Ellen, Nick, and Ryan went shopping together. One of them bought a hat, another bought sunglasses, and another bought a belt. One paid $6, another paid $8, and another paid $10.
1) Nick bought the hat.
2) Ellen spent $8.
3) The belt did not cost $10.
4) Ryan spent the most. Which of the following is true?

(a) Nick bought the hat for $10.
(b) Ellen bought the belt for $8.
(c) Ryan bought the sunglasses for $8.
(d) Ryan bought the belt for $10
(e) Ryan bought the hat for 56.​

Answer:

[tex]F = 39.47[/tex]

Step-by-step explanation:

Given

[tex]n = 30[/tex] --- observations

[tex]p = 1[/tex] -- variables

[tex]SSR = 1,297[/tex]

[tex]SSE= 920[/tex]

Required

The F statistic

This is calculated using:

[tex]F = \frac{SSR}{p} \div \frac{SSE}{n - p -1}[/tex]

[tex]F = \frac{1297}{1} \div \frac{920}{30 - 1 -1}[/tex]

[tex]F = \frac{1297}{1} \div \frac{920}{28}[/tex]

[tex]F = 1297 \div \frac{920}{28}[/tex]

Rewrite as:

[tex]F = 1297 * \frac{28}{920}[/tex]

[tex]F = \frac{1297 *28}{920}[/tex]

[tex]F = \frac{36316}{920}[/tex]

[tex]F = 39.47[/tex]

Answer:

Jon Applebe withdrew 37.15% of the amount he initially deposited.

Step-by-step explanation:

Given that Jon Applebee deposited $ 619 in his savings account, and I have later withdrew $ 230, to determine the integer that represents the amount Jon Applebee deposited the following calculation must be performed:

619 = 100

230 = X

230 x 100/619 = X

23,000 / 619 = X

37.15 = X

Therefore, Jon Applebe withdrew 37.15% of the amount he initially deposited.

Answer:

0.319 = 31.9% probability that the wait time will be more than an additional 16 minutes

Step-by-step explanation:

To solve this question, we need to understand the exponential distribution and conditional probability.

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

Which has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

The probability of finding a value higher than x is:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

Conditional Probability

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: It has already taken 11 minutes.

Event B: It will take 16 more minutes.

Exponentially distributed with an average wait time of 14 minutes.

This means that [tex]m = 14, \mu = \frac{1}{14}[/tex]

Probability of the waiting time being of at least 11 minutes:

[tex]P(A) = P(X > 11) = e^{-\frac{11}{14}} = 0.4558[/tex]

Probability of the waiting time being of at least 11 minutes, and more than an additional 16 minutes:

More than 11 + 16 = 27 minutes. So

[tex]P(A \cap B) = P(X > 27) = e^{-\frac{27}{14}} = 0.1454[/tex]

What is the probability that the wait time will be more than an additional 16 minutes?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.1454}{0.4558} = 0.319[/tex]

0.319 = 31.9% probability that the wait time will be more than an additional 16 minutes

9514 1404 393

Answer:

  11

Step-by-step explanation:

The degree of the given monomial is the sum of the exponents of the variables.

  m has degree 6

  n has degree 5

The degree of the monomial is 6+5 = 11.

Answer:

x<-12

Step-by-step explanation: hope this helps!

Answer:

x | y

0 | 2

2 | 10

4 | 18

Step-by-step explanation:

the function would be y=4x+2

just plug each x value in to get each y value

Answer:

- [tex]\frac{26}{15}[/tex]

Step-by-step explanation:

[tex]\frac{1}{5}[/tex] = -  [tex]\frac{1}{2}[/tex]w - [tex]\frac{2}{3}[/tex]

multiply equation by a common denominator. Let's use 30.  

you get :

6 = -15w - 20

26 = -15w

w = -  [tex]\frac{26}{15}[/tex]

Answer:

0.7857

Step-by-step explanation:

Given :

Mean = 69 inches

Standard deviation, = 2.8 inches

The Zscore of a man who is 71.2 inches

The ZSCORE is obtained using the relation :

Zscore = (Score, x - mean) / standard deviation

Zscore = (71.2 - 69) / 2.8

Zscore = 2.2 / 2.8

Zscore = 0.7857

Answer:

d

Step-by-step explanation:

Answer:

x=5, y=52

Step-by-step explanation:

Hi there!

1) Determine y

Because length AB is equal to length BC (making this an isosceles triangle), angle y is equal to 52 degrees.

y = 52

2) Determine x

The sum of the interior angles of a triangle will always be 180 degrees. Knowing this, we can construct the following equation and solve for x:

[tex]180=52+52+(14x+6)[/tex]

Open up the parentheses

[tex]180=52+52+14x+6\\180=104+14x+6\\180=110+14x[/tex]

Subtract 110 from both sides to isolate 14x

[tex]180-110=110+14x-110\\70=14x[/tex]

Divide both sides by 14 to isolate x

[tex]\frac{70}{14} =\frac{14x}{14} \\5=x[/tex]

Therefore, the value of x is 5.

I hope this helps!

Answer:

a triangular pyramid

Answer:

there are two solutions:

x=0

and

x=14

Step-by-step explanation:

lts suppose the numbers are x and x+2, so:

[tex]x(x+2)=8(x+(x+2))-16\\x(x+2)=8(2x+2)-16=16x+16-16=16x\\x^2+2x=16x\\x^2-14x=0\\x(x-14)=0\\x=0,~x=14[/tex]

Answer:

1,2,4,8

Step-by-step explanation:

1

2

1,2

4

4,1

4,2

4,2,1

8

8,1

8,2

8,2,1

8,4

8,4,1

8,4,2

8,4,2,1

Answer:

Step-by-step explanation:

Solution of the equation [tex]\sqrt{3} (cosec\theta) -2=0[/tex]in the  [ 0, 2π) is [tex]\frac{\pi }{3}[/tex] and [tex]\frac{2\pi }{3}[/tex].

" Trigonometric ratios are defined as relation of the ratio of the sides of the triangle to the acute angle of the given triangle enclosed in it."

Formula used

[tex]cosec\theta = \frac{1}{sin\theta}[/tex]

According to the question,

Given trigonometric ratio equation,

[tex]\sqrt{3} (cosec\theta) -2=0[/tex]

Replace trigonometric ratio [tex]cosec\theta[/tex] by [tex]sin\theta[/tex]  in the above equation we get,

[tex]\sqrt{3} (\frac{1}{sin\theta} ) -2=0\\\\\implies \sqrt{3} (\frac{1}{sin\theta} ) = 2\\\\\implies sin\theta=\frac{\sqrt{3} }{2}[/tex]

As per given condition of the interval [ 0, 2π) we have,

[tex]\theta = sin^{-1} \frac{\sqrt{3} }{2} \\\\\ implies \theta = \frac{\pi }{3} or \frac{2\pi }{3}[/tex]

Hence, solution of the equation [tex]\sqrt{3} (cosec\theta) -2=0[/tex]in the  [ 0, 2π) is

[tex]\frac{\pi }{3}[/tex] and [tex]\frac{2\pi }{3}[/tex].

Learn more about trigonometric ratio here

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Answer:

Step-by-step explanation:

Answer:

That's barely readable!  Anyway the solution is:

7x + 7x +2 +5x +7 = 180 degrees

19x + 9 = 180 degrees

19x = 171 degrees

x = 9

So the angles are:

7x = 63 degrees

7x + 2 = 65

5x + 7 = 52

Double check:

Since ALL 3 triangle sides add up to 180:

63 + 65 + 52 = 180 degrees

Step-by-step explanation:

Answer:

It would be smaller.

Step-by-step explanation:

Given that :

The number of the strawberries that are unfit for sell, x = 24

The total number of the strawberries to inspect, n = 156

Total number of the strawberries to be picked = 1000 strawberries

Therefore,

[tex]$\widehat p =\frac{x}{n}$[/tex]

  [tex]$=\frac{24}{156}$[/tex]

  = 0.1538

[tex]$\widehat p =\frac{x}{n}$[/tex]

  [tex]$=\frac{24}{1000}$[/tex]

  = 0.024

Therefore, the standard deviation of the sample proportion would be smaller.

Answer:

3z+3x=2

Step-by-step explanation:

3z+8=12+3x-2

collecting like terms

3z-3x=12-2-8

3z-3x=2

3z=2+3x

divide through by three

z= ⅔+x

Answer:

0.3968 = 39.68% probability this shipment passes inspection.

Step-by-step explanation:

The parts are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[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]

In this question:

50 parts means that [tex]N = 50[/tex]

4 defective means that [tex]k = 4[/tex]

10 are chosen, which means that [tex]n = 10[/tex]

What is the probability this shipment passes inspection?

Probability that none is defective, so:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 0) = h(0,50,10,4) = \frac{C_{4,0}*C_{46,10}}{C_{50,10}} = 0.3968[/tex]

0.3968 = 39.68% probability this shipment passes inspection.

Answer:

w = 5

y = 4

Step-by-step explanation:

w+y=9

3w-y=11

4w = 20

w = 5

y = 4

Answer:

Direct variation

[tex]k = 2.5[/tex]

Step-by-step explanation:

Given

The attached table

Required

The type of variation

First, we check for direct variation using:

[tex]k = \frac{y}{x}[/tex]

Pick corresponding points on the table

[tex](x,y) = (-2,-5)[/tex]

So:

[tex]k = \frac{-5}{-2} = 2.5[/tex]

[tex](x,y) = (4,10)[/tex]

So:

[tex]k = \frac{10}{4} = 2.5[/tex]

[tex](x,y) = (6,15)[/tex]

So:

[tex]k = \frac{15}{6} = 2.5[/tex]

Hence, the table shows direct variation with [tex]k = 2.5[/tex]

Answer:

If you buy per dozen, each buns costs about 91 cents.

You will save $4.11 if you buy per dozen.

Step-by-step explanation:

1.25 * 12= $15

10.89/12= .9075 = .91 cents

15-10.89= $4.11

Answer:

First Example: 3 1/2 + 4 3/4, Second Example: 6 3/8 + 7 9/15

Extra Example: 8 4/20 + 3 5/10

Step-by-step explanation:

First Example:

1/2 + 3/4

1/2 is equal to 2/4 so it is now compatible to be added to 3/4.

2/4 + 3/4

= 5/4

Now for the mixed numbers since its 3 and 4, 3 + 4 = 7.

Final answer is 7 5/4.

Second Example:

3/8 + 9/15

9/15 can be reduced to 3/5

Now the equation is 3/8 + 3/5

= 15/40 + 24/40 is an equivalent equation

15/40 + 24/40  

= 39/40

Now for the mixed numbers since its 6 and 7, 6 + 7 = 13

Final answer is 13 39/40.

I am going to include one last example just in case you need one:

Third Example:

4/20 + 5/10

We can reduce these to

1/5 + 1/2

= 2/10 + 5/10 is the equivalent equation

2/10 + 5/10

= 7/10

Now for the mixed numbers since its 8 and 3, 8 + 3 = 11.

Final answer is 11 7/10.

I Hope this helps!

Answer:

La suma de las dos matrices cuadradas de dimensión 2 es [tex]\vec U = \left[\begin{array}{cc}-1&11\\2&5\end{array}\right][/tex].

Step-by-step explanation:

Considerando que se tratan de dos matrices de igual dimensión y cuyos elementos son números reales, conocemos que la adición entre dos matrices consiste en las sumas de los elementos de igual posición, esto es, los elementos que están localizados en las mismas filas y columnas, entonces, la suma es:

[tex]\vec A = \left[\begin{array}{cc}1&2\\-1&0\end{array} \right][/tex], [tex]\vec B = \left[\begin{array}{cc}-2&9\\3&5\end{array}\right][/tex]

[tex]\vec U = \vec A + \vec B = \left[\begin{array}{cc}1 + (-2)&2+9\\-1 + 3&0 + 5\end{array}\right][/tex]

[tex]\vec U = \left[\begin{array}{cc}-1&11\\2&5\end{array}\right][/tex]

La suma de las dos matrices cuadradas de dimensión 2 es [tex]\vec U = \left[\begin{array}{cc}-1&11\\2&5\end{array}\right][/tex].

Answer:

The equation is

y=0.5x+2

Answer:

18

Step-by-step explanation:

3:2 means 3/2 or 3÷2

but its better to leave it as

3/2

Answer:

247372

Step-by-step explanation:

two hundreds forty seven thousand, three hundred and seventy two

The number of weddings in the UK in numerical form will be 247,372.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Last year there were two hundred and forty-seven thousand, three hundred and seventy-two weddings in the UK.

Convert the statement into a number. Then we have

⇒ 247,372

The number of weddings in the UK in numerical form will be 247,372.

More about the Algebra link is given below.

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Answer:

mehoimehoihoi

Step-by-step explanation:

Answer:

1. The slope of a line  that is perpendicular to a line whose equation

is 5y = 10 + 2x is

2.

The line y = 2x - 1 is neither parallel nor perpendicular to the line

y = -2x + 3

The line y = -2x + 5 is parallel to the line y = -2x + 3

The line y =  x + 7 is perpendicular to the line

y = -2x + 3

3. The equation of the line that passes through the point (5 , -4) and

is parallel to the line whose equation is 2x + 5y = 10 is

y =  x - 2

Step-by-step explanation:

Let us revise some rules

The slope-intercept form of the linear equation is y = m x + b, where m is the slope of the line and b is the y-intercept

The slopes of the parallel lines are equal

The product of the slopes of the perpendicular lines is -11. The slope of a line  that is perpendicular to a line whose equation

is 5y = 10 + 2x is

2.

The line y = 2x - 1 is neither parallel nor perpendicular to the line

y = -2x + 3

The line y = -2x + 5 is parallel to the line y = -2x + 3

The line y =  x + 7 is perpendicular to the line

y = -2x + 3

3. The equation of the line that passes through the point (5 , -4) and

is parallel to the line whose equation is 2x + 5y = 10 is

y =  x - 2

Step-by-step explanation:

Let us revise some rules

The slope-intercept form of the linear equation is y = m x + b, where m is the slope of the line and b is the y-intercept

The slopes of the parallel lines are equal

The product of the slopes of the perpendicular lines is -11. The slope of a line  that is perpendicular to a line whose equation

is 5y = 10 + 2x is

2.

The line y = 2x - 1 is neither parallel nor perpendicular to the line

y = -2x + 3

The line y = -2x + 5 is parallel to the line y = -2x + 3

The line y =  x + 7 is perpendicular to the line

y = -2x + 3

3. The equation of the line that passes through the point (5 , -4) and

is parallel to the line whose equation is 2x + 5y = 10 is

y =  x - 2

Step-by-step explanation:

Let us revise some rules

The slope-intercept form of the linear equation is y = m x + b, where m is the slope of the line and b is the y-intercept

The slopes of the parallel lines are equal

The product of the slopes of the perpendicular lines is -11. The slope of a line  that is perpendicular to a line whose equation

is 5y = 10 + 2x is

2.

The line y = 2x - 1 is neither parallel nor perpendicular to the line

y = -2x + 3

The line y = -2x + 5 is parallel to the line y = -2x + 3

The line y =  x + 7 is perpendicular to the line

y = -2x + 3

3. The equation of the line that passes through the point (5 , -4) and

is parallel to the line whose equation is 2x + 5y = 10 is

y =  x - 2

Step-by-step explanation:

Let us revise some rules

The slope-intercept form of the linear equation is y = m x + b, where m is the slope of the line and b is the y-intercept

The slopes of the parallel lines are equal

The product of the slopes of the perpendicular lines is -1

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

Explanation:

The phrasing "no less than" means the same as "at least".

Saying "at least 37" means 37 is the lowest we can go.

If x is the number of disconnected calls, then [tex]x \ge 37[/tex] and we want to find the probability of this happening (the max being 295).

We could use the binomial distribution to find the answer, but that would require adding 295-37+1 = 259 different values which could get tedious. So we could use the normal approximation to make things relatively straight forward.

Assuming this binomial meets the requirements of the normal approximation, then we'd look under the normal curve for the area to the right of 36.5; which is why the answer is choice A.

Why 36.5 and not 37? This has to do with the continuity correction factor when translating from a discrete distribution (binomial) to a continuous one (normal).

If we used 37, then we'd be missing out on the edge case. So we go a bit beyond 37 to capture 36.5 instead. It's like a fail safe to ensure we do account for that endpoint of 37. It's like adding a buffer or padding.

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

Side notes:

Using translation concepts, the vertex of k(x) is 6 units below the vertex of f(x) = x² for:

D. f(x) = x² and k(x) = x² - 6.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

We want to shift the vertex 6 units down, hence the transformation is y -> y - 6, so the correct pair is:

D. f(x) = x² and k(x) = x² - 6.

More can be learned about translation concepts at https://brainly.com/question/4521517

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Answer:

9ab+3a

Step-by-step explanation:

(2a+a)(3b+1)=(3a)(3b+1)

3a(3b+1)

=(3a×3b)+3a×1

=9ab+3a