3. the letters r, x, b, and q are all a. syllables. b. consonants. c. accented. d. vowels.

The shadow of a 400ft tall building is increasing at a rate of 100ft /hr

The angle of elevation of the sun is decreasing at a rate of 0.25 rad/hr

The height of the building is 400 ft tall

We need to find the rate at which the shadow is increasing

d/dθ = 1/4 rad/hr at θ = π/4

400/x = tan θ

x = 400/ tan θ

Upon derivation with t

dx/dt = 400 sec²θ/tan ²θ dθ/dt

at θ = π/4 and dθ/dt = 0.25 rad/hr

dx/dt = 400 (2x3)x0.25

dx/dt = 100ft/hr

Therefore, the shadow is increasing at the rate of 100ft/hr

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Answer:

Relation 1 & 2 are functions

Relation 3 & 4 are not functions

Step-by-step explanation:

For a relation to be a function every x must have one and only one y

This is not true for relation 3 which has 2 y's at x = m and 2 y's at x = v

This is also not true for relation 4 which has 2 y's at x = 4

The requirement is represented by the inequality y≥3x, and he caught at least 21 fish last year.

In mathematics, an inequality is a connection between two expressions or values that are not equal to each other. Inequality originates from a lack of equilibrium. To solve an inequality, isolate the variable on one side from the other constants. To do so, use opposing procedures to modify the inequality. To begin, separate the x by multiplying each side by two. Whatever you do on one side must equally be done to the other.

Here,

Let y is fishes caught in this year and x be the fishes caught in last year.

y≥3x

63≥3x

x≥21

The inequality that represent the condition is y≥3x and he caught at least 21 fishes last year.

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Answer:

h (7, - 16 )

Step-by-step explanation:

given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint M is

M = ( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] ) ← midpoint formula

let the coordinates of h be (x, y )

here (x₁, y₁ ) = g (15, 4 ) and (x₂, y₂ ) = h (x, y )

use the midpoint formula on g, h and equate to the coordinates x (11, - 6 )

[tex]\frac{15+x}{2}[/tex] = 11 ( multiply both sides by 2 )

15 + x = 22 ( subtract 15 from both sides )

x = 7

and

[tex]\frac{4+y}{2}[/tex] = - 6 ( multiply both sides by 2 )

4 + y = - 12 ( subtract 4 from both sides )

y = - 16

then

coordinates of h = (7, - 16 )

If a number is assumed then multiply it by 3 and added the result to 1 then its algebraic equation will be 3x+1

According to the question

Assume a Number and multiply it by 2.

To Find:

to write it algebraically

Let the number that was asked to think to be x.

Then it is multiplied by 2 which becomes 2x.

Now the number is multiplied by 3

So, x multiplied by 3 will become 3x.

Then, 3x is added to 1

So, we can write it as 3x+1

Therefore, the equation can be written as 3x+1 algebraically.

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Answer:

A, 74°

Step-by-step explanation:

Both of the angles are named y, so this means they are the same/have the same value!

Remember, all triangles equal 180°

To find y...

First, we subtract 32° from 180° to see what the Y angles total up to!

180° - 32° = 148°

the two y angles on the left side of the triangle equal 148°, but what does just one of them equal?

Divide by 2 to find out!

148° ÷ 2 = 74°

one y angle = 74°

y = 74°

The various reasons why rows 4 to 7 could be missing are mentioned.

Rows 4 to 7 may be missed for the following reasons:

Thus, these are various reasons why rows 4 to 7 could be missing.

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The particular solution that satisfies the given initial condition is y = 1. This is the solution to the given initial-value problem.

To solve this initial-value problem, we must first note that the given differential equation is homogeneous. This means that if y is a solution to the given equation, then so is cy, where c is an arbitrary constant. Thus, the first step in solving this initial-value problem is to find the general solution of the homogeneous equation. To do this, we can use the method of separation of variables.

This method involves separating the variables x and y on opposite sides of the equation, and then integrating both sides with respect to their respective variables. Doing this yields:

∫xy2 dy = ∫(y3 − x3) dx

Integrating both sides of the equation with respect to y yields:

y3x2/3 + C1 = x4/4 + C2

where C1 and C2 are arbitrary constants. Rearranging this equation yields:

y3 = 4x4/3 − 4C2x2/3 + 4C1

Now, we can use the given initial condition, y(1) = 1, to determine the value of the arbitrary constants. Substituting x = 1 and y = 1 into the equation yields:

13 = 4/3 − 4C2/3 + 4C1

Solving for C1 and C2 yields:

C2 = 0, C1 = 3/4

With the arbitrary constants determined, we can now find the general solution of the homogeneous differential equation. Substituting the values of C1 and C2 into the equation yields:

y3 = 4x4/3 − 3/4

This equation is the general solution of the given homogeneous differential equation. To solve the initial-value problem, we must now find the particular solution that satisfies the given initial condition. To do this, we can substitute the initial condition, y(1) = 1, into the general solution to obtain:

13 = 4/3 − 3/4

Solving for y yields:

y = 1

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Answer: Therefore, the range of values of x for which (3x-7)(x-5) ≥x+5 is x<5 or x>5, or x∈(-∞,5)∪(5,∞).

Step-by-step explanation: To find the range of values of x for which (3x-7)(x-5) ≥x+5, we first need to find the values of x for which the inequality is satisfied. We can do this by setting each factor equal to 0 and solving for x.

Setting (3x-7) equal to 0 gives us x=7/3. Setting (x-5) equal to 0 gives us x=5.

Next, we need to consider the signs of the factors. If both factors are positive or both are negative, the inequality will be satisfied. If one factor is positive and the other is negative, the inequality will not be satisfied.

For x<5, both factors are negative, so the inequality is satisfied. For x>5, both factors are positive, so the inequality is satisfied.

Therefore, the range of values of x for which (3x-7)(x-5) ≥x+5 is x<5 or x>5, or x∈(-∞,5)∪(5,∞).

The ratio of junior to adult = 6/5

What is proportion?

An equality between two ratios. According to proportion, if 2 sets of given numbers area unit increasing or decreasing within the same quantitative relation, then the ratios area unit aforesaid to be directly proportional to every different.

Main body:

Given - data in the question

To find answer the question

Solution - Let no of junior, children and adults be x, y, z respectively.

Now, ratio of junior to children = 1/3

So, x = 3y

Ratio of children to adult = 5/2

So, 5y = 2z

.(2)

So, from (1) we get, y = x / 3

So, 5x / 3 = 2z

⇒5x = 6z

⇒ x/z=6/5

Hence, the ratio of junior to adult = 6/5

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The amount of fencing needed to surround the perimeter of the picnic area of the park is 107 yards. Hence, the second option is the right choice.

In the question, we are informed that the triangle KLM, represents a section of a park set aside for picnic tables. We are also informed that the picnic area will take up approximately 400 square yards of the park.

We are asked for the amount of fencing needed to surround the perimeter of the picnic area of the park.

We know the area of a triangle can be found using the trigonometric area formula, Area = (1/2)ab sin C.

Using this in the given triangle KLM, we get:

Area = (1/2)(KL)(KM)(sin K),

or, 400 = (1/2)(KL)(45)(sin 25°),

or, KL = (400*2)/(45*sin 25°) = 800/(45*0.42262) = 800/19.017822 = 42.0658 ≈ 42 yd.

Thus, we get KL = 42 yards.

Now, the perimeter of the picnic area = the perimeter of the triangle KLM = KL + LM + MK = 42 + 20 + 45 yards = 107 yards.

Thus, the amount of fencing needed to surround the perimeter of the picnic area of the park is 107 yards. Hence, the second option is the right choice.

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Answer: b

Step-by-step explanation:

The measure of minor arc is 108°

Pentagon:

                  A pentagon is a geometrical shape, which has five sides and five angles. Here, “Penta” denotes five and “gon” denotes angle.

If a pentagon is regular, then all the sides are equal in length, and five angles are of equal measures. If the pentagon does not have equal side length and angle measure, then it is known as an irregular pentagon.

The sum of all the interior angles for a regular pentagon is 540°.

hence,

           Value of each interior angle = 540°/5

                                                       = 108°

From figure,

                    we have to find ∠AED

we can see ∠AED is one of the internal angle of pentagon.

so,

         ∠AED = 108°

The measure of minor arc is 108°

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Answer:

You must babysit for 8 weeks to earn enough money to buy the new gaming chair.

Step-by-step explanation:

To determine how many weeks you must babysit to earn enough money to buy the new gaming chair, we need to write and solve an equation that represents the relationship between the money you have saved, the money you earn each week, and the cost of the gaming chair.

First, we can let w represent the number of weeks you must babysit. Then, we can set up the equation:

Earnings + Savings = Total Cost

Substituting the known values into the equation, we have:

Earnings + Savings = Total Cost

$37.50w + $155.95 = $455.95

To solve the equation, we can first subtract $155.95 from both sides of the equation:

$37.50w + $155.95 - $155.95 = $455.95 - $155.95

$37.50w = $300.00

Next, we can divide both sides of the equation by $37.50 to find the value of w:

$37.50w / $37.50 = $300.00 / $37.50

w = 8

Therefore, you must babysit for 8 weeks to earn enough money to buy the new gaming chair.

Answer:

is your a nswer in it's simplest form

Step-by-step explanation:

Abdullah and Amna bought a car for $9000, Abdullah paid 45% of the $9000 and Amna paid

the rest.

b) Write down the ratio of the payments Abdullah: Amna in it's simplest form.

Abdullah paid 45% means Amna paid 55% (100% - 45% = 55%), so the Abdullah : Amna ratio is 45 : 55, let's simplify by dividing the two parts by 5 and we will have the ratio in its simplest form.

45 : 55

let's simplify

9 : 11 is your answer

Answer: 30

Step-by-step explanation:

6 divided by 1/5 is the same as 6/1 * 5/1

6/1 * 5/1 = 30/1

=30

30/5 = 6

Answer:

30

Step-by-step explanation:

There are a couple of ways to do this.  One way is the traditional way.

[tex]\frac{6}{1}[/tex]÷[tex]\frac{1}{5}[/tex]  Then multiply by the reciprocal

[tex]\frac{6}{1}[/tex] x [tex]\frac{5}{1}[/tex] = [tex]\frac{30}{1}[/tex] = 30

Another way that is more intuitive:

[tex]\frac{6}{1}[/tex]÷[tex]\frac{1}{5}[/tex]  Get a common denominator of 15

[tex]\frac{90}{15}[/tex]÷[tex]\frac{3}{15}[/tex] = [tex]\frac{\frac{90}{3} }{\frac{15}{15} }[/tex]= [tex]\frac{30}{1}[/tex] = 30

Answer:

-----------------------------------

Perpendicular lines have opposite-reciprocal slopes.

Given line has a slope of - 1/3, so the perpendicular slope is 3.

The matching choice is B.

Answer:

[tex]\textsf{B.} \quad y=3x+2[/tex]

Step-by-step explanation:

If two lines are perpendicular to each other, their slopes are negative reciprocals.

The negative reciprocal of a number is -1 divided by the number.

Given equation:

[tex]y=-\dfrac{1}{3}x+4[/tex]

The slope of the given equation is -¹/₃

Therefore, the slope of the perpendicular line is:

[tex]\implies -1 \div -\dfrac{1}{3}=-1 \times -3=3[/tex]

Therefore, the equation of the line that is perpendicular to the given equation is:

Answer:

1w

Step-by-step explanation:

I want points

If 4 cartons are selected at random, the the probability that exactly 3 of them are the deluxe model is 0.3231.

A shipment of 16 televisions contains 7 regular and 9 deluxe models.

The manufacturer failed to mark the model designation on the cartons.

If 4 cartons are selected at random, then we have to find the probability that exactly 3 of them are the deluxe model.

Now 4 cartons selected at random from 16 cartoons of televisions can be selected in ways = [tex]^{16}C_{4}[/tex]

Now simplifying

4 cartons selected at random from 16 cartoons of televisions can be selected in ways = [tex]\frac{16!}{4!12!}\\[/tex]

After simplification

4 cartons selected at random from 16 cartoons of televisions can be selected in ways = 1820

Now 3 of them are the deluxe model, can be selected in ways = [tex]^{9}C_{3}[/tex]

Now simplifying

3 of them are the deluxe model, can be selected in ways = [tex]\frac{9!}{3!6!}\\[/tex]

After simplification

3 of them are the deluxe model, can be selected in ways = 84

Remaining 1 selected from 7 regular model in ways = [tex]^{7}C_{1}[/tex]

Remaining 1 selected from 7 regular model in ways = 7

Therefore the probability that exactly 3 of them are the deluxe model = 84*7/1820

The probability that exactly 3 of them are the deluxe model = 0.3231

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Answer:

a)

Step-by-step explanation:

additions do not work in general that way when we consider a mixture of positive and negative numbers.

e.g.

x = 3, y = -5

|3 + -5| >= |3| + |-5|

|-2| >= 3 + 5

2 >= 8

is definitely not true.

so, for positive/negative number mixtures a) is wrong.

b) works because

if x >= y, then |x - y| >= |x| - |y|. equal when x and y > 0. larger when x and/or y < 0. correct

if x < y, then |x - y| >= |x| - |y|. larger when x and y > 0.

equal when x and/or y < 0.

c) and d) work because the signs don't change anything. either the result is positive anyway, or if negative just gets converted to the positive result.

From the triangle, the values of a and b are 5.1 units and 4.4 units respectively

You should know that a triangle is a polygon with three sides, three vertices, three angles  whose sum of angles is 180⁰

Using the trig ratio of Cosine

CosY=Adjacent/Hypothenuse

cos31=w/6

Cross multiplying we have

6*cos31=w

w=5.1 units

Then to find b, note that /VW/=/VY/=5.1

<VYX=<VWX............... base angles of isosceles triangle  WVY

Using cosine again from trig.

Cos31=b/5.1

5.1*cos31=b

simplify to get b=4.4 units

Therefore b= 4.4 units  

a=90-31       (remaining 2 angles of a right angled triangle)

a=59⁰

In conclusion, the value of a=59⁰ and the value of b=4.4 units

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Answer:

1.5A

Step-by-step explanation:

To find the current that the motor will require, we can use the formula for power, which is given by:

P = E * I

where P is the power, E is the voltage, and I is the current. Substituting the values for the power and voltage into the formula, we get:

180 = 120 * I

Dividing both sides of the equation by 120, we get:

1.5 = I

Therefore, the current that the motor will require is 1.5 amps.

Step-by-step explanation:

The formula for power is P = E x I, so the current required by the motor is equal to the power divided by the voltage. In this case, the current required by the motor is 180 watts / 120 volts = 1.5 amps.

Answer:

Step-by-step explanation:

a. 40 because 25 percent is 1/4th and 160 times 1/4=40

b. 78  because 200 times 39/100 is 78

c. 48 because 32 times 150/100=48

d. 26 because if it is 50 percent it is 1/2 of a number so just multiply

e. 15

f. 70 percent, simplify both numbers to the lowest number possible equal to 21/30 so 7/10 and that is 70 percent

The mixed fraction in simplest improper fraction is 31/5.

For the stated mixed fraction;

6 1/5

To convert this in improper fraction;

= (6x5 + 1)/5

= (30 + 1)/5

= 31/5

This, the mixed fraction in simplest improper fraction is 31/5.

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The mean, median, mode and the mean of the extra ten rolls are  

 2.96,2.5,1 and 2.9 respectively  

The mean represents the average of the dataset, the median represents the middle value of the data set, and the mode represents the repeated value in the dataset.

Using the given information we construct the following table

Score     frequency           Cumulative Frequency  (frequency*score)

1                 15                          15                                      15

2                10                          25                                     20

3                7                            32                                      21

4                 5                           37                                      20

5                 6                           43                                      30

6                 7                           50                                      42

thus N= 50 (even) The Median is the average of the 25th and 26th observations. The 25th and 26th observations corresponds to the value 3.

The Median is = 2.5

The modal score = 1

Mode = 3×(median) – 2×(mean)

mean = 2.96

The mean score for the 60 roles is 2.95×60 = 148+sum of the extra ten

                                       sum of the extra ten =29

               Thus mean of the extra ten roles is        

                                                                       = 29/10

                                                                       = 2.9

Hence the mean, median, mode and the mean of the extra ten rolls are  

 2.96,2.5,1 and 2.9 respectively

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The sample with more observations and/or more variability in the data will generally have a larger chi-square test statistic.

Chi-square test statistic is a measure of how well a set of observed data fits a theoretical model. The larger the sample size and the more variability in the data, the more likely it is that the theoretical model won't fit the data perfectly. Therefore, the larger sample size and variability in the data will lead to a larger chi-square test statistic.

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