Answers
Answer:
9 + 18 = 27
27 + n + 1
= n = 27 - 1 = 26.
n = 26
9 + 18 + 26 + n + 7 =
53 + n + 7
53 + 7 + n
60 + n = 360
n = 360 - 60 = 300
so, n 300
so = 9, 18, 300, 26
Related Questions
What is f ( 1/3)? When the function is f(x) =-3x+7
Answers
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
Which expression is equivalent to 2(5)^4
Answers
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.
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 $—
Answers
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
Please help me on question 4 and 5 I am really stuck thank you I would really appreciate it
Answers
Answer:
1. 5/4
2. 7
Step-by-step explanation:
1) Lets call the width as w
Therefore length would be:
w+4
To find the perimeter you use the formula:
2 (l+w)
Now substitute our values into this formula:
2 (w+4+w)
2( 2w+4)
4w+8
Now make this equal to 13:
4w +8 = 13
4w = 5
w = 5/4
2. In this question we will call length l
Therefore width would be:
l-5
Now we will do the steps we did above:
2 (l+l-5)
2 (2l-5)
4l -10
4l - 10 = 18
4l = 28
l = 7
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
Answers
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]
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?
$
Answers
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.
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.
Answers
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
The diameter of steel rods manufactured on two different extrusion machines is being investigated. Two random samples of sizes n1"=15 and n2"=17 are selected, and the sample means and sample variances are x1 =8.73, s2=0.35, x =8.68, and s2=0.40, respectively. Assume that σ1^2 = σ2^2 that the data are drawn from a normal distribution.
Required:
a. Is there evidence to support the claim that the two machines produce rods with different mean diameters? Use alpha=0.05 in arriving at this conclusion.
b. Find the P-value for thet-statistic you calculated in part (a).
c. Construct a 95% confidence interval for the difference in mean rod diameter. Interpret this interval.
Answers
Answer:
a) No sufficient evidence to support the claim that the two machines produce rods with different mean diameters.
b) P-value is 0.80
c) −0.3939 <μ< 0.4939
Step-by-step explanation:
Given Data:
sample sizes
n1 = 15
n2 = 17
sample means:
x1 = 8.73
x2 = 8.68
sample variances:
s1² = 0.35
s2² = 0.40
Hypothesis:
H₀ : μ₁ = μ₂
H₁ : μ₁ ≠ μ₂
Compute the pooled standard deviation:
[tex]s_{p} = \sqrt{\frac{(n_{1} - 1)s_{1}^{2} + (n_{2} - 1)s_{2}^{2}}{n_{1} +n_{2} -2} }[/tex]
[tex]= \sqrt{\frac{(15-1)0.35+(17-1)0.40}{15+7-2}}[/tex]
[tex]= \sqrt{\frac{(14)0.35+(16)0.40}{30}}[/tex]
[tex]= \sqrt{\frac{4.9+6.4}{30}}[/tex]
[tex]= \sqrt{\frac{11.3}{30}}[/tex]
[tex]= \sqrt{0.376667}[/tex]
= 0.613732
= 0.6137
Compute the test statistic:
[tex]t = \frac{x_{1} -x_{2} }{s_{p} \sqrt{\frac{1}{n_{1} }+\frac{1}{n_{2} } } }[/tex]
[tex]= \frac{8.73-8.68}{0.6137\sqrt{\frac{1}{15}+\frac{1}{17} } }[/tex]
[tex]= \frac{0.05}{0.6137\sqrt{0.06667+0.05882} } }[/tex]
[tex]= \frac{0.05}{0.6137\sqrt{0.12549} } }[/tex]
[tex]= \frac{0.05}{0.6137(0.354246)} } }[/tex]
[tex]= \frac{0.05}{0.6137(0.354246)} } }[/tex]
= 0.05 / 0.217401
= 0.22999
t = 0.230
Compute degree of freedom:
df = n1 + n2 -2 = 15 + 17 - 2 = 30
Compute the P-value from table using df = 30
P > 2 * 0.40 = 0.80
P > 0.05 ⇒ Fail to reject H₀
Null hypothesis is rejected when P-value is less than or equals to level of significance. But here the P-value = 0.80 and level of significance = 0.05. So P-value is greater than significance level. Hence there is not sufficient evidence to support the claim that population means are different.
Construct a 95% confidence interval for the difference in mean rod diameter:
confidence = c = 95% = 0.95
α = 1 - c
= 1 - 0.95
α = 0.05
Compute degree of freedom:
df = n1 + n2 -2 = 15 + 17 - 2 = 30
Compute [tex]t_{\alpha /2}[/tex] with df = 30 using table:
t₀.₀₂₅ = 2.042
Compute confidence interval:
= [tex](x_{1}-x_{2})-t_{\alpha/2} ( s_{p} )\sqrt{\frac{1}{n_{1} }+\frac{1}{n_{2} } }[/tex]
= (8.73 - 8.68) - 2.042 ( 0.6137 ) [tex]\sqrt{\frac{1}{15} +\frac{1}{17} }[/tex]
= 0.05 - 2.042 ( 0.6137 ) [tex]\sqrt{\frac{1}{15} +\frac{1}{17} }[/tex]
= 0.05 - 1.253175 [tex]\sqrt{0.06667+0.05882} } }[/tex]
= 0.05 - 1.253175 [tex]\sqrt{0.12549} } }[/tex]
= 0.05 - 1.253175 (0.35424))
= 0.05 - 0.443925
= −0.393925
= −0.3939
[tex](x_{1}-x_{2})+t_{\alpha/2} ( s_{p} )\sqrt{\frac{1}{n_{1} }+\frac{1}{n_{2} } }[/tex]
= (8.73 - 8.68) + 2.042 ( 0.6137 ) [tex]\sqrt{\frac{1}{15} +\frac{1}{17} }[/tex]
= 0.05 + 2.042 ( 0.6137 ) [tex]\sqrt{\frac{1}{15} +\frac{1}{17} }[/tex]
= 0.05 + 1.253175 [tex]\sqrt{0.06667+0.05882} } }[/tex]
= 0.05 + 1.253175 [tex]\sqrt{0.12549} } }[/tex]
= 0.05 + 1.253175 (0.35424))
= 0.05 + 0.443925
= 0.493925
= 0.4939
−0.3939 <μ₁ - μ₂< 0.4939
A soup can has a height of 4 inches and a radius of 2.5 inches. What's the volume of soup in cubic inches that would fill one soup can? Question 3 options: A) 62.8 in3 B) 125.7 in3 C) 78.5 in3 D) 314 in3
Answers
Answer:
C. 78.5 in^3
Step-by-step explanation:
A soup can is in the shape of a cylinder. The volume of a cylinder can be found using the following formula:
[tex]v=\pi r^2h[/tex]
We know that the height is 4 inches and the radius is 2.5 inches.
r= 2.5 in
h= 4 in
[tex]v=\pi (2.5in)^2*4in[/tex]
Evaluate the exponent.
[tex](2.5 in)^2=2.5 in*2.5in=6.25 in^2[/tex]
[tex]v=\pi *6.25 in^2*4 in[/tex]
Multiply 6.25 in^2 and 4 in.
[tex]6.25 in^2*4 in=25 in^3[/tex]
[tex]v=\pi*25 in^3[/tex]
Multiply pi and 25 in^3.
[tex]v=78.5398163 in^3[/tex]
Round to the nearest tenth. The 3 in the hundredth place tells us to leave the 5 in the tenth place.
[tex]v=78.5 in^3[/tex]
78.5 cubic inches can fill one soup can.
In this diagram, bac~edf. if the area of bac= 6 in.², what is the area of edf? PLZ HELP PLZ PLZ PLZ
Answers
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
if the nth term is , then the (n+1)st is: Sorry if formatting is off, check the image to see the equation better!
Answers
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]
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
Answers
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
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?
Answers
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
Answers
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:
https://brainly.com/question/22248251
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Complete question
See attached photo
it is 235 miles from tulsa to dallas. it is 390 miles from dallas to houston. a) what is the total distance of a trip from tulsa to dallas to houston? b) what is the total distance from houston to dallas to tulsa? c) explain how you can tell whether the distances described in parts (a) and (b) are equal by using reasoning.
Answers
Answer:
a- tulsa to dallas to houston is 235+390 which is 625 miles
b - houston to dallas to tulsa is 390+235 miles which is 625 miles
c - by using reasoning both are same because they are just rewritten differently but the equation is same
please give me brainliest
hope it helps buddy
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.
Answers
Answer:
The Variable has a coefficient.
Step-by-step explanation:
For a certain casino slot machine, the odds in favor of a win are given as 17 to 83. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
Answers
Step-by-step explanation:
83P (E)=17-17P (E),
P (E)=17/100=0.17
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}
Answers
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
A portion of the quadratic formula proof is shown. Fill in the missing reason.
Answers
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
if y = 2√x÷ 1–x', show that dy÷dx = x+1 ÷ √x(1–x)²
Answers
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 researcher is interested in determining whether various stimulant drugs improve maze leaming performance in rats. To find out, the researcher recruits 16 rats and assigns 4 rats to one of 4 research conditions: caffeine, nicotine, cocaine, placebo. Each rat completes the maze once and in only one research condition and is timed; time to complete the maze is the researcher's measure of performance. Answer the following questions considering the data below (alpha)
Caffeine Nicotine Cocaine Placebo
30.00 45.00 30.00 60.00
45.00 75.00 30.00 75.00
45.00 60.00 60,00 60.00
45.00 45.00 30.00
What is the dependent variable in this study?
a. Drug condition
b. Time to complete maze
c. Number of rats
d. Research conditions
16. What analysis should be used to answer the researcher's question?
a. One-way between-subjects (a.ka. independent-samples) ANOVA
b. One-way within-subjects (a.k.a. dependent-samples, repeated-measures) ANOVA
c. Factorial ANOVA
d. T-test 17.
What is the Null hypothesis for this analysis?
a. There will be no difference between any group means
b. Maze performance will get worse with stimulants
c. Maze performance of at least one group will differ from typing of at least one other group
d. Maze performance on placebo will be worse than on all drugs
What are the degrees of freedom for the numerator of the F-ratio?
2
3
8
11
What are the degrees of freedom for the denominator of the F-ratio?
2
3
8
11
What is the critical F value for this analysis?
a. 3.49
b. 4.07
c. 6.04
d. 19.00
What is the SSbetween-groups value?
a. 425.00
b. 1181.25
c. 2517.19
d. 3698.44
What is the SSwithin value?
Answers
Answer:
1) The dependent variable is : time to complete the maze
2) The analysis used should be : One -way within-subjects ANOVA ( B )
3) Null hypothesis is ; There will be no difference between any group means
4) Degrees of freedom for the numerator of the F-ratio ; 4 - 1 = 3
5) degree of freedom for the denominator = 11
6) critical F value = 3.49
Step-by-step explanation:
The dependent variable is the time to complete the maze this is because the time depends on the effects of the stimulant drugs on the rats in the maze .
The analysis used should be : One -way within-subjects ANOVA ( B )
Null hypothesis is ; There will be no difference between any group means
Degrees of freedom for the numerator of the F-ratio ; 4 - 1 = 3
degree of freedom for the denominator = N - k = 16 - 4 = 12. the closest answer from the options is 11
The critical value is 3.49 ,because at degree of freedom = 12 , ∝ = 0.05, and Dfn = 3, from the F - table the critical value would be 3.49
Match the ones on the left to the right
Answers
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.
Help pleaseeeee!!!!!!
Answers
Answer:
0.05m^2
Step-by-step explanation:
5 divided by 100
Suppose x varies directly with the square root of y and inversely with the cube root of z. What equation models this combined variation?
Answers
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.
What is the issue with the work? It is wrong. Please answer this for points!
Answers
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
Solve for x (x+4)/3 = 2.
a. x = -2
b. x=2
c. x = 2/3
d. x= -10/3
Answers
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
What is lim x → 0 e^2x - 1/ e^x - 1
Answers
Hello, please consider the following.
[tex]\displaystyle \forall x \in \mathbb{R}\\\\\dfrac{e^{2x}-1}{e^x-1}\\\\=\dfrac{(e^x)^2-1^2}{e^x-1}\\\\=\dfrac{(e^x-1)(e^x+1)}{e^x-1}\\\\=e^x+1\\\\\text{So, we can find the limit.}\\\\\lim_{x\rightarrow 0} \ {\dfrac{e^{2x}-1}{e^x-1}}\\\\=\lim_{x\rightarrow 0} \ {e^x+1}\\\\=e^0+1\\\\\large \boxed{\sf \bf \ =2 \ }[/tex]
Thank you
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?
Answers
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.
If the bathtub holds a total of 46.2 gallons, how many minutes would it take to fill the entire tub? Write an equation in one variable to help you solve the problem. The variable represents the unknown time in minutes.
Answers
Answer:
46.2÷m=x
Step-by-step explanation:
u divide the amount of water by the time it takes to fill up(m). Witch will equal the amount per minute (x).
16.5/min
time = m
gallons / minutes = rate
46.2 = 16.5 (m)
46.2 / 16.5 = 16.5 (m) / 16.5
2.8 = minutes
Multiply: (x−5)(x−7) A x2−12x+35 B x2+2x+35 C x2+35 D x2+35x−12
Answers
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
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