Answer:
(a)Mean=14
(b)Median=14.5
Step-by-step explanation:
Given the data set:
5,5, 9, 10, 13, 16, 18, 20, 22, 22
(a)Mean
[tex]\bar{x}=\dfrac{5+5+9+10+13+16+18+20+22+22}{10} \\=\dfrac{140}{10} \\Mean=14[/tex]
(b)5,5, 9, 10, 13, 16, 18, 20, 22, 22
Since we have two terms in the middle, we take the average to obtain the median.
Median
[tex]=\frac{13+16}{2}\\=\frac{29}{2}\\Median=14.5[/tex]
Shawn is buying a new Jet Ski
for $12,500. He is considering
two credit options. Option A Offers
a 6 year loan with 8.5% interest
compounded quarterly, while
Option B offers a 5 year loan with
10% interest compounded annually.
Which is the better option and
how much will he save?
Answer:
B;$573.83 crazy.
Using the compound interest principle, the best loan would be that with the lower return value, Hence, the best option is the option B. The amount saved by going for option B is $90.81
Using the compound interest formula :
[tex] A = P(1 + \frac{r}{n})^{nt} [/tex] P = principal ; r = Rate ; n = compounding time per periodOption A :
[tex] A = P(1 + \frac{r}{n})^{nt} [/tex]
[tex] A = 2000(1 + \frac{0.085}{4})^{4 \times 6} [/tex]
[tex] A = 2000(1 + \frac{0.085}{4})^{24} [/tex]
[tex] A = 2000(1 + 0.00708)^24[/tex]
[tex] A = 2000(1.6564) = 3312.83 [/tex]
Option B :
[tex] A = P(1 + \frac{r}{n})^{nt} [/tex]
[tex] A = 2000(1 + \frac{0.10}{1})^{1 \times 5} [/tex]
[tex] A = 2000(1 + 0.10)^{5} [/tex]
[tex] A = 2000(1 + 0.00708)^5[/tex]
[tex] A = 2000(1.61051) = 3257.79 [/tex]
Difference = 3312. 83 - 3221.02 = $90.81
The better loan would be option B ; as it is cheaper.
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1. What is the slope of the line passing through (-2,3) and (4, -5)?
2. Which of the following is the equation of a line that has a slope of zero and passes through the point (4,6)?
Answer:
Step-by-step explanation:
hello :
1) Hello :
let A(-2,3) B(4,-5)
the slope is : (YB - YA)/(XB -XA)
(-5-3)/(4+2) = -8/6 =-4/3
2) Use the point-slope formula.
y - y_1 = m(x - x_1) you have :
m=0 x_1=4 y_1=6
an equation for this line is : y-6 =0(x-4)
so : y=6
April received $1,800 from her grandmother as a birthday gift. She decided to put the money in an account to save for college. If the account earns 5% interest, compounded annually, how much money will be in the account after 5 years?
A. $2,408.81
B. $2,187.91
C. $2,297.31
D. $26,447.91
Answer: C
Step-by-step explanation:
Alright, first let’s review what compound interest is. Instead of simple interest which pays interest on the principal, it pays interest on the amount in the bank each year, so it basically pays interest on the principal with previous interest. Lets run this example through the years:
Year 1:
= $1800 + 5% (Of 1800)
= $1800 + $90
= $1890
Year 2:
= $1890 + 5% (of 1890)
= $1890 + $94.5
= $1984.50
Year 3:
= $1984.50 + 5% (of 1984.50)
= $1984.50 + $99.23 (I rounded it to the nearest hundredth from its original state, $99.225)
= $2083.73
Year 4:
= $2083.73 + 5% (of 2083.725)
= $2083.73+ $104.19 (I rounded it to the nearest hundredth from its original state, $104.1865)
= $2187.92
Year 5:
= $2187.92 + 5% (of $2187.92)
= $2187.92 + $109.40 (rounded to the nearest hundredth from 109.396)
= $2297.32
This is as close as you can get to answer C, it’s just off one cent because of all the rounding!
Ed is a farmer who charges $3.75
for 5
pounds of cabbage. This table shows the rates charged for cabbage by some other farmers.
Determine whether the unit rate charged for cabbage by the other farmers is less than, equal to, or greater than the unit rate charged by Ed.
Select one cell per row.
Answer:
a more b same c less d same
Step-by-step explanation:
his per pound is 75 cents
Ed charges $3.75 for 5 pounds of cabbage, which makes his unit rate $0.75 per pound. To compare his unit rate with other farmers, calculate each of their unit rates and compare them to Ed's. Farmers work with a "going rate" like most agricultural markets, which reflects the competitive nature of the industry.
Explanation:To determine whether the unit rate charged for cabbage by other farmers is less than, equal to, or greater than the unit rate charged by Ed, it is necessary to calculate Ed's unit rate first. Ed charges $3.75 for 5 pounds of cabbage, which means the unit rate is $3.75 ÷ 5 pounds = $0.75 per pound.
Once we have Ed's unit rate, we can compare it with the rates provided by other farmers. Without the rates from other farmers included in the question, the specific comparison cannot be completed. However, if another farmer is charging a different price for a quantity of cabbage, you would calculate their unit rate the same way and compare it to Ed's $0.75 per pound. If the unit rate of another farmer is less than $0.75, then they charge less than Ed. If it is greater than $0.75, they charge more than Ed. If it is equal to $0.75, then they charge the same as Ed.
Understanding unit rates is crucial as it helps consumers make informed decisions and ensures that farmers like Ed maintain competitiveness within the market, similar to the conditions agricultural growers face. Farmers generally adhere to a "going rate", which represents a price point that is influenced by supply and demand within a competitive market.
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the largest possible sum of 4 unequal numbers, none greater than 100, is A. 380 B. 388 C. 390 D. 394
Answer:
390
Step-by-step explanation:
99+98+97+96=390
Answer:
394
Step-by-step explanation:
The largest number is 100 since it says none greater than 100. We can have 100
The next number is 99 since it is not equal to 100 and is the next largest number
The next number is 98 since it is not equal to 100 or 99 and is the next largest number
The last number is 97 since it is not equal to 100 or 99 or 98 and is the next largest number
The sum of the 4 numbers is
100+99+98+97 =394
What is the approximate perimeter of the triangle below ?
256 in.
267 in.
275 in.
302 in.
Answer:
i can assure you that it is B: 267
Step-by-step explanation:
edge 2020
Answer:
B) 267 in.
Step-by-step explanation:
In Antarctica, the air temperature is -5 degrees F. The temperature of the nearby water is 33 degrees F. How much colder is the air than the water?\
Answer:
The air is 38 degrees colder.
Step-by-step explanation:
To solve for this we must understand "key words" to understand which operation we are doing. The words in this are "how much colder" this signifies we must do subtraction.
33 - (-5) = 38.
The air is 38 degrees colder.
please help answer this
Answer:
b
Step-by-step explanation:
Please help! 30 points!
Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A(-2,2), B(6,2), C(6,3), D(-2,3),
What is the area of rectangle ABCD
[Blank] Square Units
Answer:
The answer is eight.
All you have to do is graph the points and count how many boxes are inside the points.
Answer:
The Answer is 8.
Step-by-step explanation:
When you graph the plots on a graph you might look at the graph and say this looks complicated but if you count the boxes in the shape, you will get your answer as 8 square units.
The two box-and-whisker plots below represent the distribution of shoe sizes for a group of 40 two-year-old boys and a group of 80 three-year-old boys.
What is the difference of the interquartile ranges of the box-and-whisker plots?
0
0.5
1
1.5
=============================================================
Explanation:
For now, focus solely on the orange boxplot. The first quartile Q1 is the left edge of the box, which is at 3.5; while the value of Q3 is 7.5 (right edge of the box). The interquarile range (IQR) is ...
IQR = Q3 - Q1
IQR = 7.5 - 3.5
IQR = 4
This is basically the width of the box. Ignore the whiskers when it comes to the IQR.
Let A = 4 as we'll use it later.
---------------------------------
Find the IQR for the blue box plot
Q1 = 6 = left edge of the blue box
Q3 = 9.5 = right edge of the blue box
IQR = Q3 - Q1
IQR = 9.5 - 6
IQR = 3.5
Let B = 3.5 as we'll use it later
---------------------------------
Subtract the values of A and B to find the difference of the IQR values
A - B = 4 - 3.5 = 0.5
Which of the following is true for two complementary angles ∠RST and ∠TSU?
Question 4 options:
A)
m∠RST + m∠TSU = 90°
B)
m∠RST + m∠TSU = 180°
C)
m∠RST = m∠TSU
D)
m∠RST = ½ × m∠TSU
Answer:
Option "A" is the correct answer to the following question.
Step-by-step explanation:
Complementary angles ⇒ If the sum of two angles becomes 90 degrees, we can say that this is a complementary pair of angles.
In the given situation angle ∠RST and ∠TSU are a pair of complementary angles.
∠RST + ∠TSU = 90° (Complementary angles)
So, we say that the option "A" is the correct answer.
The correct statement is Option A) m∠RST + m∠TSU = 90°
To determine which statement is true for two complementary angles ∠RST and ∠TSU, we need to understand the definition of complementary angles in geometry.
Complementary angles are two angles whose measures add up to 90 degrees. Therefore, the correct option is:
A) m∠RST + m∠TSU = 90°
This is because, by definition, if two angles are complementary, their measures always sum up to 90 degrees. For instance, if m∠RST is 30 degrees, then m∠TSU must be 60 degrees so that their sum is 90 degrees.
A box of modelling clay with a mass of 6.9 kg is divided equally among 12 students.
How many grams does each student get?
Answer:
Each student gets 575 gram of clay
Step-by-step explanation:
1 kg = 1000 g
Mass of the total clay = 6.9 kg = 6.9 * 1000 = 6900.0 = 6900 g
Clay received by each student = Total / Number of students
= 6900 / 12
= 575 g
A fisherman harvested 350 kg of fishes on Monday. From Monday to Friday, the amount of fishes, be harvested increased by 10% per day. What’s the total amount of fishes did the fisherman harvest in the first five days? Round your answer to the nearest whole number.
Answer:
2137 kg
Step-by-step explanation:
The number of fish the fisherman harvest in the first five days is
512 kg.
Given,
A fisherman harvested 350 kg of fish on Monday.
From Monday to Friday, the amount of fishes, be harvested increased by
10% per day.
We need to find the total amount of fish the fisherman harvest in the
first five days.
Round your answer to the nearest whole number.
How do we find the percentage value of a given amount?We multiply the required percentage with the given amount.
Example:
10% of 500 = 10/100 x 500 = 10 x 5 = 50
We have,
Each day 10% increases.
Monday:
350 kg of fishes
Tuesday:
350 x 10%
= 350 x 10/100
=350 x 1/10
= 35
The number of fishes:
= 350 + 35
= 385 kg
Wednesday:
385 x 10%
= 385 x 1/10
= 38.5
The number of fishes:
= 385 + 38.5
= 423.5 kg
Thursday:
423.5 x 10%
= 423.5 x 1/10
= 42.35
The number of fishes:
= 423.5 + 42.35
= 465.85 kg
Friday:
465.85 x 10%
= 465.85 x 1/10
= 46.585
The number of fishes:
= 465.85 + 46.585
= 512.435 kg
Rounding to the nearest whole number we get,
= 512 kg
Thus the number of fish the fisherman harvest in the first five days is
512 kg.
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Please answer ;)
-11b+7 = 40
Answer:
b=-3
Step-by-step explanation:
Let's solve your equation step-by-step.
−11b+7=40
Step 1: Subtract 7 from both sides.
−11b+7−7=40−7
−11b=33
Step 2: Divide both sides by -11.
−11b /−11 = 33 /−11
b=−3
Answer:
The correct answer is b=(-3)
Step-by-step explanation:
First you subtract 7 from both sides and you willl get -11b=33. Then you divide both sides by -11 and you will get b=33/-11. Then you simplifty your answer and you will get b=(-3).
^^Hope this helps!^^
what does y and x equal?
Answer:
(C)
Step-by-step explanation:
I solved it by graphing.
[see picture]
Which of these triangles are definitely right triangles? Explain how you know.
Answer: A / D / E
Step-by-step explanation:
You know that because you have an angle that measures 90 degrees I’m each. You can also make the 90 degree box at the corner.
Rozonda defines the diameter of a circle as a line segment passing through the center of the circle. Is Rozonda’s definition valid?
Answer:
Step-by-step explanation:
It is not valid because not all segments that fit the description are diameters.
Yes, Rozonda's definition of the diameter of a circle as a line segment passing through the center of the circle is valid. The diameter is defined as the longest chord in a circle, and it always passes through the center.
Explanation:Yes, Rozonda's definition of the diameter of a circle as a line segment passing through the center of the circle is valid. The diameter is defined as the longest chord in a circle, and it always passes through the center. In other words, any line segment that connects two points on the circle and passes through the center can be considered a diameter.
For example, if you have a circle with a radius of 5 units, any line segment that connects two points on the circle and measures 10 units in length will be a diameter.
Keywords: diameter, circle, line segment, center
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Two buildings are 35 feet apart. The angle of elevation from the top of the smaller building to the top of the taller building is 42˚. The smaller building is 32 feet high. Find the height of the taller building.
Using trigonometry and the tangent function, the height of the taller building, with a 42˚ angle of elevation from the smaller 32-foot building 35 feet away, is calculated to be approximately 63.514 feet. The formula tan(42˚) = (h₂ - 32) / 35 is utilized where tan(42˚) ≈ 0.9004. Solving this equation gives the height of the taller building.
The question asks: Two buildings are 35 feet apart. The elevation angle from the top of the smaller building to the top of the taller building is 42˚. The smaller building is 32 feet high. Find the height of the taller building.
To solve this problem, we will use trigonometry, specifically the tangent function, which relates an angle of a right triangle to the ratio of the opposite side to the adjacent side.
Let's denote the height of the smaller building as h₁ = 32 feet, the height of the taller building as h₂, and the horizontal distance between the buildings as 35 feet. The elevation angle from the top of the smaller building to the top of the taller building is 42˚.
First, we determine the difference in height (Δh) between the two buildings:
→ tan(θ) = opposite/adjacent
In this case:
→ tan(42˚) = (h₂ - h₁) / 35
We solve for the height difference:
→ (h₂- 32) = tan(42˚) * 35
Using a calculator to find tan(42˚):
→ tan(42˚) ≈ 0.9004
Substituting the value:
→ (h₂ - 32) = 0.9004 * 35
→ h₂ - 32 ≈ 31.514
Adding 32 to both sides:
→ h₂ ≈ 31.514 + 32
→ h₂ ≈ 63.514
Therefore, the height of the taller building is approximately 63.514 feet.
Find the value of x.
A) 21
B) 27
C) 31
D) 34
Answer:
what is the equation?
Step-by-step explanation:
i only need to know the first one
Answer:
x = 9
Step-by-step explanation:
2/3x +5 = -2/6x +14
Simplify
2/3x +5 = -1/3x +14
Add 1/3x to each side
2/3x + 1/3x +5 = -1/3x +1/3x +14
3/3x +5 = 14
x+5 = 14
Subtract 5 from each side
x+5-5=14-5
x = 9
Which polynomial correctly combines the like terms and puts the given polynomial in standard form?
–5x3y3 + 8x4y2 – xy5 – 2x2y4 + 8x6 + 3x2y4 – 6xy5
Answer: [tex]-5x^3y^3+8x^4y^2-7xy^5+x^2y^4+8x^6[/tex]
Step-by-step explanation:
[tex]-5x^3y^3+8x^4y^2-xy^5-2x^2y^4+8x^6+3x^2y^4-6xy^5[/tex]
[tex]-5x^3y^3+8x^4y^2+(-xy^5-6xy^5)+(-2x^2y^4+3x^2y^4)+8x^6[/tex]
[tex]-5x^3y^3+8x^4y^2+(-7xy^5)+(x^2y^4)+8x^6[/tex]
[tex]-5x^3y^3+8x^4y^2-7xy^5+x^2y^4+8x^6[/tex]
Answer:
D. 8x6 + 8x4y2 – 5x3y3 + x2y4 – 7xy5
Step-by-step explanation:
Find the perimeter of the quarter-circle. Give your answer to the nearest whole number.
Round to the nearest hundredths.
The perimeter of the quarter- circle is ____ cm.
Answer:
The perimeter of the quarter-circle is 200 cm.
Step-by-step explanation:
Given that the angle of quarter-circle is 90°. So using Length of Arc formula, you are able to find the length of curve :
[tex]arc = \frac{θ}{360} \times 2 \: \pi \: r[/tex]
Let r be radius = 56 cm,
Let θ = 90°
[tex]arc = \frac{90}{360} \times 2 \times\pi \times 56[/tex]
[tex] = \frac{1}{4} \times 2 \times \pi \times 56[/tex]
[tex] = \frac{1}{2} \times \pi \times 56[/tex]
[tex] = 28\pi \: cm[/tex]
We have already found the arc. Next we have to add up together to find the perimeter :
[tex]p = 56 + 56 + 28\pi[/tex]
[tex]p = 112 + 28\pi[/tex]
[tex]p = 200 \: cm \: (3s.f)[/tex]
Which polygon will tessellate the plane?
Answer:
Equilateral triangles, squares and regular hexagons are the only regular polygons that will tessellate. Therefore, there are only three regular tessellations.
Step-by-step explanation:
What is the solution to 2x-8 <12?
0x<2
x <8
X <10
x <40
Answer:
c.x<10Step-by-step explanation:
Step 1: Add 8 to both sides.
2x−8+8<12+8
2x<20
Step 2: Divide both sides by 2.
2x/2<20/2
x<10
Hope this helps!Bacteria grows at an alarming rate of 75% each hour. How many bacteria will there be by the end of the day?
A. 680,634
B. 16,335,198
C. 68,633
D. 680,633
Hi.
This is a geometric sequence with the rational of the sequence : 1.75
If you start with 1,
Then U0 = 1
and U24 = 1*1.75^24≈ 680 634
Jane has saved 600 dollars in a college fund. She added money to the account over the next year and at the end of the year the account had 890 dollars. Write an equation to represent the amount she saved over the year.
which of these options ??
A. 890x = 600
B. 600 + x = 890
C. 890 + x = 600
D. 600x = 890
E. none of the above
The answer would be B)
Answer: B
Step-by-step explanation: Jane put $600 in a college fund and over the next year she got $890. You don't know how much money she added to the fund (x is added dollars) so 600+x=890.
What is the value of x, when x2 + 5 = 21? A) 2 or -2 B) 4 or -4 C) 5.5 or -5.5 D) 8 or -8
Answer:
I'm positive that the
answer is B 8
Aaliyah wants to determine how age and gender are related to movie genre preference in her town. She selects a simple random sample of 35 males from the 20- to 30-year age group and records their age, gender, and movie genre preference (comedy, romance, or horror). She also selects an independent simple random sample of 45 females from the 45- to 55-year age group and records the same information. Which is the most important observation about Aaliyah's plan? (3 points)
A. The plan is well conceived and should serve the intended purpose.
B. Her samples are too small.
C. She should have used equal sample sizes.
D. She should have selected the two age groups randomly instead of choosing them specifically.
E. She will be unable to tell whether a difference in movie genre preference is related to a difference in age or to a difference in gender.
Answer:
The correct option is;
E. She will not be able to tell whether a difference in movie genre preference is related to a difference in age or to a difference in gender
Step-by-step explanation:
The question states that Aaliyah randomly selects the following;
First sample
Sample gender = Males
Sample size = 35
Age bracket of sample = 20 to 30 years
Second sample
Sample gender = Females
Sample size = 45
Age bracket of sample = 45 to 55 years
The plan is to determine how age and gender are related to movie genre preference
Appropriate sample distribution to determine movie genre preference is as follows;
Gender = Male
Age bracket = 20 to 55 years
Gender = Female
Age bracket = 20 to 55 years
Therefore, since the samples selected do not cut across the population of the by age and gender of movie genre preference, she will not be able to tell whether a difference in movie genre preference is related to a difference in age or to a difference in gender.
Answer:
E. She will be unable to tell whether a difference in movie genre preference is related to a difference in age or to a difference in gender.
Step-by-step explanation:
What quadrilaterals can you draw that have two sides with length 7 cm and two sides with length
4 cm?
Which of these quadrilaterals can have two sides with length 7 cm and two sides with length 4 cm?
Select all that apply.
O A. Square
B. Rectangle
C. Trapezoid
OD. Parallelogram
Final answer:
Quadrilaterals that can have two sides of length 7 cm and two of length 4 cm are a rectangle and a parallelogram; a square cannot, and a trapezoid is not certain.
Explanation:
The type of quadrilaterals that can be drawn with two sides of length 7 cm and two sides of length 4 cm are a rectangle and a parallelogram. A square cannot have sides of different lengths, so it wouldn't fit the requirement. A trapezoid could possibly have these side lengths, but only if the non-parallel sides are of different lengths, which isn't stated in the question.
The reason for choosing a rectangle is because it has four right angles and the opposite sides are equal, allowing for two sides to be 7 cm and the other two to be 4 cm. A parallelogram can also have sides of these lengths as long as the opposite sides are equal, and the angles are not restricted to 90 degrees like in a rectangle.
Darius flipped a coin 500 times and it landed heads up 300 times. What is the relative frequency of the coin landing heads up based on the results of this experiment?
Group of answer choices
4%
6%
40%
60%
Answer:
Answer is D
500 times, lets divide that by 100. So... 3 out of 5 times is 60%
Step-by-step explanation: