Given that the surface are of the following prisms are equal, find y.

Answer:

BC = 10 units

Step-by-step explanation:

From the picture attached,

It's given that AD and BE are the parallel sides.

AC and DC are the transversal lines intersecting the parallel lines.

In ΔADC and ΔBEC,

∠DAC ≅ ∠EBC [Corresponding angles]

∠ADC ≅ ∠BEC [Corresponding angles]

ΔADC ~ ΔBEC [By AA property of similar triangles]

By the property of similar triangles,

Corresponding sides of the similar triangles are proportional.

\(\frac{AC}{BC}=\frac{DC}{EC}\)

\(\frac{AB+BC}{BC}=\frac{DE+EC}{EC}\)

\(\frac{2.5+BC}{BC}=\frac{2+8}{8}\)

\(\frac{2.5}{BC}+1=\frac{10}{8}\)

\(\frac{2.5}{BC}=\frac{5}{4}-1\)

\(\frac{2.5}{BC}=\frac{1}{4}\)

BC = 10

Answer:

\(x \leq -1\)

Step-by-step explanation:

divide both sides by -4

-2 >= x - 1

(FLIP THE INEQUALITY!!!)

now add 1 to both sides

-1 >= x

flip the equation

x <= -1

that is your answer

Answer:

(2,1) and (5,-5)

Step-by-step explanation:

I just truned it in and it was right.

a)The probability that a randomly selected person from this sample used the Internet Explorer or the Chrome browser is0.42

b) The probability that a randomly selected person from this sample used the Internet Explorer and the Firefox browser is :0.03

c)The probability that a randomly selected person from this sample used the Safari browser or used a laptop computer is :0.86

d) The probability that a randomly selected person from this sample used the Chrome browser and used a laptop computer is :0.32

e)the probability that the computer was a laptop is: 0.76.

a) The probability that a randomly selected person from this sample used the Internet Explorer or the Chrome browser is :

P(Internet Explorer or Chrome) = P(Internet Explorer) + P(Chrome)= (18+24)/(18+56+7+37+24+77+3+18+3+7)= 0.42

b) The probability that a randomly selected person from this sample used the Internet Explorer and the Firefox browser is :

P(Internet Explorer and Firefox) = 7/(18+56+7+37+24+77+3+18+3+7)= 0.03

c) The probability that a randomly selected person from this sample used the Safari browser or used a laptop computer is :P(Safari or Laptop) = P(Safari) + P(Laptop) - P(Safari and Laptop)= (3+56+37+77+18)/(18+56+7+37+24+77+3+18+3+7) = 0.86

d) The probability that a randomly selected person from this sample used the Chrome browser and used a laptop computer is :P(Chrome and Laptop) = 77/(18+56+7+37+24+77+3+18+3+7) = 0.32

e) Given that the randomly selected computer used the Chrome browser, the probability that the computer was a laptop is:P(Laptop|Chrome) = P(Laptop and Chrome) / P(Chrome)= 77 / (24+77) = 0.76

Hence, the required probabilities are: a) 0.42, b) 0.03, c) 0.86, d) 0.32 and e) 0.76.

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Answer:

B and E are correct

Step-by-step explanation:

Answer:

P=26 cm A=40 cm^2

Step-by-step explanation:

Perimeter:

5+5+8+8=26

Area:

8x5=40

Answer:

11

Step-by-step explanation:

11 is greater than 6, meaning it satisfies the inequality.

Answer:

GGB

GGG

GBB

GBG

BGG

BGB

BBG

BBB

Any of these has a probability of 1:8, or 1/8, or 0.125, or 12.5%

Step-by-step explanation:

GGB

GGG

GBB

GBG

BGG

BGB

BBG

BBB

Any of these has a probability of 1:8, or 1/8, or 0.125, or 12.5%

Using a hypothesis test with a significance level of 0.05, the data shows that we can conclude there is not enough evidence to support that more than 50% of all business students would rate the book as excellent.

To determine if the data allows us to conclude that more than 50% of all business students would rate the book as excellent, we need to conduct a hypothesis test.

Let p be the proportion of business students who would rate the book as excellent. The null hypothesis is that p = 0.50 (i.e., 50% of business students would rate the book as excellent). The alternative hypothesis is that p > 0.50 (i.e., more than 50% of business students would rate the book as excellent).

We can use a one-sample proportion test to test the null hypothesis. The test statistic is calculated as:

z = (P - p) / sqrt(p*(1-p)/n)

where P is the sample proportion, p is the hypothesized population proportion, and n is the sample size.

In this case, we have

P = number of students who rated the book as excellent / sample size = 25/100 = 0.25

p = 0.50

n = 100

Plugging in these values, we get:

z = (0.25 - 0.50) / sqrt(0.50*(1-0.50)/100) = -2.236

Using a standard normal distribution table, we find that the p-value for this test is approximately 0.012. This means that if the null hypothesis were true, there is only a 0.012 probability of observing a sample proportion as extreme as 0.25 or more in favor of the alternative hypothesis.

Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that more than 50% of all business students would rate the book as excellent.

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Work Shown:

n(A only) = number of items inside set A only

n(A only) = 12

n(A and B) = 16

n(B only) = 20

n(A or B) = n(A only) + n(A and B) + n(B only)

n(A or B) = 12 + 16 + 20

n(A or B) = 48

n(Total) = n(A only) + n(A and B) + n(B only) + n(Not A, not B)

n(Total) = 12+16+20+24

n(Total) = 72

P(A or B) = n(A or B)/n(Total)

P(A or B) = 48/72

P(A or B) = 0.67 approximately

The area of the rectangle in terms of b is 11b - b², and the perimeter is always 22, regardless of the value of b.

A rectangle is a four-sided flat shape with opposite sides that are equal in length and parallel to each other. It has four right angles (90-degree angles) at each corner. The two sides that are parallel to each other are called the length, and the other two sides are called the width.

The area of a rectangle is found by multiplying its length and width, and its perimeter is the sum of the lengths of all four sides. Rectangles are common in everyday life and can be found in many different contexts, such as books, doors, windows, and electronic screens.

According to given information,

Let's assume that the length of the rectangle is 'l' and the width is 'b'.

The area of a rectangle is given by the formula A = lb, where A is the area, l is the length, and b is the width.

The perimeter of a rectangle is given by the formula P = 2(l + b), where P is the perimeter, l is the length, and b is the width.

So, the area of the rectangle is:

A = lb = 28

And the perimeter of the rectangle is:

P = 2(l + b) = 40

P = (l+b) = 20

l= 20 -b

Now, we can substitute l = 20 - b into these formulas:

A = (20 - b)b

P = 2(20 - b + b)

Simplifying, we get:

A = 40b - b²

P= 40

So, the area of the rectangle in terms of b is 11b - b², and the perimeter is always 22, regardless of the value of b.

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The length of the rectangle is 10 cm and breadth of the rectangle is 4 cm.

What is rectangle?

A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees. A rectangle is a two-dimensional shape.

The longer parallel sides are called length(l) and two shorter sides are called breadth(b).

Perimeter of a rectangle is 2(l+b).

Area of rectangle is l*b.

2(l+b)=28

L+b=28/2=14

L=14-b .....eq(1)

L*b=40

(14-b)b=40

14b-b^2=40

b^2-14b+40=0

b^2-10b-4b+40=0

b(b-10)-4(b-10)=0

(b-10)(b-4)=0

Either b=10 or b=4

If b=10 then l =4 but length can't be shorter than the breadth so b=4cm and l=10 cm is the answer.

The two solutions of the system are:

(5, 6)

(-4, -3)

Here we have the system of equations:

y - x = 1

x^2 + y^2 = 41

So we have a linear eqation and a circle equation.

We can write:

y = 1 + x

From the first one, and replace that in the second equation:

x^2 + (x + 1)^2 = 41

x^2 + x^2 +2 x + 1 = 41

2x^2 + 2x - 40 = 0

x^2 + x - 20 =0

The solutions are given by the quadratic formula:

\(x = \frac{1 \pm \sqrt{1^2 - 4*1*-20} }{2} \\\\x = \frac{1 \pm 9 }{2}\)

So we have two values:

x = (1 + 9)/2 = 5

x = (1 - 9)/2 = -4

And we know that:

y = 1 + x

Replacing the solutions of x there we will get:

y = 1+ 5 =  6

y = 1 - 4 = -3

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Answer:

the line starts on (0,3) then you go down 7 points then you go 3 to the right that's thew answer

Step-by-step explanation:

Answer: the y axis is 3 and the x axis is 1

Step-by-step explanation:

The velocity of the baseball is 40 m/s

The given parameters are:

Momentum = 6.0 kgm/s

Mass = 0.15 kg

The velocity of the baseball is calculated from

Momentum = Mass * Velocity

So, we have:

6.0 kgm/s = 0.15 kg * Velocity

Divide both sides by 0.15

Velocity = 40 m/s

Hence, the velocity of the baseball is 40 m/s

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Answer:

36.1

Step-by-step explanation:

The speed of the train in china is 267.4 miles per hour.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, A train in France can travel at a speed of 217.4 miles per hour.

A train in China can travel 1.23 times this speed to obtain the speed of the train in china we have to multiply how many times it is faster by the speed of the train in France which is,

= (217.4× 1.23) miles per hour.

= 267.4 miles per hour.

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Write the coefficients of the x-terms as the numbers down the first column.

Write the coefficients of the y-terms as the numbers down the second column.

If there are z-terms, write the coefficients as the numbers down the third column.

Draw a vertical line and write the constants to the right of the line.    

Let W be the inverse of AB. Then WAB = I and (WA)B = l. Therefore, matrix B is invertible by part (j) of the IMT by letting C = WA.

We have A and B are two n × n matrices and AB is invertible. We have to prove that B is invertible by showing a valid reason given by one of the four options:

Option (a) False:

The first option is not valid proof. since W is the inverse of A B would imply WAB = I, as multiplying a matrix by its inverse will produce the identity matrix of the corresponding order. Here stated that WAB = B, which is invalid.

Option (b) False:

It is true that AB invertible implies \($(A B)^{\top}$\) is invertible but this does not imply B is invertible (not a valid statement).

Option (c) False:

A B is invertible does not mean \($A=B^{-1}$\). Since \($A=B^{-1}$\) implies AB = I, but AB need not be only the identity matrix. So these statements are invalid.

Option (d) True:

W being inverse of AB, this gives WAB = I

(WA) B = I since matrix multiplication is associative.

WA is the inverse of B, as multiplying WA by B produces the identity matrix I. Hence, this is valid proof to show that B is invertible.

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Answer:

Step-by-step explanation:

The easier way to figure this is by using the concept of torque in physics. If the torque of the man is greater than that experienced by the box, the lever will tilt in the man's favor (in other words, he will move down and the box will be lifted). Torque is found by multiplying the perpendicular force by the length of the lever arm. Because we want the man's torque to be greater than the box's torque, the inequality is:

\(\tau_{man}>\tau_{box}\) and

\(180r>500(.1524)\) That decimal is 6 inches in terms of meters.

180r > 76.2 so

r > .42 meters or `16.67 inches. The man has to sit at a distance greater than 16.67 inches in order for the box to be lifted by the lever.

Answer:

0.0016

Step-by-step explanation:

Hope this helps!

There are 84 unique 4-digit integers (excluding leading zeros) whose sum of the digits is 6.

To find the number of unique 4-digit integers (excluding leading zeros) where the sum of the digits is 6, we can use a combinatorial approach.

Let's consider the four digits as four distinct positions: A, B, C, and D. The sum of the four digits is 6, so we need to distribute these six units among these four positions.

We can solve this problem using stars and bars. Imagine we have six stars (representing the six units) and three bars (representing the three dividers between the positions). The bars help us separate the units into four distinct positions.

For example, if we have the configuration "* | * * | * * | *," it represents the digits 1, 2, 2, and 1. The sum of these digits is 6.

The number of ways to arrange the six stars and three bars is given by the binomial coefficient (6 + 3 choose 3). Using the formula for combinations, we have:

(6 + 3) C 3 = (9 C 3) = 9! / (3! * (9 - 3)!) = 84.

So, there are 84 unique 4-digit integers (excluding leading zeros) whose sum of the digits is 6.

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Answer:

The answer to the question provided is

0 = \( - \frac{6}{5} \)

It has no solutions.

Number of pens  x=10.

Number of pencils  y=30.

The Five Principles are: freedom, efficiency, mutuality, responsibility, and quality. Victoria that she always incorporates The Five Principles into her conversations with other businesses, government officials, and other partners and leaders. The writing core is tougher and leaves a lighter trace on the paper as the number increases.

Let number of pens =x

And number of pencils =y

⇒ x+y=40

⇒(5+y)+(x−5)=4x

⇒3x=y

Substituting in above equations ;

⇒x+3x=40

⇒x=10

⇒y=30

∴number of pens =x=10

⇒number of pencils =y=30

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PESTLE framework is a tool used for analyzing an organization's macro-environment. The six main types of environmental factors are Political, Economic, Sociocultural, Technological, Legal, and Environmental.

True Economic forces are one of the types of influences analyzed in the PESTLE framework. False An organization's strength is not part of the types studied in the PESTLE framework. True The PESTLE framework is designed to provide a comprehensive list of influences on the possible success or failure of strategies. It is a useful tool for identifying opportunities and threats in the external environment of a company.

PESTLE framework is a tool used for analyzing an organization's macro-environment. It categorizes environmental influences into six main types that include Political, Economic, Sociocultural, Technological, Legal, and Environmental. The PESTLE framework is designed to provide a comprehensive list of influences on the possible success or failure of strategies. It is a useful tool for identifying opportunities and threats in the external environment of a company. The PESTLE framework can be used in conjunction with other tools, such as SWOT analysis, to gain a deeper understanding of an organization's position in the market.

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Answer:

=2.17

Step-by-step explanation:

Apply BODMAS

3/6= 0.5

5/3= 1.67

Sum 0.5& 1.67

=0.5+1.67

=1.67

9514 1404 393

Answer:

Step-by-step explanation:

You can read f(0) = 3/2 from the table. The slope is 1/2, so f(4) will be 1 more than f(2): f(4) = 7/2.

Answer:

A. 24.2°

Step-by-step explanation:

I'm correct if I'm rwong

The expressions formed are,

Formation of expressions in 1, 2 and 3:

In 1, twelve times f is, 12f

Taking away 5, it becomes (12f-5)

In 2, sum of k and 6 is, (k+6)

One-half of the above quantity is, (k+6)/2

In 3, sum of 5 with x is, (x+5)

Now, x squared minus the above expression indicates (x²-x+5)

Formation of expressions in 4 and 5:

In 4, product of a and b, is ab and 3 times c is 3c

Sum of the expressions evaluated in the previous statement = ab+3c

In 5, 24 times the product of x and y is, 24xy

Adding, g in the above computed expression, we get, 24xy+g

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Answer:

answer is 10 ^ 10

Step-by-step explanation:

7.296 × 10² / 9.6 × 10^ -9

= 0.76 × 10^11

= 7.6 × 10^10