The surface area of a cone with radius r units and slant height s units is shown below:

30 points
Surface area = 3.14(rs + r2)

Part A: If r = 3 units and s = 5 units, write an expression that can be used to calculate the surface area of the cone. (4 points)

Part B: What is the surface area of the cone? Show your work. (6 points)

The value of F(G(x)) is 2x^2 - 13

The functions are given as:

F(x)=2x+1

G(x)=x^2-7

To find (FxG)(x), we make use of

(FxG)(x) = F(G(x))

So, we have:

F(G(x))=2G(x)+1

Substitute G(x)=x^2-7

F(G(x))=2(x^2-7)+1

Expand

F(G(x))=2x^2 - 14 + 1

Evaluate the like terms

F(G(x))=2x^2 - 13

Hence, the value of F(G(x)) is 2x^2 - 13

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The trigonometric function gives the ratio of different sides of a right-angle triangle. The measure of ∠C is 28°. And the value of b and c is 7.06 and 3.76, respectively.

The trigonometric function gives the ratio of different sides of a right-angle triangle.

[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}[/tex]

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite the 90° angle.

The sum of all the angles can be written as,

∠A + ∠B + ∠C = 180°

90° + 62° + ∠C = 180°

∠C = 28°

Sin(∠B) = AC/BC

Sin(∠B) = b/8

b = 8 × Sin(62°)

b = 7.06

Cos(∠B) = AB/BC

Cos(∠B) = c/8

c = 8 × Cos(62°)

c = 3.76

Hence, the measure of ∠C is 28°. And the value of b and c is 7.06 and 3.76, respectively.

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The distance from ships to the submarine is AX=1084.20

                                                                      BX=1270.69

Let X be the submarine position.

The length between a and b is AB=1425

             and the angle point a is at 59 degrees

                    the angle point b is at 47 degrees

The calculating angle at X:

∠X+∠A+∠B = 180

∠X+59°+47°=180°

∠X=180°-59°-47°

∠X=74°

Then the distance between boat A and the submarine will be found using sine law

Sine law is the ratio of each side of a plane triangle to the sine of the opposite angle is the same for all three sides and angles.

[tex]\frac{a}{sinA}=\frac{b}{sin B} = \frac{c}{sin C}[/tex]

so for Boat A and submarine, we use

[tex]\frac{AB}{sin X}=\frac{AX}{sin B}[/tex]

[tex]\frac{1425}{sin (74)} = \frac{AX}{sin (47)}[/tex]

When AX is the subject

AX=[tex]\frac{1425}{sin(74)}*sin(47)[/tex]

=[tex]\frac{1425}{0.9613}*0.7314[/tex]

AX=1042.245/0.9613

AX=1084.20

The distance between ship B and the submarine

The sine formula we use is

[tex]\frac{AB}{sin X}=\frac{BX}{sin A}[/tex]

[tex]\frac{1425}{sin 74}=\frac{BX}{sin 59}[/tex]

When BX is the subject

BX=[tex]\frac{1425}{sin 74}*sin(59)[/tex]

= 1425/0.9613 * 0.8572

=1221.51/0.9613

=1270.69

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Answer:

Ships A and B are 1,425 feet apart and detect a submarine below them. The angle of depression from ship A to the submarine is 59°, and the angle of depression from ship B to the submarine is 47°.

How far away is the submarine from the two ships? Round to the nearest hundredth of a foot.

The distance from ship A to the submarine is about

✔ 1,084.18

feet.

The distance from ship B to the submarine is about

✔ 1,270.69

feet.

Step-by-step explanation:

The value of the hypotenuse is C = 11.73

We can see that C is the hypotenuse of the right triangle.

We can see that the top angle measures 43°, and the opposite cathetus to that angle measures 8 units.

Then we can use the rule:

Sin(a) = (opposite cathetus)/(hypotenuse).

Replacing what we know:

Sin(43°) = 8/C

Solving for C:

C = 8/Sin(43°) = 11.73

The value of the hypotenuse is C = 11.73

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Answer:

operator

Step-by-step explanation:

Operator is represented as any symbol that indicates an operation to be performed.

