the larger leg of a right triangle is 7cm more than the smaller leg the hypotenuse is 17cm find each leg

The area of the bigger solid is  67.24 cm².

Assume the smaller shape has a length of 2x and a width of 2y. The larger shape would then have 5x length and 5y width.

Because the area of a rectangle is the product of its length and width, the area of the smaller shape is:

Area of smaller shape = 2x * 2y = 4xy

We know that the similar shapes have an area of 78 cm2. As a result, we can write:

4xy + larger area = 78

(larger shape area) / (smaller shape area) = (linear scale factor)²

Substituting the values from the problem yields:

(larger shape area) / (4xy) = (5/2)2 = 25/4

When we multiply both sides by 4xy, we get:

larger shape area = (25/4) * 4xy = 25xy

Now we can plug the expression we discovered for the area of the smaller shape into the equation we found earlier:

4xy + 25xy = 78

29xy = 78

xy = 78/29

Substituting this xy value into the expression we discovered for the area of the larger shape yields:

larger shape area = 25xy = 25 * (78/29) = 67.24 cm2 (rounded to two decimal places)

As a result, the larger shape has an area of approximately 67.24 cm2.

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Answer:

m = -4

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 Points (4,7) (5,3)

We see the y decrease by 4 and the x increase by 1, so the slope is

m = -4

Answer:

-4

Step-by-step explanation:

because the slope goes down by 4 according to the table, from 7 to 3 to -1 to -5. hope that makes sense.

The probability that X takes the value 1 is 1/4 and the probability that X takes the value 2 is 1/12.

The given CDF of a random variable X is F(X)=-*- on the support of X, where the support of X is x = 1,2,3,... The task is to determine P(X = 1) and P(X = 2).

To find P(X = 1), we need to find the probability that X takes the value 1. From the given CDF, we can see that F(1) = 1/4. Therefore, P(X = 1) = F(1) - F(1-) = 1/4 - 0 = 1/4.

To find P(X = 2), we need to find the probability that X takes the value 2. From the given CDF, we can see that F(2) = 7/12. Therefore, P(X = 2) = F(2) - F(2-) = 7/12 - 1/2 = 1/12.

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Question:-

The CDF Of A Random Variable X Is Given The Function F(X)=-*- On The Support Of X, Where The Support Of X Is X = 1,2,3,... Determine P(X = 1) And P(X = 2). 3x + X

Answer:

6188 ways

Step-by-step explanation:

there ate 5 objects to be choosen and there is no replacement of the object therefore you got

17 choices for the first selection of the object and 16 objects for the selection of the second object and so on until you get 13 objects for the last selection

totally you have 5 selections also arrangement does not matter there fore you have 17!/12!5! which is 6188

note we used 5! cause there are 5 placed objects and 12! are unplaced objects

note

that you have used one so you have to deduct one every time you use one

Answer:

The total labor charges for the job are P3,500.

Step-by-step explanation:

To find the total labor charges for a job that takes 2 1/2 hours, we need to look at the labor charges for each hour and a half-hour fraction and add them up.

For the first hour, the charges are P1,200. For the second hour, the charges are P1,400. For the third hour (the half-hour fraction), the charges are P1,800 / 2 = P900.

So, the total labor charges for 2 1/2 hours of work are

P1,200 + P1,400 + P900 = P3,500

Therefore, the total labor charges for the job are P3,500.

Sure! The general term of a sequence is a formula which describes the nth term of the sequence. In this case, the pattern is that each term is increased by 3 when compared to the previous term. This pattern can be expressed as a formula - an=a1+(n-1)d, where a1 is the first term, n is the term number and d is the common difference.

For the sequence given -2,1,4,7

a1=-2

n=4

d=3

Substituting these values in the formula will give us the general term of the sequence an = -2 + 3(n-1)

Hence, the general term of the sequence -2,1,4,7 is an = -2 + 3(n-1).

Answer:

11

Step-by-step explanation:

[tex]61 {}^{2} - {60 }^{2} = 121[/tex]

[tex] \sqrt{121} = 11[/tex]

Here is the stem and leaf plot:

5  4

6   0, 1, 2, 2

7    1, 2, 4, 6, 8

8    2, 3, 4,  6, 7,

9   0, 2, 5, 5, 9

The range is 45.

A stem-and-leaf plot is a table that is used to display a dataset. A stem-and-leaf plot divides a number into a stem and a leaf. The stem is the tens digit and the leaf is the units digit. For example, in the number 54, 5 is the stem and 4 is the leaf.

Range is used to measure the variation of a dataset by finding the difference between the highest number and the lowest number.

Range = highest value - lowest value

99 - 54 = 45

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Answer: C

Step-by-step explanation:

The correct answer is C.

The slope of the line represents the hourly wage, so Hunter's wage is $35 an hour, as given in option A and B. However, the y-intercept of the line represents the starting pay or the pay for zero hours worked. In this case, the y-intercept is 25, which means Hunter received $25 even if he did not work any hours. Hence, option C is correct as it states that Hunter's wage is $25 an hour, but it appears that he received no signing bonus.

The given statement "Star clusters with lots of bright, blue stars of spectral type O and B are generally younger than clusters that don't have any such stars." is True. The reason for this is that O and B stars are short-lived and burn through their fuel quickly.

The reason for this is that O and B stars burn through their fuel quickly, causing them to exhaust their nuclear fuel and end their lives in a relatively short period, typically within a few tens of millions of years.

On the other hand, stars of lower mass and cooler temperatures, like G and K type stars like our sun, have longer lifetimes and take billions of years to exhaust their nuclear fuel.

Therefore, clusters without any bright, blue stars are likely to have evolved for longer periods, allowing these short-lived stars to have already expired.

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Instead of 2.00 as mentioned in the question, the semester GPA is 1.38. Please double-check your calculations or provide more details if you made an error when reporting your grades or computing your GPA.

Students must devote approximately 135 hours (45 x 3) of class, instructional, and independent time to a three credit unit course. Students who enroll in a course for four credit hours must dedicate around 180 (45 x 4) hours to it, split between in-class and out-of-class work.

You must first translate each letter grade using the common 4.0 scale into its equivalent numerical number before you can determine your semester GPA:

A = 4.0

B = 3.0

C = 2.0

D = 1.0

F = 0.0

E = 0.0 (equivalent to F)

Then, you can use the formula:

(Total grade points) / GPA (total credit hours)

Using this formula, we can calculate your semester GPA as follows:

FYE 105: F (0.0) x 3 credit hours = 0.0 grade points

MAT 150: E (0.0) x 3 credit hours = 0.0 grade points

ENG 101: D (1.0) x 3 credit hours = 3.0 grade points

BIO 112: A (4.0) x 3 credit hours = 12.0 grade points

BIO 113: B (3.0) x 1 credit hour = 3.0 grade points

Total grade points = 0.0 + 0.0 + 3.0 + 12.0 + 3.0 = 18.0

Total credits earned is 13 (3 + 3 + 3 + 3 + 1)

GPA = 18.0 / 13 = 1.3846

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Answer:

It is a tangent

Step-by-step explanation:

A tangent is a straight line that brushes the circumference of a circle.

Answer:

D. 7/5

Step-by-step explanation:

In right triangle ABC with right angle C,

sinA = 4/5 = cosB

cosA = 3/5 = sinB

sinB + cosB = 3/5 + 4/5 = 7/5

Answer:

103%

Step-by-step explanation:

1.03/1 x 100% = 103%

To convert the decimal 1.03 into a percentage, you multiply it by 100 which gives you 103%, so 1.03 is equal to 103%.

To express 1.03 as a percentage, we need to multiply the decimal by 100.

This is because the word percent in terms of mathematics means 'per hundred'. So, 1.03 multiplied by 100 equals 103.

Hence, 1.03 expressed as a percentage is 103%.

Rewrite your decimal as a fraction with a denominator of 100 to change it into a percentage.

For example, 1.03 can be written as 103/100 which translates into 103% in percentage format.

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a) The probability the sum is 6 is equals to the 77/144.

b) The probability event that sum is 6 in case of both dice are 6 -sided is equals to the 5/36.

c) The probability event that sum is 6 in case of both dice are 4 -sided is equals to the 3/16.

d) The probability event that sum is 6 in case of one die is 4 -sided and one is 6 sided is equals to 5/24.

There are five fair dice in my pocket, three are 4-sided and two are 6-sided. Randomly select two of the dice, roll them, and record the sum. We have to determine the probabilities for different events. First, When two six-sided dice are rolled, total possible outcomes = 36

= {1,2,3,4,5,6}{1,2,3,4,5,6}

Similarly, When two four-sided dice are rolled, total possible outcomes = 16 = {1,2,3,4}{1,2,3,4}

Also, when one 4-sided and othe 6-sided faire dice are rolled, total possible outcomes = 24 = {1,2,3,4 } {1,2,3,4,5,6}

a) Let the event for sum is 6 be 'E'. The probability the sum is 6, P(E) = 5/36 + 3/16 + 5/24 = ( 20 + 27 + 30)/144

= 77/144

b) The probability that sum of the dice is 6 for both dice are 6 -sided = 5/36

c) Possible outcomes of occurrence of event E in case of both dice are 4 -sided = 3

The probability of occurrence of event E in case of both dice are 4 -sided, P(E)

= 3/16

d) Possible outcomes of occurrence of event E in case of one die is 4 -sided and one is 6 sided = 5

The probability one die is 4 -sided and one is 6 sided = 5/24

Hence, required probability is 5/24.

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The area is multiplied by 1/16 and the correct option is (a) The area is multiplied by 1/16.

When the radius of a circle is multiplied by 1/4, the effect on the area can be calculated using the formula A = πr², where A is the area and r is the radius. The new radius becomes (1/4)r, so the new area can be calculated by substituting (1/4)r for r in the original formula. Simplifying this expression, we get A' = π((1/4)r)² = (1/16)πr². This shows that the area is multiplied by 1/16, so the correct answer is (a) The area is multiplied by 1/16.

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Complete question:

The radius of a circle is multiplied by 1/4. Which of the following describes the effect of this change on the area?

a. The area is multiplied by 1/16.

b. The area is multiplied by 1/4.

c. The area is multiplied by 1/8.

d. The area is multiplied by 4.

The point of intersection of the two lines is (-3.4, -1.2).

Step 1: The slope of a line passing through two points (x1,y1) and (x2,y2) can be found using the formula:

m = (y2-y1)/(x2-x1)

Using this formula, we can find the slope of the first line:

m1 = (−2−3)/(-5 -5) = −5/(-10) = 1/2

And the slope of the second line:

m2 = (−4−4)/(2 -(-6)) = -8/4 = -2

Step 2: Find the y-intercept of each line

The y-intercept of a line in slope-intercept form (y = mx + b) is the value of y when x=0. We can use one of the two given points on each line to find the y-intercept:

For the first line passing through points (5,3) and (−5,−2):

y = mx + b

3 = (1/2)(5) + b

b = 3 - 5/2

b = 1/2

So the first line can be written as y = 1/2x + 1/2

For the second line passing through points (−6,4) and (2,−4):

y = mx + b

4 = (-2)(−6) + b

b = 4 - 12

b = -8

So the second line can be written as y = -2x - 8

Step 3: Each line in slope-intercept form (y = mx + b):

First line: y = 1/2x + 1/2

Second line: y = -2x - 8

Step 4: To find the point of intersection of the two lines, we need to solve the system of equations. We can solve for x by setting the two right-hand sides equal to each other:

1/2x + 1/2 = -2x - 8

(x + 1)/2 = -2x - 8

x + 1 = -4x - 16

5x = -16 - 1

5x = -17

x = -17/5

x = -3.4

Now that we know x, we can find y by substituting x=10 into one of the two equations:

y = -2x - 8

y = -2(-3.4) - 8

y = - 1.2

Thus, the point of intersection of the two lines is (-3.4, -1.2).

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Answer: I got you!

Step-by-step explanation:

a) Sophie's distance is given by the formula: distance = rate × time. Therefore, her distance yesterday is s × t miles.

b) Rana's time is given by the formula: time = distance ÷ rate. Therefore, her time yesterday is m ÷ r hours.

c) Sophie's time is given by the formula: time = distance ÷ rate. Let's call the time Sophie waits for Rana "w". Then we have two equations:

Sophie's distance: s × (w + t) = 20

Rana's distance: r × (w + t) = 20 - m

We can solve for "w" by substituting the second equation into the first equation:

s × (w + t) = 20 - r × (w + t) + m

(s + r) × (w + t) = 20 + m

w + t = (20 + m) ÷ (s + r)

w = (20 + m) ÷ (s + r) - t

Therefore, Sophie waits for Rana for (20 + m) ÷ (s + r) - t hours.

d) Sophie's distance tomorrow is s × 3 miles, and Rana's distance tomorrow is r × 3 miles. Therefore, the difference in distance is (s - r) × 3 miles.

The area of the living room is 24.7 m², and the area of the game room is 37.05 m².

Area is the measure of the two-dimensional space occupied by a figure or an object. It is usually expressed in square units such as cm2, m2, or in2. It is used to measure the size of a figure or object, and can also be used to calculate the amount of material required for a project.

The area of a living room measuring 4.75 m by 5.2 m can be calculated using the formula A = l × w, where A is the area, l is the length and w is the width. In this case, A = 4.75 m × 5.2 m = 24.7 m².

To calculate the area of the game room, we must multiply the area of the living room by 1.5. Therefore, the area of the game room is 1.5 × 24.7 m² = 37.05 m².

The area of the living room is 24.7 m², and the area of the game room is 37.05 m².

The area of a room can be used to determine how much furniture can fit in the room or how much floor space is available for activities. Knowing the area of a room is also important for calculating the cost of painting, wallpapering, carpeting, and other flooring materials.

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Graph D of the given function has the smallest value for b.

As per name signifies, exponents are used in exponential functions. But take note that an exponential function does not have a constant as its base and a variable as its exponent. One of the following forms can be used for an exponential function.

f (x) = aˣ

y=f(x) >0

f(x)=abˣ , where a>0

So, f(x)=abˣ

When, b<1 f(x) decreases

When, b>1 f(x) increases and the larger the b the steeper the graph

So, graph of D is increasing and is steepest

So, graph D has the smallest value for b.

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Using ratios and proportionality, we can find that the length of the missing part is 18 units.

By comparing two amounts of the same unit and establishing the ratio, we can work out how much of one quantity is contained in the other. Two categories of ratios exist.

The part to whole ratio is one, and the part-to-part ratio is another category that exists. The part-to-part ratio illustrates the relationship between two separate entities or groupings.

Here,

Let the missing length be = x.

Given,

The upper segment is 24.

One part of it is 16.

So, the other part is = 24 - 16 = 8

Now as per the ratios,

16/36 = 8/x

⇒ x = 8 × 36/16

⇒ x = 18 units.

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If d is not a prime number and n^2 is divisible by d, it does not necessarily mean that n is also divisible by d, example is d = 6 and n = 3, where n^2 = 9 is divisible by 6, but n = 3 is not divisible by 6.

A prime number is a positive integer greater than 1 that has exactly two distinct factors: 1 and itself. For example, 2, 3, 5, 7, 11, 13, and 17 are all prime numbers.

If a number d is not prime, then it has at least one factor other than 1 and itself. Let's assume that d is not prime, and let p be a factor of d such that p is not equal to 1 or d. Then, by definition, p divides d evenly with no remainder.

Consider the case where d = 6 and n = 3.

Here, d is not a prime number, and n^2 = 9, which is divisible by d since 9 is a multiple of 6. However, n = 3 is not divisible by d = 6, as 6 does not divide 3 evenly.

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Answer:

7:42

Explanation: Since, the ratio was 4:24, it equals to 1:6, and the only one with a factor of 6 for the second number is C

Step-by-step explanation:

x = weeks

Yours    75 + 5x

Friend's 30 + 10x

When are they equal ?

75 + 5x     =     30 + 10x

45 = 5x

x = 9 weeks

The number of lionfish after 6 years will be 85,609. The recursive equation for [tex]f(n)[/tex] will be [tex]f(n) = 4242.42(1.65)^n - 1300n[/tex].

Consider the function:

[tex]y = a (1 \pm r)^x[/tex]

Where x is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.

lionfish are considered an invasive species, with an annual growth rate of 65%.

Then the equation will be

[tex]f(n) = P(1.65)^n[/tex]

[tex]\text{P = initial population}[/tex]

A scientist estimates there are 7,000 lionfish in a certain bay after the first year.

[tex]7000 = P(1.65)[/tex]

    [tex]P = 4242.42[/tex]

Then the equation will be

[tex]f(n) = 4242.42(1.65)^n[/tex]

The number of lionfish after 6 years will be

[tex]f(n) = 4242.42(1.65)^6[/tex]

[tex]f(n) = 85608.58[/tex]

[tex]f(n) \cong 85,609[/tex]

If scientists remove 1,300 fish per year from the bay after the first year.

Then the recursive equation for f(n) will be

[tex]f(n) = 4242.42(1.65)^n - 1300n[/tex]

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If we cοnsider (x, y) tο be a pοint οn the unit circle, we get:

[tex]x^2 + y^2 = 1[/tex] (because the pοint is οn the unit circle) (since the pοint is οn the unit circle)

All real numbers must be determined in such a way that:

tan(s) = y / x

The trigοnοmetric identity can be applied:

Tan is equal tο Sin / Cοs.

We thus have:

Y/X = Tan(S), Sin(S), and Cοs (s)

Using the identity cοs(s) + sin(s) = 1, we square bοth sides tο οbtain:

[tex](y/x)^2 = sin^2(s) / cos^2(s) = 1 - cos^2(s)[/tex]

Rearranging and applying the equatiοn x2 + y2 = 1 results in:

cοs2(s) equals 1 - (y/x).

[tex]^2 = x^2[/tex]

Given that (x, y) is in the first οr fοurth quadrant and that x is pοsitive, we can take the square rοοt tο get the fοllοwing result:

cοs(s) = ± x

Sο, s is determined by:

S equals arccοs(x) + n, where n is any pοsitive integer.

The range οf x's value is limited tο [-1, 1] because it is οn the unit circle. As a result, the values οf s are prοvided by:

S = arccοs(x) + n, where n is any pοsitive integer and x is within the range [-1, 1].

The pοssible values οf s in exact radian measure in [0, 2] are as fοllοws:

S = arccοs(-1) + = S = arccοs(1) = 0

S is equal tο arccοs(0) + n + (n + 1/2)

where any integer n is used.

As n can be any integer, the pοssible pοssibilities οf s are s = 0,, and (n + 1/2).

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Therefore, the answers are: (i) ZADB = 48.5 degrees, and (ii) ZEAO = 54 degrees.

An angle is a geometric concept that describes the amount of rotation between two intersecting lines or planes. It is defined as the figure formed by two rays with a common endpoint, called the vertex. The two rays are called the sides of the angle, and they can be measured in degrees or radians.

In the degree measurement system, a full rotation is 360 degrees, and an angle that is one quarter of a rotation (90 degrees) is called a right angle. Angles that are less than 90 degrees are called acute angles, while angles greater than 90 degrees but less than 180 degrees are called obtuse angles. An angle that measures exactly 180 degrees is called a straight angle, and an angle that measures greater than 180 degrees, but less than 360 degrees is called a reflex angle.

by the question.

ZOAB + ZEDA = 32 + 15 = 47 degrees. Since these two angles are opposite each other, they must add up to 180 degrees (straight angle) and therefore, ZAOB + ZEDC = 180 - 47 = 133 degrees.

Angle D is given as 37 degrees, and since ZEDC is a straight line, ZEDD = 180 - 37 = 143 degrees.

ZADB = ZAOB + ZOAB + BAD. Since ZAOB + ZOAB = 180 - ZEDC = 180 - 133 = 47 degrees, we have ZADB + BAD = 37 + 47 = 84 degrees. Also, BAD is an exterior angle of triangle ABD, so it is equal to the sum of the two opposite interior angles, which are ZADB and ABD. Therefore, ZADB + ABD + BAD = 180 degrees. Substituting the value of BAD and simplifying, we get ZADB = 48.5 degrees.

ZEAO = ZEDC - ZEDA - ZOAD. We already know ZEDC and ZEDA, so we need to find ZOAD. Since ZOAB and ZOAD are opposite each other, they must add up to 180 degrees. Also, ZOAB is equal to half the central angle ZODB (since it subtends the same arc), which is equal to 2ZOAD (since it is an inscribed angle subtended by the same arc). Therefore, we have ZOAB + ZOAD = 180 and ZOAB = ZOAD/2. Substituting the value of ZOAB from the given information, we get ZOAD = 64 degrees. Substituting all the values, we get ZEAO = 54 degrees.

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Answer: C

Step-by-step explanation:

For any function, a value plugged in (x) cannot have more than 1 outcome (y). C states that when x = 10, y has 2 values; 30 and 35. This means C is not a function.

The relation between a point and a circle is relative to the location of the point relative to the circumference of the circle, which can be inside, at the circumference, or outside.

The relationship between a point and a circle can be described as follows:

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