What is 33⁄5 as an improper fractions

Answer:

dL/dt  = - 2,019 m/h

Step-by-step explanation:

L²  =  x²  +  y²   (1)    Where  x, and  y are the legs of the right triangle and L the hypotenuse

If the base of the triangle, let´s call x is increasing at the rate of 2 m/h

then  dx/dt =  2 m/h. And the height is decreasing at the rate of 3 m/h or dy/dt = - 3 m/h

If we take differentials on both sides of the equation (1)

2*L*dL/dt = 2*x*dx/dt  + 2*y*dy/dt

L*dL/dt  = x*dx/dt + y*dy/dt         (2)

When  the base is 9  and the height is 22 according to equation (1) the hypotenuse is:

L = √ (9)² + (22)²       ⇒    L = √565       ⇒  L  = 23,77

Therefore we got all the information to get dL/dt .

L*dL/dt  = x*dx/dt + y*dy/dt

23,77 * dL/dt  = 9*2 + 22* ( - 3)

dL/dt  =  ( 18 - 66 ) / 23,77

dL/dt  = - 2,019 m/h

Using implicit differentiation and the Pythagorean Theorem, it is found that the hypotenuse is changing at a rate of -2.02 meters per hour.

The Pythagorean Theorem states that the square of the hypotenuse h is the sum of the squares of the base x and of the height h, hence:

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

In this problem, [tex]x = 9, y = 22[/tex], hence, the hypotenuse is:

[tex]h^2 = 9^2 + 22^2[/tex]

[tex]h = \sqrt{9^2 + 22^2}[/tex]

[tex]h = 23.77[/tex]

Applying implicit differentiation, the rate of change is given by:

[tex]2h\frac{dh}{dt} = 2x\frac{dx}{dt} + 2y\frac{dy}{dt}[/tex]

Simplifying by 2:

[tex]h\frac{dh}{dt} = x\frac{dx}{dt} + y\frac{dy}{dt}[/tex]

The rates of change given are: [tex]\frac{dx}{dt} = 2, \frac{dy}{dt} = -3[/tex].

We want to find [tex]\frac{dh}{dt}[/tex], hence:

[tex]h\frac{dh}{dt} = x\frac{dx}{dt} + y\frac{dy}{dt}[/tex]

[tex]23.77\frac{dh}{dt} = 9(2) + 22(-3)[/tex]

[tex]\frac{dh}{dt} = \frac{18 - 66}{23.77}[/tex]

[tex]\frac{dh}{dt} = -2.02[/tex]

The hypotenuse is changing at a rate of -2.02 meters per hour.

A similar problem is given at https://brainly.com/question/19954153

Answer:

1 mile/hour is equivalent to 1.47 feet/seconds

Step-by-step explanation:

Given

[tex]88 ft/s= 60 miles/hr[/tex]

Required

Determine the equivalent of 1 mile/hour

[tex]88\ ft/s= 60\ miles/hr[/tex]

Express 60 as 60 * 1

[tex]88\ ft/s= 60 * 1\ mile/hr[/tex]

Divide both sides by 60

[tex]\frac{88\ ft/s}{60}= \frac{60 * 1\ mile/hr}{60}[/tex]

[tex]\frac{88\ ft/s}{60}= 1\ mile/hr[/tex]

Reorder

[tex]1\ mile/hr = \frac{88\ ft/s}{60}[/tex]

Divide 88 by 60

[tex]1\ mile/hr = 1.46666666667\ ft/s[/tex]

Approximate to 3 significant figures

[tex]1\ mile/hr = 1.47\ ft/s[/tex]

Hence;

1 mile/hour is equivalent to 1.47 feet/seconds

Answer:

18.18 min

Step-by-step explanation:

The complete question is

On a cold February morning, the radiator fluid in Stanley’s car is -18F. When the engine is running, the temperature goes up 5.4 F per minute. Approximately how long will it take before the radiator fluid temperature reaches 80 F?

The initial temperature of the engine [tex]T_{1}[/tex] = -18 F

rate of increase in temperature r = 5.4 F/min

Final temperature [tex]T_{2}[/tex]  = 80 F

Difference in temperature ΔT = [tex]T_{1} -T_{2}[/tex] = 80 - (-18) = 98 F

time taken to reach this 80 F will be = ΔT/r

where ΔT is the difference in temperature

r is the rate of change of temperature

time taken = 98/5.4 = 18.18 min

Answer:

Step-by-step explanation:

Since the figure above is a right angled triangle we can use trigonometric ratios to find x

To find x we use cosine

cos∅ = adjacent / hypotenuse

From the question

The hypotenuse is x

The adjacent is 10

Substitute these values into the above formula and solve for x

That's

Divide both sides by cos 37

x = 12.52135

We have the final answer as

Hope this helps you

Answer:

probably 16.5

Step-by-step explanation:

Answer:  48

There are many approaches to estimating stuff like this, so there isn't one set answer. My approach is shown below.

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

1 min = 60 sec

30 min = 1800 sec (multiply both sides by 30)

1/2 hr = 1800 sec (replace "30 min" with "1/2 hr")

The value 2014 is fairly close to 1800, so roughly every half hour we have a prize being won. This is an overestimate.

There are 24 hours in a day, so 24*2 = 48 half-hour periods in a day, meaning we have an estimated 48 prizes in a full day. This is an overestimate as well.

--------------------

Extra info:

If you're curious about finding the more accurate value, then you could follow these steps

1 prize = 2014 seconds

x prizes = 86400 seconds (number of seconds in a full day)

1/x = 2014/86400

1*86400 = x*2014

86400 = 2014x

2014x = 86400

x = 86400/2014

x = 42.8997020854021

Round down to get x = 43. We round down because there isn't enough time to get that 44th prize. The value 43 is fairly close to 48, and we can see our earlier estimate of 48 was an overestimate.

Answer:

(3/2, 0, 1)

Step-by-step explanation:

From 2x+y=3 we have => y=3-2x

From 2y-4z=-4 we have -4z=-2y-4 => z=1/2y+1 => z=1/2 (3-2x) +1 => z=5/2-x

Plug in y & z to find x

2x−y+3z=6 => 2x+(3-2x)+3(5/2-x)=6 => 2x+3-2x+15/2-3x=6 => 21/2-3x =6 => x=3/2

plug in x to find y

2x+y=3 => 2(1.5) + y =3 => y=0

plug in y to find z

2y -4z =-4 => 2(0)-4z=-4 => -4z=-4 => z=1

Answer:

C. x-2

Step-by-step explanation:

edge

Answer: the 3rd the answer c

x-2

Step-by-step explanation:

Answer:

$2 per pound = $0.125. per pound

Step-by-step explanation:

The unit of weight conversion from pound to ounce is given as follows;

1 pound weight  = 16 ounces weight

1 ounce weight = 1/16 pound weight

Therefore, whereby the cost of 1 pound weight of an item is two dollars, we have;

The cost of one ounce weight of the item will be the cost of 1 pound weight, divided by 16 and given as follows;

$2 per pound = $2/16 per pound  = $0.125. per pound

Therefore;

$2 per pound = $0.125. per pound.

Answer:

16x^2 + 24x + 9  

Step-by-step explanation:

perfect square trinomial is of the form

a^2 + 2 * a * b + b^2

9x^2 + 9x + 1   = (3x)^2 + 3*3x*1 + 1^2  not a perfect square trinomial

36b^2 − 24b + 8  = ( 6b)^2  -2 * 6b *2 + ( 2 sqrt(2)) ^2  not a perfect square trinomial

16x^2 + 24x + 9  = ( 4x) ^2 + 2 * ( 4x) * 3 + 3^2 = perfect square trinomial

4a^2 − 10a + 25 = ( 2a) ^2 -  1 * 2a *5 + 5^2   not a perfect square trinomial

Answer:

The third answer listed:

[tex]16x^2+24x+9[/tex]

Step-by-step explanation:

The trinomial:  

[tex]16x^2+24x+9[/tex]

can be factored out as follows:

[tex]16x^2+24x+9\\(4x)^2+24x+3^2\\(4x)^2+12x+12x+3^2\\4x(4x+3)+3(4x+3)\\(4x+3)\,(4x+3)\\(4x+3)^2[/tex]

which as can be seen,is the perfect square of a binomial, so this trinomial is what is called a perfect square trinomial.

Answer:

Step-by-step explanation:

If you plot the focus and the directrix on a coordinate plane, because the parabola wraps itself around the focus away from the directrix, we know that this parabola opens to the left. That means its general form is

[tex]4p(x-h)=-(y-k)^2[/tex] where h and k are the coordinates of the vertex and p is the distance between the vertex and either the focus or the directrix because both distances are the same. Knowing that both distances are the same, it logically follows that the vertex is directly in between the focus and the directrix. So the vertex is at the origin, (0, 0). p is 2 because the vertex is at an x value of 0 and the directrix is at the x value of 2, and because the focus is at an x value of -2. Filling in the equation, then:

[tex]4(2)(x-0)=-(y-0)^2[/tex] which simplifies to

[tex]8x=-y^2[/tex] and, solving for x:

[tex]x=-\frac{1}{8}y^2[/tex]

Answer:

9

Step-by-step explanation:

We can set up a systems of equations to find the value of the third side.

Let's assume that [tex]x[/tex] is the length of both sides 1 and 2. Let's also assume that [tex]y[/tex] is the length of the third side.

We know that [tex]x + x + y = 23[/tex], and looking at the first clue we can make the equation [tex]y = 2x-5[/tex].

We can substitute y into the equation [tex]x + x + y = 23[/tex].

[tex]x + x + (2x-5) = 23\\\\2x + 2x-5 = 23\\4x-5 = 23\\4x = 28\\x = 7[/tex]

So the length of the side that is the same as the second is 7.

Now we can plug this into the equation [tex]y = 2x-5[/tex] to find [tex]y[/tex].

[tex]y = 2(7) - 5\\\\y = 14-5\\\\y = 9[/tex]

Hope this helped!

Answer:

9 cm

Step-by-step explanation:

Let's say that the length of the 2 equal sides is x.

That means:

Side 1 = x

Side 2 = x

We know that the third side is 5 less than twice the length of the 2 equal sides, or 2x-5

Side 3 = 2x-5

The perimeter is all sides together.

Side 1 + Side 2 + Side 3

We know the length of each side, so let's put that in instead.

x + x + 2x-5

Let's simplify this expression:

x + x + 2x - 5

2x + 2x - 5

4x - 5

We know the perimeter, 4x-5, is 23 cm.

4x - 5 = 23

4x = 28

x = 7

The third side is 2x-5. If x is 7...

2*7 - 5 = 14-5 = 9

Answer: 9 cm

Answer:

x₁ = 2

x₂ = 10

Step-by-step explanation:

x² + 20 = 12x

x² - 12x + 20 = 0

(x-2)(x-10) = 0

then:

x₁ = 2

x₂ = 10

Check:

x₁

2² + 20 = 12*2

3 + 20 = 24

x₂

10² + 20 = 12*10

100 + 20 = 120

Answer:

=2x+3/4=5.50

x=19/8 or 2 3/8

hope this helps

Step-by-step explanation:

━━━━━━━☆☆━━━━━━━

▹ Answer

q = 16

▹ Step-by-Step Explanation

3(q - 7) = 27

3q - 21 = 27

Add 21 to both sides:

21 + 21 = na

27 + 21 = 48

3q = 48

Divide both sides by 3:

3/3 = q

48/3 = 16

q = 16

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

q=16

Step-by-step explanation:

3q-21=27

27+21=48

48/3=16

Answer:

H. b/a

Step-by-step explanation:

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Step 1: Label our variables

y₂ = 2b

y₁ = b

x₂ = 2a

x₁ = a

Step 2: Plug into formula

m = (2b - b)/(2a - a)

Step 3: Evaluate

m = b/a

Answer:

b/a

Step-by-step explanation:

We have two points so we can use the slope formula

m = (y2-y1)/(x2-x1)

    = ( 2b - b)/ ( 2a -a)

   = b/a

Answer:

Step-by-step explanation:

9x^3,15x^5= 3x^3

The GCF is constructed by multiplying all the factors that are common to all the given expressions, exponentiated to the smallest power.

In our example, the following factors are common to all the given expressions: 3, x^3

Therefore, the GCF is equal to 3x^3.

Answer:

x= 24

Step-by-step explanation:

open the bracket

4×3x =12x + 4 × 2 =8

12×+ 8-6×6

12×+ 12

x= 24

Answer:

12x - 28

Step-by-step explanation:

Because of PEMDAS you start with the parentheses and distribute the 4.

So,

(12x + 8) -6 x 6

Then, solve for the 6's

(12x + 8) -36

Remove the parentheses

12x + 8 - 36

Lastly, you get

12x - 28.

This is as far as you can go because there is no equals sign so you cannot actually solve for x.

Answer:

$76

Step-by-step explanation:

The amount changed is the total amount of the whole entire thing.

Therefore, we use absolute value or simply find the difference.

21 - (-55) = 76

So the bank account changed $76 over the 2 days.

Answer:

2040 miles

Step-by-step explanation

Gas costs 1.35 per gallon and Jose had 81 dollars for gasoline

with this info we can find out how many gallons of gas Jose can buy.

81 divided by 1.35 is 60 gallons of gas

we also know that he can travel 34 miles for each gallon of gas

with this we can find out how far jose can travel

34 multiplied by 60 is 2040 miles

so, with $81, Jose can travel 2040 miles if gas prices are $1.35

Answer:

14/9 inches, or an inch and 5/9 of an inch.

Step-by-step explanation:

If 2/3 inch is the same as 9 miles, then x inches represents 21 miles. We can then set up a proportion.

[tex]\frac{\frac{2}{3} }{9} =\frac{x}{21}[/tex]

9 * x = (2/3) * 21

9x = 2 * 7

9x = 14

x = 14/9 inches.

Hope this helps!

Answer:

1 5/9 ich represent 21 miles

Step-by-step explanation:

Proportions:

2/3  inch  ⇔   9 miles

M  inch   ⇔    21 miles

M = 21*(2/3) / 9

M = 14/9

14/9 = 9/9 + 5/9 = 1 + 5/9 = 1 5/9 inch

Answer:

x=45

Step-by-step explanation:

2x+45+x=180

Combine 2x and x to get 3x.

3x+45=180

Subtract 45 from both sides.

3x=180−45

Subtract 45 from 180 to get 135.

3x=135

Divide both sides by 3.

x=135/3

Divide 135 by 3

x=45

Answer:

(x - 1)² + (y + 4)² = 81

Step-by-step explanation:

Circle Formula: (x - h)² + (y - k)² = r²

(h, k) is the center

2r = d

Step 1: Find r

18 = 2r

r = 9

Step 2: Plug known variables into formula

(x - 1)² + (y + 4)² = 9²

Step 3: Evaluate

(x - 1)² + (y + 4)² = 81

Answer:

(x-1)^2 + (y+4)^2 = 81

Step-by-step explanation:

The equation of a circle can be written as

(x-h)^2 + (y-k)^2 = r^2

where ( h,k) is the center and r is the radius

The center is ( 1,-4)

and the radius is d/2 = 18/2 = 9

(x-1)^2 + (y- -4)^2 = 9^2

(x-1)^2 + (y+4)^2 = 81

Average rate of change ... of what?

Given some continuous function [tex]f(x)[/tex] and some interval [tex][a,b][/tex], its average rate of change over the interval is

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

Without knowing what your function is exactly, I can only give a symbolic answer,

[tex]\dfrac{f(18)-f(0)}{18}[/tex]

Answer: -5/18

Step-by-step explanation: edg

Answer:

a. [tex]\mathtt{P(X \geq 25) =0.0170}[/tex]     ( to four decimal places)

b. [tex]P(22.5<X<25) = 0.9043[/tex]   ( to four decimal places )

c. The limits will be between the interval of   ( 22.33,24.67 )

Step-by-step explanation:

Given that :

mean = 23.50

standard deviation = 5.00

sample size = 50

The objective is to calculate the following:

(a)  What is the likelihood the sample mean is at least $25.00?

Let X be the random variable, the probability that the sample mean is at least 25.00 is:

[tex]P(X \geq 25) = 1 - P(\dfrac{X - \mu}{\dfrac{\sigma}{\sqrt{n}}} < \dfrac{25- 23.50}{ \dfrac{5}{\sqrt{ 50}} })[/tex]

[tex]P(X \geq 25) = 1 - P(Z< \dfrac{1.5}{ \dfrac{5}{7.07107}} })[/tex]

[tex]P(X \geq 25) = 1 - P(Z< \dfrac{1.5 \times 7.071}{ {5}})[/tex]

[tex]P(X \geq 25) = 1 - P(Z< 2.1213)[/tex]

[tex]P(X \geq 25) = 1 - P(Z< 2.12)[/tex]   to two decimal places

From the normal tables :

[tex]P(X \geq 25) = 1 - 0.9830[/tex]

[tex]\mathtt{P(X \geq 25) =0.0170}[/tex]     ( to four decimal places)

(b) What is the likelihood the sample mean is greater than $22.50 but less than $25.00?

[tex]P(22.5<X<25) = P(\dfrac{X-\mu}{\dfrac{\sigma}{\sqrt{n}}} <\dfrac{25-23.5}{\dfrac{5}{\sqrt{50}}} ) - P(\dfrac{X-\mu}{\dfrac{\sigma}{\sqrt{n}}} <\dfrac{22.5-23.5}{\dfrac{5}{\sqrt{50}}} )[/tex]

[tex]P(22.5<X<25) = P(Z<\dfrac{1.5}{\dfrac{5}{7.071}} ) - P(Z<\dfrac{-1}{\dfrac{5}{7.071}} )[/tex]

[tex]P(22.5<X<25) = P(Z<2.12) - (Z<-1.41 )[/tex]

[tex]P(22.5<X<25) = (0.9830 ) - (0.0787)[/tex]

[tex]P(22.5<X<25) = 0.9043[/tex]  to four decimal places

(c) Within what limits will 90 percent of the sample means occur?

At 90 % confidence interval, level of significance = 1 - 0.90 = 0.10

The critical value for the [tex]z_{\alpha/2} = 0.05[/tex] = 1.65

Standard Error = [tex]\dfrac{\sigma}{\sqrt{n}}[/tex]

Standard Error =  [tex]\dfrac{5}{\sqrt{50}}[/tex]

Standard Error = 0.7071

Therefore, at 90 percent of the sample means, the limits will be between the intervals of : [tex](\mu \pm z_{\alpha/2} \times S.E)[/tex]

Lower limit =  ( 23.5 - (1.65×0.707) )

Lower limit =  ( 23.5 - 1.16655 )

Lower limit = 22.33345

Lower limit = 22.33    (to two decimal places).

Upper Limit = ( 23.5 + (1.65*0.707) )

Upper Limit = ( 23.5 + 1.16655 )

Upper Limit = 24.66655

Upper Limit = 24.67

The limits will be between the interval of   ( 22.33,24.67 )

Answer:

(n^(2)+6n-4)(2n-4)

Answer:

We conclude that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has​ decreased.

Step-by-step explanation:

The complete question is: In a previous​ poll, ​46% of adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Suppose​ that, in a more recent​ poll, 480 of 1081 adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Is there sufficient evidence that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has​ decreased? Use the [tex]\alpha[/tex] = 0.10 significance level.

Let p = population proportion of families with children under the age of 18 who eat dinner together seven nights a week.

So, Null Hypothesis, : p 46%      {means that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has increased or remains same}

Alternate Hypothesis, : p < 46%      {means that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has​ decreased}

The test statistics that will be used here is One-sample z-test for proportions;

                             T.S.  =    ~  N(0,1)

where, [tex]\hat p[/tex] = sample proportion of families = [tex]\frac{480}{1081}[/tex] = 0.44

           n = sample of adults with children under the age of 18 = 1081

So, the test statistics =    

                                   =  -1.32

The value of z-statistics is -1.32.

Also, the P-value of the test statistics is given by;

                    P-value = P(Z < -1.32) = 1 - P(Z [tex]\leq[/tex] 1.32)

                                  = 1 - 0.9066 = 0.0934

Since the P-value of our test statistics is less than the level of significance as 0.0934 < 0.10, so we have sufficient evidence to reject our null hypothesis as the test statistics will fall in the rejection region.

Therefore, we conclude that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has​ decreased.

Answer:

The greatest common factor of the expression is 25x

Step-by-step explanation:

Here, we are interested in giving the greatest common factor of the expression.

We can do this by factorization till we have no common factors left.

the expression is;

100x^2 -250xy + 75x

we start with the common factor x;

x(100x -250y + 75)

The next thing to do here is to find the greatest common factor of 100,250 and 75.

The greatest common factor here is 25.

Thus, we have;

25x(4x -10y + 3)

There is no more factor to get from the terms in the bracket. This simply means that the terms in the bracket are no longer factorizable

So the greatest common factor we have is 25x

Answer:

[tex](-5)^{11}[/tex]

Step-by-step explanation:

We can use the exponent rules. If we have [tex]\frac{a^b}{a^c}[/tex], then it will simplify to [tex]a^{b-c}[/tex].

b is 5, c is -6, and a is -5 so:

[tex]-5^{5-(-6)}\\-5^{11}[/tex]

Hope this helped!

Answer:

A = 36 cm^2

Step-by-step explanation:

The perimeter of a square is given by

P =4s

24 = 4s

Divide by 4

24/4 = 4s/4

6 =s

The area of a square is

A =s^2

A = 6^2

A = 36 cm^2

Answer:

we can set the 9 as a benchmark to be the score for the passing grade so that probability of passing a student who guesses every question is less than 0.10

Step-by-step explanation:

From the given information;

Sample  size n = 12

the probability of passing a student who guesses on every question is less than 0.10

In a alternative - response question (true/false) question, the probability of answering  a question correctly  = 1/2 = 0.5

Let X be the random variable that is represent number of correct answers out of 12.

The X [tex]\sim[/tex] BInomial (12, 0.5)

The probability mass function :

[tex]P(X = k) = \dfrac{n!}{k!(n-k)!} \times p^k\times (1-p)^{n-k}[/tex]

[tex]P(X = 12) = \dfrac{12!}{12!(12-12)!} \times 0.5^{12}\times (1-0.5)^{12-12}[/tex]

P(X = 12) = 2.44 × 10⁻⁴

[tex]P(X = 11) = \dfrac{12!}{11!(12-11)!} \times 0.5^{11}\times (1-0.5)^{12-11}[/tex]

P(X =11 ) = 0.00293

[tex]P(X = 10) = \dfrac{12!}{10!(12-10)!} \times 0.5^{10}\times (1-0.5)^{12-10}[/tex]

P(X = 10) = 0.01611

[tex]P(X = 9) = \dfrac{12!}{9!(12-9)!} \times 0.5^{19}\times (1-0.5)^{12-9}[/tex]

P(X = 9) = 0.0537

[tex]P(X = 8) = \dfrac{12!}{8!(12-8)!} \times 0.5^{8}\times (1-0.5)^{12-8}[/tex]

P(X = 8)  = 0.12085

[tex]P(X = 7) = \dfrac{12!}{7!(12-7)!} \times 0.5^{7}\times (1-0.5)^{12-7}[/tex]

P(X = 7) = 0.19335

.........

We can see that,a t P(X = 9) , the probability is 0.0537 which less than 0.10 but starting from P(X = 8) downwards the probability is more than 0.01

As such, we can set the 9 as a benchmark to be the score for the passing grade so that probability of passing a student who guesses every question is less than 0.10