Answers
Area= 12
Cost= 84
a. The perimeter of the triangle is 18 cm. b. The area of the triangle is 24 cm². c. Tiling the triangle at $7 per square centimeter would cost $168.
a. Perimeter:
Perimeter} = 5 + 5 + 8 = 18 cm
b. Area:
Use Heron's formula since the sides are known:
[tex]\[ s = \frac{5 + 5 + 8}{2} = 9 \] \[ \text{Area} = \sqrt{s(s-5)(s-5)(s-8)} \] \[ \text{Area} = \sqrt{9 \times 4 \times 4 \times 1} = \sqrt{576} = 24 \, \text{cm}^2 \][/tex]
c. Cost to Tile:
If the cost is $7 per square centimeter:
[tex]\[ \text{Cost} = \text{Area} \times \text{Cost per square centimeter} \] \[ \text{Cost} = 24 \times 7 = 168 \][/tex]
Therefore,
a. Perimeter = 18 cm
b. Area = 24 cm²
c. Cost to Tile = $168
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Related Questions
You received 1⁄3 pound of candy from your grandmother, 1⁄2 pound of candy from your sister, but your best friend ate 1⁄5 pound of candy. How much candy do you have left?
Answers
The total amount of candy left after adding the candy received from the grandmother and the sister, and subtracting the candy eaten by the friend, is approximately 0.63 pounds.
Explanation:First, we add up the amounts of candy you received. You started with 1/3 pound from your grandmother and received an additional 1/2 pound from your sister, for a total of 5/6 pound of candy. However, because your friend ate some, we subtract 1/5 pound from this total. To do this, we need to convert all fractions to have a common denominator, which is 30 in this case. Therefore, 5/6 becomes 25/30, and 1/5 becomes 6/30. Subtraction gives us (25-6)/30 = 19/30 or approximately 0.63 pounds of candy left.
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An item is regularly priced at
$80
. It is now priced at a discount of
85%
off the regular price. What is the price now?
Answers
85% = 0.85
1-0.85 = 0.15
80 x 0.15 = 12
the price now is $12
BC is tangent to circle A at B and to circle D at C. What is AD to the nearest tenth?
Answers
The parallelogram EBCD parallelogram forms. In fact, this figure is actually a rectangle due to the right (90 degree) angles. By definition, the opposite sides are parallel. Consequently, the opposite sides are congruent.
So,
BC = ED = 24
EB = CD = 4
AE+EB = AB
AE+4 = 5
AE = 1
Note how triangle AED is a right triangle with the right angle at angle E.
We can use the pythagorean theorem to find x
a^2 + b^2 = c^2
1^2 + 24^2 = c^2
1 + 576 = c^2
577 = c^2
c^2 = 577
c = sqrt(577)
c = 24.0208
If we round to the nearest tenth, then we get 24.0 which is the final answer (so the answer is choice C)
Note: this is misleading as this implies that the hypotenuse is the same length as the leg, which is not the case. So this is one drawback to rounding.
You attend an amusement park with your family. Your parents buy you an all-ride pass for $20, shown as fx. Instead of getting a pass, your parents decide to pay $4 for each ride they take, shown as gx. What function shows the correct combination of these two functions to represent the total cost to them of attending the amusement park that day, shown as hx?
A. fx = 20x, gx = 4, hx = 20x + 4
B. fx = 20, gx = 4, hx = 4 + 20
C. fx = 20, gx) = 4x, hx = 4x + 20
D. fx = 20x, gx = 4x, hx = 20x + 4x
Answers
because the $20 dollars is a one time thing so that equals fx, then since the parents pay per ride and its $4 then gx=4x, add them together to give you hx
h(x)=f(x)+g(x)
h(x)=4x+20
An employee earns $36 per hour and 1.5 times that rate for all hours in excess of 40 hours per week. assume that the employee worked 60 hours during the week, and that the gross pay prior to the current week totaled $52,200. assume further that the social security tax rate was 6.0%, the medicare tax rate was 1.5%, and federal income tax to be withheld was $605.
Answers
Answer:
An employee’s rate of pay is $36 per hour, with time and a half for all hours worked in excess of 40 during a week. The employee worked 48 hours during the week. The amount of the employee’s gross pay for the week is:
Step-by-step explanation:
You arrive in your history class today only to discover there is a pop quiz! You haven't studied and you aren't at all prepared. Fortunately, the quiz is multiple choice. Each question has five answer choices. You happen to have a die in your pocket. For each question you roll the die and answer A if the die shows 1, B if the die shows 2, etc, leaving the question blank if the die shows a six. For each question you are given one point if you answer it correctly and lose 1/4 point if you answer it incorrectly. You aren't penalized if you leave it blank, you just don't earn a point. What is the expected value for points earned on each question? Enter your answer as a decimal, rounded to two decimal places if necessary
Answers
The probability of getting a wrong answer is 4/6 with, a value of -1/4.
The probability of leaving a question empty is 1/6, with a value 0.
The Expected value is
[tex]1* \frac{1}{6}+( -\frac{1}{4} )* \frac{1}{6}+( -\frac{1}{4} )* \frac{1}{6}+( -\frac{1}{4} )* \frac{1}{6}+( -\frac{1}{4} )* \frac{1}{6}+0* \frac{1}{6}[/tex]
[tex]= \frac{1}{6} +4( -\frac{1}{4} )* \frac{1}{6}=\frac{1}{6}-\frac{1}{6}=0[/tex]
find the slope of each line 5x-y=-7
Answers
5x-y=-7
-5x -5x
-------------
-y=-5x-7
--- ------
-1 -1
y=5x+7
A copy machine makes 28 copies per minute. How long does it take to make 154 copies?
Answers
A $33$-gon $P_1$ is drawn in the Cartesian plane. The sum of the $x$-coordinates of the $33$ vertices equals $99$. The midpoints of the sides of $P_1$ form a second $33$-gon, $P_2$. Finally, the midpoints of the sides of $P_2$ form a third $33$-gon, $P_3$. Find the sum of the $x$-coordinates of the vertices of $P_3$.
Answers
1.
The midpoint MPQ of PQ is given by (a + c /
2, b + d / 2)
2.
Let the x coordinates of the vertices of P_1 be :
x1, x2, x3,…x33
the x coordinates of P_2 be :
z1, x2, x3,…z33
and the x coordinates of P_3 be:
w1, w2, w3,…w33
3.
We are given with:
X1 + x2 + x3… + x33 = 99
We also want to find the value of w1 + w2 + w3… + w33.
4.
Now, based from the midpoint formula:
Z1 = (x1 + x2) / 2
Z2 = (x2 + x3) / 2
Z3 = (x3 + x4) / 2
Z33 = (x33 + x1) / 2
and
W1
= (z1 + z1) / 2
W2 = (z2 + z3) / 2
W3
= (z3 + z4) / 2
W13 = (z33 + z1) / 2
.
.
5.
W1 + w1 + w3… + w33 = (z1 + z1) / 2 + (z2 + z3) / 2 + (z33 + z1) / 2 = 2 (z1 + z2 + z3… + z33) / 2
Z1
+ z1 + z3… + z33 = (x1 + x2) / 2 + (x2 + x3) / 2
+ (x33 + x1) / 2
2 (x1 + x2 + x3… + x33) / 2 = (x1 + x2 +
x3… + x33 = 99
Answer: 99
at the beginning of a lesson, a piece of chalk is 4.875 inches long. at the end of the lesson, it is 3.125 inches long. writ the two amounts in expanded form using fractiones.
Answers
Let's see number 4.875.
Digit 4 is in the place of the units so it is 4 * 1
8 is in the place of the tenths, so it is 8/10 = 8 * 1/10
7 is in the place of the hundreths, so it is 7/100 = 7 * 1 /100
5 is in the place of the thousanths, so it is 5/1000 = 5 * 1 / 1000
So, the number 4.875 written in expanded form using fractions is:
4*1 + 8 * 1/10 + 7 * 1/100 + 5 * 1/100.
Now, see the next amount, 3.125, which using the same procedure leads to:
3 *1 + 1 * 1/10 + 2 * 1/100 + 5 * 1/ 1000
Do the side lengths of 5, 6, and 8 form a Pythagorean triple?
Yes
No
Answers
A golden rectangle is to be constructed such that the longest side is 18 inches long. How long is the other side? (Round your answer to the nearest tenth of an inch.)
Answers
a/b=b/(a+b) multiply both sides by (a+b)
(a^2+ab)/b=b multiply both sides by b
a^2+ab=b^2 subtract a^2+ab from both sides
b^2-ab-a^2=0 using the quadratic formula for expediency
b=(a±√(a^2+4a^2))/2 and we know b>0
b=(a+a√5)/2
b=(a/2)(1+√5)
If we let a=1
b=(1+√5)/2
So the golden ratio is (1+√5)/2
Since the longest side is 18in:
(1+√5)/2=18/s
s(1+√5)=36
s=36/(1+√5) in
s≈11.1 in (to nearest tenth of an inch)
Sam took his family to the zoo. An adult's ticket is two times the cost of a child's ticket. The total cost for two adults' tickets and three children's tickets was $28. How much do the tickets cost? A. Child's ticket = $5.60, adult's ticket = $11.20 B. Child's ticket = $2, adult's ticket = $4 C. Child's ticket = $4, adult's ticket = $8 D. Child's ticket = $7, adult's ticket = $14 \
Answers
a = 2c
2(2c) + 3c = 28
4c + 3c = 28
7c = 28
c = 28/7
c = 4 <== childs ticket
a = 2c
a = 2(4)
a = 8 <== adults ticket
The Rectangles are similar. Find the value of the variable (Picture Included)
Answers
On which number line do the points represent negative seven and one over two and +1?
Answers
Answer:
d
Step-by-step explanation:
k friends evenly divided up a 12-slice pizza. One of the friends, Harris, ate 1 fewer slice than he was given. How many slices of pizza did Harris eat? Write your answer as an expression.
Answers
Final answer:
Harris ate 12/k - 1 slices of pizza after a 12-slice pizza was divided evenly among k friends and he ate one less than he was given.
Explanation:
To find out how many slices of pizza Harris ate, we initially need to determine how many slices each person would get if the 12-slice pizza is divided evenly among k friends.
Each friend would get 12/k slices.
Since Harris ate 1 fewer slice than he was given, we subtract 1 from the number of slices he was supposed to get.
Therefore, the expression for the number of slices Harris ate is 12/k - 1.
A home has dimensions of 35 feet by 57 feet that include an attached 24-foot by 22-foot garage and a 200-square-foot screened porch. how many square feet of gross living area does the home have
Answers
1995 - ((24*22)+200) = 1267
1267 is your answer.
If 3✖️/4 =7 ➖x/3,then x=
Answers
9x/4 = 21 - x -> multiply both sides by 4
9x = 84 - 4x
13x = 84
x = 84/13
The City Housing Authority has received 75 applications from qualified applicants for ten low-income apartments. Five of the apartments are on the north side of town, and five are on the south side. If the apartments are to be assigned by means of a lottery, find the following probabilities. (a) A specific qualified applicant will be selected for one of these apartments. (Round your answer to three decimal places.) (b) Two specific qualified applicants will be selected for apartments on the same side of town. (Round your answer to five decimal places.)
Answers
(a) A specific qualified applicant will be selected for one of these apartments.
(b) Two specific qualified applicants will be selected for apartments on the same side of town.
This problem is an example of combination of ways. There are 75C2 position pairs for a [articular pair of names to be placed in. About 5C2 of these position pairs are selected in the north and 5C2 are selected in the south. So the probability that a specific pair are both north or both south is
(5C2 + 5C2)/(75C2) = (10 + 10)/2775
= 4/555
A person 5.4 feet tall stands in line of a shadow cast from the top of the house. The shadow hits the top of the person's head, and continues until the shadow ends on the ground 2.4 feet from the person's shoes. The distance along the ground from the tip of the shadow to the house is 14.6 feet. Find the height of the house. Do not round your answer.
Answers
Let h = the height of the building.
Because triangles ABC and ADE are similar (due to AAA), therefore
DE/BC = AD/AB
That is,
h/5.4 = 14.6/2.4
h/5.4 = 6.0833
h = 6.0833*5.4 = 32.8498 ft
Answer: The height of the house is 32.8498 ft
Which set of coordinates, when paired with (-3, -2) and (-5, -2), result in a square?
Answers
greens theorem. find the max value of the line integral where f=(13x^2y+3y^3-y)i-12x^3j and C is any positively oriented closed curve. max=?
Answers
[tex]\displaystyle\int_C\mathbf f\cdot\mathrm d\mathbf r=\int_C((13x^2y+3y^3-y)\,\mathrm dx-12x^3\,\mathrm dy)[/tex]
By Green's theorem, the line integral along [tex]C[/tex] is equivalent to the double integral over [tex]R[/tex] (the region bounded by [tex]C[/tex])
[tex]\displaystyle\iint_R\left(\frac{\partial(-12x^3)}{\partial x}-\frac{\partial(13x^2y+3y^3-y)}{\partial y}\right)\,\mathrm dx\,\mathrm dy[/tex]
[tex]=\displaystyle\iint_R(-36x^2-(13x^2+9y^2-1))\,\mathrm dx\,\mathrm dy[/tex]
[tex]=\displaystyle\iint_R(1-49x^2-9y^2)\,\mathrm dx\,\mathrm dy[/tex]
Now consider the function [tex]g(x,y)=1-49x^2-9y^2[/tex]. We can think of the double integral above as a volume integral; namely, it's the volume of the region below [tex]g(x,y)[/tex] and above the region [tex]R[/tex] in the [tex]x[/tex]-[tex]y[/tex] plane (i.e. [tex]z=0[/tex]). This volume will be maximized if [tex]C[/tex] is taken to be the intersection of [tex]g(x,y)[/tex] with the plane, which means [tex]C[/tex] is the ellipse [tex]49x^2+9y^2=1[/tex].
For the double integral, we can convert to an augmented system of polar coordinates using
[tex]\begin{cases}x=\frac17r\cos\theta\\\\y=\frac13r\sin\theta\end{cases}[/tex]
where [tex]0\le r\le1[/tex] and [tex]0\le\theta\le2\pi[/tex]. We have the Jacobian determinant
[tex]\det\mathbf J=\left|\dfrac{\partial(x,y)}{\partial(r,\theta)}\right|=\begin{vmatrix}\frac{\partial x}{\partial r}&\frac{\partial x}{\partial\theta}\\\\\frac{\partial y}{\partial r}&\frac{\partial y}{\partial\theta}\end{vmatrix}[/tex]
[tex]\det\mathbf J=\begin{vmatrix}\frac17\cos\theta&-\frac17r\sin\theta\\\\\frac13\sin\theta&\frac3r\cos\theta\end{vmatrix}=\dfrac r{21}[/tex]
So the double integral, upon converting to our polar coordinates, is equivalent to
[tex]=\displaystyle\frac1{21}\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}\left(1-49\left(\frac r7\cos\theta)^2-9\left(\frac r3\sin\theta\right)^2\right)r\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle\frac1{21}\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}(1-r^2\cos^2\theta-r^2\sin^2\theta)r\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle\frac1{21}\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}(r-r^3)\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle\frac{2\pi}{21}\int_{r=0}^{r=1}(r-r^3)\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\dfrac\pi{42}[/tex]
Final answer:
To find the max value of a line integral over a closed curve using Green's Theorem, consider the curl of the given vector field and apply the theorem to express the result. The maximum value of the line integral is -2y²dy, determined through vector calculus and Green's Theorem application.
Explanation:
Green's Theorem states that for a vector field f in the form given, the max value of the line integral over any positively oriented closed curve C can be found by considering the curl of f.
By applying Green's Theorem, we can find that the maximum value of the line integral is -2 y²dy.
This computation involves utilizing vector calculus and understanding how to apply Green's Theorem to find the extremum of the line integral.
Find the sum of the series. 1 + z/5 + z^2/25 + z^3.125
Answers
[tex]=\dfrac1{1-\frac z5}=\dfrac5{5-z}[/tex]
provided that [tex]\left|\dfrac z5\right|<1\iff|z|<5[/tex].
How did he get this 1/2i ? I dont remember studying this definition in calc 1 neither calc 2!
Answers
[tex]\sin at=\dfrac{e^{iat}-e^{-iat}}{2i}[/tex]
This follows from
[tex]e^{iat}=\cos at+i\sin at[/tex]
[tex]e^{-iat}=\cos at-i\sin at[/tex]
[tex]\implies e^{iat}-e^{-iat}=2i\sin at[/tex]
[tex]\implies \sin at=\dfrac{e^{iat}-e^{-iat}}{2i}[/tex]
Final answer:
The term 1/2i most likely pertains to complex numbers, where 'i' is the imaginary unit. It's not typically covered in Calculus I or II but in pre-calculus or algebra courses. The principles of working with fractions apply similarly for complex numbers as they do with real numbers.
Explanation:
The term 1/2i likely refers to the fractional unit in the context of complex numbers, where 'i' is the imaginary unit. This concept is not commonly taught in Calculus I or II but is a part of complex number arithmetic, which is sometimes covered in pre-calculus or algebra. When calculating with complex numbers, it is crucial to remember that 'i' represents the square root of -1.
Let's consider the calculation of 'half' of something in more familiar terms. If you have half a pie, and you're looking to find half of that, you would intuitively know that you now have one-quarter of a pie. Likewise, if you are trying to understand how to combine fractions such as 1/2 and 1/3, you look for a common denominator. Multiplying denominators can often provide this common base for addition, just like multiplying 2 and 3 to get 6 as a common denominator.
However, when working with complex numbers and encountering a term like 1/2i, it can seem less intuitive. Nonetheless, the basic principles of fraction manipulation remain the same. The student might be looking at a problem involving complex fractions, which would require familiarity with the algebraic rules governing complex numbers.
Sarah bought a lawnmower for $320. She signed up for the buy now pay later plan at the store with the following conditions: $100 down and payments of $25 for the next 12 months. The extra cost paid by taking this plan is equivalent to what actual yearly rate of interest?
Answers
300+100=400
400-320=80
$80
Answer:
25%
Step-by-step explanation:
Just here to help cause im doing this too lol
Find f. (use c for the constant of the first antiderivative and d for the constant of the second antiderivative.) f ''(x) = 12x + sin x
Answers
[tex]\text{Integrating f''(x), we get: }f'(x) = 6x^{2} - cosx + C[/tex]
[tex]\text{Integrating f'(x), we get: } f(x) = 2x^{3} - sinx + Cx + D[/tex]
Using rectangles whose height is given by the value of the function at the midpoint of the rectangle's base, estimate the area under the graph using first two and then four rectangles. f(x)equals=x squared2 between xequals=1 and xequals=2
Answers
The area under the graph by using the first two and then four rectangles is [tex]2.958[/tex] units square.
For reference use the below-given graph.
Given function is
[tex]f(x)=x^{2}[/tex] when [tex]x=1[/tex] to [tex]x=2[/tex] .
The first rectangle of the first part graph goes from [tex]1.0[/tex] to [tex]1.6[/tex], so the width will be [tex]0.6[/tex] units. And the height measured from the middle point i.e. [tex]1.3[/tex] is
[tex]f(1.3)=(1.3)^{2}[/tex]
[tex]=1.69[/tex] units.
Then the area of the first rectangle is [tex]0.6\times1.69=1.014[/tex] units square.
Similarly, the second rectangle of the first part graph goes from [tex]1.6[/tex] to [tex]2.0[/tex], so the width will be [tex]0.4[/tex] units. And the height measured from the middle point i.e. [tex]1.8[/tex] is
[tex]f(1.8)=(1.8)^{2}[/tex]
[tex]=3.24[/tex] units.
So, the area of the second rectangle is [tex]0.6\times3.24=1.944[/tex] units square.
Hence, the final area under the graph will be [tex]1.014+1.944=2.958[/tex] units square.
Further, we can do the same for another part of the graph to find the area under the graph by using four rectangles.
For example, the first rectangle of the four has a width of [tex]0.6[/tex] units and a height of [tex]f(1.1)=(1.1)^{2}[/tex]
[tex]=1.21[/tex] units.
Therefore, the area under the graph by using the first two and then four rectangles is [tex]2.958[/tex] units square.
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The estimated areas under the curve of the function f(x)=x^2 between x = 1 and x = 2 are 2.3125 using two rectangles and 2.3281 using four rectangles
Explanation:To estimate the area under the graph of the function f(x)=x^2 between x = 1 and x = 2 using rectangles, we use the method of midpoint Riemann sums. For this question, let's use 2 rectangles and then 4 rectangles.
First, for 2 rectangles, the interval from 1 to 2 is divided into 2 equal parts: [1, 1.5] and [1.5, 2]. The midpoints of these intervals are 1.25 and 1.75. The height of each rectangle is given by the function value at these midpoints: [tex]f(1.25) = (1.25)^2 =1.5625, and f(1.75) = (1.75)^2 = 3.0625.[/tex] The total area of the rectangles is thus (0.5 * 1.5625) + (0.5 * 3.0625) = 2.3125.
Next, for 4 rectangles, the interval from 1 to 2 is divided into 4 equal parts: [1, 1.25], [1.25, 1.5], [1.5, 1.75], [1.75, 2]. The midpoints of these intervals are 1.125, 1.375, 1.625, 1.875. The height of each rectangle is given by the function value at these midpoints: [tex]f(1.125) = (1.125)^2 = 1.26562, f(1.375) = (1.375)^2 = 1.8906, f(1.625) = (1.625)^2 = 2.6406[/tex], and f(1.875) = (1.875)^2 = 3.5156. The total area of the rectangles is thus [tex](0.25 * 1.26562) + (0.25 * 1.8906) + (0.25 * 2.6406) + (0.25 * 3.5156) = 2.3281.[/tex]
These are the estimated areas under the curve for 2 rectangles and 4 rectangles respectively. And as you can see, the more rectangles we use, the closer we get to the actual area under the curve.
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A distribution x is known to have a mean value of 5 and a standard deviation of 5. what is its mean square value (i.e., the expected value of x2)?
Answers
[tex]\implies 5^2=\mathbb E(X^2)-5^2[/tex]
[tex]\implies\mathbb E(X^2)=50[/tex]
The expected mean square value (E(x^2)) can be found using the formula E(x^2) = μ^2 + σ^2. With the given mean (μ) and standard deviation (σ) as 5, insertion into the formula gives E(x^2) = 5^2 + 5^2 = 50.
Explanation:The mean square value, often denoted as E(x2), is calculated from the mean (μ) and standard deviation (σ) using this formula: E(x2) = μ2 + σ2. Based on the given distribution values, you're provided with a mean (μ) of 5 and a standard deviation (σ) of 5. By following the formula, you input these values, and it becomes E(x2) = 52 + 52. Thus, E(x2) = 25 + 25 which is equal to 50. So, the mean square value or the expected value of x2 for this distribution is 50.
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In a kitchen there are four containers that can hold different quantities of water as shown in the figure below
1-(x-2) liters
2- x liters
3- (x+2)liters
4- (x+4) liters
How many liters of water can the four containers hold in all
X^4+4
2x+4
X^2+2x
4x+4
Answers
Crestwood Paint Supply had a beginning inventory of 10 cans of paint at $25.00 per can. They purchased 20 cans during the month at $30.00 per can. They had an ending inventory valued at $500. How much paint in dollars was used for the month? A. $250 B. $1,350 C. $850 D. $350
Answers
10×25=$250
Purchase
20×30=$600
So
Beginning inventory 250
Add purchase 600
Less ending inventory 500
Material used. 350
The answer is 350