( n - 1)-6
= 38 - 6n + 6
We have the final answer as
A(n) = 44 - 6nHope this helps you
Answer:
[tex]\huge\boxed{a_n=-6n+44}[/tex]
Step-by-step explanation:
This is an arithmetic sequence:
32 - 38 = -6
26 - 32 = -6
20 - 26 = -6
14 - 20 = -6
The common difference d = -6.
The explicit formula of an arithmetic formula:
[tex]a_n=a_1+(n-1)(d)[/tex]
Substitute:
[tex]a_1=38;\ d=-6[/tex]
[tex]a_n=38+(n-1)(-6)[/tex] use the distributive property
[tex]a_n=38+(n)(-6)+(-1)(-6)\\\\a_n=38-6n+6\\\\a_n=-6n+(38+6)\\\\a_n=-6n+44[/tex]
the dot plot shows the number of text messages mr.garcia sent each day so far this month. which statement best describes the shape of the graph?
Answers
Answer:
where is the dot plot also describe if it increases or decreases
For the following systems of equations, match each diagram on the left with its solution on the right.
Answers
Answer:
1. (2,1)
2. (6,-1)
3.(-2,3)
Answer:
1. (2,1)
2. (6,-1)
3. (-2,3)
Step-by-step explanation:
Each of the answer is consistent system because the lines intersect at one point, which is one solution.
I WILL GIVE BRAINLIEST!!!! Calculate cos M if a= 4, b= 12.5, c= 13.1244 **Round your answer up to four decimal places.
Answers
Answer:
cosM ≈ 0.3048
Step-by-step explanation:
remember SOH CAH TOA = sine: opposite/hypotenuse; cosine: adjacent/hypotenuse; tangent: opposite/adjacent
cos = CAH
cosM= a / c
cosM = 4.0 / 13.1244
cosM = 0.30477
cosM ≈ 0.3048
what is the exact area of a circle having diameter 4in
Answers
need help a s a p HURRYYYYY
Answers
Step-by-step explanation:
v= 4/3πr³
4/3×314/100×8×8×8
•
= 2,143.573
Help!!!!
Find the slope of the line on the graph.
Write your answer as a fraction or a whole
number, not a mixed number or decimal.
Enter the correct answer.
Answers
Answer:
[tex]Slope (m) = -\frac{2}{3}[/tex]
Step-by-step explanation:
To find the slope of the line of the graph, pick any 2 points on the line as your coordinate pairs.
Thus, on the line, let's pick 2 points as our coordinate pairs at:
When x = -6, y = 5 => (-6, 5), and
When x = 3, y = -1 => (3, -1)
Let (-6, 5) be (x1, y1), and (3, -1) be (x2, y2)
[tex] Slope (m) = \frac{y2 - y1}{x2 - x1} [/tex]
[tex] Slope (m) = \frac{-1 - 5}{3 - (-6)} [/tex]
[tex] Slope (m) = \frac{-1 - 5}{3 + 6} [/tex]
[tex] Slope (m) = \frac{-6}{9} [/tex]
[tex]Slope (m) = -\frac{2}{3}[/tex]
I need help with this problem! Must explain why.
Answers
Answer:
95°
Step-by-step explanation:
Angle 1 and 4 are opposite angles, thus equal, so:
3x+10 = 4x-15 =>
x = 25
Angle 1 and 4 are 85°
Angle 4 and angle 6 are called allied (or co-interior) angles, which are supplementary, i.e., angle 6 = 180 - angle 4, so angle 6 = 95°.
Angle 6 and 7 are again opposite, so angle 7 is 95° as well!
En un rectangulo el ancho es menor en 5cm al largo . si el P= 38cm calcule su area
Answers
Answer:
84cm²
Step-by-step explanation:
Perímetro de un rectángulo = 2L + 2W
Representemos la longitud del rectángulo = L
En la pregunta anterior se nos dijo que el ancho del rectángulo = es menor que 5 en la longitud
Por lo tanto, ancho del rectángulo = L - 5
Perímetro del rectángulo = 38 cm
Por lo tanto
38 = 2 (L) + 2 (L - 5)
38 = 2L + 2L - 10
38 + 10 = 4L
48 = 4L
L = 48/4
L = 12 cm
La longitud del rectángulo = 12 cm
Como L = 12, encontramos el ancho
Ancho = L - 5
= 12 cm - 5 cm
= 7 cm
El ancho del rectángulo = 7 cm
En la pregunta nos pidieron encontrar el área del rectángulo.
Área del rectángulo = Largo × Ancho
Área del rectángulo = 12 cm × 7 cm
Área del rectángulo = 84cm²
A box is filled with 9 red crayons, 2 blue crayons, and 5 yellow crayons. A crayon is chosen at random from the box. Find the probability that it is a red or a blue crayon. Write your answer as a fraction in simplest form.
Answers
Answer:
[tex]P(Red\ or\ Blue) = \frac{11}{16}[/tex]
Step-by-step explanation:
Given
[tex]Red = 9[/tex]
[tex]Blue = 2[/tex]
[tex]Yellow = 5[/tex]
Required
Probability of Red or Blue
First, it should be noted that the event described in the question are mutually exclusive or disjoint events;
Meaning that the probability of one have no effect the other;
Having said that; the Probability of Red ot Blue is as follows
[tex]P(Red\ or\ Blue) = P(Red) + P(Blue)[/tex]
Calculating [tex]P(Blue)[/tex]
[tex]P(Blue) = Number\ of\ blue\ crayon / total\ crayon[/tex]
[tex]P(Blue) = \frac{2}{9+ 2 + 5}[/tex]
[tex]P(Blue) = \frac{2}{16}[/tex]
Calculating [tex]P(Red)[/tex]
[tex]P(Red) = Number\ of\ red\ crayon / total\ crayon[/tex]
[tex]P(Red) = \frac{9}{9+ 2 + 5}[/tex]
[tex]P(Red) = \frac{9}{16}[/tex]
Substitute these values in the formula given above
[tex]P(Red\ or\ Blue) = P(Red) + P(Blue)[/tex]
[tex]P(Red\ or\ Blue) = \frac{9}{16} + \frac{2}{16}[/tex]
Take LCM
[tex]P(Red\ or\ Blue) = \frac{9 + 2}{16}[/tex]
[tex]P(Red\ or\ Blue) = \frac{11}{16}[/tex]
Hence, the probability of a red or blue crayon is
[tex]P(Red\ or\ Blue) = \frac{11}{16}[/tex]
For what values of x is x2 + 2x = 24 true?
–6 and –4
–4 and 6
4 and –6
6 and 4
Answers
Answer:
Option C
x²+ 2x -24=0
x²+6x-4x-24= 0
x(x+6) -4(x+6) = 0
(x+6)(x-4) = 0
x= -6 and 4
Therefore, for x = 4 and -6 , the above given equation is true.
A cylinder shaped storage tank has a radius of (x+5) metres and a height of x metres. Determine the dimensions (round to two decimal places) of the tank if the volume is about 192 cubic metres.
Answers
Answer:
Radius = 6.46 meters
Height = 1.46 meters
Step-by-step explanation:
The volume of a cylinder = πr²h
In the above question, we were given
r = (x + 5) meters
h = x meters
Volume = 192 cubic meters
Hence,
192 = π × (x + 5)² × x
192 = π × (x² + 10x + 25) × x
192 = π × (x³ + 10x² + 25x)
Divide both sides by π
192/π = x³ + 10x² + 25x
61.115498147 = x³ + 10x² + 25x
x³ + 10x² + 25x - 61.12
This Quadratic equation is a polynomial
x = 1.46119
From the above:
Radius = (x + 5)meters
Radius = 1.46119 + 5 = 6.46119 meters
Approximately to 2 decimal places = 6.46 meters
Height = x meters
Height = 1.46119 meters
Approximately to 2 decimal places = 1.46 meters
Starting from an airport, an airplane flies 290 miles east and then 290 miles northwest. How far, in miles, from the airport is the plane? (Round your answer to the nearest mile.)
Answers
Answer:
The airplane is 222 miles far from the airport.
Step-by-step explanation:
After a careful reading of the statement, distances can be described in a vectorial way. A vector is represented by a magnitude and direction. That is:
Airplane flies 290 miles (east) (290 km with an angle of 0º)
[tex]\vec r_{A} = (290\,mi)\cdot i[/tex]
Airplane flies 290 miles (northwest) (290 km with and angle of 135º)
[tex]\vec r_{B} = [(290\,mi)\cdot \cos 135^{\circ}]\cdot i + [(290\,mi)\cdot \sin 135^{\circ}]\cdot j[/tex]
The resultant vector is equal to the sum of the two vectors:
[tex]\vec r_{C} = \vec r_{A} + \vec r_{B}[/tex]
[tex]\vec r_{C} = \{(290\,mi) + \left[(290\,mi)\cdot \cos 135^{\circ}\right]\}\cdot i + \left[(290\,mi)\cdot \sin 135^{\circ}\right]\cdot j[/tex]
[tex]\vec r_{C} = (84.939\,mi)\cdot i + (205.061\,mi)\cdot j[/tex]
The magnitude of the final distance of the airplane from the airport is obtained by the Pythagorean Theorem:
[tex]\|\vec r_{C}\|=\sqrt{(84.939\,mi)^{2}+(205.061\,mi)^{2}}[/tex]
[tex]\|\vec r_{C}\| = 221.956\,mi[/tex]
The airplane is 222 miles far from the airport.
what is known as terms of ratio
Answers
Answer: The mathematics terms of ratio are the indicates many times one number contains to the another number.
Step-by-step explanation:Terms of ratio may be specified both constitution number or value to the equal correspond to the equal ratio.
"a to b"
"a:b"
There are Sixteen and eight apples and lemon in the table of fruit the ratio(that is 16:8 to the equivalent the ratio 8:4).
a:b=(a+b):a or ratio is equivalently a:b=(1+b/a):1.
The number in a terms ratio quantities of both numbers are to be positive
A group of students made trees out of paper for a scene in a school play. The trees are shaped like square pyramids. 70 cm70\text{ cm} 70 cm 140 cm140\text{ cm} 140 cm How much paper will it take to make each tree, including the bottom?
Answers
Answer:
24500 cm^2
Step-by-step explanation:
52.85 rounded to the nearest tenth
Answers
Answer: 52.9
Step-by-step explanation:
The value 5 is rounded up.
Hope it helps <3
Answer:
52.9
Step-by-step explanation:
round up using the last number. since its 5, you round up
4xy-3x+8y2-6y 8y-6 please help someone thank you
Answers
Answer:
x=6, y=2.5
Step-by-step explanation:
Help me pLEASSSSE ! do it step by step so I can see how y'all do it.
Answers
Answer:
5
Step-by-step explanation:
Since y equals 200 + 10x and y also equals 5x, then
200 + 10x = 50x
Subtract 10x from both sides.
200 = 40x
Divide both sides by 40.
5 = x
Answer: He must sell 5 sculptures.
AB is tangent to circle D. Find the value of x.
Answers
Answer:
c 15
Step-by-step explanation:
Tangent AB is tangent to circle D at point A. The angle made by a tangent to a circle and a radius of the circle at the point of tangency is a right angle. That means that angle is a right angle, and triangle ABD is a right triangle.
We can use the Pythagoren theorem.
a^2 + b^2 = c^2
x^2 + 20^2 = (x + 10)^2
x^2 + 400 = (x + 10)(x + 10)
x^2 + 400 = x^2 + 10x + 10x + 100
400 = 20x + 100
20x = 300
x = 15
I need help with this please answer
Answers
Answer:
B. [tex]1\frac{1}{7}[/tex]
Step-by-step explanation:
[tex]-9\frac{2}{7}[/tex]=[tex]-\frac{65}{7}[/tex]
[tex]-10\frac{3}{7}[/tex]=[tex]-\frac{73}{7}[/tex]
[tex]-\frac{65}{7}[/tex]-([tex]-\frac{73}{7}[/tex])=8/7
8/7=[tex]1\frac{1}{7}[/tex]
Hope this helped!!!
which of the following is equivalent to (x+4)(3x^2+2x)??
Answers
Answer:
c
Step-by-step explanation:
I NEED HELP QUICK like very quick
Answers
Answer:
2.5 or 2 1/2
Step-by-step explanation:
i caculated do order of operations
A hair color manufacturer performed a survey which was normally distributed. They found that the average age at which a person's hair starts turning gray is 32 years, with a standard deviation of 4 years. Which of the following graphs displays the normal distribution of the average age at which a person's hair starts turning gray?
W.
X.
Y.
Z.
Answers
Answer: X
Step-by-step explanation:
g(x)= √x+3 help plsss
Answers
Answer:
All real values of x such that x ≥-3
Step-by-step explanation:
g(x) = sqrt(x+3)
A sqrt must be greater than or equal to zero
sqrt (x+3) ≥ 0
Square each side
x+3≥ 0
Subtract 3 from each side
x ≥-3
The restrictions on x are x ≥-3
That means the domain is x ≥-3
All real values of x such that x ≥-3
Answer:
[tex]\boxed{\mathrm{B}}[/tex]
Step-by-step explanation:
[tex]g(x)=\sqrt{x+3}[/tex]
A square root must have a value of greater than or equal to 0.
[tex]\sqrt{x+3}\geq 0[/tex]
Square both sides.
[tex]x+3\geq 0[/tex]
Subtract 3 from both sides.
[tex]x\geq -3[/tex]
Explain why 7 x 9 x 11 x 13 + 13 is a composite number.
Answers
Answer:
7 x 9 x 11 x 13 + 13 is a composite number because the answer is a positive number which is 9022.
7 x 9 x 11 x 13 + 13 is a positive integer that can be formed by multiplying small positive numbers which are 7, 9, 11 and 13. Equivalently, 9022 is a positive integer that has at least one divisor other than 1 and itself. For example, 9022 can be divided by 2. 9022 is exactly a number but it is not a prime number.
I hope you will understand my explanation!
A piece of string 8 inches long is cut into two pieces, one of which is of length x inches. If this piece is made into the circumference of a circle, and the other piece is made into the circumference of a square, then the combined area of the circle and square, as a function of x, is:
Answers
Answer:
2πr + 4a = 8
Step-by-step explanation:
The length of the room is 2½ times the breadth. The perimeter of the room is 70 m. What are the length and breadth of the room.
Answers
Answer:
Length = 25 cmBreadth = 10 cmStep-by-step explanation:
Let breadth of the room be 'x'
Let length of the room be '[tex]2 \frac{1}{2} x = \frac{5}{2} = 2.5 \: x[/tex]'
Perimeter ( P ) = 70 cm
Now, let's find the breadth of the room 'x '
Perimeter of rectangle = [tex]2(l + b)[/tex]
plug the values
[tex]70 = 2(2.5x + x)[/tex]
Collect the like terms
[tex]70 = 2 \times 3.5x[/tex]
Calculate the product
[tex]70 = 7x[/tex]
Swap the sides of the equation
[tex]7x = 70[/tex]
Divide both sides of the equation by 7
[tex] \frac{7x}{7} = \frac{70}{7} [/tex]
Calculate
[tex]x = 10 \: cm[/tex]
Breadth = 10 cm
Now, Let's find the length of the room ' 2.5x '
Length of the room = [tex]2.5x[/tex]
Plug the value of X
[tex] = 2.5 \times 10[/tex]
Calculate the product
[tex] = 25 \: cm[/tex]
Thus , The length and breadth of the room is 25 cm and 10 cm respectively.
Hope this helps..
Best regards!!
WILL GIVE BRAILIEST! Find the mean of the data in the bar chart below. _________puppets
Answers
Answer: 2.5
Step-by-step explanation:
To find a mean, the average, we have to add everything together.
So we add 1 + 4 + 3 + 2, which is equal to 10. The next step to find the average is to divide by the total number of “things” which is the 4 puppeteers.
10/4 is 2.5