Answer:
A computer parts company wants to make a rectangular memory board that has a perimeter of 28 centimeters and a diagonal length of 10 centimeters. Find the dimensions of the board. Consider the length to be the longer side.: Call the two sides L & W: the perimeter 2L + 2W = 28 Simplify, divide by 2 L + W = 14 L = (14-W); use this form for substitution
Step-by-step explanation:
==========================================================
Explanation:
x = width
y = length
both x and y are positive real numbers, and the units of which are in cm.
The perimeter of any rectangle is found by saying
P = 2*(length+width)
P = 2*(x+y)
Plugging in P = 14 leads us to
P = 2*(x+y)
14 = 2*(x+y)
14/2 = x+y
7 = x+y
Solve for one of the variables. Let's say we solve for y. That should get us y = 7-x which we'll use a bit later.
--------------
Notice how the diagonal forms two identical right triangles. The legs of which are x and y as defined earlier. The hypotenuse is 5, which is the diagonal length.
Use the pythagorean theorem to help solve for x
a^2 + b^2 = c^2
x^2 + y^2 = 5^2
x^2 + (7-x)^2 = 25 ... plug in y = 7-x
x^2 + 49 - 14x + x^2 = 25 ... use FOIL rule
2x^2-14x+49 = 25
2x^2-14x+49-25 = 0
2x^2-14x+24 = 0
2(x^2-7x+12) = 0
x^2-7x+12 = 0
(x-3)(x-4) = 0
x-3 = 0 or x-4 = 0
x = 3 or x = 4
If x = 3, then y = 7-x = 7-3 = 4
If x = 4, then y = 7-x = 7-4 = 3
We have this symmetry going on. If x is one of 3 or 4, then y is the other of those values. Because x = 3 and y = 4, or vice versa, this means we have a 3-4-5 right triangle (well to be fair we have two identical copies of such a triangle to form the rectangle).
Therefore, the dimensions of the rectangular board is 3 cm by 4 cm. The order doesn't matter so you could easily say "4 cm by 3 cm" to mean the same thing.
--------------
Check:
P = perimeter
P = 2*(length+width)
P = 2*(x+y)
P = 2*(3+4)
P = 2*7
P = 14
That helps confirm the answer.
Solve for x and y simultaneous equations: 2x+y=10
-3x+y=-5
Step-by-step explanation:
Hey, there!
Given, equations are,
2x+y=10.............(i)
-3x+y= -5...........(ii)
From equation (i)
y=10- 2x...........(iii)
Putting the value of "y" from equation (iii) in equation (ii).
-3x+y= -5
-3x + (10-2x)= -5
-3x + 10-2x= -5
- 5x = -15
[tex]x = \frac{ - 15}{ - 5} [/tex]
Therefore, x= 3.
Now, putting the value of "x" in equation (iii).
y= 10- 2x
y= 10- 2×3
Therefore, y= 4.
Hope it helps...
Gina, Sam, and Robby all rented movies from the same video store. They each rented some dramas, comedies, and documentaries. Gina rented 11 movies total. Sam rented twice as many dramas, three times as many comedies, and twice as many documentaries as Gina. He rented 27 movies total. If Robby rented 19 movies total with the same number of dramas, twice as many comedies, and twice as many documentaries as Gina, how many movies of each type did Gina rent?
Hi there! :)
Answer:
Gina rented 3 dramas, 5 comedies, and 3 documentaries.
Step-by-step explanation:
To solve, we will need to set up a system of equations:
Let x = # of dramas, y = # of comedies, and z = # of documentaries:
Write equations to represent each person:
Gina:
x + y + z = 11
Sam:
2x + 3y + 2z = 27
Robby:
x + 2y + 2z = 19
Write the system:
x + y + z = 11
2x + 3y + 2z = 27
x + 2y + 2z = 19
Begin by subtracting the third equation from the second:
2x + 3y + 2z = 27
x + 2y + 2z = 19
-----------------------
x + y = 8
If x + y = 8, plug this into the first equation:
(8) + z = 11
z = 11 - 8
z = 3
We found the # of documentaries Gina rented, now we must solve for the other variables:
Subtract the top equation from the third. Substitute in the value of z we solved for:
x + 2y + 2(3) = 19
x + y + (3) = 11
-------------------------
y + 3 = 8
y = 5
Substitute in the values for y and z to solve for x:
x + 5 + 3 = 11
x + 8 = 11
x = 11 - 8
x = 3.
Therefore, Gina rented 3 dramas, 5 comedies, and 3 documentaries.
Answer:
B- x + y + z = 11
2x + 3y + 2z = 27
x + 2y + 2z = 19
Step-by-step explanation:
I took the quiz
What year was it when I was a freshman if I graduated this year(2021)?
Answer:
2019
Step-by-step explanation:
I am assuming you mean graduated from high school. If that's the case it's 2019. Sophmore year means 9th grade. which is 2019!
The sum of two positive integers is 67. When the smaller integer is subtracted from twice the larger, the result is 38. Find the two integers.
Answer:
Step-by-step explanation:
x+y = 67
2x-y = 38
Add the equations together
3x = 108
x = 36
y = 67-x = 31
The circle below is centered at (2, 3) and has a radius of 4. What is its
equation?
A. (x-3)2 + (y - 2)2 = 16
O B. (x-3)2 + (y-2)2 = 4
C. (x - 2)2 + (y - 3)2 = 16
O D. (x-2)2 + (y-6)2 = 4
The equation of the circle is [tex](x - 2)^2 + (y - 3)^2 = 16[/tex] . The option C is the correct option.
Given that the centre of the circle is (2,3) and circle has radius 4.
To find the equation of the circle, use the general equation of the circle as:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where (h, k) is the centre of the circle and r is the radius of the circle.
Since, h = 2, k = 3 and radius r = 4.
Therefore, the equation of the circle:
[tex](x-h)^2+(y-k)^2=r^2\\(x-2)^2+(y-3)^2=4^2\\(x-2)^2+(y-3)^2=16[/tex]
The equation of the circle cantered at (2,3) and has a radius of 4 is [tex](x - 2)^2 + (y - 3)^2 = 16[/tex] .
Therefore, The equation of the circle cantered at (2,3) and has a radius of 4 is [tex](x - 2)^2 + (y - 3)^2 = 16[/tex] .
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You calculate the correlation between height and weight for a simple random sample of 50 students from your college. Another student does the same for a simple random sample of 200 students from the college. The other student should get:_________.
A. a correlation greater than 1.
B. a higher value for the correlation.
C. about the same value for the correlation.
D. a lower value for the correlation.
E. a correlation less than-1.
Answer:
B
Step-by-step explanation:
What is 7 x -5?........
Answer:
-35
Step-by-step explanation:
7*5*(-1)
The solution to the expression 7 * -5 is -35
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
7 * -5
Evaluate all the products in the expression
so, we have the following representation
7 * -5 = -35/1
Evaluate all the quotients in the expression
so, we have the following representation
7 * -5 = -35
Lastly, we have
7 * -5 = -35
Hence, the solution is -35
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please help me answer these questions :(
Answer:
a) ∠X = 67.4°
ii) ∠Y = 22.6°
b) Hypotenuse = 13 miles
ii) Length of each congruent = 4.33 miles
c) Distance of mall from point A = 5.21 miles
d) Distance os mall from point B = 8.17 miles
e) Difference = 2.96 miles
ii) Amount it will cost = $1,628,000
Step-by-step explanation:
Because of the length of the solution, I sent it as an attachment to this answer.
(a) A square has a perimeter of 56cm. What is the length of each side? (b) A square has an area of 62cm. What is the length of each side?
Answer:
A) 14
B) 7.874
Step-by-step explanation:
perimeter is all 4 sides add
area is l*w
56/4
√62
An animal population is increasing at a rate of 13 51t13 51t per year (where t is measured in years). By how much does the animal population increase between the fourth and tenth years.
Answer:
ΔP = 567
Step-by-step explanation:
The increasing rate of the population is 13,51*t.
That rate by definition is:
dP/dt where P is the population therefore
dP/dt = 13,51*t
dt = 13,51*t*dt
Integrating on both sides of the equation we get:
∫dp = ∫ 13,51*t*dt
P = 13,51*t²/2 + K ( K is population for t = 0 )
Now the population in 10 years P(₁₀)
P(₁₀) = 13,51* (10)² /2 + K
P(₁₀) = 675,5 + K (1)
And P(₄) is
P(₄) = 13,51*(4)²/2 * K
P(₄) = 108,08 + K (2)
Then substracting
P(₁₀) - P(₄) = ( 675,5 + K ) - ( 108,08 + K )
ΔP = 567,42
But we don´t have fraction of animal, then
ΔP = 567
The ratio of red beads to blue beads on a necklace is 4:7. If there are 16 red beads, how many blue ones are there?
Answer:
There are 28 beads
Step-by-step explanation:
Total ratio:
[tex]{ \sf{ (4 + 7) = 11}}[/tex]
let total beads be x:
[tex]{ \sf{ \frac{4}{11} \times x = 16 }} \\ \\ { \sf{x = \frac{11 \times 16}{4} }} \\ x = 44 \: beads[/tex]
Blue beads:
[tex] = 44 - 16 \\ = 28 \: \: beads[/tex]
A shopping centre wants to examine the amount of space required for parking. Studies indicated that 50% of staff and shoppers use public transportation. A survey of 1002 was taken, and 483 responded that they used public transportation. At 5% level of significance, is it reasonable to conclude that the survey results indicate a change?
Answer:
We accept H₀ data from the survey is not enough to claim that 50% of the proportion indicated in previous studies have change
Step-by-step explanation:
To get conclusions about the survey we need to develop a hypothesis test of proportion
According to previous studies, (p₀ ) 50 % of staff and customers use public transportation, and we got from a survey 0f 1002 people 483 responded they also use then p = 483/1002 then
n sample size is 1002 and p = 0,482 (48,2 % )
Test Hypothesis
Null hypothesis H₀ p = p₀
Alternative hypothesis Hₐ p < p₀
CI = 95 % α = 5 % α = 0,05 and from z-table we find z score for that value z(c) = - 1,64
z(s) = ( p - p₀ ) / √ (p₀*q₀)/ n p₀ = q₀ = 0,5
z(s) = - 0,018* 31,65 / 0,5
z(s) = - 1,1394
To compare
z(s) and z(c) -1,1394 > 1,64
Then z(s) is inside the acceptance region. We accept H₀ , because we don´t have enough evidence to claim that the survey results indicate a change in
the original proportion
Cancel the common factor of the numerator and the denominator and write specified expression
Step-by-step explanation:
Hello,
I hope you mean to cancel the common factor that exists in numerator and denominator,right.
so, Let's look for the common factor,
here, the expression is,
=4(x-2)/ (x+5)(x-2)
so, here we find the common factor is (x-2)
now, we have to cancel it. And after cancelling we get,
=4/(x+5)
Note:{ we cancel the common factor if the common factors are in multiply form.}
Hope it helps
Can someone help me, please?
Answer:
16
Step-by-step explanation:
7x+20+2x-5=159
9x+15=159
9x=159-15
9x=144
x=16
1f 12% of x is equal to 6% of y, then 18% of x will be equal to how much percent ofy?
Answer:
9%
Step-by-step explanation:
12x=6y eq 1
18x=9y eq 2
Simplify to create an equivalent expression. 7n-(4n-3) a=3n+3 b=3n−3 c=11n+3 d=11n−3 I will rate you brainliest. :)
Answer:
3n +3
Step-by-step explanation:
7n-(4n-3)
Distribute the minus sign
7n -4n +3
3n +3
What is the absolute value of the difference in the x-values between (1,7) and (3,11)
Answer:
2.
Step-by-step explanation:
The first numbers in the ordered pairs are the x values;
Difference = 1 - 3 = -1
The absolute value is 2.
An absolute value of |x| {modulus of x} is the value of a real number x. The absolute value of the difference in the x-values between (1,7) and (3,11) is 2.
What is Absolute Value?An absolute value of |x| {modulus of x} is the value of a real number x, the value we get is always a non-negative number, for example, |-5| will give 5, and also, |5| will give 5 as well.
Given the two coordinates (1, 7) and (3, 11) this can be written as,
(x₁ , y₁) = (1, 7)
(x₂ , y₂) = (3, 11)
Now, the absolute value of the difference in the x-values between (1,7) and (3,11) can be written as,
Absolute difference = |x₁ - x₂|
= |1 - 3|
= |-2|
= 2
Hence, the absolute value of the difference in the x-values between (1,7) and (3,11) is 2.
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What is the value of 2 in 9,274
Answer:
200
Step-by-step explanation:
4 is in the ones place so 4 just 4
7 is in the tens place so it is 70
2 is the hundreds place so 200
9 is in the thousands place so 9.000
What is the square root of -1
Answer:
the awnser is sqrt(-1) = i
Which choice is equivalent to the expression below? √-12
A. 12i
B. -12i
C. -2√3
D. 2i √3
E. -2√3i
PLEASE DON’T GUESS
Answer:
D. 2i√3
Step-by-step explanation:
You have the expression √-12. You can divide the number in the radical sign into the numbers that make up the expression. After you do this, you will be able to take numbers out of the radical sign
√(-12)
√(-1 × 4 × 3)
√-1 = i
√4 = 2
√3 = √3
2i√3
The answer is D.
even though the elimination method is easy I still have trouble with it
Answer:
(1,2)
Step-by-step explanation:
x+4y = 9
2x -4y= -6
Add the equations together
x+4y = 9
2x -4y= -6
-------------------
3x +0y = 3
3x=3
Divide by 3
3x/3 = 3/3
x=1
Now find y
x+4y = 9
1 +4y =9
Subtract 1 from each side
4y = 8
Divide by 4
4y/4 = 8/4
y =2
Bighorn sheep are beautiful wild animals found throughout the western United States. Data for this problem are based on information taken from The Desert Bighorn, edited by Monson and Sumner 9University of Arizona Press). Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information:
x 1 2 3 4 5
y 14 18.9 14.4 19.6 20.0
∑x=15 ; ∑y=87.3;∑x2=55; ∑y2=1569.77; ∑xy=275
(a) Draw a scatter diagram.
(b) Find the equation of the least-squares line, and plot the line on the scatter diagram of part (a).
(c) Find the correlation coefficient r. Find the coefficient of determination . What percentage of variation in y is explained by the variation in x and the least squares model?
Answer:
The answer and explanation are below
Step-by-step explanation:
i followed the data that was given in the question.
∑x=15 ; ∑y=87.3;∑x2=55; ∑y2=1569.77; ∑xy=275
a.) please refer to the attachment for the scatter diagram. Y was plotted against X.
b. The equation is given as:
Y = b₁ + b₀X
∑x=15 ; ∑y=87.3;∑x2=55; ∑y2=1569.77; ∑xy=275
b₁ = n∑xy - (∑x)(∑y)/n(∑x²) - (∑x)²
b₁ = 5 x 275 - 15 x 87.3/5 x 55 - (15²)
= 1375-1309.5/275-225
= 65.5/50
= 1.31
b₀ = 87.3/5 - 1.31(15/5)
= 87.3/5 - 1.31x3
= 13.53
the regression line is
Y = 13.53 + 1.31X
please refer to the attachment for the diagram for the regression line.
c. we are required to find r.
r = n∑XY - (∑X)(∑Y)/√n∑X²-(∑X)² × √n∑y²-(∑y)²
∑x=15 ; ∑y=87.3;∑x2=55; ∑y2=1569.77; ∑xy=275
inserting these values:
r = 5 x 275-(15)(87.3)/√275-225 x √7848.85 - 7621.29
= 65.5/106.69
= 0.6139
Coefficient of determination = r²
r = 0.6139
r² = 0.3769 = 37.69%
Therefore 37.69% variation in y is explained by variation in x and the least square model.
Let f(x)=−5x+18 and g(x)=x2+15.
Find f(−2)−g(−2).
Answer:
21
Step-by-step explanation:
-5(-2)-(-2)²+15
10-(4)+15
10-4+15
21
Answer:
9
Step-by-step explanation:
f(x)=−5x+18
f(-2) = -5(-2)+18 = 10+18 = 28
g(x)=x^2+15
g(-2) = (-2)^2 +15 = 4+15 = 19
f(02) - g(-2) = 28 - 19 = 9
What is the simplified form of x minus 5 over x squared minus 3x minus 10⋅ x plus 2 over x squared plus x minus 12 ? (6 points) Select one: a. 1 over the quantity x minus 3 times the quantity x plus 4 b. 1 over the quantity x minus 3 times the quantity x plus 2 c. 1 over the quantity x plus 4 times the quantity x minus 5 d. 1 over the quantity x plus 2 times the quantity x minus 5
Answer:
[tex]\ \text{a. }\quad\dfrac{1}{(x-3)(x+4)}[/tex]
Step-by-step explanation:
Maybe you want the product ...
[tex]\dfrac{x-5}{x^2-3x-10}\cdot\dfrac{x+2}{x^2+x-12}=\dfrac{x-5}{(x-5)(x+2)}\cdot\dfrac{x+2}{(x-3)(x+4)}\\\\=\boxed{\dfrac{1}{(x-3)(x+4)}}[/tex]
__
Numerator factors of (x-5) and (x+2) cancel those in the denominator.
Simplify -2x^3 y x xy^2
Answer:
(4,4)⋅(4,4)
Step-by-step explanation:
Algebraic Expressions
Evaluate
The weight of a bag of oranges is 1.3 pounds. There are 9 bags of oranges. What is the total weight?
Help please :)
Answer:
11.7 pounds
Step-by-step explanation:
Multiply the weight of one bag of oranges by 9 bags.
A die is rolled five times and the number of fours that come up is tallied. Find the probability of getting the given result. Exactly 3 fours.
A. 0.161
B. 0.002
C. 0.116
D. 0.216
Answer:
0.0321
Step-by-step explanation:
This can be found by binomial probability distribution as the probability of success is constant. There are a given number of trials. the successive tosses are independent.
Here n= 5
The probability of getting a four in a roll of a die = 1/6
The probability of not getting a four in a roll of a die = 5/6
The probability of getting exactly three 4s in five throws is given by
5C3 (1/6)³ (5/6)² = 10 (0.0046) (0.694)= 0.0321
A car dealership is advertising a car for $16,299.99. If the sales tax rate is 6.5 percent, what
is the total tax paid for the car?
A. S993 34
B. $1.000.00
CS1.059 50
DS1.359.19
Answer:
C.
Step-by-step explanation:
16,299.99*0.065=1059.50
A. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 1; B: the numbers add to 4; C: at least one of the numbers is 1; and D: the numbers do not add to 10. Express the given event in symbols.
The red die shows 1 and the numbers add to 4.
How many elements does it contain?
B. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 3; B: the numbers add to 2; C: at least one of the numbers is 1; and D: the numbers do not add to 10. Express the given event in symbols. HINT [See Example 5.]
The numbers do not add to 2.
How many elements does it contain?
C. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 1; B: the numbers add to 2; C: at least one of the numbers is 3; and D: the numbers do not add to 11. Express the given event in symbols. HINT [See Example 5.]
Either the numbers add to 11 or the red die shows a 1.
How many elements does it contain?
D. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 4; B: the numbers add to 5; C: at least one of the numbers is 1; and D: the numbers do not add to 9. Express the given event in symbols. HINT [See Example 5.]
Either the numbers add to 5, or they add to 9, or at least one of them is 1.
How many elements does it contain?
Answer:
1. elements it contains = (1,3)
2. elements it contains = 35
3. elements it contains = 8
4. elements it contains = 17
Step-by-step explanation:
A. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 1; B: the numbers add to 4; C: at least one of the numbers is 1; and D: the numbers do not add to 10. Express the given event in symbols.
The red die shows 1 and the numbers add to 4.
How many elements does it contain?
B. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 3; B: the numbers add to 2; C: at least one of the numbers is 1; and D: the numbers do not add to 10. Express the given event in symbols. HINT [See Example 5.]
The numbers do not add to 2.
How many elements does it contain?
C. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 1; B: the numbers add to 2; C: at least one of the numbers is 3; and D: the numbers do not add to 11. Express the given event in symbols. HINT [See Example 5.]
Either the numbers add to 11 or the red die shows a 1.
How many elements does it contain?
D. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 4; B: the numbers add to 5; C: at least one of the numbers is 1; and D: the numbers do not add to 9. Express the given event in symbols. HINT [See Example 5.]
Either the numbers add to 5, or they add to 9, or at least one of them is 1.
How many elements does it contain?
NB. Attached is the solution to the problems stated above
What is (2/3 x 3/5) - (3/4 x 1/6)
Answer:
2/3×3/5=2/3. 3/4×1/6=1/8
2/3-1/8=11/40
Answer:
[tex] \boxed{ \frac{11}{40} }[/tex]Step-by-step explanation:
[tex]( \frac{2}{3} \times \frac{3}{5} ) - ( \frac{3}{4} \times \frac{1}{6} )[/tex]
Reduce the numbers with Greatest common factor 3
⇒[tex] \mathsf{(2 \times \frac{1}{5} ) - ( \frac{1}{4} \times \frac{1}{2} )}[/tex]
Calculate the product
⇒[tex] \mathsf{( \frac{2}{5} )- ( \frac{1}{4} \times \frac{1}{2}) }[/tex]
Subtract the fractions
⇒[tex] \mathsf{ \frac{2 \times 8 - 1 \times 5}{40} }[/tex]
⇒[tex] \mathsf{ \frac{16 - 5}{40} }[/tex]
⇒[tex] \mathsf{ \frac{11}{40} }[/tex]
Hope I helped!
Best regards!