The annual rate of interest have to be 3.87%.
How to determine the annual rate of interest?Mathematically, compound interest can be calculated by using this formula:
A = P(1 + r/n)^{nt}
Where:
A represents the future value.P represents the principal.r represents the interest rate.n represents the number of times compounded.T represents the time measured in years.Making the interest rate (r) the subject of formula, we have:
r = n[(A/P)^{1/nt} - 1]
Note: A = SI + P = 600 + 30,000 = $36,000
Substituting the given parameters into the formula, we have;
Interest rate, r = 1[(36,000/30,000)^{1/1 × 4.8} - 1]
Interest rate, r = [(1.2)^{0.20833333333} - 1]
Interest rate, r = [1.0387 - 1]
Interest rate, r = 0.0387
Interest rate, r = 3.87%.
Read more on annual rate of interest here: https://brainly.com/question/20253688
#SPJ1
(-2,6), m = 4 !!!!!!!!!!!!
Answer:
y=4x+14
Step-by-step explanation:
Una grúa está elevando 5 /7 de los 224 kg que puede elevar como máximo ¿Cuántos kilos está elevando?
The number of kilograms that the crane is lifting, based on the maximum it can lift and the proportion being lifted is 160 kilos
How to find the number of kilos?The number of kilos that the crane is lifting can be found by the formula :
= Maximum kilogram capacity x Proportion of maximum being lifted
Maximum kilogram capacity = 224 kg
Proportion of maximum being lifted = 5 / 7
The kilos being lifted by the crane is therefore :
= 224 x 5/7
= 1, 120 / 7
= 160 kilos
Find out more on kilos lifted at https://brainly.com/question/11970392
#SPJ1
need help with this asap first answer will get brainliest
Answer:
x° = 34°
Step-by-step explanation:
First, find the interior angle supplementary to the given exterior angle 124°.
I will label it y.
124° + y° = 180°
y° = 180° - 124°
y° = 56°
Next, solve for x° by equating the sum of the interior angles of the triangle to 180° and plugging in the y-value that we just solved for.
x° + y° + 90° = 180°
x° + y° = 90°
x° + 56° = 90°
x° = 90° - 56°
x° = 34°
Answer:
x = 34---------------------------
Exterior angle in the triangle is the sum of remote interior angles124 = x + 90x = 124 - 90x = 34India's hourly wage is $10.50. If she
regularly works 40 hours per week, what is
her regular weekly pay?
Step-by-step explanation:
10 hours per week: $10.50 x 10 = $105.00
20 hours per week: $105.00 x 2 = $210.00
40 hours per week: $210.00 x 2 = $420.00
If f(x) = 4x² and g(x)=3x, what is (fg)(x)?
(fg)(x)=
(Simplify your answer.)
The multiplication of the given function is (fg)(x) = 12[tex]x^3[/tex]
What is operations of the function ?
Similar to how a function's constituent terms can be added, subtracted, multiplied, and divided, so can functions. These are to be noted as follows:
Addition f( x ) + g ( x ) means to combine two functions, and it may alternatively be expressed as ( f + g ) ( x )
It is possible to write ( f g ) ( x ) to represent the operation of subtracting the g(x) function from the f(x) function.
The two functions are multiplied together when you multiply f (x ) g (x), which can also be represented as (f g ) (x).
Division f (x)/g (x) means to split the two functions in half, and it can alternatively be expressed as (f/g)(x).
Here the given function ,
=> f(x) = 4[tex]x^2[/tex]
=> g(x)= 3x
Now (fg)(x) = f(x)*g(x)
=> (fg)(x)= 4[tex]x^2[/tex]*3x
=> (fg)(x) = 12[tex]x^3[/tex]
Hence the (fg)(x) = 12[tex]x^3[/tex].
To learn more about operations of the function
https://brainly.com/question/28726030
#SPJ13
Find the slope of the line
Answer:
-3
Step-by-step explanation:
we sure y2-y1/x2-x1 to find slope
6+6/-4+0
12/-4
-3 is the slope
Hopes this helps please mark brainliest
A caterer charges a $40 fee plus an additional $6.25 per person. She determines the total cost, C, for x people by using the equation shown above. How much will a party cost for 80 people?
The measurements of two sides of a triangle are 12cm and 17cm Which side length could be the measurement of the third side of the triangle
Using the triangle rule, the length of the third side falls between 5 cm and 29 cm.
In the given question,
The measurements of two sides of a triangle are 12 cm and 17 cm.
We have to find which side length could be the measurement of the third side of the triangle.
We know that,
The sum of the length of any two sides is always greater than the third side.
The given sides of triangles are 12 cm and 17 cm.
Hence, the length of the third side should be shorter than the total of the other two sides,
12 + 17 = 29 cm.
Considering that the third side must be less than the difference between the first two sides,
17 – 12 = 5 cm
So, the length of the third side falls between 5 cm and 29 cm.
To learn more about triangle link is here
brainly.com/question/25813512
#SPJ1
find the missing number of each unit rate 24/8=?/1 40/20 = ?/1
Answer:
24/8 = 3/1
40/20 = 20/1
Step-by-step explanation:
I hope this helps!
Factor the given number 102 Input the number's prime factors in ascending order.
The dimensions of the old stage at the concert hall were 30 feet wide and 15 feet deep. The new stage has a total area of 1000 square feet. The
dimensions of the new stage were created by adding the same distance x to the width and the length of the old stage. What deepth of the new stage?
The 30 feet by 15 feet dimension of the old stage and the 1,000 square feet of the new stage generates equations that gives the depth of the new stage;
The depth of the new stage is 25 feetWhat is an equation?An equation states the relationships between two expressions as being of the same value.
The width and depth of the concert hall for the old stage are 30 feet and 15 feet respectively
Area of the new stage = 1000 ft.²
The dimensions of the new stage are;
Width = 30 + x
Depth = 15 + x
Which gives;
(30 + x) × (15 + x) = 1,000
(30 + x) × (15 + x) - 1,000 = 0
x² + 45·x - 550 = 0
(x + 55)·(x - 10) = 0
The distance added to the width and length of the old stage, x = 10
The width of the new stage = 30 feet + 10 feet = 40 feet
The depth of the new stage = 15 feet + 10 feet = 25 feet
Learn more about writing algebraic equations here:
https://brainly.com/question/10892115
#SPJ1
determine the degree, leading coefficient and constant term or each polynomial
1. x+5
degree:______
leading coefficient:_____
constant term:____
For the given polynomial the degree is 1, the leading coefficient is 1, and the constant term is 5.
What are polynomials?A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.
The given polynomial is x+5.
(1) The degree is the highest power of the polynomial.
Degree = 1
(2) The leading coefficient is 1.
(3) The constant term is 5
Therefore, the given polynomial degree is 1, the leading coefficient is 1, and the constant term is 5.
To know more about polynomials follow
https://brainly.com/question/24662212
#SPJ1
2. Determine if the diagram is a function.
Why or why not?
Please
Answer:
IT IS A FUNCTION
It is specifically a Surjective/ onto Mapping/function
Step-by-step explanation:
surjective or onto function is when y has an image in x
Answer:
The graph is a function
Step-by-step explanation:
-For every input (x) there is only one output value (y)
Since the function does not have two of the same x values for several inputs, its considered a function. If the x values do not repeat values, or if you graph the function and it does not cross on more than one point, it is also considered a function.
Ex.
X: 2, 4, 7 , 2, 5 This is not a function. More than one input for each output.
Y: 1, 2, 4, -3, 7
Ex.
X: 5, 6, -5, 8 this is a function. Exactly one input for every output.
Y: 1, 4, 5, 9
For the experiment of rolling an ordinary pair of dice, find the probability that the sum will be less than 6 or greater than 9.
The probability that the sum will be less than 6 or greater than 9 is
The probability that the sum is 5/9.The additive dice roll has 36 different results, as explained. A sum of 9 is rolled using the numbers 6 (and vice versa) and 3 or 5 and 4. (and vice versa).
What is the likelihood of rolling two dice together?The additive dice roll has 36 different results, as explained. A sum of 9 is rolled using the numbers 6 (and vice versa) and 3 or 5 and 4. (and vice versa). Given that this is feasible 4 times out of 36, the probability calculated by adding the two dice is 4/36, or 1/9.
I am assuming that you are rolling two dice.
Probability of even: 18 "evens" out of 36 total outcomes = 18/36
→(1,1), (1,3), (1,5), (2,2), (2,4), (2,6), (3,1), (3,3), (3,5),(4,2), (4,4), (4,6), (5,1), (5,3), (5,5), (6,2), (6,4), (6,6)
Probability of greater than 9: 6 ">9s" out of 36 total outcomes = 6/36
→(4,6), (5,5), (5,6), (6,4), (6,5), (6,6)
Probability of both evens and >9s: 4 "both" out of 36 total outcomes = 4/36
→(4,6), (5,5), (6,4), (6,6)
evens OR >9s NOT both
18/36 + 6/8 - 4/36 = 20/36 = 5/9.
The probability that the sum is 5/9.
To learn more about additive dice roll refer to:
https://brainly.com/question/14192140
#SPJ1
A scientist mixes water (containing no salt) with a solution that contains 20% salt. she wants to obtain 120 ounces of the mixture that is 15 % salt. How many ounces of water and how many ounces of the 20% salt solution should she use?
Answer:Say w= the amount of water in oz, then the 60% of the solution is 250 - w
Set up the equation:
Use distributive property first
0.60(250-w) = 0.15 x 250
Isolate to solve for w
150- 0.60w= 37.5
-0.60w= 37.5-150
0.60w= -112.5
w= 187.5 ounces
250-187.5= 62.5 ounces salt solution
Therefore, she must use 187.5 ounces of water and 62.5 ounces of salt solution for her experiment.
Hope this helps!
Step-by-step explanation:
Describe the graph of g?
The given points gives us a line with constant slope of -2.
What are coordinates?
A pair of numbers that use the separations between the two reference axes to define the location of a point on a coordinate plane. usually represented by the x- and y-values, respectively, (x, y).
The position of a point or a shape in a given space is determined by coordinates, which are numbers (a map or a graph ).
The points are in the form of ( x, y) , where y= g(x)
Plot these points on the graph and join the points through a line.
Refer to the attachment for the graph.
The slope is constant.
consider any 2 points:
(x,y) = (0,7)
(m,n) =(2,3)
Slope = change in y values/ change in x values
= (7-3)/(0-2) = 4/-2 = -2
The given points gives us a line with constant slope of -2.
To learn more about the coordinates from the given link
https://brainly.com/question/17206319
#SPJ1
I need help with number 2...
For isosceles triangle RST the measure of angle T is 34 degree
In this question, we have been given a isosceles triangle RST with RS = RT.
So, by isosceles triangle theorem,
angle S = angle T
So, angle T = (3x - 2)°
We know that the sum of all angles of triangle is 180°
∠R + ∠S + ∠T = 180°
9x + 4 + 3x - 2 + 3x - 2 = 180°
15x + 4 - 4 = 180°
15x = 180°
x = 12
So, 3x - 2 = 3(12) - 2
= 34°
Therefore, for triangle RST the measure of angle T is 34 degree
Learn more about isosceles triangle here:
https://brainly.com/question/2456591
#SPJ1
what is the sum of 3x and -3x + 4?
5x-3(x-3)=-5+4x+6 x=?????????
Answer:
[tex]\frac{7}{4}[/tex] or 1 [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
I am not sure if you meant 6x or 6+x at the end of the equation. I went with what was written.
5x -3(x-3) = -5 +4x +6x Distribute the -3
5x -3x + 9 = -5 + 4x + 6x Combine like terms
2x + 9 = -5 + 10x Subtract 2x from both sides
9 = -5 + 8x Add 5 to both sides
14 = 8x Divide both sides by 5
[tex]\frac{14}{8}[/tex] = x
[tex]\frac{7}{4}[/tex] o r 1 [tex]\frac{3}{4}[/tex]
solve 4x + 2=(1/8)x-2
Answer:
x = -32/31
Step-by-step explanation:
4x - 1/8 x = -2 -2
(32 - 1)/8 x = -4
31/8 x = -4
x = -4 * 8/31
x = -32/31
What is 624×8 please answer this
A number line going from negative 20 to positive 20.
What is the absolute value of –20?
Use the number line to answer the question.
–20
0
20
40
Answer:
20
Step-by-step explanation:
Absolute value is the distance from zero. Absolute value is always positive.
| -20 | is positive. It is 20 units from 0. So it is 20.
| -20 | = 20
(Be careful, absolute value doesn't just flip the sign to the opposite.
| 20 | = 20 also because the distance from 0 to 20 is also 20.)
HELP 50 POINT MATH QUESTION MIDDLE SCHOOL
In the proportional relationship table, x would represent distance and y, weight.
The complete table is given in the explanation below.
What is a Proportional Relationship?If two variables that have quantities that vary proportionately are x and y, then the constant of proportionality that lies between both varies can be calculated as k = y/x. The equation for the proportional relationship would be expressed as y = kx.
x represents distance (cm)
y represents weight (newtons).
Using the pair of value that is given in the table, (20, 28), the constant of proportionality, k, would be:
k = y/x = 28/20
k = 1.4
The equation would be y = 1.4x.
Use the equation to complete the table by substituting the value of each missing variables:
Row 2, when x = 55:
y = 1.4(55)
y = 77
Row 3, when y = 140:
140 = 1.4x
140/1.4 = x
100 = x
x = 100
Row 4, when x = 1:
y = 1.4(1)
y = 1.4
The table would be:
Distance (cm) Weight (newtons)
Row 1 20 28
Row 2 55 77
Row 3 100 140
Row 4 1 1.4
Learn more about the proportional relationship on:
https://brainly.com/question/28777033
#SPJ1
8.7% increase of 525 what is answer
Answer:
Step-by-step explanation:
570.675
What is the equation of the line that passes through the point (2,-7) and has a slope of -4
Answer: y+7=-4(x-2)
Step-by-step explanation:Point slope form is: y - y1 = m(x-x1)2 = x1-7 = y1 substituteAnswer: y+7=-4(x-2)
Use I=PRT
p=12,000
r=4%
t=3year
find I
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$12000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &3 \end{cases} \\\\\\ I = (12000)(0.04)(3) \implies I = 1440[/tex]
The sum of four positive integers is 125. If you increase the first number by 4, decrease the second by 4, multiply the third by 4, and divide the fourth by 4, you produce four equal numbers. What is the smallest of the original numbers
Step-by-step explanation:
a + b + c + d = 125
a + 4 = b - 4 = 4c = d/4
a + 8 = b
a = b - 8
16c = d
b = 4c + 4
4a + 16 = d
b - 8 + 4c + 4 + c + 16c = 125
4c + 4 - 8 + 4c + 4 + c + 16c = 125
25c = 125
c = 5
d = 16c = 80
4a + 16 = d = 80
4a = 64
a = 16
b = a + 8 = 16 + 8 = 24
so, the numbers are
16, 24, 5, 80
Find the dimensions of the rectangle with the largest area; it has two vertices on the x-axis and two vertices above the x-axis on the graph of
y = 5 − x^2.
Answer:
(2/3)√15 wide by 10/3 tall, approx 2.582 by 3.333
Step-by-step explanation:
You want the dimensions of the largest rectangle that fits under the graph of y = 5 -x² above the x-axis.
DimensionsThe graph of y=5-x² is symmetrical about the y-axis, so the width of it will be x -(-x) = 2x and the height will be 5-x².
AreaThe area will be the product of the width and height:
A = WH
A = (2x)(5 -x²) = 10x -2x³
Maximum areaThe area will be a maximum where the derivative of the area function is zero.
dA/dx = 10 -6x² = 0
x² = 10/6
x = (√15)/3
The corresponding rectangle dimensions are ...
width = 2x = (2/3)√15
height = 5 -x² = 5 -5/3 = 10/3
The rectangle with largest area is (2/3)√15 wide by 10/3 tall.
Created a painting with an area of 48 in.² and a length of 6 inches they create a second painting with an area of 64 in.² it has the same width as the first painting what is the length of the second painting
The length of the second rectangle is 8 in
How to find the length of the second painting?Since we have painting with an area of 48 in.² and a length of 6 inches, since it is a rectangle, its area is A = LW where
L = length of rectangle = 6 in and W = width of rectangleSo, making Wsubject of the formula, we have
W = A/L
Since
A = 48 in² and L = 6 inSubstituting these into the equation, we have
W = A/L
W = 48 in²/6 in
W = 8 in
Now, since the second painting with an area of 64 in.² it has the same width as the first painting, since it is also a rectangle, its area is A = LW where
L = length of rectangle and W = width of rectangleSo, making L subject of the formula, we have
L = A/W
Since
A = 64 in² and W = 8 inSubstituting these into the equation, we have
L = A/W
L = 64 in²/8 in
L = 8 in
So, the length of the second rectangle is 8 in
Learn more about length of rectangle here:
https://brainly.com/question/28497588
#SPJ1
Please help me verify. I am stuck.
The trigonometric identity presented in this problem is proved trough the answer, reaching an answer 1 = 1.
Proving the identityThe identity is presented as follows:
[tex]\csc{\beta} + 1 = \frac{\cot{\beta}}{\sec{\beta} - \tan{\beta}}[/tex]
Then we take the right side of the denominator, and apply the subtraction of perfect squares to the denominator, as follows:
[tex]\frac{\cot{\beta}}{\sec{\beta} - \tan{\beta}} \times \frac{\sec{\beta} + \tan{\beta}}{\sec{\beta} + \tan{\beta}} = \frac{\cot{\beta}(\sec{\beta} + \tan{\beta})}{\sec^{2}{\beta} - \tan^2{\beta}}[/tex]
The following identity relates the square of the secant and of the tangent:
[tex]\tan^2{\beta} + 1 = \sec^2{\beta}[/tex]
Hence:
[tex]\sec^2{\beta} - \tan^2{\beta} = 1[/tex]
Thus the remaining expression is:
[tex]\frac{\cot{\beta}(\sec{\beta} + \tan{\beta})}{\sec^{2}{\beta} - \tan^2{\beta}} = \cot{\beta}(\sec{\beta} + \tan{\beta})[/tex]
The equations of the cotangent, secant and tangent are given as follows:
Cotangent: cosine/sine.Secant: 1/cosine.Tangent: sine/cosine.Hence:
[tex]\cot{\beta}(\sec{\beta} + \tan{\beta}) = \frac{\cos{\beta}}{\sin{\beta}}\left(\frac{1}{\cos{\beta}} + \frac{\sin{\beta}}{\cos{\beta}}\right) = \frac{1}{\sin{\beta}} + 1[/tex]
One divided by the sine is the cosecant, as follows:
[tex]\frac{1}{\sin{\beta}} = \csc{\beta}[/tex]
Hence the simplified expression is:
[tex]\csc{\beta} + 1[/tex]
Which is equivalent to the right side of the expression, hence an identity of the format 1 = 1 is reached and the identity is proven.
More can be learned about trigonometric identities at https://brainly.com/question/7331447
#SPJ1