Alex rides his bike to visit two friends and returned home. Interpret the graph to answer questions about his activities.

1. How long did it take Alec to get to his friends house?

2. How long did he stay at his first friends house?

3. How long did it take alec ti ride his bike from his first friends house to his second friends house?

4. How much longer did alec stay at his first friends house than at his second friends house?

5. In which parts of the graph is alec riding his bike toward his home?

6. In which parts of the graph is alec traveling the fastest?

7. How long was alec away from his house?

The number of tests that it would take for the probability of committing at least one type I error to be at least 0.7 is 118   .

In the question ,

it is given that ,

the probability of committing at least , type I error is = 0.7

we  have to find the number of tests ,

let the number of test be n ,

the above mentioned situation can be written as

1 - P(no type I error is committed) ≥ P(at least type I error is committed)

which is written as ,

1 - (1 - 0.01)ⁿ ≥ 0.7

-(0.99)ⁿ ≥ 0.7 - 1

(0.99)ⁿ ≤ 0.3

On further simplification ,

we get ,

n ≈ 118 .

Therefore , the number of tests are 118 .

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The dimension of the cylindrical container  that will minimize the cost of the container is a radius of 4.371 and a height of 25.85

since we know that the volume of a cylinder is :

355=πr²h, where r is the radius of the base and  h is the height

So, we can say h=355/πr², here we have two circular components with the areas 2A=2πr² , for the cost of   0. 02 cents per cm² and a rectangular  component  of area  A=2πrh , with cost of 0. 03 cents per cm².So the cost function will be :

C=0.02(2πr²)+0.03(2πrh)

C=0.04(πr²)+0.06(πrh), substuting the vale of h  

C=0.04(πr²)+0.06(πr(350/πr²))

C=0.04(πr²)+(21/r), differentiating both sides  we get .

C'=0

=>0.08(πr)-(21/r²)= 0, simplifying the equation we get

=>r= 3√525/2π =4.371

so for h, it will be: 355/π(3√(525/2π))  = 355/π(3√(83.55))  =350/π( 4.371) =25.85

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Logarithmic function log₍ₓ₊₂₎(4) = 3x can be written in exponential form as  4 = 3x ⁽ˣ⁺²⁾

Which property of log function is used?

The properties of log are nothing but the rules of logarithms and these are derived from the exponent rules.

These properties of logarithms are used to solve the logarithmic equations and to simplify logarithmic expressions.

A log function can be written in exponential form using

logₐ m = x ⇒ m = ax

According to the given question:

The given logarithmic function is

log₍ₓ₊₂₎(4) = 3x

On applying the property we get

4 = 3x ⁽ˣ⁺²⁾

Hence the required exponential form is 4 = 3x ⁽ˣ⁺²⁾

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No, the mean time to spoil is not necessarily greater if the banana is hung from the ceiling.

This can only be determined by analyzing the data from the experiment with 15 bananas. If the sample mean is greater than 6.5 days, then the mean time to spoil is greater when the banana is hung from the ceiling. If the sample mean is less than or equal to 6.5 days, then the mean time to spoil is not necessarily greater when the banana is hung from the ceiling.

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Sum of the 15 two elements subset of $\{1,2,3,4,5,6} = ( N-1) (N)(N+1)/2

Three elements....two at  time  (1,2) (1,3) (2,3)....sum  =   12

Four elements .... two at a time  (1,2) (1,3) (1,4) (2,3) (2,4) (3,4)  .....sum  =  30

Five elements....two at a time  (1,2) (1,3) (1,4) (1,5) (2,3) (2,4) (2,5) (3,4) (3,5) (4,5)

Note that for N elements taken 2 at a time....the pattern of sums seems to be

= (N-1)(N)(N+1) / 2

For taking 6 elements taking 2 at a time the sum should be

=(5)(6)(7) /2

=210 /2

=105

Therefore, total sum  of those 15 sums  of the elements of each of the 15 two-element subsets of $\{1,2,3,4,5,6\}$ = 105

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We can prove that the given triangles GHL and KHJ are congruent using the ASA theorem. So, the second option is the correct answer.

We can say any two shapes are congruent if they have the same shape and size. For this, their sides and angles need to be mirror images of each other. We have four congruency theorems at hand here. These are side-side-side(SSS), angle-side-angle(ASA), side-angle-side(SAS), and angle-angle-side(AAS).

According to the ASA congruency theorem, one side and two angles of the triangles in question need to be similar. In the given image, we can see that two of the angles i.e., HGL and HKJ are congruent while GHL and KHJ are congruent. The sides GH and KH are also congruent. This makes the two triangles  △GHL ≅ △KHJ by the ASA theorem. So, the second option is the correct answer.

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The measure of the value of [x] is x = √5/2

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given is a triangle as shown in the image.

We can write -

sin(30) = x/(√5)

x = √5 sin (30)

x = √5/2

Therefore, the measure of the value of [x] is x = √5/2.

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Answer:

You can draw a picture like this:

Step-by-step explanation:

If we are working with fractions, then think of it as a circle.

3 circles divided by 8 people

(Draw 3 circles divided into eighths)

Now, on the first circle, write the number one into one of the slices.

Do the same to the second circle.

Now the third.

How many slices have the number 1 in it?

3 slices have the number 1 in it.

And each whole circle has 8 pieces.

3 (slices) divided by 8 (People) = 3/8

Fewer families with kids under 18 now have dinner together seven nights a week

Given,

Let p represent the percentage of households with kids under 18 that have supper together every night.

So, Null Hypothesis, : p 38%    (meaning that more or the same number of families with children under the age of 18 now have dinner together seven nights a week.)

Alternate Hypothesis, : p < 38%     {means that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has​ decreased}

The test statistics that will be used here is One-sample z-test for proportions;

T.S.  =    ~  N(0,1)

Where,

p  = sample proportion of families = 403/1122 = 0.36

n = sample of adults with children under the age of 18 = 1122

So,

The test statistics =     -1.32

The value of z-statistics is -1.32.

Also, the P-value of the test statistics is given by;

 P-value = P(Z < -1.32) = 1 - P(Z  1.32)

= 1 - 0.9066 = 0.0934

We have enough data to reject our null hypothesis since the test statistics will fall in the rejection region because the P-value for our test statistics is less than the level of significance, which in this case is 0.0934 <  0.10.

As a result, we draw the conclusion that fewer families with children under the age of 18 now have supper together seven nights a week.

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The required number of ways to arrange the letters in the word mississippi so that either all the is are consecutive are 11!/4!2!4!..

factorial, in science, the result of all certain whole numbers not exactly or equivalent to a given positive whole number and meant by that whole number and an interjection point. Subsequently, factorial seven is composed 7!, meaning 1 × 2 × 3 × 4 × 5 × 6 × 7. Factorial zero is characterized as equivalent to 1.

We have,

All out no. of words = 11

Had all letters been unmistakable, the response would have been =11!. However, as it isn't the case we want a method for diminishing it to consider the way that a portion of its letter sets are same.

In each game plan of the expressions of "mississippi" :

Presently taking into truth the over three focuses decrease 11! by separating it by 4!2!4! also, you have your response.

Thus, required arrangement is 11!/4!2!4!.

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The factor by which the volume of cube increased is 0.0030

What is a cube ?

A cube is a three-dimensional solid object in geometry that is surrounded by six square faces, facets, or sides, three of which meet at each vertex. One of the five Platonic solids, the cube is the only regular hexahedron. It contains 8 vertices, 6 faces, and 12 edges.

The fundamental distinction between a cube and a square is that the former has three dimensions—length, breadth, and height—while the latter only has two. A cube is composed of squares, which are a type of 2-dimensional (2D) shape (such as a circle, square, triangle, etc.).

let l be the side of a cube

the new length of cube is l' = 1.001l

Initial volume (v1) = l³

final volume (v2) = (1.001)³l³

The factor by which the volume increased is  = v1 / v2

                                                                           = ((1.001)³l³ - l³)/l³

                                                                           = 0.003003

                                                                           = 3 x 0.001

                                                                           ≅ 0.0030

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Answer:

48

Step-by-step explanation:

the ratio of blue cards to yellow cards can be expressed with

4:3.

the total amount of blue and yellow cards can be interpreted as 4x+3x=7x

then you can find the value of x by dividing 84/7, which is 12

since the value of blue cards is 4x, 4(12) = 48

The given expression can be simplified as (x³ + 3x + 5)/(x² - x).

If the fractions have the same denominators then their numerators are added keeping the denominators as the same.

For fractions with different denominators the LCM of the denominators are taken then that is divided by the numerators of each fraction and the number obtained is multiplied to each of them to get the equivalent fraction.

The given expression is as below,

(x² - 5)/x + (x + 8)/(x - 1)

It can be simplified as follows,

(x² - 5)/x + (x + 8)/(x - 1)

= ((x² - 5)(x - 1) + x(x + 8))/(x(x - 1))

= ((x³ - x² - 5x + 5) + x² + 8x)/(x² - x)

= (x³ + 3x + 5)/(x² - x)

Hence, the given expression can be written in the form of single fraction as (x³ + 3x + 5)/(x² - x).

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Answer: x = 18

Step-by-step explanation:

1) 100% - 54.5% = 45.5%.

2) 45.5/100 = 0.455.

3) 0.455 * X = 8.19g.

4) x = 8.19/0.455.

5) x = 18.

For the square on the diagram, we can see that:

Remember that all the sides of a square have the same length.

Here we know that AC, the diagonal of the square, has a measure of 20 cm.

Then the length of DE, which is half of the diagonal of the square, is half of that, then:

20cm/2 = 10cm

DE = 10cm

DC is one of the sides of the square. Remember that for a square of sidelength S, the diagonal is:

D = √2*S

Then the sidelength is:

S = D/√2

Here we know that the diagonal measures 20 cm, then:

DC = S = 20cm/√2 = 14.14 cm

DC = 14.14cm

Finally, mADE refers to the measure located at the vertex D on the triangle on the angle ADE.

Remember that all the angles of a square measure 90°, and here the ray DE divides that angle in two halves, then mADE = 90°/2 = 45°

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At 0.01 significance level the hypothesis is rejected.

Null Hypothesis (H₀): The sample data occurs purely from chance.

Alternative Hypothesis (H₁): The sample data is influenced by some non-random cause.

If the p-value of the hypothesis test is less than some significance level (e.g. α = .01), then we can reject the null hypothesis and conclude that we have sufficient evidence to say that the alternative hypothesis is true.

Given that,

x = 28

s = 2.9

μ = 31

n = 8

α = 0.01

Then, the Null Hypothesis : H₀ = 31

          The Alternate Hypothesis : H₁ < 31

The average number of cigeratte smoker  per day is less than 31.

Test Statistics:

t = x -μ / s√n

   = 28 - 31/ 2.9√8

   = -3/ 8.41

   = -0.356

Since the p-value of 0.0046 is less than the significance level of 0.01, the auditor rejects the null hypothesis.

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Answer:

no it wont

Step-by-step explanation:

The expressions of the total cost are 1.15t and t * (1 + 0.15)

From the question, we have the following parameters that can be used in our computation:

Cost of a ticket = t dollars

Amusement tax on each ticket = 15%

The above parameters mean that the total cost of a ticket can be calculated using the following equation

The total cost of a ticket = Cost of a ticket * (1 + Amusement tax on each ticket)

Substitute the known values in the above equation, so, we have the following representation

The total cost of a ticket = t * (1 + 15%)

Evaluate the percentage

The total cost of a ticket = t * (1 + 0.15)

So, we have

The total cost of a ticket = t * (1.15)

Evaluate the product

The total cost of a ticket = 1.15t

Hence, the expression is 1.15t

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There are 207 students in the 9 classes at East Middle School. At this rate, how many students are in 6 classes?

1: 54 students

2: 138 students

3: 69 students

4: 250 students

207 / 9 = 23

23 * 6 = 138

The correct option for the lines of symmetry of a regular pentagon-

An image of a pentagon's five lines of symmetry is included below.

We can observe from the following photo that the lines for symmetry cut through a vertex angle, a side, and are perpendicular to either a side.

Options C, D, and E are the appropriate choices.

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Complete question is;

Which statements are true about the lines of symmetry of a regular pentagon? Check all that apply.

A) Every line connects two vertices.

B) Every line connects the midpoints of 2 sides.

C) Every line bisects a vertex angle.

D) Every line bisects a side.

E) Every line is perpendicular to a side.

When the population of a protozoa develops with a constant relative growth rate of 0.6685 per member per day, and there are two members on the day zero, the population after will consist of 7 at the end of seven days period.

The total population of the protozoa at the end of the seven days can be computed using the calculations given below,

Total Population = Growth Rate x Number of Days + Day zero Population

Total Population = (0.6685 x 7) + 2

Total Population = 6.667, or ~ 7.

Therefore, there will be 7 protozoa at the end of seven days.

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Answer: the one in blue

Step-by-step explanation:

This table illustrates how many trials out of 100 resulted in each number of heads out of ten flips. Because it precisely depicts the possibility of each occurrence, this frequency table is the most likely to include the outcomes of the 100 trials.

The likelihood of receiving any number of heads out of ten flips is the same in a fair coin flip, therefore the table should show a fairly uniform distribution of trials across each number of heads. Overall, the frequency table most likely to capture the outcomes of the 100 trials has the number of heads out of 10 flips as rows and the number of trials out of 100 as columns.

This table may be used to precisely depict the data as well as determine the likelihood of each occurrence.

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Answer:

The letter [tex]r[/tex] in the given formula represents the rate of interest.

Explanation:

Where I is the amount of interest, P is the principal (amount of money borrowed), r is the interest rate (per year), and t is the time (expressed in years).

Hope this helps!

[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-5)}}} \implies \cfrac{-3 +5}{1 +5} \implies \cfrac{ 2 }{ 6 } \implies \cfrac{1 }{ 3 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{ \cfrac{1 }{ 3 }}(x-\stackrel{x_1}{(-5)}) \implies y +5 = \cfrac{1 }{ 3 } ( x +5)[/tex]

An Endure chosen randomly the likelihood of any battery lasting longer than 550 hours is 10.56%.

These steps are used to determine the Z score:

z = (x - μ)/σ

As mentioned in question-

x > 550 and μ = 500, σ = 40:

z = 550 - 500 / 40

z = 1.25

Obtain the p-value from normal distribution chart,

P(z > 1.25) = 1 - P(z < 1.25)

P(z > 1.25) = 1 - 0.8944

P(z > 1.25) = 0.1056

Thus, an Endure chosen at random the likelihood of any battery lasting longer than 550 hours is 10.56%.

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Answer:

6, 7, 10

Step-by-step explanation:

7 > x - 4 ( add 4 to both sides )

11 > x , then

x < 11

the values from the table which are solutions are 6, 7, 10

Answer:

Answer is 11

Step-by-step explanation:

7+4>z-4+4

11>z

Answer:

8

Step-by-step explanation:

23:41

41+23=64

64/8=8

Answer:

0.2

Step-by-step explanation:

First part yields 0.008 if you take sqrt((1/25)^3).

Then the cuberoot of 0.008 is 0.2.

Answer:

Look at the attachment! :D

Hope this helps!

Step-by-step explanation: