Distance walked = 85.088 feet
The distance Sina walked would be equal to the length of the diagonal of rectangle.
As every angle in a rectangle is 90 degree. So, we can apply Pythagoras theorem in right triangle formed by sides,
Base- 74 feet, Altitude- 42 feet and Hypotenuse- Diagonal
Base^2 + Altitude ^ 2 = Hypotenuse ^2
74^2 + 42 ^ 2 = Diagonal ^2
On solving,
Diagonal = 85.088 feet
To calculate the distance Sina walked diagonally across the basketball court, we utilize the Pythagorean theorem using the court's length and width. The calculation gives us a diagonal distance of approximately 85 feet.
To calculate the distance Sina walked across the rectangular basketball court diagonally, we can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Since the court is 74 feet long and 42 feet wide, these dimensions can be considered the two shorter sides of a right triangle, with the diagonal Sina walked being the hypotenuse.
The Pythagorean theorem formula is:
[tex]c^2 = a^2 + b^2[/tex]
Where c is the length of the hypotenuse, and a and b are the lengths of the other two sides. Substituting the known values:
[tex]c^2 = 742 + 422\\c^2 = 5476 + 1764\\c^2 = 7240[/tex]
To find c, we take the square root of 7240:
c ≈ 85.09 feet
Therefore, Sina walked approximately 85 feet diagonally across the basketball court.
what is the slant height of the cone
A test was marked out of 80. A boy scored 60% of the marks on the test. How many marks did he score?
Anybody know the answer to this question?
The two triangular prisms shown are similar. The dimensions of the larger prism were multiplied by a scale factor of to create the smaller prism.
When the large prism was reduced, the surface area changed by a factor of
A.64/125
B.16/25
C.4/5
D.10/8
Answer: B. [tex]\frac{16}{25}[/tex]
Step-by-step explanation:
We know that if a figure or solid shape is dilated to create a new shape then the new shape is similar to the original shape.
Also, the scale factor of dilation is the ratio of the sides of new shape to the corresponding sides of the original shape .
Let k be the scale factor of dilation, then
Given : Original shape - larger prism
New shape - smaller prism
Surface area of prism with all sides equal (a)=[tex]4a^2[/tex]
Surface area of original prism =[tex]4(10)^2=400[/tex]
Surface area of new prism =[tex]4(8)^2=256[/tex]
[tex]\Rightarrow k=\frac{256}{400}=\frac{16}{25}[/tex]
Hence, the scale factor = [tex]\frac{16}{25}[/tex]
A and b are independent events. the probability that a will happen is 1/4 and the probability that b will happen is also 1/4. what is the probability they will both happen?
For independent events A and B, the probability of both happening is the product of their individual probabilities. In this case, the probability of both A and B happening is 1/16.
Explanation:In the field of probability in mathematics, when dealing with independent events like A and B in your question, the probability of both A and B happening (denoted as P(A AND B)) is calculated by multiplying the probability of A happening (P(A)) by the probability of B happening (P(B)) This is known as the multiplication rule for independent events.
So, if the probability that A will happen (P(A)) is 1/4, and the probability that B will happen (P(B)) is also 1/4, then the probability that both A and B will happen (P(A AND B)) is (1/4) * (1/4) = 1/16.
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This image shows a square pyramid. What is the surface area of this square pyramid? 36 ft² 72 ft² 78 ft² 84 ft² Note: Image not drawn to scale. The figure shows a square pyramid. The slant height is shown as a dashed line perpendicular to the base edge. The length of the base edge is 6 feet. The lateral edge makes a 45 degree angle with the base edge.
The square's area is relatively simple:
A=b²
A=6²=36 ft²
But now let's observe the triangles, a triangle's area is:
A=(1/2)*b*h
the base is equal to 6 ft
b=6 ft
AC=BC----------> because the angle is 45°
AC=6 ft/2----> 3 ft
so
BC=3 ft
A=(1/2)*6*3----> 9 ft²
Multiply the triangle's area by four to account for all four triangular faces and add the squares area for your answer
Surface area=36 +4*9-----> 72 ft²
the answer is
72 ft²
Answer:
72
Step-by-step explanation:
just took quiz
does the lateral area in a prism include the base?
There are 10 red and blue marbles, among which r are red. How many are blue? Denote blue marbles as b
Answer:
equation=r+b=10
answer=10-r
Its common sense y'all! IF you don't have enough information,just make up a equation! And use the variables as your numbers!
There are 10 - r blue marbles
How to determine the number of blue marbles?The distribution of the marbles are given as:
Red = r
Blue = b
Total = 10
This means that:
b + r = 10
Solve for b
b = 10 - r
Hence, there are 10 - r blue marbles
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$8000 at 3% annually for 4 years
Why does it take more centimeters than inches to measure the same distance?
Which correlation coefficient obtained from modeling advertising and sales data of tutti frutti ice cream expresses the strongest correlation of the data?
a.r = .10
b.r = .50
c.r = .75
d.r = .90
Answer:
d) r=0.90
Step-by-step explanation:
When the r value is closer to +1 or -1, it indicates that there is a stronger linear relationship between the two variables. A correlation nearerto -1 is a strong negative correlation while a correlation of 0.10 would be a weak positive correlation.
Correlation coefficient measures the strength of association between two variables.
It may be positive or negative.
If nearer to 1 or - there is strong correlation
Since here is it 0.90 positive and nearer to 1 out of all 4 options
option d is correct
Aaron is rolling the fair number cubes. What is the probability both cubes show a 5
a ice cream shop offers 5 different flavors of ice cream and 12 different toppings how many choices are possible for a single serving of ice cream with one topping
a. 18
b. 22
c. 46
d. 60
PLZ HELP
Answer:
D)60
Step-by-step explanation:
All you do is multiply 5 by 12.
5x12=60
What is the value of x
What is the interquartile range of this data? A.6 B.7 C.8 D.9
Rent-a-car rents compact cars for a fixed amount per day plus a fixed amount for each mile driven Benito rented a car for 6 days drove it 550 miles and spent $337. Lisa rented the same car for 3 days drove it 350 miles and spent $185. What is the charge per day and charge per mile for the compact car?
Please show all work! TYSM! ☺♥♫
The charge per day and charge per mile for the compact car is $36 and $0.22 respectively
let
x = charge per day
y = charge per mile
6x + 550y = 337 (1)
3x + 350y = 185 (2)
multiply (2) by 2
6x + 700y = 370 (3)
6x + 550y = 337 (1)
subtract (1) from (3)
700y - 550y = 370 - 337
150y = 33
y = 33/150
y = 0.22
substitute y = 0.22 into (2)
3x + 350y = 185
3x + 350(0.22) = 185
3x + 77 = 185
3x = 185 - 77
3x = 108
x = 108/3
x = 36
Therefore, charge per day and charge per mile for the compact car is $36 and $0.22 respectively
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A professional golfer gets a hole-in-one 0.003% of the time they try on a hole. If the golfer plays 32,000 holes over the course of their professional career, about how many hole-in-ones should they expect over their career?
96 holes I think is the correct answer
Karla and her dad were nailing up plywood, they started at 10:00. Karla drove 30 nails in 10 minutes, the time it took her dad to drive 50 nails. At that rate for each, when did they finish driving 392 nails in all ?
15 min left! Anyone know this geometry question?
You purchase a new desktop computer for $2,200. you put a 6% down payment and $100 per month on a 24 month purchase plan. determine the total finance
Someone please help me?
The equation for a projectile's height versus time is h(t)=-16t^2+Vt+h. A tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 130 feet per second. Which equation correctly models the ball's height as a function of time?
The maximum height at the moment is 266.0625 ft.
Projectile's heightThe equation for a projectile's height versus time is
[tex]&h(t)=-16 t^{2}+V t+h \\[/tex]
h = 2
V = 130
Substitute these values into the function
[tex]$h(t)=-16 t^{2}+130 t+2$[/tex]
Take the first derivative
[tex]$h^{\prime}(t)=-16* 2 t+130[/tex]
[tex]=-32 t+130$[/tex]
Equate the derivative with zero [tex]$h^{\prime}(t)=0$[/tex].
Solve the equation -32 t + 130=0
32 t = -130
t = -130 /(-32)
= 4.0625(s) .
Find the maximum height at the moment
t = 4.0625 (s)
h(4.0625) [tex]= -16(4.0625)^{2}+130 * 4.0625+2[/tex]
= - 264.0625+528.125+2
= 266.0625 ft.
Therefore, the maximum height at the moment is 266.0625 ft.
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A standard number cube is tossed. Find P (3 or odd)
A. 1/2
B. 2/3
C. 1/3
D. 1/6
what is the 14 letter word with the definition of an example showing a statement is not true. it is c--n-e-t--m-l-
Mattie uses the discriminant to determine the number of zeros the quadratic equation 0 = 3x2 – 7x + 4 has. Which best describes the discriminant and the number of zeros?
What is the equation of the quadratic graph with a focus of 4,0 and a directrix of y=10
Help me with this algebra problem. Thank you :)
Food costs are expected to rise 6% each month for the next year. which series correctly depicts the cost (to the nearest cent) for the next three months if the current cost is $150 per month? $150.00 + $159.00 + $168.00 $150.00 + $159.00 + $168.54 $159.00 + $168.00 + $177.00 $159.00 + $168.54 + $178.65
A sporting goods store sells 2 fishing reels and 5 fishing rods for $195. Later, they sell 4 fishing reels and 3 fishing rods for $131. Find the price of each item.
Write an equation of the direct variation that includes the point (6, –2). y = –3x
Answer:
-1/3x is the answer
Step-by-step explanation:
Do the problem.
An equation of the direct variation that includes the point (6, –2) is y = -1/3(x).
What is a direct variation?In Mathematics, a direct variation is also referred to as direct proportion and it can be modeled by using the following mathematical expression or function:
y = kx
Where:
y represents the y-variable or dependent variable.x represents the x-variable or independent variable.k represents the constant of proportionality.Under direct variation, the value of x represent an independent variable while the value of y represents the dependent variable. Therefore, the constant of proportionality (variation) can be calculated as follows:
Constant of proportionality (k) = y/x
Constant of proportionality (k) = -2/6
Constant of proportionality (k) = -1/3
Therefore, the required equation is given by;
y = kx
y = -1/3(x)
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