A boat traveled 27 miles in 2 hours at this rate how many miles will the boat travel in 1\2 hour??

Answer:

Well a number is (x) {unknown}

Its 17 more

So x+17=85

Now solve

subtract 17 on both sides

x=68

So the number is 68

Answer:

1 rectangle

Step-by-step explanation

Area= lxb

So 7.7 x 11 = 84.7

3 trapezoid

Area =(a+b/2)

Base a=13

Base b = 6

Height = 5

By 2

Answer= 47.5

4 Right angled triangle

Ab/2

Axb

Multiply each legs of the right angle triangle

So 3 1by4 x 4

By 2

Answer: See explanation

Step-by-step explanation:

1. That's a rectangle, the area of a rectangle is l (length) × w (width)

l = 11 cm

w = 7.7 cm

11 × 7.7 = 84.7

Area = 84.7 cm²

2. That is a triangle, the area of a triangle is 1/2 × b (base) × h (height)

b = 12 ft

h = 4ft

1/2 × 12 × 4 = 1/2 × 48 = 24

Area = 24 cm²

3. That is a trapezoid, the area of a trapezoid is \(\frac{a (base) + b(base)}{2} h(height)\)

a = 6 cm

b = 13 cm

h = 5cm

((6 + 13) ÷ 2) x 5

(19 ÷ 2) x 5 = 9.5 × 5 = 47.5

Area = 47.5 cm²

4. Same formula: 1/2 × b × h

b = 3 1/4 in

h = 4 in

1/2 × 3 1/4 × 4 = 1/2 × 13/4 × 4

1/2 × 13 = 6.5

Area = 6.5 in²

Hope I helped!

Answer:

4,767 seconds

Step-by-step explanation:

The speed of light is actually 3x10^8 m/s, not "3 × 10 ms-¹."

Convert 1.43 × 10⁹ km = 1.43 × 10^12 m

(1.43 × 10⁹ km = 1.43 × 10^12 m)/(3x10^8 m/s) = 4,767 seconds

Based on the transformation of the given parent function f(x), the function g(x) is: C. g(x) = ∛(x) + 2

In Mathematics, the translation of a geometric figure to the right is a type of transformation which simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image while translating a geometric figure up is a type of transformation that simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.

Translating the parent function f(x) = ∛(x) two (2) units up, would produce an image of function f(x):

g(x) = f(x) + 2

g(x) = ∛(x) + 2

In this context, we can reasonably infer and logically deduce that the parent function f(x) was shifted 2 units up to produce function g(x).

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Answer:

2/17

Step-by-step explanation:

Add all the marbles and add the 2 in front because 2 is what you are taking, and 17 is the total of marbles.

The probability of selecting the marble is 2 / 17.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of samples

Given that you randomly select 2 marbles from a mug containing 5 blue marbles, 4 red marbles, and 3 white marbles.

The probability will be calculated as:-

Probability = Number of favourable outcomes / Number of samples

Probability = 2 / 17

Therefore, the probability of selecting the marble is 2 / 17.

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The directional derivative of f at P(ln2, ln3) in the direction of (2,2) is e^(-(ln2+ln3)/sqrt(2)).

To compute the directional derivative of the function f(x,y) = e^(-x-y) at point P(ln2, ln3) in the direction of the vector (2,2), we need to first find the gradient of f at P.

The gradient of f is given by:

grad(f) = (-∂f/∂x, -∂f/∂y)

So, we have:

∂f/∂x = -e^(-x-y)

∂f/∂y = -e^(-x-y)

Therefore, the gradient of f is:

grad(f) = (e^(-x-y), e^(-x-y)) evaluated at P(ln2, ln3), this gives us:

grad(f)|P = (e^(-ln2-ln3), e^(-ln2-ln3))

Next, we need to normalize the given direction vector (2,2) to obtain a unit vector. The length of the vector (2,2) is sqrt(2^2 + 2^2) = 2sqrt(2). So, the unit vector in the direction of (2,2) is:

u = (2/sqrt(8), 2/sqrt(8)) = (sqrt(2)/2, sqrt(2)/2)

Finally, the directional derivative of f at P in the direction of u is given by:

D_u f(P) = grad(f)|P · u

where · denotes the dot product.

Substituting the values we have calculated, we get:

D_u f(P) = (e^(-ln2-ln3), e^(-ln2-ln3)) · (sqrt(2)/2, sqrt(2)/2)

Simplifying, we get:

D_u f(P) = e^(-ln2-ln3)·sqrt(2)/2 + e^(-ln2-ln3)·sqrt(2)/2

D_u f(P) = e^(-ln2-ln3)·sqrt(2)

Simplifying further, we get:

D_u f(P) = e^(-(ln2+ln3)/sqrt(2))

Therefore, the directional derivative of f at P(ln2, ln3) in the direction of (2,2) is e^(-(ln2+ln3)/sqrt(2)).

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In the quadrilateral ABCD if AB ||CD and  AB=9 as well as are CD=9. Then, quadrilateral ABCD is both parallelogram and trapezium.

Parallelogram's characteristics

In the quadrilateral ABCD:

Thus, the quadrilateral ABCD is both parallelogram and trapezium.

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A metric can be used to help us determine the extent of how much an outcome is achieved.

A metric is a quantifiable gauge that is employed to assess, scrutinize, and appraise diverse facets of a system, procedure, or outcome. It furnishes a standardized and unbiased approach to gauge and monitor performance or advancement towards particular objectives or goals. Metrics are commonly formulated based on precise criteria or prerequisites and can manifest as numerical or qualitative in essence.

They find application in various domains such as commerce, finance, science, engineering, and myriad others to evaluate performance, facilitate well-informed decisions, and oversee progress over time.

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At the 0.1 level of significance, the conclusion we come up with is to reject the null hypothesis.

we are given that a random sample of 150 people was taken. 98 of the people in the sample favored the candidate, were it to determine whether or not the proportion of the population in favor of candidate a is significantly more than 57%.So we need to find the test statistic, which is 1.98  determined from the z score, here the rejection region is the number more than 1.28, and 1.98 is greater than 1.28, so it is better to simply reject the null hypothesis.

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Answer:

x = 15p

-75

Explanation:

remove brackets:

4px + 4 = 64

solving for x --> 4px = 64 - 4 then--> 4px = 60

then diving both sides by 4p --> x = 60\4p --> x = 15p

now solving for x when p is -5

we will substitute the -5 in the equation we got --> x= 15 (-5)

which will give us --> x = -75

Answer:

2n + 9 = - 25

Step-by-step explanation:

let the number be n then twice the number is 2n

The sum of 2n and 9 is 2n + 9

the result is - 25 , that is

2n + 9 = - 25

Answer:

Step-by-step explanation:

The sum of twice a number and 9 is -25."

2x + 9 = -25

2x = -34

x = -17

-----------------------------------------

check

2 * (-17) + 9 = -25

-25 = -25

the answer is good

Answer:

4502 pieces of grass

Step-by-step explanation:

The radius of the semicircle is 36 meters, so its perimeter is:

Perimeter = pi * radius = 113.097 m

The perimeter of both semicircles is 2 * 113.097 = 226.194 m

So if the total perimeter is 395, the length of the rectangle is:

395 = 226.194 + 2*length

2*length = 168.8

length = 84.4 m

The width of the rectangle is 2 times the radius of the semicircle, so:

width = 2 * 36 = 72 m

Then the area of the rectangle is:

Area = length * width = 84.4 * 72 = 6076.8 m2

To find the number of grass pieces, we divide the rectangle area by the grass piece area:

number of pieces = 6076.8 / 1.35 = 4501.33 pieces

So we will need 4502 pieces to cover the rectangular area.

a. Σ2^(-1) = 1 matches with option (c) -39.9951.

b. 3 + 6 + 12 + 24 + ... + 3072 matches with option (d) -20 - 10 - 5 -...

c. Σ3(27^(-1)) matches with option (a) 1.

d. -2 + 4 + -8 + 16 + ... matches with option (b) 3072.

In a geometric series, each term is obtained by multiplying the previous term by a common ratio. To determine the equivalent expression, we need to identify the common ratio and the first term of the geometric series.

Option (a) has a common ratio of 2 and the first term of 1, resulting in the series Σ2^(-1) = 1. This matches with Σ3(27^(-1)).

Option (b) has a common ratio of 2 and the first term of 3, resulting in the series 3 + 6 + 12 + 24 + ... + 3072. This matches with -20 - 10 - 5 -...

Option (c) has a common ratio of -3 and the first term of -39.9951, resulting in the series Σ2(-3)*. This matches with -39.9951.

Option (d) has a common ratio of -2 and the first term of -2, resulting in the series -2 + 4 + -8 + 16 + ... This matches with 3072.

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Answer:

9:00 pm to 6:45 am = 9 hours 45 minutes = 9.75 hours

Water level drops 3/16" (or .1875") every 9.75 hours

.1875 / 9.75 = 0.0192307692  inches per hour

Step-by-step explanation:

Answer:

39.6 cm²

Step-by-step explanation:

The formula for the area of a trapezoid is given as:

Area of a Trapezoid = 1/2(a + b) h

Where, from the question:

a = 8.9 cm

b = 5.5 cm

h = 5.5cm

Hence,

1/2 (8.9cm + 5.5cm) × 5.5cm

= 1/2 × 14.4 cm × 5.5 cm

= 39.6 cm²

Area of the Trapezoid = 39.6 cm²

In response to the query, we can state that Therefore, the value of x trigonometry rounded to 1 decimal place is 19.4 cm.

The area of mathematics called trigonometry examines how triangle side lengths and angles relate to one another. The subject first came to light in the Hellenistic era, roughly in the third century BC, as a result of the use of geometry in astronomical investigations. The area of mathematics known as exact techniques deals with several trigonometric functions and possible computations using them. There are six common trigonometric functions in trigonometry. These go by the designations sine, cosine, tangent, cotangent, secant, and cosecant, respectively (csc). The study of triangle properties, particularly those of right triangles, is known as trigonometry. Consequently, studying geometry entails learning about the characteristics of all geometric shapes.

Based on the information given in the diagram, we can use trigonometry to find the value of x.

tan(θ) = opposite / adjacent

tan(25°) = y / x

x = y / tan(θ)

x = 9 / tan(25°)

x ≈ 19.4 cm (rounded to 1 decimal place)

Therefore, the value of x rounded to 1 decimal place is 19.4 cm.

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Answer:

24=10

Step-by-step explanation:

The value of y when  x = 10 is 5/4

If y varies directly as x, this is expressed as:

\(y \alpha x\\y = kx\\\)

where

k is the constant of proportionality

If y = 3 when x = 24, then:

3 = 24k

k = 3/24

k = 1/8

In order to get the value of x when y = 10

Recall that y = kx

y = 1/8 * 10

x = 10/8

y = 5/4

Hence the value of y when  x = 10 is 5/4

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The function is best represented by f (x) = x² + 2x.

option C is the correct answer.

The values of x in the given function can be determined as follows;

From one of the solution of x = - 2 and the second solution = 0

Now, we already know that the function has no y intercept, so we will eliminate option A,  and B because they have values for y intercept.

Since one of the solutions of x, is negative 2, we will consider a function with positive equation.

f (x) = x² + 2x

solve for x;

x ( x + 2 ) = 0

x = 0  or  x + 2 = 0

x = 0 or - 2

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Answer:

A

Step-by-step explanation:

when you divide a fraction, you actually multiply by the reciprocal

Answer:

The correct answer is A, 4/5 x 5/4.

Step-by-step explanation:

I just remember to Keep Change Flip which means keep the first fraction exactly how it is, change the sign to a division sign, and flip the last fraction. So, go from 4/5 ÷ 4/5 = 4/5 x 5/4.

Hope this helps! If you have any additional questions please don't hesitate to ask me or your teacher to be sure you master the subject. :) Stay safe and please mark brainliest!

The size of the square that should be cut out of each corner to get a box with a maximum volume is 3 inches x 3 inches.

To calculate this, we need to first find the equation for the volume of the box in terms of the length of the square cut out from each corner. Let x be the length of the square cut out from each corner. Then the length of the base of the box is (63-2x) inches and the width of the base is (15-2x) inches. The height of the box is x inches.

The volume of the box is therefore given by:

V(x) = x(63-2x)(15-2x)

We need to find the value of x that maximizes the volume V(x). To do this, we take the derivative of V(x) with respect to x and set it equal to zero:

dV/dx = 6x² - 156x + 945 = 0

Solving this quadratic equation gives us:

x = 3 inches (ignoring the negative root)

Therefore, the size of the square that should be cut out of each corner to get a box with a maximum volume is 3 inches x 3 inches.

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Answer:

The answer is below

Step-by-step explanation:

So first to find a prime number, you need to know some multiplication skills.

So prime number is a number that is only divisible by itself or 1.

______

For example

3 is a prime number because it can't be divisible by any number

but

9 is not a prime number, because it can be divisible by 3

3 x 3 = 9

______________________

So you get it now

Now if you get a some number between 1 - 10

you have to use your multiplication skills to see if there are any prime numbers.

_____________________________

so

1  - not a prime number, can't be divisible by any number.

2 - not a prime number, can't be divisible by any number.

3 - not a prime number, can't be divisible by any number

4 - is a prime number, can be divisible a number (2 x 2 = 4)

5 - not a prime number, can't be divisible by any number

6 - is a prime number, can be divisible a number (3 x 2 = 6)

7 - not a prime number, can't be divisible by any number

8 - is a prime number, can be divisible a number (4 x 2 = 8)

9 - is a prime number, can be divisible a number (3 x 3 = 9)

10 - is a prime number, can be divisible a number (5 x 2 = 10)

__________________________________________________________

Answer:

13 gallons

Step-by-step explanation:

42 / 3.19 = 13.166144200626959,

which can be rounded down to 13 whole gallons.

Answer:

13 GALLONS

Step-by-step explanation:

If gas costs $3.19 per gallon, how many WHOLE

gallons of gas could you buy with $42.00?

$42= 13.17 gallons

how many WHOLE gallons? :

13 gallons

Using a trigonometric relation we can see that the correct option is A, 370 ft.

We know that the angle of depression is 14°, and the height of the tower is 1,483ft.

The distance between the object and the bottom of the tower would be the opposite cathetus to the known angle, then we can use the trigonometric relation:

tan(14°) = (opposite cathetus)/1,483ft.

1,483ft*tan(14°) = 370ft

The correct option is A.

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The distance from the object to the

base of the tower to the nearest foot is equal to 5948 feet. Option D is correct.

The angle of depression is an angle formed between the horizontal line and the line of sight when an observer looks downwards.

Considering the right triangle formed by the height of the tower and the complementary angle 76°, we shall represent the distance from the object to the base of the tower with x so that;

tan 76° = x/1483 {opposite/adjacent}

note that 90° - 14° = 76°

x = 1483 × tan 76° {cross multiplication}

x = 1483 × 4.0108

x = 5948.0164

Therefore, the distance from the object to the

base of the tower to the nearest foot is equal to 5948 feet. Using the trigonometric ratio of tangent for the angle 76° which is complementary to the angle of depression 14°

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Answer:

70000

Step-by-step explanation:

you simply just add all the zeros in the equation.

(side note: that wording messed me up so much)

Answer:

G

Step-by-step explanation:

I did this assignment yesterday

Answer:

x = 91

y = 98

Your answer is F.

Step-by-step explanation:

Since a straight angle is 180° you have to subtract 89 from 180 and 82 from 180.

180 - 89 = 91

180 - 82 = 98

Hope this helps, and have a wonderful day! :)

Answer: D

Step-by-step explanation:

The given statement is true, according to the question.

Exponents with the same base have a ratio that is equal to the difference between their exponents with the same base. The division rule of exponents with the same base is another name for the quotient law of exponents with the same base.

According to the question,

Division in mathematics involves two exponents with the same base, however unlike dividing numbers, it is not possible to divide one exponential expression by another. As a result, the indices with the same base must be divided using a particular quotient rule.

By subtracting any two exponents with the same base, you may apply the property for dividing powers with the same base to calculate the quotient of any two exponents with the same base.

f'(x) equals [u(x)/v(x)]. '= [v(x) u'(x) - v'(x) u(x)] /[v(x)] 2

where,

The function of the form u(x)/v(x) for which the derivative must be determined is denoted by f(x).

u(x) = A differentiable function that serves as the function f's numerator (x).

Function derivative u'(x) equals u (x).

v(x) = A differentiable function that creates the supplied function f's numerator (x).

V'(x) = The function's derivative v(x).

The quotient rule says that when you are dividing x^m by x^n, you can simply subtract the two exponents (m-n) and keep the same base.

Therefore, the statement is true.

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Answer:

Step-by-step explanation:

slope formula: \(\frac{y2-y1}{x2-x1}\)

                       : \(\frac{-2--5}{1--11}\)

                       : \(\frac{1}{4}\) ............this is our slope, m.

using y - y1 = m ( x - x1 )

⇒     y - 2 = \(\frac{1}{4}\) ( x - 1 )

⇒      \(y =\) \(\frac{x}{4}\) + \(\frac{7}{4}\)

Answer:

\(y=\frac{1}{4}x - \frac{9}{4}\)

Step-by-step explanation:

\(m= \frac{y2-y1}{x2-x1}\)

So, plug in (-11,-5) and (1,-2),

\(m=\frac{(-2) - (-5)}{1-(-11)}\)

Subtract,

\(m=\frac{3}{12}\)

Divide 3 by 12:

\(m=\frac{3}{12} = .25\) or \(\frac{1}{4}\)

The slope is .25 or \(\frac{1}{4}\)

So, the equation so far is:

\(y=\frac{1}{4} x + b\)

Now, we have to find the y-intercept.

\(y=\frac{1}{4}x+b\)

Substitute the x for 1 and -2 in place of y.

\(-2=\frac{1}{4}(1) +b\)

Now solve.

\(-2=\frac{1}{4}(1) +b\\-2=\frac{1}{4} +b\\-\frac{1}{4} -\frac{1}{4} \\\\-2\frac{1}{4} =b\)

the y-intercept is: \(-2\frac{1}{4}\) or \(-\frac{9}{4}\)

The full equation is : \(y=\frac{1}{4}x - \frac{9}{4}\)

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Answer:

The value of x is 18°

Step-by-step explanation:

Sum of the angles are 180°

3x+126=180

3x=180-126

3x=54

x=18

Answered by GAUTHMATH