A nationwide survey found that 62% of American adults drink coffee regularly. A professor wondered if the proportion of coffee drinkers among MU students would differ from this nationwide proportion. He planned to conduct a hypothesis test at the .05 level of significance.
Question F1: Formulate the hypotheses for the test. (Note: Some of the choices are about p and others are about p¯. Decide which is correct and choose your response accordingly.)
Group of answer choices
H0: p¯=.62
HA: p¯≠.62
H0: p≠.62
HA: p=.62
H0: p¯≠.62
HA: p¯=.62
H0: p=.62
HA: p≠.62
Flag question: Question 20
Question 205 pts
Question F2: He selected a random sample of 100 MU students and found that 72 of them drank coffee regularly. Choose the appropriate formula for the test statistic and find its value.
Group of answer choices
2.22
2.06
2.34
1.98
2.14
Flag question: Question 21
Question 215 pts

Answer:

y = x^2 - 6x + 3

Step-by-step explanation:

let the equation of the parabola (in standard form) be y = ax^2 + bx + c

sub (3,-6), (1,-2) and (6,3):

-6 = a(3)^2 + b(3) + c

-6 = 9a + 3b + c

c = -6 - 9a - 3b --(1)

-2 = a(1)^2 + b(1) + c

-2 = a + b + c --(2)

3 = a(6)^2 + b(6) + c

3 = 36a + 6b + c --(3)

sub (1) into (2):

-2 = a + b - 6 - 9a - 3b

b = -(4a + 2) --(4)

sub (1) and (4) into (3):

3 = 36a + 6(-4a-2) - 6 - 9a - 3(-4a-2)

3 = 36a -24a - 12 - 6 - 9a + 12a + 6

15a = 15

a = 1

sub a = 1 into (4):

b = -(4(1) + 2)

b = -6

sub a = 1 and b = -6 into (1):

c = -6 - 9(1) - 3(-6)

c = 3

therefore, equation of parabola is y = x^2 - 6x + 3

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Answer:

A

Step-by-step explanation:

Given

x = y² + 6y + 1

To complete the square

add/subtract ( half the coefficient of the y- term )² to y² + 6y

x = y² + 2(3)y + 9 - 9 + 1

  = (y + 3)² - 8

The vertex form of the equation of a parabola is,

⇒ x = (y + 3)² - 8

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The standard form of the equation of a parabola is,

⇒ x = y² + 6y + 1.

Now, We can simplify as;

⇒ x = y² + 6y + 1

⇒ x = y² + 6y + 9 - 9 + 1

⇒ x = (y + 3)² - 8

Thus, The vertex form of the equation of a parabola is,

⇒ x = (y + 3)² - 8

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Answer:

Step-by-step explanation:

If the graphs intersect at one point, the solution is the point of intersection.

If the graphs are parallel, there is no solution.

If the graphs are identical, there are infinitely many solutions.

The cost of 1 shirt and 1 tie in the clothing store is $15 and $3 respectively.

Let the cost of 1 shirt be $x.

Let the cost of 1 tie be $y.

Hence we get

3x + 5y = 60                                [1]

2x + 3y = 39                                [2]

Multiplying equation [1] by 2 and equation [2] by 3 we get

6x + 10y = 120                                [3]

6x + 9y = 117                                   [4]

Subtracting equation [4] from equation [3] we get

y = 3

Putting the value of y in equation [1] gives us

3x + 15 = 60

or, 3x = 45

or, x = 15

Hence one shirt costs $15 and 1 tie costs $3.

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Answer:

Step-by-step explanation:

85 degrees. Step-by-step explanation: From the diagram, it is clearly visible that the angle ∠ABC is formed by intersections of two chords AE and CD of the circle.

Answer:

85 degrees

Step-by-step explanation:

Juliet was charged $18 for driving 120 miles.

Given,

The rent of car per day = $80

The charge for per miles driven = $0.15

Juliet was charged a total of $98 for the rental and mileage.

We have to find the total miles of driving;

Here,

Charge for miles driven = Total charge - Rent of car for a day

Charge for miles driven = 98 - 80

Charge for miles driven = $18

Now,

Total miles driven = Charge for miles driven / Charge for one mile

Total miles driven = 18/0.15

Total miles driven = 120

That is,

Juliet was charged $18 for 120 miles of driving.

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The function f(x) = −3x+2, implies that the corresponding values of f(−4), f(5)+8 and  f(3)−f(6) are 14, -5 and 9

A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

Given: f(x)=−3x+2, We are to evaluate: a. f(−4) b. f(5)+8 c. f(3)−f(6)

a. For f(−4), substitute x = -4 into f(x):

f(x)=−3x+2

f(−4) = -3(-4) + 2  = 12 + 2 = 14

b. For f(5)+8, substitute x = 5 into f(x) and then add 8:

f(5)+8 = (-3(5) +2)+ 8 = -15 +2 + 8 = -5

c.  For f(3)−f(6) substitute x = 3 and x = 6 into f(x) and evaluate separately and then subtract:

f(3)−f(6) = (-3(3)+2) − (-3(6)+2)

           = (-9+2) − (-18+2)

           = -7-(-16)  =  -7 + 16 = 9

Therefore, the values of f(−4), f(5)+8 and  f(3)−f(6) are 14, -5 and 9 respectively

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Answer:

c

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

2.39/16 =$0.206

3.19/20=$0.159

the better buy : 20 ounces for $3.19

Step-by-step explanation:

Step-by-step explanation:

7x+3y=42.

y=-5x+30.

7x+3(-5x+30)=42

7x-15x+90=42

8x=42-90

-8x=-48

x=-48/-8

x=6

y=-5x+30

y=-5×6+30

=-30+30

y=0

(6,0)

The 95% confidence interval for the population mean SAT score is given as follows:

(1340, 1460).

The confidence interval is calculated using the t-distribution, as the standard deviation for the population is not known, only for the sample.

The bounds are obtained according to the equation defined as follows:

\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)

In which the variables of the equation are presented as follows:

In the context of this problem, the values of these parameters are given as follows:

\(\overline{x} = 1400, n = 64, s = 240\)

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 64 - 1 = 63 df, is t = 1.998.

Then the lower bound of the interval is of:

1400 - 1.998 x 240/sqrt(64) = 1340.

The upper bound of the interval is of:

1400 + 1.998 x 240/sqrt(64) = 1460.

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Answer:

80 = x

Step-by-step explanation:

The base angles are the same if the side lengths are the same

The unmarked angle is 50 degrees

The sum of the angles is a triangle is 180 degrees

180= 50+50+x

180 = 100 +x

180 -100 = 100+x-100

80 = x

Answer:

80°

Step-by-step explanation:

In an isosceles triangle, if the two sides are the same length, then the two angles formed on the base line are equal.

The other angle on the base line is also equal to 50°.

Angles in a triangle add up to 180°.

x° + 50° + 50° = 180°

x° + 100° = 180°

x° = 180° - 100°

x° = 80°

The statement "If y1 and y2 are solutions to y''-6y²+5y=4x, then 2y1+3y2 is also a solution to the ODE" is false.

The given ODE is:

y'' - 6y² + 5y = 4x

Now, let y1 and y2 be two solutions of the above ODE. Then,

y1'' - 6y1² + 5y1 = 4x ... (1)

y2'' - 6y2² + 5y2 = 4x ... (2)

Now, we need to show whether 2y1 + 3y2 is also a solution of the ODE. So, let's find its second derivative:

(2y1 + 3y2)'' = 2y1'' + 3y2''

Substituting the values from equations (1) and (2), we get:

(2y1 + 3y2)'' = 2(6y1² - 5y1 + 4x) + 3(6y2² - 5y2 + 4x)

Simplifying, we get:

(2y1 + 3y2)'' = 12(y1² + y2²) - 10(2y1 + 3y2) + 10x

So, we can see that 2y1 + 3y2 is not a solution of the ODE, as it does not satisfy the ODE. Therefore, the statement "If y1 and y2 are solutions to y''-6y²+5y=4x, then 2y1+3y2 is also a solution to the ODE" is false.

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Answer:

x = 68°

Step-by-step explanation:

This is an isosceles triangle, which means the two base angles will be the same. (56° and 56°)

All triangles angles must add up to 180, so if we take 180-56-56 we will find the missing angle (x).

180-56-56 = 68

x = 68°

The given information is:

- The function of decay is:

Where A0 is the initial amount of strontium-90, A is the amount present at time t (in years).

- The initial amount is 800 grams.

a. What is the decay rate of strontium-90?

The given formula is written in the form:

Where r is the decay rate in decimal form, so:

The decay rate is -2.44%.

b. How much strontium-90 is left after 30 years?

Replace t=30 and solve:

There is 384.8 grams after 30 years.

c. When will only 200 g of strontium-90 be left?

A(t)=200g, then replace it and solve for t:

There will be 200 g left after 56.8 years.

d. What is the half-life of strontium-90?

The half-life is when A(t)=A0/2, then if we replace this into the decay formula we obtain:

The half-life of strontium-90 is 28.4 years.

Answer: 3\(\sqrt{x} 7\)

Step-by-step explanation:

3 under root 7

\( \sf {3{\sqrt{7}}} \\\\ \implies \sf{3.7^{\dfrac{1}{2}}} \\\\ \implies \sf{ (3^2)^{\dfrac{1}{2}}} \times 7^{\dfrac{1}{2}} \\\\ \implies \sf{ (9\times7)^{\dfrac{1}{2}}} \\\\ \implies \sf{63^{\dfrac{1}{2}}} \)

2.4329268293

if you rounded the answer will be 2

Answer:

the answer for c is 2

Step-by-step explanation:

\(\frac{798}{8* 41} = \frac{399}{164} = 2.43\)

2.43≈ 2

According to given triangle the value of cos A = 3/5

We know that cos theta = Adjacent Side / Hypotenuse Side

According to the question given that Adjacent side = 3

And Hypotenuse Side  = 5

Then cos A = 3/5

Hence, option 3 is correct

Each geometrical shape has unique side and angle characteristics that enable us to recognize it. The following is a list of a triangle's key characteristics.

Three vertices, three internal angles, and three sides make up a triangle.

According to the triangle's "angle sum property," a triangle's three inner angles can never add up to more than 180 degrees. Take note of the triangle PQR shown above, where the angles P, Q, and R all add up to 180 degrees.

A closed triangle has three vertices, three sides, and three angles. The symbol for a triangle with the three vertices P, Q, and R is PQR. Sandwiches and signboards in the shape of triangles are the most prevalent triangle-shaped objects.

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In the picture there is a triangle with ABC angles. Sides AB=5, BC=3, CA=4. The ratio of CosA=4/5.

Given that,

In the picture there is a triangle with ABC angles.

Sides AB=5, BC=3, CA=4

Trigonometric ratios, which contain the values of all trigonometric functions, are based on the ratio of sides of a right-angled triangle. The ratios of a right-angled triangle's sides with regard to a certain acute angle are known as its trigonometric ratios.

The right triangle's three sides are as follows:

Hypotenuse (the longest side)

Perpendicular (opposite side to the angle)

Base (Adjacent side to the angle)

According to the cos theta formula, the cos of an angle in a right-angled triangle is equal to the ratio of the Adjacent side to the hypotenuse.

Cos A = Adjacent side / hypotenuse

CosA=4/5

Therefore, CosA=4/5.

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Answer:

18 because 6 x 3 = 18 and 9 x 2 =18

Step-by-step explanation:

Answer:

2.8

Step-by-step explanation:

Just substract 7.2 from 10

You get: 2.8

Answer:

2.8

Step-by-step explanation:

because 7.2 plus 2.8 equals

Answer:

X = -2 or X = 8

Explanation:

Answer:

7

Step-by-step explanation:

as it does that F thing where its equal to it....

Answer:

I wont answer for you, but ill guide you in the right direction

Step-by-step explanation:

The table shows the estimated digit and significant figures of each measurement and their representation with x.

Number of Measurement Estimated Digit Significant Figures

14.8 m 3 ✓

$10.25 - ✓

0.05 L - ✓

1.000 g/mL - ✓

1.200 - ✓

6200 cm - ✓

403 kg - ✓

For each measurement, the estimated digit is replaced with an x to represent the number with the correct number of significant figures. The correct representations for each measurement are:

Note that in some cases, the representation requires adding zeros to the right of the decimal point to indicate the number of significant figures. In other cases, the representation requires rounding up or down to the correct number of significant figures.

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Let's see

L=

The arc length with central angle 60° and radius 10 cm is 10.47 cm.

An angle exists the figure formed by two rays, named the sides of the angle, sharing a common endpoint, reaching the vertex of the angle. Angles formed by two rays lie in the plane that includes the rays. Angles are also created by the intersection of two planes. These exist named dihedral angles.

If length of arc with central angle 360° is 2*\(\pi\)*r (r-Radius)

Then length of arc with central angle 60° is \(\dfrac{2\pi r}{6}\).

That is \(\pi\)r/3 =3.14*10/3

                   =10.47 cm

Therefore, the arc length is 10.47 cm.

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Hence, the length of the curve defined by the parametric equations x = 4sin^2(t) and y = 4cos^2(t) over the interval 0 ≤ t ≤ 5π is 20π units.

To find the distance traveled by the particle, we need to calculate the length of the curve defined by the parametric equations x = 4sin^2(t) and y = 4cos^2(t) over the given time interval 0 ≤ t ≤ 5π.

We can use the arc length formula to calculate the length of the curve. The arc length formula for a parametric curve defined by x = f(t) and y = g(t) is given by:

L = ∫[a, b] √[f'(t)^2 + g'(t)^2] dt

where f'(t) and g'(t) are the derivatives of f(t) and g(t) with respect to t.

Let's start by finding the derivatives of x and y with respect to t:

x = 4sin^2(t)

x' = d/dt(4sin^2(t))

= 8sin(t)cos(t)

= 4sin(2t)

y = 4cos^2(t)

y' = d/dt(4cos^2(t))

= -8cos(t)sin(t)

= -4sin(2t)

Now, let's calculate the length of the curve using the arc length formula:

L = ∫[0, 5π] √[x'(t)^2 + y'(t)^2] dt

= ∫[0, 5π] √[16sin^2(2t) + 16sin^2(2t)] dt

= ∫[0, 5π] √[32sin^2(2t)] dt

= ∫[0, 5π] √[32sin^2(2t)] dt

= ∫[0, 5π] 4√[2sin^2(2t)] dt

= 4∫[0, 5π] √[2sin^2(2t)] dt

= 4∫[0, 5π] √[2(1 - cos^2(2t))] dt

= 4∫[0, 5π] √[2(1 - (1 - 2sin^2(t))^2)] dt

= 4∫[0, 5π] √[2(2sin^4(t))] dt

= 4∫[0, 5π] √[8sin^4(t)] dt

= 4∫[0, 5π] 2sin^2(t) dt

= 8∫[0, 5π] sin^2(t) dt

We can use the trigonometric identity sin^2(t) = (1 - cos(2t))/2 to simplify the integral further:

L = 8∫[0, 5π] sin^2(t) dt

= 8∫[0, 5π] (1 - cos(2t))/2 dt

= 4∫[0, 5π] (1 - cos(2t)) dt

= 4∫[0, 5π] dt - 4∫[0, 5π] cos(2t) dt

The integral of dt over the interval [0, 5π] is simply the length of the interval, which is 5π - 0 = 5π. The integral of cos(2t) over the same interval is zero since the cosine function is periodic with period π.

Therefore, the length of the curve is given by:

L = 4(5π) - 4(0)

= 20π

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Answer:

c = 17 ft

Step-by-step explanation:

c=a2+b2=82+152=17ft

Answer:

17

Step-by-step explanation:

a2+b2=c2

8^2+15^2=c2

64 + 225 = 289

√289 = 17

hope it helps :-)

Answer:

Step-by-step explanation:

Area of a triangle: .5(b*h)

which means that

.5(4(x-1)*(2x+5))=30

mulitply the two equations

(4x-4)(2x+5) = 8x²+12x-20

distribute the 1/2

.5(8x²+12x-20)

4x²+6x-10 = 30

divide both sides by 2

2x²+3x-5= 15

move everything to one side

2x²+3x-20=0

not sure if you need to solve it but x= 2.5 or x= -4

Answer:

50+((10n) =

so 50 is how much it cost to walk in the park and 10 is how much each ride (n) cost soif you know how many rides your ride you times that by 10 the add 10 to 50 and you get how much it will cost you for the day