The surface area of the square pyramid is 224 square centimeters.
Since the base of the square pyramid is a square, all sides are equal in length.
Let's call the length of one side of the square base "s".
Then the surface area of the pyramid can be found using the formula:
Surface area = Area of base + Area of four triangles
The area of the base is just s², and the height of each triangle can be found using the Pythagorean theorem.
Let's call the height "h". Then:
h² = 14² - (s/2)² (using the longer side of the triangle as the hypotenuse)
h² = 196 - (s²/4)
Now, we need to find the surface area in terms of "s" and simplify:
Surface area = s² + 4(1/2)(s)(h)
Surface area = s² + 2sh
Surface area = s² + 2s√196 - s²/4))
Surface area = s²+ 2s√(784 - s²))/2
Surface area = s² + s√(784 - s²))
We are given that one side of the square base is 8cm, so:
Surface area = 8² + 8√784 - 8²
Surface area = 64 + 8√400
Surface area = 64 + 8(20)
Surface area = 224
Therefore, the surface area of the square pyramid is 224 square centimeters.
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Find the point of intersection for the pair of linear equations. A. (5.1, 2.6) B. (-3.1, 2.4) C. (3.6, 2.2) D. (-4.6, 4.1) √x+y=-0.7 y = 3x + 11.7
The point of intersection for the pair of linear equations is (-5.5, -4.8)
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the point of intersection for the pair?The pair of linear equations is given as:
x + y = 0.7
y = 3x + 11.7
Substitute y = 3x + 11.7 in x + y = 0.7
x + 3x + 11.7 = 0.7
Evaluate the like terms
2x = -11
Divide both sides by 2
x = -5.5
Substitute x = -5.5 in y = 3x + 11.7
y = 3*-5.5 + 11.7
Evaluate
y = -4.8
So, we have
x = -5.5 and y = -4.8
Express the above points as an ordered pair, to determine the point of intersection
(x, y) = (-5.5, -4.8)
Hence, the point of intersection for the pair of linear equations is (-5.5, -4.8)
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What is the measure of
Evaluate 2a x 3 + b, if a = 5 and b = 1.
Answer:
31
Step-by-step explanation:
replace the values of a and b in the given term
=2a x 3 + b
2(5) x 3 + (1)
2x5 x 3 + 1
10 x 3 + 1
30 + 1
31
The demand for a given product demand is formulated by the linear trend equation: y= 50 – 6t.
Based on this information, when would be the first period that there is NO demand at all for this product?
Answer:
t >= [tex]\frac{25}{3}[/tex] or 8.33333333333
Step-by-step explanation:
We need to set up an inequality where demand is less than or equal to 0. The inequality looks like this:
50 - 6t <= 0
50 <= 6t
t >= [tex]\frac{25}{3}[/tex] or 8.33333333333
I am odd I am less than 40 both of my digits are perfect squares t-u=0
Answer:
19 or 14
Step-by-step explanation:
Since the number is odd you can disqualify all even numbers up to 40 including 0.
Next since this number has 2 digits you can take out all 1 digit numbers.
After that, find perfect squares that also are 1 digit each.
Lastly merge the combination of the numbers as each digit on each sides in such a way that the result is less than 40.
Lamonte has 50 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. (The fourth side of the enclosure would be the river.) The area of the land is 288 square meters. List each set of possible dimensions (length and width) of the field.
The dimensions of the length and width are 25 meters and 12. 5 meters respectively.
How to determine the valuesArea of a rectangle
area of rectangle = l × w
where
l = length
w = width
Note that,
Perimeter = 2w+ l
50 = 2w + l
l = 50 - 2w
Hence,
area = w(50 - 2w)
288 = 50w - 2w²
-2w² + 50w - 288 = 0
-w² + 25w - 144 = 0
The dimension w can be found as follows;
w = - b / 2a
where
a = -1
b = 25
w = - 25 / 2 × -1
w = 12.5 meters
Then, we have that
l = 50 - 2w
Substitute the value of w
l = 50 - 2(12.5)
l = 50 - 25
I = 25 meters
Thus, the dimensions of the length and width are 25 meters and 12. 5 meters respectively.
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I need help figuring out any details that are in this graph and what you can make of it.
The graph shows the comparison of the human welfare and ecological footprints.
What is a graph?A graph simply means a diagram that shows the relationship between variables.
From the graph, it can be seen that countries such as Norway, Canada, USA, and Australia meet the minimum criteria for sustainability.
The graph also shows that Sierra Leone is the least developed country among the countries compared as it has the lowest human development index.
The threshold for high human development as given as 0.8. Most African countries had a human development index of 0.5 and below.
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Which function is graphed?
Answer: [tex]f(x)=\begin{cases} x^2 +4, x < 3 \\ -x+4, x \geq 3 \end{cases}[/tex]
Step-by-step explanation:
By inspection, we know the equation of the parabola is [tex]y=x^2 +4[/tex] and the equation of the line is [tex]y=-x+4[/tex].
Since there is an open hole at x=3 for the parabola and a closed hole at x=3 for the line, the function is
[tex]f(x)=\begin{cases} x^2 +4, x < 3 \\ -x+4, x \geq 3 \end{cases}[/tex]
Which statement is true about the function f(x) = 6x7?
The function is even because f(–x) = f(x).
The function is odd because f(–x) = –f(x).
The function is odd because f(–x) = f(x).
The function is even because f(–x) = –f(x).
Answer: The function is odd because f(–x) = –f(x).
Step-by-step explanation:
[tex]f(x)=6x^7\\\\f(-x)=6(-x)^7 = -6x^7\\\\\therefore f(x)=-f(-x)[/tex]
The function is odd because f(–x) = –f(x).
How to determine the true statement?The function is given as:
f(x) = 6x^7
A function is odd if the following is true
f(-x) = -f(x)
Calculate f(-x)
f(-x) = 6(-x)^7
f(-x) = -6x^7
Calculate -f(x)
-f(x) = -6x^7
By comparison;
f(-x) = -f(x) = -6x^7
Hence, the function is odd because f(–x) = –f(x).
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15) Mr. and Mrs. Rupe and their 4 sons are taking a 2500 mile camping trip across country. They plan to spend $120 for campsites per
day. The camper rental fee is $65 a day. While pulling the camper their car has a fuel economy of 8 miles per gallon. They estimate $85
per day for food for the 5-day trip. If gasoline is $1.92 per gallon how much will their trip cost?
O a.) $1950
Ob.) $1850
Oc.) $2950
Od.) $1750
Answer:
A $1950
Step-by-step explanation:
Food, camper rental and camp site will cost 1350
(120 + 65 + 85)5 = 1350
The trip is 2500 and the car gets 8 miles per gallon 2500/8 = 31.5. The will need to buy 31.5 gallons of gas at 1.92 a gallon or $600 (31.5 x 1.92).
When we add the cost of gas to the other costs, we get a total of 1950 (1350 + 600)
Can you guys show me what process you would use for this? I mostly need the process
The value of the expression for the given values of the variables is 1/9
Evaluating an ExpressionFrom the question, we are to determine the value of the expression for the given values of the variables
The given expression is
[tex](\frac{4x^{3} -2y-2z^{3} }{4y^{2}-16x^{2} }) ^{2}[/tex]
From the given information,
x = 2
y = -5
z = 3
Putting the values of the variables into the expression
[tex](\frac{4(2)^{3} -2(-5)-2(3)^{3} }{4(-5)^{2}-16(2)^{2} }) ^{2}[/tex]
[tex](\frac{4(8) +10-2(27) }{4(25)-16(4) }) ^{2}[/tex]
[tex](\frac{32 +10-54 }{100-64 }) ^{2}[/tex]
[tex](\frac{-12 }{36 }) ^{2}[/tex]
[tex](\frac{-1 }{3 }) ^{2}[/tex]
[tex]= \frac{1}{9}[/tex]
Hence, the value of the expression for the given values of the variables is 1/9
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A line passes through the point −8, 4 and has a slope of −3/4.
Answer:
y = (-3/4)x + 2
Step-by-step explanation:
y = m * x + b where m is the slope and b is the y-intercept
y = (-3/4)x + b substituting the slope
4 = 6 + b => b = 2 substituting the point given
y = (-3/4)x + 2
Johnny picks up a baseball and throws it to Rob who is exactly 130 feet away at a direction of 50 degrees. Rob then throws the ball to Patrick who is 50 feet from Rob in a direction of 30 degrees. Find the exact distance and direction that Patrick is from Johnny.
I need to sketch a triangle.
The exact distance and direction that Patrick is from Johnny is; 177.81 ft and 215.52°
How to utilize trigonometric ratios?Let the distance of Johnny to Patrick be x.
The angle opposite x would be; (90 - 50) + 90 + 30 = 160°
We will therefore use the cosine rule to find x;
X² = A² + B² - 2ABcosx
Where;
A and B are the distance of Johnny to Rob and Rob to Patrick respectively. Thus;
X² = 130² + 50² - 2(130)(50)cos160
X²= 16900 + 2500 + 12216.004
X² = 31616.004
X = 177.81 ft
To get the direction "y" we will use sine rule;
50/siny = 177.809/sin160
50/siny = 177.809/0.342
50/siny = 519.9094
Siny = 50/519.904
Siny = 0.09617
y = sin⁻¹(0.09617)
y = 5.52°
The bearing of Patrick from Johnny is;
5.52 + 30 + 180 = 215.52°
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(2^x+y , 3^x-y )= (16,9) find the value of x and y
Answer:
x=3,y=1
Step-by-step explanation:
2^x+y=16,3^x-y=9
16=2^4,9=3^2
x+y=4,x-y=2 add both
2x=6,x=3
3-y=2,y=1
A farmer harvests 70 apples and 98 peaches. They want to make baskets that have both apples and peaches to sell at the market. Each basket should contain the same combinations of fruit. They want to sell all the apples and peaches and as many baskets as possible. they can use the greatest common factor to help them divide up the fruit.
This means the farm can make x baskets of apples and y peaches.
Farmer will made 14 basket each of 5 apple and 7 peaches.
what is greatest common factor?
Greatest common factor (GCF) is largest common factor in the given number.
first find common factor of numbers 70 and 98
70 = 2*5*7
98 = 2*7*7
the common factor are 2 and 7
the greatest common factor is 2*7=14
70 apples = 14*5
98 peaches = 14*7
farmer will made 14 basket each of 5 apple and 7 peaches.
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The farmer will make 14 baskets containing each of 5 apples and 7 peaches.
How many baskets can be made which contain both apples and peaches and each basket should contain the same combinations of fruits?Given:
A farmer harvests 70 apples and 98 peaches.They want to make baskets that have both apples and peaches to sell at the market.Each basket should contain the same combinations of fruit. They want to sell all the apples and peaches and as many baskets as possible.Find:
How many baskets can the farm make having x apples and y peaches in the baskets?Solution:
So, for solving this kind of question first we have to find the greatest common factor, we get;
70 = 2*5*7
98 = 2*7*7
the common factor are 2 and 7
the greatest common factor is 2*7=14
70 apples = 14*5
98 peaches = 14*7
So, the farmer will make 14 baskets each of 5 apples and 7 peaches.
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Practise the Skill
A container holds 4 yellow balls, 3 blue balls and 1 red ball.
Luke chooses a ball at random.
What is the probability that Luke will pick a blue ball?
Give your answer as a fraction in its lowest terms.
The probability that Luke will pick a blue ball is 3/8.
We have,
To find the probability of Luke picking a blue ball, we need to determine the total number of balls in the container and the number of blue balls.
Total number of balls
= 4 (yellow balls) + 3 (blue balls) + 1 (red ball)
= 8 balls
Number of blue balls = 3
Now, the probability (P) of picking a blue ball is given by:
P = Number of favorable outcomes (picking a blue ball) / Total number of possible outcomes
P = 3 (number of blue balls) / 8 (total number of balls)
Now, we can simplify the fraction to its lowest terms:
P = 3/8
Thus,
The probability that Luke will pick a blue ball is 3/8.
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Suppose that X is a Bernoulli random variable with success probability 0.8. (Note: If this number is not already rounded to two decimal places, round it to two decimal places before proceeding.)
Calculate the probability of failure.Round your answer to two decimal places and enter it as a decimal number (as opposed to a fraction percentage or a fraction).
Considering the probability of success of 0.8 in the Bernoulli trial, the probability of failure is of 0.2.
What is the probability of failure in a Bernoulli trial?
The probability of failure in a Bernoulli trial is one subtracted by the probability of a success.
In this problem, the probability of a success is of 0.8, hence the probability of failure is:
pF = 1 - 0.8 = 0.2.
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An ice chest contains 9 cans of apple juice6 cans of grape juice5 cans of orange juiceand 4 cans of pineapple juice Suppose that you reach the container and randomly select three cans in successionFind the probability of selecting no grape juice Select one 243 506 6 17/45; c * 5/506; d * 102/253
Answer:
243/506
Step-by-step explanation:
There are 24 total juice boxes.
18 of them are not grape
You have an 18/24 chance of picking not grape juice
The second time, 1 is removed, then another is removed. This creates:
(18/24)*(18/23)*(18/22) = 243/506
Math man fell from the top of a 500 meter building. The equation d = t squared * 0.25 describes math man's distance from the ground as he falls. How long does math man spend falling if he falls all the way from the top of the building to the ground? Round your answer to the nearest tenth.
Based on the equation of the function of the height of the building, it takes the man 44.7 seconds to fall from the top
How to determine how long it takes the math man to fall?The function of the height where the man falls is a quadratic function, and the equation of the function is given as:
d = t^2 * 0.25
The height of the building is 500
This means that the value of d is 500.
So, we have;
d = 500
Substitute 500 for d in the equation d = t^2 * 0.25
500 = t^2 * 0.25
Divide both sides of the above equation by 0.25
500/0.25 = t^2 * 0.25/0.25
Evaluate the quotient in the above equation
t^2 = 2000
Take the square root of both sides in the above equation
√t^2 = √2000
Evaluate the exponent
t = 44.7
Hence, it takes the man 44.7 seconds to fall
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Pamela is 9 years younger than Jiri and the sum of their ages is 41 what is jiri's age
Answer:
Jiri is 25 years old.
Step-by-step explanation:
1)Pamela =Jiri-9 ( Pamela is 9 years younger than Jiri)
2)Pamela +Jiri=41
Substitute equation 1 into equation 2
(J-9)+J= 41
2J-9=41
Add 9 to both sides:
2J=41+9
Divide by 2:
2J=50
J=25
the required Jiri's age is 25 years.
Pamela is 9 years younger than Jiri and the sum of their ages is 41. What is Jiri's age is to be determined.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements.
Let the age of Pamela and Jiri is x and y respectively
Pamela is 9 years younger than Jiri. so,
y = x + 9 - - - - (1)
the sum of their ages is 41
x + y = 41 - - - - (2)
From equation 1 put y in equation 2
x + x + 9 = 41
2x + 9 = 41
2x = 41 - 9
2x = 32
x = 32/2
x = 16
Now put this x =16 in equation 1
y = 16 + 9
y = 25
Thus, the required Jiri age is 25 years
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There are 18 apple candies and 12 cherry candies mixed in a bag. If one candy is chosen from that bad, the odds of picking an apple candy are:
A: 1 out of 18
B: 2 out of 5
C: 3 out of 5
D: 3 out of 8
Which is the graph of the function f(x) = 1/2x^2+2x-6?
See the graph in the attached image.
If $11,000 is invested in an account for 25 years. Find the value of the investment at the end of 25 years if the interest is:
If $11,000 is invested, $33,000 is the value of the investment at the end of 25 years if the interest is 8% simple interest and $75,333.23 is the value of the investment at the end of 25 years if the interest is 8% compounded annually. This can be obtained by using formulas for simple interest and compound interest.
What is the formulas of simple interest and compound interest?Simple interestA = P(1 +Rt/100) , P = principle amount ,R = rate of interest, t = time(in years)
Compound interest (annually)A = P(1 + R/100)^t , P = principal amount, R = rate of interest, t = time(in years)
What is the value of investment?
Given that,
P = $11,000 , R = 8%, t = 25 years
8% simple interestA = P(1 +Rt/100) = [tex]11000(1+\frac{(8)(25)}{100} )[/tex] = $33,000
8% compounded annuallyA = P(1 + R/100)^t = [tex]11000(1+\frac{8}{100} )^{25}[/tex] = [tex]11000(1.08 )^{25}[/tex] = $75,333.23
Hence If $11,000 is invested, $33,000 is the value of the investment at the end of 25 years if the interest is 8% simple interest and $75,333.23 is the value of the investment at the end of 25 years if the interest is 8% compounded annually.
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Disclaimer: The question was given incomplete on the portal. Here is the complete question.
Question: If $11,000 is invested in an account for 25 years. Find the value of the investment at the end of 25 years if the interest is:
(a) 8% simple interest
(b) 8% compounded annually
(07.06) There are currently 4 people signed up to play on a baseball team. The team must have at least 9 players.
Which of the following graphs includes the possible values for the number of people who still need to sign up for the team?
Number line with closed circle on 5 and shading to the left
Number line with closed circle on 5 and shading to the right.
Number line with open circle on 5 and shading to the left.
Number line with open circle on 5 and shading to the right.
A graph which includes the possible values for number of people who can still sign up for the team is: B. number line with closed circle on 5 and shading to the right.
What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains numerical values (positive and negative numbers) that are placed at equal intervals along its length.
Let the number of people who can still sign up for the team be represented by x. Thus, the inequality is given by:
x + 4 ≥ 9
x ≥ 9 - 4
x ≥ 5.
This ultimately implies that, there could be five (5) or more people that can still sign up for the team and a graph which includes these possible values is a number line with closed circle on five (5) and shading to the right because it can get larger.
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can two equilateral triangles always be congrunet ? give resons
SOLUTION :
YES as well as NO , two equilateral ∆s can be congruent if any of their side matched to one another,
& CANNOT be congruent if any of their side didn't matched in terms of length (magnitude).
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Explain the difference between using area and volume with 2-D and 3-D figures.
The difference between Area and Volume lies in the fact that the former relates to plane shapes while the latter takes the concept of solid shapes into account.
What is the difference between Area and Volume?The distinctive characteristic of area is the space occupied by a two-dimensional, 2D flat object in a plane while Volume on the other hand is defined as the space covered by a three-dimensional, solid object. The area is quantised in square units while the volume is quantised in cubic units.
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_ May Occur if the chosen sample is too small for a study.
a) Participation Bias
b) response Bias
c)non-response Bias
d) sampling Bias
e) Reasearcher Bias
The non response bias can happen if the chosen sample is too small for a study.
What is the non response bias?This is the term that is used to refer to the type of bias that happens in a research study because the some of the study participants could not participate in the study.
This type of bias is a very serious matter of concern while carrying out research.
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Please Solve the equation by factoring: x2+2x−15=0
Answer:
x = 3, -5
Step-by-step explanation:
I just know
Answer:
x= -5
x=3
Step-by-step explanation:
You are factoring here. The standard form of an equation is Ax² + Bx + C.
The 2 factors must multiple together to be C, but add together to be B. The easiest way to do this is to factor C.
C is -15. Factoring this, we find the only factors of 15 that will add together to be 2 are 5 & -3.
Therefore, the factors are (x+5) and (x-3). If you set each of these factor pairs to 0 and solve, the answers are:
x+5=0
x = -5
x-3 = 0
x=3
Planes A and B intersect.
n
772
W
k
Mark this and return
V
19
Z
X
2
Which describes the intersection of line m and line nº
O point W
point X
point Y
O point Z
The point that describes the intersection of line m and line n is; Point W
How to interpret Intersection of Planes?
Intersection of the two lines is defined as the point where the two lines cross or meet each other.
It is given that the lines m and n intersect each other, which means that they must be intersecting each other at some point.
From the figure, it can be seen that in plane A, the lines m and n intersect each other at point W, thus point W is the point of intersection of the two line m and n.
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????????????????????????????????????????????
Please help
Answer: (-2,2)
Step-by-step explanation:
The solution to a system of equations represented graphically is the point where the graphs intersect.