Select True or False for each statement.

Anya her distance back to camp and the bearing angle from her starting point is 4.78 km North 26.3° West.

Define direction ?

Direction gives the information about the way towards which an object moves or tends.

The angle formed by the 2 km and 3 km is the supplement of the 35 ° angle west of north;

  180°- 35° = 145°

We know that the length of two sides and one angle.

The opposite side know angle is the direct distance between the starting and ending points.

Using the law of cosines.

[tex]a^{2} = b^{2} + c^{2} - 2bc (cosA)[/tex]

[tex]a^{2} = 2^{2} + 3^{2} - 2(2)(3)(cos 145)[/tex]

[tex]a^{2} = 4 + 9 - 12 (-0.8192)[/tex]

[tex]a^{2} = 22.83[/tex]

a = 4.78 km

To determine the bearing from the starting point , we must determine the angle between the first leg and the direct path.

Using the law of sines

[tex]\frac{4.78}{sin(145)} = \frac{3}{sin C}[/tex] sin(145°)

4.78 sin C = 3 sin 145°

sin C = [tex]\frac{3 sin (145^ 0)}{4.78}[/tex]

sin C = 0.4438

C = 26.3°

Therefore, the distance and bearing of the end point from the starting point is 4.78 km North 26.3 ° West.

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Answer:

He has $9.24 left of his gift certificate

Step-by-step explanation:

Given that,

He bought two baseballs for $1.79

Baseball= 1.79+1.79 or 1.79 × 2 (because there are two baseballs.

= $3.58

Baseball Glove = $49.99

Baseball Bat = $12.19

Altogether = $3.58 + $49.99 + $12.19

= $65.76

So you subtract $65.76 from the Original amount in the gift certificate,

=> $75 - $65.76

= $9.24

Answer:

The normal price of a pen is £8

Step-by-step explanation:

let p be the normal price.

The statement : “normal prices are reduced by 15%. The normal price of a pen is reduced by £1.20”

Means

[tex]p \times \frac{15}{100} = 1.20[/tex]

Then

[tex]p = 1.20 \times \frac{100}{15} = \frac{120}{15} = 8[/tex]

Answer:

The normal price of the pen is £8

Step-by-step explanation:

Reduced by 15%

Reduced by £1.20

Meaning that 15% is £1.20

To find the 100% or the normal price of the pen we find the 1% first then the 100%

So, 1% = £1.20/15

100% =£1.20/15 x 100

= 8

Checking..

If normal price was 8 and reduction is 15%

8(1- R/100) {R = %}

8(1 -15/100) = 6.8 (Reduced price)

8 - 6.8 = £1.20 ( Reduction price aka the 15%)

Therefore, the normal price of the pen is £8.

The probability of observing at least one Type I Error is 16.67%.

Probability is the likelihood of an event occurring, expressed as a number between 0 and 1. It is a measure of how likely it is that something will happen, given the conditions and information available. Probability is the foundation of statistics, which is the science of making decisions when faced with uncertainty. Probability can be used to make predictions about future events and to help us understand how likely various outcomes are.

A Type I Error, also known as a false positive, occurs when an experiment incorrectly rejects a true null hypothesis. This probability can be calculated by multiplying the probability of a Type I Error occurring in each test (0.05) three times, yielding 0.125 (or 12.5%).

We then add 1 minus that probability, which yields 0.167 (or 16.67%). In other words, the probability of observing at least one Type I Error in the three tests is 16.67%.

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Since, U = FY(Y) is uniform distribution (i.e. U(0, 1)).

In the given question, suppose continuous random variable Y has cumulative distribution function FY (y), and density function fY (y) > 0.

Let random variable U = FY (Y ).

We have to find the density function of U, and identify its distribution (name and parameter(s)) if possible.

A random variable Y has cumulative distribution function FY (y).

A random variable Y has density function f(y).

Let U = FY(Y)

Now we have to find the density function of U using cumulative distribution function method

FU(u) = P(U≤u)

FU(u) = P(FY(Y) ≤ u)

FU(u) = P(Y ≤ F (u))

FU(u) = FY(F (u))

FU(u) = u

fU(u) = F'U(u).1

fU(u) = 1

fU(u) = 1,     0<u<1

Here U = FY(Y) is uniform distribution (i.e. U(0, 1)).

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Answer:

1 × ( –6 × – 18 – 8) ÷ 4=[tex]\frac{1}{404}[/tex]

–4 – –20 + –5 ×( –11 – –18)=[tex]18[/tex]

13 – –10 × 16 ÷(14 + –16)=[tex]173[/tex]

1– –9 × 12 × (–19 + 20)=[tex]110[/tex]

The logic diagram, characteristic table, and equation of the SR flip-flip are shown. (Refer to the images attached below)

A gated set-reset flip-flop is an SR flip-flop.

The flip-flop is controlled by the S and R inputs when the clock pulse changes from LOW to HIGH.

Till the clock pulse is on a rising edge, the flip-flop won't alter.

There is a chance that the outputs will be HIGH or LOW when S and R are both HIGH at the same time.

A global flip flop with two inputs, the JK flip flop has the letters "J" and "K."

While J and K are not the reduced abbreviated letters for Set and Reset in the SR flip flop, S and R are.

SR flip-flop equation: Qn+1 = S + QnR'

(Refer to the images attached below)

Therefore, the logic diagram, characteristic table, and equation of the SR flip-flip are shown. (Refer to the images attached below)

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At t = 0.6, the instantaneous velocity of the bug is equal to the average velocity of the bug on [0,6], so the bug is neither speeding up nor slowing down.

The instantaneous velocity of a bug at any particular moment in time is the rate at which the bug is changing its position. The average velocity of the bug over a particular interval (in this case, [0,6]) is the average rate at which the bug changes its position over the entire interval. To compare the instantaneous velocity to the average velocity, the two velocities need to be measured at the same time.

At t = 0.6, the instantaneous velocity of the bug is equal to the average velocity of the bug on [0,6]. That means that the bug is neither speeding up nor slowing down.

The Complete the question is :

at what time t is the instaneous velocity equal to the averge equal to the equal to the average velocity of the bug on 0,6 is the bug speeding up or slowing down at t = 0.6

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Answer:

Area = 2 10/27 inch²

Step-by-step explanation:

Length: 1 7/9 inches

Width: (3/4)(1 7/9 inches)

Area = Length × Width

Area = (1 7/9 inches) × (3/4)(1 7/9 inches)

Area = 16/9 inches × 16/9 inches × 3/4

Area = 768/324 inch²

Area = 256/108 inch²

Area = 128/54 inch²

Area = 64/27 inch²

Area = 2 10/27 inch²

Answer:

y = 3/4 x + 3

Step-by-step explanation:

slope of the line :

(0-3)/(-4-0)

-3/-4

3/4

y = 3/4 x + 3

Answer:139 is the answer

Step-by-step explanation:

The solution is A = 4000

The equation after rounding up numbers is A = 10 x 400 = 4000

What is rounding up numbers?

There are basically two rules while rounding up numbers

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down and if the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

Non-zero digits are always significant

Zeros between non-zero digits are always significant

Leading zeros are never significant

Trailing zeros are only significant if the number contains a decimal point

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the first number be = p

The value of p = 13

Let the second number be = q

The value of q = 378

Rounding the number p to 1 significant figure , p = 10

Rounding the number q to 1 significant number q = 400

So , the equation is A = p x q

Substituting the values in the equation , we get

A = 10 x 400

The value of A = 4000

Hence , The equation after rounding up numbers is A = 10 x 400 = 4000

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Answer:

0

Step-by-step explanation:

0 divided by any nonzero quantity is zero.

The percentage of boys in the class is 60% and the percentage of girls in the class is 40%.

The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.

As per the given information in the question,

Total number of students in class = 45

Total number of boys in the class = 27

Then, the percentage of boys in the class will be,

Let the percentage of boys be x.

x% Of 45 = 27

x = (27 × 100)/45

x = 2700/45

x = 60%

Then, total number of girls in the class = 45 - 27 = 18

Assume the percentage of girls in the class be y.

y% Of 45 = 18

y = (18 × 100)/45

y = 1800/45

y = 40%

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Step-by-step explanation:

To find the simple interest rate that Savannah is being charged, we can use the formula for simple interest:

I = P * r * t

where I is the total interest paid, P is the principal (the amount borrowed), r is the interest rate, and t is the time period over which the interest is paid.

Since Savannah must pay back the $2,900.00 principal plus a $1,375.00 fee, the total interest paid is $1,375.00. The time period is 8 months, which is equal to 8/12 = 2/3 of a year. Substituting these values into the formula and solving for r, we get:

$1,375.00 = $2,900.00 * r * (2/3)

r = $1,375.00 / ($2,900.00 * (2/3)) = 0.1429

This is the interest rate that Savannah is being charged. To express this rate as a percentage, we can multiply it by 100% to get:

r = 0.1429 * 100% = 14.3%

Therefore, Savannah is being charged a simple interest rate of approximately 14.3%.

Answer:

s² = lw

s = 40      w= 25cm

s² = lh

(40cm)² = (25cm)

1 600 cm² = 25cm L

L = 64 cm

Area of Rectangle = length(width)

Area = 64cm(25cm)

Area = 1 600 cm²

Step-by-step explanation:

By using circle model the images are attached below:

A circle with a diameter of one has n firms distributed uniformly around it. In light of this, every company's distance from each of its closest neighbors is 1/n.

We must first create two circles in order to compare the ratios of 2 to 7 and 5:7 using a circle model.

Then, we must divide each circle into seven pieces.

We must shade 2 of the circle's total 7 portions in order to maintain the 2:7 ratio.

We must shade 5 of the circle's total 7 portions in order to maintain the 5:7 ratio.

As a result, the first circle symbolizes a 2:7 ratio, while the second circle a 5:7 ratio.

By using circle model the images are attached below:

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Answer: using circles to model the ratios, divide both circles into

7

equal parts.

For the ratio 2 to 7,

2

parts should be shaded.

For the ratio 5:7,

5

parts should be shaded.

The ratio 2 to 7 is

less than

the ratio 5:7

Answer:

(1, 3)

Step-by-step explanation:

Using a graphing website like Desmos or a graphing calculator, we can figure out the solution: (1, 3)

Answer:

8

Step-by-step explanation:

x+7=15 so x=15-7 which is x=8

Answer:

8 ft

Step-by-step explanation:

The length of the shape is 15 ft. The length on the bottom is equal to the length on the top.

We are given 2 "sides" or lines on the bottom. One of them is 7 ft. Find the other "side" length.

x + 7 =15

x = 15 - 7

x = 8

Answer:

26

Step-by-step explanation:

a_n = 1/2 (n^2 + 3 n - 2) (for all terms given)

1, 4, 8, 13, 19, 26, 34, 43, 53, 64, 76, 89, 103, 118, 134, 151, 169, 188, 208, 229, ...

Answer:

26

Step-by-step explanation:

The difference between 1 and 4 is 3

The difference between 4 and 8 is 4

The difference between 8 and 13 is 5

The difference between 13 and 19 is 6

The difference between 19 and 26  is 7

To create a 95% confidence interval for the population proportion of adults who ate fast food at least once in the past month, we need to first calculate the sample proportion.

The sample proportion is calculated by dividing the number of adults who ate fast food at least once in the past month (722) by the total number of adults surveyed (1000). This gives us a sample proportion of 0.722.

To calculate the confidence interval, we can use the following formula:

Plugging in the values, we get:

This gives us a 95% confidence interval of (0.6901, 0.7539). Rounded to four decimal places, the confidence interval is (0.6901, 0.7539).

Note: To calculate the confidence interval using Excel, you can use the following formula:

Where "alpha" is the desired confidence level (e.g., 0.95 for a 95% confidence interval), "standard_dev" is the standard deviation of the sample, and "size" is the sample size. To calculate the standard deviation, you can use the STDEV.P function.

For example, to calculate the lower and upper bounds of the 95% confidence interval, you could use the following formulas:

Where A1:A1000 is a range containing the values "1" for those adults who ate fast food at least once in the past month and "0" for those who did not. This will give you the same result as the manual calculation above.

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The Solution set of the given quadratic equations are

1. x = 5 or x = 3

2. x= -3/2 or x =  5

A Quadratic equation is an algebraic expression in which highest degree of the given variable is 2.

Formula used as x² +ax + b = (x + c)(x + d)

Where 'a' is the sum 'c' and 'd' and 'b' is the product of 'c' and 'd'

According to the information, Factorize all the given quadratic equations we get;

1. x² - 8x + 15 =0

Now Split middle term of quadratic equation using formula we get,

 x² - 5x - 3x + 15 =0

⇒ x(x- 5) -3(x - 5) =0

⇒(x -5)(x - 3) =0

⇒ x- 5 =0 or x - 3 =0

⇒ x= 5 or x = 3

2. 20x² + 10x -8=0

Now Split middle term of quadratic equation using formula we get,

10x² + 5x - 4 = 0

⇒ 2x(x-5) +3(x-5)=0

⇒(2x+3)(x-5)=0

⇒2x+3 =0 or x-5 =0

⇒ x= -3/2 or x=5

Hence, the solution set are

1. x = 5 or x = 3

2. x= -3/2 or x =  5

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In order to prevent such factors from influencing the treatment's outcomes, randomization tends to reduce the impact of uncontrollable variables like water temperature.

A variable in mathematics is a symbol that designates a mathematical object. A variable can represent any of the following: a number, a vector, a matrix, a function, its argument, a set, or an element of a set. An unknown numerical value in an equation or algebraic expression is represented by a symbol (often a letter) in algebra. A variable is, to put it simply, a quantity that may be altered and is not fixed. Because they make up a significant portion of mathematics, variables are crucial.

The impact of water pH on moon jellyfish mating behavior is being studied by researchers. In a scientific experiment, the water in the tanks containing the jellyfish will be randomly assigned to one of three treatments: low pH, medium pH, or high ph.

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The original price P will be $72

If we know that the ratio from P to Q is 4:5, we can multiply both sides by y (y = amount multiplied) to get our numbers.

4 × y =?

5 × y =?

We need to input a value in for y.

Let's put 9.

4 × 9 = 36 (P)

5 × 9 = 45 (Q)

Now adding 12 to P, and take away 6 from Q.

36 + 12 = 48

45 - 6 = 39

The numbers aren't the same yet.

Let's use a different value for y.

y = 18

The equations will now look like this:

4 × 18 = 72 (P)

5 × 18 = 90 (Q)

Let's add 12 and 6 to the numbers again.

72 + 12 = 84

90 - 6 = 84

The numbers are now equal

Therefore, the original price of P = $72

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Using the area of rectangle formula, w = A/l, determine the width of the rectangle first before determining its length.

In conclusion, you must divide a rectangle's area by its known width in order to determine its length.If you have an area A and a width w, you can calculate the length w using the formula h = A/w.

If you know the perimeter P and the width w, you can calculate the length using the formula h = P/2w.

Given a diagonal (d) and a width (w), its length is given by h = (d2w2).The basic formula for volume is length, breadth, and height, as opposed to length, width, and height for the area of a rectangular shape.

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Answer:

  C.  C = $10 +$5h

Step-by-step explanation:

The cost is a $10 admission fee plus $5 per hour for sledding. You want an equation representing the cost C in terms of hours h.

The cost is ...

   cost = admission fee + hourly charge

The hourly charge is the product of the cost per hour ($5) and the number of hours (h).

  C = $10 +$5h

The value of dc/dt due to changes in p and c variables is 0.364.

The positive variables p and c change with respect to time 1. The relationship between p and c is given by the equation p^2 = (20-c)^3. Now the dp/dt value is 41 and c is 15.

Differentiate the given equation to obtain the following:

2p dp/dt = 3(20-c)^2 dc/dt

Substitute the given values in the equation to obtain the following:

2p (41) = 3(20 - 15)^2 dc/dt

Simplify the equation to obtain the following:

82 = 225 dc/dt

Divide both sides of the equation by 225 to obtain the following:

dc/dt = 82/225

Simplify the equation to obtain the following:

dc/dt = 0.364

Hence, the value of dc/dt is 0.364.

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The function f has a real zero between -1 and 0. Therefore, statement c) is true.

To evaluate the function for the given values of a and b, we can plug in the values of a and b into the function and solve.

For a=-1, we get:

For b=0, we get:

Therefore, f(-1) and f(0) have opposite signs (one is positive and one is negative).

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