A straight line passes through the points (-4, 7), (6,-5) and (8, t)
Use an algebraic method to work out the value of t.
Answers
Answer:
-9.2
Step-by-step explanation:
equation of the line is
y = (-6/5)x + (7/5)
put 8 from (8, t) where the x is to get the y
t = (-6/5)(8) + (7/5)
t = -9.2
steps
1. get slope : -6/5
2. equation of the line is : y = (-6/5)x + (7/5)
3. put 8 from (8, t) where the x is to get the y
t = (-6/5)(8) + (7/5)
t = -9.2
detailed steps
We can use the slope-intercept form of the equation of a line, which is y = mx + b, where m is the slope of the line and b is the y-intercept.
First, we can find the slope of the line using the two given points (-4, 7) and (6, -5):
slope = (y2 - y1)/(x2 - x1)
slope = (-5 - 7)/(6 - (-4))
slope = -12/10
slope = -6/5
Now we can use the point-slope form of the equation of a line to find the equation of the line passing through (-4, 7) with slope -6/5:
y - y1 = m(x - x1)
y - 7 = (-6/5)(x - (-4))
y - 7 = (-6/5)(x + 4)
y - 7 = (-6/5)x - (24/5)
y = (-6/5)x + (7/5)
We can now substitute the x and y coordinates of the third point (8, t) into this equation to find the value of t:
t = (-6/5)(8) + (7/5)
t = -9.2
Therefore, the value of t is -9.2 when the straight line passes through the points (-4, 7), (6,-5) and (8, t).
chatgpt
Related Questions
convert 81 sq. ft. to sq. yd.
Answers
Answer:
81 sq. ft. = 9 sq. yd.
Explanation:
The ratio between sq. ft and sq. yd is:
\(1ft^2=\frac{1}{9}yd^2\)Then:
\(\frac{81ft^2}{9}=9yd^2\)Select the answer that contains all of the expressions that give the number of small squares in Step n. Step 1 Step 2 Step 3 A.n²+1 B. n(n + 1) C. n²+n D. n+ n+ 1 В. С . A.B.C. B.CD AD
Answers
In the given figure:
step 1 has 2 blocks
step 2 has 6 blocks
step 3 has 12 blocks
1)
\(\begin{gathered} n^2+1 \\ \text{for step1, n =1} \\ 1^2+1=2 \\ \text{for step2, n=2} \\ 2^2+1=5 \\ \text{ but in step 2, there are 6 blocks} \\ \text{ So, expression: n}^2+1\text{ is not valid} \end{gathered}\)2) n( n + 1 )
\(\begin{gathered} \text{ for step 1, n=1} \\ n(n+1) \\ 1(1+1)_{} \\ 1(2)=2 \\ \text{Step 1 has two blocks} \\ \text{for step 2, n=2} \\ n(n+1)=2(2+1) \\ n(n+1)=2(3) \\ n(n+1)=6 \\ \text{step 2 has 6 blocks} \\ \text{for step 3, }n=3 \\ n(n+1)=3(3+1) \\ n(n+1)=3(4) \\ n(n+1)=12 \\ \text{ step 3 has 12 blocks} \\ \text{Thus, expression : n(n+1) is valid} \end{gathered}\)n( n + 1 ) is valid
3)
\(n^2+n\)Since the expression can also write as:
\(n^2+n=n(n+1)\)Thus, n^2 +n is also valid
4)
\(\begin{gathered} n+n+1 \\ \text{for step 1, n = 1} \\ 1+1+1=3 \\ \text{but step 1 has 2 block not 3,} \\ \text{thus, the expression is not valid} \end{gathered}\)n + n + 1 is not valid
Answer :
b) n( n + 1 )
c) n^2 + n
-5/6 as decimal show work
Answers
Answer:
0.83
Step-by-step explanation:
Divide: -5 / 6 = -0.83333333
Answer:
Today : Saturday, 07 November 2020
Hour: 14.40 WIB (Indonesia)
_______________________________
-5/6 = -0,83 or - 0,833
6/-5 = -0,833
0
__-
50
48
___-
20
18
___-
20
18
____-
etc
solve for x
in the box below but i dont know how
Answers
Answer:
x=8
Step-by-step explanation:
15/12 = 1.25
1.25x = 10
x = 8
Literally the first thing i saw was Xbox. lol :)
Answer:
8
Step-by-step explanation:
15/12=10/x
15x=120
x=120/15
x=8
Write out a power set in roster notation. Write the power set of each set in roster notation. (a) {a} (b) {1,2}
Answers
The power set in roster notation requires listing all the possible subsets of a set, including the empty set and the set itself. The number of subsets in a power set can be calculated using the formula 2^n, where n is the number of elements in the original set.
The power set of a set is the set of all its subsets, including the empty set and the set itself. To write out the power set in roster notation, we need to list all the possible subsets of a given set.
(a) The set {a} has two subsets: {a} and {}. Therefore, the power set of {a} in roster notation is {{}, {a}}.
(b) The set {1,2} has four subsets: {1,2}, {1}, {2}, and {}. Therefore, the power set of {1,2} in roster notation is {{}, {1}, {2}, {1,2}}.
It is important to note that the cardinality (number of elements) of the power set of a set with n elements is 2^n. For example, the set {1,2} has two elements, so its power set has 2^2 = 4 subsets. Similarly, the set {a} has one element, so its power set has 2^1 = 2 subsets.
In conclusion, writing out the power set in roster notation requires listing all the possible subsets of a set, including the empty set and the set itself. The number of subsets in a power set can be calculated using the formula 2^n, where n is the number of elements in the original set.
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what is pi and why do we need it
Answers
Answer:
See below
Step-by-step explanation:
π, pronounced as pi is the ratio between 2πr which is circumference to 2r which is diameter.
In word, π is circumference/diameter which has exact value of 3.14159... and it is also an irrational number too.
π is often used to be defined as 3, 3.14 or 22/7 [Keep in mind, these numbers are only approximation.] in some fields. In trigonometry, π is mostly used to refer as π radians or π rad which is equivalent to 180°.
Why do we need it? Because it’s useful in a field that requires rotation. If you notice, figure with circular base will always have π with it, the volume is an example.
In calculus, you need π to do solid of revolution method which is:
\(\displaystyle \large{V =\pi \int\limits^a_b {[f(x)]^2} \ dx }\\\\\displaystyle \large{V = \pi \int\limits^a_b {[g(y)]^2} \ dy}\)
In trigonometry, you need it for measurement/angle.
So anything that’s related to revolution, rotation or related to circle must require π at least.
In general life, you do not use it but this is mostly applied in engineering field and anything related to science that involves with circle or revolve.
Let me know if you have any questions!
4. There are major chords built on what three notes (with all white notes and no accidentals)? O CFG O ABC GEB OCDE
Answers
The three major chords built on white notes without accidentals are:
1. C major chord (C, E, G)
2. F major chord (F, A, C)
3. G major chord (G, B, D)
These chords are formed by taking the root note, skipping one white note, and adding the next white note on top. For example, in the C major chord, the notes C, E, and G are played together to create a harmonious sound.
Similarly, the F major chord is formed by playing F, A, and C, and the G major chord is formed by playing G, B, and D. These three major chords are commonly used in various musical compositions and are fundamental building blocks in music theory.
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you have 26 dogs and 69 cats . what is your ratio of dogs to cats?
Answers
Answer:
Ratio is 26:69
Step-by-step explanation:
\({ \tt{dogs : cats = \frac{dogs}{cas} }} \\ \)
dogs → 26cats → 69\({ \tt{dogs : cats = \frac{26}{69} }} \\ \\ { \underline{ \tt{ \: dogs :cats = 26 : 69 \: }}}\)
Answer:
Step-by-step explanation:
dogs : Cats = 26 : 69
It is in the simplest form as they have no common terms.
After spending $300,000 for researcl and development, chemists it a new breakfast drink, The Diversified Citrus Industries have developeder with twice the amount of vitamin C currently available we introduced to the breakfast dion 8 -ounce cans nationally. which is estimated to bement concern is the decided to use newspaper One major managely, management Zap in the introductory year and dis. marketing. According to promote Zap ar that account for 65 percent of tribute Zap in major metropolitan aper advertising will carry a coupon U.S. breakfast drink volume. Newser to receive $0.20 off the price of the first can that will entitle the consumer receive the regular margin and be will restries. Past experied purchased. The retailer will bectiversified Citrus ind be introductory year, one indicates that for every five cans sold during the introductory year, one adverting campaign coupon will be returned. The cost of the $250,000. Other fixed overhead costs (excluding coupon returns) will be $25. are expected to be $90,000 per year. Management has decided that the $0.50. The only unit variable costs for sumer for the 8 -ounce can will be $0.50. The only $0 for labor. The company inthe product are $0.18 for materials and $0.06 percent off the suggested retail price tends to give retailers a margin of 20 percent of the retailers' cost of the item. a. At what price will Diversified Citrus Industries be selling its prod. uct to wholesalers? b. What is the contribution per unit for Zap? c. What is the break-even unit volume in the first year? d. What is the first-year break-even share of market?
Answers
Diversified Citrus Industries will sell Zap to wholesalers at a price of $0.035 per 8-ounce can. The contribution per unit for Zap is -$0.205, indicating potential profitability issues.
a. To determine the price at which Diversified Citrus Industries will be selling its product to wholesalers, we need to consider the suggested retail price, the unit variable costs, and the desired margins for retailers and wholesalers. The suggested retail price to the consumer for the 8-ounce can is $0.05. The unit variable costs for the product are $0.18 for materials and $0.06 for labor. The company intends to give retailers a margin of 20% off the suggested retail price and wholesalers a margin of 10% of the retailer's cost.
Price to Wholesalers = Suggested Retail Price - Retailer's Margin - Wholesaler's Margin
Price to Wholesalers = $0.05 - ($0.05 * 20%) - ($0.05 * 10%)
Price to Wholesalers = $0.05 - $0.01 - $0.005
Price to Wholesalers = $0.035
Therefore, Diversified Citrus Industries will be selling its product to wholesalers at a price of $0.035 per 8-ounce can.
The contribution per unit for Zap can be calculated by subtracting the unit variable costs from the selling price to wholesalers:
Contribution per Unit = Price to Wholesalers - Unit Variable Costs
Contribution per Unit = $0.035 - ($0.18 + $0.06)
Contribution per Unit = $0.035 - $0.24
Contribution per Unit = -$0.205
Since the contribution per unit is negative, it means that the variable costs exceed the price to wholesalers. This suggests that the product may not be profitable in its current pricing and cost structure.
The break-even unit volume in the first year can be calculated by dividing the fixed overhead costs by the contribution per unit:
Break-even Unit Volume = Fixed Overhead Costs / Contribution per Unit
Break-even Unit Volume = $90,000 / (-$0.205)
However, since the contribution per unit is negative, the break-even unit volume cannot be determined using this approach.
The first-year break-even share of the market cannot be determined based on the information provided. The total market size and the expected sales volume of Zap are not specified, making it impossible to calculate the market share at the break-even point.
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3x^2-8x+4=0 Solve quadratic equations by completing the square.
Answers
Answer:
x = ⅔ Or x = 2Explanation:
3x² − 8x + 4 = 0
Factor left side of equation
(3x − 2)(x − 2) = 0
Set factors equal to 0
3x − 2 = 0 or x − 2 = 0
x = ⅔ or x = 2Quadratic equations are a form of algebraic equations that can or cannot be factorized.
The value of x is 2 and 2/3
Quadratic equations come in the form: ax²+ bx + c = 0
Solution by completing the square for:
3x²− 8x + 4 = 0
a = 3 , a≠1 so we divide through by 3
3x²/3 − 8x/3 +4/3 = 0/3
which gives us
x²− 8x/3 + 4/3 = 0
Subtract 4/3 from both sides
x²− 8x/3 + 4/3 - 4/3 = 0 - 4/3
x² − 8x/3 = −4/3
Take half of the x term and square it and add the result to both sides
x² − 8x/3 + 16/9 = −4/3 + 16/9
Rewrite the perfect square on the left
(x − 4/3)² = −4/3 + 16/9
and combine terms on the right
(x − 4/3)²= 4/9
Take the square root of both sides
x − 4/3 = ±√4/9
Simplify
x − 4/3 = ±2/3
Collect like terms
x = 4/3 ± 2/3
Solving for xx = 4/3 + 2/3
x = 6/3
x = 2
Also:
x=4/3 − 2/3
which becomes
x = 2/3
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Find the value of x.
Explain your answer.
Answers
The value of variable x for the given expression is equal to 4.
Expression is equal to,
( 3x + 2 ) / 7 + 4( x + 1 ) / 5 = (2/3) ( 2x + 1)
To simplify the equation begin by getting rid of the fractions.
Find a common denominator for the fractions involved,
= 7 × 5 × 3
= 105.
Multiplying every term by 105 will eliminate the denominators
⇒105 × [(3x + 2) / 7] + 105 × [4(x + 1) / 5] = 105 × [(2/3)(2x + 1)]
Simplifying further,
⇒15(3x + 2) + 21(4)(x + 1) = 35(2)(2x + 1)
Now, distribute the coefficients,
⇒45x + 30 + 84x + 84 = 140x + 70
Combine like terms,
⇒45x + 84x - 140x = 70 - 30 - 84
⇒-11x = -44
Divide both sides by -11 to isolate x,
⇒x = 44 / 11
Therefore, the value of x is equal to 4 .
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The above question is incomplete, the complete question is:
Find the value of x.
( 3x + 2 ) / 7 + 4( x + 1 ) / 5 = (2/3) ( 2x + 1)
Explain your answer.
. The middle school girls' softball team only won 14 games last year. This year,
they won 26 games. What is the percent increase of games won this year over
last year?
Answers
Answer:
85.71 %
Step-by-step explanation:
26-14=12
12/14= 0.8571
0.8571x100= 85.71
Answer:
A change from 14 to 26 represents a positive change (increase) of 85.7142857143%
Step-by-step explanation:
Use the formula:
New - Old / Old x 100%
In other words, new(26) minus old(14) divided by old(14) time 100%
14 is the old value and 26 is the new value. In this case we have a positive change (increase) of 85.7142857143 percent because the new value is greater than the old value.
Shelley is searching online for airline tickets. Two weeks ago, the cost to fly from Orlando to Hartford was $200. Now the cost is $280. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price?
Answers
What is the percent increase from $200 to $280?
\(\frac{280}{200} *100 -100\) → \(140 -100\) → 40%There was 40% increase from $200 to $280
What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price?
increase with baggage fee:new ticket cost + baggage free280 + 50 $330 \(\frac{330}{200} *100 - 100\) → 165% - 100% → 65%There was 65% increase with the baggage fee.
#1
Old price=200$New price=280$Increase=280-200=80$Rate of increase (Percent increase)
\(\\ \tt\hookrightarrow \dfrac{80}{200}\times 100\)
\(\\ \tt\hookrightarrow 40\%\)
#2
New price=280+50=330$Increase=330-200=130$Percent increase:-
\(\\ \tt\hookrightarrow \dfrac{130}{200}(100)\)
\(\\ \tt\hookrightarrow 65\%\)
GIVING 50 POINTS
Find the missing length indicated. Pls show your work
Answers
Answer:
Here Both the triangle are similar ...
So by similiarty
\( \frac{7}{13} = \frac{x}{26} \)
\(x = 14\)
Missing length = 14
mark me as brainliest ❤️
\(\\ \sf\longmapsto \dfrac{7}{6}=\dfrac{x}{26-x}\)
\(\\ \sf\longmapsto 7(26-x)=6x\)
\(\\ \sf\longmapsto 182-7x=6x\)
\(\\ \sf\longmapsto 6x+7x=182\)
\(\\ \sf\longmapsto 13x=182\)
\(\\ \sf\longmapsto x=\dfrac{182}{13}\)
\(\\ \sf\longmapsto x=14\)
Show whether the values x = 5 and y = 6 make the equation 7x - 3y = 19 true
Answers
Mel makes arm bracelets . she is making one for each arm of her six friends . How
many should she make
Answers
Mel should make 12 bracelets.
Here, we are given that Mel makes arm bracelets.
She is making a bracelet for each arm of her 6 friends.
We know that a humans by default have 2 arms each.
We will assume that all of her 6 friends have 2 arms each.
Thus, 6 of her friends will get 2 bracelets each, one for each arm.
This means that the total number of bracelets Mel should make will be given by-
2 + 2 + 2 + 2 + 2 + 2
or we can also write this as
2 × 6
6 times 2 is equal to 12.
Thus, Mel should make 12 bracelets.
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can someone help pleas
Answers
Step-by-step explanation:
According to picture 1, it is A. corresponding.
Also according to picture 2, it is E. same side interior.
And according to picture 3, it is D. vertical
Find the exact solutions to x2 – 3x + 1 = 0 by using the Quadratic Formula.
Answers
Answer:
Step-by-step explanation:
3 +- \/5 over 2
Determine whether the claim stated below represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that (a) rejects the null hypothesis or (b) fails to reject the null hypothesis? A scientist claims that the mean incubation period for the eggs of a species of bird is at least 31 days. Does the claim represent the null hypothesis or the alternative hypothesis?
Answers
a. If the null hypothesis is rejected, the alternative hypothesis is accepted, and the outcomes are statistically significant.
b. When the null hypothesis is not rejected, the alternate hypothesis is not accepted, and it does not imply that the null hypothesis is true; instead, it means that the available evidence is insufficient to establish a statistically significant difference between the data and the null hypothesis.
The claim, "The mean incubation period for the eggs of a species of bird is at least 31 days" represents the alternative hypothesis.
How to interpret a decision that (a) rejects the null hypothesis or (b) fails to reject the null hypothesis?
If the null hypothesis is rejected, the alternative hypothesis is accepted, and the outcomes are statistically significant.
When the null hypothesis is not rejected, the alternate hypothesis is not accepted, and it does not imply that the null hypothesis is true; instead, it means that the available evidence is insufficient to establish a statistically significant difference between the data and the null hypothesis.
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If we invest $100,000 today in an account earning 7% per year,
how many years until we have $500,000? Round to two decimals.
Answers
It would take approximately 19.65 years for an investment of $100,000 at a 7% annual interest rate to grow to $500,000. Rounded to two decimal places, the answer is 19.65 years.
To determine the number of years it will take for an investment of $100,000 at a 7% annual interest rate to grow to $500,000, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment ($500,000)
P = the initial principal amount ($100,000)
r = the annual interest rate (7% or 0.07)
n = the number of times that interest is compounded per year (assuming annually, so n = 1)
t = the number of years
Plugging in the values we know, we get:
$500,000 = $100,000(1 + 0.07/1)^(1*t)
Dividing both sides of the equation by $100,000 and simplifying:
5 = (1.07)^t
To solve for t, we can take the logarithm of both sides:
log(5) = log[(1.07)^t]
Using logarithmic properties, we can bring down the exponent:
log(5) = t * log(1.07)
Finally, we can solve for t by dividing both sides by log(1.07):
t = log(5) / log(1.07)
Using a calculator, we find:
t ≈ 19.65
Therefore, it would take approximately 19.65 years for an investment of $100,000 at a 7% annual interest rate to grow to $500,000. Rounded to two decimal places, the answer is 19.65 years.
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Explain how you can solve inequality-2x +4 <16
Answers
The solution to the inequality -2x + 4 < 16 is x > -6.
To solve the inequality -2x + 4 < 16, you can follow these steps:
Start by isolating the variable term. In this case, the variable term is -2x. Move the constant term, which is +4, to the other side of the inequality by subtracting 4 from both sides:
-2x + 4 - 4 < 16 - 4
-2x < 12
Next, divide both sides of the inequality by the coefficient of x, which is -2. It's important to note that when you divide or multiply an inequality by a negative number, you need to reverse the direction of the inequality sign:
(-2x) / -2 > 12 / -2
x > -6
The solution to the inequality is x > -6. This means that any value of x greater than -6 would satisfy the original inequality. Graphically, this represents all the numbers to the right of -6 on the number line.
So, the solution to the inequality -2x + 4 < 16 is x > -6.
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How to solve a function?
Answers
To solve a function, you must determine the value of the function for a given input. This requires finding the equation for the function and then plugging in the given input to find the output. For example, if the function is f(x) = x2 + 2x - 5, and the given input is 3, then the output of the function is f(3) = 12.
1. Substitute the given input, x = 3, into the equation.
2. Simplify the equation: f(3) = 32 + 2(3) - 5
3. Solve the equation: f(3) = 9 + 6 - 5
4. Simplify the equation: f(3) = 12
5. Therefore, the output of the function is f(3) = 12.
To solve a given function, you must first determine the equation for the function. Then, you must substitute the given input into the equation and solve it. In this example, the given input was 3 and the equation for the function was f(x) = x2 + 2x - 5. After plugging in the input of 3, the equation was simplified to f(3) = 9 + 6 - 5, which was further simplified to f(3) = 12. Therefore, the output of the function is f(3) = 12.
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Answer:
do it
Step-by-step explanation:
a wire of length 26 m is divided into two pieces and each piece is bent into a square. how should this be done in order to minimize the sum of the areas of the two squares?
Answers
Answer:
A = a/2^2 + b/2^2 where b = 26 - a (a/2 and b/2 sides of square)
A = a^2 / 4 + 1/4 (a^2 - 52 a + 676)
4 * A= 2 a^2 - 52 a + 676
4 dA / da =4 a - 52 = 0
Area will be minimized when a = 13 and b = 13
Check:
n A
13 13 0 84.5
12 14 1 85
11 15 2 86.5
10 16 3 89
9 17 4 92.5
8 18 5 97
7 19 6 102.5
6 20 7 109
5 21 8 116.5
4 22 9 125
3 23 10 134.5
2 24 11 145
1 25 12 156.5
0 26 13 169
A company is designing a new cylindrical water bottle. The volume of the bottle will be 124 cmcubed. The height of the water bottle is 7.1 cm. What is the radius of the water bottle? Use 3.14 for pi.
Answers
Answer:
2.35cm
Step-by-step explanation:
Given data
Volume= 124cm^3
Height= 7.1cm
The expression for the volume of a cylinder is given as
V= πr^2h
substitute
124=3.142*r^2*7.1
124=22.3082r^2
r^2= 124/22.3082
r^2= 5.55
r= √5.55
r=2.35cm
Hence the radius of the cylindrical bottle is 2.35cm
5. What's the critical value of t necessary to construct a 90% confidence interval for the difference between the means of two distinct populations of sizes 7 and 8. (Assume that the conditions necessary to justify pooling variances have been met.)
a. 1.943
b. 1.771
c. 1.895
d. 1.753
e. 1.761
Answers
To determine the critical value of t for constructing a 90% confidence interval for the difference between the means of two populations, we need to consider the degrees of freedom and the desired confidence level.
In this case, we have two distinct populations with sizes 7 and 8, which gives us (7-1) + (8-1) = 13 degrees of freedom.
Looking up the critical value of t for a 90% confidence level and 13 degrees of freedom in a t-table or using statistical software, we find that the critical value is approximately 1.771.
Therefore, the correct answer is option b) 1.771.
The critical value of t is necessary to account for the uncertainty in the estimate of the difference between the population means. By selecting the appropriate critical value, we can construct a confidence interval that is likely to contain the true difference between the means with a specified confidence level. In this case, a 90% confidence interval is desired.
The critical value is determined based on the desired confidence level and the degrees of freedom, which depend on the sample sizes of the two populations. Since we have populations of sizes 7 and 8, the total degrees of freedom is 13. By looking up the critical value of t for a 90% confidence level and 13 degrees of freedom, we find that it is approximately 1.771. This value indicates the number of standard errors away from the sample mean difference that corresponds to the desired confidence level.
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There are 10 workers in a factory making widgets. They work 8-hour days and must complete their orders by the end of the day. The foreman walks in on Monday and tells the workers that they have an order for 100 widgets, which is promptly finished before lunchtime. On Tuesday, the foreman gives them an order for 200 widgets and they tinish some time after lunch. On Wednesday, the workers get an order for 275 widgets. They work harder and finish right at the end of the day. Then on Thursday, there is an order for 325 widgets and again, they get the job
done on time.
How do you think the workers will fair if on Friday, they get an order for 350 widgets? 400? or 450?
Answers
Based on the workers performance of consistently meeting orders for 100, 200, 275, and 325 widgets within the workday, it is likely that they will successfully complete the order for 350 widgets on Friday. However, fulfilling orders for 400 or 450 widgets may present a challenge and require additional resources or extended work hours.
Based on the information, it seems that the workers have been consistently meeting their production targets within the allocated time. They have successfully completed orders for 100, 200, 275, and 325 widgets within the workday.
Based on their previous performance, it is likely that the workers will continue to work diligently and efficiently to meet the order for 350 widgets on Friday.
However, meeting an order for 400 or 450 widgets may pose a challenge as it exceeds the previous order quantities.
The workers may need to work extra hours, increase their pace, or employ additional resources to complete these larger orders within the same time frame. It is important to consider the capacity and capabilities of the workers and the factory to determine if such larger orders can be fulfilled successfully.
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true or false we can represent the pdf of a discrete random variable x with a histogram. group of answer choices
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The given statement "We can represent the pdf of a discrete random variable x with a histogram." is True, because histograms are often used to graphically represent the distribution of a discrete random variable.
In a histogram, the x-axis represents the different possible values of the discrete random variable, and the y-axis represents the probability or frequency of observing each value. The bars in the histogram represent the probabilities or frequencies of the different values, and the height of each bar corresponds to the probability or frequency.
Note that for a discrete random variable, the PDF is actually a probability mass function (PMF), which gives the probability of each possible value of X. However, the histogram can be used to represent the PMF by scaling the heights of the bars appropriately so that they represent probabilities rather than frequencies.
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solve the first equation for x.
X+ 5y = 0 20y = -4x
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The answer for the first equation x + 5y = 0 is,
\(x = - 5y\)
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Which statement correctly describes the relationship between the graph of f(x) and g(x)=f(x−7)? Responses The graph of g(x) is the graph of f(x) translated 7 units left. The graph of , g begin argument x end argument, is the graph of , , f open argument x close argument, , translated 7 units left. The graph of g(x) is the graph of f(x) translated 7 units down. The graph of , g begin argument x end argument, is the graph of , , f open argument x close argument, , translated 7 units down. The graph of g(x) is the graph of f(x) translated 7 units right. The graph of , g begin argument x end argument, is the graph of , , f open argument x close argument, , translated 7 units right. The graph of g(x) is the graph of f(x) translated 7 units up.
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The statement correctly describes the relationship between the graph of f(x) and g(x)=f(x−7) is the graph of f(x) translated 7 units right.
What is Graph?The graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them.
According to the question we have
g(x)=f(x−7).
Given that f(x) then f(x + a) represents a horizontal translation of f(x).
If a > 0 then shift units left
If a < 0 then shift units right
Therefore, f(x - 7) represents a shift right of 7 units.
Hence, The statement correctly describes the relationship between the graph of f(x) and g(x)=f(x−7) is the graph of f(x) translated 7 units right.
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If 6J of work is needed to stretch a spring from 10 cm to 12 cm and another 10J is needed to stertch it from 12 cm to 14 cm, what is the natural length of the spring?
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To solve this problem, we can use the formula for the potential energy stored in the spring:
U = 1/2 k x^2
where U is the potential energy stored in the spring, k is the spring constant, and x is the displacement of the spring from its natural length.
From the given information, we can set up two equations:
6J = 1/2 k (0.02)^2
10J = 1/2 k (0.02)^2 + 1/2 k (0.02)^2
Simplifying the equations, we get:
6J = 0.0002 k
10J = 0.0004 k
Dividing the second equation by the first, we get:
10J/6J = 0.0004 k/0.0002 k
Simplifying, we get:
5/3 = 2
This is not possible, so there must be an error in the problem. Therefore, we cannot determine the natural length of the spring with the given information.
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