The speed of airplane in miles per hour (mph) is 380.2968 .
What is speed?
Speed is the time rate at which an object is moving along a path. The SI unit of speed is meter per second ( m/s ). Miles per hour ( mph ) is a British imperial and United States customary unit of speed expressing the number of miles travelled in one hour.
Given that
Speed of a certain airplane = 170 m/s or m[tex]s^{-1}[/tex]
We know that
In 1 meter = 0.0006214 miles
In 1 sec = [tex]\frac{1}{3600}[/tex] hour
but 1 [tex]sec^{-1}[/tex] = 3600 hour
Speed of this airplane in miles per hour = 170 × 0.0006214 × 3600 mph
= 0.105638 × 3600 mph
= 380.2968 mph
Hence, the speed of airplane in miles per hour (mph) is 380.2968 .
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The height of the real painting is 24 inches. What is the height of the painting in the scale drawing? (b)In the scale drawing, the length of the painting is 7 centimeters. What is the length of the real painting?
The scale drawing height is 4 cm and the actual drawing length is 42 in
The height of the painting in the scale drawingThe complete question is added as an attachment
From the attachment, we have the ratio to be given as
Scale ratio, 1 cm : 6 in
Rewrite as
Scale measurement : Actual measurement = 1 cm : 6 in
In this question, we have
Actual measurement = 24 inches
This means that
Scale measurement : 24 in = 1 cm : 6 in
Multiply 1 cm : 6 in by 4
Scale measurement : 24 in = 4 cm : 24 in
By comparison, we have
Scale measurement = 4 cm
Hence, the scale drawing height is 4 cm
What is the length of the real painting?Recall that
Scale ratio, 1 cm : 6 in
Rewrite as
Scale measurement : Actual measurement = 1 cm : 6 in
In this question, we have
Scale measurement = 7 cm
This means that
7 cm : Actual measurement = 1 cm : 6 in
Multiply 1 cm : 6 in by 7
7 cm : Actual measurement = 7 cm : 42 in
By comparison, we have
Actual measurement = 42 in
Hence, the actual drawing length is 42 in
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What is another way to represent an angle in standard position that has a measure of 530º
By finding coterminal angles, we conclude that another way of writing the angle 530° is 170°.
In which other way can we represent the angle?For any angle A, we define the family of coterminal angles B as:
B = A + n*360°.
Where n is an integer different than zero.
In this case we have A = 530°
Then the coterminal angles are:
B = 530° + n*360°
If we define n = -1, then:
B = 530° - 360° = 170°
So 170° is another way of writing 530°.
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Any buyer of a new sports car has to pick between 2 of 5 seat colors and 3 of 4 options for dashboard accessories. How many different combinations of colors and dashboard options are available to this buyer?
Different combinations of colors and dashboard options are available to the buyer who can pick between 2 of 5 seat colors and 3 of 4 options for dashboard accessories is 40.
As given in the question,
Possible combination for any buyer of a new sports car
Pick between 2 of 5 seat colors
⁵C₂ = 5! / (2!)(5-2)!
= 5!/ (2!)(3!)
= 10
Pick between 3 of 4 options for dashboard accessories
⁴C₃ = (4!)/ (3!)(4-3)!
= (4!)/ (3!)(1!)
= 4
Total different combinations of colors and dashboard options = 10 × 4
= 40
Therefore, different combinations of colors and dashboard options are available to the buyer is 40.
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What is the exact circumference of the circle if the diameter is 16?
Carmen has 4 tomatoes she will eat this week. The first tomato Carmen will eat weighs 2/8 of a pound .which point on the number line represents the first tomato Carmen will eat
The point on the number line which represents the first tomato Carmen will eat is: B. K.
What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.
In Mathematics, a number line typically increases in numerical value towards the right and decreases in numerical value towards the left.
By critically observing the number line (see attachment) which models the weight of the tomatoes Carmen would eat, we can logically deduce that each of the interval represent 1/8 pound.
First tomato = 2/8
First tomato = 1/8 + 1/8 ≡ 2/8 = point K.
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Complete Question:
Carmen has 4 tomatoes she will eat this week. The first tomato Carmen will eat weighs 2/8 of a pound. Which point on the number line represents the first tomato Carmen will eat?
A. J
B. K
C. L
D. M
Find the value of x.
57°
79°
X
what is the multiplicative inverse of -7 / 5
That is the answer
PLS HELP GAVE ME THE RIGTH ASWER AND I WILL GIVE LOTS OF POINTS I NEED IT RIGHT CAUSE ITS A GRADE PLS
What is the correct answer to this question
Answer:
The transversal is not part of this triangle.
2/7 of 5/6 (3 1/3 * 2/5) by 1/5 equals to
[tex] \frac{2}{7} \times \frac{5}{6} ( \frac{10}{3} \times \frac{2}{5} ) \times \frac{1}{5} \\ = \frac{2}{7} \times \frac{5}{6} ( \frac{20}{15} ) \times \frac{1}{5} \\ = \frac{2}{7} \times \frac{100}{90} \times \frac{1}{5} \\ = ( \frac{2}{7} \times \frac{10}{9}) \times \frac{1}{5} \\ = \frac{20}{63} \times \frac{1}{5} \\ = \frac{20}{315} \\ = \frac{4}{63} [/tex]
ATTACHED IS THE SOLUTION
Which expression is equivalent to (4.3x + 4)(-1.8x)?
A.-4.14x² +0.08x
B.-7.74x2 - 7.2
C.-7.74x² - 7.2x
D.-7.74x² + 7.2x
PLSSS ANSWER QUICK
Step-by-step explanation:
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Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production
process. Assume a production process produces items with a mean weight of 15 ounces.
a. The process standard deviation is 0.20, and the process control is set at plus or minus 0.75 standard deviation. Units with
weights less than 14.85 or greater than 15.15 ounces will be classified as defects. What is the probability of a defect (to 4
decimals)?
In a production run of 1000 parts, how many defects would be found (round to the nearest whole number?
b. Through process design improvements, the process standard deviation can be reduced to 0.07. Assume the process control
remains the same, with weights less than 14.85 or greater than 15.15 ounces being classified as defects. What is the probability of
a defect (round to 4 decimals; if necessary)?
In a production run of 1000 parts, how many defects would be found (to the nearest whole number)?
c. What is the advantage of reducing process variation, thereby causing a problem limits to be at a greater number of standard
deviations from the mean?
Using the normal distribution, it is found that:
a) The probability of a defect is of 0.4532, and out of 1000 parts, 453 will be classified as defective.
b) The probability of a defect is of 0.0324, and out of 1000 parts, 32 will be classified as defective.
c) The reduction in the variability also reduces the number of defective parts.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable that has mean given by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above(in case the score is positive) or below(in case the score is negative) the mean. From the z-score table, the p-value associated with the z-score is found, which represents the percentile of the measure X.For item a, the mean and the standard deviation are given as follows:
[tex]\mu = 15, \sigma = 0.2[/tex]
The proportion of defectives is two times the p-value of Z when X = 14.85, as 14.85 and 15.15 are the same distance from the mean and the normal distribution is symmetric, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (14.85 - 15)/0.2
Z = -0.75
Z = -0.75 has a p-value of 0.2266.
2 x 0.2266 = 0.4532 = 45.32%
Out of 1000, the number of defectives is:
0.453 x 1000 = 453.
For item b, we have that [tex]\sigma = 0.07[/tex], hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (14.85 - 15)/0.07
Z = -2.14
Z = -2.14 has a p-value of 0.0162.
2 x 0.0162 = 0.0324.
Out of 1000, the number of defectives is:
0.032 x 1000 = 32.
For item c, we can see that the reduction of variability will make the parts having measures closer to the desired, hence reducing the number of defectives.
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A principal of $3100 is invested at 3.75% interest, compounded annually. How much will the investment be worth after 9 years? Use the calculator provided and round your answer to the nearest dollar
he Solution:
iven:
[tex]\begin{gathered} P=Principal=\text{ \$}3100 \\ \\ r=rate=3.75\text{\%} \\ \\ t=time=9years \end{gathered}[/tex]We are required to find the amount the investment will be worth after 9 years.
he Compound interest formula:
[tex]A=P(1+\frac{r}{100})^n[/tex]In this case:
[tex]\begin{gathered} A=amount=? \\ P=\text{ \$3100} \\ r=3.75\text{ \%} \\ n=9\text{ years} \end{gathered}[/tex]Substitute:
[tex]A=3100(1+\frac{3.75}{100})^9=3100(1.0375)^9=4317.7217\approx\text{ \$}4318[/tex]Therefore, the correct answer is $4318
5s • 2 to the power of 3 + (h-1)to the power of 2
What is the value of the expression when: h= 4 and s = -1?
A -49
B -31
C 49
D 164
The most appropriate choice for exponent will be given by-
-31 is the required answer. The second option is correct
What are exponent?
Exponent tells us how many times a number is multiplied by itself.
For example : In [tex]2^4 = 2\times 2\times 2\times 2[/tex]
Here, 2 is multiplied by itself 4 times.
If [tex]a^m = a \times a \times a \times.....\times a[/tex] (m times), a is the base and m is the index.
The laws of index are
[tex]a^m \times a^n = a^{m + n}\\\frac{a^m}{a^n} = a^{m - n}\\a^ 0 =1\\(a^m)^n = a^{mn}\\(\frac{a}{b})^m = \frac{a^m}{b^m}\\a^{-m} = \frac{1}{a^m}[/tex]
Here,
[tex]5s \times 2^3 + (h-1)^2\\h = 4, s = -1\\5(-1) \times 8 + (4 - 1)^2\\-40 + 9\\-31[/tex]
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The length of a swimming pool is triple the width. The area of the pool is 6627 ft2. Find the length and width of the pool.
For the given statement, the length and width of the pool are 141 feet and 47 feet respectively.
What is meant by the area of the rectangle?The area occupied by the rectangle within its perimeter can be calculated using the formula for the area of a rectangle. In the aforementioned illustration, a rectangle with dimensions of 4 inches long by 3 inches wide has a surface area of 12 square inches. 4 plus 3 equals 12, so. A rectangle's area is calculated by multiplying its length by its width. Therefore, the product "l w" is the formula for the area, "A," of a rectangle whose length and breadth are "l" and "w," respectively.
Rectangular area is equal to (length breadth) square units.
Given,
length of the pool = 3 (width of the pool)
Let width of the pool = x
Length of the pool = 3x
Area of the pool = Length × Width
6627 = x × 3x
⇒ 3x² = 6627
⇒ x² = 2209
⇒ x = 47
⇒ 3x = 47 × 3
⇒ 141
This implies that the length and width of the pool are 141 feet and 47 feet respectively.
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Find domain and range of this function using h interval motion
Answer:
Domain: [-1, 4)Range: [-5, 4]Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Find the circumference of a circle with diameter, d = 2.76m. Give your answer rounded to 2 DP.
The circumference of a circle with diameter 2.76 m is 8.66 m.
What is Circumference?
Circumference of a circle is perimeter of circle.
Given that;
Diameter of a circle = 2.76 m
Since, Circumference of a circle = 2πr
Where, r is radius of circle.
Now, Diameter of a circle = 2.76 m
Then, Radius of a circle = 2.76/2 = 1.38 m
Hence, Circumference of a circle = 2πr
Substitute all the values;
Circumference of a circle = 2 x 3.14 x 1.38
= 8.66 m
Thus, The circumference of a circle with diameter 2.76 m is 8.66 m.
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The table shows the linear relationship between the amount of water being pumped
out of a pool over time.
Based on the table, what was the rate of change of the amount of water being
pumped out of the pool over time?
The rate of change of water being pumped out of the pool over time is (C) -2.
What is a linear relationship?A straight-line relationship between two variables is referred to statistically as a linear relationship (or linear association). Linear relationships can be represented graphically or mathematically as the equation y = mx + b.So, the linear relationship is:
x = 1, y = 8x = 2, y = 6x = 3, y = 4x = 4, y = 2Look at the values of y: 8, 6, 4, 2
The pattern is 8 - 2 = 6; 6 - 2 = 4; 4 - 2 = 2So, the rate of change will be -2.
Therefore, the rate of change of water being pumped out of the pool over time is (C) -2.
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The complete question is given below:
The table shows the linear relationship between the amount of water being pumped out of a pool over time. Based on the table, what was the rate of change in the amount of water being pumped out of the pool over time?
(A) 2
(B) 10
(C) -2
(D) -10
Only questions #9,13,17,21,25 please show work
THANK YOU
Simplification of the given expression to single complex number are as follow :
9. -11 +4i
13. 30 - 10i
17.20
21. (3 + 5i)/2
25. -1
As given,
To simplify the following expressions to a single complex number,
9) (- 5 + 3 i) - (6 - i)
= - 5 + 3 i - 6 + i
= - 5 - 6 +3i + i
= - 11 + 4 i
13) (6 - 2 i) 5
= (6 x 5) - (2 x 5) i
= 30 - 10 i
17) (4 - 2 i) (4 + 2 i)
= [tex]4^{2} - (2i)^{2}[/tex]
= 16 - 4 [tex]i^{2}[/tex]
= 16 - 4 (-1)
= 16 + 4
= 20
21) [tex]\frac{-5+3i}{2i} = \frac{i(-5+3i)}{2i^{2}} = \frac{-5i + 3i^{2} }{2(-1)}[/tex]
= [tex]\frac{-5i+3(-1)}{-2} = \frac{3+5i}{2}[/tex]
25) [tex]i^{6} = (i^{2})^{3} = (-1)^{3} = -1[/tex]
Note: To simplify a fraction where denominator has complex component (i) as coefficient, multiply both numerator and denominator by i to eliminate i from denominator (by converting it to real number)
Therefore, simplification of the given expression to single complex number are as follow :
9. -11 +4i
13. 30 - 10i
17.20
21. (3 + 5i)/2
25. -1
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the temperature at sunrise is 25° each hour the temperature rises 5° write an equation that models the temperature y in degrees Fahrenheit after x hours . what is the graph of the equation
EXPLANATION
Let's see the facts:
Sunrise temperature = 25°
Rate= 5°/hour
So, the temperature after x hours is given by the expression:
Temperature after x hours= Sunrise temperature + Number of hours*Rate
Substituting terms:
T= 25 + 5x
Now, with this relationship we can build the graph:
Which of the following expressions are equivalent? Justify your reasoning.Question 5
Answer:
Explanation:
A) Given the below expression;
[tex]\sqrt[4]{x^3}[/tex]The above can be written as;
[tex]\sqrt[4]{x^3}=(x^3)^{\frac{1}{4}}[/tex]Recall the below law of exponent;
[tex](a^n)^m=a^{nm}[/tex]Applying the above law of exponent to the expression, we'll have;
[tex](x^3)^{\frac{1}{4}}=x^{\frac{3}{4}}[/tex]B) Given the below expression;
[tex]\frac{1}{x^{-1}}[/tex]Recall the below law of exponent;
[tex]\frac{1}{a}=a^{-1}[/tex]Applying the above law of exponent to the expression, we'll have;
[tex]\frac{1}{x^{-1}}=x^{-1(-1)}=x^1=x[/tex]C) Given the below expression;
[tex]\sqrt[10]{x^5\cdot x^4\cdot x^2}[/tex]Recall the below laws of exponents;
[tex]\begin{gathered} a^m\cdot a^n=a^{m+n} \\ (a^n)^m=a^{^{nm}} \end{gathered}[/tex]Applying the above law of exponent to the expression, we'll have;
[tex]\begin{gathered} \sqrt[10]{x^{5+4+2}}=\sqrt[10]{x^{11}}^{}^{} \\ =(x^{11})^{\frac{1}{10}}=x^{\frac{11}{10}}^{}^{} \end{gathered}[/tex]D) Given the below expression;
[tex]x^{\frac{1}{3}}\cdot x^{\frac{1}{3}}\cdot x^{\frac{1}{3}}[/tex]Recall the below law of exponents;
[tex]a^n\cdot a^m=a^{n+m}[/tex]Applying the above law of exponent to the expression, we'll have;
[tex]x^{\frac{1}{3}}\cdot x^{\frac{1}{3}}\cdot x^{\frac{1}{3}}=x^{\frac{1}{3}+\frac{1}{3}+\frac{1}{3}}=x^{\frac{1+1+1}{3}}=x^{\frac{3}{3}}=x^1=x[/tex]We can see from the above that the below expressions are equivalent because they both yield the same result as x;
[tex]\begin{gathered} A)\sqrt[4]{x^3} \\ D)x^{\frac{1}{3}}\cdot x^{\frac{1}{3}}\cdot x^{\frac{1}{3}} \end{gathered}[/tex]The path of a diver is modeled by
f(x) = −
4
9
x2 +
24
9
x + 13
where f(x) is the height (in feet) and x is the horizontal distance (in feet) from the end of the diving board. What is the maximum height of the diver?
Answer:
Here's your answer :)
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A tank has 500 litres of salt water, which includes 10 kg of salt. At time t = 0, a solution of salt water (concentration 0.01 kg/l) is pumped in the tank at a rate of 10 l/min. At the same time, the tank starts to be emptied at rate of 20 l/min.
Use your knowledge of differential equations to solve an equation of the amount (mass) of salt within the tank at any given time t.
The differential equation used to solve an equation of the amount (mass) of salt within the tank at any given time t is [tex]\frac{ds}{0.04s-0.1} = dt[/tex].
What are differential equations?A differential equation in mathematics is an equation that connects the derivatives of one or more unknown functions. Applications often involve functions that reflect physical quantities, derivatives that depict the rates at which those values change, and a differential equation that establishes a connection between the two.Let the amount of salt any time t is given by s kg then the rate of change of s with respect to t is given by,
[tex]\frac{ds}{dt}[/tex] = (rate of salt out) - (rate of salt in)
Rate of salt in = 0.01 kg/litre × 10 litre/min = 0.1 kg/min
Rate of salt out = s/500 kg/litre × 20 litre/min = (20s/500) kg/min
A differential equation can be made on the concept that the rate of change of salt is the difference between the rate of in and the rate of out.
That gives us when combined,
[tex]\frac{ds}{dt} = 0.04s -0.1[/tex]
Now solving this differential equation,
[tex]\frac{ds}{0.04s-0.1} = dt[/tex]
Integrating both sides,
[tex]\int\ {\frac{ds}{0.04s-0.1} } \, = \int dt[/tex]
[tex]\frac{ln(0.04s -0.1)}{0.04} = t+C_{1}[/tex]
[tex]ln(0.04s - 0.1) = 0.04t +0.04C = 0.04t +C_{2}[/tex]
[tex]0.04s - 0.1 =e^{0.04t + C_{2} } =Ae^{0.04t}[/tex]
Now at t = 0, s = 10 kg
0.04(10) - 0.1 = A
A = 0.3
So the differential equation can be written as,
[tex]0.04s - 0.1 = 0.3e^{0.04t}[/tex]
Now time at which no salt is left which means s = 0 at some time t
[tex]0.1 - 0.04(0) = -0.3e^{-20t}[/tex]
The equation is not further solvable as we can see.
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If Kerel has 9 quarters and nickels in his pocket, and they have a combined value of 125 cents, how many of each coin does he have?
nickels
quarters
By using substitution method, if Kerel has 9 quarters and nickels in his pocket and they have a combined value of 125 cents, then he has 4 quarters and 5 nickels
Total number of coins = 9
Consider the number of quarters as x and number of nickels as y
Then the equation will be
x+y =9
x= 9-y
The combined value of the coins = 125 cents
We know
1 quarter = 25 cents
1 nickel = 5 cents
Then the equation will be
25x+5y = 125
Here we have to use the substitution method
Substitute the value of x in the equation
25(9-y)+5y = 125
225-25y+5y = 125
-20y = -100
y = 5
Substitute the value of y in the first equation
x = 9-y
x = 9-5
x= 4
Hence, by using substitution method, if Kerel has 9 quarters and nickels in his pocket and they have a combined value of 125 cents, then he has 4 quarters and 5 nickels
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Describe the transformation of f(x)=x2 represent by g. (Show Work)
Answer:
Shifty to right 1
Not shift to
2
Step-by-step explanation:
The transformation has a horizontal shift right by 1 units and vertical shift upwards by 3 units. The graph is shown below.
What do you mean by transformation of a graph ?
The modification of an existing graph or graphed equation to create a different version of the following graph is known as transformation.
The functions given are :
f(x) = x²
and
g(x) = (x - 1)² + 3
Now , we know that , the horizontal shift depends on the value of h. The horizontal shift is described as:
g(x) = f (x + h)
Then , the graph is shifted to left by h units.
and
g(x) = f (x - h)
Then , the graph is shifted to right by h units.
If we compare f(x) with g(x) , their is a difference of -1 , it meant shift is right by 1 units.
Now , we know that , the vertical shift depends on the value of k. The vertical shift is described as:
g(x) = f(x) + k
Then , the graph is shifted up by k units.
and
g(x) = f(x) - k
Then , the graph is shifted down by k units.
Here , if we compare f(x) with g(x) there is addition of 3 in g(x) , this meant the graph is shifted upward by 3 units.
The graph of the function is attached below. Here , both of the functions are graphed.
Therefore , the transformation has a horizontal shift right by 1 units and vertical shift upwards by 3 units. The graph is shown below.
Can someone help with this question?✨
The expression (-6 - 5i) + (-1 + 7i) in this form a + bi is -7 + 2i
How to evaluate an expression?The expression to be evaluated is as follows:
Therefore,
(-6 - 5i) + (-1 + 7i)
The expression can be express in the form a + bi as follows:
(-6 - 5i) + (-1 + 7i)
- 6 - 5i - 1 + 7i
Let's combine the like terms
- 6 - 5i - 1 + 7i
-6 - 1 - 5i + 7i
Let's do the arithmetic
-6 - 1 - 5i + 7i
Therefore,
-7 + 2i
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Shawn found it took him 429 steps to get from home to the outside basketball court. How many steps does it take to make 8 one-way trips? Choose the best estimate.
Based on the number of steps it took Shawn to get home from outside the basketball court, the number of steps needed for 8 one-way trips is 3,432 steps
How to find the number of steps?Each trip that Shawn takes from outside the basketball court to his house, and from his house to outside the basketball court, will take 429 steps.
If Shawn then takes 8 one - way trips, the number of steps till he gets either home or the basketball courts is:
= Number of steps per trip x Number of trips
= 429 x 8
= 3,432 steps
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The average price of gas in 1990 was $1.22 per gallon. The average price of gas in 2022 was $4.62 per gallon. What was the percent increase in the price of gas?
12. Evelyn deposited $5,000 into a savings
account that earns an annual simple
interest rate of 0.1%. To the nearest tenth
of a year, how long will it take for the
account to reach $5,750?
It takes 1.5 years for Evelyn to reach $5,750.
In this question, it is clear that principal amount that Evelyn deposited is $5,000. The annual interest rate as per the question is 0.1%. The final amount that Evelyn gets is $5,750.
Lets assume that it will take t years for Evelyn to get a final amount of $5,750.
So,
Principal amount, P = $5,000
annual rate, r = 0.1%
Final amount, A = $5,750
From the formula for simple interest, we have,
A = P( 1 + rt)
Hence, t = (1/r) x { (A/P) -1 }
= 1/0.1 x { (5750/5000) - 1}
= 10 x { 1.15 - 1 }
= 10 x 0.15
=1.5
Therefore it will take 1.5 years for Evelyn to get a total amount of $5,750 provided she deposited an amount of $5,000 at an annual simple interest rate of 0.1%
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any body help me please. I need answer of this question as soon as possible.
The number of ways to choose the total number of participants required by the event coordinator is 54,600.
The total number of boys who want to participate in the science competition organised by the Physics Department is 15.The total number of girls who want to participate in the science competition organised by the Physics Department is 10.The number of boys required by the event coordinator is 3.The number of girls required by the event coordinator is 3.The number of ways to choose the total number of participants required by the event coordinator is calculated by choosing 3 boys out of 15 boys and 3 girls out of 10 girls.Let "n" be the required number of ways.The concept of permutations and combinations is used here.n = (15C3)*(10C3)n = 455*120n = 54,600To learn more about permutations and combinations, visit :
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