Jayden is folding a paper strip of 66 cm into a 6 sided honeycomb. So the length of each side will be 11cm.
Jayden has a paper strip of length 66 cm. He had to make a honeycomb with it. It will have six equal sides. To calculate the length we have to formulate the equation.
Total length = number of sides × length of one side
66 = 6 × x
Dividing by 6 on both sides,
66÷6 = 6x ÷ 6
11 = x
So the length of the side of honeycomb will be of 11 cm.
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The complete question is as below
Jayden folded a 66cm strip of paper into 6 equal parts to model a honeycomb cell's. Each part was one side of the model. What is the length of one side of the model?
Need help finding the slope of the line on the graph
Answer:
2/3-3/4-2undefined40Step-by-step explanation:
You want to find the slopes of the lines shown in the attached graphs.
SlopeThe slope of a line is its "rise" divided by its "run":
m = rise/run
To determine slope from a graph, start at an identified point on the left, and count the grid squares up (+) or down (-) to the same horizontal line as the identified point on the right. This is the "rise". Then count the grid squares horizontally to the identified point. This is the "run". The slope is the ratio of these numbers.
1. rise 4, run 6, slope 4/6 = 2/3
2. rise -3, run 4, slope -3/4
3. rise -6, run 3, slope -6/3 = -2
4. run = 0; division by 0 is "undefined", so the slope is "undefined"
5. rise 4, run 1, slope 4/1 = 4
6. rise 0, run (anything), slope 0/1 = 0
__
Additional comment
It is helpful to remember that a horizontal line has a slope of 0, and a vertical line has a slope that is "undefined." Slope is positive if the line goes up to the right. It is negative if the slope goes down to the right.
Because the slope of a vertical line is "undefined," its equation cannot be written in "slope-intercept" form.
Here, points are marked on the lines. When that is not the case, it usually works well to identify points where the line crosses an intersection of grid lines.
You can also use grid crossings to check your answer for the slope. For example, the line on graph 3 crosses grid intersections that are 2 down and 1 over from the marked points (and other grid intersections), confirming a slope of -2.
There are 50 marbles in a bag. 35 of the marbles are brown. Otti takes at random a marble from the bag. He records the colour of the marble and puts the marble back in the bag. He does this 300 times. Work out an estimate for the number of brown marbles he takes.
If there are 50 marbles in a bag and 35 of them are brown, and Otti takes one marble and put it back afterwards and does it 300 times, then the estimated number of brown marbles Otti takes is around 105.
The expected number of brown marbles Otti takes can be estimated by multiplying the probability of drawing a brown marble (35/50) by the number of times he draws (300).
(35/50) × 300 = 105
This gives an estimated result of 105 brown marbles. It's important to note that this is just an estimate and the actual number could be different. The variation in the actual number of brown marbles Otti takes can be attributed to the randomness of the process.
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√52x^4 solve ……………….
Answer:
2[tex]\sqrt{13x^{2} }[/tex]
Step-by-step explanation:
To simplify the expression √52x^4, we can break it down as follows:
√(52x^4) = √(4 * 13 * x^4)
Since the square root of a product is equal to the product of the square roots, we can simplify further:
√(4 * 13 * x^4) = √4 * √13 * √(x^4)
The square root of 4 is 2, and the square root of x^4 is x^2:
2 * √13 * x^2
Therefore, the simplified expression is 2√13x^2.
Answer:
[tex]\large\text{$2\sqrt{13}\;x^2$}[/tex]
Step-by-step explanation:
Given expression:
[tex]\sqrt{52x^4}[/tex]
Prime factorization is the process of representing a positive integer as a product of its prime factors.
The prime factorization of 52 is 2² · 13. Therefore, rewrite 52 as 2² · 13:
[tex]\sqrt{2^2 \cdot 13 \cdot x^4}[/tex]
[tex]\textsf{Apply the radical rule:} \quad \sqrt{abc}=\sqrt{\vphantom{b}a}\sqrt{b}\sqrt{c}[/tex]
[tex]\sqrt{2^2} \sqrt{13} \sqrt{x^4}[/tex]
[tex]\textsf{Apply the radical rule:} \quad \sqrt{a^2}=a, \quad a \geq 0[/tex]
[tex]2\sqrt{13} \sqrt{x^4}[/tex]
[tex]\textsf{Apply the radical rule:} \quad \sqrt[n]{a^m}=a^{\frac{m}{n}},\quad \textsf{assuming} \;a\geq 0[/tex]
[tex]2\sqrt{13} \;x^{\frac{4}{2}}[/tex]
[tex]2\sqrt{13} \;x^2[/tex]
Therefore, the simplified expression is:
[tex]\large\boxed{2\sqrt{13}\;x^2}[/tex]
If 6x + 7y= 2007 and 7x+6y= 7002, then what is the value of x + y?
bryan takes out a loan of £800. This debt increases by 28% every year. How much money will bryan owe after 14 years?
Answer: £3136
Step-by-step explanation:
First you want to find 28% of 800 to find out how much it increases by every year.
So 800*0.28= 224
And then you want to multiply 224 to 14 years to see how much he has to pay in 14 years
224*14=3136
Your answer: £3136
For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 27 N acts on a certain object, the acceleration of the object is 3 /ms2. If the acceleration of the object becomes 2 /ms2, what is the force?
If the acceleration of the object becomes 2 m/s², the value of force is,
⇒ 18 N
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
For a moving object, the force acting on the object varies directly with the object's acceleration.
Hence, We get;
⇒ F = k × a
Where, F is force of the object and 'a' is acceleration of the object.
Here, When a force of 27 N acts on a certain object, the acceleration of the object is 3 m/s².
So, We get;
⇒ F = k × a
⇒ 27 = k × 3
⇒ k = 9
Thus, If the acceleration of the object becomes 2 m/s², the value of force is,
⇒ F = k × a
⇒ F = 9 × 2
⇒ F = 18 N
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cos(θ)=15/17, 15/17<θ<2(pi)
find cotθ
Step-by-step explanation:
cot(θ) = 1/tan(θ)
tan(θ) = sin(θ) / cos(θ)
Given cos(θ) = 15/17, we can find sin(θ) using the Pythagorean identity:
sin(θ) = sqrt(1 - (cos(θ))^2) = sqrt(1 - (15/17)^2) = 4/17
So, tan(θ) = 4/15
And, cot(θ) = 1/tan(θ) = 15/4
Answer: 15/8
Step-by-step explanation: We know that sin(0) will equal 8 by the 8,15,17 triangle. We using the restricted domain value for theta and using the pythagorean identities to get cot(0) as cos(0)/sin(0) and substitute the values. The denominators cancel and the result is 15/8.
a fair coin is tossed 4 times. what is the probability that there are more heads than tails given that the number of tails is divisible by 3?
The probability of more heads than tails is 1/2 since the number of tails is divisible by 3.
A fair coin is one that has equal chances of being heads or tails when it is tossed. When a fair coin is tossed four times, the probability of getting more heads than tails is 1/2. This is because for each toss, the probability of getting a head or a tail is equal (1/2). This means that the probability of getting more heads than tails is the same as the probability of getting more tails than heads, which is 1/2.
Since the number of tails is divisible by 3, this means that in the four tosses, there must either be 0, 3, or 6 tails. Since there are no other possibilities, the probability of more heads than tails is 1/2 since it is equally likely to get more heads than tails or more tails than heads.
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HELP QUICK (5 star and brainliest if correct) If masha buys three roses she will have 7 dollars left. To buy nine roses, Masha will need to borrow 11 dollars from her father. How many dollars does Masha have?
Let's start by setting up a system of equations to represent the given information:
3r = m - 7
9r = m + 11
where r is the cost of one rose, and m is the total amount of money that Masha has.
We can solve this system of equations using the elimination method:
Multiplying the first equation by 3, we get:
9r = 3m - 21
Subtracting the second equation from this, we get:
0 = -4m - 32
Simplifying, we get:
m = -8
Therefore, Masha has $-8, which means she owes money. This indicates that there may be an error in the problem statement or data provided.
Answer:
Masha has 16 dollars.
Step-by-step explanation:
3x + 7 = Masha's total money
9x = Masha's total money + 11 (after borrowing)
We can use the first equation to find the value of 3x, which is Masha's total money if she buys three roses:
3x + 7 = Masha's total money
3x + 7 = Masha's total money
3x = Masha's total money - 7
We can substitute the second equation to solve for Masha's total money:
9x = Masha's total money + 11
9x = (3x + 7) + 11
9x = 3x + 18
6x = 18
x = 3
Now we know that one rose costs 3 dollars. We can use the first equation to find Masha's total money if she buys three roses:
3x + 7 = Masha's total money
3(3) + 7 = Masha's total money
9 + 7 = Masha's total money
Masha's total money = 16
the cost in dollars of a custom made t shirt is represented by 0.75n+9.99 where n is the number of words in the design. Write and iterpret a simplifies expression that represents the cost of 12 shirts.
Answer:
Step-by-step explanation:
First you would take .75n = .75 * 12 shirts
.75 * 12 = 9
You then would take 9 + 9.99 which obviously is 18.99$
Answer = 18.99$ per 12 T-shirts
Which statements are true the ordered pair (1, 2) and the system of equations?
y=-2x+4
7z-2y=3
Select each correct answer.
O The ordered pair (1, 2) is not a solution to the system of linear equations.
When (1, 2) is substituted into the second equation, the equation is true.
Q. When (1, 2) is substituted into the first equation, the equation is false.
□ When (1, 2) is substituted into the second equation, the equation is false
When (1, 2) is substituted into the first equation, the equation is true.
The ordered pair (1, 2) is a solution to the system of inear equations.
Answer:
The statements that are true about the ordered pair (1, 2) and the system of equations are:
When (1, 2) is substituted into the first equation, the equation is true.
The ordered pair (1, 2) is a solution to the system of linear equations.
So, the correct options are:
When (1, 2) is substituted into the first equation, the equation is true.
The ordered pair (1, 2) is a solution to the system of linear equations.
Step-by-step explanation:
At the beginning of an environmental study, a forest covered an area of 1500 km^2. Since then, this area has decreased by 4.25% each year. Let t be the number of years since the start of the study. Let y be the area that the forest covers in km^2. Write an exponential function showing the relationship between y and t.
Answer:
y = 1500 * 0.9575^t
Step-by-step explanation:
Where 0.9575 is equal to 1 - 0.0425, which represents a decrease of 4.25% each year.
I need help , come on ! Please
(a) The equation to find x is 4x + 22 = 90.
(b) The degree of each angle:
m∠1 = 51°m∠2 = 39°The sum of angle 1 and 2 is equal to right angle.
What is the value of right angle?The value of a right angle is equal to 90°.
In the figure, we have a right angle and one line in it. It makes two angles 1 and 2 with
m∠1 = (3x)°m∠2 = (x + 22)°(a) Find an equation to find x!
(b) Find the degree measure of each angle!
The sum of angle 1 and 2 is equal to 90°. So,
m∠1 + m∠2 = 90
3x + x + 22 = 90
4x + 22 = 90
This is the equation to find x. Then, we find x.
4x + 22 = 90
4x = 90 - 22
4x = 68
x = 68/4
x = 17°
The degree measure of each angle will be
m∠1 = 3x
m∠1 = 3(17)
m∠1 = 51°
m∠2 = x + 22
m∠2 = 17 + 22
m∠2 = 39°
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GARDEN Camila put a frame around a triangular garden in her yard. The two legs of the triangle are 8 feet long each, and the third side is equal to the length of a leg times 2⎯⎯√ . What is the perimeter of the triangle? Give your answer as a simplified radical expression,
The perimeter of the triangle is 16+8√2.
The sum of the lengths of the sides is the perimeter of any polygon.
Perimeter = Sum of the three sides
There is a general formula for the perimeter of a triangle:
P=a+b+c
There are three steps to calculate the perimeter of a triangle:
Step 1: write the measurements of all the sides, and check that all the sides should have the same unit.
Step 2: Now, calculate the sum of all the sides.
Step 3: Then, give the answer along with the unit.
The given information is the two sides of a triangle are a=b=8 and c=8√2.
Now substitute all the given values in the above formula we get:
P=8+8+8√2
P=16+8√2.
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Joey is training for a 5k race. She runs the same distance two days in a row. On the first day, she runs 5 laps around the track, and then runs additional 1. 5 miles. The next day she runs 3 laps, and an additional 4 miles. Analyze the text to answer the following questions
Answer:
Step-by-step explanation:
What is Joey's total distance run on the first day?
Joey runs 5 laps around the track, which we can assume is 1 mile per lap. So, she runs 5 miles. Additionally, she runs 1.5 miles, so her total distance run on the first day is 5 + 1.5 = 6.5 miles.
What is Joey's total distance run on the second day?
Joey runs 3 laps around the track, which we can assume is 1 mile per lap. So, she runs 3 miles. Additionally, she runs 4 miles, so her total distance run on the second day is 3 + 4 = 7 miles.
the distance between the earth and the moon is approximately feet, and a rocket can travel there at a speed of about 1,540,000 ft/min. how long will it take the rocket ship to travel to the moon and back, in minutes? express your final answer in minutes and round to the nearest minute.
The average distance between the Earth and the Moon is about 238,855 miles or 1.28 light-seconds.
To convert miles to feet, multiply by 5,280, giving us approximately 1.27 million feet. A rocket traveling at a speed of 1,540,000 ft/min would take approximately 82.5 minutes to travel to the Moon. The round trip to the Moon and back would take approximately 165 minutes, or about 2 hours and 45 minutes.
It's important to note that this is an estimate and the actual time it takes may vary due to various factors such as the rocket's trajectory, speed, and other environmental conditions. Also, it's worth noting that this speed is significantly faster than current spacecraft speeds, so the actual time it would take a rocket to travel to the Moon and back is likely to be much longer.
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can someone please help me(15 points will give brainliest!!!)
Answer:
m = -2
b = -3
Step-by-step explanation:
Point slope formula of a line = [tex]y-y_{1} = M(x-x_{1} )[/tex]
Where x1 and y1 are the coordinates of the point and M is the slope.
Given slope = -2
Point = (-7,11)
So x1 = -7 and y1 = 11
Substituting the values in the point-slope formula, we get:
[tex]y-11 = -2(x - (-7))[/tex]
[tex]= > y = -2x -14 + 11[/tex]
Or
[tex]y = -2x -3[/tex]
Thus, m = -2 and b = -3
The area model shows 14 x 16 what number is missing
By using Area Model of Multiplication and Division, it can be concluded that the missing number in the area model is 40.
Area Model of Multiplication and Division is a rectangular chart used to multiply and divide two numbers or expressions, where the quotient and divisor determine the length and width of the rectangle.
In this model, we split up a large rectangular area into several smaller rectangular, using number bounds, to make calculations easier.
Now we take a look at our area model 14 x 16 in size.
Area I = 10 x 10 = 100
Area II = 6 x 10 = 60
Area III = 6 x 4 = 24
Using the same way, the missing number, area IV, can be calculated as follows:
Area IV = 10 x 4 = 40
Thus, it can be concluded that the missing number in the area model is 40.
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(2+5root7)/(2-5root7) = a+b root7
class 9
with complete explanation pls
The value of a and b are -179/171 and -20/171 respectively.
What is rationalization of surd?Rationalising surds is where we convert the denominator of a fraction from an irrational number to a rational number. In more complex cases, it is useful to multiply the denominator by its conjugate to cancel out the surds in the denominator.
(2+5√7)/(2-5√7)
by rationalization
(2+5√7)/(2-5√7) × (2+5√7)/(2+5√7)
=( 4+10√7 + 10√7 + 175)/4+10√7 - 10√7- 175
= (20√7+179)/-171
= -20/171 √7 -179/171
therefore the value of a = -179/171 and b = -20/171
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A fish has a mass of 75kg plus one quarter of its mass while the fisherman has a mass of 100kg plus one fifth of his mass. What is the positive difference between their masses, in kg?
Using simple mathematical operations, we know that the positive difference between the mass of the fish and fisherman is 26.25.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.
The operation's arity is determined by the number of operands.
The addition, subtraction, multiplication, division, exponentiation, and modulus operations are carried out via the arithmetic operators.
So, we know that:
Fish: 75kg + 75/4
75 + 18.75
93.75
Fisherman: 100kg + 100/5
100 + 20
120
Positive difference: 120 - 93.75 = 26.25
Therefore, using simple mathematical operations, we know that the positive difference between the mass of the fish and fisherman is 26.25.
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A truck that can carry no more than 7100 lb is being used to transport refrigerators and upright pianos. Each refrigerator weighs 250 lb and each piano weighs 425 lb. Write and graph an inequality to show how many refrigerators and how many pianos the truck could carry. Will 12 refrigerators and 11 pianos overload the truck? Explain
Yes, 12 refrigerators and 11 pianos overload the truck, because 12 refrigerators and 11 pianos weighs more than 7100 lb.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Given that, a truck that can carry no more than 7100 lb is being used to transport refrigerators and upright pianos
Let the number of refrigerators be x and the number of pianos be y.
Each refrigerator weighs 250 lb and each piano weighs 425 lb.
Here, 250x+425y≤7100
Will 12 refrigerators and 11 pianos overload the truck
Now, put x=12 and y=11 in the inequality 250x+425y≤7100, we get
250×12+425×11≤7100
7675≤7100 not true
Therefore, the inequality represent the given scenario is 250x+425y≤7100.
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I need help solving this problem
The width of the rectangular will be x+4.
What is a rectangle?
Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees. Quadrilaterals are typically four-sided closed shapes, and there are numerous varieties of them. Square, rectangle, rhombus, kite, and trapezoid are the most typical shapes. Four closed sides make up a quadrilateral. Quadrilaterals are the following figures: a four-sided figure. The form features a single set of parallel sides and no right angles.
Area of the rectangle is A = a*b
Given Length is = x+7
And the area is x² +11x+28
So the width is = x² +11x+28 / x+7
x² +7x+4x+28/x+7
=(x+7)(x+4)/x+7
=x+4
Hence the width of the rectangular will be x+4.
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Can someone please tell me the specific solving steps for this equation.
I stopped after changing log10(10x) into ln10x/ln10.
The integral ∫₁/₁₀¹⁰[㏒₁₀(10x)/x]dx = 2㏑10
What is integration?Integration is the process of finding the antiderivative of a fuinction.
How to find the given integral.Given the integral
[tex]\int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}10x }{x} } \, dx[/tex]
We evaluate the integral as follows
[tex]\int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}10x }{x} } \, dx[/tex]
Now, using the properties of the laws of logarithms, we have ㏒ab = ㏒a + ㏒b
So, [tex]\int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}10x }{x} } \, dx = \int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}10 + log_{10}x }{x} } \, dx \\= \int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}10}{x} } \, dx + \int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}x}{x} } \, dx \\= \int\limits^{10}_{\frac{1}{10} } {\frac{1}{x} } \, dx + \int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}x}{x} } \, dx\\[/tex]
So, using the property of change of base of logarithm, we have that
logx = lnx/ln10
, [tex]\int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}10x }{x} } \, dx = \int\limits^{10}_{\frac{1}{10} } {\frac{1}{x} } \, dx + \int\limits^{10}_{\frac{1}{10} } {\frac{\frac{lnx}{ln10} }{x} } \, dx\\= \int\limits^{10}_{\frac{1}{10} } {\frac{1}{x} } \, dx + \frac{1}{ln10}\int\limits^{10}_{\frac{1}{10} } {\frac{lnx}{x} } \, dx\\= \int\limits^{10}_{\frac{1}{10} } {\frac{1}{x} } \, dx + \frac{1}{ln10}\int\limits^{10}_{\frac{1}{10} } {{lnx} \, dlnx[/tex]
[tex]\int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}10x }{x} } \, dx = {[lnx]_{\frac{1}{10}}^{10} } + {\frac{[lnx]^{2}}{2} }_{\frac{1}{10}}^{10} } \\= ln10 - ln\frac{1}{10} + \frac{1}{2}[[ln10]^{2} - [ln\frac{1}{10}]^{2} ] \\= ln10 + ln10 + \frac{1}{2}[[ln10]^{2} - [-ln10}]^{2} ]\\= ln10 + ln10 + \frac{1}{2}[[ln10]^{2} - [ln10}]^{2} ]\\= 2ln10 + 0\\= 2ln10[/tex]
So, the we see that the integral [tex]\int\limits^{10}_{\frac{1}{10} } {\frac{log_{10}10x }{x} } \, dx = 2ln10[/tex]
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karan bought a few kg of rice for Rs 60 per kg and equal quantity of rice for Rs30. If he mixed both kinds of rice together and sells at Rs70 per kg find gain and loss %
Answer:
60x
30x
after mixing (60+30)x=90x
sold for=70x
gain=(90x-70x)/90x×100
20x/90x×100%
=22.22%
Given that f(x)= ax/bx-4, x≠4/b, x≠0. If f(1)=-2 and f(2)=2, find a+b.
The sum of a and b is obtained as follows:
a + b = 5.
How to obtain the values of a and b?The function for this problem is defined as follows:
f(x) = ax/[bx - 4]
f(1) = -2 means that when x = 1, y = -2, hence:
-2 = a/(b - 4)
a = -2b + 8
f(2) = 2 means that when x = 2, y = 2, hence:
2 = 2a/(2b - 4)
2a = 4b - 8
a = 2b - 4.
Equaling the two equations, the value of b is obtained as follows:
-2b + 8 = 2b - 4
4b = 12
b = 3.
Hence the value of a is ob:
a = 2b - 4
a = 2(3) - 4
a = 2.
Hence the sum is of:
a + b = 2 + 3
a + b = 5.
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what is the sum of x+52+67+75=1
Answer:
-193
Step-by-step explanation:
x+52+67+75=1
x+119+75=1
x+194=1
-194. -194
x=-193
What proportion of trucks can be expected to travel between 34 and 50 thousand miles in a year? b. What percentage of trucks can be expected to travel either less than 30 or more than 60 thousand miles in a year? c. How many miles will be traveled by at least eighty percent of the trucks? d. What are your answers to (a) through (c) if the standard devia- tion is 10 thousand miles?
The values of the proportion will be calculated by standardizing the normal distribution and using the Z table to find the values.
Here we are given that the mean distance traveled is 50,000 miles
with a standard deviation of 10,000
Now we need to find the proportion of trucks expected to travel between 34,000 and 50,000
(a)
Now for this, we need to find the area under the given normal curve between 34,000 and 50,000
For this, we need to first find the standard value. Hence we get
(X - μ)/σ
where μ = mean = 50,000
σ = standard deviation = 10,000
Hence we get
(34000 - 50000)/10000
= -1.6
(50000-50000)/10000 = 0
Looking up the value we will get
0.4452
(b)
The percentage of trucks to travel less than 30,000 will be
Z(30,000 - 50,000)/10000
= Z(-2)
looking the value up we will get
0.02275
= 2.275 %
More than 60,00 will be
1 - Z(60000-50000)/10000
= 1 - Z(1)
= 1 - 0.84134
= 0.15866
= 15.866%
Since the question asks "or" it will be a union of the 2 values to get
18.141%
(c)
Now the miles traveled by at least 80% of trucks will have a Z score of 0.8
Now in the Z table, we get the closest to be 0.80234 which has a Z value of 0.85
Now the no. of trucks will be
0.85 X 10000 + 50000
= 8500 + 50000
= 58,500
d)
Now if the standard deviation was 7000 instead of 10,000
The proportion of trucks to travel between 34 and 50 would be
Z(-16000/7000) = Z(-2.29)
0.48713
Percentage of trucks to travel less than 30 or more than 60 thousand miles in a year
is 100[ Z(-20000/7000) + 1 - Z(10000/7000) ]
= 100[Z (-2.86) + 1 - Z(1.43)]
= 100[0.00212 + 1 - 0.92364]
= 100 X 0.07849
= 7.849%
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A. Has a slope of 4/3 and passes through the point (1,0)
B. Has a slope of 4/3 and passes through the point (0,1)
C. Has a slope of 3/4 and passes through the point (1,0)
D. Has a slope of 3/4 and passes through the point (0,1)
Answer:
D. Has a slope of 3/4 and passes through the point (0,1)
Step-by-step explanation:
The y-intercept is (0, 1), so this line passes through (0, 1).
slope = m = rise/run
Start at (0, 1). Go up 3. That is a rise of 3. Now go right 4. That is a run of 4.
slope = rise/run = 3/4
Answer: D. Has a slope of 3/4 and passes through the point (0,1)
Alison made a chain using 220 beads colored,red green and black. She placed the beads in the following pattern, 5 red , 3 green, 2 black. What color is the 138th beads on the chain?
Answer:
Green
Step-by-step explanation:
All you have to do is retrace retrace Alison’s steps. Note that there are 10 beads in the pattern, the 10th bead black. 210, 200, 190, 180, 170, 160, 150, 140. The 140th bead is black, because it is a multiple of 10. The 139 bead is black as well, because the end of Alison’s pattern contained 2 black beads. The next bead, bead 138, is green. So your answer would be green.
PLSSS HELPP ASAP LAST QUESTION ****** An employee is 25 years old and starting a Roth IRA. The employee plans to invest $200 per month with an expected interest rate of 2.85%, compounded monthly. After 30 years of working, the employee wants to have $150,000 in the retirement account. What is the difference between the actual balance and the employee's goal?
A spreadsheet was used to calculate the correct answer. Your answer may vary slightly depending on the technology used.
The actual balance is $34,600.86 higher than the goal.
The actual balance is $34,600.86 lower than the goal.
The actual balance is $36,400.68 higher than the goal.
The actual balance is $36,400.68 lower than the goal.
The actual balance is $36,400.68 which lower than the goal of $150,000. The Option D is correct.
How do we derive the difference between the actual balance and the employee's goal?The Formula to use to derive the actual balance is: P[((1 + r/n)^(n*t)) - 1) / (r/n)] where: FV = future value, P = monthly deposits, r = interest rate, t = time in years, n = number of compound in a year
From the given:
P = 200
r = 2.85% 0.0285
t = 30 years
n = 12 (compounded monthly)
Future value = 200((1 + 0.0285/12)^(12(30)) - 1) / (0.0285 / 12)
Future value = $113,599.32
The difference between the actual balance and the employee's goal is:
= $150,000 - $113,599.32
= $36,400.86
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