The constant of proportionality will be 3.
The complete question ks given below:-
Explain how to find the constant of proportionality for the ratio of robins to cardinals. A 2-column table with 4 rows. Column1 is labelled Cardinals with entries 5, 6, 9, and 10. Column 2 is labelled Robins with entries 15, 18, 27, and 30.
What is the ratio?In mathematics, ratios are used to determine the relationship between two numbers it indicates how many times is one number to another number.
Given data will be arranged as follows:-
robins 15, 18, 27, 30.
cardinals 5, 6, 9, 10.
The constant of proportionality will be calculated by taking a ratio of the data:-
[tex]\dfrac{Cardinals}{Robins} =\dfrac{15}{5}=\dfrac{18}{6}=\dfrac{27}{9}=\dfrac{30}{10}=3[/tex]
Therefore the constant of proportionality will be 3.
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a tissue box has a lentgh of 11 inches a width of 5 inches and a height of 4 inches
find lim x->2 for f(x)=
{2x+1, x greater than or equal to 2
{x^2, x>2
a. 5
b. 4
c. 5 or 4
d. dne
LHL in not equal to RHL , Therefore the limit does not exists , Option D is the answer.(none)
What is the limit of a function ?The limit of a function at a certain point is the value that the function approaches as the argument of the function approaches the same point.
It is given that
lim x->2 for f(x)
[tex]\lim_{x \rightarrow 2^-}f(x) = \lim_{x\rightarrow 2^+}f(x)[/tex]
f(x) = 2x+1 x ≤2
f(x)= x² , x >2
When both the function tends to 2
Left Hand Limit
f(x) = 2 *2 +1
f(x) = 5
Right Hand Limit
f(x) = x² ,
f(x) = 4
LHL in not equal to RHL , Therefore the limit does not exists.
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The height in feet, h, of a model rocket t seconds after launch is given by the equation h (t) = 3 + 70 t minus 16 t squared. The average rate of change in h(t) between t = 1 second and t = 3 second is 6. What does the average rate of change tell you about the rocket?
The rocket is traveling six times as fast when t = 3 than it is when t = 1.
The rocket is at a greater height when t = 3 than it is when t = 1.
The rocket is 6 feet higher above the ground when t = 3 than it is when t = 1.
The rocket is traveling at a constant rate of 6 feet per second between t = 1 and t = 3.
The average rate of change in h(t) is 6.
What is Average Rate of change?It is a measure of how much the function changed per unit, on average, over that interval.
h(t) = 3 + 70t - 16t²
Average rate of change
At t = 1 second
h(1) = 3 + 70(1) - 16(1)^2
h(1) = 57
At t = 3 second
h(3) = 3 + 70(3) - 16(3)^2
h(3) = 69
Average rate of change = Δh / Δt
=[h(3) - h(1)] / (3 - 1)
= (69 - 57) / 2
= 12 / 2
= 6.
Hence, the rate of change is 6.
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Mr. Ramirez purchased 20 concert tickets for a total of $225. The concert tickets cost $15 for adults and $10 for children under the age of 12.
(AKS 16) What does the solution to the system of equations represent in the context of the problem? Explain.
Answer:
See below
Step-by-step explanation:
The solution will show the NUMBER Of adult and the NUMBER of child tickets purchased .
a = adult tickets cost = 15 a
c = children's tickets <=== this is equal to 20 - a
cost for children's tickets equals 10(20 - a)
15 a + 10c = 225 rememeber c = 20 -a <===put that in
15 a + 10 ( 20 -a) = 225 solve for a
15a + 200 - 10 a = 225
5 a = 25
a = 5 tix then c = 20 - a = 15 tix
When 7/11 is written as a decimal, what is the sum of the first 20 digits after the decimal point? Pls Help
There's a neat trick to finding the rational form of a repeating decimal number. Take for instance [tex]x=0.123123123\ldots[/tex]. Then
[tex]x = 0.123123123\ldots \\\\ \implies 1000x = 123.123123\ldots \\\\ \implies 1000x - x = 123.123123\ldots - 0.123123\ldots \\\\ \implies 999x = 123 \\\\ \implies x = \dfrac{123}{999}[/tex]
It's easy to reverse this method to find the repeating decimal form of [tex]\frac7{11}[/tex]. Let
[tex]x = \dfrac7{11}[/tex]
Multiply the numerator and denominator by 9,
[tex]x = \dfrac{63}{99}[/tex]
It follows that
[tex]x = \dfrac{63}{99} \\\\ \implies 99x = 63 \\\\ 100x - x = 63.6363\ldots - 0.6363\ldots \\\\ \implies x = 0.636363\ldots[/tex]
The first 20 digits after the decimal are made up of 10 each of 3 and 6, so the sum is 10 × (3 + 6) = 90.
Answer:
90
Step-by-step explanation:
Using long division, we find that Every group of two digits after the decimal point has a sum of 9 so the sum of the first 20 digits after the decimal point is 10*9=90
Simplify each expression
3+8b+4+7b-3
Answer:
9. 15b + 4
10. 4y + 6
11. 15r+72
12. 130n + 20
Step-by-step explanation:
9. Combine Like terms
10. Combine Like terms
11. Distribute the 8 into (r + 9) then combine like terms
12. Distribute 10 into (3n + 2 + 10n) then combine like terms
Answer:
[tex]\mathsf {9) 15b + 4}\\\mathsf {10) 4y + 6}\\\mathsf {11) 15r + 72}\\\mathsf {12) 130n + 20}[/tex]
Step-by-step explanation:
[tex]\textsf {Question 9}[/tex]
[tex]\mathsf {3 + 8b + 4 + 7b - 3}[/tex]
[tex]\mathsf {8b + 7b + 4 + 3 - 3}[/tex]
[tex]\mathsf {15b + 4}[/tex]
[tex]\textsf {Question 10}[/tex]
[tex]\mathsf {8 + 7y - 3y + 2 - 4}[/tex]
[tex]\mathsf {7y - 3y + 8 + 2 - 4}[/tex]
[tex]\mathsf {4y + 6}[/tex]
[tex]\textsf {Question 11}[/tex]
[tex]\mathsf {8(r + 9) + 7r}[/tex]
[tex]\mathsf {8r + 8(9) + 7r}[/tex]
[tex]\mathsf {8r + 7r + 72}[/tex]
[tex]\mathsf {15r + 72}[/tex]
[tex]\textsf {Question 12}[/tex]
[tex]\mathsf {10(3n + 2 + 10n)}[/tex]
[tex]\mathsf {10(13n + 2)}[/tex]
[tex]\mathsf {10(13n) + 10(2)}[/tex]
[tex]\mathsf {130n + 20}[/tex]
The volume of a cylinder with a height of 4 feet is 144n cubic feet what is the radius of the base of the cylinder V=nr2h
Answer: 6 ft
Step-by-step explanation:
[tex]144\pi =\pi(r^{2})(4)\\\\144\pi=4\pi r^{2}\\\\36=r^{2}\\\\r=\boxed{6 \text{ ft}}[/tex]
Use the FOIL method to evaluate the expression:
Answer:
[tex]\sf b.) \ 1 +2\sqrt{7}[/tex]
Explanation:
Foil method: (a + b)(c + d) = ac + ad + bc + bd
Solving steps:
[tex](4 - \sqrt{7} )(2 + \sqrt{7} )[/tex]
[tex](4)(2) + 4(\sqrt{7} ) + (-\sqrt{7} )(2) + (-\sqrt{7} )(\sqrt{7} )[/tex]
[tex]8 + 4\sqrt{7} - 2\sqrt{7} - 7[/tex]
[tex]8 -7 + 4\sqrt{7} - 2\sqrt{7}[/tex]
[tex]1 +2\sqrt{7}[/tex]
option b) 1 + 2√7
Step-by-step explanation:Foil property method :-
[tex] \red{ \boxed{ \orange{ \rm (a + b)(c + d) = ac + ad + bc + bd}}}[/tex]
then, on substituting the values,
[tex]\sf⇒ \: \: 8 + 4 \sqrt{7} - 2 \sqrt{7} - 7[/tex]
[tex]\sf⇒ \: \: \green{ \underline{\bold{ \red{1 + 2 \sqrt{7} }}}}[/tex]
Find the measure of a.
Answer:
10
Step-by-step explanation:
By the geometric mean theorem,
4/a = a/25100=a² (cross multiply)a=10 (square root both sides and take the positive solution)X Y
-2 6
0 3.5
2 1
4 -1.5
Which equations represent the data in the table?
Check all that apply.
y-6= =5 (x+2)
y-2=-(x-1)
y + 2 = S(x-6)
y-1=-(x-2)
y-3.5 = -1.25.x
Using the point-slope equation, the equations that represent the data are:
y - 6 = -1.25(x + 2)
y -3.5 = -1.25x
What is the Point-Slope Equation?Given a point (a, b) and slope (m), the point-slope equation is expressed as, y - b = m(x - a).
Find the slope (m) using two pairs from the table of values say, (-2, 6) and (2, 1):
Slope (m) = change in y / change in x = (6 - 1)/(-2 - 2) = 5/-4 = -1.25
Using the point, (a, b) = (-2, 6) and m = -1.25, plug the values into y - b = m(x - a):
y - 6 = -1.25(x - (-2))
y - 6 = -1.25(x + 2)
This cam be rewritten as:
y - 6 = -1.25x - 2.5
y - 6 + 2.5 = -1.25x
y -3.5 = -1.25x
The equations that represent the data in the table are:
y - 6 = -1.25(x + 2)
y -3.5 = -1.25x
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Ethan is using 30 cupcakes . he spreads mint icing on 1/5 of the cupcakes and chocolate on 1/2 of the reimagining cupcakes . the rest will get vanilla frosting. how many will have vanilla frosting
Answer:
12 Vanilla Frosted Cupcakes
Step-by-step explanation:
30 Cupcakes.
1/5 Of 30 is 6.
30 - 6 = 24.
24/2 = 12.
Im in math 2 and I just need help with this to pass please
Answer:
.7 I your answer to your question hope it's help
Answer:
[tex]\frac{7}{10}[/tex]
Step-by-step explanation:
35/50 --> [tex]\frac{7}{10}[/tex]
divide 35 by 5 = 7
divide 50 by 5 = 10
Otto used 5.5 cups of whole wheat flour and x cups of white flour in the recipe. What is the equation that can be used to find the value of y, the total amount of flour that Otto used in the recipe, and what are the constraints on the values of x and y? y=5.5x; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 5. y=5.5x; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 5.5. y=x+5.5; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 5. y=x+5.5; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 5.5.
Answer:
This situation of the recipe can be represented as y=x+5.5 and it is expected that x is ≥ 0 and y is ≥ 5.5.
What is the equation for this situation?
It is known the total amount of flour (y) is equivalent to the total amount of whole wheat flour (5.5) added to the total white flour (x). Therefore, the equation is:
y = x + 5.5
The possible values are
x = It is expected x is equalthan 0 or greater to it since the minimum amount of white flour that can be added is 0.
y = It is expected y is equal than 5.5 or greater to it since even if no
white flour is added the minimum total is 5.5.
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Step-by-step explanation:
This situation of the recipe can be represented as equation y = x+5.5 and it is expected that x is ≥ 0 and y is ≥ 5.5.
What is function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
For the given expression
y = x + 5.5
The possible values are
x = It is expected x is equal to 0 or greater to it
since the minimum amount of white flour that can be added is 0.
y = It is expected y is equal than 5.5 or greater to it since even if no
white flour is added the minimum total is 5.5.
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The radius is
cm.
The circumference in terms of is
✓ cm.
7
Using 3.14 for л, the approximate circumference of the
circle is
cm.
The circumference of this circle with a radius of 7 cm is equal to 44 cm.
Given the following data:
Radius of circular rug = 7 cm.π = 3.14.How to calculate the circumference of a circle?Mathematically, the circumference of a circle can be calculated by using this formula:
Circumference = 2πr
Where:
r is the radius of a circle.
Substituting the given parameters into the formula, we have;
Circumference = 2 × 3.14 × 7
Circumference = 43.96 ≈ 44 cm.
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There are 8 kids at a birthday party. If there are 6 girls and 2 boys at a party what fraction of the kids are girls?
Okay, so out of 8 kids, we know that 6/8 are girls and 2/8 are boys. Its asking us what fraction of the kids are girls. The denominator (the bottom part of the fraction will be the amount of kids at the party, 8) and the top part, the numerator, will be 6 as there are 6 girls at the party of the 8 attendees.
So the fraction is 6/8. However we can reduce this by dividing both sides of the fraction by a common factor, 2!
So your final answer is 3/4.
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Tom was able to save 35% more this year than he did last year. If he saved $140 last year, how much did he save this year?
Answer:
$189
Step-by-step explanation:
35% of 140 = 49
140 + 149 = 189
Tom's total saving this year is $189.
It is a 35 percent increased saving from last year's $140.
What are percentages?Percentages are fractional values where the denominator is fixed to be 100.
To convert percentage into number, we multiply by 100.
How to solve the question?In the question, we are informed that Tom was able to save 35% more this year than he did last year.
We are asked if he saved $140 last year, then how much did he save this year.
The increase in Tom's savings = 35% of last year's savings,
or, the increase = 35/100 * 140 (To convert percentage into quantity, we divide by 100).
or, the increase = $49.
Therefore, Tom's total savings this year = Last year's savings + Increase,
or, Tom's total saving this year = $140 + $49 = $189.
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To eliminate the y terms and solve for x in the fewest steps, by which constants should the equations be multiplied by before adding the equations together? first equation: 4x − 3y = 34 second equation: 3x 2y = 17
To eliminate the y terms and solve for x in the fewest steps, the first equation 4x - 3y = 34 should be multiplied by 2, and the second equation 3x + 2y = 17 should be multiplied by 3 before adding them.
Elimination is a process of solving a system of equations to eliminate one variable and solve for the other.
To eliminate the y terms from the equations,
first equation: 4x - 3y = 34, and
second equation: 3x + 2y = 17,
we take the L.C.M. of the coefficients of y, that is 3 and 2, which is 6, and multiply the equation by the value = (LCM of the coefficients/respective coefficient of y).
That is, for :
the first equation, we multiply the equation by (LCM of the coefficients/respective coefficient of y) = 6/3 = 2.
the second equation, we multiply by (LCM of the coefficients/respective coefficient of y) = 6/2 = 3.
Thus, to eliminate the y terms and solve for x in the fewest steps, the first equation 4x - 3y = 34 should be multiplied by 2, and the second equation 3x + 2y = 17 should be multiplied by 3 before adding them.
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Please Help! What is tan A?
Answer:
[tex]\fbox {tan A = 0.5333}[/tex]
Step-by-step explanation:
tan A = opposite side of ∠A / hypotenuse
tan A = 8 / 15
tan A = 0.5333
Answer:
tan A = perpendicular/ base
tan A = 8/15
tan A=0.5333
Step-by-step explanation:
please mark me as brainlest
If * >0 and y > 0, which expression is equivalent to √768x1937?
A. 8r4y6/12r4y
B. 16r4y6√3x¹y
C. 8r9y18/12xy
D. 16r9y18√3xy
The local public pool is a rectangle with two semicircles.
The area of the rectangle is
.
Using 3.14 for π and rounding to the nearest meter, the area of each half circle is
m2.
The area of the surface of the pool is
m2.
The area of the surface of the pool is 7322.64 m².
What is Area of rectangle?The area of rectangle is product of length and its breadth.
i.e., length * breadth
Given: Length = 100 m, Width = 52 m and Diameter = 52 m
Area of rectangle,
= 100 × 52
= 5200 m²
Now,
Area of semicircle = 1/2 × πr²
=1/2 × 3.14 × 26²
= 1061.32 m²
Hence, area of the surface of the pool is
= 1061.32 + 1061.32 + 5200
= 7322.64 m²
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5200 square meters, 1061, 7322
Solve ly + 21 > 6
() {yly <-8 or y> 4]
O (yly<-4 or y> 4}
(yly <-6 or y> 6}
[tex] |y + 2| > 6 \\ y + 2 > 6 \: \: \: or \: \: \: y + 2 < - 6 \\ y > 6 - 2 \: \: \: or \: \: \: y < - 6 - 2 \\ y > 4 \: \: \: or \: \: \: y < - 8[/tex]
Solution : ] -♾️ , -8 [ U ] 4, + ♾️ [
PLEASE GIVE BRAINLIEST
The graph of a system of inequalities shown
What is the inverse of the fraction FX = 1/4 x = -12
The inverse function of the function f(x) will be f⁻¹(x) = 4x + 48. Then the correct option is D.
The complete question is attached below.
What is inverse of a function?Suppose that the given function is
f: X → Y
Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is
f⁻¹: Y → X
It simply means, inverse of 'f' is an undo operator, that takes back the effect of 'f'
The function is given below.
f(x) = (1/4)x – 12
Then the inverse function of the function f(x) will be
(1/4)f⁻¹(x) - 12 = x
f⁻¹(x) = 4x + 48
Then the correct option is D.
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Hey need help on this question. Could I have a simple explaination please as I find it difficult to understand things
Answer:
y = 1.5x + 1
Step-by-step explanation:
→ Choose 2 points
( 2 , 4 ) ( -2 , -2 )
→ Find the gradient
-6 ÷ -4 = 1.5
→ Write into format
y = 1.5x + c
→ Substitute in ( 2 , 4 )
4 = 3 + c
→ Minus 3 from both sides
1 = c
y = 1.5x + 1
whats 10 + 4? i need to know if you answer you get 25 points
\frac { 6 ^ { n + 2 } - 6 ^ { n } } { 6 ^ { n + 1 } + 6 ^ { n } }
Solve this ...
this is the question of laws of indices(exponent)
Work Shown:
[tex]m = \frac{6^{n+2}-6^{n}}{6^{n+1}+6^{n}}\\\\m = \frac{6^{n}*6^2-6^{n}}{6^{n}*6^1+6^{n}}\\\\m = \frac{6^{n}*36-6^{n}}{6^{n}*6+6^{n}}\\\\m = \frac{6^{n}(36-1)}{6^{n}(6+1)}\\\\m = \frac{6^{n}(35)}{6^{n}(7)}\\\\m = \frac{35}{7}\\\\m = 5\\\\[/tex]
Therefore,
[tex]\frac{6^{n+2}-6^{n}}{6^{n+1}+6^{n}}=5\\\\[/tex]
Prove: 45= m/ZXY
Complete the proof. Number your reasons in the textbox below.
Step-by-step explanation:
since the two angles from a straight line, they make a linear pair and linear pairs are supplementery. by the angle addition postulate, you can determine that the two angles sum to 180. substituting the one angle mearsure that you are guven and using a bit of simple arithmetic and the subtraction property of equality, you can determine that the other angle,angle YXZ, is 45 degrees. I hope this is helpful
Question 3 of 32
Which of the following could be the equation for a parabola that opens to the
left with vertex (-17, 2)?
A. x=-3(y-2)² - 17
OB. x-3(y +17)² +2
OC. y-3(x-2)² - 17
D. y=3(x+17)² +2
Answer:
A
Step-by-step explanation:
The parabola opens to the left, so this eliminates C and D.
Also, the vertex is at (-17, 2), and out of A and B, the only parabola with this vertex is A.
Points A, B, and C, form a triangle. The distance between point A and point B is 15 yards. The distance between point B and point C is 25 yards. Pete walks directly from point A to point C, without passing through point B. What is the direct distance from A to C?
How far would Pete walk if he went from A to B to C? yards
The direct distance from A to C is more than yards.
The inequality w < represents the distance, w, that Pete might save by taking the direct path.
The total distance if Pete walks from A to B to C is 40 yards, the direct distance from A to C is more than 10 yards, and an inequality w < 30
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have:
Points A, B, and C, form a triangle. The distance between point A and point B is 15 yards. The distance between point B and point C is 25 yards.
Total distance if Pete walks from A to B to C:
= 15 + 25 = 40 yards
As we know in the triangle the sum of the two sides is greater than the third side.
25 + 15 > AC
40 > AC
or
AC < 40
The direct distance from A to C is more than 10(25-15) yards.
The inequality w < 30 represents the distance, w, that Pete might save by taking the direct path.
Thus, the total distance if Pete walks from A to B to C is 40 yards, the direct distance from A to C is more than 10 yards, and an inequality w < 30
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Answer:
40, 10, 30
see picture
Step-by-step explanation:
How do I solve the following system of inequalities graphically on the set of axes below?
y> x-3 y≥− 6/1 x+4