Answer:
y = -1/4x + 1
Step-by-step explanation:
that is (0,1) and (4,0)
gradient
can be -1/4
c can be y = mx + c
we'll take anyone of the equation
1 = 0 + c
c = 1
You would like to have $4000 in 3 years for a special vacation following graduation by making deposits at the end of every six months in an annuity that pays 4.5% compounded semiannually. a. Use one of the formulas below to determine how much you should deposit at the end of every six months.
Answer:
666.70 at the end of every six months.
Step-by-step explanation:
At the end of every six months deposit amount is 666.70
What is compound interest ?Compound interest is the interest paid on both principal and interest, compounded at regular intervals.
Formula of compound interest :
[tex]A = P(1+\frac{r}{100} )^{n}[/tex]
where,
A = final amount
P = initial principal
n = time in years
r = rate per annum
According to the question
Final Amount needed for a special vacation (A) = $4000
Time in years needed to collect Amount (n) = 3 years
Rate per compounded semiannually (r) = 4.5%
Substituting values in formula for six months
Now time (n) = 3 * 6 = 18 years
using formula of compound interest
[tex]A = P(1+\frac{r}{100} )^{n}[/tex]
[tex]4000 = P(1+\frac{4.5}{100} )^{18}[/tex]
[tex]4000 = P(1.045 )^{18}[/tex]
now,
P = 666.70
Hence, at the end of every six months deposit amount is 666.70
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-
Given the graph of y = f(x), shown as a red dashed curve, drag the movable blue point to obtain the graph of
y = f(x - 4) + 3.
Answer:
The blue point will be at (4, 3)
Step-by-step explanation:
Numbers inside the parenthases only affect x, but are revered. If it is -4, move right 4. lf it is 4, move left 4.
Numbers after the patentheses affect the movement of y. When the point is at (4, 0), move up 3.
A company wants to administer a satisfaction survey to its current customers. Using their customer database, the company randomly selects 100 customers and asks them about their level of satisfaction with the company.what type of sampling method is use
Answer:
The type of sampling method used is:
Simple random sampling.Step-by-step explanation:
A simple random sampling is a method where the pollster, in this case, the company, from a finite or infinite population (the costumers in the database) takes a representative sampling (in this case 100 costumers) to apply the survey and obtain data that can be used to deduce the way of thinking of all the costumers, though to actually identify this way of thinking, the sampling must be proportional to the size of the population, on the contrary, the data obtained won't be useful to reveal the real level of the satisfaction (In this case securely the database is 10,000 costumers or less, then the sampling is at least the 1% of the population). Another characteristic is all the people in the population should have the same opportunity to be part of the sampling, this is identified in the paragraph where says that the selection was random.
Answer:
B. simple random sampling
Step-by-step explanation:
right on edge
A nautical mile is the unit of length used in sea and air navigation. A
nautical mile is equal to 6,174 feet. What percent of a statute mile, (5,360
feet) is a nautical mile? (Round to the nearest hundredth.)
Answer:
86.82%
Step-by-step explanation:
A nautical mile = 6,174 feet.
Statute mile =5,360 feet
The percentage of a statute mile to a nautical mile is calculated as:
5360/6174 × 100
= 0.8681567865 × 100
= 86.81567865%
Approximately to the nearest hundredth = 86.82%
Therefore, the percent of a statute mile that is a nautical mile rounded to the nearest hundredth is 86.82%
A team of 15 soccer players needs to choose a captain and a co-captain. Is this an example of permutations or combination. Then find the number of possiblities.
Answer:
Permuation; 210 possibilites
Step-by-step explanation:
With permutations we care about the order of the elements, whereas with combinations we don’t. For this question order matters, because you have two different positions you want to fill (captain, and co-captain).
This would be written as 15p2
To find the number of possibilities we want to use the permuation equation.
(,)=!(−)!
P=permutation
n= the set or population (15 soccer players)
r= subset (1 captain and 1 co-captain, total of 2)
(,)=(15,2)
=15!(15−2)!
= 210
If u are confused about !(factorial) in the equation here is a quick explanation
Many calculators have a factorial key (look for the ! symbol). This function of the calculator will automate the multiplications, but if you do not have a calculator that can compute factorials you just have to go like this
1! = 1
2! = 2 x 1 = 2
3! = 3 x 2 x 1 = 6
4! = 4 x 3 x 2 x 1 = 24
5! = 5 x 4 x 3 x 2 x 1 = 120
6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40320
9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362880
10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3628800
etc
Hope this helps!!
The number of possibilities in choosing captain and co-captain are 210 ways.
What is the Permutations?Permutations are different ways of arranging objects in a definite order. It can also be expressed as the rearrangement of items in a linear order of an already ordered set. The symbol nPr is used to denote the number of permutations of n distinct objects, taken r at a time.
Given that, a team of 15 soccer players needs to choose a captain and a co-captain.
Number of captains can be choose from 15 players.
Number of co-captains can be choose from 15-1=14 players.
So, the number of possibilities= 15×14
= 210 ways
Therefore, the number of possibilities in choosing captain and co-captain are 210 ways.
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Find the missing length indicated.
Answer:
Step-by-step explanation:
x=✓25*9
x=✓5^2*3^2
x=5*3
x=15
2. Points A, B and C are all on the
circumference of the circle.o
represents the centre.
DA and DB are tangents to the
circle. Angle BDO = 31
Work out the size of angle.
Question
Points A, B and C are all on the
circumference of the circle. O represents the centre. DA and DB are tangents to the circle. Angle BDO = 31°
Work out the size of angle x
Answer:
62°
Step-by-step explanation:
To solve for the above question, we would be using circle theorems.
Step 1
Angle OBD = 90° This is because a radius and a tangent meet at 90°
Step 2
The sum of Angles in a triangle = 180°
180° = Angle OBD + Angle BDO + Angle BOD
180° = 90° + 31° + Angle BOD
Angle BOD = 180° - (90° + 31°)
= 180° - 121°
Angle BOD = 59°
Step 3
Angle BOD = Angle AOD because they are congruent ,therefore, Angle AOD = 59°
Step 4
The sum of angles of a straight line = 180°
Angle BOD, Angle AOD and Angle x are angles on a straight line
Hence,
180° = Angle BOD + Angle AOD + Angle x
180° = 59° + 59° + x
x = 180° - ( 59 + 59)°
x = 180° - 118°
x = 62°
Therefore Angle x = 62°
Determine the surface area of a sphere with a diameter of 16 cm. Question 4 options: A) 804.2 cm2 B) 1,024 cm2 C) 201.0 cm2 D) 3,216.9 cm2
Answer:
The answer is option A.
804.2cm²Step-by-step explanation:
Surface area of a sphere is 4πr²
where r is the radius
radius = diameter / 2
radius = 16/2 = 8cm
Surface area of the sphere is
4π (8)²
= 4(64)π
= 256π
= 804.2cm²
Hope this helps you.
PLEASEEEE HELPP !!In each figure, a//b . Determine whether the third figure is a translation image of the first figure. Write yes or no. Explain your answer.
Answer:
No it’s not a translation
Step-by-step explanation:
No it’s not a translation because a translation is when you are just moving a shape not resizing or rotating the shape.
explain the words and the connections of population ,area, urban,and density
Step-by-step explanation:
1. Population Area: this can be defined as a group of similar species
inhabiting/ co-existing in a defined location or space
2. Urban population: urban areas are often more developed areas with greater population than rural environments
it's the people living in cities.
3. Population density: this is a measurement of population per unit area..
Draw a vector representing the course of a ship that goes 50 miles on a
course with direction 2400.
Answer:
The answer is below
Step-by-step explanation:
We have a vector with a magnitude of 50 miles and a direction of 240 °.
To draw it, the first thing is to make a Cartesian plane, the first thing is to know in which quadrant it would be, 240 ° is in the third quadrant (180 ° - 270 °), that is, it would be 30 ° (270 ° - 240 °) with respect to to the y axis negative.
Knowing this angle, we calculate the value of x and y, knowing that the magnitude of the vector is 50 miles, that is, this value would be the hypotenuse.
The value on the x-axis can be calculated using the sine of the angle, like this:
sin 30 ° = x / 50
x = sin 30 ° * 50
x = 25, how is the third quadrant would be -25
Now to calculate the value on the y-axis it would be by means of Pythagoras and it would be:
y ^ 2 = 50 ^ 2 - 25 ^ 2
y ^ 2 = 1875
y = 43.3, -43.3 because it must be located in the fourth quadrant
Which means that to draw the vector that we are asked to do, we must draw a point from origin (0,0) to (-25, -43.3).
Then I leave a sketch of what it would be:
Which function has the same graph as x+y= 11?
A. Ax) = -y + 11
B.
Rx) = -x + 11
C.
A x) = x-11
D.
*x) = y- 11
Answer:
the answer is b= -x+11
Answer:b
Step-by-step explanation:
I need help !!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
This is just comparing what is bigger, I don't see what's so hard about it.
Step-by-step explanation:
1. >
2.>
3.>
4.>
5.<
6.<
7.>
8.<
b.
1.>
2.<
3.>
4.<
5.>
6.>
7.>
8.>
approximately 13% of the USA population is left handed. Hiw many lefties would expect in a school of 420 students
Answer:
Approximately 55 students
Step-by-step explanation:
13% of 420 is 54.6 which you can then round up to 55
Hope this helped!
Answer:
55 students
Step-by-step explanation:
Take the percent and multiply by the number of students
13% * 420
.13 * 420
54.6
Rounding up
55 students
if straykids hyunjin had 50,000 won and wanted to by lots of 45rings for 500 won how much will he have left? b) if changbin and han had 145 lightsicks and sold 75? how much lighsticks will they have now?
Answer:
a) he would have 27500 won
b) changbin and han would have 70 lightsticks
Step-by-step explanation:
a)
multiply 45 rings by 500 won to get the total expense
45 x 500 = 22500
then subtract 22500 won from 50000 to get the amount left after the purchase
50000 - 22500 = 27500
this results in 27500 won total
b)
subtract 75 from 145 to get the amount left
145 - 75 = 70
Answer:
Hyunjin has 27,500 left.
Changbin & Han have 70 lightsticks left.
Step-by-step explanation:
A) 45 × 500 = 22500 50,000 - 22500 = 27500
B) 145 - 75 = 70
Please hurry❗️❗️❗️!!!!!!
Which expression is equivalent to a+(C+7)?
О 7ac
O a-(C+7)
O (C+7)-a
0 (a+c) + 7
Answer:
The answer is (a+c) + 7
Since addition is associative a + ( C + 7) can also be written as (a+c) + 7
Hope this helps you
Answer:
(a+c)+7
Step-by-step explanation: This method is called associative property.
On addition changing the order brings no change to the answer. For example:- 2+3=3+2. but don't confuse this with multiplication. For example, if the question was a(c+7), then you are supposed to multiply c, + and 7 by a.
Hope it would help :)
Find the missing segment in the attached image
Answer:
The length of the missing segment is 24
Step-by-step explanation:
Given
The figure above
Required
Determine the missing segment
Let the missing segment be represented with x
Given that, there exist parallel lines between the two triangles;
The relationship between the sides of the triangles is as follows;
[tex]\frac{15}{x} = \frac{15+5}{8+x}[/tex]
[tex]\frac{15}{x} = \frac{20}{8+x}[/tex]
Cross Multiply
[tex]15 * (8 + x) = 20 * x[/tex]
Open bracket
[tex]15*8 + 15 * x = 20 * x[/tex]
[tex]120 + 15x = 20x[/tex]
Subtract 15x from both sides
[tex]120 + 15x -15x= 20x-15x[/tex]
[tex]120 = 20x-15x[/tex]
[tex]120 = 5x[/tex]
Divide both sides by 5
[tex]\frac{120}{5} = \frac{5x}{5}[/tex]
[tex]\frac{120}{5} = x[/tex]
[tex]24 = x[/tex]
[tex]x = 24[/tex]
Hence, the length of the missing segment is 24
HELP!!! How far have I travelled if I biked at 10mph for hhrs, I walked at 3mph for twice as long as I biked, and ran at 10mph for one quarter as long as I walked?
Answer:
21h miles
Step-by-step explanation:
The appropriate relation is ...
distance = speed · time
__
We are given that ...
biking time = h
walking time = 2h
running time = (1/4)(2h) = h/2
The total distance traveled is ...
total distance = biking distance + walking distance + running distance
= (10)(h) +(3)(2h) +(10)(h/2)
= 10h + 6h + 5h
total distance = 21h . . . miles
Answer:
21h miles
Step-by-step explanation:
The appropriate relation is ...
distance = speed · time
__
We are given that ...
biking time = h
walking time = 2h
running time = (1/4)(2h) = h/2
The total distance traveled is ...
total distance = biking distance + walking distance + running distance
= (10)(h) +(3)(2h) +(10)(h/2)
= 10h + 6h + 5h
total distance = 21h . . . miles:
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!
GPAs at CCSU are normally distributed with a mean of 2.38 and a standard deviation of 0.45. Find the z-score for a GPA of 3.06. and discuss the significance of the z-score.
Step-by-step explanation:
Z-score = (score-mean)/standard deviation
= (3.06-2.38)/0.45
= +1.51
The significance of z-score will be "1.5111".
Given values are:
Mean,
[tex]\mu = 2.38[/tex]
Standard deviation,
[tex]\sigma = 0.45[/tex]
GPA,
[tex]\bar x = 3.06[/tex]
Now,
→ The z-score will be:
= [tex]\frac{\bar x - \mu}{\sigma}[/tex]
By putting the given values, we get
= [tex]\frac{3.06-2.38}{0.45}[/tex]
= [tex]\frac{0.68}{0.45}[/tex]
= [tex]1.5111[/tex]
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Angelo cuts a piece of wood for a project. The first cut is shown and can be represented by the equation y - 5x-1. The second cut needs to be parallel to the first. It will pass through the point (0,6). Identify the equation that
represents Angelo's second cut.
PLEASE HELP!
Answer:
y=5x+6
Step-by-step explanation:
Please see attached
310
Which law would you use to simplify the expression
quotient of powers
power of a quotient
product of powers
power of a product
power of a quotient
edge 2021
The law used to simplify the expression is quotient of powers.
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given is an expression, 3¹⁰ / 3⁴, we need to determine the law used to simply the expression,
3¹⁰ / 3⁴
For this case we have an expression formed by a division of powers of the same base in which we must apply a law to simplify said expression.
By the definition we have the property of the power quotient of the same base set:
xᵃ / xᵇ = x⁽ᵃ⁻ᵇ⁾
So, using the same,
3¹⁰ / 3⁴ = 3⁽¹⁰⁻⁴⁾ = 3⁶
Thus, to simplify the expression we must use the property of the power quotient of the same base.
Hence, the law used to simplify the expression is quotient of powers.
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A gambler loses $100 Saturday night and wins $65 on Sunday. What is the gambler’s total loss or gain? Express your answer as an integer.
Answer:
-35 dollar net loss
Step-by-step explanation:
Since the gambler won $65 but still lost $100, we can see that we would still have a negative net loss.
Find a quadratic polynomial the sum and product of whose zeroes are -8 and 12 respectively. Hence find the zeroes.
Step-by-step explanation:
We khow the sum and the product of the zeroes of this quadratic polynomial
Here is a trick :
when we khow the sum S and the product P ofvtwo numbers we can find them by solving :
x²-Sx+p=0
here S= -8 and P=12
so:
x²+8x+12=0
Let Δ be the discrminant of this equation: a= 1 , b= 8 and c=12
Δ= 8²-4*12 =16
the zeros are:
(-8-4)/2= -6
(-8+4)/2 = -2
verify:
-6+(-2)= -8
-2*(-6)= 12
now the polynomial quadratic is:
(x+6)(x+2)
A motor is 85.4 % efficient: that is, the output is 85.4 % of the input.
What is the input if the motor delivers 10.75 hp. ( Round your answer to 1
decimal place.)
Answer:
12.6 hp
Step-by-step explanation:
output of motor = 85.4% of input of motor.
Given that motor delivers 10.75 hp, it means output of motor is 10.75hp
Using both the given conditions
10.75 = 85.4% of input of motor
=> 10.75 = 85.4/100 * input of motor
=> input of motor = 10.75*100/85.4 = 1075/85.5 hp = 12.57 hp.
Input of motor rounded to 1 decimal place = 12.6 hp
If a sample consists of the following data values, what is the sample mean?
13, 91, 44, 68, 54, 16, 88, 74
Answer:
mean =sum of all data values
total number of data
13+91+44+68+54+16+88+74
8
448
8
=56
therefore the mean is 56
Answer: 51
Step-by-step explanation:
Answer PLS !!! Need it now
Answer:
area = 25.12
Step-by-step explanation:
area of circle = pi(r)^2
area = 3.14 (4)^2 /2
area = 3.14 (16) / 2
area = 50.24 / 2
area = 25.12
Answer:
A = 78.9568350285
Step-by-step explanation:
A = TTr^2/2
A = TT4^2/2
A = 12.5663706^2/2
A = 157.913670057/2
A = 78.9568350285
The sum of two numbers is 88; one number is 12 less than the other. What is the larger number? 1. Cut the _______ number in half. Write both halves on your paper. 2. Cut the ______________in half. 3. Now ADD half and SUBTRACT half from each side.
Answer:
50
Step-by-step explanation:
I have set up an equation, where 'x' is the larger number:
x + (x - 12) = 88
Solve for 'x':
x + (x - 12) = 88
x + x - 12 = 88
2x - 12 = 88
2x -12 + 12 = 88 + 12
2x = 100
2x/2 = 100/2
x = 50
The larger number should be 50.
Answer:50
Step-by-step explanation:
What transformations were applied to ABC to obtain A'B'C'?
A. rotate 180 degrees counterclockwise, then shift 3 units down
B. rotate 270 degrees counterclockwise, then shift 3 units down
c. rotate 180 degrees counterclockwise, then shift 3 units up
D. rotate 270 degrees counterclockwise, then shift 3 units up
O
The required transformation is to rotate 270 degrees counterclockwise, then shift 3 units down. Option B is correct.
What is the geometry across the coordinate plane transformation?Transform the coordinate plane's shapes by translating, rotating, or reflecting them. In the 19th century, Felix Klein introduced transformational geometry, a novel perspective on geometry.
Here,
In the graph, triangle ABC is transformed into triangle A'B'C' by a combination of rotation and translation. First, the triangle is rotated 270 degrees counterclockwise around the origin. Then, the resulting triangle is shifted 3 units down.
Thus, the required transformation is to rotate 270 degrees counterclockwise, then shift 3 units down. Option B is correct.
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Which expression is equivalent to (x Superscript one-half Baseline y Superscript negative one-fourth Baseline z) Superscript negative 2? StartFraction x Superscript one-half baseline Over y z squared EndFraction StartFraction x Superscript one-half baseline Over y Superscript one-fourth Baseline z squared EndFraction StartFraction y Superscript one-half Baseline Over x z squared EndFraction
Answer:
[tex]\frac{x^{\frac{1}{2}}}{y^{\frac{1}{4}}z^2}[/tex]
Step-by-step explanation:
Given
[tex]x^{\frac{1}{2}}y^{-\frac{1}{4}}z^{-2}[/tex]
Required
Find the equivalent
To find the equivalent of the given expression; we have to apply laws of indices;
As a law;
[tex]a^{-m} = \frac{1}{a^m}[/tex]
So; the expression [tex]x^{\frac{1}{2}}y^{-\frac{1}{4}}z^{-2}[/tex] becomes
[tex]x^{\frac{1}{2}}*\frac{1}{y^{\frac{1}{4}}}*\frac{1}{z^2}[/tex]
This is further simplified to
[tex]x^{\frac{1}{2}}*\frac{1}{y^{\frac{1}{4}} * z^2}[/tex]
[tex]x^{\frac{1}{2}}*\frac{1}{y^{\frac{1}{4}}z^2}[/tex]
Combine to form a single fraction
[tex]\frac{x^{\frac{1}{2}}*1}{y^{\frac{1}{4}}z^2}[/tex]
Multiply numerator
[tex]\frac{x^{\frac{1}{2}}}{y^{\frac{1}{4}}z^2}[/tex]
The expression can not be further simplified
Hence [tex]x^{\frac{1}{2}}y^{-\frac{1}{4}}z^{-2}[/tex] is equivalent to [tex]\frac{x^{\frac{1}{2}}}{y^{\frac{1}{4}}z^2}[/tex]
Answer:
c
Step-by-step explanation:
x has a exponent of -1 after multiplying 1/2 and -2, so x has to be in the denominator of the answer no matter what.
Hope this helped other than the guy above lol