Mathematics High School

Find the surface area of a pyramid with a square base with dimensions 100 mm by 100 mm and height of 75 mm.

Answers

Answer 1

To solve for the surface area of the pyramid, we make use of the formula:

A= l w + l [sqrt ((w / 2)^2 + h^2)] + w [sqrt ((l / 2)^2 + h^2))

where,

l and w are the base of the pyramid = 100 mm

h is the height of the pyramid = 75 mm

Substituting the given values into the equation:

A= 100 * 100 + 100 [sqrt ((100 / 2)^2 + 75^2)] + 100 [sqrt ((100 / 2)^2 + 75^2))

A = 10,000 + 100 (sqrt 2575) + 100 (sqrt 2575)

A = 20,148.90 mm^2

Therefore the surface area of the pyramid is about 20,149 mm^2.

Related Questions

Find the equation of the tangent line of f^-1(x) at the point where it intersects the x-axis

Answers

hello :
note :
1 ) f(X0) = Y0 equiv : X0 = f^-1(Y0)
2 ) ( f^-1(Y0) )' = 1/ f'(X0)
in this exercice : X0 = 0
he equation of the tangent line for graph of : f
Y - Y0 = f'(X0) (X- 0)
sp : he equation of the tangent line for graph of : f^-1(x) is :
X -X0 = f'(Y0) (Y -0)

WILL GIVE A BRAINLIEST IF UR RIGHT PLEASE HELP!!

Determine which ordered pair is NOT a solution of y=3x-8.

a.
(8, 16)
b.
(3, 4)
c.
(–6, –26)
d.
(–10, –38)

Answers

A is the correct answer because 16=3(8) - 8 = 16=16

Option B;
The coordinates (3, 4) are not of this function:

y = 3x - 8
x = 3:
y = 3(3) -8
= 9 - 8
= 1 ≠ 4
∴ (3, 4) does not lie on the line y = 3x - 8

A triangle has one leg measuring 10 inches and the hypotenuse measuring 20 inches. the other leg measures 10\sqrt[]{3} 10 3 inches. what type of triangle is represented here?

Answers

From the description given for the triangle above, I think the type of triangle that is represented would be a right triangle. This type of triangle contains a right angle and two acute angles. In order to say or prove that it is a right triangle, it should be able to satisfy the Pythagorean Theorem which relates the sides of the triangle. It is expressed as follows:

c^2 = a^2 + b^2

where c is the hypotenuse or the longest side and a, b are the two shorter sides.

To prove that the triangle is indeed a right triangle, we use the equation above.

c^2 = a^2 + b^2
c^2 = 20^2 = 10^2 + (10sqrt(3))^2
400 = 100 + (100(3))
400 = 400

Student identification codes at a high school are 4-digit randomly generated codes beginning with 1 letter and ending with 3 numbers. there are 26,000 possible codes. what is the probability that you will be assigned the code a123?

Answers

[tex]\dfrac{1}{26,000}\approx3.8\%[/tex]

Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n equals 123n=123, p equals 0.85

Answers

Mean = n.p = (123).(0.4) = 49.2
Variance = np(1-p) = (123)(0.4)(1-0.4) =(123)(0.4)(0.6) = 29.52
Standard. Deviation = √variance = √29.52 = 5.43

The mean of the binomial distribution is [tex]$ 104.55 $[/tex], the variance is [tex]$ 15.6825 $[/tex], and the standard deviation is approximately .

To find the mean, variance, and standard deviation of a binomial distribution with given values of [tex]$ n $[/tex] and [tex]$ p $[/tex], we use the following formulas:

Mean [tex]($ \mu $) = $ n \times p $[/tex]

Variance [tex]($ \sigma^2 $) = $ n \times p \times (1 - p) $[/tex]

Standard Deviation [tex]($ \sigma $) = $ \sqrt{\text{Variance}} $[/tex]

Given:

[tex]$ n = 123 $[/tex]

[tex]$ p = 0.85 $[/tex]

Let's calculate each of these:

Mean [tex]($ \mu $)[/tex]:

[tex]$ \mu = n \times p $[/tex]

[tex]$ \mu = 123 \times 0.85 $[/tex]

[tex]$ \mu = 104.55 $[/tex]

Variance [tex]($ \sigma^2 $)[/tex]:

[tex]$ \sigma^2 = n \times p \times (1 - p) $[/tex]

[tex]$ \sigma^2 = 123 \times 0.85 \times (1 - 0.85) $[/tex]

