Jerome won the lottery! He donated 1/2 of the money to charity and gave his parents 1/6 of the winnings. The remaining 1/3 was divided equally among his 5 friends. The expression given represents the part of the lottery money for each friend received. "1/3 (divided by) 5" Which expression is equivalent to the amount of money each friend received? A: 1/5 (divided by) 1/3 B: 1/5 x 1/3 C: 1/3 (divided by) 1/5 D: 5/1 x 1/3

From Central limit theorem, we must consider a sample based in at least 30 or more obwervations. That is, the sample is not significant to consider the service costs as normally distributed.

Answer:

Ddkdkdckkpooooooopppppp

Step-by-step explanation:

The rear windshield wiper of a car rotated 120 degrees, as shown in the figure. The area cleared by the wiper blade is approximately 205.875 square inches.

The problem states that a car’s rear windshield wiper rotates 120 degrees, as shown in the figure. Our aim is to find the area cleared by the wiper.

The wiper's arm is represented by a line segment and has a length of 14 inches.

The wiper's blade is perpendicular to the arm and has a length of 25 inches.

Angular degree measure indicates how far around a central point an object has traveled, relative to a complete circle. A full circle is 360 degrees, and 120 degrees is a third of that.

As a result, the area cleared by the wiper blade is the sector of a circle with radius 25 inches and central angle 120 degrees.

The formula for calculating the area of a sector of a circle is: A = (θ/360)πr², where A is the area of the sector, θ is the central angle of the sector, π is the mathematical constant pi (3.14), and r is the radius of the circle.

In this situation, the sector's central angle θ is 120 degrees, the radius r is 25 inches, and π is a constant of 3.14.A = (120/360) x 3.14 x 25²= 0.33 x 3.14 x 625= 205.875 square inches, rounded to the nearest thousandth.

Therefore, the area cleared by the wiper blade is approximately 205.875 square inches.

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Answer:

284=5(40)+4r

Step-by-step explanation:

The least amount of paint that is needed to paint the walls of a room with a rectangular prism shape is 1. 8 gallons.

There would be two walls with 10 x 16 dimensions so the area is :

= 2 x 10 x 16

= 320 square feet

Two walls with 20 x 10 dimensions :

= 2 x 20 x 10

= 400 square feet

The total area is :

= 400 + 320

= 720 square feet

One gallon of paint can cover 400 square feet so the number of gallons needed is:

= 720 / 400

= 1. 8 gallons

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Full question is:

One gallon of paint covers 400 square feet. What is the least amount of paint needed to paint the walls of a room in the shape of a rectangular prism with a length of 20 feet, a width of 16 feet, and a height of 10 feet? Write your answer as a decimal.

You transfer $100 from your savings account to your checking account as a result, m1 will Remains unchanged and m2 will  increase by $100.

Hence, You transfer $100 from your savings account to your checking account as a result, m1 will Remains unchanged and m2 will  increase by $100.

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Answer:

The answer of the first on is 15 b because to find the perimeter of 2d shapes we have to add all the sides given ex: 5+5+5=15 so the answer of first question if 15.

Step-by-step explanation:

Step-by-step explanation:

Answer:

2 i think and 1

Step-by-step explanation:

hope it helps ☺️ tnxx

The value of the expression is 1.766.

To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. By eliminating all common factors from the numerator and denominator and putting the fraction in its simplest/lowest form, we can simplify fractions.

Given the expression,

2\(e^{3x}\) = 400

divide by 2 into both sides

\(e^{3x}\) =  400/2

\(e^{3x}\) = 200

converting the expression in form of a log,

ln(\(e^{3x}\))= ln(200)

log(aⁿ) = n log(a)

3x ln(e) = ln(200)  [ln(e) = 1 and ln(200) = 5.2931]

3x = 5.2931

x = 1.766

Hence Option B is correct.

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Answer:

p = $12,000

c = $4,500

b = $3,000

Step-by-step explanation:

Denote the variables as follows:

p = amount borrowed from parents

c = amount borrowed from the credit union

b = amount borrowed from the bank

The equations that can be formed using the given information are as follows:

p + c + b = 19500... (i)

p = 4b... (ii)

The formula to compute simple interest is:

SI = P × (R/100) × T

So, the equation for the total interest paid at the end of 1 year is:

0.05p + 0.04c + 0.03b = 870

5p + 4c + 3b = 87000... (iii)

Substitute (ii) in (i) and (iii) and simplify as follows:

4b + c + b = 19500

⇒ c + 5b = 19500... (iv)

5(4b) + 4c + 3b = 87000

⇒ 4c + 23b = 87000... (v)

Subtract (iv) from (v):

4c + 23b = 87000

(-)c + (-)5b = (-)19500 ] × 4

⇒

4c + 23b = 87000

-4c - 20b = -78000

⇒

3b = 9000

b = 3000

Compute the value of p as follows:

p = 4b = 4 × 3000 = 12000

p = 12000

Compute the value of c as follows:

p + c + b = 19500

12000 + c + 3000 = 19500

c + 15000 = 19500

c = 4500

Thus, the amount borrowed from each source is:

p = $12,000

c = $4,500

b = $3,000

Answer:

180 degrees

Step-by-step explanation:

The sum of all the interior angles in a triangle is always equal to 180 degrees.

Answer:

The correct answer is TRUE.

Step-by-step explanation:

Find the measure of x.

Begin by setting up an equation of the five angles equal to 180°.

x + 37° + 41° + 29° + 51°  = 180° • The sum of the angles is 180°.

x + 158° = 180°       • Add the known values on the left side.

x = 22° • Subtract 158° from both sides.

The measure of angle x is 22°.

The recursive relation of the data distribution a(n) = a ( n - 1 ) x n - ( n - 1 ).

A sequence of values is defined by a mathematical equation termed as a recursive relation, also known as recursive relation. It derives current value(s) through specified initial value(s) and previous value dependent rule(s). In essence, it generates numeric sequences.

Note that every individual unit can be derived by multiplying the preceding one with a rising integer, and subsequently subtracting a descending integer:

1 x 1 - 0 = 1

1 x 2 - 1 = 1

1 x 3 - 2 = 5

5 x 4 - 3 = 17

17 x  5 - 4 = 71

71 x 6 - 5 = 247

We can deduce the relation of a(n) = a ( n - 1 ) x n - ( n - 1 ).

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Answer:

95

Step-by-step explanation:

The equation to solving this would be 203 - (9 multiply 12). If you multiply 9 and 12 you get 108. Minus 108 from 203 and you get 95.

In the question, we can draw the conclusion that, according to the formula, it will take them 10 days to get from City A to City B if they continue travelling at their current average speed of \(415 miles\)per day.

A formula is a set of mathematical signs and figures that demonstrate how to solve a problem.

Formulas for calculating the volume of \(3D\) objects and formulas for measuring the perimeter and area of \(2D\) shapes are two examples.

A formula is a fact or a rule in mathematical symbols. In most cases, an equal sign connects two or more values. If you know the value of one, you can use a formula to calculate the value of another quantity.

We need to know the average pace at which they went to figure how long it would take to get from City A to City B at the same rate.

total distance / time taken = average speed

\(415 miles\) per day \(2075/ 5\), it would take them \(10\) days to get from City A to City B because

Time taken = \(2075/415\) per days \(= 5 days\)

Therefore it will take them 10 days to get from City A to City B if they continue travelling at their current average speed of \(415 miles\)per day.

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Answer:

Side a = 10.44031

Side b = 10

Side c = 3

Angle ∠A = 90° = 1.5708 rad = π/2

Angle ∠B = 73.301° = 73°18'3" = 1.27934 rad

Angle ∠C = 16.699° = 16°41'57" = 0.29146 rad

Answer:

t5ju8i8

Step-by-step explanation:

Answer:

click the paperclip

Step-by-step explanation:

you can click the paperclip and paste multiple pictures

Answer:

the y intercept is 5/3

the y intercept is 3/5

Answer:

0.0225 for every inch increased in size for the printing the the photo

Step-by-step explanation:

*I'll start off by using this section to show my work...*

4 x 5 = 20 \(in^{2}\) meaning that for every number multiplied with another, the total area of inches will be "Χ".

20 inches = [$]0.45

Meaning, for every 20 inches, 0.45 will duplicate... For example, 40 (Which is 20 + 20..) will be .45 + .45 = 0.9 (0.90), but half of 0.45 will be 0.225 making the area of inches 10.

0.45/20 = 0.0225 per inch squared.

Therefore, the answer for the cost to print the enlarged photo will be 0.0225 per inch upped.

The perimeter of the triangle is 30 units

The vertices are (−7,−1), (5,−1), and (5,4).

Start by calculating the distance between the vertices using:

\(d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2\)

So, we have:

\(d1 = \sqrt{(-1 + 1)^2 + (5 + 7)^2\)

d1 = 12

\(d2 = \sqrt{(-1 - 4)^2 + (5 - 5)^2\)

d2 =5

\(d3 = \sqrt{(-1 - 4)^2 + (-7 - 5)^2\)

d3 = 13

The perimeter is then calculated as:

P = d1 + d2 + d3

This gives

P = 12 + 5 + 13

Evaluate

P = 30

Hence, the perimeter of the triangle is 30 units

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To find the height of the shuttle, we can use trigonometry and the concept of similar triangles. The height of the shuttle is approximately 468.675 meters.

Let's assume that the height of the shuttle is represented by 'h' meters. From the information given, we know that the distance between the camera and the launch pad is 750 meters, and the angle of elevation from the camera to the shuttle is 32 degrees.

Using trigonometry, we can set up the following equation:

tan(32°) = h / 750

To find the value of h, we can rearrange the equation:

h = tan(32°) * 750

Using a calculator, we can find the value of tan(32°) ≈ 0.6249.

Now we can calculate the height of the shuttle:

h ≈ 0.6249 * 750

h ≈ 468.675 meters

Therefore, the height of the shuttle is approximately 468.675 meters.

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The number of strides the runner will make during 1 hour run will be =

10,800.

To calculate the distance or number of strides made by the runner in an

hour, the graph given above is considered as follows;

The y-axis which represents the number of strides is plotted against the x-axis which is the number of hours.

From the graph

20 minutes= 3600 strides

60 minutes = X strides

make X the subject of formula;

x= 3600×60/20

= 216000/20

= 10,800

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Answer:

NO

Step-by-step explanation:

The surface area of a sphere can be expressed as:

A = 4πr^2

where r is the radius of the sphere. We can express the radius in terms of the diameter as:

r = d/2

where d is the diameter.

Differentiating both sides of the surface area equation with respect to time t gives:

dA/dt = 8πr (dr/dt)

where dr/dt is the rate of change of the radius with respect to time.

We are given that the surface area is decreasing at a rate of 0.3 cm²/min, so we have:

dA/dt = -0.3 cm²/min

We are also given that the diameter is 18 cm, so we can find the radius as:

r = d/2 = 9 cm

Substituting these values into the equation above gives:

-0.3 = 8π(9) (dr/dt)

Solving for dr/dt gives:

dr/dt = -0.3 / (8π(9)) = -0.001326 cm/min

Therefore, the rate at which the diameter is decreasing when the diameter is 18 cm is approximately 0.001326 cm/min.

Answer:

(2, -1)

Step-by-step explanation:

I just plugged (y-x<-3) into desmos (if you haven't used desmos, use it. Its a lifesaver) and the only coordinate pair that was part of the line, is (2,-1)

Hope that helps!

Answer:

(6,2)

coz if y=2 & x=6

then substitute in to the equation

and we get 2-6=-4

so -4 is less than -3; in number line. thats it!!!!!

The graph of the option in the question has a domain of -∞ < x < 3.5.

The domain of a graph are the possible x-values that can be obtained from the graph.

A graph that has a domain given by the inequality, -∞ < x < ∞ does not have a vertical asymptote.

An asymptote is a straight line to which a graph approaches, as either the x or y-value approaches infinity.

The given graph has a vertical asymptote at y ≈ 3.5

The domain of the given graph is therefore, -∞ < x < 3.5

Similarly, the graph has a horizontal asymptote at x ≈ 3

The range of the given graph is therefore, -∞ < y < 3.

A graph that has a domain of -∞ < x < ∞, extends to infinity to the left and the right of the graph.

A function that has a graph with a domain of -∞ < x < ∞ is one of direct proportionality.

An example is, y = x

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The required value of \(\sin(\alpha + \beta) = \frac{15\sqrt{15} - 21}{175}$\).

To find \($\sin(\alpha + \beta)$\), we will need to use the trigonometric identity:

\($\sin(\alpha + \beta) = \sin(\alpha)\cos(\beta) + \cos(\alpha)\sin(\beta)$\)

We are given that \(\cos(\alpha) = \frac{3}{7}$\) in quadrant IV. Since cosine is positive in quadrant IV, we can draw a reference triangle in quadrant IV with adjacent side 3 and hypotenuse 7. We can use the Pythagorean theorem to find the opposite side:

\($\sin(\alpha) = \frac{\sqrt{7^2-3^2}}{7} = \frac{\sqrt{40}}{7} = \frac{2\sqrt{10}}{7}$\)

We are also given that \(\sin(\beta) = \frac{7}{25}$\) in quadrant II. Since sine is positive in quadrant II, we can draw a reference triangle in quadrant II with opposite side 7 and hypotenuse 25. We can use the Pythagorean theorem to find the adjacent side:

\($\cos(\beta) = -\frac{\sqrt{25^2-7^2}}{25} = -\frac{6\sqrt{6}}{25}$\)

Now we can substitute these values into the formula for \($\sin(\alpha + \beta)$\):

\($\sin(\alpha + \beta) = \sin(\alpha)\cos(\beta) + \cos(\alpha)\sin(\beta)$\)

\($= \left(\frac{2\sqrt{10}}{7}\right)\left(-\frac{6\sqrt{6}}{25}\right) + \left(\frac{3}{7}\right)\left(\frac{7}{25}\right)$\)

\($= -\frac{12\sqrt{15}}{175} + \frac{3}{25}$\)

\($= \frac{15\sqrt{15} - 21}{175}$\)

Therefore, \($\sin(\alpha + \beta) = \frac{15\sqrt{15} - 21}{175}$\).

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Answer:

The answer is:-

(2x+1)(4-7)