Help with homework please!

This is an algebraic word problem that is evaluated to give the total pieces of cake Mary distributed to be 35.

In algebraic word problems, we can represent an unknown number using letters and then carry out basic mathematics operations to get the value of the unknown number.

We shall represent the total pieces of cake Mary distributed with the letter x, so that:

x - 4x/5 = 7 {the pieces left that got to the 7}

(5x - 4x)/5 = 7

x/5 = 7

x = 5 × 7 {cross multiplication}

x = 35.

Therefore, the algebraic word problem is solved to give us the total pieces of cake Mary distributed to be 35.

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Let x be the total amount of money .

Emily's share =(1/3)x

Given Emily's share = 45000

so (1/3)x = 45000

x = 135000

Eric's share = (2/5)x

Eric puts 75% of his share in bank

= (2/5)*x*0.75

= (2/5)*135000*0.75

= 40500

Cat's share

= 1-([(1/3)*x] + [(2/5)*x])

= (4/15)*x

= (4/15)*135000

= 36000

Answer:

m = 2/3

Step-by-step explanation:

Take two random points, I personally picked (-2, 0) and (1, 2)

Slope = rise/run = [tex]\frac{2-0}{1-(-2)} = \frac{2}{3}[/tex]

Answer:

21x+35y=?

Step-by-step explanation:

multiply 3 by 7

multiply 5 by 7

you can't add different variables together

There are a total of 27 steps on the staircase.

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

Let x be the total number of steps in the staircase.

Larry climbs exactly 2/3 of the stairs.

Number of steps Larry climbed = 2x/3

She goes back exactly 1/2 of the way to the bottom.

Number of steps returned = (2x/3) (1/2) = 2x/6 = x/3

She is at x/3 steps from the bottom.

From that spot, she climbs exactly 2/3 of the way to the top.

Remaining steps to the top = x - x/3 = 2x/3

Number of steps Larry climbed = 2/3 of the way to the top = (2/3)(2x/3) = 4x/9

So we get,

x/3 + 4x/9 + 6 = x

x - x/3 - 4x/9 = 6

x - 7x/9 = 6

2x/9 = 6

2x = 54

x = 27

Hence there are 27 steps in the staircase.

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The complete question is as follows :

Lara starts at the bottom of a long staircase. She climbs exactly 2/3 of the stairs. Then, she goes back down exactly 1/2 of the way to the bottom. From that spot, she climbs exactly 2/3 of the way to the top. Finally from there, she climbs 6 stairs to reach the top. How many stairs are in the staircase?

Here we are interested in finding the slope of the line. From the given graph we can see that that the line passes through points (-6,0) and (0,3) . We know that slope can be calculated by ,

[tex]\longrightarrow slope \ (m)=\dfrac{y_2-y_1}{x_2-x_1} =\tan\theta =\dfrac{rise}{run}[/tex]

[tex]\longrightarrow m =\dfrac{y_2-y_1}{x_2-x_1}\\[/tex]

[tex]\longrightarrow m =\dfrac{0-3}{-6-0}\\[/tex]

[tex]\longrightarrow m =\dfrac{-3}{-6}\\ [/tex]

[tex]\longrightarrow m =\dfrac{1}{2}=0.5[/tex]

And we are done!

Answer: Figure 2 (The rectangle)

Hope this helps :)

Step-by-step explanation:

Quadrilaterals are shapes that have 4 (connected) sides

Answer:

the second figure

Step-by-step explanation:

Quadrilaterals have a maximum and minimum of four

The amount that Kim Barney spends is $342 for medical expenses.

Given that,

Kim Barney pays a $290.00 yearly premium for a $500.00 deductible insurance plan. 80 percent of the remaining cost is covered by the business. If Kim has medical costs of $2,500.00

To find : The amount that Kim barney spends for the medical expenses.

If the business covers 80% of the remaining balance ($1710), they will be responsible for paying $1368 of it.

10% of 1710 is 171

171x8=1368

The insurance provider covers the $1368.

Kim Barney spends $342.

Consequently, Kim Barney spends the following amount on medical costs $342.

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the bicycle has a frame size of 22.04 in.

What is unit conversion?

Units of measure are needed in order to measure these values. Sometimes the units of measurement used may not correspond to the standards required for a particular process or application, as well as the measuring choice and convenience. It's crucial to convert these units in a way that makes sense and can be used effectively. Let's use the example of someone who is only familiar with the metric system to better grasp the statement. The person finds it difficult to determine the height of a 25-foot tree. The person will comprehend the height of the tree better if they convert 25 feet to meters. Let's use a unit conversion table to learn about converting between different units.

A bicycle has a 56 cm frame.

As given 1 in = 2.54cm

so 2.54 cm =1 inc

1 cm = 1/2.54

56 cm for the frame = 56*1/2.54 = 22.04 in

Hence the bicycle has a frame size of 22.04 in.

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Answer:

Parallel Line: [tex]y=-\frac{4}{5}x+\frac{1}{5}[/tex]

Perpendicular Line: [tex]y=\frac{5}{4}x-8[/tex]

Step-by-step explanation:

Perpendicular lines have a slope that is the negative reciprocal of each other. So for example if one line has a slope of: [tex]\frac{a}{b}[/tex], where "a" and "b" are just some constants, then a perpendicular line would have a slope of: [tex]-\frac{b}{a}[/tex], so the slope fraction is just flipped and it's the opposite sign.

Parallel lines never intersect meaning they will have the same slope, since as one goes to the right one and up or down some amount, the only way for the other line to never intersect is to also go up or down by the same amount, which is essentially the slope. The only other condition is that parallel lines must have different y-intercepts, otherwise they have the same slope and y-intercepts meaning they're just the same line and instead of never intersecting they actually intersect at infinitely many points.

The slope-intercept form is especially useful as we can simply look at it and determine the slope and y-intercept, hence the name slope-intercept form. We want to convert into this form to determine the slope of the equation given to us so we can find the perpendicular and parallel lines.

We're given the equation in standard form:

[tex]4x+5y=9[/tex]

We want to convert this into slope-intercept form, which we can do by isolating the y variable. We want to get rid of the 4x term on the left side by subtracting 4x, and we want to do this to both sides to maintain equality:

[tex]4x-4x+5y=9-4x[/tex]

Simplify:
[tex]5y=-4x+9[/tex]

Now we want to get rid of the coefficient of 5 from the left side, and this coefficient is just multiplication so to cancel out multiplication, we divide, specifically by 5 in this case, and on both sides to maintain equality:

[tex]\frac{5y}{5}=\frac{-4x+9}{5}[/tex]

Simplify:
[tex]y=-\frac{4}{5}x+\frac{9}{5}[/tex]

Now we know the slope is: [tex]-\frac{4}{5}[/tex]

For this we simplify find the negative reciprocal so we flip the fraction and "flip" the sign, or in other words if it's negative it becomes positive, if it's positive it becomes negative so: [tex]-\frac{4}{5}\to \frac{5}{4}[/tex]

We can represent the general equation of a perpendicular line in slope-intercept form: [tex]y=\frac{5}{4}x+b[/tex], where "b" is some constant number. We're given that it passes through the point (4, -3) which we can plug in as (x, y) to solve for that value "b"

[tex]-3=\frac{5}{4}(4)+b[/tex]

Simplify on the right side

[tex]-3=5+b[/tex]

Subtract 5 from both sides

[tex]-8=b[/tex]

So now we have the perpendicular line equation: [tex]y=\frac{5}{4}x-8[/tex]

For this we don't have to do anything to the slope, since for parallel lines the slope is the same, so we know the slope is: [tex]-\frac{4}{5}[/tex] and we can plug this into the slope-intercept form to get a general equation for a parallel line: [tex]y=-\frac{4}{5}x+b\text{ where }b\ne\frac{9}{5}[/tex]

Since we're given that it passes through the point (4, -3) we can plug this in as (x, y) to find a definitive equation.

[tex]-3=-\frac{4}{5}(4)+b[/tex]

Simplify on the right side:

[tex]-3=-\frac{16}{5}+b[/tex]

Rewrite the left side to have a denominator of 5:

[tex]-\frac{15}{5}=-\frac{16}{5}+b[/tex]

Add 16/5 to both sides:

[tex]\frac{1}{5}=b[/tex]

So now let's plug this into a general equation we had above to get:
[tex]y=-\frac{4}{5}x+\frac{1}{5}[/tex]

Option A) The statement 12 / 3 = 4 can be justified by the equation 4x = 12 as 12 divided by 4 gives 3.

One of the four fundamental arithmetic operations, or how numbers are joined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.

A quotient is the amount that results from dividing two integers. The term "quotient" is used frequently in mathematics and is sometimes known as the integer portion of a division, a fraction, or a ratio.

According to the division property of equality, the quotients of an equation remain equal when both sides are divided by a common real integer that is not equal to 0. The same formula may be expressed in writing as follows: If real numbers a, b, and c are present, with a = b and c 0, then a c = b c.

The statement 12 / 3 = 4 can be justified by the equation 4x = 12 as

12 divided by 4 gives 3.

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Option A) The statement 12 / 3 = 4 can be justified by the equation 4x = 12 as 12 divided by 4 gives 3.

One of the four fundamental arithmetic operations, or how numbers are joined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.

A quotient is the amount that results from dividing two integers. The term "quotient" is used frequently in mathematics and is sometimes known as the integer portion of a division, a fraction, or a ratio.

According to the division property of equality, the quotients of an equation remain equal when both sides are divided by a common real integer that is not equal to 0. The same formula may be expressed in writing as follows: If real numbers a, b, and c are present, with a = b and c 0, then a c = b c.

The statement 12 / 3 = 4 can be justified by the equation 4x = 12 as

12 divided by 4 gives 3.

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The expression that represents the length of the rectangle is x + 5

The area of a rectangle is described as follows:

area = lw

where

l = length

w = width

Therefore,

area = x² + 8x + 15

w = x + 3

Therefore,

x² + 8x + 15 = (x + 3)l

divide both sides by x + 3

l =  x² + 8x + 15 / x + 3

l = (x+3)(x+5) / (x + 3)

Finally,

length = x + 5

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a. -79, -41, -31, 54, 57

b. -56, -55, -54, -43, -39, -37, 18, 22, 43, 44, 52

In both cases, I have put the integers in order from smallest to greatest by comparing each number and placing them in the correct order. Starting with the smallest number and moving to the largest.

The weights (in pounds) of a sample of 13 male eleventh graders ,so the median weight of these students is 159.

Calculate the mean by summing the centre values and dividing them by the number. From there, you may obtain the median.

To arrange the data points in ascending order for a small data set, count the number of data points (n). To get the rank of the data point whose value is the median when the number of data points is unequal, multiply the total by 1 and divide the results by 2.

148, 140, 159, 141, 151, 156, 173, 167, 160, 159, 146, 174, 170

140 , 141 , 146 , 148, 151 ,156,  159 ,159, 160, 167 , 170, 173, 174.

The median weight of these students is 159.

The weights (in pounds) of a sample of 13 male eleventh graders ,so the median weight of these students is 159.

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To find the number of years it takes for an investment to grow to a certain value at a certain interest rate, you can use the formula:

n = (future value - principal) / (principal * interest rate)

Where:

n = number of years

future value = the final value of the investment

principal = the initial amount invested

interest rate = the annual interest rate as a decimal

Plugging in the given values:

n = (21150 - 5000) / (5000 * 0.17)

n = 16.65

Rounding to the nearest whole number, it would take approximately 17 years for the investment to be worth $21,150.00.

A vector is a quantity that has both magnitude, as well as direction. A vector that has a magnitude of 1 is a unit vector. It is also known as Direction Vector.

Unit Vector is represented by the symbol ‘^’, which is called a cap or hat, such as: â. It is given by   â  = a / |a|

Where |a| is for norm or magnitude of vector a.

It can be calculated using a Unit vector formula.

Unit vectors are usually determined to form the base of a vector space. Every vector in the space can be expressed as a linear combination of unit vectors. The dot products of two unit vectors is a scalar quantity whereas the cross product of two arbitrary unit vectors results in third vector orthogonal to both of them. As explained above vectors have both magnitude (Value) and a direction. They are shown with an arrow.

And, â denotes a unit vector. If we want to change any vector in unit vector, divide it by the vector’s magnitude. Usually, xyz coordinates are used to write any vector.

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The height of both trees at the time when they have an equal height will be 48 inches.

Given is that Evelyn planted two trees in her backyard. At the time of planting, Tree A was 32 inches tall and Tree B was 16 inches tall. Each year thereafter, Tree A grew by 4 inches per year and Tree B grew by 8 inches per year.

       Tree {A} : y {A} = 4x + 32

       Tree {B} : y {B} = 8x + 16

Therefore, the height of both trees at the time when they have an equal height will be 48 inches.

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It is a structured visual representation of simplified thoughts, ideas, structures, relationships, statistical data, anatomy, etc. It can be used in any part of human activity to clarify a topic or provide an example of a topic.

Mind maps, flowcharts, fishbone diagrams, hierarchy/org charts, and SWOT analysis charts are the most common types of diagrams covered in this article. It is a structured visual representation of simplified thoughts, ideas, structures, relationships, statistical data, anatomy, etc. It can be used in any part of human activity to clarify a topic or provide an example of a topic.

A diagram that shows the parts of an object and their interrelationships is called a diagram.

It is a structured visual representation of thoughts, ideas, structures, relationships, statistical data, anatomy, etc. It's a simplification. It can be used in any part of human activity to clarify a topic or provide an example of a topic.

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If the sample size is large (typically n > 30), then it is generally appropriate to use the standard normal distribution (z-distribution) to approximate the sampling distribution of the sample mean.

What are the standard's mean and variance?

Standard deviation is the square root of the number, while variance is equal to the average squared deviations from the mean. Additionally, the variance's square root is the standard deviation.

This is because as the sample size increases, the Central Limit Theorem states that the sample mean will become more normally distributed, regardless of the underlying distribution of the population.

This is due to the fact that the standard error of the sample mean, which is the standard deviation of the sampling distribution of the mean, decreases as the sample size increases. When the sample size is large, the sample mean will be approximately normally distributed with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size.

However, it is important to note that in order to use the z-distribution to approximate the sampling distribution of the sample mean, it is necessary to know the population mean and population standard deviation. If these values are not known, it is appropriate to use the t-distribution, which does not require knowledge of the population parameters.

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The number of ways randomly an  integer which is a composite number generated by a computer between 10 and 20 is equal to option c. 6.

As given in the question,

Total number of integer between 10 and 20 where 20 is inclusive = 10

Composite numbers between 10 and 20 where 20 is inclusive are :

12, 14, 15, 16, 18 ,20

Total number of ways an integer which is a composite number generated between 10 and 20( inclusive )

= 6

Therefore, the number of ways randomly an integer which represents a composite number generated by a computer between 10 and 20 ( inclusive ) is equal to option C. 6.

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The height that represents the middle 80 percent of the heights is 64.87 inches and 74.13 inches and this can be determined by using the given data.

Given :

The distribution of heights for adult men in a certain population is approximately normal with a mean of 70 inches and a standard deviation of 4 inches.

The heights that represent the middle 80 percent of the heights are:

P(-z < Z < z) = 0.80

P(Z < z) - P(Z < -z) = 0.80

P(Z < z) - (1 - P(Z < z)) = 0.80

2P(Z < z) = 1.80

P(Z < z) = 0.90

So, the value of z is 1.282.

Now, put the values of height as follows:

x1= 64.87

x2= 75.13

Therefore, the height that represents the middle 80 percent of the heights is 64.87 inches and 74.13 inches.

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The radioactive substance cesium-137 has a half-life of 30 years.  For the given compound, Initial amount is 647 grams and Amount after 100 years is 64 grams.

A sample's half-life is the amount of time it takes for half of its unstable nuclei to decay, for its activity to halve, or for its count rate to decrease by half. The number of decays that a detector, like the Geiger-Muller tube, records each second is known as the count-rate.

For radioactive compounds, a general exponential function is provided by

Ao(1/2)t/t1/2 = A(t)

Where,

A(t) is the sum that is left after t years.

Ao is the radioactive substance's initial concentration.

The time it takes for a radioactive substance to degrade to A is measured in years.

The radioactive substance's half-life is represented by t1/2.

A(t) = 523(1/2)t/30 in comparison to the general exponential function

A starting point (Ao) of 523 grams

A(t) = 647(1/2)^t/30

t = 100

A(100) equals [647 × (1/2) × 100] /30

=647 × 0.53.333

=647 × 0.0992

=64.182

=64 grams (to the nearest gram)

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The correct option for an adjoining situation in which liquid is flowing through a pipe of variable cross-section representing pressure is  (a) V1>V2 if L1>L2.

This is because, in a pipe of variable cross-section, the velocity of the liquid (V) is directly proportional to the cross-sectional area of the pipe (L). Therefore, if the cross-sectional area of one section of the pipe (L1) is greater than that of another section (L2), then the velocity of the liquid flowing through the first section (V1) will be greater than that of the second section (V2). This is due to the fact that in the area of the pipe where the cross-sectional area is greater, the liquid will have more space to flow and thus will have a higher velocity.

The other options are incorrect because these situations are not possible.

In fluid mechanics, The pressure drop is directly proportional to the fluid velocity, as well as the density of the fluid and the length of the pipe. The pressure drop is inversely proportional to the cross-sectional area of the pipe. So if the cross-sectional area of the pipe is increasing, the pressure is decreasing. And if the cross-sectional area of the pipe is decreasing, the pressure is increasing.

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The complete question is:

Select the correct option for the adjoining situation in which liquid is flowing through a pipe of variable cross-section (P1, P2 represent pressure(a) V1>V2 if L1>L2 (b) V1<V2 for all values of L1 and L2 (c) P1<P2 for all values of L1 and L2 (d) P1>P2 values of L1 and L2

Answer:

x=10

Step-by-step explanation:

The triangles CAB and PMB are similar. And since each side of CAB is 2 times longer than the side of PMB, we can write the equation:

3x=2(x+5)

3x=2x+10

x=10

Two events are said to be mutually exclusive in the framework of probability theory if they cannot occur simultaneously or at the same time.

In the context of probability theory, two events are said to be mutually exclusive if they cannot happen simultaneously or at the same time. Alternatively, disjunct occurrences are those that are mutually exclusive. The likelihood that two events will occur simultaneously is 0 if they are deemed to be disconnected events.

Events that cannot exist or occur at the same moment are referred to as mutually exclusive events. There are never two occurrences that can happen at the same moment. The probability of A and B occurring simultaneously is P(A and B)= 0 if A and B are two mathematical events that are mutually exclusive.

a. Being female and preferring basketball are mutually exclusive.

b. Being male and preferring football are mutually exclusive.

c. Being female and preferring hockey are mutually exclusive.

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The volume of ice in Antarctica can be calculated by first determining the area of the semicircle.

This can be done by multiplying the radius (2000 km) of the semicircle (2πr2) by half, resulting in a total area of 3,14159265 x (2 x 20002) = 628318530 km2. To calculate the volume of ice, this area must be multiplied by the average thickness of the ice cover (3000 m). This results in a total volume of 18,8547595 x 1012 cm3 of ice in Antarctica. To put this into perspective, this is the equivalent of roughly 6.5 billion Olympic swimming pools of ice.The volume of ice in Antarctica can be calculated by first determining the area of the semicircle.

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3 of them would not be good, 9-6= 3 non-shiny gold rings.

Using two expressions, a mathematical sentence declares two things. The two expressions either employ variables, numbers, or a combination of the two. Symbols or words like equal, greater than, or less than may also be used in a mathematical sentence.

An accurate arrangement of mathematical symbols that expresses a coherent idea constitutes a mathematical sentence, which is equivalent to an English sentence in meaning. Verbs are used in sentences. The verb "=" is used in the mathematical formula "3+4=7 3 + 4 = 7".

The answer is b c 3 9-6=3

3 of them would not be good

9-6= 3 non shiny gold rings

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square side ²= area

s =√81

S = 9

perimeter= 9×4 = 36