The equation that represents one sixth of the number n is given as follows:
n/6.
How to define an equation?The equation is a fraction of an amount. A fraction has the following format:
x/y.
In which:
The top term x is the numerator.The bottom term y is the denominator.One sixth is a fraction in which the numerator is one and the denominator is six, as follows:
1/6.
To obtain one six of a number n, the above fraction is multiplied by n, as follows:
n x 1/6.
When two fractions are multiplied, the numerators multiply themselves, as do the denominators, hence the product is given as follows:
n x 1/6 = n/6.
Hence the equation that represents one sixth of the number n is given as follows:
n/6.
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The equation that represents twenty-five is one-sixth of the number n is;
25 equals n over 6
How to solve Algebra Word Problems?We want to find the equation that represents twenty-five is one-sixth of the number n.
Now, to say that twenty-five is one-sixth of the number n simply means that twenty five is equal to one-sixth of the number n.
Expressing this algebraic statement as an algebraic expression gives us; 25 = ¹/₆n
So we can see that this represents the given algebraic statement and as such looking at the options, we can conclude that the correct one is Option A.
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Complete question is;
Which equation represents twenty-five is one-sixth of the number n?
25 equals n over 6
25 = 6n
6 = 25n
one sixth equals n over 25
Which statement describes the rate of change of the line?
Answer:
20$
Step-by-step explanation:
30 to 50 is 20, 50 to 70 is 20
15. Graph the inequality y> |x + 1|-1. Which point is NOT part of the solution?
O
O
O
O
(-1,2)
(1,3)
(-1,0)
(1,-1)
The solution for the inequality y > |x + 1| - 1 is -x - 2 > y > x and the coordinate (1, -1) is not a part of the solution so, option D is correct. The graph is attached below.
What is inequality?An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. It is most frequently used to compare the sizes of two numbers on the number line.
Given:
y > |x + 1| - 1
Solve the inequality as shown below,
y + 1 > |x + 1|
y + 1 > -(x + 1) and y + 1 > x + 1
y + 1 < -x - 1 and y + 1 > x + 1
y < -x - 1 - 1 and y > x + 1 - 1
y < - x -2 and y > x + 0
y < -x - 2 and y > x
Thus, the solution is -x - 2 > y > x.
Plot the graph by putting the values of x and find y then join the points.
Put the values from the option to check,
From y > x option 4 is not part of the solution as -1 < 1.
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A Web site sells baseball caps for $12 each. There's a $4 shipping charge no matter
how many hats you order. The equation c = 12h + 4 gives the total cost to buy h hats.
Which statement correctly describes what happens when h increases?
Answer:
0
Step-by-step explanation:
A line that includes the point (0, 0) has a slope of 2. What is its equation in slope-intercept
form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
The equation of a line that passes through (0, 0) and has a slope of 2 is y = 2x.
How to represent equation in slope intercept form?Equation of a line can be represented in slope intercept form as follows
y = mx + b
where
m = slopeb = y-interceptA line that includes the point (0, 0) has a slope of 2. The equation of the line in slope intercept form is as follows:
y = 2x + b
using (0, 0) let's find y-intercept.
0 = 2(0) + b
Hence,
b = 0
Therefore, the equation is y = 2x
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nine congruent circles are inscribed in a square with a side length of 126. if a point in the square is chosen at random, what is the probability that the point is not in a circle?
There is a 21.5% chance that a point in a square with nine congruent circles drawn there won't be within one if it is chosen at random.
It is given to us that :
Nine congruent circles are inscribed in a square
The square has a side length of 126
We have to find out the probability that the point is not in a circle, if a point in the square is chosen at random.
It is known that the square has a side length of 126.
=> Area of the square = [tex](Length)^{2}[/tex]
=> Area of the square = [tex]126^{2}[/tex]
=> Area of the square = 15876 ------ (1)
It is also known to us that nine congruent circles are inscribed in the square that has a side length of 126.
=> Diameter of each circle = 126/3
=> Diameter of each circle = 42
=> Radius of each circle = 21 ------ (2)
We know that the area of a circle is given as -
Area of circle = [tex]\pi r^{2}[/tex] ------ (3)
where,
r = radius of the circle
Substituting the value of r from equation (2) in equation (1), we have
Area of circle = [tex]\pi r^{2}[/tex]
=> Area of circle = [tex]\pi (21)^{2}[/tex]
=> Area of circle = 1385.44
=> Area of 9 circles = 12468.96 ----- (4)
Now, we can say that -
Area not in a circle = Area of square - Area of 9 circles
=> Area not in a circle = 15876 - 12468.96 [From equation (1) and (4)]
=> Area not in a circle = 3407.04 ------ (5)
We know that the probability of a outcome is given as -
Probability = Number of favorable outcomes/Total number of outcomes
So, the probability that the point is not in a circle can be calculated as -
Probability = Area not in a circle/Area of square
=> Probability = 3407.04/15876
=> Probability = 0.215
=> Probability = 21.5%
Thus, if there are nine congruent circles inscribed in a square and a point in the square is chosen at random, the probability that the point is not in a circle is 21.5%.
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find the exact length of the curve. y = 3 + 4x3/2, 0 ≤ x ≤ 1
So the exact length of the curve is given by [tex]L=(1/36)*[\frac{37^{3/2}}{3/2} - 1][/tex]
Given the equation of curve:
[tex]y = 3+ 4x^\frac{3}{2}[/tex]
The length of the curve is given by [tex]L= \int\limits^a_b {\sqrt{1+(y^[/tex]
Where y^ is derivative of y with respect to x
So [tex]y= 4*(3/2) * \sqrt{x}= > 6 \sqrt{x}[/tex]
Given a=1 and b=0
So [tex]L= \int\limits^1_0 {\sqrt{1+(6\sqrt{x})^2 } } \, dx[/tex]
[tex]L= \int\limits^1_0 {\sqrt{1+36x } } \, dx[/tex]
let 1+36x be t
36dx = dt
As the value of x changes after the substitution of the value.
So now the L changes as:
[tex]L= 1/36 \int\limits{\sqrt{t } } \, dt[/tex]
[tex]L=1/36* \left \{ {{t=37} \atop {t=1}} \right. \frac{t^\frac{3}{2} }{\frac{3}{2} }[/tex]
[tex](1/36)*[\frac{37^{3/2}}{3/2} - 1][/tex]
the min value of t=1 and max value of t=37
[tex]L=(1/36)*[\frac{37^{3/2}}{3/2} - 1][/tex]
[tex]L=(1/36)*[\frac{37^{3/2}}{3/2} - 1][/tex]
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Karen earns £12.80 an hour for a 35 hour week, time and a half on the next 6 hours and double time after that. How much does she earn for a 43 hour week?
Answer:
I hope the image helps!
Marissa just bought 100 acres of land. She wants to grow apple, peach, and cherry trees on her land. Color the
model to show how the acres could be distributed for each type of tree. Using your model, complete the table.
Answer:
Step-by-step explanation:
Robb’s Fruit Farm consists of 100 acres on which three different types of apples grow. On 25 acres, the farm grows Empire apples. Mcintosh apples grow on 30% of the farm.
The area of the figure above is
blank + 25pi/4
Answer:
Add 75 for the blank number----------------------------
Divide the figure by three parts for easy calculation of its area:
Rectangle of 5 by 10 units, Square of 5 units,Quarter-circle of 5 units radius.Find each area and add up:
A = 5*10 + 5*5 + π*5²/4 A = 50 + 25 + 25π/4A = 75 + 25π/4The blank is 75.
Find the percent the first number is of the second.
(1.) 1.5 and 7.5,
(2.) 5ft 37.5ft
To find the percent that 1.5 is of 7.5, we need to divide 1.5 by 7.5 and multiply the result by 100% to convert it to a percentage:
1.5 / 7.5 = 0.2
0.2 * 100% = 20%
Therefore, 1.5 is 20% of 7.5.
To find the percent that 5ft is of 37.5ft, we need to divide 5 by 37.5 and multiply the result by 100% to convert it to a percentage:
5ft / 37.5ft = 0.1333
0.1333 * 100% = 13.33%
Therefore, 5ft is 13.33% of 37.5ft.
You are given the difference of the numbers of boys and girls in a class and the ratio of boys to girls. How many boys and girls are in class?
3 more boys; 5 for every 4
Answer:
By using the given ratio, we will see that there are 15 boys and 12 girls.
How we can find the number of boys and girls in the class?
The given information is:
There are 3 more boys.
There are 5 boys for every 4 girls.
Now, notice that in the ratio we have a difference of 1 boy, so if we want to have a difference of 3 boys, we must multiplicate it by 3, then we get:
3*15 boys for every 3*4 girls (remember that you can multiply both quantities on the ratio and it does not change).
15 boys for every 12 girls.
Now the difference is 3.
15 - 12 = 3
So we can conclude that there are 15 boys and 12 girls.
Step-by-step explanation:
81 of [60-{8*7-(13-3*5)}] find simply
Answer:
Step-by-step explanation:
81 of [60-{(8*7)-(13-(3*5))}] =
81 of [60-{56}-(13-15)] =
81 of [60-{56}-(-2) =
81 of [60-{56}+2] =
81 of [6] =
81% of 6 = 4.86
Hamburger Heaven is having a lunch special where customers buy one 1/2-* 1 p
pound cheeseburger and get one free. If they set aside 48 pounds of meat,
how many 1/2-pound cheeseburgers can they make?
24
96
O 144
O48
Answer:
hshsjsjs
Step-by-step explanation:
shhshshsjdjdjdjdj
PLEASE HURRY! Brody works at the ticket booth at the movie theater and sold 25 adult tickets and several child tickets during the first hour at work. Each adult ticket costs $12, and each child ticket costs $6. Brody collected $360 during that hour.
How many child tickets did he sell?
___ child tickets
Answer:
10 Child Tickets
Step-by-step explanation:
25 x 12 = 300
So we need 60
6 x 10 = 60
Step-by-step explanation:
25 x 13 = 300
6 x 10 = 60300 + 60 = 360
A dance squad needs at least $800 to buy new dance outfits. They have saved $350
already. -They are selling tickets to a dance performance for $10 each. They need to sell
x tickets to have enough money to buy the new dance outfits. Which inequality
represents the situation?
Answer:
x>=45 is the req. inequality
The inequality equation for the number of tickets to be sold is x ≥ 45
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the number of tickets to be sold be x
Let the total amount of money to be saved be = $ 800
The amount of money already saved = $ 350
So , the remaining amount of money = $ 800 - $ 350 = $ 450
The cost of each ticket = $ 10
So , the cost of x tickets = 10x
Now , the number of tickets to be sold to raise $ 450 is given by
10x ≥ 450 be equation (1)
On simplifying the equation , we get
Divide by 10 on both sides of the equation , we get
x ≥ 45
Therefore , the number of tickets to be sold is 45
Hence , the inequality is x ≥ 45
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If m<2 = 63°, then m<3 is:
63°.
27°
117°
None of these choices are correct.
Answer:
63°
Step-by-step explanation:
since they are in the form of vertically opposite angle.
answer these questions. ( find the variables)
1. n + 7 = 10
2. c - 2+ = 7
3. a x 3 = 15
4. a / 5 = 9
5. 9z + 2 = 38
6. 17 + 3n = 47
7. 7y - 7 = 21
8. 3x + 90 = 147
9. 26/ y + 3 = 16
10. 147 - 3x + 90
Answer:
1)3
2)9
3)5
4)45
5)4
6)10
7)4
8)19
9)2
10)unable (no equal sign?)
Step-by-step explanation:
The weights of a pack of chewing gum for a certain brand have a mean of 47.1 grams and a standard deviation of 2.4 grams. what is the weight of a randomly selected pack of gum that has a z-score of 3.11? a. 39.6 grams b. 44.7 grams c. 49.5 grams d. 54.6 grams
Answer:
Step 1: Obtain the mean and standard deviation of the weights of packs of chewing gum. The weights of packs of chewing gum for a certain brand have a mean of 47.1 grams and a standard deviation 2.- grams. Step 2: Obtain the z-score of the randomly selected pack of gum. The z-score of the randomly selected pack of gum is 3.11. Step 3: Determine which of the following statements is true: The weight of this pack of gum is lighter than the mean weight by 3.11 standard deviations The weight of this pack Of gum is heavier than the mean weight by 3.11 standard deviations The weight of this pack Of gum is lighter than the mean weight by 2.4 standard deviations The weight of this pack Of gum is heavier than the mean weight by 2.4 standard deviations
you are making a cake and have already put in all of the ingredients except the eggs. you go to the refrigerator and find that there are no eggs, which results in the condition known as
The condition known as "eggless baking" is a common problem when baking cakes and other desserts.
It can be caused by not having eggs in the refrigerator or by forgetting to add them to the recipe. Without eggs, the cake batter lacks structure and will not hold together when baked. Without the proteins from the eggs, the cake will be denser and less moist.
Additionally, the cake may not rise as much as desired and the texture may be crumbly or gummy. To solve this problem, you can try substituting other ingredients such as mashed bananas, applesauce, or yogurt. However, it is best to add eggs if possible to ensure the best results.
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Larry has decided that the above ground swimming
pools business is not the best way to earn a living
(see practice problem e). He now thinks the big
money is in rowing machines. If Larry switches jobs,
he will earn a 12% commission on all the machines he
sells. For Larry to receive $15,000 in commissions,
how many dollars worth of machines must he sell?
The amount of worth of machine Larry needs to sell to recieve 15,000 dollars is 125, 000 dollars.
How to find the worth of machine he can sell to earn a particular amount?Larry thinks the big money is in rowing machines. If Larry switches jobs,
he will earn a 12% commission on all the machines he sells. For Larry to
receive $15,000 in commissions, the worth of dollars of machines he must
sell can be computed as follows:
Therefore,
let
x = amount he will earn
Hence,
15, 000 = 12% of x
15,000 = 12 / 100 × x
15000 = 12x / 100
cross multiply
1500000 = 12x
divide both sides by 12
x = 1,500,000 / 12
x = 125,000
Therefore, he needs to sell $125, 000 worth of machine.
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Which of the following statements is always true?
A. A linear paris formed by complementary angles.
B. If two angles are adjacent, then they are linear pair.
C. If two angles for a linear pair
, then their sum measures 1800
D. In a linear pair, one of the two angles is an acute angle and the other is an obtuse angle.
The true statement is that A. A linear pair is formed by complementary angles.
What is a linear pair?When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. These are also referred to as supplementary angles.
Complementary angles are those whose combined angle is exactly 90 degrees. For instance, p angles include 30 degrees and 60 degrees.
In conclusion, based on the information, the correct option is A.
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HELPPP Determine the value of h in the equation one third plus h equals five thirds.
six thirds
fourth thirds
six over nine
four ninths
Answer:
h = [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] + h = [tex]\frac{5}{3}[/tex] ( subtract [tex]\frac{1}{3}[/tex] from both sides )
h = [tex]\frac{5}{3}[/tex] - [tex]\frac{1}{3}[/tex] = [tex]\frac{4}{3}[/tex]
The perimeter of a rectangle i 80 inche. The length of the rectangle i 12 inche. Which equation could repreent the width of the rectangle, w? Repone w = 2(80 – 12) w, = 2(80 – 12) w = (80 – 12) ÷ ÷ 2 w, = (80 – 12) divided by 2 w = 2(80 – 24) w , = 2(80 – 24) w = (80 – 24) ÷ ÷ 2
The perimeter of a rectangle i 80 inche. The length of the rectangle i 12 inchs then width is equal to 28 inch
What is length area and perimeter?
