73.
ILLUSTRATION 7
Find a. the length and b. the diameter of the shaft in

Answer:

Step-by-step explanation:

We can write the area of the rug as:

Area = 49x^2 - 25y^2

To find possible dimensions of the rug, we need to factor the expression on the right side. We can factor out 49 and 25 to get:

Area = 49 * x^2 - 25 * y^2

Area = 7 * 7 * x^2 - 5 * 5 * y^2

So, the area of the rug can be written as the product of two binomials, each of which represents one of the side lengths.

Therefore, one possible set of dimensions for the rug is 7x and 5y, and another possible set is -7x and -5y. Note that the dimensions are related in that the width of the rug is proportional to 7x, and the length is proportional to 5y.

To make the rug a square, the sides must be equal in length. To find the value that would need to be subtracted from the longer side and added to the shorter side, we take the difference between the two possible side lengths:

7x - 5y = (7x + 5y) - 2 * 5y = (7x + 5y) - 10y

So, to make the rug a square, you would need to subtract 10y from the longer side (7x) and add 10y to the shorter side (5y). This would result in both sides being equal to (7x + 5y)/2, making the rug a square.

Answer:

C.

Step-by-step explanation:

area = length × width

5/8 = 1/6 × w

w = (5/8) / (1/6)

Answer: C.

Answer:

Step-by-step explanation:30 x 2 = 60 because 8:9 get simplify by 2 and you just times the 30 with 2

Answer:

Let the common multiple be x

John's score is 8x Peter's is 9x

8x/9x-30=4/3

24x=36x-120

12x=120

x=10

John's score is 8 x 10=80

Correct me if im wrong:)

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The shape of the distribution is normal

The probability is 0.7764

What is Standard Deviation?

The standard deviation is a measure of the spread or dispersion of a set of data around its mean. It is calculated by finding the square root of the variance, which is the average of the squared differences between each data point and the mean. It is used to quantify the degree of variability or diversity in the data.

(a)

The distribution of heights of young men follows a normal distribution with a mean of 69.3 inches and a standard deviation of 2.8 inches. The distribution of heights of young women also follows a normal distribution with a mean of 64.5 inches and a standard deviation of 2.5 inches.

The difference between the height of a randomly selected young man (m) and a randomly selected young woman (w) follows a normal distribution with a mean of 69.3 - 64.5 = 4.8 inches (the difference in the means) and a standard deviation of √(2.8² + 2.5²) = 3.67 inches (the square root of the sum of the variances).

The shape of the distribution of the difference between the heights of a randomly selected young man and a randomly selected young woman is also normal, since the original distributions are normal. The centre of the distribution is 4.8 inches, and the spread is 3.67 inches.

(b)

We need to find the probability that a randomly selected young man is at least 2 inches taller than a randomly selected young woman, or in other words, we need to find P(m - w > 2).

Using the formula for the difference of two normal distributions, we have:

z = (2 - 4.8) / 3.67 = -0.76

We need to find the probability that a standard normal variable Z is greater than -0.76. Using a standard normal table or calculator, we find that P(Z > -0.76) = 0.7764.

Therefore, the probability that a randomly selected young man is at least 2 inches taller than a randomly selected young woman is approximately 0.7764.

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Answer:

hope this helps

Step-by-step explanation:

Answer:

2(fx-2cosx)

Step-by-step explanation:

regroup terms

factor out the common term 2

Answer:

5x + y = 17

Step-by-step explanation:

y -2 = -5(x -3)

y-2 = -5x + 15  Add 5x to both sides

5x + y - 2 = 5x - 5x + 15

5x + y - 2 = 15   Add 2 to both sides

5x + y + 2 - 2 = 15 + 2

5x + y = 17

If A, B, and C are n×n invertible matrices, then the solution for "x" in the equation "C⁻¹(A+X)B⁻¹ = Iₙ" is X = BC⁻¹ - A .

The Equation is ⇒ C⁻¹(A+X)B⁻¹ = Iₙ,

We first  multiply both sides by B and C to remove the inverses ;

⇒ C⁻¹(A+X)B⁻¹×BC = I×BC  ;

Simplifying, we get ;

⇒ C⁻¹(A+X)C = B ;

Next, we can multiply both sides by C⁻¹ to separate (A+X) ;

⇒ (A+X)C×C⁻¹= B×C⁻¹  ;

Simplifying, we get:

⇒ (A+X) = BC⁻¹  ;

Now , we subtract "A" from both sides, we get ;

⇒ X = BC⁻¹ - A  ;

So , the solution for X is : X = BC⁻¹ - A  . This solution exists because A, B, and C are all n×n invertible matrices, which means that their inverses exist and the product of invertible matrices is also invertible.

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The given question is incomplete , the complete question is

If A, B, and C are n×n invertible matrices, does the equation C⁻¹(A+X)B⁻¹ = Iₙ have a solution, X ? If so, find it.

Answer:

10/x is a nonlinear equation. Linear equations represent a straight line in a graph, whereas nonlinear equations are used to represent curves. In this case, the degree of variable y is 1 and the degrees of the variables in the equation violate the linear equation definition, which means that the equation is not a linear equation.

Answer:

36°

--------------------

Incenter is the intersection of angle bisectors.

It means ST is angle bisector of ∠VSW, therefore:

The measure of ∠R =49, ∠T = 61 , ∠M = 70 , ∠N = 61, x = 7 and y = 13.

What are Congruent triangles?

When all three corresponding sides are the same length and all three corresponding angles are the same size, two triangles are said to be congruent.

Given, ΔLMN ≅ ΔRST,

So, ∠L = ∠R  = 49

     ∠M = ∠S = 70

     ∠N = ∠T = 4y + 9

Now, In triangle RST,

∠R + ∠S + ∠T = 180 ( sum of all angles of a triangle is 180 )

49 + 70 + ∠T = 180

   ∴ ∠T = 61 = ∠N

and, 4y + 9 = 61

       y = 13.

Now, In triangle LMN ,

∠L + ∠M + ∠N = 180

49 + 10x + 61 = 180

    10x = 70

       x = 7

∴ ∠M = 70.

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Answer:

Two geometric objects are perpendicular if they intersect at a right angle.

Step-by-step explanation:

How you know:

The condition of perpendicularity may be represented graphically using the perpendicular symbol, ⟂.

An equation that uses a unit fraction and a whole number to write a multiplication equation equal to 712 can be represented as:

712 = (1/N) * X

Where N is the unit fraction and X is the whole number. To find the values of N and X, we can isolate X on one side of the equation and divide both sides by (1/N):

X = (712 * N) / (1)

X = 712 * N

Now we can substitute the value 712 for the right side of the equation:

X = 712 * N

X = 712 / (1/N)

Finally, we can simplify the equation by dividing 712 by the reciprocal of N:

X = 712 * N

X = 712 / (1/N)

X = 712 * N / (1/N)

X = 712 * N * N

Now we have an equation in which X is equal to 712 times N times N. To find the values of N and X, we can use trial and error or other mathematical methods.

It is important to note that there may be multiple solutions to this equation, as there can be many unit fractions and whole numbers that multiply to equal 712. The goal is to find a combination of N and X that satisfies the equation and produces the desired result.

In conclusion, writing a multiplication equation equal to 712 using a unit fraction and a whole number is a common mathematical problem that can be solved by isolating the variable and dividing both sides by the unit fraction.

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If the ratio of winners to players remains the same as last year, the balloon dart booth can expect to have 85 winners among 204 players and lose $136.

A ratio compares two quantities or values. In this case, the ratio we are interested in is the ratio of winners to players.

Last year, out of 12 players, 4 popped 2 balloons and 1 player popped 3 balloons. Therefore, the total number of players who won prizes was 4+1=5. The ratio of winners to players is 5/12.

To calculate the number of winners this year, we can use the same ratio. If we assume that the ratio of winners to players is constant, we can set up the following proportion:

(winners/players) = (5/12)

Let's solve for the number of winners among 204 players:

(winners/204) = (5/12)

winners = (5/12) * 204

winners = 85

Therefore, we can expect 85 winners among 204 players if the ratio of winners to players remains the same as last year.

Now let's calculate the potential earnings or losses for the booth. Each player pays $1 for three darts, so the booth will earn 204*1 = $204.

Out of the 204 players, we expect 85 winners. Each winner receives a prize worth $4, so the total cost of prizes is 85*4 = $340.

The booth earns $204 and spends $340 on prizes, resulting in a loss of $136.

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Complete Question:

At the balloon dart booth, players are charged $1 for the chance to throw 3 darts. Prizes worth $4 each are awarded to players who pop at least 2 balloons. Last year, 4 out of 12 players popped 2 balloons, and 1 out of 12 players popped 3 balloons.

If the ratio of winners to players is the same this year and 204 people play the game, how much money will the booth earn or lose?

The correlation between x and y is 0.5. This indicates a positive correlation, meaning that as values of x increase, so do the values of y.

The correlation coefficient (denoted by ρ) between x and y can be calculated as:

ρ = covariance(x,y) / (standard deviation of x * standard deviation of y)

A measure of the link between two random variables and how much they fluctuate together is called covariance. Alternately, we may say that it establishes the relationship between the two variables' changes, i.e., that a change in one variable is equivalent to a change in the other. When the variables are translated linearly, a function has the property of preserving its shape.

We are given that the covariance between x and y is 25, the standard deviation of x is 10, and the standard deviation of y is 5. Substituting these values into the formula, we get:

ρ = 25 / (10 * 5) = 0.5

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This means car traveled 18 miles on ONE gallon of gas.

You should get 20 to 30 miles per gallon of petrol on average when driving your car. Some automobiles, nevertheless, can go up to 60 miles per gallon. Your car's efficiency varies depending on a number of factors, including miles. Car weight, unsafe driving practices, the environment, and shoddy maintenance are a few of the contributing causes.

Vehicle mileage was x miles.

x miles of gasoline equals x gallons of fuel.

Gasoline consumption is inversely proportional with the distance driven by an automobile.

distance traveled by car  = K× Gasoline used  

Using unitary method,

Distance traveled by car in 1 gallon of gas  = 18 × 1 miles.

Distance traveled by car in 1 gallon of gas  = 18 miles

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The number of days until recovery is noted for each patient is option d) Experimental group the half in yellow rooms

Health psychologists are interested in understanding the factors that can impact a patient's recovery time following a surgical procedure. One hypothesis that they may want to test is whether the color of the hospital room can influence recovery time.

In experimental research, we often manipulate one variable to see if it has an effect on another variable. The variable that is being manipulated is called the independent variable, while the variable that is being measured is called the dependent variable. In this case, the independent variable is the color of the hospital room, and the dependent variable is the length of recovery time.

To test the hypothesis that yellow hospital rooms will shorten recovery time, the researchers randomly assign half of the patients to yellow rooms and the other half to white rooms. By randomly assigning the patients to the different conditions, the researchers can be sure that any differences in recovery time between the two groups are not due to pre-existing differences between the patients.

In order to make sure that the color of the room is the only thing that is different between the two groups, the researchers use a control group. The control group is the group of patients who are placed in white rooms. By comparing the recovery time of the patients in the yellow room group to the recovery time of the patients in the white room group, the researchers can determine whether the color of the room had an effect on recovery time.

Finally, the group of patients who are placed in the yellow rooms is called the experimental group. This is because they are the group that is being exposed to the independent variable (the yellow color of the room). By comparing the recovery time of the experimental group to the recovery time of the control group, the researchers can determine whether the yellow color of the room had an effect on recovery time.

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Complete Question:

A health psychologist wants to test the hypothesis that yellow hospital rooms will shorten the recovery time for surgical patients when compared to recovery times of patients in standard white hospital rooms. Half of the patients are randomly assigned to yellow rooms, the other half to white rooms. The number of days until recovery is noted for each patient.

1a) Independent variable color of the walls

1b) Dependent variable the length of recovery time

1c) Control group the half in white rooms

1d) Experimental group the half in yellow rooms

The Translation to  algebraic expression is shown below.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

To create a variable expression for a circumstance in the actual world:

For example, the sum of a and b can be written as

= a+ b

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Answer: 52 Degrees

Step-by-step explanation:

HZA is a 90 degree angle so since we know that HZJ is 38 degrees then we will subtract 38 from 90 which will be 52 degrees.

Answer:

The minimum value is 2.5.

Step-by-step explanation:

This is a sine wave that is parallel to the x axis.  It will never go below 2.5, as shown on the graph.

Answer:

---------------------------

Given function:

This is the vertex form and the standard form is:

Convert the given equation into standard form:

Answer:

The standard form of the given quadratic function is:

[tex]g(x)=-2x^2+20x-33[/tex]

Step-by-step explanation:

The standard form of a quadratic function is f(x) = ax² + bx + c.

To write the given function in standard form, expand the brackets:

[tex]\implies g(x)=-2(x-5)(x-5)+17[/tex]

[tex]\implies g(x)=-2(x^2-10x+25)+17[/tex]

Apply the distributive law:  m(a + b + c) = ma + mb + mc

[tex]\implies g(x)=-2x^2+20x-50+17[/tex]

Add the numbers:  -50 + 17 = -33

[tex]\implies g(x)=-2x^2+20x-33[/tex]

The scale factor of the smaller figure to the larger figure in the first instance is 1. 25 .

The scale factor in the second instance is 3. 75 .

To find the scale factor, the formula is :

= Length of side of larger figure / Length of corresponding side of smaller figure

The scale factor in the first instance is :

= 30 / 24

= 1. 25

The scale factor in the second instance is :

= 15 / 4

= 3. 75

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The probability that randomly selected mechanical component weighs: more than 11.5 lbf is 0.0099, less than 8.7 lbf is 0.3208,  less than 5.0 lbf is 0.0228, between 6.2 lbf and 7.0 lbf is 0.1314, between 10.3 lbf and 14.0 lbf is 0.0436, between 6.8 lbf and 8.9 lbf is 0.3464.

We can use the standard normal distribution and z-scores to answer these questions:

P(X > 11.5) = P(Z > (11.5 - 8) / 1.5) = P(Z > 2.33) = 0.0099

Therefore, the probability that a randomly selected mechanical component weighs more than 11.5 lbf is 0.0099, or about 1%.

P(X < 8.7) = P(Z < (8.7 - 8) / 1.5) = P(Z < 0.47) = 0.3208

Therefore, the probability that a randomly selected mechanical component weighs less than 8.7 lbf is 0.3208, or about 32%.

P(X < 5.0) = P(Z < (5 - 8) / 1.5) = P(Z < -2) = 0.0228

Therefore, the probability that a randomly selected mechanical component weighs less than 5.0 lbf is 0.0228, or about 2%.

P(6.2 < X < 7.0) = P((6.2 - 8) / 1.5 < Z < (7 - 8) / 1.5) = P(-1.2 < Z < -0.67) = 0.1314

Therefore, the probability that a randomly selected mechanical component weighs between 6.2 lbf and 7.0 lbf is 0.1314, or about 13%.

P(10.3 < X < 14.0) = P((10.3 - 8) / 1.5 < Z < (14 - 8) / 1.5) = P(1.53 < Z < 2.67) = 0.0436

Therefore, the probability that a randomly selected mechanical component weighs between 10.3 lbf and 14.0 lbf is 0.0436, or about 4%.

P(6.8 < X < 8.9) = P((6.8 - 8) / 1.5 < Z < (8.9 - 8) / 1.5) = P(-0.47 < Z < 0.60) = 0.3464

Therefore, the probability that a randomly selected mechanical component weighs between 6.8 lbf and 8.9 lbf is 0.3464, or about 35%.

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____The given question is incomplete, the complete question is given below:

Suppose that the weight of a mechanical component is normally distributed with mean p = 8.0 Ibf and standard deviation = 1.5 lbf. Answer the following questions: 1. If you randomly select a mechanical component, what is the probability that it weighs more than 11.5 lbf? 2. If you randomly select a mechanical component, what is the probability that it weighs less than 8.7 lbf? 3. If you randomly select a mechanical component, what is the probability that it weighs less than 5.0 lbf? 5. If you randomly select a mechanical component, what is the probability that it weighs between 6.2 lbf and 7.0 lbf? 6. If you randomly select a mechanical component, what is the probability that it weighs between 10.3 lbf and 14.0 lbf? 7. If you randomly select a mechanical component, what is the probability that it weighs between 6.8 lbf and 8.9 lbf?

Based on the information and the dimensions of the scaled figure, we can infer that the dimensions of the actual figure are 2.1 meters by 3.9 meters.

To calculate the measures of the original figure we must apply a rule of three. In this case, the logic that we must use is: if 2 centimeters are equivalent to 1 meter, how much is 4.2 cm and 7.8 cm respectively.

According to the above, the measurements of the original figure are: 2.1 meters by 3.9 meters.

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Whitney drank a total of 2.15 liters of liquid.

Liquids are those substances that can flow or be poured, are incomprehensible, and are more rigid than gases.

From the given table we can say that the drinks Whitney takes over a day, which are juice, milk, and water, all come in the liquid category.

Therefore, the total amount of liquid that Whitney drinks today will be the sum of the volume of all of the above

which is 250 ml + 400 ml + 1,500 ml

=2,150 ml

For converting ml in liters we can divide the given volume by 1000 after which we get,

2,150/1000 = 2.15 Litres.

The complete question that you might be looking for is given below -

From the given table, What is the total amount of liquid in liters that Whitney drinks today?

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Approximate year when the Europe began circulating the printed newsletters is given by option c. 1600.

Therefore, the year when first printed newsletter began circulating in the Europe is equal to option c. 1600.

The above question is incomplete , the complete question is :

In approximately what year did printed newsletters begin circulating in Europe?

a]  1200     b]  1450      c] 1600         d ] 1850

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After 13 hours the population of bacteria in the culture is approximately 5,905,820, rounded to the nearest whole number.

we can use the formula for exponential growth

P = P0 * 2^(t/k)

Where:

P = population at time t

P0 = initial population = 74000

t = time = 13 hours

k = time for population to double = 3 hours

Plugging in the values:

P = 74000 * 2^(13/3)

P = 74000 * 2^4.33

P = 74000 * 79.83

P = 5905820

Answer:

y-intercept: (0,-1)

Step-by-step explanation:

please verify

The proportion of the committee that is left-handed is 4/15, which is equivalent to 0.267 when rounded to three decimal places.

A proportion is a way of expressing the relationship between two quantities. It is often written as a fraction, where the numerator represents the quantity of interest, and the denominator represents the total quantity.

In this case, we are interested in the proportion of left-handed senators, so the numerator will be the number of left-handed senators, which is 4. The denominator will be the total number of senators in the committee, which is 15. Therefore, the proportion of left-handed senators can be written as:

4/15

This fraction can also be expressed as a decimal by dividing the numerator (4) by the denominator (15) using a calculator or long division. When rounded to three decimal places, the decimal equivalent of the fraction is:

0.267

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Answer: The total number of members in the club is 140 + 695 + 210 = 1,045.

The number of non-senior members is 140 + 695 = 835.

The probability that the first member selected at random will not be a senior member is 835 / 1,045 = 0.798 or 79.8%.

So, the answer is 0.798 or 79.8%.

Step-by-step explanation: