Use trigonometry to find QP. Round to the nearest tenth.

Answer:

\( {48 \: m}^{3} \)

Step-by-step explanation:

First, we can find the area of the base:

\(a(base) = {s}^{2} = {6}^{2} = 36 \: {m}^{2} \)

Now, we can find the volume:

\(v = \frac{1}{3} \times a(base) \times h = \frac{1}{3} \times 36 \times 4 = 48 \: {m}^{3} \)

Answer:

x = 21

Step-by-step explanation:

ABF is a right angle and m∠EBA + m∠EBF = m∠ABF

3x - 1 + x + 7 = 90 add like terms

4x + 6 = 90 subtract 6 from both sides

4x = 84 divide both sides by 4

x = 21

Answer: The area and perimeter of the square whose length of one side is of p cm are p^2 square cm and 4p cm respectively.

Step-by-step explanation: We know,

Area of the square = p^2 where p is the side of the square.

The perimeter of the square = 4p cm where p is the side of the square.

thus, The area and perimeter of the square whose length of one side is of p cm are p^2 square cm and 4p cm respectively.

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True, the given function f has an inverse.

A function that can reverse into another function is known as an inverse function or anti-function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y.  Inverse functions f and g result in f(x) = y if and only if g(y) = x.

Under the given condition, we can define the function g on the set of the images  {b | b = f(a), a belongs to A}  in a way

   g(b) = a,   if f(a) = b.

This function is defined correctly on this set and is the inverse function to f.

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Now we know PR∥QX , according to construction with transversal line TX.

∠PTS=∠QXS (Alternate angle)

In △PTS and △QSX

∠PTS=∠QXS (Alternate angle)

∠PST=∠QSX(vertically opposite angles)

PS=SQ(S is mid point of PQ)

△PTS≅△QSX(AAS rule)

So, TP=QX(CPCT)

As we know, TP=TR (T is midpoint)

Hence, TR=QX

Now, in quadrilateral TSQR

TS∥QR

Hence proved.

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Answer:

24

Step-by-step explanation:

By BODMAS rule,

[ ( 15 + 1 ) / 2 - 4 ] * 6

= [ 16 / 2 - 4 ] * 6

= [ 8 - 4 ] * 6

= 4 * 6

= 24

Based on the information given, the value of the equation will be -48.

From the information given, the expression is given as:

= (15+1)/2-4]*6

We'll solve the bracket first.

= (15+1)/2-4]*6

= (16 / 2 - 4) × 6

= (16/-2) × 6

= -8 × 6

= -48

In conclusion, the value of the equation will be -48.

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Answer: The answer is A. 3/5

Step-by-step explanation:

Cos is the X coordinate given in parenthesis.

The X coordinate is 0.6, so find the fraction which equals 0.6.

3/5 = 0.6

Check the picture below.

a) Composite function fog(x) = 3/(x+3)

b) Domain of fog(x) in interval notation = (-∞,-3)∪(-3,∞)

A function is a process or a relation that associates each element 'a' of a set A , to a single element 'b' of another set B.

Given functions,

f(x) = x/(x+2)

g(x) = 6/x

a) (fog)(x) = f(g(x))

= f(6/x)

= (6/x)/((6/x) + 2)

= 6/x((6/x) + 2)

= 6/(6 + 2x)

= 3/(x+3)

fog(x) = 3/(x+3)

b) Domain of (fog)(x)

y = 3/(x+3)

For domain y = 0

⇒ x+3  = 0

⇒ x  = -3

But the function gets undefined for x = -3

So, Domain x ≠ -3

⇒ x > -3 or x < -3

Domain set Interval Notation : (-∞,-3)∪(-3,∞)

Hence, value of composite function

fog(x) = 3/(x + 3)

Domain of fog(x) : (-∞,-3)∪(-3,∞)

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Answer:

4(3+5). the sum in the parenthesis is 8 and the gcf is four. 4*8=32

Step-by-step explanation:

The required expression that is equivalent to 5z  is √[5z]², [5z]²/5z, and 5z + 1 - 1.

Given that,
To create 3 expressions equivalent expression to 5z,

The algebraic expression consists of constant and variable. eg x, y, z, etc.

Here,
The expression can be created by applying the mathematical operation to the parent expression such as by squaring, division and multiplication, and so on.
The equivalent expression is deduced as, √[5z]², [5z]²/5z, and 5z + 1 - 1.

Thus, The required expression that is equivalent to 5z  is √[5z]², [5z]²/5z, and 5z + 1 - 1.

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The sequence is will always have even numbers, is hence proved.

Given, the quadratic sequence is: 44:52:64:80

Sequences with a term are known as quadratic sequences. They can be distinguished by the fact that the first differences between terms are not equal but the second differences between terms are. Utilizing the term sum in an arithmetic progression formula, the sum of even numbers formula is achieved. The equation is Sum of Even Numbers Formula = n(n+1), where n is the total number of terms in the series.

The formula is: Tₙ = 2n² ₊ 2n  ₊ 40

take 2 common

Tₙ = 2(n² ₊ n  ₊ 20)

in other words n² ₊ n  ₊ 20  = y

therefore , Tₙ = 2y

which by definition makes Tₙ an even number at all times.

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The percentage change in Corey's average in math is -5.21%

Here, we want to get the percentage of change

Mathematically, we can use the formula below;

From the question, the new value is 91, while the old value is 96

Substituting these values in the equation above, we have;

The steps in solving the given expression shows that the result is:

0.92 * 10²

The expression is given as:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

The steps that Maggie followed are:

Step 1: Rewrite the given expression:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

Step 2: Divide the coefficients:

The coefficient of the numerator (6.89) is divided by the coefficient of the denominator (7.5) to get:

6.89 / 7.5 = 0.9186667.

Step 3: Divide the powers of 10:

This is done by subtracting the exponent of the denominator 10⁻⁶ from the exponent of the numerator 10⁻⁴ to get: 10²

Step 4: Combine the results:

This gives:

0.9186667 * 10²

Step 5: Simplify the coefficient:

She rounded the coefficient (0.9186667) to two decimal places, resulting in 0.92.

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Answer:

1) 7/8     8/7

2) 4.4

3) 3.7

4) 2.8

Step-by-step explanation:

Length of bottom side of Figure A: 8 cm

Length of bottom side of Figure B: 7 cm

From Figure A to Figure B, the scale factor is 7/8.

7/8

8/7

5 × 7/8 = 35/8 = 4.375

4.4

3.2 × 8/7 = 3.657...

3.7

3.2 × 7/8 = 2.8

2.8

Answer:

Time taken by Duke on the highway = 3 hours

Time spent on the construction = 6 hours

Time spent in the city = 2 hours

Step-by-step explanation:

Speed by which Duke travels a distance on highway \(d_1\) = 60 mph

Let the time taken to travel on highway = \(t_1\) hours

Distance traveled = \(60t_1\) miles

Speed in the city = 40 mph

Let the time taken = \(t_2\) hours

Distance traveled in the city = \(40t_2\) miles

Speed on the construction = 20 mph

Let the time spend on the construction = \(t_3\) hours

Distance traveled on the construction = \(20t_3\) miles

Since, total distance covered = 380 miles

\(d_1+d_2+d_3=60t_1+40t_2+20t_3\)

He spends one half the time on the highway as he does on the construction,

\(t_3=2t_1\)

Total time spent in the trip = 11 hours

Therefore, \(t_1+t_2+t_3=11\)

\(t_1+t_2+2t_1=11\)

\(t_2=11-3t_1\)

From equation (1),

\(60t_1+40(11-3t_1)+20(2t_1)=380\)

\(60t_1-120t_1+40t_1+440=380\)

\(440-20t_1=380\)

\(20t_1=440-380\)

\(t_1=\frac{60}{20}\)

\(t_1=3\) hours

\(t_2=11-3t_1=2\) hours

\(t_3=2t_1=6\) hours

Therefore, time taken by Duke on the highway = 3 hours

Time spent on the construction = 6 hours

Time spent in the city = 2 hours

Answer:

We conclude that there is difference in the proportion of deaths between the 2 groups.

Step-by-step explanation:

We are given that among 2823 drivers not wearing seat belts, 31 died as a result of injuries, and among 7765 drivers wearing seat belts 16 were killed.

Let \(p_1\) = proportion of deaths when drivers were not wearing seat belts.

\(p_2\) = proportion of deaths when drivers were wearing seat belts.

So, Null Hypothesis, \(H_0\) : \(p_1=p_2\)      {means that there is no difference in the proportion of deaths between the 2 groups}

Alternate Hypothesis, \(H_A\) : \(p_1\neq p_2\)     {means that there is difference in the proportion of deaths between the 2 groups}

The test statistics that would be used here Two-sample z test for proportions;

                          T.S. =  \(\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }\)  ~ N(0,1)

where, \(\hat p_1\) = sample proportion of deaths when drivers were not wearing seat belts = \(\frac{31}{2823}\) = 0.011

\(\hat p_2\) = sample proportion of deaths when drivers were wearing seat belts = \(\frac{16}{7765}\) = 0.002

\(n_1\) = sample of drivers not wearing seat belts = 2823

\(n_2\) = sample of drivers wearing seat belts = 7765

So, the test statistics  =  \(\frac{(0.011-0.002)-(0)}{\sqrt{\frac{0.011(1-0.011)}{2823}+\frac{0.002(1-0.002)}{7765} } }\)

                                       =  4.438

The value of z test statistics is 4.438.

Now, at 5% significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.

Since our test statistic doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that there is difference in the proportion of deaths between the 2 groups.

Also, Margin of error (E) =  \(1.96 \times \sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} }\)

                                        =  \(1.96 \times \sqrt{\frac{0.011(1-0.011)}{2823}+\frac{0.002(1-0.002)}{7765} }\)

                                        =  0.00397

On average, someone who buys a ticket can expect to make a profit of $2.43 as the expected value for someone who buys a ticket is $2.43.

It is the average amount of money that an individual can expect to win or lose on an investment. It is calculated by multiplying the probability of each outcome by its payoff and then adding the expected values of all outcomes.

In this case, the probability of winning= 1/737

and the payoff = $1800 - $8

= $1792.

The expected value (EV) is calculated by multiplying the probability of each outcome by its payoff.

EV = (1/737) x (1792)

EV = $2.43

Therefore, the expected value for someone who buys a ticket is $2.43. This means that, on average, someone who buys a ticket can expect to make a profit of $2.43.

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Solution

For this case we have the following values:

50, 55, 56, 57

68, 69, 73, 74,

74, 75, 76, 76,

78, 79, 82, 84

Then we can find the mean like this:

And then since we have 16 values we can find the medain with the following operation:

Median = (74+74)/2 = 74

Then the correct answer is:

b) Median = 74 and Mean = 70.38

Answer:

B. The company should have 8 production runs each year.

Step-by-step explanation:

From the given information:

A paint manufacturer has a uniform annual demand for 16,000 cans of automobile primer

It costs $4 to store one can of paint for one year

$500 to set up the plan for production of the primer

Let x be the number of cans of paint produced during each production run

Let y be the number of production runs.

If the total storage and setup cost is C = 500y + 2c

and cy = 16000

Then c = 16000/y

From;

C = 500y + 2c

Replacing c with 16000/y,  we have;

C = 500y + 2(16000/y)

C = 500y + 32000/y

in order to minimize the total storage and setup costs  \(C_{min} = C\)

Therefore \(\dfrac{dc}{dy}=0\)

⇒ 500 - 32000/y² =0

y² = 32000/500

y² = 320/5

y² = 64

y = (√64)

y = 8

Therefore; The company should have 8 production runs each year in order to minimize the total storage and setup costs

Answer:

..........

Step-by-step explanation:

.....????......Ummmmm

Answer:

D

Step-by-step explanation:

just took that test

Answer:

\(\cos G=\dfrac{2}{3}\)

\(\csc E=\dfrac{3}{2}\)

\(\cot G=\dfrac{2}{\sqrt{5}}\)

Step-by-step explanation:

If the right angle of right triangle EFG is ∠F, then EG is the hypotenuse, and EF and FG are the legs of the triangle. (Refer to attached diagram).

Given ΔEFG is a right triangle, and EG = 6 and FG = 4, we can use Pythagoras Theorem to calculate the length of EF.

\(\begin{aligned}EF^2+FG^2&=EG^2\\EF^2+4^2&=6^2\\EF^2+16&=36\\EF^2&=20\\\sqrt{EF^2}&=\sqrt{20}\\EF&=2\sqrt{5}\end{aligned}\)

Therefore:

\(\hrulefill\)

To find cos G, use the cosine trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle G, the adjacent side is FG and the hypotenuse is EG.

Therefore:

\(\cos G=\dfrac{FG}{EG}=\dfrac{4}{6}=\dfrac{2}{3}\)

\(\hrulefill\)

To find csc E, use the cosecant trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cosecant trigonometric ratio} \\\\$\sf \csc(\theta)=\dfrac{H}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle E, the hypotenuse is EG and the opposite side is FG.

Therefore:

\(\csc E=\dfrac{EG}{FG}=\dfrac{6}{4}=\dfrac{3}{2}\)

\(\hrulefill\)

To find cot G, use the cotangent trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cotangent trigonometric ratio} \\\\$\sf \cot(\theta)=\dfrac{A}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle G, the adjacent side is FG and the opposite side is EF.

Therefore:

\(\cot G=\dfrac{FG}{EF}=\dfrac{4}{2\sqrt{5}}=\dfrac{2}{\sqrt{5}}\)

Answer:

maybe this will help

Step-by-step explanation:

The area of the rhombus, obtained from the dimensions, of the diagonals, found from the trigonometric of sines of the angle can be presented as follows;

Area = 8·√3

The area of a plane figure is the two dimensional space occupied by the figure on a plane.

The measure of the angle ABC, m∠ABC = 60°

The length of the segment AE = 2 units

The diagonals of a rhombus bisect each other at right angles, and the right angles through which they pass, therefore;

BE = ED, m∠AEB = 90°

m∠ABE = 30°

sin(30°) = AE/AB

sin(30°) = 2/AB

AB = 2/(sin(30°)) = 4

AB = 4

BE = √(4² - 2²) = √(12) = 2·√3

Therefore; AC = 2 + 2 = 4

BD = 2·√3 + 2·√3 = 4·√3

The area of a rhombus = (1/2) × The product of the length of the diagonals

Therefore;

Area of the rhombus = (1/2) × (4·√3) × 4 = 8·√3

The area of the rhombus = 8·√3

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The median margin for victory will be 1.89.

The median of the data is the value of the middle observation discovered after the data are organized in ascending order. The median is useful in situations where it is difficult to express anything while taking into account all of the data.

One of the easy to calculate statistical summary metrics is the median. Since it bases its value on the data that is in the middle of a sequence, the median is often referred to as the place average.

Given Data:-

1.89,2.32,0.08,4.74,0.30

Mean margin of victory= 1.866

Median margin of victory= 1.89

So the median margin for victory will be 1.89.

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Complete question -

Answer:

It takes takes them 31.67 secs to meet after Person A starts walking

OR

34.67 secs after Person B starts walking

Step-by-step explanation:

First, we will find the perimeter of the rectangle

From,

Perimeter of rectangle = 2 (\(l\) + \(b\))

Where \(l\) is the length

and \(b\) is the breadth

From the question, \(l\) = 100m

and \(b\) = 50m

Hence,

Perimeter of the rectangle = 2 (100+50)

= 2(150) = 300m

Hence, the perimeter of the rectangle is 300m

This is the total distance that will be covered by both persons by the time they meet.

Let the distance covered by person A be \(S_{1}\)

and the distance covered by person B be \(S_{2}\)

We can write that

\(S_{1}\) + \(S_{2}\) = 300m

Velocity of person A, \(V_{A}\) = 4 m/s

and velocity of person B, \(V_{B}\) = 5 m/s

From the question, Person A starts walking 3 seconds after person B,

This means, if person A spends \(t\) secs before they meet, then person B would spend (3 + \(t\)) secs.

For Person A,

Velocity = 4 m/s

Time = \(t\) secs

Distance = \(S_{1}\)

From,

\(Velocity = \frac{Distance}{Time}\)

Then,

\(Distance = Velocity \times time\)

\(S_{1} = 4 \times t\)

\(S_{1} = 4t\) ...... (1)

For Person B

Velocity = 5 m/s

Time = (t + 3) secs

Distance = \(S_{2}\)

Also, from

\(Distance = Velocity \times time\)

\(S_{2} = 5 \times (3+t)\)

\(S_{2} = 5(3+t)\) ...... (2)

Recall that, \(S_{1}\) + \(S_{2}\) = 300m

Then, \(S_{2}\) = 300m - \(S_{1}\)

We can then write that,

300m - \(S_{1}\) \(= 5(3+t)\)

Then,

\(S_{1} = 300 - 5(3+t)\) ..... (3)

Equating equations (1) and (3), we get

\(300 - 5(3+t) = 4t\)

\(300 - 15 -5t = 4t\\9t = 285\\t = \frac{285}{9}\\\)

\(t = 31.67 secs\)

This is the time spent by Person A

Hence, it takes takes them 31.67 secs to meet after Person A starts walking OR

34.67 secs after Person B starts walking

Answer:

I mistakenly rated Abdulazeez10's answer 2 stars because I thought he mixed up his variables, but I was actually the one who mixed up my variables.

Step-by-step explanation:

Sorry, Abdulazeez10 :( I can't change my rating, but just so everyone else knows, his answer is 100% correct!

Answer:

39.1 megabytes

Step-by-step explanation:

Percentages are out of a hundred, so 15.7% is 15.7 out of 100, aka 15.7/100, which is 0.157.

Now, you just need to multiple this number by 249 megabytes to get 0.157 * 249 = 39.093 which rounds to 39.1