Find f(5)+j(-2) if f(x)=12-3x and j(x)=x² + 4x - 1.

The volume of the solid that results, when the region enclosed by the curves, is revolved about the x-axis is 3.35 cubic units.

When a figure is revolved around some fixed axis, the whole three-dimensional solid formed from the area that it swaps out is called a solid of revolution.

The function is given below.

y = - x² + 1

y = 0

Then the volume of the solid will be

[tex]\rm Volume = 2\int \pi y^2 dx\\\\\\Volume = 2 \int _0^1 \pi (-x^2 + 1)^2 dx\\\\\\Volume = 2 \pi \int _0^1 (x^4 - 2x^2 + 1)dx\\\\\\Volume = 2 \pi \left [ \dfrac{x^5}{5} - \dfrac{2x^3}{3} + x \right]^1_0\\\\\\[/tex]

On solving further, we have

Volume = 2π [(1/5 - 2/3 + 1) - 0]

Volume = 2π [8/15]

Volume = 3.35

Then the volume of the solid will be 3.35 cubic units.

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Answer:

y= ⅓x +2

Step-by-step explanation:

Since the graph is a linear graph, let's use the slope-intercept form to find its equation.

Slope-intercept form

y= mx +c, where m is the slope and c is the y-intercept.

The y-intercept is the point at which the graph cuts through the y-axis. In this case, the y-intercept is 2.

Thus, y= mx +2.

Let's find the slope of the graph.

First, identify 2 pairs of coordinates from the graph:

(0, 2) and (3, 3)

Next, substitute these coordinates into the slope formula below:

[tex]\boxed{ \text{slope} = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]

slope

[tex] = \frac{3 - 2}{3 - 0} [/tex]

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

Thus, the equation of the graph is y= ⅓x +2.

Answer:

Step-by-step explanation:

Comment

There are 9 marbles all together.

The important  fact is that he draws 1 marble to begin with and does not replace it. That means that the next marble is out of 8.

Solution

First marble: Blue = 3/9 = 1/3

Second marble: Green 2/8 = 1/4

The probability of that happening is

P(blue,Green) = 1/3 * 1/4 = 1/12

Answer P(blue, green) = 1/12

Answer:

Question 23: 39

Question 24: 10

Question 25: Airline B

Question 26: 20 to 50

Step-by-step explanation:

Answer

whats the question

Step-by-step explanation:

Answer:

36 students.

Step-by-step explanation:

5 + 7 = 12.

So the number of students must be a multiple of 12.

So as the number is  between 25 and 43 it must be 36.

Answer:

143.8 m²

Explanation:

Surface Area of cylinder = 2πr(r + h)

Here given,

Surface Area of cylinder:

⇒ 2π(1.6)(1.6+ 12.7)

⇒ 174.2955 m²

⇒ 143.8 m²        (rounded to nearest 1 decimal place)

Answer:The answer is A: b^4/a

Step-by-step explanation:now i dont rly have an explaination but i got this in my test so ik its right!

100% verrified!

Answer:

x >/= 8.6

Add 9.5 to 42.1 then divide by 6

Step-by-step explanation:

Total pounds of yogurt they buy (as a mixed number) : [tex]1\dfrac{5}{16}[/tex]

Mass is one of the principal quantities, which is related to the matter in the object  

The main mass unit consists of 7 units of other than other units of mass such as quintals, tons, pounds, ounces:  

Kilogram, kg  

Hectogram, hg  

Decagram, dag  

gram, g  

Decigram, dg  

centigram, cg  

milligrams, mg  

Each unit descends then multiplied by 10, and if one unit increases then divided by 10  

Fraction numbers are known as numerator and denominator

On a number line, fractions are expressed in points that lie between two integers

The general form of fractions is

[tex]\dfrac{a}{b}[/tex]

Mixed fractions consist of integers and ordinary fractions

A mixed number is a combination of a whole number and a fraction

Sara has 14 ounces of vanilla yogurt

Her father's yogurt weighs half of much, so her fathers have yogurt :

= 0.5 x 14 ounces

= 7 ounces

Total ounces of yogurt they buy

= 14 + 7 = 21 ounces

for 1 ounces (oz) the conversion = 0.0625 pounds(lbs)

So for 21 ounces there will be

= 21 x 0.0625

= 1.3125 pounds

if we express as a mixed number , it will be :

[tex]=\dfrac{13125}{10000}[/tex]

[tex]=1\dfrac{5}{16}[/tex]

Hence Total pounds of yogurt they buy (as a mixed number) : [tex]1\dfrac{5}{16}[/tex]

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The statistical test would be a Z-test for the difference between the proportions.

The Z test is a parametric procedure that is used on data that is dispersed in a normal fashion. For testing hypotheses, the z test can be used on one sample, two samples, or proportions. When the population variance is known, it analyzes if the means of two big groups are dissimilar.

We have:

In a recent poll among 500 students, it was found that 60% of women and 68% of men eat meals on campus at least 3 times a week.

From the above data and the definition of the Z-test, the statistical test would be a Z-test for the difference between the proportions.

Thus, the statistical test would be a Z-test for the difference between the proportions.

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Answer:

4 quarts

Step-by-step explanation:

1 gallon is equal to 4 quarts

Answer:

See below

Step-by-step explanation:

Expand it a bit to see:

= [tex]\sqrt[5]{ 2^5 * 7 * x^5 * x^5 * x * y^5 * y^3}[/tex]

=[tex]2x^2y \sqrt[5]{7xy^3}[/tex]

its true

they are both already right triangles so if both have acute angles that are congruent then the right triangles are similar

if one of the acute angles of a right triangle is congruent to an acute angle of another right triangle then by angle angle Similarity the triangles are similar

[tex]v = \frac{4}{3} \pi {r}^{3} [/tex]

[tex]v = \frac{4}{3} \times \pi \times {2}^{3} [/tex]

[tex]v = 33.51 \: {m}^{3} [/tex]

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

[tex]v = \pi \times {2}^{2} \times 6[/tex]

[tex]v = 75.40 \: {m}^{3} [/tex]

[tex]v = 75.40 + 33.51[/tex]

[tex]v = 108.91 \: {m}^{3} [/tex]

Hence, the volume of the given compound shape is 108.91 cubic meters.

sphere:

= 33.51 m^3

cylinder:

= 75.40 m^3

all together:

= 108.91 m^3

It's not hemisphere,It's a complete sphere .

Volume

Volume of each hemisphere.

Answer:

9. Median: 14

10. Mean: 14.1

11. Mode: No Mode

12. New Median: 14.5

13. New Mean: 14.625

Answer:

[tex] \frac{8}{5} = \frac{2}{m - 3} \\ \\ \implies \: 8(m - 3) = 2 \times 5 \\ \\ \implies \: 8m - 24 = 10 \\ \\ \implies \: 8m = 10 + 24 \\ \\ \implies \: 8m = 34 \\ \\ \implies \: m = \frac{34}{8} \\ \\ \implies \: \boxed{m = 4.25}[/tex]

therefore , second option is correct.

hope helpful ~

Answer:

36

Step-by-step explanation:

We know all angles in a triangle must add up to 180°

The square in the triangle that angle is equal to 90°

We can now solve for x

90 + 54 + x = 180

144 + x = 180

x = 36

That is your answer

- Kan Academy Advance

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:

y=2/3x+4

Step-by-step explanation:

4 is y-intercept

2/3 is  the slope (rise/run)

Answer: y = [tex]\frac{2}{3}[/tex]x + 4

Step-by-step explanation:

    This is in slope-intercept form. We are missing the m and the b value. See attached for more information.

[m aka the slope]

   Starting from point (-6, 0), counting up 2 units, then right 3 units to point (-3, 2), gives us a slope of [tex]\frac{2}{3}[/tex] via rise-over-run

[b aka the y-intercept]

   The line intersects the y-axis at positive 4.

-> This value is "4"

s = area = 11.76

p = perimeter = 16.8

r=2*11.76/16.8=23.52/16.8=1.4

r=1.4

a= 90 degrees

b=36.87 degrees

c=53.13 degrees

triangle is in a circle

Circumradius: R = 3.5

Using it's formula, it is found that the accuracy of the test was of 0.85 = 85%.

The accuracy of a test is given by the number of correct results divided by the number of results.

In this problem, there are 80 tests, and of those, 5 + 7 = 12 had incorrect results, hence 68 had correct results.

Hence the accuracy of the test is given by:

a = 68/80 = 0.85 = 85%.

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Answer:

B

Step-by-step explanation:

Answer:

the answer is b

Step-by-step explanation:

Answer:

the answer is 11 because there are so many no. repeating so in this case we count total no of terms and say it n if terms are odd then mode

Step-by-step explanation:

mode = n+1÷2

Step-by-step explanation:

144 degree is right answer.

Answer:

144°

Step-by-step explanation:

The central angle is 360°. Since it has 5 divisions, the angle of each division is 72°.

From B to D, it requires 2 rotations.

Answer:

Getting sum 6 when rolling two dice

7000_1.8%=61.2%this is the answer

Answer:

a.

Step-by-step explanation:

the area of a whole circle (360°) is

pi×r²

in our case

pi×10² = 100pi

but here we don't need the full circle. we only need a fraction of the whole circle : 128/360

so, the area of the sector is

100pi × 128/360 = 100pi × 16/45 = 20pi × 16/9 =

= 111.7010721... cm² ≈ 111.7 cm²