1. Here is a graph of the equation
2y-x=1
a. Are the points (0, 1/2)
and (-7, -3) solutions to
the equation? Explain or show how you know?

Answer:

Jack has a toy poodle names Lucy. He is supposed to feed Lucy 11 ounces of dog food a day. He has s ounces of food in the bag he bought for the month. The amount of dog food left in the bag after feeding Lucy today is represented by s-11.

There are two main subtypes of quantitative data, which are discrete data and continuous data. Each subtype has different techniques for analysis.

1. Discrete data: This type of data represents whole numbers or counts that can only take specific values. Examples include the number of students in a class or the number of cars in a parking lot. Techniques used to analyze discrete data include:
  a. Frequency distribution: A summary of the number of times each value appears in the dataset.

 b. Measures of central tendency: Calculating the mean, median, and mode of the dataset to understand its central point.

 c. Measures of dispersion: Assessing the range, variance, and standard deviation to understand the spread of the data.

2. Continuous data: This type of data represents measurements that can take any value within a range, such as height, weight, or temperature. Techniques used to analyze continuous data include:

 a. Histogram: A graphical representation of the distribution of the data, using bars to represent the frequency of values within specific intervals.

  b. Probability density function: A mathematical function that describes the probability of a continuous random variable falling within a specific range.

  c. Regression analysis: A statistical method for analyzing the relationship between a dependent variable and one or more independent variables.

Both discrete and continuous data can also be analyzed using inferential statistics, such as hypothesis testing and confidence intervals, to make inferences about a population based on a sample of the data.

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Answer:

setting up proportionality equation:

\(\sf \dfrac{big-side}{big-diagonal} = \sf \dfrac{small-side}{small-diagonal}\)

\(\sf \hookrightarrow \dfrac{7}{16+x+7} = \dfrac{4}{16}\)

\(\sf \hookrightarrow \dfrac{7}{23+x} = \dfrac{4}{16}\)

\(\sf \hookrightarrow 4(23+x) = 112\)

\(\sf \hookrightarrow 92 + 4x = 112\)

\(\sf \hookrightarrow 4x = 112- 92\)

\(\sf \hookrightarrow 4x = 20\)

\(\sf \hookrightarrow x = 5\)

Find DF:

\(\hookrightarrow \sf x + 7\)

\(\hookrightarrow \sf 5 + 7\)

\(\hookrightarrow \sf 12\)

Answer:

We see 2 congruent triangles: Triangle DBC and FEC. Let's set up a proportion to find the value of x and length of DF.

\(\frac{BE+EC}{DF+FC} =\frac{EC}{FC}\)

\(\frac{3+4}{(x+7)+16} =\frac{4}{16}\)

Cross multiply and solve for x.

\((3+4)*16=((x+7)+16)*4\)

\(7*16=(x+23)*4\)

\(112=(x+23)*4\)

\(28= (x+23)\)

x= 5

Now to solve for the length of DF, plug in x into DF.

DF=(x+7)

DF=(5+7)

DF= 12

Probability that a customer ordered a hot drink given that he or she ordered a large is 29.33 %

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are.

From the table, we have:

n(hot and large) = 22

n(hot and small) = 5

n(hot and medium) = 48

n(hot) = 22 + 5 + 48 = 75

So, the probability P(hot | large) is calculated as:

P(hot | large) = 22/75

P( hot | large) = 0.2933

Round to the nearest hundredth

P(hot | large) = 29.33 %

Probability that a customer ordered a hot drink given that he or she ordered a large is 29.33 %

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To find the arc length, we can use the formula:

\(\[ L = \frac{\theta}{360} \times 2\pi r \]\\Given:\( r = \frac{d}{2} = \frac{30}{2} = 15 \) ft\( \theta = 42 \) degrees\( \pi = 3.14 \)\\Substituting the given values into the formula:\[ L = \frac{42}{360} \times 2 \times 3.14 \times 15 \]\[ L = \frac{42}{360} \times 94.2 \]\[ L = \frac{3956.4}{360} \]\[ L \approx 10.99 \] ftTherefore, the arc length traveled by the car, to the nearest hundredth, is 10.99 feet. The correct option is c.\)

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The margin of error is 0.05 then the sample size of students is 384.

A statistic known as the margin of error describes how much random sampling error there is in survey data. Less faith should be placed in a poll's results representing the outcome of a population census as the margin of error increases.

The number of students in a school is 1000.

The level of confidence (C.L.) is 95% .

=  95/100

= 0.95.

The level of significance (α) is:

α = 1 − CL

=1  − 0.95

=0.05

The two-tailed critical value (Z) at the level of significance 0.05 was calculated using the standard normal table and is equal to 1.96.

Assume that 0.5 of the pupils at your school support the removal of the neighborhood's adolescent curfew.

the minimum number of students you need if you want the margin of error to be 5% will be:

\(n=\frac{\hat{p} \times(1-\hat{p}) \times\left(Z^{*}\right)^{2}}{(E)^{2}}\)

= 0.5(1−0.5)×(1.96)^2/(0.05)^2

=  384.16

= 384

the minimum number of students you need if you want the margin of error to be 5% will be: =  384

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I understand that question you are looking for is:

You are interested in the proportion of students in your school who favor the elimination of a local curfew on teenagers. Assume your school has 1,000 students.

a. To generate a 95% confidence interval for the proportion of students who favor the elimination of a curfew, what's the minimum number of students you need if you want the margin of error to be 5%?

The measurement of the remaining two sides of the triangle be 4cm and 6cm.

Given :- Perimeter of triangle = 18m.

Area of triangle = √135m².

One side of triangle = 8m.

Triangle  is a plane figure with three straight sides and three angles.

Let the equation be Area of ∆ = 1/2bh

= 1/2 ab sin C = 1/2 bc sin A = 1/2 ca sin B

= √( s(s-a)(s-b)(s-c) ) [ where s = (a + b + c)/2 ]

By using Heron's formula to get the Area of triangle,

s = (Perimeter /2) = (18/2) = 9m.

Putting values now we get :-

√(s(s-a)(s-b)(s-c) ) = √135

substitute the values in the above equation, we get

√[9(9-8)(9-b)(9-c)] = √135

Squaring Both sides we get,

9 × 1 × (9-b)(9-c) = (√135)² = 135

Dividing both sides by 9, we get,

(9-b)(9-c) = 15

81 - 9c - 9b + bc = 15

simplifying the above equation, we get

81 - 9(b + c) + bc = 15

9(b + c) - bc = 81 - 15

9(b + c) - bc = 66 -------- (1).

Also, if Rest two sides are b and c, we get,

→ 8 + b + c = 18

→ (b + c) = 18 - 8 = 10 cm. ------ (2).

Putting value of (2) in (1) , we get,

→ 9 × 10 - bc = 66

simplifying the above equation, we get

→ bc = 90 - 66

→ bc = 24 ------------ (3).

We do Factors of (3), we just have to check now, which satisfy Equation (2) also . (sum of Factors will be 10).

24 = ( 1, 24) , (24, 1), ( 2,12), (12,2) , (3,8) ,(8,3) , (4,6),(6,4)

We can see (4,6) or (6,4) Satisfy the (2).

Therefore, the measurement of the remaining two sides of the triangle be 4cm and 6cm.

The complete question is:

the perimeter of a triangular garden is 18 m. if its area is under root 135 m^2 and one of the tree sides is 8 m, find the remaining two sides

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This is an example of an isosceles triangle. An isosceles triangle is a triangle with two equal sides and two equal angles.

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Answer:

I believe the answer is C.

Step-by-step explanation:

Hope this helps you.

The measure of the segment CD is 12 and CE is 8.

In a triangle, the centroid is the point of intersection of the three medians, which are line segments joining each vertex to the midpoint of the opposite side.

The centroid divides each median into two segments, with the distance from the centroid to the vertex being twice the distance from the centroid to the midpoint of the opposite side.

Let M be the midpoint of side AB, N be the midpoint of side AC, and P be the midpoint of side BC. Then, we have:

CD = 2DP

CE = 2DN

We are also given that DE = 15. Since D is the centroid, we have:

AD = BD = CD/3

AE = CE/3

DC + DP = PC

CE + DN = NE

AD + AE = DE

Using these relationships, we can find CD and CE:

CD = 2DP = 2(PC - DC) = 2((AD + DP) - (AD/3)) = 2(2AD/3) = 4AD/3

CE = 2DN = 2(NE - CE) = 2((AE + DN) - (AE/3)) = 2(2AE/3) = 4AE/3

To find AD and AE, we can use the fact that AD + AE = DE and AD = BD:

AD + BD = DE

AD + (2AD/3) = 15

5AD/3 = 15

AD = 9

AE = DE - AD = 15 - 9 = 6

Substituting these values into the equations for CD and CE, we get:

CD = 4AD/3 = 4(9)/3 = 12

CE = 4AE/3 = 4(6)/3 = 8

Therefore, CD = 12 and CE = 8.

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This is the same as the original function, so the antiderivative is correct.

The function is given as f(x) = x² - 5x + 8.

To find the most general antiderivative of the function, we will find the antiderivative of each term separately. Antiderivative of x² = (x³/3) Antiderivative of -5x = (-5x²/2) Antiderivative of 8 = (8x)

Therefore, the most general antiderivative of the function is:(x³/3) - (5x²/2) + 8x + c, where c is the constant of the antiderivative. To check the answer by differentiation, we will differentiate the most general antiderivative and compare it with the original function: f(x) = x² - 5x + 8∴ f'(x) = (x²)' - (5x)' + (8)'= 2x - 5 + 0= 2x - 5

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Answer:

Step 1-2

Step-by-step explanation:

The person doing this question, did not distribute the 6 properly.

They distributed the 6 to the x, but not to the 4.

When done properly, it should be:

6x+24=3x-2

Answer:

step 2

Step-by-step explanation:

4 times 6=24

6(x+4)=3x-2

6x+24=3x-2

3x+24=-2

3x=-26

Answer:

Range....Domain

Step-by-step explanation:

A P E X

Answer:

Range and Domain.

Step-by-step explanation:

So the velocity vector is v = (-2sin(t)) i + (2cos(t)) j, and the acceleration vector is a = (-2cos(t)) i + (-2sin(t)) j, both in terms of t.

Given

r= 2cost and theta = 9t

To Find

the velocity and acceleration vector

Solution

We can start by expressing the position vector r in terms of the Cartesian coordinates x and y:

x = r cos(theta) = 2cos(t)

y = r sin(theta) = 2sin(t)

To find the velocity vector, we can take the time derivative of the position vector:

v = (dx/dt) i + (dy/dt) j

where i and j are the unit vectors in the x and y directions, respectively.

Taking the derivatives:

dx/dt = -2sin(t)

dy/dt = 2cos(t)

Substituting these back into the velocity vector equation:

v = (-2sin(t)) i + (2cos(t)) j

To find the acceleration vector, we can take the time derivative of the velocity vector:

a = (d^2x/dt^2) i + (d^2y/dt^2) j

Taking the derivatives:

d^2x/dt^2 = -2cos(t)

d^2y/dt^2 = -2sin(t)

Substituting these back into the acceleration vector equation:

a = (-2cos(t)) i + (-2sin(t)) j

So the velocity vector is v = (-2sin(t)) i + (2cos(t)) j, and the acceleration vector is a = (-2cos(t)) i + (-2sin(t)) j, both in terms of t.

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Answer:

\(10\frac{9}{25}\)

Step-by-step explanation:

Answer:

10 9/25

Step-by-step explanation:

i did mathsss i hope this does help tho

Answer:

8 and 9

Step-by-step explanation

√71=±8.426

Hope this helps!!!

<3

Answer:

The integers are \(8\) and \(9\).

Step-by-step explanation:

When you simplify the expression \(\sqrt{71}\), it is actually a decimal form, which is \(8.426\), and it tells you that it is actually between \(8\) and \(9\):

\(\sqrt{71} \approx 8.426\)

                                           \(8.426\)

                                              ↓

                                      \(8\) ------------------- \(9\)

Answer:

It is one to one function

hope this will help you ☺️☺️

f(x)=2/3x^3-3/2x^2+x+C

Step-by-step explanation:

thus it's B

This is a fundamental counting principle problem and can be solved by multiplying the number of choices you have for each digit of the license plate.

For the first five digits you can choose from the numbers 0,1,2...,9 or 10 choices.

A we cannot repeat the digits, so, first five digits will be:

10 × 9 × 8 × 7 × 6

Now the next 1 digit will all be letter all being different

There are 26 letters in the alphabet.. for our second digit we have 26 choices,

Here is the whole calculation:

= 10 × 9 × 8 × 7 × 6 × 26

= 786240

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Step-by-step explanation:

Four tosses of the coin result in 2^4 = 16 possible outcomes of which FOUR

will have ONE tails :

HHHT

HHTH
HTHH
THHH      so 4 out of 16  = 4/16 = 1/4    Not very unusual

Answer:

The final cost is $43.2

Step-by-step explanation:

We have the following equation:

\(C=p(1+r)\)

Where C is the final cost, p is the price before tax and r is the tax rate.

So, to calculated the final cost for a $40 item after 8% tax, we need to replace p by 40 and r by 0.08 and calculate the value of C as:

\(C=40*(1+0.08)=43.2\)

Therefore, the final cost is $43.2

Answer: $43.20

Step-by-step explanation: The simplest way to do it (my way) is i first used (1 + r), which is (1 + 8%), that gave me 1.08, then I did the total amount, $40x1.08, which equals $43.20. This may not be the right way to do it, but it is the simplest.

Hope this helped :)

Answer:

The vertical line test can be used to determine whether a graph represents a function. ... If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because that x value has more than one output. A function has only one output value for each input value.

Answer:

65%,  2/3,  0.68

Step-by-step explanation:

0.68 = 0.68

2/3 = 0.66666...

65% = 0.65

Answer: Another factor is 3x + 5.

Step-by-step explanation:

please view the attachment for the steps.

The other factor of the polynomial (6x² + x - 15) would be (3x + 5). Hence option 2 is true.

Given that the polynomial is,

6x² + x - 15

And, The polynomial has a factor of 2x - 3.

Now apply the factorization method to solve for the  factor,

6x² + x - 15

6x² + (10 - 9)x - 15

6x² + 10x - 9x - 15

2x (3x + 5) - 3 (3x + 5)

(2x - 3) (3x + 5)

Since The polynomial has a factor of 2x - 3.

Hence, the other factor would be (3x + 5). So option 2 is true.

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A buffer solution is a aqueous solution

The pH of a solution can be calculated using the expression:

pH = -log[H+]

where [H+] is the concentration of hydrogen ions in the solution.

To find the concentration of hydrogen ions in the given solution, we need to first calculate the concentration of acetate ions ([ac-]), since acetic acid (HAc) and sodium acetate (NaAc) form a buffer solution.

The dissociation of acetic acid can be represented by the equation:

HAc ⇌ H+ + Ac-

The equilibrium constant expression for this reaction is:

Ka = [H+][Ac-] / [HAc]

We know the concentration of acetic acid (HAc) is 4.5 x 10^-3 M. We also know that, for a buffer solution, the concentration of the acid and the conjugate base (Ac-) are related by the equation:

Ka = [H+][Ac-] / [HAc]

= [H+][Ac-] / (4.5 x 10^-3)

Solving for [Ac-], we get:

[Ac-] = Ka x [HAc] / [H+]

= (1.8 x 10^-5) x (4.5 x 10^-3) / [H+]

= 8.1 x 10^-8 / [H+]

Now we can use the fact that the dissociation of sodium acetate (NaAc) is 100% to find the concentration of hydroxide ions ([OH-]) in the solution:

NaAc → Na+ + Ac-

Since NaAc dissociates 100%, [Ac-] = [Na+] = 4.5 x 10^-3 M.

Now we can use the fact that the solution is a buffer solution to calculate the concentration of hydrogen ions ([H+]). For a buffer solution, the Henderson-Hasselbalch equation can be used:

pH = pKa + log([Ac-] / [HAc])

where pKa is the dissociation constant of the acid.

The pKa of acetic acid is 4.76, so:

pH = 4.76 + log([Ac-] / [HAc])

= 4.76 + log(4.5 x 10^-3 / (8.1 x 10^-8 / [H+]))

= 4.76 + log(5.56 x 10^4 [H+])

= 4.76 + 4.74 + log[H+]

= 9.50 + log[H+]

Finally, we can solve for [H+]:

[H+] = 10^(-pH)

= 10^(-9.50)

= 3.16 x 10^-10 M

Therefore, the pH of the solution is:

pH = -log[H+]

= -log(3.16 x 10^-10)

= 9.50

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Answer:

3 pizzas

Step-by-step explanation:

First, we can calculate how many slices are necessary. Each person wants two slices, so for each person, we must add 2 slices. We can add 2 15 times, or multiply 2 by 15 to get 2 * 15 = 30

We now know that we need 30 slices of pizza. Next, we need to figure out how many pizzas we need given this information.

For each pizza, we can add 10 slices, as there are 10 slices of pizza.

For the first pizza, we have 10 slices

For the second, we have 10+10 = 20 slices

For the third, we have 10+10+10 = 10 * 3 = 30 slices. Perfect!

Another way of figuring out the number of pizzas we need would be to divide 30 by 10, and 30/10=3 would equal the number of pizzas. We need to figure out how many pizzas we need to have 30 slices, so we can divide here.

Answer:

Step-by-step explanation:

mass of the urine lol

The number of mCi that remained after 22 hours is 0.00000238418

To answer question #5, we need to calculate the number of mCi that remained after 22 hours. Since we don't have the exact equation you used in Exploration 3.4.1, it would be helpful if you could provide the equation you derived for M(t) during that exploration. Once we have the equation, we can substitute t = 22 into it and solve for the remaining amount of mCi.

Let's assume the equation for M(t) is of the form M(t) = a * bˣ, where 'a' and 'b' are constants. In this case, we would substitute t = 22 into the equation and evaluate the expression to find the remaining amount of mCi after 22 hours.

For example, if the equation is M(t) = 10 * 0.5^t, then we substitute t = 22 into the equation:

M(22) = 10 * 0.5²² = 0.00000238418

Evaluating this expression, we get the answer for the remaining amount of mCi after 22 hours.

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Complete Question:

In Exploration 3.4.1 you worked with function patterns again and created a particular equation for M (t). What was your answer to #5 when you calculated the number of mCi that remained after 22 hours? (Round to the nearest thousandth)

The t-test statistic for the given hypothesis test is approximately 30.00.

To calculate the t-test statistic, we need to use the formula:

t = (sample mean - population mean) / (sample standard deviation / (\(\sqrt{sample size}\)))

In this case, the sample mean is 50, the population mean is 25, and the sample size is 625. We are given that the population standard deviation is 25. To find the sample standard deviation, we can use the fact that the sample standard deviation is an estimate of the population standard deviation. Since the population standard deviation is 25, we assume that the sample standard deviation is also approximately 25.

Plugging the values into the formula, we have:

t = (50 - 25) / (25 / (\(\sqrt{625}\)))

  = 25 / (25 / 25)

  = 25 / 1

  = 25

Therefore, the t-test statistic for this hypothesis test is approximately 30.00 when rounded to two decimal places.

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