What is the point-slope form of a line that has a slope of 3 and passes through point (1, 4)?
BRE
BE
y-4=3(x-1)
1-y=3(x-4)
Y,-4 = 3(1-x)
1-Y, = 3(4-x,)

I hope this will help uh.....

Answer:

value of Ft(-15,50) = 1.3

Value of Fv(-15,50) = -0.15

Step-by-step explanation:

W = perceived temperature

T = actual temperature

W = f( T,V)

Estimate the values of  ft ( -15,50) and  fv(-15,50)

calculate the Linear approximation of   f at(-15,50)

[tex]f_{t}[/tex] (-15,50) =  [tex]\lim_{h \to \o}[/tex] [tex]\frac{f(-15+h,40)-f(-15,40)}{h}[/tex]

from the table take h = 5, -5

[tex]f_{t}(-15,40) = \frac{f(-10,40)-f(-15,40)}{5}[/tex]  = [tex]\frac{-21+27}{5} = 1.2[/tex]

[tex]f_{t} = \frac{f(-20,40)-f(-15,40)}{-5}[/tex] = 1.4

therefore the average value of [tex]f_{t} (-15,40) = 1.3[/tex]

This means that when the Temperature is -15⁰c and the 40 km/h the  value of Ft (-15,40) = 1.3

calculate the linear approximation of

[tex]f_{v} (-15,40) = \lim_{h \to \o} \frac{f(-15,40+h)-f(-15,40)}{h}[/tex]

from the table take h = 10, -10

[tex]f_{v}(-15,40) = \frac{f(-15,50)-f(-15,40)}{10}[/tex]  = [tex]\frac{-29+27}{10} = -0.2[/tex]

[tex]f_{v} (-15,40) = \frac{f(-15,30)-f(-15,40)}{-10}[/tex]  = [tex]\frac{-26+27}{-10}[/tex]  = -0.1

therefore the average value of [tex]f_{v} (-15,40) = -0.15[/tex]

This means that when the temperature = -15⁰c and the wind speed is 40 km/h the temperature will decrease by 0.15⁰c

w = f(T,v)

   = -27 + 1.3(T+15) - 0.15(v-40)

   = -27 + 1.3T + 19.5 - 0.15v + 6

   = 1.3T - 0.15v -1.5  

calculate the linear approximation

[tex]\lim_{v \to \infty}[/tex][tex]\frac{dw}{dv} = \lim_{v \to \infty} \frac{d(1.3T-0.15v-1.5)}{dv}[/tex]  = -0.15

Answer:

a

The Margin of error is correct  

b

No the polls does not provide convincing evidence that more than 70% of the population think that licensed drivers should be required to retake their road test once they turn 65.

Step-by-step explanation:

From the question we are told that

     The  population proportion is  [tex]p = 66[/tex]%  =  0.66

     The  sample size is  n =  1018

     The margin of error is  MOE  =  3 %  =  0.03

     The  confidence level is  C =  95%

Given that the confidence level is 95% , then the level of significance is mathematically evaluated as

       [tex]\alpha = 100 - 95[/tex]

      [tex]\alpha = 5[/tex]%

       [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the standardized normal distribution table, the value is  

       [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

The  reason we are obtaining critical values for [tex]\frac{\alpha }{2}[/tex] instead of  [tex]\alpha[/tex] is because [tex]\alpha[/tex] represents the area under the normal curve where the confidence level ([tex]1-\alpha[/tex]) did not cover which include both the left and right tail while [tex]\frac{\alpha }{2}[/tex]  is just considering the area of one tail which what we required to calculate the margin of error

Generally the margin of error is mathematically represented as

       [tex]MOE = Z_{\frac{\alpha }{2} } * \sqrt{\frac{p (1-p )}{n} }[/tex]

substituting values

     [tex]MOE = 1.96 * \sqrt{\frac{0.66 (1-66 )}{1018} }[/tex]

      [tex]MOE = 0.03[/tex]  

      [tex]MOE = 3[/tex]%

The 95% is mathematically represented as

      [tex]p - MOE < p < p +MOE[/tex]

substituting values

     [tex]0.66 -0.03 < p < 0.66 +0.03[/tex]

     [tex]0.63 < p < 0.69[/tex]

Looking at  the confidence level interval we see that the population proportion is between

     63%  and  69%

shown that the population proportion is less than 70%

Which means that the polls does not provide convincing evidence that more than 70% of the population think that licensed drivers should be required to retake their road test once they turn 65.

Answer:

x(3x+5)

Step-by-step explanation:

3x^2+5x

take out common factor x

= x(3x+5)

Answer:

Step-by-step explanation:

3x² + 5x

Factor out X from the expression

= x ( 3x + 5 )

Hope this helps...

Best regards!!

Answer:

72.5 feet

Step-by-step explanation:

The height of each level from floor to ceiling is 14 1/2 feet.

We want to find the net change in elevation going from the floor of the underground level to the ceiling of the 4th level above ground.

In other words, the change in elevation in going 5 floors up.

Each level has a height of 14 1/2 feet (29/2 feet).

Therefore, the height of the fourth level above ground from the underground level will be 5 times the height of one level:

h = 5 * 29/2 = 72.5 feet

The net change in elevation from the floor of the underground level to the 4th level above ground is:

ΔE = [tex]h_4 - h_0[/tex]

[tex]h_0 = 0 feet\\\\h_4 = 72.5 feet[/tex]

Therefore:

ΔE = 72.5 - 0 = 72.5 feet

Answer:

72.5

Step-by-step explanation:

Answer:

nine hundred five thousand two hundred thirty-eight

Answer:

a. Normally distributed with a mean of $2700 and a standard deviation of $40

Step-by-step explanation:

Given that:

the mean daily revenue is $2700

the standard deviation is $400

sample size n is 100

According to the Central Limit Theorem, the sampling distribution of the sample mean can be computed as follows:

[tex]\mathbf{standard \ deviation =\dfrac{ \sigma}{\sqrt{n}}}[/tex]

standard deviation = [tex]\dfrac{400}{\sqrt{100}}[/tex]

standard deviation = [tex]\dfrac{400}{10}}[/tex]

standard deviation = 40

This is because the sample size n is large ( i,e n > 30) as a result of that  the sampling distribution is normally distributed.

Therefore;

the statement that  describes the sampling distribution of the sample mean is : option A.

a. Normally distributed with a mean of $2700 and a standard deviation of $40

Answer:

  60%

Step-by-step explanation:

Reducing the rental cost by a factor of 6 makes it be 90%/6 = 15% of the original costs of the company. The non-rental costs are 100% -90% = 10% of the original costs of running the company.

Now, the rental costs are 15%/(15%+10%) = 3/5 of the present costs of the company.

Rental cost constitutes 60% in the total costs of the company.

Answer:

D. [tex]70.34 cm^2[/tex]

Step-by-step explanation:

Area of sector of a circle is given as θ/360*πr²

Where,

r = radius = 12 cm

θ = 56°

Use 3.14 as π

Plug in the values into the formula and solve

[tex] area = \frac{56}{360}*3.14*12^2 [/tex]

[tex] area = 70.34 [/tex]

Area of the sector ABC = [tex] 70.34 cm^2 [/tex]

The answer is D

Answer:

The z-score for a sales associate from this store who earns $37,500 is 2

Step-by-step explanation:

From the given information:

mean [tex]\mu[/tex] = 32500

standard deviation = 2500

Sample mean X = 37500

From the given information;

The value for z can be computed as :

[tex]z= \dfrac{X- \mu}{\sigma}[/tex]

[tex]z= \dfrac{37500- 32500}{2500}[/tex]

[tex]z= \dfrac{5000}{2500}[/tex]

z = 2

The z-score for a sales associate from this store who earns $37,500 is 2

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

cot A = [tex]\frac{cosA}{sinA}[/tex], tanA = [tex]\frac{sinA}{cosA}[/tex], cscA  = [tex]\frac{1}{sinA}[/tex], secA = [tex]\frac{1}{cosA}[/tex]

Consider the right side

[tex]\frac{cotA-tanA}{cscAsecA}[/tex]

= [tex]\frac{\frac{cosA}{sinA}-\frac{sinA}{cosA} }{\frac{1}{sinA}.\frac{1}{cosA} }[/tex]

= [tex]\frac{\frac{cos^2A-sin^2A}{sinAcosA} }{\frac{1}{sinAcosA} }[/tex]

= [tex]\frac{cos^2A-sin^2A}{sinAcosA}[/tex] × sinAcosA ( cancel sinAcosA )

= cos²A - sin²A

= cos2A

= left side ⇒ verified

Answer:

28

Step-by-step explanation:

12+[(15-5)]+(9-3)]

PEMDAS

Parentheses first

12+[(10)]+(6)]

Then add

12+10+6

Answer: 28

Step-by-step explanation:

Answer:

wrong thing

Step-by-step explanation:

13 arent shaded of the 20 units

7/20 are shaded, 7X1=7, 2X5=10

Answer:

B

Step-by-step explanation:

B is the only set of ordered pairs to represent a function because it is the only one that has no repeating x values while the others do.

Answer:

A = $211.50

A = P + I where

P (principal) = $100.00

I (interest) = $111.50

Step-by-step explanation:

$209.37 will the account be worth in 25 years.

Compound Interest is defined as interest earn on interest.

[tex]A = P(1 + \frac{r}{100})^{t}[/tex]

P= $100

r = 3%

t=25 years

substitute the values in formula,

[tex]A = 100(1 + \frac{3}{100})^{25}[/tex]

[tex]A = 100(1 + 0.03)^{25}[/tex]

[tex]A = 100(1.03)^{25}[/tex]

[tex]A=100(2.0937)[/tex]

[tex]A=209.37[/tex]

Hence, $209.37 will the account be worth in 25 years.

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Answer:

P [ Z < 66 ]  = 35,15 %

Step-by-step explanation:

Normal Distribution

Population mean μ₀  = 75,4

Standard deviation  σ = 5,2

Then:

P [ Z < 66 ]  =  ( 66 - 75,4 ) / 5,2

P [ Z < 66 ]  = - 9,4 / 5,2

P [ Z < 66 ]  = - 1,81

In z-table we look for the reciprocate area for that  z score and find

P [ Z < 66 ]  = 0,3515

P [ Z < 66 ]  = 35,15 %

Answer:

I NEED POINTS

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

Vincent’s construction method produces a hexagon that may not be equilateral and may not be equiangular. The correct option is D.

A regular polygon is a polygon that is equiangular and equilateral. Therefore, the measure of all the internal angles and the measure of all the sides of the polygon are equal to each other.

Given that Vincent wants to construct a regular hexagon inscribed in a circle. He draws a circle on a piece of paper. He then folds the paper circle three times to create three folds representing the diameters of the circle.

Now as it can be seen as the paper is folded as shown in the below image but it does not create a hexagon that is equilateral and equiangular.

Hence, Vincent’s construction method produces a hexagon that may not be equilateral and may not be equiangular.

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Answer:

At 95% confidence limits for the true difference between the  average Miles per Gallon for the two models is -1.8210  to  4.1789

Yes 95 % confidence means  that there's conclusive evidence to indicate that one model gets a higher MPG than the other.

Step-by-step explanation:

                              Model A              Model B

Sample Size              50                          55

Sample Mean  x`         32                           35

Sample Variance  s²    9                            10

At 95 % confidence limits are given by

x1`-x2` ± 1.96 [tex]\sqrt{\frac{s^{2} }{n1} +\frac{s^{2}}{n2} }[/tex]

Putting the values

32-35  ± 1.96  [tex]\sqrt\frac{9}{50}+\frac{10}{55}[/tex]        ( the variance is the square of  standard deviation)

-3 ± 1.96 [tex]\sqrt{ \frac{495+500}{2750}[/tex]

-3 ± 1.96( 0.6015)

-3 ± 1.17896

-1.8210; 4.1789

Thus the 95% confidence limits for the true difference between the  average Miles per Gallon for the two models is -1.8210  to  4.1789.

Yes 95 % confidence means  that there's conclusive evidence to indicate that one model gets a higher MPG than the other.

Answer:

[tex]x=8[/tex]

Step-by-step explanation:

We can solve this equation by isolating the variable x.

First let’s apply the distributive property:

[tex]5(x+3)-12=43\\5\cdot x + 5\cdot3 - 12=43\\5x + 15 - 12 = 43[/tex]

Combine like terms:

[tex]5x + 3 = 43[/tex]

Now we can subtract 3 from both sides:

[tex]5x + 3 - 3 = 43-3\\5x = 40[/tex]

Divide both sides by 5:

[tex]5x\div5 = 40\div5\\x = 8[/tex]

So [tex]x=8[/tex].

Hope this helped!

Answer:

x = 8

Step-by-step explanation:

5(x + 3) – 12 = 43

Add 12 to each side

5(x + 3) – 12+12 = 43+12

5(x+3) =45

Divide each side by 5

5(x+3)/5 = 55/5

x+3 = 11

Subtract 3 from each side

x+3-3 = 11-3

x = 8

Answer:

[tex]\huge \boxed{{x\geq -3, \ x \neq 2}}[/tex]

Step-by-step explanation:

The function is given,

[tex]\displaystyle f(x)=\frac{\sqrt{x+3 }}{(x+8)(x-2)}[/tex]

The domain of a function are all possible values of x.

There are restrictions for the value of x.

The denominator of the function cannot equal 0, if 0 is the divisor then the fraction would be undefined.

[tex]x+8\neq 0[/tex]

Subtract 8 from both parts.

[tex]x\neq -8[/tex]

[tex]x-2\neq 0[/tex]

Add 2 on both parts.

[tex]x\neq 2[/tex]

The square root of x + 3 cannot be a negative number, because the square root of a negative number is undefined. x + 3 has to equal to 0 or be greater than 0.

[tex]x+3\geq 0[/tex]

Subtract 3 from both parts.

[tex]x\geq -3[/tex]

The domain of the function is [tex]x\geq -3[/tex], [tex]x\neq 2[/tex].

The domain of the given function will be x ≥ -3 and x ≠ 2.

The entire range of independent input variables that can exist is referred to as a function's domain or,

The set of all x-values that can be used to make the function "work" and produce actual y-values is referred to as the domain.

As per the data given in the question,

The given expression of function is,

f(x) = [tex]\sqrt{\frac{x+3}{(x-8)(x-2)} }[/tex]

The fraction would indeed be undefined if the base of the function were equal to zero, which is not allowed.

x + 8 ≠ 0

x ≠ -8

And, x - 2 ≠ 0

x ≠ 2

Since the square root of a negative number is undefined, x+3 cannot have a negative square root. x+3 must be bigger than zero or identical to zero.

So,

x + 3 ≥ 0

x ≥ -3

So, the domain of the function will be x ≥ -3 and x ≠ 2.

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Answer:

The number must be divisible by 6

Step-by-step explanation:

Being divisible by 2 means that 2 is a factor of the number. Same with being divisible by 3, so that means the number has 2 and 3 as factors, therefore, 6 is also a factor, and the number will be divisible by it.

Answer:

The answer is 2 1/5 miles.

Step-by-step explanation:

You have to multiply 5/9 with 4 since you are going around 4 times. You could also use addition which is 5/9 + 5/9 + 5/9 + 5/9.

Answer:

Hey there!

The person jogged a total of 20/9 miles.

Hope this helps :)

Answer:

first number(x) = 2 second number(y)= 6

Step-by-step explanation:

This is an example of a simultaneous equation.

First write this word problem as equations, where x is the "first number" that you've mentioned and y is the "second number".

x + 2y = 14  (equation 1)

2x + y = 10  (equation 2)

This is solved using the elimination method.

We need to make one of the coefficients the same - in this case we can make y the same. In order to do this we need to multiply equation 2 by 2, so that y becomes 2y.

2x + y = 10 MULTIPLY BY 2

4x + 2y = 20 (this is now our new equation 2 with the same y coefficient)

Now subtract equation 1 from equation 2.

4x - x + 2y - 2y = 20 - 14  (2y cancels out here)

3x = 6

x = 2

Now we substitute our x value into equation 1 to find the value of y.

2 + 2y = 14

2y = 12

y = 6

Hope this has answered your question.

Answer:

6 and 2

Step-by-step explanation:

Let the first number =a

Let the second number =b

A first number plus twice a second number is 14.

Twice the first number plus the second totals 10.

We solve the two equations simultaneously

[tex]a+2b=14 \implies a=14-2b\\$Substitute into the second equation$\\2(14-2b)+b=10\\28-4b+b=10\\-3b=10-28\\-3b=-18\\b=6[/tex]

Recall:

a=14-2b

=14-2(6)

=14-12

a=2

The two numbers are 6 and 2.

Answer:

x= 5,77 *∛ K₂ / ( K₁ + K₅ ) the side f the square bottom-top

h = 2,88/ [∛ K₂ / ( K₁ + K₅ ) ]² heigh of the box

Step-by-step explanation:

Data from problem statement only gives one relation between dimensions of the box, we need two, in order to express surface area as a function of just one variable. In such a case we must assume the box is of square bottom and top.

Then

Area of the bottom                      A(b) = x²          ⇒  C(b) = K₁*x²

Area of the top                              A(t)  = x²         ⇒  C(t)  = K₅*x²

Total lateral area ( 4 sides)          A(l)  = 4*x*h   ⇒   C(l)  = 4*K₂*x*h

V(bx) = 96 in³

V(bx) = x²*h = 96

h = 96/x²

Then total cost as a function of x

C(x) =  K₁*x² +  K₅*x² + 4*K₂*(96)/x

Taking derivatives on both sides of the equation

C´(x) = 2*K₁*x + 2*K₅*x - 384*K₂/x²

C´(x) = 0         ⇒     2*K₁*x + 2*K₅*x - 384*K₂/x² = 0

2*K₁*x³ + 2*K₅*x³ = 384*K₂       or      K₁*x³ + k₅*x³ =  192*K₂

x³ ( K₁ + K₅ ) = 192*K₂

x  = ∛192*K₂ / ( K₁ + K₅ )

x= 5,77 *∛ K₂ / ( K₁ + K₅ )

If we obtain the second derivative

C´´(x)  = 2*K₁ + 2*K₅ - (-2*x)*384*K₂/x⁴

C´´(x)  = 2*K₁ + 2*K₅ + 768*K₂/x³

As x can not be negative  the expression C´´ wil be  C´´> 0

then we have a minimum for the function for x = 5,77 *∛ K₂ / ( K₁ + K₅ )

and  h = 96 / [ 5,77 *∛ K₂ / ( K₁ + K₅ )]²

h = 2,88/ [∛ K₂ / ( K₁ + K₅ ) ]²

Answer: Price-earnings ratio= 22.0

Step-by-step explanation:

Given: A company had a market price of $38.50 per share, earnings per share of $1.75, and dividends per share of $0.90

To find: price-earnings ratio

Required formula: [tex]\text{price-earnings ratio }=\dfrac{\text{ Market Price per Share}}{\text{Earnings Per Share}}[/tex]

Then, Price-earnings ratio = [tex]\dfrac{\$38.50}{\$1.75}[/tex]

⇒Price-earnings ratio = [tex]\dfrac{22}{1}[/tex]

Hence, the price-earnings ratio= 22.0

sum of angles = 10800

measurement of a single angle= 1350

Therefore,

No. of sides = sum of angles / single angle

No of sides = 10800 / 1350

No of sides = 8

Answer:

8 sides.

Step-by-step explanation:

If the sum of the angles is 10,800 degrees, and each angle is 1,350 degrees, the deck will have the number of sides of the sum of the angle measurements divided by each angle's measurements.

10,800 / 1,350 = 1,080 / 135 = 8 sides.

Hope this helps!

Answer:

B. The weather on a particular day a year from now

Step-by-step explanation:

We can only predict the weather in the near future, not long term or all time. The rest of the answer choices are predictable. We will always know the age of a person 10 years from now, we can predict the rating of the movie if we preview and watch it, and if a student studies enough/not enough we can predict the type of grade they will get on a test.

I believe the answer is B since to find the age of a person ten years from now, just add their age by ten. You can predict the rating of an upcoming movie by watching the trailer and seeing if it is good or bad. You can predict the grade a student gets on a test if you know that person is smart or not. You can’t predict weather from a year in the future because anything could happen in a year. This is why I think the answer is B.

Answer:

-16

Step-by-step explanation:

I solved it out.

Answer:

its d 16

Step-by-step explanation:

i did the test