Which is the largest fraction?
7/8
8/10
12/15
3/4​

The company has the total number of employees as 140.

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

We are given that company has two offices - one in Portlee and one in Queentown.

The ratio of the number of employees at Portlee to the number at Queentown is given as;

3:4

Now we know that 20% of the employees at Portlee are part-time.

25% of the employees at Queentown are part-time.

Therefore, 3x of 20% are part- time

4x of 25%

Then we have 32 part-time employees.

0.6x + 1x = 32

1.6x = 32

x = 32/1.6

x = 20

Hence, the total number of employees the company has

3x + 4x = 7x

7(20) = 140

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The solution to the given IVP is.[tex]$i(t)-\frac{E}{R}+\left(i_0-\frac{E}{R}\right) e^{-\frac{R}{L}}$[/tex]

Initial value problems describe a type of problem in calculus. Initial value problems in calculus concern differential equations with a known initial condition that specifies the value of the function at some point. The purpose of these problems is to find the function that describes the system, which can be done by integrating the differential equation.

Consider the initial value problem,

L [tex]\frac{d i}{d t}+R i=E \text {. }[/tex]

The initial condition is. [tex]$i(0)=i_0$[/tex]

Rewrite the DE as,

[tex]\begin{gathered}L \frac{d i}{d t}+R i=E \\\frac{d i}{d t}+\frac{R}{L} i=\frac{E}{L}\end{gathered}$$[/tex]

This is a linear DE.

Compare the DE  [tex]\frac{d i}{d t}+\frac{R}{L} i=\frac{E}{L}$[/tex] with the general DE [tex]\frac{d i}{d t}+P(t) i=Q(t)$[/tex]. Then [tex]$P(t)=\frac{R}{L}$[/tex] and [tex]$Q(t)=\frac{E}{L}$[/tex].

Find the integrating factor (IF).

                                     [tex]$$\begin{aligned}I F & =e^{\int P(t) \vec{t}} \\& =e^{\int\left(\frac{\pi}{\mathrm{I}}\right) \mathrm{A}} \\& =e^{\frac{\pi}{l^2}}\end{aligned}$$[/tex]

Thus, the integrating factor is [tex]$I F=e^{\frac{R^2}{2^2}}$[/tex].

Now multiply both sides of the DE with the IF.

                                   [tex]$$\begin{array}{r}e^{\frac{R}{\bar{L}^t}}\left(\frac{d i}{d t}+\frac{R}{L} i\right)=\frac{E}{L} e^{\frac{R}{L^t}} \\\frac{d i}{d t} e^{\frac{\pi}{L^t}}+\frac{R}{L} e^{\frac{R}{\bar{L}^t}} i=\frac{E}{L} e^{\frac{\pi}{\bar{L}^t}} \\{\left[i e^{\frac{R}{L^2}}\right]=\frac{E}{L} e^{\frac{R^L}{L^t}}}\end{array}$$[/tex]

Integrate on both sides.

        [tex]$$\begin{aligned}& \int\left[i e^{\frac{R}{L}}\right] d t=\int \frac{E}{L} e^{\frac{R}{L^t}} d t \\& i e^{\frac{R}{L^{\mathrm{r}}}}=\frac{E}{L} \int e^{\frac{\pi}{L^t}} d t \\& i e^{\frac{R}{\perp} r}=\frac{E}{L}\left[\frac{e^{\frac{R}{2}}}{\frac{R}{L}}\right]+C \\& i e^{\frac{R}{\Gamma}+}=\frac{E}{R} e^{\frac{R^2}{I^{+}}}+C \\& i(t)=\frac{\frac{E}{R} e^{\frac{R}{L^2}}+C}{e^{\frac{R}{D^2}}} \\& t(t)=\frac{E}{R}+C e^{-\frac{R}{L^t}} \\&\end{aligned}$$[/tex]

Thus, the general solution to the [tex]\mathrm{DE}[/tex] is [tex]$i(t)=\frac{E}{R}+C e^{-\frac{R}{t^*}}$[/tex].

Use the initial condition. [tex]$i(0)=i_0$[/tex]

Substitute [tex]$t=0$[/tex] and [tex]$i(0)=i_0$[/tex] in [tex]$i(t)=\frac{E}{R}+C e^{-\frac{R}{I^t}}$[/tex].

[tex]$$\begin{aligned}& i(0)=\frac{E}{R}+C e^{-\frac{R}{I}(0)} \\& i_0=\frac{E}{R}+C e^0 \\& i_0=\frac{E}{R}+C \quad \text { use } e^0=1 \\& C=i_0-\frac{E}{R}\end{aligned}$$[/tex]

Substitute  [tex]$C=i_0-\frac{E}{R}$[/tex] in [tex]$i(t)=\frac{E}{R}+C e^{-\frac{R}{L^1}}$[/tex].

[tex]$$\begin{aligned}& i(t)=\frac{E}{R}+C e^{-\frac{R}{I}} \\& i(t)=\frac{E}{R}+\left(i_0-\frac{E}{R}\right) e^{-\frac{\pi}{t^t}}\end{aligned}$$[/tex]

Therefore, the solution to the given IVP is. [tex]$i(t)-\frac{E}{R}+\left(i_0-\frac{E}{R}\right) e^{-\frac{R}{L}}$[/tex].

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A dot plot that corresponds to the values in the table include the following: dot plot B.

In Mathematics, a dot plot can be defined as a type of line plot that is typically used for the graphical representation of a data set above a number line, especially through the use of dots.

Based on the values contained in the table, the high school students' essays score on a scale of 0 to 10 should be plotted on a dot plot as follows:

An essay score of 3 would have 1 dot.

An essay score of 4 would have 1 dot.

An essay score of 5 would have 2 dots.

An essay score of 6 would have 5 dots.

An essay score of 7 would have 4 dots.

An essay score of 8 would have 7 dots.

An essay score of 9 would have 3 dots.

An essay score of 10 would have 2 dots.

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Answer:

140 square meters

Step-by-step explanation:

A= lw

A= 10 times 14 = 140

Answer:

<2 = 45

< 7 = 135

< 3 = 135

< 5 = 135

<8  = 45

< 6 = 45

Step-by-step explanation:

Angles 2 and 7 are supplemental angles.  This means that together they add to 180.

x + 3x = 180  Combine like terms

4x = 180  Divide both sides by 4

x = 45

<2 = 45

Angle 7

3x   Substitute 45 for x

3(45)

135

Angle 3

Corresponding angle to 7.  Corresponding angles are congruent (equal).

Angle 5

Vertical to angle 7.  Vertical angles are congruent.

Angle 8

Alternate exterior angle to 7.  Alternate exterior angels are congruent.

Angle 6

Vertical angle to 8.  Vertical angles are congruent.

Answer:

Range: 20.

Step-by-step explanation:

Put in order:

12, 13, 13, 15, 16, 19, 32

Subtract smallest number from largest number

32 - 12 =20

The p-value of 0.017 suggests that there is a statistically significant difference in the proportion of high school seniors who own their own cars, indicating that more high schoolers now have cars than before.

The p-value of 0.017 indicates that there is a statistically significant difference between the proportion of high school seniors who own their own cars today compared to a decade ago. This suggests that there is a real, measurable difference in the number of high school seniors who own cars, meaning that it is reasonable to conclude that more high schoolers have cars now than they did a decade ago. This conclusion is supported by the statistical significance of the data, which indicates that the difference between the proportions is not likely due to chance. It is also likely that changes in technology and access to transportation options have contributed to the increase in the proportion of high school seniors who own cars.

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Answer: 789

Step-by-step explanation:

No offense but this was an easy question

Sorry hope this helps

Answer:

789

Step-by-step explanation:

Step 1: add 7

Step 2: answer is 789

The number of weeks that it will take for Aaliyah yo have enough money is 13.4 weeks.

The equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

It is important to note that an equation is the mathematical statement which can be made up of two expressions which are connected by an equal sign.

The number of weeks will be calculated thus:

25 + 8.25w = 135.75

where w = number of weeks.

Collect the like terms

8.25w = 135.75 - 25

8.25w = 110.75.

Divide

w = 110.75 / 8.25

w = 13.4 weeks

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Answer:

Step-by-step explanation:

8g=9.6

Divide both sides by 8 to isolate the variable

g=1.2

Answer:

[tex] \sf \: g = 1.2[/tex]

Step-by-step explanation:

Now we have to,

→ find the required value of g.

The equation is,

→ 8g = 9.6

Then the value of g will be,

→ 8g = 9.6

→ g = 9.6 ÷ 8

→ [ g = 1.2 ]

Hence, the value of g is 1.2.

Answer:

2) [tex]f(-2)=3[/tex]

Step-by-step explanation:

[tex]f(3)=(3-1)^2+3(3)=13 \\ \\ f(-2)=(-2-1)^2+3(-2)=3 \\ \\ f(-15)=(-15-1)^2+3(-15)=211[/tex]

It is less likely to randomly meet someone who obtained a SAT score of over 1150.

Z score or standard score is defined as the number of standard deviations by which the observed value is above or below the mean value.

The formula for calculating z score is,

z = (x - μ) / σ

where x is the observed value, μ is the population mean and σ is the population standard deviation.

For IQ scores,

z = (80 - 100) / 16 = -1.25

For SAT scores,

z = (1150 - 1000) / 100 = 150/100 = 1.5

z score is closer to 0 for IQ scores and far to 0 for SAT scores.

Hence it is less likely to meet someone who obtained a SAT score of over 1150.

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If the value of x is greater than 0.01, then Tanya finished the race first.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

Tanya ran the 200-meter race in 24 +(6x) seconds.

Cecella ran the same race in 24 and 6 hundredths seconds.

That means,

Cecella ran the same race in 24 and 6/100 seconds.

Cecella ran the same race in 24 and 0.06 seconds.

Cecella ran the same race in 24.06 seconds.

And if,

Then, 6x = 0.06

x = 0.01 seconds.

If the value of x is greater than 0.01.

x > 0.01

Then Tanya finished the race first.

Therefore, if x > 0.01, then Tanya finished the race first.

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The solution to the inequality is x ≤ 3.75 and is shown on the number line.

An inequality shows the nonequal comparison of numbers and variables arranged in an expression.

Given the expression:

(-1/3)x + 1/2 ≥ -3/4

Multiply through by 12:

-4x + 6 ≥ -9

Subtract 6 from both sides:

-4x ≥ -15

Divide through by -4:

x ≤ 3.75

The solution to the inequality is x ≤ 3.75

See attachment for the number line

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Using the fact that the sum of the interior angles must be 180°, we will get the measures:

Here we have a triangle, and we know that the measures of the interior angles are:

C = 15x

T = 10x + 20

A = 5x + 40

We know that the sum of the interior angles of a triangle must be 180°, then we can write the linear equation:

15x + 10x + 20 + 5x + 40 = 180

(15 + 10 + 5)*x = 180 - 20 - 40

30x = 120

x = 120/30

x = 4

Then the measures of the interior angles are:

C = 15x = 15*4 = 60

T = 10x + 20 = 10*4 + 20 = 60

A = 5x + 40 = 5*4 + 40 = 60

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The vertex and equation of the line of symmetry will be (1, 3) and x = 1.

It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

The lowest points of the parabola from the table represent the vertex of the parabola. Then we have

Vertex = (1, 3)

The axis of symmetry is parallel to the y-axis. Then the equation of the axis of symmetry will be given as,

x = 1

The vertex and equation of the line of symmetry will be (1, 3) and x = 1.

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The length of the missing side is 19 units

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

In the given triangle there is a bisector which is bisecting on hypotenuse of length 25.

The length of opposite side will be 25-9=16

From pythagoras theorem we can find the length x

x²+16²=25²

x²=25²-16²

=625-256

=369

x=19

Hence, the length of the missing side is 19 units

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The resultant vector on the car would be a vector pointing north with a magnitude of 2 miles per hour.

The resultant vector is the net effect of two or more individual vectors on an object. It is the overall force or movement that is produced when all the individual vectors are combined. To find the resultant vector, you would add together all of the individual vectors using vector addition. The resultant vector would be represented by a single vector with a certain magnitude and direction.

If a car is rolling south at 8 miles per hour, and a man pushes the car north at 10 miles per hour, subtract the southward velocity from the northward velocity.

10 mph northward - 8 mph southward= 2 mph northward

Therefore, the resultant vector on the car is 2 mph northward.

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Using the velocity of 64 meters per second, we know that the air pressure is 910 millibars.

Everything you touch is pressed upon by the weighty air that surrounds you.

This pressure is referred to as air pressure or atmospheric pressure.

It is the force that the air above a surface applies to it while gravity pulls the surface toward Earth.

A barometer is frequently used to measure atmospheric pressure.

So, we know that:

The calculation for mean sustained wind speed.

64 M/s is the average sustained wind speed.

The equation for mean sustained wind speed:

v = 6.3√1013 - p

Hurricane's means sustained wind speed is 64 m/s,

With the help of the following equation, we can determine the air pressure.

v = 6.3√1013 - p

64/6.3 = √1013 - p

Making both sides square:

(10.1587)² = 1013 - p

p = 910 millibars

Therefore, using the velocity of 64 meters per second, we know that the air pressure is 910 millibars.

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Answer:-32

Step-by-step explanation:

p=-32

7Answer:

-7

-Step-by-step explanation:

Answer: $14.84

Step-by-step explanation: 14 + 6% = 14.84

Yes, a triangle can have three equal angles. The term "equilateral triangle" is used to describe this.

A 60-degree equilateral triangle has the same length for all three angles. This is due to the fact that all three angles in a triangle have to add up to 180 degrees, and when three angles are equal, the sum is divided equally between them.

An equiangular triangle is another name for an equilateral triangle. An equilateral triangle takes on the form of an equilateral triangle because all of its sides are equally angled. The term "congruent" refers to the fact that all three sides of the triangle are the same length.

Numerous mathematical disciplines, including geometry and trigonometry, make use of equilateral triangles. They are often used to show how other shapes, like parallelograms and rhombi, work. Additionally, they are utilized in the process of determining the perimeter, angles, and area of a triangle.

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The clock minutes rotate 270 degrees in 45 minutes.

While rotating, the clock's hands are seen to move at a speed of six degrees per minute.

The number of degrees for a clock minute is solved by

60 minutes  = 360 degrees

1 minute = ?

cross multiplying

60 * ? = 360

? = 360 / 60

? = 6

hence 1 minute is 6 degrees

The formula to use to get the calculation is multiplying the number of minutes by 6

Number of degrees in 45 minutes = 45 * 6

Number of degrees in 45 minutes = 270 degrees

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As a result, you are turning the entire trapezium figure 90 degrees clockwise in order to change the trapezoid LMNQ into L′M′NQ′.

In American and Canadian English, a trapezoid is a quadrilateral with at least one set of parallel sides. In British and other versions of English, the word is a trapezium. A trapezoid is always a convex quadrilateral in Euclidean geometry. The parallel sides of the trapezoid are referred to as its bases.

Given: When (-7,-2) to L, L becomes L' (-2,7)

You will often obtain a rotation of 90 degrees clockwise or 270 degrees counterclockwise around the origin (0,0), as well as a reflection across the x-axis and across the line of symmetry of the image, if you have (x,y) and it becomes (y,-x).

The entire graphic is therefore rotated 90 degrees in a clockwise orientation.

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The image point which results from the transformation R180° of the point (-6, -1) is; (6, 1).

It follows from the task content that the image point of the point (-6, -1) is to be determined after a transformation R180°.

Recall that a rotation of 180° in the clockwise or anticlockwise direction is such that;

( x, y ) =====>. ( -x, -y )

On this note, since the pre-image point is; ( -6, -1 ), it therefore follows that the image point which corresponds to the given transformation is; (6, 1).

Ultimately, the required image point is; (6,1).

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The average value of f(x) = 8x sec^2(x) on the interval [0, π/4] is -4/3.

To find the average value of a function f(x) on an interval [a, b], we need to evaluate the definite integral of the function over that interval and divide it by the length of the interval.

The definite integral of f(x) = 8x sec^2(x) over the interval [0, π/4] is given by:

∫[0,π/4] 8x sec^2(x) dx

This integral can be evaluated by substitution. Let u = sec(x) and du = sec(x)tan(x)dxmthen the integral becomes:

∫[0,π/4] 8x sec^2(x) dx = ∫[1,sec(π/4)] 8xu^2du

= 8/3u^3 evaluated at u = sec(π/4) - 8/3u^3 evaluated at u = 1

= 8/3sec^3(π/4) - 8/3 = 8/3(1/cos^3(π/4)) - 8/3 = 8/3*(1/1/2) - 8/3 = 4/3 - 8/3 = -4/3

Thus, The average value of f(x) = 8x sec^2(x) on the interval [0, π/4] is -4/3.

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