Xochitl spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. The plane maintains a constant altitude of 7425 feet. Xochitl initially measures an angle of elevation of 19° to the plane at point A. At some later time, she measures an angle of elevation of 37° to the plane at point B.
Find the distance the plane traveled from point A to point B. Round your answer to the nearest foot if necessary.
Answer:
d1 - d2 ≈ 9917.4 feet ≈ 3021 meters
Step-by-step explanation:
tan(19°) = 7425/d1
tan(37°) = 7425/d2
Solving for d1 and d2, we get:
d1 = 7425/tan(19°) ≈ 22977.6 feet
d2 = 7425/tan(37°) ≈ 13060.2 feet
Therefore, the distance the plane traveled from point A to point B is:
d1 - d2 ≈ 9917.4 feet ≈ 3021 meters
URGENT ! 100 POINTS
It's the age of Vikings! You are an archer on a boat approaching the London bridge in England with troops ready to ambush and secure London, England. Your leader yells
to ready your aim to fire as the boat rushes at full speed towards your enemies ahead!
Steadily, you line up the shot and the arrow is launched from your bow into the air with an upward velocity of 60ft/sec. The equation that gives the height (h) of the arrow at any time (t), in seconds, is modeled by:
h(t) = − 16t²+60t + 9.5
How long will it take the arrow to reach the enemy on the bridge and nail him with a
perfect headshot?
(The enemies head is about 45 feet from ground level as he is located on top of the London bridge)
To find out how long it will take for the arrow to hit the enemy on the bridge, we need to find the time when the height of the arrow is 45 feet (the height of the enemy's head above the ground).
So, we can set h(t) equal to 45 and solve for t:
h(t) = − 16t²+60t + 9.5
45 = −16t² + 60t + 9.5
Rearranging the equation, we get:
16t² - 60t - 35.5 = 0
To solve for t, we can use the quadratic formula:
t = (-b ± sqrt(b² - 4ac)) / 2a
where a = 16, b = -60, and c = -35.5
Plugging in the values, we get:
t = (-(-60) ± sqrt((-60)² - 4(16)(-35.5))) / 2(16)
Simplifying the expression inside the square root, we get:
t = (60 ± sqrt(3600 + 2272)) / 32
t = (60 ± sqrt(5872)) / 32
t ≈ 0.81 or t ≈ 3.69
Since we're looking for the time when the arrow hits the enemy, we need to choose the positive solution: t ≈ 3.69 seconds.
Therefore, it will take approximately 3.69 seconds for the arrow to hit the enemy on the bridge with a perfect headshot.
Prove the first associative law from Table 1 by show-
ing that if A, B, and C are sets, then A ∪ (B ∪ C) =
(A ∪ B) ∪ C.
Answer:
Step-by-step explanation:
o prove the first associative law of set theory, we need to show that for any sets A, B, and C:
A ∪ (B ∪ C) = (A ∪ B) ∪ C
To do this, we need to show that any element that is in the left-hand side of the equation is also in the right-hand side, and vice versa.
First, let's consider an arbitrary element x.
If x ∈ A ∪ (B ∪ C), then x must be in A, or in B, or in C (or in two or more of these sets).
If x ∈ A, then x ∈ A ∪ B, and so x ∈ (A ∪ B) ∪ C.
If x ∈ B, then x ∈ B ∪ C, and so x ∈ A ∪ (B ∪ C), which means that x ∈ (A ∪ B) ∪ C.
If x ∈ C, then x ∈ B ∪ C, and so x ∈ A ∪ (B ∪ C), which means that x ∈ (A ∪ B) ∪ C.
Therefore, we have shown that if x ∈ A ∪ (B ∪ C), then x ∈ (A ∪ B) ∪ C.
Next, let's consider an arbitrary element y.
If y ∈ (A ∪ B) ∪ C, then y must be in A, or in B, or in C (or in two or more of these sets).