Firstly, the area of a shape is the surface or flat space that the shape covers whereas the perimeter of a shape represents the distance around its boundary. Secondly, the area is measured in square units, whereas the perimeter is measured in linear units.
given that the perimeter of a rectangle is 80 inch
we know that
perimeter = 2 ( L +B)
putting the values we get
80 = 2 ( 12 + B)
40= 12+B
B= 28
then the width is equal to 28inch
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The graph of f(x) = 7x is stretched vertically by a factor of five. Which of the following is the equation of the new graph, g(x)? A. g(x) = 5(7x) B. g(x) = 7(5x) C. g(x) = 5(7x) D. g(x) = 7(5x)
The solution is Option D.
The graph of the function after a vertical stretch of 5 is given by the equation g ( x ) = 5 ( 7ˣ )
How does the transformation of a function happen?
The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
Let the function be represented as A
Now , the value of A is
f ( x ) = 7ˣ
The function f ( x ) is stretched vertically by a factor of 5
Let the new function be represented as g ( x )
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
So , the value of the function g ( x ) is given by the equation
g ( x ) = 5 ( f ( x ) )
g ( x ) = 5 ( 7ˣ )
Hence , the function is g ( x ) = 5 ( 7ˣ )
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The U.S. Weather Bureau has a station on Mauna Loa in Hawali that has measured carbon dioxide levels since 1959. At that time , there were 312 parts per million of carbon dioxide in the atmosphere. In 2005 , the figure was 389 parts per million. Find the increase in carbon dioxide levels and the percent of increase . Percent increase:96
a) By the subtraction operation, the increase in carbon dioxide levels between 1959 and 2005 is 77 parts.
b) The percentage increase in carbon dioxide levels between 1959 and 2005 is 24.7%.
What is the percentage increase?The percentage increase is found by determining the difference between the original and final values through subtraction operation.
The difference is then divided by the original value, multiplied by 100.
The carbon dioxide levels in 1959 = 312 parts per million
The carbon dioxide levels in 2005 = 389 parts per million
The increase in dioxide levels from 1959 to 2005 = 77 parts per million (389 - 312)
The percentage increase = 24.68% (77/312 x 100)
= 24.7%
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The function shown in the graph below is modeled by:
a linear function.
an exponential function.
a quadratic function.
Jamie has 2 ½ packs of sunflower seeds to cover 150 sq ft. Based on this
information, what is the number of sq ft that 1 pack of sunflower seeds will
cover?
Answer:
60 ft.^2
Step-by-step explanation:
Known area/number of packs= A / number of packs for A, where A= area of interest
150/2.5=A/1
A=60
in how many ways can a committee with 4 democrats and 2 republicans be formed from a group of 7 democrats and 5 republicans?
A committee with 4 democrats and 2 republicans formed from a group of 7 democrats and 5 republicans can be created in a total of 350 ways. Therefore, the option C holds true.
The calculation of the same has been shown as below,
A group has 7 Democrats and 5 Republicans.
Committee with 4 Democrats and 2 Republicans = 7C4 x 5C2
7C4 x 5C2 = 7! / (4! 3!) x 5! / (2! 3!)
7C4 x 5C2 =(7×6×5 / 3×2×1) x (5×4 / 2×1)
7C4 x 5C2 = 35 × 10
7C4 x 5C2 = 350
Therefore, a committee can be created in 350 ways.
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Complete Question
In how many ways can a committee with 4 Democrats and 2 Republicans be formed from a group of 7 Democrats and 5 Republicans?
A 105
B 924
C 350
D 1680
if a sample includes 27 people, the degrees of freedom used in the formula to estimate the population variance would be
The degrees of freedom for the sample variance is equal to the number of data points in the sample minus 1, so for a sample of 27 people, the degrees of freedom would be 26.
The degrees of freedom for the sample variance is calculated by taking the number of data points in the sample and subtracting 1. In this case, the sample size is 27 people, so the number of degrees of freedom is 26. This is because we need to account for one degree of freedom in order to calculate the overall variance of the sample. The degrees of freedom is important in estimating the population variance because it helps to determine the size of the sample necessary to accurately estimate the population variance. By knowing the degrees of freedom, we can better understand the accuracy of our estimates and adjust our sample size accordingly.
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Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.