The cost of bananas varies directly with the number of pounds bought. If 6 pounds
cost $5.22, find the cost of 3 pounds.

The probability that a call lasts less than 4 minutes is 0.1474.

Given, Mean = μ = 6.3 minutes

Standard deviation = σ = 2.2 minutes

Using z-score formula, z = (X - μ) / σ(a) To find P(5 < X < 10), we have to calculate z1 and z2 respectively, z1 = (5 - 6.3) / 2.2 = -0.59z2 = (10 - 6.3) / 2.2 = 1.68

Now, we can find the probability, P(5 < X < 10) = P(-0.59 < z < 1.68)P(-0.59 < z < 1.68) = Φ(1.68) - Φ(-0.59)  ≈ 0.833 - 0.2778 = 0.5552

Therefore, the probability that a call lasts between 5 and 10 minutes is 0.5552.

(b) To find P(X > 7), we have to calculate the z-score first,z = (X - μ) / σz = (7 - 6.3) / 2.2 = 0.32

Now, we can find the probability, P(X > 7) = P(z > 0.32) = 1 - Φ(0.32)≈ 1 - 0.6255 = 0.3745

Therefore, the probability that a call lasts more than 7 minutes is 0.3745.

(c) To find P(X < 4), we have to calculate the z-score first,z = (X - μ) / σz = (4 - 6.3) / 2.2 = -1.05Now, we can find the probability, P(X < 4) = P(z < -1.05) = Φ(-1.05)≈ 0.1474

Therefore, the probability that a call lasts less than 4 minutes is 0.1474.

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Answer:

13.2 miles

Step-by-step explanation:

To solve this, we will need to first solve for the base of the triangle and then use the information we find to solve for the shortest route.

(5.5 + 3.5)² + b² = 15²

9² + b² = 15²

81 + b² = 225

b² = 144

b = 12

Now that we know that the base is 12 miles, we can use that and the 5.5 miles in between Adamsburg and Chenoa to find the shortest route (hypotenuse).

5.5² + 12² = c²

30.25 + 144 = c²

174.25 = c²

13.2 ≈ c

Therefore, the shortest route from Chenoa to Robertsville is about 13.2 miles.

Answer:

Step-by-step explanation:

Remark

It's a permutation question, Order does not matter.

Answer

Most people will try and tell you that the answer is 20 * 19. That would make a pure pure permutation question. The problem is that the actual answer is 20 * 20  because she can have 2 scoops are the same. I would still answer permutation but be prepared to get it incorrect.

When two lines intersect they form two pairs of opposite angles, A + C and B + D. Another word for opposite angles are vertical angles.

figure51

Vertical angles are always congruent, which means that they are equal.

Adjacent angles are angles that come out of the same vertex. Adjacent angles share a common ray and do not overlap.

figure52

The size of the angle xzy in the picture above is the sum of the angles A and B.

Two angles are said to be complementary when the sum of the two angles is 90°.

figure53

Two angles are said to be supplementary when the sum of the two angles is 180°.

figure54

If we have two parallel lines and have a third line that crosses them as in the ficture below - the crossing line is called a transversal

When a transversal intersects with two parallel lines eight angles are produced.

figure55

The eight angles will together form four pairs of corresponding angles. Angles 1 and 5 constitutes one of the pairs. Corresponding angles are congruent. All angles that have the same position with regards to the parallel lines and the transversal are corresponding pairs e.g. 3 + 7, 4 + 8 and 2 + 6.

Angles that are in the area between the parallel lines like angle 2 and 8 above are called interior angles whereas the angles that are on the outside of the two parallel lines like 1 and 6 are called exterior angles.

Angles that are on the opposite sides of the transversal are called alternate angles e.g. 1 + 8.

All angles that are either exterior angles, interior angles, alternate angles or corresponding angles are all congruent.

Example

figure56

The picture above shows two parallel lines with a transversal. The angle 6 is 65°. Is there any other angle that also measures 65°?

6 and 8 are vertical angles and are thus congruent which means angle 8 is also 65°.

6 and 2 are corresponding angles and are thus congruent which means angle 2 is 65°.

6 and 4 are alternate exterior angles and thus congruent which means angle 4 is 65°.

Step-by-step explanation:

2x 3x5 = 30 ÷ 3 = 10

hope this helps

Answer:

5.59

Step-by-step explanation:

22.36/4 = 5.59

hope this helps!

Im so sorry that people these days are racist towards black people i just wish that people could protest not riot people are dying and and suffering i cant  believe that is alright not all white people are racist  and i just want peace in this world people losing there homes their cars their money i will not stand up for the rioting or the violince but i will not stand for racisim either srew every racist b**ch out there. please give me feedback i want to know your point of view

\(\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a=12\\ b=6\\ h=9 \end{cases}\implies A=\cfrac{9(12+6)}{2}\implies A=81~ft^2\)

Answer:

1. -2 degrees

2. 10 feet below sea level

Step-by-step explanation:

To find the values of trigonometric functions, we can use the acronym SOHCAHTOA, which stands for:

Because we are only looking for sin A and cos A, we'll use SOH and CAH. Remember that the positions are relative to angle A. So side BC would be the opposite and side AC would be the adjacent sides.

The answer is the third option, sin A = 24/26, cos A = 10/26.

The value of b² - 4ac for the equation x² + 5x + 4 = 0 is 9.

What is the discriminant of a polynomial?

The discriminant of a polynomial is a function of its coefficients and is represented by the capital ‘D’ or Delta symbol (Δ). It shows the nature of the roots of any quadratic equations where a, b, and c are real numbers.

It is represented as ‘D’

D = b² - 4ac

Where,

a is the coefficient of x²

b is the coefficient of x

c is a constant term

x² + 5x + 4 = 0

We have given:

x² + 5x + 4 = 0

Comparing the equation with the standard form.

a = 1, b = 5 and c = 4

Substituting it in the formula

D = 5² - 4 × 1 + 4

By further calculation

D = 25 - 16

D = 9,

The quadratic roots are real and distinct

Therefore, the value of b² - 4ac is 9.

Hence, The value of b² - 4ac for the equation x² + 5x + 4 = 0 is 9.

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Answer:

can you expand on your question?

Step-by-step explanation:

Answer:

If the family has $800 for sit-down restaurant meals and fast food and they budgeted all of it for fast food, then they can buy $800/$20 = 40 fast food meals.

Step-by-step explanation:

yw;)

Answer:

40

Step-by-step explanation:

No. Of Meal=Budget/price of Meal

=800/ 20

=40

Given that sec(t) = -2.475 and angle t is in Quadrant III, the other five trigonometric ratios are as follows: cos(t) ≈ 0.404, sin(t) ≈ -0.916, tan(t) ≈ 2.268, csc(t) ≈ -1.092, and cot(t) ≈ 0.441.

We are given that sec(t) = -2.475, which represents the reciprocal of the cosine of angle t. Since sec(t) is negative and angle t is in Quadrant III, we can deduce that the cosine of t is negative. To find cos(t), we can use the identity sec(t) = 1/cos(t) and solve for cos(t), resulting in cos(t) ≈ 0.404.

Using the Pythagorean identity \(sin^2(t) + cos^2(t)\) = 1, we can find sin(t) as sin(t) = ±\(\sqrt(1 - cos^2(t))\). Since angle t is in Quadrant III, where sine is negative, we take the negative value. Thus, sin(t) ≈ -0.916.

By dividing sin(t) by cos(t), we obtain the tangent of t. Hence, tan(t) ≈ sin(t)/cos(t) ≈ -0.916/0.404 ≈ 2.268.

Cosecant (csc) is the reciprocal of sine, so csc(t) ≈ 1/sin(t) ≈ -1.092.

Similarly, cotangent (cot) is the reciprocal of tangent, so cot(t) ≈ 1/tan(t) ≈ 1/2.268 ≈ 0.441.

In conclusion, when sec(t) = -2.475 and angle t is in Quadrant III, the other five trigonometric ratios are approximately: cos(t) ≈ 0.404, sin(t) ≈ -0.916, tan(t) ≈ 2.268, csc(t) ≈ -1.092, and cot(t) ≈ 0.441.

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The sine of the angle θ is 3/5 and the cosine of the angle θ is 4/5.

What is triangle ?

Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.

The image you provided is a right triangle with a hypotenuse of 10 and one leg of 6. To find the length of the other leg, you can use the Pythagorean theorem:

\(a^2 + b^2 = c^2\)

where a and b are the lengths of the legs of the triangle, and c is the length of the hypotenuse.

In this case, you know that c = 10 and a = 6, so you can solve for b:

\(b^2 = c^2 - a^2\)

\(b^2 = 10^2 - 6^2\)

\(b^2 = 64\)

b = 8

Therefore, the length of the other leg is 8.

Now that you know the lengths of the legs of the triangle, you can use trigonometric ratios to find the measures of the angles.

The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, the angle opposite the side of length 6 is the angle θ, so:

sin θ = opposite/hypotenuse = 6/10 = 3/5

The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. In this case, the adjacent side is the side of length 8, so:

cos θ = adjacent/hypotenuse = 8/10 = 4/5

Therefore, the sine of the angle θ is 3/5 and the cosine of the angle θ is 4/5.

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Answer:

Domain: all real numbers

Step-by-step explanation:

This graph is a parabola. It's equation looks like it should be:

y = x^2 - 1

If you have a graph and are looking for the domain, you are determining where the graph exists. For what x's the graph exists. If you have the equation then the domain is what x's may be put into the equation. There are no limitations on what numbers can go into this equation so the domain is all real numbers.

There are several ways to write the domain is all real numbers, set builder notation and interval notation. But the main idea is that it is all real numbers.

Answer:

segun yo es asi no confies mucho en mi

Step-by-step explanation:

200 kg total de papel

primer grupo= 60kg

segundo= 13kg

tercero= 45.93

cuarto= x

si sumamos el total recolectado por los tres primero grupos

60+13+45.93

esto nos da

118.93

si en total se recgio 200kg de basura y tenemos que los tres primeros grupos recogieron 118.93, entonces solo queda restar el total menos lo recolectado

200-188.93= cuarto grupo

cuarto grupo=81.07kg

Answer:

21

Step-by-step explanation:

straight line = 180 degrees ( H,D,R)

180 = 7x - 3 + 2x  - 6    

180 = 7x + 2x - 3 - 6     (group the same type number together)

180 = 9x -9           (simplify the numbers)

189 = 9x    (+9)

21 = x    (divide by 9)

Answer:

A = 28.3 cubic inches; P = 20.1 inches

Step-by-step explanation:

Looks like 3/4 of a full circle

The area of a circle is calculated with the formula: \(\pi r^{2}\)

Since the problem wants pi = 3.14, we use 3.14 instead of pi in the equation.

The radius is given as 3 inches

Area = \(3.14*3^{2} = 3.14*9 = 28.26\) cubic inches = 28.3 cubic inches

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

Perimeter is calculated with \(2\pi r\).

But this is 3/4 of a circle with an additional two 3-inch sides

Perimeter = \(\frac{3}{4}*2\pi r\) + 2(3) = 14.1 + 6 = 20.1 inches

Answer:

Step-by-step explanation:

Answer:

4 pies

Step-by-step explanation:

Hello!

We know that 12 apple pies are 75 percent of the total apple pies.

Let x = # of pies total.

This means that 75% of x, or 0.75x is 12

Solve:

Now, 16 is the total number of pies. To find the number thrown out, we subtract 12.

16 - 12 = 4

4 pies were thrown out

Solution:

Let "a" represent total apple pies.

Note that:

Simplify the LHS:

Use cross multiplication:

Divide 75 both sides:

If there were 16 apples and 12 were sold, 4 apple pies were thrown out.

Step-by-step explanation:

4.5÷4= 1.125

so each time she goes around the rectangle she's covering 1.125 km and we seed the length is twice the breadth x+2x=1.125

so 1.125 / 3 to give x which is the breadth=0.375 x 2 is equal to 0.75 km or 750 m this is the length of the field

Step-by-step explanation:

The length of a rectangular field is twice it's breadth. A girl jogged around it 4 times and covered a distance of 4.5 km. What is the length of the field?

The distance cover in 4 laps is 4.5 km, So one lap is 4.5/4 = 1.125 km.

Let the breadth of the field be B so the length will be L or 2B.

The perimeter of the field is 2L+2B or 4B+2B = 6B = 1.125, so B = 1.125/6 = 0.1875 km and the length is 2*0.1875 = 0.375 km.

Check: perimeter = 2*0.375 + 2*0.1875 = 1.125 km and 4 laps covers 4*1.125 = 4.5 km. correct.

The field is 375 m long.

An writing format called R Markdown (. Rmd) makes it simple to create dynamic documents, presentations, and reports with R.

It mixes R code chunks that are embedded and run so that their result can be included in the final document with the basic grammar of R markdown, a simple plain text format. The following are some benefits of utilizing R markdown: explicitly connects your data, R code, and output to produce a workflow that is completely reproducible. You can include ALL of the R code that was used to explore, summarize, and analyze your data in a single, simple-to-read document.

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Answer:

v= -2

Step-by-step explanation:

2v+7=3 ------> 2v = 3 - 7 ----------> 2v = -4 ( divide by 2)

v = -2

The value of QR is 5

A line segment can be defined as the part of a straight line bounded by two different end points, and also contains every point on the line between its endpoints.

From the information given, the line QS has segments, line QR , RS and QS with R and the midpoint between Q and S

Given the points;

We have that;

QR + RS = QS

substitute the values

5x + x + 3 = 9

collect like terms

6x = 9 - 3

6x = 6

Make 'x' the subject

x = 6/ 6

x = 1

But QR = 5x = 5(1) = 5

Thus, the value of QR is 5

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The complete question;

If R is the midpoint of QS and QR = 5x, RS = x + 3, and QS = 9, what is QR?

Third quartile Q₃ of the given data is 11

correct option is: b

What is the 75th percentile value?

0.675

For instance, the median represents the 50th percentile, the first quartile represents the 25th percentile, and the third quartile represents the 75th percentile.

What exactly is Q3?

Q3, the third quartile, is known as the 'upper quartile,' and represents the 75th percentile, which means that only 25% of the values in the set are greater than this value.

given data:

7,14,8,10,7,8,9,7,14,6.

In ascending, order data is 6,7,7,7,8,8,9,10,14,14.

number of terms N = 10

therefore, third quartile Q₃ = \(\frac{3}{4} (n + 1)\)

Q₃ = \(\frac{3}{4} (10 + 1)\)

Q₃ = 8.25th term

Q₃ = 8th term + 0.25 = 11

therefore, therefore, third quartile Q₃ of the given data is 10

correct option is: b

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Answer: 30

Step-by-step explanation: So clearly we want 45 to be divided into x and 2x. Because the sum of the two parts is 45, so x + 2x = 45 which gives us the value of x = 15.

So the boy has 15 while the girl has 30