Cecilia plots the points (–2, 2), (–2, –2), (3, 2) and (3, –2) in the coordinate plane. She connects the points to form a polygon. Explain how she could find the distance around the figure.

The approximate mean age is [tex]\(45.15\)[/tex] years, and the approximate standard deviation for age is [tex]\(9.22\)[/tex] years, both rounded to two decimal places.

To approximate the mean and standard deviation for the age groups provided, we can calculate the weighted average based on the midpoint of each age group and use the formula for the standard deviation of a weighted dataset.

First, calculate the midpoints of the age groups:

- For 25-34 years: midpoint = (25 + 34) / 2 = 29.5

- For 35-44 years: midpoint = (35 + 44) / 2 = 39.5

- For 45-54 years: midpoint = (45 + 54) / 2 = 49.5

- For 55-64 years: midpoint = (55 + 64) / 2 = 59.5

Next, calculate the weighted mean using the formula:

[tex]\[ \text{Weighted Mean} = \frac{\sum (\text{Midpoint} \times \text{Number of People})}{\sum \text{Number of People}} \][/tex]

[tex]\[ \text{Weighted Mean} = \frac{(29.5 \times 22.1) + (39.5 \times 31.5) + (49.5 \times 37.7) + (59.5 \times 25.3)}{22.1 + 31.5 + 37.7 + 25.3} \][/tex]

[tex]\[ \text{Weighted Mean} \approx \frac{651.45 + 1244.25 + 1867.35 + 1503.35}{116.6} \][/tex]

[tex]\[ \text{Weighted Mean} \approx \frac{5266.4}{116.6} \][/tex]

[tex]\[ \text{Weighted Mean} \approx 45.15 \text{ years (approx)} \][/tex]

Now, calculate the standard deviation using the formula:

[tex]\[ \text{Weighted SD} = \sqrt{\frac{\sum (\text{Number of People} \times (\text{Midpoint} - \text{Weighted Mean})^2)}{\sum \text{Number of People}}} \][/tex]

[tex]\[ \text{Weighted SD} = \sqrt{\frac{(22.1 \times (29.5 - 45.15)^2) + (31.5 \times (39.5 - 45.15)^2) + (37.7 \times (49.5 - 45.15)^2) + (25.3 \times (59.5 - 45.15)^2)}{116.6}} \][/tex]

[tex]\[ \text{Weighted SD} \approx \sqrt{\frac{9919.575}{116.6}} \][/tex]

[tex]\[ \text{Weighted SD} \approx \sqrt{85.004} \][/tex]

[tex]\[ \text{Weighted SD} \approx 9.22 \text{ years (approx)} \][/tex]

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Answer:

x = 29

y = 6

Step-by-step explanation:

Let the two numbers be represented as x and y

x + y = 35

x = 5y - 1

Substitute x as 5y -1 in equation one

5y -1 + y = 35

5y + y -1 = 35

Add 1 to both sides

6y - 1 + 1 = 35 + 1

6y = 36

Divide both sides by 6

6y/6= 36/6

y = 6

Now substitute y as 6 in any of the equations to get x.

Using equation one ,

We have

x + y = 35

x +6 = 35

Subtract 6 from both sides

x + 6 - 6 = 35 - 6

x = 29

Answer:

       _

-0.416       or for rounded     0.417

Step-by-step explanation:

when you multiply  -1/4 and 5/3 you will get a repeating decimal so what you will do is ether round it or put a line on top of the 6 showing that the number six never ends so when you round it you should round the thousandths plae making it -0.417

Answer:

bunches up in the middle and tapers off symmetrically at either end

Step-by-step explanation:

By definition a normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Because the data towards the mean is more frequent in occurrence, the graph peaks at the center. The data occurs less frequently at the tail ends of the distribution, thus the shape of the distribution is a bell shape that peaks at the center and tapers off towards the tails.  The key characteristic is that the distribution of data is perfectly symmetrical.

This is why the answer is:

The data depicted in a histogram show approximately a normal distribution if the distribution bunches up in the middle and tapers off symmetrically at either end.

Step-by-step explanation:

We have,,

6x and 2x

To find, the value of x = ?

According to question,

The sum of 6x and 2x is at least 39

∴ 6x + 2x = 39

⇒ 8x = 39

⇒  x = [tex]\dfrac{39}{8}[/tex]

∴ The value of x = [tex]\dfrac{39}{8}[/tex]

Thus, put x = [tex]\dfrac{39}{8}[/tex] I write the sum of 6x and 2x is at least 39 .

Step-by-step explanation:

We have,

[tex]\dfrac{x+16}{3}=3x[/tex]

To find, the value of x in the given equation = ?

∴ [tex]\dfrac{x+16}{3}=3x[/tex]

By crossmultiplication, we get

3(3x) = x + 16

⇒ 9x = x + 16

⇒  9x - x = 16

⇒  8x = 16

⇒  x = [tex]\dfrac{16}{8}[/tex]

⇒  x = 2

∴ The value of x = 2

Thus, the required value of x is equal to 2.

Answer:

Step-by-step explanation:

The function that will have the domain [tex](\infty, \infty)[/tex] and a range of [tex](-3, \infty)[/tex] is the

function in option d.) [tex]f(x) = e^x - 3[/tex]

Answer:

[tex]\cos B=0.4[/tex]

Step-by-step explanation:

Given

[tex]\Sin A=0.4=\frac{4}{10}=\frac{2}{5}\\\\In\ right\ triangle\\\\\sin A=\frac{Perpendicular}{Hypotenuse}=\frac{BC}{AB}=\frac{2}{5}\\\\Then\ \ \cos B=\frac{Base}{Hypotenuse}=\frac{BC}{AB}=\frac{2}{5}=0.4[/tex]

Answer:

Part a)

[tex]c=9.3\ units\\b=7.2\ units[/tex]

Part b) [tex]cos(B)=0.4[/tex]  see the explanation

Step-by-step explanation:

The correct question is

In right triangle ABC, C is the right angle. Given measure of angle A = 40 degrees and a =6

Part a) which of the following are the lengths of the remaining two side, rounded to the nearest tenth?

Part b) Which of the following is cos B if sin A=0.4?

see the attached figure to better understand the problem

Part a)

step 1

Find the length of side c

Applying the law of sines

[tex]\frac{a}{sin(A)}=\frac{c}{sin(C)}[/tex]

we have

[tex]a=6\ units\\A=40^o\\C=90^o[/tex]

substitute

[tex]\frac{6}{sin(40^o)}=\frac{c}{sin(90^o)}[/tex]

solve for c

[tex]c=\frac{6}{sin(40^o)}=9.3\ units[/tex]

step 2

Find the length of side b

In the right triangle ABC

[tex]tan(40^o)=\frac{BC}{AC}[/tex] ----> by TOA (opposite side divided by the adjacent side)

substitute the values

[tex]tan(40^o)=\frac{6}{AC}[/tex]

[tex]AC=\frac{6}{tan(40^o)}=7.2\ units[/tex]

therefore

[tex]b=7.2\ units[/tex]

Part b) we know that

If two angles are complementary, the cofunction identities state that the sine of one equals the cosine of the other and vice versa

In this problem

Angle A and angle B are complementary

therefore

the sine of angle A equals the cosine of angle B

we have

sin(A)=0.4

so

cos(B)=0.4

Answer:

2.5 minutes or 150 seconds

Step-by-step explanation:

Time = Distance / speed

300/2 = 150.

150 seconds, or 2 and a half minutes

The height of tree is 32 meter

Solution:

Given that,  The sun is at an angle of elevation of 58 degree

A tree casts a shadow 20 meters long on  the ground

The sun, tree and shadow forms a right angled triangle

The figure is attached below

ABC is  a right angled triangle

AC is the height of tree

AB is the length of shadow

AB = 20 meters

Angle of elevation, angle B = 58 degree

By definition of tan,

[tex]tan \theta = \frac{opposite}{adjacent}[/tex]

In this right angled triangle ABC,

opposite = AC and adjacent = AB

Therefore,

[tex]tan\ 58 = \frac{AC}{AB}\\\\tan\ 58 = \frac{AC}{20}\\\\1.6 = \frac{AC}{20}\\\\AC = 1.6 \times 20\\\\AC = 32[/tex]

Thus height of tree is 32 meter

Answer:

0.743ml=0.000743

Step-by-step explanation:

Answer:

a 90° clockwise rotation about the origin

a 180° rotation about the origin

a 90° counterclockwise rotation about the origin

Step-by-step explanation:

Transformations are done on a Cartesian Plane, which is the grid with four quadrants. (See picture) Each quadrant is 90°, so two quadrants is 180°.

When you rotate counterclockwise it is like in the picture. When you want to rotate clockwise, it's the other way.

When we rotate 180°, it does not matter if it is counterclockwise or clockwise because the result is the same (both move two quadrants).

We can imagine an example to help us solve the problem. Let's say we are rotating an object starting in first quadrant. (Upper right quadrant).

Find out which quadrant the object ends up with each instruction:

FROM THE PICTURE:

"a 90° counterclockwise rotation about the origin (Q2) and then a 180° rotation about the origin"

End: Quadrant 4

"a reflection across the x-axis (Q4) and then a reflection across the y-axis"

End: Quadrant 3

"a 90° clockwise rotation about the origin (Q4) and then a rotation 180° about the origin"

End: Quadrant 2

FROM YOUR LIST:

"a 90° counterclockwise rotation about the origin " Quadrant 2

"a 180° rotation about the origin " Quadrant 3

"a 90° clockwise rotation about the origin" Quadrant 4

Match each ending quadrant from your list with the same ending quadrant from the picture.

The order that you should put your list into the boxes is:

a 90° clockwise rotation about the origin

a 180° rotation about the origin

a 90° counterclockwise rotation about the origin

The solution set is x = 3, y = 4 (or) x = 3, y = –4.

Solution:

Given system of algebraic equations are

[tex]y^{2}+(x-8)^{2}=41[/tex] – – – – – (1)

[tex]y^{2}-25=-x^{2}[/tex] – – – – – (2)

Expand equation (1) using algebraic identity: [tex](a-b)^2=a^2-2ab+b^2[/tex]

[tex]y^{2}+x^2-16x+64=41[/tex]

subtract 64 from both sides of the equation

[tex]y^{2}+x^2-16x+64-64=41-64[/tex]

[tex]y^{2}+x^2-16x=-23[/tex] – – – – – (3)

Now, to arrange equation (2) in order, add [tex]x^2[/tex] on both sides.

[tex]y^{2}-25+x^2=-x^{2}+x^2[/tex]

[tex]y^{2}-25+x^2=0[/tex]

Add 25 on both sides of the equation,

[tex]y^{2}+x^2=25[/tex] – – – – – (4)

To solve this subtract equation (4) from equation (3)

[tex]\Rightarrow y^{2}+x^2-16x-(y^{2}+x^2)=-23-25[/tex]

[tex]\Rightarrow y^{2}+x^2-16x-y^{2}-x^2=-23-25[/tex]

[tex]\Rightarrow -16x=-48[/tex]

Divide both sides of the equation by –16,

⇒ x = 3

Substitute x = 3 in equation (4), we get

[tex]\Rightarrow y^{2}+3^2=25[/tex]

[tex]\Rightarrow y^{2}=25-9[/tex]

[tex]\Rightarrow y^{2}=16[/tex]

[tex]\Rightarrow y=\pm 4[/tex]

i. e. y = 4 (or) y = –4

The solution set is x = 3, y = 4 (or) x = 3, y = –4.

Answer:

f(-9) = -23

Step-by-step explanation:

Step 1:  Identify the function

f(x) = 3x + 4

Step 2:  Set x to -9 in the function

f(-9) = 3(-9) + 4

Step 3:  Multiply

f(-9) = -27 + 4

Step 4:  Add

f(-9) = -23

Answer:  f(-9) = -23

Answer:

5.5 pounds of seeds

Step-by-step explanation:

22 pounds seeds = 4-acre field

(x) pounds seeds = 1-acre(per acre)

x= 22/4

 = 5.5 pounds of seeds

Answer:

6 combinations

Step-by-step explanation:

Pants options: Navy Blue, Khaki

Shirt options: Red, white, blue

Possible combinations:

Navy Blue with:       Khaki with:

Red                           Red

White                        White

Blue                           Blue

There are 6 outfit possibilities

Hope this helps and let me know if you have any questions about my answer :)

Answer:

The answer you have is Correct!

Answer:

10/25 or 2/5

Step-by-step explanation:

since only 10 have sport as all the other students don't

Answer:

56 football cards

Step-by-step explanation:

If 5 baseball cards multiplied by 8 is 40, then you multiply the 7 football cards by 8 as well.

7x8=56

Answer:

[tex]\frac{1}{90}[/tex]

Step-by-step explanation:

Before calculating the scale we require the dimensions to be in the same units.

Using the conversion

1 yard = 3 ft and

1 foot = 12 inches, then

5 yards = 5 × 3 × 12 = 180 inches

The scale is then

2 in : 180 in ← divide both quantities by 2

= 1 : 90

= [tex]\frac{1}{90}[/tex]

The scale of the drawing given is 1/90

Using the following conversion :

This means that ;

Then ;

Relating the expression :

2 inches = 180 inches

divide both sides by 2

1 inch : 90 inches

Hence, the scale is 1 /90

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Answer:

The area of trapezoid PQRS is 125 square units

Step-by-step explanation:

The picture of the question in the attached figure

we know that

If trapezoid PQRS with parallel sides PQ and RS is divided into four triangles by its diagonals PR and QS , intersecting at X, then the area of triangle PSX is equal to that of triangle QRX, and the product of the areas of triangle PSX and triangle QRX is equal to that of triangle PQX and triangle RSX

Let

A_1 ----> the area of triangle PSX

A_2----> the area of triangle QRX

A_3 ---> the area of triangle PQX

A_4 ---> the area of triangle RSX

[tex]A_1*A_2=A_3*A_4[/tex]

[tex]A_1=A_2[/tex]

so

[tex]A_1^2=A_3*A_4[/tex]

we have

[tex]A_3=20\ units^2\\A_4=45\ units^2[/tex]

substitute

[tex]A_1^2=(20)(45)\\A_1^2=900\\A_1=30\ units^2[/tex]

The area of trapezoid is equal to

[tex]A=A_1+A_2+A_3+A_4[/tex]

substitute

[tex]A=30+30+20+45=125\ units^2[/tex]

Final answer:

The area of trapezoid PQRS is found by adding the areas of triangle PQX (20 square units) and triangle RSX (45 square units) together, which equals 65 square units.

Explanation:

The area of trapezoid PQRS can be found by summing up the areas of triangle PQX and triangle RSX. Since diagonals PR and QS intersect at point X, both triangles share the same height, which is the perpendicular distance from point X to the bases PQ and RS. Thus, the area of trapezoid PQRS is simply the sum of the areas of the two triangles.

To calculate the area of trapezoid PQRS, we add the area of triangle PQX, which is given as 20, to the area of triangle RSX, which is given as 45. Therefore, the area of trapezoid PQRS is:

Area of trapezoid PQRS = Area of triangle PQX + Area of triangle RSX = 20 + 45 = 65

So, the area of trapezoid PQRS is 65 square units.

Answer:

a. 1/10

b. 4/10

c. 20

Step-by-step explanation:

There are 10 equal sections.

a. 1 section is labeled "Large Prize", so the probability of winning a large prize is 1/10.

b. 1 section is labeled "Large Prize" and 3 sections are labeled "Small Prize", so there's 4 prize section.  Therefore, the probability of winning a prize is 4/10.

c. Each person has a 4/10 chance of winning a prize.  So if there are 50 people, we would expect 4/10 × 50 = 20 people to win a prize.

Answer:

Step-by-step explanation:

Final answer:

The remainder when the function f(x) = 4x² + 5x + 2 is divided by x + 7 is found using the remainder theorem, which gives us a result of 163.

Explanation:

To find the remainder when the function f(x) = 4x² + 5x + 2 is divided by x + 7, we can use the remainder theorem. The remainder theorem states that if a polynomial f(x) is divided by a linear divisor of the form x - r, the remainder is f(r). Here, our linear divisor is x + 7, which we can rewrite as x - (-7). So, we substitute x = -7 into the polynomial to get the remainder.

Substituting x = -7 into the function gives us:
f(-7) = 4(-7)² + 5(-7) + 2 = 4(49) - 35 + 2 = 196 - 35 + 2 = 163.

Therefore, the remainder when f(x) is divided by x + 7 is 163.

Approximately 3 bottles are needed to buy to completely fill the 6 glasses you need

Solution:

Given that,

A small bottle of Dr.Pepper holds 31.2 cm^3 of the delicious drink

Therefore,

[tex]Volume\ of\ small\ bottle\ of\ Dr.pepper = 31.2\ cm^3[/tex]

For a New Years Eve party, you need enough juice to fill 6 cone- shaped glasses that have a 4 cm diameter and a 3 cm height

Find the volume of cone

[tex]V = \frac{\pi r^2h}{3}[/tex]

Where, r is the radius and h is the height

Diameter = 4 cm

Radius = 4/2 = 2 cm

Height = 3 cm

Therefore,

[tex]V = \frac{3.14 \times 2^2 \times 3}{3}\\\\V = \frac{3.14 \times 12}{3}\\\\V = \frac{37.68}{3}\\\\V = 12.56[/tex]

Thus, for 6 cone shaped glasses:

Volume of 6 cone shaped galsses = 12.56 x 6 = 75.36 [tex]cm^3[/tex]

How many full bottles of Dr. Pepper do you need to buy to completely fill the 6 glasses you need?​

[tex]\text{Number of Dr.pepper bottles } = \frac{\text{Volume of 6 cone shaped galsses}}{\text{Volume of small bottle of dr pepper}}\\\\\text{Number of Dr.pepper bottles } = \frac{75.36}{31.2}\\\\\text{Number of Dr.pepper bottles } = 2.4153[/tex]

Thus approximately 3 bottles are needed to buy to completely fill the 6 glasses you need

Final answer:

To fill 6 cone-shaped glasses for a New Year's Eve party, you would need to buy 3 full bottles of Dr. Pepper. The volume of each glass is calculated using the formula for the volume of a cone, and then this volume is multiplied by 6 to find the total volume required for all glasses. The number of bottles needed is found by dividing this total volume by the volume of one bottle of Dr. Pepper.

Explanation:

To determine how many full bottles of Dr. Pepper you need to buy to fill 6 cone-shaped glasses with a 4cm diameter and a 3cm height, we need to calculate the volume of one glass and then multiply it by 6 to get the total volume required. The formula to calculate the volume of a cone is V = (1/3)πr^2h, where V is the volume, r is the radius of the base, and h is the height of the cone.

First, we find the radius of the glass by dividing the diameter by two, which yields 2cm. Plugging the values into the formula, we get:

V = (1/3)π(2^2)(3) = (1/3)π(4)(3) = 4π cm^3

Since π is approximately 3.14, we can simplify this to:

V = 4(3.14) cm^3 = 12.56 cm^3 per glass.

Now, multiplying the volume of one glass by 6 gives us the total volume needed:

Total volume = 12.56 cm^3/glass × 6 glasses = 75.36 cm^3.

To find out how many bottles of Dr. Pepper are needed, we divide the total volume by the volume of one bottle:

Number of bottles = 75.36 cm^3 / 31.2 cm^3/bottle ≈ 2.415 bottles.

Since you cannot buy a fraction of a bottle, you would need to purchase 3 full bottles of Dr. Pepper to ensure you have enough to fill all 6 glasses.

Answer:

Step-by-step explanation:

Carlo's outcome will be the greatest if Sorin's number will be the highest and Jiao's number is the lowest.

Sorin choose a three digit number, the highest three digit number is 999.

After doubled the number, 999, the outcome will be 1998.

Jiao chooses two-digit number, the lowest two-digit number is 10.

Hence, the greatest number that Carlo can get is (1998 - 10) = 1988.

Final answer:

The greatest number Carlos can get is 1988, which is found by doubling the largest three-digit number, 999, to get 1998, and then subtracting the smallest two-digit number, 10.

Explanation:

To find the greatest number Carlos can get, we must consider the largest possible three-digit number that Sorin could double and the smallest possible two-digit number Jiao could choose.

The largest three-digit number is 999. When doubled, it becomes 1998. The smallest two-digit number is 10. Therefore, Carlos' greatest possible number is obtained by subtracting the smallest two-digit number from Sorin's doubled number:

1998 - 10 = 1988

Hence, the greatest number Carlos can get is 1988.

Good evening,

Answer:

Step-by-step explanation:

Two angles are supplementary if the sum of their measures is equal to 180°

then the measurement of an angle that is supplementary to an angle that measures 80° is :

180 - 80 = 100°

[tex]\frac{1}{6}[/tex] of the original pan represents each serving

Solution:

Given that,

Mrs.Rome has 2/3 of a pan of lasagna left after dinner

She wants to divide the leftover lasagna into 4 equal servings

2/3 is divided into 4 equal servings

Therefore,

[tex]1\ equal\ serving = \frac{\frac{2}{3}}{4}\\\\1\ equal\ serving = \frac{2}{12} = \frac{1}{6}[/tex]

Thus [tex]\frac{1}{6}[/tex] of the original pan represents each serving

Answer:

The answer is

[tex] \frac{48}{64} [/tex]

Step-by-step explanation:

Equivalent fractions are set of fractions which have the same value when simplified.

The equivalent fraction to 6/8 whose numerator is 16 less than its denominator can be obtained through two basic methods below.

Method 1

Multiply the numerator and denominator by 8 respectively.

[tex] \frac{6}{8} = \frac{6 \times 8}{8 \times 8} = \frac{48}{64} [/tex]

The numerator being 16 less than the denominator is:

[tex]48 - 64 = - 16[/tex]

Method 2

Find the equivalent fraction to 6/8 whose numerator is 16 less than its denominator by continuous multiplication approach. In other words, multiply 6/8 till you arrive at an equivalent fraction whose numerator is 16 less than its denominator. Simply multiply 6/8 by 2, 3, 4, 5, 6, 7, 8. Thus:

[tex] \frac{6}{8} = \frac{12}{16} = \frac{18}{24} = \frac{24}{32} = \frac{30}{40} = \frac{36}{48} = \frac{42}{56} = \frac{48}{64} [/tex]

The difference between the numerator and denominator of the equivalent fractions are: -2, -4, -6, -8, -10, -12, -14, -16

Hence, 48/64 is the equivalent fraction to 6/8 whose numerator and denominator difference is less than 16.

That is,

[tex] \frac{6}{8} = \frac{48}{64} [/tex]

Such that 48 - 64 = -16.

The fraction equivalent to 6/8 with a numerator 16 less than the denominator is 48/64, which simplifies to 3/4.

To find an equivalent fraction to 6/8 where the numerator is 16 less than the denominator, we use an equation to represent the relationship between the numerator (N) and the denominator (D): N = D - 16. Since 6/8 can be simplified to 3/4 by dividing both the numerator and denominator by 2, we set up the following equation: N/D = 3/4.

By substituting N with (D - 16), we get (D - 16)/D = 3/4. To find the value of D, we cross multiply: 4(D - 16) = 3D. Solving for this, we have 4D - 64 = 3D, and therefore D = 64. Since N is 16 less than D, N = 64 - 16, which gives us N = 48. So, the fraction we are looking for is 48/64.

We can check that 48/64 is indeed equivalent to 3/4 by simplifying. Dividing both numerator and denominator by 16, we get 48/64 = 3/4. Thus, the student's fraction is 48/64 which simplifies to 3/4.

Answer:

1, 2, 3

Step-by-step explanation:

The range includes only the y-axis. On this graph, the line only passes by the 1,2, and 3 on the y-axis.