Answer:
Consumption in the 20th year = 82252 (nearest unit)
Step-by-step explanation:
Exponential growth problem.
Current consumption (year 0), P = 31000
growth rate, r = 5%
consumption in nth year
P(n) = P(1+r)^n
for the 20th year,
P(20) = P((1+r)^20) = 31000*1.05^20 = 82252.2 m^3
(note: annual water consumption in a town is likely to be measured by m^3, please double check)
The required volume of water will be used at 82253 liters.
The annual water usage rate increase 5% annually with current usage is 31000 liters. After 20 years what will be the volume usage? To determine.
The function which is in format f(x) =a^x where a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
Here, the rate of volume of water usage increases exponentially by 5%, current usage = 31000. So Usage for the 20th year,
= 31000(1+5%)^20
=31000(1.05)^20
= 82253 liters
Thus, The required volume of water will be used at 82253 liters.
learn more about exponential function here:
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A spinner has six spaces that are all the same size. Three spaces are yellow, two are red, and one is blue. If the spinner is spun 150 times, it should land on yellow about ___ times, on red about ___ times, and on blue ___ times.
The spinner should land on yellow about 75 times, on red about 50 times, and on blue about 25 times.
How to solve the probabilityYellow: 3 spaces out of 6, so the probability is 3/6 = 1/2
Red: 2 spaces out of 6, so the probability is 2/6 = 1/3
Blue: 1 space out of 6, so the probability is 1/6
multiplying the probability of each color by 150:
Yellow: 1/2 * 150 = 75 times
Red: 1/3 * 150 = 50 times
Blue: 1/6 * 150 = 25 times
Terefore The spinner should land on yellow about 75 times, on red about 50 times, and on blue about 25 times.
Read more on probability here:https://brainly.com/question/24756209
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Solve x2 − 7x = −12. (6 points) x = 6 and x = −2 x = 4 and x = 3 x = 2 and x = 6 x = −4 and x = −3
Work Shown:
x^2 - 7x = -12
x^2 - 7x + 12 = 0
(x - 3)(x - 4) = 0 ... see note below
x - 3 = 0 or x - 4 = 0
x = 3 or x = 4
Note: we're looking for two numbers that multiply to 12 and add to -7. Those two numbers are -3 and -4, so that's where the factorization (x-3)(x-4) comes in. After this step, you set each factor equal to zero and solve for x.
Answer:
x=3 x=4
Step-by-step explanation:
x^2 − 7x = −12
Add 12 to each side
x^2 - 7x +12 =0
Factor
What 2 numbers multiply to 12 and add to -7
-3*-4 = 12
-3+-4 = -7
(x-3)(x-4) =0
Using the zero product property
x-3 =0 x-4 =0
x=3 x=4
elogram ABCD, diagonals AC and BD intersect at point E. AE=2x, BE=y+10, CE=x+2 and DE=4y−8. Find the length of BD. A. 6 B. 16 C. 18 D. 32
Answer:
D
Step-by-step explanation:
The diagonals of a parallelogram bisect each other, thus
DE = BE , substitute values
4y - 8 = y + 10 ( subtract y from both sides )
3y - 8 = 10 ( add 8 to both sides )
3y = 18 ( divide both sides by 3 )
y = 6
Thus
BD = y + 10 + 4y - 8 = 5y + 2 = 5(6) + 2 = 30 + 2 = 32 → D
Explain how the distributive property helps us multiply the following polynomials and why and how the final products differ: (a + b)^2, (a – b)^2, and (a - b)(a + b).
Answer:
(a+b)^2 = a^2 + 2ab + b^2
(a-b)^2 = a^2 - 2ab + b^2
(a-b)(a+b) = a^2 - b^2
Step-by-step explanation:
The surface area of this rectangular prism is_____square centimeters.
Answer:
Find the area of all the shapes
Length x width = area
10 x 3 = 30
6 x 3 = 18
6 x 3 = 18
6 x 10 = 60
3 x 10 = 30
6 x 10 = 60
Add them all up
30 + 18 + 18 + 60 + 30 + 60 = 216 cm^2
Hope this helps
Step-by-step explanation:
If f(x) =27, then x=?
Answer:
x=1
Step-by-step explanation:
f(x)=27
y=27(x)
x=1
y=27
224,112,56,28 what are the two next answers?
