Answer:
c = 72/0.45
c = 160
So the value of c =160
well, let's call "c" the 100%, and we know that 45% of that is 72, hmmm so
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} c & 100\\ 72& 45 \end{array} \implies \cfrac{c}{72}~~=~~\cfrac{100}{45} \\\\\\ \cfrac{ c }{ 72 } ~~=~~ \cfrac{ 20 }{ 9 }\implies 9c=1440\implies c=\cfrac{1440}{9}\implies c=160[/tex]
PLEASEEE HELP ASAPPP
Select the correct answer.
To solve this system of equations using substitution, what could be substituted in place of y in the first equation?
4x = 5 − 2y
y − 2x = 7
Answer:
2x+7
Step-by-step explanation:
this is because if you rearrange the bottom equation to be in y= format, this is the solution you will find
Law of sines: startfraction sine (uppercase a) over a endfraction = startfraction sine (uppercase b) over b endfraction = startfraction sine (uppercase c) over c endfraction 2.2 units 2.4 units 3.0 units 3.3 units
The possible approximate lengths of b are: 2.3 units and 7.8 units
We know that the law of sines for triangle is:
The ratios of the length of all sides of a triangle to the sine of the respective opposite angles are in proportion.
This means, for triangle ABC,
[tex]\frac{sin~ A}{a} =\frac{sin~B}{b} =\frac{sin~ C}{c}[/tex]
where a is the length of side BC,
b is the length of side AC,
c is the length of side AB.
For triangle ABC consider an equation from sine law,
[tex]\frac{sin~ A}{a} =\frac{sin~ C}{c}[/tex]
here, c = 5.4, a = 3.3, and m∠A = 20°
[tex]\frac{sin~ 20}{3.3} =\frac{sin~ C}{5.4}\\\\\frac{0.3420}{3.3} =\frac{sin~ C}{5.4}[/tex]
0.3420 × 5.4 = 3.3 × sin(C)
sin(C) = 0.5596
∠C = arcsin(0.5596)
∠C = 34.03° OR 145.9°
∠C ≈ 34° OR 146°
We know that the sum of all angles of triangle is 180 degrees.
so, ∠A + ∠B + ∠C = 180°
when m∠C = 34°,
20° + ∠B + 34.03° = 180°
∠B = 125.97°
m∠B = 126°
when m∠C = 146°,
20° + ∠B + 146° = 180°
m∠B = 14°
Now consider equation,
[tex]\frac{sin~ A}{a} =\frac{sin~ B}{b}\\\\\frac{sin~20^{\circ}}{3.3} =\frac{sin~ 126^{\circ}}{b}[/tex]
b × 0.3420 = 0.8090 × 3.3
b = 7.8 units
when m∠B = 14°,
[tex]\frac{sin~20^{\circ}}{3.3} =\frac{sin~ 14^{\circ}}{b}[/tex]
b × 0.3420 = 0.2419 × 3.3
b = 2.3 units
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The complete question is:
Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction
In ΔABC, c = 5.4, a = 3.3, and measure of angle A = 20 degrees. What are the possible approximate lengths of b? Use the law of sines to find the answer.
2.0 units and 4.6 units
2.1 units and 8.7 units
2.3 units and 7.8 units
2.6 units and 6.6 units
you give a test to 100 students and determine the range of the scores. after grading the test, you realize that the 10 students with the highest scores did exceptionally well. you decide to award these 10 students a bonus of 5 more points each. the range of the new score distribution will be (less than, greater than or the same as) that of the original score distribution?
The range of the new score distribution will be greater than the range of the original score distribution.
The range of a set of scores is the difference between the highest and the lowest scores in the set. Adding 5 bonus points to the 10 highest scores in the original set will increase the highest scores and therefore increase the range of the new score distribution.
The range of the original score distribution represents the spread of scores between the highest and lowest scores in the original set, and increasing the highest scores will increase the spread of scores between the highest and lowest scores in the new set, resulting in a greater range.
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rework problem 23 from section 2.2 of your text, involving the election of officers on a committee. assume that the committee consists of 13 members including caden. the same three offices are to be filled. (1) in how many different ways can the offices be filled if each person can hold at most one office? equation editorequation editor (2) in how many of these ways is caden the chairperson? equation editorequation editor (3) in how many of these ways is caden an officer? 0 equation editorequation editor
(1) By 1716 different ways can the offices be filled if each person can hold at most one office.
(2) By 132 number of ways Caden can be the chairperson.
(3) By 1320 of the 1716 total ways the offices can be filled,
(1) If each person can hold at most one office, there are 13 people to choose from for the first office, 12 people remaining to choose from for the second office, and 11 people remaining to choose from for the third office.
Therefore, the number of different ways the offices can be filled is:
13 * 12 * 11 = 1716 ways
(2) If Caden is the chairperson, there are 12 people to choose from for the second office and 11 people remaining to choose from for the third office.
Therefore, the number of ways Caden can be the chairperson is:
12 * 11 = 132 ways
(3) If Caden is an officer, there are 12 people to choose from for the first office, 11 people remaining to choose from for the second office, and 10 people remaining to choose from for the third office.
Therefore, the number of ways Caden can be an officer is:
12 * 11 * 10 = 1320 ways
So, in 1320 of the 1716 total ways the offices can be filled, Caden is one of the elected officers.
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1) The visitors rented bicycles at the resort.1
2) They hired my brother as a nutritionist.
3) Hundreds of visitors visit the spa every week.
4) They booked a spa holiday.
5) They do not allow children in this health resort.
When converted from active voice to passive voice, the sentences read as follows:
Active Voice refers to a sentence construction where the subject is performing the action described by the verb. It emphasizes the doer of the action.
On the other hand, Passive Voice refers to a sentence construction where the action is performed on the subject, rather than the subject performing the action. It emphasizes the action or the object affected by the action.
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The following equations represent linear functions. Which of the following is true about the functions?
The true statement about the functions is that that graphs are perpendicular lines
How to determine the true statementFrom the question, we have the following parameters that can be used in our computation:
y = 3/4x + 7
y = -4/3x + 7
A linear equation is represented as
y = mx + c
Where
slope = m
This means that the slopes are
3/4 and -4/3
The above slopes are opposite reciprocal
i.e.
3/4 * -4/3 = -1
Hence, they are perpendicular lines
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There are 20 cd left to be sold in a store. This is between 1% and 1.25% of the original number of copies of the CD store. The original number of CDs was between what two numbers?
The original number of CDs is between 1000 and 1500.
What is algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Number of copies of a popular CD left to be sold in the store = 20
According to question, this is between 15 and 1.5% of the original number of copies of the CD in the store.
Let the original number of copies of the CD be 'x'.
Now, 20 is equal to 1% of the original number of copies of the CD,
1% of x = 20
1/100 of x= 20
x= 2000
Or if 15 is equal to 1.5% of the original number
1.25% of x= 20
1.25/100 x = 20
x = 1600
Hence, the CDs is between 1000 and 1500.
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I NEED IMMEDIATE HELP PLEASE HELP ME SOLVE THIS PROBLEM
Answer:
No
20 inches
Step-by-step explanation:
Area of a triangle = 1/2 × breadth × height
Therefore,
[tex] \frac{1}{2} \times 5 \times 8[/tex]
[tex] = \frac{1}{2} \times 40[/tex]
That mean
[tex] = \frac{40}{2} = 20[/tex]
I need help, ASAP! I can't figure out how to solve this. The math problem is in the picture below, Thanks!
The line of best fit for the given points is as follows:
y = 1.21x + 1.57.
How to obtain the equation for the regression line?The equation for the line of fit is obtained inserting the points of the data-set into a linear regression calculator.
The points for the data-set in this problem are given as follows:
(1,2), (2,5), (3,7), (4,2), (5,10), (6,10) and (7,9).
Inserting these points into the linear regression calculator, the line of best fit for these points is defined as follows:
y = 1.21x + 1.57.
(rounding the coefficients to two decimal places).
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a combination of values that, when arranged correctly, result in a final value.
Combinations and sequences are widely used in mathematics to explain and assess situations in which the order or selection of components might influence the final result.
What is combination?A combination in mathematics is a selection of elements from a set with distinct members, where the order of selection is irrelevant. A combination is a mathematical approach for determining the number of potential arrangements in a set of objects when the order of the selection is irrelevant. You can choose the components in any order in combinations. A combination is a method of picking elements from a collection when the order of selection is irrelevant. Assume we have three integers P, Q, and R. Combination defines how many possibilities we may choose two numbers from each set.
Here,
A combination is a grouping of things from a bigger set in which the order of the components is irrelevant. A sequence is a collection of elements that are ordered in a precise order. Combinations and sequences are frequently used in mathematics to describe and evaluate situations where the order or selection of components might impact the final outcome, such as in combinatorics, probability, and statistics.
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Complete question:
A combination of values that, when arranged correctly, result in a final value. true/false
Expand to write an equivalent expression: -12(-2x+4y)
Factor to write an equivalent expression: 26a−10
26x - 52y is the equivalent expression.
2(13a - 5) is the equivalent expression.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
-13 (-2x + 4y)
= -13 x -2x+ -13 x 4y
= 26x - 52y
Now,
26a - 10
Taking out a common factor.
= 2 (13a - 5)
Thus,
26x - 52y and 2(13a - 5) are the equivalent expression.
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a salesman a car dealership earns a month salary is $2400 and $250 for each vehicle. the Salesman sells 12 cars per month for the entire year, what is the minimum amount of money the salesperson earns for the entire year. What is the maximum amount of money the salesperson earns for the entire year
The required maximum amount of money the salesperson earns for the entire year is given as $5400.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
Let the total amount earned be x,
According to the question,
x = 2400 + 250×12
x = $5400
Thus, the required maximum amount of money the salesperson earns for the entire year is given as $5400.
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Find the slope from a table?
X 3 5 8 13 16
Y 1 9 7 11 14
What is the first part of the process of investigating a question using data?  A. Describing the data
The first part of the process of investigating a question using data is C. Collecting the data.
What is the procedure for using data to investigate a question?The first ideas regarding the questions to ask guide the data exploration process. It continues with planning, data gathering and exploration, and feature reporting. There are many different ways to explain and summarize the procedure.
Data is information that has been transformed into a cycle that is useful for transfer or processing in computing. Data is information that has been transformed into binary digital form for use with modern computers and communication mediums. The topic of data may be used in either the
Therefore, option C is correct.
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missing options:
A. Describing the data
B. Describing the data
C. Collecting the data
D. Rephrasing the question
Find
(a)the largest integer which is a factor of 96 and 294
(b) The smallest positive integer
n for ehich 96n is a multiple of 294
Answer:
(a) 6
(b) 49
Step-by-step explanation:
(a) The largest integer which is a factor of 96 and 294 should be their HCF.
Therefore, 96 = 2 × 2 × 2 × 2 × 2 × 3
294 = 2 × 3 × 7 × 7
Therefore, HCF = 2 × 3 = 6
(b) 96n should be the LCM of 96 and 294.
We know, product of two numbers = HCF × LCM
or, LCM = (96 × 294)/6 = 4704
So, 96n = 4704
or n = 49
Hope it helps.
If you have any query, feel free to ask.
Solve for x.
x + 47 = -23
x =
given z1 = 8(cos 45° i sin 45°) and z2 = 4(cos 210° i sin 210°), what is z1z2?
For the required value of the given complex numbers z₁z₂ = 32(cos 255° + isin 255°).
What are complex numbers?Complex numbers are those that expand on the idea of real numbers by incorporating an illogical element.
The formula for a complex number is "a + bi," where "a" and "b" are real numbers and "i" is the imaginary unit, which is equal to the square root of -1.
"A" stands for the complex number's real component, and "b" stands for the imaginary component.
We multiply the magnitudes of two complex numbers and add their arguments to determine their product.
Let's compute z₁z₂ with the supplied values.
Given:
z₁ = 8(cos 45° + isin 45°)
z₂ = 4(cos 210° + isin 210°)
We add the arguments and multiply the magnitudes to find z₁z₂:
Magnitude of z₁ = 8
Magnitude of z₂ = 4
Argument of z₁ = 45°
Argument of z₂ = 210°
Now, let's calculate z₁z₂:
Magnitude of z₁z₂ = (Magnitude of z₁) × (Magnitude of z₂) = 8 × 4 = 32
Argument of z₁z₂ = (Argument of z₁) + (Argument of z₂) = 45° + 210° = 255°
Therefore, z₁z₂ = 32(cos 255° + isin 255°).
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The correct question =
Given z₁ = 8(cos 45° + isin 45°) and z₂ = 4(cos 210° + isin 210°), what is z₁z₂?
A photograph 10cm x 7cm is enlarged so that
the length is 24cm. What would be the width of
the enlargement?
The width of the enlargement would be 34.2857 cm.
What is the difference between length and width?The distance separating an object's ends is its length. The longest dimension is this one. The width of an object is the separation between its two sides. The shortest dimension is this one.
Initial dimension of shorter side = 10 cm
Initial dimension of longer side = 7 cm
Final dimension of shorter side = 24
Final dimension of longer side = x cm
The enlargement always ensure the aspect ratio = longer side / shorter side
10/7 = x/24
Solving for x, we get
[tex]$\frac{x}{24}=\frac{10}{7}$$[/tex]
simplifying the above equation, we get
[tex]$\frac{24 x}{24}=\frac{10 \cdot 24}{7}$$[/tex]
[tex]$x=\frac{240}{7} cm$$[/tex]
Therefore, the value of x be 34.2857 cm.
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Hans drove 536 miles in 8 hours.
At the same rate, how long would it take him to drive 737 miles?
Answer: It would take a total of 11 hours
Step-by-step explanation: here I am using the universal equation of DST, depending on which elements we have we will use this equation.
if we have D, multiply S*T
If we have S Divide D/T
If we have T Divide D/S
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diseases tend to spread according to the exponential growth model. in the early days of aids, the growth factor (i.e. common ratio; growth multiplier) was around 2.1. in 1983, about 1900 people in the u.s. died of aids. if the trend had continued unchecked, how many people would have died from aids in 2005?
According to the growth factor, starting value and the number of years passed, the number of people who would have died is 12.94×10⁷.
The number of people who would have died from AIDS in 2005 will be calculated by the formula -
f(t) = a×[tex] {b}^{t} [/tex]. In this formula, f(t) is the number of cases that occured in the mentioned number of years and t is the number of years between the start and year in question. a is strating value and b is growth.
t = 2005 - 1990
Performing subtraction on Right Hand Side of the equation
t = 15 years
Keep the values in formula
f = 1900 × 2.1¹⁵
Calculating the power
f = 1900 × 68,122.32
Performing multiplication on Right Hand Side of the equation
f = 12.94 × 10⁷
Thus 12.94×10⁷ people would have died.
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Answer the following questions:
1. Six pipes are needed to fill a tank in 1 hour and 20 minutes. How long will it take if only 4 pipes of the same type are used?
2. There are 50 students in a hostel. Food provided for them is good only for 40 days. How long will the same amount of food last if 30 more students join the group?
3. Five trucks can transport 120 tons of goods in 2 days. How many tons of goods can 3 trucks transport in 4 days?
4. In a central post office, 4 machines categorize 8 000 packages in 8 hours. How many machines are needed to categorize 4 500 packages in 6 hours?
5. A soap factory can produce 5000 units of soap in two days if five machines are used. How many units can be made in five days if 10 machines are used?
find the slope between the points (0,-5) and (-2,3)
Answer: The slope between the points (0,-5) and (-2,3) is (-3 - (-5)) / (-2 - 0) = -8 / -2 = 4.
Step-by-step explanation:
What does the transformation f(x)↦f
1
8
x do to the graph of f(x)?
The transformation f(x)↦ 1/8f(x) will shrink the graph of f(x) by 8 times.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) → 1/8 f(x)
This means,
The function f(x) will shrink by 8 times.
Thus,
f(x) ↦ 1/8f(x) will shrink the graph of f(x) by 8 times.
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Find the area. The figure is not drawn to scale.
A triangle with side 6.9 cm extends to form a second right triangle with a height of 4cm.
the area of the given figure will be 13.8 cm².
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
The area of triangle = 1/2 (hb)
The sum of all angle of triangle = 180
A triangle with side 6.9 cm extends to form a second right triangle with a height of 4cm.
So the area will be A = 1/2 *6.9 * 4
A = 13.8 cm²
Hence the area of the given figure will be 13.8 cm².
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A rancher own a rectangular piece of land that i 5. 4 mi long and 2. 5 mi wide. Find the area of the rectangle defined by thi ranch. (Give your anwer a a number. Do not include the unit in your anwer. )
The area of the rectangular piece of land owned by the rancher is:
13.5
The area of a rectangle is a measure of the size of the rectangular space it encloses.
It is calculated by multiplying the length and the width of the rectangle. In this case, the length of the rectangular piece of land owned by the rancher is 5.4 miles and the width is 2.5 miles. To find the area, we multiply these two values.
The formula for finding the area of a rectangle is:
Area = Length * WidthSubstituting the values of length and width into the formula:
Area = 5.4 miles * 2.5 miles = 13.5 square milesSo the area of the rectangular piece of land owned by the rancher is 13.5. This means that if we divide the land into unit squares of 1 square mile each, we would have 13.5 such unit squares.
The area of a rectangle is an important metric in geometry and is widely used in many fields, including construction, agriculture, and real estate.
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9. Which of the following statements are true? Check the boxes of the true statements.
The simplest form of the function is f(x) = x2. The graph is a parabola often called the basic parabola.
What is a parabola?
A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.
Three different parabolas exist. Vertex form, standard form, and intercept form are the three forms. You can access a unique key feature for the graph on each form.
Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line. A parabola is a U-shaped plane curve.
Solve f{x}=x-2?
f(x)=x-2 x∈R
x≤0
x-2≤2
Range of f(x)=[∞,2)
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Binthily travels internationally on business. On a trip to Japan, Binthily uses the exchange rates in the tables shown below. U.S. Dollar $1.00 to japanese Yen115.19¥\ Japanese Yen 1¥ to U.S. Dollar $0.008681 What is the value of 75 U.S. dollars in Japanese yen? Round your answer to the nearest yen. Show your work. Define your variable: Let _=____
15 points
8639 is the value of 75 U.S. dollars in Japanese yen.
Why is Japanese money called yen?The term "yen," which refers to Chinese round coins, dates back in time (yuan). The yen was first coined in 1869, following the Meiji Restoration, and was formally recognised as the fundamental unit in the 1871 monetary reform.
"Yen" is Japanese for "circle" or "round thing." With the "New Currency Act" of 1871, the Meiji government formally adopted this currency in an effort to stabilise the nation's monetary position at the time.
The difference between US and Japanese interest rates has been a major factor in the decline of the yen. In an effort to combat the growing cost of living, the US Federal Reserve has aggressively increased its key interest rate from 0.25% to 3.25% since March.
As we see from the table that,
1 U.S dollar = 115.19 Japanese Yen
$1 = 115.19 ¥
so, $75 = 115.19 × 75¥
$75 = 8639.25¥ ≈ 8639¥
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Find the mean,median and range of the following list of values and choose the correct result.8,9,10,10,10,11,11,11,12,13
The mean of the data be 10.5, median is 10.5 and range be 5.
How to find the mean, median and range?The numbers are sorted, added, and then divided to determine the mean.
8 + 9 + 10 + 10 + 10 + 11 + 11 + 11 + 12 + 13 = 105
Mean = 105 ÷ 10 = 10.5
Mean = 10.5
In essence, determining the median is locating the value in a data sample that lies physically between the other numbers.
The middle number, please. Your right finger should go on 8, and your left finger should go on 13. Your right finger should be at 11, while your left finger should be at 10.
10.5 is the median because it is the midpoint number.
Subtract the largest number from the smallest number to determine the range.
13 - 8 = 5
Therefore, 5 be the range of the data.
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The mean of the data be 10.5, median is 10.5 and range be 5.
Define mean and median?Mean: the average, calculated by adding all the values in a set of data and dividing them by the total number of values added together.The median is the middle number in a set of values.The mode is the number or value that appears the most frequently in the set.The range is the difference between the largest and smallest data points in a set of numerical data. The midpoint is the average of the largest and smallest data points.The mean (average) of a data set is calculated by adding all of the numbers in the set and then dividing by the number of values in the set. When a data set is ordered from least to greatest, the median is the value in the middle.To learn more about mean and median refer to:
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What is the image of (-6,-5) after a reflection over the x-axis?
Answer:
rotation on x axis;
(x, y) 》(x, -y)
So,(-6,5) is the correct answer.
Answer:
(-6,5)
Step-by-step explanation:
(x,y) ------》 (x,-y) {reflection over x-axis}
b) let v1 = 0 0 −3 , v2 = 0 −3 9 , v3 = 4 −2 −6 . does {v1, v2, v3} span r3? why or why not?
Yes, the vectors v1 = (0,0,-3), v2 = (0,-3, 9), and v3 = (4,-2,-6) do span ℝ3. This is because any 3 vectors in ℝ3 will span the entire space, meaning that any vector in ℝ3 can be written as a linear combination of these 3 vectors.
To determine if a set of vectors spans a space, we can create a matrix with the vectors as columns and row reduce it to see if there are any free variables. If there are no free variables, the vectors span the space.
The matrix with v1, v2, and v3 as columns is:
| 0 0 4 |
| 0 -3 -2 |
| -3 9 -6 |
Row reducing this matrix gives us:
| 1 0 0 |
| 0 1 0 |
| 0 0 1 |
Since, there are no free variables, the vectors v1, v2, and v3 do span ℝ3.
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