A projectile is fired straight upward from ground level with an initial velocity of 96 feet per second. During which interval of
time will the projectile's height exceed 80 feet?

Answer:

a = 11cm

Step-by-step explanation:

We can use the Pythagorean theorem to find the value of a.

Let us solve it now.

\( \sf {a}^{2} + {12}^{2} = {15}^{2} \)

Now solve for a and and find the length of the side.

\( \sf {a}^{2} + 144 = 225 \\ \sf {a}^{2} = 225 - 144 \\ \sf{a}^{2} = 121 \\ \sf \: a = \sqrt{121} \\ \sf \: a = 11\)

By mathematical induction, we have shown that a_k=n^2 for all k.

To prove that a_k=n^2 for all k, we will use mathematical induction.

Base Case:

When k=1, a_1=2(1)-1=1. This is also equal to 1^2, so the base case is true.

Inductive Step:

Assume that a_k=k^2 is true for some arbitrary positive integer k, i.e., a_k=k^2.

Now, we want to prove that a_(k+1)=(k+1)^2.

We know that a_(k+1)=2(k+1)-1=2k+2-1=2k+1.

We can use our inductive hypothesis that a_k=k^2 and simplify the expression for a_(k+1):

a_(k+1) = 2k+1 = k^2 + 2k + 1 = (k+1)^2

Therefore, by mathematical induction, we have shown that a_k=n^2 for all k.

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Based on the z-score, an Endure All battery selected at random has a 10.56% chance of lasting more than 550 hours.

How closely a value relates to the mean of a set of values is expressed by a Z-score.

The Z-score is created using standard deviations from the mean.

A data point's total value is equal to the mean value when the Z-score of the data point is equal to 0.

So, in order to determine how far the raw score deviates from the mean, the Z score is used.

The following steps are used to determine the Z score:

z = (x - μ)/σ

We know that:  x > 550 and μ = 500, σ = 40

z = 550 - 500 / 40

z = 1.25

The graph of the normal distribution indicates:

P(z > 1.25) = 1 - P(z < 1.25)

P(z > 1.25) = 1 - 0.8944

P(z > 1.25) = 0.1056

Therefore, based on the z-score, an Endure All battery selected at random has a 10.56% chance of lasting more than 550 hours.

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Slope is 0.75 or 3/4 I believe!

Answer:

C

Step-by-step explanation:

Did the test and got it right.

Answer:

c

Step-by-step explanation:

To compute the correlation between two ordinal-level variables, you should use Spearman's rank correlation coefficient.

Spearman's rank correlation coefficient is a non-parametric statistical measure that is used to assess the association between two ordinal-level (ordinal or ranked) variables.

This type of correlation calculates the correlation between the ranks of the data rather than the actual values, making it suitable for ordinal data where the difference between the levels is not well defined.

The coefficient ranges from -1 to 1, where a value of 1 indicates a perfect positive correlation, a value of -1 indicates a perfect negative correlation, and a value of 0 indicates no correlation.

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Answer:

Step-by-step explanation:

150 - 15w

where w is the number of weeks he payed his mother the $15

Answer:

cobra $46,6

Step-by-step explanation:

la respuesta se obtiene dividiendo 140 entre 3 y el resultado es lo que cobra el carpintero como mano de obra

Answer:

$11.78

Step-by-step explanation:

14.89+9.33=24.22

36-24.22=11.78

A map uses scaled drawings. The distance between the two considered cities on that specified map is 6.25 inches

How are scale drawings formed?

For a particular scale drawing, it is already specified that all the measurements' some constant scaled version will be taken. For example, let the scale be K feet to s inches.

Then it means

1ft : s/k in.

All feet measurements will then we multiplied by s/k to get the drawing's corresponding lengths.

For this case, it is specified that the map uses scaling such that:

3/4 of an inch on map = 3 miles in reality.

Dividing both the quantities by 3, we get:

1 mile in reality = 3/4  / 3  inches on map = 1/4 inches on map

Multiplying both the quantities by 25, we get:

25 miles in reality = 25/4 = 6.25  in map

Since 25 miles is the distance between those two considered cities.

Therefore, the distance between those two cities on map would be of 6.25 inches.

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Answer:

  C.  142°

Step-by-step explanation:

You want the angle between vectors u=3i+√3j and v=-2i-5j.

There are a number of ways the angle between the vectors can be found. For example, the dot-product relation can give you the cosine of the angle:

  u•v = |u|·|v|·cos(θ) . . . . . . where θ is the angle of interest

You can find the angles of the vectors individually, and subtract those:

  u = |u|∠α

  v = |v|∠β

  θ = α - β

When the vectors are expressed as complex numbers, the angle between them is the angle of their quotient:

  \(\dfrac{\vec{u}}{\vec{v}}=\dfrac{|\vec{u}|\angle\alpha}{|\vec{v}|\angle\beta}=\dfrac{|\vec{u}|}{|\vec{v}|}\angle(\alpha-\beta)=\dfrac{|\vec{u}|}{|\vec{v}|}\angle\theta\)

This method is used in the calculation shown in the first attachment. The angle between u and v is about 142°.

A graphing program can draw the vectors and measure the angle between them. This is shown in the second attachment.

__

Additional comment

The approach using the quotient of the vectors written as complex numbers is simply computed using a calculator with appropriate complex number functions. There doesn't seem to be any 3D equivalent.

The dot-product relation will work with 3D vectors as well as 2D vectors.

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The proportionate reduction in error for knowing the value of the independent variable is 0.54.

The variable which does not depend on any variable and hence independent are known as independent variable.

Given that,

sum of squares for a regression equation was 153.7 = SST

error sum of squares was 82.6 = SSE

SS (reg) = SST - SSE

                153.7 - 82.6

                 SS(reg) = 71.1

The proportionate reduction in error for knowing the value of the independent.

             = 1 - \(\frac{(SS)reg}{SST}\)

             = 1 - \(\frac{71.1}{153.7}\)

             = 1 - 0.46

             = 0.54

The proportionate reduction in error for knowing the value of the independent variable is 0.54.

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Answer:

C

Step-by-step explanation:

By the side splitter theorem,

\(\frac{x}{15}=\frac{2}{10} \\ \\ x=3\)

\(\huge\text{Hey there!}\)

\(\large\textbf{E}\frak{quation:}\)

\(\mathsf{\dfrac{x}{15} = \dfrac{2}{10}}\)

\(\large\textbf{C}\frak{ross\ multipl\mathsf{y}\ the\ numbers }\)

\(\mathsf{x \times 10 = 2 \times 15}\)

\(\mathsf{ 10 \times x= 2 \times 15}\)

\(\large\textbf{S}\frak{implif\mathsf y\ it:}\)

\(\mathsf{10x = 30}\)

\(\large\textbf{D}\frak{ivide\ b\mathsf{y}\ \mathsf{10}}\)

\(\mathsf{\dfrac{10x}{10} = \dfrac{30}{10}}\)

\(\large\textbf{S}\frak{implif\mathsf y\ it:}\)

\(\mathsf{x = \dfrac{30}{10}}\)

\(\mathsf{x = 3}\)

\(\huge\boxed{\textbf T\frak{herefore, \textsf your\ ans\textsf wer\ should\ be: }}\)

\(\huge\boxed{\boxed{\mathsf x = \frak{3}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

To estimate the solution to the differential equation Y' = C using Euler's method with two steps, we need to divide the interval [0, 1] into two subintervals.

Let's denote the step size as h, where h = (1 - 0) / 2 = 0.5.

Using Euler's method, the general formula for the next approximation Y(i+1) is given by:

Y(i+1) = Y(i) + h * C

Given the initial condition Y(0) = 0, we can calculate the two approximations:

First step:

Y(1) = Y(0) + h * C

= 0 + 0.5 * C

= 0.5C

Second step:

Y(2) = Y(1) + h * C

= 0.5C + 0.5 * C

= C

So, the two Euler approximations with two steps are:

Y(1) = 0.5C

Y(2) = C

Now, let's calculate the magnitude of the error in these approximations compared to the exact solution.

The exact solution to the differential equation Y' = C is given by integrating both sides:

Y = C * t + K

Using the initial condition Y(0) = 0, we find that K = 0.

Therefore, the exact solution to the differential equation is Y = C * t.

Now, we can compare the Euler approximations with the exact solution.

Magnitude of error in Euler with 2 steps:

Error_2 = |Y_exact(1) - Y(1)|

= |C * 1 - 0.5C|

= 0.5C

Magnitude of error in Euler with 4 steps:

To calculate the error in the Euler approximation with four steps, we need to divide the interval [0, 1] into four subintervals. The step size would be h = (1 - 0) / 4 = 0.25.

Using the same formula as before, we can calculate the Euler approximation with four steps:

Y(1) = Y(0) + h * C

= 0 + 0.25 * C

= 0.25C

Y(2) = Y(1) + h * C

= 0.25C + 0.25 * C

= 0.5C

Y(3) = Y(2) + h * C

= 0.5C + 0.25 * C

= 0.75C

Y(4) = Y(3) + h * C

= 0.75C + 0.25 * C

= C

So, the Euler approximation with four steps is:

Y(1) = 0.25C

Y(2) = 0.5C

Y(3) = 0.75C

Y(4) = C

Magnitude of error in Euler with 4 steps:

Error_4 = |Y_exact(1) - Y(4)|

= |C * 1 - C|

= 0

Therefore, the magnitude of the error in the Euler approximation with 2 steps is 0.5C, and the magnitude of the error in the Euler approximation with 4 steps is 0.

The factor by which the error in the approximations with two steps should change compared to the error with four steps is given by:

Factor = Error_2 / Error_4

= (0.5C) / 0

= undefined

Since the error in the Euler approximation with four steps is 0, the factor is undefined.

The solution to the differential equation Y' = C with the given initial condition Y(0) = 0 is Y = Ct.

Using the exact solution, we can evaluate Y(1):

Y(1) = C * 1

= C

So, the solution to the differential equation with the given initial condition is Y = Ct, and Y(1) = C.

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Answer:

last one

Step-by-step explanation:

point slope form:

\((y - y1 )= m(x - x1)\)

just plug in the numbers and you will get the answer:

\((y - 4) = 3(x + 1)\)

Answer:

\(y = \frac{6}{7}x - 1\)

Explanation:

\(Point 1: (-7, -7)\\Point 2: (7, -5)\)

\(\frac{y_{2} - y_{1} }{x_{2} - x_{1}}\)

\(\frac{(-5) - (-7)}{(-7) - (7)}\)

\(\frac{-12}{-14}\)

\(\frac{12}{14}\)

\(m = \frac{6}{7}\)

\(y - y_{1} = m(x - x_{1})\)

\(y - (-7) = \frac{6}{7}(x - (-7))\)

\(y + 7 = \frac{6}{7}(x + 7)\)

\(y = \frac{6}{7}x + \frac{42}{7} - 7\)

\(y = \frac{6}{7}x + (\frac{42}{7} - \frac{49}{7})\)

\(y = \frac{6}{7}x - 1\)

Answer:

(8,-4,-10,-16)

Step-by-step explanation:

Here, we are told to find the range from the given points set

The range are simply the y-values

These are;

(8,-4, -10, -16)

The probability is 0.6480.

The probability is 0.9629.

1. This can be computed using the standard normal distribution as follows:

z = (70 - 69.0) / 2.8 = 0.357

Using a standard normal table or calculator, we find that P(Z ≤ 0.357) ≈ 0.6480. Therefore, the probability that a male passenger can fit through the doorway without bending is approximately 0.6480.

2. = 2.8/√25 = 0.56 inches.

We want to find P(x < 70), which is the probability that the mean height of the 25 men is less than 70 inches. This can be standardized using the standard normal distribution as follows:

z = (70 - 69.0) / 0.56 = 1.79

Using a standard normal table or calculator, we find that P(Z < 1.79) ≈ 0.9629. Therefore, the probability that the mean height of the 25 men is less than 70 inches is approximately 0.9629.

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Answer:

56ft

Step-by-step explanation:

first you need to break the shape u so 1 rectangle and 2 triangles so first we need to find the area of the rectangle

Area of rectangle= w x h so 5* 8= 40

Area of triangle = .5 x b x h so 4 x 4 x .5 = 8 and since we have 2 double that and you get 16 so then you need to add it all up and u get the answer 56

Since the points on this graph represent a relationship between x- and y-values, the statement which is true about the relationship is that: 4. It cannot be proportional because a straight line through the points does not go through the origin.

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

In Mathematics, the graph of any proportional relationship is characterized by a straight line with the points passing through the origin (0, 0) because as the values on the x-axis (x-coordinate) increases or decreases, the values on the y-axis (y-coordinate) increases or decreases simultaneously.

In this context, we can reasonably infer and logically deduce that the relationship between x-values and y-values in this graph is not proportional.

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Complete Question:

The points on this graph represent a relationship between x- and y-values. Which statement about the relationship is true?

1. It must be proportional because the points lie on the same line.

2. It must be proportional because each time x increases by 2, y stays the same.

3. It cannot be proportional because the y-values are not whole numbers.

4. It cannot be proportional because a straight line through the points does not go through the origin.

The new mean cost of a box of Cheerios Out Crunch is $4.40. This means that, on average, customers can expect to pay $0.40 more for a box of cereal after the price increase.

The new mean cost of a box of Cheerios Out Crunch after a 10% increase in price would be $4.40.

To see why, we can start with the original mean cost of $4.00 per box. To calculate a 10% increase, we can multiply the original mean cost by 1.10 (or 110% as a decimal), which gives:

$4.00 x 1.10 = $4.40

The mean cost is the proportion of the cost of the multitude of items to the absolute number of items. In Maths, we likewise have the term called "normal". The normal of some random arrangement of information is known as the mean of information.

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Answer:

Justice Department ?

Step-by-step explanation:

Answer:

816-800-0000

Step-by-step explanation:

The length of the rectangle is 7 cm and the width is 5 cm.

The whole distance covered by the rectangle's borders or its sides is known as its perimeter. As we know the rectangle will have 4 sides then the perimeter of the rectangle will be equal to the total of its four sides. And the unit will be in meters, centimeters, inches, feet, etc.        

The formula for the Perimeter of the rectangle is given by

Here we have

The length of a rectangle is 2cm greater than the width of the rectangle

And perimeter of the rectangle = 24 cm

Let x be the width of the rectangle

From the given data,

Length of the rectangle = (x + 2) cm  

As we know Perimeter of rectangle = 2(Length+width)

=> Perimeter of rectangle = 2(x+2 + x) = 2(2x +2)

From the given data,

Perimeter of rectangle =  24cm

=> 2(2x +2) = 24 cm

=> (2x +2) = 12     [ Divided by 2 into both sides ]

=>  2x = 12 - 2

=>  2x = 10

=>   x = 5         [ divided by 2 into both sides ]  

Length of rectangle, (x+2) = 5 + 2 = 7 cm

Therefore,

The length of the rectangle is 7 cm and the width is 5 cm.

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By using right tailed test the following results are obtained

a) The test is a right tailed test

b) P value = 0.0681

c) We fail to reject the null hypothesis

What is right tailed test?

Suppose there is a null hypothesis. If the alternate hypothesis claims that the true value of the parameter is greater than the null hypothesis, then the test used is called right tailed test.

a) Since p > 0.8, right tailed test is used

b) The corrosponding z is z = 1.49

P value = p(z > 1.49)

            = 1 - p(z \(\leq\) 1.49)

            = 1 - 0.9319

            = 0.0681

c) 0.0681 is greater than a = 0.05

So we fail to reject the null hypothesis \(H_0\)

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The length of the deep end is 12 feet of the swimming pool.

Given: Area of the swimming pool is 210 square feet

Width of the pool = 10 feet

The length of the shallow end is 9 feet and the length of the deep end is d.

To find the value of d.

Let's solve the problem.    

The area of the swimming pool is 210

The width is 10

The deep end length is d

The shallow end length is 9

The total length of the swimming pool = The length of the deep end + The length of the shallow end

=> d + 9

Therefore, the total length of the swimming pool is d + 9

The surface of the swimming pool is rectangular, so

The area of rectangle = width × length

Therefore,

area of swimming pool = width of the pool × length of the swimming pool

=> 210 = 10 × (9 + d)

or 10 × (9 + d) = 210

Dividing both sides by 10:

10 × (9 + d) / 10 = 210 / 10

9 + d = 21

Subtracting 9 on both sides:

9 + d - 9 = 21 - 9

d = 12

Therefore the length of the deep end is 12 feet

Hence the length of the deep end is 12 feet of the swimming pool.

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The length of the deep end of the swimming pool is 12 feet.

We are given that:

The Area of the swimming pool = 210 square feet

width of the swimming pool = 10 feet

Length of shallow end = 9 feet

Let the length of the deep end be d.

Total length of the swimming pool = length of deep end + length of shallow end =  d + 9

Area of swimming pool = width × length

Substituting the values, we get that:

210 = 10 × (9 + d)

9 + d = 21

d = 12

Therefore the length of the deep end of the swimming pool is 12 feet.

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Answer:

yall smart

Step-by-step explanation:

Answer

5x → coefficient

3y → Variable

9 → Constant