Johnny is given 18 bottles of beer and he drinks 6 of them. How much beer does Johnny have left?

Answer:

Step-by-step explanation:

Sum: 6 * 10^-4 + 1.5*10^-4 = 7.5 * 10^-4

Difference: 6 * 10^-4 - 1.5 * 10^-4 = 4.5 * 10^-4

Product: 6*10^-4 * 1.5 * 10^-4 = 9 * 10^-8

Quotient: 6*10^-4/1.5 * 10^-4 = 4

Notice the answers, because they give you the rules.

When adding exponents and rationales, if the powers are the same then the rationales merely add.

Same rule applies to subtraction. Retain the powers and subtract the rationales.

When multiplying the rationales multiply, but the rationales add. they don't stay the same.

When dividing, the rationales divide and the powers subtract -- numerator minus denominator

In set theory, intersection refers to the common elements between two or more sets. Union, on the other hand, refers to all the elements in the sets combined. The symmetric difference between two sets is the elements that are unique to each set and do not overlap.

Here's the correct pairing:

1. BΔC (Symmetric Difference): {1, 2, 3, 4, 5, 6}
2. A∩C (Intersection): {1, 3, 5}
3. A∩B (Intersection): {2, 4}
4. A∪C (Union): {1, 2, 3, 4, 5}
5. A∪B (Union): {1, 2, 3, 4, 5, 6}

So the matched pairs are:

1. BΔC: {1, 2, 3, 4, 5, 6}
2. A∩C: {1, 3, 5}
3. A∩B: {2, 4}
4. A∪C: {1, 2, 3, 4, 5}
5. A∪B: {1, 2, 3, 4, 5, 6}

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Answer:

Subtract 6 from both sides and then divide by 2. The solution is x = 8.

                                                  Thank You

Answer:

x=8

Step-by-step explanation:

Answer:

Sorry I can't help with2.08

Hope the remaining helped

PLS mark BRAINLIEST

Triangles have \(180^{\circ}\) in total, so the sum of all the angles should be \(180^{\circ}\)

First triangle

\(180 = 90 + (x + 5) + (2x - 2)\\180 = 90 + x + 5 + 2x - 2\\180 - 90 - 5 + 2 = x + 2x\\87 = 3x\\x = 29^{\circ}\)

Second triangle

\(180 = (x + 40) + (2x - 5) + (3x - 17)\\180 = x + 40 + 2x - 5 + 3x - 17\\180 - 40 + 5 + 17 = x + 2x + 3x\\162 = 6x\\x = 27^{\circ}\)

Answer:

The first one is 7 I think

Step-by-step explanation:

x+5=2x-2

subtract x from both sides.

5=x-2

add two to both sides and that is 7

Second one is -14 I think

x+40+3x-17=2x-5

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

x+40+3*x-17-(2*x-5)=0

Pull out like factors :

2x + 28  =   2 • (x + 14)

Solve  :    x+14 = 0  

Subtract  14  from both sides of the equation :  

                     x = -14

Answer:

s cos^(-1)(-(q^2 s)/2) + sqrt(4 - q^4 s^2)/q^2 + constant

Step-by-step explanation:

Take the integral:

integral cos^(-1)(-(q^2 s)/2) ds

For the integrand cos^(-1)(-(q^2 s)/2), substitute u = -(q^2 s)/2 and du = -q^2/2 ds:

= -2/q^2 integral cos^(-1)(u) du

For the integrand cos^(-1)(u), integrate by parts, integral f dg = f g - integral g df, where  

f = cos^(-1)(u), dg = du, df = -1/sqrt(1 - u^2) du, g = u:

= -(2 u cos^(-1)(u))/q^2 + 2/q^2 integral-u/sqrt(1 - u^2) du

Factor out constants:

= -(2 u cos^(-1)(u))/q^2 - 2/q^2 integral u/sqrt(1 - u^2) du

For the integrand u/sqrt(1 - u^2), substitute p = 1 - u^2 and dp = -2 u du:

= -(2 u cos^(-1)(u))/q^2 + 1/q^2 integral1/sqrt(p) dp

The integral of 1/sqrt(p) is 2 sqrt(p):

= (2 sqrt(p))/q^2 - (2 u cos^(-1)(u))/q^2 + constant

Substitute back for p = 1 - u^2:

= (2 sqrt(1 - u^2))/q^2 - (2 u cos^(-1)(u))/q^2 + constant

Substitute back for u = -(q^2 s)/2:

Answer: = s cos^(-1)(-(q^2 s)/2) + sqrt(4 - q^4 s^2)/q^2 + constant

Given data:

The given equations are x - 2y = -1 and 2x + 3y = 12.

The given point of intersection is the solution of the equation which is (3, 2).

Thus, the solution of the given equations is (3, 2).

The equation 2 = -x√(x + 2) - x has two potential solutions: x = -1 and x = -8. However, x = -8 does not satisfy the equation, so the set of all solutions is {x = -1}.

To find the set of solutions to the equation 2 = -x√(x + 2) - x, we can solve it algebraically.

Starting with the given equation, we can simplify it step by step:

2 = -x√(x + 2) - x

Adding x to both sides:

2 + x = -x√(x + 2)

Squaring both sides to eliminate the square root:

(2 + x)^2 = (-x√(x + 2))^2

Expanding and simplifying:

4 + 4x + x^2 = x^2(x + 2)

Simplifying further:

4 + 4x = x^3 + 2x^2

Rearranging terms:

x^3 + 2x^2 - 4x - 4 = 0

Factoring the equation:

(x + 1)(x^2 + x - 4) = 0

Setting each factor to zero:

x + 1 = 0 or x^2 + x - 4 = 0

Solving the first equation, we find x = -1.

For the second equation, we can use the quadratic formula:

x = (-1 ± √(1^2 - 4(1)(-4))) / (2(1))

x = (-1 ± √(1 + 16)) / 2

x = (-1 ± √17) / 2

However, when we substitute x = (-1 + √17) / 2 into the original equation, it does not satisfy the equation. Therefore, x = -8 is not a solution.

Hence, the set of all solutions to the equation is {x = -1}.

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Answer:

B) point to the left

Step-by-step explanation:

To write each of these numbers in decimal notation, you move the decimal point the same number of places as the exponent. If the exponent is positive, move thedecimal point to the right. If the exponent is negative,move the decimal point to the left

The equation of the line passing through the points (1,3) and (-2,6) is y = -x + 4.

Given that the line passes through points (1,3) and (-2,6)

First, we determine the slope (m) using the formula:

\(Slope\ m = \frac{y_2 - y_1}{x_2 - x_1} \\\\m = \frac{6-3}{-2-1} \\\\m = \frac{3}{-3} \\\\m = -1\)

Now, plug the slope m = -1 and point (1,3) into the point-slope form and simplify:

( y - y₁ ) = m( x - x₁ )

y - 3 = -1( x - 1 )

y - 3 = -x + 1

Add 3 to both sides:

y - 3 + 3 = -x + 1 + 3

y = -x + 1 + 3

y = -x + 4

Therefore, the equation of the line is y = -x + 4.

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Answer:

1

Step-by-step explanation:

The slope can be found using the RISE/RUN equaton.

Looking at both graphs we see that they are parallel so that tells us that they have the same slope.

We can count how many boxes up and then how many boxes right this line goes to find the slope.

We also know that the slope is positive because the lines are increasing from left to right.

Answer: ASAP

Step-by-step explanation:

with 10 bacteria, how many bacteria are there after 5 days? Use the exponential growth

function f(t) = ger and give your answer to the nearest whole number. Show your work.

Answer:

Hi, there!!!!

See explanation in pictures.

I hope it helps you...

Answer:

118.7 inches squared.

Step-by-step explanation:

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.

The expression for solving the area of a circle is A = π × \(r^{2}\).

To solve for the semicircle above, we can divide the diameter into 2 to get the radius.

So, the radius of the upper semicircle is 6 inches.

If the radius of a circle is 6 inches, then you can substitute r for 6 into the formula.

This simplifies to A = 36π. If a semicircle if half the size of a normal circle, then it will be A = 18π, because 36 ÷ 2 = 18.

To solve for the lower semicircle, we can do the same this as we did above.

But wait, we don't know the radius or diameter!

No worries! To solve for the diameter of the circle, we can take the line that is parallel to the semicircle (the one that has a length of 12in) and subtract 6 from it. We subtract 6 from it because the semicircle takes up the remaining length of the line, not including the 6in.

To solve for the lower semicircle, we can divide the diameter by 2 to get the radius.

So, the radius of the circle is 3.

Now we can insert 3 into the expression.

This simplifies to A = 9π. If a semicircle if half the size of a normal circle, then it will be A = 4.5π because like above, 9 ÷ 2 = 4.5.

Adding the two semicircles together:

So, the area of both semicircles is approximately 70.6858 square inches.

To solve for the area of a rectangle we use the expression:

Inserting the dimensions of the rectangle:

So, the area of the rectangle is 48 square inches.

Adding the two areas together:

Therefore, the area of the entire figure, rounded to the nearest tenth is \(118.7\) \(in^{2}\).

We have found two quadratic functions with x-intercepts (-5,0) and (5,0): f(x) =\(x^2 - 25\), which opens upward, and g(x) = \(-x^2 + 25\), which opens downward.

For the quadratic function that opens upward, we can use the x-intercepts (-5,0) and (5,0) to set up the equation:

f(x) = a(x + 5)(x - 5)

where a is a constant that determines the shape of the parabola. If this function opens upward, then a must be positive. Expanding the equation, we get:

f(x) = a(x^2 - 25)

To determine the value of a, we can use the fact that the coefficient of the x^2 term in a quadratic equation determines the shape of the parabola. Since we want the parabola to open upward, we need the coefficient of x^2 to be positive, so we can set a = 1:

f(x) = x^2 - 25

For the quadratic function that opens downward, we can use the x-intercepts (-5,0) and (5,0) to set up the equation:

g(x) = a(x + 5)(x - 5)

where a is a constant that determines the shape of the parabola. If this function opens downward, then a must be negative. Expanding the equation, we get:

g(x) = a(x^2 - 25)

To determine the value of a, we can use the fact that the coefficient of the x^2 term in a quadratic equation determines the shape of the parabola. Since we want the parabola to open downward, we need the coefficient of x^2 to be negative, so we can set a = -1:

g(x) = -x^2 + 25

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132 cm² is the area of the given figure.

To find the area of the figure we need to divide it into two parts such as a rectangle with the dimension of 20 * 6 and a triangle with the dimension of  (10 - 6) * (20 - (8 + 6)).

So,

the height of the triangle = 10 - 6 = 4 cm

the base of the triangle = 20 - (8 + 6) = 20 - 14 = 6 cm

Thus,

the area of the triangle = 1/2 * base * height

= 1/2 * 6 * 4

= 12 square cm

Area of the rectangle = length * width

= 20 * 6

= 120 square cm

Thus, the area of the figure will be = 120 + 12  = 132 square cm.

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Answer:

The sum of all the sweets is 54 sweets

Step-by-step explanation:

Here, we want to calculate the number of sweets the three have altogether.

Let the number of sweet Faith has be x

Mathematically;

Faith has 4 sweets fewer than the average number of sweets

The average is the sum of all the sweets divided by 3

The average will be (10 + 30 + x)/3

Thus;

(10 + 30 + x)/3 - 4 = x

(40 + x)/3 = x + 4

40 + x = 3(x + 4)

40 + x = 3x + 12

40-12 = 3x -x

28 = 2x

x = 28/2

x = 14 sweets

So the sum of all the sweets would be 10 + 30 + 14 = 54 sweets

Answer:

729 cubic meters

Step-by-step explanation:

Volume of cube is given by side^3

where side is length of the side

Given in the problem

side is 9 meters as length, width, and height of fort is 9 meters and it is in cube shape .

Thus,

volume of cube = 9^3 = 9*9*9 = 729

Thus, volume of Haley's fort is 729 cubic meters.

It will take more time for a bottle to fall on the Moon than on the Earth off the same height.

The time the bottle would take to land if it were to fall the same distance on the moon instead of earth is 12.1 seconds

The acceleration due to gravity on the moon is  where g (9.8 m/s²) is the acceleration due to gravity on the Earth.

Distance to the ground, s = 120 m

Initial velocity = 0

Use the second equation of motion:

s = u t + 0.5 gt²

⇒ 120.0 m = 0 + 0.5 (1.63 m/s²) t²

Time(t) = \(\sqrt{\frac{120}{0.5 \times 1.63} }\) = 12.1 seconds

Hence,

It will take more time for a bottle to fall on the Moon than on the Earth off the same height.

The time the bottle would take to land if it were to fall the same distance on the moon instead of earth is 12.1 seconds.

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Answer:

x-2=(-2)x

Step-by-step explanation:

6.56 × 1.2= 7.872 = 7.9 [ to 2 significant figures]

Significant figure

Significant figures are the number of digits in value, often measurement, that contribute to the degree of accuracy of the value. We start counting significant figures at the first non-zero digit. Calculate the number of significant figures for an assortment of numbers.

fewest; the same significant figures with; measured numbers

Without mincing words let us dive straight into the solution to the above question. In order to be able to use the significant figures properly one must know the rules attached to it uses. This is so, because they contributes to the precision of measurements.

When performing multiplication or division calculation, the number of significant figures in the answer[result] will be determined by the one with the smallest number of significant figure in the problem.

Therefore, if we have 6.56 which is three[3] significant figures and 1.2 which is two[2] significant figures, then the number of significant figures will be two[2].

6.56 × 1.2= 7.872 = 7.9[ to 2 significant figures].

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First you will get 4dz

Answer:

The 25-lb weight stretched by 0.2 inches.

According to the question, Hooke's law states that the spring can be stretched directly with a force F. Therefore, the expression for the Hooke's law can be written as: F(Force) = extension(d). constant(k)

If a spring is stretched 0.8 inches by 40-lb weight:

40 = 0.8k ⇒k = 50

Now: the stretched inches be:

25 = 50d ⇒ d = 0.2 inches

Hence, the 25-lb weight stretched by 0.2 inches.

What is Hooke's law?

The Hooke's law states that the force produced by the spring is directly proportional to the weight of the spring. And the work done can be done either in the form of stretching or compressing.

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The first step to conducting a statistical study is to clearly define the research question or problem.

This involves identifying the population of interest, the variables to be measured, and the hypothesis or objective of the study. Once the research question is clearly defined, the next step is to design the study, including selecting an appropriate sample size, choosing a sampling method, and determining the data collection method.

It is also important to consider potential sources of bias and confounding factors that may impact the study results. Overall, a well-designed statistical study should be able to produce reliable and accurate results that can be used to draw meaningful conclusions about the population of interest.

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Answer:

yes

Step-by-step explanation:

First we should find a GCF for the number of boys and girls.

The gcf for the two would be 4.

Divide.

20/4 = 5

28/4= 7

therefore the ratio for boys to girls would be 5 to 7

The equation of the tangent plane at(2,3,1) is \(\langle -2, 5, -1 \rangle \cdot \left(\langle st, s + t, s - t \rangle - \langle 2, 3, 1 \rangle\right) = 0\)

The surface area under the restriction \(s^2 + t^2 \leq 1\) is \(\mathbf{r}(s,t) = \langle st, s + t, s - t \rangle\)

Finding the equation of the tangent plane at (2, 3, 1):

To find the equation of the tangent plane at a point on a surface, we need two things: the normal vector to the surface at that point and the coordinates of the point itself.

Step 1: Determine the partial derivatives of the position vector \mathbf{r}(s,t) with respect to s and t:

\(\frac{{\partial \mathbf{r}}}{{\partial s}} = \langle t, 1, 1 \rangle \\\\\frac{{\partial \mathbf{r}}}{{\partial t}} = \langle s, 1, -1 \rangle\)

Step 2: Evaluate the partial derivatives at the point (2, 3, 1):

\(\frac{{\partial \mathbf{r}}}{{\partial s}}(2, 3, 1) = \langle 3, 1, 1 \rangle \\\\\frac{{\partial \mathbf{r}}}{{\partial t}}(2, 3, 1) = \langle 2, 1, -1 \rangle\)

Step 3: Compute the cross product of the partial derivatives:

\(\mathbf{N} = \frac{{\partial \mathbf{r}}}{{\partial s}} \times \frac{{\partial \mathbf{r}}}{{\partial t}} \\\\\mathbf{N} = \langle 3, 1, 1 \rangle \times \langle 2, 1, -1 \rangle= \langle -2, 5, -1 \rangle\)

Step 4: Substitute the point (2, 3, 1) and the normal vector \(\mathbf{N}\) into the equation of the plane, which is given by:

\(\mathbf{N} \cdot (\mathbf{r} - \mathbf{r}_0) = 0 \\\\\langle -2, 5, -1 \rangle \cdot \left(\langle st, s + t, s - t \rangle - \langle 2, 3, 1 \rangle\right) = 0\)

Simplifying this equation will give you the equation of the tangent plane at the point (2, 3, 1).

Finding the surface area under the restriction s² + t² ≤ 1:

To find the surface area under this restriction, we need to evaluate the given parametric equations within the given region and calculate the surface area using an appropriate integral.

The surface area element can be represented as:

\(dS = \left| \frac{{\partial \mathbf{r}}}{{\partial s}} \times \frac{{\partial \mathbf{r}}}{{\partial t}} \right| ds dt\)

To find the surface area, we integrate this surface area element over the restricted region.

\(A = \iint_R dS\)

where R represents the region satisfying s² + t² ≤ 1.

To evaluate this integral, we can use the parametric equations \(\mathbf{r}(s,t) = \langle st, s + t, s - t \rangle\) and compute the partial derivatives\(\frac{{\partial \mathbf{r}}}{{\partial s}}}}\)and \(\frac{{\partial \mathbf{r}}}{{\partial t}}\)as we did earlier.

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Assuming the track is straight, the distance at which they are apart one hour before they meet is; 30 km

We are told that a Nonstop trains leave Toronto and Montreal at the same time each day going to the other city along the main line.

Speed of Train 1 = 120 km/h

Speed of Train 2 = 90 km/h

Time spent by train 1 = 1 hour

Time spent train 2 = 1 hour

Formula for distance is;

Distance = Speed * time

If they leave the same time each day, it means that;

Distance of train 1 = 120 * 1 = 120 km

Distance of train 2 = 90 * 1 = 90 km

Thus, distance at which they will be apart before meeting each other is;

Distance apart = 120 - 90

Distance apart = 30 km

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When the above is simplified using Boolean Algebra, we have F = x' + y' + w'xy.

We can simplify  the Boolean function F = xy'z' + xy'z+ w'xy +   w'x'y' + w'xy using the following Boolean Algebra rules.

Absorption - x + xy = x

Commutativity -  xy = yx

Associativity - x(yz) = (xy)z

Distributivity - x(y + z) = xy + xz

Using the above , we   have

F = xy'z' + xy'z+ w'xy + w'x'y' +   w'xy

= xy'(z + z') + w'xy(x + x')

= xy' +  w'xy

= (x' + y)(x' + y')  + w'xy

= x' + y' + w'xy

This means that the simplified expression is F = x' + y' + w'xy.

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