Answer:
50
Step-by-step explanation:
Given:
140, 166, 132, 165, 152, 168, 181, 158, 173, 171, 180, 182, 163, 177, 180, 142, 147, 149, 178
Arranging in ascending order (from the lowest to the highest)
= 132, 140, 142, 147, 149, 152, 158, 163, 165, 166, 168, 171, 173, 177, 178, 180, 180 181, 182
Range = highest number - lowest number
= 182 - 132
= 50
Answer:
50
Step-by-step explanation:
None
write the following expressions as an exponential term with a single base
(4*2^5)÷(2^3 *1/16)
Answer:
2^8
Step-by-step explanation:
(4*2^5)÷(2^3 *1/16)
[tex]\left ( 4\times 2^5 \right )\div \left ( 2^3\times \frac{1}{16} \right )\\\\2^7 \div 2^{-1}\\\\2^7\times 2^1\\\\2^8[/tex]
Find the length of side AB.
Give your answer to 1 decimal place.
12 cm
62°
A
B
Hey there!
To solve this problem, we will be using Trigonometric Ratio. Trigonometry is always helpful when it comes to finding a missing side with specific measure/angle.
1. Cosine Ratio
Currently, there are 6 Trigonometric Ratios. But we will be talking about Cosine Ratio instead since it is what we will be using in your question! Cosine Ratio is defined as adjacent to hypotenuse or adjacent/hypotenuse. You know what adjacent and hypotenuse are right? If not then head to the next topic!2. Adjacent and Hypotenuse
Adjacent is basically the base of a triangle. It is basically drawn from right angle to any measure/angles. Hypotenuse is the longest side of a right triangle. It is also an opposite side of right angle.Hope you understand this topic! If not, feel free to ask!
3. Solve The Problem
Since our adjacent is length AB but we don't know its exact value. What we have to do is to determine AB as any variables which I will determine AB as "x". Next, we have the value of hypotenuse which is 12 cm. Then we also know the Cosine Ratio which is adjacent to hypotenuse.Therefore, the equation for the problem is:
[tex] \large{cos62 \degree = \frac{x}{12} }[/tex]
*cos is the short form of cosine*
At this part, we need a calculator to find the value of cos62 degrees. That's because it is not a degree like 0, 30, 45, 60 and 90 which can be found without a calculator.
When we put cos62 in a calculator, make sure to put it in degree mode since a calculator has two modes which are degree and radian.
When we put cos62 in, we should get 0.46947156... Because you want a one decimal place, we round the value up to the nearest tenth as we get 0.5 because 6 is greater than 5 and should be rounded up and not down. That makes the equation to:
[tex] \large{0.5 = \frac{x}{12} }[/tex]
Oh well! Finally to the equation part. Whenever you have to solve the equation that has decimal numbers in it, the best way to deal with decimal numbers is to make them into a whole number or integer. But how? Simply multiply the whole equation by 10. Because 0.5×10 is 5 thus 0.5 becomes an integer after multiplying 10.
[tex] \large{0.5 \times 10 = \frac{x}{12} \times 10} \\ \large{5 = \frac{10x}{12} }[/tex]
10x/12 can be simplified again.
[tex] \large{5 = \frac{5x}{6} }[/tex]
Then we isolate x-value by multiplying 6 the whole equation.
[tex] \large{5 \times 6 = \frac{5x}{6} \times 6} \\ \large{30 = 5x} \\ \large{x = 6}[/tex]
Huh, that's awkward! We want the answer in a 1 decimal place but seems like the answer for this is 6. Why? Well that is not an exact answer, but more like an approximation. Because the value of cos62 degree is actually a repeating decimal and doesn't have exact value.
When we put the equation cos62 = x/12 in the equation and solve. It appears that the the answer is 5.63365875. Because we round up to nearest tenth, it gives an approximation to 5.63365875 instead.
Hence, the equation and value above is just a rounded to the whole number from 5.63365875.
Because you want a one place decimal. Hence,
4. Final Answer
The length AB is 5.6 (rounded to nearest tenth)William needs to work out the size of angle Y in this diagram
One of William’s reasons are wrong.
Write down the correct reason.
Answer:
because internal staggal angles are equal
Step-by-step explanation:
The first reason is wrong.
Angle EGH and DEG are internal staggal angles:
the two angles are on both sides of the cut line EG, and the two angles are between the two divided lines.
{the definition of internal staggal angle}
Find an equivalent ratio for the proportional relationship. PQ restaurant offers 5 chicken rolls for $6.
Answer:
5:6 lol
Step-by-step explanation:
10 points 2 questions best one get brainliest
Answer:
9a. GCF: 16. LCM: 960
9b. GCF: 55. LCM: 275
9c. GCF: 24. LCM: 114
9d. GCF: 40. LCM: 600
10a. GCF: 120. LCM: 1440
10b. 10, 2, 5, 20
10c. 2880, 4320, 5760, 7200
the base of a right prism is an equilateral triangle each of whose sides measures 4cm.the altitude of the prism measures 5cm.Find the volume of the prism
Answer:
[tex]V=34.64\ cm^3[/tex]
Step-by-step explanation:
Given that,
The side of an equilateral prism = 4 cm
The altitude of the prism = 5 cm
We need to find the volume of the prism. The formula for the volume of a prism is as follows :
[tex]V=A\times h[/tex]
Where
A is the area of equilateral triangle, [tex]A=\dfrac{\sqrt3}{4}a^2[/tex]
So,
[tex]V=\dfrac{\sqrt3}{4}a^2\times h\\\\V=\dfrac{\sqrt3}{4}\times 4^2\times 5\\\\V=34.64\ cm^3[/tex]
So, the volume of the prism is equal to [tex]34.64\ cm^3[/tex].
Help and explain pls and ty
Answer:
(g ￮ f)(3) = 23
Step-by-step explanation:
Evaluate f(3) then substitute the value obtained into g(x)
f(3) = 2(3) + 4 = 6 + 4 = 10 , then
g(10) = 3(10) - 7 = 30 - 7 = 23
What is the equation for the diameter of a circle
Answer:
h
Step-by-step explanation:
Double radius
Determine the length of AC.
32 units
35.2 units
38.5 units
10.3 units
Answer:
38.5
Step-by-step explanation:
b^2= 29^2+20^2-2×20×29× Cos 102
b^2=841+400-1160 (-0.2079)
=1241- 241.164
b^2=1482.164
b= square root of 1482.164
AC = 38.5
Which of the following is the explicit rule for a geometric sequence defined by
a recursive formula of a, - 138-1 for which the first term is 7?
Answer:
C
Step-by-step explanation:
What you wrote is not the same thing as what the question is, or at least I don't think so. I'll answer the printed question.
First of all, the 13 is what separates each of the terms. In other words 7 is the first term. 13 must be raised to the n - 1 power.
It is written like this
an = 7 * 13^(n - 1)
you want a1 to be 7. The only way that can happen is if 13^0 which gives you 1.
So the correct answer is C
Read the following excerpt from a personal narrative essay. Based on the excerpt, what did the writer learn from her personal experience?
Have you ever been canoeing? I went on a canoeing trip with my mom, dad, and two brothers when I turned 13. It was one of the best days of my life. It was exciting, scary, and challenging all at once. At first I couldn’t believe those long, narrow pieces of wood could hold all five of us. But our instructor told us that canoes have been around for many years. He also told us some interesting facts about the history of canoe, like how American Indians used canoes as a way to travel quickly.
He patted the wood of the canoe we would be using. “It’s made of an old tree trunk,” he said.
I asked the question that had been bothering me ever since I saw our canoe. “Can it really hold all of us?” I pointed to my brothers and me. “It looks like the bottom could fall right off.”
The instructor laughed. “Oh, you’ll be surprised how strong this wood is. If our customers were always drowning, we’d have a 'sinking' business on our hands.”
He laughed some more at his own joke. Then he became serious and showed us how to keep our balance while getting into and out of the boat. He also showed me how to grip the paddle so that my left hand would guide the boat and my right hand would give the paddle power.
A.
Canoeing is dangerous, and only people who are experts can do it.
B.
Even events that seem a little scary can turn out to be great.
C.
The best age to go on a canoeing trip is 13.
D.
Canoeing can cause injury if you’re new to the sport.
What is the solution to the equation below. Round your answer to two
decimal places
In x= 3.1
The solution to the equation below rounded to 2 decimal places is 22.20.
How to simplify logarithmic equations?Given the logarithmic expressions
ln x = 3.1
We are to determine the value of "x"
ln x = 3.1
Take the exponent of both sides
e^ln x = e^3.1
The exponent will cancel out the log function to have:
x = e^3.1
x = 22.197
Hence the solution to the equation below rounded to 2 decimal places is 22.20.
Learn more on log function here: https://brainly.com/question/1695836
What is the pH of a solution with a 1.50 × 10−9 M hydroxide ion concentration? (4 points) 0.176 5.18 8.82 9.20
Answer:
5.18
Step-by-step explanation:
This is a chemistry question. However the solution to the problem is given below:
We'll begin by calculating the pOH of the solution. This can be obtained as follow:
Concentration of Hydroxide ion [OH¯] = 1.5×10¯⁹ M
pOH =?
pOH = –Log [OH¯]
pOH = –Log 1.5×10¯⁹
pOH = 8.82
Finally, we shall determine the pH of the solution. This can be obtained as follow;
pOH = 8.82
pH =?
pH + pOH = 14
pH + 8.82 = 14
Collect like terms
pH = 14 – 8.82
pH = 5.18
Therefore, the pH of the solution is 5.18
Answer:
5.18
Step-by-step explanation:
I took the test and got it right!
Solve each system of equations by substitution. Clearly identify your solution.
Answer:
(0, 2)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Coordinates (x, y)Terms/CoefficientsSolving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
y = x + 2
3x + 3y = 6
Step 2: Solve for x
Substitution
Substitute in y [2nd Equation]: 3x + 3(x + 2) = 6[Distributive Property] Distribute 3: 3x + 3x + 6 = 6Combine like terms: 6x + 6 = 6[Subtraction Property of Equality] Subtract 6 on both sides: 6x = 0[Division Property of Equality] Divide 6 on both sides: x = 0Step 3: Solve for y
Substitute in x [1st Equation]: y = 0 + 2Add: y = 2Answer:
(0, 2)
Step-by-step explanation:
Since y is x + 2, we can replace y with x + 2
3x + 3y = 6
3x + 3(x+2) = 6
3x + 3x + 6 = 6
6x + 6 = 6
6x = 0
x = 0
y = x + 2
y = 2
Now we can check by replacing x with 0
3x + 3y = 6
3(0) + 3y = 6
0 + 3y = 6
3y = 6
y = 2
The following list shows how many brothers and sisters some students have: 3, 4, 4, 5, 5, 3, 2, 4, 6, 3, 6, 4, 2 State the mode.
Answer:
mode is 4
it has the highest occurrence
Answer:
The mode is 4
Step-by-step explanation:
The mode is a value that appears most frequently in a data set.
By looking at all the numbers, the number 4 appears the most: a total of four times.
Hope it helps (●'◡'●)
Thank you very much you can help me with the others that I am uploading to my profile and there is more in case you can please
Answer: y = 2x + 20; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 20.
Step-by-step explanation:
Because it's time, it don't have to be just integers. Seconds are fractions of minutes.(0,20) is the y-intercept and there will be no smaller y-values because x(time) cannot go negative.He goes at a rate of a problem per 2 minutes, so 2 is his slope.Answer:
The second one is the answer.
Step-by-step explanation:
Objective: Linear Equation Problems.
Let model the equation given to us.
Vlad spent 20 minutes on his homework already and he complete x math problems every 2 minutes so we represent this as
[tex]y = 2x + 20[/tex]
X can be any real number greater than or equal zero because time isnt negative so anything below zero is wrong.
Y can be any real number but however since Vlad spent 20 mins on his homework already, he must spend over or equal to 20 minutes completing the total homework.
The second one is the answer
At a school picnic, your teacher asks you to mark a field every 10 yards so students can play football. The teacher accidentally gave you a meter stick instead of a yard stick. How far apart in meters should you mark the lines if you still want them?
Answer:
9.144 meters
.
Step-by-step explanation:
.
Answer:
Step-by-step explanation:
The conversion factor of meters to yards is 1 yard = 0.9144 meters
So set up a proportion
1 yard/0.9144 meters = 10 yards / x Cross multiply
x = 0.9144 * 10
x = 9.144 meters.
In the diagram, what is m NSR?
RU is a line which needs to equal 180 degrees. This means angle VSR + VSU needs to equal 180.
VSU = 100
VSR = 180 - 100 = 80
Answer: VSR = 80
Answer:
∠ VSR = 80°
Step-by-step explanation:
∠ VSR and ∠ VSU are adjacent angles and sum to 180° , then
∠ VSR + 100° = 180° ( subtract 100° from both sides )
∠ VSR = 80°
Using the table below, what is the rate of change? Don't forget to include your units.
Number of sodas 24
28
32
36
Total Cost ($)
18
21
24
27
Answer:
0.75
Step-by-step explanation:
Given the table :
Number of sodas 24
28
32
36
Total Cost ($)
18
21
24
27
The rate of change :
Rate of change = Rise / Run
Rise = y2 - y1 ; Run = x2 - x1
From the table :
Take number of sodas as X - axis
Total cost as Y - axis
Taking the points :
(24, 18) ;(36, 27)
x1 = 24 ; x2 = 36
y1 = 18 ; y2 = 27
Rise = (y2 - y1) = (27 - 18) = 9
Run = (x2 - x1) = (36 - 24) = 12
Rate of change = 9 / 12 = 0.75
Y varies directly as x and k = 5
Y=kx
Find y when x = 5
Answer:
y = 25
Step-by-step explanation:
Given y = kx and k = 5 then
y = 5x ← equation of variation
When x = 5 , then
y = 5 × 5 = 25
How do I do this problem?
Step-by-step explanation:
here is the answer to your question
Answer:
Step-by-step explanation:
I would start from the beginning and find the slope myself, just so I know what's going on (as opposed to being dropped in the middle of the problem). The slope formula is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] and for us:
[tex]m=\frac{5-3}{4-3}=2[/tex] so the slope is indeed 2. Now we need to write the equation in slope-intercept form. I find it easier to first write the equation in point-slope form and then solve it for y. Point-slope form is
[tex]y-y_1=m(x-x_1)[/tex] where m is the slope (2) and x1 and y 1 are from one of the coordinates (whichever one you want; as long as you do the math correctly, you will NOT get an incorrect answer. In other words, you can't pick the "wrong" point to use to write the equation.) I'm going to use (3, 3):
y - 3 = 2(x - 3) and
y - 3 = 2x - 6 and
y = 2x - 6 + 3 so
y = 2x - 3 and that's your equation. Of course, you will enter a (-3) in that box with the ? in it.
!!!PLEASE HELP!!!
explain the error
Answer:
Step-by-step explanation:
x is greater than minus 3. You have everything right but the graph. The arrowhead goes the other way. Around -3 is as small as x gets.
0====0====0====0====0
-3 -2 -1 O 1
O------------------------------->
Parallelogram A B C D is shown. Line segment X Y goes from point X on side A B to point Y on side C D to form 2 trapezoids.
Figure ABCD is a parallelogram. Two trapezoids are created using line segment XY such that AX ≅ CY.
What is true about the areas of the trapezoids?
Each area is equal to half of the area of ABCD.
The area of AXYD is less than the area of BXYC.
The area of AXYD is greater than the area of BXYC.
Each area is equal to the area of ABCD.
Answer:
Each area is equal to half the area of ABCD
Step-by-step explanation:
AX ≅ CY
In parallelogram, opposite sides are equal.
AB = CD
AX + XB = CY + YD
CY + XB = CY + YD
XB = CY + YD - CY
XB = CY
Both trapezoids have equal area
Area of AXYD + area of BXYC = area of ABCD
Answer:
A. ) Each area to equal to half of the area of ABCD
Step-by-step explanation:
Edge 2021
An operator in the plant receives a monthly salary. His rent, which is $849, takes up exactly 1/3 13 of his pay. What is his total pay per month?
Answer:
Below.
Step-by-step explanation:
(1/3)X = 849
x = 849*3 = 2547
The total pay per month of an operator is equal to $2547.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that an operator in the plant receives a monthly salary. His rent, which is $849, takes up exactly 1/3.
The total monthly salary will be calculated as,
(1/3)X = 849
X = 849 x 3
X= 2547
Therefore, the total pay per month of an operator is equal to $2547.
To know more about an expression follow
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A mortgage can take up to 25 years to pay off. Taking a $250,000 home, calculate the month-end payment for 15-, 20-, and 25-year periods using semi-annually compounded interest rates of 4%, 5.5%, and 7% for each period. What do you observe from your calculations?
Answer:
a-1. Using semi-annually compounded interest rates of 4%, or 0.04, we have:
M15 = $2,389.13
M20 = $2,091.10
M25 = $1,929.54
a-2. Using semi-annually compounded interest rates of 5.5%, or 0.055
M15 = $2,841.49
M20 = $2,580.47
M25 = $2,450.28
a-3. Using semi-annually compounded interest rates of 7%, or 0.07
M15 = $3,329.35
M20 = $3,108.80
M25 = $3,009.40
b-1. It can be observed that there is a negative relationship between the month-end payment and the payment period.
b-2. It can be observed that there is a positive relationship between the month-end payment and the semi-annually compounded interest rate.
Step-by-step explanation:
The month-end payment for each period can be calculated using the formula for calculating the present value (PV) of an ordinary annuity as follows:
Mn = PV / ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)
Where;
Mn = month-end payment for a particular year period = ?
PV = Present value or home value = $250,000
r = Monthly interest rate = semiannual interest rate / 6 months
n = number of months = Number of years * 12 months
Using equation (1), we have:
a. Calculate the month-end payment for 15-, 20-, and 25-year periods using semi-annually compounded interest rates of 4%, 5.5%, and 7% for each period.
a-1. Using semi-annually compounded interest rates of 4%, or 0.04
M15 = $250,000 / ((1 - (1 / (1 + (0.04/6)))^(15*12)) / (0.04 / 6)) = $2,389.13
M20 = $250,000 / ((1 - (1 / (1 + (0.04/6)))^(20*12)) / (0.04 / 6)) = $2,091.10
M25 = $250,000 / ((1 - (1 / (1 + (0.04/6)))^(25*12)) / (0.04 / 6)) = $1,929.54
a-2. Using semi-annually compounded interest rates of 5.5%, or 0.055
M15 = $250,000 / ((1 - (1 / (1 + (0.055/6)))^(15*12)) / (0.055 / 6)) = $2,841.49
M20 = $250,000 / ((1 - (1 / (1 + (0.055/6)))^(20*12)) / (0.055 / 6)) = $2,580.47
M25 = $250,000 / ((1 - (1 / (1 + (0.055/6)))^(25*12)) / (0.055 / 6)) = $2,450.28
a-3. Using semi-annually compounded interest rates of 7%, or 0.07
M15 = $250,000 / ((1 - (1 / (1 + (0.07/6)))^(15*12)) / (0.07 / 6)) = $3,329.35
M20 = $250,000 / ((1 - (1 / (1 + (0.07/6)))^(20*12)) / (0.07 / 6)) = $3,108.80
M25 = $250,000 / ((1 - (1 / (1 + (0.07/6)))^(25*12)) / (0.07 / 6)) = $3,009.40
b. What do you observe from your calculations?
Two things can be observed from the calculations:
b-1. At a particular semi-annually compounded interest rate, the month-end payment decreases as the payment period increases. This implies that there is a negative relationship between the month-end payment and the payment period.
b-2. At a particular payment period, the month-end payment increases as the semi-annually compounded interest rate increases. This implies that there is a positive relationship between the month-end payment and the semi-annually compounded interest rate.
What does 8 represent in the decimal 478.92
A. Tenths
B. Hundreds
C. Dozen
D. Units
Answer:
Units
Step-by-step explanation:
From the value above 478.92
4 represents hundreds
7 represents tens
8 represents units
Hence the answer is units
someone help me please
Answer:
1, 3, 4
Step-by-step explanation:
Points N and K are on plane A and plane S
Point P is the intersection of the line n and line g
Points M, P, and Q are noncollinear
What's the answer for m⁶ - 25
Step-by-step explanation:
[tex] {m}^{6} - 25 \\ { {m}^{3} }^{2} - {5}^{2} \\ x = {m}^{3} b = 5 \\ ( {m}^{3} - 5)( {m}^{3} + 5)[/tex]
Please someone help I can not get past this question
Answer:
65.76 m
Step-by-step explanation:
This figure is split into three shapes: a right triangle, a rectangle, and a semi- circle. To find the area of the figure you can start by figuring out the area of each of the three shapes mentioned above, then adding their areas together. I'll write the numbers without the unit to make it simpler since it won't cancel out or anything.
Starting with the triangle:
1/2(b*h)=a
We see the base is 3, and the height is 5 (because the two opposite sides of a rectangle will be congruent) so if you plug the numbers into the formula you get:
1/2*15=a or 15/2=a
a=7.5
Then we calculate the area of the rectangle:
l*w=a
5*6=a
30=a
Then the area of the semi circle:
First we find the area as if it were a full circle by the equation using 3.14 as pi and 3 as r (since the denominator is 6 and half of 6 is 3):
3.14*r^2=a
3.14*3^2=a
3.14*9=a
28.26=a
Finally, we add all three areas from above:
7.5+30 + 28.26 = 65.76
Find the area of the rhombus
Answer:
The rhombus has an area of 240 units. (2nd one on the left).
Step-by-step explanation:
The intersection of diagonals meet at right angles. That means that the labeled sides are the hypotenuse and 1 leg of a right angle triangle. You need to find the other leg by using the Pythagorean Theorem
a^2 + b^2 = c^2
a = 8
b = ?
c = 17
8^2 + b^2 = 17^2
64 + b^2 = 289 Subtract 64
b^2 = 289-64
b^2 = 225 Take the square root of both sides.
sqrt(b^) = sqrt(225)
b = 15
Find the area of 1 triangle
Area = 1/2 * a * b
a = 8
b = 15
Area = 1/2 * 8 * 15
Area = 60
Now find the area of 4 triangles.
4*60 = 240