Answer:
8 nickels and 14 pennies
Step-by-step explanation:
Let p = number of pennies
Let n = number of nickels
p + n = 22 .01p + .05n =.54
Take the second equation and multiple it through by 100 to clear the decimals.
100(.01p + .05n( = .54(100)
p + 5 n = 54 Multiply this through by -1 so that I can add it to the first equation.
-p -5n = -54
p + n = 22 Add these together
-4n = -32 Divide both sides by -4
n = 8 We have solved for n. We have 8 nickels.
Plug 8 in for n in the first equation and solve for p.
p + n = 22
p + 8 = 22 Subtract both sides by 8
p = 14 There are 14 pennies.
Check:
p + n = 22
14 + 8 = 22
22 = 22 Checks
.01p + .05n = .54
.01(14) + .05(8) = .54
.14 + .40 .54
.54 .54 check
Simplify the the following
Answer:
Answer is in the picture attached
What is the simplified form of the quantity x over 4 plus y over 3 all over the quantity x over 3 minus y over 4?
The simplified form of a given phrase x over 4 plus y over 3 all over the quantity x over 3 minus y over 4 is (3x + 4y) / (4x - 3y).
What is an expression?An expression is a combination of some mathematical symbol such that arithmetic operator and variable such that all are constrained and create an equation.
For example 3x +5y
Given the phrase,
x over 4 = x/4
y over 3 = y/3
Combine x/4 + y/3
x over 3 minus y over 4 = x/3 - y/4
Therefore ;
(x/4 + y/3) ÷ (x/3 - y/4)
⇒ (3x + 4y)/12 ÷ (4x - 3y)/12
The second fraction will inverse in multiplication
⇒ (3x + 4y)/12 × 12/(4x - 3y)
⇒ (3x + 4y) / (4x - 3y).
Hence "The simplified form of a given phrase x over 4 plus y over 3 all over the quantity x over 3 minus y over 4 is (3x + 4y) / (4x - 3y)".
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The Alden Middle School girls' soccer team won 80% of its games this season. If the team won 12 games,how many games did it play?
Answer:
15 games
Step-by-step explanation:
Since the team won 80% of the games and won 12, we can put these into an equation.
80% is also 0.8 so:
x * 0.8 = 12
To find x we can simply do 12 divided by 0.8 which equals =
15
Simplify the following. (Do NOT evaluate!) √80y^3
After simplifying the expression √80y³, we get the answer as 4 y √5 y.
We are given that:
√80y³
We have to simplify it.
We will first make the factors of it.
Factors of 80:
80 = 2 × 2 × 2 × 2 × 5
Factors of y³:
y³ = y × y × y.
Now the expression can be re- written as:
√2 × 2 × 2 × 2 × 5 × y × y × y.
Simplifying it:
2 × 2 × y √5 y
4 y √5 y
Therefore, after simplifying the expression √80y³, we get the answer as 4 y √5 y.
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I really need help on 16 and 18 I'm super confused problem because I'm tired but I really need help
Answer:
Hello,
Step-by-step explanation:
16)
Area of the square= 5²=25 (unit of square)
17)
Volume of the cube =3^3 =27 (unit of volume)
18)
side of the cube =5 (unit of lenght)
Volume of the cube = (5 (unit of lenght)) ^3
=125 * (unit of lenght)^3 =125 (unit of volume)
Find the circumference of the largest circle that will fit inside of a square that has an area of 144 square feet?
Answer:
6
Step-by-step explanation:
The square's side will be √144 = 12
The largest circle will have diameter of 12 so it's radius will be 12/2 = 6
Which graph does not represent a function?
Answer:
Choice 3
Step-by-step explanation:
The graph fails the vertical line test.
WILL CHOOSE BRAINLIEST!!!
Answer: 51.96m
Step-by-step explanation:
We can solve this using cosine, remember SOHCAHTOA, so cos is adjacent over hypotenuse.
hyp = 60
adj = ?
[tex]cos = \frac{adj}{hyp}\\cos 30 = \frac{x}{60} \\\\cos30 *60=x\\x=51.96m[/tex]
What is the mean and the median of 2, 4, 6, and 8?
In the metric system, how many milligrams are needed to make a gram?
Answer:
In one gram, there are 1000 milligrams.
To convert g to mg, multiply the gram value by 1000.
Solve 4x + 3y = 2 for y. Question 18 options: A) y = –4∕3x + 2∕3 B) y = –4x + 2 C)
Answer:
i think its answer is A or D
Answer:
y =2/3 =4/3x
Step-by-step explanation:
Solve the inequality and express your answer in interval notation.
x^2-6x+7 < 0
Solution:
A. [tex](3-\sqrt{2}, 3+\sqrt{2})[/tex]
Hope this helps!
simplify
5/8 divide by 5/6
Answer: 3/4
Step-by-step explanation:
See attached work. Remember when dividing fractions, you must multiply by the reciprocal of the second fraction.
2. Is 4x-3=19 true, false, or open? (1 point)
true
false
Open
If the 100th term of an arithmetic sequence is 609, and its common difference is 6, then
its first term a1=
It’s second term a2=
It’s third term a3=
Answer:
15, 21, 27
Step-by-step explanation:
[tex]a_n}[/tex] = [tex]a_{1}[/tex] + (n-1)d
[tex]a_{n}[/tex] is the number in the sequence we are looking for
[tex]a_{1}[/tex] This is the first term in the sequence that we do not know and we are looking for
n stands for the number of the term and d is the common difference. We will put in all that we know and solve for the first term.
609 = [tex]a_{1}[/tex] + (100-1)6
609 =[tex]a_{1}[/tex] + (99)6
609 = [tex]a_{1}[/tex] + 594 Subtract 594 from both sides of the equation
15 = [tex]a_{1}[/tex]
Now that we know that the first term is 15 we just add 6 to get the next term which is 21 and then add 6 again to get the last term 27.
value of x in the equation −3(3x−4)=15−8x?
Answer:x=−19
Step-by-step explanation: work in your head ppl
Answer: -3
Step-by-step explanation:
trust me
HELPPP QUESTION three
The image of D surely lies on the ray BA ,as ray BA is antiparallel to the ray BD.
Consider D’ to be the image of point D obtained ,when D is rotated 180 degrees anti-clockwise(or counter-clockwise),with B as center of rotation.
From the image above,it is clear that the rays BA and BD are antiparallel.
A ray is a segment of a line with a starting point and an infinite length in one direction.
Antiparallel rays are the rays which are parallel but oppositely directed.The angle between such rays is 180 degrees.
Hence,D’ must lie on the ray BA, as ray BA is antiparallel to BD(i.e the angle between the rays is also 180 degrees).
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The roof and exterior walls of a house represent intersecting planes. Using the image, name all the lines that are formed by the intersecting planes. (i dont have the picture but if you know which question im talking about please help me)
In the possible diagram of the house, the lines formed by intersecting planes are; [tex] \overline{AG}[/tex], [tex]\overline{ AB}[/tex], [tex]\overline{AH}[/tex], [tex]\overline{GF}[/tex], [tex]\overline{ BH}[/tex], [tex]\overline{HF}[/tex], [tex]\overline{BC}[/tex], [tex]\overline{ HD}[/tex], and [tex]\overline{FE} [/tex]
What are the planes and the lines formed by them on the building?The diagram found in a similar question has points A, G, B, H, and F on the roof.
The points on the walls of the house are; B, H, F, C, D, and E
A plane in Euclidean geometry is a surface that is flat, such that a line that connects two points on it lie completely on the plane.
A plane can be identified by three non collinear points that lay on it.
A line is a figure that does not have a curvature, width or depth, and it is infinitely long.
The planes on the roof are; ABH and AGHF
The planes on the walls of the house are; BCDH, and HDCF
The lines that are formed by the intersecting planes are therefore;
On the roof;
[tex] \overline{AG}, \overline{ AB}, \overline{AH}, \: \overline{GF},[/tex]Between the roof and the walls of the house;
[tex]\overline{BH}, \overline{HF}[/tex]Between the two sides of the walls;
[tex] \overline{BC}, \overline{ HD}, \overline{FE} [/tex]Learn more about lines and planes in Euclidean geometry here:
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What is the difference between positive association and negative association as it pertains to the relationship between two variables?.
A positive association occurs when an increase in one variable is generally associated with the increase in the second variable and a negative association occurs when one variable tends to decrease as the other increases.
What is meant by an association relationship between two variables?An association is any relationship between two factors that produces them subordinate, i.e. knowing the value of one variable gives us some data around the possible values of the moment variable.
The objective of this variable is to utilize clear measurements and visualisations to investigate affiliations among different kinds of factors.
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The sum of three consecutive integers is 303. If n is the smallest of the three, which equation represents this situation?
The equation that best represents a the given situation is: 3n + 3 = 303., as found by number system.
What is number system?A system of writing numbers is known as a number system. It is the mathematical notation for consistently employing digits or other symbols to represent the numbers in a particular set. It represents the arithmetic and algebraic structure of the numbers and gives each number a distinct representation.
Given: Sum of three consecutive integers is 303.
n = smallest integer.
According to question, the other two integers are: n + 1, and n + 2.Since the sum of the three consecutive integers is 303, addition operation on the values of number system
n + n + 1 + n + 2 = 303
3n + 3 = 303.
Hence, The equation that best represents a the given situation is:
3n + 3 = 303., as found by number system.
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How are defined terms and undefined terms related?
Answer:
"Defined items" are defined in terms of "undefined terms".
Step-by-step explanation:
None.
I need help −1/1/5+(−3/5)=
Answer:
- 4/5 /decimal form -0.8
Step-by-step explanation:
an independent group of food service personnel conducted a survey on tipping practices in a large metropolitan area. they collected information on the percentage of the bill left as a tip for 2525 randomly selected bills. the average tip was 13.1.1% of the bill with a standard deviation of 2.6%2.6%. assume that the tips are approximately normally distributed. construct an interval to estimate the true average tip (as a percent of the bill) with 90% confidence. round the endpoints to two decimal places, if necessary.
90% confidence interval is 11.65 <µ< 114.566 as per standard deviation data.
What is a standard deviation?
The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. When the standard deviation is low, the data are concentrated around the mean, and when it is large, the data are widely dispersed.Sample mean (T) = 13.11%
Sample standard deviation (s) = 2.6
Sample size (h) = 25
significance level = α = 1 -0.90 = 0.1
Degrees of freedom for t- distribution (df) = 24
Critical value = ta/2
df = [tex]t_{0.1}[/tex], df=24 = ±2.80
The margin of error (E) =[tex]t_\frac{a}{2} , df\frac{s}{\sqrt{h} }[/tex]
E=2.8X [tex]\frac{2.6}{\sqrt{25} }[/tex] =1.456
Limits of 90%. Confidence Interval is.
Lowest limit = X' - E = 13.11-1.456 = 11.65
Upper limit= X' + E = 13.11+1.456 = 14.566
90% confidence interval is 11.65 <µ< 114.566 as per standard deviation data.
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3.
According to the 2010 census, the population of Nebraska was 1.8 x 106 people. Which state
had a smaller population?
OCalifornia: 3.7 × 107
ORhode Island: 1.1 × 106
OTexas: 2.5 x 107
OMissouri: 6 x 106
If the population of Nebraska was 1.8×[tex]10^{6}[/tex], then the state which had a smaller population is Rhode Island
Given,
The population of Nebraska = 1.8×[tex]10^{6}[/tex]
The population of Rhode Island = 1.1×[tex]10^{6}[/tex]
1.1×[tex]10^{6}[/tex] < 1.8×[tex]10^{6}[/tex]
So, Rhode island has population less than Nebraska
Hence, if the population of Nebraska was 1.8×[tex]10^{6}[/tex], then the state which had a smaller population is Rhode Island
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the area of the rectangle is 14yd squared and the length of the rectangle is 3yds leass than twice the width
The dimensions of the rectangle are:
Length = 7/2 ydWidth = 4 ydTotal area = 14 yd²What is the area?The quantity area expresses the extent of a region on a plane or curved surface. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.To find the dimensions of the rectangle:
Let,
Area = A = 14Width = wLength = 2w-3A = lwA = (2w-3)wExtend the area equation as follows:
A = 2w2-3wRearrange:
2w2 - 3w - A = 0Substitute known information for A:
2w2 - 3w - 14 = 0To solve quickly, factor the left side (or use the quadratic formula):
(w+2)(w - 7/2) = 0The factorial solutions for w are -2 and 7/2.
Assuming this is a genuine rectangle, the width must be positive.
As a result, the length is:
2(7/2) - 3That is,
7 - 3 = 4Therefore, the dimensions of the rectangle are:
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The complete question is given below:
The area of a rectangle is 14 yd², and the length of the rectangle is 3 yd less than double the width. find the dimensions of the rectangle.
The length of a rectangle is 6 inches longer than its width. What are the possible widths if the area of the rectangle is at least 667 square inches?
Answer:
D, [tex]w\geq 23[/tex]
Step-by-step explanation:
The length is 6 inches longer than it's width, therefore:
[tex]l=w+6[/tex]
The area of the rectangle is AT LEAST 667 square inches, so:
[tex]lw\geq 667[/tex]
Now, we have a system of two equations:
[tex]\left \{ {{l=w+6} \atop {lw\geq 667}} \right.[/tex]
We want to isolate the width, so substitute the first equation into the second to eliminate the length.
[tex](w+6)w\geq 667[/tex]
Simplify:
[tex]w^2+6w\geq 667[/tex]
Since we now have a polynomial equation that needs to be factored, set the value of one side to 0.
[tex]w^2+6w-667\geq 0[/tex]
Now factor the equation:
[tex](w-23)(w+29)\geq 0[/tex]
Taking each factor individually, we find the following:
[tex]w\geq 23\\w\geq -29[/tex]
Since a negative width doesn't make any sense, we can eliminate that solution, and we are left with the correct answer!
[tex]w\geq 23[/tex]
What is constant in the simplified form of (x - 6)²?
Answer:
36
Step-by-step explanation:
The constant is the number when complete simplified, which in this case would be only formed by squaring the 6, equaling 36.
Hope this helps! :)
Answer: +36
Step-by-step explanation:
(x - 6)² simplified: x^2 -12x + 36
The constant in this algebraic expression is 36 because it's value or number doesn't change in the expression (x^2 -12x + 36)
Jonah read 5 1/2 chapters in his book in 90 minutes. How long did it take h
to read one chapter?
what is the simplest form of 3/7 of 6/1
3/7 of 6/1 means [tex]6(\frac{3}{7})=\frac{18}{7} =2\frac{4}{7}[/tex]
hope this helped
What
is the slope of the line that passes through the points (-4, 6) and (-4, 18)?
Write your answer in simplest form.