At a supermarket, there are 118 customers. If 45 have purchased shirts, 59 have
purchased pants, and 40 have purchased neither, how many purchased both shirts and
pants?

The solution to the equations are b = 15, b = 22, c = 21 and n = 28

From the question, we have the following equations that can be used in our computation:

31 - b = 16

28 + b = 50

33 + c = 54

52 - n = 24

Next, we collect the like terms in each of the equation

This gives

b = 31 - 16

b = 50 - 28

c = 54 - 33

n = 52 - 24

Lastly, we evaluate the like terms

b = 15

b = 22

c = 21

n = 28

The above are the solutions to the equations

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Question

Solve the following equations:

31 - b = 16

28 + b = 50

33 + c = 54

52 - n = 24

The airplane's groundspeed is approximately 242.25 km/h, and the resultant bearing is approximately 55.04° (relative to true north, measured clockwise).

How to solve for the airplane's groundspeed

To determine the resultant velocity of the airplane, we need to break down the airplane's velocity and the wind's velocity into their respective components and add them. Let's assume that the angles are measured clockwise from true north.

Let's denote:

Vp = airplane's speed = 250 km/h

θp = airplane's heading = 075 degrees

Vw = wind's speed = 85 km/h

θw = wind's heading = 300 degrees

We can then find the eastward (x) and northward (y) components of the velocities:

For the airplane:

Vpx = Vp * cos(θp) = 250 * cos(75 degrees) = 64.95 km/h

Vpy = Vp * sin(θp) = 250 * sin(75 degrees) = 241.92 km/h

For the wind:

Vwx = Vw * cos(θw) = 85 * cos(300 degrees) = 73.60 km/h

Vwy = Vw * sin(θw) = 85 * sin(300 degrees) = -42.50 km/h

We then sum the x and y components of the two velocities to find the resultant velocity components:

Vrx = Vpx + Vwx = 64.95 km/h + 73.60 km/h = 138.55 km/h

Vry = Vpy + Vwy = 241.92 km/h - 42.50 km/h = 199.42 km/h

The magnitude of the resultant velocity, which represents the groundspeed (Vr), is found using the Pythagorean theorem:

Vr = sqrt((Vrx)^2 + (Vry)^2) = sqrt((138.55)^2 + (199.42)^2) = 242.25 km/h

The bearing (θr) of the resultant velocity (relative to north) can be found using inverse tangent:

θr = atan2(Vry, Vrx) = atan2(199.42, 138.55) = 55.04 degrees

Therefore, the airplane's groundspeed is approximately 242.25 km/h, and the resultant bearing is approximately 55.04° (relative to true north, measured clockwise).

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Answer:

C and D

Step-by-step explanation:

[tex]\cos(2x)\\=\cos(x+x)\\=\cos(x)\cos(x)-\sin(x)\sin(x)\\=\cos^2(x)-\sin^2(x)\\=\cos^2(x)-(1-\cos^2(x))\\=2\cos^2(x)-1 \,\,\,\,\,\,\,\,\,\,\leftarrow \text{Option D}\\=2(1-\sin^2(x))-1\\=2-2\sin^2(x)-1\\=1-2\sin^2(x)\,\,\,\,\,\,\,\,\,\,\,\leftarrow \text{Option C}[/tex]

By SSS postulate, triangle SQY is similar to triangle PTY.

From the given figure, consider ΔSQY and ΔPTY.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio.

Here, SQ/PT = SY/PY = YQ/YT

8/4 = 12/6 = 4/2

2 = 2 = 2

By SSS postulate, ΔSQY~ΔPTY.

Hence, by SSS postulate, triangle SQY is similar to triangle PTY.

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An estimate of the mean age of these employees is 25.9 years.

