The materials and cost of Kara's project obtained using Pythagorean theorem, are;
(a) Distance between fence posts is 2•√(14) feet
(b) Kara needs about 12 fence posts
(c) Kara will need 22 diagonal pieces
(d) Kara's total cost is $281
What is the Pythagorean theorem?Pythagoras theorem can be stated as, the square of the length of the hypotenuse side of a right triangle is equal to the sum of the squares of the other two sides.
The drawing obtained from a similar question consists of two diagonals between consecutive posts.
(a) The given parameters are;
Height of the fence post = 5 feet
Length of the diagonal pieces = 9 feet
The distance, d, between the fence posts using Pythagorean theorem gives;
d² = 9² - 5² = 56
d = 2•√(14)
The distances between the fence posts should therefore be 2•√(14) feet
(b) The number of fence posts, n, is given by the equation;
2•√(14) × n = 93
Which gives;
[tex] \displaystyle {n = \frac{93 }{2 \cdot \sqrt{14}} \approx 12.43}[/tex]
Given that after the 12th post, the 1st post comes next and the distance remaining is less than d, the number of posts, n is 12
(c) The number of diagonal pieces, m, needed, given that there are two diagonal pieces between two posts and there is only 11 in between spaces, gives;
m = 2 × 11 = 22
There are 22 diagonal pieces
(d) Cost of a fence post = $17
Cost of a diagonal piece = $3.5
Total cost, C, is therefore;
C = 12 × 17 + 22 × 3.5 = 281
Kara's total cost is $281
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a restaurant employs 16 people, 8 of whom are women. if five employees are chosen randomly to receive tickets to a concert, what is the probability (to two decimal places) that three of them will be women? use the hypergeometric distribution.
The probability that 3 of the people chosen would be women = 0.36.
Probability is basically a numerical description of how likely an event is supposed to happen. It is a number something between 0 and 1.
total number of people = 16
total number of women = 8
number of chosen employees randomly to receive tickets to a concert = 5
probability to find = that 3 of them will be women
Therefore, we can conclude that the probability of 3 of the chosen people will be women is 0.36.
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A bag of 5 blue, 3 red, 6 green, 9 orange, and 20 black marbles. what is the ratio of the number of blue marbles to the number of marbles that are orange or green?
The ratio of the number of blue marbles to the number of marbles that are orange or green is 1 : 3.
Ratio is defined as the relationship between two quantities. It can be expressed as a to b, a/b, or a : b.
Let a = total number of blue marbles
b = total number of orange and green marbles
If the total number of blue marbles is 5 and the total number of orange and green marbles are 9 and 6, respectively, then the ratio is 5 to (9 + 6).
Simplify the ratio.
5 : (9 + 6) = 5 : 15 = 1 : 3
Hence, the ratio is 1:3.
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Draw a slope triangle, from point B, whose horizontal leg is along the x-axis. What are the lengths of the vertical and horizontal legs of your slope triangle?
Horizontal leg = 6 units
Vertical leg is 4 units
Lets Represent the diagonal as line AB where A and B are the endpoints of the line segment
The coordinates of point A is ( 12,4)
The coordinates of point B is ( 6,0)
Slope = ( Y2 - Y1 ) / (X2 -X1) = (0 - 4) / ( 6 - 12) = -4 / -6 = 2/3
or simply.
slope = rise / run = vertical leg/ horizontal leg = 4/6 = 2/3
ANSWER
Horizontal leg = 6 units
Vertical leg is 4 units
Slope = 2/3
a newsletter publisher believes that 60`% of their readers own a laptop. is there sufficient evidence at the 0.050.05 level to refute the publisher's claim? state the null and alternative hypotheses for the above scenario.
The null hypothesis is [tex]H_{0} : x=0.60[/tex] and alternative hypothesis is [tex]H_{1} :x\neq 0.60[/tex].
What is null and alternative hypothesis?
The null hypothesis is that the statement that researchers usually aim to disprove by performing tests of significance on the dataset. the most purpose of the null hypothesis is to help disprove a hypothesis or nullify it in favor of the alternate hypothesis that the researchers want to prove.
