keeping in mind that since a year is 12 months, then 4 months is really 4/12 of a year, so
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$ 20\\ P=\textit{original amount deposited}\dotfill & \$1000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\to \frac{4}{12}\dotfill &\frac{1}{3} \end{cases} \\\\\\ 20 = (1000)(\frac{r}{100})(\frac{1}{3})\implies 20=\cfrac{1000r}{300} \implies 6000=1000r \\\\\\ \cfrac{6000}{1000}=r\implies \stackrel{\%}{6}=r[/tex]
camila writes down five positive integers. the unique mode of these integers is 2 greater than their median, and the median is 2 greater than their arithmetic mean. what is the least possible value for the mode?
The least possible value for the mode is D=11
Let M be the median
According to the question, the two largest integers are M+2
Let a and b be the two smallest integers such that a<b
Accordingly, the sorted list can be concluded as a,b, M, M+2, M+2
Since the median is 2 greater than their arithmetic mean, we have,
{a+b+M+(M+2)+(M+2)/5 }+2 =M
OR, a+b+14=2M
Note that a+b must be even.
We minimize this sum so that the arithmetic mean, the median, and the unique mode is minimized.
Let a=1 and b=3
from which M=9 and
M+2=11
Therefore, The least possible value for the mode is D=11
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Find the minimum value of fsx, y, zd − x2 1 2y2 1 3z2 subject to the constraint x 1 2y 1 3z − 10. Show that f has no maximum value with this constraint
50/3 is the minimum function value.
∇f(x,y,z)=(2x,4y,6z)
∇g(x,y.z)=(1,2,3)
set up the system of equations:
2x=λ
4y=2λ
6z=3λ
x+2y+3z=10-----(1)
solve the first three equations for λ.
2x=λ
2y=λ
2z=λ
From these three equations, we conclude that
x=y=z.
Plug this into the constant equation.
x+2y+3z=10
x+2x+3x=10
6x=10
x=3/5
Therefore, there is one point of interest and it occurs at (5/3,5/3,5/3).
f (5/3,5/3,5/3)=50/3
This is the minimum function value. Notice that the function is unbounded above and therefore has no maximum.
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In ΔSTU, t = 390 cm, s = 900 cm and ∠S=48°. Find all possible values of ∠T, to the nearest degree
The values of ∠T is 18.78 degree.
In ΔSTU ,
We have:
T = 390 cm,
S = 900 cm
and ∠S=48°.
Using the sine rule which works law of sin with the formula:
[tex]\frac{SinT}{T} = \frac{SinS}{S}[/tex]
Plug all the values in above formula:
sinT/ 390 = sin48°/900
sin T = 0.743 × 390 / 900
sin T = 0.3220
T = [tex]sin^-^1[/tex](0.3220)
T = 18.78 degree.
Hence, The values of ∠T is 18.78 degree.
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I need help ASAP thanks if you do help!
Ty and Harrison are building signs for an upcoming craft fair. The relationship between x (the number of hours spent working) and y (the number of signs built) for each person is shown below.
Who is building signs at a faster rate?
Answer:
Harrison has the greater rate
If Ty can make 7 signs in 2 hours that means in 4 hours he could double that output to make 14 signs. Harrison, on the other hand, makes 15 signs every 4 hours.
Step-by-step explanation:
Convert each equation from slope-form to standard form
The conversion of the equation from slope-form to standard form is 3x + y = 2.
What is the slope-intercept form?In Mathematics, the slope-intercept form of a line is generally modeled by using this linear equation:
y = mx + b
Where:
m represents the slope.b represents the y-intercept.x and y are the data points.In Mathematics, the standard form of a linear function is is generally modeled by this mathematical expression:
Ax + By = C
Where:
A, B, and C represents a number, numeral or numerical value.
Next, we would convert the given linear function in slope-intercept form to standard form as follows:
3x + y = 2.
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Evaluate: 3(x+4)(x+1) / (x+2)(x-2) for x = 4
A.10/3
B.10
C.-10/3
D.-10
A mountain has a snow line at an elevation of 9000 feet which runs parallel to its base. The mountain is a triangle, the length of the snow line is 2. 4 times the height of the snow covered part of the mountain. If the snow covers 1,200,000 square feet of part of the mountain, how high is the mountain?
The height of the mountain is 10000ft.
Now, According to the question:
A mountain has a snow line at an elevation of 9000 feet which runs parallel to its base.
The snow covers 1,200,000 square feet of part of the mountain.
We know that:
Area of triangle = 1/2 × base × height
Area of a triangle = 1/2 × 2.4 h × h
1200000 = 2.4[tex]h^2[/tex]/2
cross multiply
1200000 × 2 = 2.4[tex]h^2[/tex]
2400000 = 2.4[tex]h^2[/tex]
Divide both sides by 2.4
[tex]h^2[/tex] = 2400000/2.4
[tex]h^2[/tex] = 1000000
h = √1000000
h = 1000 ft.
The height of the mountain = 1000 ft. + 9000 ft. = 10000 ft.
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whats the mean median mode and range of 75 55 68 44 82 28 19 31 75 36 59 93 48
The mean ,median ,mode and range of 75 55 68 44 82 28 19 31 75 36 59 93 48 are:
mean = 49.7
media = 55
mode=75
Range=74
How can the mean median mode and range be calculated?The concept that can be used here is mean median and mode.
We will need to arrange the value from the lowest to the biggest as :
75 55 68 44 82 28 19 31 75 36 59 93 48
19 28 31 36 44 48 55 59 68 75 75 82 93
The mean can be calculated by adding all numbers in the data set and then dividing by the number of values in the set.
= (19+ 28+ 44 +48+55+ 59+ 68+ 75+ 75+ 82+ 93 )/13 =646/13= 49.7
Median = (n + 1)/2th value
Where n = numner of the given digits which is 13
= (13 + 1)/2th value
= 7th value
=55
Mode = is the number that occurs most often = 75
Range = highest value - lowet value = 93-19 =74
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If point A (-4,5) is reflected over the line y=2 and then translated according to the rule open parentheses (x-1, y-4), what quadrant will point A be in?
The new point A(-5,1) will lie in quadrant 3.
what is the Cartesian coordinate system?A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates,
Given here: The point A(-4,5) is translated over y=2
Thus after the transformation( translation), the new points are
A(-4,5)→A(-4-1,5-4)=A(-5,1)
The point was translated horizontally by 1 to the left and then translated vertically by 4 units downwards.
Hence, The new point will lie in quadrant 3.
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What is the measure of the missing angle?
46°
73°
for
The third angle of the triangle must have a measure of 180° minus the sum of the other two angles, which is 180° - (46° + 73°) = 61°. Therefore, the measure of the missing angle is 61°.
What are the angles of a triangle?The internal angles of a triangle are measured in degrees and are known as triangle angles. The sum of a triangle's angles is always 180°.
Triangle angles are classified into three types: acute angles, right angles, and obtuse angles.
An acute angle is one that is smaller than 90 degrees. This is the most common form of angle in a triangle and is regarded the most desirable.
A right angle is one that is exactly 90 degrees. This sort of angle is the most stable and sturdy in a triangle, therefore it is usually employed to make a triangle.
An obtuse angle is one that is larger than 90 degrees but less than 180 degrees. This form of angle is common in triangles, however it is less desirable than an acute angle.
The sum of the three angles of a triangle is always 180°. Acute angles are the most desirable and stable, whereas obtuse angles are present in certain triangles but are not as ideal.
In the given question,
The measure of the missing angle is 180° - (46° + 73°).
180° - (46° + 73°) = 180° - 119° = 61°
Therefore, the measure of the missing angle is 61°.
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4 is 20% of what number
Answer:
20
Step-by-step explanation:
Solve these equations for x.
-(3x - 12) = 9x -4
Answer:
x= 4/3
Step-by-step explanation:
Think the negative sign outside the parentheses as -1. Then do distributive property to the numbers inside the parentheses.
-1 x 3x and -1 x -12
That equals to -3x + 12 so now your entire equation is -3x + 12 = 9x - 4. Now lets take away 9x from both sides like this,
9x - 9x and -3x - 9x.
That equation is now -12x + 12 = -4.
Now subtract 12 from both sides like this,
12 - 12 and -4 - 12.
And then you have -12x = -16.
Now you divide both numbers by -12 like this,
-12x/-12 which equals to just x and then do -16/-12 which would equal as 1.3333 and repeating but, it can be put as 4/3 for a clearer answer.
So your answer is
x = 4/3
Write 5y without exponents.
Answer:
Step-by-step explanation:
5y/5=y+y+y+y+y
A large district employs 3,461 teacher. If there are 28 students per teacher, how many students are there?
Answer:
If there are 3,461 teachers and 28 students per teacher, to find the total number of students, you can multiply the number of teachers by the number of students per teacher:
3,461 teachers * 28 students/teacher = 97,268 students
So there are 97,268 students in the district.
a personal trainer analyzes the progress of her clients. so she calculates the body mass index (bmi) for each. the bmis for all of her current clients are summarized in the histogram below. histogram with 5 bars of heights 1, 3, 5, 2, 1 and bar edges of 18.1, 20.7, 23.3, 25.9, 28.5, and 31.1. the horizontal axis is labeled bmi and the vertical axis is labeled clients. she would like to offer a discount to her clients that have a current bmi of at least 25.9 in order to encourage them to keep working with her. the discount is for $50 off of their next month's training. if she were to offer these, how much total money would she give in discounts next month?
The total number of clients with a BMI of 25.9 or higher is therefore equal to 1 * 2.6 + 3 * 2
The total amount of money she would need to give in discounts next month can be found by calculating the total number of clients with a BMI of 25.9 or higher. To calculate this, the frequencies of each BMI range need to be multiplied by the width of the corresponding bar. The total amount of money she would need to give in discounts is then equal to the total number of clients with a BMI of 25.9 or higher multiplied by $50.
Using the histogram, the number of clients in each BMI range are: 18.1-20.7 (1), 20.7-23.3 (3), 23.3-25.9 (5), 25.9-28.5 (2), 28.5-31.1 (1).
The width of each bar is: 18.1-20.7 (2.6), 20.7-23.3 (2.6), 23.3-25.9 (2.6), 25.9-28.5 (2.6), 28.5-31.1 (2.6).
The total number of clients with a BMI of 25.9 or higher is therefore equal to 1 * 2.6 + 3 * 2
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13y+7-11-4y as a sum
Answer: 9y-4
Step-by-step explanation:
13y-4y=9y
7-11=-4
Answer:
13y+7-11-4y
13y-4y+7-11
9y-4 ans
Step-by-step explanation:
first combine the like terms along with their front sign
then sbtract 13y by 4y ,after subtract 7 from 11
[ here 7 have (+) and 11 have (-) before itself
according to the rule,(+) + (-) = (-)
hence we have to subtract 7 from 11 and put the (-) before answer]
but put sign (-) before the answer because we should always put that sign before answer which have more value
If a figure is a quadrilateral, then it has four sides.
A triangle does not have four sides.
A closed quadrilateral is a kind of polygon having 4 sides, 4 vertices, and 4 angles. A triangle doesn't have four sides because if it did, it wouldn't be a triangle. It would be a quadrilateral, the term used to describe geometric objects with four sides.
Three line segments combine to form a triangle, which is a straightforward closed curve or polygon. In Euclidean geometry, any three points, notably non-collinear ones, independently create a singular triangle and a singular plane.
In Euclidean geometry, any three points, notably non-collinear ones, independently create a singular triangle and a singular plane. polygon with 4 sides that is a quadrilateral.
One fascinating feature of a quadrilateral is that its opposite parallel sides are possible. Four non-collinear points are joined to create it. Since a triangle would not have four sides
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imagine that a recent study found that people who eat large amounts of bananas get bitten by mosquitoes on average more often than people who eat smaller amounts of bananas. what causal relationship can we conclude from this study alone?
It is not possible to conclude a causal relationship from this study alone. This is because the study only shows a correlation between eating large amounts of bananas and being bitten by mosquitoes, it does not demonstrate that one causes the other. There could be other factors that are not controlled for in the study that could be the true cause of the relationship, such as people who eat more bananas also spend more time outdoors. To establish a causal relationship, further research would be needed such as a randomized control trial.
Cause and Effect of Bananas and Mosquito BitesTo determine a causal relationship between eating bananas and being bitten by mosquitoes, a randomized controlled trial could be conducted. This type of study would involve randomly assigning participants to two groups: one group would eat a large amount of bananas, while the other group would eat a smaller amount of bananas. The number of mosquito bites each participant receives would be recorded and compared between the two groups.
If the group that ate a large amount of bananas had a significantly higher rate of mosquito bites than the group that ate a smaller amount of bananas, it would suggest that eating bananas may cause an increase in the number of mosquito bites.
Additionally, other variables that could influence the result should be controlled or measured, such as time spent outdoors, skin type, or use of mosquito repellent.
It's important to note that even if the study shows a correlation between eating bananas and being bitten by mosquitoes, it doesn't mean that the banana causes the bites, there could be other factors that are not controlled for in the study that could be the true cause of the relationship.
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How might I rewrite 125% of 440 is B as a simpler equation?
Answer:1.25(400)
Step-by-step explanation:
If the perimeter of an equilateral triangle is 36 yards, what is the length of its altitude?
The length of the altitude is 10. 4 yards
How to determine the altitiude of the triangleThe formula for the perimeter of an equilateral triangle is expressed as;
P = 3a
Where;
P is the perimeter of the trianglea is the length of the side of the triangleSubstitute the values
36 = 3a
Divide the value by the coefficient of a
a = 36/3
a = 12 yards
Using the Pythagorean theorem, we get;
12² = h² + 6²
Find the square values
144 = h² + 36
collect like terms
h² = 108
Find the square root
h = 10. 4 yards
Hence, the value is 10. 4 yards
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Find the slope of a line parallel to the line whose equation is 2x+4y=56, fully simplify your answer.
Answer:
Step-by-step explanation:
m= -1/2
Simplify
3√x^5/
5√x^2
Answer:
3√x^5/=15√x
5√x^2=10√x
Step-by-step explanation:
multiply 5 by 3.
multiply 2 by 5.
Netflix is raising its prices from $15. 99 a month to $17. 99 a month. Mr.
Leone is annoyed and will cancel if this is more than a 20% increase in
the price. Based on this information, will he cancel? Explain.
If Netflix is raising it's prices from $15.99 a month to $17.99 a month , then Mr. Leone will not cancel his subscription because the percent increase is 12.507% .
The old subscription price of the Netflix is = $15.99 ;
the new subscription price of Netflix is = $17.99 ;
the percent increase of Netflix can be calculated by using formula :
⇒ (new price - old price)/old price × 100 ;
substituting the values of Netflix prices ,
we get ;
⇒ (17.99 - 15.99)/15.99 × 100 ;
⇒ 2/15.99 × 100
⇒ 0.12507 × 100 ;
⇒ 12.507 % .
Therefore , the percent increase is less than 20% , so he will not cancel the Netflix Subscription .
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What is the Value of X
3x=17x
Answer:
14X
Step-by-step explanation:
9. Joseph is teaching a PE class today and he has a bag of balls for the students to play with.
The bag has 5 timers as many basketballs as soccer balls in the bag. If there is a total of 63 balls
in the bag, how many basketballs and soccer balls are there?
The number of basketballs and soccer balls that there are in the bag are;
Soccer balls = 10
Basketballs = 53
How to solve Algebra Word Problems?We are told that Joseph has a bag of balls for the students to play with. The bag has 5 times as many basketballs as soccer balls in the bag.
Let basketballs be b
Let soccer balls be s.
Thus;
b = 5s
Total number of balls is 63 balls. Thus;
5s + s = 63
6s = 63
s = 63/6
s = 10.5
b = 5(10.5)
b = 52.5
We can estimate an approximate value of s = 10 and b = 53
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a spherical balloon is inflated so that its volume is increasing at the rate 6 cm^3/min. at what rate is the radius increasing when the radius is 3 cm
The radius is increasing at rate of [tex]\frac{10}{36\pi } \\[/tex]
What is volume ?
Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.
As we know Volume of sphere V=
[tex]V=\frac{4}{3} \pi r^3\\dv/dt=6\\Given\\radius=3cm\\[/tex]
so, we need to find dr/dt
Since there is no t in our equation. So differentiate using chain rule
[tex]\frac{dv}{dt} =\frac{dv}{dr} *\frac{dr}{dt} \\[/tex]
Since, in question it is given dv/dt=6
[tex]6=\frac{dv}{dr} .\frac{dr}{dt} \\[/tex]
To find dv/dr differentiate
[tex]4/3\pi r^3\\dv/dr(\frac{4}{3} \pi r^3)=4\pi r^2\\6=4\pi r^2\frac{dr}{dt} \\[/tex]
Dividing
[tex]\frac{10}{4\pi (3)^2} =dr/dt\\dr/dt=\frac{10}{36\pi } \\[/tex]
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The radius is increasing at rate of 10/36π
What is volume ?
Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.
As we know Volume of sphere V= 4/3 πr³
dv/dt =6
Given r = 3 cm.
so, we need to find dr/dt
Since there is not in our equation. So differentiate using chain rule
dv/dt =dv/dr * dr/dt
Since, in question it is given dv/dt=6
6 =dv/dr * dr/dt
To find dv/dr differentiate
dv/dr (4/3πr³) = 4πr²
6 = 4πr² dr/dt
Finally,
dv/dt = 10/36π
Hence, The radius is increasing at rate of 10/36π
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Tomas is planning out a rail trail using a map with a marked grid. The head of the trail, which has an information kiosk, is located at (3, 0). He moves 1 unit east and 3 units north and places a pin at (4, 3) to represent the location of another information kiosk. He continues placing pins so that each pin is 1 unit east and 3 units north in relation to the previous pin. Where is the fifth information kiosk located?
Answer:
(7,12)
Step-by-step explanation:
We are add 1 to the x value each time and 3 to the y value
1st: (3,0)
2nd: (4,3)
3rd: (5,6)
4th: (6,9)
5th: (7,12)
what is the Inequality for this?
The inequality for the goal that Miles set for the number of steps to be taken each day is x > 10, 000.
How to write the inequality ?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Miles is to take over 10, 000 steps every day which means that if the number of steps is denoted as x, the inequality would be:
x > 10, 000
This shows that the steps are greater than 10, 000 steps.
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Complete the table to combine like terms when adding Expression One and Expression Two. Expression One Expression Two 14−3a 7a−9
The addition of the two expression is 4a + 23
The term called expression in math is defined as the mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Here we know that the following expression are known.
=> 14 - 3a
=> 7a - 9
Now, we have to perform the addition operation on it.
Then the expression can be written as
=> (14 - 3a) + (7a + 9)
Now, we have to combine the similar term of the expressions, then we get,
=> (14 + 9) + (-3a + 7a)
When we simplify this one then we get,
=> 23 + 4a
When we write it as the standard form, then we get,
=> 4a + 23.
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marco made 124 free throws this season.ryan made132,if each free throw is worth 2 points,how many points did the boys score together?
Answer:
512 points altogether.
Step-by-step explanation:
This is a guess hope it helps :D
Answer:
512
Step-by-step explanation:
&:(::6)6/$/):&;!4):$:$:$:&):=512