After considering all the given data we conclude that the probability of randomly choosing a specified point within the circle that comes in the red-shaded square is 0.06.
Now we can clearly evaluate the possible probability of selecting a point randomly inside the circle under the section of red shaded square and derive a formula
[tex]P = (d - 4r)^2 / d^2[/tex]
Here,
d = diameter of the circle
r = square side length
For the given case,
d = 4 and r = 3.
Then,
P = (4 - 4×3)² / 4²
P = (4 - 12)²/ 4²
P = 0.06
Rounding to the nearest hundredth, P = 0.06.
Hence, the evaluated probability of selecting a point randomly inside a circle which falls in the red-shaded square is approximately 0.06.
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an elephant skeleton has about
345 bones. at Birth a human skeleton has about 3/5 x 345 bones which has more bones an elephant or a human? explain.
Answer: elephant
Step-by-step explanation:
3/5 x 345 = 207
345 > 207
A dentist office is getting ready to order toothbrushes to give to their patients after checkups. The toothbrush company charges a base cost of $48 to have the dentist's name and address printed on the toothbrushes, regardless of how many are ordered. Each toothbrush will cost $2.58 if the dentist office orders less than 50 toothbrushes. However, if the dentist orders 50 or more toothbrushes, then each toothbrush will only cost $1.24. If the dentist budgets $110 for the order, what is the maximum number of toothbrushes they can purchase?
The maximum number of toothbrushes the dentist can purchase is 50.
Let's denote the number of toothbrushes the dentist orders by "x".
If the dentist orders less than 50 toothbrushes, then the cost of the toothbrushes will be 2.58x.
If the dentist orders 50 or more toothbrushes, then the cost of the toothbrushes will be 1.24x.
There is a base cost of [tex]$48[/tex] for printing the dentist's name and address on the toothbrushes.
The total cost of the order can be expressed as:
Total cost = 48 + (2.58x) for x < 50
Total cost = 48 + (1.24x) for x ≥ 50
The maximum number of toothbrushes the dentist can purchase, given that the budget is [tex]$110[/tex].
So we can set up an equation:
Total cost = 110
For x < 50:
48 + 2.58x = 110
2.58x = 62
x ≈ 24.03
For x ≥ 50:
48 + 1.24x = 110
1.24x = 62
x ≈ 50
The maximize number of toothbrushes, we choose the larger value of x, which is x ≈ 50.
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Hey guys i need your help please
The matrix after the row operation is:
[tex]\left[\begin{array}{ccc}1&4/9&-1\\-43&-19&44\end{array}\right][/tex]
We have,
We use the operation R1 → R1/9.
This will give us,
Row 1 values will change to 9/9, 4/9, -9/9
So,
1, 4/9, -1
Now,
[tex]\left[\begin{array}{ccc}1&4/9&-1\\-43&-19&44\end{array}\right][/tex]
Thus,
The matrix after the row operation is:
[tex]\left[\begin{array}{ccc}1&4/9&-1\\-43&-19&44\end{array}\right][/tex]
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Which components are a possible representation of vector u if ||-4u|| ≈ 14.42?
Answer: <3, -2>
One possible representation of such a vector is u = (3, 2), which has a magnitude of approximately 3.605 and makes an angle of about 33.69 degrees with the positive x-axis in the standard Cartesian coordinate system.
Firstly, it is important to understand the meaning of the double vertical bars (|| ||), which denote the magnitude or length of a vector. For instance, if we have a vector
=> v = (2, 3),
then its magnitude can be computed as
=> ||v|| = √(2² + 3²) = √13.
Similarly, if we have a vector u = (u₁, u₂), then its magnitude can be expressed as
=> ||u|| = √(u₁² + u₂²).
The given condition
=> ||-4u|| ≈ 14.42
can be rewritten as
=> 4||u|| ≈ 14.42
=> ||u|| ≈ 3.605.
This means that the magnitude of vector u is approximately equal to 3.605.
Therefore, to obtain a possible representation of vector u with a magnitude of approximately 3.605, we can solve the following system of equations:
||u|| = √(u₁² + u₂²) ≈ 3.605
θ = tan⁻¹(u₂/u₁)
Note that there are infinitely many solutions to this system, since the direction of u is not uniquely determined.
However, one possible solution is u = (3, 2), which has a magnitude of
=> ||u|| = √(3² + 2²) = √13 ≈ 3.605
and makes an angle of
=> θ = tan⁻¹(2/3) ≈ 33.69 degrees
with the positive x-axis.
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20 points PLS HELPP marking as BRAINLIST
Answer:
25% probability
Step-by-step explanation:
2x2=4
1x1=1
1 out 4 is shaded red
1 out of 4 is 1/4 which is 25%
Helen is building a rectangular garden in her backyard and she wants to have a fence around it.The perimeter of her garden is 20 yards. She is buying wood fence panels that cost $2 per foot. How many feet of fence panels does she need
Based on the calculations, Helen needs to buy 60 feet of fence panels for her rectangular garden in the backyard
How many feet of fence panels does she needFrom the question, we have the following parameters that can be used in our computation:
The perimeter of her garden is 20 yards. She is buying wood fence panels that cost $2 per footThis means that
Perimeter = 20 yards
By metrric unit of conversion, we have
1 yard = 3 feet
So, we have
Perimeter = 20 * 3 feet
Evaluate
Perimeter = 60 feet
Hence, she needs to buy 60 feet of fence panels
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please help with this question
Answer:
Step-by-step explanation: Here if we put [tex]x=0[/tex] then we will get initial temperature. That is [tex]T_0=70+20=90[/tex].
The temperature will cools down [tex]70(0.8)^{10}+20=27.52(approx)[/tex].
So the final temperature after 10 minutes will be :[tex]90-27.52=62.48(approx)[/tex].
Final Answer: The temperature is 62.48 degree Celsius.
Analyze the diagram below and complete the instructions that follow.
Find cos 45°.
A 1
NI-
2
45°
B. √√√2
2
Answer:
cos(45°) = √2/2
B is correct.
12. ABC-A'B'C' is a reflection. Use this to answer the questions below.
(A) Which figure is the preimage?
(B) Which figure is the images
(C) What are the coordinates of the output?
Input. Output
A(0,9). A
B(-4,4) B
C(0,4). C
(A) The preimage is ABC.
(B) The image is A'B'C'.
(C) The coordinates of the output are:
A(0,9) reflects over the line of reflection to A'(0,-9).
B(-4,4) reflects over the line of reflection to B'(4,-4).
C(0,4) reflects over the line of reflection to C'(0,-4).
In geometry, a reflection is a type of transformation where a figure is flipped over a line, called the line of reflection. In this problem, ABC-A'B'C' is a reflection, which means that it is a transformation of a figure where each point of the original figure has a corresponding point in the reflected figure such that the line of reflection is the perpendicular bisector of the line segment joining each point to its corresponding point.
A) The preimage is the original figure, which is ABC.
B) The image is the reflected figure, which is A'B'C'.
C) The coordinates of the output are:
A(0,9) reflects over the line of reflection to A'(0,-9).
B(-4,4) reflects over the line of reflection to B'(4,-4).
C(0,4) reflects over the line of reflection to C'(0,-4).
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(8,-5)(4,7) 1:3 find the partitions the segment with the two given endpoints with the given ratio
The partitions coordinate are (7, -2).
We have the coordinates (8, -5) and (4, 7)
Ratio = 1 :3
Using Section Formula
x = ( 4 + 24)/ 4
x = 28/4
x= 7
and, y= (7 - 15)/4
y = -8/4
y= -2
Thus, the partitions coordinate are (7, -2).
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What measurement is equivalent to 1 2 3 1 2 3 yards?
Probability Digital Escape! puzzle 3 answer
Probability of landing on space with polka dots = 3/8.
Probability of landing on space with stripes = 1/2.
Probability of landing on space with stripes and even numbers = 1/4.
Probability of landing on space with stripes or even numbers = 5/8.
Hence the code is 'AFCH'.
From the definition of Probability we know that,
Probability of event = (Number of Favorable outcomes)/(Total number of outcomes)
Here total number of spaces = 8.
Number of space with polka dots = 3 [space numbered 1, 4, 6]
Number of space with stripes = 4 [space numbered 0, 2, 3, 5, 7]
Number of space with stripes and even numbers = 2 [the space numbered 0 and 2]
Probability of landing on space with polka dots = 3/8 (A)
Probability of landing on space with stripes = 4/8 = 1/2 (F)
Probability of landing on space with stripes and even numbers = 2/8 = 1/4 (C)
So, Probability of landing on space with stripes or even numbers
= Probability of landing on space with polka dots + Probability of landing on space with stripes - Probability of landing on space with stripes and even numbers
= 3/8 + 1/2 - 1/4
= (3 + 4 - 2)/8
= 5/8 (H).
Hence the code will be 'AFCH'.
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Find the value of x if log6 36 = x
Answer:
The answer for x is 2
Step-by-step explanation:
write the equation
log6(36)= x
rewrite the equation as, x = log6(36) [ formula used; logb x=y; x=y^b]
so, x^6=36
x^6=2^6[ 36=2^6=2*2*2*2*2*2]
thus, x=2
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Please help me please 5th grade math
The length of the given rectangular cuboid is: 9 cm
How to find the volume of the rectangular prism?In geometry, a rectangular prism is defined as a polyhedron with two congruent as well as parallel bases. It is also referred to as a cuboid. A rectangular prism is one that possesses six faces, and then all the faces are located in a rectangle shape and possess twelve edges. Whenever its cross-section along the length, it is referred to as a prism.
The formula for the volume of a prism is given by the formula:
V = L * W * H
Where:
L is length
W is width
H is height
We have that Volume = 432 cm³
Thus:
6 * L * 8 = 432
48L = 432
L = 432/48
L = 9 cm
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The net below shows a square pyramid. What is the lateral surface area?
The lateral surface area of the pyramid is 112 sq. in.
The correct answer is an option (B)
From the attached figure of the net of a square pyramid, we can observe that the side length of the square base is 8 in and height of the lateral triangular face is 7 in.
The lateral surface area of the pyramid is equal to the area of the four triangular faces of the pyramid.
Using the formula of the area of triangle, the lateral surface area would be,
A = 4 × (1/2 × base × height)
A = 4 × (1/2 × 8 × 7)
A = 4 × (4 × 7)
A = 4 × 28
A = 112 sq. in.
This is the required lateral surface area.
The correct answer is an option (B) 112 in²
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Find the complete question below.
The net below shows a square pyramid. What is the lateral surface area? A. 176 in^2
B. 112 in^2
C. 64 in^2
D. 210 in^2
Calculate the price of a zero-coupon bond that matures in five years if the market interest rate is 7.50 percent. (Assume semiannual
compounding and $1,000 par value.)
Multiple Choice
Based on the information given, the price of the zero coupon bond is $692.04.
How to solveTo calculate the price of a zero coupon bond, we need to use the following formula:
[tex]\sf P =\dfrac{F}{1+r\div n}^{(nt)[/tex]
Where:
P = price of the bondF = face value of the bondr = annual interest raten = number of compounding periods per yeart = time to maturity in yearsAlso, the annual interest rate is 7.50%, which is the market interest rate, and the compounding is semiannual, which means n = 2. Finally, the time to maturity is 5 years.
Plugging in the values into the formula, we get:
[tex]\sf P = \dfrac{1000}{(1+0.075\div2)^{(2\times5)}}[/tex]
[tex]\sf P = \dfrac{1000}{(1.0375)^{10}}[/tex]
[tex]\sf P = \dfrac{1000}{1.4450}[/tex]
[tex]\sf P = \$692.04 \ \ (rounded \ to \ the \ nearest \ cent)[/tex]
Therefore, the price of the zero coupon bond is $692.04.
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Solve for x.
10 cm
X
8 cm
X = = [?]°
Round to the nearest hundredth.
The value of the variable x is 51.340 degrees
How to determine the valueNote that their are six different trigonometric identities in mathematics.
These identities are;
sinecosinetangentcotangentsecantcosecantAlso, these identities have their different ratios, they are;
sin θ= opposite/hypotenuse
tan θ = opposite/adjacent
cos θ = adjacent/hypotenuse
From the information given, we have that;
Opposite = 10cm
Adjacent = 8cm
Substitute the values
tan x = 10/8
Divide the value, we have;
tan x = 1.25
Find the tangent inverse, we get;
x = 51. 340 degrees
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Can someone help me
Answer:
Y = -½x + 3/2
Y = -3x + 5
Y = 1/4x - 3¼
Step-by-step explanation:
Parallel implies they have the same gradient
Perpendicular implies the gradient is a negative reciprocal of the other.
What's the value of x in the figure?
A) 33°
B) 57°
C) 76°
D) 78°
Answer:
x = 78°
Step-by-step explanation:
Line q pass through the parallel line of s and r so their alternet interior angles are equal. the alternet interior angles of 135° is 57°+ x so they are equal .
57° + x = 135°
x = 135° - 57°
x = 78°
So the answer is D, 78°
HELP PLEASE! Which reason is the justification for the statement that angle A ≅ angle B?
A) Vertical angles are congruent.
B) Linear angles are equal.
C) Intersecting lines form opposing angles.
D) Lines intersect at one point.
what is 10x10 to the second power of 10
Answer:
10 * 10^10 is equal to 100,000,000,000
A dilation is a transformation in which the _____, but not the shape, of a geometric figure is changed.
Emily's score for a Mathematics test was 5% higher than her score for an English test. If Emily scored 84 points for the Mathematics test, how many points did she score for the English test?
Answer:
80 points
Step-by-step explanation:
If score in English is x points and score in math is 5% higher then score in math
y = x + 0.05x
where 0.05 = 5% expressed as decimal
0.05x refers to the 5% increase in score
y = math score
y = x(1 + 0.05)
y = 1.05x
Given score in math = 84 this becomes
84 = 1.05x
x = 84/1.05
x = 80
So Emily's score in English was 80 points
Amy is going on a roadtrip with her friends and needs to save $160. If she starts saving 18% of her weekly earnings at the pool, how many whole weeks will it take her to save $160?
There are 6 whole weeks will it take her to save $160.
We have to given that;
Amy is going on a road trip with her friends and needs to save $160.
And, she starts saving 18% of her weekly earnings at the pool,
Now, Let number of weeks it take her to save $160 is, x
Hence, We get;
160 = 160 x 0.18 x t
t = 1/0.18
t = 5.55 weeks
Thus, There are 6 whole weeks will it take her to save $160.
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A GROUP OF 6 ADULTS PAY A TOTAL OF $105 FOR THEIR ADMISSION TO A MUSEUM. EACH PERSON HAS A COUPON FOR $5 OFF THE REGULAR ADMISSION PRICE. THEY WANT TO KNOW WHAT THE REGULAR ADMISSION PRICE IS FOR ONE ADULT.
LET A EQUAL THE REGULAR ADMISSION PRICE. WRITE AN EQUATION THAT REPRESENTS THE SITUATION
The regular admission price for one adult is $17.50.
We have,
Let's first determine the total cost of admission after the coupons have been applied.
Since each person has a coupon for $5 off, the total discount for the group is $5 x 6 = $30.
The total cost of admission after the discount.
$105 - $30
= $75.
Let A be the regular admission price.
Since each person paid the same price after the discount, we can set up the following equation:
6(A - $5) = $75
We subtract $5 from the regular price A because that is the amount of the coupon discount.
We can simplify the equation as follows:
6A - $30 = $75
6A = $105
A = $17.50
Therefore,
The regular admission price for one adult is $17.50.
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not typing itttt cause yes :)
The value of x in the quadrilateral is 70 degrees
To find the value of the fourth interior angle, we can use the fact that the sum of all four interior angles is equal to 360 degrees. We can set up an equation:
85 + 150 + 55 + x = 360
where x is the fourth interior angle we want to find. To solve for x, we can first simplify the left side of the equation by adding the known angles:
290 + x = 360
Then, we can isolate x by subtracting 290 from both sides:
x = 360 - 290
x = 70
Therefore, the value of x when the interior angles of the quadrilateral are 85, 150, and 55 degrees is 70 degrees. This means that the four interior angles of the quadrilateral are 85, 150, 55, and 70 degrees, and their sum is indeed equal to 360 degrees.
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The perimeter of the pentagon below is 64 units. Find the length of side AB
Step-by-step explanation:
If this is a regular pentagon , it has FIVE sides of equal length
64 ÷ 5 = 12.8 units = AB
if 1 cm is 20 km then how many km equals 9 cm
-
Which of the following is equivalent to 2.76?
The expression that is equivalent to 2.76 is two and nineteen twenty fifths
Which of the expressions is equivalent to 2.76?The number in the question is given as 2.76
This means that we have
Number = 2.76
We can rewrite this as a mixed number.
2 + a/b
Such that:
a/b = 0.76
From the list of options, we have
two and nineteen twenty fifths = 2 + 19/25 = 2.76
This means that the correct expression is two and nineteen twenty fifths
Hence, the expression that is equivalent to 2.76 is two and nineteen twenty fifths
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Complete question
Which of the following is equivalent to 2.76?
2.76%
27.6%
two and nineteen twenty fifths
twenty five over nineteen
Find the height of the tower using the information given in the illustration.
using SOH CAH TOA
Tan 85.144 =h/130
h=tan 85.144*130
h=1530.19 fr