If B=16°45’ and c=13 then find a (picture provided)

Answer:

50 teachers

Step-by-step explanation:

step 1

Find the number of teachers for a ratio of 1:12

1/12=x/2,400

x=2,400/12=200 teachers

step 2

Find the number of teachers for a ratio of 5:48

5/48=x/2,400

x=2,400*5/48=250 teachers

step 3

Find the difference

250-200=50 teachers

The number of teachers who joined the school is 50.

Step 1:

Let's denote the number of teachers initially as x and the number of students initially as 12x, based on the initial ratio of 1 teacher to 12 students.

So, initially, the total number of people in the school is x + 12x = 13x.

Step 2:

After some teachers join the school, the new ratio becomes 5 teachers to 48 students.

Now, the number of teachers is [tex]\(x + \text{number of teachers who joined}\)[/tex], and the number of students remains 12x.

Step 3:

So, the new total number of people in the school becomes [tex]\(x + \text{number of teachers who joined} + 12x\).[/tex]

According to the new ratio, [tex]\(\frac{x + \text{number of teachers who joined}}{12x} = \frac{5}{48}\)[/tex].

We can set up the equation:

[tex]\[\frac{x + \text{number of teachers who joined}}{12x} = \frac{5}{48}\][/tex]

Step 4:

Cross-multiply:

[tex]\[48(x + \text{number of teachers who joined}) = 5 \times 12x\][/tex]

Simplify:

[tex]\[48x + 48(\text{number of teachers who joined}) = 60x\][/tex]

[tex]\[48(\text{number of teachers who joined}) = 12x\][/tex]

Divide both sides by 48:

[tex]\[\text{number of teachers who joined} = \frac{12x}{48} = \frac{x}{4}\][/tex]

Step 5:

Given that there are initially 2400 students, we can set up another equation:

[tex]\[12x = 2400\][/tex]

Solve for x:

[tex]\[x = \frac{2400}{12} = 200\][/tex]

Now, plug in the value of x to find the number of teachers who joined:

[tex]\[\text{number of teachers who joined} = \frac{x}{4} = \frac{200}{4} = 50\][/tex]

Therefore, the number of teachers who joined the school is 50.

ANSWER

[tex]a_ {10} = \frac{25}{32} [/tex]

EXPLANATION

The given geometric sequence is

400, 200, 100...

The first term is

[tex]a_1=400[/tex]

The common ratio is

[tex]r = \frac{200}{400} = \frac{1}{2} [/tex]

The nth term is

[tex]a_n=a_1( {r}^{n - 1} )[/tex]

We substitute the known values to get;

[tex]a_n=400( \frac{1}{2} )^{n - 1} [/tex]

[tex]a_ {10} =400( \frac{1}{2} )^{10 - 1} [/tex]

[tex]a_ {10} =400( \frac{1}{2} )^{9} [/tex]

[tex]a_ {10} = \frac{25}{32} [/tex]

Answer:

2x + 11 = 20

Step-by-step explanation:

let's start by assigning the variable x to certain number , if we two times a certain number we got 2x, and if we added to 11 the result is 20. So, ordering the equation we will obtain:

2x + 11 = 20

ANSWER

2x+11=20

EXPLANATION

Let the number be x.

Two times this number is 2x

If 11 is added to two times the number, the expression becomes;

2x+11

If the result is 20, then we equate the expression to 20 to get:

2x+11=20

The correct choice is the last option;

Answer:

I think the answer is "How much pineapple juice is needed to make 5 pitchers of punch?"

