Solution
- The solution steps are given below:
[tex]\begin{gathered} \sqrt{n}=4 \\ \text{ Square both sides} \\ n=4^2 \\ n=16 \end{gathered}[/tex]Final Answer
The answer is 16
Find the exact value of sin A and cos A where a = 9 and b = 10 and
Given data:
a=9 , b = 10
use the phythagoras theorem,
[tex]c=\sqrt[]{a^2+b}^2[/tex][tex]\begin{gathered} c=\sqrt[]{9^2+10^2} \\ c=\sqrt[]{81+100} \\ =\sqrt[]{181} \end{gathered}[/tex]thus,
[tex]\sin A=\frac{opp}{\text{hypo}}[/tex][tex]\text{sinA}=\frac{9}{\sqrt[]{181}}[/tex]and,
[tex]undefined[/tex]When you convert 0.0045 to scientific notation, the exponent will be
positive.
Or
negative.
Factor completely. (3.2² - 12x)(x2 – 2x + 1) =
We will have the following:
21.) Determine the distance between the points (-2, 3) and (4,9).A 142B 7146C 413D 6V222.) Infigure
The distance formula can be represented below
[tex]\begin{gathered} c^{}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} c=\sqrt[]{(4+2)^2+(9-3)^2} \\ c=\sqrt[]{(6)^2+(6)^2} \\ c=\sqrt[]{36+36} \\ c=\sqrt[]{72} \\ c=\sqrt[]{36\times2} \\ c=6\sqrt[]{2} \end{gathered}[/tex]The answer is D.
Trini Cars break down on the highway.show me estimates that she is 20 to 30 miles from the nearest car repair shop she calls a towing company that charges a fee of $80 plus $3 per mile to tow a car.if training uses this towing company, which is the best estimate for the amount of money,m,she will pay for the company to tow her car.a .103 greater than sign and greater than sign 113 b.140 greater than sign M greater than sign 150 c.114 greater than 5 m greater than 170 d. 560 greater than 10 m > 70
We have that the cost is $80 plus $3 per mile, and also we now that the car is 20 to 30 miles from the car repair shop. So we have that Trini have to pay
[tex]\begin{gathered} 80\text{ + 3(20) }\leq\text{ M }\leq\text{ 80 + 3(30)} \\ 80\text{ + 60 }\leq\text{ M }\leq\text{ 80 + 90} \\ 140\text{ }\leq\text{ M }\leq170 \end{gathered}[/tex]So the answer is: b.140 greater than sign M greater than sign 150.
A spinner has the sections A through F. The spinner is spun and a 6-sided die is rolled. What is the probability that the outcome will be D and 5?1/361/181/121/6
To find the probability of having a D and %, we would use the concept of mutually exclusive events here
But probability is given as
[tex]P=\frac{\text{ number of favourable outcomes}}{\text{total number of }possible\text{ outcomes}}[/tex]The probability of choosing a D is
A, B, C, D, E and F. This can be found as
[tex]P_a=\frac{1}{6}[/tex]The probabilty of choosing a 5 out of 6 possible outcomes is
[tex]P_n=\frac{1}{6}[/tex]The probability of having a D and 5 would be
[tex]\begin{gathered} P=P_a\times P_n \\ P=\frac{1}{6}\times\frac{1}{6} \\ P=\frac{1}{36} \end{gathered}[/tex]From the calculations above, the answer to this question is 1/36
Belinda wants to invest $1,000. The table below shows the value of her investment under two different options for three different years:
Number of years 1 2 3
Option 1 (amount in dollars) 1100 1200 1300
Option 2 (amount in dollars) 1100 1210 1331
Part A: What type of function, linear or exponential, can be used to describe the value of the investment after a fixed number of years using option 1 and option 2? Explain your answer. (2 points)
Part B: Write one function for each option to describe the value of the investment f(n), in dollars, after n years. (4 points)
Part C: Belinda wants to invest in an option that would help to increase her investment value by the greatest amount in 20 years. Will there be any significant difference in the value of Belinda's investment after 20 years if she uses option 2 over option 1? Explain your answer, and show the investment value after 20 years for each option. (4 points)
The result from using Option 2 will be significantly less than the result from using Option 1 over a period of 20 years.
Given,
Belinda wants to invest $1,000.
The Table is:
Number of years 1 2 3
Option 1 (amount in dollars) 1100 1200 1300
Option 2 (amount in dollars) 1100 1210 1331
Now, According to the question:
When the x-values are sequential (1, 2, 3, ...), the y-values will have a common difference for a linear function, and a common ratio for an exponential function.
For the two investment options, we notice Belinda earns 1300 -1000 = 300 the first year for either option. The difference is the same the next year for Option 2 (1600 -1300 = 300), but is not the same for Option 1. For that option, the ratio is the same for the second year as it was for the first year:
1690/1300 = 1.3 = 1300/1000
Part A :
(Option 1) can be represented by exponential function.
(Option 2) can be represented by a linear function.
Part B:
For Option 1:
To find the value of the investment f(n), in dollars, after n years.
The generic form of an exponential function is ...
f(n) = a·b^n
Now, Amount after 1 year = 1100
Principle (P) is = 1000
Using the formula :
A = P[tex](1+r)^n[/tex]
1100 = 1000[tex]([/tex][tex]1 + r)^1[/tex]
1.10 = 1 + r
r = 0.10
Amount after t years can be given by :
A = 1000(1.10)^t
For Option 2,
The generic form of an exponential function is ...
f(n) = a·n + b
Rate of change (m) = (1100 - 1000) / 1 = 100
Amount after t years can be given by
A = 1000 + 100 x t .
Part C:
Investment in (1) : 1000 [tex](1.10)^2^0[/tex]= $6727
Investment in (2): $3000
Hence, The result from using Option 2 will be significantly less than the result from using Option 1 over a period of 20 years.
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i need help on number 7. Please use 4 points
In order to graph this equation, we need at least two points that are solution to the equation.
To find these points, we can choose values for x and then calculate the corresponding values of y.
Choosing the x-values of -2, -1, 0 and 1, we have:
[tex]\begin{gathered} x=-2\colon \\ y=-\frac{5}{2}\cdot(-2)-1 \\ y=5-1 \\ y=4 \\ \\ x=-1\colon \\ y=-\frac{5}{2}(-1)-1 \\ y=2.5-1 \\ y=1.5 \\ \\ x=0\colon \\ y=-\frac{5}{2}\cdot0-1 \\ y=-1 \\ \\ x=1\colon \\ y=-\frac{5}{2}\cdot1-1 \\ y=-2.5-1 \\ y=-3.5 \end{gathered}[/tex]So we have the points (-2, 4), (-1, 1.5), (0, -1) and (1, -3.5). Graphing these points and the line that passes through them, we have:
Identify the x intercept(s) from the graphType your answer using set notation {x,x} listing x values in order from least to greatest
The x-intercept is where the graph passes the x-axis.
The graph extends from {-5 ≤ x ≤ 3}
The x-intercept is {x = -1}.
The semi annual compound interest of a sum of money in 1 year and 2years are Rs400 and Rs441 respectively.Find the annual compound interest for 2years
Answer:
Step-by-step explanation
Correct option is A)
C.I. for the third year = Rs. 1,452.
C.I. for the second year = Rs. 1,320
∴ S.I on Rs. 1,320 for one year = Rs. 1,452− Rs. 1,320= Rs. 132.
Rate of interest =
1,320
132×100
=10%.
Let the original money be Rs. P.
Amount after 2 year − amount after one year =C.I. for second year.
P(1+
100
10
)
2
−P(1+
100
10
)=1,320
P[(
100
110
)
2
−
100
110
]=1,320
⇒P[(
10
11
)
2
−
10
11
]=1,320⇒P(
100
121
−
10
11
)= Rs. 1,320
⇒P×
100
11
=Rs.1,320⇒P=
11
1,320×100
= Rs. 12,000
∴ Rate of interest =10%
and Original sum of money = Rs. 12,000
A rectangular room is twice as long as it is wide, and its perimeter is 60 meters. Find the dimensions of the
room.
