Francis, Georgie, and Harrieta go to the library to study every few days. Francis goes to the library every eighth day, Georgie goes every 18th day, and Harrieta goes every ninth day. In how many days will Francis, Georgie, and Harrieta all be at the library together?

The measure of angle B is approximately equal to 56.31 degrees, rounded to two decimal places.

An angle measure is a numerical value that represents the amount of rotation between two intersecting lines, line segments or rays. It is typically measured in degrees, although other units of measurement such as radians and grads may also be used. The size of an angle can range from 0 degrees (corresponding to no rotation or a straight line) to 360 degrees (corresponding to a full rotation). In geometry, angles are used to describe the relationships between lines and shapes, and are an important concept in fields such as trigonometry and calculus.

To find the measure of angle B given cot B = 0.57736, we can use the inverse tangent function.

The tangent of an angle is the ratio of the opposite side to the adjacent side,

So cot B = adjacent side / opposite side.

By taking the inverse tangent of both sides and substituting cot B for adjacent side / opposite side, we arrive at the equation

B = arctan(cot B).

Evaluating arctan(cot B) using a calculator gives us the measure of angle B as,

B = arctan(cot B) = 56.31° (rounded to two decimal places)

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The complete question is: "Given cot B = 0.57736, determine the measure of angle B".

By the fundamental theorem of calculus,

\(\displaystyle y = \int_0^v \sqrt{3+4t^2} \, dt \implies \boxed{\frac{dy}{dv} = \sqrt{3+4v^2}}\)

In general,

\(\displaystyle \frac{d}{dx} \int_0^{g(x)} f(u) \, du = f(g(x)) \frac{dg}{dx}\)

Answer:

52/15

Step-by-step explanation:

1 3/10 = 33/10 + 1/6 = 198/60 + 10/60

208/60 = 52/15

Based on the information, it should be noted that the value of tan(A-B) is 234/583.

Given:

tanA = 60/11

sinB = 45/53

A and B are in Quadrant I

We can use the following identity to find tan(A-B):

tan(A-B) = (tanA - tanB)/(1 + tanA*tanB)

Substituting the given values, we get:

tan(A-B) = (60/11 - 45/53)/(1 + (60/11)*(45/53))

= (15/53)/(295/583)

= 234/583

Therefore, the value of tan(A-B) is 234/583.

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Answer:

4

Step-by-step explanation:

2:3

4:6

6:9

8:12

8 girls in Ronna’s class

Half of 8 is 4

The situation Veronica receives $21 for babysitting, and then spends the same amount, $21, on a new shirt quantities combine to make 0.The correct answer is option C.

When we add +21 (the money she receives) and subtract -21 (the money she spends), the result is 0. This means that the net change in Veronica's money is zero, indicating that the quantities combine to make 0.

In situations A, B, and D, the quantities do not combine to make 0. In situation A, the player earns 4 points for getting an answer right and then earns an additional 4 points for making it around the board.

The total points earned in this situation would be 8, which is not equal to 0.

In situation B, the car is initially filled with 10 gallons of gas, but then half of that, which is 5 gallons, is used on a day's drive. The remaining fuel in the car would be 5 gallons, which is also not equal to 0.

In situation D, the bird flies 25 feet up in the air and then 25 feet across to its nest. The total distance traveled by the bird would be 50 feet, which is not equal to 0.

Therefore, only in situation C, where Veronica receives and spends the same amount of money, do the quantities combine to make 0.

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The probable question may be:

In which of these situations do the quantities combine to make 0?

A. A player a game earns 4 points for getting an answer right. She then earns 4 points for making it around the board.

B. A car is filled with 10 gallons of gas. Half of the 10 gallons are then used on a day's drive.

C. Veronica receives $21 for babysitting. She then spends $21 on a new shirt.

D. A bird flies 25 feet up in the air. It then flies 25 feet across to its nest.

Answer:

When 6514 is divided by 214, it equals approximately 30.4. So Daniel will have filled 30 smaller bags.

Answer:

n=335

Step-by-step explanation:

Answer:

Step-by-step explanation:

Here you go mate

Step 1

n − 325 = 10  equation

Step 2

n − 325 = 10  simplify by adding 325 to both sides

Answer

n=335

Answer:

the correct ans should be 88/15

Step-by-step explanation:

since, y is directly proportional to x then,

y=kx where k=proportionality constant

when y=22/5 and x=3/5

or,22/5=k*3/5

or,22/5*5/3=k

•°•k=22/3

now, when x=4/5

we know,

y=kx

or,y=22/3*4/5

•°•y=88/15

The surface area of a rectangular prism is 48 5/6 mi².

In Mathematics and Geometry, the surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:

Surface area of a rectangular prism = 2(LH + LW + WH)

Where:

By substituting the given side lengths into the formula for the surface area of a rectangular prism, we have the following;

Surface area of rectangular prism = 2[6 × 2 1/3 + (1 1/4 × 6) + (1 1/4 × 2 1 /3)]

Surface area of rectangular prism = 2[14 + 15/2 + 35/12]

Surface area of rectangular prism = 48 5/6 mi².

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The indefinite integral of  ∫(2ti+j+8k)dt is  t²i +tj+8tk+c.

Given the expression is ∫(2ti+j+8k)dt

The indefinite integrals, also known as the derivatives of functions, are integrals that can be computed using the process of differentiation in reverse.

Further approaches for resolving indefinite integrals include integration by parts, substitution, integration of partial fractions, and integration of inverse trigonometric functions.

now, ∫(2ti+j+8k)dt

= 2t²/2 i + tj +8tk

= t²i +tj+8tk+c

hence we get the indefinite integral as  t²i +tj+8tk+c

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Answer:

ok

Step-by-step explanation:

Answer:

y > Two-thirds x + 1     /c

\(\large\huge\red{\sf{➡ANSWER ⤵}}\)

Answer:

-25x-45y, because if we have got + and -, so we will write minus.

The length in feet of the longest part of the garden would be = 6ft

A garden is defined as an area that is prepared and set aside for the purpose of growing various flowers, shrubs and grasses.

The area of the given triangle = 54in²

The perimeter of the given triangle = 36 in.

Using the formula for area of a triangle ;

Area = ½ base(b) ×height(h)

where base = 9 in

54 = 1/2 × 9 × h

Make h the subject of formula;

h = 54×2/9

h = 108/9

h = 12

But the perimeter = sum of the whole sides of the triangle

perimeter = 36

side a = 9

side b = 12

side c = X

that is , 36 = 9+12+X

make X the subject of formula;

X = 36-21

X = 15in

Therefore, 15 in when converted to feet;

2 ft = 5 in

X ft = 15 in

xft = 2 × 15/5

X ft = 30/5

X ft = 6ft

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Answer:

D

Step-by-step explanation:

if x =4 and y =5

the expression = 818.3396

and D the only expression done the same result

Answer:

360 - 98 = 262

Step-by-step explanation:

Answer:

The sample mean is of 1970 daily calories.

The margin of error is of 120 daily calories.

The sample standard deviation is of 12.3 daily calories.

Step-by-step explanation:

Mean number of daily calories consumed by participants in a medical study is (1850, 2090).

The sample mean is the mean of the bounds of the confidence interval. So

\(M = \frac{1850 + 2090}{2} = 1970\)

The sample mean is of 1970 daily calories.

Margin of error:

The margin of error is the difference between the bounds and the sample mean. So

2090 - 1970 = 1970 - 1850 = 120

The margin of error is of 120 daily calories.

Sample standard deviation:

Now I have to expand a bit into the t-distribution. So

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 22 - 1 = 21

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 21 degrees of freedom(y-axis) and a confidence level of \(1 - \frac{1 - 0.95}{2} = 0.975\). So we have T = 2.08

The margin of error is:

\(M = T\frac{s}{\sqrt{n}}\)

In which s is the standard deviation of the sample.

Since \(M = 120, T = 2.08, n = 22\)

\(120 = 2.08\frac{s}{\sqrt{22}}\)

\(s = \frac{120}{2.08\sqrt{22}} = 12.3\)

The sample standard deviation is of 12.3 calories.

The Reflexive Property is a property of equality that states that anything is equal to itself. This property is true for numbers, shapes, angles, and more.

In the context of geometry, the Reflexive Property of Congruence states that any geometric figure is congruent to itself. This includes angles, segments, triangles, and other polygons.

So, when you see "<J ≅ <J", it's saying that angle J is congruent to angle J, which is an application of the Reflexive Property. In other words, any angle is congruent (equal in measure) to itself.

The expression factoring out the greatest common factor is  (3pf - 21p²)(f + 2).

We have the expression as

3pf² - 21p²f + 6pf - 42p²

Now, factorising the expression as

= 3pf² + 6pf - 21p²f - 42p²

= 3pf(f +2) - 21p²(f + 2)

= (3pf - 21p²)(f +2)

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The pattern for the sequence 1.3, 8.3, 27.3, 64.3,… is f(n) = (n)³.3

The pattern in the question is given as

1.3, 8.3, 27.3, 64.3,…

In the above expressions and pattern, we can see that

From the above, we have the following

Current term = (n)³.3

Note that the decimal does not represent product

And also the pattern is a geometric sequence

Hence, the pattern for the sequence is f(n) = (n)³.3

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Answer:

7: 63

8: 73

arithmetic sequence

y = 10x - 7

or f(n) = 10x -7

or

\(a_{n}\) = 3 + (n-1)10

Step-by-step explanation:

the output increases by 10 every time that the input increases by 1.  That gives us our common difference or slope.  The y intercept is -7. That is the value is you worked backwards until you get to n = 0.  The initial value  is 3.  That is when n is 1.

When n is 3, f(n) is 23

When n is 2, f(n) is 13

When n is 1, f(n) is 3

When n is 0, f(n) is -7

I am not sure if this is clear.  I am assuming that you have a lot of knowledge of linear equations and how to write arithmetic sequence.  If my explanation is confusing it is me and not you.

Answer:

a. 63,73

b. Arithmetic sequence

c.t(n)=10n-7

Explanation:

a. Here is the completed table:

n | t(n)

4 | 33

5 | 43

6 | 53

7 | 63

8 | 73

b.

The type of sequence is arithmetic.

An arithmetic sequence is a sequence of numbers where the difference between any two consecutive terms is constant.

In this case, the difference between any two consecutive terms is 10.

c.

The equation for the arithmetic sequence is:

t(n)=a+(n-1)d

where:

For Question:

Now

equation becomes:

t(4) = a+(4-1)10

33=a+30

a=33-30

a=3

Now, the Equation becomes

t(n) = 3+(n-1)10

t(n) = 3+10n-10

t(n)=10n-7

Answer:

Step-by-step explanation:

Answer:

The value of x=34 will make parallelogram ABCD a rhombus.

Answer:

10

Step-by-step explanation:

Since G = B (and 284 + 76 = 360), then FE = CD

Answer:

Option B: 3:8 is the right answer.

Step-by-step explanation:

Given that:

There are a total of eight circles.

The number of black circles is three.

Ratio is defined as quantitative relationship between two quantities.

As the statement demands ratio of black circles to total number of circles,therefore,

Ratio of black circles to total circles is 3:8

Hence,

Option B: 3:8 is the right answer.