A bed room set is being sold for $5500 if bought cash. The set can be bought on
hire purchase by making a down payment of $1500 followed by 24 months
payments of $175 each. Calculate:
the total installments paid
the hire purchase price
the amount saved by paying cash.
Dion bought a new keyboard on hire-purchase. The cash price was $2400. He
paid a 25% deposit followed by 24 monthly payments of $120 each. Calculate
the amount of the deposit paid
the total monthly payments made
the hire purchase price
the difference between the cash price and the hire purchase price
Mr. Baker bought a gas stove on hire-purchase. The cash price was $850. H
a 15% deposit followed by 18 monthly payments of $42 cach.
Calculate:​

For this case we must solve the following inequality:

[tex]8x-5 \geq27[/tex]

We add 5 to both sides of the inequality:

[tex]8x\geq27 + 5\\8x\geq32[/tex]

DIviding between 8 on both sides of the equation:

[tex]x \geq \frac {32} {8}\\x \geq4[/tex]

Thus, the solution is given by all the numbers greater than or equal to 4

Answer:

[tex]x \geq4[/tex]

Answer: [tex]x\geq4[/tex]

Step-by-step explanation:

Given the inequality [tex]8x-5\geq27[/tex], you need to solve for the variable "x".

You must follow these steps to solve for the variable "x":

- First, you need to add 5 to both sides of the inequality. Then:

[tex]8x-5+(5)\geq27+(5)\\\\8x\geq32[/tex]

- And finally, you need to divide both sides of the inequality by 8.

Therefore, you get:

[tex]\frac{8x}{8}\geq\frac{32}{8}\\\\x\geq4[/tex]

Answer:

Step-by-step explanation:

Hello There!

First let me say this. I did not like how this question was worded I am a tutor in math and I had to read this problem over and over 5 times. It was confusing but I managed to figure it out. The answer is 61%

My work is shown on paper

Answer:

The probability that a student buys a drink  is 0.47

Step-by-step explanation:

The probability that a student buys a drink will be given by;

( the number of students who bought a drink)/(the total number of students)

We are told that;

Of the 100 students who came to the movie, 62 bought popcorn and 47 bought a drink. Therefore, the required probability is;

47/100= 0.47

Answer:

C) 50,653

Step-by-step explanation:

y = 1000(3.7)^x

After 3 hours   x=3

y = 1000(3.7)^3

y = 1000(50.653)

y =50653

Answer: OPTION C

Step-by-step explanation:

You know that in the function [tex]y = 1000(3.7^x)[/tex] the variable "y" is the number of bacterias in a petri dish  and the variable "x" is the number of hours.

Then, to answer the question "How many bacteria will there be after 3 hours?", you need to substitute [tex]x=3[/tex] into the function.

Therefore, the number of baterias after 3 hours will be:

[tex]y = 1000(3.7^3)[/tex]

[tex]y = 1000(50.653)[/tex]

[tex]y = 50,653[/tex]

This matches with the option C.

The rate of change of the function can be determined by finding the slope of the function at different points in the table.

The rate of change of a function can be determined by finding the slope of the function at different points. In this case, we can use the values provided in the table to find the rate of change. The rate of change is equal to the difference in the y-values divided by the difference in the x-values.

Let's take the first two points in the table as an example. The first point is (12/5, 5) and the second point is (5, 25/2). The difference in the y-values is 25/2 - 5 = 15/2, and the difference in the x-values is 5 - 12/5 = 23/5. Therefore, the rate of change is (15/2) / (23/5) = 15/2 * 5/23 = 75/46. So, the rate of change of the function for these two points is 75/46.

Answer:

A

Step-by-step explanation:

If the corresponding parts of the triangles are congruent then the triangles are congruent.

Here there are 2 corresponding congruent angles, that is 51° and 80°

The non- included corresponding sides are congruent both 10

Then by AAS postulate the triangles are congruent- True

Answer:

True

Step-by-step explanation:

A pex

Answer:30

Step-by-step explanation: V=1/3 Bh, 9x10=90 divide that by 3 for 30

The volume of a triangular pyramid that is 10 inches tall and has a base area of 9 square inches is 30 cubics in.

Take a triangle. This is a base.

Now take 3 triangles such that each of them is connected to the one-one side of the first triangle and when they're taken together, they form a closed object, called a triangular pyramid.

The volume of a triangular pyramid that is 10 inches tall and has a base area of 9 square inches

The volume of a triangular pyramid

V = 1/3 x B x h,

V = 1/3 x 9 x 10

V = 3 x 10

V = 30

Hence, the volume will be 30 cubics in.

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Answer:

Step-by-step explanation:

pyramids have 5 surfaces and a point. a cube has 6 surfaces and is a square

Answer:

The correct answer option is B. [tex]1[/tex], [tex]\frac{1}{2}[/tex], [tex]\frac{1}{4}[/tex].

Step-by-step explanation:

We are given the following geometric sequence and we are to find its 8th term:

[tex]16, 8, 4, 2,...[/tex]  

Here [tex]a_1=16[/tex] and common ratio [tex](r) = \frac{2}{4}=0.5[/tex].

The formula we will use to find the next three terms is:  

nth term = [tex]a_1 \times r^{(n-1)}[/tex]  

5th term = [tex]16 \times 0.5^{(5-1)} = 1[/tex]

6th term = [tex]16 \times 0.5^{(6-1)}[/tex] = [tex]\frac{1}{2}[/tex]

7th term = [tex]16 \times 0.5^{(7-1)}[/tex] = [tex]\frac{1}{4}[/tex]

Answer:

K = (e, d)

Step-by-step explanation:

We are given the coordinates of three vertices of a rectangle and we are to find the coordinates of the fourth point J.

H (0, 0)

I (0, d)

K (e, 0)

J = ?

We can find this using the following formula:

K = H + (I - H) + (K - H)

K = H + I - H + K - H

K = I + K - H

Substituting the given values in it to get:

K = [tex](0, d) + (e, 0) - (0, 0)[/tex]

K = [tex](0+e-0, d+0-0)[/tex]

K = (e, d)

For this case we must simplify the following expression:

[tex](3 ^ {-2}) ^ 4[/tex]

By definition of power properties we have to:[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

So, rewriting the expression we have:

[tex](\frac {1} {3 ^ 2}) ^ 4 = \frac {1 ^ 4} {(3 ^ 2) ^ 4} = \frac {1} {(3 ^ 2) ^ 4}[/tex]

By definition of power properties we have:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

So:

[tex]\frac {1} {(3 ^ 2) ^ 4} = \frac {1} {3 ^ 8}[/tex]

Answer:

Option D

The solution is X=0.4

The answer is the first one

Final answer:

The Ishango bone, found in the Congo with scratches believed to represent counting, shows evidence of prehistoric mathematical activity 20,000 years ago. It suggests early numerical understanding and supports the theory that Stone Age humans engaged in proto-mathematics.

Explanation:

The Ishango bone is a significant archaeological find believed by many archaeologists to be evidence of prehistoric mathematical activity. Found 20,000 years ago in what is now the Democratic Republic of Congo, the bone has a series of noticeable scratches that many scholars interpret as a form of counting. The precise nature of these markings is still the subject of debate, but the prevailing theory is that they were used for arithmetic operations, such as keeping track of numbers or simple calculations.

The archaeological context of the Ishango bone, being from the Stone Age, highlights the early presence of numerical comprehension, which could suggest that the humans of that era had some sense of numbers and possibly even a form of proto-mathematics. This idea is reinforced not just by the Ishango bone, but also by the evidence from various archaeological sites across Africa, where other mathematical tools and representations, such as carved stones with depictions of animal figures, which date back tens of thousands of years, have been found.

The discovery of the Ishango bone adds to a growing body of evidence that early humans had the ability to count and perform simple mathematical operations long before the establishment of formal systems of writing or the development of modern number systems. Such artifacts are invaluable for understanding the cognitive abilities of our early ancestors and the origins of mathematical practices.

Answer:

C [tex]4\log_w(x^2-6)-\dfrac{1}{3}\log_w(x^2+8)[/tex]

Step-by-step explanation:

First use the property of logarithms

[tex]\log _ab-\log_ac=\log_a\dfrac{b}{c}.[/tex]

For the given expression you get

[tex]\log_w\dfrac{(x^2-6)^4}{\sqrt[3]{x^2+8} }=\log_w(x^2-6)^4-\log_w\sqrt[3]{x^2+8}=\log_w(x^2-6)^4-\log_w(x^2+8)^{\frac{1}{3}}[/tex]

Now use property of logarithms

[tex]\log_ab^k=k\log_ab.[/tex]

For your simplified expression, you get

[tex]\log_w(x^2-6)^4-\log_w(x^2+8)^{\frac{1}{3}}=4\log_w(x^2-6)-\dfrac{1}{3}\log_w(x^2+8).[/tex]

Answer: C

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

Try the points and see:

(x, y) = (-1, 3) . . . . x + y = -1 + 3 = 2 . . . . yes

(x, y) = (3, -1) . . . . x + y = 3 + (-1) = 2 . . . yes

The remaining points lie on the line connecting these points, so they, too will be on the graph of that line.

if its diameter is 8 cm, then its radius is half that, or 4 cm.

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=4\\ h=13 \end{cases}\implies V=\cfrac{\pi (4)^2(13)}{2} \\\\\\ V=104\pi \implies \stackrel{\pi =3.14}{V=326.7}[/tex]

ANSWER

See below

EXPLANATION

The given function is

[tex]f(x)= {x}^{2} + 2x - 3[/tex]

We complete the square to rewrite this function in the vertex form.

[tex]f(x)= {x}^{2} + 2x + 1 - 1- 3[/tex]

[tex]f(x)= {(x + 1)}^{2} - 4[/tex]

The vertex is (-1,-4).

The axis of symmetry is x=-1

To find x-intercepts , put f(x)=0.

[tex]{(x + 1)}^{2} = 4[/tex]

[tex]x + 1 = \pm \sqrt{4} [/tex]

[tex]x = - 1\pm2[/tex]

[tex]x = - 3 \: or \: x = 1[/tex]

The x-intercepts are (-3,0), (1,0)

To find y-intercept , put x=0.

[tex]f(x)= {0}^{2} + 2(0) - 3 = - 3[/tex]

The graph is shown in the attachment.

Answer:

The difference of the original two-digit number and the number with reversed digits is 98 - 89 = 9

Step-by-step explanation:

Let the digit at unit(one's) place = y

Let the digit at ten's place =  x

So, the two-digit number will be: 10x +y

According to given condition:

Five times the sum of the digits of a two-digit number is 13 less than the original number. This statement can be written as:

5(x +y) = (10x +y) - 13

If you reverse the digits in the two-digit number, four times the sum of its two digits is 21 less than the reversed two-digit number.

if digits are reserved the two digit will be 10y + x

4(x + y) = (10y + x) -21

So, we have 2 equations, solving these 2 equations we can find the 2 digit number.

5(x +y) = (10x +y) - 13

5x + 5y = 10x +y -13

Rearranging:

5x -10x +5y -y = -13

-5x + 4y = -13 (eq1)

4(x + y) = (10y + x) -21

4x +4y = 10y +x =-21

4x -x +4y -10y = -21

3x -6y = -21 (eq2)

Solving:

Multiply eq 1 with 3 and eq 2 with 2

-15x + 12 y = -39

6x - 12y = -42

_______________

-9x = -81

x = -81/-9

x = 9

Putting in eq(1)

-5x + 4y = -13

-5(9) +4y = -13

-45 + 4y = -13

4y = -13 + 45

4y = 32

y = 32/4

y = 8

So, y =8 and x = 9

The 2 digit number is:

10x + y = 10(9) + 8 = 90+8 = 98

The reversed 2 digit number is:

10y + x = 10(8) + 9 = 80+9 = 89

The difference of the original two-digit number and the number with reversed digits is 98 - 89 = 9

Answer:

5(1248 lb/horse + t lb) ≤ 8000 lb

Step-by-step explanation:

One way to do this is to find the average weight of the 5 horses:

It is:

6,240 lb

---------------- = 1248 lb/horse

  5 horses

and to this, for each horse, we must add t lbs tack.

Thus, 5(1248 lb/horse + t lb) ≤ 8000 lb

would be an appropriate inequality.

Please note that your question mentions "the following inequalities;" that means you are expected to share them!  Please do so next time.  Thanks.

Answer:

The cost of one pack of paper was $0.90 and the cost of one box of pens was $2.00

Step-by-step explanation:

Let

x----> the cost of one pack of paper

y---> the cost of one box of pens

we know that

10x+12y=33 ----> equation A

15x+7y=27.50 ---> equation B

Solve the system of equations by graphing

Remember that the solution of the system of equations is the intersection point both graphs

The solution is the point (0.9,2)

see the attached figure

Therefore

The cost of one pack of paper was $0.90

The cost of one box of pens was $2.00

Answer:

pens = $2

paper = .9

Step-by-step explanation:

p = price of a pack of paper

n =  price of a box of pens

10p + 12n = 33

15p + 7n = 27.50

Multiply the first equation by 3

3(10p + 12n )= 33*3

30p +36n = 99

Multiply the second equation by -2

-2(15p + 7n) = 27.50*-2

-30p -14n = -55

Add the 2 modified equations together

30p +36n = 99

-30p -14n = -55

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

    22n = 44

Divide each side by 22

22n/22 = 44/22

n =2

Each box of pens is $2

Now we can find the price of the paper

10p + 12n = 33

10p +12(2) = 33

10p +24 =33

Subtract 24 from each side

10p+24-24=33-24

10p = 9

Divide by 10

10p/10 =9/10

p = .9

Answer: Option D

D. $108

Step-by-step explanation:

We must calculate the expected cost per patient to use treatment method B.

The expected cost for a discrete random variable x is:

[tex]C = \sum x_i * P (x_i)[/tex]

Where [tex]x_i[/tex] is the cost associated with the probability [tex]P(x_i)[/tex]

In this case, the random variable x is represented by the cost of each treatment.

For treatment B there is a possibility that antibiotic 2 works, in that case the cost x would be $ 100 and [tex]P (x) = 0.9[/tex]

There is also the possibility that it does not work, in this case the cost x would be $180 and the probability [tex]P (x) = 0.10[/tex]

The expected cost  is:

[tex]C =\$100*0.9 + \$180*0.1\\\\C = \$108[/tex]

Answer:

1) 45 minutes or 0.75 hours

2) 45 minutes or 0.75 hours

Step-by-step explanation:

We are given the graph that shows Miriam's bike ride.

The x-axis represents the time (in minutes) and the y-axis represents the distance traveled in miles.

1) How many hours did Miriam stop to rest?

The graphs stays the same from 45 minutes to 90 minutes, where he took the rest. No distance covered in that time.

Rest time = 90 minutes - 45 minutes = 45 minutes

He took rest for 45 minutes.

In hours, it is 45/60 = 0.75 hours

2) How many hours did it take Miriam to bike the initial 8 miles.

Look at the graph, the graph reached 8 miles when the time was 45 minutes.

It took 45 minutest to reach 8 miles initially.

In hours, it is 45/60 = 0.75 hours

Answer:

y=6(x+1)^(2)-16

Step-by-step explanation:

Use the formula x=-b/2a

Plug it in for x to get y. That will give you the vertex. Plug the numbers in where they go. There will be one number left that hasn't been filled out. The first number in the equation id 6, so it goes out front.

The equation is y = 6x2 + 12x – 10 rewritten in vertex form is y=6(x+1)²-16

By using the formula   x=-b/2a

simplify

y = 6x2 + 12x – 10

as y=6(x+1)²-16

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Answer:

x=35

Step-by-step explanation:

The angles are alternate interior angles.  Alternate interior angles are equal if the lines are parallel.

3x+16 = 5x-54

Subtract 3x from each side

3x -3x+16 = 5x-3x-54

16 = 2x-54

Add 54 to each side

16+54 = 2x-54+54

70 = 2x

Divide each side by 2

70/2 = 2x/2

35 =x

The answer is 96 you’re welcome

Answer:

10 pairs of earrings and 5 necklaces (the maximum profit will be $250)

Step-by-step explanation:

Let x be the number of earrings and y be the number of necklaces Lisa makes.

1.  Lisa only has enough materials to make 15 total jewelry items per week, then

[tex]x+y\le 15.[/tex]

2.  It takes half an hour to make a pair of earrings, so it takes her [tex]\dfrac{1}{2}x[/tex] hours to make x earrings. It takes her 1 hour to make a necklace, so it takes her y hours to make y necklaces. Lisa only has 10 hours a week to make jewelry, thus

[tex]\dfrac{x}{2}+y\le 10[/tex]

3. Lisa makes a profit of $15 on each pair of earrings and $20 on each necklace. In total her profit is

[tex]P=15x+20y.[/tex]

You have to find the maximum value of the function [tex]P=15x+20y[/tex] with respect to inequalities

[tex]x+y\le 15\\ \\\dfrac{x}{2}+y\le 10[/tex]

Draw the solution set on the coordinate plane (see attached diagram). The maximum value of the efunction P is at point (10,5) and is

[tex]P=15\cdot 10+20\cdot 5=150+100=\$250[/tex]

Answer:

(4, 5)

Step-by-step explanation:

Answer:

New x-coordinate: 4

New y-coordinate: 5

New point: (4,5)

Step-by-step explanation:

You know that the coordinates of a point of this triangle are the following:

[tex]x_1=8\\y_1=10[/tex]

And you know that it is dilated with a scale factor of [tex]\frac{1}{2}[/tex], then, to find the new coordinates of the point, you need to multiply the original coordinates by the scale factor:

New x-coordinate:

[tex]x_2=\frac{1}{2}x_1[/tex]

[tex]x_2=\frac{1}{2}(8)[/tex]

[tex]x_2=4[/tex]

New y-coordinate:

[tex]y_2=\frac{1}{2}y_1[/tex]

[tex]y_2=\frac{1}{2}(10)[/tex]

[tex]y_2=5[/tex]

The new point is (4,5)

Answer:

3.6 hours

Step-by-step explanation:

Blake can do work in hours = 9

Blake can do a part of work in 1 hour = [tex]\frac{1}{9}[/tex]

Ned can paint the same room in six hours.

Ned can do a part of work in 1 hour = [tex]\frac{1}{6}[/tex]

They can do a part of work together in 1 hour =  [tex]\frac{1}{9}+\frac{1}{6}[/tex]

                                                                           =  [tex]\frac{5}{18}[/tex]  

Now they can do [tex]\frac{5}{18}[/tex]  part of work in hour = 1

So, they can do whole work in hours =  [tex]\frac{1}{\frac{5}{18}}[/tex]

                                                             =  [tex]3.6[/tex]

Hence it will take 3.6 hours to paint the room if they work together.

Answer:

Addition of two vectors Will make an resultant vector or a third vectors

Step-by-step explanation:

When two vectors represents in both magnitude and direction as two sides of triangle then resultant will represent as both as third side of triangle but in opposite order