In order to determine the volume of the sand inside the box, take into account that the shape of the volume of the sand inside the box is the same that the rectangular prism. Then, you can use the folowing formula for the volume of the sand:
V = w·h·l
where w is the width, h the height and l the length. In this case, the height of the sand is 0.25m and the width and the length are the same of the box.
w = 2 m
l = 2.6 m
h = 0.25 m
replace the previous values of the parameters into the formula for V:
V = (2 m)(2.6 m)(0.25 m)
V = 1.3 m³
Hence, the volume of the sand inside the box is 1.3 m³
Find the mass of a cylinder with a volume of 157.08 ft^3 and a density of 0.900 g/cm^3. Final answer should be in kilograms (kg).
Okay, here we have this:
Considering the provided information, we are going to calculate the requested mass, so we obtain the following:
Then we will substitute in the following formula:
density=mass/volume
0.9 g/cm^3=mass/157.08 ft^3
mass=0.9 g/cm^3*157.08 ft^3
Then we will convert the volume from cubic feet to cubic centimeters in order to operate:
mass=0.9 g/cm^3*(157.08 ft^3*(28317 cm^3/1 ft^3)
mass=0.9 g/cm^3*4448034.36cm^3
mass=4003230.924 g
Finally let's convert the mass to kilograms:
mass=4003230.924 g*(1kg/1000g)
mass=4003.230924 kg
Finally we obtain that the mass of the cylinder is approximately 4003.230924 kg.
Solve by graphing. If the radioactive half-life of a substance is 20 days, and there are 5 grams of it initally. When will the amount left be 2 grams? Round to the nearest tenth of a day. Be sure to label your answer.
The exercise describes an exponential decay, you can express this using the general form:
[tex]y=ab^x[/tex]Where
a is the initial amount
b is the decay factor
x is the time intervals
y is the amount after x time intervals
The half-life of a substance indicates the time it takes for the amount to decrease by half.
If the initial amount is a=5 grams, the half-life indicates that after x=20 days, the amount will be
y= 5/2 = 2.5 grams.
You can replace these values on the formula above to obtain an expression where the decay factor will be the only unknown:
[tex]\begin{gathered} y=ab^x \\ 2.5=5b^{20} \end{gathered}[/tex]To solve for b, first, divide both sides of the equation by 5:
[tex]\begin{gathered} \frac{2.5}{5}=\frac{5b^{20}}{5} \\ 0.5=b^{20} \end{gathered}[/tex]Then apply the square root with index 20 to both sides of the equal sign no reach the value of b:
[tex]\begin{gathered} \sqrt[20]{0.5}=\sqrt[20]{b^{20}} \\ b=0.97 \end{gathered}[/tex]Now that you know the value of the decay factor, you can determine how much time it will take for the substance to decrease to 2grams.
The expression for the exponential decay in this case is:
[tex]y=5\cdot0.97^x[/tex]For y=2grams:
[tex]2=5\cdot0.97^x[/tex]Now, you have to solve the expression for x:
-Divide both sides by 5:
[tex]\begin{gathered} \frac{2}{5}=\frac{5\cdot0.97^x}{5} \\ 0.4=0.97^x \end{gathered}[/tex]-Apply the logarithm to both sides of the equal sign:
[tex]\begin{gathered} \log (0.4)=\log (0.97^x) \\ \log (0.4)=x\log (0.97) \end{gathered}[/tex]-Divide both sides by the logarithm of 0.97 to determine the value of x:
[tex]\begin{gathered} \frac{\log(0.4)}{\log(0.97)}=\frac{x\log (0.97)}{\log (0.97)} \\ x=30.08\approx30.1 \end{gathered}[/tex]It will take approximately 30.10 days to have 2 grams of substance left.
the volume of a cylinder is 1269 pi cm^3 and its height is 16 cmthe length of the cylinders radius is ___ cm
The volume of cylinder is.
[tex]V=1296\pi[/tex]The height of cylinder is h = 16.
The formula for the volume of the cylinder is,
[tex]V=\pi(r)^2h[/tex]Determine the length of radius of cylinder.
[tex]\begin{gathered} 1296\pi=\pi(r)^216 \\ r^2=\frac{1296\pi}{16\pi} \\ =81 \\ r=\sqrt[]{81} \\ =9 \end{gathered}[/tex]So length of cylinder radius is 9 cm.
ā has an initial point, at (4,-8) and a terminal point at (5,2). Write ā in component form
Ok, here we have this data:
I: Initial point (4,-8)
T: Terminal Point (5,2)
IT==<5-4, 2-(-8)>=<1, 10>
The component form is <1,10>
Claudia dumped her 200-penny coin collection on the floor and counted the number of pennies that landed heads up. Claudia repeated this process 5 times and had an average of 84 pennies landing heads up on each try. Which of the following statements is true?A. Each penny has a greater probability of landing heads up than tails up.B. If Claudia had repeated this process more times, the average number of pennies landing heads up would be closer to 100.C. The theoretical probability of a penny landing heads up is 21/50.D. If Claudia had repeated this process fewer times, the average number of pennies landing heads up would be closer to 100.
Given:
Claudia dumped her 200-penny coin.
Claudia repeated this process 5 times and had an average of 84 pennies landing heads up.
The theoretical probability of a penny landing heads up is 21/50.
Option C is the final answer.
7.If you raised $15 byday 2 and by day 7 youhad $75. What is therate of change?
We have the following:
the rate of change is equal to a slope, therefore we can calculate it as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{75-15}{7-2}=\frac{60}{5}=12[/tex]The rate of change is $12/day
Construct an isosceles right triangle.
Take into account that an isosceles triangle has two sides with equal lengthd and two internal angles with the same measure.
Then, for instance, you have the following triangle:
As you can notice, you have two angles with the same measure and two sides with the same lengths.
What is the midpoint of the segment shown below?
-10
(-8,-7)
(-7,-8) -10-
10
OA (-15-15)
A.
O B. (-15,-15)
O C. (-15, -15)
OD. (-15, -15)
Remember that the formula to calculate the midpoint between two points is given by
[tex]M(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]substitute given coordinates
[tex]\begin{gathered} M(\frac{-8-7}{2},\frac{-7-8}{2}) \\ \\ M(-\frac{15}{2},-\frac{15}{2}) \end{gathered}[/tex]The answer is option BSimplify the expression⅜b - ¾b
-3b / 8
Explanations:The given expression is:
[tex]\frac{3}{8}b\text{ - }\frac{3}{4}b[/tex]Which can be re-written as:
[tex]\frac{3b}{8}-\frac{3b}{4}[/tex]Note that the LCM of 8 and 4 is 8
Therefore, the expression can be simplified as:
[tex]\begin{gathered} \frac{3b-2(3b)}{8} \\ \frac{3b-6b}{8} \\ \frac{-3b}{8} \end{gathered}[/tex]The simplified expression is -3b/8
Task:Dilate the extra gum package by a scale factor of 8.Will the small pack of gum cover the whole billboard given thedimensions? Explain your answer in complete sentences.
No, because the length of the billboard is larger than the dilated gum cover length.
If we dilate the gum package by a scale factor of 8:
Original = 3 x 2.5 in
3 x8 = 24 (length)
2.5x8 = 20 (width)
New measures: 24 x 20 ( Lenght by width)
Since the billboard is 48x14, the small pack of gum can't cover the billboard.
24<48
The length of the gum cover can't cover the length of the billboard.
Write the coordinates of the vertices after a rotation of 90 degrees counter clock wise around the origin. Give me the coordinates and that’s it no explanation
Isabelle is designing a sandbox for her backyard. the sandbox will be a regular pentagon 3 ft each side. how much wood does she need to enclose the entire sandbox? how many square ft will the sandbox take up?
Area of rectangular Pentagon = 5 * s^2 / (4tan(36°)) =5 × (3)^2 / (4*tan(36) ) = 17.73
the sides of the box are squares. their sides are 3 ft long. So the area of each square is 25 ft^2
Now, there are 5 sides, so if we mutiply 5 * 25 ft^ = 125 ft^2
So the answers are:
She needs 125 ft^2 to enclose the entire sandbox
and it would take up 142.73 ft^2
find the slope of the line that passes through (-82, -25) and (-81, 4)
The slope is 29
Explanation:The slope of a line is given as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where -82 and -81 are the coordinates for x, and
-25 and 4 are the coordinates for y.
[tex]\begin{gathered} m=\frac{4-(-25)}{-81-(-82)} \\ \\ =\frac{4+25}{-81+82} \\ \\ =\frac{29}{1}=29 \end{gathered}[/tex]Use associative property of addition to rewrite the following statement -1+(2.8+(-2))
Step 1
Write the additive property of addition.
[tex](a+b)+c=\text{ a+(b+c)}[/tex]Where
[tex]\begin{gathered} a=\text{ -1} \\ b=2.8 \\ c=-2 \end{gathered}[/tex]Step 2
Find the simplified form of the problem using the property in step 1
[tex](-1+2.8)+(-2)=-1+(2.8+(-2))[/tex][tex]\begin{gathered} 1.8-2=-1+0.8 \\ -0.2=-0.2 \end{gathered}[/tex]Hence the rewritten form of the problem using the additive property is
(-1+2.8)+(-2) and the simplified form of the problem = -0.2
Question number 2.7T: (Please help!)
The values of function F(5) is 35 and F(-10) is 4.
For F(5), x≥5
So, the appropriate function will be
[tex]F(x)=6x+5\\\\F(5)=6(5)+5\\\\F(5)=30+5\\\\F(5)=35[/tex]
For f(-10), x≤-8
So, the appropriate function will be
[tex]F(x)=4\\\\F(-10)=4[/tex]
Thus, the values of function F(5) is 35 and F(-10) is 4.
To learn more about value of function refer here
https://brainly.com/question/24704755
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Which of the following exponential functions is represented by the data in the table?Question 12 options:A) ƒ(x) = x3B) ƒ(x) = 3xC) ƒ(x) = (1∕3)xD) ƒ(x) = x1∕3
ANSWER:
C.
[tex]f(x)=(\frac{1}{3})^x[/tex]EXPLANATION:
Given:
To find:
The exponential function represented by the data in the given table
Let's go ahead and check each of the given functions to determine the right function;
*For the first function;
[tex]\begin{gathered} f(x)=x^3 \\ f(-3)=(-3)^3=-27 \end{gathered}[/tex]We can see that the first function is not the right function
*For the second function:
[tex]\begin{gathered} f(x)=3^x \\ f(-3)=3^{-3}=\frac{1}{27} \end{gathered}[/tex]We can see that the first function is not the right function
*For the third function:
[tex]\begin{gathered} f(x)=(\frac{1}{3})^x \\ f(-3)=(\frac{1}{3})^{-3}=27 \\ f(-2)=(\frac{1}{3})^{-2}=9 \\ f(-1)=(\frac{1}{3})^{-1}=3 \\ f(0)=(\frac{1}{3})^0=1 \\ f(1)=(\frac{1}{3})^1=\frac{1}{3} \\ f(2)=(\frac{1}{3})^2=\frac{1}{9} \\ f(3)=(\frac{1}{3})^3=\frac{1}{27} \end{gathered}[/tex]We can see that the third function is the right function
how much is 1 + 1 bc i’ve been failing high school
Explanation
to add two natural numbers, just move n units the initial to the rigth in the numeric line, so
fo
If x = 11 and y=5, what is the value of the following expression?X-9 + 2y
Given:-
[tex]x=11,y=5[/tex]To find the value of x-9+2y.
So now we substitute the known values. we get,
[tex]x-9+2y=11-9+2(5)=11-9+10=12[/tex]So the required solution is 12.
Claire wants to determine how her math score, 690, on a standardized college entrance exam compares to her mother's score, 680, when she took the exam 20 years earlier. The year Claire took the exam, the mean math score was 510 with a standard deviation of 110 points. When Claire's mother took the exam, the mean math score was 490 with a standard deviation of 100 points. Who had the better relative performance? Claire did better because her Z-score is greater than her mother's. Claire's mother did better because her z-score is greater than Claire's. Claire did better because her z-score is closer to the mean than her mother's. Claire's mother did better because her z-score is closer to the mean than Claire's.
The z score tells us the number of standard deviations that a given value is from the mean. Recall, standard deviation tells us the spread of the values from the mean
For Claire, the mean score was 510 but she scored 690 which was higher than the mean score
The z score would be
(690 - 510)/110 = 1.63
For Claire's mother, the mean score was 490 but she scored 680 which was higher than the mean score
The z score would be
(680 - 490)/100 = 1.9
We can see that her mother had a higher z score. Compared to the average score, she had a better performance. Therefore, the correct option is
Claire's mother did better because her z-score is greater than Claire's.
Write the standard form of the equation and the generalform of the equation of the circle with radius r and center(h,k). Then graph the circle.AY6r=2; (h,k) = (0,2)4The standard form of the equation of this circle is2The general form of the equation of this circle is(Simplify your answer.)-4-2Graph the circle.-2Click toenlargegraph4
coordiantes of the circle center = (h, k) = (0, 2)
h = 0, k = 2
r = 2
[tex]\begin{gathered} Standardform\text{ of the equation of circle:} \\ \text{ }(x-h)^2+(y-k)^2=r^2 \end{gathered}[/tex][tex]\begin{gathered} \text{ }(x-0)^2+(y-2)^2=2^2 \\ x^2+(y-2)^2\text{ = 4} \end{gathered}[/tex][tex]\begin{gathered} \text{General form of the equation of circle:} \\ x^2+y^2\text{ }+\text{ 2gx + 2fy + c = 0} \end{gathered}[/tex][tex]\begin{gathered} center\text{ of circle = (-g, -f)} \\ given\text{ }center\text{ of circle = (0, 2)} \\ -g\text{ = 0 } \\ g\text{ = 0} \\ -f\text{ = 2} \\ f\text{ = -2} \end{gathered}[/tex][tex]\begin{gathered} radius\text{ = }\sqrt[]{g^2+f^2-c} \\ 2\text{ = }\sqrt[]{0^2+(-2)^2\text{ + c}} \\ 2\text{ = }\sqrt[]{0+4\text{ + c}} \\ \text{square both sides:} \\ 2^2\text{ = }4\text{ + c} \\ 4\text{ = 4 + c} \\ c\text{ = 4-4 = 0} \end{gathered}[/tex][tex]\begin{gathered} \text{General form of the equation of circle:} \\ x^2+y^2\text{ }+\text{ 2(0)x + 2(-2)y + 0 = 0} \\ x^2+y^2\text{ - 4y = 0} \end{gathered}[/tex]plotting the graph:
The graph of the function()=1/ has origin symmetry as well as which of the following symmetries?A. y-axisB. x-axisC. y=x
We will graph a plot of this expression, we have:
[tex]undefined[/tex]The graph is neither symmetric to the x-axis nor the y-axis. Hence, y = x
The graph of F(x), shown below, has the same shape as the graph of G(x) = x4, but it is shifted to the right 1 unit. What is its equation?
Given:-
The graph of x power 4.
To find the equation when the graph is shifted right 1 unit.
So the equation in vertex form is,
[tex]y=a(x-h)^2+k[/tex]Substituting the values. we get,
[tex]g(x)=1(x-1)^4+0[/tex]Since the graph is shifted right side the value will be in negative. so we get,
[tex]g(x)=(x-1)^4[/tex]For the data shown, answer the questions. Round to 2 decimal places. 5.2 18.8 5.7 5 14.9 4.4 Find the mean : Find the median : Find the standard deviation :
Median:
1. Order the data from less to greater:
4.4
5
5.2
5.7
14.9
18.8
2. As it is a even number of data you take the average of the two data in the middle to find the median:
[tex]\frac{5.2+5.7}{2}=5.45[/tex]The median is 5.45Standard deviation formula (for a sample):
[tex]s=\sqrt{\frac{\Sigma(x_i-\bar{x})\placeholder{⬚}^2}{n-1}}[/tex]To find the standard deviation of the given data:
1. Find the difference between each data and the mean:
[tex]\begin{gathered} (x_i-\bar{x}) \\ \\ 5.2-9=-3.8 \\ 18.8-9=9.8 \\ 5.7-9=-3.3 \\ 5-9=-4 \\ 14.9-9=5.9 \\ 4.4-9=-4.6 \end{gathered}[/tex]2. Find the square of each difference:
[tex]\begin{gathered} (x_i-\bar{x})\placeholder{⬚}^2 \\ \\ (-3.8)\placeholder{⬚}^2=14.44 \\ (9.8)\placeholder{⬚}^2=96.04 \\ (-3.3)\placeholder{⬚}^2=10.89 \\ (-4)\placeholder{⬚}^2=16 \\ (5.9)\placeholder{⬚}^2=34.81 \\ (-4.6)\placeholder{⬚}^2=21.16 \end{gathered}[/tex]3. Find the sum of the squares:
[tex]\begin{gathered} \Sigma(x_i-\bar{x})\placeholder{⬚}^2 \\ \\ 14.44+96.04+10.89+16+34.81+21.16=193.34 \end{gathered}[/tex]4. Use the formula of the standard deviation for n=6:
[tex]s=\sqrt{\frac{193.34}{6-1}}=\sqrt{\frac{193.34}{5}}=\sqrt{38.668}\approx6.22[/tex]Then, the standard deviation is 6.22(b)A sight-seeing ship is stopped in the water for an hour, miles from the shore. Then the captain heads the ship back to the shore at a constant rate. The ship docks at the shore for a while and then returns to the open sea.Choose the graph that gives the best representation.
We have the following information from the question:
• A sight-seeing ship is stopped in the water for an hour, miles from the shore.
,• Then the captain heads the ship back to the shore at a constant rate.
,• The ship docks at the shore for a while and then return to the open sea.
Then we have to choose the graph that best represents the situation.
To do this, we need to analyze the three situations separately by knowing that on the y-axis we have graphed a distance relative to the shore (dependent variable), and on the x-axis, we have the time as an independent variable:
1. A sight-seeing ship is stopped in the water for an hour, miles from the shore:
If we see this situation, we have to check a distance larger than zero at x = 0. Then we have to see a horizontal line for an hour since the ship is stopped in the water for an hour, and this is because the ship is stopped, and the ship remains in the same place for an hour.
2. Then the captain heads the ship back to the shore at a constant rate:
It means that the ship will shorten the distance with respect to the shore, and this will be verified at a constant rate. Then we need to check in the graph a segment with a negative slope.
3. The ship docks at the shore for a while and then return to the open sea:
We need to check on the graph that the distance from the shore will be zero, and then we will have a horizontal line since the ship will remain for a while in the shore. Then the ship will return to the open sea, and we will check that the distance to shore will increase constantly.
Therefore, the graph that gives the best representation is the second graph from the left, that is:
Therefore, in summary, the
Rashad is having a picnic for 62 guests. He plans to serve each guest at least one hamburger. Ifeach package, p, contains eight hamburgers, wirte the inequality that could be used to determinehow many packages of hamburgers Rashad will need to buy.a. What are the key words and information needed to solve this problem? (2 points)b. Write the inequality that describes this situation. (2 points)C. How many packages of hamburgers will Rashad need to purchase to feed his guests? Work outthe problem, showing all of your work, including computation and explanation. (4 points)
a. What are the keywords and information needed to solve this problem?
The keywords are the words that allow us to solve the problem, So they are:
The picnic is for 62 guests
Each guest will receive at least 1 hamburger
Every package contains 8 hamburgers
b. Write the inequality that describes this situation.
Now, we can formulate an equation for the number of hamburgers H that each guest is going to receive if Radash buys p packages:
H = 8p/62
Because 8p is the number of total hamburgers and there are 62 guests.
Then, we know that H needs to be at least 1, so:
H ≥ 1
8p/62 ≥ 1
c. How many packages of hamburgers will Rashad need to purchase to feed his guests?
Then, we need to solve for p as:
Multiplying by 62 on both sides:
(8p/62)*62 ≥ 1 * 62
8p ≥ 62
Dividing by 8:
8p/8 ≥ 62/8
p ≥ 7.75
Therefore, Radash needs to buy at least 8 packages of hamburgers.
Answers:
a. The picnic is for 62 guests
Each guest will receive at least 1 hamburger
Every package contains 8 hamburgers
b. 8p/62 ≥ 1
c. At least 8 packages
List all the possible rational roots, then find all the roots of the function
Take into account that for a polynomial function, the possible roots are given by the following quotient:
roots = p/q
where p is the constant of the function (and its factors) and q is the coefficient of the term with the greates degree (variable with greatest exponent) or its factors.
Then, based on the previous explanation, you have:
p = -9
q = 5
factors -9: -1, 1, -3, 3, -9, 9
factors 5: -1, 1, -5, 5
Hence, the possible factors are:
±1, ±3, ±9, ±1/5, ±3/5, ±9/5
and the roots:
roots = {i(√15)/5 , -i(√15)/5, √3, -√3}
The roots can be also obtained by using quadratic formula for x^2, and then, by applying square root to the result to obtain x.
Watch help video Find the length of the third side. If necessary, write in simplest radical form. 7 4√2
9
1) In this right triangle we can find the missing leg by using the Pythagorean Theorem.
2)
a² = b² + c² Note that the hypotenuse is unknown so far
a² = 7² + (4√2)²
a² = 49 +(16 x2)
a² = 49 +32
a² =81 Take the square root on both sides
√a² = √81
a = -9, 9 Negative numbers for dimensions are not convenient.
a = 9
3) Hence, the answer is 9
Which of the following is correct based on this picture? A. sinY=38/63B. none of these are correctC. tanY=38/63D. cosY=38/63
Answer
A. sin Y = 38/63
Explanation
Given:
What to find:
To find the correct trigonometric function of the given diagram.
Step-by-step solution:
Using the trigonometric function: SOH CAH TOA
[tex]\begin{gathered} SOH\text{ }is\text{ }sin\text{ }\theta=\frac{Opposite}{Hypotenuse} \\ \\ CAH\text{ }is\text{ }cos\text{ }\theta=\frac{Adjacent}{Hypotenuse} \\ \\ TOA\text{ }is\text{ }tan\text{ }\theta=\frac{Oppos\imaginaryI te}{Adjacent} \end{gathered}[/tex]From the diagram, θ = Y, Opposite = 38, Hypotenuse = 63
So the correct trigonometric function based on the given picture will be:
[tex]sin\text{ }Y=\frac{38}{63}[/tex]Thus, the correct answer is option A. sin Y = 38/63
this is the question
Kelly, this is the solution:
We have the following system of equations:
y = 1/4x + 4
x + y = - 1
___________
Solving it algebraically:
x + (1/4x + 4) = -1
5/4x + 4 = -1
5/4x = -1 - 4
5/4x = -5
x = -4
-4 + y = -1
y = -1 + 4
y = 3
Solving it graphically:
Mr Tcha's recipe for fruit protein shake states that 2/3 of the total amount of ingredients should be fruit. The amount of yogurt in the recipe should be 1/4 of the amount of the fruit. If Mr. Tcha has 24 grams of fruits left over, how many grams of fruits and grams of yogurt did he use? What fraction of the total amount of ingredients is neither fruit nor yogurt?
A1Okay, here we have this:
Considering the provided information, we are going to calculate the requested questions, so we obtain the following:
To know how many grams of fruit and yogurt I use then let's consider that I use 2/3 of the total fruit,