Jennifer is saving money to buy a bike. The bike costs $227. She has $106 saved, and each week she adds
$11 to her savings.
How long will it take her to save enough money to buy tho hilo?

According to the manufacturer's claim, we build an hypothesis test, find the test statistic and the p-value relative to this test statistic, we have that:

As the test involves a comparison of samples, it involves subtraction of normal variables, and for this, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Before:

Average of 0.250 in 56 at bats, so:

[tex]p_B = 0.25[/tex]

[tex]s_B = \sqrt{\frac{0.25*0.75}{56}} = 0.0579[/tex]

After:

Average of 0.44 in 25 at bats, so:

[tex]p_A = 0.44[/tex]

[tex]s_A = \sqrt{\frac{0.44*0.56}{25}} = 0.0993[/tex]

Test if there was improvement:

At the null hypothesis, we test if there was no improvement, that is, the subtraction of the proportions is 0:

[tex]H_0: p_A - p_B = 0[/tex]

At the alternative hypothesis, we test if there was improvement, that is, the subtraction of the proportions is positive, so:

[tex]H_1: p_A - p_B > 0[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

From the samples:

[tex]X = p_B - p_A = 0.44 - 0.25 = 0.19[/tex]

[tex]s = \sqrt{s_A^2 + s_B^2} = \sqrt{0.0579^2 + 0.0993^2} = 0.1149[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{s}[/tex]

[tex]z = \frac{0.19 - 0}{0.1149}[/tex]

[tex]z = 1.65[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a difference of at least 0.19, which is 1 subtracted by the p-value of z = 1.65.

Looking at the z-table, z = 1.65 has a p-value of 0.9505.

1 - 0.9505 = 0.0495.

The p-value of the test is of 0.0495 > 0.02, which means that there is not sufficient evidence to say that his batting average has improved at the 0.02 level of significance.

A similar question is found at https://brainly.com/question/23827843

Answer:

x = -5 or x = 1

Step-by-step explanation:

[tex] 3{x}^{2} + 12x - 15 = 0 \\ {x}^{2} + 4x - 5 = 0 \\ (x + 5)(x - 1) = 0 \\ x = - 5 \: or \: x = 1[/tex]

hope this makes sense:)

Answer:

3)  20% of the students earned a D

Step-by-step explanation:

9 students got a D.

5 students got a C.

14 students got a B.

17 students got an A.

Total number of students:

9 + 5 + 14 + 17 = 45

1)  1/5 of the students earned a C

1/5 of 45 = 9

5 students got a C

False

2) 3% more students earned an A then B

3 more students got an A than a B, but not 3%.

False

3)  20% of the students earned a D

20% of 45 = 9

9 students got a D.

True

4)  1/4 of the class earned a B​

1/4 of 45 = 11.25

There were 14 B's.

False

Answer: 3)  20% of the students earned a D

Answer:

See the explanation and attached images for the answers.

Step-by-step explanation:

a) 1-step transition matrix:

See the attached image for transition matrix.

Let the matrix be M

if the stock closes higher on a day, the probability that it closes higher the next day is 0.65.

If the stock closes lower on a day, the probability that it closes higher the next day is 0.45

if the stock closes higher on a day, the probability that it closes lower the next day is 1 - 0.65 = 0.35

if the stock closes lower on a day, the probability that it closes lower the next day is 1 - 0.45 =0.55

b)

To compute probability for 3 days later multiply matrix M (from part a) thrice i.e. M*M *M

[tex]M^{3} = \left[\begin{array}{ccc}0.65&0.35\\0.45&0.55\end{array}\right]*\left[\begin{array}{ccc}0.65&0.35\\0.45&0.55\end{array}\right]*\left[\begin{array}{ccc}0.65&0.35\\0.45&0.55\end{array}\right][/tex]

[tex]M^{3} = \left[\begin{array}{ccc}0.65 * 0.65 + 0.35 * 0.45 &0.65 * 0.35 + 0.35 * 0.55 \\0.45 * 0.65 + 0.55 * 0.45 &0.45 * 0.35 + 0.55 * 0.55 \end{array}\right] * \left[\begin{array}{ccc}0.65&0.35\\0.45&0.55\end{array}\right][/tex]

[tex]M^{3} = \left[\begin{array}{ccc}0.58&0.42\\0.54&0.46\end{array}\right]*\left[\begin{array}{ccc}0.65&0.35\\0.45&0.55\end{array}\right][/tex]

[tex]M^{3} = \left[\begin{array}{ccc} 0.58 * 0.65 + 0.42 x 0.45&0.58 * 0.35 + 0.42 * 0.55 \\0.54 * 0.65 + 0.46 * 0.45 &0.54 * 0.35 + 0.46 * 0.55 \end{array}\right][/tex]

[tex]M^{3} = \left[\begin{array}{ccc}0.566&0.434\\0.558&0.442\end{array}\right][/tex]

The probability that it will close higher on Thursday is 0.566. See the transmission matrix of M³ for higher-higher. This can be interpreted as:

if the stock closed higher on Monday, the probability that it closes higher the on Thursday (three days later) is 0.566

Answer:

The equation is y= -4x -8

Step-by-step explanation:

The -4 is the slope and the -8 is the y intercept

Answer:

Slope: -4

Line type: Straight and diagonal from left to right going down.

Rate of change: a decrease by 4 for every x vaule

y-intercept is: (0,-8)

x-intercept is: (-2,0)

Step-by-step explanation:

Slope calculations:

y2 - y1 over x2 - x1

0 - 4

-2 - ( -3) or -2 + 3

=

-4/1 =

-4

More slope info on my answer here: https://brainly.com/question/17148844

Hope this helps, and have a good day.

Answer:

32.8 miles

Step-by-step explanation:

Amy is driving to Seattle. Suppose that the remaining distance to drive (in miles) is a linear function of her driving time (in minutes). When graphed, the function gives a line with a slope of -0.95. See the figure below. Amy has 48 miles remaining after 31 minutes of driving. How many miles will be remaining after 47 minutes of driving?

Answer: The general equation of a line is given as y = mx + c, where m is the slope of the line and c is the intercept on the y axis. Given that the slope is -0.95, substituting in the general equation :

y = -0.95x + c

Amy has 48 miles remaining after 31 minutes of driving, to find c, we substitute y = 48 and x = 31. Therefore:

48 = -0.95(31) + c

c = 48 + 0.95(31)

c = 48 + 29.45

c = 77.45

The equation of the line is

y = -0.95x + 77.45

After 47 minutes of driving, the miles remaining can be gotten by substituting x = 47 and finding y.

y = -0.95(47) + 77.45

y = -44.65 + 77.45

y = 32.8 miles

The telescope shape and the characteristic equations of the telescope parameters are the same as parabolic equations

The distance between the focus and the vertex, of the parabola is 3.375 meters

The process for obtain the above values is as follows:

The known parameters of the parabola are;

The location of the vertex of the parabola= The origin = (0, 0)

The height of the parabola = 9 meters

The width of the parabola = 12 meters

The unknown parameter;

The distance between the focus and the vertex

Method:

Finding the coordinate of the focus from the general equations of the the parameters of a parabola

The equation of the parabola in standard form is y = a·(x - h)² + k

From which we have;

(x - h)² = 4·p·(y - k)

The coordinates of the focus, f = (h, k + p)

Where;

(h, k) = The coordinates of the vertex of the parabola = (0, 0)

∴ a = 1/(4·p)

From the question, we have the following two points on the parabola,

given that the parabola is 12 meters wide at 9 meters above the origin and

it is symmetric about the y-axis;

Points on the parabola = (9, 6), and (9, -6)

Plugging in the values of the vertex, (h, k) and the two known points, in the equation, y = a·(x - h)² + k, we get;

6 = a·(9 - 0)² + 0 = 81·a

a = 6/81 = 2/27

p = 1/(4·a)

∴ p = 1/(4 × 2/27) = 27/8

The coordinate of the focus, f =  (h, k + p)

∴ f = (0, 0 + 27/8) = (0, 27/8)

The coordinate of the focus f = (0, 27/8)

Given the vertex and the focus of the parabola have the same x-values of 0, we have;

The distance between the focus and the vertex, d = the difference in their y-values;

∴ d = 27/8 - 0 = 27/8 = 3.375

The distance between the focus and the vertex, d = 3.375 meters

Learn more about parabola here;

https://brainly.com/question/22404310

answer is 71.08745247

in mix form or in short form it is =

71/23/263

Answer:

[tex]\pi[/tex] radian

Step-by-step explanation:

We know that angle for a full circle is 2[tex]\pi[/tex]

In the given figure shape is semicircle

hence,

angle for semicircle will be half of angle of full circle

thus, angle for given figure = half of  angle for a full circle = 1/2 * 2[tex]\pi[/tex] = [tex]\pi[/tex]

Thus, answer is [tex]\pi[/tex] radian

alternatively, we also know that angle for a straight line is 180 degrees

and 180 degrees is same as [tex]\pi[/tex] radian.

Complete Question

An IQ test is designed so that the mean is 100 and the standard deviation is 24 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 95% confidence that the simple mean is with in 3 IQ points of the true mean. Assume that standard deviation  = 24 and determine the required sample size using technology. Determine if this is a reasonable sample size for a real world calculation.

The required sample size ______ (round up to the nearest integer.

Answer:

The sample size is  [tex]n = 246[/tex]

Step-by-step explanation:

From the question we are told that

    The  mean is  [tex]\mu = 100[/tex]

     The  standard deviation is  [tex]\sigma = 24[/tex]

     The  margin of error is  [tex]E = 3[/tex]

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 normal distribution table the value is

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

The sample size is evaluated as

          [tex]n = [ \frac{ Z_{\frac{\alpha }{2} } * \sigma }{E }]^2[/tex]

=>       [tex]n = [ \frac{ 1.96 * 24 }{3 }]^2[/tex]        

=>      [tex]n = 246[/tex]

to check if this n is applicable in real world then we calculate E and  compare it with the given E

By Green's theorem,

[tex]\displaystyle\int_{x^2+y^2=16}(3y-e^{\sin x})\,\mathrm dx+(7x+y^4+1)\,\mathrm dy[/tex]

[tex]=\displaystyle\iint_{x^2+y^2\le16}\frac{\partial(7x+y^4+1)}{\partial x}-\frac{\partial(3y-e^{\sin x})}{\partial y}\,\mathrm dx\,\mathrm dy[/tex]

[tex]=\displaystyle4\iint_{x^2+y^2\le16}\mathrm dx\,\mathrm dy[/tex]

The remaining integral is just the area of the circle; its radius is 4, so it has an area of 16π, and the value of the integral is 64π.

We'll verify this by actually computing the integral. Convert to polar coordinates, setting

[tex]\begin{cases}x=r\cos\theta\\y=r\sin\theta\end{cases}\implies\mathrm dx\,\mathrm dy=r\,\mathrm dr\,\mathrm d\theta[/tex]

The interior of the circle is the set

[tex]\{(r,\theta)\mid0\le r\le4\land0\le\theta\le2\pi\}[/tex]

So we have

[tex]\displaystyle4\iint_{x^2+y^2\le16}\mathrm dx\,\mathrm dy=4\int_0^{2\pi}\int_0^4r\,\mathrm dr\,\mathrm d\theta=8\pi\int_0^4r\,\mathrm dr=64\pi[/tex]

as expected.

the answer is 11/7.you can see the image

Answer:

[tex]\boxed {\boxed {\sf \frac{11}{7}}}[/tex]

Step-by-step explanation:

The slope describes the direction and steepness of a line. The formula is:

[tex]m= \frac{y_2-y_1}{x_2-x_1}[/tex]

Where (x₁, y₁) and (x₂, y₂) are the points the line contains. For this problem, the line contains the points (2,7) and (-5, -4). Therefore:

Substitute these values into the formula.

[tex]m= \frac{ -4 -7}{-5-2}[/tex]

Solve the numerator (-4 -7 = -11).

[tex]m= \frac{ -11}{-5-2}[/tex]

Solve the denominator (-5-2 = -7).

[tex]m= \frac{ -11}{-7}[/tex]

Simplify the fraction. The 2 negative signs cancel each other out.

[tex]m= \frac{11}{7}[/tex]

The slope of the line is 11/7

Answer:

[tex]\mathbf{P(X=5) =0.0888}[/tex]    

P(x ≤ 5 ) = 0.9707

P ( x ≥ 6) = 0.0293

Step-by-step explanation:

The probability of a binomial mass distribution can be expressed with the formula:

[tex]\mathtt{P(X=x) =(^{n}_{x} ) \ \pi^x \ (1-\pi)^{n-x}}[/tex]

[tex]\mathtt{P(X=x) =(\dfrac{n!}{x!(n-x)!} ) \ \pi^x \ (1-\pi)^{n-x}}[/tex]

where;

n = 8 and π = 0.36

For x = 5

The probability [tex]\mathtt{P(X=5) =(\dfrac{8!}{5!(8-5)!} ) \ 0.36^5 \ (1-0.36)^{8-5}}[/tex]

[tex]\mathtt{P(X=5) =(\dfrac{8!}{5!(3)!} ) \ 0.36^5 \ (0.64)^{3}}[/tex]

[tex]\mathtt{P(X=5) =(\dfrac{8 \times 7 \times 6 \times 5!}{5!(3)!} ) \times \ 0.0060466 \ \times 0.262144}[/tex]

[tex]\mathtt{P(X=5) =(\dfrac{8 \times 7 \times 6 }{3 \times 2 \times 1} ) \times \ 0.0060466 \ \times 0.262144}[/tex]

[tex]\mathtt{P(X=5) =({8 \times 7 } ) \times \ 0.0060466 \ \times 0.262144}[/tex]

[tex]\mathtt{P(X=5) =0.0887645}[/tex]

[tex]\mathbf{P(X=5) =0.0888}[/tex]     to 4 decimal places

b. x ≤ 5

The probability of P ( x ≤ 5)[tex]\mathtt{P(x \leq 5) = P(x = 0)+ P(x = 1)+ P(x = 2)+ P(x = 3)+ P(x = 4)+ P(x = 5})[/tex]

[tex]{P(x \leq 5) = ( \dfrac{8!}{0!(8!)} \times (0.36)^0 \times (1-0.36)^8 \ ) + \dfrac{8!}{1!(7!)} \times (0.36)^1 \times (1-0.36)^7 \ +[/tex][tex]\dfrac{8!}{2!(6!)} \times (0.36)^2 \times (1-0.36)^6 \ + \dfrac{8!}{3!(5!)} \times (0.36)^3 \times (1-0.36)^5 + \dfrac{8!}{4!(4!)} \times (0.36)^4 \times (1-0.36)^4 \ + \dfrac{8!}{5!(3!)} \times (0.36)^5 \times (1-0.36)^3 \ )[/tex]

P(x ≤ 5 ) = 0.0281+0.1267+0.2494+0.2805+0.1972+0.0888

P(x ≤ 5 ) = 0.9707

c. x ≥ 6

The probability of P ( x ≥ 6) = 1  - P( x  ≤ 5 )

P ( x ≥ 6) = 1  - 0.9707

P ( x ≥ 6) = 0.0293

Answer:

1/6 or 16.6%

Step-by-step explanation:

There are 6 possible combinations, one of which being whole wheat with thick crust. Therefore there is a 1/6 chance.

Answer:

cccccccccccccccçccccccccc

Answer:

if the dot is filled (black) it is ≤ or ≥

if it is not filled it is  < or >

you graph goes from 6 to 10

the unfilled one is 6 the filled one is 10

thus 6 < x ≤ 10

which says x is greater than 6 and also less than or equal to 10

Step-by-step explanation:

Answer:

675 km/hr and 75 km/hr

Step-by-step explanation:

Let the speed of plane in still air be x and the speed of wind be y.

ATQ, (x+y)*(40/60)=500 and (x-y)*(50/60)=500. Solving it, we get x=675 and y=75

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

Explanation:

Count out the spaces, or use subtraction, to find the horizontal side BC is 2 units long. Similarly, you'll find the vertical side AC is 4 units long.

Use the pythagorean theorem to find the length of segment AB.

a^2 + b^2 = c^2

2^2 + 4^2 = c^2

4 + 16 = c^2

20 = c^2

c^2 = 20

c = sqrt(20)

We stop here since it matches with choice B.

-----------------

Optionally, we can simplify like so

sqrt(20) = sqrt(4*5)

sqrt(20) = sqrt(4)*sqrt(5)

sqrt(20) = 2*sqrt(5)

Answer:

The answer is [tex]\sqrt{20}[/tex].

Step-by-step explanation:

Use the Pythagorean Theorem.  

[tex]2^{2} + 4^{2} = c^{2} \\4+16 = c^{2} \\\sqrt{20} = c[/tex]

Answer:

work is shown and pictured

Answer:

Hi, there!!!

The answer would be 2(2x-1)/x(x-4).

See explanation in picture.

Hope it helps...

Distance:-

[tex]\\ \sf\longmapsto \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]\\ \sf\longmapsto \sqrt{(3+2)^2+(7-5)^2}[/tex]

[tex]\\ \sf\longmapsto \sqrt{5^2+2^2}[/tex]

[tex]\\ \sf\longmapsto \sqrt{25+4}[/tex]

[tex]\\ \sf\longmapsto \sqrt{29}[/tex]

[tex]\\ \sf\longmapsto 5.2[/tex]

[tex]\begin{gathered} {\underline{\boxed{ \rm {\red{Distance \: = \: \sqrt{(x_2 - x_1) \: + \: (y_2 - y_1)} }}}}}\end{gathered}[/tex]

[tex] \begin{cases}\large\bf{\blue{ \implies}} \tt \: Distance \: = \: \sqrt{ \bigg(3 - [ - 2] \bigg) \: + \: (7 - 5)}\\ \\ \large\bf{\blue{ \implies}} \tt \: Distance \: = \: \sqrt{ (3 + 2 ) \: + \: (7 - 5)} \\ \\ \large\bf{\blue{ \implies}} \tt \: Distance \: = \: \sqrt{ {5} \: ^{2} + \: {2}^{2} } \\ \\ \large\bf{\blue{ \implies}} \tt \: Distance \: = \: \: \sqrt{25 \: + \: 4} \\ \\ \large\bf{\blue{ \implies}} \tt \: Distance \: = \: \: \ \sqrt{29} \\ \\\large\bf{\blue{ \implies}} \tt \: Distance \: = \: \:5.38 \: \: units \end{cases}[/tex]

Answer:

the answer is c

Step-by-step explanation:

Answer:

Hello,

Step-by-step explanation:

This a method knowing nothing.

1+3+5+7+9=25

425-25=400

400/5=80

Numbers are 80+1,80+,80+5,80+7,80+9 whose sum is 425.

Answer:

26ft

Step-by-step explanation:

10^2 +24^2 =AB^2

AB=26

Answer: 26 ft

Step-by-step explanation:

a^2+b^2=c^2

10^2+24^2 = c^2

100+576=c^2

Sqrt 676 = c

C = 26

Step-by-step explanation:

Hey, there!!

Look this figure, simply we find that;

In triangle ABC,

angle CBD is an exterior angle of a triangle.

and its measure is 90°

Then,

angle CBD= y +48° {sum of interior opposite angle is equal to exterior angle or from theorem}.

or, 90°= y + 48°

Shifting, 48° in left side,

90°-48°= y

Therefore, the value of y is 42°.

Hope it helps...

Answer:

90 degrees

Step-by-step explanation:

the right angles in the top right and bottom left mean its a square

[tex]\\ \sf\longmapsto \dfrac{AK}{DK}=\dfrac{CK}{BK}[/tex]

[tex]\\ \sf\longmapsto \dfrac{14}{12}=\dfrac{4x+1}{3x+3}[/tex]

[tex]\\ \sf\longmapsto \dfrac{7}{6}=\dfrac{4x+1}{3x+3}[/tex]

[tex]\\ \sf\longmapsto 7(3x+3)=6(4x+1)[/tex]

[tex]\\ \sf\longmapsto 21x+21=24x+6[/tex]

[tex]\\ \sf\longmapsto 24x-21x=21-6[/tex]

[tex]\\ \sf\longmapsto 3x=15[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{15}{3}[/tex]

[tex]\\ \sf\longmapsto x=5[/tex]

Answer:

The mean is about 68 (67.5555)

Step-by-step explanation:

(63+64+66+66+67+68+69+71+74) / 9 ≈ 68

Answer:

(5*sqrt(2), 5pi/4)

Step-by-step explanation:

In Polar coordinates, tan(theta)=y/x and r=sqrt(x^2+y^2)

tan(theta)=-5/5=-1. Theta=5pi/4

r=sqrt(5^2+5^2)=5*sqrt(2)

Hence the Polar coordinate is (5*sqrt(2), 5pi/4)

The polar coordinate is [tex](5\sqrt{2},\frac{-\pi }{4} )[/tex].

The polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.

To convert rectangular coordinate (x, y) to polar coordinate(r, θ) by using some formula

tanθ = y/x and [tex]r =\sqrt{x^{2} +y^{2} }[/tex]

According to the given question

We have

A rectangular coordinate (5, -5).

⇒ x = 5 and y = -5

Therefore,

[tex]r=\sqrt{(5)^{2} +(-5)^{2} } =\sqrt{25+25} =\sqrt{50} =5\sqrt{2}[/tex]

and

tanθ = [tex]\frac{-5}{5} =-1[/tex]

⇒ θ = [tex]tan^{-1} (-1)[/tex] = [tex]-\frac{\pi }{4}[/tex]

Therefore, the polar coordinate is [tex](5\sqrt{2},\frac{-\pi }{4} )[/tex].

Learn more about polar coordinates here:

https://brainly.com/question/1269731

#SPJ2

Answer:

(a) The 26th percentile for the number of chocolate chips in a bag is 1185

(b) The number of chocolate chips in a bag that makes up the middle 96% of the bags is between 1020 and 1504

Step-by-step explanation:

From the question, we have the following values:

μ =1262 and σ =118

(a) Let the value of x represents the 26th percentile. So the 26th percentile means 26% data is less than x. We can use the standard normal table to get the particular z-value that corresponds to this percentile.

P( Z<-0.65 )=0.2578 which is approximately 0.26

So for 26th percentile z-score will be -0.65.

Mathematically;

z-score = (x-mean)/SD

-0.65 = (x-1262)/118

-76.7 = x -1262

x = 1262-76.7 = 1185.3

This value is approximately 1,185

(b) Using a graph of standard normal distribution curve, if middle is 96% , then at both tails 2% each.

From z-table, we can find the closest probability;

P(-2.05<z<2.05) = 0.96

So we have two x values to get from the individual z-scores

-2.05 = (x-1262)/118

x = 1020(approximately)

For 2.05, we have

2.05 = (x-1262)/118

x = 1262 + 2.05(118) = 1504 (approximately)