Step-by-step explanation:

I believe it's the second one, from 5 cups of juice, since you would divide 5 by 3 1/2

To find the exact length of the curve defined by [tex]\( x = 9 + 9t^2 \) and \( y = 6 + 6t^3 \) for \( 0 \leq t \leq 4 \):[/tex]

1. Compute derivatives: [tex]\( \frac{dx}{dt} = 18t \) and \( \frac{dy}{dt} = 18t^2 \).[/tex]

2. Substitute into arc length formula:

[tex]\[L = \int_{0}^{4} \sqrt{(18t)^2 + (18t^2)^2} \, dt = \int_{0}^{4} 18t \sqrt{1 + t^2} \, dt\][/tex]

3. Use substitution [tex]\( u = 1 + t^2 \), \( du = 2t \, dt \):[/tex]

[tex]\[L = 9 \int_{1}^{17} \sqrt{u} \, du = 9 \left[ \frac{2}{3} u^{3/2} \right]_{1}^{17} = 6 (\sqrt{4913} - 1)\][/tex]

Final answer: The exact length of the curve is [tex]\( \boxed{6 (\sqrt{4913} - 1)} \).[/tex]

To find the exact length of the curve defined by the parametric equations [tex]\( x = 9 + 9t^2 \) and \( y = 6 + 6t^3 \) for \( 0 \leq t \leq 4 \),[/tex] we use the arc length formula for parametric curves:

[tex]\[L = \int_{a}^{b} \sqrt{\left( \frac{dx}{dt} \right)^2 + \left( \frac{dy}{dt} \right)^2} \, dt\][/tex]

Here, ( a = 0 ) and ( b = 4 ). First, we need to find the derivatives

Given [tex]\( x = 9 + 9t^2 \):[/tex]

[tex]\[\frac{dx}{dt} = \frac{d}{dt}(9 + 9t^2) = 18t\][/tex]

Given [tex]\( y = 6 + 6t^3 \):[/tex]

[tex]\[\frac{dy}{dt} = \frac{d}{dt}(6 + 6t^3) = 18t^2\][/tex]

Next, we substitute these derivatives into the arc length formula:

[tex]\[L = \int_{0}^{4} \sqrt{(18t)^2 + (18t^2)^2} \, dt\][/tex]

Simplify the expression inside the square root:

[tex]\[(18t)^2 + (18t^2)^2 = 324t^2 + 324t^4 = 324t^2 (1 + t^2)\][/tex]

Therefore, the integrand becomes:

[tex]\[L = \int_{0}^{4} \sqrt{324t^2 (1 + t^2)} \, dt = \int_{0}^{4} \sqrt{324} \sqrt{t^2 (1 + t^2)} \, dt\][/tex]

[tex]\[L = \int_{0}^{4} 18 \sqrt{t^2 (1 + t^2)} \, dt = \int_{0}^{4} 18 t \sqrt{1 + t^2} \, dt\][/tex]

We can simplify this integral by using the substitution[tex]\( u = 1 + t^2 \), hence \( du = 2t \, dt \). When \( t = 0 \), \( u = 1 \), and when \( t = 4 \), \( u = 17 \):[/tex]

[tex]\[L = 18 \int_{0}^{4} t \sqrt{1 + t^2} \, dt = 18 \int_{1}^{17} \sqrt{u} \cdot \frac{1}{2} \, du\][/tex]

[tex]\[L = 9 \int_{1}^{17} \sqrt{u} \, du = 9 \int_{1}^{17} u^{1/2} \, du\][/tex]

Integrate[tex]\( u^{1/2} \):[/tex]

[tex]\[\int u^{1/2} \, du = \frac{2}{3} u^{3/2}\][/tex]

Evaluate the definite integral:

[tex]\[L = 9 \left[ \frac{2}{3} u^{3/2} \right]_{1}^{17} = 9 \left( \frac{2}{3} \left[ 17^{3/2} - 1^{3/2} \right] \right)\][/tex]

[tex]\[L = 9 \cdot \frac{2}{3} \left( 17^{3/2} - 1 \right) = 6 \left( 17^{3/2} - 1 \right)\][/tex]

[tex]\[L = 6 \left( \sqrt{17^3} - 1 \right) = 6 \left( \sqrt{4913} - 1 \right)\][/tex]

Thus, the exact length of the curve is:

[tex]\[\boxed{6 (\sqrt{4913} - 1)}\][/tex]

The area of the cross section that is parallel to side PQRS in this rectangular box is: A. 12 square units.

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = LW

Where:

A represent the area of a rectangle.

W represent the width of a rectangle.

L represent the length of a rectangle.

By substituting the given side lengths into the formula for the area of a rectangle (PQRS), we have the following;

Area of rectangle = PQ × QR

Area of rectangle = 4 × 3

Area of rectangle = 12 square units.

Complete Question:

What is the area of the cross section that is parallel to side PQRS in this rectangular box?

A. 12 square units

B. 16 square units C. 30 square units D. 40 square units

The volume of the rectangular box is 60 cubic units.

Given that the area of one side of the box is 12 and the area of another side is 15, and both dimensions are integers greater than 1, we can find the dimensions and the volume of the box as follows:

Possible dimensions:

For the side with area 12, the possible integer dimensions are (3, 4) and (4, 3) since 3 x 4 = 4 x 3 = 12.

For the side with area 15, the possible integer dimensions are (3, 5) and (5, 3) since 3 x 5 = 5 x 3 = 15.

Valid dimensions combination:

We need to find a combination of dimensions where the two sides mentioned above are not the same.

The only valid combination is (3, 4) for the side with area 12 and (5, 3) for the side with area 15.

Volume of the box:

The volume of the box is calculated by multiplying the length, width, and height.

In this case, the volume is 3 (length) x 4 (width) x 5 (height) = 60 cubic units.

Therefore, the volume of the rectangular box is 60 cubic units.

Question

The dimensions of a rectangular box are integers greater than 1. If the area of one side of this box is 12 and the area of another side 15, what is the volume of the box?

Answer:

37%

Step-by-step explanation:

35% of 55% is equal to the percent of boys on honor roll in the student body.

100 - 55 = 45%, which is the percent of girls in the student body.

40% of 45% is equal to the percent of girls on honor roll in the student body.

35% * 55% = 19.25%

40% * 45% = 18%

Adding them up, we get:

19.25 + 18 = 37.25%

Round it to the nearest percent.

37.25 --> 37%

Rounded to the nearest percent, 37% of the student body is on honor roll.

Answer:

B. 1/2 tespoon of salt per 1 teaspoon of baking soda.

Step-by-step explanation:

If you're starting with 1/2 tsp of baking soda and 1/4 tsp of salt, you can multiply that by two and still have the same ratio of salt to baking soda.

Answer:

B. 1/2 tespoon of salt per 1 teaspoon of baking soda.

Step-by-step explanation:

If you're starting with 1/2 tsp of baking soda and 1/4 tsp of salt, you can multiply that by two and still have the same ratio of salt to baking soda.

Answer: y=12.287

Step-by-step explanation:

Answer:

y = 12.3 cm

Step-by-step explanation:

Using the cosine ratio in the right triangle to solve for y

cos35° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{y}{15}[/tex]

Multiply both sides by 15

15 × cos35° = y, thus

y ≈ 12.3 cm

Answer:

The area is 154 cm²

Step-by-step explanation:

Since the formula for the area of a circle is pi times the radius squared, divide the diameter in half to get the radius (7). Then, square the radius (49). Next, multiply that by pi (153.938). After that round to the nearest whole number (154). Hope that helps!

-Kyra

Answer:

A = 154 cm^2

Step-by-step explanation:

We know the diameter of the circle

We need to find the radius

d = 2r

14 = 2r

Divide by 2

14/2 = 2r/2

7=r

Now we can use the formula for area

A = pi r^2

A = pi (7)^2

A = 49pi

Replace pi with 3.14

A = 49(3.14)

A = 153.83

Rounding to the nearest whole number

A = 154 cm^2

I'll assume you're supposed to compute the line integral of [tex]\nabla f[/tex] over the given path [tex]C[/tex]. By the fundamental theorem of calculus,

[tex]\displaystyle\int_C\nabla f(x,y)\cdot\mathrm d\vec r=f(4,48)-f(1,3)[/tex]

so evaluating the integral is as simple as evaluting [tex]f[/tex] at the endpoints of [tex]C[/tex]. But first we need to determine [tex]f[/tex] given its gradient.

We have

[tex]\dfrac{\partial f}{\partial x}=3y\sin(xy)\implies f(x,y)=-3\cos(xy)+g(y)[/tex]

Differentiating with respect to [tex]y[/tex] gives

[tex]\dfrac{\partial f}{\partial y}=3x\sin(xy)=3x\sin(xy)+\dfrac{\mathrm dg}{\mathrm dy}\implies\dfrac{\mathrm dg}{\mathrm dy}=0\implies g(y)=C[/tex]

and we end up with

[tex]f(x,y)=-3\cos(xy)+C[/tex]

for some constant [tex]C[/tex]. Then the value of the line integral is [tex]-3\cos192+3\cos3[/tex].

This question involves vector calculus and requires finding the line integral along a segment of a parabola.

The given question is related to the subject of Mathematics. It involves the application of vector calculus and requires analyzing a segment of the parabola using vector analysis and gradient fields.

To find the ∫f vector, we need to evaluate the partial derivatives of f(x, y) and multiply them with the corresponding unit vectors. Plugging in the given values, we find that ∫f = 3y·sin(xy)·ᵢ + 3x·sin(xy)·ᵢ.

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[tex]\bf \cfrac{1}{2}\div 3\implies \cfrac{1}{2}\div \cfrac{3}{1}\implies \cfrac{1}{2}\cdot \cfrac{1}{3}\implies \cfrac{1}{6}[/tex]

3 friends equally shared 1/2 pound of trail mix, during the hike.

Total quantity of trail mix = 1/2 pound

Quantity shared by each friend is 1/3 rd of the trial mix

= 1/3 * 1/2 pound

= 1/6 pound

Therefore, during the hike, each friend shared 1/6 pound of the trail mix.

Hope this helps ..!!

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Answer:

The value of x is 45

Step-by-step explanation:

The value of x is 45 degrees as per the concept of the polygon's interior angle.

To find the value of x in the irregular pentagon with interior angles measuring 90 degrees, 112 degrees, x degrees, (3x + 10) degrees, and 148 degrees, we can use the fact that the sum of the interior angles in any pentagon is 540 degrees.

Summing up the given interior angles, we have:

90 + 112 + x + (3x + 10) + 148 = 540

Combine like terms:

4x + 360 = 540

Subtract 360 from both sides:

4x = 180

Divide both sides by 4:

x = 45

Therefore, the value of x is 45 degrees.

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Answer:

d

Step-by-step explanation:

Here the sum of 5+1 golf scores, divided by 6, must be 118:

120 + 112 + 130 + 128 + 124 + x

--------------------------------------------- = 118

                         6

Here, 120 + 112 + 130 + 128 + 124 + x is the total number of points needed to have an average of 118.  Answer d is the correct one.

Answer:

Jacob has golf scores of 120, 112, 130, 128, and 124.

He wants to have an average golf score of 118.

a. Find the sum of all the numbers in the problem, 120+112+130+128+124+118.

[tex]120+112+130+128+124+118[/tex]

= 732

b. Find the average score for the five golf games that Jacob has played.

[tex]\frac{120+112+130+128+124}{5}[/tex]

= 122.8

c. Determine the number of points that he needs in his next golf game.

Jacob will need a golf score of 94  in next game to achieve the average of 118.

Total score = [tex]120+112+130+128+124+x[/tex]

number of matches = 6

Average score = [tex]\frac{614+x}{6}=118[/tex]

[tex]614+x=708[/tex]

[tex]x=708-614[/tex]

x = 94

d. Determine how many total points are needed to have an average of 118.

Total points needed are [tex]614+94=708[/tex]

The phase shift is 7.2 right

first use the formula it is 1/3 × base area × height =volume of pyramid

so we just need to replace some of the information given in the statement to our formula

so it's going to be,i'll let the height as unknown X

128=1/3 × (8 × 8) × X

so it's going to be

128=64/3X

so X is 128 ÷ 64/3=6cm

Answer:

I'm Sure the answer is 6 cm.

