A light bulb can be at most 50 watts to be safely used in this light fixture

[tex]\dfrac{2x-3}x = \dfrac{14}{x+5}\\\\\implies (2x-3)(x+5) = 14x\\\\\implies 2x^2 +10x -3x -15 -14x=0\\\\\implies 2x^2-7x-15=0\\\\\text{Apply quadratic formula,}~~x= \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}.\\\\\text{In this case,}~ a=2, b=-7~ \text{and}~ c = -15. \\\\\\x = \dfrac{-(-7) \pm \sqrt{(-7)^2 -4\cdot 2 \cdot (-15)}}{2(2)}\\\\\\\implies x = \dfrac{7 \pm \sqrt{169}}{4}\\\\\\\implies x = \dfrac{7 \pm 13}4\\\\\\[/tex]

[tex]\text{Hence} ~x = \dfrac{7+13}{4} = \dfrac{20}4 = 5 ~\text{or}~ x = \dfrac{7-13}4 = -\dfrac{6}4 = -\dfrac 32[/tex]

Answer:

Step-by-step explanation:

2

Answer:

The weather forecast says that there is a "30% chance of rain," and we think we understand what it means. This quantitative statement is assumed to be unambiguous and to convey more information than does a qualitative statement like "It might rain tomorrow." Because the forecast is expressed as a single-event probability, however, it does not specify the class of events it refers to. Therefore, even numerical probabilities can be interpreted by members of the public in multiple, mutually contradictory ways. To find out whether the same statement about rain probability evokes various interpretations, we randomly surveyed pedestrians in five metropolises located in countries that have had different degrees of exposure to probabilistic forecasts--Amsterdam, Athens, Berlin, Milan, and New York. They were asked what a "30% chance of rain tomorrow" means both in a multiple-choice and a free-response format. Only in New York did a majority of them supply the standard meteorological interpretation, namely, that when the weather conditions are like today, in 3 out of 10 cases there will be (at least a trace of) rain the next day. In each of the European cities, this alternative was judged as the least appropriate. The preferred interpretation in Europe was that it will rain tomorrow "30% of the time," followed by "in 30% of the area." To improve risk communication with the public, experts need to specify the reference class, that is, the class of events to which a single-event probability refers.

Answer:

See answer below.

Step-by-step explanation:

3x - 2 =  4                Given

   +2  =  +2

  3x     =  6               Addition Property of Equality

3x/3  = 6/3

     x = 2                  Division Property of Equality

Answer:

Thats one heck of a whole lot nuts

Step-by-step explanation:

Answer:

4 1/9

Step-by-step explanation:

Well we can infer that the whole number will be 4. And 0.111 repeating is 1/9 as a fraction.

Answer:

Answer is A and C on edge

Step-by-step explanation:

The composite function that can be used to determine the volume of the balloon after t seconds, when V is composed with r is 1/48πt⁶ and after 6 second it is 972π.

When the two or more than two functions are written in the form of single function. Then such function is called the composite function.

Let suppose there is a function f(x) and another function g(x). Then the composite function can be given as,

[tex]f[g(x)][/tex]

The volume of air in a balloon is represented by the function,

[tex]V(r)=\dfrac{4}{3}\pi r^3[/tex]

Here, r is the radius of the balloon, in inches.

The radius of the balloon increases with time, in seconds, by the function,

[tex]r(t) = \dfrac{1}{4}t^2[/tex]

The composite function that can be used to determine the volume of the balloon after t seconds is,

[tex]V(r(t))=\dfrac{4}{3}\pi (\dfrac{1}{4}t^2)^3\\V(r(t))=\dfrac{4}{3}\pi (\dfrac{1}{64}t^6)\\V(r(t))=\dfrac{1}{48}\pi t^6[/tex]

After the 6 seconds,

[tex]V(r(6))=\dfrac{1}{48}\pi (6)^6\\V(r(6))=\dfrac{1}{48}\pi \times46656\\V(r(6))=972\pi[/tex]

Thus, the composite function that can be used to determine the volume of the balloon after t seconds, when V is composed with r is 1/48πt⁶ and after 6 second it is 972π.

Learn more about the composite function here;

https://brainly.com/question/10687170

#SPJ2

The Answer there are 9*8 = 72 ways to choose a president and vice president

Step-by-step explanation:

Answer:

- 90

Step-by-step explanation:

Evaluate 1*- 5 then the outer one

1*- 5 ( with x = 1 and y = - 5 )

= 1(- 5) + 2(- 5)

= - 5 - 10

= - 15

Then

4*- 15 ( with x = 4 and y = - 15 )

= 4(- 15) + 2(- 15)

= - 60 - 30

= - 90

[tex]0.\overline{36} = \dfrac{36-0}{99} = \dfrac{36}{99} = \dfrac{4}{11}\\\\\\0.3\overline{6}= \dfrac{36-3}{90} = \dfrac{33}{90} = \dfrac{11}{30}\\\\\\0.36 = \dfrac{36}{100} = \dfrac{9}{25}[/tex]

Answer: One crate of peaches is $5

Step-by-step explanation:

All you do for this question is divide 125 by 25 gives us 5

Answer:

5

Step-by-step explanation:

Just decide 125 by 25 and get the answer :)

The completed proof is presented as follows;

By definition of a rhombus [tex]\overline{JK} \cong \overline{KM}[/tex] and by the reflexive property of

congruence [tex]\overline{KP} \cong \overline{KP}[/tex], because the diagonals of a rhombus bisect a pair

of opposite angles, ∠JKP ≅ ∠MKP, making ΔJKP ≅ ΔMKP by the SAS

congruency postulate, because CPCTC, ∠JPK ≅ ∠MPK, and these angles

are right angles because two angles that form a linear pair are congruent,

thereby making, [tex]\overline{JK} \perp \overline{KM}[/tex] by definition of perpendicular segments.

Reasons:

Please find attached the drawing of the given rhombus JKMH, that show

the point of intersection of the diagonals JM and HK at point P.

Learn more about the properties of a rhombus here:

https://brainly.com/question/10618409

The equivalent value of the expression 1, point, 86, divided by, 2 is given by A = 0.93.

Given data:

Let the expression be represented as A.

Now, the value of A is

A = 1, point, 86, divided by, 2.

Substituting the values in the equation:

[tex]A=\frac{1.86}{2}[/tex]

On simplifying the equation:

[tex]A=0.93[/tex]

Therefore, the value of A is 0.93

Hence, the equation is A = 0.93

To learn more about equations, refer:

https://brainly.com/question/19297665

#SPJ6

The complete question is attached below:

Find the equivalent value of the expression "1, point, 86, divided by, 2".

Answer:

Step-by-step explanation:

Exact Form:

2

√

2

+

3

√

5

−

2

2

2

+

3

5

-

2

Decimal Form:

7.53663105

…

Answer:

28

Step-by-step explanation:

2(√2+3)² -3(√2+3*√2-2)

expand collect like terms

2(2+6√2+9)-3(4√2-2)

2(2+6√2+9)-3(4√2-2)

calculate remove parentheses

2(11+6√2)-12√2+6

remove parentheses

22+12√2-12√2+6

remove opposite and calculate

solution= *28*

was this helpful???!

Answer:

hope this helps

Step-by-step explanation:

192 fl oz. = 6 quarts

to get this you divide the fluid ounces by 32.

Answer:

A = 9.2 cm²

Step-by-step explanation:

A = 1/2 bh, you know the base = 4.6 and you need to find the height of the triangle.

Drawn the attitude of the equilateral triangle to the base and use a² + b² = c²

c = side of the triangle = 4.6 , b = 1/2 0f 4.6 = 2.3 . the attitude to the base ÷ the base in half.

a² + (2.3)² = (4.6)²

a² + 5.29 = 21.16

a² = 21.16 - 5.29

a² = 15.87

[tex]a = \sqrt{15.87}[/tex]  

Now we know the height of the triangle = [tex]\sqrt{15.87}[/tex] , the base = 4.6

A = 1/2bh

A = 1/2 (4.6)([tex]\sqrt{15.87}[/tex] )

A  = 9.1625

A = 9.2 cm²    or the A of any equilateral triangle = [tex]\frac{\sqrt{3} }{4} s^2[/tex]

                                              A = [tex]\frac{\sqrt{3} }{4} (4.6)^2[/tex]

                                              A = 9.1625

                                              A = 9.2

Answer:

SU + UT = RT

Step-by-step explanation:

Given that TU = 6 units, RT = 12 units and RS = 24 units.

So,

For finding US, we will subtract the length of RT and TU from RS.

US = RS - RT - TU

US = 24 - 12 - 6

US = 6 units

Putting all the given values in the given conditions, we get the first option right, which is:

SU + UT = RT

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

Answer: C) Move it 3 places to the left

Explanation:

We're dividing the number [tex]34.62[/tex] by [tex]10^3[/tex], which is the same as dividing by 1000.

The exponent 3 tells us how many spots to move the decimal point. We move to the left because the number gets smaller. If we multiplied by [tex]10^3[/tex], then we'd move the decimal point 3 spots to the right.

So, [tex]34.62 \div 10^3 = 34.62 \div 1000 = 0.03462[/tex]

Answer:

12 km

Step-by-step explanation:

20 minutes = 20 * 60 = 1200 second

distance = velocity * time

car 1 = 1200 * 20 = 24000 m = 24km

car 2= 1200 * 10 = 12000 m = 12km

so distance between them after 20 minutes is 24 -12 = 12 km

Answer:  It is highly unlikely to get both multiplication cards on the first try.

Part A      The question asked is: there are two multiplication cards out of one hundred cards including forty-two addition problem cards and fifty-six subtraction cards.What are the odds of getting just the multiplication cards.The assumption is this we are talking about the first try.

Part B       You make the multiplication cards,  card#1 and card#2. All other cards are #3-100. Then you use the random number generator to see odds of two numbers out of one hundred, which is 0.02%. as I did 2/100 x 1/99 then multiply by 100 so.02

Part C      I got 83 and 27as my first two numbers with my random number generator, So Malachi didn't get a multiplication card in this random test. card #1 and card #2 are the multiplication cards

Part D    The percentage of the time that you'd expect both multiplication cards to be picked is 0.002 or .2%. The proportion of the time that it happened here is 5/1500=.00333 or .33%, which means that this is pretty much in line with what you'd expect

Step-by-step explanation: I got a 10/10 on 3.07 essay test for honors statistics.

Answer:

Asapa

[tex] (sin2(0) [/tex]

Answer:

A

Step-by-step explanation:

Can't have 0 in the denominator

The corresponding values of d, e ad f are 1, 1/16, and 1/256 respectively

Find the table of values attached. From the given table the function of the output is expressed as [tex]g(x) = 4^{-x}[/tex]

If x = 0, then;

[tex]g(0) = 4^{-0}\\g(0) = 1/4^0\\g(0)=1/1 = 1\\[/tex]

If x  = 2

[tex]g(2) = 4^{-2}\\g(2) = 1/4^2\\g(2)=1/16[/tex]

If x = 4;

[tex]g(4) = 4^{-4}\\g(4) = 1/4^4\\g(4)=1/256[/tex]

Therefore the corresponding values of d, e ad f are 1, 1/16 and 1/256 respectively

Learn more on table of functions here: https://brainly.com/question/3632175

Answer:

a =  ⇒ 1 

b = ⇒ 1/16

c = ⇒ 1/256

d =  ⇒ 1 

e =  ⇒ 4/9

f =   ⇒ 16/81

[tex]\frac{13^5}{13^x} =13^4 =>13^{5-x} =13^4\\ =>5-x=4=> x=5-4=1[/tex]

ANSWER: x = 1

ok done. Thank to me :>

Answer:

a = 19.6 (rounded to the nearest tenth)

Step-by-step explanation:

a^2 + b^2 = c^2

Hypotenuse - 35 m, Legs - 29 m, x

a^2 +29^2 = 35^2

a^2 + 841 = 1225

Subtract 841 from both sides

a^2 = 384

Square root both sides

√a^2 = √384

a = 19.595

Answer:

$35

Step-by-step explanation:

if $7 is only 20% of the original price multiply 7×5

-20%×5=100%

same thing as 7×5=35

just switch the percent by its worth

Answer:

8/3

Step-by-step explanation:

The square root of 8 can actually be written [tex]2\sqrt2[/tex], so [tex]4\sqrt2 = 4 \cdot 2\sqrt2 = 8\sqrt2[/tex]

Now, we are looking for [tex]\frac{8\sqrt2}{3\sqrt2}[/tex]. Both the square root of 2s cancel, so we are left with 8/3

Answer:

34.5

Step-by-step explanation:

The absolute value of -|-34.5| is -34.5. So, -34.5 is 34.5 away from 0.

Answer:

34.5 units.

Step-by-step explanation:

When we simplify -|-34.5|, we get -34.5, which is basically 34.5 units away from 0.

Hoped this helped.

Answer:

  x³ +7x² +7x -15

Step-by-step explanation:

Apply the distributive property repeatedly, and/or recognize the ways that the coefficients of the product are formed.

distributive property

  (x -1)(x +3)(x +5)

  = (x -1)(x(x +5) +3(x +5))

  = (x -1)(x² +5x +3x +15) = (x -1)(x² +8x +15)

  = x(x² +8x +15) -1(x² +8x +15)

  = x³ +8x² +15x -x² -8x -15

  = x³ +7x² +7x -15

__

using knowledge of products of powers

The x³ term will be the product of all of the x-terms.

The x² term will be the pairwise sum of products of two x-terms and the third constant.

The x term will be the pairwise sum of products of one x-term and the two other constants.

The constant term will be the product of all of the constants.

These computations are simplified a bit because all of the x-coefficients are 1.

  = x³ +(-1 +3 +5)x² +(-1·3 +(-1)·5 +3·5)x +(-1)·3·5

  = x³ +7x² +7x -15

The sum in terms of p of four consecutive even integers with p been the smallest is 4(p + 3)

Even numbers are numbers that can be divided into two equal groups and they can be easily divisible by 2 without any remainder.

p is the smallest of the four consecutive even integers. This means p come first and it is the first term of the numbers.

Therefore, the 4 consecutive even integers is represented as follows;

p, p + 2, p + 4, p + 6

So the sum is equal to:

sum = p + p + 2 + p + 4 + p + 6

sum = 4p + 12

sum = 4(p + 3)

learn more on even numbers here: https://brainly.com/question/21514478?referrer=searchResults