find the value of trig function indicated, use Pythagorean theorem to find the third side if you need it. Part 4​

r:-

\(\\ \rm\hookrightarrow r+60+50=180\)(Supplementary)

\(\\ \rm\hookrightarrow r+110=180\)

\(\\ \rm\hookrightarrow r=180-110\)

\(\\ \rm\hookrightarrow r=70\)

\(\\ \rm\hookrightarrow p=50(Opposite\: angles)\)

q:-

\(\\ \rm\hookrightarrow q=70+60(Opposite \:angles)\)

\(\\ \rm\hookrightarrow q=130\)

Answer:

\({ \sf{60 \degree + r + 50\degree = 180\degree}} \\ { \sf{ \{angles \: on \: straight \: line \}}} \\ { \sf{r + 110\degree = 180\degree}} \\ { \underline{ \sf{r = 70\degree}}}\)

\({ \sf{q + 50\degree = 180\degree}} \\ { \sf{ \{angles \: on \: straight \: line \}}} \\ { \sf{q = 180\degree - 50\degree}} \\ { \underline{ \sf{q = 130\degree}}}\)

\({ \sf{p + q = 180\degree}} \\ { \sf{ \{angles \: on \: straight \: line \}}} \\ { \sf{p + 130\degree = 180\degree}} \\ { \sf{ \underline{p = 50\degree}}}\)

or:

\({ \underline{ \sf{p = 50\degree \: \{alternate \: angles \}}}}\)

The MLE for both scenarios is equal to the fraction (number of successes)/(number of failures), confirming that the answer is: Yes, both MLEs are equal to the fraction (number of successes)/(number of failures).

The maximum likelihood estimate (MLE) of p, the proportion of all mechanics who would correctly diagnose the problem, is the fraction (number of successes)/(number of failures). The MLE for a random sample of 20 mechanics resulting in 6 correct diagnoses is also the same, as it follows the same formula.

The maximum likelihood estimate (MLE) is a statistical method used to estimate the parameters of a statistical model based on observed data. In this case, the MLE of p, the proportion of all mechanics who would correctly diagnose the problem, can be calculated as the fraction (number of successes)/(number of failures). The number of successes refers to the number of mechanics who correctly diagnosed the problem (r = 6), and the number of failures refers to the number of mechanics who incorrectly diagnosed the problem (14).

Now, if we consider a random sample of 20 mechanics and the outcome is 6 correct diagnoses, the MLE in this scenario remains the same. Both situations involve estimating the same parameter, p, and the formula for the MLE remains consistent: (number of successes)/(number of failures). The only difference is the context in which the data is collected, but the calculation for the MLE remains unchanged.

Therefore, the MLE for both scenarios is equal to the fraction (number of successes)/(number of failures), confirming that the answer is: Yes, both MLEs are equal to the fraction (number of successes)/(number of failures).

Learn more about maximum likelihood estimate here:

https://brainly.com/question/31962065

#SPJ11

Answer:

Kindly Refer to the attachment :)

The amount of money saved by Andre in 40 weeks is $1280.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.

Given is Andre saves up the same amount of money each week.

We can write the equation, equating the total amount of money saved and the number of weeks as follows. Assume the equation to be -

y = mx + c

Then -

m = (288 - 224)/(9 - 7)

m = 64/2

m = 32

Now -

y = 32x + c

For the point (7, 224), we can write -

224 = 32 x 7 + c

c = 0

For {x} = 48, we can write the amount of money saved as -

y = 32 x 40

y = 1280

Therefore, the amount of money saved by Andre in 40 weeks is $1280.

To solve more questions on equations & expressions, visit the link below-

brainly.com/question/17421223

#SPJ1

Answer:

Solution:

f(5)=2×5+7

=10+7

=17

Answer:

\(f(5)=17\)

Step-by-step explanation:

\(f(5)=2(5)+7\\f(5)=10+7\\f(5)=17\)

The complete statement:

The area of Charlene's rhombus is 1/9 (or 1 out of 9) of the area of Jerry's rhombus, which has an area of 135 square inches.

The base of Charlene's rhombus is 5 inches and the height is 3 inches, giving it an area of 15 square inches.

Jerry's rhombus has a base of 15 inches and a height of 9 inches, so its area is given by:

Area of Jerry's rhombus = base × height = 15 inches × 9 inches = 135 square inches.

Now, Charlene's rhombus has a base and height that are 1/3 the base and height of Jerry's rhombus. Therefore:

Base of Charlene's rhombus = (1/3) × 15 inches = 5 inches.

Height of Charlene's rhombus = (1/3) × 9 inches = 3 inches.

The area of Charlene's rhombus can be calculated as:

Area of Charlene's rhombus = base × height = 5 inches × 3 inches = 15 square inches.

To compare the areas of the two rhombuses:

Area of Charlene's rhombus / Area of Jerry's rhombus = 15 square inches / 135 square inches.

Simplifying the fraction, we get:

Area of Charlene's rhombus / Area of Jerry's rhombus = 1/9.

Therefore, the area of Charlene's rhombus is 1/9 (or 1 out of 9) of the area of Jerry's rhombus.

To learn more about the rhombus;

https://brainly.com/question/12665650

#SPJ1

Answer:

41

Step-by-step explanation:

b^2 -2ac

Let  a=4  b=3  c=-4

( 3)^2 -2 (4) (-4)

Exponents first

9 - 2 (4) (-4)

Multiply

9 + 32

41

Answer:

41

Step-by-step explanation:

b^2 - 2ac                plug in the values

3^2 -2(4)(-4)             start with the exponent (remember PEMDAS)

9  -2(4)(-4)                start multiplying from left to right

9  -8(-4)                    multiply

9 + 32                       add

41                              that's your answer :)  

Answer:

72

Step-by-step explanation:

This shape is a prism; it's a 3-D shape with 6 sides. Basically, it's a box.

All 6 sides are rectangles.

Surface area means that we'll find the area of all 6 rectangles and add them up.

There's a front and back, left and right, and a top and bottom.

The area of a rectangle is length×width or base×height.



The front and back are identical.

Area = length×width

Area = 6×3 = 18

Since the front and back are the same, two of the rectangles have area = 18.



The left and right are the same:

Area = 3 × 2

Area = 6

Two faces have area = 6.

The top and bottom are the same.

Area = 6 × 2

Area = 12

Again, two faces have area = 12.

To find the total surface area, add up all 6 areas.

A =18+18+6+6+12+12

A = 72

Answer:

46.80

Step-by-step explanation:

because 45/4%=1.80 and 45+1.80=46.80

Answer: John is 29 years old and Jane is 36 years old.

Step-by-step explanation:

There are many parts to this problem, so let's start by defining John as x and Jane as y.

We know that the sum of their age 10 years ago was 55, which gives us x+y-10=55. The reason we put -10 is because of 10 years ago. If you think about it in terms of now, 10 years back is 55, so now they would be 65 years old. So we can have either x+y-10=55 or x+y=65. For simplicity, I will use x+y=65.

We also know that John is 7 years younger than Jane, which gives x=y-7.

Luckily, we have x defined for us, so we can directly substitute that into our equation.

\((y-7)+y=65\)         [combine like terms]

\(2y-7=65\)                [add both sides by 7]

\(2y=72\)                      [divide both sides by 2]

\(y=36\)

Now we know that y=36, we can plug that into either equations to find x.

\(x+36=65\)                [subtract both sides by 36]

\(x=29\)

This concludes that John is 29 years old and Jane is 36 years old.

The equation of the tangent line at x=0 is y = x.

To find the equation of the tangent line at the given value of x, we need to find the derivative of the function y with respect to x and evaluate it at x=0.

Taking the derivative of y=∫[0 to x] sin(2t^2+π/2) dt using the Fundamental Theorem of Calculus, we get:

dy/dx = sin(2x^2+π/2)

Now we can evaluate this derivative at x=0:

dy/dx |x=0 = sin(2(0)^2+π/2)

        = sin(π/2)

        = 1

So, the slope of the tangent line at x=0 is 1.

To find the equation of the tangent line, we also need a point on the line. In this case, the point is (0, y(x=0)).

Substituting x=0 into the original function y=∫[0 to x] sin(2t^2+π/2) dt, we get:

y(x=0) = ∫[0 to 0] sin(2t^2+π/2) dt

      = 0

Therefore, the point on the tangent line is (0, 0).

Using the point-slope form of a linear equation, we can write the equation of the tangent line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line.

Plugging in the values, we have:

y - 0 = 1(x - 0)

Simplifying, we get:

y = x

So, the equation of the tangent line at x=0 is y = x.

Learn more about Fundamental Theorem of Calculus here:

brainly.com/question/30761130

#SPJ11

Step-by-step explanation:

they are similar by AA .

plz mark my answer as brainlist plzzzz . hope this will be helpful to you.

Answer:

i think it is 24

i think it is Step-by-step explanation:

Answer:

The players club is playing with the players

Step-by-step explanation:

give me a good Answer to my Question

What is the scale factor of this dilation? a:1/2 b:2/3 c:3/4 d:3/2

The length of a piece that can be cut from the three parts to obtain a whole number of tape from each part is 1.

To find the length of a piece that can be cut from the three parts to obtain a whole number of tape from each part, find the greatest common divisor (GCD) of the lengths of the three colored sections: white, red, and blue.

First, let's convert the lengths to improper fractions:

White: 7 and 3/4 = (4 * 7 + 3)/4 = 31/4

Red: 6 and 1/3 = (3 * 6 + 1)/3 = 19/3

Blue: Remainder = Total Length - (White + Red)

= 20 - (31/4 + 19/3)

= 80/4 - 31/4 - 57/3

= (80 - 31 - 76)/12

= 23/12

Now, the three lengths as fractions: 31/4, 19/3, and 23/12.

To find the GCD, convert the fractions to a common denominator. The common denominator for 4, 3, and 12 is 12.

White: (31/4) x (3/3) = 93/12

Red: (19/3) x (4/4) = 76/12

Blue: 23/12 (already in terms of 12)

Now, the lengths exist as fractions with a common denominator: 93/12, 76/12, and 23/12.

The GCD of these fractions can be found by determining the GCD of the numerators: 93, 76, and 23.

GCD(93, 76, 23) = 1

Therefore, the length of a piece that can be cut from the three parts to obtain a whole number of tape from each part is 1.

learn more about length: https://brainly.com/question/28108430

#SPJ1

Answer:
Cluster : 60,61,62,63
Gaps: 64,65 , 69,70
Outlier: 71
This is what I learned so don't blame me please!

Step-by-step explanation:

Cluster is numbers all on one side. Outlier can be the largest number or lowest. Normally the alone one.

Firstly we will analyze the question statement to determine the best possible answer.

So, the statement tells us about a person named Natalie,, the owner of an App designed for teenagers. Currently, the New Mindfulness app has One thousand two hundred and sixty-two downloads. Natalie sets a target to take her App downloads to double every month.

We are expected here to provide her with the best possible exponential equation to make her achieve the set goal.

We can use two variables for our exponential equation:

y for the number of downloads.

And x for the months.

We can use any value (Whole numbers, decimals, or fractions) in our exponential equation.

Now while keeping in mind all the necessary details, we can make the exponential equation as below:

Y= 1262 (2 x b) ^ x

Where Y are the downloads

X= 1 month or 30 days

By putting the values:

Y=1262 (2) ^ 1 month

Y=2524 after one month

So, the total number of downloads will double using the above exponential equation.

The pictures below show a relationship between the number of downloads Y and the month X.

More problems related to the exponential equations are solved in the link below.

https://brainly.com/question/15269424?referrer=searchResults

#SPJ4

Answer: 1262(2)^x

Step-by-step explanation:

The probability of drawing a yellow marble on the next draw is 13/48, which is option A, 13%.

The probability of drawing a yellow marble in the next draw depends on whether the drawing process is with or without replacement.

If the drawing process is with replacement, meaning that the marble is put back into the bag after each draw, then the probability of drawing a yellow marble remains the same at 13/48.

If the drawing process is without replacement, meaning that the marble is not put back into the bag after each draw, then the probability of drawing a yellow marble changes. After 48 draws, there are 35 white marbles and 13 yellow marbles left in the bag.

Therefore, the correct answer is A) 13%.

Learn more about probability at: https://brainly.com/question/13604758

#SPJ1

Answer:

7.5 for 6 pounds

Step-by-step explanation:

The above question is a mathematical proof of the relationship between Lines and angles related to a Rhombus. See the proof below.

We know,

A Rhombus is a parallelogram with four sides (that is a quadrilateral). It's sides however are all of equal length.

we have,

∠DEC ≅ ∠BFC  Reason = All Right Angles with Equal dimensions are congruent.

∠C ≅ ∠C  Reason = It is the same angle for the two Right angles above which are congruent, hence Reflexive Property.

Δ DEC ≅ Δ BFC  Reason = Angle Angle Side. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

 ≅   Reason = The corresponding parts of congruent triangles are congruent. Also, it is a parallelogram with all congruent sides.

ABCD is a Rhombus Reason = Its sides are all congruent.

Learn more about Rhombus at;

brainly.com/question/20627264

#SPJ1

complete question:

Given: ABCD is a parallelogram, FC is congruent to EC, DE bisects BC and BF bisects DC Prove: ABCD is a rhombus

The probability that a randomly selected point within the circle falls in the red shaded area is 15.9%

The radius is given s:

r = 4 cm

So, the area of the triangle is

A1 = 0.5r^2

Similarly, the area of the circle is

A2 = πr^2

The probability that a randomly selected point within the circle falls in the red shaded area is

P = A1/A2

This gives

P = 0.5r^2/πr^2

Evaluate

P = 15.9%

Hence, the probability that a randomly selected point within the circle falls in the red shaded area is 15.9%

Read more about probability at:

https://brainly.com/question/24756209

#SPJ1

The pair of lines perpendicular to RS are EA and FG.

A flat surface on which a straight line joining any two points on it would wholly lie is known as a plane.

What is plane?

A plane is a point, a line, and three-dimensional space's equivalent in two dimensions.

Main Body:

Given

E,F and G are on plane X. R and S are in both planes X and Y. EA and FG are parallel. AE and FG are vertical lines and are present on plane X. RS is present at the intersection of the 2 planes.

Explanation:

The lines which together could be perpendicular to RS are EA and FG.

We have to first draw both the planes according to the given information in question.

X is a vertical plane so draw a plane vertical on the horizontal plane that is Y plane. Now plot A and F And G in X plane and R,S in such a way that they  are in both plane so they will be at the intersection of both the planes. Now draw lines from A and F to form lines EA and FG.

Hence we can observe that lines EA and FD are perpendicular on line RS.

To learn more about plane : visit

https://brainly.com/question/28247880

#SPJ4

Answer:

35 months

Step-by-step explanation:

Given that,

You deposit a total of $780 in 1 year i.e. in 12 months

We need to find how many months does it take for you to deposit $2275.

$780 in 12 months

1$ in \(\dfrac{12}{780}\ \text{months}\)

$2275 in,

\(\dfrac{12}{780}\times 2275\ \text{months}\\\\=35\ \text{months}\)

Hence, it will take 35 months to deposit $2275.

Answer:

I think its 30 meters. The bottom rectangle is 21 Meters and the top square is 9 Meters

A unit rate is about finding the quantity of one unit at a rate of one of another given unit.

3.6 pounds of ground beef is needed to make 10 hamburgers.

Option D is the correct answer.

A unit rate is about finding the quantity of one unit at a rate of one of another given unit.

We have,

Recipe:

25 hamburgers = 9 pounds of ground beef.

Divide both sides by 25.

1 hamburger = 9/25 pounds of ground beef.

Now,

The number of pounds of ground beef to make 10 hamburgers:

1 hamburger = 9/25 pounds of ground beef

Multiply 10 on both sides.

10 hamburgers = 10 x 9/25 pounds of ground beef

10 hamburgers = 3.6 pounds of ground beef.

Thus,

3.6 pounds of ground beef is needed to make 10 hamburgers.

Learn more about unit rates here:

https://brainly.com/question/28394073

#SPJ2

AB = 3

The area of the square ABCD

= (3)^2 square units

= 9 square units.

The answer is 9 square units

We can claim that after answering the above question, the  This function would simulate the car's resale value if it depreciated at a rate of 15% each year.

In mathematics, a function is a relationship between two sets of numbers in which each member of the first set (known as the domain) corresponds to a single element in the second set (called the range). In other words, a function takes inputs from one set and produces outputs from another. Inputs are commonly represented by the variable x, while outputs are represented by the variable y. A function can be described using an equation or a graph. The equation y = 2x + 1 represents a linear function in which each value of x yields a distinct value of y.

1.1) Both Kala and Remy are incorrect. The given function, \(p(x) = 30,000(0.68)^x\), models the resale value of an automobile after x years, with a starting value of $30,000. The function's exponent x reflects the number of years since the car was purchased, and the base 0.68 is the percentage of the original value that remains after each year.

1.2) If the car's value fell by 15% per year, the function would be\(p(x) = 30,000(1 - 0.15)^x\). This means that the car loses 15% of its worth each year, leaving 85% of the value. This function would simulate the car's resale value if it depreciated at a rate of 15% each year.

To know more about function visit:

https://brainly.com/question/28193995

#SPJ1

The probability of this is (1/6) x (3/6) or 1/12. So, the total probability is 3/36 + 1/12, which simplifies to 1/6.

To find the probability that the sum of two numbers rolled is greater than 3, given that the sum is not greater than 5, we need to first find the probability of the sum being less than or equal to 5. This can be done by finding the probability of rolling a 2, 3, 4 or 5 on the two dice. This probability is 4/36 or 1/9. Now, to find the probability that the sum is greater than 3, given that the sum is not greater than 5, we need to use Bayes' theorem. This gives us (probability of sum>3 and sum<=5)/ (probability of sum<=5), which is (2/36)/(4/36) or 1/2.

The probability that one of the numbers is a 6 and the sum of the two numbers is an odd number can be found by considering the cases where the other number is odd or even. If the other number is odd, then the sum will be even and the probability is 3/36. If the other number is even, then the sum will be odd only if the other number is 1, 3 or 5.

To know more about probability visit:-

https://brainly.com/question/31828911

#SPJ11

Answer:

24hr/1dy

Step-by-step explanation: