7-18 use part 1 of the fundamental theorem of calculus to find the derivative of the function.
14. [tex]h(x)=\int_{1}^{\sqrt{x}} \frac{z^{2}}{z^{4}+1} d z[/tex]

Answer:

in fractions

16/18 = 8/9

4/18 = 2/9

Answer:

8/9 and 2/9

Step-by-step explanation:

for 16/18

divide the numerator and denominator by 2 to option it's simplest form

16/18÷2/2 = 8/9

for 4/18

also divide the numerator and denominator by 2 to get the simplest form.

4/18 ÷2/2= 2/9

Answer:

15) A

Step-by-step explanation:

4x-2 + 7x + 17 = 180

11x + 15 = 180

11x = 165

x = 15

Because the two angles (4x-2 and 7x+17) are linear, we can say that they add up to 180 degrees.

4x-2+7x+17 = 180   Now, simplify like terms

11x + 15 = 180

11x = 165

x = 15

Thus, the value of x would be 15 (choice 1)

Answer:

339.12 cm²

Explanation:

surface area of cone: πr² + πrl

where "r" is radius, "l" is slant height

Here given:

Solve for surface area:

So

TSA

Answer:

   45. (4) (2, 2)

Step-by-step explanation:

Question 45

Solutions

We'll take x = 2 as no options with x = 3 are listed.

Ordered pair

Answer:

262 Masks

Step-by-step explanation:

190×0.38=72.2 but there cannot be 0.2 masks so it becomes 72. 190+72=262.

The total number of masks in Emma's collection is 262 Masks.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that Emma has a mask collection. she keeps 190 of the masks on her wall, which is 38% of her entire collection.

The total number of masks will be calculated as,

190×0.38=72.2

But there cannot be 0.2 masks so it becomes 72.

Total mask = 190+72

Total mask =262.

Therefore, the total number of masks in Emma's collection is 262 Masks.

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Answer:

5/8

Step-by-step explanation:

Answer:

h=3

Step-by-step explanation:

Here's the explanation

Move 10 to the other side

5h=25-10

5h=15

h=15/5

h=3

10+5h=25

10+5h-10=25-10

5h=15

[tex]\frac{5h}{5}=\frac{15}{5}[/tex]

h=3

the answer is 3

Answer:

No and the density changes along with the weight.

Answer:

  (a) No. The weight is more than 150 lb.

  (b) No. Density is not a function of volume.

Step-by-step explanation:

The weight of the aquarium is the product of the volume and the density of the contents.

The volume of the aquarium is the product of its dimensions:

  V = LWH = (1.75 ft)(1.75 ft)(1.75 ft) = 1.75³ ft³ = 5.359375 ft³

The weight of its contents, at 72 lb/ft³ will be ...

  (72 lb/ft³)(5.359375 ft³) = 385.875 lb

The aquarium should not be placed on the table. The weight of the aquarium is too great for the load limit of the table.

__

The density of water is the ratio of its mass to its volume. Density does not change with depth or volume. It is essentially constant. (Water is considered to be virtually incompressible. Its density changes slightly with temperature,)

No, the density of the water would not change.

_____

Additional comments

The half-full aquarium would weigh about 385.875/2 lb ≈ 194 lb. This is still too heavy for the table.

The density of water is actually about 62.4 lb/ft³. We assume the extra 10 lb/ft³ might take into account the weight of the aquarium and any gravel or other non-water content.

Volume of a Cylinder = pi x r^2 x height

diameter = 10, so radius = 5

height = 6

Volume = pi x 5^2 x 6

Volume = pi x 25 x 6

Volume = 150pi

Answer: 150pi cubic feet

Hope this helps!

Hi Student!

The first step that we need to take before trying to solve the problem is that we need to take out important information from the problem.  The first important piece of information that is given to us is that we are trying to find an equation of a line that is parallel to a different line.  This means that our slope is going to be the same as the initial line given.  The second piece of information that is given is a point through which our line passes through which will help us greatly when solving for our line.

The next step that we must take is to solve for y in the given equation so we can see what the slope is.

Subtract 6x from both sides

Divide both sides by 5

Now that we have completely solved for y, we can see that the slope is -1.2 using the y = mx + b formula which states that m is the slope.

Moving onto the next step, we must use the point-slope formula to determine what the new equation is that has the same slope and passes through (-4, -2).

Insert the Values

Simplify the Equation

Distribute the Equation

Subtract 2 from both sides (to isolate y)

Therefore, our final answer for the equation of the line parallel to 6x + 5y = 1 and that passes through (-4, -2) is y = -1.2x - 6.8.

Answer:

-24 + (-55) = -79

Step-by-step explanation:

-4x+6+11x - 5​

Step-by-step explanation:

[tex] = x + 6 + 11x - 5[/tex]

Organize the expression....

[tex] = x + 11x + 6 - 5[/tex]

Simplify the expression...

[tex] = 12x + 1[/tex]

...

Answer:

I think the full amount was $a18.50

Answer:

6/63

Step-by-step explanation:

To find the probability in fraction form you must first add all the evidence together and then use that number as the denominator

Answer:

2/21

Step-by-step explanation:

There were a total of 7+6+12+19+19=63 spins, 6 of which blue.

So, you can make the fraction 6/63=2/21 to represent the probability of the spinner landing on blue the next spin

Answer:

54.59

Step-by-step explanation:

carry the 10 over and 1-.41 is .59

Answer:

x = 6, y = 0, m = -1
y = mx + b
0 = -1(6) + b
0 = -6 + b
6 = b
y = -1x + (6)

Step-by-step explanation:

^^^
See answer, pretty simple.

So

equation

So equation

Part A

y-intercept: 3

It represents that after 0 months practice, the number of matches won is 3.

Part B

slope intercept form: y = mx + b

Here to find slope,

take two points: (5, 12), (0, 3)

[tex]\sf slope: \dfrac{y_2-y_1}{x_2-x_1} = \dfrac{rise}{run}[/tex]

[tex]\rightarrow \sf slope = \dfrac{3-12}{0-5} = 1.8[/tex]

Equation:

y - y1 = m(x- x1)

y - 12 = 1.8(x - 5)

y = 1.8x - 9 + 12

y = 1.8x + 3

To find Matches won after 13 months

insert x = 13

y = 1.8(13) + 3

y = 26.4 ≈ 26 matches

The team could have won 26 matches after 13 months practice.

Answer:

See below ~

Step-by-step explanation:

Part A :

Part B :

Forming the equation :

Predicting how many matches can be won with 13 months of practice :

Answer:

Step-by-step explanation:

How do you tell if a relation is a function using domain and range?

Find the domain by listing all the x values from the relation. Find the range by listing all the y values from the ordered pairs. Repeated values within the domain or range don't have to be listed more than once. In order for a relation to be a function, each x must correspond with only one y value.

which means

There is not a function

because the domain value 10 is paired with both and 10 and 1

and the domain is 10,26,40,56

Step-by-step explanation:

[tex]3 \sqrt{3 \:} + \sqrt{3} [/tex]

Simplify,then combine each:

[tex] = 4 \sqrt{3} [/tex]

or

[tex]3 \sqrt{3 \:} + \sqrt{3} [/tex]

=5.196+1.732

=6.928

[tex] \approx6.930[/tex]

If the height of a right triangular prism is 1 5/6 inches. The surface area of the solid formed is: 598.33 in².

First step

Right triangular prism=1 5/6 inches= 11/6 inches

Height of the base=8 2/3 inches = 26/3 inches

Second step

Surface area = 5(10× 10) + (0.5÷ 10 × 26/3) + 3(10× 11/6)

Surface area = 5(100) +43.33+ 3(18.33)

Surface area = 500) +43.33 + 55

Surface area = 598.33 in²

Therefore the surface area of the solid formed is about 598.33 in²

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Answer:

47/6cm or [tex]7\frac{5}{6}[/tex]cm

Step-by-step explanation:

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

FA= 5/12

AB= 2/3

CD=2

ED=[tex]1\frac{1}{4}[/tex]

BC= 5/6

All=47/6 or [tex]7\frac{5}{6}[/tex]

Answer:

56.549 feet

Step-by-step explanation:

Diameter. ft in m

18′0″ 56.55. 678.6 17.24

18′1″ 56.81.

18′2″ 57.07. 684.9

18′3″ 57.33. 688.0

18′4″ 57.60. 691.2

18′5″ 57.86. 694.3 17.64

18′6″ 58.12. 697.4 17.71

18′7″ 58.38 700.6 17.79

18′8″ 58.64 703.7 17.87

18′9″ 58.90. 706.9 17.95

18′10″ 59.17. 710.0 18.03

18′11″ 59.43. 713.1 18.11

The graph can be seen at the end, and the piecewise function for the part above the x-axis is:

f(x) = x^2 - 4 if  x ∈ (-∞, -2] or x ∈ [2, ∞)

f(x) = 4 - x^2 if x  ∈ (-2, 2).

First, we need to graph both functions, so we can see when each one is positive, the graphs of:

y = x^2 - 4

y = 4 - x^2

Can be seen at the end.

So, the first function is positive in the interval (-∞, -2] and [2, ∞), and the second function is positive in the interval (-2, 2)

So for the part of the function above the x-axis we have a piecewise function:

f(x) = x^2 - 4 if  x ∈ (-∞, -2] or x ∈ [2, ∞)

f(x) = 4 - x^2 if x  ∈ (-2, 2).

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Answer:

y= |x^2-4|

Step-by-step explanation:

Once you graph y=x^2-4 and y=4-x^2, you will get a graph like the first picture. The equation for the parts above the x-axis would be y=|x^2-4| and would graph like the second picture.

Answer:

A.) X greater than 3/5


Open circles are used for numbers that are less than or greater than (< or >). Closed circles are used for numbers that are less than or equal to and greater than or equal to (≤ or ≥).

Step-by-step explanation:

Have a great rest of your day
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The correct inequality that  has an open circle when it is graphed on a number line is,

1) x greater-than three-fifths

We have to given that,

All the expressions are,

1) x greater-than three-fifths

2) Start Fraction 4 over 7 End Fraction greater-than-or-equal-to x

3) x less-than-or-equal-to 12

4) x greater-than-or-equal-to negative 6.

We can write all the inequality as,

1)  x greater-than three-fifths

⇒ x > 3/5

Since, it has symbol '>' which represent open circle.

Hence, It is true.

2) Start Fraction 4 over 7 End Fraction greater-than-or-equal-to x.

4/7 ≥ x

Since, it has symbol '≥' which represent closed circle.

Hence, It is not true.

3) x less-than-or-equal-to 12

x ≤ 12

Since, it has symbol '≥' which represent closed circle.

Hence, It is not true.

4) x greater-than-or-equal-to negative 6.

x ≥ - 6

Since, it has symbol '≥' which represent closed circle.

Hence, It is not true.

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The table shows the correct residual values for the data set regarding the scatterplot is D. A 3-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5.

It should be noted that a scatterplot simply means a type of data display which shows the relationship between the variables.

In this case, the table shows the correct residual values for the data set regarding the scatterplot is a 3-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5.

The second column is labeled given with entries 14.95, 25.50, 32, 38.95, 42.50. The third column is labeled residual value with entries negative 2.12, 1.575, negative 1.22, 1.315, negative 1.99.

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The amount of force that is required to lift the rock if the distance from the fulcrum is 6 feet is 10 lb of force.

Based on the given graph, we can see the curve passing through the point (1.5,40), (2,30), (2.5,24), (3,20), and (4,15).

These points satisfy by the equation

y= 60/x

and,

If we input the value of x into the equation,

y= 60/6

= 10 lbs of force.

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Answer:

Keep it simple: answer 10

Step-by-step explanation:

The expected value of the defective skateboard will be 4/25. Then the correct option is B.

Probability distribution of a random variable is the collection of value and its probability pair for values of that considered random variable.

It might be a function, a table, etc.

The table is shown below.

Then the expected value of the defected skateboard will be

p = 0 x 9/10 + 1 x 1/20 + 2 x 1/25 + 3 x 1/100

p = 1/20 + 2/25 + 3/100

p = 5/100 + 8/100 + 3/100

p = 16/100

p = 4/25

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Answer:

the answer is j because it's impossible to draw a line through the center of any parallelogram that divides the figure into two equal halves that are mirror images of each other

Out of the given options, the shape that does not have a vertical line of symmetry is J. Parallelogram.

The correct answer is J. Parallelogram.

A vertical line of symmetry means that if a line is drawn vertically through the shape, the two halves will be mirror images of each other.

In the case of a line (F), it is one-dimensional and does not have an area, so it does not have any symmetry.

A square (G) has four sides of equal length and four right angles. It has both vertical and horizontal lines of symmetry, dividing it into four congruent quadrants.

A pentagon (H) is a five-sided polygon. Depending on its shape and orientation, it may or may not have a vertical line of symmetry. For example, a regular pentagon does have a vertical line of symmetry, while an irregular pentagon may not.

A parallelogram (J) is a four-sided polygon with opposite sides that are parallel and equal in length. It does not have a vertical line of symmetry because its opposite sides are not mirror images of each other.

A scalene triangle (K) is a triangle with no equal sides or equal angles. It does not have a vertical line of symmetry because its sides and angles are not symmetric.

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Answer:

the perimeter is the width added to the length