Using a graphing calculator find the value of tα/2 for a 95% confidence interval when the sample size is 24.

Examining the figure, quadrilateral PQUV is a parallelogram

A parallelogram is a quadrilateral, which is a polygon with four sides. It is a special type of quadrilateral characterized by several distinct properties.

In this case, we assumed that

In addition, the sides as mentioned are parallel to each other

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Answer:  I can't find the answer :(

Step-by-step explanation: :(                                                                                                  

Answer:

-4*100^2 + 8 *100 + 8

-4 * 100^2 + 800 + 8

-4 * 10000 + 808

-40000 + 808

= -39192

-39192 is the answer

Step-by-step explanation:

Based on the information in the graph, we can infer that the total mass of the six samples of magnesium sulfate is 33.87g.

To calculate the total mass of the magnesium sulfate samples we must perform the following operation; We must add all the values as shown below.

According to the previous operation, the total mass of the samples would be 33.87g of magnesium sulfate.

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Answer:

Step-by-step explanation:

10: 10 same denominator

10: 10

5/10 - 3/10 = 2/10 5 - 2 = 3

Answer: 3 2/10

The work required to pump the water out of the spout is approximately 64,307,077 ft-lb

To find the work required to pump the water out of the spout, we need to calculate the weight of the water in the tank and then convert it to work using the formula: work = force × distance.

First, let's calculate the volume of water in the tank. The frustum of a cone can be represented by the formula: V = (1/3)πh(r1² + r2² + r1r2), where r1 and r2 are the radii of the two bases and h is the height.

Given r1 = 3 ft, r2 = 6 ft, and h = 12 ft, we can calculate the volume:

V = (1/3)π(12)(9 + 36 + 18) = 270π ft³

Now, we can calculate the weight of the water using the density of water:

Weight = density × volume = 62.5 lb/ft³ × 270π ft³ ≈ 53125π lb

Next, we convert the weight to force by multiplying it by the acceleration due to gravity (32.2 ft/s²):

Force = Weight × acceleration due to gravity = 53125π lb × 32.2 ft/s² ≈ 1709125π lb·ft/s²

Finally, we can calculate the work by multiplying the force by the distance. Since the water is being pumped out of the spout, the distance is equal to the height of the frustum, which is 12 ft:

Work = Force × distance = 1709125π lb·ft/s² × 12 ft ≈ 20509500π lb·ft ≈ 64307077 lb·ft

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Answer:

7.2 million dollars

Step-by-step explanation:

The domain of the function the complete set of possible values of the independent variable. In this case the domain includes all real numbers except 189.

From;

T(p) = 0.50 (p - 189)

When p = 203.4 million dollars

T(p) = 0.50 (203.4 - 189)

T(p) = 7.2 million dollars

Label XY with 3.

Label angle X with 53 degrees.

Label angle Y with 90 degrees.

Label angle C with 37 degrees.

Label angle A with 53 degrees.

Label BC with 4.

Label AC with 5.

Answer: i don't know if you want degrees or the lengths so i did both

∠ACB = 37°

∠BAC = 53°

∠ZXY = 53°

∠XYZ = 90°

∠XZY = 37°

∠ABC = 90°

BC = 4

AC = 5

AB = 3

YZ = 4

XY = 3

XZ = 5

Step-by-step explanation:

37 + 90 = 127

180 - 127 = 53

37 + 90 + 53 = 180

Answer:

It produces 120 bottles in one hour.

Step-by-step explanation:

This question can be solved by proportions.

24 Pepsi bottles of one liter capacity each in 12 minutes

24/12 = 2 bottles per minute.

How many Pepsi bottles does it produce in one hour?​

One hour has 60 minutes. So

60*2 = 120

It produces 120 bottles in one hour.

Answer:

\(\frac{31}{50}-\frac{4i}{25}\)

Step-by-step explanation:

The statistical technique used to summarize the degree to which two sets of data points fall on a straight line is called linear regression analysis.

Linear regression analysis is a statistical method that examines the relationship between two quantitative variables, typically represented by an independent variable (x) and a dependent variable (y). The technique determines the best-fit line that describes the relationship between these two variables based on the given data points.

The line is determined using a mathematical formula that minimizes the sum of the squared differences between the observed data points and the predicted values on the line. This line is known as the regression line, and the process of finding it is known as regression analysis.

The slope of the regression line represents the degree of the relationship between the two variables, with a positive slope indicating a positive relationship and a negative slope indicating a negative relationship.

The correlation coefficient, also calculated during regression analysis, provides a measure of the strength and direction of the linear relationship between the two variables.

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The sum of the terms is x^7+10x^4+4x^3-5x^11-10x^6

To determine the value, we need to know that algebraic expressions are described as expressions that are composed of factors, constants, variables, terms and coefficients.

These algebraic expressions are also identified with the presence of arithmetic operations,

These operations are;

From the information given, we have that;

7x^7+10x^4+4x^3-5x^11-10x^6-6x^7

collect the like terms

7x^7 - 6x^7+10x^4+4x^3-5x^11-10x^6

add the like terms

x^7+10x^4+4x^3-5x^11-10x^6

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14. The trigonometric equation (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = 4

15. In the trigonometric equation 2(cos²θ - sin²θ) = 1, θ = 15°

A trigonometric equation is an equation that contains a trigonometric ration.

14. To find the value of (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45°, we proceed as follows

Since we have the trigonometric equation (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45°,

We know that sin47° = sin(90 - 43°) = cos43°. So, substituting this into the equation, we have that

(sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = (cos43°/cos43°)² + (cos43°/cos43°)² - 4cos²45°

= 1² + 1² - 4cos²45°

We know that cos45° = 1/√2. So, we have

1² + 1² - 4cos²45° = 1² + 1² - 4(1/√2)²

= 1 + 1 + 4/2

= 2 + 2

= 4

So, (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = 4

15. If 2(cos²θ - sin²θ) = 1 and θ is a positive acute angle, we need to find the value of θ. We proceed as follows

Since we have the trigonometric equation 2(cos²θ - sin²θ) = 1

We know that cos2θ = cos²θ - sin²θ. so, substituting this into the equation, we have that

2(cos²θ - sin²θ) = 1

2(cos2θ) = 1

cos2θ = 1/2

Taking inverse cosine, we have that

2θ = cos⁻¹(1/2)

2θ = 30°

θ = 30°/2

θ = 15°

So, θ = 15°

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Answer:

0.325

Step-by-step explanation:

Let A represent the event: winning a prestigious scholarship
Let B represent the event: plays a varsity sport

Given

Therefore the probability that someone wins the scholarship given that they play a varsity sport is 0.325

Answer:

Step-by-step explanation:

We can use the method of undetermined coefficients to solve this differential equation. First, we will need to find the solution to the homogeneous equation and the particular solution to the non-homogeneous equation.

For the homogeneous equation, we will use the form y"+ky=0, where k is a constant. We can find the solutions to this equation by letting y=e^mx,

y"=m^2e^mx -> (m^2)e^mx+k*e^mx=0, therefore (m^2+k)e^mx=0

(m^2+k) should equal 0 for the equation to have a non-trivial solution. Therefore, m=±i√(k), and the general solution to the homogenous equation is y=A*e^i√(k)x+Be^-i√(k)*x.

Now, we need to find the particular solution to the non-homogeneous equation. We can use the method of undetermined coefficients to find the particular solution. We will let yp=a0+a1x+a2x^2+.... As the derivative of a sum of functions is the sum of the derivatives, we get

yp″=a1+2a2x....yp‴=2a2+3a3x+....

Substituting the general solution into the non-homogeneous equation, we get

a0+a1x+a2x^2+...+2a2x+3a3x^2+...=Y(4)

So, the coefficient of each term in the expansion of the left hand side should equal the coefficient of each term in the expansion of the right hand side. Since there is only one term on the right hand side, we get the recurrence relation:

a(n+1)=Y(n-2)/n^2

From this relation, we can find all the coefficients in the expansion for the particular solution. Using this particular solution, we can find the total solution to the differential equation as the sum of the homogeneous solution and the particular solution.

Answer:

  S = W/4

Step-by-step explanation:

To solve the equation for S, divide by its coefficient.

  W = 4S

  W/4 = (4S)/4 . . . . . . . . . . divide both sides by 4

  W/4 = S(4/4) = S(1) = S . . . simplify

  S = W/4

The correct answer is A) The recipe will need 16 cups of sauce and three and a half teaspoons of oregano for 8 servings.

To determine the amount of sauce and oregano needed to make 8 servings, we can use the ratio of sauce to oregano from the table.

According to the table, for 3 servings, 6 cups of sauce are used along with 1 & 1/2 teaspoons of oregano. We need to find the ratio of sauce to oregano to scale it up for 8 servings.

Ratio of sauce to oregano:

6 cups of sauce / 1 & 1/2 teaspoons of oregano = 6/1.5 = 4 cups of sauce per teaspoon of oregano

Now, for 8 servings, we need to multiply the ratio by the number of teaspoons of oregano required:

8 servings * 1 teaspoon of oregano = 8 teaspoons of oregano

Therefore, for 8 servings, we would need:

8 teaspoons of oregano * 4 cups of sauce per teaspoon of oregano = 32 cups of sauce

Therefore, the correct answer is A) The recipe will need 16 cups of sauce and three and a half teaspoons of oregano for 8 servings.

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Translate the word problem into a system of equations, with x representing true/false questions and y representing multiple choice questions:

(1) \(x+y=20\) <-- a test has 20 total questions

(2) \(4x+8y=100\) <-- the test is worth 100 total points

Now we have a system of two equations with two unknowns, which we can solve with the elimination method.

Let's multiply equation (1) by -4 so that we can eliminate x from the system:

\(-4x-4y=-80\)

Now, add this new equation to equation (2) to eliminate x so that we only have one variable left:

\(4y=20\)

Solve for y:

\(y=5\)

Now, substitute this value for y into either the original equation (1) or (2). I will do equation 1 for simplicity:

\(x+5=20\)

Solve for x:

\(x=15\\\)

Notice that we now have values for both x and y, so we are done. We now know that there are 15 true/false questions and 5 multiple choice questions on the test!

The number is 6.35.

The Natural numbers are all numbers 1, 2, 3, 4… They are the numbers you usually count and they will continue on into infinity.

6.35 is a natural number.

The total amount paid in the first month would be $32 for the minimum payment plus $9.20 for the interest, totaling $41.20.

If you have a credit card with an annual percentage rate (APR) of 30% and a minimum payment requirement of 8% of the balance, and you have a balance of $400 on the credit card, you decide to stop charging and pay it off by making the minimum monthly payment each month, here's how it would work:

The minimum monthly payment would be 8% of the balance, which is 0.08 x $400 = $32.

Each month, you would make a payment of $32 towards your credit card balance. However, keep in mind that the interest will continue to accrue on the remaining balance.

Since the APR is 30%, the monthly interest rate would be 30% / 12 = 2.5%.

To calculate the interest charged each month, you multiply the remaining balance by the monthly interest rate. For example, after the first payment, the remaining balance is $400 - $32 = $368. The interest charged for that month would be 2.5% x $368 = $9.20.

Therefore, the total amount paid in the first month would be $32 for the minimum payment plus $9.20 for the interest, totaling $41.20.

Each month, you would continue making the minimum payment, and the interest charged would be based on the remaining balance. The process would continue until the balance is paid off in full.

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Answer:

11 cows and 6 ducks

Step-by-step explanation:

if all are cow then 68 legs.

68 - 56 = 12

12÷(4-2) = 6

6 ducks = 12 legs

17 - 6 = 11

11 cows = 44 legs

check: 12+44 = 56 (correct)

Answer:

Step-by-step explanation:

let c= cows, d= duck

cows=4 legs

dock=2 legs

we know that are in total 17 heads

c+d=17

d=17-c

4c+2d=56

4c+2(17-c)=56

4c+34-2c=56

2c=56-34=22

c=22/2=11

we have 11 cows

and 6 ducks  17-11=6

12 legs (ducks)+44 legs(cows)=56

Answer:

what are the options???

Answer: They are like terms and terms

Hope this helps :)

Step-by-step explanation:

18p and 3p are terms that happen to have the same variable to be like terms.

Answer:

x is -1/b yw

Step-by-step explanation:

The arrow is at a height of 48 ft after approx. 3 - √6 s and after 3 + √6 s.

To find the time it takes for the arrow to reach a height of 48 ft, we can use the formula for the height of the arrow:

s = v0t - 16t^2

Here, s represents the height of the arrow, v0 is the initial velocity, and t is the time.

Given that the initial velocity, v0, is 96 ft/s and the height, s, is 48 ft, we can set up the equation:

48 = 96t - 16t^2

Now, let's solve this equation to find the time it takes for the arrow to reach a height of 48 ft.

Rearranging the equation:

16t^2 - 96t + 48 = 0

Dividing the equation by 16 to simplify:

t^2 - 6*t + 3 = 0

We now have a quadratic equation in the form of at^2 + bt + c = 0, where a = 1, b = -6, and c = 3.

Using the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values:

t = (6 ± √((-6)^2 - 413)) / (2*1)

t = (6 ± √(36 - 12)) / 2

t = (6 ± √24) / 2

Simplifying the square root:

t = (6 ± 2√6) / 2

t = 3 ± √6

Therefore, the arrow reaches a height of 48 ft after approximately 3 + √6 seconds and 3 - √6 seconds.

In summary, the arrow takes approximately 3 + √6 seconds and 3 - √6 seconds to reach a height of 48 ft, assuming an initial velocity of 96 ft/s.

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Note the complete question is

The height of an arrow shot upward can be given by the formula s = v0*t - 16*t², where v0 is the initial velocity and t is time.How long does it take for the arrow to reach a height of 48 ft if it has an initial velocity of 96 ft/s?  

Solve (t-3)^2=6

The arrow is at a height of 48 ft after approx. ___ s and after ___ s.

The distance travelled by the driver on the 4th day has a value of 972 km

If the driver traveled 1,087 km in the first three days, her average daily distance over the first three days was:

distance = 1,087 km / 3 days = 362.33 km/day (rounded to two decimal places)

If she has 972 km left to travel at the end of the fourth day, she has already traveled:

distance = 1,087 km

Therefore, the total distance she needs to travel is the remaining distance to go i.e. 972 km

Therefore, the driver traveled 972 km on the fourth day.

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The mean of the data set is 82.77

If we want to find the mean, we would have to put it at the back of our minds that the mean is the same as the average. As such, we would have to take the sum of all the values that have been listed in the data set and divide by the total number of the data.

The first step is to arrange the data set orderly from smallest to largest;

70, 71,79, 82,88,85,87,91,92

We have nine values in the data set thus the mean is;

70+71+79+82+88+85+87+91+92/9= 745/9= 82.77

Hence the mean of the data set is 82.77

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Answer:

Step-by-step explanation:

(0,0)

i hope this helps

Answer:

Y=KX so its 10=K2

Step-by-step explanation:

Plug in the Number OR K=y/x

Answer:

A.  (x - 80)² = -320(y = 20)

B.  Focus:  (80, -60)

     Directrix:  y = 100

     Axis of symmetry:  x = 80

Step-by-step explanation:

If the spider's movement is modeled by a parabola, and its maximum height is 20 mm halfway across a horizontal distance of 160 mm, then:

Standard form of a parabola with a vertical axis of symmetry:

\(\boxed{(x-h)^2=4p(y-k) \quad \textsf{where}\:p\neq 0}\)

If p > 0, the parabola opens upwards, and if p < 0, the parabola opens downwards.

Substitute one of the x-intercepts and the vertex into the formula and solve for p:

\(\implies (0-80)^2=4p(0-20)\)

\(\implies (-80)^2=4p(-20)\)

\(\implies 6400=-80p\)

\(\implies p=-80\)

Substitute the found value of p and the vertex into the formula to create the equation of the parabola in standard form:

\(\implies (x-80)^2=4(-80)(y-20)\)

\(\implies (x-80)^2=-320(y-20)\)

Given:

\(\begin{aligned}\textsf{Focus}&=(h,k+p)\\&=(80,20-80)\\&=(80,-60)\end{aligned}\)

\(\begin{aligned}\textsf{Directrix}:y&=(k-p)\\ \implies y&=(20-(-80))\\ \implies y&=100\end{aligned}\)

\(\begin{aligned}\textsf{Axis of symmetry}:x&=h\\ \implies x&=80\end{aligned}\)