Please help with this problem

Answer:

43

Step-by-step explanation:

the true values of each number is 26 and 17 so adding them gives you 26+17

The ratio of Mary's share to Katherine's share to Alex's share is 5:4:1, which means Mary pays 5/10 of the bill, Katherine pays 4/10 of the bill, and Alex pays 1/10 of the bill.

To find the ratio, we can write their contribution as a fraction of the total parts and then solve the fractions then they'll have the same denominator.

So, Mary's share is 5/10, Katherine's share is 4/10, and Alex's share is 1/10.

To convert this as a ratio, we write 5:4:1, where each number represents the number of parts each person pays, and the colon separates each person's contribution.

Therefore, the ratio of Mary's share to Katherine's share to Alex's share is 5:4:1

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Minimization of  f(x) = |x+3| + x^3 at the endpoints (-2 and 6)  the minimum value of the function is approximately 3.84, which occurs at x= \sqrt{1/3}

within the given interval.

To minimize the function subject to the constraint f(x) = |x+3| + x^3 that x lies in the interval [-2, 6], we need to find the value of x that minimizes f(x) within that interval.

First, let's analyze the function f(x). The absolute value term |x+3| can be rewritten as:

|x+3| =

x+3 if x+3 >= 0

-(x+3) if x+3 < 0

Since the interval [-2, 6] includes both positive and negative values of x+3, we need to consider both cases.

Case 1: x+3 >= 0

In this case, f(x) = (x+3) + x^3 = 2x + x^3 + 3

Case 2: x+3 < 0

In this case, f(x) = -(x+3) + x^3 = -2x + x^3 - 3

Now, we can find the minimum of f(x) within the given interval by evaluating the function at the endpoints (-2 and 6) and at any critical points within the interval.

Calculating the values of f(x) at x = -2, 6, and the critical points, we can determine the minimum value of f(x) and the corresponding value of x.

Since the equation involves both absolute value and a cubic term, it is not possible to find a closed-form solution or an exact minimum value without numerical methods or approximation techniques.

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The combined mass of the pebbles that are 4 1/2 grams more is 66 grams.

In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation.

Given:

The mass of the pebbles is shown in the image attached below,

Calculate the combined mass as shown below,

The combined mass = 4.5 × 5 + 5 × 4 + 5.5 × 3 + 1 × 7

The combined mass = 22.5 + 20 + 16.5 + 7

The combined mass = 39 + 20 + 7

The combined mass = 66

Thus, the combined mass is 66 grams.

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If a and b are n × n, b is invertible, and ab is invertible, then a is also invertible.

To show that a is invertible, we need to find an inverse matrix \(A^-^1\)such that A\(A^-^1 = A^-^1A\) = I (the identity matrix).

Let's begin by using the hint provided and letting c = ab. We know that b is invertible, so we can multiply both sides of c = ab by b^-1 (the inverse of b) to get:

\(c(b^-^1) = ab(b^-^1)c(b^-^1) = a(bb^-^1)c(b^-^1) = aIc(b^-^1) = a\)

Now we substitute c = ab back into the equation to get:

\(ab(b^-^1) = a\)

Next, we can use the fact that ab is invertible to say that there exists some inverse matrix\((ab)^-^1\) such that \((ab)(ab)^-^1 = (ab)^-^1(ab)\) = I. Multiplying both sides of this equation by \(b^-^1\), we get:

\(a(bb^-^1)(ab)^-^1 = (ab)^-^1(bb^-^1)a^-^1\)
\(aI(ab)^-^1 = (ab)^-^1I\)
\(a(ab)^-^1 = (ab)^-^1\)

So we have shown that a multiplied by the inverse of ab is equal to the inverse of ab. This means that a must also be invertible, since the inverse of ab exists and we can simply multiply it by a to get the inverse of a. Therefore, we have proven that if a and b are n × n, b is invertible, and ab is invertible, then a is also invertible.

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Answer:

 5.6666666666667                              

Step-by-step explanation:

             if you don't believe me plug it in yourself http://www.alcula.com/calculators/statistics/mean-absolute-deviation/

Answer:

36 ounces or if over 150 lbs drink more water than 36 ounces

Step-by-step explanation:

For every pound of sweat you lose you need to drink 16 ounces of water!

The capacity of fish tank in quarts is 246.

Therefore the answer is 246.

A pint is a unit of volume in the US customary system of measurement and is equal to 16 fluid ounces. A quart is also a unit of volume in the US customary system of measurement and is equal to 32 fluid ounces or 2 pints.

There are 2 pints in 1 quart, so to convert from pints to quarts, we need to divide by 2.

The capacity of the fish tank in pints is 492.

Therefore, the capacity of the fish tank in quarts is

= 492 pints / 2 pints per quart

= 246 quarts

So, the capacity of the tank in quarts is 246 quarts.

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-24d -31.8

Simplifying process:

6(-4d-8.3+3d)

-24d -49.8 +18

-24d -31.8

When waves travel from one medium to another the frequency never changes. As waves travel into the denser medium, they slow down and wavelength decreases. Part of the wave travels faster for longer causing the wave to turn. The wave is slower but the wavelength is shorter meaning frequency remains the same

Answer: When waves travel from one medium to another the frequency never changes. As waves travel into the denser medium, they slow down and wavelength decreases. Part of the wave travels faster for longer causing the wave to turn. The wave is slower but the wavelength is shorter meaning frequency remains the same.

Step-by-step explanation:

Answer:

$1605

Step-by-step explanation:

1500 ⋅ 0.07 = 105

Add 105 to 1500

$1605

Hope I helped :)

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The measure of the arc PR, m\(\widehat{PR}\), found using the properties of the interior angle of a right triangle is; m\(\widehat{PR}\) = 120°

A right triangle is a triangle that has an interior angle of 90°.

The two tangents to the circle, QP and QR indicates that the angle formed by the radius of the circle and the point of tangency are both 90°, therefore, the two triangles formed by the radii of the circle to the points of tangency are right angle triangles, with the vertex angles at the center of the circle of 90° - 60°/2 = 60° each.

The angle formed at the center of the circle by the two right triangles, which is the same as the measure of the arc PR, m\(\widehat{PR}\) is therefore;

m\(\widehat{PR}\) = 60° + 60° = 120°

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To duplicate angle ABC, draw a line segment, position the compass on point A, and then draw an arc that intersects the line segment. Next, position the compass on point B, and then draw a second arc that intersects the first arc at a point on the line segment. Finally, position the compass on the point where the two arcs intersect, but without changing the width, and draw a third arc that intersects the line segment.

When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.

Common instruments used to measure angles are:

1. Protractor

2.Compass

3.Digital Angle finder

4.Angle finder

5.Clinometer

6. Inclinometer

You can take the following actions to copy angle ABC:

Create a line segment that will serve as the foundation for the new angle you're going to create.

Draw an arc that crosses the line segment you produced in step 1 by positioning the compass on point A.

Draw a second arc that crosses the previous arc at a point on the line segment by setting the compass on point B.

Place the compass on the intersection of the two arcs without adjusting the compass's width, then create another arc that crosses the line segment.

Point D is where the second arc crosses the line segment. To finish the new angle, join points D and C.

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The calculated probability of spending $240 or more on a party at the first given venture is 0.62% while for the given second venture it is 1.5%.

Probability refers to chances that are linked to the suitable number of outcomes available concerning the initiation or occurrence of a given event taking place in a certain time at a dignified place.

To find the probability we are using the formula

z = (μ-x)/σ

for the first case the possible probability calculated is

z = (250-240)/16

z = 0.62%

for the second case the possible probability calculated is

z = (260 - 230)/16

z = 1.5%

The calculated probability of spending $240 or more on a party at the first given venture is 0.62% while for the given second venture it is 1.5%.

Therefore, the answer to the given question is simple we should go with the second venture cause it has higher probability in comparison with the first venture.

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Answer:

\({ \tt{ {4x}^{6} - {16x}^{2} = {(2x {}^{3}) }^{2} - {(4x)}^{2} }} \\ \)

• from difference of squares:

\({ \boxed{ \rm{( {a}^{2} - {b}^{2} ) = (a - b)(a + b)}}}\)

• a → 2x³

• b → 4x

\({ \underline{ \underline{ \tt{ = \: (2 {x}^{3} - 4x)(2 {x}^{3} + 4x) \: }}}}\)

Answer:

158 is the 38th term of the sequence

Step-by-step explanation:

1. Add 4 to 6 and tap the equal sign 37 times and the answer will be visible. it is 158

Answers:

Slope = 3/4

y intercept = -1/2

================================================

Explanation:

The form y = mx+b is known as slope intercept form

m is the slope and b is the y intercept

Comparing y = (3/4)x - 1/2 to y = mx+b, we see that

m = 3/4

b = -1/2

The area enclosed by the ellipse \(\frac{x^2}{4}+\frac{y^2}{81}=1\) is 60 square units.

The general form of the equation of ellipse is  \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)

Given the equation of ellipse is,  \(\frac{x^2}{4}+\frac{y^2}{81}=1\)

⇒ \(\frac{x^2}{2^2}+\frac{y^2}{9^2}=1\)

That is, a = 2 and b = 9

Now,  \(\frac{y^2}{9^2} = 1 -\frac{x^2}{2^2}\)

⇒ \(y=\frac{9}{2} \sqrt{4-x^2}\)

Area enclosed by the ellipse = 4 x Area of ellipse in the first quadrant

Therefore, Area of ellipse in the first quadrant, A = \(\int\limits^a_0{\frac{9}{2} \sqrt{4-x^2}} \, dx\)

Using Substitution ,x = 2cosθ, then dx = -2sinθdθ and x = 0⇒ θ = π/2 and x = 2⇒ θ = 0

A = \(\int\limits^a_0{\frac{9}{2} \sqrt{4-4cos^2\theta}} \, dx\)

  = \(\int\limits^2_0{\frac{9}{2}\times2 \sqrt{1-cos^2\theta}} \, dx\)

  = \(\int\limits^2_0{9 sin^2\theta} \, dx\)

 = \(\int\limits^0_\frac{\pi}{2} {9 sin^2\theta} (-2sinx)\, d\theta\)

  = \(\int\limits^\frac{\pi}{2} _0{18 sin^3\theta} \, d\theta\)

  = \(\int\limits^\frac{\pi}{2} _0{18 (\frac{3sin\theta-sin3\theta}{4} )} \, d\theta\)

  = \(\frac{9}{2} \int\limits^\frac{\pi}{2} _b {3sin\theta} \, d\theta -\frac{9}{2} \int\limits^\frac{\pi}{2} _0 {sin3\theta} \, d\theta\)

  = 27/2 x (-cosθ) - 9/6 x (-cos3θ) |  θ = 0 to  θ =  π/2

  = 15 square units.

Therefore, the area enclosed by ellipse  \(\frac{x^2}{4}+\frac{y^2}{81}=1\) = 4 x A = 4 x 15 = 60 square units.

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The area of the base of the prism would be = 290cm²

To calculate the base area of the prism, the formula that should be used would be given below as follows:

The area of a triangle = 1/2× base × height.

Where;

Base = 20cm

Height = 29

Area = 1/2 × 20 × 29

Area = 290cm²

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Answer:

\(x=2.8\)

Step-by-step explanation:

\(7x+3=10x-5.4\)

Subtract 3 from both sides:

\(7x+3-3=10x-5.4-3\)

\(7x=10x-8.4\)

Subtract 10x from both sides:

\(7x-10x=10x-8.4-10x\)

\(-3x=-8.4\)

Divide both sides by -3:

\(\frac{-3x}{-3}=\frac{-8.4}{-3}\)

\(x=2.8\)

Answer:

1. (x,y)=

2. (3, 480°), (3,-240°), (-3, -60°)

3. (-17, -1.08)

4. on the second circle from the center and 153° clockwise from the horizontal axis

Step-by-step explanation:

took quiz...100%

The equilibrium constant (Kc) for the reaction ni₂⁺ + 6nh₃ is [Ni(NH₃)₆]²⁺ / [Ni²⁺][NH₃]₆.

The given reaction is:

Ni₂+ + 6NH₃ ⇌ [Ni(NH₃)₆]²⁺

The equilibrium constant (Kc) for this reaction can be obtained by the formula given below

[Ni(NH₃)₆]²⁺ / [Ni²⁺][NH₃]₆

The equilibrium constant (Kc) for the reaction ni²⁺ + 6nh₃ is given as

[Ni(NH₃)₆]²⁺ / [Ni²⁺][NH₃]₆

Thus, the equilibrium constant (Kc) for the reaction ni²⁺ + 6nh₃ is [Ni(NH₃)₆]²⁺ / [Ni²⁺][NH₃]₆.

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Answer:

the answer is 17/12 all u have to do is change it into a mix fraction

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{ \frac{17}{12}}}}}} \)

Step-by-step explanation:

\( \sf{ \frac{7}{12} + \frac{5}{6} }\)

Take the L.C.M of 12 and 6

To find L.C.M , first of all find the prime factors of each numbers.

12 = 2 × 2 × 3

6 = 2 × 3

Take out the common prime factors i.e 2 and 3

Also take out the other remaining prime factors : 2

Multiply those all prime factors and obtain L.C.M

L.C.M = Common factors × Remaining factors

= 2 × 3 × 2

= 12

\( \dashrightarrow{ \sf{ \frac{7 \times 1 + 5 \times 2}{12}}} \)

\( \dashrightarrow{ \sf{ \frac{7 + 10}{12}}} \)

\( \dashrightarrow{ \sf{ \frac{17}{12}}} \)

Hope I helped!

Best regards! :D

Answer:

89,470

Step-by-step explanation:

Answer:

I think the answer is A

1,2

The volume of the solid generated by rotating the region enclosed by the curve of $f(x) = x^2 - 1$ and the x-axis around the x-axis is $\frac{16\pi}{15}$.

To find the volume of the solid generated by rotating the region enclosed by the curve of a function $f(x)$ and the x-axis around the x-axis, we use the formula:

$V = \int_{a}^{b} \pi [f(x)]^2 dx$

where $a$ and $b$ are the limits of integration.

Let's assume the function $f(x) = x^2 - 1$, then we have:

$V = \int_{-1}^{1} \pi [(x^2 - 1)]^2 dx$

$V = \int_{-1}^{1} \pi (x^4 - 2x^2 + 1) dx$

$V = \pi \left[\frac{x^5}{5} - \frac{2x^3}{3} + x\right]_{-1}^{1}$

$V = \pi \left[\left(\frac{1}{5} - \frac{2}{3} + 1\right) - \left(-\frac{1}{5} + \frac{2}{3} - 1\right)\right]$

$V = \pi \left[\frac{16}{15}\right]$

$V = \frac{16\pi}{15}$

Therefore, the volume of the solid generated by rotating the region enclosed by the curve of $f(x) = x^2 - 1$ and the x-axis around the x-axis is $\frac{16\pi}{15}$.

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