Answer:
The series is given as follows;
[tex]-\dfrac{161}{8} , \ -\dfrac{59}{4} , \ -\dfrac{75}{8}, \ -4, \ \dfrac{22}{16} ......[/tex]
Step-by-step explanation:
Assuming the series is an arithmetic progression, (AP), series, we have
The nth term of the desired series = a + (n - 1)×d
Where;
a = The first term
n = The position of the term in the series
d = The common difference
Given that the 5th term = 22/16 and the 4th term = -4, we have;
d = The difference between consecutive terms = Difference between the 5th term and the 4th term
∴ d = 22/16 - (-4) = 43/8 = 5.375
22/16 = a + (5 - 1)×5.375
∴ a = 22/16 - 4×5.375 = -20.625
The series is therefore;
[tex]-\dfrac{161}{8} , \ -\dfrac{59}{4} , \ -\dfrac{75}{8}, \ -4, \ \dfrac{22}{16} ......[/tex]
Jacob is playing a game where he earns 3 points for a correct answer and loses 2 points for an incorrect answer. He
currently has 6 points. What situation would end with him breaking even?
Answer:
Step-by-step explanation:
If he answers the next 3 questions incorrectly he will break even:
6 - 3(2) = 0.
Answer:
C. answering the last two questions correctly
Step-by-step explanation:
Did it on edge, hope this helps :) Brainliest?
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HELPP PLEASE I’ll give a brainlist
16. Expand (2x - 1)(x - 3).
A. 2x2 - 7X+3 B. 2x2 +7x+3
C. 2x2-7X-3 D. 2x2+7X-3 E. x2+7X-3
Answer:
Hey there!
[tex](2x-1)(x-3)[/tex]
[tex]2x^2-1x-6x+3[/tex]
[tex]2x^2-7x+3[/tex]
Hope this helps :)
Answer:
see below
Step-by-step explanation:
the simple answer is a if you need an explanation just comment
Triangle A' B' C' is a dilation of a triangle ABC. The scale factor is [tex]\frac{3}{4}[/tex]. Point B is 11 inches away from the center of dilation is point B'?
Answer:
None of the options are correct
Step-by-step explanation:
Let us assume point B is at (x, y) and the center of dilation is at (a, b). Therefore the distance between the two points is:
[tex]Distance =\sqrt{(b-y)^2+(a-x)^2}=11 \\\\\sqrt{(b-y)^2+(a-x)^2}=11[/tex]
If Triangle ABC is then dilated by 3/4, the new coordinate is B'(3/4 (x-a) + a, 3/4 (y - b) + b). The distance between B' and the center of dilation would be:
[tex]Distance =\sqrt{(b-[\frac{3}{4}( y-b)+b])^2+(a-[\frac{3}{4} (x-a)+a])^2}[/tex]
Therefore the distance cannot be gotten until the center of dilation is given
20 POINTS!!! Please Help! No nonsense answers please!
Answer:
[tex](2-\sqrt{7}, 2+\sqrt{7})[/tex]
Step-by-step explanation:
13) The diameter of a plant cell is 1.26 m and the length of a bacterium is 5.1 m. Compare their diameters.
Answer:
The diameter of the bacterium is 4.05 times the diameter of the plant cell
Step-by-step explanation:
Given
The given parameters both represent diameters
Plant Cell; P = 1.26m
Bacterium; B = 5.1m
Required
Compare both diameters;
Write out both expressions
[tex]P = 1.26[/tex]
[tex]B = 5.1[/tex]
Divide B by P
[tex]\frac{B}{P} = \frac{5.1}{1.26}[/tex]
[tex]\frac{B}{P} = 4.04761904762[/tex]
Approximate
[tex]\frac{B}{P} = 4.05[/tex]
Multiply both sides by P
[tex]P * \frac{B}{P} = 4.05 * P[/tex]
[tex]B = 4.05 * P[/tex]
[tex]B = 4.05P[/tex]
This implies that;
The diameter of the bacterium is 4.05 times the diameter of the plant cell
Usha had a balance of -$84. She worked for 6 days and put half the money in the bank. Now she has a balance of -$45. How much does Usha get paid each day for newspaper delivery?
Answer:
$13
Step-by-step explanation:
First, find how much she put into the bank:
84 - 45 = $39
Then, multiply this by 2 to find how much she made, because this was half of the money she got:
39(2) = 78
Then, divide this by 6 to find how much she makes a day:
78/6 = 13
= $13
make u the subject of the formula
u-x/v-x=u/v²
Answer:
See below.
Step-by-step explanation:
[tex]\frac{u-x}{v-x}=\frac{u}{v^2} \\[/tex]
Cross multiply and distribute.
[tex]u(v-x)=v^2(u-x)\\uv-ux=uv^2-xv^2[/tex]
Move all the u to the left side:
[tex]uv-ux-uv^2=-xv^2[/tex]
Factor out a u:
[tex]u(v-x-v^2)=-xv^2[/tex]
Divide:
[tex]u=\frac{-xv^2}{v-x-v^2}=\frac{xv^2}{x+v^2-v}[/tex]
(I factored out a negative in the second term.)
Which pair of parallelograms is similar?
Answer:
EFGH ~ IJKL
Step-by-step explanation:
There sides are both parallel.
Hope this helped you :)
40 POINTS!!!!
ANSWER ASAP!!!
What is the value of y?
O 3 sqrt 3 units
O 6 sqrt 3 units
O 9 sqrt 3 units
O 12 sqrt 3 units
Answer:
6 sqrt(3) = y
Step-by-step explanation:
We can use the leg rule to find y
hyp leg
----- = -------
leg part
9+3 y
----- = -------
y 9
Using cross products
12*9 = y^2
108 = y^2
Taking the square root of each side
sqrt(108) = sqrt(y^2)
sqrt(36 *3) = y
6 sqrt(3) = y
Answer: B) 6/3 units
Step-by-step explanation:
The basic unit in which data are stored in an accounting system is called an __________. These storage units should be so constructed as to readily receive money measurements of the __________ or ___________ in the items for which they are established. The basic unit in which data are stored in an accounting system is called an __________. These storage units should be so constructed as to readily receive money measurements of the __________ or ___________ in the items for which they are established.
Answer:
an accounts; credit or debit.
Step-by-step explanation:
Remember, accounting involves activities done to keep financial records. Interestingly, a similar term is used to refer to the basic unit in which data are stored in an accounting system called accounts.
Also, we need to bear in mind that this financial records written as storage units would include incoming or outgoing money measurements often called debit or credit transactions in the items for which they are established.
Define the six trigonometric functions in terms of x and y
Answer: Since y = tan θ = y / x , and y and x are coordinates of a point, y can be any real number and x can be any real number except 0. Thus, the ratio y / x can be any real number, and we conclude that the range of y = tan θ is all real numbers. ... y = csc θ = r/ y , since sin θ and csc θ are reciprocals of one another.
Step-by-step explanation:
Since y = tan θ = y / x , and y and x are coordinates of a point, y can be any real number and x can be any real number except 0. Thus, the ratio y / x can be any real number, and we conclude that the range of y = tan θ is all real numbers. ... y = csc θ = r/ y , since sin θ and csc θ are reciprocals of one another.
The period of the function is the interval between repetitions of any function. A trigonometric function's period is the length of one whole cycle. As a starting point, we can use x = 0 for any trigonometry graph function. Trigonometric functions have a periodic nature. As opposed to tangent and cotangent, which have period, sine, cosine, secant, and cosecant all have period 2.
What is trigonometry?Studying the correlations between triangle side lengths and angles is the subject of trigonometry, a branch of mathematics. By using geometry to study astronomy, the field first appeared in the Hellenistic civilization during the third century BC. The earliest documented tables of values for trigonometric ratios (sometimes called trigonometric functions) such as sine were developed by mathematicians in India, while the Greeks concentrated on chord calculation.
Geodesy, surveying, celestial mechanics, and navigation are just a few of the fields where trigonometry has been used historically. The various identities of trigonometry are well recognized.
These trigonometric identities are frequently used to simplify, discover a more practical form for, or solve equations involving trigonometric expressions.
To know more about trigonometry visit:
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complete question:
Explain what is meant by the period of a trigonometric function. what are the periods of the six trigonometric functions?
What is the measure of circumscribed LX?
O 45°
O 50°
O 90°
O 950
Answer:
90°
Step-by-step explanation:
The angle a tangent makes with a radius at the point of tangency is 90 deg.
There are three 90-deg angles in the quadrilateral, so the 4th angle must also measure 90 deg.
Answer: 90°
Based on the tangent theorem the measure of the circumscribed ∠X is: 90°.
What is the Tangent Theorem?The tangent theorem states that an angle of 90 degrees is formed at the point of tangency where a tangent meets the radius of a circle.
YX and WX are tangents of the circle.
m∠Y = m∠W = 90°
Sum of interior angles of a quadrilateral is 360°
m∠X = 360 - 90 - 90 - 90
m∠X = 90°
Therefore, based on the tangent theorem the measure of the circumscribed ∠X is: 90°.
Learn more about the tangent theorem on:
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Which statement is true regarding the traits of scatterplots?
A) The strength of a correlation is independent of whether the correlation of a scatterplot is positive or negative. A scatterplot with positive correlation can have either weak correlation or strong correlation.
B) The slope of a line is independent of whether the correlation of a scatterplot has positive or negative correlation. A scatterplot with a negative slope can have either positive correlation or negative correlation.
C) The nonlinear association of a scatterplot depends on whether it has a weak or strong correlation. A scatterplot with nonlinear association will have a strong correlation.
D) The nonlinear association of a scatterplot depends on whether it has a positive or negative correlation. A scatterplot with nonlinear correlation will have a negative correlation.
Answer:
The strength of a correlation is independent of whether the correlation of a scatterplot is positive or negative. A scatterplot with positive correlation can have either a weak correlation or strong correlation.
Step-by-step explanation:
Answer:
The answer to your question would be A.) The strength of a correlation is independent of whether the correlation of a scatterplot is positive or negative. A scatterplot with positive correlation can have either weak correlation or strong correlation.
Step-by-step explanation:
I got it right on edge 2020
Which of the following are not natural numbers? There may be more than one correct answer. Select all that apply. If only one answer is correct, select "only" and the answer that applies. A.)−1,−2,−3,… B.) 0 C.) 1,2,3,… D.) only E.) fractions
Answer:
A,E
Step-by-step explanation:
Natural numbers include the normal counting number like 1, 2, 3, and so on and also 0.
B) does not work as negative numbers are not numbers we start counting in
E) does not work as we don't count in fractions
The diagonal of rhombus measure 16 cm and 30 cm. Find it's perimeter
Answer:
P = 68 cmStep-by-step explanation:
The diagonals of the rhombus divide it into 4 congruent right triangles.
So we can use Pythagorean theorem to calculate side of a rhombus.
[tex](\frac e2)^2+(\frac f2)^2=s^2\\\\e=30\,cm\quad\implies\quad\frac e2=15\,cm\\\\f=16\,cm\quad\implies\quad\frac f2=8\,cm\\\\15^2+8^2=s^2\\\\s^2=225+64\\\\s^2=289\\\\s=17[/tex]
Perimeter:
P = 4s = 4•17 = 68 cm
Figure ABCD is a rectangle with point A (−2, 5). What rule would rotate the figure 90° clockwise?
Answer:
(5,2)
Step-by-step explanation:
The 90° clockwise rule (for around the origin) is: [tex](x,y)\rightarrow(y,-x)[/tex]
Apply the rule to point A:
[tex]\left \{ {(-2,5)\rightarrow(5,2)} \atop {(x,y)\rightarrow(y,-x)}} \right.[/tex]
A' should be (5,2).
Answer:
Step-by-step explanation:
The general rule for rotation of an object 90 degrees is (x, y) to (-y, x)
so for point A(-2,5), A' will be (5,2)
to find the new
X=xcos(θ)+ysin(θ)
X=-2(cos90)+5sin90 ( cos90=0, sin 90=1)
X=5to find the new
Y=−xsin(θ)+ycos(θ)
Y=-(-2)sin90+5cos90
Y=2The number of pages per book on a bookshelf is normally distributed with mean 248 pages and standard deviation 21 pages. Using the empirical rule, what is the probability that a randomly selected book has less than 206 pages?
Answer:
The probability is 0.0228
Step-by-step explanation:
We proceed by calculating the z-score value
Mathematically;
z-score = (x - mean)/SD
where x = 206, mean = 248 and SD = 21
Substituting these values, we have;
z-score = (206-248)/21 = -42/21 = -2
So the probability we want to calculate is;
P(z < -2)
We can use the standard normal distribution table for this;
P(z < -2) = 0.0228
Answer:
i need this as a percentage
Step-by-step explanation:
Question. 1 The product of a monomial and a binomial is a (a) monomial (b) binomial (c) trinomial (d) None of these
Answer:
The answer to this question is (D)
What are the factors of the quadratic function represented by this graph?
A.
(x − 1) and (x − 5)
B.
(x + 1) and (x + 5)
C.
(x − 1) and (x + 5)
D.
(x + 1) and (x − 5)
The factors of the quadratic equations are (x + 1) and (x + 5) which is represented on the graph.
What is quadratic equation?A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is [tex]ax^2 + bx + c = 0,[/tex]
Here in the graph we can see that the x coordinate cut by the curve of the quadratic equation is in the negative side of x at -1 and -5.
So the factors of the quadratic equations are (x + 1) and (x + 5) which is represented on the graph.
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Answer:
Check Screenshot
Step-by-step explanation:
A certain pole has a cylinder-like shape, where the base's radius is 10 centimeters and the height is 2 meters. What calculation will give us the estimated surface area of the pole in square centimeters?
Answer:
2 pi •10•210
Step-by-step explanation:
Khan academy
What is the square root of 48? what is the square root of 1/49 ? what is the square root of 4/100 ?
Answer:
Step-by-step explanation:
√48 = √(3*16) = 4√3
√1
√(1/49) = ------- = 1/7
√49
√4
√(4/100) = --------------- = ±2/10 =
√100
i need help please i give 5 stars ;(
Answer:
D. [tex]\sqrt{\frac{2*2*2*2*3}{5*5*7} }[/tex]
Step-by-step explanation:
48 divided by 2 is 24. Insert the 2.
24 divided by 2 is 12. Insert the 2.
12 divided by 2 is 6. Insert the 2.
6 divided by 2 is 3. Insert the 2 and 3:
[tex]48=2*2*2*2*3[/tex]
175 divided by 5 is 35. Insert the 5.
35 divided by 5 is 7. Insert the 5 and 7:
[tex]175=5*5*7[/tex]
:Done
need help pls will give you 5 stars
Answer:
f(x + k)
Step-by-step explanation:
A horizontal shift moves to the left or right
y = f(x + k) k > 0 moves it left
k < 0 moves it right
(01.02 HC)Morris is showing his work in simplifying (−6.7 + 4.3) − 1.2. Step 1: (4.3 − 6.7) − 1.2 Step 2: 4.3 − (6.7 + 1.2) Step 3: 4.3 − (7.9) Step 4: −3.6
Answer:
Option (C)
Step-by-step explanation:
This question is incomplete; here is the complete question.
Morris is showing his work in simplifying,
(-6.7 + 4.3) - 1.2
Step 1: (4.3 - 6.7) - 1.2
Step 2: 4.3 - (6.7 + 1.2)
Step 3: 4.3 - 7.9
Step 4: -3.6
Which statement is true ?
A). Step 1, Morris used the commutative property.
B). Step 2, Morris used the distributive property.
C). Step 3, Morris used the associative property.
D). Step 4, Morris's answer is incorrect.
In associative property,
a + (b + c) = (a + b) + c
By this property,
(-6.7 + 4.3) - 1.2
Step 1, (-6.7 + 4.3) - 1.2 = (4.3 - 6.7) - 1.2
Step 2, (4.3 - 6.7) - 1.2 = 4.3 - (6.7 + 1.2) [Use of associative property]
Step 3, 4.3 - 7.9
Step 4, -3.6
Help ASAP please show work I need this done ASAP
Answer:
Step-by-step explanation:
Graph shows the distance traveled by a biker as a function of time.
Velocity of the biker changes in the different intervals.
1). In the interval 0 < t < 2, biker is moving with a constant velocity.
Velocity = [tex]\frac{\text{Displacement}}{\text{Time}}[/tex]
= [tex]\frac{0-4}{0-2}[/tex]
= 2 km per hour
2). In the interval 2 < t < 5,
Velocity = [tex]\frac{4-4}{4-2}[/tex]
= 0
Therefore, biker stopped between 2 to 5 hours.
3). In the interval 5 < t < 6,
Velocity = [tex]\frac{\triangle x}{\triangle t}[/tex]
= [tex]\frac{4-3}{6-5}[/tex]
= 1 km per hour
4). In the interval 6 < t < 7,
Velocity = [tex]\frac{6-3}{7-6}[/tex]
= 3 km per hour
Here are the ages (in years) of 10 professors at a college. , 47, 44, 48, 43, 35, 65, 56, 37, 7351 What is the percentage of these professors who are younger than 50?
Answer:
50%
Step-by-step explanation:
We are given this set of data: Age of professors in years
47, 44, 48, 43, 35, 65, 56, 37, 73,51
We can firstly rearrange the years properly in ascending order.
Hence we have:
35, 37, 43, 44, 48, 51, 53 56, 65, 73
The number of the professor given = 10 professors
The number of professors younger 50 years = 5
Therefore, the percentage of these professors who are younger than 50
Is:
5/10 × 100 = 50%
Therefore, 50% of the professors are younger than 50
help! ill give brainliest
Answer:
84 square inches is the correct answer.
Step-by-step explanation:
I am 100% sure of that.
Hope this helps....
Have a nice day!!!!
Evaluate the expression using the values in the left column to complete the table
Answer/Step-by-step explanation:
A. [tex] 4b + 3b [/tex]
Using b = 2
[tex] 4(2) + 3(2) = 8 + 6 = 14 [/tex]
Using b = 4
[tex] 4(4) + 3(4) = 16 + 12 = 28 [/tex]
Using b = 6
[tex] 4(6) + 3(6) = 24 + 18 = 42 [/tex]
Using b = 8
[tex] 4(8) + 3(8) = 32 + 24 = 56 [/tex]
Using b = 10
[tex] 4(10) + 3(10) = 40 + 30 = 70 [/tex]
Using b = 2
[tex] 4(12) + 3(12) = 48 + 36 = 84 [/tex]
B. [tex] 3(x - 2) [/tex]
Using x = 3
[tex] 3(3 - 2) = 3(1) = 3 [/tex]
Using x = 5
[tex] 3(5 - 2) = 3(3) = 9 [/tex]
Using x = 7
[tex] 3(7 - 2) = 3(5) = 15 [/tex]
Using x = 9
[tex] 3(9 - 2) = 3(7) = 21 [/tex]
Using x = 11
[tex] 3(11 - 2) = 3(9) = 27 [/tex]
Using x = 13
[tex] 3(13 - 2) = 3(11) = 33 [/tex]
C. [tex] 5(4a - 1) [/tex]
Using a = 2
[tex] 5(4(2) - 1) = 5(8 - 1) = 5(7) = 35 [/tex]
Using a = 3
[tex] 5(4(3) - 1) = 5(12 - 1) = 5(11) = 55 [/tex]
Using a = 4
[tex] 5(4(4) - 1) = 5(16 - 1) = 5(15) = 75 [/tex]
Using a = 5
[tex] 5(4(5) - 1) = 5(20 - 1) = 5(19) = 95 [/tex]
Using a = 6
[tex] 5(4(6) - 1) = 5(24 - 1) = 5(23) = 115 [/tex]
Using a = 7
[tex] 5(4(7) - 1) = 5(28 - 1) = 5(27) = 135 [/tex]
D. [tex] 6y - 2y + 4 [/tex]
Using y = 2
[tex] 6(2) - 2(2) + 4 = 12 - 4 + 4 = 12 [/tex]
Using y = 3
[tex] 6(3) - 2(3) + 4 = 18 - 6 + 4 = 18 - 2 = 16 [/tex]
Using y = 5
[tex] 6(5) - 2(5) + 4 = 30 - 10 + 4 = 30 - 6 = 24 [/tex]
Using y = 10
[tex] 6(10) - 2(10) + 4 = 60 - 20 + 4 = 60 - 16 = 44 [/tex]
Using y = 8
[tex] 6(8) - 2(8) + 4 = 48 - 16 + 4 = 48 - 12 = 36 [/tex]
Using y = 6
[tex] 6(6) - 2(6) + 4 = 36 - 12 + 4 = 36 - 8 = 28 [/tex]
A box contain 12 balls in which 4 are white 3blue and 5 are red.3 balls are drawn at random from the box. Find the chance that all three balls are of different colour
Answer:
white: 1/3, blue: 1/4, red: 5/12
Step-by-step explanation:
Take the amount of balls each color has and divide by 12.
White:
4/12 = 1/3
Blue:
3/12 = 1/4
Red:
5/12 (can't simplify)
Answer:
3/44 or 0.068
Step-by-step explanation:
(3/12 × 2/11 × 1/10)+(5/12 × 4/11 × 3/10)+(4/12 × 3/11 × 2/10)
=3/44
