Pls help solve these three

Answer:

5

Step-by-step explanation:

Answer:

The Answer is a

Step-by-step explanation:

General equation of direct variation: y = kx, where k is the constant of proportionality. y = 5x, so 5 is the constant of proportionality

Answer:

(7x+3) (x-1)

hope this helps!!:)

Step-by-step explanation:

Answer:

We use similar triangles to get

16

15

25

brainliest pls

Answer:

I'm not sure if it is the correct answer but I believe it is 14

Answer:

14 i think

Step-by-step explanation:

The current market price for the bond is $870 the yield to maturity is 14.13%

The approximate yield to maturity of this bond is 11.25%, which is above the annual coupon rate of 10% by 1.25%. You can then use this value as the rate (r) in the following formula: C = future cash flows/coupon payments. r = discount rate (the yield to maturity)

knowing that:

the formula is:

\(P = (C / (1 + r))^1 + (C / (1 + r))^2 + ... + (C + F) / (1 + r)^n\)

Putting the values:

\($870 = (130 / (1 + r))^1 + (130 / (1 + r))^2 + ... + (130 + 1,000) / (1 + r)^13\)

Using the math we find that the percentage is  approximately 14.13%;

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Answer:

Mean = 59.1, Median = 61

(there might have been a mistake in calculation (a lot of numbers!))

Step-by-step explanation:

The sample size is 40,

Now, the formula for the mean is,

Mean = (sum of the sample values)/(sample size)

so we get,

\(Mean = (49+63+78+22+41+39+75+61+63+65+58+37+45+52+81+75+78+72+68+59+72+85+63+61+75+39+41+48+59+55+61+25+61+52+58+71+75+82+49+51)/40\\Mean = 2364/40\\Mean = 59.1\)

To find the median, we have to sort the list in ascending (or descending)order,

we get the list,

22,25,37,39,39,41,41,45,48,49,

49,51,52, 52,55,58, 58, 59, 59, 61,

61, 61, 61, 63, 63, 63, 65, 68, 71, 72,

72, 75, 75, 75, 75, 78, 78, 81, 82, 85

Now, we have to find the median,

since there are 40 values, we divide by 2 to get, 40/2 = 20

now, to find the median, we takethe average of the values above and below this value,

\(Median = ((n/2+1)th \ value + (n/2)th \ value )/2\\where, \ the\ (n/2)th \ value \ is,\\n/2 = (total \ number \ of \ samples) /2\\n/2=40/2\\(n/2)th = 20\\Hence\ the (n/2)th \ value \ is \ the \ 20th \ value\)

And the (n+1)th value is the 21st value

Now,

The ((n/2)+1)th value is 61 and the nth value is 61, so the median is,

Median = (61+61)/2

Median = 61

Answer:

Bicycle : $117

Tricycle : $87

Unicycle : $183

Step-by-step explanation:

Write a system of equations:

x + 3y + z = 561

7x + y = 906

2x + 7y + 5z = 1758

Where:

x = price of bicycle

y = price of tricycle

z = price of unicycle

Solve for x, y, and z.

It would take Fran and Denise (working together) approximately \(\frac{24}{7}\) hours to paint the living room.

To solve this problem, we can use the concept of "work rates."

Let's find out how much work Fran and Denise can do individually in one hour.

If Fran takes 6 hours to paint the living room alone, her work rate is \(\frac{1}{6}\) of the room per hour \((\frac{1 room}{6 hours } = \frac{1}{6}room/hour )\).

Similarly, if Denise takes 8 hours to paint the living room alone, her work rate is \(\frac{1}{8}\) of the room per hour \((\frac{1 room}{8 hours } =\frac{1}{8}room/hour )\).

When they work together, their work rates are additive.

So, their combined work rate would be:

\(\frac{1}{6} room/hour+\frac{1}{8} room/hour\)

\(=(\frac{4}{24} )room/hour + (\frac{3}{24} )room/hour\)

\(=\frac{7}{24} room/hour\)

This means that working together, Fran and Denise can paint \(\frac{7}{24}\) of the living room in one hour.

To determine the total time required for them to paint the entire room, we can invert their combined work rate:

\(\frac{(1 room) }{(\frac{7}{24}room/hour) } =\frac{24}{7}hour\)

Therefore, it would take Fran and Denise (working together) approximately \(\frac{24}{7}\) hours to paint the living room.

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Answer:

y = -x + 8

Step-by-step explanation:

First, plug in the slope.

y = mx + b

y = -1x + b

y = -x + b

Then, plug in the point.

7 = -(1) + b

7 = -1 + b

8 = b

Answer:

we need to add the money Andy earned to the negative balance he had. So, we have:

-$45 + $30 + $25 = $10

Therefore, Andy now has $10 in his checking account.

Answer:

Andy now has $10 in his checking account.

Step-by-step explanation:

Andy starts the week with -$45 in his checking account. When he gets paid $30 for mowing the grass and $25 for vacuuming the house, his total earnings for the week are:

$30 + $25 = $55

To find out how much money he now has in his checking account, we need to add his earnings to his starting balance of -$45. Adding a negative number is the same as subtracting a positive number, so we can write this as:

-$45 + $55 = $10

Therefore, Andy now has $10 in his checking account.

Answer:

Yes, multiplication and division are inverse. yes, for the inverse equation. Yes, addition and subtraction are inverse. yes, for the inverse equation.

Step-by-step explanation:

EXAMPLES.

E.g 21 = 3x division

3x x = 21 inverse

E.g 5+x =8 addition

5=8-x inverse.

Thank you! :)

Solution:

Given:

Part A:

Part B:

The identities used in student A verification are

Answer:

I just solved this as well and I got 102m as well.

Step-by-step explanation:

56 and -56 cancek eachother out. 57m + 45m can be added since they have the same variable. 57 + 45 is 102. So the answer is 102m.

Answer:

102

Step-by-step explanation:

The percent change in Pilar's shell collection from the beginning of the day to the end is,  22.5%

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

Given that,

Pilar has 40 shells in her collection.

She collects 6 more shells in the morning and 3 more shells in the afternoon.

The percent change in Pilar's shell collection from the beginning of the day to the end = ?

At the beginning of the day, Pilar has 40 shells.

In the morning, she collects 6 more shells, bringing her total to

= 40 + 6

= 46 shells.

Then, in the afternoon, she collects 3 more shells, bringing her total to

=46 + 3

= 49 shells.

To find the percent change in Pilar's shell collection from the beginning of the day to the end, we can use the formula:

percent change = (final value - initial value) / initial value * 100%

Plugging in the values we have:

percent change = (49 - 40) / 40 x 100%

percent change = 9 / 40 x 100%

percent change = 22.5%

Therefore, there is a 22.5% increase in Pilar's shell collection from the beginning of the day to the end.

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Answer:

44/3

Step-by-step explanation:

Let A be the line joining the vertices (0, 1) and (1,2) while B be the equation of the line joining (1, 2) and (4, 1).

The equation of a line joining points \((x_1,y_1) \ and\ (x_2,y_2)\ is:\\\\\)

\(y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\)

The equation of line A joining (0, 1) and (1,2) is:

\(y-1=\frac{2-1}{1-0} (x-0)\\\\y-1=x\\\\x=y-1\)

The equation of line D joining (1, 2) and (4,1) is:

\(y-2=\frac{1-2}{4-1} (x-1)\\\\y-2=-\frac{1}{3} (x-1)\\\\3y-6=-x+1\\\\x=-3y+7\)

Therefore the change in y is: 1 ≤ y ≤ 2, while change in x is: y-1 ≤ x ≤ -3y + 7. Hence the double integral is:

\(\int\limits^2_1\int\limits^{-3y+7}_{y-1} {4y^2} \, dx dy\\\\=4\int\limits^2_1\int\limits^{-3y+7}_{y-1} {y^2} \, dx dy\\\\=4\int\limits^2_1y^2dy[x]^{-3y+7}_{y-1} \\\\=4\int\limits^2_1y^2dy(-3y+7-(y-1))\\\\=4\int\limits^2_1y^2dy(-4y+8)\\\\=4\int\limits^2_1(-4y^3+8y^2)dy\\\\=4[-y^4+\frac{8}{3}y^3 ]^2_1\\\\=4(\frac{11}{3} )\\\\=\frac{44}{3 }\)

To answer this question, we need, first get the equations for the lines that enclosed the surface, and integrate according to the limits obtained from these equations give.

The solution is:

A = 44/3 square units  

Let´s call points:

P ( 0 , 1 )    Q ( 1 , 2 ) and R ( 4 , 1 )

The equation for the line between, P and R is:

y = 1

The equation for the line between, P and Q is:

Slope-intercept equation is  y = m×x + b

The slope   m₁ = ( 2 - 1 ) / ( 1 - 0 )    m₁ = 1

and the line passes over the point  x = 0  y = 1   ; then

1 = 0 +b           b = 1

y = x + 1            ⇒    x = y - 1  

The equation  for the line between Q and R is:

m₂ = ( 1 - 2 ) / ( 4 - 1)    m₂ = - 1/3

y = ( -1/3)× x + b

when x = 1    y = 2

2 = ( - 1/3)×(1) + b

2 + 1/3 = b

b = 7/3

y = - (x/3) + 7/3           ⇒  x = 7 - 3×y

The double  integral becomes:

A = 4×∫∫ y² dx dy          ⇒   A = 4 ×∫₁² y²dy ∫dx  | (y - 1 ) y ( 7 - 3y)

A = 4×∫₁² y²dy  × x |  ( y - 1 ) y ( 7 - 3y)

A = 4 ×∫₁² y²dy  × [ 7 - 3×y - ( y - 1 )]

A = 4 ×∫₁² y²dy  × (8 - 4×y )      ⇒     A = 4 ×∫₁² (8×y² - 4×y³ ) dy

A = 4 × [ (8/3)×y³ - y⁴ | ₁²

A = 4 × [ 64/3 - 16 - (8/3) + 1 ]

A = 4  × ( 56/3 - 15 )

A = 4  × ( 56 - 45 /3)

A = 4 × 11/3

A = 44/3 square units

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Answer: 304.8 milimeter

Step-by-step explanation:

Explanation:

Tangent lines touch the circle at exactly one point.

The solution of the given equation are; (x + 8)(x − 9)

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

We have been given the quadratic equation as;

x² − x − 72

Solving;

x² − (9-8)x − 72

x² − 9x +8x− 72

The factors are;

(x + 8)(x − 9)

Therefore, the solution of the given equation are; (x + 8)(x − 9)

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a .

Apply the slope formula (m)

Use two points from the graph:

(x1,y1) = (2,4)

(x2,y2) = (5,13)

Replace in the formula:

b. equation of the line:

y=mx+b

where:

m= slope

b= y-intercept

Replace (x,y) by a point from the graph, for example (2,4) and solve for b

4 = 3(2)+b

4=6+b

4-6 =b

-2=b

y= 3x-2

c. value of c

Replace the y coordinate (10) ans solve for x:

10= 3x-2

10+2=3x

12 =3x

12/3 = x

4=x

c=4

d. replace (0,2) in the equation and check if the equality remains:

y=3x-2

2 = 3(0)-2

2=-2

2 is not equal to -2.

So, (0,2) is no on this line.

It will take 150 minutes for the two containers to have the same amount of water.

To find the number of minutes it will take for the two containers to have the same amount of water, we need to use the following formula:

m = |A - B| / (a - b)

where m is the number of minutes, A is the initial amount of water in Container A, B is the initial amount of water in Container B, a is the rate at which water is being added to Container A, and b is the rate at which water is being drained from Container B.

In this case, the initial amount of water in Container A is 300 liters, the initial amount of water in Container B is 900 liters, the rate at which water is being added to Container A is 6 liters per minute, and the rate at which water is being drained from Container B is 2 liters per minute. Substituting these values into the formula, we get:

m = |300 - 900| / (6 - 2)

m = |-600| / 4

m = 600 / 4

m = 150 minutes

Therefore, it will take 150 minutes for the two containers to have the same amount of water.

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Step-by-step explanation:

I'm going to lay this out in a chart so it's a little easier to see:

F(x) = f(g(x))

x | f (x) | f ' (x) | g (x) | g ' (x)

--------------------------------------

-2 | 8 | 4 |

5 | | 3 | -2 | 6

Remember the chain rule, which says

(f (g (x))) ' = g ' (x) f ' (g (x))

When they ask for F ' (5), they are asking for (f (g (x))) ' when x = 5.

Using the chain rule, that's

F ' (5) = g ' (5) f ' (g (5))

We can simplify using the numbers provided.

F ' (5) = (6) f ' (-2)

F ' (5) = (6) (4)

F ' (5) = 24

I hope that helps!

The required simplified solution of the F'(5) is 24

Given that,
F(x) = f(g(x)), where f(-2) = 8, f'(-2) = 4, f'(5) = 3, g(5)=-2, gʻ(5) = 6..
To determine F'(5),

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
F(x) = f(g(x))
Now,
F'(x) = (f (g (x))) '
Following the chain rule
F'(x) = g ' (x) f ' (g (x))
Now,
x = 5
F'(5) = g'(5)f'(g(5))
substitute the value in the above equation,
F'(5) = 6 × f'(-2)
F'(5) = 6 × 4
F'(5) = 24

Thus, the required simplified solution of the F'(5) is 24.