A.Conjunction

Step-by-step explanation:

Perimeter = 2w+2l. 2(6)+2l = 36 subtract 12 to get 2l=24 then divide by 2 so the length is 12 inches

Answer:

(6 , -3)

Step-by-step explanation:

Given in the question,

point J(8,-6)

x1 = 8

y1 = -6

point L(-2,9)

x2 = -2

y2 = 9

Location of point K which is 1/5 of the way from J to L

which means ratio of point K from J to L is 1 : 4

a : b

1 : 4

xk = [tex]x1+\frac{a}{a+b}(x2-x1)[/tex]

yk = [tex]y1+\frac{a}{a+b}(y2-y1)[/tex]

Plug values in the equation

xk = 8 + (1)/(1+4) (-2-8)

xk = 6

yk = -6 (1)/(1+4)(9+6)

yk = -3

Answer:

what he said

Step-by-step explanation:

Answer:

The answer is the letter B.

The first column represents the x-values, and the second row represents the y-values.

For that reason, if we have:

2x - 7y = -1

x + 3y = -5

Then, the matrix will be given by:

[ 2      -7

 1        3]

Then, the third colum will be the equality:

[ -1

 -5]

So the correct option is the letter B.

B

[tex]2x - 7y = - 1 \\ \\ \\ 1. \: 2x = - 1 + 7y \\ 2. \: 2x = 7y - 1 \\ 3. \: x = \frac{7y - 1}{2} [/tex]

1.25 meters im pretty sure. i hope i helped

Answer:

  a.  12/37

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you ...

  Sin = Opposite/Hypotenuse

  sin(A) = BC/AB = 12/37

The value of sin A in triangle ABC, where AB = 37 and BC = 12, is 12/37.

In a right-angled triangle, the sine of one of the non-right angles (A in this case) is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. The hypotenuse is the side opposite the right angle (side AB in this case).

To find the value of sin A in triangle ABC, we can use the formula:

sin A = BC / AB

Given that AB = 37 and BC = 12, we have:

sin A = 12 / 37

So, the correct answer is: a. 12/37

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Answer: Option A.

Step-by-step explanation:

You need to remember the Quotient property of powers, which states the following:

[tex]\frac{p^m}{p^n}=p^{(m-n)}[/tex]

Then, given the expression [tex]\frac{a^3b^2}{a^2b}[/tex], you need to apply this property to simplify this expression.

Therefore, you get:

[tex]=a^{(3-2)}b^{(2-1)}\\\\=a^1b^1\\\\=ab[/tex]

As you can observe, this matches with the option A.

Answer:

The correct answer is option A.  ab

Step-by-step explanation:

Points to remember

Identities

Xᵃ * Xᵇ = X⁽ᵃ ⁺ ᵇ⁾

X⁻ᵃ = 1/Xᵃ

Xᵃ/Xᵇ = X⁽ᵃ ⁻ ᵇ⁾

To find the correct answer

It is given that,

a³b²/a²b

By using above identities we can write,

a³b²/a²b = a⁽³ ⁻ ²⁾b⁽² ⁻ ¹⁾

 = a¹b¹ = ab

Therefore the answer is ab

The correct option is option A.  ab

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}6x+3y=-21&\text{divide both sides by (-3)}\\2x+5y=5\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-2x-y=7\\2x+5y=5\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad4y=12\qquad\text{divide both sides by 4}\\.\qquad\qquad y=3\\\\\text{Put it to the second equation:}\\2x+5(3)=5\\2x+15=5\qquad\text{subtract 15 from both sides}\\2x=-10\qquad\text{divide both sides by 2}\\x=-5[/tex]

Answer:

$135

Step-by-step explanation:

step 1

Let

x----> amount of money shared by Danny

y----> amount of money shared by Amira

z----> amount of money shared by Tyler

we know that

x/y=6/4 ----> x=1.5y ----> equation A

x/z=6/3 ---> z=x/2 ---> equation B

Amira used 1/2 of her money to buy a watch that costs $30

so

(1/2)y=$30

y=$60

Substitute the value of y in the equation A and solve for x

x=1.5y ----> x=1.5(60)=$90

Substitute the value of x in the equation B and solve for z

z=x/2 -----> z=90/2=$45

so

The amount of money shared by Danny was $90

The amount of money shared by Amira was $60

The amount of money shared by Tyler was $45

step 2

Find out how much money they have left in total.

Danny gave 1/3 of his money to his sister ----> left --> (2/3)($90)=$60

Amira used 1/2 of her money -----> left --> $60/2=$30

Tyler --------> left ----> $45

Total=$60+$30+$45=$135

Total left = Danny + Amira + Tyler = $60 + $30 + $45 = $135.

The question deals with dividing a sum of money among Danny, Amira, and Tyler by the ratio 6 : 4 : 3, calculating how much Amira spent, and how much Danny gave away.

Let's assume the total sum of money is M, shared according to the ratio 6x : 4x : 3x, which means:

Since Amira spent 1/2 of her money on a watch costing $30, we can deduce:

Therefore, the total sum of money M is 6x + 4x + 3x = 13x, which gives us:

Danny gave away 1/3 of his share to his sister, which is:

After spending and giving money away, they have left:

Total left = Danny + Amira + Tyler = $60 + $30 + $45 = $135.

Answer:

14.2

Step-by-step explanation:

For this case, we have to define trigonometric relations in a rectangle triangle that, the tangent of an angle is given by the leg opposite the angle on the leg adayed to it. According to the figure we have:[tex]tg (35) = \frac {c} {5}\\c = tg (35) * 5\\c = 0.70020754 * 5[/tex]

[tex]c = 3.5010377[/tex]

Answer:

Option D

Answer:

  4/r

Step-by-step explanation:

The side lengths s of an equilateral triangle inscribed in a circle of radius r will be ...

  s = r√3

The perimeter of the triangle will be 3s.

The area of the triangle will be s^2·(√3)/4.

Then the ratio P/A is ...

  P/A = (3s)/(s^2·(√3)/4) = (4√3)/s

Substituting the above expression for s, we have ...

  P/A = 4√3/(r√3)

  P/A = 4/r

The expression for the ratio of the perimeter to the area of an equilateral triangle, whose vertices lie on a circle with radius r, is 2√3/r.

The ratio of the perimeter to the area of an equilateral triangle is derived using the formulae related to the triangle and the circle on which it lies. Let's start with the formulas for the circumference of a circle C = 2πr, and the area of an equilateral triangle A = (√3/4)*s², where s is the side length of the triangle.

As the vertices of the triangle are on the circle, the side length s is equal to the diameter of the circle. Therefore, s = 2r. Also, the perimeter P = 3*s = 6r. Substituting the terms for A and P, we find that P/A = 6r/((√3/4)*(2r)²) = (24/√3)/4r = 6/√3r. This simplifies to 2√3/r after rationalizing the denominator.

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Answer:

The height of the rectangular prism is [tex]58.36\ m[/tex]

Step-by-step explanation:

we know that

The surface area of the rectangular prism is equal to

[tex]SA=2B+PH[/tex]

where

B is the area of the rectangular base

P is the perimeter of the rectangular base

H is the height of the prism

Find the area of the base B

[tex]B=14.2*15=213\ m^{2}[/tex]

Find the perimeter of the base P

[tex]P=2(14.2+15)=58.4\ m[/tex]

we have

[tex]SA=3,834\ m^{2}[/tex]

substitute and solve for H

[tex]SA=2B+PH[/tex]

[tex]3,834=2(213)+(58.4)H[/tex]

[tex]3,834=426+(58.4)H[/tex]

[tex]H=(3,834-426)/(58.4)[/tex]

[tex]H=58.36\ m[/tex]

Answer:

174 cm²

Step-by-step explanation:

The figure is composed of a rectangle and a triangle, so

area of figure = area of rectangle + area of triangle

area of rectangle = 8 × 15 = 120 cm²

area of triangle = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

here b = 12 and h = 15 - 6 = 9 cm

area of triangle = 0.5 × 12 × 9 = 6 × 9 = 54 cm²

Hence

area of figure = 120 + 54 = 174 cm²

Answer:

c because is right

Step-by-step explanation: