Write an expression for [tex]\sqrt{32}[/tex] without any perfect square factors other than 1 in the radicand. Explain your steps.

The required amount invested in accounts with 8% and 12% are $1470 and $1820 respectively.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Lydia has money in two savings accounts one rate is 8% and the other is 12%  and the total interest is $336. Let the amount invest in accounts be x and y respectively.
According to the question,
0.08x + 0.12y = 336 - - - - - -(1)

Again,
she has $350 more in 12% account
y = x + 350 - - - - - -(2)

Put y in equation 1,
0.08x + 0.12[x + 350] =336
0.08x + 0.12x + 42 = 336
0.20x = 336 - 42
x = 294/0.20
x = $1470

Now

y = 1470 + 350
y = $1820

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Answer:

1/2 bucket

Step-by-step explanation:

Each of the 8 buckets is 1/4 full.

The total amount of paint at the beginning is 8 × 1/4 bucket = 2 buckets.

Each student uses 1/4 of his paint. Combined, they use 1/4 of the total amount of paint in the buckets.

1/4 × 2 buckets = 1/2 bucket

Answer: 1/2 bucket

The experimental probability that the team made a goal on any given shot is 0.0625

From the question, we have the following parameters that can be used in our computation:

A soccer team made 2 goals out of 32 attempts in a game

The experimental probability that the team made a goal on any given shot is calculated as:

P = 2/32

Evaluate the quotient

P = 0.0625

Hence, the probability is 0.0625

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The ratio of y to x gives the constant of proportionality, k = 5, therefore, they are proportional quantities.

If two variables of two quantities, x and y, are represented on a graph to show their relationship, they are proportional quantities if for every ratio of y to x, the value we get is the same, which means they have a constant of proportionality, k.

Using the points on the graph in the image attached below, the table can be completed as follows:

Part A:

Number of T-shirts (x): 1   2   3   4

Time in minutes (y):     5  10  15 20

Part B: Find the ratio of y to x for each of the points on the graph.

5/1 = 5

10/2 = 5

15/3 = 5

20/4 = 5

The table derived from the graph is:

Number of T-shirts (x): 1   2   3   4

Time in minutes (y):     5  10  15 20

B. The quantities are proportional.

The ratio of y to x gives the constant of proportionality, k = 5, therefore, they are proportional quantities.

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"Your question is incomplete, probably the complete question/missing part is:"

The missing information are in the attachment below.

Answer:

f'(2)=64

Step-by-step explanation:

After plugging in 2 for x our equation would look like

log(2^2+(3×2))×2^(3x2)

Now just follow PEMDAS, starting with the left.

1: 2^2=4, 3×2=6, 4+6= 10

2: 3×2=6, 2^6=64

3: log(10)=1

4: 1×64=64

5: f'(2)=64

Answer: pls braiinliest :D

To find the equation of the line passing through the point (8, -2) that is perpendicular to the line y = 4/5x + 4, we can use the concept of the slope of a line. The slope of a line perpendicular to another line has a negative reciprocal slope.

The slope of the line y = 4/5x + 4 is 4/5. The negative reciprocal of 4/5 is -5/4.

So, the slope of the line passing through (8, -2) and perpendicular to y = 4/5x + 4 is -5/4.

Next, we can use the point-slope form of a line to find the equation of the line:

y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point.

Substituting the values, we get:

y - (-2) = -5/4 (x - 8)

Expanding and solving for y, we get:

y = -5/4x + 26/2

y = -5/4x + 13

The equation of the line passing through the point (8, -2) that is perpendicular to the line y = 4/5x + 4 is y = -5/4x + 13.

Step-by-step explanation:

Answer:

There are 0

Step-by-step explanation:

Absolute value is the positive distance a number is away from 0, so no value of x will make the equation true

Answer:

A 0

Step-by-step explanation:

There are no solutions. Because the absolute value always returns a positive value, there are no solutions to this equation.

If x is negative, the answer will be positive. If x is positive the answer will still be positive. No value of x will give a value of -4. So there is no solution.

Answer:

50to70

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

You are given distance (30 km)  and time  ( 3/4 hr) and want km/hr

soooo    30 km / ( 3/4 hr) = 40 km/hr

The result of the product for the following pairs of number is irrational for 1. Option d √2(4). 2. Option a. 3. Option d. 4. Option b.

A real number that cannot be stated as a ratio of integers is said to be irrational; an example of this is the number √2. Any irrational number, such as p/q, where p and q are integers, q≠0, cannot be expressed as a ratio. Once more, an irrational number's decimal expansion is neither ending nor recurrent.

1. The product of the numbers are:

a. √2 (√8) = √16 = 4

b. √49 (∛ 8) = 14

c. √3 (2/ √3) = 2

d. √2(4)

Option d is the correct answer.

Similarly, taking the product:

2. Option a is correct.

3. Option d is correct.

4. Option b is correct.

Hence, the result of the product for the following pairs of number is irrational for 1. Option d √2(4). 2. Option a. 3. Option d. 4. Option b.

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Answer:

3734.24100725

Step-by-step explanation:

This is related for all problems like this, not just this one:

When you see the key words below, this is what it means, and you can craft an equation from it:

Per = division

Of = multiplication

Using this above, we can replace the words with an equation:

The question is asking the amount of money per person.

Remember above, per means division:

Money/person

We know the amount of money and the number of people, so let's plug it in:

1,130,000,000/302,605

After division:

3734.24100725, final answer.

Hope this helps :D

The percentage of vehicles whose speeds are between 52 miles per hour and 70 miles per hour is 75%.

A statistical principle known as the empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, holds that with a normal distribution, almost all observed data will fall within three standard deviations of the mean.

Given, The mean speed of a sample of vehicles along a stretch of highway is 64 miles per​ hour, with a standard deviation of 4 miles per hour.

[tex]\mu = 64[/tex] and [tex]\sigma = 4[/tex].

Now, 52 is 3 standard deviations away from the mean so 50% of the data falls into this category and 70 is 1.5 standard deviations away from the mean and 25% of the data falls into this category.

Therefore, 75% of the vehicles would fall into this category.

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The angles  on the quadrilaterals she drew are 47 in number.

A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles

As there are four rectangles, The total number of angles in a rectangle are 4 × 4 = 16 angles.

The number of triangles is 3, the total number of angles is 3 × 3 = 9 angles.

Number of pentagons are 2,  the total number of angles is 2 × 5 = 10 angles.

The number of trapezoids are 3, the total number of angles is 3 × 4 = 12 angles.

Total number of angles on the quadrilaterals she drew is 16 + 9 + 10 + 12 = 47 angles.

Hence, the angles  on the quadrilaterals she drew 47.

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The statement “Every sample space S is a finite set” is false because some sample spaces can be infinite, such as rolling a continuous random variable.

The statement “Every sample space S is a finite set” is false. A sample space is the set of all possible outcomes of a random experiment. While some sample spaces may be finite, not all sample spaces are. There are situations where the sample space can be infinite, such as when rolling a continuous random variable like a dice.

For example, the sample space of rolling a fair six-sided die is finite, consisting of the numbers {1, 2, 3, 4, 5, 6}. However, the sample space of choosing a real number between 0 and 1 is infinite, as there are infinitely many possible outcomes between 0 and 1.

Therefore, it is incorrect to say that every sample space is a finite set.

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The length of CE in the triangle is 20.

A triangle is a three-sided polygon that consists of three edges and three vertices.

From the given triangle ABC

BC=CD which are congruent sides

x-5=14

x=19

AB=DE

2x+3=6

2x=3

x=3/2

Now DE 2x+3=2(3/2)+3=6

CE=CD+DE

=14+6

=20

Hence, the length of CE in the triangle is 20.

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The number of students who got actually enrolled are, 5400

A percentage is a number or ratio that can be expressed as a fraction of 100.

Given that, a large university accepts ​60% of the students who apply. Of the students the university​ accepts, ​45% actually enroll, there are 20,000 students​ apply,

Since, the students whose application has been accepted = 20000 × 60%

= 12000

Now, the students who got admission = 12000 × 45%

= 5400

Hence, the number of students who got actually enrolled are, 5400

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The solution of the expression is, 15.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ h (9) = 2x - 3

Now, Substitute x = 9, we get;

⇒ h (9) = 2 × 9 - 3

⇒ h (9) = 18 - 3

⇒ h (9) = 15

Thus, The solution of the expression is,

⇒ h (9) = 15

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The following mathematical expression matched with its translation:

1. x + y = 6 (the sum of two numbers is six)

2. x + y (the sum of x and y)

3. xy (the product of two numbers)

4. x ÷ y (x divided by y)

5. y ÷ x (y divided by x)

6. y = x - 6 (six less than a number is y)

7. x - y (x minus y)

8. 6 x = y (six times a number equals y)

9. xy = 6 (the product of two numbers is six)

10. y - x (x subtracted from y)

Mathematical expression can be translated as thus;

the sum of two numbers is six

Let the unknown numbers be x and y respectively

So,

x + y = 6

six less than a number is y

x - 6 = y

also written as

y = x - 6

six times a number equals y

6 × x = y

6x = y

also written as

y = 6x

Therefore, mathematical expressions are algebraic representation of mathematics in words.

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The potential energy increases as the charges or the poles get further apart.

Static charges does not build up by polarization.

A field force is a force that acts on a particle without physical contact. It arises from the presence of a field, such as an electric field, magnetic field, or gravitational field.

The field exerts a force on a particle based on its charge, mass, or other property, and the strength of the force is determined by the field intensity and the properties of the particle. For example, an electric field exerts a force on a charged particle, while a gravitational field exerts a force on a mass.

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The horizontal distance which the car must have travelled is equal to 450 meters.

Mathematically, the gradient (slope) of a geometric figure or line can be calculated by using this formula:

Pitch (slope) = V/H

Where:

Based on the given image, we have the following distances and gradient (slope):

Rising vertical distance = 60

Horizontal distance (Run) = x

Gradient (slope) = 2/15

Substituting the given parameters into the formula, we have;

2/15 = 60/x

2x = 900

x = 450

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Answer: The perimeter triples.

Step-by-step explanation:

Since there is a direct variation, if the side length triples, so does the perimeter.

The set of pairs for which x and y vary inversely is given as follows:

{(-1, -2/7), (4, 1/14), (6, 1/21)}.

(third set).

A direct proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

For an inverse relation, the relation is modeled as follows:

y = k/x.

Meaning that when x increases, y decreases at a constant rate.

The constant is then obtained as follows:

k = yx.

Hence the third relation is then the relation for which x and y vary inversely, as:

k = -1 x -2/7 = 4 x 1/14 = 6 x 1/21.

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Line AB and CD are two parallel lines

The slope of a line is defined as the change in y- the coordinate with respect to the x-coordinate and the formula is given by    

Note:

Here we have  

AB formed by (-4, 7) and (-2, 6)

Slope of AB = (6 - 7)/(-2 + 4) = -1/2

CD formed by (2, -2) and (-8, 3)

Slope of CD = (3 + 2)/(-8 - 2) = 5/-10 = -1/2

Here Slope of AB = Slope of CD  

As we know the slope of parallel lines is equal

Therefore,

Line AB and CD are two parallel lines

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The function which models the data as represented on the graph will be; [tex]f(x) = 0.8(1/2)^x[/tex].

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

The given graph is an exponential function and should take the form;

[tex]f (x) = a (b)^x[/tex]

Hence, using values from the graph;

For ( -1, 0.2 ) = a • b..........(i)

For (0, 0.8); 10.5 = a • b².........(ii)

=> x=0 and y= 0.8

So.

0.8=a(1/2)^0

0.8=a

Thus, the rule for the function is; y=0.8(1/2)^x

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Answer:

"of -1 and 2."

Step-by-step explanation:

The quadratic function has a maximum value between the two input values of -1 and 2, with a maximum output of 9.

Answer:

The possible numbers of players are multiples of 6 (6, 12, 18, etc.).

Step-by-step explanation:

For the coach to be able to form teams of 6 players each, the total number of players must be divisible by 6. This means that if there are 6, 12, 18, 24, 30, etc. players, the coach can divide them evenly into teams of 6. Any other number of players would result in either having a team with more or fewer than 6 players, or leaving some players out. Hence, the possible numbers of players are multiples of 6.

Explanation:

The two horizontal sides are parallel. The side marked 34 is half as long as side x.

In other words, side x is twice as long as the side marked 34.

x = 2*34 = 68

For more information, search out "midsegment of a triangle".

The cost of 1 hot dog is $2.25

Proportion is a mathematical comparison between two numbers.

Given that, the cost of 4 hot dogs are $9, we need to find the cost of 1 hot dog,

Let the cost of 1 hot dog be x, therefore, setting the proportion,

4 / 9 = 1 / x

x = 9/4

x = 2.25

Hence, the cost of 1 hot dog is $2.25

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Answer:

Step-by-step explanation:

The reflection of point A will be at (3, -4) - that is 2 units directly below the red X.

Answer:

It's the third choice.

Step-by-step explanation:

IF y varies inversely as x then y = k/x   where k is a constant,

and k = xy    

For the 3rd choice

-1 * -2/7 = 2/7

4 * 1/14 = 2/7 and

6 * 1/21 = 2/7

so, this is inverse variation.