A clothing store orders 15 boxes of shirts to restock their shelves. There are 125 shirts in each box. How many shirts does the clothing store order?

Step-by-step explanation:

law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

a,b,c being the sides of the triangle, A, B, C are the corresponding opposite angles in the triangle.

the angle of depression is the external angle of the triangle vertex at the balloon. that means the internal angle is 60°, as both together must be 90° (the angle between the height of the balloon and the horizontal line at the balloon).

the angles at the ground at the fire are mirrored : the internal angle there is 30°, the external angle is 60°.

and so,

height/sin(30) = 150/0.5 = distance/sin(60)

distance = sin(60)×150/0.5 = sin(60)×300 =

= 259.8076211... ft ≈ 260 ft

Answer:

x = 10/243

Step-by-step explanation:

3^5x = 10

243x = 10

Divide 243 on both sides

10/243

Answer:

Answer:

131°

Step-by-step explanation:

Since KNJ is a straight line,

∡KNM +∡MNJ= 180° (adj. ∡s on a str. line)

(8x -5)° +(4x -19)°= 180°

Simplify:

12x -24= 180

+24 on both sides:

12x= 180 +24

12x= 204

Divide both sides by 12:

x= 204 ÷12

x= 17

∡KNM

= (8x -5)°

= [8(17) -5]°

= (136 -5)°

= 131°

The mechanical advantage of the given machine is 40, Velocity ratio is 80 and efficiency is 0.5.

The given question is concerned with finding the mechanical advantage, velocity ratio and efficiency of a weight lifting machine.

The problem has provided the following information:

Weight of the object, W = 1 kN = 1000 NEffort applied, E = 25 NHeight through which the object is lifted, h = 100 mm = 0.1 m Distance through which the effort is applied, d = 8 m

We know that, mechanical advantage = load/effort = W/E and velocity ratio = distance moved by effort/distance moved by the load.Mechanical advantage

The mechanical advantage of the given machine is given by; Mechanical advantage = load/effort = W/E= 1000/25= 40Velocity ratioThe velocity ratio of the given machine is given by;

Velocity ratio = distance moved by effort/distance moved by the load.= d/h = 8/0.1= 80EfficiencyThe efficiency of the given machine is given by;

Efficiency = (load × distance moved by load) / (effort × distance moved by effort)Efficiency = (W × h) / (E × d)= (1000 × 0.1) / (25 × 8)= 0.5

Therefore, the mechanical advantage of the given machine is 40, velocity ratio is 80 and efficiency is 0.5.

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Answer:

3.125π m²

Step-by-step explanation:

First let's find the area of a full circle with diameter of 5m. Since we need the radius to find the area, we divide the diameter by two to get the radius.

5m/2=2.5m

Now let's find the area of a full circle

A=πr²

A=π2.5²

A=6.25π

Now we divide it by two to get the area of a semicircle

6.25π/2=3.125π m²

The fraction that represents the rate between PKR and Paisas is given as follows:

1/50.

A fraction is a numerical representation of the division of the two terms x and y, as follows:

Fraction = x/y.

As the rate is PKR 1 = 50 paisas, we have that the fraction that represents the rate between PKR and Paisas is given as follows:

1/50.

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The addition equation or a subtraction equation to describe the diagram is (-9)—(-4) = -13

We know that,

In a mathematical operation we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

We have a line graph shown in the picture.

The small arrow represents the length of 4 but as it is indicating negative direction, so we take -4

Similarly, the big arrow represents the length of 9 as it is indicating negative direction, so we take -9

The sum of the lengths:

(-9)—(-4) = -13

Thus, the addition equation or a subtraction equation to describe the diagram is (-9)—(-4) = -13

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The end behavior of the polynomials are as follows;

(a) y = x³ - 9·x² + 8·x - 14

End behavior; y → ∞ as x → ∞

\({}\)                        y → -∞ as x → -∞

(b) y = -8·x⁴ + 13·x + 800

End behavior; y → -∞ as x → -∞

\({}\)                        y → -∞ as x → ∞

The end behavior of a polynomial is the characteristics of the graph of the polynomial as the input (x-values), tends to plus and minus infinity.

The factors that effect the end behavior of a polynomial are;

The degree of the polynomial, (even or odd)

The sign of the leading coefficient of the polynomial (positive or negative)

The leading coefficient is the coefficient of the term with the highest degree.

(a) The polynomial, function, y = x³ - 9·x² + 8·x  - 14

The specified polynomial is a third degree polynomial, with a positive leading coefficient of 1, the end behavior is therefore;

y tends to positive infinity as x tends to positive infinity

y tends to negative infinity as x tends to negative infinity

End behavior;

y → ∞ as x → ∞

y → -∞ as x → -∞

(b) The polynomial function can be expressed as follows;

y = -8·x⁴ + 13·x + 800

The above polynomial of degree 4 is an even degree polynomial

The leading coefficient of the polynomial is -8, therefore, the leading coefficient is negative

The shape of the graph of the polynomial is therefore ∩ shaped, such that the end behavior is as follows;

y-values approaches negative infinity as x approaches negative infinity

y-values approaches negative infinity as x approaches positive infinity

End behavior;

y → -∞ as x → -∞

y → -∞ as x → ∞

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Answer:

height of the balloon = 6.32 km

Step-by-step explanation:

The question wants us to find the height of the balloon .

They are observing the balloon from two tracking stations on the ground.  The tracking stations are 6 km apart . From Dominic point of view the hair balloon is at an angle of elevation of 72° and from Adriana point of view the elevation is 58° . The illustration forms a triangle containing 2 right angles with a similar height.

To find the height we must find the hypotenuse of one of the right angle triangle. WE are given 2 angle and a side of 6 km. The third angle is 180 - 72 - 58 = 50°.

Using sin rule

6/sin 50° = b/sin 72°

cross multiply

6 sin 72° = b sin 50°

divide both sides by sin 50°

b = 6 sin 72°/sin 50°

b = 6 × 0.95105651629 /0.76604444311

b = 5.70633909777 /0.76604444311

b = 7.44909665372

b ≈ 7.45 km

The height can be found since we know the hypotenuse of one side of one of the right angle triangle.

sin 58° = opposite/hypotenuse

sin 58° = h/7.45

cross multiply

h = 7.45 × sin 58°

h = 7.45 × 0.84804809615

h = 6.31795831637

h ≈ 6.32 km

The cost of gas is proportional to the volume of gas because a constant rate of $3.15 to 1 gallon of gas.

From the given table;

The volume of the first gas Layla bought = 3 gallons.

The cost of the 3 gallons = 9.45

Therefore the cost of 1 gallon = ?

That is:

3 gallons = $9.45

1 gallon = X

Make X the subject of formula:

X = 9.45/3 = $3.15

Therefore, the cost of 11 gallons of gas would be = 11×3.15 = $34.65. This is because the cost of 1 gallon would be = $3.15.

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Answer:18

Step-by-step explanation:15 + 6 u add the 15 and the 6 for it to be 18

The answers are 4. a) 15.7 cm, b) 26.25 m, 5. a) 128.74 cm, b) 40.82 mm, c) 45 cm and 6. 777.28 cm

Given are the circles and the circular items we need to find their circumference,

Circumference of a circle = 2π × radius = Diameter × π

4. a) Circumference = 5 × 3.14 = 15.7 cm

b) Circumference = 8.36 × 3.14 = 26.25 m

5. a) Circumference = 41 × 3.14 = 128.74 cm

b) Circumference = 13 × 3.14 = 40.82 mm

c) Circumference = 14.3 × 3.14 = 45 cm

6.

The perimeter of the cloth = circumference of the circular ends plus length in the middle,

= 76 × 2 × 3.14 + 150 × 2

= 477.28 + 300

= 777.28 cm

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The probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing is 8/25 or 0.32 (rounded to the nearest millionth).

1. Calculate the total number of students on the Student Government Board by summing up the numbers in the table:

  Total Students = 2 + 2 + 2 + 4 + 0 + 3 + 4 + 2 = 19

2. Calculate the total number of graduate students on the Student Government Board:

  Total Graduate Students = 2 + 0 = 2

3. Calculate the total number of students living in on-campus housing:

  Total On-Campus Housing = 2 + 2 + 0 + 4 + 2 = 10

4. Calculate the probability of selecting a graduate student from the Student Government Board by dividing the total number of graduate students by the total number of students:

  Probability of Graduate Student = Total Graduate Students / Total Students = 2 / 19

5. Calculate the probability of selecting a student living in on-campus housing by dividing the total number of students in on-campus housing by the total number of students:

  Probability of On-Campus Housing = Total On-Campus Housing / Total Students = 10 / 19

6. Calculate the probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing by summing up the probabilities from steps 4 and 5:

  Probability = Probability of Graduate Student + Probability of On-Campus Housing = 2 / 19 + 10 / 19

7. Simplify the fraction if necessary. In this case, the fraction cannot be simplified further, so the final probability is 2 / 19 + 10 / 19 = 12 / 19.

8. Convert the fraction to a decimal by dividing the numerator by the denominator: 12 / 19 ≈ 0.631578947, which rounds to 0.632 (rounded to the nearest thousandth).

9. Finally, express the probability as a fraction in lowest terms: 12 / 19 is already in lowest terms.

Therefore, the probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing is 12/19 or approximately 0.632 (rounded to the nearest thousandth).

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Answer:

x = 6

Step-by-step explanation: (See picture)

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Hope this helps!

Have a great day and God bless! :)

The Maclaurin series of xcos(-x) up to n = 3 is

\(m(x)= xcos(-x)= x-\frac{1}{2}x^3+\frac{1}{24}x^5-\frac{1}{720}x^7+\frac{1}{40320}x^9+\ldots \:\)

The function is given in the question as

m(x) = xcos(-x)

Taylor (Maclaurin) series of xcos(x) up to n=5

A Maclaurin series is given by  f(x),

\(f\left(x\right)=f\left(a\right)+\frac{f^'\left(a\right)}{1!}\left(x-a\right)+\frac{f^{''}\left(a\right)}{2!}\left(x-a\right)^2+\frac{f^{'''}\left(a\right)}{3!}\left(x-a\right)^3+\ldots\)

\(f\left(x\right)=f\left(0\right)+\frac{f^'\left(0\right)}{1!}\left(x\right)+\frac{f^{''}\left(0\right)}{2!}\left(x\right)^2+\frac{f^{'''}\left(0\right)}{3!}\left(x\right)^3+\ldots\)

We need to do to get the desired polynomial is to calculate the derivatives, evaluate them at the given point, and plug the results into the given formula.

f⁽⁰⁾(x) = f(x) = xcos(x)

Evaluate the function at the point: f(0)=0

1st derivative: f(1)(x)=(f(0)(x))′=(xcos(x))′=−xsin(x)+cos(x)

1st derivative at the given point: (f(0))′=1

2nd derivative: f(2)(x)=(f(1)(x))′=(−xsin(x)+cos(x))′=−xcos(x)−2sin(x)

Evaluate the 2nd derivative at the given point: (f(0))′′=0

3rd derivative: f(3)(x)=(f(2)(x))′=(−xcos(x)−2sin(x))′=xsin(x)−3cos(x)

Evaluate the 3rd derivative at the given point: (f(0))′′′=−3

Now, use the calculated values to get a polynomial:

\(m(x)=0+\frac{1}{1!}x+\frac{0}{2!}x^2+\frac{-3}{3!}x^3+.....\)

\(m(x)=x-\frac{1}{2}x^3+\frac{1}{24}x^5-\frac{1}{720}x^7+\frac{1}{40320}x^9+\ldots \:\)

Thus, the Maclaurin series of xcos(-x) up to n = 3 is

\(m(x)= xcos(-x)= x-\frac{1}{2}x^3+\frac{1}{24}x^5-\frac{1}{720}x^7+\frac{1}{40320}x^9+\ldots \:\)

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Answer:

B: rectangle JKLM ~ rectangle QRSP

Step-by-step explanation:

5/6=0.83

12.5=0.83

JK corresponds to QR

JM corresponds to PQ

rectangle JKLM ~ rectangle QRSP

Answer:

8 tickets

Step-by-step explanation:

Take the total cost and divide by the cost of one ticket to get the number of tickets purchased

66 / 8.25

8

Answer:

3.00/8

Step-by-step explanation:

because u simplify 15/5 and u get 3

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

\(y = \frac{1}{2} \times \frac{8 \sqrt{3} }{3} \\ \)

\(y = \frac{4 \sqrt{3} }{3} \\ \)

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

\(x = \frac{ \sqrt{3} }{2} \times \frac{8 \sqrt{3} }{3} \\ \)

\(x = \frac{8 \times { \sqrt{3} }^{2} }{2 \times 3} \\ \)

\(x = \frac{8 \times 3}{2 \times 3} \\ \)

\(x = \frac{8}{2} \\ \)

\(x = 4\)

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The function has three distinct real zeros.

The correct answer is A.

To determine the statement about the zeros of the graphed function, let's analyze the given information.

We have the following points on the graph:

(0.8, 4), (2, -4), (4.6, 0.5), (6, 0), and (7.5, 8)

Additionally, the function intercepts the x-axis at 1, 4, and 6 units.

To find the zeros of the function, we need to identify the x-values where the function intersects the x-axis.

From the given information, we know that the function intersects the x-axis at 1, 4, and 6 units.

These three x-values correspond to three distinct real zeros of the function.

The correct statement about the zeros of the graphed function is:

The function has three distinct real zeros.

The correct answer is A.

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5x+7x=660;

12x=660;

x=660:12;

x=55 (kg).

Then 5x=5×55=275 kg and 7x=7×55= 385 kg.

The required ratio is therefore

660= 275:385.

Answer:

D

Step-by-step explanation:

In total, the number of greetings will be 1159.

Mathematical symbols used to represent quantities or values include numbers. They are employed in the measurement, comparison, addition, subtraction, multiplication, and division processes in mathematics. According to their qualities and properties, numbers can be categorized into a variety of groups, including natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, and complex numbers. There are specific properties and guidelines for mathematical operations for each group of numbers. Mathematics depends on numbers, which are also utilized in many other disciplines, including science, engineering, economics, and statistics.

The number of greetings exchanged between the host and the other mothers and daughters must be counted first. Since there is only one host, the number of mother-daughter pairs is 20 - 1 = 19. There are thus a total of 38 greetings, 19 between the host and the other moms, and 19 between the host and the other daughters.

The number of pleasantries exchanged between the guest mums and everyone else must next be tallied. The host, the other mothers, and the daughters must all be greeted, making a total of 20 - 1 = 19 guest mothers. Thus, each host mother must extend 1 + 19 + 20 = 40 greetings. There will be 760 greetings exchanged between the guest mothers and everyone, or 19 x 40.

The number of pleasantries exchanged between the mothers and the invited girls must also be tallied. Moreover, there are 20 guest girls, so 19 of them must welcome the mothers. As a result, there will be 361 pleasantries exchanged between the mothers and the guest daughters.

In total, the number of greetings will be 38 + 760 + 361 = 1159.

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Answer:

400 litres

Step-by-step explanation:

Answer:

Since M1 has the higher probability of being in the desired range, we choose M1.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Two machines M1, M2 are used to manufacture resistors with a design specification of 1000 ohm with 10% tolerance.

So we need the machines to be within 1000 - 0.1*1000 = 900 ohms and 1000 + 0.1*1000 = 1100 ohms.

For each machine, we need to find the probabilty of the machine being in this range. We choose the one with the higher probability.

M1:

Resistors of M1 are found to follow normal distribution with mean 1050 ohm and standard deviation of 100 ohm. This means that \(\mu = 1050, \sigma = 100\)

The probability is the pvalue of Z when X = 1100 subtracted by the pvalue of Z when X = 900. So

X = 1100

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{1100 - 1050}{100}\)

\(Z = 0.5\)

\(Z = 0.5\) has a pvalue of 0.6915.

X = 900

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{900 - 1050}{100}\)

\(Z = -1.5\)

\(Z = -1.5\) has a pvalue of 0.0668

0.6915 - 0.0668 = 0.6247.

M1 has a 62.47% probability of being in the desired range.

M2:

M2 are found to follow normal distribution with mean 1000 ohm and standard deviation of 120 ohm. This means that \(\mu = 1000, \sigma = 120\)

X = 1100

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{1100 - 1000}{120}\)

\(Z = 0.83\)

\(Z = 0.83\) has a pvalue of 0.7967.

X = 900

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{900 - 1000}{120}\)

\(Z = -0.83\)

\(Z = -0.83\) has a pvalue of 0.2033

0.7967 - 0.2033 = 0.5934

M2 has a 59.34% probability of being in the desired range.

Since M1 has the higher probability of being in the desired range, we choose M1.

Answer:

There are 54 granola bars left.

Answer:

y=5

Step-by-step explanation:

If it is perpendicular to the y-axis, that means it is a horizontal line so the slope m=0.

Use the equation

y-y=m(x-x)

y-5=0(x-(-4))

y-5=0

y=5

Answer:

y=5

Step-by-step explanation:

9514 1404 393

Answer:

  x = 5

Step-by-step explanation:

The sum of the base lengths is twice the length of the midline.

  EF +HG = 2JK

  (3x +2) +(7x -2) = 2(25)

  10x = 50 . . . . . . simplify

  x = 5 . . . . . . . . . divide by 10

Answer:

the answer is x=5

Step-by-step explanation:

:)))))

Answer:

B.)

Step-by-step explanation:

baby :p