Answer:
3/8
Step-by-step explanation:
Answer:
3/8
Step-by-step explanation:
Find the GCD (or HCF) of numerator and denominator
GCD of 45 and 120 is 15
Divide both the numerator and denominator by the GCD
45 ÷ 15
120 ÷ 15
Reduced fraction:
3
8
Therefore, 45/120 simplified to lowest terms is 3/8.
Cristina is sending out thank you cards for birthday presents. She has pink (P), blue (B), and green (G) cards, and white (W) and yellow (Y) envelopes to send them in. She chooses a card and an envelope at random for each person. What is the sample space for possible combinations? Enter a list of text [more] Enter each outcome as a two-letter "word", with the first letter for the card and the second letter for the envelope. For example, PW would be a pink card in a white envelope. Separate each element by a comma.
Answer:
PW, BW, GW, PY, BY, GY
Step-by-step explanation:
We need to determine the sample space
pink(P), blue (B), and green (G) cards, (W) and yellow (Y) envelopes
Each color card can match with each color envelope
Start with the white envelopes and each color card
and then the yellow envelopes with each color card
PW BW GW
PY BY GY
-9x - 5 = 67
Pls help me
Answer:
x = -8
Step-by-step explanation:
-9x = 67+ 5
x = 72/-9
x = -8
Answer:
x=-8
Step-by-step explanation:
A car insurance company has determined that6% of all drivers were involved in a car accident last year. If14drivers are randomly selected, what is the probability of getting at most 3 who were involved in a car accidentlast year
Answer:
[tex]P(x \le 3) = 0.9920[/tex]
Step-by-step explanation:
Given
[tex]p = 6\%[/tex] --- proportion of drivers that had accident
[tex]n = 14[/tex] -- selected drivers
Required
[tex]P(x \le 3)[/tex]
The question is an illustration of binomial probability, and it is calculated using:
[tex]P(x ) = ^nC_x * p^x * (1 - p)^{n-x}[/tex]
So, we have:
[tex]P(x \le 3) = P(x = 0) +P(x = 1) +P(x = 2) +P(x = 3)[/tex]
[tex]P(x=0 ) = ^{14}C_0 * (6\%)^0 * (1 - 6\%)^{14-0} = 0.42052319017[/tex]
[tex]P(x=1 ) = ^{14}C_1 * (6\%)^1 * (1 - 6\%)^{14-1} = 0.37578668057[/tex]
[tex]P(x=2 ) = ^{14}C_2 * (6\%)^2 * (1 - 6\%)^{14-2} = 0.15591149513[/tex]
[tex]P(x=3 ) = ^{14}C_3 * (6\%)^3 * (1 - 6\%)^{14-3} = 0.03980719024[/tex]
So, we have:
[tex]P(x \le 3) = 0.42052319017+0.37578668057+0.15591149513+0.03980719024[/tex]
[tex]P(x \le 3) = 0.99202855611[/tex]
[tex]P(x \le 3) = 0.9920[/tex] -- approximated
evaluate (5^0-4^-1)×3/4
Answer:
[tex](5^{0} -4^{-1} )(\frac{3}{4} )\\\\=(1-\frac{1}{4^{1}} )(\frac{3}{4} )\\\\=(\frac{4}{4} -\frac{1}{4} )(\frac{3}{4} )\\\\=(\frac{3}{4} )(\frac{3}{4} )\\\\=\frac{9}{16}[/tex]
Two identical lines are graphed below. How many solutions are there to the
system of equations?
5
A. Infinitely many
B. Zero
C. One
D. Two
Two identical lines have, A. Infinitely many solutions.
What are the three types of solutions for a system of linear equations?If a system of equations only contains two linear equations with two variables,
The system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.
There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.
Given are two identical lines,
Now we know the solution of two lines is where they intersect.
We also know that a line is made up of infinite points, So if two lines are identical every point of one line lies with every other point of the other line.
Therefore they have an infinite number of solutions.
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The length side of xy is?
Answer:
10
Step-by-step explanation:
ok so you do 12/30 and u get a 0.4 ratio. boom multiply 0.4 by 25 and u get 10. so boom the length is 10
Answer:
XY=10
Step-by-step explanation:
Since they are similar the ratio between each sides should be the same.
