What is the area of the base, B,
of the prism?
B = Ft
4 ft
6 ft
3 ft

Answer:57

Step-by-step explanation:

y = 5x+1. ____equ(1)

4x + y = 10. ____equ (2)

substituting equ(1) into equ(2)

4x + y = 10

4x + 5x + 1 = 10

9x = 10 -1

9x = 9

x = 1

x = 1 into equ (1)

y = 5x + 1

y = (5 ×1) + 1

y = 5 + 1

y = 6

I hope this will help.

have a nice day dear :)

The equation for the situation is f(x) = 40(1+1)^x, which simplifies to f(x) = 40(2)^x.

Exponential growth is a process where a quantity increases at a constant percentage rate per unit of time. It can be represented by:

The equation f(x) = a(1+r)^x,

where "a" is the initial value, "r" is the growth rate, and "x" is the number of time periods.

This is exponential growth because the growth rate is given as 100%, which means the value is doubling with each step.

The formula for exponential growth is f(x) = a(1+r)^x,

where

r is the growth rate expressed as a decimal.

In this case, r = 1, since the growth rate is 100%, or 1.00 as a decimal.

So, the equation for the situation is f(x) = 40(1+1)^x, which simplifies to f(x) = 40(2)^x.

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Answer:

you go queen

Step-by-step explanation:

yas

Answer: Let x be the measure of the angle in degrees. Then, the measure of its supplementary angle is 180 - x degrees.

We are told that the angle measures 153.4 degrees more than its supplementary angle. Using this information, we can set up an equation:

x = (180 - x) + 153.4

Simplifying this equation, we get:

2x = 180 + 153.4

2x = 333.4

x = 166.7

Therefore, the angle measures 166.7 degrees, and its supplementary angle measures:

180 - x = 180 - 166.7 = 13.3 degrees

We can check that the angle and its supplementary angle add up to 180 degrees:

166.7 + 13.3 = 180

So our solution is correct.

Step-by-step explanation:

This is not a fair game since P + Q is greater than 1. To make game fair, we can modify conditions for scoring points. One possible modification is to give Pietro a point if all three toss results match (HHH or TTT).

This gives Pietro an additional outcome to score a point, which makes the game fair. Another modification is to give Eva a point if any two toss results match (H-T-H, T-H-T, T-T-H, H-T-T, HHT, TTH, THT, HTT). This also makes the game fair since both players have 3 possible outcomes to score a point.

There are 2³ = 8 possible outcomes when a coin is tossed three times. We can list them as follows:

HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

Let E be the event that no two consecutive toss results match and let P(E) be the probability of event E. We can count the number of outcomes that satisfy E as follows:

HTH

HTT

THT

TTH

THT

TTT

Therefore, there are 6 outcomes that satisfy E and P(E) = 6/8 = 0.75.

Let P be the probability that Pietro scores a point and let Q be the probability that Eva scores a point. We can count the number of outcomes that satisfy each player's condition as follows:

Pietro: HHT, HTH, THH (3 outcomes)

Eva: H-T-H, T-H-T, T-T-H, H-T-T (4 outcomes)

Therefore, P = 3/8 and Q = 4/8 = 1/2.

The game is not fair since P+Q is greater than 1. This means that the players have a greater than 50% chance of scoring a point on each turn, so the first player to reach 10 points will have an advantage.

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Reason:

The graph starts off very steep at x = 0. As x increases, the steepness goes down. Meaning the tangent lines become more shallow as you move to the right.

This tells us that the person learning the new task learns a lot at first. Then as time wears on, they learn less and less, until leveling off at some plateau.

If your teacher has covered derivatives, then you'll find the derivative of y = 1-e^(-0.28x) is dy/dx = 0.28e^(-0.28x)

Graph this derivative function using something like GeoGebra. Notice how the derivative curve is always decreasing. Therefore, x = 0 is when the derivative is largest, which points to the original function having the steepest increase (aka largest instantaneous rate of change).

See the graph below.

The value of x is 47 from the given figure.

An angle is formed when two straight lines or rays meet at a common endpoint.

The sum of angles is 180 degrees from the figure.

x-2+x-2+x-2+x-2=180

Add the like terms

4x-8=180

Add 8 on both sides

4x=188

Divide both sides by 4

x=188/4

x=47

Hence, the value of x is 47 from the given figure.

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Answer:

To find the area of the shaded segment of the circle, we need to first find the area of the sector formed by the 60 degrees angle, and then subtract the area of the triangle formed by the radii and the chord.

The formula for the area of a sector of a circle is:

A_sector = (θ/360) x πr^2

where θ is the central angle in degrees, and r is the radius.

Substituting the given values, we get:

A_sector = (60/360) x π x 18^2

A_sector = 113.04 cm^2

Next, we need to find the area of the triangle formed by the radii and the chord. To do this, we need to first find the length of the chord using the formula:

c = 2r sin(θ/2)

where θ is the central angle in radians.

Converting the given 60 degrees angle to radians, we get:

θ = 60 x (π/180) = π/3 radians

Substituting the values, we get:

c = 2 x 18 x sin(π/6)

c = 18√3 cm

Now, we can find the area of the triangle using the formula:

A_triangle = (1/2) x base x height

where the base is the chord length c, and the height is half the length of the chord, which is:

h = r - r cos(θ/2)

Substituting the values, we get:

h = 18 - 18 cos(π/6)

h = 18 - 9√3 cm

Therefore, the area of the triangle is:

A_triangle = (1/2) x 18√3 x (18 - 9√3)

A_triangle = 243 cm^2

Finally, the area of the shaded segment is the difference between the area of the sector and the area of the triangle:

A_shaded = A_sector - A_triangle

A_shaded = 113.04 - 243

A_shaded = -129.96

However, the result is negative because the triangle is larger than the sector in this case. Therefore, there is no shaded area in this situation.

Step-by-step explanation:

Answer:

Where is the picture???

Step-by-step explanation:

The amount of water left in the cubical tank would be; 3040000 mm³

A cube is a three-dimensional representation of a square. it has 6 faces 2 on the bottom and top, 4 on the sides faces.

We know that Volume of a cube = a³ ; a = size of edge

Volume of cubical tank = 12³

= 1728 cm³

Now, Half filled cube = 1728 / 2

= 864 cm³

Volume is f rectangular tank :

V = length x width x height

V = 10 * 8 * 7 = 560 cm³

Volume of water left in cubical tank will be;

(864 - 560) = 304cm³

1cm³ = 1000mm³

Therefore,

304cm³ = 304 x 1000 = 3040000mm³

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Given, P(X=15) and using the probability mass function we get

(27C15)(0.546)¹⁵(1-0.546)²⁷⁻¹⁵=0.1523

What is Probability?

Probability is simply how likely something is to happen. The occurrence of an event will be in the range of 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

What is the Probability mass function?

The probability distribution of a discrete random variable, or probability mass function, gives the potential values and the corresponding probabilities. 

According to the problem,

Let X be the random variable of interest, on this case we know that:

 X∼Binom (n=27,p=0.546)

The probability mass function for the Binomial distribution is given as:

                              P(X)=(nCx) (pˣ) (1-p)ⁿ⁻ˣ,

                              here,

                                      (nCx) =  n !/(n-x)!( x)!

For finding Probability and by using the mass function :

P(X=15) = (27C15)(0.546)¹⁵(1-0.546)²⁷⁻¹⁵ = 0.1523

The value of p will be 0.546

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Current yield = 4.51%

The price of a bond is equal to the future cash flows' present value, discounted at the appropriate discount rate—the yield to maturity.

The price of a bond is the amount that investors are willing to spend on an existing bond. Bond prices are stated as a percentage of face (par) value in the online offering table and statements you get.

Current Yield=Annual Cash Inflows/Market Price

Annual cash flow is 4.75% of 100 = $4.75

Market Price of Bond = $105.25

Current Yield = 4.75/105.25

=4.51%

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1) The amount is 307 g

2) The rate of change is 0.088

3) The time taken  is 8 days

Exponential decay is a mathematical process in which the value of a quantity decreases over time or space at a rate proportional to its current value.

We know that the exponential decay can be given by;

N =No[tex]e^-0.088t[/tex]

After 3 days;

N =400[tex]e^-0.088(3)[/tex]

N = 307 g

The rate of change after 3 days;

307 = 400[tex]e^-3r[/tex]

307/400 = [tex]e^-3r[/tex]

0.7675 =[tex]e^-3r[/tex]

-3r = ln(0.7675)

r = ln(0.7675)/-3

r = 0.088

1/2(400) = 400[tex]e^-0.088t[/tex]

200/400 = [tex]e^-0.088t[/tex]

1/2 =[tex]e^-0.088t[/tex]

t = ln0.5/-0.088

t = 8 days

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The value of the function f(-10), f(2) and f(3) is 20201, 17 and 142 respectively.

According to the remainder theorem, when a polynomial p(x) is divided by a linear polynomial q(x) whose zero is x = a, the remainder is given by r = p(a). The remainder theorem enables us to calculate the remainder of the division of any polynomial by a linear polynomial, without actually carrying out the steps of the long division.

Given that, f(x)=2x⁴+x²-10x+1.

Here, f(-10)

Substitute x=-10 in the given function, we get

f(-10)= 2(-10)⁴+(-10)²-10(-10)+1

= 20000+100+100+1

= 20201

Substitute x=2 in the given function, we get

f(2)= 2(2)⁴+(2)²-10(2)+1

= 32+4-20+1

= 17

Substitute x=3 in the given function, we get

f(3)= 2(3)⁴+(3)²-10(3)+1

= 162+9-30+1

= 142

Therefore, the value of the function for x=-10 is 20201.

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In response to the aforementioned query, we may say that The loan's interest future value is $8640 as a result.

By dividing the principal by the interest rate, the passage of time, and other factors, simple interest is determined. Simple return equals principle plus interest plus hours is the formula used in marketing. The easiest way to compute interest is by using this method. The most typical method for calculating interest is as a portion of the principle amount. For example, if he borrows $100 from a buddy and agrees to pay back the loan at 5% interest, he will only pay his share of the 100% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and you must charge interest when you lend it. Typically, interest is determined as an annual percentage of the loan total. The loan's interest is the name given to this percentage.

Interest is calculated as follows: Principal x Interest Rate x Time

where Principle represents the loan amount, Rate is the interest rate, and Time represents the loan's term in years. We may enter the figures since the loan is for 9 months, or 0.75 years:

Interest: $540 ($8000 x 0.09 x 0.75);

As a result, the student is required to pay interest of $540.

b. The following formula can be used to determine the loan's future value:

Principle x (1 + Rate x Time) = Future Value

where the same values for Principle, Rate, and Time apply as in section a. When we enter the values, we obtain:

Future Value = $8000 x (1 + 0.09 x 0.75), which is $8640.

The loan's future value is $8640 as a result.

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Answer:

To find the average speed in miles per hour, we need to divide the total distance by the time taken:

Average speed = Total distance / Time taken

Average speed = 234 miles / 6 hours

Average speed = 39 miles per hour

Therefore, Nathan's average speed was 39 miles per hour.

Step-by-step explanation:

Answer:

Nathan drove an average of 39mph

Step-by-step explanation:

r=d/t

rate=234/6

234+6=240

240/6=40

Because we added a six, we need to subtract one:

40-1=39

Nathan drove an average of 39mph

The center of this circle is (3,0) and its radius is 3.

It is required to find the center and radius of the circle.

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. The perimeter around the circle is known as the circumference.

here, we have,

Given that: (X-3)^2+y^2=9

The equation of a circle in standard form is:

(x -a)² + (y-b)² = r²

The x-coordinate of the center is a the y-coordinate of the center is b

, and r is the radius.

In this case,

a=3

b=0

and

r=3.

Hence, the center of this circle is (3,0) and its radius is 3.

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In this case, the equation is 6/2 = x/3, so x = 6/2 * 3/1 = 9/2.Therefore, the two possible values of x are 11/6 and 9/2.

Corresponding angles are angles that have the same relative position when two parallel lines are cut by a transversal line. When two parallel lines are cut by a transversal, corresponding angles are the same size. Corresponding angles are also known as vertically opposite angles.

In order to determine the value of x, we must assume that the two triangles in the diagram are similar. This means that the corresponding angles are equal and the corresponding sides are proportional. We will also assume that the angles of the triangle are in degrees and the sides are in the same unit of length.

Using the properties of similar triangles, we can calculate the value of x. We start by looking at the given angles, which are both 60°. Since the sides are proportional, we can set up a proportion equation between the two sides. We will use the side lengths given in the diagram to solve the proportion equation.

The proportion equation is: 11/3 = x/2.

Solving this equation for x, we get x = 11/3 * 2/1, which simplifies to x = 11/6.

We can also use the same equation to solve for x using the second given side length, which is 6. In this case, the equation is 6/2 = x/3, so x = 6/2 * 3/1 = 9/2.

Therefore, the two possible values of x are 11/6 and 9/2.

* The assumptions that I made in my working are that the two triangles in the diagram are similar and that the angles are measured in degrees and the sides are measured in the same unit of length.

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Answer:

C. Simple interest involves interest calculated only on the principal. Compound interest is interest computed on the original principal as well as on any accumulated interest.

Step-by-step explanation:

Answer:

Mean = 325.6

Range = 80

Median = 49

Step-by-step explanation:

Mean= All numbers added dividend by 10 (amount of digits)

Range= Highest number minus lowest number

Median= Middle number (process of cancellation)

Answer:

x=9

Step-by-step explanation:

Equation of best fit line on scatter plot is y = 30x + 40

Correct option is D.

A straight line is an infinite one-dimensional shape with no width. An infinite combination of points connected on either side of the point. A straight line has no curves. It can be horizontal, vertical, or slanted. An angle drawn between any two points on a straight line is always 180 degrees.

Given,

Scatter plot of the data of studying time of students

By the graph, point on the line are (0, 40) and (2,70)

Equation of the line

y - y₁ = ((y₂-y₁)/(x₂-x₁))(x-x₁)

y - 40 = ((70-40)/(2-1))(x-0)

y - 40 = (30/1)x

y - 40 = 30x

y = 30x + 40

Hence, y = 30x + 40 is the equation of the best fit line in scatter plot.

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The surface area of the pyramid, given the dimensions of the pyramid can be found to be 1, 188 m ²

The surface area of a pyramid can be found by the formula :

= Base area of pyramid + 12 x ( Perimeter of the base x Slant height )

The surface area of this pyramid is :

= ( 6 x 6 ) + 12 x ( ( 6 + 6 + 6 + 6 ) x 4 )

= 36 + 12 x ( 24 x 4 )

= 36 + 12 x 96

= 1, 188 m ²

In conclusion, the surface area of the pyramid is 1, 188 m ².

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The sum of the first 30 consecutive whole numbers is 465.

What are consecutive numbers?

Consecutive numbers are numbers that follow each other in order without interruption, with a difference of 1 between each two adjacent numbers. For example, 3, 4, 5, 6, and 7 are consecutive numbers.

The formula n x (n+1)/2 is used to find the sum of the first n consecutive whole numbers because it provides a quick and efficient way to calculate the sum without having to add all the numbers individually.

To understand why the formula works, consider the sum of the first n numbers: 1 + 2 + 3 + ... + (n-1) + n. We can rewrite this sum in reverse order, starting with n and working down to 1: n + (n-1) + (n-2) + ... + 2 + 1.

If we add these two expressions together, we get:

(1 + n) + (2 + n-1) + (3 + n-2) + ... + (n-1 + 2) + (n + 1)

Notice that each pair of terms in parentheses adds up to n+1. There are n/2 pairs of terms, so the sum of the first n numbers is:

n/2 x (n+1)

Simplifying this expression gives the formula:

n x (n+1)/2

So to find the sum of the first 30 consecutive whole numbers, we can substitute n=30 into the formula:

30 x (30+1)/2 = 15 x 31 = 465

Therefore, the sum of the first 30 consecutive whole numbers is 465.

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The solution to the equation is 7.8075 or -12.8075

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

We have the Quadratic Equation: 0.02 x² + 0.1 x - 2 = 0

2x² + 10x - 200 = 0

Using Discriminant Method

D = √b² - 4ac

D = √10² - 4(2)(-200)

D = √100 + 1600

D = √1700

D = 41.23

So, x = -b± D/2a

x = -10 ± 41.23 / 4

x= -10 + 41.23/4  or x= -10 -41.23 /4

x= 31.23/4 or x= -51.23/4

x= 7.8075 or x = -12.8075

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Answer:

16°

Step-by-step explanation:

10p+20=180

10p=120

p=16

Answer:

-21/5

Step-by-step explanation:

The given series is:-7(3/8)^1 - 7(3/8)^2 - 7(3/8)^3 - ...

We can see that this is a geometric series with first term a = -7(3/8)^1 = -21/8 and common ratio r = 3/8.

The sum of an infinite geometric series with first term a and common ratio r (where |r| < 1) is given by:

sum = a/(1-r)

Substituting the values for a and r, we get:sum = (-21/8)/(1-3/8) = (-21/8)/(5/8) = -21/5Therefore, the sum of the given series is -21/5.

The required correct match for the given problem has been shown below.

A number system is described as a process of composing to designate digits. It is the mathematical inscription for describing the numbers of a given set by using numbers or other symbols in a uniform method. It delivers a special presentation of every digit and describes the arithmetic structure.

Here,
3 2/7 = 23/7 = 3.2                      between 3 and 4
-3 7/8 = -31/8 = -3.875               between -3 and -4

-3/8 = -0.375                             between 0 and -1
-0.9                                          between 0 and -1
1/7                                             between 0 and 1.

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With given linear equations of lines, the straight lines AB and CD are not  parallel.

What is a linear equation?

In mathematics, a linear equation is an equation that can be written in the form:

y = mx + b

where "y" and "x" are variables, "m" is the slope of the line, and "b" is the y-intercept, which is the point where the line crosses the y-axis.

A linear equation represents a straight line on a graph and describes a linear relationship between two variables. The slope "m" determines how steep the line is, while the y-intercept "b" determines where the line crosses the y-axis.

Now,

To determine if the lines AB and CD are parallel, we need to compare their slopes. If the slopes are equal, then the lines are parallel.

The slope of a line is given by the coefficient of "x" in its equation when it is written in the form of y = mx + b, where "m" is the slope.

For line AB, we have:

OA = 3x + 7y

OB = 5x + 6y

Subtracting the equation for OA from the equation for OB, we get:

OB - OA = (5x + 6y) - (3x + 7y)

= 2x - y

So the slope of line AB is:

m_AB = (change in y) / (change in x) = -2 / 1 = -2

Now, for line CD, we have:

CD = 6x - 3y

So the slope of line CD is:

m_CD = (change in y) / (change in x) = -3 / 6 = -1/2

Since the slopes of line AB and line CD are not equal, i.e., m_AB ≠ m_CD, we can conclude that the lines are not parallel to each other.

Therefore, the geometrical relationship between the straight lines AB and CD is that they are not parallel to each other.

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