[tex]$ \sigma^2 = 123 \times 0.85 \times 0.15 $[/tex]

[tex]$ \sigma^2 = 104.55 \times 0.15 $[/tex]

[tex]$ \sigma^2 = 15.6825 $[/tex]

Standard Deviation [tex]($ \sigma $)[/tex]:

[tex]$ \sigma = \sqrt{\sigma^2} $[/tex]

[tex]$ \sigma = \sqrt{15.6825} $[/tex]

[tex]$ \sigma \approx 3.9599 $[/tex]

Therefore, the mean of the binomial distribution is [tex]$ 104.55 $[/tex], the variance is [tex]$ 15.6825 $[/tex], and the standard deviation is approximately .

What is the simplified expression for ?

Answers

The simplified expression is 16

Find three consecutive odd integers with the sum of 51.

Answers

well.. hmmmm

bear in mind that, if you multiply any integer, odd or even, by 2, you get an even, no matter how you slice it and dice it, you always get an even number, 17 *2, 34*2, or whatever * 2, is always an EVEN integer.

you can always get an ODD integer, by simply adding or subtracting 1 from any even, say 4 - 1, or 4 + 1, is 3 and 5 respectively, both odd ones.

and you can always get another consecutive odd integer, by simply jumping 2 units from any odd, so 3, 5, 7, 9, 11 and so on, notice, you simply hop two spots from one, on either direction back or forth, and you get another ODD integer.

alrite, with that in mind, let's pick a reference value, say "a" is our reference integer.

so, 2*a or 2a, we know is an EVEN integer, however, we also know that 2a + 1 is an ODD integer, well, there you have it, our first odd integer is 2a + 1.

now, let's hop twice from there to get our second consecutive odd one, (2a + 1) + 2, or 2a + 3, now, let's hop again to get the next consecutive odd one, (2a + 3) + 2, or 2a + 5.

there you have it, our reference integer is "a", our odd integers are those.

alrite... now, we know their sum gives 51, alrite

[tex]\bf (2a + 1) + (2a + 3) + ( 2a + 5) = 51 \\\\\\ 2a + 1 + 2a + 3 + 2a + 5 = 51 \\\\\\ 2a + 2a + 2a +1 + 3 ++ 5 = 51\implies 6a+9=51\implies 6a=51-9 \\\\\\ 6a=42\implies a=\cfrac{42}{6}\implies \boxed{a=7}[/tex]

now, recall, "a" is only our reference integer, so... if you want to get the consecutive odd integers, well, they're just 2a + 1, 2a + 3 and 2a + 5, and since you already know what "a" is, well, just plug it in to get the integers.

What is the sum of the arithmetic sequence 3, 9, 15..., if there are 26 terms?

Answers

9 - 3 = 6, 15-9 = 6 the difference is 6, So d = 6

First term: a1 = 3

Sn = n*(a1 + an)/2

Sn = n*(a1 + a1 + (n-1)*d)/2

Sn = n*(2*a1 + (n-1)*d)/2

substitute 26 for n
S26 = 26*(2*a1 + (26-1)*d)/2

substitute 3 for a1

S26 = 26*(2*3 + (26-1)*d)/2

substitute 6 for d

S26 = 26*(2*3 + (26-1)*6)/2

S26 = 2,028

Sum of an arithmetic series is:

S = n*(a_1+a_n)/2, that easy.

n is the number of terms, 26 in your case. a_n is a_26. We need to find the series!

a_n = a_1 + (n-1)*d, the difference, d, is 6.

So a_n = 3 + (n-1)*6 = 6*n-3 (check it works: 3, 9, 15, ...)

Now a_26 = 6*26-3 = 153, so finally:

S = 26*(3+153)/2 = 26*78 = 2028

2028 is the answer

Assume that adults have iq scores that are normally distributed with a mean of 100100 and a standard deviation of 15. find the third quartile upper q 3q3, which is the iq score separating the top 25% from the others.

Answers

Final answer:

The third quartile (Q3) of IQ scores, which separates the top 25% of scores, is approximately 110.125 for a normal distribution with a mean of 100 and a standard deviation of 15.

Explanation:

To find the third quartile (Q3) of IQ scores, which is the value that separates the top 25% from the others in a normally distributed data set, we use the properties of the normal distribution. The mean IQ score is 100 and the standard deviation is 15. Q3 corresponds to the 75th percentile in a normal distribution.

To find the third quartile (Q3), we often refer to the z-score table or use a statistical software or calculator that can handle normal distribution calculations. The z-score corresponding to the 75th percentile is approximately 0.675. We can then use the formula for z-scores:

Q3 = mean + z*(standard deviation)

Q3 = 100 + 0.675*15

Q3 = 100 + 10.125

Q3 = 110.125

Thus, the third quartile IQ score, separating the top 25% of scores from the rest, is approximately 110.125.

To find Q3 for IQ scores (mean 100, SD 15), calculate 75th percentile: [tex]$ Q3 = 100 + 0.674 \times 15 = 110.11 $.[/tex]

To find the third quartile (upper Q3) of IQ scores, we need to determine the IQ score that separates the top 25% from the rest. Given that IQ scores are normally distributed with a mean of 100 and a standard deviation of 15, we can use the properties of the normal distribution to find this value.

1. Identify the z-score corresponding to the third quartile (Q3):

- The third quartile (Q3) corresponds to the 75th percentile of the normal distribution.

- Using the standard normal distribution table or a calculator, the z-score for the 75th percentile is approximately 0.674.

2. Convert the z-score to an IQ score:

- Use the formula for converting a z-score to a value in a normal distribution:

[tex]\[ X = \mu + z \sigma \][/tex]

where:

- [tex]$ \mu $[/tex] is the mean (100)

- [tex]$ \sigma $[/tex] is the standard deviation (15)

- [tex]$ z $[/tex] is the z-score (0.674)

3. Calculate the IQ score:

[tex]\[ Q3 = 100 + (0.674 \times 15) = 100 + 10.11 = 110.11 \][/tex]

Therefore, the third quartile (Q3) IQ score, which separates the top 25% from the others, is approximately 110.

Solve |x| + 7 < 4.
........................

Answers

hello :
|x| + 7 < 4.
|x| < 4.-7
|x| < -3
no reals solutions because for all reals x : |x| ≥ 0

Write the equation in logarithmic form.

25 = 32

A. log32 = 5 • 2

B. log232 = 5

C. log32 = 5

D. log532 = 2

Answers

The equation in logarithmic form is B.log₂32 = 2.

To convert the equation 2⁵ = 32 into logarithmic form, you need to identify the base, the exponent, and the result. The given equation can be interpreted as 2 raised to the power of 5 equals 32.

The general form of a logarithmic equation is: log_base (result) = exponent

In this specific case, we have:

base = 2
result = 32
exponent = 5

Putting it into the logarithmic form, we get: log₂32 = 5

So, the correct option is: B.log₂32 = 2

How many three-letter "words" can be made from 5 letters "fghij" if repetition of letters (a) is allowed?

Answers

From the given, there are 5 letters to choose from. For the first letter of the three-letter word, we can choose from all 5 of them.

Also, for the second letter of the word, we can also have 5 choices because it is stated that repetition is allowed. Similarly, there are also 5 choices for the last letter of the word. By fundamental principle of counting, we multiply the numbers identified in the sentences above,

n = 5 x 5 x 5 = 125

Thus, 125 words can be formed from the given letters.

solve for x in the diagram (right triangle smallest side 9,bottom side 12,longest x)

Answers

The hypotenuse (x) is 15, use the Pythagorean Theorem.

For Jane's Uber business, she charges $5 initial fee and $0.10 a mile. Joe's Uber business charges $4 initial fee and $0.20 per mile.
1. Write a function for jane's Uber buisiness
2. write a function for joe's Uber business

Answers

Jane : y = 0.10x + 5...or f(x) = 0.10x + 5
Joe : y = 0.20x + 4...or f(x) = 0.20x + 4

The linear equations to calculate the earning by Jane and Joe's Uber business per ride, given the initial fee and charge per mile:

Jane: y = 5 + 0.1x

Joe: y = 4 + 0.2x

What is a linear equation ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

For Jane's Uber business, she charges $5 initial fee and $0.10 a mile.

Let Jane's earning from a ride be $y.

Let the number of miles she drove in that ride be x miles.

Linear equation to calculate the earning from a ride given the number of miles rode: y = 5 + 0.1x

For Joe's Uber business, he charges $4 initial fee and $0.20 a mile.

Let Joe's earning from a ride be $y.

Let the number of miles he drove in that ride be x miles.

Linear equation to calculate the earning from a ride given the number of miles rode: y = 4 + 0.2x

Learn more about linear equation here

https://brainly.com/question/14056312

#SPJ2

If a rope 36 feet long is cut into two pieces in such a way that one piece is twice as long as the other piece, how long must the long piece be

Answers

rope = 36 feet

first piece = x

2nd piece = 2x ( twice as long as the first piece)

3x=36

x=12

first piece = 12 feet

2nd piece = 2 x 12 = 24 feet

If y = 4x + 3 were changed to y = -4x + 3, how would the graph of the new function compare with the original?

Answers

4x+3 times -1 reflects the graph about the x axis

-4x-3 adding 6 moves the graph upwards by 6 units

-4x-3+6

-4x+3

Answer:

The graph of y=-4x+3 will be as a reflexion in a mirror of y=4x+3

Step-by-step explanation:

y=4x+3 y=-4x+3

. .

A group of hikers are 675 ft from the base of Guadalupe Peak, which is 8,749 ft tall. What is the angle of elevation when they look at the top of the Peak? Round to the nearest hundredth.

Answers

tan x = 8749/675
x= arctan (8749/675) arctan = tan^-1
x=85.59 degrees

(05.02 LC)

Which equation does the graph below represent?

y = fraction 1 over 4x
y = 4x y
fraction negative 1 over 4x
y = −4x

Answers

Answer:

y=-4x

Step-by-step explanation:

WE need to write the equation for the given graph

In the graph y intercept is (0,0)

The equation of linear graph is y=mx+b

where m is the slope and b is the y intercept

From the given graph y intercept is 0 so b=0

to find slope pick two points from the graph

(0,0) and (1, -4)

slope = [tex]\frac{y_2-y_1}{x_2-x_1} = \frac{-4-0}{1-0} = -4[/tex]

m=-4 and b=0

So the equation becomes

y= -4x+0

y= -4x

A rectangle has an area of k2 + 19k + 60 square inches. If the value of k and the dimensions of the rectangle are all natural numbers, which statement about the rectangle could be true?

Answers

the width of the rectangle is k+4 inches

Tiffany put a $1550 item on layaway by making a 20% down payment and agreeing to pay $120 a month. How many months sooner would she pay off the item if she increased her monthly payment to $180?
A. 18 months sooner
B. 11 months sooner
C. 4 months sooner
D 7 months sooner

Answers

1550*0.8=1240

1240/120 = approximately 11 months to pay off

1240/180=approximately 7 months to pay off

11-7 =4

so it would be paid off 4 months sooner, so C is the answer

Answer:

Option: C is the correct answer.

C. 4 months sooner.

Step-by-step explanation:

Total amount of the item is: $ 1550

Also, Tiffany paid 20% of the amount by down payment.

Hence, the amount left to pay after the down payment is:80% of total amount.

i.e. 0.80 of total amount.

= 0.80×1550

= $ 1240

Now the number of month it will take if she pay $ 120 a month is:

[tex]=\dfrac{1240}{120}=10.3333[/tex]

which is approximately equal to 11 months.

Similarly, the number of month it will take if she pay $ 180 a month is:

[tex]=\dfrac{1240}{180}=6.8889[/tex]

which is approximately equal to 7 months.

Hence, the number of months sooner she will pay off is:

11-7=4 months.

A bond payable is similar to which of the following?

Answers

A Bond payable is are likely similar to note payable. They are similar because they have both written premises to pay the interest and the principal amount on a specific futures dates. They are both liability and also the interest is accrued in current liability.

The answer to your question is "Notes Payable."

Find all solutions in the interval [0, 2pi): sin5x+sinx=sin3x

Answers

this is the concept of trigonometry, to solve for the value of x we proceed as follows;
sin5x+sinx=sin3x
this can be written as:
(sinx)^5+sinx=(sinx)^3
dividing through by sin x we get:
(sinx)^4+1=(sinx)^2
let y=(sinx)^2
thus our expression will be given by:
y^2+1=y
y^2-y+1=0
solving the quadratic equation above we get:
y=(-1)^(1/3) or -(-1)^(2/3)
the above is a complex equation, therefore our expression has no defined answer

Name a pair of supplementary angles.

A. angle A E B and angle C E D
B. angle A E B and angle B E D
C. angle A E C and angle B E D
D. angle B E A and angle C E B

Answers

Well, supplementary angles = 180 degrees. So, B is the answer.

Answer:

B.angle AEB and angle BED.

Step-by-step explanation:

We are given that a diagram .

We have to find a pair of supplementary angles.

Supplementary angles:The pair of angles whose sum is 180 degrees is called supplementary angles.

From given diagram

[tex]\angle AEB+\angle BED=180^{\circ}[/tex]

[tex]\angle AEC+\angle CED=180^{\circ}[/tex]

Hence, option B is true.

Answer:B.angle AEB and angle BED.

Which function represents g(x), a reflection of f(x) = 6(1/3)^x across the y-axis?

Answers

Given that our function is given by f(x)=6(1/3)^x, when this polynomial is reflected along the y-axis, the formula for the new function will be given as follows;
g(x)=6(1/3)^(-x)
this will give us the reflection of the f(x) along the y-axis because the only term that is affected upon this transformation is the x-term.

Answer:

its b

Step-by-step explanation:

i got u homies

Line EF has an equation of a line y = −2x + 7. Which of the following could be an equation for a line that is perpendicular to line EF?

y = 2x − 3
y = 1 over 2x − 3
y = −2x − 3
y = −1 over 2x − 3

Answers

1.

When a line is given in the form y=mx+n,

m is the slope of this line.

For example, the slope of the line y=-2x+7 is -2.

2.

If lines y=mx+n and y=kx+t are perpendicular, then the multiplication of their slopes is -1, that is

m*k = -1, so k=-1/m

3.

any line perpendicular to y=-2x+7 has slope = -1/(-2)=1/2

4.

Among the choices, y=(1/2)x-3 is a line perpendicular to the given line.

Answer:

b. y=(1/2)x-3

Answer:

[tex]y=\frac{1}{2} x-3[/tex]

Step-by-step explanation:

Step 1

Find the slope of the line EF

we have

[tex]y=-2x+7[/tex]

The slope of the line EF is equal to

[tex]m=-2[/tex]

Step 2

Find the slope of the line perpendicular to the line EF

we know that

If two lines are perpendicular, then the product of its slopes is equal to minus one

[tex]m1*m2=-1[/tex]

we have

[tex]m1=-2[/tex] -----> slope of the line EF

Find the value of m2

substitute

[tex](-2)*m2=-1[/tex]

[tex]m2=1/2[/tex]

therefore

the equation [tex]y=\frac{1}{2} x-3[/tex] could be an equation for a line that is perpendicular to line EF

What are the amplitude, period, and midline of f(x) = −7 sin(4x − π) + 2?

Answers

This is an example of a sine wave function. A given sine wave function has a standard form of:

y = A sin [B (x + C)] + D

Where,

A = absolute value of amplitude

2 π / B = the period of the sine wave

D = is the midline of y

C = phase of the sine wave

Rewriting the given equation into this form will yield:

f (x) = -7 sin[4 (x – π / 4)] + 2

Therefore from this form, we can get the answers:

Amplitude = 7

Period = 2π / 4 = π / 2

Midline = 2

Use these values to solve this problem. X=2,y=3,z=4. 21xy/x+z

Answers

21 x 2 x 3 / 2 + 4 = 126/6 = 21

x=2. y=3, z=4
21xy/x+z
Substitute x with 12, y with 3, z with 4
21xy/x+z
=21(2)(3)/(2+4)
=42(3)/16
=126/16
=21. As a result, 21 is your correct answer. Hope it help!

If there is a 0.3% chance of something happening one day, what is the possibility of it happening throughout twenty days?

Answers

try by multiplying 0.3x20

You mean of it happening within 20 days?

Well if there is a 3/10 probability of it happening in any given day, there is a 7/10 probability of it not happening on any given day. The probability of it not happening at all in 20 consecutive days is:

(7/10)^20

So the probability of it happening at least once in 20 days is:

1-(7/10)^20≈9992/10000 (about 99.92%)

Simplify 10x - 3x + (-5x).
-2x
2x
18x
-18x

Answers

This answer is 2x. Hope it helps!

+(-5x) = -5x so

its 10x - 3x - 5x

= 10x - 8x = 2x Answer

How much money should be deposited today in an account that earns 6% compounded monthly so that it will accumulate to $9000 in three years?

Answers

The formula is
A=p (1+r/k)^kt
A future value 9000
P present value?
R interest rate 0.06
K compounded monthly 12
T time 3years
We need to solve for p
P=A÷(1+r/k)^kt
P=9,000÷(1+0.06÷12)^(12×3)
P=7,520.80

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