Answer:
3.25 US Quarts
Step-by-step explanation:
Find the surface area of the regular pyramid shown in the accompanying diagram. If necessary, express your answer in simplest radical form.
Answer:
The area of the pyramid is 360 unit²
Step-by-step explanation:
Given
Base Edge, a = 10
Height, h = 12
Required
Determine the surface area
The surface area of a regular pyramid is calculated as thus;
[tex]A = a^2 + 2a\sqrt{\frac{a^2}{4} + h^2}[/tex]
Substitute values for a and h
[tex]A = 10^2 + 2 * 10 * \sqrt{\frac{10^2}{4} + 12^2}[/tex]
Evaluate all squares
[tex]A = 100 + 2 * 10 * \sqrt{\frac{100}{4} + 144}[/tex]
[tex]A = 100 + 2 * 10 * \sqrt{25 + 144}[/tex]
[tex]A = 100 + 2 * 10 * \sqrt{169}[/tex]
Take positive square root of 169
[tex]A = 100 + 2 * 10 * 13[/tex]
[tex]A = 100 + 260[/tex]
[tex]A = 360[/tex]
Hence, the area of the pyramid is 360 unit²
Answer:
B.) 360 units2
Step-by-step explanation:
I got it correct on founders education
What is the solution to the linear equation?
2/5 + p = 4/5 + 3/5p
Answer:
p = 1Step-by-step explanation:
[tex] \frac{2}{5} + p = \frac{4}{5} + \frac{3}{5} p[/tex]
Multiply through by the LCM
The LCM for the equation is 5
That's
[tex]5 \times \frac{2}{5} + 5p = 5 \times \frac{4}{5} + \frac{3}{5}p \times 5[/tex]
We have
2 + 5p = 4 + 3p
Group like terms
5p - 3p = 4 - 2
2p = 2
Divide both sides by 2
We have the final answer as
p = 1Hope this helps you
Is the square root of 65 a rational number
Answer:
No
Step-by-step explanation:
The square root of 65 is irrational.
It is not a rational number because 65 is not a perfect square.
The square root of 65 is 8.06225775...
The square root of 65 is not a rational number.
65 is not a perfect square which means it's impossible to
find a whole number times itself to give us 65.
On a calculator if you type in the square root of 65,
you will get an infinite decimal number.
The decimal values never end and never have same repeated pattern.
Hellllppp!!!! Please!Match the numbers with the correct label.
Answer:
(a = 1/7 (b = .2 (c = 3/9
Step-by-step explanation:
1/7 = .14
1/4 = .25
3/9 = .33
a & b are lower than 1/4 and c is higher
Find the measure of ∠BEF
Please HELP ASAP
Answer:
100°
Step-by-step explanation:
We know that angles EFD and AEF are the same as they are alternate interior angles.
We also can note that BEF and AEF are supplementary, meaning their angle lengths will add up to 180°.
So we can create an equation:
(2x + 60) + (3x + 20) = 180
Combine like terms:
5x + 80 = 180
Subtract 80 from both sides
5x = 100
Divide both sides by 5
x = 20.
Now we can use this to find the measure of BEF.
[tex]2\cdot20 + 60[/tex]
[tex]40 + 60 = 100[/tex]
Hope this helped!
Answer:
BEF = 100
Step-by-step explanation:
The angles are same side interior angles and same side interior angles add to 180 degrees
2x+60 + 3x+20 = 180
Combine like terms
5x+80 = 180
Subtract 80
5x = 100
Divide by 5
5x/5 = 100/5
x = 20
We want BEF
BEF = 2x+60
= 2x+60
= 2*20 +60
= 40+60
= 100
please help with this
Answer:
[tex]\sin \left(\theta \right)-\frac{1}{2}\cos \left(2\theta \rightt)+C[/tex]
Step-by-step explanation:
We are given the graph of r = cos( θ ) + sin( 2θ ) so that we are being asked to determine the integral. Remember that [tex]\:r=cos\left(\theta \right)+sin\left(2\theta \right)[/tex] can also be rewritten as [tex]\int \cos \left(\theta \right)+\sin \left(2\theta \right)d\theta \right[/tex].
Let's apply the functional rule [tex]\int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx[/tex],
[tex]\int \cos \left(\theta \right)+\sin \left(2\theta \right)d\theta \right[/tex] = [tex]\int \cos \left(\theta \right)d\theta \right+\int \sin \left(2\theta \right)d\theta \right[/tex]
At the same time [tex]\int \cos \left(\theta \right)d\theta \right=\sin \left(\theta \right)[/tex] = [tex]sin( \theta \right ))[/tex], and [tex]\int \sin \left(2\theta \right)d\theta \right[/tex] = [tex]-\frac{1}{2}\cos \left(2\theta \right)[/tex]. Let's substitute,
[tex]\int \cos \left(\theta \right)d\theta \right+\int \sin \left(2\theta \right)d\theta \right[/tex] = [tex]\sin \left(\theta \right)-\frac{1}{2}\cos \left(2\theta \right)[/tex]
And adding a constant C, we receive our final solution.
[tex]\sin \left(\theta \right)-\frac{1}{2}\cos \left(2\theta \rightt)+C[/tex] - this is our integral
(SAT Prep) Find the value of x.
Answer:
The value of x is 30°
Step-by-step explanation:
We are given that the outer angle of the parallelogram is 60 degrees. Therefore it's respective inner angle will be 180 - 60 = 120 degrees. And, by properties of a parallelogram, the angle opposite to this angle will be 120 degrees as well.
If we draw extend the line creating angle 2x, then we will make ( 1 ) a vertical angle to 2x, ( 2 ) a 90 degree angle, and ( 3 ) and angle that we can let be y. Therefore, 2x + y = 90, and 3x + y = 120.
[tex]\begin{bmatrix}2x+y=90\\ 3x+y=120\end{bmatrix}[/tex] ,
[tex]\begin{bmatrix}6x+3y=270\\ 6x+2y=240\end{bmatrix}[/tex] ,
[tex]6x+2y=240\\-\\\underline{6x+3y=270}\\y=30[/tex],
[tex]2x + (30) = 90,\\2x = 60,\\x = 30[/tex]
Solution : x = 30°
Answer:
x = 30
Step-by-step explanation:
a+ 60 = 180
a = 120
3x+b = 120 because opposite angles in a parallelogram are equal
2x+90+b = 180 since it forms a line
2x+b = 90
We have 2 equations and 2 unknowns
3x+b = 120
2x+b = 90
Subtracting
3x+b = 120
-2x-b = -90
---------------------
x = 30
Need Help
Please Show Work
Answer:
-36
Step-by-step explanation:
3*12=36
she is going down (negative) so, it is -36
not sure if this is what you are asking for, if not try this
0-12-12-12=-36
Are we adding all 4 sides ?
Answer:
Yes
Step-by-step explanation:
you would do 2(5x-10) + 2(8x+4)= 26x-12
Answer:
26x - 12
Step-by-step explanation:
The perimeter is the sum of all the exterior sides of a figure.
Here, we have a parallelogram, and its sides are 5x - 10, 8x + 4, 5x - 10, and 8x + 4. Adding these, we get:
(5x - 10) + (8x + 4) + (5x - 10) + (8x + 4) = 26x - 12
Thus, the answer is 26x - 12. Note that since the problem doesn't give a value for x, this cannot be simplified further.
~ an aesthetics lover
Nour drove from the Dead Sea up to Amman, and her altitude changed at a constant rate. When she began driving, her altitude was 400400400 meters below sea level. When she arrived in Amman 222 hours later, her altitude was 100010001000 meters above sea level. Let yyy represent Nour's altitude (in meters) relative to sea level after xxx hours.
Answer:
y = 700x - 400
Step-by-step explanation:
A negative number represents an altitude below sea level.
Beginning: -400
y = mx + b
y = mx - 400
In 2 hours the altitude was now 1000 m.
1000 m - (400 m) = 1400 m
The altitude went up 1400 m in 2 hours. The rate of change is
1400/2 m/h = 700 m/h
The rate of change is the slope.
y = 700x - 400
Answer:
The graph answer is below :)
Step-by-step explanation:
Could anyone help me with this question please? Thank you.
Answer:
C) 549 km²
Step-by-step explanation:
The area of the regular pentagon is given by ...
A = (1/2)Pa
where P represents the perimeter, and 'a' represents the apothem (6.2 km). Of course, the perimeter is 5 times the side length.
The lateral area is the product of the perimeter and the height:
LA = Ph
Using these formulas, and recognizing the total area includes two (2) pentagons, we have ...
total area = (LA) +2(A) = Ph +2(1/2)Pa = P(h +a)
= (45 km)(6 km +6.2 km) = 549 km^2
What does the tape measure say Measurement # 4 is?
Answer:
It looks like 6 and one eighth of an inch.
Solve for W.
W/9 = g
Answer:
W = 9 * g
Step-by-step explanation:
W/9 = g
W = 9 * g
The expression W/9 = g can be written as W = 9g after cross multiplication.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have an expression:
W/9 = g
To solve for W
Make subject as W:
W = 9g
By cross multiplication.
Thus, the expression W/9 = g can be written as W = 9g after cross multiplication.
Learn more about the expression here:
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The table shows the probability distribution of student ages in a high school
with 1500 students. What is the expected value for the age of a randomly
chosen student?
Age
13
14
15
16
17
18
Probability 0.01 0.23 0.26 0.28 0.20 0.02
Answer:
Exoected age is 15.49 years
Step-by-step explanation:
Expected age
= E(x)
= sum (p(i)*i)
= 13*0.01+14*0.23+15*0.26+16*0.28+17*0.20+18*0.02
= 15.49
Find the domain and the range of the relation.
Find the domain of the relation. Select the correct choice below and fill in the answer box to
complete your choice.
O A. The domain is _
(Type your answer in interval notation.)
B. The domain is {_}
(Type an integer or a fraction. Use a comma to separate answers as needed.)
Find the range of the relation. Select the correct choice below and fill in the answer box to
complete your choice.
O A. The range is _
(Type an integer or a fraction. Use a comma to separate answers as needed.)
OB. The range is {_}
Answer:
1) the domain is all real numbers
2) the range is
[tex]y \geqslant 3[/tex]
Find the length of GV¯¯¯¯¯¯¯¯ A. 43.92 B. 33.1 C. 41.45 D. 68.87
Answer:
The answer is option AStep-by-step explanation:
Since the figure above is a right angled triangle we can use trigonometric ratios to find GV
To find GV we use cosine
cos∅ = adjacent / hypotenuse
From the question
GV is the adjacent
GC is the hypotenuse
So we have
[tex] \cos(37) = \frac{GV}{GC} [/tex]GC = 55°
GV[tex] \cos(37) = \frac{GV}{55} [/tex]GV = 55 cos 37
GV = 43.92495
We have the final answer as
GV = 43.92Hope this helps you
23. f(x) is vertically shrank by a factor of 1/3. How will you represent f(x) after transformation?
A. f(3x)
B. 3f(x)
C. 13f(x)
D. f(13x)
Answer:
Step-by-step explanation:
vertical stretching / shrinking has the following transformation.
f(x) -> a * f(x)
when a > 1, it is stretching
when 0< a < 1, it is shrinking.
when -1 < a < 0, it is shringking + reflection about the x-axis
when a < -1, it is stretching + reflection about the x axis.
Here it is simple shrinking, so 0 < a < 1.
I expect the answer choice to show (1/3) f(x).
However, if the question plays with the words
"shrink by a factor of 1/3" to actually mean a "stretching by a factor of three", then B is the answer (stretch by a factor of three).
Ava placed the point of her pencil on the origin of a regular coordinate plane. She marked a point after moving her pencil 4 units to the left and 7 units up. Which ordered pair identifies where Ava marked her point?
[tex] \Large{ \boxed{ \bold{ \color{lightgreen}{Solution:}}}}[/tex]
So, Let's solve this question by using cartesian plane.
Here, Origin is shown by (0, 0)Ava moves 4 units left from origin. On the left side of origin, negative x axis begins. So, she reached (-4, 0) now.Then, from that point she moved 7 units upwards. On the upper side, there is positive y axis. So, Finally she will reach point (-4, 7).(-4, 7) is the coordinate of point which is 4 units left from y axis and 7 units up from x axis.It lies on the second quadrant.Well, What is cartesian plane?
A - A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a set of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length.
━━━━━━━━━━━━━━━━━━━━
Please Solve
F/Z=T for Z
Answer:
F /T = Z
Step-by-step explanation:
F/Z=T
Multiply each side by Z
F/Z *Z=T*Z
F = ZT
Divide each side by T
F /T = ZT/T
F /T = Z
Answer:
[tex]\boxed{\red{ z = \frac{f}{t} }}[/tex]
Step-by-step explanation:
[tex] \frac{f}{z} = t \\ \frac{f}{z} = \frac{t}{1} \\ zt = f \\ \frac{zt}{t} = \frac{f}{t} \\ z = \frac{f}{t} [/tex]
Solve 2x+2y=6 and 3x-2y=11
Answer:
x = 17/5
y = -2/5
Step-by-step explanation:
2x + 2y = 6
3x - 2y = 11
sum both equations results
5x + 0 = 17
x = 17/5
2x + 2y = 6
2*17/5 + 2y = 6
34/5 + 2y = 6
2y = 6 - 34/5
2y = 30/5 - 34/5
2y = -4/5
y = (-4/5)/2
y = -2/5
verify:
3x - 2y = 11
3*17/5 - 2*-2/5 = 11
51/5 + 4/5 = 55/5
51 + 4 = 55
Suppose your weekly local lottery has a winning chance of 1/106. You buy lottery from them for x weeks in a row. What is the probability that you never win?
Answer:
The probability mass function that you never win [tex]^xC_o[/tex] = [tex](\dfrac{999999}{1000000})^x[/tex]
Step-by-step explanation:
Given that;
the winning chance of a weekly local lottery = [tex]\dfrac{1}{10^6}[/tex]
= [tex]\dfrac{1}{1000000}[/tex]
The probability of losing = 1 - probability of winning (winning chance)
The probability of losing = [tex]1- \dfrac{1}{1000000}[/tex]
The probability of losing =[tex]\dfrac{999999}{1000000}[/tex]
The probability mass function that you never win [tex]^xC_o[/tex] = [tex](\dfrac{1}{10^6} )^0 ( \dfrac{999999}{1000000})^x[/tex]
The probability mass function that you never win [tex]^xC_o[/tex] = [tex](\dfrac{999999}{1000000})^x[/tex]
HELP PLEASE 50 POINTS
A mechanic charges $125 plus $25 per hour of labor. The equation c=25n+125
describes the total she would charge for a service visit, where n represents the number of
hours of labor and c is the total cost. Graph the equation and using the graph, find how
much he charges when she works 3 hours.
Answer:
See Attachment for graph
Charges = $200 when number of she works for 3 hours
Step-by-step explanation:
Given
Charges = $25 per hour + $125 (c = 25n + 125)
Required
Graph the equation.
From the graph, determine c when n = 3
To plot the graph; first, we have to determine the points to use;
When n = 1
[tex]c = 25 * 1 + 125[/tex]
[tex]c = 25 + 125[/tex]
[tex]c = 150[/tex]
When n = 2
[tex]c = 25 * 2 + 125[/tex]
[tex]c = 50 + 125[/tex]
[tex]c = 175[/tex]
When n = 3
[tex]c = 25 * 3 + 125[/tex]
[tex]c = 75 + 125[/tex]
[tex]c = 200[/tex]
When n = 4
[tex]c = 25 * 4 + 125[/tex]
[tex]c = 100 + 125[/tex]
[tex]c = 225[/tex]
Plotting n on the x axis and c on the y axis; we have
c || n
1 || 150
2 || 175
3 || 200
4 || 225
(See attachment)
From the attachment;
When she works for 3 hour; This implies that n = 3
And c = $200 when n = 3
See Proof
[tex]c = 25n + 125[/tex]
Substitute 3 for n
[tex]c = 25 * 3 + 125[/tex]
[tex]c = 75 + 125[/tex]
[tex]c = 200[/tex]
When a constant force acts upon an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object with mass 4kg, the acceleration of the object is 15/ms2. If the same force acts upon another object whose mass is
10kg, what is this object's acceleration?
Answer:
[tex]a = 6m/s^2[/tex]
Step-by-step explanation:
Given
When mass = 4kg; Acceleration = 15m/s²
Required
Determine the acceleration when mass = 10kg, provided force is constant;
Represent mass with m and acceleration with a
The question says there's an inverse variation between acceleration and mass; This is represented as thus;
[tex]a\ \alpha\ \frac{1}{m}[/tex]
Convert variation to equality
[tex]a = \frac{F}{m}[/tex]; Where F is the constant of variation (Force)
Make F the subject of formula;
[tex]F = ma[/tex]
When mass = 4kg; Acceleration = 15m/s²
[tex]F = 4 * 15[/tex]
[tex]F = 60N[/tex]
When mass = 10kg; Substitute 60 for Force
[tex]F = ma[/tex]
[tex]60 = 10 * a[/tex]
[tex]60 = 10a[/tex]
Divide both sides by 10
[tex]\frac{60}{10} = \frac{10a}{10}[/tex]
[tex]a = 6m/s^2[/tex]
Hence, the acceleration is [tex]a = 6m/s^2[/tex]
What is the solution set for StartAbsoluteValue z + 4 EndAbsoluteValue greater-than 15? 11 less-than z less-than 19 Negative 19 less than z less-than 11 z less-than negative 19 or z greater-than 11 z less-than 19 or z greater-than 11
Answer:
z less-than negative 19 or z greater-than 11Step-by-step explanation:
Given the inequality [tex]|z+4|>15[/tex], we are to find the solution set of the inequality. Since the the function is an absolute value, this means that the function will be positive and negative.
For the positive value of the function;
[tex]z+4>15\\\\subtract\ 4\ from \ both \ sides\\z+4-4 > 15 -4\\\\z>11[/tex]
For the negative value of the function we have;
[tex]-(z+4) > 15\\\\-z-4> 15\\add\ 4 \ to\ both \ sides\\\\-z-4+4> 15+4\\\\-z> 19\\\\[/tex]
Multiplying both sides of the inequality by -1 will change the sense of the inequality sign;'
[tex]-(-z)< -19\\\\z<-19[/tex]
Hence the solution sets are [tex]z> 11 \ and \ z< -19 \\[/tex] OR z less-than negative 19 or z greater-than 11
Answer:
z less-than negative 19 or z greater-than 11
Step-by-step explanation:
When you enter the Texas Turnpike, they give you a ticket showing the time and place of your entry. When you exit, you turn in this ticket and they use it to figure your toll. Because they know the distance between toll stations, they can also use it to check your average speed against the turnpike limit of 65 mph. On your trip, heavy snow limits your speed to 40 mph for the first 120 mi. At what average speed can you drive for the remaining 300 mi without having your ticket prove that you broke the speed limit?
Answer:
87 mph
Step-by-step explanation:
Total distance needed is 120 mi + 300 mi and that is 420 mi.
Driving at 65 mph means that it would take
420 / 65 hours to reach his destination.
6.46 hours .
at the first phase, he drove at 40 mph for 120 mi, this means that it took him
120 / 40 hours to complete the journey.
3 hours.
the total time needed for the whole journey is 6.46 hours, and he already spent 3 hours in the first phase. To keep up with the 6.46 hours required, in the second phase, he has to drive at a speed of
6.46 - 3 hours = 3.46 hours.
300 mi / 3.46 hours => 86.71 mph approximately 87 mph
Therefore, he needs to drive at not more than 87 mph to keep up with the journey while not breaking his speed limit
Chen is bringing fruit and veggies to serve at an afternoon meeting. He spends a total of $28.70 on 5 pints of cut veggies and 7 pints of cut fruit. The food cost is modeled by the equation 5 v plus 7 f equals 28.70, where v represents the cost of one pint of cut veggies and f represents the cost of one pint of cut fruit. If the cost of each pint of fruit is $2.85, what is the approximate price of a pint of veggies?
Answer:
(7 x 2.85) + 5v = 28.70. 19.95 + 5v = 28.70. 5v = 28.70 - 19.95. 5v = 8.75. v = 8.75/5. v = 1.75. A pint of veggies costs $1.75.
Find X using the Angle Sum Theorem
Answer:
Step-by-step explanation:
x + 30 + 25 = 180
x + 55 = 180
x = 125
y + 125 = 180
y = 55
What is the range of g?
Answer:
R: {y∈R | -1 ≤ y ≤ 5}
Step-by-step explanation:
the lowest point is -1 and the highest point is 5.
Consider the age distribution in the United States in the year 2075 (as projected by the Census Bureau). Construct a cumulative frequency plot and describe what information the plot communicates about the distribution of ages in the future.
Answer:
The cumulative frequency plot is also attached below.
Step-by-step explanation:
The data provided is as follows:
Age Group Frequency
0 - 9 34.9
10 - 19 35.7
20 - 29 36.8
30 - 39 38.1
40 - 49 37.8
50 - 59 37.8
60 - 69 34.5
70 - 79 27.2
80 - 89 18.8
90 - 99 7.7
100 - 109 1.7
Consider the Excel output attached.
The cumulative frequency are computed in the Excel sheet.
The cumulative frequency plot is also attached below.
From the cumulative frequency plot it can be seen that in the future most people will belong to a higher age group rather then the lower ones.
Look at the figure below. which ratio represents tan 0?
A -5/4, B -4/5, C -3/4, D 3/5.
The required value of the tanФ is given as -3/4. C option is correct.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
What are trigonometric equations?These are the equation that contains trigonometric operators such as sin, cos.. etc. In algebraic operations.
here,
Tan(180 - Ф) = -tanФ = perpendicular / base
From figure, perpendicular= 12 and base = 16
-tanФ = 12 / 16
tanФ = -3/4
Thus, the required value of the tanФ is given as -3/4. C option is correct.
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