Answer:
[tex]42.7\,\,cubic\,\, meters[/tex]
Step-by-step explanation:
Given: Perimeter of base of a pyramid = 12.8 m
Height of the pyramid = 12.5 m
To find: volume of a pyramid
Solution:
Perimeter of base of a pyramid = 12.8 m
As base of the pyramid is a square,
12.8 = [tex]4(side\,\,of\,\,a\,\,square)[/tex]
side of a square = [tex]\frac{12.8}{4}=3.2\,\,m[/tex]
Area of a square (A) = [tex](side\,\,of\,\,a\,\,square)^2=(3.2)^2=10.24\,\,m^2[/tex]
Height of the pyramid (h) = 12.5 m
Volume of the pyramid = [tex]\frac{Ah}{3}=\frac{1}{3}(10.24)(12.5)=42.7\,\,cubic \,\,meters[/tex]
Which inverse operations could you use to solve the equation m5−8=−6? Select all that apply.
A
Multiply each side by 5 and then add 8 to each side.
B
Add 8 to each side and then multiply each side by 5.
C
Add 8 to each side and then divide each side by 5.
D
Subtract 8 from each side and then multiply each side by 5.
E
Subtract 6 from each side and then multiply each side by 8.
F
Multiply each side by 5 and then add 40 to each side.
Answer:
Correct option: C
Step-by-step explanation:
To solve the equation m*5 - 8 = -6, we can use the following steps:
step1: sum 8 in both sides, to make m*5 be the only term in the left side.
m*5 = 2
step2: divide both sides by 5, then we will have 'm' isolated in the left side.
m = 2/5
So the operations we could use is: add 8 to each side and then divide each side by 5.
Correct option: C
What is the value of 1 over 2 x+3.4y when x=3 and y = 4?
Answer:
The value of the given expression is 27.1
Step-by-step explanation:
We are given an expression of two variable x and y.
We need to find the value of expression at x = 3 and y = 4
So first put x = 3 and y = 4 into expression and simplify
1/2 x 3 (3) + 3.4 x 4
➡️ 1/2 x 27 + 13.6
➡️ 27/2 + 13.6
➡️ 13.5 + 13.6
Now, add both of the numbers together. ( as an addition problem)
Therefore, when you ad the 2 together, you get the total of 27.1
Select all of the following statements that are true.
All real numbers are natural numbers.
All whole numbers are integers.
All integers are whole numbers.
All natural numbers are rational numbers.
All irrational numbers are dense.
DONE
Answer:
All whole numbers are integer
All natural numbers are rational numbers
Step-by-step explanation:
Answer:
2, 4, 5
Step-by-step explanation:
edge 2021 :)
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Answer:
$12,000,000
Step-by-step explanation:
The maximum will be the vertex and because this is written in vertex form the vertex will be (5, 12) so the maximum income will be 12 million dollars.
Starting with $5,000, you invest in an account that pays 2% APR, compounded quarterly, and plan to leave the money there and not touch it for at least 12 years. How much MORE money would you have after 12 years if the interest had been compounded continuously instead? Round to the nearest cent.
Answer:
$1,352.5
Step-by-step explanation:
A=p(1+r/n)^nt
Where,
P=principal
r=interest rate
n=no of periods
t=time
P=$5,000
r=2%
n=4
t=12
A=5000(1+0.02/4)^4*12
=5000(1+0.005)^48
=5000(1.005)^48
=5000(1.2705)
=$6,352.5
How much more money after 12 years
=$6,352.5-$5000
=$1,352.5
Add
(4-4i)+(3-2i)
Write as complex number in standard form
Answer: (4-4i)+(3-2i) = 7-6i
Step-by-step explanation:
To add or subtract two complex numbers, just add or subtract the corresponding real and imaginary parts. For instance, the sum of 4 -4i and 3 - 2i is 7 -6i. The numbers in standard form will be a + bi, where a is the real part and bi is the imaginary part.
Find the value of x.
Answer:
x = 27
Step-by-step explanation:
(whole secant) * (external part) = (tangent)^2
(x+48)* 48 = 60^2
(x+48)* 48 = 3600
Divide each side by 48
x+48 =75
Subtract 48 from each side
x = 75-48
x=27
The area of the rectangle is 20 square inches. The rectangle is enlarged by a factor of 6.
What is the area of the enlarged rectangle?
120 in.²
720 in.²
2,400 in.²
14,400 in.²
Answer:
B
Step-by-step explanation:
Here, we are told that the rectangle is enlarged by a factor of 6, we now want to calculate the new area of the said rectangle.
Now, for the rectangle to have an area of 20, mathematically the area of a triangle can be calculated using the formula L * B
where L is the length and B is the breadth
our product here is 20, so any product that gives 20 would be a good fit as the value of the width and length of the rectangle
So, let’s say the sides measure 5 inches by 4 inches
Enlarging these by a factor of 6, we have 30 inches by 24 inches
The new area of the rectangle would thus be ;
30 inches * 24 inches = 720 inches^2
Answer:
b
Step-by-step explanation:
What is the value of p ?
Answer:
B.
Step-by-step explanation:
First find the other two angles in the triangle using supplementary angles.
They are 90° and 55°
Now just subtract them from 180
180 - 90 - 55 = 35°
A recipe for stew calls for 2 1/2 pounds of meat, 22 ounces of beans, 14 ounces of carrots, and 2 pounds 6 ounces of potatoes. Which is the weight of the ingredients in the stew in pounds?
Answer:
7.125pounds
Step-by-step explanation:
if a recipe for stew calls for 2 1/2 pounds of meat, 22 ounces of beans, 14 ounces of carrots, and 2 pounds 6 ounces of potatoes, in order to get the weight of the ingredients in the stew in pounds, we will convert all the units to pounds first and then add them together.
On conversion;
since 1 ounce = 0.0625pounds
Weight of beans in pounds = 22 * 0.0625 = 1.375pounds
Weight of meats = 2 1/2 pounds
Weight of carrots in pounds = 14*0.0625 = 0.875pounds
Weight of potatoes in pounds = 2+(6*0.0625) = 2+0.375 = 2.375pounds
weight of the ingredients in the stew in pounds = 1.375+2.5+0.875+2.375
weight of the ingredients in the stew in pounds = 7.125pounds
LeBron James shot 30 shots per game last season. His season high in shots was 2,000. He wants to earn a different shot per game record next season. How many shots shouldn’t LeBron take per game next season?
Answer:
1700
Step-by-step explanation:
I Need Help With This Question
Attachment below
Answer & Step-by-step explanation:
For this problem, all we have to do is add f(x) to g(x). So, we will add (x -2) to (x² + x - 6).
(x - 2) + (x² + x - 6)
Combine like terms.
x² + (x + x) + (-2 + (-6))
x² + 2x - 8
So, (f + g)(x) is equal to x² + 2x - 8
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Answer:
x^2+6x+8
Step-by-step explanation:
x x x=x^2
x x2= 2x
4 x x=4x
4 x 2= 8
x^2+2x+4x+8
x^2+6x+8
(2n + 4) + 6 = –9 + 4(2n + 1)
Answer:
n=2.5
Step-by-step explanation:
(2n+4)+6=-9+4(2n+1)
Expand parentheses:
2n+10=-9+8n+4
Combine like terms:
15=6n
Divide both sides by 6:
n=2.5
Hope this helps!
Find the 64th term of the following arithmetic sequence.
29,38,47...
Answer:
596
Step-by-step explanation:
I typed in 656 as the other person it was but it wasn't
An arithmetic sequence is a sequence where the difference between each consecutive term is the same.
The nth term of an arithmetic series is given as:
a(n) = a(1) + (n - 1)d
The 64th term of the arithmetic sequence is 596.
What is an arithmetic sequence?It is a sequence where the difference between each consecutive term is the same.
Example:
2, 4, 6, 8, 10 is an arithmetic sequence.
common difference = 2
The first term = 2.
We have,
29, 38, 47,.....
First term = 29
a(1) = 29
Common difference:
= 38 - 29
= 9
Now,
The nth term of an arithmetic series is given as:
a(n) = a(1) + (n - 1)d
The value of the 64th term in the arithmetic sequence.
a(64) = a(1) + (64 - ) x 9
a(64) = 29 + 63 x 9
a(64) = 29 + 567
a(64) = 596
Thus,
The 64th term of the arithmetic sequence is 596.
Learn more about arithmetic sequence here:
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Answer:
first box: -14[tex](x+7)^2-49=0\\(x+7)^2=49\\(x+7)=\sqrt{49} \\(x+7)=+/-7\\x=-7+/-7\\x=-7+7\,\,and\,\,-7-7\\x=0\,\,and\,\,-14[/tex]
second box: zero
Step-by-step explanation:
at which value(s) of x does the graph of the function f(x) have a vertical asymptote?
Answer:
E. x = 4
F. x = -2
Step-by-step explanation:
Asymptotes occur when you have an undefined (a divide by 0 error). So x in the denominator can't equal zero. The 2 values that make the denominator zero are 4 and -2.
what is the rate of change between (29,9) and (33,10)?
Answer:
m= 1/4
Step-by-step explanation:
tried helping I don't know if this is the right way to do it for you
A scatter plot and a possible line of best fit is shown:
Is the line of best fit accurate for the data shown?
No, because the line does not touch any points
No, because the line should touch every point
Yes, because it touches the y-axis
Yes, because it passes through the center of the data points
Answer: No, because the line does not touch any points.
Step-by-step explanation:
A line of best fit should pass through most if not all of the points on a graph. If it does not, it can't be considered a line of best fit.
Answer:
Yes, because it passes through the center of the data points.
Step-by-step explanation :
Its D because, the line of best fit does not have to touch any points, it has to be the closest possible to the points.
A rectangular piece of metal is 25in longer than it is wide . Squares with sides 5in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 750in, what were the original dimensions of the piece of metal
Answer:
Step-by-step explanation:
Let width be x
Let lenght be 25 + x
Total ax = (25+x) * x
Square with 5in long are cut from the four corner formed = 750in
(25+x-10) * (x-10) * 5 = 750
(15+x) (x-10) = 150
15x-150+x^2-10x =150
15x -150-150+x^2-10x+0
x^2+15x-300=0
(ax^2+bx+c=0)
Researchers are interested in determining whether more women than men prefer the beach to the mountains. In a random sample of 200 women, 45% prefer the beach, whereas in a random sample of 300 men, 52% prefer the beach. What is the 99% confidence interval estimate for the difference between the percentages of women and men who prefer the beach over the mountains?
Answer:
The 99% confidence interval estimate for the difference between the percentage of women and men who prefer the beach over the mountains is -18.72% < (p₁ - p₂) < 4.72%
Step-by-step explanation:
The given parameters are;
Sample size of the women sample, n₁ = 200
Percentage of the women that prefer beach, p₁ = 45%, [tex]\hat p_1[/tex] = 0.45
Sample size of the men sample n₂ = 300
Percentage of the men that prefer beach, p₂ = 52%, [tex]\hat p_2[/tex] = 0.52
Confidence level of the confidence interval = 99%
α = 1 - 0.99 = 0.01, therefore, α/2 = 0.005
The equation for the confidence interval for the difference between two proportions is given as follows;
[tex]\left (\hat{p}_{1} - \hat{p}_{2} \right )\pm z_{\alpha /2}\sqrt{\dfrac{\hat{p}_{1}(1-\hat{p}_{1})}{n_{1}}+\dfrac{\hat{p}_{2}(1-\hat{p}_{2})}{n_{2}}}[/tex]
[tex]z_{\alpha /2}[/tex] = ±2.57 from the z score tables
Plugging in the vales, we have;
[tex]\left (0.45 - 0.52 \right )\pm 2.57\sqrt{\dfrac{0.45(1-0.45)}{200}+\dfrac{0.52(1-0.52)}{300}}[/tex]
Which gives;
-0.1872 < [tex](\hat p_1 - \hat p_2)[/tex] < 0.0472
The 99% confidence interval estimate for the difference between the percentage of women and men who prefer the beach over the mountains = -18.72% < (p₁ - p₂) < 4.72%.
Find the value of sinY
Answer:
[tex] \frac{63}{65} [/tex]
Step-by-step explanation:
Please see the attached picture.
Let's find the value of the opposite side, XZ.
Applying Pythagoras' Theorem,
(XZ)² +(XY)²= (ZY)²
(XZ)² +16²= 65²
(XZ)²= 4225 -256 (bring constant to 1 side)
(XZ)²= 3969 (simplify)
Square root both sides,
XZ= [tex] \sqrt{3969} [/tex]
XZ= 63 (simplify)
sinY
= XZ/ ZY
[tex] = \frac{63}{65} [/tex]
Answer:
63/65
Step-by-step explanation:
Write the simplest form of the expression (64/729)^(−1/6)
Answer:
3/2
Step-by-step explanation:
(64/729)^(−1/6)=(2^6/3^6)^(-1/6)=(2/3)^-1=3/2
Harpreet took out a payday loan of $500.00. He had to repay $540.00 within 7 days.
A) What was the daily interest on the loan
B) What was the annual interest?
Answer:
a) 1,14%
b) 317%
Step-by-step explanation
J = C . i . t
540 - 500 = 500 . i . 7
40 = 500 . 7 . i
i = 0,0114 = 1,14% within day
-------------------------------------------
J = 500 . 0,0114 . 365 = 2085,71
2085,71 - 500 = 500 . i . 1
1585,71 = 500 . i
i = 3,17 = 317% annual
Check the consistency of 2x-3y=7 and x-2y+1=0
Answer:
x = 17, y = 9
or as an ordered pair, (17, 9).
The equations are consistent.
Step-by-step explanation:
2x - 3y = 7
x - 2y = -1 Multiply this equation by -2:
-2x + 4y = 2 Add this to the first equation:
y = 9.
Plug y = 9 into the second equation:
x - 2*9 = -1
x = -1 + 18 = 17.
Solve
4(2x - 3) = 6x + 2
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4(2x - 3) = 6x + 2
Expand it:
8x - 12 = 6x + 2
+ 12 to both sides
8x = 6x + 14
- 6x from both sides
2x = 14
Divide both sides by 2:
x = 7
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Answer:
between step 1 and 2 he left off the 5
Consider the system of inequalities and its graph. y ≤ –0.75x y ≤ 3x – 2 On a coordinate plane, 2 solid straight lines are shown. The first line has a negative slope and goes through (negative 8, 6) and (0, 0). Everything below the line is shaded. The second line has a positive slope and goes through (negative 2, negative 8) and (2, 4). Everything to the right of the line is shaded. The section in quadrant 1 is labeled 3, the section in quadrant 2 is labeled 2, the section in quadrant 3 is labeled 1, and the section in quadrant 4 is labeled 4. In which section of the graph does the actual solution to the system lie? 1 2 3 4
Answer:
4
Step-by-step explanation:
the answer is 4 so d on edge .
Based on the information given regarding the graph, it should be noted that the correct option is graph 4.
What is a graph?
It should be noted that a graph is a diagram that shows the relationship between two or more sets of numbers.
From the information given, the system of inequalities and its graph is given is y ≤ –0.75x y ≤ 3x – 2 and the first line has a negative slope and goes through (negative 8, 6) and (0, 0).
Therefore, the section of the graph where the actual solution to the system lie is in graph 4.
Learn more about graphs on;
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Find the volume of the cylinder Either enter an exact answer in terms of Pi or use 3.14 or Pi
Answer:
[tex]Volume = 54\,\pi[/tex]
Step-by-step explanation:
Recall the formula for the volume of a cylinder:
[tex]Volume=\pi \,R^2\,H[/tex]
where R is the radius of the cylinder's base, and H is the cylinder's height.
Therefore, in our case the volume becomes:
[tex]Volume=\pi \,R^2\,H\\Volume=\pi \,3^2\,*\,6\\Volume = 54\,\pi[/tex]
An object is launched directly in the air at a speed of 64 feet per second from a platform located 16 feet in the air. The motion of the object can be modeled using the function f(t)=−16t2+64t+16, where t is the time in seconds and f(t) is the height of the object. When, in seconds, will the object reach its maximum height?
Answer:
Step-by-step explanation:
x= -b/2a = -64/2(-16) = 2
showing that the object will reach its highest point at 2 seconds