Which ratios below are equivalent?
6 to 13 and 12 to 39
5
5 to 15 and 10 to 30
12 to 15 and 5 to 10

Answer:

  B)  15/17

Step-by-step explanation:

You want the sine of acute angle A in the right triangle shown.

The sine of the angle is the ratio ...

  Sin = Opposite/Hypotenuse

We can go to the trouble to figure the hypotenuse, or we can choose the only suitable answer from the list provided. (It is the one marked already.)

The leg lengths of the triangle shown are 8 and 15, with leg 15 being opposite angle A. This is the first clue that the ratio will have 15 in the numerator. Only answer choice B matches.

The value of the sine function is never greater than 1, eliminating answer choices A, C, and E, leaving choices B and D.

Since the side opposite angle A is the longest of the two legs, we know that angle A is more than 45°, and its sine is more than √2/2. That means choice D can be eliminated, since it is less than 1/2.

The sine of angle A is 15/17.

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Answer:

21 cm increase over 14 days

Step-by-step explanation:

14 days / 2 days = 7 days.

3 cm every 2 days * 7 days =

3 * 7 = 21 cm

Answer:

x= 12/5

Step-by-step explanation:

Distribute the fraction and solve for x.

Answer:

A

Step-by-step explanation:

Using the properties of logarithms, we can simplify the expression:

4 log3x + 6 log3y - 7 log3z = log3x^4 + log3y^6 - log3z^7

Now, we can use another property of logarithms, which states that:

loga (mn) = loga m + loga n

Using this property, we can combine the logarithms with addition or subtraction:

log3x^4 + log3y^6 - log3z^7 = log3(x^4 * y^6 / z^7)

Therefore, the simplified form of 4 log3x + 6 log3y - 7 log3z is log3(x^4 * y^6 / z^7).

The solution that is the closest estimate of the amount of glass Maria will need to construct her pyramid would be =5289.25 cm squared. That is option C.

To calculate the area of a square based pyramid, the formula that should be used would be given below as follows:

\(area = {a}^{2} + 2a \sqrt{ \frac{a2}{4} } + {h}^{2} \)

Where:

a= 44cm

height= 44²-22²= 38.1cm

Area= 44²+ 2(44) × √44²/4 + 38.1²

= 1936+88 × √ 484+1452

= 2024× √1936

= 5807.61 cm².

Therefore the closest estimate to the final answer would be 5289.25 cm squared

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You cannot divide any number by zero since it is meaningless to say that we are dividing a number or object in zero groups or in 0 size parts

Answer: 60

30

Step-by-step explanation: that’s the first two, good luck!

Answer:

$5×30days= $150 for the whole month

Answer: $90 saved

Step-by-step explanation:

8 - 5 = $3 dollars saved each day

Multiply daily amount saved by number of days

$3 × 30 = $90 saved

Answer:A,C,D

Step-by-step explanation:

Answer:

A, C, D

Step-by-step explanation:

The equation of the line is y = x + 6

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

The graph

On the graph, we have the following highlights

The graph intersect the y-axis at y = 6

This means that the intercept c is 6

Also, as x changes by 1, the y values changes by 1

This mean sthat the slope is 1

So, we have

y = mx + c

This gives

y = x + 6

Hence, the equation is y = x + 6

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The linear equation on the graph can be written as:

y = (3/2)*x + 6

A general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x₁, y₁), then the slope will be:

a = (y₂ - y₁)/(x₂ - x₁)

In this case we can see the points (0, 6)  (so the y-intercept is b = 6)  and (4, 10)

Then the slope will be:

a = (10 - 6)/(4 - 0) = 6/4 = 3/2

Then the linaer equation is:

y = (3/2)*x + 6

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The Greyhound bus going to Michigan leaves the station every 20 minutes.

it's 10:40

so next departure on 10:60 => 11:00 then 11:20 then 11:40...

Another bus going to Arkansas leaves the station every 40 minutes.

it is 10:40

so next departure on 11:20 then 12:00

=> 11:20

The five fractions can be arranged in order, from the left to right, from least to greatest as : 5/17 , 3/10 , 4/13 , 1 /3.

The fraction can be arranged from the  from least to greatest by firstly convert the fraction to the decimal numbers so that one c b able to identify the highest and the lowest values.

The given fractions  1 /3 2 /7 3/10 4/13 5/17 can be converted to decimal numbers as 0.33 , 0.67 , 0.30 , 0.31 , 0.29 respectively and this can be arranged as 5/17 , 3/10 , 4/13 , 1 /3.

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Answer:

605

Step-by-step explanation:

11x55=605

A

Or maybe something else is not sure

Answer:

£0

Step-by-step explanation:

To calculate the outstanding loan balance for each person after 10 years, we can use the following formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = the final amount

P = the principal (initial loan amount)

r = the annual interest rate (as a decimal)

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

t = the time in years

For Olivia, we can calculate her outstanding balance after 10 years as follows:

P = £2000

r = 6.5% per year = 0.065

n = 1 (compounded annually)

t = 10 years

A = £2000(1 + 0.065/1)^(1*10) = £3829.71

After paying back £1000, Olivia's outstanding balance would be £2829.71.

For Sadie, we can calculate her outstanding balance after 10 years as follows:

P = £2000

r = 6.5% per year = 0.065

n = 1 (compounded annually)

t = 10 years

A = £2000(1 + 0.065/1)^(1*10) = £3829.71

After paying back £1000, Sadie's outstanding balance would be £2829.71.

To find the difference between Sadie's outstanding balance and Olivia's outstanding balance, we can subtract Olivia's balance from Sadie's balance:

£2829.71 - £2829.71 = £0

Therefore, Sadie does not owe more money than Olivia after 10 years, as both of their outstanding balances are the same at that point in time.

This text describes a scenario where two individuals, Olivia and Sadie, take out a loan of £2000 each at the same time. The loans have a compound interest rate of 6.5% per year. Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods.

Two years after taking out the loan, Olivia pays back £1000, which reduces her outstanding loan balance to £2000 plus accumulated interest. Three years after taking out the loan, Sadie pays back £1000, which also reduces her outstanding loan balance to £2000 plus accumulated interest.

The question asks how much more money Sadie owes than Olivia 10 years after taking out the loan. To solve this problem, we need to calculate the outstanding loan balance for both Olivia and Sadie after 10 years, using the compound interest formula. We can then subtract Olivia's outstanding balance from Sadie's outstanding balance to find the difference.

It's worth noting that the question specifies that the answer should be given in pounds to the nearest 1p, which means we need to round our final answer to the nearest penny.

Answer:

9x - 6

Hope this helps! <3

(If you need a step by step lmk)

Answer:

6x+3(x-2)

6x+3x-6

9x-6

Using proportions, it is found that:

A. The equation is 0.95x = 456.

B. The original price of the television was $480.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The television was sold with a 5% discount at $456, that is, 95% of the original price is of $456, hence:

0.95x = 456

x = 456/0.95

x = $480.

Thus:

A. The equation is 0.95x = 456.

B. The original price of the television was $480.

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The unadjusted cost of goods sold for the year is calculated by subtracting the ending inventory from the sum of beginning inventory and purchases. The formula is as follows:

Unadjusted Cost of Goods Sold = Beginning Inventory + Purchases - Ending Inventory

Without knowing the values for beginning inventory, purchases, and ending inventory, we cannot compute the unadjusted cost of goods sold for the year.

5. Given that the $70,000 ending balance in Work in Process includes $24,000 of direct materials, we can calculate the missing information as follows:

Direct Labor = Total Work in Process - Direct Materials - Overhead
Direct Labor = $70,000 - $24,000 - Overhead

Without knowing the value for overhead, we cannot compute the direct labor cost. However, we can rearrange the formula to solve for overhead:

Overhead = Total Work in Process - Direct Materials - Direct Labor
Overhead = $70,000 - $24,000 - Direct Labor

Without knowing the value for direct labor, we cannot compute the overhead cost.

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Answer:

Step-by-step explanation:

For step explanation:

1. write the problem

2. distinguishing the neg sign

3. distributing 3

4. moving like terms next to each other through commutative property

5.  Combining like terms

6. getting rid of parentheses

Answer:

\(x = 5\)

\(R = C = 225\)

Step-by-step explanation:

Given

\(C = 15x + 150\)

\(R = 45x\)

Required

The break even point

To do this, we make use of:

\(R =C\)

\(45x=15x + 150\)

Collect Like Terms

\(45x-15x = 150\)

\(30x = 150\)

\(x = 5\)

Substitute 5 for x in \(R = 45x\)

\(R = 45 * 5\)

\(R = 225\)

Hence, the break even point is:

\(x = 5\)

\(R = C = 225\)

The scale used by Johan is 1: 252.

Here, we are given that Jonah made a scale drawing of the picnic area in which the 70 yards wide picnic area in real life, was 10 inches wide in the drawing.

As per mathematical measurements-

1 yard = 3 feet

and 1 feet = 12 inches

Thus, 3 feet = 12 x 3 inches

= 36 inches

Therefore, we get that 1 yard = 36 inches

Now, the picnic area is 70 yards

the picnic area in inches is = 70 x 36 inches wide

= 2520 inches

Thus the scale used by Johan will be-

10 : 2520

= 1 : 252

Thus, the scale used by Johan is 1 : 252.

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Answer:

  a) 10

  b) 7.5

  c) 8

  d) 75

Step-by-step explanation:

Pick's theorem tells you the area of a figure drawn on grid points is ...

  A = i +b/2 -1

where i is the number of interior grid points, b is the number of boundary grid points.

__

a) b = 12 (The verticals cross a grid point, but the diagonals don't. The number of boundary points is the number of vertices +2.)

  i = 5

  Area = 5 +12/2 -1 = 10 . . . square units

__

b) b = 5 (The horizontal crosses a grid point, but none of the diagonals do. The number of boundary points is the number of vertices +1.)

  i = 6

  Area = 6 +5/2 -1 = 7.5 . . . square units

__

c) b = 8 (The upper left diagonal crosses 2 grid points, so the number of boundary points is the number of vertices +2.)

  i = 5

  Area = 5 +8/2 -1 = 8 . . . square units

__

d) b = 3, i = 6

  Area = 6 +3/2 -1 = 7.5 . . . square units

_____

Additional comment

The first figure can be divided by vertical lines into 4 congruent trapezoids with bases 3 and 2. Then the area is (4)(1/2(3+2)(1) = 10.

The remaining figures can be considered as the area of the bounding box less the areas of triangles discarded when the figure is cut out. (No additional lines need be drawn.) The areas figured this way agree with the area values shown above. The area of a triangle is A=1/2bh, so is not difficult to figure mentally.

Answer:

412.92

Step-by-step explanation:

\(A = P(1+\frac{r}{n} )^{nt}\)

A: Amount, P: Principal, r: interest, n: no.of times compounded yearly and t: time in years

We have P = 300

r = 4% = 0.04

n = 12 (compounded monthly)

t = 8

\(A = 300(1+\frac{0.04}{12} )^{12*8}\\\\300(\frac{12.04}{12} )^{96}\\\\= 412.92\)

Answer:

19 or -28

Step-by-step explanation:

is it 24 - 5 or 24 - 52?

Answer:19

Step-by-step explanation:

Answer:

A) 0.1855

B) 0.0010376

C) 0.0001297

D) 0.006363

E) 0.000007629

Step-by-step explanation:

In calculation of a probability, we normally take the ratio of the number of ways to meet a certain condition (i.e. the numerator) divided by the number of ways to pick from a pool (i.e. the denominator).

So what are the number of ways the flip of a coin 17 times can come out?

A coin has a head and tail, so each toss will have two possible results. If we toss once, we have 2 possible results. If we toss, twice we have 2² = 4 possible results.

If we toss thrice, we have 2³ = 8 possible results, etc.

Thus, for 17 tosses, we will have 2^(17) = 131072 possible results.

A) To achieve the probability of getting 9 heads, we will use combination formula;

C(n, k) = n! / (k!(n - k)!)

In this case, n = 17 and k = 9

So,

P(9 heads) = 17! / (9!(17 - 9)!) = 24310

Thus,

P(9 heads in 17 tosses of a fair coin) = 24310/131072 = 0.1855

B) Similar to A above;

P(2 heads) = 17! / (2!(17 - 2)!) = 136

Thus,

P(2 heads in 17 tosses of a fair coin) = 136/131072 = 0.0010376

C) Similar to A above;

P(1 tail) = 17! / (1!(17 - 1)!) = 17

Thus,

P(1 tail in 17 tosses of a fair coin) = 17/131072 = 0.0001297

D) probability of getting 14 or more heads?

Since, there are 17 tosses, this will be;

P(14 or more heads in 17 tosses) = P(14 heads in 17 tosses) + P(15 heads in 17 tosses) + P(16 heads in 17 tosses) + P(17 heads in 17 tosses)

P(14 heads) = 17! / (14!(17 - 14)!) = 680

P(15 heads) = 17! / (15!(17 - 15)!) = 136

P(16 heads) = 17! / (16!(17 - 16)!) = 17

P(17 heads) = 17! / (1!(17 - 17)!) = 1

Thus;

P(14 heads in 17 tosses) = 680/131072 = 0.005188

P(15 heads in 17 tosses) = 136/131072 = 0.0010376

P(16 heads in 17 tosses) = 17/131072 = 0.0001297

P(1 head in 17 tosses) = 1/131072 = 0.00000763

P(14 or more heads in 17 tosses) = 0.005188 + 0.0010376 + 0.0001297 + 0.00000763 = 0.006363

E) Similar to A above;

P(17 tails) = 17! / (17!(17 - 17)!) = 1

Thus,

P(17 tails in 17 tosses of a fair coin) = 1/131072 = 0.000007629

The length of BD is 18.5 units.

In the given right triangle ABC, with altitude BD drawn to hypotenuse AC, we are given the lengths AD = 22 and DC = 15. We need to find the length of BD.

Let's consider triangle ABD. Since BD is the altitude, it divides the right triangle ABC into two smaller right triangles: ABD and CBD.

In triangle ABD, we have the following sides:

AB = AD = 22 (given)

BD = ?

Now, let's consider triangle CBD. In this triangle, we have the following sides:

BC = DC = 15 (given)

BD = ?

Since triangles ABD and CBD share the same base BD, and their heights are the same (BD), we can say that the areas of these triangles are equal.

The area of triangle ABD can be calculated as:

Area(ABD) = (1/2) * AB * BD

Similarly, the area of triangle CBD can be calculated as:

Area(CBD) = (1/2) * BC * BD

Since the areas of ABD and CBD are equal, we can equate their expressions:

(1/2) * AB * BD = (1/2) * BC * BD

We can cancel out the common factor (1/2) and solve for BD:

AB * BD = BC * BD

Dividing both sides of the equation by BD (assuming BD ≠ 0), we get:

AB = BC

In triangle ABC, the lengths AB and BC are equal, which implies that triangle ABC is an isosceles right triangle. In an isosceles right triangle, the leg's length are congruent, so AB = BC = AD = DC.

BD is equal to half of the hypotenuse AC:

BD = (1/2) * AC

Substituting the given values, we have:

BD = (1/2) * (AD + DC) = (1/2) * (22 + 15) = (1/2) * 37 = 18.5

Therefore, the length of BD is 18.5 units.

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Answer:

so you have $12.95. then you multiply it by 8% which gives you $13.986. Then you take 10% off of it, which gives you $12.5874.

Answer:

The new price would be 108% of last year’s price. Multiply the new price by 4 and then multiply that amount by 90% to find the sale price.

Step-by-step explanation:

sample response