The solution is X=0.4
The answer is the first one
QUESTION 6
The growth of a population each year is given by the function f(x)=250,000(1.17)* At what percent is the population growing each year?
A. 250,000%
B. 1.17%
C. 292,500%
D. 17%
Answer:
Option D. 17%
Step-by-step explanation:
we have
[tex]f(x)=250,000(1.17)^{x}[/tex]
This is a exponential function of the form
[tex]f(x)=a(b)^{x}[/tex]
where
a is the initial value
b is the base
In this problem
a=250,000 people
b=1.17
Remember that
b=1+r
so
1+r=1.17
r=1.17-1=0.17
Convert to percentage
0.17*100=17%
Solve: a^2+4(3+a)
a=5
Answer:
57
Step-by-step explanation:
[tex] {a}^{2} + 4(3 + a)[/tex]
[tex] {5}^{2} + 4(3 + 5)[/tex]
[tex]25 + 12 + 20[/tex]
[tex]57[/tex]
What is the solution to the system of equations below?
y= 4x+6 and Y= 2x-4
0 (-8, 2)
(-8,-1)
(8, 10)
(8, -10
The solution to the system of equations y=4x+6 and y=2x-4 is (-5, -14) by solving the equations simultaneously.
Explanation:The solution to the system of equations y = 4x + 6 and y = 2x - 4 is found by setting the two equations equal to each other since they both equal y. This gives us 4x + 6 = 2x - 4. By subtracting 2x from both sides, we get 2x + 6 = -4. Subtracting 6 from both sides gives us 2x = -10. Dividing both sides by 2 gives us x = -5. Substitute x = -5 into either original equation to find y. Let's use the first equation: y = 4(-5) + 6, which simplifies to y = -20 + 6, and finally y = -14. Hence, the solution to the system of equations is (-5, -14).
What is the total of the Thompson’s liabilities? NEED HELP ASAP NO ROCKY
The liabilities only is 57,379
Fishing rods are discounted at 50% off the regular price of $25. How much money will be saved?
Answer:
$12.50
Step-by-step explanation:
two circles have the same center one circle has the radius of 3 centimeters and the orner has a radius of 1 centimeter what is the locus of the points equidistant from the two circles?
Answer:
Step-by-step explanation:
It has to be another circle with its center as the same center as the other two.
It must be equadistant from both.
The circle must have a radius of 2 which makes it one away from the 3 cm circle and 1 away from the 1 cm circle.
Which expression represents the distance between point (0,a) and point (a,0) on a coordinate grid?
You can always compute the distance between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] using the pythagorean theorem:
[tex]d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
In your case, we have
[tex]d = \sqrt{(0-a)^2+(a-0)^2} = \sqrt{2a^2}=a\sqrt{2}[/tex]
Answer:
[tex]\sqrt{2}a[/tex]
Step-by-step explanation:
We are asked to find the distance between point (0,a) and point (a,0) on a coordinate grid.
We will use distance formula to solve our given problem.
The distance between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by formula:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex], where D represents distance between two points.
Let point [tex](0,a)=(x_1,y_1)[/tex] and point [tex](a,0)=(x_2,y_2)[/tex].
Substitute the values in distance formula:
[tex]D=\sqrt{(0-a)^2+(a-0)^2}[/tex]
[tex]D=\sqrt{(-a)^2+(a)^2}[/tex]
[tex]D=\sqrt{a^2+a^2}[/tex]
[tex]D=\sqrt{2a^2}[/tex]
Factor out perfect square:
[tex]D=\sqrt{2}a[/tex]
Therefore, the distance between two points would be [tex]\sqrt{2}a[/tex].
Simplify expression 8- ( 8-2) \ 3
Answer:
6
Step-by-step explanation:
In order to solve this we must use order of operations or PEMDAS.
Parentheses:
First perform operations within parentheses. In this case, do 8-2.
Now we have 8 - 6 / 3.
Exponents:
There are no exponents.
Multiplication or Division:
Divide 6 by 3.
Now we have 8 - 2.
Addition or Subtraction:
Subtract 8-2.
The answer is 6
negative two and one thirds minus negative five
If your "and" means multiplication than:
[tex]-2\times\frac{1}{3}-(-5) \\
\frac{-2}{3}+5 \\
\frac{-2+15}{3} \\
\boxed{\frac{13}{3}\approx4.33\dots}
[/tex]
If it is a logical and than we are unable to solve the problem since you didn't provide any variables that would have a meaningful values.
Hope this helps.
if f(x)=2(x)^2+5sqrt(x+2), complete the follwoing statement ( round your answer to the nearest hundreth) : f(0)=_____
Answer:
[tex]f(0)=7.07[/tex]
Step-by-step explanation:
We have the function [tex]f(x)=2(x)^2+5\sqrt{(x+2)}[/tex]
In this case we want to find the value of f0)
To find f(0) you must replace the x in the function with the number 0 and solve as shown below
[tex]f(0)=2(0)^2+5\sqrt{(0+2)}[/tex]
[tex]f(0)=0+5\sqrt{(0+2)}[/tex]
[tex]f(0)=5\sqrt{(2)}[/tex]
Therefore
[tex]f(0)=7.07[/tex]
Question 18.
A population of students in a summer program for students in
grades kindergarten to grade 8 is surveyed. Which statement
demonstrates sampling variability?
A.
In one random sample chosen from the population, the
mean age was 9.4 years. In another random sample, the
mean age was 9.8 years.
B. In one random sample chosen from the population, the
mean age was identical to that from another random sample.
C. The mean age of the population is 8.8 years, and the mean
age from a random sample was 9.2 years.
D.In one random sample chosen from the population, the
mean age was 9.4 years.
Answer: c
Step-by-step explanation:
sampling variability is the difference between the measured value of the random sample and the mean age of the population
Option A demonstrates sampling variability because the mean age changes between two random samples chosen from the same population, illustrating the concept of sampling variability in statistics.
Explanation:The subject of this question is a concept in statistics known as sampling variability. Sampling variability refers to the idea that the statistics of a random sample of a population (like mean, median, etc.) will vary from one sample to another. In essence, if we were to keep pulling samples from the same population, it's expected that our sample statistics will not always be the same.
In this context, the statement that demonstrates sampling variability is Option A: 'In one random sample chosen from the population, the mean age was 9.4 years. In another random sample, the mean age was 9.8 years.'. This demonstrates sampling variability because the mean age changes (varies) depending on the sample chosen from the population.
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A flagpole broke in a storm. 777 meters are still sticking straight out of the ground, where it snapped, but the remaining piece has hinged over and touches the ground at a point 242424 meters away horizontally.
How tall was the flagpole before it broke?
The broken flagpole forms a right triangle, where the vertical leg is the piece still standing and the hypotenuse is the broken piece.
So, the original length is the sum of the hypotenuse and the vertical leg.
The hypotenuse can be found using the pythagorean theorem:
[tex]h=\sqrt{7^2+24^2}=25[/tex]
So, the flag was originally [tex]7+25=32[/tex] meters long.
volume of cylinder with radius of base 7cm is 102cm³.what will be the volume of cone having same radius of base and same height
3 I believe the answer
sandra brings cheese and crakers for lunch every 6 days, and lily brings cheese and crakers every 8 days. if they both brought cheese and crakers today, how many days will it be before both girls bring cheese and crakers again
Answer:
24 Days
Step-by-step explanation:
The smallest common multiple of 6 and 8 is 24. Therefore, both girls will bring cheese and crackers for lunch on the same day 24 days from today.
Explanation:This question is about finding the least common multiple (LCM) of the two numbers. Sandra brings cheese and crackers for lunch every 6 days and Lily every 8 days. The first step in solving this problem is to list the first few multiples of each number to find the smallest number that both numbers have in common.
So, for Sandra, the multiples of 6 are 6, 12, 18, 24, 30, 36, etc. And for Lily, the multiples of 8 are 8, 16, 24, 32, 40, etc. The least common multiple of 6 and 8 is 24.
Therefore, it will be 24 days before both Sandra and Lily bring cheese and crackers for lunch on the same day again.
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Help! What is the probability that a card drawn from a standard 52 card deck is a diamond or a three?
Answer:6.5%
Step-by-step explanation:
There are 4, number three cards and 4 diamond cards in a deck of 52 cards. Divide 52 by 8.
Answer:
30.8% or 4/13
Step-by-step explanation:
There are 52 cards in a deck of cards.
There are 4 nines (4/52) and 13 (13/52) diamonds in a deck of cards.
When you add them together, you get 17/52. Then, you have to subtract the card that is both a nine and in a diamond suite, so you subtract -1 because there is only one card that fits both categories. You should have 16/52, which simplifies to 4/13 / 30.8%.
find the equation!!! asap. 10 points
Answer:
[tex]y=\frac{1}{60}x^2[/tex]
Step-by-step explanation:
The focus of the parabola is (0,15)
and the directrix is y=-15.
The equation of this parabola is given by:
[tex]x^2=4py[/tex]
The vertex of this parabola is at the origin (0,0)
The value of p is the distance from the vertex to the focus.
p=15-0=15
The equation of the parabola is
[tex]x^2=4(15)y[/tex]
[tex]x^2=60y[/tex]
Or
[tex]y=\frac{1}{60}x^2[/tex]
The top if an end table is in the shape of a trapezoid. The area is 152 square inches. The bases are 11 inches and 27 inches. What is the height?
Answer:
The height is [tex]h=8\ in[/tex]
Step-by-step explanation:
we know that
The area of a trapezoid is equal to
[tex]A=\frac{1}{2}[b1+b2]h[/tex]
we have
[tex]b1=11\ in[/tex]
[tex]b2=27\ in[/tex]
[tex]A=152\ in^{2}[/tex]
substitute in the formula and solve for h
[tex]152=\frac{1}{2}[11+27]h[/tex]
[tex]304=[38]h[/tex]
[tex]h=304/38[/tex]
[tex]h=8\ in[/tex]
Books at a library sale are sold for $3.50 each. A function, y = 3.50x can be used to generate an input/output table for this scenario. Which statement is true about an accurate graph of this data?
The data is discrete, so the points are connected with a line.
The data is discrete, so the graph is a series of unconnected points.
The data is continuous, so the graph is a series of unconnected points.
The data is continuous, so it does not matter whether or not the points are in a line.
Using the concept of discrete and continuous variables, the correct option is given by:
The data is discrete, so the graph is a series of unconnected points.
What are continuous and discrete variables?Continuous variables: Can assume decimal values.Discrete variables: Assume only countable values, such as 0, 1, 2, 3, …In this problem, the input is the number of books, which is a countable amount, that is, discrete, hence the graph is a series of unconnected points.
The graph is given at the end of the answer.
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x/8 = 13. what does X equal?
Answer:
x equal 104
Step-by-step explanation:
since 8 needs to go into something 13 times we can multiply
8 x 13 to get
104
104 divided by 8
equals 13
Answer:
x=104
Step-by-step explanation:
x/8 = 13
Multiply each side by 8
x/8 *8 = 13*8
x = 104
What is 1/8 of 480? Make sure it is fully reduced as well
1/8 of 480 is 480 ÷ 8
480/80 is 60
Answer ^^^^
The Answer Would Be 60
Someone help me with this pls
Solve the equation of exponential decay.
A website had 342,000 hits in 2011. This is a decline of 2.3% from the previous year. Assuming this continued how many hits would the website get in 2019? Round to the nearest thousand.
Answer:
There will be approx 283908 hits.
Step-by-step explanation:
A website had 342,000 hits in 2011.
This is a decline of 2.3% from the previous year.
Decline rate = 2.3% or 0.023
So, increase rate will be [tex]1-.023=0.977[/tex]
Time = [tex]2019-2011=8[/tex]
We can calculate the answer as:
[tex]342000\times(0.977)^{8}[/tex]
= [tex]342000\times0.83014[/tex]
= 283907.88 rounding to 283908.
Therefore, there will be approx 283908 hits.
1) Name a pair of complementary angles. 2)Name a pair of vertical angles. 3)Name a pair of supplementary angles.
Answer:
1)m<AOB,m<BOC
2)m<EOD,m<AOB
3)m<AOE,m<EOD
Step-by-step explanation:
Complementary Angles-either of two angles whose sum is 90°.
Vertical Angles-each of the pairs of opposite angles made by two intersecting lines.
Supplementary Angles-either of two angles whose sum is 180°.
Answer:2 and 5
Step-by-step explanation:
A basketball is thrown upwards. The height f(t), in feet, of the basketball at time t, in seconds, is given by the following function:
f(t) = −16t2 + 94t + 12
Which of the following is a reasonable domain of the graph of the function when the basketball falls from its maximum height to the ground?
2.9375 < t < 6
2 < t < 5
1 < t < 4
0 < t < 3
Answer:
Well I think it is A because domain is the x values.
Step-by-step explanation:
So when you plug this in your calculator (mine is a ti-84 plus ce) you would hit graph. After it graphs it press Zoom, 0 to center it then press 2nd, trace which pulls up parabola menu's. Press 0 and find the left bound, right bound and then press enter which would give you x values of 2.9375 < t< 6
At the same time I don't know if this is right. I never really excelled at parabolas just trying to help.
Check the picture below.
so the domain will be the values that "x" gets, now, the maximum height of the ball is when it reaches the vertex or U-turn up above, well, what is the x-coordinate anyway?
[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ f(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+94}t\stackrel{\stackrel{c}{\downarrow }}{+12} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left( -\cfrac{94}{2(-16),}\qquad \qquad \right)\implies \left( \cfrac{487}{16},\qquad \qquad \right)\implies (2.9375,\qquad \qquad )[/tex]
so then x = 2.9375 at the vertex, now, what is "x" when it hits the ground? recall y = 0 at that instant.
[tex]\bf \stackrel{f(t)}{0}=-16t^2+94t+12\implies 0=-2(8t^2-47t-6) \\\\\\ 0=(8t+1)(t-6)\implies t= \begin{cases} \boxed{6}\\ \begin{matrix} -\frac{1}{8} \\[-0.5em]\cline{1-1}\\[-5pt]\end{matrix} \end{cases}[/tex]
so then, the values for "x" or namely the domain from the vertex till the ball hits the ground is 2.9375 < t < 6.
simply (6^5/7^3) ^2
[tex]\bf \left( \cfrac{6^5}{7^3} \right)^2\implies \left( \cfrac{6^{5\cdot 2}}{7^{3\cdot 2}} \right)\implies \cfrac{6^{10}}{7^6}\implies \cfrac{60466176}{117649}\implies 513\frac{112239}{117649}[/tex]
Help please I can’t solve please
Answer:
d = 52 inC = 6π mm²Step-by-step explanation:
The formula of a circumference:
[tex]C=2\pi r=d\pi[/tex]
r - radius
d - diameter
We have [tex]C=52\pi\ in[/tex].
Calculate the diameter using [tex]C=d\pi[/tex]:
[tex]d\pi=52\pi[/tex] divide both sides by π
[tex]d=52\ in[/tex]
-------------------------------------------------------------------------
If a circle inscribed in a square, then the diameter of a circle and a side of a square are congruent (have the same length).
We have the area of the square:
[tex]A=36\ mm^2[/tex]
The formula of an area of a square:
[tex]A=s^2[/tex]
s - side
Substitute:
[tex]s^2=36\to s=\sqrt{36}\\\\s=6\ mm[/tex]
The formula of a circumference [tex]C=d\pi[/tex]
d - diameter
d = s → d = 6 mm
Substitute:
[tex]C=6\pi\ mm[/tex]
There are 75 houses in the troll's street. If in every 4th house there is a pink troll, a blue troll in every 6th house and a yellow troll in every 8th house, then in how many houses are there all of pink, blue and yellow trolls?
Answer:
3 houses have all pink, blue, and yellow.
Answer:
The answer is 3 houses.
Step-by-step explanation:
This question is based on the Least Common Multiple (LCM) method. We will find the LCM of the numbers 4, 6 and 8.
4 = 2 x 2 = [tex]2^{2}[/tex]
6 = 2 x 3 = 2 x 3
8 = 2 x 2 x 2 = [tex]2^{3}[/tex]
So, LCM is = [tex]2^{3}\times3=24[/tex]
Therefore, at every 24th houses, we will find all three trolls colors.
And 24 is the number of houses we will find all color trolls. Then in a group of 75 houses, it will occur thrice and at every 24th place. Means. 3 houses will have all color trolls.
What are the domain and range of f(x) =(1/6)^x + 2?
A.domain: {x | x > - 1/6} ; range: {y | y > 0}
B.domain: {x | x > 1/6} ; range: {y | y > 2}
C.domain: {x | x is a real number}; range: {y | y > 2}
D.domain: {x | x is a real number}; range: {y | y > –2}
Answer:
[tex]\large\boxed{C.\ domain:\ \{x\ |\ x\ \text{is a real number}\};\ range:\ \{y\ |\ y>2\}}[/tex]
Step-by-step explanation:
[tex]f(x)=\left(\dfrac{1}{6}\right)^x+2\\\\\text{The domain:}\ x\in\mathbb{R}\to\{x\ |\ x\ \text{is a real number\}}\\\\\lim\limits_{x\to\infty}\bigg[\left(\dfrac{1}{6}\right)^x+2\bigg]=\lim\limits_{x\to\infty}\left(\dfrac{1}{6}\right)^x+\lim\limits_{x\to\infty}2=0+2=2\\\\\lim\limits_{x\to-\infty}\bigg[\left(\dfrac{1}{6}\right)^x+2\bigg]=\lim\limits_{x\to-\infty}\left(\dfrac{1}{6}\right)^x+\lim\limits_{x\to\infty}2=\infty+2=\infty\\\\\text{The range:}\ y\in(2,\ \infty)\to\{y\ |\ y>2\}\\\\\bold{Look\ at\ the\ picture}[/tex]
Answer: Option C
domain: {x | x is a real number}; range: {y | y > 2}
Step-by-step explanation:
We have the function [tex]f(x) =(\frac{1}{6})^x + 2[/tex]
Note that f(x) is an exponential function.
By definition the exponential functions of the form [tex]a(b)^x +k[/tex] have as domain all real numbers and as range {y | y > k} if [tex]a>0[/tex], [tex]b>0[/tex]
Where a is the main coefficient, b is the base and k is the vertical displacement.
In this case [tex]k = 2[/tex], [tex]b=\frac{1}{6}[/tex], [tex]a=1[/tex]
Therefore the domain of f(x) is all real numbers and the range of f(x) is
{y | y > 2}
| What is the factored form of 2x2 – 200 ?
Answer:
2(x - 10)(x + 10)
Step-by-step explanation:
Given
2x² - 200 ← factor out 2 from each term
= 2(x² - 100) ← x² - 100 is a difference of squares and factors as
x² - 100 = x² - 10² = (x - 10)(x + 10), hence
2x² - 200 = 2(x - 10)(x + 10)
Answer:
Step-by-step explanation:
If your equation is [tex]2x^2-200[/tex] and you're to factor it, the first thing you do is set the expression equal to 0 so you can solve for x.
[tex]2x^2-200=0[/tex]
There's a couple of different ways in which to approach this. You can factor out a 2:
[tex]2(x^2-100)=0[/tex]
and solve it from there. The Zero Product Property says that if the equation is equal to 0, then either 2 has to equal 0 or [tex]x^2-100[/tex] has to equal 0. We know that 2 does not equal 0, so [tex]x^2-100=0[/tex]
Add 100 to both sides in the equation:
[tex]x^2=100[/tex]
and then take the square root of both sides. Because this is a second degree polynomial, we expect to have 2 solutions, and we do. Don't forget that when you take the square root of a number you have to alow for both the positive and the negative of the result. Our factored form of the given equation then is that x = 10 and x = -10.
1. What are the mean, median, mode and range of the data set given the altitude of lakes in feet: –
11, –28, –17, –25, –28, –39, –6, and –46?
(1 point)
A. mean = –25; median = –26.5; mode = –28; range = 40
B. mean = –25; median = –40; mode = –26.5; range = 28
C. mean = –26.5; median = –25; mode = –28; range = 28
D. mean = –26.5; median = –28; mode = –25; range = 40
2. Given the data 21, 13, 13, 37, 13, 23, 25, 15:
A. What is the outlier in the data?
B. What is the mean with the outlier?
C. What is the mean without the outlier?
A. 13; 21; 17.6
B. 37; 20; 17.6
C. 37; 17.6; 20
D. 13; 17.6; 21
Answer:
cdc
Step-by-step explanation:
1. The option is (A) mean = –25; median = –26.5; mode = –28; range = 40.
2. The option is (C) 13; 17.6; 20.
What is the median?The median is the value that splits the mathematical numbers or expressions in the half. The median value is the middle number of data points. to find the median first arrange the data points in ascending order.
To find the mean, median, mode, and range of the data set, we first need to arrange the data in order:
–46, –39, –28, –28, –25, –17, –11, –6
Mean: To find the mean, we add up all the values and divide by the total number of values:
Mean = (-46 + -39 + -28 + -28 + -25 + -17 + -11 + -6) / 8
Mean = -25
Median: To find the median, we need to find the middle value of the data set.
Since there are 8 values, the median is the average of the 4th and 5th values:
Median = (-28 + -25) / 2
Median = -26.5
Mode: The mode is the value that appears most frequently in the data set. In this case, the mode is –28, since it appears twice and no other value appears more than once.
Range: To find the range, we subtract the smallest value from the largest value:
Range = -6 - (-46)
Range = 40
Therefore, the answer is (A) mean = –25; median = –26.5; mode = –28; range = 40.
2.
A. The outlier in the data set is 37, since it is much larger than the other values.
B. To find the mean with the outlier, we add up all the values and divide by the total number of values:
Mean = (21 + 13 + 13 + 37 + 13 + 23 + 25 + 15) / 8
Mean = 17.6
C. To find the mean without the outlier, we need to exclude the value 37 and then calculate the mean using the remaining values:
Mean = (21 + 13 + 13 + 13 + 23 + 25 + 15) / 7
Mean = 17.6
Therefore, the answer is (C) 13; 17.6; 20.
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find the midpoint of the line segment with the given endpoints.
(14, -6), (13, 14)
Answer:
Step-by-step explanation:
23
Answer:
([tex]\frac{27}{2}[/tex], 4 )
Step-by-step explanation:
Use the midpoint formula
midpoint = [[tex]\frac{1}{2}[/tex](x₁ + x₂), [tex]\frac{1}{2}[/tex](y₁ + y₂ ) ]
with (x₁, y₁ ) = (14, - 6) and (x₂, y₂ ) = (13, 14), hence
[[tex]\frac{1}{2}[/tex](14 + 13), [tex]\frac{1}{2}[/tex](- 6 + 14) ]
= ([tex]\frac{27}{2}[/tex], 4)