Erica works in a soda-bottling factory. As bottles pass her on a conveyer belt, she puts caps on them. Unfortunately, Erica sometimes breaks a bottle before she can cap it. She gets paid 10 cents for each bottle she successfully caps, but her boss deducts 1 cent from her pay for each bottle she breaks. Erica is having a bad morning. 26 bottles have come her way, but she has been breaking some and has only earned 18 cents so far today. How many bottles has Erica capped and how many has she broken?

Complete question:

A police car is located 50 feet to the side of a straight road. A red car is driving along the road in the direction of the police car and is 130 feet up the road from the location of the police car. The police radar reads that the distance between the police car and the red car is decreasing at a rate of 75 feet per second. How fast is the red car actually traveling along the road.

Answer:

The red car is traveling along the road at 80.356 ft/s

Step-by-step explanation:

Given

Police car is 50 feet side off the road

Red car is 130 feet up the road

Distance between them is decreasing at the rate of 75 feet per sec

Let x be how far the police is off the road.

Let y be how far the red car is up the road.  

Let h be the distance between the police and the red car.

This forms a right triangle so we can use the Pythagorean theorem, to solve for h

h² = x² + y²

h² = 50² + 130²

h² = 19400

h = √19400

h = 139.284 ft

Again;

Let dx/dt be how fast the police is traveling toward the road.

Let dy/dt  be how fast the red car is traveling along the road.

Let dh/dt be how fast the distance between the police and the car is decreasing.

Recall that, h² = x² + y² (now differentiate with respect to time, t)

2h(dh/dt) = 2x(dx/dt) + 2y(dy/dt)

divide through by 2

h(dh/dt) = x(dx/dt) + y(dy/dt)

since the police car is not, dx/dt = 0

and dy/dt is the how fast is the red car actually traveling along the road

139.284(75) = 50(0) + 130(dy/dt)

10446.3 = 0 + 130(dy/dt)

dy/dt = 10446.3 / 130

dy/dt = 80.356 ft/s

Therefore, the red car is traveling along the road at 80.356 ft/s

Answer:

A

Step-by-step explanation:

Draw a circle and cut it into 3 equal parts. shade 1 part

hope this helps please mark as brainliest

Draw a circle and cut it into 3 equal parts best describe to show 1/3 shaded, option A is correct

Since 1/3 represents one out of three equal parts, drawing a circle and dividing it into 3 equal parts allows you to shade one of those parts to accurately represent 1/3.

This method ensures that each part represents an equal fraction of the whole, which is necessary to accurately show 1/3 shaded.

Hence, one-way to show 1/3 shaded is draw a circle and cut it into 3 equal parts. shade 1 part.

To learn more on Fractions click:

https://brainly.com/question/10354322

The complete question is:

which best describe one-way to show 1/3 shaded?​

(A) Draw a circle and cut it into 3 equal parts. shade 1 part

(B) Draw a circle and cut it into 3 unequal parts. shade 1 part

Answer:

y = x + 1

Step-by-step explanation:

Parallel lines have same slope.

y = x - 1

Compare with the equation of line in slope y-intercept form: y = mx +b

Here, m is the slope and b is the y-intercept.

m =1

Now, the equation is,

         y = x + b

The required line passes through (-3 ,-2). Substitute in the above equation and find y-intercept,

        -2 = -3 + b

  -2 + 3 = b

         \(\boxed{b= 1}\)

    Equation of line in slope-intercept form:

                  \(\boxed{\bf y = x + 1}\)      

The equation is :

Solution:

If two lines are parallel to each other, then their slopes are equal. The slope of y = x - 1 is 1. Hence, the slope of the line that is parallel to that line is 1.

We shouldn't forget about a point on the line : (-3, -2).

I plug that into a point-slope which is :

\(\sf{y-y_1=m(x-x_1)}\)

Slope is 1 so

\(\sf{y-y_1=1(x-x_1)}\)

Simplify

\(\sf{y-y_1=x-x_1}\)

Now I plug in the other numbers.

-3 and -2 are x and y, respectively.

\(\sf{y-(-2)=x-(-3)}\)

Simplify

\(\sf{y+2=x+3}\)

We're almost there, the objective is to have an equation in y = mx + b form.

So now I subtract 2 from each side

\(\sf{y=x+1}\)

Answer: the second one

Step-by-step explanation:

Answer:

330ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

The required permutation of the letters of the word coefficient provided that all words start with coe is equals to 40,320.

The number of permutations of the letters of  word coefficient

With the condition that all words start with 'coe'.

Since we are given that the first three letters must be "coe",

Required to permute the remaining 8 letters.

The number of permutations of 8 letters can be found,

Using the formula for permutations of n distinct objects, which is,

P(n) = n!

where n is the number of objects.

Since the first three letters are fixed as 'coe',

The order of these letters is not counted in the permutation.

So, the number of permutations of the 8 remaining letters is,

⇒P(8) = 8!

⇒P(8) = 40,320

Therefore, the total number of permutations of the letters in the word 'coefficient' that start with 'coe' is P(8) = 40,320.

Learn more about permutations here

brainly.com/question/28067377

#SPJ4

Answer:

The Area of the trapezium is \(60cm^2\)

Step-by-step explanation:

Given,

Height (h)= 8cm

Sum of the parallel sides (a+b)= 15cm

Area of trapezium = \(1/2*h*(a+b)\)

                              =\(1/2*8*15\)

                              =\(4*15\)

Area of trapezium=60cm^2

Answer: Area = 60 cm²

Step-by-step explanation:

To find the area of a trapezium we use the formula

Area of trapezium = 1/2 (sum of parallel sides) × height

∴ Area = 1/2 ×15 cm × 8 cm

           = 60 cm²

To solve more questions related to the Area

https://brainly.com/question/16519513

https://brainly.com/question/76387

Answer:

Dominique should buy 4 200-milliliter containers of juice. This will cost her $4.76, which is the lowest price for 2 liters of juice. By buying the smaller containers, Dominique can save $0.45 compared to buying the larger container.

The solution to the equation is x = 10 or x = -2.

An equation refers to a mathematical expression showing that two expressions are equal.

It must have variables (e.g. a, c, x, y), constants (like 1, 13, 50, etc), and mathematical operations (like +, -, *, /).

To solve for x, we shall start with the given equation:

x + 6 = √(2x + 29) + 9

Subtract 9 from both sides:

x - 3 = √(2x + 29)

Square both sides:

\((x - 3)^2\) = 2x + 29

Expand the left side:

\(x^2\) - 6x + 9 = 2x + 29

We then subtract 2x and 9 from both sides:

\(x^2\) - 8x - 20 = 0

Next, actor the quadratic equation:

(x - 10)(x + 2) = 0

Therefore, the equation x = 10 or x = -2

Learn more about equation at brainly.com/question/29174899

#SPJ1

Answer:

each freind would get 1/15 of the pie

Step-by-step explanation:

1/5 divide by 3 equals 1/15

Answer:

5

Step-by-step explanation:

Common factor: 4. Divide 20 by 4 to get 5

Answer: X=5

Step-by-step explanation:

Since the triangles are similar shape-wise, then that means that the sides are going to be similar numerically.

12/4 got us 3, which is the side of that smaller triangle. Since we divided 12 by 4, then we need to divide 20 by 4 to get the unknown side. 20/4 is 5, therefore x is 5.

Answer:

i say it is  1.78 because you are didving the sum and the prat

Step-by-step explanation:

The cost of the molding is given as follows:

$119.30.

The circumference of a circle of radius r is given by the equation presented as follows:

C = 2πr.

The parameters for this problem are given as follows:

d = 9 -> r = 4.5.

(as the radius is half the diameter)

Hence the circumference is given as follows:

C = 2 x π x 4.5

C = 28.27 ft.

The cost is of $4.22 per ft, hence the total cost is given as follows:

4.22 x 28.27 = $119.30.

More can be learned about the circumference of a circle at brainly.com/question/12823137

#SPJ1

1. 76.56.

2. 96

3. The largest solution to the equation x²+16x+28=138 is 6.71.

4. The smallest solution to the equation x²+14x+14=145 is 5.96.

Equations are used to express relationships between variables and solve mathematical problems.

1. This is calculated by taking the coefficient of x (19) and dividing it by two (19/2) and then squaring the result (19/2)² = 76.56.

2. This is calculated by taking the coefficient of x (30) and dividing it by two (30/2) and then squaring the result (30/2)² = 96.

3. This is calculated by using the quadratic formula, by taking the opposite of the coefficient of x (16) plus or minus the square root of the coefficient of x squared (16²) minus 4 times the coefficient of the x term (4x16) minus the constant (28) divided by 2 times the coefficient of the x term (2x16).

4.  This is calculated by using the quadratic formula, by taking the opposite of the coefficient of x (14) plus or minus the square root of the coefficient of x squared (14²) minus 4 times the coefficient of the x term (4x14) minus the constant (14) divided by 2 times the coefficient of the x term (2x14).

For more questions related to coefficient

https://brainly.com/question/24881460

#SPJ1

1.  For the given equation, c need to be 90.25 to complete the square.

2. 225

3. The largest solution to the equation x²+16x+28=138 is 6.

4. The smallest solution to the equation x²+14x+14=145 is -14.

Equations are used to express relationships between variables and solve mathematical problems.

1. This is calculated by taking the coefficient of x (19) and dividing it by two (19/2) and then squaring the result

(19/2)² = 90.25.

2. This is calculated by taking the coefficient of x (30) and dividing it by two which is (30/2) and then squaring the result

(30/2)² = 225.

3. The largest solution to the equation x²+16x+28=138 is 6.

This can be calculated by using the quadratic formula to solve the equation.

(a=1, b=16, c=28)

x = -8 ± √((16)² - 4(1)(28))/2(1).

x = -8 ± √(240)/2

x = 6 or -14.

Since 6 is the larger solution, it is the largest solution to the equation.

4.  The smallest solution for x2+14x+14=145 can be determined by using the Quadratic Formula.

a=1, b=14, and c=14

x = [-14 ± √(142-4(1)(14))]/(2(1))

x = [-14 ± √(196)]/2

x = [-28/2] or [14/2]

x = -14 or 7

Therefore, the smallest solution for x2+14x+14=145 is x=-14.

For more questions related to coefficient

https://brainly.com/question/24881460

#SPJ1

Answer:

9

Step-by-step explanation:

If A = - 3, than A^2 is equal to (-3)^2

If a number is squared (to power of 2), it is multiplied by itself (there are two of that number being multiplied together) so it is - 3x-3

-3 x - 3 = 9,

Because 3x3 =9 and a negative multiplied by a negative makes a positive.

Hope this helped!

Answer:

9

Step-by-step explanation:

(A)^2 is a better way to write it. That way the answer is unambiguous (-3)^2 = -3 * - 3 = 9

That is the answer.

Answer:

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    3*x-(4*y-7)=0

STEP

1

:

Equation of a Straight Line

1.1     Solve   3x-4y+7  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  3x-4y+7  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 7/4 so this line "cuts" the y axis at y= 1.75000

 y-intercept = 7/4  =  1.75000

Calculate the X-Intercept :

When y = 0 the value of x is -7/3 Our line therefore "cuts" the x axis at x=-2.33333

 x-intercept = -7/3  = -2.33333

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 1.750 and for x=2.000, the value of y is 3.250. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 3.250 - 1.750 = 1.500 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     =  1.500/2.000 =  0.750

Geometric figure: Straight Line

 Slope = 1.500/2.000 = 0.750

 x-intercept = -7/3 = -2.33333

 y-intercept = 7/4 = 1.75000

Answer: There is a small relationship between IQ an productivity.

Step-by-step explanation:

Given: The correlation between employee IQ and productivity in a factory is .12.

Null hypothesis : There is no relationship between employee IQ and productivity.

Alternative hypothesis : There is relationship

between employee IQ and productivity.

Since, p < .01 , where 0.01 is the significance level.

So, we reject the null hypothesis.

That means, there is a relationship between employeeIQ and productivity.

Since correlation coefficient is near to 0, so it represent weak correlation.

Conclusion: There is a small relationship between IQ an productivity.

I think it is C. Hope it helps you! :)

The speed of the second pedestrian is 5 kilometers per hour.

Let's say that the speed of the second pedestrian is S.

We know that the other pedestrian walks at a speed of 4km/h, and they (together) travel a distance of 27km in 3 hours, then we can write the linear equation:

(4km/h + S)*3h = 27km

It says that both pedestrians work, together, a total of 27km in 3 hours.

Now we can solve that linear equation for S, to do this, we need to isolate S in the left side of the equation.

4km/h + S = 27km/3h = 9 km/h

S = 9km/h - 4km/h = 5km/h

The speed of the second pedestrian is 5 kilometers per hour.

If you want to learn more about speed:

https://brainly.com/question/4931057

#SPJ1

Answer:

\(14 \ 100 \1800\)

Answer:

b

Step-by-step explanation:

Answer:

a rectangle would provide the largest area for the pigs

According to the information, the perimeter of the triangle is ≈ 31.18

To find the distance between two points, we can use the distance formula:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Let's label the coordinates as follows:

Point 1: (-2, 3)

Point 2: (3, -2)

Now we can substitute these values into the distance formula:

distance = sqrt((3 - (-2))^2 + (-2 - 3)^2)

distance = sqrt((5)^2 + (-5)^2)

distance = sqrt(25 + 25)

distance = sqrt(50)

distance ≈ 7.07

Therefore, the distance from (-2, 3) to (3, -2) is approximately 7.07 units.

To find the perimeter of the triangle, we need to find the length of all three sides of the triangle and then add them up.

Using the distance formula, we can find the length of the sides:

Side 1: (-2,3) to (3,-2)

d = √[(3 - (-2))^2 + (-2 - 3)^2]

= √[5^2 + (-5)^2]

= √50

= 5√2

Side 2: (3,-2) to (-7,-2)

d = √[(-7 - 3)^2 + (-2 - (-2))^2]

= √[(-10)^2 + 0^2]

= 10

Side 3: (-7,-2) to (-2,3)

d = √[(-2 - (-7))^2 + (3 - (-2))^2]

= √[5^2 + 5^2]

= 5√2

Therefore, the perimeter of the triangle is:

5√2 + 10 + 5√2 = 15√2 + 10 ≈ 31.18 (rounded to two decimal places)

An two of the three sides are equal, so it is an isosceles triangle.

Lean more about isosceles triangle in: https://brainly.com/question/2456591
#SPJ1

Answer:

  -4

Step-by-step explanation:

You want the value of (f·g)(-1) when f(x) = x² +3x and g(x) = 2x².

The product of the functions is the product of their values for each value of x.

  (f·g)(-1) = f(-1)·g(-1) = ((-1)² +3(-1)) × (2(-1)²) = (1-3)(2·1) = (-2)(2)

  (f·g)(-1) = -4

Answer:

C.) sin(11pi/6)

Step-by-step explanation:

construct triangle with a side perpendicular to x-axis

y=(-1)sin(pi/6)

y=sin(-pi/6)

y=sin((-pi/6)+2pi)

y=sin(11pi/6)

Complete Question

The complete question is shown on the first uploaded image

Answer:

a

The expected amount to be lost is  0.5263 cents per game

b

The expected amount to be lost is  

     \(P = \$ 526 .3 \)

Step-by-step explanation:

From the question we are told that

   The probability of winning is  \(p = \frac{1}{38} = 0.0263\)

Generally the probability of losing is mathematically evaluated as

            \(q =  1-p \)

=>        \(q = 1-0.0263 \)

=>        \(q = 0.9737\)

Generally the expected value is mathematically represented as

      \(E(X) =  \sum x_i *  P(x_i)\)

Here \(x_i\) is a discrete variable (i.e it is a countable )  are outcomes of the player winning and the player losing

So

     \(E(X) =   x_1 *  P(x_1) + x_2 *  P(x_2)  \)

Now the outcome of winning is  making $350  so

       \(x_1 = \$ 350\)

        the outcome of losing is losing $10  so  

        \(x_2 = - \$10\)

So

     \(E(X) =  350* 0.0263 -10 *  0.9737  \)

       \(E(X) = -0.5263 \)

hence the expected amount to be lost is  0.5263 cents per game

If you played the game 1000​ times, the amount that is expected to be lost is  

    \(P =  1000 * -0.5263\)

=> \(P = -\$ 526 .3 \)

Hence the expected amount to be lost is  

     \(P = \$ 526 .3 \)

A statistic is a function of the random variables of the sample, also know as the sample points.

A. A statistic is a function of sample data that provides information about a population parameter. It is used to estimate or infer information about the population from a sample.

B.

i. (X1+X4)/2 is a statistic because it is a function of the sample data (X1, X2, X3, X4, ..., Xn) and provides information about the population parameter (the mean).

ii. There is no statement provided for this part.

C. To test the claim that the mean breaking strength of cables has increased, we can use a one-sample t-test. The null hypothesis is that the population mean breaking strength is still 1800 Kg, and the alternative hypothesis is that the population mean breaking strength is greater than 1800 Kg.

We calculate the t -value using the formula:

t = (sample mean - hypothesized mean)/(standard deviation/sqrt(sample size))

\(t = (1850 - 1800)/(100/ \sqrt{(50)}) = 2.236\)\(t = (1850 - 1800)/(100/ \sqrt{(50)}) = 2.236\)

At the 0.01 significance level with 49 degrees of freedom (sample size - 1), the critical t-value is 2.681. Since our calculated t-value (2.236) is less than the critical t-value, we fail to reject the null hypothesis. Therefore, we do not have enough evidence to support the claim that the mean breaking strength has increased at the 0.01 significance level.

D. To determine if the two judges agree in their standard, we can use the Kendall's coefficient of concordance (W). W measures the degree of agreement among multiple raters for the same set of objects.

To calculate W, we assign ranks to the competitors based on their positions (1 for the first place, 2 for the second place, etc.) and calculate the sum of squares of the ranks for each judge (SSj). We then calculate the total sum of squares (SST) and the degrees of freedom (df) using the formulae:

\(SST = (n^3 - n)/12\)

df = k - 1, where k is the number of judges

Using the given data, we obtain:

\(SS1 = 30\\SS2 = 22\\SST = (10^3 - 10)/12 = 825\\df = 2 - 1 = 1\)

We can then calculate W using the formula:

\(W = 1 - (6/[(n^3 - n)k]) \times sum(SSj)\\W = 1 - (6/(10^3 - 10)) \times (30 + 22) = 0.733\)

Since W is greater than 0.5 ,we can conclude that there is moderate agreement between the two judges in their standard.

E. The procedure for carrying out a test of hypothesis involves the following steps:

State the null and alternative hypotheses.

Determine the level of significance (alpha).

Calculate the test statistic.

Determine the critical value.

Make a decision to reject or fail to reject the null hypothesis based on the calculated test statistic and the critical value.

Interpret the results in the context of the problem.

f.

To calculate the Spearman’s Rank Correlation coefficient, we need to rank the scores for each subject separately, and then find the difference in ranks for each student.

Subject A:

Ranking the scores for subject A, we get:

(Image 1)

Subject B:

Ranking the scores for subject B, we get:

(Image 2)

Next, we calculate the difference in ranks for each student:

(Image 3)

To calculate the Spearman’s Rank Correlation coefficient, we use the formula:

\(r = 1 - (6 * \sum d^2)/(n(n^2-1))\)

where d is the difference in ranks for each student, and n is the number of students.

Plugging in the values, we get:

\(r = 1 - (6 \times (0^2 + 0^2 + 0^2 + 1^2 + 1^2 + 0^2))/(6(6^2-1)) \\r = 1 - (6 \times 2)/(6(35))\\r = 1 - 0.1714\\r = 0.8286\\\)

The Spearman’s Rank Correlation coefficient is 0.8286, which indicates a strong positive correlation between the two subjects. This means that students who perform well in subject A tend to perform well in subject B as well.

To know more about statistics visit:

brainly.com/question/29093686

#SPJ1