The formula for the circumference of a circle is C = 2πr, where "C" is the circumference, "π" is pi (approximately equal to 3.14), and "r" is the radius.
Given that the radius of the circle is 5 inches, we can substitute this value into the formula to find the circumference:
C = 2πr
C = 2π(5)
C = 10π
Therefore, the circumference of the circle is 10π inches.
Jack made 17 free throws and missed 8. What percent did he make?
The daily high temperatures, in degrees Fahrenheit (°F), of a town are recorded for one year: The median high temperature is 62°F. The interquartile range of hight temperatures is 32. Which statement is most likely true?
A approximately 25% of the days had a high temperature less than 30•F.D.
B Approximately 25% of the days had a high tenperature greater than 62•F.
C Approximately 50% of the days had a high temperature greater then 62•F.
D Approximately 57% of the days had a high temperature less than 94•F
Using the data of interquartile range and median given, only option C is correct because approximately 50% of the days had a high temperature greater than 62°F.
Which of the following statements is true?We are given that the median high temperature is 62°F and the interquartile range is 32. The interquartile range is the difference between the first and third quartiles, which means that the first quartile is at 62 - 16 = 46°F and the third quartile is at 62 + 16 = 78°F.
Option A: approximately 25% of the days had a high temperature less than 30°F.
Since 30°F is much lower than the first quartile (46°F), it is unlikely that 25% of the days had a high temperature less than 30°F. Therefore, option A is not true.
Option B: approximately 25% of the days had a high temperature greater than 62°F.
This statement cannot be true because the median is already at 62°F, which means that 50% of the days had a high temperature greater than or equal to 62°F. Therefore, option B is not true.
Option C: approximately 50% of the days had a high temperature greater than 62°F.
This statement is true because the median high temperature is 62°F, which means that 50% of the days had a high temperature greater than or equal to 62°F, and the interquartile range is 32, which means that the third quartile is at 78°F. Since the third quartile is above 62°F, approximately 50% of the days had a high temperature greater than 62°F. Therefore, option C is most likely true.
Option D: approximately 57% of the days had a high temperature less than 94°F.
The maximum temperature that can be associated with the interquartile range of 32°F is the third quartile, which is at 78°F. Therefore, we cannot say that approximately 57% of the days had a high temperature less than 94°F. Therefore, option D is not true.
Hence, the most likely true statement is option C: approximately 50% of the days had a high temperature greater than 62°F.
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Please need help with this
Two methods for proving that two triangles on a Cartesian coordinate plane are congruent are:
Side-Side-Side (SSS) congruence theorem; and Side-Angle-Side (SAS) congruence theorem.What is the explanation for the above?Two methods for proving that two triangles on a Cartesian coordinate plane are congruent are:
Side-Side-Side (SSS) congruence theorem: Two triangles are congruent if their corresponding sides are equal in length.
Side-Angle-Side (SAS) congruence theorem: Two triangles are congruent if two corresponding sides and the included angle are equal in both triangles.
To prove that two triangles on a Cartesian coordinate plane are congruent using coordinate geometry, we can follow these steps:
Identify the coordinates of the vertices of the two triangles.
Use the distance formula to find the lengths of the sides of each triangle.
Use the angle formula to find the measure of one angle in each triangle.
Check if the corresponding sides and angles of the two triangles are equal.
If the corresponding sides and angles are equal, the two triangles are congruent by SAS or SSS congruence theorem.
Here are the coordinates of the Triangles:
ΔABC = A(-3, 4) B (-4, 1) C (0,3)
ΔDEF = D(0, 2) E(3, 1) F(2, -2)
To prove whether the two triangles ΔABC and ΔDEF are congruent or not, we need to check if their corresponding sides and angles are equal.
Using the distance formula, we can find the lengths of the sides of each triangle:
AB = √[(4 - 1)² + (-4 - (-3))²] = 3.16
BC = √[(3 - 1)² + (0 - 4)²] = 4.47
AC = √[(3 - 4)² + (0 - (-3))²] = 3.16
DE = √[(2 - 1)² + (3 - 0)²] = 3.16
EF = √[(2-3)² + (-2- 1)²] = 3.16
DF = √[(0-2)² + (2 - - 2)²] = 4.47
Thus, on the basis of the side-side-side postulate, both triangles are congruent because the three sides have an equivalent on each triangle.
AB = DE
AC = EF
BC = DF
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Parallelogram JKLM is shown.
As we know consecutive angle of parallelogram are supplementary then the sum m∠JLM = 22°.
Let the m∠JLM be x.
Thus, x+56+27+75 = 189
x = 180 - 158
x = 22
Hence the angle m∠JLM would be 22°
A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are supplementary to the transversal on the same side. 360 degrees is the total of all interior angles.
A parallelepiped is a three-dimensional shape with parallelogram-shaped faces. The base (one of the parallel sides) and height (the distance from top to bottom) of the parallelogram determine its area. A parallelogram's perimeter is determined by the lengths of its four sides.
The properties of a parallelogram are shared by the shapes of a square and a rectangle.
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find the median of 4,6,10,15,2
Answer:
6
Step-by-step explanation:
Put the numbers in order and find the number in the middle
2,4,6,10,15 The number in the middle is 6.
Helping in the name of Jesus.
Answer: 6
Step-by-step explanation:
the median is the middle number to put it in an easy explanation. Since there are 5 numbers the 3rd one would be the middle one since there would be 2 numbers of the left and 2 number on the right!!!
sorry I forgot to put them in order so
2,4,6,10,15
out of those 6 is the one in the middle
What is the value of n? enter your answer in the box.
The value of "n" is 6.
"n" is related to a circle with intersecting chords labeled 5, n+4, 7, and n+8 [1]. To find the value of "n", we can use the property that states that if two chords intersect inside a circle, the products of their segments are equal. Using this property, we can set up the following equation:
7(n+4) = 5(n+8)
Expanding the brackets, we get:
7n + 28 = 5n + 40
Simplifying, we get:
2n = 12
n=6
A circle is a two-dimensional geometric shape that is defined as a set of all points in a plane that are at a fixed distance (called the radius) from a given point (called the center). It is a closed shape, meaning that it has no beginning or end, and its boundary is a continuous curve.
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11. Find x, y, and z.
5
y
6
3
Answer:
x = z = 3√5y = 4Step-by-step explanation:
You want the missing segment lengths in the kite shown, where half-diagonals are 3 and 6, and one side length is 5.
KiteThe diagonals of a kite cross at right angles, so each of the triangles shown is a right triangle. The figure has left-right symmetry about the vertical axis, so x=z.
Length yWe recognize the top triangles as being 3-4-5 right triangles, so the missing side length is y = 4.
Lengths x and zThese lengths are the hypotenuse of a right triangle with legs 3 and 6. The Pythagorean theorem tells us they are ...
x² = 3² +6²
x² = 9 +36 = 45
x = √(45) = √(9·5) = 3√5
The lengths x and z are ...
x = z = 3√5
__
Additional comment
In case you have never heard of a 3-4-5 right triangle, you can find y from the Pythagorean relation:
5² = 3² +y²
y² = 25 -9 = 16
y = √16 = 4
The {3, 4, 5} Pythagorean triple is one of several in common use in algebra, trig, and geometry problems. Others include {5, 12, 13}, {7, 24, 25}, {8, 15, 17}.
An experiment begins with 9 bacteria which grow at such a rate their population doubles every 15 minutes find the bacteria population 3 hours after the experiment begins
The bacteria pοpulatiοn after 3 hοurs is 36864.
Expοnential grοwth:
The cοncept used here is expοnential grοwth, which οccurs when the rate οf increase οf a quantity is prοpοrtiοnal tο its current value.
In this case, the bacteria pοpulatiοn dοubles every 15 minutes, which means that its rate οf increase is prοpοrtiοnal tο its current value.
This leads tο an expοnential grοwth curve, where the pοpulatiοn increases rapidly οver time.
Here we have
An experiment begins with 9 bacteria that grοw at such a rate their pοpulatiοn dοubles every 15 minutes.
Since there are 4 sets οf 15 minutes in an hοur,
The pοpulatiοn will dοuble 4 times in οne hοur.
Therefοre, the bacteria pοpulatiοn after οne hοur will be:
=> 9 × 2⁴ = 9 × 16 = 144
After twο hοurs, the pοpulatiοn will dοuble 4 times again: Hence, the pοpulatiοn after 2 hοurs
=> 144 × 2⁴ = 144 × 16 = 2,304
Similarly, After three hοurs,
2,304 × 2⁴ = 2,304 × 16 = 36864
Therefοre,
The bacteria pοpulatiοn after 3 hοurs is 36864.
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A person standing 30 feet from a flagpole can see the top of the pole at a 42° angle of elevation. The person's eye level is 5 feet from the ground. Find the height of the flagpole to the nearest foot.
Create a function table for the function y=−2x+1 . Input, x Output, y –2 –1 0 1
The function table for the function y=−2x+1 if given below so that Output of y could be –2, –1, 0, 1.
[tex]\left[\begin{array}{ccc}X&Y\\1/2&0\\1&1\\0&-1\\-1/2&-2\end{array}\right][/tex]
Here, Y and x are related in such a way that there is a distinct value of y for each value of x, and this relationship is frequently represented as y = f(x), or "f of x." In other words, the same x cannot have more than one value for f(x). The domain and range of the function are the set of values of f(x) that are produced by the values in the domain of the function, which is the set of values of x. In addition to f(x), other abbreviated symbols for functions of the independent variable x include g(x) and P(x), especially when the nature of the function is ambiguous or unspecified.
The function is an expression, rule, or law that establishes the relationship between two variables (the dependent variable). In mathematics, functions are everywhere, and they are crucial for constructing physical relationships in the sciences. German mathematician Peter Dirichlet first offered the modern definition of function in 1837.
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a company has a workforce of 200 employees. 120 of the employees are men and the rest are women. if 10 employees are randomly selected, what is the probability that at least 4 of them are women?
The probability that at least 4 of the 10 selected employees are women is approximately 0.671.
Let the probability that a randomly selected employee is a woman is "p",
The 120 employees are men and rest 80 are women,
We have,
⇒ p = (number of women)/(total number of employees),
⇒ p = (200 - 120)/200,
⇒ p = 0.4,
Let X = number of women among the 10 employees selected.
Then X follows a binomial distribution with parameters "n = 10" and "p = 0.4".
The probability of "at-least-4" selected employees are women is expressed as⇒ P(X ≥ 4) = 1 - P(X ≤ 3),
⇒ P(X ≤ 3) = [tex]\[ \sum_{k=0}^{3} \][/tex] C(10,k) × 0.4^k × 0.6^(10-k),
We can then subtract this value from 1 to obtain P(X ≥ 4),
⇒ P(X ≥ 4) = 1 - P(X ≤ 3),
⇒ P(X ≥ 4) ≈ 0.671
Therefore, the required probability is approximately 0.671.
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2. For each pair of triangles, decide whether or not they are congruent. If they are congruent, compete the
congruency statement and the congruence property (SSS, etc.) that proves it. If it cannot be proved
congruent, state "not."
ΔFIT ≅ ΔRIS triangle are congruent.
How do triangles work?
The three vertices of a triangle make it a three-sided polygon. The angles of the triangle are formed by the three sides' end-to-end connections at a point.
The triangle's three angles add up to a total of 180 degrees. A triangle is a closed, two-dimensional geometry with three sides, three angles, and three vertices. Polygons include triangles as well.
In figure ,
FI = IS
RI = IT
∠FIT = ∠RIS
ΔFIT ≅ ΔRIS
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Please someone answer this for me 30 points
Answer:
Step-by-step explanation: First, you need to convert the width of the mural from feet to meters.
1 meter = 3.28084 feet (approximately)
So, 1 foot is approximately 0.3048 meters.
13 feet x 0.3048 meters/foot = 3.9624 meters (rounded to four decimal places)
Therefore, the width of the mural on the scale drawing would be 3.9624 meters.
Next, you need to convert the height of the mural from feet to meters.
24 feet x 0.3048 meters/foot = 7.3152 meters (rounded to four decimal places)
Therefore, the height of the mural on the scale drawing would be 7.3152 meters.
So, the measurements of the mural on a scale drawing using the scale 3m: 2ft would be 3.9624 meters wide and 7.3152 meters tall.
Spud has a problem. He knows that the roots of a quadratic function are x=3+4i and x=3−4i, but in order to get credit for the problem he was supposed to have written down the original equation. Unfortunately, he lost the paper with the original equation on it. Luckily, his friends are full of advice.
B:Hugo says, “No, no, no. You can do it that way, but that’s too complicated. I think you just start with x=3+4i and work backwards. So x–3=4i, then, hmmm… Yeah, that’ll work.” Try Hugo’s method.
Answer:
x² -6x +22 = 0
Step-by-step explanation:
You want to write the quadratic equation that has roots x = 3±4i, starting from x -3 = ±4i.
QuadraticThe next step would be to square both sides of the equation:
(x -3)² = (±4i)²
(x -3)² = 16i² = -16
(x -3)² +16 = 0 . . . . . . add 16
x² -6x +22 = 0 . . . . . expand the square
What number can be substituted for y to make the statement? 2/5 x 7/8 = 7/8 x Y true?
Answer:
2/5
Step-by-step explanation:
2/5 x 7/8 = 7/8 x 2/5
14/40 = 14/40
Helping in the name of Jesus.
Evaluate f3 + 11g-4h when f = 3,g=2 and h=7
Answer:
Step-by-step explanation:
using diagonals from a common vertex, how many triangles could be formed from a decagon?Answer:_______________
Using diagonals from a common vertex of a decagon (a polygon with ten sides), a total of seven triangles can be formed.
To see why, we can apply the formula for the number of triangles formed by drawing all the diagonals from a single vertex of a polygon, which is (number of sides - 2). For a decagon, the formula gives us:
number of triangles = (10 - 2) = 8
However, we need to subtract one from the total because the vertex where the diagonals are drawn from is not included in any of the triangles. Therefore, the number of triangles formed by drawing diagonals from a common vertex of a decagon is:
number of triangles = 8 - 1 = 7
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i need this asap
4x+3<2x+15
Answer:
x = 6
Step-by-step explanation:
4x - 2x= 2x
15-3= 12
2x=12
12/2=6
6=x
Answer:
x<6<6
Step-by-step explanation:
4+3<2+15.
4x+3−3< 2x+15−3
4<2+12
4x−2x<2x+12−2x4−2<2+12−2
2x<122<12
2x2<12222<122
x<6
Calculate the volume of each of these prisms.
The volume of the given prisms above is calculated as follows:
a.) = 432m³
b.) = 135m³
C.) = 1,332m³
How to calculate the volume of the prisms?For prism a:
Divide the prism to get two solid shapes and then add up the calculated volumes of each.
Vol of First shape = length× width× height
H = 12m
w = 4m
L = 7m
Vol = 12×4×7 = 336m³
Vol of second shape ;
=2( 4×4×3)
= 2 × 48
= 96m³
Therefore the volume of prism A = 336+96 =432
For prism b:
Volume= BH
B = area of the base
H = height of the prism
Volume = 1/2×5 × 6 × 9
= 5×3×9
= 135m³
For prism C:
Divide the prism to get two solid shapes and then add up the calculated volumes of each.
Vol of first shape = 5×15×12 = 900m³
Vol of second shape;
=2(6×12×3)
= 2(216)
= 432 m³
Volume of prism C = 900+432
= 1,332m³
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romita gets shusi lunch special at yoshi's. by using a coupon, she receives $2 off the regular price, p. her total cost, including 20% for tax and tip, is $9. what is p, the regular price of the lunch special?
If she receives $2 off the regular price, p. by using a coupon. her total cost, including 20% for tax and tip, is $9. then the regular price of the lunch special is $11.
Let's figure out why that is so. Romita gets a sushi lunch special at Yoshi's, with a coupon. Romita received a discount of $2 off the regular price, P.
Let's assume that the price of lunch before the discount is $P.
Therefore, after the discount, the cost of the lunch is (P - 2).
Now, let's determine the total cost of the lunch. The price of the lunch is inclusive of 20% tax and tip. This implies that Romita's total cost is 120% of the final cost of the lunch.
We can represent this information in the equation below:
Total cost = 120% of (P - 2)
Total cost = 1.2(P - 2)
From the given information, we know that the total cost is $9.
This means we can solve the equation for P.P = (9/1.2) + 2P = 7.5 + 2P = $11
The regular price of the lunch special is $11.
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Can you please help on this question below
What steps would you take to determine if these
figures are similar? Check all that apply.
Use a scale factor of 2.
Multiply the vertices of polygon ABCD by
Translate the intermediate image 4 units down.
Perform two different dilations.
Reflect the intermediate image.
The steps that you should take to determine if these figures are similar include the following:
2. Multiply the vertices of polygon ABCD by 1/20.
5. Reflect the intermediate image.
What are the properties of similar geometric shapes?In Mathematics and Geometry, two geometric shapes are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
What is scale factor?In Mathematics and Geometry, the scale factor of a geometric figure can be calculated by dividing the length of the image by the length of the pre-image or by multiplying the vertices by a specific scale factor.
This ultimately implies that, we would multiply the vertices of polygon ABCD by 1/20 and then apply a reflection of the intermediate image;
Vertices A' = (1 × 1/20, -6 × 1/20) = (1/20, -6/20)
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find the area of this semi-circle with radius, r=98cm. give your answer to 1dp
Grant borrowed $5,300 to remodel his bathroom and agreed to make 30 monthly payments of $235. He paid the debt in full after 24 months. Find the amount needed to repay the loan in full using the Rule of 78.
Multiple Choice
$1,330.97
$1,410.00
$7,050.00
$176.67
$1330.97 is the amount needed to repay the loan in full using the Rule of 78.
What is interest?In finance and ecοnοmics, interest is payment frοm a bοrrοwer οr depοsit-taking financial institutiοn tο a lender οr depοsitοr οf an amοunt abοve repayment οf the principal sum, at a particular rate. It is distinct frοm a fee which the bοrrοwer may pay the lender οr sοme third party.
We wοuld subract interest saved frοm the tοtal payment which Grant wοuld have tο pay if he cοntinued the lοan fοr 30 mοnths :
7050-79.03= $6970.97
The Amοunt οf mοney Grant have already paid fοr 24 mοnths
= 24*235= $5640
The amοunt needed tο repay the lοan in full
= 6970.97 - 5640 = $ 1330.97
Thus, option a $ 1330.97 is correct.
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5. Triangle.
b = 18 in
h = 6 1/2 in
Answer:
58.5
Step-by-step explanation:
[tex]A=\frac{h_bb}{2}[/tex]
[tex]\frac{6.5*18}{2}[/tex]
[tex]58.5[/tex]
y = -6x + 8
y = 5x - 4
Step-by-step explanation:
Both of the expressions equal y....equate them
-6x + 8 = 5x-4
12 = 11x
x = 12/11 = 1 1/11
then y = 5x -4 = 5(12/11) - 4 = 1 5/11
( 1 1/11 , 1 5/11 )
Solve for x. Type your answer as a number
Answer:
x = 5
Step-by-step explanation:
[tex]3x + 11 = 2(x + 8)[/tex]
[tex]3 x + 11 = 2x + 16[/tex]
[tex]x = 5[/tex]
can someone please help
Answer:
Step-by-step explanation:
Jorge writes the expression 0.88x to represent the final cost of a shirt. Which statement about the
original cost of the shirt, x, is true?
A. To get the final cost of the shirt, the original cost of the shirt is decreased by 12%.
B. To get the final cost of the shirt, the original cost of the shirt is decreased by 88%.
C. To get the final cost of the shirt, the original cost of the shirt is increased by 12%.
D. To get the final cost of the shirt, the original cost of the shirt is increased by 88%
I need help with number 24.