The formula for finding the volume of a rectangular prism (the cargo area of the truck is the shape of a rectangle in 3D; a rectangular prism) is V = (l)(w)(h); where l = length, w = width, and h = height.
First, substitute the known values into the equation:
l = 8.5
w = 6
h = 10.5
V = (8.5)(6)(10.5)
(Note: .5 = 1/2)
Now, all we need to do is simplify:
V = 535.5 ft³ OR 535 1/2 ft³
(Note: ft³ is the condensed form of cubic feet)
You can pick whichever form your test directs you to use. They are both the same value though.
Hope this helps!
The volume of the cargo area of the truck is 519.75 cubic feet.
The volume of the cargo area of the truck can be calculated by multiplying its length, width, and height. Given the dimensions in feet are:
Length = 8 1/2 feet = 8.5 feet = 8 + 1/2 feet
Width = 6 feet
Height = 10 1/2 feet = 10.5 feet = 10 + 1/2 feet
To find the volume, we convert the mixed numbers to improper fractions and then multiply:
Length in fractions = 8 + 1/2 = 17/2 feet
Width in fractions = 6 = 6 * 2/2 = 12/2 feet
Height in fractions = 10 + 1/2 = 21/2 feet
Now, multiply the dimensions to find the volume:
Volume = Length * Width * Height
Volume = (17/2 feet) * (12/2 feet) * (21/2 feet)
Volume = (17 * 12 * 21) / (2 * 2 * 2) cubic feet
Volume = 4158 / 8 cubic feet
Simplifying the fraction, we get:
Volume = 519.75 cubic feet
6. 2× =5
7. y +1.8=14.7
8. 6=1/2 z
9. 3 1/4=1/2 +w
10. 2.5t=10
Answer:
6=1/2z
6÷1/2=1/2÷1/2z
6÷1/2=z
6×2/1 = z
z=12
h(x)= 6-3x when x=-1/4
Answer:
6 [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Substitute x = - [tex]\frac{1}{4}[/tex] into h(x)
h(- [tex]\frac{1}{4}[/tex]) = 6 - (3 × - [tex]\frac{1}{4}[/tex])
= 6 - (- [tex]\frac{3}{4}[/tex])
= 6 + [tex]\frac{3}{4}[/tex] = 6 [tex]\frac{3}{4}[/tex]
what is the value of the expression 10/5!x2!
Answer:
[tex]\large\boxed{\dfrac{10}{5!\times2!}=\dfrac{1}{24}}[/tex]
Step-by-step explanation:
[tex]n!=1\cdot2\cdot3\cdot...\cdot n\\\\5!=1\cdot2\cdot3\cdot4\cdot5=120\\2!=1\cdot2=2\\\\\dfrac{10}{5!\times2!}=\dfrac{10}{120\cdot2}=\dfrac{1}{24}[/tex]
convert 150 degrees to radian
Answer:
A
Step-by-step explanation:
To convert degrees to radians
radian measure = degree measure × [tex]\frac{\pi }{180}[/tex]
Hence
radian measure = 150° × [tex]\frac{\pi }{180}[/tex]
Cancel both 150 and 180 by 30, then
radian measure = 5 × [tex]\frac{\pi }{6}[/tex] = [tex]\frac{5\pi }{6}[/tex]
Final answer:
To convert 150 degrees to radians, multiply 150 by π/180 to get 5/6 * π or approximately 2.61799 radians.
Explanation:
To convert 150 degrees to radians, we use the fact that one complete revolution is 360 degrees which is equal to 2π radians (approximately 6.28318 radians). From this, we can derive that 1 degree is equal to π/180 radians. We multiply the value in degrees by π/180 to get the equivalent in radians.
150 degrees * π/180 radians/degree = 150/180 * π radians = 5/6 * π radians.
Therefore, 150 degrees is equal to 5/6 times π or approximately 2.61799 radians.
A lawnmower blade has a diameter of 36 inches and spins at a rate of 60 revolutions per minute.
Answer:
C. 2,160π
Step-by-step explanation:
took test
The linear velocity at the end of the blade is 13571.7 inches per minute by using the circumference of the circle that the blade makes to calculate the linear velocity at the end of the blade.
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Here, The total distance in 1 minute is 60 times circumference of the circle made by the end of the blade of the lawnmower.
Since, The blade is 36 inches long, it can be taken as radius of that circle.
The circumference is thus calculated as;
⇒ linear velocity = 226.19 × 60
= 13571.7 inches per minute
Thus, The linear velocity at the end of the blade is 13571.7 inches per minute.
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FIND THE SURFACE AREA HELP ASAP GET BRAINLISTS
Answer:
[tex]\large\boxed{a.\ 7200\pi\ mm^2}[/tex]
Step-by-step explanation:
The formula of a surface area of a cylinder:
[tex]S.A.=2\pi r(r+H)[/tex]
r - radius
H - height
We have r = 40mm and H = 50mm. Substitute:
[tex]S.A.=2\pi(40)(40+50)=80\pi(90)=7200\pi\ mm^2[/tex]
Jon has to choose which variable to solve for in order to be able to do the problem below in the most efficient manner.
6x + 3y = 27 5x+ 2y + 21
Which variable should he choose so that he can use substitution to solve the system?
Jon should solve for y in the first equation because the coefficients can be reduced by a common factor to eliminate the coefficient for y.
Jon should solve for x in the first equation because the coefficients can be reduced by a common factor to eliminate the coefficient for x.
Jon should solve for y in the second equation because the coefficients can be reduced by a common factor to eliminate the coefficient for y.
Jon should solve for x in the second equation because the coefficients can be reduced by a common factor to eliminate the coefficient for x.
The most efficient way to solve this problem is isolating the y in the first equation because:
6x + 3y = 27
3y = 27 - 6x
y = 9 - 2x
Since all the numbers have a common factor of 3, it can be easily simplified/reduce.
If you used any other variable, you would have gotten a fraction.
Now that you found y, you can substitute it into the other equation to solve for x.
ANYWAYS, your answer is A
Answer:
A
Step-by-step explanation:
Jon should solve for y in the first equation because the coefficients can be reduced by a common factor to eliminate the coefficient for y.
-1 1/5 divided by -1 5/6
Answer:
0.65454545454 or -30/46 or 65.454545454%
Hope This Helps! Have A Nice Day!!
Answer:
-36/55
Step-by-step explanation:
Jamie and Chris both started a stamp collection at the same time. Jamie started her stamp collection with 100 stamps and added 13 stamps to her collection each week. Chris started his stamp collection with 130 stamps and added 8 stamps to his collection each week. After how many weeks did Jamie and Chris have the same number of stamps in their collections?
a.) 6
b.) 230
c.) 10
d.) 178
Answer:
A) 6
Step-by-step explanation:
8 (6) = 48
130 + 48 = 178
13 (6) = 78
100 + 78 = 178
178 = 178
BRAINLIEST, BLANK POINTS, AND THANKS/GOOD RATINGS
Kevin, a 13-year-old boy, has a resting heart rate of 67 beats per minute. Using the lower and upper limit reserve training percentages of 50% and 85% respectively, what is Kevins's target heart rate range?
A) 137-186
B) 140-194
C) 147-200
D) 153-207
I believe that the answer is A 137-186,
that is the answer if you use the Karvonen formula
Karvonen formula : target training HR = resting HR + (0.6 [maximum HR -resting HR]).
1. Resting Heart Rate (RHR) = your pulse at rest
2. Maximum Heart Rate (MHR) = 220- your age
3. Heart Rate Reserve (HRR)= Maximum Heart Rate - Resting Heart Rate
sorry idk why my answer was deleted
Answer: That would be A mate 137-186
Step-by-step explanation:
Write an equation of an exponential function of the form y=ab^x passing through the points (0,8) and (6,0.125)
Answer:
[tex]y=8\cdot \left(\dfrac{1}{2}\right)^x.[/tex]
Step-by-step explanation:
If the graph of exponential function passes through the points (0,8) and (6,0.125), then the coordinates of these points sutisfy the equation [tex]y=a\cdot b^x:\\[/tex]
[tex]8=a\cdot b^0\Rightarrow a=8,\\ \\0.125=8\cdot b^6\Rightarrow \dfrac{1}{8}=8\cdot b^6,\\ \\b^6=\dfrac{1}{64},\\ \\b^6=\dfrac{1}{2^6}\Rightarrow b=\dfrac{1}{2}.[/tex]
Thus, the equation of exponential function is
[tex]y=8\cdot \left(\dfrac{1}{2}\right)^x.[/tex]
Find the product of 1 3/5 and 8 (show work please tysm)
Answer:
20 4/5
Step-by-step explanation
13/5 x 8/1 = 104/5= 20 4/5
The product of [tex]\(1 \frac{3}{5}\)[/tex] and [tex]\(8\)[/tex] is calculated by first converting the mixed number to an improper fraction and then multiplying the two fractions together.
Step 1: Convert [tex]\(1 \frac{3}{5}\)[/tex] to an improper fraction.
To convert a mixed number to an improper fraction, multiply the whole number by the denominator of the fractional part and add the numerator of the fractional part. Then, place the result over the original denominator.
For [tex]\(1 \frac{3}{5}\)[/tex] , the whole number is [tex]\(1\)[/tex], and the fractional part is [tex]\(\frac{3}{5}\)[/tex]. So, we have:
[tex]\[ 1 \times 5 + 3 = 5 + 3 = 8 \][/tex]
Thus, [tex]\(1 \frac{3}{5}\)[/tex] as an improper fraction is [tex]\(\frac{8}{5}\)[/tex].
Step 2: Multiply the improper fraction by \(8\).
Now, we multiply [tex]\(\frac{8}{5}\)[/tex] by [tex]\(8\)[/tex] . When multiplying fractions, we multiply the numerators together and the denominators together:
[tex]\[ \frac{8}{5} \times 8 = \frac{8 \times 8}{5} \][/tex]
Step 3: Simplify the product.
[tex]\[ \frac{8 \times 8}{5} = \frac{64}{5} \][/tex]
So, the product of [tex]\(1 \frac{3}{5}\)[/tex] and [tex]\(8\)[/tex] is [tex]\(\frac{64}{5}\)[/tex].
To express this as a mixed number, we divide [tex]\(64\)[/tex] by [tex]\(5\):[/tex]
[tex]\[ 64 \div 5 = 12 \text{ remainder } 4 \][/tex]
Thus, [tex]\(\frac{64}{5}\)[/tex] as a mixed number is [tex]\(12 \frac{4}{5}\)[/tex].
The final answer is[tex]\(12 \frac{4}{5}\) or \(\frac{64}{5}\).[/tex]
Analyze the table of values for the continuous function, f(x), to complete the statements.
A local maximum occurs over the interval .
A local minimum occurs over the interval .
Answer:
1. (-2,0)
2. (0,2)
I'm confirming the answer above. These are also the answers on Edge-nuity. I use Edge-nuity
Step-by-step explanation:
A local maximum occurs over the interval (-2,0)
A local minimum occurs over the interval (0,2)
How do you find a function's maximum value?We may calculate the maximum of a continuous and twice differentiable function f(x) by first differentiating it with respect to x and then equating it to 0.
A local maximum occurs over the interval (-2,0)
A local minimum occurs over the interval (0,2)
Hence, local maximum and local minimum occurs at (-2,0) and (0,2).
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Choose the set of equations that best represent the following information:
The sum of two numbers, a and b, is 12. The first number, a, is 8 more than the second number.
A. ab = 12, a + 8 > b
B. a + b = 12, a = b + 8
C. a + a = 12, b - 8 = a
D. a + b = 8, a > b + 12
Answer:
b
Step-by-step explanation:
The set of equations that best represent the given information is B. a + b = 12, a = b + 8. This represents both conditions: the sum of the two numbers is 12 and a is 8 more than b.
Explanation:The best representation of the given information is provided by option B. a + b = 12, a = b + 8. This is because it accurately portrays both conditions mentioned in the question. The first part of the equation, a + b = 12, represents the information that the sum of the two numbers a and b is 12. The second part of the equation, a = b + 8, represents the information that the first number, a, is 8 more than the second number, b.
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Iterations question one, thanks for the help :)
Answer:
option d
13 , 173 , 29933
Step-by-step explanation:
Given in the question a function, f(x) = x² + 4
initial value x0 = -3
4 times iteration means f(f(f(x)))First iteration
f(x0) = f(-3) = (-3)² + 4 = 13
x1 = 13
Second iteration
f(x1) = f(13) = (13)² + 4 = 173
x2 = 173
Third iteration
f(x2) = f(173) = (173)² + 4 = 29933
x3 = 29933
Four students had the following amounts of money in their pockets: $3.14, $.67, $2.45, and $1.14. How much money did they have total?
A. $7.44
B. $7.40
C. $7.00
D. $7.04
ANSWER
C. $ 7.00
EXPLANATION
It was given that four students had the following amounts of money in their pockets: $3.14, $.67, $2.45, and $1.14.
To find the amount of money they have in total, we add all their monies together to get:
$3.14+$0.67+$2.45+$1.14
This will give us a total of $7.00
Answer:
7.40
Step-by-step explanation:
to get the total money for the four student you have to do addition.
3.14
2.45
1.14
+0.65 to get $7.40
A happy graduate throws her cap into the air. It comes back to her hand (at the same height) in exactly 2.0 seconds. With what velocity did she originally throw the cap? Assume the acceleration due to gravity is -10
m
s2
.
A) 5
m
s
B) 10
m
s
C) 15
m
s
D) 20
m
s
Final answer:
The initial velocity at which she threw the cap is 20 m/s.
Explanation:
Since the cap comes back to her hand at the same height, the initial vertical velocity of the cap is 0 m/s. The acceleration due to gravity is -10 m/s². Using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can solve for the initial velocity. In this case, v = 0 m/s, a = -10 m/s², and t = 2.0 s. Plugging in these values, we get:
0 = u + (-10)(2.0)
0 = u - 20
u = 20 m/s
So the initial velocity at which she threw the cap is 20 m/s.
What is 7 more then 5 times the number 9 divided by 15
5•(9/15)+7= 9/3 +21/3= 30/3=10
What is the distance between point A and point B? Round your answer to the nearest tenth.
A. 5
B 3.6
C. 6
D. 2.2
Answer:
(B) 3.6
Step-by-step explanation:
Coordinate of A = (-3, 9)
Coordinate of B = (-1, 6)
[tex]\text {Distance = }\sqrt{(- 3 - (-1) )^2 + (9 - 6)^2}[/tex]
[tex]\text {Distance = }\sqrt{(- 2 )^2 + (3)^2}[/tex]
[tex]\text {Distance = }\sqrt{13}[/tex]
[tex]\text {Distance = }3.6[/tex]
Answer:
B
Step-by-step explanation:
Calculate the distance using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = A(- 3,9) and (x₂, y₂ ) = B(- 1, 6)
d = [tex]\sqrt{-1+3)^2+(6-9)^2}[/tex]
= [tex]\sqrt{2^2+(-3)^2}[/tex]
= [tex]\sqrt{4+9}[/tex]
= [tex]\sqrt{13}[/tex] ≈ 3.6 → B
What is the value of h when the function is converted to vertex form? Note: Vertex form is g(x)=a(x−h)2+k . g(x)=x2−6x+14 Enter your answer in the box. h =
Answer:
h=3
Step-by-step explanation:
The given function is
[tex]g(x)=x^2-6x+14[/tex]
We add and subtract the square of half the coefficient of x to obtain;
[tex]g(x)=x^2-6x+(-3)^2-(-3)^2+14[/tex]
Identify the first three terms as a perfect square trinomial;
[tex]g(x)=(x-3)^2-9+14[/tex]
Simplify;
[tex]g(x)=(x-3)^2+5[/tex]
Comparing this to
[tex]g(x)=a(x-h)^2+k[/tex]
We have h=3 and k=5
Answer: h=3
the other answer on this page is right
Step-by-step explanation:
x=88 ?89 ? Or 90?
What is x= ?
Answer:
The measure of angle x is 90°
Step-by-step explanation:
Given the figure in which
∠1=88°, ∠6=89°
we have to find the value of x.
∠5=∠6=89° (∵ Vertically opposite angles)
∠1+∠4=∠6 ( ∵ By exterior angle property)
88°+∠4=89°
∠4=89°-88°=1°
As AC=CB (both are radii of same circle)
∴ ∠4=∠3=1°
Now, by exterior angle property
x=∠5+∠3=89°+1°=90°
Hence, the measure of angle x is 90°
Applying the angle of intersecting chords theorem, the value of x in the diagram showing the circle is: C. 90.
What is the Angle of Intersecting Chords Theorem?According to the angle of intersecting chords theorem, the measure of the angle formed at the point of intersection of two chords inside a circle equals half the sum of the intercepted arcs.
89 = 1/2(88 + x) [based on the angle of intersecting chords theorem]
2(89) = 88 + x
178 = 88 + x
178 - 88 = x
x = 90° (Option C).
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solve equation for y .x - y= -1
Answer:
y = -1-x
Step-by-step explanation:
a cube had a side length of 13 millimeters. what is the surface area of the cube
Answer:
[tex]S_a = (13mm)^2 \cdot 6 = 1014 mm^2[/tex]
Step-by-step explanation:
the axis in the coordinate plane, which runs horizontally, is the _ _ _ _ _ _ axis.
a. x
b. y
c. origin
d. none of these
X axis is the answer to you question because it’s going across not up nor down
The answer is A. The x-axis
Solve for in simplest form
2x < 15
it can be 2, 3, 4, 5, 6, or 7.
only for sutff to do
Hey, so sorry for answer so late! I wasn't on here for a while, and I didn't get your message until I logged back in.
1.) C. 8, because if you add 3 and 5, you get 8, which is your answer.
2.) D. 9, because 9/2 equals 4.5
3.) A. 0, because if you start off with zero and add 6, you will get 6.
4.) D. y = x - 5, because when you subtract 5 from 42.50, you get 37.50, which is our desired result.
Hope this helps ya, and again, sorry about the inconvenience of answering so late. Feel free to ask more questions by messaging me on this question. Have a good day :D
If the output of the function is 5, then the input is
1. 8. ( optionC)
2. 9 ( Option D)
3. 0( option A)
4. The equation for the situation is y = x -5 ( option D).
It expresses a unique output for each input, exemplified by f(x) in algebraic terms.
In the equation;
y = x -3
the output is y
therefore;
5 = x -3
x = 5+3 = 8
Therefore the input value is 8.
2. The input value will be
x = y × 2
x = 4.5 ×2 = 9
3. The input value will be
x = 6 - 6
= 0
4. let y be the cost after the coupon and x is before the coupon
y = x - 5
A car rental agency has 15 vehicles available, of which 3 are minivans.
What is the probability that a randomly selected vehicle will be a minivan?
Simplify your answer and write it as a fraction or whole number.
P(minivan) =
Answer:
i am pretty sure its 1/5
Step-by-step explanation:
Answer:
1/5
Step-by-step explanation:
P (minivan) = number of minivans / total number of vehicles
We have 3 minivans and 15 vehicles
P (minivan) = 3/15 = 1/5
The ornament below is composed of two congruent square pyramids. Each square pyramid has base side lengths of 2 inches and a height of 2.5 inches.
What is the volume, in cubic inches, of the ornament?
Answer:
The volume of the ornament is [tex]6\frac{2}{3}\ in^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the ornament is equal to the sum of the volume of the two congruent square pyramids
so
[tex]V=2[\frac{1}{3}b^{2} h][/tex]
we have
[tex]b=2\ in[/tex]
[tex]h=2.5\ in[/tex]
substitute
[tex]V=2[\frac{1}{3}(2)^{2} (2.5)][/tex]
[tex]V=\frac{20}{3}\ in^{3}[/tex]
Convert to mixed number
[tex]\frac{20}{3}=\frac{18}{3}+\frac{2}{3}=6\frac{2}{3}\ in^{3}[/tex]
Answer:
C
Step-by-step explanation:
Use basic trigonometric identities to simplify the expression: 2 sin (x) cos (x) sec (x) csc (x) = ?
Answer:
[tex]2sin(x)*cos(x)*sec(x)*csc (x)=2[/tex]
Step-by-step explanation:
Remember the identities:
[tex]sec(x)=\frac{1}{cos(x)}\\\\csc(x)=\frac{1}{sin(x)}[/tex]
Ginven the expression:
[tex]2sin(x)*cos(x)*sec(x)*csc (x)[/tex]
You need to substitute [tex]sec(x)=\frac{1}{cos(x)}[/tex] and [tex]csc(x)=\frac{1}{sin(x)}[/tex] into it:
[tex]2sin(x)*cos(x)*sec(x)*csc (x)=2sin(x)*cos(x)*\frac{1}{cos(x)}*\frac{1}{sin(x)}[/tex]
Now, you need to simplify.
Remember that:
[tex]\frac{a}{b}*\frac{c}{d}=\frac{a*c}{b*d}[/tex]
And:
[tex]\frac{a}{a}=1[/tex]
Then, you get:
[tex]=\frac{2sin(x)*cos(x)}{cos(x)*sin(x)}}=2[/tex]
Solve for x in the following equation.
For this case we must find the value of "x" of the following equation:
[tex]x ^ 2-9 = 0[/tex]
So:
We add 9 to both sides of the equation:
[tex]x ^ 2-9 + 9 = 9\\x ^ 2 = 9[/tex]
We apply square root on both sides of the equation to eliminate the exponent on the left side:
[tex]x = \pm \sqrt {9}[/tex]
Thus, the solutions are:
[tex]x_ {1} = + 3\\x_ {2} = - 3[/tex]
ANswer:
[tex]x_ {1} = + 3\\x_ {2} = - 3[/tex]
Opcion C