Answer:
7.62
Step-by-step explanation:
Simplify the following:
7 + 6/10 + 2/100
Express 6/10 in its lowest form by cancelling out gcd(6, 10) = 2 from the numerator and denominator. 6/10 = (2×3)/(2×5) = 3/5:
7 + 3/5 + 2/100
Express 2/100 in its lowest form by cancelling out gcd(2, 100) = 2 from the numerator and denominator. 2/100 = (2×1)/(2×50) = 1/50:
7 + 3/5 + 1/50
Put 7 + 3/5 + 1/50 over the common denominator 50. 7 + 3/5 + 1/50 = (50×7)/50 + (10×3)/50 + 1/50:
(50×7)/50 + (10×3)/50 + 1/50
50×7 = 350:
350/50 + (10×3)/50 + 1/50
10×3 = 30:
350/50 + 30/50 + 1/50
350/50 + 30/50 + 1/50 = (350 + 30 + 1)/50:
(350 + 30 + 1)/50
| 3 | 5 | 0
| | 3 | 0
+ | | | 1
| 3 | 8 | 1:
Answer: |
| 381/50
3) n+ 5(n-1) = 7
4) 15=-2(2t - 1)
Answer:
3. n = 2
4. t = -13/4
Step-by-step explanation:
3)
. . . . (3a) Distribute (multiply) +5 into the expression (n-1)
. . . . . . . . [tex]n + 5n - 5 = 7[/tex]
. . . . (3b) Add like terms (terms with the same variable)
. . . . . . . . [tex]6n - 5 = 7[/tex]
. . . . (3c) Add 5 on both sides of the equation to "get rid" of the -5
. . . . . . . . [tex]6n -5 +5 = 7 +5[/tex]
. . . . . . . . [tex]6n = 12[/tex]
. . . . (3d) Divide both sides by 6 to isolate the variable
. . . . . . . . [tex]6n/6 = 12/6[/tex]
. . . . . . . . [tex]n = 2[/tex]
4)
. . . . (4a) Distribute (multiply) -2 into the expression (2t-1)
. . . . . . . . [tex]15 = -4t + 2[/tex]
. . . . (4b) Subtract 2 on both sides of the equation to "get rid" of the +2
. . . . . . . . [tex]15 -2 = -4t +2 -2[/tex]
. . . . . . . . [tex]13 = -4t[/tex]
. . . . (4c) Divide both sides by -4 to isolate the variable
. . . . . . . . [tex]13/-4 = -4t/-4[/tex]
. . . . . . . . [tex]-13/4 = t[/tex]
HELP
Michelle jogs 3 miles in 36 minutes. At the same rate, how many miles would she jog in 60 minutes?
A. 6.5
B. 6
C. 4.5
D. 5
Explain you work pls
Answer:
d) 5 miles
Step-by-step explanation:
Minutes for jogging 1 mile is,
→ 36/3
→ 12 minutes
Formula we use,
→ Total time ÷ Time needed for 1 mile
Then the distance she cross in 60 min,
→ 60 ÷ 12
→ 5 miles
Hence, she will cross 5 miles.
Sofia is 1. 35 meters tall. At 11 a. M. , she measures the length of a tree's shadow to be 23. 55 meters. She stands 18. 1 meters away from the tree, so that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
The height of the tree, calculated according to the details of shadow and Sofia's height, to the nearest hundredth of a meter is 5.83 meters.
The tangent of angle of elevation will be equal to the ratio of height of tree ÷ distance from the tip shadow. The tangent will be same for both tree and the girl. Le the height of tree be x.
x/23.55 = 1.35/(23.55-18.1)
Performing subtraction on Right Hand Side of the equation
x/23.55 = 1.35/5.45
Rewriting the equation with x
x = (1.35×23.55)/5.45
Performing multiplication on Right Hand Side of the equation
x = 31.79/5.45
Performing division on Right Hand Side of the equation
x = 5.83 meters
Thus, tree is 5.83 meters tall.
Learn more about angle of elevation -
https://brainly.com/question/88158
#SPJ4
f central pennsylvania had a really dry year, and received only one-third of our usual rainfall, we would be just dry enough to be a called a desert if such dry years stayed for a long time. how much rainfall per year would we be receiving per year then? (in an average year, pennsylvania gets about the same amount
Approximately 3.3 inches of rainfall per year.
If central Pennsylvania received only one-third of the usual rainfall in a really dry year, it would be receiving 1/3 * the usual amount of rainfall per year.
In an average year,
Pennsylvania gets about the same amount of rainfall as a desert, which is typically defined as an area that receives less than 10 inches of precipitation per year.
Therefore, if central Pennsylvania received only one-third of the usual amount of rainfall in a really dry year, it would be receiving,
1/3 * 10 inches = approximately 3.3 inches of rainfall per year.
This amount of rainfall is significantly less than the average rainfall in Pennsylvania and would qualify as a desert if it persisted over a long period of time.
Hence, Approximately 3.3 inches of rainfall per year.
To know more about Average visit,
https://brainly.com/question/20118982
#SPJ4
How do you prove AAS congruence?
To prove AAS congruence, we need to show that the angles and included sides of the two triangles are equal.
For example, consider two triangles ABC and DEF. If we know that ∠A = ∠D, ∠B = ∠E, and BC = DE, we can use the AAS theorem to conclude that triangle ABC is congruent to triangle DEF. To prove this congruence, we can set up the following system of equations:
∠A = ∠D∠B = ∠EBC = DESolving this system of equations will show that all of the angles and included sides of the two triangles are equal, thereby proving that the triangles are congruent.
Learn more about AAS Theorem here:
https://brainly.com/question/19938973
#SPJ4
4(2x + 5) = [ ]x + [ ]
rewrite using the distributive property
Answer:
Step-by-step explanation:
first you do 4 x 2x=8x
next you do 4 x 5=20
then you get 8x + 20 :)
Which financial tool is most important?
The financial tool that is most important is creating a budget.
What is the financial toll about?The ideal financial instrument for long-term planning objectives is You'll be able to set away money each week or month with the use of a budget.
You may track where your money is going and determine how much you have to spend on items besides expenses by utilizing a budget.
A budget can help you prioritize your spending and saving, and ensure that you have enough money set aside to reach your goals. Here is a step-by-step explanation of how to create a budget:
Learn more about financial tool from
https://brainly.com/question/14234253
#SPJ1
if f(x)=(2x)^2, find f(-4)
Answer:
y=32
Step-by-step explanation:
substitute x for (-4)
(2 x -4)^2= 32
John deposits $500 into a CD that compounds interest monthly. The account pays 5.2% interest. How much is in the account after 2 non-leap years?
By using compound interest, there will be$554.68in the account after 2 years.
What is compound interest?Compound interest is interest that is calculated on the original principal of a loan or deposit, as well as on any accumulated interest from previous periods.
What is the formula to calculate the compound interest?Compound interest is calculated using the following formula:
Compound interest = P * (1 + r/n)^(nt) - P
To calculate the total amount in the account after 2 years, we can use the following formula:
Total amount = P * (1 + r/n)^(nt)
In this formula, P is the principal amount (the initial deposit of $500), r is the annual interest rate (5.2%), n is the number of times that interest is compounded per year (12 in this case, since the interest is compounded monthly), and t is the number of years for which the interest is compounded (2 in this case).
Substituting the given values into the formula, we get:
Total amount = $500 * (1 + 0.052/12)^(12*2) = $554.68
To learn more about compound interest visit:
https://brainly.com/question/14295570
#SPJ1
For what value of A is x 5 a factor of x³ 3x² ax 10?
The Value of a for which (x - 5) is a factor of x³ -3x² +ax -10 is a = -8 .
The Equation is given as x³ -3x² +ax -10 ;
the factor of the above equation is given as (x - 5) ;
Since (x - 5) is given to be a factor ,
we have , x - 5 [tex]=[/tex] 0 ;
On solving ,
we have , x = 5 .
For (x - 5) to be a factor of x³ -3x² +ax -10 ,
x = 5 should satisfy the given equation .
that means ; (5)³ -3(5)² +a(5) -10 = 0 ;
⇒ 125 - 3×25 + 5a - 10 = 0 ;
⇒ 125 - 75 + 5a - 10 = 0 ;
⇒ 50 + 5a - 10 = 0 ;
⇒ 40 + 5a = 0 ;
⇒ 5a = -40 ;
dividing both sides by 5 ,
we get ;
a = -40/5 = -8 .
Therefore , the value of a is "-8" .
The given question is incomplete , the complete question is
For what value of a is (x - 5) a factor of x³ -3x² +ax -10 ?
Learn more about Factors here
https://brainly.com/question/30095829
#SPJ4
How many terms are there in 4xy 5?
The number of terms that the expression 4xy +5 has is 2 terms.
What is an algebraic expression?
An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.
How to determine terms?
To determine the number of terms in an algebraic expression, we only have to count the spaces (addition and/or subtraction symbols) and add the unit, in this way we will have the number of terms.
4xy +5 has 2 spaces
1 + 1 = 2 terms.
Learn more about expression in:
brainly.com/question/27578903
#SPJ4
How do you solve log2 value?
We solve log2 value by following logarithm laws.
What is logarithm?Logarithm is the alternating way of expressing an exponent. The power at which a number is needed to raise so as to obtain the other values is called logarithm.
What does mean by log2?log2 is termed as log base 2 or binary logarithm. It is called the inverse of the power of two function.
How do we solve log2?As stated earlier that Log base 2 is an inverse expression of the power 2.
Suppose N is a real positive number and x is the number of exponents.
Now, logarithm form of this exponent is written
as log2 N = x
2∧x = N
Besides, we can directly get the log2 value by using calculator.
To learn more about logarithm visit:
https://brainly.com/question/14175590
#SPJ4
Lamonte earned $269.10 at his job when he worked for 13 hours. How much money did he earn each hour?
Answer:
Step-by-step explanation:
To solve this problem, we need to divide the total amount of money Lamonte earned ($269.10) by the number of hours he worked (13 hours).
We can write this as an equation as follows:
earnings per hour = $269.10 / 13 hours
To solve for earnings per hour, we can divide both sides of the equation by 13:
earnings per hour = $269.10 / 13 hours / 13 = $269.10 / 13^2 = $269.10 / 169 = $1.60
Therefore, Lamonte earned $1.60 per hour.
What are the factors of x³ Y³?
The factor for (x³ + y³) is (x+ y) (x² + y² - xy).
and, factor for (x³ - y³) is (x - y) (x² + y² + xy)
What are Factors?A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.
Given:
(x³ + y³) or (x³ - y³)
Now using Algebraic identities we have
(x³ + y³)
Using (x+ y)³ = x³ + y³ + 3xy(x+ y)
(x+ y)³ - 3xy(x+ y)= x³ + y³
x³ + y³= (x+y)[ (x+y)² - 3xy]
x³ + y³ = (x+ y) [ x² + y² + 2xy - 3xy]
x³ + y³ = (x+ y) (x² + y² - xy)
and, (x³ - y³)
Using (x- y)³ = x³ - y³ - 3xy(x+ y)
(x - y)³ + 3xy(x- y)= x³ - y³
x³ - y³= (x-y)[ (x-y)² + 3xy]
x³ - y³ = (x - y) [ x² + y² - 2xy + 3xy]
x³ - y³ = (x - y) (x² + y² + xy)
Learn more about factors here:
https://brainly.com/question/14209188
#SPJ4
Convert 39 cups into cubic feet. Round your answer to the nearest hundredth.
Answer: 0.34 cubic feet
What is the variance if the standard deviation is 4?
A candy machine contains over 1{,}0001,0001, comma, 000 pieces of candy, 30\%30%30, percent of which are blue. Customers get an srs of 151515 candies in a purchase. Let x=x=x, equals the number of blue candies that a random customer gets in a purchase.
The mean and the standard deviation of the data of the purchase are 4.5 and 1.8 respectively.
According to the question we can interpret that either the candy will be blue or it will not be blue. We use the method of Binomial distribution because the probability of getting a blue candy is not dependent on any other candy. The formula for expected value of the distribution will be
Expected value = E(X) = np
The standard deviation will be
SD = √(np(1 - p))
Now, from the question, n = 15 and the value of p = 30% = 0.3
putting these values we get
Expected value = E(X) = 15×0.3 = 4.5
SD = √(15×0.3(1 - 0.3))
SD = √4.5×0.7
SD = 1.8
Learn more about Standard deviation at:
brainly.com/question/24261244
#SPJ4
Complete Question:
A candy machine contains over 1,000 pieces of candy, 30% of which are blue. Customers get an SRS of 15 candies in a purchase. Let X= the number of blue candies that a random customer gets in a purchase. Find the mean and standard deviation of X. You may round your answers to the nearest tenth.
The diameter of a circle is 6 meters. What is the length of a 30° arc?
The length of a 30° arc of a circle with a diameter of 6 meters can be calculated using the formula L = θ/360 * π * d, where L is the length of the arc, θ is the angle of the arc in degrees, d is the diameter of the circle, and π is the mathematical constant approximately equal to 3.14. Plugging in the values given in the question, we get L = 30/360 * 3.14 * 6 = 3.14 meters. So, the length of the 30° arc is approximately 3.14 meters.
the primary function of jails is to: group of answer choices a. hold persons for less than 1 year. b. hold persons for more than 1 year. c. hold persons for more than 5 years. d. hold persons for more than 10 years.
The jail's function is to hold inmates (A) for terms that are shorter than a year.
What do we mean by jails?A prison sometimes referred to as a jail, jail, penitentiary, detention center, correction center, correctional institution, lock-up, hoosegow, or remand center, is a place where people are imprisoned against their choice and typically denied a range of freedoms as retribution for various offenses.
The only purpose of a jail is to house inmates for a period of time shorter than a year.
With very few exceptions, modern jails are municipal or county-level detention centers run by local police departments or correctional facilities.
Like their historical forebears, they are employed to hold those who pose a flight risk or a threat to public safety while they await trial.
Therefore, the jail's function is to hold inmates (A) for terms that are shorter than a year.
Know more about jails here:
https://brainly.com/question/10190308
#SPJ4
Statements and Reasons
1) Quadrilateral [tex]ABCD[/tex] with diagonal [tex]\overline{AEC}[/tex] bisecting [tex]\angle DAB[/tex], [tex]\overline{BE}[/tex], [tex]\overline{DE}[/tex], [tex]\angle 1 \cong \angle 2[/tex] (given)
2) [tex]\angle BAE \cong \angle EAD[/tex] (definition of an angle bisector)
3) [tex]\overline{AE} \cong \overline{AE}[/tex] (reflexive property)
4) [tex]\triangle BAE \cong \triangle DAE[/tex] (AAS)
5) [tex]\overline{AB} \cong \overline{AD}[/tex] (CPCTC)
6) [tex]\overline{AC} \cong \overline{AC}[/tex] (reflexive property)
7) [tex]\triangle BAC \cong \triangle DAC[/tex] (SAS)
8) [tex]\overline{BC} \cong \overline{DC}[/tex] (CPCTC)
Answer number 2 or number 3 thank you
Jose can build a wall in 10 hours. Frank can build the same wall in 15 hours. If they work together, they can paint wall in 6 hours.
Define LCM.The least common multiple, or LCM, of two numbers, such as a and b, is written as LCM in mathematics (a,b). The smallest or least positive integer that is divisible by both a and b is known as the LCM. Finding the prime factors of the provided integers and determining the least common multiple are both steps in the prime factorization process (LCM). For instance, use the prime factorization to couple the multiples that are shown to determine the least common multiple of 12 and 16. Together with the other multiples, list them.
Given,
Jose can build a wall in 10 hours
Frank can build the same wall in 15 hours
Together they can paint in,
Taking LCM
1/10 + 1/15
3/30 + 2/30
5/30
1/6
Time taken = 6 hours
If they work together, they can paint wall in 6 hours.
To learn more about LCM, visit:
https://brainly.com/question/20739723
#SPJ1
which expressions are equivalent to -6+3(2+(-4t) choose all that apply A)-12t , B) 12t-12, C) none of the above
The correct answer is A) -12t.
To evaluate this expression, we need to use the order of operations. The order of operations is a set of rules that specifies the sequence in which operations should be performed in a math expression to get the correct result. The order of operations is typically abbreviated as PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
Following the order of operations, we first need to evaluate the expression inside the parentheses, which is 2+(-4t). This gives us 2-4t. Next, we need to perform the multiplication, which gives us 3(2-4t) = 6-12t. Finally, we need to perform the addition, which gives us -6+6-12t = -12t. Therefore, the expression -6+3(2+(-4t)) is equivalent to -12t.
Option B) 12t-12 is incorrect because the multiplication and addition operations are not performed in the correct order.
Option C) none of the above is incorrect because the correct answer is A) -12t.
To learn more about Expression Equivalence follow link : https://brainly.com/question/9657981
#SPJ1
What two arguments did Mary Wollstonecraft?
Both men and women have duties to their families and duties to the state.
According to Wollstonecraft, women are important to the country because they educate their children and because they have the potential to be "companions" to their husbands rather than merely spouses. She also contends that women should have an education appropriate to their status in society.
She asserts that in God's view, men and women are on an equal footing. But these affirmations of equality conflict with her assertions that the strength and bravery of males are superior. It is now challenging to label Wollstonecraft as a modern feminist due to her equivocal views on gender equality.
Wollstonecraft differs from the majority of her male Enlightenment contemporaries because of her emphasis on the rights of women.
To learn more about Wollstonecraft's arguments refer to:
brainly.com/question/28006055
#SPJ4
According to her, men and women are treated equally in God's eyes. However, these claims of equality run counter to her claims that men are stronger and bolder than women. Due to Wollstonecraft's conflicted opinions on gender equality, it is currently difficult to categorize her as a modern feminist.
Wollstonecraft's emphasis on women's rights sets her apart from the rest of her male Enlightenment peers.
The sum of present age of father and son is 50years.After 5years the age of father is thrice the age of son .Find their present age
Answer:
age of father is 40 and son is 10
Step-by-step explanation:
let age of father be x
and age of son is y
At present,
x+y=50 eq 1
After 5 years,
Ages are,
Father = x+5
Son = y+5
As age of father is thrice so,
x+5 = 3(y+5)
x+5 = 3y+15
x-3y= 10 eq 2
Multiply eq 1 by 3
3x + 3y = 150 eq 3
Now, Add eq 2 and 3
4x = 160
x = 40 .................... ....... Age of father
Put x in eq 1
40 + y = 50
y = 10 ......................... Age of Son
Is it possible to make an equation from these two equations? If so, do they have infinite solutions, no solutions, or one solution?
Consider the mathematical sentence 2 = 2.
Is there any variable or constant that you could add to or subtract from both sides, or multiply or divide both sides by using the Properties of Equality to make this true sentence false? Choose variables and constants to create new mathematical sentences to justify your conclusion
Consider the mathematical sentence 2 ≠ 3.
Is there any variable or constant that you could add to or subtract from both sides, or
multiply or divide both sides by using the Properties of Equality to make both sides equal? Choose variables and constants to create new mathematical sentences to justify your conclusion.
Answer:
For the equation 2 = 2, it is not possible to make this equation false by using the Properties of Equality. This is because the equation is already true, and any manipulation of the equation using the Properties of Equality would not change this fact. Therefore, this equation has one solution.
For the equation 2 ≠ 3, it is not possible to make both sides equal by using the Properties of Equality. This is because the equation is stating that the two sides are not equal, and any manipulation of the equation using the Properties of Equality would not change this fact. Therefore, this equation has no solutions.
What are some domain examples?
The allowable set of values makes up a function's domain. The set of authorized values is the domain of a function.
what is domain ?The set of authorized values is the domain of a function. The x values of a function, like f, are included in this collection (x). The collection of such values serves as a representation of the range of values that can be used as input for a function. The function returns this set of values when we enter an x value.
here ,
Consider the function represented by y = f(x), where x and y are independent variables. If a function f provides a method of efficiently generating a single value y while employing a value for x to that end, the selected x-value is said to fall inside the domain of f.
The range of values that a function can accept is referred to as the domain.
To know more about domain visit :-
https://brainly.com/question/28135761
#SPJ4
What is the value of 994 1/3 According binomial theorem?
The value of 994 to the power 1/3 is 9.97.
The binomial theorem involves the method of expanding an expression which is raised to a finite power. A binomial theorem has its application in probability, algebra, etc.
A binomial expression is said to have two dissimilar terms.
The total number of terms in (x + y)ⁿ are n+1.
The expansion of (1 + x)ⁿ can be written as,
(1 + x)ⁿ = 1 + nx + [n*(n-1)]/2! x² + [n*(n-1)*(n-2)]/3! x³ + ....
Let us find the value of 994 to the power 1/3,
⇒ (993 + 1)¹/³
⇒ 1 + 993/3 + 993* 993* [1/3* (-2/3)]/2! + 993* 993* 993* [1/3* (-2/3)* (-5/3)]/3! + ...
⇒ 1 + 331 - 54780.5 + 60441151.67 - ...
⇒ 9.97
Thus, the required value is 9.97.
To know more about binomial theorem:
https://brainly.com/question/20411764
#SPJ4
How much paint do I need for 2200 square feet?
6 cans are needed to paint an area of 2200 units square.
The cans of paints and areas are illustrations of equivalent ratios.
The quantity of paint required for a certain area of house can be found out using the area of the house.
As the area is given in this problem, it is easier to calculate the amount of paint.
The given parameter is,
Cans: area = 1: 400
Putting it in the form of fraction,
Cans/area = 1/400
Cross multiplying, we have,
Cans = 1/400 × 2200 = 5.5 ≈ 6
Thus, 6 cans are needed to paint a 2200 square feet.
The question is incomplete. The complete question is 'How many cans of paint are needed to cover an area of 2200 square units if one can of paint covers in area 400 square units.'
To know more about paint:
https://brainly.com/question/12799603
#SPJ4
A recipe calls for 112 1 1 2 teaspoons of cinnamon to make 2 dozen oatmeal cookies. How many teaspoons of cinnamon are needed to make 60 oatmeal cookies?.
Fraction [tex]3 \frac{3}{4}[/tex] teaspoons of cinnamon are needed to make 60 oatmeal cookies.
Given that,
A recipe calls for [tex]1\frac{1}{2}[/tex] teaspoons of cinnamon to make 2 dozen oatmeal cookies.
A fraction is numerical value that is a part of a whole. It is evaluated by dividing a whole into number of parts. For example, ½ represents half of a whole number or a thing.
Then,
We will find number of teaspoons needed to make one oatmeal cookies.
1 dozen = 12
2 dozens = 24
So,
We can write,
[tex]1\frac{1}{2}[/tex] divide by 24,
Convert mixed fraction into improper fraction:
[tex]\frac{3}{2}[/tex] divide by 24
Convert to division problem by flipping the second fraction as:
= [tex]\frac{3}{2}[/tex] * [tex]\frac{24}{1}[/tex]
= [tex]\frac{3}{48}[/tex]
= [tex]\frac{1}{16}[/tex]
Now, we will multiply amount needed for one cookie by 60 to find amount needed to make 60 cookies as:
= [tex]\frac{1}{16}[/tex] * 60
= [tex]\frac{15*4}{4*4}[/tex]
= [tex]\frac{15}{4}[/tex]
= [tex]3 \frac{3}{4}[/tex]
Therefore,
Fraction [tex]3 \frac{3}{4}[/tex] teaspoons of cinnamon are needed to make 60 oatmeal cookies.
To learn more about Fraction problems visit :
brainly.com/question/10708469
#SPJ4
Is physics 100 hard?
Yes, it is hard but with a lot of practice and putting effort one cam also find it easy.
Why physics is hard?Physics requires the ability to solve problems, which can only be acquired via practice. In addition to these difficult ideas, there are theoretical concepts, mathematical calculations, and laboratory experiments.
How to deal with physics?It is better to comprehend the derivations than to memorize the formulas. Making a mess of several formulas will just increase your anxiety over the topic. Instead, if you strive to comprehend where they originate, you will begin to appreciate physics and its applications.
Physics is a difficult topic since it combines science and arithmetic, which may be challenging for the best of us. Nevertheless, despite how difficult it is, you can achieve if you follow a few simple guidelines and put yourself through some practice.
To learn more about physics visit the link:
https://brainly.com/question/28021242
#SPJ4