The total cost of four pens and seven mechanical pencils is $13.25. The cost of each pencil is 75 cents.
a. Using an arithmetic approach, find the cost of a pen.
b. Let the cost of a pen be dollars. Write an expression for the total cost of four pens and seven mechanical pencils in terms of .
c. Write an equation that could be used to find the cost of a pen.
d. Determine a value for for which the equation you wrote in part (b) is true.

By using the given fraction of rock 'a' against the total weight of two rocks, we can find that rock 'a' weighs approximately 0.357 lbs.

The student's question involves calculating the weight of a rock, given as a fraction of a total weight. In this case, they are talking about a scenario where a geologist uses a scale to weigh two rocks together, with a total weight of 2 1/2 lbs, and rock 'a' is specified to be 1/7 of this total weight. To determine the weight of rock 'a', we simply divide the total weight by 7.

So, 2 1/2 lbs is equivalent to 2.5 lbs (since 1/2 is the same as 0.5). To find the weight of rock 'a', we take this total weight and perform the operation: 2.5 ÷ 7 = 0.357 lbs.

Therefore, rock 'a' weighs approximately 0.357 lbs. Remember, this is an estimation because the weight of the rock is being given as a fraction of the total weight, and actual weights can vary based on factors such as density and volume.

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we know that

Amanda can jog [tex]18[/tex] miles in [tex]5[/tex] hours

so

by proportion

Find the number of miles that Amanda  can jog in [tex]4[/tex] hours

[tex]\frac{18}{5} \frac{miles}{hours} =\frac{x}{4} \frac{miles}{hours} \\ \\5*x=18*4 \\ \\x=72/5 \\ \\ x=14.4\ miles[/tex]

therefore

the answer is

[tex]14.4\ miles[/tex]

The volume of a cuboid is given as length × width × height thus the volume of the paperback book will be 882 cm².

Volume is the scalar quantity of any object that specified occupied space in 3D.

Volume has units of cube example meter³,cm³, etc.

Given a paperback book shape as cuboid

Length(tall) = 21 cm

Width(wide) = 12cm

Height (thick) = 3.5 cm

The volume of the cuboid is given as

Volume = length × height × width.

Volume = 21 × 12 × 3.5

Volume = 882 cm²

Hence" The volume of a cuboid is given as length × width × height thus the volume of the paperback book will be 882 cm²".

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Answer:

[tex](4 \times 1)+(3 \times \frac{1}{100})+(5 \times \frac{1}{1000})[/tex]

Step-by-step explanation:

Given : MARIA WALKED 4.035 KILOMETERS.

To Find :WHAT IS 4.035 WRITTEN IN AS EXPANDED FORM ?

Solution :

Number = 4.035

The numbers after decimals when read from first to last has positions tenth , hundredth , thousandth and so ...

The number before the decimal part has positions ones , tens , hundreds and so on when read from last to first

Now 4 is at ones place

0 is at tenth place

3 is at hundredth place

5 is at thousandth place

So, Expanded form : [tex](4 \times 1)+(3 \times \frac{1}{100})+(5 \times \frac{1}{1000})[/tex]

Answer with Step-by-step explanation:

p is true then ~p is false.

q is false then ~q is true.

A. p -> q

if p is true and q is false then this gives false truth value.

Hence, here truth value is F

B. ~p/\~q

if any one of them is false then it gives false truth value.

Hence, here truth value is F(since,~p is false)

C. p->~q

true statement implies a true statement hence, truth value will be true

Hence, here truth value is T(p true implies ~q true)

D. q\/~p

if any one of them is true then compound statement is true.

Hence, here truth value is F(since, ~p and q both are false)

E. p/\~q

if both true then compound statement is also true.

Hence, here truth value is T(since p and ~q both are true)

Final answer:

The volume of the rectangular block of ice is 85.5 cubic feet. This was found by converting the mixed numbers into improper fractions, then multiplying the length, width, and height together using the formula volume = length × width × height.

Explanation:

To find the volume of a rectangular block of ice with the given dimensions, we simply need to multiply the length, width, and height together. The formula to calculate volume is Volume = length × width × height. First, however, we need to convert the mixed numbers into improper fractions so we can multiply them easily.

The length is given as 6 1/3 feet, which can be converted to an improper fraction: (6 × 3) + 1 = 19/3 feet. The height is given as 1 1/2 feet, which is (1 × 2) + 1 = 3/2 feet.

Now, to find the volume, we multiply these dimensions with the width, which is 3 feet.

Volume = (19/3) feet × 3 feet × (3/2) feet
The feet × feet × feet will give us cubic feet.

Multiplying these together:
Volume = (19 × 3 × 3) / (3 × 2) cubic feet
Volume = 171/2 cubic feet or 85.5 cubic feet

Thus, the volume of the block of ice is 85.5 cubic feet.

To ascertain if a vector field is conservative or not, you need to calculate the curl of the field or integrate over the components of the vector field. If the curl is zero, it's conservative. If the curl isn't zero or an integral doesn't exist, the field is not conservative.

To determine if the vector field f(x, y, z) = ye−xi + e−xj + 2zk is conservative, we need to find if there exists a function f such that f is the gradient (denoted by ∇) of f. This can be done by checking if the cross product of the vector field is equal to zero, which signifies that the field is conservative.

First, we calculate the curl (∇ x F) of the vector field, which gives us the derivatives of the field components. If the curl is zero, then the vector field is conservative. If it is not zero, this indicates that the vector field is non-conservative.

Alternatively, we can integrate over the components of the vector field to try and find a potential function. If an integral exists, then we can say that the vector field is conservative.

However, if it fails these conditions, then the vector field is not conservative and the function f does not exist for it (dne). Thus, in the case where the vector field is not conservative, enter 'dne'.

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Answer:

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

Where, x = total friends

Step-by-step explanation:

Given,

The part of the salad has eaten = [tex]\frac{1}{3}[/tex]

Total part of the salad = 1,

Thus, the remaining part of the salad = original part - part has eaten

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

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

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

If there are x friends,

Then the portion of the original bowl of salad received by each friend

[tex]=\frac{\text{Remaining part}}{\text{Total friends}}[/tex] [tex]=\frac{2}{3x}[/tex]

f(x)=x2-10x+22 domain of f

Answer: all real numbers

Range of F

Answer: y> -3

The equation of the parabola is y = ax² = (-1/2)x² where a = -2 and b = -8 are the required values of a and b.

The first derivative of y = ax² that represents the slope of the tangent line to the curve of y = ax² .  

Here, dy/dx = 2ax.  

When x = 2,

dy/dx = 2a(2) = 4a.

The point of tangency is (2,y), where y = a(2)², or y=4a;

thus, the point of tangency is; (2, 4a).  

The equation of the tangent line to y=ax² at (2,4a)

Now differentiating y=ax² with respect to x,

   dy/dx = 2ax  

dy/dx (at 2,4a) = 2a(2) = 4a

The line 2x + y = b is tangent to y = ax² at (2,4a).

The slope of 2x + y = b can be found by solving 2x + y = b for y:

y = b - 2x        

Slope m = -2

Thus, dy/dx = 4a = - 2, and thus a = -2/4, or a = -1/2.  All we have to do now is to find the value of b.  

We know that 2x + y = b, then if x=-2 and y=-8,

2(-2) + [-8] = b = -4 - 8 = -12

Thus, the equation of the parabola is y = ax² = (-1/2)x² where a = -2 and b = -8 are the required values of a and b.

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Answer:

The maximum number of students that can attend each meeting is:

40

Step-by-step explanation:

A school conference room can seat a maximum of 83 people.

The principal and two counselors need to meet with the school’s student athletes to discuss eligibility requirements.

Let there be x students,there will be x parents

that means x+x+3≤83

Subtracting both sides by 3,we get

2x≤80

dividing both sides by 2,we get

x≤40

Hence, the maximum number of students that can attend each meeting is:

40

The acceleration after 5 seconds is 20 m/s^2.

To find the acceleration, we need to take the second derivative of the position function.

x(t) = 5 + 10t^2

Taking the derivative with respect to time, we get:

v(t) = 20t

Taking the derivative again, we get the acceleration:

a(t) = 20

Therefore, the acceleration after 5 seconds is 20 m/s^2.

Answer:

the answer is A they plan to sell it in 5 years

Step-by-step explanation:

Answer:

263.56 :)

Step-by-step explanation: