Answer:
[tex]\cos(\frac{1}{2}A) = {\frac{\sqrt{3}}{2}[/tex]
Step-by-step explanation:
Given
[tex]\cos A = \frac{1}{2}[/tex]
Required
Determine [tex]\cos(\frac{1}{2}A)[/tex]
To do this, we make use of the following identity
[tex]\cos(\frac{1}{2}A) = \sqrt{\frac{\cos A+1}{2}}[/tex]
Substitute: [tex]\cos A = \frac{1}{2}[/tex]
[tex]\cos(\frac{1}{2}A) = \sqrt{\frac{\frac{1}{2}+1}{2}}[/tex]
Solve the numerator
[tex]\cos(\frac{1}{2}A) = \sqrt{\frac{\frac{2+1}{2}}{2}}[/tex]
[tex]\cos(\frac{1}{2}A) = \sqrt{\frac{\frac{3}{2}}{2}}[/tex]
Rewrite as:
[tex]\cos(\frac{1}{2}A) = \sqrt{\frac{3}{2} * \frac{1}{2}}[/tex]
[tex]\cos(\frac{1}{2}A) = \sqrt{\frac{3}{4}}[/tex]
Take square roots
[tex]\cos(\frac{1}{2}A) = {\frac{\sqrt{3}}{2}[/tex]
Item 22
At the beginning of the week, a puppy weighed 514 pounds. During the week, the puppy gains 8 ounces.
How much does the puppy weigh, in pounds, at the end of the week?
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answer:
five and three fourths
Step-by-step explanation:
eight ounces is 0.5 of a pound with is half of a pound
Find the slope… and can u explain how u got it.. mark brainliest:)
Answer:
slope is (1,1) (0,3) just count number of squares, if there was an equation involved use y=mx+b
Step-by-step explanation:
A motorcycle can go 50 miles on 1 gallon of gas. How many gallons will be used to go 150 km? I mile is about 1.6 km. Round to the nearest gallon.
Answer:
1.875 gallons
Step-by-step explanation:
Data
distance = 50 mi
volume of gas = 1 gal
volume for 150 km = ?
Process
1.- Convert 50 mi into kilometers
1 mile ------------------- 1.6 km
x ------------------ 150 km
x = (150 x 1)/1.6
x = 93.75 mi
2.- Calculate the gallons wasted
1 gallon ----------------- 50 mi
x ---------------- 93.75 mi
x = (93.75 x 1)/50
x = 93.75/50
x = 1.875 gallons
Help help yes plsssssssss
What is the correct answer?
PLZZZ HELP FAST
what is the value of y
[tex]y ^3 = 5[/tex]
Answer: y= [tex]\sqrt[3]{5}[/tex]
Step-by-step explanation:
A quantity with an initial value of 7200 decays exponentially at a rate of 0.3% every
day. What is the value of the quantity after 10 weeks, to the nearest hundredth?
Answer:5834.36 You're welcome
Answer:5834.36
Step-by-step explanation:
Los boletos para la obra de teatro "Los Miserables" cuestan 15 dólares para adultos y 5 dólares para estudiantes. Si se vendieron 227 boletos y los ingresos fueron de 2,375 dólares. ¿Cuántos boletos de cada clase se vendieron?
Answer:
Se vendieron 124 boletos para adultos y 103 boletos para estudiantes.
Step-by-step explanation:
Un sistema de ecuaciones es un conjunto de ecuaciones con las mismas incógnitas. Un sistema de ecuaciones lineales es un sistema de ecuaciones en el que cada ecuación es lineal.
En otras palabras, un sistema de ecuaciones lineales es un conjunto de dos o más ecuaciones de primer grado, en el cual se relacionan dos o más incógnitas.
Resolver un sistema de ecuaciones significa encontrar valores para las incógnitas que hace verdadera cada una de las ecuaciones.
En este caso, las variables son:
x: cantidad de boletos para adultos.y: cantidad de boletos para estudiantes.Los boletos para la obra de teatro "Los Miserables" cuestan 15 dólares para adultos y 5 dólares para estudiantes. Si se vendieron 227 boletos y los ingresos fueron de 2,375 dólares, se puede expresar el siguiente sistema de ecuaciones:
[tex]\left \{ {{x+y=227} \atop {15*x+5*y=2375}} \right.[/tex]
Se elige resolver por el método de sustitución, cuyo primer paso consiste escoger una ecuación y despejar una incógnita en términos de la otra incógnita. En este caso, se despeja la variable "y" de la primer ecuación, obteniendo:
y=227 - x
A continuación se sustituye la expresión hallada en la otra ecuación, para obtener una ecuación con una incógnita y, luego despejar esa incógnita. En este caso, reemplazando la anterior expresión en la segunda ecuación del sistema de ecuaciones:
15*x + 5*(227 -x)= 2375
Resolviendo:
15*x + 5*227 - 5*x= 2375
15*x + 1135 - 5*x= 2375
15*x - 5*x= 2375 - 1135
10*x= 1240
x= 1240 ÷10
x= 124
Finalmente se sustituye el valor hallado en la expresión y=227 - x para despejar la incógnita restante:
y=227 - 124
y= 103
Entonces se vendieron 124 boletos para adultos y 103 boletos para estudiantes.
∠2 ≅ ∠ because they are corresponding angles of parallel lines cut by a transversal. ∠5 ≅ ∠ by the Vertical Angles Theorem.
*see diagram in the attachement below
Answer:
∠2 ≅ ∠6 because they are corresponding angles of parallel lines cut by a transversal. ∠5 ≅ ∠8 by the Vertical Angles Theorem.
Step-by-step explanation:
We are required to find the angle that is congruent to <2 and the angle that is congruent to <5.
Already, we are given the reasons to justify the answers we get.
Thus:
<2 has matching corner as <6. Hence they are corresponding angles
<5 and <8 are vertical angles having the same vertex and are directly opposite each other. Therefore, based on the vertical angles theorem, <5 ≅ <8
Given that the student chosen was a female, find the probability that the student chose invisibility as their superpower. P\left( \text{invisibility }| \text{ female} \right)=P(invisibility ∣ female
Answer:
[tex]P(Invisibility | Female) = \frac{2}{3}[/tex]
Step-by-step explanation:
Given
See attachment for two-way table
Required
Determine [tex]P(Invisibility | Female)[/tex]
This is calculated using the following formula for conditional probability:
[tex]P(Invisibility | Female) = \frac{n(Invisibility \& Female)}{n(Female)}[/tex]
From the attached table
[tex]n(Invisibility \& Female) = 32[/tex]
[tex]n(Female) = 48[/tex]
So, the equation becomes:
[tex]P(Invisibility | Female) = \frac{32}{48}[/tex]
Simplify
[tex]P(Invisibility | Female) = \frac{32/16}{48/16}[/tex]
[tex]P(Invisibility | Female) = \frac{2}{3}[/tex]
How many different sandwiches can be made from the following options?
4 types of bread
3 types of cheese
6 types of meat
a: 13
b: 72
C: 42
Answer:
72
Step-by-step explanation:
By using the fundamental counting principle, we can do 4 x 3 x 6 = 72 to find how many different sandwiches can be made.
k heres the actual question
Answer:
It's most likely spposed to be 22
Step-by-step explanation:
Answer: 91.65
Part 1: You will need to find the average by adding 108, 72, and 95. This will give you 275. Now you divide the sum by the amount of numbers there are which is 3 numbers. 275/3 would be 91.6
Part 2: Now that you have all four numbers you should repeat the process, 108 + 72 + 95 + 91.6 which is 366.6 now divide by four, and you have 91.65.
Let me know if this was correct!
Ok here is the question I need it answered fast I'll give brainliest!
The point P (x,y) lies on the terminal side of an angle 0= 195 in standard position. What are the signs of the value of x and y
Answer:
When we have a point (x, y), the angle that defines this point in polar coordinates is given by:
Tan(θ) = y/x
In this case, we know that θ = 195°
Then replacing that, we get:
Tan(195°) = y/x
0.268 = y/x
Now, there is a problem, we have a single equation and two variables.
So we will get:
y = (0.268)*x
This equation defines all the possible values that x and y could take such the angle in standard position is 195°.
So we only can conclude that:
x and y have the same sign.
For a given value of x, the correspondent y-value is:
y = (0.268)*x
1. Find mYX.
50 points if answer.
Answer:
m<YX=60° is a required answer
Answer:
m<YX=60° is a required answer
Step-by-step explanation:
You and a friend are playing a game of chance. Every time you roll (using a fair die) a 1, 2, 3, or 4, you are successful, and your friend will pay you $1. Every time you roll a 5 or 6, you must pay your friend $2. If 65% of your rolls are successful and 35% of your rolls are unsuccessful, how much money do you expect to have won/owe by the end of the game?
You owe 41 cents
You have won 5 cents
You owe 5 cents
You have won 41 cents
Answer:
you owe $5
Step-by-step explanation:
65% wins means $65
35% losses means -$70
Answer:
You owe 5 cents.
Step-by-step explanation:
(the amount of money won)(the number of successful rolls)+(the amount of money lost)(the number of unsuccessful rolls)=expected value
65% of rolls are successful which means that 13/20 of the rolls are successful (simply convert to a fraction).
35% of the rolls are unsuccessful which means that 7/20 of the rolls are unsuccessful.
Using the equation above we can use,
(1)(13/20)+(-2)(7/20)
to find the expected value.
(1)(13/20)+(-2)(7/20)=0.05
What is the value of x?
Answer:
141°
Step-by-step explanation:
The sum of the internal angles can be calculated using the following formula:
(number of sides - 2) x 180°
This polygon has 7 sides, so (7 - 2) x 180° = 900° total internal angle.
Subtract the other given angles from 900°.
(900 - 131 - 122 - 125 - 148 - 107 - 126)° = 141°
Answer:
x equals 141°
Step-by-step explanation:
The sum of interior angles of this figure is 900°. This was found using the formula (n-2) x 180 where 'n' means number of sides. This figure has 7 sides. So the sum of interior angles would be:-
(7 - 2) x 180°
5 x 180°
= 900°
All the given angles + x gives 900°.
So, to find 'x' we can do the following:-
148° + 125° + 122° + 131° + x° + 126° + 107° = 900°
759 + x = 900
x = 900 - 759
x = 141°
Which equation represents a parabola opening to the right with a vertex at the origin and focus at (9,0) A. X = - 1/36y^2 B. X = - 1/6y^2 C. X = 1/36y^2 D. X = 1/6y^2
Answer:
Option C: x = (1/36)*y^2
Step-by-step explanation:
A horizontal parabola is written as
x = f(y) = a*y^2 + b*y + c
If a is positive, the parabola opens to the right.
if a is negative, the parabola opens to the left.
And the vertex of the parabola has the y-value:
y = -b/2a
and the x value
x = f(-b/2a)
For our parabola, we know that:
Opens to the right:
Then the only options left are:
C) x = (1/36)*y^2
D) x = (1/6)*y^2
Because in both cases b = 0, both of the equations have the vertex in the point (0, 0).
Now let's see wich one has a focus at (9, 0)
If the vertex of our equation is:
(h, k)
Then the focus will be:
(h + a, k)
Where a is the directrix of the equation.
Here we know that the vertex is (0, 0) and the focus is (9, 0)
Then:
(0 + a, 0) = (9, 0)
The directrix is 9.
And the directrix is such that:
(x - h)^2 = 4*a*(y - k)
Replacing the values of h and k (both are zero) we get:
x^2 = 4*a*y
And we know that: a = 9
x^2 = 4*9*y
x^2 = 36*y
if we isolate y, we get:
(1/36)*x^2 = y
This is option C.
Then the correct option is C.
2. Given: g(x) = x2
What is g(4) = ?
4
0
16
49
Answer:
16
Step-by-step explanation:
Simply plug 4 into g(x)
g(x) = x^2
g(4) = (4)^2 = 16
What is the median of the stem and lear plot
Answer:The median is the middle number of a set of data. The mode is the number that occurs the most in a set of data. You can use a stem-and-leaf plot to find the mean, median and mode of a set of data. ... Sometimes there will only be one number in the middle, and sometimes there will be two numbers
Step-by-step explanation:
The point B(-6, -2) is rotated 90° counterclockwise
coordinates of the resulting point, B'?
Answer:
(2, -6)
Step-by-step explanation:
Draw a picture woth a point at (-6, -2)
the rotate it.
Need help only on 12
Answer:
y = 3
Step-by-step explanation:
4 (1/2) + y = 10 (1/2)
2 + y = 5
-2 -2
y = 3
PLEASE HELP
Cal uses the equation y = 2.92
+ 2.4 to model his data. Use this equation to make the
following predictions.
Enter a number in each space provided
After 25 weeks, Cal will have saved a total of $____
The least number of whole weeks Cal must save to have a total of $100 saved is ____
Answer:
(a) $62.92 saved in 25 weeks
(b) 41 weeks to save $100
Step-by-step explanation:
Given
[tex]y = 2.92 + 2.4x[/tex]
[tex]x \to weeks[/tex]
[tex]y \to savings[/tex]
Solving (a): Savings in 25 weeks.
This means that: x = 25
So:
[tex]y = 2.92 + 2.4x[/tex]
[tex]y = 2.92 + 2.4 * 25[/tex]
[tex]y = 2.92 + 60[/tex]
[tex]y = 62.92[/tex]
Solving (b): Whole weeks to save $100
This means that x = 100
So:
[tex]y = 2.92 + 2.4x[/tex]
[tex]100 = 2.92 + 2.4x[/tex]
Collect like terms
[tex]2.4x = 100 - 2.92[/tex]
[tex]2.4x = 97.08[/tex]
Solve for x
[tex]x = 97.08/2.4[/tex]
[tex]x = 40.45[/tex]
Round up
[tex]x = 41[/tex]
What is the value of 3n +1 when n = 4?
A. 12
B. 13
C. 7
D. 8
Answer:
B. 13
Step-by-step explanation:
3(4) + 1 = 13
Answer:
13
Step-by-step explanation:
3n=3x4=12
12+1=13
A rock climber is standing at the edge of a cliff looking down into a valley and sees a lion laying 120 feet from
the base of the cliff. The angle of depression of the rock climber to the lion is 35º. How high is the cliff in feet?
What is the solution of the equation? √2x – 5+ 4 = x
Answer:
2x−1
Step-by-step explanation:
Kevin works at an electronics store. He is paid $500 every week plus a 4% commission on anything he sells. Select TWO statements about Kevin's weekly paycheck that are true.
A Kevin's paycheck is for $600 when he sells $250 of merchandise in a week.
B Kevin's paycheck is for $620 when he sells $600 of merchandise in a week.
C Kevin's paycheck is for $620 when he sells $3,000 of merchandise in a week.
D Kevin's paycheck is for $820 when he sells $800 of merchandise in a week.
E Kevin's paycheck is for $900 when he sells $10,000 of merchandise in a week.
F Kevin's paycheck is for $1,000 when he sells $1,250 of merchandise in a week.
Answer:
b) (d
Step-by-step explanation:
no words
Combine like terms in 3x + 2y + 2x + 4y + 1
Answer: 5x+6y+1 is the answer
Step-by-step explanation: to combine like terms that have to have the same variable so you can add them so for example you have 3x+2x which is equal to 5x then 2y+4y which is = to 6y and you also have 1 that isn't adding to anything because the others have variables
Answer:
5x + 6y + 1
Step-by-step explanation:
You are also simplifing and collecting the like terms. 3x + 2x = 5x. So that goes first as it appears first in the equation. Secondly, 2y + 4y = 6y, and that adds on to the previous answer. So far we have 5x + 6y. Now just add te 1, as it has no like value.
Help me - prime factorization of 136
Answer:
136 = 2³ x 17.
Step-by-step explanation: Factors of 136: 1, 2, 4, 8, 17, 34, 68, 136. Prime factorization: 136 = 2 x 2 x 2 x 17, which can also be written 136 = 2³ x 17.
(NEED DONE SOON) The measure of two supplementary angles are 4x - 24 and 4(2x - 3).
What is x
Answer:
X=18
Step-by-step explanation:
since angles are supplementary that means their sum is 180
[tex]4x - 24 + 4(2x - 3) = 180 \\ 4x - 24 + 8x - 12 = 180 \\ 12x - 36 = 180 \\ 12x = 216 \\ x = 18[/tex]