The volume of a cube is given by >>>
[tex]V=s^3[/tex]Where
V is the volume
s is the side length
Given volume = 64, let's find side length >>>
[tex]\begin{gathered} V=s^3 \\ 64=s^3 \\ s=\sqrt[3]{64} \\ s=4 \end{gathered}[/tex]Each face of a cube is a square. The area of a face is given by:
[tex]A=s^2[/tex]So,
[tex]\begin{gathered} A=4^2 \\ A=16in^3 \end{gathered}[/tex]Answer16 cubic inches
The graph below shows a displacement(m)-time(s) graph for a particle moving in a straight line.The speed of the particle in the first T seconds was half the speed of the particle in the last 3 seconds.Find the value of T.
The value of T = 6 sec
Explanation:We need to find the relationship between displacement, speed and time
The formula relating the displacement to speed and time:
[tex]\text{speed = }\frac{displacement}{time}[/tex]For the first T seconds:
time = T
displacement = 4m
[tex]speed_1\text{ = }\frac{4}{T}[/tex]For the last 3 seconds:
time = 14 sec - 11 sec = 3 sec
displacement = 4 - 0 = 4 m
[tex]speed_3\text{ = }\frac{4}{3}\text{ m/s}[/tex]From the question:
The speed of the particle in the first T seconds was half the speed of the particle in the last 3 seconds
[tex]\begin{gathered} speed_1\text{ = }\frac{1}{2}(speed_3) \\ \frac{4}{T}\text{ = }\frac{1}{2}(\frac{4}{3}) \\ \frac{4}{T}=\text{ }\frac{4}{6} \\ \frac{4}{T}=\text{ }\frac{4}{6} \\ \text{cross multiply:} \\ 4(6)\text{ = 4(T)} \\ 24\text{ = 4T} \end{gathered}[/tex][tex]\begin{gathered} \frac{24}{4}\text{ = }\frac{4T}{4} \\ T\text{ = 6 sec} \end{gathered}[/tex]Use the sum and difference identities to rewrite the following expression as a trigonometric function of a single number.2лम2л五COS(15) w() - Sin(ਤੋਂ ) sin()-(COS
The sum identity for Cosine is given as:
[tex]\cos (A+B)=\cos A\cos B-\sin A\sin B[/tex]This is the same for the given equation in the equation, assuming:
[tex]\begin{gathered} A=\frac{2\pi}{5} \\ B=\frac{\pi}{12} \end{gathered}[/tex]Hence, the correct answer is:
[tex]\cos (A+B)=\cos A\cos B-\sin A\sin B[/tex]Pogle Translate Ethics related to aging.docx Х + a/courses/_19560_1/outline/assessment/_1482899_1/overview/attempt/_2637749-1/review?courseld=_19560_1 Show answer choices x Question 18 Suppose the triangles shown are similar with angle A = angle D, angle Bº-angle E, and angle C = angle F. Answer the question. B 10 22 20 A 2x-7 C D 2x +4 F What is the value of x?
Looking at the diagram, we can see that twice the sides of the first triangle is equakL
Write As An Algebraic Expression For The Following:3 Times A Number Decreased By 5The Quotient Of A Number and 3The Product Of Three Times A Number And 62 Less Than The Product Of A Number And 6
3x - 5
In answering the question, our chosen unknown number will be represented by a variable x
3 times a number
= 3 * x = 3x
decreased by 5 means we are going to subtract 5 from our previous answer
Thus, we have 3x - 5
Hong is participating in a 6-day cross-country biking challenge. He biked for 71, 59, 68, 70, and 68 miles on the first five days. How many miles does he need to bike on the last day so that his average (mean) is 64 miles per day?
Based on the given information, we can express the following
[tex]64=\frac{71+59+68+70+68+x}{6}[/tex]We formed that equation from the mean formula. Now, we solve for x,
[tex]\begin{gathered} 64\cdot6=336+x \\ x=384-336 \\ x=48 \end{gathered}[/tex]Hence, he needs to bike 48 miles on the last day to have an average of 64 miles per day.Find the volume of saup in a cylindricd can thatBaches til and inches across the lid
The volume of the cylinder is
[tex]V=\pi\times r^2\times h[/tex]Where:
r is the radius of the base of the cylinder
h is the height of the cylinder
Since the cylinder is 8 inches tall, then
h = 8 inches
Since it is 4 inches across the lid, then
The diameter of the base is 4 inches
Divide it by to get the radius of it, then
r = 2 inches
Now, substitute them in the rule above
[tex]\begin{gathered} V=\pi\times2^2\times8 \\ V=\pi\times4\times8 \\ V=32\pi in^3 \end{gathered}[/tex]We can use pi = 3.14, then
[tex]V=100.48in^3[/tex]The volume of the soup is 100.48 inches^3
Which one of the following graphs represents the solution of the inequality2x + 1 ≥ 3?
Given
The inequality,
[tex]2x+1≥3[/tex]To find:
The graph representing the inequality.
Explanation:
It is given that,
[tex]2x+1≥3[/tex]That implies,
[tex]\begin{gathered} 2x+1≥3 \\ 2x\ge3-1 \\ 2x\ge2 \\ x\ge1 \end{gathered}[/tex]Therefore, the graph representing the above inequality is,
how is 2/4 and 3/6 related
Stacy is building a candy house. She worked on it 3 2/3 hours before lunch and 6 1/4 hours after lunch. How many total hours did Stacy spend working on the candy house?
To calculate the total nmber of hours, we will simply add
[tex]3\frac{2}{3}+6\frac{1}{4}[/tex]Let's add the whole number part, then add the fraction part
That is;
[tex]3+6+\frac{2}{3}+\frac{1}{4}[/tex][tex]=9+\frac{8+3}{12}[/tex][tex]=9\frac{11}{12}\text{ hours}[/tex]The above is the total number of hour she spent.
a windshield wiper sweeps out a circular sector with radius r inches, and arc length = 1.4 times the radius.Write a SIMPLIFIED EXPRESSION in the box below that represents the area, in square inches, of the sector the wiper sweeps out.
The central angle θ in radians is given by
[tex]\begin{gathered} \theta=\frac{arc\text{ length}}{radius} \\ \text{ Therefore,} \\ \theta=\frac{1.4r}{r}=1.4 \end{gathered}[/tex]Area A of a sector with a radius r and a central angle θ in radians is given by:
[tex]A=\frac{1}{2}r^2\theta[/tex]Hence, the area A is:
[tex]\begin{gathered} A=\frac{1}{2}r^2(1.4) \\ A=0.7r^2 \end{gathered}[/tex]Therefore, the required simplified expression for the area is
A = 0.7r²
The concession stand sells pizza slices and nachos during football games. Pizza slices cost $0.55 and nachos cost $0.75. James bought 10 items for $6.30 (he was given a box to carry them all in). How many slices of pizza did he buy? How many orders of nachos did he buy? Slices of Pizza: Orders of Nachos:
We will determine the number of pizza slices and nachos he bought as follows:
[tex]p+n=10[/tex]Here, p represents pizza slices and n nachos.
and:
[tex]0.55p+0.75n=3.60[/tex]***
We solve the first function for either p or n:
[tex]\Rightarrow p=10-n[/tex]And using this, we replace in the second function:
[tex]\Rightarrow0.55(10-n)+0.75n=6.30[/tex]Now, we determine the value of n:
[tex]\Rightarrow5.5-0.55n+0.75n=6.30\Rightarrow0.2n=0.8\Rightarrow n=4[/tex]Now, we replace the value of n in the first equation and determine the value of p:
[tex]\Rightarrow p+4=10\Rightarrow p=6[/tex]So, he bought 6 slices of pizza and 4 units of nachos.
Is the answer A. or C.? Can you explain, please?
The correct answer is A.
In Panel 3, option C is what you found on the top of the box with a smiley face, if you flip it side ways like in panel 4, the direction of the shape will also change that is the same with option A.
A target with a diameter of 70 cm has 4 scoring zones formed by concentriccircles. The diameter of the center circle is 10 cm. The width of each ring is 10cm. A dart hits the target at a random point. Find the probability that it will hit apoint in the yellow region.
The probability is equal to divide the area of the yellow region by the area of the complete circle
so
step 1
Find the area of teh complete circle
r=70/2=35 cm
substitute
[tex]\begin{gathered} A=\pi\cdot35^2 \\ A=1,225\pi\text{ cm2} \end{gathered}[/tex]step 2
Find the area of the yellow region
[tex]\begin{gathered} A=\pi(35^2-25^2) \\ A=600\pi\text{ cm2} \end{gathered}[/tex]step 3
find the probability
P=600pi/1,225pi
P=0.4898
or
P=48.98%
3)225 using partial quotients.
75
-----------
3I225 I
- 210 I 70 ( because 70*3 = 210)
-------------- I +
15 I5 (because 5*3=15)
- 15 I
--------------------
0 75
Quotient is 75 and the remainder is 0
The function G (X) was obtained by transforming F (X)=1/x. The function F (X) is reflected about the x-axis and translate it up 12 units. Which equation represents G(x)?
EXPLANATION
Given the function f(x)= 1/ x
Reflecting it about the x-axis, give us the function f(x) = -1/x
Translating it up 12 units will give us the following function:
[tex]f_{\text{transformed}}(x)=-\frac{1}{x}+12[/tex]The function g(x) is as shown as follows:
[tex]g(x)=-\frac{1}{x}+12[/tex]The area of the triangle has a height of 10.2ft and base of 28ft. What is the area of the shaded region
The area of a triangle is computed as follows:
[tex]A=\text{base}\cdot\text{height}\cdot\frac{1}{2}[/tex]Substituting with base = 28 ft, height = 10.2 ft, we get:
[tex]A=28\cdot10.2\cdot\frac{1}{2}=142.8ft^2[/tex]The area of a rectangle is computed as follows:
[tex]A=\text{base}\cdot\text{height}[/tex]The rectangle of the graph has a base of 29.8 ft and a height of 23 ft. Its area is:
[tex]A=29.8\cdot23=685.4ft^2[/tex]Therefore, the area of the shaded region is:
[tex]\text{area of the rectangle - area of the triangle = 685.4-142.8 = }542.6\text{ sq. ft}[/tex]Evaluate.36² + 6 + - 15 + (30/-6)
Solving the operation in parenthesis gives us:
[tex]36^2+\text{ 6 + - 15 +}-5[/tex]Now we need to solve the power, which is done below:
[tex]1296\text{ + 6 + - 15 + - 5}[/tex]Adjusting all the signals:
[tex]1296+6-15-5[/tex]Performing the operations:
[tex]\begin{gathered} 1302\text{ -15 -5} \\ 1287\text{ -5} \\ 1282 \end{gathered}[/tex]how would you draw a machine diagram for the function: f(x)=the square root of x-1
We want to draw a machine diagram for the function;
[tex]f(x)\text{ = }\sqrt{x-1}[/tex]For the machine, x enters as the input to the machine and the machine produces f(x) as its output.
For this case, according to the equation the function applies a square root operation to the value of input decreased by 1.
Lets get the Output of the machine at x = 2, x=5, x=10 and x = 17.
[tex]\begin{gathered} at\text{ x=2} \\ f(x)\text{ = f(2) = }\sqrt{2-1}=\sqrt{1}=\text{ 1} \end{gathered}[/tex][tex]\begin{gathered} at\text{ x=5} \\ f(5)\text{ =}\sqrt{5-1}=\sqrt{4}=2 \\ \\ atx=10^{\square} \\ f(10)\text{ =}\sqrt{10-1}=\sqrt{9}=3 \\ \\ at\text{ x=17} \\ f(17)\text{ =}\sqrt{17-1}=\sqrt{16}=4 \end{gathered}[/tex]If 6/7 of a class was absent due to illness and 2/5 of the school was absent due to illness, is the fraction of the class that was absent equivalent to the fraction of the entire school that was absent?
We have to convert the fraction to a decimal number, because the fractions given are in the simplest form
[tex]\frac{6}{7}=0.86[/tex][tex]\frac{2}{5}=0.4[/tex]as we can see the fractions given are not equivalent because the decimal number must be the same in equivalent fractions.
Therefore
Rex wanted to estimate the mean finishing time for the finishers at the New York CityMarathon. He took a random sample of 10 finishers' times, which were skewed to the right witha sample mean of 271.5 minutes. He's considering using his data to make a confidence intervalfor the mean finishing time, has he met the conditions for creating a confidence interval for thetrue mean finishing time?
No, he isn't the sample is just a few finishers. He must increase the size of the sample. Or at least calculate which could be the size of the sample to determine if he's right or wrong.
0 / 8 pts Question 6 Your uncle plants a white pine that has a 15-centimeter diameter. The diameter of the trunk grows an average of 0.5 centimeter every year. Write an expression that shows the diameter of the tree in years y. Question 7 0 / 8 pts
we are asked to find an expression to determine the diameter of a tree as a function of time. Since we are told that the initial diameter is 15 cm and that the diameter increases 0.5 cm/year. This means that to the 15 cm of the initial diameter we need to add the amount that the diameter increased per year by the number of years, that is, is "x" is the number of years, that we need to add 0.5x. The equation is then:
[tex]D=15+0.5x[/tex]Where D is the diameter.
What is the solution to the equation 4x = 44?x = 10x = 40x = 11x = 4
Dividing the given equation by 4 we get:
[tex]\frac{4x}{4}=\frac{44}{4}.[/tex]Simplifying the above result we get:
[tex]x=11.[/tex]Answer: Third option.
[tex]x=11.[/tex]
How do I solve for 15? It says to use tan30=20/a
Since we have a right triangle, we can relate the given angle and the legs a and 20 by means of the tangent function ,that is,
[tex]\tan 30=\frac{20}{a}[/tex]Since tangent of 30 degrees is
[tex]\text{tan}30=\frac{\text{ opposite side to angle 30}}{\text{ adjacent side to angle 30}}=\frac{1}{\sqrt[]{3}}[/tex]we have that
[tex]\frac{1}{\sqrt[]{3}}=\frac{20}{a}[/tex]Then, by cross multiplying the numbers, we have
[tex]1\times a=20\times\sqrt[]{3}[/tex]Therefore, we have:
[tex]a=20\sqrt[]{3}=34.64[/tex]By rounding to the nearest whole number, the answer is: 35 units
1. A chocolate chip cookie recipe calls for 1/2 cup of chocolate chips per batch. Alonzo wants to make 3 1/2 batches. a. How many chocolate chips will he need?
Given:
1 chocolate chip cookie recipe = 1/2 cup of chocolate chips per batch.
Number of batches he wants to make = 3½
Let's find the number of chocolate chips he will need.
The number of chips he will need are:
[tex]\begin{gathered} \\ N\text{ = number of batches }\ast\text{ amount of cup per batch} \\ \\ N=\frac{1}{2}\ast3\frac{1}{2} \\ \end{gathered}[/tex]Rewrite the mixed fraction to improper fraction:
[tex]\begin{gathered} N=\frac{1}{2}\ast\frac{7}{2} \\ \\ N=\frac{7}{4} \\ \\ N=1\frac{3}{4} \end{gathered}[/tex]Therefore, the amount of chocolate chips he will need is:
[tex]1\frac{3}{4}\text{ cups of chocolate chips}[/tex]ANSWER:
[tex]1\frac{3}{4}\text{ cups of chocolate chips}[/tex]What is the value of the expression 7x2+ 9x-3 when x = 3?
Answer:
87
Explanation:
To find the value of the expression at x = 6, we simply replace x with 6. This gives
[tex]7(3)^2+9(3)-3[/tex]which we simplify to get:
[tex]\begin{gathered} 7\times9+27+-3 \\ =63+27-3 \\ =\boxed{87.} \end{gathered}[/tex]Hence, the value of the expression is 87 when x = 3.
PreviousProblem ListNext(1 point)emsIf you borrow $49000 at a fixed annual interest rate of 9.1% annual interest and pay it back in equal monthly payments for 9 years, thenthe formula says that your payment amount isPA (5)1-(1+)-nitwhere (fill in the blanks):A=r=(round to four decimal places).na, andt =Note: You can earn partial credit on this problem2:43 PM
We have the following formula:
[tex]P=\frac{A\cdot(\frac{r}{n})}{1-(1+\frac{r}{n})^{-n\cdot t}}.[/tex]Where:
• A = the money borrowed,
,• r = the annual interest rate in decimals,
,• n = the number of annual payments,
,• t = the number of years.
In this problem, we have:
• A = $49000,
,• r = 9.1% = 9.1/100 = 0.091,
,• n = 12 (we have monthly payments),
,• t = 9 years.
Answer
• A = 49000
,• r = 0.091
,• n = 12
,• t = 9
If you wanted to make $501 by investing $3692 ofor 7 years in an account that pays simple interest, what interest rate you would need to achieve your goal?
The formula for simple interest is:
[tex]i=\text{Prt}[/tex]Where
i is the interest amount
P is the initial amount invested
r is the rate of interest [in years]
t is the time period [in years]
We are given
i = 501 [wants to achieve interest of 501 dollars\
P = 3692
r is what we need to figure out
t is 7
Substituting, we get:
[tex]\begin{gathered} i=\text{Prt} \\ 501=3692(r)(7) \\ r=\frac{501}{3692\times7} \\ r=0.019385 \end{gathered}[/tex]Mulitplying by 100, we get the percentage interest rate.
0.019385 * 100 = 1.94%
Could you please check my answer? Use elimnation to solve the system of equations:3x+4y=82x+3y=8My answer: (-8, 8)
According to the given data we have the following system of equations:
3x+4y=8
2x+3y=8
In order to calculate the variables x and y we would make the following calculations:
3x+4y=8
2x+3y=8
First we would multiply 3x+4y=8 times 2 and 2x+3y=8 times -3 So:
3x+4y=8
2x+3y=8
0 -y=-8
y=8
If y=8, hence, we would substitute the value of y into the first equation so we can finally calculate the variable x.
So:
plug y=8 into 3x+4y=8
3x + 4(8)=8
3x+ 32=8
3x=-24
x=-24/3
x=-8
Hence, the values of x and y would be (-8,8)
Luther started collecting lunch boxes when he was 5 years old. He had 12 superhero lunch boxes, 19 outer space lunch boxes, and 26 rock band lunch boxes.Then Luther's cousin started her own lunch box collection. Luther wanted to help her get started, so he gave his cousin 17 lunch boxes from his collection. How many lunch boxes does Luther have left in his collection?
Solution
For this case we have the following lunch boxes
12 from superhero
19 from outer space
26 from rock bands
A total of: 12+19+26= 57 lunch boxes
And he gave to his cousin 17 lunch boxes so then the remaining are:
57-17= 40 lunch boxes
find the value of 3√x +7 if x = 25
Given the expression
[tex]\begin{gathered} 3\sqrt[]{x}+7 \\ \end{gathered}[/tex]Given that x = 25
Substitute 25 for x into the expression above
[tex]\begin{gathered} \text{Where x = 25} \\ 3\sqrt[]{x}+7=3\sqrt[]{25}+7 \\ =3\sqrt[]{25}+7=3(5)+7 \\ =3(5)+7=15+7 \\ =15+7=22 \end{gathered}[/tex]Hence, the answer is 22