Which expression is equivalent to −1.3+(−4.9)+(−2.6) ?

−(1.3−4.9)+(−2.6)

−1.3+(4.9+2.6)

−1.3−(4.9+2.6)

(1.3+4.9+2.6)

Sales tax is .07 of the price. That is:

0.07 x $12.00m = $0.84 (Sales tax)

Total price including sales tax = Jacket cost + Sales tax

=$12.00+$0.84

=$12.84

The total price is $12.84

The coupon rate of the bonds by King of Diamonds Industries would be 7 %.

The formula for the bond price shows the coupon payment and so can be used to find the coupon rate:

= (Coupon payment  x ( 1 - ( 1 + r ) ^ ( - number of years till maturity ) ) ) / r + Face value /  (1  + rate )^ number of years

1,482.01 = (C x (1 - (1 + 0.07 )^ (- 14) ) ) / 0.07 + F / (1 + 0.07 ) ^ 14

103.7407 - 0.07 x (F / (1 + 0.07) ^14 ) = C x  (1 - ( 1 + 0.07) ^ ( - 14) )

Using a calculator, C is $ 70.

This means that the coupon rate is:

= 70 / 1, 000

= 7 %

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Answer:

$394.50

Step-by-step explanation:

Just do the cost times 10 then add additional costs.

:)

Answer:

the answer is the first one, Cara multiplied only 4 and 7 together and did not multiply 4 and 13

Step-by-step explanation:

if you look through the question you can see that Cara evaluated the (-4)^2 correctly because a negative multiplied by a negative gives you a positive thus (-4)*(-4)= 16, then next you can see that Cara subtracted 2 from 6 correctly because (6-2)= (4), and last but not least Cara did multiply 2 by 4 correctly because 2*4 or 2(4) =8 so as you can see the answer is the first one

Answer:

A is correct answer

Step-by-step explanation:

Answer:

when x=-9, y=1

Step-by-step explanation:

the graph shows when the x is at -9, the y is at 1

Answer

Measure the shape yourself and follow the explanation.

Step-by-step explanation:

Measure each side of the Triangles with your ruler. Record it.

For example,

I measured and got 3cm, 3.5cm, 3.5cm.

Multiply by scale factor r 2.

for example, 3cm × 2 = 6cm

3.5cm × 2 = 7.0cm

3.5cm × 2 = 7.0cm

Use your pencil to draw your new numbers to form the new Triangle.

As for the second shape, measure each four sides using ruler

for example, I measured and had 4cm, 6cm, 4cm, 6m.

Multiply by scale factor r 2.

for example, 4cm × 1/4 = 1 cm

6cm × 1/4 = 1.5cm

4cm × 1/4 = 1 cm

6cm × 1/4 = 1.5cm

Use your ruler to measure 1cm, 1.5cm, 1cm and 1.5cm, then to draw your new shape

What's the question?

This problem can be solved using a system of equations.

What is the system of equations?

A set or group of equations that are solved collectively is referred to as a system of equations. Both algebraic and graphical solutions are possible for these equations. The point of intersection of two lines represents the system of equations' solution.

Line 1

Taking two points on this line (0,300) and (4,450)

Equation of line y = mx+c

m = \(\frac{450 - 300}{4 - 0}\) = 37.5

y = 37.5x + c

Substituting (0,300) in the above equation

300 = 37.5 * 0 + c

c = 300

Line equation y = 37.5x + 300

Line 2

Taking two points on this line (0,400) and (5,500)

m = \(\frac{500 - 400}{5 - 0}\) = 20

y = 20x + c

Substituting (0,400) in the above equation

400 = 250* 0 + c

c = 400

Line equation y = 20x + 400

a) The solution of the system is when both lines coincide

     37.5 x + 300 = 20x + 400

     17.5 x = 100

           x = 5.7

            y = 20 * 5.7 + 400 = 514

Therefore the solution of the system is ( 5.7 , 514)

b) In terms of saving money scenario. This means that Dave and Joe have the same amount of savings at this point.

Therefore these are the solutions to the above system of equations.

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Answer:

0.74

Step-by-step explanation:

The middle age citizens are those in the age group of 18-55.

We solve this question using z score formula

z = (x-μ)/σ, where

x is the raw score

μ is the population mean

σ is the population standard deviation.

Mean 46 years

Standard deviation 13 years

For x = 18 years

z = 18 - 46/13

z = -2.15385

Probability value from Z-Table:

P(x = 18) = 0.015626

For x = 55 years

z = 55 - 46/13

= 0.69231

Probability value from Z-Table:

P(x = 55) = 0.75563

The probability that he/she is middle age is

P(x = 55) - P( x = 18)

= 0.75563 - 0.015626

= 0.740004

Approximately = 0.74

Answer:

?=6x-(x+3)-(2x+4)

=6x-x-3-2x-4

=3x-7

The probability that the couple will have 3 normal girls is approximately 0.422

Since both parents are normal, they both have to be heterozygous carriers for the recessive allele that causes albinism. We can represent the normal allele with the letter N and the albino allele with the letter n. Then, we can write the genotypes of the parents as Nn x Nn.

The daughter is albino, so her genotype must be nn. The son is normal, so his genotype must be Nn.

We want to find the probability that the couple will have 3 normal girls. We can use the multiplication rule of probability to find this probability:

P(3 normal girls) = P(normal girl) x P(normal girl) x P(normal girl)

The probability of having a normal girl is 3/4 since there are three possible genotypes that result in a normal phenotype (NN, Nn, Nn) out of a total of four possible genotypes. The probability of having a normal boy is also 3/4, for the same reason.

Therefore, the probability of having 3 normal children (in this case, girls) is:

P(3 normal girls) = (3/4) x (3/4) x (3/4) = 27/64 ≈ 0.422

So, the probability that the couple will have 3 normal girls is approximately 0.422, or about 42.2%.

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Answer:

  about 33.3%

Step-by-step explanation:

The fraction of space not occupied will be the same as the unoccupied fraction of a cylinder of the same height and diameter as a sphere.

The volume of a cylinder of diameter d and height d will be ...

  V = πr²h = π(d/2)²(d) = (π/4)d³

The volume of a sphere of diameter d is ...

  V = 4/3πr³ = 4/3π(d/2)³ = (π/6)d³

The fraction of space that is occupied is ...

  occupied space = (sphere volume)/(cylinder volume)

  occupied space = ((π/6)d³) / ((π/4)d³) = 4/6 = 2/3

The fraction of unoccupied space is ...

  unoccupied fraction = 1 -2/3 = 1/3

  unoccupied fraction ≈ 33.3%

Answer:

Putangina okay

Step-by-step explanation:

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Answer:

b

Step-by-step explanation:

Answer:

Step-by-step explanation:

If cakes of 4 small and 4 large tiers serve 288 guests, and 3 small and 5 large tiers serve 316 guests, you want to know the number of guests served by a tier of each size.

Let 's' and 'l' represent the numbers of guests served by small and large cake tiers, respectively. The first cake serves ...

  4s +4l = 288

And the second cake serves ...

  3s +5l = 316

Subtracting 3/4 of the first equation from the second gives ...

  (3x +5l) -3/4(4s +4l) = (316) -3/4(288)

  2l = 100

  l = 50

  4s +4(50) = 288 . . . substitute for l in the first equation

  4s = 88 . . . . . . . . . . subtract 200

  s = 22 . . . . . . . divide by 4

A small tier will serve 22 guests; a large tier will serve 50 guests.

Answer:

nub 5

Step-by-step explanation:

The Least Common Multiple, LCM, also known as the Lowest Common Multiple or  Least Common Divisor, LCD, of two numbers is the smallest natural number that can be divided evenly by either of the two numbers

Reason:

The given parameters, starting from the runner on the outer track are;

Number of spaces covered by the runner on the outer track, n₁ = 5 spaces

Number of spaces covered by the next inner runner, n₂ = 1 space

Number of spaces covered by the next inner runner, n₃ = 3 spaces

Number of spaces covered by the next runner, n₄ = 2 spaces

The numbered spot at which all the runners will be next to one another = Required

Solution:

A spot where all the runners will be next to one another is given by the Lowest Common Multiple, LCM, of their speeds or number of spaces traveled in the same time as follows;

The LCM of 5, 1, 3, and 2 = 5 × 1 × 3 × 2 = 30

Therefore, when the first runner runs 30 spaces, we have;

\(Time = \dfrac{30}{5} = 6\)

The time taken is 6 time units

The point the runner stops is at space 30- (30 -19) = Spot 19

The distance traveled by the runner 2 at the same time is 6 × 1 = 6

∴ The distance traveled by the runner 2 at the same time = 6 spaces

The distance traveled by the runner 3 at the same time is 6 × 3 = 18

∴ The distance runner 3 travels at the same time = 18 spaces

Runner 4 travels a distance at the same time of  6 × 2 = 12

∴ Distance runner 4 travels = 12 spaces

Therefore;

The numbered spot at which all the runners will be next to one another is spot 19

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Answer:

1 over 2

Step-by-step explanation:

9-(-7)=-2

-8-(-4)-4

-6-(-3)=-3

-2-4=-6

When you simplify both of the fractions -2 over -4 and -3 over -6

You get 1 over 2 as the slope for both. 1/2

Answer:

10 010 10 10 10 10 101 01 mo1

Step-by-step explanation:

Given:

u varies directly with the square of p and inversely with d.

To find:

The equation for the given situation.

Solution:

If y is directly proportional to x, then

\(y\propto x\)

If y is inversely proportional to x, then

\(y\propto \dfrac{1}{x}\)

It is given that u varies directly with the square of p and inversely with d. So,

\(u\propto \dfrac{p^2}{d}\)

It can be written as:

\(u=k\dfrac{p^2}{d}\)

Where, k is the constant of proportionality.

Therefore, the required equation is \(u=\dfrac{kp^2}{d}\).

Answer:

1) A, B, C

2) D, E, F

3) Q

4) R, L(but lowercase), m, S, n

If tan Ф = 15/8 then we have these trigonometric functions cosec Ф = 17/15, sec Ф = 17/8 and cot Ф = 8/15.

According to the question,

We have the following information:

Tan Ф = 15/8

We know that in this trigonometric function we have perpendicular divided by base.

Now, we can find the hypotenuse using the Pythagoras theorem:

Let's denote hypotenuse with h, perpendicular with p and base with b.

\(h^{2} =p^{2} +b^{2}\)

\(h^{2}\) = \((15)^{2} +(8)^{2}\)

\(h^{2} = 225+64\\h^{2} = 289\\h = \sqrt{289}\)

h = 17 units

Now, we have the following values:

Cosec Ф = 17/15 (Hypotenuse/perpendicular)

Sec Ф = 17/8 (h/b)

Cos Ф = 8/17 (b/h)

Cot Ф = 8/15 (b/p)

Hence, the correct options are A, B and D.

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Answer:

  7. P(q) = 60 -0.03(x -80)²

  8. P(q) = -0.03x² +4.8x -132

  9. q = 35 balloons

  10. see attached

Step-by-step explanation:

You want the profit equation, break-even sales, and a graph for a party supply company that makes a maximum profit of $60 when they sell 80 balloons, and a profit of $33 when they sell 50 balloons.

If the profit is described by a quadratic equation with a maximum at (quantity, dollars) = (80, 60), and a point on the curve of (50, 33), we can write the equation in two steps.

The vertex-form equation will look like ...

  P(q) = 60 -a(q -80)² . . . . . for some scale factor 'a'

We want P(50) = 33, so we have ...

  P(50) = 33 = 60 -a(50 -80)²

  33 = 60 -900a

  a = (60 -33)/900 = 3/100 = 0.03

The profit equation is ...

  P(q) = 60 -0.03(q -80)²

Expanding the equation gives ...

  P(q) = 60 -0.03(q² -160q +6400)

  P(q) = -0.03q² +4.8q -132

The profit is zero at ...

  P(q) = 0 = 60 -0.03(q -80)²

  0.03(q -80)² = 60

  (q -80)² = 2000 . . . . . . . . divide by 0.03

  q = 80 ±20√5 = 35.3 or 124.7 . . . . . take the square root, add 80

The store will no longer make a profit when sales drops to 35 balloons.

The attachment shows a graph of the profit function.

__

Additional comment

You can find where the profit goes to zero using the graph, the quadratic formula, or by solving it using vertex form, as above. The graph is quick and easy; using the vertex form equation works nicely.

Selling 36 balloons will result in a profit of $1.92.

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Answer:

-101 feet

Step-by-step explanation:

Answer:

101 feet.

Step-by-step explanation:

82 + 19 = 101.

Answer:

I think :

c is 30 triangle

b is 60 triangle

d is 90 triangle

Answer:

a) 24

b) f^-1 = \(\sqrt{x+1}\)

c) 3

Step-by-step explanation:

Just plug the numbers in for x:

(5)^2 -1 = 24

Switch x and y then solve for y and replace y with f^-1(x):

x = y^2 -1

sqrt(x +1) = y = f^-1(x)

Now plug in 8:

f^-1(x) = sqrt(8 +1)  = 3

Answer:

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

When the ball is punted the value of x is zero, therefore f(0) is:

Answer:

1.5 feet

Step-by-step explanation:

Given function,

→ f(x) = (-16/1225)x² + (7/5)x + 1.5

Required function,

→ f(x) = f(0)

→ f(0) = (-16/1225)x² + (7/5)x + 1.5

Now the needed height is,

→ (-16/1225)x² + (7/5)x + 1.5

→ (-16/1225)(0)² + (7/5)(0) + 1.5

→ 0 + 0 + 1.5

→ 1.5 feet

Hence, the height is 1.5 feet.

Answer:

i doesn,t understand this language

A. The solution of  linear equation is (x, y) = (-3, 8).

B. The solution is (x, y) = (3/4, -1).

C. The solution is (x, y) = (-31/8, 3/8).

D. The solution is (x, y) = (55/7, -117/14).

A. 3x - y = -11 --- (1)

-x + y = 5 --- (2)

From equation (2), we can write y = x + 5, and substitute it in equation (1):

3x - (x + 5) = -11

2x = -6

x = -3

Substituting x in equation (2):

-y = -8

y = 8

Therefore, the solution of the system is (x, y) = (-3, 8).

To check the solution, we substitute the values of x and y in the original equations:

3(-3) - 8 = -11 (True)

-(-3) + 8 = 5 (True)

So, the solution is correct.

B. -2y + 3 = 4x + 2 --- (1)

6x + 4y = 1 --- (2)

From equation (1), we can write 4x + 2 = -2y + 3, and substitute it in equation (2):

6x + 4y = 1

6x - 4y = 8 (rearranging)

12x = 9

x = 3/4

Substituting x in equation (1):

-2y + 3 = 4(3/4) + 2

-2y + 3 = 5

-2y = 2

y = -1

Therefore, the solution of the system is (x, y) = (3/4, -1).

To check the solution, we substitute the values of x and y in the original equations:

-2(-1) + 3 = 4(3/4) + 2 (True)

6(3/4) + 4(-1) = 1 (True)

So, the solution is correct.

C. 32y - x = -25 --- (1)

5x = 100 + x - 8y --- (2)

From equation (2), we can write 4x = 100 - 8y, and substitute it in equation (1):

32y - x = -25

32y - (100 - 8y) = -25

40y = 75

y = 3/8

Substituting y in equation (1):

32(3/8) - x = -25

x = -31/8.

Therefore, the solution of the system is (x, y) = (-31/8, 3/8).

To check the solution, we substitute the values of x and y in the original equations:

32(3/8) - (-31/8) = -25 (True)

5(-31/8) = 100 + (-31/8) - 8(3/8) (True)

So, the solution is correct.

D. To solve the system of equations:

2y + 3x = 6 --- (1)

4x + 5y + 20 = 0 --- (2)

We can rearrange equation (2) to isolate one of the variables:

4x + 5y = -20 (subtracting 20 from both sides)

5y = -4x - 20 (subtracting 4x from both sides)

y = (-4/5)x - 4 (dividing both sides by 5)

Substituting this value of y in equation (1):

2((-4/5)x - 4) + 3x = 6

(-8/5)x - 8 + 3x = 6

(-8/5)x + 3x = 14

(-8/5 + 3)x = 14

(-8/5 + 15/5)x = 14

(7/5)x = 14

x = 10

Substituting this value of x in the equation for y:

y = (-4/5)(10) - 4

y = -12.

Therefore, the solution of the system is (x, y) = (10, -12).

To check the solution, we substitute the values of x and y in the original equations:

2(-12) + 3(10) = 6 (True)

4(10) + 5(-12) + 20 = 0 (True)

So, the solution is correct.

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∠X = 89°, ∠Y = 90°, ∠Z = 40° ∠X+∠Z=180---------> ∠X=180-∠Z-----> ∠X=180-40°----> ∠X=140°

→ (2b+6)+(3b-1)=90----> 5b+5=90----> 5b=85----> b=17°

→ ∠Z=2b+6---- 2*17+6-----> ∠Z=40°

→ ∠Y=3b-1---> ∠Y=3*17-1---> ∠Y=50°

angle Y and W are supplementary angles

so

→ ∠Y+∠W=180---------> ∠W=180-∠Y------> ∠W=180-50----> ∠W=130°

angle X and Z are supplementary angles

so

→ ∠X+∠Z=180---------> ∠X=180-∠Z-----> ∠X=180-40°----> ∠X=140°

Therefore, the answer is