Answer:
[tex]2 \, \dfrac{4}{25} \textrm{ ft}[/tex]
Step-by-step explanation:
First, solve for how many feet Jason has dug after 40 minutes:
[tex]\dfrac{\dfrac{3}{5} \textrm{ ft}}{10 \textrm{ min}} \times 40 \, \textrm{min} = 2 \dfrac{2}{5} \, \textrm{ft}[/tex]
So, the hole he has dug is 2 2/5 ft deep.
Next, we can solve for how deep the hole will be after placing a plant in by simply multiplying 9/10 by the depth of the hole dug.
[tex]2\, \dfrac{2}{5} \times \dfrac{9}{10} = \dfrac{12}{5} \times \dfrac{9}{10} = \dfrac{6 \times 9}{5 \times 5} = \dfrac{54}{25} = 2 \, \dfrac{4}{25} \textrm{ ft}[/tex]
Christine is putting money into a savings account. She starts with $650 in the savings account, and each week she adds $60. Let S represent the total amount of money in the savings account (in dollars), and let W represent the number of weeks Christine has been adding money. Write an equation relating S to W. Then use this equation to find the total amount of money in the savings account after 11 weeks.
Total amount of money in the savings account after 11 weeks is $1310.
Total money in the account =
Initial Money + Money added per week x Number of weeks
Given:
Initial Money = $650
Money added per week = $60
Total money in the account = S
Number of weeks = W
Substituting it in the above equation we get,
S = $650 + $60xW (General Equation)
Total amount of money in the savings account after 11 weeks
S = $650 + $60x11
S = $650 + $660
S = $1310
Thus total amount of money in the savings account after 11 weeks is $1310.
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Use an outside source to search for a quadratic equation that models something from your daily life. (Be sure to cite the source you use.)
Solve the equation in two ways.
Discuss which method you liked better and why.
In your responses to peers, compare and contrast your preferences for how to solve quadratic equations.
A quadratic equation that models something from one's daily life is when calculating areas, and determining a product's profit.
What is a quadratic equation?It should be noted that a quadratic equation means an algebraic equation of the second degree in x.
The quadratic equation in its standard form is ax² + bx + c = 0. Here, a and b are the coefficients, x is the variable, while c is the constant term.
Quadratic equations are used in everyday life, as when calculating areas, and the determination of a product's profit and formulating the speed of an object.
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Factor x2 − 2x + 3. (1 point) (x − 3)(x − 1) (x + 3)(x + 1) (x − 3)(x + 1) Prime
Answer: for the factor one: The expression isn't factorable with rational numbers
Step-by-step explanation: Since the polynomial can be factored it isn't prime (i don't know if that is what you meant or not but I hope this helps and I got all of them correct )
Two friends, Jamie and Devin, are working together at the Sparrowtown Cafe today. Jamie works every 2 days, and Devin works every 7 days. How many days do they have to wait until they next get to work together?
Using the least common factor, they need to wait 14 days until they next get to work together.
How to find the time it takes for periodic events to repeat at the same time?To find the time that passes between the events happening at the same time, we need to find the least common multiple of the periods.
In this problem, the periods are of 2 days and 7 days, which already are prime numbers, hence:
lcm(2,7) = 2 x 7 = 14.
They need to wait 14 days until they next get to work together.
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18. Find the value of 3x² x 2(x-3y) divide by 6 when x is 6 and y is 1
Answer:
11664
Step by Step:
Evaluate for x=6,y=1
3(6^2)(6^2)(6−(3)(1))
3(6^2)(6^2)(6−(3)(1))
=11664
Does this table represent a function? Why or why not
Answer:
No
Step-by-step explanation:
This table does not represent a function. The domain(x) can have only one range(y) in order for a set of data to represent a function. However, the domain value 2 has the range of both 1 and 4. Therefore, the table does not represent a function.
Find the angle between the vectors.
U=< -4,-3>
V = < -1,5>
Step-by-step explanation:
The formula for the angle between vectors
[tex] \alpha = \cos {}^{ - 1} ( \frac{uv}{ |u| |v| } ) [/tex]
To multiply vectors, multiply the first component and multiply the second component and add them.
(-4*-1) + (-3*5)= 4-15=-11.
To find magnitude of vectors, use the Pythagorean theorem
[tex]u = \sqrt{ { - 4}^{2} + { - 3}^{2} } = 5[/tex]
[tex]v = \sqrt{ - 1 {}^{2} + 5 {}^{2} } = \sqrt{26} [/tex]
so
[tex] |u| |v| = 5 \sqrt{26} [/tex]
Know we have,
[tex] \alpha = \cos {}^{ - 1} ( \frac{7}{5 \sqrt{26} } ) [/tex]
[tex] \alpha = 105.94[/tex]
in degrees,
[tex] \alpha = 1.849[/tex]
in radians
Answer:
115.6° (1 d.p.)
Step-by-step explanation:
To find the angle between two vectors:
Create a triangle with the vectors as two sides and the included angle θ between them.Find the magnitude of each vector (the length of each side of the triangle).Use the cosine rule to find the angle θ.**Please see attached for the triangle diagram**
Given vectors:
[tex]\textbf{u}=-4\textbf{i}-3\textbf{j}[/tex]
[tex]\textbf{v}=-\textbf{i}+5\textbf{j}[/tex]
Use Pythagoras Theorem to find the magnitude of each vector:
[tex]\implies |\textbf{u}|=\sqrt{(-4)^2+(-3)^2}=5[/tex]
[tex]\implies |\textbf{v}|=\sqrt{(-1)^2+5^2}=\sqrt{26}[/tex]
[tex]\overrightarrow{\text{UV}}=\textbf{v}-\textbf{u}=(-\textbf{i}+5\textbf{j})-(-4\textbf{i}-3\textbf{j})=3\textbf{i}+8\textbf{j}[/tex]
[tex]|\overrightarrow{\text{UV}}|=\sqrt{3^2+8^2}=\sqrt{73}[/tex]
Cosine Rule (for finding angles)
[tex]\sf \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}[/tex]
where:
C = anglea and b = sides adjacent the anglec = side opposite the angleFind angle θ using the cosine rule:
[tex]\implies \cos(\theta)=\dfrac{|\textbf{u}|^2+|\textbf{v}|^2-|\overrightarrow{\text{UV}}|^2}{2|\textbf{u}||\textbf{v}|}[/tex]
[tex]\implies \cos(\theta)=\dfrac{5^2+\left(\sqrt{26}\right)^2-\left(\sqrt{73}\right)^2}{2(5)\left(\sqrt{26}\right)}[/tex]
[tex]\implies \cos(\theta)=\dfrac{-22}{10\sqrt{26}}[/tex]
[tex]\implies \theta=\cos^{-1}\left(\dfrac{-22}{10\sqrt{26}}\right)[/tex]
[tex]\implies \theta=115.5599652...^{\circ}[/tex]
Therefore, the angle between the vectors is 115.6° (1 d.p.).
a polygon has two interior angles of 120 degree each and the others are 150 degree each calculate the number of sides and the sum of interior angles in a polygon
Answer:
10 sidesangles total 1440°Step-by-step explanation:
The formula for the total of interior angles can be used together with the given angle values to write an equation for the number of sides.
SetupThe total of interior angles of an n-sided polygon is 180°×(n -2). In the given n-sided polygon, two angles are 120° and (n -2) angles are 150°. The total of angles is the same either way it is computed:
2×120 +(n -2)150 = (n -2)180
SolutionSubtracting (n-2)150, we have ...
240 = 30(n -2)
8 = n -2 . . . . . . . . divide by 30
10 = n . . . . . . . . add 2
The polygon has 10 sides.
The total of interior angles is ...
angle sum = 180°×(10 -2) = 1440°
The sum of interior angles is 1440°.
Answer:
10 sides and
1440° total of interior angles.
Step-by-step explanation:
The number of degrees in a polygon (sum of interior angles) is:
(n - 2)×180
This is the total. Here, n is the number of sides (same as the number of angles)
In your question, 2 of the angles are 120° and the remaining angles are 150°.
If n is ALL the angles, then (n-2) is all the 150° angles because the other 2 are 120°
So we can write an equation:
Our polygon:
120°+120°+(n-2)150°
=
(n-2)180°
Combine like terms:
240+(n-2)150=(n-2)180
Use Distributive property.
240+150n-300=180n-360
Again, combine like terms.
300 = 30n
Divide.
10 = n
n is the number of sides (and angles).
Check:
Ten-sided shape:
(10-2)180
= 1440°
Our shape:
120°+120°+ 8(150°)
= 240° + 1200°
= 1440° Check!
While traveling in Europe, you notice that the price of gas is $1.12 per liter. What is the price per gallon?
Mr. Bellman orders a cube of clay for each of his art classes. The height of the
cube is 20 inches. How much clay, in cubic inches, would Mr. Bellman order
for three classes?
Write and evaluate an expression to find your answer.
20 cubed is 20 times 20 and then that answer times 20.
length X width x height = cube
20 to the 3rd power or 203
A
B
C
60 cubic inches
400 cubic inches
8,000 cubic inches
Answer:
20 x 20 x 20 = 8000
A regular-size box of cereal measures 3 1/2 inches by 8 1/2 inches by 15 inches. The manufacturer also sells an individual-size box that has a volume that is 1 1/0 of the volume of the regular-size box.
What is the volume of the individual-size box of cereal?
Enter your answer as a mixed number in simplest form by filling in the boxes.
The individual-size box of cereal is a rectangular prism with a volume of 44.625 inches³.
What is the volume of a rectangular prism?The volume of rectangular prism of length l, width w and height h is given by:
V = lwh.
In this problem, the standard dimensions are:
l = 3(1/2) = 3 + 0.5 = 3.5 inches.w = 8(1/2) = 8 + 0.5 = 8.5 inches.h = 15 inches.The individual-size box has a 1/10 of the volume of the original box, hence:
V = 0.1 x 3.5 x 8.5 x 15 = 44.625 inches³.
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Tornadoes Use the frequency distribution from Exercise 12 in Section on page 49 to construct a frequency polygon. Does the graph suggest that the distribution is skewed? If so, how?
The distribution is skewed because it's on the right side of the polygon and this illustrates that's it's positively skewed.
How to illustrate the information?It should be noted that the polygon can be gotten by plotting the data.
After the analysis of the distribution, the distribution is skewed to the right.
This illustrates that it is skewed.
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What type of polynomial is: 3x4−2x3−2
The given polynomial is a Quartic trinomial
Types of polynomialFrom the question, we are to determine the type of the given polynomial
The given polynomial is
3x⁴−2x³−2
The highest degree of the polynomial is 4. Thus, it is a Quartic Polynomial.
Also, the expression contains exactly 3 terms. Thus, it is a trinomial.
Hence, the given polynomial is a Quartic trinomial
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Find the missing coordinate.
x = cos t
y = sin t
(-1, [?])
Answer:
0
Step-by-step explanation:
sin²t + cos²t = 1, so since cos²t = 1, sin²t = 0, and thus sint = y = 0.
Can you help me with this please?
The half-life of the given exponential function is of 346.57 years.
What is the half-life of an exponential function?It is the value of t when A(t) = 0.5A(0).
In this problem, the equation is:
[tex]A(t) = A(0)e^{-0.002t}[/tex].
In which t is measured in years.
Hence the half-life is found as follows:
[tex]0.5A(0) = A(0)e^{-0.002t}[/tex]
[tex]e^{-0.002t} = 0.5[/tex]
[tex]\ln{e^{-0.002t}} = \ln{0.5}[/tex]
[tex]0.002t = -\ln{0.5}[/tex]
[tex]t = -\frac{\ln{0.5}}{0.002}[/tex]
t = 346.57 years.
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Find the slope between the two points given. Then, use the slope and Point One to write the equation of the line in Point-Slope form. State the slope. Point One: (4,−3) Point Two: (−2,2)
The equation in point slope form is given as y+3 = -5/8(x-4)
Equation of a lineThe formula for calculating the equation of a line in point-slope form is expressed as:
y-y1= m(x-x1)
Given the coordinate point
Slope = 2-(-3)/-2-4
Slope = 5/-8
Determine the equation
y-(-3) =-5/8(x-4)
y+3 = -5/8(x-4)
Hence the equation in point slope form is given as y+3 = -5/8(x-4)
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How many cubicle blocks each with ages of length 2 cm are needed to fill a rectangular box that has inside dimensions 10 cm x 12 cm x 60 cm
we conclude that 900 cubes enter in the given box.
How many blocks are needed to fill the box?
We need to find the volumes of both figures.
The blocks are cubes of 2cm by 2cm by 2cm, then the volume of each block is:
[tex]V = (2cm)^3 = 8cm^3[/tex]
The box has dimensions of 10cm by 12cm by 60cm, then the volume is:
[tex]V = 10cm*12cm*60cm = 7,200 cm^3[/tex]
The number of cubes that enter in the box is N such that:
[tex]N*8cm^3 = 7,200cm^3[/tex]
Solving for N, we get:
[tex]N = 7200cm^3/8cm^3 = 900[/tex]
In this way, we conclude that 900 cubes enter in the given box.
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Preeta’s book has 300 pages. Each day she reads 10 more pages than the day before. She finishes her book in 6 days. How many pages does she read?
Step-by-step explanation:
1. if the number of pages in the 1st day is 'x', then the 2d day - 'x+10', the 3d day - 'x+20', the 4th day - 'x+30', the 5th day - 'x+40' and the last day - 'x+50' pages;
2. if the sum of all the pages is 300, then it is possible to make up the equation:
x+x+10+x+20+x+30+x+40+x+50=300;
3. x=25, it means:
1st day - 25;
2d day - 35;
3d day - 45;
4th day - 55;
5th day - 65;
6th day - 75 pages.
You deposit $2000 in an account earning 2% interest compounded monthly. How much will you have in the account in 10 years?
Answer:Principal P = 2000
Amount= A
years=n 10.00
compounded 12 times a year t
Rate = 2.00 0.02
Amount = P*((n+r)/n)^n*t
Amount = = 2000 *( 1 + 0.02 /t)^ 10 * 12
Amount = 2000 *( 1 + 0 )^ 120
2000 *( 1 )^ 120
Amount = 2442.4
Step-by-step explanation:
A group of yeast cells grows by 75% every 3hrs. At 9am, there are 200 yeast cells [9 marks].
a) write an equation that models the number of cells, given the number of hours after 9am
b) Determine the number of yeast cells after 10 hours.
a) The exponential function that models the number of cells is: [tex]A(t) = 200(1.75)^{\frac{t}{3}}[/tex]
b) There will be 1292 cells after 10 hours.
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^{\frac{t}{n}}[/tex]
In which:
A(t) is the amount after t hours.A(0) is the initial amount.r is the rate of change, as a decimal.n is the time it takes to change.For this problem, the parameters are:
A(0) = 200, r = 0.75, n = 3.
Hence the equation is:
[tex]A(t) = A(0)(1 + r)^{\frac{t}{n}}[/tex]
[tex]A(t) = 200(1 + 0.75)^{\frac{t}{3}}[/tex]
[tex]A(t) = 200(1.75)^{\frac{t}{3}}[/tex]
The number of cells after 10 hours is:
[tex]A(t) = 200(1.75)^{\frac{t}{3}}[/tex]
[tex]A(10) = 200(1.75)^{\frac{10}{3}}[/tex]
A(10) = 1292.
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The method in which all the elements of the set are written within brackets is called
Answer:
The set can be defined by listing all its elements, separated by commas and enclosed within braces. This is called the roster method.
Step-by-step explanation:
Mark me as Brainy.
Which inequality in standard form represents the
shaded region?
The figure is represented by the inequality y ≥ 5 · x² - 40 · x - 45. (Correct choice: C)
What inequality represents the figure
In accordance with the figure, we have an inequation of the form y ≥ f(x). Now we proceed to find the quadratic equation of the parabola:
f(x) = a · (x + 1) · (x - 9)
- 125 = a · (4 + 1) · (4 - 9)
- 125 = a · 5 · (- 5)
- 125 = - 25 · a
a = - 5
f(x) = 5 · (x + 1) · (x - 9)
f(x) = 5 · (x² - 8 · x - 9)
f(x) = 5 · x² - 40 · x - 45
The figure is represented by the inequality y ≥ 5 · x² - 40 · x - 45. (Correct choice: C)
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If two numbers are selected at random ,one after the other with replacement from the set A=(5,6,7,8,9) find the probability of selecting at least one prime number
Answer:
16/25
Step-by-step explanation:
(at least 1 prime selected)=1−(no primes selected)
There are 3 numbers in the set that are not prime (6,8,9)
(no primes selected)=(35)2=925
(at least 1 prime selected)=1−925
=1625
Rollin Corporation has 410,000 shares of 5$ per value common stock issued and outstanding. Record the following entries into the general journal
Answer:3522
Step-by-step explanation:222
2
solve each equation.
a)2/3-5/6=1/x
b)x+6/x=5
c)x+1/3-x-1/2=1
d)x-5/x+1=3/5
Answer:
a.
2 / 3 + 5 / 6 - 1 / 2a.
2 / 3 + 5 / 6 - 1 / 2
= 0,66... + 0,833... - 0,5
= 1,5 - 0,5
= 1
Step-by-step explanation:
sorry I only know the letter A hope I helped anyway
z^4-4z^3+4z^2+48=0 how to find value of z?
There are no real solutions to solve Z. If there may be a typo or something, there are no solutions.
Max is thinking of a number, which he calls n. He adds 8 and then doubles the sum. What is Max's final number if his starting number is 7? i need help pls
Based on the given situation, Max final number if his starting number is 7 is -4.5
AlgebraUnknown number = nHe adds 8n + 8
then doubles the sum2(n + 8)
starting number = 7So,
2(n + 8) = 7
2n + 16 = 7
2b = 7 - 16
2n = -9
n = -9/2
n = -4.5
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11. You want to save all the money you earn to buy a guitar that costs $400. You earn $9 per hour and
plan to work 15 hours each week for the next 3 weeks. Will you earn enough money in that time to buy
the guitar? Explain your answer.
Answer:
The answer is YES
Step-by-step explanation:
You want to save all the money you earn to buy a guitar that costs $400. You earn $9 per hour and
plan to work 15 hours each week for the next 3 weeks. Will you earn enough money in that time to buy
the guitar? Explain your answer.
15 hours × 3 weeks × $9 per hour
15 × 3 × 9 =
45 × 9 = 405$
The answer is YES
F(x)=x^3*125 complex zeros
Answer: 0
Step-by-step explanation:
[tex]125x^3 =0\\\\x^3 =0\\\\x=0[/tex]
Please Evaluate C(6,3)
The value of the expression C(6,3) is 20
How to evaluate the expression?The expression is given as:
C(6, 3)
This means 6 combination 3.
And it can be written as:
[tex]^6C_3[/tex]
Apply the combination formula
[tex]^6C_3 = \frac{6!}{3!3!}[/tex]
Evaluate the expression
[tex]^6C_3 = 20[/tex]
Hence, the value of the expression C(6,3) is 20
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