The geometric progression has the form:
[tex]\mleft\lbrace a,ar,ar^2,ar^3,\ldots,ar^n\mright\rbrace[/tex]We have the information about the second term, a*r:
[tex]ar=\frac{1}{2}[/tex]We know that the common ratio is
[tex]r=\frac{1}{4}[/tex]So from this information we can get the coefficient a:
[tex]\begin{gathered} ar=\frac{1}{2} \\ a\cdot\frac{1}{4}=\frac{1}{2} \\ a=\frac{4}{2}=2 \end{gathered}[/tex]And we also know that the last term is 1/128, that is
[tex]ar^n=\frac{1}{128}[/tex]From this one we can find n:
[tex]\begin{gathered} 2\cdot(\frac{1}{4})^n=\frac{1}{128} \\ (\frac{1}{4})^n=\frac{1}{128\cdot2} \end{gathered}[/tex]We can apply the property of the logarithm of power to get n:
[tex]\begin{gathered} \log ((\frac{1}{4})^n)=\log (\frac{1}{256}) \\ n\cdot\log (\frac{1}{4})^{}=\log (\frac{1}{256}) \\ n=\frac{\log (\frac{1}{256})}{\log (\frac{1}{4})} \\ n=4 \end{gathered}[/tex]Be careful, because n is not the number of terms. The number of terms is n+1, so the G.P. has 5 terms
Evaluate when n=5 4n
We are given an expression "4n"
The question says to evaluate this expression when n = 5
Here, evaluation simply means, finding the value of "4n" when n = 5. This is a simple problem of substitution. By substitution I mean replacing every occurence of n in the given expression by 5. This would be done as follows:
Given expression = 4n
Note that here 4 is being multiplied to n.
Replacing n by 5, we get the result as:
[tex]4\text{ }\times\text{ 5 = 20 }[/tex]From here, we can conclude that the value of expression "4n" for n = 5 will be 20.
im confused on premtier
we have to calculate the perimeter of the semicircle which radius is 16 mm
[tex]P_{sc}=\frac{2\pi\cdot r}{2}=\pi\cdot r=16\pi\approx50.26\operatorname{mm}[/tex]Now we have to add the outter sides of the triangle
[tex]P=20+20+50.26=90.26\operatorname{mm}[/tex]A loaf of bread is cut into slices size. Some of the loaf us used in a recipe and 4/8 of the loaf is used to make a sandwich. The remaining 2/8 of the loaf is put into the remaining
We have
[tex]\frac{7}{10}-\frac{2}{10}[/tex]in order to know what expression is equivalent, we need to solve and simplify the expression above
[tex]\frac{7}{10}-\frac{2}{10}=\frac{5}{10}=\frac{1}{2}[/tex]Then we will solve the next expressions in order to find the equivalent expression
[tex]undefined[/tex]Joe earned 2,100$. He spent 1/5 on rent and 1/4 on food. How much money did he have left?
The amount of money that Joe has left is $1155
How to calculate the amount of money left ?
Joe earned $2100
He spent 1/5 of the money on rent
1/5 × 2100
= 420
$420 was spent on rent
He spent 1/4 of the money on food
= 1/4 × 2100
= 525
$525 was spent on food
The amount of money left can be calculated as follows
Total amount spent = 525 + 420
= 945
Amount left= 2100 - 945
= 1155
Hence Joe has $1155 left
Read more on amount here
https://brainly.com/question/13576984
#SPJ1
HElP
pls pretty pls its due today
z
The equation of the line in slope intercept form is y = -2x - 70
How to find the equation of a line?The equation of a line can be represented in different form such as slope intercept form, point slope form and standard form.
The equation of the line can be written is slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, using the coordinates (0, - 70)(-20, -30)
Let's find the slope,
m = slope = -30 + 70 / -20 - 0
m = 40 / - 20
m = - 2
Let's find the y-intercept using (0, -70)
-70 = -2(0) + b
b = - 70
Therefore, the equation of the line is y = -2x - 70
learn more on equation of a line here: https://brainly.com/question/12952118
#SPJ1
Evaluate : g(x) = x^2 + 4x ; find g(2)
Given the function
[tex]g(x)=x^2+4x[/tex]We want to evaluate this function at x = 2.
When we evaluate a function at a given value, we just need to substitute the terms with a variable by the given value.
[tex]g(2)=(2)^2+4\cdot(2)=4+8=12[/tex]Brayden was given a box of assorted chocolates for his birthday. Each night, Brayden
treats himself to some chocolates. The number of chocolates remaining in the box t
days after Brayden's birthday can be modeled by the equation C = -3t+ 12. What
is the slope of the equation and what is its interpretation in the context of the
problem?
Answer:
Step-by-step explanation:
The slope of the function is -3 which reveals the number of chocolates Brayden eats each night.
Cameron has 21 coins in his pocket, all of which are dimes and quarters. If the total value of his change is315 cents, how many dimes and how many quarters does he have?
Given:
Cameron has 21 coins in his pocket, all of which are dimes and quarters.
Let, x be the number of quarters and y be the number of dimes.
The total cost is 315 cents.
The equations are,
[tex]\begin{gathered} x+y=21\ldots\ldots\ldots\text{.}(1) \\ 25x+10y=315\ldots.\ldots\ldots....\ldots(2) \end{gathered}[/tex]Solve the equation,
[tex]\begin{gathered} x+y=21 \\ x=21-y\text{ put this value in equation (2)} \\ 25(21-y)+10y=315 \\ 525-25y+10y=315 \\ 525-315=15y \\ y=\frac{210}{15} \\ y=14 \end{gathered}[/tex]Put the value of y in equation (1),
[tex]\begin{gathered} x+y=21 \\ x+14=21 \\ x=21-14 \\ x=7 \end{gathered}[/tex]Thus, the number of quarters are 7 and dimes are 14 .
Find the equation of a line passing through (-7,9) with a slope of -5.
y=-5x-26
Explanationthe equation of a line can be written as:
[tex]\begin{gathered} y=mx+b \\ where\text{ m is the slope} \\ and\text{ b is the y-intercept} \end{gathered}[/tex]now, when we have the slope and a passing point, we need to use the slope-point formula , it says
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ where\text{ m is the slope and \lparen x}_1,y_1)\text{ is a point from the line} \end{gathered}[/tex]so
Step 1
a)let
[tex]\begin{gathered} slope=-5 \\ (x_1,y_1)=(-7,9) \end{gathered}[/tex]b) now replace in the slope-point formula and solve for y
[tex]\begin{gathered} y-y_{1}=m(x-x_{1}) \\ replace \\ y-9=-5(x-(-7)) \\ y-9=-5(x+7) \\ y-9=-5x-35 \\ add\text{ 9 in both sides} \\ y-9+9=-5x-35+9 \\ y=-5x-26 \end{gathered}[/tex]therefore, the equaton of the line is
y=-5x-26
I hope this helps you
A delivery company uses robot dogs to deliver packages in anoffice building. The graph shows how long a robot dog can operatetor each hour its battery is charged.Pickany two points on the line. Find the slope of the line betweenInesetwo points. Can you find another pair of points on the linehat gives you a different slope?
Given:
Let the two points from the graph are
[tex](1,30)\text{ and (}2,60)[/tex][tex]\begin{gathered} \text{Slope}=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{60-30}{2-1} \\ =30 \end{gathered}[/tex]No, its impossible to find the another pair of points to give a different slope.
Only one slope from a line.
I’ve been stuck for a while and it logged me out:(
Solution
A polynomial is a function in the form of ; where n is non- negative integers which is known as the degree of polynomial. from this definition, it is clear that only option (2) √2 x -1 , is polynomial. because coefficient of variables ; √2, -1 are real number and also power of variable is non-negative integer.
I have selected the options , the ones I have ticked are polynomials, while the one cancelled are none polynomials:
What feature of Kelth's graph makes it difficult to visually compare the responses of those with some college to those shown in the other graphs? (Select all that apply.) (A)The donut hole in the graph made by Keith is a different size than in the graphs made by Ramon. (B)The graphs do not have data labels showing the percentages.(C)The graphs made by Keith and Ramon are all donut pie charts. (D)The graphs made by Keith and Ramon compare groups across education level. (E)The graphs made by Keith and Ramon use the same colors for each of the corresponding responses. 2 How would you change Keith's graph for easier comparison? (Select all that apply.) (A) Make all donuts exactly the same size, with the radius of the holes the same as well. (B)Change the graphs from donut ple charts to time series graphs. (C)Use different sets of colors in each of the donut ple charts.(D)Combine the graphs into one donut pie chart.(E) Add data labels showing the percentages,
Answer:
(A)The donut hole in the graph made by Keith is a different size than in the graphs made by Ramon.
Explanations:
Ex
Considering the graph made by Keith and those made by Ramon, we would observe that Keith's graph ( Some college) has a smaller donut hole that Ramons's graphs ( High school or less, and college graduate). This difference in the donut holes will make any comparism made between the " some college" graph and other graphs to be inaccurate.
what is 3 to the negative 8th power divided by 3 to the negative 4th power
Answer
Answer = 3⁻⁴ = (1/3⁴) = (1/81)
The answer is 3 raised to the power of negative 4 or 3 to the negative 4th power.
Explanation
The law of indices is usually applied when questions that involve same numbers with (different or the same) powers are considered.
When a number carrying a particular power is divided by the same number also carrying another power, the result is that same number raised to the power of the difference between the power of the numerator and the power of the denominator.
It'll be clearer in practice now.
[tex]\frac{3^{-8}}{3^{-4}}=3^{-8\text{ - (-4)}}=3^{-8+4}=3^{-4}[/tex]Hence, the answer is 3 raised to the power of negative 4 or 3 to the negative 4th power.
Hope this Helps!!!
Determine if the figures below are similar. If they are, identify the similarity statement.E70F50GK5060L
We have the following triangles:
And we need to determine if they are similar by identifying the similarity statement.
To determine that similarity statement, we can proceed as follows:
1. Check the measures of the internal angles of the triangles. We need to remember that the sum of the internal angles of a triangle is 180 degrees. Then we have:
2. We can see that to find the angles in the first triangle, EFG, and in the second triangle, JKL, we have that the sum of the three angles must be 180 degrees, and we obtained the other angles as follows:
[tex]\begin{gathered} \text{ Triangle EFG}\rightarrow50+70+x=180 \\ \\ x=180-(50+70)=180-120=60 \\ \\ \text{ Triangle JKL}\rightarrow50+60+y=180 \\ \\ y=180-(50+60)=180-110=70 \end{gathered}[/tex]3. Then we can redraw the triangles as follows:
4. Now, since we can see that, at least, two of the angles of the triangles are congruent (then the third one is also congruent, that is, has the same measure), we also have that to prove that if two triangles are similar it is sufficient that two of the corresponding angles of one triangle are congruent to the two corresponding angles of the other triangle, and this is known as the Angle-Angle method for proving similar triangles, then we can conclude that:
Triangle EFG is similar to triangle JKL by the Angle-Angle method.
Therefore, in summary, we have that:
Triangle EFG is similar to Triangle JKL by Angle-Angle similarity
[tex]\text{ Triangle EFG \textasciitilde Triangle JKL by Angle-Angle similarity}[/tex]
[Last option]
Consider the polynomial function q ( x ) = − 2 x 8 + 5 x 6 − 3 x 5 + 50
The function has an end behaviour of x → ∞, q(x) → -∞ and x → -∞, q(x) → -∞
How to determine the end behaviour of the function?The equation of the polynomial function is given as
q(x) = -2x⁸ + 5x⁶ - 3x⁵ + 50
To determine the end behaviour of the function, we calculate
q(∞) and q(-∞)
So, we have
q(∞) = -2(∞)⁸ + 5(∞)⁶ - 3(∞)⁵ + 50
Evaluate the exponents
q(∞) = -2(∞) + 5(∞) - 3(∞) + 50
This gives
q(∞) = -∞ + ∞ - ∞ + 50
q(∞) = -∞
Also, we have
q(-∞) = -2(-∞)⁸ + 5(-∞)⁶ - 3(-∞)⁵ + 50
Evaluate the exponents
q(-∞) = -2(∞) + 5(∞) - 3(-∞) + 50
This gives
q(-∞) = -∞ + ∞ + ∞ + 50
q(-∞) = -∞
Hence, the end behaviour of the graph is x → ∞, q(x) → -∞ and x → -∞, q(x) → -∞
Read more about end behaviour at:
https://brainly.com/question/1365136
#SPJ1
Complete question
Consider the polynomial function q(x) = -2x⁸ + 5x⁶ - 3x⁵ + 50
Calculate the end behaviour
43/1/2 divided by 1/1/4
When 43/1/2 is divided by 1/1/4 , the value will be 34 4/5.
What is a fraction?A fraction simply means a numbers that's represented as a/b where a = numerator and b = denominator
In this case, the division of the fraction will be:
43 1/2 ÷ 1 1/4
= 87/2 ÷ 5/4
= 87/2 × 4/5
= 174 / 5
= 34 4/5
This shows the. concept of fractions.
Learn more about fractions on:
brainly.com/question/17220365
#SPJ1
Alex has a $100 budget to buy food for his birthday
party. Each pizza costs $10 and each soda bottle
costs $3. Alex will buy 7 pizzas.
What is the greatest number of soda bottles Alex can
buy without going over budget?
If Alex has a $100 budget to buy food for his birthday, each pizza cost $10 and each soda bottle cost $3, and Alex bought 7 pizzas, then the greatest number of soda bottles Alex can buy without over budget 10 soda bottles
The total budget = $100
The cost of one pizza = $10
Number of pizza he bought = 7
The total cost of pizza = 7×10 = $70
The remaining money = 100-70
= $30
The cost of one soda bottle = $3
Number of soda bottle can he buy using the remaining money = 30/3
= 10 soda bottles
Hence, if Alex has a $100 budget to buy food for his birthday, each pizza cost $10 and each soda bottle cost $3, and Alex bought 7 pizzas, then the greatest number of soda bottles Alex can buy without over budget 10 soda bottles
Learn more about budget here
brainly.com/question/19297741
#SPJ1
As Mars revolves around the sun, it travels at a rate of approximately 15 miles per second. Convert this rate to miles per minute. At this rate, how many miles will Mars travel in 3 minutes? Do not round your answers. Rate:mi/minDistance traveled in 3 minutes:mi
We have:
1 minute = 60 seconds
Then, 15 miles per second to miles per minute is:
[tex]15\frac{miles}{second}\times\frac{60\text{ seconds}}{1\text{ minute}}=15\times60=900\frac{miles}{minute}[/tex]Next, Distance traveled in 3 minutes is given by:
[tex]distance=900\times3=2700\text{ miles}[/tex]Answer:
rate = 900 mi/min
distance = 2700 miles
Which type of statically graphic uses bars to describe the data ?Dot plot Box plot Histogram
HISTOGRAM
Explanations:
Data are reported using visuals to make reporting easier and ease the understanding of the audience.
Some of the graphic used in statistics to report data and make inference include:
• Bar charts
,• line charts
,• Dot plot
,• Box plot
,• Histogram etc.
Bar charts and histograms make use of bars to report data. This charts are important to detect outliers that may be present in our data.
We can therefore conclude that the type of statically graphic that uses bars to describe data is the HISTOGRAM
The cost of 5 gallons of ice cream has a varianceof 36 with a mean of 36 dollars during the summer.What is the probability that the samplean would differ from the true mean by more than 0.6 dollars if a sample of 107 5-gallon pails is randomly selected? Roundyour answer to four decimal places.
Given:
[tex]\begin{gathered} Variance=36 \\ mean=36 \end{gathered}[/tex]To Determine: The samplean would differ from the true mean by more than 0.6 dollars
Solution
Please note that standard deviation is the square root of variance
[tex]\begin{gathered} SD=\sqrt{Variance} \\ SD=Standard-deviation \\ SD=\sqrt{36}=6 \end{gathered}[/tex][tex]\begin{gathered} S.E=\frac{SD}{\sqrt{n}} \\ S.E=Standard-Error \\ n=107 \\ S.E=\frac{6}{\sqrt{107}}=0.5800 \end{gathered}[/tex]Please note that Z is the number of SE(standard error away from the mean. Therefore
[tex]\begin{gathered} Z=\frac{0.6}{0.5800} \\ Z=1.0345 \end{gathered}[/tex][tex]P(|Z|<1.0345)[/tex][tex]P(|Z|<1.0345)=1-P(Z<-1.0345)=1-0.1515=0.8485[/tex]Hence the probability is 0.8485
Spilt each number into its prime factors. Please enter the prime factors from smallest to largest.84 =
Let's make the table of the prime factors of 84:
then we have that 84=2x2x3x7, therefore, the prime factors are 2, 3 and 7
In parallelogram ABCD… Justify your answer with the applicable property.
Solution
For this case we have the following measures:
m <1= x+12
m < 2= 6x -18
We can set up both angles equal:
x +12 = 6x -18
Solving for x we have:
12+18 = 5x
5x = 30
x= 30/5= 6
Then the value of m< 2 is:
m< 2= 6*6 -18= 36-18= 18
the best second answer is:
If a quadrilateral is ||gram the opposite angles are congruent
Find the length of the missing side. Round answers to the nearest tenth if necessary. * S sva Your answer
Question:
Solution:
Notice that the angle between the sides of the square is 90 degrees:
Therefore, the angle of the vertex of the triangle measures 45 degrees:
thus, we obtain the following right triangle:
Now, apply the following trigonometric identity:
[tex]\cos \text{ (45) = }\frac{s}{5\sqrt[]{2}}[/tex]solving for s, we get:
[tex]s\text{ = cos(45) . 5 }\sqrt[]{2}\text{ = 5}[/tex]then, we can conclude that the correct answer is:
[tex]s\text{ = 5}[/tex]in a dog show there are 31 dogs competing in the terror group the top three dogs with we'll all wind crash price of $500 and moved on to complete for a place in the larger Best in Show competition how many ways can the top three dogs be determined if they are finishing position is not important
The selection of three dogs out of 31 dogs can be done in
[tex]31C3\text{ ways}[/tex]i.e.
[tex]\begin{gathered} =\frac{31!}{(31-3)!\times3!} \\ =\frac{31\times29\times28!}{28!\times3!} \\ =\frac{31\times29}{6} \\ =149.8 \\ \cong\text{ 150} \end{gathered}[/tex]The figure shows two right triangles, each with its longest side on the same line. Z 3 X T y 2 R. S 1. Explain how you know the two triangles are similar 2. How long is XY? 3. For each triangle, calculate (vertical side) = (horizontal side). 4. What is the slope of the line? Explain how you know.
The triangle are similar because the ratio between 2 sides is the same as the ratio between another 2 sides.
The included angle(angle S and Y) are equal( 90 degree)
A triangle has vertices on a coordinate grid at D(-10, -1), E(-10,6), and F(2,6). What is the length, in units, of DE?
A triangle has vertices on a coordinate grid at D(-10, -1), E(-10,6), and F(2,6). What is the length, in units, of DE?
we know that
The formula to calculate the distance between two points is equal to
[tex]d=\sqrt[]{(y2-y1)^2+(x2-x1)^2}[/tex]we have
D(-10, -1), E(-10,6)
substitute the given values in the formula
[tex]\begin{gathered} d=\sqrt[]{(6+1)^2+(-10+10)^2} \\ d=\sqrt[]{(7)^2+(0)^2} \\ d=\sqrt[]{49} \\ d=7\text{ units} \end{gathered}[/tex]therefore
the distance DE is 7 unitsThe hands of a clock show 11:20. Express the obtuse angle formed by the hour and minute hands in radian measure.
ANSWER
[tex]2.44\text{ }rad[/tex]EXPLANATION
First, let us make a sketch of the clock:
We have that for a minute hand:
[tex]1\text{ }min=6\degree[/tex]For hour hand:
[tex]1\text{ }min=0.5\degree[/tex]The hour and minute hand have their origin at 12.
At 11:20, the minute hand had moved 20 mins. This means that:
[tex]20\text{ }min=20*6=120\degree[/tex]The hour hand had moved at 11 (and 20 mins more), which means:
[tex]\begin{gathered} 11*60\text{ }min+20\text{ }min \\ \Rightarrow660\text{ }min+20\text{ }min \\ 680\text{ }min \end{gathered}[/tex]Hence, in 680 mins:
[tex]\begin{gathered} 680*0.5 \\ \Rightarrow340\degree \end{gathered}[/tex]Therefore, the angle formed between 11 and 12 at 11:20 is:
[tex]\begin{gathered} 360-340 \\ \Rightarrow20\degree \end{gathered}[/tex]Hence, the angle formed at 11:20 is:
[tex]\begin{gathered} 120\degree+20\degree \\ 140\degree \end{gathered}[/tex]Now, let us convert to radians:
[tex]\begin{gathered} 1\degree=\frac{\pi}{180}rad \\ 140\degree=140*\frac{\pi}{180}=2.44\text{ }rad \end{gathered}[/tex]That is the obtuse angle formed in radians.
Michael wants to save $55,000.00 for a down payment on a home. How much will he need to invest in anaccount with 8.5% APR, compounding daily, in order to reach his goal in 3 years?
Step 1. The information that we have is:
The final amount that Michael wants to save is:
[tex]A=55,000[/tex]We will call that amount A.
The annual percentage rate of the investment, which we will label as r, is:
[tex]r=8.5[/tex]We will need this annual percentage rate represented as a decimal number, therefore, we divide it by 100:
[tex]\begin{gathered} r=8.5/100 \\ r=0.085 \end{gathered}[/tex]The time of the investment, t, is 3 years:
[tex]t=3[/tex]And it is compounded daily, let n be the number of times of compounding in a year:
[tex]n=365[/tex]Step 2. We need to find the initial amount of the investment, which will be called P or principal.
The formula we will use to find it is:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Step 3. Substituting the known values:
[tex]55,000=P(1+\frac{0.085}{365})^{(365)(3)}[/tex]From this equation, we need to solve the operations and solve for P, the principal amount of the investment.
Step 4. Simplifying the equation:
[tex]55,000=P(1+0.0002328767)^{1095}[/tex]Continue simplifying:
[tex]\begin{gathered} 55,000=P(1.0002328767)^{1,095} \\ 55,000=P(1.2904233) \end{gathered}[/tex]Then, we solve for P:
[tex]\begin{gathered} \frac{55,000}{1.2904233}=P \\ 42,621.6726=P \end{gathered}[/tex]Rounding to the nearest cent (2 decimal places) The amount that he needs to invest is $42,621.67
Answer: $42,621.67
3.In the figure. What are the coordinates of the image of point B after a translation (x+4, y-7) ?
Answer:
(5, -5)
Explanation:
The coordinate of Point B is: (1,2)
If we carry out the translation (x+4, y-7) on point B, we have:
[tex]B(1,2)\rightarrow (1+4,2-7)=B^{\prime}(5,-5)[/tex]The coordinates of the image of point B is (5, -5)
Find an equation of the line, and write it in (a) slope-intercept form if possible and (b) standard form.
1) Note that we need to find a perpendicular line. Perpendicular lines have reciprocal and opposite slopes. So we know that the slope we need is -3
2) We also know that it must pass through (-2,-6), so let's plug the slope -3 the point (-2,-6) so that we can find the linear coefficient:
[tex]\begin{gathered} y=mx+b \\ -6=-3(-2)+b \\ -6=6+b \\ -6-6=b \\ b=-12 \end{gathered}[/tex]