a) The fraction of chocolate distributed is given as follows: 4/3.
b) The fraction of chocolates left with Paul is given as follows: 8/3.
How to obtain the fractions?The fractions are obtained applying the proportions used in the context of this problem.
He distributes 1/3 of each bar to 4 children, hence the total number of bars distributed is given as follows:
4 x 1/3 = 4/3.
(multiplication of fractions, multiply the numerators and the denominators, keeping the quotient).
The total number of bars that Paul had initially is given as follows:
4 bars.
Then the fraction of chocolate remaining with Paul is given by the subtraction of the total amount of bars by the amount given to the children, as follows:
4 - 4/3 = 12/3 - 4/3 = 8/3 bars.
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Find the quotient and remainder using synthetic division for
1³ + 31² + 8x + 14
------------------------
x + 2
The quotient is
The remainder is
Therefore , the solution to the given problem of equation comes out to be quotient : x² +x+6+ [tex]\frac{2}{x+2}[/tex] and remainder is 2
Explain equationA mathematical depiction of two equal variables, one on either side of a "equals" sign, is called an equation. Equations can be used to solve common problems. To solve challenges in real life, we frequently turn for pre algebra assistance. Lessons in pre-algebra cover the foundational ideas of mathematics.
Here,
Given : synthetic division for
x³ + 3x² + 8x + 14
------------------------
x + 2
Write the problem in synthetic division format
-2 | 1 3 8 14
-2 -2
------------------------
1 1 6
Carry down the leading coefficient, unchanged, to below the division symbol
-2 | 1 3 8 14
-2 -2
---------------------------
1 1 6
Multiply the carry - down value by the zero of the denominator, and carry the result up into the next column:
1(-2)=-2
-2 | 1 3 8 14
-2 - 2
------------------
1 1 6
=> We get:
As
x² +x+6+ [tex]\frac{2}{x+2}[/tex]
and remainder is 2
Therefore , the solution to the given problem of equation comes out to be quotient : x² +x+6+ [tex]\frac{2}{x+2}[/tex] and remainder is 2.
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can someone help me please i really have to do this right now
Answer: Angles 2 and 4 = 38, Angle 1 = 142
Step-by-step explanation:
Given that angle 3 is equal to 142, the angle between 2 and 3 has to add up to 180. 142 + 38 = 180. The same applies for angle 4 and 3. So, angle 1 + angle 2 has to add up to 180. We already know angle 2, so now we just have to subtract that from 180 to find angle 1.
Adrian bought a jacket that costs 11 dollars and a scarf that costs 15 dollars. At the counter, he received a discount. If he only paid 22 dollars total, how many dollars was the discount?
There was 4 dollar of discount on the total amount.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.
We are given that Adrian bought a jacket that costs 11 dollars and a scarf that costs 15 dollars.
At the counter, he received a discount. If he only paid 22 dollars total, then
Total cost 11 + 15 = 26
But 26 - 22 = 4
Therefore, the discount was 4 dollar.
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What is the common denominator of y + StartFraction y minus 3 Over 3 EndFraction in the complex fraction y + StartFraction y minus 3 Over 3 EndFraction divided by five-ninths + StartFraction 2 Over 3 y EndFraction?
The common denominator of the given expression is 5y+6.
What is division?Division is the process of splitting a number or an amount into equal parts.
here, we have,
Given expression,
(y+(y-3)/3)/(5/9+2/3y)
We have to find the common denominator.
On solving the numerator and denominator of the given expression,
=3y(4y-3)/5y+6
Hence the common denominator of the above expression is given by 5y+6
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A small town surveyed 250 adults,
150 of the adults who
180 of whom were parents, about whether a park should be expanded The results showed that
were parents and 40
of the adults who were not parents thought the park should be expanded.
Use this information to complete the two-way table.
Enter your answer by filling in the boxes to complete the table.
Should the park be expanded?
Yes
No
Parents
Not parents
According to the findings, 40 of the adults who were not parents and 150 of the adults who were parents believed that the park should be expanded.
