Answer:
Most likely 4cm and 5cm
Step-by-step explanation:
Where 5cm=length
And 4cm=width
A Finnish registration consists of 3 letters and 3 numbers with empty spaces possible.
Numbers do not have leading zeroes and the number part cannot be only zero (for example AAA-001 isn't a valid plate but AAA-1 is). The registration plate must have at least one letter and one number. How many possible Finnish registration plates are possible to exist when the letters used are the 26 letters of the latin alphabet?
Answer:
How many possible plates there could be if we also allowed the letters Å, Ä and Ö?
Answer:
Using the Fundamental Counting Theorem, the number of plates for each case is obtained as follows:
Latin Alphabet: 17,558,424.Extra Letters: 24,364,611.What is the Fundamental Counting Theorem?The Fundamental Counting Theorem is a theorem that states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is calculated by the multiplication of the factorials as presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
With the Latin letters, it is found that for the letters, there are 26 outcomes, hence:
[tex]n_1 = n_2 = n_3 = 3[/tex]
With one number, the number of outcomes for the digit is:
[tex]n_4 = 9[/tex]
(as the digit cannot be zero).
With two numbers, the number of outcomes for the digit are:
[tex]n_4 = 9, n_5 = 10[/tex]
With three numbers, the parameters are:
[tex]n_4 = 9, n_5 = 10, n_6 = 10[/tex]
Hence the total number of plates is obtained as follows:
T = 26³ x (9 + 9 x 10 + 9 x 10 x 10) = 17,558,424.
With the extra letters, each letter can assume 29 outcomes, hence the number of plates is:
T = 29³ x (9 + 9 x 10 + 9 x 10 x 10) = 24,364,611.
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Identify the property used to solve and the solution for each.
x/2 = 4
1 x/5= 10
2 5x = -35
5x = 10
When driving mountain roads, road signs often indicate the steepness of the road as a % grade which represents the angle of elevation as the road rises. Imagine your job is to collect or measure the data that is needed to determine the % grade of mountain roads in a certain region of the U.S. Which of these quantities is needed for you to be able to use arcsine to calculate the % grade? Select all that apply.
a) The length of a section of the road
b) The angle of depression
c) The horizontal distance travelled
d) The change in elevation along a section of road
The quantity that is needed for you to be able to use arcsine to calculate the percentage grade is D. The change in elevation along a section of road
What is an elevation?A geographic location's elevation is its height above or below a set reference point, most typically a reference geoid, which is a mathematical model of the Earth's sea level as an equipotential gravitational surface.
Elevation is described as the height above the ground or other surface, as well as a location or position of elevation. A plane flying 36,000 feet above the ground is an illustration of elevation. A pope being elevated to the position of saint is an example of elevation.
When driving on mountain roads, road signs frequently reflect the route's steepness as a percentage grade, which represents the angle of elevation as the road increases. In this case, the correct option is D.
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pls help! thanks in advance :)
Equation of the perpendicular line in slope intercept form is [tex]y = \frac{5}{2}x + 2[/tex]
Option A is correct
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Here, the given line is
2x + 5y = 10
5y = -2x + 10
[tex]y = -\frac{2}{5}x + \frac{10}{5}\\y = -\frac{2}{5}x + 2[/tex]
Slope of the given line is [tex]-\frac{2}{5}[/tex]
Slope of the line perpendicular to this given line is [tex]\frac{5}{2}[/tex]
The line passes through (-2, -3)
Equation of the required line
[tex]y - (-3) = \frac{5}{2}(x - (-2))\\y + 3 = \frac{5}{2}(x + 2)\\2y + 6 = 5x + 10\\2y = 5x + 10 - 6\\2y = 5x + 4\\y = \frac{5}{2}x + \frac{4}{2}\\y = \frac{5}{2}x + 2[/tex]
Equation of the perpendicular line in slope intercept form is [tex]y = \frac{5}{2}x + 2[/tex]
Option A is correct
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Finding a missing side length given two similar triangles
4). $1,200, 3.9%, 8 months
The simple interest on $1,200, 3.9%, 8 months is $31.356.
How to calculate the interest?From the informationm, we want to calculate the simple interest of the amount that is given.
The simple interest is calculated thus:
Simple interest = PRT / 100
where
P = Principal = $1200
R = Rate = 3.9%
T = Time = 8 months = 8/12 = 0.67 years
The interest will be:
Simple interest = PRT / 100
Simple interest = (1200 × 3.9 × 0.67) / 100
Simple interest = 31.356
The interest is $31.356.
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Complete question
Calculate the simple interest on $1,200, 3.9%, 8 months
A bag contains 35 coins, some dimes and some quarters. The total amount of money in the bag is $4.85. How many dimes and how many quarters are in the bag?
Answer:
9 quarters and 26 dimes
Step-by-step explanation:
your welcome :)
32/25 fraction as a mixed number
The value of 32/25 as mixed number is 1 7/25
What are mixed fraction?A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/7 is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.
A mixed fraction can be obtained wen there is improper fraction. Improper fraction is a fraction that it's numerator is larger than denominator for example 32/25.
To convert to mixed fraction we find the number of times 25 can go in 32, which is 1 and the remainder is 7
Therefore 32/25 = 1 7/25.
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You want to open an account with $1,700. You can earn 2.7% interest each year, and you plan to leave this account for 9 years. How much more would the account be worth after 9 years by calculating interest compounded quarterly versus calculating simple interest?
$2322.2 more the account be worth after 9 years by calculating interest compounded quarterly versus calculating simple interest.
Given that, principal = $1700, rate of interest = 2.7% and time period = 9 years.
What is the simple interest?Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.
Simple interest is calculated with the following formula: S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years.
Here, simple interest = (1700×2.7×9)/100
= 41310/100
= $413.10
Amount = Principal + Simple interest
= 1700+413.10
= $2113.1
Compound interest:
[tex]Amount=P(1+\frac{R}{100} )^{nt}[/tex]
[tex]=1700(1+\frac{2.7}{100} )^{4\times9}[/tex]
[tex]=1700(1.027)^{36}[/tex]
= 1700×2.609
= $4435.3
Now, 4435.3-2113.1=$2322.2
Therefore, $2322.2 more the account be worth after 9 years by calculating interest compounded quarterly versus calculating simple interest.
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A farmer owns a total of 8 4/5 acres of land. The land is separated into 4 equally sized sections. How many acres are in each section?
Write your answer as a mixed number or simplest form
Answer:
2 1/5
Step-by-step explanation:
8 4/5=44/5
(44/5)/(4)=(44/5)*(1/4)
(44/5)*(1/4)=44/20
44/20=2 1/5
solve the expression when a= 0.25 and b = -1
36a + 42b - 18a +6
The solution to the expression is -31.5
Algebraic expression
An algebraic expression in mathematical is statement that comprises of numbers, variables, symbols and mathematical operators.
Given, when a= 0.25 and b = -1
Step 1: Substitute the given into the expression 36a + 42b - 18a +6
we have; 36(0.25) + 42(-1) - 18(0.25) +6
= 9 - 42 - 4.5 +6
Step 2; use BODMAS to evaluate
we have; 9 - 42 - 4.5 +6= -31.5
Therefore the solution to the expression is -31.5
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Can you guys awnser this ?
a. Jays total income is $93.50 and total spending is $103.25.
b. Jays Spending is greater than income.
c. Total saving is -9.75
d. Jays savings are negative. Since Jays spending is greater than income it does not make sense.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Jays Income:
Part time job: $83.50
Allowance: $10
Spending:
Clothing: $32.50
Lunches: $19.75
Entertainment: $29.00
Transportantion: $22.50
a. Jays total income and total spending
Total income = $83.50+$10.00
=$93.50
Total spending = $32.50+$19.75+$29.00+$22.50
=$103.25
b. Spending is greater than income.
c. Jays saving=Total income - Total spending
=93.50-103.25
=-9.75
d. Jays savings are negative. Since Jays spending is greater than income it doesnt make sense.
Hence,
a. Jays total income is $93.50 and total spending is $103.25.
b. Jays Spending is greater than income.
c. Total saving is -9.75
d. Jays savings are negative. Since Jays spending is greater than income it doesnt make sense.
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Lenny and Lashae are shopping for new guitar strings in a music store. Lenny buys 2 packs of strings. Lashae buys 2 packs of strings and
a music book. The book cost $16. Their total cost is $72. How much is 1 pack of strings?
Answer:
Strings packs cost $14 each
Step-by-step explanation:
Lenny and Lashae are shopping for new guitar strings in a music store. Lenny buys 2 packs of strings. Lashae buys 2 packs of strings and a music book. The book cost $16. Their total cost is $72. How much is 1 pack of strings?
Lenny: 2s
Lashae: 2s + b
when b = $16 then these equations are:
Lenny: 2s
Lashae: 2s + 16
together they spent $72 so:
lenny + Lashae = $72 or:
2s + 2s + 16 = 72
subtract 26 from both sides:
2s + 2s + 16 - 16 = 72 - 16
2s + 2s = 56
combine s terms:
4s = 56
divide both sides by 4:
4s/4 = 56/4
s = $14
Need answer ASAP
QUESTION 16
Write an inequality of the form |x-al k so that the inequality has the given solution
set.
(-5,5)
An inequality of the form |x-al<k so that the inequality has the given solution set (-5,5) is |x|<10.
In the given question,
We have to write an inequality of the form |x-a|<k so that the inequality has the given solution set (-5,5).
We first learn about modulus,
A modulus function is a function that determines a number or variable's absolute value. It generates the size of the variable count. A function with absolute values is another name for it. No matter what input was provided to this function, the outcome is always positive.
The given set is (-5,5).
For x<(-5,5)
The mean value of x should be between -5 and 5.
-5<x<5
|x|<10
Hence, an inequality of the form |x-a l<k so that the inequality has the given solution set (-5,5) is |x|<10.
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Simplify: 2cd3(c − d + 5)
Responses
A 2cd3 − 2c2d4 + 10c2d32 cd 3 − 2 c 2 d 4 + 10 c 2 d 3
B 2c2d3 − 2cd4 + 10cd32 c 2 d 3 − 2 cd 4 + 10 cd 3
C 2cd3 − 2cd3 + 10cd32 cd 3 − 2 cd 3 + 10 cd 3
D 2c2d3 − 2c2d4 + 10cd2
Simplification of the given expression 2cd³ (c - d +5) is given by
2c²d³ − 2cd⁴ + 10cd³.
As given in the question,
Given expression is equal to :
2cd³ (c - d +5)
Law of exponents for multiplication is given by:
mᵃ × mᵇ =mᵃ⁺ᵇ
Simplification of the given expression by open the parenthesis we have,
= 2cd³ × c - 2cd³ × d + 2cd³ × 5
Apply law of exponents for multiplication we get,
= 2c¹⁺¹d³ -2cd³⁺¹ + (2×5)cd³
= 2c²d³ -2cd⁴ + 10cd³
Therefore, simplification of the given expression 2cd³ (c - d +5) is given by 2c²d³ − 2cd⁴ + 10cd³.
The complete question is:
Simplify : 2cd³ (c - d +5)
a. 2cd³− 2c²d⁴ + 10c²d³
b. 2c²d³ − 2cd⁴ + 10cd³
c. 2cd³ − 2cd³ + 10cd³
d. 2c²d³− 2c²d⁴ + 10cd²
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Compute the probability of tossing a six sided die with sides numbered 1 through 6 and getting a 5
The probability of tossing a six-sided die with sides numbered 1 through 6 and getting a 5 is 0.166666 or 1/6.
Here in the question, we see that a six-sided die is tossed. So there will be a total of 6 outcomes.
So the sample space will be {1,2,3,4,5,6}
Of which the possible outcome of getting a 5 is 1
Let A be the event of getting a 5 on tossing a six-sided die
∴ the probability of getting a 5 on tossing a six-sided die is P(A)=1/6
∵ we know that the probability of an event is the possible outcome of the event divided by the total outcomes of that event.
So here the probability of getting a 5 is 0.166666 or 1/6.
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Weight of pennies.
The distribution of weights of United States pennies is approximately normal with a mean of 2.4 grams and a standard deviation of
0.04 grams.
What is the probability that a randomly chosen penny weighs less than 2.4 grams? 6%
What is the probability that the mean weight of 15 pennies is less than 2.4 grams?
1) The probability that a randomly chosen penny weighs less than 2.4 grams is; 0.00621.
2) The probability that the mean weight of 15 pennies is less than 2.4 grams is; 0
How to apply the central limit theorem?The central limit theorem in statistics tells us that the sampling distribution of the mean will usually be normally distributed, provided that the sample size is large enough.
We are given the following parameter;
Population mean; μ = 2.4 grams
Standard deviation; σ = 0.04 grams
1) The probability that a randomly chosen penny weighs less than 2.4 grams is: P(X < 2.4)
Formula for z-score is;
z = (X - μ)/σ
z = (2.4 - 2.5)/0.04
z = -2.5
The p-value from z-score calculator is; p = 0.00621.
2) The standard deviation for these 15 pennies will now be;
σ' = 0.04/√15
σ' = 0.0103
The probability that the mean weight of 15 pennies is less than 2.4 grams is expressed as;
P(X' < 2.4)
z = (2.4 - 2.5)/0.0103
z = -9.709
The p-value from z-score calculator is; p = 0
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A 6-sided die with faces labeled1 to 6 will be rolled once.
The 6 possible outcomes are listed below.
Note that each outcome has the same probability.
Complete parts (a) through (c). Write the probabilities as fractions.
(chart attached below)
(a) Check the outcomes for each event below. Then, enter the probability of the event.
(b) P(A) + P(B) -P(A and B)=
(c) Select the answer that makes the equation true.
P(A) +P(B) - P(A and B)=
Answer:
A is shown in the attached image.
B. 5/6
C. P(A or B)
Step-by-step explanation:
B. 1/2 + 2/3 - 1/3 = 5/6 or 3/6 + 4/6 - 2/6 = 5/6
C. P(A or B) = 5/6. P(A) + P(B) - P(A and B) = 5/6. Therefore, P(A) + P(B) - P(A and B) = P(A or B).
Jim borrows $200 at 18% per annum compounded quarterly for 7 years. Determine the interest due on the loan.
The interest on the borrowed amount after 7 years is $486.
What is compound interest?The compound interest is a form of interest where the rate of interest is applied on the amount obtained after every interval of time.
Given that,
The amount borrowed is P = $200.
Rate of interest is r = 18% per annum compounded quarterly.
Total time is t = 7 years
Then, the rate of interest for quarterly compounding is given by,
r = 18 / 4%
= 4.5%
And, total time period for compounding is,
n = 7 × 4
= 28
The formula for compound interest is given as,
P[(1 + r / 100)ⁿ - 1]
Substitute the respective values to get,
200 × [(1 + 4.5 / 100)²⁸ - 1]
= 200 × 2.43
= 486
Hence, the interest due on the loan is given as $486.
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write the equation of the line that is perpendicular to the line y=-2 and passes through (4,-2)
the equation of the perpendicular line is x = 4, as the line vertical and the slope is undefined
What is the equation of the line that passes through the given point and is perpendicular to the given line?The point-slope formula is expressed as
y - y₁ = m( x - x₁ )
The slope intercept formula is expressed as;
y = mx + b
Where m is the slope and b is y-intercept.
Given the data in the question;
Equation: y = -2Point (x,y) : (4,-2)First, we determine the slope of the initial line by comparing to the slope intercept form y = mx + b
y = -2
Hence
Slope of initial line m = 0
Slope of the perpendicular line will be negative reciprocal of the initial line
m = -1/0
Slope m is undefined
Therefore, the perpendicular line is vertical and the slope is undefined
Hence.
x = 4.
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Jada claims that B'C'D' is a dilation of BCD using A as the center of dilation.
What are someways you can convince Jada that her claim is not true?
Dilation entails altering a figure's size.
Because the is larger than, Isaiah's assertion is untrue.
What is dilation?A transformation that alters the size of a figure is called a dilation (similarity transformation). It needs a scale factor and a central point. Depending on the value of k, the dilatation is either an enlargement or a reduction.The dilatation is an expansion if | k | > 1The dilation is a decrease if | k | 1.The new image's size in relation to the old image's size is determined by the scale factor's absolute value. The original image and the new image are on the same side of the center when k is positive. They are on opposing sides of the center when k is negative. A dilatation always has its own picture at its center.Although dilation is not a hard transformation, the angles of the figures it dilates remain unchanged.
The aforementioned claim suggests that,
The dimensions of and should be equal.
However, it is evident that;
are not equivalent.
In reality
greater than
Therefore, Isaiah's assertion is false.
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What is the solution to this system of equations?
3b + 4c = 3
8b+ 5c = 27
2b + 6c = 1
Here ya are hope this helps! :]]
What is the remainder of 233 Divided by 6
Answer:
38.8333333
sorry if it's wrong.
Match each number with its divisibility numbers.
3. 60
4. 48
5. 81
A. 3,9
B. 2,3
C.
2, 3, 5, 10
The numbers matched with its divisibility numbers is
for 60 the divisibility numbers are 2,3,5,10 .
for 48 the divisibility numbers are 2,3 and
for 81 the divisibility numbers are 3,9 .
In the question ,
three numbers are given as 60 , 48 and 81
we need to match them with their , respective divisibility numbers that are given in the option
For the first number 60 ,
we see that 60 is divisible by 2 , 3 , 5 and 10 because
30*2 [tex]=[/tex] 60 , 3*20 [tex]=[/tex] 60 , 5*12 [tex]=[/tex] 60 and 10*6 [tex]=[/tex]60 ,
So, for 60 the divisibility numbers are 2,3,5,10
that is option(c)
For the second number 48 ,
we see that 48 is divisible by 2 and 3 because
2*24 [tex]=[/tex] 48 , 3*16 [tex]=[/tex] 48 ,
So , for 48 the divisibility numbers are 2,3
that is option(b)
For the third number 81
we see that 81 is divisible by 3 and 9 because
3*27 [tex]=[/tex] 81 , 9*9 [tex]=[/tex] 81
So , for 81 the divisibility numbers are 3 an 9
that is option(a)
Therefore , The numbers matched with its divisibility numbers is
for 60 the divisibility numbers are 2,3,5,10 .
for 48 the divisibility numbers are 2,3 and
for 81 the divisibility numbers are 3,9 .
The given question is incomplete , the complete question is
Match the numbers 60 , 48 and 81 with its divisibility numbers
(a) 3,9
(b) 2,3
(c) 2,3,5,10
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Graph the polynomial equation by making a table of values. f (x)
=2x4 − 5x³+x²–2x+4
The graph of the function y = 2x⁴ - 5x³ + x² - 2x + 4 is plotted and attached.
What is a polynomial?Polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s). For example -
y = 4x⁴ + 3x³ + 2x² + 6x + 7
We have the following polynomial -
y = 2x⁴ - 5x³ + x² - 2x + 4
Now -
at x = 0, y = 4
at x = 1, y = 0
at x = 2, y = 32 - 40 + 4 - 4 + 4 = - 4
Refer to the graph attached. The points (0, 4), (1, 0) and (2, - 4) are plotted.
Therefore, the graph of the function y = 2x⁴ - 5x³ + x² - 2x + 4 is plotted and attached.
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Line n contains points (4, –1) and (4, 9). Point p has coordinates (1, 6).
The distance between the line containing points (4, –1) and (4, 9) and point p (1,6) is of:
3 units.
Distance of point and lineThe standard equation of a line is given by the rule presented as follows:
ax + by + c = 0.
The coordinates of the points which we want to find the distance from the line are given as follows:
(x0,y0).
Then the shortest distance is given by the equation presented as follows:
D = |a(x0) + b(y0) + c|/sqrt(a²+b²).
The two points of the line are given as follows:
(4, –1) and (4, 9).
Since the x-coordinate is constant, the line has a slope of infinite, meaning that it is a vertical line defined as follows:
x = 4.
x - 4 = 0.
The point p has these following coordinates:
p(1,6).
Hence the distance between the point and the line is:
D = |a(x0) + b(y0) + c|/sqrt(a²+b²).
D = |1(1) + 0(6) - 4|/sqrt(1² + 0²).
D = |-3|
D = 3 units.
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The length of a rectangle is 6 m longer than its width. If the perimeter of the rectangle is 64 m find its length and width in meters
The length and width of the rectangle with a perimeter of 64m are 19m and 13m respectively.
What is the length and width of the rectangle?The perimeter of a rectangle is expressed as;
P = 2( l + w )
Where l is length and w is width.
Given the data in the question;
Let x represent the width be represented by variable x.
Width w = xLength l = x + 6Perimeter = 64Plug the values into the equation above above.
P = 2( l + w )
64 = 2( (x + 6 ) + x )
64 = 2( 2x + 6 )
64 = 4x + 12
64 - 12 = 4x
52 = 4x
x = 52/4
x = 13
Hence, the dimensions of the rectangle are;
Width = x = 13m
Length = x + 6 = 13 + 6 = 19m
Therefore, the dimension of the rectangle are 13m by 19m.
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which function has the greater y-intercept?
y=-x+6 x: -1, 0, 1, 2, 3
y: 7,6,5,4,3
y=2x-3 x: -1, 0, 1, 2, 3
y: -5, -3, -1, 1, 3
By evaluating in x = 0, we can see that the function with the greater y-intercept is the first one:
y=-x+6
Which function has the greater y-intercept?
For any function y = f(x), we define the y-intercept as the value that y takes when we evaluate the function in x = 0.
For the first function:
y = -x + 6
The y-intercept is:
y = -0 + 6 = 6
While for the second function:
y = 2x - 3
Evaluating in 0 we get:
y = 2*0 - 3 = -3
So the y-intercept of the first function is 6, and the one of the second function is -3.
Then the first function has the greater y-intercept.
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Population: The Henry family has 5 children: Abby (age 15), Brian (age 10), Colin (age 9), Deena (age 7), and
Elise (age 5).
Sample
n = 2
Ages
Sample
range
A, B
15, 10
5
A, C
15,9
6
A, D
15,7
8
Α, Ε
15, 5
10
B, C
10,9
1
B, D B, E
00000000
10,7
3
10, 5
The last sample range in this table is missing. What is the missing value? 2
C, D
9,7
5 2
C, E
9,5
4
D, E
7,5
The last sample range in this table is missing,the missing value is 2.
Given:
The Henry family has 5 children: Abby (age 15), Brian (age 10), Colin (age 9), Deena (age 7), and Elise (age 5).
Sample(n = 2) A, B A, C A, D Α, Ε B, C ........ D,E
Ages 15, 10 15,9 15,7 15, 5 10,9 ....... 7,5
Sample range 5 6 8 10 1 ...........
Let x be the sample range missing.
sample range = ages difference
= Age of D - Age of E
= 7 - 5
= 2
Therefore The last sample range in this table is missing,the missing value is 2.
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Answer:
answer is 2 i did it and got it right
Step-by-step explanation:
What is the y-intercept of x = -4?
Answer:
DNE
Step-by-step explanation:
You want to know the y-intercept of x = -4.
Y-interceptThe y-intercept is the point where a graph crosses the y-axis.
The line x=-4 is a vertical line parallel to the y-axis, so does not cross the y-axis.
There is no y-intercept. It does not exist (DNE).