The simple interest rate on the account is 13%
Here Sunil deposited $400 for one and a half years, and the interest he gets is $78. He deposits in at the simple rate of interest.
We know that the simple interest formula is
Simple interest = Principle × time × rate/ 100
It is given that,
simple interest = $78
time = 1 [tex]\frac{1}{2}[/tex] year = 3/2 year
Principle = $400
Let the rate of interest be r
So we have
78 =( 400 × 3/2 × r )/100
r =( 78 × 2×100) / (400 × 3)
r = 39%
Therefore the simple interest rate on the account is 13%.
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7. Kevin can run a lap around the field in 4-6 minutes. If he has 30 minutes to run, how
many laps is he able to finish?
The number of laps that Kevin can run is 5 laps.
How to calculate the number of laps?From the information, Kevin can run a lap around the field in 4-6 minutes and he has 30 minutes to run.
Therefore, the number of laps that he can run will be:
= Total minutes / Time taken for each lap
= 30 minutes / 6
= 5 laps.
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f(x) = x²
What is f(x) + f(x) + f(x)?
The result of the given expression f(x) + f(x) + f(x) = 3x².
What is defined as the quadratic function?A quadratic function is one of the following: f(x) = ax² + bx + c, where a, b, and c are positive integers and an is not equal to zero.
A parabola is a curve that represents the graph of a quadratic function. Parabolas can open up or down, and their "width" or "steepness" can vary, but they all share the identical basic "U" shape.A quadratic equation is defined in mathematics as an equation of degree 2, which means that the highest exponent of the this function is 2.As per the given question;
f(x) = x²
Now, we have to estimate the value of the function;
= f(x) + f(x) + f(x)
Substitute the value of f(x).
= x² + x² + x²
= 3x²
Thus, the value of the given function is found as 3x².
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The graph shows the cost, c, in dollars of using a carpooling
service for d days. Which equation represents the cost of the carpooling service?
A c = = d
B c = 6d
C d = 6c
D c = 6
Answer: where is the graph?
suppose that a function f has domain (-2,2) and range (-3,5). what is the domain of the function f(2x)?
The domain of the function f(2x) is (-1, 1).
Given that a function f has domain (-2,2) and range (-3,5).
We need to determine the domain of the function f(2x).
To determine the domain of the function f(2x), we need to consider how the original domain (-2,2) is affected by the transformation of multiplying the input by 2.
When we multiply x by 2, it stretches or compresses the function horizontally.
In this case, multiplying by 2 will stretch the original domain by a factor of 1/2.
To find the new domain, we divide the original domain endpoints by 2:
New domain = (-2/2, 2/2) = (-1, 1)
Therefore, the domain of the function f(2x) is (-1, 1).
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Where on the number line would you plot the square roots of the numbers 70, 85, 99, and 112?
a. 4
b. 5
c. between 4 and 5
d. between 64 and 125
We have to plot the square roots of the numbers 70, 85, 99, and 112 between 64 and 125 ( d )
First, we must evaluate the square root of given numbers.
√70 = √ ( 2 × 5 ×7 ) = 8.36
√85 = √ ( 5 × 17 ) = 9.22
√99 = √( 9 × 11 ) = 3√11 = 9.95
√112 = √( 4 × 4 × 7 ) = 4 √7 = 10.58
All these numbers ( 8.36, 9.22, 9.95 , 10.58 ) belong between, square roots of √64 and √125 which are 8 and 15. So we have to put these numbers in between the square roots of 64 and 125 on the number table.
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Simplify the expression.
a + b + 2a + 2b + 5 - b
3a + 2b + 5
3a + 4b + 5
2a + 4b + 5
2a + 2b + 5
Answer:
the answer is 3a+2b+5.
I hope this will help
Evaluate the expression with its given values. 5 x − 2 y ; x = 2 , y = − 1
The value of the given expression (5 x − 2 y) = 12.
What is substituting method:The substitution technique is an algebraic approach for solving simultaneous linear equations. In this procedure, the value of one variable through one equation is substituted in the second equation, as the name implies.
What is the substitution technique formula?Three phases are involved in the substitution method: Solve one equation for one of the variables. Substitute (plug-in) this expression in the other equation as well as solve. Replace the value in the original equation to obtain the equivalent variable.
According to the given data:5 x − 2 y
x = 2;
y = -1;
substituting the value in the given equation:
5 x − 2 y
5(2) - 2(-1)
5(2) - (-2)
5(2) +2
10+2
12
The value of the given expression (5 x − 2 y) = 12
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Rosa ran the hurdles in 58.32 seconds. maya ran the hurdles in 54.078 seconds. what is the difference between the two times? 3.954 seconds 4.242 seconds 4.258 seconds 5.758 seconds
Answer:
Step-by-step explanation: 4.242
The difference of time taken by Rosa and Maya to ran the hurdles is 4.242 seconds .
The correct option is B .
Given, time taken by Rosa and Maya to ran the hurdles.
Time taken by Rosa to ran the hurdle = 58.32 seconds .
Time taken by Maya to ran the hurdle = 54.078 seconds .
Difference between the time taken:
Rosa is taking more time to cover the distance than Maya . Thus the speed of Rosa is less than the speed of Maya .
Relationship between speed, time and distance.
Distance = Speed × Time
Subtract time taken by Rosa to ran the hurdle from time taken by Maya to ran the hurdle.
= 58.32 - 54.078
= 4.242 seconds
Therefore the correct option is B .
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Name the geometric term modeled by the given object.
a telephone pole
The geometric term modeled by the given object (a telephone pole) is a line
How to determine the geometric term?The given object is a telephone pole
The pole of a telephone pole is often straight.
This means that the telephone pole can be modelled by a line segment
Hence, the geometric term modeled by the given object (a telephone pole) is a line
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. Tell whether (7,-4) is a solution of y ≥ 5 - x.
(7,-4) is not a solution of the inequality y ≥ 5 - x
How to tell whether (7,-4) is a solution of y ≥ 5 - x?The inequality expression is given as
y ≥ 5 - x
The solution is given as:
(7, -4)
This means that
(x, y) = (7, -4)
Substitute (x, y) = (7, -4) in the inequality y ≥ 5 - x
So, we have
-4 ≥ 5 - 7
Evaluate the difference
-4 ≥ -2
On the numbering system, -4 is less than -2
Hence, (7,-4) is not a solution of the inequality y ≥ 5 - x
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Randy's swimming coach kept track of his average 50-meter lap times during the first 3 weeks of training. How much greater was the percent of change from Week 1 to Week 2 than from Week 2 to Week 3? Round to the nearest tenth of a percent.
The percent of the first change is greater by 2.36%.
Time in 1st week = 28.8 sec
Time in 2nd week = 27.6 sec
Time in 3rd week = 27.1 sec
∴ Change of time from week 1 to week 2 = (28.8 - 27.6) sec
= 1.2 sec
∴ Percent of change from week 1 to week 2 = [tex]\frac{time change}{1st week time} \times 100[/tex] %
= [tex]\frac{1.2}{28.8} \times 100[/tex] %
= 4.17%
∴ Change of time from week 2 to week 3 = (27.6 - 27.1) sec
= 0.5 sec
∴ Percent of change from week 2 to week 3 = [tex]\frac{Time change}{2nd week time} \times 100[/tex] %
= [tex]\frac{0.5}{27.6} \times 100[/tex] %
= 1.81%
∴ The greater change was in the first week. The amount by which it was greater is = (4.17 - 1.81) %
= 2.36%
Answer) The percent of the first change is greater by 2.36%.
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25 ft
2 ft
24 ft
Is it impossible?
By applying the criterion of the law of cosine, the triangle presented in the picture is possible.
Is this triangle possible?
Herein we find an hypothetical triangles with all side lengths known. A criterion is using the law of cosine, a possible triangle has cosine values between - 1 and 1. Then, we proceed to check for each side:
cos A = - (a² - b² - c²) / (2 · b · c)
cos A = - (25² - 2² - 24²) / (2 · 2 · 24)
cos A = - 0.469
cos B = - (b² - a² - c²) / (2 · a · c)
cos B = - (2² - 25² - 24²) / (2 · 25 · 24)
cos B = 0.998
cos C = - (c² - a² - b²) / (2 · a · b)
cos C = - (24² - 25² - 2²) / (2 · 25 · 2)
cos C = 0.53
Since the law of cosine gives realistic results, then the triangle presented in the picture is possible.
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Andrea, Roberto, Charlene, Maria, and Nguyen volunteer their time as computer science tutors after school. Due to their
schedules, though, they are only able to tutor on certain school days:
Andrea is able to tutor every second school day (every other school day).
Roberto is able to tutor every third school day.
Charlene is able to tutor every fourth school day.
Maria is able to tutor every sixth school day.
Nguyen is able to tutor every ninth school day.
If all five people are tutoring together today, how many school days from today will be the next time all five tutor together again?
From today 36 days later, all five will be tutoring again.
As we have given that,
Andrea is able to tutor every second school day
Roberto is able to tutor every third school day.
Charlene is able to tutor every fourth school day.
Maria is able to tutor every sixth school day.
Nguyen is able to tutor every ninth school day.
So, as a result, our working days are 2, 3, 4, 6, and 9 days.
Today's tutoring session will involve all five participants.
Next time, all five tutors will work together = LCM (2, 3, 4, 6, 9) = 36
Therefore, from today 36 days later, all five will be tutoring again.
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Yo help please I need this done it's about rational or irrational numbers u have to figure out if it's either rat or irr. If it's rational then figure out if it is a integers. If it's a integers then figure out if it's a whole number if it is then figure out if it's a natural number. Here's the order of it. R I W N and if it's irr then it's just I
All the numbers have been analyzed for being rational and irrational .
For -1 :
It is a rational number = R
It is an integer = I
For 2 / 3:
It is a rational number = R
For - 4.8 :
It is a rational number = R
For 7:
It is a rational number = R
It is an integer = I
It is an whole number = W
It is a natural number = N
For - 32 / 95
It is a rational number = R
For - 20 / 4 = -5:
It is a rational number = R
It is an integer = I
For 0:
It is a rational number = R
It is an integer = I
It is an whole number = W
For - 7.34:
It is a rational number = R
For 7 / 1239:
It is a irrational number = I
For √5:
It is a irrational number = I
Therefore, all the numbers have been analyzed for being rational and irrational .
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which is the midpoint of AB?
Please help I’ll give Brainliest answer to whoever is correct
NEED HELP FAST, GIVING AWAY 99 POINTS.
Evaluate the numerical expression.
3/2 − (−1/4)
A -1/2
B -3/2
C 7/4
D 4/5
Answer:
The answer is C. 7/4 :)
5 1-3a
Note: Please make sure to properly format your answers. All dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include the comma
($2,354.67). All percentage values in the answers need to include a percentage sign (%). For all items without specific rounding instructions, round your answers to two decimal
places, show both decimal places (5.06).
The variance of a distribution is 195. What is the standard deviation, rounded to the nearest thousandth?
Applying the square root of the variance, the standard deviation of the distribution is of 13.964.
What is the standard deviation of a distribution?The standard deviation of a distribution is given by the square root of the variance of the distribution.
For this problem, the variance of the distribution is of 195, hence the standard deviation is:
s = sqrt(195) = 13.964.
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How many times greater is 70,000 than 7,000?
Answer
70.000 в 10 раз больше 7.000
Step-by-step explanation:
Evaluate the expression when x=3 , y=−4 , and z=−6.
z−2xy=
x = 3 , y = −4 , and z = −6
z-2xy =
Substitute the value of x,y and z in the expression.
-6-2(3)(-4)
-6-2(-12)
-6+24
18
Determine which sequences of transformations could be applied to the parent function, f(x) = x, to obtain the graph above. Reflect over the y-axis, vertically stretch by a factor of 2, and then shift up 6 units Shift left 3 units, reflect over the y-axis, and then vertically stretch by a factor of 2 Shift up 6 units, reflect over the x-axis, and then vertically stretch by a factor of 2 Shift left 2 units, reflect over the y-axis, and then vertically stretch by a factor of 6 Reflect over the x-axis, vertically stretch by a factor of 2, and then shift up 6 units Shift right 3 units, reflect over the y-axis, and then vertically stretch by a factor of 2
The sequence of transformations could be applied to the parent function, f(x) = x, to obtain the graph is E. Shift up 6 units, reflect over the x-axis, and then vertically stretch by a factor of 2.
What is transformation?It should be noted that transformation simply means the movement of an object from a position to another position.
In this case, the sequence of transformations could be applied to the parent function, f(x) = x, to obtain the graph is to shift up 6 units, reflect over the x-axis, and then vertically stretch by a factor of 2.
Therefore sequence of transformations could be applied to the parent function, f(x) = x, to obtain the graph is E. Shift up 6 units, reflect over the x-axis, and then vertically stretch by a factor of 2.
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Solve for X
4(5x+6)=12
-3(2x-4)=18
26=2(3x-2)
The value of x in the equations are:
1. x = -3/5
2. x = -1
3. x = 5
How to Solve an Equation?Given the equations above, to solve for x, isolate x as the variable in the equation to one side of the equation.
a. 4(5x+6) = 12
Apply the distributive property
20x + 24 = 12
20x = 12 - 24
20x = -12
x = -12/20
x = -3/5
b. -3(2x - 4) = 18
Apply the distributive property
-6x + 12 = 18
-6x + 12 - 12 = 18 - 12
-6x = 6
x = 6/-6
x = -1
c. 26 = 2(3x - 2)
Apply the distributive property
26 = 6x - 4
26 + 4 = 6x
30 = 6x
5 = x
x = 5
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The recommended mass of a Soccer ball is 0.43 kilogram. The actual mass is allowed
to vary by up to 20 grams.
a. Write and solve an absolute value equation to find
the minimum and maximum acceptable soccer ball
masses.
b. A soccer ball has a mass of 423 grams. The soccer
ball loses 0.016 kilogram of mass over time. Is the
mass now acceptable? Explain.
The absolute value equation is:
|M - 430g| = 20g
And the solutions are M = 410g and M = 450g
b) No, the mass is not acceptable.
How to write the absolute value equation?We know that the recomended mass is 0.43kg, with an accepted error of 20 grams.
Where:
0.43kg = 0.43*1000g = 430g
Then the minimum mass accepted is: 430g - 20g = 410g
The maximum mass accepted is: 430g + 20g = 450g
These are the solutions, and the absolute value equation is, if M is the mass:
|M - 430g| = 20g
b) If the ball has a mass of 423g it is in the accepted range, if now it loses 0.016kg:
0.016kg = 0.016*1000g = 16g
The new mass is:
423g - 16g = 407g
This is smaller than the minimum accepted mass, then this mass is not acceptable.
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So i am have homework and it is asking me to show the ratios are equivalent by simplifying any 4 of them and i am stuck in that one i don't understant that can you help me pls can u explain me
The ratios are shown equivalent as by simplification done below.
Ratio is the representative of comparison of part of things in a complete thing. Equivalent ratios are collection of ratios that show same comparison. As per the given question, the equivalent ratios are calculated as follows -
First column -
Ratio = 6:2
Dividing both the parts of ratio by 2
Ratio = 3:1
Second column -
Ratio = 9:3
Dividing both the parts of ratio by 3
Ratio = 3:1
Third column -
Ratio = 12:4
Dividing both the parts of ratio by 4
Ratio = 3:1
Fourth column -
Ratio = 15:5
Dividing both the parts of ratio by 5
Ratio = 3:1
Similarly, for rest of the columns, division by 6, 7 and 8 of both parts of ratio will give the result 3:1. Hence, the given rations are shown as equivalent ratios, by simplifying into 3:1.
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How many 5-letter words can be made from the letters WASTEFUL if
repetition of letters is allowed? And if repetition is not allowed
Answer w a s t e f u l
Step-by-step explanation:
theres 7 words on it
Any genius willing to help :) , I'll give you a brainliest if you do.
Answer:
00
Step-by-step explanation:
a certain composer wrote 10 symphonies, 4 piano concertos (music for piano and orchestra), and 35 piano sonatas (music for solo piano). a. how many ways are there to play first a symphony and and then a piano concerto? b. the manager of a radio station decides that on each successive evening (7 days a week), a symphony will be played followed by a piano concerto followed by a piano sonata. for how many nights could this be carried out before exactly the same program would have to be repeated? about how many years would this be? (round to the nearest year).
(a) According to the question, a composer wrote [tex]10[/tex] symphonies, [tex]4[/tex] piano concerts (piano and orchestra) and [tex]35[/tex] piano sonatas (solo piano):
Here, determine how many ways are there to play first a symphony and then piano concerto.
So, the probability is [tex](10P1) (4P1) = (10)(4)= 40[/tex]
Therefore, there are [tex]40[/tex] ways to play first a symphony and then piano concerto.
(b)The manager of a radio station decides that on each successive evening, a symphony will be played followed by a piano concerto followed by a sonata.
Here determine how many nights could be carried out before the same program would get repeated.
So, the probability would be [tex](35)(10)(4)=1440[/tex]
Therefore, [tex]1440[/tex] nights are carried out before the same program gets repeated.
Now, to calculate the years: [tex]\frac{1440 nights}{365days} = 3.95 years[/tex]
Therefore, it would be [tex]3.95[/tex] years.
What is probability?
Probability is the method to measure the occurred events or the occurrence of the events. It is also used to analyze the outcomes of random events. For example, to calculate the probability of a playing card which is 52 in numbers. And it is divided into four cards and each are in the count of 13.These four cards are heart, spades, diamond and club.
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It takes Mike 18 minutes to finish reading 4 pages of a book. How
long does it take for him to finish reading 30 pages?
Answer:
135 minutes
Step-by-step explanation:
18 divided by 4
4.5 pages per minute
4.5 times 30 = 135
Answer: 135 minutes
Step-by-step explanation: 18 times 30, then divide by 4
Evaluate the expression when a = 7 and c= -3.
-a+4c
Hello,
[tex] - a + 4c = - 7 + 4 \times ( - 3) = - 7 - 12 =- 19[/tex]
Answer:
-19
Step-by-step explanation:
-7 + 4(-3)
-7 - 12= -19
State the property that justifies the statement.
If x/3=-15, then x=-45.
The value of x will be -45 by the multiplicative property for the given expression x/3=-15.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
The given expression is x/3=-15. The value of x will be calculated as below:-
x/3=-15.
x = -15 x 3
x = -45
Therefore, the value of x will be -45 by the multiplicative property.
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1. Turn this standard notation 25,000,000 into scientific notation.
Answer:
25,000,000 = 2.5 × 10^7
The ^ is raised to the power.
Hope this helps :)
Step-by-step explanation:
2.5 × 10^7 = 25,000,000