Answer:
5/8
Step-by-step explanation:
Let the numerator = n.
Let the denominator = d.
The fraction is
n/d
"The denominator of a rational number is greater than its numerator by 3."
d = n + 3
The fraction is
n/(n + 3)
"If 3 is subtracted from the numerator and 2 is added to its denominator, the new number becomes 1/5."
(n - 3)/(n + 3 + 2) = 1/5
(n - 3)/(n + 5) = 1/5
Cross multiply.
5(n - 3) = 1(n + 5)
5n - 15 = n + 5
4n = 20
n = 5
d = n + 3 = 5 + 3 = 8
n/d = 5/8
The original number is 5/8.
Last trigonometry question... plzzz heelllppp...thx
Answer:
8.86 ( 3 S.F)
Step-by-step explanation:
Using Sine Rule,
AB/ Sin (41) = 13.5/ Sin (90)
AB = 8.856796891
= 8.86 cm (3 s.f.)
The Hernandez family ordered one jumbo pizza with a diameter of 20 inches, cut it into 15 equal slices, and had 3 slices left over after dinner. The Mullins family ordered two medium pizzas, each with a diameter of 12 inches, cut them into 8 equal slices each, and had 6 slices left over after dinner. How much pizza did the Mullins family eat as a fraction of the pizza the Hernandez family ate?
Answer: Mullins family eat [tex]\dfrac{9}{20}[/tex] of the pizza the Hernandez family ate.
Step-by-step explanation:
Area of circle = [tex]\pi r^2[/tex] , where r is the radius
Given, Diameter of Hernandez family's pizza = 20 inches
Radius = [tex]\dfrac{20}{2}[/tex] = 10 inches
Area of Hernandez family's pizza = [tex]\pi (10)^2=100\pi \text{ in.}^2[/tex]
Since, they divide pizza into 15 pieces , area of each slice = [tex]\dfrac{100\pi}{15}=\dfrac{20}{3}\pi\text{ in.}^2[/tex]
They left with 3 slices i.e. they ate 12 slices, area of all 12 slices = 12 x (area of each slice)
= [tex]12\times\dfrac{20}{3}\pi\text{ in.}^2= 80\pi\text{ in.}^2[/tex]
Diameter of Mullins family's pizza = 12 inches
Radius = [tex]\dfrac{12}{2}[/tex] = 6 inches
Area of Mullins family's pizza = [tex]\pi (12)^2=144\pi \text{ in.}^2[/tex]
Since, they divide pizza into 8 pieces , area of each slice = [tex]\dfrac{144\pi}{8}=18\pi\text{ in.}^2[/tex]
They left with 6 slices i.e. they ate 2 slices, area of all 2 slices = 2 x (area of each slice)
= [tex]2\times18\pi\text{ in.}^2=36\pi\text{ in.}^2[/tex]
Since, [tex]\dfrac{36\pi}{80\pi}=\dfrac{9}{20}[/tex]
Hence, Mullins family eat [tex]\dfrac{9}{20}[/tex] of the pizza the Hernandez family ate.
Triangle A B C is shown with its exterior angles. Angle B A C is (p + 4) degrees and angle A C B is 84 degrees. Exterior angle X B C is (3 p minus 6 degrees).
What is the measure of ∠XBC?
m∠XBC = m∠BAC + m∠BCA
3p – 6 = p + 4 + 84
3p – 6 = p + 88
2p – 6 = 88
2p = 94
m∠XBC =
°
Answer: 135
Step-by-step explanation:
took it on edg2020
Answer:
135
Step-by-step explanation:
Just took the test and got it right
A group of students were given a spelling test the table shows their mark Mark: 6,7,8,9,10 frequency:5,4,7,10,4 a) work out the range of the marks. B)how many students are in a group C) work out the mean mark of the group
Answer:
Step-by-step explanation:
From the information given,
Mark: 6,7,8,9,10
frequency:5,4,7,10,4
a) Range = highest mark - lowest mark
Range = 10 - 6 = 4
b) The number of students in the group is the sum of the frequency. Therefore,
Number of students = 5 + 4 + 7 + 10 + 4 = 30 students
c) Mean mark = (mark × frequency)/total frequency
[(6 × 5) + (7 × 4) + (8 × 7) + (9 × 10) + 10 × 4)]/ 30
Mean mark = (30 + 28 + 56 + 90 + 40)/30 = 244/30
Mean mark = 8.1
Answer: From the information given, Mark: 6,7,8,9,10 frequency:5,4,7,10,4 a) Range = highest mark - lowest markRange = 10 - 6 = 4b) The number of students in the group is the sum of the frequency. Therefore, Number of students = 5 + 4 + 7 + 10 + 4 = 30 studentsc) Mean mark = (mark × frequency)/total frequency[(6 × 5) + (7 × 4) + (8 × 7) + (9 × 10) + 10 × 4)]/ 30Mean mark = (30 + 28 + 56 + 90 + 40)/30 = 244/30Mean mark = 8.1
Step-by-step explanation:
HELP ASAP PLEASE answer quickly
Answer:
A. [tex]\frac{3}{5}[/tex]
B. [tex]\frac{7}{10}[/tex]
C. B (you already got that right)
Step-by-step explanation:
To find the probability of something, we have to see how many times it happened over the total amount of attempts.
On Tuesday the target was hit 18 times in 30 attempts. So our probability fraction is [tex]\frac{18}{30}[/tex] which simplifies to [tex]\frac{3}{5}[/tex].
Looking at the total results, we can see Ben hit the target 84 times out of 120, so the fraction is [tex]\frac{84}{120}[/tex] which simplifies to [tex]\frac{7}{10}[/tex].
There’s always one rule of statistics/probability - the more data the better. If we want to create a more reliable probability, we’d want more data, and the total data gives us more than just Tuesday’s Data.
Hope this helped!
What is the area of the trapezoid shown below?
Answer: 78 units²
Step-by-step explanation:
Use Pythagorean Theorem to find the base of the triangle:
x² + 12² = 15²
x² + 144 = 225
x² = 81
x = 9
Now, separate the figure into two shapes --> triangle and rectangle.
[tex]A_{\triangle}=\dfrac{base\times height}{2}=\dfrac{9\times 12}{2}=54\\\\A_{\square}=length \times width = 12 \times 2 =24\\\\A_{trapezoid}=A_{\triangle}+A_{\square}=54+24=\large\boxed{78}[/tex]
You can also use the trapezoid rule:
[tex]A=\dfrac{b_1+b_2}{2}\cdot h\\\\\\.\quad = \dfrac{(9+2)+(2)}{2}\cdot 12\\\\\\.\quad = \dfrac{13}{2}\cdot 12\\\\\\.\quad =13\cdot 6\\\\\\.\quad = \large\boxed{78}[/tex]
Examine the diagram of circle A. Circle A has a radius of 4 and arc BD has length of 6.5. Circle C is a different circle with radius 6 and arc EF. Angle ECF is congruent to angle BAD. What is the length of arc EF? Enter your answer as a number, like this: 42.25
Answer:
the answer is 9.75 :)
Step-by-step explanation:
Using the given information, the length of arc EF in circle C is 9.75
Calculating the length of an arcFrom the question, we are to calculate the length of arc EF
First, we will determine the measure of angle BAD
Let angle BAD = θ
From the question,
Length of arc BD = 6.5
Radius of circle A = 4
Using the formua,
[tex]Length \ of \ an \ arc = \frac{\theta}{360 ^\circ}\times 2\pi r[/tex]
Then,
[tex]6.5 = \frac{\theta}{360 ^\circ} \times 2\pi \times 4[/tex]
[tex]\theta = \frac{360 \times 6.5}{2\pi \times 4}[/tex]
[tex]\theta = \frac{2340}{8\pi }[/tex]
[tex]\theta = \frac{292.5}{\pi }^\circ[/tex]
Now, for the measure of arc EF in circle C
Since angle ECF and angle BAD are congruent, then
Angle ECF = [tex]\frac{292.5}{\pi }^\circ[/tex]
Thus,
Length of arc EF = [tex]\frac{\frac{292.5}{\pi}^\circ }{360 ^\circ} \times 2 \pi \times 6\\[/tex]
Length of arc EF = [tex]\frac{292.5^\circ }{\pi \times 360 ^\circ} \times 12 \pi[/tex]
Length of arc EF = [tex]\frac{292.5 \times 12}{360}[/tex]
Length of arc EF = 9.75
Hence, using the given information, the length of arc EF in circle C is 9.75
Learn more on Calculating the length of an arc here: https://brainly.com/question/12152333
#SPJ 2
Instructions: Find the missing side. Round your answer to the
nearest ten
Answer:
trig function is tangent
tan(63)=x/19
multiply each side by 19:
tan(63)19=x
x=37.3
Find the value of x.
08*
ος
Ο Α. 58ο
Ο Ο Ο
Ο Β. 32ο
C. 669
D. 68ο
Answer:
x = 66°
Step-by-step explanation:
Hello,
This question involves use of rules or theorems of angles in a right angled triangle
<DAB + <BAC = 180°
Sum of angles on a straight line = 180°
98° + <BAC = 180°
<BAC = 180° - 98°
<BAC = 82°
Now, we can use <BAC to find x because some of angles in a triangle is equal to 180°
32° + 82° + x = 180°
Sum of angles in a triangle = 180°
114° + x = 180°
x = 180° - 114°
x = 66°
Angle x = 66°
Express 429 as a product of its prime factors
Answer:
The answer is 429 = 3×11×13.
Step-by-step explanation:
You have to divide by prime number :
429 ÷ 3 = 143
143 ÷ 11 = 13
13 ÷ 13 = 1
Answer:
3×11×13
Step-by-step explanation:
Start dividing by prime numbers. Since the number is even two won't work so next is three. If you divide 429 by 3 you get 143. You continue doing this with primes going up (5, 7, 11, 13, etc.) until you get to the final prime. 5 and 7 don't work if you try dividing them by 143 individually so next up is 11. If you divide 11 by 143 you get 13 which is also a prime number. Therefore, 3×11×13 is a product of prime factors.The sum of the digits of a two-digit number is 5. If nine is subtracted from the number, the digits will be reversed. Find the number. If the numbers 32, What's the equation?
Answer:
Step-by-step explanation:
Hello,
let's note a and b the two digits, the number is then a*10+b
and the digits in revers mode give b*10 + a so we can write
(1) a + b = 5
(2) 10a+ b - 9 =10b + a
From(1) I get b = 5-a
I replace in (2)
10a + 5 - a - 9 = 10(5-a) + a = 50 - 10a = a = 50 - 9a
9a - 4 = 50 - 9a
18a = 50 + 4 = 54 so
a = 54/18 = 3
and then from (1) b = 5 - 3 = 2
So the number is 32
According to the graph, what is the value of the constant in the equation
below?
A. 10
B. 20
C. 100
D. 4
Answer:
C. 100
Step-by-step explanation:
You can rearrange the equation to say ...
(Height)(Width) = Constant
Multiply any of the coordinate values shown, and you will see the constant is 100.
4×25 = 5×20 = 10×10 = 20×5 = 100
The constant is 100.
Solve the following system using substitution. 1/3 x+2y=1 y=2/3 x-4
Answer:
4x+4y=1, 6x-y=1
x+y=4, x-y=2
x-y=9, x+y=6
Step-by-step explanation:
Answer:
x equals 27/5
Step-by-step explanation:
just substitute y into the first equation
Divide. 1 ÷ 0.0064. please my dear friend
Answer:
156.25
Step-by-step explanation:
[tex]\frac{1}{0.0064}\\\\\frac{10000}{64}\\ then divide \[/tex]
[tex]\frac{10000}{64} = \frac{2500}{16} =\frac{625}{4} = 156.25[/tex]
Does the relation define a function? If it does, state the domain of the function.
Does the relation define a function? If it does, state the domain of the function
Answer: Choice A
Yes; Domain = {m, n, p, q}
We have the inputs (think of them as the x values) as m, n, p and q. They make up the domain. The domain is the set of all allowed inputs. We do not have any repeated inputs, which is why we have a function. Any given input leads to exactly one output.
What are transformation possible to change f(x) to g(x) on graph linear equation
Answer:
Vertical stretch or compression and vertical shift.Step-by-step explanation:
When we talk about the transformation of functions, we can mention stretching, rotating, dilating, shifting. However, when we want to transform linear functions, there are only two transformations that are worthy in that case, those are vertical stretch or compression and vertical shift.
Now, you may ask, why only vertical transformation? the reason behind that is because horizontal transformation would give the exact same result because it's only a straight line which we are transforming.
Another common question would be, why only two transformations? it's because with these two you can get all the results because it's a straight line.
The image attached shows examples of this.
The table compares the daily average temperature in a park (in degrees Celsius) and the number of people who visited the park that day. Can the number of people who visited the park be represented as a function of the daily average temperature?
Answer:
YES, the number of people who visited the park can be represented as a function of the daily average temperature.
Step-by-step explanation:
From the table of values given which defines the number of visitors to the park as a function of daily temperature, the temperature is the domain values (independent variable), while the number of visitors is the range values (dependent variable).
For any relation to be considered a function, as a principle, any given domain value must have exactly one range value. In other words, there must not be two different range values assign to one domain value.
This means, for the relation between temperature and number of visitors to be considered a function, it must not have a domain value that is mapped to more than one range value.
Examining the table given, if we map each domain value to the range value, we will find out that there are only 1 exact range value for a domain value.
Therefore, we can say: YES, the number of people who visited the park can be represented as a function of the daily average temperature.
Answer:
yes
Step-by-step explanation:
In a study with four groups and 10 participants in each group, the sum of squares for the between-groups source of variation is 60. What is the value for the mean square between groups in this study
Answer:
20
Step-by-step explanation:
Given that:
The study group n = 4
number of participants = 10
the sum of squares for the between-groups source of variation is 60
The objective is to determine the mean square between groups in this study
The mean square between groups in this study compares the means of the group with the sum of squares for the between-groups source (i.e the grand mean)
For this analysis;
the degree of freedom = n-1
the degree of freedom = 4 - 1
the degree of freedom = 3
Thus; the mean square between groups = [tex]\dfrac{60}{3}[/tex]
the mean square between groups = 20
El equipo de béisbol de los Gatos Salvajes de Ludlow, un equipo de las ligas menores de la organización de los Indios de Cleveland, juega 70% de sus partidos por la noche y 30% de día. El equipo gana 50% de los juegos nocturnos y 90% de los diurnos. De acuerdo con el periódico de hoy, ganaron el día de ayer. ¿Cuál es la probabilidad de que el partido se haya jugado de noche?
Answer:
0.5645
Step-by-step explanation:
De la pregunta anterior, se nos dan los siguientes valores para el equipo de Ludlow
Probabilidad de jugar de noche = 70% = 0.7
Probabilidad de ganar en la noche = 50% = 0.5
Probabilidad de jugar durante el día = 30% = 0.3
Probabilidad de ganar durante el día = 90% = 0.9
Probabilidad de que cuando ganaron ayer, el juego se jugó por la noche =
(Probabilidad de jugar de noche × Probabilidad de ganar de noche) ÷ [(Probabilidad de jugar de noche × Probabilidad de ganar de noche) + (Probabilidad de jugar de día × Probabilidad de ganar de día)]
Probabilidad de que cuando ganaron ayer, el juego se jugó de noche = (0.5 × 0.7) ÷ (0.5 × 0.7) + (0.9 × 0.3)
= 0.35 ÷ 0.35 + 0.27
= 0.35 ÷ 0.62
= 0.5645
La probabilidad de que el partido se haya jugado de noche = 0.5645
If AD is the altitude to BC, what is the slope of AD?
A. 2/5
B. -5/2
C. 5/2
D. -2/5
Answer:
Option (C)
Step-by-step explanation:
If AD is the altitude to BC, both the segments AD and BC will be perpendicular to each other.
By the property of perpendicular lines,
[tex]m_1\times m_2=-1[/tex]
where [tex]m_1[/tex] is the slope of the line AD and [tex]m_2[/tex] is the slope of BC.
[tex]m_2=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]=\frac{8+2}{3-7}[/tex]
[tex]=-\frac{5}{2}[/tex]
Now from the given property,
[tex]m_1\times (-\frac{2}{5})=-1[/tex]
[tex]m_1=\frac{5}{2}[/tex]
Therefore, slope of altitude BC = [tex]\frac{5}{2}[/tex]
Option (C) will be the answer.
formula of minimmum pressure
Solve for x. Enter your answer in the box. x =
Answer:
X =6
Step-by-step explanation:
24/12 : (5x+2)/16
Solve
Answer:
X=6
Step-by-step explanation:
Got right on test.
Can someone please explain The measure of angle A to the nearest tenth of a degree is:
Answer:
A =19.5
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin A= opp/ hyp
sin A = 3/9
Take the inverse sin of each side
sin ^-1 sin A = sin ^-1 (3/9)
A =19.47122063
To the nearest tenth of a degree
A =19.5
Answer:
19
Step-by-step explanation:
inverse sin (1/3) = 19.47122060852
HELLLLLLPPPPPP MEEEE PLEASEEEEE!!!!!! Find the times (to the nearest hundredth of a second) that the weight is halfway to its maximum negative position over the interval . Solve algebraically, and show your work and final answer in the response box. Hint: Use the amplitude to determine what y(t) must be when the weight is halfway to its maximum negative position. Graph the equation and explain how it confirms your solution(s).
Answer:
0.20, 0.36 seconds
Step-by-step explanation:
We have already seen that the equation for y(t) can be written as ...
y(t) = √29·sin(4πt +arctan(5/2))
The sine function will have a value of -1/2 for the angles 7π/6 and 11π/6. Then the weight will be halfway from its equilibrium position to the maximum negative position when ...
4πt +arctan(5/2) = 7π/6 or 11π/6
t = (7π/6 -arctan(5/2))/(4π) ≈ 0.196946 . . . seconds
and
t = (11π/6 -arctan(5/2))/(4π) ≈ 0.363613 . . . seconds
The weight will be halfway from equilibrium to the maximum negative position at approximately 0.20 seconds and 0.36 seconds and every half-second thereafter.
here are some facts about units of length 18 ft=____yd and 3 ft= ___in
Answer:
18 ft = 6 yds
3 ft = 36 inches
Step-by-step explanation:
We know that 3 ft = 1 yd
Divide 18 ft by 3
18 ft /3 ft = 6 yds
We know that 1 ft = 12 inches
3 ft * 12 inches /ft = 36 inches
Answer:
[tex]\large \boxed{18 feet = 6 yards}[/tex]
[tex]\large \boxed{3 feet = 36 inches}[/tex]
Step-by-step explanation:
1 foot = 1/3 of a yard
Multiply both sides of this equation by 18
[tex]\large \boxed{18 feet = 6 yards}[/tex]
1 foot = 12 inches
Multiply both sides of the equation by 3
[tex]\large \boxed{3 feet = 36 inches}[/tex]
Hope this helps!
Suppose a triangle has two sides of length 2 and 3 and that the angle between these two sides is 60°. What is the length of the third side of the triangle?
Answer:
I hope it will surely help uh.....
Answer:
sqrt of 7
Step-by-step explanation:
An ancient Greek was born on April 1st, 35 B.C. and died on April 1st, 35 A.D. How many years did he live?
Answer:
69 years
Step-by-step explanation:
Data provided in the question
Born date of an Ancient Greek = April 1st 35 BC
Diet date of an Ancient Greek = Aril 1st 35 AD
Based on the above information
We can say that
35 + 35 = 70
We deduct 1 as there is no zero
So, it would be
= 70 - 1 year
= 69 years
Hence, An ancient greek lives 69 years and the same is to be considered
I don't know this question. Help.
Answer:
-60
Step-by-step explanation:
-3 · 2 = -6 and 10⁴ · 10⁻³ = 10⁽⁴⁺⁽⁻³⁾⁾ = 10¹ = 10 so the answer is -6 · 10 = -60.
The number of people contacted at each level of a phone tree can be represented by f(x) = 3^x where x represents the level.
What is x when f(x) = 27?
A. X = 2; At level 2, 27 people will be contacted.
B. x = 24; At level 24, 27 people will be contacted.
C. x = 3; At level 3, 27 people will be contacted.
D. x = 9; At level 9,27 people will be contacted.
Answer:
3
Step-by-step explanation:
Answer:
c is the correct answer
Step-by-step explanation:
Choose the equation that represents the line that passes through the point (2, 6) and has a slope of −5.
Answer:
y=-5x+16
Explanation:
We already know the slope, and in y=mx+b, m is the slope. So now we have y=-5x+b.
Next, since we do not know the y-intercept, we can substitute the y and x values we are given in the current equation we have, y=-5+b. Now we have 6=-5(2)+b.
Now we can solve for b.
6=-10+b
16=b. We know that b=16.
Therefore, the equation is y=-5x+16