Ratio is .4. Found by dividing 12/30.
Multiply .4 by 25= 10
Point-Slope Form of a Line
A ball is thrown straight up from a rooftop 320 feet high. The formula below describes the ball's height above the ground, h, in feet, t seconds after it was thrown. The ball misses the rooftop on its way down and eventually strikes the ground. How long will it take for the ball to hit the ground? Use this information to provide tick marks with appropriate numbers along the horizontal axis in the figure shown.
h=-16t^2+16t+320
The ball hits the ground after____ seconds
Answer:
28 seconds ..............
Answer by formula please
Answer:
Step-by-step explanation:
I honestly have no idea what you mean by answer by formula, but I'm going to give it my best. I began by squaring both sides to get:
(a² - b²) tan²θ = b² and then distributed to get:
a² tan²θ - b² tan²θ = b² and then got the b terms on the side to get:
a² tan²θ = b² + b² tan²θ and then changed the tans to sin/cos to get:
[tex]\frac{a^2sin^2\theta}{cos^2\theta}=b^2+\frac{b^2sin^2\theta}{cos^2\theta}[/tex] and isolated the sin-squared on the left to get:
[tex]a^2sin^2\theta=cos^2\theta(b^2+\frac{b^2sin^2\theta}{cos^2\theta})[/tex] and distributed to get:
***[tex]a^2sin^2\theta=b^2cos^2\theta+b^2sin^2\theta[/tex]*** and factored the right side to get:
[tex]a^2sin^2\theta=b^2(sin^2\theta+cos^2\theta)[/tex] and utilized a trig Pythagorean identity to get:
[tex]a^2sin^2\theta=b^2(1)[/tex] and then solved for sinθ in the following way:
[tex]sin^2\theta=\frac{b^2}{a^2}[/tex] so
[tex]sin\theta=\frac{b}{a}[/tex] This, along with the *** expression above will be important. I'm picking up at the *** to solve for cosθ:
[tex]a^2sin^2\theta=b^2cos^2\theta+b^2sin^2\theta[/tex] and get the cos²θ alone on the right by subtracting to get:
[tex]a^2sin^2\theta-b^2sin^2\theta=b^2cos^2\theta[/tex] and divide by b² to get:
[tex]\frac{a^2sin^2\theta}{b^2}-sin^2\theta=cos^2\theta[/tex] and factor on the left to get:
[tex]sin^2\theta(\frac{a^2}{b^2}-1)=cos^2\theta[/tex] and take the square root of both sides to get:
[tex]\sqrt{sin^2\theta(\frac{a^2}{b^2}-1) }=cos\theta[/tex] and simplify to get:
[tex]\frac{sin\theta}{b}\sqrt{a^2-b^2}=cos\theta[/tex] and go back to the identity we found for sinθ and sub it in to get:
[tex]\frac{\frac{b}{a} }{b}\sqrt{a^2-b^2}=cos\theta[/tex] and simplifying a bit gives us:
[tex]\frac{1}{a}\sqrt{a^2-b^2}=cos\theta[/tex]
That's my spin on things....not sure if it's what you were looking for. If not.....YIKES
What percent is modeled by the grid?
A grid model with 100 squares. 33 squares are shaded.
23%
30%
33%
40%
Answer
33 percent
Step-by-step explanation:
Answer:
33 squares are shaded 23%
Step-by-step explanation:
I hope this answer works out for you if it doesn't I'm really sorry have a great day
The height and weight of several adults were recorded:
Using this model, what would be the weight of someone who is 5.8 ft tall? Round your answer to the nearest tenth. You must find the quadratic regression equation first.
Weight of someone who is 5.8ft tall is 149.8 lbs.
What is a quadratic equation?A quadratic equation is a method of representation of a unknown variable by some variable of degree upto 2.
How to find the weight?a=5.607,b=-12.009,c=30.648
Let, y= weight(lbs) and x=height(ft)
y=5.61*x*x-12x+30.65
y=5.61*5.8*5.8-12*5.8+30.65
y=149.77
y≈149.8lbs.
Weight of someone having height 5.8ft tall is 149.8lbs.
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Express -6 as the sum of a negative integer and a whole number
The polygons in each pair are similar. Find the missing side length.
Let missing one be x
If both are similar
[tex]\\ \sf\longmapsto \dfrac{20}{25}=\dfrac{16}{x}[/tex]
[tex]\\ \sf\longmapsto \dfrac{4}{5}=\dfrac{16}{x}[/tex]
[tex]\\ \sf\longmapsto 4x=16(5)[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{16(5)}{4}[/tex]
[tex]\\ \sf\longmapsto x=20[/tex]
An Experiment to investigate the relation between two physical quantities was performed where 10 data pairs were collected. You are to perform regression analysis to describe the relation between the two quantities using a polynomial. What are the possible values for the order of that polynomial?
a) from 0 to 10
b) from 1 to 9
c) from 1 to 10
d) Any integer
Answer:
d). Any Integer.
Step-by-step explanation:
Regression analysis is characterized as the statistical method that is employed to determine the association between a dependent, as well as, the independent variable(one or more). It
As per the question, the probable values for the arrangement of a polynomial would be 'any integer' in order to determine the relationship among the different variables(the two physical quantities). Since a regression analysis helps in knowing the factors that influence the other and the factors that do not affect much in order to reach a reliable conclusion. Thus, any of the values can be examined to examine the association among them. Hence, option d is the correct answer.
Slope - 9; through (6,-9)
Answer:
Y= -9x+45
y = -9 X + b
-9 = -9(6) + b
-9 = -54 + b
b=45
Step-by-step explanation:
Which confidence level would produce the widest interval when estimating the mean of a population from the mean and standard deviation of a sample of that population?
Answer:
54% ...
Step-by-step explanation:
this is the answer I guess
The confidence level that produces the widest interval is the one with the highest percentage, which is 54%.
Option B is the correct answer.
What is z-score?A z-score also called a standard score is a measure of how many standard deviations a data point is away from the given mean of a distribution.
It measures the unusual or extreme a particular data point is compared to the rest of the distribution
We have,
The width of a confidence interval is proportional to the critical value of the corresponding confidence level.
The critical value is determined by the standard normal distribution or t-distribution, depending on the sample size and whether the population standard deviation is known.
In general,
The wider the confidence interval, the less precise the estimate of the population means.
Therefore, we want to choose the confidence level that produces the widest interval, which corresponds to the largest critical value.
For a given sample size,
The critical value increases as the confidence level increases.
For example, the critical value for a 95% confidence level is larger than the critical value for a 90% confidence level.
Therefore,
The confidence level that produces the widest interval is the one with the highest percentage, which is 54%.
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In ∆ ABC,AD is the altitude from A to BC .Angle B is 48°,angle C is 52° and BC is 12,8 cm. Determine the length of AD
9514 1404 393
Answer:
7,6 cm
Step-by-step explanation:
The law of sines can be used to find the length AB.
AB/sin(C) = BC/sin(A)
A = 180° -48° -52° = 80°
AB = BC·sin(C)/sin(A) = 12,8·sin(52°)/sin(80°)
The sine function can be used to find AD from AB.
AD/AB = sin(48°)
AD = AB·sin(48°) = 12,8·sin(48°)sin(52°)/sin(80°)
AD ≈ 7,61 cm
__
The dimension of interest is ha in the attachment, the height from vertex A.
please answer this……
Answer:
no no no no no no no no no no no no
Can anyone please help me out?
find the missing length indicated
============================================================
Explanation:
Let y be the length of the vertical dashed red line in the drawing. More specifically, this dashed line is an altitude.
Along the top, the entire segment is 400 units long. The right piece is 144 units long, so the left piece is 400-144 = 256 units long.
The triangles are similar, allowing us to set up a proportion like so:
144/y = y/256
144*256 = y*y
36864 = y^2
y^2 = 36864
y = sqrt(36864)
y = 192
So this is the length of that vertical dashed red line.
--------------------------------
Now shift your attention solely on the smaller triangle on the right side. It is a right triangle with legs 144 and 192. The hypotenuse is x.
We can use the pythagorean theorem to find x.
a^2 + b^2 = c^2
c = sqrt( a^2 + b^2 )
x = sqrt( 144^2 + 192^2 )
x = 240
240.
Let y be the length of the vertical dashed red line in the drawing. More specifically, this dashed line is an altitude.
Along the top, the entire segment is 400 units long. The right piece is 144 units long, so the left piece is 400-144 = 256 units long.
The triangles are similar, allowing us to set up a proportion like so:
144/y = y/256
144*256 = y*y
36864 = y^2
y^2 = 36864
y = sqrt(36864)
y = 192
So this is the length of that vertical dashed red line.
Now shift your attention solely to the smaller triangle on the right side. It is a right triangle with legs 144 and 192. The hypotenuse is x.
We can use the Pythagorean theorem to find x.
a^2 + b^2 = c^2
c = sqrt( a^2 + b^2 )
x = sqrt( 144^2 + 192^2 )
x = 240
What is Pythagorean Theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.
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plzzzzz helppp i will give brainlyist
Answer:
C. (2)
Step-by-step explanation:
an integer is a WHOLE NUMBER
have an amazing day :)
Answer:
2 is an integer
Step-by-step explanation:
An integer is a whole number, it does not have a fractional part
An amortized loan of RM60,000 has annual payments for fifteen years, the first occurring exactly one year after the loan is made. The first four payments will be for only half as much as the next five payments, whereas the remaining payments are twice as much as the previous five payments. The annual effective interest rate for the loan is 5%. I If the first four payments are X each, calculate the amount of principal repaid in the eighth payment and the amount of interest in the twelfth payment.
9514 1404 393
Answer:
a) RM2256.09 . . . principal paid by 8th payment
b) RM1791.10 . . . . interest paid by 12th payment
Step-by-step explanation:
First of all, we need to find the payments.
The payment amount is the amount that makes the future value of the series of payments equal to the future value of the loan at the given interest rate.
The future value of a single amount is ...
FV = P(1 +r)^n . . . . . where r is the annual rate, and n is the number of years in the future
The future value of a series of payments is ...
FV = P((1 +r)^n -1)/r . . . . . where n is the number of payments of P earning annual rate r
For payments in a series that does not end at the end of the loan, the future value is the product of that of the series and the effect of the accumulation of interest for the remaining time.
__
The first 4 payments will have a future value at the end of the loan period of ...
s1 = X((1 +0.05)^4 -1)/0.05×(1 +0.05)^11 = X(1.05^15 -1.05^11)/0.05
s1 = 7.3717764259X
The next 5 payments will have a future value at the end of the loan period of ...
s2 = 2X((1 +0.05)^5 -1)/0.05×(1 +0.05)^6 = 2X(1.05^11 -1.05^6)/0.05
s2 = 14.8097486997X
The last 6 payments will have a future value at the end of the loan period of ...
s3 = 4X((1 +0.05)^6 -1)/0.05 = 27.20765125X
So, the total future value of the series of payments is ...
payment value = 7.3717764259X +14.8097486997X +27.20765125X
= 49.3891763756X
__
The future value of the loan amount after 15 years is ...
loan value = 60,000(1 +0.05)^15 = 124,735.69
In order for these amounts to be the same, we must have ...
49.3891763756X = 124,735.69
X = 124,735.69/49.3891763756 = 2,525.57
__
At this point, it is convenient to use a spreadsheet to find the interest and principal portions of each of the loan payments. (We find the interest charge to be greater than the payment amount for the first 4 payments. So, the loan balance is increasing during those years.)
In the attached, we have shown the interest on the beginning balance, and the principal that changes the beginning balance to the ending balance after each payment. (That is, the interest portion of the payment is on the row above the payment number.)
The spreadsheet tells us ...
A) the principal repaid in the 8th payment is RM2,256.09
B) the interest paid in the 12th payment is RM1,791.10
_____
Additional comment
The spreadsheet "goal seek" function could be used to find the payment amount that makes the loan balance zero at the end of the term.
We have used rounding to sen (RM0.01) in the calculation of interest payments. The effect of that is that the "goal seek" solution is a payment value of 2525.56707 instead of the 2525.56734 that we calculated above. The value rounded to RM0.01 is the same in each case: 2525.57.
Andrew buys 27 identical small cubes, each with two adjacent faces painted red. He then uses all of these cubes to build a large cube. What is the largest number of completely red faces of the large cube that he can make
Answer:
4
Step-by-step explanation:
Number of Identical small cubes = 27
Determine the largest number of completely red faces of the large cube that he can make
Given that 2 adjacent faces of each cube is painted
and the number of cubes = 27
The number of complete red face Large cube he can make = 4
For this problem, I got 2 for the median however my answer seems to be incorrect. Can someone help me figure out this problem please? Thank you for your help!
Answer:
11
Step-by-step explanation:
we have as many numbers as dots
like 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 12 12 12 13 13 14 15 15 16 16 17 18
so in the middle it's 11 and 11
(11+11)÷2=11
Given two dependent random samples with the following results: Population 1 30 35 23 22 28 39 21 Population 2 45 49 15 34 20 49 36 Use this data to find the 90% confidence interval for the true difference between the population means. Assume that both populations are normally distributed. Step 1 of 4: Find the point estimate for the population mean of the paired differences. Let x1 be the value from Population 1 and x2 be the value from Population 2 and use the formula d=x2−x1 to calculate the paired differences. Round your answer to one decimal place.
Answer:
(-14.8504 ; 0.5644)
Step-by-step explanation:
Given the data:
Population 1 : 30 35 23 22 28 39 21
Population 2: 45 49 15 34 20 49 36
The difference, d = population 1 - population 2
d = -15, -14, 8, -12, 8, -10, -15
The confidence interval, C. I ;
C.I = dbar ± tα/2 * Sd/√n
n = 7
dbar = Σd/ n = - 7.143
Sd = standard deviation of d = 10.495 (using calculator)
tα/2 ; df = 7 - 1 = 6
t(0.10/2,6) = 1.943
Hence,
C.I = - 7.143 ± 1.943 * (10.495/√7)
C.I = - 7.143 ± 7.7074
(-14.8504 ; 0.5644)
Identify the transformed function that represents f(x) = ln x stretched vertically by a factor of 17, reflected across the x-axis, and shifted by 19 units left.
A. g(x) = −17ln (x + 19)
B. g(x) = 17ln (x − 19)
C. g(x) = 17ln (x + 19)
D. g(x) = −17ln (x − 19)
Answer:
b
Step-by-step explanation:
ANSWER. EXPLANATION. The given logarithmic function is. The transformation,. stretches the graph of y=f(x) vertically by a factor of c units ...
4 votes
ANSWER[tex]y = - 3 ln(x - 7) [/tex]EXPLANATIONThe given logarithmic function is [tex]f(x) = ln(x) [/tex]The transformation, [tex]y = - cf(x - k)[/tex]stretches
Is interquartile range a measure of center or a measure of variation?
Answer:
The interquartile range is the middle half of the data that is in between the upper and lower quartiles. ... The interquartile range is a robust measure of variability in a similar manner that the median is a robust measure of central tendency.
A teacher designs a test so a student who studies will pass94% of the time, but a student who does not studywill pass14% of the time. A certain student studies for91% of the tests taken. On a given test, what is theprobability that student passes
Answer:
0.868 = 86.8% probability that the student passes.
Step-by-step explanation:
Probability of the student passing:
94% of 91%(when the student studies for the test).
14% of 100 - 91 = 9%(when the student does not study for the test). So
[tex]p = 0.94*0.91 + 0.14*0.09 = 0.868[/tex]
0.868 = 86.8% probability that the student passes.
Word problem help please
Answer:
C(M) = 0.65*M + 22.55
Step-by-step explanation:
We know that the cost to rent and drive for M miles is given by:
S(M) = 0.40*M + 17.75
And the insurance, also a function of M, is given by:
I(M) = 0.25*M + 4.80
We want to find the equation of the total cost for a rental that includes insurance.
This would be just the sum of the two above functions:
C(M) = S(M) + I(M)
C(M) = (0.40*M + 17.75) + (0.25*M + 4.80)
Now we just need to simplify this:
Taking M as a common factor, we get:
C(M) = (0.40 + 0.25)*M + 17.75 + 4.80
C(M) = 0.65*M + 22.55
Then the total cost equation, as a function of M, is given by:
C(M) = 0.65*M + 22.55
What is the mapping for a reflection in the line y=-1
Answer:
0
Step-by-step explanation:
the key mapping for a reflection in the line y=-1 is 0
