the APR on leslie's credit card is currently 21.6%. what is the monthly periodic rate?

x - number of polio vaccinations

y - number of measles vaccinations:

x + y = 60    / * ( - 2 )

4 x + 2 y = 184

--------------------------

- 2 x - 2 y = - 120

+

4 x + 2 y = 184

--------------------------

2 x = 64

x = 64 : 2

x = 32

32 + y = 60

y = 60 - 32

y = 28

Answer: There were 32 polio and 28 measles vaccinations.

Answer:

32 and 28

Step-by-step explanation:

ANSWER

[tex]( - \frac{23}{5} , - 4)[/tex]

EXPLANATION

Given the points P(2,-1) and Q(-9,-6),the coordinates of the point that partition the directed line segment PQ in the ratio 3:2 is given by

[tex]x = \frac{ mx_2+nx_1}{m + n} [/tex]

[tex]y= \frac{ my_2+ny_1}{m + n} [/tex]

Where m=3 and n=2

[tex]x = \frac{ 3 ( - 9)+2(2)}{3+ 2} [/tex]

[tex]x = \frac{ - 23}{5} [/tex]

[tex]y= \frac{ 3( - 6)+2( - 1)}{3 + 2} [/tex]

[tex]y= \frac{ - 20}{5} = - 4[/tex]

The point is

[tex]( - \frac{23}{5} , - 4)[/tex]

The coordinates of the point on the directed line segment PQ that partitions it in the ratio 3/2 are (-21/5, -17/5).

To find the coordinates of the point on the directed line segment PQ that partitions it in the ratio 3/2, we can use the section formula. The section formula states that the coordinates of a point dividing a line segment with endpoints (x1,y1) and (x2,y2) in the ratio m:n are given by:

x = (m*x2 + n*x1)/(m+n)

y = (m*y2 + n*y1)/(m+n)

Plugging in the values from the given points P(2,-1) and Q(-9,-6) into the formula, we get:

x = (3*(-9) + 2*2)/(3+2) = -21/5

y = (3*(-6) + 2*(-1))/(3+2) = -17/5

So, the coordinates of the point are (-21/5, -17/5).

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Answer:

c. 1 and 3

Step-by-step explanation:

To quickly solve this problem, we can use a graphing tool or a calculator to plot each equation.

Please see the attached image below, to find more information about the graph

s

The equations are:

1) y = sin (3x + π/6)

2) y = cos (3x - π/6)

3) y = cos (3x - π/3)

Looking at the graphs, we can see that the identical ones

are equations one and three

Correct option:

c. 1 and 3

Answer:

C. 6 feet

Step-by-step explanation:

The answer is:

The correct option is B. the string is 3.9 feet long.

To solve the problem, we need to use the given formula, substituting "T" equal to 2.2 seconds, and then, isolating "L".

Also, we need to remember the formula to calculate a simple pendulum:

[tex]T=2\pi \sqrt{\frac{L}{g} }[/tex]

Where,

T, is the period in seconds

L, is the longitud in meters or feet

g, is the acceleration of the gravity wich is equal to:

[tex]g=9.81\frac{m}{s^{2} }[/tex]

or

[tex]g=32\frac{feet}{s^{2} }[/tex]

We are given the formula:

[tex]T=2\pi \sqrt{\frac{L}{32} }[/tex]

Where,

T, is the period of the pendulum (in seconds).

L, is the length of the string.

32, is the acceleration of the gravity in feet.

So, substituting "T" and isolating "L", we have:

[tex]2.2seconds=2\pi \sqrt{\frac{L}{32\frac{feet}{seconds^{2}} }}\\\\2\pi \sqrt{\frac{L}{32\frac{feet}{seconds^{2}}}}=2.2seconds\\\\\sqrt{\frac{L}{32\frac{feet}{seconds^{2}}}}=\frac{2.2seconds}{2\pi }[/tex]

Then, squaring both sides of the equation, to cancel the square root, we have:

[tex]\sqrt{\frac{L}{32\frac{feet}{seconds^{2} }}}=\frac{2.2seconds}{2\pi}\\\\(\sqrt{\frac{L}{32\frac{feet}{seconds^{2}}}})^{2}=(\frac{2.2seconds}{2\pi})^{2}=(0.35seconds)^{2} }\\\\\frac{L}{32\frac{feet}{seconds^{2}}}}=0.123seconds^{2}\\\\L=32\frac{feet}{seconds^{2}}*0.123seconds^{2}\\\\L=3.94feet=3.9feet[/tex]

Hence, we have that the answer is:

B. the string is 3.9 feet long.

Have a nice day!

Answer:

D. The graph of d(x) is 25 units below the graph of f(x)

ANSWER

D. the graph of d(x) will be 25 units below the graph of f(x).

EXPLANATION

The graph of

[tex]f(x) = {x}^{2} [/tex]

is the base function.

The graph of

[tex]d(x) = {x}^{2} - 25[/tex]

is a vertical translation of the base function 25 units down.

This implies that, the graph of d(x) will be 25 units below the graph of f(x).

Therefore the correct answer is D.

Answer:

C = 13

Step-by-step explanation:

C = 3(5) - 2

C = 15 - 2

C = 13

Answer:

C = 13

Step-by-step explanation:

Substitute x = 5 into the expression for C

C = (3 × 5) - 2 = 15 - 2 = 13

Answer:

84.463°

Step-by-step explanation:

Determine the x- and y-components of these two vectors.  Sum up the x-comps and the y-comps separately, and then find the magnitude and direction of the vector sum:

x-comps:

5 cos 30° + 7 cos 120° = 5(0.866) + 7(-0.5) = 0.83

y-comps:

5 sin 30° + 7 sin 120° = 5(0.5) + 7(0.866) = 2.5 + 6.062 = 8.562

Both components are in Quadrant I, so the direction angle ∅ is between 0° and 90°:  ∅ = arcctan 8.562/0.83 = arctan 10.316 = 1.474 radian, or

1.474 rad       180°

-------------- * -----------  =  84.463°

       1                π

Answer:

[tex]a=9\ in\\b= 9\ in[/tex]

Step-by-step explanation:

This straight triangle has two angles equal to 45 ° and two equal sides.

We know that the side opposite the 90 degree angle is:

[tex]c =9\sqrt{2}\ in[/tex]

Since the triangle has two equal angles, then it is an iscoceles triangle.

This means that

[tex]a = b[/tex]

We use the Pythagorean theorem to find b

[tex]c^2 = a^2 + b^2\\\\c^2 = b^2 + b^2\\\\c^2 = 2b^2\\\\(9\sqrt{2})^2 =2b^2\\\\b^2=\frac{(9\sqrt{2})^2}{2}\\\\\sqrt{b^2}=\sqrt{\frac{(9\sqrt{2})^2}{2}}\\\\b=\frac{(9\sqrt{2})}{\sqrt{2}}\\\\b=a=9[/tex]

Conditional probability means that an event happening only happened because another even had already occurred , Mean while independent probabilitty is like if two events, A and B, are independent if the fact that A occurs does not affect the probability of B occurring.

The addition is a Conditional probability.

The Addition Rule, used for calculating the probability of either event A or B occurring, applies to both independent and dependent events, requiring adjustment for overlapping probabilities.

The difference between independent and conditional probability is that independent events do not affect each other's occurrence, whereas conditional probability is the likelihood of one event given that another has occurred. The Addition Rule of probability is used with either independent or dependent events when you are calculating the probability of either event A or event B occurring (denoted as P(A OR B)). However, the rule requires an adjustment in the case of dependent events. The Addition Rule is P(A OR B) = P(A) + P(B) - P(A AND B). It is used to make sure that the probability of the intersection of A and B (which is counted in both P(A) and P(B)) is not counted twice.

