The standard equation for the position s of a body moving with a constant acceleration a along a coordinate line is s = a/2 t^2 + v_0 t + s_0, where v_0 and s_0 are the body’s velocity and position at time t = 0. Derive this equation by solving the initial value problem Differential equation: d^2s/dt^2 = a Initial conditions: ds/dt = v_0 and s = s_0 when t = 0.

The numbers are -5 and 2

Explanation:

let the 1st number = x

second number = y

Seven times a number plus three times another number equals negitive one:

7 × x + 3 × y = -1

7x + 3y = -1

The sum of the two numbers is negitive three:

x + y = -3

7x + 3y = -1 ....equation 1

x + y = -3 .....equation 2

using elimination method:

multiply equation 2 by 7:

7x + 7y = -21

7x + 3y = -1

7x + 7y = -21

subtract equation 1 from 2:

7x - 7x + 7y - 3y = -21 -(-1)

4y = -20

y = -20/4

y = -5

substitute the value of y in equation 2:

x + (-5) = -3

x - 5 = -3

x = -3 + 5

x = 2

The numbers are -5 and 2

Answer:

0. 3

1. 1

2. -1

3. -3

4. -5

y- intercept is 3 then remember rise over run for the slope

Answer:

B

Step-by-step explanation:

Answer:

The more confident the manager can be that the parameter estimates reflect the true values.

Step-by-step explanation:

Standard error:

The standard error is a parameter that is direct proportional to the margin of error of a confidence interval, that is, the higher the standard error, the higher the margin of error of the confidence interval.

A lower margin of error leads to a more precise interval, thus, a lower standard error will also mean a higher confidence for the estimate, and thus, the correct option is:

The more confident the manager can be that the parameter estimates reflect the true values.

The Distance will be  5.

The distance between two points is the length of the line segment connecting the two points on the plane. The formula for finding the distance between two points is usually d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on the coordinate or x-y plane.

Let point (7,5) be A and point (4,9) be B

Distance formula =

Ab  = √(x1- x2) ² + (y1 -y2) ²

Then Distance AB will be

Ab  = √(7-4) ² + (5 -9) ²

= √ 3² + 4²

= √ 9 + 16

= 5

Hence the distance  will be 5.

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The points \((7,5)\)  \((4,9)\) are separated by a distance of \(5\) units.

The distance between the two points is given by the length of the segment between them.

The Distance Formula is a helpful tool for figuring out how far apart two points are when they are arbitrarily represented on a coordinate plane as points A\((x_{1},y_{1})\) and B\((x_{2},y_{2})\).

The Pythagorean Theorem is essentially the source of the Distance Formula. Calculating the right triangle's hypotenuse's length is the fundamental purpose of the distance formula.

Use the distance formula to get the distance between two places.

\(d = \sqrt{ (x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} }\)

In the posted query,

\((x_{1},y_{1})=(7,5)\\\\(x_{2},y_{2})=(4,9)\)

Distance formula,

\(d = \sqrt{ (x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} }\)

\(d = \sqrt{ (4-7)^{2} +(9-5)^{2} }\)

\(d = \sqrt{ (-3)^{2} +(4)^{2} }\)

\(d = \sqrt{ 9+16 }\)

\(d = \sqrt{ 25 }\)

\(d = 5\)

Therefore, the points \((7,5)\)  \((4,9)\) are at a distance of \(5\) units.

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The solutions of the equation of the graph is -4 and 2.

An placement of values to the uncertainties that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself. Particularly but not exclusively for polynomial equations, the solution of an equation is frequently referred to as the equation's root. An equation's solution set is the collection of all possible solutions.

We know that the solution of the equation is determined using the graph by obtaining the point of intersection of the equation.

In the given graph the point of intersection of the two equations are at x = -4 and x = 2.

Hence, the solutions of the equation of the graph is -4 and 2.

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The complete question is:

The simplified expression is m^1 or simply m.

To simplify the expression −m^(-8) * m^9 without using negative exponents, we can utilize the properties of exponents.

First, let's deal with the negative exponent. A negative exponent indicates that the term should be moved to the denominator. So, we can rewrite −m^(-8) as 1/m^8.

Now, we can simplify the expression further: 1/m^8 * m^9.

When multiplying terms with the same base, we add the exponents. In this case, we have m^(-8) * m^9, which becomes m^(-8 + 9) = m^1 = m.

Finally, multiplying 1/m^8 by m gives us (1/m^8) * m = 1/m^(8-1) = 1/m^7.

Therefore, the simplified expression is 1/m^7, where m is the variable restricted to those numbers for which the expression is defined. By eliminating the negative exponent and combining like terms, we've simplified the expression without using negative exponents.

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Answer:

One plane has a speed of 450 km/h and the other has a speed of 900 km/h.

Step-by-step explanation:

I am going to say that:

The speed of the first plane is x.

The speed of the second plane is y.

One plane is flying at twice the speed of the other.

I will say that y = 2x. We could also say that x = 2y.

Two airplanes leave an airport at the same time, flying in the same direction

They fly in the same direction, so their relative speed(difference) at the end of each hour is y - x = 2x - x = x.

If after 4 hours they are 1800 km apart, find the speed of each plane

After 1 hour, they will be x km apart. After 4, 1800. So

1 hour - x km apart

4 hours - 1800 km apart

4x = 1800

x = 1800/4

x = 450

2x = 2*450 = 900

One plane has a speed of 450 km/h and the other has a speed of 900 km/h.

The blue curve of the image attached below represents the graph of the function f(x) = 3 · x².

In this question we have a power function formed by the product of a primitive function g(x) = x² and vertical dilation h(x) = 3, then:

f(x) = h(x) · g(x)

f(x) = 3 · x²

Now we proceed to graph both the primitive function and the transformed function with a graphing tool. Please notice that the primitive function is the red curve.

The statement presents typing mistakes. Correct form is shown below:

Show a graph for the following: f(x) = 3 · x².

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The coordinates of the y-intercept are (0, 3.5) and the coordinates of the x-intercepts are (-17.5, 0). Using these coordinates, the graph of the equation is shown below.

From the question, we are to graph the given linear equation.

To graph the equation,

We will determine the coordinates of the x-intercepts and y-intercepts.

When x = 0

y = 1/5x + 3.5

y = 1/5(0) + 3.5

y = 3.5

(0, 3.5)

When y = 0

y = 1/5x + 3.5

0 = 1/5x + 3.5

Multiply through by 5

0 = x + 17.5

x = -17.5

(-17.5, 0)

Using the coordinates of the x-axis and y-axis, the graph of the equation is shown below.

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Answer:

15/9

Step-by-step explanation:

2/9+7/9+6/9

2×1, 7×1,6×1

2/9,7/9,6/9=15/9

If u want u can devide it

Answer: YES

Step-by-step explanation: both equal 5 when divided.

95% confidence interval for the ratio of medians is a range of values that we are confident contains the true population ratio, with a specified level of confidence.

A confidence interval is a range of values that we are confident contains the true population parameter, with a specified level of confidence. In this case, we are looking at the ratio of medians in the Verizon data and finding a 95% confidence interval for the ratio.

Let's say the sample median for the first data set is M1 and the sample median for the second data set is M2. The standard error for M1 and M2 can be calculated using the formula for the standard error of the median.

Next, we use the formula for a confidence interval for the ratio of medians:

=> (M1/M2) +/- (Z * SE(M1/M2)),

where Z is the critical value from a standard normal distribution for a 95% confidence level.

The percent bias is the difference between the estimated value and the true value, divided by the true value and expressed as a percentage. In this case, we will calculate the percent bias of the confidence interval for the ratio of medians relative to the standard error.

Finally, we compare the results for the ratio of medians with the results for the ratio of means. This comparison can give us an idea of the difference in the level of accuracy and precision between the two estimates.

Complete Question:

Consider the Verizon data. find a 95% confidence interval for the ratio of medians. estimate the percent bias (relative to the standard error) and compare with the results for the ratio of means

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Answer:

11

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

Answer:

6) x=5

7)x=6

8)x=10

9)x=12

Step-by-step explanation:

6) 3x-5=10. 7) 36=4x+12. 8) 3(x+2)=36

+5 +5. - 12. - 12. 3x + 6=36

3x = 15. 24 = 4x. - 6. -6

÷3. ÷3. ÷4. ÷4. 3x=30

x=5. 6 = x. x = 10

9) 7(2x-15)=63

14x - 105=63

+105. +105

14x = 168

÷14. ÷14

x=12

Expanding the square of the binomial (x + 5)^2, we get:

(x + 5)^2 = (x + 5)(x + 5) = x^2 + 10x + 25

Now, let's subtract (x + 5)^2 from 6x^2 + 3:

(6x^2 + 3) - (x^2 + 10x + 25)

Simplifying, we get:

6x^2 + 3 - x^2 - 10x - 25

Combining like terms, we get:

5x^2 - 10x - 22

Therefore, the result of subtracting (x + 5)^2 from 6x^2 + 3 is 5x^2 - 10x - 22, written in standard form.

Answer:

The Distance the handler will move from the starting point to the return point will be approximately 439.8204 feet.

The distance the handler will move from the starting point to the return point when creating an arc of a circle with a radius of 70 feet, we need to find the length of the arc.

The formula to calculate the length of an arc is given by:

Length of arc = (θ/360) * 2πr

Where:

θ is the central angle of the arc (in degrees)

r is the radius of the circle

In this case, since the handler is creating a full circle, the central angle is 360 degrees.

Length of arc = (360/360) * 2π * 70

Length of arc = (1) * 2π * 70

Length of arc = 2π * 70

Length of arc = 140π

To find the approximate value in feet, we can use the approximation π ≈ 3.14159.

Length of arc ≈ 140 * 3.14159

Length of arc ≈ 439.8204 feet

Therefore, based on the given theory and using a circle with a radius of 70 feet, the distance the handler will move from the starting point to the return point will be approximately 439.8204 feet.

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Answer:

x = 5

Step-by-step explanation:

Angles in a triangle add up to equal 180

Hence, 10x - 1 + 78 + 53 = 180

( Note that we just created an equation that we can use to solve for x )

We now solve for x using the equation we created

10x - 1 + 78 + 53 = 180

Combine like terms

10x + 130 = 180

Subtract 130 from both sides

10x = 50

Divide both sides by 10

x = 5

Answer:

For this case we have the following confidence interval given:

\( 0.345 \leq p \leq 0.895 \)

And for this case we want to find the estimated proportion like this:

\(\hat p= \frac{0.345 +0.895}{2}= 0.62\)

And the margin of error for this case would be given by:

\( ME= \frac{0.895-0.345}{2}= 0.275\)

Step-by-step explanation:

For this case we have the following confidence interval given:

\( 0.345 \leq p \leq 0.895 \)

And for this case we want to find the estimated proportion like this:

\(\hat p= \frac{0.345 +0.895}{2}= 0.62\)

And the margin of error for this case would be given by:

\( ME= \frac{0.895-0.345}{2}= 0.275\)

Answer:

4- 3a .............................

The transformation in the picture is option c Reflection.

Given,

Reflection transformation:

A reflection is a transformation that works similarly to a mirror by switching all pairs of points that are directly across from one another along the line of reflection. A mathematical formula or the two sites it passes through can be used to define the line of reflection.

According to the law of reflection, r = I the angle of incidence and reflection are equal. θ r = θ I . At the point where the ray strikes the surface, the angles are measured in relation to the perpendicular to the surface.

Here,

In the picture the transformation is reflection.

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Answer:

(3x) ° + (x+ 10)° = 90°

Step-by-step explanation:

(3x) ° + (x+ 10)° = 90°

3x + x + 10 = 90

4x = 90 - 10

4x = 80

x = 20

(3x) ° = 3 x 20 = 60°

(x + 10)° = 20 + 10 = 30°

Answer: you can either do 3x°(x+10)° or (x+10)°+3x°

the choice is yours. Hope this helps

Hello!

We will go tu use the pythagorean theorem!

So:

BA² = BC² + AC²

AC² = BA² - BC²

AC² = 52² - 20²

AC² = 2304

AC = √2304

AC = 48

The joint relative frequency for school children who plan to attend camp and have swimming lesson is 44%.

The correct option to the given question is option d.

We are required to find the joint relative frequency for school children who plan to attend camp and have swimming lessons, rounded to the nearest percent.

To find the joint relative frequency, we use the formula as follows:

Joint relative frequency = frequency of interest / total frequency

Joint relative frequency for school children who plan to attend camp and have swimming lessons = 42 / 96

(As we are looking for the students who plan to attend camp and have swimming lessons, we are interested in the first column of the table and the entry at the intersection of the first row and second column.)

Joint relative frequency for school children who plan to attend camp and have swimming lessons = 0.4375

Joint relative frequency for school children who plan to attend camp and have swimming lessons (rounded to the nearest percent) = 44%(option d).

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-5( x - 5) - 28 = -3

-5x + 25 - 28 = -3

-5x - 3 = -3

collect like terms

-5x = -3 + 3

-5x = 0

x = 0/-5

x = 0

Answer:

Step-by-step explanation:

-5x+25-28=3

-5x-3=3

-5x=6

==> x=-6/5

The ratio of the volume of water in Jug B to the volume of water in Jug C is 35:18.

Let's assume the volume of water in Jug B is x.

According to the given information, Jug A contains 6/7 as much water as Jug B. Therefore, the volume of water in Jug A can be calculated as (6/7) * x.

Similarly, Jug C contains 3/5 as much water as Jug A. Hence, the volume of water in Jug C can be expressed as (3/5) * [(6/7) * x].

To find the ratio of the volume of water in Jug B to the volume of water in Jug C, we divide the volume of water in Jug B by the volume of water in Jug C:

(x) / [(3/5) * (6/7) * x]

Simplifying the expression, we get:

x / (18/35 * x)

The x values cancel out, leaving us with:

1 / (18/35)

To simplify further, we multiply the numerator and denominator by the reciprocal of the denominator:

1 * (35/18)

The final ratio is:

35/18

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True, While "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

The statement "-1000 2/3 is not a real fraction" is true. A real fraction is a mathematical expression that represents a ratio of two real numbers. In a fraction, the numerator and denominator are both real numbers, and they can be positive, negative, or zero.

In the given statement, "-1000 2/3" is not a valid representation of a fraction. The presence of a space between "-1000" and "2/3" suggests that they are separate entities rather than being part of a single fraction.

To represent a mixed number (a whole number combined with a fraction), a space or a plus sign is typically used between the whole number and the fraction. For example, a valid representation of a mixed number would be "-1000 2/3" or "-1000 + 2/3". However, without the proper formatting, "-1000 2/3" is not considered a real fraction.

It's important to note that "-1000 2/3" can still be expressed as an improper fraction. To convert it into an improper fraction, we multiply the whole number (-1000) by the denominator of the fraction (3) and add the numerator (2). The result would be (-1000 * 3 + 2) / 3 = (-3000 + 2) / 3 = -2998/3.

In conclusion, while "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

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