I need help with the 1st question please

Answer: 13 27 to 15 27 = 2 hours

15 27 to 16 00 = 33 mins

1600 to 16 12 = 12 mins

Total = 2hours + 33 mins + 12 mins = 2 hours 45 mins = 2.75 hours

Distance = Speed x time = 56 x 2.75 = 154 km

Answer: 154 km

Step-by-step explanation:

The number of pizzas delivered to a customer who pays $ 80 is 7 pizzas

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the number of pizzas be x₁ = 2

Let the cost of 2 pizzas be y₁ = $ 25

So , the first point A ( x₁ , y₁ ) = A ( 2 , 25 )

Now ,

Let the number of pizzas be x₂ = 5

Let the cost of 5 pizzas be y₂ = $ 58

So , the second point B ( x₂ , y₂ ) = B ( 5 , 58 )

Therefore , the slope of the 2 points is given by

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 58 - 25 ) / ( 5 - 2 )

Slope m = 33 / 3

Slope m = 11

Therefore , the equation of the line is given by

y - y₁ = m ( x - x₁ )

Substitute the value of m in the equation , we get

y - 25 = 11 ( x - 2 )

y - 25 = 11x - 22

Adding 25 on both sides of the equation , we get

y = 11x + 3

So , the equation of line is y = 11x + 3

Now , the customer pays $ 80 , so to find the number of pizzas the customer gets can be calculated by substituting the value of y = 80

And ,

y = 11x + 3

80 = 11x + 3

Subtracting 3 on both sides of the equation , we get

11x = 77

Divide by 11 on both sides of the equation , we get

x = 7 pizzas

Therefore , the number of pizzas is 7 pizzas

Hence ,

The number of pizzas delivered to a customer who pays $ 80 is 7 pizzas

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If the function f(x)= 2x – 3 and g(x) = 3/2x + 1 then g(4) < f(4) is a true statement?

A function is a relationship or expression involving one or more variables.  It has a set of input and outputs.  Each input has only one output.  The function is the description of how the inputs relate to the output.

A function can also be said to be a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Let A & B be any two non-empty sets; mapping from A to B will be a function only when every element in set A has one end, only one image in set B.

Functions are generally represented as f(x).

Let , f(x) = [tex]x^{3\\}[/tex].

It is said as f of x is equal to x cube.

Functions can also be represented by g(), t(),… etc.

For g(4) < f(4);

g(4) = 3/2(4) + 1

g(4) = 3/9

f(4) = 2(4) - 3

f(4) = 8 - 3

f(4) = 5

Therefore; g(4) < f(4)

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Answer: $6,000,000 = 40%

               $2,800,000 = 18.66666667%

Step-by-step explanation:

Divide the sales by the total sale.

Ex:

6,000,000/15,000,000 = .4

2,800,000/15,000,000 = .1866666667

The required simplified value of the x is given as 5.

Given that,
In triangle DEF, if m∠D = (2x)°, m∠E = (2x − 4)°, and m∠F = (x + 9)°.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
for the triangle sum of the interior angles is equal to 180°.
∠D + ∠E + ∠F = 180
2x + 2x - 4 + x + 9 = 180
5x  + 5 = 180
5x = 175
x = 35

Thus, the required simplified value of the x is given as 5.

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Answer:1/12

Step-by-step explanation:

Answer:

[tex]a_{n}[/tex] = 8n + 17

Step-by-step explanation:

there is a common difference between consecutive terms in the sequence

33 - 25 = 41 - 33 = 8

this indicates the sequence is arithmetic with explicit formula

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 25 and d = 8 , then explicit formula is

[tex]a_{n}[/tex] = 25 + 8(n - 1) = 25 + 8n - 8 = 8n + 17

The measure of the central angles of the circle are, respectively:

m ∠ BOC = 60°

m ∠ COD = 120°

m ∠ AOD = 60°

m ∠ AOB = 120°

m ∠ DOB = 180°

In this problem we find a geometric system formed by a circle, two parallel lines and two additional lines that intersect each other at the center of the circle. Then, the angles DOC, COB, AOB and DOB are central angles of the circle such that:

m ∠ DOC + m ∠ COB + m ∠ AOB + m ∠ DOB = 360°

Then, by direct inspection, we find that the measures of the central angles are, respectively:

m ∠ BOC = 60°

m ∠ COD = 120°

m ∠ AOD = 60°

m ∠ AOB = 120°

m ∠ DOB = m ∠ COD + m ∠ BOC = 120° + 60° = 180°

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Answer:

y=5x

Step-by-step explanation:

Because we already know we need atleast 5 quarters to complete a full load (Wash and dry) so we would multiply that number by how many loads were doing (x) and y is the amount we need. For example five loads is y=5x5 and then we can find y which would be y=25

The amount of Amy earn if she sold her shares today will be;

⇒ $8,038

What is an expression?

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

Given that;

Amy purchased 100 shares of Monsanto Company for $66.10 per share.

Today the stock is selling for $80.45.

And, a charge of $7.00 to buy and sell.

Now,

Since, Today the stock is selling for $80.45.

And, A charge of $7.00 to buy and sell.

Hence, The amount for Amy earn if she sold her shares today is;

⇒ $80.45 × 100 - $7

⇒ $8,045 - 7

⇒ $8,038

Thus, The amount of Amy earn if she sold her shares today will be;

⇒ $8,038

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The function that represents how much more water can be added to the bucket before it overflows is given as follows:

c(x) = 6x³ + 3x² - 2x - 2.

The function to calculate the space remaining in the pool is given by the subtraction of the capacity function by the function representing the current amount of water in the pool.

The functions in this problem are defined as follows:

Then the capacity function is obtained as follows:

c(x) = f(x) - g(x)

c(x) = 8x³ + 4x² - 6x + 5 - (2x³ + x² - 4x + 7)

Then the distributive property is applied to the negative sign as follows:

c(x) = 8x³ + 4x² - 6x + 5 - 2x³ - x² + 4x - 7.

Finally, the like terms are combined, that is, the terms that have the same variable and exponent, as follows:

c(x) = 6x³ + 3x² - 2x - 2.

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Answer:

2,144

Step-by-step explanation:

[tex]\frac{15000 - 1600}{6.25}[/tex]  The number of visitors during the time period divided by the total hours.  

2,144

Sampling distribution of mean, Sampling distribution of proportion and T-distribution.

An example of a sampling distribution is a probability distribution of a statistic that is derived by repeated sampling of a particular population. It describes a variety of potential possibilities for a statistic, such the mean or mode of some variable in a population.

When you repeat your survey or poll for all potential samples of the population, you get the sampling distribution of a proportion. For instance, you may conduct many polls rather than asking 1000 cat owners which cat food they prefer.

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Answer:

μ = 150

σ = 18

n = 35

μx¯ = 150

σx¯ = 3.04

Step-by-step explanation:

We are given population mean μ=150 and population standard deviation σ=18, and want to find the mean and standard error of the sampling distribution, μx¯ and σx¯ for samples of size n=36.

By the Central Limit Theorem, the means of the two distributions are the same:

μx¯=μ=150

To find the Standard Deviation of the sampling distribution, we divide the population standard deviation by the square root of the sample size:

σx¯=σn−−√=1835−−√≈3.04

Answer: The number line that you really want to move is the right side. Then, at that point, the right choice is C.

What is a number line?

A number line alludes to a straight line in science that has numbers organized at customary stretches or divides along its width. A number line is frequently shown on a level plane and can be delayed toward any path.

On the off chance that you are at - 15 on the number line and you needed to push toward the positive numbers

The number line that you need to move in the right side. Then the correct option is C.

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Step-by-step explanation:

The angle with a positive sine and negative cosine among the options is [tex]\frac{3\pi }{4}[/tex]

What is an obtuse angle?

Obtuse angle is any angle greater than 90°: Straight angle is an angle measured equal to 180°: Zero angle is an angle measured equal to 0°: Complementary angles are angles whose measures have a sum equal to 90°:

All obtuse angles usually have positive sine and negative cosine.

Amongst all the options  [tex]\frac{3\pi }{4}[/tex] is the only obtuse angle . which if you convert to degrees

using π rad = 180 degrees, 3/4 x 180  you get  135°

In conclusion  [tex]\frac{3\pi }{4}[/tex] is the angle with a positive sine and negative cosine.

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Acceleration resulting from gravity will be = (-9.8 ms sq.)

First of all we have to know more about gravity which means it is the force by which a planet or other body draws objects toward its center. The force of gravity keeps all of the planets in orbit around the sun.

When you throw a ball up in the air, its speed decreases, until it momentarily stops at the very top of the ball's motion. Its acceleration is

(−9.8 ms sq )

at the very top since the body is moving upward against the gravity. In other words, the acceleration due to gravity will be

g = 9.8 ms -sq

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The amount must Lance Industries pay into the fund each period is $2,054.49

Define Sinking Funds

A fund set aside to cover a certain future expense is known as a sinking fund. The sinking fund can be thought of as an annuity if equal contributions are made on a regular basis; its value will rise until it is sufficient to pay the future expense.

Given,

Lance Industries borrowed = $130,000

Time = 18 years

Interest rate = 6%

The future value is,

FVₙ =PMT( (1+i/m)ⁿ - 1 ) / (i/m) )

PMT = payment fund semiannually.

i = 6% or 0.06

m = 2  (semiannually will be 2 times per year)

n = 18 * 2 = 36 periods

FV₃₆ = $130,000

Now, plug in the values in formula

FVₙ =PMT( (1+i/m)ⁿ - 1 ) / (i/m) )

130,000 = PMT ( (1 + 0.06/2)³⁶ - 1 ) / (0.06/2) )

130,000 = PMT ( (1.03)³⁶ - 1 ) / (0.03) )

PMT = 130,000 * ( 0.03 / (1.03)³⁶ - 1 ) )

        = $2,054.49

Hence, the amount must Lance Industries pay into the fund each period is $2,054.49.

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The distributive property of 25+45 is 25+45 = 5(5+9).

The distributive property of binary operations in mathematics generalizes the distributive law, which states that in elementary algebra, equality is always true.

For instance, in basic mathematics, one has to According to one, addition is distributed more evenly than multiplication.

This property states that multiplying the total of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.

Say you wish to multiply 5 by the product of 10 plus 3.

When two terms are similar, we often sum the two amounts before multiplying by 5. 5(10 + 3) = 5(13) = 65.

So, the distributive property of 25+45:

25+45 = 5(5+9)

Therefore, the distributive property of 25+45 is 25+45 = 5(5+9).

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1) To determine the surface area of a right cone, we must know the radius of the circular base and height of the cone.

2) To determine the surface area and volume of a sphere, we must know the radius of the sphere.

3) The volume of the sphere with a great circle of radius 7 cm is 1436.75 cubic centimeters

4) The area of a regular pentagon with radius 5, and each side of length 6 is 45 square units

To determine the surface area of a right cone:

The formula for the surface area of a right cone is,

A = πr[r + √(h² + r²)]

this means, to determine the surface area of a right cone, we must know the radius of the circular base and height of the cone.

To find the surface area and volume of a sphere:

The formula for the surface area of sphere is,

A = 4πr²

and the formula for the volume of sphere is,

V = 4/3 πr³

This means, to determine the surface area and volume of a sphere, we must know the radius of the sphere.

For a sphere with radius r = 7 cm the volume would be,

V = 4/3 * π * 7³

V = 1436.75 cubic centimeters

Now we need to find the area of a regular pentagon with radius 5, and each side of length 6.

The formula for the area of a regular pentagon is:

A = 1/2 × P × a

where 'p' is the perimeter of the pentagon and 'a' is the apothem of a pentagon.

The perimeter of the pentagon is:

P = 5 * side lengths

P = 5 * 6

P = 30 units

We know that an apothem of a regular polygon is a radius of the inscribed circle.

From given dimensions, a = 5 units

so, the area of a regular pentagon would be,

A = 1/2 × 30 × 5

A = 45 square units

Therefore, the area of a regular pentagon is 45 square units

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Answer:

In step 2 you would multiply both sides by 2 not divide by 2

Step-by-step explanation:

1/2w=30

 *2      *2

w=60

Answer:

The mistake is between Step 1 and Step 2.

Step-by-step explanation:

Leon is isolating the variable, w. In this case, he should have multiplied 2 to both sides of the equation to isolate the variable, w.

[tex]2 * (\frac{1}{2})w = 3 * 2\\ w = 3 * 2\\w = 6[/tex]

For the whole question

1) Add 12 to both sides of the equation:

[tex]\frac{1}{2} w - 12 = 18\\\frac{1}{2} w - 12 (+12) = 18 (+12)\\\frac{1}{2} w = 18 + 12\\\frac{1}{2} w = 30[/tex]

2) Multiply 2 to both sides of the equation:

[tex](2 *) (\frac{1}{2}w) = 30 (* 2)\\w = 30 * 2\\w = 60[/tex]

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The maximum height will be 141.5 feet.

What is quadratic equation

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.

The function will be f(t) = -16t² + 60t + 20

at ground f(t) = 0

So, 4t² - 15t - 5 = 0

t = (15+√305) / 8

t = 4.05sec.

The maximum height will be in 2.025 sec = 60 * 2.025 = 121.5 feet. + 20feet.

Hence the maximum height will be 141.5 feet.

Hence the value of k is 0.33.

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Answer:

17 $

Step-by-step explanation:

let y  - total cost of a gift

x - price of the gift

the total cost of the gift is its price + 14% delivery, which can be written as:

y = x + 14% * x = x + 0.14x = 1.14 x

by making the substitution with the data from the task

19.38 = 1.14*x

x = 19.38/1.14 = 17

The sphere with 16 inches diameter would hold 2144in^3 of air.

A sphere is a three-dimensional object that is round in shape. The sphere is defined in three axes, i.e., x-axis, y-axis and z-axis. This is the main difference between circle and sphere. A sphere does not have any edges or vertices, like other 3D shapes.

The points on the surface of the sphere are equidistant from the center. Hence, the distance between the center and the surface of the sphere are equal at any point.

The radius of spere = diameter / 2 which is 16/2

radius = 8 inches.

The volume(V) of a sphere is 4/3 πr^3

where r = radius of sphere,  π = constant = 3.14

V = 4/3 x 3.14 x (8)^3

V = 2144 in^3

In conclusion the sphere can hold 2144in^3 of air

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The equivalent measure of the angle when converted from radians to degrees is 128.57 degrees

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

Angle = \large \frac{5\pi}{7}radians to degrees.

This angle can be properly expressed

So, we have the following representation

Angle = 5π/7 radians

Also, the angle can be further expressed

So, we have the following representation

Angle = 5/7 π radians

As a general rule of angle conversion, we have

π radians = 180 degrees

Substitute the known values in the above equation, so, we have the following representation

Angle = 5/7 * 180 degrees

Evaluate the products

Angle = 128.57 degrees

Hence, the measure of the angle in degrees is 128.57 degrees

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Answer the angle when converted from radians to degrees is 128.57 degrees

Angle = 5π/7 radians

Angle = 5/7 π radians

π radians = 180 degrees

Angle = 5/7 * 180 degrees

Evaluate the products

Angle = 128.57 degrees

Answer: Unimodal and Right Skewed

Explanation:

When almost all the data is falls to the right of the graph's peak is known as a right skewed histogram.

A left skewed histogram would have almost all the data falling to the left of the graph's peak.

A histogram is described as uniform if every value in a dataset occurs roughly the same number of times. There are usually no peaks and the data set looks similar to a rectangle.

A Symmetric histogram would be symmetrical, both side of the peak of the graph are mirrored/completely identical.

I hope this helps to better understand :)

The fraction 2/5 added by 3/4 will be 1 3/20.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers. On the other hand, a fraction appears in the numerator or the denominator of a complex fraction.

The fraction will be illustrated thus:

=✓2/5 + 3/4

= 8/20 + 15/20

= 23/20

= 1 3/20

The value is 1 3/20.

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The Orthogonal projection of A on Z i.e subspace formed by X and Y is A cos (90- θ) = A sin (θ)

What is Orthogonal projection ?

A parallel ray projection of a figure. Tangencies are kept in such a projection. Parallel lines converge on parallel lines. The length-to-area ratio of parallel segments is retained, as is the length-to-area ratio. Any triangle can be positioned so that its shadow is equilateral under an orthogonal projection.

Let's say we have a vector. A and vector X and Y

Consider the vector-formed subspace. X and Y is Z = [tex]\alpha[/tex]X + [tex]\beta[/tex]Y perpendicular to subspace vector Z is X * Y

Angle between X * Y and A can be found by cosθ = (X * Y).A/|(X * Y)| * |A|

Now the angle between Z and A is 90 - θ

So the projection of A on Z i.e subspace formed by X and Y is A cos (90 - θ) = A sin (θ)

Finally, in order to discover the projection, we must determine the angle between the subspace and the vector whose projection we must locate

Use MATLAB Code for locating a projection on vector a on the subspace defined by vectors x and y. so that it will be more easy to understand

% cross product of x and y vector

xCrossY = cross(x, y);

% angle between xCrossY and vector 'a'

angle_radian = dot(xCrossY,a)/(norm(xCrossY)*norm(a));

% angle in degrees

angle_deg = rad2deg(angle_radian);

% projection of a on subspace made by x and y is asin(angle_deg)

projection = norm(a)*sin(angle_deg);

A cos (90- ) = A sin () is the orthogonal projection of A on Z, i.e. the subspace created by X and Y.

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The difference between living with family and on campus is 27299 and she will be able to save an average of $4549.9 every month.

To determine how much she will save, we have to find the total cost of living with parents or relative and the cost of living on/off campus and then divide it by the total number of months which is six and the find their difference.

The total cost of living with parents or relative for 6 months is = 900 + 4158 + 2259 + 675 + 11205 + 19197 + 36587 + 44579 = 119560

The cost of living on or off campus for 6 months = 900 + 12798 + 2259 + 468 + 11205 + 27630 + 36587 + 55012 = 146859

The average cost of living with relative or family for 6 months = 119560 / 6 = 19926.6

The average cost of living on or off campus for 6 months = 146859 / 6 = 24476.5

The difference is = 24476.5 - 19926.6 = 4549.9

Amy will save approximately $4549.9 monthly

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The expected mean of the sampling distribution and the standard deviation of the sampling distribution is $29.50.

Standard deviation

In statistics, standard deviation refers  the square root of variance by determining each data point's deviation relative to the mean.

Given,

Here we know that a statistics student is trying to decide whether she should take a gamble and play bingo. And the average bingo player earns $9 per game, distributed normally, with a population standard deviation of $8.

And we need to find if a sample of 25 bingo players are selected at random from the population, select the expected mean of the sampling distribution and the standard deviation of the sampling distribution below.

0; = $0.32 0; = $8 O = $1.60 Mi = $9 Hi = $1.80

Here the standard deviation of the sample distribution is calculated as,

=> σₓ = √1.80 = 1.34

Here we know that the distribution is normal then the mean of the sampling distribution is equal to the mean of the population, based on this theory, the resulting value is $29.50.

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(a) SST = 1772,   SSR= 1420.79,  SSE=353.05

(b) Coefficient of determination is 0.8018.

(c) Sample correlation coefficient is 0.8954.

The average score can be obtained as

y = ∑y / n

  = 330 / 6

y = 55

The least-square regression line is given as:

y' = 23.221 + 0.318x

Using the above stated regression equation; the predicted values of overall score can be obtained for the given values of price.

y' = 23.321 + 0.318(170) = 77.281

(a) The formula for computing SST is given as:

SST = ∑ (yi - y)²

SST = 1772

Hence the value of SST is 1772.

The formula for computing SSR is given as:

SSR = ∑ (yi' - y)²

SSR = 1420.79

Hence the value of SSR is 1420.79.

The formula for computing SSE is given as:

SSE = ∑(yi - y')²

SSE = 353.05

(b) The coefficient of determination is given by the formula:

R² = [tex]\frac{SSR}{SST}[/tex]

   = [tex]\frac{1420.79}{1772}[/tex]

R²= 0.8954

Hence the value of the coefficient of determination is 0.8018.

(c) The correlation coefficient is computed as:

r = [tex]\sqrt{R^{2} }[/tex]

 = [tex]\sqrt{0.8018}[/tex]

r = 0.8954

Hence the value of the correlation coefficient is 0.8954.

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