Let the percentage of readers who own a laptop be [tex]x.[/tex]
As newsletter publisher believes that [tex]60[/tex]`% of their readers own a laptop.
Therefore the null hypothesis is [tex]H_{0} : x=0.60[/tex] and alternative hypothesis is [tex]H_{1} :x\neq 0.60[/tex].
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factor this polynomial completely[tex]10 {x}^{2} - 11x + 3[/tex]
Given:
There are given the equation:
[tex]10x^2-11x+3=0[/tex]Explanation:
According to the question:
we need to find the factor of the given equation:
So,
From the equation:
[tex]\begin{gathered} 10x^{2}-11x+3=0 \\ 10x^2-6x-5x+3=0 \\ (2x-1)(5x-3)=0 \end{gathered}[/tex]Final answer:
Hence, the factor of the given equation is shown below:
[tex](2x-1)(5x-3)=0[/tex]What is 4x + y = -3?
Answer:x=
−1/4y+ −3/4
Step-by-step explanation
FREE BRAINlIEST IF CORRECT: Find an equation of the perpendicular bisector of the segment AB with endpoints A(1, 2) and B(–3, 4). If the perpendicular bisector of AB intersects the x‑axis at point P, what are the lengths of PA and PB ?
The lengths of PA and PB are 3.1622 units if the point is P (0, 5).
What is the distance between two points?The distance between two points is defined as the length of the line segment between two places representing their distance. Most significantly, segments that have the same length are referred to as congruent segments and the distance between two places is always positive.
The formula of the distance between two points exists P(x₁, y₁) and Q(x₂, y₂) is given by:
d (P, Q) = √ (x₂ – x₁)² + (y₂ – y₁) ².
The given points exists A(1, 2) and B(–3, 4).
The perpendicular bisector of AB will pass through the midpoint of AB.
Now the perpendicular bisector of AB will meet the Y-axis at P(0, y).
∴ AP = BP
Applying the distance formula, we get4
⇒ PA² = PB²
⇒ (x₁ – 0)² + (y₁ – y)² = (x₂ – 0)² + (y₂ – y)²
⇒ (1 – 0)² + (2 – y)² = (–3 – 0)² + (4 – y)²
After solving, we get y = 5
Therefore, the point is P (0, 5).
Now calculating the lengths of PA and PB
PA = √(1 – 0)² + (2 – 5)² = 3.1622
PB = √(-3 – 0)² + (4 – 5)² = 3.1622
Therefore, the lengths of PA and PB are 3.1622 units.
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please help thank you, due soon
Answer:
8.1
Step-by-step explanation:
just calculate 45 of 18%
The temperature is −4°F. What will the temperature be if the temperature rises 20°F?
Answer:
16°F
Step-by-step explanation:
The temperature is −4°F. What will the temperature be if the temperature rises 20°F?
-4 + 20 = 16
so:
16°F
Please help me, it is important
Examining the given figure it can be calculated that
GI = 15 unitsm< IEH = 65 degrees How to get the required angel and length of side in the given figureGiven that
EI = 2x + 1
FH = 3x + 9
m< FIG = 50 degrees
The length of diagonals of rectangles are equal and when they bisect each other the divide each other into equal halves
EI is the half of FH, therefore we have that
( 3x + 9 ) / 2 = 2x + 1
3x + 9 = 2(2x + 1)
3x + 9 = 4x + 2
9 - 2 = 4x - 3x
7 = x
GI = EI (half diagonal of rectangle are equal)
GI = 2 * 7 + 1
= 15
m< FIG = 50 degrees = m< EIH (vertical opposite angles)
m< EIH + m< IEH + m< IHE = 180
m< IEH = m< IHE = y (base angles of isosceles triangle)
m< EIH + 2y = 180
50 + 2y = 180
2y = 180 - 50
2y = 130
y = 65 degrees
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the heights of men in a certain population follow a normal distribution with mean 69.7 inches and standard deviation 2.8 inches. (a) if 10 men are selected at random, what is the probability their average height is above 72 inches? (b) if exactly one man is selected at random, what is the probability his average height is above 72 inches? (c) what is the 80th percentile for the average height of 10 men? (d) what is the probability the average height of 10 men is between 70 and 71 inches?
a) 10 men are selected at random, the probability their average height is above 72 inches is 0.0122.
b) Exactly one man is selected at random, the probability his average height is above 72 inches is 0.0122.
c) The 80th percentile for the average height of 10 men is 0.0097%.
d) The probability the average height of 10 men is between 70 and 71 inches is 0.13607.
Mean = 69.7 inches
Standard Deviation = 2.8 inches
a) Using normal distribution,
P(Y > 72) = P(Y - mean > 72 - mean)
P(Y > 72) = P((Y - mean ÷ SD) > (72 - mean ÷ SD))
P(Y > 72) = P(Z > (72 - mean ÷ SD))
P(Y > 72) = P(Z > (72 - 69.7 ÷ 2.8))
P(Y > 72) = P(Z > 2.25)
P(Y > 72) = 1 - P(Z ≤ 2.25)
P(Y > 72) = 0.0122
b) P(man's height is above 72 inches) = 0.0122
c) (80 × 0.0122) ÷ 100
= 0.0097%
d) P( 70 > Y > 71) = P(70 - mean > Y - mean > 71 - mean)
P( 70 > Y > 71) = P((70 - mean ÷ SD) > (Y - mean ÷ SD) > (71 - mean ÷ SD))
P( 70 > Y > 71) = P((70 - mean ÷ SD) > Z > (71 - mean ÷ SD))
P( 70 > Y > 71) = P((70 - 69.7 ÷ 2.8) > Z > (71 - 69.7 ÷ 2.8))
P( 70 > Y > 71) = P(0.107 > Z > 0.464)
P( 70 > Y > 71) = 0.13607
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Use BIMDAS to calculate my fortnightly earnings.
I have two part-time jobs.
3 days per week I work for 6 hours each day and I earn $20.00 per hour. For 2 days per week, I earn $25.00 per hour, working an 8-hour day.
Based on your earnings from each of the part-time jobs, your fortnightly earnings would be $1,520
How to find the earnings?First, find out how much you earn in the first part-time job per week:
= (Number of days per week x Number of hours per day x Pay per hour)
= (3 x 6 x 20)
The find out how much you earn in the second part-time job:
= (Number of days per week x Number of hours per day x Pay per hour)
= (2 x 8 x 25)
In a fortnight (two weeks), your earnings would be:
= (2 weeks x (3 x 6 x 20)) + (2 weeks x (2 x 8 x 25))
= (2 x 360) + (2 x 400)
= 720 + 800
= $1,520
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Fortnightly earnings would be $1,520 based on previous earnings.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that there are two part time jobs.
For first part time
3 days per week I work for 6 hours each day and I earn $20.00 per hour
(3 x 6 x 20)
=360
Second part time
2 days per week, I earn $25.00 per hour, working an 8-hour day.
=2×25×8
=400
Now we need to calculate, the total fortnightly earnings.
= (2 weeks x360) + (2 weeks x 400)
= (2 x 360) + (2 x 400)
= 720 + 800
= $1,520
Hence $1520 is the fortnightly earnings.
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One month Ivan rented 8 movies and 3 video games for a total of $43. The next month he rented 2 movies and 5 video games for a total of $32. Find the rental cost for each movie and each video game.
Given
Let's represent movies with M
Let's represent video with V
[tex]\begin{gathered} 8m+3v=43\ldots\text{Equation 1} \\ 2m+5v=32\ldots\text{Equation 2} \end{gathered}[/tex]Solution
Using substitution method
I will solve your system by substitution.
[tex]\begin{gathered} 8m+3v=43\ldots\text{Equation 1} \\ \text{Make M the subject of the formula} \\ 8m=43-3v \\ \text{Divide both sides by 8} \\ m=\frac{43-3v}{8}\ldots\text{Equation 3} \end{gathered}[/tex]Substitute for m in Equation 2
[tex]\begin{gathered} 2(\frac{43-3v}{8})+5v=32 \\ \\ \frac{43-3v}{4}+5v=32 \\ \end{gathered}[/tex]To clear the fraction multiply all through by 4
[tex]\begin{gathered} \frac{43-3v}{4}\times4+5v\times4=32\times4 \\ \\ \\ 43-3v+20v=128 \end{gathered}[/tex]Separate the similar term
[tex]\begin{gathered} -3v+20v=128-43 \\ 17v=85 \\ \text{Divide both sides by 17} \\ \frac{17v}{17}=\frac{85}{17} \\ \\ v=5 \end{gathered}[/tex]Substitute for v =5 in equation 3
[tex]\begin{gathered} m=\frac{43-3v}{8}\ldots\text{Equation 3} \\ m=\frac{43-3(5)}{8} \\ m=\frac{43-15}{8} \\ \\ m=\frac{28}{8} \\ \\ m=\frac{7}{2}=3.5 \end{gathered}[/tex]The rental cost for each movie
[tex]m=\text{ \$}3.50[/tex]The rental cost for each video game.
[tex]v=\text{ \$5}[/tex]x+6x-5x=x+114 Please help.
11.4.4 Set F 10. The area of the trapezoid below is 24 square meters, the altitude is 4 meters, and the length of one base is 2 meters, What is the length, *, of the other base, in meters? 4 H. 10 K, 1211.4.4 Set F 10. The area of the trapezoid below is 24 square meters, the altitude is 4 meters, and the length of one base is 2 meters. What is the length, x, of the other base, in meters?
The length, [tex]x[/tex], of the other base, in meters is 10.
The area of trapezoid = 24 square meters
The altitude = 4 meters
The length of one base = 2 meters
We have to find the length [tex]x[/tex] of the other base in meters.
To find the value of the length [tex]x[/tex] we use formula of area of trapezoid.
We use the area of trapezoid to find the value of length [tex]x[/tex] because we know the value of area of trapezoid, length of one base and altitude.
As we know the formula of area of the trapezoid
[tex]A=\frac{a+b}{2}\times H[/tex]
In the formula,
[tex]A=[/tex] area of trapezoid
[tex]a[/tex] and [tex]b[/tex] are the two length of two different base of the trapezoid
[tex]H=[/tex] height or altitude of the trapezoid
From the given question, [tex]A[/tex] = 24 square meters, [tex]a=x[/tex] meter, [tex]b[/tex] = 2 meters and [tex]h[/tex] = 4 meters.
Now putting the values in the formula.
[tex]24=\frac{x+2}{2}\times 4[/tex]
[tex]24=(x+2)\times 2[/tex]
Divide by [tex]2[/tex] on both side
[tex]\frac{24}{2} =\frac{(x+2)\times 2}{2}[/tex]
[tex]12=x+2[/tex]
Subtract [tex]2[/tex] on both side
[tex]12-2=x+2-2[/tex]
[tex]10=x[/tex]
[tex]x=10[/tex]
Hence, the length, [tex]x[/tex], of the other base, in meters is 10.
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Rewrite the following calculation so it involves addition only and then determine the result. Show your work.
-3+1-7- (-4)+10
URGENT PLEASE HELP FOR HW
The given calculation, -3+1-7- (-4)+10, can be rewritten as (1+4) so that it only involves addition and the result is 5.
According to the question,
We have the following expression:
-3+1-7- (-4)+10
Now, we have to remove all the negative signs from this expression.
So, we will first solve this expression to the step where we have only addition.
Now, we know that the multiplication of two negative integers is always positive.
-3+1-7+4+10
Adding the numbers with the negative sign:
-10+10+1+4
1+4
5
Hence, -3+1-7- (-4)+10 can be rewritten as (1+4) so that it only involves addition and the result is 5.
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answer pls
1. A surfer paddles out past breaking waves, rides a
wave, paddles back out past the breaking waves,
rides another wave back to the beach. Draw a sketch
of a graph (with labels) that shows the surfer’s
possible distance from the beach over time.
2. For the table, identify the independent and
dependent variables, Represent the relationship
using words, an equation and a graph.
# of cases of
bottled
water, c
# of bottles
of water,
b
1 24
2 48
5 120
10 240
20 480
for this one i only need the graph cannot find it out
3. Sketch a graph of the function shown by the table. Is
its linear or nonlinear?
x y
1 0
2 1
3 8
4 20
5. Write a function rule to represent the situation:
The volume, V, remaining in a 243 ft3 pile of gravel
decreases by .2 ft3 with each shovelful, s, of gravel
spread in a walkway
Tell whether the relation is a function. Explain your
reasoning.
{(-1, 7), (9, 4), (3, -2), (5, 3) , (9, 1)
7. Tell whether the relation is a function. Explain your
reasoning. find graph below
Describe the pattern in the sequence. Find the next
two terms of the difference.
-2, -5, -8, -11,
the graph for 7
Answer:
V = 243 - 0.2s
Step-by-step explanation:
See attached document for questions 1 - 3.
5. Write a function rule to represent the situation:
The volume, V, remaining in a 243 ft3 pile of gravel
decreases by .2 ft3 with each shovelful, s, of gravel
spread in a walkway.
Volume Remaining (V) = Initial - Used
Volume Remaining (V) = 243 ft^3 - (0.2 ft^3/shovel)(s shovels)
V = 243 - 0.2s
6. Tell whether the relation is a function. Explain your
reasoning.
{(-1, 7), (9, 4), (3, -2), (5, 3) , (9, 1)
This is not a function. When x = 8, it results in more than one output.
7. Pattern:
-2
-5
-8
-11
Each step decreases by 3
-14
-17
8.
solve by graphing 6X + 3y equals 12 x + 4y equals 24
The system of equations is:
[tex]\begin{gathered} 6x+3y=12 \\ 8x+4y=24 \end{gathered}[/tex]To solve the system of equations by graphing, we need to make a graph of each equation. For that, we solve for y in both equations:
[tex]\begin{gathered} \text{Solving the first equation for y:} \\ 6x+3y=12 \\ 3x=-6x+12 \\ y=-2x+4 \\ \text{Solving the second equation for y:} \\ 8x+4y=24 \\ 4y=-8x+24 \\ y=-2x+6 \end{gathered}[/tex]We have two equations to graph:
[tex]\begin{gathered} y=-2x+4 \\ y=-2x+6 \end{gathered}[/tex]Comparing with the slope-intercept equation:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
We can see that the slope of the two equations is m=-2, this means that the lines will have the same rate of change of -2 in y for every 1 in x. And one graph will cross the y-axis at 4 and the other at +6.
The graph of the two equations is shown in the following image:
Where the green line is the first equation, and the red line is the second equation.
There is no solution to this system of equations because the lines do not intersect each other.
A given triangle has vertices at (-3, 1) (2, 4) and (5, -3). If the triangle were rotated 180 degrees counterclockwise, the new coordinates would be:
The new coordinates when we rotate the triangle counterclockwise is (3, -1), (-2, -4), (-5, 3).
Given,
The triangle with vertices;
(-3, 1) (2, 4) and (5, -3).
We have to find the new coordinates, when the triangle rotated 180 degrees counter clockwise;
Here,
The vertices;
(-3, 1) (2, 4) and (5, -3).
When we rotate 180 degree counter clockwise, the plane changes not the point.
That is,
(-3, 1) becomes (3, -1)
(2, 4) becomes (-2, -4)
(5, -3) becomes (-5, 3)
That is,
The new coordinates when we rotate the triangle counterclockwise is (3, -1), (-2, -4), (-5, 3).
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The new coordinates when we rotate the triangle counterclockwise is (3, -1), (-2, -4), (-5, 3).
Given,
The triangle with vertices;
(-3, 1) (2, 4) and (5, -3).
We have to find the new coordinates, when the triangle rotated 180 degrees counter clockwise;
Here,
The vertices;
(-3, 1) (2, 4) and (5, -3).
When we rotate 180 degree counter clockwise, the plane changes not the point.
That is,
(-3, 1) becomes (3, -1)
(2, 4) becomes (-2, -4)
(5, -3) becomes (-5, 3)
That is,
The new coordinates when we rotate the triangle counterclockwise is (3, -1), (-2, -4), (-5, 3).
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Rewrite 20 − 4x3 using a common factor.
Using a common factor, 20 - 4x³ can be rewritten as 4(5 - x³).
What is a Common Factor?A common factor of two or more numbers is any number that the two numbers can be divided by and will leave no remainder.
For example, a common factor of 4 and 8 is 2. This is because:
2 into 4 will give us 2 without a remainder.
2 into 8 will give us 4 without a remainder.
To rewrite the expression, 20 - 4x³ using a common factor, find the factor that will go into each of the terms without a remainder.
4 into 20 will give us 5 without a remainder.
4 into 4x³ will give us x³ without a remainder.
Therefore, we can factor out the common factor from the expression to rewrite 20 - 4x³ as 4(5 - x³).
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write the linear equation in slope-intercept form passing through the point with the given slope. 1. (0,3):slope = -2 2. (-5,-3); slope = -3/5 3. (-8,6); slope 1/4 write the linear equation in slope-intercept form that passes through the given points. 4.
The equation of each line in slope-intercept form are:
1. y = -2x + 3
2. y = -3/5x - 6
3. y = 1/4x + 8
How to Write the Equation of a Line in Slope-intercept Form?If we are given a point (a, b) and the slope of a line (m), we can write the linear equation in slope-intercept form by first plugging in the given values into y - b = m(x - a), then rewrite it in the slope-intercept form as y = mx + b.
1. Slope (m) = -2
Point (a, b) = (0, 3)
Plug in the values into y - b = m(x - a):
y - 3 = -2(x - 0)
y - 3 = -2x + 0
y = -2x + 0 + 3
y = -2x + 3 [slope-intercept form]
2. Slope (m) = -3/5
Point (a, b) = (-5, -3)
Plug in the values into y - b = m(x - a):
y - (-3) = -3/5(x - (-5))
y + 3 = -3/5x - 3
y + 3 - 3 = -3/5x - 3 - 3
y = -3/5x - 6 [slope-intercept form]
3. Slope (m) = 1/4
Point (a, b) = (-8, 6)
Plug in the values into y - b = m(x - a):
y - 6 = 1/4(x - (-8))
y - 6 = 1/4(x + 8)
y - 6 = 1/4x + 2
y - 6 + 6 = 1/4x + 2 + 6
y = 1/4x + 8 [slope-intercept form]
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Good Morning please help outt
The solution to the inequality given as 3 - x/2x + 1 ≥ 2 is (-oo, -1/2) u [1/5, oo]
How to determine the solution to the inequality?The inequality expression is given as
3 - x/2x + 1 ≥ 2
Cross multiply in the above inequality
So, we have
3 - x ≥ 2(2x + 1)
Open the brackets in the inequality
So, we have
3 - x ≥ 4x + 2
Collect the like terms
4x + x ≤ 3 - 2
Evaluate the like terms
5x ≤ 1
Divide by 5
x ≤ 1/5
Because of the denominator 2x + 1, we have
x > -1/2
This means that the solution is (-oo, -1/2) u [1/5, oo]
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Write a multiplication problem with two fractions that has a simplified product of 4/5.
A problem that consists of the multiplication of two fractions, and in which the simplified product is 4/5 is presented as follows;
[tex] \displaystyle {\frac{14}{15} \times \frac{6}{7} = \frac{4}{5} }[/tex]
What is a fraction in mathematics?A fraction consists of a number that is expressed as a quotient, such that the numerator is being divided by the value in the denominator.
The multiplication problem with two fractions that ha a simplified product of 4/5 is found as follows;
let the fractions be [tex] \displaystyle \frac{a}{b} [/tex] and [tex] \displaystyle \frac{c}{d} [/tex]
The multiplication product is therefore;
[tex] \displaystyle \frac{a}{b} \times \frac{c}{d} = \frac{a \cdot c}{b\cdot d} = \frac{4}{5}[/tex]
The lowest common multiple of a and c is 4, while the lowest common multiple of b and d is 5
Taking b as 15, and a as 14 and c as 6, while d is taken as 7, such that we have;
[tex] \displaystyle {\frac{14}{15} \times \frac{6}{7} =\frac{2 \times 7}{5 \times 3} \times \frac{2 \times 3}{7} = \frac{2 \times 2}{5 \times 1} =\frac{4}{5} }[/tex]
The multiplication problem is therefore;
[tex] \displaystyle {\frac{14}{15} \times \frac{6}{7} = \frac{4}{5} }[/tex]
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combine the like terms to create an equivalent expression -4r - 2r + 5
Answer:8r+7-6r-5Combine the like terms=8r-6r+7-5Thenafter, simplify=2r+2
good luck
Step-by-step explanation:
Emilio borrows $1200 from a bank with 8% simple interest per year.How much will he have to pay back total in 2 years
The amount of money that Emilio will pay back in two years is $1392.00.
What is the accrued amount of the loan?The accrued amount includes principal plus interest.
Simple interest formula can be expressed as;
A = P( 1 + rt )
Where A is accrued amount, P is principal, r is rate and t is time elapsed.
Given the data in the question;
Principal P = $1200Simple interest rate r = 8%Time t = 2 yearsAccrued amount A = ?First, converting percent to decimal.
Rate r = 8% = 8/100 = 0.08
Now, plug the given values into the above formula and solve for the accrued amount.
A = P( 1 + rt )
A = $1200( 1 + 0.08 × 2 )
A = $1200( 1 + 0.16 )
A = $1200( 1.16 )
A = $1392.00
Therefore, the accrued amount is $1392.00.
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A scientist has 2 3rd liter of solution. He uses 1 halfof the solution for an experiment. Howmuch solution does the scientist use forthe experiment?
SOLUTION
The total amout of solution given is
[tex]\frac{2}{3}\text{liter}[/tex]From thequestion, 1/2 of the solution is used, then the amount of solution used for the experiment will be
[tex]\frac{2}{3}\times\frac{1}{2}=\frac{2\times1}{3\times2}=\frac{2}{6}=\frac{1}{3}\text{liters }[/tex]Hence
The amount of solution the scientist use is 1/3 litres
Change baseround final answer to nearest ten thousandONLY INCLUDE THE NUMBER OF YOUR FINAL ANSWER
We can solve this by means of the change of base formula:
[tex]a^y=x,y=\log _ax[/tex]By replacing x for y, 3 for a, and 27.3 for x into the above formula, we get:
[tex]x=\log _327.3=3.0101[/tex]Then, x = 3.0101
What is the slope of this line?
Enter your answer as a whole number or a fraction in simplest form in the box.
Answer:
1/4
Step-by-step explanation:
The points (-4, 5) and (0, 6) lie on the line. Substituting into the slope formula,
[tex]\frac{6-5}{0-(-4)}=\frac{1}{4}[/tex]
5. Which equation is solved for the height of the cone based on theinformation given below?The equation V = 1 r represents the volume of a cone, where is the radius of the cone andh is the height of the coneh=V - Tr?h= } #r?VB3V - #r2 = h3Vha?D
We need to make h the subject of formula:
[tex]\begin{gathered} All\text{ the variables on the right are multiplied together.} \\ \text{First we get rid of the 1/3 by multiplying both sides by 3:} \\ 3(V)\text{ =3( }\frac{1}{3}\pi r^{2}h) \\ 3V\text{ = }\pi r^{2}h \end{gathered}[/tex][tex]\begin{gathered} \text{For h to stand alone on the right side, we divide both sides by }\pi r^2h \\ We\text{ apply division beause all the variables were ultiplied together} \\ So\text{ to undo it, we divide} \\ \frac{3V}{\pi r^{2}}=\text{ }\frac{\pi r^{2}h}{\pi r^{2}} \\ \frac{3V}{\pi r^2}=\text{ }h \end{gathered}[/tex][tex]h\text{ = }\frac{3V}{\pi r^{2}}\text{ (option D)}[/tex]Pls pls help due tomorrow!
If the equation y = -x, then the equation of the line that is parallel to the given line and passes through the point (-8,2) is y = -x-6
The equation is
y = -x
The slope intercept form
y = mx+b
Where m is the slope of the line
Comparing the slope intercept form and the given equation
Slope of the line m = -1
The line is passing through the points (-8,2)
The point slope form of the line
[tex](y-y_1)=m(x-x_1)[/tex]
Substitute the values in the equation
y-2 = -1(x-(-8))
y-2 = -1(x+8)
y-2 = -x-8
y = -x-8+2
y = -x-6
Hence, if the equation y = -x, then the equation of the line that is parallel to the given line and passes through the point (-8,2) is y = -x-6
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