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Answer:

B. 9/20\(\pi\)

Step-by-step explanation:

the circumference is 2\(\pi\)r. Since the radius is one, that would be 2\(\pi\).

81/360=0.225, or 22.5% of the circumference.  22.5% of 2\(\pi\) is 0.45\(\pi\).  0.45=9/20, so the answer is B.

CHECK: 2\(\pi\) = 6.283

6.283x0.225=0.14137, or 9/20\(\pi\)

The expression is given as:

According to the question:

Substitute the values of x and y into the given expression:

The logarithmic function f(x) = a·log₃(x - 4), passing through the points (13, 7), has the values;

5 a. The value of a is 3.5

b. Please find attached the graph of the function, f(x) = 3.5·log₃(x - 4), created with MS Excel

A logarithmic function is a function that contain and involves logarithm operation and it is the inverse of an exponential  function

The function is f(x) = a·log₃(x - 4),

x > 4 and a > 0

The coordinates of a point on the graph of the function, f is A(13, 7)

5 a. The value of a can be found by plugging in the value of (13, 7) = (x, f(x)), as follows

f(13) = 7 = a·log₃(13 - 4) = a·log₃9 = a·log₃3²

7 = a·log₃3²

7 = 2·a·log₃3 = 2·a·1 = 2·a

2·a = 7

a = 7 ÷ 2 = 3.5

a = 3.5

5 b. The coordinates of the x-intercept of the graph = (5, 0)

The equation of the function is;

f(x) = 3.5·log₃(x - 4)

A third point on the graph is given when f(x) = 14 as follows;

f(x) = 14 = 3.5·log₃(x - 4)

log₃(x - 4) = 14 ÷ 3.5 = 4

3⁴ = x - 4

x = 3⁴ + 4 = 85

Which gives the point, (85, 14)

Similarly, we have the point (31, 10.5), (7, 3.5)

Please find attached the graph of f(x) created with MS Excel

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The area of a shaded region is the amount of space it occupies

The measurement that is closest to the area of the shaded region is 19 square inches

Start by calculating the area of the big rectangle.

Assume the dimensions of the rectangle are 10 by 15 inches.

The area would be

\(A_1 =10* 15\)

\(A_1 = 150 in^2\)

Next, calculate the area of the small rectangle.

Assume the dimensions of the rectangle are 13 by 10 inches.

The area would be

\(A_2 =13* 10\)

\(A_2 =130 in^2\)

Next, calculate the difference between both areas

\(d = 150 - 130\)

\(d = 20\ in^2\)

19 is the closest to 20

Hence, the measurement that is closest to the area of the shaded region is 19 square inches (using the assumed values)

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Answer:

I think it c=4p

Step-by-step explanation:

I’m sorry if it wrong

Answer:

Below.

Step-by-step explanation:

0.1, 0.1003, 0.102, 0.11

Answer: 0

Explanation: Divide 2 and 11, and you get 2/11 and multiply that with 55 you get 10 and 10 - 10 equals 0! ^^

Here are some useful theorems and definitions for these problems:

1. Alternate interior angle theorem: when you have 2 parallel lines with a transversal passing through both of them,  the 2 alternate interior angles such as <3, <1 are equal.

2.Alternate exterior angles theorem: when you have 2 parallel lines with a transversal passing through both of them, the 2 alternate exterior angles such as <8 and <6 are equal

3. Corresponding angles theorem: when you have 2 parallel lines with a transversal passing through both of them, the 2 corresponding angles such as <8 and <1 are equal.

4.Same-side interior angles theorem: when you have 2 parallel lines with a transversal passing through both of them, the 2 angles on the same side interior, such as <4 and <1, adds up to 180 degrees.

5. Vertical angles theorem: vertical angles, angles that are opposite each other and formed by two intersecting straight lines, are congruent (or equal)

6. Supplementary angles: when 2 angles combine to make a line these 2 angles adds up to 180 degrees and are called supplementary angles.

Now apply one or more of these theorems to each of the problems to find out the answer!

1. Same side interior angle theorem: 56 degrees.

2. Same side interior angle theorem: 132 degrees.

3. Alt. Interior angles theorem: 55 degrees.

4. Alt. exterior angles theorem: 120 degrees

5. <7 --> <2 corresponding angles theorem: <2=50.5 degrees

   <2 --> <6 supplementary angles: <6=129.5 degrees

6.Same side interior angles theorem: 61.3 degrees