Using the formula 1/a+1/b=1/c, express the variable b in terms of the variables a and c. Find b.

b =

All the zeroes of f(x) are, - 4, 3/2, - 5/3

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The function is,

⇒ f(x) = 9x³ + 45x² + 26x - 40

And,  (x + 4) is a factor of f(x).

Now, Divide the function as;

⇒ x + 4 ) 9x³ + 45x² + 26x - 40 ( 9x² + 9x - 10

             9x³  + 36x²

          -          -

       ------------------------

                    9x² + 26x

                    9x² + 36x

                 -         -

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

                            - 10x - 40

                            - 10x  - 40

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

                            0

Thus, All the factors of function f (x) is,

⇒ (x + 4) (9x² + 9x - 10)

⇒ (x + 4) (9x² + 15x - 6x - 10)

⇒ (x + 4) (3x(3x + 5) - 2(3x + 5))

⇒ (x + 4) (3x - 2) (3x + 5)

Thus, All the zeroes are,

⇒ x + 4 = 0 ⇒ x = - 4

⇒ 3x - 2 = 0 ⇒ x = 2/3

⇒ 3x + 5 = 0 ⇒ x = - 5/3

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The value of the segment FE for the similar triangles is equal to 6.

The triangles EFG and ECD are similar, this implies that the length FE of the smaller triangle is similar to the length CE of the larger triangle

and the length FG of the smaller triangle is similar to the length CD of the larger triangle

so;

FE/12= 6/2FE

2(FE)² = 12 × 6 {cross multiplication}

2(FE)² = 72

(FE)² = 72/2

(FE)² = 36

FE = √36 {take square root of both sides}

FE = 6.

Therefore, the value of the segment FE for the similar triangles is equal to 6.

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The value of angle A is 100⁰.

option D is the correct answer.

The measure of angle A is calculated by applying the following formula as shown below;

If line AB is similar to line AC, then angle B must be equal to angle C.

∠ B = ∠ C = 40 ⁰

The value of angle A is calculated as follows;

∠ A = 180⁰ - ( ∠ B + ∠ C ) ( sum of angles in a triangle )

∠ A = 180⁰  -  ( 40⁰ + 40⁰ )

∠ A = 180⁰ - ( 80 ⁰ )

∠ A = 100⁰

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La pieza de hierro pesó (2 + 2/8) libras más que la pieza de aluminio.

Para ver esto, debemos tomar la diferencia entre los pesos de las dos piezas de metal.

Sabemos que:

La diferencia entre esos valores nos dará:

(9 + 3/8) libras - (7 + 1/8) libras.

Podemos reagrupar los numeros como:

(9 - 7) libras + (3/8 - 1/8) libras

2 libras + 2/8 libras

(2 + 2/8) libras

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Answer:

Hello!

a) Melody's average 4 year salary = (56,000 + 60,000 + 73,000 + 75,000) / 4

= 264,000 / 4

= 66,000

So, Melody's average 4 year salary is $66,000.

Step-by-step explanation:

Melody has worked for 30 years at Fancy Pet magazine and is planning to retire at the end of the year. As per her employer's pension formula, she will receive 2.5% of her average salary over the last four (4) years of employment for every year worked.

To calculate Melody's average salary over the last four years, we first need to add up her salary from the last four years: 56,000 + 60,000 + 73,000 + 75,000 = 264,000. Then, we divide this sum by 4 to find the average: 264,000 / 4 = 66,000.

Therefore, Melody's average 4 year salary is $66,000. With this information, we can calculate the amount of pension she will receive based on her years of employment and the pension formula offered by her employer.

If Luis trains two times per week with 12-pound weights , then to improve his strength, he should (d) Increase to three times per week.

By Increasing the frequency of his strength training sessions from two times per week to three times per week can help Luis improve his strength by exposing his muscles to more stimulation and allowing for more adaptations to occur.

It is important to remember to progress gradually and listen to his body to avoid injury.

The option (d) ;  involves increasing the frequency of his strength training sessions from two times per week to three times per week. By exposing his muscles to more stimulation, he will be allowing for more adaptations to occur and potentially leading to greater strength gains.

The given question is incomplete , the complete question is

Luis strength trains two times per week. He uses 12-pound weights and performs three sets of eight repetitions. He wants to improve his frequency. What should he do?

(a) Increase to 10 repetitions.

(b) Increase to 15-pound weights.

(c) Increase to four sets.

(d) Increase to three times per week.

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The trapezoidal rule is a numerical integration method that frequently overestimates the real value of a function's definite integral.

The trapezoidal rule is a strategy for approximating the definite integral in calculus. The trapezoidal rule works by computing the area of the region under the graph of the function f(x) that is approximated as a trapezoid. The trapezoidal rule is commonly used to calculate the area under curves. This is achievable if the overall area is divided into smaller trapezoids rather than rectangles. The Trapezoidal Rule integration determines the area by approximating the area under a function's graph as a trapezoid. The midway rule uses rectangular areas to approximate the definite integral, whereas the trapezoidal rule uses trapezoidal approximations to approximate the definite integral. Simpson's approach works by first approximating the original function with piecewise quadratic functions.

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Sampling distribution type distribution is simulated with the sample proportion with n = 15 and p = 0.65.

It is defined as a probability distribution of a statistic that is from a larger number of samples from a specific population.

We are given that

The probability of tails of a weighted coin, p=0.65 and n=15

We have to find the type of distribution that is simulated if this procedure is repeated 100 times.

The random variable is a proportion of a number of tails therefore, the type of distribution is the sampling distribution of the sample proportion.

Probability is something that is to happen.

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Approximately 90.7% of measurements will be between 31.88 and 41.54.

To find the percentage of measurements that will be between 31.88 and 41.54, we need to use the standard deviation to find the number of standard deviations away from the mean that 31.88 and 41.54 are, and then use a standard normal table to find the corresponding proportion of data within that range.

First, we'll find the z-score for 31.88:

z = (31.88 - 36.71) / 3.22 = -1.49.

Similarly, the z-score for 41.54 is:

z = (41.54 - 36.71) / 3.22 = 1.34.

Now we can use a standard normal table to find the proportion of data between -1.49 and 1.34 standard deviations from the mean. This proportion is approximately 0.907, meaning that approximately 90.7% of measurements will be between 31.88 and 41.54.

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The percentage of the time will its value falls in the indicated region are (a) 68.54%, (b) 95.44%, (c) 95.99%, (d) 99.48%, (e) 5.54%, (f) 97.19%, and (g) 15.96%.

(a) The percentage of time that a variable with 10 degrees of freedom will fall between -1.81 and 1.81 is 68.54%.

(b) The percentage of the time that a variable with 10 degrees of freedom will fall between -3.17 and 3.17 is 95.44%.

(c) The percentage of the time that a variable with 24 degrees of freedom will fall between -2.06 and 2.06 is 95.99%.

(d) The percentage of the time that a variable with 24 degrees of freedom will fall between -3.75 and 3.75 is 99.48%.

(e) The percentage of the time that a variable with 23 degrees of freedom will fall outside the interval from -2.81 to 2.81 is 5.54%.

(f) The percentage of the time that a variable with 24 degrees of freedom will fall to the right of 2.80 is 97.19%.

(g) The percentage of the time that a variable with 10 degrees of freedom will fall to the left of -1.81 is 15.96%.

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--The given question is incomplete; the complete question is

"Given a variable that has a t distribution with the specified degrees of freedom, what percentage of the time will its value fall in the indicated region? (Round your answers to one decimal place.)

(a) 10 df, between -1.81 and 1.81

(b) 10 df, between -3.17 and 3.17

(c) 24 df, between -2.06 and 2.06

(d) 24 df, between -3.75 and 3.75

(e) 23 df, outside the interval from -2.81 to 2.81

(f) 24 df, to the right of 2.80

(g) 10 df, to the left of -1.81"--

Currently, Michael is 72 years old

Let's represent Michael's current age as "x".

Then Brandon's current age is x/3.

18 years ago, Michael's age was x-18

Brandon's age was x/3-18.

18 years ago, we can write the equation:

x - 18 = 9 * (x/3 - 18)

So, we have

x - 18 = 3x - 162

Evaluate the like terms

2x = 144

Divide by 2

x = 72

So, Michael is 72 years old now.

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The total cost predicted for a month with 2,000 units of production  using the equation of the regression line $197,042.

The total cost predicted by Star, Inc. for a month in which production is 2,000 units would be calculated using the equation of the regression line:

y = intercept + (slope * x)

where y is the total cost, x is the production, intercept is the y-intercept (174,182), and slope is the coefficient of production (11.93).

Plugging in the values, we get:

y = 174,182 + (11.93 * 2,000) = 174,182 + 23,860 = 197,042

So the total cost predicted for a month with 2,000 units of production is $197,042.

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Answer:

C

Step-by-step explanation:

slope is 3/2  - use any diff in Y divide by diff in x, easiest one is BC/BA = 3/2

the line goes upwards, so slope must be positive

every triangle has the same slope cause their long sides share the same line

only C is right

Answer: The slope answer is A but my also have an extra which is e so C an E are the correct answer

Step-by-step explanation:

I just did them and it was correct hope it help :)

Answer: The slope of the line is 3; option A is correct.

Step-by-step explanation:

Each circle represents a number. The left side of the equation (4(x+5)) can be divided by 4 to find the value of x+5. The value of x is 4.70

The distance between a circle's center and periphery is referred as the radius. Always, the diameter is twice the radius. As a conclusion, the diameter is multiplied by two to obtain the formula.

The ratio of a circle's circumference to diameter serves as the basis for the traditional definition of Pi (). The diameter or length of such a circle is its circumference. A straight line connecting a point on one end of both the ring to a place on the opposite end, through the center, is the diameter.

Diameter = 2r -----------(1)

where r is the radius

The value of the diameter = 32 m   and  radius is given to be 4(x+5)

substitute the above into equation (1)   and then solve for x

32  =  2 [ 4(x + 5)]

first open the inner bracket

32 = 5[4x + 20}

then open the outer bracket

32 = 20x + 100

subtract 16 from both-side of the equation

20x=100-32

20x=68

x=3.4

Divide both-side of the equation by 3.4

16/3.4  = 8x/3.4

4.70 = x

x = 4.70

Therefore, the value of x is 4.70

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The caramel topping demand curve will not change:

The cost of caramel topping is falling; there will be an increase in demand for caramel topping:

Butterscotch topping costs more money;

There will be less demand for caramel topping:

Ice cream now costs more money.

The quantity of caramel topping demanded would increase if the price of the topping dropped. Consequently, the demand curve for caramel topping would go lower.

Ice cream and caramel toppings are complementary products.

Products that are consumed together are said to be complementary.

The amount of ice cream demanded would drop if the price went up. There would be a drop in the number of caramel toppings needed as a result of the fall in demand.

a decline in the popularity of caramel toppings. With less demand, the demand curve for caramel toppings would move inward.

Butterscotch and caramel ice cream toppings serve as stand-ins.

Products that can be used in place of one another are known as substitute goods.

The quantity demanded for butterscotch topping would decline if the price of butterscotch topping rose, making it more expensive overall. Customers might switch to caramel topping. As a result, demand for caramel topping would rise and the demand curve would move outward.

Demand curve: what is it?

The demand curve is a graphical representation of how the cost of an item or service relates to how much is demanded over a given period of time.

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Answer:

Step-by-step explanation:

Answer:

w = 25

Step-by-step explanation:

8/5w = 40

Divided both sides by 8/5

w = 25

Let's check

8/5(25) = 40

40 = 40

So, w = 25 is the correct answer.

Answer: w = 25

Step-by-step explanation:

    To solve for w, we will isolate the variable by using inverse operations.

    Given:

[tex]\displaystyle \frac{8}{5} w=40[/tex]

    Divide both sides of the equation by [tex]\frac{8}{5}[/tex]:

* Note: w is being multiplied by [tex]\frac{8}{5}[/tex], so the inverse operation is division

[tex]\displaystyle w=\frac{40}{\frac{8}{5 } } \mapsto w=40*\frac{5}{8} \mapsto w=*\frac{40*5}{8} \mapsto\frac{200}{8} \mapsto \boxed{w=25}[/tex]

Answer: 816.4 [tex]ft^2[/tex]

Step-by-step explanation: The formula is A=2[tex]\pi[/tex]rh

9.42 m and 3 m are the missing lengths. 30 degrees is the missing angle.

A triangle is a three-sided polygon that is sometimes (but not always) referred to as the trigon. Every triangle has three sides and three angles, which may or may not be the same. A triangle is a three-sided polygon with three edges and three vertices in geometry. The total of a triangle's interior angles equals 180 degrees, which is its most essential feature. This is known as the angle sum property of a triangle. This figure is two-dimensional and has three straight sides. A triangle is a three-sided polygon. A triangle's three angles added together equals 180°. A single plane contains the triangle.

Here,

sin 60=p/h

√3/2=p/6

p=3√3 m

cos 60=b/h

1/2=b/6

b=3 m

90+60+x=180

x=30 degrees

The missing lengths are 9.42 m and 3 m. The missing angle is 30 degrees.

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Answer:

2x x 3y x 3x is 18x4y  hope it helps

Step-by-step explanation:

It is referred to as "simple random sampling" when a sample of size n is taken from such a population of size N and any conceivable sample of that size has an equal likelihood of occuring.

A selection of participants from such a population are chosen at random by the researcher using simple random sampling, a sort of probability sampling.

Thus, it is referred to as "simple random sampling" when a sample of size n is taken from such a population of size N and any conceivable sample of that size has an equal likelihood of occuring.

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The numerical value of the standard deviation is never (B) less than the variance and is never negative.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers.

While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean (also known as the anticipated value) of the collection.

The standard deviation's numerical value is always greater than the variance and can never be negative.

The lowercase Greek letter (sigma), for the population standard deviation, or the Latin symbol s, for the sample standard deviation, are most frequently used in mathematical texts and equations to indicate standard deviation.

Standard deviation may be written as SD.

Therefore, the numerical value of the standard deviation is never (B) less than the variance and is never negative.

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Answer:

You are

Step-by-step explanation:

25% is 1/4 of the total value

100/400 = 1/4

So, 100g is 25%

25% * 3 = 75%, so 100 * 3 = 300

Thus, you are correct.

I have no idea how to explain where 'your friend' went wrong :D

Hope this helped!

The solution is, for, x = -1, 0, 1, 3, the value of f(x) is, -1, 2, 5, 11.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

f^-¹(x) = 1/3(x) - 2/3

so, by solving we get,

the real function is,

f(x) = 3x+2

as, we get,

let, y= f^-¹(x)= x/3 - 2/3

i.e. x = 3y+2

so, we get , inverse of f^-¹(x) is, f(x)

now, f(x)= 3x+2

Hence, The solution is, for, x = -1, 0, 1, 3, the value of f(x) is, -1, 2, 5, 11.

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Triangle ABC with a hypotenuse of 7 units and angle B equal to 70 degrees,

Since triangle ABC is a right triangle and angle B is 70 degrees, it can be deduced that angle C must be 90 - 70 = 20 degrees.

assuming

length of side AC  = a

length of side BC = b.

Using the Pythagorean theorem, we can find the values of a and b.

a^2 + b^2 = 7^2

a^2 = 7^2 - b^2

a = √(7^2 - b^2)

Using the tangent function

tan C = b/a

tan 20 = b/√(7^2 - b^2)

Solving for b, we get:

b = tan(20) * √(7^2 - b^2)

We can use numerical methods to find the approximate value of b. Using a calculator, we can find that b is approximately 4.7. Rounding to the nearest tenth, b is 4.7 units.

Finally, using the Pythagorean theorem again, we can find the value of a:

a^2 + b^2 = 7^2

a^2 = 7^2 - b^2 = 7^2 - 4.7^2

a = √(7^2 - 4.7^2)

a = √(7^2 - 22.09)

Using a calculator, we can find that a is approximately 5.3. Rounding to the nearest tenth, a is 5.3 units.

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The other angles of the triangle are x = 28° and y = 62°. The result is obtained by using the trigonometric ratios.

Where opp is opposite, hyp is hypotenuse, and adj is adjacent.

In Pythagorean Theorem, the triangle is a right triangle. It means that one angle is 90° and two others added equal to 90°. The two angles can be found by the trigonometric ratios.

A triangle with side lengths 8, 15, and 17 is a right triangle by the converse of the Pythagorean Theorem.

Find the measures of the other 2 angles! (x and y)

Let θ = x.

sin x = opp/hyp

sin x = 8/17

x = 28°

If x = 28, then y will be

y = 180 - (90 + 28)

y = 180 - 118

y = 62°

Hence, the right triangle has the other angles of 28° and 62°.

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Answer:

576 minutes

Step-by-step explanation:

You first must convert the time of a day into minutes.

24 hours x 60 minutes = 1440 minutes in a day.

Now you need to multiply the sum by 2/5

1440/1 x 2/5  =  2880/5
Simplify the number into a whole number.

2880 divided by 5 = 576

The number of students present at the dinner is 17

As stated in the question, a group of students had dinner at a local restaurant.

The total bill for the dinner was $364.99 and each student paid an equal share of the bill which is $21.47. according to the question we have to find the number of students present at the dinner,

To find the number of students we have to divide the total bill by the amount paid by each student,

Let the number of students who were present at the dinner be x

Now number of students = total bill/amount paid by each student

Hence, x = $364.99 ÷ $21.47

So the value of x is 17

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The number of cubes fitted in the storage box is 448.

The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Given:

Edge length of cube = 1/2 inch

So, volume of a cube = (Side)³

                                    = (1/2)³

                                    = (1/8)

Now, Volume of the storage box = 56 cubic inches.

So, number of cubes fitted in the storage box

= Volume of the storage box / volume of a cube

= 56/ (1/8)

= 56 x8

= 448 cubes

Hence, number of cubes fitted is 448.

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