Simplify: 45 ÷ 3 + 2 × 8 - 12 + 42

Answer:

a) 128°

b) Opposite angles of a cyclic quadrilateral add up 180°

Step-by-step explanation:

→ Work out ABD

180 - 116 = 64°

→ Use the theorem 'The angle at the centre is twice the angle at the centre'

2 × 64 = 128°

→ Use the cyclic quadrilateral theorem

Opposite angles of a cyclic quadrilateral add up 180°

The value of x is 128 degree when the angle CBD is of 116 degree.

It is a four sided polygon having four angles and four corners.

Firstly we find angle ABD which is 180-116=64 Degrees because the angle at the center is twice the angle on the any point of circle.

So the value of x becomes 2*64=128 degrees.

By using the cyclic quadrilateral theorem opposite angles of a cyclic quadrilateral has a sum of 180 degrees.

Learn more about cyclic quadrilateral theorem at https://brainly.com/question/27420229

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Answer:

Let the MP of 1 article = Rs 1

MP of 15 article = Rs 15

SP of (15+1) articles = 15 x 96/100

= Rs 14.40

CP of 16 article = 14.40/135 x 100

= Rs 32/3

CP of 1 article = 32/3x16

= Rs 2/3

Required % = 1/3 x 3/2 x 100

= 50

Answer:

A.) 6.4 units

Step-by-step explanation:

We can use the Pythagorean theorem to find the length of AB.

If we find the horizontal and vertical distance of A and B, we form a triangle, with leg lengths of 5 and 4.

Now, we just solve using the Pythagorean theorem.

5^2 = 25

4^2 = 16

25 + 16 = 41

sqrt 41 ≈ 6.4 units.

Hope this helps!

If there is something wrong, just let me know.

x=119

hope it doesn't help you!!

Complete Question

The reading speed of second grade students in a large city is approximately normal, with a mean of 90 words per minute (wpm) and a standard deviation of 10 wpm.

What is the probability that a random sample of 12 second grade students from the city in a mean reading rate of more than 96 words per minute?

Answer:

[tex]P(\=x >96 )=0.01884[/tex]

Step-by-step explanation:

From the question we are told that:

Sample size [tex]n=12[/tex]

Sample mean [tex]\=x =90[/tex]

Standard Deviation [tex]\sigma=10[/tex]

Generally

[tex]\sigma_x=\frac{\sigma}{\sqrt{10}}[/tex]

[tex]\sigma_x=\frac{10}{\sqrt{12}}[/tex]

[tex]\sigma_x=2.887[/tex]

Generally the equation for P(\=x >96 ) is mathematically given by

[tex]P(\=x >96 )=P(Z>\frac{\=x-\mu_x}{\sigma_x})[/tex]

[tex]P(\=x >96 )=P*(Z>\frac{90-96}{2.887})[/tex]

[tex]P(\=x >96 )=1-P(Z<2.08)[/tex]

[tex]P(\=x >96 )=1-0.98116[/tex]

[tex]P(\=x >96 )=0.01884[/tex]

Answer:

25%

Step-by-step explanation:

We know that there are ten purple popsicles. Together without the purple popsicles, there are 40 popsicles in total. Therefore there is a 10/40 chance to get purple. We need to turn this into a percentage so we do (10 / 40) x 100. This would equal to 25%, therefore, there is a 25% probability to get a purple popsicle.

Answer:

The domain is;

0 < c ≤ 15

Step-by-step explanation:

We are told that Levi's average calories consumed per day is denoted by c.

Now, we are told it is subject to a maximum of 15 calories.

Thus; c ≤ 15

Now,if he is losing weight consistently, then c must be greater than 0.

Thus,the domain is;

0 < c ≤ 15

Answer:

57.5

Step-by-step explanation:

20x - (10 x 110) = 50

=> 20x - 1100 = 50

=> 20x = 1150

=> x = 1150/20

=> x = 115/2

=> x = 57.5

Answer:

Surface area = 726 cm²

None of the options is correct.

Step-by-step explanation:

Surface area of the composite figure = surface area of cone + surface area of cylinder - 2(area of base of cone)

✔️Surface area of cone = πr(r + l)

Where,

Radius (r) = 5 cm

Slant height (l) = √(10² + 5²) (Pythagorean theorem)

Slant height (l) = 11.2 cm

Plug in the values

= π*5(5 + 11.2)

= 254.5 cm²

✔️Surface area of the cylinder = 2πr(h + r)

r = 5 cm

h = 15 cm

Plug in the values into the formula

S.A = 2*π*5(15 + 5)

S.A = 628.3 cm²

✔️area of base of cone = πr²

r = 5 cm

Area = π*5² = 78.5 cm²

✅Surface area of the composite figure = 254.5 + 628.3 - 2(78.5)

= 882.8 - 157

= 726 cm² (nearest square meter)

None of the options is correct.

Answer:

B. domain is all integers 0 through 9

Step-by-step explanation:

Domain values area usually plotted along the horizontal axis. In this case, the number of days is the domain of the of the function.

The domain of the function that is plotted on the graph ranges from 0, 1, 2 to 9.

1, 2, 3 to 9 are all integers. Therefore, we can conclude that the "domain is all integers 0 through 9."

Answer:

B could be (4,8), (6,11), (8,14), (10,17), (12,20), etc.

Step-by-step explanation:

quick mafhs

Answer:

C. 13

Step-by-step explanation:

Quarters are worth 25 cents each

Nickels are worth 5 cents each

Let n be the number of nickels that Jamar as in his pocket.

We already know that he only has 1 quarter in his pocket which is worth 25 cents, so we can form this equation:

5n + 25 = 90

5 meaning that each nickel is worth 5 cents, 25 meaning that he has only 1 quarter in his pocket (25 cents) and 90 meaning that he has a total of 25 cents in his pocket.

We have to isolate the n so we can subtract 25 from both sides to get:

5n = 65

After that we can get n by dividing 5 from both sides:

n = 13

Therefore there are 13 nickels in his pocket.

Let me know if I did anything incorrectly.

The number of nickels he has is 13. The correct option is C.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that quarters are worth 25 cents each and nickels are worth 5 cents each.

Let n be the number of nickels that Jamar has in his pocket.

We already know that he only has 1 quarter in his pocket which is worth 25 cents, so we can form this equation:

5n + 25 = 90

5 meaning that each nickel is worth 5 cents, 25 meaning that he has only 1 quarter in his pocket (25 cents), and 90 meaning that he has a total of 25 cents in his pocket.

We have to isolate the n so we can subtract 25 from both sides to get:

5n = 65

After that we can get n by dividing 5 from both sides:

n = 13

Therefore, the number of nickels he has is 13. The correct option is C.

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Part A

Explanation:

A histogram is best because it helps show how the scores breakdown for the various bins or intervals or classes. It's effectively a visual summary of a grouped frequency table.

A dot plot would not work because we don't know the specific scores, but rather just the general region of where they fall.

A box plot doesn't work well either because we lose information on how the distribution is broken down. Sure we get the five number summary out of it, but we don't see how the bins are set up.

============================================================

Part B

We have the categories or bins of 0-4, 5-9, 10-14, 15-19, 20-24. Each bin will correspond to a bar that tells us how frequently the values show up. It tells us how frequent or how many scores we got in that sub-interval.

And so on. This all leads to the histogram shown below.

Answer:

Part A is a histogram.

Part B draw a histogram

Step-by-step explanation:

This is because a dot plot and a box plot are too specific for how the data was given. We don't know the exact number for each student.

Part B The x axis would be labeled by the groups, 0-4, 5-9, 10-14, 15-19, 20-24. The y axis would be labeled number of students. Then you could color in the area matching the correct number of students for each category.

Answer: $15927.183

Step-by-step explanation:

Price of good= $29,000

Trade discount = 40½ 20¼/5

The first discount will be:

= 40½ × $29000

= $11745

Then, the price after the first discount will be:

= $29000 - $11475

= $17255

Then, the second discount will be:

= $17255 × 20¼%

= $3494.14

Then, the price after the second discount will be:

= $17255 - $3494.14

= $13760.86

The third discount will be:

= $13760.86 × 5%

= $688.043

Then, the total discount will be:

= $11745 + $3494.14 + $688.043

= $15927.183

Therefore, the trade discount is $15927.183.

Answer:

$368,640

Step-by-step explanation:

288,000 * .28 = 80640

288,000 + 80640 = 368640

Answer:

The answer is number 2. hope that helps

Answer:

(3,-12)

Step-by-step explanation:

the triangle has points A(-2,-2) B(1,-5) and C(-5,-5) the translation of (2 horizontally,-7 vertically)  will cause B to translate to coordinates (3, -12)

Answer:

Step-by-step explanation:

Prime factorize 121 and 99

121 = 11 * 11

99 = 11 * 3 * 3

Common factor = 11

Answer:

uwuwhwhwnwjwjwiwieiwiwjwjjejeejjwje

Step-by-step explanation:

euwwuwjw

Answer:

A.

Step-by-step explanation:

Basically.. when you draw a line from the vertex of a right triangle's 90 degree angle to its hypotenuse, it'll make two triangles with the same angles. Then you can use ratios to discern the size of said rectangles. I hope that helps.

Answer:

20 unit²

Step-by-step explanation:

A trapezium is given to us on the grid and we need to find out the area of the trapezium . In order to find the area , we need to find the measure of the parallel sides and the distance between the parallel sides.

From the grid :-

[tex]\rm\implies Side_1 = 7 \ units [/tex]

[tex]\rm\implies Side_2 = 3 \ units [/tex]

[tex]\rm\implies \perp \ Distance =4 \ units [/tex]

Now here we got the two parallel sides of the trapezium and the distance between the two parallel sides. Now we can find the area as ,

[tex]\rm\implies Area_{Trapezium}= \dfrac{1}{2}\times ( s_1 + s_2) \times \perp \ Distance \\\\\rm\implies Area = \dfrac{1}{2} \times ( 7 + 3 ) \times 4 \ unit^2 \\\\\rm\implies Area = \dfrac{1}{2} \times ( 10) \times 4 \ unit^2 \\\\\rm\implies\boxed{\rm Area = 20 \ unit^2}[/tex]

Step-by-step explanation:

Answer:f(x)=-5x^(2)-3x+9 this is the standard form

Answer:

11

Step-by-step explanation:

because line AD divided the triangle ABC into two equal halves

Answer:

The inequality is 0.6x < 12.5

The maximum number of days that Diego's father can drive the car without the warning light coming on is 20 days

Step-by-step explanation:

14 gallons-1.5 gallons=12.5 gallons    

we know that  

If the remaining fuel is greater than  1.5 gallons Diego's father can drive the car without the warning light coming on    

so  

Let  

x ----> the number of days

0.6x < 12.5 inequality that represent the situation  

Solve for x

x < 12.5/0.6

x < 20.8 days

The maximum number of days that Diego's father can drive the car without the warning light coming on is 20 days

Answer:

one side should be given.

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

hope it helps...

have a great day!!

Answer: [tex]26,400\ ft[/tex]

Step-by-step explanation:

Given

Each side of the pentagon measures [tex]1760\ ft[/tex]

A complete trip is equivalent to the perimeter of the perimeter

[tex]\Rightarrow \text{Perimeter of the Pentagon P=}5\times 1760\\\Rightarrow P=8800\ ft[/tex]

For Three rounds, he completed a distance of  

[tex]\Rightarrow P=3\times 8800\\\Rightarrow P=26,400\ ft[/tex]

Step-by-step explanation:

the equation is

3n-1 = 5n-7

2n= 6

n= 3

Answer:

0.2210

Step-by-step explanation:

If p = 0.04

then 1-p = 1 - 0.04 = 0.96

So we have the probability distribution value

as;

n C r * p^r * (1-p)^(n-r)

Thus;

64 C 3 * p^3 * (1-p)^(64-3)

= 64 C3 * 0.04^3 * 0.96^61

where 64 C 3 is 64 combination 3

= 41,664 * 0.04^3 * 0.96^61

= 0.2210

Answer:

Rs. 28,571.4

Step-by-step explanation:

Let

Cost price = x

Profit = 5% of x

= 0.05x

Selling price = Rs.30, 000

Profit = Selling price - cost price

0.05x = 30,000 - x

Collect like terms

0.05x + x = 30,000

1.05x = 30,000

x = 30,000/1.05

x = Rs. 28,571.428571428

Approximately,

Cost price = x = Rs. 28,571.4