A grocery store recently sold a bag of peanuts for $0.76 and a bag of pistachios for $3.68. At the end of that day, 50 bags of peanuts and pistachios were sold for a total of $128.52. How many bags of each were sold?

9514 1404 393

Answer:

  23°

Step-by-step explanation:

The angle a vector makes relative to the +x axis is found as ...

  α = arctan(y/x) = arctan(4.30/10.3) ≈ 22.66°

The angle is about 23°.

__

Additional comment

This vector resides in the first quadrant, so no adjustment of the angle is needed. In other quadrants, 180° may need to be added or subtracted from the angle given by the arctan function to arrive at the correct value. (Some calculators and spreadsheets have an ATAN2(x, y) function that takes signs into account.)

Answer:

He detailed 16 cars.

912/57=16

Step-by-step explanation:

Answer:

Step-by-step explanation:

You have three data points. Equation of the line passing through (30,2), (45,2.75), and (60,3.50):

y = 0.5x + 0.5

It takes 0.5 hour to clean up.

Answer:

441

Step-by-step explanation:

Answer:

x=8

Step-by-step explanation:

Answer:

The sample observations are not a random​sample, so a test about a population proportion using the normal approximating method cannot be used.

Step-by-step explanation:

The necessary conditions are

The sample must be random and independently selected from the normally distributed population.

n*p and n*q both must be greater than 5

There must be two outcomes "success" and "failure"

The number of trials must be fixed.

From the given information 2), 3)and 4) conditions are satisfied, but not 1) because we are not given that people are selected randomly.

Answer: The sample observations are not a random​sample, so a test about a population proportion using the normal approximating method cannot be used.

Answer:

-1/20

Step-by-step explanation:

As x approaches c,

g(x)         1/5

------ = ------------ = -1/20            (matches last of the four given possible answers)

f(x)          -4

Answer:

[tex]\displaystyle \frac{-1}{20}[/tex]

General Formulas and Concepts:

Calculus

Limit Property [Division]:                                                                                              [tex]\displaystyle \lim_{x \to c} \frac{f(x)}{g(x)} = \frac{ \lim_{x \to c} f(x)}{ \lim_{x \to c} g(x)}[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \lim_{x \to c} f(x) = -4[/tex]

[tex]\displaystyle \lim_{x \to c} g(x) = \frac{1}{5}[/tex]

Step 2: Solve

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

Book: College Calculus 10e

The triangles are congruent by SAS theorem

Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape

The three sides are equal (SSS: side, side, side)

Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)

Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)

A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)

Given data ,

Let the first triangle be represented as ΔRST

Let the second triangle be represented as ΔXYZ

Now , the measure of side RS = measure of side XY

And , the measure of side ST = measure of side YZ

The measure of angle ∠S = measure of angle ∠Y

Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)

Therefore , the triangles ΔRST and ΔXYZ are congruent triangles by the SAS theorem

Hence , they are congruent

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Answer:

same

Step-by-step explanation:

Answer:

GP=ar^{n-i}

a=1

r=8/1=8

GP=8^(5-1)

GP=8^4

5th term=4096

9514 1404 393

Answer:

  250

Step-by-step explanation:

Let 'a' represent the number of adult tickets.

  a +(a -73) = 427

  2a = 500 . . . . . add 73

  a = 250 . . . . . . divide by 2

250 adult tickets were sold.

_____

Additional comment

I call this a "sum and difference problem" because we are given the total of two values and the difference between them. As you can see here, the larger of the two values is the average of the given numbers, their sum divided by 2. This is the generic solution to such a problem: the larger number is the average of the given sum and difference.

Answer:

1. True

2. Hundreds

Step-by-step explanation:

1. Natural numbers are positive integers (whole numbers) 1, 2, 3, etc. 0 is lower than all of them.

2. 3 (ten thousands), 0 (thousands), 8 (hundreds), 4 (tens), 6 (ones). Try reading out the number.

Answer:

1/4 ÷ 3/8 = 2/3

Step-by-step explanation:

When dividing fractions, you have to take the reciprocal of the second fraction, then multiply from there. The reciprocal of a fraction is basically flipped. So then, 1/4 ÷ 3/8 becomes 1/4 x 3/8. Multiplying fractions should be pretty straight forward as you just need to multiply numerator (top number of a fraction) with numerator and vice versa for the denominators (bottom number of a fraction).

So then you get: (1 x 8)/(3 x 4) = 8/12. Then you just simplify it by dividing the numerator and denominator by their greatest possible factor, which in this case is 4. So then, (8 ÷ 4)/(12 ÷ 4) = 2/3.

Answer:

540 miles per hour and 50 miles per hour respectively.

Step-by-step explanation:

Let the speed of plane in still air be x and the speed of wind be y.

ATQ, (x+y)*7.5=4425 and (x-y)*7.5=3675. Solving it, we get x=540 and y=50

Answer:

B

Step-by-step explanation:

they have the same intercepts

Line geometry are caused from the intersection of two line. The measure of angle x from the diagram is 110degrees

Line geometry are caused from the intersection of two lines. From the given figures, you can see that <KOH and <IOK forms a linear pair, hence;

<KOH + <IOK = 180

110 + <IOK = 180
<IOK = 180 - 110
<IOK = 70 degrees

Similarly <x and MIOK are linear pair pair such that <x + 1<IOK = 180
<x + 70 =180
<x = 180 - 70
<x = 110degrees

Hence the measure of angle x from the diagram is 110degrees

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Answer:

<IOK = 70 degrees

<x and <IOK form a linear pair, so m<x is = 110

Step-by-step explanation:

i did it on khan and got it right, i hope your day goes well and you get all your other questions right :)

9514 1404 393

Answer:

  C  ∛((x+2)/5) -3

Step-by-step explanation:

To find the inverse function, solve for y:

  x = f(y)

  x = 5(y +3)³ -2 . . . . . . substitute f(y)

  x +2 = 5(y +3)³ . . . . . add 2 -- already you know C is the answer

  (x +2)/5 = (y +3)³ . . . . divide by 5

  ∛((x +2)/5) = y +3 . . . . take the cube root

  ∛((x +2)/5) -3 = y . . . . subtract 3

  f^-1(x) = ∛((x +2)/5) -3 . . . . matches expression C

Answer:

-x - 13

Step-by-step explanation:

5(x-4) + 3x - 9x + 7

First we use the distributive property to remove the parenthesis

5x -20 + 3x - 9x + 7

then we combine the like terms

-x - 13

Answer:

139 ( D )

Step-by-step explanation:

Interest rate on loan = 4% = 0.04

Number of payments = 15

First 10 payments = 100 each

last 5 payments = 200 each

Calculating the value of K

K = [ ( 100 / 0.04 * ( 1-1 / 1.04^10 ) + 200/0.04 * ( 1-1 / (1 +0.04)^5)*  1 /1.04^10)

*  1.1 - 100 / 0.04 * ( 1-1 / (1+0.04)^5 ) - 200/0.04 * (1-1 /1.04^5) * 1/1.04^10)*0.04 / ( 1-1 / 1.04^5) * (1 + 0.04)^5

= 138.6051 ≈ 139

Answer:

a

Step-by-step explanation:

The correct answer is option C which is the graph of the equation ( x-1 )² + ( y+ 2 )² = 4 will be the circle in the third and the fourth quadrant.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

Given equation is ( x-1 )² + ( y + 2 )² = 4

The graph of the equation is attached with the answer below when we plot the graph we will get the circle that is lying in the third and the fourth quadrant.

Therefore the correct answer is option C which is the graph of the equation ( x-1 )² + ( y+ 2 )² = 4 will be the circle in the third and the fourth quadrant.

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Answer:

Reject H0 ; and conclude that call length does not follow a normal distribution.

Step-by-step explanation:

Given :

The hypothesis :

H0: Call lengths outside normal customer roaming areas follows normal distribution

H1: Call lengths outside normal customer roaming areas do not follows normal distribution

Mean, μ = 14.3

Standard deviation, σ = 3.7

From the frequencies Given :

Expected values can be calculated :

Observed values :

16, 75, 139, 105, 37, 18 ; Total = 400

P(Z < (x - μ) / σ)) * total frequency

x = frequency

For x = 5 ;

P(Z < (5 - 14.3) / 3.7)) * 400 = 2.391

For x = 10;

P(Z < (10 - 14.3) / 3.7)) * 400 = 46.644

For x = 15;

P(Z < (15 - 14.3) / 3.7)) * 400 = 180.960

For x = 20;

P(Z < (20 - 14.3) / 3.7)) * 400 = 145.32

For x = 25;

P(Z < (25 - 14.3) / 3.7)) * 400 = 23.92

For x = 30;

P(Z < (30 - 14.3) / 3.7)) * 400 = 0.766

χ² = Σ(O - E)²/E

O = observed values

E = Expected values

χ² = (26-2.391)^2 / 2.391 + (75-46.644)^2 / 46.644 + (139-180.96)^2 / 180.96 + (105-145.32)^2 / 145.32 + (37-23.92)^2 / 23.92 + (18-0.766)^2 / 0.766 = 666.17

χ² = 666.17

The critical value "; df = n - 1= 6-1 = 5

α = 0.05

χ²critical(0.05 ; 5) = 11.07

χ²statistic > χ²critical ; Reject the Null, H0 ; and conclude that call length does not follow a normal distribution.

Answer:

Step-by-step explanation:

Answer:

431.2

Step-by-step explanation:

Area of a regular polygon = # of sides * side length of 1 side * apothem

We want to find the area of a regular polygon with 7 sides, an apothem of 8 meters, and a side length with 7.7 meters

So # of sides = 7

apothem = 8

side length = 7.7

so the area would equal 7 * 8 * 7.7 = 431.2

It says to round to the nearest tenth however 431.2 is already rounded to the nearest tenth

Answer:

That answer ^ is incorrect. The correct answer ( in acellus that is ) is 2

15.6

Step-by-step explanation:

Step-by-step explanation:

you have to type shift an cos button together at one time and then write 0.35 youwill get answer

Answer:

0.0765 = 7.65% probability that, for any day, the number of special orders sent out will be exactly 3

Step-by-step explanation:

We have the mean, which means that the poisson distribution is used to solve this question.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

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

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

The auto parts department of an automotive dealership sends out a mean of 6.3 special orders daily.

This means that [tex]\mu = 6.3[/tex]

What is the probability that, for any day, the number of special orders sent out will be exactly 3?

This is P(X = 3). So

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

[tex]P(X = 3) = \frac{e^{-6.3}*6.3^{3}}{(3)!} = 0.0765[/tex]

0.0765 = 7.65% probability that, for any day, the number of special orders sent out will be exactly 3

Answer:

2116.8 in^3

Step-by-step explanation:

V = l*w*h

All the units need to be the same

Convert 1.4 ft to inches

1.4 ft * 12 inches/ ft = 16.8 inches

V = 14 * 16.8  * 9

   = 2116.8 in^3

Answer:

38 ft²

Step-by-step explanation:

The shape consists of a rectangle and two triangles.

Area of the shape = area of rectangle + area of the two triangles

✔️Area if the rectangle = L × W

L = 8 + 2 = 10 ft

W = 3 ft

Area of rectangle = 10 × 3 = 30 ft²

✔️Area of the large triangle = ½ × bh

b = 4 ft

h = 3 ft

Area of large triangle = ½ × 4 × 3 = 6 ft²

✔️Area of the small triangle = ½ × bh

b = 2 ft

h = 2 ft

Area of large triangle = ½ × 2 × 2 = 2 ft²

✅Area of the shape = 30 + 6 + 2 = 38 ft²