a rectangle has a length of 7 meters longer than double the width. the perimeter is 134 meters. find the dimensions of the rectangle.
Answers
what's the length? well, l = w + 7.
Related Questions
From the 11
male and 6
female sales representatives for an insurance company, a team of 3
men and 2
women will be selected to attend a national conference on insurance fraud.
In how many ways can the team of 5
be selected?
Answers
For example selecting groups of 4 people out of 10 people can be done in
C(10, 4) many ways.
C(n, r) is calculated as follows: [tex]C(n, r)= \frac{n!}{r!(n-r!)} [/tex],
where n! is 1*2*3*...*(n-1)*n
3 men out of 11 men, and 2 women out of 6 women are to be selected.
This can be done in C(11, 3) and C(6,2) ways respectively.
Since any of the selected men group can be combined with any of the selected women group, there are C(11, 3)*C(6,2) many ways of selecting the team of 5.
[tex]C(11, 3)*C(6,2) = \frac{11!}{8!3!} * \frac{6!}{4!2!}= \frac{11*10*9*8!}{8!*3!}* \frac{6*5*4!}{4!*2!}= \frac{11*10*9}{3*2*1} * \frac{6*5}{2*1}= [/tex]
165*15=2475
Answer: 2475
Find a nonzero vector normal to the plane
Answers
Milla and Luka are 3 kilometers apart and walking toward each other. Milla's average speed is 5 kilometers per hour and Luka's is 4 kilometers per hour.
Which equation can be used to find t, the time it takes for Milla and Luka to meet?
5t + 4t = 1
5t + 4t = 3
5t – 4t = 0
5t – 4t = 3
Answers
Answer: Second option is correct.
Step-by-step explanation:
Since we have given that
Speed of Milla = 5 km per hour
Speed of Luka = 4 km per hour
Distance between Milla and Luka = 3 km
Let the time be 't'.
As we know that
[tex]Distance=Speed\times time[/tex]
So, it becomes,
Distance covered by Milla + Distance covered by Luka = Total distance
[tex]5t+4t=3[/tex]
Hence, Second option is correct.
Consider the following.
Point
(-5, 4)
Line
x + y = 7
(a) Write the slope-intercept form of the equation of the line through the given point and parallel to the given line.
(b) Write the slope-intercept form of the equation of the line through the given point and perpendicular to the given line.
Answers
A. a parallel line will have the same slope
y = mx + b
slope(m) = -1
(-5,4)...x = -5 and y = 4
sub and find b, the y int
4 = -1(-5) + b
4 = 5 + b
4 - 5 = b
-1 = b
so ur parallel line is : y = -x - 1 <==
B. perpendicular lines have negative reciprocal slopes. That means our perpendicular line will have a slope of 1
y = mx + b
slope(m) = 1
(-5,4)...x = -5 and y = 4
now we sub and find b, the y int
4 = 1(-5) + b
4 = -5 + b
4 + 5 = b
9 = b
so ur perpendicular line is : y = x + 9 <==
(03.03 HC)
The table shows the outputs, y, for different inputs, x:
Input (x) 6 12 15 25
Output (y) 14 15 15 16
Part A: Do the data in this table represent a function? Justify your answer. (3 points)
Part B: Compare the data in the table with the relation f(x) = 7x − 15. Which relation has a greater value when x = 6? (2 points)
Part C: Using the relation in Part B, what is the value of x if f(x) = 6? (5 points)
Answers
One card is selected at random from an ordinary deck of 52 playing cards. let a = event a face card is selected
Answers
3*4=12
12/52=3/13
p(a)=3/13
WILL GIVE BRAINLIEST...
You have 45 ft of the fence you enclose your yard, you are going to use the side of your house as one of the sides and put a fence down the width of the yard so your dog as a place to play, the length is three less than the width. What is the area of your yard?
Answers
L = W - 3
2 W + L = 45
2 W + W - 3 = 45
3 W = 45 + 3
3 W = 48
W = 48 : 3
W = 16 ft
L = 16 - 3 = 13 ft
A = 16 * 13 = 208 ft²
Answer: The area of the yard is 208 ft².
What is 18a and 12ab's GCF
Answers
Answer:
6a
Step-by-step explanation:
18a = 2 · 3² · a
12ab = 2² · 3 · a · b
Factors common to both lists are 2, 3, a, so the GCF is 2·3·a = 6a.
i need to know the solution using a fraction or integer to 3 more than the product of 7 and a number x is less than 26
Answers
3 more than that? is just 7x + 3
so, we know is less than 26, 7x + 3 < 26
[tex]\bf 7x+3\ \textless \ 26\implies 7x\ \textless \ 26-3\implies 7x\ \textless \ 23\implies x\ \textless \ \cfrac{23}{7} \\\\\\ \boxed{x\ \textless \ 3\frac{2}{7}}\qquad \qquad 3\frac{2}{7}\implies \cfrac{3\cdot 7+2}{7}\implies \cfrac{23}{7}[/tex]
Find the surface area of x^2+y^2+z^2=9 that lies above the cone z= sqrt(x^@+y^2)
Answers
[tex]z=\sqrt{x^2+y^2}\implies z^2=x^2+y^2[/tex]
which means that the intersection of the cone and sphere occurs at
[tex]x^2+y^2+(x^2+y^2)=9\implies x^2+y^2=\dfrac92[/tex]
i.e. along the vertical cylinder of radius [tex]\dfrac3{\sqrt2}[/tex] when [tex]z=\dfrac3{\sqrt2}[/tex].
We can parameterize the spherical cap in spherical coordinates by
[tex]\mathbf r(\theta,\varphi)=\langle3\cos\theta\sin\varphi,3\sin\theta\sin\varphi,3\cos\varphi\right\rangle[/tex]
where [tex]0\le\theta\le2\pi[/tex] and [tex]0\le\varphi\le\dfrac\pi4[/tex], which follows from the fact that the radius of the sphere is 3 and the height at which the sphere and cone intersect is [tex]\dfrac3{\sqrt2}[/tex]. So the angle between the vertical line through the origin and any line through the origin normal to the sphere along the cone's surface is
[tex]\varphi=\cos^{-1}\left(\dfrac{\frac3{\sqrt2}}3\right)=\cos^{-1}\left(\dfrac1{\sqrt2}\right)=\dfrac\pi4[/tex]
Now the surface area of the cap is given by the surface integral,
[tex]\displaystyle\iint_{\text{cap}}\mathrm dS=\int_{\theta=0}^{\theta=2\pi}\int_{\varphi=0}^{\varphi=\pi/4}\|\mathbf r_u\times\mathbf r_v\|\,\mathrm dv\,\mathrm du[/tex]
[tex]=\displaystyle\int_{u=0}^{u=2\pi}\int_{\varphi=0}^{\varphi=\pi/4}9\sin v\,\mathrm dv\,\mathrm du[/tex]
[tex]=-18\pi\cos v\bigg|_{v=0}^{v=\pi/4}[/tex]
[tex]=18\pi\left(1-\dfrac1{\sqrt2}\right)[/tex]
[tex]=9(2-\sqrt2)\pi[/tex]
Between 2005 and 2008, the average rate of inflation was about3.4 per year. If a cart of groceries cost $140 in 2005, what did it cost in 2008
Answers
A=p (1+r)^t
A future value?
P current value 140
R rate of inflation 0.034
T time 2008-2005=3 years
A=140×(1+0.034)^(3)
A=154.77 round your answer to get
A=155
Find the volume: in cm 7cm high 3cm wide 2 cm long
Answers
so 7×3×2=42 cm3
Anoav uses which statistical distribution to determine the significance of the results
Answers
What is the answer, with the correct number of decimal places, for this problem? 4.392 g + 102.40 g + 2.51 g =?
Answers
The summation of 4.392 g + 102.40 g + 2.51 g with three decimal places is 109.302 g.
What is summation?A summation, also abbreviated as a sum, is the outcome of adding two or more numbers or quantities. Here are always an integer number of terms in a summation. There could be only two terms, but there could be one hundred, thousand, or a million.
Given the expression for sum,
4.392 g + 102.40 g + 2.51 g
⇒ (4.392 + 102.40 + 2.51)g
⇒ 109.302 g
Hence "The summation of 4.392 g + 102.40 g + 2.51 g with three decimal places is 109.302 g".
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The sum of the masses 4.392 g, 102.40 g, and 2.51 g is 109.30 g.
Explanation:A summation, which can sometimes be shortened to "sum," is the result of multiplying two or more quantities by one another. A summation always has an integer number of terms. One hundred, thousand, or a million phrases could exist, but there could only be two.
The sum of the masses 4.392 g, 102.40 g, and 2.51 g is 109.302 g.
To ensure the correct number of decimal places, we need to consider the measurement with the least number of decimal places, which is 2.51 g.
Since 2.51 g has two decimal places, we round the sum to two decimal places as well.
Therefore, the answer is 109.30 g.
How do you convert 6 feet into meters?
Answers
ok so what is is the square root of 1234 i dot know
Answers
sqrt(1234) = 35.1283
you don't say how it should be rounded, so round off as needed
The equation d=13/v shows that the density of a particular substance equals a mass of 13 grams divided by the volume of the substance. What happens to the density as the volume approaches 0?
Answers
Assume the Mass is 1 kg and the Volume = 1 cm³, so d= 1/1 kg/cm³
for V=0.1 → d = 1/0.1 = 10 kg.cm³
for V = 0.01 → d = 100.kg.cm³
for V = 0.001 → d = 1000.kg.cm³
for V = 0.000001 → d = 1,000,000.kg.cm³
and when Volume → 0. density →∞
.
Answer: the density approaches infinity
Step-by-step explanation:
negative 2 to the 3 power
Answers
What is the reciprocal of 2 2/3
Answers
8meters long 4 meters wide and 2 meters deep.What is the volume of the pond.
Answers
8 x 4=32 x 2=64
The volume of the pond is 64 meters
Which of the following is closest to 27.8 times 9.6? A. 280. B 300. C 2,800. D 3,000
Answers
Find The Perimeter Of The Shaded Region
90 ft
58 ft
24 ft
38 ft
Answers
w = 15 - 4 = 11
P of shaded = 2(8+9) = 2 (19) = 38
answer
last one 38ft
Answer:
38 ft
Step-by-step explanation:
Perimeter of the rectangle = 2* length + 2* width
Length of shaded part = Length of the larger rectangle - 4 = 11ft
width of the shaded part = width of the larger rectangle - 6 = 8 ft
Perimeter of the rectangle = 2* length + 2* width
Plug in the values of length and width
Perimeter of the shaded rectangle= 2(11) + 2(8)= 22+ 16= 38 feet
A new basketball costs $25.00 at the sporting goods store. If the store is having a going-out-of-business sale and everything is 60% off, what is the actual cost of the basketball?
Answers
Final answer:
To calculate the discounted price of the basketball, multiply the original price ($25.00) by 60% to find the discount ($15.00), and subtract this from the original price to get the final price ($10.00).
Explanation:
To find out the actual cost of the basketball after a 60% discount, we start by calculating the amount of the discount. A 60% discount on a $25.00 basketball means the discount is 60/100 times $25.00. To do the calculation:
First, we convert the percentage to a decimal: 60% = 0.60.Then, we multiply the original price by the decimal: $25.00 × 0.60 = $15.00.This $15.00 is the amount of the discount.To find the discounted price, we subtract the discount from the original price: $25.00 - $15.00 = $10.00. Therefore, the discounted price of the basketball is $10.00.
Two trains leave a train station traveling different directions. The first train travels 12 miles west, then 6 miles north. The second train travels 20 miles east, then 35 miles north.
a. The train station is the origin. What is the coordinate of each train?
b. Using the city center and the stop point of the first train, what is the slope of the line? Is it horizontal, vertical or neither? Write the equation of the line in slope-intercept form and standard form.
c. The city wants to build a train station 2 miles directly north of the first train station. They are going to build a train track parallel to the path the first train would’ve traveled if it were a direct route from the city center. What would be the equation of the line in slope intercept form of the new track?
Answers
The origin (0, 0) is the train station.
Part a.
The first train travels 12 miles west and 6 miles north to arrive at A.
It's coordinate is (-12, 6).
The second train travels 20 miles east and 35 miles north to arrive at B.
It's coordinate is (20, 35).
Part b.
The slope of the line from the origin to A is
m = (6 - 0)/(-12 - 0) = -1/2.
The slope is neither vertical nor horizontal.
The y-intercept is 0.
The line OA is given in slope-intercept form by
y = -(1/2)x
In standard form, the line is
y - 6 = -(1/2)*(x - (-12))
or
y - 6 = -(1/2)*(x + 12)
Part c.
The new train station is located at (0, 2) because it is 2 miles north of the old station.
If a new track is built parallel to OA, then it should have a slope of -1/2.
Because it's y-intercept is 2, its equation in slope-intercept form is
y = -(1/2)x + 2.
Answer:a. first (-12,6) second (20,35)
b. y = -1/2x, 2y + 1x = 0 (neither horizontal or vertical)
c. y= -1/2x + 2.
Step-by-step explanation:
The casino la bella fortuna is for sale and you think you might want to buy it, but you wantto know how much money you are going to make. all the present owner can tell you is thatthe roulette game red or black is played about 1000 times a night, 365 days a year. eachtime it is played you have probability 19/37 of winning the player’s bet of $10 and probability18/37 of having to pay the player $10.
Answers
10*(19/37)-10*(18/37)=0.27027
Expected gain per player per night (1000 games per night)
=1000*0.27027
=270.27
Expected gain per player per year (365 nights per year)
=270.27*365
=98648.65
Revenue is 98648.65 times the average number of players per game.
The expected value of the roulette game red or black is -$0.62 per game, indicating an expected average loss.
Explanation:The expected value of the roulette game red or black can be calculated by multiplying the probabilities of winning and losing by their corresponding outcomes. In this case, the probability of winning ($10) is 19/37, and the probability of losing ($-10) is 18/37. Multiply these probabilities by their corresponding outcomes and subtract to get the expected value:
Expected value = (19/37 * $10) + (18/37 * -$10) = -$0.54 + (-$0.54) = -$0.62
This means that if you play this game repeatedly, over a long string of games, you would expect to lose an average of 62 cents per game.
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Suppose a least-squares regression line is given by modifyingabove y with caret equals 4.302 x minus 3.293y=4.302x−3.293. what is the mean value of the response variable if x equals 20x=20
Answers
The mean value of the response variable y when x equals 20 in the least-squares regression line equation y = 4.302x - 3.293 is 82.041.
Explanation:The given equation is y = 4.302x - 3.293, which is a least-squares regression line. In this formula, x is the independent variable and y is the resulting dependent variable or response. The goal is to find the mean value of the response variable when x is 20. This can be achieved simply by plugging 20 in place of x in our equation and calculating the resulting value for y.
We will substitute x = 20 into the equation y = 4.302x - 3.293. Therefore, the value of y when x is 20 is:
y = 4.302(20) - 3.293 = 82.041
So, when x = 20, the mean value of the response variable y or the predicted y value is 82.041.
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If $3500 is invested at the rate of 8%, compounded quarterly, what will be the value of the investment 17 years from now, assuming no withdrawals?
Answers
A = P(1+r/n)^(n*t)
The variables are
A = amount in the account after t years
P = initial amount invested
r = interest rate (in decimal form)
n = compounding frequency
t = number of years
In this case
A = unknown (we're solving for this)
P = 3500
r = 0.08 (8% = 8/100 = 0.08)
n = 4 (compound quarterly ---> compound 4 times a year)
t = 17
------------------------------------------
Plug all these values into the equation to get...
A = P(1+r/n)^(n*t)
A = 3500(1+0.08/4)^(4*17)
A = 3500(1+0.02)^(4*17)
A = 3500(1.02)^(4*17)
A = 3500(1.02)^(68)
A = 3500(3.8442505025456)
A = 13454.8767589096
A = 13454.88
This means that you will have $13454.88 in the account after 17 years
Final Answer: 13454.88
How do you interpret algebraic expressions in terms of their context
Answers
a garden table and a bench cost 817 dollars combined. The garden table costs 83 less than the bench. what is the cost of the bench
Answers
bench=b
t=b-83
t+b=817
b-83+b=817
2b=900
b=450 ($)
"Non nobis, Domine, non nobis, sed Nomini tuo da gloriam."
Regards M.Y.
3 1/6 divided by 5/8
Answers
The result of 3 1/6 divided by 5/8 is equal to 76/15.
To divide a mixed number by a fraction, we need to convert the mixed number into an improper fraction.
In this case, 3 1/6 can be written as an improper fraction as (3 × 6 + 1) / 6 = 19/6.
Next, we can multiply the numerator of the fraction by the reciprocal of the divisor.
The reciprocal of 5/8 is 8/5.
So, (19/6) ÷ (5/8) = (19/6) × (8/5) = (19 × 8) / (6 × 5) = 152/30.
The fraction 152/30 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which in this case is 2. So, (152/30) ÷ 2 = 76/15.
Therefore, 3 1/6 divided by 5/8 is equal to 76/15.
Final answer:
To find the result of 3 1/6 divided by 5/8, convert the mixed number to an improper fraction, multiply by the reciprocal of the divisor, and simplify the resulting fraction. The answer is 5 1/15.
Explanation:
The student's question 3 1/6 divided by 5/8 is a mathematics problem that involves division of mixed numbers and fractions. To solve this problem, the student first needs to convert the mixed number into an improper fraction. To do this, the student multiplies the whole number by the denominator of the fractional part and then adds the numerator:
Multiply 3 (the whole number) by 6 (the denominator of the fractional part): 3 x 6 = 18.
Add the numerator (the fractional part's numerator, which is 1): 18 + 1 = 19. So, 3 1/6 becomes 19/6.
The next step is to divide 19/6 by 5/8. In division of fractions, you multiply by the reciprocal of the divisor. The reciprocal of 5/8 is 8/5.
Therefore, you multiply 19/6 by 8/5: 19/6 x 8/5.
Perform the multiplication of numerators and denominators: 19 x 8 = 152 and 6 x 5 = 30.
The result is 152/30. This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
The simplified answer is 76/15, or as a mixed number, 5 1/15.
This shows that 3 1/6 divided by 5/8 is 5 1/15.