Answer:
14,7
Step-by-step explanation: if it is being divided by 2 it is 14 and 7
PLEASE ASWER FASTThe x-intercept of the equation 2y – x = -6 is: 3. -3. 6. None of these choices are correct.
Answer:
6
Step-by-step explanation:
Well first we need to tfraph the following equation,
2y - x = -6
Look at the image below
Thus,
by looking at the graph we can tell that the x-intercept is 6.
Hope this helps :)
Answer:
x -intercept = 6Step-by-step explanation:
Method 1
[tex]2y -x = -6\\Let ; y =0\\2(0) -x =-6\\-x =-6\\x = 6\\\\ (6 , 0 )[/tex]
Method 2
[tex]x - interept = -c/a\\a = -1\\b =2\\c = 6\\\\x - intercept =\frac{ -(6)}{-1} \\\\x - intercept = 6[/tex]
The height of a cone is two times its base diameter. What is the volume of the cone in terms of its base radius r?
A.
IR
V =
2
3
V=4
B.
Oc. v=1
V = 1/2
v=1
D.
3
.
Answer:
[tex]\frac{4}{3} \pi r^3[/tex].
Step-by-step explanation:
Let's say that the radius is r. The base diameter is two times the radius, or 2r.
Since the height is two times the diameter, the height is 2 * 2r = 4r.
The volume of a cone is 1/3 * h * pi * r^2. So, the volume of the cone is 1/3 * 4r * pi * r^2 = 1/3 * pi * 4r^3 = 4/3 * pi * r^3.
So, the volume of the cone is [tex]\frac{4}{3} \pi r^3[/tex].
Hope this helps!
The box plot shows the total amount of time, in minutes, the students of a class spend studying each day: A box plot is titled Daily Study Time and labeled Time (min). The left most point on the number line is 40 and the right most point is 120. The box is labeled 57 on the left edge and 112 on the right edge. A vertical line is drawn inside the rectangle at the point 88. The whiskers are labeled as 43 and 116. What information is provided by the box plot? The lower quartile for the data The number of students who provided information The mean for the data The number of students who studied for more than 112.5 minutes
Answer:
Step-by-step explanation:
Hello!
The box plot is a graph that shows the summary of a data set.
If for example the graphic is on the side:
Box
The left limit of the box is determined by the first quantile of the data set Q₁= 57
The right limit of the box is determined by the third quantile Q₃= 112
The vertical line inside the box represents the second quantile or median Me= 88
Depending on of the symmetry of the distribution you may find it in the middle of the box (symmetrical distribution), closer to the left limit (right skewed) or closer to the right limit of the box (left skewed)
Whiskers
The whiskers of the graphic are a line between the first quantile and the minimum value and the third quantile and the maximum value.
Left whisker goes from Q₁ to the minimum value min= 40
Right whisker goes from Q₃ to the maximum value max= 120
I hope this helps!
Answer:
for the people who don't understand, its A
Step-by-step explanation:
variance of 147,141,120,124,128
Answer:
Variance population of 147,141,120,124,128 = 106
Variance sample of 147,141,120,124,128 = 132.5
Hope this helps and PLSSS MARK AS BRAINLIEST :)
Answer:
See below.
Step-by-step explanation:
The mean = (120+124+128+141+147) / 5
= 660 / 5
= 132
Difference between the values and the mean = -12, -8, -4, 9, 15.
Squares of these differences = 144, 64, 16, 81, 225
Sum of these squared differences = 530
So the variance = 530 / 5
= 106.
This is the population variance.
The sample variance = 530 / (5-1)
= 132.5.
what is 9393 divided by 81x1 ?
Answer:
115.96
Step-by-step explanation:
=> [tex]9393 / 81 * 1[/tex]
By BODMAS, Dividing first
=> 115.96 * 1
Now, Multiplying
=> 115.96
Answer:
115.962963
Step-by-step explanation:
81 x 1 = 81
9393 ÷ 81 = 115.96
Which graph shows the solution to the system of linear inequalities? 2x -3y ≤ 12 y < -3
Answer: The third graph (the one on the right side)
Step-by-step explanation:
The inequalities are:
2x -3y ≤ 12
y < -3
First, for the second inequality, we can see that y must be strictly less than -3, so we should see a dotted line at y = 3, and a shaded section under that line.
From this, we can discard the second graph (the middle one).
The first inequality can be rewritten as:
2x - 3y ≤ 12
-3y ≤ 12 - 2x
Now we divide by -3 on both sides, as we are dividing by a negative number, the direction of the ≤ sign changes:
y ≥ (12/-3) + (-2/-3)x = -4 + (2/3)*x
This means that the shaded section must be above the line:
y = -4 + (2/3)*x
Then the correct option is the third graph (rightmost graph).
Answer: c on edge 2021
Step-by-step explanation:
An insect is 3.5 millimeters long. Which expression finds the length of the insect in decimeters? Use the metric table to
help answer the question.
Metric Table
kilo-
1,000
hecto-
100
unit
deka-
10
centi-
deci-
0.1
1
milli-
0.001
0.01
A.) 3.5 x 100
B.) 3.5-100
C.) 3.5-10
D.) 3.5x 10
Answer:b
Step-by-step explanation:
C and D are wrong because both of them should be divided and by 100. A is wrong because you are supposed to divide because if you multiply 3.5 x 100 its 350 and it just doesn’t make any sense because milli is smaller than deci. So by process of elimination b is the right answer.
Answer:
b
Step-by-step explanation:
:D
Please answer it now in two minutes
Answer:3.2 ft
Step-by-step explanation:
sin 32°=[tex]\frac{yz}{6}[/tex]
cross multiply
sin 32° x 6=yz
0.5299 x 6 =yz
yz=3.1795
≅3.2ft
Complete the steps used to slove a system of liner equations by substituting the value of y into one of the original equations to find the value of x. What is the solution?
Answer:
Solve one of the equations for y, take that answer and plug into the second equation in place of y. Then solve for x.
Step-by-step explanation:
Need equations if you want actual answer
Instructions: Find the measure of the indicated angle to the
nearest degree
Answer:
See below.
Step-by-step explanation:
We want to find the unknown angle and we know the sides opposite to it and the hypotenuse. Therefore, we can use sine.
Recall that sine is the ratio of the opposite to the hypotenuse:
[tex]\sin(\theta)=opp/hyp[/tex]
Plug in the numbers. The opposite is 20 and the hypotenuse is 55.
[tex]\sin(\theta)=20/55[/tex]
Solve for theta (use a calculator):
[tex]\sin(\theta)=20/55\\\theta=\arcsin(4/11)\\\theta\approx21.23\approx21\textdegree[/tex]
What are the measures of angles M and N?
mM = 61° and mN = 113
mM = 67 and mN= 119
mM = 113 and mN = 61
mM = 119 and mN = 67
Answer:
mM = 113 and mN = 61
Step-by-step explanation:
In a Cyclic quadrilateral, the rule states that:
The sum opposite interior angles is equal to 180°
In the above diagram, we have cyclic quadrilateral KLMN
According to the rule stated above:
Angle K is Opposite to Angle M
So, Angle K + Angle M = 180°
Angle K = 67°
67° + Angle M = 180°
Angle M = 180° - 67°
Angle M = 113°
Angle L is Opposite to Angle N
so Angle L + Angle N = 180°
Angle L is given as = 119°
119° + Angle N = 180°
Angle N = 180° - 119°
Angle N = 61°
Therefore, Angle M = 113° and Angle N = 61°
At Camp Sunshine, 4 kids went home sick. Of the remaining campers, 18 kids went hiking and the other 41 kids spent the day swimming. how many kids started the day at camp sunshine!?!??!?!?!?!?!?!?! I NEED TO KNOWWW
What is the measure of each intercepted arc for each inscribed angle of a square inscribed in a circle?
Answer:
The measure of the angle of each of the intercepted arc is 180°
Step-by-step explanation:
An intercepted arc is an encased (between chords) portion of the circumference of the circle. The chords that form the intercepted arc meet at a point
An inscribed angle is the angle is an angle formed between two chords that meet at a point called the end point
For the inscribed square, the symmetry has it that the diagonal is the same as the diameter of the circle as the diagonals bisect each other having equal distances on either side to the circumference of the circle.
Given that the angles in the vertices of the square are 90° and the point of intersection of the two chords forming the vertex are at the ends of the diameter of the circle, which passes through the center of the circle, the angle 90° at the vertex is half the angle at the center which is the angle of the intercepted arc
∴ The measure of the angle of each of the intercepted arc = 2× 90 = 180°.
☆*☆=3x, if x is even and negative OR ☆*☆=4x, if x is odd. Following the rule above, what is the value of ☆ - 23 ☆?
A. 92
B. -92
C. 529
D. -529
Answer:
okay... Thanks have a great day!
If a line crosses the x-axis at (4,0), what is the x-intercept?
Answer:
x = 4
Step-by-step explanation:
The y- intercept is the value of the x- coordinate where the line crosses the x- axis.
Given the line crosses the x- axis at (4, 0 ), then
the x- intercept is x = 4
Which is the solution to the equation 3.5 (2 h + 4.5) = 57.75? Round to the nearest tenth if necessary.
Answer:
h = 6
Step-by-step explanation:
Step 1: Distribute
7h + 15.75 = 57.75
Step 2: Subtract 15.75 on both sides
7h = 42
Step 3: Divide both sides by 7
h = 6
Find the surface area of the right rectangular prism shown below. units²
Answer:
67 units^2
Step-by-step explanation:
The surface area of the prism is found by
SA = 2 ( lw+lh + wh)
= 2 ( 5*1.5+ 4*1.5 + 5*4)
= 2 ( 7.5+6+20)
= 2 (33.5)
= 67
Answer:
67units²
Step-by-step explanation:
Which answer choice is equivalent to the expression below? Negative 7 (2 + n) + one-third (negative 9 minus 6 n) Negative 17 minus 9 n Negative 14 minus 12 n 11 + 5 n 14 + 2n
Answer:
a. -17 -9n
Step-by-step explanation:
Question written clearly below:
Which answer choice is equivalent to the expression below?
-7(2+n)+1/3(-9-6n)
a.-17 -9n
b, -14-12n
c. 11+5n
d. 14+2n
Solution
-7(2+n)+1/3(-9-6n)
Open parenthesis
(-14-7n)+(-9/3-6/3n)
= -14-7n+(-3-2n)
= -14-7n-3-2n
Collect like terms
= -14-3-7n-2n
= -17-9n
The answer is option a. -17 -9n
Answer:
-17 -9n
Step-by-step explanation:
i got it right on edge
y=6x 2x+3y=20 solving equation using substitution
Answer:
x = 1, y = 6
Step-by-step explanation:
y = 6x
2x + 3y = 20
Plug y as 6x in the second equation and solve for x.
2x + 3(6x) = 20
2x + 18x = 20
20x = 20
[tex]\frac{20x}{20}= \frac{20}{20}[/tex]
x = 1
Plug x as 1 in the first equation and solve for y.
y = 6(1)
y = 6
Answer:
y=6 , x=1
Step-by-step explanation:
y=6x
2x+3y=20
Substitute 6x into y because y=6x.
2x+3(6x)=20
2x+18x=20
20x=20
x=1
Then subsitiute 1 into the first equation in x value
y=6(1)
y=6
11. Which of the following lines is perpendicular to the line 3x-9y = 17?
A) 12x + y = 4
B) 9x - 3y = 11
C) 6x + 2y = 8
D) 3x - y = 5
Step-by-step explanation:
When using the equation of a line, one calculates the value of
y
in terms of
x
, say
y
=
m
x
+
c
, then
m
is the slope of the line and
c
is its intercept on
y
-axis.
As
3
x
−
9
y
=
15
can be written as
3
x
−
15
=
9
y
or
y
=
3
9
x
−
15
9
or
y
=
1
3
x
−
5
3
Hence slope of
3
x
−
9
y
=
15
is
1
3
Product of slopes of two perpendicular lines is
−
1
Hence, the slope of the line that is perpendicular to the line
3
x
−
9
y
=
15
is
−
1
1
3
=
−
1
×
3
1
=
−
3
graph{(3x-9y-15)(3x+y+5)=0 [-10, 10, -7.04, 2.96]}
If you wrote the numbers from 1-8, and it equals to three, how do you make the statement true if you can't change the 3 but you could connect two or more numbers to make the statement true if you also can only do subtraction?
Answer:
Just add 6 to the right side of 3 which will make as 36
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36
Hope it helps u...pls mark as brainliest
can you please help me
Apply the rule x^m/n = nsqrt(x^m)
(2) ^x/12 = 12sqrt(2^x)
The answer is the 3rd choice
what is the 6th term in the geometric sequence described by this explicit formula ?
Answer:
the answer is d. -5120
Step-by-step explanation:
[tex]a_{n} =-5(4)^{n-1}\\a_{6}=-5(4)^{6-1} \\a_{6}=-5(4)^{5} \\a_{6}=-5(1024)\\a_{6}=-5,120[/tex]