A soccer game lasts 90 minutes without running into overtime. The coach
plans to switch players out every 12 1/2 minutes. Approximately how many
switches will the coach make in one game?

When an spherical balloon volume is increasing at the rate of [tex]3ft^3/min[/tex] then the diameter of the balloon is increasing [tex]\frac{3}{2\pi }ft /min[/tex]

How can we find the rate of change of balloon's diameter ?

The volume of a spherical balloon is [tex]v=\frac{4}{3} \pi r^3[/tex]

In form of diameter we can write as

[tex]v=\frac{4}{3} \pi (\frac{D}{2} )^3\\=\frac{1}{6} \pi D^3[/tex]

Now we will differentiate both sides wrt to [tex]t[/tex] we get

[tex]\frac{dv}{dt} =\frac{1}{6} \pi 3D^2 \frac{dD}{dt} \\\frac{dD}{dt} =\frac{2}{\pi D^2} \frac{dv}{dt} \\\\when r=1\\D=2ft[/tex]

Given in the question [tex]\frac{dv}{dt} =3ft^3/min[/tex]

thus when we substitute the values we get

[tex]\frac{dD}{dt} =\frac{2}{\pi *2^2} (3)\\\frac{dD}{dt}=\frac{3}{2\pi } ft/min[/tex]

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The expression 3 - 7p² + 11(4 + n) to find an example of each kind of expression is;

3 - 7p² + 11(4 + n)

The expression has 3 parts

3 - 7p² + 11(4 + n)

= 3 - 7p² + 44 + 11n

= 47 + 7p² + 11n

Complete question:

Use the expression 3 — 7p2 + 11(4 + n ) to find an example of each kind of expression

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Thus, distribution is a function that shows the possible values for a variable and how often they occur and categorical values are summarized by counts and/or percents

In statistics, the distribution is a function that shows the possible values for a variable and how often they occur.

The distribution of a data set is the shape of the graph when all possible values are plotted on a frequency graph. Usually, we are not able to collect all the data for our variable of interest. Therefore we take a sample. This sample is used to make conclusions about the whole data set.

The categorical variable is a data in which individuals are placed into groups or categories.

One way to summarize categorical data is to simply count (frequency), or tally up, the number of individuals that fall into each category. Another way is to show the percentage of individuals who fall into each category, thereby creating a relative frequency.

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Answer:

1

Step-by-step explanation:

[tex]\cos A=\frac{3}{4.24} \\ \\ \cos B=\frac{3}{4.24} \\ \\ \frac{\cos A}{\cos B}=1[/tex]

#1

h(2.5)

After 2.5s the ball was at 47ft

#2

g(0)

g(4)

g(7)

Range

#3

Answer:

the scale factor from triangle ABC to triangle DEF would be 8

Step-by-step explanation:

the triangle DEF was actually flipped from triangle ABC

1.line AB corresponds to line EF

AB = 6 , and EF = 48

we multiply 6 by "8" to get to 48

2.line BC corresponds to line ED

BC = 6 , and ED = 48

we multiply 6 by "8" to get to 48

3.line AC corresponds to line FD

AC = 6 , and FD = 48

we multiply 4 by "8" to get to 32

I hope this help

Answer:

  (b)  I, III

Step-by-step explanation:

The correct answer can be chosen based on your knowledge of the shape of the graph of f(x).

The leading coefficient of this quadratic function being positive tells you the graph will be a parabola that opens upward. The left branch of the parabola will extend to positive infinity, as will the right branch.

If there are x-intercepts, the x-values between those will be where the graph has crossed the x-axis and function values are negative.

The answer choices suggest that x=2 and x=5 are x-intercepts of the function's graph. These can be checked, if you like, by evaluating f(2) and f(5).

  f(2) = 2² -7·2 +10 = 4 -14 +10 = 0

  f(5) = 5² -7·5 +10 = 25 -35 +10 = 0

This means the function will be positive for x < 2 and for x > 5. These intervals are described by I and III.

As currently written, solving for [tex]x[/tex], we have

[tex]\sqrt{15} - x + \sqrt3 - x = 6[/tex]

[tex]2x = \sqrt{15} + \sqrt3 - 6[/tex]

[tex]x = \dfrac{\sqrt{15} +\sqrt3 - 6}2[/tex]

I suspect you meant to write

[tex]\sqrt{15 - x} + \sqrt{3 - x} = 6[/tex]

Move one of the roots to the other side, then take squares on both sides.

[tex]\sqrt{15 - x} = 6 - \sqrt{3 - x}[/tex]

[tex]\left(\sqrt{15 - x}\right)^2 = \left(6 - \sqrt{3 - x}\right)^2[/tex]

[tex]15 - x = 36 - 12 \sqrt{3 - x} + (3 - x)[/tex]

[tex]12 \sqrt{3 - x} = 24[/tex]

Take squares again

[tex]\left(12\sqrt{3-x}\right)^2 = 24^2[/tex]

[tex]144 (3 - x) = 576[/tex]

[tex]432 - 144x = 576[/tex]

[tex]144x = -144[/tex]

[tex]\boxed{x = -1}[/tex]

Question 2

1) [tex]\overline{PR} \perp \overline{QS}[/tex], [tex]\overline{PQ} \cong \overline{PS}[/tex] (given)

2) [tex]\overline{PR} \cong \overline{PR}[/tex] (reflexive property)

3) [tex]\angle PRQ[/tex] and [tex]\angle PRS[/tex] are right angles (perpendicular lines form right angles)

4) [tex]\triangle PRQ[/tex] and [tex]\triangle PRS[/tex] are right triangles (a triangle with a right angle is a right triangle)

5) [tex]\triangle PRQ \cong \triangle PRS[/tex] (HL)

Question 3

1) [tex]\angle C[/tex] is a right angle, [tex]\overline{AC} \cong \overline{AE}[/tex], [tex]\overline{DE} \perp \overline{AB}[/tex] (given)

2) [tex]\angle DEA[/tex] is a right angle (perpendicular lines form right angles)

3) [tex]\triangle ACD[/tex] and [tex]\triangle DAE[/tex] are right triangles (a triangle with a right triangle is a right angle)

4) [tex]\overline{AD} \cong \overline{AD}[/tex] (reflexive property)

5) [tex]\triangle ACD \cong \triangle AED[/tex] (HL)

6) [tex]\angle CAD \cong \angle DAE[/tex] (CPCTC)

7) [tex]\overline{AD}[/tex] bisects [tex]\angle BAC[/tex] (if a segment splits an angle into two congruent parts, it is an angle bisector)

Answer:

[tex]\frac{3}{8}[/tex]

Step-by-step explanation:

[tex]\frac{3}{4}[/tex] * [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{8}[/tex]

Step-by-step explanation:

we use the point-slope approach :

y - y1 = m(x - x1)

m is the slope, and (x1, y1) is a point on the line.

so,

1.

y - 2 = 7(x - 1) = 7x - 7

y = 7x - 5

2.

y - -1 = -1×(x - 3) = -x + 3

y + 1 = -x + 3

y = -x + 2

3.

y - 5 = -4(x - -2) = -4x - 8 (3x a "-" is a "-" for 8)

y = -4x - 3

4.

y - 5 = 5/3 × (x - 3) = 5x/3 - 5

y = 5x/3 or 5/3 × x

Answer:

1. [tex]7x-y=5[/tex]

2. [tex]x+y=2[/tex]

3. [tex]4x+y=-3[/tex]

4. [tex]5x-3y=0[/tex]

Step-by-step explanation:

Since we already know the slope and the coordinates of one point, first use the point-slope form to create an equation.

[tex]y-k=m(x-h)[/tex]

[tex]y-2=7(x-1)[/tex]

[tex]y-2=7x-7[/tex]

[tex]7x-y=5[/tex]

[tex]y+1=-1(x-3)[/tex]

[tex]y+1=-x+3[/tex]

[tex]x+y=2[/tex]

[tex]y-5=-4(x+2)[/tex]

[tex]y-5=-4x-8[/tex]

[tex]4x+y=-3[/tex]

[tex]y-5=\frac{5}{3} (x-3)[/tex]

[tex]y-5=\frac{5}{3}x-5[/tex]

[tex]3y-15=5x-15[/tex]

[tex]5x-3y=0[/tex]

Using the surface area formula for rectangular and triangular prism, the surface area of the composite figure is: 444 m².

Total surface area = surface area of the top triangular prism + surface area of the bottom rectangular prism - area of the surface both share together.

Surface area of the top triangular prism = (S1 + S2+ S3)L + bh = (10 + 10 + 16)5 + (16)(6) = 276 m².

Surface area of the bottom rectangular prism = 2(wl + hl + hw) = 2·(5·16+4·16+4·5) = 328 m²

Area of the surface both share together = 2(16)(5) = 160 m²

Total surface area = 276 + 328 - 160 = 444 m².

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The ratio of distance travelled by walking to distance travelled by bus is 1 : 6.

When two quantities of the same units are compared, the ratio is what shows how much of one quantity is included in the other.

Total no. of Feet in a Mile = 5280

Distance Gary walked to the bus stop = 220 feet

Distance travelled by bus = 1/4 mile = (1 / 4)*5280 = 1320 feet

Ratio of distance walking to distance by bus = 220 / 1320 = 1 : 6

Hence, the ratio of distance travelled by walking to distance travelled by bus is 1 : 6.

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The missing angle of the right trapezoid is 126°.

There are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. The trapezoid is a quadrilateral that presents at least one set of parallel sides and the sum of the internal angles is 360°. The trapezoid classifications are:

From the figure, it is possible to see that the image has two right angles. Thus, you have a right trapezoid.

Therefore, from the sum of internal angles, you can find the missing angle:

u+54+90+90=360

u=360-234

u=126

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Answer:

15

Step-by-step explanation:

The blue angle and the yellow angle form a linear pair, so they are supplementary (angle measures add up to 180).

180 - 165 = 15

The machine produces 3000 nails in the month of April 2007.

Production of Nails in the Month of April

According to the given information,

Number of nails manufactured per day by the machine, x = 300  

And, we know that April is the fourth month of a year which has total 30 days.

Hence, number of days the machine is manufacturing nails in the month of April, y = 30

So, the number of nails that will be produced by the machine in the month of April is given by,

N = Number of nails produced per day × Number of days in April

N = xy

N = 300 × 30

N = 9000

Therefore, the machine produces 9000 nails in the April month of year 2007.

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Answer:

Perimeter: 4+[tex]\pi \\[/tex] mm

Area: [tex]\pi[/tex] mm^2

Step-by-step explanation:

Perimeter:

90/360 * 4[tex]\pi \\[/tex] +2 + 2 = 4+ [tex]\pi \\[/tex]

Area:

90/360 * 4[tex]\pi[/tex] = [tex]\pi[/tex]

Answer: 7.14 mm and 3.14 mm²

Step-by-step explanation:

The perimeter of a figure is the total length on the outside of the figure. A regular circle has a perimeter of [tex]2\pi r[/tex], where r is the radius and [tex]\pi[/tex] is an irrational constant, approximately 3.14.

Due to the right angle, we know that this is a quarter circle, as it is a quarter of 360°, or a full circle. Hence, the curved portion of the quarter circle is [tex]\frac{1}{4}* 2\pi r[/tex] or [tex]\frac{1}{2} \pi r[/tex]. The radius is 2 mm, so this value is

[tex]\frac{1}{2} \pi*2=\pi[/tex]

However, this isn't the total perimeter, as there are straight edges in the figure too. Both edges are radii of the whole circle, so both would be 2mm. Their total is

[tex]2+2=4[/tex]

By adding [tex]\pi[/tex] to 4 we get [tex]\pi +4[/tex] or 7.14 mm.

The  area is the total space enclosed by a figure. The total area of a whole circle is [tex]\pi r^2[/tex], where r is still the radius. Since this is a quarter circle, it would take up a quarter of the area, or [tex]\frac{1}{4} \pi r^2[/tex]. We can plug in 2 for r and solve to get the area.

[tex]\frac{1}{4}\pi*2^2\\\frac{1}{4}\pi*4\\\pi[/tex]

Hence, the area is [tex]\pi[/tex], or around 3.14 mm².

Answer:

See below

Step-by-step explanation:

Looks like positive linear to me....slope is up and to the right (positive) and the line drawn shows it ot be approx linear

Answer:-2.4+3.2t

Step-by-step explanation:

-3.6+1.2-1.9t+5.1t

= -2.4+3.2t

The amount of paint needed to cover the wall is 112 square feet

The given parameters are:

Parallel bases = 8 feet and 20 feet

Height = 8 feet

The area is calculated as:

Area = 0.5 * (Sum of parallel bases) * Height

So, we have;

Area = 0.5 * (8 + 20) * 8

Evaluate

Area = 112

Hence, the amount of paint needed to cover the wall is 112 square feet

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Answer: 3n+3

Step-by-step explanation:

Adding 1 to an odd number results in an even number.

The surface area of the composite figure is 524 square meters

The given composite figure is made up of a triangular prism and a rectangular prism. The surface area of the figure is given as:

Surface area = 2(16*5+5*4+16*4) + (16*6) + 2(50)

Take the sum

Surface area = 2(80+20+64) + 96 + 100

Surface area = 2(164) +196

Surface area = 328 + 196

Surface area = 524 square meters

Hence the surface area of the composite figure is 524 square meters

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The percentage of great lakes states would we expect the economic impact from fishing to be between $234.5 and $401.5 is 50%.

Given that mean is $318 , standard deviation is $83.5 and confidence interval is $234.5 and $401.5.

We have to calculate the percentage of great  lakes that we would expect the economic impact from fishing to be between $234.5 and $401.5.

Because we have not given the sample size taken so we will use any test.We are using z test.

We know that,

z=X-μ/σ

where μ is population mean and σ is population standard deviation.

We cannot find p value between $234.5 and $401.5. We have to find the p value between $234.5 and $318 and then add the p value between $318 and $401.5 by calculating.

P value between $234.5 and $318:

z=234.5-318/83.5

=-83.5/83.5

=-1

p value of -1 is 0.1587

P value between $318 and $401.5:

z=401.5-318.5/83.5

=83.5/83.5

=1

p value of z=1 is 0.3413

Total p value=0.1587+0.3413

=0.5

Total percentage=0.5*100

=50%

Hence the percentage that we would expect the impact to be between $234.5 and $401.5 is 50%.

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Answer: The answer is factor 3 out the variable terms

Step-by-step explanation:

The value of f from the given expression is 3

Given the expression below

cos(22f-1) = sin(7f+4),

This can also be expressed

cos(22f-1) = cos(90-7f-4)

cos(22f-1) = cos(86-7f)

22f - 1 = 86 - 7f

Collect the like terms

22f+7f = 86 + 1

29f = 87

f = 3

Hence the value of f from the given expression is 3

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Let X be the number of times you win.

The total number of ways to select 2 balls (order does not matter) =>

The number of ways so that two balls are white:

= 3/55

The number of ways so that two balls are red:

= 3/55

The number of ways so that one ball is red, one is white:

= 9

The number of ways so that two balls are blue:

= 10

i.e. p = 10+9/55 = 19/55

The number of ways so that one ball is blue, one is white:

p = 15/55 = 3/11

The number of ways so that one ball is blue, one is red:

15/55 = 3/11

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Answer:

f-¹(x) = (x + 6)/2

Step-by-step explanation:

Replace f(x) with y.

y = 2x – 6

Interchange x and y.

x = 2y – 6

Solve for y.

y = (x + 6)/2

Replace y with  f-¹(x)

f-¹(x) = (x + 6)/2