p,3,5,7,q,13 is a sequence of prime numbers.Find the value of p+q.
A.10
B.12
C.13
D.14

The water level rise when it is 6 feet deep is 0.318 feet/min when a conical tank is filled with water at a pace of 9 feet per minute.

Given that,

A conical tank is filled with water at a pace of 9 feet per minute. The tank is 10 feet tall and has a base radius of 5 feet. It stands pointed down.

We have to find how quickly does the water level rise when it is 6 feet deep.

We know that,

dv/dt= 9 feet³/min

x=5 feet

y=10 feet

And we have x/y=1/2 ----->equation(1)

We know the formula

V=1/3πx²y

Differentiating on both sides

dv/dt=9

1/3πy(2x) dx/dt+π/3(x²)dy/dt

=π/3[2xy dx/dt+x² dy/dt]

From equation(1)

x/y=1/2       or     y=2x

dy/dt= 2dx/dt

Now,

9=π/3[xy dy/dt+x² dy/dt]

9= π/3 dy/dt[xy+x²]

dy/dt=9×3/π×(18+9)

dy/dt=27/π×27

dy/dt= 1/π

dy/dt=0.318 feet/min

Therefore, The water level rise when it is 6 feet deep is 0.318 feet/min when a conical tank is filled with water at a pace of 9 feet per minute.

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Answer:     the mathematics books must be together but the other books can be arranged in any order? Answer:

Step-by-step explanation:

We know that the required zero of the given polynomial 3x²+4x²-7=0 is (B) x = 1.

A polynomial is a mathematical formula that involves only the operations of addition, subtraction, multiplication, and powers of positive integers of the variables and is composed of coefficients and indeterminates.

An example of a polynomial with a single indeterminate x is x² - 4x + 7.

So, we have the equation:

3x²+4x²-7=0

Now, calculate the zero of the polynomial as follows:

When x = 0:

P(x) = 3x² + 4x² - 7 = 0

P(0) = 3(0)² + 4(0)² - 7

P(0) = - 7

Not zero

When x = 1:

P(x) = 3x² + 4x² - 7 = 0

P(1) = 3(1)² + 4(1)² - 7

P(1) = 3 + 4 - 7

P(1) = 0

Zero of the polynomial.

Therefore, we know that the required zero of the given polynomial 3x²+4x²-7=0 is (B) x = 1.

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Answer:

The lowest common denominator is 12

Step-by-step explanation:

Finding the lowest common denominator

Multiples of 6: 6,12,18,24

Multiples of 4: 4,8,12,16,20

The lowest common multiple is 12

The lowest common denominator is 12

F= k*a*v^2

a= 250

v=190

30300=k*250*{190^2}

k= 0.003357

F= 0.003357*250*180*180

F=27135

The lifting force is 27135

The total area that all of a 3D object's faces cover is the surface area. The surface area of a cube is its surface area, for instance, if we are trying to determine how much paint is needed to paint it. Always expressed in square units.

The entire surface of a three-dimensional shape is referred to as its surface area. A cuboid with six rectangular faces has a surface area equal to the sum of the areas of each face. Alternatively, you can label the cuboid's length, width, and height (l, w, and h), then calculate its surface area (SA) using the formula: SA=2lw+2lh+2hw.

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Answer: c<4

Step-by-step explanation:

C fewer than 4 means that c is smaller than 4! So we use this mark <

So the answer is c<4

Answer:

X=1

Step-by-step explanation:

For step one you have to Distribute

2x-1(4x+3)=-7x+2 --> 2x-4x-3=-7x+2

For step two you have to Combine Like Terms

2x-4x-3=-7x+2 --> -2x-3=-7x+2

For step three you have to Add Three To Both Sides

-2x-3=-7x+2 --> -2x=-7x+5

For step four you have to Add 7x To Both Sides

-2x=-7x+5 --> 5x=5

For step 5 you have to Divide Both Sides By The Same Factor (5)

5x=5 --> x=1

Hope This Helps!

Answer:

the last one is obviously represent a linear of function

Answer:

P(A) =0.5 obviously since it didn't say like P(AC) or P(AD)

The slopes of the lines are 2/3, 5, 5/6 and 1 respectively

The slope of a line is a measure of its steepness or incline. It is defined as the ratio of the vertical change (called the "rise") to the horizontal change (called the "run") between two points on the line.

The slope of a line can be expressed using the following formula:

Slope = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are two points on the line.

1.  P₁(0,2) and P₂(3,4):

Slope = (4-2)/(3-0) = 2/3

2.  P₁(1,2) and P₂(3, 7):

Slope = (7-2)/(3-2) = 5/1 = 5

3. P₁(-1,1) and P₂(5,6):

Slope = (6-1) / (5-(-1)) = 5/6

4. P₁(-1,-2) and P₂(10,11)

Slope = (11-(-1)) / (10-(-2)) = 12/12 = 1

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Answer:

Step-by-step explanation:

Based on the graph, it appears that Giselle's grandma is offering to pay for a certain percentage of the cost of the book for every weed that Giselle pulls in her garden. The more weeds Giselle pulls, the more money her grandma will contribute, which will reduce the amount that Giselle has to pay for the book. This can be a good way for Giselle to save money on the book without using all of her savings.

1. True, the graph's beginning represents cost before she picks any weeds.

2. False, the graph shows that the cost for he goes into the negatives, showing that she is still able to earn more money from picking weeds.

3.True, from 0 weeds to 5 weeks picked you can see the price change from $18 to $17.

4. True, once she picks 90 weeds she earns the exact amount of money needed to buy the book.

5. False, she would need to pull 90 weeds in order to not spend her own money.

-57 decrease

In this equation.

The value of the function at x=0 is 17.78(4.86)^0 = 17.78(1) = 17.78.

ii. The ratio of output values ​​corresponding to an increment of 1 in input values ​​is (4.86)^1 = 4.86.

iii. A percent change of 1 unit is (4.86 - 1) × 100% = 286% increase.

For the function h(x) = 94.71(0.57)^x:

Thus, the value of the function at x=0 is 94.71(0.57)^0 = 94.71(1) = 94.71.

ii. The ratio of the output value corresponding to an increment of 1 in the input value is (0.57)^2 = 0.57.

iii. Percentage change of 1 unit is (0.57 - 1) × 100% = -57 reduction

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On solving the provided question we can say that  the equation of the line will be  y+11 = 0.

The slope of a line is how steeply it slopes from left to right. The slope of a line is determined by dividing its rise (vertical change) by its slope, which is its horizontal change. Regardless of whatever two locations on the line you pick, the slope of the line is always constant (it never changes).

To find the coordinates of two points on the line, choose two. Find the difference between these two locations' y-coordinates (gradients). Find the difference between these two places' x coordinates (runs). Divide the change in the y coordinate by the difference in the x coordinate (slope/history or slope).

Here,

slope, m= 0 as these are parallel line.

so the equation of the line will be

y-y1 = m(x-x1)

y+11 = 0

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The numbers which are greater than 1 are 2 ÷ 1/3 and 3/4 ÷ 2/3 so options (B) and (D) are correct.

In such a fraction, the value that appears above the horizontal line is referred to as the numerator.

In another word, the fraction is the division of the two numbers but the division is not wholly complete.

As per the given fractions,

2 ÷ 1/3 = 2 x 3/1 = 6 > 1

3/4 ÷ 2/3 = 3/4 x 3/2 = 9/8 > 1

Hence "The numbers which are greater than 1 are 2 ÷ 1/3 and 3/4 ÷ 2/3".

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The complete question below,

The inequality to describe the number of subscriptions Andre must sell to reach his goal is  3s + 25 ≥ C.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Assuming the cost of soccer cleats to be 'C' and the number of subscriptions to be 's'.

∴ The inequality that represents this situation is 3s + 25 ≥ C to real his goal.

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Answer:

the first number is 20, second is 9

Step-by-step explanation:

y=3x-7

y+x=29

rearrange the first equation

y-3x=-7

and

y+x=29

solving the simultaneous equation:

y-3x=-7

            -

y+x=29

= -4x=-36

divide both sides by -4

x = 9

now substitute the x value into the equation: y+x=29

= y + 9 = 29

y = 20

The function lim x-->a [sin(x) + a₀ + a₁x + ...+ aₙxⁿ ] has lim x-->a [sin(a) + a₀ + a₁a + ...+ aₙaⁿ] as the limit of the function as x approaches a.

Generally, To evaluate the limit of a function as x approaches a certain value, we need to substitute the value of x with the limit value and see what the function evaluates to.

In this case, we have:

lim x-->a [sin(x) + a₀ + a₁x + ...+ aₙxⁿ]

Substituting x with a, we get:

lim x-->a [sin(a) + a₀ + a₁a + ...+ aₙaⁿ]

This is the limit of the function as x approaches a.

Note that the terms a₀, a₁x, etc. are constants and will not affect the limit of the function. Therefore, the limit of the function as x approaches a is simply sin(a).

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The cost of plowing the roads after 24 inches have fallen is increasing at a rate of $0.4 million per inch.

Evaluate this expression, we need to break this into two pieces. First, we have the value of c(15), so thankfully, we don't need to run any calculations to find it. This means that we just need to evaluate this definite integral, which is the integral of the derivative of c(n) from 15 to 24.

The Fundamental Theorem of Calculus relates a function to its antiderivative as a way to find the value of the integral of that function. Since the antiderivative of  , which we have the value for at the endpoints of this integral, we can evaluate this integral as follows.

[tex]\int\limits^a_b {c'(n)} \, dn = c(24 ) - c(15) = 0.4 - 0.6 = -0.2[/tex]

We can now find the value of this entire expression as follows.

[tex]c(15) +\int\limits^a_b {c'(n)} \, dn = 0.6 + (-0.2) = 0.4[/tex]

Since this represents the derivative of C(n), the cost for plowing the roads, this tells us that the cost of plowing the roads after 24 inches have fallen is increasing at a rate of $0.4 million per inch.

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The value of [tex]f_{x}[/tex](3,2)≈12.2, [tex]f_{x}[/tex](3,2.2)≈16.8, [tex]f_{x}[/tex](3,2)≈23.25

This problem aims to find the values of a function having alternate independent variables.

A-

[tex]f_{x}(3,2) f_{x} (x,y)=lim_{h-0} \frac{(3+0.5,2)-f(3,2)}{0.5}[/tex]    considering h =±0.5

Solving for h=0.5

⇒[tex]\frac{f(3.5,2)-f(3,2)}{0.5}[/tex]

Using the table to plug in the values of the function: 22.4-17.5/0.5=9.8

Now, solving for h=-0.5

⇒[tex]\frac{f(3.5,2)-f(3,2)}{-0.5}[/tex]

Using the table to plug in the values of the function: 22.4-17.5/(-0.5)=14.6

Taking the average of both ±0.5 answers for the final answer of f(3,2)

[tex]f_{x}(3,2)=\frac{9.8+14.6}{2} \\or, f_{x}(3,2)=12.2[/tex]

B-

[tex]f_{x}(3,2.2)=lim_{h-0} \frac{(3+0.5,2.2)-f(3,2.2)}{0.5}[/tex]    considering h =±0.5

Solving for h=0.5

⇒[tex]\frac{f(3.5,2.2)-f(3,2.2)}{-0.5}[/tex]

Using the table to plug in the values of the function: 26.1-15.9/0.5=20.4

Now, solving for h=-0.5

⇒[tex]\frac{f(2.5,2.2)-f(3,2.2)}{-0.5}[/tex]

Using the table to plug in the values of the function: 9.3-15.9/(-0.5)=13.2

Taking the average of both ±0.5 answers for the final answer of f(3,2.2)

[tex]f_{x}(3,2.2)=\frac{20.4+13.2}{2} \\or, f_{x}(3,2.2)=16.8[/tex]

C-

[tex]f_{xy} (3,2)=lim_{h-0} \frac{f_{x}(3,2+h)-f_{x} (3,2) }{h} \\[/tex]     considering h =±0.2

Solving for h=0.2

⇒[tex]\frac{f_{x} (3,2.2)-f_{x} (3,2)}{0.2}[/tex]

Plugging in the answers from A and B: 16.8-12.2/0.2= 23

Now solving for h= -0.2

⇒[tex]\frac{f_{x} (3,1.8)-f_{x} (3,2)}{-0.2}[/tex]

Plugging in the values: 7.5-12.2/-0.2= 23.5

Taking an average of h=±0.2 answers to find the final answer:

[tex]f_{x}(3,2)=\frac{23+23.5}{2} \\or, f_{x}(3,2)=23.25[/tex]

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The equation that can be used to find {p}, the number of pieces Joy and her brother ate is : {p} + 4 = 16.

Given is that Joy baked 2 pizzas and cut each pizza into 8 pieces. Joy and her brother ate all but 4 pieces of pizza.

We can write the equation {p} as -

2 x 8 = 4 + {p}

{p} + 4 = 16

Therefore, the equation that can be used to find {p}, the number of pieces Joy and her brother ate is : {p} + 4 = 16.

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{Question in english language is -

Joy baked 2 pizzas and cut each pizza into 8 pieces. Joy and her brother ate all but 4 pieces of pizza. What equation can be used to find p, the number of pieces Joy and her brother ate?

The formula E3 + E4 can b expressed in the form of absolute cell address, that is option (a) $E$3+$E$4

The given formula is

E3 + E4

In the absolute cell address the coordinates of the column and row will be constant while copying a formula from one cell to the other. Here we use the dollar sign "$" before the coordinates of the column and row to correct them.

The given formula is E3 + E4

The E is the name and 3 and 4 are the coordinates of the column and row

The absolute cell address =  $E$3+$E$4

Therefore, the absolute cell address of the given formula is $E$3+$E$4

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Answer:

11x - 2 = 6x + 13 (corresponding angles)

5x = 15

x = 3

The simplified form of the expression [tex]\frac{2}{\frac{3}{11}}[/tex] is [tex]\frac{22}{3}[/tex].

To simplify the expression [tex]\frac{2}{\frac{3}{11}}[/tex], you can start by performing the division in the parentheses first:

[tex]\frac{2}{\frac{3}{11}}[/tex] = [tex]\frac{2}{\frac{3}{11}}[/tex] × [tex]\frac{11}{11}[/tex]

= 2 × [tex]\frac{11}{3}[/tex]

Then, you can simplify the fraction by dividing both the numerator and the denominator by their greatest common factor:

2 × [tex]\frac{11}{3}[/tex] = [tex]\frac{(2 * 11)}{(3 * 1)}[/tex]

= [tex]\frac{22}{3}[/tex]

So the simplified form of the expression [tex]\frac{2}{\frac{3}{11}}[/tex] is [tex]\frac{22}{3}[/tex].

Simplification is a process of making something simpler or easier to understand by reducing the amount of complexity or detail. This can be done by removing or combining elements, or by reorganizing the structure. Simplification can be used in problem-solving, decision-making, or other tasks to make it easier to understand, interpret, or use the information.

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Answer:  10

Step-by-step explanation:

As shown below, ∠ABD = ∠DAC = x.

That means tan(x) = 5 by AD and that tan(x) = AD by 20

You can set those two equations equal to each other to find the length of AD:

5 by AD = AD by 20

5 = AD square by 20

100 = AD square

AD = Square root 100 = 10

Answer:

12

Step-by-step explanation:

let a = AB b=AD c=AC

from the pythagorean theorem:

(1)a² + c² = (16+9)² = 625

(2) b² +16² = a²

(3) 81+ b² = c²

by substitution into (1):

(b²+16²) + (81+b²) = 625

2b² = 625-81-256 = 288

b² = 144

b = 12

Yes, the data in this sample indicate that these individuals have average total cholesterol levels that are desirable.

Average:

In math average refers mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.

Given,

Here we have the data of the national health and nutrition examination survey contains data on 2,263 US. adults. one of the variables is total cholesterol. total cholesterol levels less than 200 milligrams per deciliter (mg/dl) are considered desirable for adults. a reading between 200 and 239 mg/dl is considered borderline high and a reading of 240 mg/dl and above is considered high.

And we need to find that does the data in this sample indicate that these individuals have average total cholesterol levels that are desirable.

While we looking into the given question,

Total number pf participants = 2,263

Desirable level of cholesterol = less than 200 milligram

Border line level of cholesterol = Between 200 and 239 mg

Higher level of cholesterol = 240 mg

So, based on the given details, we know that at least 25% of people must have the desirable.

Therefore, the given level is a desirable one.

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Answer:

The answer is -15

Answer:

SSA

Step-by-step explanation:

If you have 2 triangles that have 2 congruent sides, and a congruent non-included angle, there is 2 possible values for the third side, so SSA does not work

Answer: Congruent

Step-by-step explanation:

Answer:

f(8) = 216

Step-by-step explanation:

f(x) = (2x - 10)³

So f(8) = (2(8) - 10)³

==> f(8) = (16 - 10)³

==> f(8) = (6)³

==> f(8) = 216