The formula for the given arithmetic series for the term aₙ will be aₙ=a₁+(n-1)d.
What is arithmetic series?An arithmetic series is the sum of a sequence like 2,..., where each term is calculated by adding (or subtracting) a constant from the previous one. An ordered group of numbers with a shared difference between each succeeding term is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.So, the possible sequence of -64, -16, 4:
We can notice the sequence as -(4³), -(4²), 4, 4², 4³.So, the formula for the aₙ term will be:
aₙ = a₁ + (n - 1)dTherefore, the formula for the given arithmetic series for the term aₙ will be aₙ = a₁ + (n - 1)d.
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The correct question is given below:
Write an explicit formula for an, the nth term of the sequence
-64, -16, 4,....
REVIEW & REFRESH
42. Tell whether x and y are proportional.
43. What number is 60% of 35?
44. 27 is what percent of 75?
Just do 42 and 44
Using proportions, it is found that:
42. x and y are not proportional.
43. The number 21 is 60% of 35.
44. The number 27 is 36% of the number 75.
How to verify if two variables are proportional?Two variables, x and y, will represent a proportional relationship if the ratio between them is always the same.
From the table, the ratios are given as follows:
6/4 = 1.5.8/6 = 1.25.Different ratios, hence the variables x and y are not proportional.
Percentage of a numberTo find the percentage of a number, the decimal equivalent of the percentage is multiplied by the number.
The decimal equivalent of a percentage of 60% is:
60/100 = 0.6.
Hence the percentage of 35 is calculated as follows:
0.6 x 35 = 21.
The percentage that the number 27 represents of the number 75 is given by the division of 27 by 75 multiplied by 100%, hence:
27/75 x 100% = 36%.
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Name the object below.
Thank you :’)
Answer:
The answer is option A.
2. Write three decimals that
have a sum of 114.056.
Three decimal that sum of 114.056 is 52.2+34.15+28.5.
What is decimal?
decimal is a term that describes the base-10 number system, probably of the most commonly used the number system. The decimal number system of consists of ten single-digit numbers.
We will represent this as 1.5 pizzas in decimal form. In this case, the dot stands in for the decimal point, the number before the dot, in this case "1," represents one whole pizza, and the number after the decimal point, or the fractional part, represents the other half of the pizza. You may have seen decimal numbers similar to these while grocery shopping, on a scale, or even during a baseball game.
Sol- we have to add three decimal that have a sum of 114.056 no parts are given here.
Let's take
X+Y+Z = 114.056
We need to add any particular number here
Let's put 52+34+28
Still we need .056 extra
So we have to add points here
52.2+34.15+28.5
So these are 3 decimal point.
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i-Ready
Dilations and Similarity -
-
Figure LMNO is dilated to form figure L'M'NO'.
Where is the center of dilation located?
on a vertex of figure LMNO
What is the scale factor of the dilation?
pls help quickly;;;
The location of the center of dilation in the figure and the image formed following the dilation is the point N
The scale factor of the dilation is 0.5
What is a dilation transformation?A dilation transformation resizes an object such that the lengths of the sides of the image (the object formed) following the dilation of the original image has sides that are a constant multiple of the side lengths of the original object.
The center of dilation is a reference and fixed point, such that the center of is in the same location relative to the preimage and the image.
The location or point shared by both the figure LMNO and the image of LMNO formed following the dilation, which is figure L'M'N'O' is the point N.
Therefore;
The center of dilation is the point NThe scale factor of the dilation is found using the definition of a scale factor, which is the ratio of the scale of a new figure to the scale of an original figure, therefore:
[tex]The \ scale \ factor,\, s.f. = \mathrm{\dfrac{Length \ of \ the \ sides \ of \ L'M'N'O'}{Length \ of \ the \ sides \ of \ LMNO}}[/tex]
MN = 6 units
LO = 6 units
ML = ON = √(6² + 2²) = 2·√(10)
M'N' = L'O' = 3 units
M'L' = O'N' = √(3² + 1²) = √(10)
Which gives:
[tex]s.f. = \dfrac{M'L'}{ML} =\dfrac{\sqrt{10} }{2 \cdot \sqrt{10} } = \dfrac{1}{2}=0.5[/tex]
The scale factor of the dilation is, s.f. = 0.5
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Where do I put the dots at
What is the length of the dotted line in the
diagram below? Round to the nearest
tenth.
Answer: Length = 10√2
Step-by-step explanation: You have to use the pythagorean theorem
4(8g+5)+6
I thought the answer was 32g+26 but its not on there
Answer:
32g + 6(you got it right, not quite sure why it isn't there though!)
Step-by-step explanation:
remember PEMDAS
parentheses first
(8g+5) but we can't add them up since they not like terms
now we go from left to right (since we have Multiplication first and then Addition)
distribute the 4 to the (8g+5)
which makes it 32g +20
now we go back to the equation,
32g +20 + 6
are there any like terms we can combine?
yes, the 20 and the 6
20+6=26
leaving us with
32g + 26The numbered disks shown are placed in a boxand one disk is selected at random. Find theprobability of selecting an odd number, given that agreen disk is selected.Find the probability of selecting an odd number, given that a green disk is selected.(Type an integer or a simplified fraction.)
Given that the numbered disks are placed in a box, you need to find the probability of selecting an odd number, given that a green disk is selected.
Therefore, you need to use the Conditional Probability Formula:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]In this case, let be "A" the event of selecting an odd number, and "B" the event of selecting a green disk.
You can identify that:
- There are a total of 8 disks.
- There are 4 green disks that have odd numbers.
- There are a total of 7 green disks.
Therefore, you can determine that:
[tex]P(A\cap B)=\frac{4}{8}=\frac{1}{2}[/tex]And:
[tex]P(B)=\frac{7}{8}[/tex]Then, you can substitute values into the formula and evaluate:
[tex]P(A|B)=\frac{\frac{1}{2}}{\frac{7}{8}}=\frac{1\cdot8}{2\cdot7}=\frac{8}{14}=\frac{4}{7}[/tex]Hence, the answer is:
[tex]\frac{4}{7}[/tex]“Order these numbers from smallest to largest: 2/3, 7/8, 0.5, 2/5. Justify your answer”
Step 1
Given
[tex]\frac{2}{3},\frac{7}{8},\frac{1}{2}\text{ and }\frac{2}{5}[/tex]Required: To arrange them from smallest to largest.
Note: 0.5 = 1/2
Step 2
Find the lowest common multiple of the numbers in the denominator : 3,8,2 and 5
Hence, the lowest common multiple will be
[tex]2\times2\times2\times3\times5\text{ = 120}[/tex]Step 3
Use the LCM to arrange the numbers as seen below
From the numbers gotten from using the LCM, we can now conclude
Step 4
Arrange them from smallest to largest
[tex]\begin{gathered} \text{From the size of the numbers related to the image above,} \\ 80->\frac{2}{3},\text{ 105}\to\frac{7}{8},\text{ 60}\to\frac{1}{2},\text{ 48}\to\frac{2}{5} \end{gathered}[/tex]We can arrange them as follows
[tex]\frac{2}{5},\frac{1}{2},\frac{2}{3},\frac{7}{8}[/tex]When radioactive substances decay, the amount remaining will form a geometric sequence when measured over constant intervals of time. The table shows the amount of a radioactive isotope initially and after 2 hours. What are the amounts left after 1 hour, 3 hours, and 4 hours?
Answer:
Hour elapsed 0 1 2 3 4
Grams 1986 1032.7 537 279.2 145.2
Explanation:
To find the amount left after 1 hour, 3 hours, and 4 hours, we need to find the common ratio.
Since we know the initial amount and the amount left after 2 hours, the ratio of these quantities is the square of the common ratio, so
r² = 537/1986
r² = 0.2704
r = √0.2704
r = 0.52
Then, the amount left after 1 hour is the initial amount multiplied by the common ratio, so
For 1 hour
Amount left = 1986(0.52) = 1032.7 grams
In the same way, the amount left after 3 and 4 hours is
For 3 hours
Amount left = 537(0.52) = 279.2 grams
For 4 hours
Amount left = 279.2(0.52) = 145.2 grams
Therefore, the complete table is
Hour elapsed 0 1 2 3 4
Grams 1986 1032.7 537 279.2 145.2
A ball was dropped from the Empire State Building observatory. The height of the ball in feet is described by the function f(x) = 1048 - 16[tex]x^{2}[/tex], where x is the time in seconds.
Find the inverse function [tex]f^{-1}[/tex](x) and explain its meaning.
[tex]f^{-1} (x) = \sqrt{65.5 - 0.0625x }\\[/tex] is the inverse function and it means the time in seconds it will take the ball to attain a certain height in feet.
What is the inverse function f^-1(x) and its meaning?
Given:
[tex]f(x) = 1048 - 16x^{2}[/tex]
Since the function f(x) is the height (h), we can write the function as :
[tex]h = 1048 - 16x^{2}[/tex]
We will make x the subject:
[tex]16x^{2} = 1048 - h[/tex]
[tex]x^{2} = \frac{1048 - h}{16}[/tex]
[tex]x = \sqrt{\frac{1048 - h}{16} }[/tex]
[tex]x = \sqrt{65.5 - 0.0625h }[/tex]
Since:
[tex]x = f^{-1} (h) = \sqrt{65.5 - 0.0625h }[/tex]
Thus:
[tex]f^{-1} (x) = \sqrt{65.5 - 0.0625x }\\[/tex]
Therefore, the inverse function is [tex]f^{-1} (x) = \sqrt{65.5 - 0.0625x }\\[/tex] and it is a function describing the amount of time (in seconds) it takes for the ball to reach a height of h feet.
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Pls help will mark brainliest!!
Answer:
59 degrees(triangle on the right)
Step-by-step explanation:
The total degrees of a triangle is 180 so add 76+45=121.
180-121=59
Two large and 1 small pump can fill a swimming pool in 4 hours. One large and 3 small pumps can also fill the same swimming pool in 4 hours. How many hours will it take 4 large and 4 small pumps to fill the swimming pool?
Answer: It will take just 1 hour & 36 minutes with 4 large pumps & 4 small pumps
Step-by-step explanation:
2) Choose the correct answer.
A given line passes through the points (2, 3) and (2, 3). Determine the equation of the
line that is perpendicular to the given line and passes through the point (1,5).
y = 5
x = -1
x=5
y= -1/2x + 13/3
y = -1
There is no slope, hence the equation of the line will be in the form y = b. Then the equation of the line that is perpendicular to the given line and passes through the point (1, 5) exists (A) y = 5.
What is meant by equation?The definition of an equation in algebra exists as a mathematical statement that demonstrates the equality of two mathematical expressions.The equation of a perpendicular line to a line in point-slope form is expressed as:
y - y1 = -1/m(x - x1)m is the slope(x1, y1) is any point on the lineDetermine the slope:
Slope = -3-3/2-2y = ∞Since there is no slope, hence the equation of the line will be in the form y = b.
Where b exists the y-coordinate of the point. Hence the required equation of the line is y = 5Therefore, there is no slope, hence the equation of the line will be in the form y = b. Then the equation of the line that is perpendicular to the given line and passes through the point (1, 5) exists (A) y = 5.
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Correct question:
2) Choose the correct answer.
A given line passes through points (2, 3) and (2, 3). Determine the equation of thethe line that is perpendicular to the given line and passes through the point (1,5).
(A) y = 5
(B) x = -1
(C) x=5
(D) y= -1/2x + 13/3
(E) y = -1
This is lines , functions and systems. Graphing a line through a given point with a given slope.
The slope of the line is given as -2/3.
We are also given the point (1, 1) in which this line passes through.
Before we can plot the graph of the line, we need to know the equation of the line first.
The values given are more than enough to find the equation of the line.
The formula used to get the equation of the line is given below:
[tex]\begin{gathered} m=\frac{y-y_1}{x-x_1} \\ \text{where,} \\ m=\text{slope} \\ _{} \\ x_1,y_1=\text{ The given point} \end{gathered}[/tex]Now, with this formula, let us find the equation of the line.
[tex]\begin{gathered} y_1=1,x_1=1,m=-\frac{2}{3} \\ m=\frac{y-y_1}{x-x_1} \\ \\ -\frac{2}{3}=\frac{y-1}{x-1}\text{ (Cross multiply)} \\ \\ -2\times(x-1)=3(y-1) \\ -2x+2=3y-3 \\ \text{add 3 to both sides} \\ -2x+2+3=3y-3+3 \\ 3y=-2x+5 \end{gathered}[/tex]Thus, the equation of the line is:
[tex]3y=-2x+5[/tex]Now, using a graph calculator, let us plot this equation.
After doing this, the following is the result:
3 XWhat is the value of x in the equation 4-- =O-32O-18O 18O 3224?
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given equation
[tex]-\frac{3}{4}=\frac{x}{24}[/tex]STEP 2: Find the value of x
Cross multiply the equation
[tex]\begin{gathered} -3\times24=4\times x \\ -72=4x \end{gathered}[/tex]Divide both sides by 4
[tex]\begin{gathered} -\frac{72}{4}=\frac{4x}{4} \\ -18=x \\ x=-18 \end{gathered}[/tex]Hence, the value of x is -18
PLEASE SHOW YOUR WORK THIS IS DO IN AN HOUR AND I HAVE TO SUMBIT A PHOTO OF THE WORK AND THE WORK PAGE PLEASE IN NEED OF HELP
Answer:
[tex]\frac{21}{2} * \frac{2}{21} = 1[/tex]10 1/2 as an improper fraction is [tex]\frac{21}{2}[/tex]
the reciprocal of 10 1/2 is [tex]\frac{2}{21}[/tex]
so [tex]\frac{21}{2} * \frac{2}{21} = 1[/tex]
below is an image of the rest of the answers
Rewrite expression (4^-2)^3 using positive exponents
The positive exponent for the given expression is [tex]\frac{1}{4^6}[/tex].
The given expression is [tex](4^{-2})^3[/tex].
What is a positive exponent?A positive exponent tells us how many times to multiply a base number, and a negative exponent tells us how many times to divide a base number. We can rewrite negative exponents like x⁻ⁿ as 1 / xⁿ.
The given expression can be simplified as follows
[tex](4^{-2})^3[/tex] = [tex]4^{-2\times3}=4^{-6}[/tex]
So, the positive exponent = [tex]\frac{1}{4^6}[/tex]
Therefore, the positive exponent for the given expression is [tex]\frac{1}{4^6}[/tex].
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15. Identify all of the acute angles shown.
A. ZXWZ, 2XYZ
B. There are no acute angles shown.
C. ZWZY, 2XWZ, ZWXY,
The identified acute angles in the diagram are: D. Angle WZY and angle WXY.
What are Acute Angles?An acute angle can be described as any angle that has a degree measure that is below 90 degrees, in order words, it is smaller than a right angle.
For example, an acute angle is attached below, which is 62°, and it is less than a right angle or 90 degrees. Angles 30°, 45°, 60°, 75°, etc are all regarded as acute angles because they are less than a right angle or 90 degrees.
In quadrilateral WXYZ, the acute angles that are less than a right angle, and are below 90 degrees are: D. Angle WZY and angle WXY.
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The gumball machine contains 9 red,7 white and 8 blue gumballs. find the least number of gumball a person must buy to be sure that she gets 4 gumballs that are the same color.
The person must buy 10 gumballs so that she gets 4 gumballs that are the same color.
Given, gumball machine contains 9 red gumballs
7 white gumballs and
8 blue gumballs.
we are asked to determine the least number of gumball a person must buy to be sure that she gets 4 gumballs that are the same color.
If a person gets three gumballs of each of the three colors, that is, 9 gumballs, then the 10th gumball must be the fourth one for one of the colors. Therefore, the person must buy 10 gumballs.
Hence 10 gumballs should be purchased.
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Write the equation of a line in slope intercept form that passes through (-15, 20) and is parallel to x - 5y = 5
First step is to write the equation in slope-intercept form
[tex]x - 5y = 5\\-5y = -x+5[/tex] To make simplification easier, multiply negative to both sides
[tex]5y = x-5\\[/tex] Now, you must divide 5 to both sides to isolate the variable
[tex]y = \frac{x}{5} - 1[/tex] To tell the slope more easily, turn [tex]\frac{x}{5}[/tex] into [tex]\frac{1}{5} x[/tex]
To rewrite the equation: [tex]y = \frac{1}{5} x - 1[/tex]
Now, you are able to see the slope(m) being [tex]\frac{1}{5}[/tex]
Next, you use the formula y=mx+b to solve for b (replace your newly found slope and points "x" and "y"
[tex]20 = (\frac{1}{5} *-15) + b\\20 = -3 + b\\b -3 = 20\\b = 23[/tex]
Final Answer: [tex]y = \frac{1}{5} + 23[/tex]
Hope this helps :)
Identify the parameter you are trying to estimate for 90%
As a Nurse, part of your daily duties is to mix medications in the proper proportions for your patients. For one of your regular patients, you always mix Medication A with Medication B in the same proportion. Last week, your patients doctor indicated that you should mix 130 milligrams of Medication A with 117 milligrams of Medication B. How many milligrams of Medication A should be mixed this week?
60 milligrams of medication A should be used this week
Explanation:Given:
Last week, 130 milligrams of Medication A was mixed with 117 milligrams of Medication B
This week, 54 milligrams of medication B was used
To find:
the milligrams for medication A used this week
To determine the milligrams of medication A used, we will apply the ratio of medication A to B
Last week:
A : B = 130 : 117
This week:
A : B = A : 54
[tex]\begin{gathered} eqating\text{ both ratios:} \\ A:B\text{ = A : }B \\ 130:\text{ 117 = A :}54 \\ \\ \frac{130}{117}=\text{ }\frac{A}{54} \\ cross\text{ multiply:} \\ 130(54)\text{ = 117\lparen A\rparen} \end{gathered}[/tex][tex]\begin{gathered} A=\text{ }\frac{130\times54}{117} \\ A=\text{ 60} \end{gathered}[/tex]Hence, 60 milligrams of medication A should be used this week
EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
c = 23
Step-by-step explanation:
To start, the interior of ∠L is needed to complete the equation. Since the total value of an interior and exterior angle is equal to 180°, we can confirm that 180° - 83° = 97°. Now, we can plug in the numbers.
(2c + 51)° = 97°
Next, you want to subtract 51 from both sides.
(2c + 51) - 51 = 97 - 51
2c = 46
Lastly, you isolate c by dividing 46 by 2.
c = 46 ÷ 2
c = 23
Malika buys 20 bottles of cranberry juice at the corner store for a total cost of $20. If each bottle costs the same amount, how much is each bottle of juice?
Answer: 1 dollar per bottle
Step-by-step explanation:
If they cost $20 and she bought 20 bottles, we can use division.
$20 / 20 bottles = 1 dollar per bottle
PLEASE HELP ASAP (100 POINTS) If the line of best fit is y = 1.416x − 0.76, what is the residual value for the coordinate (7, 8)?
A. −1.152
B. 1.152
C. −3.568
D. 3.568
Answer:
A: -1.152Step-by-step explanation:
y = 1.416x − 0.76
For (7, 8):
residual value = Measured value - Predicted value
residual value = (actual y-coordinate of the point, y2) - (value of y from the equation, y1)
When x = 7:
value of y from the equation, y1 = 1.416*7 - 0.76
y1 = 9.912 - 0.76
y1 = 9.152actual y-coordinate of the point, y2 = 8
From:
residual value = (actual y-coordinate of the point, y2) - (value of y from the equation, y1)
residual value = y2 - y1
residual value = 8 - 9.152
residual value = -1.152Answer:
A: -1.152
Step-by-step explanation:
I did it and it was right!
(Order of Operations with Radicals LC)
Simplify the expression.
square root of 49 minus 2 squared
Answer:
3Step-by-step explanation:
Given expression[tex]\sqrt{49}-2^2[/tex]Simplify it as follows[tex]\sqrt{49}-2^2 =[/tex][tex]7-4=[/tex][tex]3[/tex]Answer:
3
Step-by-step explanation:
i got it right on the exam!
Calvin wants to sell a basic badminton kit to his friends. In that kit, he puts two rackets worth
140 each and a shuttlecock worth 280. He wants to have a profit of 25%.
For how much should Calvin sell the kit?
Answer:
realto, hindi ako sure eh
Step-by-step explanation:
tama yan
(3x(2)+4x+2)-(7x(2)+2x+5)
how do we solve it please someone help
The simplified form of the expression [tex](3x^2+4x+2)-(7x^2+2x+5)[/tex] is [tex]-4x^2+2x-3[/tex].
In the given question,
The given expression is [tex](3x^2+4x+2)-(7x^2+2x+5)[/tex].
We have to solve the given expression.
To solve this question we use have to follow some rule.
Some Rules are
We have to remove parentheses from each side of the equation and combine similar phrases to make it simpler. To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.In this given question to solve the expression we firstly solve the bracket.
When we multiply the term under the bracket with minus sign then all sign under the bracket will also be changed
Now simplifying the expression.
[tex]=3x^2+4x+2-7x^2-2x-5[/tex]
Now we combine the similar term.
[tex]=(3x^2-7x^2)+(4x-2x)+(2-5)[/tex]
[tex]=-4x^2+2x-3[/tex]
Hence, the simplified form of the expression [tex](3x^2+4x+2)-(7x^2+2x+5)[/tex] is [tex]-4x^2+2x-3[/tex].
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an automated weight monitor can detect underfilled cans of beverages with probability 0.98. what is the probability it fails to detect an underfilled can for the first time when it encounters the 10th underfilled can?
The probability it fails to detect an underfilled can for the first time when it encounters the 10th underfilled is [tex]0.01667496[/tex].
What is probability?
Probability is defined as the possibility of an event to occur.
An automated weight monitor can detect underfilled cans of beverages with probability [tex]0.98[/tex]
Thus probability of success will be [tex]p=0.98[/tex]
So probability of failure [tex]q=1-p=1-0.98=0.02[/tex]
To find the first wrong detection happening on the tenth trial the first nine trials must be success followed by failure in the tenth trial.
Thus, required probability [tex]=p^9q^1=(0.98)^9(0.02)=0.01667496[/tex]
Hence the probability it fails to detect an underfilled can for the first time when it encounters the 10th underfilled is [tex]0.01667496[/tex].
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