Which equation is true for the value b=2 ?

Answer:

See below.

Step-by-step explanation:

RSTV is a quadrilateral. We see that segments RV and RS are congruent. We also see that segments TV and TS are congruent. That makes quadrilateral RSTV a kite. A kite is a quadrilateral that has one set of congruent adjacent sides and a second set of congruent adjacent sides. One set of congruent adjacent sides may or may not be congruent to the second set of congruent adjacent sides. In this case they are not.

The diagonals of a kite are perpendicular which is shown in your figure with segment VS perpendicular to segment RT. The diagonals form 4 right triangles. The 4 right triangles are VRW, SRW, VTW, and STW.

Triangles VRW and SRW are congruent.

Triangles VTW and STW are congruent.

Let's work on the angles first.

Let's work on triangle VTW.

Angle VWT is a right angle.

m<VWT = 90

m<WVT = 42

m<VWT + m<VTW + m<WVT = 180

90 + 42 + m<WVT = 180

m<WVT + 132 = 180

m<WVT = 48

Triangle SWR is a right triangle.

m<RWS + m<RSW + m<SRW = 180

90 + m<RSW + 21 = 180

m<RSW + 111 = 180

m<RSW = 69

Triangles WVR and WSR are congruent with corresponding angles WVR and WSR.

m<WVR = m<WSR = 69

m<TVR = m<WVT + m<WVR

m<TVR = 48 + 69 = 117

m<TVR = 117

Now we deal with sides.

Let's look at triangle VWT.

Side VT is the hypotenuse.

m<VTW = 42 deg

VT = 15

For angle VTW, VW is the opposite leg, and VT is the hypotenuse.

The trig ratio that relates the opposite leg and the hypotenuse is the sine.

[tex] \sin \angle A = \dfrac{opp}{hyp} [/tex]

[tex] \sin \angle VTW = \dfrac{VW}{VT} [/tex]

[tex]\sin 42^\circ = \dfrac{VW}{15}[/tex]

[tex]VW = 15 \sin 42^\circ[/tex]

VW = 10

Since triangles RVW and RSW are congruent, corresponding sides VW and SW are congruent.

SW = VW = 10

Trianlge RSW is a right triangle with right angle RWS.

For angle WRS, SW is the opposite leg. RW is the adjacent leg.

[tex] \tan A = \dfrac{opp}{adj} [/tex]

[tex] \tan \angle WRS = \dfrac{SW}{RW} [/tex]

[tex] \tan 21^\circ = \dfrac{10}{RW} [/tex]

[tex] RW \tan 21^\circ = 10 [/tex]

[tex] RW = \dfrac{10}{\tan 21^\circ} [/tex]

RW = 26

We now know VW and RW. Using the Pythagorean theorem we can find RV.

(RW)^2 + (VW)^2 = (RV)^2

26^2 + 10^2 = (RV)^2

RV = 28

Perimeter:

Triangles RVT and RST are congruent, so we have:

RV = RS = 28

VT = ST = 15

perimeter = RS + RV + VT + ST

perimeter = 28 + 28 + 15 + 15

perimeter = 86

Answer:

x = - 2, y = 3

Step-by-step explanation:

Given

22 + yi = 20 - x + 3i

Compare the coefficients of like terms on both sides, that is

22 = 20 - x ( subtract 20 from both sides )

2 = - x ( multiply both sides by - 1 )

x = - 2

And

yi = 3i , hence y = 3

Step-by-step explanation:

1 pie in total: $13.66

1 slice: $1.70

1 pie in total: $20.11 (75+1.36×4)÷4

1 slice: $1.67

108 / 1376 is the probability that a student participates in both sports and music.

Step-by-step explanation:

It is given that,

A suburban high school has a population of 1376 students.

The number of students who participate in sports is 649.

The number of students who participate in music is 433.

To find the probability of event A (sports) :

P(sports) = No.of students participated in sports / Total students.

⇒ 649 / 1376

∴ P(A) = 649 / 1376

To find the probability of event B (music) :

P(music) = No.of students participated in music / Total students.

⇒ 433 / 1376

∴ P(B) = 443 / 1376

From the question, we know that the probability that a student participates in either sports or music is 974 /1376.

∴ P(A∪B) = 974 / 1376

To find the probability that a student participates in both sports and music :

The formula used here is,

P(A∩B) = P(A) + P(B) - P(A∪B)

⇒ 649 / 1376 + 433 / 1376 - 974 /1376

⇒ 108 / 1376

∴ P(A∩B) = 108 / 1376

The probability that a student participates in both sports and music is 108/1376

The given parameters are:
Total = 1376

Sport = 649

Music = 433

P(Sport or Music) = 974/1376

The required probability is:

P(Sport and Music) = P(Sport) + P(Music) - P(Sport or Music)

This gives

P(Sport and Music) = 649/1376 + 433/1376 - 974/1376

Evaluate the expression

P(Sport and Music) = 108/1376

Hence, the probability that a student participates in both sports and music is 108/1376

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Answer:

12:27

Step-by-step explanation:

Answer:

12:27

Step-by-step explanation:

Answer:

[tex]=50m^{\frac{5}{3}}n^{\frac{3}{8}}[/tex]

Step-by-step explanation:

[tex]\left(5m^{\frac{4}{3}}\cdot \:5n^{\frac{1}{4}}\right)\left(m^{\frac{1}{3}}\cdot \:2n^{\frac{1}{8}}\right)[/tex]

[tex]=m^{\frac{4}{3}}\cdot \:5^{1+1}n^{\frac{1}{4}}m^{\frac{1}{3}}\cdot \:2n^{\frac{1}{8}}[/tex]

[tex]=m^{\frac{4}{3}}\cdot \:5^2n^{\frac{1}{4}}m^{\frac{1}{3}}\cdot \:2n^{\frac{1}{8}}[/tex]

[tex]=5^2n^{\frac{1}{4}}m^{\frac{4}{3}+\frac{1}{3}}\cdot \:2n^{\frac{1}{8}}[/tex]

[tex]=5^2m^{\frac{4}{3}+\frac{1}{3}}\cdot \:2n^{\frac{1}{4}+\frac{1}{8}}[/tex]

[tex]=5^2\cdot \:2m^{\frac{5}{3}}n^{\frac{1}{4}+\frac{1}{8}}[/tex]

[tex]=5^2\cdot \:2m^{\frac{5}{3}}n^{\frac{3}{8}}[/tex]

[tex]=50m^{\frac{5}{3}}n^{\frac{3}{8}}[/tex]

A geometric random variable represents the number of games played until a player loses. The probability can be calculated using the formula P(X = k) = (1-p)^(k-1) * p, where p is the probability of losing a game and k is the number of games.

A geometric random variable, denoted as X, represents the number of games played until a player loses. It is a type of random variable in probability theory. We can calculate the probability that it takes a certain number of games until the player loses by using the formula P(X = k) = (1-p)^(k-1) * p, where p is the probability of losing a game and k is the number of games. For example, if p = 0.57 and we want to find the probability that it takes five games until the player loses, we can calculate P(X = 5) = (1-0.57)^(5-1) * 0.57.

There is no answer, there is no table.

The midpoint of the line segment AB with points A at (-5, -4) and B at (5, -3) can be found by averaging the x and y coordinates of the two points. The x-coordinate of the midpoint is 0 and the y-coordinate is -3.5, hence the midpoint is (0, -3.5).

The subject of this question is Mathematics, specifically discussing the concept of finding the midpoint of a line segment in a 2D coordinate system. The midpoint of a line segment can be calculated using the coordinates of the two ends of the line segment. To find it, you add the coordinates (x, y) of the two points and divide each sum by 2. In this case, the coordinates of points A and B are (-5, -4) and (5, -3) respectively. Thus, the x-coordinate of the midpoint is (-5 + 5)/2 = 0 and the y-coordinate of the midpoint is (-3 - 4)/2 = -3.5. Therefore, the midpoint of line segment AB is at (0, -3.5).

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Answer:

1 metre = 100 centimetres

Step-by-step explanation:

Answer:

The domain is all real numbers

The y-intercept is 3.

Step-by-step explanation:

Let's analyze each statement separately. The function is

[tex]f(x)=(x+1)^2+2[/tex]

We have the following statements:

The domain is all real numbers, --> TRUE. The domain of a function is the set of values that the variable x can take. For this function, there are no restriction on the values that x can take, so the domain is all real numbers.

The range is all real numbers greater than or equal to 1  --> FALSE. The range of a function is the set of values that the variable y can take. For this function, we see that the factor [tex](x+1)^2[/tex] is always equal or greater than zero; this means that the minimum of the function is [tex]f(x)=2[/tex], so the range is all real numbers greater than or equal to 2.

The y-intercept is 3.  --> TRUE. The y-intercept is the value of the function when x = 0. For this function, if we substitute x = 0, we find:

[tex]f(0)=(0+1)^2+2=1^2+2=3[/tex]

The graph of the function is 1 unit up and 2 units to the left from the graph of [tex]y=x^2[/tex] --> FALSE. The graph of a function is scaled n units up when [tex]g(x)=f(x)+n[/tex]; in this case, we see that the factor n in our fuction is n = 2, so the function is actually scaled 2 units up, not 1.

The graph has two x-intercepts --> FALSE. The x-intercept of a graph is the value of x when [tex]f(x)=0[/tex]. If we require [tex]f(x)=0[/tex] for our function, we get:

[tex]0=(x+1)^2+2\\\rightarrow (x+1)^2=-2[/tex]

However, this equation has no solutions: so, the graph has no x-intercepts.

The graph of the function [tex]f(x) = (x + 1)^2 + 2[/tex] has a domain of all real numbers, a range of all real numbers greater than or equal to 2, a y-intercept of 3, and is 1 unit left and 2 units upwards shifted from the base graph [tex]y = x^2[/tex]. It has one x-intercept, not two.

The function in question is f(x) = (x + 1)2 + 2. To analyze its characteristics, we first need to look at its general shape, domain, and range. Since it is based on the parent function f(x) = x2, which is a parabola, the transformations will affect the position but not the overall shape or domain.

Answer:

Step-by-step explanation:

Answer:

The factors are 7 * 2 * 2 * 2

Step-by-step explanation:

Step 1:  Find all of the factors

                     56

               28        2

          14        2

      7        2

Answer: The factors are 7 * 2 * 2 * 2

Answer:

209

Step-by-step explanation:

i hoped this helped saying no one else wanted to answer have a nice day

The solution is , 209 is the area of this composite figure, in square centimeters.

Area of triangle is defined as the total region that is enclosed by the three sides of any particular triangle.

Formula: area= 1/2× base × height

here, we have,

given that,

A triangle with base of 11 centimeters and height of 6 centimeters is on top of a rectangle with length 16 centimeters and width 11 centimeters.

now, we know,

area of triangle:

area= 1/2× base × height

A = 1/2 * 11 * 6

   =33

again,

we have,

Area of a rectangle (A) is the product of its length (l) and width (w).

A= l. w

so, A = 16* 11

        =176

finally, the area of this composite figure, in square centimeters is,

33+176 = 209

Hence, The solution is , 209 is the area of this composite figure, in square centimeters.

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Answer:

Step-by-step explanation:

[tex]\frac{4}{5}(\frac{1}{4}-5)=\frac{4}{5}*\frac{1}{4}-\frac{4}{5}*5\\\\=\frac{1}{5}-4\\\\=\frac{1}{5}-\frac{4*5}{1*5}\\\\=\frac{1}{5}-\frac{20}{5}\\\\=\frac{1-20}{5}\\\\=\frac{-19}{5}[/tex]

$ 1,100

Step-by-step explanation:

Well use the simple interest equation;

A = P(1 + rt)

Where:

   A = Total Accrued Amount (principal + interest)

   P = Principal Amount

   I = Interest Amount

   r = Rate of Interest per year in decimal; r = R/100

   R = Rate of Interest per year as a percent; R = r * 100

   t = Time Period involved in months or years

A = 500 (1 + 0.15*8)

A = 500 (2.2)

= 1100

Answer:

The independent variable is the variable that can be changed.

