What is the solution to the equation A + 5 2/3 = 9​

Answer:

the gcf for 12,78 would be 6

Answer:

So the second one is 3

The first one is 3

Step-by-step explanation:

You just divide the first one 4.02/1.34

The second one

1) 2x-5=1

2) add  5 on to both sides= 6

3) divide 2 by 6 = 3

Answer:

Step-by-step explanation:

From the given information;

The null and alternative hypothesis is:

\(\mathbf{H_o: \mu =0}\)

\(\mathbf{H_a: \mu \ne 0}\)

sample mean x = -2

population mean = 0

SD = 6

sample size n = 25

Using t-test statistics:

\(t = \dfrac{x- \mu}{\dfrac{\sigma}{\sqrt{n}}}\)

\(t = \dfrac{-2- 0}{\dfrac{6}{\sqrt{25}}}\)

t = -1.667

P-value = P(t ≤ -1.667) + P(t ≥ 1.667)

P-value = 0.1086

Since P-value is greater than \(H_o\) , we fail to reject \(H_o\).

Answer:

80

Step-by-step explanation:

1. 76.56.

2. 96

3. The largest solution to the equation x²+16x+28=138 is 6.71.

4. The smallest solution to the equation x²+14x+14=145 is 5.96.

Equations are used to express relationships between variables and solve mathematical problems.

1. This is calculated by taking the coefficient of x (19) and dividing it by two (19/2) and then squaring the result (19/2)² = 76.56.

2. This is calculated by taking the coefficient of x (30) and dividing it by two (30/2) and then squaring the result (30/2)² = 96.

3. This is calculated by using the quadratic formula, by taking the opposite of the coefficient of x (16) plus or minus the square root of the coefficient of x squared (16²) minus 4 times the coefficient of the x term (4x16) minus the constant (28) divided by 2 times the coefficient of the x term (2x16).

4.  This is calculated by using the quadratic formula, by taking the opposite of the coefficient of x (14) plus or minus the square root of the coefficient of x squared (14²) minus 4 times the coefficient of the x term (4x14) minus the constant (14) divided by 2 times the coefficient of the x term (2x14).

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1.  For the given equation, c need to be 90.25 to complete the square.

2. 225

3. The largest solution to the equation x²+16x+28=138 is 6.

4. The smallest solution to the equation x²+14x+14=145 is -14.

Equations are used to express relationships between variables and solve mathematical problems.

1. This is calculated by taking the coefficient of x (19) and dividing it by two (19/2) and then squaring the result

(19/2)² = 90.25.

2. This is calculated by taking the coefficient of x (30) and dividing it by two which is (30/2) and then squaring the result

(30/2)² = 225.

3. The largest solution to the equation x²+16x+28=138 is 6.

This can be calculated by using the quadratic formula to solve the equation.

(a=1, b=16, c=28)

x = -8 ± √((16)² - 4(1)(28))/2(1).

x = -8 ± √(240)/2

x = 6 or -14.

Since 6 is the larger solution, it is the largest solution to the equation.

4.  The smallest solution for x2+14x+14=145 can be determined by using the Quadratic Formula.

a=1, b=14, and c=14

x = [-14 ± √(142-4(1)(14))]/(2(1))

x = [-14 ± √(196)]/2

x = [-28/2] or [14/2]

x = -14 or 7

Therefore, the smallest solution for x2+14x+14=145 is x=-14.

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Answer:

Y=-4x 2

Step-by-step explanation:

The missing variables on item 2 are given as follows:

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the formulas presented as follows:

For the angle of 60º, we have that:

Hence the length o is given as follows:

tan(60º) = o/12.

\(\sqrt{3} = \frac{o}{12}\)

\(o = 12\sqrt{3}\)

Applying the Pythagorean Theorem, the length i is given as follows:

i² = 12² + \((12\sqrt{3})^2\)

i² = 576

i² = 24²

i = 24.

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Answer:

o = 12√3

i = 24

Step-by-step explanation:

From observation of the given right triangle, we can see that two of its interior angles measure 60° and 90°. As the interior angles of a triangle sum to 180°, this means that the remaining interior angle must be 30°, since 30° + 60° + 90° = 180°. Therefore, the triangle is a special 30-60-90 triangle.

The side lengths in a 30-60-90 triangle have a special relationship, which can be represented by the ratio formula a : a√3 : 2a, where "a" represents a scaling factor that can be any positive real number.

In triangle #2, the shortest leg is 12 units.

As "a" is the shortest leg, the scale factor "a" is 12.

The side labelled "o" is the longest leg opposite the 60° angle. Therefore:

\(o = a\sqrt{3}=12\sqrt{3}\)

The side labelled "i" is the hypotenuse of the triangle. Therefore:

\(i= 2a = 2 \cdot 12=24\)

Therefore:

Answer:

The slope would be 1/2.

