So the numbers we have are:
-2, 3/4, -1/3, 0.2, -1, 1/2 & -0.8
So the numbers from least to greatest go as follows:
-2, -1, -0.8, -1/3, 0.2, 1/2, 3/4
how many cubic blocks with a side length of 1/6 cm are needed to fill the volume of this prism?
To answer this question we will compute the volume of the given rectangular prism, and the volume of a cube with a side of 1/6cm, and then we will divide the volume of the given prism by the volume of the cube.
The volume of the given rectangular prism is:
[tex]V_p=\frac{1}{6}cm\times\frac{1}{2}cm\times\frac{1}{2}cm.[/tex]Simplifying the above result we get:
[tex]V_p=\frac{1}{24}cm^3.[/tex]The volume of a cube with a side length of 1/6cm is:
[tex]V_c=(\frac{1}{6}cm)^3=\frac{1}{216}cm^3.[/tex]Therefore we need
[tex]\frac{V_p}{V_c}=\frac{\frac{1}{24}cm^3}{\frac{1}{216}cm^3}=\frac{216}{24}=9[/tex]cubic blocks with a side length of 1/6cm in order to fill the volume of the given prism.
Answer: 9.
Direction. Write the letter of the correct answer on a separate answer sheet.
1. The composite functions are two o more functions combining within another to create a new function.
So the correct notion is:
a. h(p(x))
b. ( s o t) (x)
c. f(g(x))
So the b. f(x) g(x) is not a notation of a composite function.
Solve the equation. Enter the answer as an equation that shows the value ofthe variable, for example f = 7, or 6 = W.p+ 3 = 1
Let the given equation is p+3=1
The objective is to find the value of p.
[tex]\begin{gathered} p+3=1 \\ p=1-3 \\ p=-2 \end{gathered}[/tex]Hence the value of p is -2.
sugar cookies require 2 cups of flour for every 2/3 cups of sugar. how much sugar for 5 cups of flour
Billy, this is the solution to the exercise:
For answering it, we will use the Direct Rule of Three, this way:
Sugar (cups) Flour (cups)
2/3 2
x 5
____________________________
x * 2 = 5 * 2/3
2x = 10/3
Dividing by 2 at both sides:
2x/2 = 10/3 / 2
x = 10/3 * 1/2
x = 10/6
x = 1 2/3 (simplifying)
We will need 1 2/3 cups of sugar for 5 cups of flour
Calculate the second and third derivative of y =9x-1/x
y = 9x - 1/x
I like to rewrite 1/x as x^-1
y = 9x - x^-1
Taking the derivative
dy/dx = 9 - -1 x^-2
= 9 + 1/x^2
That is the first derivative
Now we do it again
dy^2/dx^2 = d/dx ( 9 + 1/x^2)
= d/dx( 9 + x^-2)
= 0 -2x^-3
=-2/x^3
The second derivative is -2 / x^3
in the interactive below, fill out five products for a company and sells in column A and their respective prices in column B. Inter five as the quantity in cells C2 through C6. write an expression in column D to find the value of each cell by multiplying the corresponding B and C cells. for example the cell D2 should use the formula =B2*C2. The cell D7 should be determined by writing an expression to add cells D2 through D6.type in the items you’re purchasing in column A, type in the price of the items in column B. Enter an expression using an asterisk in columb D to multiply two cells together. For example in D2, type “=B2*C2” without the quotation marks.
We are tasked to complete a table by providing information on the prices of 5 items and finding their total cost.
To do this, we must first think of 5 items and find out (or at least estimate) their unit prices.
Item Price
pencil $2
notebook $4
Chapstick $3
book $7
bookmark $1
Then, in column D, we need to type the following formulas:
=B2*C2
=B3*C3
=B4*C4
=B5*C5
=B6*C6
And finally, in cell D7, type in =D2+D3+D4+D5+D6 or =sum(D2:D6).
write an inequality to represent each situation. Do not solve the inequality. define the variable 3. Leslie is driving 850 miles home from vacation. She drives a constant speed of 65 miles per hour. She wants to stopfor the night when she is no more than 300 miles from home. How many hours will she need to drive?4. Steve earns $16 per hour plus $150 in bonuses. Carly earns $14 per hour and $200 in bonuses. After how many hourswill Steve's pay be more than Carly's?5. The science club is going on a field trip to the science museum. The club has at most $800 to spend on the trip. Thebus for the trip costs $100, and meals at the museum cost $4.50 per student. If admission to the museum is $12 perstudent and $16 per adult, and there are six chaperones attending, how many students can go on the trip?
