If 30 gumballs can be purchased for 3 dollars, write a function that represents the cost in cents of ‘d' dozen gumballs.

Final answer:

The test statistic for the hypothesis test regarding the proportion of veterinary clinics that do not treat large animals is approximately 5.11, calculated using the formula for the test statistic of a proportion.

Explanation:

The student is asking about calculating a test statistic for a hypothesis test concerning the proportion of veterinary clinics that do not treat large animals such as cows and horses. The proportion as per the American Veterinary Medical Association's belief is 0.5, and the survey conducted has resulted in 88 out of 120 clinics stating they do not treat large animals. To find the test statistic, we can use the formula for the test statistic of a proportion:

Test Statistic (Z) = (p - P₀) / √(P₀(1 - P₀)/n), where p is the sample proportion, P₀ is the null hypothesis proportion, and n is the sample size.

In this case:

p = 88/120

P₀ = 0.5 (as per the hypothesis)

n = 120

Substituting these values, we get:

Z = (88/120 - 0.5) / √(0.5 * (1 - 0.5) / 120) = (0.7333 - 0.5) / √(0.25 / 120) = 0.2333 / √(0.0020833) = 0.2333 / 0.04564 ≈ 5.11

Therefore, the test statistic is approximately 5.11, when rounded to two decimal places.

Question: if a parabola never touches the x axis, then it doesn't have any real roots or solutions

Answer: True

A real solution only occurs if the graph touches or crosses  the x axis, as the x intercept (or root) is a visual indication of a real number solution. In this case, we have 2 complex solutions for the parabola

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Question: What number is equivalent to sqrt(-49) ?

Answer: choice A) 7i

Simplify as follows

sqrt(-49) = sqrt(-1*7^2)

sqrt(-49) = sqrt(-1)*sqrt(7^2)

sqrt(-49) = i*7

sqrt(-49) = 7i

note: be careful not to toss in -7i as one of the answers, because it's not. The square root of a number is exactly one output. For instance, if you take the square root of 25, the result is 5 (not plus or minus 5).

Answer:

(16)

Given the statement: Elmwood st. and oak Dr. are the same distance.

All intersection are perpendicular.

To prove that: Peach Dr. tree is the same distance as Sycamore Ln.

It given that all the intersection are perpendicular which means each interior angles are of [tex]90^{\circ}[/tex]

By rectangle properties:

Since, Elmwood st. and oak Dr. are the same distance.

then, by rectangle properties;

Peach Dr. tree is the same distance as Sycamore Ln            proved!

6.10

(11)

Given: [tex]\angle A \cong \angle T[/tex] , [tex]\overline{MA} \cong \overline{HT}[/tex]

To prove: [tex]\triangle MAX \cong \triangle HTX[/tex]

In ΔMAX and ΔHTX

[tex]\angle A \cong \angle T[/tex]    [Angle]               [Given]

[tex]\overline{MA} \cong \overline{HT}[/tex]      [Side]     [Given]

Vertical angle theorem states that angles that are opposite each other.

Since, these angles are formed when two lines cross each other.

And also vertical angles are congruent to each other.

Since,  [tex]\angle MXA[/tex] , [tex]\angle HXT[/tex]  are vertical angles

[tex]\angle MXA \cong \angle HXT[/tex]      [Vertical angles are congruent]

AAS (Angle-Angle-Side) theorem states that if two angles and a non-included side in one triangle are congruent to two corresponding angles and a non-included side in another triangle, then those triangles are congruent.

Then, by AAS theorem,

[tex]\triangle MAX \cong \triangle HTX[/tex]

(14)

Given: [tex]\overline{AX} \cong \overline{TX}[/tex] , [tex]\angle A \cong \angle T[/tex]

Prove that:  [tex]\overline{MX} \cong \overline{HX}[/tex]

In [tex]\triangle MXA[/tex] and [tex]\triangle HXT[/tex]

[tex]\overline{AX} \cong \overline{TX}[/tex]   [Side]          [Given]

[tex]\angle A \cong \angle T[/tex]       [Angle]                  [Given]

[tex]\angle MXA \cong \angle HXT[/tex]      [Vertical angles are congruent]

ASA (Angle -Side-Angle) theorem states that if two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then these triangles are congruent.

then by ASA theorem;

[tex]\triangle MAX \cong \triangle HTX[/tex]

CPCT [Corresponding Part of Congruent triangles are congruent.]

⇒[tex]\overline{MX} \cong \overline{HX}[/tex] [By CPCT]        proved!

Answer:

Correct choices are A and D.

Step-by-step explanation:

According to the table for the given function [tex]h(x),[/tex] you can write the same table for the inverse function [tex]h^{-1}(x).[/tex] With this aim change [tex]x[/tex] into [tex]h^{-1}(x)[/tex] and [tex]h(x)[/tex] into x:

[tex]\begin{array}{ccccccc}x&2&5&8&11&14&17\\h^{-1}(x)&0&1&2&3&4&5\end{array}[/tex]

Then you can see that points (5,1) and (2,0) are on the graph of the inverse function.

[tex]7x+10=13(12x-3)+14x\qquad\text{use distributive property}\\\\7x+10=(13)(12x)+(13)(-3)+14x\\\\7x+10=156x-39+14x\\\\7x+10=170x-39\qquad\text{subtract 10 from both sides}\\\\7x=170x-49\qquad\text{subtract 170x from both sides}\\\\-163x=-49\qquad\text{divide both sides by (-163)}\\\\\boxed{x=\dfrac{49}{163}}[/tex]

Answer:

Probability states the ratio of number of favorable outcomes to the total number of possible outcomes.

i.e,  [tex]probability = \frac{Number of favourable outcomes }{Total number of possible outcomes}[/tex]

A bag contains:

Brown marble = 4

Green marbles = 3

Red marbles = 2

Purple marble = 1

Total number of possible outcomes = (4+3+2+1) = 10 marbles

P(Brown marbles) = [tex]\frac{4}{10}=\frac{2}{5} = 40\% = 0.4[/tex]

P(Green marbles) = [tex]\frac{3}{10} = 30\% = 0.3[/tex]

P(Red marbles) = [tex]\frac{2}{10}=\frac{1}{5} = 20\% = 0.2[/tex]

and

P(Purple marbles) = [tex]\frac{1}{10}= 10\% = 0.1[/tex]

Answer:The possible outcome would be 10, because 4 brown marbles + 2 red marbles + 1 purple marble+3 green marbles = 10 outcomes!

Step-by-step explanation:

I just did it =w=

Answer:

The correct answer option is [tex]f(x)=-\frac{1}{2} x+3[/tex].

Step-by-step explanation:

We will take easy (clear) points on the graph i.e. (0, 3) and (6, 0) and use them to find the equation of the line given on the graph.

To find the slope:

Slope = [tex]\frac{0-3}{6-0} =-\frac{1}{2}[/tex]

Putting the values of the coordinates of one of the chosen points and slope of the line in the standard form of equation of a line to find the y-intercept (c).

[tex]y=mx+c[/tex]

[tex]3=-\frac{1}{2} (0)+c\\\\c=3[/tex]

So the equation of the graphed line in terms of f(x) will be:

[tex]f(x)=-\frac{1}{2} x+3[/tex]

Answer:

B. 5x - 4y = 12

Step-by-step explanation:

Let's convert this to slope-intercept form to interpret the equation easier.

5x - 4y = 12

Subtract 5x from both sides.

-4y = -5x + 12

Divide both sides by -4.

y = 5/4x - 3

Based on this, we know the slope is 5/4 and the y-intercept is (0, -3). When you count the rise over run in the picture and look at the y-intercept, they match.

The height of Cone Mountain, given the trail length and the radius, would be C. 2,520 feet

How to find the height ?

To find the height of Cone Mountain, we can use the properties of a right circular cone. The key relationship we'll use is the Pythagorean theorem :

[tex]l^2 = r^2 + h^2[/tex]

The slant height (l) is the length of the trail, which is 3,150 feet.

The radius (r) is 1,890 feet.

Pythagorean theorem:

[tex](3,150)^2 = (1,890)^2 + h^29,922,500 = 3,572,100 + h^2[/tex]

Make h the subject:

[tex]h^2 = 9,922,500 - 3,572,100\\h^2 = 6,350,400[/tex]

Take the square root of both sides to find h:

h = √(6,350,400)

h = 2,520 feet

Answer:

Dec % = 340/1360*100= 25%

[tex]7x+10=\dfrac{1}{3}(12x-3)+14x\qquad\text{use distributive property}\\\\7x+10=\dfrac{1}{3}\cdot12x-\dfrac{1}{3}\cdot3+14x\\\\7x+10=4x-1+14x\\\\7x+10=18x-1\qquad\text{substitute 10 from both sides}\\\\7x=18x-11\qquad\text{subtract 18x from both sides}\\\\-11x=-11\qquad\text{divide both sides by (-11)}\\\\\boxed{x=1}[/tex]

Answer:

I believe the correct awnser is x=1 I took the test

Answer: B

Step-by-step explanation:

  3x³ - 7x² +  0x + 12       →          3x³ - 7x² +  0x + 12

- (3x³ + 6x² + 10x + 0)      →    +   (-3x³ - 6x² - 10x - 0)

                                                            -13x²  - 10x  + 12

Answer:

Option b is correct.

Linear function ;

y =2x

Step-by-step explanation:

The formula y=f(x)=mx +c  ......[1]  is said to be a linear function. That means the graph of this function will be a straight line on the (x, y) plane, where m represents slope and b is the y-intercepts.

Consider any points from the table;

(1, 2) and (2, 4)

substitute these point in [1] we get;

for (1, 2)

⇒x = 1 and f(x) = 2 we have

2 = m + c      

or

c = 2- m                       ......[1]

for (2, 4) we have;

4 = 2m + c                       .....[2]

Now, substitute equation [1] into [2] we get;

4 = 2m + 2 -m

Combine like terms;

4 = m + 2

Subtract 2 from both sides we get;

4 -2 = m +2 -2

Simplify:

2 = m or

m = 2

Substitute the value of m = 2 in [1] to solve for c;

c = 2 -2 = 0

c =0

⇒ y = 2x +0

y = 2x

therefore, the data in the table represents the Linear function and a possible formula for the linear function is; y = 2x

Answer:

Option B. y = 2x

Step-by-step explanation:

The given table in the question is

x      0       1       2       3      4      

f(x)   0       2      4       6      8

As we know if the function is exponential or in the form of [tex]f(x) = (a)^{x}[/tex] then for x  = 0 value of this exponential function will be f(0) = 1 but as per table f(0) = 0, so the given function is not an exponential function.

Therefore the given function is a linear function.

Linear function is always in the form of y = mx + c

Now f(0) = m×0 + c = 0

c = 0

f(1) = m×1 = 2

m = 2

Now we replace the values of m and c in y = mx + c

The equation will be y = 2x.

Option B. y = 2x is the answer.

Answer:

<1 and <3

Step-by-step explanation:

The pairs of angles on one side of the line but in between the other two lines are called consecutive interior angles.

<1 and <3

<2 and <6

Billy wants tickets huh okay.....

Alright so first off what information do we have?

We know that 4 adult tickets are 15 Euros each

2 child tickets are 10 Euros each

Ok simple calculations here

4*15 = 60

2*10 = 20

Total is 80 Euros charge

10% booking fee

so 10% of 80 is 8 (Add this onto the total bill) = 88

3% of 88 is (well 1% is 0.88 3% is 0.88 * 3 = 2.64)

Total bill now is 90.64 (Might aswell add taxes now poor billy spending a 100)

By the way your answer is 90.64

Answer: [tex]\bold{[\dfrac{\pi}{4},\dfrac{5\pi}{4}]}[/tex]

Step-by-step explanation:

Step 1: Create a table

x    |   5sinx + 5cosx = y

0    |       0    +     5     =   5

[tex]\frac{\pi}{2}[/tex]   |        5    +     0    =   5

π    |        0    +    -5    =  -5

[tex]\frac{3\pi}{2}[/tex]    |       -5    +     0    =  -5

2π |        0    +      5    =   5

Notice that y = 5 at 0 and [tex]\frac{\pi}{2}[/tex] , so there will be a vertex at their midpoint.  Similarly at y = -5.

Midpoint of 0 and [tex]\frac{\pi}{2}[/tex]  is [tex]\dfrac{\pi}{4}[/tex] . Midpoint of π and [tex]\frac{3\pi}{2}[/tex] is [tex]\dfrac{5\pi}{4}[/tex]

(graph is attached to confirm interval)

Answer:

f(5)=469

Step-by-step explanation:

To find the value of the polynomial at x=5, we substitute the value 5 in for x into the polynomial. We then simplify using PEMDAS or order of operations.

[tex]x^4-2x^3+5x^2-7x+4\\(5)^4-2(5)^3+5(5)^2-7(5)+4\\625-250+125-35+4\\375+125-35+4\\500-35+4\\465+4\\469\\f(5)=469[/tex]

Answer:

469

Step-by-step explanation:

Answer: Cancellation method

Step-by-step explanation:

You divide the denominator by  the denominator number to cancel the fraction out.

The Cancellation method is used to simplify a fraction to its lowest form. It is done by finding the Greatest Common Divisor (GCD) of the numerator and the denominator and dividing both by this number.

The method used to reduce a fraction to its lowest form is the Cancellation method. This method involves finding the greatest common divisor (GCD) of the numerator and the denominator of the fraction. Once the GCD is found, divide both the numerator and the denominator by this number. This will reduce the fraction to its simplest or lowest form. For example, if we have the fraction 6/8, the GCD of 6 and 8 is 2. Dividing both 6 and 8 by 2, we retrieve the reduced fraction which is 3/4.

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Answer: 1/4

Step-by-step explanation:

Take any two point on the line: my starting point is -4,0 and I will be moving to 0,1.

Remember that slope = rise/run, so count up one and go to the right 4 to get to 0,1, so it would be 1/4.

Hopefully that explains it!

We can use the points (4, 0) and (0, 1) to solve.

Slope formula: y2-y1/x2-x1

= 1-0/0-4

= 1/4

Best of Luck!

S(r) = 2pi*r*h + 2pi*r^2

S ' (r) = 2pi*h + 2*2*pi*r .... differentiate with respect to r

S ' (r) = 2pi*h + 4pi*r

S ' (3) = 2pi*h + 4pi*3 ... plug in r = 3

S ' (3) = 2pi*h + 12pi

S ' (3) = 2pi*2 + 12pi .... plug in h = 2

S ' (3) = 4pi + 12pi

S ' (3) = 16pi

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Answer: D) 16pi

The instantaneous rate of change of the surface area with respect to the radius, r, when r = 3, is 16π

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder.

Given that, the surface area of a right circular cylinder of height 2 feet and radius r feet is given by S(r) = 2πrh+2πr².

We need to find, the instantaneous rate of change of the surface area with respect to the radius, r, when r = 3.

Taking the differentiation, of the formula given, S(r) = 2πrh+2πr². w.r.t radius r,

d [S(r)] / dr = 2πh + 4πr

= 2π [h + 2r]

Put h = 2, r = 3

= 16π

Hence, the instantaneous rate of change of the surface area with respect to the radius, r, when r = 3, is 16π

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Answer:

y = x + 20

Step-by-step explanation:

Isolate the variable you are solving for, y. Note the equal sign, what you do to one side, you do to the other. Add 20 to both sides

x (+20) = y - 20 (+20)

y = x + 20

y = x + 20 is your answer

Answer: Y= x+20

Step-by-step explanation: x = y-20, you must first add 20 to both sides to get Y on its own. So x+20 = y - 20 + 20, the twenties cancel each other out giving us x+20 = y or y=x+20

[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\\text{We have the line in point-slope form:}\\\\y-y_1=m(x-x_1)\\\\m-slope\\\\y-2=\dfrac{7}{3}(x+5)\to m_1=\dfrac{7}{3}\\\\\text{therefore}\ m_2=-\dfrac{1}{\frac{7}{3}}=-\dfrac{3}{7}.\\\\\text{We have the slope}\ m=-\dfrac{3}{7}\ \text{and the point}\ (-4,\ 9).\ \text{Substitute:}\\\\y-9=-\dfrac{3}{7}(x-4))\\\\\boxed{y-9=-\dfrac{3}{7}(x+4)}[/tex]

Answer:

The amount owed is greater than the cars worth (apex)

Step-by-step explanation:

Answer:

The correct answer option is: [tex]S_9=\frac{9}{2} (2+26)[/tex]

Step-by-step explanation:

We know that,

the sum of the first [tex]n[/tex] terms of an Arithmetic Sequence is given by:

[tex]S_9=\frac{n(a_1+a_n)}{2}[/tex]

where [tex]n[/tex] is the number of terms,

[tex]a_1[/tex] is the first term of the sequence; and

[tex]a_n[/tex] is the first term of the sequence.

So for [tex]a_n=3n-1[/tex],

[tex]a_1=3(1)-1=2[/tex]

and

[tex]a_9=3(9)-1=26[/tex]

Putting these values in the formula to get:

[tex]S_9=\frac{9(a_1+a_9)}{2}[/tex]

[tex]S_9=\frac{9(2+26)}{2} \\\\S_9=\frac{9}{2} (2+26)[/tex]

First five terms:

[tex]a_1=3(1)-1=2[/tex]

[tex]S_1=\frac{1(2+2)}{2}[/tex]=2

[tex]a_2=3(2)-1=5[/tex]

[tex]S_2=\frac{2(2+5)}{2}[/tex]=7

[tex]a_3=3(3)-1=8[/tex]

[tex]S_2=\frac{3(2+8)}{2}[/tex]=15

[tex]a_4=3(4)-1=11[/tex]

[tex]S_4=\frac{4(2+11)}{2}[/tex]=26

[tex]a_5=3(5)-1=14[/tex]

[tex]S_5=\frac{5(2+14)}{2}[/tex]=40

Answer: the corrrect one is A s9=9/2(2+26)

Final answer:

To adjust the fruit punch from 50% to 70% juice, Sara needs to add 4 gallons of fruit juice to the existing 6 gallons of punch.

Explanation:

The student is attempting to adjust the concentration of juice in a fruit punch mixture from 50% to 70%. Initially, Sara has 6 gallons of punch which is 50% juice. To find out how much fruit juice should be added to reach a 70% juice mixture, we can use the equation of concentration:

Let the amount of juice to be added be x gallons. The total amount of juice in the mixture would then be 50% of 6 gallons plus x gallons, and the total volume of the mixture would be 6 gallons plus x gallons.

The equation representing the new concentration is:

(3 + x) / (6 + x) = 70/100

To solve for x, multiply both sides by (6 + x) and then by 100 to clear the percentage and denominator:

3 + x = 0.7 * (6 + x)

3 + x = 4.2 + 0.7x

Now, subtract 0.7x from both sides:

3 + 0.3x = 4.2

And then subtract 3 from both sides:

0.3x = 1.2

Divide both sides by 0.3 to solve for x:

x = 4 gallons

Therefore, Sara needs to add 4 gallons of fruit juice to the existing punch to create a mixture that is 70% juice, rounding to the nearest hundredth.

Answer:

Option B is correct.

Rotation matrix = [tex]\begin{bmatrix} -3.96 \\ -1.13 \end{bmatrix}[/tex]

Step-by-step explanation:

Given a vector : [tex]<1 , 4>[/tex] , rotation by [tex]\frac{2\pi}{3}[/tex] radian.

A rotation matrix is a matrix that is used to perform a rotation in Euclidean space.

The standard rotation matrix is given by;

R = [tex]\begin{bmatrix}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}[/tex]

Then, the matrix of rotation by [tex]\frac{2\pi}{3}[/tex] radian  is:

[tex]\begin{bmatrix}x' \\ y'\end{bmatrix}[/tex] = [tex]\begin{bmatrix}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}[/tex] [tex]\begin{bmatrix}x \\ y\end{bmatrix}[/tex]

Then; substitute [tex]\theta = 120^{\circ}[/tex]

[tex]\begin{bmatrix}x' \\ y'\end{bmatrix}= \begin{bmatrix}\cos 120^{\circ} & -\sin 120^{\circ} \\ \sin 120^{\circ} & \cos 120^{\circ}\end{bmatrix}\begin{bmatrix}1 \\ 4 \end{bmatrix}[/tex]

or

[tex]\begin{bmatrix}x' \\ y'\end{bmatrix}= \begin{bmatrix} -0.5 & -0.866 \\ 0.866 & -0.5 \end{bmatrix}\begin{bmatrix}1 \\ 4 \end{bmatrix}[/tex]

or

[tex]\begin{bmatrix}x' \\ y'\end{bmatrix}= \begin{bmatrix} -0.5 +4(-0.866) \\ 0.866+4(-0.5)\end{bmatrix}[/tex]

Simplify:

[tex]\begin{bmatrix}x' \\ y'\end{bmatrix} = \begin{bmatrix} -3.96 \\ -1.13 \end{bmatrix}[/tex]

Therefore, the rotation matrix of a given vector is, [tex]\begin{bmatrix} -3.96 \\ -1.13 \end{bmatrix}[/tex]

The matrix that represents the rotation of the vector 1,4 by 2pi/3 radians is : (B) [tex]\left[\begin{array}{ccc}-3.96\\-1.13\\\end{array}\right][/tex]

A matrix can be defined as a rectangular array of numbers table of numbers, symbols, or expressions that are arranged into column and rows.A matrix can take different forms which gave rise to the types of matrices.

Given that standard rotation matrix is expressed as :

[tex]R = \left[\begin{array}{ccc}cos\beta &-sin\beta \\sin\beta &cos\beta \\\end{array}\right][/tex]

therefore the matrix by rotation of [tex]\frac{2\pi }{3}[/tex]

[tex]\left[\begin{array}{ccc}x'\\y'\\\end{array}\right] = \left[\begin{array}{ccc}cos\beta &-sin\beta \\sin\beta &cos\beta \\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex]

substituting the value of [tex]\beta = 120^o[/tex]

[tex]\left[\begin{array}{ccc}x'\\y'\\\end{array}\right] = \left[\begin{array}{ccc}-0.5 &+4(-0.866) \\0.866 &+4(-0.5) \\\end{array}\right] \left[\begin{array}{ccc}\\\\\end{array}[/tex]

Therefore the rotation of the vector is

[tex]\left[\begin{array}{ccc}-3.96\\-1.13\\\end{array}\right][/tex]

In conclusion, The matrix that represents the rotation of the vector 1,4 by 2pi/3 radians is : (B).

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