An archer fires two arrows into a raised target, as represented in the diagram below. About how much greater of an angle did the archer need to use in order for the second arrow to land 7 feet higher than the first arrow?.

Answer:

d.y=x/3+4

Step-by-step explanation:

we have

slope=(y-b)÷(x-a)

1/3=(y-2)÷(x--6)

(x+6)=3(y-2)

x+6=3y-6

x+6+6=3y

(x+12)÷3=y

y=x/3+4

Answer:

C) 3(13) - 3(5)

Step-by-step explanation:

Using the distributive property of multiplication, you will distribute the outer term (3 in this case) with all terms within the parentheses (13 and 5 respectively:

Solve:

3(13 - 5)

Multiply 3 with 13, and 3 with -5:

\(3(13 - 5)\\(3 * 13) + (3 * -5)\\(3 * 13) - (3 * 5)\)

C) 3(13) - 3(5) is your answer.

~

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Answer:

Step-by-step explanation:

2.8 × (-11) - 3 × 8 =

-30.8 - 24 =

-54.8 ( in fraction -274/5)

Answer:

259.5

Step-by-step explanation:

8.1*12=97.2
Area of trapiezium = 1/2(b+a)h
(2.8+8.1)=10.9
10.9*3/2=16.35
16.35*2=32.7
2.8*12=33.6
33.6+32.7+97.2=163.5
4*12*2=96
163.5+96=259.5

Answer: 2304

Step-by-step explanation: 18 x 16 x 8

The length of the radius of the circle is 44cm.

This problem bothers on the mensuration of flat shapes, a circular shape.

Given data

Circumference of circle C= 88πcm

Radius of circle r=?

To find the length of the radius of the circle.

To solve for the radius let us apply the formula for the circumference of a circle

C=2πr

Substituting our given data

88π=2πr

Making r subject of formula we have

r= 88π/2π

r= 44cm

Hence, The length of the radius of the circle is 44cm.

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The percentage of patients with type-B blood that are 50 years old or younger is calculated as follows:

P = number of patients with type B blood that are 50 years or younger / number of patients with type B blood x 100%

Two parameters are used to calculate a percentage, as follows:

The proportion is given by the number of desired outcomes divided by the number of total outcomes, while the percentage is the proportion multiplied by 100%.

Hence the rule is given as follows:

P = a/b x 100%.

The problem is incomplete and the table could not be found on the internet, hence the general procedure to obtain the percentage is presented.

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Formula :

Perimeter of Trapezium = sum of all sides

AB + BD + EC + BC [Refer to the attachment]

AB = 14 cm

EC = 6 cm

BD = 8 cm

Let's find the length of side BC

In right angle triangle , BDC

EC = 14 cm

AB = 6 cm

DC = EC - AB

= 14 - 6

= 8 cm

According to Pythagoras theorem,

BC² = DC² + BD²

BC² = 8² + 8²

BC² = 64 + 64

BC = √128

Perimeter = sum of all sides

= 14 + 6 + 8 +11.31

= 20 + 8 + 11.31

= 28 + 11.31

Given:

Number of green peas = 475

Number of yellow peas = 193

Let's find the 94% confidence interval to estimate the percentage of yellow peas.

Where:

Total number of peas = 475 + 193 = 668

For the sample proportion, we have:

For a 94% confidence interval, the significance level will be:

1 - 0.94 = 0.06

For the critical value, using the z-table, we have:

Now, to find the 94% confidence interval, apply the formula::

Where:

To find the margin of error E, we have:

Thus, we have:

Hence the confidence interval will be:

Lower limit = 0.2559 ==> 25.59%

Upper limit = 0.3219 ==> 32.19 %

The confidence interval does not contain 0.25, hence we can say that the true results contradicts the expectations.

ANSWER:

The confidence interval does not contain the expectation of 25%, hence, the true results contradicts the expectation.

Answer:

A

Have a great day!

Answer:

58.75

Step-by-step explanation:

You add all the numbers and get 470 then divide it by the amount of numbers there which is 8 so 470 divided by 8 is 58.75

The approximate volume of the sphere is 6.01 ft³.

A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.

The volume of a sphere is expressed as:

Volume =  (4/3)πr³

Where r is the radius of the sphere and π is the mathematical constant pi (approximately equal to 3.14).

Given that the surface area of the sphere is 16 square feet.

First, we determine the radius r:

Surface area = 4πr²

Hence

16 = 4πr²

Dividing both sides by 4π, we get:

r² = 16/4πr

r = √( 16/4πr )

r = 1.128 ft

Plugging in the value of r that we just found, we get:

Volume =  (4/3)πr³

Volume =  (4/3) × 3.14 × (1.128 ft)³

Volume =  6.01 ft³

Therefore, teh volume is 6.01 ft³.

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Answer:

x = 4, x = 10

Step-by-step explanation:

(x - 7)²  - 5 = 4 ( add 5 to both sides )

(x - 7)² = 9 ( take square root of both sides )

x - 7 = ± \(\sqrt{9}\) = ± 3 ( add 7 to both sides )

x = 7 ± 3

Then

x = 7 - 3 = 4

x = 7 + 3 = 10

The best diagram to use to display data dispersion is a box plot. A box plot is a diagram that shows how a dataset is distributed and helps to identify any outliers.

The diagram that is best at displaying data dispersion is a box plot. Here's the main answer:When there is a need to compare the distribution of data, a box plot is often the best method.

A box plot is a diagram that shows how a dataset is distributed. It shows how data is spread out and helps to identify any outliers. It is most effective for comparing data sets that have a large number of data points and when the data is not normal (not evenly distributed).

A box plot is a great way to summarize large amounts of data and it is also very easy to read and interpret. It shows a number of statistical values, including the median (the middle value of the data set), the quartiles (the values that divide the data set into four equal parts) and the range (the difference between the maximum and minimum values).

Additionally, it can identify any outliers in the data, which are values that are significantly different from the rest of the data.A box plot is created by drawing a rectangle between the first and third quartiles (the middle 50% of the data) with a line drawn inside it to show the median.

Lines are then drawn from the edges of the rectangle to the minimum and maximum values. Any outliers are marked with a point outside of the rectangle.

The box plot is a great way to compare data sets and to visualize the dispersion of the data

The best diagram to use to display data dispersion is a box plot. A box plot is a diagram that shows how a dataset is distributed and helps to identify any outliers. It is most effective for comparing data sets that have a large number of data points and when the data is not normal. A box plot is created by drawing a rectangle between the first and third quartiles with a line drawn inside it to show the median.

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Answer:

I believe the answer 16

Step-by-step explanation:

All you have to do is count.

Answer:

(4,8)

Step-by-step explanation:

The solution is where the two lines intersect.

The graphs intersect at x=4 and y = 8

(4,8)

Answer:    B: (4,8)

Step-by-step explanation:

y = 3x +2           you will go to positive to on the graph and go up 3 and to the right two because it is positive until you can't no more.

y = -6x + 32

you will go to +32 on the graph and then go down six and since there is no number under -6 you will replace it with one so it will look like this -6x/1

Answer:

x=-14

Y=40

Perimeter=(4×14+3)×4=236

Step-by-step explanation:

as long as it's a square then

\(3x + 17 = 4x + 3 \\ 4 x - 3x = 3 - 17 \\ x = - 14 \\ \\ any \: angle \: in \: the \: square \: equal \: 90degrees \\ then \\ 5x + 4y = 90 \: \: when \: x = -14 \\ 4y = 5 \times 14 + 90 \\ 4y = 16 \\ y = 40\)

\(perimeter =( 4 \times 14 + 3)\times 4 = 236\)

X = 14

Y = 5

The perimeter of the square = 236

It's square so

3x + 17 = 4x + 3

3x + 17 - 4x - 3 = 0

-x + 14 = 0

X = 14

And

5x + 4y = 90, x = 14

5(14) + 4y = 90

70 + 4y = 90

4y = 20

Y = 5

The perimeter of a square is the total length of all the sides of the square, length = 59

The perimeter of the square = 4 × 59 = 236

The values of the sides are;

41. x = 18√3. Option D

42. x = 6√3. Option A

Using the different trigonometric identities, we have;

41. Using the tangent identity, we have;

tan 60 = 9√2/y

cross multiply the values

y =9√2 ×√3

y = 9√6

Using the sine identity;

sin 45 = y/x

1/√2 = 9√6/x

cross multiply the values, we have;

x = 9√2 ×√3 ×√2

x = 18√3

42. Using the cosine identity

cos 60 = 3√3 /x

cross multiply, we have;

x = 6√3

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Point B shares its coordinates with the given midpoint P, while point A is found using the midpoint formula with the given midpoint M. The coordinates of A and B are (2, 5) and (4, -1) respectively.

To find the coordinates of points A and B, we can use the given information about the slope and midpoint.

First, let's find the coordinates of point B. We know that point B shares its coordinates with the midpoint P(4, -1) of the perpendicular segment. So, B(4, -1).

Next, let's find the coordinates of point A. We have the midpoint M(3, 2) of segment AB. We can use the midpoint formula to find the coordinates of A:

Midpoint formula:

(x₁ + x₂)/2 = x-coordinate of midpoint

(y₁ + y₂)/2 = y-coordinate of midpoint

Using the coordinates of M(3, 2) and B(4, -1), we can substitute them into the midpoint formula:

(x + 4)/2 = 3

(y + (-1))/2 = 2

Solving these equations, we can find the values of x and y:

(x + 4)/2 = 3

x + 4 = 6

x = 6 - 4

x = 2

(y - 1)/2 = 2

y - 1 = 4

y = 4 + 1

y = 5

Therefore, point A is located at A(2, 5), and point B is located at B(4, -1).

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Therefore , it means if an equation have 2 roots , it means it is a quadratic function .

A number's  root is that factor of the number that, when multiplied by itself, yields the original number. Specifically, squares and square roots are exponents. Think of the number nine. This can be expressed as  or as 3 x 3.

Here,

If an equation have 2 roots , it means it is a quadratic function

If D=0, a quadratic function has two roots that are equal.

D (discriminant) = 0

=>b24ac=0 is required for a polynomial function to have equal roots.

Therefore , it means if an equation have 2 roots , it means it is a quadratic function .

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The expression 3a^-5 - a + 3 + 4a^ - 5 is simplified to 7a⁻⁵ - a + 3

Algebraic expressions are described as expressions that are composed of variables, coefficients, constants, terms and factors.

They are also expressions that are composed of mathematical or arithmetic operations, which includes;

From the information given, we have the algebraic expression;

3a^-5 - a + 3 + 4a^ - 5

To simply the expression, we have to collect like terms, we get;

3a⁻⁵ + 4a⁻⁵ - a + 3

Now, add or subtract the like terms, we get;

7a⁻⁵ - a + 3

Hence, the expression is 7a⁻⁵ - a + 3

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The complete question:

Simply the expression;

3a^-5 - a + 3 + 4a^ - 5

This statement is False as the probability of intersection of two events is always less than the probability of union.

This assertion is untrue. Contrary to popular belief, the likelihood of two occurrences coming together is always higher than or on pair with the likelihood of them colliding.

The chance of two events A and B occurring together can be calculated using the following formula to see why:

According to this equation, the probability of A and B joining together is equal to the total of their individual probabilities less the likelihood of their colliding.

When we rewrite this calculation and focus only on the likelihood of the intersection, we obtain:

Now it is clear that the probability of the intersection is determined by subtracting the probability of their union from the sum of the probabilities of A and B.

P(A) and P(B) are both less than or equal to P(A B), since probabilities can never be negative. P(A + B) is therefore less than or equal to twice P(A + B) when they are added together. Thus, it follows:

This indicates that, contrary to what the original statement implied, the probability of the intersection is not greater than or equal to the probability of the union.

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Let A be a given matrix and b be a given vector. The QR factorization of the matrix A involves finding two matrices Q and R, where Q is orthogonal and R is upper-triangular.

To solve the least squares problem Ax = b using QR factorization, we first find the QR factorization of A:

A = QR

Next, we express the problem as:

QRx = b

Now, we can multiply both sides by the transpose of Q (since Q is orthogonal, its transpose is its inverse):

(Q^T)QRx = (Q^T)b

This simplifies to:

Rx = (Q^T)b

Since R is an upper-triangular matrix, we can use back-substitution to solve the system Rx = (Q^T)b and find the least squares solution.

1. Compute the matrix product (Q^T)b.
2. Use back-substitution to solve the upper-triangular system Rx = (Q^T)b, starting with the last equation and working upward.

The solution x obtained through this process is the least squares solution for Ax = b.

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If you  deposit $5,000 in a savings account and will earn 6. 5% simple interest over the first 10 years, then will earn $3,250 in interest over the 10-year period

Simple interest is a type of interest that is calculated only on the principal amount of an investment, and not on any interest that has been earned previously. It is typically expressed as a percentage of the principal amount and is applied over a fixed period of time.

To calculate the interest earned on the account over the 10-year period, we can use the formula for simple interest:

Interest = Principal x Rate x Time

Here, the principal is $5,000, the interest rate is 6.5%, and the time is 10 years.

Plugging in the values, we get:

Interest = $5,000 x 0.065 x 10

Interest = $3,250

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The given question is incomplete, the complete question is:

Big Money Bank has an offer for new customers: if you deposit $5,000 in a savings account, you will earn 6.5% simple interest over the first 10 years. How much interest will the account earn over this period?

The voltage across the capacitor at t=0+ is 4 volts (c \(V_c(t=0+)\) )is 4V). As time approaches infinity, the voltage across the capacitor becomes 6 volts ( \(V_c( t \to\infty)\) )is 6V). The current through the capacitor at t=0+ is -2 milliamperes ( \(i_c(t=0+)\) )is -2mA).

At t=0+, the switch opens and the circuit transitions into a new steady state. Initially, the capacitor is fully charged to 4V, so \(V_c(t=0+)\)is 4V. In the new steady state, the capacitor is connected to a series combination of R1, R2, R3, and R4. Since R1 and R2 are in series, their total resistance is 3kΩ. Thus, the time constant of the circuit is given by τ = (R1+R2+R3+R4)C = 6kΩ * 1μF = 6ms.

To determine\(V_c( t \to\infty)\) , we consider the steady state behavior of the circuit. In steady state, the capacitor acts as an open circuit. Therefore, the current flowing through R4 is zero, and the voltage drop across R4 is also zero. Thus, \(V_c( t \to\infty)\) is equal to the voltage drop across R3, which is 6V.

At t=0+, the current through R1, R2, and R3 will be the same as the current through the capacitor, ( \(i_c(t=0+)\) ). Applying Kirchhoff's current law at the node connecting R1, R2, R3, and the capacitor, we find that ( \(i_c(t=0+)\) )= I - (Vc(t=0+)/R1+R2+R3) = 4mA - (4V/3kΩ) = -2mA.

In summary, \(V_c(t=0+)\) is 4V, \(V_c( t \to\infty)\) is 6V, and \(i_c(t=0+)\)is -2mA.

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Answer:

The second one the amount of monthly sales

Step-by-step explanation:

The 2000 is the total

The complete question is

"Find the general solution of the given differential equation

y''-y=0, y1(t)=e^t , y2(t)=cosht

The function \(y(t)=e^t\)  is the solution of the given differential equation.

The function y(t)=cosht is the solution of given differential equation.

The function is a type of relation, or rule, that maps one input to specific single output.

Given;

\(y_1(t) = e^t\)

Given differential equations are,

y''-y = 0

 So that,  

\(y' (t) = e^t, y'' (t) = e^t\)

Substitute values in the given differential equation.

\(e^t -e^t=0\)

Therefore, the function \(y(t)=e^t\)  is the solution of the given differential equation.

Another function;

\(y(t)=cosht\)  

So that,  

\(y"(t)=sinht\\\\y"(t)=cosht\)

Hence, function y(t)=cosht is solution of given differential equation.

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The slope of the line that divides the region bounded by the parabola \(y=5x-3x^2\)and the x-axis into two regions with equal area is 5.

To find the slope of the line that divides the region into two equal areas, we need to determine the point of intersection between the parabola and the x-axis. Since the line passes through the origin, its equation will be y = mx, where m represents the slope.

Setting the equation of the parabola equal to zero, we find the x-values where the parabola intersects the x-axis. By solving the equation\(5x - 3x^2 = 0\), we get x = 0 and x = 5/3.

To divide the region into two equal areas, the line must pass through the midpoint between these x-values, which is x = 5/6. Plugging this value into the equation of the line, we have y = (5/6)m.

Since the areas on both sides of the line need to be equal, we can set up an equation using definite integrals. By integrating the equation of the parabola from 0 to 5/6 and setting it equal to the integral of the line from 0 to 5/6, we can solve for m. After performing the integration, we find that m = 5.

Therefore, the slope of the line that divides the region into two equal areas is 5.

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