According to the problem, Leslie will need to drive 850. As she is driving at a constant speed of 65 miles per hour, if you take h as the number of hours she drives, the distance she covers in h hours is 65h. She wants to stop when she is not more than 300 miles from home, which means that she wants to stop when the difference between 850 and 65h is less than or equal to 300.
This expressed as an inequality is:
[tex]850-65h\leq300[/tex]How many lines are determined by 18 points, no 3 of which are collinear?
First, consider the 3 points, no 3 of which are collinear; as shown in the diagram below
As one can see, we can form 3 different lines, lines 12, 13, and 23 (this is 2+1=3).
Similarly, in the case of 4 points,
There are 6 possible lines when considering 4 points on the plane (3+2+1=6).
Finally, in the case of 5 points on the plane,
4+3+2+1=10 lines when 5 points.
Therefore, for 18 points, there are 17+16+15+14+...+3+2+1=153
Given the equation y = 3x + 8, what would the value of y be when x= 3?14O 151O 17
y = 3x + 8
When x = 3, we substitute the value of x into the equation
y = 3(3) + 8
y = 9 + 8
y = 17
what is the value of a in the function's equation? please help asap.
The general equation for a quadratic function is,
[tex]f(x)=cx^2+bx+a[/tex]The zeros of equation is -8 and 4, means that f(-8) = 0 and f(4) = 0.
Determine the equation for a, b and c.
[tex]\begin{gathered} f(-8)=c(-8)^2+b(-8)+a \\ 0=64c-8b+a \\ a=-64c+8b \end{gathered}[/tex][tex]\begin{gathered} f(4)=c(4)^2+b(4)+a \\ 0=16c+4b+a \\ a=-16c-4b \end{gathered}[/tex]So equation is,
[tex]\begin{gathered} -16c-4b=-64c+8b \\ 48c=12b \\ b=4c \end{gathered}[/tex]Differentiate the function
Which describes the transformation shown below?AAdc4b1af2565e7f59d96219e110571cd3.webm 11988O aOьReflection over the y-axisRotation 270 clockwiseRotation 90' clockwiseTranslation leftOd
Looking at the picture. the image, A' is on the left hand side of the object A. This could mean rotation about the origin or reflection about the y axis. Since the positions of the coordinate changed, it means that it is rotation. For 270 degrees, an object with coordinates, (x, y
what is the perimeter of a triangle with vertices located at (1,3), (2,6), (0,4)
ANSWER
EXPLANATION
The perimeter of a triangle is the sum of the length of its three sides. For this triangle we know the location of the vertices. The length of each side is the distance between each pair of points:
At basketball tryouts, Jeremiah will shoot a 1-point shot, 2-point shot, and a 3-point shot one after theother. The table below shows Jeremiah's probability of making each shot:ShotProbability of making1-point80%2-point50%3-point30%Assume the outcome of one shot doesn't change the probability of other shots.The coach will record the total points Jeremiah scores from these 3 shots.Which graph represents the theoretical probability distribution of Jeremiah's total points?Choose 1 answer:
The graph that represents the theoretical probability distribution of Jeremiah's total points is given by:
Graph A.
What is a probability distribution?The probability of an event in an experiment is calculated as the absolute frequency of the desired outcomes in the experiment divided by the total number of outcomes in the experiment.
The probability distribution gives the probability of all possible events in the context of the problem.
For Jeremiah to make zero points, he needs to:
Miss the 1 - point shot: 0.2 probability.Miss the 2 - point shot: 0.5 probability.Miss the 3 - point shot: 0.7 probability.Hence:
P(X = 1) = 0.2 x 0.5 x 0.7 = 0.07 = 7%.
For Jeremiah to make one point, he needs to:
Make the 1 - point shot: 0.8 probability.Miss the 2 - point shot: 0.5 probability.Miss the 3 - point shot: 0.7 probability.Hence:
P(X = 1) = 0.8 x 0.5 x 0.7 = 0.28 = 28%.
For Jeremiah to make two points, he needs to:
Miss the 1 - point shot: 0.2 probability.Make the 2 - point shot: 0.5 probability.Miss the 3 - point shot: 0.7 probability.Hence:
P(X = 2) = 0.2 x 0.5 x 0.7 = 0.07.
For Jeremiah to make three points, he needs to either:
Miss the 1 - point shot: 0.2 probability.Miss the 2 - point shot: 0.5 probability.Make the 3 - point shot: 0.3 probability.Or:
Make the 1 - point shot: 0.8 probability.Make the 2 - point shot: 0.5 probability.Miss the 3 - point show: 0.7 probability.Hence:
P(X = 3) = 0.2 x 0.5 x 0.3 + 0.8 x 0.5 x 0.7 = 0.31.
For Jeremiah to make four points, he needs to:
Make the 1 - point shot: 0.8 probability.Miss the 2 - point shot: 0.5 probability.Make the 3 - point shot: 0.3 probability.Hence:
P(X = 4) = 0.8 x 0.5 x 0.3 = 0.12.
For Jeremiah to make five points, he needs to:
Miss the 1 - point shot: 0.2 probability.Make the 2 - point shot: 0.5 probability.Make the 3 - point shot: 0.3 probability.Hence:
P(X = 5) = 0.2 x 0.5 x 0.3 = 0.03.
For Jeremiah to make six points, he needs to:
Make the 1 - point shot: 0.8 probability.Make the 2 - point shot: 0.5 probability.Make the 3 - point shot: 0.3 probability.Hence:
P(X = 6) = 0.8 x 0.5 x 0.3 = 0.12.
Hence Graph A is correct, as it contains these probabilities.
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What is the distance between -3 and 2 on the number line? O -5O -1O 1O 5
The distance between two numbers on the number line can be found by counting the units between those two numbers:
Also it's de difference between the greater number and the lower one:
[tex]2-(-3)=2+3=5[/tex]Are [3/6 -4/5] and [5/-6 4/3] inverses? Why or why not?
Answer:
A.
Explanation:
Two matrices are inverses if when we multiply them, we get the identity matrix with 1 in the diagonal and 0 on the other entries.
In this case, we get that the multiplication of the matrices is equal to
[tex]\begin{bmatrix}{3} & {-4} \\ {6} & {5}\end{bmatrix}\begin{bmatrix}{5} & {4} \\ {-6} & {3}\end{bmatrix}=\begin{bmatrix}{3(5)-4(-6)} & {3(4)-4(3)} \\ {6(5)+5(-6)} & {6(4)+5(3)}\end{bmatrix}=\begin{bmatrix}{15+24} & {12-12} \\ {30-30} & {24+15}\end{bmatrix}=\begin{bmatrix}{39} & {0} \\ {0} & {39}\end{bmatrix}[/tex]Since
[tex]\begin{bmatrix}{39} & {0} \\ {0} & {39}\end{bmatrix}\ne\begin{bmatrix}{1} & {0} \\ {0} & {1}\end{bmatrix}[/tex]We get that the matrices are not inverses.
So, the answer is A.
you are visiting new Orleans, la and a taxi company charges a flat fee of $2.75 for using the taxi and $0.35 per mile write an equation
We have a fixed fee of $2.75, independent of the miles.
We also have to add a variable fee, the depends on the number of miles (lets call them x), that is $0.35 per mile.
Then, we can write the total fee as:
[tex]C(x)=2.75+0.35\cdot x[/tex]The hydrogen ion concentration of a solution is 0.0001mol/L. Calculate the pH (given pH = -log[H]+
Given:
The hydrogen ion concentration of a solution is 0.0001 mol/L
we will find the value of pH
The relation between pH and the hydrogen ion concentration H will be:
[tex]pH=-\log H^+[/tex]Given H = 0.0001 mol/L
so, the value of pH will be as follows:
[tex]pH=-\log (0.0001)=-\log 10^{-4}=-(-4\log 10)=4[/tex]so, the answer will be pH = 4
find the slope of the equation. y=-(-x+1)
The form of the linear equation is
[tex]y=mx+b[/tex]m is the slope
b is the y-intercept
Since the given equation is
[tex]y=-(-x+1)[/tex]Simplify it by multiplying each term in the bracket by (-)
[tex]\begin{gathered} y=-(-x)+-(1) \\ y=x+-1 \\ y=x-1 \end{gathered}[/tex]Compare it with the form above to find the value of m
[tex]m=1[/tex]The slope of the equation is 1
Find the 12th term of the arithmetic sequence whose common difference is d = -7 and whose first term is a 1 = 30 .(Picture is more understandable)
T12 = -47
Explanations:The nth term of an arithmetic sequence is expressed as:
[tex]T_n=a+(n-1)\cdot d[/tex]where:
• a is the, first term
,• n is the ,number of terms
,• d is the ,common difference
Given the following parameters
a = 30
n = 12 (12th term)
d = -7 (common difference)
Substitute the given parameters into the formula
[tex]\begin{gathered} T_{12}=30+(12-1)\cdot(-7) \\ T_{12}=30+11(-7) \\ T_{12}=30-77 \\ T_{12}=-47 \end{gathered}[/tex]Hence the 12th term of the arithmetic sequence is -47
TRIGfind the following in triangle CAT.lineAT is 16.5angleT is 43degrees how do I solve?
h= 22.6, CT =47º, CA=15.4
1) We're going to use trig ratios for that. So to find CT, the hypotenuse, and considering the angle 43º as our reference, we can write:
[tex]\begin{gathered} \cos (43)=\frac{adjacent}{\text{hypotenuse}} \\ \cos (43)\text{ =}\frac{16.5}{h} \\ \cos (43)h=16.5 \\ h=\frac{16.5}{\cos (43)} \\ h=22.5609\approx22.6 \end{gathered}[/tex]So the CT is equal approximately to 22.6.
2) Now let's find out the measure of angle C. The simplest way is to consider the fact that every triangle has the sum of its interior angles as 180º
90º +43º + C = 180º
133º + C = 180º
C =180º -133º
C = 47º
3) Let's focus on CA leg.
Concerning that, we can make use of another trig ratio. Since we know the measure of angle C
[tex]\begin{gathered} \tan (47)=\frac{opposite}{\text{adjacent}} \\ \tan (47)\text{ =}\frac{16.5}{CA} \\ CA=\frac{16.5}{\tan (47)} \\ CA\text{ =15.38649}\approx15.4 \end{gathered}[/tex]CA is approximately 15.4
What linear equation represents the graph of a horizontal line, parallel to the x-axis, that travels through the point (0,4)? Use the grid or a piece of paper if needed. LY 2 1 X 5 2 2 0 1 2 3 4 1 -2
It's important to know that all horizontal lines can be represented as y = k, where k is a real number.
In this case, we know that the horizontal line passes through (0,4).
Therefore, the equation of the line is y = 4.can someone please help me find the value degree of 33-gon
the sum of exterior angles of any n-gon is 360.
Sum of exterior angles of a 33-gon is 360°
For the image above, find the following:
x =
ACB =
Answer:
x = 25
m∠ACB = 115°
Step-by-step explanation:
A full circle measures 360°: 92 + (4x+15) + (6x+3) = 360
10x + 110 = 360
10x = 250
x = 25
Central angles have the same measure as the intercepted arc:
ACB = 4x + 15 = 4(25) + 15 = 115°
Answer:
Answer:
x = 25
m∠ACB = 115°
Step-by-step explanation:
ACB = 4x + 15 = 4(25) + 15 = 115°
1. You invest $28,000 into an account earning 9.3% interest compounded monthly. This interest is used for both parts.A. How much money is in the account after 5 years? Be sure to show the formula you used with the numbers plugged in to find the solution.B. How much money is in the account after 29 years? Be sure to show the equation you used with the numbers plugged in to find the solution.
A.
In order to calculate the amount after 5 years for compound interest, we can use the formula:
[tex]P=P_0\cdot(1+\frac{i}{n})^{nt}[/tex]Where P is the final amount after t years, P0 is the initial value, i is the interest rate and n depends on the compound period (since it's monthly, let's use n = 12).
So we have:
[tex]\begin{gathered} P=28000(1+\frac{0.093}{12})^{5\cdot12} \\ P=28000\cdot(1+0.00775)^{60} \\ P=44496.56 \end{gathered}[/tex]B.
For t = 29, we have:
[tex]\begin{gathered} P=28000\cdot(1.00775)^{12\cdot29} \\ P=411088.01 \end{gathered}[/tex]Annie has 13 yards of string. She uses 12 1 yards to fix her backpack. About how much string does she have left? 9 10
Annie will be left with 0.9 yd of string with her.
What is subtraction?In maths, to subtract means to take away from a group or a number of things.
Given that, Annie had a string of 13 yd, and she used 12.1 yd of the string for her backpack.
The length of string left with her after using for backpack = 13-12.1 = 0.9 yd
Hence, Annie will be left with 0.9 yd of string with her.
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Solve: Show your work.
-2-(-5)=
Answer:
3
Step-by-step explanation:
First you turn the two negatives/minuses in -(-5 into a plus (you will get it later)
Next you have -2 + 5 which is 3
Or is you want to do it the less lazy way
First you gotta know that subtracting a negative number means you are adding to the first number
You have -2 Minus -5 so you add five to -2 which is 3
inverse functionf(x)= 1/2 (3-3x)
f(x)= 1/2 (3-3x)
First, write as a linear equation: (replace f(x) by y)
y= 1/2 (3-3x)
Swap x and y variables:
x = 1/2 (3-3y)
Solve for y:
x = 1/2(3)+1/2(-3y)
x= 3/2 -3/2y
x-3/2 = -3/2y
(x-3/2) / -3/2 = y
-2/3x+1=y
Write in inverse notation
f-1(x) = -2/3x+1
14) The angle of elevationfrom a point 116 meters fromthe base of the Eiffel Towerto the top of the tower is68.9°. Find the approximateheight of the tower to thenearest meter.
Given data:
The given angle of elevation is θ= 68.9°.
The horizontal distance is d=116 m.
The expression for tanθ is,
[tex]\begin{gathered} \tan \theta=\frac{h}{d} \\ \tan (68.9^{\circ})=\frac{h}{116\text{ m}} \\ h=300.62\text{ m} \\ \approx301\text{ m} \end{gathered}[/tex]Thus, the height of the tower is 301 m.
The total volume of a tree increases 8% each year. What will its volume be after 7 years if it’s volume is 5 m³ now?
The volume of trees after 7 years if it’s volume is 5 m cube now is 8.57 m cube.
In the given question we have to find the volume be after 7 years if it’s volume is 5 meter cube now.
The increment in tree each year = 8%
At now the volume is 5 meter cube.
Time = 7 years
So the formula is used to find the volume after 7 years
A=P(1+ r/100)^n
A=volume after 7 years
P=now the volume of tree
n=time
Putting the values
A=5(1+ 8/100)^7
A=5((100+8)/100)^7
A=5(108/100)^7
A=5(1.08)^7
A=5×1.714
A=8.57
Hence, volume of trees after 7 years if it’s volume is 5 m cube now is 8.57 m cube.
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The United States Department of Agriculture (USDA) found that the proportion of young adults ages 20–39 who regularly skip eating breakfast is 0.238 . Suppose that Lance, a nutritionist, surveys the dietary habits of a random sample of size =500 of young adults ages 20–39 in the United States.Use a normal approximation to find the probability that the number of individuals, , in Lance's sample who regularly skip breakfast is greater than 124 .(>124)= (Round to 3 decimal places)
Answer
The answer is 0.300
Problem Statement
We are asked to find the probability that the number of individuals in a survey of 500 people would skip breakfast given that the proportion of people who skip breakfast, in general, is 0.238.
Method
- The proportion of people greater than 124 out of 500 is easily gotten to be:
[tex]\begin{gathered} p>\frac{124}{500} \\ p>0.248 \end{gathered}[/tex]- We now need to know the probability that the proportion of people that skip breakfast would be greater than 0.248.
- To calculate this probability, we need to find the Z-score associated with this value. This is a good way to approximate the probability because the number of people in the survey is well above 30 and we have been told to apply a normal approximation.
- Once we have the Z-score associated with this proportion of 0.248 in relation to the general population proportion statistic of 0.238, we can then convert the Z-score into a probability using a Z-score calculator or a Z-table.
- If the Z-score is "z", then, the probability we are looking for on the Z-score table or calculator is P(x > z).
- Thus, we can solve the question using the following steps:
1. Calculate the Z-score using the formula below:
[tex]\begin{gathered} z=\frac{p-p_0}{\sqrt[]{\frac{p_0(1-p_0)}{n}}} \\ \\ \text{where,} \\ p=\text{sample proportion} \\ p_0=\text{population proportion} \\ n=\text{ Total number of people in the survey} \end{gathered}[/tex]2. Convert the Z-score into probability
Implementation
Step 1: Calculate the Z-score:
[tex]\begin{gathered} p=0.248,p_0=0.238 \\ \\ z=\frac{0.248-0.238}{\sqrt[]{\frac{0.238(1-0.238)}{500}}} \\ \\ z=\frac{0.01}{0.019045} \\ \\ z=0.5251 \end{gathered}[/tex]2. Convert the Z-score into probability:
Using the Z-score calculator, we have:
Because we are asked to find the probability that the number of people who skipped breakfast is greater than 124, the correct probability here is P(x > Z).
Thus, the probability that the number of individuals that skipped breakfast is greater than 124 is 0.29977 ≅ 0.300 (To 3 decimal places)
Final Answer
The answer is 0.300.