Ben watched 3/8 of his television show. There are still 40 minutes left. How long does the whole program last?

Answer:2/5=4/10 and 1/4=2/8

Step-by-step explanation: you can simplify 4/10 to get 2/5 and same with 2/8. You would divide the fraction by two.

The plane which is parallel to the line WXT is UVZW

two segments parallel to VU is ST and WX

two segments skew to XY is UT

two segments skew to VZ is YU and TX

Lines that are always the same distance apart in a plane are said to be parallel. Lines that are parallel never cross. Lines that cross at a straight angle (90 degrees) are said to be perpendicular.

Given : The quadrilateral prism

Parallel lines means lines which does not interact and run parallel meaning they have equal distance between them.

The plane which is parallel to the line WXT is UVZW

two segments parallel to VU is ST and WX

two segments skew to XY is UT

two segments skew to VZ is YU and TX

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Answer:

x=21

Step-by-step explanation:

The angles of a triangle always add up to 180°

71+62+(2x+5)=180

First add 71 and 62

133+(2x+5)=180

Then you subtract 133

2x+5=47

Subtract 5 too

2x=42

Then divide by 2

x=21

We can check our answer by adding all the angles

71+62+(2*21+5)

71+62+(42+5)

71+62+47=180

The null hypothesis is a statement which describe the claim of 'no difference'.

Let μ be the population mean.

Given claim : The mean age of bus drivers in Chicago is 50.2 years.

i.e. μ = 50.2

Since "no difference with mean" or statements with an equal sign are used as the null hypothesis.

Then, the null hypothesis for the given situation is

Ηο : μ = 50.2

If the test fails to reject the null hypothesis, it means there is evidence to support the claim that the the mean age of bus drivers in Chicago is 50.2 years.

A statistical hypothesis known as a null hypothesis asserts that no statistical significance can be found in a collection of provided data. Using sample data, hypothesis testing is performed to evaluate a theory' veracity. It is often referred to as just "the null," and its symbol is Hο.

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The output value of g( -3 ) in the function g( a ) = 3a + 2 is -7.

A function is simply a relationship that maps one input to one output. For relation to qualify as a function,  each x-value can only have one y-value.

Given the data in the question;

To determine the output value of g( -3 ), replace all the occurrence of 'a' with -3 in the function and simplify.

g( a ) = 3a + 2

g( -3 ) = 3( -3 ) + 2

Multiply 3 and -3

g( -3 ) = -9 + 2

Add -9 and 2

g( -3 ) = -7

Therefore, the output value is -7, this forms an ordered pair of (-3,-7).

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Answer:

B is correct: also if u add C and D together there both different and if u added B and A correctly u would have got B as your answer.

Step-by-step explanation:

3Justin's estimated Vo2 max is 25.8(mL*kg*min)

What is Vo2 max ?

 The amount (volume) of oxygen used by your body while exercising as hard as you can is referred to as VO2 max. It's a common tool for determining your level of fitness. Knowing your VO2 max can assist you in training for sports, tracking fitness progress, and improving your heart health.

Here using vo2 max fomula 1.5 miles ,

=> VO2 max = 3.5+483/Time

Here Time= 11 min 25 sec = 25/60 = 0.41 min

Then time=11.42 mins. Now,

=> VO2 max = 3.5+ 483/11.41

=> VO2 max = 3.5+42.3

=>VO2 max = 25.8(mL*kg*min)

Hence His estimated Vo2 max is 25.8(mL*kg*min)

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There is no vertex in the graph and the transformations from the parent function are

The graph represents the given parameter

As a general rule, the maximum or the minimum of a graph is the vertex

In this case, there is no maximum or minimum in the graph

This means that that there is no vertex in the graph

Here, we have:

We can see that:

The graph is 4 units to the left of the origin and 2 units below the origin

This means that the function has been shifted down and shifted to the left

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The probability that the area covered by a can of spray paint is 0.251

The variable of interest is:

X: are objects that can be painted with a single can of spray paint.

This variable has a normal distribution, with a mean of 25 feet square and a standard deviation of 3 feet square.

Symbolically:

P(X≥27)

To calculate the probability, use the standard normal distribution, so first standardize the value of X using:

Z= (X-μ)/σ

P(X≥27)= P(Z≥(27-25)/3)= P(Z≥0.67)

Now, because the Z-table contains cumulative probability information:

P(Zα≤Z₀)=1-α

you must perform the following conversion to calculate the requested probability:

1 - P(Z<0.67)= 1 - 0.749= 0.251

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As per given data of at least 48inches height is required to ride in amusement park , Michael is 42 inches tall and grow 1/2 in. every month then total months after which Michael can ride is 12 months.

As given in the question,

Minimum height require to ride in amusement park = at least 48 inches

Present height of Michael is 42 inches tall

Increase in height every month 1/2 inch.

Let 'm' months taken by Michael to ride in amusement park.

Required equation is:

48 = 42 + (1/2)m

⇒(1/2)m = 48 -42

⇒ m = 6×2

⇒ m =12 months

Therefore, for the given data of at least 48inches height is required to ride in amusement park , Michael is 42 inches tall and grow 1/2 in. every month then total months after which Michael can ride is 12 months.

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Answer:

As a product of prime numbers:

420 = 2 × 2 × 3 × 5 × 7

Using system of linear equation, the complementary angles (x, y) are 27 and 63 degrees respectively.

When the sum of two angles is equal to 90 degrees, they are called complementary angles. For example, 30 degrees and 60 degrees are complementary angles. However, when the sum of the two angles is equal to 180 degrees, the angles are supplementary angles

In this case, we have two angles x, y which are complimentary to one another.

We can represent this with system of equations;

solving equation (i) and (ii)

The value of x and y are 27 and 63

The complementary angles are 27 and 63

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Answer:

Total Cost = $186

Step-by-step explanation:

All but 8 means that All of them participated except for 8 of them

Since there is 39 Students in the Club

Then the Number of Students participated = 39 - 8 = 31 Students

Total Cost = (Cost per Student ) * ( Number of Students )

                 =$6 * 31 = $186

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The vertex of the graph is (-2, 2), the axis of symmetry of parabola is -2 and the parabola opens downwards.

In the given question we have to find the vertex, axis of symmetry and whether the parabola opens upwards and downwards.

Firstly we find ing the vertex of the graph.

As we know that vertex is the highest and lowest point of the graph.

From the graph the highest point is (-2, 2).

So the vertex of the graph is (-2, 2).

As we know that the axis of symmetry always passes through the vertex of parabola. The x coordinate of the vertex of parabola is the axis of symmetry of parabola.

So the axis of symmetry of parabola is -2.

As we can see that the parabola opens downwards.

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The statements that are true are:

It should be noted that the two figures can be regrdedas as one that are similar in the case whereby their corresponding angles are congruent ,also their ratios of the lengths with respect to their corresponding sides would also be equal.

In conclusion, when two figures are similar then it can be concluded that their  corresponding angles are congruent .

Hence, the second and third options are correct.

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Answer:

Corresponding angles of congruent figures are the same.

The corresponding sides of congruent figures are the same.

Step-by-step explanation:

Answer:

0,3

Step-by-step explanation:

it between the 2 and it is negative and positive cases in the -2

Equation of the parabola with focus (-3,-3) and a directrix x=5 is given by x = (-1/16)(y² +6y -7).

As given in the question,

Focus of the parabola is equal to (-3, -3)

Directrix of the parabola is given by x = 5

Let (x, y) be the point on the parabola.

Distance between the (-3,-3) and (x, y) = Distance between (x, y) and x=5

⇒√(x +3)² + (y +3)² = | x -5|

⇒(x² +6x +9) +(y² + 6y +9) = (x-5)²

⇒x² +6x +y² +6y +18 = x² -10x +25

⇒y² +6y -7 = -16x

⇒x = (-1/16) (y² +6y -7) represents the equation of the parabola.

Therefore, equation of the parabola with focus (-3,-3) and a directrix x=5 is given by  x = (-1/16)(y² +6y -7).

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By solving the equations 2x+y=4, x-y=11 we get values x=5/3 and y=2/3

An equation is a formula in mathematics that expresses the equality of two expressions by linking them with the equals sign =. In French, an equation is defined as including one or more variables, but in English, an equation is any well-formed formula consisting of two expressions coupled with an equals sign.

An equation is composed of two expressions joined by an equals sign (=). The expressions on the two sides of the equals sign are referred to as the equation's left-hand side and right-hand side. The right side of an equation is frequently considered to be zero.

Given,

2x+y=4

x-y=1

By solving above two equations we get,

2x+y=4

x-y=1

3x=5

x=5/3

y=-1+x

y=(5/3)-1

y=2/3

Therefore, by solving the equations 2x+y=4, x-y=11 we get values x=5/3 and y=2/3

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The length of the diagonal for the given rectangular book using Pythagoras' theorem will be 5.8.

A rectangle is a geometrical figure in which opposite sides are equal.

Area of rectangle = length × width.

The angle between any two consecutive sides will be 90 degrees.

As per the given rectangle with dimensions 3 × 5.

The rectangle has been attached below,

The length of the diagonal using Pythagoras' theorem is,

x = √(3² + 5²)

x = √34 = 5.8

Hence "The length of the diagonal for the given rectangular book using Pythagoras' theorem will be 5.8".

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The number of ways a photographer can arrange 6 people in a row from a group of 10 people if the bride must be in the picture is 15120.

What is permutation and combination?
A permutation is an orderly arrangement of things or numbers.
Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.
The amount of two-letter words that can be created using the letters in a word, like GREAT, is an illustration of permutations: ⁵P₂ = 5!/(5-2)!
How many different ways we may write the words utilizing the vowels in the word GREAT is an example of a combination: ⁵C₂ = 5!/[2! × (5-2)!]

Given, 6 people are to be selected from a group of 10, where the bride must be in the picture.
Following the statements in question, the bride since always there assists for filling five empty spaces using 9 people.
Since five positions are to be filled by nine people, the total number of ways possible = 9 × 8 × 7 × 6 × 5 = 15120
Thus, the number of ways a photographer can arrange 6 people in a row from a group of 10 people if the bride must be in the picture is 15120.

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Answer:

y=-3/32

Step-by-step explanation:

2-18y=11+78y

-18y-78y=11-2

-96y=9

y=-3/32

The probability that Laura does not win the prize is 119 / 175.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

Given that,

Total number of raffle rickets to be sold is 350.

The number of tickets bought by Laura is 12.

Since, the probability of an event is defined as the ratio of favorable outcome to the total outcomes, the probability of winning the prize is,

P = 12 / 350

Thus, the probability of not winning the prize is,

1 - 12 / 350

= 338 / 350

= 119 / 175

Hence, the probability of not winning a prize is 119 / 175.

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The probability that the transistor will last between 12 and 24 weeks is 0.424

the probability that a transistor will last at most 24 weeks is 0.567

The median of the lifetime distribution is less than 24

X= lifetime of the transistor in weeks E(X)= 24 weeks

O,= 12 weeks

The anticipated value, variance, and distribution of the random variable X were all provided to us. Finding the parameters alpha and beta is necessary before we can discover the solutions to the difficulties.

a) X~gamma([tex]\alpha , \beta[/tex])

E(X)= [tex]\alpha \beta[/tex]             [tex]\beta[/tex] =[tex]12^{2}/24[/tex] =6 weeks

V(x)=[tex]\alpha \beta ^{2}[/tex]                 [tex]\alpha[/tex]=24/6= 4

Now we can find the solutions:

The excel formula used to create Figure one is as follows:

=gammadist(X,[tex]\alpha[/tex] ,[tex]\beta[/tex] , False)

P([tex]12\leq X\leq 24[/tex])

P([tex]12/6 \leq X\leq 24/6[/tex])

P([tex]2\leq X\leq 4[/tex])

P= 0.424

Therefore, the probability that the transistor will last between 12 and 24 weeks is 0.424

b) For this case we want this probability:

[tex]P(X\geq 24)=1-P(X\leq 24)[/tex]

In order to find this probability we can use excel with the following code:

=1-GAMMA.DIST(24,4,6,TRUE)

And we got:

[tex]P(X\geq 24)=P(1-X\leq 24)= 0.567[/tex]

c) For this case the median of the lifetime distribution is less than 24

[tex]P(X\leq \alpha )[/tex] = 0.5  (by definition)    So [tex]\alpha[/tex]< 24 because P([tex]X\leq 24[/tex])=0.567 which is greater than 0.5

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Answer:

slope=5/4 y intercept=-3/4

Step-by-step explanation:

put it into slope intercept form y=5/4x-3/4

pull out 5/4 as slope and -3/4 as y intercept

Work Shown:

45 beats = 15 seconds

45/15 beats = 15/15 seconds

3 beats = 1 second

To convert to beats per minute (bpm), multiply by 60.

A correlation coefficient is a numerical measure of some type of correlation, meaning a statistical relationship between two variables.

Hence, the correlation coefficient is [tex]-0.9[/tex], i.e., [tex]x[/tex] and [tex]y[/tex] have a strong, negative correlation

What is a correlation coefficient?

A correlation coefficient is a numerical measure of some type of correlation, meaning a statistical relationship between two variables.

The variables may be two columns of a given data set of observations, often called a sample or two components of a multivariate random variable with a known distribution.

As we know that the correlation coefficient is a measure of the strength of the straight line or linear relationship between two variables. Correlation coefficients are expressed as values between [tex]+1[/tex] and [tex]-1[/tex].

So,

[tex](1,8),(2,3),(3,0),(4,1),(5,2),(6,1)[/tex]

As per the Excel tools i.e., CORREL function the correlation coefficient is [tex]-0.9[/tex].

Hence, the correlation coefficient is [tex]-0.9[/tex], i.e., [tex]x[/tex] and [tex]y[/tex] has a strong, negative correlation.

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Answer:

82 rooms

Step-by-step explanation:

1459/18=81.05

so 82 rooms

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Answer:

82

Step-by-step explanation:

1459/18

[tex]1459 \div 18[/tex]

for each cabin there 18 And there are 1459

81.05 \times 48=159

since you can't have a half a cabinet the answer is 82

Using the concept of average speed we conclude that the space-mean speed of the vehicles is 0.69 km/min.

The average speed of a vehicle traveling a given segment of a highway in a specific time period is called space-mean speed, i.e.

Average mean speed = total distance traveled / average time travel

Given for vehicles are traversing a 1 km segment of highway. Hence total distance is 4km.

Average time = (1.2 + 1.5 + 1.7 + 1.4)/4

= 5.8/4

= 1.45 min

Now Average mean speed = 1/1.45

=0.689

=0.69 km/min

Hence the space-mean speed of the vehicles is 0.69 km/min

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The rectangle has its dimensions to be 8.8 units by 12.4 units

From the question, the equation is given as

2x(x + 8) = 110

This equation represents the area of the rectangle

So, we have

2x(x + 8) = 110

Divide by 2

x(x + 8) = 55

Open the brackets

This gives

x² + 8x = 55

Rewrite as

x² + 8x - 55 = 0

Using a graphing calculator, we have the solutions to be

x = -12.4 and x = 4.4

The variable x cannot be negative

So, we have

x = 4.4

In 2x(x + 8) = 110, we have

Length = 2x

Width = x + 8

So, we have

Length = 2 x 4.4

Width = 4.4 + 8

Evaluate

Length = 8.8

Width = 12.4

Hence, the dimensions of the rectangle are 8.8 units by 12.4 units

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