Barbara got a flat tire and does not have a spare. She needs her car for work, so she goes to a business that offers payday loans in order to get the money to buy a new tire. She borrows $75 and plans to pay it back when she gets paid in 8 days. Barbara is charged a fee of $15 and the term on her loan is 8 days. Approximately what is the annual percentage rate on her loan?

Answer:

a) Probability of getting exactly 7 hits = 0.001075

b)  Probability of getting fewer than seven = 0.999

c) Probability of getting at least seven hits = 0.001

Step-by-step explanation:

The process is a Poisson process.

Rate, [tex]\lambda = 0.4[/tex]

The probability is to be calculated between 8:27 PM and 8:31 PM

t = 4

[tex]\lambda t = 0.4 * 4 = 1.6[/tex]

If the number of hits is represented by X

[tex]P(X = x) = \frac{e^{- \lambda t} (\lambda t)^x}{x!}[/tex]

a) Probability of getting exactly 7 hits

[tex]P(X = x) = \frac{e^{- 1.6} (1.6)^7}{7!}\\P(X= 7) = 0.001075[/tex]

b) Probability of getting fewer than seven

[tex]P(X < 7) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6)\\P(X < 7) = e^{- 1.6} [ \frac{1.6^0}{0!} + \frac{1.6^1}{1!} + \frac{1.6^2}{2!} + \frac{1.6^3}{3!} + \frac{1.6^4}{4!} + \frac{1.6^5}{5!} + \frac{1.6^6}{6!} ][/tex]

P(X < 7) = 0.999

c) Probability of getting at least seven hits

[tex]P(X \geq 7) = 1 - P(x < 7)\\P(X \geq 7) = 1 - 0.999\\P(X \geq 7) = 0.001[/tex]

Using the Poisson distribution, it is found that:

a) 0.0011 = 0.11% probability of exactly 7 hits in a 4 minute interval, which means that over many 4 minute intervals between 7 and 10 PM, 0.11% of them will have exactly 7 hits.

b) 0.9985 = 99.85% probability of fewer than seven hits in a 4 minute interval, which means that over many 4 minute intervals between 7 and 10 PM, 99.95% of them will have fewer than 7 hits.

c) 0.0015 = 0.15% probability of at least seven hits in a 4 minute interval, which means that over many 4 minute intervals between 7 and 10 PM, 0.15% of them will have at least 7 hits.

In a Poisson distribution, the probability is:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

In this problem, we have a mean of 0.4 hits per minute, interval of 4 minutes, thus:

[tex]\mu = 0.4(4) = 1.6[/tex]

The probabilities we are going to use are:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-1.6}1.6^{0}}{(0)!} = 0.2019[/tex]

[tex]P(X = 1) = \frac{e^{-1.6}1.6^{1}}{(1)!} = 0.3230[/tex]

[tex]P(X = 2) = \frac{e^{-1.6}1.6^{2}}{(2)!} = 0.2584[/tex]

[tex]P(X = 3) = \frac{e^{-1.6}1.6^{3}}{(3)!} = 0.1378[/tex]

[tex]P(X = 4) = \frac{e^{-1.6}1.6^{4}}{(4)!} = 0.0551[/tex]

[tex]P(X = 5) = \frac{e^{-1.6}1.6^{5}}{(5)!} = 0.0176[/tex]

[tex]P(X = 6) = \frac{e^{-1.6}1.6^{6}}{(6)!} = 0.0047[/tex]

[tex]P(X = 7) = \frac{e^{-1.6}1.6^{7}}{(7)!} = 0.0011[/tex]

Item a:

P(X = 7) = 0.0011, thus:

0.0011 = 0.11% probability of exactly 7 hits in a 4 minute interval, which means that over many 4 minute intervals between 7 and 10 PM, 0.11% of them will have exactly 7 hits.

Item b:

This probability is:

[tex]P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)[/tex]

Then, with the values we found:

[tex]P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) = 0.2019 + 0.3230 + 0.2584 + 0.1378 + 0.0551 + 0.0176 + 0.0047 = 0.9985[/tex]

0.9985 = 99.85% probability of fewer than seven hits in a 4 minute interval, which means that over many 4 minute intervals between 7 and 10 PM, 99.95% of them will have fewer than 7 hits.

Item c:

This probability is:

[tex]P(X \geq 7) = 1 - P(X < 7) = 1 - 0.9985 = 0.0015[/tex]

0.0015 = 0.15% probability of at least seven hits in a 4 minute interval, which means that over many 4 minute intervals between 7 and 10 PM, 0.15% of them will have at least 7 hits.

A similar problem is given at https://brainly.com/question/24098004

Answer: 3600

Step-by-step explanation:

Area of a square = side^2

Area = √2500 = 50

If side is increased by 10, length if side becomes 60 inches

Area = 60^2

Area = 3600 sq. in.

Area of the circle = π * (35 yd)^2

Let A be the area of the sector subtended by a central angle measuring 80º. Then

A / (π * (35 yd)^2) = 80º / 360º  ==>  A = 2450π/9 yd^2 ≈ 854.78 yd^2

Subtract from A the area of the triangle, whose base has length 45 yd and with height 25 yd:

A - 1/2 * (45 yd) * (25 yd)  ≈ 292.28 yd^2

This is the area of the missing circular segment.

Then the area of the playground is equal to the area of the circle minus this area,

π * (35 yd)^2 - 292.28 yd^2 ≈ 3554 yd^2

Answer:

y = 5x-38

Step-by-step explanation:

The slope is m = (y2-y1)/(x2-x1)

                          = (-8 - -3)/(6-7)

                          = ( -8+3)/(-1)

                           =-5/-1

                            =5

Slope intercept form is

y = mx+b  where m is the slope and b is the y intercept

y = 5x+b

Substitute a point into the equation

-8 = 5(6) +b

-8 = 30+b

-8-30 = 30-30+b

-38 = b

y = 5x-38

Slope formula: y2-y1/x2-x1

-8-(-3)/6-7

-5/-1

5

Find the y-intercept with the formula for slope intercept form.

y = mx + b

-3 = 5(7) + b

-3 = 35 + b

-3 - 35 = 35 - 35 + b

-38 = b

Fill in what we have:

y = 5x - 38

Best of Luck!

Answer:

x= 48

Step-by-step explanation:

x∝ y

x= ky

24= 8k

k= 3

Now solve for x

x= ky

x= 3x 26

x= 48

I hope it helped

Answer:

4/5

Step-by-step explanation:

t + b = 2.50

t = b+1.50

Substitute

b+1.50+ b = 2.50

Combine like terms

2b + 1.50=2.50

2b =1

b = .5

t = b+ 1.5

t = .5+ 1.5

t = 2

The fraction of the total price

t/2.50

2/2.50

20/25

4/5

Answer:

80% of the total price is torch.

Step-by-step explanation:

Let

t=cost of torch

b=cost of battery

A torch and battery cost £2.50 altogether.

t+b=2.5

The torch costs £1.50 more than the battery.

t-b=1.5

Keep in mind:

When equations of the form

a+b = Sum

a-b = Diff

then the solution is immediately

a=(Sum+Difference)/2

b=(Sum-Difference)/2

and apply the rule,

t=(2.5+1.5)/2 = £2

b=(2.5-1.5)/2 = £1

Torch / total

= 2/2.5

= 80%

Answer:

[tex]|3r-15| = -3r+15[/tex] if [tex]r<5[/tex]

Step-by-step explanation:

Given that:

r < 5

To simplify:

|3r−15|

Solution:

First of all, let us learn about Modulus function:

[tex]f(x) =|x| =\left \{ {x, \ if\ {x>0} \atop -x\ if\ {x<0}} \right.[/tex]

In other words, we can say:

Modulus function has a role to make its contents positive.

If the contents are positive, the result will be equal to its contents only.

If the contents are negative, it will add a negative sign to the contents to make it positive.

Now, let us consider the given condition:

[tex]r < 5[/tex]

Multiply both sides with 3. (As 3 is a positive number, the equality sign will not change.)

[tex]3r < 15[/tex]

Subtracting 15 from both sides:

[tex]3r-15<15-15\\\Rightarrow 3r-15<0[/tex]

Now, we know that [tex]3r-15<0[/tex], let us use the definition of Modulus function.

Add a negative sign to the contents because the contents are already negative.

[tex]\\\Rightarrow |3r-15| = -(3r-15)\\\Rightarrow -3r+15[/tex]

So, the answer is:

[tex]|3r-15| = -3r+15[/tex] if [tex]r<5[/tex]

Answer: x=6, y=20

Step-by-step explanation:

Since ΔBCD and ΔTUS are congruent triangles, we can set the sides equal to each other.

y=2y-20                           [subtract both sides by 2y]

-y=-20                              [divide both sides by -1]

y=20

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

3x+32=9x-4                    [add both sides by 4, and subtract both sides by 3x]

36=6x                              [divide both sides by 6]

x=6

Answer:

Side FE < Side DE < Side DF

Step-by-step explanation:

Side FE < Side DE < Side DF are in ascending order.  Side FE is the shortest because it is opposite the smallest angle (47 degrees).

Answer:

$5.25

Step-by-step explanation:

Take $150.00 times 3.5% to get $5.25

150(.035) = 5.25

Answer:

$5.25

Step-by-step explanation:

She earned 3.5% of $150.00.

To find a percent of a number, multiply the percent by the number.

3.5% * $150.00 =

= 0.035 * $150.00

= $5.25

Answer:

50

Step-by-step explanation:

For this question you would follow the BIDMAS rule - (Brackets, Indices, Division, Multiplication, Addition, Subtraction.)

The first thing in this question you need to solve it (9 + 8)

we do this because, when we follow BIDMAS, the first rule is brackets

so, 9 + 8 = 17

The second step is to multiply, as this rule is second,

so, 17 x 2 = 34

Our final step is to solve the last bit, which is 6 x 14

and we know that 6 x 14 = 84

So now that we have 84 and 34, we need to subtract the two numbers as shown,

84 - 34 = 50

And this is how you get the answer 50

i hope this has helped you, please comment if you did not understand it and i will explain it in another way : )

Use pemdas

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

Do parenthesis first: (9+8)=17

6x14-17x2

Then do multiplication

6x14=84 17x2=34

Now do subtraction

84-34=50

Therefore your answer is 50

Answer:

Perimetro = 4 cm + 7 cm + 12 cm

                = 23 cm

Step-by-step explanation:

Answer:

to the nearest hundreths or any one

Step-by-step explanation:

Answer:May be 12

Step-by-step explanation:

Answer: The surface area of the rectangular prism is 114 cm^2.

Step-by-step explanation:

1) Formula:  A = 2wl + 2lh + 2hw

( W=width, l= length, h=height)

2) Plug it in: A=2(3)(8) + 2(8)(3) + 2(3)(3)  

3) A= 2( 24) + 2(24) + 2(9)

4) A= 48+ 48+ 18= 114

Answer:

111111 [tex]\times[/tex] 1111110 is the simple expression.

Step-by-step explanation:

The expression to be solved:

[tex]\dfrac{6,666,666\times666,666 }{1+2+3+4+5+6+5+4+3+2+1} - \dfrac{777,777\times777,777}{1+2+3+4+5+6+7+6+5+4+3+2+1}[/tex]

First of all, let us solve the first term:

[tex]\dfrac{6,666,666\times666,666 }{1+2+3+4+5+6+5+4+3+2+1}\\\Rightarrow \dfrac{6666666\times666666 }{36}\\\Rightarrow \dfrac{6666666\times666666 }{6\times 6}\\\Rightarrow 1111111\times 111111[/tex]

Now, the right term:

[tex]\dfrac{777777\times777777}{1+2+3+4+5+6+7+6+5+4+3+2+1}\\\Rightarrow \dfrac{777777\times777777}{49}\\\Rightarrow \dfrac{777777\times777777}{7 \times 7}\\\Rightarrow 111111 \times 111111[/tex]

So, the expression to be solved becomes:

[tex]1111111\times 111111-111111\times 111111\\\Rightarrow 111111(1111111-1)\\\Rightarrow 111111\times 1111110[/tex]

Step-by-step explanation:

Start with the average. (of your data set)

Find how much each data value deviates from the average (difference of average and data value).

Take the absolute value of each difference.  

Add all of these absolute values.

Divide by the total number of data values.

How to find the MAD (Mean Absolute Deviation):

Let's use these numbers to figure out the MAD:

[tex]5, 2, 1, 3[/tex]

1. First thing you want to do is add the numbers together:

[tex]5+2+1+3=11[/tex]

2. Second thing you want to do is divide it by 4 because there are 4 numbers in the data set:

[tex]\frac{11}{4} =2.75[/tex]

3. Third thing you want to do is subtract the data set from 2.75:

[tex]5-2.75=2.25\\2.75-2=0.75\\2.75-1=1.75\\3-2.75=0.25[/tex]

4. Fourth thing you want to do is add all the differences:

[tex]2.25+0.75+1.75+0.25=5[/tex]

5. Last thing you want to do is now divide the sum (5) by 4 again:

[tex]\frac{5}{4}= 1.25[/tex]

So, the answer (MAD) would be 1.25

That's how you find the MAD to any data set in steps.

Hope this helped!

I know I'm 2 years late btw, you've probably already mastered this subject, sorry!

           - June 7, 2022 (6/7/22)

Answer:

Existen 6 formas posibles de cambiar un billete de 5000 por monedas de 200 y 500.

Step-by-step explanation:

En primer lugar, se determina el mínimo común múltiplo de 500 y 200. Si se multiplica a 500 por 2 y a 200 por 5, se encuentra que el mínimo común múltiplo es 1000. Entonces, se encuentra las siguientes dos conclusiones:

1) Se requiere dos monedas de 500 para obtener 1000.

2) Se requiere cinco monedas de 200 para obtener 1000.

Para determinar todas las formas posibles sin considerar el orden de las monedas, se requiere estudiar tres escenarios:

(i) Todas las monedas son de 200.

(ii) Todas las monedas son de 500.

(iii) Hay monedas de 200 y 500.

Caso 1 - Todas las monedas son de 200:

Es evidente que solo existe una forma.

Caso 2 - Todas las monedas son de 500:

Es evidente que solo existe una forma.

Caso 3 - Hay monedas de 200 y 500:

Existen las siguientes formas:

- 1000 en monedas de 200, 4000 en monedas de 500.

- 2000 en monedas de 200, 3000 en monedas de 500.

- 3000 en monedas de 200, 2000 en monedas de 500.

- 4000 en monedas de 200, 1000 en monedas de 500.

En resumen, existen 4 escenarios.

Finalmente, existen 6 formas posibles de cambiar un billete de 5000 por monedas de 200 y 500.

Answer: 1035 cm^2

Step-by-step explanation:

Given that the shape s is exactly one quarter of solid sphere.

Where the volume of the shape s is 1994πcm^3.

The formula for volume of a sphere is

V = 4/3πr^3

The volume will be divided by 4 since the given solid is exactly quarter of solid sphere. Then equate it to the given value

1994π = 4/3πr^3 × 1/4

The π will cancel out

1994 = r^3/3

Cross multiply

5982 = r^3

r = cube root of 5982

r = 18.2 cm

The surface area of a sphere is

A = 4πr^2

Substitute r in the formula

A = 4× π × 18.2^2

A = 4141

Since the shape is exactly one quarter of solid sphere. Divide the answer by 4

A = 4141/4

A = 1035.3 cm^2

The surface area of s is therefore 1035.3 cm^2

The surface area of the shape s is approximately 329.53 cm².

Important information:

Volume of a sphere is:

[tex]V=\dfrac{4}{3}\pi r^3[/tex]

The volume of one-quarter of a solid sphere is 1994π cm².

[tex]1994\pi=\dfrac{1}{4}\times \dfrac{4}{3}\pi r^3[/tex]

[tex]1994\pi=\dfrac{1}{3}\pi r^3[/tex]

[tex]\dfrac{1994\pi\times 3}{\pi}=r^3[/tex]

[tex]5982=r^3[/tex]

Taking cube root on both sides, we get

[tex]\sqrt[3]{5982}=r[/tex]

[tex]r\approx 18.153[/tex]

Surface area of a sphere is:

[tex]S=4\pi r^2[/tex]

Surface area of one quarter of solid sphere is:

[tex]S=\pi r^2[/tex]

[tex]S=\pi (18.153)^2[/tex]

[tex]S=329.5314\pi[/tex]

[tex]S\approx 329.53\pi[/tex]

Therefore, the surface area of the shape s is 329.53 cm².

Find out more about 'Sphere' here:

https://brainly.com/question/16415229

Answer:

Hey there!

We want to change the equation for each line into slope intercept form, or y=mx+b form.

Luckily, the first one is already in slope intercept form.

The second line can be converted to: y=-3/4x-7/4.

The third line can be converted to: -8y=-6x+4, or y=3/4x-1/2

Line one and line two are neither perpendicular or parallel.

Line one and line three are perpendicular.

Lines two and three are neither perpendicular or parallel.

This is because parallel lines have same slope, and perpendicular lines have opposite reciprocal slopes.

Hope this helps :)

Answer:

Line 1 and Line 2: Neither

Line 1 and Line 3: Perpendicular

Line 2 and Line 3: Neither

Step-by-step explanation:

To make the answering process easier, begin by converting each formula into the format y = mx +b:

Line 1: y = -4/3x + 1 (already in format)

Line 2:

-4y = 3x + 7

Divide all terms by -4:

y = -3/4x - 7/4

Line 3:

6x - 8y = 4

Subtract both sides by 6x:

-8y = -6x + 4

Divide all terms by -8:

y = 3/4x - 1/2

We can determine the relationships of the lines:

Line 1 and Line 2: Neither. They do not have the same slope, and they are not opposite reciprocals of each other.

Line 1 and Line 3: Perpendicular. The slopes of each line are opposite reciprocals: (-4/3 and 3/4)

Line 2 and Line 3: Neither. The slopes are the same but one is negative.

Answer:

34

Step-by-step explanation:

For √34 and the multiplication of √y to be equal to 34 y must be 34

Answer:

Average rate of change in dollars per year between years 15 to 20 is:

$5300 per year.

Step-by-step explanation:

Given that:

Initial Investment, P  = $5000

Formula:

[tex]A(t) = P(1.06)t[/tex]

To find: If James invests $5000,

average rate of change in dollars per year (rounded to the nearest dollar) between years 15 and 20=?

Solution:

First of all, let us find out A(15) and A(20):

Putting t = 15 first,

[tex]A(15) = 5000(1.06)\times 15 ....... (1)[/tex]

Putting t = 20,

[tex]A(20) = 5000(1.06)\times 20 ....... (2)[/tex]

Average rate of change / year is defined as:

[tex]\dfrac{\text{Change in value of A}}{\text{Number of years}}[/tex]

So, required rate of change:

[tex]\dfrac{A(20)-A(15)}{5}\\\Rightarrow \dfrac{5000 \times 1.06 \times 20-5000 \times 1.06 \times 15}{5}\\\Rightarrow \dfrac{5000 \times 1.06 \times (20-15)}{5}\\\Rightarrow \dfrac{5000 \times 1.06 \times 5}{5}\\\Rightarrow 5000 \times 1.06\\\Rightarrow \$5300\ per \ year[/tex]

So, the answer is:

Average rate of change in dollars per year between years 15 to 20 is:

$5300 per year.

Answer:

78/4=19.5, 68/7=9.71, 98/6=16.3

Step-by-step explanation:

Answer:

let alpha be x and beta be y

Step-by-step explanation:

x+y= -b/a

x+y=-1/6

and xy= c/a

xy= -1/3

according to question

1/x+1/y -xy =(x+y)/xy-xy

(-1/6)/(-1/3)-(-1/3)

1/2+1/3

the answer is 5/6

Answer:

D

Step-by-step explanation:

the answer is D

Answer:

1.

a. 5p + 3

b. 26p + 6

2.

a r = (v ÷(pi)h)½

b. r = 3.74 to the nearest hundredth

Step-by-step explanation:

1.

Area of deck = 40p² + 24p

Width of deck = 8p

Area = length × width(breadth)

a. Area = length × width

40p² + 24p = length × 8p

Factorise out 8p from the left hand side

8p(5p + 3) = length × 8p

Divide both sides by 8p

5p + 3 = length

b Perimeter of deck = 2 (length + width)

"" = 2(5p+3 + 8p)

"" = 2 (13p + 3)

"" = 26p + 6

2.

Volume = 200 mm³

Height = 17mm

a. isolate the r in the equation v = (pi)r²h

v = (pi)r²h

Divide both sides by (pi)h

v ÷ (pi)h = r²

Take the square roots of both sides

(v ÷ (pi)h)½ = r

b. find r using your answer in a.

r = (v ÷ (pi)h)½

r = (200 ÷ ( 22/7 × 17))½

r = (200 ÷ 53.4286)

r = 3.7433

r = 3.74 to the nearest hundredth

Answer: 1 3/4

Step-by-step explanation:

Step 1: Subtraction

1/4+1 1/2

Step 2: Addition

1 3/4

Hope it helps <3

Answer:

1 3/4

Step-by-step explanation:

Simplify 1/2 -1/4+1 1/2​

1/2 - 1/4 + 1 1/2 =

= 2/4 - 1/4 + 1 2/4

= 1/4 + 1 2/4

= 1 3/4

Answer:

[tex]\huge\boxed{j=38}[/tex]

Step-by-step explanation:

[tex]\dfrac{j}{-2}+7=-12\qquad\text{subtract 7 from both sides}\\\\\dfrac{j}{-2}+7-7=-12-7\\\\\dfrac{j}{-2}=-19\qquad\text{multiply both sides by (-2)}\\\\(-2)\!\!\!\!\!\!\!\diagup\cdot\dfrac{j}{-2\!\!\!\!\!\diagup}=(-2)(-19)\\\\j=38[/tex]

Answer: j = 38

Step-by-step explanation: First isolate j/-2 by subtracting

7 from both sides of the equation.

That gives you j/-2 = -19.

From here, since j is being divided by -2, multiply

both sides of the equation by -2 so j = 38.

Answer:

Angle B =  75 degrees

AC =  35.7

BC =  9.6

Step-by-step explanation:

Angle A = 15 degrees (given)

Angle C = 90 degrees (given)

c = 37 (given)

Angle B = 90-15 = 75 degrees

AC = AB cos(A) = 37 cos(15) = 35.7

BC = AB sin(A) = 37 sin(15) = 9.6

Answer: 3/4 cups per cake.

Step-by-step explanation:

He needs 3 cups for 4 cakes.

Then, if you want to know the amount that he needs for each cake, you need to see the quotient between the number of cups and the number of cakes:

S = 3cups/4 cakes = (3/4) cups per cake.

In the number line, 3/4 will be:

0--I--I--(here)--1--I--I--I--2