The hypotenuse of the right triangle is 7.93 inches.
According to the question,
We have the following information:
A right triangle has a leg that measures 7 in. The angle opposite this side measures 62°.
Now, the hypotenuse can be easily found using the trigonometric function.
(More to know: in a right triangle, we can use the Pythagoras theorem. This theorem can not used in any other triangle.)
We will use sin 62 to find hypotenuse.
Sin 62 = perpendicular/hypotenuse
Hypotenuse = perpendicular/sin 62
Hypotenuse = 7/0.88295
Hypotenuse = 7.93 inches
Hence, the hypotenuse of the right triangle is 7.93 inches.
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The values of a and r in the series 3 + 12 + 48 + are
a. a = 3, r = 4 c. a = 3, r = –4
b. a = 4, r = 3 d. a = 4, r = –3
Option a is correct.
The first term, a is 3;
Common ratio, r = +4;
What is Geometric Series?
The total of a geometric sequence's finite or infinite terms is known as a geometric series. The analogous geometric series is a + ar + ar2 +..., arn-1 + for the geometric sequence a, ar, ar2,..., arn-1,... The word "series" is known to mean "sum." The geometric series specifically refers to the total of phrases with a common ratio between every pair of neighboring terms. Geometric series can be of two different types: finite and infinite.
In the given question, we have:
The series: 3 + 12 + 48 +
So, here the first term (a) = 3;
The second term = +12;
and, we know that the common ratio in the geometric series is the ratio of the second term and the first term.
So,
Common ratio, r = [tex]\frac{12}{3}[/tex]
r = 4;
so, The common ratio will be the same everywhere. So, It will be 4 in all the cases.
And, The first term, a is 3;
Hence,
Option a is correct.
The first term, a is 3;
Common ratio, r = +4;
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Why does completing the square always result in a perfect square trinomial?
Answer: Adding will make a perfect square trinomial. It is always positive because it is the square of the number.
When a binomial is squared, the result is the square of the first term added to twice the product of the two terms and the square of the last term. a2+2ab+b2=(a+b)2anda2−2ab+b2=(a−b)2.
Hope this helps.
Step-by-step explanation:
Triangle EFG is similar to triangle HIJ. Find JH. Round your answer to
the nearest tenth if necessary. Figures are not drawn to scale.
The length of the side JH in the triangle ΔHIJ is 97.9.
We are given two triangles. The vertices of the first triangle are E, F, and G. The vertices of the second triangle are H, I, and J. The triangles ΔEFG and ΔHIJ are similar to each other. The lengths of the sides FG, GE, and IJ are 12, 25, and 47, respectively. We need to find the length of the side, JH. The figure of the triangles is attached below.
Let the length of the side JH in the triangle ΔHIJ be represented by the variable "x". The side IJ is proportional to the side FG. Let the constant of proportionality be "k".
IJ ∝ FG
IJ = k*FG
k = IJ/FG
k = 47/12
The side JH is proportional to the side GE.
JH = k*GE
x = (47/12)*25
x = 97.9
Hence, the length of the side JH is 97.9 units.
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Help please! 15 points!!!!! give me an answer!!!!!
Billy has 15 apples he eats 3 ands sells 4 for $4 dollars each, How many apples are left. And what's Billy's total profit at the end of the day?
Answer:
Step-by-step explanation:
7*5
Answer:
he got 8 apples left and made a profit of 16
Step-by-step explanation:
Question 6(Multiple Choice Worth 2 points)
(Pythagorean Theorem MC)
Determine which set of side measurements could be used to form a right triangle.
O 4, 8, 11
O 6, 8, 13
O√3, √5,8
O√3, √13, 4
K
The set of side that could be used to form a right triangle is {√3 , √13 , 4} , the correct option is (d) .
In the question ,
four set of sides is given ,
we need to find the set of side that forms a right triangle ,
we know that for right triangle , By Pythagoras Theorem , the sum of square of two shorter side is equal to the square of the longest side .
Option(a)
the sides are 4 , 8 , 11.
4 + 8 = 11
16 + 64 = 121
80 = 121
we know that 80 121 ,
So , the sides do not form a right triangle
Option(b)
the sides are 6 , 8 , 13
6 + 8 = 13
36 + 64 = 169
100 169
we know that 100 169 ,
So , the sides do not form a right triangle .
Option(c)
the sides are √3, √5 , 8
√3 + √5 = 8
3 + 5 = 64
8 = 64
we know that 8 64 ,
So , the sides do not form a right triangle .
Option(d)
the sides are √3, √13 , 4
√3 + √13 = 4
3 + 13 = 16
16 = 16
Yes , the sides form a right triangle .
Therefore , The sides {√3 , √13 , 4} forms a right triangle .
The given question is incomplete , the complete question is
Determine which set of side measurements could be used to form a right triangle ?
(a) 4, 8, 11
(b) 6, 8, 13
(c)√3, √5,8
(d)√3, √13, 4
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Complete the table representing a linear function.
Answer:
x y
1 0
2 10
5 40
10 90
Step-by-step explanation:
In a linear function, every time x is increased by 1, y is increased by a set amount. The only two complete rows in the table are when x = 1 and x = 5. x is increased four times in that interval while y has increased by 40(40 - 0). This means that every time x increases by 1, y increases by 10(40/4).
Therefore, when x is 2, y will be 10.
To get to ninety, 10 will needed to be added to 0(when x=1) 9 times. 1 + 9 is 10, so x = 10 when y = 90.
Answer:
Step-by-step explanation:
(1,0) (5,40)
Using these coordinates we find the line equation y=mx+b:
[tex]\displaystyle\\m=\frac{y_2-y_1}{x_2-x_1} \\\\x_1=1\ \ \ \ \ x_2=5\ \ \ \ \ y_1=0\ \ \ \ y_2=40\\\\m=\frac{40-0}{5-1} \\\\m=\frac{40}{4} \\\\m=10\\\\Thus,\ y=10x+b \ \ \ \ (1)\\[/tex]
We substitute the value of coordinate (1,0) into equation (1):
[tex]0=10(1)+b\\\\0=10+b\\\\-10=b\\\\Thus, \ b=-10\\\\Hence,\\\\ y=10x-10\\\\x=2\\\\y=10(2)-10\\\\y=20-10\\\\y=10\\\\Thus,(2,10)\\\\y=90\\\\90=10x-10\\\\100=10x[/tex]
Divide both parts of the equation by 10:
[tex]10=x\\\\Thus, (10,90)[/tex]
x | y
-----------------
1 | 0
------------------
2 | 10
------------------
5 | 40
------------------
10 | 90
La duración de las llamadas telefónicas de larga distancia realizadas desde una central telefónica tiene distribución normal con media de 130 segundos y desviación estándar de 30 segundos. Si en un día cualquiera se realizaron 500 llamadas telefónicas desde esta central, ¿cuál es la probabilidad que la duración total de estas llamadas supere las 18 horas? Considere independencia en la duración de las llamadas.
El valor de la probabilidad es: ______ (escriba su respuesta con tres decimales)
The probability that the total duration of the 500 calls is greater than 18 hours, using the normal distribution, is of:
0.618 = 61.8%.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, for n instances of a normal variable, the mean is of [tex]\mu n[/tex] and the standard deviation is of [tex]\sigma\sqrt{500}[/tex]Hence, for the total duration of the 500 calls, in seconds, the mean and the standard deviation are given as follows:
[tex]\mu = 500 \times 130 = 65000, \sigma = 30\sqrt{500} = 670.82[/tex]
Each hour has 3600 seconds, hence the number of seconds in 18 hours is given as follows:
3600 x 18 = 64800.
The probability that the total time is greater than 18 hours is one subtracted by the p-value of Z when X = 64800, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (64800 - 65000)/670.82
Z = -0.3.
Z = -0.3 has a p-value of 0.382.
1 - 0.382 = 0.618 = 61.8% probability.
TranslationThe problem says that:
Telephone calls are normally distributed with mean of 130 seconds and standard deviation of 30 seconds.A sample of 500 calls is taken.The problem asks for the probability that the total duration of these calls is greater than 18 hours.Calls are independent.More can be learned about the normal distribution at https://brainly.com/question/25800303
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Suppose you know that f(x) is an odd function on the domain of all real numbers and that the function is concave up on the intervals 0 < x < 3 and 5 < x and concave down on the interval 3 < x < 5.
List ALL intervals on which the function f(x) is concave up and ALL intervals on which the function f(x) is concave down; explain how you know these to be correct
The intervals for the concavity of the odd function are given as follows:
Concave down: x < -5, -3 < x < 0, 3 < x < 5.Concave up: -5 < x < -3, 0 < x < 3, x > 5.What are even and odd functions?The definition of even and odd functions depends on the relation between f(x) and f(-x), as explained as follows:
In even functions, we have that the statement f(x) = f(-x) is true for all values of x.In odd functions, we have that the statement f(-x) = -f(x) is true for all values of x.If none of the above statements are true for all values of x, the function is neither even nor odd.In this problem, we have that the function is odd, hence the following statement is true:
f(-x) = -f(x) for all values of x.
This means that the concavity intervals are exchanged, hence:
f(x) is concave down on -3 < x < 0, as it is concave up of 0 < x < 3.f(x) is concave down on x < -5, as it concave up on x > 5. f(x) is concave up on -5 < x < -3, as it is concave down of 3 < x < 5.More can be learned about even and odd functions at https://brainly.com/question/13048723
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In triangle XYZ, m∠Y = 43.85° and m∠Z = 38.6°. Determine the measure of the exterior angle to ∠X.
25.65°
41.25°
82.45°
97.55°
The measure of the exterior angle to triangle X is D. 97.55°.
How to calculate the angle?It is important to note that the sum of the angles in a triangle is 180°.
In this case, triangle XYZ, m∠Y = 43.85° and m∠Z = 38.6.
The exterior angle to X will be:
= Total angle - (43.85 + 38.6)
= 180 - 82.45
= 97.55°
In conclusion, the correct option is D.
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Answer:
I got the answer d when I took the test
Step-by-step explanation:
I hope this helps...
Find the equation (in slope-intercept form) of the line with the given slope that passes through the point with the given coordinates.
slope: −43, ordered pair: (−4,1)
Answer:
[tex]y=-43x-173[/tex]
Step-by-step explanation:
[tex]y+1=-43(x+4) \\ \\ y+1=-43x-172 \\ \\ y=-43x-173[/tex]
At his most recent medical checkup, a boy was 40 inches tall. Currently, he is 46 inches tall. What percent taller is the boy now?
im not smart at this lol
Answer:
15%
Step-by-step explanation:
15%*40=46
Answer:
15%
Step-by-step explanation:
[tex]Percent of change =\frac{new -old}{ old} *100\\[/tex]
The boy was 40 inches tall so that means 40 inches is the old value
The boy is currently 46 inches tall now, so 46 is the new value
Plug these values into the equation:
[tex]Percent of change =\frac{46 -40}{ 40} *100\\[/tex]
Simplify:
[tex]Percent of change =\frac{6}{ 40} *100\\[/tex]
[tex]Percent of change =\frac{600}{ 40} \\[/tex]
[tex]Percent of change =15[/tex]
I hope this answers your question :)
Given (x – 7)2 = 36, select the values of x :x = 13 x = 1 x = –29 x = 42
The solution to the equation given as (x - 7)² = 36 are x = 1 and x = 13
How to determine the values of x?From the question, the equation is given as
(x - 7)² = 36
To start with, we take the square roots of both sides
This gives
x - 7 = ±6
Add 7 to both sides of the equation
So, we have
x = 7 ± 6
Evaluate the like terms
x = 1 and x = 13
Hence, the values of x are x = 1 and x = 13
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what is 2 1/2 + 1 1/8 + 1 1/4 - 1 1/2
Answer:
27/8 or 3.375 or 3 3/8
Step-by-step explanation:
QUATIONS
Use the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 to make true equations of
the following. Use each digit once
The true equations are :
2 + 7 = 9
8 × 5 = 4 0
6 ÷ 3 = 2
2 - 1 = 1
We are given a total of ten digits. The digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. We are given four equations with blanks. An equation is a mathematical statement that proves the equality of two mathematical expressions. The first equation involves addition. The second equation involves multiplication. The third equation involves division. The fourth equation involves subtraction. We need to use every digit only once.
The first true equation is 2 + 7 = 9.
The second true equation is 8 × 5 = 4 0.
The third true equation is 6 ÷ 3 = 2.
The fourth true equation is 2 - 1 = 1.
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In the figure, A.ABC is congruent to AADC t the square ABCD is dilated by a factor of 2 to form ABCD, what
ASCO to the area of ABCD?
A 2:1
B 3:1
c. 4:1
d 5:1
Answer:
C. Trust me on this one, it is an easy one.
if I make 11 dollars an hour and i worked 20 hours for 4 days, how much would I earn?
Answer: I think you would earn $8.35 per hour
Step-by-step explanation:
Answer: $880
Step-by-step explanation:
As I understand you are working 20 hours a day for 4 days.
[tex]\frac{11 dollars}{hour} * \frac{20 hours}{day} * 4 days[/tex] = $880
If
a + 86 = 48,
what is
a − 86?
Answer:-48
Step-by-step explanation:
a + 85 = 48
first we need to find what a
86-48=a
a=38
now we calculate
a-86?
38 - 86 = -48
Answer:
a - 86 = -124
Step-by-step explanation:
a + 86 = 48
a = 48 - 86
a = -38
Then:
a - 86 = -38 - 86
= -124
The last time it placed an order for ingredients, Sweet Treats Bakery ordered 1,090 kilograms of sugar. This time, the bakery is ordering 654 kilograms. What is the percent of the decrease in the size of the sugar order?
somebody hwelp pwease
Answer:
40% decrease
Step-by-step explanation:
[tex]\frac{1090-654}{1090}[/tex] = .4 x 100 to make a percent equals 40%
Answer:There is no decrease from 2,820 kilograms to 2,820 kilograms.
The percent of decrease in the size of the sugar order is 0%.
Step-by-step explanation:
Find the perimeter and area of the polygon shown below 15 8 17 16
The perimeter and area of the polygon is B. Perimeter = 72 feet; Area = 308 square feet.
How to calculate the perimeter?It is important to note that the perimeter is the addition of all the sides. Therefore, the perimeter will:
= 16 + 15 + 16 + 8 + 17
= 72 feet
The area will be:
= Area of triangle + Area of rectangle
= (1/2 × base × height) + (length × width)
= (1/2 × 8 × 17) + (15 × 16)
= 68 + 240
= 308ft²
Therefore, the correct option is B.
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4. Using the Place Value Method, order the following from least to greatest.
.134
.2
.051
.46
Answer: 0.051, 0.134, 0.2, 0.46
Step-by-step explanation:
Nicole charges a flat fee of $3, plus $5 per hour. Write an equation for the cost, after h hours
The equation when Nicole charges a flat fee of $3, plus $5 per hour is c = 3 + 5h.
What is an equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario
Let the number of hours be given as h.
Since Nicole charges a flat fee of $3, plus $5 per hour, this will be:
c = 3 + (5 × h)
c = 3 + 5h
where c = total cost
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I need help with this please help me
The measurement of angles ∠1 is 126° and ∠2 is 154°.
According to the question,
We have the following information:
We have a figure of two triangles and some of the measurements of the angles are given.
We know that the sum of three angles of a triangle is 180°.
So, for the larger triangle, we have the following expression:
96+30+third angle = 180
Third angle = 180-126
Third angle = 54°
We know that sum of angles on a straight line is 180°.
So, we have:
∠1+54 = 180
∠1 = 180-54
∠1 = 126°
Now, finding the sum of angles in smaller triangle:
126+28+third angle = 180
Third angle = 180-154
Third angle = 26°
Now, angle 2 and this angle will make a straight line.
∠2+26 = 180
∠2 = 180-26
∠2 = 154°
Hence, the measurement of angles ∠1 is 126° and ∠2 is 154°.
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José is climbing a mountain. Using a rope, José climbs down from the top of a steep cliff for 4 minutes at a rate of 12.2 feet per minute. He then climbs back up for 10 minutes at a rate of 3.6 feet per minute. How far from the top of the cliff is he after 14 minutes?
Enter the correct answer in the box.
Please help this is due tomorrow
The distance from the top of the cliff that Jose is after 14 minutes is 12.8 feet downward.
What is an elevation?An elevation simply means the height above sea level.
In this case, José climbs down from the top of a steep cliff for 4 minutes at a rate of 12.2 feet per minute. The total feet will be:
= 12.2 × 4
= 48.8 feet
He then climbs back up for 10 minutes at a rate of 3.6 feet per minute. This will be:
= 3.6 × 10
= 36 feet.
Therefore, the change in elevation will be:
= Elevation up - Elevation down
= 36 - 48.8
= 12.8 feet.
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can you help me use compatible numbers to find two estimates of 478/12 i will give you 100000 points
Answer:
48
Step-by-step explanation:
19. Barney divides a rectangle into fourths.
Show two ways he could do this. That’s the space or something in the picture
Answer:
slice it in the middle in the top and bottom or do it corner to corner.
Step-by-step explanation:
1. have 2 braincells
2. put them toghether and think.
Assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of μ = 1.1 kg and a standard deviation of o= 4.6 kg.
Complete parts (a) through (c) below.
b. If 25 male college students are randomly selected, find the probability that their mean weight gain during freshman year is between 0 kg and 3 kg.
The probability is
(Round to four decimal places as needed.)
The probability that their mean weight gain during freshman year is between 0 kg and 3 kg is 70%
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given,
Amounts of weight that male college students gain during their freshman year are normally distributed
mean of μ = 1.1 kg and
Standard deviation of o= 4.6 kg.
Z score=x-μ/o
=25-1.1/4.6
=23.9/4.6
=5.196
Z score=x-μ/o
=25-1.1/0
=0
Z score=25-1.1/3
=23.9/3
=7.966
By observing the z table the probability that their mean weight gain during freshman year is between 0 kg and 3 kg is 70%
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For questions 9-11, find the values of x and y if l || m.
The values of x and y using angle relationships are as follows:
x = 9, y = 13x = 22, y = 15x = 7, y = 24How to find angles in parallel line cut by a transversal?When parallel lines are cut by a transversal, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles.
Therefore, the angle relationship can be used to find the value of x and y in the diagram.
In the diagram, l and m are parallel lines and are cut by a transversal line.
Therefore,
10.
10x - 17 = 8x + 1(alternate exterior angles are congruent)
10x - 8x = 1 + 17
2x = 18
x = 18 / 2
x = 9
8x + 1 + 6y + 29 = 180(sum of angles on a straight line is 180 degrees)
72 + 1 + 29 + 6y = 180
102 + 6y = 180
6y = 180 - 102
6y = 78
y = 78 / 6
y = 13
11.
7x - 30 = 5x + 14(Corresponding angles)
Corresponding angles are congruent.
7x - 5x = 14 + 30
2x = 44
x = 44 / 2
x = 22
3y + 11 + 7x - 30 = 180(sum of angles on a straight line)
3y + 11 + 7(22) - 30 = 180
3y + 11 + 154 - 30 = 180
3y = 180 - 11 - 154 + 30
3y = 45
y = 45 / 3
y = 15
12.
7y - 23 = 23x - 16 (vertically opposite angles)
7y - 23x = 7
8x - 21 + 23x - 16 = 180 (same interior angles are supplementary)
31x - 37 = 180
31x = 180 + 37
31x = 217
x = 217 / 31
x = 7
7y - 23(7) = 7
7y = 7 + 161
7y = 168
y = 168 / 7
y = 24
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Stanley thinks of a positive number, n, which is less than 1. He adds this number to its reciprocal and gets 2.05. Work out the value of n. Give your answer as a fraction in its simplest form.
The value of n is given by either 4/5 or 16/25.
Given that the positive number is n which is n<1.
Reciprocal of the number is = 1/n
Addition of the number and the reciprocal is 2.05.
So the suitable equation for this,
n + 1/n = 2.05
[tex]n^2+1=\frac{41}{20}n\\20n^2-41n+20=0\\n=\frac{41\pm\sqrt{1681-1600}}{40}=\frac{41\pm9}{40}=\frac{50}{40},\frac{32}{50}=\frac{4}{5},\frac{16}{25}[/tex]
So the number can be either 4/5 or 16/25.
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20 points and brainliest <3 (added photo)
The measure of angles are
∠a = 48 degrees, it is an acute angle∠b = 140 degrees, it is an obtuse angle∠c = 324 degrees, its a reflex angleThe sum of angles around a point is equal to 360 degrees
The consider the angle a
The equation will be
∠a + 312 = 360 degrees
∠a = 360 - 312
∠a = 48 degree
The angle a is less than 90 degrees then it is an acute angles
Consider the angle b
∠b + 220 = 360
∠b = 360 -220
∠b = 140 degrees
Angle b is greater than 90 degrees and less than 180 degrees then it is an obtuse angle
Consider the angle c
∠c + 36 = 360
∠c = 360 - 36
∠c = 324 degrees
Angle c is grater than 180 degrees and less than 360 degrees then it is a reflex angle
Hence, the measure of angles are
∠a = 48 degrees, it is an acute angle∠b = 140 degrees, it is an obtuse angle∠c = 324 degrees, its a reflex angleLearn more about angles here
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Solve the system of equations by graphing. List the coordinates.
u=v
4u=2v-12
By using the graphing method, an ordered pair which represent a solution to the given system of equations is (-6, -6).
What is a graph?A graph simply refers to a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.
In order to plot the system of equations on a graph, we would simplify the second equation as follows:
4u = 2v - 12
Dividing both sides of the equation by 4, we have the following:
4u/4 = 2v/4 - 12/4
u = v/2 - 3
Note: The values of v would be plotted on the y-axis of a graph while the values of u would be plotted on the y-axis of a graph.
By critically observing the graph (see attachment) of the given system of equations, we can logically deduce that its solution occur at this point of intersection (-6, -6).
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