Answer:
the total mass is 212.5 kg
Step-by-step explanation:
The computation of the total mass is as follows;
Given that
Number of family members = 5
And, the average mass is 42.5 kg
Now based on the above information
The total mass is
= Number of family members × average mass
= 5 × 42.5 kg
= 212.5 kg
Hence, the total mass is 212.5 kg
The golden ratio is a solution to a quadratic equation.
a. Find the precise value for Φ by solving Φ2 − Φ − 1 = 0.
b. Which method of solving a quadratic equation did you use? Explain your reasoning.
c. What type of number is Φ? Why can it only be approximated by a decimal value?
Answer:
Below.
Step-by-step explanation:
a. Φ^2 − Φ − 1 = 0
Φ2 − Φ = 1
(Φ - 0.5)^2 - 0.25 = 1
(Φ - 0.5)^2 = 1.25
Φ - 0.5 = √(1.25) (We only take the positive root).
Φ = 0.5 + √(1.25)
b. I used Completing the square.
c. Φ is irrational That is it cannot be represented as a fraction a/b and because of this it can only be approximated by a decimal.
Each polio vaccination consists of 4 doses, and each measles vaccination consists of 2 doses. Last year, Dr. Potter gave a total of 606060 vaccinations that consisted of a total of 184 doses. How many polio vaccinations and how many measles vaccinations did Dr. Potter give last year?
I think there is a little error in your question. I guess You mean 60 vaccinations instead of 606060. I solved using 60 vaccinations.
Answer:Dr. Potter gave 32 polio vaccines and 28 measles vaccinations that year.
Step-by-step explanation:
STEP 1
Let number of polio vaccines be x
and number of measles vaccine be y
such that
total does of 60 vaccinations be expressed as
x+y = 60---- equation 1
And number of doses for both vaccine to total 184 doses taken be expressed as
4x + 2y= 184 ---- equation 2
Step 2--- solving
x+y = 60---- equation 1
4x + 2y= 184 ---- equation 2
Making x the subject of formula in equation 1 and substituting it in equation 2
x= 60-y
4(60-y) +2y- 184
240-4y+2y=184
240-184= 4y-3y
56= 2y
y= 58/2 = 28
To get x , put the value of y=28 in equation 1 and solve
x+y=60
x=60-28
x=32
Therefore Dr. Potter gave 32 polio vaccines and 28 measles vaccinations that year.
Can anyone simplify
3y+2y+y
Answer:
there all the same variables so it'll be 6y
5(x + 4) help plssssss
Answer:
5x + 20
Step-by-step explanation:
5(x +4)
= 5x + 20
multiply x + 4 by 5
In ΔFGH, \text{m}\angle F = (6x-14)^{\circ}m∠F=(6x−14) ∘ , \text{m}\angle G = (4x-8)^{\circ}m∠G=(4x−8) ∘ , and \text{m}\angle H = (x+15)^{\circ}m∠H=(x+15) ∘ . Find \text{m}\angle F.M∠F.
Answer:
[tex]\angle F =\bold{88^\circ}[/tex]
Step-by-step explanation:
Given a [tex]\triangle FGH[/tex] with the following angles:
[tex]\text{m}\angle F = (6x-14)^{\circ}[/tex]
[tex]\text{m}\angle G = (4x-8)^{\circ}[/tex]
[tex]\text{m}\angle H = (x+15)^{\circ}[/tex]
To find:
[tex]\text{m}\angle F[/tex] = ?
Solution:
Here, we can simply use the angle sum property of a triangle to find the value of [tex]\text{m}\angle F[/tex].
As per the angle sum property of a triangle, the sum of all the interior angles a triangle is equal to [tex]180^\circ[/tex].
[tex]\angle F + \angle G + \angle H = 180^\circ[/tex]
Putting all the given values in the above equation, we get:
[tex](6x-14)^{\circ} + (4x-8)^{\circ} + (x+15)^{\circ} = 180^\circ\\\Rightarrow 11x-7=180^\circ\\\Rightarrow 11x=180+7\\\Rightarrow 11x=187\\\Rightarrow x = \bold{17}[/tex]
Putting the value of [tex]x[/tex] in [tex]\angle F[/tex]
[tex]\text{m}\angle F = (6x-14)^\circ\\\Rightarrow \text{m}\angle F = (6\times 17-14)^\circ\\\Rightarrow \text{m}\angle F = \bold{88^\circ}[/tex]
A car travels at a constant speed of 45 km per hour for 5 min each wheel has a radius of 25 centimeters calculate the number of complete revolutions that the wheel makes in 5 min
Answer:
477.47 revolutions
Step-by-step explanation:
From the information given:
The formula for calculating the circumference = 2π r
Given that the radius of each wheel = 25 centimeter
Then, the circumference = 2 π (25)
= 50π cm
The distance traveled in 5 minutes is as follows:
Given that:
The speed = 45 km/ hour
i.e.
1 hour = 45 km
In an hour, we have 60 minutes
So, 60 minutes = 45 km
1 minute = 45/60 = 0.75 km
To cm;
0.75 km = (0.75 × 1000) m = 750 m
750 m = 750 × 100 = 75,000 cm
∴
The number of revolution in 5 minutes sInce 1 revolution = 50π cm is:
= 75,000 cm/ 50π cm
= 477.47 revolutions in 5 minutes
Sally paid $2.40 for 4 ounces of cinnamon. If there are 16 ounces in 1 pound, how much does cinnamon cost per pound
Answer:
$12.80 per pound
Step-by-step explanation:
Since there are 16 ounces in 1 pound, we multiply $0.80 by 16 ounces to find how much cinnamon costs per pound. The answer is $12.80.
Hope this helped, Have a Wonderful Day!!
Answer:
$9.60 per pound
Step-by-step explanation:
- 4 ounces = 2.40 each
- 2.40 x 4 (4 because 4x4 is 16 and there are 16 ounces in a pound)
= $9.60
Three ballet dancers are positioned on stage. Greta is straight behind Bryan and directly left of Alice. If Bryan and Greta are 12 meters apart, and Alice and Bryan are 13 meters apart, what is the distance between Greta and Alice?
Answer:
12
Step-by-step explanation:
A local charity receives 13of a fundraiser during a craft fair and a bake sale. The total amount given to charity was $137.45. How much did the bake sale raise?
Complete question :
A local Charity receives 1/3 of funds raised during a craft fair and bake sale. The total amount given to the charity was $137.45. How much did the bake sale raise
Answer:
$412.35
Step-by-step explanation:
Given that:
Fraction Given to charity from bake sale = 1/3 of amount raised
Amount given to charity = $137.45
Let amount raised from bake sale = x
Hence,
1/3 of x = 137.45
x / 3 = 137.45
x = 137.45 * 3
x = $412.35
Amount raised from bake sale = $412.35
Simplify this expression.
–6w + (–8) + 1 + (–7w)
A. –w – 7
B. –13w – 7
C. w + 9
D. 13w + 9
HELP ME PLEASE
Answer:
B. -13w - 7
Step-by-step explanation:
Combine -6w and -7w together to get -13w as the first part of your answer since you are subtracting from a negative to get a negative answer and combine -8 and 1 together to get -7 since you are adding 1 from -8 to go up.
Answer:
d
Step-by-step explanation:
A train leaves at 5.35 and arrives at 18.20 how long its journey . how long is the journey
Answer:
13 hours 55 minutes
Step-by-step explanation:
A train leaves at 5:35
The train arrives at its destination at 18:20
Therefore the time interval between 5:35 and 18:20 is
13 hours 55 minutes
Hence the journey is 13 hours 55 minutes long
If A = 50 degrees, B = 62 degrees, and a = 4, find b.
Round to the nearest tenth.
Answer:
[tex]b \approx 4.6[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Pre-Calculus
Law of Sines: [tex]\frac{sin(A)}{a} = \frac{sin(B)}{b}[/tex]Step-by-step explanation:
Step 1: Define
A = 50°
B = 62°
a = 4
Step 2: Solve for b
Substitute [LOS]: [tex]\frac{sin(50)}{4} = \frac{sin(62)}{b}[/tex]Cross-multiply: [tex]bsin(50) = 4sin(62)[/tex]Isolate b: [tex]b = \frac{4sin(62)}{sin(50)}[/tex]Evaluate: [tex]b = 4.61042[/tex]Round: [tex]b \approx 4.6[/tex]At the beginning of the month, Rachel's Used Car Dealership had 80 cars on
the lot. Today, there are 100 cars on thelot. What is the percent change in the
number of cars on the lot this month?"
Answer:
25%
Step-by-step explanation:
Solve for x.
7 - (2x + 11) + 3(3 - x) = 20
Answer:
your answer should be x = -3
Answer:
x=-3
Step-by-step explanation:
7-2x-11+9-3x=20
5-5x=20
-5x=15
x=-3
What is the equation in point slope form of the line that passes through the point (1 , 8) and (2 , 10)?
y-8=2(x-1)
y+8=2(x+1)
y=2x-7
2x-y=7
Help please !! Right answer
Answer:
6^10
Step-by-step explanation:
Answer:
6¹⁹
Step-by-step explanation:
2 + 11 + 3 = 6¹⁹
if A is= 31×37 to the power of 2, how many factors does A have
Answer:
A has 3 factors: 31 x 37 x 37
Step-by-step explanation:
31 and 37 are prime numbers so there are no other factors. due to the square the factor 37 shows up twice.
Use substitution to solve the system of equations.
x-2y=1
3x-6y=3
In the coordinate plane, the point A, 4− 2 is translated to the point A′, 1− 5. Under the same translation, the points B, 7− 4 and C, 2− 5 are translated to B′ and C′, respectively. What are the coordinates of B′ and C′?
Answer:
The coordinates of B' and C' are [tex]B'(x,y) = (4, -7)[/tex] and [tex]C'(x,y) = (-1, -8)[/tex], respectively.
Step-by-step explanation:
From the Linear Algebra, we define the translation of a given point as:
[tex]O'(x,y) = O(x,y) + T(x,y)[/tex] (1)
Where:
[tex]O(x,y)[/tex] - Original point, dimensionless.
[tex]T(x,y)[/tex] - Translation vector, dimensionless.
[tex]O'(x,y)[/tex] - Translated point, dimensionless.
If we know that [tex]A'(x,y) = (1, -5)[/tex] and [tex]A(x,y) = (4,-2)[/tex], then the translation vector is:
[tex]T(x,y) = A'(x,y)-A(x,y)[/tex] (2)
[tex]T(x,y) = (1,-5)-(4,-2)[/tex]
[tex]T(x,y) = (-3,-3)[/tex]
If we know that [tex]B(x,y) = (7,-4)[/tex], [tex]C(x,y) = (2,-5)[/tex] and [tex]T(x,y) = (-3,-3)[/tex], then the translated points are, respectively:
[tex]B'(x,y) = B(x,y)+T(x,y)[/tex] (3)
[tex]B'(x,y) = (7,-4) +(-3,-3)[/tex]
[tex]B'(x,y) = (4, -7)[/tex]
[tex]C'(x,y) = C(x,y) +T(x,y)[/tex]
[tex]C'(x,y) = (2,-5) + (-3,-3)[/tex]
[tex]C'(x,y) = (-1, -8)[/tex]
The coordinates of B' and C' are [tex]B'(x,y) = (4, -7)[/tex] and [tex]C'(x,y) = (-1, -8)[/tex], respectively.
Factorise y² + 5y-84
Answer:
(y-7) (y+12)
Step-by-step explanation:
Factor y2+5y−84y2+5y-84 using the AC method.
Mario spent $23.85 at the bookstore on one book and some magazines. The book cost $12.60 and the magazines cost $2.25 each. How many magazines did Mario buy?
Answer:
Mario brought 5 magazines
Step-by-step explanation:
If you just add $12.60 and $2.25 together then keep adding $2.25 until you get to $23.85, you'll get your answer.
So like,
(1) 12.60 + 2.25 = 14.85
(2) 14.85 + 2.25 = 17.1
(3) 17.1 + 2.25 = 19.35
(4) 19.35 + 2.25 = 21.6
(5) 21.6 + 2.25 = 23.85
So the total would be 5. Mario bought 5 magazines.
8 1/4 x 1 7/11 as a whole number
Answer:
(I don't know what you mean) but the answer to that question would be 13.5 or 13 and a half
Step-by-step explanation:
Please can I have an explanation also, I am terrible at these kinds of questions!
Q- A bag contain red, yellow and blue beads.
The ratio of red beads to yellow beads is 2:3
The ratio of yellow beads to blue beads is 5:4
Work out what fraction of the beads are red.
Answer:
The fraction of the beads that are red is
Step-by-step explanation:
Algebraic Expressions
A bag contains red (r), yellow (y), and blue (b) beads. We are given the following ratios:
r:y = 2:3
y:b = 5:4
We are required to find r:s, where s is the total of beads in the bag, or
s = r + y + b
Thus, we need to calculate:
[tex]\displaystyle \frac{r}{r+y+b} \qquad\qquad [1][/tex]
Knowing that:
[tex]\displaystyle \frac{r}{y}=\frac{2}{3} \qquad\qquad [2][/tex]
[tex]\displaystyle \frac{y}{b}=\frac{5}{4}[/tex]
Multiplying the equations above:
[tex]\displaystyle \frac{r}{y}\frac{y}{b}=\frac{2}{3}\frac{5}{4}[/tex]
Simplifying:
[tex]\displaystyle \frac{r}{b}=\frac{5}{6} \qquad\qquad [3][/tex]
Dividing [1] by r:
[tex]\displaystyle \frac{r}{r+y+b}=\displaystyle \frac{1}{1+y/r+b/r}[/tex]
Substituting from [2] and [3]:
[tex]\displaystyle \frac{r}{r+y+b}=\displaystyle \frac{1}{1+3/2+6/5}[/tex]
Operating:
[tex]\displaystyle \frac{r}{r+y+b}=\displaystyle \frac{1}{\frac{10+3*5+6*2}{10}}[/tex]
[tex]\displaystyle \frac{r}{r+y+b}=\displaystyle \frac{10}{10+15+12}[/tex]
[tex]\displaystyle \frac{r}{r+y+b}=\displaystyle \frac{10}{37}[/tex]
The fraction of the beads that are red is [tex]\mathbf{\frac{10}{37}}[/tex]
multiply this please
Answer: C is the answer hope this helps!
Step-by-step explanation: Merry Christmas!
Answer:
A. 12x^4 + 10x^3 - 22x^2 - 15x
Step-by-step explanation:
(6x^2 - 4x - 5)(2x^2 + 3x)
2x^2 (6x^2 - 4x - 5) + 3x(6x^2 - 4x - 5)
12x^4 - 8x^3 - 10x^2 + 18x^3 - 12x^2 -15x
12x^4 + 10x^3 - 22x^2 - 15x
402 = 2 x 3 x ____
help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
67
Step-by-step explanation:
2x3=6
402/6=67
2x3x67=402
hope this helped:)
HELP !!!!!!! Speed = Distance divided by Time. A Race-car traveling at 75 miles an hour for 4 hours would travel... * THIS IS A REBEMTION TEST 275 miles 300 miles 325 miles 350 miles
compare the graph of g(x)=6x−5 to the graph of f(x)=6x
a. g(x) shifted up 5 units
b. g(x) shifted down 5 units
c. g(x) is 6 units steeper
d. f(x) shifted down 5 units
Answer:
D
Step-by-step explanation:
Here, we want to compare the graph of g(x) and f(x)
Looking at the given equations, the difference between the two is that we have 5 subtracted from one of the equations
What this means is that we are moving down 5 units away from the graph of f(x) to get the graph of g(x)
Thus, option D is the correct answer
Question 11
Write the following in order of size, largest first.
sin 1580
cos 1589
cos 38°
sin 38
Answer:
cos 38, sin 38, sin 1580, cos 1589
simply cscx*cosx+cotx/secx*cotx
Answer: is that the question??
Step-by-step explanation:
What is the slope of the line that passes through the points
(8,−4) and (6,2)? Write your answer in simplest form.
Answer: -3
Step-by-step explanation:
(this is just my way):
1. First create an equation: 2-(-4) over 6-8
2. Simplify: 6/-2 => -3
Tada, you already go your slope
Have a nice day :)