A textbook store sold a combined total of 447 biology and sociology textbooks in a week. The number of sociology textbooks sold was 63 less than the number of biology textbooks sold. How many textbooks of each type were sold?
255 biology and 192 sociology textbooks were sold in a week.
What is linear equation?Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.
While the graph of a linear equation with two variables, x and y, creates a straight line, the graph of a linear equation with just one variable, x, forms a vertical line that is parallel to the y-axis.
Step 1:
Let x be the number of biology textbooks and y be number of sociology textbooks.
x + y = 447 ------(1)
x - y = 63 ------(2)
Step 2:
Adding (1) and (2), we get
2x = 510
x = 255
Step 3:
Subtracting (1) from (2), we get
2y = 384
y = 192
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An art museum gift shop sells prints of a famous painting. The original
painting is 120 cm wide and 85 cm tall. If the print is 50 cm wide, how tall
is the print?
SOLUTION
The print is 35.41 cm tall.
What is Proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
The original painting is 120 cm wide and 85 cm tall.
and, the print is 50 cm wide.
let the print is x cm tall
So, x/ 50 = 85 / 120
120x = 4250
x= 35.41 cm
Hence, the print is 35.41 cm tall.
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Molly works at an electronics store. Her last customer purchased a DVD player for $63.48 and five DVDs for $52.02, including taxes. If the customer paid her with two $100 bills, how much change should she give him?
Answer:
$84.50
Step-by-step explanation:
Add the amounts:
$63.48 + $52.02 = $115.50
Two $100 bills add to $200.
To find the change, subtract the total cost from the amount of money handed over.
$200 - $115.50 = $84.50
Molly should give him $84.50. Thus option B is the correct answer.
The change given must be equal to the balance left after deducting the price of the goods from the total money received.
In this case,
Price of goods = Price of DVD player + Price of five DVDs
= $63.48 + $52.02
=$115.50
Total Money Received = 2 x $100 = $200
Therefore, Change = Total Money Received - Price of goods
= $200 - $115.50
= $84.50
Easy i just want confirmation What is 3 to the power of three halves equal to?
- cube root of 9
- square root of 9
- cube root of 27
- square root of 27
The 3 to the power of three halves equal to square root of 27 sqrt(27).
What is the square root?
A square root of a number x is a number y such that y² = x; in other words, a number y whose square is x. For example, 4 and −4 are square roots of 16, because 4² = ² = 16.
A square root is a number that can be multiplied by itself to give the original number.
3 to the power of 3/2 is equal to the square root of 3 to the power of 3, which is equal to the square root of 27. The square root of 27 is approximately 3.872983346207417.
To calculate this value, you can use a calculator or you can use the following formula:
3^(3/2) = sqrt(3^3) = sqrt(27) = 3.872983346207417
Hence, the 3 to the power of three halves equal to square root of 27 sqrt(27).
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Which is a solution of the inequality 7 ≤ −2x + 3 ?
A.) 1
B.) 2
C.) −2
D.) −1
Answer: x ≤ -2
Option C is correct
Answer:
x ≤ -2 then it is C) -2
Step-by-step explanation:
7 ≤ −2x + 3
2x+7 ≤ + 3
2x ≤ 3-7
2x ≤ -4
x ≤ -4/2
x ≤ -2
An airplane travels 100 miles in 0.4 hour. Which speeds represents the rate of the airplane?
The speed represents the rate of the plane is 250 miles/ hour.
What is speed?
The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.
An object is considered to be moving at constant speed when it travels an equal distance in an equal amount of time.
When an object travels a different distance at equal intervals of time, it is said to be moving at variable speed.
Average speed is the constant speed determined by the ratio of the total distance travelled by an object to the total amount of time it took to travel that distance.
Immediately speed is When an object is travelling at a variable pace, its speed at every given moment
Speed =distance/ time taken
= 100/0.4
= 250 miles/ hour
Hence, the speed represents the rate of the plane is 250 miles/ hour.
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Mr. Tull bought 6 videotapes and 5 audio tapes. What is the ratio of videotapes to the total number of tapes?
Answer: 6:11
Step-by-step explanation:
Find the total by 6 + 5 =11
He bought 6 videotapes so ratio is 6:11
2 1/2 + 3 1/5 x 5 5/8
The solution to the expression 2 1/2 + 3 1/5 x 5 5/8 is 223/2
What is Fraction?fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
2 1/2 + 3 1/5 x 5 5/8 can be solved by converting all the mixed fraction to improper fraction
2 1/2 = 5/2
3 1/5 = 16/5
5 5/8 = 45/8
which reduces it to
5/2 + 45/8 x 16/5
using BODMAS we taking care of the multiplication section first
45/8 x 16/5 = 18
5/2 + 18
18 can be writen as a fraction which is 36/2
5/2 + 36/2 = 41/2
in conclusion the simplified form of the expression is 41/2
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8. Model Real Life A window cleaner has cleaned 467 windows
of a skyscraper. He cleans some more. Now there are 967 clean
windows. Each floor of the skyscraper has 100 windows. How
many floors of windows does the window cleaner clean?
The number of floors of windows that the window cleaner cleans will be 10.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
A window cleaner has cleaned 467 windows of a high rise. He cleans some more. Presently there are 967 clean windows. Each floor of the high rise has 100 windows.
The number of floors of windows that the window cleaner cleans will be given as,
⇒ 967 / 100
⇒ 9.67
⇒ 10 floors
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Please help with these two questions!
The inverse of the function g(x) = ∛(2x + 4) is equal to: D. g(x)⁻¹ = 1/2(x³) - 2.
The domain of the function shown in the graph is: B. [-2, 1].
What is an inverse function?In Mathematics, an inverse function can be defined as a type of function that is obtained by reversing (undoing) the operation of a given function (f(x)).
In order to determine the inverse of the given function, we would interchange input value (x) and the output value (y) as follows:
g(x) = ∛(2x + 4)
x = ∛(2y + 4)
Next, we would take the cube root of both sides of the function;
x³ = 2y + 4
2y = x³ - 4
y = (x³ - 4)/2
y = x³/2 - 2
g(x)⁻¹ = 1/2(x³) - 2
How to identify the domain any graph?In Mathematics, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right as follows;
Domain = [-2, 1].
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6am air traffic controller i tracking two plane to tart plane A wa at an altitude of 1500 meter and plane B wa at an altitude of 1115 meter plane A i going altitude at 19 meter per econd and plan B wa gaining altitude at 26 meter per econd let x be the number of econd that have pae
At 55 seconds , both the plane A and plane B will have same altitude.
According to the question,
The altitude of plane A = 1500m
The altitude of plane B = 1115m
Altitude plane A gained = 19m/s
Altitude plane B gained = 26m/s
Let "x" be the number of second
Let the equation of plan A and plane B is
a(x) = m₁ x + 1500
b(x) = m₂ x + 1115
We know how fast they are gaining altitude. The are the m values
m₁ = 19
m₂ = 26
So, now we have
a(x) = 19 x + 1500
b(x) = 26 x + 1115
So , to have same altitude ,
a(x) = b(x)
=> 19 x + 1500 = 26 x + 1115
Solving for x,
=> 26x-19x = 1500 - 1115
=> 17x = 385
=> x = 55 seconds
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Jacob distributed a survey to his fellow students asking them how many hours they'd spent playing sports in the past day. He also asked them to rate their mood on a scale from 0 00 to 10 1010, with 10 1010 being the happiest. A line was fit to the data to model the relationship.
The best estimate of the average change in mood rating linked with an additional hour spent playing sports is 1.5 points, according to the presented linear function.
Modeling a linear function involves:
y = mx + b
The slope, or m, measures how quickly y changes when x changes by one.
The value of y at x = 0 is represented by the y-intercept, or b.
In the given problem
The amount of time they invested in sports is x.
Their mood score is y.
The required equation is ,
y =1.5 + 5
Given that the slope is m = 1.5, the best estimate of the average change in mood rating resulting from an extra hour spent playing sports is 1.5 points.
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i tried the cosine rule and the sine rule but i dont get why the answer is wrong.
Answer:
93.2° (nearest tenth)
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Sine Rule} \\\\\\$\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c} $\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}[/tex]
From inspection of the given triangle:
B = 38°b = 9 cmc = 11 cmSubstitute the values into the sine rule to find the measure of angle C:
[tex]\implies \dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]
[tex]\implies \dfrac{\sin 38^{\circ}}{9}=\dfrac{\sin C}{11}[/tex]
[tex]\implies \sin C=\dfrac{11\sin 38^{\circ}}{9}[/tex]
[tex]\implies C=\sin ^{-1} \left(\dfrac{11\sin 38^{\circ}}{9}\right)[/tex]
[tex]\implies C=48.80523914...^{\circ}[/tex]
Interior angles of a triangle sum to 180°.
[tex]\implies A+B+C=180^{\circ}[/tex]
[tex]\implies A+38^{\circ}+48.80523914...^{\circ}=180^{\circ}[/tex]
[tex]\implies A=93.19476086...^{\circ}[/tex]
Therefore, the size of angle A is 93.2° (nearest tenth).
Write the equation of the line that goes through the point (4, -7) and is perpendicular to the line
y +6=-2/5(x-1). Use the table to show your work, if needed, to determine each form, and then give each form.
Point-Slope Form
Slope-Intercept Form
Show your work.
The point-slope form with a slope of 5/2 and a point of (4,-7) is 5x-2y=34.
What is line equation?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10. Linear equations are classified into three types: point-slope, standard, and slope-intercept.
Here,
The slope of line perpendicular to the line y +6=-2/5(x-1)
m1=5/2
point=(4,-7)
y-y1=m(x-x1)
y+7=5/2(x-4)
2y+14=5x-20
5x-2y=34
The point-slope form for slope given as 5/2 and point as (4,-7) will be 5x-2y=34.
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A construction worker must raise to the top of a 20-foot-tall building using a computer-controlled crane. If the materials are 28 feet away from the base of the building. What slope needs to be programmed into the computer to accomplish the delivery? State your answer as a fraction in lowest terms
The slope that needs to be programmed into the computer to accomplish the delivery is x=3441/100.
What is meant by Pythagorean theorem?A fundamental relationship in Euclidean geometry between a right triangle's three sides is known as the Pythagorean theorem or Pythagoras theorem in mathematics. It is believed that the area of the square with the hypotenuse equals the sum of the areas of the squares on the other two sides.
Pythagoras, a Greek philosopher who was born around 570 BC, is honored in the name of the theorem. Perhaps more than any other mathematical theorem, the theorem has been demonstrated several times using a variety of techniques. There are many different types of proofs, some of which go back thousands of years, including both geometric proofs and algebraic proofs.
By using Pythagorean theorem,
x²=20²+28²
x²=400+784
x²=1184
x=34.41
x=3441/100
Therefore, the slope that needs to be programmed into the computer to accomplish the delivery is x=3441/100.
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what does x equal? ???
Answer: 6.1
Step-by-step explanation:
The sine rule states that the length of one side of a triangle divided by the sine of the angle opposing the side will be equal to the length of the other side divided by the sine of its opposing angle and the same for the last side.
This means [tex]\frac{14}{sin (90)}[/tex] = [tex]\frac{x}{sin(180-90-64)}[/tex]
14 = [tex]\frac{x}{sin(26)}[/tex]
x = 14sin(26) ≈ 6.1
Which of the following is a solution to the inequality below?
4>102/z+11
A=3 B=1 C=2 D=6
None of the option are correct for the solution to inequality.
Explain the term solution to inequality?Finding a range, and ranges within ranges, of values which an unknown x can have while still satisfying the inequality is referred to as "solving" an inequality. In this lesson, inequalities are resolved using graphs and algebra.A number is solution to an inequality of x if it can be used to replace x with a statement that is true.For the given inequality:
4 > 102/z + 11
Subtract both side by 11
4 - 11 > 102/z + 11 - 11
-7 > 102/z
Divide both sides by 102
-7/102 > 1/z
Taking reciprocal of each;
z < -102/7
z < -14.5
Thus, none of the option are correct for the solution to the inequality.
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What expreion repreent the um of 2 divided by x and 15
215÷x215÷x
(215)÷x(215)÷x
152÷x152÷x
(152)÷x
The required expression will be 2/x+15 as the problem says "the sum of 2 divided by x and 15".
What is expression?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. 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. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases. A phrase in language may contain an action on its own, but it does not constitute a complete sentence.
Here,
2 divided by x,
=2/x
sum of 2/x and 15,
2/x+15
The conclusion is "the sum of 2 divided by x and 15," hence the necessary equation will be "2/x+15."
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Uma fábrica de peças automotivas produz dois tipos de peça: A e B. Sabe-se que o custo
unitário de produção da peça A é de R$ 180. Já, para a peça B, o custo direto é de R$ 290 a unidade
produzida. Estes custos referem-se à matéria-prima, mão de obra empregada etc. Aos custos diretos,
somam-se os custos fixos semanais, que incluem energia elétrica, aluguel de espaços de produção
etc, que equivalem a R$ 15.000,00. A partir disso, responda o que se pede:
Because m < n m = n am < bn am = bn this is where the function is undefined
Answer: This is where the answer is undefined
Step-by-step explanation:
Edge 2022 :)
Answer: 5th option
Step-by-step explanation:
edge 2023
Carol has 123 pounds of beans. She fills jars by putting 23 pound of the beans into each jar. What number of jars can be filled with the beans?
119
2
212
3
The number of jars that are fully filled is 5 and one jar filled partially is 8 out of 23 parts.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Song has 123 pounds of beans. She fills containers by placing 23 pounds of beans into each container.
⇒ 123 / 23
⇒ 5 ⁸/₂₃
The number of jars that are fully filled is 5 and one jar filled partially is 8 out of 23 parts.
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HELP. ITS AN EMERGENCY. ANSWER WITHIN 20MINS FOR 100 CREDITS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
12: This one if fairy simple: all you need is a line that is not parallel to the line provided, and combined with it, it will provide a solution that's on that line. For example:
y = 2x
x - y = 10
13: Just find two lines that cross (6, -4).
You can use point-slope form:
y - y1 = m(x-x1)
y + 4 = m(x - 6)
then choose two equations with different m's
y = 2(x-6) - 4
y = 3(x-6) - 4
14:
Line one has a slope of two and an intercept at y=0 so it is y = 2x
Line two has a slope of one and an intercept at y=-1 so it is y = x - 1
To find the solution of the system, substitute y:
2x = x - 1
x = -1
Then plug back in:
y = 2 * -1 = -2
So the solution is: (-1, -2)
Solve this problem
-20 < 2x6 ≤2
Answer: -20<12<=2
Step-by-step explanation:
First, you simplify the expression.
-20<2*6<=2
And then perform any multiplication or division, from left to right...
-20<2*6<=2
-20<12<=2
And there you have it!
I hope this helped!
Have a great rest of your day and Merry Christmas (and Happy New Year)!
50 POINTS IF ANSWERED!!!!
Find the value of x
Answer:
The answer is 45
Step-by-step explanation:
the way to find this answer is by, first, knowing that each angle of a triangle adds up to 180. So, we must first add the 85 and 50 which will give us 135. After, you subtract it all from 180, which gives you 45.
In the triangle, the value of x is,
⇒ x = 45°
We have to given that;
In triangle;
The angles are 85 degree, 50 degree and x.
Since, We know that;
Sum of all interior angle of a triangle are 180 degree.
Hence, We get;
⇒ x + 85 + 50 = 180
⇒ x + 135 = 180
⇒ x = 180 - 135
⇒ x = 45°
Thus, the value of x is,
⇒ x = 45°
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Luis solves the following system of equations by elimination. {5s+3t=30 2s+3t=-3
The Elimination equations: 3s = 33, s = 11.
What is Equation?A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance.
Equations come in a variety of forms, including linear, quadratic, cubic, etc
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" symbol in it.
According to our question-
5s+3t=30
-1(2s+3t=-3)
which will eventually
5s+3t=30
-2s-3t=3
which then becomes
3s = 33, s=11
Hence, The Elimination equations: 3s = 33, s = 11.
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PLEASE HELP ITS GEOMETRY ASAP HELP ME
elimination method. please help
3x+4y=21
3x-2y=11
Answer:
(x, y) = (4 7/9, 1 2/3)
Step-by-step explanation:
You want to solve this system of equations using the elimination method.
3x +4y = 213x -2y = 11AnalysisFirst of all, take a look at the coefficients of the variables:
x: 3 and 3. Subtracting one from the other will eliminate x
y: 4 and -2. Adding twice the second to the first will eliminate y.
ExecutionThe easiest elimination is accomplished by subtracting the second equation from the first:
(3x +4y) -(3x -2y) = (21) -(11)
6y = 10 . . . . . . . . . . simplify
y = 10/6 = 5/3 = 1 2/3 . . . . divide by the coefficient of y
Finding xSubstitute for y to find x.
3x +4(5/3) = 21
x +20/9 = 7 . . . . . . divide by 3
x = 7 -(2 2/9) = 4 7/9
The solution is (x, y) = (4 7/9, 1 2/3).
__
Additional comment
A graphing calculator confirms this solution.
Students are making lemonade from a powdered lemon drink mix. Ariana
mixes 3 cups of water and 17 cups of powdered lemon mix. Andres mixes 1
cup of water and 10 cups of powdered lemon mix. Use Ariana and Andres's
percent of pewdered lemon mix to determine whose mix will be more lemony.
Ariana percent of powdered lemon mix (to nearest whole number) =
Andres percent of powdered lemon mix (to nearest whole number) =
Answer: Ariana uses 85% drink mix, and Andres uses 90% drink mix. Therefore, Andres's drink will taste more lemony.
Step-by-step explanation:
Ariana uses 17 cups of mix out of the 20 total cups which is 85%
Andres uses 10 cups of mix out of the 11 total cups which is around 90%
Answer:
Ariana percent: 85Andres percent: 91Step-by-step explanation:
You want the percent of powdered lemon mix in two recipes:
Ariana: 3 c water, 17 c lemon mixAndres: 1 c water, 20 c lemon mixPercentThe desired percent can be found from ...
(lemon mix)/(water + lemon mix) × 100%
For Ariana, this is ...
17/(3 +17) × 100% = 17/20 × 100% = 85%
For Andres, this is ...
10/(1 +10) × 100% = 10/11 × 100% ≈ 91%
__
Additional comment
There aren't many powders that will dissolve 10 cups of powder in 1 cup of water. Even if there were, the resulting combination would not have a volume of 11 cups. This might be a mildly interesting math problem, but it has little relevance to any real-world lemonade recipe.
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if the histogram of monica's tips does not follow the normal curve, is the confidence interval still valid?
Yes , the confidence interval still valid because the sample size is large ( n = 100 is greater than 30 ).
Given :
Monica delivers pizza. She takes a simple random sample of 100 of her deliveries from the first 11 months of 2020 and finds that her tips average $3.66 with an SD of $2.19.The 90% confidence interval for Monica’s average tip size for these months has the form A + - B * C .
if the histogram of monica's tips does not follow the normal curve, is the confidence interval still valid .
Here
sample size n = 100
The sample size is a term used in market research for defining the number of subjects included in a sample size.
here
n > 30
Hence the confidence interval is still valid .
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Full question:
Monica delivers pizza. She takes a simple random sample of 100 of her deliveries from the first 11 months of 2020 and finds that her tips average $3.66 with an SD of $2.19.The 90% confidence interval for Monica’s average tip size for these months has the form A + - B * C .
if the histogram of monica's tips does not follow the normal curve, is the confidence interval still valid?
An equiangular triangle has one side of length six inches. What is the height of the triangle, drawn from that side, to the nearest tenth of an inch?
height = ------------- in.
Answer:
5.2
Step-by-step explanation:
Construct an altitude. Using the Pythagorean theorem, the height is [tex]\sqrt{6^2-3^2} \approx 5.2[/tex]