The length is __
meters and the width is __
meters.
Answer: 20, 10
Step-by-step explanation:
Let the width be w. Then, the length is 2w. Substituting into the formula for the perimeter of a rectangle,
[tex]2(w+2w)=60\\\\w+2w=30\\\\3w=30\\\\w=10\\\\\implies 2w=2(10)=20[/tex]
Reduce the rational expression to lowest terms. If it is already in lowest terms, enter the expression in the answerbox. Also, specify any restrictions on the variable.a²-3a-4/a² + 5a + 4Rational expression in lowest terms:Variable restrictions for the original expression: a
Factorize both quadratic polynomials, as shown below
[tex]\begin{gathered} a^2-3a-4=0 \\ \Rightarrow a=\frac{3\pm\sqrt{9+16}}{2}=\frac{3\pm\sqrt{25}}{2}=\frac{3\pm5}{2}\Rightarrow a=-1,4 \\ \Rightarrow a^2-3a-4=(a+1)(a-4) \\ \end{gathered}[/tex]Similarly,
[tex]\begin{gathered} a^2+5a+4=0 \\ \Rightarrow a=\frac{-5\pm\sqrt{25-16}}{2}=\frac{-5\pm3}{2}\Rightarrow a=-1,-4 \\ \Rightarrow a^2+5a+4=(a+1)(a+4) \end{gathered}[/tex]Thus,
[tex]\Rightarrow\frac{a^2-3a-4}{a^2+5a+4}=\frac{(a+1)(a-4)}{(a+1)(a+4)}[/tex]Therefore, since the denominator cannot be equal to zero.
The variable restrictions for the original expression are a≠-1,-4Then, provided that a is different than -1,
[tex]\Rightarrow\frac{a^2-3a-4}{a^2+5a+4}=\frac{x-4}{x+4}[/tex]The rational expression in the lowest terms is (x-4)/(x+4)i need help with my homework PLEASEMCHECK WORK WHEN FINISHED
Given:
The population of a town increases by 9 % annually.
The current population is 4,500.
Required:
We need to find the equation that gives the population of the town.
Explanation:
The population can be found by the following equation.
[tex]Th\text{e population =4500+9 \% of 4500}[/tex]Let now be the current population of the town =4500.
Let Next be the population of the town.
The population can be found by the following equation.
[tex]Next\text{ =Now+9\% of Now.}[/tex][tex]Next\text{ =Now+}\frac{9}{100}\times\text{Now.}[/tex]Take the common term now out.
[tex]Next\text{ =Now\lparen1+}\frac{9}{100})[/tex][tex]Use\text{ }\frac{9}{100}=0.09.[/tex][tex]Next\text{ =Now\lparen1+0.09})[/tex][tex]Next\text{ =Now\lparen1.09})[/tex][tex]Next\text{ =Now}\times\text{1.09}[/tex]Final answer:
[tex]Next\text{ =Now}\times\text{1.09}[/tex]Can you help me figure this out
By using the fact that the interior angles of a triangle must add up to 180, we will see that the value of x is 15.
How to get the value of x?Here we have 3 expressions for the measures of the interior angles of a triangle.
Now, remember that the sum of the interior angles of a triangle is always equal to 180°, then we can write:
(8x - 7)° + (x + 7)° + (2x + 15)° = 180°
Ignoring the degrees and solving this for x, we get:
8x - 7 + x + 7 + 2x + 15 = 180
11x + 15 = 180
11x = 180 - 15 = 165
x = 165/11 =15
The value of x is 15.
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y - 7.8= 5.5 I got 2.9 but I want to be sure I understand and took the right steps
Given the equation:
[tex]y-7.8=5.5[/tex]You need to solve for "y" in order to find its value. In this case, you need to apply the Addition Property of Equality, which states that, if:
[tex]a=b[/tex]Then:
[tex]a+c=b+c[/tex]Therefore, you need to add 7.8 to both sides of the equation in order to solve for "y":
[tex]\begin{gathered} y-7.8+(7.8)=5.5+(7.8) \\ y=13.3 \end{gathered}[/tex]Hence, the answer is:
[tex]y=13.3[/tex]i have to find is they similar or not. help im lost
First we have to find the missing angle on each case.
In the first triangle we have
180°-(28°+80°)=72°
In the second triangle we have
180°-(28°+71°)=81°
Since the values of the angles are not the same for both triangles they are not similar.
10 pts What is x and y intercept for the following equation? 8x + y = 12 A. x intercept = 0 y intercept = 4 B. x intercept = 12 y intercept = 0 C. x intercept = 4 y intercept = 6 D. x intercept = 3/4 y intercept = 12 OB ОА Oc
To find the x intercept of the equation make y=0 and solve for x.
[tex]\begin{gathered} 8x+y=12 \\ 8x=12 \\ x=\frac{12}{8} \\ x=\frac{6}{4} \\ x=\frac{3}{2} \end{gathered}[/tex]The x intercept is 3/2
To find the y intercept, make x=0 and solve for y
[tex]\begin{gathered} 8x+y=12 \\ 8(0)+y=12 \\ y\text{=}12 \end{gathered}[/tex]The y intercept is 12.
If the LM follows the reference trajectory, what is the reference velocity vref (t) ?
Answer:
Explanation:
you guess there are 80 marbles in a jar but there are actually 50. what is the percent of error
Calculate value = 80
Actual value = 50
[tex]\begin{gathered} \text{Percentage error = }\frac{Calculated\text{ value - Actual vale}}{\text{Actual value}}\text{ X 100\%} \\ =\text{ }\frac{80\text{ - 50}}{50}\text{ x 100} \\ =\text{ }\frac{30\text{ x 100}}{50} \\ =\text{ }\frac{3000}{50} \\ =\text{ 60\%} \end{gathered}[/tex]y-intercept of y=3/2|x-2|
Answer:
Combine [tex]\frac{3}{2 }[/tex] and | x - 2 |
[tex]y\frac{3|x-2|}{2}[/tex]
how do you calculate the volume of water in a lake? given is the area of the lake at 1.35 km2 and its depth is 4.0 m
Given
Area of lake = 1.35 square km
Depth = 4.0m
Find
Volume of water in a lake
Explanation
Volume of water in a lake is given by
[tex]area\times depth[/tex]first we have to make the units same
as we know 1 square km = 1000000
so , 1.35 square km = 1.35 * 1000000= 1350000 square meter
so , volume of water in a lake =
[tex]\begin{gathered} volume=1350000\times4 \\ volume=5400000\text{ }cubic\text{ meter} \end{gathered}[/tex]Final Answer
Therefore , the volume of water in a lake is 5400000 cubic meter
you pull with 45nm on a torque wrench of 1m what's the tourqe at the end
The torque at the end is equal to 45 Nm.
What is torque?Torque can be defined as a measure of the amount of force which causes a physical object to rotate about an axis. This ultimately implies that, torque is a force which tends to cause the rotation of a physical object about an axis.
Mathematically, torque can be calculated by using this formula:
τ = Fd
Where:
τ represents the torque.F represents the force.d represents the perpendicular distance.In this scenario, we can reasonably infer and logically deduce that the torque at the end would be equal to 45 Newton meter (Nm) because the force was not applied over a perpendicular distance.
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Zaria is making pipe cleaner flowers for
her friends. She has 215 pipe cleaners.
How many flowers can she make with 3
pipe cleaners in each?
[?] flowers and pipe cleaners leftover
I
Answer
Enter
We can get the answer by dividing 215 by 3
What is dividing?
One of the four fundamental arithmetic operations, or ways to combine numbers to create new ones, is division. The other operations are multiplication, addition, and subtraction. The process of counting the instances in which one integer is included into the others is the most fundamental definition of the division of two natural numbers. This amount need not be an integer. For instance, if twenty apples are divided equally among four people, everyone will get five of them.
We can get the answer by dividing 215 by 3
215/3 = 71.67
Hence, 71 flowers are made
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(8x+6)=mL(blank)
8x+6) =
8x=
x=
the L is an angle
The value of the unknown angle is as follows;
∠ = 62 degreesHow to find the unknown angle?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles etc.
Therefore, the angle 4 can be found as follows:
∠4 = 8x + 6 (alternate angles)
Hence,
8x + 6 + 118 = 180(sum of angles on a straight line)
8x = 180 - 118 - 6
8x = 56
divide both sides by 8
x = 56 / 8
x = 7
Therefore,
∠4 = 8(7) + 6 = 56 + 6 = 62 degrees
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Check each answer to see whether the students evaluated the expression correctly. If the answer is incorrect cross out the answer and write the correct answer. 8(x+2)when x= 68(6+2) = 48 +2 = 50
The answer is not correct. There is a mistake applying the distributive property.
The distributive property says:
[tex]a(b+c)=ab+ac[/tex]But in this case, the 8 only multiplies the 6, and not the 2. The correct procedure is:
[tex]8(6+2)=8\cdot6+8\cdot2=48+16=64[/tex]The correct answer is 64
Which equation is the best approximation of the trend line
approximatesThe equation of a line is given by
[tex]\begin{gathered} y=mx+c \\ m=\frac{change\text{ in y}}{change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1} \end{gathered}[/tex]Taking two points from the line of best fit
Point A(14,200) and Point B (18,400)
[tex]\begin{gathered} x_1=14;y_1=200;x_2=18;y_2=400 \\ \frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1} \\ \frac{400-200}{18-14}=\frac{y-200}{x-14} \\ \frac{200}{4}=\frac{y-200}{x-14} \\ \frac{50}{1}=\frac{y-200}{x-14} \\ y-200=50(x-14) \\ y-200=50x-700 \\ y=50x-700+200 \\ y=50x-500 \end{gathered}[/tex]Hence, the equation that best approximate the trend line is y=50x-500
For the equation, complete the given table.
Answer:
Step-by-step explanation:
first row: 4
second: 2
third: 6
fourth: 9
plug in x for x in the equation/plug in y for y in the equation for whichever is given.
Fill in the blanks to find other expressions for 8%a. __ for every 100, b. __for every 50, c. 1 for every __, d. 0.5 for every __. 150
Using ratios, the sentences regarding a percentage of 8% are given as follows:
a. 8 for every 100.
b. 4 for every 50.
c. 1 for every 12.5.
d. 0.5 for every 6.25.
Ratio between two amountsThe ratio between two amounts a and b is given by the division of a by b, as follows:
r = a/b.
One example of ratio is a percentage, as a percentage of x% is equivalent to the ratio of x to 100, that is:
r = x/100.
Hence a percentage of 8% is equivalent to the following ratio:
r = 8/100.
That is, 8 for every 8.
Ratios are fractions, and they can be simplified, dividing both the numerator and the denominator by the same amount, as is the case in this problem:
r = 4/50 (simplifying by 2, four for every 50).r = 1/12.5 (simplifying by 4, one for every 12.5).r = 0.5/6.25 (simplifying by 2, 0.5 for every 6.25).More can be learned about ratios at https://brainly.com/question/2328454
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What point in the feasible reign maximizes the objective function? constraints: x => 0 y => 0 y<= x - 4 x + y <= 6
Objective Function: C = 2x + y
The point in the feasible region maximizes the objective function is (5, 1)
How to determine the feasible region?The given parameters are
Objective function: C = 2x + y
Subject to (i.e. the constraints)
x >= 0, y >= 0
y <= x - 4, x + y <= 6
Represent y <= x - 4, x + y <= 6 as equations
y = x - 4 and x + y = 6
Substitute y = x - 4 in x + y = 6
So, we have
x + x - 4 = 6
Evaluate the like terms
2x = 10
This gives
x = 5
Substitute x = 5 in y = 6 - x
y = 6 - 5
Evaluate
y = 1
So, we have
(x, y)= (5, 1)
Hence, the coordinates is (5, 1)
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(Solve the problem & round to four decimal places as needed.)
SOLUTION
Given:
[tex]ln0.0664=-2.7121[/tex]Final answer:
-2.7121