Answer:
∠ A = 23.6°
Step-by-step explanation:
complementary angles sum to 90°
sum the 2 angles and equate to 90
2x - 20 + 3x + 1 = 90
5x - 19 = 90 ( add 19 to both sides )
5x = 109 ( divide both sides by 5 )
x = 21.8
Then
∠ A = 2x - 20 = 2(21.8) - 20 = 43.6 - 20 = 23.6°
If the car climbs 60 m vertically how far must the car have travelled horizontally?
The the gradient of the slope is 2/15
The horizontal distance is 150 meters
How to determine the horizontal distanceFrom the question, we have the following parameters that can be used in our computation:
Gradient = 2/15
Vertical distance = 60 meters
The gradient is calculaed as
Gradient = Vertical distance/Horizontal distance
So, we have
Horizontal distance = Vertical distance/Gradient
This gives
Horizontal distance = (60)/(2/5)
Evaluate
Horizontal distance = 150
Hence, the distance is 150 meters
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1522 customers at a major retailer were surveyed whether or not they made a purchase and were satisfied with the service they received. The table below organizes the responses.
Satisfied with Service
Not Satisfied with Service
Total
Made a Purchase
130
494
624
Did Not Make a Purchase
715
183
898
Total
845
677
1522
What are the odds that a shopper selected at random was satisfied with the service they received?
Probability that the shopper selected at random was satisfied with the service they received is 845 / 1522.
What is Probability?Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
Total number of customers = 1522
Out of these,
Number of customers made a purchase = 624
Number of customers not made a purchase = 898
Number of customers who purchased satisfied with the service = 130
Number of customers who does not purchase satisfied with the service = 715
Total number of customers who are satisfied with the service = 130 + 715 = 845
Probability that the randomly selected shopper satisfied with the service = 845 / 1522
Hence the probability is 845 / 1522.
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The length of a string in yards is a function ƒ(n) of the length n in inches. Write a function rule for this situation.
The function rule for this situation is f(n) = 1/36n
How to write a function rule for this situation.From the question, we have the following parameters that can be used in our computation:
The length of a string in yards is a function ƒ(n) of the length n in inches.
The conversion of yards to inches is
Yard = 1/36 * Inches
When represeted as a function, we have
f(n) = 1/36n
Hence, the function is f(n) = 1/36n
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PLEASE YALL HELP ME WITH THIS I NEED IT FOR RN
The piecewise function for the Tax due on an income of x dollars are:
T(x) = 0.035x; if 0 < x ≤ $15,000T(x) = 525 + 0.0625 (x- 15,000); if 15,000 < x ≤ 30,000 T(x) = 1462.50 + 0.068 (x - 30,000); if 30,000 < xFrom the case, we know that there are 3 scenariois for filling tax due based on an individual's income, where:
Between $0 until $15,000 is taxed 3.5% of taxable incomeBetween $15,000 until $30,000 is taxed $525 plus 6.25% of excess over $15,000Over $30,000 is taxed $1462.50 plus 6.8% of excess over $30,000.To construct the piecewise function for the Tax due, we need to translate the given conditions into mathematical formulation.
We assume that:
T(x) = tax due
x = $ amount of taxable income
For taxable income between $0 until $15,000, the tax is 3.5% of taxable income; then:
T(x) = 3.5% x
T(x) = 0.035x
For taxable income between $15,000 until $30,000, the tax is $525 plus 6.25% of excess over $15,000. Then:
T(x) = 525 + 6.25% (x - 15,000)
T(x) = 525 + 0.0625 (x- 15,000)
Please note that the additional 6.25% only will be counted based on the remaining of the taxable income deducted by $15,000.
For taxable income over than $30,000, the tax is $1462.50 plus 6.8% of excess over $30,000. Then:
T(x) = 1462.50 + 6.8% (x - 30,000)
T(x) = 1462.50 + 0.068 (x - 30,000)
Please note that the additional 6.8% only will be counted based on the remaining of the taxable income deducted by $30,000.
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On his sixth birthday, a boy inherits $6000 which is to be used for his college education. The money is deposited into a trust fund that will pay him
R dollars on his 18th, 19th, 20th, and 21st birthdays. Find R if the money earns 8% interest compounded annually.
The money deposited will pay the boy $ on his 18th, 19th, 20th and 21st birthdays.
(Round the final apower to the nearest cent as needed Round all intermediate values to six decimal places as needed.)
On solving the provided question, we can say that by solving the interest the amount after his 21st birthday = $ 10,806
what is interest ?Simple interest is calculated by dividing the principal by the interest rate, the passage of time, and other elements. The formula used in marketing is simple return = principal + interest + hours. Using this approach, interest may be calculated most easily. The most common way to calculate interest is as a percentage of the principal balance. If he borrows $100 from a friend and agrees to pay it back with 5% interest, for instance, he will only pay his proportion of the 100% interest. $100 (0.05) = $5. You must pay interest when you borrow money and charge interest when you lend it. The majority of the time, interest is calculated as an annual percentage of the loan balance. This proportion is referred to as the loan's interest rate.
P = $6000
Rate= 4 %
Time, t= 12 years
Formula of Compound Interest
[tex]A = P(1+R/100)^T\\A = 6000(1+4/100)^{12}\\A = 9606.19332[/tex]
On his 19 th birthday
[tex]A = P(1+R/100)^T\\A = 6000(1+4/100)^{13}\\A = 9990. 44106[/tex]
After 21st year S. I is
S. I = 10390.058700 × 4/100
S. I = 415.602348
A= 415.602348 + 10390.058700
A = $ 10,805.661.
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If f(1) = 5 and f(n) = 5f(n-1) + 5 then find the value of f(3)
The value of function for f(5) is 3125.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given that, f(1) = 5 and f(n) = 5f(n − 1)
Now, for finding the the 5th term we have to find the remaining four term before the 5th term.
So, n=2
f(2) = 5f(1)
f(2)= 5(5)
f(2)= 25
Now, n=3
f(3) = 5f(2)
f(3)= 5(25)
f(3)= 125
Now, n=4
f(4) = 5f(3)
f(4)= 5(125)
f(4)= 625
Now, n=5
f(5) = 5f(4)
f(5)= 5(625)
f(5)= 3125
Hence, the value of function for f(5) is 3125.
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Lily is working two summer jobs, making $11 per hour babysitting and $14 per hour clearing tables. Lily must earn a minimum of $180 this week. Write an inequality that would represent the possible values for the number of hours babysitting,
�
b, and the number of hours clearing tables,
�
c, that Lily can work in a given week.
how do I solve for x
Answer:x=1
Step-by-step explanation:
For this, you will need to use substitution.
we know that a²+b²=c²
plug it in
[tex]x^2+3^2=y^2[/tex]
simplify to find
[tex]x^2+9=y^2[/tex]
[tex]y=\sqrt{x^2+9}[/tex]
repeat with the other side
[tex](x+8)^2+3^2=z^2[/tex]
[tex]x^2+16x+73=z^2[/tex]
[tex]z=\sqrt{x^2+16x+73}[/tex]
plug these in for the larger triangle
[tex]y^2+z^2=(2x+8)^2[/tex]
[tex]x^2+9+x^2+16x+73=4x^2+32x+64[/tex]
[tex]2x^2+16x+82=4x^2+32x+64[/tex]
set equal to 0 and simplify
[tex]-2x^2-16x+18=0[/tex]
pull out a -2
[tex]x^2+8x-9=0[/tex]
factor
[tex](x-1)(x+9)=0[/tex]
x=-9,1
x cannot be negative since it a measurement so x=1
Use Cramer's rule to solve the following system. Determine D, Dx, Dy and use these values to
solve x and y.
- 8x+4y=8
3x - 5y = 4
D=
(Type an integer)
Dx =
(Type an integer)
D₁ = 0
(Type an integer)
X =
(Type an integer or fraction. Do not simplify fraction.)
y =
(Type an integer or fraction. Do not simplify fraction.)
The values of D, Dx, Dy , x and y are
D=28
Dx= -56
Dy= -56
x=-2
y=-2
What are matrices ?
The word "matrix" can be used to refer to a rectangular array or table with numbers or other components arranged in rows and columns. Any number of columns and rows are allowed. Matrix operations include addition, multiplication, transposition, scalar multiplication, and many others.
Write the matrices by taking coefficients of x and y in different columns as:
[tex]\begin{bmatrix} -8 & 4 \\ 3 & -5 \end{bmatrix} =\begin{bmatrix} 8 \\ 4&\end{bmatrix}[/tex]
Determinant of LHS = D
[tex]D=\begin{vmatrix} -8 & 4 \\ 3 & -5 \end{vmatrix}[/tex]
D=28
Substitute the x-column with the RHS to find Dx
Substitute the y-column with the RHS to find Dy
[tex]Dx=\begin{vmatrix} 8 & 4 \\ 4 & -5 \end{vmatrix}[/tex]
Dx= -56
[tex]Dy=\begin{vmatrix} -8 & 8 \\ 3 & 4 \end{vmatrix}[/tex]
Dy= -56
x=Dx / D = -56/28 = -2
y=Dy / D = -56/28 = -2
The values of D, Dx, Dy , x and y are
D=28
Dx= -56
Dy= -56
x=-2
y=-2
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Two of the interior angles of a polygon are 140° and 160° , the remaining and 150°. Find the number of sides of the polygon
the number of sides of the polygon 12 sides
Which polygon has a space inside?An interior angle is a shape's internal angle. The closed shape with sides and vertices is a polygon. All of the inner angles of a regular polygon are equal to one another. For instance, a square has interior angles that are all exactly right angles, or 90 degrees.
In a regular polygon, all internal angles are equal. Interior angle of a polygon = sum of interior angles number of sides is the formula for determining the amount of an interior angle.
The n-sided polygon's inner angle total equals (n-2).
180°, thus as follows:
140°+160°+ (n-2)150 = (n-2)180°
or, 300° = (n-2)(180° - 150°).
or, 300° = (n-2) 30°
or, 10= n - 2.
alternately, n = 10 + 2 = 12 sides.
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Work out the following sheet,please
a) The measure of <ABC is 131 degree.
What is Angle sum property?According to the triangle's "angle sum property," a triangle's angles add up to 180 degrees. Three sides and three angles, one at each vertex, make up a triangle.
The total of a triangle's three internal angles is 180 degrees, as stated by the angle sum feature of a triangle.
Given:
a) As <ACD= 90
and Triangle BCD is an equilateral triangle then each of its angle measure 60 degree.
So, <ACD= 90
<ACB + <BCD = 90
<ACB = 90 - 60
<ACB = 30
and, <BAC = 19
Using Angle sum property in Triangle ACB
19 + <ABC + 30 = 180
<ABC = 180 - 49
<ABC = 131 degree.
b) Bow, In Triangle HEF using Angle sum property
<E + <F + <EHF = 180
<EHF = 180 - (69+ 40)
<EHF = 71 degree.
Then, <GHE + <EHF + <FHI
= 72 + 71 + 37
= 180, which forms on straight line.
Thus, GHI is a straight line.
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Determine the solution to the inequality.
1/4|x+1|>4
a. x ≥ -1 or x ≥ 17
b. x < -17 or x ≥ 15
c. x < -9 or x > 7
d. x < -2 or x > 0
Answer:
bbbbbbbbbbbbbb
see attched image for sol
I need a detailed explanation of how 0.667 as a fraction equals 2/3. this isn't making sense.
The reason 0.667 is equal to 2/3 is because when you divide:
2 ÷ 3 = 0.6666666667.
You can shorten 0.6666666667 to 0.667.
That is how 2/3 is equal to 0.667.
Mark me Brainliest. :D
help me i need help whats the answer
Answer:
17
degree
jjaokaohshdh
Step-by-step explanation:
Joppa
also
aijsiwso
akoakwbd
Choose the justification for each step in the solution to the given equation.
- division property of equality
- simplification
- multiplication property of equality
-Addition property of equality
-Subtraction property of equality
The properties are used to manipulate equations in order to isolate a variable, find a solution, or simplify the equation
What are the properties of equality?
The "division property of equality" states that if you divide both sides of an equation by the same non-zero number, the two sides will remain equal.
The "simplification" step is used to simplify an expression by combining like terms, reducing fractions, or performing other operations to simplify the expression.
The "multiplication property of equality" states that if you multiply both sides of an equation by the same non-zero number, the two sides will remain equal.
The "addition property of equality" states that if you add the same number to both sides of an equation, the two sides will remain equal.
The "subtraction property of equality" states that if you subtract the same number from both sides of an equation, the two sides will remain equal.
These properties are used to manipulate equations in order to isolate a variable, find a solution, or simplify the equation.
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Suppose that a desktop computer system consists of a monitor, a mouse, a keyboard, the computer processor itself, and storage devices such as a disk drive. Most computer system problems due to manufacturing defects occur soon in the system’s lifetime. Purchasers of new computer systems are advised to turn their computers on as soon as they are purchased and then to let them run for a few hours to see if any problems crop up. Let
A=Event that a newly purchased monitor operates properly.
B=Event that a newly purchased mouse operates properly.
C=Event that a newly purchased disk drive operates properly.
D=Event that a newly purchased computer processor operates properly.
Suppose that the four events are independent, with
P(A)=P(B)=0.98, P(C)=0.97, P(D)=0.99
Find the following probabilities:
All 4 components are working properly.
All components are working properly except for the monitor.
The monitor or the processor operates properly.
SHOW ALL YOUR WORK and Round your answers to nearest four decimal places.
Physics shows that when an object is thrown upward with an initial velocity of v_0, then its approximate height is given by this quadratic function.
s = -4.9t^2 + v_0^t + h
A ball is thrown upward from the top of a building 15 meters high, at a velocity of 3.1m/sec. Answer the following questions. Be sure to show and explain all work.
A. Find the maximum height and the time in which it was attained (round to 3 decimal places)
B. When does it reach the ground? (round to 3 decimal places)
C. Sketch a graph to illustrate your answers.
The answers to each part is given above.
Explain Maxima and Minima in mathematics?Maxima and Minima are known as the extrema of a function. Maxima and minima are the maximum or the minimum value of a function within the given set of ranges. For the function, under the entire range, the maximum value of the function is known as the absolute maxima and the minimum value is known as the absolute minima.Local Maxima : A point x = b is a point of local maximum for f(x) if in the neighborhood of b i.e in (b−, b+) where can be made arbitrarily small, f(x) < f(b) for all x ∈ (b−, b+)∖{b}. This simply means that if we consider a small region (interval) around x = b, f(b) should be the maximum in that interval.Local Minima : A point x = a is a point of local minimum for f(x) if in the neighbourhood of a, i.e. in (a−,a+), (where can have arbitrarily small values), f(x) > f(a) for all x ∈ (a−,a+)∖{a}. This means that if we consider a small interval around x = a, f(a) should be the minimum in that interval.Given is that when an object is thrown upward with an initial velocity of v{0}, then its approximate height is given by this quadratic function -
S = - 4.9t² + [tex]$v_{o} ^{t}[/tex] + h
The approximate height is given by this quadratic function -
S = - 4.9t² + [tex]$v_{o} ^{t}[/tex] + h
{ 1 } - For the maximum height :
dS/dt = 0 ... Eq{ 1 }
dS/dt = -9.8t + [tex]$3.1^{t}[/tex] log(3.1) + 0 = 0
- 9.8t + [tex]$3.1^{t}[/tex] log(3.1) = 0
Refer to the graph attached. At t = 3.8 {possible value}, the function is 0.
So we get -
t = 3.8 s ... Eq{ 2 }
Maximum height achieved -
h{max} = - 9.8t + [tex]$3.1^{t}[/tex] log(3.1) + 15
h{max} = - 9.8 x 3.8 + [tex]$3.1^{3.8}[/tex] log(3.1) + 15
h{max} = - 37.24 + 73.65 x 0.50 + 15
h{max} = 14.585 m
{ 2 } -
0 = 3.1 t + 9.8/2 t²
0 = 3.1 t + 4.9 t²
Solving graphically, we get -
|t| = 0.6 s
Total time taken to reach ground -
T = 2 x 3.8 + 0.6
T = 8.2 seconds ... Eq{ 3 }
Therefore, the answers to each part is given above.
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Select the correct answer.
Where does the graph of y= sin x from x = 0 to x = 277 start?
OA.
OB.
O C.
O D.
at its minimum
at an x-intercept
at its maximum
between an x-intercept and its maximum
Answer:
At an x-intercept
Step-by-step explanation:
y = sin x
y = sin 0
y = 0
(0,0) is an x-intercept but not it's maximum or minimum.
To prove KLM = KLN, which triangle congruence postulate could you use? (last option is F. AAA)
The congruence postulate used to prove the congruence of triangles KLM and KLN is given as follows:
E. ASA.
What is the Angle-Side-Angle congruence theorem?The Angle-Side-Angle (ASA) congruence theorem states that if any of the two angles on a triangle are the same, along with the side between them, then the two triangles are congruent.
For this problem, we have that the two angles between segment LK are equal for each triangle, as LK is a bisection of these two angles, along with segment LK, hence the ASA congruence postulate was used and the correct option is given by option E.
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12x - 3у = -3
6x + y = 1
Use elimination
Pls hurry I need it now
The solution of the system of equations is (0, 1).
How to solve the system of equations?Here we want to solve the system of equations:
12x - 3y = -3
6x + y = 1
To use the elimination method, we can take the difference between the first equation and two times the second one, then we will get:
12x - 3y - 2*(6x + y) = -3 - 2*1
12x - 3y - 12x - 2y = -5
-5y = -5
y = -5/-5 = 1
Now we know the value of y, we can replace it in one of the equations ot find the value of x.
6x + y = 1
6x + 1 = 1
6x = 1 - 1 = 0
x = 0
The solution is (0, 1)
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Seth owns a printing shop that makes customized T-shirts. The cost to make T-shirts is proportional to the number of T-shirts he makes. Seth graphs a line that shows the cost per customized T-shirt. Two points on the line are (2, 8) and (4, 16). What does the slope of the line mean in this situation?
Group of answer choices
a. The cost is $4 per T-shirt.
b. The cost is $2 per T-shirt.
c. The cost is $0.25 per T-shirt.
d. The cost is $8 per T-shirt.
the slope of the line means in this situation "a. The cost is $4 per T-shirt".
What is a Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given, Seth owns a printing shop that makes customized T-shirts.
Since The cost to make T-shirts is proportional to the number of T-shirts he makes.
Thus,
The y-intercept of the line will be 0 cause the line is passing through the origin point.
The general formula of the equation of a line:
y=mx+b,
where m is the slope
b is the y-intercept
since, slope = (y - y')/(x -x')
In our case,
b = 0
m = (8 - 4)(2-1)
m = 4
And m represents The cost is $4 per T-shirt.
therefore, the slope of the line means in this situation "a. The cost is $4 per T-shirt".
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please explain how we measure the range and the domain in the following graphs, please
For the first function, the domain and the range are given as follows:
Domain: (-∞, ∞).Range: (-∞, -4].For the second function, the domain and the range are given as follows:
Domain: [-6, 0]Range: [3,6].How to obtain the domain and the range of a function?The domain of a function is the set that contains all the input values that can be assumed by the function, hence it is given by the set that contains all the values of x in the graph of the function.
The range of a function is the set that contains all the output values that can be assumed by the function, hence it is given by the set that contains all the values of y in the graph of the function.
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determine whether or not the function f(x)= x^2 +2x if x<0 x^3-2x if x>0 is continuous at x=0
The given function f(x) = x² + 2x when x <0 and f(x) = x³ - 2x when x > 0 is continuous at x=0
What is continuity ?In mathematics, The function is called as continuous at the particular value of x, if right hand limit, left hand limit and the value of function at x all are equal.
RHL = LHL = F(x)
Limit exist and continuous
Given that,
F(x) = x² + 2x {x ≤ 0}
= x³ - 2x { x > 0}
To check whether it is continuous at x = 0
First taking LHL,
F(0) = 0² + 2x0
= 0
Now, taking RHL
F(0) = 0³ - 2x0
At x = 0
F(0) = 0² + 2x0
= 0
RHL = LHL = F(0)
Hence, the given function is continuous at x =0
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Reuben and Maria walk around a track. Reuben walks each lap in 9 minutes. Maria walks each lap in 6 minutes. The two of them begin at the starting line at the same time. They walk until they meet again at the starting line. how many laps does Reuben complete? how many laps does maria complete? and how much time does it take for them to meet again at the starting line?
1) The number of laps that Reuben completes is; 2 laps
2) The number of laps that Maria completes is; 3 laps
3. It will take 18 minutes for Reuben and Maria to meet again at the starting line.
How to solve Algebra Word problems?The parameters to solve the problem are;
Time for each lap by Reuben = 9 minutes
Time for each lap by Maria = 6 minutes
Let us find the L.C.M(Lowest common multiple) of 6 and 9;
Factors of 6 = 2 * 3
Factor of 9 = 3 * 3
Thus, L.C.M = 2 * 3 * 3 = 18 Minutes
This represents the time it will take for them to meet again at the starting line.
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Cody purchased a bag of carrots costing $1.54. If Cody received $4.41 in change, how much money did he give to the cashier?
Answer: Cody gave the cashier $2.87.
Step-by-step explanation:
To determine the amount of money Cody gave to the cashier, you can subtract the amount of change he received from the cost of the carrots.
$4.41 (change) - $1.54 (cost of carrots) = $2.87
So, Cody gave the cashier $2.87.
what is the value of the expression hurry please!
Answer:
50
Step-by-step explanation:
Reid found 6 coins that totaled 61c in all. What coins did the find?
Answer:
1 quarter, 3 dimes, 1 nickel, 1 penny
Step-by-step explanation:
25c + 10c+10c+10c+5c+1c =61c
Help pic is included y(x^2+1)=1
Answer:
C.
Step-by-step explanation:
The answer is C (-1, 1/2)
An artist creates a cone-shaped sculpture for an art exhibit. If the sculpture is 5 feet tall and has a base with a circumference of 26.376 feet, what is the volume of the sculpture? Use 3.14 for 1.
The volume of the sculpture is 92.316 feet³.
What is a cone?It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.
The volume of a cone is (1/3)πr²h.
We have,
Cone-shaped sculpture:
Height = 5 feet
Base circumference = 26.376
This means,
2πr = 26.376
r = 26.376/(2 x 3.14)
r = 4.2 feet
Now,
The volume of the sculpture.
= 1/3 x 3.14 x 4.2 x 4.2 x 5
= 92.316 feet³.
Thus,
92.316 feet³ is the volume of the sculpture.
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(100 POINTS!) What is the sum of 6 of the interior angles of a regular octagon?
[tex]\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ S = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\[-0.5em] \hrulefill\\ n=8 \end{cases}\implies S=180(8-2)\implies S=1080 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{just one angle is}}{\cfrac{1080}{8}\implies 135^o}\hspace{5em}\stackrel{\textit{for six angles}}{(6)(135)\implies \boxed{810^o}}[/tex]