Answer: 24,000 tickets
Step-by-step explanation: The idea is just to round up the original ticket sold to the nearest thousand. That is 23,847 tickets to the nearest thousand is 24,000 since the next number after 3 is 8 which is greater or equal to five so you take it as 1 and add it to 3 making the total number of tickets sold as 24,000.
Universal pet house sells vinyl doghouses and treated lumber doghouses. It takes the company 5 hours to build a vinyl doghouse and 2 hours to build a treated lumber doghouse
Answer:
Step-by-step explanation:
What is the question
What is the equation of the circle with center (1, −1) that passes through the point (5, 7)?
Find all solutions to the equation in the interval [0, 2π). (3 points) sin 2x - sin 4x = 0
pi divided by six , pi divided by two , five pi divided by six , seven pi divided by six , three pi divided by two , eleven pi divided by six
0, pi divided by six , pi divided by two , five pi divided by six , π, seven pi divided by six , three pi divided by two , eleven pi divided by six
0, two pi divided by three , four pi divided by three
0, pi divided by three. , two pi divided by three. , π, four pi divided by three. , five pi divided by three.
To solve the equation sin 2x - sin 4x = 0, we apply the identity for the difference of two sines and set each term equal to zero. The solutions in the interval [0, 2π) are x = 0, π/6, 5π/6, π.
The equation given is sin 2x - sin 4x = 0. To find the solutions to this equation in the interval [0, 2π), we can use the trigonometric identity for the difference of two sines, sin A - sin B = 2 sin((A - B)/2) cos((A + B)/2). Applying this identity:
2 sin(-2x/2) cos(6x/2) = 0
2 sin(-x) cos(3x) = 0
Since sin(-x) = -sin(x), we can rewrite the equation further:
-2 sin(x) cos(3x) = 0
To find the solutions, set each part equal to zero:
sin(x) = 0
cos(3x) = 0
For sin(x) = 0, the solutions in [0, 2π) are x = 0, π, 2π. However, since the interval is [0, 2π), 2π is not included.
For cos(3x) = 0, the solutions are x = π/6, 5π/6 since cos(x) has a period of 2π and 3x adds additional repetitions of the solutions in the interval.
The complete set of solutions in the interval [0, 2π) are therefore:
0
π/6
5π/6
π
Someone please help me... I need it with step by step explanation!
Assuming it is .005y^2 + 10y not .005*y*2 + 10y
Profit = Revenue - Cost
Profit = (.005y^2 + 10y) - (20y + 1,000,000)
Profit at 30,000 cars so y = 30000
Profit = (.005(30000)^2 + 10(30000)) - (20(30000) + 1,000,000)
Profit = $3,200,000
Find the derivative of f(x) = 5 divided by x at x = -1. (1 point)
Answer:
-5
Step-by-step explanation:
The power rule can be used.
f(x) = 5x^-1
f'(x) = 5(-1)x^(-1-1)
f'(x) = -5x^-2
Then ...
f'(-1) = -5(-1)^-2
f'(-1) = -5
_____
The attached graph shows the value of the derivative at x=-1, along with a tangent line having that slope at the point (-1, f(-1)).
Prime numbers problem
Answer:
The answer to your question is 2² 3² or (4)(9)
Step-by-step explanation:
Data
factor 36
Process
1.- Divide 36 by prime numbers starting from 2, then 3, 5, 7, etc.
36 2
18 2
9 3
3 3
1
2.- Write 36 as a composition of prime numbers
36 = 2²3²
3.- The prime factors of 36 are 2² x 3²
Solve the following equation: [tex]p-\frac{1}{4} = \frac{7}{8}[/tex]
The solution for the equation is [tex]p=\frac{9}{8}[/tex]
Explanation:
The given equation is [tex]p-\frac{1}{4}=\frac{7}{8}[/tex]
We need to solve the equation.
The solution of the equation can be determined by finding the value for p.
Thus, from the equation, let us add both sides of the equation by [tex]\frac{1}{4}[/tex]
Hence, we have,
[tex]p-\frac{1}{4}+\frac{1}{4}=\frac{7}{8}+\frac{1}{4}[/tex]
Simplifying the equation, we get,
[tex]p=\frac{7}{8}+\frac{1}{4}[/tex]
Taking LCM for 4 and 8, we get,
[tex]p=\frac{7+2}{8}[/tex]
Adding the numerator, we have,
[tex]p=\frac{9}{8}[/tex]
Thus, the value of p is [tex]p=\frac{9}{8}[/tex]
Hence, the solution for the equation is [tex]p=\frac{9}{8}[/tex]
A researcher selects a sample of 25 participants from a population with a mean of 20 and a standard deviation of 10. What is the range of values for the sample mean that fall within 1 standard error of the mean in a sampling distribution?
Answer:
The range of values for the sample mean is between a lower limit of 19 and an upper limit of 21.
Step-by-step explanation:
sample mean = 20
sd = 10
n = 25
standard error = 1
Lower limit of sample mean = sample mean - standard error = 20 - 1 = 19
Upper limit of sample mean = sample mean + standard error = 20 + 1 = 21
The range of values for the sample mean is between 19 and 21.
Half of Frank's weight added to Gary's weight equals 234. Half of Gary's weight added to Frank's weight is equal to 222 pounds. How much does Gary weigh?
Answer:
164 pounds
Step-by-step explanation:
Please see attached picture for full solution.
There are 5 blue chips, 4 red chips and 3 yellow chips in a bag. One chip is drawn from the bag. That chip is placed back into the bag, and a second chip is drawn. What is the probability that the two selected chips are of different colors? Express your answer as a common fraction.
The probability of drawing two chips of different colors from the bag is 35/33.
The probability of drawing the chips:
Calculate the total number of ways to draw 2 chips: 12 chips total, so 12C2 = 66 ways.
Calculate the number of ways to draw 2 chips of different colors: (5 blue chips × 7 non-blue chips) + (7 non-blue chips × 5 blue chips) = 70 ways.
Probability = Number of favorable outcomes / Total outcomes = 70/66 = 35/33.
the probability that the two selected chips are of different colors is [tex]\( \frac{94}{144} \), which simplifies to \( \frac{47}{72} \).[/tex]
To find the probability that the two selected chips are of different colors, we can use the concept of complementary probability.
The complementary event of selecting two chips of different colors is selecting two chips of the same color.
Let's calculate the probability of selecting two chips of the same color and then subtract that from 1 to find the probability of selecting two chips of different colors.
1. Probability of selecting two blue chips:
[tex]\[ P(\text{blue, blue}) = \frac{5}{12} \times \frac{5}{12} = \frac{25}{144} \][/tex]
2. Probability of selecting two red chips:
[tex]\[ P(\text{red, red}) = \frac{4}{12} \times \frac{4}{12} = \frac{16}{144} \][/tex]
3. Probability of selecting two yellow chips:
[tex]\[ P(\text{yellow, yellow}) = \frac{3}{12} \times \frac{3}{12} = \frac{9}{144} \][/tex]
Now, let's add these probabilities together because any of these scenarios results in two chips of the same color:
[tex]\[ P(\text{same color}) = P(\text{blue, blue}) + P(\text{red, red}) + P(\text{yellow, yellow}) \]\[ P(\text{same color}) = \frac{25}{144} + \frac{16}{144} + \frac{9}{144} = \frac{50}{144} \][/tex]
Finally, we subtract this probability from 1 to find the probability of selecting two chips of different colors:
[tex]\[ P(\text{different colors}) = 1 - P(\text{same color}) \]\[ P(\text{different colors}) = 1 - \frac{50}{144} = \frac{144}{144} - \frac{50}{144} = \frac{94}{144} \][/tex]
So, the probability that the two selected chips are of different colors is [tex]\( \frac{94}{144} \), which simplifies to \( \frac{47}{72} \).[/tex]
What value of x satisfies the equation x + 3 = -(x + 1)? a. x = 8
b.x = 8/3
c.x=-8/3
d.x=-8
The solution to the equation x + 3 = -(x + 1) is x = -2, which is not listed among the provided options. There may be an error in the question or provided options.
Explanation:To find the value of x that satisfies the equation x + 3 = -(x + 1), we need to solve for x.
First, expand the right side of the equation: x + 3 = -x - 1. Then, add x to both sides of the equation to get 2x + 3 = -1. Finally, subtract 3 from both sides to obtain 2x = -4. Dividing both sides by 2 yields x = -2.
Upon examining the options provided, none of them match our solution. Therefore, there must be a mistake in the provided options or in the question as posed, because our correct solution is x = -2. This means the correct answer is not listed among the options a. x = 8, b. x = 8/3, c. x = -8/3, or d. x = -8.
Which expression is a sum of cubes?
A) -27a^ b^6 + 8a^9 b^12
B) -9a^3 b^6 + a^9 b^10
C) 9a^3 b^6 + 8a^9 b^12
D) 27a^3 b^6 + 8a^9 b^12
[tex]A) -27a^3 b^6 + 8a^9 b^{12}\\D) 27a^3 b^6 + 8a^9 b^{12}[/tex]
Step-by-step explanation:
Here, the given expressions are:
[tex]A) -27a^3 b^6 + 8a^9 b^{12}\\= (-3)^3(a^3)(b^2)^3 + (2)^3(a^3)3(b^4)^3\\= (-3ab^2)^3 +(2a^3b^4)^3[/tex]
So, the above expression is "sum of cubes".
[tex]B) -9a^3 b^6 + a^9 b^{10}\\[/tex]
But (-9) can not be expressed as a Perfect cube root.
So, the above expression is not "sum of cubes".
[tex]C) 9a^3 b^6 + 8a^9 b^{12}\\[/tex]
But (9) can not be expressed as a Perfect cube root.
So, the above expression is not "sum of cubes".
[tex]D) 27a^3 b^6 + 8a^9 b^{12}\\\\= (3)^3a^3(b^2)^3 + (2)^3(a^3)^3(b^4)^3\\= (3ab^2)^3+ (2a^3b^4)^3[/tex]
So, the above expression is "sum of cubes".
A common computer programming rule is that names of variables must be between one and eight characters long. The first character can be any of the 26 letters, while successive characters can be any of the 26 letters or any of the 10 digits. For example, allowable variable names include A, BB, and M3477K. How many different variable names are possible? (Ignore the difference between uppercase and lowercase letters.)
Answer:
Total number of possibilities 2,095,681,645,538.
Step-by-step explanation:
The variables can be 1 to 8 characters long.
The first space can be filled by any of the 26 letters.
The remaining n places can be filled by any of the 26 letters or any of the 10 digits.
For a single character variable the number of ways to select a variable name is,
n (1 character) = 26
For two character variable the number of ways to select a variable name is,
n (2 character) = 26 × 36 = 936
For three character variable the number of ways to select a variable name is,
n (3 character) = 26 × 36 × 36 = 26 × 36² = 33,696
For four character variable the number of ways to select a variable name is,
n (4 character) = 26 × 36 × 36 × 36 = 26 × 36³ = 1,213,056
And so on.
Similarly for the eight character variable the number of ways to select a variable name is,
n (8 character) = 26 × 36 × 36... × 36 = 26 × 36⁷ = 2,037,468,266,496
Total number of possibilities 2,095,681,645,538.
If an object is shot upward with an initial velocity, v 0 v0 , in feet per second (ft/s), the velocity, v, in ft/s is given by the formula v= v 0 −32t v=v0−32t , where t is time in seconds. Find the initial velocity of an object if the velocity after 3 3 seconds is 28ft/s 28ft/s
We are given a velocity equation, and from that, we want to find the initial velocity such that we know the velocity for a given time.
We will see that the initial velocity is 124 ft/s
-------------------------------
Let's see how to solve this:
We have that the velocity equation:
v(t) = v₀ - (32 ft/s^2)*t
Where I added the units of the gravitational acceleration, which are in ft over seconds squared.
We want to get the value of the initial velocity, v₀, given that after 3 seconds the velocity is 28ft/s.
This means that:
v(3s) = 28 ft/s = v₀ - (32 ft/s^2)*3s
We can solve this for v₀:
28 ft/s = v₀ - (32 ft/s^2)*3s
28 ft/s + (32 ft/s^2)*3s = v₀
124 ft/s = v₀
So we can see that the initial velocity is 124 ft/s
If you want to learn more, you can read:
https://brainly.com/question/9163788
Suppose that 4 fair coins are tossed. Let Equals The event that exactly 2 coins show tails and Equal The event that at least 2 coins show tails. Find Upper P (Upper E | Upper F )and Upper P (Upper E | Upper F prime ).
Answer:
a) P ( E | F ) = 0.54545
b) P ( E | F' ) = 0
Step-by-step explanation:
Given:
- 4 Coins are tossed
- Event E exactly 2 coins shows tail
- Event F at-least two coins show tail
Find:
- Find P ( E | F )
- Find P ( E | F prime )
Solution:
- The probability of head H and tail T = 0.5, and all events are independent
So,
P ( Exactly 2 T ) = ( TTHH ) + ( THHT ) + ( THTH ) + ( HTTH ) + ( HHTT) + ( HTHT) = 6*(1/2)^4 = 0.375
P ( At-least 2 T ) = P ( Exactly 2 T ) + P ( Exactly 3 T ) + P ( Exactly 4 T) = 0.375 + ( HTTT) + (THTT) + (TTHT) + (TTTH) + ( TTTT)
= 0.375 + 5*(1/2)^4 = 0.375 + 0.3125 = 0.6875
- The probabilities for each events are:
P ( E ) = 0.375
P ( F ) = 0.6875
- The Probability to get exactly two tails given that at-least 2 tails were achieved:
P ( E | F ) = P ( E & F ) / P ( F )
P ( E | F ) = 0.375 / 0.6875
P ( E | F ) = 0.54545
- The Probability to get exactly two tails given that less than 2 tails were achieved:
P ( E | F' ) = P ( E & F' ) / P ( F )
P ( E | F' ) = 0 / 0.6875
P ( E | F' ) = 0
HRLP HELP HELP!!!!! nearest foot
The horizontal distance the plane has covered is 3940 feet
Explanation:
The plane makes an angle 10° with the ground when it took off from the field.
We need to find the horizontal distance the plane when it has flown 4000 feet.
The length of the hypotenuse is 4000 feet.
Let the horizontal distance be x.
We shall find the value of x using the cosine formula.
The formula is given by
[tex]cos \theta=\frac{adj}{hyp}[/tex]
Substituting the values, we have,
[tex]cos \ 10^{\circ}=\frac{x}{4000}[/tex]
Substituting the value for cos 10°, we get,
[tex]0.985=\frac{x}{4000}[/tex]
Multiplying both sides of the equation by 4000, we get,
[tex]0.985\times 4000=x[/tex]
Simplifying, we get,
[tex]3940=x[/tex]
Thus, the horizontal distance the plane has covered is 3940 feet
plz help i really need it
Answer:
y=\frac{1}{8}x+4
Step-by-step explanation:
first, we can quickly get rid of options 1 and 2, since the y-intercept is not -4, but +4.
this leaves us with options 3 and 4.
we can rule out option3, since the slope is not 4, but 1/8.
hope this helps :)
please help!
"solving proportions" is what needs done
please show all work clearly!
23) x = [tex]\frac{-60}{9}[/tex] = -6.666.
24) x = [tex]\frac{-12}{7}[/tex] = -1.7142.
25) x = [tex]\frac{-37}{5}[/tex] = -7.4.
Step-by-step explanation:
Step 1; For [tex]\frac{x+6}{3}[/tex] = [tex]\frac{x+4}{12}[/tex], we cross multiply the denominators and get,
3 × (x + 4) = 12 × (x + 6),
3x + 12 = 12x + 72.
We take all the x terms to the LHS and keep the constants on the RHS.
3x - 12x = 72 - 12,
-9x = 60, x = [tex]\frac{-60}{9}[/tex] = -6.6666.
Step 2; For [tex]\frac{-5}{x-4}[/tex] = [tex]\frac{9}{x+12}[/tex], we cross multiply the denominators and get,
-5 × (x + 12) = 9 × (x - 4),
-5x - 60 = 9x - 36.
We take all the x terms to the LHS and keep the constants on the RHS.
-5x - 9x = -36 + 60,
-14x = 24, x = [tex]\frac{-24}{14}[/tex] = -1.7142.
Step 3; For [tex]\frac{6}{11}[/tex] = [tex]\frac{x-1}{x-8}[/tex], we cross multiply the denominators and get,
6 × (x - 8) = 11 × (x - 1),
6x - 48 = 11x - 11.
We take all the x terms to the LHS and keep the constants on the RHS.
6x - 11x = -11 + 48,
-5x = 37, x = [tex]\frac{-37}{5}[/tex] = -7.4.
Rectangle N has an area of 5 square units. James drew a scaled version of Rectangle N and labeled it P. What scale factor did James use to go from Rectangle N to Rectangle P
Answer:3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
khan acadamy hope this helps
A ladder 5 feet long leans against a wall and makes an angle of 65% with the ground. a. Find, to the nearest tenth of a foot, the distance from the wall to the base of the ladder.
Answer: 2.1 feet
Step-by-step explanation:
The ladder forms a right angle triangle with the wall and the ground. The length of the ladder represents the hypotenuse of the right angle triangle. The height from the top of the ladder to the base of the wall represents the opposite side of the right angle triangle.
The distance, d from the bottom of the ladder to the base of the wall represents the adjacent side of the right angle triangle.
To determine the distance, d from the bottom of the ladder to the base of the wall, we would apply we would apply the cosine trigonometric ratio.
Cos θ = adjacent side/hypotenuse. Therefore,
Cos 65 = d/5
d = 5Cos 65 = 5 × 0.4226
d = 2.1 feet
Which system of equations could be graphed to solve the equation below?
Answer:
B
Step-by-step explanation:
I think this is your full question and hope it is correct.
Which system of equations could be graphed to solve the equation below?
log(2x+1)=3x-2
A. y1=3x, y2=2x
B. y1=log(2x+1), y2=3x-2
C. y1=log2x+1, y2=3x-2
D. y1=log(2x+1+2), y2=3x
My answer:
We know that: log(2x+1)=3x-2 and they are a equation of log and linear so we need to make system of equation.
The left side is: [tex]y_{1}[/tex] => [tex]y_{1} = log( 2x+1)[/tex]
The right side is : [tex]y_{2} = 3x -2[/tex]
The system of equations are:
[tex]\left \{ {{y_{1} =log(3x+1)} \atop {y_{2} =3x -2}} \right.[/tex]
Now we have two new function with x and y.
The volume of a gas in a container at a constant temperature varies inversely as the pressure. The volume is 25 cubic centimeter at a pressure of 11 pounds. Use a proportion to find the pressure when the volume is 59 cubic centimeters.
Answer:
Pressure would be approximately 4.66 pounds.
Step-by-step explanation:
Given:
Volume of gas (V) = 25 cubic cm
Pressure of the gas (P) = 11 pounds
We need to find the pressure when volume is 59 cubic cm.
Solution:
Now Given:
[tex]V[/tex] ∝ [tex]\frac{1}{P}[/tex]
so we can say that;
[tex]V =\frac kP[/tex]
where k is a constant.
When V = 25 cubic cm, P =11 pounds.
[tex]25 = \frac{k}{11}\\\\k= 25\times 11 = 275\ cm^3.pounds[/tex]
So the equation becomes as.
[tex]V = \frac{275}{P}[/tex]
Now we need to find the pressure when Volume is 59 cubic cm.
[tex]59 =\frac{275}{P}\\\\P=\frac{275}{59}\\\\P\approx 4.66\ pounds[/tex]
Hence Pressure would be approximately 4.66 pounds.
Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even.
C(x)= 9000x +72,000
R(x)= 15,000x
Answer:
12
Step-by-step explanation:
15000x = 9000x +72000
6000x = 72000
x = 12
Answer: the number of units that must be sold to break even is 12
Step-by-step explanation:
The cost function is expressed as
C(x)= 9000x +72000
The revenue function is expressed as
R(x) = 15000x
Profit = Revenue - cost
At the point of break even, the total revenue is equal to the total cost. This means that profit is zero. The expression becomes
Revenue - cost = 0
Revenue = cost
R(x) = C(x)
Therefore,
15000x = 9000x +72000
15000x - 9000x = 72000
6000x = 72000
x = 72000/6000
x = 12
A pool charges $4 each visit or you can buy a membership. Right and solve an inequality to find how many times a person should use a pool so that the membership is less expensive than paying each time. Interpret the solution
The inequality is:
[tex]n > \frac{m}{4}[/tex]
Membership of the pool will be less expensive until number of visits to the pool is one fourth of the membership amount
Solution:
Given that,
A pool charges $4 each visit or you can buy a membership
Let "n" be the number of times you visit the pool
Let the membership amount of the pool be "m"
A pool charges $4 each visit
Therefore, cost for "n" visit is: $ 4n
The inequality showing that a membership is less expensive than paying each visit to the pool is:
4n > m
Divide both sides by "4"
[tex]n > \frac{m}{4}[/tex]
Therefore, membership of the pool will be less expensive until number of visits to the pool is one fourth of the membership amount
Help with this please! a, b, and c
Answer:
y = 3.6(sine( 6.2(x-4.2))+4.4
Step-by-step explanation:
(8.2-.6)/2 = altitude = 3.6
6.2 = Wavelength
(8.2+.6)/2 = 4.4 The "line" (the horizontal central line thingy whose name I forgot cuz it's 12:00)
4.2 = x shift
y = 3.6(sine( 6.2(x-4.2))+4.4
A painting is drawn on a cardboard 22cm long and 12cm wide such that there is a margin of 2.5 meter cm along each side. Find the total are of the margin
Answer:
[tex]\text{Area of margin}=145\text{ cm}^2[/tex]
Step-by-step explanation:
We have been given that a painting is drawn on a cardboard 22 cm long and 12 cm wide such that there is a margin of 2.5 meter cm along each side. We are asked to find the area of the margin.
The total area of the margin would be equal to area of whole cardboard minus area of painting.
[tex]\text{Area of whole cardboard}=22\text{ cm}\times 12\text{ cm}[/tex]
[tex]\text{Area of whole cardboard}=264\text{ cm}^2[/tex]
Since there is a margin of 2.5 meter cm along each side, so sides of painting would be 2,5 cm smaller on four sides. The sides painting would be [tex]22-5=17[/tex] and [tex]12-5=7[/tex].
[tex]\text{Area of painting}=17\text{ cm}\times 7\text{ cm}[/tex]
[tex]\text{Area of painting}=119\text{ cm}^2[/tex]
[tex]\text{Area of margin}=264\text{ cm}^2-119\text{ cm}^2[/tex]
[tex]\text{Area of margin}=145\text{ cm}^2[/tex]
Therefore, the total area of the margin is 145 squared cm.
Its 10 3/5 miles from Alston to Barton and 12 1/2 miles from Barton to Chester. The distance from Alston to Durbin, via barton and Chester, is 35 miles how far is it from Chester to durbin
Answer:
It is [tex]11\frac{9}{10}[/tex] miles far from Chester to Durbin.
Step-by-step explanation:
Given:
Its 10 3/5 miles from Alston to Barton and 12 1/2 miles from Barton to Chester. The distance from Alston to Durbin, via barton and Chester, is 35 miles.
Now, to find the distance from Chester to durbin.
Distance from Alston to Barton = [tex]10\frac{3}{5} =\frac{53}{5} \ miles.[/tex]
Distance from Barton to Chester = [tex]12\frac{1}{2}\ miles =\frac{25}{2} \ miles.[/tex]
As, given the distance from Alston to Durbin, via barton and Chester, is 35 miles.
Thus, the total distance = 35 miles.
So, we add the distance of Alston to Barton and Barton to Chester and get the distance from Alston to Chester:
[tex]\frac{53}{5} +\frac{25}{2}[/tex]
[tex]=\frac{106+125}{10}[/tex]
[tex]=\frac{231}{10} \ miles.[/tex]
Distance from Alston to Chester [tex]=\frac{231}{10} \ miles.[/tex]
Now, to get the distance from Chester to durbin we subtract distance from Alston to Chester from the total distance:
[tex]35-\frac{231}{10} \\\\=\frac{350-231}{10} \\\\=\frac{119}{10} \\\\=11\frac{9}{10}\ miles.[/tex]
Therefore, it is [tex]11\frac{9}{10}[/tex] miles far from Chester to Durbin.
I need help plz and I have to show work
This is a very simple and easy problem. I'm not sure why you need someone else to solve it, but I hope this helps
a. Linear equation:
Let x be amount of movies rented
$8 + ($2.50 * x)
b.
$8 + ($2.50 * 10)
= $8 + $25.0
= $33
Jake buys a fruit smoothie and a protein bar for $5.90. Kobe buys 2 fruit smoothies and 4 protein bars. He pays $16.80. What is the cost of each fruit smoothie and each protein bar?
Answer:
Fruit smoothie: $3.4
Protein bar: $2.5
Step-by-step explanation:
Let x represent cost of fruit smoothie and y represent cost of protein bar.
We have been given that Jake buys a fruit smoothie and a protein bar for $5.90. We can represent this information in an equation as:
[tex]x+y=5.90...(1)[/tex]
[tex]x=5.90-y...(1)[/tex]
We are also told that Kobe buys 2 fruit smoothies and 4 protein bars. He pays $16.80. We can represent this information in an equation as:
[tex]2x+4y=16.80...(2)[/tex]
Upon substituting equation (1) in equation (2), we will get:
[tex]2(5.90-y)+4y=16.80[/tex]
[tex]11.80-2y+4y=16.80[/tex]
[tex]2y=16.80-11.80[/tex]
[tex]2y=5[/tex]
[tex]y=\frac{5}{2}=2.5[/tex]
Therefore, each protein bar costs $2.5.
Upon substituting [tex]y=2.5[/tex] in equation (1), we will get:
[tex]x=5.90-2.5=3.4[/tex]
Therefore, each fruit smoothie costs $3.4.
Each fruit smoothie costs [tex]3.40\ dollars[/tex], and each protein bar costs [tex]2.50\ dollars[/tex].
To solve for the cost of each fruit smoothie [tex](\( x \))[/tex] and each protein bar [tex](\( y \))[/tex], we'll use the given system of equations:
1. [tex]\( x + y = 5.90 \)[/tex]
2. [tex]\( 2x + 4y = 16.80 \)[/tex]
Let's solve this step by step.
Step 1: Solve the first equation for [tex]\( x \)[/tex]
[tex]\[ x + y = 5.90 \][/tex]
[tex]\[ x = 5.90 - y \][/tex]
Step 2: Substitute [tex]\( x = 5.90 - y \)[/tex] into the second equation:
[tex]\[ 2(5.90 - y) + 4y = 16.80 \][/tex]
[tex]\[ 11.80 - 2y + 4y = 16.80 \][/tex]
[tex]\[ 2y = 16.80 - 11.80 \][/tex]
[tex]\[ 2y = 5 \][/tex]
[tex]\[ y = \frac{5}{2} \][/tex]
[tex]\[ y = 2.50 \][/tex]
Step 3: Substitute [tex]\( y = 2.50 \)[/tex] back into [tex]\( x = 5.90 - y \)[/tex]
[tex]\[ x = 5.90 - 2.50 \][/tex]
[tex]\[ x = 3.40 \][/tex]
Can someone help me on this?? I'm stuck!
Find the total area for the regular pyramid.
T. A. =
Answer:
[tex]TA=(144+36\sqrt{3})\ units^2[/tex]
Step-by-step explanation:
we know that
The total area or surface area of the regular pyramid is equal to the area of the triangular base plus the area of its three lateral triangular faces
so
step 1
Find the area of the triangular base B
Is an equilateral triangle
Applying the law of sines
[tex]B=\frac{1}{2}(12^2)sin(60^o)[/tex]
[tex]B=\frac{1}{2}(144)\frac{\sqrt{3}}{2}[/tex]
[tex]B=36\sqrt{3}\ units^2[/tex]
step 2
Find the area of the lateral triangular faces
[tex]A=3[\frac{1}{2}(12)h][/tex]
Find the height
Applying the Pythagorean Theorem
[tex]10^2=6^2+h^2[/tex]
[tex]h^2=100-36\\h^2=64\\h=8\ units[/tex]
Find the area of the lateral triangular faces
[tex]A=3[\frac{1}{2}(12)8]=144\ units^2[/tex]
therefore
The total area is
[tex]TA=(144+36\sqrt{3})\ units^2[/tex]