A relief organization supplies blankets, cots, and lanterns to victims of fires, floods, and other natural disasters. One week the organization purchased 25 blankets, 10 cots, and 5 lanterns for a total cost of $1275. The next week, at the same price, the organization purchased 5 blankets, 20 cots, and 5 lanterns for a total cost of $1425. The next week, at the same price, the
organization purchased 5 blankets, 30 cots, and 5 lanterns for a total cost of $1975. Find the cost of each item.

Answer:

56.57 km/h.

Step-by-step explanation:

Distance traveled:

First, we need to convert the time into hours to have the same unit. 1 hour 30 minutes is equivalent to 1.5 hours.

The total time the van traveled is 2 hours + 1.5 hours = 3.5 hours.

The distance traveled during the first 2 hours is 36 km/h * 2 hours = 72 km.

The distance traveled during the next 1.5 hours is 84 km/h * 1.5 hours = 126 km.

The total distance traveled is 72 km + 126 km = 198 km.

Average speed over the whole journey:

The average speed is the total distance traveled divided by the total time traveled.

Average speed = Total distance traveled / Total time traveled = 198 km / 3.5 hours = 56.57 km/h.

Answer:

56.6km/hr

Step-by-step explanation:

2 hours with a speed of 36km/hr is with a distance of (36×2) = 72km

1.5 hours with a speed of 84km/hr = 126km

Total distance = 72+126 = 198km

Average speed = 198/ total time taken = 198/3.5 = 56.6km/hr

the equation of the Linear function will be f(x) = -19x + 14.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given a data set of a linear function

The slope-intercept form of the equation of a line

y=mx+b,

where m is the slope

b is the y-intercept (the value of y, at x = 0)

since, slope = (y - y')/(x -x')

In our case,

Slope = (128 -90)/ (-6 + 4)

Slope = 38/-2

Slope = -19

And b = 14 (Given)

Thus,

The equation of Line:

y = -19x + 14

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The volume of the trapezoidal prism shown is 168 in³

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

The volume of the figure is the product of its base area and height. Hence:

Volume = area of base * height

The base is a trapezoid with parallel sides 3 in and 9 in, hence:

Area of base = 3 in * 9 in = 24 in²

Volume = area of base * height = 24 in² * 7 in = 168 in³

The volume of the figure is 168 in³

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The length of the third side is 14.4 units.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We find the third side of a triangle by using Pythagoras theorem.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides

8²+12²=x²

64+144=x²

208=x²

Take square root on both sides

x=14.4

Hence, the length of the third side is 14.4 units.

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The expressions are solved and answered below.

Given are the expressions as shown in the image.

{ 1 } -

2[tex]$\frac{5}{6}[/tex] - 2[tex]$\frac{1}{5}[/tex]

17/6 - 11/5

17/6 - (11 x 1.2/5 x 1.2)

17/6 - 13.2/6

3.8/6

38/60

19/30

{ 2 } -

3[tex]$\frac{5}{8}[/tex] + 7/3

29/8 + 7/3

(29 x 3)/(8 x 3) + (7 x 8)/(3 x 8)

87/24 + 56/24

143/24

Similarly the remaining expressions can be evaluated.

Therefore, the expressions are solved and answered above.

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{Question in english -

Please help urgently with all the answers}

Answer:

D

Step-by-step explanation:

Therefore , X is a continuous random variable, the probability of getting exactly X = 80 is zero. We can only find the probability of a range of values, such as P(79.5 < X < 80.5).

Calculating the likelihood that a statement is true or that a particular event will take place is the centre of probability theory, a branch of mathematics. Any number between  range 0 and 1, where 1 is usually used to express confidence as well as 0 is routinely used it to convey possibility, can be used to represent chance. A probability diagram shows the likelihood that a particular occurrence will occur.

Here,

For P(78 < X < 127):

We first convert the values to standard scores:

Z1 = (78 - 72) / 22 = 0.27

Z2 = (127 - 72) / 22 = 2.50

Using a standard normal distribution table or a calculator, we find the area to the left of Z1 and the area to the left of Z2:

P(Z < 0.27) = 0.6064

P(Z < 2.50) = 0.9938

Then we subtract the smaller area from the larger area to find the area between Z1 and Z2:

P(0.27 < Z < 2.50) = 0.9938 - 0.6064 = 0.3874

So the probability that 78 < X < 127 is approximately 0.3874.

For P(60 < X < 90):

We first convert the values to standard scores:

Z1 = (60 - 72) / 22 = -0.55

Z2 = (90 - 72) / 22 = 0.82

Using a standard normal distribution table or a calculator, we find the area to the left of Z1 and the area to the left of Z2:

P(Z < -0.55) = 0.2912

P(Z < 0.82) = 0.7939

Then we subtract the smaller area from the larger area to find the area between Z1 and Z2:

P(-0.55 < Z < 0.82) = 0.7939 - 0.2912 = 0.5027

So the probability that 60 < X < 90 is approximately 0.5027.

For P(X = 80):

Since X is a continuous random variable, the probability of getting exactly X = 80 is zero. We can only find the probability of a range of values, such as P(79.5 < X < 80.5).

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The complete question is " X Is A Normally Distributed Random Variable With Mean 72 And Standard Deviation 22. Use Calculator To Find The Probability Indicated. P(78&Lt;X&Lt;127) P(60&Lt;X&Lt;90) P(X=80)

X is a normally distributed random variable with mean 72 and standard deviation 22. Use calculator to find the probability indicated.

P(78<X<127)

P(60<X<90)

P(X=80)"

For Ф=-π/3 it is found in second quadrant, Ф=-π/4 is also found in second quadrant and Ф=-5π/6 in fourth quadrant.

What exactly are quadrants?

A quadrant is an area specified by the coordinate system's two axes (x and y). When the two axes, x and y, cross at 90 degrees, the four areas generated are known as quadrants. These areas include both positive and negative x- and y-axis coordinate values. The coordinates reflect a point's location in a quadrant.

In the Coordinate Plane, there are four quadrants.

Based on such values, the graph is split into parts or four quadrants.

The first quadrant is located in the upper right-hand corner of the graph. Both x and y values are positive in this quadrant.

The second quadrant is located in the upper left-hand corner of the graph. The value of x in this quadrant is negative, whereas the value of y is positive.

The third quadrant is located in the graph's lower left-hand corner. It has negative values for both x and y.

Fourth Quadrant: Finally, the fourth quarter is in the lower right-hand corner, with a positive x and a negative y value.

Now,

For quadrants, upto value of π/2 angles are in first qudrants

and upto -π/2 and π/2 to π are in second quadrant

and -π/2 to -π are in fourth quadrant.

Hence,  

          For Ф=-π/3 it is found in second quadrant, Ф=-π/4 is also found in second quadrant and Ф=-5π/6 in fourth quadrant.

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The required terminal point is Q(0,2).

By using the symbol |v|, the magnitude of a vector formula can be utilized to determine the length for a given vector (let's say v). In essence, this measurement represents the separation between the vector's starting and ending points.

For a vector v with endpoints at [tex](x_1,y_1)[/tex] and [tex](x_2, y_2)[/tex], its magnitude is

[tex]v=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We are given the following in the question:

Initial point of vector, P(1,0)

The terminal point Q has coordinates in the following format because it is on the y-axis:

Q(0,y)

The magnitude of the vector is [tex]\sqrt{5}[/tex].

Magnitude is given by,

[tex]v=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\ \sqrt{5} =\sqrt{(0-1)^2+(y-0)^2} \\5=1+y^2\\y^2=4\\y=_-^+2[/tex]

But because the terminal position is higher than the starting point,

y is greater than 0.

Therefore,

y=2

Thus, the terminal point is Q(0,2)

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The value of cot θ is [tex]\frac{15}{4\sqrt{9} }[/tex].

Trigonometric functions are defined as the real functions which are simply the functions of an angle of a triangle. They are basically the periodic functions which relate an angle in a right angled triangle to the ratios of the length of two sides.

Given that, the circle is unit circle.

In polar form, x = r cos(θ)

Since it is unit circle, r = 1

x = Cos (θ)

Cos (θ) = 15/23

Sin (θ) = [tex]\sqrt{1 - (15/23)^2}[/tex]

           = [tex]\sqrt{\frac{304}{529} }[/tex]

           = [tex]\sqrt{\frac{19*16}{23^2} }[/tex]

           = [tex]\frac{4\sqrt{19} }{23}[/tex]

Cot (θ) = cos (θ) / sin (θ)

           = (15/23) /  ([tex]\frac{4\sqrt{19} }{23}[/tex])

           = [tex]\frac{15}{4\sqrt{9} }[/tex]

Hence the value of cot (θ) is [tex]\frac{15}{4\sqrt{9} }[/tex].

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Note that given the question which is related to Dimensional Analysis, Sam's Club package is more expensive. This means WalMarts prices are a better option.

Dimensional analysis is the examination of the connection between physical quantities using dimensions and measuring units.

To determine the better option, we simply derive the cost per sheet as follows:

For Sam's Club we have:

26.99/ (36 x 248)

= $0.0030230735/ Sheet

For Walmart, we have:

5.99/ (8 * 350)

= $0.0021392857/ Sheet

So based the above, it clear that the Sam's Club package is more expensive because:

$0.0021392857 < $0.0030230735

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Full Question:

A particular brand of toilet paper is offered at two stores in different kinds of packaging. To practice using rates, for each package determine both the number of sheets per dollar and the cost in dollars per sheet. Then determine which package is the better buy.

Sam's Club sells a 36-pack of toilet paper with 248 sheets per roll for $26.99

Walmart sells the toilet paper for $5.99 in an 8-pack with 350 sheets per roll. The Sam's Club package: ?

The only restriction on the domain is that x can't be zero.

Here we have the following equation:

(7/5)*x - 8/5 = 3/x

And we want to see if there is a value of x that caueses a problem here.

We can see that on the right side, we have an x on the denominator. And remember that the division by zero is undefined, then we know that:

x ≠ 0

That is the only restriction, because x = 0 can't be on the domain.

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Answer: X and Y values

Step-by-step explanation:

The expression for the number of sundaes shop owner needs to sell in September is 3x.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Given that, the ice cream shop owner wants to triple her sale of sundaes from August to September.

If the ice cream shop owner sold x sundaes in August, then she will sell

3×x=3x sundaes in September.

Therefore, number of sundaes shop owner sold in September is 3x.

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The quadratic regression equation is y = 2x^2 + 16x - 0.75

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

x 0 2 4 6 8

f(x) 2 31 54 71 82

Using a graphing calculator, we have the following summary:

The equation is represented as

y = ax^2 + bx + c

So,, we have

y = 2x^2 + 16x - 0.75

Hence, the equation is y = 2x^2 + 16x - 0.75

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The values of t that satisfy the inequality are less than 1.25

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

8 > 3+ 4t​

Evaluate the like terms

So, we have

5 > 4t

Divide both sides by 4

So, we have the following representation

1.25 > t

Rewrite as

t < 1.25

This means that the values of t that satisfy the inequality are less than 1.25

None of the options are applicable

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Complete question

Which of the t-values satisfy the following inequality?

8 > 3+ 4t​

Choose all answers that apply:

(Choice A) t = 12

(Choice B)t = 16

(Choice C)t = 20

The function f(x-3) is simplified to have x² - 6x + 13

Given the following quadratic function below

f(x) = x² + 4

We need to determine the value of the function f(x-3). Replace x with x -3 in f(x) to have:

f(x-3) = (x-3)² + 4

Expand the equivalent expression

f(x-3) = x² - 6x + 9 + 4

f(x-3) = x² - 6x + 13

Hence the simplified form of the expression is x² - 6x + 13

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Answer:First, use the positive value of the

±

to find the first solution.

x

=

7

Next, use the negative value of the

±

to find the second solution.

x

=

−

7

The complete solution is the result of both the positive and negative portions of the solution.

x

=

7

,

−

7

Step-by-step explanation: First, use the positive value of the

±

to find the first solution.

x

=

7

Next, use the negative value of the

±

to find the second solution.

x

=

−

7

The complete solution is the result of both the positive and negative portions of the solution.

x

=

7

,

−

7

The probability values are obtained as -

P(X + Y > 3) = 0.45

P(XY = 2) = 0.10

P(XY > 1) = 0.55

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

The joint probability mass function XX and YY is given as -

p(1,1)=0.45p(2,1)=0.05p(3,1)=0.05p(1,2)=0.05p(2,2)=0.1p(3,2)=0.1p(1,3)=0.05p(2,3)=0.05p(3,3)=0.1p(1,1)=0.45p(1,2)=0.05p(1,3)=0.05p(2,1)=0.05p(2,2)=0.1p(2,3)=0.05p(3,1)=0.05p(3,2)=0.1p(3,3)=0.1.

The first operation is -

P(X + Y > 3)

Substitute the values in the equation -

P(X + Y > 3) = P(3,1) + P(2,2) + P(3,2) + P(1,3) + P(2,3) + P(3,3)

P(X + Y > 3) = 0.05 + 0.1 + 0.1 + 0.05 + 0.05 + 0.1

P(X + Y > 3) = 0.45

Therefore, the value is obtained as 0.45.

The second operation is -

P(XY = 2)

Substitute the values in the equation -

P(XY = 2) = P(2,1) + P(1,2)

P(XY = 2) = 0.05 + 0.05

P(XY = 2) = 0.10

Therefore, the value is obtained as 0.10.

The third operation is -

P(XY > 1)

Substitute the values in the equation -

P(XY > 1) = 1 - [P(XY ≤ 1)]

P(XY > 1) = 1 - [P(1,1)]

P(XY > 1) = 1 - 0.45

P(XY > 1) = 0.55

Therefore, the value is obtained as 0.55.

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The joint probability mass function of XX and YY is given by

p(1,1)=0.45p(2,1)=0.05p(3,1)=0.05p(1,2)=0.05p(2,2)=0.1p(3,2)=0.1p(1,3)=0.05p(2,3)=0.05p(3,3)=0.1p(1,1)=0.45p(1,2)=0.05p(1,3)=0.05p(2,1)=0.05p(2,2)=0.1p(2,3)=0.05p(3,1)=0.05p(3,2)=0.1p(3,3)=0.1

Compute the following probabilities:

P(X+Y>3)=

P(XY=2)=

P(XY>1)=

Answer: Account 1 earns a higher return over 3 years, with a total of $515.64.

To calculate the return of Account 1:

$500 * (1 + 0.012/12)^(12*3) = $515.64

To calculate the return of Account 2:

$500 * (1 + 0.013/2)^(2*3) = $515.16

Therefore, Account 1 earns a higher return of $515.64 compared to Account 2's return of $515.16.

Step-by-step explanation:

The image quadrilateral is identical to the original quadrilateral but has been mirrored across the x- and y-axes.

The coordinates W(-2, 1), X(-1, 3), Y(3, 3), and Z(3, 3) can be plotted to form the quadrilateral's graph as follows:

code is as follows:

     |

     | Y(3,3)

     |

     |

------Z(3,-3)

------

     |

     |

     |

     | X(-1,3)

     |

     |

     |

W(-2,-1)

We may use the following transformation on each vertex to determine the image of this quadrilateral following a 180-degree rotation of the origin:

(x, y) -> (-x, -y) (-x, -y)

As a result, the picture quadrilateral's new vertices are:

W' = (-(-2), -(-1)) = (2, 1) (2, 1)\sX' = (-(-1), -(3)) = (1, -3) (1, -3)\sY' = (-3, -3) = (-3, -3) (-3, -3)\sZ' = (-3, 3) = (3, -3) (3, -3) (3, -3)

To create a quadrilateral image, we can plot these points on the same coordinate plane:

code

     |

     | Y'(3,-3)

     |

     |

------

Z'(3,-3)

------

     |

     |

     |

     | X'(1,-3)

     |

     |

     |

W'(2,1)

It should be noted that the image quadrilateral is identical to the original quadrilateral but has been mirrored across the x- and y-axes.

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Answer:

96cm

Step-by-step explanation:

scale of 4cm : 1'    

actual: length 3 feet,  width is 2 feet.

so 12 cm & 8 cm

so area. = 12*8 = 96cm

Answer:

Step-by-step explanation:

The simple interest can be calculated as follows:

I = P * r * t

Where:

I = interest

P = principal amount (3000)

r = interest rate (0.10)

t = time in years (5)

So,

I = 3000 * 0.10 * 5

I = 1500

The final balance would be:

P + I = 3000 + 1500

P + I = 4500

The final balance, rounded to the nearest cent, is $4500.

In the following option n log n seems to grow the fastest amongst all according to the size of inputs.

In computer science and mathematics, the running time or complexity of an algorithm is often measured in terms of the size of the input, usually denoted by n. The notation O(f(n)) is used to describe the upper bound on the running time of an algorithm, where f(n) is a function of n.

In the context of comparing growth rates of functions, we usually only consider the highest-degree term of the function. For example, we would say that f(n) = n^2 + n grows as O(n^2), because n^2 grows much faster than n and dominates the running time as n grows larger.

Now, let's consider the functions n, n / log n, n - log n, n log n, and n^2. As n grows, each of these functions grows at a different rate.

1. n grows linearly with n, so it takes more time as the size of the input grows.

2. n / log n grows faster than n, but slower than n log n. This is because logarithms grow much slower than linear functions, but as n grows larger, the difference between n and log n becomes larger, so n / log n grows faster.

3. n - log n grows slower than n and n / log n, because log n grows much slower than n, so as n grows larger, n - log n becomes closer to n.

4. n log n grows faster than n, n / log n, and n - log n, but slower than n^2. This is because logarithms grow much slower than linear functions, but as n grows larger, the difference between n and log n becomes larger, so n log n grows faster.

5.n^2 grows much faster than n, n / log n, n - log n, and n log n, so as n grows larger, n^2 becomes much larger than any of these functions.

So, of the options given, n log n grows the fastest, meaning that an algorithm that takes time proportional to n log n will become slower faster as the size of the input grows than an algorithm that takes time proportional to n, n / log n, or n - log n.

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Answer: B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The sum of y and 3 means addition, but twice means to multiply the sum of y and 3. So, the answer would be 2(y+3).

The better promotion is at the campus canteen and it is the best to by a can of tab with a discount of about R600.

We come across phrases like cost price, tagged price, discount, and selling price when making a purchase. Shop owners give discounts to customers to encourage product sales. Discount is the term used to describe a rebate or an offer made to clients on the listed price of goods.

Discounts are price reductions that store owners make on items or services that are otherwise priced as marked. This portion of the rebate is typically provided to boost sales or get rid of excess inventory.

Given that, a can of Tab costs R7, 20 at Timber City.

Then 6 packs will cost = 6(720) = R4320

At promotion the cost is R3960 the discount offered is:

D = R4320 - R3960

D = R360

At campus Canteen a can of tab is for R7, 50.

6 packs = 6(750) = R4500

Discount = 4500 - 3900 = R600

Hence, the better promotion is at the campus canteen and it is the best to by a can of tab with a discount of about R600.

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The expression 5(AB)+3(AB) = 8(A^2)(B^2)​ are not equal

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

5(AB)+3(AB) = 8(A^2)(B^2)​

The left side of the equation represents the sum of two products of A and B, while the right side represents the product of 8 and A^2 times B^2,

These are two completely different expressions and their values are unlikely to be equal unless A, B, and the specific values involved are known.

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Answer:

the income affect is changed drastically as now for every person they loose $3.00

The factorization of  9x^5 + x^2 is  x^2 (9x^3 + 1).

The factorization of algebraic expressions is the process of identifying two or more expressions whose product is the given expression. A factor is a number that evenly divides the inputted number or expression.

Algebraic expressions can be factored by identifying two or more expressions whose product is the provided expression, which is known as finding the factors of the given expression.

Given that:

9x^5+x^2

Factor x^2 out of 9x^5.

= x^2 (9x^3 ) + x^2

= x^2 (9x^3 + 1)

Therefore, we can conclude that the factorization of  9x^5 + x^2 is  x^2 (9x^3 + 1).

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The area of the composite figure is equal to 26 square units.

Herein we find a composite figure formed by a parallelogram and a rectangle, whose area formula is described below:

Parallelogram / Rectangle

A = b · h

Where:

Now we determine the area of the composite figure:

Rectangle

b = √(3² + 1²)

b = √10

h = √(2² + 6²)

h = 2√10

A = √10 · 2√10

A = 20

Parallelogram

A = 6 · 1

A = 6

Composite figure

A = 20 + 6

A = 26

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