The park be expanded?250 adults, 180 of whom are parents, leaving 70 adults who are not parents (250 - 180). According to the findings, 40 adults without children and 150 adults with children said the park should be expanded. Thus, 180 – 150 = 30 parents.
Parents: YES OR NO Not parents: 40 | 30 of 150
In this exercise, we must determine the values of the voters who supported expanding the parking lot, which requires that we:
In fact, parents will be 150, not 40.
Parents won't be 30 in total; they'll be 40. Instead, a park should be built to accommodate 250 persons, 180 of whom were parents.
The park should be extended, according to 40 of the people who weren't parents.
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mr.jim would like to plant carrots all around base of the fence surrounding his square feet. the area of his garden is 100 sq feet. in feet what is tje perimeter
4. Find the sum of the first 21 terms in a series where a = 20 and t21= 400.
5. Find the sum of the first 100 terms in a series where a = 0 and t100= 99.
6. Find the sum of the first 50 terms in a series where a = 4 and t50= 196.
7. Find the sum of the first 100 terms in a series where a = 0 and t100= 99.
8. Find the sum of the first 10 terms in an arithmetic series where t7= 7 and t10= 13.
9. Find the sum of the first 10 terms in an arithmetic series where t5= 15 and t10= 45.
10. Find the sum of the first 30 positive multiples of 5.
The first 100 terms of a series add up to 4950, and the first 21 terms of a series where a = 20 and t21 = 400 add up to 4410
what is arithmetic progression ?An arithmetic progression is when the difference between each phrase that follows another in a sequence is always the same. For instance, the sequence 5, 7, 9, 11, 13, and 15 is an example of an arithmetic progression with a 2 tolerance. A progression having a set tolerance between any two consecutive numbers is known as a "arithmetic progression" (A.P.). Two alternative types of mathematical progression exist: finite-length mathematical series A series that has a limited number of terms is a finite geometric progression. One may calculate the early, late, tolerance, and number of terms in a series using the terms in the series.
given
1) n6 = 6 where a = 5 and d = 5 = 105
2)n6 =6 where a = 9 and d = 12 = 234
3) n5= 5 where a = 5.7 and d = 1.4 = 42.5
4) a = 20 and t₂₁ = 400 ,
= 380
Therefore, Sum of 21 terms = 4410
5) In series a = 0 and t₁₀₀ = 99 = 4950
The first 100 terms of a series add up to 4950, and the first 21 terms of a series where a = 20 and t21 = 400 add up to 4410
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In triangle JKL, angles J and L each measure 51° and JK = 18. Triangle PQR is similar to triangle JKL, where J corresponds to P, K corresponds to Q, and QR = 36. Which expression represents the length of segment PR?
Answer:
Step-by-step explanation:
Triangle JKL is a 51-51-78 triangle, since the angles in a triangle must add up to 180°. Since triangle PQR is similar to triangle JKL, it must also be a 51-51-78 triangle. Since corresponding sides in similar figures are in proportion, we can set up a proportion to find the length of PR:
(PR)/(JK) = (PQ)/(JL) = (36)/(18)
Cross multiplying and solving for PR, we find:
PR = (JK) * (PQ)/(JL) = 18 * 36/18 = 36
5 pizzas cost £35.00. How much do 3 pizzas cost?
Answer:£21.00
Step-by-step explanation:
One pizza: (£35/5) =£7
Three pizza's: (£7x3)=£21
Choose the expression that is equivalent to fraction with 7 raised to the negative tenth power in the numerator and 7 raised to the fourth power times seven raised to the zero power in the denominator.
negative 1 divided by 7 raised to the fourteenth power
−714
1 divided by 7 raised to the fourteenth power
714
The equation that corresponds to fraction [tex]\frac{7^{-10} }{(7^{4} )(7^{0} )}[/tex] is [tex]\frac{1}{7^{14} }[/tex] . A phrase by itself could contain an action .
what is expression ?It is possible to multiply, divide, add, or subtract in math. An expression has the following structure: Expression: (Math Operator, Number/Variable, Math Operator). A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to compare expressions and phrases. In English, a phrase by itself could contain an action, but it doesn't constitute a full sentence.
given
[tex]\frac{7^{-10} }{(7^{4} )(7^{0} )} \\= \frac{1}{7^{4} } *\frac{1}{7^{10} } * 1\\= \frac{1}{7^{14} }[/tex]
The equation that corresponds to fraction [tex]\frac{7^{-10} }{(7^{4} )(7^{0} )}[/tex] is [tex]\frac{1}{7^{14} }[/tex] .
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A movie studio keeps 240 dresses in its wardrobe for historical films. Three-fifths of them can be used for movies that take place in the 1700s and 15% of them can be used for movies in the civil war era. A. What percent of the dresses are for films set in the 1700s? B. What percent of the dresses are for films not set in the 1700s? Explain how you found your answer. C. What percent of the dresses are for films set in the 1700s or during the civil war era? Explain how you found your answer. D. What percent of the dresses are not for films set during the civil war era? Explain how you found your answer.
A) The dresses for films set in the 1700s would be 60%.
B) The percentage of dresses that are not for films set in the 1700s is 40%.
C) The percentage of dresses that can be used for films set in the 1700s or during the civil war era is 75%.
D) The percentage of dresses that are not for films set during the civil war era is 85%.
What is a percentage?
The percentage is a way of expressing a number as a fraction of 100. It is often denoted using the symbol "%". It is used to express a proportion of a number out of 100. It is useful in many applications such as finance, statistics, and other fields.
A. Three-fifths of the dresses can be used for movies that take place in the 1700s, which is 3/5 * 100 = 60%.
B. The percent of the dresses that are not for films set in the 1700s is 100% - 60% = 40%. This is found by subtracting the percentage of dresses that are used for 1700s movies from 100%.
C. The percent of the dresses that can be used for films set in the 1700s or during the civil war era is 60% + 15% = 75%. This is found by adding the percentage of dresses that can be used for 1700s movies and the percentage of dresses that can be used for civil war era movies.
D. The percent of the dresses that are not for films set during the civil war era is 100% - 15% = 85%. This is found by subtracting the percentage of dresses that are used for civil war era movies from 100%.
Hence,
A) The dresses for films set in the 1700s would be 60%.
B) The percentage of dresses that are not for films set in the 1700s is 40%.
C) The percentage of dresses that can be used for films set in the 1700s or during the civil war era is 75%.
D) The percentage of dresses that are not for films set during the civil war era is 85%.
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1 Chinese yuan= $0.14567. How many Chinese yuan can u buy for a dollar
The Chinese yuan you can buy for a dollar is 6.86483 Chinese yuan
How to determine how many Chinese yuan you can buy for a dollarFrom the question, we have the following parameters that can be used in our computation:
1 Chinese yuan= $0.14567
Divide both sides of the equation by 0.14567
So, we have the following representation
1/0.14567 Chinese yuan= $0.14567/0.14567
Evaluate the quotient
1/0.14567 Chinese yuan= $1
Evaluate the other quotient
6.86483 Chinese yuan= $1
This means that
$1 = 6.86483 Chinese yuan
Hence, you can buy 6.86483 Chinese yuan for $1
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write each percent as a fraction and
as a decimal.
7/100%
I NEED THIS BY 2:30PM
7/100% can be written as a fraction as 7/100, and as a decimal as 0.07.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{7}{100}\%}[/tex]
[tex]\mathsf{= \dfrac{7}{100} \div 100}[/tex]
[tex]\mathsf{= \dfrac{7}{100}\times \dfrac{1}{100}}[/tex]
[tex]\mathsf{= \dfrac{7(1)}{100(100)}}[/tex]
[tex]\mathsf{= \dfrac{7}{1,000}}[/tex]
[tex]\mathsf{= 0.0007}[/tex]
[tex]\huge\text{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{\dfrac{7}{1,000} \ \& \ 0.0007}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
For Exercises 13-17, given A(6,-4), B(3, 8), and
C(-7, 9), determine the coordinates of the vertices
of AA'B'C' for each glide reflection. Suppose p is
the line with equation x = -3,q is the line with
equation y = 9, and r is the line with equation
y=-2. SEE EXAMPLE 3
Answer
A(-10, 9), A'(-4, 9)
B(-4, 2), B'(-10, 2)
C(-7, 9), C'(-7, -4)
Example 3:
A(-3, 5), A'(3, 5)
B(-3, 0), B'(3, 0)
C(-3, 5), C'(-3, -10)
Lorraine prepared a 2.5-gallon pot filled with tomatoes to be canned in jars. Each jar will hold 1.25 quarts of tomatoes. If 1 gallon equals 4 quarts, how many jars can Lorraine fill?
4 jars
5 jars
8 jars
10 jars
Answer:
(c) 8 jars
Step-by-step explanation:
You want to know the number of 1.25 quart jars that can be filled from a 2.5 gallon container.
JarsThe number of jars can be found from ...
(2.5 gal) × (4 qt/gal) × (1 jar)/(1.25 qt) = (2.5·4/1.25) jars = 8 jars
Lorraine can fill 8 jars from the 2.5 gallon pot.
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The pairs of polygons below are similar. Give the sale factor of figure A to figure B
Answer:
Given that Figure A and Figure B are similar polygons, the scale factor of Figure A to Figure B = 5/2.
Recall:
Similar Polygons have corresponding side lengths whose ratio are equal. That is, their pairs of corresponding sides are proportional.
The ratio of any of their corresponding side length = scale factor
Given the two pairs of similar polygons, the scale factor of figure A to figure B will be calculated as follows:
A side length of Figure A = 10
Corresponding side length of Figure B = 4
Scale factor of Figure A to Figure B = 10/4 = 5/2
Step-by-step explanation:
the quotient of x divided by 5 is greater than or equal to 6. Write an inequality and graph its solution
So i am trying to help out my son with his homework and i do not remember this at all if anyone could help me it would greatly be appreciated
Answer:51x900/100
Step-by-step explanation:
So you’ll do 51 x 900
And then at the denominator when there is no number it is automatically 1 so the denominator will be 100.
find the value of x !
Answer:
x = 7
Step-by-step explanation:
You want to know the value of x when the base of a triangle measures 5x+35, and its midsegment measures 35.
MidsegmentThe base of the triangle is twice the length of the midsegment, so you have ...
5x +35 = 2(35)
5x = 35 . . . . . . . . . . subtract 35
x = 7 . . . . . . . . . . divide by 5
__
Additional comment
The midsegment joins the midpoints of the sides of the triangle.
In more formal terms, the smaller triangle is similar to the larger one with a scale factor of 1/2. That means the parallel segments are related by that scale factor of 1/2: (1/2)(5x +35) = 35.
8+ ((3² x 6)- 18) ÷ 9
Solve the system of equations -x-y=-2 and 5x + 7y= 28 by combining the
equations.
The value of x = -7 and y = 9 from the system of equations .
What is System of Equation ?A finite collection of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.
simultaneous equations, system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.
To create an equation in one variable using the elimination approach, you may either add or subtract the equations. To remove a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.
The equations are :
-x - y = -2 (i)
and
5x + 7y = 28 (ii)
multipling eqation (i) with 5 and then adding both equations we get,
-5x - 5y +5x + 7y = -10 + 28
⇒ 2y = 18
⇒ y = 9
Again, -x -9 = -2
or, x = -7
The value of x = -7 and y = 9 from the system of equations
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Convert:
25 decimeters
=
Round to the tenths.
meters
Answer:
2.5
Step-by-step explanation:
Decimeter is 0.1 meter (10 centimeters). That means 25 decimeters is 2.5 meters.
Itzel purchased 18 pounds of oranges.
How many ounces of oranges did she
purchase?
Answer:
288
Step-by-step explanation:
1 pound is equal to 16 ounces
if Itzel purchases 18 pounds, to convert to ounces simply multiply 18 by 16.
Answer:
288
I wish you luck in your assignments.
(I just noticed someone got here in before me and answered WAY better. So I edited this to tell you to give them brainliest.)
Need Help With This
Step-by-step explanation:
a) x+20+x+90=180 [sum of 3 angel of triangle]
2x + 110 = 180
2x = 180- 110
2x = 70
x = 70÷2
x = 35
b) 2y + y + y = 180
4y = 180
y = 180÷4
y= 45
c) 4z-30 + 2z = 180
6z = 180 + 30
6z = 210
z = 35
Can someone help with these 2 questions please :) or 1 whichever one u know
1. Overall, how successful were resistors to Spanish colonial rule? What factors prevented them from being more successful?
2. What lasting impacts do you think Spanish colonial rule will have on Native American cultures and civilizations? Explain.
After conquering indigenous civilizations in Mexico and South America, Spanish Colonial Rule became wealthy thanks to the gold and silver it discovered.
What is Spanish Colonial Rule?The objectives of Spanish Colonial Rule were to take gold and silver from the Americas, to boost the Spanish economy, and to increase Spain's might. Additionally, Spain sought to evangelize Native Americans.
Further Spanish conquistadors, who were mostly poor nobility from Spain's destitute west and south, were able to conquer the vast empires of the New World with the aid of sickness (which reduced native resistance), superior military equipment, and tactical strategies such as surprise attacks and strong.
However, it was challenging to convince immigrants to colonize there due to friction with the local Indian population and the absence of significant silver or gold discoveries.
Thus these are the most leading factors that prevent to become more successful for Spanish Colonial Rule.
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Find f(g(x)) f(x)= 2x^2-4x-6. G(x)= 2x+7
if functions f(x) = 2x²-4x-6 and g(x)= 2x+7 then f(g(x)) is 8(x+2)(x+4)
What is a function?A relation is a function if it has only One y-value for each x-value.
Given functions are f(x)= 2x²-4x-6
g(x)=2x+7
We need to find expression of f(g(x))
f(g(x))=f(2x+7)
Now replace x with 2x+7 in f(x)
f(2x+7)=2(2x+7)²-4(2x+7)-6
=2(4x²+49+28x)-8x-28-6
Apply distributive property
=8x²+98+56x-8x-28-6
Add the like terms
=8x²+48x+64
f(g(x))=8(x+2)(x+4)
Hence, if functions f(x) = 2x²-4x-6 and g(x)= 2x+7 then f(g(x)) is 8(x+2)(x+4)
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What is the length x of a diagonal support, to the nearest tenth of a foot?
CORRECT ANSWER
PROVIDE EXPLANATION
The length of x of a diagonal support is 13.8 feet.
What is the hypotenuse of a triangle.The hypotenuse of a triangle is the length of the longest side of the triangle. So that it is always opposite to the measure of the largest angle of a triangle.
In the question given, divide the length of the footbridge into 2 parts.
So that,
Half of the footbridge = 25/ 2
= 12.5 ft
So that applying the appropriate trigonometric function to determine the value of x using any of the congruent triangles. We have;
Sin θ = opposite/ hypotenuse
Sin 65 = 12.5/ x
x = 12.5/ Sin 65
= 12.5/ 0.90631
x = 13.792 feet
The length x of a diagonal support is 13.8 feet.
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Jamie has 18/5 cups of frosting she uses 2/5 cups of frosting for each cupcake how many cupcakes will Savannah be able to frost
Answer:
9
Step-by-step explanation:
18/5 ÷ 2/5 = 18/5 x 5/2 = 9
A triangular side panel for a roof has the dimensions shown.
26 ft
30°
What is the approximate area, in square feet, of the side panel?
OA.
О в.
O C.
O D.
239
146.4
119.5
60°
292.7
Answer:
d
Step-by-step explanation:
fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
4. The Jerico family went ice skating on the
frozen lake. The 2 parents and 4 children each
had ice skates. They brought an extra pair of
ice skates in case anyone else wanted to join
them. How many ice skates did the family
bring?
Answer:
10
I wish you luck in your assignments.