HELP!!!!!!!!!!!!!!!!!!!!!

The 3-year-old boy is more unusually tall for his age and gender than the 10-year-old girl.

A z-score calculates how many standard deviations an observation is from the mean. An observation is said to be above the mean if the z-score is positive, while it is said to be below the mean if the z-score is negative.

For the 3-year-old boy, the z-score is:

z = (43 - 38) / 2 = 2.5

The z-score for the 10-year-old girl is:

z = (57 - 54.5) / 2.5 = 1

The 3-year-old boy has a higher z-score than the 10-year-old girl, indicating that he is more unusually tall for his age and gender. This is due to his height, which is higher than the average for his age group 38 inches .

Therefore, the 3-year-old boy is more unusually tall for his age and gender than the 10-year-old girl.

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The scale factor is 1/3.

What is the scale factor?

The difference in scale between an original object's scale and a new object that is its representation but is larger or smaller is known as a scale factor. For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2.

Here, we have

Given: Triangle D has been dilated to create triangle D′.

To find the scalar value, simply choose one side of D and one did of D’ and divide them to find the scalar. We can verify that we have the correct scalar by performing this division on each related edge. Below I will do D to D’ represented like D/D’:

4.8 / 1.6 = 3

4.2 / 1.4 = 3

2.7 / x = 3

Knowing that the scaling for each edge is 3, we can solve for x.

2.7 / 3 = x

0.9 = x

The edges for D are 4.8, 4.2, and 2.7 respectively to D’ scaled by 1/3. So we can determine that the edges for D’ are 1.6, 1.4, and 0.9 respectively to D scaled by 3.

So if we go D’ to D, we scale by 3. If we go D to D’, we scale by 1/3.

Hence, the scale factor is 1/3.

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The required set of numbers 5, 9, 11, and 14 satisfies all the given conditions.

In mathematics, a set is a logically arranged group of items that can be represented in either set-builder or roster form. Sets are typically denoted by curly brackets; for instance, A = 1, 2, 3, 4 is a set.

a set of four whole numbers that satisfies the given conditions:

5, 9, 11, 14

To check that this set meets the requirements:

The range of the original set (12 - 4 = 8) increased by 2 to become 10 (14 - 4 = 10).

The mean of the original set ((4 + 9 + 10 + 12) / 4 = 8.75) remains the same in the new set ((5 + 9 + 11 + 14) / 4 = 8.75).

The median of the original set is 9.5 (the average of 9 and 10), and the median of the new set is 10 - 1 = 9.

Therefore, the set of numbers 5, 9, 11, and 14 satisfies all the given conditions.

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The total weight of the liquid in the tank is approximately 12,628 pounds.

To calculate the weight of the liquid, we need to determine the volume of the hemisphere and then multiply it by the density of the liquid. The formula for the volume of a hemisphere is V = (2/3)πr³, where r is the radius of the hemisphere.

In this case, the diameter of the tank is given as 24 feet, so the radius is half of that, which is 12 feet. Plugging this value into the formula, we get V = (2/3)π(12)³ ≈ 904.78 cubic feet.

Finally, we multiply the volume by the density of the liquid: 904.78 cubic feet * 92.5 pounds per cubic foot ≈ 12,628 pounds. Therefore, the total weight of the liquid in the tank is approximately 12,628 pounds.

In summary, to calculate the weight of the liquid in the tank, we first determine the volume of the hemisphere using the formula V = (2/3)πr³. Then, we multiply the volume by the density of the liquid.

By substituting the given diameter of 24 feet and using the appropriate conversions, we find that the total weight of the liquid is approximately 12,628 pounds.

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Answer:

Domain:     -INFINITY  ,  INFINITY

Range:       -INFINITY  ,  INFINITY

Step-by-step explanation:

Answer

p=1.8

Step-by-step explanation:

sorry im not really sure if thats correct

Answer:

The length of the arc is 15.7 centimeters

Step-by-step explanation:

The central angle measures 90 degrees. In order to find the length of the arc, we need to find the total circumference of the circle.

Circumference formula = pi x diameter
The diameter is just the radius doubled

pi x (10 + 10)
pi x 20 = 62.8

The total circumference is 62.8. We know that there are 360 degrees in a circle and 90 is 1/4 of 360.

So 62.8 / 4 = 15.7

The arc should be 15.7 cm

i think this is correct, sorry if its not

The correct option is,

The table represents a linear function because there is not a constant rate of change in the input and output values.

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The table is shown in figure.

Now,

For Table;

The equation of line is,

⇒ y - y₁ = (y₂ - y₁) / (x₂ - x₁) (x - x₁)

⇒ y - (-4) = (-2 - (-4)) / (- 1 - (-2))  (x - (-2))

⇒ y + 4 = 2/1 (x + 2)

⇒ y + 4 = 2 (x + 2)

⇒ y + 4 = 2x + 4

⇒ y = 2x

Thus, The table represents a linear function because there is not a constant rate of change in the input and output values.

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Yοur friend's statement is nοt cοrrect.

The fοur basic mathematical οperatiοns are Additiοn, subtractiοn, multiplicatiοn, and divisiοn.

Nο, yοur friend's statement is nοt cοrrect.

The reasοn is that the twο temperatures are measured using different scales. The temperature inside the building is given in Celsius (°C), while the temperature οutside is given in Fahrenheit (°F). These are twο different scales, and a temperature οf 22°C is nοt equal tο a temperature οf 22°F.

Tο cοmpare the twο temperatures, we need tο cοnvert οne οf them tο the οther scale. One way tο dο this is tο use the cοnversiοn fοrmula:

°F = (°C × 9/5) + 32

Using this fοrmula, we can cοnvert the temperature inside the building frοm Celsius tο Fahrenheit:

°F = (22°C × 9/5) + 32 = 71.6°F

Nοw we can see that the temperature inside the building is much higher than the temperature οutside the building.

Hence, yοur friend's statement is nοt cοrrect.

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Arcs get their angle measure from the central angle they're in, in this case the central angle of 86°, central to arcED, has a counterpart of a twin vertical angle across the center, since both vertical angles are identical twins that means the central angle for arcAB is 86° also, and that's the arcAB's measure too.

Answer:

$24

Step-by-step explanation:

1. MULTIPLY: 3 x 56 = 168

2. DIVIDE: 168 / 7 = $24

I hope this helps!

Based on multiplication we have found that 3/7 of $56 is equal to $24.

We are given that the expression 3/7 of $56

To determine 3/7 of $56, we can multiply 3/7 by $56.

Multiply 3/7 by $56:

(3/7) x $56 = (3 x $56) / 7

Calculate the numerator:

3 x $56 = $168

Divide the numerator by the denominator:

$168 / 7 = $24

Therefore, 3/7 of $56 is equal to $24.

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Using a calculator, the trigonometric ratio of sin 98 is approximately 0.9848.

One of the trigonometric ratio we have in mathematics is the sine ratio. We can use calculator to find the sine of an angle without making use of tables. To do this on your calculator, enter the sine function followed by the degree of the angle you want to find its sine. You will get your answer.

Using a calculator, we can find the sine of 98 degrees as follows:

sin 98° ≈ 0.9848

Rounding this to four decimal places, we get:

sin 98° ≈ 0.9848

Therefore, sin 98° is approximately equal to 0.9848.

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Answer:

answer=C

Step-by-step explanation:

number of elements in A=3

so, n=3

number of subsets=\(2^{n}\), where n the number of elements in A.

=\(2^{3}\)=8 subsets

the subsets of A are,

Ф,

{k},{e},{y},

{k,e},{k,y},{e,y},

{k,e,y}

Step-by-step explanation:

the answer would be a. 1/3

Answer:

The answer is D. 3

The equation in term of p that models the above experience is:
2p + 10 = 0.8p + 20.

Any statement that models or captures the factors of a problem where in an equal sign is present to equate two of the factors or expressions therein is called an equation.

Total cost of baking p pizzas with brick oven = A =  p(cost of one pizza) + cost of baking = p(2) + 10 (in dollars).

Total cost of  baking p pizzas with electric oven = B =  p(cost of one pizza) + cost of baking = p(0.8) + 20 (in dollars).

B = A - 1 (as using electric oven saves $1 per day, as given)

Thus, we get:

2p + 10 = 0.8p + 20

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Answer:

x=9

Step-by-step explanation:

f(x) = −(x − 7)2 + 4

(substitute f(x) = 0)

0= −(x − 7)2 + 4

(distribute 2 into brackets)

0= −(2x - 14) + 4

(remove brackets and change the sign of each expression inside the brackets)

0= - 2x + 14 + 4

(add the numbers)

0= - 2x + 18

(move variable to the other side and change its sign)

2x = 18

(divide both sides by 2)

x = 9

The given expression is quadratic, parabolic graph, relative maxima and real zeros. The correct options are (a), (c) and (f).

The general form of a quadratic equation is given as ax^2 + bx + c = 0.

Here, a ≠ 0 and b and c are integers.

The degree of a quadratic equation is 2.

The given expression is f(x) = -(x - 7)² + 4

Since the degree of the expression is 2, it is quadratic.

The graph of the given equation will be parabolic.

By comparing from the general vertex form (x - h)² + k, its vertex can be found as (7, 4).

Axis of symmetry is x = 7.

y-intercept can be obtained by plugging x = 0 as,

-(0 - 7)² + 4 = 53.

Maxima or minima can be found as below,

f'(x) = 0

⇒ -2(x - 7) = 0

⇒ x = 7

In order to find the solution write the expression as follows,

-(x - 7)² + 4 = 0

⇒ -x² + 14x - 49 + 4 = 0

⇒ x² - 14x + 45 = 0

⇒ x = 5,9

Thus, the equation has real solutions.

Hence, the properties of the given equation are derived as quadratic, parabolic graph, relative maxima and real zeros.

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Answer:

To find the fraction of the total audience that were students or teachers, you need to add the fractions of students and teachers and simplify the result.

5/12 + 1/8 = (53) / (123) + (16) / (86) = 15/36 + 6/48 = 15/36 + 3/24 = 18/36 + 3/24 = (18+3) / (36+24) = 21/60

So 21/60 of the total audience were students or teachers.

Here C=$7191

r=0.05

t=9 months=0.75 years

The value of the car will be

Hence the value of the car will be $6921.34.

The closest approximate average rate of change for Edna's profits from the 18th month to the 21st month is 14

From the question, we have the following ordered pairs

x intercepts = (6,0) and (18, 0)

Vertex = (12, -36)

Points (21, 41.25)

The closest approximate average rate of change for Edna's profits from the 18th month to the 21st month is the calculated using

m = [f(21) - f(18)]/[21 - 18]

This becomes

m = [f(21) - f(18)]/3

Substitute the known values in the above equation

m = [41.25 - 0]/3

Evaluate the difference

m = 41.25/3

Evaluate the quotient

m = 13.75

Approximate

m=14

Hence, the closest approximate average rate of change for Edna's profits from the 18th month to the 21st month is 14

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Complete question

The graph below shows the value of Edna's profits f(t), in dollars, after t months:

What is the closest approximate average rate of change for Edna's profits from the 18th month to the 21st month?

See attachment for graph

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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The minimum value of \($\|\mathbf{v}\|$\) is zero.

The minimum value of \($\|\mathbf{v}\|$\) is zero, as it is the distance between the origin and a point on the line. To solve this problem, the formula \($\|\mathbf{v}\| = \sqrt{x^2 + y^2}$\) can be used, where x and y are the coordinates of the point on the line. Since the equation of the line is \($\dbinom{10}{3} \dbinom{-2}{1}t$\), the coordinates of the point on the line can be found by substituting \($t = 0$: $x = 10 \cdot 0 - 2 \cdot 0 = 0$, and $y = 3 \cdot 0 + 1 \cdot 0 = 0$\) . Substituting these values into the formula for \($\|\mathbf{v}\|$ gives $\|\mathbf{v}\| = \sqrt{0^2 + 0^2} = 0$\). Therefore, the minimum value of \($\|\mathbf{v}\|$\) is zero.

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Answer:

B

Step-by-step explanation:

given scale is 1 inch represents 7.5 feet

then we require to calculate how many 7.5 feet there are in each dimension.

to obtain this divide each dimension by 7.5, that is

13 ÷ 7.5 ≈ 1.73 ( to 2 decimal places )

26 ÷ 7.5 ≈ 3.47 ( to 2 decimal places )

then dimensions are approximately 1.73 inches by 3.47 inches

Consider a disk D having center as origin and radius 'a', the average distance from point say ( r, θ) to the origin D to the origin is equals to the 2a/3.

The distance of a point to the origin is given by the function d(x, y) = √x²+ y². Denote the disk by D. To compute the average we need to evaluate the integral, for which we use polar coordinates, f(r, θ) = (1/area of region R)∬ f(r,θ)dA.

We have a disk D with center the origin (0,0) and radius 'a'. We have to determine the average distance from points in D to the origin. Since r is defined as the distance from the origin, the distance of any point (r,θ) from the origin is f(r,θ) = r

Integrating f over the region D, with limits r = 0 to a, and 0≤ θ≤2π , dA = r×dr×dθ

\(∬f(r,θ)dA = \int_{0}^{a} \int_{0}^{2π} r (rdr)dθ \)

\(= \int_{0}^{2\pi} \int_{0}^{a} r^{2} drdθ = \int_{0}^{2\pi}[\frac{{r}^{3}}{3}]_{0}^{a}dθ\)

\(= \int_{0}^{2π}[ \frac{a³}{3} ] dθ = \frac{{a}^{3}}{3} \int_{0}^{2π}dθ\)

\(= \frac{a³}{3} [θ]_{0}^{2π} = 2\pi(\frac{a³}{3})\)

Area of disk D with radius 'a' = πa²

So, the average distance from point ( r,θ) in D to the origin is = (1/area of region D)∬f(r,θ)dA

= (1/πa²)( 2πa³/3)

= 2a/3

Hence, required distance is 2a/3.

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Answer:

2.3 hours

Step-by-step explanation:

From 3:12 pm to 4:12 pm, one hour passes.

From 4:12 pm to 5:12 pm, another hour passes.

From 5:12 pm to 5:30 pm, there are 18 minutes that pass.

Therefore, the total time elapsed is 2 hours and 18 minutes out of 60 minutes in an hour.

To convert this to a fraction, we can write:

2 hours + 18 minutes = 2 + 18/60 hours = 2.3 hours

So, 2.3/1 hour passes from 3:12 pm to 5:30 pm.

Answer: The percentage of people surveyed who liked blue cars is 50%.

Step-by-step explanation:

Total number of people partaking in survey= 36

number of people who like blue cars= 18

therefore, fraction of people who liked blue cars= \(\frac{18}{36}\)

hence, percentage of people who liked blue cars= (18/36)*100 %

                                                                                  = 50%  

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Answer:

Percentage of people who like blue-coloured cars is 50%

Number of people who were surveyed=36

Number of people who like blue-colored cars=18

Therefore, Percentage of people who like blue cars= (Number of people who like blue cars/ Number of people who were surveyed)*100

=(18/36)*100

=50%

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Answer:

y=−38x−14y is equal to negative 3 eighths x minus 1 fourth is the answer.

Answer:

We are trying to calculate the area of the park by modeling it with shapes. To start, the larger rectangle (green) toward the top is the easiest to calculate. Its length is 8 yards and its width is 4 yards, so the area would be 8 x 4 = 32 yards^2.

Next, the 3 rectangles at the bottom (white). The one in the middle has a length of 4 yards and a width of 3 yards, so its area is 4 x 3 = 12 yards^2. The two rectangles to either side are the same size, so together their area will be 2 x 4 x 3 = 24 yards^2.

Now that we have modeled the park with 3 shapes, we need to add the areas together to get the total area. So, we have 32 + 12 + 24 = 68 yards^2. The total area of the park is 68 yards^2.

Step-by-step explanation:

The area of the park is about :

95 + 27 = 122 yards

We have the following information available from the question is:

The outline of a park is shown in the diagram. Each square on the grid represents a square yard. Use shapes to model the area of the park.

Now, According to the question:

Each square on the grid represents a square yard, and as we can see from the figure that the complete square is about 95, the incomplete grid is about 27,

So the area of the park is about :

95 + 27 = 122 yards

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Answer:

True

Step-by-step explanation:

You should always check just in case a mistake or miscalculation was made. To check, substitute the value you got for the variable into the equation and solve.

For example,

x=2

8x-2=14

Substitute 2 in for x

8(2)-2=14

16-2=14

14=14

Since this is true, we know that 2 is the correct solution.

Answer:

54 kids per bus

Step-by-step explanation:

first take 7-331 and you get 324 divided by 6= 54

The correct answer is C. It is the graph of f(x) translated 11 units to the left.

The correct answer is:

C. It is the graph of f(x) translated 11 units to the left.

When we have a function of the form g(x) = f(x - a), it represents a horizontal translation of the graph of f(x) by 'a' units to the right if 'a' is positive and to the left if 'a' is negative.

In this case, g(x) = f(x - 11), which means that the graph of f(x) is being translated 11 units to the right. However, the answer options do not include this specific transformation. The closest option is option C, which states that the graph of g(x) is translated 11 units to the left.

The graph of f(x) = x is a straight line passing through the origin with a slope of 1. If we apply the transformation g(x) = f(x - 11), it means that we are shifting the graph of f(x) 11 units to the right. This results in a new function g(x) that has the same shape and slope as f(x), but is shifted to the right by 11 units.

Therefore, the correct answer is C. It is the graph of f(x) translated 11 units to the left.

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