11. The relationship between adult dog weight x in pounds and the daily
recommended amount of dog food y in cups is proportional.
Dog weight (lb)
Dog food (cups)
10
116
40
W|N
2
3
50
556
100
13
Write an equation for the relationship. How much dog food is
recommended for a 25-pound adult dog?

A graph of the given equation (y= -2(x - 1)² - 4) is shown in the image attached below.

An equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

In Science, there are different types of graph and these include the following:

In this scenario, we can reasonably infer and logically deduce that the graph of the given equation is a parabolic because it represents or indicates a quadratic equation.

In conclusion, a graph which represents or indicates the given quadratic equation (y= -2(x - 1)² - 4) is shown in the image attached below.

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The probability that a score will be greater than 82 in a normal distribution with a mean of 78 and a standard deviation of 7 is 28.43%. Correct option is D.

To calculate the probability that a score will be greater than 82 in a normal distribution with a mean of 78 and a standard deviation of 7, we need to use the standard normal distribution and the z-score.

First, we can find the z-score for 82 using the formula:

z = (x - mu) / sigma

where x is the value of interest (in this case, 82), mu is the mean (78), and sigma is the standard deviation (7).

z = (82 - 78) / 7

z = 0.57

Next, we can use a z-table or a calculator to find the area under the standard normal curve corresponding to a z-score of 0.57. The area represents the probability that a score will be greater than 82.

Using a standard normal table, we find that the area to the right of z = 0.57 is 0.2843 or approximately 28.43%. Therefore , correct option is D.

In conclusion, by calculating the z-score and using a standard normal distribution table, we can find the probability that a score will be greater than a certain value in a normal distribution with a known mean and standard deviation.

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Complete question is:

A normal distribution with a mean of 78 and a standard deviation of 7, what is the probability that a score will be greater than 82?

group of answer choices

A. 23.89%

B. 26.11%

C. 76.11%

D. 28.43%

E. 52.22%

Answer:

B. RZ =R BZ

Step-by-step explanation:

Since point Z is equidistant from the sides of ARST, it lies on the perpendicular bisectors of both sides. Therefore, CZ and SZ are perpendicular bisectors of AB and ST, respectively.

Option B is true because point R lies on the perpendicular bisector of AB, and therefore RZ = RB.

Answer: vv

Step-by-step explanation:

Since point Z is equidistant from the sides of ARST, it lies on the perpendicular bisector of the sides ST and AR.

Therefore, we can draw perpendiculars from point Z to the sides ST and AR, which intersect them at points T' and R', respectively.

Now, let's examine the options:

A. SZ & TZ: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of ST, and the distance from Z to S and T could be different.

B. RZ = RB: This is true, as point Z lies on the perpendicular bisector of AR, and is therefore equidistant from R and B.

C. CTZ = ASZ: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of AR, and the distances from Z to C and A could be different.

D. ASZ = ZSB: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of ST, and the distances from Z to A and B could be different.

Therefore, the only statement that must be true is option B: RZ = RB.

Answer: the correct answer is A. Between 0 and 90

If an angle is between 0 and 90 it is acute

If an angle is EXACTLY 90 it is a right angle

If an angle is between 90 and 180 it is obtuse angle

If it's 360 then it is a full circle

The hypotenuse of a right triangle = 19.31cm

What is Hypotenuse?

The longest side of a right-angled triangle, or the side across from the right angle, is called the hypotenuse. The Pythagorean theorem, which asserts that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse.

Let the measure be,

Perpendicular = 18cm

Base = 7cm

Hypotenuse = ?

To find the Hypotenuse we can Pythagoras Theorem:

Hypotenuse² = Perpendicular²+ Base²

H² = (18)² + (7)²

H² = 324 + 49

H² = 373

H = \(\sqrt{373}\)

H = 19.31cm

Hence, The measure of the other leg is²

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There are 256 possible outcomes for the string of 8 heads/tails that can be produced when flipping a coin eight times.

