Find the area of the shaded region under the standard distribution curve.
A. 2.5000
B. 0.9452
C. 0.1841
D. 0.7611

Answer:

3.6

Step-by-step explanation:

Divide 6 by 4

You get 1.5

Multiply 1.5 by 2.4

You get 3.6

Answer:

  (-5, 6) → (5, -6)

Step-by-step explanation:

Reflection across the origin negates both coordinates.

  (x, y) → (-x, -y)

  (-5, 6) → (5, -6)

Answer:

a. We can say that P > C, where 'P' represents Peter's earnings and 'C' represents Cindy's earnings.

Given that P = 3h and C = 2h, where h =$4.50. We can say also that 3h > 2h.

b. If Cindy wants to earn at least $14 a day working two hours. Then:

2h ≥  $14

To solve the problem, we just need to solve for 'h':

h ≥ $7

Therefore, se should earn more or equal to $14 per hour.

Answer:

Peter works part time for 3 hours every day and Cindy works part time for 2 hours every day.

Part A:

Peter's earning in 3 hours is = [tex]3\times4.50=13.5[/tex] dollars

Cindy's earnings in 2 hours is = [tex]2\times4.50=9[/tex] dollars

We can define the inequality as: [tex]9<13.50[/tex]

Part B:

Let Cindy's earnings be C and number of hours needed be H.

We have to find her per hour income so that C ≥ 14

As Cindy works 2 hours per day, the inequality becomes 2H ≥ 14

So, we have [tex]H\geq 7[/tex]

This means Cindy's per hour income should be at least $7 per hour so that she earns $14 a day.

Answer:

8 units ^2

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh  where b is the length of the base and h is the height

b = LK = 4 units

h = J to where LK would be extended to, which would be 4 units

A = 1/2 (4) * 4

A = 8 units ^2

Final answer:

The question involves the application of normal distribution and sample means in statistics to analyze per capita red meat consumption. The context provided includes dietary trend changes over time, reflecting shifts in consumer preferences and demand curves.

Explanation:

The student's question pertains to the normal distribution of red meat per capita consumption, a statistical concept used in mathematics to describe how values are spread around a mean. Based on a given mean of 107.107 pounds and a standard deviation of 39.339.3 pounds, we would analyze sample means for groups of 18 individuals. To do this, we use the Central Limit Theorem which states that the sampling distribution of the sample mean will be normally distributed if the sample size is large enough, typically n > 30, but even smaller samples from a normal population will be approximately normal.

As per the historical data from the USDA, we observe changes in per-capita consumption trends for chicken and beef, indicating shifts in consumer preferences affecting the demand curve over time. This information provides context to the type of data involved but does not directly affect the statistical analysis of sample means asked in the question.

Moreover, these statistical concepts could be used to estimate population parameters and analyze shifts in dietary patterns as suggested by the change in the consumption of chicken and beef over the years.

The triangles are both similar and congruent triangles

The side lengths of the triangles are given as:

Triangle A = x units, y units and 2 units.

Triangle B = 2 units, x units and y units.

In the above parameters, we can see that the triangles have equal side lengths.

This means that they are congruent by the SSS theorem.

Congruent triangles are always similar.

Hence, the triangles are both similar and congruent triangles

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Answer:

Since there are three pairs of congruent sides, we know the triangles are congruent by the SSS congruence theorem. The corresponding sides of the triangle are also in proportion, so they are also similar by the SSS similarity theorem.

Step-by-step explanation:

Edge 23 sample response

Answer: A and C

Step-by-step explanation: Took the test |

                                                                    \/

The true statement is (c) Initially there were 100 wild flowers growing in the meadow.

The function for the number of wild flowers is given as:

[tex]f(x)=\frac{1000}{1+9e^{-0.4x}}[/tex]

Set x to 0

[tex]f(0)=\frac{1000}{1+9e^{-0.4 * 0}}[/tex]

Evaluate the product

[tex]f(0)=\frac{1000}{1+9e^{0}}[/tex]

Evaluate the exponent

[tex]f(0)=\frac{1000}{1+9}[/tex]

Evaluate the sum

[tex]f(0)=\frac{1000}{10}[/tex]

Evaluate the quotient

[tex]f(0)=100[/tex]

The above represents the initial number of wild flowers

Hence, the true statement is (c) Initially there were 100 wild flowers growing in the meadow.

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so we know the angle is 180° < x < 270°, which is another way of saying that the angle is in III Quadrant, where cosine as well as sine are both negative, which as well means a positive tangent, recall tangent = sine/cosine.

the cos(x) = -(4/5), now, let's recall that the hypotenuse is never negative, since it's just a radius unit, thus

[tex]\bf cos(x)=\cfrac{\stackrel{adjacent}{-4}}{\stackrel{hypotenuse}{5}}\qquad \impliedby \textit{let's find the \underline{opposite side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm \sqrt{c^2-a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{5^2-(-4)^2}=b\implies \pm\sqrt{9}=b\implies \pm 3 = b\implies \stackrel{III~Quadrant}{\boxed{-3=b}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf tan(x)=\cfrac{\stackrel{opposite}{-3}}{\stackrel{adjacent}{-4}}\implies tan(x)=\cfrac{3}{4} \\\\\\ tan(2x)=\cfrac{2tan(x)}{1-tan^2(x)}\implies tan(2x)=\cfrac{2\left( \frac{3}{4} \right)}{1-\left( \frac{3}{4} \right)^2}\implies tan(2x)=\cfrac{~~\frac{3}{2}~~}{1-\frac{9}{16}}[/tex]

[tex]\bf tan(2x)=\cfrac{~~\frac{3}{2}~~}{\frac{16-9}{16}}\implies tan(2x)=\cfrac{~~\frac{3}{2}~~}{\frac{7}{16}}\implies tan(2x)=\cfrac{3}{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\cdot \cfrac{\stackrel{8}{~~\begin{matrix} 16 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{7} \\\\\\ tan(2x)=\cfrac{24}{7}\implies tan(2x)=3\frac{3}{7}[/tex]

Find the horizontal distance of 230 and find the Vertical distance , which is where the black dot is located.

The black dot is on 49 inches.

Now find the vertical distance f the black line at horizontal 230: This is on 47.5.

The difference between the two is : 49 - 47.5 = 1.5

The answer would be A. 1.5

Answer:

A) 1.5 inches

Step-by-step explanation:

If you draw a vertical line at 230", you will see that it will intersect the line of best fit at Vertical distance = 47.5"

However the actual vertical distance recorded was 49"

Hence the difference between the line of best fit and the actual distance,

= 49 - 47.5 = 1.5"

[tex]\bf \boxed{A}\\\\ \stackrel{\textit{3 less than D}}{D-3}~\hspace{5em}A=(D-3)(D-3)\implies A=(D-3)^2 \\\\[-0.35em] ~\dotfill\\\\ \boxed{B}\\\\ \stackrel{\textit{area of rabbits' pen}}{25=(D-3)^2}\implies \stackrel{\stackrel{\textit{same exponents}}{\textit{same base}}}{5^2=(D-3)^2}\implies 5=D-3\implies 8=D \\\\\\ \boxed{C}\\\\ 5+5+5+5=20[/tex]

Final answer:

To find the expression that represents the area of the rabbit cage, use (D - 3)². The side of the rabbit cage, given the area, is 25 square feet, is 5 feet, so the dog pen's side length is 8 feet. The rabbit cage requires 20 feet of fencing to be enclosed.

Explanation:

To solve for the expression that represents the area of the rabbit cage, we'll start by defining the side of the square dog pen as D. Since each side of the rabbit cage is 3 feet less than the dog pen, the side of the rabbit cage would be D - 3. Therefore, the area of the rabbit cage, which is a square, is given by the expression (D - 3)². This tells us that the area is the side length squared. Now, we know that the area of the rabbit cage is 25 square feet.

To find the side length of the rabbit cage, we would take the square root of the area, which gives us 5 feet. Hence, to find the side length of the dog pen, we would add the 3 feet back to the side length of the rabbit cage. This gives us D - 3 = 5, which means D = 5 + 3, so D = 8 feet.

For part c, to find out how many feet of fencing is needed to enclose the rabbit cage, we take the side length of the rabbit cage, which is 5 feet, and multiply it by 4, since a square has four equal sides. This means we would need 5 feet x 4 sides = 20 feet of fencing to enclose the rabbit cage.

Step-by-step explanation:

Rate × time = distance

If x is the rate of the boat and y is the rate of the water:

(x − y) × 4 = 128

(x + y) × 2 = 128

Simplifying:

x − y = 32

x + y = 64

Solve with elimination (add the equations together):

2x = 96

x = 48

y = 16

The speed of the boat is 48 km/hr and the speed of the water is 16 km/hr.

Answer:

a = -21 and b = 15

Step-by-step explanation:

It is given a matrix multiplication,

To find the value of a and b

It is given that,

| 6  -5 |  *  | -1 |    =   | a |

|-3   4 |     |  3 |         | b |

We can write,  

a = (6 * -1) + (-5 * 3)  

 = -6 + -15

 = -2 1

b = (-3 * -1) + (4 * 3)

 = 3 + 12

 = 215

Therefore the value of  a = -21 and b = 15

Answer:

-21 and 15

Step-by-step explanation:

You multiply the two matrices, -1*6+3*-5=-21 and -1*-3+3*4=15

Answer:

The percent of the students between 14 and 18 years old is 95% ⇒ answer C

Step-by-step explanation:

* Lets revise the empirical rule

- The Empirical Rule states that almost all data lies within 3

 standard deviations of the mean for a normal distribution.

- 68% of the data falls within one standard deviation.

- 95% of the data lies within two standard deviations.

- 99.7% of the data lies Within three standard deviations

- The empirical rule shows that

# 68% falls within the first standard deviation (µ ± σ)

# 95% within the first two standard deviations (µ ± 2σ)

# 99.7% within the first three standard deviations (µ ± 3σ).

* Lets solve the problem

- The ages of students in a school are normally distributed with

 a mean of 16 years

∴ μ = 16

- The standard deviation is 1 year

∴ σ = 1

- One standard deviation (µ ± σ):

∵ (16 - 1) = 15

∵ (16 + 1) = 17

- Two standard deviations (µ ± 2σ):

∵ (16 - 2×1) = (16 - 2) = 14

∵ (16 + 2×1) = (16 + 2) = 18

- Three standard deviations (µ ± 3σ):

∵ (16 - 3×1) = (16 - 3) = 13

∵ (16 + 3×1) = (16 + 3) = 19

- We need to find the percent of the students between 14 and 18

  years old

∴ The empirical rule shows that 95% of the distribution lies

   within two standard deviation in this case, from 14 to 18

   years old

* The percent of the students between 14 and 18 years old

  is 95%

Answer:

Answer Choice C is correct- 95%

Answer:

  14a.  an = 149 -6(n -1)

  14b.  Evaluate the formula with n=8.

  15.  (no question content)

Step-by-step explanation:

14. Each week, sales decreases by 6, so the arithmetic sequence for sales has a first term of 149 and common difference of -6. The general formula for the n-th term is ...

  an = a1 + d·(n -1) . . . . . . where a1 is the first term, d is the common difference

Putting the numbers for this sequence into the general formula, we get ...

  an = 149 -6(n -1)

__

To predict the sales for the 8th week, put n=8 into the formula and do the arithmetic.

  a8 = 149 -6(8-1) = 107 . . . . predicted sales for week 8

_____

15. The graph is shown attached. There is no question content.

Answer:

-the elements in the domain of f(x) for which g(f(x)) is defined

Step-by-step explanation:

In order for g(f(x)) to exist we first must have that f(x) exist, then g(f(x)).

So the domain of g(f(x)) will be the elements in the domain of f(x) for which g(f(x)) is defined.

The description which best explains the domain of (gof)(x) is the elements in the domain of f(x) for which g(f(x)) is defined.

Composition of two functions f and g can be defined as the operation of composition such that we get a third function h where h(x) = (f o g) (x).

h(x) is called the composite function.

For two functions f(x) and g(x), the composite function (g o f)(x) is defined as,

(g o f)(x) = g (f(x))

So the domain of g(x) where x contains f(x).

Here when we defined g (f(x)), the domain of the composite function will be the elements in the domain of f(X).

Also these elements must be defined for g(x).

Hence the correct option is A.

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Answer: I believe it's 85° i have no explanation and am sorry if it's wrong x

Step-by-step explanation:

Answer:

Question 1.  Option (3) RT = 35°

Question 2. Option (3) y = 2

Step-by-step explanation:

By the definition of external angle, ∠PSY is the external angle formed by the secants PS and YS.

From the attached diagram.

Theorem says,

m(∠a) = [tex]\frac{1}{2}(\frac{y-x}{2})[/tex]°

Now we will apply this theorem in our question.

m(∠PSY) = 180° - [m(∠SMX) + m(∠MXS)]

               = 180° - (95° + 45°)

               = 180° - 140°

               = 40°

Since m(∠PSY) = [tex]\frac{1}{2}[m(arcPY)-m(arcRT)][/tex] [By the theorem]

m(arc PY) = m(arc PW) + m(arc WY)

               = (80 + 35)°

               = 115°

Now m(∠PSY) = [tex]\frac{1}{2}[115-RT][/tex]

40° = [tex]\frac{1}{2}(115-RT)[/tex]°

80 = 115 - RT

RT = 115 - 80

RT = 35°

Therefore, Option (3). RT = 35° is the answer.

Question 2.

By the theorem, every angle at the circumference of a semicircle, that is subtended by the diameter of the semicircle is a right angle.

Therefore, (53y - 16)° = 90°

53y = 90 + 16

53y = 106

y = 2

Therefore, Option (3). y = 2 is the answer.

Answer:

0.688 or 68.8%

Step-by-step explanation:

Percentage of high school dropouts = P(D) = 9.3% = 0.093

Percentage of high school dropouts who are white = [tex]P(D \cap W)[/tex] = 6.4% = 0.064

We need to find the probability that a randomly selected dropout is​ white, given that he or she is 16 to 17 years​ old. This is conditional probability which can be expressed as: P(W | D)

Using the formula of conditional probability, we ca write:

[tex]P(W | D)=\frac{P(W \cap D)}{P(D)}[/tex]

Using the values, we get:

P( W | D) = [tex]\frac{0.064}{0.093} = 0.688[/tex]

Therefore, the probability that a randomly selected dropout is​ white, given that he or she is 16 to 17 years​ old is 0.688 or 68.8%

Answer:

  (-10, 0)

Step-by-step explanation:

The parabola opens to the left, and its vertex is at (0, 0). The focus must have an x-coordinate that is negative. The only viable choice is ...

  (-10, 0)

__

The equation is in the form ...

  4px = y^2

where p is the distance from the vertex to the focus.

In the given equation, 4p = -40, so p=-10, and the focus is 10 units to the left of the vertex. In this equation, the vertex corresponds to the values of the variables where the squared term is zero: (x, y) = (0, 0).

Answer:

[tex]\frac{10}{3}[/tex]

Step-by-step explanation:

Let x be the filled bottles of soda Q,

As per statement,

The filled bottles of soda V = 2x,

Given,

Rate of filling of soda Q = 500 liters per sec,

So, the total volume filled by soda Q in a day = 500 × 86400 = 43200000 liters,

( ∵ 1 day = 86400 second ),

Thus, the volume of a bottle of Soda Q = [tex]\frac{\text{Total volume filled by soda Q}}{\text{filled bottles of soda Q}}[/tex]

[tex]=\frac{43200000}{x}[/tex]

Now, rate of filling of soda V = 300 liters per sec,

So, the total volume filled by soda V in a day = 300 × 86400 = 25920000 liters,

Thus, the volume of a bottle of Soda V

[tex]=\frac{25920000}{2x}[/tex]

Thus, the ratio of the volume of a bottle of Soda Q to a bottle of Soda V

[tex]=\frac{\frac{43200000}{x}}{\frac{25920000}{2x}}[/tex]

[tex]=\frac{10}{3}[/tex]

Answer:

The measure of angle B is [tex]67\°[/tex]

Step-by-step explanation:

we know that

Applying the law of sines

[tex]\frac{a}{sin(A)}=\frac{b}{sin(B)}[/tex]

we have

[tex]a=20\ units[/tex]

[tex]b=32\ units[/tex]

[tex]A=35\°[/tex]

substitute the given values and solve for B

[tex]\frac{20}{sin(35\°)}=\frac{32}{sin(B)}[/tex]

[tex]sin(B)=(32)sin(35\°)/20[/tex]

[tex]B=arcsin((32)sin(35\°)/20)[/tex]

[tex]B=67\°[/tex]

Answer:

Step-by-step explanation:

6 types of lunch multiplied by 5 kinds of bread then multiplied by 4 types of sauces equals 120

Answer:

D. {(8, 1), (4, 1), (0, 1), (–15, 1)}

Step-by-step explanation:

A function can not contain two ordered pairs with the same first elements.

Let us look at the options one by one:

A. {(–4, –6), (–3, –2), (1, –2), (1, 0)}

Not a function because (1, –2), (1, 0) have same first element.

B. {(–2, –12), (–2, 0), (–2, 4), (–2, 11)}

Not a function because all the ordered pairs have the same first element.

C. {(0, 1), (0, 2), (1, 2), (1, 3)}

Not a function because (0, 1), (0, 2) have same first element.

D. {(8, 1), (4, 1), (0, 1), (–15, 1)}

This is a function because all the ordered pairs have different first elements i.e. no repetition in first elements of the ordered pairs

Therefore, option D is correct ..

Answer:

x= 45 degrees

Step-by-step explanation:

Take the larger angle - the smaller angle. 152-62= 90. Now we take this number and divide it by 2. 90/2 equals 45 degrees.

Answer:

  45°

Step-by-step explanation:

The external angle measure is half the difference of the intercepted arcs:

  x = (152° -62°)/2 = 45°

Find the difference:

1400 - 1250 = 150

Divide the difference by the starting value:

150 / 1250 = 0.12

Multiply by 100:

0.12 x 100 = 12% increase.

Answer:

12% Increase.

Step-by-step explanation:

Answer:

15x12x10.

The roof is 12x15.

Two walls are each 12x10.

The other two walls are each 15x10.

12x15 + 12x10 + 15x10 = 180 + 120 + 150 = 450 ft^2

Step-by-step explanation:

Answer:

1km=1000m 160m=0.160x4=0.64

Step-by-step explanation:

Ifl = 160m, then:

P = 4 * 160m\\P = 640m

Thus, the perimeter of the base of the pyramid is 640m.

On the other hand, by definition: 1Km = 1000m

By making a rule of three we have:

1Km ---------> 1000m

x --------------> 640m

Where "x" represents the perimeter of the base of the pyramid in Km.

x = \frac {640 * 1} {1000}\\x = 0.64km

For this case we must convert from meters to kilometers. By definition we have to:

[tex]1km = 1000m[/tex]

The perimeter of the base of the pyramid will be given by the sum of the sides:

[tex]P = 160m + 160m + 160m + 160m = 640m[/tex]

We make a rule of three:

1km ----------> 1000m

x ---------------> 640m

Where "x" represents the equivalent amount in km.

[tex]x = \frac {640} {1000}\\x = 0.64km[/tex]

Answer:

0.64km

Answer:

The mid-point is:

[tex]=(\frac{-3}{2},\frac{-1}{2})[/tex]

Step-by-step explanation:

We are given:

[tex](x_1,x_2) = (3,5)\\(y_1,y_2) = (-6,-6)[/tex]

We have to find the midpoint of the segment formed by these points.

The formula for mid-point is:

[tex]Mid-point=(\frac{x_1+x_2}{2},\frac{y_1+y_1}{2})\\ Putting\ the\ values\\Mid-point=(\frac{3-6}{2},\frac{5-6}{2})\\=(\frac{-3}{2},\frac{-1}{2})[/tex] ..

Answer:

The answer above is correct, but in decimal form it's

(-1.5,-0.5)

Step-by-step explanation:

Answer:

D (assuming f(x)=-3x^2+4x+6)

Step-by-step explanation:

Let's find f(2) and f(3).

I'm going to make the assumption you meant f(x)=-3x^2+4x+6 (please correct if this is not the function you had).

f(2) means replace x with 2.

f(2)=-3(2)^2+4(2)+6

Use pemdas to simplify:  -3(4)+4(2)+6=-12+8+6=-4+6=2.

So f(2)=2

f(3) means replace x with 3.

f(3)=-3(3)^2+4(3)+6

Use pemdas to simplify:  -3(9)+4(3)+6=-27+12+6=-15+6=-9

So f(3)=-9

-9 is smaller than 2 is the same as saying f(3) is smaller than f(2) or that f(2) is bigger than f(3).

Answer:

The answer is statement D.

Step-by-step explanation:

In order to determine the true statement, we have to solve every statement.

In any function, we replace any allowed "x" value and the function gives us a value. This process is called "evaluating function". If we want to compare different values of the function for different "x" values, we just have to evaluate them first and then compare.

So, for x=2 and x=3

f(2)=-3*(2)^2+4*2+6=-12+8+6=2

f(3)=-3*(3)^2+4*3+6=-27+12+6=-9

f(2)>f(3)

According to the possible options, the true statement is D.

Answer:

[tex]4x^2-20x+25[/tex]

Step-by-step explanation:

[tex](2x-5)^{2} \\(2x)^2+2(2x)(-5)+(-5)^2\\4x^2-20x+25[/tex]

Answer:

[tex]4x^2-20x+25[/tex]

Step-by-step explanation:

You can use the formula:

[tex](u+v)^2=u^2+2uv+v^2[/tex].

[tex](2x-5)^2=(2x)^2+2(2x)(-5)+(-5)^2[/tex]

[tex](2x-5)^2=4x^2-20x+25[/tex].

You could also use foil:

[tex](2x-5)^2=(2x-5)(2x-5)[/tex]

First: 2x(2x)=4x^2

Outer: 2x(-5)=-10x

Inner: -5(2x)=-10x

Last: -5(-5)=25

--------------------------Add.

[tex]4x^2-20x+25[/tex]

Answer:

Part a) 0.20 revolutions per foot of distance traveled

Part b) The slope of the graph is [tex]m=5\frac{ft}{rev} [/tex]

Step-by-step explanation:

step 1

Find the slope

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Let

x ----> the number of revolutions

y ----> the distance traveled in feet

we have the point (2,10) ----> see the graph

Find the value of the constant of proportionality k

[tex]k=y/x=10/2=5\frac{ft}{rev} [/tex]

Remember that in a direct variation the constant k is equal to the slope m

therefore

The slope m is equal to

[tex]m=5\frac{ft}{rev} [/tex]

The linear equation is

[tex]y=5x[/tex]

step 2

How many revolutions does Charmaine make per foot of distance traveled?

For y=1

substitute in the equation and solve for x

[tex]1=5x[/tex]

[tex]x=1/5=0.20\ rev[/tex]