Solution
Question 1:
[tex]\begin{gathered} \text{ On day 1, 3 rabbits hopped out} \\ \text{ On day 2, }3\times2=6\text{ rabbits hopped out} \\ \text{ On day 3, }3\times2\times2=3\times2^2\text{ rabbits hopped out} \\ \text{ On day 4, }3\times2\times2\times2=3\times2^3\text{ rabbits hopped out} \\ \\ \text{Following this pattern, we can find the number of rabbits that will hop out on a day n.} \\ \\ \text{ On day }n,3\times2\times2\times2\ldots\times2=3\times2^{n-1}\text{ rabbits hopped out} \\ \\ \text{Thus, the exponential function to model this scenario is given below as } \\ \\ f(n)=3\times2^{n-1} \end{gathered}[/tex]Question 2:
[tex]\begin{gathered} \text{The question is asking for the number of rabbits that will hop out on day 13} \\ \text{ We can simply apply our formula and this implies that }n=13 \\ \\ \therefore f(13)=3\times2^{13-1} \\ \\ f(13)=3\times2^{12}=12,288 \\ \\ \text{Thus, the number of rabbits that will hop out of the hat on the 13th Day is 12,288} \end{gathered}[/tex]Final Answer
Question 1:
The exponential function to model the scenario is
[tex]f(n)=3\times2^{n-1}[/tex]
Question 2:
The number of rabbits that will hop out of the hat on the 13th Day is 12,288 rabbits
#3 iFind the volume of the sphere. Round your answer to the nearest hundredth.4 ftThe volume is aboutcubic feet.
Given: A sphere with a radius of 4 ft.
Required: To determine the volume of the sphere.
Explanation: The volume of a sphere is given by the formula-
[tex]V=\frac{4}{3}\pi r^3[/tex]Substituting the value of the radius, r=4 into the formula as-
[tex]V=\frac{4}{3}\times3.14\times4^3[/tex]Further solving-
[tex]\begin{gathered} V=267.946\text{ ft}^3 \\ \approx267.95\text{ ft}^3 \end{gathered}[/tex]Final Answer: The volume is about 267.95 cubic feet.
F=9/5C + 32 solve for C
To solve for C let us do these steps
1. Put the term of C on one side and the other terms on the other side
Subtract 32 from both sides to move the term 32 to the other side
[tex]\begin{gathered} F-32=\frac{9}{5}C+32-32 \\ F-32=\frac{9}{5}C \end{gathered}[/tex]2. Make the coefficient of C = 1
Divide both sides by 9/5
[tex]\begin{gathered} \frac{F-32}{\frac{9}{5}}=\frac{\frac{9}{5}C}{\frac{9}{5}} \\ \frac{5}{9}(F-32)=C \\ C=\frac{5}{9}(F-32) \end{gathered}[/tex]You can Multiply the bracket (F- 32) by 5/9
[tex]C=\frac{5}{9}F-\frac{160}{9}[/tex]Which is the best estimate for the sum 2/9+10/11? * O A. 0 + 0 = 0 OB. 1/2 + 1/2=1 O C. 1 + 1 = 2 O D. 0 + 1 = 1 Please explain the process of how you at your answer
this is because 9 is bigger than 2 almost 4 times, so the answer of the division must be close to 0.
now on the other side
[tex]\frac{10}{11}\approx1[/tex]10 is still smaller than 11 but the difference is small causing that the division be aroun 0.9 or 1.
when you add the estimates together you obtain
[tex]\begin{gathered} \frac{2}{9}+\frac{10}{11}=\text{?} \\ 0+1=1 \end{gathered}[/tex]with the polynomial provided I need help finding the zeros and putting them onto the graph as well as drawing the line correctly
Let's multiply out the polynomial first:
[tex]\begin{gathered} f(x)=(x-1)(x+3)^2 \\ f(x)=(x-1)(x^2+6x+9) \\ f(x)=x^3+6x^2+9x-x^2-6x-9 \\ f(x)=x^3+5x^2+3x-9 \end{gathered}[/tex]As we can see clearly that this is a cubic function, the highest degree is "3", which is odd. Hence,
This is an odd function.
Leading Coefficient is the number in front of the highest degree variable, that is x^3. So, there is "1" in front, thus the leading coefficient is positive.
Since we have one factor that is (x-1), it cuts the x-axis at:
x - 1 = 0
x = 1
We have another factor (x+3)^2. Since this is squared, here, the curve will bounce and touch the x-axis at:
(x+3)^2 = 0
x + 3 = 0
x = -3
Thus, the zeros are at x = 1 (cuts) and at x = -3 (bounces).
From basic cubic function (leading coefficient 0) we know as that x goes to infinity, the funtion goes to infinity. As x goes towards negative infinity, the function also approaches negative infinity.
Now, we can draw the curve:
Mr adams shares out 24 pencils between niamh and jack in the ratio 3:5
The number of pencils taken by Niamh is 9 and by jack is 15.
\What are ratios and proportions?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.
Given that Mr Adams shares out 24 pencils between Niamh and Jack in a ratio of 3:5.
Let the common factor between the sharing be x. Form an equation and solve.
Niamh's share = 3x
Jack's share = 5x
3x+ 5x = 24
8x = 24
x = 3
Niamh's share = 3x = 3 x 3 = 9 Pencils
Jack's share = 5x = 5 x 3 = 15 Pencils
Therefore, the number of pencils taken by Niamh is 9 and by jack is 15.
The complete question is given below.
Mr Adams shares out 24 pencils between Niamh and jack in a ratio 3:5. Find the number of pencils taken by Niamh and Jack.
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Ryan's motorcycle is now worth $2500. Ithas depreciated 12% each year since itwas purchased. If he bought it four yearsago, what did it cost brand new? Roundto the nearest dollar
Given a principal of P and a depreciation rate of r %,
after n years the new amount A is given by
[tex]A=P(1-r^{})^n[/tex]In this case,
[tex]A=\text{ \$2500 r = 12\% n = 4years}[/tex]Then, we have
[tex]\begin{gathered} 2500=P(1-0.12^4) \\ \text{ Which implies that } \\ P=\frac{2500}{(1-0.12)^4}=\frac{2500}{0.88^4}=\frac{2500}{0.5997}=\text{ \$4169} \end{gathered}[/tex]Hence the cost brand new is $4169
Draw parallel to . You can draw any length and place it anywhere on the coordinate plane, but not on top of .Find and record the ratio, n, of the length of to the length of . Then, multiply the length of by n and record the resulting length.
In a diagram,
Then,
[tex]\frac{DE}{BC}=n[/tex]For example, suppose that n=2; thus,
[tex]DE=2BC[/tex][tex]\Rightarrow2\cdot CA[/tex]We can form a new triangle DEF whose side EF is parallel to CA; therefore,
[tex]\Rightarrow EF=2CA[/tex]A pail of ice cream contains 5 quarts. Convert the volume to pints.
ANSWER
[tex]10pints[/tex]EXPLANATION
Given That the pail of ice cream contains 5 quarts
Recall 1 quarts gives 2 pints
Hence, 5 quarts will give;
[tex]5\times2=10[/tex]the mean of the ages of 5 brothers is 13 years. If the ages of four of the brothers are 12, 16, 14, and 8, how old is the fifth brother
Brothers
1. 12
2. 16
3. 14
4. 8
5. ?
___________________
mean of the ages of 5 brothers is 13 years
[tex]13\text{ = }\frac{12\text{ + 16 + 14 + 8 + x}}{5}[/tex][tex]13\cdot5\text{ = x + 50}[/tex][tex]65-50\text{ = x }[/tex][tex]\text{ x = 15 }[/tex]If W (-10,4),X(-3,-1)and Y (-5,11) classify angle WXY by its sides
So,
Let me graph the three points here below:
To classify this triangle by its sides, the first thing we need to do is to find the measure of each segment. For this, we could use the formula for the distance between two points for each one.
Let's start with segment WX.
[tex]\begin{gathered} WX=\sqrt[]{(4-(-1))^2+(-10-(-3))^2} \\ WX=\sqrt[]{(5^2)+(-7)^2} \\ WX=\sqrt[]{25+49} \\ WX=\sqrt[]{74} \end{gathered}[/tex]Now, continue with XY:
[tex]\begin{gathered} XY=\sqrt[]{(11-(-1))^2+(-5-(-3))^2} \\ XY=\sqrt[]{12^2+(-2)^2} \\ XY=\sqrt[]{148} \end{gathered}[/tex]And finally, WY:
[tex]\begin{gathered} WY=\sqrt[]{(11-4)^2+(-5-(-10))^2} \\ WY=\sqrt[]{7^2+5^2} \\ WY=\sqrt[]{74} \end{gathered}[/tex]As you can see, sides WY and WX are equal. So, the triangle has two equal sides and one different.
For this reason, the triangle is an isosceles triangle.
what is the mean and the mode of the dot plot
The mean of the data plot is approximately 12.2
Explanation:The data is: 6, 8, 8, 10, 11, 12, 12, 15, 15, 15, 16, 18
The mean of the given dot plot is:
[tex]\begin{gathered} \frac{6+2(8)+10+11+2(12)+3(15)+16+18}{12} \\ \\ =\frac{146}{12}=12.2 \end{gathered}[/tex]Calculate the distance between two points (-8,9) and (4,4)
If A=(-8,9) and B=(4,4), using the formula for distance between two points, we get:
[tex]\begin{gathered} d(A,B)=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \Rightarrow d(A,B)=\sqrt[]{(4-(-8))^2+(4-9)^2}=\sqrt[]{(12)^2+(-5)^2} \\ \Rightarrow d(A,B)=\sqrt[]{144+25}=\sqrt[]{169}=13 \\ d(A,B)=13 \end{gathered}[/tex]Therefore, the distance between A and B is 13 units
Formula for distance between two points:
[tex]d(A,B)=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Find the product (-10) (-2)
Remember that in a multiplication between two negative numbers the result always will be positive
(-10)(-2)=20
The result is 20
Answer:
20
Step-by-step explanation:
the product just means to multiply, so you do:
-10 x -2 = 20
If AB has length 10 and BC has length 19, findlength of AC:measure of angle B in degrees:measure of angle C in degrees:Answer should be in degrees and not radians.
Given a right angle triangle ABC
As shown in the figure:
The hypotenuse = BC = 19
One of the legs = AB = 10
We will use the Pythagorean theorem to find the other leg:
[tex]\begin{gathered} AB^2+AC^2=BC^2 \\ 10^2+AC^2=19^2 \\ AC^2=19^2-10^2 \\ AC^2=361-100=261 \\ AC=\sqrt[]{261}=16.16 \end{gathered}[/tex]Now, we will find the measure of the angle B:
[tex]\begin{gathered} \cos B=\frac{adjacent}{hypotenuse}=\frac{10}{19} \\ B=\cos ^{-1}\frac{10}{19}\approx58.24 \end{gathered}[/tex]The sum of the angles of the triangle = 180
so, the measure of angle C will be =
[tex]\begin{gathered} 180-(\angle A+\angle B) \\ =180-(90+58.24) \\ =180-148.24 \\ =31.76 \end{gathered}[/tex]So, as a conclusion to the answer:
[tex]\begin{gathered} AC=16.16 \\ \angle B=58.24 \\ \angle C=31.76 \end{gathered}[/tex]You hang two strands of decorative lights.
a strand of red and blue decorative lights a strand of yellow and green decorative lights
Strand 1: changes color every 16 seconds Strand 2: changes color every 28 seconds
Both strands just changed color. After how many seconds will the strands change color at the same time again?
The strands will change color at the same time again after
seconds.
Both the decorative light strands will change change the colors at the same time again after 448 seconds
In the above question, it is given that,
Two strands of decorative lights, red and blue is one strand and green and yellow is another are hanged
Strand one changes colors in = 16 seconds
Strand two changes colors in = 28 seconds
We need to find, after how many seconds will the strands change color at the same time again
To find this, we will take the LCM(Lowest Common Multiple) of both strands time
Factors of 16 = 2 x 2 x 2 x 2
Factors of 28 = 2 x 2 x 7
LCM( 16 and 28) = 2 x 2 x 2 x 2 x 2 x 2 x 7 = 448
Therefore, It can be concluded that, both the decorative light strands will change change the colors at the same time again after 448 seconds
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The table shows the number of gallons of paint Mrs. Brown used to paint the of rooms in her house. Find the slope of the line
Answer:
The slope is [tex]\frac{3}{2}[/tex] or [tex]1.5[/tex]
Step-by-step explanation:
The slope formula: [tex]\frac{y2-y1}{x2-x1}[/tex]
Now, in this case, when you get tables, you could choose two coordinates.
So, for instance, you chose the coordinates: (2,3) and (6,9)
Since we have the two coordinates, we now could solve for the slope.
-
Substituting and finding the slope:
1) [tex]m =\frac{9-3}{6-2} \\[/tex]
2) [tex]m = \frac{6}{4} = \frac{3}{2}[/tex]
3) [tex]m = \frac{3}{2}[/tex] or [tex]1.5[/tex]
Mr. Emmer gave a test in his Chemistry class. The scores were normally distributed with a mean of 82 and a standard deviation of 4. A student is randomly chosen. What is the probability that the student scores a 70 or below?
The probability that a randomly chosen student scores 70 or below is 0.0013
Firstly, we want to calculate the z-score
We have this as;
[tex]\begin{gathered} z-\text{score = }\frac{x-\mu}{\sigma} \\ \text{where x = 70} \\ \mu\text{ = mean = 82} \\ \sigma\text{ = standard deviation = 4} \\ z-\text{score = }\frac{70-82}{4}\text{ = -3} \end{gathered}[/tex]Using this z-score, we proceed to calculate the probability as follows;
[tex]P\text{ (X }\leq-3)[/tex]We use the standard normal distribution table for this
As we can see, this z-score value falls within 3 standard deviation from the mean
According to the empirical rule, the probability value here is 0.0013
15. What is missing in the problem, 48 is ____ % of 120? A. base B. percentage C. rateD. time
The following equation-definition will be consider to solve the problem:
[tex]Base*Rate=Part[/tex]Where the base in this case is 120.
The rate is the porcentage, which is the missing part in the problem.
And 48 is the part. Hence, the solution is:
The solution is C. rate
Consider the following expression -2m(m+n-4)+5(-2m+2n)+n(m+4n-5) which of the following is an equivalent expression
The given expression is
[tex]-2m(m+n-4)+5(-2m+2n)+n(m+4n-5)[/tex]First, we use the distributive property
[tex]-2m^2-2mn+8m-10m+10n+mn+4n^2-5n[/tex]Then, we reduce like terms
[tex]-2m^2+4n^2-mn-2m+5n[/tex]Hence, the equivalent expression is[tex]-2m^2+4n^2-mn-2m+5n[/tex]Hey I got the the idea! But it looks like the answer doesn’t have the other number? Which kinda makes me think it if we even did this lol!
The area of a right triangle can be calculated as half the product of each leg length.
So, if the legs measure 4 cm and 3 cm, we have:
[tex]\begin{gathered} A=\frac{4\cdot3}{2} \\ A=2\cdot3 \\ A=6\text{ cm}^2 \end{gathered}[/tex]Therefore the triangle area is 6 cm².
Which of the following shows the prime factorization of 72 using exponential notation?2.6²8.923 . 322².32O
Remember that any natural number can be written as a product of prime numbers. Prime numbers are those numbers that are only divisible by one and themselves.
In the case of 72:
[tex]\begin{gathered} 72=9\cdot8 \\ \Rightarrow72=(3\cdot3)\cdot(2\cdot2\cdot2) \\ \Rightarrow72=2^3\cdot3^2 \end{gathered}[/tex]Therefore, the answer is the third option 72=2^3*3^2
Please explain how Pascals triangle works?
Pascals triangle or Pascal's triangle is a special triangle that is named after Blaise Pascal, in this triangle, we start with 1 at the top, then 1s at both sides of the triangle until the end. The middle numbers are so filled that each number is the sum of the two numbers just above it.
Generally, we can use Pascals' triangle to find the coefficients of binomial expansion
For example, we want to expand
[tex](x\text{ + y\rparen}^2[/tex]Using Pascal's triangle, we can get the coefficients of the expansion:
[tex](x\text{ + y\rparen}^2\text{ = 1x}^2\text{ + 2xy + 1y}^2[/tex]Hong Tang's gross weekly salary is $615. His weekly federal withholding is $55. The Social Security tax is 6.2 percent of the first $90,000. The Medicare tax is 1.45 percent of gross pay. The state tax is 1.5 percent of gross pay. Each week he pays $22.40 for medical insurance. How much is deducted from Tang's weekly wages for state tax and Medicare tax combined?
We have that the Medicare tax is 1.45% of gross pay, and the state tax is 1.5%. Then, if Hong Tang's gross weekly salary is $615, then::
[tex]\begin{gathered} (615)(0.0145)=8.92 \\ (615)(0.015)=9.22 \\ \Rightarrow8.92+9.22=18.14 \end{gathered}[/tex]therefore, from state tax and Medicare tax combined, Hong Tang gets deducted $18.14
I need so help with my math
We have to change the oz to lb. So we get that
[tex]\begin{gathered} 5oz=0.3125lb \\ 10oz=0.625lb \end{gathered}[/tex]so the problem goes as
[tex]9.3125-6.625=2.6875lb[/tex]and that is
[tex]2lb11oz[/tex]What's the perimeter of rectangle DEFG, shown?
The perimeter is the sum of the length of all the sides.
1. A segment has a left end named P (0,14) and a midpoint named F (-1,-2). Find the
coordinates of x and y of the other end of the segment.
( -2,-18 ) is the coordinate of the other endpoint of the segment.
What are the coordinates of the endpoint?
The midpoint formula is expressed as;
M = ( (x₁+x₂)/2, (y₁+y₂)/2 )
Given the data in the question;
Endpoint P (0,14)
x₁ = 0y₁ = 14Midpoint F (-1,-2)
x = -1y = -2Endpoint 2
x₂ = ?y₂ = ?To determine the other endpoint, plug the given points into the midpoint formula above and solve for x₂ and y₂.
(x,y) = ( (x₁+x₂)/2, (y₁+y₂)/2 )
(-1,-2) = ( (0 + x₂ )/2, ( 14 +y₂ )/2 )
(-1,-2) = ( (0 + x₂ )/2, ( 14 +y₂ )/2 )
First we solve for x₂.
-1 = (0 + x₂ )/2
-1 × 2 = 0 + x₂
-2 = x₂
x₂ = -2
Next, solve for y₂.
-2 = ( 14 + y₂ )/2
-2 × 2 = ( 14 + y₂ )
-4 = 14 + y₂
y₂ = -4 - 14
y₂ = -18
Therefore, the coordinates of the endpoint are ( -2,-18 ).
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1. Use a calculator to find each angle measure to the nearest degree.a) sin A = 0.4848b) cos Y = 0.7431c) cos X = 0.4226d) tan B = 19.0811
Given
a) sin A = 0.4848
b) cos Y = 0.7431
c) cos X = 0.4226
d) tan B = 19.0811
To find:
Each angle measure to the nearest degree.
Explanation:
It is given that,
a) sin A = 0.4848
b) cos Y = 0.7431
c) cos X = 0.4226
d) tan B = 19.0811
That implies,
a) sin A = 0.4848.
Then,
[tex]\begin{gathered} A=\sin^{-1}(0.4848) \\ =28.99\degree \\ =30\degree \end{gathered}[/tex]b) cos Y = 0.7431.
Then,
[tex]\begin{gathered} Y=\cos^{-1}(0.7431) \\ =42.0038\degree \\ =42\degree \end{gathered}[/tex]c) cos X = 0.4226.
Then,
[tex]\begin{gathered} X=\cos^{-1}(0.4226) \\ =65.001\degree \\ =65\degree \end{gathered}[/tex]d) tan B = 19.0811.
Then,
[tex]\begin{gathered} B=\tan^{-1}(19.0811) \\ =86.99\degree \\ =87\degree \end{gathered}[/tex]Hence, the measure of each angle is,
a) A = 30°.
b) Y = 42°.
c) X = 65°.
d) B=87°.
the diagram below is a picture of a broken post. determine the height of the post before it was broken.
step 1
Find the hypotenuse of the right triangle
Applying Pythagorean Theorem
c^2=7^2+24^2
c^2=625
c=25 ft
therefore
the height is equal to
h=25+24=49 ft
answer is 49 ftGiven f of x find g of z and h of x such that
ANSWER
[tex]\begin{equation*} \begin{cases}{g(x)=\sqrt[3]{x}}+1 \\ {} \\ {h(x)=4x^2-2}\end{cases} \end{equation*}[/tex]EXPLANATION
If f(x) is,
[tex]f(x)=\sqrt[3]{4x^2-2}+1[/tex]There are many possibilities for functions g(x) and h(x) such that f(x) = g(h(x)). One of them is that g(x) is,
[tex]g(x)=\sqrt[3]{x}+1[/tex]And h(x) is,
[tex]h(x)=4x^2-2[/tex]This way, in the composition g(h(x)), when we replace x in g(x) with h(x) we will get function f(x),
[tex]g(h(x))=\sqrt[3]{h(x)}+1=\sqrt[3]{4x^2-2}+1[/tex]Hence, one of the possible equations for g(x) and h(x) such that f(x) = g(h(x)) is:
[tex]\begin{cases}{g(x)=\sqrt[3]{x}}+1 \\ {} \\ {h(x)=4x^2-2}\end{cases}[/tex]What is the value of x?M (3x - 16) O (x + 6)N (x) A 5B 38 C 22D 42
From , the properties of triangle;
Angle M + Angle N + Angle O = 180
(3x -16) + (x + 6) + x = 180
3x - 16 + x + 6 + x = 180
5x - 10 = 180
5x = 180 + 10
5x = 190
x = 190/5
...