Line p has an equation of y=5/3x-4 Line q includes the point
(-10,-3) and is perpendicular to line p. What is the equation of line q?

The distance between the points in radical form is [tex]\sqrt{52}[/tex]

What is distance formula ?

Formula for distances between pairs of points, an algebraic expression that expresses distances as a function of the coordinates of the points The Pythagorean theorem is the foundation for distance formulas for points in rectangular coordinates in two- and three-dimensional Euclidean space.

To calculate the distance we use distance formula

[tex]d = \sqrt{(x_{2} - x_{1} )^{2} + (y_{2} - y_{1} )^{2} }[/tex]

where [tex](x_{1},y_{1} )[/tex] and [tex](x_{2} , y_{2} )[/tex] are the 2 coordinates

[tex](x_{1},y_{1} )[/tex] = (-2,-4)

[tex](x_{2} , y_{2} )[/tex] = (4,0)

d = √(4 - (-2))² + (0 - (-4))²

d = √6² + 4²

d = √36 + 16

d = √52

√52 → radical form

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The solution of the polynomial equation x(x - 2) = 48 by factoring is x = 8 or x = -6

Given the polynomial equation x(x−2) = 48

x(x−2) = 48

x² - 2x = 48

x² - 2x - 48 = 0

x² -8x+6x - 48 = 0

By factoring the equation, we have:

x(x-8) + 6(x-8) = 0

(x-8) (x+6) = 0

x-8 = 0 or x+6 = 0

x = 8 or x = -6

Therefore, the solution of the polynomial equation is x = 8 or x = -6. Type x = 8 or x = -6 in the answer box

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Answer

314

Step-by-step explanation:

hope this helps ya

Answer:

Parent function:

f(x) = √x

Add a number to the value of the function, such as k:

f(x) = (√x) + k

If k is positive, the function moves up. If k is negative, the function moves down.

Answer:

78 children

266 Adults

Step-by-step explanation:

Find the picture attached.

Remember rules with angles when parallels are present (alternate interior/exterior angles, corresponding angles, same side interior/exterior angles, etc.)

Statements                         Reasons

∠3 = ∠5                            m || n, alternate interior angles

∠5 = ∠13                          a || b, corresponding angles

∠3 = ∠13                          substitution property: ∠3 =∠5 and ∠5 =∠13

The volume of the right circular cylinder is 3141592.65 centimeter cube  and the surface area is 125663.70 centimeter square

The diameter of the right circular cylinder = 200 cm

The radius = 200/2

= 100 cm

The height of the right circular cylinder = 100 cm

The volume of the right circular cylinder = π × [tex]r^2[/tex] × h

Where r is the radius

h is the height

Substitute the values in the equation

The volume = π × [tex]100^2[/tex] × 100

= 3141592.65 centimeter cube

The Surface area = 2πrh + 2π[tex]r^2[/tex]

Substitute the values in the equation

= 2×π×100×100 + 2×π×[tex]100^2[/tex]

= 62831.85 + 62831.85

= 125663.70 centimeter square

Hence, the volume of the right circular cylinder is 3141592.65 centimeter cube  and the surface area is 125663.70 centimeter square

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Answer: 68.61/6 = 11.435

Answer:

So you see what happened there

the sides are not equal so there is no answer

the answer that is the closest is 8 = 0

Step-by-step explanation:

Add x to both sides

2 - x + 6 + x = -x + x

simplify

2 + 6 = 0

simplify 2 + 6: 8

8 = 0

The amount of saline and water in the solution is given as 27.9 cm³ and 282.1 cm³ respectively.

Given,

A patient is administered 310cm^3 of a saline and water solution that is labeled as 9% saline.

What is saline solution?

Salt and water are combined to make saline. Because of its salt content (0.9% saline), which is comparable to that of tears, blood, and other bodily fluids, a normal saline solution is known as normal. Isotonic solution is another name for it.

Here,

Amount of saline = 0.09 × 310 = 27.9

Amount of water = 310 - 27.9 = 282.1

Thus, the amount of saline and water in the solution is given as 27.9 cm³ and 282.1 cm³ respectively.

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Answer: B

Step-by-step explanation:

B

Reason: supplimentry angles as the line is transervsal of line m and n .

Which means that 132°=2x

and using algebra you know that x=66°

Answer: x = 5

Step-by-step explanation:

3x + 6 = 21

3x = 21 - 6

3x = 15

x = 15/3

x = 5

Answer: X =5

Step-by-step explanation:  Subtract both sides by 6 to isolate 3x:

3x+6-6=21-6

3x=15

Divide both side by 3 to come up with x:

X=5.

A shortcut method but it does not follow the correct rules of math but if you're in a hurry it works:

3x+6=21

transfer +6 converting the sign to a -6

3x-=21-6

Subtract 3x=15

Divide by the number with x (3)

x=5

The value of the scale on the map is 18 cm 1 mi

Knowing the distance between two places on the map and measuring that distance on the map will yield the scale. Additionally, if a map has division lines, they are normally spaced apart by a mile. Example 4: On the map, the separation between points A and B is 6 inches

The ratio between a distance on a map and its corresponding distance on the ground is referred to as the "map scale."

People can accurately visualise how the distances mentioned on the map are plotted by using map scales. This is helpful in figuring out how to get from one place to another, especially if one travels or works in a profession that requires similar knowledge.

Given,

Model cm/actual miles

12/2/3

= 12/1,3/2

=18/1

=18:1

Therefore the value of the scale on the map is 18 cm 1 mi

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This is the way to find the endpoint if a confidence interval in the TI calculator:

An estimate's level of uncertainty is described by a confidence interval, which is a range of numbers.

A confidence interval is used to calculate an estimate for an unknown population parameter. Specifically, to provide an interval so that any value of the parameter falling inside the range is a credible value, and values falling outside the interval are implausible

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62 hours is 86% percent of 3 days

What is percentage and how to calculate it?

Percentage is the ratio in which the denominator is 100. To calculate the percentage we multiply the obtained value by 100.

We are given 62 hours and 3 days

Now 1 day has 24 hours

Hence 3 days will have 3*24 = 72 hours

Now To find the percentage we first have to find the ratio of 62 and 72

And to do that we divide 62 by 72

we get 62/72 = 0.86

To get the percentage we multiply this value by 100

0.86 * 100= 86%

Hence, 62 is 86% of 3 days

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As per the given demand function and equilibrium point, the consumers' surplus is 852.072.

What is consumer surplus?

Consumer advantages from market competition are measured economically as consumer surplus. When customers pay less for a good or service than they are willing to, this is known as a consumer surplus.

Given demand function,

[tex]D(q) = \frac{3000}{(3q+1)^2}[/tex]

at q = 4

putting value of q in function,

[tex]q' = \frac{3000}{(3(4)+1)^2}[/tex]

[tex]q' = \frac{3000}{169}[/tex]

Finding Consumer Surplus

[tex]CS = \int\limits^q_0 {D(q) - q'} \, dq[/tex]

[tex]CS = \int\limits^4_0 {\frac{3000}{(3q+1)^2} - \frac{3000}{169} } \, dq[/tex]

[tex]CS = [-\frac{1000}{3q+1} - \frac{3000q}{169}]^4_0[/tex]

CS = [-(76.923)-(71.005)] - [-1000]

CS = -147.928+1000

CS = 852.072

Therefore, consumers' surplus is 852.072.

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Complete Question

Find the consumers surplus if the demand function for a particular beverage is given by D(q)=(3000)/((3q+1)^(2)) and if the supply and demand are in equilibrium at q=4

Answer:

y=-2/5x+4/5

Step-by-step explanation:

it’s parallel so it will have the same slope

2=-2/5(-3)+4

2=6/5+4

2=1 1/5+4

2=5 1/5

5 1/5-2=3 1/5

We know this is 3 1/5 to big so we subtract it from y intercept

4-3 1/5

4/5 is the new y intercept

2=-2/5(-3)+4/5

2=6/5+4/5

2=10/5

2=2

So now the equation is true

Hopes this helps

Answer:

1/2

Step-by-step explanation:

The equation given is put in slope intercept form

y = mx + b

where m = slope and b = y intercept

In the equation y = 1/2x + 3/2,
"1/2" takes the spot of "m" meaning that the slope of the equation is 1/2

The area of the sector is 8800cm²

What is an area of the sector?

The area of the sector refers to the area encircled by a circle's sector. A sector always originates from the center of the circle.

What is curved surface area?

The area with just curved surfaces, leaving the circular top and base, is referred to as the curved surface area. Total Surface Area: This is the combined area of the bases and the curved surface.

Here, we have

Radius = 28cm,  Height = 96cm

L² = 96² + 28²

= 9216 + 784

= 10000

L = √10000

= 100cm

curved surface area = πrl

= 22/7×28×100

= 8800cm²

area of cone = area of sector

area of sector = 8800cm2

Hence, the area of the sector is 8800cm²

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The parabola's graph leads us to deduce that the quadratic equation is

x² + 5x + 1.

An algebraic expression with variables and constants is known as a quadratic equation.

Since the degree of a quadratic equation is two, it has two roots.

We are aware that the roots of a quadratic equation can be found at the vertex of a parabola, which is the graph of a quadratic function.

Given, The roots of the equation are x = - 4 and x = - 1, and the quadratic expression is, as the vertex of the parabola is at (-4, -1),

(x + 4)(x + 1).

= x² + x + 4x + 1.

= x² + 5x + 1.

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Answer:

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

Slope-intercept form:

Find the value of b:

The line is:

Answer:

y = (-5/4)x + 13

Step-by-step explanation:

Formula we use,

→ y = mx + b

Now the value of b will be,

→ 3 = (-5/4)8 + b

→ 3 = -40/4 + b

→ 3 = -10 + b

→ 3 + 10 = b

→ [ b = 13 ]

Then the equation will be,

→ y = mx + b

→ 3 = (-5/4)8 + 13

→ y = (-5/4)x + 13

Thus, answer is y = (-5/4)x + 13.

System of linear equations for the graph below are y = -1/3(x) + 6 and

y = 4/3(x) + 1.

From the graph:

points for the line (0,1) and (3,5) .

points for the line (0,6) and (3,5)

slope m = y2 - y1 / x2 -x1

= 5 - 1 / 3 - 0

= 4/3

substitute (0,1) and m value in y = mx + c

1 = 4/3*0 + c

1 = 0 + c

c = 1

c and m value substitute

y = mx +c

y = 4/3(x) + 1

slope of (0,6) and (3,5) m = 5 - 6 / 3 - 0

= -1/3

substitute (0,6) and m value in y = mx + c

6 = -1/3*0 + c

6 = 0 + c

c = 6

c and m value substitute

y = mx + c

y = -1/3(x) + 6

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We conclude that 80% of patients stop smoking when given sustained care.

Given,

The number of patients given sustained care = 175

Patients who were no longer smoking after one month = 82.3%

Significance level = 0.05

We have to claim that 80% of patients stop smoking when given sustained care.

Let p = percentage of patients stop smoking when given sustained care.

So, Null Hypothesis, H₀ : p = 80%     {means that 80% of patients stop smoking when given sustained care}

Alternate Hypothesis, Hₐ : p  80%     {means that different from 80% of patients stop smoking when given sustained care}

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

                      T.S. =  [tex]\frac{p_{0} -p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]  ~ N(0,1)

where,  p₀ = sample proportion of patients who stop smoking when given sustained care = 82.3%

n = sample of patients = 175

So, the test statistics  =  [tex]\frac{0.823-0.80}{\sqrt{\frac{0.823(1-0.823)}{175} } }[/tex]

                                    =  0.80

The value of z test statistics is 0.80

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

 P-value = P(Z > 0.80) = 1 - P(Z  > 0.80)

  = 1 - 0.21185 = 0.78815

Now, at 0.05 significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.

Since our test statistic lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that 80% of patients stop smoking when given sustained care.

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Answer:

See below

Step-by-step explanation:

Amount of water in pool = 14 000 -  .5 x       where x is in minutes

1.5 hr = 90 minutes

amount of water in pool =  14 000 - .5(90) = 13 955 gal

Answer:

  t(r) = log(r)/log(5) = log₅(r)

Step-by-step explanation:

You want the inverse of r(t)=5^t.

An exponential function is solved using logarithms.

  [tex]r = 5^t\qquad\text{given}\\\\\log(r)=t\cdot\log(5)\qquad\text{take logarithms}\\\\\boxed{t(r)=\dfrac{\log(r)}{\log(5)}}\qquad\text{divide by the coefficient of t}[/tex]

The change of base formula can be used to simplify this a bit.

  [tex]\boxed{t(r)=\log_5(r)}[/tex]

__

Additional comment

The latter form of the inverse function can be found directly at the first step by taking logarithms base 5.

The notation here is slightly different from the usual "inverse function" notation, where we designate the inverse of f(x) using f⁻¹(x). The notation we have used recognizes that the function r(t) generates ordered pairs (t, r), and the inverse function t(r) generates ordered pairs (r, t).

You are welcome to make use of whatever inverse function notation will satisfy your grader.

The sixth term of an arithmetic sequence is 3/2 and the twelfth term is 5/2. The common difference is 1/6.

A common difference in an arithmetic series is one between any term and its predecessor, and it is typically denoted by the letter "d". So, subtract the first term from the second term, the second term from the third term, etc. to find the common difference of an arithmetic sequence. The common difference is the difference that exists between every pair of phrases that follow one another in a series. For instance, the number 3 is a common difference in the series 4, 7, 10, 13, etc. An arithmetic progression is a series of differences.

Given,

a₆ = 3/2

a₁₂ = 5/2

Arithmetic sequence:

a₇ = a₆ + d

a₈ = a₇ + d

a₈ = a₆ + 2d

a₉ = a₈ + d

a₉ = a₆ + 3d

...

a₁₂ = a₁₁ + d

a₁₂ = a₆ + 6d

As given,

a₆ = 3/2

a₁₂ = 5/2

Equating,

5/2 = 3/2 + 6d

6d = 1

d = 1/6

The sixth term of an arithmetic sequence is 3/2 and the twelfth term is 5/2. The common difference is 1/6.

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Answer:

[tex]\dfrac{1}{6}[/tex]

Step-by-step explanation:

General form of an arithmetic sequence:

[tex]\boxed{a_n=a+(n-1)d}[/tex]

Where:

Given terms:

  [tex]a_6=\dfrac{3}{2}[/tex]

  [tex]a_{12}=\dfrac{5}{2}[/tex]

Substitute the given terms into the formula to create two equations for a:

Equation 1

[tex]\begin{aligned}a_6=a+(6-1)d&=\dfrac{3}{2}\\\\a+5d&=\dfrac{3}{2}\\\\a&=\dfrac{3}{2}-5d\end{aligned}[/tex]

Equation 2

[tex]\begin{aligned}a_{12}=a+(12-1)d&=\dfrac{5}{2}\\\\a+11d&=\dfrac{5}{2}\\\\a&=\dfrac{5}{2}-11d\end{aligned}[/tex]

Substitute the second equation into the first equation and solve for d:

[tex]\begin{aligned}\implies \dfrac{5}{2}-11d&=\dfrac{3}{2}-5d\\\\\dfrac{5}{2}-11d-\dfrac{3}{2}&=\dfrac{3}{2}-5d-\dfrac{3}{2}\\\\\dfrac{2}{2}-11d&=-5d\\\\1-11d&=-5d\\\\1-11d+11d&=-5d+11d\\\\1&=6d\\\\\dfrac{1}{6}&=\dfrac{6d}{6}\\\\\dfrac{1}{6}&=d\end{aligned}[/tex]

Therefore, the common difference of the arithmetic sequence is ¹/₆.

Using probability of a randomly chosen person, 270 people should have age less than or equal to 25.

From the given question,

Mean = 48.69

Standard Deviation = 17.993

We have to find the distribution of age is normal calculate the number of people who should be 25 years of age or less.

If 'X' is the age of a randomly selected individual in the sample, and that individual has a mean and a standard deviation that are normally distributed, then that individual's age has a standard normal score of -

Z = X- Mean/standard deviation

Z = X-48.69/17.993

Thus, Z-score for 25 year old is -

Z = 25 -48.69/17.993

Z = -23.69/17.993

Z = -1.317

Z= -1.317(approx)

The probability of a randomly chosen person to be 25 years of age or less in the sample is -

P(X < 25) = P(Z < -1.317)

P(X < 25) = 0.0939

As there are N = 2867 people in the data, so number of people expected to have age less than 25 is -

n = N x P(X < 25)

n = 2867 x 0.0939

n = 269.21

n = 270(approx)

Thus, 270 people should have age less than or equal to 25.

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Right question

"If the mean is 48.69 and the standard deviation 17.993. Assuming the distribution of age is normal calculate the number of people who should be 25 years of age or less.

Statistic

Number valid = 2867

The expectation, E(3y +2) and variance, Var(3y+2) of the random variable are 13.4 and 19.44 respectively

The expectations or expected value E(y) of a random variable can be thought of as the “average” value of the random variable. It is also called its mean

By definition:

if y = ax + b

then E(y) = aE(x) + b

where a,b = constant

The variance V(y) of  a random variable is the measure of spread for the distribution of a random variable that determines the degree to which the values of a random variable differ from the expected value

By definition

if y = ax + b

V(b) = 0

V(y) = V(ax) + V(b)

      = a²V(x) + 0

where a,b = constant

Given: E(y)= 3.8 and Var(y)= 2.16

Calculate E( 3y +2) and Var( 3y+ 2)

E(3y +2) = 3E(y) + 2            since E(y) = 3.8

           = 3×3.8 + 2

          = 11.4+2

          = 13.4

Var(3y+2) =  3²Var(y) + 0

               = 9×2.16

               = 19.44

Therefore, E(3y +2) is 13.4 and Var(3y+2) is 19.44

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Rotation is represented by a table fan, Dilation enlargement by flowers, reflection by ducks building a heart, and translation by a window picture.

Compared to translation, reflection, and rotation, what is a dilation?

Dilation:

Translation:

Reflection:

Rotation:

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