Lee spent $29 to purchase a combination of drinks, sandwiches, and chips for himself and his friends. A drink costs $1.50, a sandwich costs $5, and chips cost $1.25. Identify the linear equation that represents this situation.

Answer:

Step-by-step explanation:

Let be [tex]f(x) = \frac{1}{8\cdot x}\cdot \ln(2\cdot x) -7[/tex], the first and second derivatives of the function are, respectively:

[tex]f'(x) = \frac{\left(\frac{2}{2\cdot x}\right)\cdot 8\cdot x-8\cdot \ln (2\cdot x) }{64\cdot x^{2}}[/tex]

[tex]f'(x) = \frac{8-8\cdot \ln (2\cdot x)}{64\cdot x^{2}}[/tex]

[tex]f'(x) = \frac{1-\ln(2\cdot x)}{8\cdot x^{2}}[/tex]

[tex]f''(x) = \frac{\left(-\frac{2}{2\cdot x} \right)\cdot (8\cdot x^{2})-[1-\ln(2\cdot x)]\cdot (16\cdot x)}{64\cdot x^{4}}[/tex]

[tex]f''(x) = \frac{-8\cdot x-16\cdot x+16\cdot x\cdot \ln (2\cdot x)}{64\cdot x^{4}}[/tex]

[tex]f''(x) = \frac{-24\cdot x+16\cdot x \cdot \ln (2\cdot x)}{64\cdot x^{4}}[/tex]

[tex]f''(x) = -\frac{3}{8\cdot x^{3}}+\frac{\ln (2\cdot x)}{4\cdot x^{3}}[/tex]

Now, let equalise the first derivative to zero and solve the resulting expression:

[tex]\frac{1-\ln(2\cdot x)}{8\cdot x^{2}} = 0[/tex]

[tex]1-\ln(2\cdot x) = 0[/tex]

[tex]\ln(2\cdot x) = 1[/tex]

[tex]\ln 2 +\ln x = 1[/tex]

[tex]\ln x = 1-\ln 2[/tex]

[tex]x = e^{1-\ln 2}[/tex]

[tex]x = \frac{e}{e^{\ln 2}}[/tex]

[tex]x = \frac{e}{2}[/tex]

[tex]x \approx 1.359[/tex]

This result is evaluated at the second derivative expression:

[tex]f''(1.359) =-\frac{3}{8\cdot (1.359)^{3}}+\frac{\ln [2\cdot (1.359)]}{4\cdot (1.359)^{3}}[/tex]

[tex]f''(1.359)\approx -0.050[/tex]

The critical value leads to a critical maximum and there are two intervals:

[tex](0, 1.359)[/tex] - Increasing

[tex](1.359,+\infty )[/tex] - Decreasing

The graphic of the function is presented below as attachment.

Answer:

  increasing: x > 0

  decreasing: x < 0

Step-by-step explanation:

It should be no mystery that the graph attached is decreasing where the graph is blue, and increasing where the graph is red. The turning point is the vertex.

  increasing: x > 0

  decreasing: x < 0

Answer:

22

Step-by-step explanation:

2x+4+x-10=60

3x-6=60

3x=66

x=22

Answer:

[tex]\boxed{\bold{\huge{\boxed{Option \ 4: \ x = 22}}}}[/tex]

Step-by-step explanation:

If AD is a ray inside angle ABC

Then

∠ABD + ∠DBC = ∠ABC

2x + 4 + x - 10 = 60

3x - 6 = 60

Adding 6 to both sides

3x = 60 + 6

3x = 66

Dividing both sides by 3

x = 22

Step-by-step explanation:

In expression:25w+55

variable=w

cofficient = coefficient of variable (w)=25

constant=55

In the given expression variable is "w", the coefficient is "25" and the constant is"55".

An expression is a combination of some mathematical symbol such that arithmetic operator and variable such that all are constrained and create an equation.

In other meaning, expression is very useful to determine the end or root value of constraint.

For example 3x +5y

The constraint of expression is represented as = or <, >.

Given the expression

25w+55

Now, in general, the variable is given by an English symbol so "w" will be the variable.

The constant which in multiply of variable is called coefficient so "25" will be coefficient.

Now,

The only remaining term "55" is a constant.

Hence "In the given expression variable is "w", the coefficient is "25" and the constant is"55".

To learn more about expression,

https://brainly.com/question/14083225

#SPJ2

Answer:

3/4=.75

i wish i could explain but i dont really know but there's the anwser at least

Hope i helped

SJ

Answer:

the answer is 0.75

Step-by-step explanation:

You can put that into a decimal. 3/4 = 0.75 . Dividing a number by a larger number ends in an answer that is less than one always!.

Answer:

JL = 21

Step-by-step explanation:

Given that K is on line segment JL, therefore:

KL + JK = JL (according to segment addition postulate)

KL = 2x - 2

JK = 5x + 2

JL = 4x + 9

Thus:

[tex] (2x - 2) + (5x + 2) = (4x + 9) [/tex]

Solve for x

[tex] 2x - 2 + 5x + 2 = 4x + 9 [/tex]

[tex] 2x +5x - 2 + 2 = 4x + 9 [/tex]

[tex] 7x = 4x + 9 [/tex]

Subtract 4x from both sides

[tex] 7x - 4x = 4x + 9 - 4x [/tex]

[tex] 3x = 9 [/tex]

Divide both sides by 3

[tex] \frac{3x}{3} = \frac{9}{3} [/tex]

[tex] x = 3 [/tex]

Find the numerical length of JL

[tex] JL = 4x + 9 [/tex]

Plug in the value of x

[tex] JL = 4(3) + 9 = 12 + 9 = 21 [/tex]

Answer:

1 1/200

Step-by-step explanation:

1 1/200

one and one two-hundreth

Answer:

135 square centimeters.

Step-by-step explanation:

The area of a triangle is given by the formula:

[tex]A=\frac{1}{2}bh[/tex]

Where b is the base length and h is the length of the vertical height.

From the triangle, we can see that the base is 18 and the vertical height is 15. Thus:

[tex]A=\frac{1}{2}(18)(15)[/tex]

Multiply:

[tex]A=(9)(15)\\A=135\text{ cm}^2[/tex]

The area of the triangle is 135 square centimeters.

Answer:

135 cm

Step-by-step explanation:

Hi there! :)

Answer:

[tex]\huge\boxed{15.87kg}[/tex]

To solve, simply set up a proportion. Let "x" represent the mass of a 95 kg person on the moon:

[tex]\frac{14.2kg}{85kg} = \frac{x}{95kg}[/tex]

Cross multiply:

[tex]14.2 * 95 = 85 * x[/tex]

[tex]1349 = 85x[/tex]

Divide both sides by 85:

[tex]1349/85 = 85x/85[/tex]

[tex]x = 15.87 kg[/tex]

Answer:

15kg

Step-by-step explanation:

85/14.2=5.98

95/6=15

Answer:

See below.

Step-by-step explanation:

So we have a function f(x) which is:

[tex]f(x)=5+350x[/tex]

And this represents the total cost (f(x)) in dollars for renting a beach house for x days.

If we use 5 for x:

[tex]f(5)=5+350(5)[/tex]

Multiply:

[tex]f(5)=5+1750=1755[/tex]

This means that the total cost to rent the beach house for 5 days is $1755.

Answer:

The cost of renting the house for 5 days

$1755 for 5 days

Step-by-step explanation:

We are given the function:

f(x) = 5+350x

f(x) represents the total cost in dollars and x represents the days.

If we want to find f(5), we must substitute 5 in for x.

f(5) = 5+350(5)

Multiply 350 and 5.

f(5)= 5+ 1750

Add 5 and 1750.

f(5)= 1755

x represents days and we substituted 5 in for x. Therefore, f(5) represents the cost of renting the beach house for 5 days. f(5) is equal to 1755.

So, It will cost $1755 to rent the beach house for 5 days.

Answer:

3/4+(-2 1/2)

Exact form -7/4

Decimal form -1.75

mixed number -1 3/4

Answer:

Quadrant 2 I think.

Step-by-step explanation:

You stet on the x axis wich is positive and you second number on the y axis is negitive

Answer:

c

Step-by-step explanation:

cc

Answer:

the anser of this question for a is 17

Step-by-step explanation:

all sides are the same

Answer:

B) There is NOT sufficient evidence to conclude the proportion of work time linguists study a new language is more than 10%.

Step-by-step explanation:

Given that:

the null hypothesis is;

[tex]H_o : p =0.10[/tex]

the alternative hypothesis is:

[tex]H_a : p >0.10[/tex]

The p - value for the hypothesis is 0.09

The level of significance ∝ = 0.025

The Decision rule is that to reject the null hypothesis if the p-value is less than the level of significance ∝.

Conclusion: We fail to reject the null hypothesis because the p-value is  greater than the level of significance , therefore:

There is NOT sufficient evidence to conclude the proportion of work time linguists study a new language is more than 10%.

Answer:

Step-by-step explanation:

Let b be the length of the second parallel side

Area of a trapezium is given by

[tex]A = \frac{1}{2} (a + b)h[/tex]

where

h is the height

a and b are the parallel sides

From the question

Area = 230 cm²

height = 20cm

one of parallel side / a = 8 cm

Substitute the values into the above formula and solve for b

That's

[tex]230 = \frac{1}{2} ( 8 + b) 20[/tex]

Reduce the fraction with 2

That's

[tex]230 = (8 + b) \times 10[/tex]

Expand the terms

That's

[tex]230 = 80 + 10b[/tex]

[tex]10b = 230 - 80 \\ 10b = 150[/tex]

Divide both sides by 10

We have the final answer as

Hope this helps you

Answer:

Step-by-step explanation:

Since ∠3 and ∠4 are supplementary it means the the sum of their angles is equal to 180°

To find the angles add both ∠3 and ∠4 and equate it to 180° solve for x and substitute it into their various expressions

That's

∠3 + ∠4 = 180

5x + 22 + 7x + 2 = 180

12x + 24 = 180°

12x = 180 - 24

12x = 156

Divide both sides by 12

x = 13

So for ∠3

∠3 = 5x + 22

∠3 = 5(13) + 22

= 65 + 22

∠3 = 87°

For ∠4

∠4 = 7x + 2

∠4 = 7(13) + 2

= 91 + 2

∠4 = 93°

We have the answers as

Hope this helps you

Answer:

[tex] \boxed{ \bold{ \boxed{ \sf{ m \: ∠ \: 3 = 87 °}}}}[/tex]

[tex] \boxed{ \bold{\boxed{ \sf{m \: ∠4 = 93 °}}}}[/tex]

Step-by-step explanation:

We know that the sum of supplementary angle adds up to 180 °

So,

[tex] \sf{5x + 22 + 7x + 2 = 180°}[/tex]

Collect like terms

⇒[tex] \sf{12x + 22 + 2 = 180°}[/tex]

Add the numbers

⇒[tex] \sf{12x + 24 = 180°}[/tex]

Move 24 to right hand side and change it's sign

⇒[tex] \sf{12x = 180 - 24}[/tex]

Subtract 24 from 180

⇒[tex] \sf{12x = 156}[/tex]

Divide both sides of the equation by 12

⇒[tex] \sf{ \frac{12x}{12} = \frac{156}{12} }[/tex]

Calculate

⇒[tex] \sf{x = 13}[/tex]

Value of x = 13

Now, substituting / Replacing the value of x

[tex] \sf{m ∠ 3 = 5x + 22}[/tex]

⇒[tex] \sf{ m \: ∠ \: 3 = 5 \times 13 + 22}[/tex]

⇒[tex] \sf{m \: ∠ \: 3 = 65 + 22}[/tex]

⇒[tex] \sf{ \: m \: ∠ \: 3 = 87}[/tex]

Again,

[tex] \sf{ \: m \: ∠ \: 4 = 7x + 2 }[/tex]

⇒[tex] \sf{m \: ∠ \: 4 = 7 \times 13 + 2}[/tex]

⇒[tex] \sf{ \: m \: ∠ \: 4 \: = 91 + 2 }[/tex]

⇒[tex] \sf{m \: ∠ \: 4 = 93 }[/tex]

m ∠ 3 = 87

m ∠ 4 = 93

Hope I helped!

Best regards!!

Answer:

[tex]g(-3) = 2[/tex]

[tex]g(0) = 3[/tex]

Step-by-step explanation:

Given

The attached graph

Required

Determine

[tex]g(-3)[/tex]

[tex]g(x) = 3[/tex]

Since a graph has been provided, the question will be solved graphically;

Solving g(-3)

This implies that;

x = -3

And the interpretation is to solve for the y value when x = -3

From the attached graph;

When x = -3; y = 2

Hence;

[tex]g(-3) = 2[/tex]

Solving g(x) = 3

This implies that;

y = 3

And the interpretation is to solve for the x value when y = 3

From the attached graph;

When y = 3; x = 0

Hence;

[tex]g(0) = 3[/tex]

Answer:

-6

Step-by-step explanation:

2x = x-6

subtract x from both sides

x = -6

Answer:

2x=x-6

Step-by-step explanation:

2 times a number -> 2x

6 less than x -> x-6

Our equation would be:

2x=x-6

Subtract x from both sides.

2x-x=x-x-6

Combine like terms

x=-6

Answer:

375 miles

Step-by-step explanation:

Set it up as an equation where m=miles

$75 +.6m=.80m

Answer:

(-3, -2)

Step-by-step explanation:

y = -2x + 4; y = -2

plug in y

-2 = -2x + 4

subtract 4 from each side

-6 = 2x

divide by 2

x = -3

Answer:

The null hypothesis will not be rejected at 5% significance level.

Step-by-step explanation:

Consider a Chi-square test for goodness of fit.

The hypothesis can be defined as:

H₀: The observed frequencies are same as the expected frequencies.

Hₐ: The observed frequencies are not same as the expected frequencies.

The test statistic is given as follows:

 [tex]\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}[/tex]

The information provided is:

Observed values:

Half Pint: 36  

XXX: 35  

Dark Night: 9  

TOTAL: 80

The expected proportions are:  

Half Pint: 40%

XXX: 40%  

Dark Night: 20%  

Compute the expected values as follows:

E (Half Pint)  

 [tex]=\frac{40}{100}\times80=32[/tex]

E (XXX)  

 [tex]=\frac{40}{100}\times80=32[/tex]

E (Dark night)  

 [tex]=\frac{20}{100}\times80=16[/tex]

Compute the test statistic as follows:

 [tex]\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}[/tex]

     [tex]=\frac{(36-32)^{2}}{32}+\frac{(35-32)^{2}}{32}+\frac{(9-16)^{2}}{16}\\\\=3.844[/tex]

The test statistic value is, 5.382.

The degrees of freedom of the test is:

n - 1 = 3 - 1 = 2

The significance level is, α = 0.05.

Compute the p-value of the test as follows:

p-value = 0.1463

*Use a Chi-square table.

p-value = 0.1463 > α = 0.05.

So, the null hypothesis will not be rejected at 5% significance level.

Answer:

Total # of marbles: 10

# of red marbles: 7

Probability of choosing a red marble out of 10 marbles: 7/10

Then in the second round, you replace that marble so you still have a total of 10 marbles and 7 of them will still be red: 7/10

Multiply...

7/10 x 7/10 = 49/100

PROBABILITY: 49/100 (or 49%)

Hoped I helped

Answer:

10 hundreds or 1 thousand

Step-by-step explanation:

1 hundred is 100. 10 * 100 = 1,000. Just count the zeros in the factors (there's 1 zero in 10 and 2 zeros in 100) and then put them all at the end of the answer to get 3 zeros, which is 1,000, or one thousand.

Answer:

Add −11 and 5.

−6

Move 5 spaces to the right starting from -11 and you will end up at -6! (●'◡'●)

Answer:

-6

Step-by-step explanation:

So we want to find the value of:

[tex](-11)+5[/tex]

Simply add:

[tex](-11)+5=-6[/tex]

Further notes:

Again, to use the number line, place the first point at -11. Since we are adding, we move to the right.

So, starting at -11, move 5 spaces to the right. You should end up at -6, confirming our previous answer.

Answer:

8 km

Step-by-step explanation:

Write and solve an equation of ratios, as follows:

  x           8000 km

--------- = -----------------

2 km       2000 m

Cross-multiplying, we get (2000 m)x = (8000 m)(2 km),

which reduces to x = 8 km

Answer:

Step-by-step explanation:

Since the table showed her that  2 km = 2000m.

To determine, how many km in 2000m, she would divide by 1000.

= 2000 / 1000 = 2 km.

Similarly, for 8000m = 8000 / 1000 = 8 km

Answer:

9.33

Step-by-step explanation:

12( 4 + 3 ) / 6 + 3

48 + 36 / 6 + 3

84 / 9

9.33

Answer:

Here is an example

Use distributive property to write an expression that is equivalent to 5 x + 25. Solution : 5x + 25 = 5x + 5(5) 5x + 25 = 5(x + 5) Example 7 : Use distributive property to write an expression that is equivalent to 7y + 5y. Solution : 7y + 5y = y(7 + 5) Example 8 : Use distributive property to write an expression that is equivalent to 0.2y + z.

Step-by-step explanation:

Answer:

38 people

Step-by-step explanation:

add 11, 18, and 9 together