Answer
you do 420x0.7= 29.40
Answer:
The sales tax is 29.4
Step-by-step explanation:
Just divide in half until you reach 5 and then calculate the other 2 percent of it and add the 2 percent back onto it.
Write the prime factorization of 27.
Order the factors from least to greatest (for example, 2 × 2 × 3 × 5).
Answer:
3*3*3 or 3^3
Step-by-step explanation:
27/3=9/3=3
so 3*3*3 or 3^3
i will literally do ANYTHING for doordash mcdonalds literally Anything for 20 dollars
Answer: Nice
Step-by-step explanation:
James knows that he eventually wants to buy a motocycle, and the model he has in mind cost $5000. he has found a bank that will let him open a saving account with 7% interest that is compounded monthly. if he wants to buy his motocycle in 5 years ( he's still nervious) how much money should he invest in the account now
He should invest $86.29 in the account now, which has a 7% interest compounded monthly.
Compound interest refers to the amount of interest added on the principal amount plus interest. The formula for compound interest is:
B = P(1 + r/n)^t
where B is the ending balance, P is the principal amount or original balance, r is the interest rate in decimal form, n = number of times interest is compounded monthly, and t is the time in number of months
Based on the given information, P is the unknown and
B = $5000
t = 5 years = 60 months
r = 7% = 0.07
n = 1
Plug in the values and solve for P or the amount that should be invested today.
B = P(1 + r/n)^t
$5000 = P(1 + 0.07/1)^60
$5000 = P(1.07)^60
P = $5000/(1.07)^60
P = $86.29
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[tex]a(n)=a(n-1)-5[/tex]a(n)=a(n-1)-5
The first five terms of the arithmetic sequence with the formula a(n) = a(n - 1) - 5 is; -5, -10, -15. -20, -25
What is the nth term of the arithmetic sequence?
The general formula for an arithmetic sequence is;
aₙ = a + (n - 1)d
where;
a is first term
d is common difference
aₙ is the nth term of the sequence
Now we are given the formula for the nth term of a sequence as;
a(n) = a(n - 1) - 5
Thus;
1) First term is when n = 1;
a(1) = a(1 - 1) - 5
a(1) = -5
2) Second term is when n = 2;
a(2) = -5(2 - 1) - 5
a(2) = -5 - 5
a(2) = -10
3) Third term is when n = 3;
a(3) = -5(3 - 1) - 5
a(3) = -15
4) Fourth term is when n = 4;
a(4) = -5(4 - 1) - 5
a(4) = -20
5) Fifth term is when n = 5;
a(5) = -5(5 - 1) - 5
a(5) = -25
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Complete question is;
Write the first five terms sequence defined by a(n) = a(n - 1) - 5
Can someone help me on this question? I think it’s the 2nd answer but I’m not sure
From the properties of a right triangle is found that the missing length x= [tex]5\sqrt{3}[/tex].
RIGHT TRIANGLEA triangle is classified as a right triangle when it presents one of your angles equal to 90º. The greatest side of a right triangle is called the hypotenuse. And, the other two sides are called legs.
The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.
The Pythagorean Theorem says: (hypotenuse)²= (leg1)²+(leg2)² . And the main trigonometric ratios are: sin (x) , cos (x) and tan (x) .
The sum of the internal angles of a right triangle also is equal to 180°.
The question gives a figure which is compound for two right triangles.
For each triangle is informed two angles, then:
Triangle 1 - It is given the angle 45° and 90°, thus the third angle will be:45+90+ x = 180
135 + x =180
x=180-135
x=45°
Triangle 2 - It is given the angle 60° and 90°, thus the third angle will be:60+90+ y = 180
150+ y =180
y=180-150
y=30°
Thus, the angles for the given triangle are:
Triangle 1 - 45°, 45° and 90°Triangle 2 - 60°, 30° and 90°From the trigonometric ratio sinФ, you can find the hypotenuse the triangle 2. See below.
[tex]sin \theta =\frac{opposite\ leg }{hypotenuse} \\ \\ sin 45 =\frac{hypotenuse \ triangle 2 }{hypotenuse \ triangle 1} \\ \\ \frac{\sqrt{2} }{2}=\frac{hypotenuse \ triangle 2 }{10\sqrt{2} }\\ \\ 2*hypotenuse \ triangle 2 = 10*2\\ \\ hypotenuse \ triangle 2 = \frac{10*2}{2} \\ \\ hypotenuse \ triangle 2 =10[/tex]
If the hypotenuse of triangle 2 is 10, you can apply again the trigonometric ratio sinФ for finding x
[tex]sin \theta =\frac{opposite\ leg }{hypotenuse} \\ \\ sin 60=\frac{x }{hypotenuse \ triangle 2} \\ \\ \frac{\sqrt{3} }{2}=\frac{x }{10}\\ \\2x=10 \sqrt3\\ \\ x=5\sqrt3[/tex]
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equation of the line that passes through the points (1,-4)(1,−4) and (5,-1)(5,−1). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
The equation of the line in the slope-intercept form will be y = (3/4)x + 13/4.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The points are given below.
(1, −4) and (5, −1)
The equation of the line that passes through (1, −4) and (5, −1) will be given as,
(y + 4) = [(−1 + 4) / (5 − 1)](x − 1)
y + 4 = (3/4)x − 3/4
y = (3/4)x + 13/4
The equation of the line in the slope-intercept form will be y = (3/4)x + 13/4.
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I NEED HELP!!
Information:
Ryan conducted a 6-day study observing the effects of an organic plant food on the growth of his sprouting bean plant. He tracked these two pieces of information:
1. the amount of plant food remaining in the container after each day’s feeding
2. the height of the plant over time
(There was a total of 72 millimeters of plant food)
Question:
Write a function rule for the relationship between the amount of plant food remaining, f(x), and the number of days that have passed, x.
This relationship is not a function because more than one amount of plant food remains each day.
What is a function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that, Ryan did an experiment by observing the effects of plant food and the growth of the sprouting bean plant. He made a note of the height of the bean plant and the amount of food remaining in the container for the plant after feeding each day.
Thus, he observed that the plant food in the container decreases by an equal amount every day as the bean plant grew. Thus, this states that it is not a function between the two, as there are more than one plant food remaining each day for the plant.
Hence, This relationship is not a function because more than one amount of plant food remains each day.
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The sequence below is arithmetic. Complete parts (a) through (d) below.
- 1, 2, 5, 8, ...
(a) Find the common difference.
The common difference is d= . (Type a whole number.)
(b) Find the eighth term.
The eighth term is ag =
(Type a whole number.)
(c) Find a recursive rule for the nth term.
(Type an equation.)
(d) Find an explicit rule for the nth term.
(Type an equation.)
Answer:
see explanation
Step-by-step explanation:
- 1, 2, 5, 8
(a)
the common difference
d = a₂ - a₁ = 2 - (- 1) = 2 + 1 = 3
(b)
to find a term in the sequence add d = 3 to the previous term
a₅ = = 8 + 3 = 11
a₆ = 11 + 3 = 14
a₇ = 14 + 3 = 17
a₈ = 17 + 3 = 20
(c)
the recursive rule is
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 3 : a₁ = - 1
(d)
the explicit rule for an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = - 1 and d = 3 , then
[tex]a_{n}[/tex] = - 1 + 3(n - 1) = - 1 + 3n - 3 = 3n - 4
a random sample of 42 college graduates revealed that they worked an average of 7.3 years on the job before being promoted. the sample standard deviation was 2.9 years. using the 0.99 degree of confidence, what is the confidence interval for the population mean?
The confidence interval for the population mean with 99% confidence interval is (6.90;8.50).
What is meant by confidence interval?A confidence interval is a set of values that, with a particular level of certainty, includes a population value. When a population mean is between an upper and lower interval, it is frequently stated as a percentage.
The population mean is mean [tex]\bar{x}[/tex]=7.3.
The sample's standard deviation is 2. 9
Number of samples: 42
The range of possibilities for the mean, [tex]\bar{x}[/tex]
The confidence interval for the mean is
[tex]\bar{x}[/tex] ± (σ/√n)
To calculate the critical value, we must first determine the degrees of freedom, which are given by:
df=n-1
df=42-1
df=41.
Since the confidence level is 0.99 or 99%, the values of and can be used to calculate the critical value using Excel, a calculator, or a table is 2.701
7.3-2.701(2.9/√42)=6.9013
7.3+2.701(2.9/√42)=8.5086
The 99% confidence interval in this instance would therefore be provided by (6.90;8.50).
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kumiko decides to buy the same number of apps and games, and she decides to spend as much of the $50 as possible. how many apps and games does she buy? how much money does she have left on her gift card?
The linear inequality representing the number of apps and games that Kumiko can buy is [tex]1.25a+2.5g\leq50[/tex].
Expressions using linear inequalities compare any two values using inequality symbols like "," ">," "," or "."
The linear inequality representing the number of apps and games that Kumiko can buy is [tex]1.25a+2.5g\leq50[/tex].
What is Inequality?Expressions using linear inequalities compare any two values using inequality symbols like "," ">," "," or "." These values might be either numerical, algebraic, or both.
The number of apps Kumiko buy is a and the number of games she can buy is g.
The gift card has 50$.
Total amount of apps = 1.25a
Total amount of games = 2.5g
So, the linear equality will be [tex]1.25a+2.5g\leq50[/tex].
She can can only games and apps for amount less than and equal to $50.
Therefore, The linear inequality representing the number of apps and games that Kumiko can buy is [tex]1.25a+2.5g\leq50[/tex].
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The given question is Incomplete. Here is the complete question:
Kumiko has a $50 gift card for a Web site that sells apps and games. Games cost $2.50 each, and apps cost $1.25 each. Write an inequality that represents the number of apps a and the number of games g that Kumiko can buy and describe any constraints.
Students in a classroom have eaten 20% of jellybeans from a jar. There are now only 100 jellybeans left! How many jellybeans were in the jar to begin with?
Using percentages we calculate in the beginning there were 125 jellybeans in the jar.
Let the number of jellybeans in the jar was x.
Now student ate 20% of the jellybeans.
Number of jellybeans students ate = 20% of x = 0.2x
Number of jellybeans left = x - 0.2x = 0.8x
But the number of jellybeans is given as 100.
Therefore 0.8x = 100
or, x = 100 /0.8 = 125
Hence there were 125 jellybeans in the jar.
The English word "percentage" derives from the Latin phrase "per centum," which means "by the hundred." Percentages are fractions with a denominator of 100.
In other words, that is a relationship where it is always assumed that the value of the whole is 100.
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In a wildlife park they were 18 gray wolves after three years they were 27 gray wolves. What is the percent gain?
Answer: 66.66.....% (6 recurring) / 66.67%
Step-by-step explanation: To get the percent form of this, you'll need to turn this into a fraction, which would be 18/27, then you can simplify it to 2/3 and convert it to a percent which would be 66.66..... .
Joe and Chris share a locker at school. if they each have 8 classes and each class has 2 books, how many books are in the locker. Please show the work! :)
Answer:
32 books
Step-by-step explanation:
Well if each have 8 classes and 2 books per class then to get the total of books you'd multiply 8x2 and you get 16 for one alone. Since its two people sharing a single locker than add 16 with another 16 and you get 32!
sorry I can't physically show the work but writing down a 8x2 on the side and then adding 16 to that answer should show it off! :]
700% of what number is 1,540
If 700% of a number is 1540, then the number is 220
The given percentage = 700%
The percentage of a number is defined as the ratio that can be expressed as the fraction of 100.
Consider the number as x
Here the 700% of the number is 1540
Then the equation will become
x × 700% = 1540
Solve the equation and find the value of x
x × (700/100) = 1540
Divide the terms first
x × 7 = 1540
Move the 7 to the right hand side of the equation
x = 1540/7
Divide the terms
x = 220
Hence, if 700% of a number is 1540, then the number is 220
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23.45+1.9-5.78-2.6 ?
Answer:
16.97
Step-by-step explanation:
The shaded area below is 79 m².
Work out the area of the smaller rectangle.
If your answer is a decimal, give it to 2 d.p.
x+4 m
x + 3 m
x+2m
2x+5 m
Not drawn accurately
Answer:
[tex](x + 4)(2x + 5) - (x + 3)(x + 2) = 79 \\ 2x {}^{2} + 5x + 8x + 20 - {x}^{2} - 2x - 3x - 6 = 79 \\ {x}^{2} + 8x + 14 = 79 \\ {x}^{2} + 8x - 65 = 0 \\ {x}^{2} + 13x - 5x - 65 = 0 \\ x(x + 13) - 5( x + 13) = 0 \\ (x - 5)(x + 13) = 0[/tex]
x-5=0
x=5
the length of smaller rectangle= 8 m
and breadth of s. rectangle= 7 m
l x b = 8 x 7
[tex]56 {m}^{2} [/tex]
hopefully this will u
Fill in the missing values from the similar figures in the table
Step-by-step explanation:
9 × 1/2 = 4.5
8 × 1/2 = 4
hope it's helpful
3. One batch of pancakes needs 1½ cups of pancake mix. One box has 9 cups of pancake mix.
How many batches of pancakes can be made with one box of pancake mix?
In linear equation, 27/2 pancakes are in the box .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a " of two variables," where x and y are the variables.Number of b pancake mix to be need = 1½ cups
Number of box has pancake mix = 9 cups
Therefore, in order to get the total number of batches of pancakes needed for the batches will be calculated thus
= 1½ * 9
= 3/2 * 9
= 27/2
therefore 27/2 pancakes are in the box .
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Suppose U = {2,3,6,9,10,13,14,17,19) is the universal set and A = {2,9,10). What is A'?
The complement of set A is { 3, 6, 13, 14, 17, 19}
What is the complement of a given set?The complement of a set is the set that includes all the elements of the universal set that are not present in the given set. Let's say A is a set of all coins which is a subset of a universal set that contains all coins and notes, so the complement of set A is a set of notes (which do not includes coins).
U = {2,3,6,9,10,13,14,17,19}, A = {2,9,10}
set A complement are all the elements in the Universal set U not contained in set A. Those elements are in set A' = { 3, 6, 13, 14, 17, 19}
In conclusion the complement of set A is { 3, 6, 13, 14, 17, 19}
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Jeremy has a huge display of holiday decorations outside his home. He used 6 kilowatt hours (KWH) of electricity in November and used a total of 120KWH during the holiday season until he took them down on December 30. Set up and solve an equation that can be used to calculate the amount of electricity Jeremy used per day during the month of December.
The equation that can be used to find the amount of electricity Jeremy used per day during the month of December is 3.8KWH per day and Jeremy used 3.8KWH per day electricity in the month of December.
How to write and solve an equation?Electricity Jeremy used in November = 6 kilowatt hours (KWH)
Total electricity used in the holiday season = 120KWH
He took the decorations down on December 30
Amount of electricity Jeremy used per day during the month of December =
(Total electricity used in the holiday season - Electricity Jeremy used in November) / 30 days
= (120KWH - 6KWH) / 30
= 114KWH / 30
= 3.8KWH per day
In conclusion, the amount of electricity Jeremy used per day in December is 3.8KWH per day.
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lify.
(√-4)(4√-25) help me i dont get how to do this
Answer:
-40
Step-by-step explanation:
The Concept here is Complex Numbers
where [tex]\sqrt{-1}=i \ and \ i^{2} = -1[/tex]
Then [tex]\sqrt{-4}=\sqrt{4i^{2} } =\sqrt{(2i)^{2} } =2i[/tex]
Also [tex]\sqrt{-25}=\sqrt{25i^{2} } =\sqrt{(5i)^{2} } =5i[/tex]
Then [tex](\sqrt{-4} )(4\sqrt{-25} )=(2i)(4*5i)=40i^{2} =40*-1=-40[/tex]
Glad to Help:)
when x = -2, y = []
when x = 0, y = []
when x = 2, y = []
when x = 4, y = []
The values of y respective to x values are when x = -2 then y = 12 when x = 0 then y = 2 when x = 2 then y = -8, & when x = 4 then y = -18.
What is a function rule?
The equation-based relationship between the dependent and independent variables is known as a function rule. In simple words, a function is an association between inputs in which each input is connected to precisely one output.
Given, y = -5x + 2
when x= -2, y = (-5)* (-2) + 2 = 10 + 2 = 12, y = 12
when x= 0, y = (-5)* (0) + 2 = 0 + 2 = 2, y = 2
when x= 2, y = (-5)* (2) + 2 = -10 + 2 = -8, y = -8
when x= 4, y = (-5)* (4) + 2 = -20 + 2 = -18, y = -18
Hence, these are the required values of y to the respective input value of x.
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A: 10:00 am a truck started traveling from point A with a speed of 40mph. 3 hours
and 10 minutes later a car started to drive from point A in the same direction
with an
average speed of 60mph. At what time will the car catch up with
the truck?
Answer:h
Step-by-step explanation:
ihlug
Find the least common denominator. Then express each fraction using the least common denominator. 3/4 and 5/6
I need a answer
Answer:
The least coomon denominator is 12, so
9/12 and 10/12
a circle is always sometimes or never similar to the other circle because we can always sometimes or never map one onto the other using dilations and rigid transformations
Answer: always, always
Step-by-step explanation:
Every circle is similar to every other circle.
F(x,y) = x^2 + y^2 - 2x, D is the closed triangular region with vertices (0,0), (0,2), and (0,-2). Find the absolute maximum and minimum values of f on the set D. I know the maximum and minimum are f(0,+-2) = 4, minimum f(1,0) = -1. I need a step by step process on how to get to this answer
The absolute maximum value is f(0,±2) = 4 and the absolute minimum value is f(1,0) = -1.
The given function is F(x,y) = [tex]x^{2}[/tex] + [tex]y^{2}[/tex] - [tex]2x[/tex] → 1
D is the closed triangular region with the vertices (0,0), (0,2) and (0,-2).
Differentiate 1 partially with respect to x:
df/dx = [tex]x^{2}[/tex] + [tex]y^{2}[/tex] - [tex]2x[/tex]
[tex]f^{'}[/tex](x) = 2x - 2
Differentiate 1 partially with respect to y:
df/dy = [tex]x^{2}[/tex] + [tex]y^{2}[/tex] - [tex]2x[/tex]
[tex]f^{'}[/tex](y) = 2y
Consider [tex]f^{'}[/tex](x) = 0 and [tex]f^{'}[/tex](y) = 0 to find the critical points.
[tex]f^{'}[/tex](x) ⇒ 2x -2 =0
x = 1
[tex]f^{'}[/tex](y) ⇒ 2y
y = 0
Thus, the critical point is (x,y) = (1,0).
Calculate the values of f(x,y) at (0,0), (0,2), (0,-2) and (1,0).
At (x,y) = (0,0)
f(0,0) ⇒ 0 + 0 - 0 = 0
At (x,y) = (0,2)
f(0,2) ⇒ 0 + 4 - 0 = 4
At (x,y) = (0,-2)
f(0,-2) ⇒ 0 + 4 - 0 = 4
At (x,y) = (1,0)
f(1,0) ⇒ 1 + 0 - 2 = -1
Therefore, the absolute maximum is f(0,±2) = 4 and the absolute minimum is f(1,0) = -1.
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g in october 2012, apple introduced a much smaller version of the apple ipad, known as the ipad mini. weighing less than 11 ounces, it was 50% lighter than the standard ipad. battery tests for the mini ipad showed that battery life is uniformly distributed between 8.5 and 12 hours. calculate the expected value to two decimals.
Using the concepts of probability, we got that 0.4286 is the probability that the battery life for an iPad Mini will be 10 hours or less which is about 42.86%.
From the given information;
Let X represent the continuous random variable with uniform distribution U (A, B) . Therefore the probability density function can now be determined as :
[tex]f_X(x)[/tex] = [tex]\frac{1}{B-A}[/tex] where A<x<B
where A and B are the two parameters of the uniform distribution
From the question;
Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours
So; Let A = 8,5 and B = 12
Therefore; the mathematical expression for the probability density function of battery life is :
[tex]f_X(x)[/tex] = [1 / (12-8.5)]8.5<x<12
[tex]f_X(x)=[/tex](1/3.5)8.5<x<12
The probability that the battery life for an iPad Mini will be 10 hours or less can be calculated as:
F(x) = P(X ≤x)
F(10)=[tex](x-A)/(B-A)[/tex]
F(10)=(10-8.5)/(12-8.5)
F(10)=1.5/3.5
F(10)=0.4286
Hence, the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286
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(Complete question)
In October of 2012, Apple introduced a much smaller variant of the Apple iPad, known at the iPad Mini. Weighing less than 11 ounces, it was about 50% lighter than the standard iPad. Battery tests for the iPad Mini showed a mean life of 10.25 hours (The Wall Street Journal, October 31, 2012). Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?
A right triangle's hypotenuse is 1 cm longer than twice the length of the shortest side.
The third side is 1 cm less than twice the shortest side.
Find the length (in cm) of the hypotenuse.
The length (in cm) of the hypotenuse is 17 cm.
What is Pythagoras' theorem?According to Pythagoras' theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides.
H² = P² + B²
Let the hypotenuse = H
Shortest side = B
Third side = P
So, according to the question
H = 2B +1 ..... (1)
P = 2B -1 ..... (2)
Use Pythagoras' theorem,
H² = P² + B²
(2B+1)² = (2B-1)² + B²
4B² + 1 + 4B = 4B² + 1 - 4B + B²
4B = - 4B +B²
B² =-8B
B = - 8
But the length cannot be negative, so B = 8 cm
The length of the shortest side = 8 cm
So the hypotenuse will be
H = 2B + 1
= 2(8) + 1
= 17 cm
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assume that the heights of men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. the u.s. marine corps requires that the heights of men be between 64 and 78 inches. if 500 men want to enlist in the u.s. marine corps, how many would you not expect to meet the height requirements?
The percentage of men who didn't expect to meet the height requirements be 96.29%
Given, that the heights of men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches.
Find the percentage of men who meet the height requirements.
z(64) = (64-69)/2.8 = 1.7857
z(78) = (78-69)/2.8 = 3.2143
P(64 <= x <= 78) = P(1.78457<= z <=3.2143) = 0.0371 = 3.71%
So, the percentage of men who meet the height requirements be 3.71%
Now, the percentage men who didn't expect to meet the height requirements be
100 - 3.71 = 96.29%
Hence, the percentage of men who didn't expect to meet the height requirements be
96.29%
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(y+6) (y+13) find the product
step by step explanation pls
Answer:
(y + 6)(y + 13) = y² + 19y + 78
Step-by-step explanation:
[tex] \rm \implies (y + 6)(y + 13) \\ \\ \rm \implies y(y + 13) + 6(y + 13) \\ \\ \rm \implies {y}^{2} + 13y + 6y + 78 \\ \\ \rm \implies {y}^{2} + 19y + 78[/tex]