Answer:
x = -1/5
Step-by-step explanation:
*Steps as a proof*
_________
(-4x + 5)-(6x + 7) = 0
[given]
_____________
1(-4x + 5)-1(6x + 7) = 0 [identity property of multiplication]
1(-4x + 5) + -1(6x + 7) = 0. [additive inverse property]
___________________________________
1(-4x + 5) + -1(6x) + -1(7) = 0 [distributive property]
___________________________________
(-4x + 5) + (-6x - 7) = 0 [multiplying anything by 1 is the same]
___________________________________
(-4x + -6x) + (5 + -7) = 0 [associative property of addition]
_____________________________________
-4x + -6x + (5 + -7) = 0 [subtraction property of equality] - (5 + -7). - (5 + -7)
_______________________
-4x + -6x = -(5 + -7) [simplification]
-4x + 6x = -1(5 + -7) [identity property of multiplication]
-4x + -6x = -1(5) + -1(-7) [distributive property]
-4x + -6x = -5 + 7 [simplification]
-4x + -6x = 2 [simplification]
-10x = 2 [division property of equality]
÷10 ÷10
______
-x = 2/10 [negative one property of multiplication]
×-1 ×-1
x = -2/10 [simplification]
x = -1/5 [simplification]
__________________________
Three watches and five lamps cost $176 in all. Five watches and three lamps cost $208 in all. What is the cost of one lamp?
$200/5 lamps= $40 per lamp
Final answer: $40
Using the elimination principle, the cost of one lamp is $16
Let :
watches = a Lamps = b3a + 5b = 176 - - - - (1)
5a + 3b = 208 - - - (2)
Multiply (1) by 5 and (2) by 3
15a + 25b = 880 - - - - (3)
15a + 9b = 624 - - - - - (4)
Subtract (3) and (4)
16b = 256
b = (256 ÷ 16)
b = $16
Therefore, the cost of one lamp is $16
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Functionally important traits in animals tend to vary little from one individual to the next within populations, possibly because individuals who deviate too much from the mean have lower fitness. If this is the case, does variance in a trait rise after it becomes less functionally important? Billet et al. (2012) investigated this question with the semicircular canals (SC) of the three-toed sloth (Bradypus variegatus). The authors proposed that since sloths don't move their heads much, the functional importance of SC is reduced, and may vary more than it does in more active animals. They obtained the following measurements of the ratio of the length to width of the anterior SC in 6 sloths. Assume this represents a random sample. In other, more active animals, the standard deviation of this ratio is 0.09.
Answer:
The 95% confidence interval for the standard deviation is (0.14, 0.54).
Step-by-step explanation:
The complete data and question is:
Sloth CW Ratios ; {1.5 , 1.09 , 0.98 , 1.42 , 1.49 , 1.25}
The 95% confidence interval for the standard deviation of this data is < σ < (two decimals - include the leading zero) .
Solution:
Compute the sample standard deviation as follows:
[tex]\bar x=\frac{1}{n}\sum x=\frac{1}{6}\times 7.73=1.2883\\\\s=\sqrt{\frac{1}{n-1}\sum (x-\bar x)^{2}}=\sqrt{\frac{1}{6-1}\times 0.2387}=0.2185[/tex]
The (1 - α)% confidence interval for the variance is:
[tex]CI=\frac{(n-1)s^{2}}{\chi^{2}_{\alpha/2}}<\sigma^{2}<\frac{(n-1)s^{2}}{\chi^{2}_{1-\alpha/2}}[/tex]
Confidence level = 95%
⇒ α = 0.05
The degrees of freedom is,
df = n - 1 = 6 - 1 = 5
Compute the critical values of Chi-square:
[tex]\chi^{2}_{\alpha/2, (n-1)}=\chi^{2}_{0.025,5}=12.833\\\\\chi^{2}_{1-\alpha/2, (n-1)}=\chi^{2}_{0.975,5}=0.831[/tex]
*Use a Chi-square table.
Compute the 95% confidence interval for the variance as follows:
[tex]CI=\frac{(n-1)s^{2}}{\chi^{2}_{\alpha/2}}<\sigma^{2}<\frac{(n-1)s^{2}}{\chi^{2}_{1-\alpha/2}}[/tex]
[tex]=\frac{5\times (0.2185)^{2}}{12.833}<\sigma^{2}<\frac{5\times (0.2185)^{2}}{0.831}\\\\=0.0186<\sigma^{2}<0.2873\\\\=\sqrt{0.0186}<\sigma<\sqrt{0.2873}\\\\=0.1364<\sigma<0.5360\\\\\approx 0.14<\sigma<0.54[/tex]
Thus, the 95% confidence interval for the standard deviation is (0.14, 0.54).
Rachel baked 3 cakes in 2 hours, 4 cakes in 3 hours, and 5 cakes in 4 hours. Determine whether the number of cakes baked is proportional to the number of hours.
Answer:
Its not proportional and not combarable
-7x+3y=1 and 3y+12=-6
Answer:
the sums are given in explainationhope you like the answerplease mark the answer as brainliestDescribe two different ways to use transformations to change f(x) = x into g(x)=-3x-12
Answer:
See below
Step-by-step explanation:
GivenFunction f(x) = xTransformation ways1. Reflection by a factor of (-3) and vertical shift down -12 units
f(x) = x → (-3) ⇒ h(x) = -3x → (-12) ⇒ g(x) = -3x - 122. Vertical shift up by 4 units and reflection by a factor of (-3)
f(x) = x → (+4) ⇒ h(x) = x + 4 → (-3) ⇒ g(x) = -3x - 12The sum of a twice a number and three is 15. What is the number?
Answer:
The answer is 6. Does that help?
A proportion often shows the relationship between:
Answer:
It compares two numbers that can represent many of things. For example, people, food & items.
Step-by-step explanation:
Which function is graphed below? pls help
Answer:
its b Brother
Step-by-step explanation:
27=p(1+r3) solve for r
p = 27
r = 0
p(1+r3) = 27
27(1+0(3)) = 27
27(1+0) = 27
27(1) = 27
27 = 27
what is the equivalent of 3-(-6)
Answer:
3-(-6) = 9
Step-by-step explanation:
3-(-6) simplifies to 3 + 6.
We would have to distribute the outside negative into the inside to get rid of the parenthesis. Then, we would add.
[tex]3-(-6)\\\\-1 * -6 = 6\\\\3-(-6)=\boxed{3+6}=9[/tex]
Hope this helps.
FIRST TO ANSWER GETS BRAINLIEST
The product of 1.3 times 10 Superscript negative 4 and a number n results in 2.6 times 10 Superscript 12. What is the value of n?
A. 2 times 10 Superscript negative 8
B. 2 times 10 Superscript negative 3
C. 2 times 10 Superscript 16
D. 2 times 10 superscript 48
Answer:
The answer is c
Step-by-step explanation:
got it right on edge
Answer:
C / 2 times 10 Superscript 16
Step-by-step explanation:
Convert 255 mL to L / Convertir 820 cm a m
Answer:
255 mL = .255 L
Step-by-step explanation:
820 cm = 8.2 m
IF U CAN HELP ME ILL BRAINIFY U AND U GET ALL MY POINTS. IT HAS TO BE A GOOD ANSWER, AS I THINKING I GOT THE CORRECT ANSWER, SO YOU CANT FOOL ME!!
Sherie makes a canvas frame for a painting using stretcher bars. The retuangular painting will be 12 inches long and 9 inches wide. What should be the diagonal length of the painting in Sherie's question? Record your numerical response. Do not include words, units or spaces
it would be 15 in. diagonal
Find the slope of the line that passes through the points: (1, 1) and (7, 5) . If you get stuck , try plotting the points on graph paper and drawing the line through them with a ruler.
Answer:
2,3
Step-by-step explanation:
The slope of the line that passes through points (1, 1) and (7, 5) is 2/3.
What is slope ?Slope is a notation that shows that a surface of which one end or side is at a higher level than another surface.
The formula for slope of a line that passes through two points (x₁.y₁) and (x₂,y₂) is,
y₂ - y₁ = m(x₂ - x₁)
The given points are, (1, 1) and (7, 5).
The slope of the line is given by formula m = (y₂-y1)/(x₂-x₁)
m= (5-1)/(7-1)
m = 4/6
m = 2/3
The slope of the line that passes through points (1, 1) and (7, 5) is 2/3.
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If f(x) = 5x - 6, which of these is the inverse of f(x)?
O A. f'(x) = 5 +6
O B. :'(x)= -6
C. F'(x) = *+6
+ LO
X-6
O D. 8'(X) = *
Answer:
A
Step-by-step explanation:
Because subtraction and addition are alike just how multiplication and division are.
The inverse of f(x) is (x+6)/5, the correct option is A
What is inverse of a function?Suppose that the given function is
[tex]f:X\rightarrow Y[/tex]
Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is
[tex]f^{-1}: Y \rightarrow X[/tex]
such that:
[tex]\forall \: x \in X : f(x) \in Y, \exists \: y \in Y : f^{-1}(y) \in X[/tex]
It simply means, inverse of 'f' is undo operator, that takes back the effect of 'f'
Given;
f(x) = 5x - 6
f^-1 (x ) = x+6/5
Let, y = f(x) and rearrange making x the subject;
y = 5x - 6 ( add 6 to both sides )
y + 6 = 5x ( divide both sides by 5 )
x = (y+6)/5
Change y back into terms of x
x = (x+6)/5
Therefore, the answer in inverse will be (x+6)/5
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The ratio of Green marbles to total marbles in a bag is 2 to 9. The ratio of red marbles to total marbles in th same bag is 1 to 3 which of the following statements is true
PLEASE HELP ME!! WILL MARK BRIANLIEST!
Answer:
462
Step-by-step explanation:
15 x 11 + 33 x 9 = 462
100% sure gimme brainliest please thanks
Answer:
Its 462
Step-by-step explanation:
Olivia chose 10/21 . How did she get that answer?
5x- 13x - 44 = 2 please help!!!!!!!!!!!!!
y = 3x + 3
Is this non linear
It is linear. Not non-linear. The line goes straight, even if it has a y axis, it does not curve and the change in y is constant and same each time.
Work out the value of X
Answer:
x = 39
Step-by-step explanation:
3x - 15 + 2x + 2x + 2x +24 = 360
9x = 360 + 15 - 24
9x = 351
x = 39
The diagram below represents the side view of a bike ramp.
Which of the following is closest to the value of x ?
Answer:
32
Step-by-step explanation:
We are finding X and it connects to the base and the height, so it is going upward only a bit, so you add the base to the height or 26 + 6 = 32.
Answer:
32
Step-by-step explanation:
All you need to do is add 26 + 6=32
what is the value of k
Answer:
k = 10
Step-by-step explanation:
180° - 115° = 65°
(4k + 5) + (6k + 10) + 65 = 180
4k + 5 + 6k + 10 + 65 = 180
10k + 80 = 180
10k = 100
k = 10
Answer:
solution:
ang.XZY+ang.ZXY=ang.ZYM reason: the exterior angle of a triangle is equal to the sum of opposite interior angles 2.(4k+5)+(6K+10)=115 3. 10k +15=115 4. 10k =100 5 k= 10j(2x+9) m(6x-1)
i don’t get this at all
Answer:
omg that one is hard but it is 18j-6m
Which of the following are exterior angles? Check all that apply.
The answer is A, D, and F.
We have given that the following are exterior angles.
What is the exterior angle?
The angle between a side of a polygon and an extended adjacent side. an angle formed by a transversal as it cuts one of two lines and is situated on the outside of the line.
Therefore, The answer is A, D, and F.
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Answer: D, F
Step-by-step explanation:
The answer is D: <2 and F: <4
will give brainlist
Answer:
B is the correct answer I the math hopes this helped!
A bag contains 12 red marbles the ratio of red marbles to blue marbles is 3:4 find the number of blue marbles in the bag
Answer:
16
Step-by-step explanation:
If the ratio is 3 red marbles to 4 blue marbles we can solve this using the following:
[tex]\frac{12}{b} = \frac{3}{4}[/tex]
[tex]12 * 4 = 3b\\48 = 3b\\\frac{48}{3} = b\\b = 16[/tex]
So we have 16 blue marbles.
Based on the ratio of red to blue marbles, the number of blue marbles in the bag is 16 marbles.
The bag has red marbles to blue marbles in a ratio of 3:4.
If there are 12 red marbles, the number of blue marbles can be found by direct proportion:
3 : 4
12 : x
Cross-multiply:
3x = 48
x = 48/3
x = 16 blue marbles
In conclusion, there are 16 blue marbles in the bag.
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Find the mean
5,-15,7,-13,1
Answer:
− 4
Step-by-step explanation:
The mean of a set of numbers is the sum divided by the number of terms.
Please answer I need help badly
what is 1.25x1.19 pls hurry
