Using Pythagorean theorem, the triangle is an acute triangle.
What is Pythagorean theorem?
The Pythagorean theorem is a fundamental result in Euclidean geometry that describes the relationship between the three sides of a right-angled triangle.
In equation form, this can be written as:
[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 (also known as the legs) of the right-angled triangle.
If the triangle is not a right triangle, then the inequality [tex]c^2 < a^2 + b^2[/tex]holds for an acute triangle and [tex]c^2 > a^2 + b^2[/tex] holds for an obtuse triangle.
Using this formula, we can check if the given triangle is right, acute, or obtuse:
a = 43, b = 96, and c = 89
[tex]c^2 = 89^2 = 7921[/tex]
[tex]a^2 + b^2 = 43^2 + 96^2 = 1849 + 9216 = 11065[/tex]
Since [tex]c^2 < a^2 + b^2[/tex], we can see that:
[tex]c^2 < a^2 + b^2[/tex]
So the triangle is an acute triangle.
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Find the value of x .
The angles (x + 7)° and (3x - 21)° are vertical angles and the value of x is equal to 14.
What are vertically opposite anglesVertical angles also called vertically opposite angles are formed when two lines intersect each other, the opposite angles formed by these lines are vertically opposite angles and are equal to each other.
so we shall solve for x and y as follows:
3x - 21 = x + 7
3x - x = 21 + 7 {collect like terms}
2x = 28
2x/2 = 28/2 {divide through by 2}
x = 14
Therefore, the value of x is equal to 14 for the vertical angles (x + 7)° and (3x - 21)°.
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I need help on this asap!!
The inequality and the shaded region are added as attachment
How to graph the inequality and show the shaded regionThe given parameter from the question is represented as
0.4r ≤ 120 and r ≥ 4(360/5)
Evaluate the expression by products and quotients
So, the expression becomes
r ≤ 300 and r ≥ 288
When these inequalities are combined, we have the following compound expression of inequality
288 ≤ r ≤ 300
Next, we plot the graph of the inequality
The inequality is added as an attachment
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Decrease R1400 in the ratio 7:3
Based on the given task content; the decrease of R1400 in the ratio 7:3 is R980 and R420 respectively.
How to solve ratio:Ratio refers to the number representing a comparison between two different quantities. It is expressed as a quotient which is the relative magnitudes of two quantities.
Amount given = R1400
Ratio = 7 : 3
Total ratio = 7 + 3 = 10
Rate 1 for 7:
= 7/10 × R1400
= 0.7 × R1400
= R980
Rate 2 for 3:
= 3/10 × R1400
= 0.3 × R1400
= R420
In conclusion, R1400 decreased in the ratio 7:3 is R980 and R420.
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A miniature golf course recently provided its customers with a variety of colored golf balls.
red 2
white 1
pink 10
blue 2
green 5
What is the experimental probability that the next customer will receive a pink golf ball?
Write your answer as a fraction or whole number.
P(pink)=
Consider data Y1,Y2,…Yn that is a random (i.e. independent) sample from a Normal distribution with unknown mean μ and known variance σ2. You wish to infer μ from the data using a Bayesian approach and select a prior on μthat is Normal with mean μ0 and variance τ2. a. Derive the posterior distribution for μ. Since you should know the final result, credit will only be given for the derivation. b. Write down the posterior mean as a function of the posterior variance. Explain what happens to the posterior mean as a function of increasing n. c. Confirm your answer from part b) by plotting your results in R assuming μ0=0,τ2=1,σ2=100, and with the data Yˉ=5 for n=1,10,100,1000.
The value of t such that the area under the curve between 1 and 11 equals 0.95, assuming the degrees of freedom is 8, is 1.86.
What is degree of freedom?Degree of freedom refers to the number of independent variables that can be varied in a statistical experiment or analysis. It is a measure of the flexibility of the experiment or analysis to accommodate new data or observations.
In this case, the degrees of freedom is 8. To find the t-value, the t-table must be consulted. The t-table is a chart of t-values for different degrees of freedom. The t-value is the value at which the area under the curve between 1 and 11 equals 0.95. The t-table is organized such that the rows represent the degrees of freedom and the columns represent the area under the curve. For example, if the degrees of freedom is 8 and the area under the curve is 0.95, the t-value can be found in the row for 8 degrees of freedom and the column for 0.95 area under the curve. The t-value from the t-table in this case is 1.86.
Therefore, the value of t such that the area under the curve between 1 and 11 equals 0.95, assuming the degrees of freedom is 8, is 1.86.
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complete ques is:
Consider data Y1,Y2,…Yn that is a random (i.e. independent) sample from a Normal distribution with unknown mean μ and known variance σ2. You wish to infer μ from the data using a Bayesian approach and select a prior on μthat is Normal with mean μ0 and variance τ2. a. Derive the posterior distribution for μ. Since you should know the final result, credit will only be given for the derivation. b. Write down the posterior mean as a function of the posterior variance. Explain what happens to the posterior mean as a function of increasing n. c. Confirm your answer from part b) by plotting your results in R assuming μ0=0,τ2=1,σ2=100, and with the data Yˉ=5 for n=1,10,100,1000.
Find the volume of this sphere.
Use 3 for TT.
7cm
Va [?]cm³
3
V = πr³
Answer:
Step-by-step explanation:
To find the volume of a sphere, we use the formula:
V = (4/3) * π * r^3
where r is the radius of the sphere.
We are given that the radius of the sphere is 7 cm and we can use 3 as an approximation for π. Substituting these values in the formula, we get:
V = (4/3) * 3 * 7^3
V = (4/3) * 3 * 343
V = 4 * 343
V = 1372
Therefore, the volume of the sphere is 1372 cubic centimeters.
please help me i really need it
The simplified expression, given the rule for exponentiation of powers, is 1, 024 x ³⁰.
How to simplify the expression ?To simplify the expression ((2x³) ⁵ ) ², we need to apply the rule for exponentiation of powers which states " When an expression is raised to a power, and that result is raised to another power, we can simplify by multiplying the exponents."
Using this rule, we can simplify the expression as follows:
( ( 2 x ³ ) ⁵ ) ² = (2 ⁵ x (3 x 5) ) ^ 2
= ( 32 x ¹⁵ ) ²
= 1, 024 x ³⁰
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Ms. Katie had a pizza party with the art club theres 8 students and each student ate 1/3 of a pizza how many pizzas did they eat altogther
The 8 students at the pizza party ate 2 and 2/3 pizzas if each student ate 1/3 of a pizza.
If each of the 8 students ate 1/3 of a pizza, we can find the total number of pizzas by multiplying the number of students by the fraction of a pizza each student ate:
8 students × 1/3 pizza per student = 8/3 pizzas
However, it's more common to express the result as a mixed number or decimal. To convert the improper fraction 8/3 to a mixed number, we can divide the numerator by the denominator:
8 ÷ 3 = 2 with a remainder of 2
Therefore, the students ate 2 and 2/3 pizzas altogether. Alternatively, we can convert the improper fraction to a decimal by dividing the numerator by the denominator:
8/3 = 2.67
Therefore, the students ate approximately 2.67 pizzas altogether.
To recap, if each of the 8 students at the pizza party ate 1/3 of a pizza, they ate 8/3 pizzas altogether, which is equal to 2 and 2/3 pizzas or approximately 2.67 pizzas.
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Marika Perez's gross biweekly pay is 2,768 her earnings to date for the year total 80,272 what amount is deducted from her paycheck for social security taxes if the rate is 6.2% what amount is deducted for medicare which is taxed at 1.45%?
Answer: there you go :)
$171.62 for social security.
$40.14 for Medicare.
Step-by-step explanation:
We have been given that Marika Perez’s gross biweekly pay is $2,768.
To find the amount deducted from her pay for social security tax, we will find 6.2% of her biweekly pay.
Therefore, $171.62 is deducted from Marika's biweekly pay.
Now let us find 1.45% of $2768 to find the amount of medicare deducted from her pay.
Therefore, an amount of $40.14 is deducted from Marika's biweekly pay for medicare.
(Help ASAP pls/50 points) Solve the equation by completing the square. Show your work on the canvas.
x^2- 8x - 20 = 0
(canvas is a piece of paper btw)
Which is a recursive formula for this geometric sequence?
-18, -14, -12, -1, . . .
A. a1 = -1/8
an = (an – 1)(1/8)
B. a1 = -1/8
an = (an – 1)(1/2)
C. a1 = 2
an = (an – 1)(-1/8)
D. a1 = -1/8
an = (an – 1)(2)
A recursive formula for this geometric sequence is;
Option C:
a₁ = -1/8
aₙ = (-1/8)a⁽ⁿ⁻¹⁾
How to find the recursive formula?The geometric sequence is given as;
-1/8, -1/4, -1/2, -1, . . .
The general formula used to find the nth term of a geometric sequence is;
aₙ = a(r)⁽ⁿ⁻¹⁾
where;
a is first term
d is common ratio
where;
r = (-1/4)/(-1/8)
r = 2
Thus;
aₙ = -1/8(2)⁽ⁿ⁻¹⁾
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[CALCULATOR OK] Many years back, Mr. Yang invested a sum of $1000 into a savings account that earned interest at 6% compounded semiannually (twice per year). This sum is now worth $1435.77. How long ago did he invest that $1000? Round to two decimal places.
Mr. Yang invested the $1000 approximately 8.55 years ago
To calculate the time that Mr. Yang invested the money, you can use the formula for compound interest: A=P(1+r/n)^nt where A is the amount of money after t years, P is the initial principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years. We are given A= $1435.77, P=$1000, r=0.06, and n=2 (since interest is compounded twice per year). We want to solve for t, so we will rearrange the formula to solve for t:t=ln(A/P)/(n ln(1+r/n))Plugging in the values, we have: t= ln(1435.77/1000)/(2 ln(1+0.06/2)) ≈ 8.55 years, rounded to two decimal places.Therefore, Mr. Yang invested the $1000 approximately 8.55 years ago.
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the angle of elevation from a pack bench 778 feet from the base of the getaway arch in St. Louis Missouri is 39 degrees how tall is the getaway arch ?
630 .18 feet tall is the gateway arch by the trigonometric ratio
Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios (sec). A branch of mathematics called trigonometry in geometry deals with the sides and angles of a right-angled triangle. Trig ratios are therefore assessed in relation to sides and angles.
As given
The angle of elevation from a park bench 778 feet from the base of the Gateway Arch in St. Louis, Missouri is 39 degrees.
Now by using the trigonometric property
[tex]tan\theta=\frac{P}{B}[/tex]
As the diagram is given below.
AB=CB tan39
AB = 778 tan 39
AB= 630.18 feet
Hence the gateway arch is 630.18 feet tall.
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10
9
=
k
10
start fraction, 9, divided by, 10, end fraction, equals, start fraction, 10, divided by, k, end fraction
k =
The value of k that solves the proportion is given as follows:
k = 100/9.
How to solve the proportion?The proportional relationship for this problem is defined as follows:
9/10 = 10/k.
Then we cross-multiply, that is we multiply the numerator of one ratio by the denominator of the other ratio, and vice versa, hence:
9k = 10 x 10
9k = 100.
Then we solve for the unknown variable k, applying the division, which is the inverse operation of the multiplication, hence the value of k that solves the proportion is given as follows:
k = 100/9.
Missing InformationThe proportional equation for this problem is defined as follows:
9/10 = 10/k.
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For each expression, select all equivalent expressions from the list. Check all that apply.
8x + 56 -
☐ 8·x + 8·7
☐ 8(x + 7)
☐ 64x
☐ 8(7x + 1)
9 + 16y - 8 - y -
☐ y + 15
☐ 15 + y
☐ y + 15y
☐ 15y + 1
Answer:
8x + 8·7
8(x + 7)
15y - 1
Step-by-step explanation:
8x + 8·7
8x + 56
8(x + 7)
8(x) + 8(7)
8x + 56
9 + 16y - 8 - y Combine like terms
15y - 1
Helping in the name of Jesus.
Hannah makes and sells bags. It used to be that she could only make 4 bags in one day. Then she got a new sewing machine. Now she can make 7 bags in one day. What is the percent increase in the number of bags she can make?
If she can make 7 bags in one day, the percent increase in the number of bags Hannah can make is 75%.
To calculate the percent increase in the number of bags Hannah can make, we need to find the difference between the number of bags she can make now and the number she could make before, and then express this difference as a percentage of the original number of bags she could make.
The difference between the number of bags she can make now and the number she could make before is:
7 bags - 4 bags = 3 bags
To express this difference as a percentage of the original number of bags she could make, we can use the following formula:
percent increase = (difference ÷ original value) x 100%
In this case, the original value is 4 bags, so we have:
percent increase = (3 bags ÷ 4 bags) x 100% = 75%
This means that she can now make 75% more bags per day than she could before she got her new sewing machine.
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A circular watch has a minute hand that is 2.5 cm long.
(a) What distance does the tip of the hand move through in 20 minutes?
(b)What area of the watch face is covered by the minute hand in 30 minutes?
Answer:
a) 20 minute=2pi/3 rad
angle=arc length/radius
arc length= angle×radius
=2pi/3×2.5
=5pi/3 cm
b)area= pi(radius)²/2
=pi×6.25
=25pi/4cm²
i hope you find it helpful
Step-by-step explanation:
Answer:
[tex]L=\frac{5}{3} \pi cm. \\ A=3.125\pi cm^{2}[/tex]
Step-by-step explanation:
a)
L - is how far does the tip of the hand move in diameter.
m - is how much time does the tip of the hand move in minutes.
m=20
r =2,5cm
[tex]L=\frac{m}{60} *2\pi r\\L=\frac{20}{60} *2\pi *2,5cm\\L=\frac{5}{3} \pi cm[/tex]
In a formula, we have [tex]\frac{m}{60}[/tex] because the minute hand needs 60 minutes to make one circle. L = 2πr is a formula for the full length of a circle.
b)
A- Area
r=2,5cm
m - is how much time does the tip of the hand move in minutes.
[tex]A=\frac{m}{60} *\pi r^{2} \\A=\frac{30}{60} *\pi *(2,5cm)^{2} \\A=\frac{1}{2} *\pi *6.25cm^{2} \\A=3.125\pi cm^{2}[/tex]
In the formula, we have [tex]\frac{m}{60}[/tex] because the minute hand needs 60 minutes to make one circle. The formula for the full area of a circle is A=πr².
Rosalind drew a rectangle with a width of 11 centimeters and a length of 14 centimeters. Which equation can be used to determine P, the perimeter of this rectangle in millimeters
Answer:
P=(1100+1400)2
Step-by-step explanation:
Write the polynomial in standard form. Then classify its degree and by number of terms
7x²+10+4x³
Step-by-step explanation:
4x^3 + 7x^2 + 10 <====standard form
degree is 3 (this is the largest exponent) and there is three terms
solve and graph the inequality 4x>16
Answer: X>4
Step-by-step explanation:
First divide both sides by 4 and then
4 divided by 4 is 1 so what remains is x>16/4 and that is x>4
(12+13)(-2) work show
Answer:
To solve this expression, we can use the order of operations, which tells us to perform the operations inside the parentheses first, and then multiply by -2.
So, we have:
(12 + 13) (-2)
= (25) (-2) // simplify the parentheses by adding 12 and 13
= -50 // multiply 25 by -2
Therefore, (12+13)(-2) equals -50.
in a small county, there are 150 people on any given day who are eligible for jury duty. of the 150 eligible people, 80 are women. (a) determine whether the following statement is true or false. this is an example of sampling without replacement. true false (b) if four potential jurors are excused from jury duty for medical reasons, what is the probability that all four of them are women? (round your answer to four decimal places.)
a) True. This is an example of sampling without replacement because once a person is selected for jury duty, they are no longer available for selection again.
b) 0.5238 is the probability.
a) Sampling without replacement is the technique of choosing a sample from a population without replacing the selected individuals in the population after each selection. In this case, once an eligible person is chosen, they cannot be chosen again.
Hence, the given statement is true.
b) We have to find the probability of all four of the excused jurors being women. We are picking four people out of 70 men and 80 women, or 150 people in total. Since we are dealing with independent events, we may use the multiplication principle for probabilities.
There are 80 women in the 150-person sample, so the probability of selecting one woman is 80/150.
After the first woman is selected, there are 79 women remaining in the 149-person sample, so the probability of selecting another woman is 79/149.
Similarly, the probabilities of selecting a third and fourth woman are 78/148 and 77/147, respectively.
Therefore, the probability that all four excused jurors are women is:
P(4 women) = (80/150) × (79/149) × (78/148) × (77/147)
P(4 women) = 0.5238 (rounded to four decimal places)
The probability that all four of the excused jurors are women is 0.5238.
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In a right triangle, angle A measures 20°. The side opposite angle A is 10 centimeters long. Approximately how long is the hypotenuse of the triangle?
3.4 centimeters
10.6 centimeters
27.5 centimeters
29.2 centimeters
Answer: 27.5 centimeters
Step-by-step explanation:
angle A measures 20 degrees and we know it's a write tringle so 180-(90+20)=70 degrees
so, angle B measures 70 degrees.
using the law of cosines:
[tex]\frac{sin70}{b} =\frac{sin20}{10}[/tex]
[tex]b=\frac{10sin(70)}{sin(20)}[/tex]
so, side b =[tex]\frac{10sin(70)}{sin(20)}[/tex]
Using the Pythagorean theorem to find the hypotenuse:
hypotenuse[tex]=\sqrt{(\frac{10 sin70}{sin20})^{2} + 10^{2} }[/tex]
approximately = 27.5 centimeters
Alvin is 12 years younger than Elga. The sum of their ages is 66 . What is Elga's age?
According to the problem, Alvin is 12 years younger than Elga, and the sum of their ages is 66. So, we have to use algebra to find Elga's age.
Step-by-step explanation:
Let's assume Elga's age to be x.
Alvin's age can be found as: x - 12
The sum of their ages is 66. So,
x + (x - 12) = 66 ⇒ 2x - 12 = 66
⇒ 2x = 78
⇒ x = 39
Therefore, Elga's age is 39 years old.
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Find the median of 16 even number
Answer:
17
Step-by-step explanation:
To find the median of 16 even numbers, we need to arrange the numbers in order from least to greatest, and then find the middle value.
Since the numbers are even, the middle two values will need to be averaged to find the median.
Let's assume the 16 even numbers are:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32
Now, we arrange them in order from least to greatest:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32
The middle two numbers are 16 and 18. So, we need to average them to find the median:
Median = (16 + 18) / 2 = 17
Therefore, the median of 16 even numbers is 17.
NEED HELP PLEASE HELP
Answer:
y = 2/3x - 2
Step-by-step explanation:
A car is driving at 35 kilometers per hour. How far, in meters, does it travel in 4 seconds?
Answer: The answer would be about 38.88 meters
Step-by-step explanation:
First you transfer Kilometers per hour into Meters per second.
35 KM/H = 9.72 M/S
The formula for distance is D = Speed x Time
9.72 x 4 seconds = 38.88 Meters that he will travel in 4 seconds
Isabella built a time travel machine, but she can't control the destination of her trip. Each time she uses the machine she has a 0. 250. 250, point, 25 probability of traveling to a time before she was born. During the first year of testing, Isabella uses her machine 555 times. Assuming that each trip is equally likely to travel before Isabella was born, what is the probability that at least one trip will travel before Isabella was born? Round your answer to the nearest hundredth. P(\text{at least one before she's born})=P(at least one before she’s born)=P, (, start text, a, t, space, l, e, a, s, t, space, o, n, e, space, b, e, f, o, r, e, space, s, h, e, apostrophe, s, space, b, o, r, n, end text, ), equals
The probability that at least one trip will travel before Isabella was born is 0.9999, or 99.99% (rounded to the nearest hundredth).
We can use the complement rule to find the probability that at least one trip will travel before Isabella was born. The complement rule states that the probability of an event happening is equal to 1 minus the probability of the event not happening. In this case, the event we are interested in is at least one trip traveling before Isabella was born.
The probability of none of the 555 trips traveling before Isabella was born is (1-0.25) raised to the power of 555, since the probability of each trip not traveling before Isabella was born is 1 - 0.25 = 0.75.
So, the probability of at least one trip traveling before Isabella was born is:
P(at least one before she's born) = 1 - (1-0.25)^{555}
P(at least one before she's born) = 1 - 0.75^{555}
P(at least one before she's born) = 0.9999 (rounded to the nearest hundredth)
Therefore, the probability that at least one trip will travel before Isabella was born is 0.9999, or 99.99% (rounded to the nearest hundredth).
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Lourdes garage is in the shape of a square pyramid. The garage is shown, with dimensions given in feet (ft).
Lourdes is replacing the roof and installing shingles. What is the surface area of the roof?
The slant height of the roof is 18ft the base of the roof is 40ft
Since Lourdes garage is in the shape of a square pyramid, the surface area of the square pyramid roof is 1440 ft²
What is an equation?An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.
The surface area (SA) of a pyramid is given as:SA = B + (1/2)Ph
where B is the base area, P is the perimeter and h is the slant height
Since the roof is a square pyramid with base 40 feet and slant height of 18 ft, hence:
h = 18 ftP = 40 + 40 + 40 + 40 = 160 ft.
Surface area of only roof = (1/2)Ph
Therefore, Substituting:
SA = (1/2)(160)(18) = 1440 ft²
The surface area of the roof is 1440 ft²
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Point m is on line segment ln. given ln=20 and lm=7,determine the length mn
27 mn is the length of line segment .
What in mathematics is a line segment?
A line segment has two unique points on the line defining its boundaries. Or, a line segment is a section of the line that links two points, as another alternative.
In contrast to a line, which has no endpoints and can go on forever, a line segment has two distinct endpoints that are fixed or identifiable.
The value of the line segment will be calculated as:-
Point M is on the line segment MN.
In = 20
Im = 7
MN = In+ Im
= 20 + 7
= 27
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