1/4 of all the students in the orchestra are girls who play string instruments.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
Let's assume there are a total of 100 students in the school orchestra. Then, according to the problem, 2/5 of them are string players.
The number of string players is:
2/5 x 100 = 40
Out of these 40 string players, 5/8 are girls.
The number of girls who play string instruments is:
5/8 x 40 = 25
Therefore, the fraction of all the students in the orchestra who are girls who play string instruments is:
25/100 = 1/4
Therefore, 1/4 of all the students in the orchestra are girls who play string instruments.
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What is the domain and range of R(c)
The domain of the function; R (c) as required is; [0, 150].
The range of the function; R (c) as required is; [0, 450].
Which intervals represent the domain and range of the function?As evident in the task content; the given function is; R (c) = 3c and the class has a maximum of 150 bags to sell.
In Essence, the possible values of c are such that; 0 ≤ c ≤ 150.
The domain is therefore; [0, 150].
Hence, the range is; 3(0) ≤ R(c) ≤ 3(150).
Ultimately, the range of the function is; 0 ≤ R (c) ≤ 450.
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What is an algebra over a field F?
An algebra over a field F is a vector space over F equipped with a bilinear operation called multiplication.
Let F be a field and let A be a vector space over F. An algebra over F is a triple (A, ×, 1) where × is a bilinear operation A x A -> A, and 1 is an element of A such that:
a × (b × c) = (a × b) × c for all a,b,c in A (associativity)
There exists an element 1 in A such that a × 1 = a = 1 × a for all a in A (existence of identity)
a × (b + c) = (a × b) + (a × c) and (a + b) × c = (a × c) + (b × c) for all a,b,c in A (distributivity)
a × b = b × a for all a,b in A if and only if A is commutative
The operation × is usually referred to as multiplication and the element 1 as the unit or identity element.
Examples of algebras over a field F include the set of n x n matrices over F, the polynomial ring F[x], and the complex numbers C, which can be viewed as an algebra over the field of real numbers R.
Therefore, the algebra over a field F has been explained
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Hannah is getting balloons for her father's birthday party. She wants each balloon strain to be 12 ft long. At the party store string is sold by the yard. If Hannah wants to get 48 balloons how many yards of string was she need.
Explanation:
1 balloon needs 12 ft of string.
48 balloons need 48*12 = 576 ft of string.
Divide by 3 to convert from feet to yards. This is because 1 yard = 3 ft.
576 ft = 576/3 = 192 yards
In the Normal model N(100, 15) from Exercise 10, what cutoff value bounds
the highest 5% of all IQs?
the lowest 30% of the IQs?
the middle 80% of the IQs?
The highest 5% of all IQs in the N(100, 15) Normal model are bounded by a value of 124.68, while the lowest 30% are bounded by a value of 92.64. The middle 80% of IQs are bounded by values between 80.77 and 119.23.
In the Normal model N(100, 15):
The highest 5% of all IQs are bounded by a z-score of 1.645, which corresponds to a value of 100 + (1.645 * 15) = 124.68. This means that an IQ of 124.68 or higher is in the top 5% of all IQs in this model.
The lowest 30% of the IQs are bounded by a z-score of -0.524, which corresponds to a value of 100 + (-0.524 * 15) = 92.64. This means that an IQ of 92.64 or lower is in the lowest 30% of all IQs in this model.
The middle 80% of the IQs are bounded by z-scores of -1.282 and 1.282, which correspond to values of 100 + (-1.282 * 15) = 80.77 and 100 + (1.282 * 15) = 119.23, respectively. This means that IQs falling between 80.77 and 119.23 are in the middle 80% of all IQs in this model.
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scientists determined that the equation y=0.5x+26 models the amount of shoreline at the beach, y, in feet, x decades after 1950. Which statement is true based on the model
The shoreline is reduced by 0.5 feet every 10 years. Then the correct option is A.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
A group of scientists studied the amount of erosion at a beach. The scientist determined that the equation is given below.
y = -0.5 x + 26
Hence, The shoreline is reduced by 0.5 feet every 10 years. Then the correct option is A.
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scientists determined that the equation y=0.5x+26 models the amount of shoreline at the beach, y, in feet, x decades after 1950. Which statement is true based on the model
The shoreline is reduced by 0.5 feet every 10 years.
The shoreline is increased by 0.5 feet every 10 years.
The shoreline is reduced by 26 feet every 10 years.
The shoreline is increased by 26 feet every 10 years.
Mrs. Mack is looking at the blueprints for a new factory. On the blueprint, the factory floor is a rectangle with a length of 0.3 meter and a width of
0.25 meter. The factory will be built by using a scale factor of 140.
Mrs. Mack wants to know the area of the factory floor. She decides to do this by first determining the dimensions of the factory floor.
What will be the length of the factory floor?
Enter your answer in the box
Answer:
42 meters
Step-by-step explanation:
The length of the factory floor will be 42 meters. This is found by multiplying the length of 0.3 meters by the scale factor of 140, which yields 42 meters.
Answer:
42 meters
Step-by-step explanation:
its correct :)
what is 23 out of 25 as a percentage
Answer:
92%
Step-by-step explanation:
a cylinder is sliced such that the cross section is parallel to its bases. what is the shape of the cross section?RectangleCircleTriangleTrapezoid
The shape of the cross section is circle from the following option given.
A cylinder has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes.
When a cylinder is sliced parallel to its bases, the shape of the cross section will be a circle. This is because the bases of a cylinder are circular, and any plane that is parallel to the bases will intersect the cylinder in a circle of the same radius as the bases. Therefore, regardless of the position of the slice, the shape of the cross section will always be a circle.
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what is log base 2 calculator
A log base 2 calculator calculates the logarithm of a number with respect to base 2.
A tool that helps in calculating a number's logarithm in relation to base 2 is a log base 2 calculators. A base must be increased to the logarithm, or exponent, in order to yield a given number.
The base in this situation is 2, and the exponent to which 2 must be increased in order to equal the supplied number is the logarithm. The base-2 logarithm offers a measure of the number of bits necessary to express a particular amount, making it important in computer science, information theory, and other fields that need computations involving binary integers.
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Which graph represents the linear equation y = −5x − 4?
a graph of a line that passes through the points negative 2 comma 5 and 0 comma negative 3
a graph of a line that passes through the points negative 4 comma negative 1 and 0 comma negative 2
a graph of a line that passes through the points negative 1 comma 1 and 0 comma negative 4
a graph of a line that passes through the points negative 4 comma 3 and negative 2 comma negative 3
The linear equation y = -5x - 4 has a slope of -5 and a y-intercept of -4. Therefore, the correct graph should be a straight line with a slope of -5 and a y-intercept of -4.
Out of the four given options, the graph of a line that passes through the points (-1, 1) and (0, -4) represents the linear equation y = -5x - 4. To see why, we can use the two given points to find the slope of the line:
slope = (change in y) / (change in x) = (-4 - 1) / (0 - (-1)) = -5
The y-intercept is -4, so the equation of the line can be written in slope-intercept form as y = -5x - 4.
Therefore, the graph that represents the linear equation y = -5x - 4 is the graph of a line that passes through the points (-1, 1) and (0, -4).
Answer:
The linear equation y = -5x - 4 has a slope of -5 and a y-intercept of -4. Therefore, the correct graph should be a straight line with a slope of -5 and a y-intercept of -4.
Out of the four given options, the graph of a line that passes through the points (-1, 1) and (0, -4) represents the linear equation y = -5x - 4. To see why, we can use the two given points to find the slope of the line:
slope = (change in y) / (change in x) = (-4 - 1) / (0 - (-1)) = -5
The y-intercept is -4, so the equation of the line can be written in slope-intercept form as y = -5x - 4.
Therefore, the graph that represents the linear equation y = -5x - 4 is the graph of a line that passes through the points (-1, 1) and (0, -4).
Step-by-step explanation:
Suav deposits $450 every quarter into an account earning a quarterly interest rate of 2.225%. How much would he have in the account after 10 years, to the nearest dollar?
Suav deposits $450 every quarter into an account earning a quarterly interest rate of 2.225%. After 10 years, he would have $7,395 in the account to the nearest dollar.
The formula for calculating the future value (FV) of an investment is: FV = PV(1 + r/n)nt, where PV is the present value, r is the interest rate per period, n is the number of compounding periods per year, and t is the number of years.
In this problem, PV is $450, r is 2.225%, n is 4 (quarters in a year), and t is 10 years. Plugging these values into the formula gives us:
FV = 450(1 + 0.02225/4)4*10 = 450(1.0055625)40 = 450(2.7326) = $7,395
Therefore, after 10 years, Suav would have $7,395 in the account to the nearest dollar.
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Hi , please help ( see images)
This is a word problem and the value of the unknown number is equal to 5.5.
We can write algebraically the second question as 3(x - 1).
Simplifying fully 15xy ÷ 15xy = 1/y
Word problems in mathematicsWord problems are mathematical problems which involves the use of ordinary words, instead of mathematical symbols.
Let us represent the unknown number with the letter x so that we derive the equation;
2x - 2 = 9
we add 2 from both sides of the equation
2x - 2 + 2 = 9 + 2
2x = 11
divide through by the coefficient of x which is 2
2x/2 = 11/2
x = 5.5.
Using x as the unknown, we can write the statement in the second question as 3(x - 1).
15xy ÷ 15xy = 1/y
Therefore, the value of the unknown number for the word problem is equal to 5.5
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Answer:
in order from last to first
3y
(x-1)3
x2-2=9
Step-by-step explanation:
(I also included the image for your previous question))
what is 1 1/2 cups divided by 2?
The 1 1/2 cups divided by 2 is 0.75 cups
Division is the opposite of multiplication. If 3 groups of 4 are multiplied by 12, then dividing 12 into 3 equal groups yields 4 in each group when divided.
Dividend: The dividend is the number that is being divided in the division process.
Divisor: The number by which the dividend is being divided by is called the divisor.
Quotient: The quotient is a result obtained in the division process.
Remainder: Sometimes, we cannot divide things exactly. There may be a leftover number. That leftover number is called the remainder.
The relationship between these four parts can be expressed as follows:
Dividend = Divisor x Quotient + Remainder
The main purpose of sharing is to see how many equal groups form, or how many people belong to each group, when sharing equitably.
In the above example, to divide the 12 donuts into 3 similar groups, we need to place 4 donuts in each group. So dividing 12 by 3 gives 4.
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Reflect the figure over the line l
The required reflection of the given figure across the line y = x is shown.
What is the transformation of geometry over the coordinate plane?Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Felix Klein introduced transformational geometry, a fresh viewpoint on geometry, in the 19th century.
Here,
A figure on a coordinate plane is shown, and we have to determine the reflection of that figure across the line y = x,
In order to determine the reflection across the line y = x,
The Abscissa inside the line gets interchanged by the ordinate of the corresponding Absciss as.
(x, y) ⇒ (y, x)
Thus, the required reflection of the given figure across the line y = x is shown.
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What is the conversion of 152cm in feet ?
The conversied value of 152 centimetres in feet is equals to the 4.98 feet.
Unit conversion, by definition, is the conversion between different units and measurements of the same quantity done in the process of multiplication or division. In mathematics, conversion is the process of changing a value from one form to another, such as converting a value from inches to millimeters, for time minutes to hours, or other units.
How to convert centimeters to feet : 1 meter is a measure of length and equals approximately 3.28 feet.
152 meters = 152×3.28 feet = 498.56 feet --(1)
But we need to convert 152 centimeters to feet. So change meters to centimeters. As you know, 1 meter is 100 centimeters, so 152 meters = 15200 centimeters --(2). Now from equations (1) and (2),
15200 centimeters = 498.56 feet,
Divide both parts by 100,
=> 152 centimetres = 498.56/100 feet
= 4.98 feet
Hence required value is 4.98 feet.
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Find the length of AC
The length of the side AC of the right-angled triangle is equal to 24cm by comparison using the trigonometric ratio of sine of angle B.
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
Considering the right-angled triangles ABC and DBC, we shall evaluate for the length AC using the trigonometric ratio of sine for the angle B° to derive an equation as follows:
For ∆ABC;
sin B = AC/BC {opposite/hypotenuse}
For ∆DBC;
sin B = 24cm/BC {opposite/hypotenuse}
thus;
AC/BC = 24cm/BC
Therefore, by comparison using the trigonometric ratio of sine for the angle B, we have the length of AC equal to 24cm.
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A town is designing a rectangular park that will be 600 feet by 1000 feet. A rectangular area of the park for swing sets will be 25 feet by 100 feet. On a scale drawing of the park the swing set area is 0. 5 inch by 2 inches. What is the dimensions of the park on the scale drawing?
The dimensions of the park on the scale drawing are 2 inches by 0.5 inches
The dimensions of the park on the scale drawing can be determined by using the scale factor between the actual dimensions and the scale drawing dimensions. The scale factor can be found by dividing the actual dimensions by the scale drawing dimensions.
Scale factor for length = Actual length / Scale drawing length = 1000 feet / 2 inches = 500 feet per inch
Scale factor for width = Actual width / Scale drawing width = 600 feet / 0.5 inches = 1200 feet per inch
Now, we can use the scale factor to determine the dimensions of the park on the scale drawing.
Length of park on scale drawing = Actual length / Scale factor for length = 1000 feet / 500 feet per inch = 2 inches
Width of park on scale drawing = Actual width / Scale factor for width = 600 feet / 1200 feet per inch = 0.5 inches
Therefore, on the scale drawing, the park measures 2 inches by 0.5 inches.
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what is balance chemical equations calculator
A balanced chemical equation calculator is an online tool that assists in the balancing of chemical equations by automatically computing the coefficients for each reactant and product to verify that the equation obeys the rule of mass conservation.
According to the law of conservation of mass, matter cannot be generated or destroyed in a chemical process, just rearranged.
A balanced chemical equation includes the chemical formulae for the reactants and products of a chemical reaction, as well as the factors that balance the amount of atoms of each element on both sides of the equation. Balancing a chemical equation is a necessary step in addressing many sorts of chemistry issues, such as forecasting the quantity of product generated or reactant required in a reaction.
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a mug slides across a horizontal counter with initial speed v. it slides off the 0.86 m high counter and lands 1 m from the base. what was its initial speed?
slides off the 0.86 m high counter and lands 1 m from the base. what was its initial speed ⇒ Ø = 56.87˚ beneath the horizontal
A. Suppose the horizontal component of the velocity is vx and the vertical is vy.
At first at t=0 (as the mug leaves the counter) the components are v0x and v0y.
v0y = 0 since the customer slides it horizontally so applied force is in the x component as it were.
The equations for horizontal and vertical shot movement are:
x = x0 + v0x t
y = y0 + v0y t - 1/2 g t^2 = y0 - 1/2 g t^2
Setting the beginning to be the end corner of the counter so that x0=0 and y0=0, thus:
x = v0x t
y = - 1/2 g t^2
Given esteem are: x=1.50m and y=-1.15m (y is negative since mug is going down)
1.50m = v0x t - - - - > v0x= 1.50/t
-1.15m = - (1/2) (9.81) t^2 - - - - - > t =0.4842 s
Working out for v0x:
v0x = 3.10 m/s
B. v0x is constant since there could be no other horizontal forces so, v0x=vx=3.10m/s
vy can be calculated from the recipe:
vy = v0y + at where a=-g (negative since going down)
vy = - gt = - 9.81 (0.4842)
vy = - 4.75 m/s
Presently to get the point beneath the horizontal, tan(90-Ø) = - vx/vy
tan(90-Ø )= 3.1/4.75
Ø = 56.87˚ beneath the horizontal
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Square root of 2.75?
Answer: 1.65831239518
Step-by-step explanation:
The square root of 2.75 is defined as the only positive real number such that, multiplied by itself, it is equal to 2.75.The square root of 2.75 can be written as
(2.75)1/2. So,(2.75)1/2 = (1.6583123951777 × 1.6583123951777)1/2(2.75)1/2 = [(1.6583123951777)2]1/2(2.75)1/2 = (1.6583123951777)2/2(2.75)1/2 = (1.6583123951777)1Thus,√2.75 = 1.6583123951777
Assume that births of girls and boys are equally likely. If a family has six children. What the number of outcomes in the sample space?
Group of answer choices
8
12
64
36
The number outcomes in the sample space is option (3) 64
In mathematics, combination is a way of selecting a group of objects from a larger set, where the order in which the objects are selected does not matter.
The number of outcomes in the sample space can be calculated by finding the total number of possible combinations of genders for the six children.
For each child, there are two possible genders: male or female. Therefore, the number of possible outcomes for one child is 2.
To find the total number of outcomes for six children, we need to multiply the number of possible outcomes for each child together:
2 × 2 × 2 × 2 × 2 × 2 = 64
Therefore, the correct option is (3) 64
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What are the initial and final potition respectively
The initial position is the starting point, and the final position is the endpoint.
We proceed to explain the initial and final position:
The initial position is the starting point or location of an object before any movement or displacement occurs. It is often denoted as x0 or xi. The final position is the ending point or location of an object after it has undergone movement or displacement. It is often denoted as xf.For example, if an object starts at the 2 meter mark (initial position) and moves 3 meters to the right, its final position would be at the 5 meter mark.
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How much water should be added to 14 mL of 14% alcohol solution to reduce the concentration to 7%?
We need to add approximately 14.86 mL of water to 14 mL of 14% alcohol solution to reduce the concentration to 7%.
First, let's figure out how much alcohol is in the first 14 mL of the 14% alcohol solution.
Alcohol is equal to 0.14 x 14 (14%) times 14%, or 1.96 mL.
We need to add water so that the amount of alcohol stays the same while the overall volume grows in order to lower the concentration to 7%.
Assume that x mL of water needs to be added.
The volume of the solution will be (14 + x) mL with the addition of x mL of water, while the amount of alcohol will remain at 1.96 mL.
The equation for the ultimate concentration can be written as follows:
1.96 mL / (14 + x) mL = 0.07
When we find x and simplify, we get:
x = (1.96 mL / 0.07) - 14 mL
x ≈ 14.86mL
In order to lower the concentration to 7%, we must therefore add around 14.86 mL of water to 14 mL of 14% alcohol solution.
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I Need help plssssssss
Answer: 5, 6, 7, 8, 9, or the numbers 5-9 inclusive.
Step-by-step explanation: The Triangle Inequality Conjecture states that any two sides of a triangle added up will be larger than the third. To easily prove this, you can add the two smaller sides to see if it is bigger than the larger side. Using this conjecture, we can calculate that 5 works, 6 works, 7 works, 8 works (8 is larger than 7 so now we do 3+7), and 9 works.
You choose between red, blue, yellow, or green wallpaper and purple or yellow carpet. Find the total number of possible outcomes when you select one color of wallpaper and one color of carpet.
Answer: there are 8 outcomes
Step-by-step explanation:
1: red wallpaper and purple carpet
2: blue wallpaper and purple carpet
3: yellow wallpaper and purple carpet
4: green wallpaper and purple carpet
5: red wallpaper and yellow carpet
6: blue wallpaper and yellow carpet
7: yellow wallpaper and yellow carpet
8: green wallpaper and yellow carpet
A cone with a volume 1,780.38 and a height of 7. What is the radius
Answer:
15.585 is the radius of the cone
3.8 Thabo kept a diary of his activities during the week. He then drew up a table to show an average day. Look at his table Activity Sleeping At school PS Doing homework Playing sport Watching TV Eating Time 8 hours 7 hours 1 hour 2 hours 4 hours 2 hours a. What is the ratio of the time spent doing homework to the time spent at school? (1)
The ratio of the time Thabo spent doing homework to the time he spent at school is 2:7.
What is the ratio?Ratio refers to the relative size of a quantity compared to another.
Ratios are expressed as percentages, from 0% to 100%, as fractions, as proportions or decimals, from zero to one, and in ratio forms (:).
To compute the ratio as a decimal, it is the quotient of one quantity and another comparative quantity.
Activity Time
Sleeping 8 hours
At school 7 hours
Doing homework 2 hours
Playing sport 4 hours
Watching TV 2 hours
Eating 1 hour
Total hours = 24 hours
Ratio of time doing homework to the time spent at school = 2:7
The sum of ratios = 9 (2 + 7)
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What is 20% of 2000?
Answer:
Step-by-step explanation:
of is *
20% is 1/5
1/5 *2000= 2000/5= 400
The total area under the frequency polygon for a continuous random variable equals 1? True or False
The given statement "The total area under the frequency polygon for a continuous random variable equals 1" is true because the total area under the frequency polygon is a measure of the probability of the variable and the probability of a continuous random variable is always equal to 1
Frequency polygons are graphical representations of a continuous random variable. The total area under the frequency polygon for a continuous random variable is a measure of the probability of the variable. In this problem, we are asked if the total area under the frequency polygon for a continuous random variable equals 1.
The answer is true. The total area under the frequency polygon for a continuous random variable indicates the probability of the variable. Since the probability of a continuous random variable is always 1, the total area under the frequency polygon also equals 1.
Therefore, it is true that the total area under the frequency polygon for a continuous random variable equals 1.
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when I solved that i got no real solutions, is that true? please help tyvm
Answer:
true
Step-by-step explanation:
log2(5x+3)=log2(4x-3)
log2(5x+3)/log2(4x-3)
division turns to minus
log2(5x+3-4x-3)
log2(x)