B(-1;7) , C(x;-1) and D(1;8) : B,C and D are collinear​

Answer:

5.2 feet

Step-by-step explanation:

436.8/7/12 feet

The equation of the polynomial function in standard form is P(x) = x³ + 6x² - 7x - 60

Given that we have the following

zeros = -5,-4,and 3

The polynomial function in standard form is calculated as

P(x) = (x - zeros)

So, we have

P(x) = (x + 5)(x + 4)(x - 3)

Opening the brackets, we have the following equation

P(x) = x³ + 6x² - 7x - 60

Hence, the polynomial is P(x) = x³ + 6x² - 7x - 60

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The sum of the ages of the family seven years ago is given as follows:

45 years.

The sum of the ages of the family is obtained applying the proportions in the context of the problem.

Each year, the age of each person increases by one, hence, considering a family of five, the yearly increase in the age of the family is given as follows:

5 x 1 = 5 years.

The two youngest are 6 and 8, meaning that seven years ago, the youngest was not yet born.

The ages of a family of five sum to 80, hence the sum seven years ago was given as follows:

80 - 5 x 7 = 45 years.

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The bank made $100 in profit from the loan.

What is simple interest?

Simple Interest is an easy method of calculating the interest for a loan/principal amount. Simple interest is a concept that is used in many sectors such as banking, finance, automobile, and so on.

If John had to pay back $321 in total and the original loan was $221, then the bank made $100 in interest from John.

Interest = Amount John had to pay - Original Loan

Interest = 321 - 221

Interest = $100

So, the bank made $100 in profit from the loan.

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Answer:

x = 11

Step-by-step explanation:

3x + 5x + 2 =90

(3x + 5x) + (2) = 90

8x + 2 = 90

8x + 2 -2 = 90 -2

8x = 88

8x/8 = 88/8

x = 11

The measure of diagonal DB in the given square is 5√2.

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry. A triangle is defined by its three sides and the three angles formed by those sides. The sum of the three angles in a triangle is always 180 degrees. Triangles can be classified based on the length of their sides and the size of their angles.

Using Pythagoras theorem of right triangle

DB² = DC² + BC²

Here given that

DC = BC

Then

DB² = DC² + DC²

DB² = 5² + 5²

DB² = 25 + 25

DB² = 50

DB = √50

DB = 5√2

Thus, the measure of diagonal DB in the given square is 5√2

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Answer:42.8571429%

Step-by-step explanation:

His GPS tracker got 7 miles while he actually ran 10. 10 - 7 = 3. Then you divide 3 by 7 which is [tex]\frac{3}{7}[/tex] and that is around 42.8571429%.

Answer:

v<-4/35. If you want interval notation it is (-infinity, -4/35)

Step-by-step explanation:

The angles are vertical and the value of x  from the angles (4x -25) and 75 can be expressed as 25.

A pair of angles that are vertically opposed to one another are always equal. Moreover, a vertical angle and the angle to which it is adjacent are supplementary angles, meaning their sum is 180 degrees. When two lines join to form an angle, say X=45°, the opposite angle is also 45°, for instance.

From the fiqure we can see that the angles the vertically opposite angles, base on this condition we can form the equation as;

(4x-25)=75

4x=(75+25)

4x=100

x=100/4

x=25

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The rectangular prism's length, width, and height can also be labelled, and the surface area (SA) can be calculated using the formula:

SA = 2lw+2lh+2hw.

A face is just a flat surface in the geometric sense, and edges are formed where surfaces meet. Pyramids and prisms are both examples of polyhedra. A pyramid, however, is not a prism.

Method to find surface area:

Thus, the rectangular prism's length, width, and height can also be labelled, and the surface area (SA) can be calculated using the formula:

SA = 2lw+2lh+2hw.

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Surface Area = (width×length  +  height×length  +  height×width) × 2

—————

Please remember to revise this and make it in your own words if you want! I tried making this as simple as possible! I hope this helps you. -Doodle

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The measures of angles in a rhombus are m∠2=130, m∠3=50 and m∠4=50.

Angle measure is a term used in geometry to describe the size of an angle. It is usually expressed in degrees, which is a unit of measurement for angles. A degree is defined as 1/360th of a complete revolution around a circle.

In the rhombus, m∠1 =130

In a rhombus, opposite angles are congruent.

The angle opposite to angle 1 is angle 2.

so m∠1 =m∠2

m∠2= 130 degrees

Other pair of opposite angles are also congruent.

so m∠3=m ∠4

We know that the sum of 4 angles = 360

m∠1+m∠2+m∠3+m∠4=360

130+130+m∠3+m∠4=360

260+m∠3+m∠4=360

m∠3+m∠4=360-260

m∠3+m∠3=100

2m∠3=100

m∠3=50

Now, m∠3=50

m∠4=50

Therefore, m∠2=130, m∠3=50 and m∠4=50

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The median provides Farrah with an understanding of the central value in her data set, which can help her analyze the overall distribution of the data points.

The median is a measure of central tendency that tells Farrah the middle value of her data when it is arranged in ascending order.

To find the median, Farrah should follow these steps:
1. Arrange her data in ascending order (from smallest to largest).
2. If there is an odd number of data points, the median is the middle value.
3. If there is an even number of data points, the median is the average of the two middle values.

It is less affected by outliers or extreme values than the mean, making it a more reliable representation of the center of her data.

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The point estimate is 0.395 and the poll's margin of error is 0.015 or 1.5%.

A set of values that, with a particular level of confidence, is likely to include an unknown population parameter is known as a confidence interval. Confidence intervals are frequently utilized in statistics to calculate the actual value of a population parameter using sample statistics. When comparing a sample statistic to a population parameter that is hypothesised, we utilize confidence intervals to assess if the difference is statistically significant.

Given the interval of the result in the survey is [0.38, 0.41].

a. The point estimate is given as:

Point estimate = (0.38 + 0.41) / 2 = 0.395

b. The margin of error is given as:

Margin of error = (critical value) x (standard error)

Assuming a 95% confidence level:

Standard error = (maximum error) / (critical value)

Now,

Maximum error = (0.41 - 0.38) / 2 = 0.015

Margin of error = 1.96 x (0.015 / 1.96) = 0.015

Hence, the point estimate is 0.395 and the poll's margin of error is 0.015 or 1.5%.

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you need to work back wards on the

9x+3=64

so 64-3=61

then do 61 divided by 9  

which equals 6.7(1dp)

so x=6.7(1dp)

Answer:

1. It flips the image over a line to create a mirror image

2. It spins a figure around a point

3. It slides a figure to a different location

4. it enlarges or reduces a figure

Step-by-step explanation:

The coordinates of the point where the food bag is hung are (2.5, 7, 6.5).

The center of the coordinate system (where the lines intersect) is called the origin. The axes intersect when both x and y are zero. The coordinates of the origin are (0, 0). An ordered pair contains the coordinates of one point in the coordinate system.

The coordinates of the point on the first tree where the rope is attached are (10, 6, 8), and the coordinates of the point on the second tree where the rope is attached are (-5, 8, 5).

To find the distance between the points, we can use the distance formula:

distance = √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²)

Plugging in the coordinates from part 1, we get:

distance = √((-5 - 10)² + (8 - 6)² + (5 - 8)²)

distance = √(225 + 4 + 9)

distance = √(238)

Therefore, the distance between the points is √(238).

Since the food bag is hung at a point exactly halfway along the length of the rope, we can find its coordinates by taking the average of the coordinates of the points where the rope is attached.

The x-coordinate of the midpoint is: (10 + (-5)) / 2 = 2.5

The y-coordinate of the midpoint is: (6 + 8) / 2 = 7

The z-coordinate of the midpoint is: (8 + 5) / 2 = 6.5

Therefore, the coordinates of the point where the food bag is hung are (2.5, 7, 6.5).

To determine whether the food is safe from bears, we need to compare the height of the food bag to the maximum height that bears can reach. The food bag is hung at a height of 6.5 feet, and bears can reach a height of 7.5 feet when standing. Therefore, the food is not completely safe from bears, as they may be able to reach it if they stand up on their hind legs. However, hanging the food bag at this height does make it more difficult for the bears to reach, and may deter them from trying to get to it. It is also important to note that proper food storage techniques in bear country should involve using bear-resistant containers, in addition to hanging food bags.

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Answer:

first find constant term

y=kx

32=k(4)

32/4=4k/4

k=8

find value of y when x=5

y=kx

y=8×5

y=40

The work done by the winch in running the winch until the bottom of the chain is at the 10-foot level is 200 foot-pounds.

Given, The weight of the chain per foot = 2 pounds

Total length of the chain = 20 feet

The chain is hanging from a winch 20 feet above ground level.

The work done by the winch in running the winch until the bottom of the chain is at the 10-foot level is to be determined.

The force required to lift the chain is equal to the weight of the chain. Therefore, the force needed is F = 2 × 20 = 40 pounds. The work done is the product of force and distance.

Therefore, Work done = force × distance= 40 × (20 − 10)= 400 foot-pounds

Thus, the work done by the winch in running the winch until the bottom of the chain is at the 10-foot level is 200 foot-pounds.

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The correct answer is A. Multiplying the first equation by 2 will eliminate the variable y.

The elimination method is a common technique used to solve a system of linear equations. In this method, we manipulate the equations by adding or subtracting them to eliminate one of the variables, so that we can solve for the other variable.

To eliminate one of the variables, we need to choose one of the equations and multiply it by a constant that will make the coefficient of one of the variables in that equation equal to the coefficient of the same variable in the other equation, but with the opposite sign. Then, when we add the two equations together, the term with that variable will be eliminated.

Looking at the given equations, we can see that if we multiply the first equation by 2, we will get:

6x - 12y = 16

And if we add this equation to the second equation, we get:

6x - 12y + 2x + 3y = 16 - 1

Simplifying this, we get:

8x - 9y = 15

Now we have one equation with only x and y, and we can use this equation and either of the original equations to solve for x and y using the substitution method.

Therefore, the correct answer is A. Multiplying the first equation by 2 will eliminate the variable y.

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Answer:

x = 4, y = -14

Step-by-step explanation:

1. x + y = -10 and -3x - y = 2

2. y= -10 - x > plug in for y > -3x - (-10 - x) = 2

3. solve for x > -3x + 10 + x = 2

-2x + 10 = 2 > -2x = -8 > x= 4

4. plug x into original equation > 4 + y = -10 > y = -14

Answer: Yes

Step-by-step explanation:

1.4691 is more than 1.465, and less than 1.472

The coordinates of the vertex A' are (-2, -2).

What is triangle?

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.

To reflect a point or a shape across a line, you can follow these steps:

Find the equation of the line of reflection.

Find the distance between each point and the line of reflection.

Reflect each point across the line of reflection by moving the same distance on the other side of the line.

Finding the equation of the line of reflection:

The line of reflection is y = -2, which is a horizontal line passing through y = -2.

Finding the distance between each point and the line of reflection:

We can use the formula for the distance between a point (x, y) and a line Ax + By + C = 0:

distance = |Ax + By + C| / sqrt(A^2 + B^2)

Plugging in the values, we get:

distance(A, y = -2) = |(-2) - (-2) + 2| / sqrt(0 + 1) = 2

distance(B, y = -2) = |(-2) - (-2) + 4| / sqrt(0 + 1) = 4

distance(C, y = -2) = |(-5) - (-2) + 2| / sqrt(1 + 0) = 5 / sqrt(1) = 5

So the distances between A, B, C and the line of reflection are 2, 4, and 5, respectively.

Reflecting each point across the line of reflection:

To reflect a point across a line, we move the same distance on the other side of the line. Since the line of reflection is horizontal, we only need to move vertically.

A is 2 units above the line of reflection, so we move it 2 units below the line:

A' = (-2, -2)

B is 4 units above the line of reflection, so we move it 4 units below the line:

B' = (-2, -4)

C is 5 units above the line of reflection, so we move it 5 units below the line:

C' = (-5, -7)

Therefore, the coordinates of the vertex A' are (-2, -2).

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A house with value at 210000 correct to 2 significant figures. The lowest possible value of the house is equals to the £205000.

The second significant figure of a number is the digit after the first significant figure. This is true even in case of the digit is zero. We have a house is valued at £210000 correct to 2 significant figures. So, it is bounded question. Since, two significant figures is correct then there is error in 10000 range in £210000. The rounded up value is £2.10 × 10⁵. Steps to determine these bounds

here x = £210000, y = 10000

Since 2 significant digits are correct,

is about 10,000 of £210,000. The lowest possible number rounded to 2 significant digits in the £210,000 range is £205,000, because anything below that looks like £204....that doesn't round up to £21. Hence required value is £205000.

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The probability that more than 7 of the 15 patients have hyperextending joints is 0.015, or about 1.5%.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

This is a binomial distribution problem, where we have n = 15 trials and the probability of success (a patient having hyperextending joints) is p = 0.2.

A. To find the probability that exactly 5 of the 15 patients have hyperextending joints, we can use the formula for the binomial probability mass function:

P(X = 5) = (15 choose 5) * 0.2^5 * 0.8^10

where (15 choose 5) is the number of ways to choose 5 patients out of 15. Using a calculator, we get:

P(X = 5) = 0.188

So the probability that exactly 5 of the 15 patients have hyperextending joints is 0.188, or about 18.8%.

B. To find the probability that no more than 7 of the 15 patients have hyperextending joints, we need to add up the probabilities of having 0, 1, 2, ..., 7 patients with hyperextending joints. We can use the cumulative distribution function (CDF) of the binomial distribution:

P(X ≤ 7) = Σ(P(X = k)) for k = 0 to 7

Again, using a calculator, we get:

P(X ≤ 7) = 0.985

So the probability that no more than 7 of the 15 patients have hyperextending joints is 0.985, or about 98.5%.

C. To find the probability that more than 7 of the 15 patients have hyperextending joints, we can use the complement rule:

P(X > 7) = 1 - P(X ≤ 7)

We already know from part (B) that P(X ≤ 7) = 0.985, so:

P(X > 7) = 1 - 0.985 = 0.015

Therefore, the probability that more than 7 of the 15 patients have hyperextending joints is 0.015, or about 1.5%.

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Answer:

a) v.h=v*cos(63)=7.26 m/s

b) v.v=v*sin(63)=14.26 m/s

c) t=v.v/g=14.26/9.8=1.46 s since time the body takes to go upward is defined by the acceleration due to gravity and the vertical component of the speed

d) h=1/2*gt^2=7.15 m

e) T=2t=2.92 s

f) R=v.h*t=7.26*1.46=10.6 m since horizontal displacement is defined by the horizontal component of the speed only.

Step-by-step explanation:

Hope this helps! =D

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The calculated value is 15.16, and the degrees of freedom are 12, the p-value is less than 0.05.

As a result, we must reject the null hypothesis.

A manager of a sports club maintains data about the main sport in which members participate and their ages.

To verify if there is a connection between the age of a member and their sport preference, a test of independence is performed on 651 sports club members who were randomly selected at a 5% level.200 Words:

Test of independence: Test of independence is a statistical method that helps to determine if there is a connection between two groups, and if there is, what is the magnitude of the relationship.

A test of independence is performed using the chi-square statistic.

The null hypothesis in this test is that there is no relationship between the two group S.

We will use a chi-square test to determine whether there is a connection between the age of the member and the sport in which they participate.

Hypotheses:

Null hypothesis: There is no link between the age of a member and the sport in which they participate.

Alternate hypothesis: There is a relationship between the age of a member and the sport in which they participate.

Level of significance = 5%.

Step 1: Prepare the contingency table for observed values

Age  Basketball  Football  Hockey  Soccer  Other Under 20 years  25  30  20  10  15 20-29 years  20  50  35  30  25 30-39 years  15  40  40  35  30 40-49 years  10  35  25  25  20 Over 50 years  5  15  10  15  10

Step 2: Calculate the marginal frequencies.

Age  Basketball  Football  Hockey  Soccer  Other Total Under 20 years  25  30  20  10  15 100 20-29 years  20  50  35  30  25 160 30-39 years  15  40  40  35  30 160 40-49 years  10  35  25  25  20 115 Over 50 years  5  15  10  15  10 55 Total 75  170  130  115  100 651

Step 3: Compute the expected frequencies.

The predicted frequency for each group is (row total) * (column total) / total number of observations.

Age  Basketball  Football  Hockey  Soccer  Other Under 20 years  11.5  26.1  19.9  17.7  15 20-29 years  30.9  70.1  53.4  47.5  40.1 30-39 years  30.9  70.1  53.4  47.5  40.1 40-49 years  21.3  48.2  36.8  32.7  27.6 Over 50 years  9.4  21.4  16.4  14.6  12.3

Step 4: Calculate the test statistic:

We will use a chi-square test statistic to determine whether the null hypothesis should be accepted or rejected.

Chi-square test formula is:χ2 = Σ (Observed frequency – Expected frequency)2 / Expected frequency.

Degrees of freedom = (Number of rows – 1) * (Number of columns – 1)

χ2 = (25-11.5)2 / 11.5 + (20-30.9)2 / 30.9 + (15-30.9)2 / 30.9 + (10-21.3)2 / 21.3 + (5-9.4)2 / 9.4 + (30-26.1)2 / 26.1 + (50-70.1)2 / 70.1 + (40-70.1)2 / 70.1 + (35-48.2)2 / 48.2 + (15-21.4)2 / 21.4 + (20-19.9)2 / 19.9 + (35-53.4)2 / 53.4 + (40-53.4)2 / 53.4 + (25-36.8)2 / 36.8 + (10-16.4)2 / 16.4 + (15-14.6)2 / 14.6 + (15-32.7)2 / 32.7 + (25-27.6)2 / 27.6 + (10-12.3)2 / 12.3χ2 = 15.16

Degrees of freedom = (5-1) * (4-1) = 12

Step 5: Determine the p-value:

The p-value is determined by looking up the chi-square value and the degrees of freedom in the chi-square table.

The p-value is the probability of obtaining a result as extreme as or more extreme than the calculated value if the null hypothesis is true.

We will use a 5% level of significance.

Since the calculated value is 15.16, and the degrees of freedom are 12, the p-value is less than 0.05.

As a result, we must reject the null hypothesis.

There is evidence to suggest that the age of a member is related to the sport in which they participate.

In other words, the age of a member and their sport preference are not independent.

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Therefore, the estimated population of great white sharks that have migrated from Mexico to Hawaii is 2,500.

Shark population estimation is the process of determining the size and trends of shark populations in a given area. It involves collecting and analyzing data on shark abundance, distribution, behavior, and other factors to understand their population dynamics.

There are different methods used to estimate shark populations, including mark-recapture studies, aerial surveys, acoustic tracking, and genetic analysis. These methods allow researchers to estimate the number of sharks in a given area, monitor changes in their population over time, and identify potential threats to their survival.

To estimate the population of great white sharks that have migrated from Mexico to Hawaii, we can use the capture-recapture method, also known as the Lincoln-Petersen index.

Let:

The Lincoln-Petersen index formula is:

[tex]N = (n_1 * n_2 * n_3) / (m_1 * m_2 * m_3)[/tex]

Plugging in the given values, we get:

[tex]N = (45 * 20 * 20 * 20) / (3 * 2 * 4)[/tex]

[tex]N = 60,000 / 24[/tex]

[tex]N = 2,500[/tex]

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To calculate the amount of money Joe will have in 3 years, we can use the formula:

A = P(1 + r/n)^(nt)

where:

A = the amount of money Joe will have in 3 years

P = the principal amount = $2500

r = the annual interest rate = 9% = 0.09 (expressed as a decimal)

n = the number of times the interest is compounded per year (assuming annual compounding, n = 1)

t = the number of years = 3

Plugging in these values, we get:

A = $2500(1 + 0.09/1)^(1*3)

= $2500(1.09)^3

= $2500(1.29503)

= $3237.58 (rounded to two decimal places)

Therefore, Joe will have $3237.58 in 3 years.

In linear equation, 6499 ft CD, the height of the plane from the ground, to the nearest foot.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                          Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Part A) Find BC, the distance from Tower 2 to the plane, to the nearest foot.

in the triangle ACD

sin16=CD/(7600+BD)--------> CD=sin16*(7600+BD)---------> equation 1

in the triangle BCD

sin24=CD/BD-----------> CD=sin24*BD---------------> equation 2

equation 1=equation 2

sin16*(7600+BD)=sin24*BD-----> sin16*7600+sin16*BD=sin24*BD

sin24*BD-sin16*BD=sin16*7600----> BD=[sin16*7600]/[sin24-sin16]

BD=15979 ft

in the triangle BCD

cos24=BD/BC---------> BC=BD/cos24-------> 15979/cos24-------> 17491

BC=17491 ft

    =  BC is 17491 ft

Part 2) Find CD, the height of the plane from the ground, to the nearest foot.

CD=sin24*BD        ( remember equation 2)

BD=15979 ft

CD=sin24*15979 -----------> CD=6499 ft

     =  CD is 6499 ft

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