The makers of a popular brand of laundry detergent have discovered a new secret ingredient that they believe will boost the cleaning power of their detergent. The new ingredient is expensive, and if they use it, they would have to increase the retail price of the detergent (and they worry that the price increase will cause them to lose customers). However, they believe that if the improved detergent gets clothes drastically cleaner, customers will recognize that it is worth the extra cost. They conduct an experiment to compare the performance of the new and old formulas at removing grass stains, red wine, and chocolate from white t-shirts. Each cleaned shirt was rated on a scale from 1 (stain did not get removed) to 10 (no evidence of the stain) by trained experts. They compared the average rating for the new and old formulas. Suppose, at the 5% significance level, they find that the new formula cleaned the shirts significantly better than the old formula, with a p-value of 0.046. Interpret the p-value, in terms of the probability of the results happening by random chance, in this context.

Answer:

38.10

38.00

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

nre, nre

Step-by-step explanation:

Given

[tex]4b^2 + 16 = 0[/tex]

Required

Solve

[tex]4b^2 + 16 = 0[/tex]

Subtract 16 from both sides

[tex]4b^2 +16 -16 = 0 - 16[/tex]

[tex]4b^2 = - 16[/tex]

Divide both sides by 4

[tex]b^2 = -4[/tex]

Take square roots of both sides

[tex]b = \sqrt{-4[/tex]

[tex]\sqrt{-4} \to[/tex] Complex number

Hence, no real root exist

Answer:

Their are 166 students

are brought food

Answer:

5/6x^2 + 1/2x + 1/15

Step-by-step explanation:

(1/2x + 1/5)(5/3x + 1/3)

5/6x^2 + 1/6x + 1/3x + 1/15

5/6x^2 + 1/6x + 2/6x + 1/15

5/6x^2 + 3/6x + 1/15

5/6x^2 + 1/2x + 1/15

Answer:

16

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Have a great day, be safe and healthy  

Thank u  

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Answer:

16

Step-by-step explanation:

The equation of the exponential function represented by the table will be y = 4(3)ˣ.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

Take two points from the table, then the points are (0, 4) and (1, 12).

The equation passes through (0, 4), then we have

4 = a(b)⁰

a = 4

The equation passes through (1, 12), then we have

12 = 4(b)¹

b = 3

Then the equation of the exponential function represented by the table will be y = 4(3)ˣ.

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Answer:

0.3172 rounded to the nearest tenth would be 0.3.

This is because you would first look at the number in the tenths place which is 3.

Then you would look to the number to the right to determine if you would round up or down.

If the number in the hundredths place is bellow 5, the number would remain the same, and if it were above 5, it would round up by one number.

If the number were 5, you would look to the number in the thousandths place and then go from there.

Since the number in the hundredths place is 1, then you will ignore the other numbers to the right and, you would have a result of 0.3.

Step-by-step explanation:

Hope it helps! =D

Answer: 0.3171 rounded to the nearest tenth is 0.3.

Step-by-step explanation:

Follow these steps for rounding the decimal number 0.3171 to the nearest tenth (one decimal place):

Find the tenth digit, = 3 in the 0.3171. 

Find the digit immediately to the right of the tenth place. If this number is greater than or equal to 5, round up; otherwise, round down. 

= 1 in the 0.3171

Because 1 is less than 5, the tenth position digit 3 remains constant.

Remove all digits to the right of the rounding digit and rewrite the number.

As a result, 0.3171 rounded to the nearest tenth is 0.3.

Answer:

B

Step-by-step explanation:

Let, number of children and adults swam at the public pool that day is x and y.

So, x + y = 379   .....1)

It is given that daily prices are $1.75 for children and $2.00 for adults.

Also, the  receipts for admission totaled $693.50.

So, 1.75x + 2y = 693.50  .....2)

Putting value of y from equation 1 to equation 2 , we get :

1.75x + 2( 379 - x ) = 693.50

758 - 2x + 1.75x = 693.50

0.25x = 64.5

x = 258

So, y = 379 - 258 = 121

Therefore, number of children are 258 and adults are 121.

Answer:

Percent change = 15 - 25/25 × 100% = -10/25 × 100 = -40%

Step-by-step explanation:

Answer:

5 percent

Step-by-step explanation:

divide 25 by5 which gives you percent

Answer:

Step-by-step explanation:

You want to know the translation effected by subtracting -2 from the x-coordinate, and subtracting -4 from the y-coordinate of the vertices of a triangle.

You have correctly observed that the triangle vertex (-2, 0) is translated to (0, -4) by the subtraction of the translation matrix. That is, the x-coordinate is increased by 2, moving the point 2 units to the right, while the y-coordinate is decreased by 4, moving the point 4 units down.

The translation is to the right by 2 units, and a translation down by 4 units.

Answer: 2 units right  4 units down

Step-by-step explanation: trust

The perimeter of the considered isosceles triangle is  28.8 in. approx.

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

Considering the attached image below, which has same isosceles triangle with same measurements, we see that:

|AC| = |AB| (because perpendicular dropped leaves two congruent triangles in ABC, as ADC and ADB)

similarly, we have:

|BD| = |DC|

But |BC| = 6 =  |BD| + |DC|,

Thus, 6 = |BD| + |DC| = |BD| + |BD| =2|BD|

|BD| = 6/2 = 3 inches = |DC|

From Pythagoras theorem for triangle ADB, we get:

[tex]|AB|^2 = |AD|^2 + |BD|^2\\|AB|^2 = 11^2 + 3^2 = 121 + 9 = 130\\|AB| = \sqrt{130} \approx 11.4 \: \rm in. = |AC|[/tex]

(positive square root since |AB| is length, which is a non-negative measure).

Thus, we get:

Perimeter of the rectangle = |AB| + |BC| + |AC| ≈ 11.4 + 6 + 11.4 = 28.8 in.

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Her class of 30 pupils can be divided into 10 groups using 5 groups of 2 students and 5 groups of 4 students each.

A circle is created in the plane by each point that is a specific distance from another point (center). Thus, it is a curve made up of points that are separated from one another by a defined distance in the plane. Every pair of points in a circle's closed, two-dimensional plane are evenly spaced apart from the "center." A circular symmetry line is made by drawing a line through the circle.

given

10 groups of 3 students = 30 students :

5 groups of 2 students + 5 groups of 4 students = 30 students : 7 groups of 3 students + 3 groups of 3 students = 30 students

so Her class of 30 pupils can be divided into 10 groups using 5 groups of 2 students and 5 groups of 4 students each.

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Answer:

the graph would show a line with a y-intercept of 7 and a slope of -2/3

Step-by-step explanation:

y - 3 = -2/3x + 4

y = -2/3x + 7

the graph would show a line with a y-intercept of 7 and a slope of -2/3

Answer:21/2

Step-by-step explanation:

Answer:

It means that if the system of equations has an infinite number of solution, then the system is said to be consistent.

Their Customer Acquisition cost was $10

Customer Acquisition Cost is the cost of winning a customer to purchase a product or service. As an important unit economic, customer acquisition costs are often related to customer lifetime value. Customer acquisition cost can also be referred as the fee associated with convincing a customer to buy your product or service.

To calculate customer acquisition cost

Customer Acquisition Cost (CAC) = Customer Acquisition Cost/total marketing cost

From the question,

The business gained 50+100+150= 300 new customers

Campaign budget = $30000

Customer Acquisition Cost (CAC) = $3000/300

=$10

Hence, it cost the business $10 to acquire a new customer

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Answer:

27/8

Step-by-step explanation:

First, note that 3 3/8 is a mixed number, also know as mixed fraction. It has a whole number and a proper fraction. The numbers in the mixed fraction are defined as follow:

3 = whole number

3 = numerator

8 = denominator

To convert mixed number 3 3/8 to improper fraction, you follow these steps:

1. Multiply the whole number by the denominator

  3 × 8 = 24

2. Add the product from Step 1 to the numerator

   24 + 3 = 27

3. Write answer from Step 2 over the denominator

   27/8

The mixed number 3 3/8 converted to improper fraction is therefore :

27/8

[tex]1024 \div 4 = 256[/tex]

Answer:

32 feet

Step-by-step explanation:

area= length * width

squares have the same length and width

so therefore, you have to find the square root of 1024

1024= length*width, but the length is the same as the width

1024= length^2

The value of π can be written with upper and lower limits as -

3.12 ± 0.062.

Significant figures of a number in positional notation are digits in the number that are reliable and necessary to indicate the quantity of something.

Given is that Helen draws a random circle, she then measures the circumference and diameter. She gets a circumference {C} of 405mm correct to 2 significant figures She gets a diameter {D} of 130mm correct to 2 significant figures.

We can write -

Circumference {C} = (405 ± 2) mm

Diameter {D} = (130 ± 2) mm

The value of π can be calculated as -

π = {C}/{D}

π = (405 ± 2)/(130 ± 2)

Now, divide the numbers without errors first -

405/130

3.12

Now, we will calculate the relative errors in each number -

2/405 = 0.004

2/130 = 0.016

Adding the relative errors -

0.004 + 0.016

0.02

Absolute error = 0.02 x 3.12 = 0.062

The value of π can be written with upper and lower limits as -

3.12 ± 0.062

Therefore, the value of π can be written with upper and lower limits as -

3.12 ± 0.062.

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Answer:

a.

The 95% confidence interval for the proportion of all American adults who have a gun in their home is (0.4066, 0.4734). This means that we are 95% sure that the true population proportions of American adults who have a gun in their home is between these two values.

b.

The confidence level is the probability of the confidence interval containing the population proportion.

Step-by-step explanation:

Question a:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

Poll of 850 randomly selected American adults and finds that 44% of those surveyed have a gun in their home.

This means that [tex]n = 850, \pi = 0.44[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.44 - 1.96\sqrt{\frac{0.44*0.56}{850}} = 0.4066[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.44 + 1.96\sqrt{\frac{0.44*0.56}{850}} = 0.4734[/tex]

The 95% confidence interval for the proportion of all American adults who have a gun in their home is (0.4066, 0.4734). This means that we are 95% sure that the true population proportions of American adults who have a gun in their home is between these two values.

b. Explain what is meant by 95% confidence in this context.

The confidence level is the probability of the confidence interval containing the population proportion.

Therefore , the solution of the given problem of domain is The range of f(x) is a subset of this range, which is the range of -3x-2 (-14,), after answering the given question.

A function's domain is the set of values that can be sent into it. This collection represents all x values in a function like f. (x). A function's range is the set of possible values that it can accept. This collection includes the values that the return statement when we enter an x value. Assume that x and y are indeed the independent and dependent variables of a function with the formula y = f(x). If a function f provides a way to generate a single value y successfully while using a value of x .

Here,

In this case, f(x)=-3x-2 x < 4

3/4x-1 x≥ 4

Domain

This range, which is the range of -3x-2 (-14,), is a subset of the range of f(x).

Therefore , the solution of the given problem is The range of f(x) is a subset of this range, which is the range of -3x-2 (-14,), after answering the given question.

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Answer:

Third Option!

Step-by-step explanation:

Sorry if i'm wrong :(

Answer:

Third option is the correct answer.

[tex] 2log_{5}x - 2log_{5}4[/tex]

Step-by-step explanation:

[tex] log_{5} \bigg( \frac{x}{4} \bigg) ^{2} \\ \\ = 2log_{5} \bigg( \frac{x}{4} \bigg) \\ \\ = 2log_{5}x - 2log_{5}4[/tex]

Answer:

1 ≤ x < 6

Step-by-step explanation:

Okay so the answer is 1 ≤ x < 6, and the way you solve it is pretty simple :)

First: Eliminate the functions of the inequality, leaving it to just being an inequality. You have to understand that the function is decreasing on its domain, so the sign will reverse itself once you take away g(x)

This should take you from having [tex]g(x^{2} )>g(5x+6)[/tex]  to having [tex]x^2<5x+6[/tex]. From here you solve the inequality to get [tex]-1<x<6[/tex], although you aren't done.

Afterwards you take into account the domain, which restricts everything to being greater than or equal to one. This means that your inequality changes to 1 ≤ x < 6.

yw and good luck w ur rsm hw haha

lmk if this was helpful :P

The solution of inequality is 1 ≤ x < 6.

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Remove the inequality's functions, leaving it as an inequality alone.

As, the function is decreasing on its domain, the sign will change if g(x) is removed.

We have

g (x²) > g (5x+6)

x² > 5x +6

For the above equation the interval is -1 < x < 6.

The domain, which limits everything to being larger than or equal to one, is then taken into consideration.

So, the inequality is 1 ≤ x <6.

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Answer:

See below for answers and explanations

Step-by-step explanation:

Part A:

Check conditions for a 2-sample t-interval:

Random sample? √

Is the sample size no more than 10% of the population? √

Are both samples approximately normal? √

Construct the 95% confidence interval:

On a TI-84, click on "Stat", scroll to "Tests", and select "2-SampTInt". Put your data into 2 lists and set C-Level to be 0.95 to represent a 95% confidence level. Make sure the data isn't pooled, and press "Calculate" to obtain your results. You will see that the 95% confidence interval for the difference between the mean scores for the two types of instruction is {-6.042,8.1175}

Part B:

The confidence interval does not contradict the claim because 0 is contained within the 95% confidence interval, so it is quite possible that there is no difference between the mean scores for the two types of instruction.

Answer:

2x^5+y^12*x^2/3

Step-by-step explanation:

Step-by-step explanation:

okay

I think you should use the method of tan 30

and then find x by using pythagorean theorem