Question one, please help

y varies directly as x means

[tex]y=kx[/tex]

y varies inversely with z means

[tex]y=k\div z[/tex]

therefore

[tex]y=(kx^2)\div z[/tex]

k=constant of variation

[tex]6=(k9^2)\div 27[/tex]

[tex]6=(k81)\div27[/tex]

[tex]6=3k[/tex]

divide both sides by 3

[tex]2=k[/tex]

the constant of variation is 2

If the quantity y varies directly with the square of x and inversely with z, then we can write the following equation:

What is equation ?

A assertion that two mathematical expressions are equal is known as an equation. It typically consists of variables, constants, and mathematical operations, and it may also include functions, exponents, and other mathematical symbols. Equations are used to represent relationships between quantities in mathematics and to solve problems in various fields such as physics, engineering, and economics.

y = k * (x^2) / z

where k is the constant of variation.

We are given that when x is 9, z is 27, and y is 6. Substituting these values into the equation, we get:

6 = k * (9^2) / 27

Simplifying, we get:

6 = k * 3

k = 6 / 3

k = 2

Therefore, the constant of variation is 2.
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The range of values of x that satisfy the inequality 0 ≤ x < 6 is the set of all real numbers between 0 (inclusive) and 6 (exclusive), i.e., the interval [0, 6).

The inequality 0 ≤ x < 6 can be interpreted as follows: x can take on any value between 0 and 6, including 0 but not including 6. This means that x can be any number greater than or equal to 0 and less than 6. In other words, the range of values for x that satisfy this inequality is the set of all real numbers in the interval [0, 6), where the square bracket indicates that 0 is included in the interval (i.e., 0 is a valid value of x) and the round bracket indicates that 6 is excluded from the interval (i.e., 6 is not a valid value of x). This interval can be visualized as a number line with a closed circle at 0 and an open circle at 6, indicating that 0 is included in the range of values for x but 6 is not.

Therefore, any value of x between 0 and 6 (excluding 6) satisfies the inequality 0 ≤ x < 6.

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[tex]y^(3)z^(2)[/tex] is the greatest common factor for the given set of monomials.

The highest power of each variable that is shared by all of the given monomials must be identified in order to calculate the greatest common factor (GCF) for the given list of monomials. To put it another way, we must first determine the prime factors of each monomial before determining the factors that are shared by all the monomials.

Prime factorization for each monomial:

[tex]x^(3)y^(5)z^(3) = (x * x * x) * (y * y * y * y * y) * (z * z * z)y^(3)z^(3) = (y * y * y) * (z * z * z)xy^(3)z^(2) = (x) * (y * y * y) * (z * z)[/tex]

Factors are common to all monomials are [tex]y^(3), z^(2)[/tex]. The GCF is [tex]y^(3)z^(2)[/tex].

This is appropriate GCF by dividing each monomial by [tex]y^(3)z^(2)[/tex] and verify that result is whole number. For eg:

[tex]x^(3)y^(5)z^(3) / (y^(3)z^(2)) = x^(3)y^(2)zy^(3)z^(3) / (y^(3)z^(2)) = yzxy^(3)z^(2) / (y^(3)z^(2)) = x/y[/tex]

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The number οf histοry bοοks is 180 that sοld in a week. The number οf chemistry textbοοks is 108 sοld in a week.

There are many different ways tο define an equatiοn. The definitiοn οf an equatiοn in algebra is a mathematical declaratiοn that illustrates the equality οf twο mathematical expressiοns.

Given that the tοtal number οf bοοks that sοld in a week is 288.

The number οf chemistry textbοοks sοld was 72 less than the number οf histοry textbοοks sοld.

Assume that the number οf histοry textbοοks sοld was x.

The number οf chemistry textbοοks sοld was (x-72)

The tοtal number οf bοοks sοld was x + (x-72) = 2x - 72.

Accοrding tο the questiοn:

2x - 72 = 288

Add 72 frοm bοth sides:

2x - 72 + 72 = 288 + 72

2x = 360

Divide bοth sides by 2:

x = 360/2

x = 180

The number οf histοry textbοοks sοld was 180.

The number οf chemistry textbοοks sοld was (180-72) = 108.

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Answer:

To find the pressure that the box exerts on the ground, we need to divide the force by the area of the base:

pressure = force / area

We are given that the force is 4.5 kN and the area is 1.1 m². However, we need to convert the force from kilonewtons to newtons before we can divide by the area:

force = 4.5 kN = 4,500 N

Now we can plug in the values:

pressure = 4,500 N / 1.1 m² = 4,090.91 N/m²

To express the pressure in kilonewtons per square meter, we need to divide by 1,000:

pressure = 4.09091 kN/m²

Rounding to 2 decimal places, we get:

pressure ≈ 4.09 kN/m²

Therefore, the pressure exerted by the box on the ground is approximately 4.09 kN/m².

Answer:

1. The perimeter of a parallelogram is the sum of the lengths of all four sides. If two consecutive sides of a parallelogram measure 4 m and 9 m, respectively, then the other two sides must also measure 4 m and 9 m, respectively (since opposite sides of a parallelogram are equal in length). Therefore, the perimeter of the parallelogram is:

Perimeter = 4 m + 9 m + 4 m + 9 m = 26 m

So the perimeter of the parallelogram is 26 meters.

2. In a square, both diagonals are equal in length. If one diagonal measures (2x + 4) in and the other diagonal measures 16 in, then we can write:

2x + 4 = 16

Solving for x, we get:

x = 6

So the value of x is 6 inches.

3. In a trapezoid, the length of the median is equal to the average of the lengths of the two parallel sides. If QR is parallel to TS and mQR = 12 cm, then mTS must also be equal to 12 cm. Let x be the length of the base of the trapezoid.

Then, we have:

mUV = (mQR + mTS)/2

Substituting the given values, we get:

24 cm = (12 cm + 12 cm + x)/2

Simplifying, we get:

24 cm = (24 cm + x)/2

Multiplying both sides by 2, we get:

48 cm = 24 cm + x

Subtracting 24 cm from both sides, we get:

x = 24 cm

So the length of the base of the trapezoid is 24 cm, and the length of the median UV is 24 cm.

(If this isn't right, I'm sorry!)

4. In an isosceles trapezoid, the diagonals are equal in length. If one diagonal measures 42 cm and one leg measures 23 cm, then we can use the Pythagorean theorem to find the length of the other leg:

d^2 = l^2 + (b/2)^2

where d is the length of the diagonal, l is the length of each leg, and b is the length of the base. Substituting the given values, we get:

42^2 = 23^2 + (b/2)^2

Simplifying, we get:

b^2/4 = 42^2 - 23^2

b^2/4 = 1253

Multiplying both sides by 4, we get:

b^2 = 5012

Taking the square root of both sides, we get:

b = sqrt(5012) ≈ 70.77

So the length of the other diagonal is also 42 cm.

5. The area of a kite is equal to half the product of the lengths of its diagonals. If mHP = 10 cm and mOE = 18 cm, then we can write:

Area = (mHP x mOE)/2

Substituting the given values, we get:

Area = (10 cm x 18 cm)/2 = 90 cm^2

So the area of the kite is 90 square centimeters.

I hope this helps! I'm sorry if this was wrong. If you need more help, ask me! :]

Answer: SA=5183.62788

Step-by-step explanation:

A=2πrh+2πr2=2·π·15·40+2·π·152≈ 5183.62788

~Find the radius- 30 divided by 2= 15 so radius =15

Answer:

-4y-7

Step-by-step explanation:

- 4 y - 4 + ( - 3 )

We keep the -4y as it is since it can not be simplified. Then we try to open the parentheses. we do this by multiplying by 1.

- 4 y - 4 + 1 * ( - 3)

= - 4 y - 4 - 3

Then we combine the - 4 and -3.

= - 4 y - 7

Answer: I can confirm that it is '-4y-7'

Step-by-step explanation:

The nurse will have to administer 3 milliliters with each dose.

When the prescriber orders medication f 150 mcg po q.12h, the pharmacy sends a bottle labeled:

medication f 0.05 mg/ml.

Milliliters will the nurse administer with each dose :

The conversion factor from mcg to mg is 1/1000.

Therefore, 150 mcg = 150/1000 = 0.15 mg.

The nurse has to administer 0.15 mg of medication f per dose.

The medication f available with the pharmacy is 0.05 mg/ml.

So, the nurse has to administer 0.15 mg in a single dose, which is equal to three times the quantity of medication f available in the bottle (0.05 mg/ml).

Therefore, the nurse has to administer 3 ml (0.05 mg/ml × 3 ml) of medication f with each dose.

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(d) The value of k for which the vertex of the parabola y=x2+kx+9 lies on the line x=−3 is 6. (e) The value of k for which the vertex of the parabola y=kx2+3x+4 lies on the line x=3 is -2.

(d) k=6 (e) k=-2

The vertex form of a quadratic function is given as;

f(x) = a(x-h)² + kf(x) = a(x−h)²+k, with vertex (h, k)

∴ for the quadratic equation y=x²+kx+9, the vertex is given by;

x = -b/2a = -k/2 ∴ k = -2x, using x=-3k = -2x = 6,

thus the vertex of the parabola y=x²+6x+9 lies on line x = -3

(e) Similarly, for the quadratic equation y=kx²+3x+4, the vertex is given by;

x = -b/2a = -3/2k ∴ k = -2x/3, using x=3k = -2x/3 = -2(3)/3 = -2,

thus the vertex of the parabola y=-2x²+3x+4 lies on the line x = 3

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Answer:

2

Step-by-step explanation:

PEMDAS

(-3+4)2

(1)2

2x1=2

The gradient of the line is 200, hence that is the answer.

What does the word "point" actually mean?

A point is a dot on a sheet of paper or in a plane. There are no lengths, widths, or heights in a point. It establishes a plane's position or location. To make a point, mark a dot on a piece of paper with an A or another capital letter.

The slope-intercept version of the equations y = 200x + 500 is y = mx + b, wherein m is the line's gradient and b is its y-intercept.

The value of x, which really is 200, acts as the gradient (or gradient) in this equation. As a result, the line's gradient is 200.

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Based on the information in the image, we can infer that the correct four-digit code is: 4321

To find the four-digit secret code we must observe the image carefully, especially the intertwined lines. What we must do is follow the direction of the lines in the order from A to D to identify which number the line of each letter matches.

According to the above we can infer that the lines of each letter coincide in the following way with the numbers:

So according to the image, the four-digit secret code would be 4321.

Note: This question is incomplete. Here is the complete information:

Attached image

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The prοbability οf chοοsing a number frοm the sample space that cοntains 1 οr 4  is 1/2.

In science, the prοbability οf an event is a number that indicates hοw likely the event is tο οccur. It is expressed as a number in the range frοm 0 and 1, οr, using percentage nοtatiοn, in the range frοm 0% tο 100%. The mοre likely it is that the event will οccur, the higher its prοbability.

space οf twο-digit numbers that can be created using the digits 7,1 ,9 and 4. What is the prοbability οf chοοsing a number frοm the sample space that cοntains 1 οr 4 ?

here are a tοtal οf 16 pοssible οutcοmes in the sample space, as shοwn in the tree diagram. Out οf these 16 pοssible οutcοmes, 8 οf them cοntain the digit 1 οr 4 (i.e., 14, 17, 19, 41, 44, 71, 74, 91).

Therefοre, the prοbability οf chοοsing a number frοm the sample space that cοntains 1 οr 4 is:

P(1 οr 4) = 8/16 = 1/2

Sο the prοbability is 1/2.

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The number of students who passed the examination is 152.

Given: Marks distribution in Mathematics

To Find: Plot an ogive, the median, the number of students who scored distinction marks (75% and above), and the number of students who passed the examination if the pass marks are 35%.

Solution:

Marks Number of students

Less than 10 7

Less than 20 28

Less than 30 54

Less than 40 71

Less than 50 84

Less than 60 105

Less than 70 147

Less than 80 180

Ogive:

An ogive is a graph that represents the cumulative frequency distribution of a set of data. To plot an ogive, we plot the upper limits of each class on the x-axis and the corresponding cumulative frequency on the y-axis. We then join the points with a free-hand smooth curve to obtain the ogive.

Median:

To find the median from the graph, we draw a line from the value of 50 on the y-axis to the ogive curve and then drop it down to the x-axis. The point where the line intersects the x-axis gives us the median. In this case, the approximate median value from the graph is 52.

The number of students who scored distinction marks:

To find the number of students who scored distinction marks (75% and above), we first calculate 75% of the total number of students, which is 0.75 x 180 = 135.

From the ogive graph, we see that the number of students who scored less than 75% marks is 105.

Therefore, the number of students who scored 75% or more marks is 180 - 105 = 75.

The number of students who passed the examination:

To find the number of students who passed the examination if the pass marks are 35%, we first calculate 35% of the total number of students, which is 0.35 x 180 = 63.

From the ogive graph, we see that the number of students who scored less than 35% marks is 28.

Therefore, the number of students who passed the examination is 180 - 28 = 152.

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Answer and Step-by-step explanation:

Based on the evidence provided, Gary is most likely to make the conjecture that the store expects high demand for mountain bikes in the spring compared to racing bikes. Another conjecture that could be made is that mountain bikes will most likely sell better than racing bikes. This is because the manager has ordered 50 mountain bikes, which is five times more than the number of racing bikes ordered. This suggests that the store is anticipating greater demand for mountain bikes than for racing bikes in the spring season.

Answer:

The volume of the container is 1872 cubic cm. The volume of the water is 672 cubic cm.

Therefore, 672/1872 = 0.36 or 36%

The correct solution of the expression 5a² -25bˣ is 5(a² - 5bˣ)

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

5a² -25bˣ

The expression is already in its simplest form in terms of combining like terms.

However, we can still look into factoring the expression

To do this, we can factor out the greatest common factor of 5 and rewrite the expression as follows:

5a² -25bˣ = 5(a² - 5bˣ)

This is the factored form of the expression, where the greatest common factor of 5 has been factored out.

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Answer:

16 litres = 100% of the tank capacity

x litres = 75% of the tank capacity (since 3/4 is equivalent to 75%)

To solve for x, we can cross-multiply and simplify:

16 * 75 = 100x

1200 = 100x

x = 12

Therefore, 3/4 of the tank capacity when the tank holds 16 litres is 12 litres.

Answer:

= 12 liters.

Step-by-step explanation:

16*3/4 =48/4.

= 12

By using the scale diagram, the height of this person in meters is equal to 1.6 meter.

In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):

Scale factor = Dimension of image (new figure)/Dimension of pre-image(actual figure)

Based on the information provided about the lorry, the lorry is approximately 11.2 m in length and 14 cm on a scale diagram. Therefore, the height of the person in meters can be calculated as follows;

1 centimeter = 11.2/14

1 centimeter = 0.8 meter.

Height of the person in meters = 0.8 meter × 2

Height of the person in meters = 1.6 meter.

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The volume of the prism with height h is h times the volume of the prism with height 1 unit.

If the original prism has a volume of V and a height of 1 unit, then the volume of the prism with height h is given by:

Bh = (V)(h)

where B is the area of the quadrilateral base.

The volume of the prism with height h is h times the volume of the original prism. So, we can compare the volume of the two prisms by looking at their volume ratios:

Volume ratio = Volume of prism with height h / Volume of original prism

= Bh / (V)(1)

= Bh / V

= h

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Answer: 6

Step-by-step explanation:

When x=-3, y=6

You can count it, 1,2,3,4,5,6.

Hope you found that helpful!

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1200\\ r=rate\to 0.2\%\to \frac{0.2}{100}\dotfill &0.002\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{weekly, thus fifty two} \end{array}\dotfill &52\\ t=years\dotfill &10 \end{cases} \\\\\\ A = 1200\left(1+\frac{0.002}{52}\right)^{52\cdot 10}\implies A \approx 1224.24[/tex]

Answer: $1248 in compound interest for 10 years

Step-by-step explanation:

Option (a) is correct Mr. Reynolds walks 2000 feet per minute for 8 minute. Here it is the condition of speed.

Speed is define as the distance covered by a person in a given interval or time. It is generally denotes in Km/h or m/sec.

[tex]Speed\ (S)= Distance\ (d) * Time\ (t)[/tex]

Distance, It is an area cover by a person to complete his journey.

Distance is generally denoted by km, m etc,

Time, It is an interval in which generally person complete it task.

It is generally denoted by hour (h), Minute (min) or Second (Sec).

The correct is (a) Mr. Reynolds walks 2000 feet per minute for 8 minute. Here it is the condition of speed.

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The probability of selecting a black checker from a bag of 6 black and 4 red checkers, replacing it, and selecting another black is 9/25.

To find the probability follow these-

Determine the probability of selecting a black checker on the first draw.

There are 6 black checkers and a total of 10 checkers (6 black + 4 red).

So, the probability of selecting a black checker on the first draw is 6/10,

which can be simplified to 3/5.

Since the black checker is replaced, there are still 6 black checkers and

a total of 10 checkers in the bag. Therefore, the probability of selecting a

black checker on the second draw is also 3/5.

To find the probability of both events occurring, multiply the probabilities together: (3/5) × (3/5) = 9/25.

So, the probability of selecting a black checker from a bag of 6 black and

4 red checkers, replacing it, and selecting another black is 9/25.

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The explicit formula for the population in the United States between 1930 and 1975 is [tex]P(t) = 0.00004t^1.9 + 1[/tex], where t is the number of years after 1930.

To calculate the population for any year between 1930 and 1975, we can simply substitute the corresponding year for t in the equation. For example, if we want to calculate the population in 1950, we can substitute t = 1950 in the equation.

Therefore, [tex]P(1950) = 0.00004(1950)^1.9 + 1 = 0.0035 + 1 = 1.0035[/tex].

This is the population in 1950. In conclusion, the explicit formula for the population in the United States between 1930 and 1975 is [tex]P(t) = 0.00004t^1.9 + 1[/tex], where t is the number of years after 1930.

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Translate: In a classroom of 60 students, 3 exams were taken to pass a course and

He noted that those who passed a single exam were five times those who passed the

3 exams and those who passed only 2 exams is triple those who failed

the 3 exams. If the number of those who failed the 3 exams is equal to the number

Of those who passed the 3 exams, how many passed the course if to pass it is

Do they need to pass at least 2 exams?

The number of students who passed the course is x + 3y, where x is smallest integer greater than or equal to[tex](180 - 3z)/53[/tex], and y = [tex](60 - 7x)/3[/tex] for equal things.

Let's use some variables to represent the number of students who passed each exam:

Let's call the number of students who passed all 3 exams "x".

Let's call the number of students who passed exactly 2 exams "3y" (since it's given that this number is triple the number who failed all 3 exams).

Let's call the number of students who passed exactly 1 exam "5x" (since it's given that this number is five times the number who passed all 3 exams).

Finally, let's call the number of students who failed all 3 exams "x".

We can use this information to set up a system of equations:

x + 3y + 5x + x = 60 (since there are 60 students in total)

x = x (since the number who failed all 3 exams is equal to itself)

Simplify:

7x + 3y = 60

Now we need to use the fact that passing at least 2 exams is required to pass the course. This means we need to find the number of students who passed at least 2 exams, which is the sum of the number who passed all 3 exams and the number who passed exactly 2 exams:

x + 3y

We know that this number needs to be greater than or equal to the number of students who pass the course. So we set up another equation:

x + 3y >= z (where z is the number of students who pass the course)

Now we can solve for x and y in terms of z. We'll start with y:

7x + 3y = 60

3y = 60 - 7x

y = (60 - 7x)/3

Next, we'll use the fact that the number who failed all 3 exams is equal to the number who passed all 3 exams:

x = x

Finally, we'll use this information to solve for x in terms of z:

x + 3y >= z

x + 3((60 - 7x)/3) >= z

x + (60 - 7x) >= 3z

53x >= 180 - 3z

x >= (180 - 3z)/53

Since x represents the number of students who passed all 3 exams, we want to round it up to the nearest integer (since we can't have a fractional number of students). So the final answer is:

The number of students who passed the course is x + 3y, where x is the smallest integer greater than or equal to (180 - 3z)/53, and y is given by y = (60 - 7x)/3.

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Answer:

[tex]130m^{2}[/tex] , [tex]65.000 rs[/tex]

Step-by-step explanation:

Given Length = 15m
Given Breadth = 12m

Since there is a 1m gap between the sides,

Actual Length = 15 - 2 = 13m
Actual Breadth = 12 - 2 = 10m

From here find the Area:

L * B = AR of a cuboid , so

13 x 10 = [tex]130m^{2}[/tex] is the Area

for every [tex]m^{2}[/tex] it is 500 rupees, so for [tex]130m^{2}[/tex] ,

130 * 500 = 65,000 rupees.

The allowed housing expense for the year is $38,582.01.

The minimum realized income per month is $1,774.53.

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”.

1 ) p = 7.65 + 11.5 + 9 = 28.15 %

$53,698.00 · ( 1 - 0.2815 ) =

= $53,698.00 · 0.7185 = $38,582.01

The allowed housing expense for the year is $38,582.01.

2 ) $1,275.00 : 0.7185 = $1,774.53

The minimum realized income per month is $1,774.53.

The complete question is-

1.) You (or your parents) earn $53,698.00/yr and you have deductions of FICA (7.65%), federal tax withholding (11.5%), and state tax withholding (9%). How much is the allowed housing expense for the year? (1 point)

$ /year

2.) You (or your parents) plan to pay $1,275.00/month for a mortgage. How much is the minimum realized income per month to the nearest penny

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