Solve the system of equations. \begin{aligned} & -10x+3y = 5 \\\\ & x=y-4 \end{aligned} ​ −10x+3y=5 x=y−4 ​

Answer:

[tex]z=\frac{0.60 -0.65}{\sqrt{\frac{0.65(1-0.65)}{340}}}=-1.933[/tex]  

The p value for this case can be calculated with this probability:

[tex]p_v =2*P(z<-1.933)=0.0532[/tex]  

For this case is we use a significance level of 5% we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true proportion is different from 0.65 or 65%. We need to be careful since if we use a value higher than 65 for the significance the result would change

Step-by-step explanation:

Information given

n=340 represent the random sample taken

[tex]\hat p=0.60[/tex] estimated proportion of readers owned a laptop

[tex]p_o=0.65[/tex] is the value that we want to test

z would represent the statistic

[tex]p_v{/tex} represent the p value

Hypothesis to test

We want to check if the true proportion of readers owned a laptop if different from 0.65

Null hypothesis:[tex]p=0.65[/tex]  

Alternative hypothesis:[tex]p \neq 0.65[/tex]  

The statistic is given by:

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

Replacing we got:

[tex]z=\frac{0.60 -0.65}{\sqrt{\frac{0.65(1-0.65)}{340}}}=-1.933[/tex]  

The p value for this case can be calculated with this probability:

[tex]p_v =2*P(z<-1.933)=0.0532[/tex]  

For this case is we use a significance level of 5% we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true proportion is different from 0.65 or 65%. We need to be careful since if we use a value higher than 65 for the significance the result would change

Answer:

Step-by-step explanation:

Time = distance/speed

Considering the first stage,

Speed = 20km/hr

Distance = 5km

Time = 5/20 = 0.25 hour

Considering the second stage,

Speed = 10km/hr

Distance = 5km

Time = 5/10 = 0.5 hour

Considering the third stage,

Speed = 25km/hr

Distance = 5km

Time = 5/25 = 0.2 hour

Considering the third stage,

Speed = 20km/hr

Distance = 5km

Time = 5/20 = 0.25 hour

Therefore, the time it took the biker to complete the race is

0.25 + 0.5 + 0.2 + 0.25 = 1.2 hours

Answer:

0.5934% probability that a baseball player will play at an NCAA college and will also go on to be drafted by the MLB

Step-by-step explanation:

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Playing at an NCAA college.

Event B: Being drafted by the MLB.

6.9% will play in an NCAA college

This means that [tex]P(A) = 0.069[/tex]

8.6% of the college players will go on to be drafted by the MLB.

This means that [tex]P(B|A) = 0.086[/tex]

What is the probability that a baseball player will play at an NCAA college and will also go on to be drafted by the MLB?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

[tex]P(A \cap B) = P(A) \times P(B|A)[/tex]

[tex]P(A \cap B) = 0.069*0.086 = 0.005934[/tex]

0.5934% probability that a baseball player will play at an NCAA college and will also go on to be drafted by the MLB

Answer:

B:<

Step-by-step explanation:

You can solve this question with fractions. The way I did it was by changing both equations into fractions like this: 6÷7=6/1x1/7=6/7 and     7÷8=7/1x1/8=7/8. Since they don't have a common denomintor and you still dont know which fraction is bigger/smaller, we are going to find a common denominator which is 56. After converting both fractions, (6/7=48/56 and 7/8=49/56)  Now you can see that 7/8 is bigger than 6/7, which shows that 6÷7<7÷8.

Answer:

y=4

Step-by-step explanation:

A line that is parallel to the x-axis would have an equation of y= ______.

This is because a horizontal graph has a gradient of zero, thus the value of m in y=mx+c is zero.

y=0x +c

y= c

Since it passed through the point (1,4):

When x=1, y=4,

4= 0(1) +c

c= 4

Thus, the equation of the line is y=4.

Answer:

y =4

Step-by-step explanation:

Parallel to x axis means a horizontal line

Horizontal lines are of the form

y =

Since it goes through the point (1,4)

y =4

Answer:

Step-by-step explanation:

let s estimate the following

[tex](secA-tanA)(secA+tanA)=sec^2A-tan^2A=\dfrac{1}{cos^2A}-\dfrac{sin^2A}{cos^2A}=\dfrac{1-sin^2A}{cos^2A}=\dfrac{cos^2A}{cos^2A}=1[/tex]

as [tex]cos^2A+sin^2A=1[/tex]

it means that

[tex]\dfrac{1}{secA-tanA}=secA+tanA[/tex]

hope this helps

Let [tex]f(x,y,z)=z-\ln(x+y)[/tex]. The gradient of [tex]f[/tex] at the point (1, 0, 0) is the normal vector to the surface, which is also orthogonal to the tangent plane at this point.

So the tangent plane has equation

[tex]\nabla f(1,0,0)\cdot(x-1,y,z)=0[/tex]

Compute the gradient:

[tex]\nabla f(x,y,z)=\left(\dfrac{\partial f}{\partial x},\dfrac{\partial f}{\partial y},\dfrac{\partial f}{\partial z}\right)=\left(-\dfrac1{x+y},-\dfrac1{x+y},1\right)[/tex]

Evaluate the gradient at the given point:

[tex]\nabla f(1,0,0)=(-1,-1,1)[/tex]

Then the equation of the tangent plane is

[tex](-1,-1,1)\cdot(x-1,y,z)=0\implies-(x-1)-y+z=0\implies\boxed{z=x+y-1}[/tex]

Answer:

a. Probability density function for the battery life

[tex]f(x)={\begin{cases}{\dfrac {1}{12-8.5}}=\dfrac{1}{3.5}&\mathrm {for} \ 8.5\leq x\leq 12,\\[8pt]0&\mathrm {for} \ x<8.5\ \mathrm {or} \ x>12\end{cases}}[/tex]

b. P(x<11) = 0.7143

Step-by-step explanation:

The question is incomplete

In October, Apple introduced a much smaller variant of the Apple iPad, known as the iPad Mini. Weighing less than 11 ounces, it was about 50% lighter than the standard iPad. Battery tests for the iPad Mini showed a mean life of hours (The Wall Street Journal, October 31, 2012). Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours.

a. Give a mathematical expression for the probability density function of battery life.

b. What is the probability that the battery life for an iPad Mini will be 11 hours or less (to 4 decimals).

a. We model the battery life as random variable with an uniform distribution with parameters a (min. value)=8.5 hours and b (max. value)=12 hours.

The probability that the battery life takes any value between 8.5 and 12 is constant. Also, the probability that takes any value outside the interval (8.5, 12) is 0.

We can express that as:

[tex]f(x)={\begin{cases}{\dfrac {1}{12-8.5}}=\dfrac{1}{3.5}&\mathrm {for} \ 8.5\leq x\leq 12,\\[8pt]0&\mathrm {for} \ x<8.5\ \mathrm {or} \ x>12\end{cases}}[/tex]

The last is the probability density function for the battery life.

b. We can calculate P(x<11) using the cumulative density function or integrating the density function between x=0 (or x=a=8.5) and x=11.

[tex]P(x<11)=\int\limits^{11}_{8.5} \dfrac{1}{3.5} \, dx=\dfrac{1}{3.5}(x_2-x_1)=\dfrac{1}{3.5}(11-8.5)=\dfrac{2.5}{3.5}= 0.7143[/tex]

Answer:

7/15

Step-by-step explanation:

There are 15 marbles total. -->

3 of them are yellow => 4 of them are green

3 + 4 = 7

7/15

Hope This Helps!

Answer: 7/15=46%

Step-by-step explanation:

There is in total of 15 marbles

but 3 of them are yellow and 4 are green.

4+3=7

7/15=0.466...

7/15≈0.46

0.46=46%

Answer: 1/8

Step-by-step explanation:

Unit Fractions: A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer. A unit fraction is therefore the reciprocal of a positive integer, 1/n.

Example of Unit Fractions: 1/1, 1/2, 1/3, 1/4 ,1/5, etc.

Hope this helps! Please mark as brainliest!

The unit fraction of the cake is 1/8

A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer.

A unit fraction is therefore the reciprocal of a positive integer, 1/n.

Examples are 1/1, 1/2, 1/3, 1/4, 1/5, etc.

Given that, George cut a cake into 8 equal pieces, we need to find the unit fraction for the cake

Since, George cut the cake in 8 equal pieces so, 1 part will be shown by 1/8 of the cake, that mean 1/8 is one unit of the cake, we can say that 1/8 is the unit of the whole cake.

Hence, the unit fraction of the cake is 1/8

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Answer:

  11.82 mph

Step-by-step explanation:

The angle between the direction of travel and the direction to the city of Hartville is ...

  arctan(180/49) ≈ 74.77°

The speed from the direction of Hartville is the the actual speed multiplied by the cosine of this angle:

  speed from Hartville = (45 mph)×cos(74.77°) ≈ 11.82 mph

_____

Comment on the solution

There are other approaches you can use to solve this. One is to compute the  change in distance over a small period of time, such as 0.02 hours.

0.01 hours before the time of interest, the distance to the city is ...

  d1 = √(180² +(49-.01(45))²) ≈ 186.4326 . . . miles

0.01 hours after the time of interest, the distance to the city is ...

  d2 = √(180² +(49+.01(45))²) ≈ 186.6690 . . . miles

Then the rate of change of distance is ...

  (d2 -d1)/(t2 -t1) = (186.6690 -186.4326)/0.02 = 11.82 . . . mi/h

__

Another is to write the distance equation and differentiate it. (You will find the solution looks very much like the trig solution above.)

  d = √(180² +(45t)²)

  dd/dt = 45²t/√(180² +(45t)²) . . . . . to be evaluated at t=49/45

  rate of change = 45(49/√(180²+49²)) ≈ 11.82 . . . mi/h

It's pretty easy not college levlel just some simple high school geomerty.

Answer: 12

Step-by-step explanation: Because $\overline{PQ}$, $\overline{UV}$, and $\overline{SR}$ are all perpendicular to $\overline{QR}$, we have $\overline{PQ} \parallel \overline{UV} \parallel \overline{SR}$. Therefore, we have $\angle UPQ = \angle UTS$ and $\angle UQP = \angle UST$, which means that $\triangle UPQ \sim \triangle UTS$. So, we have $UQ/US = PQ/ST$.

Because $ST/SR = 2/3$ and $PQ = SR$, we have

\[\frac{UQ}{US} = \frac{PQ}{ST} = \frac{SR}{ST} = \frac{3}{2}.\]Since $UQ/US = 3/2$, we have $UQ/QS = 3/5$.

We have $\triangle UQV \sim \triangle SQR$ by AA Similarity, so $UV/SR = UQ/QS = 3/5$. Therefore, we have $UV = (3/5)SR = \boxed{12}$.

Answer:

Step-by-step explanation:

hello,

[tex]36=6*6=6^2[/tex]

and

[tex](x+6)^2=x^2+12x+36[/tex]

so the missing term is 12 to get a perfect square trinomial

hope this helps

Answer: The answer is "12".

Step-by-step explanation: Correct on edgen. (2022)

Answer:

The solution for this is:

y = (0.6 * x) + 1.25

Hope it helps! :)

Answer:

Having 3.2 liters of water for 3 hours of hiking

Step-by-step explanation:

If x represents the number of hours and y represents the number of liters of water, then we can plug the possible solutions into our inequality to see which solution(s) work.

The first option is having 3 liters of water for 3.5 hours of hiking. We will plug 3 in for y and 3.5 in for x:

y > 0.6x + 1.25

3 > 0.6(3.5) + 1.25

3 > 3.35

But since 3 is not greater than 3.35, this does not work.

The next option is having 2 liters of water for 2.5 hours of hiking:

2 > 0.6(2.5) + 1.25

2 > 2.75

But 2 is not greater than 2.75, so this does not work.

Option c is having 2.3 liters of water for 2 hours of hiking:

2.3 > 0.6(2) + 1.25

2.3 > 2.45

Since 2.3 is not greater than 2.45, this solution does not work.

The last option is having 3.2 liters of water for 3 hours of hiking:

3.2 > 0.6(3) + 1.25

3.2 > 3.05

3.2 IS greater than 3.05, so this solution works!

Answer:

The standard form of a circle is (x - c)² + (y - d)² = r² where (c, d) is the center and r is the radius. This means that the center is (0, -7) and the radius is 8.

Answer:  Center = (0, -7)

                Radius = 8

Step-by-step explanation:

The equation of a circle is: (x - h)² + (y - k)² = r²     where

       x²   + (y + 7)² = 64

→   (x - 0)² + (y - (-7))² = 8²

           ↓              ↓       ↓

          h=0        k=-7     r=8

Answer:

81

Step-by-step explanation:

let the terms be a,ar,ar²

r=2/3

a+a(2/3)+a(2/3)²=171

multiply by 9

9a+6a+4a=171×9

19 a=171×9

a=(171×9)/(19)

a=9×9=81

Answer:

The claim has no evidence to be supported.

On the contrary, there is enough evidence to support the claim that less than 25% of gamers prefer consoles.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The sample has a size n=503.

The sample proportion is p=0.211.

p=X/n=106/503=0.211

The sample proportion is less than 25%, so we will test the claim that less than 25% of gamers prefer consoles.  

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.25\\\\H_a:\pi<0.25[/tex]

The significance level is assumed to be 0.05.

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.25*0.75}{503}}\\\\\\ \sigma_p=\sqrt{0.000373}=0.019[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.211-0.25+0.5/503}{0.019}=\dfrac{-0.038}{0.019}=-1.9685[/tex]

This test is a left-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=P(z<-1.9685)=0.0245[/tex]

As the P-value (0.0245) is smaller than the significance level (0.05), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that less than 25% of gamers prefer consoles.

Answer:

its 4x

Step-by-step explanation:

Answer:

4x

Step-by-step explanation:

Answer:

[tex]n=(\frac{1.440(2.3)}{0.12})^2 =761.76 \approx 762[/tex]

So the answer for this case would be n=762 rounded up to the nearest integer

Step-by-step explanation:

Information given

[tex]\bar X = 17[/tex] represent the mean

[tex]\mu[/tex] population mean (variable of interest)

[tex]\sigma= \sqrt{5.29}= 2.3[/tex] represent the standard deviation

Solution to the problem

The margin of error is given by this formula:

[tex] ME=z_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]    (a)

And on this case we have that ME =0.12 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex]   (b)

The confidence level is 85%, the significance level would be [tex] \alpha=1-0.85 = 0.15[/tex] and [tex]\alpha/2 =0.075[/tex] the critical value for this case would be [tex]z_{\alpha/2}=1.440[/tex], replacing into formula (b) we got:

[tex]n=(\frac{1.440(2.3)}{0.12})^2 =761.76 \approx 762[/tex]

So the answer for this case would be n=762 rounded up to the nearest integer

Answer:

y+2=4(x-1)

y-6=4(x-3)

Step-by-step explanation:

Slope between (3, 6) and (1, -2)

6-(-2)/3-1

8/2

4

y+2=4(x-1)

y-6=4(x-3)

The mean and the standard deviation of the sampling distribution of the sample means are 36 and 1.94 respectively.

Hence option B is correct.

Given Data

Population Mean, μ = 36.0

Population Standard Deviation, σ = 8

Sample size n = 17

Mean standard deviation, μ = 36.0

[tex]\sigma_\bar x[/tex] = [tex]\sigma/\sqrt{n}[/tex]

= [tex]8/\sqrt{17}[/tex]

= 1.94

The mean and the standard σ/√n of the sampling distribution of the sample means are 36 and 1.94 respectively.

Therefore correct option is B .

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Answer:

$706.50 to rent one water tank.

Step-by-step explanation:

The volume of the tank can be calculated by taking the area of the base times the height.

The area of the base is found by taking the radius²×pi: 5²×3.14=78.5.

The multiply that by the height to find the volume: 78.5×3=235.5.

To find the cost of renting the tank, multiply the volume of the tank by the price per cubic foot : 235.5×3=$706.50

Step-by-step explanation:

positive angle =300+180=480.

negative angle = 300 -180=120

Answer: (fоg)(24)=5

Step-by-step explanation:

(fоg)(24) is f of g of 24. This means you plug in g(24) into f(x).

[tex]g(24)=\sqrt{24-8}[/tex]

[tex]g(24)=\sqrt{16}[/tex]

[tex]g(24)=4[/tex]

Now that we know g(24), we can plug it into f(x).

f(4)=2(4)-3

f(4)=8-3

f(4)=5

Answer:

The answer is 100.

Step-by-step explanation:

The original figure has 3 significant figures

Rounded to 1 significant figure is 100

Answer:

384cm2

Step-by-step explanation:

surface area

12×12=144

10×12/2=60

60×4=240

240+144=384cm2

Answer:

differential coefficient of 5x⁴

The solution is : the particular integral is,  yp = -x/8.

and, y = A+Be^8x-x/8

In Mathematics, a differential equation is an equation with one or more derivatives of a function. The derivative of the function is given by dy/dx. In other words, it is defined as the equation that contains derivatives of one or more dependent variables with respect to one or more independent variables.

here, we have,

Given the differential equation: y′′−8y′=7x+1,

The solution of the DE will be the sum of the complementary solution (yc) and the particular integral (yp)

First we will calculate the complimentary solution by solving the homogenous part of the DE first i.e by equating the DE to zero and solving to have;

y′′−8y′=0

The auxiliary equation will give us;

m²-8m = 0

m(m-8) = 0

m = 0 and m-8 = 0

m1 = 0 and m2 = 8

Since the value of the roots are real and different, the complementary solution (yc) will give us

yc = Ae^m1x + Be^m2x

yc = Ae^0+Be^8x

yc = A+Be^8x

To get yp we will differentiate yc twice and substitute the answers into the original DE

yp = Ax+B (using the method of undetermined coefficients

y'p = A

y"p = 0

Substituting the differentials into the general DE to get the constants we have;

0-8A = 7x+1

Comparing coefficients

-8A = 1

A = -1/8

B = 0

yp = -1/8x+0

yp = -x/8 (particular integral)

y = yc+yp

y = A+Be^8x-x/8

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Complete question:

Consider the differential equation: y′′−8y′=7x+1. Find the general solution to the corresponding homogeneous equation. In your answer, use c1 and c2 to denote arbitrary constants. Enter c1 as c1 and c2 as c2. yc= Apply the method of undetermined coefficients to find a particular solution. yp=

Answer:

The right graph (one on your right side)

Step-by-step explanation:

The left one it incorrect because there is 0 data showing 0-9 so it's going to be the right sided graph.

Answer:

none of the choices are correct

Step-by-step explanation:

it's 4/3

20/15=4.3333333333333

4/3=4.333333333333333

8/6=4.33333333333

The scale factor of the two triangles is [tex]\frac{3}{4}[/tex].

When two triangles are similar, the reduced ratio of any corresponding sides is called  the scale factor of the similar triangles.

Similar triangles are triangles that have the same shape, but their sizes may vary.

According to the given question

We have two triangles NGK and ALH

In which

NG = 15, GK = 6, NK = 3

And, AL =  20, LH = 8 and AH = 4

Since, we have to find the scale factor of these two triangles so the two triangles must be similar.

As, ΔNGK is similar to ΔALH

⇒ [tex]\frac{NG}{AL} = \frac{GK}{LH} = \frac{NK}{AH}[/tex]

⇒ [tex]\frac{15}{20} = \frac{6}{8} =\frac{3}{4}[/tex]

⇒ [tex]\frac{3}{4} = \frac{3}{4} =\frac{3}{4}[/tex]

Hence, the scale factor of the two triangles is [tex]\frac{3}{4}[/tex].

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Answer:

3| 4 4 7

4| 0 3 4

5| 5 5 5

6| 0 1 3 8 9

7| 9

8| 1 4 6 8

hope it helps!

Step-by-step explanation:

Check the numbers and list out the tens digit in stem (that is 3-8) and then write the corresponding leaf values