The slant height of the pyramid will be 5 inches.
Given Information and Formula Used
Volume of the clay = 48 cubic inches
Edge of the square base of the pyramid, a= 6 inches
Volume of the pyramid = (1/3) × Base Area × Height
Pythagoras Theorem, l² = x² + h²
Here, l is the hypotenuse, x is the base and [tex]h[/tex] is the height in a right angle triangle.
Calculating the Height, h of the Pyramid
Volume of the pyramid = Volume of the clay
Volume of the pyramid, V= 48 cubic inches
Base Area of the pyramid, B = a²
⇒ B = 6² square inches
⇒ B = 36 square inches
∵ V = (1/3)×B×H
[tex]\frac{1}{3}*36*h = 48[/tex]
∴ [tex]h = \frac{48*3}{36}[/tex]
⇒ h = 4 inches
Calculating the Slant Height, l of the Pyramid
Applying Pythagoras Theorem to determine the slant height,
l² = x² + h²
Here, we have x=a/2
[tex]l^{2} = \frac{a^{2} }{4} + b^{2}[/tex]
[tex]l^{2} = \frac{6^{2} }{4} + 4^{2}[/tex]
[tex]l = \sqrt{9+16}[/tex]
[tex]l=\sqrt{25}[/tex]
l =5 inches
Thus, the slant height of the solid right pyramid with a square base made by Helen is 5 inches.
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What is this function written in vertex form? f(x) = (x 2)2 3 f(x) = (x2 2x)2 3 f(x) = (x 1)2 2 f(x) = (x 3)2 2x
The vertex form of the give quadratic equation is f(x) = (x+1)² + 2
Vertex form of an equationThe standard vertex form of a quadratic equation is expressed as
y = a(x -h)² + k
where (h, k) is the vertex
Given the quadratic equation
f(x) = x^2 + 2x + 3
Complete the question
f(x) = (x^2+2x) + 3
f(x) = (x^2+2x+1)-1 + 3
f(x) = (x+1)² + 2
Hence the vertex form of the give quadratic equation is f(x) = (x+1)² + 2
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What is the measure (in radians) of central angle & in the circle below?
O
O
O
옥
26
ㅇ 역
12 cmy
0
14 cm
Answer:
7pi/6
Step-by-step explanation:
Using the formula for arc length in radians, we get:
14pi = 12(theta)theta = 7pi/6 [divide both sides by 12]While traveling to Europe, Phelan exchanged 250 US dollars for euros. He spent 150 euros on his trip. After returning to the United States he converts his money back to US dollars. How much of the original 250 US dollars does Phelan now have? Round to the nearest cent.
1 European euro = 1.3687 US dollars
Answer:
44.70 US dollars
Step-by-step explanation:
Begin by converting the Euros to US dollars by dividing 250 by 1.3687
250/1.3687=182.655
Then subtract 150
182.655-150=32.655
Multiply by 1.3687 to convert back to US dollars
32.655x1.3687=44.70
Solve for w.
w^2-9w+18=0
Answer:
w = 3 or 6
Step-by-step explanation:
[tex]w {}^{2} - 9w + 18 = 0 \\ w {}^{2} - 6w - 3w + 18 = 0 \\w(w - 6) - 3(w - 6) = 0 \\ w - 3 = 0 \\ w - 6 = 0 \\ w = 3 \: or \: 6[/tex]
Suppose a simple random sample of size n = 36 is obtained from a population that is skewed right with μ = 75 and o = 24. What is P x > 80 ? Suppose a simple random sample of size n = 36 is obtained from a population that is skewed right with μ = 75 and o = 24. What is P x > 80 ?
Using the normal distribution, it is found that the probability that the sample mean is above 80 is of 0.1056 = 10.56%.
Normal Probability Distribution
The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters are given as follows:
[tex]\mu = 75, \sigma = 24, n = 36, s = \frac{24}{\sqrt{36}} = 4[/tex].
The probability that the sample mean is above 80 is one subtracted by the p-value of Z when X = 80, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{80 - 75}{4}[/tex]
Z = 1.25
Z = 1.25 has a p-value of 0.8944.
1 - 0.8944 = 0.1056.
0.1056 = 10.56% probability that the sample mean is greater than 80.
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please help me on how to solve for the distances
Answer:
B
Step-by-step explanation:
Solve this question, and I'll be extremely thankful (:
Thanks to whoever can do this for me!
-
Problem:
Using Scratch (or whatever programming language you are comfortable with), create code that would allow a user to input the legs of a right triangle and the output would be the length of the hypotenuse.
Create a program that finds the leg of a triangle given the hypotenuse and another leg and add an error message if the leg is longer than the hypotenuse.
Send a screenshot when you're done.
Answer:
it is in java and it is also can be done in BlueJ
Step-by-step explanation:
please mark me brainlist
The table shows the outputs, y, for different inputs, x: Input (x) 2 5 9 12 Output (y) 20 15 12 8 Part A: Do the data in this table represent a function? Justify your answer. (3 points) Part B: Compare the data in the table with the relation f(x) = 5x + 14. Which relation has a greater value when x = 9? (2 points) Part C: Using the relation in Part B, what is the value of x if f(x) = 64? (5 points) (10 points)
The table is a function and the relation f(x) = 5x + 14 has a greater value when x = 9
Is the table a function?The table of values is given as:
Input (x) 2 5 9 12
Output (y) 20 15 12 8
In the above table of values, each x value have a unique y value.
This means that the table is a one-to-one relation
A one-to-one relation is a function
Hence, the table is a function.
The greater relation at x = 9The function is given as:
f(x) = 5x + 14
This gives
f(9) = 5 * 9 + 14
Evaluate
f(9) = 59
From the table, we have:
y = 12 when x = 9
Hence, the relation f(x) = 5x + 14 has a greater value when x = 9
The value of x if f(x) = 64We have
f(x) = 5x + 14
This gives
5x + 14 = 64
Subtract 14 from both sides
5x = 50
Divide by 5
x = 10
Hence, the value of x when f(x) = 64 is 10
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What is (-2)-(-2 1/6) and how do i get that answer?
Answer:
1/6
Step-by-step explanation:
-2 - (-2 1/6)
multiply the number in the parentheses by -1
-2 + 2 1/6
-2 + 2 cancels out
Leaving 1/6 as your answer.
solve the linear system by elimination. 4x-2y=15 2x+2y=3
Answer:
x=3 and y = -3/2
What is the elimination method?A method for solving a system of linear equations where you add or subtract equations to eliminate a variable. Eliminating one variable by combining two equations with a common term with adding or subtracting.
___________________________________
Let's solve your system by elimination.
4x−2y=15;2x+2y=3
4x−2y=15
2x+2y=3
Add these equations to eliminate y:
6x=18
Then solve 6x=18 for x:
6x=18
6x/6 = 18/6 (Divide both sides by 6)
x=3
Now that we've found x let's plug it back in to solve for y.
Write down an original equation:
4x−2y=15
Substitute3 for x in 4x−2y=15:
(4)(3)−2y=15
−2y+12=15(Simplify both sides of the equation)
−2y+12+−12=15+−12(Add -12 to both sides)
−2y=3
-2y/-2 = 3/-2 (Divide both sides by -2)
y = -3/2
Answer:
x=3 and y = -3/2
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Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of pi (no approximations)
Answer:
A = 27π cm²
Step-by-step explanation:
the area (A) of the sector is calculated as
A = area of circle × fraction of circle
the central angle of the shaded sector = 360° - 90° = 270° , then
A = πr² × [tex]\frac{270}{360}[/tex]
= π × 6² × [tex]\frac{3}{4}[/tex]
= 36π × [tex]\frac{3}{4}[/tex]
= 9π × 3
= 27π cm²
Solve this question please
The expansion of the polynomial is given as:
[tex](5x^3+\frac{14}{3x^4})=15625x^{18}+87500x^{11} +\frac{612500}{3}x^3+\frac{6860000}{27x^3}+\frac{4802000}{27x^{10}}+\frac{5378280}{81x^{17}}+\frac{7529536}{729x^{24}}[/tex]
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The expansion is given as:
[tex](5x^3+\frac{14}{3x^4})=15625x^{18}+87500x^{11} +\frac{612500}{3}x^3+\frac{6860000}{27x^3}+\frac{4802000}{27x^{10}}+\frac{5378280}{81x^{17}}+\frac{7529536}{729x^{24}}[/tex]
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Helpppppp pleaseeee shoe your work
2p-4p ≤ -2
-2p ≤ 2
[tex]\frac{-2p}{-2} \leq \frac{-2}{-2}[/tex] (Sign flips as both sides it is getting divided by NEGATIVE 2)
p≥1
Interval notation: [1, infinity)
Hope it helps!
please help!!!!
picture below
Answer:
7 ^ 6x + 2 = 7^15
taking log on both the sides
log 7^6x + 2 = log 7^15
6x + 2 log 7 = 15 log 7
log 7
the tabel show the time merrida spent driving and the number of miles she drove she drove the same number of miles each other
Answer:
35 miles per hour
Step-by-step explanation:
Speed of a car or any other object is given by distance divided by time taken.
therefore,
according to the given data in the table :
speed = miles covered/ time taken
= 140/4 = 35 miles per hour
= 175/5 = 35 miles per hour
= 210/6 = 35 miles per hour
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georgia drew a scale model of one of the stepping stones in her garden. the two shapes are similar, and the ratio of the lengths of the sides is 4:1. if the length of side dc equals twelve inches, what is the length of side ut in the scale drawing?
The length of the UT is 3 inches if the ratio of the lengths of the sides is 4:1. if the length of side DC equals 12 inches,
What is a scale factor?The ratio among comparable dimensions of an object and a model with that object is known as an exponent in algebra. The replica will be larger if the scale factor is a whole number. The duplicate will be lowered if the step size is a fraction.
We have:
Georgia drew a scale model of one of the stepping stones in her garden. the two shapes are similar, and the ratio of the lengths of the sides is 4:1.
The length DC = 12 inches
DC/UT = 4/1
12/UT = 4/1
UT = 12/4 = 3 inches
Thus, the length of the UT is 3 inches if the ratio of the lengths of the sides is 4:1. if the length of side DC equals 12 inches,
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Answer:
3 in.
Step-by-step explanation:
Keep it simple :)
12.
(05.05 MC)
A survey asked, "If you were to buy a new vehicle, would you want a sport car or a sedan?" The results are presented in the following two-way table:
table:
Sedan Sport Total
Male 21 39 60
Female 135 45 180
Total 156 84 240
Which of the following is a two-way conditional frequency table for gender? (1 point)
A two-way conditional frequency table for this gender is shown in table A.
What is a frequency table?A frequency table can be defined as a type of table which is typically used to graphically represent the frequencies or relative frequencies that are associated with a categorical variable.
In this scenario, a two-way conditional frequency table for this gender would be constructed as follows:
Gender Sedan Sport Total
Male 0.35 0.65 1
Female 0.75 0.25 1
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2+2 I
dont know how but 4 was wrong guys am I not thinking right?
Answer:
Maybe the question could've been 2+2+1. I'd say read the question properly.
Step-by-step explanation:
In which case, 2+2+1= 5
What is the method used when the objective is to determine the cause and effect relationship of a certain phenomenon under controlled condition?
Answer: A
Explaination:
The cause and effect relationship of a certain phenomenon under controlled condition
30 POINTS AND BRAINLIEST PLS HELPP - Vanessa's bedroom floor is a rectangle 3m wide and 5m long. She chooses a new carpet that costs £20 per m squared. How much does the carpet cost??
Answer:
Carpet costs = 300£
Step-by-step explanation:
• First calculate the area of the floor:
Area of floor = length x width
= 5m² x 3m²
= 15m²
• As one m² of carpet costs £20, 15m² of carpet costs:
15 x 20
= 300£
Absolute value of (-1, -3/7)
The absolute value of -1 is 1 and -3/7 is 3/7.
We have given that,
(-1, -3/7)
We have to determine the absolute value of (-1, -3/7)
What is the absolute value?The absolute value or modulus of a real number x denoted |x|, is the non-negative value of x without regard to its sign. Namely, [tex]{\displaystyle |x|=x}[/tex]if x is a positive number, and [tex]{\displaystyle |x|=-x}[/tex] if x is negative, and[tex]{\displaystyle |0|=0}[/tex].
Therefore the absolute value of -1 is 1 and -3/7 is 3/7.
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There is a bag filled with 6 blue and 5 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting at least 1 blue?
Answer:
1/11
Step-by-step explanation:
probability =total number of items ÷ 1
=11÷1
=1/11
О A. 24
B. 12
О с. 92
D. 46
A
12
46°
46°
C
Answer:
I think A or C.
Step-by-step explanation:
what is the gradient and y-intercept of y+2n=5
Answer:
Step-by-step explanation:
Here is an equation: 5x - 2y = 10
Create 3 equations that result in…
1. 1 solution
2. No Solutions
3. Infinitely many solutions
You should provide three different answers and an explanation why your equations work.
Answer:
one solution from the amount of numbers
Find the perimeter.
15 ft
25 ft
if the 25ft is diagonal in a rectangle
Answer:
P=70ft
Step-by-step explanation:
25^2-15^2=400
Sqrt400=20
2l+2w=P
40+30=70
What do you consider to be the advantages of the numerical values? What do you consider to be the advantages of the visual representations? Which do you prefer working with, and why?
Visual representation is preferable for working for its attractive charts, graphs etc.
The advantages of the numerical values :
1. Numerical values are present in numerical methods. Numerical methods are easier to calculate with the help of mathematical operations like addition, subtraction, multiplication, division & others.
2. No analytical solution is present in numerical methods, only the numerical values are there. So, this is an advantage of numerical values.
The advantages of the visual representations
1. Visual representation gives us an easier way of understanding.
2. Visual representation makes something more interesting to read or solve.
3. Visual representation is best to arrange quantitative datas by using charts, graphs, attractive colors etc.
Which is preferable for working and why?
Visual representation is preferable for working. Because it is more easier way to solve something. The gained interest from visual representation also help to solve something quicker.
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Answer:
I myself prefer visual representation because to me it helps to see things visually and for understanding and working with charts and graphs.
Numerical methods make equations easier to calculate because they give us help of mathematical operations like in addition, subtraction, multiplication, division & others.
Visual representations give us easier ways of understanding and makes something more interesting to read or solve by simply looking at the visual.
Step-by-step explanation:
Someone please explain this step by step:
If\begin{align*}
2x-y&=3,\\
x+y &=1,
\end{align*}compute $8x-7y$.
Answer:
13
Step-by-step explanation:
Perhaps the most straightforward way to find the value of the given function is to first solve the equations for x and y. The results can be substituted into your expression to find the value you want.
__
solving the systemWe notice the y-coefficients are opposites, so we can eliminate the y-variable by adding the equations.
(2x -y) +(x +y) = (3) +(1)
3x = 4 . . . . . . simplify
x = 4/3 . . . . . divide by 3
The value of y can be found from the second equation:
4/3 +y = 1 . . . . substitute for x
y = -1/3 . . . . . . subtract 4/3
expression valueThe value of 8x-7y is found by substituting the x- and y-values into this expression:
8(4/3) -7(-1/3) = 32/3 +7/3 = 39/3 = 13
The value of 8x-7y is 13.
_____
Additional comment
You can also work out what combination of the two equations will give 8x -7y. That turns out to be 5 times the first minus 2 times the second:
5(2x -y) -2(x +y) = 5(3) -2(1)
10x -5y -2x -2y = 15 -2
8x -7y = 13
__
The coefficients 5 and -2 are found by solving the system of equations ...
a(2x -y) +b(x +y) ≡ 8x -7y ⇒ {2a +b = 8, -a +b = -7}
Which statements about the location of the point are true? Select three options.
A square garden has a side length of 5 ft. What is the area of the garden?
O 5ft²
O 10ft²
O 20ft²
O 25 ft²
formula is lsquare so answer is 25ft