If y ∈ A, then y ∈ A ∪ (B ∪ C), and so y ∈ (A ∪ B) ∪ C.
If y ∈ B, then y ∈ A ∪ B, and so y ∈ A ∪ (B ∪ C), which means that y ∈ (A ∪ B) ∪ C.
If y ∈ C, then y ∈ (A ∪ B) ∪ C.
Therefore, we have shown that if y ∈ (A ∪ B) ∪ C, then y ∈ A ∪ (B ∪ C).
Since we have shown that any element that is in the left-hand side of the equation is also in the right-hand side, and vice versa, we can conclude that:
A ∪ (B ∪ C) = (A ∪ B) ∪ C
This proves the first associative law of set theory.
Weight on Earth (pounds) a. If a person weighs 12 pounds on the Moon, how much does the person weigh on Earth? Explain your answer. b. If a person weighs 126 pounds on Earth, how much does the person weight on the Moon? Explain your answer.
Answer: I gave you two answers if you can try them both :)
Step-by-step explanation:
If his weight on Earth is 126lb and only 21lb on moon, you can divide to see what is the ratio of those weights.
It means that your weight on moon will be 6 times less than on Earth.
Now we have to multiply 31lb which is weight of the person on moon by 6 to get his weight on Earth
On moon our mass becomes 1/6 of actual mass so if you weigh 60 kg then your mass on moon will be 10 kg..
Similarly if your mass on moon is 31 lbs then your mass on earth will be 31*6=186 lbs.
please help me out with this question! i appreciate it :))
Answer:
144,000
Step-by-step explanation:
you multiply 18,000 by 8 since its after one year and you get 144,000.
I will mark you brainiest!
Given the diagram above, m∠Z is:
A) 180°
B) 120°
C) 60°
D) 30°
Answer:
B. 120o
Step-by-step explanation:
A parallelogram is a flat 2d shape which has four angles. The opposite interior angles are equal. The angles on the same side of the transversal are supplementary, that means they add up to 180 degrees. Hence, the sum of the interior angles of a parallelogram is 360 degrees.
t + 2t = 180
3t = 180
t = 180/3 = 60
m∠Z = 2t = 2(60) = 120
if 2^x=x^2 , find x.
Answer:
x = 2 or x = 4
Step-by-step explanation:
The equation:
[tex]2^{x} = x^{2}[/tex]Has two solutions:
x = 2 or x = 4.The values of x can be found by graphing the two functions ([tex]y = 2^{x}[/tex] and [tex]y = x^{2}[/tex]) and finding their points of intersection, or you can use numerical methods to solve the equation.
To check our work, we can simply insert 2 and 4 in as y.
For 2:
[tex]2^{2} = 2^{2}[/tex]You can see that it is the same.
For 4:
[tex]2^{4} = 4^{2}[/tex](2 × 2 × 2 × 2) = (4 × 4)16 = 16They are also the same.
Therefore, x can equal either 2 or 4.
Write the polynomial in standard form. Identify the degree and leading coefficient of the polynomial. Then classify the polynomial by the number of terms. 5z + 2z³ + 3z4 Standard form: Degree: Leading coefficient: Classification:
The given polynomial written in standard form is: 3z⁴ + 2z³ + 5z
Degree: 4
Leading Coefficient: 3
Classification: Trinomial
How to write polynomial in standard form?Writing a polynomial in standard form simply means that we put the term with the highest exponent in it first and then the one with the second highest exponents second, and so on.
The polynomial we are given is: 5z + 2z³ + 3z4
Writing it in standard form gives us:
3z⁴ + 2z³ + 5z
The degree of the polynomial is defined as the value of the exponent in the leading term (if we are assuming a single variable). Thus, this given polynomial is of degree 4.
The leading coefficient is the number that the first term is multiplied by and in this problem that would be 3.
There are three terms in the given polynomial (the first term is 3z⁴, the second term is 2z³, and the 3rd term is 5z). Thus, it is a trinomial.
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The weights of ice cream cartons are normally distributed with a mean weight of 7 ounces and a standard deviation of 0.6 ounces. A sample of 25 cartons is randomly selected. What is the probability that their mean weight is greater than 7.19 ounces?
The probability that the mean weight of the sample of 25 cartons is greater than 7.19 ounces is given as follows:
0.0571 = 5.71%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 7, \sigma = 0.6, n = 25, s = \frac{0.6}{\sqrt{25}} = 0.12[/tex]
The probability that the mean weight is greater than 7.19 ounces is one subtracted by the p-value of Z when X = 7.19, considering the standard error s, hence:
Z = (7.19 - 7)/0.12
Z = 1.58
Z = 1.58 has a p-value of 0.9429.
Hence:
1 - 0.9429 = 0.0571 = 5.71%.
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The gas/oil ratio for a certain chainsaw is 50 to 1 .
a. How much oil (in gallons) should be mixed with 12 gallons of gasoline?
b. If 1 gallon equals 128 fluid ounces, write the answer to part a in fluid ounces.
0.24 gallons of oil should be mixed with 12 gallons of gasoline.
Therefore, 30.72 fluid ounces of oil should be mixed with 12 gallons of gasoline.
Step-by-step explanation:
a. To calculate the amount of oil needed, we need to know the ratio of gas to oil in terms of units. Since 50 parts of gas are mixed with 1 part of oil, we have:
1 gallon of gas / 50 = x gallons of oil
To find x, we substitute the given value of gas (12 gallons) and solve for x:
1 gallon of gas / 50 = x gallons of oil
12 gallons of gas / 50 = x
0.24 gallons of oil = x
Therefore, 0.24 gallons of oil should be mixed with 12 gallons of gasoline.
b. To convert gallons to fluid ounces, we multiply by 128:
0.24 gallons of oil * 128 fluid ounces/gallon = 30.72 fluid ounces of oil
Therefore, 30.72 fluid ounces of oil should be mixed with 12 gallons of gasoline.
what is the value of the expression (-5)-³
Answer:
[tex]\frac{1}{-125}[/tex]
x = -125
Step-by-step explanation:
It shows the steps in the pic you attached so I didn't add those steps.
(-5)(-5)(-5) = -125
multiply. round your answer to the nearest hundredeth: 2.56x0.03=
0.08 rounded for the nearest hundredth
If x = 37 degrees, how many degrees is Angle y? (Include only numerals in your response.)
Answer:
143 degrees
Step-by-step explanation:
angles on a straight line add up to 180 degrees
[tex]x + y = 180 \\ 37 + y = 180 \\ y = 180 - 37 \\ y = 143 \: degrees[/tex]
(Stock Level). A.S. Ltd. produces a product 'RED' using two components X and Y. Each unit of 'RED' requires 0.4 kg. of X and 0.6 kg. of Y. Weekly production varies from 350 units to 450 units averaging 400 units. Delivery period for both the components is 1 to 3 weeks. The economic is 600 kgs. and for Y is 1,000 kgs. Calculate: (1) Re-order level of X; (ii) Maximum level of X; (iii) Maximum level of Y.
Answer:
Step-by-step explanation:
To calculate the reorder level of component X, we need to find out the average weekly consumption of X.
Average consumption of X per unit of 'RED' = 0.4 kg
Average weekly production of 'RED' = 400 units
Average weekly consumption of X for producing 400 units of 'RED' = 0.4 kg/unit x 400 units/week = 160 kg/week
Assuming lead time of 3 weeks for delivery of X, the reorder level of X would be:
Reorder level of X = Average weekly consumption of X x Lead time for delivery of X
Reorder level of X = 160 kg/week x 3 weeks = 480 kg
To calculate the maximum level of X, we need to take into account the economic order quantity and the maximum storage capacity.
Economic order quantity of X = Square root of [(2 x Annual consumption of X x Ordering cost per order) / Cost per unit of X]
Assuming 52 weeks in a year:
Annual consumption of X = Average weekly consumption of X x 52 weeks/year = 160 kg/week x 52 weeks/year = 8,320 kg/year
Ordering cost per order of X = 600
Cost per unit of X = 1
Economic order quantity of X = Square root of [(2 x 8,320 kg x 600) / 1] = 2,771.28 kg (approx.)
Maximum storage capacity of X = Economic order quantity of X + Safety stock - Average weekly consumption x Maximum lead time
Assuming a safety stock of 20% of the economic order quantity and a maximum lead time of 3 weeks:
Maximum storage capacity of X = 2,771.28 kg + (0.2 x 2,771.28 kg) - (160 kg/week x 3 weeks) = 2,815.82 kg (approx.)
To calculate the maximum level of Y, we follow the same approach as for X:
Annual consumption of Y = Average weekly consumption of Y x 52 weeks/year
Average consumption of Y per unit of 'RED' = 0.6 kg
Average weekly consumption of Y for producing 400 units of 'RED' = 0.6 kg/unit x 400 units/week = 240 kg/week
Annual consumption of Y = 240 kg/week x 52 weeks/year = 12,480 kg/year
Economic order quantity of Y = Square root of [(2 x Annual consumption of Y x Ordering cost per order) / Cost per unit of Y]
Ordering cost per order of Y = 1,000
Cost per unit of Y = 1.5
Economic order quantity of Y = Square root of [(2 x 12,480 kg x 1,000) / 1.5] = 915.65 kg (approx.)
Maximum storage capacity of Y = Economic order quantity of Y + Safety stock - Average weekly consumption x Maximum lead time
Assuming a safety stock of 20% of the economic order quantity and a maximum lead time of 3 weeks:
Maximum storage capacity of Y = 915.65 kg + (0.2 x 915.65 kg) - (240 kg/week x 3 weeks) = 732.52 kg (approx.)
Fuel wood is measured in cords. The number of cords in a pile l ft long, w ft wide, and h ft tall can be estimated using the equation number of cords=lwh128.
Hannah measures a pile of wood to be 14 ft long by 20 ft wide.
Which equation can be used to determine the number of cords in a pile of wood h ft tall?
The equation that is used to determine the number of cords in a pile of wood h ft tallis is the number of cords = 280×h×128.
What is an equation?
There are many different ways to define an equation. The definition of an equation in algebra is a mathematical declaration that illustrates the equality of two mathematical expressions.
Given that
The number of cords in a pile l ft long, w ft wide, and h ft tall can be estimated using the equation number of cords=lwh128.
The length of the wood pile is 14 ft and the wide is 20 ft.
The product of length and width is lw = 14×20 = 280 ft².
Putting lw= 280 in the equation number of cords=lwh128:
number of cords = 280×h×128
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Calculate the volume of sand needed to fill the long jump pit to a depth of 0,07m
Answer:
Step-by-step explanation:
To calculate the volume of sand needed to fill the long jump pit to a depth of 0.07 meters, we need to know the length and width of the pit.
Assuming that the long jump pit is a rectangular prism, we can use the formula:
Volume = length x width x depth
Let's say the length of the pit is 8 meters and the width is 3 meters. Then the volume of sand needed to fill the pit to a depth of 0.07 meters would be:
Volume = 8m x 3m x 0.07m
Volume = 1.68 cubic meters
Therefore, we would need 1.68 cubic meters of sand to fill the long jump pit to a depth of 0.07 meters.
please help me with question one it should not be to long as you see the space provided thanks
Answer:
1. Draw a coordinate plane with a circle on it somewhere
2. B. and C.
Step-by-step explanation:
1. What is a function?A function is a set of points that has a specific input (x-value) and a specific output (y-value). Let's take the example of y = 2x. Let's start by plugging in 1 for x. 1 will be our input value, and 2• 1 = 2 will be our y-value because the x-value was changed to get to our output, the y-value.
In a function, it is possible to have the same y-value for different x-values; take the example of y = x^2. X can have 2 values, but because it is squared, it will give the same y-value. However, a function that has the same x-values for one y-value is not a function. For example, take a circle, with the equation x^2 + y^2 = 0. This is not a function, because, for 2 y-values, it will equal the same x-value. For your answer, you can draw a coordinate plane with a circle on it. IMPORTANT: 2 x-values cannot equal one y-values in a function.
2. What is a linear function?
A linear function is a function that has an x and y-value, as well as sometimes a coefficient to either variable and a constant. For example, the equation y = 5x +4 is a linear function because there is one y and one x-value, a coefficient (even though it is not necessary), and a constant (even though it is not necessary). It doesn't matter where the coefficients are, but there has to be one y-value and one x-value. Since there can be only one x and y, equations like y = x^2 does not work, because there are 2 x's (in the x^2). Using this information, we can figure out the correct solutions:
A. doesn't work, because there are 3 y-values.
B. works because there is one x and y, and a coefficient (although it isn't necessary)
C. works because like b, it has only one x and y, a coefficient (although it isn't necessary)
D. doesn't work because there is only one y-value and no x-value.
If you liked this answer, please brainliest!
Find the value of x. Round your answer to the nearest tenth.
Answer:
19.4
Step-by-step explanation:
cosФ=adjacent ÷hypotenuse
cos72° =6/x
0.309016994=6/x
∴x=6/0.31
=19.35
=19.4
Question
K
31
L
119°
N
45
M
MN =
KN =
m/K=
m/L=
m/M =
The measure of length MN is 31.
The measure of length KN is 45.
The measure of m∠K is 61⁰.
The measure of m∠L is 119⁰.
What is a parallelogram?A parallelogram is a four-sided plane figure in which opposite sides are parallel and congruent (having the same length) and opposite angles are congruent (having the same measure). In other words, a parallelogram is a quadrilateral with two pairs of parallel sides.
The properties of a parallelogram include:
Opposite sides are parallel and congruentOpposite angles are congruentConsecutive angles are supplementary (their measures add up to 180 degrees)Diagonals bisect each other (they intersect at their midpoint)So the length MN = Length KL = 31
Length KN = Length LM = 45
Angle K = angle M = ( 180 - 119) = 61⁰
Angle L = angle N = 119⁰
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10 1/3 is how much more than 7 8/9?
Answer:2 4/9
Step-by-step explanation:
A his herd of cows among his 4 sons he gave one son half the herd a second son one fourth of the herd a third son one fith of the herd and the fourth son 48 cows how many cows were in the herd originally
Answer:
Let the total number of cows in the herd be represented by "x". Then, according to the problem:
The first son received half the herd, or (1/2)x cows.
The second son received one fourth of the herd, or (1/4)x cows.
The third son received one fifth of the herd, or (1/5)x cows.
The fourth son received 48 cows.
We can write an equation to represent the total number of cows in the herd:
(1/2)x + (1/4)x + (1/5)x + 48 = x
To solve for "x", we can start by simplifying the fractions:
5/10x + 2/10x + 2/10x + 48 = x
Combining like terms, we get:
9/10x + 48 = x
Subtracting 9/10x from both sides, we get:
48 = 1/10x
Multiplying both sides by 10, we get:
x = 480
Therefore, the original herd had 480 cows.
find thenonpermissible replacment for x in this expression 1/-8x
If any number is divided by zero. the result is indeterminate.
Therefore, zero is the non-permissible replacement for x.
Find the equation of the line that passes through the given point and has the given slope. (Use x as your variable.) (-9,- 9 ) , m = 0
The linear equation that passes through (-9, -9) and has the slope m = 0 is:
y = -9
How to find the equation of the line?A general linear equation can be written in slope-intercept form as.
y = m*x + b
Where m is the slope and b is the y-intercept.
Here we want to find the equation of a line that passes through (-9, -9) and that has the slope m = 0.
Repplacing the slope we will get:
y = 0*x + b
And no we want it to pass throug (-9, -9), replacing these values we will get:
-9 = 0*-9 + b
-9 = b
Then the linear equation is:
y = -9
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if 24 x 18 and x 1 are in proportion find the value of x
Answer:
x = 432.
Step-by-step explanation:
We know that 24 x 18 and x x 1 are in proportion, which can be written as:
(24 x 18) / (x x 1) = k, where k is a constant of proportionality.
Simplifying the left-hand side, we get:
24 x 18 = 432
x x 1 = x
Substituting these values, we get:
432 / x = k
To solve for x, we need to find the value of k. We can do this by using the fact that the two ratios are in proportion. That is:
24 x 18 : x x 1 = 432 : k
Simplifying the left-hand side, we get:
(24 x 18) / x = 432 / k
Multiplying both sides by x and k, we get:
24 x 18 k = 432 x
Dividing both sides by 24 x, we get:
18 k / 1 = 18
Solving for k, we get:
k = 1
Substituting k = 1 into the equation 432 / x = k, we get:
432 / x = 1
Multiplying both sides by x, we get:
432 = x
Therefore, x = 432.
PLS HELP , in need to solve by using substitution and with checks
Answer:
(0, 2)Step-by-step explanation:
[tex]\tt y=x+2\\3x+3y=6[/tex]
Substitute y= y=x+2 into 3x+3y=6
[tex]\tt 3x+3(x+2)=6[/tex][tex]\tt 6x+6=6[/tex]Solve for x :-
[tex]\tt 6x+6=6[/tex]Cancel 6 from both sides:-
[tex]\tt 6x=0[/tex]Divide both sides by 6:-
[tex]\tt \cfrac{6x}{6} =\cfrac{0}{6}[/tex][tex]\boxed{\bf x=0}[/tex]Now, Let's solve for y:-
Substitute x = 0 into y=x+2
[tex]\tt y=0+2[/tex][tex]\boxed{\bf y=2}[/tex]Therefore, x = 0 and y = 2.
_________________
Check:-
To check a system of equations by substitution, we plug the values for x and y into the equations, If both simplified are true then your answer is correct.
Equation 1 :-
y = x + 2
(2) = 0 + (2)2=2 ✓Equation 2 :-
3x+3y=6
3(0)+3(2)=60+6=66=6 ✓__________________________
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Assume that when adults with smartphones are randomly selected, 44% use them in meetings or classes. If 25 adult smartphone users are randomly selected, find the probability that exactly 20 of them use their smartphones in meetings or classes.
Answer:
The probability that exactly 20 out of 25 adult smartphone users use their smartphones in meetings or classes is approximately 0.002.
Question 9
The volume of a cube can be found using the equation V = s³, where V is the volume and s is the measure of one side of the cube.
Match the equation for how to solve for the side length of a cube to its description.
Drag the equation into the box to match the description.
The equation for solving the side length of a cube is s = ∛V, where s is the side length of the cube, and V is the volume.
The equation for solving the side length of a cube can be expressed as s = ∛V, where s is the side length of the cube, and V is the volume. This equation can be used to calculate the side length of a cube when the volume is known. For example, if the volume of a cube is 125 cubic units, the side length can be calculated by substituting 125 for V and solving the equation: s = ∛125 = 5. This means that the side length of the cube is 5 units.
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In ΔLMN, l = 150 inches, n = 890 inches and ∠N=61°. Find all possible values of ∠L, to the nearest 10th of a degree.
The possible values of ∠L are 118.9 degrees (rounded to 10th of a degree).
What is a triangle?A polygon with three sides and three angles is a triangle. It is one of the simplest geometric shapes.
To find the measure of angle L in ΔLMN, we can use the fact that the sum of the angles in a triangle is 180 degrees:
∠L + ∠M + ∠N = 180
We know that ∠N = 61 degrees, so we can substitute that value in and simplify:
∠L + ∠M + 61 = 180
∠L + ∠M = 119
We also know that the length of LM is 150 inches and the length of LN is 890 inches. We can use the Law of Cosines to find the measure of angle M:
cos M = (150² + 890² - LM²) / (2 × 150 × 890)
cos M = 0.999989 (rounded to 6 decimal places)
M = cos⁻¹(0.999989)
M ≈ 0.00114 radians
M ≈ 0.0655 degrees (rounded to 10th of a degree)
Now we can substitute the value of M into the equation we derived earlier and solve for angle L:
∠L + 0.0655 + 61 = 180
∠L = 118.9345
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A chemist has two alloys, one of which is 10% gold and 20% lead in the other which is 40% gold and 30% lead. How many grams of each of the two alloys should be used to make an alloy that contains 57 g of gold and 94 g of lead 
Answer:
The chemist should use 410 grams of the first alloy (which is 10% gold and 20% lead) and 40 grams of the second alloy (which is 40% gold and 30% lead) to make an alloy that contains 57 grams of gold and 94 grams of lead.
Step-by-step explanation:
Let's call the amount of the first alloy used "x" and the amount of the second alloy used "y". We can set up a system of two equations based on the amount of gold and lead needed in the final alloy:
Equation 1: 0.10x + 0.40y = 57 (the amount of gold in the first alloy is 10%, and in the second alloy is 40%)
Equation 2: 0.20x + 0.30y = 94 (the amount of lead in the first alloy is 20%, and in the second alloy is 30%)
We can then solve for x and y using any method of solving systems of equations. One way is to use substitution:
Solve equation 1 for x: x = (57 - 0.40y)/0.10 = 570 - 4ySubstitute this expression for x in equation 2: 0.20(570 - 4y) + 0.30y = 94Simplify and solve for y: 114 - 0.8y + 0.3y = 94 → -0.5y = -20 → y = 40Substitute this value of y into the expression for x: x = 570 - 4y = 410Therefore, the chemist should use 410 grams of the first alloy (which is 10% gold and 20% lead) and 40 grams of the second alloy (which is 40% gold and 30% lead) to make an alloy that contains 57 grams of gold and 94 grams of lead.
If $5,000 is invested at 9% annual interest compounded quarterly, how long would it take for the account balance to reach $20,000? Round your answer to the nearest tenth.
Using the compound interest formula, it is obtained that it would take approximately 9.9 years for the account balance to reach $20,000.
What is Compound Interest?
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.
We can use the formula for compound interest to solve this problem -
[tex]A = P(1 + \frac{r}{n})^{(nt)}[/tex]
where A is the account balance, P is the principal (the initial investment), r is the annual interest rate (as a decimal), n is the number of times per year the interest is compounded, and t is the time (in years).
In this case, we have P = 5000, r = 0.09 (9% annual interest), n = 4 (compounded quarterly), and A = 20000. We want to find t.
Substituting these values into the equation, we get -
[tex]20000 = 5000 \big(1 + \frac{0.09}{4} \big)^{(4t)}[/tex]
Dividing both sides by 5000, we get -
[tex]4 = \big(1 + \frac{0.09}{4} \big)^{(4t)}[/tex]
Taking the natural logarithm of both sides, we get -
ln(4) = 4t ln(1 + 0.09/4)
Solving for t, we get -
t = ln(4) / (4 ln(1 + 0.09/4))
Simplifying the equation, we get -
t ≈ 9.9
Therefore, the time value is obtained as 9.9 years.
To learn more about compound interest from the given link
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