See attached image and answer questions.

Answer: 6.38

.................

Answer: 87.96m

Step-by-step explanation:

Circumference of a circle = 2[tex]\pi[/tex][tex]r^{2}[/tex] --> 2[tex]\pi[/tex]14² = 87.96m

In 30 minutes the two friends 2 miles apart.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Given that, Wendy headed due north at 3 miles per hour, and Roger hiked due south at 6 miles per hour.

We know that, Time= Distance/Speed

Now, T₁= 2/3

T₂= 2/6 =1/3

T=T₁-T₂

T=2/3+1/3

T=1/3

T=0.33 hours

= 30 minutes

Therefore, in 30 minutes the two friends 2 miles apart.

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Answer:

  6.8 ft

Step-by-step explanation:

You want the height of a tank with a base of 5.5 ft by 4 ft if adding 74.8 ft³ of water fills it halfway.

The volume of a rectangular prism is given by the formula ...

  V = LWH

The filled volume of the tank h feet high is ...

  74.8 ft³ = (5.5 ft)(4 ft)(h/2) . . . . . . the filled height is h/2

  74.8 ft³/(11 ft²) = h ≈ 6.8 ft . . . . . . divide by the coefficient of h

The height of the tank is 6.8 feet.

The revenue corresponding to break even condition for selling x units is $4.28.

An evaluation of the model's accuracy in estimating the link between X and y is done using a cost function. In most cases, this is represented as a difference or distance between the projected value and the actual value. The price element (you may also see this referred to as loss or error.)

To break even (R = C) we have:

7.8 √x + 22,000 = 13.82x

Substitute the value of x = u² thus:

7.8u +22000 = 13.8u²

13.8u² - 7.8u - 22000 = 0

The quadratic formula is given as:

u = -b ± √b² - 4ac / 2a

u = -(-7.8) ± √(-7.8)²- (4)(13.82)(22000) / 2(13.82)

u = 7.8 ± 7.8 / 27.64

u = 7.8 + 7.8 / 27.64

u = 0.56

Back substituting the value of u:

x = u²

x = (0.56)²

x = 0.31

Substituting the value of x is R:

R = 13.82 (0.31)

R = 4.28

Hence, the revenue corresponding to break even condition for selling x units is $4.28.

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Answer:

C

Step-by-step explanation:

consider the coordinates of the same points on both figures

top left vertex of figure P (- 8, 8 )

top left vertex of figure Q (- 4, 4 )

note that both coordinates from Q are half the coordinates of P

then to obtain Q from P multiply each coordinate by [tex]\frac{1}{2}[/tex] , that is

(x, y ) → ([tex]\frac{1}{2}[/tex] x , [tex]\frac{1}{2}[/tex] y )

Answer:

The answer to your question is, 0.484

Step-by-step explanation:

The actual chances of an event occurring are defined by a probability. Probability has several uses in games, and in business to create probability-based forecasts which bascially how it works.

Lets graph it out:

Let A signify that the selected employee participates to a workplace retirement savings plan. Let P stand for the male employes.

P(A∩P) the intersection of male & female.

P(A\P)  is the probability that a randomly picked worker participates to a workplace retirement savings plan is the option male

The probability that a randomly selected worker contributes to a retirement savings plan at work is male is found in this formula :

P(A\P)=P(A∩P)/A(P)

P(A\P)=(121/500)/(250/500)

P(A\P)=0.484

Thus, the probability that a randomly selected worker contributes to a retirement savings plan at work that is male will be,

0.484.

68 students said that Mr.Lopez should buy jumbo chocolate chip cookies.

What is a circle graph?

A pie chart, often known as a circle chart, is a visual representation of the various values of a specific variable or a means to summarise a set of nominal data (e.g. percentage distribution). This kind of chart consists of a circle with numerous segments.

Let's say the total number of students = X.

From the circle graph, we can say that 15% of students chose cinnamon twists and their count is 12.

Which means that

[tex]X*\frac{15}{100}=12\\ X=80[/tex]

Therefore the total number of students is 80.

Among the 80 students except for 12 students, the remaining students asked for jumbo chocolate chip cookies.

Which is equal to 80-12=68.

Therefore 68 students said that Mr.Lopez should buy jumbo chocolate chip cookies.

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Answer:

£76

Step-by-step explanation:

[tex]28+16(1.5/0.5)=28+16(3)=28+48=76[/tex]

Answer:

W =1 1/4Step-by-step explanation: Let W = what. W - 1/2 = 3/4. Add 1/2 to each side. W -1/2 +1/2 = 3/4+1/2. W = 3/4+1/2.

Step-by-step explanation:

Answer: the probability of selecting the first urn and then drawing two white balls from the first urn is 0.027.

Step-by-step explanation:

Let's call the event of selecting the first urn "A" and the event of drawing two white balls from the selected urn "B". The probability we want to find is P(A and B), which can be found using the formula for the intersection of two events:

P(A and B) = P(A) * P(B|A)

where P(B|A) is the probability of drawing two white balls from the first urn given that the first urn was selected.

First, let's find P(A):

P(A) = 0.3

Next, let's find P(B|A):

P(B|A) = (3/10) * (3/10) = 9/100

Finally, let's find P(A and B):

P(A and B) = P(A) * P(B|A) = 0.3 * 9/100 = 0.027

So the probability of selecting the first urn and then drawing two white balls from the first urn is 0.027.

The correct answer for given dilation will be A and D i.e. Point P is midpoint of AA' and XY⊥AA'.

What precisely is dilation?

Dilation is the process of changing the size of an object or form by shrinking or extending its dimensions based on certain scale variables. For example, a circle with radius 10 unit is decreased to a circle with radius 5 unit. This method is used in photography, arts and crafts, and logo design, among other things. In geometry, there are four basic types of transformations. These are their names:

Properties of Rotation, Translation, Reflection, and Resizing

Dilation properties

The following are some features of shapes that remain constant with dilation changes:

Now,

As The image of A is made on line XY and the image will be A'

then XY⊥AA' because line formed between images is always perpendicular to the plane it is formed on and

P is the midpoint of AA' because we know that AP and A'P are same in a image formation.

Hence,

           Point P is midpoint of AA' and XY⊥AA'.

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The mean for this population is 55. The variance and standard deviation for this population are 94.8 and 9.74

The data is given for five families and their children are tested to see how many words they can speak in Swahili.

Toddler     Number of words(X)        X - M         (X - M)²

   A                        47                          - 8                64

   B                        73                           18               324

   C                        56                            1                  1

   D                        46                          -9                 81

   E                        53                          -2                  4

                                                                              424

Mean of the population(M) = (∑X)/n

                                             = (47 + 73 + 56 + 46 + 53)/5

                                             = 275/5 = 55

Variance f population (σ²) = (X - M)²/n = 474/5 = 94.8

Standard deviation of population(σ) = √94.8 = 9.74

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The lowest common denominator of the fraction is 6

The lowest common denominator (LCD) is the smallest common multiple of the denominators of a set of fractions. It is used to add or subtract fractions with different denominators.

The LCD of a set of fractions is the smallest number that is divisible by all the denominators in the set. When all the denominators are divided into the LCD, each fraction has an equivalent fraction with the same value and a denominator equal to the LCD.

In the fraction given;

x / 3 + x / 2 = 20

The lowest common denominator is 6

Using 6, we can divide through each of the fraction.

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The sample standard deviation weight of the 50 candies is, 0.07 grams.

The amount of variation or dispersion in a set of data values is measured by standard deviation. A statistical calculation is used to determine how far the values vary from the mean (average) value. While a high standard deviation suggests that the data values are more dispersed, a low standard deviation suggests that the data values tend to be close to the mean.

To find the sample standard deviation weight,

we can use the formula:

[tex]s = \sqrt{((1/(n-1))} \sum((x - \bar x)^{2} ))[/tex]

where n is the sample size, x is the weight of each candy, [tex]\bar x[/tex] is the sample mean weight, and sum() means to add up the values.

We can first find the sample mean weight:

[tex]\bar x[/tex]= (0.98 + 0.85 + 0.92 + 0.98 + 0.71 + 0.88 + 0.86 + 0.75 + 0.85 + 0.85 + 0.86 + 0.78 + 0.75 + 0.75 + 0.74 + 0.82 + 0.85 + 0.91 + 0.78 + 0.72 + 0.81 + 0.81 + 0.81 + 0.84 + 0.87 + 0.85 + 0.89 + 0.77 + 0.85 + 0.97 + 0.74 + 0.89 + 0.82 + 0.86 + 0.82 + 0.84 + 0.91 + 0.87 + 0.94 + 0.85 + 0.71 + 0.83 + 0.87 + 0.94 + 0.81 + 0.81 + 0.78 + 0.77 + 0.85) / 50

[tex]\bar x[/tex] = 0.8456

Next, we can calculate the sample standard deviation:

s = √((1/(50-1)) x ((0.98-0.8456)² + (0.85-0.8456)² + ... + (0.77-0.8456)² + (0.85-0.8456)²))

s = sqrt(0.0045916)

s = 0.0678

Rounding to two decimal places, the sample standard deviation weight is 0.07 grams.

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The graphing points of the equation is given in the table.

An equation is a statement that asserts the equality of two expressions, the expressions are written one on each side of an '=' equal to sign.

Given equation is [tex]y=2^{x+5} +1[/tex].

To find the graphing points of the functions:

By assuming the value for x and substitute in the given function to find the values of y.

[tex]if x=-2,y=2^{-2+5} +1=9\\ifx=-1, y=2^{-1+5} +1=17\\if x=0,y=2^{0+5} +1=33\\if x=1,y=2^{1+5} +1=65\\ifx=2,y=2^{2+5} +1=129[/tex]

It is given the table format as,

                 x                [tex]y=2^{x+5} +1[/tex]

                -2                     9

                -1                      17

                 0                     33

                  1                     65

                  2                   129  

Hence, these are all the graphing points of the equation.

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The volume of the rectangular prism is 140 cubic meters

The volume of a figure is a measure of the amount of space it occupies in three-dimensional space. It is a scalar quantity, meaning that it is a single numerical value with no direction.

The volume of a rectangular prism is given by the formula V = l * w * h, where l is the length, w is the width, and h is the height.

This problem is a two rectangular prism joined together.

The volume can be calculated as;

V = l * w * h

v = (4 * 7 * 3) + (2 * 7 * 4)

v = 140m³

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Its 10/29 so its answers this

Answer:

16 inches

Step-by-step explanation:

28 - 12 = 16 inches

1 foot = 12 inches

The average rate of change over each specified interval is 8/3 and -10.

The average rate shows the change in the function per unit, over an interval.

Given that, find the average rate of change over each specified interval.

The average rate of change is given by

f(b)-f(a) / b-a

a) [2, 5] :-

To find the average rate of change we will take the change in the function over the change in x,

f(5)-f(2) / 5-2 = 24-16 / 3 = 8/3

Therefore, the average rate of change in interval [2, 5] is 8/3

b) [3.8, 4] :-

Similarly,

f(4)-f(3.8) / 4-3.8 = 17-19 / 0.2 = -2/0.2

= -10

Therefore, the average rate of change in interval [3.8, 4] is -10

Hence, the average rate of change over each specified interval is 8/3 and -10.

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Answer:

4 would be the rate of change

Step-by-step explanation:

y=mx+b mx = slope

The slope represents the rate of change. Then the rate of change will be 4.

Answer:2304.9

Step-by-step explanation:

Answer:

  2304.9 ft

Step-by-step explanation:

You want the distance from point A, which is 1246 ft horizontally from a lighthouse to point B, given the angles of elevation to the light are 14° and 5° from points A and B, respectively.

The tangent relation for sides in a right triangle is ...

  Tan = Opposite/Adjacent

In a model of this geometry, the height (h) of the lighthouse is the side opposite the angle of elevation. This lets us write two equations:

  tan(14°) = h/1246

  tan(5°) = h/(1246 +d) . . . . . where d is the distance from A to B

Solving these equations for d, we have ...

  h = 1246·tan(14°) = (1246+d)·tan(5°)

  d·tan(5°) = 1246·(tan(14°) -tan(5°))

  d = 1246·(tan(14°)/tan(5°) -1) ≈ 2304.9 . . . . feet

The distance from point A to point B is about 2304.9 feet.

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Answer:

C

Step-by-step explanation:

In this equation, you would need to do 32/5 to figure out how much each person will get. 32/5=6.4 feet

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Answer:

m∠2=12°

Step-by-step explanation:

some of two angles is 90

90 -78=12

The next step in the solution to this equation is to evaluate the exponents

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

The steps 1 to 4

Using the above as a guide, we have the following:

Step 4: (3x - 11)² =(√4x)²

At this point,, we open the bracket

This is done by evaluating the exponents

So, we have

9x² - 66x + 121 = 4x

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The value of a, b, and c are 1, -2, and 6 respectively.

The y-intercept of this quadratic function is 6.

The axis of symmetry of this quadratic function is 1.

The vertex of this quadratic function is (1, 5).

Mathematically, the axis of symmetry of a quadratic function can be calculated by using this mathematical expression:

Axis of symmetry, Xmax = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

For the given quadratic function f(x) = x² - 2x + 6, we have:

Axis of symmetry, Xmax = -b/2a

Axis of symmetry, Xmax = -(-2)/2(1)

Axis of symmetry, Xmax = 2/2 = 1.

Vertex (h, k) = (1, 5).

In Mathematics, the y-intercept of any graph such as a quadratic function, generally occur at the point where the value of "x" is equal to zero (x = 0).

y-intercept = 6.

Lastly, we would create a table and then graph the quadratic function as follows;

x         y

0         6

2         2

5         11

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The expression to be added is 9mn +3m² - 12n²

These are expressions having terms, variables, coefficients, factors and constants.

They are also known to be composed of arithmetic operations, such as;

From the information given, we have the expression;

-7 mm + 2m ²+ 3n²

To make it up to 5m² +2mn-9n²., we have

-7mn + 9mn + 2m² + 3m² + 3n² - 12n²

Hence, the expression is 9mn +3m² - 12n²

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The 52nd term of the arithmetic sequence -3, 12, 27, ..... is equal to 762.

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

aₙ =  a₁ + (n - 1)d

Where:

Next, we would determine the common difference as follows.

Common difference, d = a₂ - a₁

Common difference, d = 12 - (-3)

Common difference, d = 12 + 3

Common difference, d = 15

Substituting the given parameters into the formula, the 52nd term of this arithmetic sequence is given by;

a₅₂ = a₁ + (52 - 1)d

a₅₂ = -3 + (51)(15)

a₅₂ = -3 + 765

a₅₂ = 762.

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The solution is, (17)(0.25)(4) = 17.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

given that,

(17)(0.25)(4)

=(17)*1

=17

at first we have to multiply the last two terms i.e. (0.25) and (4), then, we multiply the result 1 with 17, and get the result 17.

Hence, The solution is, (17)(0.25)(4) = 17.

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