The cost of one granola bar is $0.60 and cost of one apple is $0.35
Step-by-step explanation:
Let,
Cost of one granola bar = x
Cost of one apple = y
According to given statement;
4x+y=2.75 Eqn 1
2x+3y=2.25 Eqn 2
Multiplying Eqn 2 by 2
[tex]2(2x+3y=2.25)\\4x+6y=4.50\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 1 from Eqn 3
[tex](4x+6y)-(4x+y)=4.50-2.75\\4x+6y-4x-y=1.75\\5y=1.75[/tex]
Dividing both sides by 5
[tex]\frac{5y}{5}=\frac{1.75}{5}\\y=0.35[/tex]
Putting y=0.35 in Eqn 2
[tex]4x+0.35=2.75\\4x=2.75-0.35\\4x=2.40[/tex]
Dividing both sides by 4
[tex]\frac{4x}{4}=\frac{2.4}{4}\\x=0.60[/tex]
The cost of one granola bar is $0.60 and cost of one apple is $0.35
Keywords: linear equation, elimination method
Learn more about elimination method at:
brainly.com/question/9196410brainly.com/question/9178881#LearnwithBrainly
The cost of one granola bar is $0.60, and the cost of one apple is $0.35.
To solve the problem, we need to set up a system of linear equations based on the information given:
Georgia paid $2.75 for 4 granola bars and 1 apple.
Addison paid $2.25 for 2 granola bars and 3 apples.
Let G be the cost of one granola bar and A be the cost of one apple.
4G + A = 2.75
2G + 3A = 2.25
Multiply the first equation by 3
3(4G + A = 2.75)
=> 12G + 3A = 8.25
(12G + 3A) - (2G + 3A) = 8.25 - 2.25
10G = 6
G = 0.60
Substitute the value of G back into the first equation,
4(0.60) + A = 2.75
2.40 + A = 2.75
A = 0.35
Therefore, the cost of one granola bar is $0.60 and the cost of one apple is $0.35.
Im in desperate need of help!
Answer:
umm, my regards, how should I help lol
Complete the following statement. The number of iPhones sold today at an Apple store is an example of ________ data.
a. interval,
b. classified as discrete ratio,
c. classified as continuous interval,
d. classified as continuous ratio,
e. classified as discrete
Answer: Option 'e' is correct.
Step-by-step explanation:
Since we know that
Discrete data are those data which is countable and it is expressed in exact numerical form.
Continuous data are those data which is lie within the interval and it varies so it does not expressed in exact numerical form.
Here, the number of iphones sold today at an Apple store is countable and it can be expressed in exact numbers.
So, it is considered as discrete.
Hence, Option 'e' is correct.
Final answer:
The number of iPhones sold today at an Apple store represents an example of quantitative discrete data.
Explanation:
The number of iPhones sold today at an Apple store is an example of classified as discrete data. This is because the number of iPhones can only take on specific numerical values and cannot be a fraction or a decimal. In other words, you cannot sell half an iPhone, so the data is quantitative discrete.
If you invested $100 at an interest rate of 5% per year compounded quarterly, how much will the investment be worth at the end of two years? *
50 points
Answer: the investment would be
$110.45
Step-by-step explanation:
Initial amount deposited into the account is $100 This means that the principal is
P = 100
It was compounded quarterly. This means that it was compounded 4 times in a year. So
n = 4
The rate at which the principal was compounded is 5%. So
r = 5/100 = 0.05
It was compounded for 2 years. So
t = 2
The formula for compound interest is
A = P(1+r/n)^nt
A = total amount in the account at the end of t years. Therefore
A = 100 (1+0.05/4)^4×2
A = 100 (1.0125)^8
A = $110.45
Out of 200 people sampled, 110 had kids. Based on this, construct a 95% confidence interval for the true population proportion of people with kids.
Answer:
From the sample of n= 200 people,
The proportion of people with kids is:
p'= 110/200= 0.55
The confidence interval for population proportion is given by:
[tex]p' - Z_{\alpha /2} \sqrt[]{\frac{p'(1-p')}{n} } } \leq P\leq p' + Z_{\alpha /2}\sqrt[]{\frac{p'(1-p')}{n} } }[/tex]
[tex]= p' - Z_{\alpha /2} \sqrt[]{\frac{0.55(0.45)}{200} } } \leq P \le p' + Z_{\alpha /2} \sqrt[]{\frac{0.55(0.45)}{200} } }[/tex]
[tex]= p' - Z_{\alpha /2} 0.0352} } } \leq P\le p' + Z_{\alpha /2} 0.0352} }[/tex]
Where P is the population proportion and Z is the critical value at a given level of significance α.
Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth. x2 – 6 = x
A. x = 2, 3
B. x = –2, 3
C. x = 2, –3
D. x = –2, –3.
Answer:
3, -2
Step-by-step explanation:
Can someone please help me with my homework page 17, 19, and 20. Thank you!
Answer:
17.B
19. C
20.C
Step-by-step explanation:
17.
[tex]\frac{m^2n^3}{p^3} \div \frac{mp}{n^2}\\=\frac{m^2n^3}{p^3} \times \frac{n^2}{mp}\\=\frac{mn^5}{p^4}[/tex]
19.
[tex]w^{2} +w-20=w^2+5w-4w-20=w(w+5)-4(w+5)=(w+5)(w-4)\\(w-3)(w-4)=w(w-4)-3(w-4)=w^2-4w-3w+12=w^2-7w+12\\reqd.~fraction ~is~ \frac{w^2-7w+12}{w^2+w-20}[/tex]
20.
[tex]\frac{w^2+5w+6}{w^2-w-12} =\frac{w^2+3w+2w+6}{w^2-4w+3w-12} =\frac{w(w+3)+2(w+3)}{w(w-4)+3(w-4)} =\frac{(w+3)(w+2)}{(w-4)(w+3)} =\frac{w+2}{w-4}[/tex]
Simplify the following expressions by combining like terms.
10z-11z+2-5=
Answer:
-1z-3
Step-by-step explanation:
10z-11z = -1z
+2-5= -3
= -z-3
Answer:
-z - 3
Step-by-step explanation:
10z - 11z + 2 - 5
Simplifying:
10z - 11z = -z
+2 - 5 = -3
Theresfore; 10z - 11z +2 - 5 = -z - 3
Write the expression in radical form. x 1/5
Answer:
[tex]x^{\frac{1}{5} } = \sqrt[5]{x}[/tex]
Step-by-step explanation:
A radical expression is an expression with a variable, number, or combination of both of them under a root symbol.
A radical expression has a general form of [tex]\sqrt[n]{x}[/tex]
For the given expression [tex]x^{\frac{1}{5} }[/tex]
So, [tex]x^{\frac{1}{5} } = \sqrt[5]{x}[/tex]
[tex]x^{1/5}[/tex] in radical form is √5x.
To write the expression [tex]x^{1/5}[/tex] in radical form, we use the property of exponents where a fractional exponent represents a root. Specifically, the exponent 1/5 indicates the fifth root of the base.
Here are the steps:
Identify the base and the fractional exponent: base = x, exponent = 1/5.Rewrite the expression using the radical symbol, where the denominator of the exponent (5) becomes the index of the root.So,[tex]x^{1/5}[/tex] is equivalent to √5x.Therefore, the radical form of [tex]x^{1/5}[/tex] is √5x.
Determine algebraically whether the function is even, odd, or neither even nor odd.
f(x) = -9 x^3 + 8x
Odd
Even
Neither
Answer: The function will be ODD.
Hope this helps! :)
QuezoMartiinez
The function f(x) = -9x³ + 8x is odd.
Option A is the correct answer.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
A function f(x) is even if f(-x) = f(x).
A function is odd if f(-x) = -f(x).
Using the above definition.
f(x) = -9x³ + 8x
Put x = -x
f(-x) = -9 x (-x³) + 8 x (-x)
f(-x) = 9x³ - 8x
f(-x) = - ( -9x³ + 8x)
f(-x) = -f(x)
This means,
The function is odd.
Thus,
f(x) is odd.
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ2
A manufacturing company with 450 employees begins a new project line and must increase their number of employees by 18% how many total employees does the company have now
Answer: the company now have 531 employees.
Step-by-step explanation:
The initial number of employees that the company had was 450.
The company began a new project line and must increase their number of employees by 18% . it means that the number of new employees that the company employed would be
18/100 × 450 = 0.18 × 450 = 81
Therefore, the total number of employees that the company have now would be
450 + 81 = 531
Assume that the mean of a normal distribution of IQ scores is 102 and the standard deviation is 15. You have been told that your test score is 1 standard deviation above the mean. What is your IQ test score?
Answer: your IQ test score is 117
Step-by-step explanation:
Assume that the mean of a normal distribution of IQ scores is 102 and the standard deviation is 15.
If you have been told that your test score is 1 standard deviation above the mean, it means that your score would be
102 + 15 = 117
According to the empirical rule, 68% of data falls within the first standard deviation from the mean. This means that 117 falls within 68% of the scores.
Jack decides to grow and sell bean plants. Let P represent the number of plants he will grow and sell. After considering his expenses, the expression -3p(p-10)-6p(p-10) represents his profit.
a. Rewrite and simplify the profit expression by factoring out the greatest common factor.
b. Rewrite the expression in simplest form with no parentheses.
Answer:
b. [tex]\displaystyle 90 - 9p^2[/tex]
a. [tex]\displaystyle -9[-10 + p^2][/tex]
Step-by-step explanation:
b. [tex]\displaystyle 90 - 9p^2 = -3p^2 + 30 - 6p^2 + 60 = -3p(p - 10) - 6p(p - 10)[/tex]
a. [tex]\displaystyle -9[-10 + p^2] = 90 - 9p^2[/tex]
I am joyous to assist you anytime.
Final answer:
The profit expression -3p(p-10)-6p(p-10) simplifies first by factoring out the greatest common factor to -9p(p-10), and then further simplifies to -9p² + 90p by distributing the -9p across the parentheses.
Explanation:
The student is tasked with simplifying the profit expression given by -3p(p-10)-6p(p-10), first by factoring out the greatest common factor, and then by writing the expression in the simplest form without parentheses.
To begin, we notice that both terms in the expression share a common factor of p(p-10), so we can factor this out:
-3p(p-10) - 6p(p-10) = -9p(p-10).
Upon factoring out the common factor, our expression simplifies to -9p(p-10). Next, we simplify this expression by removing the parentheses and multiplying through by the common factor:
-9p(p - 10) = -9p² + 90p.
Therefore, the simplified profit expression with no parentheses is -9p² + 90p.
When randomly selecting an adult, A denotes the event of selecting someone with blue eyes. What do Upper P(Upper A)P(A) and Upper P(Upper A overbar)PA represent?
Answer:
When randomly selecting an adult, A denotes the event of selecting someone with blue eyes. What do P(A) and P([math] \overline A [/math]) represent?
Step-by-step explanation:
Solve for x.
x−11−−−−−√=5
A 14
B 16
C 25
D 36
The value of x in the expression will be 36.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is;
⇒ √x - 11 = 5
Now,
Solve the expression for x as;
⇒ √x - 11 = 5
Squaring on both side;
⇒ (√x - 11)² = 5²
⇒ x - 11 = 25
Add 11 both side;
⇒ x - 11 + 11 = 25 + 11
⇒ x = 36
Thus, The value of x in the expression will be 36.
Learn more about the mathematical expression visit:
https://brainly.com/question/1859113
#SPJ2
The correct answer is option D. 36.
We need to solve the equation:
√(x - 11) = 5
To solve this, follow these steps:
Square both sides to eliminate the square root.
√(x - 11)2 = 52
x - 11 = 25
Isolate x by adding 11 to both sides:
x - 11 + 11 = 25 + 11
x = 36
So, the correct answer is 36 (option D).
The point of a square pyramid is cut off, making each lateral face of the pyramid a trapezoid with the dimensions shown. What is the area of one trapezoidal face of the figure?
The area of one trapezoidal face of the figure is 2 square inches
How to determine the area?The dimensions of the trapezoid are given as:
Base = 3 inchesHeight = 1 inchTop side length = 1 inch.The area of one trapezoidal face of the figure is the calculated using:
Area = 0.5 * (base + top side) * height
So, we have:
Area = 0.5 * (3 + 1) * 1
Evaluate
Area = 2
Hence, the area of one trapezoidal face of the figure is 2 square inches
Read more about areas at:
https://brainly.com/question/15944318
#SPJ2
Answer: 2
Step-by-step explanation:
The Masterfoods Company says that before the introduction of purple, yellow candies made up 20% of their plain candies, red another 20%, and orange, blue and green each made up 10%. The rest were brown. If you pick a THREE M&Ms in a row (assume with replacement), what is the probability that they are all Brown?
a. 0.09
b. 0.027
c. 0.3
d. 0.6
Answer:
b. 0.027
Step-by-step explanation:
We have been given that the Masterfoods Company says that before the introduction of purple, yellow candies made up 20% of their plain candies, red another 20%, and orange, blue and green each made up 10%.
Probability of a yellow candy would be 0.20 and probability of a red candy would be 0.20.
Probability of orange candy would be 0.10, probability of blue candy would be 0.10 and probability of green candy would be 0.10.
The probability of brown candy would be [tex]1-0.20-0.20-0.10-0.10-0.10=0.30[/tex]
To find the probability that three candies are all Brown, we will use multiplication rule of independent events as:
[tex]0.30\times 0.30\times 0.30=0.027[/tex]
Therefore, the probability that that three candies are Brown would be 0.027 and option 'b' is the correct choice.
The probability that they are all Brown is option b. 0.027.
The calculation is as follows;The probability of brown candy should be
= 1-0.20 -0.20 -0.10 - 0.10-0.10
= 0.30
Now
the probability should be
[tex]= 0.3^3[/tex]
= 0.027
Learn more: https://brainly.com/question/537797?referrer=searchResults
Consider triangle GHJ. Triangle G H J is shown. Angle G H J is a right angle. The length of the hypotenuse is 10 and the length of another side is 5. What is the length of line segment HJ? 5 units 5 StartRoot 3 EndRoot units 10 units 10 StartRoot 3 EndRoot units
Length of segment HJ is 5√3 units
Step-by-step explanation:
Here, apply the Pythagorean relationship where sum of squares of the sides equals the square of the hypotenuse.
Given that the hypotenuse, c= 10 units, and one of the side, a=5 units, then the other side can be calculated as;
a²+b²=c²
5²+b²=10²
b²=10²-5²
b²=100-25
b²=75
b=√75 = √3*25 = √3 *√25 = √3 *5 = 5√3
Length of segment HJ is 5√3 units
Learn More
Pythagorean relationship:https://brainly.com/question/14532944
Keywords :triangle, right-angle, side, hypotenuse,line segment
#LearnwithBrainly
Answer:
B
Step-by-step explanation:
Find the value of x.
logx 8 = 0.5
А. 4
В. 16
C.32
D. 64
Answer:
The answer to your question is letter D. x = 64
Step-by-step explanation:
Equation
log x 8 = 0.5
Express the log as a exponential equation
x[tex]x^{0.5}[/tex] = 8
Express the power as a fraction
[tex]x^{1/2} = 8[/tex]
[tex]\sqrt{x^{2}}[/tex]
Look for a number which squared root is 8
[tex]\sqrt{64} = 8[/tex]
Then
x = 64
Answer:
Please mark as brainliest :)
Step-by-step explanation:
need help asap
Solve the equation by completing the square
-2x^2+x=0
a. {0,-0.5}
b. {1,0}
c. {0.5,0}
d. {0}
Answer:
Option C) [tex]{\{0.5,0}\}[/tex] is correct
The solution to the given equation is [tex]{\{0.5,0}\}[/tex]
Step-by-step explanation:
Given quadratic equation is [tex]-2x^2+x=0[/tex]
To solve the equation by completing the square :
[tex]-2x^2+x=0[/tex]
[tex]-2(x^2-\frac{x}{2})=0[/tex]
[tex]x^2-\frac{x}{2}=0[/tex]
Rewritting the above equation as below :
[tex]x^2-2(x)\frac{1}{4}+\frac{1}{4^2}-\frac{1}{4^2}=0[/tex]
[tex](x-\frac{1}{4})^2-\frac{1}{4^2}=0[/tex]
[tex](x-\frac{1}{4})^2=\frac{1}{4^2}[/tex]
Taking square root on both sides we get
[tex]\sqrt{(x-\frac{1}{4})^2}=\sqrt{\frac{1}{4^2}}[/tex]
[tex](x-\frac{1}{4})=\pm\frac{1}{4}[/tex]
[tex]x=\pm\frac{1}{4}+\frac{1}{4}[/tex]
[tex]x=+\frac{1}{4}+\frac{1}{4}[/tex] and [tex]x=-\frac{1}{4}+\frac{1}{4}[/tex]
[tex]x=\frac{2}{4}[/tex] and [tex]x=0[/tex]
Therefore [tex]x=\frac{1}{2}[/tex] and x=0
[tex]x=0.5[/tex] and x=0
Therefore the solution to the given equation is [tex]{\{0.5,0}\}[/tex]
Option C) [tex]{\{0.5,0}\}[/tex] is correct
I need help with 2b.
The topic is rational equations and restrictions are 2 and 0.
As my answer I got 0 = 8 but I’m unsure if that’s correct...
Answer:
The answer to your question
a) Values excluded = -2, 0
b) solutions = -2/3, 2
Step-by-step explanation:
Equation
[tex]\frac{4x}{2x + 4} = \frac{x+ 2}{2x}[/tex]
a) x is restricted when the denominators equal zero, so let's get them.
2x + 4 = 0 2x = 0
2x = - 4 x = 0 / 2
x = -4 / 2 x = 0
x = -2
x must be different to -2, 0
b) [tex]\frac{4x}{2x + 4} = \frac{x+ 2}{2x}[/tex]
[tex]\frac{2x}{x + 2} = \frac{x + 2}{2x}[/tex]
4x² = (x + 2)²
4x² = x² + 4x + 4
4x² - x² - 4x - 4 = 0
3x² - 4x - 4 = 0
3x² - 6x + 2x - 4 = 0
3x(x - 2) + 2(x - 2) = 0
(x - 2)(3x + 2) = 0
x₁ - 2 = 0 3x₂ + 2 = 0
x₁ = 2 x₂ = -2/3
A 28ft ladder leans against a wall so that the base of the ladder is 5ft away from the base of the wall. How far up the wall does the ladder reach?
Round to the nearest tenth.
Answer:
the top of the ladder is 27.5ft above the ground.
Step-by-step explanation:
The ladder makes an angle, θ with the ground thus forming a right angle triangle with the wall of the house.
The length of the ladder represents the hypotenuse of the right angle triangle.
The ground distance from the base of the wall to the foot of the ladder represents the adjacent side of the right angle triangle.
Therefore, to determine how high up is the top of the ladder on the wall, x, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
28² = x² + 5²
784 = x² + 25
x² = 784 - 25 = 759
x = √759 = 27.5ft
Using the Pythagorean theorem, the ladder reaches approximately 27.5 feet up the wall when the base is 5 feet from the wall.
Explanation:The question involves finding the height up a wall that a 28ft ladder reaches when its base is 5ft from the wall. To solve this, we will use the Pythagorean theorem which relates the sides of a right-angled triangle. The ladder, wall, and ground form a right-angled triangle with the ladder as the hypotenuse and the wall and ground as the other two sides.
Let h be the height the ladder reaches up the wall. Using the Pythagorean theorem, we have:
28² = h² + 5²
Solving for h:
28² - 5² = h²
784 - 25 = h²
759 = h²
h ≈ √759
h ≈ 27.5 (to the nearest tenth)
Therefore, the ladder reaches approximately 27.5 feet up the wall.
The Hall family and the Nguyen family each used their sprinklers last summer. The water output rate for the Hall family's sprinkler was 35L per hour. The water output rate for the Nguyen family's sprinkler was 15L per hour. The families used their sprinklers for a combined total of 50 hours, resulting in a total water output of 1050L. How long was each sprinkler used?
Answer:
Nguyen family uses sprinkler for 35 hours while the Hall family uses sprinkler for 15 hours
Step-by-step explanation:
Let h and n be the number of hours that the Hall and Nguyen family individually use their sprinkler for, respectively. Since they use for a combined total of 50 hours, h + n = 50, or h = 50 - n
Also their total water output is 1050 L, we can have the following equation
35h + 15n = 1050
Substitute h = 50 - n and we have
35(50 - n) + 15n = 1050
1750 - 35n + 15n = 1050
35n - 15n = 1750 - 1050
20n = 700
n = 35 hours
h = 50 - n = 50 - 35 = 15 hours
* ANSWER ASAP PLEASE *
- can anyone answer this question?? you have to find x.
Answer:
The answer is the last one
Step-by-step explanation:
Answer:
Step-by-step explanation:
X= 11/tan17
Where tan17= 3.494
Therefore, X = 3.148
A parachute rate during a free fall reaches 70 meters per second. What is the rate in feet per second? At this rate how many feet will the parachute fall during 20 seconds of free fall
Answer:
229.659 ft/s4,593.18 ftStep-by-step explanation:
1 foot is 0.3048 meters, so ...
70 m/s = (70 m/s)×(1 ft)/(0.3048 m) ≈ 229.659 ft/s
At that speed, the distance covered in 20 seconds is ...
(20 s)(229.659 ft/s) = 4,593.18 ft
The parachutist will fall 4593 feet during 20 seconds of free fall at 229.7 ft per second.
_____
Final answers are rounded. Intermediate values are not.
I got 13.7 is that correct
Answer:
The answer to your question is 10.5 in
Step-by-step explanation:
Data
First triangle
height = x
base = 7 in
Second triangle
height = 12 in
base = 8 in
Process
1.- Use proportions to solve this problem, relates the sides of a triangle with the same sides of the other triangle.
[tex]\frac{x}{7} = \frac{12}{8}[/tex]
2.- Multiply both sides by 7
[tex]7\frac{x}{7} = \frac{7(12)}{8}[/tex]
3.- Simplify
x = [tex]\frac{84}{8}[/tex]
4.- Result
x = 10.5 in
Joey spent $.75 on a bus ticket. Then he spent 1/2 of his money on the soccer ball. After that, he spent 1/4 of his money on lunch. With the last of his money, Joey spent $14.95 for soccer tickets. In the end, Joey had 5 cents left. How much money did he start out with?
Joey started his day with $63.
Step-by-step explanation:
Let,
x be the amount Joey started with.
Amount left = 5 cent = $0.05
Amount spent on bus ticket = $0.75
Amount spent on soccer ball = [tex]\frac{1}{2}x[/tex]
Amount spent on lunch = [tex]\frac{1}{4}x[/tex]
Amount spent on soccer tickets = $14.95
According to given statement;
Total amount - bus ticket - soccer ball - lunch - soccer tickets = Amount left
[tex]x-0.75-\frac{1}{2}x-\frac{1}{4}x-14.95=0.05\\\\x-\frac{1}{2}x-\frac{1}{4}x=0.05+0.75+14.95\\\\\frac{4x-2x-x}{4}=15.75\\\\\frac{x}{4}=15.75[/tex]
Multiplying both sides by 4
[tex]4*\frac{x}{4}=15.75*4\\x=63[/tex]
Joey started his day with $63.
Keywords: variable, addition
Learn more about addition at:
brainly.com/question/10081622brainly.com/question/10341324#LearnwithBrainly
Robert is Running in a race that is 3 miles long. A Distance marker is placed evenly every 1/2 mile from the beginning of the race until the end. What is the total number of distance markers on the trail?
Answer: the total number of distance markers on the trail is 6
Step-by-step explanation:
The total distance that Robert covers in the race is 3 miles.
If a distance marker is placed evenly every 1/2 mile from the beginning of the race until the end, then the total number of distance markers on the trail would be
3/0.5 = 6
To make lemonade, use 1 cup of lemon juice for every 3 cups of water. If you use 12 cups of water, how many cups of lemon juice will you need? Use a double number lineto solve.
Answer:
4 cups of lemon juice is required for 12 cups of water to make lemonade.
Step-by-step explanation:
Given:
To make lemonade 1 cup of lemon juice is required with 3 cups of water.
To find how many cups of lemon juice is required with 12 cups of water.
Solution:
We will construct a double number line of which one represents the cups of lemon juice and the other represents the cups of water.
From the number lines we can see that with 1 cup of lemon juice there are 3 cups of water.
So, ratio of cups of lemon juice to cups of water = 1 : 3
If we require [tex]x[/tex] cups of lemon juice with 12 cups of water then ratio = x : 12
Since ratio will always be equivalent, so we can write it as:
[tex]\frac{x}{12}=\frac{1}{3}[/tex]
Multiplying both sides by 12.
[tex]12.\frac{x}{12}=12\times\frac{1}{3}[/tex]
∴ [tex]x=4[/tex]
Thus, 4 cups of lemon juice is required for 12 cups of water to make lemonade.
The probability that an event will not happen is Upper P (Upper E prime) = 0.94. Find the probability that the event will happen.
Answer: P(Upper E' prime) = 0.06
Step-by-step explanation:
Not happen:P(Upper E prime) = 0.94
Happen: P(Upper E' prime) = ?
P(Upper E' prime) + P(Upper E' prime) = 1
Therefore
P(Upper E' prime) + 0.94= 1
P(Upper E' prime) =1- 0.94
P(Upper E' prime) = 0.06
a. Show that the following statement forms are all logically equivalent. p → q ∨ r, p ∧ ∼q → r, and p ∧ ∼r → q b. Use the logical equivalences established in part (a) to rewrite the following sentence in two different ways. (Assume that n represents a fixed integer.) If n is prime, then n is odd or n is 2.
Final answer:
The statement forms p → q ∨ r, p ∧ ¬q → r, and p ∧ ¬r → q are shown to be logically equivalent using principles of logical equivalence and contraposition. The original statement 'If n is prime, then n is odd or n is 2' can thus be rephrased in different ways while retaining the same meaning.
Explanation:
Logical Equivalences
To show that the statement forms p → q ∨ r, p ∧ ¬q → r, and p ∧ ¬r → q are all logically equivalent, we need to understand that logical equivalence means that the statements have the same truth value in every possible scenario. The implication p → q is equivalent to p∨ q, as a truth table would confirm. Likewise, by using the principle of contraposition, which states that p → q is equivalent to ¬q → ¬p, we can transform the given implications accordingly.
Considering the sentence "If n is prime, then n is odd or n is 2" and denoting p as "n is prime", q as "n is odd", and r as "n is 2", the original statement can be represented as p → q ∨ r. Using logical equivalences established earlier, two different ways to rewrite this sentence could be:
The logical equivalences show that all these forms express the same condition from different perspectives but with the same meaning.