Examples:

- Square root of√x, which indicates the square root is to be taken

- d/dx, which indicates differentiation with respect to x is to be performed

Answer:

OPERATION

OF ALGEBRA IN MATH

Answer :

X*2-16

Explanation :

The square of x is x*2 and the square of 8 is 64

Answer:

C. [tex]1\frac{1}{2} x - 1\frac{3}{4}[/tex]

Step-by-step explanation:

c

Answer:

[tex]1\frac{1}{2}x - 1\frac{3}{4}[/tex]

Step-by-step explanation:

So the first step is to distribute the [tex]\frac{1}{4}[/tex] to the (3x - 7) this gives you:

[tex]\frac{3}{4}x-\frac{7}{4} + \frac{3}{4}x[/tex]

Add like terms:

[tex]\frac{6}{4}x-\frac{7}{4}[/tex]

Simplify the fractions:

[tex]\frac{3}{2}x-\frac{7}{4}[/tex]

Convert it to a mixed fraction:

[tex]1\frac{1}{2}x - 1\frac{3}{4}[/tex]

Volume is a three-dimensional scalar quantity. The length of the square base side is 5 meters.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

The volume of the square pyramid is one-third of the product of the base area and the height. Therefore, the area of the base of the pyramid will be,

The volume of pyramid = (1/3) × Height × (Base length)²

75 m³ = (1/3) × 9 × (Base length)²

Base length)² = 25 m²

Base length = 5 m

Hence, the length of the square base side is 5 meters.

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Answer: 754

Step-by-step explanation:

Divide 683/11 to get the unit rate of 58. That means she is driving 58mph.

Multiply that by how many hours you have, 13, and you get 754.

The area of the shaded triangle BDE is 4 cm²

The area is the amount of space within the perimeter of a 2D shape.

area of ΔADE= / *b *h

=1/2 * 8 *5

= 20 cm²

area of ΔBCD

= 26-20

= 6 cm²

area of CDE

= 1/2* 5 * 4

= 10 cm²

Area of shaded triangle,

=10-6

=4 cm²

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The total finance charge is $611.20 (Option c) for this compound interest.

Data Given

Principal, P = $4250

Rate of Compound Interest, R = 13.25%

Time, t = 24 months, i.e., 2 years

Since it is compounded monthly, n = 12

Calculating the Total Finance Charge

We know that the formula for total amount of finance charge in a Compound Interest is,

[tex]A=P\frac{r(1+r)^{n} }{(1+r)^{n} - 1}[/tex]

Substituting the values of P, R and n, we get,

[tex]A=4250\frac{13.25(1+13.25)^{24} }{(1+13.25)^{24} - 1}[/tex]

[tex]A = 611.20[/tex]

Thus, the total finance charge is $611.20

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Answer:

(B). roots

Step-by-step explanation:

(a ± b)² = a² ± 2ab + b²

~~~~~~~~

( [tex]\sqrt{4x+5}[/tex] - [tex]\sqrt{x-1}[/tex] )² = ( [tex]\sqrt{x+4}[/tex] )²

( [tex]\sqrt{4x+5}[/tex] )² - 2[tex]\sqrt{(4x+5)(x-1)}[/tex] + ( [tex]\sqrt{x-1}[/tex] )² = ( [tex]\sqrt{x+4}[/tex] )²

4x + 5 - 2[tex]\sqrt{(4x+5)(x-1)}[/tex] + x - 1 = x + 4

2[tex]\sqrt{(4x+5)(x-1)}[/tex] = 4x + 5 + x - 1 - x - 4

[tex]\sqrt{(4x+5)(x-1)}[/tex] = 2x

( [tex]\sqrt{(4x+5)(x-1)}[/tex] )² = ( 2x )²

( 4x + 5 )( x - 1 ) = 4x²

4x² + x - 5 = 4x² ⇒ x = 5

Answer:

Step-by-step explanation:

Answer:

4 5/18 ≈ 4.278

Step-by-step explanation:

1/2 of 8 5/9

8 5/9 = 77/9

1/2 x 77/9

= 77 over 18

= 77/18

= 4 and 5/18

≈ 4.278

Hope this helps!

Answer:

a. n+5

b. n+ 7

c. 1\2(n×2n)

d. n +n+1 n+2

0.3:0.1

Step-by-step explanation:

first convert the % to decimals.

75%=0.75

25%=0.25

then look for a common factor and divide be that, in this case its 5.

0.75/5=0.15

0.25/5=0.5

now since these arent in the simplified form, you gotta divide again by 5.

0.15/5=0.3

0.5/5=0.1

The ratio to adults to children is 3:1

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

75% of the people are adults and 25% are children.

So, the ratio of adult to children

= (75%) / (25%)

= 0.75 / 0.25

= 75/25

= 3/1

Hence, the ratio to adults to children is 3:1

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The width of the rectangle is 6.82 meters, while the length of the rectangle is 8.184 meters.

A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.

Let the width of the rectangle be x.

Given that a rectangular room is 1.2 times as long as it is wide. Therefore, the length is 1.2x.

Perimeter = 2(x + 1.2x)

30 meters = 2(2.2x)

30 = 4.4x

x = 6.82

Hence, the width of the rectangle is 6.82 meters, while the length of the rectangle is 8.184 meters.

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a. The probability of rolling a sum of 7 or 11. (sum of 7 or 11) is 2/9. b. the probability of not rolling a sum of 7 nor 11. (not sum of 7 nor 11) is 7/9.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The probability of getting a total of 7 = 6/36

The probability of getting total of 11 = 2/36

a. The probability of rolling a sum of 7 or 11. (sum of 7 or 11)

= 6/36 + 2/36

= 2/9

b. Find the probability of not rolling a sum of 7 nor 11. (not sum of 7 nor 11)

= 1- 2/ 9

= 7/9

c. Find the odds against rolling a sum of 7 or 11.

= 2/9

d. The money you will win, If you make a $10 bet that you will roll a sum of 7 or 11, and the dice land on a sum of 7 or 11.

10 x  2/9 = 20/9

10 x 7/9 = 70/9

Thus, The money you will win $10.

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The true statement is (b) use of incorrect header

The product expression is given as:

(-2x - 1)(2x - 1)

Expand the expression

(-x - x - 1)(x + x - 1)

This means that the header of the algebra tiles would be:

-x, -x, 1 and x, x and -1

From the figure, we can see that this is incorrectly represented

Hence, the true statement is (b)

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Answer:

no because 1 x value cannot have 2 y values , i hope the helps

Choose C.

Draw the graph:

f(x) = |x-1|

f(x) = -(x-1) when x-1 is negative

f(x) = (x-1) when x-1 is positive

when x = -2, f(x) = 3

when x = -1, f(x) = 2

when x = 0, f(x) = 1

when x = 1, f(x) = 0

when x = 2, f(x) = 1

Using this values, draw the graph of f(x) = |x-1|

Hence, the required modulus of x-1 graph.

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The area of the shaded region for a z-score of -0.92 is 0.1788, which means the area that will be shadeded in the normal distribution graph is 17.88% of the total.

The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.

1.) The area of the shaded region for a z-score of -0.92 is 0.1788, which means the area that will be shadeded in the normal distribution graph is 17.88% of the total.

2.) The area of the shaded region for a z-score of 1.23 is 0.8907, which means the area that will be shadeded in the normal distribution graph is 89.07% of the total.

Now, the area of the shaded region will be,

Area = 0.8907 - 0.1788

        = 0.7119

        = 71.19%

Hence, the area of the shaded region is 71.19%.

The complete question is mentioned in the below image.

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The linear equation passes through (0, -4) and (1, 0), so we conclude that the correct option is the first one.

Here we have the linear equation:

y - 6 = 4*(x - 3) + 2

if we rewrite the line in slope-intercept form, we get:

y = 4x - 12 + 2 + 6

y = 4x - 4

Then the y-intercept of the line is (0, -4). And when x = 1, we have:

y = 4*1 - 4 = 0

So the line also passes through (1, 0).

Then the correct option is the first one:

"Number graph ranging from negative four to three on the x-axis and negative five to two on the y-axis. A line is drawn on the graph that passes through the points (zero, negative four) and (one, zero)."

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Hello!

Let the missing number be x.

⇒ 3 1/3 × x = 8

⇒ 10/3 × x = 8

⇒ x = 24/10

⇒ x = 12/5

The other number is [tex]\boxed {\frac{12}{5}}[/tex]

Answer:

The other number ia:

12/5

Step-by-step explanation:

3 1/3 = 3 + 1/3 = 9/3 + 1/3 = 10/3

a * 10/3 = 8

a = 8*3/10

a = 24/10

a = 12/5

a = 2.4

Check:

(12/5) * (10/3) = 8

(12*10) / (5*3) = 8

120 / 15 = 8

Answer:

x = -36

Step-by-step explanation:

x/4 + 10 = 1

To solve this two step equation, first subtract 10 from each side.

x/4 + 10 -10 = 1-10

x/4 = -9

Then multiply each side by 4 to isolate x

x/4 * 4 = -9*4

x = -36

The graph of R intersects with the horizontal or oblique asymptote at (-3, 0)

The function is given as:

[tex]R(x)=\frac{x+3}{x\left(x+8\right)}[/tex]

Set the numerator to 0

[tex]R(x)=\frac{0}{x\left(x+8\right)}[/tex]

Evaluate

R(x) = 0

This means that the horizontal asymptote of R(x) is y = 0

The function is given as:

[tex]R(x)=\frac{x+3}{x\left(x+8\right)}[/tex]

The numerator has a degree of 1, while the denominator has a degree of 2

When the degree of the numerator is less than the degree of denominator, then the function has no oblique asymptote

Hence, the function has no oblique asymptote.

In (a), we have:

R(x) = 0

Substitute R(x) = 0 in [tex]R(x)=\frac{x+3}{x\left(x+8\right)}[/tex]

[tex]\frac{x+3}{x\left(x+8\right)} = 0[/tex]

Cross multiply

x + 3 = 0

Solve for x

x = -3

So, we have:

(x, y) = (-3, 0)

Hence, the graph of R intersects with the horizontal or oblique asymptote at (-3, 0)

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Answer:

$1756

Step-by-step explanation:

1.  More = Addition

2. Twice = Multiplication by 2

3. Tuition costs $100 more than twice room and board

   Tuition = 2x + 100

   $2584 = (2x + 100) + x

   $2584 = 3x + 100

4. Subtract 100 on both sides: $2484 = 3x

5. Divide both sides by 3: $828 = x

6. Plug it in to the tuition equation: Tuition = 2(828) + 100

                                                                       = $1756

Check Work: (828*2) + 100 = $1756

                      $1756 + 828  = $2584

When t is between 2 and 5, the ball will be above 10 feet.so answer is:

C. 2 ≤ t ≤ 5

Given, height h(t) = ₋t² ₊ 7t

At what values of time t is the ball 10 feet above the ground = ?

To find out the time we need to set up an inequality.

Inequality expression is given as = ₋t² ₊ 7t ≥ 10

                                                       = ₋t² ₊ 7t ₋ 10 ≥ 0

                                                       = ₋(t² ₋ 7t ₊ 10) ≥ 0

                                                       = t² ₋ 7t ₊10 ≥ 0

Now, factorize the expression and get the factors.

= t² ₋ 2t ₋ 5t ₊ 10 ≥ 0

=t(t ₋ 2) ₋ 5(t ₋ 2) ≥ 0

=(t ₋ 2) (t ₋ 5) ≥ 0

Hence t value ranges from t = 2 and 5.

As a result, when t is between 2 and 5 seconds, the ball will be farther than 10 feet, 2 ≤ t ≤ 5

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Answer:

refer to the above attachment

Answer:

Twenty - one miles per gallon

Step-by-step explanation:

⇒ 550/26 = Amount per gallon which is one

⇒21.15384615384615

[tex] \approx [/tex] 21.2 miles per gallon

The distance travelled by truck in one gallon of fuel is 21.2 miles per gallon.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a truck can travel 550 miles on a tank of gasoline. The distance travelled by truck will be calculated as,

550 miles = 26 gallons

1 gallon = 550 / 26

1 gallon = 21.2 miles per gallon

Therefore, the distance travelled by truck in one gallon of fuel is 21.2 miles per gallon.

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