Answer:
6400
Step-by-step explanation:
We have 1 + 3 + 5 + ... + 155 + 157 + 159.
We can use Gauss's strategy.
Since we are adding 80 numbers, there are 40 pairs. Each pair adds up to 1 + 159 = 160. (Notice that 3 + 157, 5 + 155 = 160)
Thus, because there are 40 pairs and each pair adds up to 160, we have 160 * 40 = 6400.
I hope this helps!
5. Which of the following is an arithmetic
sequence?
A
B
C
D
-2, -5, -8, -11, -14, -17, ...
0,5, 0, 10, 0, 15, ...
2, 4, 8, 16, 32, ...
5, 11, 17, 23, 29, 36, ...
Answer:
A. -2, -5, -8, -11, -14, -17, ...
Step-by-step explanation:
The difference between consecutive terms is constant.
Which of the following expressions are equivalent to 16/24? Select all that apply.
After evaluation, we can conclude that the expression (E) 8/2 * 2/12 is equivalent to the given expresion 16/24.
What are expressions?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
It's possible to multiply, divide, add, or subtract with this mathematical operation.
You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression.
So, we have the expression:
16/24
We need to find the equivalent expression from the options as follows:
So, let's take option (E) as it seems the answer and evaluation is:
8/2 * 2/12 (Be LHS)
Now, multiply:
8/2 * 2/12 = 16/24
16/24 = 16/24
Therefore, after evaluation, we can conclude that the expression (E) 8/2 * 2/12 is equivalent to the given expression 16/24.
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which statement must be true?
Answer:
DF=FE
Step-by-step explanation:
first to make it easier we can find the angles to each side
the sum of all angles of a triangle equal 180 degrees so to find x we set all the angles equal to 180
(3x+5)+(4x-15)+(2x+10)=180
9x+0=180
/9. /9
x=20
now we can find each angle
3(20)+5
60+5
D=65 degrees
4(20)-15
80-15
E= 65 degrees
2(20)+10
40+10
F=50 degrees
Angle D and E are the only angles equal to each other so answer C and d ARE INCORRECT
Since there are 2 of the same angles this is an isosceles triangle
the 2 of the same angles are the base so the side going up are connecting to the top angle F so the sides will be DF and FE and these are equal
hopes this helps
complete this working to write 9³ as a power of 3
9³=9x9x9
so 9³= 3x3x3x ____
so 9³=3^y where y=____
Answer: y=6
Step-by-step explanation:
Describe the 3-D figure that would be formed if the figure is rotated about the y-axis. (You can say what it looks like.)
By completing a complete revolution on the soda can-like profile about the y-axis to generates a cylinder-like solid that is the result of the combination of three cones and a cylinder.
What kind of solid is generated by rotating a profile about the y-axis?
In this problem we find a representation of a soda can-like profile, whose complete revolution generates a cylinder-like solid. This solid is the result of the combination of three truncated cones (lower trucated cone, middle cone, upper cone) and a cylinder (right cylinder). There are two axes for the rotation, a horizontal axis (x-axis) and a vertical axis (y-axis).
The first axis, that is, the horizontal axis, is along the base of the can-like profile and the second axis, that is, the vertical axis, is along a side of the can-like profile. The solid of revolution is generated by rotating around the y-axis.
In consequence, the solid generated by a revolution creates a soda can-like profiles as the result of combining three truncated cones and a cylinder.
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PLEASE EXPLAIN WHY YOU GOT YOUR ANSWER PLEASEE!!!!
When Skip was a puppy, he weighed 5.6 lbs. When he visited the vet, he weighed 13.3 lbs. How much weight did Skip gain between the time he was a puppy and his vet visit?
Answer:
7.7
Step-by-step explanation:
I got this by subtracting 13.3 - 5.6
Alonso went to the market with \$55$55dollar sign, 55 to buy eggs and sugar. He knows he needs a package of 121212 eggs that costs \$2.75$2.75dollar sign, 2, point, 75. After getting the eggs, he wants to buy as much sugar as he can with his remaining money. The sugar he likes comes in boxes that each cost \$11.50$11.50dollar sign, 11, point, 50
The number of boxes of sugar that Alonso can buy are 4.5 boxes.
What is a mathematical function, equation and expression? function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that Alonso went to the market with $55 to buy eggs and sugar. He knows he needs a package of 12 eggs that costs $2.75. After getting the eggs, he wants to buy as much sugar as he can with his remaining money.
The money remaining after buying 12 eggs : {r} = $(55 -2.75).
Cost of one box of sugar = $11.5
The number of boxes that he can buy are -
n = (55 - 2.75)/11.5
n = 4.5 boxes {approx.}
Therefore, the number of boxes of sugar that Alonso can buy are 4.5 boxes.
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A beetle is moving along a straight line at a constant rate. It moves 23 of a foot in 15 of a minute.
What is the average speed of the beetle?
The average speed of the beetle is 1.53 feet per minute.
What is the average speed?Average speed is calculated by dividing a quantity by the time required to obtain that quantity. Meters per second is the SI unit of speed. The formula S = d/t, where S is the average speed, d is the total distance, and t is the total time, is used to determine average speed.
Given that, it moves 23 of a foot in 15 of a minute.
Here, the average speed
= 23/15
= 1.53 feet per minute
Therefore, the average speed of the beetle is 1.53 feet per minute.
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the interior angles of a regular polygon each measures 165 degrees. how many sides does the polygon have
Number 49. Please help Graphing inequalities? Why is the answer A? Please do a step by step explanation for each answer choice.
I don't see the picture. Can you send it in the message.
what is the product of each equation?
[tex]\left(3a^{2}b^{4}\right)\left(-8ab^{3}\right)[/tex]
[tex]\left(3a^{2}b^{7}\right)\left(5a^{3}b^{8}\right)[/tex]
[tex]\left(-2d^{2}+s\right)\left(5d^{2}-6s\right)[/tex]
[tex]\left(3x-6\right)\left(2x^{2}-7x+1\right)[/tex])
[tex]\left(7x^{2}y^{3}\right)\left(3x^{5}y^{8}\right)[/tex]
[tex]\left(y^{2}+3y+7\right)\left(8y^{2}+y+1\right)[/tex]
[tex]\left(4s+2\right)\left(5s^{2}+10s+3\right)[/tex]
The solution to the products of exponents is as follows;
1) -24a³b⁷
2) 15a⁵b¹⁵
3) -10d⁴ + 17sd² - 6s²
4) 6x³ - 33x² + 45x - 6
5) 21x⁷y¹¹
6) 8y⁴ + 25y³ + 60y² + 10y + 7
7) 20s³ + 50s² + 32s + 6
How to find product of exponents?The Product of Powers Property of exponents states that when we multiply two powers with the same base, we add the exponents.
1) (3a²b⁴) * (-8ab³)
= -24a³b⁷
2) (3a²b⁷) * (5a³b⁸)
= 15a⁵b¹⁵
3) (-2d² + s)(5d² - 6s)
Expanding the bracket to get;
(-10d⁴ + 5sd² + 12sd² - 6s²)
= -10d⁴ + 17sd² - 6s²
4) (3x - 6) * (2x² - 7x + 1)
= 6x³ - 33x² + 45x - 6
5) (7x²y³) * (3x⁵y⁸)
= 21x⁷y¹¹
6) (y² + 3y + 7) * (8y² + y + 1)
= 8y⁴ + 25y³ + 60y² + 10y + 7
7) (4s + 2) * (5s² + 10s + 3)
= 20s³ + 50s² + 32s + 6
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what is the slope if the line that passes through the points (10,8) and (7,14)? write your answer in simplest form
Answer:
-2
Step-by-step explanation:
we use the y2-y1/x2-x1 fomrula to find slope
14-8/7-10
6/-3
-2 is the slope
hopes this helps
will mark brainliest pls
-photo is attached ! :)
The figures are similar, and the ratio of the perimeters is 2: 5. Find x.
Answer: x=3.2
Ste by Step
We have that for the Question "The figures are similar, and the ratio of the perimeters is 2 : 5. Find x." it can be said that the perimeters of x is
x=3.2
From the question we are told
The figures are similar, and the ratio of the perimeters is 2 : 5. Find x.
Generally the equation for the the ratio is mathematically given as
2=x
and
5=8
Therefore
x=3.2
Therefore
the perimeters of x is
x=3.2
Yujin Pon has a principal of $900 in her savings Iccount on October 1. The money earns interest at a rate of 6.5% compounded quarterly until July 1 of the following year. What is the amount in the account on July 1?
а.$914.63
b. $943.75
c.$943.87
d. $944.59
Answer: The correct answer is c. $943.87.
Step-by-step explanation: To solve this problem, we need to first determine the length of time between October 1 and July 1 of the following year. This is a period of 9 months, or 3 quarters. We can then use this information to calculate the amount of interest earned over this time period.
The principal in Yujin Pon's account is $900, and the interest rate is 6.5% compounded quarterly. This means that for each quarter, the account will earn 6.5/4 = 1.625% in interest. Over the 3 quarters between October 1 and July 1 of the following year, the account will earn a total of 1.625% * 3 = 4.875% in interest.
To calculate the amount of interest earned, we can multiply the principal by the interest rate:
Interest = Principal * Interest Rate
= $900 * 0.04875
= $43.87
The total amount in the account on July 1 will be the original principal plus the amount of interest earned over the 3 quarters:
Total = Principal + Interest
= $900 + $43.87
= $943.87
Therefore, the correct answer is c. $943.87.
PLease help meh im begging you
Determine the measurement of ∠A, the angle marked in red.
The measure of ∠A is __________Degrees?
Answer:
x= 222 degress
Step-by-step explanation:
Name the property of real numbers illustrated by the equation. -2(x 4)=-2x-8
Distributive property of real numbers illustrated by the equation. -2(x 4)=-2x-8
The equation -2(x 4)=-2x-8 is an example of the distributive property of real numbers. This property states that when a number is multiplied by a group of numbers that are being added together, the number can be distributed to each of the terms in the group. To rewrite this equation as -2x + (-2)(-4) = -2x - 8, the number -2 is allocated to each of the terms in the group (x and -4) in this equation.Simplifying further, we get -2x - 8 = -2x - 8.
-2(x 4) = -2x - 8
Distribute -2 to each term in the group
-2x + (-2)(-4) = -2x - 8
Simplify
-2x - 8 = -2x – 8
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Which number line shows the solutions to n > -2?
++++
+
-6-5-4-3-2-1 0 1 2 3 4 5 6
←++++
H
-6-5-4-3 -2 -1 0 1 2 3 4 5 6
+++
++++++
-6-5-4-3-2-1 0 1 2 3 4 5 6
+++++
-6-5-4-3-2-1 0 1 2
3 14 5 6
Done -
2
what is the value of 18 to the third power
Answer:
5832
Step-by-step explanation:
A kangaroo hopped directly toward a lake at a constant velocity for 30seconds. In one-third of that time, the kangaroo hopped 60meters. What was the kangaroo's velocity?
Answer: The animal hopped 60 meters in 10 seconds
6 m/s (lol)
Step-by-step explanation:
First off ok and second off bye <3
17. Select the correct inequality and graph for the statement.
The highest temperature possible today is 95 °F.
The correct inequality for the statement - highest temperature possible today is 95 °F
x ≤ 95 °F
How to identify the correct statementThe statement saying the highest temperature possible today is 95 °F is represented by
knowing that the temperature will never be greater than 95 °F, hence the temperature values is from 95 °F and downwards
assuming x represents the measles of the temperatures then
x is less than or equal to 95 °F means x can be any value but never greater than 95 °F
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If using the method of completing the square to solve the quadratic equation x 2 + 2 x + 16 = 0
Answer:
Step-by-step explanation:
[tex]x^{2} +2x+16=0\\x^{2} +2x+1-1+16=0\\(x^{2} +2x+1)-1+16=0\\(x+1)^{2} +15=0\\(x+1)^{2}=-15[/tex]
The solution does not exist because all numbers squared are greater than zero.
write 987.6 in scientific notation
987.6 million written in scientific notation is 9.876 × [tex]10^{8}[/tex]
What is scientific notation?
Scientific notation is basically a shortcut for writing numbers. It is a method of expressing real numbers in terms of a significand, multiplied by a power of 10.
When using scientific notation, you're allowed to simplify all the zeros that you have in the number by writing the number as a product of a number and a power of 10. 987.6 million in exponential form is [tex]a^{b}[/tex], a is the base, and b is called the exponent . The term [tex]a^{b}[/tex] is called the exponential expression. 987.6 million = 9.876 x 100,000,000 = 9.876 ×[tex]10^{8}[/tex].
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49: 1 of 1 question 2 with 1 blank 97: 1 of 1 question 3 with 1 blank 113: 1 of 1 question 4 with 1 blank 632: 1 of 1 question 5 with 1 blank 1.781: 1 of 1 question 6 with 1 blank 3.558: 1 of 1 question 7 with 1 blank 1.006.015: 1 of 1 question 8 with 1 blank 67.224.370: 1 of 1 3
Spanish is a Romance language of the Indo-European language family that emerged from the Iberian peninsula's colloquial Latin. It is now a worldwide language with around 500 million native speakers, primarily in the Americas and Spain. Twenty nations have Spanish as their official language.
These numbers in Spanish are:
1. 49: cuarenta y nueve
2. 97: noventa y siete
3. 113: ciento trece
4. 632: seiscientos treinta y dos
5. 1.781: mil setecientos ochenta y uno
6. 3.558: tres mil quinientos cincuenta y ocho
7. 1.006.015: un millon seis mil quince
8. 67.224.370: sesenta y siete millones doscientos veinte y cuatro mil trescientos setenta
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Answer:
49: cuarenta y nueve
2. 97: noventa y siete
3. 113: ciento trece
4. 632: seiscientos treinta y dos
5. 1.781: mil setecientos ochenta y uno
6. 3.558: tres mil quinientos cincuenta y ocho
7. 1.006.015: un millon seis mil quince
8. 67.224.370: sesenta y siete millones doscientos veinte y cuatro mil trescientos setenta
Step-by-step explanation:
browns are expected to win with probability of 60% against their opponent, while steelers are also expected to win with probability of 40% against their opponent. the outcome of each game can be either a win or a loss (i.e., no ties). if you bet $10 on one of these two teams to win and another one to lose, no matter which one wins or loses, i.e., your bet is that only one team (browns or steelers) wins, what net payout will you be promised in a fair betting game in case your bet works out?
Net payout will you be promised in a fair betting game in case your bet works out is $0 .
Given :
browns are expected to win with probability of 60% against their opponent, while steelers are also expected to win with probability of 40% against their opponent. the outcome of each game can be either a win or a loss (i.e., no ties). if you bet $10 on one of these two teams to win and another one to lose, no matter which one wins or loses, i.e., your bet is that only one team (browns or steelers) wins .
P ( browns ) = 60 / 100 = 0.60
P ( steelers ) = 40 / 100 = 0.40
Net payout = Number of wins * 10 - Number of loses * 10
= 1 * 10 - 1 * 10
= 10 - 10
= $0.
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What is 213 divided? Also how do you break 23 into tens and ones?
Answer:
What is 213 divided? 2 I think
Also how do you break 23 into tens and ones? It would be 2 tens and then it would be 3 ones
What is the area of triangle lmn? round to the nearest square meter. 3 square meters 9 square meters 28 square meters 34 square meters
9 square meters is the area of triangle LMN. Using the concept of Heron's formula.
What is Heron's formula?Heron of Alexandria is credited with creating Heron's formula, which determines a triangle's area by dividing the lengths of its sides. if the side lengths are represented in symbols by a, b, and c.
According to Heron's formula the area = √s (s - a)(s - b)(s - c)
A triangle's semi-perimeter, whose area has to be calculated, is represented by the letter s in Heron's formula. s = (a+b+c)/2 is the formula for the triangle's semi-perimeter, which is the sum of its three sides.
a triangle with three sides, a, b, and c.
given data was LM = 7,MN = 6 and perimeter was given by 16m
As we know perimeter is the sum of all the sides
so, Perimeter=LM + MN + NL
NL=Perimeter-(LM+MN)
NL=16 - 7 - 6
NL= 3
By Heron's formula,
Area = √[(s(s-a)(s-b)(s-c)].
where s = perimeter/2
so, s = 16/2 = 8
area = √[(8(8-7)(8-6)(8-3)]
area = 8.94427191 ≈ 9 square meters.
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Answer: 9m
Step-by-step explanation:
Find the sum of 5.21 × 1019 and 3.149 × 1017.
A. 8.359 × 1019
b. 5.24149 × 1019
c. 5.24149 × 1036
d. 8.359 × 1036
Answer:
B
Step-by-step explanation:
5.21 x 10^19 + 3.149 x 10^17
10^17(5.21 x 10^2 + 3.149)
10^17(521 + 3.149)
10^17(524.149)
5.24149 x 10^17 x 10^2
5.24149 x 10^(17+2)
5.24149 x 10^19
Answer: b. 5.24149 × 1019
Step-by-step explanation: I took the test
A manager of a self-service car wash charges a flat fee in addition to a fee per minute, x, for use of the services. The expression 5+0.75x models the scenario.
Which statement is true?
Responses
The coefficient 5 represents a cost of $5 per minute for use of the services, while the term 0.75x represents the flat fee of $0.75.
The coefficient 5 represents the flat fee of $5, while the term 0.75x represents a cost of $0.75 per minute for use of the services for x minutes.
The constant 5 represents a cost of $5 per minute for use of the services, while the term 0.75x represents the flat fee of $0.75.
The constant 5 represents the flat fee of $5, while the term 0.75x represents a cost of $0.75 per minute for use of the services for x minutes.
The constant 5 represents the flat fee of $5, while the term 0.75x represents a cost of $0.75 per minute for use of the services for x minutes. Therefore, option D is the correct answer.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given expression is 5+0.75x.
In the given expression, 5 is constant term and 0.75x is another term.
In the term 0.75x, 0.75 is the coefficient of x
In the expression 5+0.75x, 5 is fixed price and 0.75 is price for second or minute or hour or year and x can be number seconds or minutes or hours or years.
Therefore, option D is the correct answer.
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Insert terms to make a identity replace *
(15x+*)^2=225x^2+90xy+*
Answer:
3y, 9y²
Step-by-step explanation:
We use laws of binomial
(a+b)²=a²+2ab+b²
From this, we get
15x × * × 2 = 90xy
2×*=6y
*=3y
Now, we square this term to get the last term
3y×3y=9y²
If using the method of completing the square to solve the quadratic equation x 2 + x + 9 = 0, which number would have to be added to "complete the square"?
Answer:
Below
Step-by-step explanation:
To complete the square, the coefficient of x^2 must be 1 ( it is already)
then take 1/2 of the x coefficient .... 1/2.... square it and add it to both sides of the equation
x^2 + x + 1/4 + 9 = 1/4
then you can reduce this to
( x+ 1/2)^2 + 9 = 1/4 for further 'solving'
