Is f(x)=4x^2 linear,quadratic,or exponential

Answer:

The amount of the loan is going to be $ 182,700, and the monthly payments, if the interest is 6%, are going to be $ 537.95, while if the interest is 7%, are going to be $ 543.02.

Step-by-step explanation:

Given that you want to buy a $ 203,000 home, and you plan to pay 10% as a down payment, and take out a 30 year loan for the rest, for A) determine how much is the loan amount going to be, B) determine what will your monthly payments be if the interest rate is 6%, and C) determine what will your monthly payments be if the interest rate is 7%, the following calculations must be made:

A) 100 - 10 = 90

203,000 x 0.90 = X

182,700 = X

B) (182,700 x 1.06) / (30 x 12) = X

193,662 / 360 = X

537.95 = X

C) (182,700 x 1.07) / (30 x 12) = X

195,489 / 360 = X

543.025 = X

Therefore, the amount of the loan is going to be $ 182,700, and the monthly payments, if the interest is 6%, are going to be $ 537.95, while if the interest is 7%, are going to be $ 543.02.

Answer:

Step-by-step explanation:

This is a related rates problem from calculus using implicit differentiation. The main equation is going to be Pythagorean's Theorem and then the derivative of that. Pythagorean's Theorem is

[tex]x^2+y^2=c^2[/tex] where c is the hypotenuse and is a constant. Therefore, the derivative of this with respect to time, and using implicit differentiation is

[tex]2x\frac{dx}{dt}+2y\frac{dy}{dt}=0[/tex] and dividing everything by 2 to simplify a bit:

[tex]x\frac{dx}{dt}+y\frac{dy}{dt}=0[/tex]. Upon analyzing that equation, it looks like we need values for x, y, [tex]\frac{dx}{dt}[/tex], and [tex]\frac{dy}{dt}[/tex]. And here's what we were given:

[tex]\theta=45[/tex] and [tex]\frac{dx}{dt}=.5[/tex]  In the greater realm of things, that's nothing at all.

BUT we can use the right triangle and the angle we were given to find both x and y. The problem we are looking to solve is to

Find [tex]\frac{dy}{dt}[/tex] at the instant that [tex]\frac{dx}{dt}[/tex] = .5.

Solving for x and y:

[tex]tan45=\frac{x}{6}[/tex] and

6tan45 = x ( and since this is a 45-45-90 triangle, y = x):

[tex]6(\frac{\sqrt{2} }{2})=x=y[/tex] so

[tex]x=y=3\sqrt{2}[/tex] and now we can fill in our derivative. Remember the derivative was found to be

[tex]x\frac{dx}{dt}+y\frac{dy}{dt}=0[/tex] so

[tex]3\sqrt{2}(\frac{1}{2})+3\sqrt{2}\frac{dy}{dt}=0[/tex] and

[tex]\frac{3\sqrt{2} }{2}+3\sqrt{2} \frac{dy}{dt}=0[/tex] and

[tex]3\sqrt{2}\frac{dy}{dt}=-\frac{3\sqrt{2} }{2}[/tex] and multiplying by the reciprocal of the left gives us:

[tex]\frac{dy}{dt}=-\frac{3\sqrt{2} }{2}(\frac{1}{3\sqrt{2} })[/tex] so

[tex]\frac{dy}{dt}=-\frac{1}{2}\frac{m}{s}[/tex]

Answer:

option a.

[tex] + - \frac{13}{5} [/tex]

Step-by-step explanation:

[tex]25x^2\: - \:169 = 0 [/tex]

[tex]25x^2 = 169[/tex]

[tex] {x}^{2} = \frac{169}{25} [/tex]

[tex]x = + - \sqrt{ \frac{169}{25} } [/tex]

[tex]x = + - \frac{13}{5} [/tex]

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { A. \:2 \sqrt{30} }}}}}}[/tex]

[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}[/tex]

[tex] = \sqrt{3} \times \sqrt{8} \times \sqrt{5} [/tex]

[tex] = \sqrt{3 \times 2 \times 2 \times 2 \times 5} [/tex]

[tex] = \sqrt{ ({2})^{2} \times 2 \times 3 \times 5} [/tex]

[tex] = 2 \sqrt{2 \times 3\times 5} [/tex]

[tex] = 2 \sqrt{30} [/tex]

[tex] \sqrt{ ({a})^{2} } = a[/tex]

[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]

Answer:

A. 2√30

Step-by-step explanation:

[tex] \small \sf \: \sqrt{3} \times \sqrt{8} \times \sqrt{5} \\ [/tex]

split √8

[tex] \small \sf \leadsto \sqrt{3 × 2 × 2 × 2 × 5} [/tex]

[tex] \small \sf \leadsto \: 2 \sqrt{2 \times 3 \times 5} [/tex]

[tex] \small \sf \leadsto \: 2 \sqrt{30} [/tex]

Answer:

equation : y= -6 + 1

Step-by-step explanation:

Step-by-step explanation:

6/10 > _ > 1/3

3/5 > _ > 1/3

½(⅗+⅓)

½(9+5/15)

½(14/5)

=7/15

Answer:

7/15

Step-by-step explanation: 10 and 3 LCM is 30

6/10 x 3 =18/30 and 1/3x 10= 10/30

10/30 and 18/30 average is 14/30 which simplified is 7/15

The answer is 7/15

Hope it helps

Answer:

4 places after the decimal.

the result is 0.0215

Step-by-step explanation:

I assume the expression is really

43 / (2⁴ × 5³)

this is the same as

(((((((43 / 2) / 2) / 2) / 2) / 5) / 5) / 5)

since the starting value is an odd number, the first division by 2 creates a first position after the decimal point, and it must be a 5, as the result is xx.5

the second division by 2 splits again the uneven end .5 in half, creating a second position after the decimal point again ending in 5, as the result is now xx.x5

the third division by 2 does the same thing with that last 5 and creates a third position after the decimal point ending again in 5, as the result is now xx.xx5

the fourth division by 2 does again the same thing, a fourth position after the decimal point is created ending in 5. now xx.xxx5

in essence, every division of the 0.5 part by 2 is the same as a multiplication by 0.5, which squares 0.5 leading to 0.5². the next division did the same thing leading to 0.5³.

and finally the fourth division to 0.5⁴.

0.5⁴ = (5/10)⁴ = 5⁴/10⁴

so, now we start to divide this result by 5. since the positions after the decimal point are divisible by 5 without remainder, as we have 5⁴ to work with.

every divisible by 5 takes one of these powers away.

so, we go from 5⁴/10⁴ to 5³/10⁴ to 5²/10⁴ to 5/10⁴.

all the time we maintain the 10⁴ in the denominator of the fraction. and that determines the positions after the decimal point.

so, after all the individual divisions we come to and end and are still limited to the 4 positions after the decimal point.

Answer:

The possible values are a = -2.5 or a = 4.5.

Step-by-step explanation:

Composite function:

The composite function of f(x) and g(x) is given by:

[tex](f \circ g)(x) = f(g(x))[/tex]

In this case:

[tex]f(x) = 4x^2 - 8x - 20[/tex]

[tex]g(x) = 2x + a[/tex]

So

[tex](f \circ g)(x) = f(g(x)) = f(2x + a) = 4(2x + a)^2 - 8(2x + a) - 20 = 4(4x^2 + 4ax + a^2) - 16x - 8a - 20 = 16x^2 + 16ax + 4a^2 - 16x - 8a - 20 = 16x^2 +(16a-16)x + 4a^2 - 8a - 20[/tex]

Value of a so that the y-intercept of the graph of the composite function (fog)(x) is (0, 25).

This means that when [tex]x = 0, f(g(x)) = 25[/tex]. So

[tex]4a^2 - 8a - 20 = 25[/tex]

[tex]4a^2 - 8a - 45 = 0[/tex]

Solving a quadratic equation, by Bhaskara:

[tex]\Delta = (-8)^2 - 4(4)(-45) = 784[/tex]

[tex]x_{1} = \frac{-(-8) + \sqrt{784}}{2*(4)} = \frac{36}{8} = 4.5[/tex]

[tex]x_{2} = \frac{-(-8) - \sqrt{784}}{2*(4)} = -\frac{20}{8} = -2.5[/tex]

The possible values are a = -2.5 or a = 4.5.

Answer:

6/7

Step-by-step explanation:

7 days make a week. 7 would go into the denominator and 6 would go in the numerator. 6 is the amount of days through the week that it is dry.

Answer:

6/7

Step-by-step explanation:

[tex]\frac{number \ of \ dry \ days}{total \ number \ of \ days \ in \ a \ week} =\frac{6}{7}[/tex]

Answer:

Place value of 1 = 1 × 10 = 10

Step-by-step explanation:

In 382619,

Place of 1 = Tens

Place value of 1 = 1 × 10 = 10

Answer:

We reject the Null and conclude that There is significant evidence that the slope values are greater than 0.

Step-by-step explanation:

Based on the ANOVA output given :

The F critical value can be obtained thus ;

F(df regression, df error)

Using an α-value of 0.01

F(2, 12) at α = 0.01 is 6.927

The F statistic as obtained from the ANOVA table = 134.65

Since, F statistic > F critical we reject the Null and conclude that slope values are significantly > 0

Similarly,

Using the Pvalue :

The Pvalue of the slope are extremely small :

Viscosity <0.0001

Load <0.0001

At α = 0.01, 0.025

The Pvalue < α ; The null will be rejected.

Answer:

how accurate the statistic is when using it to estimate the parameter.

Step-by-step explanation:

The margin of error may be referred to as a range or interval around a calculated statistic. The margin of error usually employed when calculating the confidence interval, will give a certain range of value within the sample statistic. This is sample statistic and margin is used to estimate the parameter albeit a certain percentage or proportion within the sample statistic. This provides the accuracy level at which the statistic will estimate the parameter.

Margin of Error :

Margin of Error = Zcritical * σ/√n ; OR

Margin of Error = Tcritical * s/√n

Where ;

σ = population standard deviation

s = sample standard deviation

The limit of the difference quotient of the above function [tex]f(x)[/tex] at [tex]x=3[/tex] is [tex]3[/tex] such that [tex]f(x)=x^{3} - 4x^{2} + 2[/tex].

The difference quotient of a function [tex]f(x)[/tex] is [tex]\frac{f(x+h)-f(x)}{h}[/tex].

The given equation is, [tex]f(x)=x^{3} -4x^{2} +2[/tex]

So, [tex]f(x+h)=(x+h)^{3} -4(x+h)^{2} +2= x^{3} +h^{3}+3x^{2} h+3xh^{2} -4x^{2} -4h^{2} -8xh+2[/tex]

Now, [tex]f(x+h)-f(x)[/tex]

[tex]=x^{3}+h^{3}+3x^{2}h+3xh^{2}-4x^{2}-4h^{2}-8xh+2-x^{3}+4x^{2}-2[/tex]

[tex]=h^{3}+3x^{2}h+3xh^{2}-4h^{2}-8xh[/tex]

So, [tex]\frac{f(x+h)-f(x)}{h} =\frac{h^{3}+3x^{2}h+3xh^{2} -4h^{2}-8xh }{h}[/tex]

[tex]=h^{2}+3x^{2}+3xh-4h-8x[/tex]

Now, at [tex]x=3[/tex],

[tex]h^{2}+3x^{2}+3xh-4h-8x=h^{2}+27+9h-4h-24=h^{2}+5h+3[/tex]

If   [tex]h[/tex]→[tex]0[/tex], the value of [tex]h^{2}+5h+3=3[/tex]

Thus, the limit of the difference quotient of the above function [tex]f(x)[/tex] at [tex]x=3[/tex] is [tex]3[/tex].

Learn more about the limit of the difference quotient here- https://brainly.com/question/17008881

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Answer:

Step-by-step explanation:

The only mistake is in the last line. You need to replace the y by x, So:

f-1(x) = (x - 4)/-8

It's usual to put the negative on the top so it becomes

-(x -4)/8

- and we can simplify this a bit more to give

f-1(x) = (4 - x)/5

Answer:

A seems to be correct

Step-by-step explanation:

Answer:

b) Then z(s) is in the rejection region for H₀. We reject H₀. The p-value is smaller than α/2

c)CI 95 %  =  ( 0.00002 ;  0.09998)

Step-by-step explanation: In both cases, the size of the samples are big enough to make use of the approximation of normality of the difference of the proportions.

Recent Sample

Sample size    n₁  =  1000

Number of events of people with financial fitness more than fair

x₁  =  410

p₁ =  410/ 1000  =  0.4     then q₁ = 1 - p₁    q₁ =  1 -  0.4    q₁  = 0.6

Sample a year ago

Sample size    n₂ =  1200

Number of events of people with financial fitness more than fair

x₂  =  420

p₂  =  420/1200     p₂ = 0.35   q₂  =  1 - p₂    q₂  = 1 - 0.35   q₂ = 0.65

Test Hypothesis

Null Hypothesis                                  H₀              p₁  =  p₂

Alternative Hypothesis                      Hₐ              p₁  ≠  p₂

CI  95 % then significance level  α  =  5%   α  = 0.05    α/2  = 0.025

To calculate p-value:

SE  =  √ (p₁*q₁)/n₁  +  (p₂*q₂)/n₂

SE  =  √ 0.4*0.6/1000 +  0.65*0.35/1200

SE  =  √ 0.00024 + 0.000189

SE = 0.021

z(s) =  ( p₁ - p₂ ) / SE

z(s) = ( 0.4 - 0.35 )/0.021

z(s) = 0.05/ 0.021

z(s) =  2.38

We find p-value from z-table to be   p-value = 0.00842

Comparing

p-value with  α/2   = 0.025

α/2 >  p-value  

Then z(s) is in the rejection region for H₀. We reject H₀

CI 95 %  =  ( p₁  -  p₂ )  ±  2.38*SE

CI 95 %  =  ( 0.05 ± 2.38*0.021 )

CI 95 %  =  ( 0.05 ± 0.04998)

CI 95 %  =  ( 0.00002 ;  0.09998)

CI 95 % does not contain the 0 value affirming what the hypothesis Test already demonstrate

Answer:

a)  [tex]h=286.8ft[/tex]

b)  [tex]\frac{dh}{dt}=5.7ft/s[/tex]

Step-by-step explanation:

From the question we are told that:

Angle [tex]\theta=35[/tex]

a)

Slant height [tex]h_s=500ft[/tex]

Generally the trigonometric equation for Height is mathematically given by

[tex]h=h_ssin\theta[/tex]

[tex]h=500sin35[/tex]

[tex]h=286.8ft[/tex]

b)

Rate of release

[tex]\frac{dl}{dt}=10ft/sec[/tex]

Generally the trigonometric equation for Height is mathematically given by

[tex]h=lsin35[/tex]

Differentiate

[tex]\frac{dh}{dt}=\frac{dl}{dt}sin35[/tex]

[tex]\frac{dh}{dt}=10sin35[/tex]

[tex]\frac{dh}{dt}=5.7ft/s[/tex]

Answer:

[tex]P(X = 0) = 0.03125[/tex]

[tex]P(X = 1) = 0.15625[/tex]

[tex]P(X = 2) = 0.3125[/tex]

[tex]P(X = 3) = 0.3125[/tex]

[tex]P(X = 4) = 0.15625[/tex]

[tex]P(X = 5) = 0.03125[/tex]

Step-by-step explanation:

For each toss, there are only two possible outcomes. Either it is tails, or it is not. The probability of a toss resulting in tails is independent of any other toss, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Fair coin:

Equally as likely to be heads or tails, so [tex]p = 0.5[/tex]

5 tosses:

This means that [tex]n = 5[/tex]

Probability distribution:

Probability of each outcome, so:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{5,0}.(0.5)^{0}.(0.5)^{5} = 0.03125[/tex]

[tex]P(X = 1) = C_{5,1}.(0.5)^{1}.(0.5)^{4} = 0.15625[/tex]

[tex]P(X = 2) = C_{5,2}.(0.5)^{2}.(0.5)^{3} = 0.3125[/tex]

[tex]P(X = 3) = C_{5,3}.(0.5)^{3}.(0.5)^{2} = 0.3125[/tex]

[tex]P(X = 4) = C_{5,4}.(0.5)^{4}.(0.5)^{1} = 0.15625[/tex]

[tex]P(X = 5) = C_{5,5}.(0.5)^{5}.(0.5)^{0} = 0.03125[/tex]

Answer:

[tex]z = 1.6[/tex]

Step-by-step explanation:

Given

[tex]Pr = 0.05[/tex]

Required

The z value to the right

The z value to the right is represented as:

[tex]P(Z > z)[/tex]

So, the probability is represented as:

[tex]P(Z > z) = 0.05[/tex]

From z table, the z value that satisfies the above probability is:

[tex]z = 1.645[/tex]

[tex]z = 1.6[/tex] --- approximated

Answer:

467 muffins

Step-by-step explanation:

143 + 211 + 113 = 467

Answer:

triangle KLM

Step-by-step explanation:

x-1 meaning subtractikn so u subtract l from its original x cord making it move left 1

y-8 same thing but for the y making it move down 8 spaces

Answer:

Step-by-step explanation:

A). Volume of a rectangular prism = Length × Width × Height

                                                        = lwh

1). Volume of a rectangular prism if the measures of the sides are,

    Length (l) = 9 cm

    Width (w) = 4 cm                                              

    Height (h) = 3 cm                                            

    Therefore, volume = lwh

                                   = 9 × 4 × 3

                                   = 108 cm³

2). Length = 10 cm

     Width = 7 cm

     Height = 15 cm

     Volume = lwh

                   = 10 × 7 × 15

                   = 1050 cm³

3). Length = 14 cm

    Width = 10 cm

    Height = 9 cm

    Volume = 14 × 10 × 9

                  = 1260 cm³

B. Volume of a cube = (Side)³

4). If the measure of one side = 12 cm

    Volume of the cube = (12)³

                                      = 1728 cm³

5). If the measure of one side = 6 cm

   Volume of the cube = (6)³

                                     = 216 cm³

Answer:

4th option

Step-by-step explanation:

tanZ = [tex]\frac{opposite}{adjacent }[/tex] = [tex]\frac{XY}{ZY}[/tex]

Answer:

363,000,000

..........

Answer:

Step-by-step explanation:

because these are similar triangles, that is, one is a bigger of smaller version of the other, then we know, that the bigger triangle is just 2 times bigger than the smaller,  or   2x of any side of the small one

sooo   2(20) =40  

so we know that side n of the bigger triangle is 40

Answer:

The probability that the proportion of persons with a retirement account will be less than 57%=31.561%

Step-by-step explanation:

We are given that

n=570

p=58%=0.58

We have to find the probability that the proportion of persons with a retirement account will be less than 57%.

q=1-p=1-0.58=0.42

By takin normal approximation to binomial  then sampling distribution of sample proportion  follow normal distribution.

Therefore,[tex]\hat{p}\sim N(\mu,\sigma^2)[/tex]

[tex]\mu_{\hat{p}}=p=0.58[/tex]

[tex]\sigma_{\hat{p}}=\sqrt{\frac{p(1-p)}{n}}[/tex]

[tex]\sigma_{\hat{p}}=\sqrt{\frac{0.58\times 0.42}{570}}[/tex]

[tex]\sigma_{\hat{p}}=0.02067[/tex]

Now,

[tex]P(\hat{p}<0.57)=P(\frac{\hat{p}-\mu_{\hat{p}}}{\sigma_{\hat{p}}}<\frac{0.57-0.58}{0.02067})[/tex]

[tex]P(\hat{p}<0.57)=P(Z<-0.483)[/tex]

[tex]P(\hat{p}<0.57)=0.31561\times 100[/tex]

[tex]P(\hat{p}<0.57)[/tex]=31.561%

Hence,  the probability that the proportion of persons with a retirement account will be less than 57%=31.561%

Answer:

Step-by-step explanation:

I have this saved on my computer in notepad b/c this type of question get asked sooo often :/

point P1 (-4,-2)  in the form (x1,y1)

point P2(3,1)  in the form (x2,y2)

slope = m

m = (y2-y1) / (x2-x1)

My suggestion is copy that above and save it on your computer for questions like this

now use it

Point 1  , P1 = (2,-4)   in the form (x1,y1)

Point 2 , P2 = (4,-1)  in the form (x2,y2)

m = [ -1-(-4) ]  /  [ 4-2]

m =  (-1+4) / 2

m = 3 / 2

so now we know the slope is  3/2  :)  

[tex] cos(A) = \frac{ {b}^{2} + {c}^{2} - {a}^{2} }{2bc} [/tex]

The cos A will be b/c

Cosine function in a triangle is the ratio of the adjacent side to that of the hypotenuse

The steps are as follow:

AB = c

BC = a

AC = b

Cos A = Adjacent side to A / Hypoteneous

Cos A = AC / AB

Cos A = b / c

Therefore the value of Cos A in given figure will be b / c

Learn more about Cosine function here:

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Answer:

1/2

Step-by-step explanation:

Convert 2/3 to 4/6

Subtract: 4/6 - 1/6

You get 3/6

Simplify: 1/2

Hope this helps!

Answer: The answer is 1/2