8. Adam is 14 years old. Adam is three years younger than his brother Michael. How old is Michael?
Answers
Answer:
Michael is 17 years old.
Step-by-step explanation:
If Adam is 14 years old and he is three years younger than Michael, then Michael is:
\(14+3=17\text{ years old}\)Related Questions
Your grandmother will be giving you $10,000 every year for the next five years, the first payment beginning at the end of the first year
A) If you invest these receivables in a bank at 6%, what is the total value at the end of 10 years if you make withdrawals of $3,000 in years 9 and 10?
B) An investor expects to receive $3,000 in year 2, $5,000 in year 5, and $7,000 in year 7. What is the present value of these payments if the interest rate is 8%?
Please also write the Excel formulas.
Answers
Answer:
a. The present value of these receivables is $42,123.64
b. The total value at the end of 10 years is $69,257.02
c. The present value of these payments is $10,059.37
Step-by-step explanation:
How long is the control line? I couldn’t figure this out
Answers
Solution:
Given the circle with center A as shown below:
The plane travels 120 feet counterclockwise from B to C, thus forming an arc AC.
The length of the arc AC is expressed as
\(\begin{gathered} L=\frac{\theta}{360}\times2\pi r \\ \text{where} \\ \theta\Rightarrow angle\text{ (in degre}e)\text{subtended at the center of the circle} \\ r\Rightarrow radius\text{ of the circle, which is the }length\text{ of the control line} \\ L\Rightarrow length\text{ of the arc AC} \end{gathered}\)Given that
\(\begin{gathered} L=120\text{ f}eet \\ \theta=80\degree \\ \end{gathered}\)we have
\(\begin{gathered} L=\frac{\theta}{360}\times2\pi r \\ 120=\frac{80}{360}\times2\times\pi\times r \\ cross\text{ multiply} \\ 120\times360=80\times2\times\pi\times r \\ \text{make r the subject of the equation} \\ \Rightarrow r=\frac{120\times360}{2\times\pi\times80} \\ r=85.94366927\text{ fe}et \end{gathered}\)Hence, the length of the control line is 85.94366927 feet.
Question 10 of 25 What is the recursive formula for this geometric sequence? -2,-16, -128, -1024,... A. ○ B. C. (a, D. 3₁ = :-2 an = 2n-1 = = -2 an = an-1.8 • a₁ = 8 an = an-1• (-2) (a₁ = -8 30 = 20-1.2 SUBMIT
Answers
Answer:
\(a_{n}\) = 8\(a_{n-1}\) ; a₁ = - 2
Step-by-step explanation:
a recursive formula in a geometric sequence allows a term to be found by multiplying the preceding term by the common ratio r
here r = \(\frac{a_{2} }{a_{1} }\) = \(\frac{-16}{-2}\) = 8 , then
\(a_{n}\) = 8\(a_{n-1}\) ; a₁ = - 2
pls help oooooooooooooopoo
Answers
9514 1404 393
Answer:
140°
Step-by-step explanation:
Angles 1 and 3 are "corresponding" angles, so are congruent.
∠1 = ∠3
20x +60 = 30x +20
40 = 10x . . . . . . . . . . . . subtract 20x+20
4 = x . . . . . . . . . . . . . . divide by 10
∠1 = 20x +60 = 20(4) +60 = 80 +60
∠1 = 140°
Answer:
140°
Step-by-step explanation:
Angle 1 and angle 3 are corresponding angles ;
Corresponding angles are equal ;
Hence,
Angle 1 = Angle 3
20x + 60 = 30x + 20
Collect like terms
20x - 30x = 20 - 60
-10x = - 40
x = 4
Angle 1 is thus :
20x + 60 ; x = 4
20(4) + 60
80 + 60
= 140°
Expand using binomial theorem(3a-2)^3
Answers
Answer:
Recall that the binomial theorem states that:
\((a+b)^n=\sum ^n_{k=0}{\binom{n}{k}}a^{n-k}b^k\text{.}\)Therefore:
\(\mleft(3a-2\mright)^3=\sum ^3_{k=0}{\binom{3}{k}}(3a)^{3-k}(-2)^k.\)Then:
\(\begin{gathered} (3a-2)^3={\binom{3}{0}}(3a)^{3-0}(-2)^0+{\binom{3}{1}}(3a)^{3-1}(-2)^1+{\binom{3}{2}}(3a)^{3-2}(-2)^2 \\ +{\binom{3}{3}}(3a)^{3-3}(-2)^3\text{.} \end{gathered}\)Simplifying the above result we get
\(\begin{gathered} (3a-2)^3=(3a)^3+3(3a)^2(-2)+3(3a)(-2)^2+(-2)^3 \\ =27a^3-54a^2+36a-8. \end{gathered}\)What is the equation for this graph?
Answers
Answer:
\(y=\frac{5}{2} x\)
Step-by-step explanation:
Notice is a line, The equation for a line can be found as the following:
\(y-yo=m(x-xo)\)
We need to find the slope.
First take two points of the graph
(0,0) the origin and (4,10) for example. Notice i do assume the X value is 4 for Y=10, since the cropping for the picture doesn't show the exact values for X .
Then the slope is given by equation:
\(m=(y-yo)/(x-xo)\\\)
\(m=\frac{10-0}{4-0} =5/2\)
then the equation is
\(y-0=\frac{5}{2} m(x-0)\)
\(y=\frac{5}{2} x\)
Answer:
y=5/2x or y=2.5x
Step-by-step explanation:
Find the value of x.
12.1
17.6
12.4
6.3
Answers
Using Pythagorean theorem, the value of x is 12.4 units
What is the value of xTo find the value x, we need to find the radius of the circle from the diameter and then use Pythagorean theorem to find the unknown side or adjacent and then subtract the value from x.
radius = diameter / 2
radius = 44 / 2
radius = 22
Using Pythagorean theorem, the adjacent side will be;
22² = 19.8² + y²
y² = 22² - 19.8²
y = √(22² - 19.8²)
y = 9.6
The value of x will be
x = 22 - 9.6
x = 12.4
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The correct answer is 12.4
Evaluate =f(×) r 6x-2 for f (2a-3)
Answers
Answer:
\( \boxed{\sf f(2a - 3) = 12a - 20} \)
Step-by-step explanation:
Function given:
⇒f(x) = 6x - 2
Substitute 2a - 3 into the function in place of x:
⇒f(2a - 3) = 6(2a - 3) - 2
Expand bracket:
⇒f(2a - 3) = 12a - 18 - 2
Add the like terms:
⇒f(2a - 3) = 12a - 20
Select the correct answer from each drop-down menu.
The total area of the three triangles is
square units.
The area of the figure is
square units.
Answers
The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.
What is the triangle?The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.
From the figure, the area of triangles can be calculated using the:
Area = (1/2)height×base length
Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)
Area of three triangle = 1/2(24×3) = 36 square units
Area of the figure = area of three triangle + area of the rectangle
= 36 + 6×4
= 60 square units
Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.
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Find the components of the vertical force Bold Upper FFequals=left angle 0 comma negative 4 right angle0,−4 in the directions parallel to and normal to the plane that makes an angle of StartFraction pi Over 3 EndFraction π 3 with the positive x-axis. Show that the total force is the sum of the two component forces.
Answers
Answer:
\(F_p = < - \sqrt{3} , -3 >\\\\F_o = < \sqrt{3} , -1 >\)
Step-by-step explanation:
- A plane is oriented in a Cartesian coordinate system such that it makes an angle of ( π / 3 ) with the positive x - axis.
- A force ( F ) is directed along the y-axis as a vector < 0 , - 4 >
- We are to determine the the components of force ( F ) parallel and normal to the defined plane.
- We will denote two unit vectors: ( \(u_p\) ) parallel to plane and ( \(u_o\) ) orthogonal to the defined plane. We will define the two unit vectors in ( x - y ) plane as follows:
- The unit vector ( \(u_p\) ) parallel to the defined plane makes an angle of ( 30° ) with the positive y-axis and an angle of ( π / 3 = 60° ) with the x-axis. We will find the projection of the vector onto the x and y axes as follows:
\(u_o\) = < cos ( 60° ) , cos ( 30° ) >
\(u_o = < \frac{1}{2} , \frac{\sqrt{3} }{2} >\)
- Similarly, the unit vector ( \(u_o\) ) orthogonal to plane makes an angle of ( π / 3 ) with the positive x - axis and angle of ( π / 6 ) with the y-axis in negative direction. We will find the projection of the vector onto the x and y axes as follows:
\(u_p = < cos ( \frac{\pi }{6} ) , - cos ( \frac{\pi }{3} ) >\\\\u_p = < \frac{\sqrt{3} }{2} , -\frac{1}{2} >\\\)
- To find the projection of force ( F ) along and normal to the plane we will apply the dot product formulation:
- The Force vector parallel to the plane ( \(F_p\) ) would be:
\(F_p = u_p(F . u_p)\\\\F_p = < \frac{1}{2} , \frac{\sqrt{3} }{2} > [ < 0 , - 4 > . < \frac{1}{2} , \frac{\sqrt{3} }{2} > ]\\\\F_p = < \frac{1}{2} , \frac{\sqrt{3} }{2} > [ -2\sqrt{3} ]\\\\F_p = < -\sqrt{3} , -3 >\\\)
- Similarly, to find the projection of force ( \(F_o\) ) normal to the plane we again employ the dot product formulation with normal unit vector ( \(u_o\) ) as follows:
\(F_o = u_o ( F . u_o )\\\\F_o = < \frac{\sqrt{3} }{2} , - \frac{1}{2} > [ < 0 , - 4 > . < \frac{\sqrt{3} }{2} , - \frac{1}{2} > ] \\\\F_o = < \frac{\sqrt{3} }{2} , - \frac{1}{2} > [ 2 ] \\\\F_o = < \sqrt{3} , - 1 >\)
- To prove that the projected forces ( \(F_o\) ) and ( \(F_p\) ) are correct we will apply the vector summation of the two orthogonal vector which must equal to the original vector < 0 , - 4 >
\(F = F_o + F_p\\\\< 0 , - 4 > = < \sqrt{3}, -1 > + < -\sqrt{3}, -3 > \\\\< 0 , - 4 > = < \sqrt{3} - \sqrt{3} , -1 - 3 > \\\\< 0 , - 4 > = < 0 , - 4 >\) .. proven
ASSIGNMENT Question
A steel tape of nominal length \( 30 m \) was use d to measure a line AB by suspending it between supports. The following measurements were recorded Line. AB length measured 29.872 Slope angle 3.67° Mean temperature 5° Tension applied 120N The standardized length of the tape against reference tape was known to be 30.14m at 20°and 50.. if the tape weight 0.17Nm–¹ and has a cross sectional area of 2mm¹.. calculate the horizontal length of AB..young's modulus(E) for the tape 200knmm–² and the coefficient of thermal expansion (a) is 0.0000112 per °C
Answers
Step-by-step explanation:
That depends on the tension on the tape.
As defined, the tape, due to gravity would form a catenary, a curve, so the measurement would be less than 30 m. The tension on the tape would affect the degree to which the measurement would be less. A tension well within the limits of the steel used to make the tape would be would be well within the accuracy of the tape. Over 30 m, the tape is likely +/- 2 mm, the recorded value could be 30m, +1mm/-3mm. If you need more than that degree of accuracy, you don’t use a tape.
Find all solutions for the following equations. Write your answers in radians using exact values. (Enter your answers as a comma-separated list. Let k be any integer.) sin 2x cos x cos 2x sin x
Answers
Answer:
Step-by-step explanation:
Given that:
sin2xcos x + cos2xsin x = -1
Recall that;
SInAcosB + cosASinB = SIn (A+B)
SIn (2x +x) = -1
Sin (3x) = -1
\(x = \bigg [\dfrac{Sin ^{-1} (-1)}{3} \bigg ]\)
\(x = \dfrac{\pi}{2} + \dfrac{2 \pi \ k}{3}\)
\(x = \dfrac{\pi}{2}, \dfrac{7 \pi}{6}, \dfrac{11 \pi}{6}\)
Simplify write without absolute value : |1 + 2x| + |5 − 3x| − |−5x − 8| , is x < −10
Answers
Answer:
3x + 1 – 2x = 9 – 3
Step-by-step explanation:
3) 6 + 2x – 4 = x – 1
4) – 6 – 2x = - 3x – 6
5) x + x +4 +2 = 8
6) 2x + x +5 – 5 = 6
7) 2x – x – 3 – 5 = 2
8) 2x + 2 – 1 – x = 2
9) 5x – 4= 3x – 2
10) 2x – 5 +1 +x = + x – 6
11) – 2x – 5 = 6 – x – 2x
12) – 10 – 4 x + 2x = – 3 – 4x
13) – 5x – 6 + 4 = 4 + 2x – 8x
14) – x = – 6 – 2 – 2x
15) 5x – 10 – 3x +3 + 2x = 20 – x – 4 – 3 + 3x
David’s bowling score is 1 less than 3 times Aaron’s score. The sum of their scores is 179. Find the score of each student, Use the variable a for Aaron’s score
Answers
Answer: List all of the solutions.
1
=
3
=
179
=
Step-by-step explanation:
4ft - 43in write the answer in standard form
Answers
Answer:
5in.
Step-by-step explanation:
4ft * 12= 48in
48in - 43in= 5in.
Answer:
5 inches
Step-by-step explanation:
4 ft = 48 inches
48 in - 43 in = 5 in
If 3 is the input for this function machine, what is the output?
x² + 2x +1
Answers
Danielle swam a total of 266 laps in the 7 days leading up to the swimming finals. How many laps did she swim each day if she swam the same number every day?
Answers
Answer:
Step-by-step explanation:
266 divided by 7 is 38 laps a day
Each student was asked to create an expression whose quotient is 1/3. Each student and their response can be seen in the table below. Which students have answered correctly? Select all that apply. A. Angela B. Ben C. Chris D. Denice E. Elizabeth
Answers
Answer:
Pretty sure its Chris
Step-by-step explanation:
I've done this work and the only one with the answer is him.
HELP ASAP (I chose 34 as random number)
The table shows the grading scale for Ms. Gray's social studies class.
A 90%–100%
B 80%–89%
C 70%–79%
Part A: Pick a number between 28 and 39. This number will represent how many points you earned. If you have a pop quiz worth a total of 40 points, using the number you selected, calculate the percentage you earned on the test. Show each step of your work. (8 points)
Part B: Based on the percentage found in Part A, would you earn a grade of A, B, or C using the grading scale provided? Explain your answer. (4 points)
Answers
Part A: if you earned 14 points out of 17 points on the quiz, your percentage score would be 82.35%.
Part B: the grade earned for the quiz is a B.
What is the percentage?
A percentage is a means to represent a piece of 100 as a ratio or percentage. The sign for it is % (percent), which stands for "per hundred." If your state, for instance, that 50 out of 100 people like chocolate, then means that 50 out of 100 people, or 0.5 (50/100), like chocolate overall. In several disciplines, including finance, business, mathematics, and statistics, percentages are frequently used.
Here, we have
Given: Ms. Gray's social studies class.
A 90%–100%
B 80%–89%
C 70%–79%
Part A: Let's say we pick the number 17 as the number of points earned on the quiz. If the quiz is worth a total of 17 points, and you earned 14 points, then your percentage score is calculated as follows:
Percentage score = (points earned / total points) x 100%
Percentage score = (14 / 17) x 100%
Percentage score = 82.35%
Hence, if you earned 14 points out of 17 points on the quiz, your percentage score would be 82.35%.
Part B: Based on the percentage score of 82.35%, you would earn a B grade using the grading scale provided.
According to the grading scale, a B grade is earned for a percentage score between 80%-89%, and the percentage score obtained in part A is within this range.
Hence, the grade earned for the quiz is a B.
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If a cylinder has a height of 12 feet and a radius of 4 feet, what is its surface area (in square feet)? What is its volume (in cubic feet)? (Round your answers to two decimal places.)
Answers
The volume of the cylinder is 602.88 ft³.
The surface area of the cylinder is 301.44 ft²
How to find the volume and surface area of a cylinder?volume of a cylinder = πr²h
volume of a cylinder = 3.14 × 4² × 12
volume of a cylinder = 3.14 × 16 × 12
volume of a cylinder = 602.88 ft³
Surface are of a cylinder = 2πr(r + h)
Surface are of a cylinder = 2 × 3.14 × 4(4 + 8)
Surface are of a cylinder = 25.12(12)
Surface are of a cylinder = 301.44 ft²
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Which graph represents the function f (x) = StartFraction 1 Over x EndFraction minus 1?
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 0, and the horizontal asymptote is at y = 1.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = 0.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = negative 1, and the horizontal asymptote is at y = 0.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 0, and the horizontal asymptote is at y = negative 1.
Mark this and return
Answers
The correct answer is Option C. The graph represents the function f (x) = StartFraction 1 Over x EndFraction minus 1 is On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = negative 1, and the horizontal asymptote is at y = 0.
On a coordinate plane, the graph of a hyperbola is shown.
In quadrant 1, one curve opens up and to the right, while in quadrant 3, the other curve opens down and to the left.
The vertical asymptote is at x = -1, and the horizontal asymptote is at y = 0. This hyperbola is symmetrical across both the x and y axes.
The function f(x) = 1/x - 1 has a vertical asymptote at x = 0 because the denominator approaches zero as x approaches zero.
A fraction with a denominator of zero cannot exist.
The horizontal asymptote of this function is y = -1 because as x approaches infinity or negative infinity, f(x) approaches -1.
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I need help please.
Answers
Step-by-step explanation:
if I had to guess it's probably true
PLEASE HELP QUICK
What is the simplified expression for the expression below?
–1(2x + 3) – 2(x – 1)
–4x + 1
–4x – 2
–4x + 2
–4x – 1
Answers
Answer:
-4x - 1
Step-by-step explanation:
i used a calculator and got that
what is dynamic environment?
Answers
Answer:
A dynamic environment is a business environment that is rapidly changing. In a dynamic market, businesses have to adapt quickly to changes and develop new ideas, products and services to keep up with technology and new trends.
Step-by-step explanation:
please help greatly appreciated image attached (using e or in is not allowed)
Answers
Step 1
Given;
Step 2
If you plot the point P in the xy-plane, you see it lies in Quadrant II. Draw the segment from the origin O to P and find its length:
\(\begin{gathered} r=\sqrt{(-5)^2+(7)^2} \\ r=\sqrt{74} \end{gathered}\)\(cos\theta=\frac{x}{r}=\frac{-5}{\sqrt{74}}\)\(\begin{gathered} The\text{ exact value of cos}\theta=\frac{-5}{\sqrt{74}}\times\frac{\sqrt{74}}{\sqrt{74}}=\frac{-5\sqrt{74}}{74} \\ Numerical\text{ value to 2 decimal places=-0.58} \end{gathered}\)Answer;
\(\)
what are the answers? thank you.
Answers
Answer:
176.78cm squared,23.57cm,Step-by-step explanation:
inorder to solve the area of the shaded area;°/360ñRsquared
arc length you use ;°/360ñD
In a survey of 750 students in a school, it was found that 520 students liked tea, 450 liked coffee, and 90 did not like both the drinks. (i) Draw a Venn-diagram to illustrate the above information, (i) Find the number of students who liked both the drinks. (iii) Find the number of students who did not like tea only
Answers
Answer:
i: see picture attached
ii:310 of the student liked both drinks
iii: Every other student that does not like tea only should be 90+310+210=610
Step-by-step explanation:
(ii) If there are 750 students we can start by subtracting 90 since they don't like either drink. 750-90=660. 660 is the number of students that like both tea and coffee. From there we know that 450 like coffee and 520 like tea.
For the students that only like coffee subtract 660 from 450, that leaves up with 210 students.
For the students that only like tea subtract 660 from 520, that leaves 140 students that only like tea.
If you subtract 660 from the students that only like one drink. 660-( 140+210)= 310 students that like both drinks.
To double check the work, 210+140+310+90 should equal 750.
(iii) If this is asking for all other students who do not only like tea. we subtract
750-140=610
or
90+310+210=610
Hope this is what the assignment is looking for.
Plss help I’ll give Brainliest it help immediately
Answers
Answer:
3.61
Step-by-step explanation:
Find the domain of the function for this situation.
Answers
0,390 because I did a lot of test and exams on these types of questions
Andria wrote the following statements: Statement 1: If parallel lines have a transversal, then corresponding angles are congruent. Statement 2: A line has an infinite number of points extending in opposite directions. Which geometry term does each statement represent? (4 points) Statement 1: definition; Statement 2: theorem Statement 1: postulate; Statement 2: definition Statement 1: postulate; Statement 2: theorem Statement 1: theorem; Statement 2: postulate
Answers
Answer: Statement 1: postulate; Statement 2: definition
Step-by-step explanation:
A postulate is assumed to be a fact and used to derive conclusions about any argument .A definition is a brief explanatory statement of a term.A theorem is a statement that can be proved to be true by using given, definitions, postulates or prior proved theorems .Here, Statement 1:If parallel lines have a transversal, then corresponding angles are congruent.
which is a fact, and hence it is postulate.
Statement 2: A line has an infinite number of points extending in opposite directions.
which is an explanatory statement of a 'line', hence it is 'definition.
So the correct option is Statement 1: postulate; Statement 2: definition
Answer:statement 1 and statement 2 postulate
Step-by-step explanation: