Answer:
you ate 7.33333 (repeating) ounces of popcorn
Step-by-step explanation:
36 - 14 = 22
22/3 = 7.3333 (repeating)
Find the half-life (in hours) of a radioactive substance that is reduced by 5 percent in 75 hours.half life = ___ include units
Let's list down the given information.
Time = 75 hours
Final Value = reduced by 5% = 95%
To get the half life, the formula is:
[tex]t=\frac{\ln 0.5}{k}[/tex]Before we can get the half-life, we need to get the value of k or the decay rate first. The formula is:
[tex]k=\frac{\ln A}{t}[/tex]where A is the final value in percentage and t = time. Since we have this information above, let's plug it in the formula and solve for k.
[tex]k=\frac{\ln0.95}{75}=-0.0006839105918[/tex]Now that we have the value of "k", let's solve for "t" using the formula stated above as well.
[tex]t=\frac{\ln 0.5}{k}=\frac{\ln 0.5}{-0.0006839105918}=1013.51[/tex]Hence, the half life of the radioactive substance is approximately 1,013.51 hours or 1,013 hours and 30 minutes.
On Day 16, Ebony deposited $100 into her account. On each day after Day 16, segment 5, Ebony made adeposit, and those deposits were equal to each other.(a) Explain how you can determine, just by looking at the graph, whether the amounts she depositedafter Day 16 were each less than $100, $100, or more than $100.(b) Use the graph to estimate B(21) in hundreds. Explain how you determined this estimate. Then showhow you can estimate the amount of money Ebony deposited into her account each day after Day 16.
Given that on day 15 the balance was $0 and on day 16 the balance is $100, then we have:
[tex]\begin{gathered} \text{slope:} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ \Rightarrow m=\frac{100-0}{16-15}=100 \\ \text{for point (15,0) and slope m=100:} \\ y-y_0=m(x-x_0) \\ \Rightarrow y-0=100(x-15) \\ \Rightarrow y=100x-1500 \end{gathered}[/tex]we have that the relation function for this period is B(x)=100x-1500. Then for x=21 we have the following:
[tex]\begin{gathered} B(x)=100x-1500 \\ B(21)=100\cdot21-1500=2100-1500=600 \\ \end{gathered}[/tex]therefore, using the relation function, we have that B(21) = 600.
To find the amount of money deposited into the account after day 16, we have to find B(17), B(18), B(19) and B(20):
[tex]\begin{gathered} B(17)=100\cdot17-1500=1700-1200=200 \\ B(18)=100\cdot18-1500=1800-1500=300 \\ B(19)=100\cdot19-1500=1900-1500=400 \\ B(20)=100\cdot20-1500=2000-1500=500 \end{gathered}[/tex]I need to know if it’s A b c or D
The value of x is 1.
Step - by - Step Explanation
What to find? The value of x.
Given:
From the diagram,
• Inscribed angle = 70°
,• arc length = 141x - 1
The formula we can use to solve the given problem is;
[tex]\text{Inscribed angle =}\frac{1}{2}(\text{ length of arc)}[/tex]Substitute the values into the formula.
[tex]70=\frac{1}{2}(141x\text{ - 1)}[/tex]Simplify the above.
To simplify, first multiply both-side of the equation by 2.
[tex]70\times2=\cancel{2}\times\frac{1}{\cancel{2}}(141x-1)[/tex]140 = 141x - 1
Add 1 to both-side of the equation.
140 + 1 = 141x -1 + 1
141 = 141x
Divide both-side of the equation by 141.
[tex]\frac{\cancel{141}x}{\cancel{141}}=\frac{141}{141}[/tex]x = 1
a recipe for cookies calls for 1/4 cup of brown sugar for one batch how many batches can be made with 3/8 cups of brown sugar
1) Gathering the data
1/4 cup of brown sugar ------ 1 batch
3/8 ---------------------------------- x
2) Let's solve this problem by setting a proportion to solve this:
1/4 cup of brown sugar ------ 1 batch
3/8 ---------------------------------- x
Since it is a proportion then we can cross multiply those fractions:
[tex]\begin{gathered} \frac{1}{4}x=\frac{3}{8} \\ 8x=12 \\ \text{Divide both sides by 8} \\ x=\frac{12}{8}\text{ =}\frac{3}{2} \end{gathered}[/tex]3) So with 3/8 cups of sugar, we can make 3/2 batches or 1.5 batches
Parallelogram ABCD has vertices A(8,2), B(6,-4), and C(-5,-4). Find the coordinates of D.
Given:
ABCD is the parallelogram.
vertices are A(8,2), B(6,-4), and C(-5,-4)
We know the diagonals of the parallelogram bisect each other.
Find the midpoint of AC.
[tex]\begin{gathered} m=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ (x_1,y_1)=(8,2) \\ (x_2,y_2)=(-5,-4) \\ m=(\frac{8-5}{2},\frac{2-4}{2}) \\ m=(\frac{3}{2},-\frac{2}{2}) \\ m=(\frac{3}{2},-1) \end{gathered}[/tex]Now, the midpoint of BD is given as,
[tex]\begin{gathered} m=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ m=(\frac{3}{2},-1) \\ B\mleft(6,-4\mright),D(x,y) \\ (\frac{3}{2},-1)=(\frac{6+x}{2},\frac{-4+y}{2}) \\ \frac{6+x}{2}=\frac{3}{2},\frac{-4+y}{2}=-1 \\ 6+x=3,-4+y=-2 \\ x=-3,y=2 \end{gathered}[/tex]The coordinate of D is (-3,2).
function notations For the function below for which values of x does f (x)=3 ?
Answer:
x = 2
Explanation:
Each ordered pair in the function has the form (x, f(x)). So, the first coordinate is x and the second coordinate of each pair is f(x).
Then, the ordered pair that has a second coordinate equal to 3 or f(x) = 3 is the pair (2, 3). Therefore, the value of x that does f(x) = 3 is x = 2
So, the answer is x = 2
hurry and anwser please im dying
Answer:
the answers to your question would be 65 aka D
So my teacher teach us about this leason but I did not understand it at all can someone please teach me.
x + 2= 2(2x - 14 )
We will first find x
x + 2 = 4x - 28
collect like term
4x - x = 28 + 2
3x = 30
Divide both-side of the equation by 3
x = 10
But TU = 2x - 14
substitute x = 10 in the above and evaluate
TU = 2(10) - 14 = 20 - 14 = 6
Hence the length of TU is 6
Hi could you help me with my homework Number 1
Slope-intercept form:
[tex]y=mx+b[/tex]This form reveal the slope (m) that describes the steepness of a line, and the y-coordinate of the y-intercept (b) (The y-intercept has coordinates (0,b))
Find the slope of the tangent line to f(x) when x= -3. Two points on the line tangent to f(x) at x = -3 are: (-4,-7) and (1,3).
When x = -3, the line that's tangent to f(x) is shown in the given image. So, in order to find the slope of f(x) at x = -3, we need to find the slope of that line.
The slope of a line is given by the formula:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]Now, notice that the points (-4,-7) and (1,3) belong to the tangent line. Therefore, we can use them to find the slope:
y₂ = 3
y₁ = -7
x₂ = 1
x₁ = -4
So, we have:
[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{3-(-7)}{1-(-4)}=\frac{3+7}{1+4}=\frac{10}{5}=2[/tex]Therefore, the slope is 2.
Find all the roots of the following equations2x^3+x^2-7x-2=0
Let's begin by listing out the information given to us:
2x³ + x² - 7x- 2 = 0
We will proceed to factorise, we have:
(x + 2)(2x² − 3x - 1) = 0
We will proceed to equate the factors to zero, we have:
x + 2 = 0⇒ x = -2
⇒ x = -2
2x² − 3x - 1 = 0
We will use the quadratic formula, we have:
[tex]\begin{gathered} 2x^{2}-3x-1=0 \\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ a=2,b=-3,c=-1 \\ x=\frac{-(-3)\pm\sqrt[]{(-3)^2-4(2)(-1)}}{2(2)} \\ x=\frac{3\pm\sqrt[]{9+8}}{4}=\frac{3\pm\sqrt[]{17}}{4} \\ x=\frac{3\pm\sqrt[]{17}}{4}\Rightarrow x=\frac{3+\sqrt[]{17}}{4},\frac{3-\sqrt[]{17}}{4} \\ x=\frac{3+\sqrt[]{17}}{4},\frac{3-\sqrt[]{17}}{4} \end{gathered}[/tex]
Please help with this math problem so my son can understand better I have attached the image. For some reason he keeps getting it incorrect cause he's not sure were the point should be placed on the graph please help.
Step 1
Choose input values for x for both equations based on his graph. The x-values on his graph sheet range from -10 to 10. we will choose; -10, -8,0,4 and 10.
Step 2
Input these x-values in the first equation and get values for the output y.
[tex]\begin{gathered} 3x+y=6 \\ \text{Transforming the above equation we will have; y=6-3x} \\ y=6-3x \\ x=-10 \\ y=6-3(-10) \\ y=6+30 \\ y=36 \\ \text{First point(-10,36)} \end{gathered}[/tex][tex]\begin{gathered} \text{If x=-8} \\ y=6-3(-8) \\ y=6+24 \\ y=30 \\ \text{second point}(-8,30) \end{gathered}[/tex][tex]\begin{gathered} \text{If x=0} \\ y=6-3(0_{}) \\ y=6 \\ \text{Third point(0,6)} \end{gathered}[/tex][tex]\begin{gathered} \text{If x=4} \\ y=6-3(4) \\ y=6-12 \\ y=-6 \\ \text{Fourth point(4,-6)} \end{gathered}[/tex][tex]\begin{gathered} \text{If x=10} \\ y=6-3(10) \\ y=6-30=-24 \\ \text{fifth point(10,-24)} \\ \end{gathered}[/tex]Step 3
Find similar points using the same x values for line 2, the second equation
[tex]\begin{gathered} -3x-4y=12 \\ -4y=12+3x \\ -\frac{4y}{-4}=\frac{12}{-4}+(\frac{3x}{-4}) \\ y=-3-\frac{3x}{4} \end{gathered}[/tex][tex]\begin{gathered} \text{If x=-10, points are }(-10,4.5) \\ \text{If x=-8 points are (-8,}3) \\ \text{if x =0 points are (}0,-3) \\ \text{if x=4 points are (4,}-6) \\ \text{if x=10 points are (10},-10.5) \end{gathered}[/tex]What is the variable term in 2x+3?
In the expression
[tex]undefined[/tex]Can you explain/show the steps to me how to solve
Step 1: Identify the overall set
Which in this case is the Dangerous
Step2: poisonous things are dangerous
These are contained in the dangerous things, hence contained in the big circle
Step3: Some Chemicals are poisonous
Then the chemicals are contained in the poisonous things
Hence since some chemicals are poisonous then they are dangerous as in the diagram above
Therefore the argument is valid
POS The radius of a cylindrical box of oatmeal is 5 centimeters. The height of the box is 18 centimeters. 5 cm 18 cm QATMEAL Which measurement is closest to the total surface area of the oatmeal box in square centimeters? A 597 cm2 B 361 cm? C 314 cm? D 723 cm?
Explanation
Step 1
to find the area, imagine the unfolded cylindrical box
Let
length=18 cm
width=2*pi*radius
radius= 5 cm
[tex]\begin{gathered} \text{width}=2\cdot\pi\cdot5\text{ cm} \\ \text{width}=10\cdot\pi\cdot\text{cm} \\ \text{width}=31.4\text{ cm} \end{gathered}[/tex]Step 2
now, the total area would be
[tex]\begin{gathered} \text{total area= area of the rectangle+twice area of the circle} \\ \text{replacing} \\ \text{total area=(length}\cdot widht9+2(\pi\cdot radius^2) \\ \text{total area=(18 cm}\cdot31.4\text{ cm)+2(3.14}\cdot25cm^2) \\ \text{total area=565.2 cm}^2+157.07cm^2 \\ \text{total area=722.27 cm}^2 \\ \text{rounded} \\ 723cm^2 \end{gathered}[/tex]I hope this helps you
to which set or sets of numbers does the number 5 belong?A. rational numbers only b. integers c. integers and rational numbers or D. integers,whole numbers, and rational numbers
5 belongs to the set of integers, whole numbers and rational numbers, so the answer is D.
What is the length of the dotted line in the diagram below? Round to the nearesttenth.
From the given figure
The rectangle has a width of 3 and its length is the hypotenuse of a right triangle with legs 5 and 7
Then we will find at first the hypotenuse of the triangle using the Pythagoras Theorem
[tex]\begin{gathered} L=\sqrt[]{7^2+5^2} \\ L=\sqrt[]{49+25} \\ L=\sqrt[]{74} \end{gathered}[/tex]Now, to find the dotted line we will do the same with the length and the width of the rectangle
[tex]\begin{gathered} D=\sqrt[]{L^2+W^2} \\ L=\sqrt[]{74},W=3 \\ D=\sqrt[]{(\sqrt[]{74})^2+(3)^2} \\ D=\sqrt[]{74+9} \\ D=\sqrt[]{83} \\ D=9.110433579 \end{gathered}[/tex]Round it to the nearest tenth
The length of the dotted line is 9.1
in a class of 20 students, 40% of them have a pet how many students have a pet
20 students represent 100% of the class, to find how many students are 40% of the class, we can use the next proportion:
[tex]\frac{20\text{ students}}{x\text{ students}}=\frac{100\text{ \%}}{40\text{ \%}}[/tex]Solving for x,
[tex]\begin{gathered} 20\cdot40=100\cdot x \\ \frac{800}{100}=x \\ 8=x \end{gathered}[/tex]8 students have a pet
The students in Mr. Collin's class used a surveyor's measuring device to find the angle from their location the top of a building. They also measured their distance from the bottom of the building. The diagram shows the angle measure and the distance. To the nearest foot, find the height of the building. Building 100 2400 ft b. 72 ft 308 ft 33 ft D
The height of the building is 308 ft
here, we want to get the height of the building
From what we have, the angle given faces the building which makes the building the opposite
The length given does not face the angle nor the right-angle and that makes it the adjacent
The relationship between the opposite and the adjacent is the tan
In fact, tan is the ratio of the opposite to the adjacent
Let us call the height of the buliding h
Thus, we have it that;
[tex]\begin{gathered} \tan \text{ 72 = }\frac{h}{100} \\ h\text{ = 100}\times\tan \text{ 72} \\ h\text{ = 307.76} \\ h\text{ = 308 ft} \end{gathered}[/tex]does 1/2y+ 3.2y=20 have a solution?
3.7 is multiplying on the left, then it will divide on the right
[tex]\begin{gathered} y=\frac{20}{3.7} \\ y\approx5.4 \end{gathered}[/tex]Find fractional notation. 12.3% = (Simplify your answer. Type an integer or a fraction.)
The repeating decimal is 12.3.
To transform the repeating decimal into a fraction, first, we subtract all the digits 123 with the whole number 12
[tex]123-12=111[/tex]Then, we divide 111 by 9 because the repeating decimal has one digit only.
[tex]\frac{111}{9}[/tex]Hence, the fractional notation is 111/9 %How many radians are in 120°? ?7T22T30123
To convert 120 degrees to radians, we have to multiply by pi/180 and simplify the fraction:
[tex]120\cdot\frac{\pi}{180}=\frac{120}{180}\cdot\pi=\frac{12}{18}\pi=\frac{2}{3}\pi[/tex]therefore, there are 2/3 pi radians in 120 degrees
A battery is charged. The percentage of the battery's capacity that is charged as a function of time (in minutes) is graphed 0 IT) HE + What was the battery's charging level when the charging began?
look closely to the graph
when the time (which is on the x-axis) was zero (0),
the capacity of the battery (which is on y-axis) was already at 40% left
Now, the battery's charging level when the charging began was 40%
Graph the line given a point and the slope. (2,-2) ; m = 1/2
On a map, 1 inch equals 13.1 miles. If two cities are 2.5 inches apart on the map, how far are they actually apart?
EXPLANATION:
The ratio given is 1 inch equals 13.1 miles. That means 2 inches would be 13.1 miles times 2, and so on.
Therefore, if two cities are 2.5 inches apart on the map, then;
[tex]\begin{gathered} 1\text{inch}=13.1\text{mile} \\ 2.5in=13.1(2.5)\text{miles} \\ 2.5in=32.75miles \end{gathered}[/tex]Hence, the two cities are actually 32.75 miles apart
(5x-1)+2y= 194° what is x and y?
Given a cyclic quadrilateral
The sum of the opposite angles = 180
so,
[tex]\begin{gathered} 2y+90=180 \\ (5x-1)+76=180 \end{gathered}[/tex]solve the first equation to find y as follows:
[tex]\begin{gathered} 2y=180-90 \\ 2y=90 \\ y=\frac{90}{2}=45 \end{gathered}[/tex]Solve the second equation to find x as follows:
[tex]\begin{gathered} 5x-1+76=180 \\ 5x+75=180 \\ 5x=180-75 \\ 5x=105 \\ x=\frac{105}{5}=21 \end{gathered}[/tex]so, the answer will be:
x = 21
y = 45
Brenda uses 1/3 of a bag of flour in each batch of pizzas. She used 2/3 of a bag of flour on Monday. How many batches of pizzas did she make?
Given that it takes 1/3 of a bag of flour to make 1 batch.
r
Three years ago Maya was eleven times as old as her daughter Fiona. In four years time Maya will be four times as old as Fiona. How old are they now?
Let's call M the present age of Maya, and F the present age of Fiona.
Three years ago Maya was eleven times as old as Fiona. At that time, Maya's age was M-3, and Fiona's age was F-3. Thus, we have:
[tex]M-3=11(F-3)[/tex]Also, in four years Maya will be four times as old as Fiona. At that time, Maya's age will be M+4, and Fiona's age will be F+4. Thus, we have:
[tex]M+4=4(F+4)[/tex]Now, we need to solve the system of those two equations to find M and F. Subtracting the second equation from the first, we obtain:
[tex]\begin{gathered} M-3-(M+4)=11F-33-(4F+16) \\ \\ M-3-M-4=(11-4)F-33-16 \\ \\ -7=7F-49 \\ \\ -7+49=7F-49+49 \\ \\ 42=7F \\ \\ \frac{42}{7}=\frac{7F}{7} \\ \\ 6=F \\ \\ F=6 \end{gathered}[/tex]Now, we can use the above result to find M:
[tex]\begin{gathered} M+4=4(6+4) \\ \\ M+4=40 \\ \\ M+4-4=40-4 \\ \\ M=36 \end{gathered}[/tex]Therefore, now Maya is 40 years old and Fiona is 6 years old.
The formula for finding the distance traveled, base on the speed and time, is D= RT, whereD is distanceR is rateT is timeUnits must be consistent. If the unit for D is miles and the unit for T is minutes, what must the units for R be?_______Solve this formula for R.R=______If a bicyclist rides for 140 minutes at an average speed of 14 miles per hour, how far was the ride, to 1 decimal place?_______ miles.At what speed must a bicyclist ride to cover 60 miles in 1.5 hours, to 1 decimal place?______ miles/hour
Given:
a)
The formula for finding the distance traveled, based on the speed and time, is D= RT, where D is distance, R is rate and T is time.
The unit for D is miles and the unit for T is minutes.
b)
A bicyclist rides for 140 minutes at an average speed of 14 miles per hour.
c)
A bicyclist ride to cover 60 miles in 1.5 hours.
Required:
a)
We need to find the units fir R.
b)
We need to find the distance.
c)
We need to speed.
Explanation:
a)
The given formula is
[tex]D=RT[/tex]Divide both sides of the equation by T.
[tex]\frac{D}{T}=\frac{RT}{T}[/tex][tex]\frac{D}{T}=R[/tex]Substitute D =miles and T= minutes in the formula.
[tex]miles=R\times minutes[/tex][tex]\frac{miles}{minutes}=R[/tex]We can rewrite miles by the hour. since 60 minutes = one hour
[tex]60\text{ }\frac{miles}{hour}=R[/tex]The most common unit of speed is miles/ hour.
Answer:
The unit of R is miles/hour.
b)
T =140 minutes and R =14 miles per hour.
Convert the minutes onto hours.
Divide 140 by 60 to convert units.
[tex]T=\frac{140}{60}hours[/tex][tex]T=\frac{7}{3}hours[/tex]Consider the formula.
[tex]D=RT[/tex]Substitute R =14 and T=7/3 in the formula.
[tex]D=14\times\frac{7}{3}[/tex][tex]D=32.7miles[/tex]Answer:
The bicycle was ridden 32.7 miles.
c)
D =60 and T =1.5
Consider the formula.
[tex]D=RT[/tex]Substitute D =60 and T =1.5 in the formula.
[tex]60=R\times1.5[/tex]Divide both sides by 1.5.
[tex]\frac{60}{1.5}=R\times\frac{1.5}{1.5}[/tex][tex]40=R[/tex]Answer:
The speed of the bicycle is 40 miles/hour.
Final answer:
5.1234 to the thousandths 6.6666 to the thousandths
Answer:
[tex]\begin{gathered} 5.1234\approx5.123 \\ 6.6666\approx6.667 \end{gathered}[/tex]Explanation:
We want to round up the given number to the nearest thousandths.
[tex]5.1234[/tex]To the nearest thousandth which is also to 3 decimal place, we have;
[tex]\approx5.123[/tex]Also;
[tex]6.6666[/tex]To the nearest thousandth, we have;
[tex]6.667[/tex]Note that numbers from 5 above will be rounded up, while numbers below 5 will be rounded down.