We are given that;

The frequency table

Now,

To work out an estimate of the mean age of these employees, we can use the formula:

mean = (sum of (frequency x midpoint)) / (sum of frequency)

We can calculate the midpoints of each class interval by adding the lower and upper limits and dividing by 2:

(18 + 20) / 2 = 19 (20 + 22) / 2 = 21 (22 + 24) / 2 = 23 (24 + 26) / 2 = 25

Using these midpoints and the frequencies given in the table, we can calculate the sum of (frequency x midpoint):

3 x 19 + 2 x 21 + 7 x 23 + 8 x 25 = 3 x 19 + 2 x 21 + 7 x 23 + 8 x 25 = 518

We can calculate the sum of frequency by adding up all the frequencies:

3 + 2 + 7 + 8 = 20

Now we can substitute these values into the formula for mean:

mean = (sum of (frequency x midpoint)) / (sum of frequency) mean = (518) / (20) mean = 25.9

Therefore, by the frequency the answer will be 25.9 years.

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The complete question is;

The table shows the age, in years, of employees in a company.

Age (a) in years Frequency

18 < a < 20

3

20 < a < 22

2

22 < a < 24

7

24 < a < 26

8

26 0

a) Find the modal class interval.

b) Work out an estimate of the mean age of these employees.

Step-by-step explanation:

This is of the form

(x-h)^2 + ( y-k)^2 = r^2        so r^2 = 16  means r = 4   units

Approximately 34.87% of the readers surveyed don't use e-readers.

To find the approximate sample proportion of readers who use e-readers, we divide the number of readers who said they read books on e-readers (1954) by the total number of readers surveyed (3000):

Approximate sample proportion = Number of readers who use e-readers / Total number of readers surveyed

Approximate sample proportion = 1954 / 3000 ≈ 0.6513

To express this as a percentage, we multiply the sample proportion by 100:

Approximate sample proportion as a percentage = 0.6513 × 100

= 65.13%

Therefore, the approximate sample proportion of readers who use e-readers is approximately 65.13%.

This means that approximately 65.13% of the readers surveyed use e-readers.

To determine the percentage of readers who don't use e-readers, we subtract the sample proportion from 100%:

Percentage of readers who don't use e-readers = 100% - 65.13%

= 34.87%

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Answer:

A. 65

Step-by-step explanation:

To find <CAB you need to find the angle of BC and divide it by 2

To find BC add the other angles up and minus it from 360 because a full circle is = to 360

122 + 108 = 230

360 - 230 = 130

130/2 = 65

Hope this helps :)

From the given expression we can draw a rectangle and square.

The given expression is x(x+5)

We can draw a rectangle with length of x+5 and width of x.

The given expression is (y-2)²

The two factors are (y-2)(y-2).

We can draw a square of side length (y-2).

For the expression (3z)².

We can draw a square of length 3z and width of 3z.

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The capacity of the tin is  235.62 cm³ and the density of the polish is approximately 1.27 g/cm³.

The formula to calculate the volume of a cylinder is:

Volume = π r² h

where π is approximately 3.14159, r is the radius of the cylinder (half of the diameter), and h is the height of the cylinder.

Given:

Diameter = 10 cm

Radius (r) = Diameter/2 = 10 cm / 2 = 5 cm

Height (h) = 3-5 cm (range) = 3cm

Volume = 3.14159×25 cm² × 3 cm

Volume ≈ 235.62 cm³

Therefore, the capacity of the tin is approximately 235.62 cm³.

To calculate the density of the polish, we use the formula:

Density = Mass / Volume

Given:

Mass = 300 g (grams)

Volume = 235.62 cm³ (cubic centimeters)

Density = 300 g / 235.62 cm³

Density = 1.27 g/cm³

Therefore, the density of the polish is 1.27 g/cm³.

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The exact area of the triangle is 12.5√3 square units.

The area of the triangle to the nearest hundredth is 21.65 in².

We have,

Sin 30 = y/10

1/2 = y/10

y = 5

And,

Cos 30 = x / 10

√3/2 = x/10

x = √3 x 5

x = 5√3

Now,

Area of the triangle.

= 1/2 x 5 x 5√3

= 1/2 x 25√3

= 12.5√3

Now,

The area of the triangle to the nearest hundredth of a square inch.

= 12.5 x 1.732

= 21.65

Thus,

The exact area of the triangle is 12.5√3 square units.

The area of the triangle to the nearest hundredth is 21.65 in².

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The table is attached below.

The given equation is,

y = x² + 2x + 11

The given equation is a quadratic equation

Now to find X intercept put y = 0

⇒  x² + 2x + 11 = 0

Now the discriminant is,

⇒ 2² - 4x1x11 = -11 < 0

Hence there is no real solution,

Thus,

There is no x intercept.

To find Y axis is,

put x = 0

y = 11

Hence the y intercept is 11

Now plot the graph of the given equation to find the axis of symmetry.

Then we get line of symmetry is x = -1

Domain: real number

Range : [10 , ∞)

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The value of system of equations are,

⇒ 14x + 18y ≥ 320

⇒ x + y < 25

Now,

Let x be the number of hours Pa Chia works at the grocery store

And, y be the number of hours she spends walking dogs.

Hence, The amount of money Pa Chia earns per week is calculated by using the inequality,

⇒ 14x + 18y ≥ 320

And, Since, Pa Chia must also work less than 25 hours per week, which can be represented as:

⇒ x + y < 25

Thus, The value of system of equations are,

⇒ 14x + 18y ≥ 320

⇒ x + y < 25

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The equation of the red graph is g(x) = x^2 - 4x + 4.

We are given that;

The graph of functions f(x)=x^2

Now,

By using symmetry and see that the vertex of the red graph must be halfway between its x-intercepts, which are at (1, 0) and (3, 0). This also gives you (2, 0) as the vertex.

Now that you know the vertex of the red graph is at (2, 0), you can plug it into the vertex form along with a = 1:

y = a(x - h)^2 + k y = 1(x - 2)^2 + 0 y = (x - 2)^2

This is the equation of the red graph in vertex form. You can also expand it to get it in standard form:

y = (x - 2)^2 y = x^2 - 4x + 4

g(x) = (x - 2)^2

or

g(x) = x^2 - 4x + 4

Therefore, by the function answer will be g(x) = x^2 - 4x + 4.

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Monica's balance from account 2 over 5.9 years would be approximately $7892.99.

We have,

To calculate Monica's balance from account 2 over 5.9 years, we can use the formula for compound interest:

[tex]A = P(1 + r/n)^{nt}[/tex]

Where:

A = the final balance

P = the initial principal (amount deposited)

r = the annual interest rate (expressed as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

For account 2, the annual interest rate is 4% (0.04) and it compounds daily, so n = 365.

Plugging in the values into the formula, we have:

[tex]A = 6100(1 + 0.04/365)^{365 \times 5.9}[/tex]

Calculating the expression inside the parentheses:

[tex](1 + 0.04/365)^{365 \times 5.9} = 1.293082[/tex]

Now, we can calculate the final balance:

A = $6100 x 1.293082 ≈ $7892.99

Therefore,

Monica's balance from account 2 over 5.9 years would be approximately $7892.99.

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This function written in vertex form include the following: A. f(x) = (x –1)² – 7.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical equation:

Axis of symmetry = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

For the given quadratic function f(x) = x² – 2x – 6, we have:

a = 1, b = -2, and c = -6

Axis of symmetry, Xmax = -b/2a

Axis of symmetry, Xmax = -(-2)/2(1)

Axis of symmetry, Xmax = 2/2

Axis of symmetry, Xmax = 1.

Next, we would determine vertex as follows;

f(x) = x² – 2x – 6

f(x) = 1² – 2(1) – 6

f(x) = -7.

Now, we can write quadratic function in vertex form;

f(x) = a(x - h)² + k

f(x) = (x - 1)² - 7

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Complete Question:

The image shows a geometric representation of the function f(x) = x² – 2x – 6 written in standard form.

What is this function written in vertex form?

f(x) = (x –1)² – 7

f(x) = (x +1)² – 7

f(x) = (x –1)² – 5

f(x) = (x +1)² – 5

The equation of the sinusoid function is:

3 Sin πx + 2.

Let's analyze the given options to find the correct equation:

a. 3 Cos πx + 2:

This option is a cosine function with a vertical shift of 2, but it does not have the correct amplitude or period. Therefore, it is not the correct equation.

b. 3 Sin x: This option is a sine function with the correct amplitude, but it does not have the correct vertical shift or period. Therefore, it is not the correct equation.

c. 3 Sin πx + 2: This option is a sine function with the correct amplitude and vertical shift. Let's check if it has the correct period:

To determine if the period is correct, we need to calculate the x-values when the function repeats itself.

In this case, we need to find x-values such that sin(πx) = 0, since the function will reach its maximum and minimum points again at those x-values.

sin(πx) = 0 when πx = 0, π, 2π, 3π, ...

Solving for x, we have:

πx = 0 ⟹ x = 0

πx = π ⟹ x = 1

πx = 2π ⟹ x = 2

πx = 3π ⟹ x = 3

From this, we can see that the function repeats itself every integer value of x, which matches the given information.

Therefore, option (c) is the correct equation: 3 Sin πx + 2.

Option (d) 3 Cos x does not have the correct vertical shift or period, so it is not the correct equation.

Hence, the equation of the sinusoid function is:

3 Sin πx + 2.

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The general journal entries Adriana Graphic Design should record the transaction  as;  Cash 1,650 Accounts Receivable 1,650.

When Adriana Graphic Design receives $1,650 from a client billed in a previous month for services provided, the firm is collecting an amount that was previously recognized as an account receivable.

In scenario provided, the firm will decrease its Accounts Receivable a debit entry, because Accounts Receivable is an asset account and assets decrease on the credit side and increase its - Cash account a credit entry, because Cash is also an asset account and assets increase on the debit side.

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To find y when x = 4.

y = kx (k is a constant)

to find the constant:

5 = k8

8 ÷ 5 = 1.6

k = 1.6

because 5 times 1.6 = 8

so now:

y = kx

y = 1.6 x 4

y= 6.4

He went to station Y, and the cost for 20 liters is 32 pounds.

Here we know taht Daniel went to a petrol store, and bought 15 L of petrol for 24 pounds.

So we need to use the graphs of the linear relations to see which store he went to.

We can see that in store X, for 15L the cost is 28 pounds, and for store Y the cost is 24 pounds.

So the correct option is Y.

Now, for 20 litres in that station, (using the same graph) we can see that the cost will be C=  32 pounds.

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Answer:

the law of large numbers is a theorem that describes the result of performing the same experiment a large number of times.

give brainlist

Step-by-step explanation:

The angle on the unit circle is solved to be

56.01 degrees (to the nearest tenth)

To find the angle of the terminal side through the given point on the unit circle, we can use the inverse trigonometric functions.

given that P = ((√5)/4, (√11)/4)

θ = arctan ((√11)/4 / (√5)/4)

θ = arctan((√11)/(√5))

θ ≈ 56.01 degrees

hence to the nearest tenth of a degree, the angle of the terminal side through the point P = ((√5)/4, (√11)/4) on the unit circle is approximately 56.01 degrees.

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There are 87 small cubes painted on exactly 2 faces.

Now, We can assume the small cubes in the 5x5x5 cube with coordinates (x, y, z) with 1≤x,y,z≤5.

Then, the cubes with x, y, or z equal to 1, 2, 4 or 5 are painted on 3 faces, the ones with x, y, or z equal to 3 are painted on 4 faces, and the ones in the 3x3x5 hole are painted on 2 faces.

The 5x5x5 cube contains 125 small cubes, and the 3x3x5 hole contains 45 small cubes.

Therefore, the total number of small cubes outside of the hole is 80.

Since, There are 64 cubes painted on 3 faces, 27 cubes painted on 4 faces, and 4 cubes painted on 5 faces.

Therefore, the number of cubes painted on exactly 2 faces is:

64 + 27 - 4 = 87

So, there are 87 small cubes painted on exactly 2 faces.

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The volume of the sodium hydroxide is 20 mL

Titration is a laboratory technique used to determine the concentration of a substance in a solution by reacting it with a solution of known concentration. Titration is a versatile technique and can be used to determine the concentration of various substances, such as acids, bases, redox agents, and complex ions.

We know that the reaction is 1:1

Number of moles of acid = 20/1000 * 0.1

= 0.002 moles

Thus;

Number of moles = Concentration * volume

Volume = Number of moles/Concentration

Volume = 0.002 moles/ 0.100

Volume = 0.02 L or 20 mL

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Answer: See below

Step-by-step explanation:

Let's assume that there are 12 students in the school

So 9 students like hot dogs

and 8 students like ice cream

Using calculus, we round the answers to the fifth quartile and then find the standard deviation

we get 4.9823

Using the complex system, we round 4.9823 to 3.25.

3.25*(hot dogs)i is 3.25*9i

We also have the equation:

5*(ice cream)i or 5*8i

We multiply these 2 complex number and get:

16.25*72i^2

or 16.25*-72

or -1170

So out of the 12 students, -1170 like hot dogs and ice creams, because they don't go well together.

Alright sorry

Now let's completely abandon that.

(3/4)*(2/3)=6/12=1/2

The probability that all three coins will be displaying heads is 1/8 or 0.125.

When flipping a fair coin, there are two possible outcomes: heads (H) or tails (T).

Since each coin flip is independent, we can calculate the probability of all three coins displaying heads by multiplying the probabilities of each coin landing on heads.

The probability of one coin landing on heads is 1/2, or 0.5.

Since there are three coins flipped simultaneously, the probability of all three coins displaying heads is:

(1/2) × (1/2) × (1/2)

= 1/8

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Answer: The water that overflows from the rectangular tank is 4.25 liters or 4250 milliliters.

Step-by-step explanation: To calculate the volume of the rectangular tank, we need to multiply its length, width, and height. The measurements are given in centimeters, so we need to convert the result to liters.

Volume of the rectangular tank = length × width × height

= 55 cm × 35 cm × 30 cm

Converting the volume to liters:

1 liter = 1000 cubic centimeters (cm³)

Volume of the rectangular tank = (55 cm × 35 cm × 30 cm) / 1000

= 57750 cm³ / 1000

= 57.75 liters

Mr. Tay emptied 62 liters of water into the rectangular tank. Since the tank's volume is only 57.75 liters, the excess water will overflow.

Overflow = Volume of water emptied - Volume of the rectangular tank

= 62 liters - 57.75 liters

= 4.25 liters

To convert the overflow from liters to milliliters:

1 liter = 1000 milliliters (ml)

Overflow in milliliters = 4.25 liters × 1000

= 4250 milliliters

The time period with the given principal, rate of interest and amount is 10 years.

Given that,

Principal = $1000, time period = 1 year and rate of interest =$40.

We know that, Simple interest = (Principal×Rate×Time)/100

48 = (1000×r×1)/100

4800=1000r

r=4800/1000

r=4.8%

Principal=$200, time period= 3 years and amount = $248

Simple interest = 248-200

= $48

48=(200×r×3)/100

4800=600r

r=4800/600

r=8%

Principal=$5000, rate of interest=2% and amount=$6000

Simple interest =6000-5000=$1000

Here, 1000=(5000×2×t)/100

1000=(100t)

t=10 years

Therefore, the time period with the given principal, rate of interest and amount is 10 years.

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The mean should be calculated for data sets A, B, C, and D.

It is useful to take into account the nature of the data and any potential outliers when deciding whether to choose the mean or the median as the measure of center in a data set.

When the data is symmetrically distributed with no major outliers, the mean is usually a better choice. It affects extreme values and gives an indication of the average value.

The median, on the other hand, is often preferred when the data is skewed or contains outliers. It represents the middle value when the data is ordered, and it is less affected by extreme values.

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