A garden hose emits 9 quarts of water in 6 seconds. How long will it take to emit 12 quarts

Answer:

\(\frac{5}{12}\)

Step-by-step explanation:

1/4 / 3/5

To divide fractions we flip the second one and then multiply them both and this method works for any number

1/4 x5/3

5/12

Hopes this helps please mark brainliest

the dimensions that would yield the maximum area are 70ft by 70ft. The maximum area is given by the quadratic function:A = 140x - x²= 140(70) - (70)²= 4900ft².

To solve this problem, you will need to use the quadratic equation. The first step is to use the given perimeter of 280ft to find the dimensions of the rectangular room. Let's assume that the length of the room is x, and the width is y.Therefore, we have:Perimeter = 2x + 2y = 280ft=> x + y = 140fty = 140 - xNext, we can use the dimensions to find the area of the rectangular room.Area, A = xy = x(140 - x) = 140x - x²To find the maximum area, we need to find the vertex of the quadratic equation of the area. The vertex is given by:Vertex, x = -b/2aWhere a, b, and c are coefficients of the quadratic equation ax² + bx + c = 0.For the quadratic equation of the area, a = -1 and b = 140.

Therefore:Vertex, x = -b/2a= -140/2(-1) = 70Therefore, the length of the room is x = 70ft. Using the perimeter formula, we can find the width:Width, y = 140 - x= 140 - 70= 70ftTherefore, the dimensions that would yield the maximum area are 70ft by 70ft. The maximum area is given by the quadratic function:A = 140x - x²= 140(70) - (70)²= 4900ft².

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1) The statement of Lin is correct.

2) (a) When scale factor, k = 9, area of the new triangle = 8100 square inches

(b) When k = 3/4, area of the new triangle = 56.25 square inches.

Given that,

A triangle has area 100 square inches.

It's dilated by a factor of k = 0.25.

When the triangle is dilated by a scale factor of k, then, each of the base and height is dilated by the scale factor of k.

So new area of the triangle after the dilation with the original triangle having base = b and height = h is,

Area of new triangle = 1/2 (kb)(kh) = k² (1/2 bh) = k² × Area of original triangle

Here original area = 100 square inches.

k = 0.25

New area = (0.25)² 100 = 6.25 square inches

So the correct statement is that of Lin.

Mai may found the new area by just multiplying the scale factor with 100, instead of taking the square of the scale factor. That is why she got 25 square inches as the new area.

2) (a) When k = 9,

Area of the new triangle = 9² (100) = 8100 square inches

(b) When k = 3/4

Area of the new triangle = (3/4)² (100) = 56.25 square inches

Hence the areas are found.

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Answer: …………..

Step-by-step explanation:

……………..

Answer:

$48

Step-by-step explanation:

Given that he is charged $8 service fee each month if his account goes below $500. If he has $510 and withdraws $25 the amount in account would be

= $510 - $25

= $485

This is below $500 hence he will be charged $8

Since he did not have any transactions in his account for 6 months, the change in his account as a result of the monthly charge

= 6 * $8

= $48

Answer:

(1 , -2/3)

Step-by-step explanation:

when y =0

3×0-2x=-2

0-2x=-2

divide both side by -2

x=1

when x=0

3y-2×0=-2

3y-0=-2

divide both side by 3

y=-2/3

A. can be used to test joint hypotheses.

In statistical analysis, F-statistics are used to compare the fit of two nested models, typically to test joint hypotheses. Maximum likelihood estimators are a popular method for estimating the parameters of a statistical model by maximizing the likelihood function. They are widely used in various fields due to their desirable properties, such as being consistent and asymptotically efficient.

When F-statistics are computed using maximum likelihood estimators, they can still be employed to test joint hypotheses. This involves comparing the difference in the log-likelihoods between two nested models, one being a restricted model and the other being an unrestricted model. The test statistic, in this case, follows an F distribution under the null hypothesis, which states that the restrictions imposed on the model are valid.

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The kite is approximately 43.8 feet above the ground.

To solve this problem, we can use trigonometry and the concept of opposite and adjacent sides of a right triangle.

Let's call the height of the kite above the ground "h". Then, in the right triangle formed by Savannah, the kite, and the ground, the opposite side is "h", the adjacent side is 75 feet (the length of the string), and the angle of elevation is 32 degrees.

We can use the tangent function to find the value of "h":

tan(32) = h/75

To isolate "h", we can multiply both sides by 75:

h = 75 × tan(32)

Using a calculator, we find that:

h ≈ 43.8 feet

Therefore, the kite is approximately 43.8 feet above the ground.

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Answer:

Step-by-step explanation:

\(\angle 2,\angle AEG, \angle GEB\)

The derivative of F(x) is \(F'(x) = x^{(1/3)\).

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

To find the derivative of the given function F(x), we will apply the fundamental theorem of calculus and differentiate the integral with respect to x.

Let's compute F'(x):

F(x) = ∫[0 to x] \(t^{(1/3)} dt\)

To differentiate the integral with respect to x, we'll use the Leibniz integral rule:

F'(x) = d/dx ∫[0 to x] \(t^{(1/3)} dt\)

According to the Leibniz integral rule, we have to apply the chain rule to the upper limit of the integral.

\(F'(x) = x^{(1/3)} d(x)/dx - 0^{(1/3)} d(0)/dx\)   [applying the chain rule to the upper limit]

Since the upper limit of the integral is x, the derivative of x with respect to x is 1, and the derivative of 0 with respect to x is 0.

\(F'(x) = x^{(1/3)} (1) - 0^{(1/3)} (0)\)

\(F'(x) = x^{(1/3)\)

Therefore, the derivative of F(x) is \(F'(x) = x^{(1/3)\).

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Answer: 30, 60, 90 triangle ==> Option 3

Step-by-step explanation:

Lets say Angle A is the angle opposing the line of a triangle that has the length of 6. Lets say Angle B is the angle opposing the line of the same triangle that has the length of \(6\sqrt{3}\).

sin A=6/12=1/2

sin A=30 degrees.

sin B=\(\frac{6\sqrt{3}}{12}\)=\(\frac{\sqrt{3}}{2}\)

sin B=60 degrees.

Hence, triangle is 30, 60, 90 triangle ==> Option 3

The measure of <EFA is 70 degree.

We have,

arc (AB) = 72

arc (ED) = 72

We know

Inside Angle = (arc + arc) /2

So, <EFG = (72 + 64)/2

m <EFG = (136/2)

m <EFG = 68

Now, using Angle Sum property in ΔEFG

42 + 68 + <EGF = 180

<EGF = 180 - 110

<EGF = 70

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Answer:

$100.14

Step-by-step explanation:

convert to a number

Answer: -30

Step-by-step explanation:

My answer is correct because, All you have to do is subtract all the numbers by 11 and the one that has the sum -19 is the correct choice. In this case -30 does and we can make sure were orrect by subtracting 11 by -19 and that equals -30.

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Answer:

Elaine

Step-by-step explanation:

2.1 is bigger than 2.06

Answer: x= 6

Step-by-step explanation:

Since the shape is a parallelogram, the angles will either be equal to each other or add up to 180.  

You can see they do not look the same so they add up to equal 180

12x + 3 +105 = 180

12x + 108 = 180

12x = 72

x = 6

The standard deviation of x for scores on the Critical Reading part of the test is approximately 18.26.

To find the standard deviation of x for scores on the Critical Reading part of the test, we can use the formula:

\(σ(x) = σ / √n\)

where σ is the population standard deviation and n is the sample size.

Plugging in the values given in the question:

\(σ(x) = 100 / √30\)

≈ 18.26

Therefore, the standard deviation of x for scores on the Critical Reading part of the test is approximately 18.26.

(b) Using the same formula, we can find the standard deviation of x for scores on the Mathematics part of the test:

\(σ(x) = 100 / √60\)

≈ 12.91

So, the standard deviation of x for scores on the Mathematics part of the test is approximately 12.91.

(c) Again, using the same formula, we can find the standard deviation of x for scores on the Writing part of the test:

\(σ(x) = 100 / √90\)

≈ 10.58

Hence, the standard deviation of x for scores on the Writing part of the test is approximately 10.58.

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Answer:

68.9

Step-by-step explanation:

     Let's take the formula: (C*9/5)+32=F

     Now let's substitute C for 20.5:

(20*9/5)+32=F

36.9+32=F

68.9=F

     So, 20.5 centigrade/celsuis is 68 temperature in fahrenheit.

Parentheses are employed to indicate changes to the usual order of operations.

The well-known () symbols, often known as "round brackets," are used in pairs to group things together or designate the order of operations in an equation. You will frequently need to employ brackets in math when forming or resolving equations. They support number grouping and operation definition.

{}, [] are other type of brackets.

In mathematical expressions, parentheses are employed to indicate changes to the usual order of operations (precedence rules). In an expression like, the portion of the expression enclosed in parentheses,, is first assessed, and the outcome is then incorporated into the remaining portions of the expression.

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Yes, 90 degrees (clockwise) and -270 degrees (counterclockwise) are coterminal angles.

Two angles are coterminal if they share the same terminal side when drawn in standard position. In other words, coterminal angles differ by an integer multiple of 360 degrees.

To see if 90 degrees and -270 degrees are coterminal, we can add 360 degrees to the smaller angle (-270 degrees) and see if we get the other angle:

-270 + 360 = 90

Since we obtain 90 degrees after adding 360 degrees to -270 degrees, these two angles are coterminal. They share the same terminal side in standard position, even though their rotations have different directions (clockwise and counterclockwise).

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Answer:

The correct next step is the answer choice

x^2+b/a x=-c/a

Step-by-step explanation:

Using the cosine rule, the distance the plane has flown during Jack's phone call can be calculated by taking the square root of the sum of the squares of the initial and final distances, minus twice their product, multiplied by the cosine of the angle difference.

To determine the distance the plane has flown during Jack's phone call, we can use the cosine rule in trigonometry.

The cosine rule relates the lengths of the sides of a triangle to the cosine of one of its angles.

Let's denote the initial distance from Jack to the plane as d1 and the final distance as d2.

We know that the altitude of the plane remains constant at 2400 meters.

According to the cosine rule:

\(d^2 = a^2 + b^2 - 2ab \times cos(C)\)

Where d is the side opposite to the angle C, and a and b are the other two sides of the triangle.

For the initial angle of elevation (70°), we have the equation:

\(d1^2 = (2400)^2 + a^2 - 2 \times 2400 \times a \timescos(70)\)

Similarly, for the final angle of elevation (50°), we have:

\(d2^2 = (2400)^2 + a^2 - 2 \times 2400 \times a \times cos(50)\)

To find the distance the plane has flown, we subtract the two equations:

\(d2^2 - d1^2 = 2 \times 2400 \times a \times (cos(70) - cos(50))\)

Now we can solve this equation to find the value of a, which represents the distance the plane has flown.

Finally, we calculate the square root of \(a^2\) to find the distance in meters.

It's important to note that the angle of elevation assumes a straight-line path for the plane's movement and does not account for any changes in altitude or course adjustments that might occur during the phone call.

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Answer

140.29 miles

Step-by-step explanation:

477miles/ 153 gallons = x miles/45 gallons

criss-cross multiplication and solve for x

477 x 45 = 153 x

x = (45x477) / 153 =  140.29 miles

Step-by-step explanation:

100 multiple it by the percentage

Answer:

100

Step-by-step explanation:

multiply by the percentage that you have

The orthocenter of the ΔABC is ( -1,5 ).

In a right triangle, the orthocenter is the polygonal vertex of the right angle. When the triangle's vertices and orthocenter are joined, any point becomes the orthocenter of the other three points, according to Carnot (Wells 1991). These four locations thus form an orthocentric system.

Given the  co-ordinates A( -3,3 ), B( -1,7 ) and C( 3,3 ).

To find the orthocenter using below steps:

1. First, we find the equations of AB and BC.

The general form of a line is y = mx + b

where m is the slope and b is the y-intercept.

Using the formula of slope given \($m =\frac{y_2 - y_1}{x_2 - x_1}\)  , we will find the slope of AB and BC.

Now, slope of AB is m = (7-3/-1 + 3)  

i.e. m = (4/2) = 2

Putting this 'm' in the general form and using the point B(-1, 1), we get the y-intercept as,

y = mx + b

1 = 2 × (-1) + b

i.e. b = 3.

So, the equation of AB is y = 2x + 3.

Also, slope of BC is m=(3-7/3+1)  i.e. m=-4/4 i.e. m--1

Putting this 'm' in the general form and using the point B( -1,1 ), we get the y-intercept as,

y = mx + b i.e. 1 = (-1) × (-1) + b i.e. b = 0.

So, the equation of BC is y = -x.

2. We will find the slope of line perpendicular to AB and BC.

When two lines are perpendicular, then the product of their slopes is -1.

So, slope of line perpendicular to AB is \(m*2=-1\)  i.e. m = -1/2

So, slope of line perpendicular to BC is  i.e.\(m*-1=-1\) i.e. m = 1.

3. We will now find the equations of line perpendicular to AB and BC.

Using the slope of line perpendicular to AB m=-1/2 i.e.  and the point opposite to AB

i.e. C(3, 3), we get,

y = mx + b

i.e. \(3=-1/2*3+b\)  

i.e. b = 9/2

So, the equation of line perpendicular to AB is

\(y=-x/2+9/2\)

Again, using the slope of line perpendicular to BC i.e. m = 1 and the point opposite to BC

i.e. A( -3,3 ), we get,

y = mx + b

i.e. 3 = 1 × -3 + b

i.e. b = 6.

So, the equation of line perpendicular to BC is y = x+6

4. Finally, we will solve the obtained equations to find the value of (x, y).

As, we have y = x + 6 and  y = -x/2 + 9/2

This gives, y = -x/2 + 9/2 → x + 6

y = -x/2 + 9/2

simplifying the above equation, we get

2x + 12 = -x + 9

3x = -3

x = -1.

So, y = x + 6

simplifying the above equation, we get

y = -1 + 6

y = 5.

The value of x = -1 and y = 5.

Hence, the orthocenter of the ΔABC is ( -1,5 ).

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The ratio of eyes to noses in a classroom with 32 students and 1 teacher is 64:32 or 2:1. Answer: 2:1.

To find the ratio (in simplest form) of eyes to noses in a classroom with 32 students and 1 teacher, we need to follow the steps given below:

Step 1: Find the total number of eyes and noses in the classroom.  As given, there are 32 students in the classroom. Therefore, the number of eyes = 32 × 2 = 64 (since each student has 2 eyes).

Also, the total number of noses = 32 × 1 = 32 (since each student has 1 nose). Adding the number of eyes and noses, we get: Total number of eyes + Total number of noses = 64 + 32 = 96Step 2: Write the ratio of eyes to noses in the simplest form.

Now, divide both the numerator and denominator by the greatest common factor (GCF) of the numerator and denominator to obtain the simplest form of the ratio.

Therefore, the ratio of eyes to noses in a classroom with 32 students and 1 teacher is 64:32 or 2:1. Answer: 2:1.

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if f has an absolute maximum value at c, then function f '(c) = 0 is True

This statement is true. This is because the first derivative of a function, f', is equal to 0 at the point of an absolute maximum. This is because the first derivative measures the rate of change of a function, and at a maximum, the rate of change of a function is 0. Therefore, if a function has an absolute maximum value at c, then f'(c) = 0.

The statement that if f has an absolute maximum value at c, then f '(c) = 0 is true. This is because the first derivative of a function measures the rate of change of a function. At an absolute maximum, the rate of change of a function is 0, so the first derivative of a function at that point must be 0. Therefore, if a function has an absolute maximum value at c, then f'(c) = 0.

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The requried, graph is a line that goes through points (1.4) and (2,8). Option B is correct.

Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression.

Here,
The given equation is y + 4 = 4(x + 1). To determine which statement is true about its graph, we can simplify the equation into slope-intercept form, y = mx + b, where m is the slope of the line and b is the y-intercept.

y + 4 = 4(x + 1)

y + 4 = 4x + 4

y = 4x + 4 - 4

y = 4x

Now we can see that the slope of the line is 4, and the y-intercept is 0. This means that the graph passes through the origin (0,0), and any point on the line can be found by starting at the origin and moving 4 units up for every 1 unit to the right.

From the given options, the only statement that is true about the graph of this equation is, B. The graph is a line that goes through points (1.4) and (2,8).

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