prove:
[tex] \frac{1}{secθ + \tanθ} - \frac{1}{cosθ} = \frac{1}{cosθ} - \frac{1}{secθ - tanθ} [/tex]
​

Answer:

The area of the house is A. 1,108

Answer:

[tex]p(x)[/tex] and [tex]q(x)[/tex] have the same domain and the same range.

Step-by-step explanation:

[tex]p(x) = 6-x[/tex] and

[tex]q(x) = 6x[/tex]

First of all, let us have a look at the definition of domain and range.

Domain of a function [tex]y =f(x)[/tex] is the set of input value i.e. the value of [tex]x[/tex] for which the function [tex]f(x)[/tex] is defined.

Range of a function [tex]y =f(x)[/tex] is the set of output value i.e. the value of [tex]y[/tex] or [tex]f(x)[/tex] for the values of [tex]x[/tex] in the domain.

Now, let us consider the given functions one by one:

[tex]p(x) = 6-x[/tex]

Let us sketch the graph of given function.

Please find attached graph.

There are no values of [tex]x[/tex] for which p(x) is not defined so domain is All real numbers.

So, domain is [tex](-\infty, \infty)[/tex] or [tex]x\in R[/tex]

Its range is also All Real Numbers

So, Range is [tex](-\infty, \infty)[/tex] or [tex]x\in R[/tex]

[tex]q(x) = 6x[/tex]

Let us sketch the graph of given function.

Please find attached graph.

There are no values of [tex]x[/tex] for which [tex]q(x)[/tex] is not defined so domain is All real numbers.

So, domain is [tex](-\infty, \infty)[/tex] or [tex]x\in R[/tex]

Its range is also All Real Numbers

So, Range is [tex](-\infty, \infty)[/tex] or [tex]x\in R[/tex]

Hence, the correct answer is:

[tex]p(x)[/tex] and [tex]q(x)[/tex] have the same domain and the same range.

Answer:

z=65

Step-by-step explanation:

supplementary angles means sum of those angles is 180 degrees

so,

z+z+50=180

2z=130

z=65

I did the best I could, I'm 12 don't judge me.

Answer:

the probability the die chosen was green is 0.9

Step-by-step explanation:

Given that:

A bag contains two six-sided dice: one red, one green.

The red die has faces numbered 1, 2, 3, 4, 5, and 6.

The green die has faces numbered 1, 2, 3, 4, 4, and 4.

From above, the probability of obtaining 4 in a single throw of a fair die is:

P (4  | red dice) = [tex]\dfrac{1}{6}[/tex]

P (4 | green dice) = [tex]\dfrac{3}{6}[/tex] =[tex]\dfrac{1}{2}[/tex]

A die is selected at random and rolled four times.

As the die is selected randomly; the probability of the first die must be equal to the probability of the second die = [tex]\dfrac{1}{2}[/tex]

The probability of two 1's and two 4's in the first dice can be calculated as:

= [tex]\begin {pmatrix} \left \begin{array}{c}4\\2\\ \end{array} \right \end {pmatrix} \times \begin {pmatrix} \dfrac{1}{6} \end {pmatrix} ^4[/tex]

= [tex]\dfrac{4!}{2!(4-2)!} ( \dfrac{1}{6})^4[/tex]

= [tex]\dfrac{4!}{2!(2)!} \times ( \dfrac{1}{6})^4[/tex]

= [tex]6 \times ( \dfrac{1}{6})^4[/tex]

= [tex](\dfrac{1}{6})^3[/tex]

= [tex]\dfrac{1}{216}[/tex]

The probability of two 1's and two 4's in the second  dice can be calculated as:

= [tex]\begin {pmatrix} \left \begin{array}{c}4\\2\\ \end{array} \right \end {pmatrix} \times \begin {pmatrix} \dfrac{1}{6} \end {pmatrix} ^2 \times \begin {pmatrix} \dfrac{3}{6} \end {pmatrix} ^2[/tex]

= [tex]\dfrac{4!}{2!(2)!} \times ( \dfrac{1}{6})^2 \times ( \dfrac{3}{6})^2[/tex]

= [tex]6 \times ( \dfrac{1}{6})^2 \times ( \dfrac{3}{6})^2[/tex]

= [tex]( \dfrac{1}{6}) \times ( \dfrac{3}{6})^2[/tex]

= [tex]\dfrac{9}{216}[/tex]

∴

The probability of two 1's and two 4's in both dies = P( two 1s and two 4s | first dice ) P( first dice ) + P( two 1s and two 4s | second dice ) P( second dice )

The probability of two 1's and two 4's in both die = [tex]\dfrac{1}{216} \times \dfrac{1}{2} + \dfrac{9}{216} \times \dfrac{1}{2}[/tex]

The probability of two 1's and two 4's in both die = [tex]\dfrac{1}{432} + \dfrac{1}{48}[/tex]

The probability of two 1's and two 4's in both die = [tex]\dfrac{5}{216}[/tex]

By applying  Bayes Theorem; the probability that the die was green can be calculated as:

P(second die (green) | two 1's and two 4's )  = The probability of two 1's and two 4's | second dice)P (second die) ÷ P(two 1's and two 4's in both die)

P(second die (green) | two 1's and two 4's )  = [tex]\dfrac{\dfrac{1}{2} \times \dfrac{9}{216}}{\dfrac{5}{216}}[/tex]

P(second die (green) | two 1's and two 4's )  = [tex]\dfrac{0.5 \times 0.04166666667}{0.02314814815}[/tex]

P(second die (green) | two 1's and two 4's )  = 0.9

Thus; the probability the die chosen was green is 0.9

Answer:

Step-by-step explanation:

Since it's a right angled triangle we can use trigonometric ratios here.

To find FV we use cosine

cos∅ = adjacent / hypotenuse

From the question

FV is the hypotenuse

TV is the adjacent

So we have

cos 43 = TV/FV

FV = TV/ cos 43

TV =53

FV = 53/ cos 43

FV = 72.4683

We have the final answer as

Hope this helps you

Answer:

FV=72.47

Step-by-step explanation:

cos43=adj/hyp.=VT/FV

cos43=53/FV

FV=53/cos43

FV=72.46835= 72.47 rounded to the nearest hundredth

*Correct Question:

Which relationships have the same constant of proportionality between y and x as the equation 3y=27x?

Answer:

A, B, C

Step-by-step explanation:

Given that [tex] 3y = 27x [/tex] , we can simplify to get a proportionality statement that exists between X and y. Thus

[tex] 3y = 27x [/tex]

Divide both sides by 3

[tex] \frac{3y}{3} = \frac{27x}{3} [/tex]

[tex] y = 9x [/tex]

Thus, we can say, y would always be 9 times the quantity of x.

From the options given, examine which options have this proportionality statement as well.

Option A, y = 9x is same as the statement.

Option B, 2y = 18x, conforms to the same statement. If we simply further, we would have y = 9x

Option C, the graph shows that when x = 1, y = 9. This also confirms to the same constant of proportionality in the given equation.

Option D and E do not have same constant of proportionality.

The right options are A, B, and C.

Answer:

Thus percentile lies between 53.3% and 55.6 %

Step-by-step explanation:

First we arrange the data in ascending order . Then find the number of the values corresponding to the given value. Then equate it with the number of observations and x and then multiply it to get the percentile. n= P/100 *N

where n is the ordinal rank of the given value

N is the number of values in ascending order.

The data in ascending order is

0.1 0.2 0.2 0.2 0.3 0.6 0.6 0.6 0.7 0.8 0.8 0.8 0.9 1.3

1.5 1.7 1.9 2.2 2.3 2.3 2.6 2.8 3.3 3.5 5.5 6.1 6.4 6.9 7.5 7.9 8.3 9.8 10.1 11.8 11.9 12.1 12.3 12.7 12.9 13.8 13.8 14.6 14.7 14.8 27.5

Number of observation = 45

4.9 lies between 3.3 and 5.5

x*n = 24 observation x*n = 25 observation

x*45= 24 x*45= 25

x= 0.533 x= 0.556

Thus percentile lies between 53.3% and 55.6 %

Answer:

a,b and d

Step-by-step explanation:

●You can assign a probality based on your judgement and intuition.

●You can also assigni it based on the data of an histogram, in wich you see the frequency of the event you are interested in.

● Then there is the classical method based on mathematical calculations of equaly likely outcomes.

The three methods of assigning probabilities are:

b. intuition

e. relative frequency

d. equally likely outcomes

Probabilities may occasionally be determined by a person's subjective opinion or personal conviction. This approach depends on the individual's perception of an event's probability or intuition. It is crucial to remember that probabilities based on intuition may not always be precise or trustworthy.

With this approach, probabilities are calculated based on the relative frequencies of historical events that have been observed. Probabilities can be calculated based on the relative frequency of different outcomes by gathering data and calculating their frequencies.

This approach makes the supposition that each potential result has an equal likelihood of happening.

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Answer:

1, 7

Step-by-step explanation:

Because the product is 0, either (x-1) or (x-7) is equal to 0. That means that x = 1, or 7

Answer:

20 cm

Step-by-step explanation:

20 cm

8/2 = 4

6/2 = 3

3 and 4 are the sides of the triangle (four triangles in rhombus)

a²+b²=c²

4³+3²=c²

c = 5

5 x 4 = 20

Hope this helped

Answer:

perimeter = 20 cm

Step-by-step explanation:

consider breaking the rhombus into four equal parts.

and that gives you a triangle.

(refer to image attached for more clarification)

let a = 3, b = 4

to get the side c, use Pythagorean theorem = c² = a² + b²

c = sqrt (3² + 4²)

side c = 5

therefore,

perimeter = 4 x sides (c)

perimeter = 4 x 5

perimeter = 20 cm

Answer:

Step-by-step explanation:

50 : 10 = 5 speaks French only

50 -5= 45 the remainder

4/5 * 45= 36 speaks French and English

45 - 36= 9 speaks English only

The number of students who speak:

i) French only = 5 students,

ii) both French and English = 36 students,

iii) English only = 9 students.

Step 1: Find the number of students who speak French only.

Step 2: Find the remainder (students who speak both French and English) after subtracting the French-only speakers.

Step 3: Find the number of students who speak both French and English.

Step 4: Find the number of students who speak English only.

Let's calculate it step by step:

Step 1: Find the number of students who speak French only.

1/10 of 50 pupils speak French only:

French-only speakers = (1/10) * 50 = 5 students.

Step 2: Find the remainder (students who speak both French and English) after subtracting the French-only speakers.

Remaining students = Total students - French-only speakers

Remaining students = 50 - 5 = 45 students.

Step 3: Find the number of students who speak both French and English.

4/5 of the remaining students speak both French and English:

Both French and English speakers = (4/5) * 45 = 36 students.

Step 4: Find the number of students who speak English only.

To find the English-only speakers, subtract the total number of French-only speakers and both French and English speakers from the total number of students:

English-only speakers = Total students - (French-only speakers + Both French and English speakers)

English-only speakers = 50 - (5 + 36) = 50 - 41 = 9 students.

To know more about French:

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Complete question is:

There are 50 pupils in a class. Out of this number, 1/10 speak French only and 4/5 of the remainder speak both French and English. If the rest speak English only, find the number of students who speak​

i) French only,

ii) both French and English,

iii) English only,

Answer:

40.63

Step-by-step explanation:

31.25+9.38= 40.63

Hope this helps

Answer: 40.63

Look at the image for shown work.

Answer:

q =  5000/x  + 6

Step-by-step explanation:

D´= dq/dx  =  - 5000/x²

dq = -( 5000/x²)*dx

Integrating on both sides of the equation we get:

q = -5000*∫ 1/x²) *dx

q = 5000/x + K   in this equation x is the price per unit and q demanded quantity and K integration constant

If when  1006 units are demanded when the rice is 5 then

x = 5     and   q = 1006

1006  =  5000/5 +K

1006 - 1000 = K

K = 6

Then the demand function is:

q =  5000/x  + 6

Answer:

I found the answer on Yahoo

Step-by-step explanation:

P[rains in spain] = 1/9

P[hurricane in hartford & rain in spain] = 0.03*1/9 = A

P[hurricane in hartford & no rain in spain] = 0.02*8/9

P[hurricane in hartford] = 0.03*1/9 + 0.02*8/9 = 0.19/9 = B

P[rain in spain | hurricane in hartford] = A/B = 3/19 <---------

Answer:

0.00114

Step-by-step explanation:

Divide length value by 5280

Answer:

c = 468 / 13

Step-by-step explanation:

If c is the number of cans of soda in each case, we know that the number of cans in 13 cases is 13 * c = 13c, and since the number of cans in 13 cases is 468 and we know that "is" denotes that we need to use the "=" sign, the equation is 13c = 468. To get rid of the 13, we need to divide both sides of the equation by 13 because division is the opposite of multiplication, therefore the answer is c = 468 / 13.

Answer:

468/13 = c

Step-by-step explanation: Further explanation :

[tex]13 \:cases = 468\:cans\\1 \:case\:\:\:\:= c\: cans\\Cross\:Multiply \\\\13x = 468\\\\\frac{13x}{13} = \frac{468}{13} \\\\c = 36\: cans[/tex]

Answer:

x^2 +4y +z = 1

Step-by-step explanation:

Surface consisting of all points P to point (0,1,0) been equal to the plane y =1

given point, p (x,y,z ) the distance from P to the plane (y)

| y -1 |

attached is the remaining part of the solution

Answer:

All units of measurement that are not based on or do not measure mass or weight and volume are incommensurable with kilograms.

Step-by-step explanation:

A measure unit is said to be incommensurable with another if it does not have the same measurement basis with the other measure unit.  For example, a measure in time cannot be measured in kilograms because time is measured in hours, minutes, seconds, days, etc.  But, if a measurement base can be applied to two or more measurement units, then the measurement units are commensurable with the measurement base.

Answer:

2^11

Step-by-step explanation:

since the bases are the same, we can add the exponents

a^b * a^c = a^(b+c)

2^6 * 2^5

2^(6+5)

2^11

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▹ Answer

x = 5

▹ Step-by-Step Explanation

The x-axis and y-axis are labeled on the graph. The x-axis is the horizontal axis. Between 4 and 6, there is a missing number. That number should be 5, leaving us with an x-value of 5 for Point A.

Hope this helps!

CloutAnswers ❁

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Answer:

The x value is 5

Step-by-step explanation:

The x value is the value going across

Starting where the two axis meet, we go 5 units to the right

That is the x value

The normal vector to the plane x + 3y + z = 5 is n = (1, 3, 1). The line we want is parallel to this normal vector.

Scale this normal vector by any real number t to get the equation of the line through the point (1, 3, 1) and the origin, then translate it by the vector (1, 0, 6) to get the equation of the line we want:

(1, 0, 6) + (1, 3, 1)t = (1 + t, 3t, 6 + t)

This is the vector equation; getting the parametric form is just a matter of delineating

x(t) = 1 + t

y(t) = 3t

z(t) = 6 + t

The vector equation for the line through the point (1,0,6) and perpendicular to the plane x+3y+z=5 is v =(1+t)i + (3t)j + (6+t)k

The parametric equations for the line through the point (1,0,6) and perpendicular to the plane x+3y+z=5

The parametric equation of a line through the point A(x, y, z) perpendicular to the plane ax+by+cz= d is expressed generally as:

A + vt where:

A = (x, y, z)

v = (a, b, c) (normal vector)

This can then be expressed as:

s = A + vt

s = (x, y, z) + (a, b, c)t

Given the point

(x, y, z) = (1,0,6)

(a, b, c) = (1, 3, 1)

Substitute the given coordinate into the equation above:

s = (1,0,6) + (1, 3, 1)t

s = (1+t) + (0+3t) + (6+t)

The parametric equations from the equation above are:

x(t) = 1+t

y(t) = 3t

z(t) = 6+t

The vector equation will be expressed as v = xi + yj + zk

v =(1+t)i + (3t)j + (6+t)k

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Answer:

There is a positive correlation between X and Y.

Step-by-step explanation:

The estimated regression equation is:

[tex]\hat Y=20X+200[/tex]

The general form of a regression equation is:

[tex]\hat Y=b_{yx}X+a[/tex]

Here, [tex]b_{yx}[/tex] is the slope of a line of Y on X.

The formula of slope is:

[tex]b_{yx}=r(X,Y)\cdot \frac{\sigma_{y}}{\sigma_{x}}[/tex]

Here r (X, Y) is the correlation coefficient between X and Y.

The correlation coefficient is directly related to the slope.

And since the standard deviations are always positive, the sign of the slope is dependent upon the sign of the correlation coefficient.

Here the slope is positive.

This implies that the correlation coefficient must have been a positive values.

Thus, it can be concluded that there is a positive correlation between X and Y.

Answer:

b ≈ 9.2

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

b² = a² + c² = 6² +7² = 36 + 49 = 85 ( take the square root of both sides )

b = [tex]\sqrt{85}[/tex] ≈ 9.2 ( to the nearest tenth )

Answer:

9.22

Step-by-step explanation:

Since it's a 90° triangle [tex]c^{2} =a^{2} +b^{2}[/tex].

In this example they labeled the hypotenuse as b instead of c are equation is still the same just put the correct variables in the right places.

[tex]b = \sqrt{6^{2} +7^{2} }[/tex]

b = 9.22

Answer:

135 degrees

Step-by-step explanation:

3x+15 = 5x - 5 because of the alternate interior angles theorem.

20 = 2x

x = 10

3(10) + 15 = 30+15 = 45

Remember that a line has a measure of 180 degrees. So we can just subtract the angle we found from 180 degrees to get BFG.

180-45 = 135.

Answer:

yes

Step-by-step explanation:

every negative any positive number is an integer

Answer:

Step-by-step explanation:

No.  Integers do not have fractions in them.

-2.75 is equivalent to -275/100, which is a fraction that does not reduce to an integer

Answer:

B) 5

Step-by-step explanation:

Proportions:

8 ⇒ 10

20 ⇒ 5x

5x = 20*10/8

5x = 25

x = 25/5

x = 5

Answer:

Shawn is correct because two events are independent if the probability of both occurring is equal to the product of the probabilities of the two events.

Step-by-step explanation:

We are given that A represent going to the movies on Friday and let B represent going bowling on Friday night. The P(A) = 0.58 and the P(B) = 0.36. The P(A and B) = 94%.

Now, it is stated that the two events are independent only if the product of the probability of the happening of each event is equal to the probability of occurring of both events.

This means that the two events A and B are independent if;

P(A) [tex]\times[/tex] P(B) = P(A and B)

Here, P(A) = 0.58, P(B) = 0.36, and P(A and B) = 0.94

So, P(A) [tex]\times[/tex] P(B) [tex]\neq[/tex] P(A and B)

      0.58 [tex]\times[/tex] 0.36 [tex]\neq[/tex] 0.94

This shows that event a and event B are not independent.

So, the Shawn statement that both events are not independent because P(A)P(B) ≠ P(A and B) is correct.

Answer:

Shawn is correct

Step-by-step explanation:

Answer:

As the calculated value of t is greater than critical value reject H0. The tests supports the claim at ∝= 0.05

If the p-value for the test statistic for this hypothesis test is 0.014, then the critical region is t ( with df=9) for a right tailed test is 2.821

then we would accept H0. The test would not support the claim at ∝= 0.01

Step-by-step explanation:

Mean x`= 518 +548 +561 +523 + 536 + 499+  538 + 557+ 528 +563 /10

x`= 537.1

The Variance is  = 20.70

H0 μ≤ 520

Ha μ > 520

Significance level is set at ∝= 0.05

The critical region is t ( with df=9) for a right tailed test is 1.8331

The test statistic under H0 is

t=x`- x/ s/ √n

Which has t distribution with n-1 degrees of freedom which is equal to 9

t=x`- x/ s/ √n

t = 537.1- 520 / 20.7 / √10

t= 17.1 / 20.7/ 3.16227

t= 17.1/ 6.5459

t= 2.6122

As the calculated value of t is greater than critical value reject H0. The tests supports the claim at ∝= 0.05

If the p-value for the test statistic for this hypothesis test is 0.014, then the critical region is t ( with df=9) for a right tailed test is 2.821

then we would accept H0. The test would not support the claim at ∝= 0.01

Answer:

To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations. In the example above, the variable x is equal to 6 since 6 + 6 = 12. If we know the value of our variables, we can replace the variables with their values and then evaluate the expression.

Step-by-step explanation:

Evaluate Algebraic Expressions. ... To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number. To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations.