The numbers 1 to 12 must be placed in the circles of the star shown on the right. The sums of the numbers in each row, and the sum of the numbers in the six outer circles of the star, must be equal to 26. Arrange the numbers accordingly.
Answer:
The numbers 1 to 12 must be placed in the circles of the star shown on the right. The sums of the numbers in each row, and the sum of the numbers in the six outer circles of the star, must be equal to 26. Arrange the numbers accordingly.
how to find the common factors and H.C.F of 20, 35, and 40
he instructions to find the LCM of 20, 35 and 40 are the next:
1. Decompose all numbers into prime factors
20 2 10 2 5 5 1
35 5 7 7 1
40 2 20 2 10 2 5 5 1
2. Write all numbers as the product of its prime factors
Prime factors of 20 = 22 . 5
Prime factors of 35 = 5 . 7
Prime factors of 40 = 23 . 5
3. Choose the common and uncommon prime factors with the greatest exponent
Common prime factors: 5
Common prime factors with the greatest exponent: 51
Uncommon prime factors: 2 , 7
Uncommon prime factors with the greatest exponent: 23, 71
4. Calculate the Least Common Multiple or LCM
Remember, to find the LCM of several numbers you must multiply the common and uncommon prime factors with the greatest exponent of those numbers.
LCM = 51. 23. 71 = 280
At first it decreased by 60 percent and it increased by 80 percent
The quantity reported an equivalent net percentage change of 28 percent.
How to calculate the net change of a quantity in percentages
In this problem we must determine the simple percentage change equivalent to two consecutive percentual changes. The formula that describes the situation is:
1 + r/100 = (1 - 60/100) · (1 + 80/100)
1 + r/100 = 72/100
r/100 = - 28/100
r = - 28
The quantity reported an equivalent net percentage change of 28 percent.
Remark
The statement is incomplete. Complete form is presented below:
A quantity is changing. At first it descreased by 60 percent and it increased by 80 percent. What is net change of the quantity in percentage?
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Calculate the geometric center of the graph the function
The geometric center of the graph under the function is 5/3
How to determine the geometric center of the graph under the function?The equation of the function is given as:
f(x) = 3 - |x - 2|
The interval is given as:
x ∈ [0, 3]
The geometric center (gc) of the graph under the function is calculated using
gc = ∫x f(x) dx/∫f(x) dx
Substitute the known values in the above equation
gc = ∫x * (3 - |x - 2|) dx/∫3 - |x - 2| dx
Integrate the numerator and the denominator of the above equation
gc = [-1/6(x - 2)((2|x -2| - 9)x + 2|x - 2| - 18)]/[3x - 1/2[|x - 2|(x - 2)]]
Recall that the interval is given as x ∈ [0, 3]
Substitute the interval values in the above equation.
The equation is then simplified using a graphing calculator.
So, we have
gc = (65/6)/(13/2)
Express the quotient expression as a product
gc = (65/6) * (2/13)
Divide 65 by 13
gc = 5/6 * 2
Divide 2 by 6
gc = 5/3
Hence, the geometric center of the graph under the function is 5/3
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1. The correlation coefficient on a scatter plot representing the variables for the amount of weight a body builder can lift in a gym and the amount of protein the body builder takes each day is 0.76. Describe the meaning of this correlation coefficient.
A
very Strong positive linear relationship between the two variables
B
very Strong negative linear relationship between the two variables
C
moderate positive linear relationship between the two variables
D
no relationship between the two variables
A correlation coefficient of 0.76 indicates a very strong positive linear relationship between the two variables.
What does the correlation coefficient mean?Correlation is a statistical measure used to measure the linear relationship that exists between two variables.
If the sign of the correlation coefficient is positive, it means that the two variables exhibits a positive correlation. The closer to 1, the correlation coefficient is, the stronger the linear relationship.
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answers for these? pls
Answer:
6a. 13.5m
6b. 12.4m
Step-by-step explanation:
We can use trig identities to solve these problems because each triangle is a right triangle.
6a. Find the measure of the hypotenuse.
Using the angle in the top corner, which is defined as 66 degrees and its adjacent side, we can find the hypotenuse. Remember that the hypotenuse is the longest side, which in this case would be AB. The adjacent side is the side next to the angle that is not the hypotenuse, in this case it would be AC, which is shown to be 5.5m.
The trig identity cos(x) is defined as adjacent/hypotenuse, or the value of the adjacent side divided by the value of the hypotenuse, where x is the degrees of the angle.
So we can set up the equation:
cos(x)=adj/hyp
If we know that x=66 (the degree of the angle) and adj=5.5m, we can substitute this into the equation. Let c represent the hypotenuse.
cos(66)=5.5/c
Then we can multiply by c:
c*cos(66)=5.5
Then divide by cos(66):
c=5.5/cos(66)
Use a calculator to estimate that c approximately equals 13.5m when rounded to the nearest tenth (remember to use degree mode because our angle is measured in degrees).
6b. Find the measure of side a.
Side a is the side opposite to angle A. This can also be known as side CB or the bottom of the triangle.
Method 1: Use trig identity tan(x)tan(x)=opp/adj
Remember x=66 and adj=5.5m. Let a represent the opposite side. Plug in these values into the equation:
tan(66)=a/5.5
Multiply both sides by 5.5:
a=tan(66)*5.5
Use a calculator to estimate that a approximately equals 12.4m when rounded to the nearest tenth (remember to use degree mode because our angle is measured in degrees).
Method 2 (I would recommend method 1, however because you are basing this answer off of the first answer, and in a test or a quiz, you might not be sure if your first answer was correct):
Use Pythagorean Theorem:
a^2+b^2=c^2
c, or the hypotenuse is 13.5m as found in out last problem, and b, the adjacent side is 5.5m which was a given. Substitute these values into the equation:
a^2+5.5^2=13.5^2
a^2+30.25=182.25
a^2=152a=sqrt(152) which rounds to 12.3m, which is almost the same as Method 1, however our answers are different because we used a rounded value of b, rather than the approximate.
Which ordered pair is in the inverse of
the relation given by p?y + 5y= 0?
Remember that an ordered pair is of the form (x, y), then the ordered pairs on the inverse of the relation are (x, -x/5).
Which ordered pair is in the inverse of the relation given?Assuming the given relation is:
y + 5x = 0
We can rewrite it to:
y = -5x
Then the inverse will be a function g(x) such that:
y = -5*g(x) = x
Solving for g(x):
g(x) = (-x/5).
Then the inverse of the relation is:
y = -x/5
Remember that an ordered pair is of the form (x, y), then the ordered pairs on the inverse of the relation are (x, -x/5).
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Rectangle A has side lengths of 6\text{ cm}6 cm6, start text, space, c, m, end text and 3.5\text{ cm}3.5 cm3, point, 5, start text, space, c, m, end text. The side lengths of rectangle B are proportional to the side lengths of rectangle A.
What could be the side lengths of rectangle B?
Choose 2 answers:
The side lengths of rectangle is 3 cm and 1.75 cm and 5.25 cm and 9 cm.
According to the statement
we have given that Rectangle A has side lengths of 6 cm and 3.5 cm
And The side lengths of rectangle B are proportional to the side lengths of rectangle A.
And we have to Find that the What could be the side lengths of rectangle B?
A 3 cm and 1.75 cm
B 5 cm and 2.5 cm
C 7 cm and 7 cm
D 12 cm and 5 cm
E 5.25 cm and 9 cm
Here we see that the side B are proportional to side length A of rectangle.
So,
Let say sides of rectangle B are a and b corresponding to sides 6 and 3.5 cm
=> a/6 = b/3.5
=> a/b = 6/3.5
=> a/b = 12/7
A 3 cm and 1.75 cm
3/1.75 = 12/7
Hence this is proportional
B 5 cm and 2.5 cm
5/2.5 = 2 ≠ 12/7
Not Proportional
C 7 cm and 7 cm
7/7 = 1 ≠ 12/7
Not Proportional
D 12 cm and 5 cm
12/5 ≠ 12/7
Not Proportional
E 5.25 cm and 9 cm
9/5.25 = 36/21 = 12/7
Hence this is proportional
So, 3 cm and 1.75 cm and 5.25 cm and 9 cm could be the side lengths of rectangle B.
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Which of the following are true?
The company stock you are monitoring for your Economics class increases five-eighths point the first week and then it increases one- half point the second week and one-quarter point the third week. What is the total increase during the three weeks?
Based on the change in the company stock over the three weeks, the total increase in those three weeks is 1.38%.
how much did the stock increase by?assuming the stock has a value of $1, the value in the third week would be:
= 1 x (1 + 5/8%) x (1 + 1/2%) x (1 + 1/4%)
= $1.013809453125
the total increase is:
= (1.013809453125 - 1) / 1
= 1.38%
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? Question
Warm-Up
Given: AB || CD
m/ZYB = 60°
Prove: m/DXW = 120°
A
W
Z
Y/60°
X
Select the correct answer from each drop-down menu.
Statements
AB || CD
m/ZYB
ZYXDand ZDXWform a linear pair.
K
B
=
60°
m/YXD
m/DXW = 120°
Reasons
given
given
definition of a linear pair
corresponding angles have equal measures
The missing Statement and reason for the transverse line angles is; m∠YXD = 60° and Supplementary angles sum up to 180°.
How to prove congruent angles?Statement 1; AB ║ CD
Reason 1; Given
Statement 2; m∠ZYB = 60°
Reason 2; Given
Statement 3; ∠YXD and ∠DXW form a linear pair
Reason 3; Definition of Linear Pair
Statement 4; m∠YXD = 60°
Reason 4; Corresponding angles have equal measure.
Statement 5; m∠DXW = 120°
Linear pairs usually sum up to 180° because they are supplementary angles. Thus;
m∠YXD = 180° - 60° = 120°
Reason 5; Supplementary angles sum up to 180°.
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A manufacturer has a steady annual demand for 38016 cases of sugar. It costs $9 to store 1 for 1 year, $33 in set up cost to produce each batch, and $18 to produce each case. Find the number of cases per batch that should be produced to minimize cost.
Based on the setup costs, the steady annual demand, and the costs to store, the number of cases to produce to minimize cost is 528 units .
How many cases should be produced to minimize cost?This can be found by using the Economic Order Quantity.
= √ ( (2 x Setup costs x annual demand) / holding costs for the year)
Solving gives:
= √ ( ( 2 x 33 x 38,016) / 9)
= √278,784
= 528 units
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In Fig. 6.39, sides QP and RQ of ΔPQR are produced to points S and T respectively. If ∠SPR = 135° and ∠PQT = 110°, find ∠PRQ.
[tex] \: [/tex]
[tex] \leadsto \sf{ \pink{Pls \: give \: me \: correct \: answer!!}}[/tex]
Thank u :)
[tex] \huge{↬ \boxed{ \sf{ \pink{A\green{n \blue{s \color{yellow}w \red{e \orange{r}}}}}}}}[/tex]
Given: ∠SPR = 135° and ∠PQT = 110°To find: ∠PRQ[tex] \leadsto[/tex]According to Angle sum property of a triangle , sum of the interior angles of a triangle is 180°.
➱ ∠SPR + ∠QPR = 180° [Linear pair]
➱ 135° + ∠QPR = 180°
➱ ∠QPR = 180° - 135°
➱ ∠QPR = 45°.....(i)
➱ ∠PQT + ∠PQR = 180° [Linear pair]
➱ 110° + ∠PQR = 180°
➱ ∠PQR = 180° - 110°
➱ ∠PQR = 70°.....(ii)
Now,➛ ∠PQR + ∠QPR + ∠PRQ = 180° [Angle sum property of a triangle]
➱ 70°+ 45° + ∠PRQ = 180° [from (i) and (ii)]
➱ ∠PRQ = 180° - 115°
➥ ∠PRQ = 65°
hope it's help u!! :D
Sketch the graph of y = (x-3)^2 -25, than select the graph that corresponds to your sketch.
Answer: graph c
Hope I was able to help
On which intervals is the function increasing? Choose
all that apply.
The function is increasing on the intervals:
(-∞, 3] and [5, ∞)
Then the correct options are a and c.
On which intervals is the function increasing?
The function is increasing when, reading from left to right, we can see that the curve goes upwards.
By looking at the graph, we can see that the function increases between -∞ and 3, and also increases between 5 and ∞, then the correct options are a and c-
(-∞, 3] and [5, ∞)
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Which transformations could have occurred to map triangle ABC triangle A^ * B^ n C^ prime
Reflection and dilation is the transformation which will occur to map triangle ABC triangle to A^ * B^ n C^ prime.
What is a Triangle?This refers to a plane figure which has features such as three angles and three sides.
Reflection and dilation involves flipping and enlargement/reduction respectively which gives rise to the sides being changed.
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Answer:
c. a reflection and a dilation
Step-by-step explanation:
From its founding through 2012, the Rock and Roll Hall of Fame has inducted 303 groups or individuals. Forty-seven of the inductees have been female or have included female members.1 The full dataset is available in RockandRoll.
The probability of inductees who are female will be 0.155.
How to illustrate the probability?Question: What proportion of inductees have been female or have included female members?
From the information, 303 groups or individuals and forty-seven of the inductees have been female or have included female members.
Therefore, the proportion will be:
= 47/303
= 0.155
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the time between customer visits to the bank from midday to 1pm is evenly distributed over the period from 0 to 120 seconds. what is the standard deviation of the timeout?
Using the uniform distribution, the standard deviation of the timeout is of 34.64 seconds.
What is the uniform probability distribution?It is a distribution with two bounds, a and b, in which each outcome is equally as likely.
The standard deviation is:
[tex]S = \sqrt{\frac{(b - a)^2}{12}}[/tex].
For this problem, the bounds are:
a = 0, b = 120.
Hence the standard deviation is found as follows:
[tex]S = \sqrt{\frac{(120 - 0)^2}{12}} = 34.64[/tex].
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The quantities xxx and yyy are proportional. xxx yyy 777 353535 121212 606060 202020 100100100 Find the constant of proportionality (r)(r)left parenthesis, r, right parenthesis in the equation y=rxy=rxy, equals, r, x. r =r=r, equals
The constant of proportionality of our given tables is; 5.
How to find the constant of Proportionality?We are given that x and y are proportional, and this means that:
y = r*x
where;
r is the constant of proportionality.
We are given the table;
x y
7 35
12 60
20 100
Now, we can replace those values in our equation and get, for the first pair: 35 = r*7
r = 35/7 = 5
For the second pair:
60 = r*12
60/12 = r
r = 5
Thus, we can conclude that the constant of proportionality is 5.
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Answer: 3
Step-by-step explanation:
How should I solve this?
Inscribed angles that are formed by segments which extend from one side of the hypotenuse to the other are right angles.
Therefore, angle PRQ is a right angle and is equal to 90 degrees.
53y - 16 = 90
53y = 106
y = 2
Hope this helps!
Answer:
y=2
Step-by-step explanation:
the angle is 90 degrees which is equal to (53y-16).therefore find a number which you can substitute to get 90 which is y=2
answer as soon as possible
The area of the equilateral triangle is 110.9 cm
How to find area of a triangle?area of a triangle = 1 / 2 bh
where
b = baseh = heightTherefore,
tan 60 = opposite / adjacent
tan 60 = 8√3 / x
x = 8√3 / √3
x = 8
hence,
b = 8 + 8 = 16
Therefore,
area of a triangle = 1 / 2 × 16 × 8√3
area of a triangle = 64√3
area of a triangle = 110.851251684
area of a triangle = 110.9 cm
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a seller sold his house $240,000, which was 92 percent of the list price. what did the house list for?
The list price of the house is $260,869.57
What is a list price?
This is the price the property is valued to sell at in an arm's length transaction in a transaction that occurs between independent parties.
In this case, the property was sold for 92% of its list price, which means the sales price is 92% multiplied by the list price.
sales price=92%* list price
sales price=$240,000
list price=unknown(assume it is X)
$240,000=92%*X
X=$240,000/92%
X=$260,869.57
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Question 19 of 25
f(x)=√x-6. Find the inverse of f(x) and its domain.
Answer:
f¯¹(x)=x²+12x+36
Step-by-step explanation:
[tex]f(x) = \sqrt{x} - 6 \\ substitute \: y \: for \: f {}^{ - 1} (x) \\ y = \sqrt{x} - 6 \\ interchange \: x \: and \: y \\ x = \sqrt{y} - 6 \\ swap \: the \: side \: of \: the \: equation \\ \sqrt{y } - 6 = x \\ move \: the \: constant \: to \: the \: right \: hand \: side \\ \sqrt{y} = x + 6 \\ square \: both \: sides \: of \: the \: equation \\ y = x {}^{2} + 12x + 36 \\ substitute \: f \frac{}{ -1} (x) \: for \: y \\ f {}^{ - 1} (x) = x {}^{2} + 12x + 36 \\ domain \: x∈R[/tex]
The isosceles trapezoid is part of an isosceles triangle with a 34° vertex angle. What is the measure of an acute base angle of the trapezoid? Of an obtuse base angle? The diagram is not drawn to scale.
What is the values of x?
Answer:
x = 34
Step-by-step explanation:
complementary angle sum to 90°
sum the 2 angles and equate to 90
x + x + 22 = 90
2x + 22 = 90 ( subtract 22 from both sides )
2x = 68 ( divide both sides by 2 )
x = 34
A university freshman class has 9900 students 4554 of thoses students are majoring in computer science what percentage of the class is computer science majors
Given the total number of students in the university freshman class and the number of students majoring in computer science, the percentage of the class majoring in computer science is 46%.
What percentage of the class is computer science majors?Percentage is simply number or ratio expressed as a fraction of 100.
It is expressed as;
Percentage = ( Part / Whole ) × 100%
Given the data in the question;
Total number of students or Whole = 9900Number of students majoring in computer science or Part = 4554Percentage of the class majoring in computer science = ?We substitute the given values into the above equation.
Percentage = ( Part / Whole ) × 100%
Percentage = ( 4554 / 9900 ) × 100%
Percentage = ( 0.46 ) × 100%
Percentage = 46%
Given the total number of students in the university freshman class and the number of students majoring in computer science, the percentage of the class majoring in computer science is 46%.
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Reflect the given triangle over the line y=-X
TOP (3 6 3)
BOTTOM (-3 3 3)
The equation rule for the reflection of the triangle over the line y = -x is given as (x, y) ⇒ (-y, -x)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
The equation rule for the reflection of the triangle over the line y = -x is given as (x, y) ⇒ (-y, -x)
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Factories completely 2x * (2x + 1) ^ 2 + (2x + 1)(4x ^ 2 - 3)
The factored form of the polynomial is (x - 0.556) · (x + 0.528 - i 0.242) · (x + 0.528 + i 0.242).
How to factor an algebraic equation
In this question we have an algebraic expression to be expanded by means of algebraic properties, the purpose of this handling is to modify the polynomial until its standard form is finally obtained and later we find its factor form by Cardano's method. Now we proceed to show the procedure in detail:
2 · x · (2 · x + 1)² + (2 · x + 1) · (4 · x² - 3) Given
2 · x · (4 · x² + 4 · x + 1) + (2 · x + 1) · (4 · x²) + (2 · x + 1) · (- 3) Perfect square trinomial/Distributive property
8 · x³ + 4 · x² + 2 · x + 8 · x³ + 4 · x² - 6 · x - 3 Distributive property/(- 1) · a = - a
16 · x³ + 8 · x² - 4 · x - 3 Distributive property/Definitions of addition and subtraction
(x - 0.556) · (x + 0.528 - i 0.242) · (x + 0.528 + i 0.242) Cardano's method/Result
The factored form of the polynomial is (x - 0.556) · (x + 0.528 - i 0.242) · (x + 0.528 + i 0.242).
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Robert can mow a 600 square lawn in 1 hour and 20 minutes. How many lawns in the same size's can he mow in 8 hours?
Please help ASAP
What of the secants below is a secant?
The secant in the diagram is [tex]\overline{AD}[/tex]
Segment AD intersect the circle at two points. So it can be a secant.
We have been given that a circle of center O. We have to find the segment that is secant.
What is Secant?Secant : If a line which intersect the circle at two points.Then the line segment is called secant.
If the ray lies onto the considered line segment(overlapping), then it can be said belonging to the considered line segment.
(line segment has 2 fixed ends, whereas a ray has one end only, other end is not fixed)
Segment OB intersect the circle at one point B only. so OB cannot be a Secant.
Segment AD intersect the circle at two points. So it can be a secant.
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