James found a pair of shoes he wanted at two different stores. At store A they were $35 and he had a 20% off coupon. At store B they were $40 and he had a 30% off coupon. Both stores had 7% sales tax. Which would be the better deal, and by how much?

The area of the rectangle is equal to 216ft^2.

We have given that,

A flower bed is in the shape of a rectangle.

It measures 7 yards long and 3 yards wide. David wants to use a mulch to cover the flower bed.

The mulch is sold by the square foot.

A yard is equal to 3 feet.

7 yards = 7(3) = 24 feet

3 yards = 3(3) = 9 feet

Area of the rectangle=  Lw

Area of the rectangle= 24(9)

Area of the rectangle= 216 ft^2

Therefore the area of the rectangle is equal to 216ft^2.

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Correct transformation rule is (x, y) → (-x, −y).

What is angle of rotation?

The degree that a figure is rotated about a fixed point known as a point of rotation is expressed as an angle of rotation.

When a point is rotated 180° clockwise about the origin, the new coordinates can be found by taking the negative of the x and y coordinates of the original point.

For example, if the coordinates of point A are (2,3), then the coordinates of the rotated point A' would be (-2, -3), since we take the negative of both the x and y coordinates.

This rule applies to all points in the figure, so the correct transformation rule is (x, y) → (-x, −y).

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The ratios are;

Sin θ =  5/6

Cos θ = √11/6

Tan θ =  5√11/11

Sec  θ =  6√11/11

Cosec  θ = 6/5

Cot θ =  √11/5

These trigonometric ratios are used to relate the angles of a right triangle to the lengths of its sides

We can see that the hypotenuse is obtained from;

x =√\((10)^2 + (2\sqrt{} 11)^2\)

x = √100 + 44

x = 12

Then;

Sin θ = 10/12 = 5/6

Cos θ =  2√11/12

= √11/6

Tan θ = 10/2√11

= 20√11/44

= 5√11/11

Sec  θ =  1/Cos  θ

=  6/√11

= 6√11/11

Cosec  θ = 1/Sin

 θ = 6/5

Cot θ = 1/tan θ

= 11/ 5√11

= 55√11/275

= √11/5

Sinβ = 2√11/12

= √11/6

Cos β = 10/12

= 5/6

Tan β = 2√11/10

= √11/5

Sec β = 6/5

Cosec β = 6√11/11

Cot β = 5√11/11

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Answer:

3

Step-by-step explanation:

he spend 26 dollars and bought the shoes for 5 dollars

26-5=21 so therefore you have to divide the amount of money per game

26÷7=3

Answer:

Please find the complete question and its solution in the attached file.

Step-by-step explanation:

Shortest had survived after 6741 hours \(2.5\%\) of the lights burnt.

\(\to 0.15\% + 2.35\% = 2.50\%\)

Answer:

Its C

Step-by-step explanation:

So,the value of the 30th percentile of the given data will be =P30=4

The cumulative distribution function of a real-valued random variable X, or simply the distribution function of X, assessed at x, is the likelihood that X will have a value less than or equal to x in probability theory and statistics.

Using the Cumulative Distribution Function to Calculate Probabilities

F(x) is a cumulative distribution function that calculates the likelihood that the random variable X is smaller than or equal to x:

To get the cumulative probability that X is less than or equal to 1, multiply P(X=0) by P(X = 0) by (P=1):

First, we will determine the value of the cumulative probability P(X<=x):

x         f(x)       P(X<=x)

1       0.02          0.02

2       0.01          0.03

3       0.2          0.23

4       0.17           0.4

5       0.39           0.79

6       0.2           0.99

7 0.01 1

30th percentile will be the x value,

below which less than or equal to 30% of the data falls.

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The theorems that demonstrate that AC ⊥ BD are Angle Bisector Theorems and Perpendicular Bisector Postulate.

Recall that according to the angle bisector theorem, an angle bisector of a triangle divides the opposing side into two segments that are proportionate to the triangle's other two sides. An angle bisector is a ray that splits a given angle into two equal-sized angles.

In this case

∠1 ≅ ∠2 - Given

hence they is bisected by AX

Also ∠5 ≅ ∠6. This means that they are bisected by CX

Since AX and CX form AC, and

AC = CA (Reflexive Property)
Also

BD = DB  (Reflexive Property)

Then it means that AC ⊥ BC (QED)

Recall that the perpendicular bisector principle deals with congruent triangle segments, allowing for congruent diagonals from the vertices to the circumcenter.

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To find the unit rate, we need to determine how much distance Margo covers in one unit of time. We can do this by dividing the distance by the time.

Distance = 1/4 mile

Time = 1/12 hour

Unit rate = Distance ÷ Time

Unit rate = (1/4 mile) ÷ (1/12 hour)

We can simplify this division by multiplying both the numerator and denominator by the least common multiple of 4 and 12, which is 12.

Unit rate = (1/4 mile) ÷ (1/12 hour) x (12/12)

Unit rate = (3/4 mile) ÷ 1 hour

Unit rate = 3/4 mile per hour

Therefore, Margo's unit rate is 3/4 mile per hour. This means that she can cover a distance of 3/4 mile in one hour of walking.

Answer:

3mph

Step-by-step explanation:

1/12 of an hour will be 5 min. In 5 min she can walk 1/4 mile then in one hour she can walk 1/4 x 12. This means her rate will be 3 miles per hour.

60/12 = 5

12 x 1/4 = 12/4 = 3

The value of mathematical expression is,

⇒ 55 ÷ x

⇒ 55 / x

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The word phrase is,

''The quotient of 55 and x.''

Now, The value of mathematical expression is,

''The quotient of 55 and x.''

⇒ 55 ÷ x

⇒ 55 / x

Therefore, The value of mathematical expression is,

⇒ 55 ÷ x

⇒ 55 / x

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Answer:

Th correct option is (d).

Step-by-step explanation:

The given expression is :

\(16x^2 + nx + 49\) ....(1)

We know that, 16 = 4² and 49 = 7²

Also, (a+b)² = a²+2ab+b²

The given expression becomes,

\(16x^2 + nx + 49=(4x)^2+nx+7^2\\\\=(4x)^2+2(4x)(7)+7^2\\\\=16x^2+56x+49\ ......(2)\)

Comparing equations (1) and (2),

n = 56

Hence, the value of n is equal to 56.

The sum log 4(11) + log 8(11) + log 64(11) can be expressed in the form log b(n), where b and n are positive integers, and b is as small as possible.The sum of b and n is 13.

1. Use the change of base formula to convert each logarithm to the same base (in this case, base 2):

- log 4(11) = log 2(11) / log 2(4) = log 2(11) / 2

- log 8(11) = log 2(11) / log 2(8) = log 2(11) / 3

- log 64(11) = log 2(11) / log 2(64) = log 2(11) / 6

2. Find the common denominator for the fractions, which is 6:

- (log 2(11) / 2) × (3/3) = 3 × log 2(11) / 6

- (log 2(11) / 3) × (2/2) = 2 × log 2(11) / 6

- log 2(11) / 6 stays the same

3. Add the numerators together:

- (3 × log 2(11) + 2 × log 2(11) + log 2(11)) / 6

- (3 + 2 + 1) × log 2(11) / 6

- 6 × log 2(11) / 6

4. Cancel out the 6 in the numerator and denominator, resulting in log 2(11).

5. The sum is expressed as log b(n) = log 2(11), so b = 2 and n = 11.

6. Finally, find b + n: 2 + 11 = 13.

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Answer:

x=5

Step-by-step explanation:

k(x)=6x–12

18=6x–12

18+12=6x

30=6x

30/6=6x/6

x=5

i think it is clear answer.

The angle PMR in the quadrilateral is 32 degrees.

The angle PMR can be found as follows;

The line AP is an angle bisector of angle RPM. Therefore, the following relationships are formed.

∠RPM ≅ ∠WPM

Hence,

∠RPM ≅ ∠WPM = 58 degrees

Therefore,

∠WPM = 58 degrees

∠PWM = 90 degrees

Let's find ∠PMR as follows

∠PMR = 180 - 90 - 58

∠PMR = 90 - 58

∠PMR  = 32 degrees

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Answer:

can I see a copy of the picture? I will edit answer once I can see the picture of the gingerbread man

Answer:

Step-by-step explanation:

This is a case of binomial distribution. The formula used in calculations for binomial probability is:

P = nCr p^r (1-p)^(n-r)  

Where,

P = probability

nCr = combinations of r from n possibilities

p = success rate = 40% = 0.40

n = sample size = 10

1st: Let us calculate for nCr for r = 8 to 10. Formula is:

nCr = n! / r! (n-r)!  

10C8 = 10! / 8! 2! = 45

10C9 = 10! / 9! 1! = 10

10C10 = 10! / 10! 0! = 1

Calculating for probabilities when r = 8 to 10:

P (r=8) = 45 * 0.4^8 (0.6)^2 = 0.0106

P (r=9) = 10 * 0.4^9 (0.6)^1 = 0.0016

P (r=10) = 1 * 0.4^10 (0.6)^0 = 0.0001

Total probability that at least 8 were married = 0.0106 + 0.0016 + 0.0001

Total probability that at least 8 were married = 0.0123

To determine if a linear transformation is onto, we need to check if every vector in the range has at least one pre-image in the domain.

Let T be a linear transformation from R^3 to R^2 given by:

T (x, y, z) = (2x - y, x + 3y - 4z)

(a) To check if T is one-to-one, we need to check if for any two distinct vectors (x1, y1, z1) and (x2, y2, z2) in R^3, we have T (x1, y1, z1) ≠ T (x2, y2, z2). Equivalently, we can check if T (x1, y1, z1) - T (x2, y2, z2) ≠ 0 for any two distinct vectors (x1, y1, z1) and (x2, y2, z2) in R^3.

So, let (x1, y1, z1) and (x2, y2, z2) be two distinct vectors in R^3. Then:

T (x1, y1, z1) - T (x2, y2, z2) = (2x1 - y1, x1 + 3y1 - 4z1) - (2x2 - y2, x2 + 3y2 - 4z2)

= (2x1 - y1 - 2x2 + y2, x1 + 3y1 - 4z1 - x2 - 3y2 + 4z2)

= (2(x1 - x2) - (y1 - y2), x1 - x2 + 3(y1 - y2) - 4(z1 - z2))

For T to be one-to-one, the only solution to T (x1, y1, z1) - T (x2, y2, z2) = 0 must be (x1, y1, z1) = (x2, y2, z2). So, we need to solve the equation above and check if the only solution is (x1, y1, z1) = (x2, y2, z2).

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Answer: Yes, a triangle can have sides of those lengths.

Step-by-step explanation:

(a) The natural coefficient of variation for one patient is the ratio of the standard deviation to the mean, expressed as a percentage:

C0 = (standard deviation / mean) x 100% = (3 / 5) x 100% = 60%.

(b) If the admission times of patients are independent, the mean and variance of admitting a group of 50 emergency patients can be calculated as follows:

mean = n x mean time = 50 x 5 = 250 minutes

variance = n x variance of individual patient / sample size = 50 x (3)^2 / 50 = 9

The coefficient of variation for a group of 50 emergency patients is the ratio of the standard deviation to the mean, expressed as a percentage:

C0 = (standard deviation / mean) x 100% = (3 / 5) x 100% = 60%.

(c) The effective mean and coefficient of variation of the admission time for a group of 50 trauma patients can be calculated using the following formula:

te = n x mean time / (1 - p1 x p2)

where p1 is the probability of machine failure and p2 is the probability of repair completion. Assuming the machine can fail at any time, p1 can be calculated as 1 / (mean time between failures / mean admission time) = 1 / (80 x 60 / 5) = 0.001042. Assuming the repair time is also exponentially distributed, p2 can be calculated as 1 / mean repair time = 1 / 4 = 0.25. Therefore, te = 50 x 5 / (1 - 0.001042 x 0.25) = 250.14 minutes. The variance of the admission time can be calculated using the formula:

σe^2 = n x variance of individual patient / (1 - p1 x p2)^2 = 50 x (3)^2 / (1 - 0.001042 x 0.25)^2 = 10.81. The coefficient of variation for a group of 50 trauma patients is the ratio of the standard deviation to the mean, expressed as a percentage:

Ce = (standard deviation / mean) x 100% = (sqrt(10.81) / 250.14) x 100% = 2.60%.

(d) The variability class of the squared coefficients of variation can be determined as follows:

C0² (Part a): (0.6)^2 = 0.36 (low variability)

C0² (Part b): (0.6)^2 = 0.36 (low variability)

Ce² (Part c): (0.026)^2 = 0.000676 (low variability)

(e) The manager of the center can improve the inflated effective admission time in Part c by implementing preventive maintenance measures to reduce the probability of machine failure, such as regular inspection and cleaning of the X-Ray machine, and by improving the repair process to reduce the mean repair time, such as hiring more skilled technicians or improving the repair procedures.

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Answer:

12

Step-by-step explanation:

Answer:

x+2_3x_x=2^2

2_3x=4

3x=4+2

x=6÷3

×=2 is ans

Answer:

21

Step-by-step explanation:

Answer:

1. p, 7p, -4p, and 5p

2.2uv to the second power, and uv to the second power

Step-by-step explanation:

Answer:

-59

Step-by-step explanation:

x = -2

4(-2)³ - 6(-2)² + (-2) - 1

= -32 - 24 - 2 - 1

= - 59

Answer:

4ºF

Step-by-step explanation:

-4 + 8 = 4

1. The expected value of the distribution is of E(X) = 5.7.

2. The variance of the distribution is of V(X) = 2.2.

3. The standard deviation of the distribution is of S(X) = 1.5.

4. The probability is P(X < 8) = 0.8.

5. The probability is P(X > 5) = 0.5.

The expected value of the distribution is given by the sum of each outcome multiplied by it's probability, hence:

E(X) = 4 x 0.3 + 5 x 0.2 + 6 x 0.2 + 7 x 0.1 + 8 x 0.2

E(X) = 5.7.

The variance of the distribution is given by the sum of the difference squared between each observation and the mean, multiplied by it's probability, as follows:

V(X) = (4 - 5.7)² x 0.3 + (5 - 5.7)² x 0.2 + (6 - 5.7)² x 0.2 + (7 - 5.7)² x 0.1 + (8 - 5.7)² x 0.2

V(X) = 2.2.

The standard deviation is the square root of the variance, hence:

S(X) = square root (2.21) = 1.5.

The probabilities are calculated considering the table as follows:

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Answer:

  70 ft

Step-by-step explanation:

You want the actual width of a gym that is represented as 7 inches on a drawing with a scale of 1 in : 10 ft.

Each inch represents 10 feet, so 7 inches will represent ...

  7 × 10 ft = 70 ft

The gym is 70 ft wide.

__

Additional comment

You can also write and solve an equation that shows the measures are proportional:

  actual width / drawing width = (10 ft) / (1 in) = (gym width) / (7 in)

Multiplying both sides of this proportion by 7 in, we have ...

  gym width = (7 in) × (10 ft)/(1 in) = 7 × 10 ft = 70 ft