Answer:
[tex]\boxed{\sf 10}[/tex]
Step-by-step explanation:
The additive number of any number is the number when added to the number gives a result of zero.
So, if we add 10 to -10 we get a result of zero.
=> -10+10
=> Zero
if y = 2√x÷ 1–x', show that dy÷dx = x+1 ÷ √x(1–x)²
Answer: see proof below
Step-by-step explanation:
Use the Quotient rule for derivatives:
[tex]\text{If}\ y=\dfrac{a}{b}\quad \text{then}\ y'=\dfrac{a'b-ab'}{b^2}[/tex]
Given: [tex]y=\dfrac{2\sqrtx}{1-x}[/tex]
[tex]\sqrtx[/tex][tex]a=2\sqrt x\qquad \rightarrow \qquad a'=\dfrac{1}{\sqrt x}\\\\b=1-x\qquad \rightarrow \qquad b'=-1[/tex]
[tex]y'=\dfrac{\dfrac{1-x}{\sqrt x}-(-2\sqrt x)}{(1-x)^2}\\\\\\.\quad =\dfrac{\dfrac{1-x}{\sqrt x}-(-2\sqrt x)\bigg(\dfrac{\sqrt x}{\sqrt x}\bigg)}{(1-x)^2}\\\\\\.\quad =\dfrac{1-x+2x}{\sqrt x(1-x)^2}\\\\\\.\quad =\dfrac{x+1}{\sqrt x(1-x)^2}[/tex]
LHS = RHS: [tex]\dfrac{x+1}{\sqrt x(1-x)^2}=\dfrac{x+1}{\sqrt x(1-x)^2}\qquad \checkmark[/tex]
A tin of tennis balls costs $6.99, and each tin contains 4
tennis balls.
If the tennis balls were sold individually, then
approximately how much would one tennis ball cost?
$
Answer:
About $1.75 per tennis balls
Step-by-step explanation:
A tin of 4 tennis balls costs $6.99. We are asked to find the price of one tennis ball.
We need to find the unit price, or price per ball.
Divide the cost by the number of tennis balls.
cost / tennis balls
cost = $6.99
tennis balls = 4 tennis balls
$6.99 / 4 tennis balls
Divide 6.99 by 4.
$1.7475 / 1 tennis ball
Round to the nearest cent or hundredth. The 7 in the thousandth place tells us to round the 4 to a 5 in the hundredth place.
$1.75 / 1 tennis ball
It would cost approximately $1.75 for one tennis ball.
Mark has a collection of 80 coins. There are only nickels and dimes in the collection. The total value of the coins is $5.00. How many dimes does Mark have?
Answer:
number of nickel = 60
number of dimes = 20
Step-by-step explanation:
1 nickel = 5 cents
1 dimes = 10 cents
$1 = 100 cents
we will use these value to solve the questions
_______________________________
Total no of coins = 80
let the number of nickels be x
let the number of dimes be y
thus,
x+y = 80
y = 80-x equation 2
value of x nickels = 5x
value of y dimes = 10y
Total value of x nickels and y dimes = 5x+10y
The total value of the coins is $5.00
total value of the coins in cents = 5*100 = 500
thus
5x+10y = 500
using y = 80-x from equation 2
5x + 10(80 - x) = 500
5x + 800 - 10x = 500
-5x = 500 - 800 = -300
x = -300/-5 = 60
Thus,
number of nickel = 60
number of dimes = 80-60 = 20
(08.01 MC)
The volume of a pyramid that fits exactly inside a cube is 9 cubic feet. What is the volume of the cube? (5 points)
Select one:
a. 3 cubic feet
b. 6 cubic feet
c. 18 cubic feet
d. 27 cubic feet
Answer:
d. 27 cubic feet
Step-by-step explanation:
volume of cube = s^3 = B * s
volume of pyramid = (1/3) * B * h
The volume of a pyramid is 1/3 of the area of the base multiplied by the height. The volume of a cube is the area of the base multiplied by the height. Since the volume of a pyramid has the fraction 1/3 and the volume of the cube does not, then the volume of a cube is 3 times greater than the volume of a pyramid that fits inside and has the same base area.
volume of pyramid = 9 cu ft
volume of cube = 3 * 9 cu ft = 27 cu ft
Answer: d. 27 cubic feet
Answer:
27 ft^3 (Answer d)
Step-by-step explanation:
Here the volume of the pyramid is (1/3) the volume of the cube:
Letting s represent the length of one side of the base,
(1/3)(s)^2(s) = 9 ft^3, equivalent to s^3 = 27.
Solving for s, we get s = 3 ft.
Thus, the volume of the cube is V = s^3 = (3 ft)^3 = 27 ft^3 (Answer d)
What is credit?
an arrangement in which you receive money, goods, or services now in exchange for the promise of payment later
an arrangement in which you receive goods or services in exchange for other goods and services
an arrangement in which you receive money now and pay it bulk later with fees?
if the nth term is , then the (n+1)st is: Sorry if formatting is off, check the image to see the equation better!
Answer:
5
----------
( n+1)(n+2)
Step-by-step explanation:
5
----------
n ( n+1)
Replace n with n+1
5
----------
(n+1) ( n+1+1)
5
----------
( n+1)(n+2)
We replace every 'n' with n+1 and simplify
[tex]\frac{5}{(n+1)(n+1+1)} = \frac{5}{(n+1)(n+2)}[/tex]
Suppose x varies directly with the square root of y and inversely with the cube root of z. What equation models this combined variation?
Answer:
[tex]\huge\boxed{x = k \frac{\sqrt{y} }{\sqrt[3]{z} }}[/tex]
Step-by-step explanation:
Given that:
1) x ∝ √y
2) x ∝ [tex]\frac{1}{\sqrt[3]{z} }[/tex]
Combining the proportionality
=> x ∝ [tex]\frac{\sqrt{y} }{\sqrt[3]{z} }[/tex]
=> [tex]x = k \frac{\sqrt{y} }{\sqrt[3]{z} }[/tex]
Where k is the constant of proportionality.
Can someone please help me?
Negative Integers are :
Less than zeroTo the left of zero on a number line.For each ordered pair, determine whether it is a solution to y=-9.
Is it a solution?
Yes or No
(1, -9)
(7,3)
(-9,4)
(0, -9)
Answer:
(1, -9) yes
(7,3) no
(-9,4) no
(0, -9) yes
Step-by-step explanation:
The y value must be -9
The x value can be any value to satisfy the equation y = -9
Which expression is equivalent to 2(5)^4
Answer:
2·5·5·5·5
Step-by-step explanation:
2(5)^4 is equivalent to 2·5·5·5·5; 2 is used as a multiplicand just once, but 5 is used four times.
A) Which of triangle A, B, C and D is congruent to triangle E.? B) Which other two triangles (from A, B, C and D) are congruent to each other? Please help!
Answer:
c is congruent to e congruent means to be the same
Step-by-step explanation:
A portion of the quadratic formula proof is shown. Fill in the missing reason.
Answer:
Find a common denominator on the right side of the equation
Step-by-step explanation:
The equation before the problem is
X² + b/a(x) + (b/2a)²= -c/a + b²/4a²
The next step in solving the above equation is to fibd tge common denominator on the right side of the equation.
X² + b/a(x) + (b/2a)²= -c/a + b²/4a²
X² + b/a(x) + (b/2a)²= -4ac/4a² + b²/4a²
X² + b/a(x) + (b/2a)²=( b²-4ac)/4a²
The right side of the equation now has a common denominator
The next step is to factorize the left side of the equation.
(X+b/2a)²= ( b²-4ac)/4a²
Squaring both sides
X+b/2a= √(b²-4ac)/√4a²
Final equation
X=( -b+√(b²-4ac))/2a
Or
X=( -b-√(b²-4ac))/2a
Which table represents a linear function?
x y
1 5
2 10
3 15
4 20
5 25
x y
1 5
2 20
3 45
4 80
5 125
x y
1 5
2 25
3 125
4 625
5 3125
x y
1 2
2 4
3 7
4 16
5 32
Answer:
The first table on the list:
x 1 2 3 4 5
y 5 10 15 20 25
Step-by-step explanation:
A linear equation is when the slope is the exact same between each point. The way we find slope is by finding the change in "y" over the change in "x".
x-values: 1, 2/y-values: 5, 10---[tex]\frac{10-5}{2-1}[/tex]=5/1=5
x-values: 2, 3/y-values: 10, 15---[tex]\frac{15-10}{3-2}[/tex]=5/1=5
x-values: 3, 4/y-vaues: 15, 20---[tex]\frac{20-15}{4-3}[/tex]=5/1=5
x-values: 4, 5/y-values: 20, 25---[tex]\frac{25-20}{5-4}[/tex]=5/1=5
The slope for each change in points is 5, which means that this table represents a linear function.
The only table that represents a linear function is; Table 1
Linear functionA linear function is one that has the same slope for every coordinate point.
Looking at the tables, the one with same slope for all points is table 1 and we will prove that as follows;
At x = 1, y = 5 and;Slope = 5/1 = 5
At x = 2; y = 10 and;Slope = 10/2 = 5
At x = 3, y = 15 and;Slope = 15/3 = 5
At x = 4, y = 20 and;Slope = 20/4 = 5
At x = 5, y = 25 and;slope = 25/5 = 5
In conclusion, only table 1 represents a linear function.
Read more about Linear function at; https://brainly.com/question/15602982
Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. lim x→9 x − 9 x2 − 81
Without resorting to L'Hopitâl's rule,
[tex]\displaystyle\lim_{x\to9}\frac{x-9}{x^2-81}=\lim_{x\to9}\frac{x-9}{(x-9)(x+9)}=\lim_{x\to9}\frac1{x+9}=\frac1{18}[/tex]
With the rule, we get the same result:
[tex]\displaystyle\lim_{x\to9}\frac{x-9}{x^2-81}=\lim_{x\to9}\frac1{2x}=\frac1{18}[/tex]
Officer Jacobi drove 180 miles in his patrol car during part of May. The distance represents 40% of May. How many miles did he drive all of May? a) 710 miles b) 420 miles c) 720 miles d) 450 miles Need Help on How to work this problem out, what formula would I use?
Answer:
D: 450 miles
Step-by-step explanation:
So we know that Officer Jacobi drove 180 miles, which represents 40% of the total distance driven. In other words, 40% of the total distance traveled is 180. Thus (let D be the total distance traveled):
[tex]0.4D=180[/tex]
This equation is basically saying that 40% (0.4) of the total distance driven is 180 miles. To solve for the total distance D, we can divide both sides by 0.4. Thus:
[tex]0.4D=180\\D=450[/tex]
So the answer is D or 450 miles.
Note that there isn't a specific formula you would use. These types of problems require you to write out an equation yourself.
What is the issue with the work? It is wrong. Please answer this for points!
Answer:
3 ( a ) : x = 3.6,
3 ( b ) : x = 5
Step-by-step explanation:
For 3a, we can calculate the value of x through Pythagorean Theorem, which seemingly was your approach. However, the right triangle with x present as the leg, did not have respective lengths 9.6 and 12. The right angle divides 9.6 into two congruent parts, making one of the legs of this right triangle 9.6 / 2 = 4.8. The hypotenuse will be 12 / 2 as well - as this hypotenuse is the radius, half of the diameter. Note that 12 / 2 = 6.
( 4.8 )² + x² = ( 6 )²,
23.04 + x² = 36,
x² = 36 - 23.04 = 12.96,
x = √12.96, x = 3.6
Now as you can see for part b, x is present as the radius. Length 3 forms a right angle with length 8, dividing 8 into two congruent parts, each of length 4. We can form a right triangle with the legs being 4 and 3, the hypotenuse the radius. Remember that all radii are congruent, and therefore x will be the value of this hypotenuse / radius.
( 4 )² + ( 3 )² = ( x )²,
16 + 9 = x² = 25,
x = √25, x = 5
What is f ( 1/3)? When the function is f(x) =-3x+7
Answer:
f(1/3) = 6
Step-by-step explanation:
f(x) =-3x+7
Let x = 1/3
f(1/3) =-3*1/3+7
= -1 +7
= 6
Answer:
f(1/3) = 6
Step-by-step explanation:
The function is:
● f(x) = -3x+7
Replace x by 1/3 to khow the value of f(1/3)
● f(1/3) = -3×(1/3) +7 = -1 +7 = 6
Lori buys a $586 certificate of deposit (CD) that earns 6.6% interest that compounds monthly. How much will the CD be worth in 13 years? Express your answer rounded correctly to the nearest cent. Do not include units on your answer.
Answer:
$1344.9Step-by-step explanation:
This problem can be solved using the compound interest formula
[tex]A= P(1+r)^t[/tex]
Given data
A, final amount =?
P, principal = $586
rate, r= 6.6% = 0.066
Time, t= 13 years
Substituting our values into the expression we have
[tex]A= 586(1+0.066)^1^3\\\ A= 586*(1.066)^13\\\ A= 586*2.295\\\ A= 1344.87[/tex]
To the nearest cent the in 13 years the CD will be worth $1344.9
Multiply: (x−5)(x−7) A x2−12x+35 B x2+2x+35 C x2+35 D x2+35x−12
Answer:
x^2 -12x+35
Step-by-step explanation:
(x−5)(x−7)
FOIL
first x*x = x^2
outer -7x
inner -5x
last -7*-5 = 35
Add them together
x^2 -7x-5x +35
x^2 -12x+35
Answer:
Step-by-step explanation:
x*x=2x
x*-7=-7x
-5*x=-5x
-5*-7=+35
2x-12x+35
A
True or False. The statistician should use Printout C to perform a t-test on the GROUP variable in the regression model. g
Answer:
False
Step-by-step explanation:
Regression model is a set of statistical process which estimates the relationship between two variables. The one variable is dependent variable and the other is independent variable. The statistician should not use printout C to perform a t-test in regression model.
Match the ones on the left to the right
Answer/Step-by-step explanation:
[tex] (4 + 5) + 2 = 4 + (5 + 2) [/tex] => any combination of numbers were formed or grouped when adding. The associative property of addition was applied.
[tex] 2(2x + 4) = 4x + 8 [/tex] => the sum of two terms (addend) are multiplied by by a number separately (I.e., a(b + c) = a(b) + a(c) = ab + ac). The property applied is distributive property.
[tex] (7x * x) * 3 = 7 * (x * 3) [/tex] => the numbers were grouped in any combination to arrive at same result when multiplying. Associative property of multiplication was applied.
[tex] (8 * x * 2) = (x * 8 * 2) [/tex] => the numbers where ordered in any manner to arrive at same result when multiplying. Cummutative property of multiplication was applied.
[tex] (7 + 3) + 1 = (1 + (7 + 3) [/tex] => the order in which the nnumbers in the were arranged doesn't matter, as same result is arrive at. This is Cummutative property of addition.
Reducing scrap of 4-foot planks of hardwood is an important factor in reducing cost at a wood-floor manufacturing company. Accordingly, engineers at Lumberworks are investigating a potential new cutting method involving lateral sawing that may reduce the scrap rate. To examine its viability, two independent, random, representative samples of planks were examined. One sample contained 200 planks which were sawed using the old method. The other sample contained 400 planks which were sawed using the new method. Sixty-two of the 200 planks were scrapped under the old method of sawing, whereas 36 of the 400 planks were scrapped under the new method.
Required:
a. Construct the 90% confidence interval for the difference between the population scrap rates between the old and new methods, respectively.
b. Write the null and alternative hypotheses to test for differences in the population scrap rates between the old and new cutting methods, respectively.
c. Using the part a results, can we conclude at the 10% significance level that the scrap rate of the new method is different than the old method?
Answer:
The critical value for two tailed test at alpha=0.1 is ± 1.645
The calculated z= 9.406
Step-by-step explanation:
Formulate the hypotheses as
H0: p1= p2 there is no difference between the population scrap rates between the old and new cutting methods
Ha : p1≠ p2
Choose the significance level ∝= 0.1
The critical value for two tailed test at alpha=0.1 is ± 1.645
The test statistic is
Z = [tex]\frac{p_1- p_2}\sqrt pq(\frac{1}{n_1} + \frac{1}{n_2})[/tex]
p1= scrap rate of old method = 62/200=0.31
p2= scrap rate of new method = 36/400= 0.09
p = an estimate of the common scrap rate on the assumption that the two rates are same.
p = n1p1+ n2p2/ n1 + n2
p =200 (0.31) + 400 (0.09) / 600
p= 62+ 36/600= 98/600 =0.1633
now q = 1-p= 1- 0.1633= 0.8367
Thus
z= 0.31- 0.09/ √0.1633*0.8367( 1/200 + 1/400)
z= 0.301/√ 0.13663( 3/400)
z= 0.301/0.0320
z= 9.406
The calculated value of z falls in the critical region therefore we reject the null hypothesis and conclude that the 10% significance level that the scrap rate of the new method is different from the old method.
Solve for x (x+4)/3 = 2.
a. x = -2
b. x=2
c. x = 2/3
d. x= -10/3
Answer:
The answer is option BStep-by-step explanation:
[tex] \frac{x + 4}{3} = 2[/tex]
To solve it first of all cross multiply
That's
x + 4 = 6
Move 4 to the right side of the equation
The sign changes to negative
That's
x = 6 - 4
We have the final answer as
x = 2Hope this helps you
The manager of the video department at a department store plans to purchase a large number of DVDs of a recent movie. One supplier is selling boxes of 20 DVD movies for $240, and a second supplier is selling boxes of 14 DVD movies for $170. Only complete boxes of DVD movies can be purchased. Complete part a) and b) below. a)
a) If the manager can purchase boxes of DVD movies from either or both suppliers, determine the maximum number of DVD movies that can be purchased for $415. Indicate how many boxes of 20 and how many boxes of 14 will be purchased.
— box(es) of 20 and — box(es) of 14
b) How much will the DVD movies cost?
They will cost $—
Answer:
1 box of 20 and 1 box of 14
They will cost $410
Step-by-step explanation:
1. Find how many boxes of 20 DVD movies can be bought
415 - 240 = 175
1 box of 20 DVD movies can be sold
2. Find how many boxes of 14 DVD movies can be bought from $175
175 - 170 = 5
1 box of 14 DVD movies can be bought
3. Find the cost
240 + 170 = 410
Why is f (x) = (3x + 1/3)^2 + 8/9 not the vertex form of f (x)
not the vertex form of f (x) = 9x^2 +2x +1?
O The expression has a constant outside of the squared term.
O Some of the terms are fractions instead of integers.
O The expression is not the product of two binomials.
O The variable x has a coefficient.
Answer:
The Variable has a coefficient.
Step-by-step explanation:
Help pleaseeeee!!!!!!
Answer:
0.05m^2
Step-by-step explanation:
5 divided by 100
Which is an infinite arithmetic sequence? a{10, 30, 90, 270, …} b{100, 200, 300, 400} c{150, 300, 450, 600, …} d{1, 2, 4, 8}
Answer:
C
Step-by-step explanation:
An arithmetic sequence has a common difference d between consecutive terms.
Sequence a
30 - 10 = 20
90 - 30 = 60
270 - 90 = 180
This sequence is not arithmetic
Sequence b
200 - 100 = 100
300 - 200 = 100
400 - 300 = 100
This sequence is arithmetic but is finite, that is last term is 400
Sequence c
300 - 150 = 150
450 - 300 = 150
600 - 450 = 150
This sequence is arithmetic and infinite, indicated by ........ within set
Sequence d
2 - 1 = 1
4 - 2 = 2
8 - 4 = 4
This sequence is not arithmetic
Thus the infinite arithmetic sequence is sequence c
How can a company use a scatter plot to make a future sales decision?
Answer:
Hope this helps :)
Step-by-step explanation:
A scatter plot is a two-dimensional diagram that displays individual data points based on the intersection of two variables, shown as vertical and horizontal axes. Individual data points or values are plotted at particular coordinates of the two variables being studied. Patterns of data points provide a visual representation of relationship between the two variables. A wide range of jobs and careers use this valuable analytical tool for data analysis and decision making.
My conclusion,
They help organize important data for future occurences.
In this diagram, bac~edf. if the area of bac= 6 in.², what is the area of edf? PLZ HELP PLZ PLZ PLZ
Answer:
2.7 in²
Step-by-step explanation:
Given that ∆BAC ~ is similar to ∆EDF, the ratio of the area of ∆BAC to the area of ∆EDF = the square of the ratio of their corresponding sides.
Thus, let x be the area of ∆EDF
[tex] \frac{6}{x} = (\frac{3}{2})^2 [/tex]
[tex] \frac{6}{x} = \frac{9}{4} [/tex]
Cross multiply
[tex] x*9 = 4*6 [/tex]
[tex] 9x = 24 [/tex]
[tex] \frac{9x}{9} = \frac{24}{9} [/tex]
[tex] x = 2.67 [/tex]
Area of ∆EDF = 2.7 in²
Write the expression as a single term, factored completely. Do not rationalize the denominator. 54x2+1−−−−−−√+20x4x2+1√ Select one: a. 5(4x2+4x+1)4x2+1√ b. 20x2+20x+1)5x+1 c. 20x2+20x+1)4x2+1√ d. 5(4x2+4x+1)5x+1
When we write expression 5√(4x² + 1) + 20x / √(4x² + 1) as singled term factorised completely, we have 5(4x² + 4x + 1) / √(4x² + 1) (Option A)
Data obtained from the question5√(4x² + 1) + 20x / √(4x² + 1)Factorised =?How to factorised 5√(4x² + 1) + 20x / √(4x² + 1)5√(4x² + 1) / 1 + 20x / √(4x² + 1)
Least common multiple (LCM) is √(4x² + 1)
[(5√(4x² + 1) × √(4x² + 1) + 20x] / √(4x² + 1)
[5(4x² + 1) + 20x] / √(4x² + 1)
[20x² + 5 + 20x] / √(4x² + 1)
[20x² + 20x + 5] / √(4x² + 1)
5(4x² + 4x + 1) / √(4x² + 1)
Learn more about factorisation:
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Complete question
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