If X = 9 units, Y = 7 units, Z = 18 units, and h = 8 units, what is the surface area of the triangular prism shown above?

Answer:

Did you try this is a piece of cake

Step-by-step explanation:

Answer:

Blue

Step-by-step explanation:

A straight line has an angle of 180 on each side.

5a+18+24-a+8a-30=180

12a+12=180

12a=168

a=14

Green: 14x5+18=88

Blue:24-14=10

Yellow:8x14-30=82

Based on the data recorded by Anna on Saturday, we can estimate the number of people expected to visit The Youth Wing on Sunday.

Let's calculate the proportion of visitors to The Youth Wing compared to the total number of visitors on Saturday:

\(\displaystyle \text{Proportion} = \frac{\text{Visitors to The Youth Wing on Saturday}}{\text{Total visitors on Saturday}} = \frac{382}{382 + 461 + 355}\)

Next, we'll apply this proportion to the total number of visitors on Sunday to estimate the number of people expected to go to The Youth Wing:

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \text{Proportion} \times \text{Total visitors on Sunday}\)

Now, let's substitute the values into the equation and calculate the estimated number of visitors to The Youth Wing on Sunday:

\(\displaystyle \text{Proportion} = \frac{382}{382 + 461 + 355}\)

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \text{Proportion} \times 800\)

Calculating the proportion:

\(\displaystyle \text{Proportion} = \frac{382}{382 + 461 + 355} = \frac{382}{1198}\)

Calculating the estimated number of visitors to The Youth Wing on Sunday:

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \frac{382}{1198} \times 800\)

Simplifying the equation:

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} \approx \frac{382 \times 800}{1198}\)

Now, let's calculate the approximate number of visitors to The Youth Wing on Sunday:

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} \approx 254\)

Therefore, based on the data recorded on Saturday, we can estimate that around 254 people should be expected to go to The Youth Wing on Sunday.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

  (b)  (x -10)(x +10)

Step-by-step explanation:

The factorization of the difference of squares is a special form:

  a² -b² = (a -b)(a +b)

Your expression is recognizable as the difference of squares:

  x² -100 = x -10²

Using the above form, the factorization is ...

  = (x -10)(x +10) . . . . . . . . matches the second choice

Answer:

1) 114

2) 159

Step-by-step explanation:

2+8+5+9+90 = 114

3+45+111 = 159

Hope this helps.

Answer:

1)144

2)159

..........

Based on the sample data, 7th grade boys, would be more likely to hold a handstand for about 19 seconds or more.

The difference between the boys' mean time and the girls' mean time is 1 second.

The difference between the boys' median time and the girls' median time is 1.5 seconds.

A subset of data collected from a larger population. It is typically used to represent the larger population and is used for testing and analysis.

In this data set, the mean time of the 7th grade boys= 19.375 seconds, while the mean time of the 7th grade girls = 17.875 seconds.

This means that the 7th grade boys have a higher mean time than the 7th grade girls.

The difference is 1.5 seconds.

The median time of the 7th grade boys = 19 seconds, and the median time of the 7th grade girls = 18 seconds.

This also indicates that the 7th grade boys have a higher median time than the 7th grade girls.

The difference is 1 second.

Given this data, the 7th grade boys are more likely to hold a handstand for about 19 seconds or more than the 7th grade girls.

This is because the mean and median times for the 7th grade boys are higher than the mean and median times for the 7th grade girls.

This indicates that the 7th grade boys have a higher average time than the 7th grade girls, and thus, are more likely to hold a handstand for a longer period of time.

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Answer: The answer is 4.

Step-by-step explanation:

= 340/500 • 6

= .68 • 6

= 4.08

Answer:

23,7777

Step-by-step explanation:

because 13% died

The general form for the equation of a line is:

\(y = mx + c\)

Where:

m is the gradient of the line

c is the y intercept of the line  (y - intercept is where the graph crosses the y-axis)

So if you had the following equation:

\(y = 3x + 2\)

Then:

m = 3

c = 2

So gradient = 3, and y intercept = 2

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

Rearranging

So first rearrange both of the equations in the form y = mx + c :

\(3x + 2y = -1\)   becomes  \(y = -\frac{3}{2} x-\frac{1}{2}\)      \((where: \ m = -\frac{3}{2} \ and, \ c = -\frac{1}{2} )\)

and:

\(2x+7y=2\)  becomes  \(y=-\frac{2}{7}x +\frac{2}{7}\)     \((where: \ m = -\frac{2}{7} \ and, \ c = \frac{2}{7})\)

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

The question tells us that the equation of the line we are looking for has the same y-intercept as:

\(2x+7y=2\)

So the line we are trying to work out will also have a y intercept of   \(\frac{2}{7}\)

(refer to rearranging)

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

The question also tells us that the line is perpendicular to  \(3x + 2y = -1\)

Perpendicular gradient = negative reciprocal of the gradient of the line it is perpendicular to.

So the gradient of the new line will be the  negative reciprocal of the gradient of  \(3x + 2y = -1\)

Gradient of  \(3x + 2y = -1\)  is: \(-\frac{3}{2}\)

(refer to rearranging)

Gradient of new line: = negative reciprocal of  \(-\frac{3}{2}\) , which is  \(\frac{2}{3}\)

(just flip fraction and change the sign)

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

So for the new line: \(m = \frac{2}{3} \ and, \ c = \frac{2}{7}\)

So just substitute in the values for m and c into: y = mx + c

\(y = mx + c\\y = \frac{2}{3} x + \frac{2}{7}\)

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

Answer:

So equation of the new line is:

\(y = \frac{2}{3}x + \frac{2}{7}\)

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

Any questions, just ask.

Answer:

Is there a graph orrrrr?

Step-by-step explanation:

Answer:

13,15,17,19

Step-by-step explanation:

13+15+17+19=64

\(\qquad\qquad\huge\underline{{\sf Answer}}♨\)

Here's the solution ~

\(\qquad \sf  \dashrightarrow \:b(b + 12) = 0\)

Here, we have two cases :

\(\qquad \sf  \dashrightarrow \:b = 0\)

\(\qquad \sf  \dashrightarrow \:b + 12 = 0\)

\(\qquad \sf  \dashrightarrow \:b = - 12\)

Hence, 0 and -12 are the only possible solutions for given equation.

Answer:

Step-by-step explanation:

The inequality corresponding to the equation -4x + y = -3 is either y > 4x - 3 or y < 4x - 3, depending on the relationship between 4x - 3 and 0.

To write the inequality represented by the equation -4x + y = -3, we first need to manipulate the equation to express y in terms of x.

Starting with -4x + y = -3, we isolate y by adding 4x to both sides:

y = 4x - 3

Now we have y expressed in terms of x. To form the inequality, we consider the relationship between x and y. The inequality depends on whether the expression 4x - 3 is greater than or less than 0.

If 4x - 3 is greater than 0, then y is greater than 0, and we can write the inequality as:

y > 4x - 3

If 4x - 3 is less than 0, then y is less than 0, and we can write the inequality as:

y < 4x - 3

The inequality represents a region in the coordinate plane where the y-values are either greater than or less than the expression 4x - 3, depending on the direction of the inequality sign.

For example, if we choose a point (x, y) in the region above the line y = 4x - 3, where y is greater than 4x - 3, the inequality y > 4x - 3 will hold true. On the other hand, if we choose a point below the line, where y is less than 4x - 3, the inequality y < 4x - 3 will be satisfied.

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Answer:

(x + i) (x - i)

Step-by-step explanation:

The expression x^2 + 1 is a sum of squares, which means that it cannot be factored using real numbers. However, it can be factored using complex numbers.

To factor x^2 + 1, we can use the fact that i^2 = -1, where i is the imaginary unit.

We can rewrite x^2 + 1 as:

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

Now, we can use the difference of squares formula to factor x^2 - (-1):

x^2 - (-1) = (x + i)(x - i)

Therefore, the factored form of x^2 + 1 is:

(x + i)(x - i)

Answer:

  0

Step-by-step explanation:

If we solve the inequality for y, we get ...

  1/2 > y . . . . divide both sides by 2

That is true only for the value 0 from the given set.

Answer:

472 in²

Step-by-step explanation:

This net is made up of 3 identical rectangles and 2 identical triangles.