The dependent variable is wjat you measure in an experiment

Answer:

C = (13)π meters

Step-by-step explanation:

Its circumference is C = πd, which here has the value C = (13)π meters.

Final answer:

The circumference of a circle with a diameter of 13 meters is 13
meters, using the formula C =
d where C is the circumference and d is the diameter.

Explanation:

The question involves finding the circumference of a circle when given its diameter, in terms of
(pi). The diameter of the circle is provided as 13 meters. To find the circumference, we use the formula C =
d, where C is the circumference, r is the radius, and d is the diameter of the circle. Since the diameter is twice the radius (d = 2r), the formula can also be written as C = 2
r. However, since we are given the diameter, we use the first formula.

For this particular problem, we have d = 13 meters. Thus, the circumference of the circle calculated in terms of pi is:

C = imes d

C = imes 13 m

The circumference of the circle in terms of pi is therefore 13
meters.

Answer:

P(T₀ < 200) = 0.99856

P(150 < T₀ < 200) = 0.99856

Step-by-step explanation:

The expected values for each of the tasks is μ₁ = 60, μ₂ = 60, μ₃ = 60

The variances for each of the 3 tasks

σ₁² = 15, σ₂² = 15, σ₃² = 15

calculate P(T₀ < 200) and P(150 < T₀ < 200)

When independent distributions are combined, the combined mean and combined variance are given through the relation

Combined mean = Σ λᵢμᵢ

(summing all of the distributions in the manner that they are combined)

Combined variance = Σ λᵢ²σᵢ²

(summing all of the distributions in the manner that they are combined)

Distribution of total time taken for the 3 successive tasks

= X₁ + X₂ + X₃

Expected value = Combined Mean = μ₁ + μ₂ + μ₃ = 60 + 60 + 60 = 180

Combined Variance = 1²σ₁² + 1²σ₂² + 1²σ₃²

= (1² × 15) + (1² × 15) + (1² × 15)

= 45

standard deviation of the combined distribution = √(variance) = √45 = 6.708

Since each of the distributions are said to be normal, the combined distribution too, is normal.

P(T₀ < 200)

We first standardize 200

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (200 - 180)/6.708 = 2.98

The required probability

= P(T₀ < 200) = P(z < 2.98)

We'll use data from the normal probability table for these probabilities

P(T₀ < 200) = P(z < 2.98) = 0.99856

b) P(150 < T₀ < 200)

We first standardize 150 and 200

For 150

z = (x - μ)/σ = (150 - 180)/6.708 = -4.47

For 200

z = (x - μ)/σ = (200 - 180)/6.708 = 2.98

The required probability

= P(150 < T₀ < 200) = P(-4.47 < T₀ < 2.98)

We'll use data from the normal probability table for these probabilities

P(150 < T₀ < 200) = P(-4.47 < T₀ < 2.98)

= P(z < 2.98) - P(z < -4.47)

= 0.99856 - 0.0000 = 0.99856

Hope this Helps!!!

This question relates to the times needed for repair tasks at a service facility and involves concepts such as expected values, variances, and probability distributions. It also mentions sample standard deviations, estimates of population standard deviations, and sample means.

The question is about the times necessary to perform three successive repair tasks at a service facility. Let x1, x2, and x3 represent the times for each task. Assuming they are independent, normal random variables, we can calculate the expected values and variances using the given information. For example, the expected value of x1 is m1, and the variance is s21.

The question also refers to different figures that represent probability distributions for the repair times. In Figure 5.19, the shaded area represents the probability that the repair time is less than three. In Figure 5.18, the shaded area represents the probability that the repair time is greater than two. These figures provide visual representations of the probabilities associated with the repair times.

Finally, the question mentions the concepts of sample standard deviations, estimates of population standard deviations, sample means, and population means. These concepts are relevant for analyzing the repair times and understanding the characteristics of the data.

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Answer: 1.875 days

Step-by-step explanation:

Hi, to answer this question we simple have to divide the total day of the month (30 days) by the number of days that she offers tutoring (16).

Mathematically speaking:

30 /16 =1.875 days

1.875 days is equivalent to the fraction of days that tutoring was offered in November

Feel free to ask for more if needed or if you did not understand something.

Answer:0.533

Step-by-step explanation:

Sam's mathematics teacher offered after school tutoring 16 days out of the 30 days that were in November in order to help students review for the mid-term exam.

To convert this to a decimal, we divide the number of days tutorial was offered in November by the number of days in November. This will be:

= 16/30

= 0.533

The decimal that is equivalent to the fraction is 0.533.

Answer: The weight of mail at noon is 104 pounds.

Step-by-step explanation:

Given that , At a post office, the weight of the mail at 10.00 A.M was 80 pounds.

Two hours later, the weight of the mail had increased by 30%.

Since , time after 2 hours of 10 A.M would be 12 P.M which is known as noon.

Mathematically , the weight of the mail at noon = (Weight at 10 AM) +30% of (Weight at 10 AM)

= 80 + 0.30(80) pounds

= 80 (1+0.30) pounds

= 80 (1.30) pounds

= 104 pounds

Hence, the weight of mail at noon is 104 pounds.

Answer:

T=2000(x)+1200

Step-by-step explanation:

Let the number of years that you attend xollege be x.

Every year, you receive $2000 as academic scholarship hence for x years, you will receive $2000x

However, for books, you receive it once and rhe amount is $1200

The total expenditure will be expressed as

T=2000(x)+1200

Substitute the number of years for x with an integer to get equivalent amount received for scholarship

Answer:

1109

Step-by-step explanation:

The first term is -27, and the common difference is 16.

The nth term is:

a = a₁ + d (n − 1)

a = -27 + 16 (n − 1)

a = -27 + 16n − 16

a = 16n − 43

The 72nd term is:

a = 16(72) − 43

a = 1109

The 72nd term of the arithmetic sequence -27, -11, 5 is 1109.

The sequence provided, -27, -11, 5, is arithmetic, which means it has a common difference between consecutive terms. To find the 72nd term in this sequence, we first determine the common difference by subtracting the first term from the second term, so the common difference (d) is
[tex]-11 - (-27) = 16.[/tex]

The nth term of an arithmetic sequence can be found using the formula
[tex]a_n = a_1 + (n - 1) * d[/tex], where
[tex]a_n[/tex] is the nth term,
[tex]a_1[/tex] is the first term, and
n is the term number. Applying this formula to find the 72nd term, we get:

[tex]a_{72} = -27 + (72 - 1) * 16 \\a_{72} = -27 + 71 * 16 \\a_{72} = -27 + 1136 \\a_{72} = 1109.[/tex]

Therefore, the 72nd term of the sequence is 1109.

Answer:

70 yd.

Step-by-step explanation:

The three streets at the intersection form a right triangle.

For a right triangle, the length of the longest side (called hypothenuse) is given by Pythagorean's theorem:

[tex]h=\sqrt{x^2+y^2}[/tex]

where

x is the length of the 1st side

y is the length of the 2nd side

h is the length of the hypothenuse

Here we want to find the hypothenuse.

We have:

x = 42 yd (length of the 1st side)

y = 56 yd (length of the 2nd side)

Substituting, we find h:

[tex]h=\sqrt{42^2+56^2}=70 yd[/tex]

Answer:

70

Step-by-step explanation: i don't why it only says one answer i thing brainly messed up cause it says i have no brainliest ether to.

Answer:

because hygiene

Step-by-step explanation:

a

a

a

a

a

a

a

a

a

a

a

Answer:

the answer is b

Step-by-step explanation:

Answer:

143

Step-by-step explanation:

Because triangles JKL and JUV are similar, the ratio of JV:LJ also applies to the ratio of UJ:JK. JV:LJ=130:60=13:6, so 17x+7=13\6*(66).

KJ=17x+7=11*13=143

Hope this helps!

Answer:

24

Step-by-step explanation:

3t⁶ × 8(t^-6)

3 × 8 × t⁶ × t^-6

24 × t^(6-6)

24 × t⁰

24 × 1

24