Answer:
The half-life of a substance is the amount of time it takes for half of the initial amount of the substance to decay.
We can use the following formula to calculate the half-life (t1/2) of a substance with a decay rate of r:
t1/2 = (ln 2) / r
where ln 2 is the natural logarithm of 2 (approximately 0.693).
In this case, the decay rate is 2.5% per year, or 0.025 per year. Plugging this into the formula, we get:
t1/2 = (ln 2) / 0.025
t1/2 = 27.73 years (rounded to two decimal places)
Therefore, the half-life of the substance is approximately 27.73 years.
The Nutty Professor sells cashews for $6.80 per pound and Brazil nuts for $4.20 per pound. How much of each type should be used to make a 35 pound mixture that sells for $5.31 per pound?
The Nutty Prοfessοr shοuld use apprοximately 14.94 pοunds οf cashews and 35 - 14.94 = 20.06 pοunds οf Brazil nuts tο make a 35 pοund mixture that sells fοr $5.31 per pοund.
Assume the Nutty Prοfessοr makes a 35-pοund mixture with x pοunds οf cashews and (35 - x) pοunds οf Brazil nuts.
The cashews cοst $6.80 per pοund, sο the tοtal cοst οf x pοunds οf cashews is $6.8x dοllars.
Similarly, Brazil nuts cοst $4.20 per pοund, sο (35 - x) pοunds οf Brazil nuts cοst 4.2(35 - x) dοllars.
The tοtal cοst οf the mixture equals the sum οf the cashew and Brazil nut cοsts, which is:
6.8x + 4.2(35 - x) (35 - x)
When we simplify, we get:
6.8x + 147 - 4.2x
2.6x + 147
The mixture sells fοr $5.31 per pοund, sο the tοtal revenue frοm selling 35 pοunds οf the mixture is:
35(5.31) = 185.85
When we divide the tοtal cοst οf the mixture by the tοtal revenue, we get:
2.6x + 147 = 185.85
Subtractiοn οf 147 frοm bοth sides yields:
2.6x = 38.85
When we divide by 2.6, we get:
x ≈ 14.94
Tο make a 35-pοund mixture that sells fοr $5.31 per pοund, the Nutty Prοfessοr shοuld use apprοximately 14.94 pοunds οf cashews and 35 - 14.94 = 20.06 pοunds οf Brazil nuts.
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Can someone solve this
Note: in dark pen is the questions to solve in light pencil is my answer probably are wrong
The open circle at 3 indicates that 3 is not included in the solution set. This inequality can be read as "X is less than 5" or "X is strictly less than 5."
What is expression?In mathematics, an expression is a combination of numbers, symbols, and operators that represents a value. Expressions can be as simple as a single number or variable, or they can be complex combinations of mathematical operations. For example, 2 + 3 is a simple expression that represents the value 5, while (2 + 3) x 4 - 1 is a more complex expression that represents the value 19. Expressions can be evaluated or simplified using the rules of arithmetic and algebra.
Here,
1. Simplify:
3(4x-2)+ 7X (2-1) + 4 (6+4)+(-8)
Multiplying inside the parentheses first:
12x - 6 + 7x + 4 + 40 - 8
Combining like terms:
19x + 30
Final answer: 19x + 30
2. Graph:
3 > X
This is a simple inequality in one variable (X). To graph it on a number line, we first draw a dot at 3 (since the inequality is strict), and then shade all values less than 3:
<=========o---
The open circle at 3 indicates that 3 is not included in the solution set.
3. Write the inequality:
X < 5
This is a simple inequality in one variable (X). The inequality sign is "less than," and the number on the right-hand side is 5. This inequality can be read as "X is less than 5" or "X is strictly less than 5."
4. Solve for x:
3x - 7 = 42
Adding 7 to both sides to isolate the variable:
3x = 49
Dividing both sides by 3 to solve for x:
x = 16.33 (rounded to two decimal places)
Final answer: x = 16.3
5. Find 32% of $542.50:
To find 32% of $542.50, we can use the formula:
percent * amount = part
where "percent" is the percentage expressed as a decimal, "amount" is the whole amount, and "part" is the result we're looking for.In this case, we have:
0.32 * $542.50 = part
Multiplying:
$173.60 = part
Final answer: $173.60
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In a double slit experiment, it is observed that the distance between adjacent maxima on a remote screen is 1.0cm. The distance between adjacent maxima when the slit separation is cut in half decreases to 0.50cm. The speed of light in a certain material is measured to be 2.2x10^8 m/s.
The index of refraction of the material used in double slit experiment is 1.36.
The distance between adjacent maxima on a screen in a double-slit experiment is given by:
d sinθ = mλ
where d is the slit separation, θ is the angle between the screen and the line connecting the slits and the maxima, m is the order of the maximum, and λ is the wavelength of light.
The distance between adjacent maxima changes from 1.0cm to 0.50cm when the slit separation is cut in half, which means that the wavelength of light is also halved. Therefore, the ratio of the two wavelengths is:
λ1/λ2 = 2/1 = 2
The speed of light in the material is given as 2.2x10^8 m/s. The speed of light in a vacuum is c, so the index of refraction of the material is given by:
n = c/v
where v is the speed of light in the material. Therefore:
n = c/2.2x10^8 m/s = 1.36
The index of refraction of the material is 1.36.
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_____The given question is incomplete, the complete question is given below:
In a double slit experiment, it is observed that the distance between adjacent maxima on a remote screen is 1.0cm. The distance between adjacent maxima when the slit separation is cut in half decreases to 0.50cm. The speed of light in a certain material is measured to be 2.2x10^8 m/s. what is the index refraction of this material?
There are 450 seats in the lower level of a concert hall with b balcony seats in the upper level. So far, 170 tickets have been sold, which is 1/5 if the total number of seats in the concert hall. How many tickets sold are balcony seats?
Answer:
400 balcony seats
Step-by-step explanation:
We know 170 tickets have been sold which is 1/5 of the total tickets
We have to find the total number of seats by doing 170x5
Now we know that there are 850 seats (170x5)
We have to subtract the lower seats from the total number of seats to find b (balcony seats)
850-450 = 400
Therefore, b is equal to 400 balcony seats
If you start a bank account with N$15,000 and your bank compounds the interest monthly at
an interest rate of 9% p.a, how much money do you have at the year's end?
(Assume that you do not add or withdraw any money to/from the account).
Answer:
Step-by-step explanation:
16350$
Answer:
16 407.1
Step-by-step explanation:
Suppose an unknown radioactive substance produces 16000 counts per minute on a Geiger counter at a certain time, and only 1000 counts per minute 13 days later. Assuming that the amount of radioactive substance is proportional to the number of counts per minute, determine the half-life of the radioactive substance.
The radioactive substance has a half-life of __ days.
The radioactive material has a half-life of roughly 11.8 days.
What exactly does half-life mean?The amount of time it takes for an active component of a medication to degrade by half in your body is referred to as the half-life.
Let's apply the exponential decay formula:
N(t) = N0 e(-kt)
Let's calculate the decay constant using the information provided:
At time t=0, the number of counts per minute is N0 = 16000.
At time t=13 days, the number of counts per minute is N(13) = 1000.
When we enter these numbers into the equation, we obtain:
N(13) = N0 e(-k*13)
1000 = 16000 e(-k*13)
e(-k*13) = 1000/16000
When we take the natural logarithm of both sides, we obtain:
ln(e(-k*13)) = ln(1000/16000)
-k*13 = ln(1000/16000)
k = -ln(1000/16000)/13
k ≈ 0.0585
We may use the half-life formula now that we know the decay constant:
t1/2 = ln(2)/k
Substituting k = 0.0585, we get:
t1/2 = ln(2)/0.0585
t1/2 ≈ 11.8
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0.00063 / (9*10^-4)
Please answer QUIKLYYYY!!!!
