Directions: Solve for x. Round to the nearest tenth.
3.
2
.
48°
17
29
x
х
х
67°
4.
5.
29°
16°
12
X
Х
37
6.
7.
15
х
589
51°
х
22

Mean is average.

Add the speeds together and divide by number of cars:

67 + 74 + 85 + 80 + 74 + 82 = 462

462/6 = 77

Mean = 77 miles per hour

Answer:

168 = L + 2W

And you want to maximize LW.

Which means you want to maximize W (168 - 2W), or 168W - 2W^2.

To maximize that, the derivative must go to zero.

0 = 168 - 4W, or W = 42. And L = 84. Done. :-)

Step-by-step explanation:

Answer:

Area (A)  0.0682

Step-by-step explanation:

The sketch for the region enclosed by the given curves can be found in the image attached below.

From the image below;

The two curves intersect in the area of tan 9x = 2 sin 9x

Recall that:

making x the subject; then:

The subdivision of the domain is in two intervals

where;

Area (A) =

Area (A) = 0.06818

Area (A)  0.0682

We need volumes

#Chest A

V=LBH

#Chest B

V:-

Answer:

See below ~

Step-by-step explanation:

Chest A

Chest B

⇒ Chest B has more space than Chest A

⇒ Hope it helps ~

Answer:

10

Step-by-step explanation:

Since it given that:

x = 7 and y = 3

We can substitute x and y:

(7-3) + 2(3)

7 - 3 = 4

4 + 2(3)

2(3) = 6

4 + 6 =10

Thus the answer is 10.

[RevyBreeze]

Answer:

[tex]10[/tex]

Step-by-step explanation:

Sorry for messing it up last time.  The format can be really weird

Step 1:  Input x and y and solve

[tex](x - 3) + 2y[/tex]

[tex](7 - 3) + 2 * 3[/tex]

[tex]4 + 6[/tex]

[tex]10[/tex]

Answer:  [tex]10[/tex]

Answer:

  5.  ∠TSR ≅ ∠TRS = 72°

  6.  ∠ORS ≅ ∠OSR = 18°

  7.  ∠ROS = 144°

Step-by-step explanation:

Segments OT and SR can be drawn to divide the figure into similar right triangles. In these triangles, all of the smaller acute angles are congruent, and all of the larger acute angles are congruent. The smaller and larger acute angles are complementary, as they are in any right triangle.

Segment OT bisects angle T, so the smaller acute angle in each right triangle is 36°/2 = 18°.

__

∠TSR ≅ ∠TRS = 90° -18° = 72°

__

∠ORS ≅ ∠OSR = 18°

__

∠ROS = 2×∠TOS = 2×72° = 144°

Note that this is supplementary to ∠T: ∠O = 180° -36° = 144°.

The final statement is: The volume of box be is equal to 8 m³

Every three-dimensional object occupies some space. This space is measured in terms of its volume. Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

Given here: Volume of Box A= 64 m³

Let the dimensions of box  be a each

Then we have dimensions of box b are a/2 each

Therefore volume of box b is = a/2×a/2×a/2

                                                  =a³/8

                                                  = 64/8

                                                  =8

Hence, The volume of box be is equal to 8 m³

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Let p(t) be the number attendees and t be the ticket price measured in units of 10s of rupees. When the price is t = 7 (i.e. Rs70), there were p(7) = 300 people in attendance.

For each unit increase in t (i.e. for each Rs10 increase in price), p(t) is expected to fall by 20, so that

p(t + 1) = p(t) - 20

Solve for p(t). Suppose t ≥ 7. By substitution,

p(t + 1) = (p(t - 1) - 20) - 20 = p(t - 1) - 2×20

p(t + 1) = (p(t - 2) - 20) - 2×20 = p(t - 2) - 3×20

p(t + 1) = (p(t - 3) - 20) - 3×20 = p(t - 3) - 4×20

and so on, down to

p(t + 1) = p(7) - (t - 6)×20 = 420 - 20t

or

p(t) = 420 - 20 (t - 1) = 440 - 20t

With t = price per ticket (Rs/ticket) and p(t) = number of attendees = number of tickets sold, it follows that the income made from ticket sales for some fixed ticket price t would be t×p(t). If one plots p(t) in the coordinate plane, the price that maximizes income and number of attendees is such that the area of a rectangle inscribed by the line p(t) and the coordinate axes is maximized.

Let A(t) be the area of this rectangle, so

A(t) = t p(t) = 440t - 20t²

Without using calculus, complete the square:

A(t) = 440t - 20t² = 2420 - 20 (t - 11)²

This is the equation of a parabola with vertex at (11, 2420), so the optiml ticket price is Rs11, and at this price the drama club can expect an income of Rs2420.

With calculus, differentiate A with respect to t and find the critical points:

A'(t) = 440 - 40t = 0   ⇒   11 - t = 0   ⇒   t = 11

Differentiate A again and check the sign of the second derivative at this critical point:

A''(t) = -40   ⇒   A''(11) = -40 < 0

which indicates a local maximum at t = 11 of A(11) = 2420.

Using the rules of significant figures the expression 47.5-6.12 can be simplified as 41.38.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The number 6.12 has two digits after the decimal while the number 47.5 has only one digit after the decimal therefore, as per the law of significant figures, to deduct 6.12 from 47.5, we need to put one zero at the end of 47.5.

Also, there are two digits in 47.50 before the decimal while 6.12 has only one, therefore, As per the law of significant figures, one zero will be added before 6.12. Thus, the deduction now can be done as,

    4  7  .  5  0

-   0  6  .  1  2

   4   1  .  3  8

Hence, Using the rules of significant figures the expression 47.5-6.12 can be simplified as 41.38.

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Answer:

the answer is in the picture

Answer:

We know that in a triangle, given two sides, the third one must be smaller than the sum of the given sides, but greater than their difference:

z < x + y

z > x - y

Therefore, the length of the third side will be between the difference and the sum of the other two sides. In our case:

x + y = 13

x - y = 3

Hence, the correct answer is: B) The side needs a fence that is longer than 3ft. and shorter than 13ft.

Step-by-step explanation:

Using z-scores, it is found that all of the values fall within 2.46 standard deviations of the mean.

The z-score of a measure X of a variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure is above or below the mean.

In this problem, the farthest variable from the mean is of $29.95, hence X = 29.95 and:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{29.95 - 22.58}{3}[/tex]

Z = 2.46.

Hence, all of the values fall within 2.46 standard deviations of the mean.

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To determine the whether the ordered pair satisfies the equation:

     ⇒ we must plug in the values

          ⇒ since coordinates are (x,y) ⇒ (2,1)

             ⇒ there we must plug 2 into the 'x' position in the equation

                ⇒ and 1 into the 'y' position in the equation

Let's try the first equation:

   [tex]3x-y=5\\3(2)-1=5\\6-1=5\\5=5[/tex]

Let's try the second equation

   [tex]5x-2y=8\\5(2)-2(1)=8\\10-2=8\\8=8[/tex]

Thus ordered pair satisfies the following system of equations

Answer: Yes

Hope that helps!

Answer: A

Step-by-step explanation:

Answer:

Zach has 14 apples left.

Step-by-step explanation:

This equation is 12 - 4 + 18 - 6 + 14 - 20.

8 + 12 + 14 - 20

20 + 14 - 20

14

Step-by-step explanation:

Sum

(4-3i)+(-4+5i)

=4-4-3i+5i

=0+2i

=2i

Product

(4-3i)(-4+5i)

=4(-4)-3i(-4)+4(5i)-3i(5i)

=(-16)+7i+20i-15i²

-16+27i-15(-1) [i²=(-1)]

=27i-16+15

=27i-1

=(-1+27i)

I hope it helped you

Hey mate ,

In this particular question we have to find the volume of given objects and compare to find which has the greatest volume.

Lets Solve ,

Volume of cone :- 1/3πr²h

putting the known values ,

Volume = 1/3×3.14×5²×7 cubic ft.

Volume :- 183.1 cubic ft.

Volume of Sphere = 4/3πr³

putting the known values ,

Volume = 4/3×3.14×5³ cubic ft.

Volume = 523.33 cubic ft.

Volume of Cylinder = πr²h

putting the known values ,

Volume = 3.14×5²×7 cubic ft.

Volume = 549.5 cubic ft.

Volume of hemisphere = 2/3πr³

Putting the known values ,

Volume = 2/3×3.14×5³ cubic ft

Volume = 261.66 cubic ft.

Comparing the volume of each object , we can find that the Cylinder has the greatest volume

Answer:

4 3/4 liters

Step-by-step explanation:

2 1/2 + 2 1/4 = 4 3/4

Answer:

C) The range is the set of all real numbers greater than –4.

Step-by-step explanation:

Domain

Range

The correct statement is C, which states : the range is the set of all real numbers greater than -4.

D, sorry if wrong!!

have a good day

Answer:

D. 4u + 12

Step-by-step explanation:

Distributing the 4 to each term in the parenthesis:

4(u) + 4(3)

= 4u + 12

hope this helps :)

Answer:

(a) m = -7

(b) m = 1/7

Step-by-step explanation:

Since parallel lines never overlap, the slopes (m) must be equal. Therefore, a parallel line to a line with a slope of (m = -7) must also have a slope of (m = -7).

Perpendicular lines run opposite of parallel lines. As a result, the sign of the perpendicular slope must be the opposite. Since this slope is negative, the perpendicular slope must be positive. The actual numerical value of a perpendicular slope is equal to one over the slope. Therefore, if a line has a slope of (m = -7), the perpendicular line's slope must be (m = 1/7).

The value of the statistic for the annual sales in Canadian dollars; C) The standardized score of the minimum annual sales

Standardized scores are defined as scores or data values that have been given a common standard. This standard is a mean of zero and a standard deviation of 1.

Now, in this question the literacy project involved comparing the annual sales of companies. Thus, the value of the statistic for the annual sales in Canadian dollars be equal to the value of the corresponding statistic in United States dollars is the standardized score of the minimum annual sales.

The complete question is; Nyasha's financial literacy project involved comparing the annual sales of companies in Canada and companies in the US that produce software. Using the ratio of 1 CAD to 0.75 USD, she converted all annual sales from the Canadian companies into United States dollars. For which of the following will the value of the statistic for the annual sales in Canadian dollars be equal to the value of the corresponding statistic in United States dollars?

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Using proportions, it is found that there are 165 students in the school.

A proportion is a fraction of a total amount.

In the school, there are n students. Of those 1/5 of 3/8, that is, 3/15 wear glasses and identified blue as their favorite color. This amount is equivalent to 33 students, hence:

3/15n = 33

n = 33 x 15/3

n = 11 x 15

n = 165.

There are 165 students in the school.

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Answer:

Reptile, any member of the class Reptilia, the group of air-breathing vertebrates that only have:

Answer:

6854 do not have a tablet

2163 have a mobile computing device

Step-by-step explanation:

You just have to read it.

GHIJK ≅ UVWST

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

Given for 1st shape:

Given for 2nd shape:

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

WS ≅ IJ

Solve for UV:

[tex]\rightarrow \sf \dfrac{UV}{WS} =\dfrac{GH}{IJ}[/tex]

[tex]\rightarrow \sf \dfrac{UV}{18} =\dfrac{24}{24}[/tex]

[tex]\rightarrow \sf UV =18[/tex]

Solve for ST

[tex]\rightarrow \sf \dfrac{ST}{WS} =\dfrac{JK}{IJ}[/tex]

[tex]\rightarrow \sf \dfrac{ST}{18} =\dfrac{16}{24}[/tex]

[tex]\rightarrow \sf ST = 12[/tex]

Solve for VW

[tex]\sf \rightarrow \dfrac{VW}{WS} = \dfrac{HI}{IJ}[/tex]

[tex]\sf \rightarrow \dfrac{VW}{18} = \dfrac{16}{24}[/tex]

[tex]\sf \rightarrow VW = 12[/tex]

Let's see

#ST

#VW

Answer:

Below,

Step-by-step explanation:

(a) f is not defined  when x = 2 because this would make the denominator =  zero.

(i)  f-1 is the inverse of f.

Let y = (x + 1)/(x - 2)

y(x - 2) = x + 1

xy - 2y = x + 1

xy - x = 2y + 1

x(y - 1) = 2y + 1

x = (2y +1)/(y - 1)

Replace x by f-1 and y by x , we get:

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

(ii)  f-1 is not defined when x = 1 , as this makes the denominator zero.