the parabola opens downward and is congruent to y=x^2; the vertex is (2,-5)

Step-by-step explanation:

Use the arctan function

tan Φ = 45/12

Φ = arctan ( -45/12)  = 75 degrees south of east = 165 degrees on the compass

Part 1. The employee who is \(32\)  years old could have \(2\) doctor visits in one year, according to the given equation.

Part 2.The new employee is predicted to have \(3\) more doctor visits per year than the previous employee, according to the given equation.

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

For instance, \(3x+5 = 14\) is an equation, in which \(3x+5\) and \(14\) are two expressions separated by an 'equal' sign.

Part 1: To predict how many doctors' visits an employee who is \(32\)years old could have in one year, we need to substitute a = \(32\) in the equation   \(v = 1/4a - 6\) and solve for v:

\(v = 1/4a - 6\)

\(v = 1/4(32) - 6\)

\(v = 8 - 6\)

\(v = 2\)

Part 2: The previous employee's age is not given, so we cannot directly compare their doctor visits with the new employee's visits. However, we can use the same equation to predict how many doctor visits the new employee might have based on their age.

Let's assume that the age of the new employee is \(a+12\), where a is the age of the previous employee. Then, we can substitute \(a+12\) for a in the equation  \(v = 1/4a - 6\)  and solve for v:

\(v = 1/4(a + 12) - 6\)

\(v = 1/4a + 3 - 6\)

\(v = 1/4a - 3\)

Therefore, the employee who is \(32\)  years old could have \(2\) doctor visits in one year, according to the given equation.

Therefore, the new employee is predicted to have \(3\) more doctor visits per year than the previous employee, according to the given equation.

Learn more about equation here:

https://brainly.com/question/10413253

#SPJ1

The measure of indicated angle in the given triangle is 71.035°.

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

In the given right angled triangle, hypotenuse side is 74 units and the two legs of triangle are 70 units and 24 units.

Let the unknown angle be x.

We know that, tanθ =Perpendicular/Base

Now, tan x= 70/24

tan x= 2.91

x =71.035°

So, one of the angle in the triangle is 71.035°.

Therefore, the measure of unknown angle is 71.035° in the given triangle.

Learn more about the trigonometric ratios here:

brainly.com/question/25122825.

#SPJ1

If the production of wood tables on an assembly line increases from 1600 tables per shift to 2000 tables per shift, the labor productivity will increase by 25%.We need to determine the percentage change.

To calculate the increase in labor productivity, we need to compare the difference in production levels and determine the percentage change.The initial production level is 1600 tables per shift, and the increased production level is 2000 tables per shift. The difference in production is 2000 - 1600 = 400 tables.

To calculate the percentage change, we divide the difference by the initial production and multiply by 100:

Percentage Change = (Difference / Initial Production) * 100 = (400 / 1600) * 100 = 25%.

Therefore, the correct answer is option C) 25%, indicating that labor productivity will increase by 25% when the production is increased to 2000 tables per shift.

To learn more about percentage change click here : brainly.com/question/14979505

#SPJ11

Answer:

20

Step-by-step explanation:

f(x) = 30

30 = 1.8x -5.4

35.4 = 1.8x

x = 35.4/1.8

x = 19.666

Answer:

Step-by-step explanation:

a

The value of x for this problem is given as follows:

x = 5.

Hence the angle measures are given as follows:

We have that angles A and D are congruent for this problem, meaning that they have the same measure.

Hence the value of x is obtained as follows:

7x - 3 = 5x + 7

2x = 10

x = 5.

Hence the angle measures are given as follows:

More can be learned about angle measures at https://brainly.com/question/25716982

#SPJ1

Answer:

The first one

Step-by-step explanation:

I think that for you to convert miles to feet you would need to cancel out miles which means miles goes in the bottom. I'm not sure though

Answer:

mean of e + f = 18

Step-by-step explanation:

(a + b + c + d)/4 = 9         Multiply by 4

a + b + c + d = 9 * 4 = 36

(a + b + c + d + e + f ) / 6 = 12

but a + b + c + d = 36

(36 + e + f)/6 = 12             Multiply by 6

36 + e + f = 72                 Subtract 36 from both sides

e + f = 36                         Divide by 2 to find the mean.

(e + f)/2 = 36/2

mean of e + f = 18

Answer:

30

Step-by-step explanation:

Answer:

\( \tan (A +B) = - 6\frac{6}{13} \)

Step-by-step explanation:

\( \sin \: A = \frac{3}{5}...(given) \\ \\ \because\cos A = \pm \sqrt{1 - { \sin }^{2}\: A } \\ \\ \ \therefore\cos A = \pm \sqrt{1 - \bigg( \frac{3}{5} \bigg) ^{2}} \\ \\ \ \therefore\cos A = \pm \sqrt{1 - \frac{9}{25}} \\ \\ \therefore\cos A = \pm \sqrt{ \frac{25 - 9}{25} } \\ \\ \therefore\cos A = \pm \sqrt{ \frac{16}{25}} \\ \\ \therefore\cos A = \pm { \frac{4}{5}} \\ \\ \because \: \angle A \: is \: in \: quadrant \: I \\ \\ \therefore \: \cos A = { \frac{4}{5}} \\ \\ \tan \: A = \frac{ \sin \: A}{\cos \: A} \\ \\ \tan \: A = \frac{ \frac{3}{5} }{ \frac{4}{5} } \\ \\ \tan \: A = \frac{3}{4} \\ \\ \because \tan (A +B) = \frac{ \tan A + \tan B }{1 - \tan A \tan B } \\ \\ \therefore \tan (A +B) = \frac{ \frac{3}{4} + \frac{15}{8} }{1 - \frac{3}{4} \times \frac{15}{8} } \\ \\ \therefore \tan (A +B) = \frac{ \frac{6}{8} + \frac{15}{8} }{1 - \frac{45}{32}} \\ \\ \therefore \tan (A +B) = \frac{ \frac{21}{8} }{\frac{32 - 45}{32}} \\ \\ \therefore \tan (A +B) = \frac{ \frac{21}{8} }{\frac{ - 13}{32}} \\ \\ \therefore \tan (A +B) = \frac{21}{8} \times \bigg(- \frac{32}{13 } \bigg)\\ \\ \therefore \tan (A +B) = - \frac{84}{13} \\ \\ \therefore \tan (A +B) = - 6\frac{6}{13} \)

Answer:

c

Step-by-step explanation:

plato

The probability that the length of a component lies between 19 and 21 centimeters is 0.0376.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given:

Population mean, µ = 14

Population standard deviation, σ = 3

Probability that the length of a component lies between 19 and 21 centimeters

= P(19 <  X  < 21)

= P( (19 - 14) / 3 < (X - µ) / σ < (21 - 14) / 3)

= P(1.67 < z < 2.33)

= P(z < 2.33) - P(z < 1.67)

Using excel function:

= NORM.S.DIST(2.33,1) - NORM.S.DIST(1.67,1)

= 0.9901 - 0.9525

= 0.0376

Hence, the probability that the length of a component lies between 19 and 21 centimeters is 0.0376.

To know more about probability, click on the link

https://brainly.com/question/24756209

#SPJ4

From the information provided the measure of the angles are given as,

m ∠EFH = 71; and m ∠EFG = 142°.

Angles are measured in degrees, which is why they are called "degrees". A complete circle equals 360 degrees, so it is divided into 360 parts. Each part of the revolution is a degree. Any angle, whether acute, obtuse, reflected or right, can be measured with a protractor. Although based on right angles, we are able to distinguish acute, obtuse or reflex angles. But if we have two acute angles to measure, we cannot determine the greater angle between the two. Therefore, we need to use a protractor to measure angles accurately.

According to the Question:

It is to be noted that

m ∠GFH = m ∠EFH

⇒ m ∠EFH = 71°

⇒ m ∠EFG = m ∠GFH + m EFH

Hence,

m ∠EFG = 71 + 71

              = 142°

Learn more about Angle:

https://brainly.com/question/28451077

#SPJ4

Answer:

In order from top to bottom, left to right, the solutions to the equation for the graph are;

(3, 2)  

(-2, -8)

(0, -4)

(2, 0

Step-by-step explanation:

To find out if a point (a solution) is on the graph, take the x-value of each of the choices given and see if the y-value in the choice will correspond to a point on the graph

(2, 3)  ==> for x = 2, we can see that y = 0 so (2, 3) IS NOT a solution. However (2, 0) IS a solution

That means we can also eliminate (2, -4). so (2, -4) IS NOT a soluition

(3, 2) ==> for x= 3, y is indeed 2 so (3, 2) IS a solution which

(1, -6) ==> for x = 1, y = -2 so (1, -6) IS NOT a solution

(-2, -8)==> for x = -2, y = -8 so (-2, -8) IS a solution

(0, -4) ==>: for x= 0, y = -4 so (0, -4) IS a solution which means (0, 2) IS NOT a solution

(-4, 0) ==> for x = - 4, y is not 0.  So (-4, 0) IS NOT a solution

That covers all 9 options

The points that are solutions to the graph equation are (in order from top to bottom, left to right)

(3, 2)  

(-2, -8)

(0, -4)

(2, 0)

Note
We could have computed the line equation for the graph in slope intercept form , plugged in each of the x-values and see if the y value matches the corresponding y value in each of the options provided

I did not think this approach is required in this question but if you are interested, the equation for the graph is

y = 2x -4

This would have made the calculations a bit more complicated but you can plug in each of the x-values, see what the y-values are and check if they are consistent with the answer I have provided if you are interested

Answer:

(-2,-3)

Step-by-step explanation:

abscissa is always know as the x axis

ordinate is known as y axis

therefore

it lies in the fourth quadrant

Answer:

2x + 10

_______

x^3 - 4x

Step-by-step explanation:

this is the answer

The estimated temperature of the room is 105 degrees Fahrenheit (rounded to the nearest integer).

Newton's Law of Cooling states that the rate of change of the temperature of an object is proportional to the difference between the object's temperature and the temperature of its surroundings. We can use this law to estimate the temperature of the room.

Let's denote the temperature of the room as T (in degrees). According to the information given, the temperature of the soup decreases from 120 degrees to 105 degrees in 10 minutes, which means a temperature difference of 120 - 105 = 15 degrees. Similarly, in the next 10 minutes, the temperature decreases from 105 degrees to 95 degrees, which is a temperature difference of 105 - 95 = 10 degrees.

Since the rate of change of temperature is proportional to the temperature difference, we can set up the following proportion:

15 degrees / 10 minutes = (120 - T) degrees / 10 minutes

Cross-multiplying and simplifying the equation, we get:

15 = 120 - T

T = 120 - 15 = 105 degrees

Therefore, the estimated temperature of the room is 105 degrees Fahrenheit (rounded to the nearest integer).

For more questions on proportional, click on:

https://brainly.com/question/1496357

#SPJ8

Answer:

Trevon is 15

Step-by-step explanation:

If Issac is 5 years older than Trevon, and the ratio is 4:3, then we can multiply one or both of them to be compared by.

If Issac is 10, for example, then Trevon would be 5, giving a 2:1 ratio

When we multiply the ratio, we eventually see a point where Issac's (first number) age is 5 more than Trevon's (second number) age:

( 4:3 ) 3 = 12:9
( 4:3 ) 4 = 16:12
( 4:3 ) 5 = 20:15

Issac is 20 and Trevon is 15

There's probably an easier way to solve problems like these but this was what came to mind at first hope this helps

Answer:

Trevon is 15

Step-by-step explanation:

let Trevon's age be x then Issac is x + 5

the ratio of Issac : Trevon = 4 : 3

set up a proportional equation

\(\frac{Issac}{Trevon}\) , that is

\(\frac{x+5}{x}\) = \(\frac{4}{3}\) ( cross- multiply )

4x = 3(x + 5)

4x = 3x + 15 ( subtract 3x from both sides )

x = 15

So Trevon is 15 and Issac is x + 5 = 15 + 5 = 20

Answer:

1 mile per hour

Step-by-step explanation:

you just double it

The prioritized critical decision areas for P&B Inc. to achieve competitive advantage are goods and service design, human resources and job design, inventory management, and scheduling, aligned with a response strategy.

To achieve a competitive advantage in a market characterized by quick delivery, reliability of scheduling, and frequent design innovation and customer demand changes, P&B Inc. needs to prioritize critical decision areas.

Goods and service design should focus on creating innovative and differentiated products/services that meet customer needs. Human resources and job design should ensure a skilled and motivated workforce capable of delivering high-quality outputs.

Inventory management is crucial to balance stock levels, minimize costs, and meet customer demands promptly. Scheduling should prioritize efficient resource allocation and sequencing of tasks to optimize production and meet customer deadlines.

By effectively managing these decision areas, P&B Inc. can align its operations with a response strategy, delivering quick and reliable outcomes while adapting to market dynamics.

This strategic approach allows the company to differentiate itself, attract customers, and maintain a competitive edge in the industry.

Learn more about critical here: https://brainly.com/question/17259837

#SPJ11

Step-by-step explanation:

−4x+5−13x+39=180

Step 1: Simplify both sides of the equation.

−4x+5−13x+39=180

−4x+5+−13x+39=180

(−4x+−13x)+(5+39)=180(Combine Like Terms)

−17x+44=180

−17x+44=180

Step 2: Subtract 44 from both sides.

−17x+44−44=180−44

−17x=136

Step 3: Divide both sides by -17.−17x

−17

=

136

−17

x=−8

Answer:

x=−8

Answer:

100 miles

Step-by-step explanation:

Two plans are being offered for the renting of cars.

Plan A:

Cost per week = $200

Cost for each mile = $0.35

Plan B:

Cost per week = $180

Cost for each mile = $0.55

To find:

Number of miles for which the cost is same ?

Solution:

Let the number of miles driven so that the cost becomes the same = \(m\) miles

First of all, let us find the cost for each plan as per \(m\) miles.

Cost as per plan A = Cost per week + Cost for \(m\) miles = $200 + $0.35\(m\)

Cost as per plan B = Cost per week + Cost for \(m\) miles = $180 + $0.55\(m\)

Now, putting both the costs equal to find the value of \(m\):

\(200 +0.35m = 180 +0.55m\\\Rightarrow 20 = 0.20m\\\Rightarrow m = \bold{100\ miles}\)

Therefore, after 100 miles the cost from each plan will be the same.

Answer:

Step-by-step explanation:

3x - 2y = 18

x -int

3x - 2(0) = 18

3x = 18

x = 6

(6,0)

3(0) - 2y = 18

-2y = 18

y = -9

(0, -9)

Answer:

I think either way is correct.

For a point (a, b), and slope m:

point-slope form: y - b = m(x - a)

slope-intercept form: b = ma + c, where c is the y-intercept.

To find the 90% confidence interval, using the following formula: Confidence interval = sample mean ± Z* (standard error)`where `standard error = (population standard deviation / √n)`n is the sample size Z is the Z-score at the 90% confidence level which is 1.645When we substitute the values in the formula, we get:
Confidence interval = 56 ± 1.645(13.3 / √36)
                       = 56 ± 4.54
                       = (51.46, 60.54)
Hence, the 90% confidence interval for the true population mean watermelon weight is (51.46, 60.54) ounces.

Let's learn more about standard deviation :

https://brainly.com/question/475676

#SPJ11

To answer this question, we'll use the exponential distribution and the concept of the probability density function (pdf). Let X be the time until failure of a single device, with a mean lifetime of 20 months. The exponential distribution has the following pdf:

f(x) = (1/μ) * e^(-x/μ),

where μ is the mean lifetime (20 months in this case).

Now, let's find the probability that the first failure occurs at w months among the 5 independent devices. For this, we need to calculate the probability that none of the other 4 devices fail before w months and that the first device fails at w months.

The probability that a single device does not fail before w months is given by the complementary cumulative distribution function (ccdf) of the exponential distribution:

P(X > w) = e^(-w/μ).

Since the devices are independent, the probability that all 4 devices do not fail before w months is:

P(All 4 devices survive > w) = (e^(-w/μ))^4.

Now, the probability that the first device fails at w months is given by the pdf of the exponential distribution:

P(X = w) = (1/μ) * e^(-w/μ).

Finally, we multiply the two probabilities to find the chance that the first failure occurs at w months:

P(First failure at w) = P(All 4 devices survive > w) * P(X = w)
= (e^(-w/μ))^4 * (1/μ) * e^(-w/μ)
= (1/20) * e^(-5w/20).

Thus, the chance that the first failure will occur at w months is given by the expression (1/20) * e^(-5w/20).

To learn more about Exponential distribution - brainly.com/question/22692312

#SPJ11