Answer: .70
Step-by-step explanation:
10^-4 = .0001
.0001 x 9= .0009
.00063/ .0009= .70
determine, without actually computing the z transform, the rocs for the z transform of the following signals:
The ROC of a given signal's Z-transform can be determined without actually computing the Z-transform by identifying the maximum and minimum magnitude of the signal and checking for any poles of the Z-transform within the resulting annular region.
Let's take a signal as an example, suppose x[n] = {1, -2, 3, -4, 5}. In order to determine the ROC of its Z-transform, we are firstly required to first look for any regions in the complex plane where the sum of the absolute values of the Z-transform is found finite. It can be done by looking for the maximum and minimum magnitude of x[n] and denote them as R1 and R2 respectively. Then, the ROC of the Z-transform will be the annular region between R1 and R2, excluding any poles of the Z-transform that lie within this annular region.
In this case, the maximum absolute value of x[n] is 5 and the minimum is found being 1. So, the ROC of the Z-transform will be the annular region between |z| = 1 and |z| = 5. We can denote this as 1 < |z| < 5. We also need to check if there are any poles of the Z-transform within this annular region. Since we haven't actually computed the Z-transform, we cannot determine the exact location of any poles.
However, we can check for any values of z that would make the Z-transform infinite. For example, if x[n] is a causal signal (i.e., x[n] = 0 for n < 0), then the ROC cannot include any values of z for which |z| < 1, since this would make the Z-transform infinite.
So, the ROC of the Z-transform for the given signal x[n] can be written as 1 < |z| < 5, assuming that x[n] is a causal signal.
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The complete question is :
Can you explain how to determine the ROCs (regions of convergence) for the Z-transform of a given signal without actually computing the Z-transform? Please provide an example signal with random data and demonstrate how to find its ROCs using this method.
The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 360 grams and a standard deviation of 9 grams Find the weight that corresponds to each event(use excel or appendix c to calculate the z value round your final answers to the 2 decimal places)
URGENT
The weight that corresponds to this event are approximately 344.03 grams and 375.97 grams.
How to deal with normally distribution?To find the weight that corresponds to each event, we need to use the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We can convert the given mean and standard deviation to z-scores using the formula:
z = (x - μ) / σ
where x is the weight we want to find, μ is the mean (360 grams), and σ is the standard deviation (9 grams).
Then, we can use a standard normal distribution table or calculator to find the probability of each event, and convert it back to a weight using the inverse of the z-score formula:
x = μ + z * σ
where z is the z-score that corresponds to the desired probability.
Event 1: The weight is less than 345 grams.
z = (345 - 360) / 9 = -1.67
Using a standard normal distribution table or calculator, we find that the probability of a z-score less than -1.67 is approximately 0.0475.
x = 360 + (-1.67) * 9 = 344.03 grams
Therefore, the weight that corresponds to this event is approximately 344.03 grams.
Event 2: The weight is between 355 and 365 grams.
First, we need to find the z-scores that correspond to the two boundaries:
z1 = (355 - 360) / 9 = -0.56
z2 = (365 - 360) / 9 = 0.56
Using a standard normal distribution table or calculator, we find that the probability of a z-score less than -0.56 is approximately 0.2123, and the probability of a z-score less than 0.56 is approximately 0.7123. Therefore, the probability of a z-score between -0.56 and 0.56 is:
0.7123 - 0.2123 = 0.5
x1 = 360 + (-0.56) * 9 = 355.16 grams
x2 = 360 + (0.56) * 9 = 364.84 grams
Therefore, the weight that corresponds to this event is any weight between 355.16 and 364.84 grams.
Event 3: The weight is greater than 375 grams.
z = (375 - 360) / 9 = 1.67
Using a standard normal distribution table or calculator, we find that the probability of a z-score greater than 1.67 is approximately 0.0475.
x = 360 + (1.67) * 9 = 375.97 grams
Therefore, the weight that corresponds to this event is approximately 375.97 grams.
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We usually write numbers in decimal form (or base 10), meaning numbers are composed using 10 different "digits" { 0,1…,9 }. Sometimes though it is useful to write numbers hexadecimal or base 16. Now there are 16 distinct digits that can be used to form numbers: { 0,1,…,9,A,B,C,D,E,F }.
So for example, a 3 digit hexadecimal number might be 2B8.
Please answer the parts of the question below:
a) How many 5-digit hexadecimal are there in which the first digit is E or F?
b) How many 6-digit hexadecimal start with a letter (A-F) and end with a numeral (0-9)?
c) How many 3-digit hexadecimal start with a letter (A-F) or end with a numeral (0-9) (or both)?
a) 14 to 15, 5-digit hexadecimal are there in which the first digit is E or F
b) 1205 (in decimal) 6-digit hexadecimal start with a letter (A-F) and end with a numeral (0-9)
c) there is a total of 2.1875, 3-digit hexadecimal start with a letter (A-F) or end with a numeral (0-9) (or both)
The hexadecimal number system( hex) functions nearly identically to the decimal and double systems. rather of using a base of 10 or 2 independently, it uses a base of 16. Hex uses 16 integers including 0- 9, just as the decimal system does, but also uses the letters A, B, C, D, E, and F( original to a, b, c, d, e, f) to represent the figures 10- 15. Every hex number represents 4 double integers, called bites, which makes representing large double figures simpler. For illustration, the double value of 1010101010 can be represented as 2AA in hex. This helps computers to compress large double values in a manner that can be fluently converted between the two systems.
a) 14 to 15, 5-digit hexadecimal are there in which the first digit is E or F
b) 4 is in the 16 x 16 position so that means, 16 x 16 x 4 + 11 x 16 + 5 for the position of A - F we get 1205 (in decimal) 6-digit hexadecimal start with a letter (A-F) and end with a numeral (0-9)
c) there are a total of 2.1875, 3-digit hexadecimal start with a letter (A-F) or end with a numeral (0-9) (or both) as on the left side is "2", that is the whole number part and the 3 is in the "sixteenths" position, meaning "3 sixteenths", or 3/16 so, 2.3 is "2 and 3 sixteenths" (=2.1875 in Decimal)
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A line with a slope of -8/7 passes through the points (6, -10) and (-8, f). What is the
value of f?
Answer: -18
Step-by-step explanation:
Answer:
value of f is 6
Step-by-step explanation:
100% correct
the work is in the image below. Hope this help!
A boat can travel 29mph in still water. If it travels 342 miles with the current in the same length of time it travels 180 miles against the current, what is the speed of the current?
29 = speed of the boat in still water
c = speed of the current
t = time it took each way
when going Upstream, the boat is not really going "29" fast, is really going slower, is going "29 - c", because the current is subtracting speed from it, likewise, when going Downstream the boat is not going "29" fast, is really going faster, is going "29 + c", because the current is adding its speed to it.
[tex]{\Large \begin{array}{llll} \underset{distance}{d}=\underset{rate}{r} \stackrel{time}{t} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Upstream&180&29-c&t\\ Downstream&342&29+c&t \end{array}\hspace{5em} \begin{cases} 180=(29-c)(t)\\\\ 342=(29+c)(t) \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 1st equation}}{180=(29-c)t\implies \cfrac{180}{29-c}=t} \\\\\\ \stackrel{\textit{substituting on the 2nd equation from above}}{342=(29+c)\left( \cfrac{180}{29-c} \right)}\implies \cfrac{342}{29+c}=\cfrac{180}{29-c} \\\\\\ 9918-342c=5220+180c\implies 4698-342c=180c\implies 4698=522c \\\\\\ \cfrac{4698}{522}=c\implies \boxed{9=c}[/tex]
Help me find the value of x
Answer:
x = 30
Step-by-step explanation:
We know
The three angles must add up to 180°. We know one is 20°, so the other two must add up to 160°.
2x + 3x + 10 = 160
5x + 10 = 160
5x = 150
x = 30
do you mind helping me with this?
Answer:
125
Step-by-step explanation:
We Take
625 / 5 = 125
So, the answer is 125
ASAP PLEASE FOR A TEST!!!A line passes through (-1, 7) and (2, 10).
Which answer is the equation of the line?
O-3x+y=4
Ox+y=12
O = x+y=8
-3x+y=16
Answer:
i think this is the answer!! good luck
i need help on these 2 !!!
The length of RS is 13 units and the length of the hypotenuse XY is approximately 16.4 units.
15) In ΔTSR
TR² = TS² + RS²
Substituting the given values, we get:
(5√10)² = 9² + RS²
250 = 81 + RS²
RS² = 169
Taking the square root of both sides, we get:
RS = 13 units
16)In ΔYZX
XY² = YZ² + XZ²
Substituting the given values, we get:
XY² = 10² + 13²
XY² = 169 + 100
XY² = 269
Taking the square root of both sides, we get:
XY = √269
XY=16.4 units
What is Pythagorean theorem?
In a right triangle, the Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
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1) The school bake sale needs to make at least $200.
If each cake is sold for $10, how many cakes should
they sell to beat their goal? Let x represent the
number of cakes. Identify the inequality that
represents this situation.
a) 10x ≥ 200
b) 10x ≤ 200
10
c)
d)
X
-> 200
10
x
< 200
If we solve this inequality for x, we get x 20, which indicates the school equation bake sale must sell at least 20 cakes in order to meet their $200 objective.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
10x ≥ 200 accurately portrays the scenario.
To explain why, consider the following:
Because each cake costs $10, the total amount earned from selling x cakes is 10x.
The aim is to raise at least $200, thus the total amount must be larger than or equal to $200.
As a result, we may describe the circumstance by writing the inequality 10x 200.
If we solve this inequality for x, we get x 20, which indicates the school bake sale must sell at least 20 cakes in order to meet their $200 objective.
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nction value. n=4 -1,4, and 2+2i are zeros; f(1)=-30
The polynomial function with the given zeros and numeric value at x = 1 is given as follows:
f(x) = x^4 - 7x³ + 16x² - 8x - 32
How to define the polynomial function?The zeros of the polynomial function are given as follows:
x = -1.x = 4.x = 2 + 2i.x = 2 - 2i. -> complex-conjugate theorem, when a complex number is a root of a polynomial function, it's conjugate also is.Then the linear factors of the function are given as follows:
x + 1.x - 4.x - 2 - 2i.x - 2 + 2i.According to the Factor Theorem, the function with leading coefficient a can be defined as a product of it's linear factors are follows:
f(x) = a(x + 1)(x - 4)(x - 2 - 2i)(x - 2 + 2i).
f(x) = a(x² - 3x - 4)(x² - 4x + 8)
f(x) = a(x^4 - 7x³ + 16x² - 8x - 32).
When x = 1, y = -30, hence the leading coefficient a is obtained as follows:
-30 = a(1 - 7 + 16 - 8 - 32)
-30a = -30
a = 1.
Hence the function is:
f(x) = x^4 - 7x³ + 16x² - 8x - 32
Missing InformationThe problem asks for the polynomial function with the given zeros and numeric value at x = 1.
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h(n) = -4n+ 7
f(n) = -8n + 4
Find (hᵒf)(n)
Answer:
(h°f)(n) = 32n - 9
Step-by-step explanation:
h(f(n)) = h(-8n+4)
h(-8n+4) = -4(-8n+4) + 7
h(-8n+4) = 32n - 9
(h°f)(n) = 32n - 9
What is the code to this I need help asap.
Based on the information in the image, the values of the symbols in order would be: 5, 9.86, 9.93, 7.91. 10.56.
How to find the equivalent value of each symbol?To find the equivalent value of each symbol we must apply the Pythagorean theorem and find the value of the hopotenuse of all triangles as shown below:
Triangle 1:
4² + 3² = c²16 + 9 = c²c = 5Triangle 2:
5² + 8.5² = c²25 + 72.25 = c²c = 9.86Triangle 3:
9.86² + b² = 14²b² = 14² - 9.86²b² = 98.78b = 9.93Triangle 4:
a² + 6² = 9.93²a² = 9.93² - 6²a² = 62.60a = 7.91Triangle 5:
7.91² + 7² = c²62.56 + 49 = c²111.56 = c²10.56 = cAccording to the above, the values of the symbols in order would be:
5, 9.86, 9.93, 7.91. 10.56.
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Triangle XYZ is a 45°- 45°- 90° triangle with right angle Z. Find the coordinates of point X in
Quadrant I for Y(-1,2) and Z(6,2).
The coordinates of point X are (7/3, 2√(2)) in Quadrant I.
What is a quadrant?In coordinate geometry, a plane is divided into four regions called quadrants. These quadrants are numbered counterclockwise starting from the upper right quadrant, which is known as the first quadrant.The four quadrants are defined by the x-axis and y-axis. The x-axis is a horizontal line that runs left and right through the origin, while the y-axis is a vertical line that runs up and down through the origin.
What is isosceles triangle?An isosceles triangle is a type of triangle in which two sides are of equal length. In an isosceles triangle, the third side is called the base, and the two equal sides are called legs. The two angles formed by the legs and the base are also equal to each other. The angle opposite the base is called the vertex angle.
In the given question,
Since Triangle XYZ is a 45°- 45°- 90° triangle, the two legs of the triangle are congruent.
Let's call the length of each leg "x".We know that point Z is the right-angle vertex of the triangle and has coordinates (6, 2).
Since the triangle is isosceles, we can find the length of the other leg using the distance formula:x² + x² = (distance between Y and Z)²²x² = (6 - (-1))²²x² = 49x² = 24.5.
Now that we know the length of each leg, we can find the coordinates of point X. Since Triangle XYZ is a 45°- 45°- 90° triangle, we know that the hypotenuse is the square root of 2 times the length of a leg.
Let's call the coordinates of point X (x, y).x² + y² = (distance between X and Y)²x² + y² = x² + (y - 2)²y = 2√(2)Now we can find the x-coordinate of point X:x^2 + (2√(2))^2 = (distance between X and Z)^2x^2 + 8 = (6 - x)^2x^2 + 8 = 36 - 12x + x^212x = 28x = 7/3.
Therefore, the coordinates of point X are (7/3, 2√(2)) in Quadrant I.
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figure: quantity of goods y and x i) the substitution effect will be largest for indifference curve:
The magnitude of the substitution effect depends on the slope of the indifference curve and the specific prices and quantities of the goods U4 has the largest substitution effect. so the correct answer is D).
The substitution effect measures the change in the quantity demanded of a good in response to a change in its relative price, while keeping the consumer's utility constant. It depends on the slope of the indifference curve at the initial consumption bundle.
If the indifference curve is relatively steep like curve U4, then the substitution effect will be larger because a small change in the relative price of the goods will cause the consumer to switch to a consumption bundle that is further away from the original bundle.
On the other hand, if the indifference curve is relatively flat like U1, the substitution effect will be smaller because the consumer can switch between the goods while keeping the utility constant with a relatively small change in the relative prices.
So, the substitution effect will be largest for indifference curve is U4. So, option D) is correct.
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_____The given question is incomplete, the complete question is given below:
The substitution effect will be largest for indifference curve Quantity of good Y 10- 9- 5- 0123 456789 10 Quantity of good X
a) U1
b) U2.
c) U3.
d) U4.
Isaiah is a high school basketball player. In a particular game, he made some free throws (worth one point each) and some two point shots. Isaiah scored a total of 12 points and made 4 times as many free throws as two point shots. Write a system of equations that could be used to determine the number of free throws Isaiah made and the number of two point shots he made. Define the variables that you use to write the system.
In equation 1, 4t + t = 12, so t = 8.
In equation 2, 4f = 8, so f = 2.
Isaiah made two free throws and eight two point shots.
What is equation?Equations usually contain an equation symbol, such as an equals sign (=) or an inequality symbol, such as a less than sign (<).
We can define the variables as ‘f’ for the number of free throws and ‘t’ for the number of two point shots.
The system of equations for this problem is as follows:
f + t = 12 (Equation 1)
f = 4t (Equation 2)
Equation 1 states that the total number of points that Isaiah scored is equal to the sum of the number of free throws and the number of two point shots. Equation 2 states that the number of free throws is four times the number of two point shots.
To solve this system of equations, we can use the substitution method. First, substitute 4t for f in equation 1 and solve for t. 4t + t = 12, so t = 8. Then substitute 8 for t in equation 2 and solve for f. 4f = 8, so f = 2.
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In equation 1, 4t + t = 12, so t = 2.4≈3
In equation 2, f = 4t, so f = 9.6≈10
Isaiah made three free throws and ten two point shots.
What is equation?Equations usually contain an equation symbol, such as an equals sign (=) or an inequality symbol, such as a less than sign (<).
We can define the variables as ‘f’ for the number of free throws and ‘t’ for the number of two point shots.
The system of equations for this problem is as follows:
f + t = 12 (Equation 1)
f = 4t (Equation 2)
Equation 1 states that the total number of points that Isaiah scored is equal to the sum of the number of free throws and the number of two point shots.
Equation 2 states that the number of free throws is four times the number of two point shots.
To solve this system of equations, we can use the substitution method. First, substitute 4t for f in equation 1 and solve for t.
4t + t = 12
so t = 2.4
Then substitute 2.4 for t in equation 2 and solve for f.
f = 4t
so f = 9.6.
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23. What are the digits which can be put in the box in 806 so that the four digit number is divisible by 8? 3 marks
6, 14, 22, 30, 38, 46, 54, 62, 70, 78, 86, 94
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A salesperson earns 4% commission on furnace sales.
What is the commission that the salesperson earns on the sale of $33,000 worth of furnaces.
The commission earned 4 percentage on the salesperson on the sale of furnaces is $1320.
What is percentage?In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage therefore refers to a part per hundred. The word per cent means per 100. The letter "%" stands for it. The term "percentage" was adapted from the Latin word "per centum", which means "by the hundred". Percentages are fractions with 100 as the denominator.
by the question.
the commission that the salesperson earns on the sale of $33,000 worth of furnaces= 4% of 33,000 = 4× 330 = $1320
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A regular hexagon is inscribed into a circle. Find the length of the side of the hexagon, if the radius of the circle is 12 cm.
A. 20 cm
B. 18 cm
C. 16 cm
D. 12 cm
E. None of these
In response to the stated question, we may respond that As a result, the fraction length of the hexagon's side is roughly 16.97 cm, which is closest to option C. (16 cm).
what is fraction?A fraction is a number that represents a portion of a whole or a ratio between two quantities in mathematics. It is represented as a top number (numerator) over a bottom number (denominator) divided by a horizontal line, also known as a vinculum. The fraction 3/4, for example, represents three-quarters of a whole that has been divided into four equal parts. Proper fractions, improper fractions , and mixed numbers are all ways to express a fraction. A suitable fraction is one in which the numerator is less than the denominator, for example, 2/5.
We can calculate the length of the other leg of the right triangle, which is also half the side of the hexagon, using the Pythagorean theorem:
[tex]$(fracs2 )2 + (fracs2 )2 = 122$\\$fracs244 + fracs244 = 144$\\$\frac{s^2}{2} = 144$\\$s^2 = 288$\\$s = sqrt288 = about 16.97$[/tex]
As a result, the length of the hexagon's side is roughly 16.97 cm, which is closest to option C. (16 cm).
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the annual rainfall in 2017 in opuwo was 420mm.
the annual rainfall in 2018 was 12% more than in 2017.
Answer:
470.4 mm
Step-by-step explanation:
Given: the annual rainfall in 2017 in opuwo was 420 mm, the annual rainfall in 2018 was 12% more than in 2017.
First, find 12% of 420 mm:
12% of 420 mm
[tex]\frac{12}{100}[/tex] x 420 mm
1.2 x 420 mm
= 50.4 mm
Then add 50.4 mm to the previous annual rainfall of 420 mm:
50.4 mm + 420 mm
= 470.4 mm
Therefore, the annual rainfall in opuwo in 2018 is 470.4 mm.
1. Find an equation for the line with the given properties.
Perpendicular to the line x = 5; containing the point (5,6)
y =
2. Find an equation for the line with the given properties. Use lowercase letter x for the variable.
Parallel to the line 7x - y = -7; containing the point (0,0)
y =
3. Find an equation for the line with the given properties.
Slope undefined; containing the point (8,2)
For the first question, the equation for the line is y = -x + 11. This comes from the fact that the slope for a line perpendicular to the line x = 5 is -1. From there, we can use the point (5,6) to calculate the y-intercept, which is 11.
For the second question, the equation for the line is y = 7x. This comes from the fact that the slope for a line parallel to the line 7x - y = -7 is 7. Since the point (0,0) is already on the line, the equation is already solved.
For the third question, the equation for the line is x = 8. This comes from the fact that the slope for a line with an undefined slope is 0. Since the point (8,2) is already on the line, the equation is already solved.
LaShawn’s class raised $500 for a fundraiser.
They used 10% of the money to cover the cost of materials, saved 20% for the next fundraising project, and donated the rest.
How much money did LaShawn’s class donate?
LaShawn's class donated $350 for the fundraiser.
How to find Percent of amount of money?LaShawn's class raised $500 for the fundraiser, and they used 10% of the money to cover the cost of materials. That means they spent:
[tex]$$0.1 \times 500 = 50$$[/tex]
So they spent $50 on materials. Next, they saved 20% of the money for the next fundraising project. That means they saved:
[tex]$$0.2 \times 500 = 100$$[/tex]
So they saved $100 for the next project. To find out how much money they donated, we can subtract the amount spent on materials and the amount saved from the total amount raised:
500 - 50 - 100 = 350
Therefore, LaShawn's class donated $350 for the fundraiser.
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Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading greater than 0.28°C. Round your answer to 4 decimal places
The probability of obtaining a reading greater than 0.28°C is 0.3897.
What is standard normal distribution ?
The standard normal distribution is a specific type of probability distribution that has a mean of 0 and a standard deviation of 1. It is also called the Z-distribution or the Gaussian distribution.
The standard normal distribution is commonly used in statistics and probability theory to make comparisons and calculations across different normal distributions. To use the standard normal distribution for calculations involving a normal distribution with a different mean and standard deviation, the data must be standardized by subtracting the mean and dividing by the standard deviation.
According to the question:
To solve this problem, we need to standardize the value of 0.28°C using the standard normal distribution formula:
z = (x - mu) / sigma
where:
x = 0.28°C
mu = 0°C
sigma = 1.00°C
Substituting the values, we get:
z = (0.28 - 0) / 1.00
z = 0.28
Now, we need to find the probability of obtaining a reading greater than 0.28°C, which is the same as finding the area to the right of z = 0.28 on the standard normal distribution curve. We can use a standard normal distribution table or calculator to find this area.
Using a calculator or software, we find that the probability of obtaining a reading greater than 0.28°C is 0.3897, rounded to 4 decimal places.
Therefore, the probability of obtaining a reading greater than 0.28°C is 0.3897.
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