30 students, along with some of their parents, are going to a trip to Washington DC. Some of the adults are driving cars, and each car can accommodate up to 5 people including the driver. What is the smallest number of adults that should be invited on the trip to get all 30 students to Washington?

Answer:

y = -3x + 3

[tex]y=\frac{1}{3}x-7[/tex]

Step-by-step explanation:

Slope of a line passing through two points ([tex]x_1, y_1[/tex]) and [tex](x_2, y_2)[/tex] is determined by the formula,

Slope = [tex]\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]

If these points are (0, 3) and (3, -6),

Slope of the line passing through these lines = [tex]\frac{3+6}{0-3}[/tex] = (-3)

Equation of the line which passes through (0, 3) and slope = (-3),

y - y' = m(x - x')

y - 3 = (-3)(x- 0)

y - 3 = -3x

y = -3x + 3

Now slope of another line that passes through (3, -6) and (0, -7),

m' = [tex]\frac{(-6+7)}{(3-0)}[/tex]

m' = [tex]\frac{1}{3}[/tex]

Equation of the line that passes through (0, -7) and slope = [tex]\frac{1}{3}[/tex]

y - (-7) = [tex]\frac{1}{3}(x-0)[/tex]

y + 7 = [tex]\frac{1}{3}x[/tex]

y = [tex]\frac{1}{3}x-7[/tex]

Therefore, system of linear equations are,

y = -3x + 3

[tex]y=\frac{1}{3}x-7[/tex]

Answer: The mean difference is between 799586.3 and 803257.9.

Step-by-step explanation: To estimate the mean difference for confidence interval:

Find the statistic sample:

For the traffic count, mean = 1835.8 and s = 1382607.3

The confidence interval is 90%, so:

α = [tex]\frac{1-0.9}{2}[/tex]

α = 0.05

The degrees of dreedom are:

df = n - 1

df = 10 - 1

df = 9

Using a t-ditribution table, the t-score for α = 0.05 and df = 9 is: t = 1.833.

Error will be:

E = [tex]t.\frac{s}{\sqrt{n} }[/tex]

E = 1.833.([tex]\frac{1382607.3}{\sqrt{10} }[/tex])

E = 801422.1

The interval is: mean - E < μ < E + mean

1835.8 - 801422.1 < μ < 1835.8+801422.1

-799586.3 < μ < 803257.9

The estimate mean difference in trafic count between 6th and 13th using 90% level of confidence is between 799586.3 and 803257.9.

Answer:

-7/2

Step-by-step explanation:

To find the y coordinate of the midpoint and the y coordinates together and divide by 2

(2+-9)/2

-7/2

Answer:

2 goes in green box

Step-by-step explanation:

(9,2) (-7,-9)

(x1, y1) (x2,y2)

Midpoint is (x1+x2)/2 , (y1+y2)/2

(9-7)/2= 1

(2-9)/2 = -7/2

Answer:

40.5 ft

162 ft

16 in

7.2 in

13.9 ft

Step-by-step explanation:

1) V=√32d

d= ?

V=36 ⇒ 36²= 32d  ⇒ d= 1296/32=40.5 feet

2) S= 5.5√d

S= 70 mph, d=?

70²= 5.5²d ⇒ d= 4900/ 30.25≈ 162 feet

3) d= 0.25√h

d= 1 mile, h=?

1²= 0.25²h ⇒ h= 1/0.0625= 16 in

4) a= 4, b= 6, c=?

c²= a²+b² ⇒ c= √a²+b²= √4²+6² = √52≈ 7.2 in

5) c= 16 foot, b= 8 feet, a=?

c²= a²+b² ⇒ a= √c² - b²= √16²-8²= √256- 64= √192≈13.9 feet

Answer:

2 is the coefficient

Step-by-step explanation:

2 is the coefficient bc a coefficient is the number next to a variable (such as x)  and 2 is next to x and is the only one in the equation

Answer:

-2

Step-by-step explanation:

Answer:

[tex] P(X>1)= 1-P(X \leq 1)= 1- [P(X=0) +P(X=1)][/tex]

And if we use the probability mass function we got:

[tex]P(X=0)=(4C0)(0.6)^0 (1-0.6)^{4-0}=0.0256[/tex]  

[tex]P(X=1)=(4C1)(0.6)^1 (1-0.6)^{4-1}=0.1536[/tex]  

And replacing we got:

[tex] P(X>1) =1- [0.0256 +0.1536]= 0.8208[/tex]

Step-by-step explanation:

Let X the random variable of interest, on this case we now that:  

[tex]X \sim Binom(n=4, p=0.6)[/tex]  

The probability mass function for the Binomial distribution is given as:  

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]  

Where (nCx) means combinatory and it's given by this formula:  

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]  

We want to find the following probability:

[tex] P(X >1)[/tex]

And for this case we can use the complement rule and we got:

[tex] P(X>1)= 1-P(X \leq 1)= 1- [P(X=0) +P(X=1)][/tex]

And if we use the probability mass function we got:

[tex]P(X=0)=(4C0)(0.6)^0 (1-0.6)^{4-0}=0.0256[/tex]  

[tex]P(X=1)=(4C1)(0.6)^1 (1-0.6)^{4-1}=0.1536[/tex]  

And replacing we got:

[tex] P(X>1) =1- [0.0256 +0.1536]= 0.8208[/tex]

Answer:

The expected number of adult workers with a high school diploma is 4.

Step-by-step explanation:

This random variable X can be modeled with the binomial distribution, with parameters n=10 (the sample size) and p=0.4 (the probability that a adult worker have a high school diploma).

The expected value of X is then the mean of the binomial distribution with the parameters already mentioned.

This is calculated as:

[tex]E(X)=\mu_b=n\cdot p=10\cdot0.4=4[/tex]

Answer:

A linear equation is an equation with two variables whose graph is a line. The graph of the linear equation is a set of points in the coordinate plane that all are solutions to the equation. If all variables represent real numbers one can graph the equation by plotting enough points to recognize a pattern and then connect the points to include all points.If you want to graph a linear equation you have to have at least two points, but it's usually a good idea to use more than two points. When choosing your points try to include both positive and negative values as well as zero

Step-by-step explanation:

Answer:

The answer would be C because the y-intercept is when x is equal to 0

please mark me brainliest

Answer:

[tex]\frac{1}{12}[/tex]

Step-by-step explanation:

The number with the smallest denominator is the larger number and [tex]\frac{1}{12}[/tex] is the number with the smallest denominator out of [tex]\frac{1}{12} , \frac{1}{32} , \frac{1}{48} , \frac{1}{18}[/tex].

Answer:

1/12

Step-by-step explanation:

Start with a number, for example 100.

Now divide 100 by several numbers which are greater and greater:

100/1 = 100

100/2 = 50

100/4 = 25

100/10 = 10

100/100 = 1

As you divide the same number, 100, by a greater number, the result becomes smaller.

As we divide 100 by 1, then by 2, then by 4, etc., we are always dividing 100 by a greater and greater number. The result is smaller and smaller, 100, 50, 25, etc. If you always divide the same number by other numbers, the larger the number you divide by, the smaller the result.

Numbers in order from greatest to smallest:

1/12, 1/18, 1/32, 1/48

Answer: The greatest number is 1/12

Answer:

D.

Step-by-step explanation:

Deus ex machina is the plot device of using something very improbable to resolve a situation.

Answer:

[tex]\boxed{\sf \ \ \ x = -8 \ or \ x = -4 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

[tex]4x^2+48x+128=0\\<=> 4(x^2+12x+32)=0\\<=> x^2+12x+32=0\\<=> (x+6)^2 - 36 + 32= 0\\\\<=> (x+6)^2-4=0\\<=> (x+6+2)(x+6-2)=0\\<=> (x+8)(x+4) = 0\\<=> x = -8 \ or \ x = -4[/tex]

vouch, i confirm that -8, -4 are the answers

Answer:

the answer is 157

Step-by-step explanation:

7 +10= 17

17+20=37

37+40=77

77+80=157

157+160=317

At the beginning you add +10. Every sequence, you need to multiply that number x2. For example: 10 x 2=20...

Answer:

45,000 codes

Step-by-step explanation:

Given:

Code of 5 digits

Condition

Required

Calculate the number of codes available

Digits = {0,1,2....9}

n(Digits) = 10

Let the format of the code be represented as follows;

ABCDE

From the conditions given

A can't be 1;

This means that A can be any of 0,2,3,4....9

This implies that A can be any of the above 9 digits

n(A) = 9

There's no condition attached to BCD;

This means that B can be any of 10 digits

This means that C can be any of 10 digits

This means that D can be any of 10 digits

n(B) = n(C) = n(D) = 10

Lastly, E must be an even number;

This means that E can be any of 0,2,4,6,8

This implies that E can be any of the above 5 digits

n(E) = 5

So,

Number of available codes = n(A) * n(B) * n(C) * n(D) * n(E)

Number of available codes = 9 * 10 * 10 * 10 *5

Number of available codes = 45,000

Hence, there are 45,000 available codes

Answer:

The 1st graph

Step-by-step explanation:

The quickest and easiest way is to just graph y < x² + 4x + 5. When you do so you should be able to see your answer.

Answer:

We conclude that older people are more likely to be victimized.

Step-by-step explanation:

We are given that a survey shows that 10% of the population is victimized by property crime each year.

A random sample of 527 older citizens (65 years or more of age) shows a victimization rate of 12.35%

Let p = population proportion of people who are victimized.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]p \leq[/tex] 10%      {means that older people are less likely to be victimized or remains same}

Alternate Hypothesis, [tex]H_A[/tex] : p > 10%      {means that older people are more likely to be victimized}

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

                             T.S. =  [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]  ~  N(0,1)

where, [tex]\hat p[/tex] = sample proportion of older people who are victimized = 12.35%

            n = sample of older citizens = 527

So, the test statistics  =  [tex]\frac{0.1235-0.10}{\sqrt{\frac{0.10(1-0.10)}{527} } }[/tex]  

                                       =  1.798

The value of z-test statistics is 1.798.

Since in the question, we are not given with the level of significance so we assume it to be 5%. Now at 5% level of significance, the z table gives a critical value of 1.645 for right-tailed test.

Since our test statistics is more than the critical value of z as 1.798 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that older people are more likely to be victimized.

Answer:

24

Step-by-step explanation:

Use the Pythagorean theorem.

Where the sum of the two legs squared is equal to the hypotenuse squared.

10² + x² = 26²

100 + x² = 676

x² = 576

x = √576

x = 24

The value of x is 24.

Answer: the answer is c (the third answer ) ‼️

Step-by-step explanation:

The data in the given residual plot shows that model C has the best fit.

A straight line that minimizes the gap between it and some data is called a line of best fit. In a scatter plot containing various data points, a relationship is expressed using the line of best fit.

Given:

The residual plot of the values in the graph,

The points in the first graph are very far from the x-axis and y-axis so, it is not the best fit,

The points in the second graph are very far from the x-axis and y-axis, and they are symmetric to the y-axis but not the best fit.

Most of the points are close to the x-axis, so it is the best fit,

Thus, the third graph is the best line of fit.

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Answer:

csc 270° is the answer.

Answer:

(a)650 ways

(b)650 ways

(c)676 ways

Step-by-step explanation:

There are 26 red and 26 black cards.

If a card is dealt to each of 2 players, we want to find out how many different ways this can be done.

(a)Both cards are red

If both cards are red:

The first red card can be dealt in 26 ways.

The second red card can be dealt in 25 ways.

Therefore: Both Red cards can be dealt in: 26 X 25 = 650 ways

(b)Both cards are black

If both cards are black:

The first black card can be dealt in 26 ways.

The second black card can be dealt in 25 ways.

Therefore: Both black cards can be dealt in: 26 X 25 = 650 ways

(c)One card is black and the other is red.

The red card can be dealt in 26 ways.

The black card can be dealt in 26 ways.

Therefore: Both cards can be dealt in: 26 X 26 = 676 ways

Answer:

15 is the answer to the question

Answer:

15, which for some reason does not seem to be an option.

Step-by-step explanation:

Product means to multiply to numbers, items etc.

5 times 3, as you should know, is 15.

Hope this helps.

Answer:

  $106.67

Step-by-step explanation:

Using the example, for 3 hours work, Alex would be paid ...

  (2 hr)($30/hr) +(1 hr)($20/hr) = $60 +$20 = $80

At the same rate of pay, for 4 hours work, the pay would be ...

  pay/(4 hr) = $80/(3 hr)

  pay = $80(4/3) ≈ $106.67

Alex's pay for 4 hours of work is $106.67.

Answer:

a = 30

b = 6/7

Step-by-step explanation:

The number of yeast cells after t hours is modeled by the following equation:

[tex]f(t) = a(1 + be^{-0.7t})[/tex]

In which a is the initial number of cells.

At time t = 0 the population is 30 cells

This means that [tex]a = 30[/tex]

So

[tex]f(t) = 30(1 + be^{-0.7t})[/tex]

And increasing at a rate of 18 cells/hour.

This means that f'(0) = 18.

We use this to find b.

[tex]f(t) = 30(1 + be^{-0.7t})[/tex]

So

[tex]f(t) = 30 + 30be^{-0.7t}[/tex]

Then, it's derivative is:

[tex]f'(t) = -30*0.7be^{-0.7t}[/tex]

We have that:

f'(0) = 18

So

[tex]f'(0) = -30*0.7be^{-0.7*0} = -21b[/tex]

Then

[tex]-21b = 18[/tex]

[tex]21b = -18[/tex]

[tex]b = -\frac{18}{21}[/tex]

[tex]b = \frac{6}{7}[/tex]

Answer:

None

Step-by-step explanation:

The answers are:

1. g(10) -31

2. x= -17/3

3. f(3)= 2

4.x= √30

5. h(-2)= 1

6. x= 0

7. h(a)= 1

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f(x) = x² – 7

g(x) = -3x - 1

j(x)= 2x-9

h(x) = 1

1. g(10)= -3(10) -1 = -30 - 1= -31

2. g(x) = 16

-3x- 1= 16

-3x = 17

x= -17/3

3. f(3)= (3)² – 7 = 9- 7= 2

4. f(x)= 23

x² – 7=  23

x² = 30

x= √30

5. h(-2)= 1

6. x= 0

7. h(a)= 1

8. S(-1) = 3

The value of function s(a) at a=-1 is 3.

10. g(4) = -1

The value of function g(a) at a=4 is -1.

11. h(2) = 8

The value of function h(a) at a=2 is 8.

12. k(2) = 9​

The value of function k(a) at a= 2 is 9.

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Answer: time = 20 seconds

Step-by-step explanation:

h(t) = -16t² + 316t + 80

The shape of this graph is an upside parabola ∩.  

It lands on the ground when height (h) = 0

Set the equation equal to zero, factor, and solve for t.

0 =  -16t² + 316t + 80

0 =  4t² - 79t - 20              divided both sides by -4

0 = (4t + 1)(t - 20)               factored the equation

t = -1/4      t = 20              Applied Zero Product Property and solved for t

Since we know time cannot be negative, disregard t = -1/4

The only valid solution is: t = 20

Answer:

B. Length A of Rasheeda’s garden is 27 ft.

C. Length B of the book’s garden is 12 ft.

E. Length A of the book’s garden is 9 ft longer than length A of Rasheeda’s garden.

Step-by-step explanation:

step 1

Find the dimension of the book's garden

we know that

Book scale: 1 inch = 2 feet

That means

1 inch in the drawing represent 2 feet in the actual

To find out the actual dimensions, multiply the dimension in the drawing by 2

so

Length A of the book’s garden

Width B of the book’s garden

step 2

Find the dimension of Rasheeda’s garden

we know that

Rasheeda's Scale: 2 inch = 3 feet

That means

2 inch inches the drawing represent 3 feet in the actual

To find out the actual dimensions, multiply the dimension in the drawing by 3 and divided by 2

so

Length A of Rasheeda's garden

Width B of Rasheeda's garden

Verify each statement

A. Length A of the book’s garden is 18 ft.

The statement is false

Because, Length A of the book’s garden is 36 ft (see the explanation)

B. Length A of Rasheeda’s garden is 27 ft.

The statement is true (see the explanation)

C. Length B of the book’s garden is 12 ft

The statement is true (see the explanation)

D. Length B of Rasheeda’s garden is 6 ft.

The statement is false

Because, Length B of Rasheeda’s garden is 9 ft. (see the explanation)

E. Length A of the book’s garden is 9 ft longer than length A of Rasheeda’s garden.

The statement is true

Because the difference between 36 ft and 27 ft is equal to 9 ft

F. Length B of the book’s garden is 3 ft shorter than length B of Rasheeda’s garden.

The statement is false

Because, Length B of the book’s garden is 3 ft greater than length B of Rasheeda’s garden.

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Answer:

B. Length A of Rasheeda’s garden is 27 ft.

C. Length B of the book’s garden is 12 ft.

E. Length A of the book’s garden is 9 ft longer than length A of Rasheeda’s garden.

(second, third, and fifth choices)

Explanation: I did the quiz and got it right.

Hope this Helps!

Answer:

The correct answer is:

r + 0.50 = 10.25: Subtract .50 from both sides. The answer is $9.75.

This is because Juan got a $0.50 raise which means that his new rate will be $0.50 more than his original rate (r).

Answer:

$9.75

Step-by-step explanation:

The graph of the compound inequality can be seen at the end.

Here we have two inequalities that depend on p, these are:

4p + 1 > -15

6p + 3 < 45

First, we need to isolate p on both inequalities.

4p + 1 > -15

4p > -15 - 1

p > -16/4

p > - 4

6p + 3 < 45

6p < 45 - 3 = 42

p < 42/6 = 7

So we have the compound inequality:

p > -4

p < 7

or:

-4 < p < 7

Then this represents the set (-4, 7) where the values -4 and 7 are not included, so we should graph them with open circles.

The graph of the inequality is something like the one below.

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Answer:

[tex] \frac{4 {x }^{2} - 17x - 9 }{ {x}^{3} - 7 {x}^{2} + 7x + 15 } [/tex]

Step-by-step explanation:

In the picture.

I hope I am correct

I hope it helps :)

Answer:

The x intercepts are (7,0) and (-4,0)

Step-by-step explanation:

y = x^2 – 3x - 28

Set y=0

0 = x^2 – 3x - 28

Factor.  What 2 numbers multiply to -28 and add to -3

-7*4 = -28

-7+4 = -3

0 = (x-7)(x+4)

Using the zero product property

0 = (x-7)      0 = x+4

x=7              x = -4

The x intercepts are (7,0) and (-4,0)

Answer:

908360.67 lb-ft

Step-by-step explanation:

height of tank= 6 ft

diameter of the tank = 4 ft

density of water p = 62.4 lbs/ft

A is the cross sectional area of the tank

A = [tex]\pi r^{2}[/tex]

where r = diameter/2 =  4/2 = 2 ft

A = 3.142 x [tex]2^{2}[/tex] = 12.568 ft^2

work done = force x distance through which force is moved

work = F x d

Force  due to the water = pgAh

where g = acceleration due to gravity = 32.174 ft/s^2

Force  = 62.4 x 32.174 x 12.568 x 6 =  151393.44 lb

work done = force x distance moved

work = 151393.44 x 6 = 908360.67 lb-ft