Area of a rectangle = width x length

Area of a triangle = 1/2 x base x height

Rectangle

Triangle

Surface Area

SA = 3(8 x 19) + 2(0.5 x 8 x 2)

⇒ SA = 456 + 16

⇒ SA = 472 in²

Value of C = 25 when d = 625

Square root is denoted by operator√. It is a factor which can be multiplied. When a square root of a particular number is multiplied by itself, we get the original number. As example, square root of 12 is √12 is multiplied by √12 and we get (√12) ² = 12.

What is the value of C when d = 625?

As per question, C varies directly as the square root of d.

C = 16 when d = 256

C = √d

√d = √256

√d = 16

when d = 625

the value of C will be,

C = √d

C =√625

C = 25

When, d = 625, the value of C =25

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The most appropriate choice for functions will be given by -

Third option is correct

Third relation is a function.

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Here,

For a function a point in the domain has a unique image.

Here values of x axis represents domain and values of y axis represents the range

For the first option,

x = -1 has two images, y = -1 and y = 3

so x = -1 do not have a unique image

So the first relation is not a function

For the second option,

x = 0 has two images, y = -1 and y = 2

so x = 0 do not have a unique image

So the second relation is not a function

For the third option,

Every point of the domain has a unique image

So the third relation is a function

For the fourth option,

x = -2 has two images, y = 1 and y = -2

so x = -2 do not have a unique image

So the fourth relation is not a function

so, Third option is correct

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After considering the given data we conclude that the clockwise rotational path of the line segment is a rotation of -59.04 degrees about the point (-6, -1).

We have to evaluate the center and angle of rotation to explain the clockwise rotation of the line segment.

So in the first step, we can evaluate the midpoint of the line segment JK and the midpoint of the line segment J'K'. we can calculate the vector connecting the midpoint of JK to the midpoint of J'K'. This vector is (4-1, 1-(-4) = (3,5)

The center of rotation is the point that is equidistant from the midpoints of JK and J'K'. We can evaluate this point by finding the perpendicular bisector of the line segment connecting the midpoints.

The slope of this line is the negative reciprocal of the slope of the vector we just found, which is -3/5. We can apply the midpoint formula and the point-slope formula to evaluate the equation of the perpendicular bisector:

Midpoint of JK: (1, -4)

Midpoint of J'K': (4, 1)

The slope of the vector: 3/5

(x₁ + x₂)/2, (y₁ + y₂) /2

Point-slope formula: y - y₁ = m(x - x₁)

Perpendicular bisector: y - (-4) = (- 3/5)(x - 1)

Applying simplification , we get: y = (- 3/5)x - 1.2

To evaluate the center of rotation, we need to find the intersection point of the perpendicular bisector and the line passing through the midpoints of JK and J'K'. This line has slope ( 3 - (4)) /(4 - 1) = 7/3 and passes through the point (4, 1). Applying the point-slope formula, we can evaluate its equation:

y - 1 = (7/3)( x - 4)

Apply simplification , we get: y = (7/3)x - 17/3

To evaluate the intersection point, we can solve the system of equations:

y =(- 3/5)x - 1.2 = (7/3)x - 17/3

Evaluating for x and y, we get x = -6 and y = -1.

Therefore, the center of rotation is (-6, -1).

√( 4 - 1)² + ( 1 - ( - 4))²) = 5√(2)

Distance between image points and center of rotation

√( ( 6 - (-6))² + ( 3 - (-1))² = 13

The ratio of these distances gives us the scale factor of the transformation, which is 13/√2).

The angle of rotation is negative as the image moves clockwise direction. We can apply the inverse tangent function to find the angle of the vector connecting the midpoint of JK to the midpoint of J'K':

Angle of vector: arctan(5/3) = 59.04 degrees

Therefore, the clockwise rotational path of the line segment is a rotation of -59.04 degrees about the point (-6, -1).

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Answer:A

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

We have

n = 4 scores

SS = 48

For this question, we are required to find the estimated standard error

To get this, we first solve for the variance

S² = SS/n-1

= 48/4-1

= 48/3

= 16

Then S² = 16

S = √16

S = 4

Then the estimated standard error is given by:

S/√n

= 4/√4

= 4/2

= 2.

The estimated standard error is 2.

Answer:

see below

Step-by-step explanation:

h=−4.9t^2 +39.2t

When will if fall back to the ground

When will h=0

0 =−4.9t^2 +39.2t

Factor out a -t

0 = -t (4.9t -39.2)

Using the zero product property

-t =0     4.9t - 39.2 =0

t =0     4.9t = 39.2

                t =39.2 /4.9

               t =8

It will reach the ground again at 8 seconds

The maximum height is halfway between the zeros

(0+8)/2 = 4

It will reach the max height at 4 seconds, substituting this in to find the max height

h=−4.9 (4)^2 +39.2(4)

h = 78.4 meters

This will only be applicable between t=0 and t=8 seconds

0≤t≤8 seconds

The y-intercept of the line of fit is approximately 43.94 fluid ounces.

What is Probability ?

Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.

The answer is 35. If the theoretical probability of drawing two yellow socks is one fifth, then the experimental probability of drawing two yellow socks in one trial with replacement is also one fifth. Therefore, out of 175 trials, the number of times he will select two yellow socks can be predicted by multiplying the number of trials by the experimental probability: 175 * (1/5) = 35.

No, because for each input there is not exactly one output. The relation is not a function because for the input x = -5, there are two possible outputs: y = 1 and y = -1. Therefore, the relation violates the vertical line test, which requires that every vertical line intersects the graph at most once for the relation to be a function.

The y-intercept of the line of fit is approximately 43.94 fluid ounces. To find the y-intercept, we can look at the point where the line of fit intersects the y-axis (i.e., when x = 0). From the equation of the line of fit, we can see that the y-coordinate when x = 0 is approximately 43.94, which represents the initial amount of diet soda in the machine before it starts to be purchased.

Therefore,  The y-intercept of the line of fit is approximately 43.94 fluid ounces.

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Answer: the answer is for the first one is i now the fraction one is 12 the second one should be 6 the dimintions are 12 and 6

brainlyest plz

Step-by-step explanation:

The tοtal prοductiοn fοr fοοd shοuld be $1,000,000.

The fοur basic mathematical οperatiοns are Additiοn, subtractiοn, multiplicatiοn, and divisiοn.

Let F and B be the prοductiοn οf fοοd and building, respectively, in dοllars. Then, we have the fοllοwing system οf equatiοns:

Fοr the prοductiοn οf fοοd:

F = 0.20F + 0.25B + 100,000

0.20F + 0.15B = 100,000

Fοr the prοductiοn οf building:

B = 0.20F + 0.25B + 200,000

0.25B + 0.20F = 200,000

We can sοlve this system using substitutiοn οr eliminatiοn. Here, we will use eliminatiοn:

0.20F + 0.25B = 200,000 (multiply the secοnd equatiοn by -1)

0.20F + 0.15B = 100,000

0.10B = 100,000 - 0.10F (subtract the secοnd equatiοn frοm the first)

B = 1,000,000 - F

Substitute this expressiοn fοr B intο οne οf the equatiοns tο sοlve fοr F:

0.20F + 0.25(1,000,000 - F) = 200,000

0.20F + 250,000 - 0.25F = 200,000

-0.05F = -50,000

F = 1,000,000

Hence, the tοtal prοductiοn fοr fοοd shοuld be $1,000,000.

We can substitute this value intο either equatiοn tο sοlve fοr B:

0.20(1,000,000) + 0.15B = 100,000

0.15B = -80,000

B = -533,333.33

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The length of the rectangle is \(x^{4}\)- 7 units.

We know that,

                  Area of a rectangle = length* width

           So,                       Length = Area/width

According to the question,

                                    Area = \(7x^{5} - 49x\)

                                   Width = \(7x\)

             Length of the given rectangle = Area/width

                                                                = \(\frac{7x^{5}- 49x}{7x}\)

                                                                = \(\frac{7x(x^{4}- 7)}{7x}\)

                                                                = \(x^{4} - 7\)

Hence, the length of the rectangle is \(x^{4} - 7\) units.

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The complete question is:

A rectangle has an area of \(7x^{5}- 49x\). Its width is 7x units. What is its length?