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Answer:

The radius is 7, and the circumference is  43.96

Step-by-step explanation:

The radius is half of the diameter, and this would just be 14/2 which is 7. The circumference is found by C=pi(diamete) or 2pi(radius). This is found by 14*3.14 this is equals 43.96

The radius of the dartboard is 7 inches and the circumference is approximately 43.96 inches.

Radius:

The radius of a circle is half of its diameter. So, in this case, the radius is 7 inches.

Circumference:

The circumference of a circle can be found using the formula C = 2πr, where r is the radius. So, the circumference of this dartboard is 2π(7) = 14π inches, which rounds to 43.96 inches when rounded to the nearest hundredth.

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Answer:

it's false

Step-by-step explanation:

If you have the equation of a parabola in vertex form y=a(x−h)^2+k, then the vertex is at (h,k) and the focus is (h,k+14a).

In this case, h = 0,k = 0 and a = 1/4

Then the focus is at (h, k +14a) = (0, 0 + 14*1/4) = ( 0, 1)

So, it's false.

Answer:

false

Step-by-step explanation:

the expanded form of (3x + 4)(2x − 5) is 6x² - 7x - 20. The third option is the correct option.

The simplified form of (3x + 2y) - (x + 2y) is 2x. The correct option is the third option.

3x + 4y equals 36. The third option is the correct option.

To evaluate f(x) = 4x + 3x² - 5, f(x) evaluates to -1. The last option is the correct option.

The Breakdown

To expand the expression (3x + 4)(2x − 5), you can use the distributive property:

(3x + 4)(2x − 5) = 3x(2x) + 3x(-5) + 4(2x) + 4(-5)

Now, simplify each term:

= 6x² - 15x + 8x - 20

Combine like terms:

= 6x² - 7x - 20

So, the expanded form is 6x² - 7x - 20.

To simplify the expression (3x + 2y) - (x + 2y), we can remove the parentheses and combine like terms:

(3x + 2y) - (x + 2y) = 3x + 2y - x - 2y

The terms "2y" and "-2y" cancel each other out:

= 3x - x

Simplifying further:

= 2x

Therefore, the simplified form of (3x + 2y) - (x + 2y) is 2x.

To find the value of 3x + 4y, we need to solve the given equation and then substitute the values into the expression.

Given: 1/2x + 2/3y = 6

To eliminate the fractions, we can multiply the entire equation by the least common multiple (LCM) of the denominators, which is 6:

6 × (1/2x + 2/3y) = 6 × 6

This simplifies to:

3x + 4y = 36

Therefore, 3x + 4y equals 36.

To evaluate f(x) = 4x + 3x² - 5 when x = -2, we substitute -2 for x in the expression:

f(-2) = 4(-2) + 3(-2)² - 5

Simplifying:

f(-2) = -8 + 3(4) - 5

f(-2) = -8 + 12 - 5

f(-2) = -1

Therefore, when x = -2, f(x) evaluates to -1.

ANSWER

(-1,-1), (-4,-5), (-8,0)

EXPLANATION

We have a triangle with vertices:

(0,2), (-3,-2) and (-7,3).

The rule for the translation is

[tex](x, y) \to (x - 1,y - 3)[/tex]

The new vertices of the triangle will be;

[tex](0, 2) \to (0 - 1,2- 3) = ( - 1, - 1)[/tex]

[tex]( - 3, - 2) \to (- 3-1, - 2- 3) = ( -4, - 5)[/tex]

[tex]( - 7, 3) \to ( - 7 - 1,3- 3) = ( - 8, 0)[/tex]

The new vertices are:

(-1,-1), (-4,-5), (-8,0)

the answer would be 3 I believe

1-7=

-6

4-(-2)=

6

-6/6=

-1

The slope is -1

Answer: d) 2.5

Step-by-step explanation:

The mean is 16 so it has a z-score is 0

The standard deviation is 4 so:

Notice that 26 is between the z-scores of 2 and 3 = 2.5

Algebraically: [tex]\dfrac{26-16}{4}=\dfrac{10}{4}=2.5[/tex]

Answer:

  D.  7 +11i

Step-by-step explanation:

In many situations, you can treat "i" as though it were a variable. Collect terms in the usual way.

  (2 +8i) -(-5-3i) = 2 +8i +5 +3i = (2+5) +(8+3)i

  = 7 +11i

Answer:

  D)  168 ft^3

Step-by-step explanation:

The volume of a cone is given by the formula ...

  V = (1/3)πr^2·h

Putting your numbers in, we have ...

  V = (1/3)π(4 ft)^2·(10 ft) = (160π/3) ft^3 ≈ 168 ft^3

The answer is d 168ft3

Explanation:

(1/3)*(4^2)*10*pi

Answer:

The area of the circle is [tex]78.5\ units^{2}[/tex]

Step-by-step explanation:

step 1

Find the radius of the circle

we know that

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]C=31.4\ units[/tex]

assume

[tex]\pi=3.14[/tex]

substitute the values

[tex]31.4=2(3.14)r[/tex]

[tex]r=31.4/[2(3.14)]=5\ units[/tex]

step 2

Find the area of the circle

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

substitute the values

[tex]A=(3.14)(5)^{2}[/tex]

[tex]A=78.5\ units^{2}[/tex]

Answer:

78.5

Step-by-step explanation:

Answer:

sec Ф = 13/12

Step-by-step explanation:

If tan Ф = 5 / 12, we can find the third side of this triangle (that is, the hypotenuse) by applying the Pythagorean Theorem:  

hyp² = 5² + 12² = 169.  Thus, the hyp is 13.

Thus, cos Ф = adj / hyp = 12/13.

The secant function is the reciprocal of the cosine function, so

sec Ф = 13/12.

Answer:

It's the first choice (20 degrees).

Step-by-step explanation:

These angles will be equal ( by The Alternate Angle Theorem).

5(x - 2) = x + 14

5x - 10 = x + 14

4x = 24

x = 6.

So the measure of each angle =  5(6 - 2) = 6 + 14 = 20 degrees.

The angles of elevation and depression are equal because they are alternate interior angles. Solving the given expressions yields x = 6. Therefore, both the angle of elevation and the angle of depression measure 20 degrees.

First, let's set up the problem:

In any scenario involving angles of elevation and depression, these angles are equal because they are alternate interior angles formed by a horizontal line and a transversal.

Therefore, we can equate the two expressions:

5(x-2) = (x+14)

Now, solve for x:

Now substitute x back into the expressions to find the angle measures:

For the angle of elevation: 5(x-2) = 5(6-2) = 5*4 = 20 degrees

For the angle of depression: (x+14) = (6+14) = 20 degrees

Therefore, both the angle of elevation and the angle of depression measure 20 degrees.

This confirms that our setup and calculation are correct.

Answer:

  D(4, 1)

Step-by-step explanation:

The two diagonals have the same midpoint, so ...

  (A+C)/2 = (B+D)/2

  A+C = B+D . . . . multiply by 2

  A+C-B = D . . . . . subtract B

  D = (1, 1) + (5, 3) - (2, 3) = (1+5-2, 1+3-3)

 D = (4, 1)

Answer:

D(4 ; 1)

Step-by-step explanation:

vector(AB)=(2-1 ; 3-1) = (1 ; 2)

vector(DC)=(5-x ; 3-y)  and D(x ; y )

ABCD  parallelogram :vector(AB)=vector(DC)

you have the system : 5-x =1

                                       3-y =2

so : x=4 and y=1

D(4 ; 1)

Answer:x=18

Step-by-step explanation:2x-9=x+9

Answer:

She will owe $16987.35 when she begins making payments

Step-by-step explanation:

* Lets explain how to solve the problem

- The loan is $16,000

- The loan at a 4.8% APR compounded monthly

- She will begin paying off the loan in 15 months

- The rule of the future money is [tex]A=P(1 + \frac{r}{n})^{nt}[/tex], where

# A is the future value of the loan

# P is the principal value of the loan

# r is the rate in decimal

# n is the number of times that interest is compounded per unit t

# t = the time in years the money is borrowed for

∵ P = $16,000

∵ r = 4.8/100 = 0.048

∵ n = 12 ⇒ compounded monthly

∵ t = 15/12 = 1.25 years

∴ [tex]A=16000(1+\frac{0.048}{12})^{12(1.25)}=16987.35[/tex]

* She will owe $16987.35 when she begins making payments

Answer:  The correct option is

(A) The scale factor is 0.8 and the coordinates of point B" are (–3.2, –4.8).

Step-by-step explanation:  Given that the segment AB is being dilated to A''B'' with the center at the origin. The image of A, point A" has coordinates of (3.2, 6.4).

We are to find the scale factor of the dilation and the co-ordinates of the point B''.

From the given graph, we note that

the co-ordinates of point A are (4, 8).

Now, If S is the scale factor of dilation, then we must have

[tex]S\times (4,8)=(3.2,6.4)\\\\\Rightarrow (4S,8S)=(3.2,6.4)\\\\\Rightarrow S=\dfrac{3.2}{4}=\dfrac{6.4}{8}=0.8.[/tex]

So, the scale factor is 0.8.

Now, the co-ordinates of point B are (-4, -6). So, the co-ordinates of B'' will be

[tex](-4\times 0.8,-6\times 0.8)=(-3.2,-4.8).[/tex]

Thus, the correct option is

(A) The scale factor is 0.8 and the coordinates of point B" are (–3.2, –4.8).

Answer:

A) The scale factor is 0.8 and the coordinates of point B" are (–3.2, –4.8).

Step-by-step explanation:

I believe the correct answer is 4.33%.

Answer:

2.00%

Step-by-step explanation:

Answer:

its B

Step-by-step explanation:

Answer:

  you expect to win on average $1.33 per round

Step-by-step explanation:

The expected value is the sum of products of probability and value:

  2/6×$8 + 4/6×(-$2) = $8/3 - 4/3 = $4/3 ≈ $1.33

The expected value of the gambling game is calculated by taking into account the probability of winning $8 and losing $2. The final expected value is $1.33, which means on average, you would gain $1.33 per game played.

To calculate the expected value for the gambling game where you roll a die, you need to account for the different outcomes and their associated probabilities. In this game, rolling a 1 or 2 means you win $8, and there are two outcomes out of six that result in a win, giving a probability of 2/6 or 1/3 for each of these outcomes. Rolling any other number (3, 4, 5, or 6) results in losing $2, with a probability of 4/6 or 2/3 for each of these losing outcomes.

The expected value (EV) can be calculated using the formula:

EV = (Probability of Winning × Amount Won) + (Probability of Losing × Amount Lost)

Substituting the values into the formula:

EV = ‎‎(1/3 × $8) + (2/3 × -$2)

EV = ($2.67) + (-$1.33)

EV = $1.33

This means that the average gain per game, after many plays, is expected to be $1.33.

Answer:

ezpz false

Step-by-step explanation:

Answer: 1 out of 5 for the first box and 1 out of 7 for the second box

( in simplest form)

Step-by-step explanation:

Answer:

C. [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

We have been given a table showing rates of time taken by Judy and Sam to complete a puzzle.

We can see from our given table that Sal's rate is r. We are told that Judy completes a puzzle by herself, it takes her 3 hours. working with Sal, it only takes them 2 hours.

Since Judy completes the puzzle in 3 hours, so part of puzzle completed by Judy in one hour would be [tex]\frac{1}{3}[/tex], therefore, correct choice is option C.

Answer:

C.

Step-by-step explanation: