A drawer contains 60 coins consisting of dimes and quarters. If the total value of the coins is $12.30, how many dimes and how many quarters are in the drawer?

[tex]\frac{1+\tan x}{\sin x+\cos x}=\sec x[/tex] is proved

Given that,

[tex]\frac{1+\tan x}{\sin x+\cos x}=\sec x[/tex]  ------- (1)

First we will simplify the LHS and then compare it with RHS

[tex]\text { L. H.S }=\frac{1+\tan x}{\sin x+\cos x}[/tex]  ------ (2)

[tex]\text {We know that } \tan x=\frac{\sin x}{\cos x}[/tex]

Substitute this in eqn (2)

[tex]=\frac{1+\frac{\sin x}{\cos x}}{\sin x+\cos x}[/tex]

On simplification we get,

[tex]=\frac{\frac{\sin x+\cos x}{\cos x}}{\sin x+\cos x}[/tex]

[tex]=\frac{\sin x+\cos x}{\cos x} \times \frac{1}{\sin x+\cos x}[/tex]

Cancelling the common terms (sinx + cosx)

[tex]=\frac{1}{c o s x}[/tex]

We know secant is inverse of cosine

[tex]=\sec x=R . H . S[/tex]

Thus L.H.S = R.H.S

[tex]\frac{1+\tan x}{\sin x+\cos x}=\sec x[/tex]

Hence proved

Answer:

The area is 12.56, and the circumference is 12.56.

Step-by-step explanation:

For the area,

We need to use the formula A=3.14*radius*radius

So we plug it in, and we get 3.14*2*2, which is 12.56 centimeters squared.

For circumference, we need to do,

C = 3.14*diameter

To find the diameter we need to do 2 (radius) x 2 which is 4

Plugging it in that would be 3.14 * 4 which is 12.56

So, in this case, the area is 12.56, and the circumference is also 12.56.

The area of a circle with a radius of 2 cm is 12.56 cm², and the circumference is 12.56 cm, using 3.14 for pi.

To find the area and circumference of a circle with a radius of 2 cm, we can use the formulas A = πr² for the area and C = 2πr for the circumference, where π (pi) is approximately 3.14.

Area of the Circle

The area of the circle is calculated using the formula A = πr². Plugging in the radius:

A = 3.14 × (2 cm)²

A = 3.14 × 4 cm²

A = 12.56 cm²

Circumference of the Circle

The circumference of the circle is calculated using the formula C = 2πr. Plugging in the radius:

C = 2 × 3.14 × 2 cm

C = 12.56 cm

Answer: 18 question correct

Step-by-step explanation:

if she got 100% on the test:

100% x 25 question = 25 questions correct

so,

72% x 25 questions = 18 question correct

Answer:

C

Step-by-step explanation:

432×24= 10368

288×36= 10368

Answer:

BUILDING C

Step-by-step explanation:

To find the answer, we need to find the scale factor. First, divide the given numbers (measurements). So 36/24. This gives us 1.5, our scale factor. Now, to find the correct measurements of the real building, divide the values. So for example, BUILDING C = 288 feet by 432 feet. Divide the two values. You get 432/288= 1.5 Therefore, this building matches our scale factor.

Answer:

the three consecutive odd integers are 9, 11, and 13.

Step-by-step explanation:

Let's say that the first odd integer is x. The second consecutive odd integer would have to be x+2. (It would not be x+1  because that would result in an even integer. The sum of any two odd numbers is even.) The third consecutive odd integer would be (x+2) +2 or x+4.

The sum of the first, twice the second, and three times the third can be written as:

x+2(x+2)+3(x+4)

This equals 70. We can now distribute and solve for x:

x+2(x+2)+3(x+4)=70

x+2x+4+3x+12=70(distribute)

6x+16=70(combine like terms)

6x=54(subtract 16 from both sides)

x=9(divide by 9)

Thus, the three consecutive odd integers are 9, 11, and 13

hope this helps :)

Answer:

9,11 and 13

Step-by-step explanation:

X+(x+2)+(x+4)= ?

3x+6=  ?

70/2=35      35-2=33

3x+6=33

3x=27

x=9

9+22+39=70

Answer:

Step-by-step explanation:

Let's find the volume of the room in ft³ and that will give

14×22×9=2772ft³

There are deductions. Hence we subtract them from this value

3×5=15, but there are two, hence 15×2=30ft²

And 4×7=28ft²

Hence 2772-(30+28)=2714

Dividing this value by 320 gives

8.4(to 2s.f)

Answer:

A. positive slope.

Step-by-step explanation:

In the least square linear regression of Y on X, the straight line of best fit is given by,

[tex]Y_{s} = \mu_{Y} + \rho \times \frac {\sigma_{Y}}{\sigma_{X}} \times (X - \mu_{X})[/tex] ------------------(1)

[where [tex]Y_{s}[/tex] is the estimated value of Y]

Clearly,  here,

Slope pf the line = [tex]\rho \times \frac {\sigma_{Y}}{\sigma_{X}}[/tex]---------------------------------(2)

Y- intercept = [tex]\mu_{Y} - \rho \times \mu_{X} \times \frac {\sigma_{Y}}{\sigma_{X}}[/tex]-----------------(3)

and,

X - intercept = [tex]\mu_{X} - \mu_{Y} \times \frac {\sigma_{X}}{\rho \times \sigma_{Y}}[/tex]----------------(4) [putting [tex]Y_{s} = 0[/tex] in (1) and taking the value of X]

So,

since [tex]\sigma_{Y}, \sigma_{X} > 0[/tex]

[since [tex]\sigma_{Y} = 0[/tex] or [tex]\sigma_{X} = 0[/tex] will result in a degenerate distribution, hence these cases are discarded]

so, correlation coefficient = [tex]\rho[/tex] > 0 implies

A. positive slope. [as evident from (1)]

clearly from (3) and (4) all the other options are false.

Final answer:

A least squares line of best fit with a positive correlation coefficient always has a positive slope, reflecting the positive relationship between the independent and dependent variables. The y-intercept can be positive or negative and is not determined by the correlation.

Explanation:

The question is asking about the characteristics of a least squares line of best fit when there is a positive correlation coefficient. A positive correlation coefficient means that as the value of the independent variable (x) increases, the value of the dependent variable (y) also increases. From this, it follows that the slope of the line ( he m term in the equation) is positive - reflecting the concept that the slope represents the relationship between two variables, with a positive slope indicating a positive relationship.

The y-intercept (the b term in the equation) could be positive or negative, as it represents where the line crosses the y-axis when x is 0, and this point doesn't affect the direction of the relationship between the variables, just the starting level of the dependent variable. Therefore, the correct answer to the question is simply A. positive slope, as this is the only feature guaranteed by a positive correlation coefficient.

Answer:

Step-by-step explanation:

2/10+6/100 is the same as 2/10*10/10+6/100

2/10*10/10=20/100

20/100+6/100

26/100

Answer: 26/100

Step-by-step explanation: Find the common denominator, which is 100 multiply both numerator and denominator by 10 which is 20/100 and then add on 6/100 which equals 26/100

Answer:812/1000

Step-by-step explanation:

Answer:

21700

Step-by-step explanation:

23400 - 1700 = 21700

Walter's salary last year can be found by subtracting the increase from his current salary. After calculating, we find that Walter's salary last year was $21,700.

To calculate Walter's salary last year, we need to subtract the amount his salary increased this year from his current salary. Walter's current salary is $23,400, and it has increased by $1,700 from last year. Thus, his salary last year was:

$23,400 (current salary) - $1,700 (increase) = $21,700

Therefore, Walter's salary last year was $21,700.

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Answer:

The coordinates of the lines when both lines meets at point is ( 0, 0 )

Step-by-step explanation:

Given as :

The two lines are

[tex]\frac{2}{3}[/tex]x + [tex]\frac{1}{6}[/tex]y = [tex]\frac{2}{3}[/tex]

And 4 x + y = 4

The coordinate of the lines are obtained when the two lines intersect

Let the coordinate of intersection points are ( x , y )

Now , The first lines as

[tex]\frac{2}{3}[/tex]x + [tex]\frac{1}{6}[/tex]y = [tex]\frac{2}{3}[/tex]

Or, Taking LCM we get ,

[tex]\frac{4x + y}{6}[/tex] = [tex]\frac{2}{3}[/tex]

Cross multiplication both sides

Or, 3 × ( 4 x + y ) = 2 × 6

Or,  3 × 4 x +  3 × y = 12

Or, 12 x + 3 y = 12          ...........A

Other line is 4 x + y = 4

i.e 3 × ( 4 x + y ) = 3 × 4

or, 12 x + 3 y = 12          .........B

Solving both the line equations

(12 x + 3 y ) - ( 12 x + 3 y ) = 12 - 12

I.e x = 0  and  y = 0

So coordinates are ( x , y )  =  ( 0 , 0 )

Hence The coordinates of the lines when both lines meets at point is ( 0, 0 ) Answer

Answer:

x>=-1

Step-by-step explanation:

10x+4>=-6

10x>=-6-4

10x>=-10

x>=-10/10

x>=-1

Answer:

This is answer

rise/run -6/1

y intercept : 8

Step-by-step explanation:

Answer:

[tex]\displaystyle -5x + y = -92\:or\:y = 5x - 92[/tex]

Step-by-step explanation:

−12 = 5[16] + b

80

[tex]\displaystyle -92 = b \\ \\ y = 5x - 92[/tex]

If you want it in Standard Form:

y = 5x - 92

- 5x - 5x

__________

[tex]\displaystyle -5x + y = -92[/tex]

I am joyous to assist you anytime.

Answer:

Step-by-step explanation:

12/4=3 and 16/8=2

Answer:

The number of shirts to be purchased for price to be same is 6 .

Step-by-step explanation:

Given as :

The price for cool shirt = $ 8

The shipping charge for cool shirt = $ 13

The price for Tees = $ 7.50

The shipping charge for Tees = $ 16

Now, Let The number of shirts = S

So , According to question

∵ price to be same for both companies

∴ $ 8 × S + $ 13 = $ 7.50 × S + $ 16

Or, $ 8 × S - $ 7.50 × S = $ 16 - $ 13

Or, 0.5 S = 3

∴ S = [tex]\frac{3}{0.5}[/tex]

I.e  S = 6

Hence The number of shirts to be purchased for price to be same is 6 . Answer

Answer:

I believe they made $4,550 each week.

Step-by-step explanation:

If they sold 74 puppies in a week, and there are 7 days in a week, You would divide 74 by 7 to get an estimate of 10. So that means that 10 puppies were sold each day. Then, because the puppies cost $65, you would multiple 65 by 10 to get $650. $650 is the amount of money they make in a day. Than multiple 650 by 7 to get $4,550. $4,550 is the amount of money they would have made.

74÷7 = about 10

65×10 = 650

650×7 = 4550

Answer: 2.5 miles per hour

Step-by-step explanation:

this problem is all about conversions

220 ft per minute

first get it to hours, since there is 60 minute in an hour multiply by a factor of 60

220 ft per minute becomes 13200 ft per hour

then you need to covert from ft to mi, there are 5280 ft in 1 mi so divide by 5280

13200 ft per hour becomes 2.5 miles per hour

Answer:

Diameter=35

Step-by-step explanation:

If your circumstance is 35pi then the formula would be C=35pi and to find that it would have been C=2 pi r. To find the diameter it would be d=c/pi. So it would be d=35pi/pi. The pi's would cancel out and you have 35 as the diameter and 17.5 as the radius

Check:

C=2 pi r

C= 2 pi 17.5

C=35pi ✅

D=2r

D=2(17.5)

D=35✅

I hoped this helped, I am not sure but this is what I think

Answer:

The Value of x is 40.

Step-by-step explanation:

Given:

∠SRT ≅ ∠STR

∠SRT = 20

m∠SRT = 4x

To find: Value of x

Solution:

From the given data,

m ∠SRT = 20

Also ∠SRT ≅ ∠STR

Hence from congruence and equality property we can say that;

m∠STR= 20

m∠STU= 4x

Now by straight angle property which states that sum of two angles which are created by a straight line is always 180.

Hence,

∠STR +∠STU =180

Now Substituting the given values we get;

[tex]20+4x=180\\4x=180-20\\4x=160\\\\x=\frac{160}{4} =40[/tex]

Hence m∠STU = 4x =4 ×40 = 160°

Hence the value of x = 40.

2/5= 12/30

The road is 12/30 miles long, they pave 1/30 each hour.

60x12= 720 minutes= 12 hours

To repave the road that is 2/5 miles long, it will take the road crew 12 hours.

To find out how long it will take the road crew to repave the road, we need to divide the length of the road by the rate at which they can repave. The road is 2/5 miles long and the crew can repave 1/30 miles per hour. To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. So, (2/5) ÷ (1/30) = (2/5) x (30/1) = 60/5 = 12. Therefore, it will take the crew 12 hours to repave the road.

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Answer:

$16.74

Step-by-step explanation:

so for every pound is 2.79 so just so

6 times 2.79

Step-by-step explanation:

PART A

a=total amount

c=cans of oil

g=gasoline

a=2.85g+3.15c

PART B

a=2.85(8.4)+3.15(6)

a=23.94+18.90

a=42.84

Answer:

y = 0.25x - 5

Step-by-step explanation:

Given line is 4x + y = 3

or y = -4x + 3

Comparing this with slope-intercept form y = mx + c :

slope of this line is -4

Product of slopes of perpendicular lines = -1

⇒ slope of a line perpendicular to this is [tex]\frac{-1}{-4}[/tex] = [tex]\frac{1}{4}[/tex] = 0.25

This line also passes through the point (-4,-6)

The equation of a line having slope m and passing through a point (h,k) is

y - k = m(x - h)

⇒ equation of line perpendicular to given line is y - (-6) = 0.25×{x - (-4)}

⇒ y + 6 = 0.25×(x + 4)

⇒ y + 6 = 0.25x + 1

⇒ y = 0.25x - 5

This is in the slope-intercept form y = mx + c with slope m = 0.25 and y-intercept (0,-5)

Answer:

8189.11

Step-by-step explanation:

If 8900 is 100% and we need to find 15%  we would multiply 8900 and 15 then divide by 100 and that equal 1335 so we would then subtract 1335 from 8900 because it is 15% off, which equals 7565, so now 7565 is 100% and we need to add the 8.25% tax, so we multiply 7565 and 8.25 then divide by 100 which equals 625.11 then we add 7565 and 625.11 which equals 8189.11

The sale price of the car is $8,188.36.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed.

We have,

A car originally priced at $8,900 is on sale at 15% off.

If the sales tax rate is 8.25%.

So, Discount

= 15% of $8,900

= 0.15 x $8,900

= $1,335

Now, Price after discount

= $8,900 - $1,335

= $7,565

and, Sales tax

= 8.25% of $7,565

= 0.0825 x $7,565

= $623.36

So, Sale price of the car

= $7,565 + $623.36

= $8,188.36

Therefore, the sale price of the car is $8,188.36.

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Answer:

1104 miles

Step-by-step explanation:

Given

Let x be the miles he drove in the United States

⇒

The total distance traveled by him= distance traveled in mexico + distance traveled in US

1851=747+x

x=1104 miles

⇒distance traveled in US= 1104 miles

Answer:

The reason for statement #7.

C) Converse of the same side consecutive angles theorem.

Step-by-step explanation:

For  Parallel Lines:

Same side consecutive angles theorem

When the lines are parallel, the interior angles on the same side of the transversal are supplementary.

Here,

It is Converse Of above Statement

∠ 6 and ∠ 13 are supplementary

i.e

∠ 6 + ∠ 13 = 180°

Therefore the Reason  is

C) Converse of the same side consecutive angles theorem.

That is If ∠ 6 and ∠ 13 are supplementary then the Lines are Parallel

i.e        t₁ || t₂

Answer:

C) Converse of the same side consecutive angles theorem.

Step-by-step explanation:

Step-by-step explanation:

So you solve the equation for x and then solve it for y. If the x and y match the given ordered pair then the answer is yes

Four 1/4's = 1 pound

So 4 people would eat 1 pound.

15 people / 4 = 3.75 pounds of turkey is needed.

3.75 is written as 3 3/4 using fractions

Check: 3.75 / 15 = 0.25 = 1/4

Step-by-step explanation:

I think it 1,180 yeah I think it is