A toll bridge charges $1.00 for passenger cars and $2.25 for other vehicles. Suppose that during daytime hours, 60% of all vehicles are passenger cars. If 15 vehicles cross the bridge during a particular daytime period, what is the resulting expected toll revenue

Answer:

60°

Step-by-step explanation:

∠ABC-∠CBD=∠1

[tex]135-75[/tex]

[tex]=60[/tex]

Answer:

Brainliest goes to me!

Step-by-step explanation:

angle abc = 135 degrees

part of it is angle 1 and the other part is angle cbd

<abc (135) = cbd (75) + <1

angle 1 = 60 degrees

Answer:

126

Step-by-step explanation:

We multiply 42 × 3= 126

The measure of the angle is 126.

The measure of angle will be 66°.

What is Complementary angle?

The sum of two or more angle is 90 degree then the angle is called the complementary angle.

Given that;

The measure of the supplement of an angle is 42 more than 3 times the measure of the complement of an angle.

Now,

Let the measure of angle = x

So, We can formulate;

⇒ (180 - x) = 42 + 3 (90 - x)

Solve for x as;

⇒ 180 - x = 42 + 270 - 3x

⇒ 180 - x + 3x = 312

⇒ 2x = 312 - 180

⇒ 2x = 132

⇒ x = 66

Thus, The measure of angle will be 66°.

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Answer:

4a²

Step-by-step explanation:

(2a)²

Distribute the square to all the terms in the bracket.

2²a²

Solve the powers if possible.

4a²

Answer:

4a²

Step-by-step explanation:

=> [tex](2a)^2[/tex]

=> [tex](2^2*a^2)[/tex]

=> 4 * a²

=> 4a²

Answer:

  see below

Step-by-step explanation:

The construction makes ray BF a bisector of angle ABC. That bisector divides ABC into the two congruent angles DBF and EBF. As a consequence, angle EBF will be half of ABC, not equal to ABC.

[tex]solution \\ {2x}^{2} - x + ( - x - {2x}^{2} - 2) \\ = {2x}^{2} - x - x - {2x}^{2} - 2 \\ = {2x}^{2} - {2x}^{2} - x - x - 2 \\ = - 2x - 2[/tex]

Hope it helps

Good luck on your assignment

Answer:

[tex] - 2x - 2[/tex]

Step-by-step explanation:

[tex]2 {x}^{2} - x + ( - x - 2 {x}^{2} - 2) \\ 2 {x}^{2} - x - x - 2 {x}^{2} - 2 \\ 2 {x}^{2} - 2 {x}^{2} - x - x - 2 \\ - 2x - 2[/tex]

hope this helps you.

brainliest appreciated

good luck!

have a nice day!

Answer:

Step-by-step explanation:

let s estimate the following

[tex](secA-tanA)(secA+tanA)=sec^2A-tan^2A=\dfrac{1}{cos^2A}-\dfrac{sin^2A}{cos^2A}=\dfrac{1-sin^2A}{cos^2A}=\dfrac{cos^2A}{cos^2A}=1[/tex]

as [tex]cos^2A+sin^2A=1[/tex]

it means that

[tex]\dfrac{1}{secA-tanA}=secA+tanA[/tex]

hope this helps

Answer:

15 cm

Step-by-step explanation:

Median means middle number

10,15,15,18,20

Answer:

15 cm

Step-by-step explanation:

The median is the number in the middle of a data set.

First, arrange the data from least to greatest.

10 cm, 15 cm, 15 cm, 18 cm, 20 cm

Now, take one number off each end of the data set until the middle number is reached.

10 cm, 15 cm, 15 cm, 18 cm, 20 cm

15 cm, 15 cm, 18 cm

15 cm

Therefore the median of the set of measurements is 15 cm.

Answer:

Step-by-step explanation:

Hello!

The Psychomotor Development Index (PDI) has an average value of μ= 100

The Mental Development Index (MDI) has an average value of μ= 100

At an approximate age of 1 year of normal healthy infants.

Using the group data set heart = 1 for all calculations (see attachment for complete table), you can define two variables of interest and obtain the descriptive statistics:

X₁: PDI of an infant with congenital heart disease who had to undergo reparative heart surgery during the first three months of life.

n₁= 69

X[bar]₁= 97.61

S₁= 14.73

X₂: MDI of an infant with congenital heart disease who had to undergo reparative heart surgery during the first three months of life.

n₂= 69

X[bar]₂= 106.33

S₂= 14.67

a)

You have to test the hypothesis that the average PDI for kids with congenital heart disease who have to undergo reparative heart surgery during the first three months of life is equal to 100.

H₀: μ₁ = 100

H₁: μ₁ ≠ 100

α: 0.05

[tex]Z= \frac{X[bar]_1-Mu_1}{\frac{S_1}{\sqrt{n_1} } }[/tex]≈N(0;1)

[tex]Z_{H_0}= \frac{97.61-100}{\frac{14.73}{\sqrt{69} } } = -1.347[/tex]

p-value: 0.17798

Using this approach the decision rule is:

The p-value is greater than the level of significance, the decision is to not reject the null hypothesis. Then the average PDI of the kids with congenital heart disease who have to undergo reparative heart surgery during the first three months of life is equal to 100.

b)

H₀: μ₂ = 100

H₁: μ₂ ≠ 100

α: 0.05

[tex]Z= \frac{X[bar]_2-Mu_2}{\frac{S_2}{\sqrt{n_2} } }[/tex]≈N(0;1)

[tex]Z_{H_0}= \frac{106.33-100}{\frac{14.67}{\sqrt{69} } } = 3.584[/tex]

p-value: 0.000338

Using this approach the decision rule is:

The p-value is less than the level of significance, the decision is to reject the null hypothesis. Then the average MDI of the kids with congenital heart disease who have to undergo reparative heart surgery during the first three months of life is different from 100.

c)

[tex]Z_{1-\alpha /2}= Z_{0.975}= 1.96[/tex]

95% CI for PDI

X[bar]₁ ± [tex]Z_{1-\alpha /2}[/tex] * [tex]\frac{S_1}{\sqrt{n_1} }[/tex]

97.61 ± 1.96 * [tex]\frac{14.73}{\sqrt{69} }[/tex]

[94.134; 101.086]

95% CI for MDI

X[bar]₂ ± [tex]Z_{1-\alpha /2}[/tex] * [tex]\frac{S_2}{\sqrt{n_2} }[/tex]

106.33 ± 1.96 * [tex]\frac{14.67}{\sqrt{69} }[/tex]

[102.869; 109.791]

The CI for the mean PDI of the kids with congenital heart disease who have to undergo reparative heart surgery during the first three months of life contains 100, this is to be expected since the null hypothesis in the hypothesis test made at complementary confidence level, was not rejected.

I hope this helps!

Answer:

x=1/3 is the answer

Step-by-step explanation:

6x+15=3x+14

substracting 3x on both sides

6x-3x+15=3x-3x+14

3x+15=14

subtracting 15 on both sides

3x+15-15=14-15

3x=1

x=1/3

i hope this will help you

Answer:

[tex]solution \\ 6x + 5 = 3x + 14 \\ or \: 6x - 3x = 14 - 5 \\ or \: 3x = 9 \\ or \: x = \frac{9}{3} \\ x = 3[/tex]

hope this helps ..

Good luck on your assignment...

Answer:

The value of the test statistic is:

t = -1.112

Step-by-step explanation:

In this case a paired difference test is to be performed.

The hypothesis can be defined as follows:

H₀: There is no difference between the two population means, i.e. d = 0.

Hₐ: There is a significant difference between the two population means, i.e. d ≠ 0.

The significance level of the test is, α = 0.10.

Use MS-Excel to perform the analysis.

Consider the output attached below.

The value of the test statistic is:

t = -1.112

The p-value of the two-tailed test is:

p-value = 0.303.

Decision rule:

Reject the null hypothesis if the p-value is less than the significance level.

p-value = 0.303 > α = 0.10.

The null hypothesis was failed to be rejected at 10% level of significance.

Conclusion:

There is not enough evidence to support the claim that there is a difference between the two population means.

Answer: yes is it a function

Step-by-step explanation:

A graph is a function when there is only one y value for each x value. You can also use the vertical line test. This example is a “quadratic function”.

Answer:

A. Tomas is correct; AC is opposite ∠B and BC is adjacent to ∠B.

Step-by-step explanation:

edge2021

The description of Thomas is correct. AC is opposite ∠B and BC is adjacent to ∠B.

Right angled triangle are those triangle for which one of the angle is 90 degrees.

Hypotenuse of a right angled triangle is the longest side.

Opposite side with respect to an angle is the side opposite to that angle.

Adjacent side with respect to an angle is the side which is adjacent to the angle.

Given is a triangle ABC.

Here C is the right angle.

Then the side opposite to the right angle is the hypotenuse.

So AB is the hypotenuse.

Now we are describing the sides in relation to the ∠B.

Side opposite to ∠B is AC, which is the opposite side.

Side adjacent to ∠B is BC, which is the adjacent side.

This is the description of Thomas.

Hence Thomas is correct about describing the sides in relation to ∠B.

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The complete question is as follows :

Two students describe the sides of right triangle ABC in relation to ∠B. Triangle A B C is shown. Angle A C B is a right angle. Tomas : AB is the hypotenuse. AC is the opposite side. BC is the adjacent side. Iliana : AB is the hypotenuse. BC is the opposite side. AC is the adjacent side. Who is correct? Explain. Tomas is correct; AC is opposite ∠B and BC is adjacent to ∠B. Iliana is correct; BC is opposite ∠B and AC is adjacent to ∠B. Both are correct because both AC and BC are opposite ∠B. Neither is correct because neither AC nor BC is opposite ∠B.

Answer:

25 pencils.

Step-by-step explanation:

You have 30 blue pencils and 15 green ones. To find how many pencils of other colors are in the bag, we can solve: 70-15-30=25

So, there are 25 pencils of other colors in the bag.

Answer:

[tex] \boxed{\sf Volume \ of \ cone = \frac{785}{3} \: {m}^{3} \: \: or \: \: 261.67 \: {m}^{2} } [/tex]

Given:

Diameter of cone (d)= 10 m

Height of cone (h) = 10 m

To find:

Volume of cone

Step-by-step explanation:

[tex] \sf Radius = \frac{Diameter}{2} \\ \\ \sf \implies Radius = \frac{10}{2} \: m \\ \\ \sf \implies Radius \: (r) = 5 \: m[/tex]

[tex] \sf Volume \ of \ cone = \frac{1}{3} \pi {r}^{2} h \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{3} \pi {(5)}^{2} \times 10\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{3} \pi \times 25 \times 10\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{3} \pi \times 250\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{3} \times 3.14 \times 250\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{3} \times 785\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{785}{3} \: {m}^{3} \: \: \: \: or \: \: \: \: 261.67 \: {m}^{2} [/tex]

Answer:

262.

Step-by-step explanation:

w.k.t

r = 10\2

or , r = 5

h = 10

V=π r^2 h \3

hence ,

v=22\7 * 5^2 *10\3

261.8

after rounding up

262.

if it helps , please mark me as brainliest

Answer:

64

Step-by-step explanation:

There are only pink and yellow sections of the circle, so every spin will land on pink or yellow.

Answer: 64

Answer:

Brianliest!

Step-by-step explanation:

since there are only the colors pink and yellow and the prediction for the   number of times it will land on pink or yellow, it will have a 100% probability

64

Answer:

a) 0.202 = 20.2% probability that a customer has to wait more than 4 minutes.

b) 0.33 = 33% probability that a customer is served within the first minute.

c) 11.5 minutes.

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

Which has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

The probability of finding a value higher than x is:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

In this question:

[tex]m = 2.5, \mu = \frac{1}{2.5} = 0.4[/tex]

(a) Find the probability that a customer has to wait more than 4 minutes.

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

[tex]P(X > 4) = e^{-0.4*4} = 0.202[/tex]

0.202 = 20.2% probability that a customer has to wait more than 4 minutes.

(b) Find the probability that a customer is served within the first minute.

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

[tex]P(X \leq 1) = 1 - e^{-0.4*1} = 0.33[/tex]

0.33 = 33% probability that a customer is served within the first minute.

(c) The manager wants to advertise that anybody who isn't served within a certain number of minutes gets a free hamburger. But she doesn't want to give away free hamburgers to more than 1% of her customers. What number of minutes should the advertisement use

We have to find x for which:

[tex]P(X > x) = 0.01[/tex]

So

[tex]P(X > x) = e^{-0.4x}[/tex]

Then

[tex]e^{-0.4x} = 0.01[/tex]

[tex]\ln{e^{-0.4x}} = \ln{0.01}[/tex]

[tex]-0.4x = \ln{0.01}[/tex]

[tex]x = -\frac{\ln{0.01}}{0.4}[/tex]

[tex]x = 11.5[/tex]

So 11.5 minutes.

[tex]\frac{2}{3}=\frac{boys}{18}[/tex]

3*boys=2*18

3*boys=36

boys=12

12+18=30

total number of students: 30

Answer:

30 students

Step-by-step explanation:

2:3 = x:18

X = number of boys

[tex]\frac{2}{3} = \frac{x}{18}[/tex]

multiply 18 by both sides

18 × [tex]\frac{2}{3} = X[/tex]

X = 18 × [tex]\frac{2}{3} = 12[/tex]

18 + 12 = 30

Answer:

1/100

Step-by-step explanation:

Since the numerators are all the same, the lowest value will depend on the denominators. The greater the denominator, the lower the value. Thus, the answer is 1/100

Answer:

All the possible numbers she could represent using the counters are:

0.6  |  1.5  |  2.4  |  3.3  |  4.2  |  5.1  |  6

Step-by-step explanation:

Please refer to the attached diagram for this question.

We are asked to list all the possible numbers she could represent using the counters.

The possible numbers are:

When there is 0 counter in the "ones" place and 6 counters in the "tenths" place.

0.6

When there is 1 counter in the "ones" place and 5 counters in the "tenths" place.

1.5

When there are 2 counters in the "ones" place and 4 counters in the "tenths" place.

2.4

When there are 3 counters in the "ones" place and 3 counters in the "tenths" place.

3.3

When there are 4 counters in the "ones" place and 2 counters in the "tenths" place.

4.2

When there are 5 counters in the "ones" place and 1 counter in the "tenths" place.

5.1

When there are 6 counters in the "ones" place and 0 counter in the "tenths" place.

6

Therefore, all the possible numbers she could represent using the counters are:

0.6  |  1.5  |  2.4  |  3.3  |  4.2  |  5.1  |  6

9514 1404 393

Answer:

  B)  35/111

Step-by-step explanation:

  [tex]0.\overline{315}=\dfrac{315}{999}=\boxed{\dfrac{35}{111}}[/tex]

The denominator of the fraction has as many 9s as the decimal has repeating digits. Here, the numerator and denominator both have factors of 9 that can be cancelled.

Answer:

£29.37

Step-by-step explanation:

→ First step is to find the amount of hours it takes for 5 builders

[tex]\frac{3*\frac{11}{2} }{5} =\frac{33}{2} /5=\frac{33}{2} *\frac{1}{5} =\frac{33}{10} =3\frac{3}{10}[/tex]

→ Now we know how long 5 builder takes we need to multiply the hourly rate by their time worked

[tex]3\frac{3}{10} *8.90=\frac{33}{10} *8.90=3.3*8.90 = 29.37[/tex]

Answer:

Step-by-step explanation:

When the number of builders is increased, the hours worked will be reduced.

So, this is inverse proportion.

Number of hours worked by  5 builders = [tex]\frac{3*\frac{11}{2}}{5}\\\\[/tex]

                                                                  [tex]=3*\frac{11}{2}*\frac{1}{5}\\\\=\frac{33}{10}\\\\=3\frac{1}{10}[/tex]

Amount received by each builder= 33/10 * 8.90

                                                       =    £ 29.37                                                    

Answer:

Dear Yates

Answer to your query is provided below

Total Price for her vehicle will be $20600

Step-by-step explanation:

Edith's trading is worth $8000. So, without the package upgrade of the vehicle delivery charge, her cost is:

$22750 - $8000 = $14750.

Now, add the package upgrade ($5050) and the delivery charge ($800).

$14750 + $5050 + $800 = $20600.

The total cost price of the vehicle after all the expenses is given by the equation A = $ 20,500

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The initial cost of the vehicle is = $ 22,750

Now , Edith has asked for an upgrade to a premium package for which the cost is $5050

So , the new cost of the vehicle = $ 22,750 + $ 5050 = $ 27,800

Now , the delivery charge of the vehicle = $ 700

And , the updated total price = $ 27,800 + $ 700 = $ 28,500

Now , the dealer has offered her $8000

So , the final price of the vehicle = updated total price - $ 8000

On simplifying the equation , we get

The final price of the vehicle A = $ 28,500 - $ 8,000

The final price of the vehicle A = $ 20,500

Hence , the final price of the vehicle is $ 20,500

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Answer:

(x + 3)(x + 2)

Step-by-step explanation:

Given

x² + 5x + 6

Consider the factors of the constant term (+ 6) which sum to give the coefficient of the x- term (+ 5)

The factors are + 3 and + 2 , since

3 × 2 = 6 and 3 + 2 = 5 , thus

x² + 5x + 6 = (x + 3)(x + 2)

Answer:

5%

Step-by-step explanation:

Plz rate thanks

Answer:

[tex]a. \quad 8\left(x+a\right)\\\\b. \quad 8\left(2x+h\right)[/tex]

Step-by-step explanation:

Best Regards!

Answer:  (a) 8(x  + a)   -->    8x + 8a

               (b) 8(2x + h)  -->   16x + 8h  

Step-by-step explanation:

f(x) = 8x²

f(a) = 8a²

[tex]\dfrac{f(x)-f(a)}{x-a}\quad = \quad \dfrac{8x^2-8a^2}{x-a}\quad = \quad \dfrac{8(x-a)(x+a)}{x-a}=\large\boxed{8(x+a)}[/tex]

f(x + h) = 8(x + h)²

           = 8(x² + 2xh + h²)

           = 8x² + 16xh + 8h²

f(x) = 8x²

[tex]\dfrac{f(x+h)-f(x)}{h} = \dfrac{(8x^2+16xh+8h^2)-8x^2}{h}\\\\\\.\qquad \qquad \qquad \quad =\dfrac{16xh + 8h^2}{h}\\\\\\.\qquad \qquad \qquad \quad =\dfrac{8h(2x + h)}{h}\\\\\\.\qquad \qquad \qquad \quad =\large\boxed{8(2x+h)}[/tex]

Answer:

Midpoint Of AB = ( 1+1/2 , -2-1/2)

= (2/2 , -3/2)

= ( 1 , -1.5)

Hope this helps

Please mark Branliest.

Answer:

-2,0

Step-by-step explanation:

Answer:

See explanation below

Step-by-step explanation:

Here a coin was tossed three times.

Let H = head &  T = tail

Find the following:

a) The sample space:

Since a coin is tossed thrice, all possible outcome would be:

S = { HHH, HHT, HTH, HTT, TTT, TTH, THH, THT}

b) i) A = Exactly 2 tails: Here exactly 2 tails were recorded.

A = {HTT, TTH, THT}

ii) B = at least two tails: Here 2 or more tails were recorded.

B = {HTT, TTT, TTH, THT}

iii) C = the last two tosses are heads:

C = { HHH, THH}

c) List the elements of the following events:

i) A. This means all outcomes in A

= {HTT, TTH, THT}

ii) A∪B. A union B, means all possible outcomes present in A or B or in both

= {HTT, TTH, THT, TTT}

iii) A∩B. This means all possible outcomes of A that are present in B.

= {HTT, TTH, THT}

iv) A∩C. All outcomes A that are present in B

= {∅}

Answer:

Mean, median and mode are measures of central tendency. The median is a better measure of central tendency when the given data contains outliers.

Step-by-step explanation:

Mean, median and mode are all measures of central tendency. These are statistical information that gives the middle or centre of a set of data. Since the values are central, they usually represent the entire distribution.

The mean is the obtained by dividing the sum of all the scores by the number of scores. The median is the middle value when numbers are arranged in increasing or decreasing order of magnitude. The mode is the most frequently occurring score in a distribution.

Let us see an example of the median as a measure of central tendency. Given the set of values; 4, 10, 12, and 26, the median is obtained from the average of the two middle numbers in the set of values which are 10 and 12 as seen from the set of values above. Hence the median of this set of values is 11.

The median can be a very good measure of central tendency, even better than the mean mostly in situations where there are outliers, or extreme values.