Type a digit that makes this statement true. 366,5_4 is divisible by 8.​

Answer:

y-18,000=2,750(x-0) --> point-slope

y=2,750x+18,000   --> slope-intercept

-2,750x + y = 18,000  --> standard

Step-by-step explanation:

Linear Modeling

Some situations can be modeled as linear functions. If we are in a situation where a linear model is suitable, then we need two sample points to make the model and predict unknown behaviors.

The pool being drained contained initially 18,000 gallons of water. If we set the variable x as the time in hours and y as the remaining gallons of water in the pool, this first point is (0;18,000).

We are also aware that after 2 hours 12,500 gallons of water remain. This gives us the second point as (2;12,500).

The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:

\(\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\)

Let's find the equation of the line with the 2 points:

\(\displaystyle y-18,000=\frac{18,000-12,500}{2-0}(x-0)\)

Calculating:

\(\displaystyle y-18,000=\frac{5,500}{2}(x-0)\)

\(y-18,000=2,750(x-0)\)

The equation above is the point-slope form of the line

Simplifying and adding 18,000:

\(y=2,750x+18,000\)

The equation above is the slope-intercept form of the line

Moving all the variables to the left side:

\(-2,750x + y = 18,000\)

The equation above is the standard form of the line

Answer:

y-18,000=2,750(x-0) --> point-slope

y=2,750x+18,000   --> slope-intercept

-2,750x + y = 18,000  --> standard

Step-by-step explanation:

y=8tan60=8√3

x=8/cos60 = 8 × 2 =16

Answer:

no

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(2 \frac{3}{7} \times 5\frac{5}{6} \div 11 \frac{1}{3} \)

Convert the mixed number to an improper fraction

\( \frac{17}{7} \times \frac{35}{6} \div \frac{34}{3} \)

To divide by a fraction, multiply the reciprocal of that fraction

\( \frac{17}{7} \times \frac{35}{6} \times \frac{3}{34} \)

Reduce the number with the G.C.F 7

\(17 \times \frac{5}{6} \times \frac{3}{34} \)

Reduce the numbers with the G.C.F 17

\( \frac{5}{6} \times \frac{3}{2} \)

Reduce the numbers with the G.C.F 3

\( \frac{5}{2} \times \frac{1}{2} \)

Multiply the fraction

\( \frac{5}{4} \)

In mixed fraction:

\(1 \frac{1}{4} \)

Hope this helps..

Good luck on your assignment...

Answer:

Step-by-step explanation:

Since both of the terms are perfect squares, you are going to factor using the difference of squares formula.

\(a^{2} -b^{2} = (a+b)(a-b)\)

where a = 3 and b = 2t

\(2(3+2t)(3-2t)\)

Complete Question

Assume that adults have IQ scores that are normally distributed with a mean μ=100 and a standard deviation σ=15. Find the probability that a randomly selected adult has an IQ between 81 and 119.

Answer:

The probability is  \(P( x_1 < X < x_2) = 0.79474\)

Step-by-step explanation:

From the question we are told that

   The standard deviation is  σ = 15.

    The mean μ= 100

     The range we are considering is \(x_1 = 81 , \ x_2 = 119\)

Now given that IQ scores are normally distributed

    Then the probability that a randomly selected adult has an IQ between 81 and 119 is mathematically represented as

               \(P( x_1 < X < x_2) = P(\frac{x_1 - \mu }{\sigma } <\frac{X - \mu }{\sigma } < \frac{x_2- \mu }{\sigma } )\)

 Generally

                \(\frac{X - \mu }{\sigma } = Z(The \ standardized \ value \ of \ X )\)

So

              \(P( x_1 < X < x_2) = P(\frac{x_1 - \mu }{\sigma } <Z < \frac{x_2- \mu }{\sigma } )\)

substituting values

               \(P( x_1 < X < x_2) = P(\frac{81 - 100 }{15 } <Z < \frac{119- 100 }{15 } )\)

               \(P( x_1 < X < x_2) = P( -1.2667 <Z <1.2667 )\)

               \(P( x_1 < X < x_2) = P(Z <1.2667 )-P( Z < -1.2667 )\)

From the standardized Z table

               \(P(Z <-1.2667 ) = 0.10263\)

And        \(P(Z <1.2667 ) = 0.89737\)

So

            \(P( x_1 < X < x_2) = 0.89737 - 0.10263\)

            \(P( x_1 < X < x_2) = 0.79474\)

Answer:

D.

Step-by-step explanation:

Answer:

\(\frac{4}{13}\)

Step-by-step explanation:

1÷3\(\frac{1}{4}\)=3+\(\frac{1}{4}\),  3×\(\frac{4}{4}\)

1÷\(\frac{13}{4}\)

69200000 in scientific notation is  6.92 × 10⁷.

Scientific notation is a form of presenting very large numbers or very small numbers in a simpler form.

Scientific Notation is a special way of writing numbers:

For example 800 is written as 8 × 10² in Scientific Notation.

Therefore, let's write the scientific notation of the number 69200000.

Hence,

69, 200, 000 = 6.92 × 10⁷

The logic is that we will count backwards until we meet the last number. Since we counted towards the left side, the exponent will be positive.

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Answer:

4.99 + 1.99m = T. Dependent Variable = T (Total Cost), Independent Variable = M (Movies) Now, for the equation we have to input 5 for the m because he watched 5 movies. So, 4.99 + 1.99(5) = T Well, 1.99 x 5 is 9.95 so our next step is this 4.99 + 9.95 = T and that  added up together would be 14.94 dollars. $14.94 = T

Step-by-step explanation: I hope that this helps you!

cotangent ZF = adjacent side / opposite side

adjacent side = 39

opposite side = 80

cotangent ZF = 39/80

Answer:

Step-by-step explanation:

what do u need help with

Answer:

The answer is (-5)

Step-by-step explanation:

f(x)= 5x-11

[f(x)= (-36)]

-36=5x-11

-5x= -11+36

-5x=25

x= -25/5

x= (-5)

The rational function graphed in this problem is given as follows:

D. F(x) = x/[(x + 4)(x - 1)]

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator, hence they are given as follows:

x= -4 and x = 1.

Hence the denominator of the function is given as follows:

(x + 4)(x - 1).

The intercept is given as follows:

x = 0.

Hence the numerator is:

x.

Thus the function is given as follows:

D. F(x) = x/[(x + 4)(x - 1)]

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Answer:

domain t = (-∞,∞)

range D = (-∞,∞)

Step-by-step explanation:

domain t = (-∞,∞)

range D = (-∞,∞)

The shape is a triangular prism with a triangular base, base area of 24in², height of 5in and volume of 40in³

The given solid is a triangular prism since its base figure is triangular in nature.

Since the base is a triangle, the area of the base is expressed as:

Area = 1/2 * base * height

Area of base = 1/2 * 6 * 8

Area of base = 24 square inches

The height of the solid is 5 inches and the required volume is calculated as:

Volume = BH/3

Volume = 24*5/3

Volume = 40 cubic inches

The shape is a triangular prism with a triangular base, base area of 24in², height of 5in and volume of 40in³

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Answer:

0.85

Step-by-step explanation:

1.37-0.52=0.85

Answer:

-4;  -3;   -2;   0;  1;   3;

Step-by-step explanation:

The cost of the bench is $ 375 and the Cost of the garden table is $ 446.

We can Calculate unknown quantities mathematically using Algebra Expressions. Unknown values in an equation are represented by variables, which are often represented by a letter of the alphabet like x, y, and z or a, b, and c, etc.

Here we have

A garden table and a bench cost $ 821 combined

Let x, and y be the cost of the garden table and bench

Given that

The garden table costs $71 more than the bench.  

=> x = y + $ 71 ---- (1)  

It is also given that

The total cost of the garden table and a bench = $ 821  

=>  x + y = 821  

=>  y + 71 + y =  821

=>  2y = 821 - 71

=>  2y = 750

=>  y = 375

=> Cost of bench, y = $ 375

=> The cost of the garden table, x = $ 375 + $ 71 = $ 446

Therefore,

The cost of the bench is $ 375 and the Cost of the garden table is $ 446.  

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The length of b and angle B and C are 3cm, 45  degrees and 79 degrees respectively.

To determine the angles and length of sides, we use the sine rule

The sine rule is thus:

\(\frac{sin A}{a} = \frac{sin B}{b} = \frac{sin C}{c}\)

Given;

Let's find angle C

\(\frac{sin 43}{2. 5} = \frac{sin C}{3. 6}\)

cross multiply

0. 682 × 3. 6 = sin C × 2. 5

sin C = 2. 4552/ 2. 5

C = \(sin^-^1(0. 982)\)

C = 79°

To find length of b

\(b= \sqrt{c^2 - a^2}\)

substitute the values

\(b = \sqrt{3.6^2 - 2. 5^2}\)

\(b = \sqrt{6. 71}\)

b = 2. 59 cm

b = 3cm

To find angle B, we have

\(\frac{sin 43}{2. 5} = \frac{sin B}{2. 59}\)

cross multiply

0. 682 × 2. 59= sin B × 2. 5

sin B = 0. 7065

\(B = sin^-^1(0. 7065)\)

B = 45°

Hence, the length of b and angle B and C are 3cm, 45  degrees and 79 degrees respectively.

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Answer: its 2

Step-by-step explanation:

The cone will fit in 4 times and the volume of the cone is 535.89 in³

To solve this problem, we have to find the volume of the cone and the volume of the sphere.

The formula of volume of a cone is given as;

V = 1/3πr²h

We need to calculate the volume of the sphere which is given as

V = 4/3 πr³

The volume of the ball = 4/3 * 3.14 * 8³ = 2143.57in³

The volume of the cone = 1/3 * 3.14 * 8² * 8 = 535.89 in³

The number of times it will fit into will be 2143.57 / 535.89 = 4

It will fit in 4 times

b)

The volume of the cone is 535.89in³

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Answer:

12-4r

Step-by-step explanation:

4r<12 because r<3 so you flip it.

Answer:

b

Step-by-step explanation:

Answer:

I believe the correct answer would be X = \(\frac{1}{4} z\)

Step-by-step explanation:

You would set the denominator equal to 0

Then move the variable to the right

Lastly, divide both sides, which gives you your answer of X = \(\frac{1}{4} z\)

Hope this helped.

Answer:

(12(3)-3(1/3))/(4(3)-5)=5

Step-by-step explanation:

12 x 3= 36     3 x 1/3=1  

4 x 3=12

(36-1)/(12-5)

35/7

5

THE ANSWER IS 5

Answer:

B. making an inference.

Step-by-step explanation:

The drama teacher's decision to add another performance time on Saturday is a result of making an inference based on the information that 80% of last year's sold-out plays occurred during weekend performances. By observing this pattern, the drama teacher infers that adding another performance on Saturday will likely attract a larger audience and increase the chances of having a sold-out show.

Answer:

p-40=s ( as p is 40 less that is "-" than s)

k4/5=t ( divide k with 4/5 and that will be equal to t)

m2/9=n (explained above)

Answer:

the man above me is right he just didn't put a division sign

Step-by-step explanation:

the answers are

k/4/5=t

s=p+40

m/2/9=n

Answer:

The answer for the above question is:

b)2

When solving a word problem using a system of equations with two unknowns, you must create two equations. So, correct option is B.

The reason is that each unknown in the problem requires an equation to represent its relationship with the other variables.

For example, let's say you have two unknowns, x and y. You need two equations to define the relationships between these variables. These equations can be represented as:

Equation 1: x + y = 10 (This equation represents the relationship between x and y based on the given information in the problem.)

Equation 2: 2x - y = 4 (This equation represents another relationship between x and y based on additional information provided in the problem.)

With a system of two equations involving two unknowns, you can use algebraic methods such as substitution or elimination to solve for the values of x and y.

Having only one equation would not be enough to determine unique values for both x and y, as there would be an infinite number of possible solutions. On the other hand, having more than two equations might lead to over-determining the system, making it inconsistent or redundant.

Therefore, two equations are the minimum required to solve for two unknowns effectively. So, correct option is B.

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