To find the value of x for parallel lines with expressions (7x + 11) and (10x - 43), set them equal and solve the resulting equation, which gives x = 18.
If line a is parallel to line b and we have the expressions (7x + 11) for line a and (10x - 43) for line b, then the corresponding angles formed by these lines and a transversal would be equal. To solve for x, we set the two expressions equal to each other because the slopes of parallel lines are equal. The equation would be 7x + 11 = 10x - 43.
Subtract 7x from both sides: 11 = 3x - 43.Add 43 to both sides: 54 = 3x.Divide both sides by 3: x = 54 / 3.Therefore, x = 18.This is the value of x that makes the two expressions equal, thus confirming the lines are parallel.
Emma has $3.15 worth of dimes and quarters. She has twice as many dimes as quarters. Determine the number of dimes and the number of quarters that Emma has.
Answer:
Emma has 14 pennies and 7 quarters
When, Emma has $3.15 worth of dimes and quarters and she has twice as many dimes as quarters. Then, Emma has 14 dimes and 7 quarters.
To solve this, we set up two equations based on the given information. Let the number of quarters be q and the number of dimes be d.
From the information given:
Emma has twice as many dimes as quarters (d = 2q).The total value of the dimes and quarters is $3.15.The value equation can be written as 0.10d + 0.25q = 3.15 (since dimes are worth $0.10 and quarters $0.25).
Substituting the first equation into the second gives: 0.10(2q) + 0.25q = 3.15, which simplifies to 0.45q = 3.15.
Dividing both sides by 0.45 gives us q = 7. Since the number of dimes is twice the number of quarters, d = 2 x 7 = 14.
Therefore, Emma has 14 dimes and 7 quarters.
10. Sue has a boat that would go 9 miles per hour in still water. She travels downstream for a
certain distance and then back upstream to where she stared. Sue notices that it takes her 4
hours to travel upstream against the river, and only 2 hours to travel downstream with the
river. The rivers speed is r miles per hour. Write and Solve for r.
Answer:
The speed of the river is 3 miles per hour.Step-by-step explanation:
In downstream, the speed of the boat will be (9 + r) miles per hour and in upstream the speed of the boat will be (9 - r) miles per hour.
Ratio of the speed in downstream to the speed in upstream is (9 + r):(9 - r).
Hence, the ratio of the time taken by the boat to cover the distance in downstream to upstream is (9 - r):(9 + r).
[tex]\frac{9 - r}{9 + r} = \frac{2}{4} \\18 - 2r = 9 + r\\3r = 9\\r = 3[/tex]
Given: ∆ABC, AB = 12, AC = 17 Area ∆ABC = 65 Find: BC, m∠A, m∠B, m∠C
Answer:
BC = 10.89, ∠A = 39.59°, ∠B = 95.80°, ∠C = 44.61°
BC = 27.34, ∠A = 140.41°, ∠B = 23.35°, ∠C = 16.24°
Step-by-step explanation:
Using the area formula to find angle A, we get ...
Area = (1/2)bc·sin(A)
65 = (1/2)(12)(17)sin(A)
sin(A) = 65/102 . . . . divide by the coefficient of the sine term
A = arcsin(65/102) = 39.59° or 180°-39.59° = 140.41°
Then from the law of cosines*, ...
BC² = AB² +AC² -2·AB·AC·cos(A) = 12² +17² ±2·12·17·cos(39.59°)
BC² = 433 ± 314.426
BC = √118.574 or √747.426
BC = 10.89 or 27.34
___
For A = 39.59° and BC = 10.89, the remaining angles are ...
sin(C)/AB = sin(A)/BC
C = arcsin(12·(65/102)/10.89) = arcsin(.7023) = 44.61°
B = 180° -39.59° -44.61° = 95.80°
__
For A = 140.41° and BC = 27.34, the remaining angles are ...
sin(C) = AB·sin(A)/BC = 12(65/102)/27.34
C = arcsin(0.2797) = 16.24°
B = 180° -140.41° -16.24° = 23.35°
__
In summary, the solutions are ...
BC = 10.89, ∠A = 39.59°, ∠B = 95.80°, ∠C = 44.61°
BC = 27.34, ∠A = 140.41°, ∠B = 23.35°, ∠C = 16.24°
_____
* For a given value of 0 < (x=sin(α)) < 1, there are two possible positive angles: α = arcsin(x) and 180°-α. In the Law of Cosines formula, these different angles result in cos(α) and cos(180°-α) = -cos(α).
_____
The solution process is the same for the remaining sides and angles, once you recognize that the initial value of sin(A)=65/102 can have two different angles as its solution.
I
-72
–54
-36
y
25
13
1
What is the y-intercept of the line?
Answer:
-23
Step-by-step explanation:
As I increases by 18, y decreases by 12. From the last value in the table, I needs to increase by 2·18 for it to become zero. Hence the y-intercept will be 2·12 less than the last value in the table:
1 - 2·12 = -23 . . . the y-intercept
Answer:
-23
I hope this helped you and i hope you have a good day.
A store sells notebooks with each of the combinations of color, binding, and dividers shown in the table.
Which statements are true about the variety of notebooks that the store sells? Check all that apply.
-There is a greater number of combinations with pocketed dividers than with no pockets.
-There are more than 18 different combinations of features for sale.
- The number of combinations of red notebooks is the same as the number of combinations that are yellow.
- The number of combinations of black notebooks is the same as the number of combinations that have dividers with no
pockets.
-Adding one more color option would increase the number of different combinations by 4.
Answer:
These are the true statements:
1) There are more than 18 different combinations of features for sale.
2)The number of combinations of red notebooks is the same as the number of combinations that are yellow.
3)Adding one more color option would increase the number of different combinations by 4.
Step-by-step explanation:
Here, we need combination of three different things color, binding and divider.
Firstly, from color we have 5 options, so there are 5 different ways of choosing color.
Next, 2 options for binding, so 2 ways to choose the binding.
Thirdly, 2 more ways to choose divider.
So, total number of ways = 5×2×2 = 20 ways.
This is because when we fix one of the things, say color to be red, then there are 2 ways for binding and 2 ways for divider. so, we get a total of 4 different combinations.
Now, as we are having 5 different colors, total ways = 5×4 = 20.
Here, it is obvious that combinations of notebooks of any color are same(4 red, 4 blue, 4 green, 4 yellow, 4 black)
Suppose, we have one more color option then total ways = 6 ×4 =24 ways.
⇒Adding one more color option would increase the number of different combinations by 4.
Answer:
B,C,E
Step-by-step explanation:
I got it right on the test
hope this helps
If sales tax is 7.75%, what is the total cost of an 11$ purchase including tax?
Answer:
$11.8525
Step-by-step explanation:
To find the total price of purchase including sales tax, we need to add sales tax to our total. This can be done as follows: Purchase price + percentage of purchase price as according to sales tax. In the case of your problem, this takes the form of $11 + 0.0775(11). This expression is equivalent to 11.8525.
Answer:
$11.8525 rounds to 11.85. 11.85 is your answer.
Step-by-step explanation:
his converter requires the use of Javascript enabled and capable browsers. This script calculates the sales tax percentage of a given purchase amount and a given sales tax amount. It then displays the sales tax percentage and the total sales price, including tax. You (obviously) may change the default values if you desire. Enter the total amount that you wish to have calculated as the sales amount, in dollars and cents. In our example, that is $50.00 as the sales price. Then, enter in dollars and cents, the sales tax amount. In our example, that is $2.00 for the tax amount. For instance, if a shopping cart does a sales tax calculation for you based on your city, state and zip code, enter the tax amount that it displays. That entry might be something like $2.50 or something similar with dollars and cents. Then click on Calculate and the result should be YOUR local sales tax percentage and the total of the sales price and the sales tax amount. An example of the sales tax percentage might be something like this... If your sales tax has been designated as as 7.75% (7.75 percent), it can be written as .0775; we would show it as 7.75 in the Sales Tax Percentage field. If you need to calculate the sales tax amount and you know the sales amount and the sales tax rate or percentage, use our Sales Tax Calculator And De-Calculator. You can use the same page to calculate the appropriate sales tax in a transaction that includes tax.
A torch and a battery cost £2.50 altogether.
The torch costs £1.50 more than the battery.
What fraction of the total price is the torch?
Give your answer in its simplest form.
Answer:
3/5
Step-by-step explanation:
Dunno?
7. Which coordinate lies in the solution set for
graph of the system of inequalities shown
below?
Select one:
A. (0,5)
B.(3,0)
C. (0,0)
D -3.0
Answer:
The only point (0,0) lies inside the shaded region and hence it gives a solution for the set of inequalities.
Step-by-step explanation:
See the graph attached to this question.
The solution of the set of inequalities is given by the shaded region on the graph.
Now, the point (0,5) is outside this shaded region, hence it can not be the solution.
The point (3,0) also is outside this shaded region, hence it can not be the solution.
The point (-3,0) also is outside this shaded region, hence it can not be the solution.
Now, the only point (0,0) lies inside the shaded region and hence it gives a solution for the set of inequalities. (Answer)
47. What is the 12th term of the geometric sequence?
3,6, 12, 24, ...
A) 6144
B) 3072
C) 1526
D) 36
Answer:
A
Step-by-step explanation:
The rule is 2x.
So 3,6,12,24,48,96,192,384,768,1536,3072,6144,12288,....
The question asked for the 12th term so 6144.
Answer:
The answer to this is:
A. 6144
Step-by-step explanation:
3,6,12,24,48,96,192,384,768,1536,3072,6144 all you have to do is multiply the last number by 2.
The surface area of the rectangular prism can be found using the expression 6x exponent 3 + 4x exponent 2 + 12x. if the value of x is 3, what is the surface area, in square centimeters of the prism?
Answer:
234 cm²
Step-by-step explanation:
Given expression to represent the surface area of the rectangular prism is [tex]6x^{3} +4x^{2} +12x[/tex]
The given value of x is 3.
Now, finding value of expression by sustituting value of "x" as given.
Surface area of the rectangular prism = [tex]6x^{3} +4x^{2} +12x[/tex]
Surface area of the rectangular prism= [tex]6\times 3^{3} +4\times 3^{2} +12\times 3[/tex]
∴ Surface area of the rectangular prism= [tex]6\times 27+ 4\times 9+ 12\times 3[/tex]
Surface area of the rectangular prism= [tex]162+36+36= 234\ cm^{2}[/tex]
∴ Surface area of the rectangular prism= 234 cm²
financial math
8% can be written as the following decimal and fraction
a.) 0.8, 80/100
b.) 0.8, 8/10
c.) 0.008 , 8/100
Answer:
d) 0.08, 8/100
Step-by-step explanation:
Here is the correct question: Financial maths ;
8% can be written as the following decimal and fraction
a.) 0.8, 80/100
b.) 0.8, 8/10
c.) 0.008 , 8/100
d.) 0.08, 8/100
Percentage (%) is a representation for fraction of hundred.
∴ if it is given 8%, it means 8 upon 100
= [tex]\frac{8}{100} = 0.08[/tex]
∴ Answer is 0.08 in decimal and [tex]\frac{8}{100}[/tex] in fraction.
What is the quotient of 3227/555? What is the repetend?
Answer:
A repeating or recurring decimal is decimal representation of a number whose digits are periodic (repeating its values at regular intervals) and the infinitely repeated portion is not zero. It can be shown that a number is rational if and only if its decimal representation is repeating or terminating (i.e. all except finitely many digits are zero). For example, the decimal representation of
1
/
3
becomes periodic just after the decimal point, repeating the single digit "3" forever, i.e. 0.333.... A more complicated example is
3227
/
555
, whose decimal becomes periodic at the second digit following the decimal point and then repeats the sequence "144" forever, i.e. 5.8144144144.... At present, there is no single universally accepted notation or phrasing for repeating decimals.
The infinitely repeated digit sequence is called the repetend or reptend. If the repetend is a zero, this decimal representation is called a terminating decimal rather than a repeating decimal, since the zeros can be omitted and the decimal terminates before these zeros.[1] Every terminating decimal representation can be written as a decimal fraction, a fraction whose divisor is a power of 10 (e.g. 1.585 =
1585
/
1000
); it may also be written as a ratio of the form
k
/
2n5m
(e.g. 1.585 =
317
/
2352
). However, every number with a terminating decimal representation also trivially has a second, alternative representation as a repeating decimal whose repetend is the digit 9. This is obtained by decreasing the final (rightmost) non-zero digit by one and appending a repetend of 9. 1.000... = 0.999... and 1.585000... = 1.584999... are two examples of this. (This type of repeating decimal can be obtained by long division if one uses a modified form of the usual division algorithm.[2])
Step-by-step explanation:
What is the slope of the line through ( 6 , 9 ) and ( 7 , 1 )?
Answer:
m=-8
Step-by-step explanation:
Answer:
Step-by-step explanation:
slope = y₂ - y₁ / x₂ - x₁
= 1 - 9 / 7-6
= - 8/1
= -8
:
CHCK Farms raises hens and roosters. They have enough space to raise at most 300
300
birds per year. Each hen eats 80
80
pounds of food per year, and each rooster eats 60
60
pounds of food per year. The business can only afford 20,000
20
,
000
pounds of food per year. The graph below shows the solution set of a system of linear inequalities that represents this situation.
Answer:
The number of hens is 100 and the number of roosters is 200.
Step-by-step explanation:
Let the number of hens be x and the number of roosters be y
then the total number of hens and roosters, is 300
so,
[tex]x+y \leq 300[/tex]----------------------------(1)
Also the hen eats 80 pounds of food per year and roosters eats 60 pounds of food per year,
[tex]80x+60y \leq 20000[/tex]----------------(2)
To solve the equations , multilpy eq(1) by 80
[tex]80x +80y \leq 24000[/tex]------------------(3)
Subracting (2) from (3)
[tex]20y \leq 4000[/tex]
[tex]y \leq 200[/tex]
substituting y in eq(1) we get
[tex]x+200 \leq300[/tex]
[tex]x \leq300 - 200[/tex]
x = 100
After dividing a piece of wood into four equal sections,each section is 4 in.long.How long was the piece of wood I started with
I'm going to out on a limb and say 16 in.
4 pieces * 4 in. = 16
Write a two column proof.
Can someone please help me I posted this yesterday and nobody helped if you can also help me with the other that’ll be great. Happy New Years from my family’s to yours.
Step-by-step explanation:
HJ ≅ JH, by symmetric property of equality.
ΔGHJ ≅ ΔIJH, by SAS congruence.
GJ ≅ IH, corresponding parts of congruent triangles are congruent.
Lesledi has a box that is 36cm wide, 24cm high, and 20cm deep. She wants to fill the box with packages that are 12cm wide, 6cm high, and 4cm deep.
What's the greatest number of packages Lesledi can put in the box without it overflowing?
Answer:
The answer is 3
Step-by-step explanation:
36÷12=3, which is the lowest number on either side of the boxes
Lesledi can put a maximum of 60 packages in the box without it overflowing.
What is Unitary Method?The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
The maximum number of 12cm wide packages that can fit in the 36cm width of the box is
= 36 ÷ 12
= 3
and, The maximum number of 6cm high packages that can fit in the 24cm height of the box is
= 24 ÷ 6
= 4
and, The maximum number of 4cm deep packages that can fit in the 20cm depth of the box is
= 20 ÷ 4
= 5
Therefore, the maximum number of packages that can fit in the box is:
= 3 x 4 x 5
= 60
Learn more about Unitary Method here:
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For i = √−1 , what is the sum (7 + i) + (−8 + 9i ) ? √ is the square root symbol.
A) −1 + 12i
B) −1 − 6i
C) 15 + 12i
D) 15 − 6i
Question is incomplete, complete question is given below;
For i = √−1 , what is the sum (7 + 3i) + (−8 + 9i ) ? √ is the square root symbol.
Answer:
A) −1 + 12i
Step-by-step explanation:
Given,
[tex]i = \sqrt{-1 }[/tex]
We have to find the sum of[tex](7+3i)+(-8+9i)[/tex].
Solution,
Firstly we Substitute the the value of 'i' in given expression.
[tex](7 + 3\sqrt{-1}) + (-8 + 9\sqrt{-1} )[/tex]
On combining the like terms, we get;
[tex]7+(-8)+3\sqrt{-1}+9\sqrt{-1}[/tex]
On we use the addition property of equality and get;
[tex]-1+12\sqrt{-1}[/tex]
Since [tex]\sqrt{-1}[/tex] = i
Then we can say that;
[tex]-1+12\sqrt{-1}[/tex] = [tex]-1+12i[/tex]
Hence The sum of [tex](7+3i)+(-8+9i)[/tex] is [tex]-1+12i[/tex].
preliminary sample of 100 labourers was selected from a population of 5000 labourers by simple random sampling. It was found that 40 of the selected labourers opt for a new incentive scheme. How large a sample must be selected to have a precision of ± 5% with 95% confidence ?
Answer:
[tex]n=\frac{0.4(1-0.4)}{(\frac{0.05}{1.96})^2}=368.79[/tex]
n=369
Step-by-step explanation:
1) Notation and definitions
[tex]X=40[/tex] number of the selected labourers opt for a new incentive scheme.
[tex]n=100[/tex] random sample taken
[tex]\hat p=\frac{40}{100}=0.4[/tex] estimated proportion of the selected labourers opt for a new incentive scheme.
[tex]p[/tex] true population proportion of the selected labourers opt for a new incentive scheme.
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The population proportion have the following distribution
[tex]p \sim N(p,\sqrt{\frac{p(1-p)}{n}})[/tex]
2) Solution tot he problem
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
And on this case we have that [tex]ME =\pm 0.05[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.4(1-0.4)}{(\frac{0.05}{1.96})^2}=368.79[/tex]
And rounded up we have that n=369
The size of the sample that must be selected to have a precision of ± 5% with 95% confidence is 369
How to find the margin of error of sample proportion?For large enough sample, let the population proportion of a quantity be denoted by random variable [tex]p[/tex]
Then, we get:
[tex]p \sim N(\hat{p}, \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}})[/tex]
where
[tex]\hat{p}[/tex] = estimated (mean value) proportion of that quantity, andn = size of sample drawn.It is visible that as we increase the value of n, the standard deviation decreases, therefore, forcing the values of population proportion to be closer to the estimated proportion.
Margin of error is the distance between the mean and one of the end point of the confidence interval(assuming its equal on both the sides of the mean). The margin of error with level of significance [tex]\alpha[/tex] is calculated as:
[tex]MOE = Z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
where
[tex]Z_{\alpha/2}[/tex]
is the critical value of the test statistic for level of significance [tex]\alpha[/tex]
For the considered case, we have following facts:
Size of the preliminary sample = 100The precision needed = Margin of error = 5% =0.05Confidence level = 95%Count of labors in sample who opt for a new incentive scheme = 40Thus, if we denote p = proportion of labors opting for a new incentive scheme in the considered population, then,
[tex]\hat{p} = 40/100 = 0.4[/tex] (estimate from the sample about the proportion of such labors who opt for new incentive scheme to the total count of labors of the sample).
For 95% confidence interval, level of significance is 100% - 95% = 5% = 0.05
At this level of significance, the critical value of Z is ±1.96
Let the needed sample size be 'n', then:
[tex]MOE = Z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\0.05= \pm 1.96 \sqrt{\dfrac{0.4(1-04)}{n}}\\\\n = \dfrac{0.4 \times 0.6}{(0.05/1.96)^2} \approx 369[/tex]
Thus, the size of the sample that must be selected to have a precision of ± 5% with 95% confidence is 369
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If A={3,5,7,9} and
B = {1, 2, 4, 6,7,9)
Find the intersection: A B.
A. {7,9}
B. {2,4}
C. {1,3,5}
D. {1,2,3,4,5,6,7,9}
Answer:
a. (7,9) this both includes in both sets hence the right answer is a.
Find the interest earned in an account with 3,600 invested at 3 1/2% simple interest for 5 years at
Answer:
Total Interest earned is $630.
Step-by-step explanation:
Principal = $3,600
Time = 5 Years
Interest Rate = 3 1/2% = 7/2% = 3.5%
Interest = Principal x Time x Interest Rate
Interest = $3,600 x 5 x 0.035
Interest = $630
If the point (-6, 10) lies on the graph of y=f(x) then which of the following points must lie on the graph of y=1/2f(x)?
Answer:
(-6,5)
Step-by-step explanation:
we have
y=f(x) ----> the parent function
y=1/2f(x) ---> the new y-value will be 1/2 times the original value
The rule of the transformation of f(x) to 1/2f(x) is
(x,y) -----> (x,y/2)
substitute the given value
(-6,10) ------> (-6,10/2)
(-6,10) ------> (-6,5)
What subtraction sentence does this show?
A. 7.6 – 1.7 = 9.3
B. 7.6 – (–1.7) = 9.3
C. –7.6 – 1.7 = 9.3
D. –7.6 – (–1.7) = 9.3
Answer:
b
Step-by-step explanation:
Answer:
B.) 7.6 – (–1.7) = 9.3
Step-by-step explanation:
21. Alcohol's effect on the circulatory system can lead to
A. O heat loss
B. O a feeling of warmth
C. O Both A and B
A jet left Paris at the same time as a
passenger plane. The planes flew in
opposite directions. The passenger plane
flew at a speed of 450 mph. After 11 hours
they were 9460 mi. apart. How fast did the
jet fly?
Answer:
The speed of the jet is 410 mph.
Step-by-step explanation:
The jet and the passenger plane flew in opposite directions.
Given that the passenger plane flew at a speed of 450 mph, then after 11 hours, the passenger plane will fly (450 × 11) = 4950 miles.
Again, given that after 11 hours the passenger plane and the jet are 9460 miles apart.
Therefore, in 11 hours the jet flew (9460 - 4950) = 4510 miles.
Hence, the speed of the jet is [tex]\frac{4510}{11} = 410[/tex] mph. (Answer)
Final answer:
The jet flew at a speed of 410 mph. This was calculated by first determining the distance covered by the passenger plane (at 450 mph for 11 hours) and then subtracting this from the total separation distance of 9460 miles to find the distance covered by the jet.
Explanation:
To determine how fast the jet flew, we need to consider the total distance covered by both planes after 11 hours when they are 9460 miles apart. Given that the passenger plane flew at a speed of 450 mph, we can calculate the distance it covered and then subtract this from the total separation distance to find how much distance the jet covered. Since they traveled in opposite directions, their speeds add up to account for the total separation distance.
First, calculate the distance covered by the passenger plane:
Distance = Speed × Time
Distance for passenger plane = 450 mph × 11 hours = 4950 miles
Now, subtract the passenger plane's distance from the total distance to find the distance covered by the jet:
Distance for jet = Total distance - Distance for passenger plane
Distance for jet = 9460 miles - 4950 miles = 4510 miles
Finally, calculate the speed of the jet:
Speed of jet = Distance for jet / Time
Speed of jet = 4510 miles / 11 hours = 410 mph
A tree is 212
1
2
feet tall. How tall will it be in 3 years if it grows 14
1
4
foot each year?
Which method will NOT give the correct number of feet?
Answer: The incorrect choice is the one in the bottom left.
Step-by-step explanation: This is because you have to multiply the 1/4 by 3 then add it on to the 2 1/4. Hope this helped
Final answer:
The current height of the tree is 212 feet, and it grows 141 feet each year. Over 3 years, the tree will grow 4¼ feet, reaching a height of 216¼ feet. Incorrect arithmetic or unit conversion could lead to an error in calculating the tree's future height.
Explanation:
The question involves calculating the future height of a tree given its current height and its annual growth rate. The tree is currently 212 feet tall and grows 141 foot each year. After 3 years, we would expect the tree to have grown an additional 3 years × 141 feet per year = 3 × 141 feet = 4 1/4 feet. Adding this to the initial height, the tree will be 212 + 4 1/4 = 216 1/4feet tall after 3 years. To determine which method will not give the correct number of feet, students need to ensure they correctly apply arithmetic operations and unit conversion if necessary.
To measure the height of a tree, one can use a measuring tape. Trees can be measured in feet or yards, and methods can vary depending on the desired level of accuracy and the tools available. For example, measuring directly with a tape or using a mathematical model based on the tree's shadow or geometric properties are valid approaches.
Iridium-192 is an isotope of iridium and has a half life of 73.83 days. If a laboratory experiment begins with 100 grams of iridium-192, the number of grams, A, of iridium-192 present after t days would be A= 100(1/2)^t/73.83. Which equation approximates the amount of iridium-192 present after t days?
Answer:
[tex]A=100(0.990655512)^t[/tex]
Step-by-step explanation:
[tex]A=100(\frac{1}{2})^{\frac{t}{73.83}}[/tex]
It does say an approximate equation so we could play with law of exponents a little especially if you don't like that fraction in the exponent.
[tex]A=100(\frac{1}{2})^{\frac{1 \cdot t}{73.83}}[/tex]
[tex]A=100(\frac{1}{2})^{\frac{1}{73.83}t}[/tex]
[tex]A=100((\frac{1}{2})^{\frac{1}{73.83}})^t[/tex]
I'm going to put (1/2)^(1/73.83) into my calculator.
This gives me approximately: 0.990655512.
[tex]A=100(0.990655512)^t[/tex]
So maybe that is what you are looking for.
Please let me know.
A gram of the isotope of iridium is present. Then after t day, the equation is [tex]\rm A = 100*(0.990655)^t[/tex].
What is half-life?Half-Life is defined as the time required by a radioactive substance to disintegrate into a different substance. This was discovered in 1907 by Ernest Rutherford.
Given
Iridium-192 is an isotope of iridium and has a half-life of 73.83 days.
[tex]\rm A= 100(0.5)^\frac{t}{73.83}[/tex]
If A gram of the isotope of iridium is present. Then after t day, the amount will be
[tex]\rm A= 100(0.5)^{\frac{t}{73.83}}\\[/tex]
On simplifying, we have
[tex]\rm A = 100((0.5)^{\frac{1}{73.83}})^{t} \\\\A = 100*(0.990655)^t[/tex]
Thus, the required equation is [tex]\rm A = 100*(0.990655)^t[/tex].
More about the half-life link is given below.
https://brainly.com/question/24710827
Which statement is true about the equations -3x + 4y = 12
The system of the equations has exactly one solution at (-8, 3).
The system of the equations has exactly one solution at (-4, 3).
The system of the equations has no solution; the two lines are parallel.
The system of the equations has an infinite number of solutions represented by either equation.
Answer:
D)
Step-by-step explanation:
write an equation of a line that is parallel to the line containing the points (0,-7) and (5,12)
For this case we have that by definition, the equation of the line of the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut-off point with the y axis
We have the following points through which the line passes:
[tex](x_ {1}, y_ {1}) :( 0, -7)\\(x_ {2}, y_ {2}) :( 5,12)[/tex]
Thus, the slope of the line is:
[tex]m = \frac {y- {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {12 - (- 7)} {5-0} = \frac {12 + 7 } {5} = \frac {19} {5}[/tex]
By definition, if two lines are parallel then their slopes are equal. Thus, a parallel line will be of the form:
[tex]y = \frac {19} {5}x + b[/tex]
Answer:
[tex]y = \frac {19} {5}x + b[/tex]
if the relationship between distance y in feet and time x in seconds is proportional, which rate is represented by y/x=0.6
Answer:
3 feet in 5s
Step-by-step explanation:
Consider the complete question is,
'If the relationship between distance y in feet and time x in seconds is proportional, which rate is represented by y/x=0.6?
a. 3 feet in 5s
b. 3 feet in 9s
c. 10 feet in 6s
d. 18 feet in 3s'
If y = 3 ft, x = 5 sec
[tex]\frac{y}{x}=\frac{3}{5}=0.6[/tex]
If y = 3 ft, x = 9 sec
[tex]\frac{y}{x}=\frac{3}{9}=0.33...[/tex]
If y = 10 ft, x = 6 sec
[tex]\frac{y}{x}=\frac{10}{6}=1.66666...[/tex]
If y = 18 ft, x = 3 sec
[tex]\frac{y}{x}=\frac{18}{3}=6[/tex]
Hence, the required rate would be 3 feet in 5s