Step-by-step explanation:

When solving questions like these, make sure to plug in the points into the formula: \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}} = slope\) . y2 would stand for the y coordinate of the second point, y1 would stand for the y coordinate of the first point. While x2 would stand for the x coordinate of the second point and x1 for the x coordinate of the first point. Once plugged in, it should look like this: \(\frac{10-7}{-1-(-7)}\). That should then give you the slope of 1/2. Hope this helps!! :D

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The confidence level for the true average strain is (24.69,27.31) and the prediction level is (20.01,31.99) and also it is estimated that prediction level is much wider than the confidence level

Given that sample size is 20, mean is 26%, standard deviation is 3.4, confidence level is 95%.

a)

We must calculate the true average strain in a way that conveys precision and reliability.

We have to use t-test in our problem because sample size is less than 30.

We Know that,

True average value is determined by formula,

\(\mu\pm t*\frac{S}{\sqrt{n}}\)

where μ is sample mean,

s is sample standard deviation.

Degree of freedom=n-1

=20-1

=19

t-value at 95% confidence interval=1.7281

\(26\pm 1.728*\frac{3.4}{\sqrt{20}}\\\\=26\pm1.728*0.7606\\\\=26\pm1.31\\\\=24.69,\ 27.31\)

b)

predicted value can be calculated by formula,

\(\mu \pm t*S\sqrt{1+\frac{1}{n}}\\\\=26\pm 1.728*3.4\sqrt{1+\frac{1}{20}}\\\\=26\pm 1.728*3.4*1.02\\\\=26\pm5.99\\\\=20.01,\ 31.99\)

As a result, we conclude that the prediction interval is greater than the confidence interval.

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Answer:

21.17

Step-by-step explanation:

tan= opposite/ adjacent

tan(36)= x/29

0.73= x/29

x= 21.17

Juliet will earn the same amount of money whether she chooses a monthly salary of ​$1900 from the company or a base salary of ​$1800 plus a ​5% commission on furniture sales if her sales amount to $2000.

To find the amount of sales for which the two salary choices are equal, we set the equation for the base salary plus commission equal to the equation for the flat monthly salary. The equation can be written as:

1800 + 0.05x = 1900

where x is the amount of furniture sales in dollars.

Simplifying and solving for x, we get:

0.05x = 100

x = 2000

If she sells less than $2000 of furniture, she will earn more with the flat monthly salary of $1900. If she sells more than $2000 of furniture, she will earn more with the base salary plus commission. This calculation provides an important decision-making tool for Juliet, as she can tailor her salary choice based on her expected sales for the month.

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Answer:

35

Step-by-step explanation:

perimeter = sum of the lengths of the sides

In a parallelogram, opposite sides are congruent.

Two sides have length 7.5 cm.

We need the length of the top and bottom sides.

area = base × height

62 cm² = base × 6.2 cm

base = (62 cm²)/(6.2 cm)

base = 10 cm

Two sides have length 10 cm.

perimeter = 7.5 cm + 7.5 cm + 10 cm + 10 cm

perimeter = 35 cm

Answer:

\(2\frac{1}{4}\)

Step-by-step explanation:

Question has missing details (See attachment).

Given

\(Orange\ Juice = 1\frac{1}{4}quart\)

\(Pineapple\ Juice = 2\frac{1}{2}quart\)

\(Seltzer = 1\frac{1}{2}quart\)

Required

Determine how much juice than seltzer used.

To do this, we first calculate the total amount of juice

\(Juice = Orange + Pineapple\)

\(Juice = 1\frac{1}{4} + 2\frac{1}{2}\)

\(Juice = \frac{5}{4} + \frac{5}{2}\)

Take LCM

\(Juice = \frac{5+10}{4}\)

\(Juice = \frac{15}{4}\)

Then subtract the amount of seltzer used.

\(Juice - Seltzer = \frac{15}{4}-1\frac{1}{2}\)

\(Juice - Seltzer = \frac{15}{4}-\frac{3}{2}\)

Take LCM

\(Juice - Seltzer = \frac{15 - 6}{4}\)

\(Juice - Seltzer = \frac{9}{4}\)

\(Juice - Seltzer = 2\frac{1}{4}\)

The amount of juice used more than seltzer is \(2\frac{1}{4}\)

Answer: 3 3/4 quarts

Hope this helps

The inequalities that represent these constraints are x ≤ 500 + 2y and 35x + 50y > 22500²

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the number of product A and y represent the number of product B, hence:

x ≤ 500 + 2y        (1)

Also:

35x + 50y > 22500²    (2)

The inequalities that represent these constraints are x ≤ 500 + 2y and 35x + 50y > 22500²

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Well I assume you have a TI-84 or something

a)  null is  μa = μb

alternate is  μa > μb

where μa = the true mean number of fish contrained in the stomach of blue crabs in location A

μb = the true mean number of fish contrained in the stomach of blue crabs in location B×

B) this is a 2 sample t-test

t= (xa-xb)/ \(\sqrt{s1^{2} /n1+ s2^{2} /n2}\) so you find the t value and look up on the T- table

or you use your calculator

t= 0.549 ⇒ p= 0.295

since out p value of 0.295 is greater than our alpha level of 0.01, we have no evidence to conclude that the stomachs of blue crabs from Location A contain more fish than the stomachs of blue crabs from Location B.

you also might want to check the assumptions.

We can simplify cosec(t)tant(t) to sec(t). A trigonometric function is a mathematical function that relates the angles of a triangle to the ratios of its sides.

The most common trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

To simplify the expression cosec(t)tant(t), we need to use the trigonometric identity:

cosec(t) = 1/sin(t)

tant(t) = sin(t)/cos(t)

Substituting these expressions into the original expression, we get:

cosec(t)tant(t) = (1/sin(t))(sin(t)/cos(t))

The sin(t) term in the numerator and denominator cancel out, leaving:

cosec(t)tant(t) = 1/cos(t)

Recalling the definition of secant, sec(t) = 1/cos(t), we can express the simplified expression as:

cosec(t)tant(t) = 1/sec(t)

Therefore, we can simplify cosec(t)tant(t) to sec(t).

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The rate of change of the Distance between the planes is zero. This means that the distance between the planes remains constant throughout their respective flights.

The rate of change of the distance between the planes, we need to determine how the distance between them changes over time.

the distance between the two planes is represented by the variable D, and time is represented by the variable t.

At noon, the southbound plane starts flying and continues for 4 hours until 4 pm. During this time, the plane covers a distance of 900 km/h * 4 hours = 3600 km due south.

Meanwhile, the eastbound plane is also traveling towards the airport. It starts from a distance of 2000 km away from the airport at 4 pm.

To find the distance between the planes at any given time, we can use the Pythagorean theorem, as the planes are moving at right angles to each other. The distance D between the planes can be calculated as:

D^2 = (2000 km)^2 + (3600 km)^2

Simplifying the equation:

D^2 = 4000000 km^2 + 12960000 km^2

D^2 = 16960000 km^2

Taking the square root of both sides:

D = sqrt(16960000) km

D = 4120 km

Now, we can find the rate of change of the distance between the planes by calculating the derivative of the distance equation with respect to time

dD/dt = 0

Since the distance between the planes is constant, the rate of change is zero.

Therefore, the rate of change of the distance between the planes is zero. This means that the distance between the planes remains constant throughout their respective flights.

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Answer:

8 significant figures should be provided.

Step-by-step explanation:

I believe I am correct, but check your answer anyways.

Answer:

distributive property

Step-by-step explanation:

i think its distributive property

Answer:

A

Step-by-step explanation:

Two Squares

There are 2 squares at the top and bottom. All sides = 3

2* s^2

2 * 3^2

2 * 9

18

Middle Figure.

Triangles

There are many ways to solve this. I think the most easily understood is to break it into 2 triangles and a rectangle.

Base of both triangles = 5 + 5 = 10

The height of each triangle = (7 - 3)/2 = 4/2 = 2. You divide by 2 because there are 2 bases -- one in each triangle.

Area = 1/2 * 2 * 10 = 10

But there are 2 of them so the total area is 20

Rectangle

The length of the rectangle = 5 + 5 = 10

The width = 3

Area = 30

Total

Total Area = 2 squares + 2 triangles + 1 rectangle

Total Area = 18 + 20 + 30 = 68

Answer:

8inches

Step-by-step explanation:

Length of the third side = perimeter - ( side1 + side2 )

                                       = 17 - (5+4)

                                       = 17 - 9

                                       = 8 inches

The slope of the line shown in the graph is 4.5 .

In the question ,

it is given that ,

the amount of grapes is represented on x axis . and

the cost for that grape in the grocery store is represented on y axis .

to find the slope we need two points on the line ,

from the graph we can take two points as (1 , 4.5) and (2 , 9) ,

the slope can be calculated using the formula

slope = (change in y coordinate)/(change in x coordinate)

slope = (9 - 4.5)/(2 - 1)

slope = 4.5/1

slope = 4.5 .

Therefore , The slope of the line shown in the graph is 4.5 .

The given question is incomplete , the complete question is

The graph below shows the cost of grapes at a grocery store. What is the slope of the line?

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Answer:

Step-by-step explanation:

Given this information, we can determine the maximum number of units of each product (A, B, and C) that can be produced with the given quantity of resources (M1, M2, and M3). To do this, we can use the formula:

Maximum number of units of product = Minimum of (available quantity of resource / resource required per unit of product)

For example, to find the maximum number of units of product A that can be produced, we take the minimum of the following three values:

(71,000 units of M1 / 3 units of M1 per unit of A) = 23,666.67 units of A

(81,000 units of M2 / 2 units of M2 per unit of A) = 40,500 units of A

(92,000 units of M3 / 6 units of M3 per unit of A) = 15,333.33 units of A

So the maximum number of units of A that can be produced is 15,333.33 units.

Similarly, we can find the maximum number of units of B and C that can be produced:

(71,000 units of M1 / 3 units of M1 per unit of B) = 23,666.67 units of B

(81,000 units of M2 / 2 units of M2 per unit of B) = 40,500 units of B

(92,000 units of M3 / 4 units of M3 per unit of B) = 23,000 units of B

So the maximum number of units of B that can be produced is 23,000 units.

(71,000 units of M1 / 5 units of M1 per unit of C) = 14,200 units of C

(81,000 units of M2 / 7 units of M2 per unit of C) = 11,571.43 units of C

(92,000 units of M3 / 4 units of M3 per unit of C) = 23,000 units of C

So the maximum number of units of C that can be produced is 11,571.43 units.

It is important to note that these calculations are based on the assumption that all resources are used fully and no resources are left over.

Step-by-step explanation:

OK, 'Brainless'....  the triangle side length rule states that any two sides of a triangle must sum to greater than the remaining side length...

42 + 20 > x        then  12 , 20, 22, 32, 42, 50     will work here

42+x > 20            all of the possibles work here

20 + x > 42         32, 42, 50, 62 and 70 work here

   so   32 and 42 are in all of the lists ....that is your answer

Using the Trigonometry ratios, the missing sides and angles are:

1. sin R = 5/13

2. sin T = 12/13

3. cos R = 12/13

4. cos T = 5/13

5. tan R = 5/12

6. tan T = 12/5

7. x = 16.5

8. x = 58.9

9. x = 9.2

10. x = 35.9

11. x = 40.7°

12. x = 77.8°

The Trigonometry ratios that can be used to solve any right triangle are given as: SOH CAH TOA.

SOH is: sin ∅ = opp/hyp

CAH is: cos ∅ = adj/hyp

TOA is: tan ∅ = opp/adj.

1. sin R = opp/hyp = 15/39

sin R = 5/13

2. sin T = 36/39

sin T = 12/13

3. cos R = adj/hyp = 36/39

cos R = 12/13

4. cos T = 15/39

cos T = 5/13

5. tan R = opp/adj = 15/36

tan R = 5/12

6. tan T = 36/15

tan T = 12/5

7. Apply CAH:

cos 38 = x/21

x = (cos 38)(21)

x = 16.5

8. Apply TOA:

tan 23 = 25/x

x = 25/tan 23

x = 58.9

9. Apply TOA:

tan 57 = x/6

x = (tan 57)(6)

x = 9.2

10. Apply SOH:

sin 32 = 19/x

x = 19/sin 32

x = 35.9

11. Apply SOH:

sin x = 15/23

x = sin^-1(15/23)

x = 40.7°

12. Apply TOA:

tan x = 37/8

x = tan^-1(37/8)

x = 77.8°

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A: Five people each paying $14.50 means that the total bill was \(5\cdot\$14.50=\boxed{\$72.50}.\)

B: Subtract the number of people he already has from the number of people he needs to get \(42-29=\boxed{13}\) people.

C: Divide 96 by 8 to get \(\boxed{12}\) packs.

Arithmetic is where it all begins, y'know?

Answer:

Hope this helps though I m not sure about the first one since I got another answer 72.5 but it isn't there

The coefficient of determination is the square of the correlation coefficient, and the value is 0.0151

The given parameter is:

Correlation coefficient, r = 0.123

Rewrite as:

r = 0.123

Take the square of both sides

r² = 0.123²

Evaluate the square

r² = 0.015129

Approximate

r² = 0.0151

The coefficient of determination is represented by r²

Hence, the coefficient of determination is 0.0151

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Answer:

0.3632 = 36.32% probability that the mean benefit for a random sample of 20 patients is more than $4100.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

Population: \(\mu = 4064, \sigma = 460\)

Sample of 20: \(n = 20, s = \frac{460}{\sqrt{20}} = 102.86\)

Find the probability that the mean benefit for a random sample of 20 patients is more than $4100.

This is 1 subtracted by the pvalue of Z when X = 4100. So

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{4100 - 4064}{102.86}\)

\(Z = 0.35\)

\(Z = 0.35\) has a pvalue of 0.6368

1 - 0.6368 = 0.3632

0.3632 = 36.32% probability that the mean benefit for a random sample of 20 patients is more than $4100.

Answer:

dont know.

Step-by-step explanation: