b. A kennel has 90 dogs in total, some are puppies and some are adult dogs. The ratio of puppies to adult dogs in a kennel is 1:4. What fraction of dogs are adults? Use this to work out how many adult dogs there are. See the examples on the formula sheet for this assessment.​

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=0\\ k=-3\\ \end{cases}\implies y=a(~~x-0~~)^2 + (-3)\hspace{4em}\textit{we also know that} \begin{cases} x=-8\\ y=5 \end{cases} \\\\\\ 5=a(-8-0)^2-3\implies 8=64a\implies \cfrac{8}{64}=a\implies \cfrac{1}{8}=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} y=\cfrac{1}{8}x^2-3 \end{array}} ~\hfill[/tex]

Therefore, there are 20 girls in the class of fifth-graders.

In mathematics, a fraction represents a part of a whole or a division of two numbers. It is written in the form of a numerator and a denominator separated by a horizontal bar (also known as a fraction bar). The numerator represents the number of equal parts being considered, while the denominator represents the total number of equal parts in the whole or the divisor of the division.

Here,

Let the number of girls in the class be represented by 'g'.

According to the problem, the number of boys is 3/4 as many as the number of girls. This means:

Number of boys = (3/4) * number of girls

Number of boys = (3/4) * g

The total number of students in the class is given as 35. So we have:

Number of girls + Number of boys = Total number of students

g + (3/4)g = 35

Simplifying the equation, we get:

(7/4)g = 35

Dividing both sides by 7/4, we get:

g = 20

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Answer:

m = -3/4

Step-by-step explanation:

Calculation of the Slope of a line

The information provided about the line is that the line passes through the points  (-8, 9) to (-4,6)

Therefore, the first step consists in computing the slope. The formula for the slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Now, by plugging the corresponding numbers is , we get that the slope is:

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{6-9}{-4-(-8)} =\frac{6-9}{-4+8} =-\frac{3}{4}[/tex]

So then, we find that the slope is [tex]m=-\frac{3}{4}[/tex] and that the line passes through the point  [tex](-8,9)[/tex].

By answering the question the answer is So the slope intercept  expression 4x + 5y = 20 in intercept form is: x/5 + y/4 = 1 

The slope-intercept form of a linear equation in mathematics is an equation of the form y = mx + b. where m is the slope of the line and b is the y-intercept, the point where the line crosses the y-axis. The slope-intercept format is a convenient way to plot equations for straight lines because it allows you to quickly see the line and determine the slope and y-intercept. The slope indicates how steep the line is, and the y-intercept indicates where the line crosses the y-axis.  

The intercept form of a linear equation in two variables (x and y) is given by

x/a + y/b = 1

where a and b are the intercepts of x and y respectively.

To convert the given expression 4x + 5y = 20 to intercept form, we need to solve for the intercepts for x and y.

For x = 0, 4x + 5y = 20 becomes

0 + 5 years old = 20

y = 4

So the y-intercept is 4.

For y = 0, 4x + 5y = 20 becomes

4x + 0 = 20

x = 5

So the x-intercept is 5.

So the expression 4x + 5y = 20 in intercept form is:

x/5 + y/4 = 1 

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The coordinates of point P that is 3/4 of the way along the directed line segment from C(6, -5) to D(-3, 4) are (-0.75, 1.75).

To find the coordinates of point P that is 3/4 of the way along the directed line segment from C(6, -5) to D(-3, 4), we can use the following formula:

P = (1 - 3/4)C + (3/4)D

First, we find the vector CD = D - C:

CD = (-3, 4) - (6, -5) = (-9, 9)

Then we can plug in the values and simplify:

P = (1 - 3/4)C + (3/4)D

P = (1/4)(6, -5) + (3/4)(-3, 4)

P = (3/4)(-3, 4) + (1/4)(6, -5)

P = (-2.25, 3) + (1.5, -1.25)

P = (-0.75, 1.75)

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The probability of getting the toss Heads and spin a Red when A coin is tossed and then the spinner is spun is 1/6 option A.

Events classified as independent do not depend on other events for their occurrence. For instance, if we toss a coin in the air and it lands on head, we can toss it again and this time it will land on tail. Both instances include separate occurrences of the two events.

Formula for probability,

P = number of outcomes/Total outcomes

P = n/T

We have probability of getting a head is, n = 1

S = {H, T}

Total Outcome = 2

So Probability p1 = 1/2

The probability of getting the red after spun is

S = {R, R, B, B, G, G}

n = 2

Total outcome = 6

p2 = 2/6 = 1/3

Total number of probability for toss Heads and spin a Red.

P = p1 x p2

P = 1/2 x 1/3

P = 1/6

Therefore, probability is 1/6.

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Answer:

J. 2.5

Step-by-step explanation:

A reciprocal is the inverse of a number. The reciprocal of a number is 1 divided by the number.

With a decimal number, it's best to convert the number into fraction form. In fraction form, you just have to switch the numerator and denominator to find the reciprocal.

0.4 = 4/10 = 2/5

Reverse the numerator and denominator to get 5/2.

Convert 5/2 to a decimal:

5/2 = 2.5

The Length of arcXY is 4π/3

The Circle identities refer to a set of fundamental identities in trigonometry that relate the six trigonometric functions of an angle in a right-angled triangle.

Given, (radius) WX =3, it means, r = 3

given, m∠XWY = 80°

So, the length of arc XY;

arcXY = [tex]\frac{80}{360}* 2\pi r[/tex]        (by formula: length of arc)

arcXY = [tex]\frac{2}{9}* 2\pi *3[/tex]

arcXY = [tex]\frac{4}{3}\pi[/tex]

Therefore, the Length of arcXY is 4π/3

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Complete question-

Using the power property to simplify the expression (9¹⁺⁴)⁷⁺², we have 9^7/8

Given the expression

(9¹⁺⁴)⁷⁺²

To simplify this expression using the power of a power property, we need to multiply the exponents:

(9¹⁺⁴)⁷⁺² = 9(¹⁺⁴ ˣ ⁷⁺²)

Simplifying the exponents in the parentheses:

(9¹⁺⁴)⁷⁺² = 9⁷⁺⁸ or 9^7/8

Therefore, (9¹⁺⁴)⁷⁺² simplifies to 9^(7/8).

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For the given statements for domain and range, option 3 and option 4 are correct answers.

The sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively, are the domain and range of a relation. With functions, we enter various numbers, and the output is a new set of numbers. The two essential characteristics of functions are domain and range. A function's domain and range are its constituent parts.

The domain of the function are all the input values while the range are the output values of the function for the given input.

In the given options, option 3 and 4 are correct as the functions have the same input but not the same output.

That is, they have the same domain, all real numbers, but not the same range.

Hence, for the given statements for domain and range, option 3 and option 4 are correct answers.

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Days when change in temperature more than 10° F are Option B)Tuesday and E) Friday.

calculating the difference by deducting the end temperature from the initial temperature. The temperature difference is therefore 75 degrees Celsius - 50 degrees Celsius = 25 if something begins at 50 degrees Celsius and ends at 75 degrees Celsius.

Change in temperature on Monday from High to low

=15-10=5°F

Change in temperature on Tuesday from High to low

=8-(-4)=12°F

Change in temperature on Wednesday from High to low

=-2-(-5)=3°F

Change in temperature on Thursday from High to low

=-3-(-7)=4°F

Change in temperature on Friday from High to low

=-1-(-12)=11° F

Days when change in temperature more than 10° F are Tuesday and Friday.

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The Complete question is attached below:

In one of his experiments conducted with animals, Thorndike found that cats learned to escape from a puzzle box is increased gradually

To quantify the learning process, Thorndike used a mathematical formula known as the Law of Effect equation. The equation is:

B = f(log S1/S2)

where B represents the strength of the behavior, S1 represents the satisfaction of the positive consequence, and S2 represents the degree of frustration or negative consequence.

In the context of Thorndike's puzzle box experiment, the Law of Effect equation can be used to describe how the cat's behavior changed over time as it learned to escape the puzzle box more quickly and efficiently. Initially, the cat's behavior was weak because it did not know which actions would lead to a positive outcome.

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Using binomial theorem, the generating function is G(x) = x^4 + 16x^3 + 96x^2 + 256x + 256 while the associated sequence of (x+4)^4 is {1, 16, 96, 256, 256}.

To find the generating function of (x+4)^4, we expand it using the binomial theorem:

[tex](x+4)^4 = C(4,0)x^4 + C(4,1)x^3(4) + C(4,2)x^2(4^2) + C(4,3)x(4^3) + C(4,4)(4^4)[/tex]

where C(n,k) denotes the binomial coefficient "n choose k".

Simplifying the terms, we get:

[tex](x+4)^4 = x^4 + 16x^3 + 96x^2 + 256x + 256[/tex]

Therefore, the generating function of (x+4)^4 is:

[tex]G(x) = x^4 + 16x^3 + 96x^2 + 256x + 256[/tex]

The associated sequence can be read off by finding the coefficients of each power of x:

To find the generating function of (x+4)^4, we expand it using the binomial theorem:

(x+4)^4 = C(4,0)x^4 + C(4,1)x^3(4) + C(4,2)x^2(4^2) + C(4,3)x(4^3) + C(4,4)(4^4)

where C(n,k) denotes the binomial coefficient "n choose k".

Simplifying the terms, we get:

(x+4)^4 = x^4 + 16x^3 + 96x^2 + 256x + 256

Therefore, the generating function of (x+4)^4 is:

G(x) = x^4 + 16x^3 + 96x^2 + 256x + 256

The associated sequence can be read off by finding the coefficients of each power of x:

The coefficient of x^k is the k-th term of the sequence.

In this case, the sequence is given by the coefficients of G(x):

a₀ = 256

a₁ = 256

a₂ = 96

a₃ = 16

a₄ = 1

Therefore, the associated sequence of (x+4)^4 is {1, 16, 96, 256, 256}.

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Option A: The factor (96 − 2x) represents the length, in inches, of the uncovered portion of the bulletin board.

To obtain the area of a rectangle, you need to multiply the dimensions of the rectangle, which are the length and the width.

Hence the formula for the area of the rectangle is given as follows:

Area = Length x Width.

The area of the uncovered region is given by the total area subtracted by the area of the covered region.

Then the dimensions for the uncovered region are given as follows:

The area of the covered region is given as follows:

4x².

The area of the entire region is given as follows:

4x² - 288x + 4608.

Hence the correct statement is given by option A.

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y = 2x + 1...so sub in 2x + 1 for y in the other equation

x + 3y = 10

x + 3(2x + 1) = 10

x + 6x + 3 = 10

x + 6x = 10 - 3

7x = 7

x = 1

y = 2x + 1

y = 2(1) + 1

y = 2 + 1

y = 3

the difference : there can be 1 possible answer for this..

y - x = 3 - 1 = 2

The sum of the arithmetic progressive sequence will be +∞, for common difference as positive that is d >0.

The difference between every two successive terms in a sequence is the same; this is known as an arithmetic progression (AP).

A good example of an arithmetic progression (AP) is the series 2, 6, 10, 14,..., which follows a pattern in which each number is created by increasing 4 to the previous term. This annual income of a worker whose pay rises by a predetermined amount of $5000 each year serves as a real-world illustration of an AP.

The expression for an arithmetic progression:

a is the first term

l is last term

d is common difference

n is total number of terms

Sn = the sum of term

A.P =  a,a+d,a+2d,a+3d,…, a+(n-1)d

l = a+(n-1)d

Sum formula:

Sn=n/2 [a+(n-1)d]

Or, Sn=n/2 [a+l]

Thus, the sum of the arithmetic progressive sequence will be +∞, for common difference as positive that is d >0.

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The utility that maximizes the possible utility of both the agents Alice and Bob is equal to option D. $10.

Compare Alice's utility from each option and choose the one that maximizes her utility.

Let us consider each option,

If Alice offers Bob $0, her utility will be,

If XA > XB then

UA (XA , XB )= 0.3x3 + 0.72A

UA(10,0)

= 0.3(10)³ + 0.72(10)

= 307.2

If Alice offers Bob $5, Bob's utility will be,

UB(10,5)

= 0.314 + 0.72(5)

= 0.314 + 3.6

= 3.914

And Alice's utility will be,

UA(5,10)

= -0.32(5) + 1.3(10)

= 11.4

Total utility for both Alice and Bob will be,

UA(5,10) + UB(10,5)

= 11.4 + 3.914

= 15.314

If Alice offers Bob $2, Bob's utility will be,

UB(10,2)

= 0.314 + 0.72(2)

= 1.754

And Alice's utility will be,

UA(2,10)

= -0.32(2) + 1.3(10)

= 12.4

So the total utility for both Alice and Bob will be,

UA(2,10) + UB(10,2)

= 12.4 + 1.754

= 14.154

If Alice offers Bob $10, Bob's utility will be,

UB(10,10)

= 0.314 + 0.72(10)

= 7.514

And Alice's utility will be,

UA(10,10)

= 0.3(10)³ + 0.72(10)

= 307.2

So the total utility for both Alice and Bob will be,

UA(10,10) + UB(10,10)

= 307.2 + 7.514

= 314.714

Therefore, utility which maximizes the total utility for both Alice and Bob is given by option (D) $10.

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Answer:

88/25

Step-by-step explanation:

if you do 2.2 times 1.6 equals 3.52 and then a fraction.

Answer:

2.2 × 1.6 can be expressed as a fraction multiplication expression as follows:

(22/10) × (16/10)

Simplifying the expression by canceling out the common factor of 10, we get:

22 × 16 / 10 × 10

Multiplying the numerator and denominator, we get:

352 / 100

Simplifying the fraction by dividing both the numerator and denominator by 4, we get:

88 / 25

Therefore, 2.2 × 1.6 as a fraction multiplication expression is 88/25.

Since Kingsley wanted an equation to convert from inches to centimeters, the correct answer is B) c = 2.54i.

What is equation ?

An equation is a statement that asserts the equality of two expressions, usually separated by an equals sign (=). The expressions on either side of the equals sign may contain one or more variables, which are unknown values that can be determined by solving the equation.

Kingsley wants to convert a given length in inches to centimeters. He knows that 1 inch is about 2.45 centimeters.

Let's call the length in inches "i" and the length in centimeters "c".

We want to find an equation that relates i and c. We know that 1 inch is about 2.45 centimeters, so we can write:

1 inch = 2.45 centimeters

To convert from inches to centimeters, we can multiply the length in inches by 2.45. So:

c = 2.45i

This is the equation Kingsley can use to convert any given length in inches to centimeters.

Alternatively, we can rearrange this equation to solve for i:

c = 2.45i

Divide both sides by 2.45:

c/2.45 = i

So the equation for converting from centimeters to inches is:

i = c/2.45

Therefore,  since Kingsley wanted an equation to convert from inches to centimeters, the correct answer is B) c = 2.54i.

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Answer: numbers 1,3 and 4

Step-by-step explanation:

The company's price-earnings ratio for a company that reported net income of $275,270 with $20,390 for preferred dividends and 36,000 shares of common stock, is 16.79.

The price-earnings ratio represents the per-dollar amount that an investor can expect to invest in a company in order to receive $1 of that company's net earnings.

The price-earnings (P/E) ratio is also referred to as the price multiple.

The price-earnings (P/E) ratio compares the market price with the earnings per share.

Net income = $275,270

Preferred Dividends = $20,390

Net income available to Common Stockholders = $254,880 ($275,270 - $20,390)

Number of common stock outstanding = 36,000 shares

Market price per share of common stock = $118.87

Earnings per share (Common Stock) = $7.08 ($254,880/36,000)

Price-earnings ratio = Market price per share/Earnings per share

= 16.79 ($118.87/$7.08).

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The volume of the new rectangular prism is 160 in³ after it has been dilated with a scale factor of 2.

In this case, the scale factor is 2, which means that the dimensions of the original figure will be multiplied by 2 to get the dimensions of the new figure.

Volume of rectangular prism = length x width x height

20 = l x w x h

Next, we need to find the new dimensions of the rectangular prism after it has been dilated by a scale factor of 2. We can do this by multiplying each dimension of the original rectangular prism by 2.

New length = 2 x l

New width = 2 x w

New height = 2 x h

Now we can find the volume of the new rectangular prism by using the same formula as before, but with the new dimensions:

Volume of new rectangular prism = (2 x l) x (2 x w) x (2 x h)

Simplifying this expression, we get:

Volume of new rectangular prism = 8 x (l x w x h)

We know that l x w x h is equal to the volume of the original rectangular prism, which is 20 in³. So we can substitute this value into the expression to get:

Volume of new rectangular prism = 8 x 20 in³

Volume of new rectangular prism = 160 in³

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On the fifth day there were 4 tοmatοes left tο be sοld. Jοann had 71 tοmatοes tο begin with.

Prοbability is a measure οf the likelihοοd οr chance οf an event οccurring. It is a number between 0 and 1, where 0 indicates that the event is impοssible, and 1 indicates that the event is certain tο οccur.

Let's wοrk backwards frοm the last day and figure οut hοw many tοmatοes Jοann had οn the fοurth day.

On the fifth day, there were 4 tοmatοes left tο be sοld, which means she sοld half οf what was left οn the fοurth day. Sο she must have started with 8 tοmatοes οn the fοurth day (since half οf 8 is 4).

On the fοurth day, she sοld half οf what was left, which means she had 16 tοmatοes befοre she sοld any.

On the third day, she sοld 12 tοmatοes, which means she had 28 tοmatοes befοre she sοld any.

On the secοnd day, she sοld half οf what was left, which means she had 56 tοmatοes befοre she sοld any.

Finally, οn the first day, she sοld 15 tοmatοes.

Therefοre, Jοann had 71 tοmatοes tο begin with.

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Answer:

Step-by-step explanation:

circumference c=2πr=5π

[tex]r=\frac{5\pi }{2\pi } =\frac{5}{2}~cm \\area=\pi r^{2} =\pi (\frac{5}{2} )^2\\=\frac{25}{4} \pi \\=6.25 ~cm^2[/tex]

The equation of the line passing through A and B is y = (4/5)x - (2/5).

A straight line's general equation is y = mx + c, where m is the gradient and y = c is the value at which the line intersects the y-axis. The y-axis intercept is denoted by the number c. A straight line with gradient m and intercept c on the y-axis has the equation y = mx + c.

The point-slope form of a linear equation can be used to find the equation of the line passing through points A and B:

y - y1 = m(x - x1) (x - x1)

where m denotes the slope of the line, (x1, y1) denotes the coordinates of point A or B, and (x, y) denotes the coordinates of any other point on the line.

To calculate the slope, we can use points A (3, 2) and B (8, 6).

m = (y2 - y1) / (x2 - x1) = (6 - 2) / (8 - 3)\s= 4 / 5

So the equation for the line connecting A and B is:

y - 2 = (4/5)(x - 3) (x - 3)

This equation can be simplified by multiplying both sides by 5:

5y - 10 = 4x - 12

Then we can rearrange it to form the slope-intercept equation, y = mx + b:

5y = 4x - 2

y = (4/5)x - (2/5)

As a result, the equation for the line connecting A and B is y = (4/5)x - (2/5).

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The kinetic energy of particle with a de Broglie wavelength of 0.50 nm is 82.6 eV.

The given de Broglie wavelength of 0.50 nm corresponds to photons. The formula for the kinetic energy of a particle with a given de Broglie wavelength λ is given by:

K = (hc/λ) - mc^2

where h is Planck's constant, c is the speed of light, and m is the rest mass of the particle.

For photons, the rest mass is zero, so the formula simplifies to:

K = hc/λ

Plugging in the given wavelength of 0.50 nm, we get:

K = (6.626 × 10^-34 J s × 3.00 × 10^8 m/s) / (0.50 × 10^-9 m)

K = 1.3252 × 10^-17 J

Converting to electronvolts (eV), we use the conversion factor 1 eV = 1.602 × 10^-19 J:

K = (1.3252 × 10^-17 J) / (1.602 × 10^-19 J/eV)

K = 82.6 eV (rounded to three significant figures)

Therefore, the kinetic energy of photons with a de Broglie wavelength of 0.50 nm is 82.6 eV (rounded to three significant figures).

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Answer: 1/3 chance or 33.33333%

Step-by-step explanation: There are only 3 odd numbers on the die, 1,3,5 so there is a 1/3 chance it is 3

The  angles can be named with one letter  are 2.

Angles are a type of geometric shape which are formed when two straight lines intersect at a point. They are measured in degrees, usually between 0 and 360. Angles can be classified as acute, right, obtuse, straight and reflex, and the sum of any three angles in a triangle will always equal 180 degrees. Angles can be used in various ways, from providing stability in construction work to helping to identify other shapes. They can also be used to measure the size and shape of objects and to calculate distances and areas on maps. Angles are an important part of mathematics, geometry and trigonometry, and are used in a variety of applications in science and engineering.

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