The points
(−1.2,2.9) and (2.9,9.46) are on the graph of a linear relationship between two variables, x and y

Write a formula that expresses
y in terms of x

What is the value of y when x=115

1)  The empirical formula for this compound is; K₂Cr₂O₇

2) It is an Ionic compound because it has two potassium ions (K+) and a negatively charged dichromate ion (Cr2O7-).

1) Elements of the unknown compound are;

Potassium = 40 g

Chromium = 52 g

Oxygen = 56 g

Let us find the number of moles of each element;

Number of moles of Potassium = 40/39 = 1.026 mol K

Number of moles of Chromium = 52/52 = 1 mol Cr

Number of moles of oxygen = 56/16 = 3.5 mol O

Multiply through the number of moles by 2 and round up to the nearest whole number to get the empirical formula at; K₂Cr₂O₇

2) The compound K₂Cr₂O₇ is called Potassium dichromate. It is classified as an ionic compound because it has two potassium ions (K+) and a negatively charged dichromate ion (Cr2O7-).

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The answer choice which correctly draws a comparison between the end behaviours of the functions is; Choice C; They have the same end behavior as x approaches -∞ and same end behavior as x approaches ∞.

As given in the task content; the graph of the exponential function passes through (-4, 9), (0, 1), (1, 0), and (5, -2).

It therefore follows that as; x reduces (approaches -∞), the y value increases.

And, as x -increases (approaches +∞), the y-value decreases.

For the table, the values can be written as coordinates as follows; (-1,2), (0,4), (1,6), (2, 0), (3,-2).

Consequently, as x reduces (approaches -∞), the y- values decrease.

And, as x increases (approaches +∞), the y-values decrease.

Ultimately, the two functions in discuss can be concluded to have; Choice C.

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Answer:

40°, 50°, and 90°

Step-by-step explanation:

Let the smallest angle be x.

Then, the other small angle is x+10.

The acute angles of a right triangle are complementary, so x+x+10=90, and thus x=40.

So, the acute angles measure 40° and 50°.

Therefore, the three angles are 40°, 50°, and 90°.

Answer + Step-by-step explanation:

1) The probability of getting 2 white balls is equal to:

[tex]=\frac{8}{20} \times \frac{7}{19}\\\\= 0.147368421053[/tex]

2) the probability of getting 2 white balls is equal to:

[tex]=C^{2}_{5}\times (\frac{8}{20} \times \frac{7}{19}) \times (\frac{12}{18} \times \frac{11}{17} \times \frac{10}{16})\\=0.397316821465[/tex]

3) The probability of getting at least 72 white balls is:

[tex]=C^{72}_{150}\times \left( \frac{8}{20} \right)^{72} \times \left( \frac{7}{20} \right)^{78} +C^{73}_{150}\times \left( \frac{8}{20} \right)^{73} \times \left( \frac{7}{20} \right)^{77} + \cdots +C^{149}_{150}\times \left( \frac{8}{20} \right)^{149} \times \left( \frac{7}{20} \right)^{1} +\left( \frac{8}{20} \right)^{150}[/tex]

[tex]=\sum^{150}_{k=72} [C^{k}_{150}\times \left( \frac{8}{15} \right)^{k} \times \left( \frac{7}{15} \right)^{150-k}][/tex]

First of all, we would determine the total number of balls in the urn as follows:

Total number of balls = 8 + 7 + 5

Total number of balls = 20 balls.

Next, we would determine the probability of getting two (2) white balls without replacement:

P(2 white balls) = 8/20 × 7/19

P(2 white balls) = 2/5 × 7/19

P(2 white balls) = 0.1474.

When 5 balls are selected without replacement, the probability of getting two (2) white balls would be calculated as follows:

P = [⁵C₂ × (8/20 × 7/19) × (12/18 × 11/17 × 10/16)]

P = [5!/(2! × (5 - 2)!) × (2/5 × 7/19) × (2/3 × 11/17 × 5/4)]

P = [5!/(2! × 3!) × (2/5 × 7/19) × (2/3 × 11/17 × 5/4)]

P = [20/2 × (2/5 × 7/19) × (2/3 × 11/17 × 5/4)]

P = [10 × (2/5 × 7/19) × (2/3 × 11/17 × 5/4)]

P = 0.3456.

When 150 balls are randomly selected with replacement, the probability of getting at least seventy two (72) white balls would be calculated by applying binomial probability equation. Mathematically, binomial probability is given by this equation:

[tex]P =\; ^nC_r (p)^r (q)^{(n-r)}[/tex]

Substituting the given parameters into the formula, we have;

P = [¹⁵⁰C₇₂ × (8/20)⁷² × (8/20)⁽¹⁵⁰ ⁻ ⁷²⁾]

P = [150!/(72! × (150 - 72)!) × (8/20)⁷² × (8/20)⁽¹⁵⁰ ⁻ ⁷²⁾]

P = [150!/(72! × (78)!) × (4/5)⁷² × (4/5)⁽⁷⁸⁾]

P = 0.7948.

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Answer:

BA

CB

CA

Step-by-step explanation:

this simply means that such a letter combination stands for a line that goes through the points with these letters.

and a "ray" means a straight line (not one that goes around a corner). "from this figure" means lines (or connections between points) that are drawn in this graphic.

BA yes

B is just a point, no line. therefore, no.

DBA guys around a corner (from D to B, and then from there to A). therefore, no.

AD would be a straight line, but it is not drawn in the graphic. therefore, no.

ADB is partly not drawn, and it goes around a corner. therefore, no.

CB, CA are both straight lines in the graphic. yes.

Answer:

6x⁴ - 2x² +3

Step-by-step explanation:

[tex]\frac{12x^6-4x^4+6x^2}{2x^2}=6x^4 - 2x^2 + 3[/tex]

Answer: C

Step-by-step explanation:

The line [tex]y=x+2[/tex] is shaded below and is solid.

This eliminates all the options except for C.

The irrational number on set B is given by: [tex]\sqrt{5}[/tex]

Irrational numbers are numbers that cannot be represented by fractions. The two most common examples are:

In the set B given in this problem, the only number that is irrational is [tex]\sqrt{5}[/tex], as it is a non-exact root.

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Answer: Interior Angle

Step-by-step explanation:

The angle BAD is fully enclosed, it is on the inside

Answer:

AG = 17 m

AD = 25 m

GD = ?

AD = AG + GD

GD = AD - AG

= 25 - 17

= 8 m

the answer to your question is 8m

If the Hansens want to reduce their expected estate tax liability prior to the death of either of the spouses, they could initiate a Marital Transfer.

A Marital transfer simply means that the Hansens should bequest their assets to each each other in case either of them die.

If this happens, the surviving spouse will not be charged any estate taxes because bequests to spouses are not subject to taxation.

To do this, the Hansens should put it into both of their wills that they plan to gift/ bequest their assets to their spouse if they die.

The big disadvantage of using a marital transfer however, is that the estate will still be subject to taxes when the surviving spouse dies. All the estate taxes that had been avoided would then be incurred by the estate but only after the death of both spouses.

In conclusion, they should use a marital transfer.

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Answer:

  y = x +5

Step-by-step explanation:

The equation of a parallel line will have the same x- and y-coefficients, but a different constant. You need to find the constant that makes the line go through the given point.

The given line is y = x +1. The equation you're looking for is

  y = x +c . . . . . . for some new constant c

We want this equation to be true for (x, y) = (-2, 3). Putting these values into the equation, we can solve for c.

  3 = -2 +c

  5 = c . . . . . . add 2

The desired equation is y = x +5.

The chances of it happening more than once in 4 trials is 13%

From the information given, we have can deduce that;

Probability of 1 trial = 55%

= 55/ 100

Find the ratio

= 0. 55

We are to find the probability of it happening more than once in 4 different trials

If the probability of it happening in one trial is 555 which equals 0. 55

Then the probability of it happening in 1 in 4 trials is given as;

P(1/4 trials) = 1/ 4 × 55%

P(1/4 trials) = 1/ 4 × 0. 55

Put in decimal form

P(1/4 trials) = 0. 25 × 0. 55

P(1/4 trials) = 0. 138

But we have to know the percentage

= 0. 138 × 100

Multiply the values, we have

= 13. 8 %

Thus, the chances of it happening more than once in 4 trials is 13%

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The correct option regarding Talia factoring is given by:

Talia needs to factor out a negative from one of the groups so the binomials will be the same.

The expression is given by:

(15x² - 3x) + (-20x + 4).

Her first step was:

3x(5x - 1) + 4(-5x + 1)

After that, she did not factor out anything more out of the expression. However, looking at the two terms of the addition, we can realize that:

(-5x + 1) = -(5x - 1), hence she should factor out the negative.

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Answer: Madison can travel 2.2 miles less than Anthony on one gallon of gas.

Step-by-step explanation:

The equation y = 39.1[tex]x[/tex] represents the number of miles, [tex]y[/tex], that madison can drive her car for every x gallons of gas.

Question: Madison can travel _ miles _ than Anthony on one gallon of gas.

Lets find how much Madison travels on 1 gallon of gas.

39.1(1) = 39.1

Therefore, Madison travels 39.1 miles on one gallon of gas.

Now lets solve for Anthony

Anthony travels 380.7 miles on 9 gallons of gas.

Therefore we can set up the equation:

9x = 380.7 to show that 9 gallons equates to 380.7 miles

to solve divide 9 from both sides

[tex]\frac{9x}{9} =\frac{380.7}{9}[/tex]

x = 41.3

So, Anthony travels 41.3 miles on one gallon of gas

Now find whether Madison travels more or less than Anthony on one gallon.

39.1 - 41.3 = -2.2

This means that Anthony can travel 2.2 miles more than Madison.

For your answer, this means that:

Madison can travel 2.2 miles less than Anthony on one gallon of gas

Hope this helped and have a nice day :)

Answer:

-13

Step-by-step explanation:

First, we will find the value of j(2) first.

j(2) = -2(2) = -4

next, we will solve h[j(2)].

h[j(2)] = h(-4) = 3(-4) - 1 = -12 - 1 = -13

a. Recall that in polar coordinates, we can parameterize [tex]x=r\cos(\theta)[/tex] and [tex]y=r\sin(\theta)[/tex]. So, doing as the hint suggests, we have

[tex]r = 6\cos(\theta) + 8 \sin(\theta)[/tex]

[tex]\implies r^2 = 6r\cos(\theta) + 8r\sin(\theta)[/tex]

[tex]\implies \boxed{x^2 + y^2 = 6x + 8y}[/tex]

b. By completing the square, we get

[tex]x^2 + y^2 = 6x + 8y[/tex]

[tex]x^2 - 6x + y^2 - 8y = 0[/tex]

[tex]x^2 - 6x + 9 + y^2 - 8y + 16 = 25[/tex]

[tex](x-3)^2 + (y-4)^2 = 5^2[/tex]

which is the equation of the circle centered at (3, 4) with radius 5. Thus the area bounded by [tex]C[/tex] is [tex]\pi\cdot5^2 = \boxed{25\pi}[/tex].

c. This is made easier if you can consult a plot (attached). In the first quadrant, we have [tex]0\le\theta\le\frac\pi2[/tex], while the radial coordinate [tex]r[/tex] runs uninterrupted from the origin [tex]r=0[/tex] to the circle [tex]r=6\cos(\theta)+8\sin(\theta)[/tex]. So the area is

[tex]\displaystyle \int_0^{\pi/2} \int_0^{6\cos(\theta) + 8\sin(\theta)} r\,dr\,d\theta = \boxed{\frac12 \int_0^{\pi/2} \left(6\cos(\theta) + 8\sin(\theta)\right)^2 \, d\theta}[/tex]

d. Evaluate the integral.

[tex]\displaystyle \frac12 \int_0^{\pi/2} \left(36\cos^2(\theta) + 96\sin(\theta)\cos(\theta) + 64 \sin^2(\theta)\right) \, d\theta[/tex]

Simplify the integrand with the help of the identities

[tex]\cos^2(x) + \sin^2(x) = 1[/tex]

[tex]\sin(x)\cos(x) = \dfrac12 \sin(2x)[/tex]

[tex]\sin^2(x) = \dfrac{1 - \cos(2x)}2[/tex]

[tex]\displaystyle \frac12 \int_0^{\pi/2} \left(50 + 48\sin(2\theta) - 14 \cos(2\theta)\right) \, d\theta[/tex]

The rest is easy. You should end up with

[tex]\displaystyle \frac12 \int_0^{\pi/2} \left(6\cos(\theta) + 8\sin(\theta)\right)^2 \, d\theta = \boxed{24 + \frac{25\pi}2}[/tex]

a) The Cartesian equation that described curve C is x² + y² = 6 · x + 8 · y.

b) The area inside C is A = π · 5² = 25π square units.

c) The integral that computed the area inside curve C within the first quadrant is A = (1 / 2)∫ (6 · cos θ + 8 · sin θ)² dθ, for θ ∈ [0, 0.5π].

d) The integral evaluated at the given limits is equal to an area of 20.139π square units.

In this question we find a polar equation in explicit form. a) To find the equivalent form in rectangular coordinates, we must apply the following substitutions x = r · cos θ, y = r · sin θ:

r = 6 · cos θ + 8 · sin θ

r² = 6 · r · cos θ + 8 · r · sin θ

x² + y² = 6 · x + 8 · y       (1)

The Cartesian equation that described curve C is x² + y² = 6 · x + 8 · y.

b) Perhaps the equation represents a conic section, possibly a circunference. To prove this assumption, we must apply algebraic handling until standard form is obtained:

x² - 6 · x + y² - 8 · y = 0

x² - 6 · x + 9 + y² - 8 · y + 16 = 25

(x - 3)² + (y - 4)² = 5²          (1b)

Which indicates a circumference centered at point (h, k) = (3, 4) and with a radius of 5 units. By the area formula for a circle we find that the area inside C is A = π · 5² = 25π square units.

c) The polar form of the area integral is presented herein:

A = ∫ ∫ r dr dθ, for r ∈ [0, r(θ)] and θ ∈ [0, 0.5π]  

A = (1 / 2)∫ [r(θ)]² dθ, for θ ∈ [0, 0.5π]  

A = (1 / 2)∫ (6 · cos θ + 8 · sin θ)² dθ, for θ ∈ [0, 0.5π]  

The integral that computed the area inside curve C within the first quadrant is A = (1 / 2)∫ (6 · cos θ + 8 · sin θ)² dθ, for θ ∈ [0, 0.5π].

d) By algebraic handling, trigonometric formulas and integral properties:

A = 25 ∫ dθ  + 24 ∫ sin 2θ dθ - 14 ∫ cos 2θ dθ, for θ ∈ [0, 0.5π]  

A = 25 · θ - 12 · cos 2θ - 7 · sin 2θ, for θ ∈ [0, 0.5π]  

A = 20.139π

The integral evaluated at the given limits is equal to an area of 20.139π square units.  

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Step-by-step explanation:

Let ABC be the equilateral triangle. Let AE, BD and CF be the medians. A meridian divides a side into two equal parts. Hence, proved that medians of an equilateral triangle are equal .

(a) The half-life of the unknown radioactive element is 250.28 days.

(b) The time taken for a sample of 100 mg to decay to 81 mg is 76.1 days.

N(t) = N₀(0.5)^t/h

where;

in 340 days; N(340) = N₀(0.39);

1 - 0.61 = 0.39

N(340) = N₀(0.5)^340/h

N(340)/N₀ = 0.5^340/h

0.39 = 0.5^340/h

log(0.39) = 340/h x log(0.5)

log(0.39) /log(0.5) = 340/h

1.358 = 340/h

h = 340/1.358

h = 250.28 days

81 = 100(0.5)^t/250.28

81/100 = (0.5)^t/250.28

0.81 = (0.5)^t/250.28

log(0.81) = t/250.28 x log(0.5)

log(0.81) / log(0.5) = t/250.28

0.304 = t/250.28

0.304(250.28) = t

76.1 days = t

Thus, the half-life of the unknown radioactive element is 250.28 days and the time taken for a sample of 100 mg to decay to 81 mg is 76.1 days.

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Answer:

he is more likely incorrect.

Step-by-step explanation:

Z = (ps - p0)/sqrt(p0(1-p0)/n)

ps = proportion sample

p0 = proportion null hypothesis (NCAA)

n = sample size

ps = 17 / 36/100 = 17/1 / 36/100 = 1700/36 =

= 47.22222222...%

Z = (0.47222... - 0.575)/sqrt(0.575(1 - 0.575)/36) =

= -0.10277777... /sqrt(0.244375 / 36) =

= -0.10277777... / 0.0823905... =

= -1.247446952... ≈ -1.25

p(-1.25) = 0.10565

0.10565 > 0.05

the null hypothesis is therefore likely, or at least cannot be rejected.

so, his claims are not supported, as surprising as this might feel given that the sample result itself is 10 points off the NCCA result, which feels to be a solid difference.

Answer:

8.75

Step-by-step explanation:

106.75 divided by 12.20= 8.75

your mother i swear

Step-by-step explanation:

ask yo mom

Answer:

incenter

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

This is a translation 5 units left and 5 units dowh.

Here, the translation is [tex]T < 5,-5 >[/tex].

Here, the translation is given as: [tex]y=2(x-5)+5\longrightarrow y=2(x-0)+0[/tex].

i.e. [tex]y=2(x-5)+5\longrightarrow y=2(x-5+5)+(5-5)[/tex].

So, the graph of [tex]y[/tex] moves 5 units to the right and (-5) units to the up i.e., 5 units to the down.

Therefore, here, the translation is [tex]T < 5,-5 >[/tex].

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Answer:

f(x) = g(x) + 9 because it is shifted 9 to the right

On looking for a pattern in the given data set, the quadratic model best describes the data.

2nd option is correct.

A data model represents the type of relationship between the variables of a data set.

Data models are of four types, namely, Linear, Cubic, Quadratic and Exponential data models.

Given data is:

Distance Traveled                      Average Speed(miles per hour)

(miles)

1                                                                7

2                                                               6.3

3                                                              5.67

4                                                              5.103

A quadratic model is the best data model for the given data set.

The pattern observed in the given data set observes the properties of a quadratic function.

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Answer:

Exponential is the correct answer.

Step-by-step explanation:

Using the binomial distribution, the probability that:

(a) Exactly 29 of them are spayed or neutered, that is, P(X = 29) = 0.1163.

(b)  At most 29 of them are spayed or neutered, that is, P(X ≤ 29) = 0.6648.

(c)  At least 28 of them are spayed or neutered, that is, P(X ≥ 28) = 0.5714.

(d) Between 28 and 32 (including 28 and 32) of them are spayed or neutered, that is, P(28 ≤ X ≤ 32) = 0.48345.

A binomial distribution, with a success rate of p on each trial, gives us the probability of x number of success in n number of trials, using the formula:

P(X = x) nCx.pˣ.qⁿ⁻ˣ, where q = 1 - p.

In the question, we are informed that 61% of owned dogs in the United States are spayed or neutered, and are given that 46 owned dogs are randomly selected.

This can be seen as a binomial probability distribution, with n = 46, and p = 61% = 0.61, q = 1 - p = 1 - 0.61 = 0.39.

(a) We are asked for the probability of exactly 29 of them being spayed or neutered.

Thus, x = 29, and we need to find P(X = 29).

Using the given calculator, P(X = 29) = 0.1163.

(b) We are asked for the probability of at most 29 of them being spayed or neutered.

Thus, we need to find P(X ≤ 29).

Using the given calculator, P(X ≤ 29) = 0.6648.

(c) We are asked for the probability of at least 28 of them being spayed or neutered.

Thus, we need to find P(X ≥ 28).

Using the given calculator, P(X ≥ 28) = 0.5714.

(d) We are asked for the probability between 28 and 32 of them are spayed or neutered.

Thus, we need to find P(28 ≤ X ≤ 32), which can be shown as;

P(28 ≤ X ≤ 32) = P(X ≤ 32) - P(X < 28).

Using the given calculator, P(X ≤ 32) = 0.91209.

Using the given calculator, P(X < 28) = 0.42864.

Thus, P(28 ≤ X ≤ 32) = P(X ≤ 32) - P(X < 28) = 0.91209 - 0.42864 = 0.48345.

Thus, using the binomial distribution, the probability that:

(a) Exactly 29 of them are spayed or neutered, that is, P(X = 29) = 0.1163.

(b)  At most 29 of them are spayed or neutered, that is, P(X ≤ 29) = 0.6648.

(c)  At least 28 of them are spayed or neutered, that is, P(X ≥ 28) = 0.5714.

(d) Between 28 and 32 (including 28 and 32) of them are spayed or neutered, that is, P(28 ≤ X ≤ 32) = 0.48345.

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Answer:

2827 m²

Step-by-step explanation:

The equation for volume of a sphere is:

[tex]V=\frac{4}{3}\pi r^3[/tex]

Using this equation and the given volume of the sphere, we can find the radius of the sphere.

[tex]V=\frac{4}{3}\pi r^3[/tex]

[tex]4500\pi = \frac{4}{3}\pi r^3[/tex]

Divide both sides by π

[tex]4500=\frac{4}{3}(r^3)[/tex]

Multiply both sides by 3

[tex]13500=4( r^3)[/tex]

Divide both sides by 4

[tex]3375=r^3[/tex]

Take the cube root of both sides

[tex]r=15[/tex]

Thus the radius of the sphere is 15m. We can use this information to find the surface area of the sphere.

The equation for surface area of a sphere is [tex]4\pi r^2[/tex]. Substituting the value we found for the radius into the equation, we find:

[tex]SA=4\pi r^2\\SA=4\pi 15^2\\SA=4\pi 225\\SA=900\pi\\SA\approx2827$ m^2[/tex]

The surface area of the sphere, rounded to the nearest square meter, is 2827 m².

The answers to these questions are:

a. In the question we have the existence of the mean, the mode and the median hence the answer to this question is none.

b. if the measurement 14 is replaced by 2, the data that it is going to have the most effect on is going to be the mean. It would reduce the mean.

c. If the largest measurement is removed, it is going to have the most effects on the mean and the median.

d. If the data is skewed then the mean of the data set is going to be greater.

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Answer:

113

Step-by-step explanation:

first we need to divide 1000 by 8 to get 125.

Our prime number has to be less than 125.

The largest prime number less than 125 is 113.