what is (19-y)+5y=55

Answer:

The standard deviation of the sampling distribution of sample means would be of 0.6626 pounds.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Standard deviation of 5.7 pounds.

This means that \(\sigma = 5.7\)

If a sampling distribution is created using samples of the amounts of weight lost by 74 people on this diet, what would be the standard deviation of the sampling distribution of sample means?

Sample of 74 means that \(n = 74\)

The standard deviaiton is:

\(s = \frac{\sigma}{\sqrt{n}} = \frac{5.7}{\sqrt{74}} = 0.6626\)

The standard deviation of the sampling distribution of sample means would be of 0.6626 pounds.

Answer:

c= 17

Step-by-step explanation:

c² = a² + b²

c= ?

a = 8

b= 15

c² = (8)² + (15)²

c² = 64 + 225

c² = 289

\( \sqrt{c ^{2} } = \sqrt{289} \\ \\ c = 17\)

Answer:

m<ABC = 116°

m<CDE = 67°

Step-by-step explanation:

✔️m<ABC = 180 - m<BAD (adjacent angles of a parallelogram are supplementary)

m<ABC = 180 - 64° (Substitution)

m<ABC = 116°

✔️m<CDA = m<CDE + m<ADE (angle addition postulate)

m<CDA = m<CDE + 49°

m<CDA = m<ABC (opposite angles of a parallelogram are congruent)

m<CDE + 49° = 116° (substitution)

m<CDE = 116° - 49° (Substraction property of equality)

m<CDE = 67°

Step-by-step explanation:

2x+3x+x+20=180

6x+20=180

6x=160

x=160/6

x=26.667

Answer:

2X=53.2 , 3X=79.8 , X+20=46.6

Step-by-step explanation:

3X+2X+X+20=180

therefore,

6X+20=180

6X       =180-20

6X       =160

X        = 160 over 6

X        =26.6

now,

3X      = 26.6 x3

          =79.8

2X       =26.6 x2

          =53.20

X+20  =26.6+20

          =46.6

Im not sure if it's right. Because the total does not make 180 degrees.

Answer:

I don't know

Step-by-step explanation:

i don't know

Answer:Graph A.

Step-by-step explanation:

Graph A.

Step-by-step explanation:

We will try to understand the graph plotted for the change in temperature for whole day.

In the morning, temperature starts out around 50°F. As the day goes on, the temperature rises first slowly- Slope of the first line will be less.

Then temperature rises more quickly - Slope of the second line will be more than first line.

It stays constant for an hour- third line will be parallel to the x-axis for one hour gap.

Then the temperature dropped down slowly - Last line of the graph will go down.

By the understanding we made for the graph we find graph A is the answer.

Answer:

In standard form, the answer should be : 2y + x = 6.

Step-by-step explanation:

See attached image.

First, find the slope of the line between the two points using

     \(m = \dfrac{y_2-y_1}{x_2-x_1}\)

Then use one point to calculate the b for  \(y=mx+b\).

Step 1: slope

   \(\begin{aligned}m&=\dfrac{7-4}{-4-2}\\[0.5em]&=\dfrac{3}{-6}\\[0.5em]&=-\dfrac{1}{2}\end{aligned}\)

Step 2: calculate b

Right now we have \(y=\frac{1}{2}x+b\), so we'll plug in (2,4) for the x and y:

    \(\begin{aligned}\\4&=-\frac{1}{2}(2)+b\\[0.5em]4&=-1+b\\[0.5em]5&=b\end{aligned}\)

Now we build our slope-intercept equation: \(y=-\frac{1}{2}x+5\)

But, this isn't standard form.  We need to clear out the fraction and then move the x-term to the left.

Can you take it from there?

Answer:

i think it is B. x^ab, but i could be wrong

Step-by-step explanation:

pemdas so take

x^(a+b)

x^(ab)

x^ab

probably wrong

Answer:

The function f(x) to model U. S. cell phone usage over the time period of 2010 to 2016 can be expressed as f(x) = 43 * (1.23^x), where x is the number of years since 2010. Part b: The estimated cell phone usage in 2013 can be calculated by substituting x = 3 into the function f(x) = 43 * (1.23^x). This yields an estimated cell phone usage of 68.4 million in 2013, which can be rounded to the nearest ten thousand to 68 million.

Step-by-step explanation:

Where the friend made the error was in step 2. She should have squared the 4 first before multiplying by 2. The correct answer is 44

We want to simplify the mathematical expression;

2(10 - 6)² + 3*4

The correct steps are as follows;

Step 1; Using BODMAS Acronym, let us deal with the bracket first to get;

2(4)² + 3*4

Step 2; Still dealing with the bracket, we will now have;

2(16) + 3*4

Step 3; Still dealing with the bracket, we will now have; 32 + 3*4

Step 4; Next sign to be used is multiplication sign and as such we now have; 32 + 12

Step 5; Using the addition sign, we now have 44

Thus, where the friend made the error was in step 2. She should have squared the 4 first before multiplying by 2.

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Answer:solution

Step-by-step explanation:

2 (4x^3-2x^2+3x-9)

Answer:

4+52=56

\(y = 4cm and o = 52 work out x\)

56

Answer:

x=-4 is true, x=6 is not

Step-by-step explanation:

5x + 7 < 22

Plug in our X values

5(-4) + 7 < 22 ?

solve

-20 + 7 < 22

-13 < 22 ?

x=-4 is true.

Repeat steps from ^

5(6) + 7 < 22

30 + 7 < 22

37 < 22 ?

x=6 is not true.

Hope this helped

Answer:

False

Step-by-step explanation:

5(-4) + 7 < 22

-20 + 7 < 22

-14 < 22

5(6) + 7 < 22

30 + 7 < 22

37 < 22

The statement would be false because when applying 6 to the equation, the equation becomes false.

On the other hand, when applying -4 to the equation, the equation becomes true, but since both -4 and 6 HAVE to be BOTH solutions to the equation, the statement becomes false.

Answer:

answer is given in up paper. where ans is -1/2

Answer:

65 packets and 4 stamps

Step-by-step explanation:

The first thing we see is that the stamps are mixed... which means they must be added.

208 + 186 = 394 stamps total

Now we see that each packet has 6 stamps. So we divide the number of stamps in total by 6.

394/6= 65.66667

Now we see from that number that the stamps can't quite make 66 packets, so there are 65 packets.

Now we find the number of stamps left over by multiplying the number of packets by 6.

65 x 6= 390

Now we take the total number of stamps minus the number of stamps in packets.

394 - 390 = 4

Therefore, there are four stamps left over.

Hope this helps!

The intermediate step in completing the square is\($x^2 + 2ax + (a^2) = b - a^2 + (a^2)$\)

To complete the square for the equation \($(x+a)^2=b$\), we can follow these steps:

1. Expand the left side of the equation: \($(x+a)^2 = (x+a)(x+a) = x^2 + 2ax + a^2$\).

2. Rewrite the equation by isolating the squared term and the linear term: \($x^2 + 2ax = b - a^2$\).

3. To complete the square, take half of the coefficient of the linear term, square it, and add it to both sides of the equation:

\($x^2 + 2ax + (a^2) = b - a^2 + (a^2)$\).

4. Simplify the right side of the equation: \($x^2 + 2ax + (a^2) = b$\).

This step can be represented as: \(\[x^2 + 2ax + (a^2) = b - a^2 + (a^2)\]\)

This intermediate step helps us rewrite the equation in a form that allows us to factor it into a perfect square.

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Answer:

you need exactly 0.72 fertilizer but since its pounds, you round up so the answer is 1 pound.

Step-by-step explanation:

The amount of fertilizer required to cover 1 square foot of ground is 0.72

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

Given data ,

Amount of fertilizer required to cover 25 square foot ground = 18 pound

Amount of fertilizer required to cover 1 square foot ground = Amount of fertilizer required / total square foot ground

Amount of fertilizer required to cover 1 square foot ground = 18 / 25

Therefore , Amount of fertilizer = 0.72 pound

Hence , the amount of fertilizer required to cover 1 square foot of ground is 0.72

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Answer:

24

Step-by-step explanation:

2^3 * 3 = 8 * 3 = 24

Hope this helped!

Answer:

24

Step-by-step explanation:

2^3 is equal to 2 times 2 times 2 which is 8 and 8 times 3 is 24

The value of N that satisfies the following equation, 5!9!= 12N!, is 10.

Factorial notation (n!) means to multiply a series of descending natural numbers. Also stated in the problem that for positive integer n, the factorial notation n! represents the product of the integers from n to 1.

Take for example 6! which can be written as 6 x 5 x 4 x 3 x 2 x 1 = 720.

Given the equation 5!9!= 12N!, expand the factorial notation.

(5 x 4 x 3 x 2 x 1)(9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) = (4 x 3) N!

N! = (5 x 2 x 1)(9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)

N! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

N = 10

Therefore, the value of N that satisfies the following equation, 5!9!= 12N!, is 10.

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The area of the figure ABDECA, and the coordinates of the points on the quadrilateral are;

1. The area is about 15.16 units²

2. The coordinates of the points are;

(i) B(5, 8)

(ii) C(8.58, 4)

(ii) D(8,58, 1.21)

A quadrilateral is a four sided polygon.

1. The coordinate of the point C can be found as follows;

Let (x, y) represent the coordinates of the C, we get;

(x + 8)/2 = 5

x = 2 × 5 - 8 = 2

(y + 8)/2 = 6

y = 2 × 6 - 8 = 4

The coordinates ot the point C (2, 4)

The length of the segment BC = √((8 - 2)² + (8 - 4)²) = 2·√(13)

Length of the side AB = √((8 - 6)² + (8 - 11)²) = √(4 + 9) = √(13)

The area of the triangle ABC = (1/2) × 2·√(13) × √(13) = 13

CE is perpendicular to DE, let (a, b), represent the coordinates of the point E, therefore;

(4 - y)/(2 - x) = -(5 - x)/(6 - y)

y - 4 = (-4/7)(x - 2)

y - 6 = (7/4)(x - 5)

(-4/7)(x - 2) + 4 = (7/4)(x - 5) + 6

x = (17/5) = 3.4

y = (7/4)((17/5) - 5) + 6 = 3.2

The coordinates of the point E is (3.4, 3.2)

The length of the side DE = √((5 - 3.4)² + (6 - 3.2)²) = √(10.4)

Length of the side CE = √((3.2 - 2)² + (3.4 - 4)²) = √(1.8)

Area of the triangle ΔCDE = (1/2) × √(10.4) × √(1.8)

Area of the figure is therefore;

2. The equation of the line AB is; y - 6 = (1/3)·(x - (-1))

y - 6 = (1/3)·(x + 1)

y = (1/3)·(x + 1) + 6

The slope of the segment AE = (4 - 6)/(3 - (-1)) = -1/2

Slope of the segment BE = -1/(-1/2) = 2

Equation of BE is; y - 4 = 2·(x - 3)

y = 2·(x - 3) + 4 = (1/3)·(x + 1) + 6

Therefore, x = 5

y = (1/3)·(5 + 1) + 6 = 8

(ii) Area of the triangle EBC = 24 unit²

EB = (1/2) × √((5 - 3)² + (8 - 4)²) = √20

Therefore;

BC = 24/(√20) = 12/√5 = 12·√5/5 = √(28.8)

(x - 5)² + (y - 8)² = 28.8

y = 4, therefore;

(x - 5)² + (4 - 8)² = 28.8

(x - 5)² = 28.8 - (4 - 8)² = 12.8

x = √(12.8) + 5

(iii) The equation of the segment AD is; y - 4 = (-1/2)(x - 3)

x = √(12.8) + 5

Therefore;

y - 4 = (-1/2)((√(12.8) + 5) - 3)

y = (-1/2)((√(12.8) + 5) - 3) + 4 ≈ 1.21

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Answer:

m = -3 ; c = 1

Step-by-step explanation:

y = -3x + 1

y = mx + c

m = -3

c = 1

The power of 0.95 shows that there is a 95% chance of rejecting the alternative hypothesis of p = 0.16 where the true proportion is actually 0.08. That is if the proportion of users who experience abdominal pain is actually 0.08, then there is a 8% chance of supporting the claim that the proportion of users who experience abdominal pain is more than 0.08.

Given that the alternative value of p is 0.16, it means that the power of the test is 0.95.

This means that if the true proportion of drug users experiencing abdominal pain is indeed 0.16, then by conducting the hypothesis test with a significance level of 0.05, we will correctly reject the null hypothesis and support the claim that more than 8% (0.08) of the drug's users experience abdominal pain with a probability of 0.95.

In other words, the power of 0.95 indicates that the test has a high chance (95%) of correctly detecting a true difference and correctly concluding that the proportion of drug users experiencing abdominal pain is greater than 8% when the true proportion is actually 16%. It demonstrates the test's ability to identify and support the alternative hypothesis when it is true.

It's important to note that the power of the test is influenced by factors such as sample size, significance level, effect size, and variability. In this case, with a power of 0.95, there is a high probability of detecting the claimed difference if it truly exists.

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Answer: 1085

Step-by-step explanation:

Answer:

Therefore, the constant of proportionality for the given proportional relationship is 5.

Step-by-step explanation:

To determine the constant of proportionality in the given proportional relationship, we can use the formula:

Constant of Proportionality = Tickets / Games

Let's plug in the values from the table:

For the first set of values (4 games and 20 tickets):

Constant of Proportionality = 20 / 4 = 5

For the second set of values (7 games and 35 tickets):

Constant of Proportionality = 35 / 7 = 5

For the third set of values (10 games and 50 tickets):

Constant of Proportionality = 50 / 10 = 5

In all three cases, the constant of proportionality is equal to 5.

Therefore, the constant of proportionality for the given proportional relationship is 5.

Yes, Wilson is right since "negative numbers" don't exist when you find the absolute value.

Therefore, Wilson is correct as there is no negative term in absolute value.

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(a). The smallest quantity at which marginal cost is equal to 15 dollars per item is 2.76. (b). The positive value of q at which average variable cost is equal to marginal cost is \(\frac{15}{2}\). (c). The longest interval on which marginal revenue exceeds marginal cost is (1.8377, 8.1622). (d). The profit is increasing at 8.1622 at p(q) is maximum. (e). The maximum value of profit is 78.2455 dollars.

The total revenue: TR(q) = 30q

The total cost: Tc(q) = \(q^3-15 q^2+75 q+10$\)

The change in cost is referred to as the change in the cost of production when there is a need for change in the volume of production.

(a).  Marginal cost MC\(=\frac{\partial}{\partial q}(T C)$\)

\($$=3q^2-30 q+75 \text {. }$$\)

According to question.

\($$\begin{aligned}& 3 q^2-30 q+75=15 \\& 3 q^2-30 q+60=0 \\& q^2-10 q+20=0 \\& q= \frac{10 \pm \sqrt{100-80}}{2} \\&= \frac{10 \pm 2 \sqrt{5}}{2}=5 \pm \sqrt{5}\end{aligned}\)

\($$$\therefore \quad q=5+\sqrt{5} \quad$ and $q=5-\sqrt{5}$\)

we have to find smallest quantity.

\($$\therefore \quad q=5-\sqrt{5}=2.76 \text {. }$$\)

b)

\($$\begin{aligned}& F C=T C(0)=10 \\& V C(q)=T C(q)-F C \\& =q^3-15 q^2+75 q . \\& \text { AVC(q) }=\frac{V C(q)}{q}=q^2-15 q+75 .\end{aligned}$$\)

When AVC(q)=MC(q)

\($$\begin{array}{ll}\Rightarrow & q^2-15 q+7 ;=3 q^2-30 q+75 \\\Rightarrow & 2 q^2-15 q=0 .\ \Rightarrow q(2 q-15)=0 . \\\Rightarrow & q=0, \frac{15}{2} \quad \Rightarrow \quad q=\frac{15}{2}\end{array}$$\)

Therefore, the positive value of q at which average variable cost is equal to marginal cost is \(\frac{15}{2}\).

(c).

\(& M R(q)=\frac{d}{d q}(T R)=30 . \\\)

\(& M C(q)=3 q^2-30 q+75 . \\\)

Let MR(a)>MC(q)

\(& \Rightarrow \quad 30 > 3 q^2-30 q+75 \text {. } \\\)

\(& \Rightarrow \quad 3 q^2-3 p q+45 < 0 \\\)

\(& \Rightarrow \quad q^2-10 q+15 < 0 \text {. } \\\)

\(& \because \quad q=\frac{10 \pm \sqrt{100-60}}{2} \Rightarrow q=\frac{10 \pm 2 \sqrt{10}}{2} \\\)

\(& q=(5 \pm \sqrt{10}) \\\)

\(& \Rightarrow \quad(q-5+\sqrt{10})(q-5-\sqrt{10}) < 0 . \\\)

\(& \Rightarrow \(q-5+\sqrt{10}) < 0 \quad \& \quad(q-5-\sqrt{10}) > 0 \text {. } \\\)

\(& \text { or } \quad(q-5+\sqrt{10}) > 0 \quad \& \quad(q-5-\sqrt{10}) < 0 \text {. } \\\)

\(& \therefore \quad \text { other } q < 5-\sqrt{10}=1.8377 ., q > 5+\sqrt{10}=8.1622 \text {. } \\\)

\(& \Rightarrow \quad q < 1.8377 \& q > 0.1622 \text {. } \\\)

\(& \text { or } q > 5-\sqrt{10} \quad \& \quad q < 5+\sqrt{10} \text {. } \\\)

\(& \Rightarrow q > 1.8377 \quad < q < 8.1622 \text {. } \\\)

The Interval is (1.8377, 8.1622).

(d).  P(q) =TR(q)-TC(q)

\(& =30 q-\left(q^3-15 q^2+75 q+10\right) \\& =-q^3+15 q^2-75 q-10+30 q \\& =-q^3+15 q^2-45 q-10 .\)

on (1.8377,8.1622). we have to find a point such that p"(q)=0 and p"(q)<0.

\(& p^{\prime}(q)=-3 q^2+30 q-45 \\\)

\(& \Rightarrow \quad-3\left(q^2-10 q+15\right)=0 \\\)

\(& \Rightarrow \quad q^2-10 q+15=0 . \\\)

\(& \quad q=1.8377 \text { and } \quad q=8.1622 . \\\)

\(& \Rightarrow \quad p^{\prime \prime}(q)=-6 q+30 . \\\)

\(& p^{\prime \prime}(1.8377)=-6(1.8377)+30 \\\)

\(&=18.9738 \\\)

\(& p^{\prime \prime}(8.1622)=-6(8.1622)+30 . &=-18.9732 < 0 .\)

at 8.1622, p(q) is maximum.

(e).

Max profit-P(8.1622)

=78.2455 dollars

Therefore, the maximum value of profit is 78.2455 dollars.

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