At a school dance, the ratio of boys to girls is 7 to 5. What fraction of students at the dance consists of girls? (You must use the fraction form of a ratio

There are three ways to buy 66 cookies with packaging options of single cookies, or packages of 11 or 33. They are two packages of 33, six packages of 11, or sixty-six single cookies.

To find out how many ways you can buy 66 cookies using single cookies, or packages of 11 or 33, we can set up a problem using combinations of these quantities. As we know, 66 is a multiple of both 11 and 33, so we'll want to find out how many packages of 11 and how many packages of 33 can be combined without exceeding 66.

Firstly, since 33 is exactly half of 66, we can have either two packages of 33 or zero packages of 33. If we choose two packages of 33, then we have no need for additional cookies. If we choose zero packages of 33, we can then use six packages of 11 to make up the total because 6 x 11 = 66. There's also the option of buying 66 single cookies, although that tends to be inefficient.

So, our possibilities are:

Thus, there are three ways to buy 66 cookies given the packaging constraints.

Answer: (-1.5, -0.5)

Step-by-step explanation:

Answer:

1) x = 6.6.

2) x = 6.1.

Step-by-step explanation:

1) In this triangle, the hypotenuse is given, which is 8 units, and the angle is given, which is 35 degrees. The base is unknown. To find the base, following ratio will be used:

cos θ = Base/Hypotenuse.

cos 35 = x/8.

x = 8*cos 35.

x = 6.6 units (to the nearest tenth)!!!

2) In this triangle, the base is given by 12, and the angle is given by 27 degrees. The perpendicular is unknown. To find the perpendicular in this case, tangent formula will be used:

tan θ = Perpendicular/Base

tan 27 = x/12.

x = 12*tan 27.

x = 6.1 units (to the nearest tenth)!!!

Answer:

1).  x = 6.55 units

2).x = 2.55 units

Step-by-step explanation:

1). To find the value of x

From the given figure 1 we can see a right angled triangle with hypotenuse is 8 units

Cos 35 = Adjacent side/Hypotenuse

 = x/8

x = 8 * Cos 35

 = 8 * 0.8196

 = 6.55

2). To find the value of x

From the figure we can write,

Tan 27 = Opposite side/Adjacent side

 = x/12

x = 12 * Tan 27

 = 12 * 0.509

 = 2.55 units

Answer:

Step-by-step explanation:

The equation is y = 225 - 60x

y is the distance from Seattle

x is the number of driving hours.

At the start of the journey, x = 0.

y = 225 - 60*0

Therefore he has 225 miles to go.

====================

The change for every hour is the slope of the equation, which is - 60.

So the answer to the second part is - 60

Answer:

The distance was 225 miles when be began driving. The change in Milan's distance from Seattle for each hour he drives is -60.

Step-by-step explanation:

Consider the provided equation.

225 - 60x = y

Where x is the time and y is distance.

For part (A):

When she begins the drive, x = 0.

Substitute the value of x in the provided equation.

y = 225 - 60(0)

y = 225

Hence, the distance was 225 miles when be began driving.

Part (B)

The slope intercept form is: y = mx + c

Where m is the slope and c is the y intercept.

By comparing the provided equation with the slope intercept form it can be conclude that the slope is -60 or the rate of change of distance with respect to x is -60

The change for every hour is the slope of the equation, which is - 60.

Hence, the change in Milan's distance from Seattle for each hour he drives is -60.

Answer:

2

Step-by-step explanation:

Consider two functions:

[tex]y=\sin x[/tex] and [tex]y=\sin 2x[/tex]

The period of each function is

[tex]2\pi[/tex] and [tex]\pi[/tex]

This means that the graph of the function [tex]y=\sin x[/tex] (red graph) intersects by the horizontal line [tex]y=\frac{1}{2}[/tex] twice and the graph of the function [tex]y=\sin 2x[/tex] intersects by the horizontal line [tex]y=\frac{1}{2}[/tex] four times (blue graph) for [tex]x\in [0,2\pi ).[/tex]

So the equation [tex]\sin \theta=\dfrac{1}{2}[/tex] has 2 solutions and  the equation [tex]\sin 2\theta=\dfrac{1}{2}[/tex] has 4 solutions. Thus, the difference is 2.

Answer:

y=4

Step-by-step explanation:

Slope equal 0 means you have a horizontal line. Horizontal lines are all of the form y=a where a is the constant you have to figure out. Our horizontal line goes through (2,4) and the coordinate there is 4 so the line is y=4.

The equation in slope-intercept form that describes a line through (2, 4) with slope 0 is y = 4 .

The equation of a straight line in the form y = mx + c where m is the slope of the line and c is its y-intercept is known as the slope-intercept form. Here both the slope (m) and y-intercept (c) have real values. It is known as slope-intercept form as it gives the definition of both the slope and y-intercept.

It is given that the line passes through (2,4) and it has slope 0 .

Thus, general equation of straight line is y = mx + c

Slope(m) = 0

∴ y = c

The y-coordinate of the point is 4 , so c = 4

Thus, the equation of a straight line in slope-intercept form is -

  y = 0*(x) + 4

∴ y = 4 .

Therefore, the equation in slope-intercept form that describes a line through (2, 4) with slope 0 is y = 4 .

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Answer:

The number of black T-shirts in 110 experiments is 20.

Step-by-step explanation:

It is given that in 55 trials of the experiment, a black T-shirt was drawn 10 times.

Formula of probability:

[tex]P=\frac{\text{Favorable outcomes}}{\text{Total number of outcomes}}[/tex]

Since 55 trials of the experiment, a black T-shirt was drawn 10 times, therefore the probability of getting black T-shirts in 1 experiment is

[tex]P=\frac{10}{55}[/tex]

[tex]P=\frac{2}{11}[/tex]

The number of black T-shirts that would be drawn in 110 times is

[tex]T=\frac{2}{11}\times 110=20[/tex]

Therefore the number of black T-shirts in 110 experiments is 20.

To find the average temperature Tave during the period from 9 AM to 9 PM, we need to find the average value of the temperature function T(t).

To find the average temperature Tave during the period from 9 AM to 9 PM, we need to find the average value of the temperature function T(t). The formula for the average value of a function over an interval is given by:

Ave = (1/(b-a)) * ∫[a, b] f(x) dx

In this case, a = 0 (corresponding to 9 AM) and b = 12 (corresponding to 9 PM). Plugging in the temperature function T(t) = 52 + 17 sin(πt/12), we get:

Tave = (1/(12-0)) * ∫[0, 12] (52 + 17 sin(πt/12)) dt

Tave = (1/12) * (52t - 204cos(πt/12))

To find the definite integral ∫[0, 12] (52t - 204cos(πt/12)) dt, we evaluate the antiderivative at the upper and lower limits, and subtract the two values:

Tave = (1/12) * ((52(12) - 204cos(π(12)/12)) - (52(0) - 204cos(π(0)/12)))

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The value of the missing angle x° in the diagram is: 63°

By the concept of opposite angles, we know that opposite angles are defined as the angles directly opposite each other where two lines cross.

Thus:

∠ACB = 63°

Similarly, we can say that:

x° = 63°

This is because angle x is also an opposite angles to ∠ACB from the given diagram

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Answer:

73.5 kJ

Step-by-step explanation:

Mass of butane = 185 g

Heat of vaporization for butane = 23.1 kJ/mol

Molar mass of butane = 58.12 g/mol

Number of moles of butane = [tex]\frac{\text{Mass of butane}}{\text{Molar mass of butane}}=\frac{185}{58.12}=3.18\ moles[/tex]

Energy required for burning 185 g of butane = 3.18×23.1 = 73.5 kJ

∴ Energy is required to vaporize 185 g of butane at its boiling point is 73.5 kJ

Answer:

Correct arrangement of equation of displacement to find a is as follows;

1-  Vt - d = 1/2 a t^2 (^ represents exponent i.e. t square as given in equation)

2- 2(Vt - d ) = a t^2

3- a = 2(Vt - d )/ t^2   (keep in mind, 2(Vt - d) whole divided by  t^2)

Step-by-step explanation:

1-  In the first equation, Vt is taken to the left side of the equation (keep in mind, original equation of displacement used for reference as given in question) and multiplied by -1 on the both sides of the equation.

2- In the second equation, 2 is multiplied on the both sides.

3- Multiply t^2 on both sides of the equation, We will get a in correct arrangement, which is required to find.

Answer:

your answer would be 4.5 cubic feet!!! HOPE I HELPED!!!!! good luck to anyone who needs this in the future

Step-by-step explanation:

The volume of the triangular prism is 44.52 cubic feet.

A prism is a three-dimensional object.

There are triangular prism and rectangular prism.

We have,

To find the volume of a triangular prism, we need to multiply the area of the base by the height of the prism.

The base of the triangular prism is a triangle with sides of lengths 2 ft, 2.5 ft, and 18 ft.

The perimeter of the base is the sum of the lengths of these sides, which is:

2 ft + 2.5 ft + 18 ft = 22.5 ft

To find the area of the base, we can use Heron's formula, which states that for a triangle with sides of lengths a, b, and c, the area is given by:

[tex]area = \sqrt{s(s-a)(s-b)(s-c)}[/tex]

where s is half the perimeter of the triangle:

s = (a + b + c) / 2

In this case, we have:

a = 2 ft, b = 2.5 ft, c = 18 ft

s = (2 ft + 2.5 ft + 18 ft) / 2

s = 11.25 ft

Plugging these values into the formula, we get:

[tex]area = \sqrt{11.25(11.25-2)(11.25-2.5)(11.25-18)}[/tex]

area = 14.84 ft^2

The volume of the triangular prism is:

volume = area of base x height

volume = 14.84 ft² x 3 ft

volume = 44.52 ft³

Thus,

The volume of the triangular prism is 44.52 cubic feet.

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Answer:

  Obtuse

Step-by-step explanation:

The sum of squares of the short sides is 130, so is less than the square of the long side. The long side (12) is longer than it would need to be for a right triangle, so the largest angle is bigger than 90°.

The triangle is obtuse.

_____

A triangle solver app or calculator can confirm this. Note angle C is about 96°, an obtuse angle.

Answer:

Measure of <QTS = 20°

Measure or minor arc QS = 40°

Step-by-step explanation:

From the figure we can see a circle with center U.

To find the measure of <QTS

m<QTS = m<QPS   [Angles subtended by same arc are equal]

Therefore m<QTS = 20°

To find the measure of minor arc QS

Measure or minor arc QS = 2 * m<QPS

 = 2 * 20 = 40°

Measure or minor arc QS = 40°

Answer:

A) m∠QTS = 20°

B) The degree measure of minor arc QS is 40°

C) The degree measure of arc QTS is 320°

Step-by-step explanation:

* Lets revise some facts about the circle

- The inscribed angle in a circle is the angle whose vertex lies on the

 circumference of the circle and its sides are the chords in the circle

- Each inscribed angle subtended by an opposite arc to its vertex

- The measure of the arc is twice the measure of the inscribed angle

  subtended by this arc

- The measures of the inscribed angles subtended by the same arcs

  are equal

- The measure of the circle is 360°

* Lets solve the problem

- In circle U

A)

∵ ∠QPS is an inscribed angle subtended by arc QS

∵ ∠QTS is an inscribed angle subtended by arc QS

∴ m∠QPS = m∠QTS

∵ m∠QPS = 20°

∴ m∠QTS = 20°

B)

- Lets find the measure of the arc QS

∵ ∠QPS is an inscribed angle subtended by arc QS

∵ The measure of the arc is twice the measure of the inscribed angle

  subtended by this arc

∴ Measure of arc QS = 2 × m∠QPS

∵ m∠QPS = 20°

∴ Measure of arc QS = 2 × 20° = 40°

∴ The degree measure of minor arc QS is 40°

C)

∵ The arc QTS is an major arc

∵ The sum of the major arc QTS and the minor arc QS equals the

   measure of the circle

∵ The measure of the circle is 360°

∴ m of major arc QTS + m of minor arc QS = 360°

∵ m of minor arc QS = 40°

∴ m of major arc QTS + 40° = 360°

- Subtract 40° from both sides

∴ m of major arc QTS = 320°

∴ The degree measure of arc QTS is 320°

Answer:

Step-by-step explanation:

To maximize profit, the greatest possible number of the most profitable item should be manufactured. Remaining capacity should be used for the less-profitable item.

Up to 30 of model B, which has the highest profit, can be made each day. The remaining amount (20 sets) of the daily capacity of 50 sets should be used to make model A sets.

The given line is y = 3x - 5 after adding Y and subtracting 5 from both sides.

The slope of this given line is 3.

Therefore, the slope of the perpendicular line is -1/3, as it must be the negative reciprocal.

The general form of a line equation in slope intercept form is y = Mx+B where M is the slope and B is the intercept.

Solving for B is: B = y- Mx

So the intercept of the perpendicular line with slope M=-1/3 and passing through (x=4, y=-3) is

y M * x

B = -3 - (-1/3)*4 =

-3 + 1/3*4 = <-- subtracting the negative is the same as adding the positive; definition of subtraction

-3 + 4/3 = <-- multiplies the fractions first per order of mixed operations

-9/3 + 4/3 <-- common denominator is 3

= -5/3

So the equation of the perpendicular line is y = -1/3X + -5/3 = -1/3X-5/3

Notice when X=4, y = -1/3(4) - 5/3 = -4/3 - 5/3 = -9/3 = -3 as expected

Answer:

Step-by-step explanation:

Answer:

It's C.

Step-by-step explanation:

Note. x^2 + 6x - 40 = (x + 10)(x - 4) so we have

     x - 16                    1

----------------        +  ---------

(x + 10)(x - 4)          (x + 10)

=   x - 16  + (x - 4)            2x - 20

   --------------------  =     -----------------------

    (x + 10)(x - 4)            x^2 + 4x - 40

Answer:

  C. 615.7536 square inches

Step-by-step explanation:

The formula for the area of a circle is ...

  A = πr²

Fill in the given numbers and do the arithmetic.

  A = 3.1416×(14 in)² = 615.7536 in²

_____

Comment on the value of pi

We are interested to see that recent problems require use of a value of pi that has 5 significant digits, instead of 3 (as in 3.14). The only problem in this scenario is that the answer is now reported to 7 significant figures, so is still wrong. The correct 7-digit answer to this problem is 615.7522 in². It would be obtained by using a 7- or 8-digit value for pi: 3.141593 or 3.1415927 and rounding appropriately.

Answer:

Step-by-step explanation:

[tex]4^0=1\\2^2=2\cdot2=4\\3^3=3\cdot3\cdot3=27\\\\4^0\cdot2^2\cdot3^3=1\cdot4\cdot27=108[/tex]

Answer:

108

Step-by-step explanation:

4 to the power of 0 is always 1. multiply to 2 to the power of 2 gives you 4. multiplying 4 to 3 to the power of 3 gives you 108 because 3^3 is 27 but if you multiply that by 4, you get 108

Answer:

  5/3 m/s

Step-by-step explanation:

Antonio's speed in the 400 m dash was ...

  (400 m)/(80 s) = 5 m/s

Antonio's speed in the hurdles was ...

  (400 m)/(120 s) = 3 1/3 m/s

His speed in the dash was ...

  (5 -3 1/3) m/s = 1 2/3 m/s = 5/3 m/s

faster than in the hurdles.

Answer:

The ratio of the reaming apples to peaches is 3 : 4

Step-by-step explanation:

* Lets solve the problem

- There are 300 apples and peaches

- The ratio of the number of apples to the number of peaches is 7 : 8

- To find the the numbers of apples and peaches add the terms of the

  ratio and then divide the total number of apples and peaches by this

  sum and then multiply each terms of the ratio by this quotient

∵ The ratio of apples to peaches = 7 : 8

∴ apple : peach : sum

      7     :     8    :    15

       ?    :       ?    :    300

∴ The number of apples = (300 ÷ 15) × 7 = 20 × 7 = 140 apples

∴ The number of peaches = (300 ÷ 15) × 8 = 20 × 8 = 160 peaches

- 50 apples and 40 peaches are sold

∴ The remaining number of apples = 140 - 50 = 90 apples

∴ The remaining numbers of peaches = 160 - 40 = 120 peaches

- To find the ratio simplify the numbers to its simplest form

∵ There are 90 apples and 120 peaches

∴ apple : peach

      90  :   120      ⇒ divided both by 10

∴       9  :    12       ⇒ divide both by 3

∴       3  :     4    

∴ The ratio of the reaming apples to peaches is 3 : 4

Answer:

  cos(θ) = -3/5

Step-by-step explanation:

The cosine of the reference angle (in the first quadrant) is ...

  cos(θ) = √(1 -sin(θ)²) = √(1 -(4/5)²) = √(1 -16/25) = √((25-16)/25)

  = √(9/25) = 3/5 . . . . in the first quadrant

In the second quadrant, the cosine is negative, so the answer is ...

  cos(θ) = -3/5

Answer:

Reflects over the x-axis, then translate (x + 3, y + 1).

Step-by-step explanation:

Your have to flip is over the X-axis to get the short side on the bottom.

Then move is 3 places to the right, so X+3. After which it is move 1 place up, Y+1

Reflects over the x-axis, then translate (x + 3, y + 1).

Answer:

please ignore my answer

Answer:

0, 6 = x

Step-by-step explanation:

I hope you can see how and if this was alot of help to you, and as always, I am joyous to assist anyone at any time.

Answer:

3

Step-by-step explanation:

lim(t→∞) [t ln(1 + 3/t) ]

If we evaluate the limit, we get:

∞ ln(1 + 3/∞)

∞ ln(1 + 0)

∞ 0

This is undetermined.  To apply L'Hopital's rule, we need to rewrite this so the limit evaluates to ∞/∞ or 0/0.

lim(t→∞) [t ln(1 + 3/t) ]

lim(t→∞) [ln(1 + 3/t) / (1/t)]

This evaluates to 0/0.  We can simplify a little with u substitution:

lim(u→0) [ln(1 + 3u) / u]

Applying L'Hopital's rule:

lim(u→0) [1/(1 + 3u) × 3 / 1]

lim(u→0) [3 / (1 + 3u)]

3 / (1 + 0)

3

L'Hospital's Rule is a technique used to evaluate limits of indeterminate forms. It involves differentiating the numerator and denominator separately and then taking the limit again. The process is repeated until a determinate form is obtained.

L'Hospital's Rule is a technique used to evaluate limits of indeterminate forms. An indeterminate form is an expression that does not have a unique value when evaluating the limit. To use L'Hospital's Rule, we differentiate the numerator and denominator separately and then take the limit again. If the new limit is still indeterminate, we repeat the process until we get a determinate form.

For example, let's say we have the limit lim(x → 0) (sin(x) / x). This is an indeterminate form since both the numerator and denominator approach 0. Applying L'Hospital's Rule, we differentiate sin(x) and x, giving us lim(x → 0) (cos(x) / 1). Since the new limit is determinate, we can simply evaluate it as cos(0) / 1, which equals 1.

Step-by-step explanation:

1 can is to 10 liters as x cans is to 35 liters.

Write a proportion:

1 / 10 = x / 35

Cross multiply:

10x = 35

Divide:

x = 3.5

It takes 3.5 cans.

The answer is:

The line that is parallel to the given line and passes through the point (4,32) is:

[tex]y=4x+16[/tex]

To solve the problem, we need to remember that parallel lines have the same slope, so, we need to find a line that has the same slope that the given line and it also pass through the point (4,32).

So, we are given the line:

[tex]y-1=4(x+3)\\\\y=4x+12+1\\\\y=4x+13[/tex]

So, we have that the line has a slope which is equal to "4".

Now, we have to find which of the given lines that have a slope equal to "4", also pass through the point (4,32), so, we need to evaluate it into the equations.

Therefore, evaluating we have:

Third line:

[tex]y=4x-16\\\\32=4*4-16=0\\32=0[/tex]

We can see that the equation is not satisfied, so the line does not pass through the point.

So, evaluating the fourth line, we have:

[tex]y=4x+16\\\\32=4*4+16=16+16=32\\\\32=32[/tex]

We can see that the equation is satisfied, so the line does pass through the point (4,32)

Hence, we have that the line that is parallel to the given line and passes through the point (4,32) is:

[tex]y=4x+16[/tex]

Have a nice day!

Answer:

y=4x+16

Step-by-step explanation:

Let us first rearrange the equation of the given line to be in the form y=mx+c. M gives the gradient of the line and c gives the y intercept.

y-1=4(x+3)

y-1=4x+12

y=4x+13

The gradient of parallel lines is equal. For the second line m=4

m=Δy/Δx

(y-32)/(x-4)=4

y-32=4(x-4)

y-32=4x-16

y= 4x+16

The equation of line 2 will be y=4x+16

Answer:

  see below

Step-by-step explanation:

In addition to the exponent rule ...

  (a^b)^c = a^(bc)

it is helpful to know the first few powers of some small integers.

  5^3 = 125

  9^2 = 81

  4^3 = 64

  2^6 = 64

__

Answer:

KM = 10.68; angle K= 55; angle M=35  

Step-by-step explanation:

Using Law of Cosine, you can find KM. Then using Law of Sines, you can find the angle of M. Find the sum of angle M and 90. Then subtract the total of that to 180 to fine angle K.  (sidenote: your angle K should be bigger then angle M since the side measurement of K is larger than M.)

A correct option is option (b).

Given,

[tex]KL=6.2\\LM=8.7\\KM=x(let)[/tex]

Trigonometric ratios:

The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

The given triangle is right angle triangle then

[tex]KM^2=LM^2+KL^2\\KM=\sqrt{(8.7)^2+(6.2)^2}\\KM=\sqrt{114.13}\\ KM=10.68[/tex]

Now, calculate the angles.

[tex]\angle m=sinm\\=\frac{P}{H}\\ =\frac{6.2}{10.6}\\ m=35[/tex]

Again,

[tex]\angle k=sink\\=\frac{P}{H}\\ =\frac{8.7}{10.6}\\ k=55[/tex]

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Answer:

3/2π and π/480

Step-by-step explanation:

The question given says that the minute hand on a clock moves through  complete circle in 1 hour, that is 360° or 2π. It also says that the hour hand moves through 1/12 of a circle, that means 30° or π/6.

To know how many radians do the minute hand and the hour hand move between 1:00 p.m. and 1:45 p.m, it's necessary to calculate how many radians move them per minute.

Between 1:00 p.m. and 1:45 p.m 45 minutes have passed. With that information, the radians can be calculated using multiplication and division.

Minute hand: To know how many radians move the minute hand per minute division wil be used.

Movement in an hour/ minutes in an hour

2π rad/60 min= π/30 rad-min

That means the minute hand move π/30 radians in a minute.

Now, multiplication can be used to calculate how many radians move the minute hand in 1h.

(π/30 rad-min)(45 minutes)= 3/2π rad

The minute hand moves 3/2π radians between 1:00 p.m. and 1:45 p.m.

Hour hand: To know how many radians move the hour hand per minute division wil be used.

Movement in an hour/ minutes in an hour

2π rad/(60 min x 12 hours)= π/360 rad-min

That means the minute hand move π/360 radians in a minute.

Now, multiplication can be used to calculate how many radians move the hour hand in 1h.

(π/360 rad-min)(45 minutes)= π/8 rad

The minute hand moves π/8 radians between 1:00 p.m. and 1:45 p.m.

Between 1:00 p.m. and 1:45 p.m., the minute hand on a clock moves 1.5π radians and the hour hand moves π/8 radians.

In clock motion, a full circle or a complete revolution equates to 2π radians. So, in 1 hour the minute hand moving through a complete circle means it moves through 2π radians. Since the time duration considered here is 45 minutes, which is 0.75 of an hour, the minute hand sweeps 2π * 0.75 = 1.5π radians.

Similarly, for the hour hand, a one-twelfth of a circle would be 2π/12 = π/6 radians. As the time frame is again 0.75 hours, the hour hand sweeps a distance of π/6 * 0.75 = π/8 radians.

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