Answer:
[tex]Area = 1200m^2[/tex]
[tex]Perimeter = 148m[/tex]
Step-by-step explanation:
To find the area, just multiply the length by the width. In fact, we have a simple formula for this:
[tex]A(area) = lw[/tex]
[tex]l(length) = 50[/tex]
[tex]w(width)= 24[/tex]
Now, we need to plug in our values:
[tex]A(area)= 50*24[/tex]
Simplify:
[tex]A(area) = 1200[/tex]
Therfore, the area of the rectangle is:
[tex]1200m^2[/tex]
Now, lets move on to the perimeter(again, we have a simple formula!):
[tex]P(perimeter) = 2(l+w)[/tex]
Plug in our values from before:
[tex]P(perimeter)= 2(50 + 24)[/tex]
Simplify:
[tex]P(perimeter)= 2(74)[/tex]
Multiply it out:
[tex]P(perimeter) = 148[/tex]
Therfore, the perimeter of your rectangle is 148 m
Always remember to include the proper units and format your work well to minimize mistakes and leave less room for error.
I hope this helped!
~~~Harsha~~~
tions using any method: word problems WHE
Write a system of equations to describe the situation below, solve using any method, and fill
in the blanks.
Clarksville City Cafe recently introduced a new flavor of coffee. They served 60 grande cups
and 59 jumbo cups of the new coffee today, which equaled a total of 61,644 grams. The day
before, 60 grande cups and 74 jumbo cups were served, which used a total of 71,184 grams.
How much coffee is required to make each size?
There are 968
grams in a grande cup of coffee and
Submit
grams in a jumbo one.
For this reason, 968 grams of coffee are needed to make a grande cup, and 998 grams are needed to make a jumbo cup.
Let's call the amount of coffee required to make a grande cup "g" and the amount of coffee required to make a jumbo cup "j". We want to find the values of g and j.
From the first piece of information, we know that:
60g + 59j = 61,644
From the second piece of information, we know that:
60g + 74j = 71,184
We can solve this system of equations by using the method of elimination. To eliminate g, we can subtract the first equation from the second equation:
(60g + 74j) - (60g + 59j) = 71,184 - 61,644
Simplifying, we get: 15j = 9540
Dividing by 15, we get: j = 636
Now that we know j, we can substitute it into either equation to find g. Let's use the first equation:
60g + 59(636) = 61,644
Simplifying, we get: 60g = 59,880
Dividing by 60, we get: g = 998
Therefore, the amount of coffee required to make a grande cup is 968 grams, and the amount of coffee required to make a jumbo cup is 998 grams.
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A retirement account has a balance of $300,000. You want to receive monthly payments(withdrawals) from the account for a total of 25 years. The retirement account earns 4% interest. How much will you be able to receive each month?
The monthly payments you can withdraw from the retirement account is $1,583.4.
What is the amount received each month?The monthly payments you can withdraw from the retirement account, is calculated as;
PV = Px [(1 - (1 + r)⁻ⁿ) / r]
where;
PV is the present value of the annuity P is the monthly payment you want to receiver is the interest rate per period n is the total number of periodsThe total number of periods = 25 years x 12 months/year = 300 months
PV = P x [(1 - (1 + r)⁻ⁿ) / r]
$300,000 = P x [(1 - (1 + 0.04/12)⁻³⁰⁰) / (0.04/12)]
$300,000 = P x 189.47
P = $300,000 / 189.47
P= $1,583.4
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Find dx/dt when x = e^6t
2x + 8 > -4. 2.find the solution set of x and express the solutions set in number form
The solution set of this inequality is {x| x > -6.1}
How to find the solution set?Here we have the inequality:
2x + 8 > -4.2
To find the solution set, we need to isolate the variable x in one of the sides of the inequality. Doing that we will get:
2x + 8 > -4.2
2x > -4.2 - 8
2x > -12.2
x > -12.2/2
x > -6.1
So the set of all numbers larger than -6.1, this in number form is:
{x| x > -6.1}
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A bag contains red and yellow cubes in the ratio of 3:4. What is the probability that a red cube is picked at random from the bag?
Answer:
Step-by-step explanation:
ok Let me explain :
Your argument of saying that the prob is 1/2 because there are 2 colors.
Had there been red, blue and green cubes you would have ended up calculating the prob as 1/3.
But this concept is wrong.
Prob is the chance occurrence of an event given many such events.
here since we have 4 cubes , the chance to pick any one is equal and that is 1/4
chance of picking a blue cube (1/4)*1 ....since we have one blue cube
chance of picking a red cube (1/4)*3 ....since we have one red cubes
You can think in a simple manner also, when something is greater in number (3>1) , the chances to pick that would obviously be more , so the probability cannot be half.
Use spherical coordinates. Evaluate E x2 + y2 + z2 dV, where E lies above the cone z = x2 + y2 and between the spheres x2 + y2 + z2 = 1 and x2 + y2 + z2 = 64.
Answer:
To solve this problem using spherical coordinates, we need to parameterize the region E using rho, theta, and phi. The cone z = x^2 + y^2 becomes phi = arctan(sqrt(x^2+y^2)/z), and the sphere x^2 + y^2 + z^2 = 1 becomes rho = 1, while x^2 + y^2 + z^2 = 64 becomes rho = 8. Then, we can integrate over the bounds rho = 1 to rho = 8, theta = 0 to theta = 2pi, and phi = 0 to phi = arctan(sqrt(x^2+y^2)/z), using the integrand x^2 + y^2 + z^2. The final result is a numerical value that represents the volume of the region E.
Simplify the following fraction:
x² + x -6 / x²-9
pls help asap
Answer:
The answer is located inside the file sent below
9) The graph shows the amount of money Lucy makes for babysitting. a) Using the graph, give an equation in the form of d=rh , where d is dollars,r is rate, and h is hours, that accurately describes this situation.
The linear equation that gives the graph expression is: d = 2h
How to solve Linear equation Graphs?The general formula for the equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
We are given the equation as: d = rh
where:
d is dollars
r is rate
h is hours,
From the graph, we can find the rate by finding the slope of the graph.
(1, 4) and (2, 8)
Thus:
Slope = (8 - 4)/(2 - 1)
Slope = 2
Thus, r = 2
Then d = 2h
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Reflection over the x-axis of the point ( − 3 , − 7 ) (−3,−7)
The image of the point (-3, -7) after a reflection over the x-axis is (-3, 7)
Calculating the image of the point after a reflection over the x-axis?From the question, we have the following parameters that can be used in our computation:
Point = (-3, -7)
Transformation rule
A reflection over the x-axis
The rule of a reflection over the x-axis is
(x, y) = (x, -y)
Using the above as a guide, we have the following:
Image = (-3, 7)
Hence the image of the point after a reflection over the x-axis is (-3, 7)
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What value of x makes this equation true? 0.17x 0.03 0.03x - 0.002
The value of x that makes the equation true is 0.2.
We have the Equation,
0.17x - 0.03 = 0.03x - 0.002
Simplifying the equation by adding 0.002 to both sides, we get:
0.17x - 0.028 = 0.03x
Subtracting 0.03x from both sides, we get:
0.14x - 0.028 = 0
Adding 0.028 to both sides, we get:
0.14x = 0.028
Dividing both sides by 0.14, we get:
x = 0.2
Therefore, the value of x that makes the equation true is 0.2.
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Richard is selling bundles of wood. The total weight of the wood he is selling is 3,941 pounds, and there are 70 bundles. If each bundle weighs the same, how much does one bundle of wood weigh?
Answer:
Each bundle of wood weighs approximately 56.3 pounds.
Explanation:
To determine the weight of one bundle, we divide the total weight of all the bundles by the number of bundles. Thus, the weight of one bundle is equal to 3,941 pounds divided by 70 bundles, which is approximately 56.3 pounds. Therefore, each bundle of wood weighs approximately 56.3 pounds.
Amit can complete a piece of work in 2.25 days. Badri takes double the time taken by Amit. Chetan
takes double that of Badri, and Das takes double that of Chetan to complete the same task. They are
split into two groups (of one or more persons) such that the difference between the times taken by
the two groups to complete the same work is minimum. What could be the composition of the faster
group?
Answer:
Easy
Step-by-step explanation:
Let the time taken by Badri to complete the work be B. Then Amit can complete the work in 2.25 days, so we can write:
A = 2.25/B
Chetan takes double that of Badri to complete the work, so we can write:
C = 2B
Das takes double that of Chetan to complete the work, so we can write:
D = 2C = 4B
Let the first group consist of Amit and Das, and the second group consist of Badri and Chetan. Then the time taken by the first group to complete the work is:
T1 = A + D = 2.25/B + 4B
The time taken by the second group to complete the work is:
T2 = B + C = B + 2B = 3B
The difference between the times taken by the two groups to complete the work is:
T2 - T1 = 3B - (2.25/B + 4B) = 3B - 2.25/B - 4B
To minimize this difference, we take the derivative with respect to B and set it equal to zero:
d/dB (3B - 2.25/B - 4B) = 0
3 + 2.25/B^2 - 4 = 0
2.25/B^2 = 1
B = sqrt(2.25) = 1.5
Therefore, the time taken by Badri to complete the work is B = 1.5 days. Amit takes 2.25/1.5 = 1.5 days, Chetan takes 2B = 3 days, and Das takes 4B = 6 days.
To minimize the difference between the times taken by the two groups, we can take the faster group to consist of Amit and Badri, and the slower group to consist of Chetan and Das. The faster group takes 1.5 + 1.5 = 3 days to complete the work, and the slower group takes 3 + 6 = 9 days to complete the work. Therefore, the composition of the faster group could be Amit and Badri.
Which translation moves a triangle 6 units to the right and 3 units down?
Answer:
A translation of (x+6, y-3)
Step-by-step explanation:
X goes left or right, while Y goes up or down. So, to move the triangle 6 units to the right, we take our current x coordinate, and add 6 to it.
WILL MARK BRAINLIEST
An account invested in a money market fund grew from $73,310.56 to $73,608.40 in a month. What was the interest
rate to the nearest tenth?
What was the interest rate?
%
(Do not round until the final answer. Then round to the nearest tenth as needed.)
Answer:
1 - ($73,310.56/$73,608.40)^12 = .047
= 4.7%
Can anyone help me on this one
Hello !
Answer :
[tex]{x}^{ - \frac{8}{3} }[/tex][tex]\sqrt[3]{ {x}^{ - 8} }[/tex][tex]\sqrt[3]{ ({x}^{ 4}) {}^{ - 2} }[/tex]Explanation :
[tex] \to \boxed{ ({x}^{a}) {}^{b} = {x}^{ab} } [/tex]
[tex] \to \boxed{ {x}^{ \frac{1}{n} } {}^{} = \sqrt[n]{x} } [/tex]
[tex] ({x}^{4} ) {}^{ - \frac{2}{3} } = {x}^{- \frac{2}{3} \times 4} \\ \boxed{= {x}^{ - \frac{8}{3} } } \\ \boxed{= \sqrt[3]{ {x}^{ - 8} }} \\ \boxed{ = \sqrt[3]{ ({x}^{ 4}) {}^{ - 2} }}[/tex]
Have a nice day ;)
Use the functions s(x) and c(x) to determine each value.
s(5)
The Trigonometric functions sine (s) and cosine (c) c(5) ≈ -0.2837.
The trigonometric functions sine (s) and cosine (c). To determine s(5), we need to know the value of sine of 5 radians.
We can use a scientific calculator or a trigonometric table to find this value.
Using a calculator, we can simply enter "sin(5)" and get the answer. On most calculators, the answer will be displayed as a decimal.
Using a trigonometric table, we can look up the value of sine for 5 radians. The table will list the sine of angles in degrees, so we need to convert 5 radians to degrees first. One radian is equal to 180/π degrees, so
5 radians = (5 × 180)/π degrees ≈ 286.48 degrees
Looking up the sine of 286.48 degrees in the table, we get:
sin(286.48°) ≈ -0.9589
Therefore, s(5) ≈ -0.9589.
To determine c(5), we need to know the value of cosine of 5 radians.
We can again use a calculator or a trigonometric table to find this value.
Using a calculator, we can enter "cos(5)" to get the answer.
Using a trigonometric table, we can look up the cosine of 5 radians. Since we have already converted 5 radians to degrees, we can simply look up the cosine of 286.48 degrees in the table. We get:
cos(286.48°) ≈ -0.2837
Therefore, c(5) ≈ -0.2837.
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In a recent election, there were six candidates and 3200 total votes. The table below summarizes the votes by candidate. This information is also presented as a
circle graph.
Find the central angle measure, xº, for the Bowerman slice in the circle graph. Do not round.
Candidate
Mendez
Watkins
Choi
Nguyen
DeWitt
Bowerman
Number
of Votes
864
384
736
704
288
224
Choi
Watkins
Nguyen
Mendez
Bowerman
DeWitt
Español
111
K
The measure of x is 25.2 degree
Given that,
Total number of votes = 3200
Bowerman's share = 224
Now the percentage of Bowerman's share = (224/3200)x100
= 7%
Now we know that.
The complete angle of circle is 360 degree.
Therefore the value of x shown in the figure is,
x = 7% 360
= (7 x 360)/100
= 25.2 degree
Therefore,
⇒ x = 25.2 degree
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The figure shows the dimensions for a package to be shipped.
A trapezoidal prism. The front and back are trapezoids.The distance from the trapezoidal front to the trapezoidal back is 15 inches.
The slant is on the right side. The Height on the left is 6 inches, On the top, the width from the left to the top of the slanted side is 4 inches. The distance of the slant from top to bottom is 10 inches. The entire width of the base from the left to right (that is, from the left side of 6 inches to the bottom of the slant) is 12 inches.
What is the minimum amount of wrapping paper, in square inches, needed to cover the package?
The minimum amount of wrapping paper that is needed to cover the package is 576 square inches.
How to calculate the total surface area of a trapezoidal prism?In Mathematics and Geometry, the total surface area of a trapezoidal prism can be calculated and determined by using this mathematical equation or formula:
Total surface area of a trapezoidal prism, TSA = (a + b)h + (a + b + c + d)l
Where:
TSA represent the total surface area of a trapezoidal prism.l represent the length of a trapezoidal prism.a, b, c, d represent the base edges of a trapezoidal prism.h represent the height of a trapezoidal prism.By substituting the given parameters into the total surface area of a trapezoidal prism, we have:
TSA = [(12 + 4) × 6/2] × 2 + [(12 × 15) + (10 × 15) + (4 × 15) + (9 × 15)]
TSA = 96 + 180 + 150 + 60 + 90
TSA = 576 square inches.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Find the value of x
if:
a square’s perimeter is (x+7) cm
and its side length is 12 cm
.
Answer:
41
Step-by-step explanation:
Given
Perimeter of a square ( P ) = (x + 7) cm
Side length ( L ) = 12 cm
To find : The value of x
Formula :
Perimeter of a square = 4L
4 * 12 = x + 7
48 = x + 7
x + 7 = 48
x = 48 - 7
x = 41
PLEASE HELP, ANYONE WHO CAN!!! PLEASE GIVE A SERIOUS DETAILED ANSWER
King Arthur's Sword has a blade that is made of a regular hexagon and a regular pentagon. What is the amplitude of the tip of King Arthur's Sword?
As per the given scenario, the amplitude of the tip of King Arthur's Sword is equal to the length of the side of either the regular hexagon or the regular pentagon.
To decide the amplitude of the tip of King Arthur's Sword, we want to locate the gap from the center of the regular hexagon and pentagon to one in every of their vertices.
A regular hexagon has six identical aspects and 6 same angles. The distance from the center to one of the vertices of a everyday hexagon is identical to the length of its side.
Thus, a everyday pentagon has 5 equal facets and 5 same angles. The distance from the middle to one of the vertices of a everyday pentagon is also equal to the length of its aspect.
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48+24x3-x+10x4-5x2 in standard form
The Standard form of the expression is 10x^4 + 24x^3 - 5x^2 - x + 48.
To write an expression in standard form, we need to arrange the terms in descending order of degree and combine like terms.
The given expression is:
48 + 24x3 - x + 10x4 - 5x2
First, we arrange the terms in descending order of degree:
10x4 + 24x3 - 5x2 - x + 48
Next, we combine the like terms:
10x4 + 24x3 - 5x2 - x + 48 = 10x^4 + 24x^3 - 5x^2 - x + 48
Therefore, the standard form of the expression is 10x^4 + 24x^3 - 5x^2 - x + 48.
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Find the x intercepts of the parabola with vertex (-1,2) and y intercept (0,3).
The x intercepts of the parabola are -1 + i√(2) and -1 - i√(2)
How to find the x intercepts of the parabolaUsing the equation:
y = a(x - h)²+ k
where (h, k) is the vertex of the parabola
y = a(x + 1)²+ 2
solving for a at the y intercept
y = a(x + 1)²+ 2
3 = a(0 + 1)²+ 2
a = 1
To find the x intercepts we need to set y = 0 and solve for x:
0 = (x + 1)²+ 2
x + 1 = ±√(-2)
x + 1 = ±i√(2)
x = -1 ± i√(2)
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A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 13 millimeters long, and the height of the equilateral triangle is 11.3 millimeters. The pyramid's slant height is 17 millimeters. What is its surface area?
The surface area of the Triangular pyramid is approximately 331.3 square millimeters.
The surface area of a triangular pyramid, we need to calculate the area of its base and the area of each triangular face, then add them together. The formula for the surface area of a triangular pyramid is:
SA = (1/2)P*l + B
where SA is the surface area, P is the perimeter of the base, l is the slant height of each triangular face, and B is the area of the base.
In this case, the base of the triangular pyramid is an equilateral triangle with legs of 13 millimeters and a height of 11.3 millimeters. To find the area of the base, we can use the formula for the area of an equilateral triangle:
B = (sqrt(3)/4)*a^2
where a is the length of a side of the equilateral triangle.
Substituting a = 13 into the formula, we get:
B = (sqrt(3)/4)*13^2
B = (sqrt(3)/4)*169
B = 43.7 square millimeters (rounded to one decimal place)
Next, we can find the perimeter of the base:
P = 3a
P = 3*13
P = 39 millimeters
Now we can use the formula for the surface area of a triangular pyramid:
SA = (1/2)P*l + B
Substituting P = 39, l = 17, and B = 43.7, we get:
SA = (1/2)*39*17 + 43.7
SA = 331.3 square millimeters (rounded to one decimal place)
Therefore, the surface area of the triangular pyramid is approximately 331.3 square millimeters.
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If a rectangular container is 25cm by 37cm by 21cm how much does it overflow
If a rectangular container is 25cm by 37cm by 21cm, then it will overflow after reaching the volume of 19425 cm³.
To know the volume after which the container will overflow, first we have to calculate the volume it can contain.
As, Volume of cuboid= length × breadth × height
So, Volume of rectangular container = 25 × 37 × 21 cm³
Volume = 19425 cm³
So, volume of rectangular container whose dimensions are 25cm by 37cm by 21cm is 19425 cm³ and it will overflow after reaching this volume.
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Henry has 50 apples. He gives 4 apples to f friends. What is the different in the expression 50 - 4f? What does the different represent?
Answer:
I don't understand you
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
The 13.2 meters from that point on the ocean floor to the wreck.
Step-by-step explanation:
As given
A ship's sonar finds that the angle of
depression to a ship wrack on the bottom of the ocean is 12.5°.
If a point on the ocean floor is 60
meters.
Now by using the trigonometric identity.
tano = Perpendicular /Base
As shown in the figure given below.
Perpendicular CB
Base AC = 60 meters
0 = 12.5°
Put in the identity CB
tan 12.5°
AC
tan 12.5° CB 60
tan 12.5° 0.22
tan 12.5° = 0.22
0.22 CB 60
CB = 60 × 0.22
CB= 13.2 meters
Therefore the 13.2 meters from that point on the ocean floor to the wreck.
PLEASE HELP!!!
Find the x and y intercepts for8x - 16y= 64.
A. x=4; y = 8
B. x=8;y = 4
C. x=8; y = -4
D. x=1/4; y = 8
Answer:
C. x =8; y = -4
Step-by-step explanation:
To find the x and y intercepts, substitute with zero.
8x - 16y = 64
Finding the x-intercept:
8x - 16(0) = 64
8x = 64
Divide both sides by 8.
x = 8
Finding y-intercept:
8(0) - 16y = 64
-16y = 64
Divide both sides by -16.
y = -4
tly cloudy
The value of a certain investment over time is given in the table below. Answer the
questions below to determine what kind of function would best fit the data, linear or
exponential.
Number of
Years Since
Investment
Made, x
Value of
Investment
(s), f(x)
1
27,171.30
22,507.26 18,718.31
3
values change
function is approximately
function would best fit the data because as x increases, the y
The
of this
Q Search
15,412.40
GM
An exponential function would best fit the data because as x increases, the y values change multiplicatively. The rate of change of the function is of approximately 0.8275.
How to identify an exponential function?A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant, which is the rate of change of the exponential function.
The rate of change for this problem is approximated as follows:
22507.26/27171.30 = 0.828.18712.31/22507.26 = 0.831.15412.4/18712.31 = 0.824.Hence the rate can be rounded to 0.8275.
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Need help with this ASAP
a) The solution to the equation is given as follows: x = -12.
b) The solution to the inequality is given as follows: -12 ≤ x < 7.
How to solve?The equation for this problem is given as follows:
f(x) = g(x).
The point of intersection of the functions f(x) and g(x) is given as follows:
(-12, -7).
Hence the solution is given as follows:
x = -12.
For the inequality, we have that:
f(x) = g(x) at x = -12.f(x) = h(x) at x = 7.Hence the solution to the inequality is given as follows:
-12 ≤ x < 7.
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Which of the following functions M best represents the area of the figure shown ?
The function of the area of the figure is M(x) = (x + 2)(3/2x - 2)
The total area of the composite figure is the sum of the areas of the individual shapes
So, we have
Area = Rectangle + Triangle
Using the area formula, we have
M(x) = (x + 2)(x - 2) × 1/2 × x × (x + 2)
Factorize the expression to get the function
M(x) = (x + 2)(x - 2 + x/2)
So, we have
M(x) = (x + 2)(3/2x - 2)
Hence, the function of the area of the figure is M(x) = (x + 2)(3/2x - 2)
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