When a coin is flipped eight times, there are two possible outcomes for each individual flip: heads or tails.

Since each flip has two possibilities, the total number of possible outcomes for eight flips can be calculated by multiplying the number of possibilities for each flip together.

Therefore, the number of possible outcomes for eight coin flips is:

2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 2^8 = 256

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Answer:

They don't form a proportion.

When an uncertain event is expressed as a set of possible values, these values are often combined with their respective probabilities into a single mean value called the expected value or the mathematical expectation.

The expected value is a concept used in probability theory and statistics to represent the long-term average outcome of a random variable or uncertain event. It is calculated by multiplying each possible value of the event by its corresponding probability and summing up these products. The result is a single value that represents the average or mean outcome of the event.

The expected value provides a way to summarize the overall outcome of an uncertain event in a single numerical value. It serves as a useful tool in decision-making and risk analysis, as it helps to assess the potential outcomes and evaluate the potential gains or losses associated with different probabilities. By considering the expected value, individuals or organizations can make informed decisions based on the average outcome of the event and weigh the potential risks and rewards.

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Given:

The function is:

\(y=5500\ln (9t+4)\)

Where y is the sales of lawn mowers t years after a particular model is introduced.

To find:

How many mowers will be sold 3 years after a model is introduced?

Solution:

We have,

\(y=5500\ln (9t+4)\)

Substituting \(t=3\), we get

\(y=5500\ln (9(3)+4)\)

\(y=5500\ln (27+4)\)

\(y=5500\ln (31)\)

On substituting the approximate value of ln(31), we get

\(y=5500\times 3.433987\)

\(y=18886.9285\)

\(y\approx 18887\)

Therefore, the 18887 mowers will be sold 3 years after a model is introduced.

Answer:

1. Yes

2. 112 ounces

Step-by-step explanation:

To answer this question, we should first convert the amount of pounds Rick's cat weighs into ounces, so that both measurements are in the same unit. Since 1 pound is the same as 16 ounces, we can multiply 7 pounds by 16 ounces:

7 * 16 = 112

So, Rick's cat weighs 112 ounces, which is more than his neighbor's puppy, which only weighs 103 ounces. so for the first question, the answer is:

Yes, Rick's cat weighs more than the puppy.

And the second answer is:

Rick's cat weighs 112 ounces.

Hope this helps :)

y = 10 + 3 x hopefully this helps im still new tho!

Answer:

m<AOB = 50°

Step-by-step explanation:

<ACB = 25° is an inscribed angle of the circle.

<AOB is a central angle of the circle.

Thus, based on the inscribed angle theorem which states that an inscribed angle is ½ the measure of the central angle, therefore:

m<ACB = ½(m<AOB)

Substitute

25° = ½(m<AOB)

Multiply both sides by 2

2*25 = m<AOB

m<AOB = 50°

Answer:

Step-by-step explanation:

Given the coordinates D(-2, 3), E(5, 5), F(-4, 10), to find the measure of the sides, we will use the formula for calculating the distance between 2 points as shown:

D = √(y2-y1)²+(x2-x1)²

For DE;

D(-2, 3), E(5, 5),

DE = √(5-3)²+(5-(-2))²

DE = √2)²+7²

DE = √4+49

DE = √53

For DF;

D(-2, 3), F(-4, 10)

DF = √(10-3)²+(-4-(-2))²

DF = √7²+(-2)²

DF = √49+4

DF = √53

For EF;

E(5, 5) F(-4, 10)

EF = √(10-5)²+(-4-5)²

EF = √5²+(-9)²

EF = √25+81

EF = √106

Since two he sides DE and DF are equal, this shows that the triangle is an isosceles triangle. An isosceles triangle  is a triangle that has two of its sides and angle equal

To compute the z-score for the applicant, we can use the formula:

z = (x - μ) / σ

Where:

x is the applicant's score

μ is the mean

σ is the standard deviation

Given that the applicant's score is 21.0, the mean is 18.0, and the standard deviation is -3.0, we can substitute these values into the formula to calculate the z-score.

z = (21.0 - 18.0) / (-3.0)

z = 3.0 / -3.0

z = -1.0

Therefore, the z-score for the applicant is -1.0.

The correct option is O-10.

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The Correlation Strength shown by the 3 graphs are respectively; 5. No correlation; 2. Strong Positive Correlation and 4. Weak positive correlation

A graph is said to have positive correlation if the relationship between two variables move in tandem in the same direction.

No correlation is also termed as zero correlation which means there is no relationship between the two variables.

Now, the first graph shows that there is no correlation at all between the x-values and y-values. Thus, It has No correlation.

The second graph shows strong positive correlation as the relationship between the x and y values are almost perfect.

The third graph shows weak positive correlation as the relationship between the variables though positive are very weak.

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The value of y for the given equation at x=81 is 87.

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

Here, given equation;

       y = x + 6

     Put x = 81, we get

       y = 81 + 6

      y = 87

Thus, the value of y for the given equation at x=81 is 87.

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The amount that Roxana has left is $7560.

Total Amount = $12000

She spent 12% on meat and 25% on vegetables.

Therefore, the amount left will be:

= (100 - 12% - 25%) × 12000

= 63% × 12000

= 63/100 × 12000

= 0.63 × 12000

= $7560

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The profits would reach 413 thousand dollars in the year 9181.

The linear relationship between two variables is displayed by linear regression. The slope formula that we previously learnt in prior classes, such as linear equations in two variables, is similar to the equation of linear regression.

To find the linear regression equation that represents the given set of data, we can use the least squares method. Let's denote the year as x and the profits as y. We'll calculate the slope (m) and the y-intercept (b) of the regression line using the formulas:

m = (nΣ(xy) - ΣxΣy) / (nΣ(x²) - (Σx)²)

b = (Σy - mΣx) / n

where n is the number of data points, Σ represents the sum, Σxy represents the sum of the products of x and y, Σx represents the sum of x values, and Σy represents the sum of y values.

Let's calculate the values:

n = 5

Σx = 1999 + 2000 + 2001 + 2002 + 2003 = 10005

Σy = 112 + 160 + 160 + 173 + 226 = 831

Σxy = (1999 * 112) + (2000 * 160) + (2001 * 160) + (2002 * 173) + (2003 * 226) = 1072103

Σ(x²) = (1999²) + (2000²) + (2001²) + (2002²) + (2003²) = 40100245

Now, we can calculate the slope and y-intercept:

m = (5 * 1072103 - 10005 * 831) / (5 * 40100245 - 10005²) ≈ 0.0561

b = (831 - 0.0561 * 10005) / 5 ≈ -100.784

Therefore, the linear regression equation is approximately y = 0.0561x - 100.784.

To estimate the year in which the profits would reach 413 thousand dollars, we can substitute y = 413 into the equation and solve for x:

413 = 0.0561x - 100.784

0.0561x = 513.784

x ≈ 9181.155

Rounding to the nearest whole year, the profits would reach 413 thousand dollars in the year 9181.

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The average number of pending USCIS immigration cases is 3,969,000 cases.

To know average number of pending USCIS immigration cases, we will calculate number of cases pending at any given time.

This will be done by multiplying the average processing time by the average number of cases processed per year.

Given:

Average number of immigration cases processed per year = 6.3 million cases

Average processing time = 0.63 years

The number of pending cases:

= Average processing time * Average number of cases processed per year

= 0.63 years * 6.3 million cases

= 3,969,000 cases

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Answer:

100,000

Step-by-step explanation:

answer:

yes, it is a right triangle

step-by-step explanation:

a^2 + b^2 = c^2

6^2 + 8^2 = 10^2

6^2 + 8^2 = 10^2

36 + 64 = 100

100 = 100

Answer:

\(\boxed{\textsf{ \textbf{ Yes} , the given triangle is a right angled triangle .}}\)

Step-by-step explanation:

We are given three sides of the triangle and we need to say that whether the triangle is right Angled triangle or not . The given side lenghts are 6 cm , 8 cm and 10 cm . ( Units not given in Question ) .

\( \textsf{$\implies$ Sides = 6cm , 8cm and 10 cm .}\)

So , a triangle with its given sides will be a right angled triangle if it has a right angle . And the sum of squares of two smallest sides must be equal to the square of the longest side . ( According to Pythagoras Theorem ) .

Here two smallest sides are 8cm and 6cm .

\(\implies\textsf{ $\sf Sides_{(smallest)}$= 8cm and 6 cm }\)

And the largest side is 10 cm .

\(\sf\implies Side_{(largest)}= 10 cm \)

And here the sum of squares of 8cm and 6cm should be equal to the square of 10cm in order to Prove it a right angled triangle .

\(\sf\implies (8cm)^2+(6cm)^2 = (10cm)^2 \\\\\sf\implies 64 cm^2+36cm^2 = 100 cm^2 \\\\\sf\implies \boxed{\pink{\frak{ 100 cm^2=100cm^2}}}\)

Since LHS = RHS hence the triangle is a right angled triangle .

Figure :-

\(\setlength{\unitlength}{1 cm}\begin{picture}(12,8)\thicklines \put(0,0){\line(1,0){4.49}}\put(0,0.01){\line(0,1){3}}\put(0,3){\line(3,-2){4.44}}\put(4.9,-0.3){\sf C }\put(0,-0.3){\sf B }\put(0,3.3){\sf A}\put(2,-0.5){\sf 8\: cm }\put(-1,1.5){\sf 6\: cm }\put(2,2){\sf 10\: cm }\put(0.2,0){\line(0,1){0.2}}\put(0.2,0.2){\line(-1,0){0.2}}\end{picture}\)

Carolyn made an error in her work because she did not correctly distribute the negative in Step 3.

A system of equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.

You can solve a system of equations by the adding or substitution methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other.

The question gives:3x-2y=7 (1)y=x+2The question shows that Carolyn applies the substitution method because she replaces the variable y (equation 2) in equation 1. See the given step 2.

3x – 2y = 7

3x – 2(x + 2) = 7

3x – 2x - 4 = 7 - here it is the mistake. (Carolyn did not correctly distribute the negative).

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Respuesta:

1,4 kilometros

Explicación paso a paso:

Dado que :

Distancia que separa a Sandra y José en el mapa = 7cm

Dibujo a escala = 1: 20.000; Esto se puede interpretar en el sentido de que 1 cm en el mapa equivale a 20.000 cm en el suelo.

Por tanto, una distancia de 7 cm en el mapa será:

20.000 * 7 = 140.000 cm en el suelo = distancia real

Por lo tanto, la distancia real = 140.000 cm.

Recordar :

1 cm = 10 ^ -5 km

140000 cm = 1.4 kilometros

Por lo tanto, la distancia real entre Sandra y José es de 1,4 km.

the test's finding at the 5% level of significance is that the true average longevity is not less than claimed.

The following is a definition of the test's hypothesis:

H0: The actual average lifetime, which is > 750 hours, is not less than what is stated

Ha! The actual average lifespan, at 750 hours, is less than what is advertised.

The examination is left-tailed.

Making a decision:

The null hypothesis is rejected if the test's p-value is less than the significance level (), and vice versa.

The test's p-value is calculated as,

0.016 as the p-value

(a)

The level of significance is 0.05.

The p-value is equal to 0.016/0.05.

The null hypothesis was rejected since the test's p-value was lower than the threshold for significance.

Consequently, the test's finding at the 5% level of significance is that the genuine average lifetime is shorter than

(b)

The level of significance is = 0.01.

The p-value is equal to 0.016 > = 0.01.

The null hypothesis could not be rejected since the p-value of the test was greater than the level of significance.

Therefore, the test's finding at the 5% level of significance is that the true average longevity is not less than claimed.

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Answer:

x = 3, y = 1

Step-by-step explanation:

By substitution since y = -2x + 7, substitute that for the 2nd y so

-2x +7 = 3x - 8, so x = 3, then substitute the 3 in any of the equations, so y = -2(3) + 7 is equal to 1

If you use elimination you can subtract the two equations from each other to get rid of the y so

y = -2x + 7

-y = -3x + 8

so 0 = -5x + 15, 5x = 15, x=3

The derivative of the function\(f(t) = t^(88) - t^(66) + t^(3) is f'(t) = 88t^87 - 66t^65 + 3*t^2\).

To find the derivative of the function\(f(t) = t^(88) - t^(66) + t^(3),\)we can use the rules of differentiation. The power rule and the constant rule will be helpful in this case.

The power rule states that the derivative of \(t^n\), where n is a constant, is given by\(n*t^(n-1).\)Applying this rule to each term of the function f(t), we have:

\(f'(t) = d/dt (t^(88)) - d/dt (t^(66)) + d/dt (t^(3))\)

\(= 88t^(88-1) - 66t^(66-1) + 3t^(3-1)\)

\(= 88t^87 - 66t^65 + 3t^2\)

Therefore, the derivative of the function\(f(t) = t^(88) - t^(66) + t^(3) is f'(t) = 88t^87 - 66t^65 + 3*t^2.\)

It's important to note that the derivative represents the rate of change of the function with respect to the independent variable, in this case, t. The derivative gives us information about the slope or steepness of the function at any given point.

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As per the linear equation the system has one solution, which is x = 1 and y = 1.

A linear equation is a mathematical expression that represents a straight line. A linear equation has a set of variables, and the coefficients (numbers in front of the variables) are constant.

The reason why most overdetermined linear systems are inconsistent is that there are more restrictions placed on the variables than what is required to find a solution.

It is possible for an overdetermined linear system to have one solution, but this is a rare occurrence.

When an overdetermined system has infinitely many solutions, this means that there are an infinite number of combinations of values that satisfy all of the equations simultaneously.

For example, consider the following system of linear equations:

2x + 3y = 6

4x + 6y = 12

This system is overdetermined because there are two equations and only one variable (x and y). In this case, the system has one solution, which is x = 1 and y = 1.

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$65,656.57 was borrowed at 7%, $262,626.26 was borrowed at 8%, and $1,181,717.17 was borrowed at 10%.

A system of equations to determine how much was borrowed at each rate if the annual interest was $130,500 is given below.

Let X be the amount borrowed at 7%Y be the amount borrowed at 8% Z be the amount borrowed at 10%

Then, according to the question, the following equations are given:

X + Y + Z

= 1,500,000

X = Y/4Z

= 4X

Interest on the amount borrowed at 7%

= 0.07 X

Interest on the amount borrowed at 8%

= 0.08 Y

Interest on the amount borrowed at 10%

= 0.10 Z

Total annual interest

= $130,500

Then, according to the problem, the following equation is given:

0.07 X + 0.08 Y + 0.10 Z

= 130500

Substitute the values of X and Z in terms of Y as per the given conditions:

Z = 4X then

Z = 4Y

Z = 4X and

X = Y/4

Then, put the above values in the equation

0.07 X + 0.08 Y + 0.10 Z

= 1305000.07 (Y/4) + 0.08 Y + 0.10 (4Y)

= 1305000.0175 Y + 0.08 Y + 0.4

Y = 1305000.4975

Y = 130500

Y = $262,626.26

Then, X = Y/4

= $65656.57 and

Z = 4X

= $262626.26

Thus, $65,656.57 was borrowed at 7%, $262,626.26 was borrowed at 8%, and $1,181,717.17 was borrowed at 10%.

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