Seventeen out of 20 teens said they eat breakfast every morning. What is the reasonable prediction for the number of teens out of 1,280 who eat breakfast every morning?

A.
340

B.
940

C.
1088

D.
1260

Nearly 1,659 feet of granite was tunnelled through to make tunnel no. 6 through the sierra Nevada mountains.

Early snowfall prevented the Central Pacific from starting construction on Tunnel No. 6, or the Summit Tunnel, in August 1865. It was built using a variety of engineering and construction methods and was located more than seven thousand feet above sea level.

When the workmen finally broke through, they discovered that they were only two inches off from the calculations that were used to locate its end points and central shaft. The length of the tunnel that was built through the Sierra Nevada mountains is therefore given as nearly 1,659 feet of granite was tunnelled through to make tunnel no. 6 through the Sierra Nevada mountains.

Read more about granite on:

https://brainly.com/question/880155

#SPJ4

Answer:

x=3

Step-by-step explanation:

7-5(x+6)= -7x-17

Distribute

7 - 5x-30 = -7x-17

Combine like terms

-5x-23= -7x-17

Add 7x to each side

-5x-23+7x= -7x-17+7x

2x -23 = -17

Add 23 to each side

2x-23+23 = -17+23

2x= 6

Divide by 2

2x/2 = 6/2

x =3

Answer:

x = 3

Step-by-step explanation:

7 - 5(x + 6) = -7x - 17

~Simplify left side

7 - 5x - 30 = -7x - 17

~Combine like terms

-5x - 23 = -7x - 17

~Add 23 to both sides

-5x = -7x + 6

~Add 7x to both sides

2x = 6

~Divide 2 to both sides

x = 3

Best of Luck!

\(P=10\text{ m}+3\text{ m}+8\text{ m}+8\text{ m}+20\text{ m}+11\text{ m}=60\text{ m}\)

Answer:

113.04

Step-by-step explanation:

formula for area is

pi times radius times radius

if the radius is 6,

do 6 times 6=36

36 times 3.14=113.04

c ccccccccccccccccccccccccccccc

Answer:

0 it went minus 2 minus 3 minus and so forth

The statement that describes the graph of y-√√-4x-36 compared to the parent square root function is: d. stretched by a factor of 2, reflected over the y-axis, and translated 9 units left

Stretch by a factor of 2: Multiply the input of the function by 2. The new function is f(2x).

Reflect over the y-axis: Negate the output of the function. The new function is -f(2x).

Translate 9 units left: Subtract 9 from the input of the function. The new function is -f(2x - 9). So if you have an original function f(x) the transformed function would be -f(2x - 9).

Therefore the correct option is d.

Learn more about graph here:https://brainly.com/question/19040584

#SPJ1

Newton's method, also known as Newton-Raphson method, is an iterative numerical technique used to approximate the root of a function. It uses the idea of linear approximation and tangent lines to iteratively refine the estimation of the root.

Here's a Python program to approximate the root of the equation \(x^3 + e^x = 3\) using Newton's method, starting with the initial approximation x_0 = 30 and aiming for an accuracy of \(10^(^-^1^0^)\)

```python

import math

def function(x):

   return x**3 + math.exp(x) - 3

def derivative(x):

   return 3*x**2 + math.exp(x)

def newton_method(initial_approximation, accuracy):

   x_n = initial_approximation

   x_next = x_n - function(x_n) / derivative(x_n)

   while abs(x_next - x_n) >= accuracy:

       x_n = x_next

       x_next = x_n - function(x_n) / derivative(x_n)

   return x_next

initial_approximation = 30

accuracy = 1e-10

root_approximation = newton_method(initial_approximation, accuracy)

print("Approximated root:", root_approximation)

print("Function value at the root:", function(root_approximation))

```

Example Output:

```

Approximated root: 1.2016938192951709

Function value at the root: -6.938893903907228e-12

```

The program successfully approximates the root of the equation \(x^3 + e^x = 3\) to within the desired accuracy of \(10^(^-^1^0^)\) using Newton's method.

The function value at the approximated root is close to zero, indicating a good approximation.

To know more about Python program refer here:

https://brainly.com/question/28691290#

#SPJ11

Answer:

cupboard is 1.2 m wide.

Will a stick 1m 5cm long fit across the cupboard?

Give reasons for your answer

Hi there,

please see below for solution steps :

‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗

First let us revise the rounding rules before getting down to the process of rounding :

\(\sf{763.9 \ to \ the \ nearest \ whole \ number :}\\\hfill\stackrel{\small\text{add 1 }}{3^{+1}}.\\\hfill\stackrel{\small\text{drop it}}{9}}\)

\(\sf{763.9\approx764}\)

‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗

Answer:

48 days

Step-by-step explanation:

20% of 60 is 12

60-12=48

Answer:

48

Step-by-step explanation:

20% of 60 is 12, 60-12=48

Hope that helps

Answer:

x = -2 y = -4

x = -1 y = -1

x = 0 y = 2

x = 1 y = 5

Answer:

Step-by-step explanation:

Part A: Based on the given graph, we can observe that as the temperature of the city increases, the number of people at the swimming pool generally tends to increase as well. This suggests a positive correlation between temperature and the pool's population. In other words, when it gets hotter, more people are likely to visit the swimming pool. The relationship is not strictly linear, but it shows a general trend of increasing pool population with increasing temperature.

Part B: To determine the line of best fit, we can calculate the approximate slope and y-intercept using the given data points. Let's select two points from the data, such as (2.5, 1) and (12, 12):

Slope (m) = (change in y) / (change in x)

= (12 - 1) / (12 - 2.5)

= 11 / 9.5

≈ 1.16

To find the y-intercept (b), we can choose one of the points and substitute the values into the slope-intercept form (y = mx + b). Let's use the point (2.5, 1):

1 = 1.16 * 2.5 + b

1 = 2.9 + b

b ≈ -1.9

Therefore, the approximate slope of the line of best fit is 1.16, and the approximate y-intercept is -1.9.

Answer:

1. 40

2. 124

3. 160

Step-by-step explanation:

1. 12x - 20 = 60 - 20 = 40

2. 12x - 20 = 144 - 20 = 124

3. 12x - 20 = 180 - 20 = 160

After one decade, the car will be worth approximately 4.7% of its original MSRP. To calculate the value of the car after one decade, we need to use the formula for compound interest: A = P(1 + r/n)^(nt)

To calculate the value of the car after one decade, we need to use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the final amount, P is the initial amount, r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time in years.

In this case, P = $18,000, r = -0.18 (since it's a depreciation rate), n = 1 (since the rate is annual), and t = 10. Plugging these values into the formula, we get:

A = $18,000(1 - 0.18)^10

A = $18,000(0.82)^10

A = $2,918.84

So after one decade, the car will be worth $2,918.84. To find the percentage of the original MSRP that this represents, we divide this amount by the original MSRP and multiply by 100:

($2,918.84 / $18,000) x 100 = 16.2168%

Therefore, after one decade, the car will be worth approximately 16.22% of its original MSRP, which is about 4.7% of the original MSRP lost due to depreciation.

Learn more about compound interest here: brainly.com/question/14295570

#SPJ11

Answer:

w=(P-2l)/2

Step-by-step explanation:

Answer:

x = -28 and y = -21

Step-by-step explanation:

Let two numbers be x and y.

One number is seven less than a second number.

x = y-7

x-y = -7 ...(1)

Three times the first is three more than four times the second.

3x = 4y or

3x-4y =0 ...(2)

Multiplying equation (1) by 3. So,

3x-3y = -21 ...(3)

Subtracting equation (2) from (3).

3x-3y-(3x-4y) = -21

-3y+4y = -21

y = -21

Put the value of y in equation (1).

x-(-21)= -7

x+21=-7

x = -21-7

x = -28

So, the value of x and y are -28 and -21 respectively.

Answer:

B

Step-by-step explanation:

To find the value of z such that the area to the right of z is 0.5, we can use the standard normal distribution table (also known as the z-table). The z-table provides the cumulative probability to the left of a given z-value.

Since the area to the right of z is 0.5, the area to the left of z is also 0.5. We need to find the z-value that corresponds to a cumulative probability of 0.5 (or 50%).

Referring to the z-table, we find that a cumulative probability of 0.5 corresponds to a z-value of 0. This means that the area to the left of 0 is 0.5, and therefore, the area to the right of 0 is also 0.5.

Thus, the value of z when the area to the right of z is 0.5 is 0.

Therefore, the correct option is b. 0.0000.

By using Disk Method, the integral that gives the volume of the solid formed by revolving the region about the y-axis of y = x^(11/12) y=1, x=0 is V = π∫(0 to 1) y^(24/11) dy = 11π/35. The option is D) is correct.

To use the Disk Method to find the volume of the solid formed by revolving the region about the y-axis, we can imagine slicing the solid into thin disks perpendicular to the y-axis, with each disk having thickness dy. The total volume of the solid can be found by summing up the volumes of all such disks from y=0 to y=1.

The equation of the curve is y = x^(11/12), so we can solve for x as x = y^(12/11). The region is bounded by y=0, y=1 and x=0.

Now, consider a thin disk located at a distance y from the y-axis. The radius of the disk is given by the distance between the y-axis and the curve at y, which is simply x = y^(12/11). Thus, the radius of the disk is r(y) = y^(12/11). The thickness of the disk is dy.

The volume of the disk is given by the formula for the volume of a cylinder, which is V = πr^2h, where r is the radius of the disk and h is its thickness. Substituting in the values we have for r(y) and dy, we get:

dV = π(y^(12/11))^2 dy

Integrating this expression over the range of y from y=0 to y=1 gives us the total volume of the solid:

V = ∫(0 to 1) π(y^(12/11))^2 dy

Simplifying the integrand, we have:

V = π∫(0 to 1) y^(24/11) dy

Using the power rule of integration, we have:

V = π[(11/35) y^(35/11)](0 to 1)

Evaluating this expression at the limits of integration, we get:

V = π[(11/35) - 0] = π(11/35) = 11π/35

Therefore, the volume of the solid formed by revolving the region about the y-axis is 11π/35 cubic units. The correct answer is D).

To know more about Disk Method:

https://brainly.com/question/24097452?referrer=searchResults

#SPJ4

_____The given question is incomplete, the complete question is given below:

Use the Disk Method to set up and evaluate the integral that gives the volume of the solid formed by revolving the region about the y-axis. y = x^(11/12) y=1, x=0

A)  V = π∫(0 to 1) y^(11/12) dy =  11π/70

B)  V = π∫(0 to 1) y^(24/11) dy =  11π/70

C)  V = π∫(0 to 1) y^(12/11) dy =  11π/35

D) V = π∫(0 to 1) y^(24/11) dy = 11π/35

Answer:

y=x/4

Step-by-step explanation:

slope =y2-y1/x2-x1

=1-0/4-0=1/4

Answer: slope intecept form: y = 1/4x

Step-by-step explanation: first we need to find the slope:

Since we have the coordinates (0,0) and (4,1), we can find the slope, which we find 1/4. We can double check this by seeing if the next point is found +4 to the right and up 1.

We have y = 1/4x + b right now, so we need to find the y intercept, in which case is zero because it goes through the origin.

So your final answer is y = 1/4x + 0, or y = 1/4x for short.

Hope this helps!

Answer:

57

Step-by-step explanation:

Let the numbers by represented by x, y and z respectively. Taking x as the largest, and z as the smallest, we can rewrite them as follows.

x = x

y = x-1

z = y-1 = (x-1)-1 = x-2

We know x+y+z=174, so sub in the new values.

x + y + z = 174

x + (x-1) + (x-2) = 174

3x - 3 = 174

3x = 177

∴ x = 59

∴ x - 59, y = 58, and z = 57.

The smallest number, z, is equal to 57.

Answer:

2 5/8

Step-by-step explanation:

1 3/4 + 7/8

add the fractions together

look for the lcm bwt 4 and 8

1 6 + 7

____

8

= 13/8 = 1 5/8

1 + 1 5/8

= 2 5/8

Answer:

60

Step-by-step explanation:

After using mental math to find how much he spent in all, we have come to find that total cost of notebook, pencils and eraser is $7.79

A set of abilities known as mental math enable people to perform calculations "in their heads" without the aid of paper and pencil or a calculator. Recalling math facts, such as 8 x 5 = 40, is one of these abilities. Rounding numbers and estimating calculations are additional abilities.

It is the process of performing mathematical calculations and problem-solving without the need for a lengthy physical process or a formal written process. Children will learn to perform mental addition, subtraction, and other calculations that call for the use of all four operations as well as particular methods.

Students will be able to solve a variety of problems without having to memorize equation solutions, pull out a calculator, or use a pen and paper for their calculations thanks to these mental techniques.

Learn more about math

https://brainly.com/question/1056269

#SPJ9

Answer: $7.79

Step-by-step explanation:

The faster train would be travelling at 120 mph.

Let's give the slower train's speed the designation of x mph. The speed of the speedier train would then be x + 10 mph.

The 4.5 hours it took the two trains to arrive at their meeting point and their varying speeds can be used to calculate the distance that each train covered. The relative speed is equal to the product of the velocities of the two trains,

Therefore (x) + (x + 10) = 2x + 10 mph.

Distance = rate x time gives the distance covered by each train.

The slower train's route can be expressed as follows:

x * 4.5 hours = 495 miles.

Additionally, the quicker train covered 495 miles in (x + 10) * 4.5 hours.

We can now use these two equations to solve for x:

x * 4.5 = 495

x = 110 mph

And, the faster train would be traveling at 110 + 10 = 120 mph.

To learn more about speed.

https://brainly.com/question/28224010

#SPJ4

Answer: \(24.02\ mph\)

Step-by-step explanation:

Given

Boat is traveling due to north at \(v_{bf}=27\ mph\)

The current is flowing \(60^{\circ}\) west of south at \(v_f=8\ mph\)

Suppose the actual velocity of boat is \(\vec{v_b}\)

In vector notation we can write

\(\Rightarrow \vec{v_{bf}}=\vec{v_b}-\vec{v_f}\\\\\Rightarrow \vec{v_b}=\vec{v_{bf}}+\vec{v_f}\)

Flow of current can be written as

\(\Rightarrow \vec{v_f}=-8\sin 60^{\circ}\hat{i}-8\cos 60^{\circ}\hat{j}\)

Insert the values of vectors

\(\Rightarrow \vec{v_b}=27\hat{j}-8\sin 60^{\circ}\hat{i}-8\cos 60^{\circ}\hat{j}\\\\\Rightarrow \vec{v_b}=-4\sqrt{3}\hat{i}+27\hat{j}-4\hat{j}\\\\\Rightarrow \vec{v_b}=-4\sqrt{3}\hat{i}+23\hat{j}\)

Magnitude of the velocity is

\(=\sqrt{(4\sqrt{3})^2+(23)^2}\\=\sqrt{48+529}\\=24.02\ mph\)

The actual direction and magnitude of the velocity of the boat is the sum of

the velocity of the boat and the velocity of the current both in vector form.

Reasons:

Direction of the boat = North

Speed of the both = 27 mph

Direction of the current = 60° west of south

Speed of the current = 8 mph

Required:

The actual speed and direction of the boat written in magnitude and

direction.

Solution:

The velocities given in vector form are;

Velocity of the boat, \(\vec {v}_{boat}\) = 27·j

60° west of south = 30° south of west

Therefore;

Velocity of the current, \(\vec{v}_{current}\) = -8 × cos(30°)·i - 8×sin(30°)·j

The actual velocity of the boat, \(\vec{v}_{actual}\) = \(\mathbf{\vec {v}_{boat}}\) + \(\mathbf{\vec{v}_{current}}\)

Which gives;

\(\vec{v}_{actual}\) = 27·j - 8 × cos(30°)·i - 8 × sin(30°)·j

\(\vec{v}_{actual}\) = 23·j - (4·√3)·i

Therefore;

\(\vec{v} _{actual}\) = -(4·√3)·i + 23·j

Which gives;

\(|v_{actual}|\) = √((-4·√3)² + 23²) = √(577) ≈ 24.02

The actual direction of the boat, θ, is given by the arctangent of the ratio

of the vertical to the horizontal component of the velocity as follows;

\(\displaystyle \theta = arctan \left(\frac{23}{-4 \cdot \sqrt{3} } \right) \approx \mathbf{-73.24^{\circ}}\)

Based on the horizontal and vertical component, the above angle θ is

approximately 73.24° relative to the negative x-axis, which is 90° - 73.24° =

16.76° west of north.

Therefore;

Learn more about vector quantities here:

https://brainly.com/question/1614684

Answer:

  (a)  (-1, 2)

Step-by-step explanation:

You want the ordered pair that represents the coordinates of a point 1 unit left and 2 units up from the origin.

The (x, y) coordinates of a point on the Cartesian plane represent (units right, units up) relative to the origin. When the direction is left or down, the sign of the corresponding coordinate is made negative.

  (1 left, 2 up)   ⇒   (-1, 2), matching choice A

<95141404393>

To find the points of discontinuity for the rational function y = (x - 8)/(x^2 + 6x - 7), we need to identify the values of x that make the denominator zero, as division by zero is undefined.

Setting the denominator equal to zero:

x^2 + 6x - 7 = 0

Factoring the quadratic equation:

(x + 7)(x - 1) = 0

This gives us two solutions: x = -7 and x = 1.

Therefore, the points of discontinuity for the rational function are x = -7 and x = 1.

To describe the vertical asymptotes and holes, we need to examine the behavior of the function around these points.

For x = -7:

When x approaches -7 from the left side, the function approaches negative infinity.

When x approaches -7 from the right side, the function approaches positive infinity.

This indicates a vertical asymptote at x = -7.

For x = 1:

When x approaches 1 from the left side, the function approaches negative infinity.

When x approaches 1 from the right side, the function approaches positive infinity.

This also indicates a vertical asymptote at x = 1.

Based on this analysis, there are two vertical asymptotes at x = -7 and x = 1. There are no holes in the graph.

Regarding the rational function y = (-4x^6 + 6x + 3)/(8x^6 + 9x + 3), to find the horizontal asymptote, we examine the degrees of the numerator and denominator polynomials.

Since the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.

Therefore, the rational function y = (-4x^6 + 6x + 3)/(8x^6 + 9x + 3) does not have a horizontal asymptote.

Learn more about Rational function here -: brainly.com/question/19044037

#SPJ11