Please help me with this question please

The equation cos (π/6 + β) is solved to get

From the question it was given that sine β = -0.8

solving for β

sine β = -0.8

β = arc sine ( -0.8 )

β = -0.9273

β ≈ -π/3

substituting the value into cos (π/6 + β)

cos (π/6 + β)

cos (π/6 - π/3)

cos (π/6 - π/3)

= √3 / 2

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2016 is the year in which the average gas mileage is the greatest.

An equation contains one or more variables connected by an equal sign.

Example:

1x + 2 = 99 is an equation.

We have,

y = -0.4 (x - 3)² + 42

where x = the number of years since 2013.

y = average gas mileage

Now,

In 2016,

x = 3

y = -0.4 (3 - 3)² + 42

y = 0 + 42

y = 42

This is the greatest value for any x value.

Thus,

In 2016, the average gas mileage for new vehicles sold is the greatest.

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Answer:3.25

Step-by-step explanation:

Divide 325/100=3.25

The volume of the given complex structure would be = 56 m³

The structure is made up of the big and small cubes.

The volume of the big cube = length × breadth × width = 7 × 3 × 4 = 84 m³

The volume of the small cube cut out = length * breadth * width = 4 × 7 × (4 - 3) = 28 m³

Volume of the complex figure = 84 m³ - 28 m³ = 56 m³

The volume of the complex figure shown in the diagram is 56 m³.

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Answer:

1.) M=9,100(1 + 0.05)^6

Step-by-step explanation:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

In this formula the "P" represents the principle amount, or the original amount. The "r" represents the interest rate in decimal form, while the "n" represents the number of compounds in the time unit (usually years), and the "t" represents the amount of time that has passed (usually years)

In this case it says annual interest rate of 5% and nothing of compound monthly, etc... so n=1, and r=0.05. We're also given the principle amount of 9,100 and the time passed is just 6 years, so t=6. Plugging all this information into the equation we get:

[tex]A=9,100(1+0.05)^6[/tex]

which makes the first option correct.

351 and 1053 are the next terms of geometric sequence  13, -39, 117...

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

The given series is 13, -39, 117..

We need to find the fourth and fifth terms of the sequence.

The given sequence is geometric sequence.

Geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.

The general term of sequence [tex]a_{n} =ar^{n-1}[/tex]

r is the common ratio

r=-39/13

=-3

a=13 first term

a₄=13(-3)³

a₄=13(-27)

Fourth term is 351.

Now plug in n as 5 to find 5th term.

a₅=13(-3)⁴

a₅=1053

Hence, the next two terms of geometric sequence are 351 and 1053.

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Answer: god

Step-by-step explanation: god god god god god god god god

Option D is correct, SA = 2π(1.3)2 + 2.6π(4.4) square feet is used calculate the surface area of the cylinder.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Given that cylinder with diameter labeled 2.6 feet and height labeled 4.4 feet

The surface area of cylinder is given by the formula =2πrh+2πr²

The radius is Diameter/2

2.6/2=1.3

The radius is 1.3

Surface area =2π(1.3)(4.4)+2π(1.3)²

So =2.6π(4.4)+2π(1.3)²

Hence, Option D is correct, SA = 2π(1.3)² + 2.6π(4.4) square feet is used calculate the surface area of the cylinder.

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Answer:

Step-by-step explanation:

The answers include the following:

This is referred to as the ratio of distance to the time in which the distance was covered and it is a scalar quantity.

From the graph, we can deduce that Runner A won the race because it attained a greater distance when compared to the time for all the other runners.

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De acuerdo con la información, se puede inferir que Jim vendió 634 sándwiches de bistec y 351 perritos calientes.

Para identificar cuántos perros y sandwiches vendió Jim durante la feria debemos comprobar con diferentes números hasta encontrar el número correcto. En este caso, debemos multiplicar el valor de cada producto por un número específico e ir ajustado los valores hasta obtener el número total de productos.

En este caso, la cantidad de sándwiches vendidos por Jim sería 634 y perritos 351.

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Answer:

5%

Step-by-step explanation:

We can use the formula for simple interest to solve for the interest rate:

I = Prt

where:

I is the interest

P is the principal (the amount borrowed)

r is the interest rate

t is the time in years

We know the principal (P) is $8,500, the interest (I) is $1,785, and the time (t) is 42 months, or 42/12 = 3.5 years. So, we can plug in the values and solve for r:

I = Prt

$1,785 = $8,500 * r * 3.5

$1,785 / $8,500 / 3.5 = r

r = 0.05, or 5%

So, the simple interest rate on Tamaya's car loan was 5%.

The equation of the line will be y = -3/4x + 1.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

The slope of the line is -3/4 and the y-intercept is 1. The equation of the line can be written as:-

y = mx + c

y = -3/4x + 1

Therefore, the line will have the equation y = -3/4x + 1.

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The option that is true for the central limit theorem is;

C: For a large enough sample size, the Central Limit Theorem states that the sample means of repeated samples of a population are normally distributed

Let us look at all the given options to access which one clearly is correct about the central limit theorem;

a) This option is incorrect because the CLT theorem is based on ‘sample mean’ distribution.

b) This option is Incorrect because the theorem is true for any population distribution.

c) This option is correct because Irrespective of the population distribution, the sample means of repeated samples are normally distributed for larger n.

d) The “central limit theorem(CLT)” states that, the sample means of the repeated samples follows normal distribution for ‘large’ sample sizes. Thus, this option is incorrect.

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The values of the composite functions are (f + h)(5) = 7, (h - f)(2) = 0, (fh)(3) = 0 and (h/f)(0) = 3/5

From the question, we have the following parameters that can be used in our computation:

The graphs

Using the graphs as a guide, we have the following:

(f + h)(5) = f(5) + h(5)

(f + h)(5) = 3 + 4

(f + h)(5) = 7

(h - f)(2) = h(2) - f(2)

(h - f)(2) = 1 - 1

(h - f)(2) = 0

(fh)(3) = f(3) * h(3)

(fh)(3) = 4 * 0

(fh)(3) = 0

(h/f)(0) = h(0)/f(0)

(h/f)(0) = 3/5

Hence, the value of the function (h/f)(0) is 3/5

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On solving the provided question, we can say that Frequency Percentage is equal to the relative frequency times one hundred.

In order to make the information easier to understand, frequencies are organized into frequency distributions, which are visual displays. The frequencies displayed in a frequency distribution can be absolute or relative, like ratios or percentages. Both a graph and a table of frequencies can be used to represent a frequency distribution. Both the exact number of observations and the proportion of observations falling within each range can be displayed in a frequency distribution. A relative frequency distribution is the name given to the distribution in the latter scenario. The frequency of an observation is the frequency with which it appears in the data. The frequency of the number 9 in the following list of numbers, for instance, is 5. (because it occurs 5 times). 1, 2, 3, 4, 6, 9, 9, 8, 5, 1, 1, 9.

25–29 is listed as the First Class Group.

Class size is 4 (29-25).

Maintain the same class size for reminders from 89 through 93.

Count the values and record the frequency next to the appropriate class.

Midpoint equals (higher class limit plus lower class limit) / 2.

Relative Frequency is equal to Frequency/total Values.

Cumulative Frequency equals the sum of the past and current frequencies.

Frequency Percentage is equal to the relative frequency times one hundred.

Class Recurrence Point Midway Frequency relative Frequency Added Up percentage of frequency 25-29 0 27 0 0 0.00% 1.25% 1 31 0.0125

%ile Rank for 48 = 12.5

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Each worker would take home a net pay of $586.71.

What is the net pay?

The net pay is the amount of money that an employee takes home after all deductions have been made from their gross pay. Gross pay is the total amount of money an employee earns before taxes and other deductions are taken out.

To calculate net pay, you need to subtract all the required deductions from the employee's gross pay.

To calculate the net pay for each worker, we first need to determine their gross pay. The gross pay will depend on the number of hours they worked and whether they worked any overtime.

For the first 40 hours worked, each worker earns $15.90 per hour, so their gross pay for those hours would be:

Gross Pay for 40 hours = $15.90/hour x 40 hours = $636

For any hours worked beyond 40, the worker earns time and a half wages. This means they earn 1.5 times their regular hourly wage of $15.90, or $23.85 per hour. So, if they worked, for example, 45 hours in total, the additional 5 hours would be paid at the overtime rate, resulting in an additional gross pay of:

Gross Pay for 5 overtime hours = $23.85/hour x 1.5 x 5 hours = $178.88

Therefore, their total gross pay would be:

Total Gross Pay = Gross Pay for 40 hours + Gross Pay for 5 overtime hours = $636 + $178.88 = $814.88

Now, we need to calculate the deductions, which we are told are 28% of the gross pay. So the total deductions would be:

Total Deductions = 28% x $814.88 = $228.17

Finally, to determine the net pay, we need to subtract the total deductions from the gross pay:

Net Pay = Gross Pay - Total Deductions = $814.88 - $228.17 = $586.71

Therefore, each worker would take home a net pay of $586.71.

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One reason to compute a correlation coefficient to measure the strength of the relationship between two variables is that quantify the strength and direction of the correlation in a precise and standardized way..

When we have two variables that are related, we say that there is a correlation between them. The most common way to visually represent a correlation is by plotting the data on a scatter plot, where each point represents a pair of values for the two variables.

While a scatter plot is a useful tool to visualize the relationship between two variables, it doesn't tell us how strong or weak the correlation is. For instance, two variables might show a positive correlation, but the scatter plot might be quite dispersed, indicating that there is a lot of variability in the data. In this case, we would say that the correlation is weak. On the other hand, if the scatter plot is tightly clustered around the line, we would say that the correlation is strong.

This is where the correlation coefficient comes in. The correlation coefficient is a mathematical measure that quantifies the strength and direction of the relationship between two variables. It ranges from -1 to 1, where a value of -1 indicates a perfect negative correlation, a value of 0 indicates no correlation, and a value of 1 indicates a perfect positive correlation.

To compute the correlation coefficient, we first need to calculate the covariance between the two variables. Covariance is a measure of how much the two variables vary together, and it is defined as the sum of the products of the deviations of the values from their respective means. Once we have the covariance, we can divide it by the product of the standard deviations of the two variables to get the correlation coefficient.

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Jean purchased a snow thrower for $1,980 using an installment plan that required a 10% down payment of $198 and 18 monthly payments of $116. This allowed Jean to spread out the cost of the snow thrower over time, avoiding a large upfront cost.

Jean recently purchased a snow thrower for $1,980 using an installment plan. To start, Jean had to make a down payment of 10% of the total purchase price, which was $198. This down payment allowed Jean to spread the remaining cost of the snow thrower across 18 monthly payments of $116 each. After making all 18 payments, Jean will have paid the full purchase price of $1,980. This installment plan option is an excellent way for Jean to get the snow thrower he needs while avoiding a large upfront cost and spreading the payments out over a period of time. With this installment plan, Jean can pay off the purchase of the snow thrower while still having money left over each month to cover other expenses.

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The position of G in the given line segment is at point 1, which is between points F and D and the line segment between F and D in the ratio 8:5.

What is meant by line segment?

Two unique points on a line define the boundaries of a line segment. A line segment is a section of the path a line takes to join two locations. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction.

Given, the locations of D  and F on the line segment.

D = -4

F = 9

Number of units between F and D = 9 - (-4) = 13

Point G partitions the line segment from F to D in the ratio 8:5.

So distance of G from F = [8/(8+5)] * 13 = 8

Distance of G from D =  [5/(8+5)] * 13 = 5

So from F, it is 8 units behind F = 9 - 8 = 1

from D, it is 5 units in front of D = -4 + 5 = 1

Therefore the position of G in the given line segment is at point 1.

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Another way to find 4x2x5 is to multiply two of the digits and multiply the last digit with the product of two.

Multiplication is when you take one number and add it together a number of times. Example: 5 multiplied by 4 = 5 + 5 + 5 + 5 = 20. We took the number 5 and added it together 4 times. This is why multiplication is sometimes called "times".

Given are three numbers multiplied, 4x2x5, we need to find the another way to solve it,

So,

4x2x5 = 40

So, in another method,

Multiply 4 and 2, we get, 8 as product, now multiply the product 8 to the last number 5,

8x5 = 40

Hence, the another way to find 4x2x5 is to multiply two of the digits and multiply the last digit with the product of two.

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The question is incomplete solved for:

Find the another method to solve 4x2x5

A function modeling the volume of the box can be found, and the values of x for which the volume is greater than 230 in2 are x = [-2.636, 2.636]. The largest volume is 480 in2, which is achieved when x = 5.

A function that models the volume V of the box can be found by subtracting four [tex]x2[/tex]from both the length and the width, and then multiplying the result to get the volume:

V = [tex](12 - 4x2)(20 - 4x2)[/tex]

To find the values of x for which the volume is greater than 230 in2, we can solve the equation

V = [tex](12 - 4x2)(20 - 4x2) = 230[/tex] for x.

This gives x values of ±2.636

Thus, the values of x for which the volume is greater than 230 in2 are x = [[tex]-2.636, 2.636[/tex]].

The largest volume that such a box can have is 480 in2, which is obtained when x is equal to the length or width divided by two. This occurs when x = 10/2 = 5. Thus, the largest volume that such a box can have is 480 in2.

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Answer:

this is not belongs to mathematics

Step-by-step explanation:

Answer:

Length = 26 feet; Width = 8 feet

Step-by-step explanation:

Let:

x = Length of rectangle

y = Width of rectangle

4 times the width = 4y

∴ 6 less than 4 times the width = 4y - 6

Perimeter of a rectangle = 2 × [Length + Width]
                                     68 = 2 × [(4y - 6) + y]

Expand the brackets or parenthesis by applying the Distributive Law and bring the like terms together:

                                    68 = 2 × [4y - 6 + y]
                                    68 = 2 × [5y - 6]

                                    68 = 10y - 12

                             68 + 12 = 10y

Isolate y by making it the subject of the equation:

                                  80 = 10y

                                    y = [tex]\frac{80}{10}[/tex]

                            y = Width of rectangle: 8 feet

Substitute y into the equation to calculate x:

       x = 4(8) - 6

         x = Length of rectangle = [tex](32 - 6)[/tex] feet

                                               x = 26 feet

Answer: 0

Step-by-step explanation:

1/2x = -1/2x cannot be true for any other value of x except when x equals 0. In other words, we need the left and right sides to equal each other, but that would only happen when x=0.

a) The probability of rolling a 5 or a number greater than 3 is 1/2.

b) The probability of rolling a number less than 4 or an even number is 5/6.

c) The probability of rolling a 4 or an odd number is 2/3.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

In rolling a six-sided die, the total number of outcomes is 6.

The sample space is {1,2,3,4,5,6}

The probability formula is -

Probability = Number of outcomes corresponding to events / total number of outcomes.

(a)  Let A be the event of rolling a 5. Then A = {5}.

Let B be the event of rolling a number greater than 3. Then B = {4,5,6}.

The event of rolling A or B is given by A∪B = {4,5,6}.

So, apply the probability formula -

P(A∪B) = 3/6 = 1/2

Therefore, the probability value is 1/2.

(b)  Let C be the event of rolling a number less than 4. Then C = {1,2,3}.

Let D be the event of rolling an even number. Then D = {2,4,6}.

The event of rolling C or D is given by C∪D = {1,2,3,4,6}.

So, apply the probability formula -

P(C∪D) = 5/6

Therefore, the probability value is 5/6.

(c)  Let E be the event of rolling a 4. Then E = {4}.

Let F be the event of rolling an odd number. Then F = {1,3,5}.

The event of rolling E or F is given by E∪F = {1,3,4,5}.

So, apply the probability formula -

P(E∪F) = 4/6 = 2/3

Therefore, the probability value is 2/3.

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The distance from the apex, or top of the pyramid, to each vertex of base is 10.9.

A right rectangular pyramid is a pyramid, with four slant sides, and a rectangular base, such that all the sides are congruent and the vertex is atop of the midpoint of the base rectangle.

Suppose the base of the pyramid has length = l units, and width = w units.

Suppose that the height of the pyramid is of h units, then:

[tex]v = \dfrac{l \times w \times h}{3} \: \rm unit^3[/tex]

is the volume of that pyramid.

The base is a rectangle with length = L units, and width = W units, so its area is:

[tex]b = l \times w\: \rm unit^2[/tex]

Given that;

Altitude of pyramid= 10

Each side base of pyramid= 6

Now,

So using pythagorean theorem,

x2=y2+(10)2....1

with y half of the length of the diagonal of the base.

2y=length of the diagnol

and (2y)2 = 72

4y2=72

y = 3√2.

So substitute y in eq1 and get x

( 3√2)2+(10)2=(x)2

(x)2=118

x=10.86.

x≈10.9

Therefore, the side of  right square pyramid will be 10.9.

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On solving the provided question we can say that median from the vertex in an isosceles triangle is perpendicular to the base.

ƒ(x)=sin(x)

consider Asin(Bx + C) = y +D changes the amplitude of the function (how high or low it is).

if you want to

Because it has three sides and three vertices, a triangle is a polygon. It is a fundamental geometric shape. Triangle ABC is the name given to a triangle with the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered. A triangle is a polygon because it has three sides and three corners. The triangle's corners are defined as the points at which the three sides meet. The sum of three triangle angles yields 180 degrees.

Let O be the circle's centre and P be the midpoint of BC. After that, OP LBC.

Let AP =x and PB = CP -y.

Applying Pythagoras theorem in As AP B and OP B, we have

AB2 = BP2 + AP2 and OB2 = OP2 +BP2

Y2 +x2 ... (i) and, 81 = (9 —x)2 + Y2

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The y-coordinate for the solution to the system of equations is 6.

In mathematics, the value that is equally divided by the two supplied numbers is known as the LCM of any two. Least Common Multiple is its full name. Another name for it is the Least Common Divisor (LCD).

When the fractions' denominators differ, LCM can also be used to add or subtract any two fractions. LCM is used to make the denominators common when doing any arithmetic operations using fractions, such as addition and subtraction. The simplifying process is facilitated by this procedure.

The system of equation is given as:

−x + 3y = 9

y = 2/3x

The second equation can be written as:

x = 3/2y

Substituting the value of x in equation 1:

-3/2y + 3y = 9

Take the LCM:

-3y + 6y / 2 = 9

-3y + 6y = 18

3y = 18

y = 6

Hence, the y-coordinate for the solution to the system of equations is 6.

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