Answer:
11 years
Step-by-step explanation:
Set the function f(x) = 100(1.0153)^x = to 118 and solve for x:
100(1.0153)^x = 118
Taking the natural logarithm of both sides, we get:
ln 100 + x ln 1.0153 = ln 118
Then x ln 1.0153 = ln 118 - ln 100, or
= 4.7707 - 4.6052
... which leads to:
4.7707 - 4.6052
x = --------------------------- = 11 years (rounded up from 10.888 )
0.0152
Answer:
11 years
Step-by-step explanation:
The table below shows the function f.
Determine the average rate of change of the given function.
A.
B.
C.
D.
Answer:
the average rate of change is -1/6 per unit increase in x
Step-by-step explanation:
Looking at the table, we see that for each unit change in x, y decreases by 1/6. Thus, the average rate of change is -1/6 per unit increase in x.
Answer with explanation:
Average rate of Change
[tex]=\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}}\\\\=\frac{\frac{25}{3}-\frac{17}{2}}{4-3}\\\\=\frac{50-51}{6*1}\\\\=\frac{-1}{6}[/tex]
You can find average rate of change by taking any two distinct points on the curve.
Option B
What is 7.04 trillion in scientific notation
Answer:
7.04 trillion = 7.04 x 10¹²
Step-by-step explanation:
Answer: 7.04 x 10^12
Step-by-step explanation:
Just took the test :)
Find an equation, in slope-intercept form, that passes through point (-5, 6) with slope -2.
Select one:
a. y = -2x + 3
b. y = -2x - 4
c. y = 2x - 4
d. y = 2x + 3
Answer:
The desired equation is y = -2x - 4
Step-by-step explanation:
The general slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
Starting from that, substitute the given values for m, x and y and calculate b:
6 = -2(-5) + b. Then 6 = 10 + b, and b = -4.
The desired equation is y = -2x - 4.
in 18 days, 20 workers can build a school. How many days would it take if there were only 12 workers?
To build a school;
20 workers -> 18 days.
So 1 worker -> 18/20 days.
So; 12 workers -> (12×18)/20 days.
-> (12×9)/10 days
->10.8 days.
so 10.8 days is your answer.
Hope it helps...
Regards;
Leukonov/Olegion
If 20 workers can build a school in 18 days, how many days will it take 12 workers to build the same school?
☯ Explanation -:In this question we are provided that 20 workers can build a school in 18 days. We are asked to calculate how many days will 12 workers will take to do the same work.
We can solve this question using two methods :
Unitary MethodMethod of proportion[tex] \small\bf{ Unitary \: Method}[/tex]
20 workers can build a school in 18 days
1 worker can build a school in 20 × 18 days
12 workers can build a school in [tex]\dfrac{20 × 18 }{12}[/tex] = 30 days.
Hence the required number of days is 30.[tex] {{\rule{40mm}{4pt}}}[/tex]
[tex] \small\bf{ Method \: of \: proportion }[/tex]
Let us assume that 12 workers can finish the work in x days.
[tex]\begin{array}{c|c} \bf{Number \: of \: workers }& \bf{Number \: of \: days}\\ 20 & 18 \\ 12 & x\end{array}[/tex]
Ratio of workers = Inverse ratio of days
[tex] \small\sf{ 20 : 12 :: x : 18}[/tex]
Product of mean = Product of extreme
[tex] \small\rm{ 12 \times x = 20 \times 18}[/tex]
[tex] \small \rm{ \dfrac{20 \times 18}{12} = 30 \: days}[/tex]
Hence the required number of days is 30.[tex] \rule{72mm}{5pt}[/tex]
select the best definition for congruent (A same size) (B same shape but not necessarily the same size) (C same size not necessarily same shape) (D same size and same shape)
Answer:
(D same size and same shape)
Step-by-step explanation:
Congruent means the same size and shape.
Similar means the same shape, but not necessarily the same size
Answer:
The answer is : (D same size and same shape)
Step-by-step explanation:
Two shapes or figures are called congruent, when they are identical. When the angles are equal in degrees, they are called congruent angles and when sides are congruent, this means they have the same length.Two polygons are congruent if they have the same size and shape or if their corresponding sides and angles are equal.
Therefore, option D is correct.
A set of data with a mean 56 and a standard deviation 3.3 is normally distributed. find 2 standard deviations from the mean
Answer:
To the right we have 62.6 while to the left we have 49.4
Step-by-step explanation:
A normal distribution is usually symmetric with respect to the mean. The mean of the distribution is also the mode as well as the median.
The general formula for points that lie n standard deviations away from the mean on either sides of the mean is given by the formula;
mean ± n(σ)
where σ is the standard deviation of the distribution;
Two standards deviations from the mean imply that n = 2;
56 ± 2(3.3)
56 ± 6.6
To the right we have 62.6 while to the left we have 49.4
Use the Distributive Property to write each expression as an equivalent expression. Then evaluate it.
(5 +1)3
Distributive property means that you must multiply the number directly outside the parentheses to all the numbers inside the parentheses
Look at the image below for the work!
Hope this helped!
Using the Distributive Property to expand and evaluate an expression.
Given expression: (5 + 1)3
Step 1: Apply the Distributive Property to expand the expression: (5 + 1)3 = 5 x 3 + 1 x 3
Step 2: Evaluate the expression: (5 + 1)3 = 15 + 3 = 18
need help fast!!!!!!!!!!!!!!!
k(3)=13(3)-2
k(3)= 39-2
Answer is k(3)= 37
ANSWER
[tex]k(3) = 37[/tex]
EXPLANATION
The given expression is
[tex]k(t) = 13t - 2[/tex]
We want to find k(3).
We substitute t=3 into the expression to get:
[tex]k(3) = 13(3) - 2[/tex]
We multiply out to get,
[tex]k(3) = 39- 2[/tex]
Simplify to get,
[tex]k(3) = 37[/tex]
What is the equation of the line?
y=0 because no matter what x value you have, y will always be 0
Y=0 because the y-axis of the line is 0
Identify the interval that is not equal to the other three 15-19 30-34 40-45 45-49
Answer:
45-40
Step-by-step explanation:
The first interval is 15-19.
The width of this interval is: 19-15=4
The second interval is 30-34.
The width of this interval is: 34-30=4
The third interval is 40-45.
The width of this interval is: 45-40=5
The fourth interval is 45-49.
The width of this interval is: 49-45=4
Therefore the interval that is not equal to the other three is 45-40If BP PC, what is m BC?
60
90
180
Answer:
90
Step-by-step explanation:
BP PERPENDICULAR 2 PC SO
BC=90
Answer: 90
Step-by-step explanation:
Given: A circle with center P and B and C are two points on circle such that
BP is perpendicular to PC, it gives [tex]\angle{BPC}=90^{\circ}[/tex]
We know that in a circle, the degree measure of an arc is equal to the measure of the central angle that intercepts the arc.
Therefore, the measure of [tex]\overarc{BC}[/tex]= Central angle made by [tex]\overarc{BC}[/tex].
⇒ the measure of [tex]\overarc{BC}=90^{\circ}[/tex]
What is the slope-intercept form for the equation of the line passing through (-3,4) and having a slope of 5/6?
Begin answer with y=
I'd like to figure out how to do the answers following this one by myself so if you can, please explain?
[tex]\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{4})~\hspace{10em} slope = m\implies \cfrac{5}{6} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-4=\cfrac{5}{6}[x-(-3)]\implies y-4=\cfrac{5}{6}(x+3) \\\\\\ y-4=\cfrac{5}{6}x+\cfrac{5}{2}\implies y=\cfrac{5}{6}x+\cfrac{5}{2}+4\implies y=\cfrac{5}{6}x+\stackrel{\textit{LCD of 2}}{\cfrac{(1)5+(2)4}{2}}[/tex]
[tex]\bf y=\cfrac{5}{6}x+\cfrac{13}{2}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
Which of the following numbers have an absolute value of 5? Select all that apply.
-5
5
0
1/5
-1/5
Answer: -5, and 5
Step-by-step explanation: an absolute value can only be positive. So -5 and 5 are the only answers that will give you 5.
Answer:
B and D.
Step-by-step explanation:
–15
–5
0
5
15
Absolute Value Assignment
Finding Absolute Value
the first thats do 2 will get brainlist
Answer:
6
Step-by-step explanation:
Find the distance between the points given. (2, 2) and (5, 5) 3
For this case we have that by definition, the distance between two points is given by:
[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}\\(x_ {1}, y_ {1}) :( 2,2)\\(x_ {2}, y_ {2}) :( 5,5)[/tex]
Substituting the points:
[tex]d = \sqrt {(5-2) ^ 2 + (5-2) ^ 2}\\d = \sqrt {(3) ^ 2 + (3) ^ 2}\\d = \sqrt {9 + 9}\\d = \sqrt {18}\\d = 3 \sqrt {2}[/tex]
ANswer:
[tex]d = 3 \sqrt {2}[/tex]
use the system of equations and graphs below to complete the sentences
Answer:
Graph C; (2, 1)
Step-by-step explanation:
When equations are in standard form, finding the x- and y-intercepts is relatively easy. For ...
ax +by = c
x-intercept: c/ay-intercept: c/bUsing this idea on the first equation, we find its x-intercept to be -2. There is only one graph showing that has a line going through the point (-2, 0). That is Graph C. Checking the remaining intercepts for the two equations confirms that Graph C is the graph of this system of equations.
The two lines intersect at point (2, 1), so that is the solution to the system.
The correct graph is: Graph C
and the solution for this system is: (2,1)
Step-by-step explanation:The first equation is given by:
[tex]x-4y=-2-------(1)[/tex]
and the second equation is given by:
[tex]-2x-y=-5----------(2)[/tex]
from (1) we have:
[tex]x=-2+4y-------------(3)[/tex]
We put the value of x in equation (2) to get:
[tex]-2(-2+4y)-y=-5\\\\i.e.\\\\-2\times (-2)-2\times 4y-y=-5\\\\i.e.\\\\4-8y-y=-5\\\\i.e.\\\\4-9y=-5\\\\i.e.\\\\-9y=-5-4\\\\i.e.\\\\-9y=-9\\\\i.e.\\\\y=1[/tex]
Now on putting this value of y back to equation (3) we get:
[tex]x=-2+4\times 1\\\\x=-2+4\\\\x=2[/tex]
Hence, the solution to this system of equality is: (2,1)
Please help. I am a little torn with this one
Answer:
A.
Rotational symmetry is when things look the same rotated.
Answer:
A
Step-by-step explanation:
It has buttons which are on the top but not on the other faces
Joyce wants to buy a house for 129,500 with a 20% down payment. How much will her down payment be?
Answer: 29,500.
Step-by-step explanation: percentagecalculator.com
Item Prompt
Segment MP is a diameter of circle O.
150°
What is the measure of arc MN?
B
I
U
S
x, x
=:
.
Answer:
30°
Step-by-step explanation:
Segment MP is the diameter of the circle, hence angle MOP has the measure of 180°.
Angles MON and NOP are supplementary angles (add up to 180°). Thus,
m∠MON+m∠NOP=180°
m∠MON=180°-m∠NOP
m∠MON=180°-150°=30°.
Angle MON is the central angle subtended on the arc MN. Thus, the measure of the arc MN is 30°.
Answer:
Arc MN is 30°Step-by-step explanation:
It's important to know that the whole arc of a circle is 360°.
So, if MP is a diameter, that means it divides the circle in two equal parts of 180° each.
Now, one half of this arc is formed by MN and 150°, so we can formulate the expression
[tex]MN+150\° = 180\° \\MN= 30\°[/tex]
Therefore, the arc MN is 30°.
The linear equation x = -2 will be parallel to the x-axis.
True
False
Answer:
False
Step-by-step explanation:
The equation x = c represents the equation of a vertical line parallel to the y- axis.
The equation y = c represents the equation of a horizontal line parallel to the x- axis
In both cases c is a constant
Hence x = - 2 is not parallel to the x- axis
Will you help me?
A square banner had 4 feet added its width and 2 feet subtracted from its height. The banner then had an area of 91 square feet. How long was a side of the original square banner?
Answer:
The length side of the original square banner was 9 ft
Step-by-step explanation:
Let
x-----> the length side of the original square banner
we know that
The new area of the banner is equal to
[tex]91=(x+4)(x-2)[/tex]
Solve for x
[tex]91=(x+4)(x-2)\\ \\91=x^{2}-2x+4x-8\\ \\x^{2}+2x-99=0[/tex]
Solve the quadratic equation by graphing
The solution is x=9 ft
see the attached figure
To determine the length of the original square banner, we can set up an equation using the given information and solve for the side length.
Explanation:To solve this problem, let's first represent the length of the original square banner as x. According to the question, 4 feet is added to the width, so the width becomes x + 4. Also, 2 feet is subtracted from the height, so the height becomes x - 2. The area of a square is calculated by multiplying the side lengths, so we have (x + 4)(x - 2) = 91.
Expanding the equation, we get x² + 2x - 8 = 91. Rearranging the equation, we have x² + 2x - 99 = 0. This is a quadratic equation that can be solved by factoring, completing the square, or using the quadratic formula.
By factoring, we find (x + 11)(x - 9) = 0. So, x = -11 or x = 9. Since we cannot have a negative length for a banner side, we discard x = -11. Therefore, the length of the side of the original square banner is 9 feet.
Learn more about the Length of the original square banner here:https://brainly.com/question/14510781
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Ava bought a rectangular rug for her hallway. The rug is 23 yards wide and 234 yards long.
What is the area of the rug as a mixed number in simplest form?
Enter your answer in the box.
I really need help ASAP
Answer:
1 5/6
Step-by-step explanation:
This seems complicated please help me !!!!!!!
Answer:
The second answer is correct.
Step-by-step explanation:
The playlist consists of 21 songs by The Working Mamas, 12 songs
by Chef Mo Cheese, 36 songs by The Snippers, 54 by Lucy and
The Jungle Cats, and 27 by Nuestra Paradise.
What's the probability of Chef Mo Cheese playing?
Write the answer as a percent.
artist.
Answer:
8%
Step-by-step explanation:
If m=3 = what is the value of 3m?
Answer: 9
Step-by-step explanation:
M=3 and the equation is 3m so your going to multiply. So the equation would be 3*3 and 3*3=9 so that's your answer
What is the value of x?
Please answer ASAP
Answer:
x = 5
Step-by-step explanation:
You have a right triangle, so you can use the Pythagorean Theorem.
a^2 + b^2 = c^2
x^2 + 12^2 = 13^2
x^2 + 144 = 169
x^2 = 25
x = 5
Answer: x = 5
Answer:
just do 13 time 12
Step-by-step explanation:
Use a net to find the surface area of the prism please help
Finding rectangle surface areas(RSA) are: 2(14×7)+2(14×5)=336
R.S.A+side surface areas: 336+2(7×5)=406
Ans:406
To find the surface area of a prism using a net, you simply calculate the area of each individual shape in the net and then add those areas together. The sum of these areas is the prism's surface area.
Explanation:To find the surface area of the prism using a net, you need to first understand what a net of a prism is. A net of a prism is essentially a 'flat' version of the shape. It's what you would get if you cut along the edges of the prism and flattened it out.
For a rectangular prism, for instance, the net would consist of 2 rectangles (the bases) and 3 or 4 rectangles (the sides), depending on whether the prism is a right prism or an oblique prism.
To find the surface area, calculate the area of each individual shape in the net and then add all those areas together. The sum of these areas is the surface area of the prism.
As an example, suppose we have a rectangular prism with length 4 cm, width 3 cm, and height 2 cm. The areas of the two bases are each 4*3=12 square cm. The areas of the four sides are two of 4*2=8 square cm and two of 3*2=6 square cm. So the total surface area is 2*12+2*8+2*6=48 square cm.
Learn more about Surface Area here:https://brainly.com/question/35439753
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3/12 = _/4
Fill in the blank to make the fractions equivalent.
Answer:
1/4
Step-by-step explanation:
because if you use the process of breaking down the numbers they will end up going down to simplest form.
Answer:
3/12 = 1/4
Step-by-step explanation:
If we know 12 is equal to a fraction with the denominator of 4, we can divide 12 by 4 and get 3. This means we must also divide the numerator by 3 to get 3/3 = 1. Another way to solve this is to cross multiply. If 3/12 = _/4, we multiply the numerator of the first fraction by the denominator of the second fraction. Then, we get 12. Divide the 12 by the denominator of the first fraction to get 12/12. This will give you an answer of 1 as well.
Determine the intercepts of the line that correspond to the following table of values.
Answer:
Part 1) The x-intercept is the point (-5,0)
Par 2) The y-intercept is the point (0,-17.5)
Step-by-step explanation:
step 1
Find the x-intercept
we know that
The x-intercept is the value of x when the value of y is equal to zero
Observing the table
For x=-5, y=0
therefore
The x-intercept is the point (-5,0)
step 2
Find the equation of the line
Find the slope m
we have
(-7,7) and (-5,0)
[tex]m=(0-7)/(-5+7)\\ m=-3.5[/tex]
Find the equation of the line into point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-3.5[/tex]
point (-5,0)
substitute
[tex]y-0=-3.5(x+5)[/tex]
[tex]y=-3.5(x+5)[/tex]
Find the y-intercept
The y-intercept is the value of y when the value of x is equal to zero
For x=0
[tex]y=-3.5(0+5)[/tex]
[tex]y=-17.5[/tex]
therefore
The y-intercept is the point (0,-17.5)
4-2(6x-5)=-4 solve for x
Answer:
[tex]\boxed{ x = \frac{3}{2}}[/tex]
Step-by-step explanation:
[tex]\begin{array}{rcll}4 - 2(6x - 5) & = & -4 &\\- 2(6x - 5) & = & -8 &\text{Subtracted 4 from each side}\\6x - 5 & = & 4 &\text{Divided each side by -2}\\6x & = & 9 &\text{Added 5 to each side}\\x & = &\mathbf{\frac{3}{2}} &\text{Divided each side by 6}\end{array}[/tex]
Check:
[tex]\begin{array}{rlc}4 - 2(6\times\frac{3}{2} - 5)& = &-4\\4 - 2(9 - 5) & = & -4\\4 - 2\times4 & = & -4\\4 - 8 & = & -4\\-4 & = & -4\\\end{array}[/tex]
Answer:
[tex]\large\boxed{x=\dfrac{3}{2}}[/tex]
Step-by-step explanation:
[tex]4-2(6x-5)=-4\qquad\text{subtract 4 from both sides}\\\\-2(6x-5)=-8\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\(-2)(6x)+(-2)(-5)=-8\\\\-12x+10=-8\qquad\text{subtract 10 from both sides}\\\\-12x=-18\qquad\text{divide both sides by (-12)}\\\\x=\dfrac{-18\!\!\!\!\!\diagup^3}{-12\!\!\!\!\!\diagup_2}\\\\x=\dfrac{3}{2}[/tex]