There are TWO answers needed for this question John rode 2 kilometers on his bike. His sister Sally rode 300 meters on her bike. Who rode the farthest and how much farther did they ride (answer in km)?

Answer:

Let the speed of the boat in still water be x mph. As, the speed of stream is 5 mph, upstream speed will be (x−5) and downstream speed will be (x+5). and time taken by boat for travelling 13 miles downstream is 13/(x+5). The speed of boat in still water be 8 mph

Step-by-step explanation:

Answer:

\(Area = 27.5\)

Step-by-step explanation:

Given

\(J_{Area} = 440\)

\(J_{Width} = 22\)

\(K_{Width} = 5.5\)

See attachment

Required

Determine the area of K

First, we need to calculate the length of the rectangle  J

\(J_{Length} * J_{Width} = J_{Area}\)

This gives:

\(J_{Length} * 22 = 440\)

Divide both sides by 22

\(\frac{J_{Length} * 22}{22} = \frac{440}{22}\)

\(J_{Length} = 20\)

So, the length of the rectangle J is 20.

Since both shapes are similar, then:

\(J_{Length} : J_{Width} = K_{Length} : `K_{Width}\)

Substitute the known values:

\(20 : 22 = K_{Length} : `5.5\)

Express as fraction:

\(\frac{20 }{ 22 }= \frac{K_{Length} }{ `5.5}\)

Make Length, the subject of formula

\(K_{Length} = \frac{5.5 * 20}{22}\)

\(K_{Length} = \frac{110}{22}\)

\(K_{Length} = 5\)

The area of K is:

\(Area = K_{Length} * K_{Width\)

\(Area = 5.5 * 5\)

\(Area = 27.5\)

Answer:

thanks and it is 25

there are 4 prime numbers in the spinner

A 100% = 4

? = what about

100×1/4

= 25%

Using the log, the answer to (1/243) ^-x/3 = 4 is \(-x=\log _{\frac{1}{243}}(12)\).

The power to which a number must be increased in order to obtain another number is known as a logarithm.

For instance, the logarithm of 100 in base ten is 2, since ten multiplied by two equals 100: log 100 = 2, since 102 = 100.

So, solve using a log as follows: (1/243) ^-x/3 = 4

\(\begin{aligned}& \frac{\left(\frac{1}{243}\right)^{-x}}{3}=4 \\& 3 \cdot \frac{\left(\frac{1}{243}\right)^{-x}}{3}=3 \cdot 4\end{aligned}\)

\(\begin{aligned}& 3 \cdot \frac{\left(\frac{1}{243}\right)^{-x}}{3}=3 \cdot 4 \\& \left(\frac{1}{243}\right)^{-x}=3 \cdot 4\end{aligned}\)

\(\begin{aligned}& \left(\frac{1}{243}\right)^{-x}=3 \cdot 4 \\& \left(\frac{1}{243}\right)^{-x}=12\end{aligned}\)

\(\begin{aligned}& \left(\frac{1}{243}\right)^{-x}=12 \\& -x=\log _{\frac{1}{243}}(12) \\& \frac{\left(\frac{1}{243}\right)^{-x}}{3}=4 \\& -x=\log _{\frac{1}{243}}(12)\end{aligned}\)

Therefore, using the log, the answer to (1/243) ^-x/3 = 4 is \(-x=\log _{\frac{1}{243}}(12)\).

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The expression where the greatest common factor (GCF) is factored completely is \(2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)\)

The expression completely factored in is

\(2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)\)

Please refer below for the remaining answers.

We have,

Part A:

To rewrite the expression 2x³y + 18xy - 10x²y - 90y so that the greatest common factor (GCF) is factored completely, we can factor out the common terms.

GCF: 2y

\(2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)\)

Part B:

To completely factor the expression, we can further factor the quadratic term.

\(2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)\)

Now,

Part A:

To determine the length of each side of the square given the area expression (9x² + 24x + 16), we need to factor it completely.

The area expression (9x² + 24x + 16) can be factored as (3x + 4)(3x + 4) or (3x + 4)².

Therefore, the length of each side of the square is 3x + 4.

Part B:

To determine the dimensions of the rectangle given the area expression (16x² - 25y²), we need to factor it completely.

The area expression (16x² - 25y²) is a difference of squares and can be factored as (4x - 5y)(4x + 5y).

Therefore, the dimensions of the rectangle are (4x - 5y) and (4x + 5y).

Now,

f(x) = 2x² - 5x + 3

Part A:

To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x.

2x² - 5x + 3 = 0

The quadratic equation can be factored as (2x - 1)(x - 3) = 0.

Setting each factor equal to zero:

2x - 1 = 0 --> x = 1/2

x - 3 = 0 --> x = 3

Therefore, the x-intercepts of the graph of f(x) are x = 1/2 and x = 3.

Part B:

To determine if the vertex of the graph of f(x) is maximum or minimum, we can examine the coefficient of the x^2 term.

The coefficient of the x² term in f(x) is positive (2x²), indicating that the parabola opens upward and the vertex is a minimum.

To find the coordinates of the vertex, we can use the formula x = -b / (2a), where a and b are the coefficients of the quadratic equation.

For f(x),

a = 2 and b = -5.

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

To find the corresponding y-coordinate, we substitute this x-value back into the equation f(x):

f(5/4) = 25/8 - 25/4 + 3 = 25/8 - 50/8 + 24/8 = -1/8

Therefore, the vertex of the graph of f(x) is at the coordinates (5/4, -1/8), and it is a minimum point.

Part C:

To graph f(x), we can start by plotting the x-intercepts, which we found to be x = 1/2 and x = 3.

These points represent where the graph intersects the x-axis.

Next,

We can plot the vertex at (5/4, -1/8), which represents the minimum point of the graph.

Since the coefficient of the x² term is positive, the parabola opens upward.

We can use the vertex and the symmetry of the parabola to draw the rest of the graph.

The parabola will be symmetric with respect to the line x = 5/4.

We can also plot additional points by substituting other x-values into the equation f(x) = 2x² - 5x + 3.

By connecting the plotted points, we can draw the graph of f(x).

The steps to graph f(x) involve plotting the x-intercepts, the vertex, and additional points, and then connecting them to form the parabolic curve.

The answer in part A (x-intercepts) and part B (vertex) are crucial in determining these key points on the graph.

Thus,

The expression where the greatest common factor (GCF) is factored completely is \(2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)\)

The expression completely factored in is

\(2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)\)

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Answer:

5

Step-by-step explanation:

1 cup for 1 cake

cups of butter=6-1=5

5 butter left therfore. 5 cakes

Step-by-step explanation:

ans : 3

total cup of butter = 6 cups

1 cup of butter for each cake + 1 cup of butter to make frosting

so , she can make 3 of them

Answer:

18

Step-by-step explanation:

trust me

Answer:

Domain of the given function is all real numbers i.e. R.

Step-by-step explanation:

It is given that the given graph is a V shaped graph.

It is crossing x - axis at \((-2,0)\)

then y-axis at \((0,-2)\) and

then again x - axis at \((2,0)\).

If we try to plot the graph, the graph will be like it comes down from the negative x axis side and then intersect x axis at \((-2,0)\), then intersects y axis at \((0,-2)\)  and then rises towards the right side (i.e. positive x axis) intersecting the positive x axis at \((2,0)\).

Please find attached graph for the same.

This graph denotes the following function:

\(y=f(x)=|x|-2\)

Domain of a function \(y =f(x)\) is the values of \(x\) that can be provided to the function.

Here function is a modulus function and from graph we can easily infer that it can have any Real Number, R as its input.

Modulus function has R as its domain.

So, the answer is:

Domain of given function is all Real Numbers, R

Answer:

A on edg. all real numbers

Step-by-step explanation:

Answer:

Step-by-step explanation:

According to Triangle Property: Angle A + Anlge B + Angle C = 180°

             Solution:
                            1.  ∠A = 119°  ( ∵ ∠A > 90°. It is an Obtuse Angle )

                            2.  ∠B = 38°   ( ∵ ∠B < 90°. It is an Acute Angle )

                            3. ∠C = 23°   ( ∵ ∠C < 90° . It is an Acute Angle

            ∴  The triangle is an Obtuse Triangle as it consists of an Obtuse
                 Angle.                

Answer:

1\4 of the price

Step-by-step explanation:

200 -50 =150-50=100-50=50-50=0 you can do it 5 times so its reduced by 1\4

Answer:

25% off

Step-by-step explanation:

Step-by-step explanation:

(a3/2)3

(a3)3/(2)3

a9/8

Hope it is helpful for you

The maximum distance the dog can be from the house is 8 meters and the minimum distance the dog can be from the house is also 8 meters on the basis of the equation |x - 500|.

The equation |x - 500| can be used to find the maximum and minimum distances that Morgan's dog may be from her house while walking on an 8-meter-long leash.
The equation |x - 500| represents the absolute value of the difference between the dog's distance from the house (x) and 500 meters. The absolute value ensures that the result is always positive.
To find the maximum distance, we need to consider the scenario where the dog is as far away from the house as possible. In this case, the dog would be at the end of the 8-meter-long leash, which means x would equal 500 + 8 = 508 meters. Plugging this value into the equation gives us |508 - 500| = 8 meters which is the maximum distance.
To find the minimum distance, we need to consider the scenario where the dog is as close to the house as possible. In this case, the dog would be at the other end of the leash, which means x would equal 500 - 8 = 492 meters. Plugging this value into the equation gives us |492 - 500| = 8 meters which is maximum distance.
In summary, the maximum and minimum distances that the dog may be from the house while walking on an 8-meter-long leash are both 8 meters.

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Answer:

$0.88 per pound

Step-by-step explanation:

you want to divide the 3/4 pounds by 3, and when you do that, you also have to divide the 66 cents by 3 as well, then multiply the 1/4 you get from dividing 3/4 by 3, and multiply it by 4 to get 1 pound, but when you do that, you have to do the same thing with the 22 cents you get from dividing 66 cents by 3, which will give you 88 cents per pound

14 people gave the modal response

In a survey, modal response is the most frequently occurring response to a question. It can be used to identify the most important issues or concerns of a population.

You will notice the key says one circle represents 4 people. So half circle represents 2 people. Thus, we can say:

Swedish = 4 + 4 + 2 = 10

German = 4 + 4 = 8

French = 4 + 4 + 4 + 2 = 14

Since French has the highest number of people (i.e. 14 people). Therefore, 14 people gave the modal response.

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Answer:

29

Step-by-step explanation:

Investment X earns the greater amount of interest over a period of 2 years.

Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,

SI = PRT

where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.

Let's consider that Ian invests in X, then:

Principle amount, P = $6,000
Time, T = 2 Years

Rate of Interest, R = 4.5% at simple Interest = 0.045

The interest earned is:

Interest = PRT = $6,000 × 0.045 × 2 = $540

Now, consider that Ian invests in Y, then:

Principle amount, P = $6,000
Time, n = 2 Years

Rate of Interest, R = 4% at Compound Interest = 0.04

The interest earned is:

Interest = P(1+R)ⁿ - P

            = $6,000(1+0.04)² - $6,000

            = $489.6

Since $540>$489.6, therefore, Investment X earns the greater amount of interest over a period of 2 years.

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Answer:

Step-by-step explanation:

using pythagoras theorem

a^2 + b^2 = c^2

4^2 + y^2 = 21^2

16 + y^2 = 441

y^2 = 441 - 16

y^2 = 425

\(y = \sqrt{425}\)

\(y = 5\sqrt{17}\)

y = 13.2

a^2 + b^2 = c^2

4^2 + x^2 = 7^2

16 + x^2 = 49

x^2 = 40 - 16

x^2 = 33

x = \(\sqrt{33}\)

x = 5.7 m

Answer:

7.87402 C:

Step-by-step explanation:

Answer:

d or c

Step-by-step explanation:

Answer:

2/5

Step-by-step explanation:

Since the formula for grid's are y by x Y=2 X=5 put them as a fraction there you have 2/5 as I think it is

Answer:

hope this help

Step-by-step explanation:

here is the answer

The Speed of the train in Miles per hour will be 105 miles per hour.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

A train travels at a constant speed during a portion of its cross-country route the table shows the distance the train traveled over different intervals of time at this speed.

The slope represents the speed of the train. Then we have

m = (157.5 - 131.25) / (1.50 - 1.25)

m = 26.25 / 0.25

m = 105 miles per hour

The Speed of the train in Miles per hour will be 105 miles per hour.

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Answer:

a)cross-sectional correlation

Step-by-step explanation:

a test to see whether two variables, measured at the same point in time, are correlated is known as a cross-sectional correlation test

A longitudinal study is a research design that involves repeated observations of the same variables over long periods of time

and so on

9514 1404 393

Answer:

Step-by-step explanation:

The sum of angles in a triangle is 180°, so we have ...

  60° +60° +∠1 = 180°

  ∠1 = 180° -120° = 60°

The measure of angle 1 is 60°.

All of the angles are the same, so this is an equiangular triangle, better known as an equilateral triangle.

Answer:

Step-by-step explanation:

Remark

The way this is worded, it sounds like it is a horizontal distance. However by the marking it looks like they want the hypotenuse. Life can be very confusing sometimes.

The angle of the triangle that you need to know is the one on the right. The line of sight line is parallel to the base of the triangle. So the angle on the right is 8 degrees by the Z theorem.

Solution

Sin(8) = 1817 / x           Multiply both sides by x

x*sin(8) = 1817             Divide by sin(8)

x = 1817/sin(8)

sin(8) = 0.1392

x = 1817/0.1392

x = 13055.7

Note

Watch how you do this. I would put it into your calculator as

1817

÷

sin(8)

=

If you use the rounded answer I gave for sin(8), you might get it wrong. This is a big distance and you should just use the exact number you get for sin(8).

Number of students should be sampled to be within 0.5 drink of population mean with 95% probability is 617 students.

To determine the sample size required to estimate the population mean with a given level of precision, we can use the formula for the margin of error

Margin of error = Z × (standard deviation / sqrt(sample size))

where Z is the critical value of the standard normal distribution corresponding to the desired level of confidence. For a 95% confidence level, Z is 1.96.

We want the margin of error to be no more than 0.5 drinks, so we can set up the equation

0.5 = 1.96 × (6.3 / sqrt(sample size))

Solving for the sample size, we get

sqrt(sample size) = 1.96 × 6.3 / 0.5

sqrt(sample size) = 24.82

sample size = (24.82)^2

sample size = 617

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Answer:

2: 1 : 1

Step-by-step explanation:

4:2:2

Divide all sides by 2

4/2:2/2:2/2

2: 1 : 1

Answer:

Step-by-step explanation:

Step one:

given data

the cost of the laptop= $800

initial payment= $200

monthly payment = $60

let the number of months be x

the expression for the situation is the function for the equation of line

y=mx+c

Step two:

the expression for the situation is

800=200+60x

solve for x

800-200=60x

400=60x

divide both sides by 60

x=400/60

x=6.7

Approximately 7 months