Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Solve the equation .

The solution of the equation is x =
.

Answer:

The total number of feet travelled by the motorcycle is 396 feet

Step-by-step explanation:

Using the constant speed relationship with the distance:

           v = s/t

From the above equation the distance travelled will be:

          s = v * t              (i)

We are given with the v, that is:

          v = 45 miles per hour

Converting in to feet per second.

          v = (45 * 5280)/3600 feet / s

          v = 66 feet per second

Now, put that v and t in equation (i)

          s = 66 * 6

          s = 396 feet

If the speed of the ball after kicking is 48 feet per second then the ball will return on the ground after 3 seconds.

Given that the speed of the ball after kicking is 48 feet per second and the function that represents the height of the ball is [tex]-16t^{2} +48t[/tex].

We are required to find the time that the ball took to travel before returning the ground.

We know that speed is the distance a thing covers in a particular time period.

The height of the ball after t seconds is as follows:

h(t)=[tex]-16t^{2} +48t[/tex]

It is at ground at the instants of t.

Hence,

[tex]-16t^{2} +48t[/tex]=0

-16t(t-3)=0

We want value of t different of 0, hence :

t-3=0

t=3.

Hence if the speed of the ball after kicking is 48 feet per second then the ball will return on the ground after 3 seconds.

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Answer:

B. t=3

Step-by-step explanation:

i took the test and got it right

Answer:

[tex]12.50 \space\ h = 2500.75[/tex]

Step-by-step explanation:

We know from the question that the student earned $12.50 per hour.

Using this information, we can say that if the student worked for h hours, they would make a total of 12.50 × h dollars.

We also know that the total money they earned is $2500.75.

∴ Therefore, we can set up the following equation:

[tex]\boxed {12.50 \times h = 2500.75}[/tex]

From here, if we want to, we can find the number of hours worked by simply making h the subject of the equation and evaluating:

h = [tex]\frac{2500.75}{12.50}[/tex]

  = 200.6 hours

Answer: 12.50h = 2500.75

Step-by-step explanation:

We know from the question that the student earned $12.50 per hour.

Using this information, we can say that if the student worked for h hours, they would make a total of 12.50 × h dollars.

We also know that the total money they earned is $2500.75.

The side lengths of the isosceles triangle are:

AO = 16 units

AB = 16 units

OB = 6 units.

An isosceles triangle is a type of triangles that has two sides that are congruent to each other, and two base angles that are opposite these two sides that are also congruent to each other.

Referring to the isosceles triangle in the image attached below, we have the following:

One of the congruent sides = AO = 3x + 4 units

The other congruent side = AB = x + 12 units

The third side = OB = 4x - 10 units

Applying the definition of an isosceles triangle, we can create an equation as shown below to find x:

AO = AB [congruent sides]

Substitute

3x + 4 = x + 12

3x - x = - 4 + 12

2x = 8

2x/2 = 8/2

x = 4

Find the side lengths of the isosceles triangle by plugging in the value of x:

One of the congruent sides = AO = 3x + 4 = 3(4) + 4 = 16 units

The other congruent side = AB = x + 12 = 4 + 12 = 16 units

The third side = OB = 4x - 10 = 4(4) - 10 = 6 units.

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The answer is B.

If the terminal point of θ is at (0, -1), then tanθ is equal to :

The tangent of the given angle is undefined, so the correct option is B.

The tangent function is one of the main six trigonometric functions and is generally written as tan x. It is the ratio of the opposite side and the adjacent side of the angle in consideration in a right-angled triangle.

Given that on a unit circle, the terminal point of θ is (0, - 1) we need to determine tan θ,

We know that the terminal point of θ is (0, -1).

Now, the tangent of an angle is equal to the quotient between the y-component and the x-component of the terminal point, then we have:

tan(θ) = =1/0

And we can't divide by zero, so it is undefined, then the correct option is B.

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Answer: 170 marbles

Step-by-step explanation: Rani had 20 more marbles than Seema and Seema had 150. 150+20 is 170.

Answer:

not sure but I think it is this

Solving a system of equations we can see that:

Let's define:

When the airplane travels against the wind, the total speed is:

(A - W)

In this way, we know that the airplane travels 1350 miles in 5 hours, then:

(A - W) = 1350mi/5h

When the airplane travels with the wind, it takes 3.75 hours to travel the same distance, then:

(A + W) = 1350mi/3.75h

We have now a system of equations:

(A - W) = 1350mi/5h

(A + W) = 1350mi/3.75h

If we isolate A on the first equation, we get:

A = 270mi/h + W

Replacing that in the other equation we get:

270mi/h + W + W = 360 mi/h

Solving for W we get:

2*W = 360mi/h - 270mi/h = 90mi/h

W = 90mi/h = 45mi/h

And the airplane rate is:

A =  270mi/h + W = 270mi/h + 45mi/h = 315 mi/h

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[tex]4r {}^{3} s - rs + 7r {}^{3} s + 8rs - 3 + 8rs + 6 \\ add \: \: terms \: \: of \: \: same \: \: variables \\ 11r {}^{3} s + 15rs + 3[/tex]

Answer:

Width is 11 inches

Step-by-step explanation:

I am not sure what the question is.  I think you might be looking for the width length.  The perimeter is the distance around a rectangle.  If the whole distance around is 48.  We have 2 lengths and 2 widths.  They tell us that the length is 13.  We have two lengths so the lengths add up to 26.  We can subtract that from 48 and that leaves us with 22 (48-26)  This is the total for the 2 widths.  Since the 2 widths are the same length we divide that number by 2 to get 11.

11 + 11+ 13 + 13 = 48

Answer:

a = 97° , b = c = 146°

Step-by-step explanation:

a and 83° are same- side interior angles and sum to 180°

a + 83° = 180° ( subtract 83° from both sides )

a = 97°

34° and b are same- side interior angles and sum to 180°

b + 34° = 180° ( subtract 34° from both sides )

b = 146°

b and c are corresponding angles and are congruent , so

c = b = 146°

Answer:

< a = 97 degrees.

< b = 146 degrees.

< c = 146 degrees.

Step-by-step explanation:

We have 2 lines crossing 2 parallel lines.

Internal angles between the 2 parallel lines add up to 180 degrees, so

34 + <b = 180

<b = 180 - 34 = 146 degrees

Also

<a + 83 = 180 degrees (also internal angles)

---> <a = 97 degrees

< c and < b are corresponding angles so are congruent, therefore

<c = < b = 146 degrees.

Answer:

B={1,2,3,4,6and12}

n (B) =6

Step-by-step explanation:

Factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. The other factors of 12 are 1, 2, 4, and 12.

Hope it helps!

Step-by-step explanation:

I just answered this. how often did you post that question ?

she added 54-48 = 6g.

how many % of 48g are these 6g ?

100% = 48

1% = 100%/100 = 48/100 = 0.48g

how many % are 6g ?

as many as how often 1% (0.48g) fits into 6g :

6 / 0.48 = 12.5%

Answer:

ur answer is B

Step-by-step explanation:

Answer:

B

As root over 72 is 8.48 and after we round off we get 8.5 so no B is correct

The probability that the service time will be more than three minutes is 0.3012.

Given that the average wait time at the Rivertown bank's neighborhood branch is 2.5 minutes and has an exponential distribution,

The time it takes to succeed in a continuous sequence of independent trials is described by the exponential distribution, which is a continuous probability distribution.

At the River Town Bank's neighborhood branch, the random variable X service time has an exponential distribution with a mean value of 2.5 minutes. Therefore,

[tex]f(x)=\left\{\begin{array}{ll}\theta e^{-\theta x},& \theta \geq 0,0\leq x\leq \infty\\0&\text{otherwise}\end{array}[/tex]

E(x)=1/θ

θ=1/2.5

θ=0.4

The probability that the service time will be longer than three minutes:

[tex]\begin{aligned}P(X > 3)&=1-P(X\leq 3)\\ &=1-(1-e^{-0.4\times 3}\\ &=e^{-1.2}\\ &=0.3012\end[/tex]

Since the service duration has an exponential distribution and a mean of 2.5 minutes, the needed chance that it will exceed 3 minutes is 0.3012.

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(C) [tex]8x^{3} -7x^{2} -6x+5[/tex] represents a cubic expression.

To determine which expression represents a cubic expression:

Therefore, (C) [tex]8x^{3} -7x^{2} -6x+5[/tex] represents a cubic expression.

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The complete question is given below:

Choose the expression that represents a cubic expression.

(A) −7x + 14

(B) 7x2 − 5x + 6

(C) 8x3 − 7x2 − 6x + 5

(D) 9x4 + 8x3 − 6x2 − 2x + 11

The standard deviation exists as the positive square root of the variance.

So, the standard deviation = 4.47.

Given data set: 13 17  9 21

To calculate the mean of the data.

We know that mean exists as the average of the data values and exists estimated as:

Mean [tex]$=\frac{13+17+9+21}{4} \\[/tex]

Mean [tex]$=\frac{60}{4} \\[/tex]

Mean = 15

To find the difference of each data point from the mean as:

Deviation:

13 - 15 = -2

17 - 15 = 2

9 - 15 = -6

21 - 15 = 6

Now we have to square the above deviations we obtain:

4, 4, 36, 36

To estimate the variance of the above sets:

variance [tex]$=\frac{4+4+36+36}{4}$[/tex]

Variance [tex]$=\frac{80}{4}$[/tex]

Variance = 20

The standard deviation exists as the positive square root of the variance. so, the standard deviation [tex]$=\sqrt{20 }=4.47$[/tex].

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Answer:

4.4

Step-by-step explanation:

The answer above is correct.

Using proportions, it is found that the value of n is of [tex]n \geq 11[/tex].

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

On the first 15 games, the team wins 2 games and losses 13. Then, in each week, the team plays 3 games, winning 2. Then:

The proportion of wins is given as follows:

[tex]\frac{2 + 2n}{15 + 3n}[/tex]

The proportion is of at least 50%, hence:

[tex]\frac{2 + 2n}{15 + 3n} \geq 0.5[/tex]

We solve the inequality for n, similarly to how we would solve an equality, applying cross multiplication. Then:

[tex]2 + 2n \geq 7.5 + 1.5n[/tex]

[tex]0.5n \geq 5.5[/tex]

[tex]n \geq \frac{5.5}{0.5}[/tex]

[tex]n \geq 11[/tex]

The value of n is of [tex]n \geq 11[/tex].

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Answer:

10

Step-by-step explanation:

By the alternate interior angles theorem,

[tex]4x=2x+20 \\ \\ 2x=20 \\ \\ x=10[/tex]

The equation of the directrix is x = -3

A mirror-symmetrical, roughly U-shaped plane curve known as a parabola. It corresponds to a number of mathematical models that appear to be superficially dissimilar but yet all define the exact same curves. A point and a line are one way to describe a parabola.

Given the general equation of a parabola expressed as

(y-y0)² = 4a(x-x0) ... 1

Equation of the directrix will be expressed as x = x0 - a

From the equation given;

y² = 12x ... 2

Comparing 1 and 2;

x - x0 = x

-x0 = x - x

-x0 = 0

x0 = 0

Similarly;

y-y0 = y

-y0 = y - y

-y0 = 0

y0 = 0

Also;

4a = 12

a = 12/4

a = 3

Substituting x0 =0, y0 = 0 and a = 3 into the equation of the directrix above, we will have;

x = x0 - a

x = 0 - 3

x = -3

Hence,

the equation of the directrix is x = -3

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The value of the missing side x is 38.40 units given the triangle is a right angled triangle with angle 38° and side opposite to the angle is 30 units. This can be obtained by using trigonometric ratios.

Trigonometric identities,

If in a right triangle ΔABC where A is the right angle

In the question,

x is the adjacent side of the angle 38° and 30 units is the opposite side.

The ratio with opposite side and adjacent side is tan A

Therefore,

⇒ tan 38° = [tex]\frac{opposite\ side}{adjacent\ side}[/tex]

⇒ tan 38° = 30/x

⇒ x = 30/tan 38°

∵ tan 38° = 0.781285627

⇒ x = 30/0.781285627

⇒ x = 38.398249

⇒ x = 38.40

Hence the value of the missing side x is 38.40 units given the triangle is a right angled triangle with angle 38° and side opposite to the angle is 30 units.

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Answer:

7/10

Step-by-step explanation:

take 3, 2, 1 from the equation and your left with 7 numbers. Add those together you get 10. 7/10 is the probability that you will draw a number greater than 3

Answer:

Situation 2 (B)

Step-by-step explanation:

I think it would be B since the power of the gear increases proportionally with the radius.

Answer:

$0.03

Step-by-step explanation:

2.31/11 =.21

2.70/15 =.18

.21-.18 = .03

Answer:

The rope is worth 13.

The shoe is worth 5.

The clock is worth 3.

Step-by-step explanation:

We know that the weights are 8 so we will use 8 for the weights.

Let s = show

Let r = rope

Let c = clock

We have three unknowns so we need three equations.

8 + s = r                      c + s = 8                                 s= c +2

There are a number of ways that we can approach this.  Let's substitute

c + 2 for s in the first 2 equations.

8 + s = r

8 + c + 2 = r

10 + c = r

c + s = 8

c + c + 2 = 8

2c + 2 = 8  

2c = 6

c = 3  we found the value of the clock.

Now, let's substitute 3 in for 3 in the bold equation above.

10 + c = r

10 + 3 = r

13 = r we found the value of the rope.

We can use any of the equations to find the shoe.

s= c + 2

s = 3 + 2

s = 5

This is tricky.  It takes a lot of practice.  Don't give up!

Shoe= 5

Rope= 13

Clock= 3

We can start by giving each item a variable. Shoe= s, rope= r, clock= c. The weight is 8, so we don't need to give it a variable. Our equations are now:

8+s= r

c+s= 8

s= c+2

Now, we can isolate a variable to solve for it using the substitution method. Let's start with s.

c+s=8

-c    -c

s= 8-c

Now, we'll take another equation and plug s in.

8-c=c+2

 +c +c

8= 2c+2

-2      -2

6=2c

c=3

Now we know that the clock is 3. Put 3 into the last equation, and add 3+2 to get 5 for the shoe. 5 in the first equation for the shoe plus 8 as the weight means the rope is 13.

hope this helped!

Answer:

A

Step-by-step explanation:

the means is less than the median

Using the Fundamental Counting Theorem, there are 20 possibilities for their big night out.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

For this problem, we have that:

The number of possibilities is given by:

N = 5 x 4 = 20.

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Answer:

  0.33 ⋅ 10^−15

Step-by-step explanation:

Scientific notation requires exactly one non-zero digit to the left of the decimal point.

The number ...

  0.33 ⋅ 10^−15

has no non-zero digits to the left of the decimal point. It is not in "scientific notation."

__

Additional comment

Expressed in scientific notation, it would be ...

     3.3 ⋅ 10^−16

Answer:

The answer is 314

Step-by-step explanation:

You need to do

3.14(pie) times the radius times the height divided by 3

Answer:

C. 314 [tex]in^{3}[/tex]

Step-by-step explanation:

The volume of a cone is: 1/3[tex]\pi[/tex][tex]r^{2}[/tex]h'

1/3 x 3.14 x [tex]5^{2}[/tex] x 12

1/3 x 3.14 x 25 x 12

1/3 x 3.14 x 300

100 x 3.14

V = 314