Answer:
The correlation between sales and advertising is positive.
Step-by-step explanation:
For every $35 spent on advertising, sales increase by $1
Is FALSE, since y = 500 + 35 x $35, sales increase more than $1
Even if no money is spent on advertising, the company realizes $35 of sales
Is FALSE, if no money is spent, the sales amount to $ 500 (when X = 0)
The coefficient of correlation between sales and advertising is 0.81
Is FALSE, since R² = 0.9. The coefficient of correlation = R = 0.94, not 0.81
Given triangle ABC with coordinates A(−6, 4), B(−6, 1), and C(−8, 0), and its image A′B′C′ with A′(−2, 0), B′(−5, 0), and C′(−6, −2), find the line of reflection.
The line of reflection is at y=?
Answer:
The line of reflection is at y = x+6.
Step-by-step explanation:
The perpendicular bisector of AA' is a line with slope 1 through the midpoint of AA', which is (-4, 2). In point-slope form, the equation is ...
y = 1(x +4) +2
y = x + 6 . . . . . . . line of reflection
Phil, Melissa, Noah, and olivia saw a tall tree that cast a shadow 34 feet long. They observed at the same time that a 5-foot-tall person cast a shadow that was 8.5 feet long. How tall is the tree?
Answer:
20 ft
Step-by-step explanation:
The tree's shadow is 34/8.5 = 4 times the length of the person's shadow, so the tree is 4 times a tall as the person:
4×5 ft = 20 ft . . . . . the height of the tree
_____
Shadow lengths are proportional to the height of the object casting the shadow.
Using the ratio given from the shadow of the 5-foot person, we set up a proportion and solve for the height of the tree, which is 20 feet.
Explanation:The question is asking about the height of a tree, which can be figured out through a method called similar triangles in geometry. In this case, Phil, Melissa, Noah, and Olivia observed a 5-foot tall person casting an 8.5-foot shadow and a tall tree casting a 34-foot shadow.
From this, we can set up a proportion to find out the height of the tree. This would look like 5/8.5 = x/34, where x is the height of the tree. Cross multiplying and solving for x gives us x = (5*34)/8.5, which equals to 20 feet. Therefore, the height of the tree is 20 feet.
Learn more about Proportions here:https://brainly.com/question/32430980
#SPJ11
If one card is drawn from a standard 52 card playing deck, determine the probability of getting a jack, a three, a club or a diamond. Round to the nearest hundredth. Please show your work! Thanks!
0.50
0.58
0.65
0.15
Answer:
0.65
Step-by-step explanation:
we know that
The probability of an event is the ratio of the size of the event space to the size of the sample space.
The size of the sample space is the total number of possible outcomes
The event space is the number of outcomes in the event you are interested in.
so
Let
x------> size of the event space
y-----> size of the sample space
so
[tex]P=\frac{x}{y}[/tex]
In this problem we have
[tex]x=4+4+13+13=34[/tex]
because
total of three=4
total of jack=4
total of club=13
total of diamond=13
[tex]y=52\ cards[/tex]
substitute
[tex]P=\frac{34}{52}=0.65[/tex]
Please help me with this !!!!!!!
Answer:
y = 2x - 1
Step-by-step explanation:
Note the difference between consecutive terms of y are constant, that is
1 - (- 1) = 3 - 1 = 5 - 3 = 7 - 5 = 9 - 7 = 2
Thus the equation is of the form y = 2x ± c ← c is a constant
Substitute values of x to determine the required value of c
x = 0 : 2 × 0 = 0 ← require to subtract 1 for y = - 1
x = 1 : 2 × 1 = 2 ← require to subtract 1 for y = 1
x = 2 : 2 × 2 = 4 ← require to subtract 1 for y = 3, and so on
Thus the required equation is
y = 2x - 1
10 POINTS AND BRAINLIEST!!
A government agency can spend at most $125,000 on a training program. If the training program has a fixed cost of $45,000 plus a cost of $125 per employee, how many employees can be trained?
Answer:
Step-by-step explanation:
From the problem statement, we can setup the following equation:
[tex]125,000 = 45,000 + 125E[/tex]
where [tex]E[/tex] is the number of employees being trained.
Solving for [tex]E[/tex] will give us the answer:
[tex]125,000 = 45,000 + 125E[/tex]
[tex]80,000 = 125E[/tex]
[tex]E = 640[/tex]
[tex]\text{Hello there!}\\\\\text{The most that they can spend is \$125,000}\\\\\text{We know that the fixed cost of the program is \$45000}\\\\\text{They also need to pay \$125 for each employee}\\\\\text{We need to solve:}\\\\125000-45000=80000\\\\\text{Now divide 80,000 by 125 to see how many employees they can train}\\\\80000\div125=640\\\\\boxed{\text{They can train 640 employees}}[/tex]
One street light flashed every 4 seconds Another street light flashes every 6 seconds If they both just flashed as the same movement how many seconds will it take before thwart flash at the same time again
Time for light A's Flash = 4 seconds
Time for light B's Flash = 6 seconds
Duration between the lights = 6-4=2
Duration to flash again = LCM of 6, 4
2/6,4
2/3,2
3/3,1
/1,1
2x2 x 3
4 x 3
= 12 seconds
Final answer:
The two street lights will flash together again after 12 seconds. This is determined by finding the least common multiple of the intervals at which each street light flashes (4 seconds and 6 seconds), which is 12 seconds.
Explanation:
The question you've posed is about finding the least common multiple (LCM) of two numbers, which in this case are the intervals at which two street lights flash: 4 seconds and 6 seconds. To determine when the street lights will flash together again, we must find the smallest time interval that is a multiple of both 4 and 6. The multiples of 4 are 4, 8, 12, 16, and so on. The multiples of 6 are 6, 12, 18, 24, and so on. The smallest multiple they have in common is 12 seconds.
To arrive at this answer, you can either list out the multiples as above or use a shortcut by calculating the LCM. Here's a step-by-step breakdown:
Write down the prime factors of each number: 4 = 2 x 2 and 6 = 2 x 3.
For each distinct prime factor, take the highest power present in the factorization of either number. Here, this gives us 22 (from 4) and 3 (from 6).
Multiply these together to get the LCM: 22 x 3 = 4 x 3 = 12.
Therefore, the two street lights will flash together again after 12 seconds.
A real estate office manages an apartment complex with 50 units. When the rent is $780 per month, all 50 units are occupied. However, when the rent is $825, the average number of occupied units drops to 47. Assume that the relationship between the monthly rent p and the demand x is linear (Note:The term demand refers to thenumber of occupied units.)
(a) Write a linear equation giving the demand x in terms of the rent p. (b) Linear extrapolation - Use a graphing utility to graph the demand equation and use the trace feature to predict the
number of units occupied when the rent is raised to $855. (c) Linear interpolation - Predict the number of units occupied when the rent is lowered to $795.
Answer:
A) The linear equation is [tex]x=\frac{-1}{15}p+102[/tex]
B) When the rent is raised to $855 the number of units occupied is 45.
C) When the rent is lowered to $795 the number of units occupied is 49.
Step-by-step explanation:
A) A linear equation for the demand is written as [tex]x=mp+p_{0}[/tex], where [tex]m[/tex] is the slope, [tex]x[/tex] is the number of occupied units, [tex]p[/tex] is the rent.
[tex]m[/tex] is calculated using the problem information. When the rent is [tex]p=$780[/tex] then [tex]x=50[/tex] and when the rent is [tex]p=$825[/tex] then [tex]x=47[/tex].
Using the slope equation we have:
[tex]m=\frac{50-47}{780-825}=\frac{-3}{45}=\frac{-1}{15}[/tex]
Thus the linear equation is:
[tex]x=\frac{-1}{15}p+p_{0}[/tex]
In order to calculate [tex]p_{0}[/tex] we use the problem information, When the rent is [tex]p=$780[/tex] then number of occupied units is [tex]x=50[/tex], thus:
[tex]50=\frac{-1}{15}780+p_{0} \\\\50=-52+p_{0} \\\\p_{0}=102 \\[/tex]
Finally, the linear equation is:
[tex]x=\frac{-1}{15}p+102[/tex]
B) The demand equation is plot in the attached file, the number of units occupied when the rent is raised to $855 is 45.
C) In order to predict the number of occupied units lets use the equation:
[tex]x=\frac{-1}{15}p+102[/tex]
where [tex]p=$795[/tex], then:
[tex]x=\frac{-1}{15}795+102\\ \\x=-53+102\\\\x=49[/tex]
Thus, when the rent is lowered to $795 the number of units occupied is 49.
In woodshop class, you must cut several pieces of wood to within 3/16 inch of the teacher's specifications. Let (s-x) represent the difference between the specification s and the measured length x of a cut piece.
(a)Write an absolute value inequality that describes the values of x that are within the specifications.
(b) The length of one piece of wood is specified to be s=5 1/8 inches. Describe the acceptable lengths for this piece.
Answer:
(a) |s - x| ≤ 3/16
(b) 4 15/16 ≤ x ≤ 5 5/16
Step-by-step explanation:
(a) The absolute value of the difference from spec must be no greater than than the allowed tolerance:
|s - x| ≤ 3/16
__
(b) Put 5 1/8 for s in the above equation and solve.
|5 1/8 - x| ≤ 3/16
-3/16 ≤ 5 1/8 -x ≤ 3/16
3/16 ≥ x -5 1/8 ≥ -3/16 . . . . multiply by -1 to get positive x
5 5/16 ≥ x ≥ 4 15/16 . . . . . . add 5 1/8
Pieces may be between 4 15/16 and 5 5/16 inches in length.
An absolute value inequality can be used to represent the acceptable range of lengths for a piece of wood in a woodshop class. For a specified length of 5 1/8 inches, the acceptable lengths for the piece would be between 4 15/16 inches and 5 5/16 inches.
Explanation:Your task in woodshop class is to cut pieces of wood to within 3/16 inch of the teacher's specifications. The difference between the specification s and the measured length x of a cut piece is represented by (s-x).
(a) You can represent this situation with the absolute value inequality |s - x| ≤ 3/16, which shows that the difference between the specification and the measured length must be less than or equal to 3/16 inch.
(b) If the length of one piece is specified to be s = 5 1/8 inches, you can substitute that value into the inequality to find the acceptable range of lengths: |5 1/8 - x| ≤ 3/16. Solving the inequality gives you the range 5 - 3/16 inches ≤ x ≤ 5 + 3/16 inches, or between 4 15/16 inches and 5 5/16 inches.
Learn more about Absolute Value Inequality here:https://brainly.com/question/33786594
#SPJ2
The equation A=p(1+r)^t can be used to calculate compound interest on a savings account. A = future balance, p = current balance, r = rate of interest, and t = time in years. If you deposit $2,000 at 10% each year, how much money will be in your account in 10 years(Round to the nearest dollar.)
A.
$2,200
B.
$4,000
C.
$4,318
D.
$5,187
To calculate the compound interest, the formula[tex]A=p(1+r)^t[/tex] is used with the principal amount of $2,000, an annual interest rate of 10%, and a time frame of 10 years. The correct calculation results in a future balance of $5,187, when rounded to the nearest dollar. The correct option is d.
The equation [tex]A=p(1+r)^t[/tex] is used to calculate the compound interest on a savings account. To find out how much money will be in the account after a certain number of years, we can follow these steps:
Identify the principal amount (p), which is the initial amount deposited. In this case, it's $2,000.Determine the annual interest rate (r), expressed as a decimal. For a 10% interest rate, r would be 0.10.Identify the time (t) in years that the money will be invested. Here, it is 10 years.Substitute these values into the formula: [tex]A = 2000(1 + 0.10)^{10[/tex]Calculate the future balance A.After performing the calculation, we get:
A =[tex]2000(1 + 0.10)^{10[/tex] = [tex]2000(1.10)^{10[/tex] = 2000 ×2.59374 = $5,187.48
Therefore, rounded to the nearest dollar, you will have $5,187 in your account after 10 years. The correct answer is D. $5,187.
BD bisects ABC. m ABD=2y m DBC=5y-12. What is ABC?
In triangle ABC, BD bisects angle ABC into two parts with measures 2y and 5y-12. The measure of angle ABC is the sum of its parts, equating to 7y-12. Without additional information, the exact value of y and thus, the measure of angle ABC, cannot be determined.
Explanation:The given problem involves a geometrical concept related to triangles, specifically angle bisectors. In triangle ABC, BD is an angle bisector, dividing angle ABC into two angles with measures 2y for angle ABD and 5y-12 for angle DBC. To find the measure of the whole angle ABC, we need to understand that the angle bisector divides the angle into two parts, where their measures are equal to the sum of the parts' measures.
Given:
m ABD = 2ym DBC = 5y - 12Since BD is an angle bisector, the sum of the measures of angles ABD and DBC equals the measure of angle ABC. Thus, to find m ABC, we add the measures of angle ABD and angle DBC:
m ABC = m ABD + m DBC = 2y + (5y - 12) = 7y - 12
To solve for y, we note that additional information is required that is not provided in the question. However, the measure of angle ABC in terms of y is 7y - 12, showcasing the relationship between the angle and its bisector.
4. A rectangle has a width of 2 cm and a perimeter of 25 cm. Find the length and the area.
A ) ℓ = 12.5 cm and A = 21 cm2
B) ℓ = 10.5 cm and A = 25 cm2
C) ℓ = 10.5 cm and A = 21 cm2
D) ℓ = 12.5 cm and A = 25 cm2
Answer:
l = 10.5 cm and A = 21 cm2
Step-by-step explanation:
Area is w*l
Perimeter is 2(w+l)
Replacing the information known in the problem you can get the length with the perimeter
P = 2(w+l)
25 = 2(2+l)
12.5 = 2 + l
10.5 cm = l
with the length now you can find the area
A = w*l
A = 2*10.5
A = 21 cm2
A newborn calf weighs about 90 pounds. Each week, it's weight increases by 5%. a) If we were to graph this growth, would it be a linear or exponential function? b) How do you know? Support your answer.
Answer: exponential because it's a ratio :)
Step-by-step explanation:
Answer:
Exponential. Because of its cumulative nature (gain of weight) and its growth rate (5%).
Step-by-step explanation:
It's a growth graph given by an exponential function because every gain of weight is cumulative to the earlier week's. This function can be modeled this way since the rate of growth (5%) was given, which is added by 1 then plugged into the formula. [tex]y=90(1.05)^{t}[/tex] Besides, this model is identical to Interest Composite Rate, which follows the same basic structure, namely Cumulative Growth at a given rate.
How many oranges are in a crate if the price of a crate of oranges is $1.60 and the price of oranges is $0.20 per pound and there are 3 oranges per pound?
The crate contains 24 oranges.
What is unitary method ?Unitary method is a mathematical technique for first finding the value of a single unit and then deriving the given units from it by multiplying with the single unit.
According to the given question a no. of oranges are in a crate which costs 1.60 dollars also given that per pound of orange costs 0.20 dollars.
∴ The crate contains (1.60/0.20) pounds of oranges which is
= 8 pounds of oranges.
Given 3 oranges are of 1 pound
∴ In 8 pounds of oranges pieces of oranges are (8×3) = 24 oranges.
learn more about unitary method here :
https://brainly.com/question/21648365
#SPJ2
A student is running a 5 kilometer race. He runs 1 kilometer every 3 minutes. Select the function that describes his distance from the finish line after x minutes
The first one f(x) = -1/3x + 5
Answer:
f(x)=-1/3+5
Step-by-step explanation:
hope this helps
Two symptoms are associated with a certain disease.
There is a 95% probability that at least one of the symptoms occurs;
in addition, the first symptom occurs with 50% probability, the second symptom occurs with 45% probability.
Based on these probability results, answer the following two questions
1) Are the two events "first symptom occurs" and "second symptom occurs" mutually exclusive (i.e. disjoint)?
2) Are the two events "first symptom occurs" and "second symptom occurs" independent?
For each question, clearly state YES or NO and provide a brief written explanation that includes the appropriate numerical support.
Answer:
Mutually exclusive, dependent events
Step-by-step explanation:
Two events A and B are mutually exclusive if [tex]P(A\cap B)=0[/tex]
Two events A and B are independent if [tex]P(A\cap B)=P(A)\cdot P(B)[/tex]
Remark: All mutually exclusive events are dependent.
Now,
A = the first symptom occurs
B = the second symptom occurs
[tex]P(A)=0.5\ (\text{or } 50\%)[/tex]
[tex]P(B)=0.45\ (\text{or } 45\%)[/tex]
[tex]P(A\cup B)=0.95 \ (\text{or }95\%)[/tex]
Use the rule
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)\\ \\0.95=0.5+0.45-P(A\cap B)\\ \\P(A\cap B)=0.5+0.45-0.95=0.95-0.95=0[/tex]
Thus, the events A and B are mutually exclusive (disjoint) and dependent (accordint to the remark)
Find (f + g)(x) and (f g)(x) for f(x) = 6x2 + 5 and g(x) = 7 – 5x.
A.
(f + g)(x) = 6x2 + 5x – 12
(f- g)(x) = 6x2 – 5x – 2
B.
(f + g)(x) = 6x2 – 5x + 12
(f- g)(x) = 6x2 + 5x – 2
C.
(f + g)(x) = 6x2 + 0x + 7
(f- g)(x) = 6x2 + 10x – 7
D.
(f + g)(x) = 6x2 + 5x – 2
(f- g)(x) = 6x2 – 5x + 12
Answer:
B. (f + g)(x) = 6x² – 5x + 12
(f- g)(x) = 6x² + 5x – 2
Step-by-step explanation:
1) (f +g)(x) = f(x) + g(x) = (6x² + 5) + (7 -5x) = 6x² -5x +12
__
2) (f-g)(x) = f(x) -g(x) = (6x² + 5) - (7 -5x)
= 6x² +5 -7 +5x . . . the minus sign outside multiplies all the terms inside
= 6x² +5x -2
In this Mathematics problem, we are asked to add and subtract given functions f(x) and g(x). The sum results in (f+g)(x) = 6x^2 - 5x + 12 and the difference results in (f-g)(x) = 6x^2 + 5x - 2.
Explanation:The question is asking about finding the sum (f+g) and the difference (f-g) of two functions, f(x) and g(x). To answer this, we add (or subtract) the two given functions together.
For the function (f+g)(x), you simply add f(x) = 6x2 + 5 and g(x) = 7 - 5x together to get (f+g)(x) = 6x2 - 5x + 12. Thus, the sum of the two functions is 6x2 - 5x + 12.
Similarly, for the function (f-g)(x), we subtract g(x) from f(x) to get (f-g)(x) = 6x2 + 5x - 2. Thus, the difference of the two functions is 6x2 + 5x - 2.
So, the correct answer is B, (f+g)(x) = 6x2 - 5x + 12 and (f-g)(x) = 6x2 + 5x - 2.
Learn more about Function Addition and Subtraction here:https://brainly.com/question/33593405
#SPJ2
Susan needs to buy apples and oranges to make fruit salad. She needs 15 fruits in all. Apples cost $3 per piece, and oranges cost $2 per piece. Let m represent the number of apples. Identify an expression that represents the amount Susan spent on the fruits. Then identify the amount she spent if she bought 6 apples.
Answer:
Part a) 30+m
Part b) $36
Step-by-step explanation:
Part a) Identify an expression that represents the amount Susan spent on the fruits
The complete question in the attached figure
Let
m ------> the number of apples
n -----> the number of oranges
q ----> the amount Susan spent on the fruits
we know that
m+n=15 ----> (in total she needs 15 fruits)
n=15-m -----> equation A
q=3m+2n ----> equation B
Substitute equation A in equation B
q=3m+2(15-m)
q=3m+30-2m
q=30+m -----> expression that represents the amount Susan spent on the fruits
Part b) Identify the amount she spent if she bought 6 apples
we know that
If m=6 apples
substitute the value of m in the expression of Part a)
q=30+m -----> q=30+6=$36
Five friends a matinee movie spend $8 per ticket.They also purchase a small bag of popcorn each.If the friends pend a total of $62.50,how much does each bag of popcorn cost?
Five friends went to see a movie. Each person paid $5.
This is a total of $40.
$62.50 - $40 = $22.50.
We now have $22.50 to divide by 5 people.
So, $22.50/5 = $4.50.
Each person paid $4.50 for popcorn.
A spyware is trying to break into a system by guessing its password. It does not give up until it tries 1 million different passwords. What is the probability that it will guess the password and break in if by rules, the password must consist of
(a) 6 different lower-case letters
(b) 6 different letters, some may be upper-case, and it is case-sensitive
(c) any 6 letters, upper- or lower-case, and it is case-sensitive
(d) any 6 characters including letters and digits
The probability of a spyware program breaking into a system depends on the complexity of the password rules. By calculating the total number of possible passwords based on given rules and comparing it to the number of guessing attempts (1,000,000), one can determine the probability for each scenario.
Explanation:The probability of a spyware program guessing a password correctly can be calculated by determining the total number of possible unique passwords and then seeing how many attempts the spyware has in comparison.
6 different lower-case letters: There are 26 possibilities for each character, and because the letters must be different, the total number of possibilities is 26 * 25 * 24 * 23 * 22 * 21. Since the spyware makes 1 million (1,000,000) attempts, the probability of guessing correctly is 1,000,000 / (26 * 25 * 24 * 23 * 22 * 21).6 different letters, case-sensitive: There are 52 possibilities for each character (26 lower-case + 26 upper-case), and since letters must be different, the total number of possibilities is 52 * 51 * 50 * 49 * 48 * 47. So the probability is 1,000,000 / (52 * 51 * 50 * 49 * 48 * 47).Case-sensitive combination of letters: Since letters can be the same and are case-sensitive, there are 52 possibilities for each character, for a total of 52^6 possible combinations. The probability is 1,000,000 / 52^6.Any 6 characters including letters and digits: There are 62 possibilities for each position (26 lower-case + 26 upper-case + 10 digits), giving us 62^6 possible combinations. The probability is 1,000,000 / 62^6.In all cases, the probability of the spyware breaking in is the quotient of the number of attempts made (1,000,000) and the total number of possible passwords for each scenario.
Solve by Substitution
Show Steps
x = −5y + 4z + 1
x − 2y + 3z = 1
2x + 3y − z = 2
Answer:
(x, y, z) = (1-z, z, z) . . . . . . . an infinite number of solutions
Step-by-step explanation:
Use the first equation to substitute for x in the remaining two equations.
(-5y +4z +1) -2y +3z = 1 . . . . substitute for x in the second equation
-7y +7z = 0 . . . . . . . . . . . . . . simplify, subtract 1
y = z . . . . . . . . . . . . . . . . . . . . divide by -7; add z
__
2(-5y +4z +1) +3y -z = 2 . . . . substitute for x in the third equation
-7y +7z = 0 . . . . . . . . . . . . . . subtract 2; collect terms
y = z . . . . . . . . . . . . . . . . . . . . divide by -7; add z
This is a dependent set of equations, so has an infinite number of solutions. Effectively, they are ...
x = 1 -z
y = z
z is a "free variable"
What is the measure of angle BAC?
ABCD is a square
30
45
60
90
Answer:
B:45 degrees.
Step-by-step explanation:
We are given that a square ABCD .
We have to find the measure of angle BAC.
We know that each angle of square is of 90 degrees.
We know that diagonal AC bisect the angle BAD.
Therefore, measure of angle BAC=Measure of angle CAD.
Measure of angle BAD=[tex]\frac{1}{2}\times 90=45^{\circ}[/tex]
Hence, the measure of angle BAC=45 degrees.
Answer:B:45 degrees.
Answer:
45
Step-by-step explanation:
Please help me out!!!!!!!!!!!!!!!!!!
Answer: true
Step-by-step explanation: x-values are not repeated
Answer:
True
Step-by-step explanation:
For a relation to be a function, each value of x in the domain maps to exactly one unique value of y in the range.
This is the case here, thus this is a function.
The set of valid inputs for a function is called the The letter a in parentheses above a horizontal line. _____ (a) , and the input variable x is called the The letter b in parentheses above a horizontal line. _____ (b) variable.
Answer:
(a) domain
(b) "argument," or "independent variable"
Step-by-step explanation:
You may want to refer to your notes for terminology related to functions. Different terms are used, depending on the context.
__
The set of valid inputs for a function is called the domain.
__
The input variable x is called the argument, or independent variable.
The set of valid inputs for a function is referred to as the domain, and the variable x is known as the independent variable in a function or an equation.
Explanation:The set of valid inputs for a function is called the domain (a), and the input variable x is called the independent variable (b).
In the context of the equation of a line, such as y = mx + b, the independent variable x is usually plotted on the horizontal axis. When you select a value for x, it is considered independent because it can be chosen freely, and then you solve the equation for y, which is the dependent variable because its value depends on the chosen x. An example would be setting x to a specific number to see what y would be, demonstrating how the equation represents a straight line on a graph with m representing the slope and b representing the y-intercept.
Iran of paper contains 500 sheets of paper. Norm has 373 sheets of paper left from a team. Express the option of a rem Norm has as a fraction and as a decimal
Answer:
373/500 = 0.746
Step-by-step explanation:
373 out of 500 is represented by the fraction 373/500.
This value is easily converted to a decimal number by multiplying numerator and denominator by 2:
(373×2)/(500×2) = 746/1000 = 0.746
_____
You can also divide 373 by 500 using a calculator to get the decimal result.
Charles is making pumpkin latte his recipe makes five lattes and cars for 5 cups of milk for each cup of pumpkin Purée if child Charles is making 15 pumpkin lattes how many cups of milk will he need
Answer:
15 cups
Step-by-step explanation:
To make 15 lattes, Charles will triple his recipe, so use 3×5 = 15 cups of milk.
How fast must a truck travel to stay beneath an airplane that is moving 125 km/h at an angle of 35º to the ground?
Answer:
The horizontal speed of the truck is 102.39 km/hr.
Step-by-step explanation:
Given that,
Speed of airplane = 125 km/h
Angle = 35°
We need to calculate the horizontal speed
Using formula of horizontal speed
[tex]u_{x}=u\cos\theta[/tex]
Where, u = speed
Put the value into the formula
[tex]u_{x}=125\times\cos35^{\circ}[/tex]
[tex]u_{x}=102.39\ km/hr[/tex]
Hence, The horizontal speed of the truck is 102.39 km/hr.
Answer:
v = 102.4 km/h
Step-by-step explanation:
Given:-
- The speed of the airplane, u = 125 km/h
- the angle the airplane makes with the ground, θ = 35°
Find:-
How fast must a truck travel to stay beneath an airplane?
Solution:-
- For the truck to be beneath the airplane at all times it must travel with s projection of airplane speed onto the ground.
- We can determine the projected speed of the airplane by making a velocity (right angle triangle).
- The Hypotenuse will denote the speed of the airplane which is at angle of θ from the truck travelling on the ground with speed v.
- Using trigonometric ratios we can determine the speed v of the truck.
v = u*cos ( θ )
v = (125 km/h) * cos ( 35° )
v = 102.4 km/h
- The truck must travel at the speed of 102.4 km/h relative to ground to be directly beneath the airplane.
The heights of the adults in one town have a bell-shaped distribution with a mean of 67.5 inches and a standard deviation of 3.4 inches. Based on the empirical rule, what should you predict about the percentage of adults in the town whose heights are between 57.3 and 77.7 inches?
Answer:
The percentage is approximately 99.7%
Step-by-step explanation:
In order to understand this question you must understand the bell curve. (I would suggest googling a picture of the bell curve)
The mean of the bell curve is 67.5, meaning +1 standard deviation would be 70.9 (67.5+3.4). This would mean that 34% of the sample is between 67.5" and 70.9" (The bell curve % goes 34/14/2/.1 in that order)
When looking at the bell curve of this data, you would find that ±3 standard deviations gives you the range of 57.3" to 77.7". This would represent roughly (2+14+34+34+14+2)% of the sample. This excludes the .2% that are above or below 57.3" to 77.7". Therefore, the only answer that is close would be 99.7%
Using the empirical rule for a normal distribution, the calculation shows that approximately 99.7% of adults in town have heights between 57.3 and 77.7 inches.
Explanation:The heights of the adults in this town follow a bell-shaped distribution known as the normal distribution. This means that the values are symmetrically distributed around the mean, with most values close to the mean and fewer values farther away. The empirical rule states that approximately 68 percent of the data falls within one standard deviation of the mean, about 95 percent falls within two standard deviations, and about 99.7 percent falls within three standard deviations.
In this case, the mean is 67.5 inches and the standard deviation is 3.4 inches. Thus, one standard deviation away from the mean is a range from 67.5 - 3.4 = 64.1 inches to 67.5 + 3.4 = 70.9 inches. Two standard deviations away from the mean is a range from 64.1 - 3.4 = 60.7 inches to 70.9 + 3.4 = 74.3 inches. Three standard deviations away from the mean is a range from 60.7 - 3.4 = 57.3 inches to 74.3 + 3.4 = 77.7 inches.
Therefore, according to the empirical rule, we would predict that about 99.7 percent of adults in the town have heights between 57.3 and 77.7 inches.
Learn more about Empirical Rule here:https://brainly.com/question/30700783
#SPJ3
Find the equation of the line in slope-intercept form that passes through the following points. Simplify your answer.
(−5,−8) and (−7,8)
Answer:
y=-8(x+6)
Step-by-step explanation:
The equation of a line is [tex]y=mx+b[/tex] where m is the pending and b is the y intercept,
First we are going to calculate m:
If you have two points [tex]A=(x_{1},y_{1})\\B=(x_{2},y_{2})[/tex],
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
In this case we have A=(-5,-8) and B=(-7,8)
[tex]x_1=-5, y_1=-8\\x_2=-7,y_2=8[/tex]
Replacing in the formula:
[tex]m=\frac{8-(-8)}{(-7)-(-5)}\\\\m=\frac{16}{-2} \\\\m=-8[/tex]
Then [tex]y=-8x+b[/tex].
We have to find b, we can find it replacing either of the points in [tex]y=-8x+b[/tex]:
Replacing the point (-5,-8):
[tex]y=-8x+b\\-8=-8.(-5)+b\\-8=40+b\\-8-40=b\\-48=b[/tex]
Or replacing the point (-7,8):
[tex]y=-8x+b\\8=-8.(-7)+b\\8=56+b\\8-56=b\\-48=b[/tex]
The answer is the same with both points.
Then we have:
y=-8x-48
y=-8(x+6)
Complete the proof for the following conjecture.
Given: AC = BD
Prove: AB = CD
Statements Reasons
1. 1.
2. 2.
3. 3.
4. 4.
Please help!!!
Answer:
Statements Reasons
AC+CD=AD and AB+BD=AD Segment Addition Postulate
AC+CD=AB+BD Transitive/Substitution Property
AC=BD Given
BD+CD=AB+BD Substitution Property
CD=AB Subtraction Property
AB=CD Symmetric Property
Step-by-step explanation:
By segment addition postulate, we can say the following two equations:
AC+CD=AD and AB+BD=AD.
By either substitution/transitive property, you can say AC+CD=AB+BD.
You are given AC=BD, so we use substitution and write AC+CD=AB+AC.
After using subtraction property (subtracting both sides by AC), you obtain CD=AB.
By symmetric property, you may say AB=CD.
So let's write it into the 2 column-proof you have there:
Statements Reasons
AC+CD=AD and AB+BD=AD Segment Addition Postulate
AC+CD=AB+BD Transitive/Substitution Property
AC=BD Given
BD+CD=AB+BD Substitution Property
CD=AB Subtraction Property
AB=CD Symmetric Property
Properties/Postulates used:
Transitive property which says:
If a=b and b=c, then a=c.
Substitution property which says:
If a=b, then b can be substituted(replaced with) for a.
Subtraction property which says:
a=b implies a-c=b-c.
Segment Addition Postulate says:
If you break a segment into two smaller pieces then the measurement of that segment is equal to the sum of the smaller two segments' measurements.
Please help me out with this
Answer:
y = - 3x + 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (2, - 2) ← 2 points on the line
m = [tex]\frac{-2-4}{2-0}[/tex] = [tex]\frac{-6}{2}[/tex] = - 3
Note the line crosses the y- axis at (0, 4) ⇒ c = 4
y = - 3x + 4 ← equation of line